diff options
| author | Rémi Flamary <remi.flamary@gmail.com> | 2019-07-03 14:34:13 +0200 |
|---|---|---|
| committer | GitHub <noreply@github.com> | 2019-07-03 14:34:13 +0200 |
| commit | 952503e02b1fc9bdf0811b937baacca57e4a98f1 (patch) | |
| tree | c5b1b8f10eaee4c2ecaa12f629255489c2481590 | |
| parent | 8b3927bb5e8935c3dbddf054f054dc0c036fbdfe (diff) | |
| parent | 7402d344240ce94e33c53daff419d4356278d48f (diff) | |
Merge pull request #88 from rflamary/doc_modules
[MRG] Update documentation and add quick start guide
68 files changed, 4772 insertions, 156 deletions
@@ -42,10 +42,10 @@ pep8 : flake8 examples/ ot/ test/ test : FORCE pep8 - $(PYTHON) -m pytest -v test/ --cov=ot --cov-report html:cov_html + $(PYTHON) -m pytest -v test/ --doctest-modules --ignore ot/gpu/ --cov=ot --cov-report html:cov_html pytest : FORCE - $(PYTHON) -m pytest -v test/ --cov=ot + $(PYTHON) -m pytest -v test/ --doctest-modules --ignore ot/gpu/ --cov=ot uploadpypi : #python setup.py register @@ -54,6 +54,12 @@ The library has been tested on Linux, MacOSX and Windows. It requires a C++ comp #### Pip installation +Note that due to a limitation of pip, `cython` and `numpy` need to be installed +prior to installing POT. This can be done easily with +``` +pip install numpy cython +``` + You can install the toolbox through PyPI with: ``` pip install POT @@ -63,6 +69,8 @@ or get the very latest version by downloading it and then running: python setup.py install --user # for user install (no root) ``` + + #### Anaconda installation with conda-forge If you use the Anaconda python distribution, POT is available in [conda-forge](https://conda-forge.org). To install it and the required dependencies: @@ -151,7 +159,12 @@ You can also see the notebooks with [Jupyter nbviewer](https://nbviewer.jupyter. ## Acknowledgements -The contributors to this library are: +This toolbox has been created and is maintained by + +* [Rémi Flamary](http://remi.flamary.com/) +* [Nicolas Courty](http://people.irisa.fr/Nicolas.Courty/) + +The contributors to this library are * [Rémi Flamary](http://remi.flamary.com/) * [Nicolas Courty](http://people.irisa.fr/Nicolas.Courty/) diff --git a/docs/cache_nbrun b/docs/cache_nbrun index 6f10375..8a95023 100644 --- a/docs/cache_nbrun +++ b/docs/cache_nbrun @@ -1 +1 @@ -{"plot_otda_mapping_colors_images.ipynb": "cc8bf9a857f52e4a159fe71dfda19018", "plot_optim_OTreg.ipynb": "481801bb0d133ef350a65179cf8f739a", "plot_otda_color_images.ipynb": "f804d5806c7ac1a0901e4542b1eaa77b", "plot_stochastic.ipynb": "e18253354c8c1d72567a4259eb1094f7", "plot_WDA.ipynb": "27f8de4c6d7db46497076523673eedfb", "plot_otda_linear_mapping.ipynb": "a472c767abe82020e0a58125a528785c", "plot_OT_1D_smooth.ipynb": "3a059103652225a0c78ea53895cf79e5", "plot_OT_L1_vs_L2.ipynb": "5d565b8aaf03be4309eba731127851dc", "plot_barycenter_1D.ipynb": "5f6fb8aebd8e2e91ebc77c923cb112b3", "plot_otda_classes.ipynb": "39087b6e98217851575f2271c22853a4", "plot_otda_d2.ipynb": "e6feae588103f2a8fab942e5f4eff483", "plot_otda_mapping.ipynb": "2f1ebbdc0f855d9e2b7adf9edec24d25", "plot_gromov.ipynb": "24f2aea489714d34779521f46d5e2c47", "plot_compute_emd.ipynb": "f5cd71cad882ec157dc8222721e9820c", "plot_OT_1D.ipynb": "b5348bdc561c07ec168a1622e5af4b93", "plot_gromov_barycenter.ipynb": "953e5047b886ec69ec621ec52f5e21d1", "plot_free_support_barycenter.ipynb": "246dd2feff4b233a4f1a553c5a202fdc", "plot_convolutional_barycenter.ipynb": "a72bb3716a1baaffd81ae267a673f9b6", "plot_otda_semi_supervised.ipynb": "f6dfb02ba2bbd939408ffcd22a3b007c", "plot_OT_2D_samples.ipynb": "07dbc14859fa019a966caa79fa0825bd", "plot_barycenter_lp_vs_entropic.ipynb": "51833e8c76aaedeba9599ac7a30eb357"}
\ No newline at end of file +{"plot_otda_semi_supervised.ipynb": "f6dfb02ba2bbd939408ffcd22a3b007c", "plot_WDA.ipynb": "27f8de4c6d7db46497076523673eedfb", "plot_UOT_1D.ipynb": "fc7dd383e625597bd59fff03a8430c91", "plot_OT_L1_vs_L2.ipynb": "5d565b8aaf03be4309eba731127851dc", "plot_otda_color_images.ipynb": "f804d5806c7ac1a0901e4542b1eaa77b", "plot_fgw.ipynb": "2ba3e100e92ecf4dfbeb605de20b40ab", "plot_otda_d2.ipynb": "e6feae588103f2a8fab942e5f4eff483", "plot_compute_emd.ipynb": "f5cd71cad882ec157dc8222721e9820c", "plot_barycenter_fgw.ipynb": "e14100dd276bff3ffdfdf176f1b6b070", "plot_convolutional_barycenter.ipynb": "a72bb3716a1baaffd81ae267a673f9b6", "plot_optim_OTreg.ipynb": "481801bb0d133ef350a65179cf8f739a", "plot_barycenter_lp_vs_entropic.ipynb": "51833e8c76aaedeba9599ac7a30eb357", "plot_OT_1D_smooth.ipynb": "3a059103652225a0c78ea53895cf79e5", "plot_barycenter_1D.ipynb": "5f6fb8aebd8e2e91ebc77c923cb112b3", "plot_otda_mapping.ipynb": "2f1ebbdc0f855d9e2b7adf9edec24d25", "plot_OT_1D.ipynb": "b5348bdc561c07ec168a1622e5af4b93", "plot_gromov_barycenter.ipynb": "953e5047b886ec69ec621ec52f5e21d1", "plot_UOT_barycenter_1D.ipynb": "c72f0bfb6e1a79710dad3fef9f5c557c", "plot_otda_mapping_colors_images.ipynb": "cc8bf9a857f52e4a159fe71dfda19018", "plot_stochastic.ipynb": "e18253354c8c1d72567a4259eb1094f7", "plot_otda_linear_mapping.ipynb": "a472c767abe82020e0a58125a528785c", "plot_otda_classes.ipynb": "39087b6e98217851575f2271c22853a4", "plot_free_support_barycenter.ipynb": "246dd2feff4b233a4f1a553c5a202fdc", "plot_gromov.ipynb": "24f2aea489714d34779521f46d5e2c47", "plot_OT_2D_samples.ipynb": "912a77c5dd0fc0fafa03fac3d86f1502"}
\ No newline at end of file diff --git a/docs/source/auto_examples/auto_examples_jupyter.zip b/docs/source/auto_examples/auto_examples_jupyter.zip Binary files differindex 88e1e9b..901195a 100644 --- a/docs/source/auto_examples/auto_examples_jupyter.zip +++ b/docs/source/auto_examples/auto_examples_jupyter.zip diff --git a/docs/source/auto_examples/auto_examples_python.zip b/docs/source/auto_examples/auto_examples_python.zip Binary files differindex 120a586..ded2613 100644 --- a/docs/source/auto_examples/auto_examples_python.zip +++ b/docs/source/auto_examples/auto_examples_python.zip diff --git a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png Binary files differindex 2e93ed1..a5bded7 100644 --- a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png +++ b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_001.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png Binary files differindex d6db0ed..1d90c2d 100644 --- a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png +++ b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_002.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png Binary files differindex 9a215ab..ea6a405 100644 --- a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png +++ b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_005.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png Binary files differindex 81c4ddb..8bc46dc 100644 --- a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png +++ b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_006.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_009.png b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_009.png Binary files differindex 892b2a2..56d18ef 100644 --- a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_009.png +++ b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_009.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_010.png b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_010.png Binary files differindex c53717f..5aef7d2 100644 --- a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_010.png +++ b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_010.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_013.png b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_013.png Binary files differnew file mode 100644 index 0000000..bb8bd7c --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_013.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_014.png b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_014.png Binary files differnew file mode 100644 index 0000000..30cec7b --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_OT_2D_samples_014.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_UOT_1D_001.png b/docs/source/auto_examples/images/sphx_glr_plot_UOT_1D_001.png Binary files differnew file mode 100644 index 0000000..69ef5b7 --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_UOT_1D_001.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_UOT_1D_002.png b/docs/source/auto_examples/images/sphx_glr_plot_UOT_1D_002.png Binary files differnew file mode 100644 index 0000000..0407e44 --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_UOT_1D_002.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_UOT_1D_006.png b/docs/source/auto_examples/images/sphx_glr_plot_UOT_1D_006.png Binary files differnew file mode 100644 index 0000000..f58d383 --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_UOT_1D_006.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_001.png b/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_001.png Binary files differnew file mode 100644 index 0000000..ec8c51e --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_001.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_003.png b/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_003.png Binary files differnew file mode 100644 index 0000000..89ab265 --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_003.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_005.png b/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_005.png Binary files differnew file mode 100644 index 0000000..c6c49cb --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_005.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_006.png b/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_006.png Binary files differnew file mode 100644 index 0000000..8870b10 --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_006.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_barycenter_fgw_001.png b/docs/source/auto_examples/images/sphx_glr_plot_barycenter_fgw_001.png Binary files differnew file mode 100644 index 0000000..77e1282 --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_barycenter_fgw_001.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_barycenter_fgw_002.png b/docs/source/auto_examples/images/sphx_glr_plot_barycenter_fgw_002.png Binary files differnew file mode 100644 index 0000000..ca6d7f8 --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_barycenter_fgw_002.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_fgw_004.png b/docs/source/auto_examples/images/sphx_glr_plot_fgw_004.png Binary files differnew file mode 100644 index 0000000..4e0df9f --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_fgw_004.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_fgw_010.png b/docs/source/auto_examples/images/sphx_glr_plot_fgw_010.png Binary files differnew file mode 100644 index 0000000..d0e36e8 --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_fgw_010.png diff --git a/docs/source/auto_examples/images/sphx_glr_plot_fgw_011.png b/docs/source/auto_examples/images/sphx_glr_plot_fgw_011.png Binary files differnew file mode 100644 index 0000000..6d7e630 --- /dev/null +++ b/docs/source/auto_examples/images/sphx_glr_plot_fgw_011.png diff --git a/docs/source/auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png b/docs/source/auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png Binary files differindex b9135dd..ae33588 100644 --- a/docs/source/auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png +++ b/docs/source/auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png diff --git a/docs/source/auto_examples/images/thumb/sphx_glr_plot_UOT_1D_thumb.png b/docs/source/auto_examples/images/thumb/sphx_glr_plot_UOT_1D_thumb.png Binary files differnew file mode 100644 index 0000000..1d048f2 --- /dev/null +++ b/docs/source/auto_examples/images/thumb/sphx_glr_plot_UOT_1D_thumb.png diff --git a/docs/source/auto_examples/images/thumb/sphx_glr_plot_UOT_barycenter_1D_thumb.png b/docs/source/auto_examples/images/thumb/sphx_glr_plot_UOT_barycenter_1D_thumb.png Binary files differnew file mode 100644 index 0000000..999f175 --- /dev/null +++ b/docs/source/auto_examples/images/thumb/sphx_glr_plot_UOT_barycenter_1D_thumb.png diff --git a/docs/source/auto_examples/images/thumb/sphx_glr_plot_barycenter_fgw_thumb.png b/docs/source/auto_examples/images/thumb/sphx_glr_plot_barycenter_fgw_thumb.png Binary files differnew file mode 100644 index 0000000..9c3244e --- /dev/null +++ b/docs/source/auto_examples/images/thumb/sphx_glr_plot_barycenter_fgw_thumb.png diff --git a/docs/source/auto_examples/images/thumb/sphx_glr_plot_fgw_thumb.png b/docs/source/auto_examples/images/thumb/sphx_glr_plot_fgw_thumb.png Binary files differnew file mode 100644 index 0000000..609339d --- /dev/null +++ b/docs/source/auto_examples/images/thumb/sphx_glr_plot_fgw_thumb.png diff --git a/docs/source/auto_examples/index.rst b/docs/source/auto_examples/index.rst index 17a9710..fe6702d 100644 --- a/docs/source/auto_examples/index.rst +++ b/docs/source/auto_examples/index.rst @@ -29,13 +29,13 @@ This is a gallery of all the POT example files. .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="Illustrates the use of the generic solver for regularized OT with user-designed regularization ..."> + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of Unbalanced Optimal transport using a Kullback-Leibl..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_optim_OTreg_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_UOT_1D_thumb.png - :ref:`sphx_glr_auto_examples_plot_optim_OTreg.py` + :ref:`sphx_glr_auto_examples_plot_UOT_1D.py` .. raw:: html @@ -45,17 +45,17 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_optim_OTreg + /auto_examples/plot_UOT_1D .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 2D Wasserstein barycenters if discributions that are weighted sum of diracs."> + <div class="sphx-glr-thumbcontainer" tooltip="Illustrates the use of the generic solver for regularized OT with user-designed regularization ..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_free_support_barycenter_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_optim_OTreg_thumb.png - :ref:`sphx_glr_auto_examples_plot_free_support_barycenter.py` + :ref:`sphx_glr_auto_examples_plot_optim_OTreg.py` .. raw:: html @@ -65,17 +65,17 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_free_support_barycenter + /auto_examples/plot_optim_OTreg .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of EMD, Sinkhorn and smooth OT plans and their visuali..."> + <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 2D Wasserstein barycenters if discributions that are weighted sum of diracs."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_1D_smooth_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_free_support_barycenter_thumb.png - :ref:`sphx_glr_auto_examples_plot_OT_1D_smooth.py` + :ref:`sphx_glr_auto_examples_plot_free_support_barycenter.py` .. raw:: html @@ -85,17 +85,17 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_OT_1D_smooth + /auto_examples/plot_free_support_barycenter .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Gromov-Wassertsein distance computation in POT...."> + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of EMD, Sinkhorn and smooth OT plans and their visuali..."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_gromov_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_1D_smooth_thumb.png - :ref:`sphx_glr_auto_examples_plot_gromov.py` + :ref:`sphx_glr_auto_examples_plot_OT_1D_smooth.py` .. raw:: html @@ -105,17 +105,17 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_gromov + /auto_examples/plot_OT_1D_smooth .. raw:: html - <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 2D optimal transport between discributions that are weighted sum of diracs. The..."> + <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Gromov-Wassertsein distance computation in POT...."> .. only:: html - .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_gromov_thumb.png - :ref:`sphx_glr_auto_examples_plot_OT_2D_samples.py` + :ref:`sphx_glr_auto_examples_plot_gromov.py` .. raw:: html @@ -125,7 +125,7 @@ This is a gallery of all the POT example files. .. toctree:: :hidden: - /auto_examples/plot_OT_2D_samples + /auto_examples/plot_gromov .. raw:: html @@ -209,6 +209,26 @@ This is a gallery of all the POT example files. .. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="Illustration of 2D optimal transport between discributions that are weighted sum of diracs. The..."> + +.. only:: html + + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_OT_2D_samples_thumb.png + + :ref:`sphx_glr_auto_examples_plot_OT_2D_samples.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_OT_2D_samples + +.. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the stochatic optimization algorithms for descrete ..."> .. only:: html @@ -289,6 +309,26 @@ This is a gallery of all the POT example files. .. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of regularized Wassersyein Barycenter as proposed in [..."> + +.. only:: html + + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_UOT_barycenter_1D_thumb.png + + :ref:`sphx_glr_auto_examples_plot_UOT_barycenter_1D.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_UOT_barycenter_1D + +.. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example presents how to use MappingTransport to estimate at the same time both the couplin..."> .. only:: html @@ -329,6 +369,26 @@ This is a gallery of all the POT example files. .. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of FGW for 1D measures[18]."> + +.. only:: html + + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_fgw_thumb.png + + :ref:`sphx_glr_auto_examples_plot_fgw.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_fgw + +.. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example introduces a domain adaptation in a 2D setting and the 4 OTDA approaches currently..."> .. only:: html @@ -409,6 +469,26 @@ This is a gallery of all the POT example files. .. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation barycenter of labeled graphs using FGW"> + +.. only:: html + + .. figure:: /auto_examples/images/thumb/sphx_glr_plot_barycenter_fgw_thumb.png + + :ref:`sphx_glr_auto_examples_plot_barycenter_fgw.py` + +.. raw:: html + + </div> + + +.. toctree:: + :hidden: + + /auto_examples/plot_barycenter_fgw + +.. raw:: html + <div class="sphx-glr-thumbcontainer" tooltip="This example is designed to show how to use the Gromov-Wasserstein distance computation in POT...."> .. only:: html diff --git a/docs/source/auto_examples/plot_OT_2D_samples.ipynb b/docs/source/auto_examples/plot_OT_2D_samples.ipynb index 26831f9..dad138b 100644 --- a/docs/source/auto_examples/plot_OT_2D_samples.ipynb +++ b/docs/source/auto_examples/plot_OT_2D_samples.ipynb @@ -26,7 +26,7 @@ }, "outputs": [], "source": [ - "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot" + "# Author: Remi Flamary <remi.flamary@unice.fr>\n# Kilian Fatras <kilian.fatras@irisa.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot" ] }, { @@ -100,6 +100,24 @@ "source": [ "#%% sinkhorn\n\n# reg term\nlambd = 1e-3\n\nGs = ot.sinkhorn(a, b, M, lambd)\n\npl.figure(5)\npl.imshow(Gs, interpolation='nearest')\npl.title('OT matrix sinkhorn')\n\npl.figure(6)\not.plot.plot2D_samples_mat(xs, xt, Gs, color=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.legend(loc=0)\npl.title('OT matrix Sinkhorn with samples')\n\npl.show()" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Emprirical Sinkhorn\n----------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% sinkhorn\n\n# reg term\nlambd = 1e-3\n\nGes = ot.bregman.empirical_sinkhorn(xs, xt, lambd)\n\npl.figure(7)\npl.imshow(Ges, interpolation='nearest')\npl.title('OT matrix empirical sinkhorn')\n\npl.figure(8)\not.plot.plot2D_samples_mat(xs, xt, Ges, color=[.5, .5, 1])\npl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\npl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\npl.legend(loc=0)\npl.title('OT matrix Sinkhorn from samples')\n\npl.show()" + ] } ], "metadata": { @@ -118,7 +136,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.6.8" } }, "nbformat": 4, diff --git a/docs/source/auto_examples/plot_OT_2D_samples.py b/docs/source/auto_examples/plot_OT_2D_samples.py index bb952a0..63126ba 100644 --- a/docs/source/auto_examples/plot_OT_2D_samples.py +++ b/docs/source/auto_examples/plot_OT_2D_samples.py @@ -10,6 +10,7 @@ sum of diracs. The OT matrix is plotted with the samples. """ # Author: Remi Flamary <remi.flamary@unice.fr> +# Kilian Fatras <kilian.fatras@irisa.fr> # # License: MIT License @@ -100,3 +101,28 @@ pl.legend(loc=0) pl.title('OT matrix Sinkhorn with samples') pl.show() + + +############################################################################## +# Emprirical Sinkhorn +# ---------------- + +#%% sinkhorn + +# reg term +lambd = 1e-3 + +Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd) + +pl.figure(7) +pl.imshow(Ges, interpolation='nearest') +pl.title('OT matrix empirical sinkhorn') + +pl.figure(8) +ot.plot.plot2D_samples_mat(xs, xt, Ges, color=[.5, .5, 1]) +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') +pl.legend(loc=0) +pl.title('OT matrix Sinkhorn from samples') + +pl.show() diff --git a/docs/source/auto_examples/plot_OT_2D_samples.rst b/docs/source/auto_examples/plot_OT_2D_samples.rst index 624ae3e..1f1d713 100644 --- a/docs/source/auto_examples/plot_OT_2D_samples.rst +++ b/docs/source/auto_examples/plot_OT_2D_samples.rst @@ -17,6 +17,7 @@ sum of diracs. The OT matrix is plotted with the samples. # Author: Remi Flamary <remi.flamary@unice.fr> + # Kilian Fatras <kilian.fatras@irisa.fr> # # License: MIT License @@ -176,6 +177,8 @@ Compute Sinkhorn + + .. rst-class:: sphx-glr-horizontal @@ -192,7 +195,58 @@ Compute Sinkhorn -**Total running time of the script:** ( 0 minutes 3.027 seconds) +Emprirical Sinkhorn +---------------- + + + +.. code-block:: python + + + #%% sinkhorn + + # reg term + lambd = 1e-3 + + Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd) + + pl.figure(7) + pl.imshow(Ges, interpolation='nearest') + pl.title('OT matrix empirical sinkhorn') + + pl.figure(8) + ot.plot.plot2D_samples_mat(xs, xt, Ges, color=[.5, .5, 1]) + pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') + pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') + pl.legend(loc=0) + pl.title('OT matrix Sinkhorn from samples') + + pl.show() + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_013.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_OT_2D_samples_014.png + :scale: 47 + + +.. rst-class:: sphx-glr-script-out + + Out:: + + Warning: numerical errors at iteration 0 + + +**Total running time of the script:** ( 0 minutes 2.616 seconds) diff --git a/docs/source/auto_examples/plot_UOT_1D.ipynb b/docs/source/auto_examples/plot_UOT_1D.ipynb new file mode 100644 index 0000000..c695306 --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_1D.ipynb @@ -0,0 +1,108 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# 1D Unbalanced optimal transport\n\n\nThis example illustrates the computation of Unbalanced Optimal transport\nusing a Kullback-Leibler relaxation.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Hicham Janati <hicham.janati@inria.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot\nfrom ot.datasets import make_1D_gauss as gauss" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5) # m= mean, s= std\nb = gauss(n, m=60, s=10)\n\n# make distributions unbalanced\nb *= 5.\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot distributions and loss matrix\n----------------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()\n\n# plot distributions and loss matrix\n\npl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, 'Cost matrix M')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solve Unbalanced Sinkhorn\n--------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Sinkhorn\n\nepsilon = 0.1 # entropy parameter\nalpha = 1. # Unbalanced KL relaxation parameter\nGs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn')\n\npl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_UOT_1D.py b/docs/source/auto_examples/plot_UOT_1D.py new file mode 100644 index 0000000..2ea8b05 --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_1D.py @@ -0,0 +1,76 @@ +# -*- coding: utf-8 -*- +""" +=============================== +1D Unbalanced optimal transport +=============================== + +This example illustrates the computation of Unbalanced Optimal transport +using a Kullback-Leibler relaxation. +""" + +# Author: Hicham Janati <hicham.janati@inria.fr> +# +# License: MIT License + +import numpy as np +import matplotlib.pylab as pl +import ot +import ot.plot +from ot.datasets import make_1D_gauss as gauss + +############################################################################## +# Generate data +# ------------- + + +#%% parameters + +n = 100 # nb bins + +# bin positions +x = np.arange(n, dtype=np.float64) + +# Gaussian distributions +a = gauss(n, m=20, s=5) # m= mean, s= std +b = gauss(n, m=60, s=10) + +# make distributions unbalanced +b *= 5. + +# loss matrix +M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) +M /= M.max() + + +############################################################################## +# Plot distributions and loss matrix +# ---------------------------------- + +#%% plot the distributions + +pl.figure(1, figsize=(6.4, 3)) +pl.plot(x, a, 'b', label='Source distribution') +pl.plot(x, b, 'r', label='Target distribution') +pl.legend() + +# plot distributions and loss matrix + +pl.figure(2, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') + + +############################################################################## +# Solve Unbalanced Sinkhorn +# -------------- + + +# Sinkhorn + +epsilon = 0.1 # entropy parameter +alpha = 1. # Unbalanced KL relaxation parameter +Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True) + +pl.figure(4, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn') + +pl.show() diff --git a/docs/source/auto_examples/plot_UOT_1D.rst b/docs/source/auto_examples/plot_UOT_1D.rst new file mode 100644 index 0000000..8e618b4 --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_1D.rst @@ -0,0 +1,173 @@ + + +.. _sphx_glr_auto_examples_plot_UOT_1D.py: + + +=============================== +1D Unbalanced optimal transport +=============================== + +This example illustrates the computation of Unbalanced Optimal transport +using a Kullback-Leibler relaxation. + + + +.. code-block:: python + + + # Author: Hicham Janati <hicham.janati@inria.fr> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + import ot.plot + from ot.datasets import make_1D_gauss as gauss + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + + #%% parameters + + n = 100 # nb bins + + # bin positions + x = np.arange(n, dtype=np.float64) + + # Gaussian distributions + a = gauss(n, m=20, s=5) # m= mean, s= std + b = gauss(n, m=60, s=10) + + # make distributions unbalanced + b *= 5. + + # loss matrix + M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) + M /= M.max() + + + + + + + + +Plot distributions and loss matrix +---------------------------------- + + + +.. code-block:: python + + + #%% plot the distributions + + pl.figure(1, figsize=(6.4, 3)) + pl.plot(x, a, 'b', label='Source distribution') + pl.plot(x, b, 'r', label='Target distribution') + pl.legend() + + # plot distributions and loss matrix + + pl.figure(2, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') + + + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_001.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_002.png + :scale: 47 + + + + +Solve Unbalanced Sinkhorn +-------------- + + + +.. code-block:: python + + + + # Sinkhorn + + epsilon = 0.1 # entropy parameter + alpha = 1. # Unbalanced KL relaxation parameter + Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True) + + pl.figure(4, figsize=(5, 5)) + ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn') + + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_UOT_1D_006.png + :align: center + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Err + ------------------- + 0|1.838786e+00| + 10|1.242379e-01| + 20|2.581314e-03| + 30|5.674552e-05| + 40|1.252959e-06| + 50|2.768136e-08| + 60|6.116090e-10| + + +**Total running time of the script:** ( 0 minutes 0.259 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_UOT_1D.py <plot_UOT_1D.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_UOT_1D.ipynb <plot_UOT_1D.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb b/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb new file mode 100644 index 0000000..e59cdc2 --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_barycenter_1D.ipynb @@ -0,0 +1,126 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# 1D Wasserstein barycenter demo for Unbalanced distributions\n\n\nThis example illustrates the computation of regularized Wassersyein Barycenter\nas proposed in [10] for Unbalanced inputs.\n\n\n[10] Chizat, L., Peyr\u00e9, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Hicham Janati <hicham.janati@inria.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\n# necessary for 3d plot even if not used\nfrom mpl_toolkits.mplot3d import Axes3D # noqa\nfrom matplotlib.collections import PolyCollection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# parameters\n\nn = 100 # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\na2 = ot.datasets.make_1D_gauss(n, m=60, s=8)\n\n# make unbalanced dists\na2 *= 3.\n\n# creating matrix A containing all distributions\nA = np.vstack((a1, a2)).T\nn_distributions = A.shape[1]\n\n# loss matrix + normalization\nM = ot.utils.dist0(n)\nM /= M.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\npl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycenter computation\n----------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# non weighted barycenter computation\n\nweight = 0.5 # 0<=weight<=1\nweights = np.array([1 - weight, weight])\n\n# l2bary\nbary_l2 = A.dot(weights)\n\n# wasserstein\nreg = 1e-3\nalpha = 1.\n\nbary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights)\n\npl.figure(2)\npl.clf()\npl.subplot(2, 1, 1)\nfor i in range(n_distributions):\n pl.plot(x, A[:, i])\npl.title('Distributions')\n\npl.subplot(2, 1, 2)\npl.plot(x, bary_l2, 'r', label='l2')\npl.plot(x, bary_wass, 'g', label='Wasserstein')\npl.legend()\npl.title('Barycenters')\npl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycentric interpolation\n-------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# barycenter interpolation\n\nn_weight = 11\nweight_list = np.linspace(0, 1, n_weight)\n\n\nB_l2 = np.zeros((n, n_weight))\n\nB_wass = np.copy(B_l2)\n\nfor i in range(0, n_weight):\n weight = weight_list[i]\n weights = np.array([1 - weight, weight])\n B_l2[:, i] = A.dot(weights)\n B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights)\n\n\n# plot interpolation\n\npl.figure(3)\n\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = weight_list\nfor i, z in enumerate(zs):\n ys = B_l2[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel(r'$\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with l2')\npl.tight_layout()\n\npl.figure(4)\ncmap = pl.cm.get_cmap('viridis')\nverts = []\nzs = weight_list\nfor i, z in enumerate(zs):\n ys = B_wass[:, i]\n verts.append(list(zip(x, ys)))\n\nax = pl.gcf().gca(projection='3d')\n\npoly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list])\npoly.set_alpha(0.7)\nax.add_collection3d(poly, zs=zs, zdir='y')\nax.set_xlabel('x')\nax.set_xlim3d(0, n)\nax.set_ylabel(r'$\\alpha$')\nax.set_ylim3d(0, 1)\nax.set_zlabel('')\nax.set_zlim3d(0, B_l2.max() * 1.01)\npl.title('Barycenter interpolation with Wasserstein')\npl.tight_layout()\n\npl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.py b/docs/source/auto_examples/plot_UOT_barycenter_1D.py new file mode 100644 index 0000000..c8d9d3b --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_barycenter_1D.py @@ -0,0 +1,164 @@ +# -*- coding: utf-8 -*- +""" +=========================================================== +1D Wasserstein barycenter demo for Unbalanced distributions +=========================================================== + +This example illustrates the computation of regularized Wassersyein Barycenter +as proposed in [10] for Unbalanced inputs. + + +[10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. + +""" + +# Author: Hicham Janati <hicham.janati@inria.fr> +# +# License: MIT License + +import numpy as np +import matplotlib.pylab as pl +import ot +# necessary for 3d plot even if not used +from mpl_toolkits.mplot3d import Axes3D # noqa +from matplotlib.collections import PolyCollection + +############################################################################## +# Generate data +# ------------- + +# parameters + +n = 100 # nb bins + +# bin positions +x = np.arange(n, dtype=np.float64) + +# Gaussian distributions +a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std +a2 = ot.datasets.make_1D_gauss(n, m=60, s=8) + +# make unbalanced dists +a2 *= 3. + +# creating matrix A containing all distributions +A = np.vstack((a1, a2)).T +n_distributions = A.shape[1] + +# loss matrix + normalization +M = ot.utils.dist0(n) +M /= M.max() + +############################################################################## +# Plot data +# --------- + +# plot the distributions + +pl.figure(1, figsize=(6.4, 3)) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') +pl.tight_layout() + +############################################################################## +# Barycenter computation +# ---------------------- + +# non weighted barycenter computation + +weight = 0.5 # 0<=weight<=1 +weights = np.array([1 - weight, weight]) + +# l2bary +bary_l2 = A.dot(weights) + +# wasserstein +reg = 1e-3 +alpha = 1. + +bary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) + +pl.figure(2) +pl.clf() +pl.subplot(2, 1, 1) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') + +pl.subplot(2, 1, 2) +pl.plot(x, bary_l2, 'r', label='l2') +pl.plot(x, bary_wass, 'g', label='Wasserstein') +pl.legend() +pl.title('Barycenters') +pl.tight_layout() + +############################################################################## +# Barycentric interpolation +# ------------------------- + +# barycenter interpolation + +n_weight = 11 +weight_list = np.linspace(0, 1, n_weight) + + +B_l2 = np.zeros((n, n_weight)) + +B_wass = np.copy(B_l2) + +for i in range(0, n_weight): + weight = weight_list[i] + weights = np.array([1 - weight, weight]) + B_l2[:, i] = A.dot(weights) + B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) + + +# plot interpolation + +pl.figure(3) + +cmap = pl.cm.get_cmap('viridis') +verts = [] +zs = weight_list +for i, z in enumerate(zs): + ys = B_l2[:, i] + verts.append(list(zip(x, ys))) + +ax = pl.gcf().gca(projection='3d') + +poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) +poly.set_alpha(0.7) +ax.add_collection3d(poly, zs=zs, zdir='y') +ax.set_xlabel('x') +ax.set_xlim3d(0, n) +ax.set_ylabel(r'$\alpha$') +ax.set_ylim3d(0, 1) +ax.set_zlabel('') +ax.set_zlim3d(0, B_l2.max() * 1.01) +pl.title('Barycenter interpolation with l2') +pl.tight_layout() + +pl.figure(4) +cmap = pl.cm.get_cmap('viridis') +verts = [] +zs = weight_list +for i, z in enumerate(zs): + ys = B_wass[:, i] + verts.append(list(zip(x, ys))) + +ax = pl.gcf().gca(projection='3d') + +poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) +poly.set_alpha(0.7) +ax.add_collection3d(poly, zs=zs, zdir='y') +ax.set_xlabel('x') +ax.set_xlim3d(0, n) +ax.set_ylabel(r'$\alpha$') +ax.set_ylim3d(0, 1) +ax.set_zlabel('') +ax.set_zlim3d(0, B_l2.max() * 1.01) +pl.title('Barycenter interpolation with Wasserstein') +pl.tight_layout() + +pl.show() diff --git a/docs/source/auto_examples/plot_UOT_barycenter_1D.rst b/docs/source/auto_examples/plot_UOT_barycenter_1D.rst new file mode 100644 index 0000000..ac17587 --- /dev/null +++ b/docs/source/auto_examples/plot_UOT_barycenter_1D.rst @@ -0,0 +1,261 @@ + + +.. _sphx_glr_auto_examples_plot_UOT_barycenter_1D.py: + + +=========================================================== +1D Wasserstein barycenter demo for Unbalanced distributions +=========================================================== + +This example illustrates the computation of regularized Wassersyein Barycenter +as proposed in [10] for Unbalanced inputs. + + +[10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. + + + + +.. code-block:: python + + + # Author: Hicham Janati <hicham.janati@inria.fr> + # + # License: MIT License + + import numpy as np + import matplotlib.pylab as pl + import ot + # necessary for 3d plot even if not used + from mpl_toolkits.mplot3d import Axes3D # noqa + from matplotlib.collections import PolyCollection + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + # parameters + + n = 100 # nb bins + + # bin positions + x = np.arange(n, dtype=np.float64) + + # Gaussian distributions + a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std + a2 = ot.datasets.make_1D_gauss(n, m=60, s=8) + + # make unbalanced dists + a2 *= 3. + + # creating matrix A containing all distributions + A = np.vstack((a1, a2)).T + n_distributions = A.shape[1] + + # loss matrix + normalization + M = ot.utils.dist0(n) + M /= M.max() + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + + # plot the distributions + + pl.figure(1, figsize=(6.4, 3)) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + pl.tight_layout() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_001.png + :align: center + + + + +Barycenter computation +---------------------- + + + +.. code-block:: python + + + # non weighted barycenter computation + + weight = 0.5 # 0<=weight<=1 + weights = np.array([1 - weight, weight]) + + # l2bary + bary_l2 = A.dot(weights) + + # wasserstein + reg = 1e-3 + alpha = 1. + + bary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) + + pl.figure(2) + pl.clf() + pl.subplot(2, 1, 1) + for i in range(n_distributions): + pl.plot(x, A[:, i]) + pl.title('Distributions') + + pl.subplot(2, 1, 2) + pl.plot(x, bary_l2, 'r', label='l2') + pl.plot(x, bary_wass, 'g', label='Wasserstein') + pl.legend() + pl.title('Barycenters') + pl.tight_layout() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_003.png + :align: center + + + + +Barycentric interpolation +------------------------- + + + +.. code-block:: python + + + # barycenter interpolation + + n_weight = 11 + weight_list = np.linspace(0, 1, n_weight) + + + B_l2 = np.zeros((n, n_weight)) + + B_wass = np.copy(B_l2) + + for i in range(0, n_weight): + weight = weight_list[i] + weights = np.array([1 - weight, weight]) + B_l2[:, i] = A.dot(weights) + B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) + + + # plot interpolation + + pl.figure(3) + + cmap = pl.cm.get_cmap('viridis') + verts = [] + zs = weight_list + for i, z in enumerate(zs): + ys = B_l2[:, i] + verts.append(list(zip(x, ys))) + + ax = pl.gcf().gca(projection='3d') + + poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) + poly.set_alpha(0.7) + ax.add_collection3d(poly, zs=zs, zdir='y') + ax.set_xlabel('x') + ax.set_xlim3d(0, n) + ax.set_ylabel(r'$\alpha$') + ax.set_ylim3d(0, 1) + ax.set_zlabel('') + ax.set_zlim3d(0, B_l2.max() * 1.01) + pl.title('Barycenter interpolation with l2') + pl.tight_layout() + + pl.figure(4) + cmap = pl.cm.get_cmap('viridis') + verts = [] + zs = weight_list + for i, z in enumerate(zs): + ys = B_wass[:, i] + verts.append(list(zip(x, ys))) + + ax = pl.gcf().gca(projection='3d') + + poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) + poly.set_alpha(0.7) + ax.add_collection3d(poly, zs=zs, zdir='y') + ax.set_xlabel('x') + ax.set_xlim3d(0, n) + ax.set_ylabel(r'$\alpha$') + ax.set_ylim3d(0, 1) + ax.set_zlabel('') + ax.set_zlim3d(0, B_l2.max() * 1.01) + pl.title('Barycenter interpolation with Wasserstein') + pl.tight_layout() + + pl.show() + + + +.. rst-class:: sphx-glr-horizontal + + + * + + .. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_005.png + :scale: 47 + + * + + .. image:: /auto_examples/images/sphx_glr_plot_UOT_barycenter_1D_006.png + :scale: 47 + + + + +**Total running time of the script:** ( 0 minutes 0.344 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_UOT_barycenter_1D.py <plot_UOT_barycenter_1D.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_UOT_barycenter_1D.ipynb <plot_UOT_barycenter_1D.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_barycenter_fgw.ipynb b/docs/source/auto_examples/plot_barycenter_fgw.ipynb new file mode 100644 index 0000000..28229b2 --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_fgw.ipynb @@ -0,0 +1,126 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n=================================\nPlot graphs' barycenter using FGW\n=================================\n\nThis example illustrates the computation barycenter of labeled graphs using FGW\n\nRequires networkx >=2\n\n.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain\n and Courty Nicolas\n \"Optimal Transport for structured data with application on graphs\"\n International Conference on Machine Learning (ICML). 2019.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Titouan Vayer <titouan.vayer@irisa.fr>\n#\n# License: MIT License\n\n#%% load libraries\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport networkx as nx\nimport math\nfrom scipy.sparse.csgraph import shortest_path\nimport matplotlib.colors as mcol\nfrom matplotlib import cm\nfrom ot.gromov import fgw_barycenters\n#%% Graph functions\n\n\ndef find_thresh(C, inf=0.5, sup=3, step=10):\n \"\"\" Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected\n Tthe threshold is found by a linesearch between values \"inf\" and \"sup\" with \"step\" thresholds tested.\n The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix\n and the original matrix.\n Parameters\n ----------\n C : ndarray, shape (n_nodes,n_nodes)\n The structure matrix to threshold\n inf : float\n The beginning of the linesearch\n sup : float\n The end of the linesearch\n step : integer\n Number of thresholds tested\n \"\"\"\n dist = []\n search = np.linspace(inf, sup, step)\n for thresh in search:\n Cprime = sp_to_adjency(C, 0, thresh)\n SC = shortest_path(Cprime, method='D')\n SC[SC == float('inf')] = 100\n dist.append(np.linalg.norm(SC - C))\n return search[np.argmin(dist)], dist\n\n\ndef sp_to_adjency(C, threshinf=0.2, threshsup=1.8):\n \"\"\" Thresholds the structure matrix in order to compute an adjency matrix.\n All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0\n Parameters\n ----------\n C : ndarray, shape (n_nodes,n_nodes)\n The structure matrix to threshold\n threshinf : float\n The minimum value of distance from which the new value is set to 1\n threshsup : float\n The maximum value of distance from which the new value is set to 1\n Returns\n -------\n C : ndarray, shape (n_nodes,n_nodes)\n The threshold matrix. Each element is in {0,1}\n \"\"\"\n H = np.zeros_like(C)\n np.fill_diagonal(H, np.diagonal(C))\n C = C - H\n C = np.minimum(np.maximum(C, threshinf), threshsup)\n C[C == threshsup] = 0\n C[C != 0] = 1\n\n return C\n\n\ndef build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None):\n \"\"\" Create a noisy circular graph\n \"\"\"\n g = nx.Graph()\n g.add_nodes_from(list(range(N)))\n for i in range(N):\n noise = float(np.random.normal(mu, sigma, 1))\n if with_noise:\n g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise)\n else:\n g.add_node(i, attr_name=math.sin(2 * i * math.pi / N))\n g.add_edge(i, i + 1)\n if structure_noise:\n randomint = np.random.randint(0, p)\n if randomint == 0:\n if i <= N - 3:\n g.add_edge(i, i + 2)\n if i == N - 2:\n g.add_edge(i, 0)\n if i == N - 1:\n g.add_edge(i, 1)\n g.add_edge(N, 0)\n noise = float(np.random.normal(mu, sigma, 1))\n if with_noise:\n g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise)\n else:\n g.add_node(N, attr_name=math.sin(2 * N * math.pi / N))\n return g\n\n\ndef graph_colors(nx_graph, vmin=0, vmax=7):\n cnorm = mcol.Normalize(vmin=vmin, vmax=vmax)\n cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis')\n cpick.set_array([])\n val_map = {}\n for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items():\n val_map[k] = cpick.to_rgba(v)\n colors = []\n for node in nx_graph.nodes():\n colors.append(val_map[node])\n return colors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n-------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% circular dataset\n# We build a dataset of noisy circular graphs.\n# Noise is added on the structures by random connections and on the features by gaussian noise.\n\n\nnp.random.seed(30)\nX0 = []\nfor k in range(9):\n X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% Plot graphs\n\nplt.figure(figsize=(8, 10))\nfor i in range(len(X0)):\n plt.subplot(3, 3, i + 1)\n g = X0[i]\n pos = nx.kamada_kawai_layout(g)\n nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100)\nplt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20)\nplt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycenter computation\n----------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph\n# Features distances are the euclidean distances\nCs = [shortest_path(nx.adjacency_matrix(x)) for x in X0]\nps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0]\nYs = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0]\nlambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel()\nsizebary = 15 # we choose a barycenter with 15 nodes\n\nA, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot Barycenter\n-------------------------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% Create the barycenter\nbary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0]))\nfor i, v in enumerate(A.ravel()):\n bary.add_node(i, attr_name=v)\n\n#%%\npos = nx.kamada_kawai_layout(bary)\nnx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False)\nplt.suptitle('Barycenter', fontsize=20)\nplt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_barycenter_fgw.py b/docs/source/auto_examples/plot_barycenter_fgw.py new file mode 100644 index 0000000..77b0370 --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_fgw.py @@ -0,0 +1,184 @@ +# -*- coding: utf-8 -*- +""" +================================= +Plot graphs' barycenter using FGW +================================= + +This example illustrates the computation barycenter of labeled graphs using FGW + +Requires networkx >=2 + +.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain + and Courty Nicolas + "Optimal Transport for structured data with application on graphs" + International Conference on Machine Learning (ICML). 2019. + +""" + +# Author: Titouan Vayer <titouan.vayer@irisa.fr> +# +# License: MIT License + +#%% load libraries +import numpy as np +import matplotlib.pyplot as plt +import networkx as nx +import math +from scipy.sparse.csgraph import shortest_path +import matplotlib.colors as mcol +from matplotlib import cm +from ot.gromov import fgw_barycenters +#%% Graph functions + + +def find_thresh(C, inf=0.5, sup=3, step=10): + """ Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected + Tthe threshold is found by a linesearch between values "inf" and "sup" with "step" thresholds tested. + The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix + and the original matrix. + Parameters + ---------- + C : ndarray, shape (n_nodes,n_nodes) + The structure matrix to threshold + inf : float + The beginning of the linesearch + sup : float + The end of the linesearch + step : integer + Number of thresholds tested + """ + dist = [] + search = np.linspace(inf, sup, step) + for thresh in search: + Cprime = sp_to_adjency(C, 0, thresh) + SC = shortest_path(Cprime, method='D') + SC[SC == float('inf')] = 100 + dist.append(np.linalg.norm(SC - C)) + return search[np.argmin(dist)], dist + + +def sp_to_adjency(C, threshinf=0.2, threshsup=1.8): + """ Thresholds the structure matrix in order to compute an adjency matrix. + All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0 + Parameters + ---------- + C : ndarray, shape (n_nodes,n_nodes) + The structure matrix to threshold + threshinf : float + The minimum value of distance from which the new value is set to 1 + threshsup : float + The maximum value of distance from which the new value is set to 1 + Returns + ------- + C : ndarray, shape (n_nodes,n_nodes) + The threshold matrix. Each element is in {0,1} + """ + H = np.zeros_like(C) + np.fill_diagonal(H, np.diagonal(C)) + C = C - H + C = np.minimum(np.maximum(C, threshinf), threshsup) + C[C == threshsup] = 0 + C[C != 0] = 1 + + return C + + +def build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None): + """ Create a noisy circular graph + """ + g = nx.Graph() + g.add_nodes_from(list(range(N))) + for i in range(N): + noise = float(np.random.normal(mu, sigma, 1)) + if with_noise: + g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise) + else: + g.add_node(i, attr_name=math.sin(2 * i * math.pi / N)) + g.add_edge(i, i + 1) + if structure_noise: + randomint = np.random.randint(0, p) + if randomint == 0: + if i <= N - 3: + g.add_edge(i, i + 2) + if i == N - 2: + g.add_edge(i, 0) + if i == N - 1: + g.add_edge(i, 1) + g.add_edge(N, 0) + noise = float(np.random.normal(mu, sigma, 1)) + if with_noise: + g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise) + else: + g.add_node(N, attr_name=math.sin(2 * N * math.pi / N)) + return g + + +def graph_colors(nx_graph, vmin=0, vmax=7): + cnorm = mcol.Normalize(vmin=vmin, vmax=vmax) + cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis') + cpick.set_array([]) + val_map = {} + for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items(): + val_map[k] = cpick.to_rgba(v) + colors = [] + for node in nx_graph.nodes(): + colors.append(val_map[node]) + return colors + +############################################################################## +# Generate data +# ------------- + +#%% circular dataset +# We build a dataset of noisy circular graphs. +# Noise is added on the structures by random connections and on the features by gaussian noise. + + +np.random.seed(30) +X0 = [] +for k in range(9): + X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3)) + +############################################################################## +# Plot data +# --------- + +#%% Plot graphs + +plt.figure(figsize=(8, 10)) +for i in range(len(X0)): + plt.subplot(3, 3, i + 1) + g = X0[i] + pos = nx.kamada_kawai_layout(g) + nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100) +plt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20) +plt.show() + +############################################################################## +# Barycenter computation +# ---------------------- + +#%% We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph +# Features distances are the euclidean distances +Cs = [shortest_path(nx.adjacency_matrix(x)) for x in X0] +ps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0] +Ys = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0] +lambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel() +sizebary = 15 # we choose a barycenter with 15 nodes + +A, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True) + +############################################################################## +# Plot Barycenter +# ------------------------- + +#%% Create the barycenter +bary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0])) +for i, v in enumerate(A.ravel()): + bary.add_node(i, attr_name=v) + +#%% +pos = nx.kamada_kawai_layout(bary) +nx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False) +plt.suptitle('Barycenter', fontsize=20) +plt.show() diff --git a/docs/source/auto_examples/plot_barycenter_fgw.rst b/docs/source/auto_examples/plot_barycenter_fgw.rst new file mode 100644 index 0000000..2c44a65 --- /dev/null +++ b/docs/source/auto_examples/plot_barycenter_fgw.rst @@ -0,0 +1,268 @@ + + +.. _sphx_glr_auto_examples_plot_barycenter_fgw.py: + + +================================= +Plot graphs' barycenter using FGW +================================= + +This example illustrates the computation barycenter of labeled graphs using FGW + +Requires networkx >=2 + +.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain + and Courty Nicolas + "Optimal Transport for structured data with application on graphs" + International Conference on Machine Learning (ICML). 2019. + + + + +.. code-block:: python + + + # Author: Titouan Vayer <titouan.vayer@irisa.fr> + # + # License: MIT License + + #%% load libraries + import numpy as np + import matplotlib.pyplot as plt + import networkx as nx + import math + from scipy.sparse.csgraph import shortest_path + import matplotlib.colors as mcol + from matplotlib import cm + from ot.gromov import fgw_barycenters + #%% Graph functions + + + def find_thresh(C, inf=0.5, sup=3, step=10): + """ Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected + Tthe threshold is found by a linesearch between values "inf" and "sup" with "step" thresholds tested. + The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix + and the original matrix. + Parameters + ---------- + C : ndarray, shape (n_nodes,n_nodes) + The structure matrix to threshold + inf : float + The beginning of the linesearch + sup : float + The end of the linesearch + step : integer + Number of thresholds tested + """ + dist = [] + search = np.linspace(inf, sup, step) + for thresh in search: + Cprime = sp_to_adjency(C, 0, thresh) + SC = shortest_path(Cprime, method='D') + SC[SC == float('inf')] = 100 + dist.append(np.linalg.norm(SC - C)) + return search[np.argmin(dist)], dist + + + def sp_to_adjency(C, threshinf=0.2, threshsup=1.8): + """ Thresholds the structure matrix in order to compute an adjency matrix. + All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0 + Parameters + ---------- + C : ndarray, shape (n_nodes,n_nodes) + The structure matrix to threshold + threshinf : float + The minimum value of distance from which the new value is set to 1 + threshsup : float + The maximum value of distance from which the new value is set to 1 + Returns + ------- + C : ndarray, shape (n_nodes,n_nodes) + The threshold matrix. Each element is in {0,1} + """ + H = np.zeros_like(C) + np.fill_diagonal(H, np.diagonal(C)) + C = C - H + C = np.minimum(np.maximum(C, threshinf), threshsup) + C[C == threshsup] = 0 + C[C != 0] = 1 + + return C + + + def build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None): + """ Create a noisy circular graph + """ + g = nx.Graph() + g.add_nodes_from(list(range(N))) + for i in range(N): + noise = float(np.random.normal(mu, sigma, 1)) + if with_noise: + g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise) + else: + g.add_node(i, attr_name=math.sin(2 * i * math.pi / N)) + g.add_edge(i, i + 1) + if structure_noise: + randomint = np.random.randint(0, p) + if randomint == 0: + if i <= N - 3: + g.add_edge(i, i + 2) + if i == N - 2: + g.add_edge(i, 0) + if i == N - 1: + g.add_edge(i, 1) + g.add_edge(N, 0) + noise = float(np.random.normal(mu, sigma, 1)) + if with_noise: + g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise) + else: + g.add_node(N, attr_name=math.sin(2 * N * math.pi / N)) + return g + + + def graph_colors(nx_graph, vmin=0, vmax=7): + cnorm = mcol.Normalize(vmin=vmin, vmax=vmax) + cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis') + cpick.set_array([]) + val_map = {} + for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items(): + val_map[k] = cpick.to_rgba(v) + colors = [] + for node in nx_graph.nodes(): + colors.append(val_map[node]) + return colors + + + + + + + +Generate data +------------- + + + +.. code-block:: python + + + #%% circular dataset + # We build a dataset of noisy circular graphs. + # Noise is added on the structures by random connections and on the features by gaussian noise. + + + np.random.seed(30) + X0 = [] + for k in range(9): + X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3)) + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + + #%% Plot graphs + + plt.figure(figsize=(8, 10)) + for i in range(len(X0)): + plt.subplot(3, 3, i + 1) + g = X0[i] + pos = nx.kamada_kawai_layout(g) + nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100) + plt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20) + plt.show() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_barycenter_fgw_001.png + :align: center + + + + +Barycenter computation +---------------------- + + + +.. code-block:: python + + + #%% We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph + # Features distances are the euclidean distances + Cs = [shortest_path(nx.adjacency_matrix(x)) for x in X0] + ps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0] + Ys = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0] + lambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel() + sizebary = 15 # we choose a barycenter with 15 nodes + + A, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True) + + + + + + + +Plot Barycenter +------------------------- + + + +.. code-block:: python + + + #%% Create the barycenter + bary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0])) + for i, v in enumerate(A.ravel()): + bary.add_node(i, attr_name=v) + + #%% + pos = nx.kamada_kawai_layout(bary) + nx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False) + plt.suptitle('Barycenter', fontsize=20) + plt.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_barycenter_fgw_002.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 2.065 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_barycenter_fgw.py <plot_barycenter_fgw.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_barycenter_fgw.ipynb <plot_barycenter_fgw.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/auto_examples/plot_fgw.ipynb b/docs/source/auto_examples/plot_fgw.ipynb new file mode 100644 index 0000000..1b150bd --- /dev/null +++ b/docs/source/auto_examples/plot_fgw.ipynb @@ -0,0 +1,162 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Plot Fused-gromov-Wasserstein\n\n\nThis example illustrates the computation of FGW for 1D measures[18].\n\n.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain\n and Courty Nicolas\n \"Optimal Transport for structured data with application on graphs\"\n International Conference on Machine Learning (ICML). 2019.\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Titouan Vayer <titouan.vayer@irisa.fr>\n#\n# License: MIT License\n\nimport matplotlib.pyplot as pl\nimport numpy as np\nimport ot\nfrom ot.gromov import gromov_wasserstein, fused_gromov_wasserstein" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n# We create two 1D random measures\nn = 20 # number of points in the first distribution\nn2 = 30 # number of points in the second distribution\nsig = 1 # std of first distribution\nsig2 = 0.1 # std of second distribution\n\nnp.random.seed(0)\n\nphi = np.arange(n)[:, None]\nxs = phi + sig * np.random.randn(n, 1)\nys = np.vstack((np.ones((n // 2, 1)), 0 * np.ones((n // 2, 1)))) + sig2 * np.random.randn(n, 1)\n\nphi2 = np.arange(n2)[:, None]\nxt = phi2 + sig * np.random.randn(n2, 1)\nyt = np.vstack((np.ones((n2 // 2, 1)), 0 * np.ones((n2 // 2, 1)))) + sig2 * np.random.randn(n2, 1)\nyt = yt[::-1, :]\n\np = ot.unif(n)\nq = ot.unif(n2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% plot the distributions\n\npl.close(10)\npl.figure(10, (7, 7))\n\npl.subplot(2, 1, 1)\n\npl.scatter(ys, xs, c=phi, s=70)\npl.ylabel('Feature value a', fontsize=20)\npl.title('$\\mu=\\sum_i \\delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1)\npl.xticks(())\npl.yticks(())\npl.subplot(2, 1, 2)\npl.scatter(yt, xt, c=phi2, s=70)\npl.xlabel('coordinates x/y', fontsize=25)\npl.ylabel('Feature value b', fontsize=20)\npl.title('$\\\\nu=\\sum_j \\delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1)\npl.yticks(())\npl.tight_layout()\npl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create structure matrices and across-feature distance matrix\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% Structure matrices and across-features distance matrix\nC1 = ot.dist(xs)\nC2 = ot.dist(xt)\nM = ot.dist(ys, yt)\nw1 = ot.unif(C1.shape[0])\nw2 = ot.unif(C2.shape[0])\nGot = ot.emd([], [], M)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot matrices\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%%\ncmap = 'Reds'\npl.close(10)\npl.figure(10, (5, 5))\nfs = 15\nl_x = [0, 5, 10, 15]\nl_y = [0, 5, 10, 15, 20, 25]\ngs = pl.GridSpec(5, 5)\n\nax1 = pl.subplot(gs[3:, :2])\n\npl.imshow(C1, cmap=cmap, interpolation='nearest')\npl.title(\"$C_1$\", fontsize=fs)\npl.xlabel(\"$k$\", fontsize=fs)\npl.ylabel(\"$i$\", fontsize=fs)\npl.xticks(l_x)\npl.yticks(l_x)\n\nax2 = pl.subplot(gs[:3, 2:])\n\npl.imshow(C2, cmap=cmap, interpolation='nearest')\npl.title(\"$C_2$\", fontsize=fs)\npl.ylabel(\"$l$\", fontsize=fs)\n#pl.ylabel(\"$l$\",fontsize=fs)\npl.xticks(())\npl.yticks(l_y)\nax2.set_aspect('auto')\n\nax3 = pl.subplot(gs[3:, 2:], sharex=ax2, sharey=ax1)\npl.imshow(M, cmap=cmap, interpolation='nearest')\npl.yticks(l_x)\npl.xticks(l_y)\npl.ylabel(\"$i$\", fontsize=fs)\npl.title(\"$M_{AB}$\", fontsize=fs)\npl.xlabel(\"$j$\", fontsize=fs)\npl.tight_layout()\nax3.set_aspect('auto')\npl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compute FGW/GW\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% Computing FGW and GW\nalpha = 1e-3\n\not.tic()\nGwg, logw = fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=alpha, verbose=True, log=True)\not.toc()\n\n#%reload_ext WGW\nGg, log = gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', verbose=True, log=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Visualize transport matrices\n---------\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% visu OT matrix\ncmap = 'Blues'\nfs = 15\npl.figure(2, (13, 5))\npl.clf()\npl.subplot(1, 3, 1)\npl.imshow(Got, cmap=cmap, interpolation='nearest')\n#pl.xlabel(\"$y$\",fontsize=fs)\npl.ylabel(\"$i$\", fontsize=fs)\npl.xticks(())\n\npl.title('Wasserstein ($M$ only)')\n\npl.subplot(1, 3, 2)\npl.imshow(Gg, cmap=cmap, interpolation='nearest')\npl.title('Gromov ($C_1,C_2$ only)')\npl.xticks(())\npl.subplot(1, 3, 3)\npl.imshow(Gwg, cmap=cmap, interpolation='nearest')\npl.title('FGW ($M+C_1,C_2$)')\n\npl.xlabel(\"$j$\", fontsize=fs)\npl.ylabel(\"$i$\", fontsize=fs)\n\npl.tight_layout()\npl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}
\ No newline at end of file diff --git a/docs/source/auto_examples/plot_fgw.py b/docs/source/auto_examples/plot_fgw.py new file mode 100644 index 0000000..43efc94 --- /dev/null +++ b/docs/source/auto_examples/plot_fgw.py @@ -0,0 +1,173 @@ +# -*- coding: utf-8 -*- +""" +============================== +Plot Fused-gromov-Wasserstein +============================== + +This example illustrates the computation of FGW for 1D measures[18]. + +.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain + and Courty Nicolas + "Optimal Transport for structured data with application on graphs" + International Conference on Machine Learning (ICML). 2019. + +""" + +# Author: Titouan Vayer <titouan.vayer@irisa.fr> +# +# License: MIT License + +import matplotlib.pyplot as pl +import numpy as np +import ot +from ot.gromov import gromov_wasserstein, fused_gromov_wasserstein + +############################################################################## +# Generate data +# --------- + +#%% parameters +# We create two 1D random measures +n = 20 # number of points in the first distribution +n2 = 30 # number of points in the second distribution +sig = 1 # std of first distribution +sig2 = 0.1 # std of second distribution + +np.random.seed(0) + +phi = np.arange(n)[:, None] +xs = phi + sig * np.random.randn(n, 1) +ys = np.vstack((np.ones((n // 2, 1)), 0 * np.ones((n // 2, 1)))) + sig2 * np.random.randn(n, 1) + +phi2 = np.arange(n2)[:, None] +xt = phi2 + sig * np.random.randn(n2, 1) +yt = np.vstack((np.ones((n2 // 2, 1)), 0 * np.ones((n2 // 2, 1)))) + sig2 * np.random.randn(n2, 1) +yt = yt[::-1, :] + +p = ot.unif(n) +q = ot.unif(n2) + +############################################################################## +# Plot data +# --------- + +#%% plot the distributions + +pl.close(10) +pl.figure(10, (7, 7)) + +pl.subplot(2, 1, 1) + +pl.scatter(ys, xs, c=phi, s=70) +pl.ylabel('Feature value a', fontsize=20) +pl.title('$\mu=\sum_i \delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1) +pl.xticks(()) +pl.yticks(()) +pl.subplot(2, 1, 2) +pl.scatter(yt, xt, c=phi2, s=70) +pl.xlabel('coordinates x/y', fontsize=25) +pl.ylabel('Feature value b', fontsize=20) +pl.title('$\\nu=\sum_j \delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1) +pl.yticks(()) +pl.tight_layout() +pl.show() + +############################################################################## +# Create structure matrices and across-feature distance matrix +# --------- + +#%% Structure matrices and across-features distance matrix +C1 = ot.dist(xs) +C2 = ot.dist(xt) +M = ot.dist(ys, yt) +w1 = ot.unif(C1.shape[0]) +w2 = ot.unif(C2.shape[0]) +Got = ot.emd([], [], M) + +############################################################################## +# Plot matrices +# --------- + +#%% +cmap = 'Reds' +pl.close(10) +pl.figure(10, (5, 5)) +fs = 15 +l_x = [0, 5, 10, 15] +l_y = [0, 5, 10, 15, 20, 25] +gs = pl.GridSpec(5, 5) + +ax1 = pl.subplot(gs[3:, :2]) + +pl.imshow(C1, cmap=cmap, interpolation='nearest') +pl.title("$C_1$", fontsize=fs) +pl.xlabel("$k$", fontsize=fs) +pl.ylabel("$i$", fontsize=fs) +pl.xticks(l_x) +pl.yticks(l_x) + +ax2 = pl.subplot(gs[:3, 2:]) + +pl.imshow(C2, cmap=cmap, interpolation='nearest') +pl.title("$C_2$", fontsize=fs) +pl.ylabel("$l$", fontsize=fs) +#pl.ylabel("$l$",fontsize=fs) +pl.xticks(()) +pl.yticks(l_y) +ax2.set_aspect('auto') + +ax3 = pl.subplot(gs[3:, 2:], sharex=ax2, sharey=ax1) +pl.imshow(M, cmap=cmap, interpolation='nearest') +pl.yticks(l_x) +pl.xticks(l_y) +pl.ylabel("$i$", fontsize=fs) +pl.title("$M_{AB}$", fontsize=fs) +pl.xlabel("$j$", fontsize=fs) +pl.tight_layout() +ax3.set_aspect('auto') +pl.show() + +############################################################################## +# Compute FGW/GW +# --------- + +#%% Computing FGW and GW +alpha = 1e-3 + +ot.tic() +Gwg, logw = fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=alpha, verbose=True, log=True) +ot.toc() + +#%reload_ext WGW +Gg, log = gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', verbose=True, log=True) + +############################################################################## +# Visualize transport matrices +# --------- + +#%% visu OT matrix +cmap = 'Blues' +fs = 15 +pl.figure(2, (13, 5)) +pl.clf() +pl.subplot(1, 3, 1) +pl.imshow(Got, cmap=cmap, interpolation='nearest') +#pl.xlabel("$y$",fontsize=fs) +pl.ylabel("$i$", fontsize=fs) +pl.xticks(()) + +pl.title('Wasserstein ($M$ only)') + +pl.subplot(1, 3, 2) +pl.imshow(Gg, cmap=cmap, interpolation='nearest') +pl.title('Gromov ($C_1,C_2$ only)') +pl.xticks(()) +pl.subplot(1, 3, 3) +pl.imshow(Gwg, cmap=cmap, interpolation='nearest') +pl.title('FGW ($M+C_1,C_2$)') + +pl.xlabel("$j$", fontsize=fs) +pl.ylabel("$i$", fontsize=fs) + +pl.tight_layout() +pl.show() diff --git a/docs/source/auto_examples/plot_fgw.rst b/docs/source/auto_examples/plot_fgw.rst new file mode 100644 index 0000000..aec725d --- /dev/null +++ b/docs/source/auto_examples/plot_fgw.rst @@ -0,0 +1,297 @@ + + +.. _sphx_glr_auto_examples_plot_fgw.py: + + +============================== +Plot Fused-gromov-Wasserstein +============================== + +This example illustrates the computation of FGW for 1D measures[18]. + +.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain + and Courty Nicolas + "Optimal Transport for structured data with application on graphs" + International Conference on Machine Learning (ICML). 2019. + + + + +.. code-block:: python + + + # Author: Titouan Vayer <titouan.vayer@irisa.fr> + # + # License: MIT License + + import matplotlib.pyplot as pl + import numpy as np + import ot + from ot.gromov import gromov_wasserstein, fused_gromov_wasserstein + + + + + + + +Generate data +--------- + + + +.. code-block:: python + + + #%% parameters + # We create two 1D random measures + n = 20 # number of points in the first distribution + n2 = 30 # number of points in the second distribution + sig = 1 # std of first distribution + sig2 = 0.1 # std of second distribution + + np.random.seed(0) + + phi = np.arange(n)[:, None] + xs = phi + sig * np.random.randn(n, 1) + ys = np.vstack((np.ones((n // 2, 1)), 0 * np.ones((n // 2, 1)))) + sig2 * np.random.randn(n, 1) + + phi2 = np.arange(n2)[:, None] + xt = phi2 + sig * np.random.randn(n2, 1) + yt = np.vstack((np.ones((n2 // 2, 1)), 0 * np.ones((n2 // 2, 1)))) + sig2 * np.random.randn(n2, 1) + yt = yt[::-1, :] + + p = ot.unif(n) + q = ot.unif(n2) + + + + + + + +Plot data +--------- + + + +.. code-block:: python + + + #%% plot the distributions + + pl.close(10) + pl.figure(10, (7, 7)) + + pl.subplot(2, 1, 1) + + pl.scatter(ys, xs, c=phi, s=70) + pl.ylabel('Feature value a', fontsize=20) + pl.title('$\mu=\sum_i \delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1) + pl.xticks(()) + pl.yticks(()) + pl.subplot(2, 1, 2) + pl.scatter(yt, xt, c=phi2, s=70) + pl.xlabel('coordinates x/y', fontsize=25) + pl.ylabel('Feature value b', fontsize=20) + pl.title('$\\nu=\sum_j \delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1) + pl.yticks(()) + pl.tight_layout() + pl.show() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_fgw_010.png + :align: center + + + + +Create structure matrices and across-feature distance matrix +--------- + + + +.. code-block:: python + + + #%% Structure matrices and across-features distance matrix + C1 = ot.dist(xs) + C2 = ot.dist(xt) + M = ot.dist(ys, yt) + w1 = ot.unif(C1.shape[0]) + w2 = ot.unif(C2.shape[0]) + Got = ot.emd([], [], M) + + + + + + + +Plot matrices +--------- + + + +.. code-block:: python + + + #%% + cmap = 'Reds' + pl.close(10) + pl.figure(10, (5, 5)) + fs = 15 + l_x = [0, 5, 10, 15] + l_y = [0, 5, 10, 15, 20, 25] + gs = pl.GridSpec(5, 5) + + ax1 = pl.subplot(gs[3:, :2]) + + pl.imshow(C1, cmap=cmap, interpolation='nearest') + pl.title("$C_1$", fontsize=fs) + pl.xlabel("$k$", fontsize=fs) + pl.ylabel("$i$", fontsize=fs) + pl.xticks(l_x) + pl.yticks(l_x) + + ax2 = pl.subplot(gs[:3, 2:]) + + pl.imshow(C2, cmap=cmap, interpolation='nearest') + pl.title("$C_2$", fontsize=fs) + pl.ylabel("$l$", fontsize=fs) + #pl.ylabel("$l$",fontsize=fs) + pl.xticks(()) + pl.yticks(l_y) + ax2.set_aspect('auto') + + ax3 = pl.subplot(gs[3:, 2:], sharex=ax2, sharey=ax1) + pl.imshow(M, cmap=cmap, interpolation='nearest') + pl.yticks(l_x) + pl.xticks(l_y) + pl.ylabel("$i$", fontsize=fs) + pl.title("$M_{AB}$", fontsize=fs) + pl.xlabel("$j$", fontsize=fs) + pl.tight_layout() + ax3.set_aspect('auto') + pl.show() + + + + +.. image:: /auto_examples/images/sphx_glr_plot_fgw_011.png + :align: center + + + + +Compute FGW/GW +--------- + + + +.. code-block:: python + + + #%% Computing FGW and GW + alpha = 1e-3 + + ot.tic() + Gwg, logw = fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=alpha, verbose=True, log=True) + ot.toc() + + #%reload_ext WGW + Gg, log = gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', verbose=True, log=True) + + + + + +.. rst-class:: sphx-glr-script-out + + Out:: + + It. |Loss |Relative loss|Absolute loss + ------------------------------------------------ + 0|4.734462e+01|0.000000e+00|0.000000e+00 + 1|2.508258e+01|8.875498e-01|2.226204e+01 + 2|2.189329e+01|1.456747e-01|3.189297e+00 + 3|2.189329e+01|0.000000e+00|0.000000e+00 + Elapsed time : 0.0016989707946777344 s + It. |Loss |Relative loss|Absolute loss + ------------------------------------------------ + 0|4.683978e+04|0.000000e+00|0.000000e+00 + 1|3.860061e+04|2.134468e-01|8.239175e+03 + 2|2.182948e+04|7.682787e-01|1.677113e+04 + 3|2.182948e+04|0.000000e+00|0.000000e+00 + + +Visualize transport matrices +--------- + + + +.. code-block:: python + + + #%% visu OT matrix + cmap = 'Blues' + fs = 15 + pl.figure(2, (13, 5)) + pl.clf() + pl.subplot(1, 3, 1) + pl.imshow(Got, cmap=cmap, interpolation='nearest') + #pl.xlabel("$y$",fontsize=fs) + pl.ylabel("$i$", fontsize=fs) + pl.xticks(()) + + pl.title('Wasserstein ($M$ only)') + + pl.subplot(1, 3, 2) + pl.imshow(Gg, cmap=cmap, interpolation='nearest') + pl.title('Gromov ($C_1,C_2$ only)') + pl.xticks(()) + pl.subplot(1, 3, 3) + pl.imshow(Gwg, cmap=cmap, interpolation='nearest') + pl.title('FGW ($M+C_1,C_2$)') + + pl.xlabel("$j$", fontsize=fs) + pl.ylabel("$i$", fontsize=fs) + + pl.tight_layout() + pl.show() + + + +.. image:: /auto_examples/images/sphx_glr_plot_fgw_004.png + :align: center + + + + +**Total running time of the script:** ( 0 minutes 1.468 seconds) + + + +.. only :: html + + .. container:: sphx-glr-footer + + + .. container:: sphx-glr-download + + :download:`Download Python source code: plot_fgw.py <plot_fgw.py>` + + + + .. container:: sphx-glr-download + + :download:`Download Jupyter notebook: plot_fgw.ipynb <plot_fgw.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ diff --git a/docs/source/conf.py b/docs/source/conf.py index 433eca6..d29b829 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -15,7 +15,10 @@ import sys import os import re -import sphinx_gallery +try: + import sphinx_gallery +except ImportError: + print("warning sphinx-gallery not installed") # !!!! allow readthedoc compilation try: @@ -65,6 +68,8 @@ extensions = [ #'sphinx_gallery.gen_gallery', ] +napoleon_numpy_docstring = True + # Add any paths that contain templates here, relative to this directory. templates_path = ['_templates'] @@ -81,7 +86,7 @@ master_doc = 'index' # General information about the project. project = u'POT Python Optimal Transport' -copyright = u'2016-2018, Rémi Flamary, Nicolas Courty' +copyright = u'2016-2019, Rémi Flamary, Nicolas Courty' author = u'Rémi Flamary, Nicolas Courty' # The version info for the project you're documenting, acts as replacement for @@ -323,7 +328,10 @@ texinfo_documents = [ # Example configuration for intersphinx: refer to the Python standard library. -intersphinx_mapping = {'https://docs.python.org/': None} +intersphinx_mapping = {'python': ('https://docs.python.org/3', None), + 'numpy': ('http://docs.scipy.org/doc/numpy/', None), + 'scipy': ('http://docs.scipy.org/doc/scipy/reference/', None), + 'matplotlib': ('http://matplotlib.sourceforge.net/', None)} sphinx_gallery_conf = { 'examples_dirs': ['../../examples','../../examples/da'], diff --git a/docs/source/index.rst b/docs/source/index.rst index b8eabcb..9078d35 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -10,9 +10,10 @@ Contents -------- .. toctree:: - :maxdepth: 3 + :maxdepth: 2 self + quickstart all auto_examples/index diff --git a/docs/source/quickstart.rst b/docs/source/quickstart.rst new file mode 100644 index 0000000..1640d6a --- /dev/null +++ b/docs/source/quickstart.rst @@ -0,0 +1,877 @@ + +Quick start guide +================= + +In the following we provide some pointers about which functions and classes +to use for different problems related to optimal transport (OT) and machine +learning. We refer when we can to concrete examples in the documentation that +are also available as notebooks on the POT Github. + +This document is not a tutorial on numerical optimal transport. For this we strongly +recommend to read the very nice book [15]_ . + + +Optimal transport and Wasserstein distance +------------------------------------------ + +.. note:: + In POT, most functions that solve OT or regularized OT problems have two + versions that return the OT matrix or the value of the optimal solution. For + instance :any:`ot.emd` return the OT matrix and :any:`ot.emd2` return the + Wassertsein distance. This approach has been implemented in practice for all + solvers that return an OT matrix (even Gromov-Wasserstsein) + +Solving optimal transport +^^^^^^^^^^^^^^^^^^^^^^^^^ + +The optimal transport problem between discrete distributions is often expressed +as + +.. math:: + \gamma^* = arg\min_\gamma \quad \sum_{i,j}\gamma_{i,j}M_{i,j} + + s.t. \gamma 1 = a; \gamma^T 1= b; \gamma\geq 0 + +where : + +- :math:`M\in\mathbb{R}_+^{m\times n}` is the metric cost matrix defining the cost to move mass from bin :math:`a_i` to bin :math:`b_j`. +- :math:`a` and :math:`b` are histograms on the simplex (positive, sum to 1) that represent the +weights of each samples in the source an target distributions. + +Solving the linear program above can be done using the function :any:`ot.emd` +that will return the optimal transport matrix :math:`\gamma^*`: + +.. code:: python + + # a,b are 1D histograms (sum to 1 and positive) + # M is the ground cost matrix + T=ot.emd(a,b,M) # exact linear program + +The method implemented for solving the OT problem is the network simplex, it is +implemented in C from [1]_. It has a complexity of :math:`O(n^3)` but the +solver is quite efficient and uses sparsity of the solution. + +.. hint:: + Examples of use for :any:`ot.emd` are available in : + + - :any:`auto_examples/plot_OT_2D_samples` + - :any:`auto_examples/plot_OT_1D` + - :any:`auto_examples/plot_OT_L1_vs_L2` + + +Computing Wasserstein distance +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The value of the OT solution is often more of interest than the OT matrix : + +.. math:: + OT(a,b)=\min_\gamma \quad \sum_{i,j}\gamma_{i,j}M_{i,j} + + s.t. \gamma 1 = a; \gamma^T 1= b; \gamma\geq 0 + + +It can computed from an already estimated OT matrix with +:code:`np.sum(T*M)` or directly with the function :any:`ot.emd2`. + +.. code:: python + + # a,b are 1D histograms (sum to 1 and positive) + # M is the ground cost matrix + W=ot.emd2(a,b,M) # Wasserstein distance / EMD value + +Note that the well known `Wasserstein distance +<https://en.wikipedia.org/wiki/Wasserstein_metric>`_ between distributions a and +b is defined as + + + .. math:: + + W_p(a,b)=(\min_\gamma \sum_{i,j}\gamma_{i,j}\|x_i-y_j\|_p)^\frac{1}{p} + + s.t. \gamma 1 = a; \gamma^T 1= b; \gamma\geq 0 + +This means that if you want to compute the :math:`W_2` you need to compute the +square root of :any:`ot.emd2` when providing +:code:`M=ot.dist(xs,xt)` that use the squared euclidean distance by default. Computing +the :math:`W_1` wasserstein distance can be done directly with :any:`ot.emd2` +when providing :code:`M=ot.dist(xs,xt, metric='euclidean')` to use the euclidean +distance. + + +.. hint:: + An example of use for :any:`ot.emd2` is available in : + + - :any:`auto_examples/plot_compute_emd` + + +Special cases +^^^^^^^^^^^^^ + +Note that the OT problem and the corresponding Wasserstein distance can in some +special cases be computed very efficiently. + +For instance when the samples are in 1D, then the OT problem can be solved in +:math:`O(n\log(n))` by using a simple sorting. In this case we provide the +function :any:`ot.emd_1d` and :any:`ot.emd2_1d` to return respectively the OT +matrix and value. Note that since the solution is very sparse the :code:`sparse` +parameter of :any:`ot.emd_1d` allows for solving and returning the solution for +very large problems. Note that in order to compute directly the :math:`W_p` +Wasserstein distance in 1D we provide the function :any:`ot.wasserstein_1d` that +takes :code:`p` as a parameter. + +Another special case for estimating OT and Monge mapping is between Gaussian +distributions. In this case there exists a close form solution given in Remark +2.29 in [15]_ and the Monge mapping is an affine function and can be +also computed from the covariances and means of the source and target +distributions. In the case when the finite sample dataset is supposed gaussian, we provide +:any:`ot.da.OT_mapping_linear` that returns the parameters for the Monge +mapping. + + +Regularized Optimal Transport +----------------------------- + +Recent developments have shown the interest of regularized OT both in terms of +computational and statistical properties. +We address in this section the regularized OT problems that can be expressed as + +.. math:: + \gamma^* = arg\min_\gamma \quad \sum_{i,j}\gamma_{i,j}M_{i,j} + \lambda\Omega(\gamma) + + s.t. \gamma 1 = a; \gamma^T 1= b; \gamma\geq 0 + + +where : + +- :math:`M\in\mathbb{R}_+^{m\times n}` is the metric cost matrix defining the cost to move mass from bin :math:`a_i` to bin :math:`b_j`. +- :math:`a` and :math:`b` are histograms (positive, sum to 1) that represent the weights of each samples in the source an target distributions. +- :math:`\Omega` is the regularization term. + +We discuss in the following specific algorithms that can be used depending on +the regularization term. + + +Entropic regularized OT +^^^^^^^^^^^^^^^^^^^^^^^ + +This is the most common regularization used for optimal transport. It has been +proposed in the ML community by Marco Cuturi in his seminal paper [2]_. This +regularization has the following expression + +.. math:: + \Omega(\gamma)=\sum_{i,j}\gamma_{i,j}\log(\gamma_{i,j}) + + +The use of the regularization term above in the optimization problem has a very +strong impact. First it makes the problem smooth which leads to new optimization +procedures such as the well known Sinkhorn algorithm [2]_ or L-BFGS (see +:any:`ot.smooth` ). Next it makes the problem +strictly convex meaning that there will be a unique solution. Finally the +solution of the resulting optimization problem can be expressed as: + +.. math:: + + \gamma_\lambda^*=\text{diag}(u)K\text{diag}(v) + +where :math:`u` and :math:`v` are vectors and :math:`K=\exp(-M/\lambda)` where +the :math:`\exp` is taken component-wise. In order to solve the optimization +problem, on can use an alternative projection algorithm called Sinkhorn-Knopp that can be very +efficient for large values if regularization. + +The Sinkhorn-Knopp algorithm is implemented in :any:`ot.sinkhorn` and +:any:`ot.sinkhorn2` that return respectively the OT matrix and the value of the +linear term. Note that the regularization parameter :math:`\lambda` in the +equation above is given to those functions with the parameter :code:`reg`. + + >>> import ot + >>> a=[.5,.5] + >>> b=[.5,.5] + >>> M=[[0.,1.],[1.,0.]] + >>> ot.sinkhorn(a,b,M,1) + array([[ 0.36552929, 0.13447071], + [ 0.13447071, 0.36552929]]) + +More details about the algorithms used are given in the following note. + +.. note:: + The main function to solve entropic regularized OT is :any:`ot.sinkhorn`. + This function is a wrapper and the parameter :code:`method` help you select + the actual algorithm used to solve the problem: + + + :code:`method='sinkhorn'` calls :any:`ot.bregman.sinkhorn_knopp` the + classic algorithm [2]_. + + :code:`method='sinkhorn_stabilized'` calls :any:`ot.bregman.sinkhorn_stabilized` the + log stabilized version of the algorithm [9]_. + + :code:`method='sinkhorn_epsilon_scaling'` calls + :any:`ot.bregman.sinkhorn_epsilon_scaling` the epsilon scaling version + of the algorithm [9]_. + + :code:`method='greenkhorn'` calls :any:`ot.bregman.greenkhorn` the + greedy sinkhorn verison of the algorithm [22]_. + + In addition to all those variants of sinkhorn, we have another + implementation solving the problem in the smooth dual or semi-dual in + :any:`ot.smooth`. This solver uses the :any:`scipy.optimize.minimize` + function to solve the smooth problem with :code:`L-BFGS-B` algorithm. Tu use + this solver, use functions :any:`ot.smooth.smooth_ot_dual` or + :any:`ot.smooth.smooth_ot_semi_dual` with parameter :code:`reg_type='kl'` to + choose entropic/Kullbach Leibler regularization. + + +Recently [23]_ introduced the sinkhorn divergence that build from entropic +regularization to compute fast and differentiable geometric divergence between +empirical distributions. Note that we provide a function that compute directly +(with no need to pre compute the :code:`M` matrix) +the sinkhorn divergence for empirical distributions in +:any:`ot.bregman.empirical_sinkhorn_divergence`. Similarly one can compute the +OT matrix and loss for empirical distributions with respectively +:any:`ot.bregman.empirical_sinkhorn` and :any:`ot.bregman.empirical_sinkhorn2`. + + +Finally note that we also provide in :any:`ot.stochastic` several implementation +of stochastic solvers for entropic regularized OT [18]_ [19]_. Those pure Python +implementations are not optimized for speed but provide a roust implementation +of algorithms in [18]_ [19]_. + +.. hint:: + Examples of use for :any:`ot.sinkhorn` are available in : + + - :any:`auto_examples/plot_OT_2D_samples` + - :any:`auto_examples/plot_OT_1D` + - :any:`auto_examples/plot_OT_1D_smooth` + - :any:`auto_examples/plot_stochastic` + + +Other regularization +^^^^^^^^^^^^^^^^^^^^ + +While entropic OT is the most common and favored in practice, there exist other +kind of regularization. We provide in POT two specific solvers for other +regularization terms, namely quadratic regularization and group lasso +regularization. But we also provide in :any:`ot.optim` two generic solvers that allows solving any +smooth regularization in practice. + +Quadratic regularization +"""""""""""""""""""""""" + +The first general regularization term we can solve is the quadratic +regularization of the form + +.. math:: + \Omega(\gamma)=\sum_{i,j} \gamma_{i,j}^2 + +this regularization term has a similar effect to entropic regularization in +densifying the OT matrix but it keeps some sort of sparsity that is lost with +entropic regularization as soon as :math:`\lambda>0` [17]_. This problem can be +solved with POT using solvers from :any:`ot.smooth`, more specifically +functions :any:`ot.smooth.smooth_ot_dual` or +:any:`ot.smooth.smooth_ot_semi_dual` with parameter :code:`reg_type='l2'` to +choose the quadratic regularization. + +.. hint:: + Examples of quadratic regularization are available in : + + - :any:`auto_examples/plot_OT_1D_smooth` + - :any:`auto_examples/plot_optim_OTreg` + + + +Group Lasso regularization +"""""""""""""""""""""""""" + +Another regularization that has been used in recent years [5]_ is the group lasso +regularization + +.. math:: + \Omega(\gamma)=\sum_{j,G\in\mathcal{G}} \|\gamma_{G,j}\|_q^p + +where :math:`\mathcal{G}` contains non overlapping groups of lines in the OT +matrix. This regularization proposed in [5]_ will promote sparsity at the group level and for +instance will force target samples to get mass from a small number of groups. +Note that the exact OT solution is already sparse so this regularization does +not make sens if it is not combined with entropic regularization. Depending on +the choice of :code:`p` and :code:`q`, the problem can be solved with different +approaches. When :code:`q=1` and :code:`p<1` the problem is non convex but can +be solved using an efficient majoration minimization approach with +:any:`ot.sinkhorn_lpl1_mm`. When :code:`q=2` and :code:`p=1` we recover the +convex group lasso and we provide a solver using generalized conditional +gradient algorithm [7]_ in function +:any:`ot.da.sinkhorn_l1l2_gl`. + +.. hint:: + Examples of group Lasso regularization are available in : + + - :any:`auto_examples/plot_otda_classes` + - :any:`auto_examples/plot_otda_d2` + + +Generic solvers +""""""""""""""" + +Finally we propose in POT generic solvers that can be used to solve any +regularization as long as you can provide a function computing the +regularization and a function computing its gradient (or sub-gradient). + +In order to solve + +.. math:: + \gamma^* = arg\min_\gamma \quad \sum_{i,j}\gamma_{i,j}M_{i,j} + \lambda\Omega(\gamma) + + s.t. \gamma 1 = a; \gamma^T 1= b; \gamma\geq 0 + +you can use function :any:`ot.optim.cg` that will use a conditional gradient as +proposed in [6]_ . You need to provide the regularization function as parameter +``f`` and its gradient as parameter ``df``. Note that the conditional gradient relies on +iterative solving of a linearization of the problem using the exact +:any:`ot.emd` so it can be slow in practice. But, being an interior point +algorithm, it always returns a +transport matrix that does not violates the marginals. + +Another generic solver is proposed to solve the problem + +.. math:: + \gamma^* = arg\min_\gamma \quad \sum_{i,j}\gamma_{i,j}M_{i,j}+ \lambda_e\Omega_e(\gamma) + \lambda\Omega(\gamma) + + s.t. \gamma 1 = a; \gamma^T 1= b; \gamma\geq 0 + +where :math:`\Omega_e` is the entropic regularization. In this case we use a +generalized conditional gradient [7]_ implemented in :any:`ot.optim.gcg` that +does not linearize the entropic term but +relies on :any:`ot.sinkhorn` for its iterations. + +.. hint:: + An example of generic solvers are available in : + + - :any:`auto_examples/plot_optim_OTreg` + + +Wasserstein Barycenters +----------------------- + +A Wasserstein barycenter is a distribution that minimize its Wasserstein +distance with respect to other distributions [16]_. It corresponds to minimizing the +following problem by searching a distribution :math:`\mu` such that + +.. math:: + \min_\mu \quad \sum_{k} w_kW(\mu,\mu_k) + + +In practice we model a distribution with a finite number of support position: + +.. math:: + \mu=\sum_{i=1}^n a_i\delta_{x_i} + +where :math:`a` is an histogram on the simplex and the :math:`\{x_i\}` are the +position of the support. We can clearly see here that optimizing :math:`\mu` can +be done by searching for optimal weights :math:`a` or optimal support +:math:`\{x_i\}` (optimizing both is also an option). +We provide in POT solvers to estimate a discrete +Wasserstein barycenter in both cases. + +Barycenters with fixed support +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +When optimizing a barycenter with a fixed support, the optimization problem can +be expressed as + +.. math:: + \min_a \quad \sum_{k} w_k W(a,b_k) + +where :math:`b_k` are also weights in the simplex. In the non-regularized case, +the problem above is a classical linear program. In this case we propose a +solver :any:`ot.lp.barycenter` that rely on generic LP solvers. By default the +function uses :any:`scipy.optimize.linprog`, but more efficient LP solvers from +cvxopt can be also used by changing parameter :code:`solver`. Note that this problem +requires to solve a very large linear program and can be very slow in +practice. + +Similarly to the OT problem, OT barycenters can be computed in the regularized +case. When using entropic regularization is used, the problem can be solved with a +generalization of the sinkhorn algorithm based on bregman projections [3]_. This +algorithm is provided in function :any:`ot.bregman.barycenter` also available as +:any:`ot.barycenter`. In this case, the algorithm scales better to large +distributions and rely only on matrix multiplications that can be performed in +parallel. + +In addition to the speedup brought by regularization, one can also greatly +accelerate the estimation of Wasserstein barycenter when the support has a +separable structure [21]_. In the case of 2D images for instance one can replace +the matrix vector production in the Bregman projections by convolution +operators. We provide an implementation of this algorithm in function +:any:`ot.bregman.convolutional_barycenter2d`. + +.. hint:: + Examples of Wasserstein (:any:`ot.lp.barycenter`) and regularized Wasserstein + barycenter (:any:`ot.bregman.barycenter`) computation are available in : + + - :any:`auto_examples/plot_barycenter_1D` + - :any:`auto_examples/plot_barycenter_lp_vs_entropic` + + An example of convolutional barycenter + (:any:`ot.bregman.convolutional_barycenter2d`) computation + for 2D images is available + in : + + - :any:`auto_examples/plot_convolutional_barycenter` + + + +Barycenters with free support +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Estimating the Wasserstein barycenter with free support but fixed weights +corresponds to solving the following optimization problem: + +.. math:: + \min_{\{x_i\}} \quad \sum_{k} w_kW(\mu,\mu_k) + + s.t. \quad \mu=\sum_{i=1}^n a_i\delta_{x_i} + +We provide a solver based on [20]_ in +:any:`ot.lp.free_support_barycenter`. This function minimize the problem and +return a locally optimal support :math:`\{x_i\}` for uniform or given weights +:math:`a`. + + .. hint:: + + An example of the free support barycenter estimation is available + in : + + - :any:`auto_examples/plot_free_support_barycenter` + + + + +Monge mapping and Domain adaptation +----------------------------------- + +The original transport problem investigated by Gaspard Monge was seeking for a +mapping function that maps (or transports) between a source and target +distribution but that minimizes the transport loss. The existence and uniqueness of this +optimal mapping is still an open problem in the general case but has been proven +for smooth distributions by Brenier in his eponym `theorem +<https://who.rocq.inria.fr/Jean-David.Benamou/demiheure.pdf>`__. We provide in +:any:`ot.da` several solvers for smooth Monge mapping estimation and domain +adaptation from discrete distributions. + +Monge Mapping estimation +^^^^^^^^^^^^^^^^^^^^^^^^ + +We now discuss several approaches that are implemented in POT to estimate or +approximate a Monge mapping from finite distributions. + +First note that when the source and target distributions are supposed to be Gaussian +distributions, there exists a close form solution for the mapping and its an +affine function [14]_ of the form :math:`T(x)=Ax+b` . In this case we provide the function +:any:`ot.da.OT_mapping_linear` that return the operator :math:`A` and vector +:math:`b`. Note that if the number of samples is too small there is a parameter +:code:`reg` that provide a regularization for the covariance matrix estimation. + +For a more general mapping estimation we also provide the barycentric mapping +proposed in [6]_ . It is implemented in the class :any:`ot.da.EMDTransport` and +other transport based classes in :any:`ot.da` . Those classes are discussed more +in the following but follow an interface similar to sklearn classes. Finally a +method proposed in [8]_ that estimates a continuous mapping approximating the +barycentric mapping is provided in :any:`ot.da.joint_OT_mapping_linear` for +linear mapping and :any:`ot.da.joint_OT_mapping_kernel` for non linear mapping. + + .. hint:: + + An example of the linear Monge mapping estimation is available + in : + + - :any:`auto_examples/plot_otda_linear_mapping` + +Domain adaptation classes +^^^^^^^^^^^^^^^^^^^^^^^^^ + +The use of OT for domain adaptation (OTDA) has been first proposed in [5]_ that also +introduced the group Lasso regularization. The main idea of OTDA is to estimate +a mapping of the samples between source and target distributions which allows to +transport labeled source samples onto the target distribution with no labels. + +We provide several classes based on :any:`ot.da.BaseTransport` that provide +several OT and mapping estimations. The interface of those classes is similar to +classifiers in sklearn toolbox. At initialization, several parameters such as + regularization parameter value can be set. Then one needs to estimate the +mapping with function :any:`ot.da.BaseTransport.fit`. Finally one can map the +samples from source to target with :any:`ot.da.BaseTransport.transform` and +from target to source with :any:`ot.da.BaseTransport.inverse_transform`. + +Here is +an example for class :any:`ot.da.EMDTransport` : + +.. code:: + + ot_emd = ot.da.EMDTransport() + ot_emd.fit(Xs=Xs, Xt=Xt) + + Mapped_Xs= ot_emd.transform(Xs=Xs) + +A list of the provided implementation is given in the following note. + +.. note:: + + Here is a list of the OT mapping classes inheriting from + :any:`ot.da.BaseTransport` + + * :any:`ot.da.EMDTransport` : Barycentric mapping with EMD transport + * :any:`ot.da.SinkhornTransport` : Barycentric mapping with Sinkhorn transport + * :any:`ot.da.SinkhornL1l2Transport` : Barycentric mapping with Sinkhorn + + group Lasso regularization [5]_ + * :any:`ot.da.SinkhornLpl1Transport` : Barycentric mapping with Sinkhorn + + non convex group Lasso regularization [5]_ + * :any:`ot.da.LinearTransport` : Linear mapping estimation between Gaussians + [14]_ + * :any:`ot.da.MappingTransport` : Nonlinear mapping estimation [8]_ + +.. hint:: + + Example of the use of OTDA classes are available in : + + - :any:`auto_examples/plot_otda_color_images` + - :any:`auto_examples/plot_otda_mapping` + - :any:`auto_examples/plot_otda_mapping_colors_images` + - :any:`auto_examples/plot_otda_semi_supervised` + +Other applications +------------------ + +We discuss in the following several OT related problems and tools that has been +proposed in the OT and machine learning community. + +Wasserstein Discriminant Analysis +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Wasserstein Discriminant Analysis [11]_ is a generalization of `Fisher Linear Discriminant +Analysis <https://en.wikipedia.org/wiki/Linear_discriminant_analysis>`__ that +allows discrimination between classes that are not linearly separable. It +consist in finding a linear projector optimizing the following criterion + +.. math:: + P = \text{arg}\min_P \frac{\sum_i OT_e(\mu_i\#P,\mu_i\#P)}{\sum_{i,j\neq i} + OT_e(\mu_i\#P,\mu_j\#P)} + +where :math:`\#` is the push-forward operator, :math:`OT_e` is the entropic OT +loss and :math:`\mu_i` is the +distribution of samples from class :math:`i`. :math:`P` is also constrained to +be in the Stiefel manifold. WDA can be solved in POT using function +:any:`ot.dr.wda`. It requires to have installed :code:`pymanopt` and +:code:`autograd` for manifold optimization and automatic differentiation +respectively. Note that we also provide the Fisher discriminant estimator in +:any:`ot.dr.fda` for easy comparison. + +.. warning:: + Note that due to the hard dependency on :code:`pymanopt` and + :code:`autograd`, :any:`ot.dr` is not imported by default. If you want to + use it you have to specifically import it with :code:`import ot.dr` . + +.. hint:: + + An example of the use of WDA is available in : + + - :any:`auto_examples/plot_WDA` + + +Unbalanced optimal transport +^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Unbalanced OT is a relaxation of the original OT problem where the violation of +the constraint on the marginals is added to the objective of the optimization +problem: + +.. math:: + \min_\gamma \quad \sum_{i,j}\gamma_{i,j}M_{i,j} + reg\cdot\Omega(\gamma) + \alpha KL(\gamma 1, a) + \alpha KL(\gamma^T 1, b) + + s.t. \quad \gamma\geq 0 + + +where KL is the Kullback-Leibler divergence. This formulation allows for +computing approximate mapping between distributions that do not have the same +amount of mass. Interestingly the problem can be solved with a generalization of +the Bregman projections algorithm [10]_. We provide a solver for unbalanced OT +in :any:`ot.unbalanced` and more specifically +in function :any:`ot.sinkhorn_unbalanced`. A solver for unbalanced OT barycenter +is available in :any:`ot.barycenter_unbalanced`. + + +.. hint:: + + Examples of the use of :any:`ot.sinkhorn_unbalanced` and + :any:`ot.barycenter_unbalanced` are available in : + + - :any:`auto_examples/plot_UOT_1D` + - :any:`auto_examples/plot_UOT_barycenter_1D` + + +Gromov-Wasserstein +^^^^^^^^^^^^^^^^^^ + +Gromov Wasserstein (GW) is a generalization of OT to distributions that do not lie in +the same space [13]_. In this case one cannot compute distance between samples +from the two distributions. [13]_ proposed instead to realign the metric spaces +by computing a transport between distance matrices. The Gromow Wasserstein +alignement between two distributions can be expressed as the one minimizing: + +.. math:: + GW = \min_\gamma \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*\gamma_{i,j}*\gamma_{k,l} + + s.t. \gamma 1 = a; \gamma^T 1= b; \gamma\geq 0 + +where ::math:`C1` is the distance matrix between samples in the source +distribution and :math:`C2` the one between samples in the target, +:math:`L(C1_{i,k},C2_{j,l})` is a measure of similarity between +:math:`C1_{i,k}` and :math:`C2_{j,l}` often chosen as +:math:`L(C1_{i,k},C2_{j,l})=\|C1_{i,k}-C2_{j,l}\|^2`. The optimization problem +above is a non-convex quadratic program but we provide a solver that finds a +local minimum using conditional gradient in :any:`ot.gromov.gromov_wasserstein`. +There also exists an entropic regularized variant of GW that has been proposed in +[12]_ and we provide an implementation of their algorithm in +:any:`ot.gromov.entropic_gromov_wasserstein`. + +Note that similarly to Wasserstein distance GW allows for the definition of GW +barycenters that can be expressed as + +.. math:: + \min_{C\geq 0} \quad \sum_{k} w_k GW(C,Ck) + +where :math:`Ck` is the distance matrix between samples in distribution +:math:`k`. Note that interestingly the barycenter is defined as a symmetric +positive matrix. We provide a block coordinate optimization procedure in +:any:`ot.gromov.gromov_barycenters` and +:any:`ot.gromov.entropic_gromov_barycenters` for non-regularized and regularized +barycenters respectively. + +Finally note that recently a fusion between Wasserstein and GW, coined Fused +Gromov-Wasserstein (FGW) has been proposed +in [24]_. It allows to compute a similarity between objects that are only partly in +the same space. As such it can be used to measure similarity between labeled +graphs for instance and also provide computable barycenters. +The implementations of FGW and FGW barycenter is provided in functions +:any:`ot.gromov.fused_gromov_wasserstein` and :any:`ot.gromov.fgw_barycenters`. + +.. hint:: + + Examples of computation of GW, regularized G and FGW are available in : + + - :any:`auto_examples/plot_gromov` + - :any:`auto_examples/plot_fgw` + + Examples of GW, regularized GW and FGW barycenters are available in : + + - :any:`auto_examples/plot_gromov_barycenter` + - :any:`auto_examples/plot_barycenter_fgw` + + +GPU acceleration +^^^^^^^^^^^^^^^^ + +We provide several implementation of our OT solvers in :any:`ot.gpu`. Those +implementations use the :code:`cupy` toolbox that obviously need to be installed. + + +.. note:: + + Several implementations of POT functions (mainly those relying on linear + algebra) have been implemented in :any:`ot.gpu`. Here is a short list on the + main entries: + + - :any:`ot.gpu.dist` : computation of distance matrix + - :any:`ot.gpu.sinkhorn` : computation of sinkhorn + - :any:`ot.gpu.sinkhorn_lpl1_mm` : computation of sinkhorn + group lasso + +Note that while the :any:`ot.gpu` module has been designed to be compatible with +POT, calling its function with :any:`numpy` arrays will incur a large overhead due to +the memory copy of the array on GPU prior to computation and conversion of the +array after computation. To avoid this overhead, we provide functions +:any:`ot.gpu.to_gpu` and :any:`ot.gpu.to_np` that perform the conversion +explicitly. + + +.. warning:: + Note that due to the hard dependency on :code:`cupy`, :any:`ot.gpu` is not + imported by default. If you want to + use it you have to specifically import it with :code:`import ot.gpu` . + + +FAQ +--- + + + +1. **How to solve a discrete optimal transport problem ?** + + The solver for discrete OT is the function :py:mod:`ot.emd` that returns + the OT transport matrix. If you want to solve a regularized OT you can + use :py:mod:`ot.sinkhorn`. + + + Here is a simple use case: + + .. code:: python + + # a,b are 1D histograms (sum to 1 and positive) + # M is the ground cost matrix + T=ot.emd(a,b,M) # exact linear program + T_reg=ot.sinkhorn(a,b,M,reg) # entropic regularized OT + + More detailed examples can be seen on this example: + :doc:`auto_examples/plot_OT_2D_samples` + + +2. **pip install POT fails with error : ImportError: No module named Cython.Build** + + As discussed shortly in the README file. POT requires to have :code:`numpy` + and :code:`cython` installed to build. This corner case is not yet handled + by :code:`pip` and for now you need to install both library prior to + installing POT. + + Note that this problem do not occur when using conda-forge since the packages + there are pre-compiled. + + See `Issue #59 <https://github.com/rflamary/POT/issues/59>`__ for more + details. + +3. **Why is Sinkhorn slower than EMD ?** + + This might come from the choice of the regularization term. The speed of + convergence of sinkhorn depends directly on this term [22]_ and when the + regularization gets very small the problem try and approximate the exact OT + which leads to slow convergence in addition to numerical problems. In other + words, for large regularization sinkhorn will be very fast to converge, for + small regularization (when you need an OT matrix close to the true OT), it + might be quicker to use the EMD solver. + + Also note that the numpy implementation of the sinkhorn can use parallel + computation depending on the configuration of your system but very important + speedup can be obtained by using a GPU implementation since all operations + are matrix/vector products. + +4. **Using GPU fails with error: module 'ot' has no attribute 'gpu'** + + In order to limit import time and hard dependencies in POT. we do not import + some sub-modules automatically with :code:`import ot`. In order to use the + acceleration in :any:`ot.gpu` you need first to import is with + :code:`import ot.gpu`. + + See `Issue #85 <https://github.com/rflamary/POT/issues/85>`__ and :any:`ot.gpu` + for more details. + + +References +---------- + +.. [1] Bonneel, N., Van De Panne, M., Paris, S., & Heidrich, W. (2011, + December). `Displacement nterpolation using Lagrangian mass transport + <https://people.csail.mit.edu/sparis/publi/2011/sigasia/Bonneel_11_Displacement_Interpolation.pdf>`__. + In ACM Transactions on Graphics (TOG) (Vol. 30, No. 6, p. 158). ACM. + +.. [2] Cuturi, M. (2013). `Sinkhorn distances: Lightspeed computation of + optimal transport <https://arxiv.org/pdf/1306.0895.pdf>`__. In Advances + in Neural Information Processing Systems (pp. 2292-2300). + +.. [3] Benamou, J. D., Carlier, G., Cuturi, M., Nenna, L., & Peyré, G. + (2015). `Iterative Bregman projections for regularized transportation + problems <https://arxiv.org/pdf/1412.5154.pdf>`__. SIAM Journal on + Scientific Computing, 37(2), A1111-A1138. + +.. [4] S. Nakhostin, N. Courty, R. Flamary, D. Tuia, T. Corpetti, + `Supervised planetary unmixing with optimal + transport <https://hal.archives-ouvertes.fr/hal-01377236/document>`__, + Whorkshop on Hyperspectral Image and Signal Processing : Evolution in + Remote Sensing (WHISPERS), 2016. + +.. [5] N. Courty; R. Flamary; D. Tuia; A. Rakotomamonjy, `Optimal Transport + for Domain Adaptation <https://arxiv.org/pdf/1507.00504.pdf>`__, in IEEE + Transactions on Pattern Analysis and Machine Intelligence , vol.PP, + no.99, pp.1-1 + +.. [6] Ferradans, S., Papadakis, N., Peyré, G., & Aujol, J. F. (2014). + `Regularized discrete optimal + transport <https://arxiv.org/pdf/1307.5551.pdf>`__. SIAM Journal on + Imaging Sciences, 7(3), 1853-1882. + +.. [7] Rakotomamonjy, A., Flamary, R., & Courty, N. (2015). `Generalized + conditional gradient: analysis of convergence and + applications <https://arxiv.org/pdf/1510.06567.pdf>`__. arXiv preprint + arXiv:1510.06567. + +.. [8] M. Perrot, N. Courty, R. Flamary, A. Habrard (2016), `Mapping + estimation for discrete optimal + transport <http://remi.flamary.com/biblio/perrot2016mapping.pdf>`__, + Neural Information Processing Systems (NIPS). + +.. [9] Schmitzer, B. (2016). `Stabilized Sparse Scaling Algorithms for + Entropy Regularized Transport + Problems <https://arxiv.org/pdf/1610.06519.pdf>`__. arXiv preprint + arXiv:1610.06519. + +.. [10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). + `Scaling algorithms for unbalanced transport + problems <https://arxiv.org/pdf/1607.05816.pdf>`__. arXiv preprint + arXiv:1607.05816. + +.. [11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). + `Wasserstein Discriminant + Analysis <https://arxiv.org/pdf/1608.08063.pdf>`__. arXiv preprint + arXiv:1608.08063. + +.. [12] Gabriel Peyré, Marco Cuturi, and Justin Solomon (2016), + `Gromov-Wasserstein averaging of kernel and distance + matrices <http://proceedings.mlr.press/v48/peyre16.html>`__ + International Conference on Machine Learning (ICML). + +.. [13] Mémoli, Facundo (2011). `Gromov–Wasserstein distances and the + metric approach to object + matching <https://media.adelaide.edu.au/acvt/Publications/2011/2011-Gromov%E2%80%93Wasserstein%20Distances%20and%20the%20Metric%20Approach%20to%20Object%20Matching.pdf>`__. + Foundations of computational mathematics 11.4 : 417-487. + +.. [14] Knott, M. and Smith, C. S. (1984). `On the optimal mapping of + distributions <https://link.springer.com/article/10.1007/BF00934745>`__, + Journal of Optimization Theory and Applications Vol 43. + +.. [15] Peyré, G., & Cuturi, M. (2018). `Computational Optimal + Transport <https://arxiv.org/pdf/1803.00567.pdf>`__ . + +.. [16] Agueh, M., & Carlier, G. (2011). `Barycenters in the Wasserstein + space <https://hal.archives-ouvertes.fr/hal-00637399/document>`__. SIAM + Journal on Mathematical Analysis, 43(2), 904-924. + +.. [17] Blondel, M., Seguy, V., & Rolet, A. (2018). `Smooth and Sparse + Optimal Transport <https://arxiv.org/abs/1710.06276>`__. Proceedings of + the Twenty-First International Conference on Artificial Intelligence and + Statistics (AISTATS). + +.. [18] Genevay, A., Cuturi, M., Peyré, G. & Bach, F. (2016) `Stochastic + Optimization for Large-scale Optimal + Transport <https://arxiv.org/abs/1605.08527>`__. Advances in Neural + Information Processing Systems (2016). + +.. [19] Seguy, V., Bhushan Damodaran, B., Flamary, R., Courty, N., Rolet, + A.& Blondel, M. `Large-scale Optimal Transport and Mapping + Estimation <https://arxiv.org/pdf/1711.02283.pdf>`__. International + Conference on Learning Representation (2018) + +.. [20] Cuturi, M. and Doucet, A. (2014) `Fast Computation of Wasserstein + Barycenters <http://proceedings.mlr.press/v32/cuturi14.html>`__. + International Conference in Machine Learning + +.. [21] Solomon, J., De Goes, F., Peyré, G., Cuturi, M., Butscher, A., + Nguyen, A. & Guibas, L. (2015). `Convolutional wasserstein distances: + Efficient optimal transportation on geometric + domains <https://dl.acm.org/citation.cfm?id=2766963>`__. ACM + Transactions on Graphics (TOG), 34(4), 66. + +.. [22] J. Altschuler, J.Weed, P. Rigollet, (2017) `Near-linear time + approximation algorithms for optimal transport via Sinkhorn + iteration <https://papers.nips.cc/paper/6792-near-linear-time-approximation-algorithms-for-optimal-transport-via-sinkhorn-iteration.pdf>`__, + Advances in Neural Information Processing Systems (NIPS) 31 + +.. [23] Aude, G., Peyré, G., Cuturi, M., `Learning Generative Models with + Sinkhorn Divergences <https://arxiv.org/abs/1706.00292>`__, Proceedings + of the Twenty-First International Conference on Artficial Intelligence + and Statistics, (AISTATS) 21, 2018 + +.. [24] Vayer, T., Chapel, L., Flamary, R., Tavenard, R. and Courty, N. + (2019). `Optimal Transport for structured data with application on + graphs <http://proceedings.mlr.press/v97/titouan19a.html>`__ Proceedings + of the 36th International Conference on Machine Learning (ICML).
\ No newline at end of file diff --git a/docs/source/readme.rst b/docs/source/readme.rst index e7c2bd1..0871779 100644 --- a/docs/source/readme.rst +++ b/docs/source/readme.rst @@ -12,9 +12,11 @@ It provides the following solvers: - OT Network Flow solver for the linear program/ Earth Movers Distance [1]. -- Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2] - and stabilized version [9][10] and greedy SInkhorn [22] with optional - GPU implementation (requires cudamat). +- Entropic regularization OT solver with Sinkhorn Knopp Algorithm [2], + stabilized version [9][10] and greedy Sinkhorn [22] with optional GPU + implementation (requires cupy). +- Sinkhorn divergence [23] and entropic regularization OT from + empirical data. - Smooth optimal transport solvers (dual and semi-dual) for KL and squared L2 regularizations [17]. - Non regularized Wasserstein barycenters [16] with LP solver (only @@ -33,6 +35,7 @@ It provides the following solvers: - Stochastic Optimization for Large-scale Optimal Transport (semi-dual problem [18] and dual problem [19]) - Non regularized free support Wasserstein barycenters [20]. +- Unbalanced OT with KL relaxation distance and barycenter [10, 25]. Some demonstrations (both in Python and Jupyter Notebook format) are available in the examples folder. @@ -67,6 +70,13 @@ modules: Pip installation ^^^^^^^^^^^^^^^^ +Note that due to a limitation of pip, ``cython`` and ``numpy`` need to +be installed prior to installing POT. This can be done easily with + +:: + + pip install numpy cython + You can install the toolbox through PyPI with: :: @@ -115,14 +125,9 @@ below pip install pymanopt autograd -- **ot.gpu** (GPU accelerated OT) depends on cudamat that have to be - installed with: - - :: - - git clone https://github.com/cudamat/cudamat.git - cd cudamat - python setup.py install --user # for user install (no root) +- **ot.gpu** (GPU accelerated OT) depends on cupy that have to be + installed following instructions on `this + page <https://docs-cupy.chainer.org/en/stable/install.html>`__. obviously you need CUDA installed and a compatible GPU. @@ -209,10 +214,13 @@ nbviewer <https://nbviewer.jupyter.org/github/rflamary/POT/tree/master/notebooks Acknowledgements ---------------- -The contributors to this library are: +This toolbox has been created and is maintained by - `Rémi Flamary <http://remi.flamary.com/>`__ - `Nicolas Courty <http://people.irisa.fr/Nicolas.Courty/>`__ + +The contributors to this library are + - `Alexandre Gramfort <http://alexandre.gramfort.net/>`__ - `Laetitia Chapel <http://people.irisa.fr/Laetitia.Chapel/>`__ - `Michael Perrot <http://perso.univ-st-etienne.fr/pem82055/>`__ @@ -226,6 +234,9 @@ The contributors to this library are: - `Kilian Fatras <https://kilianfatras.github.io/>`__ - `Alain Rakotomamonjy <https://sites.google.com/site/alainrakotomamonjy/home>`__ +- `Vayer Titouan <https://tvayer.github.io/>`__ +- `Hicham Janati <https://hichamjanati.github.io/>`__ (Unbalanced OT) +- `Romain Tavenard <https://rtavenar.github.io/>`__ (1d Wasserstein) This toolbox benefit a lot from open source research and we would like to thank the following persons for providing some code (in various @@ -366,6 +377,20 @@ approximation algorithms for optimal transport via Sinkhorn iteration <https://papers.nips.cc/paper/6792-near-linear-time-approximation-algorithms-for-optimal-transport-via-sinkhorn-iteration.pdf>`__, Advances in Neural Information Processing Systems (NIPS) 31 +[23] Aude, G., Peyré, G., Cuturi, M., `Learning Generative Models with +Sinkhorn Divergences <https://arxiv.org/abs/1706.00292>`__, Proceedings +of the Twenty-First International Conference on Artficial Intelligence +and Statistics, (AISTATS) 21, 2018 + +[24] Vayer, T., Chapel, L., Flamary, R., Tavenard, R. and Courty, N. +(2019). `Optimal Transport for structured data with application on +graphs <http://proceedings.mlr.press/v97/titouan19a.html>`__ Proceedings +of the 36th International Conference on Machine Learning (ICML). + +[25] Frogner C., Zhang C., Mobahi H., Araya-Polo M., Poggio T. (2019). +`Learning with a Wasserstein Loss <http://cbcl.mit.edu/wasserstein/>`__ +Advances in Neural Information Processing Systems (NIPS). + .. |PyPI version| image:: https://badge.fury.io/py/POT.svg :target: https://badge.fury.io/py/POT .. |Anaconda Cloud| image:: https://anaconda.org/conda-forge/pot/badges/version.svg diff --git a/examples/plot_barycenter_fgw.py b/examples/plot_barycenter_fgw.py index e4be447..77b0370 100644 --- a/examples/plot_barycenter_fgw.py +++ b/examples/plot_barycenter_fgw.py @@ -166,7 +166,7 @@ Ys = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]) lambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel() sizebary = 15 # we choose a barycenter with 15 nodes -A, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95) +A, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True) ############################################################################## # Plot Barycenter diff --git a/notebooks/plot_OT_2D_samples.ipynb b/notebooks/plot_OT_2D_samples.ipynb index 96e84a5..cd1b541 100644 --- a/notebooks/plot_OT_2D_samples.ipynb +++ b/notebooks/plot_OT_2D_samples.ipynb @@ -34,6 +34,7 @@ "outputs": [], "source": [ "# Author: Remi Flamary <remi.flamary@unice.fr>\n", + "# Kilian Fatras <kilian.fatras@irisa.fr>\n", "#\n", "# License: MIT License\n", "\n", @@ -108,7 +109,7 @@ }, { "data": { - "image/png": "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\n", + "image/png": "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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] @@ -118,7 +119,7 @@ }, { "data": { - "image/png": "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\n", + "image/png": "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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] @@ -169,7 +170,7 @@ }, { "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAAEICAYAAAB/KknhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAEDdJREFUeJzt3XuMXPV5xvHvE+MLxDjGATnGRsFpSBBNubSWgdCkyBQFSBpbLUpBtHJUV26aViKFlFvUFKS2grQKoLSFmEuzJCg2IahGNBFyXSMaQQzmfnEBgxrF1GDANcZAjA1v/5jfpsOyuzM71zP7Ph9p5Dlnzsx5Zz3P/ub9zTmzigjMLJf39bsAM+s9B98sIQffLCEH3ywhB98sIQffLCEH39om6VOSnup3HdY8B78CJH1R0mOS3pD0gqRrJM0ut10raXe5vCVpb93yj3tQW0j66HjbRMR/RsTH29jHWZI2Snpd0vZy/cuSVG6XpCskvVIuVwzfZq1x8PtM0vnAFcBfAh8ATgA+DKyTNC0ivhQRMyNiJvB3wJrh5Yg4vX+V10jar837nw9cDfw98CFgLvAl4CRgWtlsJbAMOAY4Gvgd4E/a2W96EeFLny7ALGA38IUR62cCLwF/NGL9pcD3GjzmycBW4AJgO7CNWmjOAJ4GdgCX1G2/GLgX2Fm2/UdgWrntbiCA10udv1/3+BcCLwDfHV5X7vMrZR+/XpYPLc/l5FFq/UB57N9r8JzuAVbWLa8Aftrv/79BvnjE769PAjOA2+pXRsRu4EfAqS0+7ofK484Hvg5cB/wB8BvAp4C/krSwbPs28BfAwcCJwCnAl0sdny7bHBO1dxhr6h5/DrV3JitH1P4stV8K35N0APAvwFBE3DVKnScC04G1DZ7PrwKP1C0/UtZZixz8/joYeDki9o1y27Zyeyv2An8bEXuB1eVxro6I1yLiCeBJam+biYgHIuKnEbEvIv4b+DbwWw0e/x3gryNiT0S8OfLGiLgO2AJsBOYBXxvjcd7z/CXdI2mnpDclDf/imQm8Wne/V4GZ7vNb5+D318vAwWP0yfPK7a14JSLeLteHg/li3e1vUgsTkj4m6Y4yqbiL2jxCo184L0XELxpscx3wCeBbEbFnrDoZ8fwj4pMRMbvcNvz63E2tLRo2C9gd5X2/TZyD31/3AnuA361fKWkmcDqwvgc1XAP8F3BERMwCLgEajaTjBq7UfxVwA3CppDljbDr8/Jc22N8TlHcoxTFlnbXIwe+jiHgVuAz4lqTTJE2VdDhwC7UJtO/2oIwDgV3AbklHAn864vYXgY9M8DGvBjZFxB8D/wZcO9pGEbGT2vP/Z0lnSjpQ0vskHQu8v27Tm4DzJM2XdChwPvCdCdZkddr6KMbaFxHfkPQK8A/UZsR3Af8KnDPOW+RO+iqwitqnAA8Ba4AldbdfCgxJ2p/aRN728R5M0lLgNODXyqrzgIclnRMRN4/cvjz/58v+b6I2y/8ctQnCe8pm36b2y+exsnx9WWctktsks3z8Vt8sIQffLCEH3yyhtoJfZqKfkrRF0kWdKsrMuqvlyT1JU6gd+30qtY+e7gfOjognx7rPNE2PGe/6lMassz529BvvWn760QP6VEl//ILXeSv2NDyisZ2P8xYDWyLiOQBJq6kdiDFm8Gfwfo7XKW3s0mx8d9758LuWP3PosX2qpD82RnPHfLXzVn8+8PO65a1lnZlVXNcP4JG0knIG1wxyve0yq6p2gv88cFjd8oKy7l0iYhW1I8OYpTk+WqgJd/5P7rer7fDPqjntvNW/HzhC0kJJ04CzgNs7U5aZdVPLI35E7JP058CdwBTgxnKut5lVXFs9fkT8iNo3xZjZAPGRe2YJ+bTcCqrSBJUnGicnj/hmCTn4Zgk5+GYJuce3cfWqpx85l9DLfWfkEd8sIQffLCEH3ywh9/hWCe7na3p13IRHfLOEHHyzhBx8s4QcfLOEevontBYdMyPuu/P/v7THEzpmnbUx1rMrdjT8ll2P+GYJOfhmCTn4Zgn19ACepx89wH29TUqD9oUlHvHNEnLwzRJy8M0ScvDNEvLZeRUwaBND9l6D9n/mEd8sIQffLCEH3yyhyvX4GfvdDM/RqsUjvllCDr5ZQg6+WUKV6/FH9rsZe36zbvOIb5aQg2+WkINvllDD4Eu6UdJ2SY/XrZsjaZ2kZ8q/B3W3TDPrpIbfsivp08Bu4KaI+ERZ9w1gR0RcLuki4KCIuLDRzmZpThyvUzpQtllOjf6ceMe+ZTci7gZ2jFi9FBgq14eAZY0ex8yqo9WP8+ZGxLZy/QVg7lgbSloJrASYwQEt7s7MOqntyb2o9Qpj9gsRsSoiFkXEoqlMb3d3ZtYBrY74L0qaFxHbJM0DtneyKOsfHzBVbZ36/2h1xL8dWF6uLwfWdqQaM+uJZj7O+z5wL/BxSVslrQAuB06V9Azw22XZzAZEw7f6EXH2GDf5czmzAVW5k3Ra4b60c/yzy8GH7Jol5OCbJeTgmyXk4JslNCkm9zwhVW2NTiyx3vOIb5aQg2+WkINvltCk6PGtd1rp193PV49HfLOEHHyzhBx8s4Tc44/DJ/+8l38Gk4NHfLOEHHyzhBx8s4QcfLOEPLk3jkYTWT75xAaVR3yzhBx8s4QcfLOE+trjD3qPPEi1mtXziG+WkINvlpCDb5ZQX3t898h5+QSo/vKIb5aQg2+WkINvlpCDb5aQT9KxvvBkXnO6NQnqEd8sIQffLKGGwZd0mKQNkp6U9ISkc8v6OZLWSXqm/HtQ98s1s05QRIy/gTQPmBcRD0o6EHgAWAZ8EdgREZdLugg4KCIuHO+xZmlOHK9TOlO5VZYPzumfjbGeXbFDjbZrOOJHxLaIeLBcfw3YDMwHlgJDZbMhar8MzGwATKjHl3Q4cBywEZgbEdvKTS8AcztamZl1TdPBlzQT+CHwlYjYVX9b1PqFUXsGSSslbZK0aS972irWzDqjqeBLmkot9DdHxG1l9Yul/x+eB9g+2n0jYlVELIqIRVOZ3omazaxNDQ/gkSTgBmBzRHyz7qbbgeXA5eXftV2p0EZV5Qm0KtVio2vmyL2TgD8EHpM0/Gq7hFrgb5G0AvgZ8IXulGhmndYw+BHxE2Csjwf82ZzZAPKRe2YJpT1Jp8o9cjMGrV6rFo/4Zgk5+GYJOfhmCaXt8d0j5zTof72pUzzimyXk4Jsl5OCbJeTgmyWUdnLPchptIm/QD+ZqhUd8s4QcfLOEHHyzhNzj28DoVi+eoacfySO+WUIOvllCDr5ZQu7xB4BPLKnJ+Jy7xSO+WUIOvllCDr5ZQg6+WUKe3BsAWSe1Mp480yse8c0ScvDNEnLwzRJyj29t88kzg8cjvllCDr5ZQg6+WUID1+P7hJXq8c9/8HjEN0vIwTdLyME3S6hh8CXNkHSfpEckPSHpsrJ+oaSNkrZIWiNpWvfLNbNOaGZybw+wJCJ2S5oK/ETSj4HzgCsjYrWka4EVwDVdrBXwRJL13mScUG444kfN7rI4tVwCWALcWtYPAcu6UqGZdVxTPb6kKZIeBrYD64BngZ0Rsa9sshWYP8Z9V0raJGnTXvZ0omYza1NTwY+ItyPiWGABsBg4stkdRMSqiFgUEYumMr3FMs2skyZ0AE9E7JS0ATgRmC1pvzLqLwCe70aBneIvdbBWTcbXSjOz+odIml2u7w+cCmwGNgBnls2WA2u7VaSZdVYzI/48YEjSFGq/KG6JiDskPQmslvQ3wEPADV2s08w6qGHwI+JR4LhR1j9Hrd83swHjI/fMEhq4s/NaNRknaBrxhKaNxSO+WUIOvllCDr5ZQml6/Izc01dbP0/+8YhvlpCDb5aQg2+WkHv8DvNn59asfr42POKbJeTgmyXk4Jsl5OCbJTQpJ/f6eWCEJ/NsEHjEN0vIwTdLyME3S2hS9vjus3OYjH/hplc84psl5OCbJeTgmyU0KXv8KvFJO93jn2XrPOKbJeTgmyXk4Jsl5OCbJeTJvS7zBJR1W/0E8uLPvNHUfTzimyXk4Jsl5OCbJeQe36wFVTowq37fT8crTd3HI75ZQg6+WUJNB1/SFEkPSbqjLC+UtFHSFklrJE3rXplm1kkT6fHPBTYDs8ryFcCVEbFa0rXACuCaDtdXKVXq66y/Bv3/vqkRX9IC4LPA9WVZwBLg1rLJELCsGwWaWec1+1b/KuAC4J2y/EFgZ0TsK8tbgfmj3VHSSkmbJG3ay562ijWzzmgYfEmfA7ZHxAOt7CAiVkXEoohYNJXprTyEmXVYMz3+ScDnJZ0BzKDW418NzJa0Xxn1FwDPd69MM+ukhsGPiIuBiwEknQx8NSLOkfQD4ExgNbAcWNvFOiuhyhM6/sZZm4h2Pse/EDhP0hZqPf8NnSnJzLptQofsRsRdwF3l+nPA4s6XZGbd5iP3zBLySTo91q1e3P28TYRHfLOEHHyzhBx8s4Tc4/eYe/G8qnSSl0d8s4QcfLOEHHyzhBx8s4Q8uWc2Qrcm4ao0sesR3ywhB98sIQffLCH3+DaptdKvV6kX7xaP+GYJOfhmCTn4Zgk5+GYJeXLPJrV+TdRV/VuPPeKbJeTgmyXk4Jsl5B6/qHpPZoOl6q8dj/hmCTn4Zgk5+GYJuccvqt6TdUKVvuXV+ssjvllCDr5ZQg6+WUIOvllCntxLZORkng9ayssjvllCDr5ZQg6+WUKKiN7tTHoJ+BlwMPByz3bcnkGqFQar3kGqFQaj3g9HxCGNNupp8H+5U2lTRCzq+Y5bMEi1wmDVO0i1wuDVOx6/1TdLyME3S6hfwV/Vp/22YpBqhcGqd5BqhcGrd0x96fHNrL/8Vt8sIQffLKGeBl/SaZKekrRF0kW93HczJN0oabukx+vWzZG0TtIz5d+D+lnjMEmHSdog6UlJT0g6t6yvar0zJN0n6ZFS72Vl/UJJG8trYo2kaf2udZikKZIeknRHWa5srRPVs+BLmgL8E3A6cBRwtqSjerX/Jn0HOG3EuouA9RFxBLC+LFfBPuD8iDgKOAH4s/LzrGq9e4AlEXEMcCxwmqQTgCuAKyPio8D/Aiv6WONI5wKb65arXOuE9HLEXwxsiYjnIuItYDWwtIf7bygi7gZ2jFi9FBgq14eAZT0tagwRsS0iHizXX6P2Ap1PdeuNiNhdFqeWSwBLgFvL+srUK2kB8Fng+rIsKlprK3oZ/PnAz+uWt5Z1VTc3IraV6y8Ac/tZzGgkHQ4cB2ykwvWWt84PA9uBdcCzwM6I2Fc2qdJr4irgAuCdsvxBqlvrhHlybwKi9tlnpT7/lDQT+CHwlYjYVX9b1eqNiLcj4lhgAbV3gEf2uaRRSfocsD0iHuh3Ld3Syy/ieB44rG55QVlXdS9KmhcR2yTNozZaVYKkqdRCf3NE3FZWV7beYRGxU9IG4ERgtqT9ykhaldfEScDnJZ0BzABmAVdTzVpb0ssR/37giDIzOg04C7i9h/tv1e3A8nJ9ObC2j7X8Uuk5bwA2R8Q3626qar2HSJpdru8PnEptXmIDcGbZrBL1RsTFEbEgIg6n9jr9j4g4hwrW2rKI6NkFOAN4mlpv97Ve7rvJ+r4PbAP2UuvhVlDr7dYDzwD/Dszpd52l1t+k9jb+UeDhcjmjwvUeDTxU6n0c+HpZ/xHgPmAL8ANger9rHVH3ycAdg1DrRC4+ZNcsIU/umSXk4Jsl5OCbJeTgmyXk4Jsl5OCbJeTgmyX0f8BneHj0wfxYAAAAAElFTkSuQmCC\n", + "image/png": "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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] @@ -179,7 +180,7 @@ }, { "data": { - "image/png": "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\n", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAEICAYAAABLdt/UAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzsfXdYVGfa/v1SrBCNJTaM2AtSLNgVj4ktamw4aqKxbBq73252s1l3s9+SZGPKxux+2U32F9KbxjJqLDFqjDr2higooigKKgqC9M4w8/7+uOcwA0xDMJac+7q8ZJgz73nPOcz9PO/9PO/zCCklNGjQoEHD/QOPOz0BDRo0aNBQv9CIXYMGDRruM2jErkGDBg33GTRi16BBg4b7DBqxa9CgQcN9Bo3YNWjQoOE+g0bsGu5JCCFGCiESb/M5CoUQXZy8nyKEePR2zqE+IYTwF0JIIYTXnZ6LhtsLjdh/oRBCLBRCnBZCFAsh0oUQUUKI5pb3PrKQWqEQolwIYbR5ve1nmJsUQnRzdoyUcr+UsuftnIeU0kdKeckyp6+EEG/czvNp0FBf0Ij9FwghxB8BvAPgTwCaARgCoBOAn4QQDaSUz1tIzQfAWwDWqK+llBPv3MwJzePUoME5NGL/hUEI8QCAvwP4rZRyu5TSKKVMAaAD4A9g3i2MOVoIkSqEWCKEyBBCpAkhpgkhHhNCnBdCZAsh/mpz/CAhxGEhRK7l2P8KIRpY3ttnOSzOskKYbTP+n4UQ6QC+VH9n+UxXyzn6W163F0JkCiFG25nrIiHE9zavLwgh1tq8viqECLH8LIUQ3YQQzwJ4EsASy5y+txkyRAhxSgiRJ4RYI4Ro5OAedRNC7LUcd1MIscbmvf9YzpsvhIgRQoy0ee81IcRaIcQKIUSBZZXVQwjxsuVeXxVCjLM5fo8Q4m0hxDHLeJuEEC0czKmZEOJzyzO4JoR4Qwjh6Wq+Gu5+aMT+y8MwAI0AfGf7SyllIYCtAMbe4rhtLeN2APAKgE9BIzEAwEgAkUKIzpZjTQD+AKAVgKEAHgHwa8s8RlmOCbasENbYjN8CXFk8W23uFwH8GcAKIUQTAF8C+FpKucfOPPcCGCmE8BBCtAfQwDIHWPR0HwCnqo3/CYBvASyzzGmKzds6ABMAdAYQBGChg/uzFMAOAA8C8APwgc170QBCLNe3EsDaagZiCoDlls+eBPAj+N3tAOB1AB9XO9dTABYDaAegAsD7Dub0leX9bgD6ARgH4Gk35qvhLodG7L88tAJwU0pZYee9NMv7twIjgDellEYAqy3j/EdKWSClPAMgAUAwAEgpY6SUR6SUFZbVwscAwlyMbwbwqpSyTEpZUv1NKeWnAJIAHAUJ7X/tDWLRzAtAIh0FkuR1IUQvyxz2SynNtbju96WU16WU2QC+t4xrD0bQKLWXUpZKKQ/YzGmFlDLLcj/+BaAhANv4wX4p5Y+WZ7YWQGsA/7C51/5qfMSC5VLKeCllEYBIADrVE1chhGgD4DEAv5dSFkkpMwC8B2COq/lquPuhEfsvDzcBtHKgU7ezvH8ryJJSmiw/q8R7w+b9EtAbhkVK2GIJ2uaDOr4rg5IppSx1ccynAPoC+EBKWebkuL0ARoPEvhfAHpDUwyyva4N0m5+LYblGO1gCQAA4JoQ4I4RYrL4hhHhJCHHWInvkgnEP2/tR/T7etHOvbc971ebnywC8UfP+drL8Ps0iieWCBvYhV/PVcPdDI/ZfHg4DKAMww/aXQggfABMB7PoZ5hAF4ByA7lLKBwD8FSQRZ3BahtQy/38D+BzAa450ZQtUYh9p+XkvXBN7ncqgSinTpZTPSCnbA3gOwIcWHXskSKI6AA9KKZsDyIPr++EMHW1+fhj0vqsb7Kvg30ErKWVzy78HpJQBzuZbhzlp+BmhEfsvDFLKPDB4+oEQYoIQwlsI4Q9ADyAV1HJvN3wB5AMotEggEdXevwHAYf64A/wHwHEp5dMAfgDwkZNj9wJQADSWUqYC2A/q5C1BDdsebmVOlRBCzBJC+Fle5oCGwgzeiwoAmQC8hBCvAHjgVs9jwTwhRB9LvOF1AOtsPHwAgJQyDdTQ/yWEeMASc+gqhAhzMV8N9wA0Yv8FQkq5DPSS/wkS7FHQg3vEhYRRX3gJwBOg1v0pgOoZF68B+NoiEehcDSaEmAoSs2ogXgTQXwjxpL3jpZTnARSChA4pZT6ASwAOVidAG3wOoI9lThtdzckOQgEcFUIUAtgM4AWL3v8jgO0AzoOySSmqSim3guVgYDQdDGj/zsFxT4HB4wSQvNeBcpyz+Wq4ByC0RhsaNNw/EELsAbBCSvnZnZ6LhjsHzWPXoEGDhvsMGrFr0KBBw30GTYrRoEGDhvsMmseuQYMGDfcZ7kgxpVatWkl/f/87cWoNGjRouGcRExNzU0rZ2tVxd4TY/f39cfz48Ttxag0aNGi4ZyGEuOzOcZoUo0GDBg33GTRi16BBg4b7DBqxa9CgQcN9Bq0TjQYN9xGMRiNSU1NRWuqqEKaGuxmNGjWCn58fvL29b+nzGrFr0HAfITU1Fb6+vvD394cQdSkQqeFOQUqJrKwspKamonPnzq4/YAf1IsUIIZoLIdYJIc5Z6koPrY9xNdzFWLYMMBiq/s5g4O813DGUlpaiZcuWGqnfwxBCoGXLlnVaddWXxv4fANullL3ALjln62lcDXcrQkMBnc5K7gYDX4eG1u95NANSa2ikfu+jrs+wzsQuhGgGdqL5HACklOVSyty6jqvhLoeiAHo9jDN0yP7tKyR1vZ6/r09YDEj6KgOkxO0zIBo03EeoD4+9M9gk4EshxEkhxGdCiKbVDxJCPCuEOC6EOJ6ZmVkPp9Vwp5HYXsGhoAi0+O9SICLCPVKvrQeuKEh6Sw/fp3W4/sxtNCAa6g1vvvkmAgICEBQUhJCQEBw9evROT+lnxZ49ezB58uQ7Oof6IHYvAP0BREkp+wEoAvCX6gdJKT+RUg6UUg5s3drljlgNdzmuXweOv2vAoBNRMP01EoiKqknY9lBLCScxEViZpuDi2Ah0+LwWBkRDrfDaa/UzzuHDh7FlyxacOHECp06dws6dO9GxY0fXH3SBigp7vdc1OEJ9EHsqgFQppWqW14FEr+E+RV4ecGCpAdNX64A1eni++Tq9aFvCdgSLhGMK1yF5/iuQTjzwlBRg7VpgQL4BgQejgMhaGBANtcLf/14/46SlpaFVq1Zo2LAhAKBVq1Zo3749AGDXrl3o168fAgMDsXjxYpSVsVmXv78/bt5kS9bjx49j9OjRAIDXXnsN8+fPx/DhwzF//nyYTCa89NJL6Nu3L4KCgvDBBx8AAGJiYhAWFoYBAwZg/PjxSEtLqzGvtWvXom/fvggODsaoUaMAACkpKRg5ciT69++P/v3749ChQwDocYeFhWHq1Kno0qUL/vKXv+Dbb7/FoEGDEBgYiIsXLwIAFi5ciOeffx4DBw5Ejx49sGXLlhrnLSoqwuLFizFo0CD069cPmzZtAgCcOXMGgwYNQkhICIKCgnDhwoV6uf+VkFLW+R/YYqyn5efXALzr7PgBAwZIDfcmSkul/PBDKXdPeEdmr99d9c3du6V85x2XY6SmSnlgTKSUgDS+HGn3mGvXpHzrLSk3vLBbmlu14tjqOWxfa6iChISEW/ocUD/nLygokMHBwbJ79+4yIiJC7tmzR0opZUlJifTz85OJiYlSSinnz58v33vvPSmllJ06dZKZmZlSSimjo6NlWFiYlFLKV199Vfbv318WFxdLKaX88MMP5cyZM6XRaJRSSpmVlSXLy8vl0KFDZUZGhpRSytWrV8tFixbVmFffvn1lamqqlFLKnJwcKaWURUVFsqSkREop5fnz56XKSwaDQTZr1kxev35dlpaWyvbt28tXXnlFSinlv//9b/nCCy9IKaVcsGCBHD9+vDSZTPL8+fOyQ4cOsqSkRBoMBjlp0iQppZQvv/yyXL58eeV5u3fvLgsLC+X//M//yBUrVkgppSwrK6u8RlvYe5ZgX1+XnFxfWTG/BfCtEOIUgBAAb9XTuBruIphM9KBv3gQ6/b8leHBGNS9bUYAlS5yOkZYG7Pu7Af2PRqFsSSS8Pq3pgd+8CXz7LdC4MTChRTSErUdv8fgRHV2fl/aLxGuvAULwH2D9uS6yjI+PD2JiYvDJJ5+gdevWmD17Nr766iskJiaic+fO6NGjBwBgwYIF2Ldvn8vxHn/8cTRu3BgAsHPnTjz33HPw8uL2mxYtWiAxMRHx8fEYO3YsQkJC8MYbbyA1NbXGOMOHD8fChQvx6aefwmRiW1uj0YhnnnkGgYGBmDVrFhISEiqPDw0NRbt27dCwYUN07doV48aNAwAEBgYiJSWl8jidTgcPDw90794dXbp0wblz56qcd8eOHfjHP/6BkJAQjB49GqWlpbhy5QqGDh2Kt956C++88w4uX75ceY31hXrZoCSljAUwsD7G0nB3Qkpg61bg4kVgyhSgS5faj5GeDux51YCpK3UwrdKj8RQFmKBUCYjm5QErVpBg5s8HGrW0YygURdPZ6wGvvWYlcSH4jOsDnp6eGD16NEaPHo3AwEB8/fXX6Nevn8Pjvby8YDabAaBG7nbTpjXyMKpASomAgAAcPnzY6XEfffQRjh49ih9++AEDBgxATEwMPvjgA7Rp0wZxcXEwm81o1KhR5fGqlAQAHh4ela89PDyq6P3V0xKrv5ZSYv369ejZs2eV3/fu3RuDBw/GDz/8gMceewwff/wxxowZ4/QaagOtVowGt3DoEHDiBDBiBND/FiIoGRnA8uWAX1o0TCv18JlS0wMvLiapl5YCTz4JtGxZv9eg4fYjMTGxil4cGxuLTp06oWfPnkhJSUFSUhIAYPny5QgLCwNAjT0mJgYAsH79eodjjx07Fh9//HElsWZnZ6Nnz57IzMysJHaj0YgzZ87U+OzFixcxePBgvP7662jdujWuXr2KvLw8tGvXDh4eHli+fHmlJ18brF27FmazGRcvXsSlS5dqEPj48ePxwQcfqJI1Tp48CQC4dOkSunTpgt/97neYOnUqTp06VetzO4NG7BpcIiEB2LkTCAgAbsWpyMwEvv4a8PQEAr5eAt/Ha0o4ZS8swbffArm5wNy5QLt29TN3De7h1VfrZ5zCwkIsWLAAffr0QVBQEBISEvDaa6+hUaNG+PLLLzFr1iwEBgbCw8MDzz//vOXcr+KFF17AwIED4enp6XDsp59+Gg8//DCCgoIQHByMlStXokGDBli3bh3+/Oc/Izg4GCEhIZVBUFv86U9/QmBgIPr27Ythw4YhODgYv/71r/H1118jODgY586dc7k6sIeHH34YgwYNwsSJE/HRRx9V8foBIDIyEkajEUFBQQgICEBkZCQAQK/Xo2/fvggJCUF8fDyeeuqpWp/bGe5Iz9OBAwdKrdHGvYHUVJJyu3bAU08BXrUU727eBL76ikv9hQvte+EVFcDKlcyCmT0bqOb01C+WLWNqpa2UYzBQs3cRH7gXcPbsWfTu3ftOT+MXgYULF2Ly5MkIDw+/LePbe5ZCiBgppUvZW/PYNThETg6wahXg6wvMmVN7Us/OBr75hj8/9ZR9Ujebge++A5KTgalTbzOpAz9fKQQNGu4gtOqOGuyipIRetNlMvbtJk9p9PieHnr7JBCxYANjbkyYlsGULcPYsMH48EBxcP3N3CjWPfqYOadMj4Lc5StvJquGW8NVXX93pKTiE5rFrqAGTiVyXk0NPvbZBzNxckrrRyMyWhx6yf9zOncDJk8CoUcCQIXWft7s485CCg0ER8PtiKczPaTtZNdx/0IhdQxVICXz/PfXuxx8HOnWq3efz8kjqZWUk9bZt7R938CAzbUJDActGw58FJ08CMf80IDQmChUvR8LjY20nq4b7Dxqxa6iCffuAuDiSbVBQ7T6bn09NvaQEmDfPcWbLiRP01vv2BSZOtG6Qud04cgQ49R8DdOt18P5OD6+3alEKQYOGewgasWuoxKlTwJ491Lot5TTcRmEhSb2wkJp8hw72j0tIoK7erRswbdrPQ+pS8rp+/BHoVxFNUh+r7WTVcP9CC55qAABcvgxs3gz4+3NnaW0It6iI8kt+Pj11R8X8Ll1iBoyfH51kJynL9QYpSehHjwIhIUDfyCXwqO7OaDtZ6w1ZWVl45JFHAADp6enw9PSEWs312LFjaNCgQb2f88SJE8jIyMCECRPqfezaoKKiAq1atUJu7p1vR6ERuwZkZQFr1gDNm9eecIuL6ann5tJTf/hh+8dduwasXs1A7Ny5wC326K0VzGbGC2JjGZwdN+7nk33uCdyGnP6WLVsiNjYWAKsz+vj44KWXXnL78yaTyekmJXs4ceIE4uPj7zix303QpJhfOIqLWXBLCBJzbWoRlZSwTEB2Nsna39/+cZmZPIePDz36eq53ZBcVFcC6dST10aNvkdTv97Z8P3NO/5QpUzBgwAAEBATgs88+A0Avt3nz5vj973+PoKAgHDt2DJs3b0bPnj0xYMAA/Pa3v8W0adMAcFfrwoULK0vgfv/99ygpKcHrr7+Ob7/9FiEhIVi3bl2Vc54+fRqhoaGV5XEvXbrkci4vvvgiAgICMH78eBw9ehRhYWHo0qULtm7dCgD47LPPMH36dISFhaF79+5444037F7vP/7xDwwaNAhBQUF4/fXXAQAFBQWYOHEigoOD0bdv3xrzrTe4UwKyvv9pZXvvDhiNUn7+uZRvvCHl1au1+2xJiZQffyzl0qVSXrjg+LicHCn/9S8p//lPKbOz6zbfGnjnnZrle3fvlsY335HffCPla69JeeRIHca3lAgu2Lxbms3ynigZXOuyveo1RUbW+7W9+uqr8t133618nZWVJaVkudzevXvL7OxsaTQaJQC5fv36yvc6dOggU1JSpNlsluHh4XLq1KlSSin/9Kc/yVWrVkkppczOzpbdu3eXJSUl8tNPP60spVsdzz//vFy9erWUUsrS0tLKMr3O5rJjxw4ppZSTJ0+WEyZMkEajUR4/fryyrO+nn34q27dvL7Ozs2VhYaHs3bu3PHnypDQajbJZs2ZSSil/+OEHGRERIc1mszSZTHL8+PHy4MGDcvXq1fL555+vnF9ubq7D+3c3lO3VcI9BSmDjRuDqVQYx/fzc/2xpKYt13bjBEgDdutk5aNkylGw1YPly5rPPmwc8GFvP3q7F45S7DSgqAmAwQOp02JEbWrmTdfDgOoyvKLj2nh4ec3S49vR92pZPUdiVaunt70713nvvITg4GEOHDkVqamplw4oGDRpg+vTpAICEhAT07NkTnTp1ghACc+fOrfz8jh078OabbyIkJASKolSWwHWGYcOG4Y033sCyZctw9erVyloujubSuHFjjB07FgBL9I4ePRpeXl41yvWOHz8eDz74IJo2bYpp06bhwIEDVc67Y8cObNu2Df369UP//v2RlJSE8+fPIygoCNu3b8df/vIXHDx4EM2aNavbTXUAjdh/odi9GzhzBnj0URb3chdlZZRV0tLIc9272z+uPDgUmK3Dg7EGzJ4NtEm4Dct8RUH5Cj3KpumQEP4KzLN0+H6eHjG+CmbNYrC0LoiPB75IVpAwmpuZ6kx8d6O0YzCwK9Vt7k61c+dO7Nu3D0eOHEFcXByCgoIqS/Q2bty4Rrlbe5BSYuPGjYiNjUVsbCyuXLlSWd/dEebPn48NGzagYcOGmDBhAvbt2+d0LrbB3bqW6/3b3/5WOdekpCQsXLgQvXv3xvHjxxEQEIC//OUveOut29O6ol6IXQiRIoQ4LYSIFUJo1b3ucpw8CRw4wPK7w4a5/7nycpYZuHYNCA93XNfFaGSf0rXhesz+ToeM51+BKbz+vd2MDODj8wqO9Y9A6PaliB4YgfjWCp54AqhrHaxjx4D164GBBQYMOFZPxHe31alRz6/XA6/f3pz+vLw8tGjRAo0bN8aZM2cQ7SC9tE+fPkhMTMTVq1chpcSaNWsq31NL4KpQS+D6+vqioKDA7niXLl1Ct27d8MILL2Dy5Mk4deqU23Nxhh07diA3NxfFxcXYtGkThg8fXuX98ePH4/PPP0dRUREAIDU1FTdv3sS1a9fg4+OD+fPn449//CNOnDhR63O7g/r02BUpZYh0o/KYhjuHS5eYR961K/DYY+4HFI1GFgS7ehWYOdMxcZrNJMTLl4G+v1VwYnAEBv24FKZn6neZHx8PfPYZVwLDTkXhyNhIBB6IwtNdDeja9dbHlZK8tm0bMLLCgAlf6tjByR7x1dYDt+TMy1k6ZP3mLpB2oqOrnv825vRPmjQJxcXF6NOnD/72t79hsAONrEmTJvjvf/+LRx99FAMHDkTz5s0r5YpXX30VRUVFCAwMREBAAF6zdAkZM2YM4uLi0K9fvxrByJUrVyIgIAAhISE4f/485s2b5/ZcnCE0NBRTp05FcHAw5s6di5Bqy8PHHnsM4eHhGDJkCAIDA6HT6VBYWIi4uLjKYO5bb72Fv/71r7U+t1twR4h39Q9ACoBW7h6vBU/vDG7ckPLtt9mz1BJDcgvl5VJ+842Uf/+7lKdOOT7ObJZywwYGLY8elXLn/+6WhU1aydwX6i8wZzJJuX07z/HDn3bLigdbyVXP7pbvvitl1rq6BTdNJim3bOHYGzdKafqH/eBsZV/X6sFUN4Kr169LeXic836vdcGt9jy9m1BQUCCllNJsNstnnnlGvv/++3d4RlXhLFhbn7gbgqcSwA4hRIwQ4ll7BwghnhVCHBdCHM/MzKyn02pwF4WFlFG8vYEnngCq9QNwiIoKOnGXLjEYGRho/zh1I5BajqDhIQOGvKfDlXf1aPbv+lnmFxUxvfLIEaoXQzyisWamHmm9FCxaBLSYeeseZ0UFVxrHjwPDh7NOjsefl9T0pm37uioK5Bo9jDN0uLLQtQd+6hSw628GBB2MQsHv7fd71QBERUUhJCQEffr0QUlJCZ555pk7PaV7DvXSaEMI0UFKeU0I8RCAnwD8VkrpsFOt1mjj54XRyGYXmZlsdtG+vXufU0n9wgUSnZO2ldi3jxw1eDD7oV7+zTI0GhmKEZGKVe6pw+aX1FTOpaQEmDyZOfFr1gAPPMBiY3VJLigr41jJycDYse7HHUwm4IcfgGb/egVh+5ZC/i0SYunrNY4zm4EdO4Abqw2YvV4HuUaPxo8pVTXuepJjtEYb9w/ueKMNKeU1y/8ZADYAGFQf42qoO9RGFtevUxt3l9RNJm7wuXABmDTJOalHR5OjgoKAQYOADRuAizOXYMjLSlUN39bbrQViYmiYPD2BxYu56li5EmjRgoaqLqSulkNISWHap7ukXlLC7KCc7wwYGhdFUv+opgeurjKOHgUGe0TDe4OF1IHbpmnXh7Om4c6irs+wziUFhBBNAXhIKQssP48DUNNt0XBH8NNPwLlzbGThbncik4myRGIiqy8OdOIfxMcDW7cCPXrwWLX3wOzZdS8bUFHBsU+eZLB35kzOafNm5t3XRlKyh9xc5uPn5bHuvIvMuUpkZ1s6Sx034MnNOnhtsHjcY5QqHvj161wJFBfTaPQKtmPU6rlOTaNGjZCVlYWWLVu6lUKo4e6DlBJZWVk1+qfWBvVRK6YNgA2WPyIvACullNvrYVwNdUR0NPXoQYPcb2RhNtPjVrsaDXKy9kpK4rGdOpF0f/iBm5aeeAJ48MG6zT0vj/x4/TowciR1+2PHqON37Ur+rEs9qYwMkrraDMRRjZvquHKFZC0l8ETbaHitt59VEtdCwZYt7Dy1aJH7K6W6ws/PD6mpqdDiWPc2GjVqBL/a7BqshjoTu5TyEoCfo6mZhlrgwgWm7PXoQYJ2B2Yzd6OqG5ecGYOrV8lhDz1Ebzc2lsHB0aMdb1pyF5cuccVgMlmbW+/bx9K7vXsDM2bUvv+qLa5cocft5UUpp00bJwfbFMo6fRrYtAkIyDBg3IPRaPp2TQ/cNErBT2UKjm5k7ZzwcKBpUzcmVU8Fuby9vdG5c2e3j9dwf0LbeXofIj2d+nibNvSka5SptQO1c9Lp08CYMcwMcYQbN6hx+/qycFhGBj3pHj1qX8e9+hwOHqQn3bQp8MwzJPUdO0jqISEkyrqQ+vnz1LybNAF+9SsXpA4AoaGQOh2ilxnw3XdAaKEB01bp0HR0zU1FVfT0wSyj4BapW84DnQ55G++SzUsa7mloZXvvM+Tnk3QbNaIk4o5coZJ6bCwQFkbpwxFycki83t6UMABg7VoGMKdPv/WyuGVl1M4TEoA+fZha6eXF38XGkijHj69b2d24OHrcbdvSILlDuhUjFex+Wo/hf9fBNCICg09EccNSNV28up5e28bccrSChFf18H9Sh8wFEWi9VmuyreHWoRH7fYSyMkoMZWXMHvH1df0ZKa0BypEjSeyOUFhIj9Rkom7s68ta7GVl9E5vNdZz8yZJMSuL6YZDh1oDuAkJnFNYWN1I/fBhev6dO1PesZQAcYqiIuDzz4GcRgp8hkZg2I6ltGbV5JLrm6LxRasl8PHhfXfUEtARjEbLailLQfjECARELWUJA43UNdwiNGK/T6Bu5VeDly4lBpDUt2/nppxhw8gjjshTrehYWAg89RTQujU/e+UKNW93zmcP584xAOvlRc7s3Jk1afR64OJF1lEfOvTWxlavcdcuSjx9+nBV4Y6Uk54OfPkl59I/jymNmD+fNyEkBLmLX4TvcQNMM3X4aboeHfvVQk+3QW4ujVp6OjC9uQF99trUpdE6O2m4RWjEfh9ASgZK1Zxzu2V07Xxmxw5mmgwZwmCpI1I3GinvZGbSaPj5UYtXtWRHu1GdwWymjHzgADNGdDrKOaWlPFdqqutNUe6cQ5WYBgxgbRx34g3x8cz9lxJ4xMOA4ct1lfKLDA4BXnoJl7+JRY+L26CfqUfbuQrGjnVvbFskJ1PGMpuBX3UxwO9Fm81KinLna8louGehEft9gCNHrF63s5xzFaoXq6ZCOusuZDKRW1JT6ZF27cpVwebNTBG0lK6uFYqLSZwXL5K4H3uMXnRRER3ijAyeq0+f2o+twmi05uKPGsVsHXeknJ07AfnOMnTqEIrev1YwaI+lUBYA09vLsKnnEnQNjEVw3HLsHx2Jfi8qCAqq3dyk5L0WMzUVAAAgAElEQVT/6SegVStKQy0/d1KQSyN2DbWERuz3OM6do+fduze9bndgMFCaGDAAmDDBMeFJyWBjUhK38ffpQ496zRrq6bNm1b4hdVoa+aqggGMOGMDf5+VRv8/LY5s9d1YdjlBayv6qly/z+twp3icld5JevAh0fTgU8zbq4LlAz1RDgwHmWTpsW6BHQaIB3ZK24cjYSAyLiYJnlgLAfeKt1NNPA716MdDasCHspzRqUoyGW4SW7ngP49o1eqUdOrifkbJ3L7B/Pz3lSZOck/q2bSSgRx4hAUtJPTwvjyqBj0/t5hsXB3zxBaWHRYuspJ6VRT27sJAydl1IvbCQu1+vXqX27w6pl5QA779PUn/gAWD6+wo81+lRMVOH4pdYS37dLD2ys4HwtToc+J0eQRtfh+e62hU2y83l9Z8+bVVaGv7nLmi+cTc2ANFQJ2jEfo8iN5cZMD4+3CDkzvb9/fuZDx4cDEyZ4twQ7N1LFWDoUGtO+759zAMfPx7o2NH9uZpMzLzZuJH6/LPP0hgB1iCl0QgsWOD+DlB7yM4mcarNtd3R/tPTgffe4/3s3Bl44QXmuO8RCg4GRqDJv5biUFAEzndQ0C41Ggmv6jH2TQVNmqBWtV6Sk4FPPgF6bFyGxZ0NGDXKcv9DQ+m2P/ccD7wT+et3WwMQDXWGJsXcg1ADjBUVJEN3POdDh9gOLzCQQUlnpH70KIk9JIQauhAMzO7Zw0Jftfm+FxQwQHj1Ko3Eo49ag4xXr/I6GjSgp96qlfvjVkd6OvV5s5lZO+7sxj51isZGSsYnxo5lFszGjUDJVgN0J6Kwd1QkBh6LQkpnBW3/b0lNY+FCLrHV01u2BPo/F4pmz+iQ94AeTScr8AIghYDp29XwaN0GHh//DPnr1Xe5Kgrw8suQkycjVfdH+G2xn6uv4d6BRuz3GEwmEmVWFnPHW7d2/RmVWAIC6Bw6y944dYppjL16Wb367GwGO9u0oS7ubj755cvcAVtWxmCobW/VS5eog/v6ktSbN3dvTHtISeFYDRvS0LlzT7ZtY0aQENa55eRwnCZHDdCt10E/U4/LXRRkBCh4Yo0OnvP1qKue7u2tIP6qHp2f1CF1ZgQe3hqFHxZvwAMxBoS9+TPlr1s89OyP9Gg2TYHYY4Bp6dtI7DkTfb9aisI/RMJHI/V7GpoUcw9BShbaunSJpOtOSRC1cJZaY8UZqZ8/T2+1c2drKQKjsTIpxO2KjVLS6//mG3rjTz9dldTPnrWW3V20qG6kfu4cPXVfX24OckXqFRWUa44dA0YeWYbf9jUgIIBSyaefAg/EGDDy6LtYG65HSmcF/v7ApH9Sc69NeV17enpREfX/9dkKkidEwH85ZZ6iImD46dvfUFpF2TAFx17So+FTOiTPfwVl03TYPehldEvahqIXI+GzXGsAcq9D89jvIRw4YN0hWq3Fol3ExNAz7dnTdc2Yy5e5EmjXjgTu5UWC3rKldhUbbb3Unj3ppdruSFW39XfowDEbN3Y9piOcPMlztW/PsZo0cX58QQF17sJCGpURvw+F9zwdzqbrsfamgt7pBkxapcM6nR7J/kpV6agWGSrJyVypmEzU+rt3ZzrqTz9xrDltDfD/F2WeoUfex7CY/8Bj48bbnr8uJY3q9u1AQakCERaB0FVLcWbAfDwS/TY8N+ohxijAZC2H/l6HRuz3COLjrRq5O9+1kydJyt27U2pwlpaYns5AbLNmrKGibrePjq5dxcacHKZC3rjBOY4cWVW2OXqUpNKlC43HrZbdVYuF7drlfgnflBR69iYTi5XNmQOYzQoOvaBHyJ90GDssAkGHorBOp8eVrgpmOGkD6GxeR48y/bRlS57Dy4vnvXSJcx1lMqDVb3RYM0sP/0UKvFbcgId+jXWQ25S/npvLAPaFC8z86Z7KXa5JcyPRZ9P/sfPTGC2H/n6BRuz3AK5coUTy8MOuA58Ad1pu3mwlPWdb6LOySDwNG1LrVr3eK1dqV7HxwgXq8ACNg23KopTMyDEYqDXPnHnrFRrVHbNHjgB9+3JF4CqX/tAhessAr0VRKIusWgVcMymoGBiBsJ1LsXdUJLKDFTw9h4XCagOjkYb01Cle49SplIm2b2dAd9IkplWeXxqNYwv0UP6iMLNo1MfA3DlVSbQ2+esuyv2aTLxXe/fy3jVrBjwYa8D09TqUfKNHt5kKYLB46P363docNNx1qDeNXQjhKYQ4KYTYUl9jamDgcvVqfiFVicQZ1Jrhqlfs7Pj8fG4KkrJq31A1k6V5c9f58VKSNFau5OeffbYmqf/0E7kmOJibmm6V1E0mGji1mfWMGc5JXQ00qxKITkeuSkujlH3tGuCfbMDA45RFBp+MwvM9DbUm9bw8pmyqq5vHHmO+/6ZNwKMnluHprgYkJHDFlfPMEjz+ONBxlU2OuG3LwNrmlNukKpaXo0qq4tWrlJ527mTmVEUFDdDY5tFotEnP5t/q+W9Diz4Ndw716bG/AOAsgAfqccxfNIqLSZiAexrymTMkFH9/17ntJSX01EtKmEmiphqqvU7dqdhYWsrznT/PNMjJk6ue02ymF3vyJEsXONvl6gpGI0n6wgX7Mk91qL1MMzO5Glm8mE1B4uM5Z7OZpB6+lpuP2j+poIGHAo85tdOWU1I4L1VPNxppNIxG5vu36RwKn1/p4DFbj0kRCgbkGyBm66wR6epQiVqdg23Da3tQFJSv0ENO0yF2aAQGxUShfLkeOwoVnPiCMYyGDSmTDRzIWvuNG2u7XO931IvHLoTwAzAJwGf1MZ4Geld6PbXROXOo2TrD2bPchdqxIwnGGamXl3P7fHY2x7Zt27ZjB2WYKVOcV2zMyGAWSVISe50ylc/6vlp29+RJyh91IfWSEq4s1CJnlZt7HOD6deCDD0jqLVsCv/sds2V27eKczGYe1/5aNL6brceAlyxFvB5x33NV89O/+YYGd948euzr1jEw+6tfWTJjkhXs+JUeM/U6+L77ipXUHZGoxXs2T56MnMefqkny1Tz3pCTgw7MKjoREYPCPS5E+LQLvn1bQ+INl6HPDgJISGu1nngEmNTGg8Qd2PH9t5+l9h/ry2P8NYAkANyqAa3AFtfHF5cuUG1ztxkxMJKGomSbOAokVFQxwXr9OzrBNmTx9mmmArio2xsdTw1fzxqvPT02RTEripp9hw1xfsyPk59MIZWVRxnFVGEyNL0hJSWj2bBqZVatoGKpcx2NLMHduNT3dDc/VaGTaaVwcM3/69rU22Rgzhr/bsIFB6R49gMQrClqFRmCE3nWeupRAbHMFXj1mIvD75TA9MR+edjz34mIa4bg4IDjbgOGnoxA3NRLdVkah01MKrrUPxaxvdAj6lx4tpyloddqJ51/bVYKGux51JnYhxGQAGVLKGCHEaCfHPQvgWQB4uC77xn8B2LuX3p+iuM7MuHCB37927apmtNiD2qj60iUGYXv1sr6nVmzs1MlxxUazmXrt4cNcGcyaVbOZR2kpSVT1+vv3d++a7SEri556SQmvzVnevtnM1M7jx/l6+HDWuMnJ4Xxu3qx6fOfOzBZyJW9VR14eSTwtDRgxgqmT69dzdfPEEyTzzz5jHKF3b66k+uUaMOyU6zrrxcU06KXbDJidtA0l4fPRaNUKGM2A985tgF7PTktneK0lJcAUHwP6vqfDqhl6XO2mwL+1gqnf6BD3Vz0wfQY6vzgdR1b9DiPio+CxVs+AzerVwMcfV71/02agYroOxQsi0Hyl1r3pXkd9eOzDATwuhHgMQCMADwghVkgp59keJKX8BMAnADBw4EBZD+e9LxEXZ93O76xFHcCiVWvWkFRc6eHq5qaEBBK3bZ1ztWJj48aOUyOLirgqSEmhgzd+fM3jqpfdtd2UVFtcv05PHeCqwFYuqo7iYpJ3aiolmqlTGai9eJH6d3l51eOHDSPp17Z+uq2ePno0cOIEA80jR3KVs307VzN+ftac8bFeBgxdoYNY67zO+oULDLa2STDgiU065Hymx6p0BaMvAMGrlwPz56NgoIKtembbtGvH1UHJ69FYNU2PzD4KjEVAYaiCwkf06LA/GhsazsGs8uUYtXcpTH+N5IlWr+ZNmjOn0js3hevw/Xw9Hgxug7D3te5N9wOElPXHsRaP/SUp5WRnxw0cOFAeV10rDZVISaGH2qkTPVRnGR+XLpHMWrYk8bna6LNrFzc4jRhBUlMhJce5eBFYuNB+ca/UVBJacTEDpPb6eaoZNrm55C138t6dXduaNVbt2ll8Qa0RU1RECWrePBLr0aNM1/TwsGrqnp6MBfTtW7v5SGndwduiBY3M6dOc17RpPGb9enrzQUEMJldU8F4FbXeejmg0UlI5fpzB3XnXl+Fq21Csz1YwddtzCIhfDY+pU2Fe9x3WzPseZjMw1CsaceOX4PRpGvOyMq7Uxoyhkd+6lSuw4eUGKO9Ph7msHB4eAp4NvZhWBMAUrkPyeJY0WD1dj0aNgJlrdPD8nwiuKjSP/a6EECJGSumy64KWx36XQO372aIFidEZqaekkIxbtGDBK1ekfugQSX3AAH75bbF3L73FiRPtk7q6e1Xdsm+vn2d2NoOIpaUk1k6dXF6uQ6iZPS1bcixnfVttM1yaN+e98PW1NsAWwkrqvr40lrVt4Werp3fsSA/99Gl2nVIUGhCDgZt+goN53tatKVO1bg0gyHEGyrVrnH9WFscbNgz44YclSEwERlYYEHhmNaQQ+LH9ItyYvQhzV0yDh6fA2ic2IOkMDVlpKc87YgQlsq1bea0LHjagwx90+DZ8A3qnGxC6fSng2YRB38YKjIERGLWKufudOgGj/p8OYr3Wvel+Qb0Su5RyD4A99TnmLwFFRZQdPD1JPs4klStXmAKpEpkrjfjkSeZx9+nD/GrbbJILF0jswcE1KzZWVFibXHftyk1F9gzIjRvWXPgFC2rfyNkW0dE8p5rZ48hg2Wr9AA3JnDkk4a+/5goD4JwA6umzZtW+fIGtnu7nx2qUzZvzOlu2pKqRnMwAaWkpST04mPfZWQDbbOaGLeOby9CmWygm/UmBlxe1+ZanDFjYNBod/YCzb21ETAww4786XJ4YASkEYnvOxpWuCsylLPEwcSJXSV9+Sc19yBD+S/l1NPZO06PTw8DALdT35X/+g6Q3V+N8RyA8OgoHx0Ri+MkoeJX+CLz8co1qj3j3XY3Y71FoHvsdhtFIgigspBTirCBWaioNwAMPkNRdNU4+d47BuC5duNHIVlNWKza2bVuz4UZeHp2169epH48ebV+PVufj7c353GrZXSlZ633PHko4s2Y5TtcsKaEslJzM12rDkPR03seioqrH11VPLy/n/U5N5Ypn7FhmK330Ed8bNozefFmZez1as7PppaemAsrwUIT/V4f4XnpsyFXQN9OAqZt1yP9Uj8+zFPjrl8HcIRSxQyIwfP1S7B8diWR/BaGGZWjy2hJ07kxdv/2KZQgICUX/Pyrw8ODqqVmDUIzPWY02P3wHoWeZhCOZCqZ8OQ2zsQb7/rABQ15W4BWj8I/j73+37jx97jneTItsA6CKfKTh7odG7HcQUvK7k5rKla/afMIerl2jlty0qVVycAa1EFWHDjV3oNpWbNTpqpLopUvUi00mfs42c8YW9VV2V+3UFB1tbQDiSIa6cYMSVF4eX48bR+9U3W0rhNVL9/BgqmhtA7iqnr59Oz18k4m/e/JJbvzauZPyS5s2fH34MCWx+fOdyzxSMtj644+8vpkzgc6dFews02PYyzpMHBWBgdFROBWpx6Z4eskNOoRi9uppAAQOKJEIPfQ+Bh/7D0pXbkR0EXeVNmgADAkPRY+/6ZDcS4/VNxR0u2rAzM06eIbPgFyjx34vBYavALRT0DVwDh7uCIx9S6ExVxRgwwbIVathmqmDx68j4KEGWFVo6Y/3HDRiv4PYtcuapdK7t+Pj0tJI6o0bUwZ4wMXe3uvXSbotWtTMa1dz5G/cIFmpFRulpBa/a5dNg2UHQctz52g0WrYkodW2RZ4KtURAfDybcKhNPewhIYGerslEIzVzJiWQn34iuXp5UT4COJ9582qvp1dUcKdsXByDkSUlDIZOmMCVwOefc2XQvz/lj6NHGYidPNl5mmlREXX/8+cpC02bRs89KgoobqSgwcAIhG1fiugJkdiaR8KtvA9CQEoJb2+ggSwDpCd++gmIb01DOL6BAQ1PRePYH/Xo+zsdxgyPwKATUfBYp0fRIKUykwlg0Lfzjx+jRYuq8yserOD7DAVtE9tUqQkvdTrcmBGBNt9Va7zhoj6NhjsPjdjvEGJirA2lhw51fFx6OjVsdTOQWs/FEW7epDyiZpRU15WPHaOHO3q0taZLWRmJJyGBWvzUqY414voqu1teTgfw4kWWxlXb71WH2UzOOHCAZNekidUgrVrFTVCenlZS9/enc1kXPV0IjqnTccUSG8tVhZcX53rsGMl60iQ+P2e7YBMTeW/LypgiGhpKfX3vXq4qOl0yYJDaqWlfFBLaKLjcRYGUQIfr0VgzewP8kw0I27EUKSPno82xTegZuxohXyvoeoVNtrcv0iPaR0H5oAiM/GkpCn4fiZv+CvT/pfYvBJ/3iBE1JamLF2lcHzrDXHv5t0iIqChkBytIHhSBAZ8sRc5vI/GgLYnbbGiSo9moQ/Po7y5oxH4HcPEiMy26dasZ0LRFRgZJ3dubpO5K7sjL4/FCkNSre/ZXrjC1zrZio5qNk5VFj3noUMfzOXaMBNe5M4OVt1p2V62Bc/26c126pIRxgKQkvn7oIRqT8nIGGrOyOFeTie/fqp5++TJXOGVlfN2rF0nb05Pnj4+nwejYkYW8mjVjyQBngeLycsouJ05w5aCmpC5fzvMBQI9rBkxZp4M+XI/U7gpSOisIX6vDd7P1uNRJweGRS+CfbMDgk1E4oESi39EoXPvVq+i58m3E/a4NKg5HYb1Oj/MPKPC/yGJmhX+IRMMvorAvR0FpZwUtWjBmUb2wmdFIWenYMSA4x4DHN+ng8Z0e5jAF8a0VdHtyGgKEQGZEJFqvigKmK1WCqxUr9TBP1+H8IxEI2Ke10rvboBH7z4wbN+jYPPQQN/E4IqHMTAbBPD1JCq6aXBQVkTTKyhiErS6j2KvYeO4c5Q0vL0oqjnZ2SkmPefdubpcPD7/1Co2q8cnLo9zTs6f94zIySLY5OXzdowfll8uXrTEAdW5qeztX5QbsXZeany4lV0WTJlFeuXbNmps+ciSf2/79lMwef9x55tLVq7yvOTlciYwezXl/+aXVeLRoAbQ4EI2Nc/VI8VOACuBKVwXrZunhdz0alzopCMwyYPxaHdbM1MNrrIJuzyjwe06HhM4TMXArUxWTOip4+IIBczboULaCm5oaTaOBOPOKHv0jlBrPKj2dBiszk8XZxsVGw2OdHjcDFWz8AvA+AfT0FBCzZ6P1h68Ds6qmP6akAN+fUxAUHIGw75bC/L+REBqp31Wo1w1K7uKXukGpoICeppRsF+dIK8/KYgs1oGrlRUcoK6MRyMiwn0duMvH9tDSet1Urq7zRvj2/s44kHinp2R06RL358cdd1z93hMxMxgrKypjO6Cjf/exZa366ycQA6aOPsujWzp0k1dJSHqsGkx96qHZzqajgORIS+LpLF2rfPj68L2pu+qhRJPT8fAZrBw1yvKIxmZjds38/Pzt9utXLP3iQx3h58V9pKQ2JSvTqmF5evO62bYFOa5Yht3so+vxGQVkZDVDo/v9D2K5IHBryRww8HoVNT+jxSLNolAWGYsU1BUYj5ar5fga0vVpV85aS8Yjdu7l6mDoV6PbdMsiBoTjaRMGuXTz/09HPoUULQHxiU3bAYIDxUDS2By3BiRNA4E0Dpq7UwfM32oamnxPaBqW7DOXl1IRLStjn0xGpZ2czF9tspuftitQrKujZpqVRHrFHlmrFxpkzSVwrV1IO6tePUpAj79tspmR04gRl1YkTb71CY2oqz+vpyeuyV/NcShLq/v1Wgps0iUHCTZsYG2jY0ErqDz/Ma66tnp6by3ucm8v5TJzIgGhhIVcTycn0/tu14/Wrm7OcZS3dvElDcf065zthAkn788/5O4BGqKiI1yAE31d3xvr40PA3bcrfX78O+P1xCcaEktAvXAAG5BswbN/bWDl3C1I6KygapGDOlzoc/r0eO1NIqr17k7AbNlRg23g7P59aenKytVF5kyZAQa9QeE/VIXGmHp3HKZjWzIAm//yuhl5+tq2CrY0UFJ1klcgBX0yGWLoUePFF64aml1/mH6QWQL3j0Ij9Z4DZzKVvejqJyJE2m5NDwqmoIPm5asxsNlMuSEmhd9ijR81jTp2yVmxs2ZKldgsKmMkxYIDjsU0mEtWZM5QiFOXWST0piTzh40PJx56sZFvb3cuLhDtnDu/BV1+R6Ly8rB7u4MH0oGurp6vljU0mevlz51KeOn+exsNoJClfvswMoR496Mk7Mh5SshzAjh2MhagVKBMT+czLy3nfvLxI6k2aVM21b9iQz7GoiPPIzaUBmTSJK7fPPuPfQ3Aw0DgqGutm6ZHir2DUKCAoSMF3xXo02xsNr9EKpk+3L0edOcNsH5OJhK7GNI4fB3bEK+g0W49Zq3XIbxCBJhuqet8FBYyrnD3LWMHcuUD7FdHA0qXA228D/foxgPryy8ArrzDlyl1o2TW3DRqx/wzYsYNf9IkT7ZMvYPUiy8spv7iSFtS0xXPnSERBQTWPSU/nMZ068Uv5xRcklkWLnHuftk0tnGWsuIPTpy1ZFw8xm8VeamRmJgO42dkkah8fEkhZGQ2RmtlRUcH/Z868tfz0TZuY1QMwQ2TMGJLd9u3W3PRRoyj35Oa6DiYXFDDjJSmJu3OnTuX93brVWtLd25v3s3Fjzr+42Pr5hx6ifNa0KZ97aSkJvXdvkumZM3xOLVpY5j1sCaWnmST9Dz8EzA8paB+i4A9P1tyFXFbGceLigImnl6HnvFA0668gL4/zNu8yYFR2NAyhSxA3NAJDP7VJdZTcdbxjB+f9yCO8F56eqCRdU1A/mKbrcH5MBAL2R0F8/33t5BitXPBtg0bstxlHj/Lf4MHUZ+0hP99aa+Wpp1z321TbzcXGkogGD655TEkJvx+NG9ND3ryZmR3h4c53rJaVUTK6fNm1V+8KavNqdcu/vYBjYiI9aPW61A1VFy5QBvH2tqYyNm7MlUxt9fT8fAYuc3M5h3nzeJ6bN3nu9HQ+mxYt6GU3acLzOKsuffYsjabRSIMdGsrxP/rIWiLY09Mqs+TnWz/brh1fZ2ZyPkVFNMxjx3JlEhXF5zdiBCWz06f5ue7d+UxUSUUIx8bnyhWugPLy+DcyYHgoPObqEJusx7ZSBR2TDJi1Toe14XqEmQ0YEmstK5w/QMGGXAZJO3Wil189GH/hArAtQUFwcATCNrB6pGdtNXZFQVaUHk2n6iAiItDwC02rry9oxH4bcf489dGePSkb2ENBAT314mLKFM7K06o4eJBBsNBQZlxUh5TWL3WrVjQAQ4fS+3YmXRQXM7h54wa94tpWQbQ9v6qVO2perfZK3buXRFpcTC98yhR+9uhREmJhIY9v1473p7Z6+smTlCHMZhq2efN4D06etOamh4fTwGzfTs97+nTHxq+sjMfFxnJOM2bwHsfHk3BNJqtu7uvLZ6Beg48PpaXkZEowUvI8Oh2fuzpumzZcTfz0k3W1Mm4cj/nwQ85BLStRnXBNJt7TAwcYEF+0iAHcnBwFhjl6jP+bDoWDI9DvaBS2PKWHMgR4+CV6yeYwBWdaKejyhA7eT+gxJUJBv341y038+CMNW1CWASPiaRA8o6KAR103KbEdx2AA4s4oGDsoAsOWaeWC6xMasd8mpKVxd2bbtvzy2yPUwkKSemGh1Yt0hZgYar99+zoOZqoVG9Vel+7URrctuztnzq2X3bUNuPbrRw+z+rWXldHwJCZayXvkSGa/6PUsV9CkiZUQBwxgkLc2enppKe//xYu8R+PHc/zSUs5PzU0fOZIEn5XlupeqrRc8ciQQFkZyXr+e4wH8rIcHDVBurvWzAQH8fHIy36+o4PmGDWN6ZFQUn8GIEdwfoErVahPzU6dIqADv65QpNeeZlcUVx/XrrOc/YQLH2rOH2TqylYLWgyIw0rAUibpITPk/ttCDXo+0Xgo2fwqk5ygY9Uc9ZnpHo2F/K8maTMxK2ruX1zy9uQGB/9VBrKtdRciyMhqdI0c4zuSmBvSPc92EREPtoBH7bUBeHjNAmjShVmxvI09REeWX/Hxqz/ZK5lZHQoJ1Y9O0afYJKDGRXz6A558zx7V0kZ1NUi8urlvZ3YoKEsvZs1YNu/oc1Q1RN2/SWy0u5rW0a8dAYW4u5RdVi54+3X78wBmSkki2paWUOhYsoIFNTbXmpo8ZQ6OyahWPeeopEr09mEwkx4MHGeBUZZqbN/kMCwqsxzZvTmOqykd+fvSuz5yxpol26UKj7OtLr/zYMWt5hkOHrBuy+vblimzlSj4jb28+zy5dqs6veh0aNYCbm8tGSTk5fA7+yQYMiI5C1m8i0XNNFHBEgfEPS7BnD3D4U+vqoXfvqhk1ly/z7y4zk6vPCROA5p9EVyVxS69WREfbJWazmXPcs4d/+4GBwDhvA3wW2xgDrVxwvUHLY69nlJUxSJmXxxQ5e6RaXExPPTvbWlzKFS5e5Be8QwcSgL3qhxkZ/CKbzfS4Z8xwvpFG/czy5SSvefPck4LsoayMaZcpKVbvuDrOnyfxq/DwoDdaWsrfC8EgopS8vsWLXccbbGG72xOgsVRr5Rw8aM1NnzqVHnBsLO+9mgZqD5mZ1oymfv14bQ0bWksMq1BrxahZOw0aMPYRF2fV1318SOi9e6OyFnt2NvX9oCAavIICkvOUKXwmP/zA59mxo/3nXlRE7z4x0VqH5oEHbLx0SbnJz7KJSej1aDBeqeyctOkJPU63UtC/P/V621FbPagAACAASURBVL+XwkIGkuPiuHKYONHxhjJHkJKrx59+oiHs1MkqK2lZMbWHu3nsGrHXI8xmazeiJ5+kXlsdJSX08m7epDdf3fuyh9RUfqZFC3qL9sg6I4MZJBUVJNVx41ynJ6oVI729SRqu0isdobCQ9WkyMkia1T1sKam3GwwkiMJCerZz59KTVQlXJcAWLYBnnnFtlGxx+bJVJgGsPU8LC/n75GTKIUOHMpCckcGgYliYfYlH3ZW6cydJesoUxguMRj5jtWwwwGtSzwvQG/X2poFRK04OHkz+8vTkiurgQauRyc+3ZKmYUVkCYMcOa4BUrWJZHUlJzPQpKeG1DhnCeXzzjdVLl5Lzm5+2DC0nkERLSjh+7gYDuuVEo/2/l1TZdWw2U/LbvZvGcvhwSk+OSik7QloaCT05mSuSsWOZFXarabMafsYNSkKIRgD2AWhoGW+dlPLVuo57r0FKenBJSdSV7ZF6aSm948xM+0tqe8jIoKeuViy0R3bnz9PbM5u5dA8Lcz1ucjI97KZNHeeWu4OcHBqH/Hz72nxZGYOK585Z0/v8/elZ7thBeUnN3wYoIYSHu//lr6ggAR0+bM0XnzGDXvH58zx3RQWJ2cuLKyVvb95Le88I4LVs2kStv3t37rb18aEhVMs2APTSKyqspO7ry3u/b5/VSLVty3O3a0evf+NGBqf79WMw+8cfuXoAGEvo1YsZPOXllk5IC2oGSI1GEmZ0tKWdnqWSpcEAmN5ehmbtQ5HfTYHJBAwcyL6rDcoBOVrB2QT+nRYXA8PmKRgUplQh7GvX+P7161wBPPZY7evsVwZG4ygHTpzIa7vVHcsaao/60NjLAIyRUhYKIbwBHBBCbJNSHqmHse8ZHD5ML2f4cPspgmVl1oyT2bOtlRWdITeXn/H0tF8e17ZBBUCPzR1ST0xknro77eec4cYNzq+ighp19ThBVhYNTmYmCS49nUG9ESNoVNLTaVhUUnck4TjC9ev0xtX0QnUV8OCDDIgeO0bCmzaNm3FiYqiNz5zpeOev7WYetXojQOOxf7/1ODWTR8XQodayvwCNx7hx3NEK8DmpGUBz5/J+fPYZDaOXF2MJFy9aG3gHBnLe1VcT6emME9y8yVXAo49Svnn/faD398tg9vRC+FpWfOwVoSDgx/8DIiNRtGYLvl/DZ9+uHZ+7rcxVUsJrPH6cf2fqXoHaeNfVA6PDh/NZ12blpaF+UGdil9RyLPkL8Lb8+/n1nTuIhAR6UAEBVRtFqygr4xc2LY3LbEeblGyhbm83Gim/VPeobXdqAvQsHaVU2uLUKXqN7dtTLrrVsrtXrlCS8PZmSl31WMKFCyQgISjxpKfz3vj5MQZRXs7PFhWRvBYt4nvuwLYmi5pGqcYUCgutddMHDyaxbtjA18OHM2hqT3opLaUxOHWKcYzp02n4SkroQWdm8rgGDTh3ldQffJDkun27NYjapw/w+LllaFgQipvZCjZupCc8WhowtCQaKViCDz6gIWjdmsHITZvo5duuOGyh1svfvdtakrlLFxr1/fv5fnrHUMxYo0PK3JcxebkO5/ZPhDy9Aldf+CdWxtODHzuWxlO9B1Lymnfs4LUOHsxVX23IuHpgNCiIstOtNl/RUHfUS1aMEMITQAyAbgD+n5TyqJ1jngXwLAA87Gznxz2G1FQSh58f9dLqHk55OaWU1FRKDI46EtmitJSGoKDAfmeejAx6wjk5lAOaNiUZuPKu1ICfvz9lE2fNIZwhMZGphM2akWBsv8BSUj/etYvEaDRynrNmkTiWL+d81c5ETZoAv/mN696tKm7coGFKT7d6zWr7vrg4a2763Lkkzs8/J4nNnevYoKakcMz8fK54Ro7kKikxkQkaakNsb28+T4D3esQInn/tWv5O1cy7dAHk7lAYZ+iwfYYe2T0VPNXRAP8/63Dsj3psX8XjBw3ivVixgvfioYfsr8zy8ji/lBQS/uTJ/Bt5/32udtTnnttPwdneevT5uw7pLXsj+NRyXBgyHyubv4jO7fk52yYbGRkMzl65wr/fSZOAtt8sAxq6F9C0Fxh94olbD8BrqD/UC7FLKU0AQoQQzQFsEEL0lVLGVzvmEwCfAAye1sd57zRycui1+vqSKKsHl9RA29WrJF53ysqqn8nIIBlVlzfOnKF316ABvb2cHEo7rjys/fvp7fXoQZK91bK7sbEM9LVrxy+x7Uae8nLOLSGBxiMtzVoS+PRpLvNbtqREA9AzXrzYvfx0s5keq8HAa1f1bZ2OWvB33/He+PtTEz9yhFKMnx8Nqr3qlbb6fIsWnIufH8+1Zg3jAgBJ3mTiswFoyB55hF56URGJdfhwGgUvL5LtpqsKMFUPnV6HnNkRaPduFDY/qUdsGcvoTpnCOaalcUxHq4n4eGtmzOOPs2aMwUDjKaV1boGBNHo/FCvw7joRwaeW4/LDI9Hh9DY8sciAbvOVSgNQXk5Z6MgR3ke1fowQqNzmL9foIcY43uaflkYvPyWFz3TOnNsUGNUyZ24J9ZrHLqXMFUIYAEwAEO/q+HsZJSX0xM3mmgQHWKsuqgW63NnFaTLRE1YrMdrq8GYzMzQOHybZt2xJkp0503meupT0ng8e5Jd/6tRbD2IdOkTvrEsXftdtPf6cHF5vZia9ynPnaHimTWOA8PJlyhYqqQ8axKCaO8jKsvaGbduWBPbggzRo5eVM8VRz0/v04T28ft1a7tfe9d64wZXWjRvU0ceNo8FQC2+pFSRtG3kAlCpKS61lENq1o+Fo0aJqPrmUQPNBCo4lRyDsczaijn1QwUMPkUQ3b+a4jRrxOqqnvNpKQ35+/Bsym+ml5+VZCbRZM/4tqGUHhhz6PwSdWoG4oPnolbwN+N+X0f1/dUB3djs6e5bzy8+3BnCrrJYUBTc+0OOBqToYfxWBB76tus0/L4/G8NSpnykwqtWTuSXUR1ZMawBGC6k3BjAWwDt1ntldDJOJf1fZ2fRGq2cNVFTQ47t0yX76nz1Iae2L+dhjVQ1BUREqe1eGhnKpu2kTicuZwTCbKb3ExDA7wlm3JldzU2uyBwSQrG09/osXOT8pKTWdPUujNGoU70N+PklAbZoxYwaNjDvnVVMOvbxIfikp1NOnTeN1qSmUixfzPqn17rnRxv6YR47Q2DVqVFWiMRio3QPWVEE1G9jHh9LL3r006l5evJ8hITy2oID55BcuUJIpKACan2T3o72jIjHwWBS8xiq46KtU7iDt1Imrp+pOgZq6aSsN7d7N+w9Ya9B06cLVYHY2f9/nhgGK4RXsffyfaPvOi2iYZqgsp1u8NxobritISqK0Fx5eczWYn897fTpRwfihERjyH+s2/zsWGFUUFHyuR4NpOpQvjoDvCq2ejDuoD4+9HYCvLTq7BwC9lHJLPYx7V0JKZj6kpJBcqntaJhM116QkLnFDQtwbU017UxSSt4rUVI6n7tBs04a6cadO9LYcwbZRtKNdoO7AbCZhxcbSOEycWDXwZtsA29eXpB4ayuwTta2fhwfn7+nJ/HR3mkzn5tJ4paRQaikp4c8jR9JDXLfOmps+caK1fk67diRLe+mbtlp1z558Pmr9848+qloCQO3MJCVXARUVlF4AGpaZM60rFlUuMRrp9efnA494GDBgNbsfXeuhoNk0BcGROpwP10N0UfDIIywnYPtMqu9wXbyY53j/fY6pzkfNYrp0if83bsz3ml+Ixom/f48hf1BIuL0UmFbpkbI2Gqs6LoHnFQZqQ0OrSj4VFbx3+/fzeU/xMaDfSW7zl1FRSGyn4PtCBcXFP29gNDubc4qLU6D0j8DIf2v1ZNyFtkGplti3j55dWFjNAlyqlHLuHANRA11uIyD27uUXevBgpvypX/aYGC7HfX3peDVvbt2E9OyzjndL2pbdfeQREvutwGjk9Zw/z+sNC0MVnfb770lq3bvTQ71xg/MvLuZ9ss1P9/UFfv1r1x6eWi5W9WpDQ2lUysspR3h6WnPTJ04k6a9fTwM4cCDPby9+cPq0VaueMMGqKZ88yZVSdXh4cJz+/SmvlJeTQGfNsrYQLC7miujMGWt5Xj8/fibnr8twtU0oigYpaN3aEndINqDzzWh0jlpSw1u+eZNxgrQ0zm3sWN7DI0es85GSBlTN0PH05OsbNyjHTJlStRxEUhLnl5PDld24cVVTW9Xg5/btPKZXL+Cxxgb4/ooa+wU/BQn/z4Cxn+mw/3/0CHpB+VkCozdvktBPn+Y1PuppQOg/dfD4tdatSdt5ehtw+jS/fEFBNWu1qE0vEhJIOI5K9FaHmqkSHGzNqqmo4O9OnuQmmpkzSYjqrtaFCx3XlrEtu1sb41IdpaUc58oVSg62q4icHEosN27wOs+e5XmnTuU9OneuapC0UyfmubsKktrWN/f3J4Hu3UsDER5Ogldz08PDOY8NG6wNJOzJUiUlvJfx8VatukULkrDawMMWajqjWpDt2jX+378/76d6DWpjjpISa5XGsWNJSgcO8JjevSmVqMXMevbkPbJNMZWSBvzHH2kcpkzhamPVqqpeuo8PDYmaodO+PT1adWfoqFFWg2ZbgbFlSz6/6pvhsrJI6ElJNA4TJlg2bC1bhqwuodhSpFQGRh/3NaBjejTEn+shWOkkGJq5aAn27eOz8vLi3+7ICgOaLHSgsf8CyV1rjVfPuHyZX2S1PnV1Ulf7Z6p9Md3B6dMknZ49mfEgBL+Uej0JR03j8/CgR3/hAr+kjki9uJhpkunp7uvY9lBQwHEyM2uW7710yaqnjxrFJXzjxiTanTuZzePrayV1d8obSMkv89atNGrjxnEcg4Fa/f9n782jqzqvu/99JCEhicEIBIh5njGzJGYkgwGbwQaMsevEdpI6b/K2TYe0aX5NYpw06+2w+rZZSePE6dvWSezY2MaJJ2wmMVmAQAwSZhQICaF5nqd7z++Pj3efc6+upCsxGs53LRZI3HvOc86957v38332891Ll0L4WpuenExGd+gQJP/EE213Z+pYf/97tPekJGYuISEEnm3bjH4uwu/DwwlQEydyr71e9PunnzYL1M7mFXpNCxYwrjffNJ2exo6FWENC+BOoX2pdnVlXGTuWcsTDh826oGbpPXua4NCvH0EkLw9yX7fOSFseD3bH+/bxvuRkNk45ZzBNTWYmEBZmxhUaKtLww3+S4zJP9n6WJFFRfNdmV6VI6IljIjeD1EX+ZzG05bVtEro8SUL2p4h302Y58CfbZP/PCW4LFzLu6GgR+aeumY25AG7GHgTKytC1o6JEvvpV34zL64XwMzK61m3o0iWqSIYPZ6NQjx4Q0TvvQG6PP25q3i9eJINzZvX+qKlB09aa8WA2QQWCOj3W1VGtodvuddFx1y5IdNIk0wx7wQJkDq0e0VrvYJwZ6+p477lzZNQrVnCOvDyIuF8/MsuwMOMC+c47BNpZs5gd+ZeZtrYSZI4eZawbNjDO5mbuudPnRYSMtayMRc+QEOOzomsTiuxszq2t7caOJdPVgNrcTCCwLCNB9etH0POXMC5ehNQbG7nmoUMJDErgIr7NrsPDCXKXLvFzUhLBRGcQTgfGCRO4L/77CzIyuC+1taz9PPQQMwFdGC14PUUef2OznH9pmwx4IklGXrn52XFTk8iFX6TIuL/bLCUbvyGD3n1Z3tywTfInJklCAolAsHsa7ke4GftNQn09ZY2WRebmP41+/32z6Bksqefm8qwMHEj9b1iY2dQzYADPklbalJczGxg8GCkgEKlXVGD8VF8fvFtkIBQUQFBeLx4lKke0tHCdmZkQemQkRDBpEouk77wDQTQ2GjfB557r3F/+/HmO29REUBw2jLUBlXWysjjPqFGQc0kJpY3NzZD8jBltj1lYiFxWUkJyuGIFxK82Cs7SxV69yIZLS8l6i4r4/YAB3EclxpYWSFPb6vXuzWcxfjyzCpVe1DZBS/+0cYizLLSlhfrv48c559NPo+Hrwqw26dBm13qcigpmhGPHcm5dHK6rIxCqA+OWLW0dGPPzmWXk5fGZbNnC314vie++fXx3HlyTJCWLtsmUP9ssxz74hgw/87KEvHVzSL2xERntyBGRhoYkeXj+N2T+r38knyZ/X0Y+lySbE7q/C9pFW7jE3gG0Fr2qCqJz7trT6phTp5AKliwJ7phFRWTfffqwa9OykDbOnv18K/o6QwTNzWRxIpB9e1a9arv75S8H16wjEK5eZVyRkYxLA0tlJWMoLEQaun4dQl6wADLYuZP7oiV3vXqJfO1rgTcEKZw12oMHk9nn5hKc+vaFjFNSTG36/PmQ5/79jOvZZ9s6UTo3MEVFQczjxhk7B/U4V0yezHqFLooWFUGqy5eTNWoAvXqVINzQwP8vXkwm39xMaWVBAb/v25d7pLLHmjXo8s5AXFBA0Ckt5ZrGjydpcDa3Vtg2gW7wYNZawsMJZg8+yDH9HRgXLeI76PyO1NWRLJw8iayxfr0JhhcukL3rjtH4eAL3q7lJ8nDiN2TJ7h+J/b0br0BpbGTmdOQI/46KYhF5xuGXJefL35cFH70slp0kEunKKjcTLrG3A21+fO1a25pfdXI8cYIHKhjjLRHIz2mT29AAaZaVte1dqYGjuBiSClS+d/06pBUa2r1eoIpz58i6Y2IgdTXIys4m6Oji5JEjjPXhh3nPtWsQmpK6esV3ZFWQlYUEUVvLfZs/n+Bw4gTZ6JAh6OJam64LiVeuQGqPPtq2cUllJbOa3Fyz5T4qijFu326aXogww+jZk/+LjjakOngwNe167S0t3JMLF/h51CgCUJ8+jOWNN3hNz54ED/WJ0YVeZ0mnM+hER3Oec+cIZCJmgVRfGx1NcDl9msx+2jQkH613z89nBtGeA6PHw/tSUhijmsP17Nl2x+j69dy3t9/me/lY3xR58PP+p9bLL4skJ3WL3BsaDKE3NRl5ZXhWimz8/Wax39kmI1cmiaS4zTVuBVxibwcpKSzoPfSQb1s522bafPw4WWuw9eE1NZC6x4PhVWEhZKRb7p1+2CJMWzMz+a4HcoLUDPtGbXfT0yGJoUON1GTbPJQ7d/LwL13KNXs8kMiBAxBzz57GsnbmTMi/vcqX5maOl55Otr1lC5LGb3+LRDBvHkHs4EHu95o1ZNG/+AWZns+298+hurE2vNCMVD1ptM5bhGCwdCnXpc0s6ur4++GHOb8eW20blLg3bCC79nq5D0c/d0LSwBAZyTlnzOD+OANPZSWBKieHGdm0aRzb6QyppB4SwneqsZFMu08f3w1U/g6MGzZwPOc9yc5mNlRSQiXMqlXc76oqM0uKiuKatVxT7X2TJEUin72xjkYNDSwAp6X5Ero23o7fd0zC3nUXQ2813MXTANDaZv/ekraNnnn4cNua847Q0EBpXUUFJHzpEgQ2ZAjPjb9skZuLb/i4cRCg/zkuXuRZiInheN2x3bVt5I29eznPE09ASE49eeJEdPQPPoBk5s41Xi2Njab0ThtBtHcvcnIgt8pKiCspicxx2zYe/vh4MnatTZ8xwzgZ9uvHPfLf1FRfz7jOnSMLf/xx7uOZMxCnU0ufOROCSU0lkGoGP3Qo1633v66OTDwvj5+dvVa13WFxselrqn/bttmF6oTWzts2pHb1KkEjEPRe79vHuebNI6nQptcZGXz36utNtaBzT0BlJYHz3DlmDStXcszmZt8dowkJ5l5oA/Hk5M9lxhvwZamvN4Q+dy8lkxeGJEmvXqw9za1JkbCTQfi7uN4wHcJdPO0msrMhjDFjfBcr1XPl8GG+d8GSenMzmXVZGaWD+/ej7c6aBRn4b6apqWGR74EHICv/c2RmQpKDByPRdKeCQHe6Hj2KvLFuHZlrVRXSUEEBem1ICCQ5fDhBaNcu301HISGQbnvt0lpaIOcjRyDo55+HhNPTyRT79kXi+PRTrmfjRq7njTcIfoEWH0VM56D6evmfHZx1dQTP3Fzzuqgo7uGePcyQRCD10FAy2TlzjF598KBp1NyvH/dWSyjPnmV2pe/1eMjWq6uRvzZt8tX8nQ2zhw8nUO3ebfxnnIiJITDqLGHAACQolf6Ki7lXOTlo7n/0R1QGOe/xp5/yR8Q0yLYsMntdGJ0+nWMePkyCMXKkqcb5HwQizk6aS9fXEySOHTPrFflD58kTr22WCz/cJmO+miR9T6SIPB2kv4vrDXNT4GbsDpSUUNbYpw8PlzMjUh+ROXPar07xh8cDSV2+DAEdPw5xq3FSoNe/+iok9LWvtdXMjx+HMEaOZIreHdtdjwcCycz0nXXk5PDstLYiaVy4QJY4dSpZdVaWL6lHRjJbcJKME9rTs6yMZ3X5cgLBjh1k5yNGMJMpKTENIwoK0Hrr6hjX3Lm+99nZOSg2FtIePNjs0NUZhAizgNhYpBOv18gdw4cjYWjFS24uWnp1NePTenc9344dzOBETHbepw9BcPZsAoRzwfLqVa67poZMtbTUuEQ60aMH1xwRQZBtajILs2FhbR0Yly/3laJsm+x8507GMnUqRN2nDzM658Lo9Olcw/Xr3JPly5GWbsSJsa7OEHpLi5Gj+vZl3ST0QIpM3rpZrq/9hkzY07XdorXvp0j4M5vl8sPfkMn77u+dpv5wM/YuoraWqXZYGFqzk9T374fUZ80KntS9XjLrrCym6Pv2kUE+/3z7lSs7d7IgGcix8dAhMs8JE8gQu9p/UgSyUB+b5GRDYGlpkEu/flRe7NoF4SUk8NqyMsaupD5gAKQeqAuRx8P9OnQIiehLX2L2U1PD85mXh/Rz9SqSzlNPQTJHjkBGGlT9676d3ZI0EFRXU/6oZYoifG5btpCBp6WZ3/tr6TU1ZMJKuv6LpyUlBGVdGBbhehobITD/jVsej7HTjYnh/h46ZEoWnZg9m3Hs2cP9HTaMmcnAgYawP/64fQfG4mL+Pzub9zz7rLFJVi+c/v1JILKymIH27m1sf4OxSW4PtbUQ+vHjJAERERC7Bp/wcL4/1fVJ0uvRb8ikN4P3d8nPZ0bx2WdJsmzWN2TJ21TmWC6pdxkusQtfzDfe4Ev73HO+GzsOHYKUZ8xou+O0Pdg2mZ5uYz91igdv06a2Tn6KjAyIyN+x0Wm7O20axNsdi1S1Gb5+neuYPZsH88MPGd+ECcgv27eTAS5axMPr9XI+XewbN47rCDRbcPb0nDmTrLtnT4KV6unDhkE2o0eTcYeFIf9cuIDGvH69b1D1ek2poy4Uq3yzd6/v+adPZ4Hyd7/zJdThw7lvMTFc85EjfKYeD9fmnB2oV436yiiGDIF4nDa9ipIS7lthIWOor+cz88eQIdz7nBy6SIn4mnKVl/O9ac+BsbHRyM0RERD33LkEqXffNQujycnGMiA8nNliQkL3kgFFbS333Eno2ihl5UoC465dLFgPGiTydFyKDPoZ1TXy8svtSjq2zfWmpppgv7pnisw5c+OVOQFxn2j49z2x2zYPxfXr7LR0ZtPqXDh9utnyHwz27eMB6N2bDHX+fCNFBEJhIRt1/B0bbRuCSU/3XcjrKqqrqT4pL2excPJkfrdtG9e9ZAlk+dvfcvw5c3iIe/UyZXwiPA+rVrUdg9fL6/ftY0ru3CSjenp0NIR9/brRxQsLmUFUV0MOCQm+91i9YK5dQ2p49FHG89Of+joxhoYSJM6fN3X/urC5fLk57qVLjEXfO2wYmbcG8sZGPoezZ82xdRNTfj7yzooVZl3EtuGDXbsgzfh4goI25FD07Amh9+/P8a9fJ0CuWYN00drKjPDQIRNo4uPNffZ6Cb579hA05syBvEND4SRdGE1MNH1wvV6ue/HiG9vJWVPDZ5ueTiAMD2e8vXvzfRw/nnG///7npLyahdKQLR1X13g8yIGHDxsbiuXLRebVIsPIW+2/94Zwn2j4973GvnMnX66HH4aAFUeOIE9MnYomGyyh6vvCwiCT9et9yyX90dAQ2LHRqYUvXAgZdkcTLS2l9K+xEalh1Ciz87WlhUy2sZHpekwMMsv580gS1dXmOKtWQRSBjq89PadO5WGPimL8O3ZACLqB6YEHINKhQyHEnTu53k2bfPud2jZE9vHHXPOjjxKM1CbAicGDCUzvv8+91Kx76FCubcAAzv3JJ2jPSvgrVvh6t6g9svOaR4+G0C2LwO70d6+tpXLq0iUCstdLAHJCOystXMh37NAhSH7VKlOm2JkD47Vr3MeCAtYlVq1CftEeo/X1vC8mhnva0EAikpTU/RJYEe6DErrXa3x0YmO535Mnm16/NTVIRg89pP4u7WfFjX/2N5KebspOBw4kyE+b9vlM9BZn1F6vSM6rKRL3Z5ulOUAjkbsdrrtjENDFyHnzyDT0IVfHxcmTIaJgpY9TpyBjER60J5/svLuROjY6mzm3trKIeOHCjdnu6gamkBCqKZwLjQ88wPgyMniAR45Egy8oML1ERchEN25sW/mite579vAaZ3MQrey5ds0ECK1NtywI8exZ0zDDmVHW1RFkzp8nCD32GO9//fW2VSWJiYwzI4OftQQxKYkgrZnw4cP8v9fr26har0PtHBTh4dyPS5d4/aZNvvLchQtcQ3Mz9+X8ed/yShHev2EDs4O8P/snufTAPOmzPklWruR66z5IkctvHJN3x/9NQAfGmhoCWUYGRL9iBffw0iXfhdExY5glVFYSiFasaH9BOxhUVRGATp7kfmmf10GDDKGXlJhKnbg4xt5ZI/KqKr4v6ekcb/RoCH3s2FvQTi8A6usJhseO8X1adfgHkvDJ5/r/D3946wdwk3DbFk8tyxouIr8WkUEiYovIK7Zt/+RGj3urodPy8ePJgpwe6Oq42BVS13I1EY65YUPn3uP79xvHRn0wmppMSz1/u9yu4PJlZAnVpfv0Ias9eRIZYN06CP7cObTtvDyyvR49eAgsi/c+/XRboqio4FpzctDm1641Mw3V0/VYDQ2ca+ZMtPe33uL9y5e3bTThb4w1dy5SjH9VSc+eSAyHDpmt/l4vNqfvCAAAIABJREFUgUuz9DNnTDYZFsb/JyeTPevsS7VppymYVutcumQ2oOl3wLnJasAA7ql/XXpkJAFz8GAI+PhxkalD58kzv9ssoc9uE09Ekpz5aYqM+dvNkrFl2/+UJ6q84/Ew6ztwgH8vWsS16sxLF0aXLeO+pKRAun/0RzdGklVVLDifPEmw69GD8+sGtQkT+G5+8glrQT17Eqhnzep4NltUhKR55gzHnTqV672R4NMVFBURUDIzCfSjR4tsjEmR4UHo/zcVt1nbvxkae6uI/JVt2ycsy+otIumWZe2ybftsZ2+8UygsJCPWBSr9Yp48SbY4fjy/D5bUz5wxPTAXL+az6+wBu3gRYp8xw3imNzSQYefnB+eM2B4++4zFvNhYHngRyijVMXHePIJHfj5Z9tmzLIZ5vSbzHDTIt0pExPT03LnTyEwzZphrPXGCGZCSQmwswbF/f/5vxw6y1eeeg0AVTsIcOJBAVF4u8s//7GsHIEIA7NUL0hYxbeK0TLG42NSzq6lU//4Q/uDB5jhZWdyjhgZ+DgnhWtQL/Omn+R4o8vN5fVkZM4mcHF/bX8uCbBct4tg//zmZITbDSRKycZs0P75ZTi/4hkzZ/7Ic/ott8uhfJfnIJZcuQZxlZRDpypVc34cfmoXRRYsYy7596PNO/5juoLISQj91yhi4tbTw2S1danY9nz5NoKqrMxp/e9q9bRMsU1NJMHr04DuXmHh7Oi95vTxfaWmMIyyMe5SQIDLwMz/Hyput4beH26zt3zCx27ZdICIFn/+7xrKscyIyVETuSmLXaX1EBMSl279PnyZbHDuW+x2oC08gHD1qtGDd4t0ZysshCadjo1oOlJWR8bW36aczqIw0YgTXV1JiKlLUt/w//5OsfOJEiKxXL1+7WA1szq3x1dVk/FlZTP/XrTM7Np16umqxWpKoZZ8ZGdzbxx/3rQy6fp17UV6OfDJ/vgk6Cs3Ip07l/Hl55nfaMLt3b+PfEx4OqTc2QoTLlpkg7fGYjWZKhv36UbFy8iT3beNGE9D8F4YHDCBrdmL4cO61+vKfOUOAeuIJAlFJichvTiXJnBnfkKU7fiSl3/y+PPT3hkScawD9+xNURowwO0ZF4IWGBqPT6xpBsN9Tf1RUaNs5X0IfPBhCHzOG+1NYyH29di3wBiknPB6ShNRU3hcdTQCYO/f2ODc2NvIZpqURsPr04Ts4e7bj/P99h/zdk5Kk4dVt0mPjZrG//g3p8R+3Vtu/qRq7ZVmjROSAiEyzbbva7/9eEJEXRERGjBgxJycn56adN1g0N4v813/xID3/vMngMjN5IEeN4gENpizMuXszJIRaYmcW2tEY/t//gyhfeAFSqagwHuhbtrT1jQkGts0MYP9+IyOpj4rauVZVMVMJDydzysszerouOsbHkyk6+5pmZkLcHo+RSJQUnfXpISEEzMceI+MsLkZ6KSszTZmdlR4HDvCnd28Iv6CATDxQA4x+/fh/EUjI40HzXbiQhzklhQdb7Xc1S3dqv+XlzKycQWP6dI5bWurb2ETE11xs4ECux4mICO7ryJEQ5M6dfL660ciyCCKpqTgaPrl9s4T9yTck7Fc81M0Lk+TgQYJMaCjXM28ex9KF0alTOY9aBickcOzuEqXpI2oWkltbuYalS3kGLMv40qSnc67ly03jbn80NRFQjx7lOzZgAAH6wQe7H3i6gtJSzn36NMFpxAju06RJN1azf6NoaeG7c/kyZaBFRSLL9v5Alh7ovrZ/2xdPLcvqJSL7ReTHtm1v7+i1d2Lx1OslE8zKMptiRJAt3nmHL4M2vOgMjY0Q1pUrPJBf/WpwmqGWVmZmGlvZkhJIvbWV33XHdtfrhXiPH+fhe+QRgk56ummtl5nJzKJ/f85VWWn6dKqcoSWHCudCprMWXJGXh45fV8e1aW16795M7T/8EFLauNE3WJWVmRLT6dMh59de8y2t1LHFxEAWHo/J0gcOZCxNTVxTURH3v76e18bHQ0TOzzIjgxmHSjsqD6SlMcYNG8zipQazjz4yHYyqfdIUs2u3spJ7dOUK92jtWmYR168T8KqrRcbmpsiWdzdL2DtkaPbeFPFs2izvbtkmZwclyYwZZLYa2MrK+D7GxUFWjY3IRElJHdshd4SyMgg9I8OX0EePNuWueu0nTxKQGhoC+9IoamrMgmhjI2NesICgfqsXRLX+PS2Nv0ND+S7Fx98+/T7QmIqLDZHn5HCPQ0K4N7OrUmTKS/RutX7RvYz9tu48tSyrh4i8IyKvdUbqdwLqyKgLlUrqalc7fDjT32BIvbiYAFFRwZfpK18J/ovk79iYn4/8ciO2u62tSB2ffcZDlZhIoLh2DcJctgyySEsjaGgjZMuCOLUsc/Nm365L585BWE1NZOmJib7Zj+rpts2fhx7ifK2tLKzqpqyNG83Cqvb33LmTa96wAQ30F7/wvSbtHBQdbXZ+qkfLokUs2O3dyzX36UNmduEC//7yl32DSHMzBK0ZrwifV79+ZNKjRzMOHWNDA9elx66uNh2hRAg0zz7L648cYaZgWXyv5s5l3O+9Z2wI4uJENoce+x9SLywU2ZGTJCHrtsmkomOS+N0kCQ0l0OnCaEIC9z83l+/JQw/5rg90Bc7G0EroHg9BbMkS3w1Q169zr/LzIaJHHmlrvibCdyg1lWN6vVTKzJ/feWXMzUBTE59lWhrBqlcvnqc5c9rf/HcrUVsLiV+5AqGrpDlgAGMaO5bZUPinn2vqb39O5sm3Vtu/4YzdsixLRF4VkXLbtv88mPfc7oxda8vnz6dOWAQi2LYNbfWZZ4LzXdHKF11g1F2QwSAnB//t8eN5aJ9/nlLHqCiO48yEg0VTE9dw5QrkO3IkGXRjIxr4+PEErkuXeFBzc31LGUND+fmpp0xwamgg+8/M5HePPeYbcJx6ugjkp1pyaSkzmeLitrJGbS0Z88WLkMqcOQQk52YedZdUvVfESET9+5tdm4cO8bsZMwhgxcWQ/cqVvp+jes84bQHmzuV+VVSYxU4dY3Y2Y6qp4TjO8krLMs0zioog7/x8guEjj3AfMjJIIPR9y5ZBnpbFPd+7l4AYGQlZjx6N5KILo1Oncn3Fxdz75cvbNqEOFiUlEPqZM5zfsvjsdIexc2aoO2VPnIAoV6wg+/W3SM7JgdAvXeIzmjmTZ6o7392uoqICMj95ku/90KEEwClTurcTu7tobTXyyuXLxs4iMhISHzOGv9vYbdykqpjbJsVYlrVIRA6KSKaI6Cbs/8+27Y/ae8/tJHbdjThpEgFSdyC++SbZyJe+1HlZotdLRcDhwyabfPJJ05O0M9TU4GkSESHyx3/Ml+Dv/x6duz3Plc5QV8cicEEBJK67VHv3ZmyRkQQOJYn8fEPqamblX/ly6RLkW1fHw79oke9DU1vLMVWj1tr0nj0JBB98wAP/+OO+HvLOFnjJyQQ2tcbVTFwXcFVuETH/TkwkcOzejfQxaRIZ99GjXNPatb6zDaefvH69IyIIJvqejRsJhCI8rCkpkFbPnm3r5UeO5J726MEaRmoq93f1aojFWdctwvE3bzYbl7TphVoUz5/P73RhdNo0iCsnh+9EcnJbn/VgUVLCusWZM6au3+Phni1e7OvB49+FKSEBnd0ZHL1ePq/UVPMdio+Ho251b1KtrklLIxELCeE7Fx9/e2YHOoaSEkPk/vKKEnlc3O2px79tUoxt24dE5DZcUtehJWpDhjDdtixT3z1wIJl6Z6ReV0fWd/WqWehcvz54Uvd4yGKbm5EJtPlDbCzn787DUVmJhFNVBYFcuULgHzMGwqqooG1bczNjzs8nG66v5+/mZohw40ZTxaJdjGJjfTN4RV4egaShATJes4aM2eOB0NPTmdZv2mQChdY9nzyJlDB+POSsZKsLaxERZgrrfDj69iXBOX0aEoyNJYilpxMsnDtdFfX1ZN3a9FmE7C46GnIaN47Ao+9x+ryEhfmSelgY1zNxIg/0++8z/Z8501gLaMDXrH/0aO5rdDTfmR07CK66eSgvT+SVVxjnpEnGLiAy0njWdGfBsbiYoHP2LGPRoDhlCoTuL+Vcu0YwKixkbKtX+1oPNzczrsOH+b7FxFDBNWPGjXnOBIOWFmYxR4/y+URFkWjMndu93gNdRV2dkVb85ZXZsyHyUaPadvK6m3DP7jytrKT6JDQUC9xevYj+r7/OtP7LX+6cVHWbeX095JCT09Z6oDN89BGkW1TEXgh/vPiiyNatwR+vuBhSVzuAw4cZl/rRXLgAUfXsCek2NxvbWs3YnZUvV68iL1VVodEvW9aWWI4fNwuJ/ftTCaJb9d96C3Lw38xz7Rq6cUUF2d3582ZxVC1enbYFOosQ4e85cxjHsWMQibYf3Lu37U5XxdWr5vNSzJrF515djfyh7Qdtm0xQA43/ztHJkwkiIrwmPZ1ses0aAuj588aBUbP8JUsYZ00N6xqffWZ6uIaGcpyyMgJg376GhBMTWZ/oLMkIhKIiCP3cOc5h23ze06ZB6P7rNrW1jOP0aUhy5UrIXwNqXR33Re0Jhg3js5048dZXmFRVcd4TJzj34MHMIqZNu7XVNU555coV490fGWky8jFjur9wfTNxX1sKNDZS1lhVRcVKbCzk99prPJzPPtv5QotuvT90SOR//S8ehEWLIIdgkZEBuSUm8gApnD0uu4Jr14y18MqVpqPOunV8+XVrvM4sVDYS4Xrr69llGx9PYNizh6woJoYg4VxIE4Hs3n3X7K6cPZvMLiwMUnrvPa7lscdM3b3TtrdvXwKANpIOCyPLaWiAVJTUnfJHnz6UyZ08CcnMmkWmtmsXxD1+PNKLM3PzetGqDx40vwsPNz7kvXv7+tHU1DD2rKy2n4VW8YwfD3l/9BFkmJhI0KutNQ6MfftyT8PCmBGOGsWsQMexcCGEkJLC2GNiGMP589z/mTM5ZnekuMJC7vP586aqyba5d4sX+/ZA1XuUlsZ9amkhwC1ZYrLOsjLGfvo0n+HEiRB6MCW8NwLbhlTT0ghOIsxkEhI4962QN5zyypUrfDYqrwwfDpGPHUtguZPlkoFw3/qxq/RRWkr5YGwsX5zXXuNB/PKXOyb11lYe5pMn+XC//30eAt1tFyycjo0rVtz4dV26xEJpnz5m4bFXL6pyBg6EqE6dMoZbSpaWxb9bWsi0J0xgJvL73/Mwx8cTrPynlTU17OAsL4e4Nm7kgfN4TN9Pfx+V0lJmCwUFEFpurnFS1DrwyEgelupqzun1muAzaRK/P3SIY2/ZwntefZX/V2sC58Pu7PqkGDSI2Ul6Osdct87UfZ8/z73SHadOUp8+HbmhpYXv0NmzHGvLFsb/6aeQtuqrubnGIbKwUOTf/53rnTyZQJCeToIRFcWxs7MJ9hMmcM+7UwVVUAChX7gAoauGPnMmiYd64DiRk8N3uriY7/Tq1eZ1165B6BogZszg++4fGG42WltZBzh6lHvXsyfnjY+/NZmxyisqsejssX9/I6+MHNm95jV3I+4pYtcFxCtXeJjHjIHEXnvNlMJpWVsgVFVBnvn5ZD1KWKrlBps9NDRANpGRvpYFihdf7Np1ZWQglwwcaFrUjRpljv3b35J1PPAARKw9SdUmICyMax8wwHi7ByoNVFy5wiJpayuBUfuqVlay3nD9OhmVSgxO+9qwMGYMupYQHc19KC7mgdXm1zqr0NfExUEu0dGsYYwZg3Z/6RLXun592+3o584xo2hpMZn3xIl8fqWlZnZiWUhSH39syhCdiIyEnNVQa9cujpmcTNZ69SoyWnk5mXxNjWlEMmsW47x8mXv15JN85379a847ZQpySWamCYS6aNsV5OdD6BcvGkL3ejn/okWBnRxVEsrM5N7rjmZt5pGayljVeyc+vuPn42agpgZp7/hxZjuxschbDz54c7X71laClmblGvh79jTSypgxt8fi4E7gnpJivvIVHhqVTP7qr/jiqD9JoCnv1q38yc6GtFpbIa5///e2rw1GD7dt5JIrV3wdG7sLLdUcPpyHWQnl4Ych2tdfhyB79jS2tV4v11pTYypf6ushwfZKAxV79pAxi/Cgq0HahQtk+bZN0JwyhdfU1BB0Ll9mtlBRwWssCxK8fNnsFG1tZZwhIUYHHzoUEm5pMVUZly4RoFtbWTdw2uuK+DbcFjHVHxMnmmbOmzaZCpDr18nANag4MWMGQVvLMa9e5Tu0di1E88knZO79+/Paw4e5v6tXk2mmpZk1gJAQKlLq61mkbWjg3NpRyallB4vr141ZnEoulkWWuXBhYGLyeMiE9+/n3wsXGofQ06e5BrVRTkzk+3CrFwKvX2dMn33GNUyYwOc9evTNkVtsm++Rs3qlpcXIK87qlbtNXukK7juN/bPP0Jnffhu9s7CQB/vf/g1Sb296Z1lksLt3k9Fu3uw7De2qHq69UW/EmVGEc+7dC8mOHo1sUlcH4cyYwRf3zTd5cHVXptZ+x8aiIU6YQAVIWhoPeaDSQEVLC5LH9esQ8ZNPQk4eD+NITUVzfOIJU7d89izZanMzpKMbeQYNgsBzcnx9aHS7v4jxc6mq4oFbtYrxffQRn6W/va6ipIQZmJK0ZRHEtKmJswG22hbs39/2eqOiTPZ8+DDac2gos5AZM5iB7NvHMRYtMk2jBw7ke3b0KJ/HzJnMKA4e5DMaOpRry87mHEuXIp11tdb62jXT+FxLQkNCWG9YuLB9Xf7KFdYASkuNkVjPnlxPWhpBJy6OmciUKbeW5NQ75uhRvlcREdyv+PibU/teX+9bveKUV5TIR426d+QVkftMY9d+mCJM2YuL2X0pwkJpe6Su2u6uXXzJ1627sS/BxYsQycyZxrGxO/B6IcyTJ01jjOho0ws0IwOdWEsX9W8RQ54qE/zmN8bFcfXqwJVABQWQelMTQe3553lddTWB8to1rmflSki/qQnyOH2a+6XBJSyMh/bECYglNBRSDw9n/ErqWg0THW10/0uX0PQbGtra64q0rU3Xax46lFlCYaHZQGRZ/O611yBbf8ycyb0oK6PJSWEh2f4jjzAL+tWv+A6NH88C4549ZPITJnA9e/cyE1uxgnWN3/8eoho/nkXVsDDet2BB179PubkQutpVKBITOV575X5VVdybs2eRZZ56igB/+DDfo9ZWxrdgAcHsVtZc19WxvnDsGPcrJob7PWPGjT1fra0EbyVyp7yi0srYsfeuvNIVfOEz9q1bRV56qfPXOWWU9t4TSGpRqaYzlJdTnxwTAzF2Vy9sbWW36PnzkNb16zyITzwB2e7bR/DQ0kX1VOnRA8IsL4eAvV4IKTycBcH2ujilphoL3DlzjNtkVhbBsrUVwpw+ndfk5PD7qirf2czEiZwrM9M30AwcCIFqf1ERCHvxYhbLdDH21CmCkr+9rgjrBb/7HaQnYsolR42CcAcMIPseNMiUMX78cdtr1Y1DQ4ZwHw8fJrisXs1i6J49jKNvX2YQPXvyWTQ08Fnk5jIDWbAAUsnM5JhDh5rKitmzydK7Wm+dkwOhZ2ebDF0D5fz57Wvfra1cx8GDXPvixdyXo0eRpSwL/Xr+/O4t1nYFhYXG+9zjgWQTEpj5dSeQOOUVrV5ReWXYMFO98kWXV7qC+06KEWkrmwQjo3S39NAJdWysqcGxsbsZQ2MjPjQ5Oaa6Zd48iNq20bLPnDEVL7oJpW9fU7O+ahWZdE4OZLtmTWBSaG1Fn1ci2biRag5n6aBazw4YwPFTUpAjnLtDo6LYRHTokClfVI19wADjTRMWxjmnTUM379uXc//hD7xPfW38JYvsbO6Jzkxsm9f06UNWrRq5bsD61a98+6Eq1BwtLw8tvaLCtHM7dw5Sb26GABcvJtvcs4fra23lz9y5XPuxY1zfqFEQfF0d1TcPPdT1apKrVyH0q1cNoffoASEmJnZcwZWVxcypvJzPesIEZnM5OWTGc+dynFu5qcfrJQk5epTA16MHn0lCQvcqa5zyypUr5jsVE2OI/F6TV7oCl9gD/BzMe7oK26bE78wZdpKOHdu949TWIh0UF0PcTU1kz7NmQRxvvAEpaTcgJdahQ817Zs5ksTUkhCy0vQYMhYVUbegmoa9+1Sy2bt8OySgR/vjHIt/8Jr9XKUWRkAAZpab6kn2fPgSe5mZzfwcNYkwjR5J17d5NZh3IXlfv60cfUT0hwuvKynjAGxog2kceYZwiBKP2tHTdULVrF7JEv35Gh//oI2ZFo0ZxvF69kFYuXjQzj7Fjuc9ayTFyJIRTUcHC3PLlXav3tm1D6Dk5htDDwyHzxMSObXkrK5mRXLjA/ZgwAZIvLeXeJyYyc7iV5NfQYFrNVVWRzMTH833tykYrj8e3ekXtKnr2ZG1JK1hupH/rvYT7SmNX+JcRBlNW2NXSQ38cPQqpJyV1n9TVj12zk9BQ5Bx1Y3z9dfN/WvUiYjTd2FiI4ODBtk0wnLBtiF89zydNIiMPCSEzfucdAsr69RCmbSNZOXeFikAmK1eS0fp7lCsBKyIi0MznzOE4eXlIOeXlge11RSCuV1/l77AwzldcbNYPnDOJsjLsE3SDkzNQz5oFWV+8SBlrXR0zg4QE7tXx4xC/NkgpKKCsURfhoqJ47dmzEM/gwWS/OTlcp5YPBiszqPfJ/v1ktzo7CQtjlpCQ0DEptrQQRLVqaexY7seRI9ybxx9HcruVpljFxXznMzIIrqNGMUucMCE4OcS2+cyUyLOzTbnq8OHM2saORS67X+SVW4F7KmO/3XA6Nj75ZPd0xMJCMvXGRh6UESMgrV69+PK/9ZYpFVQ5IyQE3fLiRcimogKyf/hhCDTQOJwe8pZlary9Xkhu/37I6oknIM7qal7/ta+ZNQbLgohDQggOWnqnD2CPHr5eK84Waq2tnENr6NevD1xDf/w48oL6rtfXm5lFRQXH1JZx27aRtfpDHSv79iUjP3+e+7R2LVntzp0cV832IiJ8A15YGEGhqAgC7tcPSSQvj89l6VIy4mCJx7a57/v3k51qht6zJ3p9fHzH2bVt81l//LHxbampgRDHjOEY2vHoVkDPf/SoaTU3fTqBKJCtrz/q63mfLno65RVn9Up3LBXuN9yXUszthL9jY3e+lDk5ZONaVTJ3LoQbGmr8WdTCVjPRXr1Mezbd5DNiBETZXgnZtWssPjY0MM4vfYmMqK4OieXKFR7UNWuQA775zcC+Nn/xF2SE6syopYz+rfWGDkVGUiOxwkLkjaKi9mvoW1vZaKUOiZMnQ9qRkfyfbUPM06YZL3iduWjAEzG2B6dPQ9QeD1nguHEEjJwc3/E1NRFYr13j/ePGcbzz5zm37lwOD4dA588PvuZbm0EcOMA9U0KPjGTmMG9e58cqLze9BCIijLw1bRpj6a5PezBobGQxOS2N71mfPox59uyOfZY8Ht/qFZVXIiJ8q1dceaXrcIn9FsLjQSooLCSj7U61wfnzlBLq7X/0UR4YrxdCOnLEEIFiyBAIrLiY7NjrZcEuISFw9uhfxx0XZxwlc3KQXurrIcLZsyG5Dz4w3jAiZOsnT0ImH3zA+Xv04BhVVb4+LxERXIdaznq9yAad1dBfvUrgaW4myx48GFJ/4AEy1Lg4ql5aW3mdc3FUA56WTkZGsjiak2NkgsxMKkfCw00PTMti0XT7do4bHc0MQitJ4uKQZrxeZglLlwbfyMG2IeL9+yE1/RyjoyH0uXM7r5pqaeGzS001zUzCwxl7YuKtNaQqKzOt5pqbkUi01Vwgmce2CUBK5FevmgDkrF5x5ZUbx32psd8ufPIJGd6mTd0j9ZMnjYGWLu79x39AiNu301EoOdlX19YmDLpjU5s4O61WnXDWoIuQaeku0kOHqMXu14/ANHiw2XnrdEZUEj592jRwHjaMzLu2lmMpqc+bB2lqBlpaSpZ+/Xpge10Rru+DD8jARZg1FBVB6mphEB8Pqb7/PsFQoWWetg3ZrVxpdlv26EEQiYw06xMzZzK+6GhmLm+/bWwPRo0iWJ45QzZfXs59mzKFzyGQ/0ogqGRx4IAhdBHGsWgR4+yM0G2bwPrRR8bPJjoaMp8799bJFbYNKaelmV2u06Zx/50e7oqGBl/vFadVxIMPuvLKncbNao33nyKyRkSKbdue1tnrv8g4fZpKgMTE9mvDO8KhQyw6ipAVbtkCib30Ej+ra9/y5WR5lgVppqcbTTspybfzjz8uXGCBsqmJ16xfz8Pm9CrXDVk//jHZmHMCFRnJ/3k8nOvqVchl2DCOrRYBIsg/Tz9tyE83Eu3ZA4lt3NjWXlcE8nz1VUg3IoJM9tNPuUYl7c2bed2//IuRXbQbUEsLgeLpp/n5P/+ToDBlCp/NwYNc58CBjGHECONwuHOn0bgjIri+2FiuS/cNLF8evB2EbXNfDhwgy1dCj45mUXTmzOBsZ/PzmUVpx6cHHiCoTZ9+6xZEm5tNq7nSUsa8dClBxFkm65RXrlzhPolw/0aP5vs4Zszt6abkonPcrIz9v0XkZyLy65t0vLsShYVkmN1xbLRtNN5jx/h55kxki7Aws4POWWGiWuyUKTx0ImjrGze2r6u2tkJaeo7evU3TDPWWr61Fepk3DyL80Y98N2Bp0+R332WGsHQpQaGw0CxU6gLuI48gUygqK6lLb89eV5GaanzQR49mfHv3QtRNTRBqYiL3y9ngWssPNUtfsQIyPXIEEtq0CXL69a8Z38MPG5kqN5esv7SUY0VHs8YQEQEZlZSYJiPjxwe3EGnbzCL27+deKvn26sXO0xkzgiPk0lLut2rRMTGM/VY2hfZvNTdkiG9VTaDqFae8snSpKQN15ZW7DzeF2G3bPmBZ1qibcay7FZ05NnYEtRJWYlQfGf8dsD/4gfm3ku3SpRDt/PnIAu1lfiUlyAsaHEaNosIlMhJ9efduU7MeF2d+p+jdmwe7ulrkZz+DvB94AOJOSfGVhYYNw6pBx6Kd7T/5hJ8D2evqPfztbyGwkBBb99AkAAAgAElEQVTkkwsXTKs5bQJSWMi1OKFeNNHRkG9TE4vXlZWmafDu3WS7U6dCjGpdsHs3OruI0eS16qa4mGtftw4iDrZk79w5goqT0Pv0gdCDzbALCwleuqNWG3l0t2w2mHFfvWpazan7pLaaa2zk90rmupbxwANc09ixBGJXXrn7cdMWTz8n9g+CkWK+aIunXi+Ldt1xbGxpwZO7oICM8+mnfW1bs7Mp2/vbv+V1OTmQ+r/+q1mcfOqp9jfAKKlqhyPtEbpiBUT4hz+QVU6ciCTT3Awp/+EPbY+1dq0pl5w/n4xWHRRFIKsnnySjVdTUkAl3ZK8r4rtQqRnphx9yDssicx45krE6v5Iqy4iQpScnQ9TqPZ+cTJ352bP8/MgjEFBrK5n8gQO+DbNDQ5n5FBUZCSgxMTgLCNvmPPv3E0h1UTQmhgA8bVrngUHJNSXFrH9ERUHokyd3PobuoKWFwJaWxnVHRvI5z57N5+esXrFtI69o9Yorr9w9uOsWTy3LekFEXhARGXGr27LcZOzfT9nao48GT+pbt9J8/Je/JGt84AGCgrryqafJJ5+Ysq+cHOPJUlUFUT79dPuk09gIqZ49azy6H38c6SQ/n1lCdbWRJM6cgUznzKHsMDZW5H//b7OY6vUyllWrCBROm9tRoyiTdBKXHq+11df73ImWFmQG7Y6TkABRvPmmqeyJjWWc+hpFaCjv1yy9ooIyzIYGSg+joliE9nqZ1SxYwHu05ruiwvfexcaS0ZeUMI4lS4LrOev1sqB54IAxNxPhXi1dGpxLoh7j00/NDt6wMMadmHhr5IzqamS59HTu2cCBBMIePQguv/iFkVeGDuV+jBnDv2/lJicXtx63jdht235FRF4RIWO/Xee9Ueii2MyZvnpyZ3jpJVN3PGoU3ZxUunB2aRoxAi0zOZksKTMTsli+nGyyPVy7xkJbdTWk0KsX2fTgwTzMn3wCIT73HBnqO++YHpsinGP8eIh9924e7sWLmSH87nfmPKGhSDra+k4EycRpr/vYY4F9QZwNsHv25DinTyM/qF4eHW38ZBRal+7xEICWLuV8Fy+iBT/0ENm4OjCuXg3JlpVB6FlZZKW6yBodzfFKSsiqk5ODq6H2egleBw5wbL13/fszpsmTO9fAm5up+jlyxBiniXBdy5d3r5l5R7Bt7vvRo3zetm2aeRcXE8BFfOWVUaM6tjBw8cWDW+7YAcrLyTbj4rrWQenSJf5ubvZtViHC4uW2bRCzNqLo1YvjZ2eTTf3mN237jyq0NjwlhcBh20gYmzZBiO+8A+GOG0f2ri3b6up4/+DBEGFGBiWWS5dSE71hA6TobDE3fDhZujPrvXjRtJYLZK8rAiHv2gW5iEAey5cjxZSU+PrK1NX5bjAKCeHfWvGSny/y85/z+mXLyMLfe4+Zj27pb242tf8hIabpiP67ro6guXx54NK9QPc4MxNCLy831zdwIPcrGBuB2lqu//hxZlZaBhoXx8wvmHF0Ba2tfO5HjvCZh4aaBeLr1zn/6NHManRz0K207nVxZ3FTNHbLsn4nIstEZICIFInIi7Zt/7/2Xv9F0Ni749jYmR1wfj4ShBJNVhYPWGUlBB0TQ4bdnhtfdTWB5upVY9ur3ZSKi5FeKiog3Ph4Sg7T0sy2/+Rks81e69UTEznvjh1G2w4JQfOdNcucu6mpc3tdEaQK7eqklTPR0Yxbd9jqAqYSptfruxlr1iw0/vffJwCOHk1WefiwcWBcsoSAk5HBjKO21rf1nmrzgwZB6GPHdk5kXi/HO3DAjN/rhYyXLQuuWqa0lMXgjAyuR3cHR0UxjkCLyjeC2lpKO0+d8jVdsyyCh24OcuWVewO3VWO3bfupm3GcuwW2DakUF7NTMxhSt20eft21+PWv+y4CZmaSaUZGQohZWTzs2vdz/Hiy7va2mF+4wIJnSwvHaG6GXB98EElnxw6y02ef5Ri//KWphz5xgsXY1FTOK8IsYfVqsv8jR8x5YmPb9oZ12usuWhTYXte2TaWNbUNoTz+N9PLBB75Zuu4U1VlESAgkGBVFFn71KuPXlnOXLjFDUQfG2FiC5I4dxr8lJMR3TSAyktc++GDn+rXHYwi9stK8Xgm9s6Bg21S2pKYyowkLMxu5KiuNJ83NkjsaG9HNT5wwn7EI93TiRFO94sor9y9cKSYA1LExOTm40rOmJjLSCxcomVuzBmIXgcz27mXRLC6OTFnL/bSD0/z5xlzLH87a9L59jS/5l76E1vv730NKY8ZA9CdPYmFr2xDjww8zW5g71xDrtGnMCpyWBiKQ2JIlhsT87XW/8pXAi8dVVcwWdNPKnDkcR2cXeh9EOG9dHX+U7L1eMtlZs1iMLS5m+3rPnqapyOOPownX1xN0T5zgPoSH+/rUhIdz7oSEzjcFeTwEnoMHfQl96FDuRWf9ONWLPDWVa4+MpNIkP5+F8BEjCJ436ufi9XL8rCzkFqd75gMPELwefJCZlyuvuBBxib0NcnIg0okTTQPgjlBairxSVuZbGfLii2RW27eTcY4dS1bn8RjfD/Vcb6+NXkkJmnlREeRQWEjWumkTBPcf/8FrdHfi66/zGhE09vnzkV1EIIfwcM6VkeG78ad3b2YmTnuEYOx1bRti1MqY8HA2UEVFMTb/zUW9extSUi+ZyEgWVS9coNyzd2/kocxMrnHuXFPJkZZGkGxpMR41St66Q3fZss4zVY8H6eLgQYKSEvqIEdzLUaM6fn9LC+8/fJgZV79+3J/SUgJOr14mEHWXaCsqTBlidrZJAkS49gcfZKw3e/HVxb0B1wTMAXVs7NkTD5XONmJcvAhxa+WIkxDKymiOUVaGzHLxIg95WJjJVDdvhoD9obXp3/42waJ3b7JY1dMzMyHT8HAIpLISAlfyXruWDPqHP2x7bN3wpJg1i+Ci0kqw9rp1dUhLFy/y8/DhBJwLF3z1ehEWd/PyfPV1EWY3U6aY0spp05B7cnN9HRizszlmSYkhdKf5WFwc97+zSpfWVu6rdnvSsYwZw33prAq3ro6Z07FjBJ2hQwme9fVIRY2NfEbLlnW9yUVjI7MbJXOV6Hr0MO6WI0ey+BnszlgX9x7uujr2ux0eD9Uqzc1ozB2Rum2T7aWkkElv2eLrtpeVRaa9axc6s5Kf9v/UTUeBvKydtekpKcg65eXILFOmmCbXI0eiIe/YYeSOSZMg9agoCKFXLzK9738fklc5RIQAsHmzr9QUjL2uCOT9+98zVvWuSUggw3cadfXvzzjUileJNDKSKpzMTEor+/cnu/3sM8alTamrqvhMzp0zswX1kmlsJBitWWO6KLWH1lYy6UOHCN5KimPHQuid7U0oL0duOX2aY02YAMFalqkkGjUK2SWQKVygvrleL5KNEnlenpnJaeloRYWxT0hIaN/wzYULf7jE/jk++YSHqzPHxqYmSO38eabDa9YY0nF2KIqJoSpl8WIIaOJEyHrIEEjdvw/p1q1s93/nHchHjbMsi41NERFU6RQVIRHFxSF3tLTwf48/bkr/VIN2BhsnqY8Zw3WqZOFvr/vUU4HtdZ2VMSLMJDZvhoz+9V9NBh0Swrb+s2d9bYdt29ROv/suJYlTpnDfMzONA2N4OGM5dIix6QzHueA6eDDyUUdWui0thtDVjVKEjHfp0s5LDvPyIPRz5/gMtSl0VJTZ/dq7N/LT1KntZ9EvvcTnW1Fh3BCzs839GjIE+amlhSQgP5/PbsUKAqy7COqiq3CJXYxj4/z57Ts2bt0q8qd/ip5eWookkphoHubWVrLpf/s3Fja1Hjw2FhLKzCSj3rChrVbt9ZoWdIcPQ56Kv/xL/iQnk0Fv3gyhaHs0dWmMiPDVxXv3JuONjITERDi+9lHVcQdjrytC1r19u+l+M2UKQU1NuBQjRhAA1JtF0bMn4zx5kvMNGkRmevascWAcPhwS/eQTzqNmVNHRELPa2C5ZwjW1V+3S0kLVyKFDxrJAhMC3dGnHi5lqvZuaiiTUsyeBNCGB+3LsGDOplhZq+Jcs6bhZhnr3/PSnpoKlTx82N40dy79Pn6bevaWFmdiqVYzVNddy0V3c9xp7QQGWr8OGtd0y74Rlifyf/8P/b9pE1quoqYHwr19vO+VWPPMMroOBsrqjRwkSb78NWar8oc0tjh9nfPHxaOtNTWYn55gxvg01tH47MpLf66LbgAFk4ur74W+v+8gjge11W1tZsDx82NTDP/II5Pjb3xqyDQuD7JXQnV+radPIStVMbNQo5KOQEPTo+HgkKpWVnI0p6uogTm32vHFj+5VKLS3cq0OH0L1V+pk6lZlTR23cWlsh2MOHGUvfvgT6WbM4b04O4ysq4vyrVgXebatob0/DX/+1yD/8A3JdWhrZe2ioaTV3Kzsiufjiw+2gFAQaGkReeQXS+PrX25/WnznDg/fyy+jpzrr2vDxIvakJkn3qKXzGk5PJQF96iSw5kB1BRxuavvUtYy713e8SPLSz0dSpLGr26AEJbd9uSihFCALqGChCxpmUZP4/WHvdggKOrVa3sbG8NjXVV0uPi4NUS0t9F0d79mSWkZ7OfYqL455XVhoHxn/6JzJf3Uhl27xPN9vExqL96+Kseu040dwMoX/6qS+hT58OoXekTTc0kIWnpRFE4uLQz9X/paYGaS0zE7JfuZKZV7CLl7r5yrb5jmirOZ1Vaau5YLszubi/4RJ7JwjGsbGznaSnT6NnHzpkLGv9kZUVXC28kxDPnYN4d+8mo/7HfzR+K5s3U6Vi2+jH2vhZM+HaWkPE2p1J7Qn87XVXrQq8E9LrhSRTUkxZ4pw5BLR9+4xublkEM806nXr65MlktJ9+Ssbbvz8zGnVgHD0akpszx8xyevRgjK2tEGtZGRlyYiLau/+mqOZmSPnTT83MQYRqm8WLO+58VFGBhHTyJEFp3DgIfdQorsvjMR2ZPB7+b/Hi4Fwg/WFZVP7o7tBhw8jOJ092d4O66BrcqphOEIxjo7OawUm8Xi/keOQIRLB9u9GlLYuuRFFREFlXvLWdHiuDB2NlsGePWWTcsAEicDahFiGLnTaN8egiqVN7FwneXresDA08L4+MtUcPSO34cd+69Oho5Bd/Ug8PZ7Zy/DgBKi6OQFNUhOyycCEzgV/9ytTch4RwrOZmZhDjxhnZZvPmtna2TU1kvampZgHSsghSixZ1bDObn8/7zp7lPdOnc33OBfPsbIi4tJTxrFrVdeta2+bzSUtj1nX8uGk1N3Ro147lwkVXcV9m7BcuUGM+cybkF8y0Wom9oYHKlcuXmUavXGmm2keOQBKvvBK48qUj/O3fQmjXryNzvPFG29e8+CJE9/vfk2WGhEBk+fnGKiA0FNJW+18RX3vd5cvb2utu3cqxjx9nc5buBh0yBMJ1yjoiZMJlZcahUTFhAvJCejqBLTwc2UUdGMPCmIX85CemwbYTf/ZnfB6HDhHYnnjCl1Cbmgh6hw/7Evrs2dyH9qwfbJv7k5qK/BQRwUwhIcFX2qmqIrB+9pmxLw5UHdQRmpvZAJaWRt19dDTnmju3fQ8gFy6ChSvFtIOyMrLFmBgkmGCn1lu3YnH7xhuQ1aOPQigikOCOHRDjmTPsAO3KlP3iRapZdu6E4E+fhri0+kP12W3bTJY+bhwLe++9ZxZIBw/Ga0UJLlh7XcvCUfLyZbP4OmwYQcb59QgJgRQbGnxJPTycgHbiBNUsAwaQ7fbpAzmOHw8hHzhAZj9tGlJIbi739cwZqmm2b4d4Z80iEOg9bGw0hK7XGhICYS5c6FvW6YTHgzaemgrJ9ukDmc+Z41uf72zKYdsEiYULg+tTqqisRBY6cYLxxsVxrqlTu3YcFy46givFBEBzM+QYEkLm2xXyffpp6sZ79MBoS3cpNjVRzZKVBbn94AfBL6x5PFScpKYiBezdC5kPGsQmKZUHzpxBc1c72/XrCQZvvWWOtWwZGrAukAZjryuC7KB/W5Zp2JGXx+91puKfneu/x43j//btY4YSHs7CoJYC5uTQ0KGsDAkoLIzAFRUFeW/dSlb7yisQ4mOPoZGL8PORI8bVUYTxzZ3L8dvLgBsbCbJpachHAwdy3GnT2mraWVmUl5aVsSi6cmVwpm8ixvzr6FGzmKyt5oYPd3eHurhzuG+IvTuOjfq+Tz9F646LIyPWDLGqiuy8pIQyxa404qiuRtLJzYUMtO59wQIqWMLCyLjXruV1IhDGtGkQuurd2l1IdVt/e91nnglcQtdev1W1HIiMJCjYttG/1SpYhAA3Z46ZXfTuzZhGjjQWBe+8Q4Dp1w9JIyuL3y9eDDGHh2NT/OtfM4N65hnG3NAAoR85Ygg9LAzpa8GC9iWuqirec+IE7xszBmknkDtjZSXrJOfPc+4/+qPA9g6B0NrKTODoUdNqbsECxtfe7MGFi9uJ+0aKOXKEBzk5GWIJBi0tZL1nzkCo69aZLD8/n6qalha04K4skl6+jOzQ0oLf+C9+0fY1zz1natRjYggop0+T3SumTmVMukHGaa+7cGFge10nrl6FfL/9bbNIHBFB9Y3TAlcdGXVhduRIsv/sbEi2rg7Sf/hhNtYcOkSWHRJC5pqXx7XOmsWYeveGvN99l8XcqVMJYB6PIXTtUxoWhqQxf377JYGFhZzvzBkC0bRpvD4uru1rW1sJ1IcOQfZLllB1E4xcUl3NTCA9nQA3cCBjmz69e9UyLlx0Fa4U48Cf/znkGKxjowjE9uabZNIPPQRRatZ3/jyEGB3NpqaOLAic8HpZNDxwgNrqzZvRo19+2TSeyM2F9LX5RnIymeSbb5qdi6GhRloQCd5e1zmOffvwu3Fi8mSCjrZws21mNtqtPiyMcyqBqmWu+o1nZdGtqaaG8+sW+kmTuIeq71+/bmYdq1dD7AcPMn4l9B49INzExMA7YbXqJDWVv3v0YByJie3Pxpy9UKdOZct+Zxm2bTNebTXn9fI9SkgwpZEuXNxtuFkdlFaJyE9EJFRE/sO27X/o6PW3M2Ovrubh/elPg3NsFIFct22DZDZuNJURWvmycyfSx5YtwVe+1NYSDK5epRrnkUd8s7zaWjJZzZwHDOD4mZm+FSSDBqH3azVHMPa6TlRVibz2mm+f0fR0kW9+07SyE4Eca2tNy7qhQyG1ggIj0wwZguwSEsLicW4usottEwyGDYM8dT3Ctk0/1t69ka+ysyF0PU94ONl2QkJgjxSPh8Xgw4fJ1Hv1Mgui7XmqlJdD6JcucV9Xr/bdORwIep6jR5mdRUQw44iPD65fqgsXtwK3LWO3LCtURP5dRFaISJ6IHLMs6z3bts/e6LFvFF6vWWB88sngSP3ECUoDH3iARVLdtej1UmGSnk5m+/jjwU+/s7Mh9aYmpBNnyzndCJOSgr5tWcgV773H2LWjvQgSUlISr/G31/3ylwPb6zpx/LjZ0CRCJrxqFcTrJPVBg8x5Q0OparlwwSys2jaEPmkSmb82vYiJgUT792c24tyh2dSEPcKZM4xzwABmIUroERHMiubNC/w5NTWZptBaebNuHTJIezJKSwszgdRUxr5iBUGgI3mqtpbP+Phx/t2/P0F4xoyOPWFcuLibcDOkmHgRybJt+4qIiGVZb4jIehG5o8TuvzioconuGvWHx0MmnpaGXr5xo8kAm5og2cuXIZ+HHgpuCq72vvv2QXpf+pKvX0lWFkSrEsvGjWybz8oS+Zd/MeOMjGRxTxdIg7XXVdTXU86oG4Isi+uYPJnfa014TAx6+RtvEEAGDWIR8vx5UwY5cyby0LlzyC6NjaavZ1iYMRlzkmdxMTOgsjKCSG6uqcZRk625cwNfQ02NaQrd1GQWZzvyJLdtxvzJJ8xQpk+H1DuqIy8oMJ2zPB7kr4SE4HqlunBxt+FmEPtQEbnm+DlPRBL8X2RZ1gsi8oKIyIjOOhrcBLS3azQQ6uspWczORqNdscKUBjorX9auNbXrnaGuDonk8mWI5dFHDXFVVEA6Fy6Y8yQmkhW+/z5Tf8X48SzO9ugRvL2uwr8PqQgSxJo1BI9f/cq8VglXhOM//zyykWbD/fqRudo2Uk5REUTZ1ERmu3QplSH+Wa3aLqiBmJ4jMpIZyJw5gTPh4mLGnpHBOSdP5vid7dosLUV2uXyZYP7ccwSDQPB6CVBpaYwrPNx4n3dkR+DCxd2O27Z4atv2KyLyigga++06b2coKiJDranxraEW8a18eeaZznVZRW4ugaK+3hiAWRbZ76FDprLFskxdelERRL1vnzmOBqaLF0X+5E+Cs9dVFBSQJevCpza3GDMGV0bNmPv1g5yVcJXQrl41ZLxiBbLK3r3ozhERxtpgzhxI3X+tobWVCp0zZ3x/Hx0Noc+eHbjVXk4O9+fSJYLKnDlo7p3p2s3NLEofPsxxV61C1glUu19fj6xz7BiyTr9+zHpmzgxOrnPh4m7HzSD26yIy3PHzsM9/d9fgxRcD//78eSpQIiLI7JyVJOfO8X9dqXyxbUhpzx40+q9+lZI724bgdu2CSLQefOpUSOvjj1kEffRR9PVhw1jotW1jr/vLX0JYGzcGttdV1NczG8jIML/T0seaGtwUdfem2ueKEFACBZW/+RtI+uc/Nw2ym5qovU9ODpzZ5uYSLJ3GXL16UVo4a1ZbTVwz59RUgmlUFOOdN6/znp62TbDZuZPrmzkTqSzQonZREfcyM5NrGj2aADl+vOt97uLewg1XxViWFSYiF0XkIYHQj4nI07Ztf9bee+60V4xtk93t28fU/sknjf6q8sWuXV2rfGloIKO+eBHZYN06sr/CQog7J4fqnLo6st3VqyHhvXtNZtzaSi24ZpoVFcHZ64pAjseOIbvoguSAAcw0+vZlkXX3bn4fGQm56ianQYOYNXz6KSS5dSvX4fEw9qoqs/N0xAgy+EDllFVVyC6XL5vf9e5NRj9jRltCb27GXfHIEWYWMTEEuhkzgluYLi42Hu5xcdzT4cN9X+P1ci1pacxSwsLohJSQEHyZqgsXdwtuW1WMbdutlmX9iYh8IpQ7/mdHpH6n0dwMAZ87xwO+dq0hHI8HokhPJyN97LHgCCYvD+mlpgYJID6eRcUPP+RYPXuy+7OwEL132TKqYHJzId2qKtNFaOBAgssLL1DfLkKQCGSvq7hyhXPpIqxlmXG0tLABSqtc4uIYh8bzhx/m7//+b65/2TJ+PnoUgtZ707cvmfCECW0NxP78zwmUJ0+a3/fuzQLsgw+2rUKprYVojx8nIA4fjhQycWJwC5VNTQTltDQCjvr2OLPuxkbGk5ZG0OjTh1LQWbM6nwW4cPFFx03R2G3b/khEProZx7qVqKxEIiguJuucP98QSWMj5NyVyheVSXbtgsi+8hWIMz2dTLyxESLMy+OcDz0EEb3+Ou/X9nWJifyfZtHvv0+N+JAh7dvrivguwioGDUI6+ud/Rib53e8g7JAQMvL583ld//5IKQcOQPrjxvFzRgbkrhp8ZCQ/z5zZVq6oqDAt/TRQRERA0jNmtH19aSmzodOnGdOkSSyI+mfZHd3vzEzud20tZP7QQ75EXVoKmZ86RVDTGcakSa7c4uL+wX2x81SE6fpbb0EoTz/t6wtSWQnZlpUFX/nS2Eit+blzkPdjj0Her7wCUY4YQZZ45gy18OvXQ2rZ2ZCq7ix95hljR+C019WMO1Bw0UXYTz/1bVKtwcrjgXD1verj8skn/P/ixfz81luM8YknyIJ/8xsy6GXLCDKLFhF0/Gct5eWUcZ4+zc9K6vHxkLo/gebmop9rLfzMmYyjK5UnhYVmE5RKZFoho7a8aWnGj2b6dMYTyFbAhYt7Hfc0sWvJ47FjaMX9+lF54iSU69fJaltbqRUPpvKloABSrKyETKdOZfPSmTNmyn/yJCQUH8/53n4bAlJL24kTkVh0ITUYe11dhP3kE7R6hV5XbCzeMzojEGF94L33kEVEIO2jRyHyBQvQ7nfu5JpU6587l4VOf2+W8nIy/J/8JPBC64svonOLEHAuXIDQ8/LI/Jcs4X50pQ1cYyOzn+PHOcbataYZd1MTwSUtjaDcqxfXN3eu22rOxf2Ne9oEzLKQNdLTIbANG3zL2bTypVcvsviOemOKQKzp6QSJqCh2n+blkb16vRBlaCjkFx0NwWdkIO/ExpIlazY+ezbjc9rraoehQJJBQQHkr3a6irlzjU7+/PPUmAeDb32LRU1n9czUqUgb/qWFZWVcU2Ym1zdjBnX96qfe1GRq0VtaTFPo8nJkpPnzydK7snPTtpFTdu/m3syda1wnKyog85MnOffQoSyGTpnitppzcW/jvjcB04w2PR2yTE42hOmsfBk2jGl9Zxmec0v82LFmM1FFBfptYiKZZW4uVTGjRkHEHg8a8rVryAIbNoj87GeULAZjr1tXx3FPnDC/syxIcv16zvWtb1G6N348ZL16NQ07tm4lgKxbhzTz4oscp6GBxVsl9REjkFCGDPE9d2kphH7mDISZkMDi70cfGUvhrVsZS329aQpdX8+xNm1ifF3VtvPzOcf169y7Rx7hHqmvjG7smjKFMXVkeObCxf2Iey5j76wBtccDaZw4EXzlS1ER0kt5OURSWoqWO2AAhFhXxzFFyCqvXGGDzeDBSAmVlQSXpCTjt/Kv/9qxva7HA1GmpBhPcjXfGjHCzD527YJgf/hDApZeZyDbBBGy+wUL+Hf//ox/3Dijx2unKCV0dU2cP59AsHs3WfgTTxCovvMdJJZTp5iNTJjA8UeM6PpWfC3/TE8n0K5YQWDIzITQi4uZKc2Zw5jcVnMu7jfctxl7R1YCjY0Q9JUrLAwmJ3dMPioHfPQR1R5Tp0IwYWEQ5PTpLOidPUtmOWUK2/FbWsieL19G5nn2WTL41lZeL8Ix2rPXvXyZ15WVQewrV0KwdXWmXd7ly8wgqqvNtTobWX/veyI/+pGxA/7v/xb5r/+CdKOiIM0HH/TNpouLzaJrjx4EnfnzCTp/+AMbuoaUYdcAABBOSURBVCZNYqZQVsa9jI5GEtGm0J3JWYHg9RJotZIoIYGZRkYG6wkNDQTJ9euZ6bit5ly46Bj3zSPirHzxd1gMhOZmCP30aTLzhgYyWN3ZqBUwdXUEiZISSGjwYMjy0iUIds0aMm3/mcSf/il/nKZkzvJFDTj796PVR0QQIAYNQpP/t3/ztfP9/vfNvzdvNv/W7PzqVchcG0v4z1Kysow+v2gRhB4VZRaKq6p4f0wMJaM5OYxpwQKIuLvZc14e97mgAJln5kzunTYfmTSJ43dnBuDCxf2Ke5rY1Uqgq5UvJSWQmTZALi1FM96yBWLds4fKkgEDqPJITSUQTJ8OKXm9ZJczZvhKHCoFhYX5ziSam429rP4+Ls5kpidPUoqYk4OjYkND+8ZWIpz/1Ck0/LQ0pJ45cwhIgTzL/YPO8uX8/cd/DKFq67eTJ7kXffsyi5g1q2NXyY5QV4esc+oUs5o5cyD5P/wBiWn+fO6t22rOhYuu457T2P1x9iwui8FWvmRksChq25BwdDSEOHMmWvv27RD+rFnIBufOkaX37UumPXQo+ndMTPvnUInIf8ONCFnylSuB2+UtXUpZ4/r1vgutejwNIj/5Cdm/CAu9a9YE3+NVywg//JB7ERPDz3V1nHPBghurPvF6KV3UtYMhQ5hFNTTw2WirOdf73IWLtrhvNXaFGnLt3h1c5UtLC7r2yZOQm2UhWSxdCsmkpqIBR0UhZ6SnQ35/9VcQ8cWL/H7Jks5J78UXqfzYsYMs1f98ERHYCWh2L4Jerta4gY6vTaaXLoXUBwygHNO/0iUY/PKXLBSHhPD32LGcd/ToG5NDcnORXYqKCLRNTVz/hAkQ+o0e34ULF+CeJHaPB9I9eZIFz/XrO658KStDX9Ysd9QoSgZjY9GWt2whQ58wwdSpDxrEJp2kJLL1554zLeA6Ql0dC4O/+pVZuBw5kpI+52zCXx5RDd2/UYj+W4PW/v38efHFrpP6oUPINuXlEOy0aRC6szlId1BTwyYoLZsUIVuPj+dPR7MbFy5cdB33nBTT1coX3ZXq9UKOa9YYM6rMTALEd79Lpnn2LJnxwoXUVH/ta0gzq1d37uPt8aB379tnyhd792az0uTJ7Y/xe98T+fGPAzcKKShgRnLlCmsBf/mXXEdXsl7bZrbx4YcQsGUReBYvvnF92+MhWBw8yL9F2PykTUW6q8+7cHG/Ilgp5p4idmfly5o1HVe+NDTQcCI/38ggSUlk9g0NxiJg6FAWEbduxXkxK0vk//7ftsdrr+WeCO/5+GPGpbLLwoUEnmC0ZP+yzcpKs8FIOxHNm8fYg/04PR6u7+BBxiXCjGPz5puzHT89naCjbfdGjOB6nTXzLly46BruO409L48yPI+HXZztNXZ+8UU29Hz8Ma+NiaFSRuWA7Gxsfd97r30/FCXPzlrulZdTvnjxopFdxo4lw++K/KBB4zvfQQY6dsw3OOhsob2GIk40Npqm0Jqhh4WZGvEbgdajp6QYzX/cOMokXe9zFy5uH+4JYndWvjz3XGADLRGqWX74Q0jWstCTly7l/1pbKWM8coQdma+9ZjTqzgjcH01NZMJHjpj39e4Nofv7mQeDv/s7MvvISIh55kzG7i+VtDdjEGEj05EjEG9Tk3nvwIFk6Teiczc0UOmSmmoy9LFjCRbu7lAXLm4/bojYLct6QkS2ishkEYm3bfu2tkWybaxr9+zpuPKlsZEsMi2Nn/v0Efnyl43Lo5YxFhcbU61gGmz4Z8i2bbbd19Yat0Q19+rujkm1Kxg+nNLLrixmFhVBuGfOML4JE1gQLixES1+9uvvjKi6mnv/UKbPrdehQqnHcZtAuXNw53JDGblnWZBHxisgvReTbwRL7zdDY/StfHnusLUGpJcB3vkOtuD9+8AMWL/fsQc5Yvx4rAH905L2iuH7d9C4NDWV8kycTJIKtIQ903o58b9obp20jKaWmYj3QowckPnQo0lBzM12HnI27g4UutqalsWirs5k+fZC4nD73Lly4uLm4rYunlmXtk9tE7Fu34ly4bRvktXgxi57+8kZeHnXi+flkuqtXI9X06QMx/sVfsMsxO5sqmLVru7doWFtLYDh1yhB6TAzli9pA42YgGDnIspgxpKaSkUdHUx8+Zw6LmSkpjG3z5uA1bw0WjY1cY1oaZaHh4chXoaF8BvPnux4uLlzcatx1i6eWZb0gIi+IiIwIpuC7Hbz0EvXe5eVk2DNnmv/bulXk2982RNurF7LA9Om+xP/SS+jVHo9v44auwONBhlDTL612Wb6cCpvb6Qve3GxsfbdvZ41h7VpMvrTH66VLLI6uWdO1MsOXXqLW/PRpjjVgAAGjro4dqA8/7G77d+HibkOnxG5Z1m4RCeAULn9n2/Yfgj2RbduviMgrImTsQY/QAW0yUVtLX89Ro8z/aTu4iAgyyYULyST9SezZZ0VefdXszOzOouGlS0gaZWXG92XaNKo/+vTpzpV1jvYqXvzlGmf1zqBB1PTX1DCDmDs3+ABWXY17pIhpVNLQwO7RAQOwTQim25QLFy5uP74QUkxnWrNts5Pz61+nNn3VqraLd13VqwOhrAxCv3QJ3bqlBUlj9WrfIHMnUFFBkFIPmrQ0dnv27o13uvYHDQbt3avkZKwNEhLcTkUuXNwJ3JMaeyBnxO4QdnfKFw8coFxQfc979EDbnzfv7iE5yzJNts+eNU22Azk6dgbbxn99yhTu4/TpzEjc8kUXLu4cbguxW5b1uIj8VERiRaRSRE7Ztr2ys/fdyOJpR6QcLGEH+zrbRlvevRtNOSwMmUc92Xv16trYbzW+/W1mDuXlZNcLF3Zvl2dZGQvPly9D6tnZd35G4sKFi9u0eGrb9rsi8u6NHKOrCGZ35c04Rl6eyDe/SUWJbvuPjUV2GT78xsdws3HqFD4sTU3U6HeHiJubmZkcPsyMZNUqZicuqbtw8cXCF65ArSM9PFjS76gGvKaGqprTp/FlnzOHTUaPPkoteFcbM99qOO2GR40S2bix6zMJ20a62bmTRdMZM6ju6dULPd2FCxdfLHzhiL0jBLsIGggvvYSGfOAAWr7uPJ0zB1kjKuqmDPGmQvuOFhXhGZOU1PXAU1JCYMjOppHGpk1354zEhQsXweOeIvbu4tIl/t69mw0+27eb/1u7lr+7Uj1zO3D2LBusQkPpDBVox2xHaGrC5CwtDanpkUfM7MSFCxdfbNzXxN5RDfjWrV2vnrkd8HiwRzh6lBLGTZu6Zlng345v9mwWgu/GGYkLFy66h3vKj727aGkha/W/FXcbsVdVibz9Ngu78fHs+uxKqWVREYZiubk4Vz7ySNfq2124cHFncddZCtzNaM/J8WZU4NwsZGUhEXk8ZOlTpwb/XnW3PHYMs7Pu2ii4cOHiiwGX2D9HIBK/GzR1rxc/mgMH2OX6xBPt+837Q90td+/GDkAXgruzYcmFCxdfHLjE/jnuBhL3R12dyDvvULEyYwYll8H4xIvgarljB7LNsGHILnFxt3a8Lly4uDvgEvtditxc9PSGhq5JJw0N1OGnp+PCuH49QcGVXVy4uH/gEvtdBttm5+fu3VS7fPWr1Jd3Bq+XTUp79qCpJyTQuUn7obpw4eL+gUvsdxEaG/FOv3CB7kvr1gVHzM6mIiNHYnvQlfZ5Lly4uLfgEvtdgoICukJVV4usXEnG3Zl8UldHZq9NRTZswBfelV1cuLi/4RL7HYZto4d//DGa+HPPdb6l3+sVOX6cEsbmZpEFC0SWLOlaZyQXLlzcu3CJ/Q6iuZmG3BkZ9EfdsKHzHaC5uWwyKioSGT0a2SU29vaM14ULF18MuMR+h1BSgoFXSQmLnIsXd+zTUluLDUBGBu33nngCHd6VXVy4cOGPGyJ2y7L+WUTWikiziFwWkedt2668GQO7l5GZiSVwjx70bu2od6jHg1HXvn38e9EigoB6xLtw4cKFP240Y98lIt+1bbvVsqx/FJHvish3bnxY9yZaW+mZevw4OvqmTR03v756FdmlpERk3LjAvVxduHDhwh832kFpp+PHIyKy6caGc++iogLppaBAZP58HBXbM/CqrkZ2OXOGWvYnnxSZONGVXVy4cBEcbqbG/hURefMmHu+ewYUL1KfbNiQ9aVLg13k8NMzev5/Kl6VL6VsarI2ACxcuXIgEQeyWZe0WkUB7H//Otu0/fP6avxORVhF5rYPjvCAiL4iIjBgxoluD/aLhxRfRxFNT2T26eTN9Sf2xdSta+44ddEWaOJFa9kCvdeHChYvOcMN+7JZlPSciXxeRh2zbrg/mPXebH/utQE0N+vnWrbgqrlolEhYgjFZVIbds3SoSE8PrutoNyYULF/cHbosfu2VZq0Tkb0RkabCkfj8gP1/k9df59+OPizz4YPuv+6//4t/JyWjvgcjfhQsXLrqCG+1w+TMR6S0iuyzLOmVZ1i9uwpi+0Ni6la5Ef/3X/KzOiv62wPq6732Pn5csQUu/G+2DXbhw8cWC2xrvFiLY1np3Wws+Fy5c3J0IVopxe9K7cOHCxT0Gl9hvIYLtmXo39VZ14cLFFx+uFOPChQsXXxC4UowLFy5c3Kdwid2FCxcu7jG4xO7ChQsX9xhcYnfhwoWLewwusbtw4cLFPYY7UhVjWVaJiOTc9hPfvRggIqV3ehB3Kdx7ExjufQmMe/2+jLRtu9NmmHeE2F34wrKs48GUMN2PcO9NYLj3JTDc+wJcKcaFCxcu7jG4xO7ChQsX9xhcYr878MqdHsBdDPfeBIZ7XwLDvS/iauwuXLhwcc/BzdhduHDh4h6DS+wuXLhwcY/BJfY7DMuyVlmWdcGyrCzLsv72To/nboBlWcMty0qxLOusZVmfWZb1rTs9prsJlmWFWpZ10rKsD+70WO4WWJb1gGVZb1uWdd6yrHOWZc2/02O6k3A19jsIy7JCReSiiKwQkTwROSYiT9n2/9+u3bNGEYZRGL4PRgs/65AISSHWEbEJWGhpUEsLLewVxELQHyF2NqsiGLBQCwvBxsYqSIIgmkaCkBVFG1FsgngsdgLxFzwvM+eqdqe6WZbD7DvrD6VhxSRNA9O21yQdAFaB80P/XLZJug4cBw7aXqruaYGkh8Br2yNJe4C9tn9Ud1XJHXutE8BH2xu2t4DHwLnipnK2v9he617/AtaBmdqqNkiaBc4Ao+qWVkg6BJwE7gHY3hryqEOGvdoMsLnj/ZgM2H8kzQELwEptSTPuADeAv9UhDZkHvgMPuiOqkaR91VGVMuzRLEn7gafANds/q3uqSVoCvtlerW5pzBRwDLhrewH4DQz6eVWGvdZn4PCO97PdtcGTtJvJqC/bflbd04hF4KykT0yO7U5JelSb1IQxMLa9/avuCZOhH6wMe603wBFJ890DnwvA8+KmcpLE5Lx03fbt6p5W2L5pe9b2HJPvyivbF4uzytn+CmxKOtpdOg0M+kH7VHXAkNn+I+kK8BLYBdy3/b44qwWLwCXgnaS33bVbtl8UNkXbrgLL3Q3SBnC5uKdU/u4YEdEzOYqJiOiZDHtERM9k2CMieibDHhHRMxn2iIieybBHRPRMhj0iomf+AZcIQl0P8QqCAAAAAElFTkSuQmCC\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] @@ -223,7 +224,7 @@ "outputs": [ { "data": { - "image/png": "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\n", + "image/png": "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\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] @@ -233,7 +234,7 @@ }, { "data": { - "image/png": "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\n", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAEICAYAAABLdt/UAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzsfXd4VNeZ/nvUuwQqIIGEJBBCXQIEBptyccHYJNiOPUl2jUOycWxlkzg/2yF2NriR2DHJJk7sRG67idcNj3vFwdiDG02i9yYE6r3PaDSaOb8/3jm6IyFQQdTc93nmkWbm3tNm5v2+852vCCklDBgwYMDApQOv8z0AAwYMGDAwsjCI3YABAwYuMRjEbsCAAQOXGAxiN2DAgIFLDAaxGzBgwMAlBoPYDRgwYOASg0HsBkYEQog5QoiDZ6HdfxdCrB3ktcuEEF8N9b0LBUKIBCFEuxDC+zTXSCHEpHM5rjOBEGK+EKL8fI/jXw0GsV8gcBPPbiGEVQhRLYQoFEJEuN972v2DbxdCdAkhHB7P15yDsQ1IJlLKL6WUqcNs/wohxAYhRIsQolEI8bUQIt/d7stSymuG0+7FBinlCSlliJTSCQBCiPVCiB+e73EZuPhgEPsFACHEPQAeB/ALAOEALgMwAcAnQgg/KeWd7h98CIBHAbymnkspF52/kRNCCJ8zuDcMwAcAngQwGsA4AA8DsI/M6EYeZzJfAwbOBQxiP89wE9vDAH4qpfxYSumQUpYCMAFIBHDrMNqcL4QoF0IsF0LUCiGqhBA3CCGuE0IccmvFv/K4foYQYqMQotl97VNCCD/3e1+4L9vp3iF826P9XwohqgH83XPLLYSY6O5jqvt5nBCiTggxv5/hTgYAKeWrUkqnlNImpVwrpdzlvreXCcW9e7hTCHHYPd6/CiHEKdbh90KIr4QQ4R6v/UEI0SSEOCaEWOTxepwQ4j33uI8IIW73eO8hIcQbQoiXhBCtAJa5XzMLIf5PCNEmhNgrhJh+inE8LIR40v2/rxCiQwjxe/fzQCFEpxBitBAi0T0/HyHEbwHMAfCUe92f8mjyqkHOf4YQolgI0SqEqBFC/NHjvdfdO8MWIcQXQogMj/f+IYT4mxBijbvvr4UQY4UQT7jX7oAQIs/j+lIhxP1CiH3u9/8uhAg4xZjihBBvur8Px4QQPxvMeA0MEVJK43EeHwCuBdANwKef914A8Gqf1x4C8NIAbc53t/kAAF8AtwOoA/AKgFAAGQBsAJLc108Ddwk+oDDZD+DnHu1JAJP6af9xAP4AAt2vlXtcczuAfQCCAPwTwB9OMdYwAA3uuS4CMKrP+8sAfNVnLB8AiACQ4J7XtZ7XggrLc+5+gzzec7jH5Q2gAEAlAOF+/wsAfwMQACDX3e4CjzV3ALjB3Xag+7VOANe523sMwKZTzHEBgN3u/2cDOApgs8d7O93/J7rn5+N+vh7AD/u0dcr599PvRgBL3f+HALjM470fuL8L/gCeALDD471/AKh3fy8CAHwG4BiA29xz/Q0Ai8f1pQD2AIgHd11fA/iNx3el3P2/F4Ct4PfSD0AygBIACwcar/EY2sPQ2M8/ogDUSym7+3mvyv3+cOAA8FsppQPAanc7f5ZStkkp94KkmwMAUsqtUspNUspuyd3CMwDmDdC+C8CDUkq7lNLW900p5XMAjgDYDCAWwH/114iUshXAFSBhPQegzq05jzlN37+TUjZLKU8AsIBErOAL4FWQYL4hpbR6vHdcSvmcpA37Bfe4xggh4gFcDuCXUspOKeUOAM+DRKawUUr5jpTS5THfr6SUH7nbexHu9ewHGwGkCCEiAcwF8D8AxgkhQsB1/vw0cx3q/D3hADBJCBElpWyXUm5Sb0gp/9f9XbCDQirHc2cD4G3396ITwNsAOqWU/+ee62sA8tAbT0kpy6SUjQB+C+C7/YwnH0C0lPIRKWWXlLIE/My/M9B4DQwNBrGff9QDiDqF3TbW/f5w0OD+EQLUzgGgxuN9G6gVQQgxWQjxgXtr3gra8QcSKHXuH/3p8ByATABPugmkX0gp90spl0kpx7uvjwO1yFOh2uN/q5qHG5MALAHwsJSy61T3eRB+iLu/Rillm8e1x0F7v0LZIMYR0N/n6BYExSCJzwWJfAMoTIZD7Kebvyf+AzR1HRBCFAkhFgOAEMJbCPE7IcRR9+dd6r7e8zPv+13p97vjAc/1OQ6uaV9MABDnNiE1CyGaAfwKgBLi/Y7XwNBhEPv5x0bwoPAmzxfd2twiAJ+egzEUAjgAIEVKGQb+2Pq123rgtGlB3eN/AtROHxJCjB7MQKSUB0BTQOZgru8H+wF8H8AaIcRgvXQqAYwWQoR6vJYAoMJzaMMcj8LnoNklD0CR+/lCADNAM1B/OKM+pZSHpZTfBRADms3eEEIEA/g3UPhdBR7WJ7pvGegzPx3iPf5PANe0L8oAHJNSRng8QqWU1w0wXgNDhEHs5xlSyhbw8PRJIcS17sO1RABmAOXgFv9sIxRAK4B2IcQU0P7siRrQHjoU/BlAsZTyhwA+BPB0fxcJIaYIIe4RQox3P48Ht/HD3oZLKV8FhdM6IcTEQVxfBmrQjwkhAoQQ2aD2+NJwx9APPgdNO/vcO4n1AH4IEl3dKe4Zzrr3QAhxqxAiWkrpAtDsftkFft528GwjCNyhnSn+Uwgx3i3A/ws01/TFFgBtgofuge6dQ6Zwu7aeZrwGhgiD2C8ASClXgUT0B5BgN4PazZWnM2GMIO4Ftbg20HzS90f5EIAX3Ntn00CNCSGWgIfCSkDcDWCqEOLf+7m8DcBMAJuFEB0goe8BcM8w5tEDKeULAB4B8JlbUA6E74KaayVoU35QSrnuTMbQBxvAQ1elne8DD19Ppa0DFI43uz1N/jKMPq8FsFcI0e5u6ztus9D/geaSCvc4RsKW/QqAteBh6FHwgLUX3KbBxeCZwDHQzPg8uGs43XgNDBHKI8CAAQMGhgUhRCnovTOSgtDAGcDQ2A0YMGDgEoNB7AYMGDBwicEwxRgwYMDAJQZDYzdgwICBSwznJZlRVFSUTExMPB9dGzBgwMBFi61bt9ZLKaMHuu68EHtiYiKKi4vPR9cGDBgwcNFCCHF8MNcZphgDBgwYuMRgELsBAwYMXGIwiN2AAQMGLjEYlWAMGLiE4HA4UF5ejs7OgRJvGriQERAQgPHjx8PX13dY9xvEbsDAJYTy8nKEhoYiMTERpyisZOACh5QSDQ0NKC8vR1JS0rDaGBFTjBAiQrB02AEhxH4hxKyRaNfABYxVqwCLpfdrFgtfN3De0NnZicjISIPUL2IIIRAZGXlGu66RsrH/GcDHUsopYBWZ/SPUroELFfn5gMmkk7vFwuf5+SPbjyFAhgyD1C9+nOlneMbE7i6npcp9wV3yqvn0dxm46KFpgNmM7m+Z0PSzB0jqZjNfH0m4BUj1qxa4XDh7AsSAgUsII6GxJ4EFdf8uhNguhHi+v6onQogfuSuQF9fVnaqugIGLCUfiNey+ogCjnlwJFBQMjtSHqoFrGkp+Z0bEHSbU3nkWBYiBEcNvf/tbZGRkIDs7G7m5udi8efP5HtI5xfr167F48fmt6jcSxO4DYCqAQillHoAOAPf1vUhK+ayUcrqUcnp09IARsQYucNTUAEeftyB9fSGcv1oBFBaeTNj9YYgmnH37gK/9NJRdX4Cxzw1BgBgYEh56aGTa2bhxIz744ANs27YNu3btwrp16xAfHz/wjQOgu7u/Wu8GToWRIPZyAOVSSiWW3wCJ3sAlirY2YPdfLJj3NxO6XzHD+7ePUIv2JOxTwW3Ccd5sQvkPTq+BHzoEbNsGTCqzYNK6QmDFEASIgSHh4YdHpp2qqipERUXB398fABAVFYW4ONa1/vTTT5GXl4esrCz84Ac/gN3O4mCJiYmor2fN9uLiYsyfPx8A8NBDD2Hp0qW4/PLLsXTpUjidTtx7773IzMxEdnY2nnzySQDA1q1bMW/ePEybNg0LFy5EVVXVSeN6/fXXkZmZiZycHMydOxcAUFpaijlz5mDq1KmYOnUqNmzYAIAa97x587BkyRIkJyfjvvvuw8svv4wZM2YgKysLR48eBQAsW7YMd955J6ZPn47Jkyfjgw8+OKnfjo4O/OAHP8CMGTOQl5eHd999FwCwd+9ezJgxA7m5ucjOzsbhw4dHZP17IKU84weALwGkuv9/CMDvT3f9tGnTpIGLE3a7lK+/LmWR6XFZ//pnvd/87DMpH398wDYqKqTcfeMKKQHZdd+Kfq85ckTKF1+U8stHPpOuqCi2rfrwfG6gF/bt2zes+4CR6b+trU3m5OTIlJQUWVBQINevXy+llNJms8nx48fLgwcPSimlXLp0qfzTn/4kpZRywoQJsq6uTkopZVFRkZw3b56UUsoHH3xQTp06VVqtVimllH/729/kt771LelwOKSUUjY0NMiuri45a9YsWVtbK6WUcvXq1fL73//+SePKzMyU5eXlUkopm5qapJRSdnR0SJvNJqWU8tChQ1LxksVikeHh4bKyslJ2dnbKuLg4+cADD0gppXziiSfkXXfdJaWU8nvf+55cuHChdDqd8tChQ3LcuHHSZrNJi8Uir7/+eimllPfff7988cUXe/pNSUmR7e3t8ic/+Yl86aWXpJRS2u32njl6or/PEqwjPCAnj5RXzE8BvCyE2AXWMxyJ4rgGLjC4XMCnn1JjD1u5HJE399GyNQ1Yvvy0bVRXAwcKLUhZV4jOX6yA7/O9NXApgdJSYNMmIDgYmCGKIDw1erfGj6KiEZ7dvx4eeggQgg9A//9MzDIhISHYunUrnn32WURHR+Pb3/42/vGPf+DgwYNISkrC5MmTAQDf+9738MUXpyv3Snzzm99EYGAgAGDdunW444474OPD8JvRo0fj4MGD2LNnD66++mrk5ubiN7/5DcrLy09q5/LLL8eyZcvw3HPPwel0AmAw1+23346srCzccsst2LdvX8/1+fn5iI2Nhb+/PyZOnIhrrrkGAJCVlYXS0tKe60wmE7y8vJCSkoLk5GQcOHCgV79r167F7373O+Tm5mL+/Pno7OzEiRMnMGvWLDz66KN4/PHHcfz48Z45jhRGJEBJSrkDwPSRaMvAhQkpgQ0bgKoqIDsbcP8+h4TaWmD/3yy4/M8m2F80I2yJBizSeswxrnkaysqAjRuBgADgqqsAvxv7ERSaZtjZRwAPPaSTuBD8jEcC3t7emD9/PubPn4+srCy88MILyMvLO+X1Pj4+cLlcAHCS73Zw8El+GL0gpURGRgY2btx42uuefvppbN68GR9++CGmTZuGrVu34sknn8SYMWOwc+dOuFwuBAQE9FyvTEkA4OXl1fPcy8url72/r1ti3+dSSrz55ptITU3t9XpaWhpmzpyJDz/8ENdddx2eeeYZLFiw4LRzGAqMXDEGBoXdu2nzTkwEpg7jBKW2Fvj8cyCypAi2F9ykDvRo4K4tRaispKbu6wssWACEho7oFAycAxw8eLCXvXjHjh2YMGECUlNTUVpaiiNHjgAAXnzxRcybNw8Abexbt24FALz55punbPvqq6/GM88800OsjY2NSE1NRV1dXQ+xOxwO7N2796R7jx49ipkzZ+KRRx5BdHQ0ysrK0NLSgtjYWHh5eeHFF1/s0eSHgtdffx0ulwtHjx5FSUnJSQS+cOFCPPnkk8pkje3btwMASkpKkJycjJ/97GdYsmQJdu3aNeS+TweD2A0MiNJSYOtWIDoamDMH8Brit6a+HlC77pg/LEfEjb21bdc8DVW3LseGDdQc588HRo0akaEbGCQefHBk2mlvb8f3vvc9pKenIzs7G/v27cNDDz2EgIAA/P3vf8ctt9yCrKwseHl54c4773T3/SDuuusuTJ8+Hd7e3qds+4c//CESEhKQnZ2NnJwcvPLKK/Dz88Mbb7yBX/7yl8jJyUFubm7PIagnfvGLXyArKwuZmZmYPXs2cnJy8OMf/xgvvPACcnJycODAgQF3B/0hISEBM2bMwKJFi/D000/30voBYMWKFXA4HMjOzkZGRgZWrFgBADCbzcjMzERubi727NmD2267bch9nw7npebp9OnTpVFo4+JAfT2wZg1NI9ddR7v3UFBXR1J3uYDZs4Fx43q/73RSm9+wAejuBubOBWJjR278J2HVKrpWeppyLBba7Ac4H7gYsH//fqSlpZ3vYfxLYNmyZVi8eDFuvvnms9J+f5+lEGKrlHJAs7ehsRs4JdrbeVjq5UUeHA6pf/01SX3mTMDt9daD7m4Kjs2bAYeDxH9WSR04d6kQDBg4jzCyOxroF11dwLp1QGcnTSORkUO7v76eWrjDAUyfDowfr3tfACT1hgZgyxb2NWMGMAJxLAPDw4++9qYCxL5TaESyGhgW/vGPf5zvIZwShsZu4CS4XDzobGriQWlCQm9SHgh1dST1ri4gL4/3e9rlHQ62vXUrYLMBOTlAcvLIz+NU2BPNVAixz6+E6w4jktXApQeD2A30gpT0TCkvB1JTgYyMoZG6Mq10ddEtcsIEwPM8TJH69u30h8/IGJ7r5HDgdHJsZf9nQdr6QnTfvwJezxiRrAYuPRimGAO9sG8f3Rrj42l2HooHTF0didNuBzIz6RrpWQDGbgdaW4G9e0nukycD6elDExzDhd1O/3jrRxZc9awJ3m+a4X2VBlytGYnFDFxyMDR2Az04fhwoLgZGjwZmzQJ8hiD26+p0e3laGjV1jxgPdHaS1PfvpxdMcjJNMOeC1FtbgfXrgWPHgLS2IvgoUgeMSFYDlyQMjd0AAJpQvv4aCAoCrriCfwdLunV15MWuLmDKFNrUVYS0lNSW29q4E6iq4vtTpw7dH344qKnh2BoaaPZJXLb85HkZkawjhoaGBlx55ZUAgOrqanh7e0Nlc92yZQv8/PxGvM9t27ahtrYW11577Yi3PRR0d3cjKioKzc3nvxyFQewG0N5OjRYALruMwUFDIfXiYpJ6air91JVbpJTU1NvbgZISoKKCLo/Tp/e2u58NOJ1AWRmwcyeFSl4ekJV1bnYIFw3Ogk9/ZGQkduzYAYDZGUNCQnDvvfcO+n6n03naIKX+sG3bNuzZs+e8E/uFBMMU8y8Ou52kbrNRi+4bQHQ61NaS1B0OICUFGDMGCAvT847YbEBHByNXT5wAYmLo1jjMwuuDht0OHD7MlL82GwXJsEj9Ui/Ld459+r/xjW9g2rRpyMjIwPPPPw+AWm5ERAR+/vOfIzs7G1u2bMF7772H1NRUTJs2DT/96U9xww03AGBU67Jly3pS4L7//vuw2Wx45JFH8PLLLyM3NxdvvPFGrz53796N/Pz8nvS4JSUlA47l7rvvRkZGBhYuXIjNmzdj3rx5SE5OxkcffQQAeP7553HjjTdi3rx5SElJwW9+85t+5/u73/0OM2bMQHZ2Nh555BEAQFtbGxYtWoScnBxkZmaeNN4Rw2BSQI70w0jbe2Ggu1vKdeuk/Mc/pNy6lc9drsHdW1sr5Zo1Ur73npR79vC508n3XC4p29qkrK+Xcvt2pvldt07KfjKTnhkef/yk9L0dH3wmK+56XL7xhpRms5RHj55B++4Uwa3vXjwpg4ectlfNacWKEZ/bgw8+KH//+9/3PG9oaJBSMl1uWlqabGxslA6HQwKQb775Zs9748aNk6WlpdLlcsmbb75ZLlmyREop5S9+8Qv56quvSimlbGxslCkpKdJms8nnnnuuJ5VuX9x5551y9erVUkopOzs7e9L0nm4sa9eulVJKuXjxYnnttddKh8Mhi4uLe9L6PvfcczIuLk42NjbK9vZ2mZaWJrdv3y4dDocMDw+XUkr54YcfyoKCAulyuaTT6ZQLFy6UX3/9tVy9erW88847e8bX3Nx8yvW7ENL2GrjIICV33GVlwMSJ9GLx8hqcVltbS224u5v3RkbSfOPlxXY7OgDx+1VoftuCY8eA8HBGngZuGmFt161xOtdZ0N4ONL1lge+tJhwZlQ8h2OcZ+cdrGsr+2wzfW02ouv0SLcunaaxKtfLsV6f605/+hJycHMyaNQvl5eU9BSv8/Pxw4403AgD27duH1NRUTJgwAUIIfPe73+25f+3atfjtb3+L3NxcaJrWkwL3dJg9ezZ+85vfYNWqVSgrK+vJ5XKqsQQGBuLqq68GwBS98+fPh4+Pz0npehcuXIhRo0YhODgYN9xwA7766qte/a5duxZr1qxBXl4epk6diiNHjuDQoUPIzs7Gxx9/jPvuuw9ff/01wsPDz2xRTwGD2P9FsXcvDzPHjQNyc2keGSypb99OUk9OBiIiSOw+PrRrt7fT3l6XmI/x95gw/rAF+flASNFZ2OZrGhwvm+H8lgkltz6AkP8wYePPzWjO0zBrFg9phwuXi8LrSx8NxxcxmOmMie9CNO1YLKxKdZarU61btw5ffPEFNm3ahJ07dyI7O7snRW9gYOBJ6W77g5QS77zzDnbs2IEdO3bgxIkTPfndT4WlS5fi7bffhr+/P6699lp88cUXpx2L5+Humabr/fWvf90z1iNHjmDZsmVIS0tDcXExMjIycN999+HRR89O6YoRIXYhRKkQYrcQYocQwsjudYGjtJSHiqNG0a4+2BwwitSdTpJ6eDhJ3deXr3V00N5eVwfsitSw434z8n5nwvHvPQDnzSOv7ba1AWs6NeyeU4Dsd1ei5JoCtEzVcNllZ5Zzxm6nh9D+/UBKuQWTPxsh4rvQ8tSo/s1m4JEhlDccBlpaWjB69GgEBgZi7969KDqFe2l6ejoOHjyIsrIySCnx2muv9bynUuAqqBS4oaGhaGtr67e9kpISTJo0CXfddRcWL16MXbt2DXosp8PatWvR3NwMq9WKd999F5dffnmv9xcuXIj/+Z//QUdHBwCgvLwc9fX1qKioQEhICJYuXYp77rkH27ZtG3Lfg8FIauyalDJXDiLzmIHzh9paBhH5+9NTZPRovj6QwlRTA+zYoZN6WBjv9fPTSd3ppFvhkSPU4GO+rWHPnALkvLcS3T8c2W1+TQ3wySeA+NyCzC8LcdC0AokfF2Key4KYmOG329rKbJRlZUBmnQXTf29iBaf+iG+oGrjbZ17eYkLjTy4A005RUe/+z6JP//XXXw+r1Yr09HT8+te/xsyZM/u9LigoCE899RSuuuoqTJ8+HRERET3migcffBAdHR3IyspCRkYGHnJXCVmwYAF27tyJvLy8kw4jX3nlFWRkZCA3NxeHDh3CrbfeOuixnA75+flYsmQJcnJy8N3vfhe5ubm93r/uuutw880347LLLkNWVhZMJhPa29uxc+fOnsPcRx99FL/61a+G3PegMBhD/EAPAKUAogZ7vXF4en7Q0iLlm29K+corUh4+zMPOwRyWVldLuXatlB99JOXBg1KWlfFw1OWS0uGQsrlZysZGHlR+9JGUH3wg5bFjUn7x8GfSGhIlm382cgdzTifH/vrrUn5wz2eyMyxKbvjtZ3LNGinb3hv+4abTKWV5uZQffijl6tVSbt4spfOxkw9ne9V17XuYOojD1YoKKXffxHqvjvv7r/d6JhhuzdMLCW1tbVJKKV0ul7z99tvlX/7yl/M8ot443WHtSOJCODyVANYKIbYKIX7U3wVCiB8JIYqFEMV1dXUj1K2BwaKzE/jyS8Bq1cP9Petd9gcpWaN01y5q4ykpDFwKC+NfpakDQHMzNXV1Xeu71HbL/9uM8D+PzDbfbmclp6Ii2vInNhZh2y/NaJuu4YorgJBvDE/jdDg49u3buU5TptBF0uu+5Sdr0551Xd0aruMmEyp+eHoNXEpgzx5g95MWTPqkEG0/XwGf54w8Nf2hsLAQubm5SE9Ph81mw+23336+h3TRYUQKbQghxkkpK4QQMQA+AfBTKeUpK9UahTbOLZxOZmusqCBpZWXp4f6nInZF6nv38qB08mTeo4jd5SKpe3nppN7eDkyaxDabfrUKvrPyMe1eTY8wPYPgl+ZmjuXECfYdHU2iDwpiHvfh1AKWkmMuLWW6ASHo5TNlyuCiYru7KSyjn3wAmW+vpB3e7a/sCYcD+OorwP6xBdrTJsjVZgQs0nrbuEfIHGMU2rh0cN4LbUgpK9x/awG8DWDGSLRr4MwhJXO4VFRQS09LGxyp19QwIZjTqZO6vz/rkHqSemsro0pbW+mFEh7Og8cT316OnJ9rvQnSU9sdwvirquihUlFB231UFAOPQkOZ/mC4pF5Xx0Cm48d5ADxlyuBJva0N+Oc/AdenFqRaCiF/ffLhqpQUSB98wD5SW5mnJmDR2bVpj4SyZuD84kw/wzNOKSCECAbgJaVsc/9/DYCT1RYD5wW7d1MbjY0lqSsPmIE09f37qZGmpvKA1MdH19StVpJfezvbbm5mIY2EBGDtWrZ99dW870zgcLD9Y8fYl9oxtLeT3C+7bOhRrFJyXuXlzI9TV8d2J06k4BsMqVdXM1Nk+DYL5v7NBJ+33Br3Aj1TpGuehhMneleQSlrWj1Ab4Tw1AQEBaGhoQGRk5KBcCA1ceJBSoqGh4aT6qUPBSOSKGQPgbfeXyAfAK1LKj0egXQNniJISEnRYGEldVUEaDKk7HCR1f3+SXUQECaqzk3leVKqAhgamEkhJobdNczNw5ZVDr7jUdxydncCBA0BlJfsNDGS/bW0UUvn5Q8s+qdq12WjOaWtj6mB/f5qP4uMHJnUpuabbtnEN85zUwD29SuRrZrg2F2FnuIbduznuefO4RucC48ePR3l5OYxzrIsbAQEBGD9+/LDvP2Nil1KWAMg503YMjCyqq1mhyM+PpD6QX7cyeRw8SI12yhQWsHa5aF5xOmnT9vYmOZaW0nUyKoo51Y8fJ+llZ5MohwuXi8LhwAEKjYAAEq7KEDlhAjBt2tAyQ0rJR1MTzTnd3WzL15dmpri40xwiuxNlOedq2LWLQV3jD1uQ6yhC8KPLT+rDPkvD1y4N5buYG2f+fO4yBsQIJeTy9fVFUlLSoK83cGnCiDy9BNHczCpIAIlrwgSduPojMEXqhw5RU588mZqm06mbX+x2EmFnJ0m9uppafFYWtfdNm0iQ+fnDz6DodJJ4d+4kqYeH03SkkolNnOj2Vhkiqat2y8s5l7Y2Cqi0tAFIHYCcng9pMmHbpiClAAAgAElEQVTrHyzYuxdIPm7B7CdMCJ6f36sPKYHGRmDNGvaVmgosXDhIUgd6gpda3rlAgpcMXNQw0vZeYrDZWG+0s5PkMnGiniL3VKReWclDxK4uknpICIk8LIzX2O3U/BWpV1Xxvdxctv3ppySw+fOHl7nR5aIWXVLCwKDubpouvLxIxqp4R2bm4IWGItuuLppeOjs5tro6tjtlCncbA7l7tk3XsP0/zchfaYKvVoDcTYUQr9P8ovqQkuuyeTP/v+IKBnENRcC55mk4+LAZSbeZUHdrAaJfN4psGxg+DGK/hNDdTVJvaSGxTJzYu4pRXyhSP3JET70bFkbhEBLCaxwOtmG3k7wqK0niubm85sMPSZqLFumCYChQh7EHD9ITx9+fB7FOJ4ne4WClpdTUoZN6aysFA8AdSGWlbn6JjDz9WQPA8fzzn0BtsIbQ+QWY+sFKYOlSyPkapMs9/k8tqHyvCBtmLO8RbqNHD43UW1p4yNoySkPAkgIkFbpdJw1SNzBMGKaYSwQuF90aa2t5EJiURHdAhb5E43KR6I4epVY7aRIJqbOTJCgEydXPj+8fO0YTQ2AgUxGMGsX+qqro8TGUPO4KTifNF7t20bQTGkrPGi8vfQcxfTq168EQpZScl8tFUj5xQvekqaykvT41dWBSl5KC5t13uZ45jRbkbiokqb/0EuQf/4jmZvqlu24xYX9IPmJigOuuGxqpu1yc59q1FEL5HRYkfXz2E3IZuPRhaOyXAKQkOZaV8cAuIYF/leZ5KlI/doya+MSJNEu0tZHIvb1JugEBJNejR3m9vz+158hIvrZ7N7XftLQhmh1cbL+ykruA9nYGHI0fT+11926OfdYsuiAOdg2UK+OJE9wFjBrF+ZWV0VY/cSLPBU5lkgJ4//btPDNwOIDLbBZc8bzbhXG+BpmdC69f3IvGN3dg/J41+PwnZkTepCEvb/BpjwHuinbu5PwDA4ErHBZE3u8RrKQZRbYNDB+Gxn4J4MgRan7h4TwoHT9+YFIvLSXpJScDY8fqB4o+Prw3MJAkd/QotXJfXx6UxsTQu+Tzz4fnS+50UlgcPsyHzcYdxsSJ1Fp37GD/c+YMjtSVli4lyfzIEbYZF8fnFRUk80mTBiZ1q5Xzsq9chXGHLJg2DZjtVwS52sxD2MdWYV3W3Tg841ZM2vgiDl1ZgEm3a5g6lWs3WFKvrGSisdJSniVcfTUQWXLuEnIZuPRhaOwXOSorqa37+1NT9/SA6QuXi0R3/DhNLomJFAINDdQ2lV94QABJ/fBhmkh8fFgIOjaWpPzJJ3xt7tzBe30o8u3oIPnW1nJ3MHEiBUtlJcvseXvTTj2YtLtKSwcYbFRdzTbj46m119Vxd5GQoJfs63u/QmMjSwQePw4kJeVjyYsmiBvMEMuX0yTybRM2/tQM64cWxO9ZgwO3rEDmZ4VAiQavpMFp1HY73TiPHeN6pKXx4eeH/l0ajSLbBoYJQ2O/iNHURIXOy4sknZjYO2jHk8iUy19ZGUl9wgQSXmMjCc7Xl+0oN8fDh0mM3t60catYifXraS65/PLBByEpu3d9PRNh1dTw4HXSJNrmq6por/f2ZnDTYHzulaBwuUji1dX6jqW0lH2NGTMwqUvJNfnwQ94XGgpk/UyDeN0MaTLBeu8DcN1iwmd3mFFXB1z7dxP2P2xG0ouPAK+Z4fWdwSU2q6vjHA8fJpFPnUovH78nLoDiGxdiARADZwSD2C9SWK30gOnuJpnFx/fWnk9F6sr0kZREUlcHpELQDu100p+9vp6kl5xMchSCtufSUh6eqkPO00H5kDud7PvgQQqFqChqqmPGkJQ3baJgufpqDJhL3VNL7+yk9t/aSmEwZgz7aGri87i4k0nd836nk1G2H3/M+cbEAEuWcD03+GvYOqMAIX9aid1XFGB3lIb46iJU/NGMnJ9r8PMDvK4c2FzS1UUtfedOkvu0T1dhtt2ChAS3G2p+PnDDDcAdd/CG8+G/fqEVADFwxjBMMRchHA6Sus1Ggo2N5UFhf3Z1ReqVlbx+/Hhqyg0Nuiujlxc1VYeDxKgIPyGBphIvLxJzcTFJLz194DwwSqNWHjXV1Wxz3DgKC19fujNu2ULTz5VXkvBPBU9CFkKPIvX25hgBJi3r6CChx8RwTn1JXcFup6Dato3znjABWLCA67FmDdD1Twuu/7oQxYtWIP2zQjRmaxjz38sRH98n3fFpzCVNTRQ89fVcj6QkYMzifAQtM6EZZoR8Q4MPACkEnC+vhogaA+9nz4H/et8oV00D7r8fcvFiVH73HsS9W8jiIoYZ6KKFQewXGVwuBsI0NZEkY2Joo+4vGZzTST/uqioS3rhx9FVvaKC26+dHgg0O1km9pYX/x8XpmQ5bW6nEhYUBM2YMbFd3OnsfZtbXs69x40huAE0SxcU0/SxYMHhSV773jY005yQkcG6HD5Osx4+niciT1PuuTWsrk3gdOsTnU6bwsNZmA956C/DfYMHiF01Ys8yMylQN9tkatCdMgGaGSNAGPCTt7tZ9/tvaOM7YWAoP3xwNRx4zY/z3TKi+uQBx7xVi471vI2ybBVmPniP/dbeG3vi0GWFLNHh9boFr5WM4nvstTPyflWj/fysQYpD6RQ3DFHMRQUp6jVRX0+wQFYUeDVJB/a8yGFZX61rs5MkUCFYrNV1/f5JOdzdJXRWiHjOGh6VeXnxv3Tr+veKK/u3VCsqNUUqS+d69ND+EhFBLT0nhdQcPktSDg09P6p6RnUJQ4Bw9SlKPiaGQaG3VUyHEx7OtU5G6EFyPTz6heSTfsgoLhAWaxvG+/TZJfcYXv8eHt5lRk64hJweY/gsNeM0MUVw0IKm3tvIwu7ycgmb0aM49MVFfy6JgDWXXF2D831di/7wCdHUB6evPnf965ywNu35tRtD3TTix7AE4bjKheOH9GL9nDTruXoGQFw0f+osdhsZ+EeHQIZo1Ro0igU2YQILua4Lp7qaZoqaGpB4bS620pYXPfXyoKQcHk8gPHeLrNhuJKDNTb/err0h6V1xBX/NTZVRUB6RS0m5eUaG3l5jIe7u6aC7ZtYvkO2fOwKSu5tXaSnOQEGwvLIyeNaWlvC4+noenISG8pq+WLiXnuWULdyyhoUD0dfmY+CsTDvuZsdahYcw+auof3mZG6zQNc2boPvpigQZx5am1WLU7qqzkbsjHh33Ex3MHcfw4hbLDwYCnCWsKsfvGFZjy8V+Qtu7P8HrnnbPuvy6lXinKGq7BpRUg9+WVKLl8KaavfQzeb5vhv0ADFhs+9Bc7DGK/SFBeTg04JEQPQvL375/Uy8upKbe3U/ueMoXE2NrKa4KCSOrd3SQ7m42P8HBmZ1R+6fv28f2MDAqR/tITeHqoKI26pobPx46ltqrs97t3cw7h4fR/74/UPU0uak7V1ZxPYCDH4eenJ/Xy9qbgCgvrn9SFoOa8axf7b2tjvzNmAOPiNRQ3mZFxtwlTZxUgb3MhPrzNjO45Gq6dy/GrNk6nqbe1UeC2tZHgg4L4SEjgWhYVUdj5+gK5zRYk/sqEL39qRvBiDV6RNfB6/TW9MU//9REk1ZYWmp/q6vhZjNlnwZTPCnH8thVIeuOPECsfYT75szgGA+cOBrFfBGhoYApef3+STVwcSayvVupwkPDq60kyMTHUOK1WZnyUkqQaFKT7qdvtJPXgYJK6OhStrqa3Smwsib0/u7oidIBC5OhRmnp8fSlQkpP1lATbt1NIRESQVGNi+ndB9BRUKoq0o4Nar3KDLC3V88rExJDUVQGRvqTe1kazz6FDHEdcHEvphYbSnl5i12DLL8DcT1diy8IVCLxOw9y5vQuSnM70VFXFnYTTSS3d359zHDeOn9uePSTV0aPdmSpfL8KWe8xIulVDcjKAy54B/u07vUl0KP7rA6T7dTq5Uzh4kJ+10wnEHrDgqudMaP+7GRNu1oBlbg09L294YzBwwWHEbOxCCG8hxHYhxAcj1aYBEubGjbR3x8VR2+zrP67sz+XlJJPWVpo+0tL4Y25oIOGpItTd3dySK1JXqQJUiTmrFfjsMz6fOVPXhBU8c7IAJNn9+2n7Dg6mqWTyZJ3Ui4spREaPZu6X05G6EJyrOhBV7pkqF01JCfsLCjqZ1D3XQwhe9/nnHJvTqXu+eHkBr7xCQTShxILpxfR+ydtciGt8LT3tnS5FgNXKHU1pKXcNgYGc79ixXPsjRzjvuJdXIaPW0uPyWff95cjNBZLf8PAR9ywZOFSfcg9XRbsdvVwVKyuB997jTsVq1b2gpjqL4PuWGZE3G1GulypGUmO/C8B+AMPI8WegP3R16b7qyoYcF8f3PDVbRepNTSR15Sfe3U07tNNJu3xAAP8/epSkrqohZWfr5OhyMQ2vzUYXxLCw3nZ1paWrh3JltNv1ACFF3A4Htf6yMpJdejqJz9P/va+WDnDM1dUkoeRkfdxHjnDnERrK+YSGnryTEIJjLCnhLkFFuCYlcadQUUF3xrY25lb/1usmfP5jMyYs0+BdpUF8x8SD0gX9a6suF9s8fpz/h4VxnZVJyOGgz3pNjbtIyIx8pPzahLq7zEi8XsPUFgt8/8Ntv+4PiqiVfduz4HV/0DR0vWQGbjSh5OoCTFlfiK4XzdjkpaHsM37GLhc/w6QkmsCClxpRrpc6RkRjF0KMB3A9gOdHoj0DJLJNm6ixK9OLChTyNDd0dZHUm5v1LX96uk5ADgdNAyqi9OhRvma3s53MzN7pdjdvJqnm51NAqLKLfbV0FXhTXs72oqNpyx8zhmPs6mI+lPJykvmUKZxHf6SutHSXi4SpokgnTWL/yhWzuZlzGTVK3314FhBR/W7frtuTQ0Io5GbPJuG+9x7X1McHSKgpwua7GXA0ZQpIbG7vl75Q5foOH6bQ8PPjWLq7OcbYWPa3axf/RkRQWB6M07DhLjNmPWFC9JMPwPffBziUdGvPrsWL0fTN204m+T6a+9GjwHttGg4uKEDaGytRc1MB3mnREPTXVQjfZoGU3OEtXAhc6WVB8F/70fyNyNNLDiOlsT8BYDmA0IEuNDAwpGTgTF0dyTA4mJqwStCloDT11laS+qhRtIertLV2OwlGabzHj5P4Ojt5b2YmBYHCkSO0CaeksD+lDXsekHp5cWdw7Bj79PUlqScn64erdjtNIPX1HH9iIv+qgh99tXQhuENQ41MmJ9XWoUM0JURFcUyhoXpqYdUGQC182zY9FXF4OAVKSgq19P37de01MBDo+M/lmDOnjz19gaYfIrrhctHMVFrKdYuM5Hp2drIPX1/2WVvLeY0axffUYerxZA2RVxYg++XB+anvjtIQMu1bSHr/RTj/bSm8+9Hc29tp6qmsBOKPWJC2vhBHvrsC418tRFCIhqpx+bjmeRPK/mBGyGwNsQdOo/kPdZdg4ILHGRO7EGIxgFop5VYhxPzTXPcjAD8CgISEhDPt9pLGgQM0X4wZQ40zPl7XnBU8SV1pshkZJJbaWhLLqFEkQmXftdupYXZ1MS95dLTeXmMj8OWXfC07m/cpLdqThCsr2W9HB68ZOxZ6eDzY7/r1JP+EBJJ0XJzuaeOppStCbmykicTHh1GkimitVt1HfexY3e9eaeqe9u+6OpqIKyvRo6Wmp9MsZDbzkFPlxAkPZ6GQ6dN1M1N/h6RScs0qKrimAQH8TFpbOSZF4CdOcL5+fhx7SwvXvLvbXdLvhAWZX3r4qZ/C7NHezl2aWG/B5J1r0HHTUgS9+hK6nIDfp2uoyc/TcOgA7ft2O5BRa0H6n0xY/2MzjiVqiInRcM2zJux9wAznN29C4t034uA/f4aY9YXwfsMMrF7NxzPP9OrbecNNcN5oQsdtBRj1qlG96WLHSGjslwP4phDiOgABAMKEEC9JKW/1vEhK+SyAZwFg+vTp/cRJGgBIEvv3U5MOCyORKFOJItiuLpJNeztJPTycJCaETurh4boZo6qKJKCqFU2cqNvqAb63bh1JbuZMarM+PrrpxdNurdzlwsIocJTpBWDbFgvHNXEiyTUujoTXn5ausk02NemmJkW0bW00e0jJPnx9e2vqqk+Xi7uHnTspIAD2m5vLe199lUQLcBxRUfSfV8FSnuPxhCqqrTJhRkaStBsaeG14OP+vq+P6BQVRuDU3836bjZ9TTqMFeU+Zesrp9eenrs4qduwAIrZbMOevJtQ8ZcbmIA1Ta4Gk114Eli5FQ7aGHRbuhAIDeaDstaYIn9xuxvHxGrxcQNflGpryzRhXXIQtyd/BHMeLyHxrJZy/WsGBrV7NCXznO4CmwfWpBdJkwlc/NSNi/hjkPGlUb7oUIGR/sejDbYwa+71SysWnu2769OmyuLh4xPq9VFBXxxJpISHUnEePJnkCOina7dRKOzp0QszIIKk0NOgh7KGh1BpV5ClA0lH5XxSkZAWf8nJg3jxquJ6ulMpMolwZAZJaUhL/KrS3k9RtNrYfFkZS9zTneBKo3a6T5pgxvT1lmptpFvL25uteXrqg8rTR2+30iz98mHP08iIB5+VxjT7/nO0DJPUJEzhHzxQMfUld+eNXVnLtfH05D7ud41JZMBsbdRL39yeJd3WxreZmXpOTA2R/fHp3RKuVQun4cc5vzsZVqI7Px+4oDTP/9w4kbFoN8c0lkG+9hQ33vc+kb7VFOHzjctTWct4uF4VOejrJfs8efhcmlFgw47EbAUcXhBDw9vcB3nkHAOC82YRjCwuQ8FEh1heY4esLzH3KBO+fFHBXYWjsFySEEFullNMHus7wY79A0NbGbbi/P0k9OPjkcnOdnXoyr6YmXqNIvamJbSgbtNNJO7vVSi1Y2buTk3u3uX07zTR5eSTFwECd9Ly8SBClpWzb11cPkfc0DalcMg4HbdqBgSRPz7Y8CbSlRY8i7VvCr76e2qufH9dBaceepK7yum/fzh2Ow6Hb+nNzGV26dy9NIULw3owMRs/2FVqepO5ycZ7Hj7P9iAjOQwV7+fmR4FtauK4qh73NxvV2ufheaCgPa+PiAGT374HinKuhppKk3tLCfuLjgc1+y9HaCqRWWpC4eTWkECjO+j46kr+Pyx+/AV5C4POfv43jxzlvPz+eYWRn8/PetIljSa+xIG2VCevvehvxRyxINa8EvINYF9dfQ/CsAkx7dSW2Xb8CMTFAzqMmiDeN6k2XCkaU2KWU6wGsH8k2/xVgt1NTB0gG/v7ULj2JzJPUlb94ejqvaWnhIyCAmrLTiR5tzteX/0dH07fck8jKynjYmJhIgvX318lOSt1DpbNTty+rNAYKzc0kdZeL4/Hx0QUT0Js8paRZqL5ej8z0zBJZXU2iDgqiyUQFVCnzizLnqICt+nrO1d+fY5s8mcWnT5xge15eHMfMmcC0aVyL/khdldSrrub4vLw4toAAPrfZOOe2Nj66u9mny8W1Ubsau53CePZsvRh4f1DFu33+tAqhKfmIXqTBy4uCKmavBXnNRRg9Gji86h0cOwbMWUntWkDgyLRv40CsBi8n12jqVI7XM44gNBTwer8IX99lRkwkMPnZQshfr4Drz3/Gsd+tRl0aMH19IfbctALZlkJ41/0T4v77T8r2iN//3iD2ixSGxn6e4XTSNa+zk+Tq7a2HogMkHZuNBNPZSc08KEgn0bY2/eAuIoJk09BADVMR06hRug1eQWnZnmkEFLF3d9OerohT7R5iY3u30dDAg1IvL7YB6P7lQG/ydDgoKKxW3fbuSawqtXBoKHcF/ZG6cofctYvjV9r4+PE02bzzjm4u8vZmO/Pn6wLNM02BZ99tbRRyyoyVkMBxlpfTvALwM2hv5xhU4FVXFz8D1WdmJnc+noLPE93dXLO9e/k3IT0fl60yYVeQGYfHa0gqtWDaX0yoe8qMzyI0RDy7Cm1x+dhzRQFmvLUSxYtWoGyShhmfr4Lz7uVISOB6hD+zCgGT8hEzR0N3NzV3r8n5yN21GqMsb8H2ghlbwzQ0WzVc9bcbkLDhNRx47G2MX6rBZ5cG3Hgj8PDDeuTpHXfQFu822wDoZT4ycOHDIPbzCCnpstbURFL38iJJedqlbTaSnsNBjczfXyd1q5Wv+frq+dgbG3XtvbqaGnxWVm/btMoyKCULRiv3Py8vkltJCf+qaNXERLbviZoaetH4+NCW3N3Na0eNOjlis72dWrTLRdKMiNDfU2RdV0cij4jQSV2Ze1TWyP376SWjkmz5+dEs1N0NvP8+1wMgscbHs3DHmDH6WnqSutLS6+p0T5px4yh0amsp1BwOzqWzk5+DELo5Rrl+NjRwnJddxj77Kz7icvGeY8f46Opye/mkaNjiNCPvIRN8rixAxpeFOLTSjB3QUHcYiI3Nxzf+9wYICGxZuAI56/+C7M//jJa/v4OqIAqIri7AJz0f+Y+asN3HjPIUDcnHLch9wgTXkptQ8SczNtk0VJUAzgQNqbO/g8jRQPp/alQeNI1pLVevRve3TBAFBfBWB6wKhvvjRQeD2M8j9u4laSvzRnR0b9KzWkk6TqdO6pmZJHKbjeSjSF0IkkxzMzXsqioKiOzs3hqklCTkhgbanAMDqaV6e5PQTpzQTQ8RESROlWpAoaKCEbEBAVTyrFb2GRnZm9SlJHH2jSJVcLn0NLzKfCMl+1WeNACJdft2atCATuopKRzL7t062fr6MiBJ0/SdQ9+DW2WjV9G6yqXUx4fzb2lhe76+nFtXl07YNhv7bm9nGzExNPV4xgN4zs/p7F1ww8uLfdlsPPStH63B94oC5L+7Eoe+vQIb/DW01fBeb29AQEBCwtcP8HXaAW9vVFYClaEcb9xBC0KOFKHoXjOmP2pCkFtANBaacSBWY4WpCo558mQg+JZnMKrPzqttuoZN3Rpi68cg0yMnvDSZUH9zAaLf6HOYOkB+GgPnH0Y+9vOEY8eofSp3QOXaqNDRoZN6QwNJJiODfzs7+Zq3NzVbFTTU3EySqqnhdTk5uklHQXmRZGaSlJSb3rFjPCRVxDVmDH3d+5L6iRM8DwgK4m/batXt797eOmE4nWyvuppEnZLSm9RVZsnGRpp4goN5ryJ1heZm9ldWpqcSDgzk2HbuJOF3demvz54NLFpEUu/rM6+09Npa9t3Wxr5TUnTzU02NviNQpO7trfv/+/py7W02EqWmnZrUbTauwc6d7DMwkAKstZV9VVcDsQctyPq6EHtvWoH4DwsRtpV5ZYQAoo4V4e3b3sbu+Xch7/2VaLzyFji9vBG1bjUF6S4LMh4xoW5CPk5M1LBnTgGy3lmJE9cVYFOg1pNjPyKCwmfWrN4mMIDfhU8+AXy+tCD1M93XvrEROHxlAaKfXonmfyvoTeIe+WmkhFFK7wKEobGfB9TU0GdZFYXw86MJRv3g2tupcStN3dubpO7npx+eAnoel6Ym/eCspobv5eScnGa3qor2/Ph4kpKyqe/fT7JRKWdVvdC+vt0lJTQdhYdTU29u5phiY3vnk7FaaV7p7tbNG55QKQKsVs7bx4d9hYb2FkTl5Vwnm41CobOT18TFcdfR1KQX9oiIYIIvlT+97yGpMmtVVpKYAwNpYgoOpiZdUcE1CArSNXqAa2+1clwqTiAggN43SUknC06Xi/NuaeEa1NbyNRUMVlOjn5cklVpwzf+a8OVPqF3vidbwjf8z4f1bzSibpGHrlcuRWmVB9oZCHLt1Bca9X4jy7z+I2BceQ0X3GGRuLMS2+8w4OFbD6M0WpH9RiMPfWYGEdwuxJ1qDI0VDfDy/C0qBULDZ6D1UVcXI1cv+aoL3W2Y452o4NFbDxKU3IEQI1P94BaJeKQRu0HodrjpeZn6a49cVYNInhnvkhQaD2M8xWlqYjyUkRA+b9/Q0UaSuwti9vEjq/v4kg5YW3fYdENCb1NVh59SpvZNjKaJat47EqCIuu7qosVmtJK2QEI6lrwaqilTs3Emzz9SpenreuLjepN7QQPJUUaR9k3R1dpLUu7rYlxIeSsApEj5wgA8lbKxWPf+K8k9XpB4bC1x3nZ7Wt78c9U1NeqBWZKTuSlpRwV2ISmLmcOi+704nxxkQwPVra+O906fzs/M0cakIXZuN5qfyct1FNCREjz9oaNCThyXWFeHTH5lxIFKD08bUA+/fakZseRFaptJWPvdZE3avMKNzloamXA1pD5lQkroIM/65EntvWoHtERrGbrdg4T94XckEDQdiNVz1rAmHVpox7nINo0f3tv2fOMGdjqqZO6OkCN5vmFGdpqF4DRBcDUzyEpC3fBtRf30EuLm3++OxY8C2Ng0p8wuQ/epKuP5rBbwMUr+gMKIBSoPFv2qAUmcnd61SkvQcDmqNyjWuvZ0/foAkLQRJXWmrra0kqeBgPpqbSSLBwXrJu5yc3nZ6KUlQH31EUrn6aj3sXUVNentzDP0RsZQ03+zbRzLLzdW9QOLjdU3W5dKTkanKQX2rLbW3U5C4XCR1lVAsJEQvqm23U0s/cYL3q/OEyEg9IMnp1A82J01igqvw8JNzsas1Vy6Wfn4URKNG6WaS6mrOPyyM62e36+MAuPbqIDUxkesbHNybKJWW3trKvlSenqAg3U5/4gTfV7EAKqBMBRh5eemeScHB7vORf66CNT0fjis0lJVRCOVa/ohZH63AvkX3IGVdIT7+vhmprUVw5OZjb4yG9nbOZbbdgrFlRfD79fKetejqonAuLeXaZmYCKW+vgnNqPrZHaCgp4eva6jt4WO6ZdsBigf2rInw5a3mPlj/nSSOg6VzDCFC6wNDdzQPHri56tXR26lkbAZ3Uheif1NvbSS5BQbynpYXb/NBQveRdVpZO6orkVPHrmhqG0gcEkCA6Ojgmdfjan1lBSpLs4cO0oefkkNSVB4ki9dNFkSq0tPAA0cuLAkQRZ2ioTuqtrTx/U6YS5b8fGUkhVFbGMXd3k4CmTQPmzu1dSUpBpQSoqiKxhodzzH5+nMPhw3xf7Xza2/UdQGenHmGqok/z8k4+SPbU0hsaKLjiM0QAACAASURBVNisVt2rx+Xi/dXV+mcXFcV5NjVxHurA19+f7/v48PMICQGab18OhwM4tIfaf1KpBTM+fQxrfvwBjiZoqEjRsPg5E/asMGNriAZY+TlmZQFRURp8fbWecTY0cG3b2zmGmTPZX+PEfAR/y4SWn5oRqWmYabUgxPJWLw8Ylws4MEbDrhQN3dVAXrMFGX9YDLFyJXD33XpA0/33c1LGAep5h0Hs5wBS8kfV0kKy7uyk1qZsz21temBMXR1/SJmZJBwV+GK388cfHk5iqK7mj7+jg+2mp+vteeZLP3qU2nZGBkm/pEQnMFUYwtO+r+ByMQiopISEmJXFflwumjwCAvTw+fLy/qNI1ViamjgOFSWpTB1hYTqpV1QwWEplpLRaOc6ICGqYyszkdJJc586lSahvzVcpKTxra/nw9ub8IiP5Xnk5BUx3NwlORZsCeoWh4GC96tSoUfQsio3VBZ/aaTgcJMqaGj5UJCjAOZaX00wmBD9v5YLa0cF+fH15fWAg/w8I0KN/g4L4nSgv19dhXFUR3r/VjMpEDeNigegrNBSFm+GzoQh+39SQmamnelBmIoeDJq1Dh/g8PZ3fBaeT5pijLg1hPzZj3l9MaKkvQMibuvYtJdd9yxbOIyyMZqhxLxcBK1cCjz2m+77ffz/wwAP0Ox0sDO+aswaD2M8Bdu3ij3TKFJJOcLCehEuRure3TupKU1eJpJSnyqhRvL6ykm2o6kgpKb39tT0jNL/6iqQ0bhzJVR0mBgTQHNL3YBPgj37LFpoPJkwgGbS2cixjxujmmspKPYp0woT+DxLr60nMwcEkWJtNz/2iXBoPuLMVqqyM6nA4MJAkrKI9nU4S5DXX0ATTVxg5nfoZRXs7BZ/yuLHbqaVXVuoHvh0dukeNiiANC+Pn0NVFkpwyheuuBIgKlLJa2YdKxqaiUT0DnqxWzmH0aLZfVkaiBbj+6rDY5SJxR0Twtc5Ompza23lteDjH+tm05QgJAbJSOc79+wFbjIYxt2mYl0NBpbyLVHqDrVu5njn/XIWx38hHaLqGujqSuvcXFiQdKcK+65fj2MICpD2juzp2ddGN9OBBjiEtTY9yVaTblZEHcZMJxxe5D1Dff39o5hgjXfBZg0HsZxlHj/KhApBUZKkQJMuaGm6/6+pIDpmZJAOrVXeZU1GUyvda+XvX1lIDHj++t+kFIDFZLCSbxESaSoQgkQQF0azQX9i7w0HPmepqmkxSU0kwNpvua97drUeRRkWdHJGqCLC6mmSmKj+p/CqK1Lu6aOpRCbAiItxRk25f+MOH9QhPl4t2+2uv1YtMe/blcFCI1Nby9bFjOTblNbRvHwk3LIyP1la2qQ5LFSFWVnK9MzO5bqGhevpita4dHRSatbW6v7taO6W9AxQI6lBbkb9KG+zvr9dJjY7W0xErrxnlRqriE9ROKSODRL1jB8eVnk4hN3q0LigdDrqv7t/P/5OSgCRTPnxvNWH7UTP2j9UQtceCK54yYcPPzciss2CKha6OsrAQ9ZkavvajvT4yUi+64onDh4Fd7RomawXIenUluu9fAZ+h2tg1DY1PmxG8xAQUFMD/fw1b/UjBIPaziKoqautjx/KH29VFsvTx0W3kPj56pSOlqXd06PlHhOCPS23t1YFcaSkJPTGxt5YO8J7PPyeZTJlCYvH21tMOJCefrF0DHN/XX/P6yZM5VhVKr9IId3RQk5eSWrpnhkdAH0d5OYl99Ghq+YrUIyLYtyoyXV+vR5lWV+uRnqqknzrMzMzk771v1KqUujlEuSsqLR2g0DhyhG1FR3O9W1t123h3N8eo7N7h4fwclLlJaeguF+dutXKcSjAoAaXysivXyMhItl9ers8hLEw/5FVVp1SZv64uvfSf8snv6mJ7KrgrNlY/GwgN1bM5KrdXZVbas4ffvYAAnkPExgKVlRp2LzNj/gMm2GcXIG9zIbbca0ZKEhB/jwmu18xon6HheLSGST80IfznZkwysbKU5yF4Y6N+DpJw1IL0zykQfAoLgau1QZNyczNdVg+VaphzeQFmrDLSBY8kDGI/S2hupjlDaattbSTCgACd1FWCrq4undSV66HNpvs/q8PJgAD+4I8eJVmq9LtKm1Rmlu3beX18PAlEmV5iYk4d9m61UlNvbua2OzFRz2SoQv3r6vRanhMm9PaT99wxqBQB0dF8dHSQHMLCOOeaGpK6OmxV6YUBEmZjox6G7+PDcP38/N5Fq1Uhi8bG3r7i0dF62P++fexLJQlTqQGUycbfn2NSic7i42nWio7mGikhperDtrSwPRWJqt5T6+Jw6PltlMeL08n1Um3abBQ+Y8aQ0P39eb9K2qZ2K1Yr5xcTw8/Z5aJHi8PBcaamUnioM43ubpqF9uzhWMeO1fPWfPEF77WN1jBqdgFmrVuJY7euwLR7NQQ9tQpdL5lRGq9h91rAHqmh60EzLusoQmCmTrJ2O79XpaUc37RWCyb/xQTxxtAyQtrtdCLYuZPrp8GCvOKBi5AYGBoMYj8LsFr55VVh783N/KGFhekuin5+ultcerpuU1cBMUqTdDj4Y1LRqQcP8gedmsq+PLV0Ly9qjZs36z7fgB6M41kxyRPt7RxvezvHMn48iUSF20dEkKzb20lG48adXLsUIImVlPC+2Fheq9IGh4VxbocP034spS7wmpp0m7Aiw64uEuCCBXrErerL6dT9xZubSY5jx5LkVBCRZ9SlOnCWkuPp7OR4hKCpyMeHfSQk8FolIJ1OXm+zsU3Vho8P2+7qombc2qrnju/s1AWFtzdNGKNG6QnEIiP5OYSF8ZrSUt6vUiIoV04fH34O48bp5h0/Px7kJiSwTT8/PcPkgQO6G2N2NgVvfT2jSququHZp1RZM3VKIxp+sQOLqQrg2aqj/wXJq+MVcx/x8IDlZg7e3Tq6HD1Ng2GwUSNOmARHPFvUmcXetVhQV9UvMTifNR5s2cbwpKcACYUHIDzyEgZEueMRg+LGPMBwOmkGsVv4AGhtJLvHxJLD6ev6Aamr4Q1GautJO1fZbJd06epSkFhVFm2lYGH+4SmMEdC2vuRl47TU+nzJFL8CQmnqytwrA+1ta9B9berpuL6+upkAICyP5OZ0kYs/DVs+vjsOhH3QmJLA/q5XkpsL7d+8m8QcHk4grKnSPlMZG3Z6uzBRXXkmBpNLtKn9xJRyVhhwdzTV0uTgG5Umi3C47O/leayv7GjWK81bVp1JT9fQKal07O3UhUFnJfgH+VVk2lfYeGKjHBqizkcBAroPDoZuIVPEUVWmptpbfAbWrUjuEgAASemionhs+Koqau1IQfHz0bJG7d7OP0aPpkhoUxM901y627+MDZDVYoBWa0P2yGf7Xauj+xALvfzPh65+ZUZmqISGBMQqeuyJ1yFpfz9czM2kS6ntofTqoz+TLLznn2FgWOxk3DoZXzDAwWD92g9hHEC4XzRm1tXQLa23V7aMtLfyBBAToBTDS0kgAdju1L+U+p0wWqorQ2LE0K6ikW0pbVpqlEPzxm838m52te1qkp/cOJVdQmSBVYYaMDBKPry+JTLni1dbq1Yc8fbg9vzaq4LRKPawOfxWp2+26PT0igiR17Jju9dHQwL+KFBMTqanHxPQu0We16onO/PwoZCIi2E9rKzXLxka9SIfdrgsKlcY4NJRCy2ajoJo4kW2o7JaqTmlXF/tpaOBcVT729na9epIQ+mGy0uB9fKjVjh6tH4hHRfEzDAriGtXU6NervDCqj+Bgkl9XF8cpBJUCFRGsDrxV1PCxY1ybpCRqwY2NjDBWpq3QUJLonI2rMOqafHTP0dDURNL3/sKCuIoiBD+8HOPG6S6SVis19OPH2fbEifxO9fc9Oh2qqpjWubKSAlSVJOzPFGhgcDhnAUpCiAAAXwDwd7f3hpTywTNt92KDlLQb1tTwR6CIbcIEnSACA/mDs1qpUfv766SuDudCQvhcBfPExdF0obbhyu3OM4ticzPw8cckN5UrJTqaffTNDa4Iua6OZwBC0Ec9MpLjqahg2w4HtdKwsN7FqvvqATabXnA6JUWPtPT11SNilT1dkdvBg5y3w6Fr7O3t7CMnh8EzKlOksqV7RsqGhpI8lQ98WZmeT93TZVAJA7ud81CmKrWjiYvTPXQA3eyi6sQq05hy22xv519F4P7+7FOZUUJDKZRUAjeltatdTmMjH52dvbNRqkyOYWEUAnV1bDc0VNfSPT1pWloo6Ovr+X1JS2MfmzcDfn9eBf+YfPhM1nqqMs3osMAvArDO1HBoD3dNAJC4RENyttYTjOVyUVgcOKBH+6rKWkPR0pub6WZ78CCFqWfMgYFzg5GwsdsBLJBStgshfAF8JYRYI6XcNAJtXzRQ2tPkyXpIenKyfhgYGKgfkE2ZoheaVgeQra28RvluA7Sx7t3L9rKydDuzInUpSUDFxRQo8fH8ocfEnFzpCOjthlhcTEJLS9M11vJyjsnhIIHExurl6dT9nlApAqTknACd1AMDqfHt2cPXk5LY7v79JGqbTc+fbrVyLLNnc4cREfH/2Xvz6Ejvq8z/VmlXlZbSvkut3ve2Hbcn8ZLIzuKEsISBBjLwYzIDznQGzmESSAgzxAlhGAgMQzKAwWSYBAKBhoQlBLJM3EmwnThtx+59V0tq7buqpNJS2++Ppz+5r+S23bbVXut7jk63SlXvVu/7fO/3uc99rmuxk0n3wyko8Gi4sFDX8tIlL15qatLrACcrgvp6AeXUlCabLVsEoPD+ROnptN6HIqe4WN/L3NzqXEBxsf4+O+tVsG1t2h4Kp8ZG/UQi+uz0tK8Egi37AHUUO9BIzc36PuvrBeqFhdru5cuaSOnWtHWrjvFznzNr/+zHbClcaO/4qwP26C8dsqq9PbbjS79rBR/5VRv75D/Zd/9V5xKLiXapr/dAYWJCgQmNsm+6SffvswHjxUVNLk88oW3eeKNXuObHCzueN7DnxOVceYSs6MrPC8/vvIgDNUJrq0BpZkYPJY0wIhGBaSKhBxFQh9rAaz0aFajjpXL6tP6/b59rmlnGZjICtf5+Jc1iMYFLS4tAKyhnBJBzOR3r44+79W1VlfaLaVUqpX1t3OjL/rWADjd/8aIAZ8sWT2hSHn/ypI6vrMwTeQMDeh/7IfEXiYhPh5s309/n5nRtkkmBAzy4ma7n4KDTXfX1vr1kUiAapF6wcCDxCJcMj57J6Bjn5gRmKJbm5tx7PRRyO18KjaqrFaXPzuralpRIV779Cx+zuS032+VNPTY7K0BvOHnYai4esXM/JP8WJvbaWt8HbRHJZ+A2GY8rAh4Z8WYrDQ2iVI4evTI5dtxsP/TZAzbwkx+0/f/zgF3+8lut4Fufsf6f/x07Uthj4UV9bvt2nSMqnWPHXMKKHw7327WMdFrHQK5myxZN0jU1zy7Sz4/1G+uiigmFQgVm9piZbTKzP8jlco9c5T33mNk9ZmYdHR3rsduXxJieVvRbU6OodGxMIIOjYDSqhzGRcKtcJHAkPIuKFO1dvKjPdXV5VLZnj5tO8ZAkk1pOz80pYoamaWkRkAZ9z4P69r4+TUDRqI4lGnVQh8+NxTxhyeeDA7XMpUvaz+bNruPGnfGRRwSStbWKPOmdSkQMqKVSAqeeHo9ukXpCW5hpOxTgLC8LhKamdB0qK/W5TEbAiAUDPvU056A6NxbziRXp4/KyviOcHGdndY40DUfeiE48HHZ7hJISP7f6ev8OJjfcbNv/6wEbes8hW97WY01nDtvr7ztgj7z30PfUL9GoSyOzWZ1jS4snWaFpRkZ0PySTen3rVh3bF7+oycRME0DJ3T12fOMh2/XRAzbRsN02Pfzn1n/HT9kjr3uv1dcqQOC6ZDLa5tmzbnGxd69Z7Z9+zMKL15bQzGR0/z30kK5ZS4t49JaWPI/+Yo91AfZcLpcxs32hUKjazP4uFArtyuVyJ9a8534zu99MydP12O+LPRYWlCwtLRVVMjLiXC6gTqS+caOXnJeW6j0k4CoqBNQrKwKLixf1EOPvEuz+A6jyUKVSepg2bNDf19r10mjiwgXxsrGYjiUS0bEODLhGvrXVfdiDgB6M+Ccm9JloVJHp0pKbZi0uyu9lcdGpiTNn7HsRKzptkqQbN6r5A/4ouZznI4i4qcqkDd3wsFsX19ZqvyRHFxf1en29q16iUVEKFFiFw06JYLiGPTIa+9lZtwxADUNUjztjS8vq3Elnp76rlRUdY7ypx8bfc8hu//0Ddvy2g7bnofvskfcesoGNPZbJ6FhY+RQUaAJsaPDzLSjQ+Vy8qMmJaLq1Vd8jUXo4rAmLBh4P5HqsuPuttvfYn9v4ttut6Yl/kdPj7T3fCw4mJhSlc+z79vlkHtr/zGX+uZzO8cEHdWzV1Wbf9336Pq9W+Pa8Rl4585zGuurYc7ncbCgUOmxmd5vZiWd6/8t5rKxI+53NSgFDIUxJiR7WigqvhuzudsBFfRH0VccZkdL/eFycNQlEM6/mxILg4kVt49ZbFX2j+w56mjBOn9YkUF8vACov1357e7W/igpFtEgsryaUgpsfGlLUt3Gj0xioZ+DTUT4gt1tc9K5E8/NXClxuknwOfn95WUA5OenuiBQbYWEwPe10D06I8/M+uWCeNTGhY6uv1zWtqnIbBmxyKehZXtYEEo9r31Ta0miDzkmFhQJcotHRUW0PLp1q4nhcn8/lzE419lhk/0G79UvyTr+8qcfsyndOHiMS0efr6vTDBDc5qYiaAGHzZn3mS1/SvjFDa27Wd37u3JX74ZHftT3HPmOXbvspazv+L5b+wAet7X0HLNcqT/fjx3Xe2azuyx07/J40M7OeHhv9xCGL/dABW37XQav8i9WmYNPTCmbOnnUzNhQz14V2yfvJPKexHqqYejNLXQH1MjN7k5n91vM+spfwwAp3YUERJ3K98nL3IyHy27DBQR2dNBaxkYjAenFRADQ8rAdn82YlAoONIi5e1LZLSpRAGx7WA7V3r3OzeIUQpZsJXPv6BEitrXoYq6oUSQ8NafLYvt3L5xlrwZ1JBcopKO+7cEH7KC1VFJ9IaDJBk8/7Egkd4223rS6yIbqm2AgZIyufYAl/efnq6B7JYHW1/h0a0r/d3YqAYzFNBKhwCgpcYUOx0diYji2Z9GIh1DiU98di7teDuVdzsybFlRUd59yc5xoSCXmW3/id++zYD/6qbfnKfTayTc0yqFnA4bOuzvXtKyv6fi9d0vG2trqB29GjvuppaNB9NjXl57Jj7LC9/oEP2an/+DsW+W/vtfCFw1b6Ewcs80sftJkvHbFHFnssmdQ+9+xxczPuFWjFiWyP3fCmg7bj4yrzz72hx5ILUlEdPar33nSTftZ606/76OmxxP85ZCXv0ERT8Zm8n8y1jPWI2JvN7NNXePawmR3K5XL/tA7bfUmOXE7Jx4kJ3dhwuhTkVFUJKKanBYDwxoA67y8rE3WzsCCQw2Z2wwYlXhnz84qsSWpOTemh7+oSBcNyvKRktbUAxzk4qCi9oUGfj0YF9hMTmjxIpAXPb+359vVpv42NolgA9WxWxTHYB3R0CFg5XqJezqOiQvr0mhqnmMbHHaCrqgRynAuNO/DMiUT0N6JqgLq6WoA8O6tzxJGRSlRsGkIh0UgLC04dYaMLGKNayWa96UVDg/eeBVRra10/zzFSPZvJmHX3H7a3/eUB++bPqQBoYleP3fYJFQQlb+mxykqfeKBe4nFNkhMTnsAOh1XwNjKi48ItMpXSdWalEouZbT13xC787hes+12SMObaemzmjw7Z9JeP2ONver+VmeSLHR3uN2+mY6cBRy5nduPcYdv2jfss999U5n+2uccOmyaFrVsVzFA/cD0HBVKXJ3rsxjsO2g2/l/eTudaRL1B6lgOLWWSCPIShkH4fHb1ikNThiaqyMo/G4nG9H61yR4fAYGBAgB60o4XPLijQz/y8IuGSErMf/mGPKiMRj7wohT9yRBMMzn9E9GfPumpn82bt52pyRrZz8aKOubVVEwG6bTodLS5q4ojF9F4UKIAnkXJ9vZ5HuH108jMz7jMfi7lJ1+ioUxpMXBQJUXgE0A8P6zW8cKJRLxzCUXFuzpOchYUC47k5ryJdWnJrYDpKVVS45z0Jb2yLUyltI5FwXxsmoJoa2eSOtt9sw1t7vteQpPWcuhrN/Oz7rbZWkwMa+pERTdgkSNva9N1j34ulcFmZaBqub02NjrOmRlE48tRkUvfp8LAbttGcnHslndb9cOaMjr+uzuzfLB62yp85YJnPHrLzbT3W+6eH7Q1/eMC+/V8O2ZZ393yPdrpeahdcSx9/3Gsqbpw7bLt//YCF35Pv1pSvPL0O4/JlAWZ7u6IpGkwELWcnJ/X3WEx/40GiFL6oSEASj+vhXVpS5NXUpEgT/fbAgNsP4J1y+bK28fa3Cwhp8kxTatQm3/mOJpetV3y7KYDq6xNIdHW5dfDaRKmZHibcBhcWBAp0/sED/vRp16+Hw+J4kSbCu9MsY9MmUaXQKKheaB+HJQDFRuyHfAERfDzuMsmqKh3j2JjOoavLm4MXFHjrPKx4sROgQXgy6XJU6Bwzj36ZGEgM4zmDfn56WvtIp3WsRNP19asnCZKyKJCqqwXCFEYtLgrQ4eyJpp94whuaFxbq/fPzXtBVVaXvliKmLVv0OfIR589r23V1CkKgerimQ0OK0ufmdK779l1pV/ibH7OJrpvt66EeGxzUtXhjgSpUw7/8/udPuzxFMjT7nSM28pPvt6NHvT/Bpk0C9fJ//xQc+6sQ3POt8dZ5TE6qaUFdncCsr08PdkWFHtbxcb2nrc35YZJSLNFRwszN6X0sp9lmKCSQuXhR4FFe7lHg8rImhNe9zkG2sHC13nhlRVri2VkpaojkEwnv29ndregbUM9m/fO8hkXA8rKX3MfjOpagimbnTm95Nz/vgEyuIRRSYnnTJqcbZme92CgWU9QKWEKLmOk1Iku06em09ovH+cyM9rVpk76HsjLvDlVQ4FbHqZTb9HKMRL3o0YuLtV2+u/l5/RuNevejTEaTBDYFTLh4+ZCEhSIqKNAxcWyYf0Ui7sFPEryyUpz92JgmTUzDoPImJryxd22td1vas0fHR6R75owXxO3b571nw2FXFh07pmuN+dnOnVfO+UMfs+OlN9u3hnustNTsDW8w2z152AofP2LhX1knBcqVZOjKZw5ZwRt7LPfAYQv9+AE78ouH7OSXdEzbt+vYy8vN7GPPzmwsPzTywH4NY35egFleLl4dp8OaGv3Aj7e1eUKqtNQ5yNlZ/ZtI6MFvbnZzJPxcaLzR26u/RaNuLVtaKhnh5s3e+MLMH3ozgdjDD3tDa6JcpHvh8Go5o5knWYNyyoUFRXuZjGvdcV08fVoAg2Xw5csCTtrzZTJeZl9UpBxAQ4NABovdxUW9B86/oMAjahQqKyuuhllY8P6omF9dvqzzra8XcJWXe+KYwpvxcYFYJuMNSxIJr0BdXNQ2QyGdYyzm+m5WHNgVh8NeObq0tLqTUmWlPsuKLNghqapKx1Ze7nLL8nIvLqNgi16sR4/qWjAxRKNeDMXkUVbmKpmNG3X8iYTupaEhl0Vu2eKBBY6hJ08qIEmndd1uuEHvWVhQ0nR6+mZ766cOWPmvH7LIm3us69JhK/jJAxZaRwXK8ut67MK9h2zjjx6wwR84aK1fuM++ds8hm2ztsV1bNVEFPYmuKmnMW/s+48gD+zOM5WUVYJjJF3x4WJFidbU3WR4bE2Cy3C0t9UbPtLtDcdHYqIf49Gk9oLt36zNUUhYXeyMKDLO+8AXt63Wv8yQdnX3M9GDSKJv2ZeiwoYrKyrTvtdxokI7BIiAUctsDqj9PntR+UJtcvOidfmZnvVpzYUHH9oY36Pzww5mb0/6qq92HPJn0bRQW+gRAPgIdOV2XkklNquGwkswNDc69m7njIY6IgHoiIUCenNSxQrsQ9aK9xgmxqsq9WZaWPDnKsZi5/UMkou8VGaWZPsu9UF3tXZtKSnzyRkPe1ubSRnrKUu/Aqqy21o3hGho0cUejbunc2+vdrKBdiNDTaX2nZ8+6ayh2AisrWoU++qjOb9vbemxq/yHb9vMH7Ow3Dlr4X++z0N+sD+WRTHqfgPniHlu49aDt/4uP2rEf/FWrP9Bjd+5eXViXH89v5IH9aUYm42XSt90mQB8Z0YPb2CjQHh11T5WCAj2UKA7wMFlYELgQvZ46pfft2SMQvXjRaQU8wClYoTfwnXfqIcWKgK42icRqPT2l8eicAT18VNY6Q5p5ocyFCzr2rVv1bzyu6PjMGb1n9259/uxZnTucb2mpji2Z1HW54w63PwBU6SoEPTQ66hEuZfPoy7NZT5zCy09MOMVANArdUVion8lJTbL0L02n3etlctKbaIfDAj+07dAqpaV6nXoAonRWPEVFPnGjcpqacnlkaanAlRUEhmTQUJcvK0pfWnL1z6lT7jZJkpgVSjTqtQzRqFZ27e2rq1FnZ512aWvz75i6h9OndW/h/9LVpb+dPat7e25OQclNN2mb35zpsT13HbQ9f/dRy/7X569Aice1Erl82dVUbRcO256H7rORn/lV2/3391lovsesNB+Br+fIA/tTjFxO0czUlNn+/R4dRSJ6uMbH9UBSoAKooxggKZdMCtxog3bihLsYUtZN4weSjVRKfv3reijf/Gbtd37eeXUz/e3b39aDvH+/Pk8BU329A1ZQyRAEdM4TCSWgSS7g7FmdM8BBT9HpaS+5j0bdEXHjRlGoRN1zc67moBBpcVEPebCrEslLtrO8rM9VVTkgLix4wVFxsQM60XZfn/aHRnxpyQ29sCYw85xIQYFz5LTsq652KimR8KgfRVFpqV9/VmAAcmWlT+7UClRW6vosLbnPS2mpgHRuTvfC3JxfL1ROdLsqKtJPe7s3Y5mf17aw5e3s1HdG8tlM3+e5c1pdhsP6+9atOvaREd0zw8M6sPZhIgAAIABJREFU37e8Rft84okrnvxjh23nN9XRKHzffWZ3PTfaA5/4wUGnkwoK1Ozjjk8fMPvbQ9b85h6zd/a8qpOh12vkgf0pxunTuilJQh47pgeju1vR48iIHuTmZo+0iJaQ0S0s6EGsq9NDdOKEgHTPHlfDhMNaHs/MCDy2bFHEd+KEIuibblIkhgkVxU6TkyqSKinxhh7j4wKSjg432kJxQgS9FtTHx1dXn5rpoXziCZ1nXZ1ABZUOxT0rKzonVBo33KDPoxknP4AcD957elpAgsZ8ZcVVJVgNFBV54U9fn17btMkTraGQV/nOzIhbZr9IG1ldwXljFFZU5JMIyclYTCCMZwzukMXFTregcMLfJ+js2NSk84Qii0Zd9TI2pu95cdEnjgsXXBZKniOddo/5SMSVP7t3a2JOpwXWly65NHHrVjfaCoV0j1BNvLKiz+3cqeOJx6WWOn9e98Ntt+l4oIWiUUkdW3/zgNMvz7KjEZYTJ0/qO8Exk2bsO3aY7frnI1bw+Xwy9HqPPLBfZfT3i37o6hKoPvaYXt+2TTfu0JBAorXVfbkBnPl557fpfFNbq5s9nRaoz8569FZYKLCrrPRG1yMjAm262rDUD9IYR47o95tuchkklgHI+erq3GdlrUwNyRuR26ZN2sfIiBK1FE61t4sqQs0yOen+NnNzAsrXvtarMlHZVFa6B8zSkhdjlZR4RyX8z7HxzeXcGAtaJRLRhIH3Os0ozAT6yCahgyYm3KmSQW9QEqPIEOvrPWkK7bKwoOOIRPQZbJVLSgSW09PeIg8lS3GxR+2Aei4nIEaO2dDgq6CZGfegMdM1hJfHo72726WkIyOaDObmdG327HHaxUznNDSk72l+Xtu68UZvNvKtbyl6xkq3rU2T7LFjOrYNGzSBRP/wuSlQ0mltD1pp0+c/ZtH2m21+e8/3AoPto4et8MtHzD74DMnQvDfMuow8sK8ZVLs1NOiGfPRR3bi7dyuyGRoSYLa2epchZHnI6QB1+luePKm/7djh/jFQEImEIiuqTefnzR54QKDS0+M6abj7wUEBb1WVQP/8eT3YHR06Jgqfgn7jaxOmmYwmAypGu7rctuDoUf2fzkvI8SYmvJioqEjHGYlI+YJcMZt1nhoaZWJC121lxX3U4b6hXlZWPKorKPDkZ329m5uRBIYG6evTewoKXF45OurabzP3YSE3QQs6VDkoj+bmdCy4O+Itg+kXqwC8ZOhqVV/vtgRQL+Xluk4op8rKdB17e71zFpMfxw5Vlsnoe9u9W//i3snk0NGhSY6cxMqKru3Fi+6jvnOnrhmtCB97TPfH1q367Py8JgmcMTdtUjAQDtuzVqAsL+uanz3rrR5TKbOJrpvt7k8esIu/ccha39Jj1Y8fNnvnNfq75L1h1mXkgT0w4nHxj9GoEpFHj+qh2LlT0dbgoMC6vd3VKwAnOnMAq7ZW4EFT5e5uPQQrK/pbPC7A2bBBD3Eup98PH9Z73vpWN7kKhwU4fX2KsmhmTVPorVu98w6NFJDpXQ3UL13SsTY1aTJIpXSuZ8/qvG66SfsdHPR/6e6EkVZdnZookByGL0fPvbLiny8uVmRrttqPhZUI/jDJpECHSkmAE2oGaSS9RsvLBZLj46KKiNJDIUWlVL5ik4tKpbbWaSicHnM5TSwUlplp+8vLuq7j417l29HhdAlVrvD2fX1u0lVVpfvmwgW3TeD48JcvK3M5444dbvZFfiOV0nFt3uyJVKp28QwKh3VMmzbpWvf3e2K0tVURfjrtnjvhsO7hLVv0nT3bwQrh/HldGwqyWAW139pjp9sO2bYPHrCRbx+06i8/i2rRK94wpe84YIPff9A2fOnVXWn6XEce2K8MdODhsADr1Ck9GFu36uG/fFkPWBDUWQrTVBhQr6lRFHb+vB5oFDRI16amBAJbtzpAmLkNQE+PtkGRSkWF2+4CxqdP6zh27vQokebMdXXa3lpQJyqn6rWpyc8bSmbHDv2fpG9fn/u4UMrf1uZ5AtrOkXykCAkenmKaXE7HiBsjlZmoU8bH3SFz40ZPEKPbXl4W2CUS2gegefmyPkf1bFWVJhFMvYiOsQBGcog1ARWjjY2rQZYiJfIKZr6ygkah8rOyUu/FmZMov7/fJw9GUZEmD659Oq1k6u7d+h5HRhTdz8x4tycmKbTyw8PeYDwWc4CemhKFx3d55506X+SaNDXp6Lh6h61nGvG4Wx+gMsLgjSI7goTlaI9V/sBB2/gX1+bvghXw6dNm4/M9tufOg7brM1LmhPOg/qxHHthND8i3vqUH/dZbBWaTk/a9dm4DA3qAOjoEEHCqJL0mJx3UYzEBS2+vwA2vESRwExMCg+5uPawAEsC9a5eAjYe+rEyAdv68ACAW04MVjepBKi72ytJIROBl9mROnebHyaSX38/Oevf4tjb99Pd72T3NjLEvyOUEIjTnpnq0vl77pldoPK7jokHyyopXei4va5v4iIfDut7xuHukwKWXl3vz78FBXY/ycl33wUF9jkKjwkLfH1p15JCYjq2s6PpDGYTDAtjaWveVQR+Oa2IyqWPAjZLvBA6+uFjRK6ux4mKB/OiorhHJWySLUG7JpH+HXV065uPHPQLv7PQuVhSaTU665QI+8w0N2tY3vqHvt6zMPe4pLGMiamjwSuJrHdBmIyN6DigyA9AbGqSdp8BqevqKP3v5Yav7itQ1dt99T0nppFK6z5BuFhaq2nXHOihzrjpeJRz+qx7Yczl9p7Oz+r4nJ/VQ4rs9MKAbdS2om62O1DFvam3VjTo46CqZmho3m8IFkX0jjXzoIYHM/v2rPUrOnHHb3fJyHVt9vfejXFwUAJWXu9XvWlBfXPSmHBs3CqCGhrTPlRUt86NRgUYup3MeG3PqApnltm2atKanXTbY0OBgOj7uUXpVlRcHUemJtwqfTSY98mxr86bJAGcq5Y06iHRpNIJvu5lb3xKlh8Oe1K6r8+ODdmEVhLYfPxZAeWrK+56SWKYqtbTUbQHw7yGix5eGRiEMmpgQ2YfDAvNdu9xnZ3DQOxlt2qTjpg5gelrbnZzUMW7apAkik1G+BR/8vXt1b8Xjuk4EHjRF7+y89kYYKys6r5ERb0HI9WNS3rFD982pU7rnS0oUGG0fPWzhHw/w5FdR16DguXRJ/0cRtnP8sJV99IDZc1TmPON4lXD4r3pgP3FCD83One4tgpqjv18A1dmp3zHbopgG2Vsi4aA+PCy6w0yvNTS4YVSQNzZzud//+3/a9l13uTOfmZalQ0MCUwqG8FXH6Gp8XA8FoL5WzphMCtSzWQF4RYUexMcf1zZ27XJVQ0GBrsfsrEfLdDLau1f7oeq2qUnbymYFblAkbW1OaUxNOaACMHV1AsXpaV3r0lKBFIqfSMQLkvB5iUZ1XkEpn5lrwjMZvZ9IP2i6RYvCpSWv6sSzBb91uPrpaQHZ3JzOlVUMTUIqKvRTVOQRPUVPCwuaDLETNtOxNDToGClSq6rSNW9q0r3S3+9FRtu2CZgxB5uZ0fcyMuJgumGDzvv8eX2Hi4sCetrlzc56s21WBRs2rM4dPN1YWHB3TVo6YuwWBHSkko88on3t3KncTGmpmX3x6uqa7HeO2PTuHrt0Sff10pKu/c6dujfLyuy6e8Okb++xyx87ZC0/eMCW/8PqRiKvpPGqdnfs7ZVeu6tLDxwt36qrBSrRqCJclA0YelGpOTXlycrOTj3YTzyh93R16XUAs7vbm0MHy/i//GU94G9/u0AAPxKkcjRwTqe9BRo+KtiaNjW5hUGwmhQPkXBYD05pqbTM584JQLduXc01kywmUbm4qH3v2+fmWnV1qyea8XFPFtfV+cQ0Pu4rGao2Kd8fGPAuU01NrknH2wRqhiKl6WkvuWc0Nekckkkdf7AqNHj8+N/jo15d7Xw1Rm1ExSMjem8k4l76SCkB9VTKDchQ23AfBKN0mlyHQmbtn/2YzW6+2Sp+oMc2b74C2p8/bLnvHLHz73i/tbZ6u8JUygvAhoZ8YuvsVKAwOCil1uysvoc9e/S9oLtndZLLuY0xks2nGthJzMx4ERoROoCOSgzDu9OnXdF1yy1OAV5trKzoM1CcmOd1duoarfKGuQ6DPr2nTul5WFoyu/XLH7I9/3CF//+1X7u+B7CO4wVzdwyFQu1m9mdm1mhmOTO7P5fLffz5bvd6j9FRAVlDg8BjZMSd+AD1ri7nxvEnN3Pb1pkZPWydnYreHnlEDwE+K6OjeliDvSCD4Pvd72pfr3udjgNP75MntX1Mn6gkra11G9/hYW2jsfHqoD47q5VDcbFAPZvVyoDCqrY27QMTKToewTdTULN7t9NCcPwkuqgs7ejwAh+qXwF1mlXU1DjPj4FXLObNt+mkNDTkXHpBga9auPYkas2cbigu9upQCrioHDXzNns0sYZSQb8+NqbvLxTS9YQqgzZiFZFIuJwULxeUUBxfUZEmhcpKfz19w812x28dsORrDllfSY8lv3jY9v2PA3b6w4fspptcFTU97TUOdMvasEEAPjurIGBkROff0+NeNiSTMWMrKxOgM9E+1Uil9B1NTWnf0IokuAkadu3S+czN6Z4dHdV1vv123VtX2werRRK9dMAiV8XEfL0G+x8Z8W5huZz2e/P8YWt56Jn5/3UdLzC3vx5UTNrM3pfL5b4bCoUqzOyxUCj01Vwud2odtn1dxtycItdoVF80UXU0qhshEhGoU6CCXA4L2YkJRR61tXrf+Lj46oICRbckCwF9Eq3BB2BgQEvpzZuVfMpk3FdjdtZbn1GwA6hns3pYslkvjlkL6pOTbgWwZYvO96GHtP2ODgHD9LS2ffas6IBQSEBA9N7Q4L1US0t9kiNRu7Cgh7SxcXUZ/tiYR9bIGFFs0DSkrc0Tj6iCKLKiuGliQlE6ydGCgtUFT0TSxcVuLYDMEvMwZJbQPLyGtcHUlCd7oYS4BiUlTudks/6dowRhxQYtZKZ9tbZ6IVNZmb7bDd/fY6Mth6z2Jw9Y0d0H7Yav3GfDv3fINv5Iz/cmNLYHpdTUpO8qlZJq6eJFHeO/+Te67iTXaQk4M+OVxu3tTx8FUxVNcEKv1kTCLRKam68ULV1J/l+8KD48m1Xkvm/f1VcCmYy2RytFag2gpKDiroUWerYDa+aFBd3/ly7pHAsLtTrdu9cs9sRhs599ev7/uowXmNt/3sCey+VGzGzkyv8ToVDotJm1mtlLEtgXFwVyaHkBIXjd0lLRJnCp8OnhsBdkTEzo4dqwQSD78MN67y236EFZXhZ4NTZq22tBPR6XD0xtrZJNZvrckSPOowe71QPqRMqplFMYa0F9bEwAWlEh7nVgQNtNp7VyoAVbRYWiLzj6ykoH0fZ2gQrJw9ZWnT9RejjsyU5UEyzh5+e9cKupyQuOJid1PihoAGUUJKmUnyOt+4ISRhprQNHQPYmInfMKUgdQP6hCqMKlmGl42CWXnZ3aDrwvjbFpCsK2FxY0AdG31sw94UtL9Tcm3R079PdHHzU7Od1jN77moN32Nx+15Pt+1Zp+Qq3mqD0YG3Pte2entnXihNcq7N3rfH8q5W6R5HhKSvS91dc/dQ9SLC7oCYCN9NycotuCApdeQnONj3u/XWoXamqevO2lJc+bzMy4T31bm46ppsZzJes5cjn364/Hda/19+sZjEa1Gt66NTAJHXmR/N17emzx04es6N8esNy7D1rRJ68vt7+uHHsoFOoys2+a2a5cLhdf87d7zOweM7OOjo6b+vv7122/1zrSabNvflM3wMaNvlyjGUVpqaJUqiaDTaFTKS3nRkZ0k27cqBvo0Ufdr4Wm1hs2aBtrAZ3t/OM/6iF7xzsEsJOTmhzicbcx4EakfVou540oqJo084c4m3XZHfzu0aOKegsKXLpJAvHBB7UtQBZHxK4uAXI2qweyrk5/w9sEnXgk4s6HQ0Ne2k+bO0CfTj60gsPuNpvV9YJOgbo6f96BuKTE/e1JfhYWrj53qCmKkyoqdH1YCaTTzuHTt5Sm4XjUNzT45I3qhRzFzIznIQBB3BfNXHI4P+85ic2bNan394tKGhkx6+w9bD/81wfM/tNBK/zkfTb+vw/Z5O6e77lklpY6CJ4/720HN2/WD9cEvp8k59KSrlFrq1+X4KCAjEYowX+xnkA1g5aeVcnAgK5VaamsCLq7V9/P2ay2PTnpnvp8l7GYF8oxoa7nWFrS9Ukm9Z309ek653K6P3fuVHByXRttP8NAKn3xolcev+GBD9nrv/ncuf0XvINSKBSKmtnnzOwX1oK6mVkul7vfzO43U/J0vfZ7rSOXE/0yM+P0SDLpfHR5+dVBHcnYyIjzm11dAsyTJ/W57dsV2ZSWKnJbG0kHj+HBB3UMd9+tB3RqShrkREKRxaZNemCy2dU9MScm3KZgLahnMrqBMO1qbJQ+HS60uVkPKpQJ3u2cK6qPYHVjfb0+Oz6u4wUEkQ+ydB8a0t9RlzQ2OvWCOqi52ft1FhXpuk9OetITX3Da1wHewbaAZgJrFB+ANWZc9CPlc0FZI5YHY2MCIDzjoSygaKJRp3PwoQc8UPdQTBaLOdBNTen8W1v1Hc7NqS5ieFgAumP8sL3tbw/Y4p8fstkbeiy7vceaDx6wvg8cssW9Pdbaqs+OjmrSn50V0N5225NlltAu1Ap0dGhiKVzzJAedRck3YLM8M6PfWbXS3IJk89SUkoyplM5n3z6/D6El5+a8wQz9V/Ger6jQvcWKc70G54TKCl3/xIT2v2WLVkm1teu3z2czqGYGyPv7PUnf0WH2w7HDtuOEmoSHrjO3vy7AHgqFikyg/he5XO7z67HN9Ry5nHenIdokKsHzZNs23ZR4WQdBc3hYS8yqKj2Ap07pyysv1yQxO6sHvavr6Rv9njypz+HYODVl9tWv6mHavVsPEY5/NTX+MEEF0HfTbLWWHouA5mYd09e+pge4ttaTltGoHtZz5zyJZeZqil27PEmIU+HAgI6tqkpAg+Mi3jF4qpeUeKl+WZlHJ6WlOibAFs0+DSWKi+170jciZhQteMoA4njVm+k9GK0VFAjQq6s9GReUJ7LP4WEdL/w1VsvZrNMuWA1TIcvyHmtdM2130ybtj+i9stLleidOaD8zM3r/9u1mPfNHbPaPD9n0th6Lj5lNNvXY8AcOWePAEWv//3pscVH+QGsTo7mcrhG0INE23wkTZnAsLOjv+BUtLen/8/MeHAA0dNpCOZRKaYUxN6eJff9+v0+yWc8d4I2/tOTfMSs/KnHXC9BJ8ALmmYyuL35CkYjoaxp1v9Bjfl73e2+vm7CZKQC66Sat7Ds7zYofusKp/+0V+uXO68vtP28qJhQKhczs02Y2ncvlfuFaPvNCyx0vXNDSFr4YBUIiIdDZuVM341q/chKV/f3utz04qCihuNg7wre0eMu5pwL10VGzL35REdJDD5kdPGj2la/oRr35ZgFDIqGblw5DZg6i+LCY+X5WVnRDxePa7uKieHM4eHqAVlaKMhoa0gOH/pwqyn37vHlEJKLjoJ1fU5N7g/OADQ87SFRUeIvAVEoTx/y8zgHfmJIS9zeh8nRxURPkyoov34MumVz/YLMQbBxQpdAzNciH0xe0uFjbpjMVNsJtbV69GqxuXVnxhCJe7rQVZJAcTae90KitzaPtgQGfcEpKRF+0tzvYEt2WlSkIoOUhFaP79ul8KJgicQ4NlEjo9Zoal7iauQ0x1BiVoUwE7JfE9Q036LP00y0s1H3U16djoiEH38HCgr478gHYHdNlitUOrQuf78DCOdiTNp3Wc0dlNK6RXV3ruyq4lmODXrl4UQGMmb6njRu1itu48SoePOukirlWKmY9gP02M/tXMztuZlcWqvYruVzun5/qMy8ksJPcLClxkyQiqspKl3Kt9SvPZvWlXbigm7aiwj3Pzdx3u6vLPbGfaiSTZn/3d3qYfuiHdCx/+qfa3223if9G1VBd7T4pJBYjEYFrcOJYXtaxLS4q+hoeFqiGQk9WyzzyiFdvRqPe0AGHyKBOH/qhstKrJeloND+vh4tGyPDZqFh6e7XtpiZP7tFvk6g3m9UDQT6CaBz+3MzBhhULqhcaWtMYOhJxkKatHZbA0EQjI26LECzioik2VNT0tEfpJBd5NMrK3FVxdlbXvrpaD/DyslYdQfvh6mqBJ92QZma8gXdLi67ZyZOyEAiFFFi0tXnPVqJfbKApEqqsdC1+KOTRLD8rK+4YGo+7NLOw0Hucch3R8I+OuqX09u3eqhHtN8fOREabP7pWRSLetu/5DAqqqG7le5+f1/UdHnaL4R07nl43v54Dj3mAfC29ApA3N18fpc/a8YJx7Llc7kEzewFO6dkPOgxxQ1A2PzEhMN6925tAXE0yiA68oMCX5/iJxGL6QgGWpxqZjPTjqZQcG+Gdi4vVF7SlxStTg6COHrys7MmgvrgoEE+ndXPhg11erkgGUIzHFRAsLnpEDEfa2KiIEs4aACKR1tTkUS/FK/39bk5VV+c6dBpHlJRoMigv98ibTksU8vT1uY8LCWZ+N1vdgg6AN3NzraYmfY7zwWOdqB1P9oEBr8KE98eXnomMlRu2vfG4jpEosbBQD2xjoxfZBHXqfX3umRMKCQxbWwWQZtr/2Jivwki4f/7znhjdtMm/14oKb7mHAiiRcJUPSijqBYjOsWpglUFClsK4G27Q+dIRiq5O3/62m9TdfLPXIoyP++SWTOqzDQ2r++wC6Ey+z2XQCzjYsJzJYnTU/WOofN62zesUrufA7gAwD9IrN96o77Gr6/md+/Uer1hLgWRSicrlZUVENGDGT33XLr9Rg5lzHvZz5zyBipc3oNbWtrro6OnGI494U4N3vctf/8mf1L/vf7/ZL/zCalBHhQIoBUF9YUHHZibQQSKJAgGpYV+fR2KRiB9rOq2bcu9e/Q4fC2/b1uaAy9Iev5CVFTf9qq7WtaUpR3W1uyfCj0NrJJO69nQ5IsKDt8YGwMwpkuJi53WRXVKwxXUCDJDfLS7q+8WKIGgjzPcc9HQPeuejzWdUV+taRKMCe5wUm5oEePSBraryjlldXa49R/pZVuYOoV/8oidGb7/d5bQVFV51a+bJzmRS311trWvXg5bHVL6SB2CfqKBuvNEbjHMfYBtBncOttzpdxGRIb1KabZOsp48u3aGeS4QKDQeYs0phZdjbq/t7eVnf6223uS/S9RpBeqW319sOlpV5RN7d7fmtl8N4RVoKpFJKIE5MCNS7u8Vj9vXpIdm376mbUMzO6sYnCvzMZ8x+9mdVyFNZqSgfB8JnGufPS/Gya5cKS8zc15wlM8t6Ej8rK24V0NKy+hjjcW0zHNZDeuKEt0BDe02DBYqOysv1cGOFsGuXIkq8SOBZSShisUtJeV+fAIMCpro63eDQVJmMJ0jp90kFJAk7ZGg0scD/PBRyi9xs1i0BiFhpdI1CB+4cpQzFRqg0+vsFwrQbrKpa7R9DchWpH17rVEWaaXs4PjIpMcGaeZ6gslLHOjCg17dt02cmJ11K2d6uYw5a6e7Z43JKchpMZkTpTDDkL6CaaCOYzfo54ycD5dLZuZpyMfNr19ureyad1vFu2+bfFZMJeQ3UV7he8t2RBH82g8IhVhiAOffs7KxWnVzLjg7RLQQ16z2C9Aq5BeiV9nYB+caNug9eTLnk1cYLLnd8qYxsVpH66Khu3M2bfVlVUyNQh6Nce9MkErrxMbqqqzP7oz9SVFNdreIMEpjPNKamdBw4Npq58oB9LS/rYQHU02m3CqC4hzE9rfMg0n38cb8RKalHNjgx4SBLYrCwUJNLS4sv12kU0dHhIEgSERfFeFzbAdQLCzW5jIx4ZSeTB23+4nHtY2DAfVoaG93ThOYZnAtgUlio/SM/RO2yNkonyjXT9RwedgUPXj/w+2arE7izs05xTEysttWtq9PKjkIjipeiUee5qcKdndX3UVGh4GFlRfcYib3GRk2w587pM/v3u14e9Qj7pU8uZlto/cvLnTvnOJE7zsy46RhS1b17PSnKpIik9sEHtY+WFjd+6+/3fZrpPOlRu7SkH/rWwvlf6+C7JnHMxE1epKhI1+/UKd0z9BbYvv3qevznO6BXwALqHmprnV7p7HxmX52Xy3hFAXsup+ior09f1J49TklUV+vhgmtdO5JJ0QpTU96SjQRfVZXZ61/vD+MzjeXl1Y6NaJFpq/b+9zuowxkiq6RqMUjz0CGoqEgPAXw6nCtNk48e9cpPKAcqKe+6S79jK1tSov20tOj1bNaX+mNjykWgdW9sdAOskyfdOz0W833hxU4jCJKPgEUi4bYM9C+FWyd5SrEYCiTALRx2qRuRN4nD/n6XMdLblFUOFaoFBV5xOT//5OYX0ah7BuHZzsSSySgKRyYZi4mGmZnRym3DBgdYzLr6+83+/u+17V279JqZtskEStSK6Rc1FSUlup4knVMpz4vQTGVkxL/nzZsVoWN6lkrpnDEw+/a39QxEIgKwSMRb/GHBC2VFtWki4aovGnhf6/NHYECTE3Ia1CAsLQnMz57V/6urVR1Kv9/1GqhoiMpHRvR6aalTK93dz86b/uU0XlFUzMGDAu/WVrM77jD7wAcUpUaj3pV97U364Q+b/fIvq6BkbEyf/ad/kjpp7bj3Xr3/6cbVHBtxz8tknEbA09vMZZXLyy5TZMBvFxZ6dV8spu2SDO3rk/4Y/xTAgarEu+/2LlDJpBsxYeXKUjked9VLKOSOjdGoF15kMl7ZCTWCffHQkK4hCpfWVjc2g24I0kKRiB58rAzKy51CCXrfE1ES6UGhXL7srfegRlB0BKmpuTkdHwoPaJfiYs8ZoBOnGAhgZHJqbtbvx4+7X4qZe6S3t+vzR47oeLu7BbqoR5gE02n36UdOCajTXpD2d2b6l2IpGoKTwAXQ+Xwk4tHumTNOu3R16Rzx+U+ltC8KyiIR5+5prP1MooDgCII5kzeTMtTaxIQTVZJXAAAgAElEQVQA/dIlHWt7u67heqlJgoIH1Cs0U2lvX61eeanRK89mvGByx+cyrgewnz+vyrMvfEHR6cyMgOVzn9PvT5X4CIWkJ5+Y0MOC/M/MC5WezSV67DHRJK97nT/8WMvCVwZBPWgVwEPGAGSxC1hZ0Y0Zi3kC8ORJAXsut9opkQbXPT2K9vH0bmlxz3QAFs6Z5BnNnmMxAUB/vyaVoiJvIcfnaUyCvzZcPPQFOnWWuNmstkM/UWgX+GSKpFCZMFnRHm95WefLBALvywqHbWNYNjurFcrk5OqeoxUVblCGyiRY1BT0bq+qEiD19ur9GzYIbJnkyspU1YzCZOdO199DJREd47UeBHUKs2hSDY1xNUDv7tY9CqCbuStpOKz3Pvqo7v9g03XoHIzX+B5J/NKQG0B/JrBNpRzM02n/jvn+WJH19+senZz0Fcb27c+t1+rakUyuVq8E6RWAvKvrlUOvmL3KOPbhYRX9mAnE43ElLc3U9/GpQB1Vxfi4+Pi9e1cvB59tJLHWsdHMtcXBEvcgeEMLoMs28weCTjxQDV1d7jg5MaGIDGdKKAqScHv26OfECfc+37DBuxRlMjoeqJeBAT3gaKWrqvT7mTP6PHa5VVXaVyKhfV+65EZqOCQij4Q6QeECp4/OHOBj24BhOOwVkih90JfTmKK4WOdChE6UTsQ6Pu5uicjViCSrq92DBjsEJg9WG1VVrrZ5/HHnp8vKvINUfb1XNFdVqSUd262qcvoq2Ed1asp15mZ6vabGA4iVFZ+MAPTiYi/tZ2Vh5v1gsXh4/HFdHwCUZiKLi3qtocFXeqhoSDRj0PV093w67WCeSrkBG3YR5DS4b86c8ZqIW27RMT0fvXs6rdUrQB6kV6BWnm3rv1fqeNkD+4c/bPaRj/jva3WulEQHaZS1n0F6eDWq5d57r+041jo2EvUh7SIqCyaGeMhjMS+sCVoE0IGopMQdJ3M5PbzHjzsnzcOFWuLWW7XNRx/V762t3qWI1QfWAIODvirAERHwunhRx1NXJ/AhmhseXh01FxRoJVFW5s5+cKtEbgD88rJ+p3FFNOqRIpYByAQ5J1q00XgCWgMwhMLAn3xiwrXY0C5UckL1AFDhsE9WfEf4nMzMiOLCxphJpLNT5//YY15hioKislKfh/aA8qCCmGpKjpn7le9jfFzfB2CM3SxOmMvLHqEjxT161KWtNClnm4WFXj1cWOhKmlDIJ5+nA3SqQEnimjmFhQ1D8H4+dUpRdDbrfjetrc+NbgnSK6hXoFfa2rQafSXQK9djvGKoGDPni5/q92v5zHMZODYmk6osBYDn5z2a5SFi0JyYxFUup+1QlTk+roeYSJtGB729ioTgaouLFaHQDOPWW/V/XPk2bRIoUzCEdG5y0qNtojkKTi5fFpAWFDgVUV6u88HnmtUO2ne01GY+2UBlwatzzEwSVVW+yiBKZ5tlZR7503EJMMxkXMZYUuLywbk5geLU1OqCF6gZpIMAPpw015HVVFGRrkFfnydz8USZm1NNgplAt63NK3prapxGwXkS+SqAzutBszL6xY6OenOS7m6tuIIROkZgTJZ9fZq843GnH4KTHSqfUMg7PEFDBQvz1g6qQBcXPb/BipDiMwaeQqdOaaLHS2f79ucWOQfpFewyzNxR9ZVIrzyb8aqiYl7MkcvJSTHo2GimB4IWZUTkDJpVRKN6+CjEuXDBHfPQh7e3e1enc+cUrfPglpbqhkeR8ZrXeBecujo9BEHZH5PN0JCAa2nJ7QqImE+f9sYTjY1mf/mXZj/3cwIdpGlmAsLOTm2bSYgEKZMIUj54dvxE4NNZlkMJ0ZiDcnai9JUVb8wBBw3I05cVO15AED6bhCwJQhpJ1NZ6sjXoc5LNSrExMuKTEN/RI4/o8xs22Pd6j5aXa1uFha4x57xGRnRcrBqKitzWOJVyI7WxMW23pET8/K5d7kiJqgnrW4qfvvtdr0zGPx3TMFZeZg7oSESDqqHgCK4uAfMg777W3G55Wffj6dNem3HzzcpzPZuKzExmtXoFuW9pqa7xHXdowmLlnR/XNl5RwL6WNrkWGuVaqZanGidP6obEsdFMkSnViuiCGTQvwCqAB+r8eW9SQCl4W5seqHPnvAeqmQNWTY0e3Joa8ZfIJTds0DI4HHYFBs23e3u1fxwkq6udKmCpi5Sxutrsj/9YieD+fpev1dZqeY38zsx5fgDdzLlv+OtoVJ8NKi5IoFZX64fIv7fXm3qg6CBSx7uHxDNROkVPhYXOP1dXu+0ykws8OJE8lFEqJYqL7li0bztzxhOj+/frMyUlXglL8pVzJ28B5ZLNOvVRWOgJZzzuAfQdO7xSNAjoGL7NzOh+6+/Xfrq73TOFiTgW0/6w60Utg0VzEJyRuLK/YBUoCqS1EwC9Q1FINTVJedbefm10Sy7nls69vVr9wde3t8tmY+NGv3/z47mNVxQV80KPoGPjm97kvHqwIUYwcQtFUlSkaNzMG0739vpDvnWrgHNpSUAD5w5lwWRBC73mZo/a29oEZqg6iJhHR31pS8IO6mVoyKtLUcNQVfm2t3neoaxMkwaVe+jyi4sdBOD5qSoFnNCmQ31BvRQWeqejYJQOl4yixMwrTVG8jI8LQPk7mv7CQrdowFwNugldfEWFK4iKirStxx93v5emJtfIV1W5rTOAjoUxOQMzb+RBwhM7BCpMyRWMjXlTko0bBeoYXnGdSYomk65Y6u3VudTWOgVEspt8BIBOMpnJxMyvPWB+tSrQq1WW5nKKqk+dcoquu1vHfS2RdDKpe5ikZ5BeCapXKELLj6ceeSrmOo9kUrYFFRWKMngYUGHU1q4G9ZUVfyiowsRzhOgnFhOAtLV5s+3eXoEAkTfNq4kga2td/05BCdLHUMi16RQcBamJXE7bn552SqaqyuwP/sDs/vv92AH2H/9xvYeqTEAR1cvyskfugGYs5tWbRK5Ul5aXa3uLiwK78+c9SoefxbURKWco5E1PAAj07sjtMLkaHdXxYCEcfE9pqXPrjz2m64OLYyIh2qWsTFpxKm7r6rzHKBWb8OZQb6ySkE9WVnpRzvi495DdsUM/UC5mDuhUoqK97+tzMyy6c9Fvlu87HndrBPxcggqUq1WBsmJ5qqpSmo+fPq1rUl6ulemWLU8PwpnMavUK9Aq5g9tvF5jn6ZXrN/LA/hxG0LHxbW9zTnFqSg8kTScYQasAPEcmJ71ggyz/li0COopLLl92b+6iIjeYwkiKyBpfDx422sJRVDQ97YU2JCwXF30ZXFurSYHy8/37PTL/lV8x+5u/0YMP5RH0oDHzyBQOGaqors47MpE4BcQ45nhc14YVC5MB1AC66+JigcvwsEspAWYUONAz09MeKdNsG4oBzXskou187Wu6Fs3NujbHj2t7O3a4Vw8Tg5mraSjmITFJMROUEZ42Fy86oMOHb93qhVno9Im4p6f1/RIIDA5qH62t3gu3ocHzDUgnKazCoIvvZW0VKHkBCoeuNubmBOa0KWxoEKDTeWzt4JoD5H19nldpa8vTKy/GyAP7cxjf/rYe1jvv9KgDy9dIZLVX9FqrgHBYn33sMUWptPT6+79XJPPII2a/8zsCV+gMerGiee/oEDDSNYgldFGR/r+0pEmht9cjx0jEXQQnJ72aFeqmoED8LXp2ipHMPDkJXw5QplIubSTBVlysCJ2JAnVKKLTaAhY658KF1Qoc3mfmUTq+JpOTntgDmIKqF7y8CwvdZwazLQANvfXRo9o39QEkMbu6dH1R2yATxBd9ZcXNygDipSWXQuK4OD2t402ltE98iyj9J7KurNR7Rkd9BZJICCAXFlwN0tbmbQlzOTfvosCLhueobPCHx3s+mEu42sjldJ+eOqV7Ixy273mfX80faXFxtfcKiqhYTGqePL3y4o51AfZQKPSnZvZ2MxvP5XK71mObL9XB0nTXLi0rzdx/BGdAlrXZrEArlXKnuqEh98GuqNCDs2WL9L5veIMelC9+UQUdqBK2bHEbYSIf5Grw0NAi8bgAa3hYD3ZRkevFw2FF6XQ+am42+7M/M3vnO938zEyA2Nio43/rW3Vu2BRgNUsUyL4Bu7Y27wIEhQQPXVkpoEomdXxnznh7MySbKF6geKamBLg4D7Ivos+KCp0nhUaVlU5XBUG/pETHOjGhbloUGZlp0mhq0rVlomxq0vbn531CASSZHKFeiotX2wBPTzvVtH277pPCQm0jk3G6aHFRIIpSJxSSImdiQvvZt0+TQbCRC01LyBvU1zsXTz6BKlCSoE8XJadSul9oiUcnp23bVltbBOmV3l7dx2baz4YNbq9LUVd+vLhjvSL2T5nZ75vZn63T9l6S42qOjahcaAIRlBaiemho0MN14YJKz5eX9UDu3avl7cSEPkNbOTMBQUuLwPfUKf2+Y4ceIpKUJADh38fGvFKUhzsaFZCgp06lFIEBCPfdp20GHRUrKwVO09Oq5I1EPKlG1SGJOzNPxuL0GHRMJJpFXojXPbJN3BTxGQHQSTRDq7AqQFKJ3S28MiCHHTMRKv8uLEh/3tfnDor4yO/f79YErDSYfKBYSALH454ToXfu4KA7RpK03LlT15UOTcvLPmkkEloZraz4dTx7VoAZDnuVaZCDXlzU98qKhPzN7OzqKlAKh55Ko85IJATm5845HXfHHd5q7mrqlSC98vrXayJsbc3TKy/FsS7AnsvlvhkKhbrWY1sv1XE1x8ZkUqBMh5tgsooqw9paPXDHjkl1kcno4bnpJiUpP/pR/8x73+v//5Vf0b9vepPZj/6oNMJtba5Jptk1UkaWxRTHABjl5e6VUlKiiQTflaNHtQ/kho2NTnvA/QZ1+Wy7osKVFpGIc7/I56AEcBqsqfFy8OPHvWFJa6veBzXBNtF/o3YhciT5WVKi7fH3qiqvDCU5iu7dTGBOmzwULKGQwBMDMHxjlpb0PozJ2NbystvcsnIZGNBxoi6JRt3+tbDQX8csDatgXquo0LGdOqVr1dEhW4Jg1Lu05Bw+4J3LucyURuLYHj8dmBNsnDolqs5M9yKt5paWNMEA5uyjulq5gY0bXb+fHy/tsW5yxyvA/k/XQsW83OSOV3NsXFz0JXcsttrUaGpKP1VVev2hhxRJFxSIf6QlXy4nsPvSl8ze/W6zP/kTgdd//I9mn/qUQKCpSdERcjmcAgsKnK89fVrROja4VKPiqgfd0dSkz//e75l9+tNPPs/v/35Fbewj6M/OCoCIHJ/u9nb3OjfTZ5gAiB7n57VaOXtW72tp8bL+VMpVGvG4W8qauVwT/3Z+J4omcQzVEswjYGUMd853VVoqmgFzLL6jYANlM5coZrP6LpGbIg9F0kqB0+bN3oCFc2JCQo3CpFhQoMnj5ElXUN12m64LA66cFRKrMjOXkUYizwzmZjo3vM9nZlxSu3mz9hFUr2AdvGGDSxHz9MpLZ7zk5I6hUOgeM7vHzKyjo+OF2u26jO9+VwB8660O6igzUJkw8Hj54z+WTPCf/1mfjUa15N++XQ92JqMH+1vfWl2ZSJHTxIQA6PbbvVsOqgcKYSYntQ1c7eCd8RWfnHS6o6ZGxz08LPB+3eu0v//wH1RdSm/Oqir9wOVCj0CDwJUHo/TlZVeBpFI6BiyBR0cVpY+MeJs4My/rR0mCxziUEBLKoHUA7pihkBdQ4TuPYyYdec6fdw47Htc26DGKDDHY+JomKNA3VMNCBeGFPzDgzS1iMW0P9QzJ5JIS97ghz8G1GhtzpUwkIr+TrVsdnEm8QrtAKwWLrq5WOHS1sbCggOLsWe/UtWeP9nH+vFxNoVewuu7u1v+vZyu6/Lj+4wUD9lwud7+Z3W+miP2F2u/zHf397ti4bZsvjSnRxuvEzDvDl5WZ/e7v6iGantZD/frX64Ex04P14IN66Gjc/I536H3Hjol+ueMOfT4e99J/PFGyWS/4gI4oKPAkKR4rcMalpZpsUF4E9dxmAr/iYlEBZu61AgAWFAigiNI7Orzi0kyv47lOJevyso6PBGljo1YMwQbMFNRMTTlgEyUHvXAKC73hBKob8guUyZeV6T3nzrliZHBQ22lsFO2Cfp1JanlZ15Zzw5ArmfQ+sDTzHhx0jX1dnQC9sdGPLZXy+wAKA4UUfWNHRjSxQgPdcIN7ntAsO7iyIGhgRXKtlZ0TE16hiidOJKJJCZ+bIL3S1bU6UZofL/+Rlzs+zcD+F8fG5WV/aJHQwavPz+vBpZuQmR7SjRsli6QgaHFRkdLgoF5LpwVM73ynKJWSEkX7LS0etUWjHkUuL7vhEgU/wUrL6Wl9Bi09VX9TUw4+VE0ODpq95S2K6OvqtE2ifxKmmYxH8s3NAmesYPk7vDr0zcyMovTLl71tG4lHwHJxUccUbKJB1EvpO/1XiSopzCGRGZxYh4cFaCsr3sGppES5DCJQlEFmqzsyBfeDNS1e7hMT7oZYU6PJnWR4KqX3B/XrBQVucjY7Kw49kfBq2uZmrdxqa321EHSipKkHJmHXmpjMZPQ9nzyp+5C+sgQhxcWiV+hWxIoqP16ZY1049lAo9Fkze4OZ1ZnZmJndm8vl/s9Tvf/lwLGvdWyk2pPKSoACpcjly2Z/+Idmn/jEk7f1oQ/Jk2ZiwuyrX9XDhtytokIP5fi4oru3v92dDelbWV7ukj6oF8rDiWCpVsxmPWqemBBYx+MeDRcWurVuJCKOnIiSSJGGD0G1Cc05SOJhkUuzCzoODQy4MqemRtHg0pLOB75+elq/kwwsLnZgxNwMugp+HbtdyuRJjs7MaILCSwWP7pYWb+pM8hJ3SyggriETZDqt6wXQAoqVlaLQkKwy2dGvlesRi2k/RN5YDExM6PrccIPAlVUAVcrkI/Dkv5ZGF4zFRdVEHD/ulBLH1NLijoh5euWVMV51HZTWc+RyZocPK+F099164GZmnBpAakgi7/Jlf+D7+gQmd93lnilm4jT/9V/dJwVL3uVlbXvTJrM3vtEnkEzGo7ZUyv2ol5ZcCROJKPJLpx0o0ZAPDnqz5q98xezHfkz74n1UMPb1OT1DP850WsdMCz7UMlQ3Et1SlYnx1enTikzxBa+t9cIeGmQHmzRUVDjtYuZcOtfSzB0widDh0plMia5HR90yYft2b4oRLGQyc+oqaP1bWKhtDQ6u7j8ajep7ARRZnQSPF6fKTEbHAF2DDDKdVh3Ctm16z/y8r1yYlOvqVvPmzwTqS0uiVI4e1STC8USj2hfqlTy98sobL7nk6ctp4Nj4mtesBvXycgcPONqhIeeKx8cVLe+6ogsiOjxyRA8hvuTJpEA0kdBD+prXSOZmpn1ls24jOz+v4iESoYBeba1AdWHBDbMqKwXmQ0MO4BUV6uH6lrd4sheah+YMKCyIQqncbGnxc0aiR5Qe5LWR0M3NaTubNnmxFBbF6K2DyUCsCIjSi4ud3sAcrLpa+8L6OJsVdzwz4/JBGlo0NEi6R4s9iocKCnSNoFpQt5SV6djPnfMiJJQrra2anJhYWUGhs8eNMplcnVCNRDRZzszoODD4mp72alCS5NXVqy1unwrQaY1IIRF1D6GQJoVdu7SfYCFTfry6Rx7Y14yREZX1d3Qo8kPmVlmph5iKxlRK700mBQoLC3pYeZDvvVdgcviwgCgScXCoq3Ov9jvv1GfSaX+NptsoSrAFoDilvd1BnMi+qMgBCmVKRYVz5oAJro2JhCcCcfyDq6+rE5dOToCol+pL/F8WFpQgvXRJx9/UpMkA/nx6Wv9iEQCgp1L+GhYFNABhUsOxEClpYaH7lzNZ4C2DhfHu3S4FpRI3lXKKIqgsmZoShRG0zsUThn1DfwWTmSRuZ2Z0vVEENTUp6j9xwjsfYS0R7DdaU7Paz8Xs6mA8M+MyxGBjk+JibXfnTnH1+ag8P6428lRMYCSTZn/3d3p43vpWATHJMAqD4J9HRrwpRjispXZnpz+kMzMqaJqe1oM8MeF+MVNTevjf+EY39gq2K8tmxVP/j/8hCoXVQUWF3l9Q4FFbdbVrkYnSYzGzBx6QXcDacffdZm9+s3P3qFNoGNHQ4MlVzL7wTEcKaKbzOnFC/zJpULGJnS7+IYBvOu32AvjalJZ6NF1c7FWxUBzl5Yr8kS3STpDjyGS8xyzRNJz9/Ly3D6RZdDyuyZJSfpp7kCeoqdH14PsuK9P1jMW81+z4uEsjGxt1rkePaoJobxcVwn0SLLLChIwRBPSlJUX6gDn2DlQWl5YqX7Fnj651PjJ/dY48x/4sRyYjj5bpaTk2UjRTU+NVlyg3RkZcaVJZKekaTaJzOUXEX/+62ec+Z/Zv/63eV1wsUB8fV8T45jd7tR9J2cpKgc2jj+p9P/VTZp/9rDc06OrypB7t2DDRgiJqaRG/SnFSKiUwv/9+BzksdPHirq7WeeIPk8kIgIJdgaANUimd+5kz2mcsJjBDgXH5sq8kkEsS+VO4RNQMoNMrFL09Da5TKbcVGB93pUtNjcs5b77ZGzTDo+PZwnaJsM+eFXguLOj9LS2+GmBCwGMebh8jsbExb55SWanvO5HQdzU76ysGDM4WFvw6fuITZr/+636vQdENDzuQDw56MpwkLSuvTZtEMeWbNOdHnmN/lgPHxjvucMCjFJ6mCIWFq+mR1lYpHVgOZ7NKaj36qB7QL3xBFYWU64+OCszf/GaPbgHpj3/c7N//e2nm8RUxEzht2SIgwVOdpOt3vrOaUunuFrCgY8eYyswtApAokhzEL51eovDnmYzACTvccFj7OnbMfc47OlynPTys46NqtKJC+yJZSrUqtNHCguvH6+s1cREZM3mi6pme1v47Olz9QueeoFfO3JwrgODmZ2aU4+jr09+R/TU3++qBClsztzCGPx8cdIqsslI/y8ui64aHdX1e+1qtGlIp7R/aJRbT33/jNwTsMzNef3Dpkks9W1q0DegmWs1t26bv/tXa3zM/nvvIA7u5Y+OOHV7ZSRn1woIe/I99zOxd7xIvm8tp6b9jx2pd9De+oXL9n/gJb2PX0iKQGBpSZPvGN+qhpxdlcbEe4v/+3/Ug/8M/mP3t3/qx/diP6d+f/mntv67OTbTQwHd1aZKBKpibcxpiZcU942mCXFDgmnCscqmYDBpy0VQ6FNL+kFrW1Gh/paXeRX5qSseJ22Q67S6EQS90eOuiIl0X7GhravS5mRnv6ETk39SkCWtwUL/fcIM4bCJ0lDdIL6urNRkcOaLJZnZW7+3s1OS3vOxVoUwMDQ36KSsTOJ8/74Zs0ahez2R07Xt79fqePVqtZTJeP1BU5C3zzHQeZma///veLxb5JOX6gD3FVLfconslb66VH891vOqpmMlJRdZ1dVKn4ERo5s6BdKP5y78UQN5yi5f+mwkAvvpVAdG73331/bzrXWaf/KQX8JCUjEQUpb/2tfKjee1rBSTJpP597DGBEEocutKHw4o6sXVNJt2jZmnJLXAZFDJhkQvdgVSOiH1x0T1UaBR9/LjopVxO+2xu1v76+wWcdBEi6UuSmPZ8NJHA6pcGGE1Nuu5VVS4bpRcoNE9Xl8s3S0v1HTU3O90BoLP6oOHD0JBTXA0Nuk7hsDs20gi8tdV9zqF8WHWgfw+HdU6AfUuLKKDSUn03JJ4xXQuFZCfxa7/25Pvgl37J7Dd/U8d36pSOJxwWyG/fvrpBS37kx9qRp2KuYSwvq4NOcbEsdKFfACdoifPn9f5IRN4t2Knilkc3JVQQX/iCIsotW7wZ9K5dbigF1fLbv61InfGWt+jfD3zA7D//Z/3/4x83+y//xbnYdFoAsnmzR+l4luPtQmINYC8q8gg5GtU5ok7BpxxqBFMsM23z0UddxtjZqX+HhnQsKG7oq0lVKZJCeqouLbnuva5OkyK9VT/xCbXcGxwU/QINsWWLA/X4uD53yy1ue8u+yss9gfzII94yLxzWxIGbJa8XFQmYu7pc8z85qX0kk54DQMFDM/GhIZ37G96gSYmm22j5KSxifOQj+iFXQyL1wgUl6ONx7ePGG3Wv5B0T82M9x6s2YsexcWhIwFtT4wlQSt7/5/8UP7p23Huvfs6cMXv4YRl9ff7zV99PX5/AheV6KqXJAk078kmKluJxpyM+/Wm5PP7+7ztX3tEhIKiudo917GgLC72DDxQIiUqcD7HhDYU8iYqckpZr6bSaUeBF09IiMJ6f90YQwSbNJJepxMRugW2bub1vS4s3lZ6c1IR6333Of3d1KSIvKxPlMTenSWzzZt8PScnKSv29t1eRLyqmujqBbyTi1zMU0mvbt/sKYWxMP0TcVLZSfTswIOVPLucNUWg1R2IWvTzjamqVUEhmbxcueACwY4fONU+35MezGfmI/RnGd7+rpf/u3QJ1ovBMxrnSX/91VzNgH8t7Hn5YnHNTk2SFn/ucV5X+yZ8IHI4dc1DH6ApTLboBFRb6dimJn5kR6L797QL26Wl9bscOAWxxsUCxr8+bPdPFJ6gPp8cpBTV0P6IL0Py8jg1qxkzH+e1va59Y3EYiq/XUhYUuC0wkvLCJKJ3mEkGnx/Z2rTBiMS+66u/XPuNxb0lXXa1tnTih7d94o7ZJX08APR7Xdzg87LkK8hno14eH9Zm6Oum+YzFdn3PnNDkhIW1qch4d//pvfEP7aGkRj57Nuvd+VdVq3xmzJwN6sNXcD/yAJsSg93l+5Mf1HK/KiL2/X2X2ra0CDpQYZt6+bO2DC7AvLYl6GR5W9IeaIZMR0Ozfr+Tn3XcLEFMpAQVukGyTvqGZjADkox81+5Ef0fs/+1lROGvHz/+82cGDivymptymN5NxegKpHsnIoJthYaH72+Al3tCglckHPygu/fRpnWNjo67P3JyAMOibQis2bHopCMK6l65JGFp1dXnHpr4+Reh/8RdPPr/3vc/swAEdQySiSYXrRLu8eFzboDgMLTk6eXxSoNE6O3UM09NuGWDmSiUcH6lOffxxRerRqJK0FRWrk6iVlU+OsifdcgUAACAASURBVIOgnk57hejsrLa9davOBe19fuTHcx15HftTjLk5NY4uLpaVLnwzVAh69WA3JJJhP//zSpLOzwvQd+4U2GHDix/Mpz7lGvDpaS/tx0edhBzmWDMzmig+/WklX2kOXFCg38+cEYANDGhSQvJIcwqi5rIyd3UMNpgO2vQSSROlFxcLfP7mb7QKoMF1WZknR6FdyspcvoirYWGhuxDSMaisTMfQ3a1tRaPuXUO3KTTjN92kv5WVuYSwsVGfDR7/3JyOh+5GkYg3tsDbhabeVHjW1ur6ENVjldDU5I2dAemzZzWxmWnCbmtbTSPhoxMcQUCfn/dWcysrbidAe7z8yI/1GHkq5iojlRIwp9PSl8dietiJnJeXPdHI4OH96Z+W22NBgaLxtjbnkB94QICze7fZPfd4efzMjHOxZm5yhV3r4qJTLyUlZv/3/8oeeGVF4Eez7HRa0r1Ewrnw5WWvwkSeiVwPkMPkikkgkfDkYTSqbZMYnpjwKHZ2VpNJPO70BKX52aw3BiGazmbd1Kq8XFFyV5cAFDkknaZoPh1MNmcyZv/yL7qWW7bos7SAm5wU8I+NOaDv2aO/4aBIwVBRkRt+LS2pGjSd1me2bPGetGjXQyFPECcSWqFs2eKVpwD6WmAOJqfHxkS3DAzotc5O0S0NDfnq0Px48carBthzObNvflNAccstWp5jEAVAQ20wWNI//rhkhzU1aoKBNHBuzm14b7tNEZqZN3oAVGnATGIykXB3QoqfLl3yfW7d6u6EP/VTAh4zX11MT7v1bmmpwLi52WWHtEvDL4akY2Wl9/j8yEdWK3Le8x79+/3fr9VINuue4UTpgDqTXy7n1aTRqN6/ebMXEp06pc8ib8QiNxZzWd+73qXkc3m59tvUpOMdHfUof2lJ29+3z5t2r6wIdPG/QbefSrm1MNx+LOb7RqWC3e3goK7RzTc7nYM1cOGapwOgzmS81dz0tL6/XbsU6Qe7aeVHfrxY41VDxRw7pt6jW7d6xSJLa3pv4ldu5iXdX/+6QHfDBlE3hYXe4uxrX9NDftdd3n0IaoRm0mbu4Q71Eo9LzRIKKen6e7/35OO95x61TQPUKircXCseF1DFYtovXuhEoSQYoTvMBKzkDWjhNj4uYLvrLrM//3P9vrTkypD5ee8vauagiCFZKKTzokhqyxYdy+XLTuvgUW7mBmNmAsTvfEfA3dqq3EQ2qxUMTaKRhW7cqHNCY46PfDSqaz0z486MZWWKlpubvblJ0H/dTJTJyZP6P52QWOVQsxAcfG5tq7lYTNF5d/eTJ4H8yI/rMfJUTGC8970CnYYGd8TjYYVzpsu7mf6WSEgOOT0tHviGG1a3pfvGN/SZ7/s+jz5nZtyHJBipU46/uOieI+XlArR77lEjDzNppGn6jE1vU5P+RjcfnAhbWgTqUEhmbolbXa3Xk0lvz0ZZ+vKyjuPSJZcImum48GmnUXcupx+klCSJaa5cWiqg3rJFFMTUlI4/2HwDKqquzlc5Y2OaaFdWlLxub9dkMDDgFZwVFYr+6WE6Pq5z6OzUtjMZce6JhJfvNzbqB7qLCJ3vYXhYUXoioevX2bnahjfouMh9kMtp36dOKWmby+l4d+7Ud5OnW/LjpTjWBdhDodDdZvZxMysws0/mcrnfXI/trsdIJMz+1/8Sf33XXc4tmzkoIhc004M6PKxoPJ0W9dLZ6bzy0aMCh7o6ce20rJueFuiWlXmxSrAH5tKSovRk0j1RRkZ0fDTMMBOXnk4LaCIRb1AR5JO3bHEvEyJqeqIiBcxmNZHBEWezOobpaZf7QQm96U1+XeJxLzKCimJlQ4MMOhp1dkrtkUopAub8WS2Ul+sYslmdQyqlFcL585oUbrlF+3voIbfHxc+9vFzHNjam80OSihwR/5jmZm+sjXQUzxu+g4UF0VnDw/r83r0uA8U2Ye3CNZsVkJ86pUm2qEjR+fbtXguQH/nxUh3PG9hDoVCBmf2Bmb3JzAbN7EgoFPrHXC536vlu+/kOHBvNZLwVdMeDOzZzX49QSAD1rW8J6N76VoEJS/kHHxQodnVpkiCChTagNynql1TKy94HBx1sCwpcbVJbq9dPnVLkXlioSeNTn9LvtE9DrbJtm46VFQCFNfX12t7srNMR0E0UXPX1KaLG0gAb4ne+048TiwGidTTh2azLJSn0qalRlE3pPg0usAAOhbyXZzYrCgTVS12dVCg0b66oEKWBwRmTYVGRtlVb69a2mYz2tWmTtwU0c2dKM5enHj+ua5vLiU5raVFETzES58lYWtKK6cwZXaOqKlF3NA/Jj/x4OYz1iNj3m9mFXC7Xa2YWCoX+ysx+0MxeVGD/8IeVIGS0turfe+/V3xYXXcZHq7mHHxb4NDeL3yaRmkq5dn3PHj3odDLCGhdvFbjcZFIgMTmpqLOwUNudn/dKR6ov0bm/+90Cj0RCOu+bbhLoRaMC0qYmHffkpMAaq1u45mzWnQlJbhKlnzihyWVhwX3WAW2AHgB+4AFNXJy7mcCwoUHg2N2tYzh+XNeADkelpS61RPdeVKT3HDmi6LyhQfs6dszrBVpbdS70AmXCJfmZTrtkMRoVRRNUnTDxBlcXQ0OqK2CfGze6ygU9eRDQp6c1qV+6pO20topuaWnJ0y358fIb6wHsrWZ2OfD7oJndsvZNoVDoHjO7x8ysg0zjdRwf/rB+tO/VDzHJw5ISAU8yKepldFTL7f37XeOcSJh96UtPVr6srAjUoQkAUjPv2DM46FRLZaW3hyOROjHhqpGyMm1zetqLaHI5Acvu3XrP2Ji2QXl8Y6MXOOHjHWwEnUx6sQxe4iUlXt05P+8JUqgmM+UPenr899paj9LDYUW0S0uuyIlGtU1a+bEfyvKhl8rKvBo0EnFAZ2UTbI4NoE5M6PxKS7X/oOvh1Xj0+Xntb3hYn9m7143G1ipWslkd36lT4tELC5Vcx3YgP/Lj5TpesORpLpe738zuN5Mq5oXa79qxVto4OSnJ4sKCNORbtzqVMjamCtVMRrRMe7u2gTrFTKDBxJFOe1n/wICAqq7Omz3T3X5uzhtMVFf7BPKZz0glw3jf+/Tve96jhh1zc4qO29oEPLgowtlT+EQ5Pa6MyaT+htYbT3OqR4OgHizCoeUbPu+0pSPJGot5w+3FRU8cV1XpenznO6KusFqYm9P7KVpKp73SN2i5Gw5rAlteFli3t6/W3l8N0DMZ5T+CtEtnpxufBcfSkls1J5O6pvv3ayWwNoGaH/nxchzrAexDZtYe+L3tymsvmXHvvfoXq1eSjRcvStteWCjgbmrySP3CBUkdg8oXePnp6dX2vlAeqZQiv6EhLyRKpwWky8sOisECInqdZrNyOfx3/07//5Ef8W5Ely8LFJubnVLCY5wq0WD3IKooMb/CfZBORlA58NFmug4PPOC/s9p597s12Z0/7xLL+nqv8iTaBtDDYW3/gQfc9qCoSH9va/OOSnD5FDmhHkK2iIyyomJ1YjQoX0Teefmy2xk3Nup46+pcmcSYmRHw9/bq3JubpZ1vb8/TLfnxyhrPW8ceCoUKzeycmd1lAvQjZvbOXC538qk+82JZCiwuunLj2DEVHtXViU8O+rh897tPVr5QLUrHo5oaBygsZAcGvFqTCkscG6EngrQQ0T3AhrlWa6s44a9/XcCObruuzqP0YLVlQYFH6Y8/rgTjyop7lFPFibUvvDkDKwIzgebBg2rCXVKiSYzEcFOTjgU5IefExLKyIhrk+HH3PMcvhpULg2u6tOSdlHCiRJFDL1KOay2gx+NaFWCpC1WDnwsTweXL4s/HxnStNm4U5YbxW37kx8tlvGA69lwulw6FQj9nZl82yR3/9OlA/cUaLPtDIQFmf78ohttvX91d6JvffLLyJZv1rkS4FdKUgoRff7+2T3Xo0pI+g5YctQceK4A9+4b2aGnRZ378x92HnCYRqE9wIyRKn5iQiuPkSe2zsFDbgbtPJNwJMjhwKqTiEp7ezJUpdB4KmmVlMtpucbHZb/2W2S/+oiL6I0fcG4fuSC0tfg3NHNCD16a+Xue5suLRf2Oj5y2uRrs88YSibzM32ULaSUXsuXOiW7AHeM1rdC3z3uf58Uof68Kx53K5fzazf16PbV2PgffH/Lwki4mEFCf79gkIQiEB8Ve/ulr5YiYQobKxvNyTfYD6xIT06GYCKCL7mRkBWmur2wgQoeLCWFrqvuidnYpQL17UJHHggAqQ2ts1CaDxrqtzD/eFBa0Sjh9XVIotcHOz2V//tdnP/IwopclJ/e3wYU+KlpWtXnVgN5DNqh3f4qL2FYu5sRZVrRR4rayoG9C2bYqaKcffskUcd2mpU1SRiLYxNqZrUVKi82tu1rUYH3c/maCFMqsbvqfeXkXp9Jzdt0/HCVUzOyvAv3BBn29sFH/e0ZH3Ps+PV894VVSe0mz54YcFDnfdJeDhQZ+bk/IlHlcEv2OHa6JJ4kWj+llacr338LAAvLjYPVlmZlxnXVsrnjmZdOoA+sLMbXNpuPDYY4p4o1F5j0CFhMMCXRp0pNMC9HPn9EP15YYNrqX/q78SoNGgw8zVLnV12vbSkgAXzTvJ1J/5GR07tr9UtEIlraxoAqIsf2BAx7h1q/ZJT1dWONGoJhdyE3iv0/0JeouOUETpZp7Inp5WfcHYmCah17/eK0ezWU1sp05pgiko0Gpsx458q7n8eHWOVzSwf/jDZr/8y+LTjx4VPfCmN3nxjJmi7a9+VYCGa2Mm45E6fHZ5uQAUeeDAgKJawHZy0vn7DRuc885mvYyfJCKR7YYN2t/4uI5veVmAt3mzonH8vLG5DYe1QhgYEMVAlFtdLZArLdX2T5/WuQHqwUi9u9vb4MVioi9YUbCvigqneuDU0eb396ux91//tV/nD31I//7iL0qaOTPjBmSJhMCWUnx8X5CDYuZF83CidJLY8PZnz+p49u3zSW9lRZPL6dNPbjVH0Vl+5MercbyiTcBCIVWe9vUJMO+8c3Wzg/Pn3fPl7ru9K1A6rQgxmxVoFhQIrEiEjox4f9DFRa8MbW7Wa6OjDp54sZSXu6yP5spVVQL0vj4B1c6d3r8TfXxlpSaE+XlFpRcvrpYwUlJfXKwGFp/+9LVdmx/7Mf1gYVtT452BIpHVgL6wIGpjcFDXgO5LiYSkmMPDirqx7qWDEj1Y6+q8QAi6hOid1UKwApSV1KlTSgYvL2tCuvlmTRbxuP52/rwmUDokdXXlvc/z45U9XvUmYDRa7utTFHnrrasLW9YqX+hEhEWAmSLadFrReDarCHliwvlxilrq6gSuCwuKaOHg8XcvK9PvJSUCn89+VlHnAw8IpOrrVUhDlWhxsV7jmPr6VBHZ1+c+MLGYdyb63/9b7dduu02Tymtfq9XKb/+23vOjP2r2R39k9p/+//bOPTbO8krjz/E1CYmd+EKcm51gnCsOSXBCyAUKJYKyXRYCK4EK6kLLRcrSRSvKAmmbi9RWq5VW2+yqu0QsK1Ro2Zbdtohuu4CAammBQoAKSkiInTh2Mr7HnvH4OjPv/vHk6B07jjPEjr/x+PykaGzPePx+H+h5zzzvuTwI/PjHPtpNjpY133vmTO/9RyI8lG1s9GX/JSX8XoS9XgD+TW1L3N/P99VhHvPn+2pUTQdVC0hrANR20WyXEyc4dOPUKf7utm30ykMhju1raODrFi/mfbRRc4YxlIwT9uGtBHbs4KO2Ehie+XLttb5J1sAAo0mAwqlNsgYHKTY6cFmtFe0Hnp3tq0LjcV+2X1BAQYxGKZ4rV1Kgvv99WgrOMUWvosJvHjrZKNl2qavzaYf5+RS7lSv9oIinn2b3yZ4edqS86ipewze/6e/Dgw/y8Wc/A7Zv98JaXOwHYOTlsUf7N77BFgShkN9EFi3idRw+TOGvrOT7PfCA990Bfxis7Q40AyUc5jVqcZNG79qCQQuY3n2Xm+P06dyoKit5/W+95S2eyy/nfbNRc4YxMhkp7Lt3+97hyU5Tfz8rSTXzZcMGLy7Joj5zpvfXIxFGiL29voK0oICCXlTkDwV7e32evLbtDYe5hqoqZo6IcFMBKKL695ubGdlrS4Dubm4kR45QtK+7zjf7qqigh9zczOtoa+P7dXX5op/Vq4FHH6WwNzTQd37mGVa13n47hXX+fG+/qH/f1gbs3cu1Okdhrqjg/fj4Y65JNzO9r1/7mp/nqumIs2fzvbWfTkuLn0+q+ezJgt7X5+etxuO+i2JtLfDTn/K/W1GRF3qzWwxjdDJO2IEzW7ACQzNftmzx4gVQkDs7/ZxQjbybmrwoARTdqioKsHYa7O72+dfqi8di3BgKCxlJl5ZSMPfu9eu59VY+7tgBPPEEo+LBQb5nfT0j9cFB4KWXONVIR8LNmsWoef9+Rt/Kt77lv96+nY/Nzb6ZVyzGbJeKCq5fW+uq/XHkCO0PgL59ZSXvRXc357iGw8yfLynx1onOFhWh+OblcTPQrJ9olJ86NOrXwSMiPsqvr+c5QyTC96+qotXzi1/wteXlFHrrfW4YqZNxwp788V5bCYRCjNQTCeCGGxitaifA7m5fiJOf77Ne6ut91okWDy1dymixqYk+vProGo0WFHADSSQojNXVXjz1k4Tmwx886Ac75+b61gF1df4wVguQXn8d2LePEbqeOY9WNXngAKPdtjYK5m230b5YuNA360qOeofbV5pBc9993kevqOA1Zmf7tsCajplIeJ9ePXP92/pJRFveqtfe2soo/eRJblrLlvF33nyT92zVKut9bhjnS0ZlxSSLukZ3mvkyY8bQnuwiFKVolEKSk0ORbmtj1Nzezp8VF/OATrNVGht9WX806qPRrCxG6TNnMkqfP3/oYa32aWlupugfP04x1CybujqKXVYWI+Tnnjvz+rZvB+69l9bK3Ln+/bXASv3sH/6Q69N2v5de6rN7RirS0UrN3l6uSXuvhEIUcW06NmuWT4dsb/dVopqOCXAdzc0+TVTvjYjvi3P4MDcePVPo6fEHuStX8v7o3FbDMDxTMitG9yjtx/L++xSo0lJmVmi2RyLhx8zpMArtyHj0KAWuoMC3cO3tpaCHQn5YcjQKvPgi0/20iGnRIopu8qGeFtvoAGqA/ve0adxAjh2jdx2PUyBrauhb/+hHfrgFwIKjykpG3skDH9QW+fBDPm7bxvdavpwHtEVFvmpzJJKraHXE3ssv8/pKS5lrr217NS+9sZHXpb1c9H7rNWrbg+T73dXF6/z0U3/2kEjw3i1cSEGfN2/opmwYxvmRMcKeLOrxOKP0zz5j5svVV3sx7O+n+AwM+Ai3vZ2CEwr5Cs6aGgpZWxuwcyftDOd8v/HZs4EXXuDP8/KYY62ZIroejYRbWymUatd8/et+qIMWOa1Zw40kN5fXMNweueMOPmp2D0BRfuQRfq0tEF55hf++8x2K/NlEUkfl6YFvOMxPDTfeyJ9ppD93Ltetlba9vb6QSe/pwACjdB28XVzshTscpuAfOuTPDXJz/XnFihVDvXfDMMZORlgxyRbMwABT/kIhetw1NT5qHBz0B6Namn/iBDM++vooSOvXsximr48+e309cNNNPMwLhxlBL1lCsb75Zoroxo1De35rlN7Z6acjFRZ6m6K2lptLfj59+5qaoQO2k9m5E/je9848ENaeKKGQz6XfsoXXpNbH2e6V2kjRKCNptZ+6umidbNrETx/aFTIc9rn9xcUUYo3Su7qG9qbXYRaRCH+vtpabZk8Pr7esjNF5VZXfGEzQDSM1powVkyzq4TDw619TVDZtYgSsrV6170ss5ift6Li4nBxuAldeSfE5dYoRZkuLF51IhFH6G29wRqiybRsfNZJW4Wxu9tWhubmMduvrefAKMNtj0yafVXI2vvtdCrsSi/mpSIODtEuWLfNdGUdLBdSpSppT3tFBYW5p4XOXX841qeAmFxRNn86/pc/FYv4a9TBVD6MjEV7rRx/56U7LlvkDXL1eE3TDuDBMemFXmpr8tKPrr6dfq32943EKWH8/s0vuvJP9Y3p7KVZbt/rZmseOMcJ85hnmUCt3383HXbvO9PIBH6WHw4zm43HaDdEoPxXU1/v+LFdeySyTVLsN6qaxYwfPDDo7+QmhuppWk/rwmgU0HO0q2dXlUzi1D3pHB6PsrVu52ejru7p8C97SUm+XAP4aEwk/0EKj/+PHuWF2dnITWL2a15ucxWOCbhgXlkltxWi0fuQIC3+mTWPeth7oZWd78YpGGYFWVwM/+AGf0yKl/HxGnh9/zIyQvDz65YsX++6GI90mFXZtfdva6qck6ffHjvm5p6tXM2od7TBzJHQ+609+ws2gspLpgKn0FVf7qaGBoq69XrR1wsUX08JRK2lggMLf389DYJ1eBPB3mpt918bSUt9yQTdEtatWrBg6EDz5nhmGcX5MiBUjIn8JYDeAFQA2OOcmbCySRsgffMC87aIiVmhqrrUOu2hp8Qd4tbX83aIi4Atf8BWUTU18n0iEQqftXkfzqgEfvUciFHEdN6dWhKZMrljBMv+z+ejn4s03+VhayqybVCb/6KeH2lp+YtD0x0suoS8fDjNz5oor/MbV2enH6WlaoxKN8j7F475He3297x8fjTJCX76c/x2Gzxk1QTeMiWOsVszHALYDeHIc1vK5iMUYpX/2GW2UzZspNjqEQvPDm5rYAOv55/3vqq3y7W8zN/zwYYrbihU8zNShEspIFodzrPbUcXP9/fx34oQfvDFvHj3ruXPPT9iGZ8Zcf71fj2bGDH/97t389HHwoM9C0fzwadPYiyUW44HvkiX8Pc3c6e/3E43Uq4/H+Zx65bNne0HXzSwnh59uNm/mNSdjgm4YE8+4WDEi8gaAR1KN2MdixWiP9d/8hgK6YgWzSvLzfVFLWxvtGe06WFbmWwgUFlIYH37YdxCcM4eRa1FRar63DrVuaaEtEY3yE8GJExS6ggJm1yxdOn5Te5L9/NFe8957vsNkYSEPLRcu5Ob10UeMpLdu5XPO8fo197ykxEfaeo1PPEFvPzubB8BHj/rBIQCj+tWreX+TD25N0A1j/Em7rBgRuR/A/QBQrqd058GePRTMcJj++KpVvm/4rl3APffQK49GfZ/usrIz32PVKorX8uX8OrnoZzTUm+7ooHURiVDwIhFaLWvXcqPRSsyJQAdOABTwoiJueAsXUuB//3uusbyc9yw3lzaVRtyzZvncc71GLTbat48VuydP8uc6hAPg+61b51McARN0w0gHzinsIvIqgLIRntrpnPtlqn/IObcfwH6AEXvKK0yisZGP0SgPSSsrfUQ8MOA7E+bm8pCyqurM9L9772XHxGnTaEd8nl7eGqWrsLe3ex+9stJnf1wIcTtbxstwu0ZTMXftAh56iP58Xx83m0sv5XPt7UMHY6sw67SnlhY+r5tFYyM3CYA/LyzkJxyzXQwjPZkUVsxw8VKSc8dffBG45RYOr1i//szDu3O9x2hoSwBtlZuc7ldaStFcvDhYYTt1yg+ndo5nDx98wE8RmzczItfDZO3jogfEyQVVp05xcMe+fWf+jdtu4+a5bNlQi8kE3TAmhlStmEkh7Eosxmg8ecnnI9ip+NVKfz+9/IYGH8n29FAYq6vpL+dMmKE1Olp5+847XO/8+fxUkpvri5FycpjxMn26F3TttqgpjhdfzGi+oYH59s8+y41rzZqhfXBM0A1jYpkQYReRWwH8M4BSAJ0APnTO3XCu3xvL4eloopyqYKf6uo4OP+uzq8tXkl5yCb3qdGsp+9hjzEnv7uaGow3MWlv9jFY9IE4k+K+7m9aMiG/qFQ777o533cVHrWwFTNANIygm5PDUOfdzAD8fy3t8Xs7mNY/newwOMp1v7142xdIhGmVl9NHVb04njh7lQWYsxjzykhJfMJWbCyxYwHMFHdadSPjWu9rUKyuL9s2nnzJiX7eOKaEq6ibohjE5SBMTIXVG88NTFf3RcsBbWjjRp6WFlZ6bNvke69XV45e+OF7E44yu6+oozps2UbSPH/ddKIuK/Gu1vUBbG7/XARkNDWxz3NND22XtWto1e/aYoBvGZGPSCftonOsQdDT27AG+9CWWxmsVJsDCno0b03NwciTCrJfOTq5z5UraR93dfupTfr5vhAbwcDQcZhRfVkZf/bXXeDA8Zw4PWpMzhUzUDWPykVHCfr4cOcLH2lp2h3z2Wf+czgxNJXtmImlo4CFpVhZwzTU8zNWBHXPm+ElR8TgfBwcZpWsBVUEB8/0PHaLI19QwPdQ6LxrG5GdKC/vwjJqvfIWPKuKfJ3tmokgkOC3p0CEedm7cSPukuZnR+bx5FGqdrKTtjDs6fN56SwvH7/X28iB47Vo/gNoE3TAmP5O6u+N4od0Th9+KdBP2nh7gd79j5L10KQuOOjq4xjlzfJsA7U+vfV76+liElJNDH721la9fv56HrIAJumFMBtKupUA6c7by//HIwBkvQiHgrbco1hs3MpOlrY2PJSUU7UTCtyuORPi8CEW8tpbtBvLymKpZWWnzRQ0jUzFhP81IIp4OnrpzbN71ySf0xdes4YFnby8zWpJz6bWKtKmJ0b0O+njtNUbtVVVstaC9dQzDyExM2E+TDiI+nL4+NvBqbmbDrfJyCvr06UObdmVl8V806lsdZGVxQ2hv52uvvdanPZqoG0ZmY8KeprS20k8fGGD3yYsuYmFRcbHvgyPio/SWFj+9qamJBUv5+b7vutkuhjF1MGFPM5xj5ecf/8jIvLqavnhylK6CLsKovrmZ6Yw6MWlggIerq1efOTTEMIzMx4Q9jRgYAN5+m/noJSVswJWTQwtl5syhgu6cb78bjbLStLOTxUUbNjCP3QTdMKYmJuxpQkcHq0ijUXrpc+ey2rWoiOKuPjrADUCHSjc20nqZMYNVoxUV6df2wDCMicWEPWCco31y4AAFedky5qOXlNBX1whdo/SuLqYxhkKM0gG2GIUg0AAABSVJREFUElDLxjAMw4Q9QGIxDpeuq6PVUlVFC6W42EfpaqfEYjwgDYX4+r4+VpGuX8+NwGwXwzAUE/aA6Oqi9dLezoEYS5b4YdLJgg4w2+XECU5Fam9nPvvVVwOLFpntYhjGmYxJ2EXkHwD8OYABALUA7nHOdY7HwjKZY8d4SDo4yBmtixbRS8/NHSrU8Ti99EOH+Ds6y/Wyy1Ifvm0YxtRjrBH7KwAed87FROTvATwO4O/GvqzMJB6nl37wINMXr7iCQzs04yU5Su/pYdrjwYM8LC0vZwfGwsLg1m8YxuRgrBOUXk769m0At49tOZlLdzfw298yg2XBAuaYl5bSS08W9ESCtsuBA75Z19atjOrNRzcMIxXG02O/F8B/juP7ZQwNDRT1wUHaKFpJOlyoe3qAP/yBWTLZ2TwYveyy9BmWbRjG5OCckiEirwIoG+Gpnc65X55+zU4AMQDPjfI+9wO4HwDKy8vPa7GTjV27gJtu4kCLGTM4tq68/Eyh3rULuPNOjrjr7eVouo0b029YtmEYk4Mx92MXkb8C8ACALzrnelL5nXTrx34h6O6mMO/fTx99y5aRhfrUKR6cPvkks102b6btYhiGMZwJ6ccuIjcCeBTANamK+lTg5Eng1Vf5dU0NM1lGSksMhYBf/Ypfr10LrFvnOzYahmGcL2PNgv4XALMAvCIiH4rIv43DmiY1u3fzcPSrX+X3KtbD2wLv3s389fvu4/cbNtCiScf2wYZhTC5sNN4FJNXReuk2gs8wjPQkVSvG6hYNwzAyDBP2C0iqM1PTabaqYRiTH7NiDMMwJglmxRiGYUxRTNgNwzAyDBN2wzCMDMOE3TAMI8MwYTcMw8gwAsmKEZFWAPUT/ofTlxIAbUEvIk2xezMydl9GJtPvS4VzrvRcLwpE2I2hiMh7qaQwTUXs3oyM3ZeRsftCzIoxDMPIMEzYDcMwMgwT9vRgf9ALSGPs3oyM3ZeRsfsC89gNwzAyDovYDcMwMgwTdsMwjAzDhD1gRORGETkkIkdE5LGg15MOiMgiEXldRD4RkT+JyN8EvaZ0QkSyReQDEXkp6LWkCyIyW0ReEJFPReSgiFwV9JqCxDz2ABGRbACHAWwD0AjgXQB3Ouc+CXRhASMi8wDMc869LyKzABwAcMtUvy+KiPwtgBoABc65Lwe9nnRARJ4B8H/OuadEJA/ADOdcZ9DrCgqL2INlA4Ajzrk659wAgOcB/EXAawoc51zIOff+6a8jAA4CWBDsqtIDEVkI4M8APBX0WtIFESkEcDWAfwcA59zAVBZ1wIQ9aBYAaEj6vhEmYEMQkcUA1gJ4J9iVpA3/BOBRAImgF5JGLAHQCuA/TltUT4nIRUEvKkhM2I20RURmAvgvAA8758JBrydoROTLAFqccweCXkuakQNgHYB/dc6tBRAFMKXPq0zYg+UEgEVJ3y88/bMpj4jkgqL+nHPuv4NeT5qwGcDNInIMtO2uE5Fng11SWtAIoNE5p5/qXgCFfspiwh4s7wKoEpElpw987gDwYsBrChwREdAvPeic+8eg15MuOOced84tdM4tBv9fec05d1fAywoc51wTgAYRWXb6R18EMKUP2nOCXsBUxjkXE5G/BvC/ALIBPO2c+1PAy0oHNgO4G8BHIvLh6Z894Zz7nwDXZKQ3DwF47nSAVAfgnoDXEyiW7mgYhpFhmBVjGIaRYZiwG4ZhZBgm7IZhGBmGCbthGEaGYcJuGIaRYZiwG4ZhZBgm7IZhGBnG/wNYESnuTvA3/QAAAABJRU5ErkJggg==\n", "text/plain": [ "<Figure size 432x288 with 1 Axes>" ] @@ -263,6 +264,82 @@ "\n", "pl.show()" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Emprirical Sinkhorn\n", + "----------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Warning: numerical errors at iteration 0\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/rflamary/PYTHON/POT/ot/bregman.py:374: RuntimeWarning: divide by zero encountered in true_divide\n", + " v = np.divide(b, KtransposeU)\n", + "/home/rflamary/PYTHON/POT/ot/plot.py:83: RuntimeWarning: invalid value encountered in double_scalars\n", + " if G[i, j] / mx > thr:\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%% sinkhorn\n", + "\n", + "# reg term\n", + "lambd = 1e-3\n", + "\n", + "Ges = ot.bregman.empirical_sinkhorn(xs, xt, lambd)\n", + "\n", + "pl.figure(7)\n", + "pl.imshow(Ges, interpolation='nearest')\n", + "pl.title('OT matrix empirical sinkhorn')\n", + "\n", + "pl.figure(8)\n", + "ot.plot.plot2D_samples_mat(xs, xt, Ges, color=[.5, .5, 1])\n", + "pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')\n", + "pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples')\n", + "pl.legend(loc=0)\n", + "pl.title('OT matrix Sinkhorn from samples')\n", + "\n", + "pl.show()" + ] } ], "metadata": { @@ -281,7 +358,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.5" + "version": "3.6.8" } }, "nbformat": 4, diff --git a/notebooks/plot_UOT_1D.ipynb b/notebooks/plot_UOT_1D.ipynb new file mode 100644 index 0000000..2354d4f --- /dev/null +++ b/notebooks/plot_UOT_1D.ipynb @@ -0,0 +1,210 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# 1D Unbalanced optimal transport\n", + "\n", + "\n", + "This example illustrates the computation of Unbalanced Optimal transport\n", + "using a Kullback-Leibler relaxation.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Hicham Janati <hicham.janati@inria.fr>\n", + "#\n", + "# License: MIT License\n", + "\n", + "import numpy as np\n", + "import matplotlib.pylab as pl\n", + "import ot\n", + "import ot.plot\n", + "from ot.datasets import make_1D_gauss as gauss" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n", + "-------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n", + "\n", + "n = 100 # nb bins\n", + "\n", + "# bin positions\n", + "x = np.arange(n, dtype=np.float64)\n", + "\n", + "# Gaussian distributions\n", + "a = gauss(n, m=20, s=5) # m= mean, s= std\n", + "b = gauss(n, m=60, s=10)\n", + "\n", + "# make distributions unbalanced\n", + "b *= 5.\n", + "\n", + "# loss matrix\n", + "M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\n", + "M /= M.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot distributions and loss matrix\n", + "----------------------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 460.8x216 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%% plot the distributions\n", + "\n", + "pl.figure(1, figsize=(6.4, 3))\n", + "pl.plot(x, a, 'b', label='Source distribution')\n", + "pl.plot(x, b, 'r', label='Target distribution')\n", + "pl.legend()\n", + "\n", + "# plot distributions and loss matrix\n", + "\n", + "pl.figure(2, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, M, 'Cost matrix M')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Solve Unbalanced Sinkhorn\n", + "--------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "It. |Err \n", + "-------------------\n", + " 0|1.838786e+00|\n", + " 10|1.242379e-01|\n", + " 20|2.581314e-03|\n", + " 30|5.674552e-05|\n", + " 40|1.252959e-06|\n", + " 50|2.768136e-08|\n", + " 60|6.116090e-10|\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Sinkhorn\n", + "\n", + "epsilon = 0.1 # entropy parameter\n", + "alpha = 1. # Unbalanced KL relaxation parameter\n", + "Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True)\n", + "\n", + "pl.figure(4, figsize=(5, 5))\n", + "ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn')\n", + "\n", + "pl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks/plot_UOT_barycenter_1D.ipynb b/notebooks/plot_UOT_barycenter_1D.ipynb new file mode 100644 index 0000000..43c8105 --- /dev/null +++ b/notebooks/plot_UOT_barycenter_1D.ipynb @@ -0,0 +1,336 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# 1D Wasserstein barycenter demo for Unbalanced distributions\n", + "\n", + "\n", + "This example illustrates the computation of regularized Wassersyein Barycenter\n", + "as proposed in [10] for Unbalanced inputs.\n", + "\n", + "\n", + "[10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Hicham Janati <hicham.janati@inria.fr>\n", + "#\n", + "# License: MIT License\n", + "\n", + "import numpy as np\n", + "import matplotlib.pylab as pl\n", + "import ot\n", + "# necessary for 3d plot even if not used\n", + "from mpl_toolkits.mplot3d import Axes3D # noqa\n", + "from matplotlib.collections import PolyCollection" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n", + "-------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# parameters\n", + "\n", + "n = 100 # nb bins\n", + "\n", + "# bin positions\n", + "x = np.arange(n, dtype=np.float64)\n", + "\n", + "# Gaussian distributions\n", + "a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std\n", + "a2 = ot.datasets.make_1D_gauss(n, m=60, s=8)\n", + "\n", + "# make unbalanced dists\n", + "a2 *= 3.\n", + "\n", + "# creating matrix A containing all distributions\n", + "A = np.vstack((a1, a2)).T\n", + "n_distributions = A.shape[1]\n", + "\n", + "# loss matrix + normalization\n", + "M = ot.utils.dist0(n)\n", + "M /= M.max()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 460.8x216 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plot the distributions\n", + "\n", + "pl.figure(1, figsize=(6.4, 3))\n", + "for i in range(n_distributions):\n", + " pl.plot(x, A[:, i])\n", + "pl.title('Distributions')\n", + "pl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycenter computation\n", + "----------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/rflamary/PYTHON/POT/ot/unbalanced.py:501: RuntimeWarning: overflow encountered in square\n", + " np.sum((v - vprev) ** 2) / np.sum((v) ** 2)\n", + "/home/rflamary/PYTHON/POT/ot/unbalanced.py:501: RuntimeWarning: invalid value encountered in double_scalars\n", + " np.sum((v - vprev) ** 2) / np.sum((v) ** 2)\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 432x288 with 2 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# non weighted barycenter computation\n", + "\n", + "weight = 0.5 # 0<=weight<=1\n", + "weights = np.array([1 - weight, weight])\n", + "\n", + "# l2bary\n", + "bary_l2 = A.dot(weights)\n", + "\n", + "# wasserstein\n", + "reg = 1e-3\n", + "alpha = 1.\n", + "\n", + "bary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights)\n", + "\n", + "pl.figure(2)\n", + "pl.clf()\n", + "pl.subplot(2, 1, 1)\n", + "for i in range(n_distributions):\n", + " pl.plot(x, A[:, i])\n", + "pl.title('Distributions')\n", + "\n", + "pl.subplot(2, 1, 2)\n", + "pl.plot(x, bary_l2, 'r', label='l2')\n", + "pl.plot(x, bary_wass, 'g', label='Wasserstein')\n", + "pl.legend()\n", + "pl.title('Barycenters')\n", + "pl.tight_layout()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycentric interpolation\n", + "-------------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/rflamary/PYTHON/POT/ot/unbalanced.py:500: RuntimeWarning: overflow encountered in square\n", + " err = np.sum((u - uprev) ** 2) / np.sum((u) ** 2) + \\\n", + "/home/rflamary/PYTHON/POT/ot/unbalanced.py:500: RuntimeWarning: invalid value encountered in double_scalars\n", + " err = np.sum((u - uprev) ** 2) / np.sum((u) ** 2) + \\\n", + "/home/rflamary/PYTHON/POT/ot/unbalanced.py:501: RuntimeWarning: overflow encountered in square\n", + " np.sum((v - vprev) ** 2) / np.sum((v) ** 2)\n", + "/home/rflamary/PYTHON/POT/ot/unbalanced.py:501: RuntimeWarning: invalid value encountered in double_scalars\n", + " np.sum((v - vprev) ** 2) / np.sum((v) ** 2)\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# barycenter interpolation\n", + "\n", + "n_weight = 11\n", + "weight_list = np.linspace(0, 1, n_weight)\n", + "\n", + "\n", + "B_l2 = np.zeros((n, n_weight))\n", + "\n", + "B_wass = np.copy(B_l2)\n", + "\n", + "for i in range(0, n_weight):\n", + " weight = weight_list[i]\n", + " weights = np.array([1 - weight, weight])\n", + " B_l2[:, i] = A.dot(weights)\n", + " B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights)\n", + "\n", + "\n", + "# plot interpolation\n", + "\n", + "pl.figure(3)\n", + "\n", + "cmap = pl.cm.get_cmap('viridis')\n", + "verts = []\n", + "zs = weight_list\n", + "for i, z in enumerate(zs):\n", + " ys = B_l2[:, i]\n", + " verts.append(list(zip(x, ys)))\n", + "\n", + "ax = pl.gcf().gca(projection='3d')\n", + "\n", + "poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list])\n", + "poly.set_alpha(0.7)\n", + "ax.add_collection3d(poly, zs=zs, zdir='y')\n", + "ax.set_xlabel('x')\n", + "ax.set_xlim3d(0, n)\n", + "ax.set_ylabel(r'$\\alpha$')\n", + "ax.set_ylim3d(0, 1)\n", + "ax.set_zlabel('')\n", + "ax.set_zlim3d(0, B_l2.max() * 1.01)\n", + "pl.title('Barycenter interpolation with l2')\n", + "pl.tight_layout()\n", + "\n", + "pl.figure(4)\n", + "cmap = pl.cm.get_cmap('viridis')\n", + "verts = []\n", + "zs = weight_list\n", + "for i, z in enumerate(zs):\n", + " ys = B_wass[:, i]\n", + " verts.append(list(zip(x, ys)))\n", + "\n", + "ax = pl.gcf().gca(projection='3d')\n", + "\n", + "poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list])\n", + "poly.set_alpha(0.7)\n", + "ax.add_collection3d(poly, zs=zs, zdir='y')\n", + "ax.set_xlabel('x')\n", + "ax.set_xlim3d(0, n)\n", + "ax.set_ylabel(r'$\\alpha$')\n", + "ax.set_ylim3d(0, 1)\n", + "ax.set_zlabel('')\n", + "ax.set_zlim3d(0, B_l2.max() * 1.01)\n", + "pl.title('Barycenter interpolation with Wasserstein')\n", + "pl.tight_layout()\n", + "\n", + "pl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks/plot_barycenter_fgw.ipynb b/notebooks/plot_barycenter_fgw.ipynb new file mode 100644 index 0000000..8da80a6 --- /dev/null +++ b/notebooks/plot_barycenter_fgw.ipynb @@ -0,0 +1,312 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "=================================\n", + "Plot graphs' barycenter using FGW\n", + "=================================\n", + "\n", + "This example illustrates the computation barycenter of labeled graphs using FGW\n", + "\n", + "Requires networkx >=2\n", + "\n", + ".. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain\n", + " and Courty Nicolas\n", + " \"Optimal Transport for structured data with application on graphs\"\n", + " International Conference on Machine Learning (ICML). 2019.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Titouan Vayer <titouan.vayer@irisa.fr>\n", + "#\n", + "# License: MIT License\n", + "\n", + "#%% load libraries\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import networkx as nx\n", + "import math\n", + "from scipy.sparse.csgraph import shortest_path\n", + "import matplotlib.colors as mcol\n", + "from matplotlib import cm\n", + "from ot.gromov import fgw_barycenters\n", + "#%% Graph functions\n", + "\n", + "\n", + "def find_thresh(C, inf=0.5, sup=3, step=10):\n", + " \"\"\" Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected\n", + " Tthe threshold is found by a linesearch between values \"inf\" and \"sup\" with \"step\" thresholds tested.\n", + " The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix\n", + " and the original matrix.\n", + " Parameters\n", + " ----------\n", + " C : ndarray, shape (n_nodes,n_nodes)\n", + " The structure matrix to threshold\n", + " inf : float\n", + " The beginning of the linesearch\n", + " sup : float\n", + " The end of the linesearch\n", + " step : integer\n", + " Number of thresholds tested\n", + " \"\"\"\n", + " dist = []\n", + " search = np.linspace(inf, sup, step)\n", + " for thresh in search:\n", + " Cprime = sp_to_adjency(C, 0, thresh)\n", + " SC = shortest_path(Cprime, method='D')\n", + " SC[SC == float('inf')] = 100\n", + " dist.append(np.linalg.norm(SC - C))\n", + " return search[np.argmin(dist)], dist\n", + "\n", + "\n", + "def sp_to_adjency(C, threshinf=0.2, threshsup=1.8):\n", + " \"\"\" Thresholds the structure matrix in order to compute an adjency matrix.\n", + " All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0\n", + " Parameters\n", + " ----------\n", + " C : ndarray, shape (n_nodes,n_nodes)\n", + " The structure matrix to threshold\n", + " threshinf : float\n", + " The minimum value of distance from which the new value is set to 1\n", + " threshsup : float\n", + " The maximum value of distance from which the new value is set to 1\n", + " Returns\n", + " -------\n", + " C : ndarray, shape (n_nodes,n_nodes)\n", + " The threshold matrix. Each element is in {0,1}\n", + " \"\"\"\n", + " H = np.zeros_like(C)\n", + " np.fill_diagonal(H, np.diagonal(C))\n", + " C = C - H\n", + " C = np.minimum(np.maximum(C, threshinf), threshsup)\n", + " C[C == threshsup] = 0\n", + " C[C != 0] = 1\n", + "\n", + " return C\n", + "\n", + "\n", + "def build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None):\n", + " \"\"\" Create a noisy circular graph\n", + " \"\"\"\n", + " g = nx.Graph()\n", + " g.add_nodes_from(list(range(N)))\n", + " for i in range(N):\n", + " noise = float(np.random.normal(mu, sigma, 1))\n", + " if with_noise:\n", + " g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise)\n", + " else:\n", + " g.add_node(i, attr_name=math.sin(2 * i * math.pi / N))\n", + " g.add_edge(i, i + 1)\n", + " if structure_noise:\n", + " randomint = np.random.randint(0, p)\n", + " if randomint == 0:\n", + " if i <= N - 3:\n", + " g.add_edge(i, i + 2)\n", + " if i == N - 2:\n", + " g.add_edge(i, 0)\n", + " if i == N - 1:\n", + " g.add_edge(i, 1)\n", + " g.add_edge(N, 0)\n", + " noise = float(np.random.normal(mu, sigma, 1))\n", + " if with_noise:\n", + " g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise)\n", + " else:\n", + " g.add_node(N, attr_name=math.sin(2 * N * math.pi / N))\n", + " return g\n", + "\n", + "\n", + "def graph_colors(nx_graph, vmin=0, vmax=7):\n", + " cnorm = mcol.Normalize(vmin=vmin, vmax=vmax)\n", + " cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis')\n", + " cpick.set_array([])\n", + " val_map = {}\n", + " for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items():\n", + " val_map[k] = cpick.to_rgba(v)\n", + " colors = []\n", + " for node in nx_graph.nodes():\n", + " colors.append(val_map[node])\n", + " return colors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n", + "-------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% circular dataset\n", + "# We build a dataset of noisy circular graphs.\n", + "# Noise is added on the structures by random connections and on the features by gaussian noise.\n", + "\n", + "\n", + "np.random.seed(30)\n", + "X0 = []\n", + "for k in range(9):\n", + " X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAKGCAYAAADXppg8AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzs3Xd4U2X7wPHvSZqkTQcFypJRyqpMoQyBgkyRvWUqe6uAOH6IA1BUwBcZIkN8BUVAhiIbRNmyChSQVRCKrDI6oTvj+f1Rm7elaZuU0rTN87kuLuDM+yQn59znWUcRQggkSZIkSXJaKkcHIEmSJEmSY8lkQJIkSZKcnEwGJEmSJMnJyWRAkiRJkpycTAYkSZIkycnJZECSJEmSnJxMBgqB3377jaZNm+Lt7Y2iKHTv3t3RIbFixQoURWHFihWODqXAUhSFli1bOjqMPOfo4542bRqKorBv376nuh9rx5lX+y7oWrZsiaIoDtn3vn37UBSFadOmPdF28uIaaU+sT5QMKIqS7o9Op6NEiRIEBAQwYsQIduzYgclkepJdWBSkm0texnr9+nW6detGaGgow4YNY+rUqfTr1++p71dyXsePH2f48OH4+/vj6emJTqfD19eX3r17s27dulz7zUt5Y8iQISiKwvXr1x0dikV+jKmwc8mNjUydOhUAk8lEdHQ058+fZ+XKlfz3v/+lQYMGrFq1imrVquXGrqTH/P777yQmJjJnzhwGDBjg6HAsevToQePGjSlTpoyjQ5FyicFgYPz48SxZsgS1Wk2LFi3o1KkTOp2OW7dusWfPHn7++Wd69erFhg0bHB1ujr3++uv069ePChUqONW+JeeWK8mAtSKIe/fu8cYbb7B+/Xratm3LiRMnKFmyZG7sTkrjzp07ADzzzDMOjiS9IkWKUKRIEUeHIeWi1157jWXLllG7dm3Wr1+Pv79/uvkmk4nVq1ezefNmB0WYO3x8fPDx8XG6fUtOTjwBQGS1CZPJJFq2bCkAMWHChHTzTpw4IcaPHy/q1KkjihYtKnQ6nahSpYqYNGmSiIyMTLdsixYtLPt6/E9oaKgQQojbt2+L6dOni6ZNm4pSpUoJjUYjypQpI/r37y/Onz9vNb5NmzaJ1q1bi9KlSwutVivKlCkjXnjhBfH1119nWDYiIkJMnjxZPPvss8LV1VV4eXmJ1q1bi127dtkda3bWrl0rmjdvLry8vISrq6uoVauW+Oyzz0RiYqJlmb1792a6n71792a5/eXLlwtALF++XOzZs0e0aNFCeHh4CE9PT9GxY0dx4cIFq+vduXNHjBs3Tvj6+gqNRiN8fHxEjx49xIkTJ7LcR1pnzpwR/fr1E76+vkKr1QofHx9Rr149MWHCBJGcnCyEEGLy5MkCECtWrLAax4kTJwQgOnXqlOVxpkpMTBRTp04Vfn5+QqvViooVK4r3339fJCYmCkC0aNEi3fJTp061fI6rVq0SjRo1Eu7u7sLX1zfd8fXs2VP4+fkJV1dX4enpKZo2bSpWrlxpNYbU8yIxMVG8//77omLFikKr1YpKlSqJadOmiaSkpAzrpMb24MEDMXLkSMt5WqNGDfHdd99lWN5sNosVK1aIJk2aCB8fH6HT6US5cuVEu3btxE8//WTTZ5WZQ4cOCUAUK1ZM3LlzJ8tl056nQqRcBxYvXiwaNGgg3N3dhV6vFw0aNBCLFi0SJpMp0+N+XHR0tJg8ebKoVq2a0Ol0wtvbW7Rr107s3r07w7Kpv4+pU6eKY8eOiY4dO4qiRYva9DtM+/1bi8vW70MIIZKSksTHH38sKlWqZPe597iLFy+KoUOHWn47JUqUEM2aNROLFi1Kt9zGjRvFwIEDRdWqVYVerxd6vV4EBASI+fPnZ/i8M7uGpD3XhbD9+pd6zPPnzxf16tUT3t7ews3NTfj6+oquXbta/a4eZ0tMqb8ng8EgPv30U1GlShWh1WpFuXLlxLvvvmv195T6GQ4ePFiUK1dOaDQaUbJkSdG/f39x6dKlbONKlfbcSsuee5oQ6a+RW7duFU2aNBF6vV54e3uLXr16icuXL1vdf1xcnPjss8/Ec889J/R6vXB3dxeNGzcWq1evtjlWa3KlZCAzKpWKDz74gH379rFmzRrmzp1rafSxbNkyNm7cSIsWLWjbti1ms5mTJ0/y5ZdfsmPHDo4dO4anpyeQUn/k7e3Npk2b6NatG3Xr1rXsw9vbG4ADBw4wc+ZMWrVqRa9evfDw8ODKlSts2LCBzZs38+eff/Lcc89Z1vvmm28YPXo0pUuXpkuXLvj4+HD//n3Onj3L8uXLGTdunGXZf/75h5YtW3L9+nWaN29O+/btiYuLY+vWrbRv356lS5cycuRIm2PNypQpU/j888/x8fFhwIABeHh4sGPHDqZMmcKuXbv47bff0Gq1VKxYkalTp7Jv3z7279/P4MGDqVixIoDl7+xs3bqVTZs20aFDB8aMGcOFCxfYvn07QUFBXLhwId0TSmhoKM2aNePOnTu0bt2a/v37c/PmTdavX8+2bdv4+eef6dy5c5b7O3v2LM8//zyKotC1a1f8/Px4+PAhf//9N4sWLWLGjBloNBpGjx7N7Nmz+eabbxg8eHCG7SxduhSAMWPGZHuMQgh69erFtm3bqFq1Kq+//joGg4EVK1Zw/vz5LNedM2cOu3fvpkuXLrRq1YqYmBjLvLFjx1KzZk1eeOEFypQpQ0REBNu3b+fVV18lJCSETz75xOo2+/TpQ1BQEL1790aj0bBp0yamTZvGiRMn2Lx5c4ZGUdHR0QQGBqLVaunduzdJSUmsX7+eYcOGoVKp0n0+77//Pp9//jl+fn706dOHIkWKEBYWRlBQEOvXr6dv377Zfl6Z+eabbwAYNWpUtlU/Op0u3f9fffVVVq9eTfny5RkxYgSKorBx40bGjRvHoUOHWLVqVbb7T/0cLly4QMOGDZk4cSLh4eGsW7eOdu3asXjxYkaPHp1hvSNHjvD555/TrFkzhg0bRnh4OFqt1o4jtx6HLd+HEII+ffqwadMmKleuzOuvv05ycjLfffcdf/31l1373bZtGy+//DJJSUm0b9+e/v37Ex0dzZkzZ5g9ezZjx461LDt58mRUKhXPP/88ZcuWJSYmhj179jBhwgSCgoJYuXKlZdmpU6fy66+/cubMGSZMmGC5RqW9Vtlz/YOUa+CaNWuoVasWgwYNws3NjTt37nDo0CF27txJ27ZtszxWW2JKNWDAAA4ePEiHDh3w8vJi+/btzJ49m/v377N8+fJ0y+7cuZOePXtiMBjo0qULVapU4datW/zyyy9s27aNvXv3EhAQYMe3kp4997S0fvnlF3bs2EGPHj1o2bIlp0+f5ueff2bv3r0cPnw4XQlcdHQ0rVu3Jjg4mICAAIYNG4bZbGbXrl0MGDCA8+fPM2PGjJwdgA2JUKbIpmRAiJSnBBcXFwGIa9euWaZfv35dGI3GDMt/++23AhAzZ85MNz2zJ81U9+7dEw8fPsww/fTp08Ld3V20b98+3fSAgACh1WrFvXv3Mqzz4MGDdP9v0aKFUBRFrFmzJt30qKgo8dxzzwlXV1dx9+5dm2PNzOHDhwUgypcvL8LCwizTDQaD6Ny5swDEp59+mm6drJ4kMpMan1qtFr///nu6ealP5bNmzUo3vV27dgIQM2bMSDf9zz//FGq1WhQrVkw8evQowz7SfgaTJk0SgPj1118zxBQZGZnuqaVTp04CEH/99Ve65R4+fCg8PDxE+fLlrZ4/j/vhhx8EIJo3b57uaSEqKkr4+/tn+XSm1+vFqVOnrG7377//zjAtKSlJtG7dWri4uIhbt26lm5f6JFO1atV0TwkJCQmicePGAhA//PBDunVSf1/Dhw9Pd6znz58XarVaVK9ePd3yxYoVE2XLlhVxcXEZYnv8nLZXpUqVBGDTk11aq1evFoCoV69euvMjNjZW1K9fXwBi1apV6dax9p2MGjVKAGLUqFHCbDZbpl++fFl4eXkJrVab7ok/bcnZkiVL7Io5q5IBe76PVatWCUA0btxYJCQkWKZHRERYPk9bSgYePHggvLy8hEajEfv27csQ782bN9P939q5aTKZxKBBgwQgjh49mm7e4MGDsywxsef6Fx0dLRRFEfXr17f6+wwPD7e6j8fZEhMgAgICREREhGV6bGysqFy5slCpVOmuoZGRkcLb21sUL148Q0nxX3/9Jdzd3UW9evVsii2zp+2c3tMAsWXLlnTz5s2bJwDRunXrdNNTP5fHr88JCQnipZdeEoqiiODg4GxjteapJwNCCFGqVCkBiGPHjmW7rNlsFl5eXqJVq1bppuf0BiuEEF26dBE6nc5SDC1ESjKg1+utFt+kdfr0aQGI3r17W53/66+/CiBd1UJOYx0xYoQAxNKlSzPMCwkJESqVSvj5+aWb/iTJwMCBAzPMu3btmgBEr169LNNu3rwpAFGhQoV0n2GqV155RQDi+++/z7APa8mAtaLFx23dulUA4vXXX083fcmSJQIQ06dPt+VQRZs2bQQg9u/fn2Hejz/+mOUFeeLEiTbtI62ff/45w2chxP8uXo/f8IX43w+2ZcuW6aanJiQxMTEZ1nnhhRcEkO4GW6xYMVGxYsUMxfS5wc3NTQDi4sWLdq3Xtm3bTL/z33//XQAZfuuPfydJSUlCr9cLDw+PdBf+VB988EGGcyL1M61bt65d8QqRdTJgz/eReux79uzJsHzq78OWZOA///mPAMT48ePtPpa0Tp48afW3k9WN197rX0xMjABE06ZN0yVt9rI1GbCWnH700UcZbrCpN9eFCxda3d7EiRMFkGmVclr23GCFyP6e9vgNXwghjEajqFy5sgDE9evXhRApiZRarRYNGjSwup/U7+qdd97JUaxPtZoglfj3Lclpi0ANBgNLly7lp59+4sKFC8TExGA2my3zb9++bfd+tm3bxpIlSzhx4gTh4eEYjcZ088PDwy1FnAMHDuStt96iRo0a9OvXjxYtWhAYGEiJEiXSrXPkyBEAYmJirDaUfPDgAQAXL160O97HnTp1CoDWrVtnmFetWjXKlStHaGgoMTExudI4r0GDBhmmlS9fHoCoqCjLtODgYACaN2+ORqPJsE7r1q358ccfCQ4OZtCgQZnur2/fvsyfP5/u3bvTu3dv2rZtS2BgIJUrV86wbIcOHfDz82PlypXMmjULvV4PpBRXu7i4MGLECJuOMTg4GJVKRdOmTTPMa9asWZbrNmrUKNN5N27cYNasWfzxxx/cuHGDhISEdPMzO39btGhhNQ61Wm35nNOqWrUqXl5eGaan/Z48PDyAlHP6q6++okaNGvTp04cWLVrQpEkThzbkPHXqFCqVyuq4AS1atMj0uNMKCQkhPj6ewMBAihUrlmF+69atmTFjhtXtZPUd5oQ930fqsVs7z+wZR+Ho0aNAym/CFhEREXzxxRds376da9euERcXl26+PddWe69/Xl5edOnShS1btlC3bl169epF8+bNef755y2/4dxk6zUs9TjOnDlj9TguX74MpBxHjRo1chRLTu9p1q4JarWaZs2acfXqVYKDg/H19SUoKAiTyZTpuAEGg8FyDDnx1JOBxMREIiMjAdLdaPv27cvGjRupVKkS3bp1o3Tp0pa6xnnz5pGUlGTXfubPn8/EiRMpWrQoL774IhUqVECv16MoiqX+Ke02J02ahI+PD4sWLWLBggXMmzcPRVFo0aIFX3zxheUki4iIAGD37t3s3r070/3HxsbaFa81qXXSmdXJlilThhs3bhAdHZ0rF3hrdXAuLimnRNq+4rbEBSn1WVlp1KgRBw8e5NNPP2XDhg2Wukt/f3+mTp1K//79LcuqVCpGjx7N5MmTWbt2LUOHDuXkyZOcOnWK7t2729x7IiYmhmLFilmOK61SpUpluW7p0qWtTr927RqNGjUiKiqK5s2b065dO4oUKYJareb69et8//33mZ6/1vbp4uJiabPyuMzamVj7nubOnUulSpVYvnw5M2fOZObMmbi4uNCxY0fmzJlDlSpVsjzerJQpU4Zr165x+/Ztnn32WZvXS/38rdXTZ3Xcj28jNYbMYgPr519m32FO2fN9pB67tQTanrhSj6ts2bI2LduwYUNCQ0Np1KgRgwYNspz/0dHRzJ8/365ra06uf2vXrmXWrFmsXr3a0u3c1dWV3r1785///Cfb3509bL2GpR7HsmXLstzek1zHc3pPy+zzSD1HUs//1GMICgoiKCgo14/hqScDhw4dwmg0UqpUKUvDthMnTrBx40batm3Ljh070l2ozWYzs2fPtmsfRqORadOmUbp0aU6dOpXhopGaFT5u0KBBDBo0iOjoaA4fPszGjRv57rvveOmll7h06RIlSpSw3HTnz5/P+PHj7YrLXqn7unv3rtWn5bCwsHTL5ZW0cVljT1xNmjRh69atJCUlcfLkSXbu3MlXX33FgAEDKFGiRLrGRamDKC1dupShQ4daGg5aayiWGS8vLyIjIzEajRkSgnv37mW5bmYjnH355ZdERESwfPlyhgwZkm7emjVr+P777zPd5r179zL0ITcajYSHh1t94rSHWq1m4sSJTJw4kfv373Po0CF++ukn1q9fz/nz5zl//nyGxn22atasGdeuXeOPP/6gTZs2Nq9XpEgRIiMjMRgMGW6Kth73k5x/jhqlDrI+9syOxZrUG97t27epXbt2lst+++23hIaGMnXq1AxPj0eOHGH+/Pk27xfI0fXPzc2NadOmMW3aNG7evMmBAwdYsWIFP/74I9evX+fgwYN2xZAbUo/jzJkz1KlTJ9e3/yT3tMyuQ6nnSGrsqX+/+eabfPnll7kVusVTHY7YbDbz6aefAqQbEOfvv/8GoGvXrhku0MePH89Q5AopFzrA6uhm4eHhREdH07Rp0wyJQGxsrKX4PTPe3t507NiRZcuWMWTIECIjIzlw4AAAjRs3BrDrBM4q1qzUq1cPwOpQpH///Te3bt3Cz8/Ppl4JuSk1rtTE7nF79+4FsKslrk6no2nTpnz88ccsWLAAgE2bNqVbpkSJEvTu3Ztjx47x559/smbNGvz8/GjXrp1dsZvNZg4fPpxh3qFDh2zeTlqp52+vXr0yzNu/f3+W61qbf+jQIUwmk+Vzzg0lS5akZ8+erFu3jtatW3P16lXOnTuX4+2NGjUKSKmmyS6JSvsElPr5p/6e0jpw4AAmkynb88bf3x+9Xs+ZM2esPv3n5PzLCwEBAZjNZqvnmT3DDadeg3bs2JHtsjk5N7O6XuXk+pdW+fLlGThwILt27aJKlSocOnTI8oSblZxeQzPzpMeRnZzc01JZ+15MJpPlvEm9LjRq1AiVSvXUjuGpJQP379+nX79+7Nu3jwoVKjBlyhTLvNQSgsd/EPfv3+e1116zur3ixYsDKXW1jytZsiR6vZ6TJ0+mKyIxGAxMmDCB8PDwDOvs3bvX0pbh8RgAS/1WgwYNaN68Ob/88gvfffed1dj++uuvdEWdWcWalWHDhgEwY8YMS10cpJwYb7/9NmazmeHDh9u1zdxQrlw5XnzxRa5fv868efPSzTt27BirV6+maNGi9OjRI8vtHD582OqPIvXmYq1OMbXLVN++fYmNjWXkyJGoVLaftqltGD744AOSk5Mt02NiYjLt/pedzM7fXbt28e2332a57ieffJKuLjMxMZH33nsPgKFDh+YoHki5Af/5558ZphsMBks1XdrPNywsjEuXLqXrLpmVwMBARo4cSUREBO3bt+fKlSsZljGbzaxZs4ZXX33VMi31nH7vvfeIj4+3TI+Pj2fy5MkA2Z7TWq2WgQMH8ujRIz788MN0865evcqCBQvQaDTp9psfpH6f77//PomJiZbpkZGRdnX/Gjx4MF5eXixevNhqUnXr1i3LvzM7N4ODg/n888+tbj+r65W9178HDx5Y7TYZFxdHbGwsLi4uNnXtzOk1NDNDhw7F29ub6dOnc/z48QzzzWbzE70PIif3tFR79uxh69at6aYtXLiQq1ev0qpVK3x9fYGU+9zAgQM5ceIEn3zyidVE6erVq4SGhuboGHJ1BEKz2WwZjvjQoUMkJyfTqFEjVq1ala7PesOGDQkMDOSXX36hadOmNGvWjHv37rFjxw78/f2t1gc3adIEvV7PvHnziIiIsNSnvPHGGxQpUoTx48czc+ZMateuTbdu3UhOTmbv3r1ERkbSqlUry9NDqh49euDh4UHjxo2pWLEiQggOHjxIUFAQ9evXT1dcvXr1alq3bs3w4cNZsGABzz//PN7e3ty6dYuzZ89y7tw5jhw5YhlhMbtYM9O0aVPeffddZs+eTa1atejduzfu7u7s2LGDc+fO0axZM955552cfUlPaMmSJQQGBvLOO+/w22+/0aBBA8s4AyqViuXLl1vtQ5vW7Nmz2bNnD82bN8fPzw8PDw/Onz/Pjh07KFq0qOXpM63AwECee+45zpw5g0ajsdxcbDVo0CB++ukndu7cSa1atejatSsGg4Gff/6Zhg0bEhISYldyATBu3DiWL1/Oyy+/TO/evXnmmWc4d+4cO3fupE+fPqxduzbTdatXr07NmjXTjTNw9epVOnXq9EQ3s4SEBJo1a0aVKlWoX78+vr6+JCYmsnv3bi5evEjXrl2pXr26Zfn33nuP77//3mpVR2a+/vpr1Go1S5YsoXr16rRs2ZLnnnsOnU7H7du32bNnD7du3aJ3796WdQYMGMCmTZtYt24dNWvWpHv37pZ2PKGhofTt25eBAwdmu++ZM2dy8OBBFi5cSFBQEK1atbKMM/Do0SMWLlyIn5+f3Z/b09S/f3/Wrl3L5s2bqVWrFt26dcNgMLBhwwYaNmzI1atXbdqOj48Pq1evpnfv3rRq1YoOHTpQp04dHj58yNmzZ7l586blBjBo0CC++OILJk6cyN69e6latSpXrlxh69at9OzZ0+q52aZNG7744gtGjhxJr1698PT0xNvbm9dffx2w7/p3+/Zt6tWrR+3atalTpw7ly5fn4cOHbN26lbt37zJ+/PhsrxO2xGSv4sWLs2HDBssw6W3atKFmzZooisLNmzc5cuQIERER6ZI2e+TknpaqS5cu9OjRgx49elClShVOnz7Njh07KFasGIsWLUq37MKFC7ly5QofffQRK1eupFmzZpQqVYo7d+5w8eJFgoKCLCWodrOpb0QmeGyEKK1WK4oXLy4CAgLEiBEjxI4dO6yOMCZESl/bsWPHCl9fX6HT6USlSpXEe++9J+Li4oSvr2+GEbCEEGLHjh2icePGwt3d3bLP1K4nBoNBzJkzR1SvXl24urqKUqVKiVdeeUVcv37dajeVxYsXi+7duws/Pz/h5uYmihYtKurWrStmzZpldbyChw8fik8//VQEBAQId3d34erqKipWrCg6duwoli5dKmJjY22ONTtr1qwRgYGBwsPDQ+h0OlGjRg0xY8aMdH2VUz1J18LMuj5ipcuTEELcunVLjBkzRlSoUEFoNBpRvHhx0a1bN3H8+HGb9rFr1y4xZMgQUb16deHl5SX0er2oVq2aeOONNyzdZ6xJ7RaUWfem7CQkJIgPP/zQMuqfr6+vmDJlirh165YARLdu3dItb8tn+ueff4pWrVoJb29v4eHhIQIDA8XGjRsz7cqT2QiEfn5+Ytq0aVa7A2b2PQiRsetVcnKymDVrlmjfvr0oX7680Ol0wsfHRzz//PNi8eLFGUZkS10/J111jx49KoYNGyaqVq0q3N3dLSO/de/eXaxduzbDb95kMomvv/5a1K9fX7i5uQk3NzcREBAgFi5caNcIhFFRUeLdd9+1jDZXpEgR0bZtW6vdFu3t/pVWdiMQWpNZV7ikpCQxffp0y+iXqedeTkYgPHfunHj11VfFM888Yxk974UXXsjQFfn8+fOiS5cuokSJEpbRB5ctWyZCQ0MFIAYPHpxh23PmzBHPPvus0Gq1AjKOQGjr9S8qKkpMnz5dtGrVSjzzzDNCq9WK0qVLixYtWojVq1fb1d0wq5hSf0/WZHV9Cw0NFa+99pqoUqWK0Ol0wtPTU/j7+4tXXnlFbNy40aa4Mju37L2npY1zy5YtonHjxkKv14siRYqInj17ipCQEKv7T0pKEl999ZVo0qSJZYyN8uXLi9atW4u5c+emG8vBnt+BIoSVsnJJykeGDBnC999/z++//25X47Xs7N69m3bt2jF58uRMi1BzS8uWLdm/f7/VqilJkiRHe6oNCCXpSd28eZOffvqJ6tWrWx1/wRapL3NKKyIiwlJnnV1bB0mSpMIuTwYdkiR7rV69msuXL/PTTz+RlJTEJ598kuNuYpMmTeLMmTM0bdqUEiVKcOvWLXbs2EFkZCSjR4/O9YFpJEmSChqZDEj50jfffMOBAwcoX748c+fOtdpVylY9e/bk3r17bNmyhejoaFxdXalZsybDhw93SO8MSZKk/Ea2GZAkSZIkJyfbDEiSJEmSk5PJgCRJkiQ5OZkMSJIkSZKTk8mAJEmSJDk5mQxIkiRJkpOTyYAkSZIkOTmZDEiSJEmSk5PJgCRJkiQ5OZkMSJIkSZKTk8mAJEmSJDk5mQxIkiRJkpOTyYAkSZIkOTmZDEiSJEmSk5PJgCRJkiQ5OZkMSJIkSZKTk8mAJEmSJDk5mQxIkiRJkpOTyYAkSZIkOTmZDEiSJEmSk5PJgCRJkiQ5OZkMSJIkSZKTk8mAJEmSJDk5mQxIkiRJkpOTyYAkSZIkOTmZDEiSJEmSk5PJgCRJkiQ5OZkMSJIkSZKTk8mAJEmSJDk5mQxIkiRJkpOTyYAkSZIkOTmZDEiSJEmSk5PJgCRJkiQ5OZkMSJIkSZKTk8mAJEmSJDk5mQxIkiRJkpOTyYAkSZIkOTmZDEiSJEmSk5PJgCRJkiQ5OZkMSJIkSZKTk8mAJEmSJDk5mQxIkiRJkpOTyYAkSZIkOTmZDEiSJEmSk5PJgCRJkiQ5OZkMSJIkSZKTk8mAJEmSJDk5mQxIkiRJkpOTyYAkSZIkOTmZDEiSJEmSk5PJgCRJkiQ5OZkMSJIkSZKTk8mAJEmSJDk5mQxIkiRJkpOTyYAkSZIkOTmZDEiSJEmSk3NxdAD5yV+Rt/ntziUeGhIp716UruVrU9LN09FhSZKMJyWzAAAgAElEQVRdhDBC0h5EwiYwx4BLeRT9ABRNbUeHJklPRJijwHgNUIFLNRSVu6NDKjQUIYRwdBCOdic+hjGH13AzLookkwEzoFOpEUDX8nWYWq8jGpXa0WFKUraEIQQRNRREAoi4f6eqQNGBSy2UoktQVDLBlQoWYbyBeDQbkvalnMsIEEZw64Li+RaKqpijQyzwnD4ZiEiMo+sfS4hKjsds5aNwVWtoXqoyC55/GUVRHBChJNlGmO4gwruAeJTJElpw8Ucpvg5FkcmtVDAI49+IiL7/Jrfmx+a6gMoHpfgvKGofR4RXaDh9m4ElIQd5mJxgNREASDQZOHTvKqcjb+VxZJJkHxG7GER8Fkskg+kqJB3Is5gk6UkIIRBRY0DEkjERADCCORwRMzmvQyt0nDoZSDYZ+fn6aQzC2kn2P4kmA8uvHM2jqCTJfkIkQ8ImwJTNgvGI+O/yJCZJemKGk2AOB7IqwDZC8lGE6W5eRVUoOXUDwnuJjxBZnmQpBHA++s7TD0iScsocDthYjWUMfaqhSFKsMZqTkb9xI+4CiqJQyeM56hVti5vaw67tiKR9Ke1fsqO4QNKfoO+Vs4Al504GVHa0AbBn2dwSbwzjfvyfGM0J6DXPUFr/AipFk+dxSAWBlmxLBSzy7zmU2oRJts8pmIQQHHywgQMP1gIKRpEMwD9x59lzbxUdyoygfrGXbN5efFw4ehse2BBmIClnQUuAkycDpd280KldSDAZslxOBTzv45c3QQFJpkhO3n+fiMSTgAohTKgVLQDPFhtHJa8B8mIppacqDuqSYMqubYsGXFvnSUi2EiIZErciYpeBKaXUQrhUQXEfCa6dUBSnvkwVKEfCN3HwwXqMIv011SBSbtQ7w75Fo3KljneLDOsmJSURHBzMsWPHOHr0KEePHqVnh0Q+edcLV9esEwIzKtTqCrl3IE7IqdsMqBUVr1Z+Hp0q64uN2WBk74zFnDx58qnHlGx6yP7bAwlPCMIskjGLRAQGjCIOo4jjYuRXXIpa9NTjkAoWRVFAPwpwzXK5pGQjDw1d8yYoGwiRgIgciIiZntK4EXPKH+NlRMxHiMhBCCGf+AqCZHMie++vttz4rTGIZHaGfYvJbCQ0NJQ1a9YwYcIEGjduTLFixRg7diyXLl2iffv27Ny5ky8WXMDVVZvtviMiYnnrvQ2EhYXl5iE5FadOBgCGVW2Cr0cxtJmMI+Cm1jCyxgsM7dSTLl26MGjQIG7dsv70ZTKEkPBwLvHRU0mM/Qaz6Z7d8YRELSHRGI7AaH0fIpG/Y34gznDT7m1LhZuifxm0z5NZQiBwZfuBGtSt341jx47lbXCZENGTwXAJsFYvnACGvxAxH+V1WFIOnI/5E2wosXwUF0OjLjUIDAxkw4YNlC1bltmzZ3P//n2Cg4NZvHgxgwcPxt/fH5VLUXAfCrhlsUVXtMU+QAiFmjVrMmHCBG7fvp1rx+Us1NOmTZvm6CAcSaNS06V8bW7ERXEjNhKVyQxmM3qtDje1hgk1WjHm2ebUr1+fUaNGce7cOYYPH05cXBwNGzZEq9ViNj0gNmIgiY/mY0o+jMlwCmPSMZLivsNkvI7GtZVN/bpN5iRO3J+MOdu6LxVgppQ+MFc+A6lwUBQVuHZMaUdouMjD2EQ0Go+UYnZ1OVRFPqZGwBQqVqzIgAED0Gg0PP/88w6rchKme/BwGpCcxVKmlBHn9P1QlKxuCJKj/RV9gH/iz2W7nFql5tWuo1k843v69u1LYGAgvr6+aLWZlABoG4OIAsNFUk7u1N5fOsAFPN9BX2ww7du3Z/DgwRw9epRRo0Zx8+ZN6tSpg5eXV6axCPNDzMnBCNMNUHROPaKh05cMAHhodMxp1JN9HSbS+J6a2jcMzGnYkz87vcWgKv+7WHp6ejJjxgyCg4O5du0a/v7+/PDDIh496ILJcAZI5H+NuJKAJAwJW4iLHIktYzvFGW+i2NAiXGAgPDEox8crFV6K4oLK4zUiVVvpMzIKVdF5KYMM+exCcW0LQPfu3Tl27BirVq2iV69eREdHOybYxF3Y1ANCUUPi7qcejvRkXFTZF+cDqNUu+BQrYXMSqigKKq8pKD7bQP8KaJ4DTT1wH4VSYi8q90GWZUuXLs2cOXO4dOkSer2e5557jnHjxnHjxo102xSmCJKi3iT+XgMSo0aQGDWKhPvNSIgYjNl41faDLkRkMpBGUZ2eErfjqJOop2WZapkOQVyhQgV+/PFHNm7cyKPIRSQm3IZMivUhEWPyUYzJf2aYExcXx+nTp1m/fj2fffYZH3zwPnHxWQ0a8z8im7ERJOd28dIVHiVWReXaAkXjn+HC6+fnx6FDhyhbtiz169fPk/YwjxPmKGxqAS6SwRz11OORnkwVj3poFJ1Ny1Zyf87u7SsuFVB5TUFVfD2q4mtReb6R6aiDJUuWZPbs2Vy6dAkvLy/q1avH6NGjuX79OsL0gITwjhgTNwNJKSN2ikdAEubk/SSEd8FsuGh3fAWdTAYe8/DhwyyLldJq2LABr/RV0GVz/gtzPDevfswXX3zByJEjadmyJWXLlqVEiRK8+uqrrFmzhpiYGJ6r3gqdLvtuX0aD4MyRKHbt2oXRmFkSkp7ZFEbyo0UkxbxP0sMvMBsu2bSeVDBdvHiR6tWrZ7mMTqfjq6++YubMmXTo0IFFixbZVIKVG65du8aBg3+RmGRLyYAW5Njz+V55/bN4aIplOT6QgooyrpUornsmT2IqUaIEM2fOJCQkBB8fH+rXr8+JQy9hNj3A+gOcABFHYtTwPPst5Beyz85j7EkGhDkSYcOAGIoCatUVwsJqUb9+ffr160fVqlUpV64cKlX6fOz0g/vceLQJkUWfcY1Gh2tsCz6a8xGDBw+mb9++DBw4kIYNG2Z4AhQikaTotzEl7vp3SjKgxhj3LSpNdVyLLkNRl7DpeKWC48KFC9SoUcOmZV9++WXq1q3Lyy+/zIEDB/jmm2/S/QaMxlvEJx1AiCQ0LhVx071g97sNDAYDhw8fZuvWrWzbto2IiAj6932RwLpqMi9V+5cwgWs7u/Yn5T1FUaj9qCu/G79Gq3fJUAOkoMJN7U6v8m/leWw+Pj58+umnvDXpFdTxHVGUrEtWhTkKc/IR1LqmeRSh48mSgcfYkwykfHy2ZY/e3kX58ssvGTNmDG3atKFChQoZEgGAZ4uOQ6PyQsnkq1Errvh6dWPssKkcO3aMgwcPUrRoUQYOHIi/vz/Tp0/n77//BlKqEhIjh2NK3E1KEpDaUMsEJGI2/EVCRHeE+aGNxysVFPYkAwBVq1blyJEjFClShAYNGnDmzBmMpvuEPejLzbvNiIj+kIjo6dyLGMU/YXV4FLc+220+ePCAH374gb59+1KqVCneeust3N3d+f777wkLC2Pegh9R6zuQ0hDMOpNZA27dUFTeNh+L5BgXL15kQKdh1I3sR2XPeqgVDTqVHp1Kj4uiwd+rEaOrzMNbW9JhMXq6XcBFk3X3WwBEPMakP55+QPmILBl4jD3JgKIqiqIqhjBnNya2ChdtI5u26eriQ4tyqzl+dxKxhlBMwgCYUCtuCMxU8hpA9WKvW5avWrUq06ZNY+rUqQQFBbFq1SoCAwOpWLEik99uyovNTqKQmMnejAjTAwxxy9F6TrApPqlgsDcZAHBzc2Pp0qWsWrWK3i+3ZfP2ouhcEwCjJecVIgkhIDz6/zCbH1HEc5hlfSEEZ86csTz9X7hwgTZt2tC5c2fmzZtHmTJlMuxTKfJZypjyxnMZhp01mXUcOhZL8Uo9qGN/FbOUh27cuMFLL73E7Nmz6dPhVQAeGiK4l/gPCgpl3Crh7lLEwVFCShsBG4v/bRkGuRBx+lcYP65BgwYsXryYhg0b2rT87X9mojZ/jWtW7QYUNzyKr8VFW8+uWGKSQrgbfwCjOR53TVnKeryExoZ30RuNRn7//XdKuL/Ls1Vist+RUhR9qVMpXdOkAu/hw4eUKVOGR48eWS19ssWV0CGY2YUmiyYsCjp8ihxg797TbN26le3bt+Pq6krnzp3p3LkzzZs3R5ddgxpACCMk7uT23x9TsthDXNTqlFcte4xk3aZo3nnn/zhy5Ahly5bN0bFIT9f9+/dp3rw548aNY8KE/P1QYUo6TGLUiH9fh5wVNzSek9F6DMmLsPIFWTLwmIcPH1KkiG0Z7Lp165g06Uv27ayAqy4aqy2jFTe0bj3tTgQAiuj8KaLzt3s9FxcX2rdvT9zd/7OtFkPEgXgIiiyKLQwuXrzIs88+m+NEwGx+hItmf7anTlJyMlOn1+VMcD06derEW2+9RbVq1ewet0BRXMCtM6MnL2bkyCl0797dMq9vX7h+/QadOnXi4MGDeHpmnwxLeScmJob27dvTt2/ffJ8IAKi0jVEUd0S2yYAZjb5HnsSUX8hk4DExMTHZVhMkJCQwceJE/vjjDzZt2kHlGtWJj5mMIWE7oAZMoGgAgav7WHSe4/MidCtsvRkIbH7jnZTv5aSKIK1kw8WU81dkVr2UQqsVTJwUSIVntuR4X2mdOnWK+vXrZ5j+7rvvEhoaSp8+fdiyZQsuLvKylR8kJCTQtWtXmjZtyvTp0x0djk0URYXGaxrJ0ZMg0+pTNzTuw1FU+aFaI+/IcuHHZNdm4MKFCzRq1IhHjx5ZLl6KSo970QV4lQ5C7/0pbl7vo/eeQ5HSp3H1muCwEd7U2kbY8hUrqpKg2NpoUsrvnjQZEJhtGvwKQO2SO+f2nTt3MBqNlCtXLsM8RVFYuHAhAK+99prTdfnKjwwGA3379qVcuXIsWLCgQL04TePWCa3XdFIarqYd1VJLUjKcDamBxvNtB0XnODIZSCM5ORmDwYCbW8ZhT4UQfPfdd7Ro0YKJEyeyatWqDEmDSlUUrb43Oo+haN06oig2tFp9ijQeo8iqpTaAWehw8RhToH7MUtZsGWMgK1qXqja9HMhsdkGnaZDj/aR16tQpAgICMj0PXVxcWLduHceOHWP27Nm5sk8pZ8xmM8OHD8dkMrFixYocV0c5ksa9H/pSx9B4volK2xSVtjEu7sOJTPqRLr0PZBix0BkUvG/xKRDGm5gffoYS2ZGQw76I6NcQyUGWJ5BHjx7xyiuv8OWXX7Jv3z6GDx9eIG6eam19XNx6QCZjuhuNLpz5K5G//5FNtQuTJy0ZOHfuFieCXDBlPtQFAEaDkTEjf+Pw4cM53leqzKoI0vL09GTbtm18/fXXrF279on3KdlPCMGbb75JaGgo69evR5NVC9N8TlEVResxGrfia3Arvhad12SqVGvOpEmTGD16tNOVQDl9MmCOW4EI7wjxq1BzA78Kakj6AxE1AhE1kuBTRwkICMDd3Z3jx49Ts2ZNR4dsF22Rz9C4vwaKR8ofXEFxB3S4evbiRsR02rRpT3BwsKNDlXJBfHw8YWFhVKpUye51IyIiGDduHO3atSP+0XBcXDzJrC2JougpXnQ0HTsOo1+/fnTp0oUzZ87kOO6TJ08SEBCQ7XJly5Zl69atvPHGGxw6dCjH+5OyJsyPEIYQhPEaQvwvK/zkk0/Yv38/W7ZsQa/XOzDCp+edd94hLCyMVatWOTqUvCWcmCl+izCF1RamsKpW/yTefFb8stxXrFmzxtGhPjGzOVEYEnaJ5NiVwhD/qzCboi3zNmzYIEqWLCmOHDniwAil3HDq1ClRu3Ztu9YxGAziq6++EiVKlBCvv/66iIiIEEIIkZQcIv4JayKu3aokrt4sI67eLC2u3aokrt2sKCKiZwmz2SyEECIhIUHMnz9flCpVSvTr10+EhITYHXe5cuXE1atXbV5+586dolSpUuLy5ct270vKnNlwTZgi3xCmsJrCdLeeMN2tI0x3GwnTo6/F11/PFVWqVBF37951dJhPXVBQkChVqpS4f/++o0PJM047zoAQAvGgBWQzYJBZaFGX2I7iUiGPInOM7du3M2TIENatW0fLli0dHY6UQ6tWrWLz5s02F6Pv3buX8ePHU7JkSebPn0+tWrXSzRdCkJQcRHziHszmOLSaKnjoe6BSZWxwGhsby/z585k7dy49evTgo48+onz58tnGcP/+ffz9/YmMjLSr+m3ZsmXMnj2bw4cPU6KEHFL7SQnDOUTkq/8OtpN+uF6jyYUz55MoUW0HFStWc0yAeeztt992qhIC500GkoMRUUNBZPeWQBdwH47KM+/H085re/bsoW/fvqxcuZL27ds7OhwpB95//320Wi1Tp07Ncrl//vmHt99+m6CgIObMmUPPnj1zrR1MZGQkX3zxBUuXLmXw4MG89957lCyZfgjay/fD+e7YSfZeDSUhMQlTTBQzBvShY/Vq6OzoOjhlyhT27dvHH3/8YbXhr2QbIQyI+81AZP52SLPQonJ/BZXX5DyMzHHi4uKoU6cOCxYsoFOnTo4O56lz3jYDpjvY1rfeCMbQpx1NvtC6dWs2bdrEoEGD2Lhxo6PDkXIgu8aD8fHxTJ06lYCAAGrXrs3Fixfp1atXrjaILVasGJ9//jkXLlzAaDRSvXp1PvzwQ6KjowH479ET9F6xhk3nLxIVn0Ci2YzBswjTd+6hy7KVhMdmNyDM/8yYMQNfX18GDx6M2Sxf651jSXv437tLrFMpyZCw1qaeJoWBu7s7S5cuZdy4cTx69MjR4Tx1zpsMKHpsHmjHSpFoYdW0aVN27tzJuHHjWL16tWW6EGZE8klE4m+I5OMpQ8hK+cL9xL/ZdecLfrw2Dv/BkbjVuEuiKf3Lp4QQrF+/nurVqxMSEkJwcDAfffTRU32aLl26NF999RUnT57k1q1bVK1albEzZzP/wBESjUZM5vSFkvEGA7diYhiy5mebW3KrVCqWL19OWFgY77333tM4DKcgErbaMEQvgALJztPYuG3btrRp04YpU6Y4OpSnznmrCcxxiPtNyHwUqn8p7ijeC1F0gXkSV35x/vx52rVrx/Tp0xjWXw9xC/8dkS41gVKD+wgU95HynQbZEEJwN+EkF6J+Ijo5FJWiobx7c5717oWHpnSOt2s0J7P99mf8E3cSkzAg/q3ndVFSxpZoV+Zt/Iu04OzZs4wfP56oqCgWLFhAixYtcuW47HXx4kX6rPmFJNesW6HrNRqWvNyNxhWzb2+QKiIigqZNm/Lmm28yZswYzMLMjfjLxBjC0an0VPKoiVaV/XsSnJU5cigk/5n9gooHSpE5KK6tnn5Q+URkZCS1atViw4YNNG1aeF9p7LTjeioqd4RbT0j4GavvFEhZCpQioG2Sl6HlCzVr1mTfvn3s3/oShihXNC5WSgJiFyGMIVBkToEYd8ERDOYE/rjzNhGJlzCmeQvaxeh1XIpZT0OfCfh752wM9J13ZvFP3EmMjxXbpv5/150v+GbRcn6ct4Np06YxcuRIhw7lqy1RCsXDC4xZlyrFGwysCT5rVzJQvHhxtm3bRvPmzdE+m0RYyXMkmxNITV7NmGlUtC0dyryCi6rg9o1/atSVgKOkvN48C8IEaud6YVSxYsWYP38+I0aMIDg42KaXbxVETv1Ip3hNBpdqJBusfQxqUDxRin3rtE++VXyjGdLP3XoiAEBCSl1j0u48jasg2R/2AQ8Sz6dLBADMGDCJZILCF3Aj9oDd241MukFo7LEMiUBaJpIp0SyCixcvMnbsWIeP6f8gNg6N2rbf0vX7D+xuA1ClShU+3/Iu5/X7eGSMIsmcSJI5gSRzAgZzEscjd/Nt6MeYZBVXBoq+H2BDkqR+BkXjHL0J0urduzdVq1bls88+c3QoT41z3uX+pSiu/PPoM2YtfIRJeANu/7YlcAW3Hig+m1Fcqjg6TIcRcf9NaTSU5ULxiLhv8iagAiYq6Sp3E05hFpl/hiaRxInwhXaPdnY2aismkc1THOBeAoR7rF3bflq8XHUZ2glk5tzJk3h4eFCnTh1efvllPvjgA1auXMnx48eJibH+Wu77ibf5WxeExlVtdb5BJHM7/ipHwnfl+BgKK0VTFXRNyXr4clcUr//Lq5DyFUVRWLRoEYsWLeLcuXOODuepcNpqglRTpkyjevXRuJR+H0y3AROoS6NkMoSvU0k+ik3vQDb8hRBmpy1ByUxIzK+YhSHb5eKN4dyICEaTXJq4uDji4+Mtf6f9d9ppbs3P4Vou+2RApbjw0HCX4jrHj5PxbKkSuGu1xBuy/kzctRpmThpP4Jefc/nyZUJCQggJCWH79u3MnTuXy5cv4+Hhgb+/f7o/D/wuYM4mQTKIZA6GbybQp6Os2nqM4j0PETUWkXwKsyketTr189ECCnhNRdG1dGCEjlW2bFlmzJjBiBEjOHToELeSrnE/KQwXxYUqHjXx0hTsV8A7dTJw/PhxDhw4wLfffouiqKGQDyxkNxuePP/HhJMXNGXwMPmGpVFfVh49jGXAm10JPWnG3d0dvV6PXq/P8t9aFz1gyxO/QK3kjzpylaIwJrAh/9l7iASD9aJ6BdBrtbSpVhkXlYqAgIAMwxQLIbh9+7YlSQgJCWH37t1UfVuDe8ns63PjjA95ZIzGS1M0Nw6r0FAUVyj6Hft3f4kqcSXNm5ROeZW17kUUfT8UdcnsN1LIjRw5kq2nf+a9E8NR6VOSJQUwCRP+nrXpW340npqC+epjp00GhBC8/fbbfPzxx7i7uzs6nPxJXQ5MV7NfTlUcJZ/ccPITrdrTpuWKeBVhw9rFlNFn/aKetC7F7OX3u/MwmBOyXE4IM2Xccv4Gw9z2Sv26nAu7z85LV0h4rIRAo1aj17jw/YBeuGTxJjxFUShXrhzlypWjTZs2lumfXRjFQ2NktjEoqDDLdgNWKYrC8h/P0LjxKFqUGOfocPKd09FH8R9dEiNJjw/SyMWHZ5hz+T3e9p+Jh0vB647utI9ymzdvJioqiiFDhjg6lHxLcR9O+vd9W6MD/eC8CKfAqeT5Ii6KLS9zEZR0rW3Xtqt4BqLCet14KrWipaZ3ezQqx75KOy1FUZjZuR2zOrejZumSqBQFjUqFu1bLqw3qsm3UIKr4FM/Rtku52tb7QFHAw6VgF+k+LQaDgW3bttG1a1dHh5LvJJri+enmEkxYTyTNmIg1xPDr7R/yOLLc4ZQlAwaDgXfffZf58+ejVmd9QXVqbl0g7lsw3QSs1fOqQVUURd8/ryMrEMq5B+KicsVoynzIa7Wio5p3T9QqrV3bdlFp6V7+E3658R7JpgQUVfr6b7Wipbi2As1KDstR7E+Toii0r16N9tWrkWgwkmwy4qHToXrCOvzmJbrwT3wIyebMxw5RoaZ+0daye2EmDh06hJ+fH+XKlXN0KPnO8cgDKe1MsmhGZcLEmehj9Co7FDeXglXi7JQlA8uWLaNChQq89NJLjg4lX1MUHUrx1eBSnZQSgpTTRaAQFy+ITy6FUnwdihON0GgPleLCi2XnolG5Y+2nplZc8dFVp17xkTna/jP6mpS79TI3gxNRKxq0Kne0Kj06lTsBxXrSt+LcfFUqYI2rxgUvV9cnTgQAqnjUoZxbZVwyqbJSUHBV62lVsucT76uw2rRpE927d3d0GPnSxYfBJJuzH4rZRdFwM+FaHkSUu5xuBMKYmBj8/f3ZuXMndevWdXQ4BYYwnEXErwfTXVAXZ8tuDUv+G8SOHTsdHVq+98hwhzMR/+V67B4UVAhhJvJBLI3Lj6JBuaGolJwV0JnNZurXr8+HH35I+66tiDHcRa1oKK6riDqH2yzoks1JrPlnLldiz2IWJsz/DqJjiDdSzL0ko6tNx0dXxsFR5k9CCPz8/NiyZQu1a9tXbeUMFv89g8ux2XcrdFXpGVxxAs96PZcHUeUep7tizJo1iw4dOshEwE6Kpg5KkTqW/7fvksTrb1bh+PHjNGrUyIGR5X+emmdoVvpDnje/TbzxAWpFw4iPJqJ5wUijsTn/Ca5btw6NRkOPHj1QFAW9i2wdr1XpGOw3mQeJtwmK/IPI5Hu4qT04te8Kty8l4LNIJgKZOXv2LCqVKsNrrKUUFfRVuBZ3CWM2jU+NwkAp14I3SqNTlQzcvHmTunXrcubMGVknlgu+/vprdu3axebNmx0dSoGzZcsWZs+ezcGDB3O0vsFgoHr16nzzzTe0bt06l6MrfO7evUuNGjW4cuUKxYvnrIFiYffxxx8THR3Nl19+6ehQ8qXo5Ag+vTgRYzZjh1TxqMFrVT7Ko6hyT6FuM3An4RbBUUGcjQ4mzhjHBx98wNixY2UikEuGDx/OyZMnCQ52nreY5ZaXXnqJixcv8s8//+Ro/e+++w4/Pz+ZCNiodOnS9OjRg8WLFzs6lHzr119/pVu3bo4OI9/y1hanmc9LaJXMx7LQqnT0KDsk74LKRYWyZODyo4usvbmS+4n3UCspvQUM5mSu77vFf4etpHRRWVSYW+bNm8eBAwf45ZdfHB1KgTNmzBh8fX3tfvVufHw8VatW5ddff6Vhw4ZPKbrC5/z587Rt25bQ0FBcXfN3w8q8duPGDQICArh7967D32GRnwkh2Bb2E/sfbEdBwfDvUOMatLi6uDHc7x183QvmEPaFLhn4K+Y031z9yvIlpWNWKO5anCnVP8HdxSPvgyuE4uPjqVy5Mrt27aJOnTrZryBZHDx4kHHjxvHXX3/Ztd6sWbM4ceIE69evf0qRFV4dOnSgT58+DB061NGh5CsLFy7kxIkTrFixwtGhFAhxxkccj9xPWOJN9v2+n9pFG/Ba90moCvCQ7AU3ciuSzUl8e+1r64kAgEoQbYhm3c0f8zawQkyv1/PWW28xY8YMR4dS4AQGBhITE8PZs2dtXicqKor//Oc/8vPOoUmTJvHll1/a/WKowk5WEdjH3cWTViU7M6DCWKpG1Ofq/lsFOhGAQpYMBEUeIbsX65iEkVNRx0nIYiAYyT5jxoxh//79XLhwwdGhFCgqlYoBAwawevVqm9f54osv6NatG/7+/k8xssKrbdu2qFQqfvvtN0eHkm9ER0dz/Phx2rVr5+hQCiR+2FcAACAASURBVKSAgABOnTrl6DCeWKFKBs5EB5Nkw6AQasWF0DgbxtyXbOLh4cGbb77Jp59+6uhQCpyBAweyevVqzObsX2gUFhbG0qVLmTp1ah5EVjgpisKkSZOYM2eOo0PJN7Zv307Lli3lO1pyKCAggNOnT9v0G87PClUykF2Xj7RseRe8ZLvXXnuN3bt3ExIS4uhQCpTatWtTpEgR/vzzz2yX/eSTTxg6dCjly9s2Br9kXf/+/Tl//rxd1TOFmawieDJFixbFx8eHK1euODqUJ1KokoEK+oq42DDymkkYKe0qexTkJk9PT9544w0+++wzABKNRpJM8s1wthg4cCCrVq3KcpmrV6+ybt06Jk+enEdRFV5arZbXX39d9qcHkpKS+O233+jcubOjQynQCkNVQaFKBl4o0ZqUt0tnrZy+AiV0pZ5+QE5m1Lix7Aq/w/Pff02N7+ZT/b/zab56GT+ePy0Tgyz079+fDRs2kJycScNX4KOPPmLChAn4+PjkYWSF1+jRo9m0aRNhYWGODsWh9uzZQ61atShVSl4Pn4RMBvKZYlofmvm0RKvKalAILX3Kv5qHUTmH2ORkhu7dhnvndtxLTMAsBGYhuPkohk+P7qP3r2uIN2R+s3Nmvr6+VK9enV27dlmdf+bMGf744w/efPPNPI6s8CpWrBgDBw5k4cKFjg7FoTZt2iSrCHJBYUgGCt04A2ZhZv2tVRx8sBezyYRZldKoQ6dyRaWoGFN5Av6eNRwcZeEzatev7L8ZSpLJelsMnVpNG9/KLHpRvifdmiVLlrBv3z5++umnDPM6d+5Mu3btGD9+vAMiK7z+/vtvmjRpwvXr152m8VyCKZnf757mfPQNFBS+/XAOv37+X2r6V3d0aAXa/fv38ff3JzIyMuU1xwVQoUsGUkUlR/L5Lx+ToI+jTq3nqOtdn3reDXFRydG1cltY7CNa/vRtpolAKq1azaEBoyipd44Lrz3Cw8OpXLkyt27dwtPT0zL94MGDvPrqq4SEhKDTZV7iJeVMz549adOmDa+99pqjQ3nqttw+zrxLm1EUhQRTSimdOdGIp4c7H9bsR/OS8iHpSZQvX579+/dTqVIlR4eSI4WqmiCtotpi3NsRRUBEU0ZWep2GxZrIROAp2RlqWytalaKwy8ZlnY2Pjw/NX3iBRevX8+v5C2y7FML92Fjee+89Pv74Y5kIPCVvvfUWc+fOxZRNIlvQbbt9grmXNpNoNlgSAQCVqwtxxiSm/rWaI+GXHBhhwVfQqwoKbTIAcPnyZapWreroMAq9mKTEbEsFAJKNJh4mJeZBRAXPwdDr3G/dlm/vh/PR7j+Ysus3XliyjPsBDXipe3dHh1doNW3aFB8fH7Zs2eLoUJ6aZLOReSGbSTJn3vU6yWxg9oVf5MiMT0AmA/nY5cuXqVbt/9m77+ioqm+B4987fZIQUgiE3kNVeq/SQZAmTUCRZhc7VniIiiiKiqiI0ptUARHpRZBepAZCLwkmhPTpc+/7A+EHkmQmkMxMMuezFmu959zc2clv5t599zlnnyhvh1HgFQkIwOjG5iYGjYYiYojgHutPx/Dcr6u44XCiqDWY7HYybHYcigKly9Bz/kKuZ2R4O8wCyR+aEG3755hbx6U5zBxKOpfH0RRcIhnwUYmJiTidTiIiIrwdSoHXpXwUshtPFE5FplN5Uam5k8lm543f/8DiyHzppQzcMJn5cNMWzwbmR3r16sWVK1fYu3cvQIF7Oo5Ji8XkdN2Z1anInE2/5oGICqZ69epx8ODBfPv5KbCD6LeqAvl1Zmd+EmYMoGfl6vwacxJLFv0EDBoNfaJqUFgvto6906qTJ10e45BlNp05S5LZTKjR6IGo/ItGo2HAmy/w8u5fMMetxyY7Kaw10qd8XQZXaERRYyHXJ/FhapV7z3wSoM7nm+14U/HixVGpVFy5ciVfdgktsP/LiyECz/qweTsalyhNgEZ7z2sBGi3NS5ZlTNM2XojMt207dx6T3XUbba1azZE48dSWF2af2c3vJa0klwzCJt+c+5JiNzPnzG4e3TiV48n5uzFR7dAKGNU6N46UqBVSLq/DKbAkScrXQwUFNhmIiYkRyYAH6dRqZnTuxZR2XWkYWYpArQ7JZqdaQDBT23fjx4490KrV3g7T59id7m1uIkk3KwRC7vor/hxfndiMVXYg/ecJ2iY7SXdYGbpjDhl212V2X9UgrBKBmuwrchJQJjCCioVEm/YHIZIBHyRWEnieSpJoW7Yii7v35/jQl2m5P5o+dg2PlKmASgzXZOrh4pHo3EiSbE4nlYuEeyAi/zI1eisWZ/aVGbvsZNXl/LupkUpS8UrJTsjWzIfwJCBAref/avb3bGAFkEgGfJAYJvC+ypUr5/udvPJa/1oPubGbBtQoWowyISF5Ho8/SbaZOXoj1uVxZqedX84f8EBEeSMlJYVXew+j+ZnCVAyKRK/SonFKqOwKOpWG6oXLML3Ri5QLEvsTPKhbkwjzowI5gVCWZWJiYkRlwMuioqL45ZdfvB2GTzMqCsYzMdjKlEFRZ/51NGo0jGn3iIcjK/hSbWa0KjV2N3pkJNtMHogo91mtVnr06EHz5s35bNQHSJLEmbQ4fl6ziNOnT/PV6+MpHSg2v8otZcqUwWKxcCU2lpLFi+erCewFsjIQGxtLcHAwwcHB3g7Fr4nKQPbi4uJo1aoVdRw2nmnSBJ1ajeGOfg2BWi1hRiOz+vSmpthVLtcV1hmxK+51HgzVBeRxNLlPlmUGDx5MkSJF+Prrr2/fmCoVKk5NZ1H00SkiEchFN8xmpuzdTejoN2m5ZBGVp3zFE8uW8OfFC94OzS0FsjIghgh8Q+XKlTlz5gyyLKNyc3mTvzh58iSdO3dmxIgRvPvuu0iSxNAG9Vlx/DhTFi6kVvUaDGrVkkcqVkAj/nZ5orDOSO3QUuxLvJjtcUa1lv4V6nsoqtyhKAqvvPIK8fHx/PHHH6j/My/FYDBgsYhuoLnlfFISfZYsIsNmQ9bfXLkhKwq7r1zm72vX6FezJh+0bO3TlYICeZURKwl8Q1BQECEhIVy9etXbofiUP//8k9atWzNu3Djee++92xeIsAAjwxrUJ+LoEQaVLU37ypVEIpDHXqzWGkMWwzO36NUaupZ+2EMR5Y6JEyeybds2Vq5cicFw70oCg8GA1Zp/V0j4EocsM2j5UpLM5kzbspsddn45dpRlJ497ITr3FZgrzfnUG3ywZz1Nl37Hl5pEjjeqxIbLMTjFciyvioqK4vTp094Ow2csWbKE3r17M2/ePJ566qlMjxGVFM9pGFGOt2p2wKDW3LPiRa/SEKw1MKv5UwRq3Fmn7xtmzZrFtGnTWLt2LYULF870GL1eLyoDuWTTubOkWi1k13fQ7HDw9e7dPt2dsEAME/x8Yh+fH9qOQ5ZxKDJo1cQCr/y5moqFw5nXvj/BOrHrmzfcmjfQtm1bb4fidZMnT+aLL75g/fr11K5dO8vjRDLgWQMqNKBOeGlmxOxi/ZXjWB12igQUon/5BvSvUJ9wve/tpyErMgnWVByykyL6YPTqm82+fv/9d95++222bdtGiRIlsvx5URnIPb8cP0aGG43DbpjNnE5MpEoR35ynke+TgbUXTzHp0PZM2+BmOOxEJyUwfPNSFnca6IXoBFEZuHlzf/3111m/fj1//fUXZcqUcXm8SAY8q2rhSD6r35O+lObZZ5/lz/37vR1Spmyyg8UXd7Lw4p9kOKyoJAlFUehcoi61UkIZMmQIq1atokqVKtmeR1QGcs8Ns3srTTQqiWSLOY+juX/5OhlQFIVPD27FnEU/fLjZRexo4jWOXI/j4SKiu5anVa5cme3bt3s7DK8xm80MHjyY69evs2PHDkJDQ13+jEgGvMeX//ZWp50X908nJi3unu2IV17Zy9I0M5NmTqVx48YuzyUmEOaeYoFBwD8uj3PIsk/v2uqbn3o3nUxKIN7semtXq+xk/unDHohI+K+CXhkw2e0sP36CKbt28dP+/Zy7ceP2a4mJibRv3x6tVsu6devcSgTAt29IBZ3T6fTZv/2U02s4nRZ7TyIAIKOgDjKwMvicW+PSer1eDBPkkv41HyJQe++eLP8VGVSICm5eA7whX1cG/jGloXFjly1ZUbiUnuyBiIT/qlixIhcvXsThcKDR5OuP210URWHKrt38uG8fkiRhttvRqFRM3vkXNYoW5a1atRjUqyePPfYYn376aY5uMCIZ8B5Zlu9ZhucLTA4rv109gE3OugqKBEm2DA7cOEv98ErZnk9UBnJPy7LlKBIQiCU1BWcWiZhRo+G1Jk3F0sK8EqTVo2Q7h/N/QnRi61xv0Ov1FC9enAsXLng7lFz10dat/LhvH2aHA5PdjgLYZRmLw8HhuDj6LlnM088/z2effZbjG7tIBrzHV//2B5POufXgY3ba2HDtb5fHiQmEuUetUjG/dx8iAgMx/ueBRyVJGDUanqnfgEejsp/H4W35+lGtdkRxtzbACdTo6FWxpgciEu6kKAoHYmMp3KsXL27cSFR0NL1r1KBFuXL5euOis4k3WHTkKBZH5k9pTkVBE1QIc40a93V+X70h+QNf/dubHFY3H3sgzeF6kpqYQJi7ShQqxPrBQ1h24jjf/rWDGxYrRoOelmXL8ky9BtSK9P35avk6GdCq1Ayt1oBpx3ZnOYlQ4mZb1zYlK3o2OD+XaDLx9PLlnE9KwlSiBGkmEzGnT7Pl/HnCjEbmPv54vt14Z+bBAy772TuBpcdP8HbLlhjcGE+8k6/ekPyBr84ZKGZw77uikVSUMrre3VJUBnJfkE7HU7XrYNu3n90HDvPzzz97O6Qc8b1PfQ69+FATGkeWwai+94KrkVQU0umZ174fah/8ghdUVoeD/r/8wunr1zHZ7XBHFcBktxOblsbjixZxw+y7y2yys/9qbJZjg3dSSRKXUlJyfH6RDHiPr84ZeCikDAFuND5SSSoeK9XQ5XE6nQ6bzYYsmrLluqtXr1KqVClvh5Fj+f6Ko1Gp+OmR3oxp0IayQSHoVGrUsoJGVuhfuRZ/dBtKVEiEt8P0K6tPneJaejr2LC40sqKQZrUyO59u9ZnXRDLgPb76t1dJKp6v3AmDKusqk2xzECUVoVSA68qAJEliRUEeuXLlCiVLlvR2GDnme5/6+6BWqRgQVZutPUey6/HnedEZRpOtJ/mocQdKBIqdCz3t5/37b1YEsmFzOpl7+LBPt+fMSsNSpdC4MedBURTKZNEONju+Wqr2B76aDAB0LlGPoRXboldp7ppMKAFGtY5KughWPTmRTZs2uXU+MVSQN0RlwAdIkkS4IYBG1Wpy+mS0t8PxW1dSU906Lt1my3ISni8bUreO61Ky00nHsmVyPF8AfPuGVND5eiI2uHxr5jZ5he6lGlLSGEakIYSmRaoyqc5TzGv/FksXLWbAgAGsXr3a5bnEJMK8kV8rA/l6AmFWqlatSnR0NIqi+PS6zoLK3Z32ZEXJl7vyVQgLY1CtWiz4+2/MmSQzGklCr1Ix9+WXaaVS0a1btxyd31fHrf1Bfvjblw4swhvVemT6WosWLfjtt9/o1q0bU6ZMoW/fvlmeR1QG8sbVq1fzZTKQ/67EbggLC8NgMBAXF+ftUPxS87Jl3Vo6WLNYMbQ+fuHNyjutWvJ8o0YYtVoCtVpUkoRerUavVlOvZEk2PfcsKxYu5MUXX+T111/HZrO5fW5RGfCegvC3b9iwIRs2bOCVV15h1qxZWR4nKgO5z2QyYTKZCA93PW/D1xTIygDcrA6cPHky2527hLwxon59Np87l+0QgFGr5dkGDTwYVe6SJInnGzfi6Xp12XDmDFdSUzFqtTxSvjzl/m05GtG0KQcPHmTIkCG0bNmSX375hbJly7o8d0G4IeVXBeVv//DDD7Nlyxbat29PRkYGL7zwwj3HiC6Eue9WVSA/VqTz/6c+C7eGCgTPezgykuH16t3TjesWo0ZDh4oV6Vi5socjy31GrZbHqlXj+UaNeLpu3duJwC3h4eGsWrWKPn360LBhQ1auXOnynAXlhpQf+fqcgZyoUqUK27Zt48svv+Szzz676zWH3YlRX5jr8Sn5chKvr7py5Uq+nDwIBbgyUK1aNZEMeNGrzZpRNiSEyX/9RUJaGrLTicFgQK/R8EyDBgytVy9fZs/3Q5IkXn/9dZo1a0b//v3ZunUrEydORKfLfN24SAa8Jz/MGciJ8uXLs337dtq1a0d6ejqvjnqTJbN2snbZfkLsLfnync3M+HwvvZ9sSrd+DdFqC+wtwSPy63wBKOCVgZMnT3o7DL/Wq0YNtg8fTru0NFpaLMzq3ZvdzzzD8Pr183U74vvVuHFjDh48yLlz52jevDnnz5+/63W7zcHetYcolF6EQxuOY04XJVxPK4iJWMmSJdm2bRu/rdrAoE4TWbVwD2aTDQk1TodMYnwqs7/dyJtDZ2CzZr8kWMhefq4MFKxP/R1EZcA3SJKE7epV6kdEULdECb/vBBkWFsavv/7KE088QaNGjVixYgWKorDos5X0LT6STwZ+Q9GU8sx8azF9S4xk6iszsdvy3/LL/KogJgMAERER1CnbD4cdHI57W2lbLQ7Onb7GtElrvRBdwSEqAz6odOnSJCUlkermmnch78TFxVG8uO9v1OEpkiTxyiuv8Ntvv/Haa6/Rr87TzP94GRmpJkxpZtSosaRbsZpt/DFjC+91nYAzkwu4kPsK0pyBO508cpnE+HSkbC75NquDjasOY8oQyw3vl6gM+CCVSkVUVBSnTp3ydih+LzY2ViQDmWjYsCELv19CcrQZqynzpYdWs43oPWfYMHe7h6PzTwW1MrDtj2NYLa6HANQaNQd3n/VARAWTqAz4KDFU4BtEZSBra3/cgiRn/zW0mKwsnrTKQxH5t4I2gfCW1BSTW6sGZFnBLCoD9y2/dh+EAp4MiEmE3ud0OklISKBYsWLeDsUnHd0R7dZFOvbsP1jN7jcuEtynKAp7rl5h2G8r+CwjiR21qtF32SI2nj+Ls4Ds6le8VCgareskR1JJhBcV+7ncD4fDwfXr14mMjPR2KPelwCYDiqIQqi/B0W2xLPlhE4d2nBLbdXpBQkICoaGhWS6j83ey073PpCRJYt5AHpAVhdGb1vH06uVsuXAOCwoOjZp9cVcZtX4Ng1cuxZoP98/4rw7d67q1gkerVVOrQXkPRFTwXLt2jSJFiqC9j/1IfEGBTAZOHrzA0FYfs3HmKexXCzN70u98+MwMBjcex4HtYtjAk8QQQfbKVndvslFQaCDGIEMeR+N/vtm7i9/OnMLssPPf+ozJbufQtTje2PiHV2LLTZElQ2nUqgo6fdZ9BPQGLU8+1wa1ukDeFvJcfp48CAUwGYg+dJF3Bn7PtUuJ2CwOJFQ4HTKWDBs34lMZP3IG+7eKoQNPEclA9vq81g1DoD7bY3QGLT1f6uQ3TZo8xeKwM/3w/kw3m7p9jNPBhvNniEtP82BkeePNj3pRo3YZDMa7q3SKIqPTa+gxsDGP9s2/LcK9LT9PHoQClgwoisKk1+dnO7Zqtdj5/NX5ON0szwoPRiQD2WvSrR4VHi6L1pB5aVGtURNStDDdn+/k4cgKvq0XL6DCdYKlKLDyVP5/gNDptXzyw1OMmTyAek0rERZRiIhiwRjDTNTrYOTpl9qLhPMBiMqADzn99yUS41JcHme3Odi35YQHIhJEMpA9tUbNhLXvUq/dw+gMWtT/TvKSVBKy5KRCrbJ8s/MjAgsHeDnSgic+Ix27G/OIbLKT2AJQGYCbc0/qNq7Ix989yYINbzJ33Ru8Mb4Xi5bOEHsU3CdZVjh1OZ5jlxIoXCz/VgYKVCPq6MMX3Zr9a86wEn3wIo3b1fRAVP4tNjaWatWqeTsMn2YMNPDhijeJPXuNDXO3k3AlkcJFCvHD8m/o9fGzhEWGeDvEAilYb0CjkrC6mJepliTCDEbPBOUFzZo1Q5Ikdu7cSfPmzb0dTr4hywrzNh9k9sZ9WGwOLObCqKwazn46n1E9mtO4qusdSn1JgUoGckZkwZ4QFxdHmzZtvB1GvlCiYiRP/V/f2/+/rXQKP/74I23btvViVAVXm3Llcbjx8KBVqelauYoHIvIOSZIYPnw406dPF8mAm2RZ4Y2fVrPr5EUst9qFqzTICkRfjueVH1bx/oC2dG1U3buB5kCBGiaIeriMWzNhjYF6omrlr6wtvxLDBPdv4MCBrFu3jvj4eG+HUiAF6w30qFINgzrrZyKtSsVDRYtRKSzcg5F53uDBg1m5ciXJycneDiVf+HXXMXbfmQj8h9Xu4KOFm7iWlH+GlwpUMlC1TllCI1w3zNBo1TRqm38ytvwm2ZbMqqvL+fjEWMq9VoLDwfu4ar7i7bDynZCQEHr27Mns2bO9HUqBNa5lW2pEFEWTSaFQr1ZTPKgQ33d5zPOBeVhERAQdO3Zk/vz53g7F5ymKwox1+zC72EBMURQWb//bQ1E9uAKVDEiSxBtfPoE+i5nZcHOZ1muTBqDWFLyWo75ga/wm3j36Bn9c+52LpgsEVyjEUevffHJiHDPO/YhTEY1zcmLkyJH8+OOPYnJXHtFrNPzcqRvmtesppjegliQ0KhXhxgBGNWzKmv5PEm70j8mbI0aMYPr06eKz5sL11AwSUtJdHmdzONl4KMYDEeWOAjdnoHq98nw05xkmvjyX9FTz7c05NFoVFquJt6cMFRMH88i+G3tYemURDuXuDVFkZGTFxsHkfegu6RhUdoh3AsyHGjdujMFgYOvWrTzyyCPeDqdAmj1jBvW0BlaOeAGT3Y6sKARqtX63zK5Nmzakpqayf/9+GjQQ/QayYrU7/t2K3fWDjc2ef7pXFrhkAKBmw4rM2TWWv3edIfrQBRRZoUL1krw+5hnOxR+hCQ95O8QCR1EUllxegE3OuseDTbbx1/UddC3egxCdmCHvDkmSblcHRDKQ+ywWCxMnTmTVqpsbQQXk01ayuUGlUt2eSCiSgayFBwe6vWdF6Yj8c52TFD+qCW3atInnn3+e48ePo9EUyDzIa2LSTvFNzJdYZUu2x2kkLV1LPEaX4gV/HDa3JCUlUb58eWJiYoiIiPB2OAXK1KlTWbt2Lb/99pu3Q/EJcXFxVK9encuXLxMUFOTtcHzW+7PXsnb/KWQ569tngF7LJ093ptVDFT0Y2f0rUHMGXGnTpg1FixZl0aJF3g6lwLluTcCd5ZoOxU6cOTbvAypAQkND6d69O3PmzPF2KAWK1Wrl008/ZezYsd4OxWcUL16cVq1aiWukCyM7N8GgzfqBUsXNqkDzGvln0ye/SgYkSWLcuHF8+OGHOArATmS+RKfSI7nR2hXAoC64DVzyiphImPtmzJjBQw89JEri/3FrIqGQtTJFQ5j28uOoZDtq6X/fSQkwaNWYE6/yUpsq/84tyB/yT6S55JFHHiEyMpKFCxd6O5QCpUpwNbdWCuhVBuqE1vdARAVL06ZN0Wg0bN++3duhFAhWq5UJEyaIqkAmOnXqRGxsLEeOHPF2KD4t8eIpEtdN493+bWlYpQw1yhSjfd0opr7Yi/cfq8vTgweSmprq7TDd5ldzBm7ZsmULI0eO5OTJk2LuQC766dz3HEzaj0PJvOqiyBCmD2PCw1+gkvwuD31gX3/9NXv37hVrwXPBtGnTWLFiBX/8kf+3J84LY8eO5caNG0yZMsXbofgkp9NJvXr1ePfdd+nbt2+mx4wcOZK0tDQWLFiQL1am+OUVuXXr1pQoUYIFCxZ4O5QC5YkyTxGuK4Jsvze/lJCQrTJxM6+jZDPpRsja4MGDWbNmDYmJid4OJV+z2WyiKuDC0KFDWbBgAWaz2duh+KQZM2YQHBxMnz59sjzm66+/5vjx4/lmyMUvk4FbcwfGjx8v5g7kogBNALXO1Sd2wzX0Kj0GlQGjyohG0lA3tAFjH/qIuOPXGDx4sPi734ewsDC6desmJhI+oNmzZxMVFUWTJk28HYrPKlu2LA0bNmTp0qXeDsXnpKSkMGbMGL766qtsn/iNRiNLlizhvffe4++/80EnQsWPtWrVSpk1a5a3wygwTCaTUq5cOWXjxo2KzWlTLmVcUM6nn1PS7el3HdOhQwelb9++is1m82K0+dP27duVqlWrKrIsezuUfMlmsynlypVTduzY4e1QfN6yZcuUFi1aKDf+SVYuHL+kJMbd8HZIPuGNN95Qhg4d6vbx8+bNU6KiopTU1NQ8jOrB+eWcgVu2bt3K8OHDiY6OFnMHcsHYsWM5efIkixcvzvY4i8VCr169CAgIYOHChWj9uNFLTimKQvXq1fnxxx9p0aKFt8PJd37++WcWLlzIxo0bvR2Kz9vz+wFe6/EuwapQtHodDpuD8g+V5sn/60ejLnW9HZ5XxMTE0KRJE44dO0ZkZKTbPzdixAhMJhPz5s3z2fkDfp0MwM3VBYMHPUnNSk1I/CeVgCAD9ZpXJihYLH/LibNnz9KoUSMOHTpE6dKlXR5vtVrp3bs3Op2ORYsWodPpPBBlwTB58mQOHjzI3LlzvR1KvmK326lSpQqzZ88WiZQLy79Zw4x3FmA139tRVB+gY/DYvvR7s7sXIvOu7t2707RpU0aPHp2jnzOZTDRq1IhRo0YxfPjwPIruwfh1MqAoCpPGzGbDkqMEBRVClmVUKgmnQ6Z119o8//5j2W56JPzPY489RtOmTXn77bfd/hmr1UqfPn1QqVQsXrxYJARuSkxMpHLVGnw1fRmpGQ4CjDpa1q9EpTKiO2F2Zs2axZw5c9i8ebO3Q/FpMQfP8WqLDzJNBG7RB+j4bONYqjeO8mBk3rVx40aeeeYZTpw4gV6vz/HPR0dH06JFCzZt2sTDDz+cBxE+GL9OBqZ/toY1i/ZgNdvveU2n11AuKpLP5z2DTieGELKzZs0aXn31VY4ePZrjL4nNZqNfv344HA6WLl16++ejYxO4ciMFvVZN3XIlCdSLRAHAqTX6LwAAIABJREFUKctMmbeNxWv3o1KpcMqgUkloNWoqlArn09e7UzSskLfD9DkOh4OqVavy888/06pVK2+H49M+eeIrti3+K9tWu5Ik0bR7A/5v+ZsejMx7HA4HtWvXZvz48fTs2fO+zzN37lw+/vhj9u/f73Ptnv02GThzIpY3Bv5we1fDzOgNWoa82oEeTzb3YGT5i8VioWbNmkydOpWOHTve1znsdjsDBgzAbDbz+qeT+WLdX/yTkoZKpUICHLJM1zrVeOvRln6fFIz/fi2bd5/Gksle6mqVipBgI3MnPklosH9su+uuOXPmMGPGDLZu3ertUHxet0KDsGRYXR6n0WlYa/GP5m3fffcdS5cuZdOmTQ885j9s2DBsNhtz5szxqfkDfrm0EGD5rD+xZ3JBvZPVYmfpjD9FC9hsTJo0iYceeui+EwEArVbLwoULsRctw8tzV3HhehJmu4MMq410qw2L3cGqgycY+N0iTLask7eCLvrcP1kmAnCzapCSbmbWr3s8HJlvczgcfPTRR6KvgJvsVve+Yw6bA9nN3fvys6SkJMaNG+dyKaG7pkyZwqFDh5g5cyYA19My2HHqAjtOXSAhNf2Bz3+//Lb+/fees9mWwW5JTcogJSmDkDDfKun4gosXLzJ58mQOHDjwwOfKsDm4XrI6Shb9B2wOJxcTk5m6YRdvPtrygd8vP1r0+35s9uxbPjscMqu3HOWFAS3QZbORSkGWnG5mx6FzpGRYCCtkJDZmP5GRkbRu3drboeULhSMKcyMuyeVxweGFUOWj3vv3a9y4cfTs2TPXxvkDAgJYvHgxjzz6GFvTtRy7loROowZuXucaVizNuz0eoUy4Z7c/9s+rBbiVCMDNsTHZKSoDmXnttdcYNWoU5cqVe+BzLdt/HFdJt83hZMneI4zq2BSdHy4FPXYmDtnNKtU/19MoXTw0jyPyLVabg4mzN7J+zynUKhV2hxOtRo3JbKZ5l+E4ZQWN2nfKsr6q+wsdmf/xcmzZTCDU6rV0e66DB6PyjujoaObPn8+JEydy9bxBxUpQqt+LHLgUj6RSYXP8L8n/6/RF+n49nwUvDqBC0bBcfd/sFPy0LgsVqxZ36zitTkPhUDH+arc5uH4theTEdBRFYf369Rw+fJi33norV86/+cQZLHZ3uhJKnL52PVfeM79RuVuiVEBS+ddNz+Fw8uJnS9mw5zQ2uxOz1Y7DKWO22pFUGg6cTebdqb+JIT83dH2mA4YAfZbJuYKCQ7Hz6DPtPBuYF7z22mu88847RETk7kqdN+atwa6AlEllRVYUMqw2Xp37W66+pyv+93j1r95Pt+T4wYtYTFlnvxqtmkf7N0L9bwnHH12/lsIv321iw7J9oIAsy4QXK8zRq1uYPPkrDAZDrryP3eHe2KMkgd1Z8McpM1OnWmli41NwuqhqqdUqIsP9a0XB2r9OcupSPNYsEkqLzcGeYxf568h5mtWq4OHo8pfg8EJ8uf1D3nhkLFaTDXO65fZrhiADWp2GjCr/MPLFESxcuDDXrgHe5nDKJKWYUKskQoIDWLfuD86ePcuvv/6aq+8Tc+065+JvZFvlUxS4eiOFY5evUbO0+82NHoTfJgO1m1SkRt2yHN13Hps1kwuIBBZ7Os27+M862v+6dOYfXn/8W8wmK847btbXLt8gQnqIfSuu8WgXZ64kS1VLRBAdF+/yRmdzOD0+luYr+nepx7qdJ3FmM/FVQqZ7m5po/CyBnbNmH5bMvsd3MFvtzP19v0gG3FC2Winmnf+ObYt3sfqH9Rw9cIyKVSvQ55XHaN2/GSqNxMCBA+natSu//vqrzy2Ty4mUNDMLVu5jxfrDOBwyiqIQFKjnSvQWJk78PNf7n+yOuYTTjYmXDqeTXTGXPJYM+O0wgSRJjJn6JE3aVker06DR3vxTSCoJvUFLhSrFadqrCF26deTSpUtejtbznE6ZdwdPIyPNfFcicJui4uiec8yfsiFX3m9Qszpo1dnfwCSgccUyhAf557BN+VLhPN6hNgZ95jm8Rq1CpViZP/UDYmNjPRyd9zicMpf+cT3hDeDk+X/yOJqCQ2/U0+Gp1kzZ9Qk3ql7gpTlD6DS0DYYA/e3OoWXLlqV9+/bcuHHD2+Hel4Qb6Tz1+mx+WXOADJMNq82Bze7kRrKJgGL1WbkzGbMl6+rx/bA5nG7N/XHICnZn9hOGc5PfJgMAOp2Gt78YwM9/vE6XAfVIsp+h99AWfD7vGaaueJlxH7/PCy+8QMuWLYmJifF2uB61f2s0pnQL2X1mrRY7K2ftcLlE0x1RkUV4pFoFDNnMgDfqtLzexb97PrzwREuG9W5KgEFHgEEHihOtWkKrVdO4VnnWTH+dbl0707BhQ3bt2uXtcD0jB/MAxJyB+6PX67Fa7+49oFar+emnn2jatCmtW7fm2rVrXoru/o3+dAU3UkzYM1ulI6m5cCWRSdNzdx+LchGhGNzYjyVAr6VchJhA6FERxUNo0S2KNP0Jhr3emco1St5+7ZVXXuH999+ndevWHDt2zItRetbmXw9gznAjI1YUTh66mCvvOaFfJ8poZZCdaNX/+2gG6rWEBBj4eXhvKhUrkivvlV9JksSgbg1Y++NzfPBcJwKsZ2lfvyjLvhrO52/2oHAhI++++y7Tpk2jR48e/PTTT94OOc9pNGoiw4PdOrZiKf/+/NyvzJIBuPl5nDRpEn379qVFixZcuHDB88Hdp9Pn/uHi1USc2cxBstmdbP7rFKlp5lx735bVyqNyY4KvBLSrWTHX3tcVv50z8F8ZGRkEBgZm+trw4cMJDAykXbt2rFmzhnr16nk4Os9LSzG5d6AkYU533a3MHck3brDz249Z8OtqjqTYORufSIBOQ/uaUTxSvYLLYQR/otNqaN2wMl8TT82ygUT8pw/Go48+yp9//kmPHj04ePAgX331VYHd+0FRFKoUkbl6zYZKk/XvaNRrefLRBh6MrOAwGAyZJgNwMyF4//33KVy4MC1btmTdunVUq1bNwxHm3Jbdp7HZXJfhNWoVuw6dp2PL6rnyvlq1mtFdW/HRr5uzXEFl0Gp4tXMLjy6hFsnAv9LT07OdBDNgwAACAgLo3LkzK1asoFmzZh6MzvMiS4ejUp9x2WNBdsqERxbOlfd87733eOKJJ2jXtBEFf9FS7tDpdNhsmVdwoqKi2L17N4MHD6Zt27YsWbIkR9uu5geXL1/m2Wef5fKVWCq0fYaEFCt2x70XeL1WQ7XyxWhZ13NPWgVJVpWBO7300ksULlyYNm3asGbNGurW9e1tjlPTLW6N3TtlBVM2PRfuR48GNbh2/TpTNuxBr9dj+7c6oddoAIWXOjSlf9Naufqerohk4F/ZVQZu6d69O0ajkZ49e7JgwQLatbt5y7JZ7RzdfoL0ZBNhkSHUaFYl33fm6ty/EeuX7gEXiXNIeBAVq5d44Pfbt28fv/32GydPnnzgc/mT7JIBgODgYFasWMH48eNp2LAhy5Yto0GD/P90LMsy06ZNY8yYMbz88susGD0am0Phve/XcODkZWRFweGQ0WnVoECrehX5YFhH1Pn8e+kt7iQDAE8++STBwcF06tSJZcuW0aJFCywmK1t/+Ys9aw5gtzmoUr8iXUa0I9zLTbGKFy2MVqNyuaxZrVYRkQdLdXctmkGn4iWp2bEXe85eBqB+hVL0bliT0EBjrr+fKyIZ+JerysAtHTp0YNmyZfTu3ZvpP04n6aCZFd/8fvNF5WZDDr1Rz5P/14euz3TwqY0o3BUbG8tr7z5PhjOCQE2RzFcTADIOuj7d8IF/R1mWeeGFF5gwYQKFC+dOlcFfaLXabJMBAJVKxdixY6lduzaPPvoon332GUOGDPFMgHng1KlTjBgxAofDwbZt26he/Wb5VqeDr1/vxdWEFDbvO01SmpmIkCDaNYwiIjT/Ln3zBe4mAwA9evQgKCiIXr16MfaFj1j/5Q6A2/0KDm08wsIJK+j5UmeGTxzklWtkdHQ061ZMx2qtiEqd/W1QkqBRrXK5+v579uxh48aNREdHU6hQIZ5uXT9Xz38/RJr8L3cqA7e0aNGC1at/4+P+X7Pos18xpZpv/kszY06zkByfwrQ35jJ99Lw8jjp3KYrCnDlzqF27NnXr1mXF3q+oVKMkxoC7x2HVGhU6g5bqLYrwygdPc/z48Qd635kzZ6LRaBg8ePADnccfuaoM3Kl79+5s3bqVTz75hFGjRmG3569Nn+x2OxMmTKBZs2b06dOHP//883YicKeSEYUZ3KUBL/dryYCOdUUikAtykgwAtGvXjq/GfsuKD9dhTrfc1bjIZrFjt9pZ9f06fn5nfl6Em6UDBw7w+OOP07JlS6IqlaFds6ros9miXqdVMaR3Y7Ta3JuvJMsyo0aN4uOPP6ZQId9pDiYqA/9ytzJwS1qMhQh1JDZz5hdUq8nKqu/+oOXjjanasHJuhZlnYmNjeeaZZ7h06RLr1q2jTp06AHyx9CX2b41m6fQtHNh1jJKlStCoTXV6PN2CUhWKUn9+edq0acOKFSto2rRpjt83KSmJ9957j99//z3fD614g06ny9FNvXr16uzdu5eBAwfSvn17lixZclerVVmWuXYpEavFTpHIEAqF+EZPh4MHDzJs2DCKFSvGgQMHKFu2rLdD8is5TQYANn+/CxVZ30QtGVaWf/07vV/rRmjRnFUEU5JNbFp/lIsXrmM06mnSrDIP1ymTaZVBURS2bNnChAkTiI6O5o033mD27NkEBgZitzt59/OVHDp+GfMduzWqVBIqCa5f3E/Len1zFJsrCxYswOl08uSTT+bqeR+USAb+ldNk4JeJv2aZCNxis9hZPGkVYxa//qDh3bfkhBRiDp5HkRUqPFyGIiXD73r9VjXgzTff5Pnnn2fZsmV3zTpXq1U0aludqLrFqVChApt33t3cZeDAgYSFhdG9e3fmzJlD586dcxTfmDFj6Nmzp89PNvJVOakM3BISEsKqVasYO3YsDRo0YPny5dR6uBarZv3J0h82k5FmRq1WYbc5qdeqKk++2YXyVR98Xsj9MJvNjBs3jpkzZzJp0iQGDfJOWdnf5TQZOPv3BeIvud5DRFJJrJu5hf6je7h1XllWmP7dJlYtPwAS2KwOJAnWrDpIaGgg4yf2pWz5iH+PlVm9ejWffPIJycnJvP322wwcOPCu65tWq+azd3py8PhlFqzcx5kL8UiSRJ0apRnQrT7LfrHRs2dPtm3bRkDAgyfG6enpvP322yxZssTnHn5EMvCvjIwMt8erbRYbl6KvujxOkRUOb/ZOb4L4y9f5btRM9v1xCK3+ZoMLm8XOwy2r8cI3QyldpSRXr15l5MiRXL16lfXr11O7du0sz5ecnExISOZtgDt37syqVavo0aMHX375JQMHDnQrxr///pvFixfn+o5g/uR+kgG42TDmo48+onbt2nTs2IlutZ7lxmUz1v8kuHs2HufQjtN8OHskDzeulFth88/FBPavO4zVbKNExUgadKp9T1vr7du3M3z4cOrWrcuRI0coVqxYrr2/kDM5TQYunbya6SY8/2Uz2zhz6Lzb5/32yz9Y/8dRbHc0OlMUsJjtXLMkM+rZ2Xzz41Ns3baWiRMnYjAYeOedd+jZsyfqLJYmS5JEvZplqFezzD2vvf3225w4cYKhQ4eycOHCB05EJ06cSOvWrWnSpMkDnScviGTgX+np6ZQsWdL1gYDD7nT7Q+HMZJlTXvvnYgLP1x9NenIGslPGZvnfBf7gxqO82OgdWr9RnwnffMQLL7zAO++843INenJycrbJUpMmTdi8eTOdOnXi+vXrjBo1KtvzKYrCiy++yPjx4wkPD8/2WCFr7kwgzM7jjz9O7BELa2btRpXJ5UBRFKxmG+OG/sT8/eMwBOgfJFxuXEvi08FTOLYjGpVahex0otFp0Gg1jJg4iM7D2pKamsro0aNZvXo1U6dOpXv37g/0nsKDy2kyoNFpXG5Jfsvq31axvcNaqlSpQlRU1O1/ZcqUuesGfuVSIuvWHsl8LxluJgUZJit9e76NsfA5Jk+eTPv27R/oBi5JEtOnT6d169Z89NFHfPDBB/d9rgsXLvD9999z+PDh+z5HXvL7ZCA5zcz6vac4k1EI5Yaa87GJlC+R/c3JiQO1XuXWjV42ONi/fz/16tVz60MZf/k6fy7dTeqNdEKLFaZVnyaEFsvZxjyfDPz6diLwX4qiYEo1sfqjTazfnX014E7ZVQZuqVGjBjt27KBDhw4kJCQwfvz427/z0fh/OJWYgEpS0bBESbauWo3ZbGbYsGE5+t2Eu+l0OkwmNxtEZcLplNm56mSmicCdZFlm68qDdBpw/080yQkpPF9/NMnxqXd9d+z/XtynjprJ3r/28dP6qXTu3Jljx465/MwJnpHTZKBm86putSk3FjIw4uOXKVTRwOnTpzl58iQrV67k9OnTJCQkULFixdvJQdqNYjhcbXOuQGhwJX5Z+S3BwbmzPM9gMPDrr7/SsGFDqlevTu/eve/rPG+++SajRo2iVKlSuRJXbvPbZMDhlPliwRZW7TiGBFilCJIuWRg8bj5VyxZl4gvdCC989+qCI0eOMG3aNBYuXEjjkq1Rn9fitGe9RlUfoKNM8wj69euHVqtl0KBBDBw4kPLly99zrCnNzKeDv+HA+r9RFLBb7eiMOn58ay6t+jTh1R+fRad33c/6yulYzhw6n2ki8D8SgdpCaE3uf1ncSQYAypYty44dO+jSpQsJCQkMef9d3t+2ibj0dCRuLtNxyDLmcxeY8sWkLEt3gnt0Oh3Jycn3/fMXomNv34yzYzHZ2Lxi/wMlAz+/M5/khNQsk2irycr2Wfv47pfv6fZ41/t+HyH36fV6UlNT3T5eF6hBV1zCdl5GymbRmkajptcz3dBoNffMN8rIyODMmTOcPn2a06dPc2RvIrLs+pql12u5cukG1Wu6V+l1R2RkJCtXrqRDhw6UL18+x3Octm3bxr59+5gzZ06uxZTb/DIZUBSF96f9zs4j57DdsUGFrIDV7uDYuTieGr+ABeMGo1UpLFmyhB9++IFLly4xYsQIjhw5QnBAYUY89BrJ8amZ3ni1Og2lokrw9cIJqDWT2b17N/Pnz6dhw4ZUqVKFQYMG0adPH8LDw7FZbLzWagyXTl7FfseMVtu/Xa+2L91NYuwNJvzxvsub56FNR936G1hNNvavP0yNplXcOt7dZAAgIiKCzZs303HkCAYu/wUlk5hVpUsy5vRx6tSpQ+lg0Vvgft3vnIFbLCabW33SAfbvOUiTJk0IDQ29519YWFim/z0gIABJkjClmdmycCfOzDaEuYNepyfxaAY8ft+/kpAHclIZ2L17N08++ST16zZEbwkjJSEt0wRQH6Bn7LI30WSxOVlgYCC1atWiVq2bnfhevjSTk8dd78apAHkxN69OnTr88MMP9OjRgz179lC8eHG3fs7pdDJq1Cg+//xzjEbPNxNyl18mA0fOxLLz6HksWZSxnLJCYkoGQ974lO1LvqVBgwaMHj2aRx99FM0dvaKn7PqEdzp/TPzlRKwZN3f4U6lVaPUaqjSoxLgVb93+oDdp0oQmTZowefJk1q1bx7x58xg9ejStW7emTtHGXDkde1cicCeb2cbJ3THsXn2AZj0a3vWaoijExcURExPDmTNn2Ll8PzarlZvbXGRNURSsJvdvIikpKTkq2RoCAsh4pDmKLYsLiEpFms3KW5v+YGHPfm6fV7jbg84ZKFoy9K7JWFmRJGjUsi7dnhtBUlLS7X83btzg0qVL/P3333f9t1v/tyzLhIaGUsxQgghb+WyfEuFmRezghiMMGSc+E77EnWTAZrMxfvx4pk+fzrfffsvjjz9OckIK3740g79W7kP779bbDruT8g+V4cVvhuZo2XWDxpU4GxPv8vMqO2XKVSjq9nlzonfv3pw4cYKePXuydetWDAaDy5/5+eefKVy4MI8/7tsZrl8mA/PWHcBqy35ZoMMpEycHsXvPHipVzLyfedEyEfx0bDJH/zzJxnnbSUlIpWjpInQa1oaKWXSs0mq1dO3ala5du5Kamsry5cuZ//wqsGT/xG/JsDL9/TmcvH7k9o0/JiaGs2fPEhQURKVKlahcuTJhJYpyTZeM3ZL9F8YQqKdsdffHrnJSGQBYf/4MTiX7Np+yonDoWhxXUlMoJaoD9+VBKgNpaWnMnDedJPM1glTZ7+anN+oY9PKj1GhQIUfvYbFYSEpK4sDmw/zw7DysbuyEKbYZ9j06rQ6LyYqiKJnOfTp+/DiDBw+mePHiHDp06PZTc0hEYd5f9CqpiWmc3BOD0+GkTLVSlKrs3lP1nbp2r8OiuX9le4xGo6Z954cwGFwPqd6v999/n+PHjzN8+HDmzp2b7Vyw5ORkxowZw9q1a31+SaxfJgPHz11zawt0jVZHodDsM0xJkni4ZXUevo8drYKDgxk0cBALhv2OguuArkTHsXNnBpUqVaJfv35UqlSJihUr3jXL3+l00m/tSFIs2Y/vmUwm4rmS5Zf7v5KTk3PU6GXn5YtkuNEMR6NScSAuViQD9ymnTYfg5v+WU6ZM4ZtvvqFt27a8OWkYP49Zf9eqkztpdWoqVC9J9fr3znVxxWAwULx4cVp1KcT3zrkuj9foNNRo5t7QlZD3Dm49wS+Tf+fIjlMoiobe5V6my5CW9Hy2PeHFQ5Blma+++ooJEybwySefMHz48EyvJ8HhhWjU5cF6iYSGBTHyhbZM/24T1kzmuWg0KsKLBPH0iNYP9D6uSJLEzJkzadmyJZ9++invvPNOlsd++OGHPPbYY7ebuPkyv0wG3E3QFAVUeZzN5SRbNBqNzJw5M9tj1Go1z3/zNF8O/z7LYQB9gJ4WT9Xn62+/5tvvv+WLL76gefPmWZ4zI9XE9Ss3qFbZ/YTHIWdfFbhFARwuKghC1nQ6HVare5WB69ev89VXX/HDDz/QtWtXduzYQZUqN2+8YcFF+fyVeaDc3HjrFkOAjnJVi/PhrJEP9GRTKDSIJo814M+lu5DlrBNflUqi+wud7vt9hNzz87hlrJ6+Gcvt64iEKc3CymmbWTvnT177cRDvffwWDoeDPXv2UKFCzqpG96N77/oEFTIw7duNWCx2ZFlBJUk4nE7qN6zAG+90pVAurSLIjtFoZOXKlTRq1Ijq1avTvXt3riQks+v4Raw2B6WKhhChszF37twHbtfuKX6ZDNSJKsWGvadcbl8ZYNDes6Igt6k1akpUiuRqTJzLYyvXde/L1qZ/cyzpFqa+PBNJJWE13Rzr0/1bOhv4Xi/6v92TN5WXWbhwIQMHDqR+/fpMnDiRSpX+11jmyPYTzP1wCcd2RONw2lm+ahOnl15l8Jg+1H6kZpbvf+7cOa7sPwQ6CbTZl+sURaFqePYlauFeR05cYf6yPew5cBlZrku3Qd/Ss0ttej1al5DCd3dKu3btGpMmTWLGjBn06dOHffv23bOipXmXWtRsVJE/Fu5i++pD2K0OSpaPoMfwVtRqWjlXSpwjJg7iwIa/yUg2ZToUoA/Q89jzHSheXjQX8rZty/exavrmTB8o7DYHdpuDMf2+pcPrHRn99lseXRXUtkNNHmlXg8MHL3AtNhmtTkO9BuUJC/fsHhQlSpRg+fLldOvdj18O3uB8fBqSJOGUZXRaDWZTBr2ffYeiRfNm/kJukxQ/HKCLvvgPIyb8kuUEQgC9Vs3Qro0Y2q1xnsez9udNfPfKTCwZWU/QMQTqeW/hqzTuWs/t86YnZ7Bu5mYObjyKLCs81KIqnYe3u6cPuNls5uuvv77d7vWDDz5g9/KDfP/KLKyZ7OOtD9Ax/NOB9Hixy+3/lpiYyOLFi5k3bx4xMTH0GtCfLVHlsbl46q8UGsaGgU+7/TsJMHPRThYu24vV5rhruEunVWMwaPn20ycoVzqcy5cv89lnnzF//nwGDx7Mm2++6fU1zldi4hjbYyLxl65jNdtQZAVDoB5FVuj7VncGj+nj82Or/mBEow+4HHMt22P0Ri0vfTmYdv18r5uep9xINdHjnemkW+xIqnsTIoNOw4iujRjSuWEmP+1b/DIZAJg4dxO/7TyeaUKg06gpVTSEWR88gdGNtf0Pym6z83rr/+Ps4QvYLJncfI066rR9iHG/vpWn/azj4+MZN24cqxasobqpEbKLHgoT1r3HqbgTzJs3jy1bttC5c2cGDRpEx44d0Wq1/Hz4AF/s3oHZkXnSZdBomP1YbxqW8M0mHL5o+67TjP9yTaZjpnBzCKxQkJ5ixmOsWL6U4cOH89prrxEZGenhSLN3at8Zdv92AIvJSumoErTq15TAYN/YFMnfXbuYwMgmY7OcQ3KnGo0r8cXvoz0QlW8aN2sdv++OxpFNXxedRs3KT4ZS1Md3z/TLYQKAtwa1oUhIILN/34ckSdjtTjQaCadToVmt8owZ2tEjiQCAVqfl801jmDxyGn8u241KrcJudaAzaHE6nHQc+gjPfTkkzze2KFq0KFOnTiX4SnH2/3aY7JYnWk02hrR5ltAWOgYNGsScOXMIDg6+65hhteshAZ/v3oEKCZPj5sUlUKtFq1LzbaeuIhHIoRkLdmaZCMDNeS5JyamUDCtFTEyMz7Z6rtKgElUa5N5eB0LuSUsyodGq3UoGUm9keCAi35RhsbFu7+lsE4Fblmz9mxd6NvNAVPfPb5MBSZIY1q0xAzvWY8ff54lPSiPAoKN5rQoUyeN5ApnRG/W8Pfdlnv3yKf76dd/tdsTNezYk0MPxHN9yChTXpdqiUknWblyY7TFDa9ejb/WHWHnqJEcTrqFRqWlWqgztK1RC42O7dvm6a/EpXIlz3W1QrdajCyzls4mA4NtCihTC4aI51C1hkf67CuhcbCIatYos2sPcZnM42Rd92TNBPQC/TQZuMei0tGsQ5e0wbguJKEyXEe28GkNm8wQy47A5kGXZZcUiSKdj4EO1gFq5EJ3/SkmzoNWocKdF/UHJAAAgAElEQVStQFLq/e9XIPi3iFJhlIkqzpkjl7I9zhikp9vQ1h6JyRfdXJbt/rG+TjyaCfcILlLIreOCQgN9bk/ugiwk2Ijd3Se2EM9Xt4SCY8j7PdEbs97JVKWSCAoJpHFn/03wyxcPw+bGZnUatYralUp4IKIHI67kwj26Pdvh9jLErGj1Gh4d6d0Khr8pFhFMmVJhLo8LMGrp3tm93SgFITP129Xk6TG90Bu1qNR33yb0ATpCigbz+eo3stxXwB8UCjDQunZFl71oVCqJfm18//sokgHhHt2e64jOkPVTAYBWr6PHS12yPUbIfcMHtUCvz/oCLEkQYNTTsrH7Pd8FITM9nmnL5PXv0qZPIwILG9EZtBQvF8HQsb2Yvns8kWUjvB2i1416vCVBAfosl8MadBr6t6lNiSK+P7fCb5cWCtk7c/g8b7X7ELvFjsX0v/4HhgA9Gp2GT9d/QJX6me/ZIOStBcv3MnPhTmw2511jkXqdhgCjjm8/HUDpkq4rCIIgPLjL8cm88d1qriQkY7M7kRUFo06LrCgM6dyAEV0b5YveGSIZELJkSjOzce52Vv+wjtTEdILDgugysh0dnmzl8RUOwt1OxsSxaPk+du0/h93uIDQkkN7d6vJYx1oUCnK9k5ogCLnr5MV/2Hn0AhabndJFQ2hfP4oAFxVWXyKSAUEQBEHwc2LOgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5jbcDEHKHrMjEWS5jcZoJ1YUTpovwdkiCn3IqTmTFiVal83Yogg9QHFdQTPPAtgMUJ+geRgoYgqSt5u3QhDtIiqIo3g5CuH+yIrMtYS2b/lmNTbYiocKp2Ik0luaxEgOIKlTT2yEKfkBRFE6k/sXOhOXEWs4iAUZ1MI3Cu9IwvAtGdZC3QxS8QE6fBunfAjJg//e/qgEtGDojFf4ESVJ7L0DhNpEMeIGi2HBYNiI7zoOkR6NviVoblePzyIrMzPNfcTL1b+yK7Z7XtZKOfqWH0yC8RW6ELQiZkhWZZVe+4HTqfuyK5a7XNJIOozqI4RU+o7CoVvkV2fQLpH4CmLM4wgABfVAFf+DJsIQsiGTAw6wZc7GmTgAUUCzczJJVqLRVCQidikpT2u1z7bq+meVX5mBTrFkeo5V0vF/9S0J04Q8cuyBkZnv8Ev5MWII9i8+hhIpwXXFeqDwVSZI8HJ3gDYriQIlvCkqyiyN1SEW3I6nCPBKXkDUxgdCDrOnTsKZ+BEo6KBmAE7ABFmT7ETISuiI749w6l6IobPhnZbaJAICCwp/XNzxw7IKQGafi4K/rK7JMBAAUZFLsiVw0HfdgZIJX2f7if8MC2ZFQTCvzOhrBDSIZ8BDZmYA1dRIoWZXMZBQlFUvKh26dL9WRTIo9yeVxDsXO4aQ9OYhUENx32RSNguzyOLti5XDSZg9EJPgEZ+zNyYIuWcF5Ia+jEdwgVhN4iM00342jnDfnEjiTSEmFhIQE4uPjM/2X7Eyk8hvhaAyuJ984MplPIAiKomC1H8XhvIIkGTHqGqFSBeToHGZnGuBO6V8hw+GqZCwUGJIB9541JZAC8zoawQ0iGfAQp/UvIPuSPkBqmoXu/Utz6IiGiIgIihYtete/KlWq0KJFC8KKhrHWMAcnDpfnLKIrlgu/gVCQpJn+4HrKOJxyAjfnrSiAk+CAvhQJGYNKMmb7806nkwMHDrB27wrsjdPRGLK/8EuoCNYWybX4BR+naw5uXJvAgGTokNfRCG4QyYCPKRRUiN9/n48xqKXLY+MunOJg0q5sy7ROi0x5VY3cDFHI51LS55OQ8gHKf2b+A6RmLMJiO0Spor+ikgx3vRYXF8e6detYt24dGzZsIDIyko4dOxDWIhB7ljPGb9JIWuqGtc/V30PwXZK6CIq+NVi3kPXcARWoi4O2lgcjE7Ii5gx4iFrXCNC7PE6S7OiN7vUG6BTZG102jV3UqAlwFmJoh2cZPXo0GRkZ7oYrFFAO5zUSkt/PNBEAULBis58mKXUqVquVzZs3M3r0aGrVqkWNGjVYs2YN7dq149ChQxw7dowvvviSDqWeQitl/dlWoaaYoSwljZXz6tcSfJBU+BPsSjEs1nsXrDkcgBSMFPqjWGHiI0Qy4CG6wEEoiquJVio0hjao1O4tsylqKM7zld7DqA5Ep7r7KU6nMlDCWJaxjb/i6JFjXL16lRo1arB69er7/A0Eb5EVK0kZS4m51p7jV6I4fqU6F68/i8l6KMfnSk6fg0L2q4kVLFyO+4rIyAjeffddDAYD33//PfHx8SxZsoRhw4ZRuvT/lsDWD+tE/bBO/yYEd1/YHRYZKcPAE2XFWnJvUxSFVNtlblhjsDg9MH9DKsSA57UcjK4BUtDNuQFSEAp6lq+V2R3zDpKmTN7HIbhF9BnwkM2bN7NtwyBGPWdEo8msbKYCKZigiN9RaUrl6Nw22cbhpF3svfEnZqeJcF1RWkZ0oGJQtbuy7k2bNvHcc89Ro0YNvvnmm7su6IJvcjiTOBffG7vzCrJiuuMVFZKkp0jQMCJD3nb7fBf/aY/N7nqJn9OpIyxgCUUjGrh97sumaDZcms+ZlIMEBgUSqouknK0hT7d/jX279/P/7J1nYBTl2oavme0pJAECgYQuJUG61AACSkekdzkoShXEAwrIdxQRRbCBgBQVBJQivUV6B+kSeg0t1BRC6mbbfD8iCLItIclms3P9wp133r03zs4+89SSJeUbvyuQJAvnE1Zy+sGvpFuSEFFgxkCQriY1Cw2ikLZijrzv/PnzmT59OocOHUKplMB0HbCAIoSly9bx3XffcejQIdkzkEeQjYFcYPbs2YwfP54lS5bQoPYV0pO+BoS/ew0oQVAhKsrgVXA2orJ0jmrR6/VMnjyZ6dOnM3bsWIYPH45KpXpqTbo5kRvJ+zFYktAqAijpE44qk1nmMs+PJElcud+eNMNpbMVdBUFHcf/PKOjTw+Y+6enpXLx4kXPnzlEmdDz+AY6fCgXBhxKBq9GoM5dvsnXrViZNmsSOHf+UEU6cOJH9+/cTEREh3/hzGYtkZtedj7idegSzldCQQtDStNgXBHvXy9b3jY6OpkaNGmzfvp2qVas+q8tioXbt2owePZpu3bpl63vLZA3ZGMhBTCYT77//Ptu2bWP9+vW88MILAEiSHlPaJizma4AapfZlFKrcTfK7dOkSQ4YM4f79+8yZM4d69ephsqTz5/1viErahoACi2RCIaiwYCbUrxMvBQ5ClPuI5xqp6X8RFdMNyWZvigyUiqJUKnaU1NRULly4wNmzZzl79iznzp3j7NmzXL9+nTJlyhAaGsrAYfcoXe4aomj/ay+goUzxSBRigUxpnj59OmfPnmXWrFmPXzMajdSuXZv//ve/9O3bN1P7yTwf5x4s53jcLEw2ckQAlIKWrmXWolb4Zst7SpJE27ZtqVevHh9//LHNddu2bWPQoEGcPXsWtVoeauVq5GqCHCIhIYHu3bsjCAJ//vkn/v7+j48JghaVVwcXqoPy5cuzZcsWli5dSqdOnXi9w2u0HCXx0HwF8xN9CSxSxhPp+YerSTbdpWmxCfLTXS4Rn7IYyUGHSYDklBhatS3Nnp33KV++PGFhYYSFhdGrVy/CwsIoX77845utPv040bHdkJ4KOTyNxSJQwLtFpg0BgAsXLlCpUqWnXlOpVMybN4/WrVvTokULgoKCMr2vTOaRJAunHiyyawhARlHp5cQIwgK6Z8v7LliwgDt37jB27Fi761599VXKlSvH3Llzeffdd7PlvWWyjpxAmANcunSJevXqUalSJTZs2PCUIZCXEASBnj17cvbsWQIrP+Ru0mnMNn58TJKe6JQ/uZ16JJdVei5G021worufSqVm2vRPSUpK4uTJkyxdupSPP/6Yrl27Urly5aeeujTqGug04VgsKuubSaDXw+fj75GaattgsMX58+epWPHZGHTNmjV566235Jt+LpJovInRkuxwnVnSE5W0OVve89atW3z44Yf88ssvz4QfrTF58mQmTpxIUlJStry/TNaRjYFsZseOHTRs2JD333+fadOmoVTmfeeLv78/VdsIqHX2LweTpOdkvDOdFGWyA6XCueFSKqWSEiGhTl1rgiCg4Ut27zD+bRConjjmjUIRSOli60hK9KNBgwZcvXo1U5qteQYe8cknn3D69GlWrlyZqT1lsobJond6PLDJYj8U5QySJDFgwACGDh1KtWrO9Q6oXr06zZs35+uvv37u95d5PmRjIBOkmQysiz7K5DNr+ebsenbfO4vJ8k//7dmzZ9OzZ0+WLl3KwIEDXag0c5glI4nGaKfWxurP5bAamUcEeHdDdKJVqyAo8VLXcmpPSZIYNGgY50/2oEzxXfj7vI2Xtjm+uk4EFZxJmWLH8fOtxS+//EL//v2pX78+W7c6N+gqOTmZuLg4m1UDWq2Wn3/+mWHDhhEfH+/UnjJZx1tZBLPkeFiQJAHpz++9XLhwIbdv3+ajjz7K1HmfffYZM2bM4O7du8+tQSbryAmETrLyxiGmnc/Ihk4zZ8TUvRRqVKKSz6p047fPpj+TKOgumC0GFlx+BRzUnwMoBR19y8tTEHMDSZK4eLcRBtMNbIULBEFHkQLvUaSAc+73BQsW8PXXX3PkyBG0Wq3D9bt376Znz56MGDGCDz74wG6+yPHjx+nXrx8nT560u+fw4cNJTEzkl19+cUqzTNbZEv0ed9Lsh/YsRgXzPryFlFCcgQMH0qVLF3Q62+2oU00JRD7YxLWUv5CwEKyrTHFDLcJrvcKWLVuoXr16pnWOHDkSQUpgyoS6YDwBKEDdEEH3GoJcyZQryMaAE6y4cZDvz/+B3mLDyjaa8V19mZXf/pxn8wMcsSyqEymm+w7XBWor81rJObmgSAbAYLrJlXvtMZkfgvD0wClB8MJX+wolC81EEBw7+aKioqhbt67Nci9b3Lx5k86dO1OmTBnmzZuHt7d1b8WSJUtYvXo1v//+u939kpOTqVKlCrNmzaJVq1ZO65DJPLH6c2yKHmIzF0hERYCmHC2CZhMREcHcuXM5fPgwvXv35p133uHFF5/uhno8fj077/2IgPB4AJoCFQajEfOl4ozr/FOmE4wlSSIl5hvEtDmo1RrEx9e5FwgSFPgSUdc6059dJnPIYQIHpJrSmWbPEABQKSjUL9xtDQGAFwN6orDTUhYyvAJVC/bOJUUyAGplCcoH7eDS6eqkparIGCokEnVJJCVmACUL/eCUIWAymXjjjTf46KOPMmUIAJQoUYI9e/bg7e1N/fr1uXLlylPHzaZrpKUsQSGspmkTPxw9X/j4+DB37lwGDhwoJ47lMIW1oTQp9jlKQfvM91sp6AjQlKV58FTUajUdOnQgIiKCY8eO4efnR8uWLQkPD2fBggWkpqZyOmEbu+79jFkyPjUJ1YwRhQq8KsfxZ+zSTGuUUn7Ey7IIrUZ4whAASM0Y+f5wNJJ+Z1b/BDJOInsGHLDm5hG+O7/xcWjAFlpRxdy6A6jkF5xLyrIXk0XPuhtvk2i4hcVKgxuD3oLWWIK+NRfLvQZcQLVq1Zg2bSqNG9cFQclXU77j0qVL/PTTT06dP3HiRHbt2sWWLVsQxaw9A0iSxKxZs/j0009ZsGABzV+tTOKD4ZiMkSCIGNLTEUUlanVhfPy/RKN9xe5+/fv3R6vVMnPmzCzpkXGedHMilxI3cOlBBJeunKNWWFNCA7pTTFfLpjFpMpkeewsOHvqTkZvqodDZr25RCmqGVliCRuGca1+yJCPdr4/Dia5iMYTAXXJZcw4iGwMO+OL0atZEOy6n0ynUfBD6Gu1CnEvkyoukm5PYeedj7qVFIkkWLJgwGixoNBr8jNV4t+VS5v20gJYtW7paqkdx+vRpWrVqxY0bNx7/kN+5c4ewsDCio6Ntuu0fcfjwYV577TWOHTtGSEjmWl1bY9++fYx4rzurl2vRag1Yz2fQ4uv/PVqvtjb3SUhIoHLlyixZsoTGjR1P6ZR5fhITEwkJCSExMTFT5x2MimB30kwElX1jQCVoaBY0iGoBzoV/pNSlSImTwMHUSwQvhICfENQvOalYJrPk/bo3FyM64YJ9hLtbrRqFL61CviPRcItryTtJMz1g8oTpfDV6JeXKV6HI0q506NCBtWvX0qBBA1fL9RgWL15Mz549n3qiL1asGOHh4axYsYL//Oc/Ns9NTk6mT58+zJw5M1sMAYCGDRuycV09JMtBO6v0JD0cgUbbDEG0nozm7+/PzJkzefvtt4mMjLSbtCaTPajVatLTHTey+jcqPyPKdAVmB8PWjFI6Py6ZxtWN04GMe+Kj+6K1f7/T4zatXnairFGygOkKyMZAjiEbAw6oXagsm27/RaqDMIFZslDVv1QuqcpZCqiDqVqwDwDpVzdx8uhlypWoQnh4OIsWLaJjx45s27aNKlWquFhp/sdisbB48WLWrFnzzLE333yT6dOn2zUGRo4cSYMGDejSpUu2aTKb7yAKf2WkL9hFIF2/Dq2X7c52HTp0YMmSJXzyySdMnvwld9NOkmqKRSV6UdyrJkrRccWDjPOo1WoMBgOSJGXq4UUhqhCcSTGToGa1l2hdqh6SJD3OH7H17xdKrQf2Od5XEEBw3MRIJuvIxoADXi4SxhfCszfiJxEQCC0QTAlv55rEuBO1a9fmyJEjdOzYEYBWrVoxbdo0WrduzZ49eyhbtqyLFeZvDhw4gLe3t9UmLq+99hqDBw/mypUrlCtX7pnj69atY+vWrZw4cSJbNZkMf2XcmB21SpZSMOh32zUGIGOeQb+x4Sy4cApBYfl7CrKAJJmp6NeeOoGDUMg/BNmCKIoolUpMJpNTHQIfUdq7BpIz3TBFDS1r9CLYK9SpfaX0QkgJx8FOe2wAoyGd2JgQguXBlzmGXE3gAKWo4PPqPdCI1r84AgLeSg3/q9I5l5XlDnXq1OHw4cNPvdajRw/GjRtH8+bNuXPnjouUeQaLFy+mV69eVp/i1Go1vXr1slqvf/fuXQYOHMiiRYsoUCDzMwbs4/hH4RH37t1xGJ++Ka6n06gQTGIyRikVoyUVoyUFk6Tn/MO1bIoeiUUyPa9omb/JSqjAX10MIcEfs8ne/3sBH1Vhiuusd6C0LqYhOGisJUki1+8UpGqN1vTr14+zZ886v7+M08jGgBPUK1yeqbX+g3e6iGCyoFWo0CnUqEUlL/qH8Ev9IZT0LuxqmTlC7dq1OXr0KBbL0zeBwYMH89Zbb9GiRQsePHjgInX5G6PRyPLly+nVq5fNNW/3b0uA73zi79Yh/m41EmLaoE9dxYAB/Xj77bcJDw/Pdl0KVSg48eNsNCpYveYyxYsXp2rVqgwYMIB58+Zx7ty5x9dTfPoVTj5YAgrr+5mldGL05zifsD5bP4Mno9FoMBjshz2fJDU1lTfffJMlH57AS+mHaCU+JCCgEXV0KvFxpsIPgiAi+P8Agq18EQWC6Ef5Wiu5fPkyFSpUoFmzZnTo0IGDB+3lrGQgSUYMxosYjOexWDI/a8OTkKsJnMRisVChQgU+XzAdTcnCKAWRqgGl8q0R8CRly5YlIiLimZ7zkiQxcuRIDh48yNatWx1mtctkjo0bN/LFF1+wf/9+q8f1qatISfgQg0HPkxNgjSYVMTEWKlTej0abPUmD/+ZBTFtMRkfhBw2Fgo5jMnlx8uRJDh48yJ9//snBgweJj4+nTp06tBnhh3eZu+BgpLKPMojuZX53+yTdvEBQUBAnTpxwanrkxYsX6dKlC1WrVmXOnDlImnR23v2JS0n7UQhK+Lv5UBnvWjQNeocAdfEsaZKMZ5ESPwXj2X9yAyQDaBoiFBiPoPhHa1paGvPmzeOrr76idOnSjBkzhpYtWz51bVgsKSQkTSMp+RcyPFkCYMJb1wH/Ah+gVGZNZ35GNgacZPv27fz3v//lxIkTHndD6tGjB23atLE6i95isfDWW29x9+5d1q1bJ88lz0Z69epFeHg4Q4cOfeaYMf0giXF9AOvjaSVJgUJZEv8iu5weVpMZjIZTJMR1zGgKYw1Bh7fPSLx8B1s9fP/+fQ4ePMjtEtNQejt+ShUFFT3LrESnDHge2TJAyZIl2bt3L6VK2U94/v333xk6dCgTJ05kwIABT9339OZkYvRXkZAopCmJtzJ7Gq5JphtgugiIoKqKoLD9sGU0Gvn999/58ssvUSgUjBkzhi5duiCKqdy53xaj6SbP9i9QIIoFKFZkIyplmWzRnF+QjQEn6d69O40bN7Z6Y87vfPvtt0RFRTFjxgyrx00mE126dEGj0bB48WIUiowfH4slBYuUhCgUQJT7i2eK5ORkQkJCuHTpEoGBgc8cfxjbCZPhsJUzn0DwxjdgOmptixzRaDQcIzH+HSxSMkgpf7+a0ULW2/dDvHwGONzj1yvt0Zsdh5kUgobuZZbipcz/nricpnz58kRERFC+fHmrxw0GA6NGjWLjxo0sX76cmjVr5rLCzCFJEhEREUyaNIm7d++yaHFpihW/BNgyMkWUyjIEF93rcQ929pBzBpzg/v37bN68md69PbMVr7UkwidRKpUsXbqUmJgYhg4dSqp+L3fud+LG7UrculufG7crcS+2H+mGyFxU7d6sXbuW8PBwq4aAxXwfkzN/SykFfcr8HFCXgUpdi4JFj+IXMAed9wC0Xm/i4/cphYtGOmUIAASonXs6E1GgVbhvu++8xKPyQmtcv36dRo0acfPmTY4dO5bnDQHI6FnQtm1b9u3bx8KF31M48Cy2DQEAC2bzHdINR3NLolsgGwNOsGDBAjp27OjWsweehxo1anDmzBm7GcharZY1a9YQVHwnt+70JN3wJ2BCkvSAkTT9Fu7GdCQ5VU4Ec4bffvvNZuKgxXLf6Zprs+l2dsp6BkEQUWub4uP3Cb7+E9F590IQnc8dqVqwJ0qbyWMZiKio5N8eUZArobOKJElcTznJ79c/o/30Emy1fMWOu/N5aPhnONnGjRupU6cO3bp1Y9WqVW55v6taXY9a7dgLKUlppKZF5IIi90H+djlAkiR+/PFHFixY4GopLsPb25vy5ctz8uRJateubXOdWnOOfm8ZALOVoxKSlEbcg/fQqKuiUuaPBk05wf379zlw4IDN6X+C4OtUNj+AKGZ3WWH2EuJVh8LaCsToz2GWnn2aExBRK3yoGmC7okLGPkaLnt9vfMat1AsYpXR8iipJIZbDcWs5Er+eZoFvsfq7AyxatIiVK1fSsGFDV0vOMpIlFedKXyUskjwk60lkz4ADdu/ejUajoV69eq6W4lJq165tN1QAkJD4PbYS2h4hSSYSk37MRmX5j+XLl9O2bVt8fHysHhcVJREVRZ3YyQu1rlv2istmBEGkZfBXFPeqhUJQIzx6PpEgPdWCr7I4r5ecLScOPgerbk4mOvUcRkkP/JMiZsaESTLwR/QsotKOcezYMbc2BACUyhCcaI0JaFAq5IZpTyIbAw6YO3fuM5m0noijvAFJMqNP3+3ETkZS0ux3dPR07IUIIMNbtXt/RVJT7ef+CoICrVen7JaX7ahEHS2Dp9Cx1HyqBHSjtM/LVPRvz47vBZSRXfFVyWVgWSVGf51rKZFPjRz+Nwq1QKPBJazmp7gbWk0jBMGZiiYJH+/sa9GdH5CNATvExsYSERFBnz59XC3F5Tg2BtL4u4+sQyRb5WgyREVFcfnyZVq0sF4BEBsbS/v27flyyhmUmtdBsBYfVYDghW+hXzMVv3c1/uqS1AkczKvFJ9Ko6Ad0aDqQuXPmulqWW3P8wSbMkrWw3dOkmBK4p7+aC4pyFkFQEFDgIwQ7eShmsxof7+4oFUVyUVneRzYG7LBw4ULat29PQIDsoqxcuTI3b97k4cOHVo8Lgtc/Ll4HiGL+m+GQXSxZsoSuXbta7Ru/d+9eatasSVhYGHv37iMoZCY+/t+iUFYmI/1HC2jQ6DrjH7gZldp9x2kDdOnShaNHj3L1qvv/SLmKeMNtJKs5PE8jCiKJxphcUJTz+Pr0xs/3fQS0wJPfIwWSRcOWzXru3vLMyjB7yMaADSRJehwikMkoH6xRswZ7j+0nwZCI5V+jTAVBxEvXCYvFvndAEHQU8H4zJ6W6LZIkWQ0RmM1mPv/8c7p27cqcOXOYMmUKKpUKQRDQ6NrhX2QzAUGRBBTdR8FiZ/EJ+BZFPmiootPpeOONN/jxRznHJKtoM9HfQyVqclBJ7uJfYBjFg3bj6/MmKmVFVMryeOs6UDxoHb5e39ChQ2fi4+NdLTNPITcdssGePXsYNGgQZ86c8fh8gTSznojb21lxZT2SUkCpVKBTaGld7BXaFGuGVqEhKiqKUaN68MWUaLRa25eUKAYQHHQAheh+ZUs5gdFs5kz0PdIMRh7ciWbof/oQFRX1+Jq7d+8effr0wWAwsHjxYoKDg12sOHc5d+4czZo148aNG5masieTwYXEg6y79Q0Gi/3QnFrU8X7F31CKntFBdOTIkZw6dYqIiAiUSrmoDmTPgE3kxMEMko0pjDn5BatvbcKiAUkhYZRMJJqSWRUdwdiTk5jzy1zq1q1L48a9KBm8HCcQ0A8AACAASURBVEHw/ttF9w8CXohiAEGBq2RDgAwjYMaWAzT6bA4D5q3m/d82MHrjQYK6D+HApRtARgvsmjVr0qBBA7Zv3+5xhgBAaGgoFSpUYO3ata6W4paU962NSrD/xK8U1NQIaOUxhgDA5MmTkSSJMWPGuFpKnkH2DFghLi6OcuXKceXKFQoV8uz49udnp3Em8aLNJCTJJJF89gFTwj/mxRdfBMBsjiUp5TcePFxEQsItigRWwNe7Hz7eXRFF6+VynoTJbGHAvFVE3riD3vhsvwCNUkkV6SHbfpnFwoULeeWVV1ygMu+wePFi5s+fz9atW10txS25p49i4dUx6I0piIqnH26UgoYgbTl6l/4cpY0x7fmVuLg46tSpw4QJEzy2u+yTyJ4BKyxatIh27dp5vCFwXx/LucTLdrORBaVAwWpFKFb+n6dWhaIw/gXew5y+lC4dvAgO2k0B3zdlQ+Bvfjvwl01DACDdZOKoUcuWPfs83hAA6Ny5M5GRkVy+fNnVUtySotqyBF9szc0DaSgFNWpRh0rQ4K0MoHGRXvTxQEMAoFChQqxZs4YRI0Zw7NgxV8txOXKwBLivv82R+D08MMbio/RjyZZFfDXmO1fLcjlH4k8g4dhxJCBw9EEkLYOaPPW62Wx+PLRIJgOLRWL+nmM2DYFHqNVqdly5Q+Vy7p8I+LxoNBr69u3Ljz/+yOTJk10tx+0wGo2M/2ASM2bMoEnFRiSaYlEIKvxVRRAEz34erFKlCrNnz6ZTp04cOXKEIkU8t9zQo40BvTmNBdemciX5HGbJjAUzSFDn47IcDdhEDWNVfFWeG99ONadhcqLtrUkykWp+tvOg2WyWk3P+xa0HD0nS257x8AiDycy205cZ1qJBLqjK+7zzzjs0btyYzz77TB6TnUnmzZtHiRIlaN68OYIgUFhRwtWS8hSdO3fmxIkTdOnShW3btnns9eWxZqFZMvHD5YlcTj6LUTJkGAIAAii1Cm6lXWfqpf+hN6e6VqgLKaj2R+NEUpFaVFNQ5ffM6yaTSfYM/It0kxmF6FxSarrJufkDnkDFihUJCwtj9erVrpbiVqSmpjJhwgS+/PJLj0+Gtsenn36Kn58f77//vquluAyPNQZOJhzmXno0Jslo9bgFM0nGh+yP3ZbLyvIO9QrVwuJEfqkFC3UK1XjmdTlM8CxBfj4Yzc4MUoGyRQrmsBr3YuDAgcyZM8fVMtyKadOm0aBBA7sDxmRAFEV+/fVXtm/fzk8//UR06j1mX17GiL8mMeKvL5kXtZJ7+lhXy8xRPNYY2HF/PQaLfXetUTKwO2ZjLinKe3grvXi1aCPUdrwDGlFNq6Cm6BTaZ47JxsCz+Gg1NAsrh+jgKc1LraJvw7w/Sz436dixI6dPn+bixYuuluIWxMfH88033/D555+7Wopb4Ofnx5o1a5h7+XfeO/4FW+7u52rKLa6mRLPxzh6GHpvIkusbya8FeB5rDNxPv+PUuhRTEgaL7SEf+Z2+pbvwUkBVNKIa4cnZAxbABHUK1qBnyQ5Wz5WNAesMa94AhZ3ETLVSQaXigdQtJ8d2n0Sj0dCvXz+5I6GTTJo0ic6dO1OhQgVXS3EbjukuU6JtKCbMmJ8YhWySzBglE6tvbWf97V0u05eTeKwxIDg7VAcJ0XP/TIiCyPDy/RkbOoxaAVXwV/nhr/Kjqk8lDo/ZTmefVog2MpJlY8A6+7dE8OCPxfhqVHip/ynpEgUBrUpJjVLFmf1mRznGa4UBAwawYMEC0tMdJ2F6Mjdv3mTevHl88sknrpbiNqSa0lhzazsmwXYpdbrFwJIbGzFa8l8+j8emepfzrsTZpL8criuqDUEpeuyfCQBBEAgtUJ7QAuWfev1erSi++eYbvv76a6vnycbAs6xfv56RI0eyfft2ylesyNbTl5n86wpUOm8aVAujR71qVA4p6mqZeZYXXniBqlWrsmrVKnr27OlqOXmW8ePHM2DAAIoXl8c/O8u+2L+cekiUkDgaf5r6havngqrcw2MfeZsWfQ21gzadakHDK0Xa55Ii9+PDDz9k3rx5xMRYn3YmlxY+ze7du3nrrbdYt24dlStXRq1U0rZ6JUrcOUe/CoX5rEsL2RBwAjmR0D5nz55l3bp1jB492tVS3Ip7+ljSnQgJGy0m7unjckFR7uKxxkBZr0qknpEwp1vP7FYJasr6VKJmQHguK3MfQkJC6NGjB99++63V43Jp4T8cP36crl27snTpUurUqfPUsbi4OI/vdpkZXn/9dc6fP8+J02e4GBPL5dg4DGbHY3o9hXHjxjF69Gj8/T23R0pW0CjUToWERUFEo8h/vQg88rFNkiQ+/PBDDu05z/gVo9iXsAkLEknJifh6+yIJEg0KNadd8R424+EyGYwePZqaNWsyatSoZ37Q5DBBBufPn6dt27bMmTPHanth2RjIHA8NRqoOGUb3DZvQajQgAQL0qFaVd8Pr4qvJP6N4HZFiNHDw1k2SjQaCfQpguHqdY8eOsWTJEldLczteCniRFTc3k26xX/orSRI1A8JySVXu4ZHGwKeffsrWrVvZuXMnBQsWpGWJTlxMOk2vt3owd+ZPVAusjTofzfbOSUqVKkWnTp2YOnUqn3322VPHZGMAbty4QcuWLfniiy/o2LGj1TVxcXEULCj3FHCGWw8T6bRwCQlab8ySRIrhnz4hi47/xdZLl1nVtxf+umdLXfMTepORiQd2seL8GZSi+HdtioT+YSKd/m8sWm3+/vw5QVmfEIJ1RbmWchsL1g0CBSKhBcpSVJv/jHePe+z96quvWLp0KVu3bn18A1YISkILVOfiHzcJ9a4uGwKZZOzYscyaNYuEhISnXvd0Y+D+/fs0b96cESNG8Oabb9pcFx8fL3sGnGTwqnU8SEvDbKXW22C2cCcxiQ82bnKBstwj3Wyi+9plLD9/Br3ZRLLRQIrRQIrRiNlLxybSmXviiKtluiVjQwfgo/RCYeWnUSko8FcXYGTFfrkvLBfwKGNg5syZzJ49m+3bt9scSCGXc2WesmXL0q5dO77//vunXvcEY8BgNLH92EUWbz3O6j0nuf8gCYCHDx/SqlUrunXrZrfFqclkIjk5WY7vOsGZe/e5Gv/AbldMo8XCgWs3uJeUnIvKcpefI49xIS6WdLP18ja92cQ3h/dx/WGC1eMytimiLci0mmNpUqQOalGFl0KLGhWWdDPNizZgao0x+KsLuFpmjuAxYYL58+czefJkdu/eTXBwsNU1+bWzVG7w0UcfER4ezogRIyhQIOPLkp+NAUmS+HXzUX7ccAgA498zB75avJPalUL4a+0s6tevz4QJE+zuEx8fj7+/P6LoUXZ5lth+6QrpTiQKiqLIrqirdK9WJRdU5S4WSeLnk8fQ2zAEnlz3y6njfNKwWS4pyz8UVPsxvEIf3inXlTtp97FYLDSoVIdZh8dRQJV/x7DnmzuQRZLYe+cqnx/bzv8Obea3i8dJMmQ0Jlm2bBnjxo1j69atlCljfySs7BnIGhUqVKBly5bMnDnz8Wv5ubTw+xV7mbPuT1L1BlL1BowmM3qDCYPJzP5TVzGWacakKV87vJ7i4+PlfAEnSTYYnJqVYbZYSDNanzni7txKekiq0ZnyNwu7blzNBUX5F51CQ1mfErxQoBTNGjdl8+bNrpaUo+SLO/WpuDsM2L2SRIOeVFPGTUCnUPHZse28qizIivfGsWXLFipWrGh3H9kz8HyMGzeOJk2aMGzYMHx8fPJtaWHU7Th+33GCdKONpzNBRFB5s3DzMd7t1NDuXnIlgfOU9PdHq1SidzDNUaUQCfZ7dopmfsBkkRzOtfhnrXMDsWQc06pVKyIiIujfv7+rpeQYbu8ZuJAQQ4+tv3E3NemxIQCQZjaSbjaxIfEWb8yfStWqVZ3aT/YMZJ3Q0FCaNGnC7NmzgfwbJli89TgmB+5qg8nMip2RmEz218nGgPO8FlbRKYNdFAReLls65wW5gGI+PlaTJ/+NAFQqFJjzgjyEli1bsm3bNkz5eKy42xsD449secoI+DeCRsX6BzeISXOcUCR7Bp6f//u//+O7774hJiGCIqUjaNImigcp67BI+WfY07ELNzFbnHNX341PsrtGNgacx0+rpU/NaujshJ50SiXvNayPOh8aoQBapYoO5UNROHho0SlVvFPtpVxSlf8pVqwYJUuW5PDhw66WkmO4tTFwK+Uhf8XccmrtkksnnFonewaej9LlE/l9i5Ybce8SVGoftRveJDr+Q85EV+NBylpXy8sWMmM0OopxyzkDmWN008a0C62IVql86gdRJYpolArerF2T/9Sq4UKFOc97LzXAR62x2UVfq1BSu1gwtYtZT5SWyRotW7Zk06b8W7bq1sbAxYQY1ArHaQ/pFjN/xTpnNMhknWT9n1yNeRMfXxNK1T/eGouUgkVK5mb8qHxhELxYtpjTcduggr52j8uegcwhCgKT2rRgxRs96PBiKCV8fZDiY+lRvQob3+rLfxuH53uDvpiPL6s69iLYtwDeKhX8bXCqRBGNQkGzUmWZ06pDvv875DatWrXK10mEbp1AmJlWwc6slcMEWUeSJG7Gj0KS0uys0RMdPwY/r9aIgvv29u7Toha7/rqM3mA7fqhUiHRo9CJqlf2vWFxcHCVKlMhuifmeSkUCmdymJSkpKQQGBvLJ5M9dLSlXKRdQkL293+HArRuMXTgPjV8BmteoTffQKpTyk3tW5ATh4eGcP3+e2NhYChcu7Go52Y5bewaqFAzC4KDeFjIqCxoXs19S+AjZms4aqYbjmMyxTqyUeJj6R47ryUkqlSrKq7UqoFVb/6G3WMx4a5S81bauw71kz8Dz4e3tDUBKSoqLleQ+giAQHlKK4FMX6ecfxIf1GsmGQA6iVqtp0qQJW7dudbWUHMGtjYGCWi+ahrzgMJlGQqJTWccNSGTPQNZJM5xGkhyXMlmkFFINJ3NBUc7yvzdb0KlxVdQqxWOjQBRAo1JS3F9L1KYfMKTaTx4EOWcgOwgMDOT+/fuuluEy4uLi8uWTal6kVatW+TZvwK2NAYDxLzXHX6OzaRBIBiM9vUPwVTs3b0D2DGQVEZsZTf9CcP/LDoUo8t8eTfjjqwG817UxiriLtKxWnAXjerLh22G80aMLnTt3xmCwX0Uhewaen8DAQGJiYlwtw2XExsbK11Au0bJlSzZv3owlH/ZwcPu7clEvXza0eYu6RUuiERV4KVXoFEq8lWqK6nwZEVyV6f2Hs3//fod7yZ6BrOOtqeXUOlHwxltTJ4fV5B5+Pjq6Nq2ONv4cr7wYxAshGbXd48ePJzAwkCFDhti9rmRj4PkpUqSIRxsD8jWUe5QtW5YCBQpw8qT7ezf/jVsnED4iyMuX317tRXTyQw7eu47BbKasXyHqFimBIAiE/qqjY8eObNmyherVq9vdS/YMZA2dOgyNsjR643m76wRBQwFd/uuXrlAoMD/RiEgURRYtWkSDBg2YMWMGw4YNs3qePL74+fF0z4AcJshdHoUKHP2WuBv5whh4RIiPH118nu002LJlS2bNmkWbNm3YuXOnzbbEsmfg+ShZ6Hsu3+uIRbKezCUIWkoVnoEg5L+GMP82BgB8fHxYu3YtDRo0ICwsjFdeeeWp42lpaVgslsdJcDJZw5NzBvR6PQaDAR+f/DtAJy9htJgJblmb36OPsHP71+gUKtoEV6VzydoU0rj3/wO3DxM4S+fOnfniiy9o0aIF169ft7lO9gxkHZ06lBeKrkarqoTFosaQLiCgxWJWE3NPQZnCC/DVNnK1zBzBmjEAUKZMGZYsWUKvXr24cuXKU8ceuXfla+758GTPwCOvgHwN5Twx+iQ67/6eNYqrmEP8uKd/yLWUWH6+vIe2O79l9z37XtG8jscYAwD9+vVj5MiRvPrqq9y9e/eZ47Jn4PnRqUOpWGwr+//owPH9NSgeMI4Xii5haB81Rw+mu1pejmHLGABo0qQJ48ePp3379iQmJgJwOymRrZcu4Ff1RR7q9bkpNd/h6caAnC+Q85gsZt4++DO3UhNIMz/d/j7dYkJvNjL6+O+cfei+ze08yhgAGD58OH379qVFixbEx8cDYDCb2XPjGl41q7Pv5g0MTsxMl7HPvt230ImdKezbD1+vOowZM5ZJkya5WlaOYc8YABg8eDCNGzem88AB9Fy1jGaL5vHV2ZOkN29G3XmzGb5pAzGpnlcrnx14cgKhXEmQO+y5f4EYfRJmbFcRpFuM/HBhey6qyl48zhiAjGE6LVq0oHWbNny7bzcv/fQDQ/9YT8FunRi2eSMv/fQD0w//6dTsdBnrREZGUq1atcf/3bt3b86fP8+RI0dcqCrncGQMALzzf+O4UrsGB6Nvkm42k2axIKlVpJvN/HH5Iu2WLCLGA5vnPC+e7hmQkwdznsVX/yTVbL9MWAIOx0WRaLTdhTUv45HGgCAITJkyBUWbFsw4cpAkg4FkgwFRqyXZaCDJYGDWscO8vyVCDh1kgbS0NK5du0ZoaOjj19RqNaNGjcq33gFHxoBFkhiyeSOSSglW4rsmSSIuLZUPt+ff3uc5hScnEMqegdzhdlqCU+tUgoJYveNmY3kRjzQGAHbfuEZCYGEkG+NQ00wmtkVdYce1qFxW5v6cPn2aihUrolY/PX/g7bffZv/+/Zw9e9ZFynIOR8bA3hvXSTbYz5kwSxJ/Rt/gbrJ73kxchad7BmRjIOfxVjrXtM4kWZxem9fwWGNgzrEjpJmMdtekmozMPpY/3do5yb9DBI/w8vJi+PDhTJ482QWqchalUonJZHtOxs5rUaQY7V9vAEpR5M/om9kpLd/j4+ODxWIhNTXV1VJyHTlMkDu0C66OVlQ5XBek86eozi8XFGU/HmsMHL9726l1J+7dyWEl+Q9bxgDA0KFD2bBhA9euXctdUTmMI8+A3o6h8CQWSZITWDOJIAge6x2QwwS5Q4cSNR2Wb2oVKt554eVcUpT9eKwx4GxyoEWS5LyBTGLPGPD392fAgAF8/fXXuawqZ3FkDIQWLozORkjqSURBoGxAQHZK8wg8KW/gXlwSM5btod3wOVySqrD4YCK//XGUpBS5RDWn8FN78W2tnmgVKgQrQ1h0ChWti1elbbD1+5474LHGQEgB51w5wb4F5IYemUCSJE6ePGnTGAAYMWIEixcv5t69e7moLGdxZAx0qBjmlAHqp9HyUrHg7JTmEXiKZ2DfiSi6jZnPss1/EZOQgiQqSUgxMnflATqNmsflm/n/b+Aq6ge+wMIGA2hWNBS1qMCiN6ASFJT1CeR/VV7n4yqvu/VvhccaA+/UeMnhk5pOqeSdGi/lkqL8wfXr1/H29rYbxyxatCi9evVi6tSpuagsZ3FkDPhptQysWQeNaPsrp1UqGf9yM7e+obgKT+g1cCU6lnEzNqBPN2EwPX2t6Q0mElP0DJm0XPYQ5CAVCgTxzUs92dl8LDc+WMSq+kNY9fJw2gRXc/vvrccaA50qhVHMxxeVjZuzShQJ8vGhS2jlXFbm3tgLETzJqFGjmDt3LgkJzpXs5HWc6TPwVmhlDIeOogQ0in/mM+iUKrRKJZOaNqd52RdyWGn+xBM8A7+sO4TBaP8aSzeY2Lgv/1Xr5DW8lRpSbsYQ5JN/QnoeawzoVCpWdOnJi0WKolMqER/FgSQQzRYqBxZleZee6FSOM0hl/uHEiRNOGQOlS5emXbt2zJw5k4eGNC49jOFWykO3zc9wZAxIksTgwYNprvNh35sDGVCzNuHBJdCfO88H9cM53H8QHSqF5aLi/EV+NwZMJjM7j152GGrSG0ws33Yil1R5LhaLBZPJhNKJPCB3If98kiwQoNOxqmsvzsTcY8XZM9xPTcEHgZ/+O4pfjx7DW+flaoluR2RkJN26dXNqbdfhgxiy6mcWrfoelajALFkI1PowpHIDupVzL7ebI2Ng3rx5nDp1isOHD6PT6fhvvXAAAgcOpc0nE/FVu2dtcl4hMDCQCxcuuFpGjpGcZrCStmadhCT37IDnThiNRtRqtVvdoxzhsZ6BJ6kcWJRPXm7GzNavMbl1O+qULsOaNWtcLcstcTZMsPdOFB9e3osyrAwGi5kUkwG92cTNlAQmHNvK8P1r3KodtD1j4MyZM4wZM4Zly5ah0+meOhYSEsKtW+473CSvkN89AzqNCrPFdl/8J/HWqh0vknkuHhkD+QnZGLBC3759WbRokatluB2JiYncvXuX8uXL21330JDGoL0r0ZtNVlvzppmN7Lh1mWWX3cfdacsYSE1NpVu3bkyZMoWwsGfDACEhIURHR+eGxHxLrD6Fw+o0rlQLZsKxLfx575rbhptsoVErqRVWwuE6tUpBm4ZyuCmnMRgMqPJZCFk2Bqzw+uuvc+jQIe7ckRsOZYZTp04RFhbmMI62/Eqkw5t1mtnIrLMH3OambssYGD58ODVr1qRfv35WzwsODpaNgSxitlj49NgWGq2dwYqEa6S/WIoFF4/yzp7lNFn/A5ce5i9PwVvt66FV2/9uiaJI51fct9bdXTAYDLJnwBPw8vKiQ4cOLF682NVS3IrIyEiqV6/ucN2aa2cyvAIOiNWncDPFPaoNrBkDixcvZu/evfzwww82Y4tymCDrjDvyB79fiSTdYsYgZfztJTLaiEenPKTL1oXcSH7gWpHZSI1KIQzsEm7VIBAFsJiMvNuxBoEBPi5Q51nIxoAH8cYbb8ihgkzibL6Ao5kQj1AKIqlOrnU1/zYGLl26xHvvvceyZcvw9fW1eZ4cJsgalx/Gsu76GdLM1q8PCUgxGfjqxK5c1ZXT9GpVi6kfdKJeldIoRBEkM0pRoGWDULrULsCnHw4iRR6DnePkR2PAo6sJ7NGkSRPi4+M5deoUVapUcbUctyAyMpI+ffo4XBfi7cfVpHiH6wwWM0V1efcpR5Ik9p+4yqINRzgVVQBJgktjF9KzVXU+fv9NPv30U4eeEjlMkDV+uXgEo8V+zb1Fkth26xIPDWn4qXV217oTNSqGUOODEIwmM9179KJbl0706NEaSZI4F3mId955h99++y1fZbrnNeQEQg9CFEV69+4tewfskKY3snrHSXqNXUjLIbNIL/YqkdEm4hLsP5n0q1gbb6XjL1K9oqUI0OTN8k6zxcJH36/nfzM2EnnhFhZJQELgys1YvvhxC96V2vOfN/s73EcOE2SNyLjbmJ3IJ1ErFFxLyj+hgidRKRUEFvInISHj8wmCwKxZszh37hwzZsxwsbr8jZxA6GG88cYb/Pbbbw47y3kiN+48oNOon5m2eDdXomNJSEpD7VOQZVtP0mnUzxw8ec3muY2LlSXE2w+VYKc1r0LJf6vm3Qlgs5bt48/Ia6SlP+umtiCC2p9PfvjD4T6PwgTukiiZV1DYuXaeRJIkp9e6IwULFiQ+/h8vm06nY+XKlUycOJEDBw64UFn+Jj+GCfLvtyQbCAsLIygoiB07drhaSp4iVW9g4OfLeJCY+syPocFoRp9uYvS0dURFx1o9XyGK/PZKb8oWKIT4r/aqakFEp1Axo2EnqhYqlmOf4XlI0xtZsfUEeoPtJEijyczh09e5ff+h3b18fX0RRZGHD+2vk3mal4uVQyMqHK6zIPFCgfw74rdgwYLExcU99VrZsmX5+eef6d69e74aBpaXkI0BD0TuOfAsm/afI1VvxN7DrMFoZv66wzaPF9R6Ma1iE5LnradeYElK+vjjk2LgpUSRfR2G0iw47/boPxB5FdHOwKFHWCwSmw+cd7hODhVknt7la1rtUfEkgkWiS+mqaJX5y537JIUKFXrKM/CIdu3a0a9fP3r06IHJ5LhyRyZzyDkDHkjPnj1Zt24dycnJrpaSZ/h961/orbjHn8QiSew8cgmD0faN6IcZM+lXvxmLm/dhV/shjPGuQOrmg3k2T+ARDxJTneoGZzJbiH3g+LqRKwoyTxGdDx9VfwWtwnoOtEoQUSbr2ffptHwzDMsa/w4TPMn48eNRq9WMGzcul1Xlb0wWM3cMD1AG+aI3G1wtJ9uQjQEHFClShPDwcFavXu1qKXmGuIRUp9aJgkBSarrVY4mJiSxcuJChQ4c+fq1Ro0bs3bs3z8fP/Xx1KETHmdoKhUhBf8eGjVxRkDXeqFCLL+u0paBKi6Q3oFOo8Faq0YgKXg2pwIE3RhNW9gUaNGhAVFSUq+XmCNbCBI9QKBT89ttvLF26lFWrVgFwO+YhW/88z+b957h6y/p5MtZJMxv4+cpmXt/7KT+JB0nv+wKv7RnPlHPLiU13/zCfXFroBG+88Qbz5s3jjTfecLWUPIGXVkWiEzPTTRYLXhrrrrR58+bRokULSpT4p8VqiRIl8Pb25vz584SGhmab3uymQbUymC2ODRaFKNC8fiWH6+QwQdZpX7oytzfvZeOZ87zx3lC0CiXhQaUppPUG4Pvvv+eHH34gPDyc33//nUaNGrlYcfZiK0zwiMKFC7NixQrad+7F2qMPuXr7IUpFxjOg2SJRunhBxr7dgkpliuaWZLckxaRnyNEZ3EqLw2AxgQCoFaRbjPxx+yh7Y04z+6VhBHsVdrXULCN7Bpzg9ddf5+jRo9y+fdvVUvIErcJDUakcJ29VKVcMnfbZeK3ZbOb7779nxIgRzxx75B3Iy3jr1LR/+UU0dlrDSmYT5YL9KBnkeN65HCZ4Pjb9sYme9ZrQrVw12peu/NgQeMSQIUNYsGABnTt3ZsGCBS5SmTPYCxM8omhIOco3GcT5a7EYjGZS9UZS9UbSDSYuXLvPoM+WcvqSfG+zxzfnVxKdGpthCPwLMxYSjWl8GDkvz3s17SEbA06g0+no2LEjixcvxmQ0Y0j37ISczq9Uc+wmt5g4t38lV65ceebQ+vXrKVKkCPXq1XvmmDsYAwDv9X6Z6pWC0WmeNXa0aiWF/bVsmv8x+/fvd7iXHCbIOunp6ezcuZMWLVrYXdeiRQt27drFhAkTGDt2LBYnJwDmdR4ZDDvlOQAAIABJREFUA/Z+hD75IQKjBQQbJZb6dBNjp63H4oS3yxN5aExhT8xpjJLtEnMJiZj0h5x+eD0XlWUvsjHgBGaTmRplXmbTjAu0f2EUHSt+QJ/an7By7k7SUqzHxPMzRQr6MnFIWwTJTEbj16fRqpW83SmcDi3qUbduXaZOnfpUr4apU6fy/vvvW93bXYwBpVLBt6M68tHbzSlfKhBByEhuDy7ix/DeL7Ny2mAWzP+JDh06sGHDBrt7yWGCrLN3717CwsIoXNixezYsLIxDhw6xf/9+unbtmi/a9mo0GtRqtc0E56u34oiKjrNb+QOQkpbOkTPu+0OWkxyNu4RCcOwJTTcb2H3/VC4oyhnknAEHGA0mPu43l3PHrqGyeCMhIUkQd+8hC7+OIOLX/Xy7ZgR+BfNu29ycIPrCYZLPraVNn1EcOHkNAUg3GKlWsQRvdahL/aplgHBee+01+vfvz/Lly5k3bx6pqalcuXKFTp06Wd23UqVKpKSkcPPmzafyCfIiClGkef1KNK9fCUnKuC7EJzwmLVq0YMOGDbz++utMmTKFvn37Wt1HDhNknYiICNq0aeP0+sKFC7N161YGDhxI48aNWbduHcHBwRgtJg7G/cXOmIOkmFIpqilMy6DGhBV4Ic+39X3kHbA2A+Ovc85dV6l6I8fP3qRuldLZrM79SbMYkCTHniQJSDE7zqXKq8jGgAN+nLiWs0evYtA/W0pn0Bu5f+sBE975mW9WvucCda7h9u3bjBgxgo0bN/LSSy+hNxiJjU+kwgtl2Rcf81T9bfny5dm1axc//PADDRs2pFSpUgwePNhmK09BEB57B3r16pVbH+m5EQTBatl73bp12blzJ61atSImJoaRI0c+s6ZQoUKkpKSQlpaGTpd/eujnBn/88Qe//vprps7RaDTMnz+fKVOmUK9ePWav+onl0jZMFhNplgxP35Xk6xx7cJriuiJ8HDYMX1XeNfYfJRGWKlXqmWNmi8XpOLbJnD9CJ9lNUY0/ohNdLFWCkhCdnECYL0lN1rNl6UGrhsAjTEYzl09Fc/3CnVxU5jokSaJ///4MHjyYl156CQCtWkVIUCGKBwVaLeESRZF3332XjRs3EhkZyYoVKzhz5ozN93CXUIGzhIaGsm/fPn7++WdGjx79zM1ZEASCg4PlUEEmiYqKIj4+nho1amT6XEEQGD16NF/MmMzchBUkGVMeGwKQ8ZSnt6RzPfU2H5+ZisnBUCRXYq+8sGxwIRQKx7d5nVbFCyUCs1tavqBmwRdQOdHt0mBIx/uKc2XXeRHZGLDDsd3nEZWO/0Qmo5ld647ngiLXM3fuXGJiYqw2MqlYsSIXLlywee7GjRvp378/gwYNokmTJnz++ecYjc8aWvnNGICMssm9e/eye/du+vfv/0xXuOCQEK5EXXfrbOTc5o8//qB169ZOdYO0RXJlCZW3OqNUzApmycx9fRxHHpzM8nvkNP4FCxN9N8bqk33NsBIoBSeuKQma1i2fA+rcH4UgMqBca7Si7U6WGlHFi5YgRg4YTtu2be0+7ORVZGPADkkJqVhMjl1nFrOFhNikXFDkWq5cucK4ceNYuHChVTd/hQoVbBoDer2e2bNn89577zFgwACOHTvG3r17qVu3LpGRkY/XpZmMXPaH1AGvUm3VJF5a+xWjDq3mbMLdHPtcuUWhQoXYvn07t2/fpnPnzqSlpXHy/C1Gfb4Sc2A7PvvxL17pPY0vZ20m+k7+nLSXnWQ2X+DfGC0m9sQeRrKSBPskeks6629vy/L75ASSJLHtyEX6fLKIGz51mL3jDk2HzGDyou3cjUsEICUlhSFDhnD92CpUdrwDWrWS4X1eRqvOv22bn5fXguvRp/QrCGbA/M/1IiKgFVU0KBzG9FYjOXv2LM2bN6dp06YMGDCAu3fd574lGwN2CAj0ReGEZ0CpUlC4mH8uKHIdZrOZfv368dFHHxEWFmZ1jT3PwJIlS6hZs+bjZkIlS5bkjz/+YNiwYTRv3pxPPvmE6MQ42m6dzaRT21AWL0SaxUSiUc+G6DP02Dmfuecdl+nldby9vVm3bh0+Pj68+vogRkxYzsETVwEBSYJ0g4mInafpN2ohx0/fcLXcPEtaWhp79+6lefPmWd4j0eh8i/F7eutDt1yBJEl8Nm8LE37ezIUbMYCAWQK9wcSa3afo+b+FrPpjJzVr1iQlJYUju9bx2bB2eGlVT/X9sJgMaNRK3u31Mh2bVXPdB3IT2vhW48J7v9OqUHVKeRUhRFeYpkWrMa3WYD6t0gelqECj0TBixAguXLhAgQIFqFy5MhMmTLBbuXI99gH7Ll7j6NVo9Hbat+c0giT7JW1i0BvpUeP/HJYPqjRK5mwbQ7FS7ps84oivv/6a9evXs3PnTptu2Z07d/K///2Pffv2PfW6JElUr16dKVOm0LJly2fOu3XrFgMHDeJSm0oIgX5YbDypaRUqvq7TgRbBjrv65XWOnbrOiAnLsEi2jU2dVsXymW8T4Odtc42nsmnTJj7//PPnCiclGZN5++hYTHbqxx9RWB3AnJc+z/J7ZScrd0YydeluO1MzJcyGNEa1K0+vnt0fv5puMLHj0EWOnLmORZLYtPo3Phrem/btsu5d8STGjh3LgwcPmD17ttPnXL16lY8++og9e/bw2Wef8Z///AeFIiP/4EhUNJM37uJqzANUChFJypjp0qV2Fd5rGY5Wlbv5/bJnwA5qrYpOA5qi0dmeTmXBzIt1y+RrQ+D06dNMnjyZX375xW58tmLFily8ePGZ13ft2oXRaLTZGCY4OJjRP36HqrBtQwBAbzby7en8MU56wcqDdg0ByMgEX7ct78aqXcnzhggAfFU+FNU6/t4qBQV1C1V/rvfKLiRJYt76Q3bHZ4OAj08BCpau+tSrGrWS1o3C+HhQa8YPbkOnV6sRsWFdzgrOJ8TFxTF37lzGjh2bqfPKlCnDkiVLWLVqFfPnz6dGjRps2bKFbWcuM+iX1Zy7HYPeaCJJbyA53UCqwciyQ5H0nbOM9Fz2EsjGgAN6vdeChm2qovV61iDQeqnxKaQk4uRPxMTEuEBdzmMwGOjbty+TJk2iTJkydtcWK1YMvV7PgwdPx7unTp3KiBEj7NZrL406jsGJRKfbqYlEJeUdl21WSNMbiDznuHLAYDCzYcfpXFDkfmSHMQDQKbglGtH+KFpREGlTrMlzv1d2EHU7zubwrydJM5hYt9f+tdOxY0fWrl2bb7ox5iTfffcdnTt3tlq+6Qx169Zlz549fPrppwwd8T4jFqyxGRJIN5m5fC+OWTsOPo/kTCMbAw4QRZGR3/bm45/epmbjSui8NWi91JSvWoL/ft2LZYe/ou1rbWjWrBn37993tdxsZ+LEiRQvXpz+/fs7XCsIwjNJhJcvX+bAgQP06dPH7rl305xLwFQJInF69+4cl5JmcKrcCyDFiRu/p3Hp0iXS0tKoWrWq48UOaBxYh1oBL9o0CNSiijdLdyFImzfK7pJTDU5NzARIdHDtlC9fnkKFCnHo0KHskJZviY+PZ9asWXz00UfPtY8gCHTs2JGxP8xHobRfqphuMrPkYCQGU+6VtMpNh5xAEARqNKxAjYYVrB6fOHEiCoWCZs2asX37dooWdc8JYClJelJT0vH106HVqTl8+DBz5szhxIkTTndhe5RE+GjuwPTp03nnnXfw8rI/yjdA7VyzHbNkwVeldWptXsXXW+t0H3j/Ao5HIHsaERERtG7dOls6A4qCyPsV3mLjnZ0surAKiyih0+owSSaKaYvQp1QHagZUzgbV2UNhf2+MTlQ4AQQVfLYj4b/p2LEjq1evpn79+s8rLd8ybdo0OnToQOnSpbNlvx3nozA5U+0pwaV7sVQOzp3fE9kYyAYEQWDChAmIokjTpk3ZsWMHQUFBrpblNIf3XmTx3J1cPnsHhVLEYrZQK/wFVm6ZzvTp0ylWrJjTe1WsWJHz5y8gSRKJiYksWrSIkycdx727lqnBsbibpJgMdtf5qXVU9CvitJ68iEatpH7NMuw9ctluz3itRkWnlnkjVp2XiIiIYODAgdm2nyiIvFb8FSZ0GMMHU8ZSudKLFFT7U0yX966z4EA/Sgb5c+mm/VCZVq2kixMVAh07dqR79+5Mnjw5z7dddgUJCQnMnDmTw4cPZ9uezj7tC4Lza7MDOUyQjYwfP54ePXrQtGlT7txxj46Ei37YzuejlnL+ZDQmk5l0vRGj0czBXecJ1rxKqaLOlRylpxtZtekv/rziy56LATTq9g09h/1Io+Y9KVasuMPzmxWvgJdSbav3CwA6hYohoY3yxU2rX5f6qB1kC6tVClo3yTtPpXmBlJQUDhw4wKuvvpqt+967d49LFy/RoUE7KvtVyJOGwCOGdmlkd3y2ACTG3eH6Gcfu/xo1amA0Gt2ySU5uMG3aNF577TXKli2bbXuWL1oY0Yl7mMFkJqSgX7a9ryNkYyCb+fjjj+nduzdNmzbl9u28PSP86P5LrFiwn3Sr7ZYFkES++HAZsfcS7e6TlKKn/5hf+X/27jzOpvIP4PjnnLvf2cfY931JtuzKnrKFJJWlshSJZK30S9lCSSLKkiVKZMkalUiWECayE5oYZmHWu5/z+2MizMy9FzNzZ+Y+79drXph57jnfGXfu/Z7nPN/v8+mXO0hMcYGUVjOfkAqJcnlGvr8ap4cMVydrWNK0FyF6E/oMWn+aNDqeKPUgT5e9+9azuVHlcoX53+C2GPVatHf0slAVJ3qdxKz3uhNgNvgowtzp559/pm7dugQHB2fpcbds2ULLli1v21cjt2pSoyxDuzfDoNOmWz9gMugoUSiUjwZ3ZMyYMQwYMACLxZLpsSRJonPnzqxZsya7w85zEhISmDlz5n2vFbhTzya10XtYMwBQt2wJCgblXFmxSAaywdtvv83zzz9P8+bNc3W/+a/mbs8kEfiPoqhsWOH+CuPtD9cRdfkaVlv61bF2h8LhY1HMWrLDYzzlgyPY1GYAL1ZsQJDOgEaSkZGoFV6cjxp0YVyddvliVuCGFo0qs2T6C3RpU4vQYBNGg44iBYPp1KoSJ3fOJDxY3MW7U1ZVEdxp8+bN2XLc7PJUy5osfa8nXZrVoEBIAMFmA5VKFeSN3q34ekJvWjVrzMGDB0lISKBBgwacOHEi02OJZCBjM2fOpF27dlSsmLVtmqsWK0TjiqUxaDP//TbptAxv+0iWntcT0XQoG02dOpV58+bx888/U6JECRwOF3t+PcXfF+PQ6TTUqVeWChV9s7bAkmrjqYcn4fJip7JCRUNY8v2IDL924Z94Xhi5BLvbuue0++QbFryC2U3PhlupqorF5UAna7zaJCS/GTBgAHq9nk8++cTXoeQaqqpStmxZNm7cyAMPZN3tE6fTSeHChYmMjKREiRJZdtzcQFVVFixYwJtvvsmHH37I888/n26M0+mkaNGi7N+/P8sWyeV1iYmJVKhQgV9//ZVKlTJeOH4/7E4nI77ayI9HTqLR6bixntis1yHLEp/27kTdsjn7XBSXHtlo1KhRyLJMs2bNePftz/l2+WFUVcX6b2nZki92UrxEGP8b9yQlShXI0dgsqXY0WtmrZCD6cgwtWrQgNDT05kdYWBihoaGcuaLF6UVzDI1GZs+hc7Rq7F33QEmSMGtz/5Rtdpk4cSLVqlWjX79+WVJClx+cOHECVVUzbYd9r/bt20eJEiXyXSIAab9H/fr1o0GDBnTv3p1t27bx6aefEhj435bMWq2Wjh07snbtWoYOHerDaHOPWbNm0aZNm2xJBAD0Wi01HbEcObmXVn1f5czVOMw6HY/XqMRjD1bCkMPdB0HMDOSIIa9M5c/DqcgZ7HolSRIBAXpmL+hL0eJhORaT3e6ka5MJOOyeV6sWLh7M8yMe4vr16+k+Tl8xk+jy3MXNoNfyau9mPPl4/rjnnxM+//xzli1bxo4dO/LV7RFvWVNt/LzmAOsW/sK1mCTsTiv6wlbmfDOZsIJZt2bg7bffxul0Mnny5Cw7Zm6UkpLCkCFD2LVrF9988w01a/63OHj9+vVM+3Aa3yxZieJSiCgRjs6PNi66lpjK1bgkDHotYYE6KlaswI4dO27upZLVnE4nVapU4YsvvqBp06bZco67JWYGslnC9VTOnlAzTAQgbRovNdXOpx9vZcIH3TMck9VUVeXHH7eS4opCpxZGktzsaGbS071Pc1q2rJfh1xd9u4eF3+7B6aH2WaORCQsRNfN3o1+/fsydO5evv/6a5557ztfh5Kios1cY2XUG1lQ71tT/yk3tqXr6NBnHOwv6U/uRyllyrs2bN/PRRx9lybFys4CAABYsWMDSpUtp3bo148eP5+WXX8ZmsRN7IAV+DaFPtaHIsoQkSbTt14pn3+xCaMGcW9Ge007+dYXZX+/k8IkodFoNLkVFddmp2+pZKlXOmudXRpYvX07x4sVzTSIAYmYg232zdA9fLvwFWwaL626l02tYuvJVwgsEuh13P1RVZf369YwbNw6bzcarA0ayacn5TBcRSpJEaIEAFq5/PcN2zAD/XLlOz6ELsTvczzAYDTo2fvEKRoP/XG1khT179vDUU09x/PjxLF9Bn1ulJlvp+/A4EuJSyOzlyWDS88mmEZS6zzU30dHRVKlShZiYmAy35c6vTp06Rffu3SlfugLBp4tz5a+r2O94HdDqtQSFBzLrt/cpVDL/7b3y2x/nGT3tO2wZrHfSa2XqPFCKD0d1QeNmP5Z7oSgKDzzwAJ988sl97bqZ1UQ1QTY7fOi8x0QAQK/TcvbMFa+Pa0mxsnHJTgY0n8Az1UfTp+FYln20iWsx6csAFUVh9erV1KlTh7Fjx/LWW28RGRnJy4N6M/bj5zCa9OgNt08SGU06QgsEMG1hv0wTAYDihUOpV6M0el3mi/yMBi1d29YWicA9aNSoEW3atGH8+PG+DiXH/PTtPqyp9kwTAQCH3cE3s7be97m+//57Wrdu7VeJAEClSpXYs2cPyjEDF47/nS4RAHDanSTEJPJOpyk+iDB7JafaePOjdRkmAgB2p8Lh41Es33Qwy8+9atUqQkJCsrxXxv0SyUAuYbPbOHf2HC6X53v4f5+O5sWGY5n/3mounLxMQlwyly/EsmLmVvo0HMuhX9LKiFwuFytWrKBmzZq8//77jBs3joMHD/Lkk0/e3H2wTqMKLNr4Os/0a0qxkuGEhgdQrlIRBo5uz8INr1PMi4WN7w7tQLlSERm+2RsNOhrWLsfLzz58lz8R4YbJkyezaNEijh8/7utQcsS6RTtvuzWQEcWlsnP9YZweZqQ8yWslhVnJlmzHFqUgu3kbUFwKUacuc/rguRyMLPtt+uVPVDc7pAJY7U6+2rDf69bh3lBVlQkTJvD222/nunVAYs1ANqtVuwxHDl/0ODvgdCqMmzCKlwaeo1GjRjRp0oSHH36Y+vXrExDwX+OJ1GQrI7tMJzE+OV0r2xvZ/XsvfE6bwdWYNW86ISEhTJ06lccffzzTJ19ogUCee6kFz73U4p6+R7NJz2cTnmPbnpMsW7uPi5euIckSVcsXoWfnejSqUy7XPfHzksKFC/P2228zZMgQtm7dmu9/ltczmN3KkATJiamEFvDcgz8jTqeTH374genTp9/T4/O6fZsP/bthjvteIw6rnV9X/0bFOlnXhc/Xfth9IsO+KHeyWB2c/yeOcll0m2T9+vXIskz79u2z5HhZSSQD2axtx5os+eIXt2NkWaJ+w8qMn3qI2NhYdu/eza+//sqYMWOIjIykevXqPPzwwzRp0oTUizqsFrvbnvZWi5XVc7bxyexPaNWqVY68eeh0Gh5rWo3HmmZt2ZeQZtCgQcyfP5/Vq1fTtWtXX4eTrYxmA8kJmXfNu0FxKpjuo0Pj3r17KV26NMWKeW6XnR9ZkqxelRYrikrSteQciCjnWDw0W7tBliWsHnqoeCs3zwqAuE2Q7YJDzPQb2AKDMeN7kpIkYTbreWVoGwAiIiJ44oknmDp1Krt37yY2NpYPPviAiIgIFixYwPz3v8HmYQpVQsZsK0TzZi1y5ZNOuHtarZZZs2YxbNgwUlNTfR1OtmrR+SF0bnrv31CtXjkMXjaxysiN3Q/9VaFSER630gXQGXUULZ93Nl7zRtGC3s0m2R1OCt/jzNOdtm7dSkpKCl26dMmS42U1kQzkgC7d6vPKkEcJCDBgMuuRZQlZBhUXZcsXZOa8PhQtFprhY00mE02bNuXNN99k48aNRIR6/0uZkuj56krIO5o1a0aTJk14//33fR1Ktur4YlMk2X0S61KdWIMv4XB4d4WXkc2bN/t1MlD3sZrIHn7OADarjWNxh0hKSsqBqLLXhQsXGDlyJMvnjkdSPa03UbkefZbRI15z287ZG6qqMn78eMaMGXNzvVZukzujyofaPVGblRteZ8SbHejdtynP92vK0dNLmDTtSUqUDPf6OEYvp0UVl+K2CkDImz744APmzJnDmTNnfB1KttEYVaJ1h5E0ZDizZTDpeWpAS05fjuThhx/m9OnTd32OS5cuceHCBRo1apQVIedJWp2W3u92c/uaYjDrefipepz86wQVKlRg6tSppKSk5GCU6TkdLqIvxnH5QiwOL6bwVVVl165ddOvWjTp16uByudj+/bc8UKkEOjczIwa9js/eH0TJkiVp2rQpnTt3Zvfu3fcU844dO7h69Srdu+dML5l7oXn33Xff9XUQ/kKjkSldtiA1apXiwZql2b1nO7IsU6uW93vWX49N4nTkBRSX+xWuDzaqwOM9mtxvyEIuc6PXwNy5c3nuuee4+ncsUacv47A6CArLvh4VOSUhIYE2bdrQ9NGG/G/qMK7HJnH5Qiw6gxYJiSp1yjBoYjc6Pt+MHj16YLVa6d27NwUKFKB27dpe3xZbuXIliqLk6hfnnFClQUVSk62cOXgOUFH/XTkvSRLGAAP129bm7a+G0e3pbrRr147ly5czbNgwJEmiVq1aOVqSmZJo4auPtzDplcWsX7yTjUt3serzbSRdT6VijZIYjLdf/NjtdpYvX07fvn35+uuv6d69O4sWLeKJJ54gPDyclg0qceDPiyQmW3E4nTefO0aDFq1Ww6ShHWn8UCWaN2/OoEGDSEpKYsSIEaxcuZKIiAgqVqyY4fMtxWrnu11Hmf7tLyz/+TC/n4riywWfM+ilF3nooYdy5Gd1L0TTIR/68ssvWb169V3tGBbzzzX6P/IeNkvm06MGk56xi1+m9iPe7QMg5C12u5165RpR3VSX6/8kodVrcTlcFCxZgF5jn6ZlHi3jTEpKok2bNtSrV48ZM2bcfKG1WuwkX0/FFGggIMiU7nFHjx6lR48eVKhQgblz51KggOdy2G7dutG+fXteeOGFrP428qQLx/5m1fQNHNp2FFVRqfhQOboN70jVhpXSveEdOXKE9957j927dzNq1ChefvllTKbb/1/Onopm5dI9/LbrNE6Hi4KFguj6XCNatn0Q0z2s80i8lsLQjh8ReyUBxx1VADq9hpACQXyyYThhBYOIiYlh7ty5zJ49mypVqjB06FDatWuHRpN+FkBVVd6bMpudkZcpXKICRr2WR5tUoX3T6gQHGtONdzqdrF69+uYMyYgRI+jZsycGQ9rsyt5jFxjx2XpUwGJLe42WAMVp56GqZfnk1c6YjblzxlYkAz4UHx9P2bJluXz5Mmaz961693wfyYT+c1GcKmlPtf8YTHq6D2nDs0P9915ofrd21mY+H7kEZwalUQazgY4D2/DyB719ENm9S0lJoW3btlStWpXPPvvsrhe+Wq1W3nrrLVasWMHixYtp1apVpmMdDgeFChXi+PHjFCmSvxbG5aTDhw/z3nvvsW/fPt544w369++P0WhkxZe7+XLudhwO1201+kajjuBQMx/Pf5GIQnfXTfPtXp8Ruft0pn0lNFqZkpUL4ixxjm+//ZYnn3yS1157zatNvtq2bcuLL77I008/7XU8qqry888/M3XqVP744w9ee+01WrTvytDPN2dafaDXaniwXFHmDnsqVy7sFsmAj7Vq1YrBgwfTuXNnrx/zxx9/0LF1V3q2Hswfu86gkWWcThdVHirLs0Pb8lDz7NlcQ/C9v45eZHCDN7FZMq8oMQYYeOfbEdR7zPvbT75ksVjo0KEDpUqVYsGCBfe1wGrr1q306dOHZ555hokTJ2IwGLA5nWw+c4q5Bw9wMeE6KAqOs+f4ZtSb1CpSNAu/E/908OBB3n33XQ4dOsQLPYZzeFdqpn1VZI1E0WJhLFg5yKvFiwBXouLp32JSuhmBOymqk4eejmDo6FcoVKiQV8dOSkqiePHiREVF3XO778jISD788EMOJIViKlyWOy/QbmUy6Ph0SBdqVSh+T+fKTiIZ8LFZs2Zx4MABFi1a5NV4l8tFo0aN6N+/P/3798dmsZOckIop0Ig5g2ktIX/5sO9sfliyA8VDfXiNZtWY9vN7ORTVvbPZbHTu3Jnw8HCWLFmS4VTu3YqNjaV///789ddffL54EWOPRhKVmEDqrZUHqopJp6NXjdqMbvJIrrxSy2v279/PmCGrwOV+ltNk1jNmUlfqN67o1XE3LPmVeRO+y7Bl8q20OpnnR3bgqQEtvY555cqVLFiwgO+//97rx2QkPjGVtm/Mw+Hh91KSoHWdSkx5STQdEu7QqVMn3n33XZxOJ1qt5/+OGTNmEBAQQL9+/YC02wL3U2st5C271+73mAgAHP31BC6ny6s6cl+x2+1069aNwMBAFi9enCWJAKT16li9ejULFiyg29LF6EuWIN1PTJKwOJ18+cchSoeE8OyDNTM6lHAXihUuh0EXgs3l/k3bkmpn8dytXI0/SUJCAomJiTc/bv33jb/L8REUcFZ2u7sqgNOhYEmx3lXM69ato1OnTnf1mIxcjk/EoNPicLnvAaOqcD46/r7Plx1EMuBjJUuWpEyZMuzcuZMWLdy3Az537hyTJk1i795QtVyJAAAgAElEQVS94krGT9lt3tXVS1LaWFMuTQacTifPPfcckiTx1VdfeZUI3w1JkqjXsQMB1mRsSub15Bank49/20P36jWQxe/UfbkWn4JWK2PzYuzJ439xfs4mQkJCCA4OvvlRpEiRm3+/8bVT+6NZMeMXj83WDCY9BYuFeR2vw+Fg06ZNWdK3w6DT4vJykt3gRUMtX8idUfmZLl26sHbtWrfJgKqqvPzyy4waNYoKFSrkYHRCbhJRPJx/Tl/2OM5gMnjdkyKnuVwuevXqRWpqKmvWrMm28rQVfx7BoXqeRUl12DkcfZk6Rf2zLXFWCQo2edXeGKBe/Vq8P/NDr8ZWf8DOyo/dt3QHUBWVR9p7v07m119/pWzZspQoUcLrx2SmbNFwDDrtzQqCzBj1Wh6vW/m+z5cdRNOhXKBz586sXbvW7ZatixYtIj4+nmHDhuVgZEJu8+Rr7TEGuH+TV1Ao3qAgiuLdC3N2OHMqmsnjv+PZLp/QvdMMxoz8hsMHz+Nyuejbty+xsbGsWrXqZklWdriclITixdWaJEnEpvq2kU5+UKpsBMEhnquiTGY9bTvV8fq4RpOepwa2dHs71KU6eahNOQKC05eeZua7777LklsEABpZpmfrOhh0nq+vOzbOnfu3iGQgF6hWrRp6vZ7Dhw9n+PXo6GhGjx7NggULsnw6VchbHu3dlIDQALcrsc1BJo4m/E7dunXZuXNnDkaXNoM155MfGDpwMT//8CexMUnExyWzf+8Z/jdqBV3av8Nf587z3XffpatNz2oFzF4eX4Vgg1h8e78kSaJnv6YYM9mHJW1M2pt74+Z3d3X83GuP0ebpBhiMOmTNf29bsixhMOl4sElpZq54hy1btnh1PFVVs2y9wA292jxEjXJFM00IDDotU15qT5A5dz7XRAfCXECSJKKiojhz5kyGtwpefPFFWrduTc+ePX0QnZCb6PQ6HunakF/X7ENRFJy31DSbAo2Yg018tH0cr495jbCwMF5++WUOHDhAgwYN7rl06m6s/Hov3y7/DZvNmW5nTadTwWGTad26A60ezf4Fe0F6A9+fPY3DwwyJUadlbLOWaHJpz/i8pHylIsTFJnHxXAxO5+0/d51OgznAwLTPnyeswN11y5QkiXotq9GgdXWsFjupSVYCQ8w81Lwqr03uzrOD2tKkSRO6d+9OmTJleOCBB9we7+jRo3z99ddMmjQpy9ZfaWSZx+tXRpYlTkXFoJGlm+sDapYvxoQ+balfpVSWnCs7iNLCXGL37t0MGDCAP/7447bPr127llGjRhEZGZntV1JC3uFyutiz/gDr52wl7lI8wQWCaNu3Fc2eboT+lg5nKSkpTJ48mdmzZzNs2DCGDx+O0Zg9VyYOh4unOkwnNcX9EjKdTsOSlYOIiMia3eAyo6oqrb9cyMWE65ku7jJptQys24BX6zfM1lj8iaqq7Nt1muWLd3HsSBQSabcGOnStS5fuDQiPyL622ZGRkbRt25Zx48bdrLjKyIQJE4iNjeXjjz/OljicLoWzl2Kx2p0UDQ+mUB5oFS6SgVwiKSGFRtUeo3mdJ5BUDSXLF6blU7Xp/OxjfPXVVzRt2tTXIQp52Llz5xgxYgSRkZFMmzaNTp063bwislvt/Lx8Fys/XEf0+atotBrqtK5BtxFPUK1hJa/PsfvXU0wZ9x2pHlZ963Qanu/XjO49sn+ToH8SE+m64isSbFZsrturCkxaHS3KlOWTth1EJUE2cbkUnA4XeoM2xyqgTp8+TZs2bXjllVcYOXLkzc9bUqxcPnsFSZZ4+vmuTPlgCi1bet+TIL8TyUAu8PuOE0wYuBCb1YaqpP3CpG3hqmAIU/h65we5dmW4kLf88MMPvPbaa5QoUYIZM2ZQNKIYrzd9h9ioOKy3XNFLsoTeqKfL4Lb0fb+HV8dev+Z3Ppv1I3YPneIAOnapw5DhOdMy+7rVwpLIwyyOPEiizYYKVIkoyMCH6tOuYvre+0LeFxUVRZs2bejUqRPDB49kybsr2LZsJxqtBkVVSElOoeuQjjz/bncCQwN8HW6uIJIBHzsZeZHRz8zKdOMhnV5L9frlmPjlAPGiJWQJh8PBp59+ysQJE2mofRTHNQVXJj3fDWYDr87sw+Mvpr+CSklJ4Y8//uDgwYMcOnSIo5ExmLQ10WrcJ66yLPFMz8a8+FLzrPh2vKaqKhanE60so8+iBkdC7hUbG0u7lh0IO1MKySnjct7+HNfqtUQUD+fTfZMJLpC9t6zyArFixse+eH+d2x0IHXYnxw+e51TkxRyMSsjPdDodQ4cOZe2S9djiHZkmAgC2VBuL3/mG+Ph4tm3bxrRp0+jRowfVqlWjYMGCDB48mMOHD/PQQw8xafIITCbPpWU6nYZHWuT8jpqSJGHW6UQi4CciIiKoSWNcViVdIgDgtDuJjYpn6guzfBBd7iPq1Hwo7koCxw9d8DjOZnXw3cKdjJpROgeiEvzFnlUHwSUB7icHr16KoVqJB6lQpyx16tShdevWjBo1iqpVq6LX3177vW9XPL9sP4Ejk53bNBqZUmUiqFBR7BYoZK/TB89x+dxVJDcbBzkdTg7+eITYf+KIKO556+v8TCQDPnQlKh69XutxNy5VUfn77JUcikrwFzF/x7ptdHWDOcDMqi/X0KRTfY9jXxvZlgvnY/j7Qly6net0Og3BoWbGTfF+q1hBuFd71h/AYXW/mBXStj/et/kw7fplvu21PxC3CXxIb9Ddtt+327FuGnkIwr0ILRTi1ThJkgmJ8K5HgcmkZ8acF+jdtynhBQLQ67UYDFoCAgw82b0+cxf1y/aSQkEASE2yePX66nIqWO9yg6P8SMwM+FDZKkXR6jzfvzSY9DTrWDsHIhL8yWMvtGDPugNYkt2/EOr0Wqo29G67WQC9QcvTzzXiqWcacv1aCoqqEhYagEYrrj2EnFO8fBEMZr3HDY50ei1FyhTKoahyL/Hb6UMarYZOLzb1eNUvSdDqyXo5FJXgL2q1rE5YkVC3rY0NZgPPvNH5nrYXlmWJ8AKBREQEiURAyHHNn2mC6sXMgCRL1G8nLrbEb6iPPT2wFZVqlMSQSUJgMOoYM/sFAoJyZz9rIe+SZZkpW/9HaOEQdBk8/4wBBh5+sgFdX+/gg+gE4f4EhQXSeXBbDG56tBjNBl4Y3x2tFxsM5Xeiz0Au4LA7WTHnJ75b+AtOhwtZlrDbnVSpXZq+b3Skci1RRSBkn8T4JNbN3sLaTzaRdC0FVVGpVK88z4zuTJPO9UV/CyHPUhSFT16Zx49f/oLD7kT5d4tlrU6LrJHoProzvceKBa0gkoFcxeV08deJS9htTgqXCKdAYe8WeAlCVrFb7Wh0mnu6LSAIudX5P/9m9YyNHNt9EkmWqN3qQboMbkfRcoV9HVquIZIBQRAEQfBzYs2AIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmRDAiCIAiCnxPJgCAIgiD4OZEMCIIgCIKfE8mAIAiCIPg5kQwIgiAIgp8TyYAgCIIg+DmtrwMQ/qMq8aip34BlFShJIIeB+Tkk05NIcqCvwxPyMdUVjZq6AhxHQdIiGVqBqR2SZPJ1aIJw11yuy1hSvsCa8jWqmogkmdCbOmIOGIBWV8HX4eVKkqqqqq+DEEC170e99hKoLsD63xckE6BHCv8SSVfFV+EJ+ZSqKqhJUyB12b+fsaf9IZnT/giZjmRs4ZvgBOEeOOz7SYjrgao6uPl8BkADkp6gkI8wmp/wVXi5lkgGcgHVeRE17glQUzMfJIUgFdyKJIdlzTlVF9j3gusiYABDYyRNkSw5tpB3KIlTIPUrwJLJCCNS2DwkQ4OcDEsQ7oniiiX+ahNUNdnNKBNhBdei1VXPsbjyArFmIBdQUxaAavcwyJY2jZsFlNR1qDEPo15/FTXxfdSkcagxrVHi+6G64rLkHELup7piIPVLMk8EAKyoSeNyKiRBuC+W1C//nRFwx0ZK0qwciScvEcmAj6mqCpY1gNPDSOu/V3D3R0lZBolvgxIHakracdVUwA723ahxXVCV+Ps+j5D7qZaVgOR5oDMK1XEi2+MRhPtlTfkKsHkYpWC3fo+qenrN9S8iGfA5K+Apk03jtMewatUqdu3axdmzZ0lJSbmrM6muOEiazG1rEm4/AyixqEkf3tVxhTzKcRzPL5yApAHnuWwPRxDul6om3MXYu3v9zO9ENYHPGbweabVLLF26lCtXrhAdHc3ly5fRarUUKVLE40ehQoXQ2L7x4ixOsGxADXpLVDDkd5L3zz0kXfbFIQhZRJKCvXyTV5GkgGyPJy8RyYCPSZKMlQbolN3IbudpdAQW6M6aNe/c/IyqqiQlJREdHZ3uY9euXbf9OyYmhh1rS9DwIS9e1CUtOE+Bvs59f39C7iUZWqLafvr3dpEbqgP0D+VMUIJwH4zmZ0hNno37GS8ZvfFRJEm8/d1K/DR8yOFw8Omnn7Jlw/esWRiGXna5Ga1BCnj+ts9IkkRwcDDBwcFUqlTJ7blcLhfOmG7AUS8ikwDFi3FCnmZsDYnveBikBUNzJDk8R0IShPthCuhNUsJsNBo3gyQD5sAhORZTXiHWDPjI9u3bqVOnDps2bWL6rO3ow98AjBmMlNI+HzIZSVv6ns+n0WjQmesBXswMqDbQlrvncwl5gyTpkUI/JePnHaiqFuQIpJD3cjYwQbhHq1bvoM9LKSiKkTtf61RVBkwEhkxGp6/hk/hyM5EM5LCoqCieffZZXnjhBcaNG8eWLVuoUqUKcsDzSOHzQd+QtAmbf5/MhpZIBb5CNrW773NL5h54+i9XFFD1j4grQT8hGRpw5J9RHD6qoGIAKQikQBxOmYPHCiFFrBXPBSFPWLJkCUOGDOH9yVuJKLIDY0BvJCkIALtd5p/LDxJWcB0m81M+jjR3EslADrHZbEyZMoVatWpRsWJFjh07RpcuXZCk/0q7JH195PAlSIUOIBX8Aanw78hhc5CyqDmGpC0F5meBjFvMqkhYrBJ9Bh8nLk70G/AHqqry6tDPifx7DHLEeqSQD5BCpxMvr+Wxbn8Qf030JBNyv88//5wxY8awbds2atasiUZbgqCQcUQUPUFE0Sg2/fAO0z4OR6ur5utQcy2RDOSALVu2UKNGDXbt2sVvv/3GuHHjMJvNmY6XZDOSpjCSlPH07f2Qgt6EgOdJq2K4cXwJJDOSpgSmYmspVKwe9evX58iRI1l+fiF32bhxI9euXaN3795I2jJIxpZIhmYULVaFLl26MHv2bF+HKAhuTZ8+ncmTJ7N9+3aqVq2a7uuSJNGyZUu2bduGaLibOdGOOBv99ddfDBs2jCNHjjBjxgzat2/v65BuUpUEVMt6cJ4ByYRkbAm6ujdnKpYtW8bQoUOZM2cOTz0lptXyI5fLRc2aNZk0aRJPPJG+V/uJEydo1qwZ58+fx2QSGxYJOU9VXVxN/Ynz1+eTbD8JQKC+MmVC+1HI3IpJkyazePFifvzxR0qVKuXmOCplypS5eVtWSE8kA3dBURX+SDjBhkvb+MdyBZ2spUF4LR4v0pQChv/2DLBYLEydOpWZM2cybNgwhg0bhtGY9Vf52e3gwYN06dKFnj17Mn78eGT3tY9CHrN48WLmzZvHzp07b7tddavOnTvTpk0bXnnllRyOTsirbM4LXE1cRLJtNyoKgYZ6FArqg/EudwtUVDuHogeSYDuM6459WzSSmZioACYOimXL9z9RtGhRj8fr06cPdevWFc/lTIhkwEsWl5Xxx2ZxIeUfrMp/Naw6SQtIvFSuOy0KNWLdunUMHTqUunXrMm3aNLfZal5w9epVunXrRlBQEMuWLSMkJMTXIQlZwGq1UrlyZb766iuaNGmS6bjdu3fTq1cvTp48iVYrKpGFzKmqyuWE6VxJmoOqKvzXWVWLJGmJCOhOibD3kCTvLir+jHmb6JSNKGrGHVPtNigS0I6HSk7z6nhLly5lzZo1rFq1yqvx/kZc6nnp/eNzOJd88bZEAMChOnGoDuaeXU6HwV154403mDdvHitXrszziQBAoUKF+PHHHylTpgwNGjTg5MmTvg5JyAKzZ8+mZs2abhMBgMaNG1OsWDFWr16dQ5EJedXVpAVcTfocVbVxe4t1J6pqJS5lBZcSvGt1bnddIzplQ6aJAIDeANddP2F3XfPqmC1atGD79u0oiuihkhGRDHjhTNJ5ziRfwOFmYwsHTsI7lSIyMpLWrVvnYHTZT6fTMWvWLEaOHMkjjzzChg0bfB2ScB8SEhKYPHkykyZN8mr8qFGjmDJlilh8JWRKUW1cTvgIRc18B0xFtXA1aT4uJcnj8a6m/IB3b08SV1K2eBVj8eLFKViwIJGRkV6N9zdi3s8L30fvxKF43kzIGaQS47pGcQrnQFQ5r2/fvlSrVo1u3boxcOBA3nrrrUzvNQu519SpU2nfvj3Vq3tXstq+fXtGjx7Ntm3baNWqVTZHJ+RFCZZtgBfJoipxNmoJtoSmJCQk3Py4fv36bf8uXfsEtVtZPLRoT0tC7Hex7XqrVq3Ytm0btWvX9vox/kIkA164bL2K4sUTXStpiLVdo7gpfyYDAI0aNWLfvn107dqVQ4cOsWjRIgIDxYZGecXly5f57LPPOHTokNePkWWZkSNHMnXqVJEMCBmyO6NQVLvHcSoWFi6ZzLqvZxMSEkJoaCghISG3fZQqVYoi5UxI/IjHHV1VHXpNqNdxtmzZkgULFjB8+HCvH+MvxAJCL0w6Npvfr3vu6W+SjbzzwGAqBZXNgah8y2az8corr7B//37Wrl1LuXJp7YtV1Q62n1AdxwANkr4u6Bt7vWhIyF4DBw4kICCADz+8u22q7XY75cqVY/369eKqSkgnJulLoq6PR3Vzjz+NhqIhwygaMtjtKJsrll8vtkLBfYLhsKl8ODiQHs8M5JlnniEgwP1OhHFxcdRvVJ49v3+LTqsnUF8dnUZ02ATQvPvuu+/6Ooi84PD14zhVdxsJgUHW8UKZp5D94I1Pq9XyxBNPoKoqvXv3pnbt2pQpegzie4LtR7DvAcd+sP0AqctA9yCSprivw/YbqqoSZTnGjiuL2Be3hlNJe7h6OYb3Rk/lm+XfuG16lRGNRoOiKKxatYquXbtmU9RCXqXVFOBK4hdIkvvFeZJkoHjoW+g0Bd0fTzaT4jhLqvMiKhm/7sqSgSJBj1K9VF+WLVvGsGHDiIqKolSpUhQqVCjd+BT7KS6kvEnrrvFcs/5EnGUrUQnzSbYfI9hQF62fb9kuZga84FCc9D/wJknOzLd61ct6uhR/lKdL5p7GQjllx44dLF/Uk4/HB6HTZrbI0ogUvhhJL64qs1uqM5EVF/9HrO1vHKqNG/dyXTbQqDr6VZtBQWOZuz5uYmIi1WuUZ8PPb6AxnwJUQoz1KRz4FLq7mKoV8pfLly/zxhtv0LTjNmrV1SDJmSUEGky6qlQtusmr47oUC79Hv0iS/VS6hYmyZCJQX5G6RRahkdMaYv3999/Mnz+f+fPnU7ZsWV5++WW6deuG0Wgk2XaUyOjnUO7oV3AjLp0cQu1i32HQeu5XkF+JZMBLZ5IvMPbox6Q6LMia26/89bKOqkHlGVNtEBrJ3d6Z+ZOq2nBF10eWMl9JDICmPHLBzTkTlJ9yqU4WnhtMvO0fXGSUmEkY5AD6lZ9NsC7iro59OXE5J6++g6pIaPVpV2uyZEzr7hY2ghIhL2bBdyDkFTabjRkzZjB16lT69+/PqDdeJir5GZyuGNR09/q1aOUQKhdZj0FbwutzKKqD6OQN/JUwn1THXwCYdWUoE9KPooEdkCV9usc4HA42bNjA559/zu+//07v3r148tXdKFKsmzNpCDHWo0aRpV7Hlt+IZOAufLx4Jj+m7CWwdgE0kgYFhUBtAJ2Ltebxos38MhEAUC3rUBPfgQyz7luZkAosy7KNl4T0jifuZOM/03G4uXcro6V2WFvaFB3o9XGvJH/HmbgxmdZ9y5KJcmFvUjT4ubuOWcg9VFXBqaYgSwY0GbzR3rBp0yaGDh1K5cqV+eijj6hYsSIATtd1LidMIy5lJTdKA1WchJs7Uyx0ODrNvS+uTmtkxF2tPzp37hyrN02gRosdmALcVz5JGKhbfAtGnffJSn4ikgEvpaSkUKlSJdauXUv1Og9yzZ6AVtJS0BDu9+V1SsJ7YFnmxUgTUvBbSObu2R6Tv1p87nUuWT03htJJRl6vsgKN5LmgSFWd7P27AU4lwe04jRRAw5L7kGWD1/EKuYPFGc1fCYv4O2k1iupAxUWovjrlQ/tTyNz85mvc6dOnef311zl16hQff/wx7dplvLW6olixOv8CFAzaMmhk9wv7stO5+Pf5J3GBx3GyZKZ8+DsUCfLPvVhEaaGXZsyYQZMmTahXrx4AJlPe22sg29zVjEj+X1zpS9ccl70aZ3famPnZRwTpCxAUFERgYGCGf5rNZuItO1DdNNy6QQViU7dSKLDjfX4XQk5KtJ1gb/SLuBQL6i23lq7b/+BwzCiKBz5BKf1rTJo0ifnz5zN69GhWr16NXp/5zIEsGzHr0+8g6AuKavM8KG1kWjWUnxLJgBdiY2P56KOP2LNnj69DyZUkfT1UyypQM19gmUYFXa0ciclfeXOlD4Ckcv7cRRLjTpCcnExSUlKGf1qtVnoNKkjvwQHodO5nwBQ1hVTH2Sz4LoSc4lJs7IvujzOTroAu1cKF66t5b/IXBDibceTIEa82BcpNAvSVkSWT2+6IABIaTLpyORRV7iOSAS9MmjSJ7t2737wvJtzB0BLwYnZAWw5JJ36G2alCYAMOX/seJPd3/woaS/HWB7M8Hs/lcnE+bh6XUj8BDzXfIGe4oEvIvaJTt+LycOUsaRz0HV2axyoszJO3RAsGdOBc/ESP4zRyICHGBjkQUe4k5mw9OH/+PIsXL+Z///ufr0PJtSRJhxT6IZDxrRNFAVUyI4VMydnA/Myff/7Jp8PX4rS774ehk4w0injaq2NqNBqKhLb0qneGLBkINTby6rhC7vB30up02wNnRNIlk+I4n/0BZQOtHETJkEHIkinTMQ67ROngMXky2ckqIhnw4H//+x+vvvoqRYoU8XUouZpkaI4UNhvkIiCZcbpk7A4ZMHI+SstXmzog6Sr7Osx8KSkpiREjRtC8eXMeb9KFR0u8hFbKeBGfVjJQPrAuD4Q09/r4AfpKmHXlcfdyoSgq9tRAggziNlBe4nC5XxR6g4Q201sJeUHJkAGUCO6HhB6J/343ZMmELBnZsrwIrw/4EpfLfSKdn4lqAjcOHz7M448/zunTpwkKCvJ1OHmCqqpg38dvuxdz6uQZevX9mDPndTRq1Ij9+/dTtmz+adVsdTj5/tBJlvxykOhrSeh1GlpWL0/PR+pQrnD2tzhVVZXly5czYsQI2rRpw+TJkylcOK1061Tibn6+uogkRwyypEVFQSvpaVDgKRoU6HLX7aEtjvMcvvwkTiUZuLOpjASKkTf6JNG4Xjfef/99tFpxBzIv2B89kBjLTo/jZMlA0+LrMOvydhdRuzOGy8nLSbIeQpI0hJoeoXBgFxw2Le3ataNy5crMmTPHL2cIRDLgxuOPP06HDh149dVXfR1KnrNixQq+/fZbVqxYAcCUKVP48ccf2bp1a774RbuakEzvWd8Qn2zBYv+vwYpWltBoNIzs2JTuTWpm2/n//PNPBg0aREJCAp9++imNGzfOcFys7SJJjjgMmgCKGMsj30cvDKvjb87Evct1656bawMU1U6IsR7lC4wlNSGYHj16YLfbWb58+c3EJCcoSgKqkoQkhyH7sIwtr7mauoNDV0d6vFUQrK/Cw8W/zaGofCMpKYlWrVrRsmVLJk+e7Otwcpy4TZCJn376idOnT/PSSy/5OpQ8yWQykZr63wvM8OHDiYuLY/HixT6MKmu4FIU+c74l+nrSbYkAgFNRsTmcfLj+F3adOO/1MVXVhWr9ESXuGZQrdVGu1Ee5NgjVfvC2cYmJiQwfPpwWLVrQrVs3Dhw4kGkiABBhKEXZwNoUM1W6r0QAwKgrSfUiC6hfYjtVCk6nSsHp1CvxEw8WWYxZV46IiAg2bdrEww8/TN26ddm9e/d9nc8bNuvPxMV05OrlGsRcbcbVy9W4Fvs8DrvYs94b4fpGJMaruNxUjsqSkUphQ3IuKB8JCgpi8+bNrF+/XiQDQhpFURg9ejQTJ050W0srZM5sNt+WDGi1WhYsWMCoUaO4cuWKDyO7f7tOXiAmMRmXkvmkmtXh5JPNu7w6nqpaUON7oV4fAY6DoCaCeh1sP6JeexElYSyKorBs2TKqVq3K9evXOXr0KIMGDUKjyfmul3ptIcLNLQg3t0jXy12j0TB+/HjmzJlD586dmTVrFtk1+ZicOJ1r8f1w2H8HHKBaAAc224/ExT6JJXVjtpw3v0hJSaFr124snRiAWV8UmTsX2GmQJQNVwl6nkLmpT2LMaQUKFOCHH35g3rx5zJkzx9fh5CiRDGTg22/TpsOeftq7FddCeiaTCYvl9rre2rVr06dPH4YMydtXGct3HSbV5mGfdeBsdByX4hM9jktLAo4Ad07VqqBaUFJW8/n0ekybNo1vv/2WBQsWZLgrW27SoUMH9uzZw/z58+nVqxcpKRTvCsYAACAASURBVJ56UNwdm3Unycmz/k0A7pT2c0u4PgSXMypLz5tfREdH07x5c8LCwlj59Vaal1yHcrkDMVEyWikQvRxGicDONCm2gjIhPXwdbo4qVqwYP/zwAxMnTmTZMm86q+YPIhm4g91u56233mLKlCnIsvjx3Ks7ZwZuGDt2LAcPHmTdunU+iCprXLme7NU41eXi2w2b+O2334iKisLpTD8Xqzovgu0XIPNab1m28cLTNvbv20WjRnmndK98+fLs3r0bWZZp2LAhp0+fTjdGdf2Dao9EdV64qxmElKQZmSQCtx2clOQv7jbsfO/YsWM0atSIjh07snDhQvR6PRrZxKavYoje3YM2ZfbSuvROahR8jyB9eV+H6xPlypVjy5YtDB8+/LbXKlVJRrFHotgjUfNwdUVGxJLfO8ybN4/y5cvTqlUrX4eSp2U0M3Dj8/PmzaNXr140a9aMkJAQH0R3f4LN3rWidioKm9etZcn5M1y6dImYmBgiIiIoXrw4xYsXp1ixYjzdIZaHaznxNNtv0OuQnHtB2yILvoOcYzabWbx4MZ999hlNmjRh3rx5dOrUCdW2HTVpOjjPgaQD1QmawhA4GIwd3S4yVVUbdvtvXpzdjtWyhuDQd7LuG8rjfv75Z5555hk++OADevfuffPzqqqyceNG1q9f78PocpcHHniA9evX0759e1at/JyGNXejWDbCjS6fqhPZ1A5t0CgkTe6eqfOGSAZukZSUxIQJE9i0ybv9toXMZTYzANC8eXPatm3L6NGj+eyzz3I4svv3ZP0HOBZ1xeOtgqIFQtk07eubb2xOp5Po6GguXbrEP//8wz///EOgcR0ajRe1zaoCirstWHMvSZIYOHAgderUoVu3bsjWpbRrdhKJf3dAvNEBz3UBNfF/4PgTKfjNTI+nqqmkTWp6/rmpXjTU8RdLlixhxIgRLF++nJYtW972tePHj6MoCg888ICPosud6tWrx9rVn1Eq9HWcqTpkyZW2Cce/FMs67LYd6CO+Q9IU812gWUAkA7eYNm0arVq1onbt2r4OJc8zm80ZzgzcMHXqVKpXr86OHTto1qxZDkZ2/9rUrMTUdTvcJgNGnZaXWze47QpXq9VSokQJSpT4b4tUJckCKQtIX7t/B0kGOW/3umjQoAGH9n+DyfoCEpncElAtYFmOamiCZEhbtOZwODhy5Ah79+5l79697N+3h80b7RiNnktUZblgVn4LuZaqquA8As7zaTMt+gZIcvjNr40fP56FCxeyfft2qlWrlu7xGzZsoH379vmi7Der1a2yFJdNm5YIpOME5TqOa4PQR6zx6nh25xWSbL8DCiZdZcz63NGi3a+TgWtWC8kOOwWMJpLirzFz5kwOHDjg67DyhTtLC+8UGhrKrFmz6N+/P5GRkZhMmbcKzW0MOi1zX+pKnzkrsTqcOF23v5Gb9Fo6PFSVzvU9X2VJxvaoKV/CjavkzKgu0D98H1HnDmHGtaiqh6t61ULM+Yl8uGADe/fu5eDBg5QpU4aGDRvStGlTRo0aRUjYPGyW1e6PgxlzYJ8s/g5yH9X2C2riuH9njqS0D9WOamiO0/Q/Xhowmj///JM9e/Zk2kl148aNjBo1KkfjzgsUxxlUxwlk2V2y7kJ1nERxnEHWVch0lM15ib/i3iLRuhdJ0v37WSdGbTnKFJhAkMG3F6F+2XRoy4XTzDy8m5PXY9DKGlyKQnhcElWvJrNw8oe+Di9fUBQFrVaL0+l0uxCzW7duVKxYkUmTJuVgdFkj+loSC7cfYM2+ozhdKg6ng2JBRkY99Rgtq5f3+ipLie0KzuNAZsXeRjA9iRzyblaF7jPKlXqgem6BqygwZWFPGjRoTL169dKtLXE6zhIb8xhkehtAQpLDKVh4N3Ien1FxR7FshIQ3ySiZVNFyNVZlxMRyzJ2/goCAjJsxXbt2jdKlS3PlypU8lZTnBGfyfFxJHwCeqod0aIJGog3sl+FXbc5LHL3cEaeSQEYJrCwZqVxoIcHGhvcd873yu2Rg4v6fWXriMBbn7f+5qqJg0uqY06oLLUr47zaWWclkMhEXF4fZbM50THR0NDVq1GDr1q3UqpU3+9q7FIVkq53p0z4kJTGBDz744K4er7picFztgsN2BVO6qW8T6KojhS9Eygc7AirRNQEPVQAAaJAK/Y4kZ/7csdl2cT3uBVTVxW1vhpIZWTITHrEarZsrtbxOVZJRrzbG3ayS0ymhCeiMJizzTcKWL1/O0qVL2bBhQzZEmbc5kz7FlTwdT7fxFBVOXXwMfcgQKlasmK4d9/ErPUm07sXdTJZWDqNOiX1I3m5DnsX8qnZuy4XTGSYCAJIsY1VcvPLzd8RYsrYm2l+5W0R4Q5EiRZgyZQp9+/bNsPQuL9DIMiFmI480bsTevXvv+vGSpiC9h4aw72htkMJIu3unAU0ppOC3kMIX5YtEAEirGPCGZEr7cMNgaELBwnsJDB7Gxb9lFCUMrbYawSHvEVF4b75OBABUyxrwMPuk1apIts1uy+A2btxI+/btszq8fEHSlvT4PARwOLRs+eEYHTt2JCgoiBo1avDss88yYcIE1m34gkTLPjwteFVUO9cs27Io8rvnV8nAzMjdGSYCt1JUha9OilamWSGz8sI7vfDCC4SHhzN9+vQciCr71KtXj0OHDuFweG5IdKt169ZxOPIsjR/9EqnQXqRCvyEV+h254I9I5u633F/MB8wvQLpOd3fSgfkZr26zyJoCGE0DaNo8lvCCvxNR+EfMAT2Q3cwo5Bu27Z57LUDagkLH0Qy/5HK5+P7770UykAnZ2AYyW+x6C4NBz8i3t3DmzBni4uJYtGgR7dq1Izk5mT2/L8SS6vk1QVFTSLDsyIKo743fJAPXbRZOXovxOM7mcrH6TMa/OMLd8WZmANJKzz7//HOmTJnCmTNnciCy7BEcHEzZsmWJjPQ+mUxJSWHIkCHMnj0bg8GAJElIcpDb6fG8TDJ1AjmEzF56VBWQTEjm570+5oULFyhSpAhGo3f9H/IN9W6SzoyvSvft20fRokUpVapU1sSUz0iSEU3ga+5nByQTmsAhSFLa889sNlOnTh169erF5MmTGTb8NQICvft9Vu7q/zRr+U0ykOywo5W96+Oe6mH2QPCOp/LCW5UrV4633nqLl156CbvLwa6YI6z6ezsbLu3mqvVaNkeadRo1urtbBePHj6dJkybp6r7zK0kOQCqwHDTFQLp9QZvdoSMhSYawpUje3k4ATp8+TcWKuaM8K0fpawBe3D5S7aD9r5Ngot3KpovHWXE2knk/b6KtmBVwSxPQD01AX8DArT9vux1cihZNQB80Af0zfbxJVwlvZhdkyUSA3nd9HvymtDDcYMKleKjl/ldhc2A2R+MfPJUX3mnIkCGsOr+dztvfQKvX4VCcaCSZ2eoaaoSWY3TVnoTpc/fK8IYNG7Jt2zavtr0+duwYCxYs4MiRIzkQWe4haYpBxFawbUdN/QqUqyCFog3syuNd3+O1136nR48qXh/v1KlTVKpUKRsjzp0k87OoKe53AVUUlavXilC0cBEsTgfv/b6V7y78iVaSUVFJLaYl0BTEg6d/p2fFh3Io8rxFkiS0QcPQmLrjTP0S1f4boHL6bAAz58awcMlwt48P0D+ITlMYm/O823EqChGBXbIu8LvkN8mAWaenVcnybLlwGsVNlhag1dGnWt0cjCz/upuZAYDlUT8R8mRlHDhxuNK60jnVtOnNw9fOMOj3j/is7giCdbl3v/qGDRsyceJEj+NUVeWVV15h7NixmdZ+52eSpAVjayRj65ufk4GZM4vRuXNn2rVrR1hYmFfHOn36tH8mA5riqOZnIHUFmVVoqBgZMiaaFFdHpJc68pclAZvL+d9OGAYdyYqT9w9t44olmeE18lYDsJwkaYujC37j5r+r1Ell/aZS/PXXX5QtWzbzx0kSZcMnciqmL4qaceWHLJkoHjIYrRyc5XF7y29uEwAMqdUYgzbzWwWyJBFsMNKuTOUcjCp/UVUnqmU9SuwTbF7yN82qDkKJ7YRq2YiqZl4tEG2J5+uLP+LIpNbehcI1exKL/9qcXaFniSpVqhAXF8fVq1fdjlu6dClJSUkMHDgwhyLLGxo0aEDnzp0ZM2aM1485deqUf94mAKSgN8H8HGnT14ZbvhAAUjjaiKV8teJ3Ah9twPH4aGyujH+/LC4HC078xqkEz+uqhDRms5nevXszd+5cj2NDTI2pWHA2qsuI9ZbJUlkyIWGgWMirFA0ekI3ReuZXyUDV8ELMadEZk1aHQXP7pEiAVkdhcyAr2z2HUes3EyZZSlWtqPG9URPeBucJtBrSOnc5j6MmvoUa/yKqas/wsWv/2YnioeWFU3WxNXo/NlfGx8gNZFmmQYMG/PZb5hvpXLt2jVGjRvHZZ5+h8bRDkR+aNGkSa9asYd++fV6N99eZAQBJkpGDRyMV3AGBg/nmuxScui5IIdOQCu1C0tdEq9NxsWQwkt59VYpDcfHFCe9+5kKaAQMG8MUXX2CzZb7r6A2hphZMGVGemLOdiAjoQri5AyVChlGnxG8UD3nF562g/a7pEECsJYWvT0WyJHIf15KTqFqiNH0eeIi2pSuLROA+KNeHg3UrmW/HawRTe+SQ99N9ZcCBDzmb/I/Hc5g1BqbVGkyFoOL3F2w2Gjt2LA6HI9OuigMHDkSSJGbPnp3DkeUdS5cu5aOPPmLfvn3pGrjcymazERISQnJysttx/sDlcqHX63E6nbe9sUSnJtFiw5xMZwVuVdwczM5Onte7CP959NFHefHFF3nuuefcjjt//jx169bl4sWLbhux+YpfzQzcEGEKYHDNxrwRUJKaPx1m/RO96VL+AZEI3AfVFQPWLWSeCABYwbIeVYnHYrHwxx9/sGLFCsaNG8f5C+e9PJOE6mlTHx9zV1Gwb98+1q5d69W6An/Wo0cPQkNDPSZM586do3Tp0n6fCEBamWpAQEC6K0yXqiDj3VWny/+uDe/bwIEDvUrs58yZw/PPP58rEwHw02TgBqvV6n+1ydnFugVvnk4Wq4O3htUjLCyMZ599lm+++QabzUZ5fVGvXrCcqovipty9E139+vU5cOAALtfttd0ul4uBAwcydepUrxfH+asbMyfjx4/n0qVLmY7z5/UCd0pOTiYwMH0lVEFjoKdGhUDaFkdVwwplfWD53BNPPMH58+f5448/Mh1jsVj44osvcvUaIZEMiGQgS6hKPB533gMMBhg29EWSk5P5888/WbVqFRMnTuSNVv3Ryu6v7jTItChUG7M2d/+fhYeHU6xYMY4evb151ezZswkODqZnz54+iixvqVKlCi+//DKvv/56pmP8eb3AnZKSkjJMBvQaDd3L1ULnZsMwAJNWR/8qvtsoJ6/SarX079+fOXPm/L+9+46v+fofOP763J1EhhAkxI69V61QxKxRo0WpVdSm6KQTraoqVWpXq/amRuwYFXvW3rFXjIy7P78//ORrJPfekNyRnOfjkcejzT333nci997355z3eZ8UxyxcuJDKlStTuLD7tsjO9MmAVqu1P1CwS1JkBex/SCskHdlzFH5pWjfUOweNg6uiVSRf5KRAwkftRZcCTdIi3HRXvlYtZu7cyZL//uPozZtcv36d7777jsmTJ7u8UMiTDBs2jH379hEZGZns7WJm4H9SmhkA6FWiGn5qHVIKqwA6pYrKQaG8kUN0InwVPXr0YOHChTx69Oil22RZ5rfffnOo94grZfpkQMwMpBFdI+yd7PWEFXQNkr2lb+GWtM5TG42kwpL4pAukAgmtQk1+n2AmVRhMdq1/svd1F9cePaLD4sUcKFaM9QkJfLtlC+8tXkzE7Nk0792b4sWLuzpEj+Ll5cVvv/1G3759k+1ZIWYG/sdWMhDklYVp5d/CfPMuWkmZtCCnVijRKpQ0yFOEKeFtRKL6ikJCQqhXrx5///33S7ft3buX2NhYGjVq5ILIHJepq25EMpB2JGUQsq4+6DdhczeBrgmSIjD5x5AkuhZ8C78TJiZvm8u7vTuhU2qolq0khX3zpFvsaeX6o0c0//tvHhsMTzrBK5UkPD20SKcjOksWoi5epLaNBiXCy5o0acKsWbMYPXo033777XO3iZmB/7GVDAD8+PmXtMufn3adOrLmygkeGvXkzZKVVgVKk9vHvZNsT9C7d28GDhyYtFvoqd9++40+ffqgsLNM42oiGRDJQJqR/H9AtlwH0yle7ojmBepSSP7fJnfX52yL3EyDPJXoUahZusSZXj7bsOFJIpBCRbbebGbg2rXs7dULjegvkCrjx4+nXLlydOjQIWkmIC4ujtjYWPLkcf9E0RlsJQNr1qxh//79/PHHH3h5eVE+u/tuzfVUderUwWQyEbVzC8Uq5UbGiuWhjn/++YcJEya4Ojy7MnUyYDAY8PV17173nkSSdBD4N+jXIMdPB/MFZFnm7EUoWn4k6Bo/aUNrx4YNG1iwYIETIk471x8/Zv+1a3a3ZlmtViLPnqVZMcd77wuQJ08ehg0bRp8+fZi/aDlRu89y8swFildsyr3YeIKyiddxXFxcsu9ncXFx9OnTh5kzZ+LlZe/4aOFV6a2P6D2xBgf9f+BkjDcgYTAlMuiPcFRZ3LdR2lPuPW+RzsTMQNqTJDWS19sosq9BynkCa7ajVGl0nfsJ1R1KBC5dusSDBw8oW7asE6JNOwevX0flwNV+vMnEjsuXnRBRxtPzw948lorSpudUJs+JInLHJbyCKtG2zwyGjVlJot7933DTU0ozA19++SV16tQhIiIimXsJaSHB/ID5F3ujCL2GUgNGawJGazyS0kpA0UTmXerFfcMVV4dpk0gGRDKQbiRJQq3RULNmTbZu3erQfTZu3Ej9+vXdfn3tRVarFRxs2GK2JH+2vJAys8XKx6OW45W1EBYrGI1Pf4cKjCYLuw9cYMBXizCZMu/vNrmthfv27WP+/PmMHTvWRVFlDhtvjCHefB9rcmerSDIGazyrr36FOzf89ax33DQmkgHnqFevHps3b3ZobGRkJA0aJL/bwJ0VzZ7d7tkKAF4qFWWDg50QUcaybfcZzl64jdmc/I4Vo8nCxZi7bNp50smRuY8XZwZMJhM9evRg7NixZM+e3YWRZWyPTXeISTiUfCKQRCbefJcbif85La7UEsmASAbSXb169diyZYvdcWazmS1btlC/fn0nRJW2igYFkTcgwO44qyzTqkQJJ0SUscxdvpdEg8nmGL3BzN/LX++gHYvVSqLJ5NZXcCl5MRn45ZdfyJkzJx06dHBhVBnflfgDSNhfIjTJei7EJd+m3B1k6gJCkQw4R5kyZbh37x5Xr161Wfm9f/9+QkNDCfbQK+eRERF0WrKERHPyVwheKhUDqlXDVzS6SrWLMXcdGnflWiyyLKd6v/zuy1f4PXov0TExSIBWpeLdMqXpVqkiIX6eUZz4bDJw/vx5xowZw969e0XvgHRmlg0On5dilu13aXWVTD8zIDoQpj+FQkGdOnXsLhV46hLBUxVCQpj+9tsE6HR4PVNM6KVSoVWpGFi9Oj0qVXJhhBmfLFtZuXIl167ZPwHzqfE7/6Xn8hX8e+UKVlnGIsskmEz8fegwTf74k+M3b6VjxK/HaDKzdv8p3h83n2PeRZl3Jp65Ww/Ss08/Pv30UwoWLOjqEDO8AHUICsn+zIBK0pJVE+qEiF5Npk8GxMyAcziyVLBhwwaPTgYAquXNy55evWiTNStZr13j3VKl+KxWLfZ8+CE9KlUSV2mvqHB+xw7Q8dFamTp1KuXKlSMkJITmzZszYsQI1q1bx507d14av/HsOWbu20+i6eXZHLPVSpzRSOdFS4g3ut9Ohav3HtJ0xB+MWLiJo5duYlbpuB1vYtzKKO4WepM6b7d1dYiZQqhPBZRS8m3UnyUjU9SvrhMiejUiGRDJgFM8LSJMaS32wYMHHD16lPDwcCdHlvZUCgVcuEAjLy9+aNCAjuXKiaWB19SxZRW8tLbfcHVaNUN6NWPdunXcvn2b3bt306lTJ+Lj4xk7dixhYWHkz5+fd955hx9//JEtW7bwy/adKS7rPGWyWll98lRa/jivLcFgpMsvC7nzMJ6EF2opzFZApaH/tFXE3HngmgAzEYWkJDzoQ1RSyq9xlaSjfNbW6JTuu+QkkgGRDDhF4cKFkSSJM2fOJHv71q1bqVGjRob59zh27BilS5d2dRgZRniVwpQqFoJWk3yZk1ajomihnNSt+aSZkyRJ5MuXjzZt2jB69Gg2b97M/fv32bBhAy1btuTWrVsM//4HTt+2vwSQYDKx4EjKx9O6wpp9J4nTG2zuYDGYzMzatM+JUWVeJQIaUj3oA5SSBqWkSfq+AhVKSUNJ/0ZUD+rqwgjty9TJgMFgyDAfPu5OkiSbWww9vV7gRceOHaNUqVKuDiPDUCoVjPmiFQ1rl0CjVqLTqrFaLei0ajRqJXVrFGXcV21QKVN+S1MoFBQpUoT33nuPcePGMXvBfLJ4ezv0/A/1KZ234Rpzow6TaLQ9o2GxyqzZfwqzxbHiNuH1lA9sRddCc6gY+C6BikJcP5lI6YBmdCwwgzdz9UOS3PvjVuwmEMmA09SrV4+VK1fSp0+f574vyzKRkZH079/fRZGlrcTERGJiYsRpemlMrVbySe8G9OoYzva95+jVewCTJ42ndtUi+Pumvs1uNi9vTA5+UAb5+KT68dPTnYdxDo2zWmXi9Ub8fcT7nDP4qLJRLagLpb3a0Kt8Tn6M3+XqkBzm3qlKOhPJgHPVrVuXrVu3PunW94zz589jNBopkUH23584cYIiRYqgVtsvKhJSz8/Xi6b1SnPt7DaaRZR5pUQAIJuPN6Vz5rQ7zketpmN592qPrUthueRFVtnq8Fgh7fj4+GAwGDC6YeFpSjJlMnDj0WP+PnAYRfnKbLoUw2ODe00BZlS5c+cmKCiIw4cPP/f9p7sIMkqlvVgi8ByDwqujU6X8YSkBPloNDYu41zHJDcsXRW1jSeSpMvmD0apFMuBskiQREBDAw4cPXR2KwzJVMvBYb6DXkpVETP2DH7fuwCf8TcbsjKb6xGmM3rIdi1WsraW35LYYZrR6gePHj4viQSd53QSyWt68fFm3DjqVCuULj+WlVpHN25t57d5FayNhcIX3apeze36Hl0ZFjwZvOCki4UUBAQE8eOA5uzkyTTKQYDTx7pwF7Lh4CaPFgt5sRlIqSTCZ0JvNzD14hI//We+RbUg9Sd26dZ8rIjSZTGzbts0jWxCnROwk8Cxty5ZmRacOtCldiiwqFZjNhAb4MzQ8nI3du5I/a1ZXh/iSPNkD+LpdBLoUrvp1GhXta5WjRon8zg1MSOJpyYB7pbvp6O+Dh4l5+AhjCgVDerOZTWcvcODqdSqF5nZydJlHnTp16Nq1K0ajEY1GQ3R0NGFhYRnqIJXjx4+LZYJ0ltZJe+Fs2RjVsD7N/H0ZNGgQW6Pdt4f8U29VLk7ubP5MXvsve09fQaWQQKEg/u51fhzYhUaVirs6xEzN05KBTDEzYJVlZu09iMFOcxG9ycSMPfudFFXmFBgYSFhYGHv27AEyRtfBZ92/f5+4uDjy5s3r6lCEV2C1Wj2qdqVcwRCm9WtDzgtb6VMtL+u/7U7wtX3EXXLf0/EyC5EMuKEHiXqHigRl4PD1m+kfUCZ2Oz6OXG83p9/+aKrOnMJCzARUqYzRkjHOoT927BglS5b0qA8UT5Rey3myLNtdi3dHl86doWqZ4mT386Fr16788ccfrg4p0xPJgCCkIPLcWd78cyZnA3x5rFRwOz4ec1B2/roRQ8O/Z3M73rG90+5MFA86T3okXJ42MwBgsVi4fPkyBQoUAKBVq1b8+++/3Lhxw8WRZW4iGXBDAV46smg1dsdJQJlg+/uOhdQ7cvMGH21Yi95sxvzCVV2CycTVR49ot3QhZg/f0SGKBz2bJ84MXL16lezZs+Pl9aTfgo+PD61bt2bOnDkujixzE8mAG1JIEl0qlUersn3MpE6t5oM3xBGz6eHn6F3obdRsWGQrd+Lj2XzxvBOjSnuix4BzpNcygSfODJw/f/6lo4qfLhWI3VGu4+/vL5IBd9SpUnlC/PxQK5NPCLxUKmoXzE8VsZMgzT3QJ7L32lW74+JNJmYfPuiEiNKHLMtimcCJ0uND2xNnBi5cuEChQoWe+1716tWxWq1JhbqC84mmQ27KR6Nhcad2VArJhWwyofn/F7xWqUA2m2lVugS/tGjicVcFnuB2fDxqhe1ZmaduPH6cztGkn5iYGHx8fMiWLZurQ8nwxMzA/5w/f/6lZECSJLp06SIKCV1ILBO4MX+djnK3rlL+wimG1glnQM2qfFm/LiHbIin+4O6Tc+iFNJdFo8FsdWy3gI/Gfm2HO5JlmaNHjoolAicSMwNPJLdMAPD++++zePFiEhISXBBV5mayxqPKdZ781e9z+sFSEsx3XB2SXZmm6RA8yfonT57MnDlzqFa5QtL3tf368eOPP9K2bVsXRpdxhfj6EeLrx8UHsTbHealUtC5e0klRvT5Zltmz8yyL/tzJyWNXsVpl1JpqLJ7zL01aVsQni9bVIQqplFFmBgDy5MlDlSpVWLFiBe+9954LIst8ZNnKoXuTOfVgMbI/VGpp4cDdX9l/dwK5vatSPefXaJTudQLmU56VAr+mDRs24OfnR9WqVZ/7frNmzbh9+zbRHtB1zFP1r1IVLzv93RWSRJsSnpEMyLLMz9+t5IdhS/jvSAxW65Npa7NRwZypW/mw3WTu3n7k4igzLtFn4H+Sqxl4SvQccB5Zltl16ztOPViCRTZglQwoVdKT/5aNXIvfzfqrPTBb9a4ONVme9Vf/miZNmkTfvn1fyvyVSiUDBgxg/PjxLoos42tRtDg5Yh8gJbOjQCFJeKlUTGv6Nn5azzhSeuncaLZvOoE+0fTSbQaDmft34/ii/9+imjsdiT4DTzpel5xRYQAAIABJREFUWq3WFOtUWrRowaFDh1j77wFW7zvBxiNneZTgnh9Gnu6O/igxcduwyMn/fq2YiDNd4/SDxU6OzDGZJhm4ePEiu3fvpn379sne3rVrVzZu3EhMTIyTI8scZsyYwbW/5jHqzQiKZMuGWqHES6UGi4Wy3llY3rYD1UI9o4WvxWJl4ewdGPQvJwLPjrl14wHHD19xYmTC6/K0mYGn9QIpJTCbj18kf8dPGb44ilFLtvDV/A3U+3oaw+auJ15vdHK0GduJ2LmYZdudbi2ygRMP5rvlRYLn/NW/pilTptC5c2e8vb2Tvd3Pz49OnToxadIkJ0eW8W3bto3hw4ez5p9/aFehIus7dOHfbj2J7NiZHhYF2fceoEg2zzmo6MTRGMxm+82RDHoTG1YfdkJEmY/YTfBESvUCAH9HHeTbRZswSirMSCQYTcQbjBjMFiIPn+H9CQtIMKSc0Aqpc0d/jCdN7W0zWh5jsLrflsNMkQzo9Xr++OMPevfubXPcgAEDmDlzJvHx8U6KLOM7d+4c7dq1Y/78+YSFhSV9P5u3N3n8/GnVrBn//POPW2bKKXn8MNGhcbIM9+567lZJdyd2E6RcL3Aj9hHj/9mJ3pR8oy+j2ULM3QfM3LQ3vUMUXuSmyabn/NW/hoULF1KxYkUKFy5sc1yBAgUIDw/nr7/+clJkGduDBw9o1qwZ33zzDXXr1k12TNGiRfHx8eHQoUNOju7V+Wf1cSh5kSTInsPPCRFlHolmE4tOH+OdNQvJ8dVHtFk5j5XnTmCw2D6R1FGeMDNgtcrs232OqRM2sG/HfSRTMAnxz09PL9h5BHt/ogazhQW7jmDKIIeEuVo2bXGeNLW3Ta3wRqtwv/eFTJEMPC0cdMSgQYOYMGECVg/vke9qZrOZdu3aUb9+fXr16mVzbNOmTVm9erWTInt9xUvnQatV2x2n1alp3KKC3XGCY07eu031eVP55t/NHLlzE1WO7Oy/dY0vdmwgfP40Ljy4/9rP4e4zAyePX6VD818Y+cUSls6PJj7Wj2P74mjb5GcW/f1vUpK68+RFhz7kLVYrMXc9pzGOOyuRtQMqyXYBtAINxQPaIUnu9zfmfhGlsX379nHnzh0aN27s0Pjw8HC8vb2JjIxM58gytiFDhiDLMuPGjbM7tlmzZh6VDCgUEh2610arSzkhUKoU5MmbjWKlRHvrtHA7IY62qxcQq08kwfT8One8ycSdhHjeWTWPh4ZXr5Q3WMxcssSRkCML9/Tut1R4/sxNPu0/h3t340hM/F/xn8lkxWAwM2dGFAv+3AWA2eLYspskSQ6PFWzL6VWBEJ9qKFNICCRU+KhzUizgHSdH5pgMnwxMmjSJXr16oUzhTIIXSZLERx99xC+//JLOkWVcU6ZMYcOGDSxcuBCVnd4CADVr1uT8+fNcv37dCdGljWbvVKJh83LokkkItDo1OYMDGPVrR7efcvYUs48ftHnQlcyTpGDhqaOpfuw4k4GRhyN5Y/VYZnKZK3UK8ea6X+m+cx7nHrlP57iJP61NdivrUwa9ib9nRTF92h/cPv8fsgNdP80WC7kD3W/K2hNJkkR4ru8INFfHZLCilJ40HVOgxmqWeHDFh8ahM1Ar3LPpkCR7UuVWKt27d49ChQpx7tw5smd3vFrdYDBQoEABNm7cSMmSntEEx11s2bKF9u3bs2vXLrs1Gs9q164d9erVo0ePHukYXdo7vP8ii//axbGDlzGbLRjMjxj8RTvqNSmbbKIgvJqysyfy0Gj/qj/Yx5fdHWwvSz0rzmSg9ZaZXEt4gPGFD08J8FKq+atWJ8oEhqQ25DR1/ep9enaYgtFguzbCYjWh879N3XeqseDcIwymlBMChSTxVsVijOrQKK3DzdQ6dOhA6fJFaNWjDAmmO2iUWfDSl6JSqTocPHiQfPnyuTrEZGXomYFZs2bRokWLVCUCAFqtlt69ezNhwoR0iixjOnv2LO3bt2fBggWpSgTA85YKnipXqQCjfu3Iqp3DWLH9M/acmkJ4RBGRCKQhs9XKIwcSAYA7CXFcv37d4ZqfEUfWJ5sIwJPZhgSLiZ7/zsfs4hqiC+duo7JzBDuAUqGmcoW6DOnZhdolCqJTJz8zJwE+Og19G1dP40gzt9OnT7Nhwwb69PyIIv4tKZe9JyWyvkeB4DL07duXr7/+2tUhpijDJQPxBiMPEhIxmkz8/vvvDhcOvqhXr14sWbKEu3fvpnGEGVNsbCzNmjVj5MiR1KlTJ9X3b9y4Mdu2bSMx0bFte+5Io9FQvnx59u4V27XSklKSUDi43GIxGKlYsSJeXl4ULFiQN998k06dOjF8+HCmT59OZGQkJ0+eJD4+nscmPWtjTiSbCDzLYDGz7ebZtPhRXplS4fhyk/L/CyB/eL8xjcoXQaNSolb9/1u9LOOtURMc6MecgW0JEUsEaer7779nwIAB+Pm9/HsdMmQI69at4/jx4y6IzL4McVCR1Sqz5ugppm/fx8W791FKCiTZSpZq9SjwigffBAUF0apVK6ZOncqwYcPSOOKMxWQy8e6779K4ceNXnuYPDAykXLlybNmyhbfeeiuNI3Se6tWr8++//xIREeHqUDIMSZIIz5OfqJiLNlu6KCWJZiXKMP7GDQwGAzExMVy5ciXpa8+ePSxatCjp//3fKIlfjyZgZxYn3mwk8tpJIkKKpu0PlgpFS+bGbGPK/ymdl4ZK1Z7MyqmVSr5r35A+jauzcu9/7Dx4jPOnT/LLF4OoUjhU1LOksXPnzrFmzRrOnTuX7O3+/v58+umnDBs2jJUrVzo5Ovs8vmbAYrUyeOEadp65TOILVcYKwNdLx7yebSkQFJjqxz527BiNGjXi4sWLaDz0aF1n6NevH+fPn2f16tUOFQym5KeffuL8+fNMmTIlDaNzrhUrVjB16lTWrVvn6lAylD03YuiybgmJNooIdUoVS1u8R8nsOe0+nizLLDq5h+9PbSFRtv8h2yCkGL9Vc20V+JdD5rNv97mkQ7GSo/NSs2jd0GSXqfbu3UufPn3Yv39/eoaZaX3wwQfkyZOHb7/9NsUxer2eokWLMn/+fKpXd68lGo9fJpi5Yz87zlx6KREAsAKP9Hq6/bEUyyus+ZUuXZrixYuzeLF7HizhTPGPEtkwdydzx6xi+eQN3Lh4G3iyW2PLli0sWLDgtRIBeFI34GndCF9UrVo1oqOjRZ+KNPZGcCi9ylZJ8eRLnUrFJ1VqOZQIwJPZhlLB+cCBngJqhZLCfq5vlz3g07fw9fNCkcKSgUolMXR48xTrVXLlysXNmzfTM8RM69KlS6xYsYKBAwfaHKfT6fjmm2/47LPP3O59zqNnBswWK+Gjp/Iw0XZxkbdGzdh3m/BmsYKpfo41a9bw3ccjeT+iO7cu3cE/yI+IjrUo+2bJTDHNZrVamf3tUlZM2YRCqcCQYESlUQISwUUCWXP2b7b/uy3F/uipIcsyYWFhLF68mPLly7/247lKoUKFWLVqldiJkg4WHtrL0JWL8MoTgkapxGi1UDwwiMGValI7tECqHkuWZRpETuJyfKzNcRqFkg0N+xLi7f86oaeJ2zcfMua7FZw6fg2FUkKWnyQ2Wq2Cw6eXErVrOSEhye98MBgM+Pr6otfr3bqxkifq1asX2bJlY9SoUXbHms1mypQpw88//+xw/xtn8OiagWPXbjpU5ZtgNLHi0IlUJwPxD+PZ+vM+spwOYdWZSOT/n57bvng3gcEB/LB+OMEFHLsS8VQT+s9m27K9GJ85oc/0/9ubLh27TnjOluTKHpwmzyVJUtKuAk9OBqpXr87u3btFMpAOTq9ez1s34/jm4x7E6hPJ5uVNDu8sr/RYkiQxrGxDBuxZgj6FdsY6pZqmeUq6RSIAkCOXP2Mnd+bG9ViOHbyMyWwhb/7slCqbl2+/TaBLly6sX78+2Q97rVZLlixZiI2NTfHIYyH1YmJiWLRoEWfOnHFovEql4vvvv+fzzz+nYcOGbpOYuUcUr+ix3uBAJ+gnzsdc5dy5c5htrDk+y2K28HHEd5zYfRqFrEhKBAAS4/TcOH+LAdWG8eCO+50+lVbOHLzItmV7MSQkf9SpAiXxD/Qs/nV9mj3n06UCT/a0iFBIWyaTiWnTptGnTx9y+fhSPFuOV04EnnozOIyRFZqiVajQKf83va6UJHRKFY1yF+O7Cu5X0BockpUGTcvx1tsVKV0uH5IkMXz4cB4/fsyvv/6a4v3EUkHa+/HHH+nevXuqtrC3aNECnU7HggUL0jGy1PHomYEgXx8sNoppksgyN86fJSJiNLdu3aJgwYIULVqUYsWKUbRo0aSvrFmzJt3l35X7uHr6etJV8IusVpn4h/EsG7+GbqPeS6sfya0sm7QBk972Eacmg5l/pm/h/c9boHRgH7Q9NWvW5OzZs9y4cYPg4LSZcXC2atWq2XxDFl7NqlWrKFCgAGXKlEnTx22etzS1chVm6aXDbLp+GrPVQomAYN4vXJnCfkFp+lzpSaVSMXfuXN544w3q1q2b7O/paTIgZq3SxrVr15g3bx4nT55M1f0kSeL70d/zxbTPOV/2DNf0VwHI4xVK4+AmlA+oiMLJ5xd4dM2ALMs0GDeLa7GPbI7zUquY1a0NZUODSUhI4OzZs5w+fZrTp09z6tSppP/29vZOSgxiN5p4eMV+f3Iff2+W3fvDbaZ60tL7JYdy56r9w1+03hqm7x1FjtC0mXps27Yt9evXp3v37mnyeM5mNpsJDAzk0qVLBAamfheLkLx69erRvXt32rdv7+pQ3Nrs2bP5+eef2bdvHzrd833y27dvT9OmTenQoYOLovNsJrOFyzfvYzJbyR3kz1fDPkOhUDh0Bstzj2M1MeHsOE7c/Q+F9vnPDq1CS0GfQgwI+wi1wnnNyzx6ZkCSJD6qX4PhyzemeG63WqkgLGd2yuTJBYC3tzdly5albNmyz42TZZkbN24kJQcr/t7qUAxGvZG42Hj8svm+3g8jJKnWsh4L7+zhwL4EdEoNdXOUIyK4PF5KratDc4hKpaJy5cpER0fTpEkTV4eTIZw8eZL//vuP1q1buzoUt9e5c2fWrl3LZ599xvjx45+7TSwTvBq9wcTMf6JZvPUIVllGQsJoNhN7OZ6/fxqa6sebc/lPzsedeykRADBYDZyLO8vcy3/RpcAHaRG+Qzz+crZJmWL0qfMGOrXqpS5d3ho1BbJnZUqnlnYr/yVJIiQkhLp169K7d2/8/B37cLdaZFQaj86pUlSyaliK25iepVaryBYc8NrPZ7CY+OTQdNbluIChqC8nH13hUOw5Jp9bRasd37L/vmMFOu5A1A2krd9//53u3buLfh8OkCSJKVOmsGzZspdOX82VKxe3bt1yUWSeKdFgouv385m78SBxiUYS9Cbi9UZMZitZchdj8JQNnLp82+HHe2R6xL77ezDJKS/BmmQTe+5HE2eOS4sfwSEenwwAdK9VhYW92tOiXAmy+Xjj76WjdO6cjGhZn8V9OhDgbfuM6eRUiCiDQmn/1xNcKCfevl6vErbba92vIWqt7WkqtVZNs55106Re4Mujszn84DwG2fzc7z7RYiTRYmTYkT84/ejqaz+PM1SrVo3du3e7OowMIS4ujr///psPP/zQ1aF4jMDAQGbPnk23bt24c+d/Jy+KmYHUG7dgG5dvxWJMtgOkRILexIDxyxzuZXMgdr9D29IVkoIDsc5rEJUhkgGAsJzZGdmqATs+/5Ddw3qzsPd7NC5dFLWDRxe/6J0hzVHbueK3SlbqdKn2So/vCcLK56d4eH4sJL8Eo1IryR4cQJsBr79X9tSjKxx9cAGjNeXdHgariann1rz2czlD1apV2bt3r8O7V4SUzZ07l9q1axMaGurqUDxK3bp16dChAz169EhqcCOSgdSJTzSyNvpkConA/+iNJnYdvejQY8aZH2O0Jr9D61lGq5HHJtv1cGkpwyQDaa1w+QK0HtwMrXfy69Rabw0hJYMY8lN/Fi5c6OTonOP48eP8EfUL1VqWRuulQeejRVJIyJIVpVpB6ZpFmbD1S3z8Xn9mZFnMTpuJQFJMDy9yz+C8F8irCgwMJDQ0lGPHjrk6FI8myzKTJk165QPHMrsRI0Zw+fJlpk+fDoC3zp97N02cPBqDwc5OIQEOnb2KyoHi8AS9iY37HFvG9FH5oJbsFwaqJTU+qtfbOpsaGXOxO410HdGOXPmDmP3VQhLjEp+b2nm7fxM6ff0OR499yDvvvENUVBTjxo17qXrXU125coUmTZowfsJ42rdvT8LjRHatPsjda/fZsCWSkJKBjBqb+sKZlFyMv4XV5jE0T6glFTf198mmdf/T1p4uFXhyAyVX27VrFwaDgbp167o6FI+k1WqZN28eDeq24MS/Vs6duE2A9AZf9JmD1SrToEU5uvaLwNvHM4pznU1vdHxmL0Fv/2ofoEJAJRbF2O8vYEWmYtZKDj//6xLJgB2NP6hHw651OBl9lvs3YvHx96Z0reKoNU8yu/Lly3PgwAG6d+9O9erVWbx4cZq05nWle/fu0bBhQwYPHpy0jcvb14v679UAIEsx0nwfvdbBLTQyMhonbrd5HdWrV2dT1Dbe6doZP40WrVK83FJr0qRJ9OnTJ0Nu3XUWyeJL6TzvceLIdSQkVAotCfEGANYtPcDB6Av8+lcPfHwzxoVMWsqd3R+rA7vvVSoFBUIc20YcoAmgfEAFDj84lGIRoVpSUyFrRfzUzrvoEa8wBygUCkpWL0p466pUiCiTlAg85e/vz6JFi+jWrRvVqlVjyZIlLor09cXHx9O0aVOaN2/OoEGDkh1Ts2ZNoqOjMSVzONSrqpOzLDoHPuSVkpICPrnS7HnTy97bMawJkomOKEr4ysmUXvQzPaOWcPy+WK911M2bN1m/fj2dO3d2dSgey2K28NWAeVjMT7bDvchksnDrWiyTx6x1QXTur1i+HGTz87Y7TiFJtKzleDOsLvk/IIcyJ+bEl2ceNAoteb3z0Tl/t1TF+rpEMpBGJEmiX79+rF27lk8//ZT+/ftjMBhcHVaqmEwm2rZtS9GiRRk9enSK47JmzUrBggU5dOhQmj13w+BKdhcJtAo1rUJroFK8/s6F9PTX6f102bKAQ4/vgFKJwWLGZLWy6epZ3tkwhzWXU9etLLOaMWMG77zzDgEBr79tNbPas+MMRoOdLqImC9s3/kfc40QnReU5JElicLs30apTntXTqlXUrRBG7iDHz6/QKrUcG3mCoNM5yaUNTkrUgnXBdMjbkY+LfoZG4dxttGLeMo1VqlSJAwcO0K1bN2rWrMnChQspWDD1pyU6myzLSVXH06dPt7v1JTw8nO3bt1OlSpU0ef74e4+4O3UP/t0qYE3ms16jUBPmm5uO+eulyfOll0N3rzH60FYSkzn4Rgb0FjNDd/9DycCc5PcV3QlTYjabmTp1KqtXr3Z1KB5t5+YTJKZwtsizVColxw9eoWrtok6IyrPUKleITzrUYdSfG5GtFmTpyRuUhAyylRplCvN1t4apeszVq1dz/Ohx5v09D51Oh1V+si3R2S2InyVmBtJBQEAAS5cupWPHjlStWpXly5e7OiS7vvjiC06dOsWiRYtQq+1P19eqVYvt27enyXNfvXqV2rVr07x4bSZU6Usp//xoFCp8VDq8lVqyqHS0zVuLcRV6oVa4d/46+b/dKZ6A95TFauWPU87bP+yJVq9eTd68eSlXrpyrQ/Fo+lTsGDCmolgus2lYOYzrmybTvGphiufLSeE82YmoGMbVbbPp36w86lT0WYmPj6d///5Mnjw5qeBcISlcmgiAmBlIN5IkMXDgQKpVq0bbtm2JiopizJgxz3VQMxhMHD99A73BRK4cfhTK55pDUSZMmMCKFSvYuXMnPj4+Dt0nPDycXr16YbVaX6u468KFC0RERNC3b1+GDBkCwG+V+nFLH8vNxPtJMwLuvjQAYJVltl47b3e5wyRbWX3pBN9WbuCUuNydLMsc3nqcVZMjuXXpDlkCvDl0cw8fDu3l6tA8Xr6COdi7/QwmO/vkrVYrwXmy2hyTmc2aNYsKZUrwZc+Wz33feD6K8ePH8/PPPzv8WN9++y01a9YkIiIircN8LR59UJGniI2NpWvXrty4cYOFCxcSHJKH6XN3sGrD0aR2vxaLTI7svvTr+ibVKjpvWWHBggV8/PHH7Nq1i7x586bqvmFhYSxbtozSpUu/0nOfPHmSBg0aMGzYMHr18vw3fr3ZRMlFPztUfaxVqjjV7mMnROXeHt59xKcNRnD93E0S4/RJ37dIZgIC/Pkh8kuKVvLs3TmudPvmQ7q1+BWTnav+3HkDmbligEOd8TIbo9FIWFgYixYt4o033njutpiYGMqWLcuFCxccqm05evQoERERHDt2jJw5c6ZXyK9ELBM4QdasWVm+fDlt27alatXqvN93CsvXHyZRbyI+wUh8ghG9wcSVa/f5cswq1m457pS4Nm7cyMCBA1m3bl2qEwF4vaWCw4cPU7duXUaNGpUhEgF48gGvdXAGI1CbMVtYp4bZZGZInW+4/N/V5xIBAKWs4nFsPJ/U+5YbF0Qv/VeVI5c/EW+VRatLeelPkqx8OLSRSARSMGfOHIoWLfpSIgAQGhrKW2+9xZQpU+w+jtVqpVevXowYMcLtEgEQyYDTSJLE4MGD6ffJeK7deozRmPy0ncFo5ucpG7kXa//4ZEecPXiBMV1+o0+lTxhYczhLx/9D3IN4Dhw4QIcOHViyZAmlSpV6pceuVasWO3bsSPX9oqOjadiwIb/99hudOnV6ped2R5Ik0apgaVR21v50ShUdwio4KSr3tXvVfm5fvoM5hRNHAfQJBub9sMyJUWU8/b94i1r1S6LRqlA+c+aHVqdGo1GRoPqP+Ut/R0wSv8xsNvPDDz8wfPjwFMcMHTqUX3/91e7usRkzZgDQo0ePNI0xrYhlAieyWKw07zqZR4/1Nsdp1Eo6tKpCt3Y1Xvm5jHoj3707jsNbjmHSm7Ban/wza721yFYr53RH+XHWSN5+++1Xfo4LFy5Qs2ZNrl275vBVxbZt23j33XeZPXt2hjze98rjWBqvnUmCOeXCLT+Njq3NPiRQZ3//ckY2sMYwTuy238JV46Vh+f3ZaOwcmiXYduXiHVbO38O5UzdQqRRUrV2Mhm+XxyobqVOnDs2bN+fbb791dZhuZe7cuUybNo2oqCib4xo1asS7775Lt27J9wa4desWpUuXZtOmTZQp43g/AmcSBYROdPVGrN1CHgCjycL2PedeKxkY1X48hzYfw5j4/LYiQ8KT7LWApSQFA4u88uMDFChQAIVCwfnz5ylcuLDd8evWraNz584sXLiQOnXqvNZzu6u8vlmZ+ea7dN+2GItsfW5ngU6hIjEujj5ZwjJ9IgA4PP0vSRIP7zwiKE+2dI4oY8tbIIj+XzRN5hZvIiMjqVWrFr6+vgwdmnZtxj2Z1Wpl1KhRTJgwwe7Yjz/+mP79+9OlS5dkC6qHDh1Kly5d3DYRAJEMOJXJbHX4Cvrs2XM0b96c4OBgQkJCCAkJee6/g4KCUKZwIuPFY5fZv+HIS4nAsywmK1OH/sWkvSk3F7JHkqSkugF7ycDSpUvp06cPK1eupFq1jHvSI0DVnHmJatGb+ecOMWn3JiQvLbn8stKxSAXy3E7g/XfepX7pCh7RfyI9aXSONVWxmC1obKx5C68vR44cbNq0ifDwcPz8/OjZs6erQ3K55cuX4+vr61DVf926ddHpdKxdu5amTZ9PuDZv3syOHTv477//0ivUNCGSASfKFeSH2Wx/ZkCSoHzpQtSvWokbN25w/fp19uzZw/Xr15P+//79++TIkeOlJCEkJIQTyy5iMtrfX3zpvxiun79JSKFXb+8bHh7Ojh07UpwegycFOJ988gnr16/PNIf2ZNN5069UDZb2H87w4cOpV+//myUVg2HDhtG6dWv+/fdfvLwybyFhzVZVWDkpErOdSvfggjnxz+7+B1N5ujx58rBx40Zq166Nr69v0rkkmZEsy4wcOZLvvvvOoQs4SZIYMGgIo39bwtyNt3n4OJEs3loahhdjzDcfMXHiRIe3bbuKSAacKIuPluqVChEVfdZmsY5Wo6ZX5waUKhaS4hiTycStW7e4fv160teNGzfYvXs3V/bcB4v9f1q1RsXNi7dfKxmoVasWY8eOTfH2qVOnMnLkSDZv3kyJEiVe+Xk8VUxMDKGhoc99r3///kRHR9OnTx9mzZqVaau4W/RrzOopG22O0floaf95S5tjhLRTuHBhIiMjiYiIwMfHh+bNm7s6JJdYu3Ytsiy/dJWfkrOXbrNgSywW72JcuR4LwMPHemYvjSaoZAdCC7v/RZBIBpysR4ea7Dl0kcQUOoNpNErKFM9NyaLBNh9HrVaTJ08e8uTJ89JtX9z8nn3r7J8bkJCQwJaoLWQvEvBKWwtlWcak8kdbsC5vD5mOTquhZrmCvFOvHDmz+TJu3DgmTpzItm3bPP4kx1chyzJXr1596d9IkiSmTZvGG2+8wfTp0zPtlGyu/Dnwq6Tizi4DkvXlhEjrraVqs0pEdKzlgugyr1KlSrF69Wreeust5s+f/79ZLTd0/9ZD7t96iLefF8H5sr9SYh37OJEVO4+zaf8Z9EYz+XIGsHP5TL744guHHu/BowT6f7OIx/EGFMrnl7OssgSSiqHfL+OvsZ0Jyen4+QXOJnYTuMCpczf5eMRSDCYziYlPkgJJAtlqIfyNonw9+C20r1E5veHPbfzWf+ZLe7dfpNIq8W5kZvvOKHx9falduza1a9fmzTffJH/+/DbvazCa+XTiag6dvkqi3vjkBwDUKiWSBEX849n1z59s2rTppSvjzOL27duUKFGCu3fvJnv76dOnCQ8PZ82aNVSuXNnJ0bmWLMt8+umnREVFMfbz8cwbsZwrp66h1qiwWKx4Z9HR7rO3adGvsTi+2EW2b99OmzZtWLlGJNYeAAAUHElEQVRyJZUqVWbnppOsX3GARw8SyZ7Tj2bvVKZi9cLPbVd0lqP/nuXP0as4e/TKk78Zs4WsQX60G9SIBu2qOZwUbD10jmHT1yEB+me2uMoWE2XD8jJxUEuyeGltPsafS6OZvTQao43icJVSQfOI0gzp7l5dB58lkgEXMZst7Nx3ns07ThGfaCQ02J+JPw1hycLZVKjwenvQDYkG3g3uQcKjlE8h0+jUtOjXmJ5j3keWZU6cOEFUVFTSl1arfS45KFiw4HMvsM8mrmbXkYsYUtgjLlvMfN6lDq0iMteH3LMOHDhA9+7dbZ7uuGzZMgYPHsz+/fvJnj27E6NzrVGjRrFgwQKioqIIDHxyYNONi7e4d+0+3n7e5C8VKpIAN7Bu3Tp6df+ISoU7YTHLzx165OWtITC7L2OmdyF7DufVdGxesoeJH8/HkMzsqs5bw5tvV2LA2PfsJgSHz12jz7hlKb6HqVVKShXIxfSP37H5WG9/OJU79+Psxq3Tqtk0p7/bLguKZMCN/Pjjjxw/fpw5c+a89mMd2fYfnzb8DrPJ8tI55hovNQVK5WVc1HfJVnTLsszp06efSw4kSUpKDoqVqcQXM3bYzIQBgrP7sWLsB277x5/eVqxYwaxZs1i1apXNcZ988gmHDx9m3bp1Ke4QyUh+/fVXJk6cyI4dO8iV69XrVYT0d+/2I7q0+AVDoiXZ17FCqSAohx/TlvZF55X+R+7eirlHz1ojMNo4gEnnrWHw+PcJb2b7oqrb6IUcOX/d5hgvjZpJH7WibOHn67esVit37twhJiaGwT9tx2K1/zGqkCQ2zx2AxsZxyK7knlFlUj179qRgwYJcv36dkJCUiwcdIQVaOOG9l5al23N2/yU0WjWyVUZSSrzdtxHvDWud4tYuSZIoVqwYxYoV48MPP0SWZc6dO5eUGIyftxWf0ApIdlrvPnicyMlLtyhRIHO+4SdXPJic77//nvr16/PNN98wYsQIJ0TmOrNnz2bs2LEiEfAQS//ejdUipZjQWy1WHj6IZ9v6YzRqWTHd41k1axtWq9XmGH2CkQUTIm0mA7fuP+bkFft9LvRGE6OmLSFMfYuYmJikr6tXr5IlSxZCQ0PxKdQWJPvLupJEqk43dDaRDLiRrFmz8t577zFp0iRGjRr1yo+j1+vp2LEj3/3yNV26dOH+zVhuXryNWqumQOm8qFKZmUqSRFhYGGFhYXTv3p2h41ew/dAFu/dTSBI37j4SyYAdKpWKBQsWUKlSJapUqUKzZs2cEJ3zLV26lC+++IKtW7eSL18+V4cj2CHLMmuX7sdsZwZQn2hi6Zx/nZIM7Fh9CHMKrdyfdfHkNSb9+jtWyYxer3/p655ewizlA8n2e6EMXL8fR6m8WurUqUNoaGjSl7f3k8ZhY6dvYtXmo1gsKc8OSBJUr1jQrWdJRTLgZgYOHEiNGjUYNmxY0h9bag0fPpywsDA6d+4MQGCurATmSrvjSX28bRfUJJGeTLNlVk9PNHNEzpw5WbRoES1atGD37t0ZbvfF+vXr6dOnD5GRkRQtWtTV4QgOSEwwYrTTA+KpO7cepXM0T9haHniWjJUD+w7iE6BDp3vy5e3tTWBgIF5eXjy2qLn0XzxWGx/gTxUvWpivPn43xdvbNq3I2m3/YbGk/LvSqFV0fLuKQ7G7ikgG3EyRIkWoWrUqc+bM4cMPP0z1/bdu3cr8+fM5cuRIumWhEVWKEnXgHAl2XpgWi5XyxV7e+phZXLlyJVU7KapVq8ZXX31F69at2bBmI1ELdrNt4S708UZCiwbTcsBblKldwq2vLpKzY8cOOnXqxIoVKyhXrpyrwxEcpNYokR1YCwdQqZ0z/Z0jdyAP79kv1tOoNUyZMSHF8ywsVisbhkzlgZ0dV15aNY3fKGZzTGhwVr7o05DvJ0diNJp58Tem1ajo0yGcUkVeb+k3vYlyXTf00UcfMX78eLtrYy968OABXbp0YebMmelamV69TH687bSS1aqVNAsviVcmPlzG0WWCZ/Xt25fCAcXpWKAPf369kDP7L3Dl5FX+XbmP4c1HM6jmcOIfJaRTxGnvwIEDtG7dmnnz5lG9enVXhyOkglqtomip3HbHWWULOv/EFLfQppXY2FgM/rexyLYvQhRKBbXfrmjzYCulQkGH+hVR2fkElCRo/EZxu7FF1CjGpO/aUqNSIVQqBVqNCpVSQaXSeRk3rDVtmrj/KaUiGXBDderUQaPREBkZmar79e3bl2bNmtGoUaN0iuwJpULBhCGt8PHSoEjmKlWrVlEoT3b6t8u8zWIsFgs3b94kd277b6bPOrX3HIn7FMhmMDyzjUuWQR+n5+zBC3zR5Hu3Om720ukbTBu1iu/7zeH3b5Zz+sgVAE6cOEHTpk2ZPn26Q/3dBffT7oNa6LxsJ/RarQal722KFClC3759OX/+vMOPb3GgPXtiYiI//fQTRYoUwZLlEblCc6Cw0dtAq1PTbmBDu4+runeauJsX0SSTEUiATqNiXN8WDl/QFC+Uix8/fZsNs/ux6LcPiPyzHxO+eodyJTxjdlQsE7ghSZIYPHgwv/zyC40bN3boPgsWLODgwYMcOHAgnaN7IixvEH9/15Fpy3ezZd8ZlEolVtmKVq2iXYMKvN+kkttuoXGGGzdukC1bNjSa1G23mvnFXJsHTJkMZi4cvczxnacoHW7/iiU9xT1K5LsPZ3P6yBXMJjNWi4ykkIhcvJccuf3ZeHImP/30Ey1atHBpnMKreyO8CBHNyrFp9WH0iS9fkWt1arr0q0erDtW4efNrJk6cSNWqVXnzzTf5+OOPqVLl5XXymEt3WfzXLratP4rRaEalVlGrfkne7VSD/IVzJo0zm8389ddffP3111SuXJnt27dTvHhx7t96yCetx3P/5kMS4w1J43XeGpQqJSPm9SWkQA6bP9cff/zB8OHDWR8ZyZHrBuZs2E98ohGFQoHJbKFK8bz0bVmDIqFBqf6dabXq12oa5yqiz4CbMhgM5M+fn40bN1KqVCmbY69evUrFihVZu3YtFSumf0Xvi+ITjdy89wi1SknuHP4oRbMYdu/ezaBBg9izZ4/D97l/M5aOBfpiMtieBpUkqNmqKl8tHvK6Yb4yk9HMoJYTuHL+drLV3TJWvP00zNnxDT6+OhdEKKQVWZbZsOoQc6dF8TA2HqVSgdlkISRfNrr0rUfVWs8XhMbFxTFz5kx++eUX8uXLxyeffELjxk86Se7deYaRny7CbLJgsfxvGVShkFBrVAz95m3CI0qyatUqPv/8c4KCghg9evRLJ51aLFb2b/mPVbOiuHP1PifP/EefLzvRslsEOjsFztOmTWPEiBFs2rQpqZjVapW5cjsWo8lCjqxZCMiS+Q4QE8mAGxsxYgSXL19mxowZKY6xWq00aNCAOnXqMGzYMCdGJ7zIZLKwfd9Zlq0/zMUrN0mIe8DAnm/TMLwE3g40ZDm19yyfNRxJ/EP7NQEFSudl2pGf0yLsV7JlxUEmDl+CPiHlWQyNTs37gxrQpmcdJ0YmpBdZlom5eJe4x3qyZvMhOE+gzfFms5nFixfz008/YTAY6NVzIBsX3U62c+BTKrWCR9IuHsbfZPTo0TRu3NihgtmIiAiGDBlidyZ10qRJjBkzhs2bN9s9dj2zEcmAG7tz5w5FihTh9OnT5MiR/LTX+PHjWbRoEdu3b0elyrzT8q524/ZD+n61gEdx+ucOofLSqlGqFPwyvA0lwlI+fCoxMZFlc1byV/9lWE32X5IlqhVhwq5X70Xxuvo0+ZmLp27YHReYw4+50V85ISLBXcmyzObNm/np60VYE3OgkFLeeWCVrRQu4c9vf36Uqm6cQ4cOJVu2bHz++ecpjvnll1+YOHEimzdvpkCBAqn6GTIDMZ/rxoKCgmjTpg1TpkxJ9vbjx48zatQo5syZIxIBF0rUG+k9fD537se9dBplosFEXLyBgd8u4sbth0nft1gs7Nu3jx9++IF69eoRFBTE73/+hlJj/yVpxcKBa9FMnz6dx48fp/nP44hrlxyrHI+9+xiTg3vVhYxJkiQiIiLw1RS0mQgAKCQFV88nprotd7ly5Th8+HCKt48ZM4ZJkyaxbds2kQikQCQDbm7QoEH8Pvl3ju06QeTsrWyeu4PbV+5gMBjo2LEjo0ePznANajzN+u0neBxvwGpjT7bRZGHyX5uYMmUKbdq0IUeOHHTt2pVbt27x0Ucfcf36dXbu2kmXr99D6217ScE7iw+Df+rH2rVryZs3L927dyc6OtruDgOLxcqe7aeZOHIVP3+5jGVzdvHoQeq3KZrNZnhpN3UKZGxWfguZR0KCwf4gwGg0O7TL4Fmly5Th8PWbRF24yMnbd557LYwcOZKZM2cSFRX1Ske1ZxZimcDNHdx8jE+bf43SokGtViFJEmazBV1OFZaij1mxbpnHNaHJaDoMnMWla/ftjrNaTIT5nqJ+/Qjq1auX7PkTFouFL5v/yNGoExiSefPUemv5bsUnVIgoA8DNmzf5888/mTFjBlqtlu7du9OxY8eX+kycPnaVbwbORZ9oTDp5TqtTY7XKtO5Unc79Imz+HV27do3IyEjWrVvHpk2bKBfUHJ3ZfqV1oRIh/PbPYLvjhIzvnXo/OpR8Sgor3T8tS/369fH397c51irLTNuznxl793P/wQP8/PywyjLZvL0ZWqsGe+bPZcmSJWzevJng4JSX6QSRDLi16H8OMLLtOAzJbDWzYsU/mx9TDv5EjtDMc/StO2rQ6VfibRTSPaVWKVg9sw++Prar6y0WCyt+Xcuin1aR8DgRhVKByWCmXJ2SdBv1HoXLvzzNKcsy27dvZ8aMGaxevZpGjRrRvXt36taty6VztxncaTr6FLYsanVqmrWrQveP/tefwmg0snPnTtavX8/69eu5du0a9evXp1GjRjRo0IC7MYl81W0GhmS2mz2l89YwaPS71G4qug4KMGPCBlbMj8Zk46wDhVIitJCWqw93sGPHDipUqECTJk1o0qQJpUqVei5htcoyA1b+Q9SFSySaX16KUsoy0qH9bP91fIo1V8L/iGTATRn1Rtrk/IDExym3y1QoFVRsUJbv13zhxMiEFzX7YDL3HdgBoFBIbJ470OH+C1arlatnbmBIMBAUmo2AINtXSU/FxsYyd+5cpk+fzqNHj6hc6H0e3bH9MldrVHz3e2ui9+1g/fr1bNu2jWLFitGoUSMaNWpE5cqVn6tLkWWZ375cyublB5JNCLReasrXKMKXUzqjEFtNBeDOrYd0b/1bikkpPElMf5/fm9x5s5GQkMC2bdtYu3Yta9euxWQy0aRJExo3bky9evXYfOUqX27YTKIp5YRUq1SyvNN7FAkSF0z2iGTATW2cE8XEvjNItNM7W61V89f538geYnubj5B+xk7fxOpNRzFbbLePLlMsN7+PbO+kqP6/invDDn7+dAOybHspySpbuBV3hLI1s9GoUSPq169PUJDtZQBZllk6I4qFkzdjtViR5Sc9EGQZWnSuQcePGqEU9QLCM44euMSXA+disVgwPdOfQqVSolIpGD6mLZVrhL10P1mWOXPmTFJiEB0dTZ6PPsaUxdfm8ykliZalSjC6cYM0/1kyGpEMuKkf3v+VLXN32B3n7efF0Fl9CW/1hhOiEpJz5fp9ugz9C4ONqnmdVs2IIc2oXqGgEyOD/bvO8sMni4i3k1QClK9aiB+mdkn1c5hNFo7tOU/s3Th8A7woWy0MjVbsbhGSd+fWQ1Yt3EPkqkPEP9bj5aMl4q2yvN2uKrlyO3a66q379wmf8SeOnN6S3dub6H6pP/QtsxGvWDdlsXOGeBIZrKmsvBXSVt6QQAZ3r8e4GZuTTQh0WhUtG5ZzeiIAT5YmZAcr/1WqVzt5TqVWUr5mkVe6r5D5BOX054MBDfhgwKtfrWu8vFAplRgt9t/7TKk88C2zEsmAmypWpTDR/+x/7rCa5FjMFvKXFttlXK1p3dKE5PBn+oJdnDx/E7VKidlsIXfOALq+W4161W0fg5pewkrmxuxAYqnzUlO55svTs4Lgjvy0WtRKhUPJQL4Ax2ptMjuRDLipBl3eZNbw+XbHhRbLTb7innEqVkZXoVRefh+Zl9iH8cQ+TMDHW0vO7H4ujcnXz4sa9UqwPfL4c73gXyTLUK+ZqPoXPINSoaBtmdLMOXjY5pW/t1rNB1Wcf16LJxLVPW7KL9CX979sg9bGoRtabw0DJvdwYlSCI7L6+1Awb5DLE4GnPvy4CQHZfFIs5tPq1Hz07dv4ZBEHCgmeo3uVivhoNKRUGqtWKAj196NBmDiDwBGigNCNybLMop9W8tc3i1EoJPT/34TGy1eHWqPm66VDKVOrhIujFDxB7L04xn+zgoPR51H9//ntsgz+Wb3p83lT3njh5DlB8AQX7t2n06KlPNYbiP//LYYKSUKrUlEkezZmtmlJgJdIch0hkgEPEP8wnk1zd3Du4EVUGhWVGpSlatOKKF+x4EvIvO7decyx/RcxmSzkzpeN4mVCRQdLwaNZrFaiLlxi6fETPEhMJLe/H++VK0PZ4FzibzsVRDIgCIIgCJmcqBkQBEEQhExOJAOCIAiCkMmJZEAQBEEQMjmRDAiCIAhCJieSAUEQBEHI5EQyIAiCIAiZnEgGBEEQBCGTE8mAIAiCIGRyIhkQBEEQhExOJAOCIAiCkMmJZEAQBEEQMjmRDAiCIAhCJieSAUEQBEHI5EQyIAiCIAiZnEgGBEEQBCGTE8mAIAiCIGRyIhkQBEEQhExOJAOCIAiCkMmJZEAQBEEQMjmRDAiCIAhCJieSAUEQBEHI5EQyIAiCIAiZnEgGBEEQBCGTE8mAIAiCIGRyIhkQBEEQhExOJAOCIAiCkMmJZEAQBEEQMrn/AyA1SX6uH34DAAAAAElFTkSuQmCC\n", + "text/plain": [ + "<Figure size 576x720 with 9 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%% Plot graphs\n", + "\n", + "plt.figure(figsize=(8, 10))\n", + "for i in range(len(X0)):\n", + " plt.subplot(3, 3, i + 1)\n", + " g = X0[i]\n", + " pos = nx.kamada_kawai_layout(g)\n", + " nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100)\n", + "plt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Barycenter computation\n", + "----------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph\n", + "# Features distances are the euclidean distances\n", + "Cs = [shortest_path(nx.adjacency_matrix(x)) for x in X0]\n", + "ps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0]\n", + "Ys = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0]\n", + "lambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel()\n", + "sizebary = 15 # we choose a barycenter with 15 nodes\n", + "\n", + "A, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot Barycenter\n", + "-------------------------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeEAAAFCCAYAAADGwmVOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzs3XdcVeXjB/DPuYvLxoGogOBWNEfuco/ENLeWOZqalpaU9m2raflTi0It0285Mkcqam4TxZkbzQFuBURA9r77/P5Q+YqCAvfCuffyeb9evLLLved+cPDhec5zniOIoiiCiIiIyp1M6gBEREQVFUuYiIhIIixhIiIiibCEiYiIJMISJiIikghLmIiISCIsYSIiIomwhImIiCTCEiYiIpIIS5iIiEgiLGEiIiKJsISJiIgkwhImIiKSCEuYiIhIIixhIiIiibCEiYiIJMISJnoKQRAe+3BwcIC/vz9ee+01REVFSR3RIkRTJkTN3xBz19370OyGaMqw2PFff/11CIKAW7duWeyYRLZOIXUAIlsxbdq0/F9nZGTgxIkT+P333xEaGorDhw+jRYsWEqYrPVF/EWLOMkCzGxCUgGgEIAKCHBANENW9IDi/CUHZVOqoRHaHJUxUTNOnT3/ssUmTJmHhwoX48ccfsXz58nLPZA5RNEDM/BLI2w5AB8AEiNqHnnD/v5odEDV7IapfgOD+LQRBKUFaIvvE6WgiM7zwwgsAgKSkpAKPZ2RkYN68eejevTt8fHygUqng6emJ/v374+jRo4UeSxAEdO3aFQkJCXj77bfh7e0NuVyO5cuXY8SIERAEAQcOHCj0taGhoRAEARMnTizweGpqKj7//HM0bdoUTk5OcHd3R/PmzfGf//wH2XFj7xewBoAJqWlGfPZNMpp0ugXn2tdQqcF19Bp2G3/vzwKQB2h2Q0wbD1E0Yvny5RAEAcuXL0d4eDi6du0KV1dXuLm5oW/fvo9N0QuCgBUrVgAAateunT+t7+/v/1jeTz/9FI0bN4ajoyPc3d3Ro0cP/P333499zQ9n2LVrF7p27Qp3d3cIglDEnxaR9eFImMgMYWFhAIDWrVsXeDwqKgqff/45OnfujL59+6JSpUqIiYnBli1bsHPnTmzduhWBgYGPHS81NRXt27eHi4sLBg8eDJlMBi8vL0yYMAFr167FkiVL0KVLl8det3jxYgDA+PHj8x+7efMmunXrhujoaLRq1QoTJkyAyWTClStX8OOP3+OdofXh7GsEAETH6tF9yG3cijWgUzs1endzRk6uCdvDcvDiq3ewaG41jB0FQHcKYta3AHwBANu2bcNff/2FPn36YPz48YiMjMSOHTtw8uRJREZGomrVqgDuTeVv3rwZ//77Lz744AN4eHgAQP5/ASA6Ohpdu3bFrVu30KlTJwQGBiInJwfbtm1DYGAgFi9ejLFjxz72tW/YsAG7du3KzxAdHV3cPz4i6YlE9ES4NzErTps2Lf8jKChI7NixoygIgtivXz8xMzOzwGvS09PFpKSkx44VGxsr1qhRQ2zUqFGR7zN69GhRr9c/9vkmTZqIDg4OYnJycoHHr1+/LgqCID733HMFHu/QoYMIQPz2228LPG4ypomJFxqJOTfrisb4+qIxvr7YpYOjKAgQVy2qnv+YMb6+mHKpjti8iUpUqwXxzrna9x9vIi79bYEIQJTL5WJYWFiB43/yySciAHHOnDkFHn/ttddEAOLNmzcf/00WRbFLly6iIAjimjVrCjyelpYmNm/eXFSr1WJCQkL+48uWLRMBiIIgiDt37iz0mETWjiVM9BQPyrGwj4CAAHHVqlUlOt6kSZNEAGJ0dPRj76NSqcTExMRCX7dw4UIRgPjdd98VePxB6a1YsSL/sVOnTokAxBYtWohGo7HA841Zv4rG+GfyizYirJYIQBzSz6VAAT/42LishghAXDjb8/5jz4i/LRotAhBHjhz5WM4bN27cO96QIQUef1IJnz17VgQgDh06tNCvffPmzSIA8aeffsp/7EEJDxw4sNDXENkCTkcTFZMoivm/zsnJwcWLF/HJJ59g5MiRuHjxIr755psCzz9y5AhCQkJw9OhR3L17FzqdrsDn4+LiUKtWrQKP+fv7o1q1aoW+/5gxY/DJJ59gyZIl+OijjwAAer0ey5cvR6VKlTB8+PD85x47dgwA0Lt3b8hk/1v6IYoikLsU984D33P0VB4AICPThBnfpTz2vkkp96aso64+yK8BtIcBPD4NDwC+vvemqtPS0gr9Ogrz4Dx5RkZGoQvgHpxzL+xysLZt2xb7fYisDUuYqBScnZ3Rtm1bbNy4ET4+Ppg7dy7Gjx+fX0CbNm3C0KFDoVar0atXL9StWxfOzs6QyWTYv38/Dhw4AK1W+9hxq1evXuR7urq6YtSoUfjll18QHh6Obt26YcuWLUhISMDkyZOhVqvzn5ueng4A8Pb2LngQMR0wpRd4KDXNBAAIO5iLsIO5Rb5/do7pof+7V8gPn9N9QKG4923FaDQWeaxHpaTcK/89e/Zgz549RWfIzn7ssSf9nhFZO5Yw2RWjaEC2PgVaUy7kghLOikpQy53L7P08PDzQsGFDREREICIiIr+Ev/zyS6hUKpw6dQqNGzcu8Jp33nmnyFXOT1vZO2HCBPzyyy9YvHgxunXrlr8ga9y4cY/lAu6NtgswZd2/Flif/5C7272R8o8zPTHp7cdLtXCWvbDC3d0dABASEoL333+/RK/lamiyZSxhsguZ+iScTt2GM2nbYRKNEAQ5RNEEEwyo5dQM7asMhZ9z8zL5hv1g2tVk+t9I8dq1a2jSpMljBWwymXD48OFSv1ezZs3w/PPPY9OmTTh+/DjCwsLQuXPnx96nXbt2AIDNmzejbdu2uH37NmJjY5GVcQ3Bn+dC7fDQc5+9N4I+dDyv2CX8YJSr0Wie8sz/kcvlBV77sPbt29/LcOhQiUuYyJaxhMmmGUU9tt/5EZcyDwMiYMT9Ed7/Tt/iZk4EbudGwlHhhuG+0+Gp9rfY+2/evBk3b96EUqnEc889l/+4v78/rl69ijt37qBmzZr3Iokipk+fjsjISLPec8KECThy5AgGDBgAURTRqFEjTJ8+HbGxsYiJiUFMTAxiY2OhUChw+fJlfP755+jRowdq1aqFNm2aQaW6hJRUHZydBKjVMrRuoUandmps2pGNpWsy8OYI98fe83yUFl6eclSreu9bhoB7Rfr+++9jzpw5CAgIQEBAAJo0aYKAgIBCc1epUgUAEBMTg7p16xb4XOvWrdGpUyds3LgRS5cuxZtvvvl4hvPn4eXlVeQ5cyJbxBImm6U3abE6+hPc1dyE8aHp1UKfK2qg12ux4uaHeMXvG/g4NX7i8wvz8IKhnJwcREZGYufOnQCAb7/9Fl5eXvmfDwoKwvjx49GyZUsMGTIESqUSR44cQWRkJF566SVs3bq1yPcxmUxISEjIL9QHpfrg1w+ug01MTIRSqURubi5MJhM6dOiA4cOHo1atWvD19UVSUhK6du2KS5cuwdnZGWq1GomJiVi5LA97wmMQecgP/r73ppX/+Lk6eg6Lw9gP72Lhb+lo21IND3c5bt8x4HyUFhcu6XBkm8/9EhYgUzUEkIhFixahc+fOiIyMxMWLFxEWFob58+cDuLc4rE+fPvkF/eCHkbFjx2LIkCFwdXWFh4dH/gYjq1evRvfu3fHWW29h/vz5aNeuHTw8PHD79m2cO3cOFy5cwNGjR1nCZFdYwmSTRFHEptvf4q7mJgyi7ukvuPcq6EUN/oz5Em/UmY/Kqpoles8ZM2bk/1oul8PT0xMvvfQSJk6ciF69ehV47jvvvAMHBwf8+OOPWLFiBRwdHdGpUycsW7YMq1evxtatW3Hs2DFcunQpv2SBe8Xl6OiIypUrw9fXF7Vq1UKtWrVQu3ZtdO7cOf//Z8+ejZCQEHzwwQeYN29eoXldXFwQERGBuXPnYvPmzVi4cCHUajX8/bzw4XhPVKsiz3+uT00lTu6uhYW/pWPj9mys3pgFowmo7ilH4wYqvPemB55pfH8OW3CE4NAZwEHI5XLUr18f9evXx4ABA/KPJwgCmjdvjnfffReRkZE4cOAAIiMjoVQqER0djXnz5kEURVSpUgUtW7ZEQEAAfHx8cPr0aSxYsAChoaFYtWoVjEYjqlevjoCAAEyaNAnPPPNMif7MyoPemIz0vDDojSkQYYBC5g5Xh/ZwUjWSOhrZAEF8+LoLIhsRnfMv1sfMgF4s/jnJBwQIqOfaHkN9v7R4Lr1ej7i4uCJHsTExMTAajfDz8ytQsg9Gr7Vq1YKPjw8cHBye+D5du3bFwYMHcfnyZdSvX79EGUVRhJj8AmCMQYF5++KSeUPw3Feq8+smkwnR0dGIjIzM/7h48SKioqLg6upaYEr7wceDaWxrk6U9jYTMxcjIOwBBkMEkagGIEKACBAFqRR3UcBuPSk6BkAkqqeOSlWIJk036M/pL3MiJQKlKBIBcUOK9+ivgrCjuauB75ZWSkvLEgk1KSkKNGjUeK9iHS9bDw8OsBWInTpxAu3btEBgYmD8dXlKi4RrElGGAmFOyFwpOECr/CUHZsFTvWxSTyYTbt2/nl/LDJe3o6PjYOeeAgAB4enpaNENxiaIR0WlfICVnM0yiBk/6OygTnOCg8EXDaquhlFvnDxMkLZYw2ZwsfQoWXXvzqeeBn0QhqPBc1ZfxvOeI/Mfy8vIeK9VHFzs5OjoWKNRHC7ZGjRr518la2qJFixAXF4dly5YhISEBR48eNWujClF3FmLam/eL+GnfBoR7BVzpVwiqVqV+z5ISRRFxcXGPlfPFixehVCoLlPKDX1erVq3MLlsSRRHXUyYiI28fTGJeMV+lhEpeDU2qb4dCXvwf+qhiYAmTzTmfvhe7E36C3lTyqeiH6VNUOBMs5JdsVlYWfH19iyxYX19fuLi4WOirKDl/f3/cvn0bderUwfTp0/Hqq6+afUzRcAti5ixAdxz3ivjR8+v3p1FV7SC4fQ5BUcfs97QEURQRHx9foJQf/FcQhMdGzU2aNEH16tXNLuc7GT8hPnNhCQr4HgFKOKmaoLHXJl7XTAWwhMnmnEjZjP2Jy/53OVIpCXlqNIgelV+ynp6eBbZ4rEhEYyLE3DWAZgdgyrz3oMwVUL8IwWkEBLlt7EoliiLu3r372Kj54sWLMBqNhU5re3t7F6sYTaIWZ24/C1NJp/DvkwmOaFhtFVwcni3V68k+sYTJ5pxM+QvhiUvNLmE3ZTW8V3+5RTKR9UtKSip0Wluj0RRazr6+vgXKOSVnM26lfl7qEgZkqOTYG/U8F1nmCyK7wEuUyOY4KtwgFxRmnRMGAEe5q4USkS3w9PREly5dHrsfc3JyMqKiovLLeceOHYiMjERWVlaBVdrP998MpWNpCxgATEjP2wuDMQ0KeSXzvhiyGyxhsjl1nJ+FEQazjqEUHNDEratlApFNq1q1Kjp16oROnToVeDw1NRVRUVH5o2ZBccfs95IJDtAYbsBFXn6L28i6cTqabEpSUhIWLVqEW9V2om7HSijtKVyFoMLEBis5GqZiEUUTTsWavyhNLriiTtX58HDsZoFUZA8q5ioUsjlRUVEYN24cGjRogNjYWLzR6Qs4yJ+8oUVRBMjQwLUDC5iKTRBkAORPfV5xyAUnixyH7ANLmKyWKIrYu3cvXnzxRXTt2hXe3t64fPky/vvf/6JjwIto4PocFELJi1gtd0F3r7fKIDHZM6XM/M02TNBDpSjZdqlk33hOmKyOVqvF2rVrERwcDIPBgA8//BAbN24scNN6QRDQ1zsIebFZiM05D72ofepxBcigkjnhVb/ZcFVWLcsvgeyQp+tIxGf8DBFP/7tWFEdFHTgofC2YimwdR8JkNVJSUvDNN9+gdu3aWL16NebOnYsLFy7grbfeKlDAD8gFBYb5TkOLSi9CIaiKHBULkEEhOKCaQ228WWcBqqlrl/WXQnaomot5m6Pk5ojYtk6J27dvWygR2QOWMEnu8uXLmDBhAurVq4cbN25g9+7d2L17N3r37v3UTRRkghw9q4/FpAZ/oEu1MXBVVIEMcigEB8gFBeSCEk3cu2FM7e/xZt0F8FB5PfF4REVRyj3h4dgNApSler2LswfSExugefPmCAoKQmJiooUTki3i6miShCiK2L9/P4KDg3HixAm88847ePfdd1G9unk7M4miCL2ohdaYDYXMAQ4yJ8gEyyyoITKYMnAxvi90xngAxmK/7t5uWWvh4tAcCQkJmD17Nv744w+MGzcOU6dOReXKlcsuNFk1ljCVK51Oh3Xr1iE4OBh5eXkICgrC6NGj4ejoKHU0omLRGRJx6e7L0BnuQHxsr+1HySAT1Kjv+Svc1M8V+ExsbCxmzpyJjRs34v3338fkyZPh5uZWdsHJKrGEqVykpqZiyZIlWLBgARo3bowPP/wQgYGBFXavZrJtRlMW4jIWIil7FQDxsa0sBUENiCZ4OHaHt8cUOCrrFXmsa9euYcaMGdi9ezemTp2K9957D05OvIypomAJU5m6evUqQkJCsHr1avTv3x9BQUFo3ry51LGILMIkapGWuwtJ2etgMCVBFI2Qy9zh4dgdni4jSnQP4cjISEybNg1HjhzBZ599hrFjx8LBoXTXwpPtYAmTxYmiiEOHDiE4OBhHjhzBO++8g/feew81atSQOhqR1YuIiMBXX32F8+fP46uvvsKYMWOgVJZuMRhZP5YwWYxer8f69esRHByMrKwsBAUFYcyYMZxaIyqFf/75B19++SViYmIwffp0vPLKK5DLucjQ3rCEyWzp6en473//i/nz56NevXr48MMP0bdvX57vJbKAffv24YsvvkBmZia+/vprDBo0qFj3PybbwBKmUrtx4wZCQkKwcuVK9OvXD0FBQWjZsqXUsYjsjiiK2LlzJ7744gsIgoBZs2YhMDCQZWwHOFShEhFFEUeOHMGQIUPQtm1bODk54fz58/j9999ZwERlRBAEvPjiizh16hQ+++wzfPTRR+jUqRP2798vdTQyE0fCVCwGgwGhoaEIDg5GamoqJk+ejNdeew0uLi5SRyOqcIxGI9asWYPp06fD398fs2bNQvv27aWORaXAEqYnysjIwK+//or58+fD398fH374Ifr168cFIkRWQK/XY/ny5Zg5cyaaN2+OmTNnokWLFlLHohJgCduBDH0qbmRHIdeYDQEyuCjcUN/1GTjKS78q+datW5g/fz5WrFiBwMBABAUFoXXr1hZMTUSWotFosGTJEsyePRudOnXCjBkz0LhxY6ljUTGwhG2UKIq4nhOJ/Xe34lr2BcgFOYyiCQLu3dTAKBrQwqMDuni+hBqOtYp93GPHjiE4OBj79u3DW2+9hYkTJ8LXl7deI7IFOTk5WLhwIb7//nsEBgZi+vTpqFOnjtSx6AlYwjZIZ9Ji+a3vcSvnEnSmou9tKoMMckGB9lV64qWaoyETCl+HZzAYsHnzZgQHByMxMRGTJ0/G66+/DldX17L6EoioDGVkZODHH3/EggULMGTIEHz55Zfw8fGROhYVgiVsY/QmHX66Ng0JmlgYRH2xXqMUHNDUvQ1erTWxwCUNmZmZWLp0KUJCQuDt7Y0PP/wQAwYM4PleIjuRkpKCefPmYcmSJRgzZgw+/fRTeHnxdp7WhJco2ZjVMQuRqLld7AIGAL2oxYWMk9h3dzMAICYmBlOmTEHt2rVx7NgxrF27FocPH8bgwYNZwER2pEqVKvi///s/REZGQhRFBAQE4NNPP0VqaqrU0eg+lrANSdLGIyozAnrxabdPe5xe1OLv+FCMGP1K/vW8ERERWLt2Ldq1a2fpqERkRapXr46QkBCcPXsWKSkpaNCgAb7++mtkZmZKHa3CYwnbkMNJOyGKplK/XqPRoGnfOrh58ya+++47+Pn5WTAdEVk7X19fLFmyBMeOHcPVq1dRr149zJ07F7m5uVJHq7AUUgeg4tGbdDiZth9GGEt9DKWjHMoWebxxOFEFV69ePaxcuTL/9on16tXDp59+inHjxpXo9olZ+jQcT9mL23nXoTHmQCVzhJfaB+2q9ERVB941rTi4MMtGxOfFYOG1L6E1acw6jgABc5qtLnKlNBFVPA/fPvHLL7/Ea6+99sTbJ8bkXsXexFBczToHAAXWqMggh0yQwduxDnp6DUFDN25n+yT8TmwjNKZcCBb445IJMujMLHIisi/PPvsstm3bhjVr1mDNmjUICAjAqlWrYDQ+PvN2PCUMi69NR1TmaRhE/WOLRE0wwiDqEZ17Gb/f+h477vwBjvWKxhK2EUpBBcD8v8gm0QSFoDI/EBHZneeeew579+7F4sWL8dNPP6FZs2YIDQ2FyXRvLcrJlHBsiVtW7MWhelGLIym7sDN+VVnGtmksYRvhqvSAQTSYfRylTAWFjEsBiKho3bt3x5EjRzBv3jx88803aN26Ndb/vRqb434t8dUZepMWR5J3ISrzdBmltW0sYRvhrqyMGmrzVjPLIEerSl0slIiI7NnDt0/8/PPPsTFqKbT6onfoexK9qEVYQqiFE9oHlrAN6V6tPxxk6lK/XibI0KlqHwsmIiJ7J5PJ0HdgH9Tp5gWZQnj6C4qQoInGXU2cBZPZB5awDQlwbw2FUPSKxSeRQQZvx9qopq5p4VREZO/+TT8KAaUvYAAwikYcTfnbQonsB0vYhsgFOd6s/TFkYsm3llTLnTDab3IZpCIie5esvQOdWLqp6AdMMOKu5raFEtkPlrCNiT1zF7v+cwpysXiLq2SQwVnuinfrzYCHqkoZpyMie5RntMyOWhpjnkWOY0+4TNaGREREYPDgwVi1ahWaNGyArXd+x82cyxAhwvjIymmloIIIEU3cWqO/9xi4KytLlJqIbJ2TwsUix3GUO1nkOPaEJWwjIiMj0bdvXyxevBi9evUCALxT90uk6ZJxJHk3LmaeRJ4xFzLI4KRwQetKXdC2cjeL/eMhooqrutoXKpnarI1+5FDA26m2BVPZB25baQNu3LiBLl26YPbs2Rg1apTUcYiogtGbtJhx8W2zSlghKDG1UQgqqTwtmMz28ZywlYuLi0PPnj3x2WefsYCJSBJKmQNaV+oGGUp/v3E/54Ys4EKwhK1YUlISevbsifHjx2PChAlSxyGiCqyTZ1/IhdKdwVQKKvT0GmrhRPaBJWyl0tPT0bt3bwwZMgQff/yx1HGIqIKr4uCFkf5B9/exLz4FlOhdYwTqujQpo2S2jSVshXJyctC3b1906tQJM2fOlDoOEREAIMCtFUb6BUEpODx1alqAAMEow78rYtFSze1yi8KFWVZGo9HgpZdegq+vL3799VfIZPw5iYisS7I2HgeTtuF06gEIAqAz/W8jjweXRwa4tUEXz/74evL/ITU1FRs2bIAgmLfrlj1iCVsRvV6PYcOGQaVSYc2aNZDLS78IgoiorOmMGvybcRTxedHINWRCLXeGp7omWnh0hLPCFQCg1WrRtWtX9OvXD59//rnEia0PS9hKmEwmjBkzBqmpqdi8eTNUKt7zl4jsw507d9CmTRssWbIEffv2lTqOVWEJWwFRFDFhwgRcunQJO3fuhKOjo9SRiIgs6ujRoxgwYAAOHTqEhg0bSh3HavCEo8REUcTHH3+MiIgIbNmyhQVMRHapQ4cO+OabbzBw4EBkZmZKHcdqcCQssVmzZuHPP//E/v37UaUKb7BARPZtwoQJiI+Px8aNG7nwFBwJSyokJAQrVqzAnj17WMBEVCGEhIQgOTmZl1/exxs4SGTp0qUIDg7GwYMHUb16danjEBGVC5VKhQ0bNqBNmzZo0aIFBgwYIHUkSXE6WgLr1q3D5MmTsX//fjRo0EDqOERE5e7EiRPo168fDhw4gMaNG0sdRzKcji5n27dvx6RJk7Br1y4WMBFVWG3btsWcOXMwcOBApKenSx1HMhwJl6Pw8HAMHz4c27ZtQ7t27aSOQ0QkuUmTJuHmzZvYsmVLhVyoVfG+YokcP34cw4cPx7p161jARET3BQcHIysrC9OmTZM6iiRYwuXg3Llz6N+/P5YvX45u3bpJHYeIyGoolUqsX78ev//+OzZu3Ch1nHLH6egyduXKFXTr1g0//PADhg8fLnUcIiKrdPr0aQQGBiI8PBxNmzaVOk654Ui4DMXExKBXr16YOXMmC5iI6AlatWqF4OBgDBw4EGlpaVLHKTccCZeRhIQEdO7cGe+++y4mT54sdRwiIpsQFBSEqKgobN++vULcSY4j4TKQmpqKXr16YfTo0SxgIqISmDdvHvR6Pb744gupo5QLjoQtLCsrCz169ECXLl0wd+5c3sSaiKiEkpOT0aZNG8yZM8fuT+WxhC0oLy8Pffr0QaNGjbBo0SIWMBFRKZ05cwYvvPAC9u7di2bNmkkdp8xwOtpCdDodhg4dCh8fH/z8888sYCIiM7Rs2RLz58/HwIEDkZKSInWcMsORsAUYjUaMGDECOp0O69evh1KplDoSEZFdmDp1Ks6ePYudO3dCobC/ew6xhIsgiiJic5OQosuEwWSEi8IRtV2qQy1XFXieyWTC22+/jdjYWGzduhVqtVqixERE9sdgMODFF19E8+bNMW/ePKnjWJz9/VhhpjyjFnsTzmBNdDiStZlQyOSACIgQYRRN6F2jNYb6dkIt52oQRRFBQUG4fPky/v77bxYwEZGFKRQKrF27Fm3atEHLli3x6quvSh3JojgSfsg/yZH4+sIfEADkGXWFPkcOGeQyOZ6rGgD9+svYsXU7wsPD4eHhUb5hiYgqkPPnz6N79+74+++/0bJlS6njWAxL+L7d8acQfCkUWpO+WM+XGQFNdBo29J+Fml41yjgdERGtX78eU6dOxcmTJ+Hp6Sl1HIvg6mgAZ1KvlaiAAcAkB1zqemJR4u4yTEZERA8MGzYMI0aMwMsvvwyDwSB1HItgCQP48cqmEhXwAzrRgBMpl3El83YZpCIiokfNmjULDg4OmDp1qtRRLKLCl/DlzNtIyEst9ev1JgPWxRywYCIiIiqKXC7H6tWrsW3bNqxcuVLqOGar8CW8LuYA9KbST2uYIOJg0nlk6XMtmIqIiIpSqVIlbN68GR999BFOnToldRyzVPgSPp16FSaYtzZNKSh7P6dEAAAgAElEQVQQlRlroURERPQ0TZo0wS+//IIhQ4YgMTFR6jilVuGvE84zas0+hgiRI2EionI2ePBgnD17FsOHD0dYWFj+boUJmrvYf/cI4jWJ0Bi1cFE4o75LHXT2bA8nhZPEqQuq8Jco9dn/udlF7CR3wMeNh6OrV3MLpSIiouIwmUwYMGAA/P398ebX47A5bgdu5sTAJJpghDH/eQ4yFUyiiA5VWqO/dyC8Ha3j0tIKPx3tqnC0yHE8VC4WOQ4RERWfTCbD7yt/R2S1G/gu6idcyb4OvagvUMAAoDXpoBf1OJx8HJ+f/wYRaeckSlxQhS/hF6q3glJm3qy8TJChqbu/ZQIREVGJbEzdDu9efjDJTE99rgkmaE06hFxdgrPpF8oh3ZNV+BIe4PMczLnpoFKmwCCf5+7tMU1EROXqSPIJHEo+Bj1KdpWLzqTDj1d+QaouvYySFU+FL2FPtTtaeNSFrJRVLADo7/2cZUMREdFTiaKIDbe3QGsqfK//pzGKJuxJ3G/ZUCVU4UsYAD5qPBTOipLfAUktU2Js3RfhqXYvg1RERPQk13NuIc2MkaxBNGBPwn4YzNgrwlwsYQBe6kr44dkJcFE4FntE7CBTYohvJwyr1bmM0xERUWF2xe+DrhRbDj/MKJokPTfMEr6vnmtN/No2CE3c/aCSKaAQCj/H6yh3gLvSCZMbDsbYei+Wc0oiInrgdl4cRDM3W9KLeiRqkyyUqOQq/GYdD6vuWBkLWk/E7dxkLD2/FXsSz0Dh7ABAhEKmQENXH7zq1w3tqjaGXODPL0REUtJYYLMlo2hEnlFjgTSlwxIuhI9TVdS5qkT1v+Kxbt06mCCydImIrIxaXvK1PI9SCHI4WeA4pcVmKcLx48fRrl07CILAAiYiskJ+Tj4QzLrIFFAISlRXe1koUcmxXYpw4sQJtG3bVuoYRERUhMAa3aGSKc06hkImR3OPJhZKVHIs4UJotVqcP38erVq1kjoKEREVobazH6o6VCn165WCEoHVu0NexELc8sASLsS///6L+vXrw9nZWeooRET0BMN8+sNBpirVa+WCDD2qdbFwopJhCRfiwflgIiKybu2qtEL3ap1LXMQqmRIfNXwPHiq3MkpWPCzhQrCEiYhsx2i/YXjBq1uxilgOGRxkDviowXto6t6oHNI9WYW/n3BhGjRogNDQUDzzzDNSRyEiomK6kHEJf8XtxOWsqxBxb1vKBxxkKogAulTtgL41X4CX2lOynA9jCT8iNTUVfn5+SE9Ph1zOOyMREdmaFG0qDiYdRYL2Lu4kxePUoZP4+LWP0KFKG6jlDlLHK4Al/Ijdu3dj9uzZ2L9/v9RRiIjITHFxcWjVqhUSEhKkjlIonhN+BM8HExHZDy8vL6SkpECvN+9GD2WFJfyIEydOsISJiOyEQqFAtWrVEB8fL3WUQrGEHyKKIo4fP86dsoiI7Ii3tzfi4uKkjlEolvBDbt68CZVKBR8fH6mjEBGRhXh7e+POnTtSxygUS/gh3C+aiMj+cCRsI7goi4jI/rCEbQRHwkRE9oclbAP0ej3Onj2L1q1bSx2FiIgsiCVsA86dO4fatWvDzU3azbyJiMiyWMI2gFPRRET2qWbNmoiLi4M1bhDJEr6Pi7KIiOyTm5sbZDIZMjIypI7yGJbwfRwJExHZL2udkmYJA8jIyEBMTAyaNm0qdRQiIioDLGErdurUKbRo0QJKpVLqKEREVAasddcsljB4PpiIyN5xJGzFWMJERPaNJWyleOckIiL7xxK2UrGxsRBFEX5+flJHISKiMsIStlIPLk0SBEHqKEREVEZYwlaK54OJiOyfl5cXUlJSoNfrpY5SQIUvYW7SQURk/xQKBTw9PZGQkCB1lAIqdAkbDAZERESwhImIKoAHe0hbkwpdwhcvXoS3tzc8PDykjkJERGXMGs8LV+gS5lQ0EVHFYY27ZimkDlCeLscn4fDVW0jNzoUgCNh77hqef5YlTERUEVjjSNjuS1hvNOLvC1fx64GTiE5Jh8FogsFkuvdJJ0/cSTbi/M9r8Hbn1ugeUBdyWYWeHCAislve3t6IioqSOkYBdl3CmXkajF22CdfupiBPV8iydLkcepMJ528n4NMNu9HctwYWjO4PJxVv5EBEZG+scSRst8O+HK0Or/7yJy7HJxVewI/I1ekRER2H139dD53BUA4JiYioPLGEy9GUtTsQl5YBndFY7NdoDUZcS0zBtE17yzAZERFJ4UEJi6IodZR8dlnC0SnpOHY9BlpD8Qv4AY3egJ3nLyMlO7cMkhERkVTc3NwgCAIyMzOljpLPLkv4j3/OwGgq/U86AoB1J85ZLhAREVkFa5uStrsS1hkM2HT64v9WQJeC1mDEyn/OWNWUBRERmY8lXMaSsnIsUp7ZGh1ytDoLJCIiImthbRt22N0lStkaHWQWuNZXIZchW6uDi9rBAqmIiEhqUUlJyKxXD5sSE5F4+BCqODmhV526qCXh1sV2V8KOKqVFRsJGkwhHXi9MRGTTdEYjdl69gl9OnkR0ejp0ri4wATh38iRUcjm+O3wYzbyqY1ybNuhWuzZk5Xxvebsr4aquzjAYS38++AG5TICrA0fBRES2Kl2Th9GhobiZlobcQu4j/OAS1pN34nBxx1209/HBT/1egoOi/KrR7s4JO6mU6NLIvJ9mFDIBA58NgExWvj8RERGRZWRptRi0ejWuJCcXWsCPytXr8U9sLMaEhkJfgv0lzGV3JQwAb3ZqDQeFvNSvl8tkGP1cSwsmIiKi8jRh6xbEZ2dDX4IrZTQGAy7cTcTX+8PLMFlBdlnCzXyrw7uSe6lGwwqZDE19qqO2Z+UySEZERGXtSnIyIuLjS7Rj4gN5BgM2XLyIDI2mDJI9zi5LWBAELHptIFzUKpSkhmWCAA8nNX58tV+ZZSMiorK19EyEWVPKgiBg/YULFkxUNLssYQDwruSGVe+8jErOjlAU45IlpVwOLzcXrJnwCqq4OJVDQiIisrQ8vR5bLl2C0YyrZDQGA36LOG3BVEWz2xIGgLrVqmDz+6Pxcttn4KhUFnqLQrVCDpNOixHtnsHG90fBu5K7BEmJiMgS4jIzIbfAZUZJubmlms4uKbu7ROlRVV2d8Xn/7vioT2fsPHcZu85fQWpOHmQCUNnZCf1aNMIPUz+Ad3NvuDuqpY5LRERmyNbpLHKtr0ImQ7ZOh8qOjhZI9YT3KdOjWxG1UoFBrZpgUKsmj31OfH8Spk+fjlGjRkEo5wu1iYjIchyVSlhi13+jyQQnZdlXpF1PRxfXiy++iPT0dPzzzz9SRyEiIjNUd3GxyDSyWqGAWlH2uyayhAHIZDJMmjQJ8+fPlzoKERGZwV2tRgdf3xJdGfMopUyGV555xmKZnoQlfN8bb7yBPXv2IDY2VuooRERkhnGtW8NRWfpRrEwQMKZF+WzYxBK+z83NDaNHj8bPP/8sdRQiIjJDex9fVHVyKtUCLaVMhtbe3vB1L58rZQSRd67Pd+3aNXTo0AHR0dFwcuK1wkREtupWehoGrFqFLF3x7wsvFwR4Ojtj+6jRqFTGq6If4Ej4IfXq1UP79u2xatUqqaMQEZEZ/D0qYe3wl+GhVhfr/LBKLkcNV1dseGVEuRUwwJHwY8LCwjB58mScP3+elysREdm4K3Fx6P7pJ3Bt1QoymQx5BkOBzzsrlZAJAl5t1gwT2raDWznfwrbCXCdcXD169IAoiggPD0f37t2ljkNERGb4NSQEfRzU+HHCu9hy6RJ2Xr2KtLw8yGQCqjo5YVDjALxQrx5U8tLfec8cHAkXYvHixdixYwf++usvqaMQEVEp3bp1C61atcKFCxdQo0YNqeMUiiVciNzcXPj5+eHYsWOoW7eu1HGIiKgURo4ciXr16mHGjBlSRykSS7gI//nPf6DT6fDDDz9IHYWIiEro1KlT6N+/P65cuQIXFxep4xSJJVyEmJgYtGjRAtHR0XB1dZU6DhERFZMoiujevTtGjBiBcePGSR3niXiJUhFq1aqF7t27Y8WKFVJHISKiEti+fTsSExPx5ptvSh3lqTgSfoJDhw7hrbfewqVLlyCT8ecVIiJrZzAY0KxZM8ydOxf9+vWTOs5TsVmeoGPHjnBxccGuXbukjkJERMWwdOlSeHl5oW/fvlJHKRaOhJ9ixYoVWL16NXbv3i11FCIieoLs7Gw0aNAAW7duRatWraSOUyws4afQarXw8/NDeHg4GjduLHUcIiIqwvTp03H16lWb2nqYJVwMX331FZKTk3mHJSIiKxUfH4+mTZvi9OnT8Pf3lzpOsbGEiyE+Ph4BAQG4ceMGKlWqJHUcIiJ6xLhx4+Du7o558+ZJHaVEWMLFNGrUKLRo0QJTpkyROgoRET3k4sWL6NatGy5fvmxzAyWWcDGdPHkSw4YNw7Vr16BQ8L4XRETWol+/fujRoweCgoKkjlJivESpmNq0aYOaNWtiy5YtUkchIqL79u3bh6ioKLz77rtSRykVlnAJfPDBB5g/f77UMYiICIDJZMKUKVMwe/ZsOJTzfYAthSVcAoMHD8a1a9dw9uxZqaMQEVV4q1evhkqlwrBhw6SOUmo8J1xC3377La5du4alS5dKHYWIqMLSaDRo2LAhVq1ahY4dO0odp9RYwiWUnJyM+vXr48qVK/D09JQ6DhFRhTR37lwcPXoUmzZtkjqKWVjCpfD222/D398fX3zxhdRRiIgqnJSUFDRq1AiHDx9Gw4YNpY5jFpZwKZw7dw59+vTBzZs3oVKppI5DRFShTJ48GXq9Hj/99JPUUczGEi6lbt26Ydy4cRgxYoTUUYiIKozr16+jXbt2iIyMRLVq1aSOYzauji6lDz74ACEhIVLHICKqUD799FMEBQXZRQEDHAmXmtFoRP369bFmzRq0a9dO6jhERHbv2LFjGDZsGC5fvgwnJyep41gES9gMwcHBOHXqFFasXIlzN+ORlp0Hg8kENyc1mtbygpuTWuqIRER2QRRFdOrUCW+99RbeeOMNqeNYDEvYDFdj4tDrtYmo2aYHAOH+oyIEQYDeYESP5vUxpnsrNPaxj2kTIiKpbNq0CdOnT0dERATkcrnUcSyGJVxKK8NPY8G2I9Dp9RCFwk+tywQBKoUczzf2x/+91gcq3viBiKjE9Ho9mjRpgoULF+KFF16QOo5FcWFWKSzYdgQLd/wDrcFYZAEDgEkUodEbcCTqFt5esAF6g7EcUxIR2YfFixejdu3adlfAAEfCJfbX8Yv4dv0+aPSGEr1OrVSg6zN1MOe1vmWUjIjI/mRkZKBhw4b4+++/0axZM6njWBxHwiVgNJnw/eaDJS5gANDoDQg/fx23ElPLIBkRkX2aM2cO+vTpY5cFDLCES+TQxZvQG0s/pWw0ilh14IwFExER2a/Y2FgsXrwYM2fOlDpKmWEJl8CyvaeQq9WX+vUGkwlbTkYiT1f6YxARVRRffvklxo8fDx8fH6mjlBku1y2Bi7GJZh9DLpPhenwKmvpVt0AiIiLbpdHqcfD0dSSkZEKj1cPFSY36tTzRKsAX58+fw65du3DlyhWpY5YplnAxGYwmGCywulkAkJWnNT8QEZGNiolPw9pdEdhx6CJkMgFanQFGkwiFXAaVUg4ntQpZsafwn0+/gJubm9RxyxRLuJhkgnCvQS2wllypsJ8LzYmISmJz+Dn8sHI/jEYTDEZTgc8Z7j+Wq9FDdKqHnZEy9I2+iwZ+9rvhEc8JF5NMJsBF7WD2cQxGE6q62seep0REJbFudwR+XLkfWp3hsQJ+lCBXIjNHg3e+/hNXou+WU8LyxxIugb6tG0EhN++3zNPdBX7VKlkoERGRbTgdGYOf/jwMja5kl3jmafWYOHsDMnM0ZZRMWizhEni1c0vIBeHpTyyCo0qJN3u2hmDGMYiIbNEv645AW8ICfkCnM2DbgQsWTmQdWMIl4FetEhr7et07P1wKomhC4LONLJyKiMi6xSSk4bIZU8oanQGrd5yGyWR/GzyyhEvom9GBcFarSvw6OUQk7FuH4/8cLoNURETWa8PfZ8wu0FyNDqcjYy2UyHqwhEvIp4o7fps0DG5ODsUeETsoFZj+aiB+mzsdI0aMQHBwMLhlNxFVFOevxj91IdbT6A0mXItNslAi68ESLoWG3p74c+ootG9YCyqFHKpCLjmSCQLUKgXqeFXGwncGon+7APTs2RPHjx/H6tWrMWLECGRnZ0uQnoiofOXk6cw+ht5gRHau/e2xwOuES6lmZTcsmjAYielZWHf4X2w9GYWsXC2MoggnByXaN6iFMd1bIcDXq8Dr/Pz8cPjwYbz77rvo0KEDNm7ciPr160v0VRARlT0HlflVI5cLUDsoLZDGurCEzeTl4YpJ/TpiUr+OxX6NWq3Gb7/9hsWLF+P555/H0qVL0a9fvzJMSUQkHR8vd1yNMW8q2UGpgFdlVwslsh6cjpaIIAgYP348tmzZggkTJmDatGkwmcw7Z0JEZI2G9moBR7V5o1iTCHRuVddCiawHS1hi7du3x8mTJ7F//3689NJLSEtLkzoSEZFFPdvYF65Opd9xUCGXoW+nALucjmYJW4Hq1asjLCwMDRo0QJs2bXDu3DmpIxERWUxOTg5UOTdgMpbuNq5yuQwv937WwqmsA0vYSiiVSvzwww/4+uuv0aNHD6xevVrqSEREZjt8+DCaN28OF2MiOrSoAwdlyZYiqVUKfDi6G2rVsM/tfgWRF6xanXPnzmHQoEHo378/5s6dC6XS/qZgiMi+aTQafPXVV1i5ciV++eUXDBgwADq9AZ/N34ZTkTHQaJ++haWDSoH3XumE4S+0LIfE0mAJW6m0tDSMHDkSOTk5WLduHby8vJ7+IiIiK3DmzBmMHj0aDRs2xC+//AJPT8/8z5lMIjbu/Re/bz2BrFwtNBp9gTvEKuQyyGQCGvp7Yfyw59AqoFb5fwHliCVsxUwmE2bMmIGlS5di/fr1aN++vdSRiIiKZDAYMHv2bCxYsADBwcEYOXJkkTesEUUREVGx2LDnLOLuZkCjM8DFUYUmdWtgWO+WqFXdPqefH8UStgFbt27FW2+9hZkzZ2LcuHG8CxMRWZ1Lly5hzJgx8PDwwNKlS+Hj4yN1JJvAhVk24KWXXsKRI0ewYMECvP3229Bo7PO+mkRke0wmE0JCQtCxY0e88cYb2L17Nwu4BDgStiHZ2dl46623cP36dWzcuBG1atn3uRIism7R0dF44403oNVqsWLFCtSrV0/qSDaHI2Eb4uLigrVr12LEiBFo164d9u7dK3UkIqqARFHE0qVL0bp1a/Tu3RsHDx5kAZcSR8I2Kjw8HK+++iqCgoIwdepUnicmonKRkJCAsWPHIjY2FitXrsQzzzwjdSSbxpGwjerWrRtOnDiBDRs2YNiwYcjKypI6EhHZuQ0bNqBFixZo3rw5Tpw4wQK2AI6EbZxGo8GkSZNw5MgRbNq0CQ0bNpQ6EhHZmbS0NEycOBGnTp3C77//jnbt2kkdyW5wJGzj1Go1/vvf/yIoKAidOnXC5s2bpY5ERHZk165daNasGapUqYIzZ86wgC2MI2E7cuLECQwdOhRjxozBjBkzIJfLpY5ERDYqOzsbU6ZMwc6dO7F06VL06NFD6kh2iSNhO9K2bVucOnUKR44cQd++fZGamip1JCKyQQ9uuqDVanHu3DkWcBliCduZatWqYc+ePWjatClat26Ns2fPSh2JiGyERqPBxx9/jGHDhiE4OBjLli2Du7u71LHsGkvYDikUCnz33XeYPXs2evXqhZUrV0odiYis3JkzZ9C6dWtcv34d586dw4ABA6SOVCHwnLCdu3DhAgYNGoTAwEB8//33UKlUUkciIitSkpsukOWxhCuA9PR0jB49GmlpaVi/fj1q1KghdSQisgK86YL0WMIVhMlkwqxZs7BkyRL8+eefeP7554t87qVLd3DmTDQyM/IgV8hQubIzOnZsiGrV3MoxMRGVFZPJhPnz52PWrFmYOXMmxo8fz9GvRFjCFcyOHTvw+uuvY9q0aXj33Xfz/+HpdAbs2xuJNWuPIjkpC3q9EUajCQCgUt271KnpM754+eX2aNXKn/9giWzUrVu38MYbb0Cn0/GmC1aAJVwBXb9+HYMGDULLli3xyy+/IDfXiI8+XIWkpCxoNPonvlatVqJjxwaY+nFfKBS8DpnIVoiiiGXLluE///kPpkyZgilTpnAvASvAEq6gcnJyMHbsWFy+fAP+fq8gK0ubP/J9GgcHBVo+64+ZM4dCJuOImMja8aYL1ouXKFVQzs7O+OOPP1Cr1kCkpmYXu4ABQKs14MyZW1i+/GAZJiQiS+BNF6ybQuoAJJ3IyDvQaRWQyUo+GaLVGBC64SRGjnwODg7KMkhHRACQlZ6LlLuZ0OTp4OSiRrWaHlA7Pv1Sw9TUVEyaNAmnTp3CX3/9xT2frRRLuAJb9+cxaLVPPgf8JIIgIDw8CoGBzSyYiohEUcS5Ezew4beD+Pf4dSiVCkAQIIommIwiuvVrgYGvPQ+/el6Fvn7Xrl14++23MXjwYJw5cwZOTk7l/BVQcfGccAWVkZGLV15eCJ3OaNZx/PyqYumysRZKRURxt5Lx5bhlSEvJhjZPh8K+Q8vlMsiVcgS09MMX80fC2UUNgDddsEU8J1xB3Y5NvffTtZni4tIskIaIAODGpXi8P2whEuLSoMktvIABwGg0QafR4+LpW3h/6EJkpefypgs2itPRFVROrtYixzEY7l1PLJfz5zkicyQnZuCT1/+L3Ozi/9vU6wy4eycdYwK/xomYP/Dzop+457ONYQlXUGq1ZfaQlstlLGAiC1j10z7k5pT8h2OD3ghDpohF369B/wGdyiAZlSV+96ygvKq5Qa8373wwALi68oYQRObKy9EifOsZGA3Fv1SwAFGGXX9GWDYUlQuWcAXlVd0dtWt7mnUMQTDh0uUwtGzZErNmzUJkZKSF0hFVLOHbzpq9Feyd6BTcvBxvoURUXljCFdiIER3gWIzrDYuiUChx8OBahISEICkpCb1790bjxo3xxRdfICIiAlx4T1Q8h3dfgCZPZ9YxDAYTTh++aqFEVF5YwhXYc8/Xh1pdumUBSqUcz3dsgCpVXNG5c2eEhIQgOjoaK1asgF6vx/Dhw1G3bl1MmTIF//zzD0ymUk6zEVUAmek5Zh/DaDAiM83841D5YglXYHK5DHPmvgK1umQ7XsnlMlTzcsNHH/Up8LhMJkPbtm0xZ84cXL16FZs3b4azszPGjRsHX19fTJw4Efv27YPBYLDkl0Fk8wQL7cEu4yJJm8M/sQqubl0vzJ33CpycVMW6GYNKpYCvb2WEhIyGk5NDkc8TBAHNmjXDjBkzcOHCBezbtw/e3t74+OOPUaNGDbz99tvYsWMHtFrLXCpFZKsMBgMgN3+RpFKlgHtlZwskovLEHbMIABAfn47fVxzC/v2XIJMJj93S0NFRBYVChkGDW+Pll9uXePT8sOjoaGzcuBGhoaG4ePEi+vbti8GDByMwMJDb65HdE0URV69eRVhYGMLCwhAeHo76NdvCU2gJk7H0I2KlSoHF24JQw7eyBdNSWWMJUwHZ2Rr8vfs8jh69hsysPMjlMlSp7ILegc3QoUM9i18THB8fj82bNyM0NBQnT55Er169MHjwYPTr1w9ubm4WfS8iqdy9exd79+5FWFgY9uzZA5PJhJ49e6JXr17o0aMHqlSuileen1WijToe1bS1P+atfMeCqak8sITJaiQnJ2Pr1q0IDQ3FwYMH0blzZwwePBgDBgxAlSpVpI5HVGy5ubk4ePBg/mj31q1b6NKlC3r16oWePXuiYcOGj12S9Nt3O/HXyn+g15V8zYTaSYVPvnsF7bo1ttSXQOWEJUxWKTMzE9u3b0doaCj27NmDNm3aYPDgwRg0aBBq1KghdTyiAoxGI06fPo09e/YgLCwMJ0+exLPPPps/2m3Tpg0UiidfiZCTpcF7g+YjKT4dJlPxvy2rHBRo0aEepv00GjIZl/nYGpYwWb3c3Fzs3r0boaGh2L59O5o0aYLBgwdj8ODB8Pf3lzoeVUCiKOLatWv508vh4eHw8fFBz5490bNnT3Tp0gUuLi4lPu7dO+n4cMQiZKTlwFCMHe0c1ErUb+qNb359Eyre19smsYTJpmi1Wuzbtw+hoaH466+/4Ofnh8GDB2PIkCFo2LCh1PHIjt29exf79u3LH+0aDIb86eUePXpYbIYmIy0Hc6asxYXTtyCaxELL2EGthCiK6DWoFcZ/9hIUSrlF3pvKH0uYbJbBYMChQ4cQGhqKTZs2oVKlSvmF3KxZM7O3AXySnKw8ZCRnQa8zwNnNCZW93DgVaGdyc3Nx6NCh/NHug/O6D0a7jRo1KtO/Ywm3U7Hlj3+wa8MpaDU6yOVyGAxGVK7qisFvdESvQa3h6u5YZu9P5YMlTHbBZDLh+PHjCA0NRWhoKORyeX4ht2nTxiIFaTKZcObAJaz/eQ8uHr8OhUoBQQCMBhMcnR0wcGw3BI58Hh5VXS3wFVF5e3Be98FiqhMnTqBly5b5o902bdpAqZRmyler0UOTp4OTswOUKt78zp6whMnuiKKIM2fO5F+LnJ2djUGDBmHIkCHo2LEj5PKST91dORuNr99YjJwsDTRF3G5OdX+K8MXRHTF2+hDe4vEJsjPzEHstETlZGqgcFKji5Q5vM28oUlKiKOL69ev508vh4eGoWbNmful27twZrq78gYrKFkuY7F5kZGR+Id+5cwcDBgzAkCFD0K1bN6hUT7+BxZmDlzDj9cXQFnODfQdHFZo/3wBfLRsHuYLn6h527cJthP56AP/sPg/F/RGdgHv3xPXyqYxh47uhc9/mZbbIKCkpqcB5Xb1eX+B6Xa68p/LGEqYK5fr169i0aRNCQ0Nx+fJl9OvXD0OGDMELL7wAR8fHz6/djIzDhy99B01uye5w4+CoQpeBrRAUPMpS0W1abrYGX49fjpp5nHQAAAVVSURBVEsR0dDrDTAZC/+24+jsAEEmYNri19GsfT3z3zc3F4cPH84/r3vjxo3887q9evUq8/O6RE/DEqYK6/bt2/m7dUVERKB3794YMmQIXnzxxfxpyI8GfI/IEzdKdXyVWokfd0xF7cbeloxtc3Iy8zB58HwkxqVBry3eRhQOaiU+WTAK7Xs0KdF7GY1GREREFDiv26JFi/zFVG3btpXsvC5RYVjCRLh3+cmWLVsQGhqKI0eOoGvXrniha1/8PT+y2MXxKJlchp7D2iHoh4o7GjaZTJj68s+4ev52iXeCcnBU4rs/30O9pj5FPufBed2H92GuUaNGget1eV6XrBlLmOgR6enp2LZtG9Z+vwf6eEfIhNKf11WplVh9bjacXSvmpSSnDlzCN+/9XuLp/Aeata+LOasnFHgsOTk5fx/msLAwaLXaAtfr1qxZ0xLRicoF17oTPcLDwwOjRo3C7h+ikCykm3UshVKOiyeuo22PphZKZ1vWLw4vdQEDQNSZaERfu4MrNy/mL6a6fv06OnfujF69eiEoKAiNGzfmeV2yWSxhoiLkZmnMPoZOp8eBvYeQoouFSqUq9odSqbT5zT8S41IRdSbarGPotDr06/ga3OvloVevXliwYAHP65JdYQkTlSGDXo8DBw5g35kt0Ol0JfpQKBQlKm5zP5RKZalfV9hI9MKJm1DIZdAX8vtSXAJkaNekB37d+4kZRyGyXixhoiK4uDmaPRp2cnbCpzMnonX3kq3yFUURBoOhxMVdnI/s7GyLHUuv10Ov1xda4J7KRqgqNoEM5l0rnZdT+ulsImvHEiYqQqf+rfDXb+Ew6J5+N5uiGA0mNC3F9a6CIECpVEKpVMLZ2bnU718eRFGEXq9/rKDDNkRg85Kj0Jvx+weAO4+RXePfbqIivPRGZ7MW/MgVMvQY2hZqJwcLprI+giBApVLBxcUFlStXRvXq1VGrVi3Ub1Q7f1csc7hVtu4fQojMwRImKoKXbxUEtK6D0vawXCHHwLHdLBvKhrTq3BBGg8msYzg4qhD4clsLJSKyPixhoieY+H+vlGok6+CoQuDI5+Bbv3oZpLINTi5qdOvfEjJ56WcTRFFE94GtLJiKyLqwhImewKeeF2aufu//27l/kKjDMIDjj3eep5elpZAuFRQtETglRURgBEVBkUE19WcooikaHJpaCwoapDHaCiGClpBaGiJqK6LJsTmo5PS8X0NjmCl6j+LnM/+GZ/v+eF+ed1EhrnZ1xPDRvXH1zugKTrY2nL58KNorSzuSbq+U4/DJoah1dy7zVLB6iDAsYM++nXH/5a0Y3NEfnbWOee+Jq10d0dFZiTPXRmJs/NKa3/NdDtt3D8Spiwej2rW4vd62Ulv09nXHlbETKzQZrA6erYT/VBRFfPkwFRPjk/F+8lOUSm3RVi5FY6YRW7b2xOj1IzFydnjdPlE5n6Io4uHtiXj9/GPUpxfeGm6vlGPT5lrce3ojBrf1tWBCyCPCsASzM4348f1XzNYbsaGnK2rdnZ5O/IeiKOLF47fx5MGraM41Y/pn/a9vKtU/x9ZD+3fFzbvnorevu9VjQsuJMNAyjdm5eDf5OZ49ehNTX7/FbL0R5XIpNvbW4tj54Th+4UD0D/RkjwktI8JAmmaz6e6cdU2EASCJX1AASCLCAJBEhAEgiQgDQBIRBoAkIgwASUQYAJKIMAAkEWEASCLCAJBEhAEgiQgDQBIRBoAkIgwASUQYAJKIMAAkEWEASCLCAJBEhAEgiQgDQBIRBoAkIgwASUQYAJKIMAAkEWEASCLCAJBEhAEgiQgDQBIRBoAkIgwASX4D8cVwlrUdwoEAAAAASUVORK5CYII=\n", + "text/plain": [ + "<Figure size 432x288 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%% Create the barycenter\n", + "bary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0]))\n", + "for i, v in enumerate(A.ravel()):\n", + " bary.add_node(i, attr_name=v)\n", + "\n", + "#%%\n", + "pos = nx.kamada_kawai_layout(bary)\n", + "nx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False)\n", + "plt.suptitle('Barycenter', fontsize=20)\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/notebooks/plot_fgw.ipynb b/notebooks/plot_fgw.ipynb new file mode 100644 index 0000000..b41f280 --- /dev/null +++ b/notebooks/plot_fgw.ipynb @@ -0,0 +1,359 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "# Plot Fused-gromov-Wasserstein\n", + "\n", + "\n", + "This example illustrates the computation of FGW for 1D measures[18].\n", + "\n", + ".. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain\n", + " and Courty Nicolas\n", + " \"Optimal Transport for structured data with application on graphs\"\n", + " International Conference on Machine Learning (ICML). 2019.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "# Author: Titouan Vayer <titouan.vayer@irisa.fr>\n", + "#\n", + "# License: MIT License\n", + "\n", + "import matplotlib.pyplot as pl\n", + "import numpy as np\n", + "import ot\n", + "from ot.gromov import gromov_wasserstein, fused_gromov_wasserstein" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate data\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% parameters\n", + "# We create two 1D random measures\n", + "n = 20 # number of points in the first distribution\n", + "n2 = 30 # number of points in the second distribution\n", + "sig = 1 # std of first distribution\n", + "sig2 = 0.1 # std of second distribution\n", + "\n", + "np.random.seed(0)\n", + "\n", + "phi = np.arange(n)[:, None]\n", + "xs = phi + sig * np.random.randn(n, 1)\n", + "ys = np.vstack((np.ones((n // 2, 1)), 0 * np.ones((n // 2, 1)))) + sig2 * np.random.randn(n, 1)\n", + "\n", + "phi2 = np.arange(n2)[:, None]\n", + "xt = phi2 + sig * np.random.randn(n2, 1)\n", + "yt = np.vstack((np.ones((n2 // 2, 1)), 0 * np.ones((n2 // 2, 1)))) + sig2 * np.random.randn(n2, 1)\n", + "yt = yt[::-1, :]\n", + "\n", + "p = ot.unif(n)\n", + "q = ot.unif(n2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot data\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 504x504 with 2 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%% plot the distributions\n", + "\n", + "pl.close(10)\n", + "pl.figure(10, (7, 7))\n", + "\n", + "pl.subplot(2, 1, 1)\n", + "\n", + "pl.scatter(ys, xs, c=phi, s=70)\n", + "pl.ylabel('Feature value a', fontsize=20)\n", + "pl.title('$\\mu=\\sum_i \\delta_{x_i,a_i}$', fontsize=25, usetex=True, y=1)\n", + "pl.xticks(())\n", + "pl.yticks(())\n", + "pl.subplot(2, 1, 2)\n", + "pl.scatter(yt, xt, c=phi2, s=70)\n", + "pl.xlabel('coordinates x/y', fontsize=25)\n", + "pl.ylabel('Feature value b', fontsize=20)\n", + "pl.title('$\\\\nu=\\sum_j \\delta_{y_j,b_j}$', fontsize=25, usetex=True, y=1)\n", + "pl.yticks(())\n", + "pl.tight_layout()\n", + "pl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create structure matrices and across-feature distance matrix\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "#%% Structure matrices and across-features distance matrix\n", + "C1 = ot.dist(xs)\n", + "C2 = ot.dist(xt)\n", + "M = ot.dist(ys, yt)\n", + "w1 = ot.unif(C1.shape[0])\n", + "w2 = ot.unif(C2.shape[0])\n", + "Got = ot.emd([], [], M)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plot matrices\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV8AAAFgCAYAAAAcmXr5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzt3XuQHWd55/HvM2cu0uhmSyMLYUu+YeK7BWidIhjWbIDCbCo2bIXY7LJOQsVkC1I4IQlekkpcSW2VN8UtISkvBhxMikDYAoKLpQi2wWvMErBky7Is+Y4vkmVdLNm6zoxm5tk/TgvP6ffpUc/MOdPnnPl9qlQz5z3d/b490+dRz/v2+7zm7oiIyNzqqboBIiLzkYKviEgFFHxFRCqg4CsiUgEFXxGRCij4iohUQMFXRKQCCr4iIhVQ8BWZ58ysz8z+wMx+ZmYvm9lRM9uYlfVX3b5uZZrhJjJ/mdnJwJ3A2cBngR9nb10B/B7wfnf/ekXN62oKviLzlJkZ8APgXOCt7v5I7v31wIvu/vMq2tfteqtugIhU5lrgcuCqfOAFcPcNc96ieUR3viLzlJltBnrd/fyq2zIfacBNZB4ys9OBi4CvVN2W+UrBV2R+uij7umWqjcxsjZndZWbbzOxhM/vrrK9YZknBV2R+WpZ93XWC7caAj7n7ecDrgF8G3tPKhs0XGnATmZ92Z19fPdVG7r4T2Jl9P5r1E69pcdvmBd35isxPPwEOAL8dvWlmlwVlK4CrgH9tbdPmBz3tIDJPmdnvATcDtwP/COyhPtniN4Cl7v6mSdsOAN8DvuPun6yguV1HwVdkHjOzK4E/ot6fC/AscA9wq7v/LNumBvwz8Ky7/2ElDe1CCr4iMiUz+wJQA37HFTCaRsFXRAqZ2ZuAe6k/kjaeFd/q7n9bXau6g4KviEgF9LSDiEgFFHxFRCqgSRbSMczsncDfUB/8+YK73zTV9kNDK/yMtWtnXqFPRK2INix/zIngmNFs3Wi7orrGx8rVXdTMsdFyxyzqohwrV79Hxyw6z+CYPhHUHxSNHgnOh7j50W/z4Nh4UlYrmFF9cDxt/14m9rr7ynCHSRR8pSNkjzv9PfB2YDtwn5nd7u5bi/Y5Y+1aNtx794zr9JEjaWGtLy2bSD+s2RHSoqOH0rK+YLGI4cPxIYNg5Qf2BtsFdRe00/c+nxa+FBxzeDhu0/5g26ie/fvTwiPBzxiY2LsvKRuPgmpwns/evz085uhIEFR70z/+7919IClbXIs7Ce55+WhS9jkOPRNunKNuB+kUlwJPuPtT7j4KfA24suI2icyYgq90ilOB5ya93p6VNTCz68xsg5lt2LP3xTlrnMh0KfhKV3H3W9x9vbuvXzm0ourmiBRSn690ih00ZtM6LStrHQvuTaKBl8L0tkF5LfjIRfX0FHw0LRig6h1Iy6LBwqK+6f5g/4GF8baRhYvK1b8w6DMuGHDrGVyQFkY/52AUbdFg0C8P9Ab9trXe9Jgn9daSsgUFv+MVwbaUHP/Una90ivuAc8zszGw586upJ4QR6Ui685WO4O5jZvZh6ukMa9SnuD5ccbNEZkzBVzqGu38X+G7V7RBpBnU7iIhUQHe+IkV6ogG3qGwaM9yiY/YEgzZRWf2NtCgaMIumcxUNuA0MpmUL0skDhRaOlKrfhtNjFv7kRtJj9kQ/u6CewcE4rPUGg2vRJIulwcDcQPR7B1b1a8BNRKSjKPiKiFRAwVdEpAIKviIiFdCAm3Qvn0gzkxUMnEQDYdYbZBsruW9hk3qWpPUE+3vZugHrj2ajRekX4+EtW3xyWjgaDI4Vpa48kmYBi/jhg2ndUeY4gIMvpWUjwQy54JyWrl4dH3M0yIpWSwfM3vLAtqSsZyCeNXfB47uSso/cl2Zki+jOV0SkAgq+IiIVUPAVEamAgq+ISAU04CZdzNJlf4rSPxYNxDVbMMssHAYrmo0WDZqNHYs2LLcvxINrR9LBMY4VrI0WDbhFKSUPvZyWBbPeAHgpSIQfzHoL69lbsKxRNOAWDHYe3ZEud1Trj0Pl7t3TmAmYr3rGe4qIyIwp+IqIVEDBV0SkAurzlY5hZk8DB4FxYMzd11fbIpGZU/CVTvNWdy8YUcnzdOCqcMAtGIyaxsy10oJUkeEMt4mCuqPmB7O0QkUDbtFsugXBumy98Swviwa9gro8qr/gmESz6fqDGW6RZcvi8pIz3AZWLE7KehbE7Tz5QDAI+MyUrXvlmOU2ExGRZlLwlU7iwPfNbKOZXVd1Y0RmQ90O0kkuc/cdZnYKcIeZPeLu90zeIAvK1wGsPe20KtooUorufKVjuPuO7Otu4FvApcE2t7j7endfv3Jo+Vw3UaQ03flKRzCzRUCPux/Mvn8H8Jcn3jM/yFMw4NZuigYGo0Grom3L7Fu0f9kyKFjXbhb1QLyGXTSwODGNgdKoPDim9UV1x8es1WZ+PSn4SqdYBXzL6h/WXuCf3P171TZJZOYUfKUjuPtTwCVVt0OkWdTnKyJSAQVfEZEKqNtButfEBBw91FhWK7jko1lmwXprYarHaHCoQDSbLdyuqJ0BLzsTr2jALajL+gbS7SaCmWwAC4OfU2RJsFbcWJymkpPSNJUepbQMZtdZ0Yy/aP/gdzcQ/Zz64hluQ0PBuW98JK4/X3WprUREpKkUfEVEKqDgKyJSAfX5Svcyg75cxq6i5YLKZhuLqmlB9rMwA1j9jbQsygBWdl+I+12j/tGCpY38WMnlffL97wCjcaYyj5YcitoZ1bNvT3jMsn2+4TJEBX2+I8+nSw6VpTtfEZEKKPiKiFRAwVdEpAIKviIiFdCAm3SviQkYPtxY1lM0ySIdePFoeZ1g0Kl4yZ8041U0eSIaXLPCDGJpuVvQzqLBtZLHDCejFEyysOjnFOlfkJYVDRZGEzfGgoG9IKtZOBkDSi8jxPDRpMgKBtwG+qNz/0lcf47ufEVEKqDgKyJSAQVfEZEKKPiKiFRAA27SVszsVuDXgN3ufmFWthz4Z+AM4Gngve5eYmqRp4NEVpCZq+x9SLiMzzS2LX3MWS53FO0/nWWEopMqXPIn+NmF5xQtN1Twcw+XDArKot2Lssz1BoNm0TJCUd1FWeYKBuLK0J2vtJsvAe/Mld0A3OXu5wB3Za9FOpqCr7SVbCn4fbniK4Hbsu9vA66a00aJtICCr3SCVe6+M/v+BeqLaYbM7Doz22BmG/bsm3nSE5FWU/CVjuL1GQmFnanufou7r3f39SuXBysniLQJDbhJJ9hlZqvdfaeZrQZ2l9prfAw/kEsP2BssjwPQn5Zb/8J0u7FjaVnRsjXRbLRocCqY5RXOWitQOBuuRHvqdQWDRtFAWJS+EeLBqGjAbVqz5oI2FaS0TIwGM+EAH09/dxbNbDwSpL7MpyY9vn/UzpJ05yud4Hbg2uz7a4FvV9gWkaZQ8JW2YmZfpT45/pfMbLuZfQC4CXi7mT0OvC17LdLR1O0gbcXdryl461fntCEiLaY7XxGRCujOV7pbPuVg0aBROPurbFkLTGs22lyZRt2zbmfJWXfR76MwHWfJGXbR/oWz+2Z+nrrzFRGpgIKviEgFFHxFRCqg4CsiUgENuEn3ctJZUUWzpKLyaNCrbFkz9i97zFYMwk0nJWXZgbjomEUDVtFMwGhwLZxJF884tGjbKP1kNGutaCZbwcy3MnTnKyJSAQVfEZEKKPiKiFRAwVdEpAIacJPuNTaK732+sSxIHQnAwGBSZIuDfMCjR9Oy3oJBl2iAKUqrODZabt+C8jAl5DSEKSktSLVYtN5aODhWcruClJLhQFi4bTqIZkuH4mNGsxujn+fw4XS7ogG3WQx26s5XRKQCCr4iIhVQ8BURqYCCr8yYmWnMQGSG9OGR2ThsZg8DD2b/NgEPuvuMlw02s1uBXwN2u/uFWdmNwO8Ce7LNPu7u3z3hwcbH4KXcGm4DwbpsAAuCgbRgcM2PHAz2XRQfMxiMsb5gwO9YMOAWDczVjxAUlbyHKhzEK1iDLtm9/P4eziaL2l4w4BbOhivYNq9/QVweDdhFv6MlwUBrNAAIePS7K0nBV2bjWuBi4BLgj4HVgJvZDrJAnP3b5O5PlDzml4C/A76cK/+0u3+iGY0WaQcKvjJj7v414GvHX5vZEPVAvC77+uvAnwB9ZnbY3ZeUOOY9ZnZGSxos0kYUfKVp3H0vcFf2DwAz6wcuoH6HPBsfNrP/CmwAPlrUtWFm1wHXAawdCv58FGkTGnCTlnL3UXd/wN1vm8VhbgbOpn5HvRP45BT13eLu6919/cqlBX2xIm1Ad77S9tx91/HvzezzwHdK7gjDwzOvd3wsLYwGWKYz+yka9InSWRbN/ApTPUbblk8JGc1cKxxcKynaP659GuutlVUwOBYPVgZlUZrIgmNa0YzJEnTnK23PzFZPevluYEtVbRFpFt35Slsxs68ClwNDZrYd+AvgcjNbR/3m6Wngg5U1UKRJFHylrbj7NUHxF+e8ISItpm4HEZEK6M5XutfYGOzPzXBbWPAExMKRtOzIgaTIgzILB7yIB40Wpo86+7G0bitKUxmlZSycDZcctfwxS856m454EK4oTWVQ5iUHAYt+HuEMuWCGW38wC7IgbaYHv8+ydOcrIlIBBV8RkQoo+IqIVEDBV0SkAhpwk/mlaHCsYPZXqf2L9i07SayoTeG2QV1R2SxnqEUpIWc76616JWe4hedZfk29snTnKyJSAQVfEZEKKPiKiFRAwVdEpAIacJOu5eNj+P5czvWFcYpJGw7WazscrNd26OV0u8IBt2AwJlof7OihtKxoHbJo1lzZGW5Fg0PR7K1gvbWiIcnZDMQV7RvOfCtbTa0gxWc0sBnVH80uLEhxaUUzJkvQna+ISAUUfEVEKqDgKyJSAQVfaStmtsbMfmhmW83sYTP7SFa+3MzuMLPHs69aHVM6mgbcpN2MUV+d+H4zWwJsNLM7gN8C7nL3m8zsBuAG4GNTHmliAo4cScsC0WCSjRxJC4OBuWmt4TYWrAE3GgwCRuvHQTzwU7TeW14wiFa4v5VcF44p0kLm957GwFzZbcPBzoL0j7NLSVk0WDnzEKo7X2kr7r7T3e/Pvj8IbANOBa4Ejq+AfBtwVTUtFGkOBV9pW2Z2BvA64KfAKnffmb31ArCqYJ/rzGyDmW3YeyRIkC7SJhR8pS2Z2WLgG8D17t6wfITX/9YMHzt191vcfb27rx8anPmy3iKtpuArbcfM+qgH3q+4+zez4l3Hl5DPvu6uqn0izaABN2krVh9p+SKwzd0/Nemt24FrgZuyr98+4cHGxpjYu6+hqGewYObYSNBFcfCltOylF9OyosGxnmAdtJOCdeGCWXPRWm8A1NJjWjjgFwwQFQ1ERe0MUy1OY721QDQwN9s0leG6cNH5QPnUm9GAW9G5TycdaI6Cr7SbNwHvBx4ys01Z2cepB92vm9kHgGeA91bUPpGmUPCVtuLu91I8i/9X57ItIq2kPl8RkQoo+IqIVEDdDtK1fMIZP5KbUVYwwNMTDUaNBDPPooG5/jhNZTQ45seCGW7RrLexgmeUJ4LBpInxYMPoPAuSQkYz3Hqms65cyUGzOVsCrmi9tZKF0eBa0WBl0UBcCbrzFRGpgIKviEgFFHxFRCqgPl/pXg5M5Po5i5b8icrDsmn0hebrLto/Kov2hWncLpU8n6Jt50jREkyznXwxK3NUt+58RUQqoOArIlIBBV8RkQoo+IqIVEADbtK1Ro+M8uz92xvKFg3GS/4MDqYfhaWrV6cb7t2bli1bFjcgeDDfgokX7NuTFIWTMSDOQDYaTMgIs3XF2b5s6VBa2B9kfyvKFhYuuxNtF/zsCyYvxJnJyg2EWdGEiJK8L8oDXbSMUMHPpATd+YqIVEDBV0SkAgq+IiIVUPAVEamABtykrZjZGuDL1FcnduAWd/8bM7sR+F3g+OjUx939u1Mdyx1GRxozfvXW4vuN3t5gQGU0GPQqWwbxYFI0kBaVFR0zWDLIx4+l2wXZtqxwdl80wy6ayVc06FRy23B2X8ExwyV/4k2bL8p0VlT5zBul4CvtZgz4qLvfb2ZLgI1mdkf23qfd/RMVtk2kaRR8pa24+05gZ/b9QTPbBpxabatEmk99vtK2zOwM4HXAT7OiD5vZZjO71cxOLtjnOjPbYGYb9o9HScZF2oOCr7QlM1sMfAO43t0PADcDZwPrqN8ZfzLaz91vcff17r7+5IJJBSLtQN0O0nbMrI964P2Ku38TwN13TXr/88B3TngcoNbbeH9RiwbWgu3qhUHwjgbRioJ8uH/Jsmkc06L9w6VwCo4ZDSaVLau/Mcv9S7Zp7kbcUi1Ix6k7X2krVk/k+kVgm7t/alL55Lm+7wa2zHXbRJpJd77Sbt4EvB94yMw2ZWUfB64xs3XUbzWeBj5YTfNEmkPBV9qKu99L/PfllM/0inQadTuIiFRAd77StQ6OjXPv7gMNZSf1xoNOS4OZb295YFtSdnTH/qRsYMXi8JjWl9Y1EA3cRGkqh4/GxwwG3PzIoWDD4I+HYHYcgA8fTndfEjzJ19cft6l/Ycn6g/2L0lFG5dEgYlBPnBISWpKSsif+mZTadcZ7iojIjCn4iohUQMFXRKQCCr4iIhXQgJt0rZoZi3MDaQsKZlkNBIM5PQPpAFWtP/3I9CyIB7KI0lf2BdsGZRZtB/FAVDQQNo0Bt7C87Ew8KFiHLZrhVnK7om1LD4QVHTNKcznzGWr13TXDTUSkoyj4iohUQMFXRKQCCr4iIhXQgJt0rYPjE9zzcuNMsRUFM9xW9aflFzy+KynbvTudeXbygZHwmLVaOsAzNLQkKRt5Ppg1118wcyoanAsHzILBpYIZauEssWBdOeuPZ475wvScomPawkXpdj0FISha7y0csAsUDQyGA3HBgFkwa61oYM2mkyYzX82M9xQRkRlT8BURqYCCr4hIBRR8RUQqYLOZoSHSzsxsD/BM9nIICHI3Np3qaf+6Wl3P6e6+8kQbKfjKvGBmG9x9veppz3rmsq65PKepqNtBRKQCCr4iIhVQ8JX54hbV09b1zGVdc3lOhdTnKyJSAd35iohUQMFXRKQCCr7S1czsnWb2qJk9YWY3tLiup83sITPbZGYbmnjcW81st5ltmVS23MzuMLPHs6/BWu9NqedGM9uRndMmM3tXE+pZY2Y/NLOtZvawmX0kK2/qOU1RT9PPaUbtU5+vdCszqwGPAW8HtgP3Ade4+9YW1fc0sN7dm/oAv5m9BTgEfNndL8zK/hrY5+43Zf+pnOzuH2tBPTcCh9z9E7M5dq6e1cBqd7/fzJYAG4GrgN+iiec0RT3vpcnnNBO685VudinwhLs/5e6jwNeAKytu07S5+z3AvlzxlcBt2fe3UQ8qrain6dx9p7vfn31/ENgGnEqTz2mKetqCgq90s1OB5ya93k5rP3wOfN/MNprZdS2sB2CVu+/Mvn8BWNXCuj5sZpuzbolZd29MZmZnAK8DfkoLzylXD7TwnMpS8BVpnsvc/fXAFcCHsj/jW87rfYet6j+8GTgbWAfsBD7ZrAOb2WLgG8D17n5g8nvNPKegnpad03Qo+Eo32wGsmfT6tKysJdx9R/Z1N/At6t0erbIr69M83re5uxWVuPsudx939wng8zTpnMysj3pA/Iq7fzMrbvo5RfW06pymS8FXutl9wDlmdqaZ9QNXA7e3oiIzW5QN6mBmi4B3AFum3mtWbgeuzb6/Fvh2Kyo5Hgwz76YJ52T1tXe+CGxz909Nequp51RUTyvOaSb0tIN0tewxos8ANeBWd/8fLarnLOp3u1BfG/GfmlWXmX0VuJx6KsRdwF8A/wJ8HVhLPW3me919VoNlBfVcTv3PcweeBj44qV92pvVcBvwIeAg4vljbx6n3xzbtnKao5xqafE4zap+Cr4jI3FO3g4hIBRR8RUQqoOArIlIBBV8RkQoo+IqIVEDBV0SkAgq+IiIVUPAVEamAgq+ISAUUfEVEKqDgKyJSAQVfEZEKKPiKiFRAwVdEpAIKvk1kZn1m9gdm9jMze9nMjmbref1BlsxbpBJm9mkz88nLwk967yQz25e9/8dVtG8+6q26Ad0iW4TvTuprQ30W+PPsrSuAm6gvX/P1alonwkXAQeA1ZlZz9/FJ7/0JcPzmYPOct2yeUjL1JsiWK/kBcC7wVnd/JPf+euBFd/95Fe0TMbNdwB3AfwZe6+6PZ+WrgCepL+FzDfDqKlZ1mI/U7dAc11JfbuX38oEXwN03KPBKVbIAewrwHep3v+dOevtPgQepL9uzV4F37ij4NscfUl+kryWLGIrM0kXZ183AVuA8ADNbC3yQegC+mPpaZzJHFHxnycxOp35xf6XqtogUuAgYAR4DHiYLvsCNwD3ufne2jfp755CC7+wdv6s44fLTZnazme0wM3W0y1y6mPpfZmPUg++5ZnYu8H7gT83sJGANuTtfM/tQ9gTEWbnyq8zsRTPbZGZbzexBMzt/js6layj4zt6y7OuuEtt+FXh9C9siErmIVwLrw9T7fP8K+D/u/jPgwuy9X9z5mtlS4KPARurBe7J1wGfdfZ27nw/cR32wTqZBwXf2dmdfX32iDd39HncvE6RFmsLMeoDzeSX4bgFOAt4D/FlWdjEwQT0wH3cD8GXqT/FcRKN11IMy2V3zhcCPWtD8rqbgO3s/AQ4Avx29aWaXzW1zRBqcAywkC77ufvx587909+NdZRcBT7r7EQAzOw24GvhEtl9053uTmW0GXgC+4e7fb/WJdBtNspgldz9kZh8DbjazbwP/COyhPtniN4ClwJsqbKLMb8fvWn/Rn+vuvxlsM3mw7X8AN2XX9hbqT0MAv7jTXeLuZ2SvzwE2mNnn3P1AC9rftRR8m8Dd/5eZ7QT+CPhSVvwscA9wa1XtEqEeWPdnd7xFLgS+D2Bm64D3Apeb2ccBA15tZgvd/Sj1u96tx3d098ezAeRl1P8ClJI0w60CZubublW3QyTPzO4A/t7d/2VS2WPANe6+0cyuB85z9w9m770X+HN3vzA+ohRRn+8cMrMvmNn27PvtZvaFqtskcpyZXQEsmxx4M4/ySr/vOuDK7DGz+4D3Ab8+h83sGrrzFRGpgO58RUQq0FbB18zeaWaPmtkTZnZD1e2R9qLrQ7pJ23Q7mFmN+tzztwPbyWbNuPvWon2Ghlb4GWvXlq/EJ4Ky3Pn35P4/Gh/Lt7Tx5UTumGOjuffHyfPDh6Zu10Rjm3x4pPHt0cZjHhjJtxH6rLGdB8Ya6+jJncbzPr7X3VcmB2oTM7o+li72M1ataCycKLjeFyxMy4aPpGW14AGh6LoC6Am2HT+WlvUFefaPBnVD2E4/dDAps/7gmP0L4mPWamlZb7B/dO6QfgbqrUqLeoJ6in52+c9ZkekMW0e/+/znHYLPfMF2kMYPYOODD5X6LLXTo2aXAk+4+1MAZvY14EomPdaSd8batWy49+7CAyb/sYweTTfKfxgGFjW+PvhibofG37aPNH5IfPdzjZsffilt18afNBYMDze+PtrYztHHnm14fejZfQ2vf/DY3qSOVX19Da/vfOlww+vBWuN5/NnIS88kB2kv078+Vq3gp5/6742FoyPhtvaa/CQu8EfuTzdcHnymhoPrCmDpyWnZ/j1p2arT0rJHHoyP+ZoLkiL/tx8mZbY6OOZZ56ZlgC1dnpYtDyZsLiuIJyOH07IogC1cmpaNxb8PLAh2UVkUFItuKI8Np2X9g2lZ8Jkt/I8r+M+0Z+XppT5L7dTtcCowOXJtz8oamNl1ZrbBzDbs2ZsPjNLFpn99vHwo/7ZI22in4FuKu9/i7uvdff3KoRUn3kHmlYbrY9niqpsjUqiduh12UE9rd9xpWdnM5f/8CPpfk36gpP81v0+ukynfxzua+9Mm+pM0161wom6HsQONr48cbfyTbt9Y2m+2qNbY7hfHGl8fmei4/3enfX1M7NnL0c/9Q0PZ+KH4z9xFl69Lyg7duTEpG1ib/oc/9nLcPzuw+qSkbPiZ9K+1wfOSG3h23P1oeMxXv/HMpOz+bz+clJ2xZklStuKXz0rKAHzVqqSs96OfSrfLX+sZW1DuPzkPuiKsP+hrJ+gyrBdGWwYNiq/tqJ0+lnYb2JK0G6YV2ukTeB9wjpmdma30ezX1daVEQNeHdJm2ufN19zEz+zDwr0ANuNXd0//SZV7S9SHdpm2CL4C7fxf4btXtkPak60O6SVsF35lo6BvK9QlZ7jEUj/qXcn26lnu+0fP9RLnnZ6238ZGuRPAYDy/vb3w9ku/zbexDHBwYaHjd/3zj40pv3J/2Y64cajzXnlxfdX/uQd/P7O2+hFQ+4UwcbezTGxsJnrMFGEl/hsPDwfPTR9N+z3wdvygP9h8/ktYzcbRc3fVjpnUdDZ6zHR5JxzcmhuM+257RuDw9QNEzuSW1Yk5BdMxppayqbp5DO/X5iojMGwq+IiIVUPAVEalAZ/f5+kTjlOFc/22+j9eiuem5suT5whM9w9jX2B+b9AFHzwzm6vBjuT633DRIO2V1Y5V7Xmh4fX4t7eSqDTVObV364FONx+zLzbP/7s60nR2uZ/Egg2/OLT+Wf6Y6Y+vekJQNHQv6clemU2wHjhTkYViRPhO8ZO0LSZmtPT0pS5/mrautyy+nBm/YnfbXLzxndVJm5xWs7r4yfc7Xj6X90FYwxdZL5nY44fjI5G0t6LiNyqZx/xg9O5wf44H4eeQwLwVMkZvixHTnKyJSAQVfEZEKKPiKiFRAwVdEpAIdPuDmjfk080ly8klxipJBNxwz14GeS9KRHwhwch3x+QTateAh7oWNg3jWl0/OkxsEXLIs937jYEhtRZrAhZMay/pXNuZStf6CAYQucnjPAX5y852NZeNBciXgjReniWzueTAdhDxt4UBSdmA0nhDxqpPSAapn96eJll67Ok2C88On9yVlAJf96Mmk7LOPpTmC3/xvzyZl6097JDzmilPTPLtL3vU7SZkfKEjhumhZWhYkt/EoT+5AkE8XCpJgRYshBGXhwBzQl/4+/GiQdjQ6nygJPhQPxJWgO18RkQoo+IqIVKCtuh3M7GngIDAOjLn7+mpbJO1E14d0k7YKvpm3unu6KFmkp6dxzbVc/0+SJCdM0JwxTSF5AAASU0lEQVTbJ9eHk3/YPDlCPsH0cON6Vp5Prg74c481FpwgAbs/9/PG93fvbnj58o+3JXUseFVjv9Uzmxsf7u/t7dg/ekpfH4tfvZxf+dj7Gso8n8g+YxencfyKTT9Ltxs6Jd35SMFyRcF6b2fvej495pp0SsV/2bQhPKRdkE6y+MQP7wqOma7hZuem678BYTt9OD0nWxqvHBMlJGciSFK+KB2b8KhvF6BWbkJGOBmjQJjMfXHQpmitx2hBUYj7pkvq2E+giEgna7fg68D3zWyjmV0XbaAFNOe16V0fhwpWFRZpA+0WfC9z99cDVwAfMrO35DfQAprz2vSuj8Xx+mAi7aCt+nzdfUf2dbeZfQu4FLincIfxMTg46e43n1gnnxQnSpKTex4x38drfelznQ1y73vuWUKbCPqZzs31L+bbne9DW3NO4+uDjXf8y4IELnZyY9lrz8s9x9qb+9X/Vfr8aLuZ7vXhR44y/sCDDWUTR+LE4b19aR/j6M82J2X9p6Y/64lDcWKdnpXBYps7didlvQfSxDhH/l+8QtJg8Kzr9nufSspWnp0+U7tgLH4e2U4J+rEv/Y9JUVH/bJQwJxpfiRLw5MdYpitMllPQDxwl1gqTAgXPAxf2LXfDc75mtsjMlhz/HngHsKXaVkm70PUh3aad7nxXAd/K/ofpBf7J3b9XbZOkjej6kK7SNsHX3Z8CLqm6HdKedH1It2mb4DszRuNqebl+mRLPAKa5GuZAvp/qhK9z/VL5/ARRv9WJtinIcdBVeoyewVz/XcEijrYgHZyrDQbPdi5I+wN7CvpSGUjHC2oLg+dX+9N6ehYVPFca1L9gQdrvWBsMxiqC9tTrj5KkRz+naa1MGew+y/3DQ7agTeGinHE94dyBktqmz1dEZD5R8BURqYCCr4hIBTq7z3diAh+Z9IxlLs9C8vxh8Mxuko83n6vhRM/55uWf+4v6ivI5THPPT1pfrj922VDDS6811mGvOjWtY1njApocPti4T/453y40emCY5+5szHtx5Gicl/U142m/+bYfpM8+r35VmuP30KH4mCtOeS4pe+H5NGfCqa9JZ2pu3JjmgAB4/eH0OeW7nkhTXZyzI63n/JcOJ2UAA2vS55Fr70v7kf3owaQMgufpiftiGz6rx8uKPl8l8rAA8XhHT8E9ZZQvIsjjYEGO4XiRULCiukrQna+ISAUUfEVEKqDgKyJSgc7u+BsbxXdP6lcLcudOFs1BT9Zcy+fjDeZ5N+6f639N+oCCtaz6c8+U5vuy8jmG8+vILWjsk5pYm+YGIJenNOmBq3X/Gm5m0FNrPPOenqJ5/+nvKShKjjfdY0bbhnUX5hJIy3uDbcP9oxMqqD/esBXP+RYds+Rzxi14dniu6M5XRKQCCr4iIhWYMvha/u/dJjCzW81st5ltmVS23MzuMLPHs68nT3UMaQ+6PkRm7kR9vi+a2ZvcfauZfQDYDGxx99ksEfAl4O+AL08quwG4y91vMrMbstcfO+GRJsbh8KS8pbm1z1i6vPH1ktxrgFpj31J+zbUoH2/jBvk+pxLxKJ9XNOnzzfV39ebakN8+WIfKBpc27rI0F69mmUc109bXR/+553H6vXeXqjTKVXtRyZ9RugJasWVBWZQf4M3TyCXwm1FO2+D508I8BMG5b7v4dUnZOb9/Zbj70e/dm5SNvpQ+07vs134lKRvb+kR4zNqyNNeGLQyS4w+mz+QyMpKWAcNbn0nKFlyWnucLX7s7KVtx7qrwmCM707zJZZ0o+P4hcHw05zPAIDBhZk9R/6A9lH3dnGWdOiF3v8fMzsgVXwlcnn1/G3A3ZYKvVE3Xh8gMTRl83f0fJr1cCpwFXARcnH19H/DnQI+ZHXL3pelRSlnl7senDr1APXertDldHyIzV/pRM6//zfJk9u9fjpeb2QLgwuzfrLm7m1lhnrZs4cTrANaeojXc2kVbXh9r1jSjSpGWmPWAibsPu/sGd//SLA6zy8xWA2Rf04WuXqnvlQUST5rpjZTMlUqvDy2wKm2sXSZZ3A5cC9yUff12mZ388CF8409eKTiaG+d5eX9uh+CGaWFjUhB/7rGG18lil/lj5JJwJBMogkX7ooX8puL57XN19Kw+K90pN6HEBnPJT5r/oEIrzej6mJ7OeFg/TFhTMqF3UeJxD8oXDATXbX+cBKe2KC3vjRIYRYnoo+TygEWJ36OyIBF90cSLnqCd0f4DQXL6onaGyfFLmvNPoJl9FfgJ8Etmtj0bJb8JeLuZPQ68LXst85CuD5kv5vzO192vKXjrV+e0IdKWdH3IfNFRf3uKiHSLdunznRmfgOFJkyKGc4l1Rhpf+7E0EbX15cryyXnyD6Dn+9eS96dOkjMz+YVBe6Z+HZUlSd7nx/+7SRLsokQsx9KkTEn/ff2Awc4Fx4y2jSZujAf9o73xApo+lm4bJowK902v/3r96USiB3a+nJStefSRcPdnNqWJ3/cfTOt6w1np/nsfSBPOAyxaGiw+ujgqS/uRfThObr99WzpOe+bS9Hf84JP7k7LXHo0nW+3ZM/P5RPPjEygi0mYUfEVEKqDgKyJSgc7u853wxmd788/5Hs0l9wj69RjNJ1NvPEbSx5br800WuzxRkpyZyPdT5l9H/Yj5xCrzsc/XJ9IFUYsWPBwJ+u6iBRej/tmiBDxl+3KDRQC86JhR33T03HiQLKdwsYGgL/j7+9PEOG97OO6fffjFdGHO7SNpH+nZD+1IyrZtDxYCAJYFyf4HB9PzHAyesx0ZDc4d2Ppiuqjo0JbtSdmPD6TXwkTBx3j7aNy/XMY8+ASKiLQfBV8RkQoo+IqIVKCj+3x9eITRx579xeuxXF/NYG4uuJ2yOj3Gksb01v7czxs3WHNObodcn+6yocY68n2p+UToRH10U/fpJnPyc/t7f7DIZ5KwPddp1cELD5ZmPVj0swn44JJ09+D52ah/tTBnQtBnHCY5D/p3raDP1wcWlas/aKcvSPcFYDx9fvb9p6Rp3wfffEm4+5tfSvtIXz6Q9iOveGua2O7STU+Gx+xdliZJD5/zXZT+fidG4n7YFQ+l/bvL/v1FSdlVO9I+7DPPCRZiAPbtTvuR2bI33DZPd74iIhVQ8BURqUAVWc2iBRJvNLMdZrYp+/euuW6XtAddHzJfVNHn+yXSBRIBPu3un5jOgSZGxzn07L5fvD6Sm3/d//yehtd9e15IDzKaW2xvd27+98EXG1+PNz5D6LnnEW1Brq8qmt+fzxmQ5GqYuo83Eb2f7zMsyBXQhr5Ek66PaSm5WGZR/264bdEzxemGpY8Z9dUn+SuK6i6qJzj35UuC62VZtPwnDJ6yOCnr7U37TaP9+1fGCyLMZgHNnoIFNBcOBYtdnpQuPrtiedqP3LcyHRMAOGksfqa4jDm/83X3e4B9J9xQ5iVdHzJftFOf74fNbHP2Z+fJRRuZ2XVmtsHMNrw4doJl3aWbTPv62LP3xaLNRCrXLsH3ZuBsYB2wE/hk0YaT1+ha0dvRT8pJeTO6PrSGm7Sztohe7r7r+Pdm9nngO2X2OzAyxg8ee+WZun1jjX1fb9zf2Pdzfi3tL6utaOzzefnH2xpeL1uR+wDn+tfsVac2vr02N1d9cdqnlKy5doLcu8lzvLk+3lJrwvXF6291gpleHwXHCsuj52rL9qUWHrPkemvhdlFuhqJ2BrkZnHLPGAPhmMGac1em+59+drj7wvPSnA8DLx9M9z8j3b93vKDPdFHwPHOwBhwDQT9wkLcbIHri205P1z8cuuDRpKz3NWvDY/atCJ7pvWdzuG1eW9z5Hl+ZNvNuYEvRtjL/6PqQbjTnd77ZAomXA0Nmth34C+ByM1sHOPA08MG5bpe0B10fMl+0ywKaX5zrdkh70vUh80VbdDuIiMw3bTHgNlN9Zqzqe2VgYVGtsfN+5VBjZ3xtKHhCKfeQ9YJXNT4IbifnBtzyAwTLcsfMDbDZYPAQeT5hSzLglnudHxApOSFgstILSYpQMIgYDEBmG8+8bDrHLNq2rJILG4TnXrBv0WBrGbrzFRGpgIKviEgFFHxFRCrQ0X2+B8YmuPOlVxJ4vJhLctGTS1K+9MGnkmPkE3s8s7kx+c5rz8s9cJ3vdzrc+DB5vifVl6b9zDaYS0SS78PNv873K+WT5AQTKPJ9vKWTvHS5wsTnwUQFC5IRlZ0kAdOYpBFMqChMph4ds+QEmqKJG4yn0/QfuO/5pOxX/t394e57/+/WpCxKpn72Sen4x5EHf56UAfQGiXVqi4Jk6ovLJ1N/aXOaTH158Lt79EdPJ2VnPh8k5QH27UkXGi1Ln0gRkQoo+IqIVEDBV0SkAh3d59tjMDgpWc6Ricb/S/p7cgtR9gULFfY3lvX25hfAzP2Ics/5Wv792gn6byFInn6i1zN4JlfP8UpZwbXSG10++Wv7eHH+MwPUeoIDBFkILUh2BWC9QV214F4xaJPV4r7t5LNdsH9v0KYodgDUwh9UObrzFRGpgIKviEgFFHxFRCpgs5mbXDUz2wM8AwwBQVbjWWn2Mdu9jae7e5pBu4NNuj6gNT//iOpp/7paXU+pz1JHB9/jzGyDu69v52N2Qhu72Vz9rFRP+9fVLp8bdTuIiFRAwVdEpALdEnxv6YBjdkIbu9lc/axUT/vX1Rafm67o8xUR6TTdcucrItJRFHxFRCrQ8cHXzN5pZo+a2RNmdkMTjve0mT1kZpvMbMMMj3Grme02sy2Typab2R1m9nj2NVhQbtrHvNHMdmRt3WRm75pJe7tZs6+PE9Q162un4LhNv56mUU/TrzEzW2NmPzSzrWb2sJl9JCtv6jlNUU97fG7cvWP/ATXgSeAsoB94EDh/lsd8Ghia5THeArwe2DKp7K+BG7LvbwD+ZxOOeSPwR1X/Htr1Xyuuj1ZfO3N1PU2jnqZfY8Bq4PXZ90uAx4Dzm31OU9TTFp+bTr/zvRR4wt2fcvdR4GvAlRW3CXe/B9iXK74SuC37/jbgqiYcU6bWltfHdLXieppGPU3n7jvd/f7s+4PANuBUmnxOU9TTFjo9+J4KPDfp9XZm/8N14PtmttHMrpvlsSZb5e47s+9fAFY16bgfNrPN2Z+Ms/7Ts8u04vqYSquunUirrqdIy64xMzsDeB3wU1p4Trl6oA0+N50efFvhMnd/PXAF8CEze0uzK/D630HNeMbvZuBsYB2wE/hkE44pM9fyayfSxOsp0rJrzMwWA98Arnf3A5Pfa+Y5BfW0xeem04PvDmDNpNenZWUz5u47sq+7gW9R/9O1GXaZ2WqA7Ovu2R7Q3Xe5+7i7TwCfp3lt7RZNvz6m0sJrJ9L06ynSqmvMzPqoB8SvuPs3s+Kmn1NUT7t8bjo9+N4HnGNmZ5pZP3A1cPtMD2Zmi8xsyfHvgXcAW6beq7TbgWuz768Fvj3bAx6/UDPvpnlt7RZNvT6m0uJrJ9L06ynSimvM6ss9fxHY5u6fmvRWU8+pqJ62+dxUPeI323/Au6iPYj4J/Oksj3UW9RHxB4GHZ3o84KvU/5w5Rr2f8QPACuAu4HHgTmB5E475j8BDwGbqF+7qqn8f7favmdfHXFw7c3U9VXmNAZdR71LYDGzK/r2r2ec0RT1t8bnR9GIRkQp0ereDiEhHUvAVEamAgq+ISAUUfEVEKqDgKyJSAQVfEZEKKPi2iJldbWYj2QwbEZEGCr6tcwmw1d2PVd0Qkekys/dkNw+Lqm5Lt1LwbZ1LgAeqboTIDP0U+GV3P1x1Q7qVgm/rrKM+nREAM/sPZvaimX3GzGoVtkvkhNx9h7tvOvGWMlMKvi1gZiupZ9HflL3+feA71LP0X+/u41W2T+REzGyPmV1fdTu6WW/VDehSl1BP6LHVzD4PvAd4l7vfXWmrREows1cDQ0z6y02aT8G3NdZRX47lm8BK6n1nT1TbJJHSLsm+PlhpK7qcgm9rXAIY8GbgbQq80mEuAZ5z9/1VN6SbKfi2xiXA3wKvAf7BzN7g7nsqbpNIWReju96W04Bbk5nZAHAu9UTN1wF7gf9tZvqPTjrFJSj4tpyCb/OdD/QBD7n7UerLlFwAfLrSVomUkN08/BIKvi2n4Nt8lwCHqS9bg7s/A/wm8N/M7LcqbJdIGRcANRR8W07LCInIL5jZbwN/Byzx+uq+0iK68xWRyd4E/EyBt/UUfEUEMzvVzK4GrqY+G1NaTN0OIoKZfQ74T8DXgevdfbTiJnU9BV8RkQqo20FEpAIKviIiFVDwFRGpgIKviEgFFHxFRCqg4CsiUgEFXxGRCvx/XTXmOvJULLsAAAAASUVORK5CYII=\n", + "text/plain": [ + "<Figure size 360x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%%\n", + "cmap = 'Reds'\n", + "pl.close(10)\n", + "pl.figure(10, (5, 5))\n", + "fs = 15\n", + "l_x = [0, 5, 10, 15]\n", + "l_y = [0, 5, 10, 15, 20, 25]\n", + "gs = pl.GridSpec(5, 5)\n", + "\n", + "ax1 = pl.subplot(gs[3:, :2])\n", + "\n", + "pl.imshow(C1, cmap=cmap, interpolation='nearest')\n", + "pl.title(\"$C_1$\", fontsize=fs)\n", + "pl.xlabel(\"$k$\", fontsize=fs)\n", + "pl.ylabel(\"$i$\", fontsize=fs)\n", + "pl.xticks(l_x)\n", + "pl.yticks(l_x)\n", + "\n", + "ax2 = pl.subplot(gs[:3, 2:])\n", + "\n", + "pl.imshow(C2, cmap=cmap, interpolation='nearest')\n", + "pl.title(\"$C_2$\", fontsize=fs)\n", + "pl.ylabel(\"$l$\", fontsize=fs)\n", + "#pl.ylabel(\"$l$\",fontsize=fs)\n", + "pl.xticks(())\n", + "pl.yticks(l_y)\n", + "ax2.set_aspect('auto')\n", + "\n", + "ax3 = pl.subplot(gs[3:, 2:], sharex=ax2, sharey=ax1)\n", + "pl.imshow(M, cmap=cmap, interpolation='nearest')\n", + "pl.yticks(l_x)\n", + "pl.xticks(l_y)\n", + "pl.ylabel(\"$i$\", fontsize=fs)\n", + "pl.title(\"$M_{AB}$\", fontsize=fs)\n", + "pl.xlabel(\"$j$\", fontsize=fs)\n", + "pl.tight_layout()\n", + "ax3.set_aspect('auto')\n", + "pl.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Compute FGW/GW\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "It. |Loss |Relative loss|Absolute loss\n", + "------------------------------------------------\n", + " 0|4.734462e+01|0.000000e+00|0.000000e+00\n", + " 1|2.508258e+01|8.875498e-01|2.226204e+01\n", + " 2|2.189329e+01|1.456747e-01|3.189297e+00\n", + " 3|2.189329e+01|0.000000e+00|0.000000e+00\n", + "Elapsed time : 0.005539894104003906 s\n", + "It. |Loss |Relative loss|Absolute loss\n", + "------------------------------------------------\n", + " 0|4.683978e+04|0.000000e+00|0.000000e+00\n", + " 1|3.860061e+04|2.134468e-01|8.239175e+03\n", + " 2|2.182948e+04|7.682787e-01|1.677113e+04\n", + " 3|2.182948e+04|0.000000e+00|0.000000e+00\n" + ] + } + ], + "source": [ + "#%% Computing FGW and GW\n", + "alpha = 1e-3\n", + "\n", + "ot.tic()\n", + "Gwg, logw = fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=alpha, verbose=True, log=True)\n", + "ot.toc()\n", + "\n", + "#%reload_ext WGW\n", + "Gg, log = gromov_wasserstein(C1, C2, p, q, loss_fun='square_loss', verbose=True, log=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Visualize transport matrices\n", + "---------\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "<Figure size 936x360 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#%% visu OT matrix\n", + "cmap = 'Blues'\n", + "fs = 15\n", + "pl.figure(2, (13, 5))\n", + "pl.clf()\n", + "pl.subplot(1, 3, 1)\n", + "pl.imshow(Got, cmap=cmap, interpolation='nearest')\n", + "#pl.xlabel(\"$y$\",fontsize=fs)\n", + "pl.ylabel(\"$i$\", fontsize=fs)\n", + "pl.xticks(())\n", + "\n", + "pl.title('Wasserstein ($M$ only)')\n", + "\n", + "pl.subplot(1, 3, 2)\n", + "pl.imshow(Gg, cmap=cmap, interpolation='nearest')\n", + "pl.title('Gromov ($C_1,C_2$ only)')\n", + "pl.xticks(())\n", + "pl.subplot(1, 3, 3)\n", + "pl.imshow(Gwg, cmap=cmap, interpolation='nearest')\n", + "pl.title('FGW ($M+C_1,C_2$)')\n", + "\n", + "pl.xlabel(\"$j$\", fontsize=fs)\n", + "pl.ylabel(\"$i$\", fontsize=fs)\n", + "\n", + "pl.tight_layout()\n", + "pl.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.8" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/ot/__init__.py b/ot/__init__.py index 1b3c2fb..35ae6fc 100644 --- a/ot/__init__.py +++ b/ot/__init__.py @@ -1,6 +1,46 @@ -"""Python Optimal Transport toolbox +""" + +This is the main module of the POT toolbox. It provides easy access to +a number of sub-modules and functions described below. + +.. note:: + + + Here is a list of the submodules and short description of what they contain. + + - :any:`ot.lp` contains OT solvers for the exact (Linear Program) OT problems. + - :any:`ot.bregman` contains OT solvers for the entropic OT problems using + Bregman projections. + - :any:`ot.lp` contains OT solvers for the exact (Linear Program) OT problems. + - :any:`ot.smooth` contains OT solvers for the regularized (l2 and kl) smooth OT + problems. + - :any:`ot.gromov` contains solvers for Gromov-Wasserstein and Fused Gromov + Wasserstein problems. + - :any:`ot.optim` contains generic solvers OT based optimization problems + - :any:`ot.da` contains classes and function related to Monge mapping + estimation and Domain Adaptation (DA). + - :any:`ot.gpu` contains GPU (cupy) implementation of some OT solvers + - :any:`ot.dr` contains Dimension Reduction (DR) methods such as Wasserstein + Discriminant Analysis. + - :any:`ot.utils` contains utility functions such as distance computation and + timing. + - :any:`ot.datasets` contains toy dataset generation functions. + - :any:`ot.plot` contains visualization functions + - :any:`ot.stochastic` contains stochastic solvers for regularized OT. + - :any:`ot.unbalanced` contains solvers for regularized unbalanced OT. + +.. warning:: + The list of automatically imported sub-modules is as follows: + :py:mod:`ot.lp`, :py:mod:`ot.bregman`, :py:mod:`ot.optim` + :py:mod:`ot.utils`, :py:mod:`ot.datasets`, + :py:mod:`ot.gromov`, :py:mod:`ot.smooth` + :py:mod:`ot.stochastic` + The following sub-modules are not imported due to additional dependencies: + - :any:`ot.dr` : depends on :code:`pymanopt` and :code:`autograd`. + - :any:`ot.gpu` : depends on :code:`cupy` and a CUDA GPU. + - :any:`ot.plot` : depends on :code:`matplotlib` """ @@ -41,15 +41,15 @@ def sinkhorn_lpl1_mm(a, labels_a, b, M, reg, eta=0.1, numItermax=10, where : - M is the (ns,nt) metric cost matrix - - :math:`\Omega_e` is the entropic regularization term - :math:`\Omega_e(\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})` - - :math:`\Omega_g` is the group lasso regulaization term + - :math:`\Omega_e` is the entropic regularization term :math:`\Omega_e + (\gamma)=\sum_{i,j} \gamma_{i,j}\log(\gamma_{i,j})` + - :math:`\Omega_g` is the group lasso regularization term :math:`\Omega_g(\gamma)=\sum_{i,c} \|\gamma_{i,\mathcal{I}_c}\|^{1/2}_1` where :math:`\mathcal{I}_c` are the index of samples from class c in the source domain. - a and b are source and target weights (sum to 1) - The algorithm used for solving the problem is the generalised conditional + The algorithm used for solving the problem is the generalized conditional gradient as proposed in [5]_ [7]_ @@ -1,6 +1,12 @@ # -*- coding: utf-8 -*- """ Dimension reduction with optimal transport + + +.. warning:: + Note that by default the module is not import in :mod:`ot`. In order to + use it you need to explicitely import :mod:`ot.dr` + """ # Author: Remi Flamary <remi.flamary@unice.fr> diff --git a/ot/gpu/__init__.py b/ot/gpu/__init__.py index deda6b1..1ab95bb 100644 --- a/ot/gpu/__init__.py +++ b/ot/gpu/__init__.py @@ -5,11 +5,15 @@ This module provides GPU implementation for several OT solvers and utility functions. The GPU backend in handled by `cupy <https://cupy.chainer.org/>`_. +.. warning:: + Note that by default the module is not import in :mod:`ot`. In order to + use it you need to explicitely import :mod:`ot.gpu` . + By default, the functions in this module accept and return numpy arrays in order to proide drop-in replacement for the other POT function but the transfer between CPU en GPU comes with a significant overhead. -In order to get the best erformances, we recommend to give only cupy +In order to get the best performances, we recommend to give only cupy arrays to the functions and desactivate the conversion to numpy of the result of the function with parameter ``to_numpy=False``. diff --git a/ot/gromov.py b/ot/gromov.py index ca96b31..3a7e24c 100644 --- a/ot/gromov.py +++ b/ot/gromov.py @@ -72,8 +72,8 @@ def init_matrix(C1, C2, p, q, loss_fun='square_loss'): References
----------
.. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,
- "Gromov-Wasserstein averaging of kernel and distance matrices."
- International Conference on Machine Learning (ICML). 2016.
+ "Gromov-Wasserstein averaging of kernel and distance matrices."
+ International Conference on Machine Learning (ICML). 2016.
"""
@@ -137,8 +137,8 @@ def tensor_product(constC, hC1, hC2, T): References
----------
.. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,
- "Gromov-Wasserstein averaging of kernel and distance matrices."
- International Conference on Machine Learning (ICML). 2016.
+ "Gromov-Wasserstein averaging of kernel and distance matrices."
+ International Conference on Machine Learning (ICML). 2016.
"""
A = -np.dot(hC1, T).dot(hC2.T)
@@ -172,8 +172,8 @@ def gwloss(constC, hC1, hC2, T): References
----------
.. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,
- "Gromov-Wasserstein averaging of kernel and distance matrices."
- International Conference on Machine Learning (ICML). 2016.
+ "Gromov-Wasserstein averaging of kernel and distance matrices."
+ International Conference on Machine Learning (ICML). 2016.
"""
@@ -207,8 +207,8 @@ def gwggrad(constC, hC1, hC2, T): References
----------
.. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,
- "Gromov-Wasserstein averaging of kernel and distance matrices."
- International Conference on Machine Learning (ICML). 2016.
+ "Gromov-Wasserstein averaging of kernel and distance matrices."
+ International Conference on Machine Learning (ICML). 2016.
"""
return 2 * tensor_product(constC, hC1, hC2,
@@ -277,15 +277,15 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs The function solves the following optimization problem:
.. math::
- \GW_Dist = \min_T \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}
+ GW = \min_T \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}
Where :
- C1 : Metric cost matrix in the source space
- C2 : Metric cost matrix in the target space
- p : distribution in the source space
- q : distribution in the target space
- L : loss function to account for the misfit between the similarity matrices
- H : entropy
+ - C1 : Metric cost matrix in the source space
+ - C2 : Metric cost matrix in the target space
+ - p : distribution in the source space
+ - q : distribution in the target space
+ - L : loss function to account for the misfit between the similarity matrices
+ - H : entropy
Parameters
----------
@@ -312,7 +312,7 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs If True the steps of the line-search is found via an armijo research. Else closed form is used.
If there is convergence issues use False.
**kwargs : dict
- parameters can be directly pased to the ot.optim.cg solver
+ parameters can be directly passed to the ot.optim.cg solver
Returns
-------
@@ -355,25 +355,31 @@ def gromov_wasserstein(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwargs def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5, armijo=False, log=False, **kwargs):
"""
Computes the FGW transport between two graphs see [24]
+
.. math::
- \gamma = arg\min_\gamma (1-\alpha)*<\gamma,M>_F + alpha* \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}
+ \gamma = arg\min_\gamma (1-\\alpha)*<\gamma,M>_F + \\alpha* \sum_{i,j,k,l}
+ L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}
+
s.t. \gamma 1 = p
\gamma^T 1= q
\gamma\geq 0
+
where :
- M is the (ns,nt) metric cost matrix
- :math:`f` is the regularization term ( and df is its gradient)
- a and b are source and target weights (sum to 1)
- L is a loss function to account for the misfit between the similarity matrices
- The algorithm used for solving the problem is conditional gradient as discussed in [1]_
+
+ The algorithm used for solving the problem is conditional gradient as discussed in [24]_
+
Parameters
----------
M : ndarray, shape (ns, nt)
Metric cost matrix between features across domains
C1 : ndarray, shape (ns, ns)
- Metric cost matrix respresentative of the structure in the source space
+ Metric cost matrix representative of the structure in the source space
C2 : ndarray, shape (nt, nt)
- Metric cost matrix espresentative of the structure in the target space
+ Metric cost matrix representative of the structure in the target space
p : ndarray, shape (ns,)
distribution in the source space
q : ndarray, shape (nt,)
@@ -392,19 +398,23 @@ def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5, If True the steps of the line-search is found via an armijo research. Else closed form is used.
If there is convergence issues use False.
**kwargs : dict
- parameters can be directly pased to the ot.optim.cg solver
+ parameters can be directly passed to the ot.optim.cg solver
+
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
+
+
References
----------
.. [24] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain
- and Courty Nicolas
- "Optimal Transport for structured data with application on graphs"
- International Conference on Machine Learning (ICML). 2019.
+ and Courty Nicolas "Optimal Transport for structured data with
+ application on graphs", International Conference on Machine Learning
+ (ICML). 2019.
+
"""
constC, hC1, hC2 = init_matrix(C1, C2, p, q, loss_fun)
@@ -428,17 +438,23 @@ def fused_gromov_wasserstein(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5, def fused_gromov_wasserstein2(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5, armijo=False, log=False, **kwargs):
"""
Computes the FGW distance between two graphs see [24]
+
.. math::
- \gamma = arg\min_\gamma (1-\alpha)*<\gamma,M>_F + alpha* \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}
+ \min_\gamma (1-\\alpha)*<\gamma,M>_F + \\alpha* \sum_{i,j,k,l}
+ L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}
+
+
s.t. \gamma 1 = p
\gamma^T 1= q
\gamma\geq 0
+
where :
- M is the (ns,nt) metric cost matrix
- :math:`f` is the regularization term ( and df is its gradient)
- a and b are source and target weights (sum to 1)
- L is a loss function to account for the misfit between the similarity matrices
The algorithm used for solving the problem is conditional gradient as discussed in [1]_
+
Parameters
----------
M : ndarray, shape (ns, nt)
@@ -466,16 +482,18 @@ def fused_gromov_wasserstein2(M, C1, C2, p, q, loss_fun='square_loss', alpha=0.5 If there is convergence issues use False.
**kwargs : dict
parameters can be directly pased to the ot.optim.cg solver
+
Returns
-------
gamma : (ns x nt) ndarray
Optimal transportation matrix for the given parameters
log : dict
log dictionary return only if log==True in parameters
+
References
----------
.. [24] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain
- and Courty Nicolas
+ and Courty Nicolas
"Optimal Transport for structured data with application on graphs"
International Conference on Machine Learning (ICML). 2019.
"""
@@ -506,22 +524,22 @@ def gromov_wasserstein2(C1, C2, p, q, loss_fun, log=False, armijo=False, **kwarg The function solves the following optimization problem:
.. math::
- \GW_Dist = \min_T \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}
+ GW = \min_T \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}
Where :
- C1 : Metric cost matrix in the source space
- C2 : Metric cost matrix in the target space
- p : distribution in the source space
- q : distribution in the target space
- L : loss function to account for the misfit between the similarity matrices
- H : entropy
+ - C1 : Metric cost matrix in the source space
+ - C2 : Metric cost matrix in the target space
+ - p : distribution in the source space
+ - q : distribution in the target space
+ - L : loss function to account for the misfit between the similarity matrices
+ - H : entropy
Parameters
----------
C1 : ndarray, shape (ns, ns)
Metric cost matrix in the source space
C2 : ndarray, shape (nt, nt)
- Metric costfr matrix in the target space
+ Metric cost matrix in the target space
p : ndarray, shape (ns,)
distribution in the source space
q : ndarray, shape (nt,)
@@ -587,21 +605,21 @@ def entropic_gromov_wasserstein(C1, C2, p, q, loss_fun, epsilon, The function solves the following optimization problem:
.. math::
- \GW = arg\min_T \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}-\epsilon(H(T))
+ GW = arg\min_T \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}-\epsilon(H(T))
- s.t. \GW 1 = p
+ s.t. T 1 = p
- \GW^T 1= q
+ T^T 1= q
- \GW\geq 0
+ T\geq 0
Where :
- C1 : Metric cost matrix in the source space
- C2 : Metric cost matrix in the target space
- p : distribution in the source space
- q : distribution in the target space
- L : loss function to account for the misfit between the similarity matrices
- H : entropy
+ - C1 : Metric cost matrix in the source space
+ - C2 : Metric cost matrix in the target space
+ - p : distribution in the source space
+ - q : distribution in the target space
+ - L : loss function to account for the misfit between the similarity matrices
+ - H : entropy
Parameters
----------
@@ -629,14 +647,13 @@ def entropic_gromov_wasserstein(C1, C2, p, q, loss_fun, epsilon, Returns
-------
T : ndarray, shape (ns, nt)
- coupling between the two spaces that minimizes :
- \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}-\epsilon(H(T))
+ Optimal coupling between the two spaces
References
----------
.. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,
- "Gromov-Wasserstein averaging of kernel and distance matrices."
- International Conference on Machine Learning (ICML). 2016.
+ "Gromov-Wasserstein averaging of kernel and distance matrices."
+ International Conference on Machine Learning (ICML). 2016.
"""
@@ -695,15 +712,15 @@ def entropic_gromov_wasserstein2(C1, C2, p, q, loss_fun, epsilon, The function solves the following optimization problem:
.. math::
- \GW_Dist = \min_T \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}-\epsilon(H(T))
+ GW = \min_T \sum_{i,j,k,l} L(C1_{i,k},C2_{j,l})*T_{i,j}*T_{k,l}-\epsilon(H(T))
Where :
- C1 : Metric cost matrix in the source space
- C2 : Metric cost matrix in the target space
- p : distribution in the source space
- q : distribution in the target space
- L : loss function to account for the misfit between the similarity matrices
- H : entropy
+ - C1 : Metric cost matrix in the source space
+ - C2 : Metric cost matrix in the target space
+ - p : distribution in the source space
+ - q : distribution in the target space
+ - L : loss function to account for the misfit between the similarity matrices
+ - H : entropy
Parameters
----------
@@ -736,8 +753,8 @@ def entropic_gromov_wasserstein2(C1, C2, p, q, loss_fun, epsilon, References
----------
.. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,
- "Gromov-Wasserstein averaging of kernel and distance matrices."
- International Conference on Machine Learning (ICML). 2016.
+ "Gromov-Wasserstein averaging of kernel and distance matrices."
+ International Conference on Machine Learning (ICML). 2016.
"""
@@ -762,13 +779,13 @@ def entropic_gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, epsilon, The function solves the following optimization problem:
.. math::
- C = argmin_C\in R^{NxN} \sum_s \lambda_s GW(C,Cs,p,ps)
+ C = argmin_{C\in R^{NxN}} \sum_s \lambda_s GW(C,C_s,p,p_s)
Where :
- Cs : metric cost matrix
- ps : distribution
+ - :math:`C_s` : metric cost matrix
+ - :math:`p_s` : distribution
Parameters
----------
@@ -806,8 +823,8 @@ def entropic_gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, epsilon, References
----------
.. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,
- "Gromov-Wasserstein averaging of kernel and distance matrices."
- International Conference on Machine Learning (ICML). 2016.
+ "Gromov-Wasserstein averaging of kernel and distance matrices."
+ International Conference on Machine Learning (ICML). 2016.
"""
@@ -876,8 +893,8 @@ def gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, Where :
- Cs : metric cost matrix
- ps : distribution
+ - Cs : metric cost matrix
+ - ps : distribution
Parameters
----------
@@ -913,8 +930,8 @@ def gromov_barycenters(N, Cs, ps, p, lambdas, loss_fun, References
----------
.. [12] Peyré, Gabriel, Marco Cuturi, and Justin Solomon,
- "Gromov-Wasserstein averaging of kernel and distance matrices."
- International Conference on Machine Learning (ICML). 2016.
+ "Gromov-Wasserstein averaging of kernel and distance matrices."
+ International Conference on Machine Learning (ICML). 2016.
"""
@@ -972,6 +989,8 @@ def fgw_barycenters(N, Ys, Cs, ps, lambdas, alpha, fixed_structure=False, fixed_ verbose=False, log=False, init_C=None, init_X=None):
"""
Compute the fgw barycenter as presented eq (5) in [24].
+
+ Parameters
----------
N : integer
Desired number of samples of the target barycenter
@@ -993,8 +1012,9 @@ def fgw_barycenters(N, Ys, Cs, ps, lambdas, alpha, fixed_structure=False, fixed_ initialization for the barycenters' structure matrix. If not set random init
init_X : ndarray, shape (N,d), optional
initialization for the barycenters' features. If not set random init
+
Returns
- ----------
+ -------
X : ndarray, shape (N,d)
Barycenters' features
C : ndarray, shape (N,N)
@@ -1002,11 +1022,13 @@ def fgw_barycenters(N, Ys, Cs, ps, lambdas, alpha, fixed_structure=False, fixed_ log_: dictionary
Only returned when log=True
T : list of (N,ns) transport matrices
- Ms : all distance matrices between the feature of the barycenter and the other features dist(X,Ys) shape (N,ns)
+ Ms : all distance matrices between the feature of the barycenter and the
+ other features dist(X,Ys) shape (N,ns)
+
References
----------
.. [24] Vayer Titouan, Chapel Laetitia, Flamary R{\'e}mi, Tavenard Romain
- and Courty Nicolas
+ and Courty Nicolas
"Optimal Transport for structured data with application on graphs"
International Conference on Machine Learning (ICML). 2019.
"""
@@ -1107,6 +1129,7 @@ def update_sructure_matrix(p, lambdas, T, Cs): """
Updates C according to the L2 Loss kernel with the S Ts couplings
calculated at each iteration
+
Parameters
----------
p : ndarray, shape (N,)
@@ -1117,6 +1140,7 @@ def update_sructure_matrix(p, lambdas, T, Cs): the S Ts couplings calculated at each iteration
Cs : list of S ndarray, shape(ns,ns)
Metric cost matrices
+
Returns
----------
C : ndarray, shape (nt,nt)
@@ -1132,6 +1156,7 @@ def update_feature_matrix(lambdas, Ys, Ts, p): """
Updates the feature with respect to the S Ts couplings. See "Solving the barycenter problem with Block Coordinate Descent (BCD)" in [24]
calculated at each iteration
+
Parameters
----------
p : ndarray, shape (N,)
@@ -1142,6 +1167,7 @@ def update_feature_matrix(lambdas, Ys, Ts, p): the S Ts couplings calculated at each iteration
Ys : list of S ndarray, shape(d,ns)
The features
+
Returns
----------
X : ndarray, shape (d,N)
diff --git a/ot/lp/__init__.py b/ot/lp/__init__.py index 8ec286b..17f1731 100644 --- a/ot/lp/__init__.py +++ b/ot/lp/__init__.py @@ -1,6 +1,9 @@ # -*- coding: utf-8 -*- """ Solvers for the original linear program OT problem + + + """ # Author: Remi Flamary <remi.flamary@unice.fr> @@ -39,26 +42,30 @@ def emd(a, b, M, numItermax=100000, log=False): - M is the metric cost matrix - a and b are the sample weights + .. warning:: + Note that the M matrix needs to be a C-order numpy.array in float64 + format. + Uses the algorithm proposed in [1]_ Parameters ---------- - a : (ns,) ndarray, float64 - Source histogram (uniform weigth if empty list) - b : (nt,) ndarray, float64 - Target histogram (uniform weigth if empty list) - M : (ns,nt) ndarray, float64 - loss matrix + a : (ns,) numpy.ndarray, float64 + Source histogram (uniform weight if empty list) + b : (nt,) numpy.ndarray, float64 + Target histogram (uniform weight if empty list) + M : (ns,nt) numpy.ndarray, float64 + Loss matrix (c-order array with type float64) numItermax : int, optional (default=100000) The maximum number of iterations before stopping the optimization algorithm if it has not converged. - log: boolean, optional (default=False) + log: bool, optional (default=False) If True, returns a dictionary containing the cost and dual variables. Otherwise returns only the optimal transportation matrix. Returns ------- - gamma: (ns x nt) ndarray + gamma: (ns x nt) numpy.ndarray Optimal transportation matrix for the given parameters log: dict If input log is true, a dictionary containing the cost and dual @@ -130,16 +137,20 @@ def emd2(a, b, M, processes=multiprocessing.cpu_count(), - M is the metric cost matrix - a and b are the sample weights + .. warning:: + Note that the M matrix needs to be a C-order numpy.array in float64 + format. + Uses the algorithm proposed in [1]_ Parameters ---------- - a : (ns,) ndarray, float64 - Source histogram (uniform weigth if empty list) - b : (nt,) ndarray, float64 - Target histogram (uniform weigth if empty list) - M : (ns,nt) ndarray, float64 - loss matrix + a : (ns,) numpy.ndarray, float64 + Source histogram (uniform weight if empty list) + b : (nt,) numpy.ndarray, float64 + Target histogram (uniform weight if empty list) + M : (ns,nt) numpy.ndarray, float64 + Loss matrix (c-order array with type float64) numItermax : int, optional (default=100000) The maximum number of iterations before stopping the optimization algorithm if it has not converged. @@ -153,7 +164,7 @@ def emd2(a, b, M, processes=multiprocessing.cpu_count(), ------- gamma: (ns x nt) ndarray Optimal transportation matrix for the given parameters - log: dict + log: dictnp If input log is true, a dictionary containing the cost and dual variables and exit status @@ -233,9 +244,9 @@ def free_support_barycenter(measures_locations, measures_weights, X_init, b=None Parameters ---------- - measures_locations : list of (k_i,d) np.ndarray + measures_locations : list of (k_i,d) numpy.ndarray The discrete support of a measure supported on k_i locations of a d-dimensional space (k_i can be different for each element of the list) - measures_weights : list of (k_i,) np.ndarray + measures_weights : list of (k_i,) numpy.ndarray Numpy arrays where each numpy array has k_i non-negatives values summing to one representing the weights of each discrete input measure X_init : (k,d) np.ndarray @@ -248,7 +259,7 @@ def free_support_barycenter(measures_locations, measures_weights, X_init, b=None numItermax : int, optional Max number of iterations stopThr : float, optional - Stop threshol on error (>0) + Stop threshold on error (>0) verbose : bool, optional Print information along iterations log : bool, optional @@ -533,14 +544,13 @@ def wasserstein_1d(x_a, x_b, a=None, b=None, p=1.): r"""Solves the p-Wasserstein distance problem between 1d measures and returns the distance - .. math:: - \gamma = arg\min_\gamma \left( \sum_i \sum_j \gamma_{ij} - |x_a[i] - x_b[j]|^p \\right)^{1/p} + \min_\gamma \left( \sum_i \sum_j \gamma_{ij} \|x_a[i] - x_b[j]\|^p \right)^{1/p} s.t. \gamma 1 = a, \gamma^T 1= b, \gamma\geq 0 + where : - x_a and x_b are the samples diff --git a/ot/lp/emd_wrap.pyx b/ot/lp/emd_wrap.pyx index 8a4aec9..2b6c495 100644 --- a/ot/lp/emd_wrap.pyx +++ b/ot/lp/emd_wrap.pyx @@ -58,13 +58,16 @@ def emd_c(np.ndarray[double, ndim=1, mode="c"] a, np.ndarray[double, ndim=1, mod - M is the metric cost matrix - a and b are the sample weights + .. warning:: + Note that the M matrix needs to be a C-order :py.cls:`numpy.array` + Parameters ---------- - a : (ns,) ndarray, float64 + a : (ns,) numpy.ndarray, float64 source histogram - b : (nt,) ndarray, float64 + b : (nt,) numpy.ndarray, float64 target histogram - M : (ns,nt) ndarray, float64 + M : (ns,nt) numpy.ndarray, float64 loss matrix max_iter : int The maximum number of iterations before stopping the optimization @@ -73,7 +76,7 @@ def emd_c(np.ndarray[double, ndim=1, mode="c"] a, np.ndarray[double, ndim=1, mod Returns ------- - gamma: (ns x nt) ndarray + gamma: (ns x nt) numpy.ndarray Optimal transportation matrix for the given parameters """ @@ -1,5 +1,11 @@ """ Functions for plotting OT matrices + +.. warning:: + Note that by default the module is not import in :mod:`ot`. In order to + use it you need to explicitely import :mod:`ot.plot` + + """ # Author: Remi Flamary <remi.flamary@unice.fr> diff --git a/ot/stochastic.py b/ot/stochastic.py index bf3e7a7..5754968 100644 --- a/ot/stochastic.py +++ b/ot/stochastic.py @@ -1,3 +1,9 @@ +""" +Stochastic solvers for regularized OT. + + +""" + # Author: Kilian Fatras <kilian.fatras@gmail.com> # # License: MIT License diff --git a/ot/unbalanced.py b/ot/unbalanced.py index 44ab411..50ec03c 100644 --- a/ot/unbalanced.py +++ b/ot/unbalanced.py @@ -20,7 +20,7 @@ def sinkhorn_unbalanced(a, b, M, reg, alpha, method='sinkhorn', numItermax=1000, The function solves the following optimization problem: .. math:: - W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + \alpha KL(\gamma 1, a) + \alpha KL(\gamma^T 1, b) + W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + \\alpha KL(\gamma 1, a) + \\alpha KL(\gamma^T 1, b) s.t. \gamma\geq 0 @@ -129,7 +129,7 @@ def sinkhorn_unbalanced2(a, b, M, reg, alpha, method='sinkhorn', The function solves the following optimization problem: .. math:: - W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + \alpha KL(\gamma 1, a) + \alpha KL(\gamma^T 1, b) + W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + \\alpha KL(\gamma 1, a) + \\alpha KL(\gamma^T 1, b) s.t. \gamma\geq 0 @@ -240,7 +240,7 @@ def sinkhorn_knopp_unbalanced(a, b, M, reg, alpha, numItermax=1000, The function solves the following optimization problem: .. math:: - W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + \alpha KL(\gamma 1, a) + \alpha KL(\gamma^T 1, b) + W = \min_\gamma <\gamma,M>_F + reg\cdot\Omega(\gamma) + \\alpha KL(\gamma 1, a) + \\alpha KL(\gamma^T 1, b) s.t. \gamma\geq 0 diff --git a/ot/utils.py b/ot/utils.py index f21ceb9..e8249ef 100644 --- a/ot/utils.py +++ b/ot/utils.py @@ -1,6 +1,6 @@ # -*- coding: utf-8 -*- """ -Various function that can be usefull +Various useful functions """ # Author: Remi Flamary <remi.flamary@unice.fr> diff --git a/test/test_ot.py b/test/test_ot.py index ac86602..dacae0a 100644 --- a/test/test_ot.py +++ b/test/test_ot.py @@ -72,7 +72,8 @@ def test_emd_1d_emd2_1d(): # check AssertionError is raised if called on non 1d arrays u = np.random.randn(n, 2) v = np.random.randn(m, 2) - np.testing.assert_raises(AssertionError, ot.emd_1d, u, v, [], []) + with pytest.raises(AssertionError): + ot.emd_1d(u, v, [], []) def test_wass_1d(): |
