{ "cells": [ { "cell_type": "markdown", "id": "20778463", "metadata": {}, "source": [ "## KL Divergence: Gaussian\n", "\n", "In this example we show how the KL divergence of the surrogate model improves as a function of iteration." ] }, { "cell_type": "code", "execution_count": 1, "id": "98cd9606", "metadata": { "execution": { "iopub.execute_input": "2026-02-21T08:21:37.358443Z", "iopub.status.busy": "2026-02-21T08:21:37.358330Z", "iopub.status.idle": "2026-02-21T08:21:38.427640Z", "shell.execute_reply": "2026-02-21T08:21:38.424240Z" } }, "outputs": [], "source": [ "import alabi\n", "from alabi.core import SurrogateModel\n", "from alabi import benchmarks as bm\n", "from alabi import metrics\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import multiprocessing as mp\n", "from functools import partial\n", "from scipy.stats import multivariate_normal" ] }, { "cell_type": "markdown", "id": "ce78fb18", "metadata": {}, "source": [ "We will check how the GP converges on a 4-dimensional Gaussian after 10, 20, 30... iterations" ] }, { "cell_type": "code", "execution_count": 2, "id": "d603d220", "metadata": { "execution": { "iopub.execute_input": "2026-02-21T08:21:38.432071Z", "iopub.status.busy": "2026-02-21T08:21:38.431802Z", "iopub.status.idle": "2026-02-21T08:21:38.440062Z", "shell.execute_reply": "2026-02-21T08:21:38.439414Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mean: [0. 0. 0. 0.]\n", "cov: [[ 0.8414129 -0.33304198 0.10790599 0.16416321]\n", " [-0.33304198 1.03456341 -0.16338963 0.47298839]\n", " [ 0.10790599 -0.16338963 0.802922 -0.16358507]\n", " [ 0.16416321 0.47298839 -0.16358507 0.39199966]]\n" ] } ], "source": [ "ncore = 1\n", "ndim = 4\n", "ntrain = 10 # number of initial training samples\n", "nbatch = 5 # number of active learning iterations * 100\n", "niter_per_batch = 10 # number of iterations per batch\n", "\n", "# Define the multivariate normal likelihood function\n", "mean = np.zeros(ndim)\n", "cov = bm.random_gaussian_covariance(ndim)\n", "lnlike = partial(multivariate_normal.logpdf, mean=mean, cov=cov)\n", "\n", "print(\"mean:\", mean)\n", "print(\"cov:\", cov)" ] }, { "cell_type": "markdown", "id": "0fa5a69e", "metadata": {}, "source": [ "### Define `alabi` settings and run function" ] }, { "cell_type": "code", "execution_count": 3, "id": "8ab25337", "metadata": { "execution": { "iopub.execute_input": "2026-02-21T08:21:38.441750Z", "iopub.status.busy": "2026-02-21T08:21:38.441381Z", "iopub.status.idle": "2026-02-21T08:21:38.456589Z", "shell.execute_reply": "2026-02-21T08:21:38.455938Z" } }, "outputs": [], "source": [ "gp_kwargs = {\"kernel\": \"ExpSquaredKernel\", \n", " \"fit_amp\": True, \n", " \"fit_mean\": True, \n", " \"fit_white_noise\": False, \n", " \"white_noise\": -12,\n", " \"gp_opt_method\": \"l-bfgs-b\",\n", " \"gp_scale_rng\": [-2,2],\n", " \"optimizer_kwargs\": {\"max_iter\": 50, \"xatol\": 1e-4, \"fatol\": 1e-3, \"adaptive\": True}}\n", "\n", "al_kwargs={\"algorithm\": \"bape\", \n", " \"gp_opt_freq\": 10, \n", " \"obj_opt_method\": \"nelder-mead\", \n", " \"nopt\": 1,\n", " \"optimizer_kwargs\": {\"max_iter\": 50, \"xatol\": 1e-3, \"fatol\": 1e-2, \"adaptive\": True}}\n", "\n", "gp_opt_method = gp_kwargs[\"gp_opt_method\"]\n", "obj_opt_method = al_kwargs[\"obj_opt_method\"]\n", "save_base = f\"convergence_results\"\n", "\n", "\n", "def run_alabi(ndim, with_mcmc=True):\n", " \n", " savedir = f\"{save_base}/multivariate_normal_{ndim}d/\"\n", "\n", " dynesty_sampler_kwargs = {\"bound\": \"single\",\n", " \"nlive\": 50*ndim,\n", " \"sample\": \"auto\"}\n", " \n", " dynesty_run_kwargs = {\"wt_kwargs\": {'pfrac': 1.0},\n", " \"stop_kwargs\": {'pfrac': 1.0},\n", " \"maxiter\": int(2e4),\n", " \"dlogz_init\": 0.5}\n", "\n", " # Train surrogate model\n", " sm = SurrogateModel(lnlike_fn=lnlike,\n", " bounds=[(-3., 3.) for _ in range(ndim)],\n", " savedir=savedir,\n", " cache=True,\n", " verbose=True,\n", " ncore=ncore)\n", "\n", " # Initialize surrogate model \n", " sm.init_samples(ntrain=ntrain, sampler=\"sobol\")\n", "\n", " sm.init_gp(**gp_kwargs)\n", "\n", " if not with_mcmc:\n", " # Active training on surrogate model\n", " sm.active_train(niter=int(nbatch*niter_per_batch), **al_kwargs)\n", "\n", " else:\n", " for _ in range(nbatch):\n", " # Active training on surrogate model\n", " sm.active_train(niter=niter_per_batch, **al_kwargs)\n", "\n", " # Run MCMC on surrogate likelihood function\n", " sm.run_dynesty(like_fn=sm.surrogate_log_likelihood, \n", " sampler_kwargs=dynesty_sampler_kwargs,\n", " run_kwargs=dynesty_run_kwargs)\n", "\n", " return sm" ] }, { "cell_type": "code", "execution_count": 4, "id": "82ac080e", "metadata": { "execution": { "iopub.execute_input": "2026-02-21T08:21:38.458098Z", "iopub.status.busy": "2026-02-21T08:21:38.457921Z", "iopub.status.idle": "2026-02-21T08:27:55.440045Z", "shell.execute_reply": "2026-02-21T08:27:55.439465Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Initialized GP with squared exponential kernel.\n", "Successfully initialized GP on attempt 1\n", "\n", "Optimizing GP hyperparameters using 5-fold cross-validation...\n", "Evaluating 100 hyperparameter candidates using 5-fold CV...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Running 10 active learning iterations using bape...\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", " 0%| | 0/10 [00:00 0.500]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "254it [00:00, 1225.76it/s, batch: 0 | bound: 0 | nc: 6 | ncall: 565 | eff(%): 33.203 | loglstar: -inf < -56.612 < inf | logz: -61.235 +/- 0.137 | dlogz: 52.058 > 0.500]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "377it [00:00, 1010.78it/s, batch: 0 | bound: 0 | nc: 1 | ncall: 1134 | eff(%): 28.261 | loglstar: -inf < -40.607 < inf | logz: -45.555 +/- 0.141 | dlogz: 40.780 > 0.500]" ] }, { "name": "stderr", "output_type": "stream", "text": 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"output_type": "stream", "text": [ "\r", "12711it [05:24, 55.91it/s, batch: 13 | bound: 84 | nc: 10 | ncall: 1291488 | eff(%): 0.982 | loglstar: -7.061 < -1.153 < -0.750 | logz: -9.307 +/- 0.080 | stop: 1.014]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12898it [05:24, 115.87it/s, batch: 13 | bound: 86 | nc: 1 | ncall: 1291827 | eff(%): 0.997 | loglstar: -7.061 < -0.534 < -0.750 | logz: -9.307 +/- 0.080 | stop: 1.014]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "13024it [05:24, 166.88it/s, batch: 13 | bound: 86 | nc: 1 | ncall: 1291953 | eff(%): 1.006 | loglstar: -7.061 < 0.240 < -0.750 | logz: -9.307 +/- 0.080 | stop: 0.923]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "13024it [05:24, 40.08it/s, batch: 13 | bound: 86 | nc: 1 | ncall: 1291953 | eff(%): 1.006 | loglstar: -7.061 < 0.240 < -0.750 | logz: -9.307 +/- 0.080 | stop: 0.923] " ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Run 1 complete: 13024 samples, logZ = -9.323\n", "Total accumulated samples: 13024\n", "Caching model to convergence_results/multivariate_normal_4d/surrogate_model...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Saved dynesty samples to convergence_results/multivariate_normal_4d//dynesty_samples_final_surrogate_iter_10.npz\n", "Running 10 active learning iterations using bape...\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", " 0%| | 0/10 [00:00 0.500]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "193it [00:00, 961.17it/s, batch: 0 | bound: 0 | nc: 5 | ncall: 369 | eff(%): 33.919 | loglstar: -inf < -47.913 < inf | logz: -52.339 +/- 0.134 | dlogz: 99.230 > 0.500]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "296it [00:00, 989.14it/s, batch: 0 | bound: 0 | nc: 2 | ncall: 702 | eff(%): 32.816 | loglstar: -inf < -26.040 < inf | logz: -30.707 +/- 0.136 | dlogz: 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1.072]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12374it [00:10, 1372.94it/s, batch: 13 | bound: 8 | nc: 2 | ncall: 28736 | eff(%): 42.585 | loglstar: 61.502 < 67.228 < 67.592 | logz: 58.032 +/- 0.085 | stop: 1.072]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12630it [00:10, 1702.73it/s, batch: 13 | bound: 9 | nc: 1 | ncall: 29102 | eff(%): 43.112 | loglstar: 61.502 < 67.984 < 67.592 | logz: 58.032 +/- 0.085 | stop: 1.072]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12703it [00:10, 1154.98it/s, batch: 13 | bound: 9 | nc: 1 | ncall: 29175 | eff(%): 43.361 | loglstar: 61.502 < 68.504 < 67.592 | logz: 58.032 +/- 0.085 | stop: 0.967]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Run 1 complete: 12703 samples, logZ = 58.023\n", "Total accumulated samples: 12703\n", "Caching model to convergence_results/multivariate_normal_4d/surrogate_model...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Saved dynesty samples to convergence_results/multivariate_normal_4d//dynesty_samples_final_surrogate_iter_20.npz\n", "Running 10 active learning iterations using bape...\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", " 0%| | 0/10 [00:00 0.500]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "257it [00:00, 1286.98it/s, batch: 0 | bound: 0 | nc: 3 | ncall: 501 | eff(%): 36.662 | loglstar: -inf < -26.070 < inf | logz: -31.217 +/- 0.144 | dlogz: 97.432 > 0.500] " ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "386it [00:00, 951.27it/s, batch: 0 | bound: 0 | nc: 12 | ncall: 1181 | eff(%): 27.951 | loglstar: -inf < -1.302 < inf | logz: -6.637 +/- 0.144 | dlogz: 72.107 > 0.500] " ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "490it [00:00, 713.45it/s, batch: 0 | bound: 0 | nc: 70 | ncall: 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[00:10, 1473.18it/s, batch: 13 | bound: 11 | nc: 1 | ncall: 29642 | eff(%): 43.017 | loglstar: 69.092 < 76.239 < 75.562 | logz: 65.624 +/- 0.087 | stop: 0.967]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12791it [00:10, 1235.83it/s, batch: 13 | bound: 11 | nc: 1 | ncall: 29642 | eff(%): 43.017 | loglstar: 69.092 < 76.239 < 75.562 | logz: 65.624 +/- 0.087 | stop: 0.967]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Run 1 complete: 12791 samples, logZ = 65.651\n", "Total accumulated samples: 12791\n", "Caching model to convergence_results/multivariate_normal_4d/surrogate_model...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Saved dynesty samples to convergence_results/multivariate_normal_4d//dynesty_samples_final_surrogate_iter_30.npz\n", "Running 10 active learning iterations using bape...\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", " 0%| | 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eff(%): 40.117 | loglstar: 37.414 < 39.489 < 43.276 | logz: 34.573 +/- 0.082 | stop: 1.061]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "11974it [00:10, 1209.59it/s, batch: 14 | bound: 3 | nc: 2 | ncall: 29377 | eff(%): 40.184 | loglstar: 37.414 < 40.928 < 43.276 | logz: 34.573 +/- 0.082 | stop: 1.061]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12114it [00:10, 1254.92it/s, batch: 14 | bound: 5 | nc: 5 | ncall: 29650 | eff(%): 40.285 | loglstar: 37.414 < 41.850 < 43.276 | logz: 34.573 +/- 0.082 | stop: 1.061]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12264it [00:10, 1318.73it/s, batch: 14 | bound: 6 | nc: 7 | ncall: 29939 | eff(%): 40.395 | loglstar: 37.414 < 42.597 < 43.276 | logz: 34.573 +/- 0.082 | stop: 1.061]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12401it [00:10, 1293.58it/s, batch: 14 | bound: 8 | nc: 1 | ncall: 30264 | eff(%): 40.414 | loglstar: 37.414 < 43.129 < 43.276 | logz: 34.573 +/- 0.082 | stop: 1.061]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12645it [00:10, 1415.61it/s, batch: 14 | bound: 9 | nc: 1 | ncall: 30603 | eff(%): 41.023 | loglstar: 37.414 < 44.322 < 43.276 | logz: 34.573 +/- 0.082 | stop: 0.970]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12645it [00:10, 1169.84it/s, batch: 14 | bound: 9 | nc: 1 | ncall: 30603 | eff(%): 41.023 | loglstar: 37.414 < 44.322 < 43.276 | logz: 34.573 +/- 0.082 | stop: 0.970]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Run 1 complete: 12645 samples, logZ = 34.566\n", "Total accumulated samples: 12645\n", "Caching model to convergence_results/multivariate_normal_4d/surrogate_model...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Saved dynesty samples to convergence_results/multivariate_normal_4d//dynesty_samples_final_surrogate_iter_40.npz\n", "Running 10 active 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12 | bound: 12 | nc: 3 | ncall: 38033 | eff(%): 28.588 | loglstar: 2.323 < 8.070 < 8.479 | logz: 2.130 +/- 0.072 | stop: 1.153]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "11123it [00:12, 1018.32it/s, batch: 12 | bound: 14 | nc: 2 | ncall: 38340 | eff(%): 28.632 | loglstar: 2.323 < 8.413 < 8.479 | logz: 2.130 +/- 0.072 | stop: 1.153]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "11344it [00:12, 953.43it/s, batch: 13 | bound: 0 | nc: 1 | ncall: 38891 | eff(%): 29.169 | loglstar: 2.182 < 4.542 < 8.471 | logz: 2.115 +/- 0.069 | stop: 1.033] " ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "11447it [00:12, 967.40it/s, batch: 13 | bound: 2 | nc: 9 | ncall: 39183 | eff(%): 28.897 | loglstar: 2.182 < 3.711 < 8.471 | logz: 2.115 +/- 0.069 | stop: 1.033]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "11547it [00:13, 938.13it/s, batch: 13 | bound: 4 | nc: 4 | ncall: 39540 | eff(%): 28.889 | loglstar: 2.182 < 4.807 < 8.471 | logz: 2.115 +/- 0.069 | stop: 1.033]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "11643it [00:13, 893.30it/s, batch: 13 | bound: 6 | nc: 4 | ncall: 39935 | eff(%): 28.844 | loglstar: 2.182 < 5.664 < 8.471 | logz: 2.115 +/- 0.069 | stop: 1.033]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "11734it [00:13, 856.68it/s, batch: 13 | bound: 8 | nc: 1 | ncall: 40328 | eff(%): 28.789 | loglstar: 2.182 < 6.389 < 8.471 | logz: 2.115 +/- 0.069 | stop: 1.033]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "11844it [00:13, 918.20it/s, batch: 13 | bound: 9 | nc: 1 | ncall: 40637 | eff(%): 28.841 | loglstar: 2.182 < 7.027 < 8.471 | logz: 2.115 +/- 0.069 | stop: 1.033]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "11938it [00:13, 901.09it/s, batch: 13 | bound: 11 | nc: 1 | ncall: 40988 | eff(%): 28.823 | loglstar: 2.182 < 7.413 < 8.471 | logz: 2.115 +/- 0.069 | stop: 1.033]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12033it [00:13, 910.55it/s, batch: 13 | bound: 12 | nc: 7 | ncall: 41308 | eff(%): 28.830 | loglstar: 2.182 < 7.810 < 8.471 | logz: 2.115 +/- 0.069 | stop: 1.033]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12160it [00:13, 1010.30it/s, batch: 13 | bound: 14 | nc: 2 | ncall: 41580 | eff(%): 28.945 | loglstar: 2.182 < 8.254 < 8.471 | logz: 2.115 +/- 0.069 | stop: 1.033]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12435it [00:13, 1304.04it/s, batch: 13 | bound: 14 | nc: 1 | ncall: 41933 | eff(%): 29.493 | loglstar: 2.182 < 9.488 < 8.471 | logz: 2.115 +/- 0.069 | stop: 0.934]" ] }, { "name": "stderr", "output_type": "stream", "text": [ "\r", "12435it [00:13, 899.42it/s, batch: 13 | bound: 14 | nc: 1 | ncall: 41933 | eff(%): 29.493 | loglstar: 2.182 < 9.488 < 8.471 | logz: 2.115 +/- 0.069 | stop: 0.934] " ] }, { "name": "stderr", "output_type": "stream", "text": [ "\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Run 1 complete: 12435 samples, logZ = 2.087\n", "Total accumulated samples: 12435\n", "Caching model to convergence_results/multivariate_normal_4d/surrogate_model...\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Saved dynesty samples to convergence_results/multivariate_normal_4d//dynesty_samples_final_surrogate_iter_50.npz\n" ] } ], "source": [ "sm = run_alabi(ndim, with_mcmc=True)" ] }, { "cell_type": "markdown", "id": "5c2f9d50", "metadata": {}, "source": [ "### Measure convergence using KL divergence metric\n", "\n", "Compute the KL divergence between the surrogate model Gaussian ($P$) and the true Gaussian ($Q$) using the means and covariances:\n", "\n", "$$ D_{\\rm KL}(P \\Vert Q) = \n", " \\frac{1}{2} \\left[ \\log \\frac{\\vert K_2 \\vert}{\\vert K_1 \\vert} \n", " + \\mu^T K_2^{-1} \\mu \n", " + \\mathrm{tr} \\left(K_2^{-1} K_1\\right) - k\n", " \\right] $$\n", "where $K_1$ is the covariance matrix of $P$, $K_2$ is the covariance matrix of $Q$, and $\\mu = \\mu_1 - \\mu_2$ is the difference in the mean of $P$ and $Q$.\n", "\n", "If $D_{\\rm KL}(P \\Vert Q) = 0$, then the two distributions are identical, whereas a larger KL divergence value indicates greater divergence." ] }, { "cell_type": "code", "execution_count": 5, "id": "d75c01a1", "metadata": { "execution": { "iopub.execute_input": "2026-02-21T08:27:55.441542Z", "iopub.status.busy": "2026-02-21T08:27:55.441410Z", "iopub.status.idle": "2026-02-21T08:27:55.449863Z", "shell.execute_reply": "2026-02-21T08:27:55.449349Z" } }, "outputs": [], "source": [ "batches = np.arange(ntrain, int(nbatch * niter_per_batch)+1, niter_per_batch)\n", "metric = alabi.metrics.kl_divergence_gaussian\n", "savedir = f\"{save_base}/multivariate_normal_{ndim}d/\"\n", "\n", "kl_divergence = []\n", "for it in batches:\n", " dynesty_samples_model = np.load(f\"{savedir}dynesty_samples_final_surrogate_iter_{it}.npz\")[\"samples\"]\n", "\n", " kl_div = metrics.kl_divergence_gaussian(mean, cov, dynesty_samples_model.mean(axis=0), np.cov(dynesty_samples_model, rowvar=False))\n", " kl_divergence.append(kl_div)" ] }, { "cell_type": "markdown", "id": "be62f308", "metadata": {}, "source": [ "Plot KL divergence vs. iteration. For this 4D Gaussian example it takes roughly ~30 active learning iterations for the surrogate model to converge." ] }, { "cell_type": "code", "execution_count": 6, "id": "8ab465c2", "metadata": { "execution": { "iopub.execute_input": "2026-02-21T08:27:55.451477Z", "iopub.status.busy": "2026-02-21T08:27:55.451315Z", "iopub.status.idle": "2026-02-21T08:27:55.526234Z", "shell.execute_reply": "2026-02-21T08:27:55.525786Z" } }, "outputs": [ { "data": { "image/png": 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LIj1dv5OJ9WFx2HwmARl5RQAAM4WEJ9u4Y2J3H/Rq4crWJCKqEMNRLWI4Ml3n49Mw8tvjEAJY/3x39GzhKndJZIC8QjV2XUjChrA4hMc+0C33cbbB+EBvjOvqDTd7SxkrJCJjxHBUixiOTJNaIzDym+O4eDsdIx9rjC/Gd5a7JKoB15IzdX2TMku0Jj3Vzh0TA33Rs7kLW5OICADDUa1iODJNa07E4INtl2BvZYb/ze7HloV6JrdAjZ0XErEhLA4RcWm65b4uNpgQ6IOxXb3gasdzTtSQMRzVIoYj03M3Mw8D/n0YmflFWDSiHab08JO7JKpFV5IysCEsDlsibiMzv7g1yVwp4al2HpgU6IMezV3KnbpBrREIi76Pu5l5aGRvhcCmzpxfiageYTiqRQxHpuf1jWex7VwiOnqpsOXlIF7wGoicgiLsPJ+E9WFxOBefplve1NUWEwK9MaaLF1wetibtiUzCwh2XkZSep9vOU2WF+cPaYlB7z7ounYhqAcNRLWI4Mi3Hb6Ri0o+nIEnAtleC0NHLUe6SSAaXEtOxISwOW88mIutha5KFUoGn23ughZsdvtgfhb//MtRG6O8md2FAIqoHGI5qEcOR6cgvUmPwF0dxKzUbU3v44sMR7eUuiWSWnV+EHeeL+yadT0ivdHsJgIfKCsfefYItjkQmTt/rt6IOayKqcz8cvoVbqdlwtbPE7Kf85S6HjICtpRnGB/pg2796YeervTCgTaNHbi8AJKXnIazE40yIqH5jOKJ6K+5eDr4+eAMAMO+ZNlBZm8tcERmb9k1UGN6psV7b/u/qHWQ/vB1HRPWbmdwFENUGIQTmb49EfpEGQS1c9L4AUsPTyF6/R4/892g0VoXGIMDXGX1auaFPK1e09XTgA4uJ6iGGI6qX/ryUjIPXUmChVODDEe15AaMKBTZ1hqfKCsnpeWU6ZGvZWCjhYmuB+Ae5OHHrHk7cuodP9wBu9pbo3dIVfVu5oVcLV93INyIybQxHVO9k5xdh4Y7LAIAX+zZDczc7mSsiY6ZUSJg/rC3++XMEJKBUQNJG6mXPdsKg9p6ISc3GkespOHwtBSdu3UNKZj5+j7iN3yNuQ5KADk1U6NPSDX1auaGzjyPMley5QGSKOFrNABytZtz+b9dl/PdoNLydrbHvzb6wMueDZalyVZ3nKL9IjTOxD3AkKhWHo1JwJSmj1Hp7SzP0bOFSfAuupRu8nW1q/TMQ0aNxKH8tYjgyXleSMvDM8mNQawRWTu+G/q0fPRKJqKTqzJB9NzMPR6NSceR6Co5eT8X97IJS65u52aJPSzf0beWGx5u5wNqCoZ2ortW7cDR9+nSsXr36kdvk5ubCyqps58ozZ87gk08+wZEjR5Ceng5PT08888wzmDdvHho1qvrFk+HIOGk0AuO+P4EzsQ8wqJ0H/jOlq9wlUQOl0QhEJqbjSFQKDkelICIuDWrNX79qLZQKBDZ1Rp9WrujTyg3+7vbsF0dUB/S9fptcn6OgoCC0aNGi3HVKZdm/xDZt2oQJEyagqKgI3bp1Q9OmTREeHo6vv/4av/32G44dO1bh+5Fp2XQmAWdiH8DGQokPhrWVuxxqwBQKCR29HNHRyxH/eqIlMvIKEXrjnq6/0u20XBy7kYpjN1Lx8R9X4e5gqeur1KuFK5xsLeT+CEQNmsmFo+effx7Tp0/Xa9vExERMmzYNRUVF+P777/HCCy8AANRqNaZPn46ff/4ZEydOxKlTp/hXm4l7kF2AxbuvAADefLIVGjtay1wR0V8crMwxqL0HBrX3gBACt1Kzda1KJ2/dw52MfPx2JgG/nUmAJAGdvBzRp5Ub+rZyRScvR5ixYzdRnTK5cFQVX3zxBXJycvDkk0/qghFQ3ML03XffYceOHTh9+jT27t2Lp59+WsZKqbo+2X0VD3IK0drDHtOD/OQuh6hCkiShuZsdmrvZITioKfIK1QiPeaBrVbp2JxPn4tNwLj4NXx24DgcrM/Rq6aprWWLwJ6p99TocbdmyBQAwceLEMuvs7OwwfPhwrF27Fr///jvDkQkLj7mPX8LjAQAfjWzP4dNkUqzMlejV0hW9WrrivSFtkJyeVxyUolJw7Hoq0nML8cfFZPxxMRkA0LKR3cNJKN3QvakzR2MS1QKTC0cHDx7ExYsXkZmZCRcXFwQGBmLIkCGwtCw9+VpmZiZu3Ch+dERAQEC57xUQEIC1a9fi7NmztV431Y5CtQZzt0YCAJ4N8EKAn7PMFRFVj4fKCs8GeOPZAG+oNQIXEtIeThdwF+fi03D9bhau383CimPRsDRToHszF/R5OBFli0Z27CJAVANMLhytWbOmzDJPT0/89NNPGDRokG5ZTEyM7r99fHzKfS9vb28AQHR09COPmZ+fj/z8fN2/MzIyHrE11aXVoTG4mpwJRxtzzBncRu5yiGqUUiGhs48TOvs44fUnWyI9pxDHb6bi8LUUHLmegqT0PByJSsGRqBR8tOsKGqusdK1KQS1c+TxBIgOZTDjq1KkTvvzySwwYMAA+Pj7Izc3F+fPnsWDBAoSGhmL48OHYu3cv+vXrB6C45UjL1ta23Pe0syueObmysLN48WIsXLiwZj4I1Zik9Fx8vi8KABAyuDWcOcKH6jmVjTmGdPDEkA6eEELgxt0sHH7YsTss+j4S0/Ow8XQ8Np6Oh0ICOvs4Peyr5IqOXo56z9lE1NCZzDxHFRFCYNSoUdi2bRs6deqEc+fOAQBCQ0MRFBQEACgsLISZWdkcuG/fPjz11FOwsLAo1TL0d+W1HHl7e3OeI5n98+cz2B2ZjK6+TvjtxR5Q8Bc/NWB5hWqcir6vGwV3425WqfWONubo1cL14Sg4N7g76PfAXaL6pN7Oc/R3kiRh4cKF2LZtG86fP4/4+Hh4e3vD3t5et012djZUKlWZfbOyin95VBZwLC0ty/RpInkdvHYXuyOToVRI+GhkewYjavCszJXo+zD4zANwOy0XRx8GpWM3UpGWU4idF5Kw80ISAKC1h73u0SbdmjrB0owdu4m0TD4cAUCbNn/1NUlISIC3tzd8fX11y+Li4tChQ4cy+8XHF49w8vPzq/UaqebkFaoxf9slAEBwTz+08WTrHdHfNXG0xvhAH4wP9EGRWoPzCWk4/PA5cBcS0nA1ORNXkzPxw5FbsDZX4vFmzrr+Ss1cbdmxmxq0ehGO7t27p/tvbYuRg4MDWrRogRs3biA8PLzccBQeHg4A6NKlS90USjXim4M3EHc/Bx4OVnhjYCu5yyEyemZKBbr6OqOrrzNmDWyFB9kFOHajOCgdiUrB3cx8HLyWgoPXUgAAXk7WulaloBYusLdix25qWOpFONq4cSOA4kDk7++vWz5q1Ch89tlnWL9+PYKDg0vtk5WVhR07dgAARo8eXXfFUrXcTMnC94dvAQDmD2sLO8t68RUmqlNOthYY1qkxhnVqDCEErt3J1PVVOh39AAkPcrH+VBzWn4qDUiGhq4+T7jlw7RureBub6j2T6JB97tw5xMXFYciQIaU6Vms0GqxcuRL/+te/kJeXh7lz52LRokW69YmJiWjZsiVycnLwww8/4B//+AeA4seHBAcHY+3atejWrVuVHx/CB8/KQwiByStO4fiNe+jn74aV07ux6Z+ohuUUFOHUrfu6VqVbqdml1jvbWqD3wxm7e7dyRSN7duwm06Hv9dskwtHWrVsxatQoODk5oUuXLnB3d0daWhoiIyMRFxcHAJgwYQLWrFlTZlTab7/9hgkTJkCtVqN79+7w8/PD6dOncevWLbi7uxv04FmGI3lsO3cbr288B0szBfa92Rc+LjZyl0RU78Xfz9E92iT05j1k5ReVWt/W0+FhXyVXBPg6w8KMM9ST8apX4Sg6OhpfffUVwsPDER0djXv37kEIAXd3dwQGBiI4OBhDhgypcP8zZ87g448/xtGjR5Geng5PT08888wzmDdvHtzd3atcD8NR3cvIK8SApYeRkpmP2QNb4dUBLeUuiajBKVRrcDYuTXcL7uLt9FLrbSyU6NncRddfyc+1/DnmiORSr8KRsWE4qnvzt0Vi9YlYNHO1xe43enPYMZERuJeVX9yx+1oKjlxPRWpW6fnifF1sdA/M7dHchX0ESXYMR7WI4ahuXUxIx4hvjkEjgHXPd0dQC1e5SyKiv9FoBK4kZ+j6Kp2JfYBC9V+XF3OlhK6+TrpWpbaeDuzYTXWO4agWMRzVHbVGYPS3x3E+IR3DOzXGVxM6y10SEekhK78IJ2/eKw5L11MQey+n1HpXO0v0aVk8Aq53S1e42HGiXap9DEe1iOGo7qw9GYt5WyNhb2mGA2/15cgYIhMVey9b11cp9OY95BSoS63v0ERVPF1ASzd08XWCuZIdu6nmMRzVIoajupGSmY8nlh5CZl4RFg5vh2k9/eQuiYhqQEGRBmdiH+huwV1OKv3wbztLM13H7r6t3ODtzJGpVDMYjmoRw1HdePOXc9hy9jbaN3HAtld68YniRPXU3cw8HLtePGP30eupuJ9dUGp9M1db3XQBjzdzgY1FxR271RqBsOj7uJuZh0b2Vghs6szfHaTDcFSLGI5qX+jNVEz87ylIErD15SB08naUuyQiqgMajcClxAwcjrqLI1GpiIh7gCLNX5cpC6UC3Zo66UbBtfaw100GuycyCQt3XEZSep5ue0+VFeYPa4tB7T3r/LOQ8WE4qkUMR7WroEiDwV8ewc2UbEx+3AcfjSz7XDwiahgy8woRqu3YHZWChAe5pda7O1iid0s3qKzN8dOxaPz9gqZtM/puchcGJGI4qk0MR7Xrm4M38Nmf1+BqZ4EDs/tBZc2HXhJR8SOEolOzdUHp5K37yC1UV7qfBMBDZYVj7z7BW2wNnL7Xb87IRUYl/n4Olv/vOgDg/aFtGIyISEeSJDRzs0MzNzsEBzVFfpEa4TEPsCEsDjsvJFW4nwCQlJ6HsOj76NHcpe4KJpPFsZJkNIQQWLD9EvIKNejRzAUjH2sid0lEZMQszZQIauGKgW31ewzU3cy8yjciAsMRGZG9l+/gwNW7MFdKWDSyna6TJRHRo+g7/xnnSSN9MRyRUcjOL8LC7ZcAAP/o3QwtGtnLXBERmYrAps7wVFmhoj+nJBSPWgts6lyXZZEJq5FwtH37drzyyit45plnMGDAgFLrsrOzERoaihMnTtTEoaie+urAdSSm58HLyRqvPtFS7nKIyIQoFRLmD2sLABUGpPnD2rIzNumtWh2y4+PjMXr0aERERAAo7jPy91shFhYWmDBhAhISEhAaGoru3btX55BUD11LzsSKY9EAgIXD28HaQilzRURkaga198R3k7uUmefIXClh+YTOHMZPVWJwy1F2djaeeuopnDlzBk2aNMErr7wCW1vbMtuZm5tj5syZEEJgy5Yt1SqW6h8hBOZtjUSRRuCptu4Y0Ea/jpVERH83qL0njr37BDb843F8NLI9zBQSCtUCjRzY14iqxuBw9M033+DatWvo0qULrly5gq+++gp2dnblbjtixAgAwPHjxw09HNVTm84kICzmPqzNlZg/vJ3c5RCRiVMqJPRo7oLJj/tixMMRryuPx8hbFJkcg8PR5s2bIUkSli1bVm6LUUnt27eHUqlEVFSUoYejeuhBdgEW774KAHjjyZZo4mgtc0VEVJ8EB/kBAHZfTEJyOofxk/4MDkfXrl2DUqlEUFBQpdsqlUo4OjoiLS3N0MNRPbTkz6u4n12AVu52mNGrqdzlEFE9076JCoF+zijSCKw9GSN3OWRCDA5H+fn5sLa2hlKpX+fZnJwcWFnxvi8VOxP7ABvC4gEAH43sAHMlZ5Ugopo3o5cfAGD9qTjk6fGoESKgGuHI3d0dWVlZerUGXbp0Cbm5ufD29jb0cFSPFKk1mLs1EgAwtqsX5x4holozsK0Hmjha40FOIbaevS13OWQiDA5HvXr1AgD88ssvlW67ZMkSSJKE/v37G3o4qkdWn4jFlaQMqKzNETK4tdzlEFE9plRImNbTF0Bxx2w+a530YXA4evnll4ufhbVgASIjI8vdpqCgACEhIVi7di0kScI///lPgwul+iE5PQ/L9l4DAMwZ3BoudpYyV0RE9d1zAT6wNlfi2p1MnLh5T+5yyAQYHI569uyJV199FXfu3MHjjz+OsWPHIisrCwDw3nvvYdKkSfD29saSJUsAAHPnzkXbtm1rpmoyWYt2XkZ2gRqdfRzxXABvsxJR7VPZmGNsVy8AwE8c1k96kEQ12hiFEPjggw/wySefQK0u7uhWcoZsIQTMzMwwb948zJs3r/rVGomMjAyoVCqkp6fDwcFB7nJMxuGoFEz7KQwKCdjxai+0a6ySuyQiaiBupmRhwNLDkCTg0Fv94Ovy6CloqH7S9/pdrceHSJKERYsW4fnnn8eqVatw/PhxJCYmQq1Ww8PDA0FBQZgxYwaaNWtWncNQPZBXqMYH24pvv07v2ZTBiIjqVHM3O/Rt5YbDUSlYFRqD+cM46SxVrFrhSMvX1xfz58+vibeieuq7QzcRey8H7g6WmPVUK7nLIaIGaEavpjgclYLfwhMwa2Ar2FuZy10SGSlOLkO1Ljo1G98dugkA+OCZdrCzrJFMTkRUJX1auqK5my2y8ovwW3iC3OWQETM4HBUUFODChQu4evVqpdtevXoVFy5cQGFhoaGHIxMlhMAH2yJRoNagTys3DOngIXdJRNRASZKE6UHFs/GvPhEDtYbD+ql8BoejX375BZ07d8YXX3xR6bb/93//h86dO2PTpk2GHo5M1M4LSTh6PRUWZgp8OLxdqQ77RER1bUyXJnCwMkPsvRwcvHpX7nLISFXrwbMAMHXq1Eq3nTlzJoQQDEcNTGZeIRbtvAwAeKVfC/i5cnQIEcnLxsIMEwJ9AAArQ6NlroaMlcHhKDIyEmZmZggMDKx026CgIJiZmeHixYuGHo5M0NK9UbibmQ8/Fxu82JcjFonIOEzp4QuFBBy/cQ9XkzPkLoeMkMHhKDExESqVCmZmlXeuNTc3h0qlQlJSkqGHIxMTeTsda07EAAAWjWwPK3P9HlBMRFTbvJxs8HS74v6PqzgpJJXD4HBkYWGBzMxMvbYVQiArK4v9TRoIjUZg7tZIaATwTEdP9G7pJndJRESlBD/smL3l7G3czy6QuRoyNgaHo6ZNm6KgoAAnTpyodNvQ0FDk5+fD19fX0MORCdlwOg7n4tNgZ2mGec/wkTFEZHy6+TmhfRMH5BdpsCEsTu5yyMgYHI4GDhwIIQTmzJmDoqKiCrcrKipCSEgIJEnCU089ZejhyESkZuXj093F0zvMfqoV3B2sZK6IiKgsSZIQ3LO49WjtiVgUqjUyV0TGxOBw9Nprr8HKygrHjh3Dk08+ibNnz5bZJiIiAgMGDMCxY8dgaWmJ119/vVrFkvH7+I8ryMgrQrvGDpjyOFsKich4PdPJE652lkjOyMPuyGS5yyEjYnA48vLywvfffw8AOHr0KAICAtCkSRP07NkTPXv2RJMmTdCtWzccPXoUkiThhx9+gI+PT40VTsbn5K17+D3iNiQJ+Ghke5gpOQE7ERkvSzMlJj/+cFj/cQ7rp79U6+o1ZcoUbN++Hb6+vhBCICkpCSdPnsTJkyeRlJQEIQSaNWuGXbt2YfLkyTVVMxmhgiIN5m0tfrDshEAfdPZxkrkiIqLKTeruCwulAmfj0nA27oHc5ZCRqPZDroYOHYpBgwbh4MGDCA0NRXJyMiRJgoeHB3r27In+/ftDoWALQn234lg0rt/NgoutBd59urXc5RAR6cXN3hLPdPLE7xG3sfJ4DP+wIwCAJITgw2WqKCMjAyqVCunp6XBwcJC7HNklPMjBwGVHkFuoxtJxnTCmq5fcJRER6S3ydjqeWX4MZgoJx959Ah4qDiSpr/S9frNJh6ptwfbLyC1Uo3tTZ4zu0kTucoiIqqR9ExUC/ZxRpBH4+WSs3OWQEWA4omrZd/kO9l+5AzOFhI9GtudEn0RkkoKD/AAA607FIq9QLW8xJLtq9zk6dOgQNmzYgAsXLuD+/fsoLCyscFtJknDz5s3qHpKMRE5BERZsvwQAeL53M7R0t5e5IiIiwwxs644mjta4nZaLbedu47luHF3dkBkcjoQQmDFjBtasWaP7d2XYqlC/LP/fDdxOy0UTR2u8NqCF3OUQERnMTKnA1B6+WLz7KlYej8GzAd68ZjVgBoej5cuXY/Xq1QCArl27Yvjw4WjcuLFeD6Il03f9Tib+e+QWAGDB8HawseB5JyLTNr6bD77Yfx1XkzNx4tY99GzuKndJJBODr2grV66EJEl4/vnndZNB1rV33nkHn332GQBg0aJFmDt3brnb7d+/H8uWLUNYWBiys7Ph6+uLMWPGICQkBHZ2dnVZcr0gRPGDZYs0Ak+2ccfAtu5yl0REVG0qG3OM6doEP5+Mw0/HYhiOGjCDO2RHRUUBAD755JMaK6YqQkNDsXTp0kqbPT///HMMHDgQe/bsQbt27TBs2DCkp6fj448/RkBAAFJTU+uo4vrj94jbOBV9H9bmSiwYzgfLElH9Mf3h89YOXL2D2HvZMldDcjE4HFlZWcHR0RFOTnU/YVZOTg6mT58OT09PjBgxosLtzp49i9mzZ0OpVGLXrl04fPgwfv31V9y8eRMDBgzAtWvX8NJLL9Vh5aYvLacAH/9xBQDw2oCW8HKykbkiIqKa06KRHfq2coMQwOpQDutvqAwORx06dEBGRgaysrJqsh69hISE4Pr16/jhhx+gUqkq3G7x4sUQQiA4OBiDBw/WLbexscGKFSugUCiwefNmXL16tS7KrheW/HkN97IL0LKRHWb2aip3OURENU47rP/X8Hhk5lU8ApvqL4PD0b/+9S+o1Wr89NNPNVlPpQ4dOoTly5dj6tSpGDJkSIXbFRQUYNeuXQCAiRMnllnv6+uLoKAgAMCWLVtqp9h65mzcA2wIiwMALBrZHhZmnCaLiOqfPi3d0MzNFln5Rdh0JkHuckgGBl/dxo4di1deeQXvvvsu1q5dW5M1VSgrKwszZsyAu7s7vvjii0duGxUVhZycHABAQEBAudtol589e7ZG66yPitQazN0aCSGA0V2a4PFmLnKXRERUKxQKCcE9/QAAq0NjoNHwKVsNjcGj1WbMmAGg+BbV9OnTMW/ePHTr1g329hVPBChJElasWGHoIfHWW28hOjoaW7ZsqbSvU3R0NADA0dGxwpq8vb1LbVuR/Px85Ofn6/6dkZFRlbLrhbUnY3EpMQMqa3O8N6SN3OUQEdWq0V288Nmf1xBzLwcHr93FgDYclduQGByOVq1aBUmSdJM/xsXFIS4urtxttdtVJxzt3bsX33//PcaPH4+RI0dWun1mZiYAwNbWtsJttMP4Kws7ixcvxsKFC/Uvtp65k5GHpXuLRye+M8gfrnaWMldERFS7bC3NMD7QBz8cuYWfjkczHDUwBoejqVOn1tnsoenp6Zg5cybc3NywfPnyOjlmSSEhIZg1a5bu3xkZGbpWp4Zg0c7LyMovQidvR0zglPpE1EBM7eGLH4/ewvEb93AtORP+HnxEUkNRrZajuvLGG28gISEBv/zyC1xd9ZuUS3srLTu74nkqtCPtHBwcHvlelpaWsLRsmK0lR6+nYOeFJCgk4P9GtodCwen0iahh8HKywdPtPLA7MhmrQqOxeHRHuUuiOmISz3zYsmULzMzM8O233+Lbb78ttU47DH/FihXYv38/PDw8sHHjRvj5+QEA0tLSkJmZWW6/o/j4eADQbUul5RWqMW9rJABgag8/tG9S8bQJRET1UXBQU+yOTMbvEbfxztOt4WRrIXdJVAdMIhwBQFFREQ4fPlzh+piYGMTExMDX1xcA4O/vDxsbG+Tk5CA8PBz9+/cvs094eDgAoEuXLrVTtIn7/vAtxNzLQSN7S8x+qpXc5RAR1blufk5o19gBlxIzsD4sDq/050O2G4Iamahm+/bteOWVV/DMM89gwIABpdZlZ2cjNDQUJ06cMPj909LSIIQo9zVt2jQAxc9WE0IgJiYGAGBhYYGhQ4cCANavX1/mPWNjYxEaGgoAGDVqlMG11Vcxqdn45tANAMC8Z9rC3spc5oqIiOqeJEkIDiqe8HbtiVgUqjUyV0R1oVrhKD4+Ht26dcOoUaPwn//8B3/88QcOHTpUahsLCwtMmDABvXr1wqlTp6pzuCqbM2cOJEnCypUrsWfPHt3ynJwczJw5E2q1GmPGjEHr1q3rtC5jJ4TAB9svoaBIg94tXfFMR0+5SyIiks2wTp5wtbNAckYe9kQmy10O1QGDw1F2djaeeuopnDlzBk2aNMErr7xS7rB5c3NzzJw5E0KIOp+JukuXLli6dCnUajWGDBmC/v3747nnnkOLFi1w4MAB+Pv74z//+U+d1mQK/riYjCNRKbBQKvDhiPZ1NiqRiMgYWZopMal7cZeNn44/el48qh8MDkfffPMNrl27hi5duuDKlSv46quvdPMG/Z324bDHjx839HAGe/PNN7Fv3z48/fTTuHDhArZt2wY7OzuEhITg9OnTeo9+aygy8wrx4c5LAICX+jVHU9eK54kiImooJj3uA3OlhLNxaTgXnyZ3OVTLJKGdxbGKunfvjvDwcBw8eBB9+vQBAHh6euLu3btQq9WltlWr1bCysoKzszPu3LlT/apllpGRAZVKhfT09EqnATA1H+64jJ+OR8PXxQZ/vtEHVuZKuUsiIjIKs345h9/P3saIxxrjy/Gd5S6HDKDv9dvglqNr165BqVTqHt76KEqlEo6OjkhLSzP0cFQHLiWmY1VocZPxhyPaMxgREZWg7Zi960IS7mTkyVwN1SaDw1F+fj6sra2hVOp3Ac3JyYGVlZWhh6NaptEIzNsaCY0AhnbwRN9WbnKXRERkVDp4qdDNzwlFGoG1J2LlLodqkcHhyN3dHVlZWXq1Bl26dAm5ubkN6pEbpuaX8HhExKXB1kKJec+0lbscIiKjpG09Wh8Wh7xCdSVbk6kyOBz16tULAPDLL79Uuu2SJUsgSVK5EzGS/O5l5eOT3cUzjc96yh8eKrbwERGV56m27mjiaI372QXYfi5R7nKolhgcjl5++WUIIbBgwQJERkaWu01BQQFCQkKwdu1aSJKEf/7znwYXSrVn8e6rSM8tRBtPB0zr4St3OURERstMqcDUHn8N6zdwTBMZOYPDUc+ePfHqq6/izp07ePzxxzF27Fjdg1zfe+89TJo0Cd7e3liyZAkAYO7cuWjblrdrjE1Y9H1sOpMAAPhoZHuYKWtk0nQionprfDcfWJsrcTU5Eydu3ZO7HKoF1Xq22hdffAEHBwd88skn+P333wEUT7X+6aefAiieadnMzAzz5s3DvHnzql8t1ahCtQZzt14EAEwI9EZXXyeZKyIiMn4qG3OM7tIE607FYeXxGPRszvny6huD5zkqKTY2FqtWrcLx48eRmJgItVoNDw8PBAUFYcaMGWjWrFlN1Go06ss8R98fvonFu6/C2dYC/5vdF442fNo0EZE+btzNxJPLjkCSgMNv9YePi43cJZEe9L1+V6vlSMvX1xfz58+vibeiOnI7LRdf7L8OAAgZ3JrBiIioClo0skefVm44EpWC1SdiOMq3nmEHkwZq4fZLyC1UI9DPGWO7esldDhGRyQkO8gMA/Ho6Hln5RfIWQzWK4agBOnDlDvZevgMzhYRFI/lgWSIiQ/Rt6YZmrrbIzC/CpvB4ucuhGmTwbbUPP/ywSttbWVnB0dER7dq1Q7du3WBhwds4csgtUGP+9uIHy87s1RT+HvYyV0REZJoUCgnBQX6Yt+0SVoXGYGoPPygU/GOzPjA4HC1YsMDgFgdnZ2e8+eabmDNnDhQKNl7Vpa8PXkfCg1w0VlnhtQEt5S6HiMikje7ihSV/XkPMvRwcvHYXA9q4y10S1QCDk0mfPn3Qp08fqFQqCCEghICXlxe6d++O7t27w8vLS7fc0dERvXv3RocOHWBubo579+5h3rx5mDBhQk1+FqrEjbuZ+OHILQDA/OHtYGtZI/3xiYgaLFtLM4zvVvxorJXHY+QthmqMweHo0KFD6NmzJ9LS0jBt2jTcuHEDsbGxCA0NRWhoKGJjY3Hz5k0EBwfjwYMH6Nu3L86dO4d79+5hwYIFAIBNmzZhy5YtNfVZ6BGEEJi7NRKFaoEBrRvhqbb864aIqCZM7eEHhQQcu5GKqDuZcpdDNcDgcLR582Z88skneP3117Fy5cpy5zJq2rQpVqxYgTfeeAMfffQRtm/fDltbW3zwwQeYNWsWhBBYvXp1tT4A6Wfruds4ees+rMwVWDC8HTthExHVEG9nGzzV1gMAW4/qC4PD0ddffw1JkvSa+Xru3LkAgK+++kq37NVXXwUAhIeHG1oC6Sk9pxD/t+sKAODVJ1rC25mTlRER1STtsP7fIxLwILtA3mKo2gwORxcuXICjoyOcnZ0r3dbZ2RmOjo44e/asbpmPjw/s7e2RmppqaAmkp8/2XkVqVgGau9niH73r12zlRETGILCpM9p6OiC/SIMNp+PkLoeqyeBwlJ+fj4yMDOTk5FS6bXZ2NjIyMpCfn19mnbW1taElkB7Ox6dh3ani/6MuGtkeFmYcHUhEVNMkScKMXk0BAGtPxKJQrZG5IqoOg6+ULVu2hFqtxnfffVfptv/5z3+gVqvRsuVfQ8fT09ORmZkJNzc3Q0ugSqg1xZ2whQBGdW7ChyMSEdWiYZ084WpngaT0PPx5KVnucqgaDA5HU6ZMgRACc+bMweLFi5Gbm1tmm9zcXHzyySeYM2cOJEnClClTdOtOnjwJAGjfvr2hJVAlfj4Zi4u30+FgZYb3hrSRuxwionrN0kyJid19AQA/HYuWuRqqDoMnunnttdewbds2HD16FHPnzsXHH3+MgIAANG7cGJIkITExEeHh4cjOzoYQAr1798Zrr72m23/VqlUAgIEDB1b7Q1BZdzPy8O8/rwEA3h7UGm72ljJXRERU/01+3AffHbqBiLg0nI9PQydvR7lLIgNIQghh6M45OTmYNWsWfvzxR2g0xfdXtUPEtW+rUCgwc+ZMLFu2DLa2trp9s7KyoFarYWdnB6VSWZ3PUOcyMjKgUqmQnp4OBwcHucsp12sbzmL7+UR08lLh95eDoOSU9kREdWLWL+fw+9nbGPlYY3wxvrPc5VAJ+l6/qxWOtOLj47F582ZEREQgJSUFAODm5oYuXbpg9OjR8PHxqe4hjIqxh6Nj11MxecUpKCRg2yu90MFLJXdJREQNxsWEdAz7+hjMFBKOz3kC7g5WcpdED+l7/Tb4ttqRI0cAAB07doS3tzfeeOMNQ9+KalB+kRofbIsEAEx53JfBiIiojnXwUiHA1wnhsQ/w88lYzH7KX+6SqIoM7pDdr18/DBgwADXQ8EQ16IfDt3ArNRtu9paY/TT/D0lEJAftsP71p+KQV6iWuRqqKoPDkUqlgkqlgpOTU03WQ9UQdy8HXx+8AQCYO7QNHKzMZa6IiKhheqqtO5o4WuNedgG2n0+UuxyqIoPDUYsWLZCZmVnuxI5U94QQ+GB7JPKLNAhq4YLhnRrLXRIRUYNlplRgSo+/hvXzLotpMTgcjR8/HoWFhfj1119rsh4y0J7IZBy6lgILpQKLRrTng2WJiGQ2vps3rMwVuJqciZO37stdDlWBweHo9ddfR48ePfCvf/0Lf/zxR03WRFWUlV+EhTsuAwBe7NsMzdzsZK6IiIgcbSwwposXAGDlcU4KaUoMHq328ccfo0+fPrh48SKGDRuGdu3aISgoCI0aNXrkvEUffPCBoYekCny5PwrJGXnwcbbBK/1byF0OERE9FBzkh3Wn4rDvyh3E3cuBj4uN3CWRHgye50ihUECSpFL3UfW5laNWm36vfWOa5+hKUgaeWX4Mao3AyuBu6O/fSNZ6iIiotCkrTuHo9VTM7NUU855pK3c5DVqtz3PUp08f9muRmebhg2XVGoHB7T0YjIiIjNCMoKY4ej0Vv56Ox5sDW8HO0uBLL9URg8/QoUOHarAMMsRvZ+JxJvYBbC2U+GAY/xohIjJGfVu5oZmrLW6lZmPzmQRM6+knd0lUCYM7ZJO87mcXYPHuqwCANwe2gqfKWuaKiIioPAqFhOlBfgCAVaEx0Gg4rN/YMRyZqE92X0FaTiFae9jzrxAiIiM3posX7K3MEJ2ajUNRd+UuhypRIzc+L1y4gD///BOxsbHIzc3FihUrdOsKCwuRkpICSZLg6elZE4dr8MJj7uPX8AQAwEcj28NcyYxLRGTMbC3NML6bN/57NBorj8fgidbucpdEj1CtcJSeno4ZM2Zg69atAIpnaZYkqUw46tSpEx48eIDz58+jXbt21Sq4oStUazB3a/GDZZ8L8EaAn7PMFRERkT6m9vDDimPROHo9FVF3MtHK3V7ukqgCBjc5FBYWYvDgwdi6dStsbGwwdOhQWFlZldnOxsYGwcHB0Gg02LRpU7WKJWDV8RhcTc6Ek4055gxuLXc5RESkJ29nGwxsW9xitPJ4jLzF0CMZHI5WrFiBkydPolmzZrh27Rq2b98OlUpV7rZjxowBABw5csTQwxGAxLRcfL4/CgAQMrgNnGwtZK6IiIiqIjioKQBgy9kEpOUUyFwNVcTgcLRhwwZIkoTPP/8cjRs/+iGnnTt3hkKhwNWrVw09HAH4cMdl5BSoEeDrhLFdveQuh4iIqqh7U2e09XRAXqEGG8Li5S6HKmBwOLp48SIkScJTTz1V6bYWFhZQqVS4d++eoYdr8A5evYs9l5KhVEhYNLI9FApOwElEZGokSULww2H9a07EoFCtkbcgKpfB4SgnJwf29vawsNDv1k5hYSHMzDgrqCHyCtX4YHtxJ+wZQX5o4ynvI0uIiMhwwzo1houtBZLS8/DnpWS5y6FyGByOXF1dkZGRgaysrEq3jY6ORlZWVqW336h83xy8gfj7ufBUWeGNJ1vJXQ4REVWDlbkSk7r7AGDHbGNlcDjq3r07AGDXrl2Vbrt8+XIAQO/evQ09XIN1MyUL/zl8EwAwf1hb2PKZPEREJm/y474wV0o4E/sA5+PT5C6H/sbgcDRjxgwIITBv3jwkJiZWuN3333+PL7/8EpIk4YUXXjD0cFi3bh2mTp2KTp06oVGjRjA3N4dKpUJgYCAWL178yBas/fv3Y8iQIXB1dYW1tTVat26N999/X69WLzkJITBvayQK1QL9/d3wdDsPuUsiIqIa0MjBCs90LL6bsvJ4tMzV0N9JQgiDH/Iybtw4bN68GR4eHpg4cSJ+/PFHZGZm4rvvvkNsbCx27tyJyMhICCHwj3/8A99//73Bhfbq1QuhoaFo06YNvL294ezsjDt37uDEiRPIzc1FixYtcPjw4TK37j7//HPMmjULkiShd+/ecHd3x9GjR5GcnAx/f38cO3YMrq6uVaolIyMDKpUK6enpcHCovf4/287dxusbz8HSTIF9b/aFj4tNrR2LiIjq1oWENAz/+jjMlRKOv/sEGjmUnSuQapbe129RDbm5uWLy5MlCkiShUCjKvCRJEpIkiZkzZ4rCwsLqHEqcPHlS3Lt3r8zy1NRU0atXLwFAjB8/vtS6iIgIIUmSUCqV4o8//tAtz87OFgMGDBAAxJgxY6pcS3p6ugAg0tPTq/5B9JSWUyC6LtonfN/dKb7aH1VrxyEiIvmM+fa48H13p1j651W5S2kQ9L1+V+uhXFZWVli7di2OHDmCKVOmoHnz5rC2toaFhQV8fHwwceJEHDp0CD/++GO1R6p1794dzs5lH5Xh4uKCjz/+GACwd+/eUusWL14MIQSCg4MxePBg3XIbGxusWLECCoUCmzdvNsr5l5btvYbUrHw0c7PFC32byV0OERHVAu2kkOtOxSGvUC1zNaRVI717e/XqhV69etXEWxlEG7wsLS11ywoKCnSdxSdOnFhmH19fXwQFBeHo0aPYsmULQkJC6qbYCqg1AmHR93E3Mw/ZeUVYcyIWAPDRiPawNFPKWhsREdWOp9u5o7HKConpedh+PhHPBnjLXRKhhsKRnDIzM7FgwQIAwPDhw3XLo6KikJOTAwAICAgod9+AgAAcPXoUZ8+erfU6H2VPZBIW7riMpPS8Usu7+TmhZ4uq9YciIiLTYaZUYEoPP3y65ypWHo/BuK5ekCRO8is3g2+rDRw4ED///LMugNSVvXv3Yvr06Zg6dSqefvppNGnSBHv37sWgQYPw6aef6raLji7u/e/o6Ah7+/KffOzt7V1qWznsiUzCP3+OKBOMAOB0zAPsiUySoSoiIqorEwK9YWWuwJWkDJyKvi93OYRqhKMDBw5g2rRp8PDwwPTp07F///6arKtCly9fxurVq7F27Vrs3bsXmZmZmDhxIlatWlXqwbeZmZkAAFtb2wrfy87ODkBx7/VHyc/PR0ZGRqlXTVBrBBbuuIyKhgtKABbuuAy1xuABhUREZOQcbSwwukvx8zI5rN84GByOJk+eDBsbG2RlZWHt2rV4+umn4e3tjZCQEFy6dKkmayzljTfegBACBQUFuHHjBpYuXYrdu3ejbdu2OHLkSK0cc/HixVCpVLqXtsWpusKi75fbYqQlACSl5yGMf0kQEdVrwT39AAB7L99B/P26vSNDZRkcjtasWYM7d+5g7dq1ePLJJ6FQKHD79m0sWbIEHTt2RNeuXfHVV18hJSWlJuvVMTc3R/PmzTFr1izs3r0bDx48wOTJk5GbmwsAultp2dnZFb6HdhLIyuYqCgkJQXp6uu4VH18zT1K+m1lxMDJkOyIiMk0t3e3Ru6UrhABWh8bIXU6DV62h/DY2Npg0aRL+/PNPxMfH47PPPkPHjh0hhMDZs2fx5ptvokmTJhg2bBh+/fVX5Ofn11TdpXTv3h1t27ZFfHw8wsPDAQB+fn4AgLS0NN0ttr/ThhztthWxtLSEg4NDqVdNaGSv34Rf+m5HRESma8bDYf2/hMcjK79I5moatmqFo5I8PDwwe/ZsnD17FhcuXMBbb72Fxo0bo6ioCLt27cKECRPg6elZU4crQ9u36O7duwAAf39/2NgUzyitDUx/p13epUuXWqvrUQKbOsNTZYWKxiVIADxVVghsWnZ+JyIiql/6tnJDM1dbZOYVYfOZBLnLadBqLByV1L59eyxZsgRxcXHYt28fAgICIIRAenp6bRwOqampOH/+PACgVavip9ZbWFhg6NChAID169eX2Sc2NhahoaEAgFGjRtVKXZVRKiTMH9YWAMoEJO2/5w9rC6WCwzqJiOo7hULCtId9j1aFxkDDwTiyqZVwBABJSUlYtmwZZs+ejTNnzlTrvS5fvox169YhL69s35uoqCiMGzcO+fn5ePzxx9GhQwfdujlz5kCSJKxcuRJ79uzRLc/JycHMmTOhVqsxZswYtG7dulr1Vceg9p74bnIXeKhK3zrzUFnhu8ldMKh97bW2ERGRcRnb1Qv2VmaITs3G4aja6bNLlavWg2f/Ljc3F7///jvWrFmD//3vf9BoNNC+fZcuXTB16lS89tprVX7fQ4cOoX///rC1tUXnzp3h5eWFgoICxMXFISIiAhqNBm3atMGePXvg4+NTat+SD57t27cvGjVqhKNHjyIpKcmoHjxbcobsRvbFt9LYYkRE1PB8tPMyfjwWjd4tXbF2Zne5y6lX9L1+10g42r9/P9auXYstW7YgOztbF4i8vLwwadIkTJkyBW3btjX4/VNSUvDf//4XR48exdWrV5GSkoLCwkI4OzujQ4cOGD16NIKDg0s9PuTv9S1duhRhYWHIzs6Gj48Pxo4di5CQkAoniHyU2ghHREREABB/Pwd9PzsIjQD2vdkHLd2rfp2i8tV6OIqMjMTatWuxfv16JCYmAgCEELCzs8Po0aMxZcoUPPHEE/VyGnSGIyIiqk0vrAnH3st3MLG7Dz4e1aHyHUgv+l6/DX62WseOHSFJEoQQUCgUeOKJJzB16lSMHj1aN0qMiIiIqm5Gr6bYe/kOfo9IwDtP+8PRxkLukhqUaj14tm3btpg6dSomTZqExo0b11RNREREDVr3ps5o4+mAK0kZ2Hg6Hi/1bS53SQ2KwaPVIiIicPHiRbz99tsMRkRERDVIkiQEB/kBANaExqBIrZG3oAbG4HD02GOP1WAZREREVNLwTo3hYmuBxPQ8/HnpjtzlNCi1Ns8RERERGc7KXIlJ3Yunp1l5PFrmahoWvfocffjhhwAAV1dXvPzyy6WWVdUHH3xg0H5EREQNzeTHffHd4ZsIj32ACwlp6OjlKHdJDYJeQ/kVCgUkSYK/vz8uX75callVqdXqqldpZDiUn4iI6sobG89i67lEjOrcBJ8/95jc5Zi0Gh3K36dPH0iSVGr2ae0yIiIiqj0zejXF1nOJ2HkhESGDW6ORg1XlO1G16BWODh06pNcyIiIiqlkdvRzR1dcJZ2If4OdTcZg1sJXcJdV77JBNRERk5LTD+tedjEVeoel3TzF2DEdERERG7ul2HvBUWeFedgF2nE+Uu5x6r1ozZANAbGwsbt68ifv37wMAXFxc0Lx581L9k4iIiMhw5koFpvbww6d7rmLl8RiM7erFfr+1yKBwlJ6ejmXLlmHNmjWIi4srdxtfX18EBwfj9ddf54guIiKiapoQ6I0vD0ThclIGwqLvo3szF7lLqreqfFstIiICbdq0wUcffYTY2FgIIcp9xcTEYMGCBWjbti3Onz9fG7UTERE1GI42FhjV2QsA8BMnhaxVVWo5iouLQ//+/ZGVlQUhBNq3b48hQ4agU6dOcHZ2BgDcv38f58+fxx9//IHIyEgkJiaif//+uHDhAry8vGrlQxARETUEwUF+2BAWh32X7yD+fg68nW3kLqle0msSSK0hQ4Zgz549UKlU+PHHHzFmzJhHbr9p0yb84x//QEZGBoYOHYrt27dXu2BjwEkgiYhILlNWnMLR66n4R++meH9oW7nLMSn6Xr/1vq128+ZN7NmzB0qlEtu2bas0GAHA2LFjsXXrVigUCvzxxx+IjmYzIBERUXVoh/VvPB2P7PwieYupp/QOR7/88gsA4Nlnn0WfPn30PkDfvn0xbtw4CCF070FERESG6deqEZq62iIzrwibIxLkLqde0jscnTlzBpIkYerUqVU+yNSpUyGEQHh4eJX3JSIior8oFBKm9/QDAKw6HgONRu/eMaQnvcNRZGQkACAwMLDKB+nevXup9yAiIiLDjenqBXtLM9xKzcbh6ylyl1Pv6B2OHjx4AEtLSzg5OVX5IE5OTrCystJNFElERESGs7M0w7PdvAEAPx1jf96apnc4qu7ILAcHB2RkZBi8PxEREf1lWg8/SBJw9HoqbtzNlLucekXvcFRYWAiFwvBHsUmShMLCQoP3JyIior/4uNhgYBt3AMDK4zHyFlPP8MGzREREJio4qCkA4PeI20jLKZC5mvqjSjNkZ2Vl4cMPPzToQFlZWQbtR0REROV7vJkzWnvY42pyJjaejsdLfZvLXVK9oPcM2QqFolpPABZCQJIkqNVqg9/DWHCGbCIiMha/no7HO5svoLHKCkfe6Q8zJW8KVaTGZ8gGUOFDZvV5ERERUc0b/lhjONtaIDE9D3sv35G7nHpB73Ck0Wiq/aoPrUZERETGxMpciUndfQAAK49zWH9NYNsbERGRiZv8uC/MFBJOxzzAxYR0ucsxeQxHREREJs7dwQrPdPQEwNajmsBwREREVA9oh/XvuJCIu5l5Mldj2hiOiIiI6oFO3o7o4uOIQrXAzyfj5C7HpDEcERER1RPa1qP1p2KRX8RBUIZiOCIiIqonBrX3gKfKCqlZBdhxPknuckwWwxEREVE9Ya5UYEoPXwDFHbM5z6BhGI6IiIjqkQndfGBlrsClxAyERd+XuxyTxHBERERUjzjZWmBU5yYAgJXHY+QtxkTVSTgqLCzE9u3bsX379ro4HBERUYOm7Zi993Iy4u/nyFyN6amTcJSRkYGRI0di9OjRdXE4IiKiBq2Vuz16tXCFRgBrT8bKXY7JqdPbauwYRkREVDeCg/wAABvC4pCdXyRvMSaGfY6IiIjqof7+jeDnYoPMvCL8HpEgdzkmheGIiIioHlIoJEzv6QcAWBkaA42Gd2/0xXBERERUT40N8Ia9pRlupWTj8PUUucsxGQxHRERE9ZSdpRnGBXgD4LD+qmA4IiIiqsem9/SDJAFHolJw426W3OWYBIYjIiKieszHxQZPtnEHAKwKjZa5GtNgpu+GH374ocEHycmp3gRUhYWFOHLkCPbs2YNDhw7h+vXryM7OhouLCwIDA/Hiiy9i6NChFe6/f/9+LFu2DGFhYcjOzoavry/GjBmDkJAQ2NnZVas2IiIiYxcc5Id9l+9g85nbePup1lDZmMtdklGThJ6TDykUCkiSZPCBhBCQJAlqtbrK++7fvx8DBw4EAHh4eKBr166wtbXF5cuXERkZCQB44YUX8J///KdMjZ9//jlmzZoFSZLQu3dvuLu74+jRo0hOToa/vz+OHTsGV1fXKtWTkZEBlUqF9PR0ODg4VPnzEBER1SUhBAZ/eRRXkzMRMrg1XuzbXO6SZKHv9btKt9WEEAa/qkOhUGDMmDE4cuQIkpKSsHPnTvzyyy+4ePEiNm7cCKVSiR9++AFr164ttd/Zs2cxe/ZsKJVK7Nq1C4cPH8avv/6KmzdvYsCAAbh27RpeeumlatVGRERk7CRJwoyHjxRZcyIWRWqNzBUZN73DkUajqfbLkFYjAHjiiSewadMm9O7du8y65557DtOnTwcArFmzptS6xYsXQwiB4OBgDB48WLfcxsYGK1asgEKhwObNm3H16lWD6iIiIjIVwx9rDGdbC9xOy8W+y3fkLseo1YsO2Z07dwYAxMfH65YVFBRg165dAICJEyeW2cfX1xdBQUEAgC1bttRBlURERPKxMldiYqAPAOCn4+yY/Sh6h6PMzMxqH+yjjz6q9nuU5/r16wAAT09P3bKoqChdR/CAgIBy99MuP3v2bK3URUREZEym9PCFmULC6ZgHiLydLnc5RkvvcDRs2DDk5+cbfKD/+7//w/z58w3evyLJyclYtWoVAGDMmDG65dHRxanY0dER9vb25e7r7e1datuK5OfnIyMjo9SLiIjI1Lg7WGFox+KGBLYeVUzvcHTkyBE899xz0Giq3onrk08+wbx586q8X2WKioowefJkpKeno0OHDnjxxRd167QtXba2thXurx3GX1nYWbx4MVQqle6lDVVERESmJvhhx+wd5xNxNzNP5mqMk97hSKlUYseOHQgODq7SAZYsWYL33nsPAPDUU09VrbpKvPTSSzhw4ABcXFywadMmWFhY1Oj7a4WEhCA9PV33Ktm3iYiIyJQ85u2Izj6OKFQLrDsZJ3c5RknvcPTDDz8AAH7++We88cYbeu3z73//G3PmzAFQHIy2bt1a5QIr8vrrr2PFihVwcnLCvn370KpVq1LrtbfSsrOzK3yPrKziadQrm6vI0tISDg4OpV5ERESmSjusf92pWOQXGTaSvD7TOxwFBwfj3//+N4QQWL58eaUzZi9btgzvvPMOAODJJ5/E1q1bYWlpWb1qH5o9eza++uorODo6Yu/evbrRaiX5+fkBANLS0irsTK5tAdJuS0RE1BAMau8BDwcrpGYVYOf5JLnLMTpVGsr/5ptv4v3334cQAgsXLsQ333xT7nZffPEF3nrrLQDFcxRt374dVlZW1a8WwDvvvINly5ZBpVJh7969FY5E8/f3h42NDQAgPDy83G20y7t06VIjtREREZkCc6UCU3r4AijumF3dyZrrmyrPc7Ro0SK8/PLLEELg9ddfx/r160ut/+qrrzBr1iwAQL9+/bBjx44aC0Zz5szBZ599BpVKhX379qFbt24VbmthYaF73trfawSA2NhYhIaGAgBGjRpVI/URERGZiomBPrA0U+BSYgZOxzyQuxyjYtAkkF9//TUmTpwIjUaD4OBg/PHHHwCA5cuX48033wQA9O3bFzt37oS1tXWNFDp37lx8+umncHR0rDQYac2ZMweSJGHlypXYs2ePbnlOTg5mzpwJtVqNMWPGoHXr1jVSIxERkalwsrXA6C5NAAArOay/FL0fPPt3arUaI0eOxK5du2BtbY2ZM2fi66+/BgD07t0bu3fv1t3Wqq7t27djxIgRAIonbmzXrl2527m6uuLf//53qWUlHzzbt29fNGrUCEePHkVSUhIfPEtERA3ateRMPP3FESgk4Mg7/eHlVDPXbWOl7/Xb4HAEFE+O+PTTT+PIkSOQJAlCCAQFBWHPnj2PnF+oqlatWqXXFAK+vr6IiYkps3z//v1YunQpwsLCkJ2dDR8fH4wdOxYhISEVThD5KAxHRERUX0z68SSO37iHF/o0w3tD2shdTq2qk3AEFE+22L9/f0RERNRKMDJGDEdERFRfHLhyBzNXh8PBygwn3xsAGwszuUuqNfpev/X+CSiVykeulyQJoaGhj05ikoSioiJ9D0lERES1rL9/I/i52CDmXg42R9zGlMd95S5Jdnp3yBZC1MiLiIiIjIdCIWFaTz8AxR2zNRpeq/VuOaqNh8YSERGR/MZ29cLSvVG4lZKNI9dT0M+/kdwlyYrhiIiIqIGztzLHswHe+Ol4NFYej2nw4cigeY6IiIiofpne0w+SBByOSsGNu1lylyMrhiMiIiKCj4sNBrR2BwCsCm3Yk0IyHBEREREAYEaQHwBg85nbSM8plLcYGTEcEREREQCgR3MXtPawR26hGr+Ex8ldjmwYjoiIiAhA8XyEwQ9bj1aHxqJIrZG3IJkwHBEREZHOiMeawMnGHLfTcrHv8h25y5EFwxERERHpWJkrMal78SzZK4/HyFuMTBiOiIiIqJQpPXxhppAQFnMfkbfT5S6nzjEcERERUSnuDlYY0sETQMNsPWI4IiIiojK0HbN3nE9ESma+vMXUMYYjIiIiKqOzjxM6+ziiQK3BulOxcpdTpxiOiIiIqFzBQU0BAD+fjEN+kVrmauoOwxERERGVa3B7D3g4WCE1Kx87zyfJXU6dYTgiIiKicpkrFZjS4+Gw/tBoCCFkrqhuMBwRERFRhSYE+sDSTIHI2xkIj30gdzl1guGIiIiIKuRsa4FRnZsAAFYej5a5mrrBcERERESPNP3hsP49kclIeJAjbzF1gOGIiIiIHqm1hwOCWrhAI4C1J+r/sH6GIyIiIqpUcM/iYf0bwuKQU1AkczW1i+GIiIiIKvVE60bwdbFBRl4Rfo+4LXc5tYrhiIiIiCqlUEiY1sMPQHHHbI2m/g7rZzgiIiIivYwL8IKdpRlupmTj6I1UucupNQxHREREpBd7K3OMC/ACUL+H9TMcERERkd6m9/SDJAGHrqXgxt0sucupFQxHREREpDdfF1sMaN0IALA6NEbeYmoJwxERERFVyYyg4mH9myMSkJ5bKHM1NY/hiIiIiKqkR3MX+LvbI6dAjV9Px8tdTo1jOCIiIqIqkSQJwQ8fKbIqNAZFao28BdUwhiMiIiKqspGdm8DJxhy303Kx/8oducupUQxHREREVGVW5kpM7O4DAPjpeIy8xdQwhiMiIiIyyJTH/WCmkBAWfR+Rt9PlLqfGMBwRERGRQTxUVhjcwRMAsLIetR4xHBEREZHBZjzsmL3jfCJSMvPlLaaGMBwRERGRwTr7OOExb0cUqDVYfypO7nJqBMMRERERVYt2WP/ak7HIL1LLW0wNYDgiIiKiahnSwRPuDpZIzcrHrgtJcpdTbQxHREREVC3mSgWm9vADUNwxWwghb0HVxHBERERE1TYh0AeWZgpcvJ2OM7EP5C6nWhiOiIiIqNqcbS0w8rEmAICfjkfLXE31MBwRERFRjQju5QcA+PPSHdxOy5W3mGpgOCIiIqIa0drDAT2bu0CtEVhzIkbucgxmMuHo2rVrWL58OaZPn44OHTrAzMwMkiTho48+qnTf/fv3Y8iQIXB1dYW1tTVat26N999/H1lZWXVQORERUcMRHNQUALAxLB45BUUyV2MYkwlH3333HV577TWsXr0akZGRUKv1m0fh888/x8CBA7Fnzx60a9cOw4YNQ3p6Oj7++GMEBAQgNTW1lisnIiJqOJ5o3Qg+zjZIzy3E7xG35S7HICYTjtq3b4+33noL69atw5UrVzBlypRK9zl79ixmz54NpVKJXbt24fDhw/j1119x8+ZNDBgwANeuXcNLL71UB9UTERE1DEqFhOk9/QAAq0JNc1i/mdwF6Ov5558v9W+FovJct3jxYgghEBwcjMGDB+uW29jYYMWKFWjWrBk2b96Mq1evonXr1jVeMxERUUM0LsALy/ZF4cbdLBy9noo+rdzkLqlKTKblqKoKCgqwa9cuAMDEiRPLrPf19UVQUBAAYMuWLXVaGxERUX1mb2WOsV29AJjmsP56G46ioqKQk5MDAAgICCh3G+3ys2fP1lldREREDcH0nn6QJODQtRTcTDGtAVD1NhxFRxcnVUdHR9jb25e7jbe3d6ltK5Kfn4+MjIxSLyIiIqqYn6stBrRuBABYHRojbzFVVG/DUWZmJgDA1ta2wm3s7OwAoNKws3jxYqhUKt1LG6qIiIioYtph/ZvOJCA9t1DmavRXb8NRTQoJCUF6erruFR8fL3dJRERERq9ncxf4u9sjp0CNX0+bzrWz3oYj7a207OzsCrfRTgLp4ODwyPeytLSEg4NDqRcRERE9miRJCA7yAwCsPhEDtcY0hvXX23Dk5+cHAEhLS9PdYvs7bQuQdlsiIiKqWSM7N4GTjTkSHuRi3+U7cpejl3objvz9/WFjYwMACA8PL3cb7fIuXbrUWV1EREQNiZW5EhMCfQAAK01kWH+9DUcWFhYYOnQoAGD9+vVl1sfGxiI0NBQAMGrUqDqtjYiIqCGZ0sMXSoWEU9H3cSkxXe5yKlVvwxEAzJkzB5IkYeXKldizZ49ueU5ODmbOnAm1Wo0xY8ZwdmwiIqJa5KmyxpAOngCAlcdj5C1GD5IwkYeeRERE4OWXX9b9++bNm0hNTYWXlxeaNGmiW75lyxZ4enrq/v35559j1qxZkCQJffv2RaNGjXD06FEkJSXB398fx44dg6ura5VqycjIgEqlQnp6OjtnExER6SEi7gFGfxsKC6UCoSFPwNXOss5r0Pf6bTLPVsvIyMCpU6fKLE9ISEBCQoLu3/n5+aXWv/nmm+jQoQOWLl2KsLAwZGdnw8fHByEhIQgJCalwgkgiIiKqOV18nNDJ2xHn49Ow7mQcXn+ypdwlVchkWo6MCVuOiIiIqm7budt4feM5uNlb4vi7T8DCrG579+h7/a7XfY6IiIjIeAxu7wl3B0ukZOZj18VEucupEMMRERER1QkLMwWmPO4LoLhjtrHevGI4IiIiojozIdAHFmYKXEhIx5nYB3KXUy6GIyIiIqozLnaWGPVY8ShzYx3Wz3BEREREdSq4lx8AYM+lZCSm5cpbTDkYjoiIiKhOtfZwQI9mLlBrBNaciJW7nDIYjoiIiKjOBQf5AQA2hMUhp6BI3mL+huGIiIiI6tyANu7wcbZBem4htpy9LXc5pTAcERERUZ1TKiRM6+kHAFhlZMP6GY6IiIhIFuMCvGBrocT1u1k4diNV7nJ0GI6IiIhIFg5W5hgX4A0A+OlYtMzV/IXhiIiIiGQzracfJAk4eC0Ft1Ky5C4HAMMRERERyaipqy2e8G8EAFgdGiNvMQ8xHBEREZGsgoOaAgB+O5OA9NxCmathOCIiIiKZBbVwQSt3O+QUqPHZn1ex7dxtnLh5D2qNPCPYzGQ5KhEREdFDkiShm58zou5k4eeTcfj5ZBwAwFNlhfnD2mJQe886rYctR0RERCSrPZFJWH8qrszy5PQ8/PPnCOyJTKrTehiOiIiISDZqjcDCHZdR3g007bKFOy7X6S02hiMiIiKSTVj0fSSl51W4XgBISs9DWPT9OquJ4YiIiIhkczez4mBkyHY1geGIiIiIZNPI3qpGt6sJDEdEREQkm8CmzvBUWUGqYL2E4lFrgU2d66wmhiMiIiKSjVIhYf6wtgBQJiBp/z1/WFsoFRXFp5rHcERERESyGtTeE99N7gIPVelbZx4qK3w3uUudz3PESSCJiIhIdoPae2JgWw+ERd/H3cw8NLIvvpVWly1GWgxHREREZBSUCgk9mrvIXQZvqxERERGVxHBEREREVALDEREREVEJDEdEREREJTAcEREREZXAcERERERUAsMRERERUQkMR0REREQlMBwRERERlcAZsg0ghAAAZGRkyFwJERER6Ut73dZexyvCcGSAzMxMAIC3t7fMlRAREVFVZWZmQqVSVbheEpXFJypDo9EgMTER9vb2kKSaeyBeRkYGvL29ER8fDwcHhxp7X6o7PIemj+fQ9PEcmrbaPH9CCGRmZqJx48ZQKCruWcSWIwMoFAp4eXnV2vs7ODjw/9AmjufQ9PEcmj6eQ9NWW+fvUS1GWuyQTURERFQCwxERERFRCQxHRsTS0hLz58+HpaWl3KWQgXgOTR/PoenjOTRtxnD+2CGbiIiIqAS2HBERERGVwHBEREREVALDEREREVEJDEd14Nq1a1i+fDmmT5+ODh06wMzMDJIk4aOPPqp03/3792PIkCFwdXWFtbU1Wrdujffffx9ZWVl1UDkVFhbiwIEDePvtt9GtWzc4OjrC3NwcHh4eGD58OHbt2vXI/Xn+jMO6deswdepUdOrUCY0aNYK5uTlUKhUCAwOxePHiR54PnkPj9M4770CSpEp/l/L8GY/p06frzllFr7y8vHL3PXPmDMaNGwd3d3dYWVmhadOmePXVV3H37t3aKVZQrXv99dcFgDKvRYsWPXK/ZcuWCQBCkiTRp08fMW7cOOHh4SEACH9/f5GSklJHn6Dh2rdvn+58eXh4iKFDh4pnn31WtG/fXrf8hRdeEBqNpsy+PH/GIygoSEiSJNq2bSuefvppMWHCBPHEE08Ia2trAUC0aNFC3L59u8x+PIfG6fjx40KhUAhJkh75u5Tnz7hMmzZNABBBQUFi2rRp5b4KCgrK7Pfbb78JMzMzAUB069ZNPPvss6JZs2YCgHB3dxfXr1+v8VoZjurAf//7X/HWW2+JdevWiStXrogpU6ZUGo4iIiKEJElCqVSKP/74Q7c8OztbDBgwQAAQY8aMqYvyG7QDBw6IMWPGiCNHjpRZt3HjRqFUKgUAsXr16lLreP6My8mTJ8W9e/fKLE9NTRW9evUSAMT48eNLreM5NE7Z2dmiZcuWokmTJmLkyJEV/i7l+TM+2nC0cuVKvfe5ffu2sLGxEQDE999/r1teVFQkJk+erAtM5f2BWh0MRzLQfkEeFY7GjRsnAIjnn3++zLqYmBihUCgEAHHlypXaLJUqMXPmTAFADBgwoNRynj/TceTIEQFAODs7l1rOc2icXnvtNQFA7Nq165G/S3n+jI8h4ejtt98WAMSTTz5ZZl1mZqZQqVQCgNizZ08NVioE+xwZoYKCAl1flokTJ5ZZ7+vri6CgIADAli1b6rQ2Kq1z584AgPj4eN0ynj/TYmZW/IjJkhPO8Rwap0OHDmH58uWYOnUqhgwZUuF2PH/1h/b8lHce7ezsMHz4cADA77//XqPHZTgyQlFRUcjJyQEABAQElLuNdvnZs2frrC4q6/r16wAAT09P3TKeP9ORmZmJBQsWAIDulyzAc2iMsrKyMGPGDLi7u+OLL7545LY8f8bt4MGDmD17Nl544QWEhIRgy5YtyM/PL7NdZmYmbty4AaDuz6NZjb4b1Yjo6GgAgKOjI+zt7cvdxtvbu9S2VPeSk5OxatUqAMCYMWN0y3n+jNfevXuxfv16aDQa3LlzBydOnEBmZiYGDRqETz/9VLcdz6HxeeuttxAdHY0tW7bAycnpkdvy/Bm3NWvWlFnm6emJn376CYMGDdIti4mJ0f23j49Pue9VW+eRLUdGKDMzEwBga2tb4TZ2dnYAgIyMjDqpiUorKirC5MmTkZ6ejg4dOuDFF1/UreP5M16XL1/G6tWrsXbtWuzduxeZmZmYOHEiVq1aBZVKpduO59C47N27F99//z3Gjx+PkSNHVro9z59x6tSpE7788ktERkYiIyMDd+7cwd69e9GzZ08kJSVh+PDhOHTokG577XkEKj6XtXUeGY6IDPDSSy/hwIEDcHFxwaZNm2BhYSF3SaSHN954A0IIFBQU4MaNG1i6dCl2796Ntm3b4siRI3KXR+VIT0/HzJkz4ebmhuXLl8tdDlXDm2++iddeew3t2rWDvb09GjVqhIEDB+LYsWMYMWIECgsL8cYbb8hdJgCGI6OkbQbOzs6ucBvtBGYODg51UhP95fXXX8eKFSvg5OSEffv2oVWrVqXW8/wZP3NzczRv3hyzZs3C7t278eDBA0yePBm5ubkAeA6NyRtvvIGEhAR8/fXXcHV11Wsfnj/TIkkSFi5cCAA4f/68boBLyVuiFZ3L2jqPDEdGyM/PDwCQlpZWqlmxJO2XR7st1Y3Zs2fjq6++gqOjI/bu3asbrVYSz59p6d69O9q2bYv4+HiEh4cD4Dk0Jlu2bIGZmRm+/fZb9OvXr9Rrz549AIAVK1agX79+GD9+PACeP1PUpk0b3X8nJCQAKB5VqBUXF1fufrV1HhmOjJC/vz9sbGwAQPfL+u+0y7t06VJndTV077zzDpYtWwaVSoW9e/dWOHqC58/0aPszaB9FwHNoXIqKinD48OEyrzt37gAo7rh7+PBhnDx5EgDPnym6d++e7r+1LUYODg5o0aIFgLo/jwxHRsjCwgJDhw4FAKxfv77M+tjYWISGhgIARo0aVae1NVRz5szBZ599BpVKhX379qFbt24VbsvzZ1pSU1Nx/vx5ANDdIuU5NB5paWkQxRMWl3lNmzYNALBo0SIIIXSjm3j+TM/GjRsBFAcif39/3XLt+SnvPGZlZWHHjh0AgNGjR9dsQTU6pSTpRZ8Zss+cOaOb+n737t265Zz6vu69//77AoBwdHQUYWFheu3D82c8Ll26JH7++WeRm5tbZt21a9dEv379BADx+OOPl1rHc2j8HvW7lOfPuJw9e1Zs27ZNFBYWllquVqvFjz/+KKysrAQAMXfu3FLrSz4+5IcfftAtLyoq0j2KqzYeHyIJIUTNxi36u4iICLz88su6f9+8eROpqanw8vJCkyZNdMu3bNlSajLBzz//HLNmzYIkSejbty8aNWqEo0ePIikpCf7+/jh27JjeHRTJMNu3b8eIESMAFE821q5du3K3c3V1xb///e9Sy3j+jMOhQ4fQv39/2NraonPnzvDy8kJBQQHi4uIQEREBjUaDNm3aYM+ePWXmUuE5NG7Tp0/H6tWrsWjRIsydO7fMep4/47F161aMGjUKTk5O6NKlC9zd3ZGWlobIyEhdf6IJEyZgzZo1ulnrtX777TdMmDABarUa3bt3h5+fH06fPo1bt27B3d0dx44d091+qzE1GrWoXAcPHtQ9wf1Rr+jo6DL77tu3TwwaNEg4OzsLS0tL0bJlSxESEiIyMjLq/oM0QCtXrtTr3Pn6+pa7P8+f/O7evSv+7//+TwwaNEj4+fkJW1tbYWFhITw8PMTAgQPFd999J/Ly8ircn+fQeOnTCs/zZxxu3bol3njjDdGrVy/RpEkTYWVlJSwtLYWPj48YO3as2LVr1yP3Dw8PF6NHjxZubm7CwsJC+Pr6ildeeUUkJyfXSr1sOSIiIiIqgR2yiYiIiEpgOCIiIiIqgeGIiIiIqASGIyIiIqISGI6IiIiISmA4IiIiIiqB4YiIiIioBIYjIiIiohIYjoiIiIhKYDgiqgULFiyAJEno16+f3KVQNfFc1h/9+vWDJElYsGCB3KWQkWM4onrhwYMHsLa2hiRJkCQJ169fr5XjnDt3DgsWLMAXX3xRK+8vp0OHDul+focOHZK7HKoB06dPhyRJ8PPzK7OuPn2Xt27digULFmDr1q1yl0L1BMMR1Qvr1q1DXl6e7t8//fRTrRzn3LlzWLhwYaUXFFdXV/j7+5d5yjuZnvp6LvX9LpuCrVu3YuHChZWGIx8fH/j7+8PV1bVuCiOTxXBE9cKKFSsAAK+++ioAYPXq1VCr1bLV869//QtXr17FmjVrZKuBagbPZf2xZs0aXL16Ff/617/kLoWMHMMRmbyIiAicO3cOjo6OWLJkCZo2bYqkpCT88ccfcpdGREQmiOGITJ621ei5556DlZUVpk6dCkD/W2t79+7F+PHj4evrC2trazg7O6Njx4549dVXceLECd12kiQhODgYABAbG6vrn6N9lezkWV4n3sLCQri6ukKSJHz11VePrOmnn36CJElwcHBATk5OmfWRkZF44YUX0LJlS9jY2MDOzg4dO3bE+++/j9TUVL0+d007fvw4Jk+eDF9fX1hZWUGlUiEwMBCffvopsrKyyt0nJycHGzZswNSpU/HYY4/Bzc0NlpaWaNy4MUaOHIndu3dXeLxVq1aV6k9z8OBBjBw5Ep6enlAqlZg+fTqAsufiwIEDGDp0KNzc3GBlZYU2bdpg4cKFpW7LlvSoDtnaPj3aY23atAn9+vWDs7MzbGxs8Nhjj+HLL7+ERqOp8HMIIbBy5Ur06NED9vb2UKlU6N69O3744QcIIcocoyZU5buslZKSgrlz56Jz585QqVSwsrJCs2bNMHPmTFy6dKnc45TsxwYAZ8+exaRJk+Dl5QVzc/NSP9Pk5GQsX74cI0aMQJs2baBSqWBtbY0WLVrg+eefL/cY2vdfvXo1gOIW479/lpL95/TpkP3777/jmWeegbu7OywsLODu7o5nnnkGW7ZsqXCfmvgekJERRCYsNzdXODo6CgDi+PHjQgghbt68KSRJEmZmZiI5ObnCfbOzs8W4ceMEAN3L3t5eqFQq3b87deqk297d3V04ODgIAEKhUAh3d/dSr88++0y37fz58wUA0bdv31LHfOWVVwQAERAQ8MjP1a9fPwFATJ8+vcy6Tz/9VCgUCl2NNjY2wsLCQvdvT09PERERocdPr7SDBw/q3uPgwYN676dWq8Vrr71W6udoZ2cnlEql7t/+/v4iJiamzL4rV67UbSNJklCpVMLGxqbUe82ePbvc42r39fX1FV988YWQJEkAECqVSpibm4tp06YJIUqfiyVLlghJkoQkScLR0VG3DwDRv39/UVRUVOY4FZ1LIYSYNm2aACCmTZumO7cKhUL3ndS+pk6dWu5nKCoqEs8991ypn4GTk5Pu/E6YMKHUMapKu6+vr2+p5VX5LgshxL59+0p9JnNzc2Fra6v7t4WFhVi9enWZ45f8Tm3atEmYm5sLAMLBwUFYWVmV+plqawUgzMzMhLOzszAzM9Mts7S0FJs2bSr1/sePHxfu7u7CyspKABBWVlZlPov294IQQvTt21cAEPPnzy9Ta35+fqlzoVAoSp0L7fkoKCio8Ods6PeAjA/DEZm0n3/+WQAQLVq0KLW8d+/eAoBYsmRJhfs+++yzul9i7777roiPj9etS0lJEevWrRMvvfRSqX1KXpAfpaIL6qlTp3S/KK9cuVLuvrGxsbqL9v/+979S63788Udd+Pi///s/kZSUJIQovsiGh4eLJ554QgAQXl5eIjMz85E1/p2h4Wju3LkCgGjUqJH45ptvxL1794QQQhQUFIiDBw+Kzp07CwCiS5cuQq1Wl9p369at4q233hLHjh0T2dnZuuWJiYli4cKFuovptm3byhxXey6srKyEUqkU06dPF3Fxcbqfx40bN4QQf50LR0dHoVAoREhIiEhJSRFCCJGeni4++OAD3edesWJFmePoE46cnJyEhYWFWLZsmUhPTxdCCJGamiqef/553XsfOHCgzP6LFy/WrZ81a5ZITU3V1fXxxx/rwlJNh6OSP7/KvssXLlwQ1tbWAoD4xz/+IS5fvqwLkbGxseLll1/WBZrTp0+X2rfkd8rOzk4MGTKk1Pc+KipK99+LFi0Sn332mbh48aIoLCwUQhQH78jISDFp0iQBQNja2orbt29X+Dkr+xk9KhzNnj1bF1DnzZsnHjx4IIQQ4v79++K9997TfY533323wuMb+j0g48NwRCatf//+AoD48MMPSy3/73//KwCI1q1bl7vf/v37db+svv32W72PV91wJIQQ/v7+AoAICQkpd9+PP/5YABA+Pj5Co9HolmdkZOj+Et2zZ0+5+xYWFoquXbsKAOLzzz/X92MJIQwLR9HR0UKpVApra2tx7ty5crfJyMgQXl5eAoDYsmVLlWr67LPPBAAxYMCAMutKtjqNHj26wvfQnouKLopCCDF69GgBQDz55JMV7v+ocARArFy5stz31p6P559/vtTyrKwsXevNzJkzK61drnCkDdwVfV+FELqWwxEjRpRaXvI7FRgYWG7LnL6GDh0qAIhFixaVWVfdcJSQkKBrparoc86aNUvXapaYmFju8Q35HpBxYp8jMlm3bt3S9TmYMmVKqXXPPvssrK2tcfXqVYSGhpbZV9sfqX379vjnP/9ZJ/VqaWtdt24dhBBl1q9duxYAMGnSJF1fDQDYvHkz0tLS0LlzZzz99NPlvreZmRkmTJgAAPjzzz9ruvQyVq1aBbVajUGDBqFTp07lbmNvb4+RI0caVNPQoUMBACdOnHjk6MOQkJBK38vS0hJvvfVWuetGjBgBALhw4UKV6tPy9vbGtGnTyl03fPjwct977969yMjIAAC8//775e47e/Zs2NjYGFRTTYiJicH//vc/mJmZVfizA6Dr57d///4Kz9Pbb78NpVJpcC3a78KxY8cMfo+KbN68GUVFRbCyssKcOXPK3Wbu3LmwtLREYWEhNm3aVO42hnwPyDiZyV0AkaFWrlwJIQT69OlTZpI7BwcHjBw5Ehs2bMCKFSvQs2fPUuu1gemZZ56pq3J1pkyZgnnz5iEuLg6HDx8u1Sn1zJkzuHLlCoC/Ljhax48fBwBcuXIFHh4eFb5/bm4ugOKOtrVNW9PevXsfWZO2Q3Z5Nd25cwfffvst9u7di6ioKKSnp5e5wObk5ODBgwflzk9jbW2NLl26VFpru3btYGdnV+66xo0bAwDu379f6fuUp1u3bqWCrD7vHRERAaB47p2mTZuWu6+9vT26du2Ko0ePGlRXdWnPr0ajQdu2bSvcTnu+srOzce/ePTRq1KjMNkFBQZUe7/z58/j+++9x7NgxxMTEICsrq8wfEAkJCVX5CHoJDw8HUHweHRwcyt3GyckJAQEBOH78uG77vzPke0DGieGITJJGo8GqVasAlA0RWtOmTcOGDRvw66+/4ssvvyx1YUxOTgYA+Pr61nqtf+fj44O+ffvi0KFDWLt2balwpG016tatG1q3bl1qv8TERABAXl5ehSOrSipvlFtN09aUnZ2N7OzsSrf/e00nTpzAkCFDkJaWpltmZ2cHGxsbSJIEtVqtG32XnZ1dbjhycXGBQlF5I7i9vX2F68zMin8VFhUVVfo+hr53YWFhqeUpKSkA/rpoVqRJkyYG1VQTtOdXo9Hgzp07eu1T0feuvMBU0tdff43XX39dN6JLkiSoVCpYWloCKA79GRkZen3Pquru3bsAKv9Ze3l5ldr+7wz5HpBx4m01Mkl//vmn7i/I559/vszwXUmSMGjQIADFrRa//vprqf0r+uuurmgD3aZNm3QtPUVFRdiwYQMAlLlNCPz11/lzzz0HUdxf8JGvmJiYWv8c2preffddvWoqOay6qKgIEyZMQFpaGh577DH88ccfyMjIQGZmJu7cuYPk5GScPHlSt315tyABVOtWjTGQ+7v4KNrz6+7urtf5FUKU+6gS4NHn6cqVK3jjjTeg0Wgwbtw4hIWFIS8vDw8ePEBycjKSk5OxbNkyABV/D4hqEsMRmSTt3EaGbq+9BVQXt57KM3bsWFhbWyMjIwPbtm0DUHxr6u7duzA3N9f1GypJ7prLU52aTpw4gdjYWCiVSuzcuRODBw8u85e3toWvPnJzcwPwV+tMRW7fvl0X5ZRLe35TU1NrpcVGa9OmTVCr1WjTpg02btyIbt26wcLCotQ2tfld0LZqVXbLTru+slYwMn0MR2RyUlJSsH37dgDFv1QzMzMrfIWFhQEo7mN07do13Xto+yDt2LGjSsfW3r6p7l+vJTspa2+laf938ODB5d4+0vbZOHPmDJKSkqp1/JqirWn//v163eorKT4+HkBxSKjodsb+/furV6AR0/aTio2NrbCVLysrC2fOnKmV4+vzXdaeX7Va/cgJOatL+13o1KlThbdIH/VdqO7/LwMCAgAU9z1KT08vd5u0tLRSfZOofmM4IpOzdu1aFBYWQqVSYdiwYbCzs6vwVbLvTsnWo5kzZwIALl26hO+++07vY2s7a5bsI2Mo7a21vXv34vr167oWpIr6UI0bNw6Ojo4oLCzErFmzHnkh0Gg0NVJjZWbMmAEzMzOkpqZi/vz5j9y2oKCg1EzZKpUKQHGH7PL6syQkJFQ6k7gpe+qpp3Tfp48//rjcbT7//PNa6zumz3e5ZcuWuj5x77//foXBQcvQzsba78LFixfL/V7v3r271C3Zv6vu/y/HjBkDMzMz5OXl4dNPPy13m48//hj5+fkwNzfHmDFjDDoOmQ6GIzI52pAzYsSIMk3v5Rk3bhyA4odOajvc9u/fH+PHjwdQ/GDRkJCQUk3qqamp+PHHH3UhSqt9+/YAgIyMjDL9mKpq4MCB8PDwQFFRESZOnIjc3Fw4OTlVOILO0dFR9wT1jRs3YujQoTh16pSuA6tGo8GVK1ewdOlStGvXDjt37jS4tvT0dKSmpj7yJYRA8+bNMW/ePADAkiVLMHXqVERGRurep6ioCOfOncOHH36IFi1a4Ny5c7p1vXr1gq2tLYQQePbZZxEVFQWguJXizz//1D3qob6ytbXFu+++CwD473//i3feeUcXLjIzM/Hpp59iwYIFcHJyqpXj6/tdXr58Oezs7BAVFYXHH38c27ZtK9VKePv2baxduxYDBgzQfZ6q0vYPvHTpEl555RXdzyE7Oxvff/89xo4dCxcXl0o/y9GjR3H16tUqH79JkyZ4/fXXAQCffPIJ5s+frwtaaWlpmDdvHj777DMAwKxZs+Dp6VnlY5CJqb0plIhq3okTJ3STre3YsUOvfS5cuKDbZ+vWrbrl2dnZusn/tC8HB4cKHx+iNWDAAN16e3t74evrK3x9fUtNuvioiQNL0k4sp329+OKLlX6e7777rtTjQiwtLYWLi4tuNmnt6+eff9br56NVcsI+fV7aGYQ1Go2YN29eqUdxWFtbCxcXl1KPEAEgjh07VuazlFxvZ2enexSEq6ur2L59u25ddHR0qX1rYkLO8j57VfbXZ/LBR9VZWFgoxo4dqzu29pEV2p/blClTxNSpU/X+blRUX0U/I32+y0IIcezYMeHh4aHbVqlUChcXF93M2drX3yc4fNTP9e/Gjx9f6r0cHR11P4euXbuK5cuXV/hZ7t+/L9zc3HT7urq66j7LiRMndNtV9vgQ7az5Jc9FVR8fUhF9v69kHNhyRCZF22qkUqnw1FNP6bVPhw4d0KZNm1L7A4CNjQ02b96MnTt3YtSoUWjcuDHy8vJgZmaGjh074rXXXsMPP/xQ5v02bdqEN998E61atUJhYSFiY2MRGxtrUJP+32+hVXRLraSXXnoJ165dw1tvvYVOnTrB0tISaWlpsLOzQ0BAAF599VXs27ev3E7dtUGSJHz44Ye4cOECXn75ZbRp0wZKpRLp6elwcnJCz5498fbbbyM0NLTMXDcvvfQSdu3ahX79+sHOzg5FRUVo0qQJXn31VZw/fx4dOnSok88gFzMzM/z666/48ccfERgYCGtraxQVFSEgIAA//vgj1qxZo/teOTo61vjx9f0uBwUFISoqCv/+97/Rp08fODo6Ii0tDUqlEm3atMHkyZOxbt06XcumIbT7d+zYEZaWllCr1ejQoQMWL16M48ePVzhHFVA8B9GRI0cwfvx4NGnSBOnp6brPom9fOAsLC/zyyy/YtGkTBg8eDBcXF2RmZsLFxQWDBw/G77//jvXr18Pc3Nzgz0imQxKC4yKJiIyREAI+Pj5ISEjAmjVryp3igYhqHluOiIiM1Nq1a5GQkAAzMzM8+eSTcpdD1GAwHBERyWjChAnYtGmTbiZwoHgE3yeffIJ//OMfAIpvt7ITMFHd4W01IiIZOTo66obI29jYwNzcvNSQ+d69e2Pnzp0VPvOLiGoewxERkYzWrFmD3bt34+zZs7h79y6ysrLg6OiIxx57DOPHj8eUKVPYCZiojjEcEREREZXAPkdEREREJTAcEREREZXAcERERERUAsMRERERUQkMR0REREQlMBwRERERlcBwRERERFQCwxERERFRCf8PQ3a8G+oGAWAAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(batches, kl_divergence, marker='o')\n", "plt.xlabel(\"Active Learning Iteration\", fontsize=18)\n", "plt.ylabel(\"KL Divergence\", fontsize=18)\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "py310", "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": "3.14.2" } }, "nbformat": 4, "nbformat_minor": 5 }