seminars/seminar8/seminar8.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4c67dc94-3fad-4c53-8ead-8bcc5a642b8a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from time import time\n",
    "\n",
    "import torch\n",
    "import torch.optim as optim\n",
    "import torch.nn as nn\n",
    "import torch.utils.data as Tdata\n",
    "import torch.nn.functional as F\n",
    "import torch.distributions as TD\n",
    "\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.stats import norm\n",
    "\n",
    "#TODO: adapt for colab users\n",
    "import sys\n",
    "sys.path.append('../../homeworks') # to grab dgm_utils from ../../homeworks directory\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "if torch.cuda.is_available():\n",
    "    DEVICE = 'cuda'\n",
    "    GPU_DEVICE = 0\n",
    "    torch.cuda.set_device(GPU_DEVICE)\n",
    "else:\n",
    "    DEVICE='cpu'\n",
    "# DEVICE='cpu'\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "# dgm_utils\n",
    "from dgm_utils import train_model, show_samples, visualize_images\n",
    "from dgm_utils import visualize_2d_samples, visualize_2d_densities, visualize_2d_data\n",
    "\n",
    "def reset_seed():\n",
    "    OUTPUT_SEED = 0xBADBEEF\n",
    "    torch.manual_seed(OUTPUT_SEED)\n",
    "    np.random.seed(OUTPUT_SEED)\n",
    "\n",
    "reset_seed()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "amber-humidity",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# <center>Deep Generative Models</center>\n",
    "## <center>Seminar 8</center>\n",
    "\n",
    "<center><img src=\"pics/AIMastersLogo.png\" width=600 /></center>\n",
    "<center>03.04.2024</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8fd6b3c-d0f7-40ba-a31c-bc01f618e1ad",
   "metadata": {},
   "source": [
    "## Plan\n",
    "\n",
    "1. Forwar KL vs Reverse KL vs JSD \n",
    "    - Mode collapse\n",
    "    \n",
    "\n",
    "---\n",
    "\n",
    "2. Vanilla GAN on 1D and 2D multimodal data\n",
    "    - Non-saturating GAN"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "consolidated-filing",
   "metadata": {},
   "source": [
    "# Forward KL vs Reverse KL vs JSD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "quiet-kenya",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "X = torch.from_numpy(np.linspace(-6,6,500)).double()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "differential-directory",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "single_gaussian = TD.Normal(torch.tensor(0.), torch.tensor(1.))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "statistical-montgomery",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plt.plot(X.numpy(), single_gaussian.log_prob(X).exp().numpy())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "frequent-attempt",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# make mixture of gaussians with \n",
    "# means: (-2, 2)\n",
    "# stds: (0.5, 0.5)\n",
    "# mixture probabilities (0.8, 0.2)\n",
    "\n",
    "#YOUR CODE\n",
    "means = torch.tensor([-2., 2.])\n",
    "stds = torch.tensor([0.5, 0.5])\n",
    "probas = torch.tensor([0.8, 0.2])\n",
    "\n",
    "mixture_gaussian = TD.MixtureSameFamily(mixture_distribution=TD.Categorical(probas),\n",
    "                                        component_distribution=TD.Normal(means, stds))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "southern-kinase",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def plot_distributions(X, real_log_prob, model_log_prob=None, title=None, figsize=None, savepath=None):\n",
    "    with torch.no_grad():\n",
    "        res1 = real_log_prob(X).exp()\n",
    "        if model_log_prob is not None:\n",
    "            res2 = model_log_prob(X).exp()\n",
    "\n",
    "    if figsize is None:\n",
    "        figsize = (5, 5)\n",
    "    plt.figure(figsize=figsize)    \n",
    "    plt.plot(X.numpy(), res1.numpy(), color='b', linewidth=3, label=r'$\\pi(\\mathbf{x})$')\n",
    "    plt.fill_between(X.numpy(), np.zeros_like(X.numpy()), res1.numpy(),  color='b', alpha=0.2)\n",
    "    if model_log_prob is not None:\n",
    "        plt.plot(X.numpy(), res2.numpy(), 'g', linewidth=3, label=r'$p(\\mathbf{x} | \\mu, \\sigma)$')\n",
    "        plt.fill_between(X.numpy(), np.zeros_like(X.numpy()), res2.numpy(),  color='g', alpha=0.2)\n",
    "    if title is not None:\n",
    "        plt.title(title, fontsize=20)\n",
    "    plt.legend(fontsize=20)\n",
    "    plt.xticks(fontsize=20)\n",
    "    plt.yticks(fontsize=20)\n",
    "    if savepath is not None:\n",
    "        plt.savefig(savepath)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "closing-feedback",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plot_distributions(X, single_gaussian.log_prob, title='single gaussian')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "novel-circumstances",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plot_distributions(X, mixture_gaussian.log_prob, title='mixture of gaussian')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "final-outside",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plot_distributions(X, mixture_gaussian.log_prob, single_gaussian.log_prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "36f6a462",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "double-graph",
   "metadata": {},
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\" width=800 height=800 />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "binary-weight",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def KLD(X, log_prob1, log_prob2):\n",
    "    # p and q return log pdf\n",
    "    # X - some linspace\n",
    "    return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "otherwise-appreciation",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def JSD(X, log_prob1, log_prob2):\n",
    "    \n",
    "    def log_prob_mean(x):\n",
    "        prob_mean = (log_prob1(x).exp() + log_prob2(x).exp()) / 2\n",
    "        return prob_mean.log()\n",
    "    \n",
    "    return (KLD(X, log_prob1, log_prob_mean) + KLD(X, log_prob2, log_prob_mean)) / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "successful-marking",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "forward_KL_loss_fn = lambda X, real_log_prob, model_log_prob: KLD(X, real_log_prob, model_log_prob)\n",
    "reverse_KL_loss_fn = lambda X, real_log_prob, model_log_prob: KLD(X, model_log_prob, real_log_prob)\n",
    "JSD_loss_fn = lambda X, real_log_prob, model_log_prob: JSD(X, real_log_prob, model_log_prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "passive-neighbor",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "mu_start = -1\n",
    "sigma_start = 0.5\n",
    "\n",
    "# define trainable params\n",
    "mu = torch.tensor(mu_start, requires_grad=True, dtype=torch.double)\n",
    "sigma = torch.tensor(sigma_start, requires_grad=True, dtype=torch.double)\n",
    "single_gaussian = TD.Normal(mu, sigma)\n",
    "\n",
    "plot_distributions(X, mixture_gaussian.log_prob, single_gaussian.log_prob)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "alternate-fossil",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def solve_task(optimizer, loss_fn, real_log_prob, model_log_prob, n_iters):\n",
    "    for it in range(n_iters):\n",
    "        optimizer.zero_grad()\n",
    "\n",
    "        loss = loss_fn(X, real_log_prob, model_log_prob)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "\n",
    "        if it % 5 == 0: \n",
    "            plot_distributions(X, mixture_gaussian.log_prob,\n",
    "                               single_gaussian.log_prob, title=f'step: {it}, loss: {loss:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28dcf9ca-cea1-43a1-88d7-30917f4aa206",
   "metadata": {},
   "source": [
    "### Forward KL optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "active-interim",
   "metadata": {
    "scrolled": false,
    "tags": []
   },
   "outputs": [],
   "source": [
    "N_ITERS = 50\n",
    "LEARNING_RATE = 0.1\n",
    "\n",
    "mu_start = -1\n",
    "sigma_start = 0.5\n",
    "\n",
    "mu = torch.tensor(mu_start, requires_grad=True, dtype=torch.double)\n",
    "sigma = torch.tensor(sigma_start, requires_grad=True, dtype=torch.double)\n",
    "single_gaussian = TD.Normal(mu, sigma)\n",
    "\n",
    "optimizer = torch.optim.SGD([mu, sigma], lr=LEARNING_RATE)\n",
    "\n",
    "solve_task(optimizer, forward_KL_loss_fn, mixture_gaussian.log_prob, single_gaussian.log_prob, N_ITERS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "killing-retreat",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plot_distributions(\n",
    "    X, \n",
    "    mixture_gaussian.log_prob, \n",
    "    single_gaussian.log_prob, \n",
    "    title='forward KL', \n",
    "    #savepath='forward_KL.png'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0515f063-ed8c-42cd-a53b-9ba4ef35b628",
   "metadata": {},
   "source": [
    "### Reverse KL optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "mineral-recipe",
   "metadata": {
    "scrolled": false,
    "tags": []
   },
   "outputs": [],
   "source": [
    "N_ITERS = 50\n",
    "LEARNING_RATE = 0.1\n",
    "\n",
    "mu_start = -1\n",
    "sigma_start = 0.5\n",
    "\n",
    "mu = torch.tensor(mu_start, requires_grad=True, dtype=torch.double)\n",
    "sigma = torch.tensor(sigma_start, requires_grad=True, dtype=torch.double)\n",
    "single_gaussian = TD.Normal(mu, sigma)\n",
    "\n",
    "optimizer = torch.optim.SGD([mu, sigma], lr=LEARNING_RATE)\n",
    "\n",
    "solve_task(optimizer, reverse_KL_loss_fn, mixture_gaussian.log_prob, single_gaussian.log_prob, N_ITERS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "trained-metropolitan",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "plot_distributions(\n",
    "    X, \n",
    "    mixture_gaussian.log_prob, \n",
    "    single_gaussian.log_prob, \n",
    "    title='reverse KL', \n",
    "    #savepath='reverse_KL.png'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "saved-disabled",
   "metadata": {},
   "source": [
    "### Jensen Shannon optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "identical-edition",
   "metadata": {
    "scrolled": false,
    "tags": []
   },
   "outputs": [],
   "source": [
    "N_ITERS = 50\n",
    "LEARNING_RATE = 0.1\n",
    "\n",
    "mu_start = -1\n",
    "sigma_start = 0.5\n",
    "\n",
    "mu = torch.tensor(mu_start, requires_grad=True, dtype=torch.double)\n",
    "sigma = torch.tensor(sigma_start, requires_grad=True, dtype=torch.double)\n",
    "single_gaussian = TD.Normal(mu, sigma)\n",
    "\n",
    "optimizer = torch.optim.SGD([mu, sigma], lr=LEARNING_RATE)\n",
    "\n",
    "solve_task(optimizer, JSD_loss_fn, mixture_gaussian.log_prob, single_gaussian.log_prob, N_ITERS)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "streaming-advance",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "plot_distributions(\n",
    "    X, \n",
    "    mixture_gaussian.log_prob, \n",
    "    single_gaussian.log_prob, \n",
    "    title='JSD', \n",
    "    #savepath='JSD.png'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "systematic-alarm",
   "metadata": {},
   "source": [
    "# Vanilla GAN"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "advanced-national",
   "metadata": {},
   "source": [
    "<img 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gErBgSG2FNoxZrc5qwIwXfS1V1NW0613lTPEB8W4G/wClY+pCqCCOCqhhvgcjZKVa8dAI49fS0pWRxB9s0Mxb1KLraFqihefV7l2b0dBHM0qSjJB1+vytg6prHQavHHlb9raBEZbYUu1z1ravUgc/499jMHsZx7hP/wA9gWRxLYuRPFnd0MsQysWsTRFyMC0Sk0fvdqzr8pYMFiHrWveiC+8iRu92qWvSlE8fAmsoY4ilYtbaTG1bTyxP6Og9UY+m616MLnyrY0ccmsTB+92rOvylEIbAYfNn/wBhH2mq/YMfdjrPdbBxdLvtrQZxW42T0UiMpactU+KXiJcCnR96dGzGUxFS3xWsuixvGuzzqPPOo8EOwXLksdcdcs8MyOAqYVqRYR2V/jrSo89aW+6A9MskbC1GHrFHtz1U6rj5bpafJbCDR5nbM2UtcsowMi1j0i/3ntH6NmjLKkCcLF/FXufa/tav9PNp/TZ9rqn2bX3OzaTEuYVt8rdf9FFX3sS0BmYcJG73apa9KUZp6LVdy5kppXF+NA/6WIlEbviYa5SVZ+GTo8X654UlksqZUwStR4q0+Qbo69OLZqDlgCnWSWUGa72yZJWZXDEvfq1IGVwTdVFnUMhM7tYgmAe6TSZZERFRsap62WPIWeKlSWtbwTX5jNeD6/bS26HhMRlQihrgXJTNQWzV1sYeWuJRmt/wy0TIIFSudbxmqgxj5a4sjau7SZeNkMBootJLvSsTaQh8ig2JTamFYNsVSoKS8Fwoyy4vDwCCzV1sYeWuJxEHwIJxsrmxnZHt0p101o5Kud7lgvqYj+UNcVrVtS2hilneXejONpFG7kDyUsO0FaTWXhZPD3mfyo1+fmTdPFlFcNcIH8bNHA23C931K1WF3DKfEBazd1gOF1jIenXTh+L1xwxTgjwyrXx8jqD8W/iXobLvMhFgXl4ONf8A8wRVm4ZSDJcFYrnN63WzYxtphfRFMwDyuW3C3Bq5jNnC2bKmGOzDjdZNlyce1UnWzW0GLJktmymZ1lihkXStEkCAsWzAsZKZFEsVUWNXlricSFE5B2KmxMBRoCC/wYwOs4aC5uLipLbaV/2RAty9rjPXjoMHvbMcYxHHh6vE/wDvpzK0Zt9V0wtXDVy7VX7ZqXMFeIRK9cpY3MMfAsZXGkfx6c41w/EofbjsAtlx7MddEXYBiLzjawBrdiDr4CfQwpPaDrsCPxybzjq14978OmZ7gcCwZ+PeQwYVAVpG9AI2Ca/C52YbtDkVFUX7GHVeWbSc96DnI4Nwz6i8g9sOvzRsI9t9lmKqvxEH3Az8IjH4mD7zvY9z+Iwe6Ceim3bV9jVnqGt2QaFgR1J9HLJ4rr/EQfcCvwieZ2YPE4TjZWRsItVwDYZhkplSGTW7EuOOdDBWgOBz7OiTkWBQDWljInYBqLwGVDGBjwcS8F2ObdsXoqr+igFhSfi7YR4XDPByYSb0Z2IFhSwiIxpNtPajL+Q2UbM/zx/G9hxPKam0L8N6zGWFPiZS2JmTcwHe5lLXVA1dSnXcdhlAmWX7Qi9hRsGZSQJltIoJN4Qlj9iGbVj/AJhatHGQNoslEapjOkYeZAanXg6qlrOuFez9BviFT0J2GwvJtDGk+ZBHC5lmSPVh4eEPEqs2vYKa8pluevXNVoryLsY8Bbtmz2lru6VKBcdYGEnxb5zwv7PVR4eGZiVT2h9TXlL4idOmoha6Fb+uIZ2yw746oSleGoLnTIi4gpj0ZCidtbLOA06guYQYmbp7DeYABYyOHKbbF6Ks9G1jHXQIXegsXsBGPMxx+M8Yxjmu/fKK8Hu7Ka7Y/wAc2HPUmhco4ubBF8LjcncT2WjMdhzKaJd6Ygx/licXJW89lolHYsymkD+xLnWJsjphUaNVjrCUNIK6mQ02ykfZKoUwvm7BWN/K67ypG7D0XvoiGX21tm7KURtjcMaDAseg6v6UX7wfeirPbiJpFeNddZsTHaMfIGh+OUBO/A0gNcsCuFfZ6t/RYd7teeihCeN1YBvJXVnNuwsnuP8AMZxiUR7rNeKxsESL+gLH/wAuLHwUIAykniK68caNdQA2YmROP2L0ZZ6NrPXEeGyUdlRHxT1jf5fs69nFjnXvvrMWoW89lqng87wAI13iRf41sQt19Fb9b3dEfMnvI1wjno6ufnyNcIdMoRnzs4xjndw7XM1wlnma4Sz1Y6ZRjLkYRhyUIzxiMcY6Orov+21ePWujGMMdXX0SrhPmMdWOj8udXTKEZ8xjGMdXRnGJYjCMOnq6JQjPmI4jiVcJ86sdPV1clXCfMYxjEoRnzGOrnVzOOvka4Q/j2aq5Z/L99jGMf+ATnGuHnS/mHK/PK7IWxtthRUMcMX8d5FQ1Y5dBcfgJMHExTfWRV+2IKpFjjPXj4sEUyulLEIjsxCrhzBys/FZZCmvzpfylkHfPhBFYtC8uZo/QXdYOMEbUcN8ZD2dZ1cszqwVRmz4O8h3hpExRlzjJxfxwLosI5Oca4V2wuh0SLogT8NZdFt9hNNMvgtIpo+jbfVRGMsSjyUsQjQTUVX+8KKuHaCvo55XbC6PS39IRBUnm26wFKELSUTMyjDJYmTyW2SshDkZxn0d/V18xnGeNAvMwkyvKyrtY68zjjPMSjLjlTJnhYF5eDjOM8xOOc8ldXHOJYlh6yuXUqy5Gr+ZuqjnGevHXjr7WOv4Py+Hr6+bV9nV/p6+j8uj8uitVTUz2ayUFYYA1FYi8cLPxbHd3SdUrF8raIh7BdfOmYA3lk9xGOIx6af8AF7L0WWQqh55VPNLOVt3QB7s2Aq3lmtC+D182ZQXQwGMI4khOvYeL/dXxrfdPCh4lighQAG5+fDfd3wq/c5yqk+/nXw8nIYAJGSwWKuplzGOrHxsF9bGmmrFNHXw37HWPSfg6/wBwx9S4NIjFoeSMj9Df0jVvU+bTjHmeZyxp+r2z4Jkc81eoiOw2FhdYdHVa+4yMQDrS7JpHDQrFeuarOUhKrSPOHKjwIyqklwL/AHFTva5yjSPOWdNS1kl2tRMqj5d8Yjr1saNSsiwJ1swfc3qEuCRNkY2C1r9drLBALuVOGt06n61UbM1gsPuc9PkEiJrbLl7voutIdNc67KnO0/Z3123L563judfOtKEEjhycCqyASFXFyUAqyAQNdZnbNlDzXhaskNLXbbLbLLLXbO2qaIjZ7ZViBgnMJdGzzzZfXDu6754qH1SGe5Wf3tpljtRviSgaW3kv2lFWKKNk/tl9F8cMXMc1wj2o9IHuw/8ArtnNd/ox6Vfuni/3V0uLbQm78mVS/XyJ2hL7bDdhxC+7ZWIl6WxhZnydHbnKWmJOwlUo5iFOu9/ETJTcEIsIkUt48YSACFRETqRYsi+fXWVnbCTZG78P1Zg9Al4JWolYHsltlUXspRSgLiWgCG6+pg1vvJasw7lPA12AIazbZbQ2usg/2SydSxiVaNrwScc0SI0xE6QK9gKF36zYHZ10bbUuRxzm11qCpCPdSLVKkX9sZRbe1FQ8poqHh0t/SNYnGDG04WmDEiTdsxp8PreqZ6p5VAN8gxuV7A4jml/G6uVLAuktJqX+/ZfRtT+0X+49p9L1X05t7h2z/UN7L1P7ravUTTbQtcSrRzhx+x5/tv8ApRXV1otrhnxSe+FigjPi9iZ+4uXOQxyui+3FA4mWTmFFOaNs6EUsCNp2QqhtP2bRhJctrAYEVar+RSIJjNdkhY8KQhHzWSIXuxfeO1enUfba1/sWrhbmE9eWVR2nHyNX+not+b3HOerDdhk6YAcQQ1H9vZObCf4mxSVJMw/Pmz/8p4/LlgQ0th8hXcpTA0XdAHux38s7nbGunWIZnnBNMr+hX7p4v91SnGHTsA3iFIt3mjK6/wApc62P3Stb7s2r7E72+mhmzW9XujgedkK+H+7nvoqH0Xm0RziFN0L6E8sT2PYfUDhBTonqJp6mF2SdXTSx5LtH6X/oaX0Vb7ra4ulsWQ2DUqz/AFar9u3nGWy7R6VDFM1ZGs1wirMtLRat6UV7yeUV+e/hxbnEAV/gDUHgaFBUzFn7bqx8RNESRvwnRzGp0dYKkUDhQ8SxVyapfizVqu2vQUhXsVVDKP4VxytOPSuWKK1mTwoMBFi2CymjX6aGDECDEZavgtHJ1+kk9mrrZwrWV1qlietZNkkqZXWrqbl1Wr1wnXrg9RzFdWyGp1aqOSgaDBs6rHGVyQdfMjX6SGHCdfqKP6JRxOEdb7qwVBSKd0MU1DCUdcxOTFZBhSYBUaHXrucRWqq1uJ67iMwEtQVktcxCS5PUBZWshW1ZLosqIR7Fa9ZBfJgnoPnHXsTmyWwY0xx2Y9E9djMr8O4nwMAcGHCv8ftM49usBDQCSyT0suBj+EFJ/wAjtPQaDUdTiluPynLXvugD3YaFUeN+HyJQGGrEHtXV0PuMAMnYxrMYzDH8KMv91bLV3o0MdmHJwxZWsT1LJs09TOdNUaaR1cB2bJdFlTcNi4EAOIIhqKkq8fX4QvuVwuaGC4MECFwEJwkesqiGt9jICapeUcsgdexU1sJfhztyuFruDq1rEOMVkGODRMGhiD4EEHVwHZ30ZdP563KENfMuLFxr2ar469RAliBFiMQvqKAzrk+qhfUMAtXxXDWK4WNjA6TqPw7LGLEQ0ws65KfKKIDUfxxkBBgIu8VgXoLlfEZUu8BT8dgbOhzX2+66IjRwX0m5JiMqCNra5hGWf3hyWgy7KG63ggdIVH/qEybvxX9V0TdSx+K6zFNAtBzqAtU6Rf25BVIleM4lH4FpN1j/AOqUTdHaP4qwJkGBjYrr4GtMAA5atqa8nxysye77tYxgyGs96dE25pRgRjGRZh5/i6XBVBzEqQYFbs0umjZJSjY8ODvMK8OBU8NLpWPJFFP/AFQwusIaLRvdXU5psVVsHJNa8i8kfju4msNEUbEY154FotYlnX3Or7yqXRFBTY6QAGHJ5NNGySuqw8LHM6GbTwPLXZ4eQSDpyy5NMuWtZlXMHcgGd7pkLyoiFwvnBxtqxpIu0154FotYFnXzYNLrlzey4zYyCpVgGsZzZtvBWebsA5mHVBh0OGZGEV3iHvLbI001NGp2FpRZGJMGpFi1vMklwzmtrscsJ1VbBMqoR2R5i1OkvC86PJoUOfMcl+8GbOC2qTVsPAtrUOswa8lWHdYQJ/EHnouu0QqUusXWbDOt7OC+PkyjDu4jmr9ffWe9Oi1cyXGrXVtxZbumghyUQTa99EQRxFKHDGdw2n0w72zrvojqOKn7/wBU2rtdzGD2MBUxGaIZdqalbKLIbjL0zWvRjaIEbefnMFusRhhVs8YZVNJSnqiqOIKUkI/iDaf0R/TxxbELYW5lTeTftVpFUG0V1ADKTg2OJ7hsHonaljTFcG0VwwDHLg2iBG3flix9CV2brrtp2n0yj7bqLs2ckV0WO6rsqDhHEK1HuTl9WL6K6HKjCpvhhCT+M7arbbds2v7aMcRE1SGOy69wbL6Or9KnHFO5l+8G2L7Nmsqe214S22IfGOllYBkDxP4g2pnerUU2DqnCyR0MMXOIFgHGJBzHHh9fCJEsmHfnaejJboWwQU01x3J6pqfQ1Y2NqbL1KimwdUKGRDZdgFuLXsI5hrislkKsXLiyWTkO8hgzAixDpLcB1w84sE8ycxiiX2hD8OhK0BEPaKrsDvztMo4lGIjBKTIRi6IdiWXqQISqXqQyKG+wh3lwx+njW6edgiY0E4AdU4CqqZpZiXNSjCAyJ7O5psIVAC58lprZpZB2tSTLA787RZDvKgfM1PICMrnz4OwxaES2skzXEeMywc3YPWWHKRi3VdSUEwZpwnFuRsMXNOFiwjPAJNFUaBGNmwbCHeXT1f2deDvErahkXudl9HFLbCrkyy+JRId89mcLJmcwxc9mcW0Ftp7i6lYFavUK7DbKP5CzqnesSUWDKv2hIRoTTLNrZhMtmBX+8ej2lLAK5VLv/af/xAAdEQACAgIDAQAAAAAAAAAAAAABEQBgECAxQYCQ/9oACAEDAQE/AaocAwUvvUQ7GHicUNbKLCysr6xOoj2+4C6evRn/xAAkEQACAgIBBAIDAQAAAAAAAAABAgADERIhBDFRYCJBEBOAkP/aAAgBAgEBPwH1JVVU3eMysOBiUIp5ea4fUzqK1XlJaoXGPH4II7yxMY18Rcc5EAJ7TGYtZLawDVvkPyQR39Ab51Aj6mqGssI2iqEJluC62D7mc2NWfudQMFQfE6cfKIzOrbyx3XTXxCALHx4mwRF7zb4s6Sl3Ni5MqYtdzEH7a9fEUgucfQllgZcegK7Jysa124JjMWOTN2xiFiTtHdnOWgJHIjWu/BMF9g7GIVVS2e8W1k4EFjA7ZhsZjkw3OTtmK7IcrAxU5Ea1n7/6xN07qM+obqiAtL7Uc/Eenk5/pD9KWKMy+j9X36e3VORqOP6M/8QATRAAAgEDAQQGBwQFCgQFBQEAAQIDAAQREhMhMUEQFCIyUXEFIEJSYXLBIzCBsTM0c5GhFSRAUGBicHTR8EOCkpM1U4Oi4WOAkKCywv/aAAgBAQAGPwL/AO0XZwoZn+FapbFgtbRARy39Bh2eQDgtnoeTGdIzQiaPRq4HPR1TZ/8ANn1haaOPtdPVNLavH7hNaltXhQPj/gJoQ4aTdSuR9q+8nowihRnO6nkPsjNTXTd8tqpPeTsmpvkNLdJ3o330ko58fOh/vl6mnbpnz6E8vpWkzJnwz0ZxHtv49Gnbpnz6MyOqedYjlRj502ylCyA+O+otcy6yN++htxH8NdAMyr4ZPRpLqCeWayxAFaUmRj4Z/wAALfPDFCmjdzqXjuotEcgUkA4yGlg1LjTg76ltidx4VN8hp0bgxIqSyk4E7qH++XTHYxHTq71adJ1e9mnsJTqA7tCPUV1AbxR2WVccDnjTRPxjNL5fSo7VX0a+8a0bdNfv6qlEjathz+FPc3JJXOAtK0eYypzuNPcgHaEioZip14B41B81CQd6PfUb88YNPLxSHhXVnl2cCcaJt5kWVd47fGo3bvcD/b/Ugy8e+hGx+1TdjxqRjEhbHHFTfNTq2dlGMbq9v/qqGWHOn41Kw4GPNH5qS7j7ycailHtD6dMU79w86znd408qdxedJn4U0jnAWribkxpfL6VDLKuqJtxrIgQg1cRWyqGK4OKaE7nVs4rLsFHxo/MKhOfZqD5q0HgRiry3bivdrWe9JvqRLlQUk3jNfoFrEGNHw/wA2kbGF/hWJL1yKaOIntczT9vWznjjo2ZOnfkGuqmTVuxqxWz169+c00bcGGKWbbFtPLHTokHkfCtHXG2fhWiMeZ8a2zSEbuArEl47RjkaEcYwooeX0oxyDIrRHeusfhRCksW4k1toZDDJ8KDXNy8uOVNC27POgsl0xjHsioxtNGj4dG12mjPEYoKOA3Vh9zDgwrQ965j8KESd0f4I7W2uNnuxpprieTaSn/8ARl2G0Xa+792Xc4UcTQkicOp5j+mTbAW2iOQp2s5pdrp2mO1p4f0jJ3CtULh14ZHSu1kCatwz/S8k4ArXC4deGR99k8KLQyBwN2R6zCKQPp3HHSu1kCatwz0KJZAmrcM9AM0gQHdv6P5r1fZ4/wCJnNTbcIHjkKdjh95H1F9LZ7W/FJr72N/30UkUjJhsHSagk4lkFFicAU9wJHW1h3KAeNPN7XBfOusS755+0xPQLW0Xa3LfwrXeX7qx9leVR6bsy2x72fUhjicoztyNAn0ncAkUrvObm3Y47VLIu9HGa2PC1ueA90/eSCE4lK9nzoi9bVJq8eX393/mGo3MV3NHggaAd1dV/lC50bLXnVv40TbekpnYb9DHjWqVmZtZHa4/c2+ykZMvvwaHrnQxV3YAEVHM/pGdS4zjNdYju2uIh3g1JOm7PEeBqH0ZAcGT9IfhSxRjCr0tDIOPA+BqSynP2tucfh6kkAPbjAJ/Hp0rPJCfFKW46/ca2l2fe3ccV2fSlwp/vGntbqZ3xGTvOQd/H7lDE7IdfI1GT7o9aH0XC2NpvkPwpYoxhVGKmENi2mP/AIjcPOllmbU5J3/cMUYqzEAEVFM3pGdS4zjNdYiu2uIh3g9LOu7PEeBqL0ZAcNL3z8KWGMYVaLMcAU0Ho37OIcZTWT6Rl2lSpeS7QA9jnUdnB+muN34UsKDhxPiel4ZBub+FS2E5+1t9w+IpoX58D4GpLOf9NbnHmKaGQZVql9HTnLwd0/Dovf8AMN9xAFUFX71daWzVbfjv44oLY2uqXGXLcFo2V7EI5eWKSSNFYs2N9PcqBqC531/NLVWZe+x4Z+FSW1zGI5k8OjYbMOmnlxJpZp7SNYTRb0ba5ReLPUkM8eiaPwpIbO32jMM6jwFIb+KNon3ZTlW3tEWXng8xW1HZI7492mS3jXqycZD0Tf3e1SD3CVpPR1vvlm4/AUkCcuJ8TVla8mbJrA5VLP7i7qkv5e1I5wCfWtrfkmM/n0T6vh+dRZ8T+dRTDjG9RSe8oPQY5bhVccRX60v8a/Wl/jWzhnV38OiSdACy+NZs7VSV77Hhn4U0Mlrm6zhVXnSddtkETe7TzLvwmoVtnUKdWN1TW0duJJNWEA+tJD6QgRVk4FehJIgpJbG+tvaWi7Ec24mhFBa6ro8R7I+NJa+kIVTXwK00kURlfgFozvBDoG8rzrbQgB+GDyNPaXcYhuF4DxqO0tIxNO3HwFDXjVzx0Xf+Yan+ZfzoyTtpXq+OHxqSYKVjMXYz4ZorGukE6vW39Nt89GaU4VRRls7dEh5a+dG0uotjcry8ajggj2txJwWgt1ax5fukHdT9djjRfZ09FrbD2jmlQcFGKnDcNBqbw11eTn2Nw/Kn6vja47OaNvfBYzyPDBrq9giFc4BI4/Gt9LjcJl3+pffInqIzbgLrJ/6qhhtssqyqXbhzrbaftMadXw+5j+elmlOFVBW2tLeNIeWrnTW1xHsblOXjSW1tHtbmTgPCliubWPXJ3CDuqTrscae7pq8uD7G4dFz8hpPmP3FrajixzSIPZGKmDcNBqfw11dznfs8gfl0R2ycZjv8AKkiA38WPiek54Qit3Gj/ADaP/f40ItMTNnGAtDPGomHCYb+gY4Tjf+7otpRuEowfy6L3/MN9xZA8z9anH/0z+VSNzL1b+Q+tQ/tKl/ZioscyT/Gp/L6Dogz4Cpvw/OrfHMZq88j9KEIRppz7C19vY7CPUO0Tvq3/AGYqYWTPgr9uE4Co+q748ceiWP3lIq8MnCPtVJ6TuP0kvc+A6LH8Pz6JsfD86jA4qSDTTx3xgjRe6KllnlaTtYGfUuZ+SZ/06I/Rtv2pGbtYqOAewMU3zCrb9mOgpNLEJBxzX6aCv00FaIJIi/8Ad6J/KoMc8n+NXHwzSftPpX/ofSv+c1fNzH+tWfzH6dEf7SoVHDQKvG55xVh831FbWY7uQHOiYfRjbMji5xU/z/SopFJF5n7PTxNSuxJvM/aauI6bv/MNT/Mv50QwB/m/PzqSeJQsLx/xqS2XOuMZPSqQ/ppjoSliG88WPiehopBlWqb0fO2qSDunxXotvnqIDgXGf3VCE7ugYqxaPv7s/vq3uj2hp3jwqC0swz9rUzY4UB0IvsxfTo6rHvmm3YHhSRt3z2m86vxz1fU9C7L9P7eKkx+s88+HRZY+HRi3kWOTxYZr9cg/7dXQW5iEoVdTaNxr9cg/7dLtCC+N5HRF/m//APVQywxqJUcHw3VGH4ytpXHS83tcF862kp1Tzdpyeho3GVbcam9GzNq2e+MnmvRH89Wg9k4z+6ownd0jFWZj75xqqK5btLo3gcqtrezDMFbUzY4dF8Oer/XoufkNJ8x6GETBX5E1+uQf9uv1yD/t1+uQf9vpjTiIsfw39HVk3zTbsDwpI2757TVfjnn6notZG7mPrWVPEbqEp9Iu2psBRUO0Ys+kZJq8z4H6dBtIW+0bvHwFC7nH2jd0eA6LHHHd+fRZY+HRYY45+vRe/wCYb7i0eFNSxntb6lRd7MhAoxzppbXnjUN0qfYqN7ZqNIE1kPk76eBFzIUxioopV0uM5H41LdlPsWG5s/Doiugn2Kje2akihXU5xgVDFKNLqN4q5uXTET5wc0PSFnGJcjetaWt0jQHOjO81FDbRZn0BTvHZoo/bkk/SHxoi3Ta2Um8jPd6XUrptWkyTnlQVRgDcOi0ux7DYNBhwO+mRxlWGCKZ7DE0LeyaaHqiQq4wSaWBiC3E4pOovpwe1g4qGR+8y76fQMtjdUhSzRzJx1MP9a0bOK2B9rNGRm2s7cXPRBbL3pHqOP3VA6MtEjHxK1+gj/wCmv0Ef/TWUiRT8B0SxRLqduAqGKUaXUbxU90yYhYbjmljgTWwfPGtjjt7LTj44rZTrpfUTiruWVNKSHs7/AI1bbBNWht+/oRIE1sHzxqNTxCgVcmdNIc7t9WjwpqWM9rf8RSbHfJGc48a2PVUiOMGQ1PtYe2TlVyN9Pf8ApAfa+wnu0l9Yfpx3l96lZ02bHivh0Xf+YajbwWutDg69YrrX8n7tns9O0FaYLFYviXBq6meFmnkIwC2SaihPpEh5AWIVdyitr/Kb6Q5Hd44NWMZ4KNVPEJDGTwYcqb0WcmctpD530sckhkfiSTUJH/Fj39EAgTVpbJ30beTdkcfA11dIVuIx3T4V1/0gQZfZXwodQXaTRppcEbqLdQi089K/6UW06HQ4Zeia7S0V2kz3mFaVtoYf72a6zdSbe4PM8B0XUJ3CXePzpzbLqlx2RTXV8vb5AnO/xrrPo5crxxnh8KUuNLY3isjuwD1L75E6cwQbZvDVilt+o7xLtM7QeOa7Ho0A/GUVDc3qY0HPeGB+FWtvbSGOSV+IrrY9ISOycRwFei9X/GYE0VzjIxkUqrfXEkzcF1V/OZGZ37WD7NWTj210noRIE1sGzxoW0m46Rv8AA11dYFuEHdbwo39+wMx4L4UxsE2sipocEbqLdQi089K/6VtAuhlOGWrq3O7a7x+fRPbx2iGFuyG1b6S3FnGUB4lv/n7ia8S0Vy5PeYVpW2hh/vZrrV3Jt7jx5DouYjuEwyPz6Nmx0sN6t4VsOrrcIO6ai60kcMSHOOhWPdnFPs+/js+dbZrcO+dXaYHNfoY/4UNXHnQx3bcdBYd2AdESDeIBv6L3/MN93tJnCLWqOyuXj97TW1iDAZx2h65nkBKjdurV1C70+OijsW7Q4qeI+5eBva4HwNH0fcdm4g3D4j1dlBxk7Jb3R40sa91RgeqXc6VG8mj6QcYt4t0Wef3hjgSS5cf+WM0LdoJoZTwDD180TFZ3MgG7Krmtg6yQSHgJBj1rv/MN6t3cyIUH6KPPhTxTRlCkhxnnVhcHunsf7/fTyRRNK/JRT3sjMLwtrVaHWYWilXccjGaXHCCPf/v8fWe9sNMm070ZrQno8Rt7xNOZG1SynLY9aO/th9tBxHiKWaM8eI8D0l+Mh3IviaaWb9PN2m+HqNIFAduJ8fXiMcJm6uuSq0tutu9vbA5dn4mrOVR2YJBTSRrtDpyAOdG8u7CeduIGmmaS2e3IPB+dWyD/AIKaj60l3YBZVl7yGtCWAiJ9ommDtqkc5aovSFsMywcR4ilmiO4/w++jvrYfbQb8eIpZozx4jwPqrLD+nh7S/Gg/CRdzr4HpMh3udyL4mnnn/Tz7z8KL8ZDuRfE00s36ebtN8KaV+PsjxNSXdx+nn3+Q6L3/ADDfdy3E2+3gOETlWBXZUDnu9e1thxkelUchirV4txl7wH3WrAz4/d4O+sAY+7h9HwHDT94/ChFEuMcT40GKjUOB9eeT+7UZ5yEtW2x9pGwwahdu8UBPqzbB7fRJIX7WaXa4147WOHrGPOlxvRvA0OsRmOVdx+Px6GdIzIw4KOdSTT77ic6m+Hw+/wCyAOneAcfeXN3Iyna93HLoeB+DiurXKHMW5X5MOhmCFyPZHOpbu5/WJ+I90eH3XZAHl9/2QB624AZ6d4Bx0ZIBx0bwD0fzVoBHj2+NS7cqXkkL9n7ojxq4srg7OTVkZ50Z47uXauwAQPuqJGJJCjOfXgj9mFc/Wi80qqKb0nKpSMbogf6htL1h9lwJoEXZjTvakbFXEjSO669K6jn11iHGR8VGhZVCKBvNJaW2+3jOZJOVBRwG7+1GZost7w3Ggwh1Ee8c/cNNJGS7cTqNahBk/wB45/qIxyoHU8jWdk3lqNbOFAi+A9desJq08N+K/Qk+bGtESBF8B/8AmRyTgVjrMX/WKyjBh8D/AFxliFHxrIOR06NQ1eGfvsyOqeZxWI542PwboQSZZ3OFRd5NZxjpe0OpJV5Nz8vuMmsqwYfDo3n1CoYFhyz92dLBseB/qyVNzxhuFY1aH8G9V5n7qDNbMHjwXkortXR1fBaTJJhwTqXgfvkjEO01DPHFJJjGoZ/pE8KoVMBwSedSQ6tOsYzWxMm07Wc/fy+Y/Orb5B0n5Pp96IoRquH4Dwrb+kpXkkb2c8KzbM0MnnkUATuReJqf0jLvCnTGPD1FvYt01uc5+FRzj2hv9ef5DX/OeiLTNstFAeHTf/j+f3d/8/8Ar/Vk/wA3RgNrX3WraGNo/gel8c2Aq4fmABQM0qxg+8aCJcxsx4ANS29udLsMs3hXWDeuJSNQTJp7a4OplGQx40+mV3xIQEzuNC7lvSSTvVTjFO9w2TEd7fCtjDKYY/hyFRypdtIjeNW9xC5j2p34NLa27OdO9nz9ahigYm53BiKaV/SEhlAzjJxXVZnMikZBPKsTz7YkZB8BUEz32YcZ0ULW3bQcZZhxrbdffa41acmuqXLaye6x4077V5N5GkndTXF650svdLfSgJNvsdoePDHTJM3BBmjdrd7EHuIKk/n2xaI4KhajsLP9Yk4t4V1oXhnC73Q093A2klMj4VlbrYom7VzY1NYXj62TgaSwsv0z8W8K611zrCr30NNdQMVJQMD4UqW77NUGGlPM1BDbTBOz9pJS3IvTcJntK1RyWcuxZ8Nk1diC6Ebq3bOO9vqQyS650QnXTyiU9Y34asyHMqHDVb2NrJoJ3uajsLL9PJxbwrrQvOsBd7oajmXg4z0W5hcrk7wOdG763oONWyXkK2cUiwbPvy440tldy7ZZOBpUiGqeXcoran0gRLx0cqeC4XTcRcfjRsfR7aNHeeiJ7gXELEZ8RUUz91I80bnrXVYj3FFSej706pEGpX8RR+T6dIMkzzQk5GeBFRwej2dQfDiTSJNIZZBxY9DL1C6bBxkLxr/w67/6K/8ADrv/AKKYG2mhxzkGOme7k3iPu/St5ArAdT+NXDDjpxUX97JrRbT7F88a2svpPyUE5NNLLM7QKMHUeJqVD7SmnjPsP6l1Z3MmvT3KSK2bGhdT0bv2dGqria4kLlw2nyow20wt4kO9+ZNGwvJNrngat9hJo1Ng00778DcPE11lrw26N3VFOl3MJo8dludXcVpgSSMRqPsionlutvE5rPj0W5hcrlt+Oddb61szjVsl8K2MUiw7Pvy440lndzbZJOBpEsnEeT2mPIV1pb9ptPeU1HOBjWOFekZJG0qr7z++i0DmCzTnje1R2Fl+mfi3hXWuudYVe+hq3ktjpNx7XhWtPSjF/DlSCc5lx2j/AFNN81ZYbNPFqzp1v4t6k0a727wpllOlJRjPgaQO50qcgrUKjgJMVk8GQUjr6Un0sMimYXO0l092h/mPrR+cVfKOJz+VGJbh7dtPFedfb+kZWUb+1VrHFJtEDbm8aY8zIajig3PJv1eFdbu7yZtS6sBt1J5Go/2f1q3+QVIW+BoPns6c1GV94mowRn7Q9GyWdDJnGnPTcbTu6DSxCwkl5xsKkkn3SzHUR4UY3meDaDssvlWD6RuSDyzUsCvrCrx/Gofx/Op/I/lTxvO8G0HZZfKirekbkg8iakgVtYReP41Bjnk0llaRCSdvHgKd7ueLZ5HYUVbfJXpH5/qauPkNL8xqaBt0Mw1Crn0i/jpSijzPBtB2WXyohvSNyQeWaSBW1hOfRZ/NUvyGpfnqz8h9aspZP0e78+i6kj7mDvq+jf8ASE/Wn+YUunkimopU9ITqCO6p4UtybqSVwMduj8n06eqlQ8rb/lrTdRaC4xqPs9LJ1S6ODjIjr9Tu/wDt1+p3f/bpgIJo8f8AmLjoI8auLWTczcPMUqSlgFOeyalWLJjgzx/dU/4fnVv5fWmlkOlV41gbk/8A5WlhiGFWnPwq4bkX9S1vOCydlq9Jztv2mY0/3+6ktP8AibXZ4+FNCPYix/Cv/UNRfL9KtPnpCOCuM1Ayd3QOi+/H86t/npPlHRa/Maf5an+erH8PzqO2t4trcScBUz3M8Kx43ooqH8fzq5jR9EQclvPlTejpxolh4fGnjeZ4NoOyy+VFW9I3JB5E1HZs5Oz7r86M0F5rjTeR/wDFRzkYLcf6maURjW3P1zLC2xc8RjdWlbldPmaSeWfUyHICigr9l17rDlWygvgI/OmnlnMsrjBrrW3XRtNeMb6MCvoOc5NOjSByzZ3V1izm2L5zj41oub/7PwqGzilxsjxatizhzqzkUuG0SJwNbCe9It/cTnW3aZWAB3AUkkbhXXdv51Cbi8JSE5VFoNq2cq8GrYC9Gx8Mmi5baSndnwoXRnUqGJxjoF2ZkKhy2MdMmpdW07GKTRfbJSMhcndUS3conhkOKHa2cqd1xWyb0gAniONGxST2campLdmDFeYqS+2i6WHdpTq2cyd1xWzf0gAniONGxST2camqOBmDFOYpLu1m2Uy7q03N8D4KBuqKAnUUGM1LPZXQiWU5NPavPtXcHtn40IGYOck5FRtG4jdOZ8KSDOSOJ8TQ7WzlTuuK2T+kAE8RxpIAxbRzPRAVkVNmc76dPeGKeN3D6mzuqC8EihYvZrZybiO63hWwX0h9jwrSnaZu8x50Lu0m2M/P41/Or7U47oxuqO2fD6V0n40zejrvZo3sNXWru7MzgYA5V1/aDTjGnnw6etXc4m36sY40rKwjlXn4ilhml2pXgfh9xt4n2M/j41pPpEBfGpGMplkk4k1ND76kU8Dd+FuFJGkuzwcnPOjsb4R546citpPfGVMd3fUz8yNIpM8ZO3VmEkOkjJXPSIwwVlOQTSwZ1HiTXWtouy169GKkiBxrXFbFnDnVnIpL/aLpUd2oQkgTZtnfRhkGpWGDRWxvdMR5NTz3NyZ5WGPgKuLsyKVl5VGiSBNDZ30q+A6IdEgTZnO+iviMU6O4fU2d1W92JFCxcqjngl2U0fOilzfjHugUkDMGK8xVwzOG2rZ3VFdW8ghnTn40hZtncJwda2b+kAE8Rxq3igunjeDg3jWxnvlMR40kCd1B/YdoJeB/hWzt75GjHDWOFLcekLnbsnBRw/rPr1rGZI5d0qL+dZ6VhaNo7OE5JO7WawOArb6PtcadXw/x+trZAuiXjn75JIgpLNjfSt4jP9HeeMAsMcajnYdpk1bql2sGy0Yx8fVmjlg2Qj4Hx/s+XY4Ubya7spT39O6lSNJXDHGrTuobU5Y8FHGhE6PAzcNfOttKCVzjdXZDybt+kcK2kJ4cQeVDaklzwVeNCFkeF24a+dbaUErnG6lTLO55LyoRsHeQ79KihC6SQO3DXQ2urt7hpFSJNtCS2dwzQuC2mPTqya7MMzIPbxQmibUhrZKHlI5oKsJIWyBgHPLf07Eh5JfdSlgaGWJ33DUKCyamduCqKEUkckBbhrFNIeCjNBxrLH2AN9PljEUGe3WCkoU+1prag5TGrNawXJ4acb62Q1RvyDc6h/aUhPuiiscckwXiyjdW0hbPiOY6Gc8FGaD9sk+wBvpssYioz26xol0+9poOpyrDINGONXnI46KKxkrIPYbjUUMmcy8DypbWLU7HdqA3VssNLL7qUYgGjlHsv0zQyEpsRkk8KkEIbCczRijR52HHRRMRIZeKniKMASSWQcQorY4aKX3XqTzFW/yU5h1dg4ORTRxRSzleJQVKdEiGJdTAjlS3nb2QTHDfwpmhDdnd2hUqRasxHByKAlJLngq8aAlhmiB5kf2dk0eIz5VxTRssEfGu1wLnTVxO1q91szhVHKtH8lzJIpyr+FRlxh+zmoV0DtrlvjV9GvdB+tXFw1q90UOAB7NAD0ZMkinKvjhURcYYlc1G+gNLINRY1tp2RHIxk8aiNuSZEbjpxuoFt50fSpcgfpKghXg7b8UIF9DzaAMYr0j9jJCu7QG5Z3Uk2kGSXeTVmVUDVgnHn0vfCDbRSfwpY2j2c3s6qE1w0atjAJ40ghJaRW46a1HiYPpUk+MuW01FFpGl8FhUh0jsYx8Kj/ZmpZSgL6sZqC9iGh9W/FQN4t9KGn29K0kcfoqZt29veqd+qyW8Mq5ww59E3yGpZyMuW01BHpAWTBapewOxgj4UrKe0Rpz+NRMoGqQaiatbyHsyFt+OdWaD2938aOxjHYXOeZqW56jJcyOe+OVW1xH6OmhdG3tjiOmaOTuA6j8anMChMLgYr7P0bLKX3mQc6S4Wylt0cYfI3UzSuiSNx8TVpNak6gQGOMc6k8xUH7OrseL1LDPal1JzqFM0QxJjtAjfSjAxo+lbhir/AOb61dXU3aKHsg8q0yIrD4j+zsuGC8PxpWaznzzAbdQhg+zIG5CMU19HGZLebvgcqxbwyyyHguKUsuGJUkeFW/7MVf8An9ae8SMyW03exyrFtDLLKeAxSFlwxYZHhUHyD8qklv4TLEe5SJbQMsatnVpxSD+59Kmgnjcvq3ACopo0KTL21U/lWi7jkSZdxGONXUewaKMjCFudGzvY3Gg7iBVpLsWjTIC6uYz0yQ3FvIqg9lwONW3UYSug5Z8YrbXsRlgI7NCK1t2CBsltOBX/AKH0pv2hq38hU/4fnSfszUgmifZM3fUc/Coo4o2W2j4k1CB79bDg2kFfOha38UiPFuBxxphHbusAHfbmeib5DT/tKtPIfWrjy+tJBwLDd55rqd9DIDH3SBUbCNo7WLma9H7uf1og8DUkM0bPaucqwpIrSCSUsd5I4DpuvL/SpIDwcYo2V/E4Cd1gKWK3t32XtSNyq5/lGEu5bcxGatGhgZIlbcSMZ31J5ioP2dXZx7Vabu3kjfmMZqW8ghMVvio7qRSYynKpNETqi8C3Or/5vrUlwIy9rNxxyrTawSyyHgMUJzGX4DTUc2nTrGcf2bhkjTaCJssnjWHjMRHs6KiurW2MMEfFsYz0dlFHkPV7KKPIdPaUN5isYGOjVoXPjjoyyKT5dGWUE/Eep2gD512VC+VdpQ3nWABj1ZPlNShl/wCJz8qwoAHw6e0obzFbvX7ShvMVgDHTgjIrsqF8vV7ShvOsAAV2kU+Yrh6naRW8xWAMV2lDedbujfXZRV8h/Z7JjUny/p+7/AAu50qOJr9aSv1qOtUbh18QaMkjBUXiTR2EyyaeOPX2kzhF8TRaCQSAcceqNvKI9XDNCSJw6HmP6OGnkCA7hms+uYhKpkHs530WY4A4mjFDMHcb6YQyh9PHHrmSRtKrxNfrSVojuEZvDPQ00rYVa2zQ7JT3cniOlpY4tqV9nNCaI+Y8PuJbaOzaYx+BpXI0kjOPCtAmjLeGr1dGoa+OKMqQmZh7Ip7drcwsgycn7hoEkBkTivh0F3YKo4k1rjcOviOlYGkAlbgvrNCkgMicV8KCySqhbgCfVG1kVM8Mn7nVLIqD4mgynIPQWY4A41rhcOvDI/ps5ikK9qtNwuk+8K1RuGHw9S5+SmjnBKhc7jXYMiN45zRTO5T2hyYU0aPp2oBBqR2lD6xjcK7Tqvma7LBvLoxtUz59G45rYpIFw2c8akDSBy55VjO+sFgD59G5gai0yiPZ540sBfXg5zW45rAYE9HakUeZrKkEfCojCFy59qo5pMB2446MGRQfOsisZ31jO/7uD56Ty9dr4M20blyoKpxrcA1G8cKq+jGrnTmBdOvjv9dhzkIWoDLbozsMkkU0ltGIpkGRp50RIcvEcZ8at/RwPYHaegoGAPUaAbobneB8ekvIwVRxJr7C3uLgeKJupU6hdJq9pl3DpvfL/SobGA4ec7z8KxHqE4G5886ZJTmSE6SelOq3WwA73xq5SSQyMqkajz39F75fcXvkeh4HyFcY3VsIySuc7+m18v8AX1r78fzqOWRmBj4Y6ZZ1UMUHA1FORpLjOKj2rMNHDFY+4EcpYAHO6kiXggx0T/IaPzn+mz/N0fzfXr/u0OsgCT4dNz8lP+z6E+MdaskHZVdZYthQcVI3pK4ZM8KS4tLvaW/MZrqcbFUXccczQzcOJcfhVzHNJqffg55U9pasfte8c8BUkZm1M0gORU+picPzr7B/tWkIGaW46w8rlsNmtlNcOtvDu3cWrZxyN9m+PMVb6WIyTTtqOdLb/wAakto5mjjYZcilWGZ+GoHnWYmxNJGMHhvrN5cMZD/exSwpJqjL6D4GluNozbY908qiuesyLv7opLeFtLSbyR4Uk88r65BndyrqrOWi16CPrUrqTlX3VH6Qu5d/e086aaNTsiwPe9RpLu8ldidwU8Kb0bJIZIj3c8ul7WGUxW0XeI50Htb2VHHjUHz1ohk2chUYbwosLuYz8dWedOkx1PCcZ8an65dshU9mMHFGRLmSSLT3Gqdry7dGB7MYbFF1upJIiO41TxmRtAXu53V1nbuwd8aOQ3Us5u5Zcp3W4Vea3ZsNuyakhE+xtIfA8aimguTLbu2l1Y1AyMR2+RqO8urlo1yGWMeHTa2q8WOaVBwUYqR24KpNXEnJmAq8kPs5oqedB1ZnhPDPtDwoJDqSIf8AtHjSRKSQgxvqymHEN0m3kP8ANrYAsvvNWldIA5CuI6b3y/0q0Hhjovxyz9fUvfx/PovfL1LS4Dtsm3MM7qVImIkmYKuKaKViZIX0nNXMu0bYxbgM7quYYJNlrJ1MOQqK5hupHBbB1GppFJU7PO6kklcnGck1I7TNDaocALUclveSaQe0rcxUGwOJSoCmjdpeyvIneyahmfvMN/R9n+lkOF+FCea+lSZt+48KuxM2qQAhj476sQkjKC2/B+NW1sJTDFJ32Fa7W+lDe9qzT3HWZOwgBTkat7jrsyjvaBwq12bsmX5GpSpIO7hSST3ciLwRVq4sJpDII+Gai9GwyGJWGXYVGYrybZSnS2/fUrLPJJrHtmrjaOz4fmc1ZIsjBTjIB+NAxuyHWOBoSxk6yqjVSS9dlaVhk4bhU0UkxmIVu0aZDcPDboeCczQsjM0sUg51FY2zaZZuLeAozQX7m4QZ73GreRG0NI2h2FB4b6UufaDUkbyGRlG9jz/o8yxoWOqtVy//ACrWmJAo9S5+SnLMF7HOtT3EYHzV9ipOewgqSEexGBV0TyUU09nPsmPFcUluJA2WCtjgRUjNw1BqEoddBGc5q8MD6wvZJq5+UUfnFT/PUf7U0v7QVJ89S/OKtvM0/k351cfJUfyVamE6WcBdXhuprq7cytnGC3Ck2Xc23Z/fVt5mo2d1UAniagk9krioCGHZXB+FNst+qXdUn7QdBt3c7QHHd6XlO8IM0Z+t9WizgKg31HGZ2nIG9m8um7tZey7Hd8aLOwVRzNQfPSOi5dsKM0Jrj0myAjOEq659oUZ45NDNxKbxX8ntNto3H7qM8UhQtzTeKPo55dtGR+6rj5aj/afSo/lFXvz1c2t4CJVbs78ZrU+pQOZercctf0pPLpReIi+lb6Ho6x+0Zj22HCkgXlxPiavk8c/n0L6PgXWdW8/Hwp7W6XSH4nw6LOPmW6ZUu0ztwGjOcfhX6D/3Glkjhwy7x2j03vl/pVldHuczRlJ7IGc1dXPJ23UYRKpkHs539N7+P59F75V2mA8+lzzj7dWCneII9Tef+8Ve8lmj1r51tD3pTqq88j9Kh+epP2NaBxYMKltm3SK2cUNbBcnAzVp+FXHl9ag/3z6LWbGVRt9LKhyrDNXrKcg5/OrD5vrQgnxniu/fXW7W6YaTwNNMwwXQE1bHPs1afPUv4VbfLV7+NQ9UA6wked541Eb5EhhiOdKnjTeVXPz1ZKDvXGf30PnFRJPp2bIAc00lrcNGRvGaudsdTRgrq8d1N+0NW/kPrVu9znq8g0k1kB8fPXVAQ0TNu7XOnubW6ddn2sGo5ZO/wPx/prwtuDjFfrMn7q33En7qzEnb95uNSQMSA4xuqUB2k2owc1qguHj+HGtu0jSyDhnlQ2mVdeDCsdcbT4YqSzQtpk4nnUhSRnL+NGB2Kg78imRHZ9Rzk0LoSuSG1aa2LsV35yKMSMXyc5NG6Mrgk5K0iu7Jo8KNjqbQRjPOnZJGcuMb6WRpWQgY3ULN8lFGAeddq6kMfujdmluEkcBW1BK2Tkrg5DDlX2tw7r7o3VsJVyo4fCuxduF8q2gzJJ7zcq60ZXBJ1aeg3RmcEkHGOkqwyDuptheyxIeQpLlJXJXkefSJCTHKPbWh1m8lmUezUcbOUCHO6uryZxyPhWzkvpmi9wbqkCSM+08aLW15NDnlTStI00rDGpqJtryaEHlTS62lmb2mp77aHU4xppYncpg53Uq+AxUpWQvtTnfQly0Uw9taBuryWcD2aSNnKaDndQHh0vOLyVHc57NfaX1w6+BNaYI8eJ5noiuDujn3E0y505GMitvtGlflq5UrOSjr7QpIdo0mnm1RRjeltvbp0SbiN6sOK1pSeCdeRkGDS7ZbbZ89JOem98v9KMMvDkfChC/pBzbj2cUsMQwq1Bcxu20lckr8Mb+hMXEkOn3OdFxezhjxNLFtGlx7TcavfKrdQe2ZNKilXwHQyNwYYp2R2cvu38qRmkZCm7dSRLwQYqW8EjFpPZpY3cppOd1NbFiAV05pYFYsBzNbeORreXmV50s1xcyzshyM1FemRg0fs08DMVD8xSQKxYLzPQ0MoyrUVF7MIT7Ap5onbtDGk8qhkaRl2Jzu50rmR45E4FaHWL2WVB7NNbEYjK6d1APeStGDnSN1RBpGTZnO6mt2YqG5io4AdQQYyalvBIS0vs1LGZBCIBgeJotFfyBh41Ik7azEcavGme2vZIVbkKinE0hdDkk79VbFnKDOciltZC2lcbxWj+UJtn7tG1jyFYHJ50YVcuCc5NJfbRtSezWymXI/Ktn/AChNsvdpLYM6iM5BzzrTJfzPH7tLDGMIu4f2dMR3NxVvA0Eu0xIm7IOdXS3Vk1y8t9EyHVPJvdvuLi6tYkYSe8aXabnxv6XuCxZyMDPsj1CbRVaXkGqa6u41XaDkaBZQccP6btlZoZvfStM/pKZ092tlCuF/P/FFYNo2y093lw++skjlZFc7wOe/13lPBBmmumvXgQnCqlJHJJtHUb28f6RtJ30LnGaBHA+reRPIzIucL4b/AL63hErCIjevL+y0s6gEoOBpEtbXazkZbwFRyTL9s4/RjxrrE1kuw544iuuRKZBpyFozdSQIN+k8a2gGll3MvhSfL9OmSD0fbq4i3FmrYXloEBGda8Ka3s7TXp4u3CltvSMCxl+6y1JOoDFeRoGzstZA7ZPDNNHJbHrWcKi86TrtmEjbwqS5QBtK6h8aza2Oth3jyo2tzFspuVej/m+tNNKdw/jXWIbJdj/E097gjZ95fjW3htI9keGTxotcQbFwcY6GWGDaIyHW3u1FFHaa4NW+TNGCRRsguc86Je12VvpyrHnTW/o2DbaeLnhSwekrfY6+DjhRnRQxyBvraWdlrQcWPj8K0LbFrsnAQcKSK/tRGr8x0pFHHtbiTupQW6slBfu4NSG9gSFAMgg06+jbYPGnttT21zFsblOXjQgMWpNOd3GhLPYBITS3AOEZdVMPR1qGjX22509vcRbG4j4r40YJFGyC5zzol7XZW+Mq3jTraWQCKcan501neRbKceHOjE9vpgD9mTxqGOSx0RY7+aWCGPbXD8FpD6QtQsLbtS8qNw+9eWOdbZPR4aGruXBXWM4Pn0PI/dQZNGW0tI9lndqPGpBd2+xZP403VbICNTjL86a0uotlcL/GomRA2tsHNG4trH+bj2m4mlW1tTJcnivIULO9txEzcMUZ1QOcgYNbS0sNS43saaKRNnMvLxq2+Wgca5H7q0J7iyXYc8cRQvF7YfuihKtnFoO/HOkkli2Tniv9kbjypHA7Um8mrZI9OrSNGrhmirG2IO40euOoCsTur+a+jpZV947qvMjG8bqT5fp0yz+j8PHIcla6peQ7KblXV4o3uJhxVKtWmtDbYbdk8an8hUOOeT/Grg44ZNJ+0pv2IqLzP51ZSR99iM/vr0f831q2UcC5oBTa4HCr2O6KL1jeNHI1o2QmhT8a2gXS67mXouf2ZpfmNRRuMrgHFTlOIQ4osO8XOa1HvBxpqFm4kJVsB7gq+OO7nH76tfnodFrdPvXTvHhVva2eZG1ZJxwqfTxCYpOqG32R37+NRXdzseyMHR4Vbg+Aqb8Pzrs+59aj6qbfZHeM8ajvLnZbhg6KijkGVwCRXwox2lvJdEc14VavNb9Xfd2c+dJ+0qP5RVybbZ7VeGvwpoZTbFGr0bbzHhualVdwA3Vf/j+fQ8TcHGKKQKJoc58acSLspY+8KKWdrLdY5jhUTzQbByO7n4Vb/PQUDcExVy3PUBVh+H50fmFW37MUmz9vvfuq2+WoVi06wo0a+FNG5tirDBoWcrASo2pTyobaESxJz40s6bs8R4f2RmjiXU7DcKhjlXS6jeKSWFtNxFvU1sz6O1Se9yrROQ1yG14H5UsC+jwGUadZ3Crk3EenVjf40tzszsdPe/DpYPaC4TO4rS393FsFjHZWp5YLbrEcpqGSS10Kp3KDwqWKJdTkbhUMUq6XUbx+NXFw0ZETA4alSBC7a84qRW3ERAGlMNsLiFs6fFa6/wCkF0kd1as3ijLKh7R8N9GInS3FT4GhA9lt9O4OKnkbQkzY2aeFaD6Oy/vCpGn3SynJHh0TogyzIQBSxzJofUd1JciM7EL3vwoqd4NObOPrFu/s0nW4+r26ezWwt49RBGFFQI4wyoARV5LJGVR+6fHfVvsIy+lt+KHQvU028qJpZCMii49FRoOelacFNPsutNHDD1q2JyPhSPNCLe3XivM1DcrGTCo3tUsUS6nOMD8ajtrhMdnSwpoooetW5OV+FLJPELe3X2eZqO5EZ2IXvfhTJ7wxT262W2UnIIqC7uYMD+6e6K0wjU6tqx41BG1oI413Ox5il9IWJ+2XvL41s4/R+zf3jSROwNygzq8TQtzZamXcJGq4kuU7w7/jv6JBAcS47PnWiT0ftG94Vdz3f2clyCMDlTWwsdqM5BqO7uYcD4cBuqAQRlyrZNY54qcTxlNTbs1ZyxxlkTvHw30fmFRIloJ1K9hxyFPfXv6Z+A8KguFjJiUb2qOe3bTcRcPjWz/k77T3uVIVKNc6ssPh4U0H8naWYY1UY+M29vxpjfJofVu8v7RTxxjU7LuFRxSrpcZ3fj/RZL6yUTCTvIa0xejCj+LHcKkaZgZZTk45f00xwprfUN1QRuMMqAEf41f/xAAvEAEAAgEDAgUEAgMBAQADAAABABEhMUFREGFxgaGx8CCRwdEw4UBg8VBwgJCg/9oACAEBAAE/If8A8RUZljjcC7h5lLndjl0xxVsHMEBMjN8DpzPE+wzx0rN72L+rU/S8u19VuNa4aX/BvRtRSugv/wCCDLDy4N4COixqdollOSJ3hI5TQTeAEuuexr7+kui36BPnOJpbqo4xT95qkDDjdPQnUtFz011giWZJ6J7pRp04elfnzH95dFsE7LrpqrO6p27UZRKgTAPRFhJ8jdzNx4H5mYE0AdDOiJUWJiLVWids4v8A4A+RbyuDSoVYlC8X2mmyoqnf+BHtV0TPM1bl8x/U+c4h9W0PKLZuvf8AsnoTq0lqogN6071zMJK35xFBqh1KqAhKyW80e9awvHQNQwydqiOKwO7c1DnVtYUudE0RZ5zUXKQClvEZBVnnPUpSTR8m8tl95JnH6TBAY9bWrd4cutpaGCulnKf7+UsChybw7IFls5l5cWxvSek+0Yjcjj+53pao3eV5P6ip2ofaes/iaFnBHozbSbOHV10wGfgy3CxvLE1Ji+io6oChnwgwBWrKKUQPfoGn8i3t/wBhHOATeViFL3rEQ9YWa1O5oFXSmNlVzPUopG7b7RsKufFp+pVFl+3aKHVXTbpKS/fgYzd12Xv/APAHSK3en7TyA+f3D5XJzN8zLa4XTpkfGBuo6IynYGE5VtBUBG7iEbwhvrl+NQ1Uop8H/uWJZyusOjyCrjvCukTI9HYc6do3E3TkeSDeYD9xZ8W7VliGyuhYLAVkKIg4GzHCzZhIbqtvdcFJwTNtAAtcMehpCVnewlEGbL/cuV7rn/4idsi9aMNFh42//hlvral1c1/GbktpsTSYUtn+YznJ8bwna47jt/kI0ALV2jQueBfVAX/Lq3/LcmBau0aBzwL/AJgZAGVY9DraN/UsveXdPXUVrHVsGyyIL3l1b0c5tF0LBAI2M2f7geUs6E5aK5/kPKp8gqAJWT56z/Nql9Auz+o7rYF71BRAtXYjrGsgPa/eCZW3d1Ez3PqnQ6aDVVVn95rG1bj8IatGvoeD+PoeXRupo/7DcEUvR+8vGMbvDszQHtfDHIrl7X/T3/ktHAO6rZMs/I5aD/AfdMDpVWvzCkCLaMsKh1C0NHZjo6vKwcfwuqNWFeJn4J9by6EUm77QxP2U1fnLHi3deUBDZ+4EbqkQ24fmF/PQdbXgfYGWCsw6uj0+hmyQ1to6kjJu+mAtsX5lD8eiCXO3iZQofwt9RFqdGIstWXy+pcSQDbh9swf9cJnCi7sSHe3fzfwMbeik+VMZP+mvWdxU1XlDl2PvBLhpEtuH5g+z0fuBgFauxAq+GdveW7+Wav7xIgwlyOb1j5tmnU0esOdj7g9bQgYeWzGZJLGJz4PsDE7vIOuhKH4rweZe/WTf59+mr4tP4LxHNjNFaThKzPvOYD4Lrm/My15bHOsu0LnhiQhyaLhtGsuu0LhxzvZda46BMbIDM0JYkOhlOy3iJweObwFwUmcm40cQC98mo/KJZtBe7xSXrNWur9Rx56v2+HTSeSDyZcrn85+ZrMYVhsgfcGNxuPFr9wDCgUQdyR8W01Xn6o/VzXFer06cZBHjSN8Wnwi7AFp8f+T4Jh012yg4n/P/AEn/AD/0hxoLAPQ7QlGjWDS5s1wFxkx6KF34jA0/F3rMM712+LmV/q6cQiPWMAFtUV6lbDvrnpZVf7aiiquTlQuZ5WyYIvg0NlejrmA1SB3uD0HRyD7wNaNaf6YngMGh7RilYuj3nYR2L6v+Q4y9GAZNs0EA7iNX3uGDbQcur9ALUjXQBaA79fX/AGmYi7DAY56vXPsqony8njuxH3HWW7zHKBvv89E1vgeLR+YGjCPKVg3vvwiZOjH7Td/PtZ/AjChmw0rENVoTwjAynkLu7CWpu3qZv82H7Po+J4foW7LHBeW0k0pwCXGuveZXX0UaWWbdEC1A7zXp6T7MuaM7uNIp8yP1zcTjb4JuzY6DvNOlKSaszGe/G5ufl2s17HV3yvP8D6xFfHB+YOkjPkSkW99+EdJ0GvtH7NFn9HohfEcNvvDvY+oOvI8ftR+2ZtLpi5jFV8EDXceW/eJIapk7zZE55hPwdHs3rX7HTZE+7r+nTV8Wn8A5cUv2QMbGjBEMu3yJh8bEfC7T4jtGIUtd2MKOfQBxYJ9hhv4dErRVi8bZiJ8WNGNJ585U8iZNvCO7fiQ4zx0MwBYtuS7336fNcI8tKU5dK+5BLtHL7n46YO6X0uC9nwpGDKQ4bv8AMtH1o4ysNxIv3VGff6OS4vs6YAKTs4PzM9oNuXeVyTvk1/B00VWDkn/OJ/ziCVswDPT0r3JQCqp42i2mSjxohz9numtP4/hGKMiD4ua3eTQnyuzDVoY/KYaw+xbNfvBZWWrIVwSy0W9E0vbB+ETukYcmd0+h/wAhxgeWuBclToqNr5oiUIuPBfX0GOd42LqnLvPSn46YpBOXXa6ev+0/eJBKPa4HhECM9DeOEX+oyX6yiWWNQ6TtQV0G4035L9+l5PGw/tpF/LgbTBnQOSB2u19549d7jXTxbV93o+tDaq8OnV3yOxKxR06BChUoXpl8GuMSPJVr5uLe0SF29Tr7GDlaQczndbt5dKYeojxFz7g6ek+zDjWyEdQODpVRAVBg3yntM3INYnJcvSqKATapgrY9+o3yvPRmDMewfDr3pYXVJdZ16eLG8n5dFz6HrHxiIAr767TB3RLnMPZlBIiXKI38wHeEdwtYtTF6vy9Gis4/teLNHHz/AHvF+hn45r+700ew6dXxafwZ8cqhWTmBbQDlSXytUo4o4l+0ZQxh285h1MUMV3lHqjas4m5GYuspXjaUM4ba9L44Shw7azcmEVuTDtOy6zK1rw2cm0x8ETbFQ+NFBt82ZT8FWnLDYB2ufB4RlicGP39ckVFObWYh7B0Gx0M7Hrln5jD2NGCUYRuS8wc/mPyTO1xqx94TlKui2OaJmok85pzd8UZ1J15axKg5WiUJjiLp6seU/wCLdEzS0Hhj8yiP1J0ZPuwWf8fP+PndsIj0pfAyVeZctAsussvplhZ02lEpGUMU8xLPf3YnKzQOPKa1slG8mO9NnEVpzDRM74BQxTzALp4d6mc7eJvLxMt+1QrxPCM1aO2MiZaa9LgKjVm15hcM6uEEFsEq+gx6YsiNvE6vs4hqGjdU+EKy7Xd3dxAhd7+8pnId3Kndgy3N0uOc4mj/ABK4Ues56/my/ghoryaVK7c7Jdh/M3gfdng7Tb/D36/o6Wx+mCjzmioKGxozS5zX90V7UMWU1EH5zK6moFn7pY/2wdEg5TRC+MyIPC16sRMzvaemzZe/8XDM64azLJwbIst0HiRrSX3y2gc1CTdPEzc9Ne4ft+j5njqMtbWKvfMC8C28FRlOcsIwoNsKsAO8oAysrGn5lidF3oEDhVP+37lTLvAQHO8mg5YRUfJunE2dW7mvTIGEUMV3mIGo4RHo/N10+/vD6IazOPEQ3viBA5BflF6MpLpmxoPf+F6HH9ohHOssBFS3S5/gVEHdEL4zKg8LXqwmQ7dvR6DXYd/4vpmEeFqh4YHZdHjcXtdbnvzAoDQm3FMfEr3JtHPlpwhTMVVLvmUWn88zZmOjmDfMnyP29DqyuvgV7vTZV3yZ906avi0/jUnG7v4RaItuMRgFpQj9agoKa24MDaLNGvvLZDR9fwmESnsDAZ0g+Wn00QBrTq6wDtCLsfSbkNjQIxHAt03/AD/GoFuCa0XCsef8B+E0ItDMEa+wR7wdgBl38bx3TAaw1fvCoQ01S7ubSWp76QSBlFu2X7ODDR+YuJHrSTluW4fqVyE24rY05BB3loO31Jvi2E7+wO5uD1bnmdLXvcmo4+g44gZmmn10MP1rv7kPT0GqNpWqIrgxXtFij4O4hL/aSAfttKAEj1EGpRuzr/X1Zlha+IsbtOQEt9GnhA3RWU7Ph5N1uP8ANfsewlggeI3h+nXp8OvZCp5hdbz1QJahVn1HE+9QqWvw5NeyPVejd2iABluOup01fFp/EtFs389NT8zAAFBoEIQlbArP1vvtp6fmDoohAdq95qfxe0Vn+NEAHZgoANj+Oz78HdVfOIG4DuPliRGGjJ9ebqRh4uJdhkP3o9oDQOS87T1pUK+kKrDqnM3dq7rt9WZodoTfHD0ps8ehKM5aiFlo+j+cXQrwV1cFzRZp/JpO2NQ+V02FZfDswM9g63obbbNXsgNA1/Yv4h9C9lfzmuV4K+pVXNSGvVwXNFl10FJNCmnSsxull10R2AFy8pY7p25r+LbeiQMnBcACsJZ5ECAclatfWyzMr4/BC4La8vgQ6578nP8A4KWSa4mv4Zd4OHt5xa/2HA/79ezheQz+oUWUaDSXLUu1diEzQ0P9oJGDRPUmzlS/8Bsd2BfmGClpZ74AACg2/wDB1aFBAtI8FAIfn6zLzPg6X4QFvwCj3h4v0Gv/ANyNcXItRuBvEO6bLv8AyFAtxACxHw/npPG6ohkyaI2PX9l77fzU4nJR2fca9NLEh+ylSlYunbqTGWBqvPL+AEQA1Wd74KzpogeP0ajeBkfxoB7Vkr/zG9hQ8UdmUItdr1+lrclQGnPVqT8Lr7wCvYTY0T+ZhVW1xZhh0HXiz/Iuexjkn4iBWr25mj2xV/4CVk1Wd/eKEaptua6BoqghFzktwazXAbfG3v8ARpNgHWMJmccO/wBfy/E0/jp0MsWu13dfqZMulfzA+D3/APOQiUXuRCaLX6eoFur7xi6qXnf6jRooaLiDvoBWY8qTUbBD13I8aruK547G4xcuEd5QVBJ1FhfiWSaE1aXmCGTUHQe7WrHY5WTV8IsS1jonRx941cth2nQYDIFdbW+X3jGR1ZHF3ECxq2o7wY7xPDiNIr6ritI+bxSNAhdgvWlXct8A8wbM0SDXE5DE0oHZQ39kS5rtHe9OoN29nMKuxpYajBa3+oeEpEQO1m56o1UbAcxqofNtO5iUCKuuO8NXmfiypVmXaqBsUWtkgNN+Xxv1NHDG1srSB1hCYhuT0V43JkH87WtK46iG+0TWDjF42meu254YxrDBeH+hnLJcGWe6kaqaafpx0P2I8TWJX1p9W5XjDRAch7VxN7un0SFbd2XeWek/Q49IVpj205lPVoud88ECbg0y3iad5XeWQIeT85gY+uKTtKqhh+C7JKTwZxV+CHtDvHoPbloPcdaUr6+8E9Fouar5Yds16CFWb3aliBwCOgpU+eIKd2v3/qabGe84lrKrVyYjHGQOxAGsF6Rd2deZ9DGis2AwP6SIDNWA77/N4PnZ/bEyLghVAjPDtFo2lAUcvhY3G1E9IZIQWF3DQmqUpdvAg7SO8gEXQd5LWP8AqhHTudoRjQX0sXpXgrEWg4MqrVXjBtAc7gVNE5U76JG8ze2JVqsS4qazyPB3gILRNswpT6aPU39pWHXfFlYrNu1UKlTpbZSNZdrvCUkaNF/8YWZlmnu3ifaUuK73p9Ac0FHKZgw7S9Ni4UfYkzHOum9ZmlYDGBg0cV4xwd23QgusF29GOymipXSFWr2TtNdwd9Z7rb0whTUHyJVAZSLp2jh45qgrefP8T0P3QNYz7c0iGrwoiCDcdqhdL/b0wFQvp8+m37hlfUjSZyeEHYJRNU8wH/jt5zDiN6ns9GOThSrD6xny1PeAFPPvT4bhHrwF1Lhj0YCBqbA+sfTSD3iuFUTu2wEL3nA7jkZevNT07pF81x0GCy64Tc/JDOw+A+FTG+K6nZXowwjUqw+sefaB75vobJ5fifAcQlu7+JPjeYHT3U6FZSxLIWVkEabHuTAGyr1QV/iIO77sN7ZTwHMwR4cF7kbHgGVn0JHIMHbzMHwAc3/DBEs6JSzZAfDq99PT3dN8OnYxUHa+tyOJWXowZjQFVVbfwxa2wvRBr7M9UH+O1BNh6cfulCn0d+8BDQb6RuEK+30Cq0Sej6M0FLLt8IsPvN1MzcEfNqhBPPsk9M909d/EvfsPDSRySwFbYll1eYC7g9qeq+0+c46Zj8sTHxPtAXbp9p6H3JvmCaEB0L5lzpc9d7kv/odmzolG6mulI9cgupcMejAQNTYH1htnwRjbteXB4sRq82ByNP8A41jXWvL9erruQ3w2hgH2B6Q9NMIX3Y+D8icTi5ZYqX/OG39w7cGrbrqDgpgLMTMeVFBiXtiytDkJpBi1uCt+WJvIYK7+3jLdCmFGZykrLPBg+aLMHiuCLzAN/c0iHnAgoV4zHoKosThnZCaavCYlXatA4IchyVeb/fSpCBq83++qrhqeKaVkHEZkUDXb+4rqyNp2lNo7RkRr4rT41yywthhtuNVHBRswfqFFeEHZnCeo5EXIGHxrzB2BToOYCAdl3mANzrHvCV2YaMQRKzUvMZWJp3gQYqFGZkJoo1UJYDZeZHW3gp2lJoahkQxKK3npkDEpd6RyGlbeJFa2Sa2hZABQ20v7mS+QGrhXTDldfO8UO5Wq/pPTDRcyglUpw8rMeTRcQmwu3LUHKoHRcQ5PSdjpa1axfBUWW19pjVHcs4GETwhPIfwAnnt0/t3jtkm59ovol6pz4J47TQ0kVw/GCXwwWQMPFIQfb4Wq/vAtq8yuJSOmV56ekTg9NUBdr1YGadpzMJRUe6xS3mZd/wDYThIV2uZ5oqUZqBACGDelTKgjS7hm6Qg+U2FpPCqzl3LAS0RstuOorKbvEtxug6CCyVW7ijtK28oz2qpqsSkEtsbabmieQtyP2VxhL3l49MGMsI316aa/uKzHLMDaUhT4r9ThuUciW4V8ZzU4YQGU+0uVwLd+/wDo5UOuJquZpNEcg+zHlss1H/0zuDRW+AlXRLLz1qNSfyEMlQUHEUDFKt3Z/wDeRHRv6W+qbjOtfzXGy67VEa1Jf470pAacsCJmDRcYrqGrVfPWy6vPTv4Qbu/+vgLLY0CIsCWqwJ/Mmgtiw/L6mA7FVEYVIoc5h5Z0dF2rFC0VApU26F1qbFrKiMQEVOYWKLhvLlgBmpeamOeFdDGsvPIbQeKP2lRN29hoh3Y1Iwgm9CxEiKbB/cSkgApWx6iEouq0juOp1WE8ddopMUrlQMuNvOu0vGZQuY7zMiiCsdoiNJTwlu2UNyrl+ZNDnmf90NR8TtCaADK+HSv4TBMGkwnfpYTYVdoOEaQsY7ykpphrEGoXo8GCPrBuTCn9GwmUIiNQR23NHjHZVeAly1d0K68YIJLqpfDqiV3HeH3hcdNjV3/yYYk02E05Qeodkg7zsVwVc+V5ituxmH5pFHzJWAhQVs3pAgaR3LGkNxGLBOKJE+aQ3IqK1NMKl8ggJo/65mthK90oBr6BePvcCpyFuMfm5bAPxdoYXAhQt9Ee8iy6jWYNlpuNTCxTAPBRPI+PND6QXv7BfRFmKC7NZjBERLc5omJKjIztNxKy0OfGph4S+Ys1dx2JeNfpurQ9ZtTUNfHEdrNRHUtXlM5IJM1eCOSca1bZ62kB1rs32cRhAOBHPZ5nbbMbtLgZywxvn7RGt2GTvOTJoAfuVCq80efaZDdlTkEZS3j95qXLy0KIZpKaVpkZ2+WLq0hU4TPtLWhYTU76QIdqELH99PieJRbQF2Av8zA2MN9b9phFpRORLrCj4Cz2mn1d5bgPFRpYRG9Jo8WIXhUwZA1Wfus/jSE4fctTfHXJdWewMRmvjNVePzDFtP8AQY+N+uGtdPCZiH0L+1Ml4R2wr8z5fmeje0ydWC/Jm10Or8Hcjw50GK/knhRNd80U8BPi90LE3oaqPsE7HLsmn+uJaRdTVL0mn5DULM6uGZ2njzArf9zt/McxPnPirJMPi4jF46/fNEoPenaHR5jTEPIrSfB8IAibVWBtjeW/5HVdOIu+pIz7b1J0qbUIKe8BB/SvaMgK1Z8/epavtmPKaO1VTuOtEY1gGPiw7Ou8yiKtKsMfhhihYc1xNGIS4r9BA301+JgWvj2Iav8AjcStslwKGUaAlg+6yk3BX0mHIiDsCGbFUtTaW5F1bmnT5niBslZexC3U1Abo4eyWq3NnYJJnSQtMcf3Gtnbu/wBsTGqD7YYVhTKP07uoEsJWG89Uvpq8JrS7cRcBOeElnHKpRhiKD8cbzxBsaNlUC1l/tmA9ntFa6lwrXDLImxhvWEJNlJQr8uYh6WOyRqq2lWcKWCf3RIOvim/SEMdkoXHRy0DVXM5Kd21/627KsmyGIapema6CPCglOSW5F3AiCZL6ANAIgKSyLWi8BEHUvodRx3IUguFdLPtEvp3+EhgUVCQdo2TJoY6i0LwLh1HdlSiFcC5SS4BKxUANCpS7ouIJSXDjD/lDt4dA7J2QUKiNQPTaO7kCoAcHUDQVKXdFxBKcwAKMQavPiUIA2Ihcg9KwuBLgVFdldaXdF9AqK4FyqI4CogKJogzEFMaYiCUlyqKgNAE9GgZWkDYIEBRwuAKAHBAGgEAUBHZiF3HARBMlzT/XO7dE3ABQUdv87QAeH/wAnIbTQJ8diVHnMHsnKJlnpoiIljQ2fXVy2u5GIzXB9KqV5iaWYP8AHF4fZuYABscn164aDg8odM1o0EHEGAOkVV+W+szArTYnx2DlzTUelBDWssVXjY8nVyeYijW8xKHCavh/gVtWXW71Ud2Wn6J2NTF/T2Haua5qIagDXZr84g+FfwaSnrXoz4ARQS6KYts65ss7z9Wid61jatUS/T5a+rg2WfwEENoaswMArE0ehUB2nYmad+I/zePpNnylH5sT7Q6j7r6PVopQJKM2RMbSwvtGa0FPm4QwKJe4xdeAKqnp8BArK5VxaLZ6IKy8XtBbAdmZkwbTG3rAiqcKCoLQOy52eYwoFrRPTJbjI1sbu6/UYySIlGYLYeBnYwg9KMnwJO9ilcVtaNLoCHVcU0YenaDiSBcCO5KsDsuIlAWhess5+hTUh9INCM+D2noPtKXVl9FNTXRTUh0zm7aTVHOCpcZYXqCgyszF8p3dPQRLG/pqNr8kfaMzbs3OZsyQQptHTXlbNojYcr339veAiFQGxLuXXRaYfAF/dnn1Bq9ooJYhiU+wqsHxOvqsAWaoO6qhm9y3XgiRr0apt1ZOSaLeERZp1qDp69+P4PnOToslgOqFw5W15mkE0Nz0/wCp8Lsm+p9Kc30A6Iy6II0HNQ49mGhN2Hy8yjGxX8Ff1dlsFKV7Sl1Zc+L4nyXbrZdWX0pdWX/lQTv2IaLp9nfr6tPWvc6EU1C/uwoKnkc6xjiUJvOZrZYr347Q5BDVdusGMMVUzBVdzHoxstFGOpDAbWEoEYOBR32lsAS08vSA1CVa6xCuwQ1eqk1GWN67kthTVyOy9oqVgbXqVr94Gg2qavBHk5DLMixUtmjY+8RAspaDGaxYHg3lCJZaAfPWIwoa8N1cMpy3oVDSPNeezhjWCOrHCBV1OGG2usbZYJxrgcSuaSL4qUIb5baJ6RbcMlcY7w06qogwANodnbbzhZ19verRAJb8P2mF+f6zCdTyUwE6iwYZ9lfURZozpLOl8RYYRdeeZUBHoDtcqtDEunmJwIpKmDaFUIB/bfaBptawsIYVuWmtYq9lLQuEchbangW+XibTYj07dczmA8Wj8wNGAeUeqmH2lxlEPL/s3WqD7hB0QKajbF1Mbi7x1tELxuLvB6ACrWHQ1K/MYNg9NZWkobS4ATDFAEGaGfHr6rGfaD8uipfivo+H2dPXvx9BhbZrQ5x4MbMMOmO4cqt+aw5JZfZaaeTH/o2uw3UqVyNzvyS/Y0qpMR8jau2hnMqs39wYkt6DJdoAVS4kWh3GdplczXKY6Gb1YvUw4HVLvNDiEDupmYqijF4RuI3hYuoHaigoftEt1rN+rYWHAsctNZnhC7i5utUVOpCL8vNjd5lugLK6Rqbi1Epr+IQ1qml4TNe3Uqo7KAC1MTJI8gMVzAXU7wLbmgurY/budVxWsXpAatVgnBdKLx4bgv2sfHE530K8zaa6YnB8RsmnLVa/eDdS6iX4SjczVL/H4V+E0fgt2eCDjX6PVoHKvlVuRQJdjLQQzcJzC0p7DC04l9Y+VKvanw2mV4Q5EJHIvcxOzhBVK+joaXiDJv8AlelfQvafNd58Jwz4fYnx/BPk+Dp76J7z0X3Z4FJ4glyehdzARpU4aVogyfOiFrcWiszdxYe4/wBzBiOfUcwGYTEb06+kyL5Y6HWgQJLeoCKNTeoYjfsUZGRFm746uAap4L+5rB8SgjFzR/GC+45GNZZSVOgPGYZORzrGMKyhHwghVqZ4XfbSIgK1BHwjk00zwvynqHsT073T47iemfmJwo1xLz+Il7bAgAOCAAGgfbr2w/RfvARQBuzSSLQji/eZPK394Zk2HB9nQTatUX2CCPcHK2b4ggEbGOk1f4IKJ26VbVpBYUx3ny7xAi7LKfv19Vh6bsHBTn0YVs19iogiqfqX3hRLtODy6/H7Onr34gA2PKpr0qYtweWvpHffZ3/yOSv8Pe5Rjlp7aE+F5j5vZnyu0R6b/O4mhn3VPhNPNWKtdp6D8p6J7J6N93S8BE9D+IVsQJD8Xom8fP7J2GWoe5KKYrxP9ymwu72QLABS77z138T4PcnyO7Pg9yMBdhjXj7TWqMRf3Z6v7T0n2gAGj2R8NwzCAedDYQwvIPH3g8lnNRHwnBPkuIqnQgaqr/ZAlpZswmWt8rvOnmWzIya9Sa9607Gr/wAcBUAXX6kXV2mpP+BgckeCZPKwtcXkjHUSj2Glx8ZdB+Rh5wnqECjulFe4c/cL7/G8wjEc7duYfRQahVRxEG4EmWceK1wBBVsFhwmI1a/EeayBWP8AkVyJRN6washd5uHdxhCiaRb8NwJQuwVoxRYNQ+5BgKwKK2uEFm8igymN0UgndoOe4Y8GWozbmrR7AiU4UAqzpUbexWK/XWqY7HJE3Dev7wEP5y2qrvroEf1POKW9hqUddKXtUuaBVOqN4IANylQHQjRVQTC7Q3HKUW0OsQiF1bjtKU7UNy2FCjT9QuNnm9oILYVpmXQpVfLm2SOr5xzl2Jogq+mm9p2VV1YdNNDXaOBvaGni+rnzOg0A+IOj+IwDTbg7zSNNAy58Y3icp1OGYVBo1qg0GhO5n3o6hDUWdJyMOrvUPNqIoFuIduvqsGi2yGq5JeOmOL7yqfsd+8cD2Yllugpl+qo0ibuF84rrr5cp69+JdJTBvc7OB0KC2LzgnWMIUhjmbEbJoM0+UAYqKCi6/UPz5Zu5jwH9YjVVopzLzrnduYBhAugSEkAABTX/AGF8CnUM3NCoOo56U89nt3l8oZw3E8CpoC+Y6xoANw/iD+inQd/+xf8AZoRCbDaNUlmJMBIlLuV4UwZxHz0TUZYMy0FFyzciDEMPIljifcZjGT4Igj7Tl7CG2XeHhQ1LlYVASmzRi67uq4+8rvAXKXeJijUqMsAAoU6/uKd8iarkhWh4+PvH9YPnbVlMc7v+yqXaP9dVmqIr20Ggc9W8XwUAd8zO7/HcfwYc8COmNr7RpwIKmg79Tba23AfRaZZsK3nDcfS7I2hdpLp/zfUF54wLlfl6wFTsu6uX/wConMSvn/MZ9QZRg+vVVr8iMWDbUV5xN1Qv+QKhfIvWOHYWP05PJpx/MDGHS5a/6tcHYaDmMeqUu+WJTV2GfKF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V3g01S2gV2/rjKEzPa6FDcOXKMbA9kTkXIdIHXN4YziDRPfr5wEDjbhBT8j6/US59aCulllKXkTzirgaSvcFn851taUtwd+VX9TnTDdg35m9dlwnEanC+UeqXhUO08Q7Glw8L36Co/O1fL4/Ros2UuBesv6zFfSBaoOqU+MhAoRVwP4C75dZrb/P6nHGfCW2tge+PgvYU7FaHBkGsKiJY0a+MgKyDqaL8v2/UiiVoKWoWUtRG7wnc2Jr1Bf8Aeba6/lkBeZvfnEYhBbBvTmVHwvbDA8x8P5R+8pwsGot46pvXZcIchL8D5R+kXkrOAIp86E8nnE2JG6DzTsynqgQB5q+AOZ1cHN08baovKtfg6Y7kvLtOjXMLX/3h0r2qNo/O1fL4wMUW/bNB/PYxQw8baYHsq2eD0/ve37QESAVcmp5hKGKdeK9wwsBoCAdgxfmwAVys6v62KUYOUIPz+Ofi6yAD+MDEWahaqnkB+P2lCmJCMHa8/t62ZIUfjNSIgIHx+22w2jY4exivjB+CafMTquCs5SU3kHkv6498H5H5c1qewD/AH3ksCFoijX5+Mrkrjyo39MxXATfDNcBhIMtBRTvbcv6tN7/Ez7PD74A675V0qcnL011e07A3wd3IRHrYXYvj+8fvJeceJCoQXvr1Q7lZqvF4/cuMReheG+Aa9Ap3JFeYPIxwrJZIm4m2hpH0afUWv0FyFsdb2V78X2P2UE3jVIagBe+v3ucIBFUKnvr9TPQpYrzOfVBKVml4vHoysqWvsvHpzLNjp3Lx6H2MbPlvZOMr/wDNTNG98j+1sTkvakwVt3EwRBesBO45KeMwZtEs19uIRUoAKq8t/WgkFV0Af5ORiXaL4+RckbCcgTXtFb3fH/gTP6EUY0fk+HD1IBwY6ezfGNZgfmBu+un60SM8HXY/ODXrACC7fNxER5TQ1TrqzuvYwPxougED/tAs/iEO0c/OUDYYmnDFn4/Y3HUA2TgAcYgn6jh9kmGWBAEA/wDAgeeXh8+HziGhtuX4uJyJBwry+X9YYCaPBF5F4MPo42mfDjiFSo/9v/8AcVf1qz7kQPlzpNWqfznhA0P2f+IRIA5VmSje6v77Pm0cPlwJX0YHcT18Dro179X7wlf4GP25SB/6mH0FQAqT3OzziPAS5q6Pn1Fn8Ke8XSb/AGAwtUQDuubC/J7e56Q9nxQX9HFhnn3w2ftt1mEk+zOP/GHTIXUjg/zcE40XEvjg4NKcfog07ps4DysPnEXxkmJ1TwcvLk6GNwl+acODWKcQ6Jqae2v3tU4dwoA03hxGwc2sDPz/AMianAEWwTj3d8RuGArfWYhctVaIaivb9/8AsuzP7jt6/kv3T6feMF0I6q6Drg/YuEU6KdfBAyheiyPcdnuOFagXA3JeXWF1W4AdEO5Hyv0NadalN2PeMfa4GwiB0dD7H9f9t3+phko1j+ETj+WK3Qa7wnr/AEvH/wAv1+Z/g9F261UTsPJj6EQc+V1PVxEIDtt/jD8S11BJ/hkkjuFcwuVxyIPYOuabuhWs7BY7y2o0GkhcSnSZ1eKkBncRTeW/ZxzehTjEXeYmoQxCTjF88eMGu5N/WPRiqsOSFNdeXHk72kN3hE6++Os5uDko3I/GJQ9ChNhwHbl+MLz3Oy12jVxxaiOBeo6czOYDGpiVtEunFROdSkpeJOmsv02sl6y6JT6yEM+CdS6a2vOzIcLNKz3L4lx0sLgti3XVnXWalNfoIfAYw7Y06ssICaa0HHz5jzeOSaSfHq5AEOYNHy6xHTmvlI+KStxXIBZed2OqMuuxHk7XQ6VXgzXSoy7sq0O5HOQJlyQT3GmW/YVJbVTYFDX5zU01SFFO4REuTXISW2wLo0KvQwouQhbNpVp5InOO7YHZQe5UwroFjrXgvCaHu4cHOVsherbXX3jJJJcuNK6eKRLh8OcMZ2Xq/jFaII6LQmti/OJRAIxFUE6E6dMYRBuliRJsE464ZvRgHqQPDPhx5DgpCcbGRHyYdAgIBUsnQYKvQM1Y0Iu6lWnkiYS0Aru5Php8eirdwgOR45yVgRiw5OEHR+8ihCVPWB1Q3P8A1iPSBuuxVOzYiOPvAgoeLOu0A74KgYth5t/9GC6bEIJmnRHT04cH1WIBjk9CM1tcifkDOULtFJiyMaOYNB5WHzhCNRXUZYIp0p3vWSWEHOrnvpEeebxn5L0JUWe2PTorVu+3/SeMlzYU58PU/wBjlOsXVRqXsWHt6H8yDsmUuxz/AOC/3n/wX+8PGGNksg3n0BloCuOIrbkSh+EffB7gykL84fUeEF+LmzQZ7xfhcAICt3rP4GUutTSHNGzHQtd4QFOhtcLA4MhwV1OV/wB5R8ue6xJFg8AGfY/f6FDkpg6CByj4wCNSYiIUaJMHTi/utj7QzU+ANSah1b9ZxhsNOz2ADjvi1XXeR0HKIJHrioNhEg1se+VuQUjqfZ+MBLJTA9LQh5VXGdcc6vY3fHe++QgYwBoe+silfu0mh5Rojiv0g9kvpuq9ASFXjnGE9RWUVwx0cWg1CnXVwGDZ+MbHHs+qp2bIjhxKpbLTy3exjNwhdzLFRKnZyj1tVmoPsctW9cAZSrZqReBDt44echGImK14uhgq9D3w8uAhbNpVp5ImKp6KOoXnVrL0jgDIGNHMGonxhyMCh1KTX/hmCKIAKujHuYktjxz+5ki7Z6PjgYEIED1cCOLlJB7gmCGToQNXYbT5xPBkIonKJMRkmjygg/jIGDKNaoz2T850tt4oIYR7QCBNwV5MAAEVpx/Qd3L2pD5KqGLhe6aReZ038ZAtbqszug1m2YNhClialXC8gktsj/ObyYyBQ0dVXnpMarW60Ty42EydHH+fhyEqJACvLOsAZs7v/wCs5RYg3rkt9sDxXYdLb9ZooEFKDPyHoEeEQrFpO+n1ZIlJUlE+ZiTH1yimg0F7mGwiiM7QfNTOmMFDaywAb1Qx/wAxWB5EdjCITBBqumuXIklR9/SUs6atKQWmmHxiIQKQdRHYwa8yQRL011xmNMQ5Nz9GFSO2AtTtdCuwDAhiPUpnBw756Z/Vd3ER61h/X92f3Xcy+C060P1TJJdduh5nsR8uOWFrlkBvVDHSgVgeRHYwuMAQaXRrl9ACUSfvJAAgfy8MI6l9Kkqs4VyP4UcAEESidcVg5mr/AHI/GNAMzqhA+1hgoIwerLhuJBnav4ZvSQwO6S6j/OKqngSElVYXPyXqChhvIePC8B745VHe5A+wgv8A7wAgiUTh9FATC42VXZ5z/wC5/wB5/wDc/wC8cEk00MirX033K17kxrb4aWp7kae2R/RqWJvT3wpwls0pfdxsBufYwYENX3AxeZW/wd14DDYdg5M7Xy/Lg3AQ6rqnqrtc5kHewsZ0D/BX+T9D3qejU5vgfjIsjQ2A2TA1tSs5AT7Q+MBsBfyFXy1wxG6Hv6Lb+w7YPhSboiL8pjPgZwQBPhEzpbSy7mOYVge2f9V35/cdnoRLYk/WCACAc+eGCaBfY/79Ixpgi2GsF7qj24ydSpko6Gtzq+mRzrGuhF3NvtvADmIEbU8pzeo+MZf3aUAt4YfGUQoSDsjCYXSlENpbOE3Ewo00hHnkR3jhOUzjDIeKf+GcIkzZ4vHx+tYKkFd14K9vrPaDhvwx1+6g+Rt+jLp5SVTyJ1U4xjSGEZ7EZ8OIpBIkqK1VWjG2x8kOo48XEQRYbHDMDlamAiby96yJENdpXbDJ24LfAPzmuGGlMbejFIUYBAQu+mGoPWwDyHM0bwUQKoo5lZC9N4RxjpRCrrjHTHAbWmzhG/eJx7xCoDAHxxlW406ij1Lw9MtXhxfi048Y9815gPO+q4IZXJwAXj/09JLUgMSC8X1FQ3Mwpdr4BcQ3FSgFDWjngwMLLaFBRQCUd0c1/CLfVXcu/DkMyW75kH84hGwOqtlD5zfLKhR0H3w1al3QbeMbesm3te4l33MQDstPnAP5xizA2qlEHzjzHhJROh98H1miEWInDFHUTES6Ups5gKy9MLPUlEOoORsYJ3KEiO1RxYVR2qeVQuV/2VBcbxuq6xOk1vn+XGVKCgjV/e2KdTRV6q7l34yKJLb5kHjziCM9aqqvyvoEMcX2q1PbDZE64FC/nIEe2AIJv2xj7KVxp4w6NCTxeTudzrkOeoqD28XjphZjA0U4A6DoYLAIpoAkJwzTpHKYDUG/gBWeMB6aY0pHT0chSICH9IzvBw3LfoY3z/gMe6p3tuS8efQIGDGKUHJW4kRt6mo7eAzRhi/wBvTs+cSN6gJ5G2fsQkCp7jhZsHZgowNAx99vzk4gMxpVht2tVc1x+AH+Uzz2ngl49wZsQXAchZ25wFLCON4s5w0iAI007QnOLIv+bW/lfjGNSQkZB+A+8CpESJoFjT+PV1fQE5A1vY/jDcF8wdzvxD4y3koeYBeO7CZMlRBK4rcb1ACb9sdiBdsfLjri6NkeCGie2V9F/UnJ2euMNLs3xiXyS5YrbbotLvk6QwsoE9N2XXTFxYQAMQmOIJlOsJ6brHNizRPbAWBK4Fi4O/iECCNwfiF9d0TXXCIctABps2I37w2+2mfhYFPvESG1gqPD75JLrYTVG4AB2oi6p1OPIzJCRkYcknO2zdMSj8tPnAP5wswUjXyaCfnGCyC7wkBfZcoGg8j5V5VX/o+rkk4HgeTBfPwfQG4fDg8A3QGnbV3AP/Joy7XlXfUbL73vgBAIAiXudH1q4xvooXk6D2V6mALIAQBwGKEqRYqx05//AHkWgPDf075nQTXo3sfvDA0DIUdRO2EiBYcVB/45ACgXQHhMlZoJNFhkRRiHqOHSfn16U8Lv0goBoPIdHjp/19CW0YDarlmkfI9+b+MU4FFUKq2Htm8xI/dzoeXEHWKangpxfOsbB0oaqcp2zjUxrQtCFOszvvJeaJ/nAExsR950PLiV8Amh4L0XpcOp0iabOU7YL1Wl4UKS72FwNZ9hHDWHTExoAKXgvS+cPqjitOreuceqtYiBtvjBpFPlZd+fGOMyDD5i/wAzDUHR0k5E6J1MT3owKcxU08Y7TJt+weu/UoLFCHivfxgu46EnTTT3mch2+wlrDnHviDlOivS9+MLFBIqgrPrJqKJhyQMDtXH5IDkjmha+OcVSmiGd5bPjCe05j1Q+MKgjrYA2WBvlcLnRlVOgil8OfhP54kFwIAGq4tKoBE6ldnnjL6RP8EP88PoKyOxWCs+sHsd1CKgYG+rgBSzLHMRa+OcR+MAC7hanxh/gMaQo4z20So5i8+5rAxzES6p0Z4y4+IQ5QVLo3hv5kAUW1qa5DDfRIFfAnQ+OcelBEEc11nbn1hcswcGoarGpgXpY53SbvyxxHqis5K8zxrI1AN0OGdTyYlmpeuWK889LjIzVHU7QTrOjHP7rtweDLfrAdAeuW8b8YjAV2U0x6+8maFRVXJIxfGbDOPvA4rm0w8upSbw/xUyLU1ve1gYS0Qd3oHviGDgH0G/q44dAR8f9c4jwvPTfji4cSYt5Gic/nxWZLnzHiMIJyzTehHs/Ll/OGpHZosT/ABgStzlOE725XkSFlre/M9jCA158AM/GG9/elDCPRTyuaQvHByaLH+QwUxZxVwnvcG8TUIinAD0wQOgwCrBtlXjFV3rgS1QXRYgVW0XbS7xKZFsHI67zSSSHz+Bhs5W7DIvVXrhZL2yZCQsRmh7lEUAXgh9499nQ11eYH16iSkhTCBIGHDuOVpILWeOny7Ybho0d1g289sHvpIRjFB14YjCgPK8nGB2JFcQ7V29jHhDgigunnliuJ3iK4nbSmPiRY9iTNWE8QtC8bXNYOtjjE66R+MuWvz6cMl5ohZ9iPnAW4OtS+29PGJ/u2B+Bgbqnn0/pu/NaMaqYg7V29jJKEXg7RPILicoYiUFrtpTGPYo7QN/IxD4jhTgXsGpkAmYRYahzRR75fxPiJfzjZn01YvIamWIzaJ1httWviYRwlkOB0HAu3o+tOETsiD5KfGQ2Aj3i9djE/ELYLAGtHHPNwW4+2wRsBU+XvkqsdP0FAvHfK5LDV9RzpGf2Hbn993Y5aYQ6ULkFN9mAgxRDc6YLt2xj3Op5z4lEnsYEhTzAvpSws5pEpAfAPfHbnGYU49sAABA0f9cOAHSqVT3U6eMU0gGoDfLYvnJGjiNHSdM7c4KPkBVN122QutpgQdxI+5FfowQ6aGqn4HWFCiJrfbiQIYKS4LJ9SVZreyNRdNTCBljzPKKvwYQB3jUS/B1lhJEzDhSRrxQtAiTo7woZRjxBD3X4wiGn+6DB+xklApVJs885P/uhadSb0J7GC4JBgJSoi9nCbNImy10gOHfnIHuWQLVDKWonRxc7eUZb+6v168Tu4hNxnW8LiccELAoHEB27bMtShqKAg6dlPNxeXdLAAZ1b+MLKN1k3gUZdcmLwMNk1iTBXhC5oMImt98qgJrMz8ET3zoFb8KVcChAuXVRACwHnZkeACX32fOayDLx1RrghSjjBh3DQAdDS9V16Ggf2eDDLrkzeRhdmucIMKuswCnPNyIfFDKPiBVetoJ2DxgazBTmLvhgELDFUnAGjGyYi7iRx6ZtveB7WQS3Vx89cXHgK6O8PUKCW+a4x7hKU6Pwg4tRK5LYdyqid44UGbRgTAaKw29eMjDgQ2NFyIkSyTJw1tmqoGoQ+8JkXEF6cCoI8SeWQk2XZiQwW2orX2h+zCMw4TBANVRQcYBjbZKWzooxmJLUx26zpqd3nH4R0UlxeNwhekPZVl5HOKG57yir8Ysc2VQ3uPGGKGvVlZf8AraQr11Wbhzwj4cF5MY69Ca/jEepJ+y7hqtkOnOIgE0iUcRc9kj9GRRDslwAACB0xNVHlCXHIk0iUcY85FR+jDYQ7JcACBAwNtABE+8OmHAAHxkhDG5Tv/ky+hws4eHymAAADgM4qsgj2UxYKzwZx6+B2EfnE7ByGfxhop2DP5wEXcFD6yOAnEwWEOwTFS2HWbyCAeiXBJbSAeeGQdt4+Fzrl6EfRhUM8lzjIPZko+8GFfAQPj0QSJTDoQ7BMVLYcM3iIAPRMBAA6BMLADgKPvDHCIIHxgZUOFOPRevciD8OO2joY/HqCyS5Zv0m6OjH5wkN8CH0Zz1mAPamdEPBGvbIIDslwEAAdDLW85hMZqBx/nDAfAoQHwY6EKBgfnA5XwEDE1UeYS4n1WQo4+Qcmx9GRRDslwAAAB0P+udcA3PsmHTFwCB/zeTBYK7gn/eqNjZ+pat24LlXP/rf6YDKXuh9pnGSgH3GFKShAs/lwDhC1oeFH9as1G8K4PfL66T58g39KDYS7Z5gdqYlPUXRRiff/AB7bUi8FhgMhiHUf11qVJYc3liZPSQOVcbrFFCOUUjycYyIQFbtlvs/rYx/j+85/9b/TOBn7HsDL6FqvLl7AdV4DPtoyDSEH1JQe6R5Gmp2z+R9tfN/P7EedqaIOhQ3nOREVJVe2b8zKd9pef0/Rj+adyXrlSWY7mLoeOcQQQpiIVBOf2B8srHQg37PQDTwgO6uH0UgrJyU9THsJWbePp/VT+u5oY35c4ElTuzQ87/ShzUR6+ZeeTABBEonX9iDIVi8pXrgMVP0HYj29FeJ4oCq43LHtSOT8/wDNbKXbuo5WnDW+Kavl5Hxc4qyHfvt+naSfgOA5Pdx9yNUD5Rv7wvYCGzZHdOHkcmUKYCGnxjt8oADVVcVB143v247KOjH4wEQA2r0waa8OX9XINhpbdYsFOUHK4+zNgRUcV15XAEm+ecQtjkCnxhRw4IP1isAFVYGXdVzOPrEslVQfFx/tnPTpwLoe2PBRygzFIxyFT49ERvyg/LhFg4AH5MRA/qQHQJ3yH4OilCgrOPSJ21WfS4M2WEo/OJrNcMX6zkSygfYYkxA9r+gykd1mDS/otazmNz8n/PP6PsxEslwXfoZSHdZgiUaYZSO6zBEpsxAGmYRGavTvl0Ay5JD7DNDhQwBp613vCb22KipK65cUCujIoDuN/ToNEO5f4PyyKBPFpAr2EMSUCvrSji60nXDTm55St7uk+MGwQLs5ex+8B6EdACAYDgjOziBVA85pO44+kdxqknw9geszEDA8ri4VS5XssuV7Jj8pXR+iC6NCIiAo6Kt8GWWnj1l3wBe2zK9xTerL1SJfHqAQxfMTT2j94411VQF2v16f2nf9rTsHMoAo6vtgWpaDSrwGKBVAOrhlIdxuf1vb9T8fAM7oAB1KPUzgxNFDkGzDSMaSg2T3yjukqlSC+2B1rcRdLaPYwkihC+P2A+uZBsTqPfORwrqAC+dYjcuy7z+o78/u+3qHQQcg7PQVlhyXZ/yPzP8ABnXAUydVb7nE98pjzXX0MaH2/VsMaRZjwf8AGGeYjCIOfbGkBKx7L3hiGsuuFu6RgOCZAartCE4lbuSY7qW5GHY6FCe+CxAFoeJzL1uGf1FCoAXZd685vMy6FNvQbubdGIEnfQYbWuCoUBdm8uWchoBsJ4G/GX8kf4C05NnXNNrB1KEcg4vfLA2RFiQcNIxQtIfRCz3weQBNBRLzxrGbpcS0NmlYznxciCOznZjeNcqQnwu/vAlrjRu2z7nnE/3PaYRxeETKRETfxBvjFnpa4OmN6zEGxNCMA9K2vjIw5LhOqFXXkzdL3zLAHlsfbHg7+zRB7YTBmHUiHY74wo6DBBeuHDmgHmejw4gqTZMwW9JwGLBTacmLxSicX1ZJSNRlpZyrQOIXAnSbcbvonyOFGqIXvvi3n2XkdeLkiE4vmccxfOFhRRUjK9URL7Yt7ZPmGmnANF3mlbYK5KGOh6dcVsUVNPDSEkC98WwVkFRKsdHY5xBnDLsdQxioh9RsXn2dcIUUuaCm3iQwaeIi7qV1jUJGimXkqoy6AwUcFGHrrXFRgiecRotK0rYzpm1TLRIINADPKjfVlqD8iyBTArwA/wAYdpUvYTg1PYCoV/hnWAvehL+DK6X2RiRj0xoslut+Ae/s5p2SaOxOlf6MdR1aI5V65yHVeAb/AD955kL6ArEDI6O4Dp/vCl5UA7AYKXOAKv6IHL1Mvu/5PRFUDQ8h/qe/tO/6JP0jJ6Kqbr8Ys5isLWJ30fOL+RmoqlXbuPjDWWLbwu06mHLwrVVToqB85R0xyoLNoheTLMhWJQ6TjnGoYo2HK9gygURovoThjatlhjvxLAXJrTfJg0GsL+IArjHpZzYCodReG6xgCCXUKfmX0ROBteF90JPKYWqyCqUEu3uGAFeLQg/KZBNc11dg7xhW0lENk6ArMJywGu78H85OHFVUC3ctvHTKSFVkL16GfnNbNtdQ0x3gJ+S0PMYheMQWnPso+fOUO2dQai7iIzxh9qLRgwPMDh1XAwkWxCKo1suIRjTsAonnePf6WDoK6wry7CbGgx1itSxzE0pijDdWMV7+e7gBwhlcqlaHu4xnsna+ReDFEBiRgtewB95a8Qq6XArAoZhQ2HPMwDuRV7GIWE0AhUbp4tuOH/USLonHB15MBSUvUWxs35uDqG4vdN3/AMdZZfaNG14M++q/1+PvDnWPm9zy/P6dqbJAyvFXA2TXYfYGuXZJRodR0qr4MeAaw6ohfvHyjB4FuBHCcK7dxDzpTB7OxQpydEt8JjfRGTorX0mTMMUCxbeMNImAiCtPU3zgMhAD/Ttn9p3fT/8ApO/oQfnfWE8P6bv9c1TnIMK7jOyyfeNSiPBAa27t5kwtCUHY8XiYjNoO4jtJ8Fet9dmEKI48bE+g413IT0KdnFxw+fqACPEThFCiafOJCHTBB40ACbPcwRKejrw3NCzOhzhA7tHryvxnNeUDSVt49WvBU5SoPWgTvhBgp4PdxFBpE6l4JTOpe6u8DjBY7LLF4IceMIEYAv7MaNB6mde68xMSwSyTcIVvYTjZir3dfnexvMTG2kakZNBXgRPJ67zP9324aPf+TJxpBSCg7u0eMLLmlh8ubtxLfSsN4AwOhHrru1ZyG3+WBlaqQPnFxlKUDvoQdrjUxixyJKb+z8BhNLDD13fw50zlpdh09i72/HfJM4+LL3Dv+e+GWBRGid8DZWQ68/5stXID0r+9XNxCV1fSFVY1+QRh/RApJCE1/wCyMfbZ9ALbiRw2Tnf8JkDVEoeeX6Tv7TvkoWoI194IBGjwnp0l2O5p+R+si47rHBv5+zNYYF4GaTzWVbL05T/oX5wFJx6Vt+K/jn58rYH844xr0oAYdYw4I9aJrQF5VcNr+j/BhZg44Fhfe8cf82gTh7TLTxNQTs9IXPTsGTT3TvyYtOHC9YRNeQnGTalBoV/zlkNSADRM/oO2Pw8Qnu8vwsYslNI4wbpdjnr4zSr5HWOOSSvBcEAOiHyxkupp+eRJuRtrQfMj8+nhy4WSBBXrePOBGuomFkxPfeGRZbNqV6pZfbAehdoJCsqqDvpFPa4aFoYo73L8VIofpp0yxjVQQ3CW+wm83KaHlNo8z/jqhGoIvvk/TwmaFHqelIR7WB/OJo04J9h4D2DPP3aRRL5MNvQIk3RPdvHsM6B7AEfvK+nnKdMbVnVcGSBIwno3Q8OSFb4E/wBPxjAnb0g06EhrEBwgApIHvhFkxihTTzkZLCA0IAGQKT4KaXmFwoyBCiCSPTeKrgcDUCQ6axrUoiQGl2XBA1uVAIj7GP8AXzNkT25cVIRgA3Uyj6QIFW745yuhHRTBe+E67z09kP8AjAuFcqVOpKZKEzBgnDyI8Zw/IJvdr+MaoAJDhDuJ95xE9RX6QfrN9rBBDzDR784gjNRQ1eQZnTGiIFAkSu94CAdvQUCK+EImIiuulHagH3TE2w0bkly3b6hc4OWDgHWdHnGC3RYfdVnxgtLqSZobkVBc8qA/OvOOz7nL2O0nxjjCEKJQBPfF7ASivkRfnGfuRHpG1r3XFfKSQXyJfnFL65oPMN7ZyuIH4krA084GA8kSiJv3xmgauUCX8Y7qEzqKwmFUUBUQcR1nR04IDStJ3VX6mRw2AnhG4ASoJXrCepnOeUqoRGf6yd46R+1x875j5y38cenWaY5AW+R/OCXgcykjyc4rQaGQTnTny84Tl0iV+g874yNoUq6oa6HB7YmpuHAln2+D18CCQF6DCug4NOlaPvh3ynSPc1f0QWmg1Z+P9HXE9SRVjg3H8njNDFgtV1T1V3jqhNEjU5mw+fStwJecnOzifnLLw0a+aGuKmBblVdvizP7TvkTqcGmUb7Y6jVl7wnpJoD7gj/OVuhIgrCd9fWAqSUkjG9m/eE5PaUS4McVK5aecT23kSiTfvghFIBBAs4usFF4IlXgxKo6cO4KI+R3ivWIoKO1eTi4tNwLe5ecE0cEMBoPthjXQQUTsPf0F7OHCugeidHCvQGa+yjPmY8nxQxHXJ465d+xo4BvGG1p4uLeHz1JhtRQu/FVPcM0s86JEj2h9YP0PPo28oPkMNGKxJ6032zbcqRFDw+2RJ0ANi1D3yMuJK4dPPTEhW8SxsrVfBiYXWjm90B5ycpW7VOF6yc9kxXG9sBbLSy6phhzkg21PHbWTPrUqCTfvnACk5Z2PjEHAVCPZNPxmndqAsX0v+sRmlEhQJD2w9b11QNvP/pi6Ga06ZOjhQR0Ik7Oj8ZWxX7rC6ePEwV4B2tnuj8ZD1dFfdequ3/rpL16lS4fZ4c4CNEHxrw977+pg5vletRQ7dcmZ1sbbl7Cu+r+wnXmbrNtCNwyup9hIPFvqJAaiPaPl2vX9A8+aQdbNTp5x8moth0AKhDJgLbXeLw/800dTZFnCOr5EcE2/RSeyqPw5adKL5Q6v/wCog9ojubbPff70qVZYjvvpf1nCo+cojPxk6aLAXWD26rhCB3K+7a/8gkcCKFChoezk0nG6iUf0uPva5AIdNfvJ2ggqnM+D/qwkGWNgNz3wPDgfAE29NqGN5JsisI6wL5wODW0N6uye6fWIanBXs7tjp9saj4kWO+O14+MfuoxumiPUemfh/UQ2GHEKPUAozl1gyUykRxyFV7mO2UtGqgbD84xwTkFYXaJdUdY2ExLVBue+FgdcOZOi6847iM1jsRu5eecgj2Og6ykU7axt8qSAybPfL51u7WuBUnXDXyB1gPYR9+iajhw5hx5HFajb6XqaL7hk4Sb7rAXsqR84TuH3NClfox37VvANL0q9+PQ0eir4jrpX4x3CRmXZPGG4xs1SkBZtAxsT8BAhWGxXR05xfPqzLxrYS9V32xPEC7bxvaS9R12wMoF3Rc6wAUMewjUEUH3cozDjOba2CbMBr1BoWbKgF3x6oQCM6WEN7dB4c1m5fqcKjr3MCykvXOyuDfTOBshB+NAvQ25qO1L3zXCU76bccV2tIzBxtAw4iptjeBDBncwJIl81Vvtv6xbrz014oC9tuTRLldw1slNb5uG4xlqlICzbDFscKMAFYNFdHTNTAWLSLSJ7XDAcpTrKkVjNkUTD+q92iROnP0wp+1ZHWPMPvKnxtiF4Y2r0MTy2mqnvEfDHE0git8R7u/bBhBYRO47e2JS0vLjbyeixHEFQK/xnE+IgeUX4Mqt6DuqtXiHC84MQyO2RSh06XDvsu+RyArGN5RMt4ix0FpOuD0M0EPJQQ+8GaaeDdfWN8Y13Y2kXUKiPFHnKFJMEUtMKVqhBNCRQfnKFkQyMUHYjyPoVcmR+L7vYKe+KzgSkd1dk+T6wR4k2rtL0kb7YSQC9i2a3s/8AmFkKg1iOoO5f+pci5oK3CC9gP5y2HaTs9PcfjE/3FxCJiT0BHRwKq3WF6Vvc9wk+cEaWx58Pxxn4f1E0AYSVWgWKxG7zWKmQWFrgU2JpxXJbGPs7b7wZgCbvJqSEmvvEqPLlGbV86gX6D6x5ROjwgv5cU0IY9rmlVa5hDAFVnXIqicasEL7inx6JrwG4NgCvtzVmegAhPjFxwygOAaLNdsEi9sQO9KCe5rPBCuFRHqP+H0/uO/0mNEyricHxQwcbvg5ePbJtPFykh+H84xNYORaA+P4xR0zmKcvvhrWSHUKflXNQStOos+sNCSN6yYSu8p/j0XnUNsikfY7xyOXQQLlB3VeNYQRBB3t+BcUZ+6Og+7X1MBOGSJACTbXCv6ylKF+QyIhll6OSOwm05FH4LjqGbQlV91MBPG6JyKTbU+sFozHBEHxQx3dL7AMWO1RU7Qs8zOCpI0gTDnZ8ej/+97c595jQnyInxcKQIEIRojNNMJEjva2V8JwsJEQAQmEBCekfoN/IBKYd7xJjylDPUMLidK9ai7ASI8YyQvwLYs+DCwXKHSFYcmUDqOTrGCaBMwDnURsAp9uAWBXTlmP77vgEAW1rpwIQBrQ2T3g/PoVSJ7qYDU70fkMfyROQRxf/AHMtsTOEX2wI7mhB0V6E6plUrtVPlPX/AN/9RL6FIFQ9ddMEKQoVLdNcJg2qgYNtPRpRw8QLbE7gZ+cdgUoLiGaoLP5xRCQyBBJn04u/5gMbEfP5x6U9kGyS3l7ejxjHVvQNIXsO5c7/ADsMEE56lX2wWx7dMdFNoVG6c1VTSSqt6w+uMLBSoFDPOumCDJUKlDjXCYSPh6KRq3o9MZ+rIIDXadUx0KA8gCfeWgTGAYAbRRfnnF1l0Yx2PILtcj10ICm69hwu4UdhxfDUcZoDeQNFeWurHGgIHCwXko1t+scMBsN94KfnBYBqiFYM1anXotLl6IgN4hHG4oOjpcGQU0DCS3lOmBrXdwhEw82y29mlonFLcLjzdt6wtUarAwIFxITV1Q0Yr5vkoATWIDnQAWJG8bwt2OhYItTtjEIgH69GUnNZ2qI+NuIzJWbW8eVr+MttJewHY9RL9ZYcE0z4Nj30jzlqlGpVBzXTHoYYmMqAbq3qdMGh9MGEedcGP8PYoXUascqahHLe2x7kTqZUFzUijudMehh1DmgYSW8p0wm2WxyUL+cDvRShSWeiBp4xlPlAwBbtrevOJ1NxBAIhesr4x2XtYCMF09dDhypEACJS6daR51kOs5N9wQfzlv2s1INmju9sGrrMA0Ksjvd5FABCPpTdjt4PRrGxyDTnEzR0XuiT+MPNMyE2oHG5DxiB0Y4V1Z0muuzGFen3VBtOvPOMgQUcC7TBlfyTSYVDzSkO9LiLfWAi21vG/TxSi9qoBcvDpg9TYg9gNGtB0MPbYmgOm3qdMuIdTBMV0R2XW0ywkC0RvhZ+caa9GjYKBqnCcacNXJ2SCKC/ywUryYDQOjIMlZILIb2Tm/8AYmlpvAqmt4mP95QUOPD/AMUQF7k6aHF2UT6xzzddTvEr7wf5VbKsHq1V/wCa7CHcFB27xkXNcACf/tX/2Q==\" width=800 height=800 />"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7de23e26-9a61-4eaf-9bb1-6a613e43ac7b",
   "metadata": {},
   "source": [
    "Helpful functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "tracked-philosophy",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def get_simple_model(hiddens):\n",
    "    assert len(hiddens) > 1\n",
    "\n",
    "    modules = []\n",
    "    for in_, out_ in zip(hiddens[:-2], hiddens[1:-1]):\n",
    "        modules.extend([nn.Linear(in_, out_), nn.ReLU()])\n",
    "\n",
    "    modules.append(nn.Linear(hiddens[-2], hiddens[-1]))\n",
    "\n",
    "    return nn.Sequential(*modules)\n",
    "\n",
    "def plot_gan_data(data_fn, noise_fn, data_pdf=None):\n",
    "    noise = noise_fn(5000).numpy().flatten()\n",
    "    target = data_fn(5000).numpy().flatten()\n",
    "\n",
    "    plt.hist(noise, label='noise', alpha=0.5, density=True, color='b')\n",
    "    plt.hist(target, label='target', alpha=0.5, density=True, color='g')\n",
    "    if data_pdf is not None:\n",
    "        x = np.linspace(-6,6,100)\n",
    "        plt.plot(x, data_pdf(x), 'g', label='real distibution')\n",
    "\n",
    "    plt.legend(loc='upper left')\n",
    "    plt.show()\n",
    "\n",
    "def visualize_GAN(gan, data_pdf=None):\n",
    "    size = 500\n",
    "    x = np.linspace(-6,6,100)\n",
    "    bins = np.linspace(-6,6,60)\n",
    "    real_data = gan.data_fn(size)\n",
    "    noise = gan.noise_fn(size)\n",
    "    sampled_data = gan.generate_samples(noise)\n",
    "    \n",
    "    plt.hist(noise.numpy(), label='noise', alpha=0.5, density=True, color='b', bins=bins)\n",
    "    plt.hist(real_data.numpy(), label='real data', alpha=0.5, density=True, color='g', bins=bins)\n",
    "    plt.hist(sampled_data.numpy(), label='G samples', alpha=0.5, density=True, color='r', bins=bins)\n",
    "    \n",
    "    if data_pdf is not None:\n",
    "        plt.plot(x, data_pdf(x), 'g', label='real distibution')\n",
    "    with torch.no_grad():\n",
    "        plt.plot(x, gan.D(torch.from_numpy(x).float().unsqueeze(-1)).numpy(), 'b', label='D distibution')\n",
    "    \n",
    "    plt.legend(loc='upper left')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ba086cf",
   "metadata": {},
   "source": [
    "#### Vanila GAN code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "critical-avenue",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class VanillaGAN():\n",
    "    def __init__(self, G, D, noise_fn, data_fn,\n",
    "                 batch_size=32, device='cpu', lr_D=1e-3, lr_G=2e-4):\n",
    "        \"\"\"A GAN class for holding and training a generator and discriminator\n",
    "        Args:\n",
    "            G: a Ganerator network\n",
    "            D: A Discriminator network\n",
    "            noise_fn: function f(num: int) -> pytorch tensor, (latent vectors)\n",
    "            data_fn: function f(num: int) -> pytorch tensor, (real samples)\n",
    "            batch_size: training batch size\n",
    "            device: cpu or CUDA\n",
    "            lr_D: learning rate for the discriminator\n",
    "            lr_G: learning rate for the generator\n",
    "        \"\"\"\n",
    "        self.G = G\n",
    "        self.G = self.G.to(device)\n",
    "        self.D = D\n",
    "        self.D = self.D.to(device)\n",
    "        self.noise_fn = noise_fn\n",
    "        self.data_fn = data_fn\n",
    "        self.batch_size = batch_size\n",
    "        self.device = device\n",
    "        # !\n",
    "        self.criterion = nn.BCELoss()\n",
    "        self.optim_D = optim.Adam(D.parameters(),\n",
    "                                  lr=lr_D, betas=(0.5, 0.999))\n",
    "        self.optim_G = optim.Adam(G.parameters(),\n",
    "                                  lr=lr_G, betas=(0.5, 0.999))\n",
    "        # is needed in D train loop\n",
    "        self.target_ones = torch.ones((batch_size, 1)).to(device)\n",
    "        self.target_zeros = torch.zeros((batch_size, 1)).to(device)\n",
    "    \n",
    "    def generate_samples(self, latent_vec=None, num=None):\n",
    "        \"\"\"Sample from the generator.\n",
    "        Args:\n",
    "            latent_vec: A pytorch latent vector or None\n",
    "            num: The number of samples to generate if latent_vec is None\n",
    "        If latent_vec and num are None then us self.batch_size random latent\n",
    "        vectors.\n",
    "        ! We don't need grad for generated samples\n",
    "        \"\"\"\n",
    "        num = self.batch_size if num is None else num\n",
    "        latent_vec = self.noise_fn(num) if latent_vec is None else latent_vec\n",
    "        # your code here\n",
    "        with torch.no_grad():\n",
    "            samples = self.G(latent_vec)\n",
    "        return samples\n",
    "\n",
    "    def train_step_G(self):\n",
    "        \"\"\"Train the generator one step and return the loss.\"\"\"\n",
    "        self.G.zero_grad()\n",
    "        latent_vec = self.noise_fn(self.batch_size)\n",
    "        # your code here\n",
    "        # use self.target_ones\n",
    "        generated = self.G(latent_vec)\n",
    "        classifications = self.D(generated)\n",
    "        loss = self.criterion(classifications, self.target_ones)\n",
    "        loss.backward()\n",
    "        self.optim_G.step()\n",
    "        return loss.item()\n",
    "\n",
    "    def train_step_D(self):\n",
    "        \"\"\"Train the discriminator one step and return the losses.\"\"\"\n",
    "        self.D.zero_grad()\n",
    "\n",
    "        # real samples\n",
    "        real_samples = self.data_fn(self.batch_size)\n",
    "        # calc real loss\n",
    "        # you code here\n",
    "        pred_real = self.D(real_samples)\n",
    "        loss_real = self.criterion(pred_real, self.target_ones)\n",
    "\n",
    "        # generated samples\n",
    "        latent_vec = self.noise_fn(self.batch_size)\n",
    "        # calc fake loss\n",
    "        # you shouldn't optimize G here\n",
    "        # you code here\n",
    "        \n",
    "        with torch.no_grad():\n",
    "            fake_samples = self.G(latent_vec)\n",
    "        pred_fake = self.D(fake_samples)\n",
    "        loss_fake = self.criterion(pred_fake, self.target_zeros)\n",
    "\n",
    "        # combine\n",
    "        loss = (loss_real + loss_fake) / 2\n",
    "        loss.backward()\n",
    "        self.optim_D.step()\n",
    "        \n",
    "        return loss_real.item(), loss_fake.item()\n",
    "\n",
    "    def train_step(self):\n",
    "        \"\"\"Train both networks and return the losses.\"\"\"\n",
    "        loss_D = self.train_step_D()\n",
    "        loss_G = self.train_step_G()\n",
    "        return loss_G, loss_D"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83c47258-4e84-4132-993a-ac77af91977f",
   "metadata": {},
   "source": [
    "#### Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "65f1d28d-acd1-436a-a652-e12137c29808",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "noise_fn = lambda x: torch.rand((x, 1), device='cpu') - 0.5\n",
    "\n",
    "pi = torch.tensor([0.7, 0.3])\n",
    "mu = torch.tensor([-3., 3.])\n",
    "scale = torch.tensor([1., 1.])\n",
    "\n",
    "mixture_gaussian = TD.MixtureSameFamily(TD.Categorical(pi), TD.Normal(mu, scale))\n",
    "\n",
    "def data_fn(x):\n",
    "    return mixture_gaussian.sample((x, 1))\n",
    "\n",
    "def data_pdf(x):\n",
    "    return mixture_gaussian.log_prob(torch.tensor(x)).exp().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "fleet-miracle",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "gen_hiddens = [1, 64, 64, 64, 1]\n",
    "dis_hiddens = [1, 64, 64, 64, 1]\n",
    "G = get_simple_model(gen_hiddens)\n",
    "D = nn.Sequential(*get_simple_model(dis_hiddens), nn.Sigmoid())\n",
    "\n",
    "gan = VanillaGAN(G, D, noise_fn, data_fn, device='cpu')\n",
    "loss_g, loss_d_real, loss_d_fake = [], [], []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "5ed462f1-c1d8-489c-a23d-c7a0e5cab549",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_gan_data(data_fn, noise_fn, data_pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "silver-donna",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize_GAN(gan, data_pdf=data_pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c4b7f20-88d9-4c64-9f7f-d50da3bdb843",
   "metadata": {},
   "source": [
    "#### Training on multimodal data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "763caa60",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "step_size = 20\n",
    "n_D_steps_per_G = 20\n",
    "\n",
    "loss_g, loss_d_real, loss_d_fake = [], [], []\n",
    "start = time()\n",
    "for epoch in range(epochs):\n",
    "    # break\n",
    "    loss_g_running, loss_d_real_running, loss_d_fake_running = 0, 0, 0\n",
    "    for i, batch in enumerate(range(batches)):\n",
    "        #lg_, (ldr_, ldf_) = gan.train_step()\n",
    "        \n",
    "        for k_D_step in range(n_D_steps_per_G):\n",
    "            ldr_, ldf_ = gan.train_step_D()\n",
    "            loss_d_real_running += ldr_\n",
    "            loss_d_fake_running += ldf_\n",
    "        \n",
    "            if k_D_step == 0 and i%step_size == 0:\n",
    "                print(i)\n",
    "                print('D train step 0')\n",
    "                visualize_GAN(gan)\n",
    "\n",
    "            elif k_D_step == n_D_steps_per_G - 1 and i%step_size == 0:\n",
    "                print(f'D train step {n_D_steps_per_G - 1}')\n",
    "                visualize_GAN(gan)\n",
    "\n",
    "        lg_ = gan.train_step_G()\n",
    "        if i%step_size == 0:\n",
    "            print('G train step')\n",
    "            visualize_GAN(gan)\n",
    "\n",
    "        loss_g_running += lg_\n",
    "        \n",
    "    loss_g.append(loss_g_running / batches)\n",
    "    loss_d_real.append(loss_d_real_running / (batches * n_D_steps_per_G))\n",
    "    loss_d_fake.append(loss_d_fake_running / (batches * n_D_steps_per_G))\n",
    "    print(f\"Epoch {epoch+1}/{epochs} ({int(time() - start)}s):\"\n",
    "          f\" G={loss_g[-1]:.3f},\"\n",
    "          f\" Dr={loss_d_real[-1]:.3f},\"\n",
    "          f\" Df={loss_d_fake[-1]:.3f}\")\n",
    "    visualize_GAN(gan, data_pdf=data_pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "intelligent-healthcare",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "epochs = 20\n",
    "batches = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "associate-glasgow",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [],
   "source": [
    "start = time()\n",
    "for epoch in range(epochs):\n",
    "    # break\n",
    "    loss_g_running, loss_d_real_running, loss_d_fake_running = 0, 0, 0\n",
    "    for i,batch in enumerate(range(batches)):\n",
    "        lg_, (ldr_, ldf_) = gan.train_step()\n",
    "        loss_g_running += lg_\n",
    "        loss_d_real_running += ldr_\n",
    "        loss_d_fake_running += ldf_\n",
    "    loss_g.append(loss_g_running / batches)\n",
    "    loss_d_real.append(loss_d_real_running / batches)\n",
    "    loss_d_fake.append(loss_d_fake_running / batches)\n",
    "    print(f\"Epoch {epoch+1}/{epochs} ({int(time() - start)}s):\"\n",
    "          f\" G={loss_g[-1]:.3f},\"\n",
    "          f\" Dr={loss_d_real[-1]:.3f},\"\n",
    "          f\" Df={loss_d_fake[-1]:.3f}\")\n",
    "    visualize_GAN(gan, data_pdf=data_pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "243555e8-aa39-4a76-b7b4-f443b738595d",
   "metadata": {},
   "source": [
    "## Vanilla GAN on 2D data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "84e5957a-d855-4081-9563-0e5c2afc30e2",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def generate_2d_data(size, var=0.02):\n",
    "    scale = 2\n",
    "    centers = [\n",
    "        (1, 0),\n",
    "        (-1, 0),\n",
    "        (0, 1),\n",
    "        (0, -1),\n",
    "        (1. / np.sqrt(2), 1. / np.sqrt(2)),\n",
    "        (1. / np.sqrt(2), -1. / np.sqrt(2)),\n",
    "        (-1. / np.sqrt(2), 1. / np.sqrt(2)),\n",
    "        (-1. / np.sqrt(2), -1. / np.sqrt(2))\n",
    "    ]\n",
    "\n",
    "    centers = [(scale * x, scale * y) for x, y in centers]\n",
    "    dataset = []\n",
    "\n",
    "    for i in range(size):\n",
    "        point = np.random.randn(2) * var\n",
    "        center = centers[np.random.choice(np.arange(len(centers)))]\n",
    "        point[0] += center[0]\n",
    "        point[1] += center[1]\n",
    "        dataset.append(point)\n",
    "\n",
    "    dataset = np.array(dataset, dtype='float32')\n",
    "    dataset /= 1.414  # stdev\n",
    "\n",
    "    return dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "befb901c-5cb8-4001-a064-773d89b02472",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "reset_seed()\n",
    "COUNT = 20000\n",
    "\n",
    "train_data = generate_2d_data(COUNT, var=0.08) # 0.02, 0.1, 0.4\n",
    "visualize_2d_samples(train_data, \"Train data\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78c41590-21fb-45ff-978c-a649bf16c09d",
   "metadata": {},
   "source": [
    "Visualization functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "bcc34293-9b85-4863-a8f1-a09336b11115",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from seminar8_utils import make_inference, visualize_GAN_output\n",
    "\n",
    "def plot_losses(losses, title):\n",
    "    n_itr = len(losses)\n",
    "    xs = np.arange(n_itr)\n",
    "\n",
    "    plt.figure(figsize=(7, 5))\n",
    "    plt.plot(xs, losses)\n",
    "    plt.title(title, fontsize=14)\n",
    "    plt.xlabel('Iterations', fontsize=14)\n",
    "    plt.ylabel('Loss', fontsize=14)\n",
    "\n",
    "    plt.xticks(fontsize=12)\n",
    "    plt.yticks(fontsize=12)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0a9f19e",
   "metadata": {},
   "source": [
    "<img 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\" width=800 height=800 />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "3060ace0",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from seminar8_utils import FullyConnectedMLP"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1338129d",
   "metadata": {},
   "source": [
    "`GAN` generator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "8eccaccd",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class MLPGenerator(FullyConnectedMLP):\n",
    "\n",
    "    def sample(self, n):\n",
    "        z = torch.randn(size=(n, self.input_dim)).to(\n",
    "            next(iter(self.parameters())))\n",
    "        return self.forward(z)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a068698",
   "metadata": {},
   "source": [
    "`GAN` discriminator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "c88585da",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class MLPDiscriminator(FullyConnectedMLP):\n",
    "\n",
    "    def __init__(self, input_dim, hiddens, output_dim):\n",
    "        super().__init__(input_dim, hiddens, output_dim)\n",
    "        self._criterion = nn.BCELoss()\n",
    "\n",
    "    def forward(self, z):\n",
    "        x = super().forward(z)\n",
    "        return F.sigmoid(x)\n",
    "\n",
    "    def criterion(self, x, gt='fake'):\n",
    "        assert gt in ['fake', 'real']\n",
    "        tensor_gt = torch.zeros_like(x) if gt == 'fake' else torch.ones_like(x)\n",
    "        return self._criterion(x, tensor_gt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c581218d",
   "metadata": {},
   "source": [
    "`GAN` training loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "38eca46d",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def train_gan(\n",
    "    generator, \n",
    "    discriminator, \n",
    "    train_loader,\n",
    "    discriminator_steps, \n",
    "    batch_size,\n",
    "    n_epochs,\n",
    "    lr,\n",
    "    visualize_steps=10):\n",
    "\n",
    "    gen_optimizer = torch.optim.Adam(generator.parameters(), lr=lr, betas=(0, 0.9))\n",
    "    discriminator_optimizer = torch.optim.Adam(discriminator.parameters(), lr=lr, betas=(0, 0.9))\n",
    "\n",
    "    generator.train()\n",
    "    discriminator.train()\n",
    "\n",
    "    curr_iter = 0\n",
    "    d_loss, g_loss = torch.zeros(1), torch.zeros(1)\n",
    "    batch_loss_history = {'discriminator_losses': [], 'generator_losses': []}\n",
    "\n",
    "    for epoch_i in tqdm(range(n_epochs)):\n",
    "        for (batch_i, real_data) in enumerate(train_loader):\n",
    "            curr_iter += 1\n",
    "            real_data = real_data.to(DEVICE)\n",
    "\n",
    "            # DISCRIMINATOR UPDATE\n",
    "            with torch.no_grad():\n",
    "                fake_data = generator.sample(real_data.shape[0])\n",
    "\n",
    "            pred_real = discriminator(real_data)\n",
    "            loss_real = discriminator.criterion(pred_real, 'real')\n",
    "            pred_fake = discriminator(fake_data)\n",
    "            loss_fake = discriminator.criterion(pred_fake, 'fake')\n",
    "\n",
    "            discriminator_optimizer.zero_grad()\n",
    "            d_loss = (loss_real + loss_fake) / 2.\n",
    "            d_loss.backward()\n",
    "            discriminator_optimizer.step()\n",
    "\n",
    "            # GENERATOR UPDATE\n",
    "            if curr_iter % discriminator_steps == 0:\n",
    "                gen_optimizer.zero_grad()\n",
    "                fake_data = generator.sample(batch_size)\n",
    "                pred_fake = discriminator(fake_data).mean()\n",
    "\n",
    "                g_loss = discriminator.criterion(pred_fake, 'real')\n",
    "                g_loss.backward()\n",
    "                gen_optimizer.step()\n",
    "\n",
    "                batch_loss_history['generator_losses'].append(g_loss.data.cpu().numpy())\n",
    "                batch_loss_history['discriminator_losses'].append(d_loss.data.cpu().numpy())\n",
    "\n",
    "        if visualize_steps and epoch_i % visualize_steps == 0:\n",
    "            print('Epoch {}'.format(epoch_i))\n",
    "            samples, grid, discr_output, discr_grad_norms = make_inference(generator, discriminator)\n",
    "            visualize_GAN_output(samples, train_data, grid, discr_output, discr_grad_norms)\n",
    "\n",
    "    return batch_loss_history"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c97cac67",
   "metadata": {},
   "source": [
    "`GAN` training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ef2e975a",
   "metadata": {
    "scrolled": false,
    "tags": []
   },
   "outputs": [],
   "source": [
    "# CRITIC_STEPS = 5 => MODE COLLAPSE (SATURATING)\n",
    "# CRITIC_STEPS = 1 => NO MODE COLLAPSE \n",
    "reset_seed()\n",
    "BATCH_SIZE = 1024 # any adequate value\n",
    "GEN_HIDDENS = [32, 128, 128, 32] # 4 layers with < 128 neurons would be enough\n",
    "DISCR_HIDDENS = [64, 256, 256, 64] # 4 layers with < 128 neurons would be enough\n",
    "CRITIC_STEPS = 5 # take 1/2\n",
    "LR = 2e-4 # < 1e-2\n",
    "\n",
    "N_EPOCHS = 100 # change it if you want\n",
    "\n",
    "train_loader = Tdata.DataLoader(train_data, batch_size=BATCH_SIZE, shuffle=True)\n",
    "\n",
    "generator = MLPGenerator(16, GEN_HIDDENS, 2).to(DEVICE)\n",
    "discriminator = MLPDiscriminator(2, DISCR_HIDDENS, 1).to(DEVICE)\n",
    "\n",
    "train_losses = train_gan(\n",
    "    generator, \n",
    "    discriminator, \n",
    "    train_loader,\n",
    "    discriminator_steps=CRITIC_STEPS, \n",
    "    batch_size=BATCH_SIZE, \n",
    "    n_epochs=N_EPOCHS,\n",
    "    lr=LR,\n",
    "    visualize_steps=20\n",
    ")\n",
    "\n",
    "plot_losses(train_losses['discriminator_losses'], 'Critic loss')\n",
    "plot_losses(train_losses['generator_losses'], 'Generator loss')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d2278c42",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "samples, grid, discr_output, discr_grad_norms = make_inference(generator, discriminator)\n",
    "visualize_GAN_output(samples, train_data, grid, discr_output, discr_grad_norms)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a706ff0-be4e-4d93-b346-cd4a13851bf3",
   "metadata": {},
   "source": [
    "### Non-saturating Vanilla GAN\n",
    "\n",
    "* Consider $f(x) = - \\log(1 + \\exp(-x)) = - \\text{Softplus}(-x)$.\n",
    "\n",
    "**Practical approach for training GAN**\n",
    "\n",
    "*Note*: In what follows, **discriminator** $D_{\\theta}$ is an arbitrary functional (not restricted to produce probabilites)!\n",
    "\n",
    "1. **D** update:\n",
    "\n",
    "$$\n",
    "\\text{loss}_{D_{\\theta}} = \\frac{1}{\\vert X_{\\text{real}} \\vert} \\sum\\limits_{x_{\\text{real}} \\in X_{\\text{real}}} \\text{Softplus}(-D_{\\theta}(x_{\\text{real}})) +  \\frac{1}{\\vert Z \\vert} \\sum\\limits_{z \\in Z_{\\text{latent}}} \\text{Softplus}(D_{\\theta}(G_{\\psi}(z)))  \\rightarrow \\min_{\\theta}\n",
    "$$\n",
    "\n",
    "2. **G** update (equivalent to Non-Saturating GAN loss):\n",
    "\n",
    "$$\n",
    "\\text{loss}_{G_{\\psi}} =  \\frac{1}{\\vert Z \\vert} \\sum\\limits_{z \\in Z_{\\text{latent}}} \\text{Softplus}(-D_{\\theta}(G_{\\psi}(z)))  \\rightarrow \\min_{\\psi}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f446f164-f334-4c18-a477-48a410797e45",
   "metadata": {},
   "source": [
    "`NS GAN` generator\n",
    "\n",
    "(the same as for vanilla GAN)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a6c1896-a6cd-4c0b-a5b0-5237a9067012",
   "metadata": {},
   "source": [
    "`NS GAN` discriminator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "bc72d5b1-efb4-4eb6-90ba-d260dece33ee",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "class MLPDiscriminator(FullyConnectedMLP):\n",
    "\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d142f15-4666-4021-8932-e44be12be3ec",
   "metadata": {},
   "source": [
    "`NS GAN` training loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "9c90c6d8-7cf4-4ddd-9485-28f2014c3dfa",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def train_gan(\n",
    "    generator, \n",
    "    discriminator, \n",
    "    train_loader,\n",
    "    discriminator_steps, \n",
    "    batch_size,\n",
    "    n_epochs,\n",
    "    lr,\n",
    "    visualize_steps=10):\n",
    "\n",
    "    # \\beta_1 = 0 !!!\n",
    "    gen_optimizer = torch.optim.Adam(generator.parameters(), lr=lr, betas=(0, 0.9))\n",
    "    discriminator_optimizer = torch.optim.Adam(discriminator.parameters(), lr=lr, betas=(0, 0.9))\n",
    "\n",
    "    generator.train()\n",
    "    discriminator.train()\n",
    "\n",
    "    curr_iter = 0\n",
    "    d_loss, g_loss = torch.zeros(1), torch.zeros(1)\n",
    "    batch_loss_history = {'discriminator_losses': [], 'generator_losses': []}\n",
    "\n",
    "    for epoch_i in tqdm(range(n_epochs)):\n",
    "        for (batch_i, real_data) in enumerate(train_loader):\n",
    "            curr_iter += 1\n",
    "            real_data = real_data.to(DEVICE)\n",
    "\n",
    "            # DISCRIMINATOR UPDATE\n",
    "            with torch.no_grad():\n",
    "                fake_data = generator.sample(real_data.shape[0])\n",
    "            \n",
    "            #YOUR CODE\n",
    "            real_predict = F.softplus(-discriminator(real_data)).mean()\n",
    "            fake_predict = F.softplus(discriminator(fake_data)).mean()\n",
    "\n",
    "            discriminator_optimizer.zero_grad()\n",
    "            d_loss = real_predict + fake_predict\n",
    "            d_loss.backward()\n",
    "            discriminator_optimizer.step()\n",
    "\n",
    "            # GENERATOR UPDATE\n",
    "            if curr_iter % discriminator_steps == 0:\n",
    "                gen_optimizer.zero_grad()\n",
    "                fake_data = generator.sample(batch_size)\n",
    "                fake_scores = discriminator(fake_data)\n",
    "\n",
    "                # implements Non-saturating GAN loss\n",
    "                g_loss = F.softplus(-fake_scores).mean()\n",
    "                g_loss.backward()\n",
    "                gen_optimizer.step()\n",
    "\n",
    "                batch_loss_history['generator_losses'].append(g_loss.data.cpu().numpy())\n",
    "                batch_loss_history['discriminator_losses'].append(d_loss.data.cpu().numpy())\n",
    "\n",
    "        if visualize_steps and epoch_i % visualize_steps == 0:\n",
    "            print('Epoch {}'.format(epoch_i))\n",
    "            samples, grid, discr_output, discr_grad_norms = make_inference(generator, discriminator)\n",
    "            visualize_GAN_output(samples, train_data, grid, discr_output, discr_grad_norms)\n",
    "\n",
    "    return batch_loss_history"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d2ba2d5-e47e-48f6-899e-981bc1d68fd5",
   "metadata": {},
   "source": [
    "`NS GAN` training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ccaa59f-c1cc-455d-8c0b-403f778d49ce",
   "metadata": {
    "scrolled": false,
    "tags": []
   },
   "outputs": [],
   "source": [
    "# CRITIC_STEPS = 5 => MODE COLLAPSE (SATURATING), NO LEARNING (NOT SATURATING)\n",
    "# CRITIC_STEPS = 1 => NO MODE COLLAPSE \n",
    "reset_seed()\n",
    "BATCH_SIZE = 1024 # any adequate value\n",
    "GEN_HIDDENS = [32, 128, 128, 32] # 4 layers with < 128 neurons would be enough\n",
    "DISCR_HIDDENS = [64, 256, 256, 64] # 4 layers with < 128 neurons would be enough\n",
    "CRITIC_STEPS = 1 # take 1/2\n",
    "LR = 2e-4 # < 1e-2\n",
    "\n",
    "N_EPOCHS = 100 # change it if you want\n",
    "\n",
    "train_loader = Tdata.DataLoader(train_data, batch_size=BATCH_SIZE, shuffle=True)\n",
    "\n",
    "generator = MLPGenerator(16, GEN_HIDDENS, 2).to(DEVICE)\n",
    "discriminator = MLPDiscriminator(2, DISCR_HIDDENS, 1).to(DEVICE)\n",
    "\n",
    "train_losses = train_gan(\n",
    "    generator, \n",
    "    discriminator, \n",
    "    train_loader,\n",
    "    discriminator_steps=CRITIC_STEPS, \n",
    "    batch_size=BATCH_SIZE, \n",
    "    n_epochs=N_EPOCHS,\n",
    "    lr=LR,\n",
    "    visualize_steps=20\n",
    ")\n",
    "\n",
    "plot_losses(train_losses['discriminator_losses'], 'Critic loss')\n",
    "plot_losses(train_losses['generator_losses'], 'Generator loss')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "45ac38fc-3625-4884-a690-5d425c3698be",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "samples, grid, discr_output, discr_grad_norms = make_inference(generator, discriminator)\n",
    "visualize_GAN_output(samples, train_data, grid, discr_output, discr_grad_norms)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b278b3b-ecbe-4725-9760-2aac6d00c90e",
   "metadata": {},
   "source": [
    "**Practical Note**:\n",
    "\n",
    "Use **RMSProp** or **Adam** with $\\beta_1 = 0$ when training your GAN. Large $\\beta_1$ of Adam leads to training instabilities!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb586bdb",
   "metadata": {},
   "source": [
    "## Recap\n",
    "\n",
    "#### Vanila GAN\n",
    "1. $G$, $D$, min max objective, $D$ steps, then $G$ steps optimization\n",
    "\n",
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\" width=800 height=800 />\n",
    "\n",
    "2. Theoretical results:\n",
    "    - a global minimum exists \n",
    "    - we know the corresponding value of the loss !\n",
    "    - algorithm converges\n",
    "3. Many troubles in practice:\n",
    "    - Mode collapse (remember JSD pics)\n",
    "    - Vanishing gradients (remember very confident D in a 1d example)"
   ]
  }
 ],
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