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December 27, 2025 14:42
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Sigmoid function approximations
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 386, | |
| "id": "310ccfe6", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import matplotlib.pyplot as plt\n", | |
| "import torch\n", | |
| "import torch.nn as nn\n", | |
| "\n", | |
| "%matplotlib inline" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 387, | |
| "id": "04baf118", | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "def bf16(value):\n", | |
| " return torch.Tensor([value]).to(torch.bfloat16)\n", | |
| "\n", | |
| "# Taylor series-based implementation for exp(x)\n", | |
| "def taylor_exp(x, order):\n", | |
| " sum = np.ones_like(x) # 0th order term\n", | |
| " pow = np.ones_like(x)\n", | |
| " factorial = 1\n", | |
| " \n", | |
| " for i in range(1, order + 1):\n", | |
| " pow *= x\n", | |
| " factorial *= i\n", | |
| " sum += (pow / factorial)\n", | |
| "\n", | |
| " return sum\n", | |
| "\n", | |
| "def plot(x, y, title = \"\"):\n", | |
| " plt.plot(x, y)\n", | |
| " plt.title(title)\n", | |
| " # Should intersect with sigmoid graph at x = 0\n", | |
| " plt.axhline(y = 0.5, color = \"r\", linestyle = \"--\", label = \"y = 0.5\")\n", | |
| "\n", | |
| " plt.xlabel(\"x\")\n", | |
| " plt.ylabel(\"σ(x)\")\n", | |
| " plt.grid()\n", | |
| " plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "ecb58bbc", | |
| "metadata": {}, | |
| "source": [ | |
| "Comparison between np.exp and Taylor series exponentiation" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 388, | |
| "id": "72352a6e", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "x = np.linspace(-10, 10)\n", | |
| "\n", | |
| "plt.plot(x, taylor_exp(x, order = 5), label = \"Taylor, order = 5\")\n", | |
| "plt.plot(x, taylor_exp(x, order = 10), label = \"Taylor, order = 10\")\n", | |
| "plt.plot(x, taylor_exp(x, order = 20), label = \"Taylor, order = 20\")\n", | |
| "plt.plot(x, np.exp(x), label = \"numpy\", linestyle='--', color='black')\n", | |
| "\n", | |
| "plt.legend()\n", | |
| "plt.xlabel(\"x\")\n", | |
| "plt.ylabel(\"$e^x$\")\n", | |
| "plt.title(\"Taylor Series exp(x) Approximation, float32\")\n", | |
| "plt.grid(True)\n", | |
| "plt.show()\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 389, | |
| "id": "bbb81e3a", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# If inverseDefinition is False, calculate sigmoid as\n", | |
| "# σ(x) = 1 / (1 + exp(-x))\n", | |
| "# Else if inverseDefinition is True, calculate sigmoid as:\n", | |
| "# σ(x) = exp(x) / (1 + exp(x))\n", | |
| "def sigmoid_bf16_torch(x, invertedDefinition = False):\n", | |
| " if invertedDefinition:\n", | |
| " exp = torch.exp(bf16(x))\n", | |
| " return exp / (exp + bf16(1.0))\n", | |
| " else:\n", | |
| " exp = torch.exp(bf16(-x))\n", | |
| " return bf16(1.0) / (bf16(1.0) + exp)\n", | |
| "\n", | |
| "x = np.linspace(-10, 10)\n", | |
| "y1 = sigmoid_bf16_torch(x, invertedDefinition = True).to(torch.float32).numpy().flatten()\n", | |
| "y2 = sigmoid_bf16_torch(x, invertedDefinition = False).to(torch.float32).numpy().flatten()\n", | |
| "\n", | |
| "plot(x, y1, f\"$\\\\sigma(x) = \\\\frac{{e^x}}{{e^x + 1}}$ (bfloat16, using torch.exp)\")\n", | |
| "plot(x, y2, f\"$\\\\sigma(x) = \\\\frac{{1}}{{1 + e^{{-x}}}}$ (bfloat16, using torch.exp)\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 390, | |
| "id": "80259e17", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "def sigmoid_f32_torch(x):\n", | |
| " exp = torch.exp(-x)\n", | |
| " return 1.0 / (1.0 + exp)\n", | |
| "\n", | |
| "x = np.linspace(-10, 10)\n", | |
| "y = sigmoid_f32_torch(torch.Tensor(x)).numpy().flatten()\n", | |
| "\n", | |
| "plot(x, y, f\"$\\\\sigma(x) = \\\\frac{{1}}{{1 + e^{{-x}}}}$ (float32, using torch.exp)\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 391, | |
| "id": "ec4d6d97", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# If inverseDefinition is False, calculate sigmoid as\n", | |
| "# σ(x) = 1 / (1 + exp(-x))\n", | |
| "# Else if inverseDefinition is True, calculate sigmoid as:\n", | |
| "# σ(x) = exp(x) / (1 + exp(x))\n", | |
| "def sigmoid_f32_taylor_exp(x, order, inverseDefinition = False):\n", | |
| " if inverseDefinition:\n", | |
| " exp = taylor_exp(x, order)\n", | |
| " return exp / (exp + 1.0)\n", | |
| " else:\n", | |
| " exp = taylor_exp(-x, order)\n", | |
| " return 1.0 / (1.0 + exp)\n", | |
| "\n", | |
| "x = np.linspace(-5, 5)\n", | |
| "\n", | |
| "def compareTaylorSeries(order = 20):\n", | |
| " plt.figure(figsize = (10, 6))\n", | |
| "\n", | |
| " y = sigmoid_f32_taylor_exp(x, order = order, inverseDefinition = False)\n", | |
| " plt.plot(x, y, label = f\"Standard Sigmoid (order = {order})\")\n", | |
| "\n", | |
| " y = sigmoid_f32_taylor_exp(x, order = order, inverseDefinition = True)\n", | |
| " plt.plot(x, y, label = f\"Inverse Sigmoid (order = {order})\")\n", | |
| "\n", | |
| " y = 1.0 / (1.0 + np.exp(-x))\n", | |
| " plt.plot(x, y, label = f\"Standard Sigmoid, Numpy\")\n", | |
| "\n", | |
| " plt.xlabel(\"x\")\n", | |
| " plt.ylabel(\"σ(x)\")\n", | |
| " plt.title(\"Sigmoid Approximations (Taylor Series)\")\n", | |
| " plt.grid(True)\n", | |
| " plt.legend()\n", | |
| " plt.show()\n", | |
| "\n", | |
| "compareTaylorSeries(order = 5)\n", | |
| "compareTaylorSeries(order = 10)\n", | |
| "compareTaylorSeries(order = 20)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 392, | |
| "id": "b2d3877e", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# Exponential-less, branchless sigmoid approximation (https://stackoverflow.com/a/10733861)\n", | |
| "def fast_sigmoid(x):\n", | |
| " return 0.5 * (x / (1 + np.abs(x)) + 1) \n", | |
| "\n", | |
| "# Exponential-less, branchless tanh approximation (https://stackoverflow.com/a/10733861)\n", | |
| "def fast_tanh(x):\n", | |
| " return x / (1 + np.abs(x))\n", | |
| "\n", | |
| "plt.figure(figsize = (10, 6))\n", | |
| "\n", | |
| "x = np.linspace(-10, 10)\n", | |
| "y = fast_sigmoid(x)\n", | |
| "plt.plot(x, y, label = \"Exponential-less Sigmoid: $\\\\sigma(x) = 0.5 * (x / (1 + abs(x)) + 1)$\")\n", | |
| "\n", | |
| "y = 1.0 / (1.0 + np.exp(-x))\n", | |
| "plt.plot(x, y, label = \"Standard Sigmoid, Numpy\")\n", | |
| "\n", | |
| "plt.xlabel(\"x\")\n", | |
| "plt.ylabel(\"σ(x)\")\n", | |
| "plt.title(\"Exponential-less, Branchless Sigmoid Approximation, f32\")\n", | |
| "plt.grid(True)\n", | |
| "plt.legend()\n", | |
| "plt.show()\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 393, | |
| "id": "22ddbe3c", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# Generalization of the above branchless sigmoid function.\n", | |
| "# Used to compute the sigmoid function, with different parameters (a, b, c, d, e) based on the value of x\n", | |
| "# General formula:\n", | |
| "# σ(x) = a * (b * x / (c + d * np.abs(x)) + e), where x in [lower bound, upper bound]\n", | |
| "# Since the sigmoid function is symmetric, ie σ(-x) = 1 - σ(x), we can simply approximate the function for values >= 0\n", | |
| "# And use the above property to calculate it for negative values\n", | |
| "# Thus the formula becomes:\n", | |
| "# σ(x) = a * (b * x / (c + d * x) + e), where x in [lower bound, upper bound]\n", | |
| "def parametric_sigmoid(x, a, b, c, d, e):\n", | |
| " return a * (b * x / (c + d * x) + e)\n", | |
| "\n", | |
| "# Exponential-less, branchful approximation of sigmoid function\n", | |
| "def fast_sigmoid_branching(x_vec):\n", | |
| " output = np.empty_like(x_vec)\n", | |
| " \n", | |
| " for i, x in enumerate(x_vec):\n", | |
| " # Sigmoid is symmetrical around 0. Calculate sigmoid on abs(x), then flip it accordingly if it was negaitve\n", | |
| " x_abs = np.abs(x)\n", | |
| " y = 0\n", | |
| "\n", | |
| " if x_abs < 1:\n", | |
| " y = parametric_sigmoid(x_abs, 1.03925, 0.2839, 1.1252, 0.1417, 0.4800)\n", | |
| " elif x_abs < 2:\n", | |
| " y = parametric_sigmoid(x_abs, -0.3460, -0.6023, 0.4117, 0.2342, -1.1782)\n", | |
| " elif x_abs < 4:\n", | |
| " y = parametric_sigmoid(x_abs, -1.4539, 0.8033, -0.2292, -0.7260, 0.3473)\n", | |
| " elif x_abs < 6:\n", | |
| " y = parametric_sigmoid(x_abs, 0.2892, 0.8950, 0.0413, 0.2349, -0.2479)\n", | |
| " else:\n", | |
| " y = 0.9999\n", | |
| "\n", | |
| " # If x < 0, σ(x) = 1 - σ(|x|) due to sigmoid symmetry\n", | |
| " if x < 0:\n", | |
| " y = 1 - y\n", | |
| " output[i] = y\n", | |
| " return output\n", | |
| "\n", | |
| "plt.figure(figsize = (10, 6))\n", | |
| "\n", | |
| "y = 1.0 / (1.0 + np.exp(-x))\n", | |
| "plt.plot(x, y, label = \"Standard Sigmoid, Numpy\")\n", | |
| "\n", | |
| "y = fast_sigmoid_branching(x)\n", | |
| "plt.plot(x, y, label = \"Exponential-less Sigmoid, Branching\")\n", | |
| "\n", | |
| "plt.xlabel(\"x\")\n", | |
| "plt.ylabel(\"σ(x)\")\n", | |
| "plt.title(\"Exponential-less, Branching Sigmoid Approximation, f32\")\n", | |
| "plt.grid(True)\n", | |
| "plt.legend()\n", | |
| "plt.show()\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 394, | |
| "id": "bfb3466d", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "def create_sigmoid_lut(size):\n", | |
| " lut = np.zeros(size)\n", | |
| " for i in range(size):\n", | |
| " # Mapping index to x value, in [0, 6] range\n", | |
| " # e.g., 0 -> 0, ..., size-1 -> 6\n", | |
| " # LUT is mirrored to save space, using σ(x) = 1 - σ(|x|) property\n", | |
| " x = 6 * i / (size - 1)\n", | |
| " lut[i] = 1.0 / (1.0 + np.exp(-x))\n", | |
| " return lut\n", | |
| "\n", | |
| "def sigmoid_lut_based_single(x, lut, size):\n", | |
| " minVal = 0 # Minimum value of LUT range\n", | |
| " maxVal = 6 # Maximum value of LUT range\n", | |
| "\n", | |
| " # Our LUT only contains values from 0 to 6, to save space\n", | |
| " # If x < 0, compute it as σ(x) = 1 - σ(|x|)\n", | |
| " if (x < 0):\n", | |
| " return 1.0 - sigmoid_lut_based_single(-x, lut, size)\n", | |
| " \n", | |
| " elif (x > maxVal):\n", | |
| " return 0.9999\n", | |
| " \n", | |
| " idx = (x - minVal) * (size - 1) / (maxVal - minVal)\n", | |
| "\n", | |
| " # Get two closest indices in the LUT\n", | |
| " idxLow = int(np.floor(idx))\n", | |
| " idxHigh = int(np.ceil(idx))\n", | |
| " \n", | |
| " # If x hits one of the LUT points\n", | |
| " if idxLow == idxHigh:\n", | |
| " return lut[idxLow]\n", | |
| " \n", | |
| " # Get the fractional part and interpolate\n", | |
| " t = idx - idxLow\n", | |
| " return lut[idxLow] + (lut[idxHigh] - lut[idxLow]) * t\n", | |
| "\n", | |
| "def sigmoid_lut_based(x_vec, lut, size):\n", | |
| " output = np.empty_like(x_vec)\n", | |
| " \n", | |
| " for i, x in enumerate(x_vec):\n", | |
| " output[i] = sigmoid_lut_based_single(x, lut, size)\n", | |
| " return output\n", | |
| "\n", | |
| "lutSize = 1024\n", | |
| "lut = create_sigmoid_lut(size = lutSize)\n", | |
| "plt.figure(figsize = (10, 6))\n", | |
| "\n", | |
| "y = 1.0 / (1.0 + np.exp(-x))\n", | |
| "plt.plot(x, y, label = \"Standard Sigmoid, Numpy\")\n", | |
| "\n", | |
| "y = sigmoid_lut_based(x, lut, lutSize)\n", | |
| "plt.plot(x, y, label = f\"LUT-based ({lutSize} points)\")\n", | |
| "\n", | |
| "plt.xlabel(\"x\")\n", | |
| "plt.ylabel(\"σ(x)\")\n", | |
| "plt.title(\"LUT-based Approximation for Sigmoid Function, f32\")\n", | |
| "plt.grid(True)\n", | |
| "plt.legend()\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 395, | |
| "id": "eafeb825", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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s5bVr1w5DQ0PNe1NTUz788EN++eUX0tPTiY+P58yZM3To0AETExNNPqVSSffu3fn777+5cuWKVpmtWrXSel+hQgUAbt++DcCBAwdIS0ujR48epKWlaV6GhobUr18/28x4CoUi23ibChUqaMp7FY8fP6Z///44OTmhq6uLnp4eLi4uANm6J71ICKFV57S0tFzzFnQ/rays8PDwYM6cOcybN48LFy5k6+ZSsWJF9PX16devH+vWrePmzZuvvO8vevF4+uGHH+jZsyefffZZtq6ekPG55tQFZtu2bdSuXRsTExNNW65evTrHdmzQoAGmpqaa93Z2dpQoUULzWSYkJPDzzz/TqVOnAo0Hye9Yy0uLFi20vhNZ171y5QoPHz6kU6dOWus5OztTu3btfMsHaN68OXfu3GHnzp2MGDGCcuXKsWvXLlq1apXjmI1M8fHxnD9/njZt2qCvr69JNzExyXXsWYMGDTA2Nta89/b2BjLGgbzYFSszPXM/T506RWJiYrYuUU5OTjRs2DDHrruZjhw5AkDXrl210jt16qTVfSovISEhxMTE0KtXL01ar169EEJouqy9yNTUNNvn/vHHH6NWq/nll1+00vM7v72offv2Wu9/+ukngGzt0rFjR4yNjbXapXbt2syYMYMFCxYwYMAAunXrRu/evQuw9xldOStXrqx5b2VlRYkSJahYsSIlS5bUpGf93ADS0tL46quv8PHxQV9fH11dXfT19bl27Vqe57G8ZH6mWfe7WrVqeHt7Zzse7O3ttcYiweufn/Py/fffc+bMGbZt24aPjw/NmjXLc1bZ3377jU6dOlGjRg1mzpxZJHWSpFclAydJKmLe3t5UqVJF6/XiP7qZSpcuTd26dUlKSqJr1665jrOwt7fPMS0lJYW4uDiioqIQQuS4fuY/6pljOTJZW1trvc+cQCAxMRGAR48eAVC1alX09PS0Xlu3bs02zsjIyEjr4iezzKSkpBz3KT9qtZrGjRuzY8cORo0axeHDhzl79qxmfEtmPXOybt26bHXOTUH3U6FQcPjwYZo0acLs2bOpVKkStra2DB48mNjYWAA8PDw4dOgQJUqU4LPPPsPDwwMPDw8WLlz4Sm2Q6cXjqWnTpixfvpzGjRszatQozTiOTDkdAzt27KBTp06UKlWKjRs3curUKc6dO0evXr1y/HyyHhuQ8VlmtnlUVBTp6ekFHqye37H2OutmHtd2dnbZ1s0pLTcqlYo2bdowZ84cfv75Z65fv46Pjw/ffvutZiB8Vpnfu5fZtpWVldb7zIArt/TMzyevsVglS5bM9v1+UeayrOcRXV3dHD/rnKxevRpDQ0OaNm3K8+fPef78ORUqVMDV1ZW1a9dmC3By2v/M7Weta37ntxdl3f/IyEh0dXWzBfAKhQJ7e/ts2+ratSv6+vokJyczcuTIfPb6X1k/H8j4jPL73AC++OILJk6cSJs2bdizZw9nzpzh3Llz+Pn5Feg7kJOXPR7y+04XtnLlylGtWjU6dOjA/v37cXFxYciQITnmvXDhAoGBgXh6ehIaGvqfmMxGer/IWfUk6S2xatUq9u3bR7Vq1Vi8eDGdO3emevXq2fI9fPgwxzR9fX3NHQQdHR0ePHiQLV/mIHwbG5uXqltm/u3bt2vu8rxJf/75J7///jtr166lZ8+emvScBsxn9eGHH3Lu3LkCbedl9tPFxYXVq1cDcPXqVUJCQpgyZQopKSksW7YMgLp161K3bl3S09M5f/4833zzDUOHDsXOzo6PPvqoQHUqiAoVKnDgwAGuXr2q9UtyTs962bhxI25ubmzdulVredZJHArKysoKpVL5VgzgzrwgzAyAX5TT96agnJ2d6devH0OHDuXSpUuUK1cuWx5LS0sUCkWhbzsnmfuZ23c8r+935roPHz6kVKlSmvS0tLQ8A65MV69e5fjx40BGu+TkwIEDNG/eXPM+rzbJehGf3/ntRVmPb2tra9LS0njy5IlW8CT+mbo/c8IFyJhlsmvXrlhaWmJgYEDv3r05ceKE1t3CorBx40Z69OjBV199pZX+9OlTLCwsXqnMF4+HrD9g5Hc8vGm6urpUqlSJkJCQbMsuXLhAo0aNcHFx4ccff8Tc3LwYaihJeZN3nCTpLXDx4kUGDx5Mjx49OHbsGBUqVKBz585ERUVly7tjxw6tXzBjY2PZs2cPdevWRalUYmxsTPXq1dmxY4fWL4hqtZqNGzfi6OhImTJlXqp+TZo0QVdXlxs3bmS7e5b5elkvc6ch8wIp66+Py5cvz3dda2vrAtf1VfezTJkyTJgwAV9fX3777bdsy5VKJdWrV+fbb78FyDHP68icya8gXeUUCoXmIZWZHj58mOOsegWhUqmoX78+27ZtK5IZDl+Gl5cX9vb22S7K7ty5k+2hmzmJjY3NdlcjU2Y3qhe7Yr3I2NiYKlWqsGvXLs2zjQDi4uIK/QHFNWvWRKVSsXHjRq30v//+m59++okPPvgg13UzZyvctGmTVnpISEie3VgzZf5YsHLlSo4cOaL1Cg0NRU9PL9tzd2JjY9m9e7dW2v/93/+ho6NDvXr1tNLzO7/lJXO/s7bL999/T3x8vFa7TJ48mWPHjrFp0ya2bt3K77///lJ3nV6VQqHIdh7bt28f9+7d00p7mfNjw4YNgez7fe7cOS5fvpzn8fCmJSUlcfr0aUqXLq2VHhYWRqNGjXB0dOTgwYNYWloWUw0lKW/yjpMkFbE///wzxwsSDw8PbG1tiY+Pp1OnTri5ubFkyRL09fUJCQmhUqVKfPLJJ+zatUtrPaVSSWBgIF988QVqtZpZs2YRExOj9dyZmTNnEhgYSIMGDRgxYgT6+vosWbKEP//8k82bN7/0U+ddXV2ZNm0a48eP5+bNm5pnBz169IizZ89ibGystf2CMDU1xcXFhf/973988MEHWFlZYWNjk+OU0WXLlsXDw4MxY8YghMDKyoo9e/ZopmovLAXdzz/++INBgwbRsWNHPD090dfX56effuKPP/5gzJgxACxbtoyffvqJFi1a4OzsTFJSkuaCslGjRpptBgUFsW7dOm7dupXvdNmgfTxFRkayY8cODh48SNu2bXFzc8t3/ZYtW7Jjxw4GDhxIhw4duHv3Ll9++SUODg5cu3btFVoN5s2bR506dahevTpjxoyhdOnSPHr0iN27d7N8+XKtMVJFSUdHh6lTp/Lpp5/SoUMHevXqxfPnz5k6dSoODg5a04nn5MqVKzRp0oSPPvqI+vXr4+DgQFRUFPv27WPFihUEBARQq1atXNefNm0aLVq0oEmTJgwZMoT09HTmzJmDiYkJz549K7T9tLCwYOLEiYwbN44ePXrQpUsXIiMjmTp1KoaGhkyePDnXdb29venWrRsLFixAT0+PRo0a8eeffzJ37lzMzMzy3G5aWhrr16/H29ubPn365Jgn82HML971sba2ZsCAAdy5c4cyZcoQGhrKypUrGTBgQLa7VgU5v+UmMDCQJk2aMHr0aGJiYqhduzZ//PEHkydPxt/fn+7duwMZjzaYOXMmEydO1AQVM2fOZMSIEQQEBGgeclwUWrZsydq1aylbtiwVKlTg119/Zc6cOdnuFHl4eKBSqdi0aRPe3t6YmJhQsmTJHAN3Ly8v+vXrxzfffIOOjg7NmjUjIiKCiRMn4uTkxLBhw16prgEBAfz8888IIV5p/Vq1atGqVSu8vb0xNzcnIiKCpUuXcuPGDXbu3KnJd+XKFc05ccaMGVy7dk3rXJT5b6UkvRWKb14KSXq35TWrHiBWrlwphBCiW7duwsjISGuqayGE2LZtmwDE/PnzhRD/zjo1a9YsMXXqVOHo6Cj09fWFv7+/OHDgQLbtHzt2TDRs2FAYGxsLlUolatSoIfbs2ZNjHbPOhnTkyBEBaKbWzrRr1y7RoEEDYWZmJgwMDISLi4vo0KGDOHTokCZPz549hbGxcbb65DSF7qFDh4S/v78wMDDQmtErp9mswsPDRWBgoDA1NRWWlpaiY8eO4s6dO9lm5nvd6cgLsp+PHj0SQUFBomzZssLY2FiYmJiIChUqiPnz52tmfTt16pRo27atcHFxEQYGBsLa2lrUr18/2+xs7du3FyqVKt8pynM6nszNzUXFihXFvHnzNFMtC/HvsTJnzpwcy/r666+Fq6urMDAwEN7e3mLlypU5tgVZpozO5OLikm32tfDwcNGxY0dhbW0t9PX1hbOzswgKCtLU62WOtdxm1ctpf7J+/kIIsWLFClG6dGmhr68vypQpI7777jvRunXrbLMGZhUVFSWmT58uGjZsKEqVKiX09fWFsbGxqFixopg+fbpISEjIVqess57t3LlT+Pr6atrg66+/FoMHDxaWlpbZ6p21bXPbz8w22rZtm1b6qlWrRIUKFYS+vr4wNzcXrVu3znYeyelzTU5OFsOHDxclSpQQhoaGokaNGuLUqVM5fq4vypz1L6/ZJDNntgsODhZCZHyW5cqVE0ePHhVVqlQRBgYGwsHBQYwbN06kpqZm2/eCnN8y9+nFabYzJSYmitGjRwsXFxehp6cnHBwcxIABAzTfr/v374sSJUqIhg0bivT0dM16arVafPjhh8LCwkJz7shtVr1y5cpl266Li4to0aJFtvSsn3NUVJTo3bu3KFGihDAyMhJ16tQRx44dy3bMCyHE5s2bRdmyZYWenp7WcZ7TZ5qeni5mzZolypQpI/T09ISNjY3o1q2bZgrz/Orfs2fPbLNOVq5cWdjb22fLm1Vu3+3hw4cLPz8/YW5uLnR1dYW9vb1o27atOHHiRI7r5/bKaWZBSSouCiFe8acESZLeqIiICNzc3JgzZw4jRowo7upIhcTe3p7u3bszZ86c4q7KO+v58+eUKVOGNm3asGLFije67dTUVCpWrEipUqX48ccf3+i23wYBAQE8ffqUP//8M8988vz2domNjcXKyooFCxbw2WefFXd1JOmtIbvqSZIkFZNLly6RkJDA6NGji7sq74yHDx8yY8YMGjRogLW1Nbdv32b+/PnExsbmOpNXYerduzeBgYE4ODjw8OFDli1bxuXLl197NkVJepN++eUXSpUqRd++fYu7KpL0VpGBkyRJUjEpV64cMTExxV2Nd4qBgQEREREMHDiQZ8+eYWRkRI0aNVi2bFmOs+EVttjYWEaMGMGTJ0/Q09OjUqVKhIaGao1rk6S3XYsWLWjRokVxV0OS3jqyq54kSZIkSZIkSVI+5HTkkiRJkiRJkiRJ+ZCBkyRJkiRJkiRJUj5k4CRJkiRJkiRJkpSP925yCLVazf379zE1NX3ph4BKkiRJkiRJkvTuEEIQGxtLyZIl831Q+nsXON2/fx8nJ6firoYkSZIkSZIkSW+Ju3fv4ujomGee9y5wMjU1BTIax8zMrJhrk/FwxB9//JHGjRujp6dX3NV558j2LVqyfYuWbN+iJdu3aMn2LVqyfYuWbN+i9Ta1b0xMDE5OTpoYIS/vXeCU2T3PzMzsrQmcjIyMMDMzK/YD510k27doyfYtWrJ9i5Zs36Il27doyfYtWrJ9i9bb2L4FGcIjJ4eQJEmSJEmSJEnKhwycJEmSJEmSJEmS8iEDJ0mSJEmSJEmSpHy8d2OcCkIIQVpaGunp6UW+rdTUVHR1dUlKSnoj23vfyPYtWrJ9i1ZRtK9SqURXV1c+jkGSJEmSXpIMnLJISUnhwYMHJCQkvJHtCSGwt7fn7t278kKmCMj2LVqyfYtWUbWvkZERDg4O6OvrF1qZkiRJkvSuk4HTC9RqNbdu3UKpVFKyZEn09fWL/GJQrVYTFxeHiYlJvg/dkl6ebN+iJdu3aBV2+wohSElJ4cmTJ9y6dQtPT0/5uUmSJElSAcnA6QUpKSmo1WqcnJwwMjJ6I9tUq9WkpKRgaGgoL2CKgGzfoiXbt2gVRfuqVCr09PS4ffu2pmxJkiRJkvInr3RyIC8AJUl6l8lznCRJkiS9PPmvpyRJkiRJkiRJUj5k4CRJkiRJkiRJkpQPGThJRSIiIgKFQkFYWNhbWXZR1u9lrV27FgsLizzzTJkyhYoVK76R+kiSJEmSJEnZycDpHfH48WM+/fRTnJ2dMTAwwN7eniZNmnDq1ClNHoVCwa5du4qvkm/QzZs36dKlC46Ojtjb2+Ps7Ezr1q25evUqAE5OTjx48IDy5csXc02hc+fOmnoVpoCAABQKBVu2bNFKX7BgAa6uroW+PUmSJEmSpHeZnFXvHdG+fXtSU1NZt24d7u7uPHr0iMOHD/Ps2bPirtorS0lJeaXnzKSkpBAYGEjZsmXZvn07JiYmREdHs3//fqKjo4GMh4Da29sXdpVfiUqlQqVSFUnZhoaGTJgwgfbt26Onp1ck25AkSZIkSXofyDtO+RBCkJCSVqSvxJT0HNOFEAWq4/Pnzzl+/DizZs2iQYMGuLi4UK1aNcaOHUuLFi0ANHcY2rZti0Kh0Ly/ceMGrVu3xs7ODhMTE6pWrcqhQ4e0ynd1deWrr76iV69emJqa4uzszIoVK7TynD17Fn9/fwwNDalSpQoXLlzQWp6enk7v3r1xc3NDpVLh5eXFwoULtfIEBQXRpk0bZs6cScmSJSlTpkyBys4qPDycmzdvsmTJEmrUqIGzszO1a9dmxowZVK1aFci5q97u3bvx9PREpVLRoEED1q1bh0Kh4Pnz58C/Xer27t2Ll5cXRkZGdOjQgfj4eNatW4erqyuWlpZ8/vnnpKena8qNioqiR48eWFpaYmRkRLNmzbh27ZpmeU5d9b7++mvs7OwwNTWld+/eJCUl5bnPuenSpQvR0dGsXLky1zyZ7f6ioUOHEhAQoHkfEBDA559/ztChQ7G0tMTOzo4VK1YQHx/PZ599hrm5OR4eHvzwww+adY4ePYpCoWDfvn34+flhaGhI9erVuXjxIgDx8fGYmZmxfft2rW3v2bMHY2NjYmNjX2mfJUmSJEmSikKx3nH65ZdfmDNnDr/++isPHjxg586d2S7gsvr555/54osvuHTpEiVLlmTUqFH079+/yOqYmJqOz6QDRVZ+XsKnNcFIP/+PyMTEBBMTE3bt2kWNGjUwMDDIlufcuXOUKFGCNWvW0LRpU5RKJQBxcXE0b96c6dOnY2hoyLp16/jwww+5cuUKzs7OmvWDg4P58ssvGTduHNu3b2fAgAHUq1ePsmXLEh8fT8uWLWnYsCEbN27k1q1bDBkyRGv7arUaR0dHQkJCsLGx4eTJk/Tr1w8HBwc6deqkyXf48GHMzMw4ePAgQogClZ2Vra0tOjo6bN++ncGDB+fbfpARSHXo0IEhQ4bQp08fLly4wIgRI7LlS0hIYNGiRWzZsoXY2FjatWtHu3btsLCwIDQ0lJs3b9K+fXvq1KlD586dgYzA5Nq1a+zevRszMzNGjx5N8+bNCQ8Pz/EuUEhICJMnT+bbb7+lbt26bNiwgUWLFuHu7l6gfXmRmZkZ48aNY9q0afTs2RNjY+OXLiPTunXrGDVqFGfPnmXr1q0MGDCAnTt30rRpUyZNmsTChQvp3r07d+7c0XoO2siRI1m4cCH29vaMGzeOVq1acfXqVYyNjfnoo49Ys2YNHTp00OTPfG9qavrKdZUkSZIkSSpsxXrHKT4+Hj8/PxYvXlyg/Ldu3aJ58+bUrVuXCxcuMG7cOAYPHsz3339fxDV9u+nq6rJ27VrWrVuHhYUFtWvXZty4cfzxxx+aPLa2tgBYWFhgb2+vee/n58enn36Kr68vnp6eTJ8+HXd3d3bv3q21jebNmzNw4EBKly7N6NGjsbGx4ejRowBs2rSJ9PR0vvvuO8qVK0fLli0ZOXKk1vp6enpMnTqVqlWr4ubmRteuXQkKCiIkJEQrn7GxMatWraJcuXKUL1++QGVnVapUKRYtWsSkSZOwtramVatWTJ8+nZs3b+a6zrJly/Dy8mLOnDl4eXnx0UcfERQUlC1famoqS5cuxd/fn3r16tGhQweOHz/O6tWr8fHxoWXLljRo0IAjR44AaAKmVatWUbduXfz8/Ni0aRP37t3LdbzZggUL6NWrF3369MHLy4vp06fj4+OT5z7nZeDAgRgaGjJv3rxXLgMyjpUJEybg6enJ2LFjUalU2NjY0LNnTzw9PZk0aRKRkZFaxx3A5MmTCQwMxNfXl3Xr1vHo0SN27twJQJ8+fThw4AD3798H4OnTp+zdu5devXq9Vl0lSZIkSZIKW7HecWrWrBnNmjUrcP5ly5bh7OzMggULAPD29ub8+fPMnTuX9u3bF0kdVXpKwqc1KZKyIeNOTGxMLKZmptkeSqnSUxa4nPbt29OiRQuOHTvGqVOn2L9/P7Nnz2bVqlU5BgCZ4uPjmTp1Knv37uX+/fukpaWRmJjInTt3tPJVqFBB87dCocDe3p7Hjx8DcPnyZfz8/LTuMtSsWTPbtpYtW8aqVau4ffs2iYmJpKSkZJspztfXV2tcU0HLzuqzzz6jR48eHD58mGPHjrF9+3ZmzpzJ7t27CQwMzJb/ypUrmm58mapVq5Ytn5GRER4eHpr3dnZ2uLq6YmJiopX2Ytvo6upSvXp1zXJra2u8vLy4fPlyjnW/fPlytruoNWvW1ARjL8vAwIBp06YxaNAgBgwY8EplgPYxoFQqsba2xtfXV5NmZ2cHoNn3TC9+XlZWVlr7Xq1aNcqVK8f69esZM2YMGzZswNnZmXr16r1yPSVJkqS3gBCQngIp8YiUeFJj40iMjiMpNpHk2GTU6eo3V5V/qoMQqP95j8gYjpHx3z/LAbUAgcio363bXNr9AwqFjnY5/7xTiyzbQGT+gdBKR5OQsc0stdPK/+/SbCM2spSb276+uLLIcWFO+fNYVoBUrRwFGGmiFmqeP3jIE7+HlHR1yn+Ft8R/anKIU6dO0bhxY620Jk2asHr1alJTU3Ps9pScnExycrLmfUxMDJBx5yA1NVUrb2pqKkII1Go1avW/X2hD3aK7MSeEgjR9JSo9JQqFIssyUeBxTgD6+vp88MEHfPDBB0yYMIG+ffsyefJkevToocmTdd9GjBjBjz/+yOzZsyldujQqlYpOnTqRnJyslU9XV1frvUKhID09Xau8F5e/mKZWqwkJCWHYsGHMnTuXGjVqYGpqyty5czl79qwmrxACIyOjXMvJrezcGBsb8+GHHxIQEMCsWbNo1qwZ06dP54MPPshWRk7byRyn9GIePT29bNvMKS2zbV4s48XPN/Nzzav9Xnz/Yv6XkXk8f/zxx8ydO5cvv/xSM74tsyyFQpFteykpKdm2l9MxoKurq1U/gLS0tGz7lVO9M9N69+7Nt99+y6hRo1izZg1BQUEvfey/qzLbIPNzLCxqtRohBKmpqZpuu++jzH8Dsv5bIBUO2b5Fq0jbNz0VkqIh6TmKpGjUCVGkxj0nOSaa5NhoUuPjSU1IIC0xmZQkSElRkpKiS0qqPilpBqSkGZKsNiJJbUqS2pRktSlqrUtO5T+vt115/r6Wfy7pVVlz6/dL2JYq3sm6XuY79J8KnB4+fKj5VTuTnZ0daWlpPH36FAcHh2zrzJw5k6lTp2ZL//HHH7XuYkDGhaG9vT1xcXGaC8c3pSgGwru7uxMXF6cJFvX09LTeQ8aYsY8++ogPPvgAyBjzdOvWLWrWrKnJp1arSUpK0lovPT2d5ORkYmJicHNzY8OGDTx69EgzO1xmN774+HhiYmL46aefqFatGl27dtWUcfXqVdLT07WC2bS0NK3tFKTsgoiLi8Pd3Z2zZ88SExNDXFycVhlubm4cPHhQq7yTJ08CGZ+Njo4OSUlJCCG08iQnJ2vtQ9b9cHZ2Ji0tjZ9++klz1+nZs2dcvXoVFxcXYmJispXr6enJsWPHtMb7nTx5Mtt28pOWlkZKSopmnfHjx9OjRw969eqFWq3WpJuZmfHHH39olf3rr7+ip6enSctaFmQcF5k/Srx4/CYmJhITE0NCQgIAR44coW3btkDGRCZXr17F2dlZU1arVq0YPXo0c+bM4dKlS7Rt2/al9vN9UNjnh5SUFBITE/nll19IS0sr1LL/iw4ePFjcVXinyfYtWrm1b0oqJCRBemISJCVBUjI6qakoUtLQSU1HJ12gkw6KdB0Uah0UQgeEEiF0UQs90oQBqcKAtH9eAjvALsdtFZSSZPR04lHqJKIgPf8V3nKK/LO84YKKx+tUP+JeGk9DQwutLq8i83qlIP5TgROQ412ZnNIzjR07li+++ELzPiYmBicnJxo3boyZmZlW3qSkJO7evYuJiQmGhoaFXPOcCSGIjY3F1NQ0133IT2RkJJ07dyYoKIgKFSpgamrK+fPn+eabb2jdurVmP11dXTl16hSNGjXCwMAAS0tLypQpQ2hoKO3bt0ehUDBp0iSEEOjr62vW09HRwdDQUKu9lEolBgYGmJmZ0atXL2bMmMEXX3zB+PHjiYiIYMmSJUDGXR8zMzN8fHzYunUrp06dws3NjY0bN3LhwgXc3Nw05erp6aGrq6u1nYKUnVVYWBhTpkyhW7dueHt7k5qayq+//sqmTZsYNWoUZmZmmq51mWV8/vnnLFmyRDN7YFhYmOb5R2ZmZpiZmWFoaIhCodDapoGBAUqlUivtxf3w9/enVatWfPHFFyxduhRTU1PGjh1LqVKl+Oijj9DT08tW7rBhw/jkk0+oWbMmderU4f/+7//466+/cHd3z3F/c6Orq6v1OXbs2JFvv/2WtWvXYmdnp0lv2rQp33zzDbt27aJmzZps2rSJv/76C39/f02erGVlHheZE5G8ePyqVCrMzMw0P0wEBwfj6OiInZ0dEyZMwMbGhi5dumi6ZJqZmdG2bVsmTZpEYGAg3t7eBd7Hd11hnB9ykpSUhEqlol69em/sXPc2Sk1N5eDBgwQGBsrp+ouAbN/Ck5qm5tGTBB49jifq0TPin0SSFBVD9KNnqBR6iBQFIlWJSNdFLfRJVxsgyGzzwp5oRw2KNFCko1aoEcp00pVq1LqCNF0F6Xo6pOnrkq6vS5qhAemGhqAyQGmoRN9Aib5SBz2lAl2lDro6CnSVin/+/897nX/fK3UU6OkoUCoV6OpkLFf+89JR8M///0lTKFBkpv3z/sV8CkVGmo4i45rxxXQdBei8sAzk8VvU3qb2fZkfa/9TgZO9vT0PHz7USnv8+DG6urpYW1vnuI6BgUGOs8zp6ell+6DS09MzvkA6OtnGGxWVF7tLveo2zczMqF69OgsXLuTGjRukpqbi5ORE3759GTdunKbc4OBgvvjiC1atWkWpUqWIiIjQTERQp04dbGxsGD16NLGxsdnqk1P9MtPMzMzYs2cP/fv3p3Llyvj4+DBr1izat2+vacsBAwbw+++/06VLFxQKBV26dGHgwIH88MMPmnIVCkW27RSk7KycnZ1xc3Pjyy+/1Ew77urqytSpUxk2bJjWepl/e3h4sH37doYPH86iRYuoWbMm48ePZ8CAAahUqmzrvNgGOaW9uB9r165lyJAhtGrVipSUFOrVq0doaKjmuMxabpcuXbh16xZjx44lKSmJ9u3bM2DAAA4cOKDJc/ToURo0aMCtW7fyfJht1vacNWsWtWrV0tpes2bNmDhxImPGjCEpKYlevXrRo0cPLl68WKBjIOuyzLbKfP/1118zbNgwrl27hp+fH7t37852sd6nTx82b95M796939h377+gMM4POdHR0UGhUOR4HnwfyXYoWrJ98xYVncT1a495dPNvYh5Ekvw8EXViGiIZRJoe6nQD0tRGZJ/PyxQwJTHP0tXoKxLRUySi1ElGRycFHWUaCqVAoQ8KfSU6hnroGBigo1KhVBmhNDJGz8QUPVMzjIwMMTbSw9g442VipIeB/pu7RnobyOO3aL0N7fsy21eIt2QggUKhyHc68tGjR7Nnzx7Cw8M1aQMGDCAsLIxTp04VaDsxMTGYm5sTHR2d4x2nW7du4ebm9sZ+hc3sMmVmZvZenYjelNdp3xkzZrBs2TLu3r1bRLV7dWvXrmXGjBm5Tmn+puTVvpnBXVRUVLbnVGW1adMmhgwZwv3791/pocfvqqI6PxTHue5tlJqaSmhoKM2bNy/2f7jfRbJ9ASFIiX7K3Wu3eBhxn+gH0SQ8SyY5XkFasiHJaWakqgt6R0iNoSIWI2U0Bjox6OomoVAkYWCsg76xLgamBhiYm2BoZoqxlRWmNjaY25ZAaWoDeu/v9/xVyeO3aL1N7ZtXbJBVsd5xiouL4/r165r3t27dIiwsDCsrK5ydnRk7diz37t1j/fr1APTv35/FixfzxRdf0LdvX06dOsXq1avZvHlzce2C9A5ZsmQJVatWxdramhMnTjBnzhwGDRpU3NXK0f79+/nqq6+K/WTzuhISErh16xYzZ87k008/lUGTJEn/LalJEP03RN8h+cldIq4+4tG9JKKjDEhKNiEpzZK4dJt/JkYw++eVnaEiBhPlEwz1nmNgmIyeoUDfWBdDcxWm1maY21ljXcoefXNPMCkBeirNhWeDt+DCU5LeF8UaOJ0/f54GDRpo3meORerZsydr167lwYMHWtNiu7m5ERoayrBhw/j2228pWbIkixYtKrKpyKX3y7Vr15g+fTrPnj3D2dmZ4cOHM3bs2OKuVo4yx1/9182ePZsZM2ZQr169t7atJUl6jyVFw/M78PyuJkDi+V1Snt3nySNBVLwVT1I9eJLqTmSaM2pynlZZh1RUus/Q04tD3zAFQzMFJjZGWJeyxrG0I1aOFUFlCYU4llGSpMJXrIFTQEBAnlMOr127Nlta/fr1+e2334qwVtL7av78+cyfP7+4q/HOyO/7DTBlyhSmTJnyZiokSZJUECkJcHk3XNgIEcdIURvyNM2NJ6nuPE1150lafZ6lOSFymE5boUhCVxWLgYXAzN4UKydbHL1ccHW2RVmEjzaRJOnN+E9NDiFJkiRJklTohIC/z0PYRlL/2M39OFduJ1fi7+RORKWXJPvEDJCqk0aSiRJDe1McPczxLW+Lp5uFHK8sSe8wGThJkiRJkvR+in0Ef2wh8uRe7j+25nZKJf5OXkI62rPxxisFqWZ6mDoY4exugV8FW1wcTWWQJEnvGRk4SZIkSZL0/khPJenSfm4eOsizv3W4k1yJqHTtMZbxSgEOKkr72VK1sj1OJQv7WUiSJP0XycBJkiRJkqR33p2w37j24xHi76t5mOxDqmijWSZQE2uswLy0JdVrlcLf11beTZIkKRsZOEmSJEmS9E76+94zTmwIJekexKWWBPw1yxQ6iaTY6FKyoisNApyxtVIVX0UlSfpPkIGTJEmSJEnvlBMnbnBl72mSo2xQU/KfVDXG+g9RllTh0aAq1Ss7ypnuJEl6KfKMIb1TXF1dWbBgQYHzr127FgsLizzzBAUF0aZNm9eqV1F62X0uKhERESgUCsLCwnLNc/ToURQKBc+fP39j9SpqBdmnKVOmULFixTdWJ0l6HyUkprJl03mWDdlO2IbbJEY5oEYPa70beHpdpe2o0gQt6kb3Me2pVd1ZBk2SJL00edZ4RwQFBaFQKLK9mjZtWtxVKxK5BTznzp2jX79+b75CRSQ+Pp7Ro0fj7u6OoaEhtra2BAQEsHfvXk2et2WfnZycePDgAeXLly/UcqdMmaJ1TJubm1O3bl1+/vnnQt1OURoxYgSHDx8u7mpI0jvp1p1olgT/zNrhPxJ5LIb0ZCt0SMXV6Ax1G0Tw0fweNB7Wn5LursVdVUmS/uNkV713SNOmTVmzZo1WmoGBQS653022trbFXYVC1b9/f86ePcvixYvx8fEhMjKSkydPEhkZqcnztuyzUqnE3t6+SMouV64chw4dAuDZs2fMnTuXli1b8vfff2Nubp7jOqmpqejp6RVJfV6WiYkJJiYmxV0NSXpnqNVqjhz/m7D9f2H4TAEoARXGOk9xtziPV7PK2NUaCUp5mSNJUuGRd5zyIwSkxBftKzUh53QhXqqqBgYG2Nvba70sLS2BjO5E+vr6HDt2TJM/ODgYGxsbHjx4AEBAQACDBg1i0KBBWFhYYG1tzYQJExAv1CMqKooePXpgaWmJkZERzZo149q1a5rlmXeCDhw4gLe3NyYmJjRt2lSzjUxr1qzB29sbQ0NDypYty5IlSzTLMrt87dixgwYNGmBkZISfnx+nTp3S7Msnn3xCdHS05i7ElClTgOzd1ubPn0+tWrUwNTXFycmJgQMHEhcX91LtmpUQgtmzZ+Pu7o5KpcLPz4/t27drtVHXrl2xtbVFpVLh6empCWhTUlIYNGgQDg4OGBoa4urqysyZM3Pd1p49exg3bhzNmzfH1dWVypUr8/nnn9OzZ09Nnqz7/Ndff1GnTh0MDQ3x8fHh0KFDKBQKdu3apdW+ISEh1K1bF5VKRdWqVbl69Srnzp2jSpUqms/tyZMnmnLVajXTpk3D0dERAwMDKlasyP79+zXLc+qqFxoaSpkyZVCpVDRo0ICIiIhXanNdXV3NMe3j48PUqVOJi4vj6tWrmjwKhYJly5bRunVrjI2NmT59Ounp6fTu3Rs3NzdUKhVeXl4sXLhQq+zMrphz587FwcEBa2trPvvsM1JTUzV5kpOTGTVqFE5OThgYGODp6cnq1au1yvn111+pUqUKRkZG1KpViytXrmiWZe2qV5BtPnjwgJYtW+Lg4ICHhwf/93//99Z0y5Sk4hIbl8K6jX8yb+iP/PV/1zF8pgsoKal3idqO2+nymSn1ZszCrm5nGTRJklTo5FklP6kJ8FXJ/PO9Ih3AIreF4+6DvnGhbCcgIIChQ4fSvXt3fv/9dyIiIhg/fjybN2/GwcFBk2/dunX07t2bM2fOcP78efr164eLiwt9+/YFMi74rl27xu7duzEzM2P06NE0b96c8PBwza/7CQkJzJ07lw0bNqCjo0O3bt0YMWIEmzZtAmDlypVMnjyZxYsX4+/vz4ULF+jbty/GxsZaAcH48eOZO3cunp6ejB8/ni5dunD9+nVq1arFggULmDRpkubiNLdf83V0dJg1axY+Pj7cvn2bgQMHMmrUKK1A7WVNmDCBHTt2sHTpUjw9Pfnll1/o1q0btra21K9fn4kTJxIeHs4PP/yAjY0N169fJzExEYBFixaxe/duQkJCcHZ25u7du9y9ezfXbdnb2xMaGkq7du0wNc3/OSJqtZo2bdrg7OzMmTNniI2NZfjw4TnmnTx5MgsWLMDZ2ZlevXrRpUsXzMzMWLhwIUZGRnTq1IlJkyaxdOlSABYuXEhwcDDLly/H39+f7777jjZt2nDq1Cn8/f2zlX/37l3atWtH//79GTBgAOfPn8+1Li8jOTlZE6B7eXll26eZM2cyf/58lEolarUaR0dHQkJCsLGx4eTJk/Tr1w8HBwc6deqkWe/IkSM4ODhw5MgRrl+/TufOnalYsaLmuO/RowenTp1i0aJF+Pn5cevWLZ4+faq17fHjxxMcHIytrS39+/enV69enDhxItf9KMg2nz59yp49e7CwsGDEiBE8fvz4tdtPkv6LnjxLZMN3F1HeeI6u0EWFProkU0b1Mx7uT3Bu1RtcPs9xXZGSAkolCqXyDddakqRM6ep04tPiSUhNID41nujEaK6nXic+NR4LPYvirl6BycDpHbJ3795sAcTo0aOZOHEiANOnT+fQoUP069ePS5cu0b17d9q2bauV38nJifnz56NQKPDy8uLixYvMnz+fvn37agKmEydOUKtWLQA2bdqEk5MTu3btomPHjkBGF6lly5bh4eEBwKBBg5g2bZpmG19++SXBwcG0a9cOADc3N8LDw1m+fLlW4DRixAhatGgBwNSpUylXrhzXr1+nbNmymJubo1Ao8u0aNmTIEGJiYjAzM8PDw4Mvv/ySAQMGvHLgFB8fz7x58/jpp5+oWbMmAO7u7hw/fpzly5dTv3597ty5g7+/P1WqVAEy7ghlunPnDp6entSpUweFQoGLi0ue21uxYgVdu3bF2toaPz8/6tSpQ4cOHahdu3aO+X/88Udu3LjB0aNHNW0zY8YMAgMDs+UdMWIETZo0ATLaqUuXLhw+fFhTdu/evVm7dq0m/9y5cxk9ejQfffQRALNmzeLIkSMsXbqUFStWZCt/6dKluLu7ZzueZs2alec+5+TixYuaYzshIQFTU1O2bt2KmZmZVr6PP/6YXr16aaVNnTpV87ebmxsnT54kJCREK3CytLRk8eLFKJVKypYtS4sWLTh8+DB9+/bl6tWrhISEcPDgQRo1agRkfOZZzZgxg/r16wMwZswYWrRoQVJSEoaGhjnuU17b/Ouvvzh06BBnzpyhTJkymJmZsWrVKjw9PV+67STpv0ytVrNl+xUeHb2LgVoX0MVU5xE++gdwdUzB0KsZ6Vjy7Og10p6dJf3ZM9KinpEe+eyfv6NQx8SgtLXBYdo0TBs0KO5dkqT/DLVQk5CaQFxqHPGp8cSmxBKfGq95H5cSp/U+ITWB+LT4f//+Z1lCagJJ6Uk5bqNRTCMsjCze7I69Bhk45UfPKOPOTxFRq9XExMZiZmqa/WF7ekYvVVaDBg00dwcyWVlZaf7W19dn48aNVKhQARcXlxy7/NSoUQOFQqF5X7NmTYKDg0lPT+fy5cvo6upSvXp1zXJra2u8vLy4fPmyJs3IyEgTNAE4ODhofil/8uQJd+/epXfv3ppf1gHS0tKyjVWpUKGCVhkAjx8/pmzZsgVqD8j4VX/69OlcvXqVmJgY0tLSSEpKIj4+HmNj7bt5d+7cwcfHR/N+3LhxjBs3TitPeHg4SUlJ2QKRlJQUzV2XAQMG0L59e3777TcaN25MmzZtNIFmUFAQgYGBeHl50bRpU1q2bEnjxo1zrX+9evW4efMmp0+f5sSJE/z0008sXLiQqVOnagLiF125cgUnJyetgLJatWo5lv1i+9rZ2QHg6+urlZb5ucXExHD//v1sAVutWrX47bffciz/8uXLOR5Pr8LLy4vdu3cDEBsby9atW+nYsSNHjhzRBKiA1t+Zli1bxqpVq7h9+zaJiYmkpKRkm+GuXLlyKF/4NdrBwYGLFy8CEBYWhlKp1ARFucnteHV2ds4xf17bvHLlCrq6ulSqVEnTtbR06dKarreS9D74PfwJP3z3B6ZxCvTRxTjpAR63dmH96BIKBBkdiS8UqKz0J0/5e8BArIKCKPHFMBT6+kVZdUkqdunqdOJS44hLjSM2JZbYlFjiUuKITY3Veh+XGkdMSoxWEJQZCMWnxhd6vfR09DDWM8ZI14j0xHRQ5L/O20QGTvlRKAqtu1yO1GrQS8/Yxms+pdzY2JjSpUvnmefkyZNAxgD7Z8+eZQse8iJyGXMlhNC6OM46IF+hUGjWVavVQEZ3vRcDMEDrIjJrOZnlZ65fELdv36Zly5Z88sknzJgxAxsbG44fP07v3r21xpJkKlmypNb4nBeDzkyZ29+3bx+lSpXSWpY5EUezZs24ffs2+/bt49ChQ3zwwQd89tlnzJ07l0qVKnHr1i1++OEHDh06RKdOnWjUqJHWGKms9PT0qFu3LnXr1mXMmDFMnz6dadOmMXr0aPSz/OOf9bPIS07tmzUta3tnLTuv7eV2vLwKfX19rWPb39+fXbt2sWDBAjZu3KhJz3o8h4SEMGzYMIKDg6lZsyampqbMmTOHM2fOaOXL6ZjN3HeVqmAPxXzZ4zWvbeb1XZOkd11cfAqrV4ShvBKDKTroqFNwjdiP891D6Ij0jExKJUpLS3QtLVFaWaFrbYXS0gqllSW6VlYorazRtcpYpjQz4+nKlUSt38CztWtJ+O03Ss0LRt/RsXh3VJLyIIQgMS2R2JRYYlJiiEmJ+ffv5Bit9JjkGK08mYFPYdFV6GKib4KxnjGm+qYY6xljomfy7//1jTHWNcZYL+NlpGf079+6//5trGeMvjLjuiU1NZXQ0FB8rHzy2frbRQZO75EbN24wbNgwVq5cSUhICD169ODw4cNad7pOnz6ttc7p06fx9PREqVTi4+NDWloaZ86c0dxBiYyM5OrVq3h7exeoDnZ2dpQqVYqbN2/StWvXV94XfX190tPT88xz/vx50tLSmD59OhYWFujo6BASEpJrfl1d3XwDTx8fHwwMDLhz506edyBsbW0JCgoiKCiIunXrMnLkSObOnQuAmZkZnTt3pnPnznTo0IGmTZvy7NmzHAO13OqQeecsa+BUtmxZ7ty5w6NHjzR3kc6dO1egcvNiZmZGyZIlOX78OPXq1dOknzp1Cj8/v1zrmTkhRaasx9frUCqVmrFjuTl27Bi1atVi4MCBmrQbN2681HZ8fX1Rq9X8/PPPmq56Ra1s2bKkpaVx4cIFTfe869evv1PPv5KknOw5cIOre65jmKYH6GAdeYky17ZirJuA9ZDPMQ1slBEMmZujeIkfG+3HjcO4WjXujxtP0h9/cKttOxxmTMcsjzv+klQYhBDEpcYRnRz97ysll79feB+TEkOaOu21t2+gNMBU3xQTPRNM9U1z/NtE3+Tfv/8JhEz1/gmQ9E3Q19Ev8I+y7zoZOL1DkpOTefjwoVaarq4uNjY2pKen0717dxo3bswnn3xCs2bN8PX1JTg4mJEjR2ry3717ly+++IJPP/2U3377jW+++Ybg4GAAPD09ad26NX379mX58uWYmpoyZswYSpUqRevWrQtczylTpjB48GDMzMxo1qwZycnJnD9/nqioKL744osCleHq6kpcXByHDx/Gz88PIyMjjIy0uzZ6eHiQlpbGihUr6NChA6dOnWLZsmUFrmdOTE1NGTFiBMOGDUOtVlOnTh1iYmI4efIkJiYm9OzZk0mTJlG5cmXKlStHcnIye/fu1QSW8+fPx8HBgYoVK6Kjo8O2bduwt7fP9SG8AQEBdOnShSpVqmBtbU14eDjjxo2jQYMG2cb3AAQGBuLh4UHPnj2ZPXs2sbGxjB8/Hsh+t+hljRw5ksmTJ+Ph4UHFihVZs2YNYWFh2bqHZurfvz/BwcGa4+nXX3/VGjP1MtLS0jTHdmZXvfDwcEaPHp3neqVLl2b9+vUcOHAANzc3NmzYwLlz53Bzcyvwtl1dXenZsye9evXSTA5x+/ZtHj9+rDVOqjCVLVuWRo0a0b9/f2bPno2FhQUjR45EpVLJf7ykd9KtO9GELP8Nk0iBIXoYJEfheW07JWL+xLpnENZ9+qDM5dEDBWXaqBHu3t7c+2I4ib//zr3BQ0jo2pUSo0ai8549ukN6NUIIYlNjeZ70nKjkqOz/T35OVFIU0cnRmvSYlBjSRd4/9OZFqVBipm+GmYEZpnqmmBmYZbzXN8NU/9/3pvqmWukm+iaY6pmip3w7HsvxrpCB0ztk//79WjPkQcbYkL/++osZM2YQERHBnj17gIzZ2latWkWnTp0IDAzUjPno0aMHiYmJVKtWDaVSyeeff671cNU1a9YwZMgQWrZsSUpKCvXq1SM0NPSlnpfTp08fjIyMmDNnDqNGjcLY2BhfX1+GDh1a4DJq1apF//796dy5M5GRkUyePFkzJXmmihUrEhwczJw5c5g2bRr16tVj5syZ9OjRo8DbycmXX35JiRIlmDlzJjdv3sTCwoJKlSppxkPp6+szduxYIiIiUKlU1K1bly1btgAZs//NmjWLa9euoVQqqVq1KqGhodnHt/2jSZMmrFu3jnHjxpGQkEDJkiVp2bIlkyZNyjG/Uqlk165d9OnTh6pVq+Lu7s6cOXP48MMPc52koKAGDx5MTEwMw4cP5/Hjx5o7Si+OZ3uRs7Mz33//PcOGDWPJkiVUq1aNr776KtvkDQqFgjVr1hAUFJTrti9duqQ5tjPH0C1dujTfz7J///6EhYXRuXNnFAoFXbp0YeDAgfzwww8vte9Lly5l3LhxDBw4kMjISJydnbONfyts69evp1evXrRo0QJ7e3tmzpzJpUuXXvtzlKS3SUpKGmvX/UnKr48wQQ+FSMfx76O43w3Fpm0zbD7/Bl0bm0Lbnl6pUrhs3MCThQuJXLWaqE2bSLjwG47z56Ofz2Q90rsnMxB6lviMZ0n/viKTInka/5Tw+HB2HtpJdEq0JiBKE692F8hQaYi5gfm/L/2M/5sZmGFhYKF5b25gjpm+meb/Kl35g9nbRCHes07zMTExmJubEx0dne0X+6SkJG7duoWbm9sbuzhRq9WaWd9yu3h+UwICAqhYseI79ZyYt6l9i8uJEyeoU6cO169fzzXIeVWv274RERF4enoSHh4uZ4zLwYvte//+fZycnDTj5l5HcZzr3kaZfeybN2/+1jws+V2SX/seO32P8xvD0E/LGEdoFnMLr6tbcKzphO3Y6eiVLLpHgQDE/fwz90ePIf35c3SMjbGfNhXzf2Zy/S+Qx2/O1EJNdHI0TxOf8iTxCZGJkTxNfMrTxKdawdGzxGc8S372St3hjHSNsDS0xMLAAgtDCywNMv7WpP3zt7mBORYGFpjpm2Go+/6ea3PyNh2/ecUGWck7TpL0jtm5cycmJiZ4enpy/fp1hgwZQu3atQs9aCoM+/fvp1+/fjJoysFPP/1ETEwMbm5uxMbGMmbMGFxdXbXGmEnSf9GTZ4lsmn8Mvcc66CtU6KYm4HHzf3iVukeJzYsx8PTKv5BCYFK/Pm67dnJvxAgSz//K/eEjSDhzFrtxY9F5j39QeFulpKfwJPEJTxKeaAKhrK8niU94lvjspe8KmeiZYGVo9e9LZYWFngUPbj6gjn8dbE1sNQGRhaEFBkrZtfN9JQMnSXrHxMbGMmrUKO7evYuNjQ2NGjXSjFN72/Tv37+4q/DWSk1NZcKECdy8eRNTU1Nq1arFpk2biv2XOUl6Hbu3/869A3fRUxqBAuwfnsFXfRDnr8djWP317qS+Cj17e1zWruXJt98SuWw5z0NCSAwLo9SC+Rjk8Lw2qfAJIYhOjuZRwiMeJzzWvLK+j0qOeqlyLQ0ssVZZY6Oy0bysDa2xUllpB0mGVpqZ3l6UmppK6L1Qmrg2keddSUMGTpLG0aNHi7sKUiHo0aPHa4/jkopfkyZNCAwMfO+7mkrvjvXzDhJ7RQFKI4wSHuL7dAs+nzbHqPVPxVovha4uJYYMwbhqVe6NGk3y1avcat8B+8mTsGjTpljr9l+XOYboQdwDHsT/+3oY95BHCY94lPCIJwlPSFGnFKg8fR19bI1ssVXZZgRC/wRGme8z06wNreWkCFKRkIGTJEmSJElFJj1NzfqJISQ9twEFlHpynPoBT7D4dAsK/Zd70HtRMq5VC/edO7g3chQJp0/zYMxYEs6cxX7yJNl1Lxep6lSeJDz5NyCKf8j9uPuavx/EPyjw84QsDSwpYVRC87Izssv23tzAXE6UIBUrGThJkiRJklQkUlJh0xdbSBJOAHg++h8BUz9Ev8KbeSbay9K1tcV59SqeLl/O08XfEr1zJ0oLC+xGjyruqhULIQTPk5/zd+zf/B33t/b/Y//mYcJD1CL/B9NbGljiYOKAg3HGy97YHjtjO01wZKuyzbG7nCS9bWTgJEmSJElSoXv0KJbY0CiS9J1RqNPxfb6F2isno2PjXNxVy5NCqcR24EAMXF2598Vwnm/bhu2gz9AxNi7uqhWJlPQU7sXdyxYU/R33N/fi7uV7x0hPRw97Y3tNUJQZIGWm2Rvbo9JVvaG9kaSiJQMnSZIkSZIK1V9hNzi56ByJ+s4o0xKppLObqpuWoND778xGZtq0KfoLF5Fy+zbP//c/rD7+uLir9MrUQs3jhMfcir7F7Zjb3I65za2YW9yOvs39+Pv53jUqYVQCRxNHHE3/eZk44mTqRCmTUlirrNFRyDGY0vtBBk6SJEmSJBWas/87TNjuWFL1S2CQHEU1l9+oMGV5cVfrpSl0dLDs1o1HM2YQtXETll26vPXja2JSYoiIjsgIjF4Ikm7H3CYpPSnX9Yx0jTQB0YvBkaOpIyVNSsrptyXpHzJwkiRJkiSpUBxZuJq//iyJWs8Mk/i72Hlcw3v8lOKu1iszb9uGJwsWkHLzJvEnT2JSu3ZxVwmA2JRYrjy9wrnkc/x5/k9uxtzk+vPrPEt6lus6ugpdHE0dcTV3xdXMFRczF1zNXHE1d8Xa0PqtDwol6W0gAyfpneLq6srQoUMZOnRogfKvXbuWoUOH8vz581zzBAUF8fz5c3bt2lUodSxsL7vPRSUiIgI3NzcuXLhAxYoVc8xz9OhRGjRoQFRUFBYWFm+0fkWlIPs0ZcoUdu3aRVhY2ButmyS9MWo1B8Z+zfXn1UCpg1X0ZeoPqsi5pxbFXbPXojQxwbxtW6I2biRqw8Y3HjglpiVyM/om16Ouc/35da49v8b1qOs8Snj0b6ar2uuUMCqRLTByNXOlpElJdHXkZZ8kvQ75DXpHBAUFsW7dumzpTZo0Yf/+/cVQo6KVW8Bz7tw5jN+hAbzx8fFMmzaNbdu2cf/+fUxNTSlXrhwjRoygZcuWwNuzz05OTjx48AAbG5tCLXfKlClMnTpV897MzIwKFSowffp06tevX6jbkiTp5aXHPWP/8G+IUNQFBdhFn6f5vB7o2VhDaGhxV++1WXb9mKiNG4n7+WdS7txB37nwJ7cQQnAv7h7hkeH89ewvbjy/wfXn17kbexeByHEdOyM7zFLMqOFZAy8rL0pblMbN3A0jvbdnindJetfIwOkd0rRpU9asWaOVZmDwfvVLtrW1Le4qFKr+/ftz9uxZFi9ejI+PD5GRkZw8eZLIyEhNnrdln5VKJfb29kVSdrly5Th06BAAz549Y+7cubRs2ZK///4bc3PzHNdJTU2VT3uXpCKWcPsP9k/+gQeGdQFwTDhJizUj0DU0JDU1tZhrVzgM3NwwrleX+F+OEbXp/7AbO+a1yhNCcDf2LuGR4YQ/Cyc8MpzLkZeJSYnJMb+lgSWelp6UtihNacvSeFp44m7hjkqhIjQ0lOb+zeW5TpLeEDkNSj6EECSkJhTpKzEtMcd0IXL+lSk3BgYG2Nvba70sLS2BjO5E+vr6HDt2TJM/ODgYGxsbHjx4AEBAQACDBg1i0KBBWFhYYG1tzYQJE7TqERUVRY8ePbC0tMTIyIhmzZpx7do1zfK1a9diYWHBgQMH8Pb2xsTEhKZNm2q2kWnNmjV4e3tjaGhI2bJlWbJkiWZZREQECoWCHTt20KBBA4yMjPDz8+PUqVOaffnkk0+Ijo5GoVCgUCiYMmUKkNFtbcGCBZqy5s+fT61atTA1NcXJyYmBAwcSFxf3Uu2alRCC2bNn4+7ujkqlws/Pj+3bt2u1UdeuXbG1tUWlUuHp6akJaFNSUhg0aBAODg4YGhri6urKzJkzc93Wnj17GDduHM2bN8fV1ZXKlSvz+eef07NnT02erPv8119/UadOHQwNDfHx8eHQoUMoFApNV8PM9g0JCaFu3bqoVCqqVq3K1atXOXfuHFWqVNF8bk+ePNGUq1armTZtGo6OjhgYGFCxYkWtu5mZ5b7YHS00NJQyZcqgUqlo0KABERERr9Tmurq6mmPax8eHqVOnEhcXx9Wr//ZRUSgULFu2jNatW2NsbMz06dNJT0+nd+/euLm5oVKp8PLyYuHChVplBwUF0aZNG+bOnYuDgwPW1tZ89tlnWhd9ycnJjBo1CicnJwwMDPD09GT16tVa5fz6669UqVIFIyMjatWqxZUrV/Lcp7y+A5nHSalSpbC3t8fd3V3rOJkyZQrOzs4YGBhQsmRJBg8e/ErtKkmv4+kvIfxv0gkeGFZFoU7HVf8CrdaNR/cdfFisVbduADz//nvU8QV7oCtkzGYXER1B6M1Q5p6bS+8Dvam9uTYtdrZg5C8jWfPnGs48OENMSgy6Orp4W3nT3rM9Y6qNYVXjVRztdJRfPvqF1U1WM7b6WDqW6UjFEhUx0zcrql2VJCkP8o5TPhLTEqn+f9WLZdtnPj5TaLfcAwICGDp0KN27d+f3338nIiKC8ePHs3nzZhwcHDT51q1bR+/evTlz5gznz5+nX79+uLi40LdvXyDjIvPatWvs3r0bMzMzRo8eTfPmzQkPD9f84pWQkMDcuXPZsGEDOjo6dOvWjREjRrBp0yYAVq5cyeTJk1m8eDH+/v5cuHCBvn37YmxsrBUQjB8/nrlz5+Lp6cn48ePp0qUL169fp1atWixYsIBJkyZpLk5NTExy3G8dHR1mzZqFj48Pt2/fZuDAgYwaNUrrIvVlTZgwgR07drB06VI8PT355Zdf6NatG7a2ttSvX5+JEycSHh7ODz/8gI2NDdevXycxMRGARYsWsXv3bkJCQnB2dubu3bvcvXs3123Z29sTGhpKu3btMDU1zbduarWaNm3a4OzszJkzZ4iNjWX48OE55p08eTILFizA2dmZXr160aVLF8zMzFi4cCFGRkZ06tSJSZMmsXTpUgAWLlxIcHAwy5cvx9/fn++++442bdpw6tQp/P39s5V/9+5d2rVrR//+/RkwYADnz5/PtS4vIzk5WROge3l5ZdunmTNnMn/+fJRKJWq1GkdHR0JCQrCxseHkyZP069cPBwcHOnXqpFnvyJEjODg4cOTIEa5fv07nzp2pWLGi5rjv0aMHp06dYtGiRfj5+XHr1i2ePn2qte3x48cTHByMra0t/fv3p1evXpw4cSLHfcjvO5B5nGzZsgVLS0ueP3/OvXv3ANi+fTvz589ny5YtlCtXjocPH/L777+/drtKUoEJwZ21Uznyc2niVF4o0xIp4/mMhqNf//v9tjKuUwd9F5d8pyZ/mviUsMdhhD0O48/IP/nr2V85PgdJX0efMpZl8Lb2xsfaBx9rHzwtPNFTyjtHkvQ2k4HTO2Tv3r3ZAojRo0czceJEAKZPn86hQ4fo168fly5donv37rRt21Yrv5OTE/Pnz0ehUODl5cXFixeZP38+ffv21QRMJ06coFatWgBs2rQJJycndu3aRceOHYGMLlLLli3Dw8MDgEGDBjFt2jTNNr788kuCg4Np164dAG5uboSHh7N8+XKtwGnEiBG0aNECgKlTp1KuXDmuX79O2bJlMTc3R6FQ5Ns1bMiQIcTExGBmZoaHhwdffvklAwYMeOXAKT4+nnnz5vHTTz9Rs2ZNANzd3Tl+/DjLly+nfv363LlzB39/f6pUqQJk3BHKdOfOHTw9PalTpw4KhQIXF5c8t7dixQq6du2KtbU1fn5+1KlThw4dOlA7lwHKP/74Izdu3ODo0aOatpkxYwaBgYHZ8o4YMYImTZoAGe3UpUsXDh8+rCm7d+/erF27VpN/7ty5jB49mo8++giAWbNmceTIEZYuXcqKFSuylb906VLc3d2zHU+zZs3Kc59zcvHiRc2xnZCQgKmpKVu3bsXMTPtX148//phevXpppb04PsrNzY2TJ08SEhKiFThZWlqyePFilEolZcuWpUWLFhw+fJi+ffty9epVQkJCOHjwII0aNQIyPvOsZsyYoRlzNWbMGFq0aEFSUhKGOfz6nt934MXjJDY2lvLly6Ojk9FB4M6dO9jb29OoUSP09PRwdnamWrVqL92mkvSq/t6+mB+P+ZJsaIl+8nMqNrGg6kfdi7taRSqnqckFglvRt7jw+AIXHl8g7HEYd2LvZFvXQGmAl6WXVpDkYeGBno4MkiTpv0YGTvlQ6ao48/GZIitfrVYTGxuLqamp5sLoxW2/jAYNGmjuDmSysrLS/K2vr8/GjRupUKECLi4uWt27MtWoUUNrStKaNWsSHBxMeno6ly9fRldXl+rV/70DZ21tjZeXF5cvX9akGRkZaYImAAcHBx4/fgzAkydPuHv3Lr1799b8mg+QlpaWbaxKhQoVtMoAePz4MWXLli1Qe0DGnYTp06dz9epVYmJiSEtLIykpifj4+GwTKty5cwcfHx/N+3HjxjFu3DitPOHh4SQlJWULRFJSUjR3XQYMGED79u357bffaNy4MW3atNEEmkFBQQQGBuLl5UXTpk1p2bIljRs3zrX+9erV4+bNm5w+fZoTJ07w008/sXDhQqZOnaoJiF905coVnJyctALK3C6qX2xfOzs7AHx9fbXSMj+3mJgY7t+/ny1gq1WrFr/99luO5V++fDnH4+lVeHl5sXv3bgBiY2PZunUrHTt25MiRI5oAFdD6O9OyZctYtWoVt2/fJjExkZSUlGyz/pUrVw6lUql57+DgwMWLFwEICwtDqVTmOxFFbserc5aB5AX5DmQeJ97e3jRo0IC2bdvStGlTADp27MiCBQtwd3enadOmNG/enA8//BBdXXk6l4pe3KWjHNlrTLLKElXiI+oO8MOzhk/+K74DVK2aIeYFk3LzJrO+/Zi9NneJTo7WyqNAgYeFB/4l/KlgWwEfax/czd3lbHaS9I6Q3+R8KBSKIp2hRq1Wk6abhpGeUbbA6WUZGxtTunTpPPOcPHkSyBhg/+zZs5eajS23MVdCCK2L46yDVBUKhWZdtTrj6eQrV67UCsAArQvXrOVklp+5fkHcvn2bli1b8sknnzBjxgxsbGw4fvw4vXv3znHQcsmSJbXG57wYdGbK3P6+ffsoVaqU1rLMiTiaNWvG7du32bdvH4cOHeKDDz7gs88+Y+7cuVSqVIlbt27xww8/cOjQITp16kSjRo20xkhlpaenR926dalbty5jxoxh+vTpTJs2jdGjR6Ovr6+VN+tnkZec2jdrWtb2zlp2Xtt72TF6edHX19c6tv39/dm1axcLFixg48aNmvSsx3NISAjDhg0jODiYmjVrYmpqypw5czhzRvvHkJyO2cx9V6kK9gNGQY/XgnwHMo+Tffv2sX//fj766CPNceLk5MSVK1c4ePAghw4dYuDAgcyZM4eff/5ZDhCXilT683sc/Po0McbV0E2No+Yn5d7poCk6OZrzj84T9jiM3x7/RnhkON19kmn2Kzju/53ojkoMlYaUtymPfwl//Ev441fCT44/kqR3mAyc3iM3btxg2LBhrFy5kpCQEHr06MHhw4e1ArbTp09rrXP69Gk8PT1RKpX4+PiQlpbGmTNnNHdQIiMjuXr1Kt7e3gWqg52dHaVKleLmzZt07dr1lfdFX1+f9PT0PPOcP3+etLQ0pk+fjoWFBTo6OoSEhOSaX1dXN9/A08fHBwMDA+7cuZPnHQhbW1uCgoIICgqibt26jBw5krlz5wIZ02l37tyZzp0706FDB5o2bcqzZ89yDNRyq0PmnbOsgVPZsmW5c+cOjx490txFOnfuXIHKzYuZmRklS5bk+PHj1KtXT5N+6tQp/Pz8cq1n1mdfZT2+XodSqdSMHcvNsWPHqFWrFgMHDtSk3bhx46W24+vri1qt5ueff9Z01XsdBf0OZB4nzZo146OPPqJ58+aa40SlUtGqVStatWrFZ599RtmyZbl48SKVKlV67fpJUo7SUvhpxALuGzdDoU7Hswp4B1TIf73/kDR1Gn8+/ZMT909w8v5J/nz6J2qh/ePH6VpWNPs1kko3BP/nN4+yvgFyXJIkvUdk4PQOSU5O5uHDh1ppurq62NjYkJ6eTvfu3WncuDGffPIJzZo1w9fXl+DgYEaOHKnJf/fuXb744gs+/fRTfvvtN7755huCg4MB8PT0pHXr1vTt25fly5djamrKmDFjKFWqFK1bty5wPadMmcLgwYMxMzOjWbNmJCcnc/78eaKiovjiiy8KVIarqytxcXEcPnwYPz8/jIyMMDLSvjPo4eFBWloaK1asoEOHDpw6dYply5YVuJ45MTU1ZcSIEQwbNgy1Wk2dOnWIiYnh5MmTmJiY0LNnTyZNmkTlypUpV64cycnJ7N27VxNYzp8/HwcHBypWrIiOjg7btm3D3t4+1wenBgQE0KVLF6pUqYK1tTXh4eGMGzeOBg0aZBvfAxAYGIiHhwc9e/Zk9uzZxMbGMn78eCD73aKXNXLkSCZPnoyHhwcVK1ZkzZo1hIWFZesemql///4EBwdrjqdff/1Va8zUy0hLS9Mc25ld9cLDwxk9enSe65UuXZr169dz4MAB3Nzc2LBhA+fOncPNza3A23Z1daVnz5706tVLMznE7du3efz4sdY4qZeR33cg8zipUKECCQkJbN++XXOcrF27lvT0dKpXr46RkREbNmxApVLlO15Okl7H6QkTuKrMGBPpYHqDhgP6F3ONCsfd2Lucun+Kk/dPcubBGeJStWdddTVzpbJdZSrZVcLf1h9HU0fuhn1K/LFjlPjhV/QqZh8/KknSu0sGTu+Q/fv3a82QBxljQ/766y9mzJhBREQEe/bsATJma1u1ahWdOnUiMDBQM+ajR48eJCYmUq1aNZRKJZ9//jn9+vXTlLdmzRqGDBlCy5YtSUlJoV69eoSGhr5UF6E+ffpgZGTEnDlzGDVqFMbGxvj6+jJ06NACl1GrVi369+9P586diYyMZPLkyZopyTNVrFiR4OBg5syZw7Rp06hXrx4zZ86kR48eBd5OTr788ktKlCjBzJkzuXnzJhYWFlSqVEkzHkpfX5+xY8cSERGBSqWibt26bNmyBciY/W/WrFlcu3YNpVJJ1apVCQ0NzbWbZpMmTVi3bh3jxo0jISGBkiVL0rJlSyZNmpRjfqVSya5du+jTpw9Vq1bF3d2dOXPm8OGHH+Y4ScHLGDx4MDExMQwfPpzHjx9r7ii9OJ7tRc7Oznz//fcMGzaMJUuWUK1aNb766qtskzcoFArWrFlDUFBQrtu+dOmS5tjOHEO3dOnSfD/L/v37ExYWRufOnVEoFHTp0oWBAwfyww8/vNS+L126lHHjxjFw4EAiIyNxdnbONv7tZeT3HXjxONHR0aFatWqa48TCwoKvv/6aL774gvT0dHx9fdmzZw/W1tavXB9Jykv4qkWERQaAUgfrpIu0Wfrfnf4+NiWWsw/PaoKlu7Has5qaG5hTw6EGtUrWoqZDTRxMHLKVYdW9G/HHjvH8+++xHfw5Om/BA8glSXozFKIwByL8B8TExGBubk50dHS2X+yTkpK4desWbm5ur32RWVBqtVoz69vrjnF6XQEBAVSsWDHHSSP+q96m9i0uJ06coE6dOly/fj3XIOdVvW77RkRE4OnpSXh4OJ6enoVat3dBUR2/xXGuexulpqZmPEC0uXyAaG4enf6JfcufkGhgi2n8TTot/RhDk4KN+30b2lcIQXhkOL/c+4VT90/xx5M/SBf/dvPWVejiV8KPWiVrUatkLbytvFHqKPMoEYRazc1mzUm5fRv7yZOw7NKlqHcjR29D+77LZPsWrbepffOKDbKSd5wk6R2zc+dOTExM8PT05Pr16wwZMoTatWsXetBUGPbv30+/fv1k0CRJb6GkJ39zeMkVEo28MEx6SsNxgQUOmoqTEIKLTy/yY8SPHLx9kPvx97WWu5q5UrNkTWqVrEVV+6oY673cHSOFjg6WXbvy6KuveLZhIxYfffTaXaElSfpvkIGTJL1jYmNjGTVqFHfv3sXGxoZGjRppxqm9bfr3fzfGSUjSOyc9jQMj1hJlVAtlWhL+rUvg6P32jqNTCzW/P/mdHyN+5NCdQzyM/3e8r0pXRe2StaldqjY1S9aklEmpPEoqGPN2bXmyYAEpN28Sf/IkJrk8W0+SpHeLDJwkjaNHjxZ3FaRC0KNHj9cexyVJ0vvt0NCp/K1qAEKNu9sjKrX9pLirlE26Op3fHv/GwdsHOXT7EE8Sn2iWGekaUd+pPo1dGlO7VO2Xfi5ifpQmJpi3a0fUxo1EbdwkAydJek/IwEmSJEmSJI3TcxdyNbke6ICD4ncajx9e3FXSSFOncf7ReQ5GHOTQnUM8S3qmWWaiZ0IDpwYEugRSq1QtDJQGRVoXy64fE7VxI3FHj5Jy5w76WR52LUnSu0cGTpIkSZIkAXD1hx/447IbQk+JdfxFWq8ZUtxVQgjBn0//ZMf1HRy6fYjnyc81y8z0zWjo3JBAl0BqONRAX6mfe0GFzMDNDeO6dYk/doyoTf+H3dgxb2zbkiQVDxk4SZIkSZJE5M2bnNzylFRVKUwS7tBsbneUusV3mRCXEse+m/vYfm07fz37S5NuaWBJQ+eGNHZpTFWHqujpFN+MXHJqckl6v8jASZIkSZLec2lJyRyavJd44/Lop0RTp78v5nZWxVKXS08vse3qNkJvhZKYlgiAvo4+TVyb8KHHh1S1r4quzttx+WJcpw76Li6k3L5N9O7dxTY1uSRJb8bbceaRJEmSJKnY7BsUzFPjGuioU/GtkYxHrcpvdPvxqfGE3gpl25VtXH52WZPuZu5GxzIdaeXRCnMD8zdap4KQU5NL0vtFBk6SJEmS9B47OH4+f+vWAMDd/CI1+o14Y9u+HHmZbVe3se/mPhLSEgDQ09Ej0CWQjmU6Utmu8lsfiMipySXp/VF4j6KXpBdERESgUCgICwt7K8suyvq9rLVr12JhYZFnnilTplCxYsV8y5o4cSL9+vUrnIrlY8qUKVSqVOmNbKswBQUF0aZNm+KuRpG5ePEijo6OxMfHF3dVpP+Ac+u/5/pjbwBKJp+myZyiD5oSUhPYcW0HXfZ2odPeTmy7uo2EtARczVwZUWUEhzseZla9WVSxr/LWB03wz9TkbdsCELVxUzHXRpKkoiQDp3fE48eP+fTTT3F2dsbAwAB7e3uaNGnCqVOnNHkUCgW7du0qvkq+QTdv3qRLly44Ojpib2+Ps7MzrVu35urVqwA4OTnx4MEDypcvX8w1hc6dO2vq9ToePXrEwoULGTduHJDxeef1CgoKeu1tSoVrxYoVBAQEYGZmhkKh4Pnz59nyREVF0b17d8zNzTE3N6d79+5a+Xx9falWrRrz589/cxWX/pPuXAjn96OgVupjFR9OiyXDinR7z5KeMe/8PD7Y9gGTT07mz8g/0dXRpZlrM75r8h272+ymZ7meWBpaFmk9ioJl164AmqnJJUl6N8mueu+I9u3bk5qayrp163B3d+fRo0ccPnyYZ8+e5b/yWyolJQV9/ZefWjYlJYXAwEDKli3L9u3bMTExITo6mv379xMdHQ2AUqnE3t6+sKv8SlQqFSrV6z+ccfXq1dSsWRNXV1cAHjx4oFm2detWJk2axJUrV7S2W9xSU1PR0yuaGbGKqmwhBOnp6egWwWxjCQkJNG3alKZNmzJ27Ngc83z88cf8/fff7N+/H4B+/frRvXt39uzZo8nzySef0L9/f8aOHYtSqSz0ekrvhpPzD5Js5ItR0kMaTQhEv4jOCVFJUWz8YyNb/tqimezB2dSZDmU60Lp0a6wMi2cSisJk4C6nJpek94G845QPIQTqhISifSUm5pguhChQHZ8/f87x48eZNWsWDRo0wMXFhWrVqjF27FhatGgBoLmYbtu2LQqFQvP+xo0btG7dGjs7O0xMTKhatSqHDh3SKt/V1ZWvvvqKXr16YWpqirOzMytWrNDKc/bsWfz9/TE0NKRKlSpcuHBBa3l6ejq9e/fGzc0NlUqFl5cXCxcu1MqT2YVq5syZlCxZkjJlyhSo7KzCw8O5efMmS5YsoUaNGjg7O1O7dm1mzJhB1apVgZy76u3evRtPT09UKhUNGjRg3bp1Wr/6Z3ap27t3L15eXhgZGdGhQwfi4+NZt24drq6uWFpa8vnnn5Oenq4pNyoqih49emBpaYmRkRHNmjXj2rVrmuU5ddX7+uuvsbOzw9TUlN69e5OUlJTnPgNs2bKFVq1aad7b29trXubm5igUCs17PT09+vfvj6OjI0ZGRvj6+rJ582bNuuvXr8fa2prk5GStbbRv354ePXrkuH21Ws20adNwdHTEwMCAihUrai7uX2zzkJAQAgICMDQ0ZOPGjfnu1+uUnZ6ezhdffIGFhQXW1taMGjUq2/dKCMHs2bNxd3dHpVLh5+fH9u3bNcuPHj2KQqHgwIEDVKlSBQMDA44dO1ager+soUOHMmbMGGrUqJHj8suXL7N//35WrVpFzZo1qVmzJitXrmTv3r1aQXGTJk2IjIzk559/LpJ6Sv99R+d+R6SRLwg1fvXU2Hp5Ffo2opKi+DHxR1rubsmaP9eQmJZIOetyfPvBt+xpu4dPyn/yTgRNmay6Zdx1er5jB2rZVVaS3knyjlM+RGIiVyoV/exCj3JI8/rtVxRGRvmua2JigomJCbt27aJGjRoYGGR/Wvq5c+coUaIEa9asoWnTpppfoePi4mjevDnTp0/H0NCQdevW8eGHH3LlyhWcX3gKenBwMF9++SXjxo1j+/btDBgwgHr16lG2bFni4+Np2bIlDRs2ZOPGjdy6dYshQ7QfmqhWq3F0dCQkJAQbGxtOnjxJv379cHBwoFOnTpp8hw8fxszMjIMHDyKEKFDZWdna2qKjo8P27dsZPHhwvu0HGRfeHTp0YMiQIfTp04cLFy4wYkT2vv4JCQksWrSILVu2EBsbS7t27WjXrh0WFhaEhoZy8+ZN2rdvT506dejcuTOQERBeu3aN3bt3Y2ZmxujRo2nevDnh4eE53hEJCQlh8uTJfPvtt9StW5cNGzawaNEi3N3dc61/VFQUf/75J1WqVCnQ/iYlJVG5cmVGjx6NmZkZ+/bto3v37ri7u1O9enU6duzI4MGD2b17Nx07dgTg6dOn7N27VytgedHChQsJDg5m+fLl+Pv7891339GqVSsuXbqEp6enJt/o0aMJDg5mzZo1OR6rhVl2cHAw3333HatXr8bHx4fg4GB27txJw4YNNetMmDCBHTt2sHTpUjw9Pfnll1/o1q0btra21K9fX5Nv1KhRzJ07F3d391zHpJUrV47bt2/nuh8uLi5cunSpQPuck1OnTmFubk716tU1aTVq1MDc3JyTJ0/i9c/Fr76+Pn5+fhw7dkxrXyUJICbyOTf/NAJDKJV8lkq9xhVq+c+TnrMufB3/d/n/NBM++Fj7MNBvIPUc6/0nxi29CuO6ddFzcSb19h05NbkkvavEeyY6OloAIjo6OtuyxMREER4eLhITEzVp6fHxItyrbLG80uPjC7xf27dvF5aWlsLQ0FDUqlVLjB07Vvz+++9aeQCxc+fOfMvy8fER33zzjea9i4uL6Natm+a9Wq0WJUqUEEuXLhVCCLF8+XJhZWUl4l+o79KlSwUgLly4kOt2Bg4cKNq3b69537NnT2FnZyeSk5M1aa9a9uLFi4WRkZEwNTUVdevWFVOnThU3btzQLL9165ZWGaNHjxbly5fXKmP8+PECEFFRUUIIIdasWSMAcf36dU2eTz/9VBgZGYnY2FhNWpMmTcSnn34qhBDi6tWrAhAnTpzQLH/69KlQqVQiJCREU665ublmec2aNUX//v216lK9enXh5+eX6/5euHBBAOLOnTs5Ls+6jZw0b95cDB8+XPN+wIABolmzZpr3CxYsEO7u7kKtVgshhJg8ebLw8/MTUVFRIj09XZQsWVLMmDFDq8yqVauKgQMHCiH+bfMFCxbkWY+cvGrZDg4O4uuvv9a8T01NFY6OjqJ169ZCCCHi4uKEoaGhOHnypNZ6vXv3Fl26dBFCCHHkyBEBiF27duVbz4iICHHt2rVcXxEREQXa38xtRkZGatpXCCFmzJghPD09s+X39PQUX331lVZa27ZtRVBQUI7l53Suex+lpKSIXbt2iZSUlOKuyhu1s+/XYvGnh8XKT74XT65dLbRynyc9Fwt/XSiqbawmyq8tL8qvLS8CNwSKgzcPas4b77rIdetFuFdZcb15iyLf5/f1+H1TZPsWrbepffOKDbKSd5zyoVCp8Prt1yIrX61WExMbi5mpKTo62j0nFS/R37x9+/a0aNGCY8eOcerUKfbv38/s2bNZtWpVnpMAxMfHM3XqVPbu3cv9+/dJS0sjMTGRO1kGt1aoUOHfev3T5evx48dARvchPz8/jF64O1azZs1s21q2bBmrVq3i9u3bJCYmkpKSkm2mOF9fX61xTQUtO6vPPvuMHj16cPjwYY4dO8b27duZOXMmu3fvJjAwMFv+K1euaLrxZapWrVq2fEZGRnh4eGje29nZ4erqiomJiVbai22jq6urdYfA2toaLy8vLl/+91klL7p8+TL9+/fXSqtZsyZHjhzJdX8TEzPGDRgaGuaa50Xp6el8/fXXbN26lXv37pGcnExycjLGLzz1vm/fvlStWpV79+5RqlQp1qxZQ1BQUI6/FsfExHD//n1qZ5mGt3bt2vz+++9aaQW9K/a6ZUdHR/PgwQOt40VXV5cqVapouuuFh4eTlJSU7ZhISUnB39//pevt4uJSsJ16DTm1vxAiW7pKpSIhIaHI6yP9t4TvP8oDKgLgbncVm9LtXrvM6ORo1oevZ9PlTcSnZnRRK2tVln7l+xH/ezz1Heu/s3eZstJMTX7jBgmnTmFcq1ZxV0mSpEIkA6d8KBSKAnWXe2VqNTppaegYGWULnF6WoaEhgYGBBAYGMmnSJPr06cPkyZPzDJxGjhzJgQMHmDt3LqVLl0alUtGhQwdSUlK08mXtUqZQKFCr1QAFGosVEhLCsGHDCA4OpmbNmpiamjJnzhzOnDmjle/FC/eClp0bU1NTWrVqRUBAALNnz6ZZs2ZMnz49x8AppwvPnLadUzu8StvktL3XYWNjA2R02bO1tc03f3BwMPPnz2fBggX4+vpibGzM0KFDtT53f39//Pz8WL9+PU2aNOHixYtaExDkJKc2zJqW9TMuqKIoO/Nz2rdvH6VKldJalrUbYUHKLuquevb29jx6lL1j75MnT7Czs9NKe/bsmVaQL0np6emEbbqM2tgLq/jL1F88/LXKi06OZkP4BjZd3kRcahwAXpZeDKg4gIZODUlLSyP0j9DCqPp/RubU5FGbNvFsw0YZOEnSO0YGTu8wHx8frenH9fT0tCYtADh27BhBQUG0/ecZFHFxcURERLz0djZs2EBiYqJmprbTp09n206tWrUYOHCgJu3GjRuFUnZBKBQKypYty8mTJ3NcXrZsWUJDtf+BP3/+/EtvJysfHx/S0tI4c+YMtf75BzQyMpKrV6/i7e2d4zre3t6cPn1aaxKG/PbZw8MDMzMzwsPDNZNq5OXYsWO0bt2abt26ARkBxLVr17LVqU+fPsyfP5979+7RqFEjnJyccizPzMyMkiVLcvz4cerVq6dJP3nyZI537l7Gq5Ztbm6Og4MDp0+f1qyXlpbGr7/+qnn+lI+PDwYGBty5c0drPNOrCg0NJTU1NdflrzvLX82aNYmOjubs2bOafT9z5gzR0dGa4yvTn3/+SYcOHV5re9K75fCUb4kyLo+OOpWKHVxQ6r7a8ZiSnsKaP9ew7tI6YlNjAfC09GSg30AaOjdER/F+zztl+VFnojZtIu74cdTJyegUcCynJElvPxk4vQMiIyPp2LEjvXr1okKFCpiamnL+/Hlmz55N69atNflcXV05fPgwtWvXxsDAAEtLS0qXLs2OHTv48MMPUSgUTJw4UfMrfEF9/PHHjB8/nt69ezNhwgQiIiKYO3euVp7SpUuzfv16Dhw4gJubGxs2bODcuXO4ubm9dtlZhYWFMXnyZLp3707ZsmVJSUnh119/5bvvvmP06NE5rvPpp58yb948Ro8eTe/evQkLC2Pt2rVAzl2jCsrT05PWrVvTt29fli9fjqmpKWPGjKFUqVJan82LhgwZQs+ePalSpQp16tRh06ZNXLp0Kc/JIXR0dGjUqBHHjx8v0MNdS5cuzffff8/JkyextLRk3rx5PHz4MFvg1LVrV0aMGMHKlStZv359nmWOHDmSyZMn4+HhQcWKFVmzZg1hYWFs2vT6D4R81bKHDBnC119/jaenJ97e3sybN0/rmUempqaMGDGCYcOGoVarqVOnDjExMZw8eRITExN69uz5UvV83a56Dx8+5OHDh1y/fh3IeJitjo4O3t7e2NjY4O3tTdOmTTXHE2RMR96yZUvNxBCQMdlJZrArSQBPIu5y+54j6EMp9Vm8W098pXLCHocx+eRkbkbfBKC0RWkGVhzIB84fvPcBUyb90qVRWlmR/uwZyZcvoyrAw8slSfpvkGe5d4CJiQnVq1dn/vz51KtXj/LlyzNx4kT69u3L4sWLNfmCg4M5ePAgTk5OmvEb8+fPx9LSklq1avHhhx/SpEkTza/xL7P9PXv2EB4ejr+/P+PHj2fWrFlaefr370+7du3o3Lkz1atXJzIyUuvu0+uUnZWjoyOurq5MnTqVmjVrEhAQwDfffMPUqVMZP358juu4ubmxfft2duzYQYUKFVi6dKkmb0FnfsvNmjVrqFy5Mi1btqRmzZoIIQgNDc317kPnzp2ZNGkSo0ePpnLlyty+fZsBAwbku51+/fqxZcuWAgW+EydOpFKlSjRp0oSAgADs7e1zDLjMzMxo3749JiYm+QZkgwcPZvjw4QwfPhxfX1/279+vmeI9PwqFQhOoFmbZw4cPp0ePHgQFBWm6iGbeXc305ZdfMmnSJGbOnIm3tzdNmjRhz549+Qb1RWHZsmX4+/vTt29fAAICAqhXrx67d+/W5Nm0aRO+vr40btyYxo0bU6FCBTZs2KBVzubNm2ncuPEbGXMl/Tf8MvX/SNG3QJX0mIAZfV96/YTUBGadnUWPH3pwM/omVoZWfF33a75v9T2BLoEyaHqBQqFA9c+44MQs4zAlSfpvU4jXGUTyHxQTE4O5uTnR0dGYmZlpLUtKSuLWrVu4ubkVeJD961Kr1cTExGBmZvbaY5yk7F6nfWfMmMGyZcu4e/duEdWucAkhqFGjBkOHDqVLIU6DGxgYiLe3N4sWLcq2rDCO34iICDw9PQkPDy9QkPU+eZX2TU5OxtPTk82bN2ebUCNTcZzr3kapqamEhobSvHnzInsQ89vg1//7H6d/NgaFDhVc/qTu2II9piHTyXsnmXpqKvfj7wPQyqMVI6uMxMLQIs/13pf2zcnTZct4smAhZs2bUWrevCLZxvvcvm+CbN+i9Ta1b16xQVayq54k/WPJkiVUrVoVa2trTpw4wZw5cxg0aFBxV6vAFAoFK1as4I8//iiU8p49e8aPP/7ITz/9pHXnsrDt37+ffv36yaCpkNy+fZvx48fnGjRJ75e05FTC9z8FI1Ns48OoO2ZYgdeNTo5mzrk5/O/G/wBwMHZgcs3J1C4lj638qPz8AEj8vXDOx5IkvR1k4CRJ/7h27RrTp0/n2bNnODs7M3z4cMaOHVvc1Xopfn5++P3zD/brqlSpElFRUcyaNUtr/Exhyzr1uvR6ypQpU6AJQqT3w49jFxBjVBllWiJVP60OBRyzefD2QWacnkFkUiQKFHQp24XBlQZjrPdqs2K+bwx9fUGhIPXePdKePEG3ALOdSpL09pOBkyT9Y/78+cyfP7+4q/HWeNnZFSVJervc/f0yd6PLgh4461/Arc6EfNd5kvCEr858xaE7hwBwM3djWq1pVCxRsYhr+25RmphgULo0ydeukfjHH5h+8EFxV0mSpEIgB9VIkiRJ0jvodHAoaXrGmCTe5YNZQ/LMK4Rg57WdtP5faw7dOYSuQpd+Ffqx7cNtMmh6RaqK/3TXC5MTREjSu0LecZIkSZKkd8yJxet5bOQPQo13jXQMTE1zzXs39i7TTk3j9IOM58X5WPswrdY0vKyKrovu+0Dl58fzbdvlzHqS9A6RgZMkSZIkvUOSYuO4dk4HVGCf+CvVBuT8/Dq1ULPp8ia+ufANiWmJGCgN+KziZ3T36Y6ujrw8eF2aCSL+/BORloZCV7apJP3XyW+xJEmSJL1Dfhy1mHhVNfRSY6k9qkWOeRLTEhl7bCyH7xwGoIpdFabUmoKLmXz2V2HR9/BAx8QEdVwcydevY1i2bHFXSZKk1yTHOEmSJEnSO+Lq0ZPcS8u40+FqEY59+fLZ8jxNfErvA705fOcwejp6TKwxkdVNVsugqZApdHQw9M1ofznOSZLeDTJwkiRJkqR3xG+rz6NWGmAef50PZo3Itvzm85t0C+3GxacXMTcwZ2XjlXTy6oSOQl4OFIV/n+ckAydJehfIM6X0yo4ePYpCoeD58+fFXRUtERERKBQKwsLCirWMwrJ27VosLCzyzDNlyhQqVqz4RurzXxIUFESbNm2KuxqS9EYcmbGESOPyKNTpVGhpi1JXT2v5uYfn6PZDN+7F3cPJ1ImNzTZS2a5yMdX2/aAJnArpweSSJBUvGTi9I/K6QAwICGDo0KHZ0nft2oXin4chBgQEoFAocn25uroWXeWLwc2bN+nSpQslS5bE0NAQR0dHWrduzdWrVwFwcnLiwYMHlM+hm8ub1rlzZ029CtOOHTto0qQJNjY2uQaJycnJfP7559jY2GBsbEyrVq34+++/NcsjIiL4/PPP8fDwQKVS4eHhweTJk0lJSclxm5GRkTg6Or6xgHvhwoWsXbv2pdZRKBTs2rWrSOojSUUl+sETbl63AaBk6lkqdG6rtXzPjT30O9iP2JRY/Gz92Nh8I67mrsVQ0/dLZuCUcuMG6TExxVwbSZJelwycJCDjIvrBgwc8ePCAs2fPAnDo0CFN2rlz54q5hoUnJSWFwMBAYmJi2LFjB1euXGHr1q2UL1+e6OhoAJRKJfb29ui+BbMgqVQqSpQoUejlxsfHU7t2bb7++utc8wwdOpSdO3eyZcsWjh8/TlxcHC1btiQ9PR2Av/76C7VazdKlS7l06RLz589n2bJljBs3LsfyevfuTYUKFQp9X3Jjbm6e7906SXoX/DRhFUkGNhgmR1L/yx6adCEES39fyrjj40hTp9HYpTGrGq/CytCqGGv7/tC1skLP2RmAxD8uFnNtJEl6XTJwyocQgtTk9CJ9paXknC6EeGP7aWVlhb29Pfb29tja2gJgbW2dLS0nJ06cwM/PD0NDQ6pXr87Fi//+4xAZGUmXLl1wdHTEyMgIX19fNm/erLX+9u3b8fX1RaVSYW1tTaNGjYiPj9csX7NmDd7e3hgaGlK2bFmWLFmitf7Zs2fx9/fH0NCQKlWqcOHChTz3NTw8nJs3b7JkyRJq1KiBi4sLtWvXZsaMGVStWhXIuave7t278fT0RKVS0aBBA9atW6d15ySzS93evXvx8vLCyMiIDh06EB8fz7p163B1dcXS0pLPP/9cE3gAREVF0aNHDywtLTEyMqJZs2Zcu3ZNszynrnpff/01dnZ2mJqa0rt3b5KSkvLc55x0796dSZMm0ahRoxyXR0dHs3r1aoKDg2nUqBH+/v5s3LiRixcvcujQIQCaNm3Kt99+S+PGjXF3d6dVq1aMGDGCHTt2ZCtv6dKlPH/+nBEjso+7yIlCoWDp0qU0a9YMlUqFm5sb27Zt08pz8eJFGjZsqDl2+vXrR1xcnGZ51juxAQEBDB48mFGjRmmO+SlTpmiWZ95Zbdu2rdad1t9//50GDRpgamqKmZkZlStX5vz58wXaD0kqahd3/sADZUaXO3eXu1g6OgGQmp7KhBMTWBKWcc7sVb4Xc+rPwVDXsNjq+j76d5xTWPFWRJKk11bsP6cvWbKEOXPm8ODBA8qVK8eCBQuoW7durvk3bdrE7NmzuXbtGubm5jRt2pS5c+dibW1dJPVLS1GzYsjPRVJ2fvotrI+egbJYtv0yRo4cycKFC7G3t2fcuHG0atWKq1evoqenR1JSEpUrV2b06NGYmZmxb98+unfvjru7O9WrV+fBgwd06dKF2bNn07ZtW2JjYzl27JgmaFy5ciWTJ09m8eLF+Pv7c+HCBfr27YuxsTE9e/YkPj6eli1b0rBhQzZu3MitW7cYMmRInvW1tbVFR0eH7du3M3ToUJTK/Ns4IiKCDh06MGTIEPr06cOFCxdyDAASEhJYtGgRW7ZsITY2lnbt2tGuXTssLCwIDQ3l5s2btG/fnjp16tC5c2cg4+L+2rVr7N69GzMzM0aPHk3z5s0JDw9HT08v2zZCQkKYPHky3377LXXr1mXDhg0sWrQId3f3gnxcBfbrr7+SmppK48aNNWklS5akfPnynDx5kiZNmuS4XnR0NFZW2r9mh4eHM23aNM6cOcPNmzcLXIeJEyfy9ddfs3DhQjZs2ECXLl0oX7483t7eJCQk0LRpU2rUqMG5c+d4/Pgxffr0YdCgQXl2z1u3bh1ffPEFZ86c4dSpUwQFBVG7dm0CAwM5d+4cJUqUYM2aNTRt2lRzbHTt2hV/f3+WLl2KUqkkLCwsx89GkorDxR0RCGMvrOP/pMHkYQDEpMQw7Mgwzj48i1KhZHyN8XQs07GYa/p+Uvn5EbNnj5wgQpLeAcV6x2nr1q0MHTqU8ePHc+HCBerWrUuzZs24c+dOjvmPHz9Ojx496N27N5cuXWLbtm2cO3eOPn36vOGaSy+aPHkygYGB+Pr6sm7dOh49esTOnTsBKFWqFCNGjKBixYq4u7vz+eef06RJE82dgwcPHpCWlka7du1wdXXF19eXgQMHYmJiAsCXX35JcHAw7dq1w83NjXbt2jFs2DCWL18OZATS6enpfPfdd5QrV46WLVsycuTIPOtbqlQpFi1axKRJk7C0tKRhw4Z8+eWXeV7QL1u2DC8vL+bMmYOXlxcfffQRQUFB2fKlpqaydOlS/P39qVevHh06dOD48eOsXr0aHx8fWrZsSYMGDThy5AiAJmBatWoVdevWxc/Pj02bNnHv3r1cx9ksWLCAXr160adPH7y8vJg+fTo+Pj557vOrePjwIfr6+lhaWmql29nZ8fDhwxzXuXHjBt988w39+/fXpCUnJ9OlSxfmzJmD8z9dVgqqY8eO9OnThzJlyvDll19SpUoVvvnmGyDjs09MTGT9+vWUL1+ehg0bsnjxYjZs2MCjR49yLbNChQpMnjwZT09PevToQZUqVTh8OONZNpl3Vi0sLLTutN65c4dGjRpRtmxZPD096dixI37//IosScXp9MrNRBl7oVCn4/+xDygU3Iu7R/fQ7px9eBYjXSMWf7BYBk3F6N87Tn+80Z4kkiQVvmK94zRv3jx69+6tCXwWLFjAgQMHWLp06f+3d9/xVZb3/8dfZ2cnJCEJYYSwp0xlOHARxYGtVdHWVdFKERf96ler3zp+ddZBraK17k1VbK1FIaiACCJT9h5hJIQkkH32/fsj5EBMWCEnd8b7+fCYnOu+73Pe58pNcj7nvu7r5oknnqi1/g8//EDnzp254447AMjMzOTWW2/l6aefDltGu9PK7/46KmyPHwwGKS0tITY2Dqu1Zh1rdzadkZRjxozhu+++AyAjI4M1a9aElo0YMSL0fWJiIj179mTdunUABAIBnnzySaZNm8bu3bvxeDx4PB6io6MBGDBgAOeddx79+/fnggsuICsriyuuuII2bdqwb98+du7cyfjx47nllltCz+H3+4mPjwdg3bp1DBgwgKioqDrzHMltt93G9ddfz7fffsuiRYv4+OOPefzxx/n8888ZPXp0rfU3bNgQGsZX7bTTTqu1XlRUFF27dg3dT01NpXPnzqFCsLotPz8/lN9utzNs2LDQ8qSkpBp9+HPr1q2rUZhUv+bqYizcDMMITSpyuD179nDhhReGip1q999/P7179+baa6894ef6+c9yxIgRoeGT1T/76n0J4PTTTycYDLJhwwZSU1PrfMyfn2PVrl270M/jSCZPnszNN9/Mu+++y/nnn8+VV15Z4+csYpbt8wogOpUU9wp6jrmH1QWrmfT1JArdhaREpTD1vKn0TOxpdsxWLaJnDywuF8HiYrzbt+PKzDQ7kojUk2mFk9frZenSpdx333012rOysliwYEGd24wcOZIHHniAGTNmMGbMGPLz8/nkk0+4+OK6r4wOhN6oVys5OKuNz+fD5/PVWNfn82EYBsFgkGAwGGq3OWq/SWwoVsOK3WnD7rTWejNqGMZxfzpVve7huavFxsZy4MCBWsuKioqIi4ur1V59//B+ePXVV6msrATA4XDUWPbz/jr8cZ555hmef/55nnvuOfr37090dDR33303Ho+HYDCIxWJh5syZLFiwgOzsbP72t7/xwAMPsHDhwlAx9Pe//71GYQFVkzf8PENd+av7r66+iY6O5pJLLuGSSy7h0Ucf5cILL+TPf/4z5513Xq3XVtfzVJ+ndPg61X1zuLraAoEAwWCwxmMc/vOvzn2013j4/cPXP1FH+jmmpKTg9XopLCyscdQpPz+fESNG1Ojf3bt3c/755zN8+HBeeeWVGo/zzTffsGrVKj755JMaWZOTk/njH/9Y4xyjurL9/HVaLJZQe/X3P38t1T/vuv5d2O32I/48jvS8f/rTn7j66quZMWMGX375JQ899BAffPABv/xlzZnLGtrR9t+TUd03Pp/vuIaqtlTVfwN+/reguVj58X8pjO4LRpDuY3uSvS2bP37/R9wBNz0SevDC2S+QEpVi2utr7v3bYCwWXH364F6+nLJly7B26NAgD6v+DS/1b3g1pf49kQymFU4FBQUEAoFanwofbRjQyJEjef/99xk3bhxutxu/38/YsWNDQ3fq8sQTT/DII4/Uap81a1aNoxRQ9YYqLS2NsrKyI06nHC6lpaUntb3P58Pv94cKw8NlZmYye/bsWssWLFhAt27darVXn1xfXl4eWhYbG0tsbGxonZKSEioqKgD49ttvQ28gDxw4wMaNG+nUqRMlJSV8++23jBkzhrFjxwJVb9g2btxIjx49ajxv//796d+/P3feeSennHIKH330Ebfddhvp6emsX7+eSy+9tNbrKikpITMzMzQ0KzIyEqi6vlR1/up+PZ7+7dKlCz/++CMlJSW1+iAzM5Ps7OwamasL/NLSUqxWK263G8Mwaqzj8XgIBAI12g7/WXXq1Am/388333wTKg6LiorYuHEjGRkZlJSU1Hrc7t27891339WY9GDBggW1nud41fXzrn4eh8PB559/Hvr55uXlsXr1av70pz+F1t2zZw9jx45lwIABTJkypcbkDFA1uUd10Q2wfPlyJk2axIwZM8jMzDxq5rpeZ//+/UM/k7fffpvc3NzQUafs7GysVivt2rWjpKSk1r8Lv9+P1+ut8Zx+vx+fzxdqczgclJWV1cqVlpbGTTfdxE033cT48eN57bXXOO+8846vk0/Syf5++Dmv10tlZSXz5s3D7/c36GM3R9nZ2WZHqJfKGVsgZhDJ5Sv5ILiXL+d9iYFBd3t3xhnjWDKnaUxg0lz7tyElx0STCGz8zxfkN/Bsrerf8FL/hldT6N/q97PHw/TJIeo6ylLXMCCoOsH8jjvu4E9/+hMXXHABubm53HPPPUyYMIHXX3+9zm3uv/9+Jk+eHLpfUlJCx44dycrKIi4ursa6brebnTt3EhMTQ0RE48w6ZBgGpaWlxMbGHvF1Hw+Hw0FFRUWt83QSExO56667eO211/jjH//ILbfcQmRkJLNnz+a9997j7bffrtUP1cPKoqOjay07XHXh+eyzz9KhQwdSU1N58MEHSU5O5pprrsHpdNKrVy+mT5/O6tWradOmDc8//zz5+fn06dOHuLg4Fi1axDfffMPo0aNJSUlh0aJFFBQUMHDgQOLi4njooYe46667aNu2LRdeeCEej4clS5Zw4MAB7r77bm666SYee+wxJk+ezAMPPMD27dtDs+5FR0cTGxtbq39XrFjBww8/zLXXXkufPn1wOp3MnTuX999/n3vvvZe4uLhafXD77bczdepUHn/8cW666SZWrFjBRx99BEBcXBxxcXFERERgsVhq9JnL5cJms9Voczgc2O124uLiGDRoEGPHjmXy5Mm8/PLLxMbGcv/999O+fXuuvvpqHA5Hrce9++67+e1vf8uIESM444wz+OCDD1i/fj1dunQ56s/r54qKisjJyWHPnj0A7Nq1i+jo6NBMinFxcdx000386U9/okOHDiQmJnLvvffSv39/xo4di81mY/fu3Vx66aVkZGQwZcqUGkd309LSAGqdC1Q9A+DQoUOPOVX4559/XuN1Ll26lDfeeIO4uDjGjx/PU089xR133MFDDz3Evn37uP/++7n22mvp1q1brb6Gqg9HnE5njX6y2+04HI5QW+fOnVm4cCHnn38+LpeLiIgI7r33Xn71q1+RmZnJrl27+Omnn7j88stPqL/ro6F+P/yc2+0mMjKSs846q9F+1zVFPp+P7OxsRo8e3ewm+1g/cx7zoqv+beUO3c2MylkAXNHtCu4dei92q+l/3pt1/za0MpudvO/mk1pczNCLLmqQx1T/hpf6N7yaUv+e0IfOhkk8Ho9hs9mM6dOn12i/4447jLPOOqvOba699lrjiiuuqNH23XffGYCxZ8+e43re4uJiAzCKi4trLausrDTWrl1rVFZWHuerOHmBQMDYv3+/EQgETupxbrjhBgOodbvhhhsMwzCMJUuWGBdccIGRkpJixMXFGUOHDjU+/PDDOh9r27ZtBmAsX778qM/57bffGoDxn//8x+jbt6/hdDqNU0891VixYkVoncLCQuOyyy4zYmJijJSUFOPBBx80rr/+euOyyy4zDMMw1q5da1xwwQVG27ZtDZfLZfTo0cP429/+VuN53n//fWPgwIGG0+k02rRpY5x11lk19puFCxcaAwYMMJxOpzFw4EDj008/DeWvq3/37dtn3HHHHUa/fv2MmJgYIzY21ujfv7/xzDPPhNarqw/+/e9/G926dTNcLpdx9tlnGy+//LIBhPaXN99804iPj6+R/aGHHjIGDBhQ62dV/foNwzCKioqM6667zoiPjzciIyONCy64wNi4cWNoeV2P+9hjjxnJyclGTEyMccMNNxj33ntvjeep/tls27atrh9d6HHr2mceeuih0DqVlZXGpEmTjMTERCMyMtK45JJLjJycnNDy119/vc7HONqvlups+/fvP+I6hmEYgPHSSy8Zo0ePNlwul5GRkVFrn125cqVxzjnnGBEREUZiYqJxyy23GKWlpaHlP+/rUaNGGXfeeWeNx7jssstC/04MwzA+//xzo1u3bobdbjcyMjIMj8djXH311UbHjh0Np9NppKenG5MmTWqU3xMN9fvh58z4XdcUeb1e41//+pfh9XrNjnLCPr7+aePFW7823r7uBaPfW/2Mfm/1M95Y9YYRDAbNjhbSnPu3oXn37DHW9uxlrO3T1whUVDTMY6p/w0r9G15NqX+PVhv8nMUwzJviZdiwYQwZMqTGdXn69OnDZZddVufkEL/61a+w2+1MmzYt1LZw4UJGjhzJ7t27SU9PP+ZzlpSUEB8fT3FxcZ1HnLZt20ZmZmajfQobDAYpKSkhLq725BBy8sLZv4899hivvPIKO3fubNDHbQhvvfUWjz322BGnNG8o4exfi8XCZ599VmOoXmsTrv4143ddU+Tz+ZgxYwYXXXSR6Z94noitC5bx1VsFGFY7K1L+yg9dtzJx4ER+P+D3Zkerobn2bzgYhsHmUWfjz88n4713iRo69KQfU/0bXurf8GpK/Xu02uDnTH2nPnnyZF577TXeeOMN1q1bx913301OTk5oxrD777+f668/dAX0Sy+9lOnTp/Pyyy+zdetWvv/+e+644w5OO+204yqaRE7G1KlTWbx4MVu3buXdd9/lL3/5CzfccIPZser01Vdf8fjjj5v+y0hEGt6Kf2RjWO04KzfyQ9etZGVkMeGUCcfeUExjsVgOm5Zc13MSaa5MHQQ9btw4CgsLefTRR8nNzaVfv37MmDGDjIwMoOoaP4df0+nGG2+ktLSUF198kT/84Q8kJCRw7rnn8tRTT5n1EqQV2bRpE3/+858pKiqiU6dO/OEPf+D+++83O1adqs+/EpGWZdfK9ey1V02pv7xdNr0Te/PnM/7coOfASXhEDhxAaXY2lStUOIk0V6afPTpx4kQmTpxY57K33nqrVtvtt9/O7bffHuZUIrU9//zzPP/882bHaDVMHEUs0mQtfuEzgvZhOCt3sGbUPqad+08i7ZFmx5LjEDritGLFUSfCEpGmSyfViIiINAP523ayl/4AbGg7m7+e9wJp0Wkmp5LjFdG3L9hs+Pftw3+Ey66ISNOmwqkO+qRbRFoy/Y5rnmY+9ToBexROdy4jb7qMgSkDzY4kJ8AaGUlEz56AznMSaa5UOB2m+kT6E7kQlohIc1P9O06ThzQfSzcsosI3CAB/4hIu73OVyYmkPiIGVJ2fpvOcRJon089xakpsNhsJCQnk5+cDVRd4DfcY5GAwiNfrxe12azryMFD/hpf6N7waun8Nw6CiooL8/HwSEhKw2WwNkFLCraCygOy/vkes45c4PQX8+okHzI4k9RQ5YAAHPvyIypUrzY4iIvWgwuln0tKqxotXF0/hZhgGlZWVREZG6kTRMFD/hpf6N7zC1b8JCQmh33XStHkDXiZ/dSdnuH+JzwnpMWuJbqOjTc1V9QQR7jVrMLxeLE6nyYlE5ESocPoZi8VCu3btSElJwefzhf35fD4f8+bN46yzztKwmTBQ/4aX+je8wtG/DodDR5qaCcMweHTho3T6NgKfMxGn9wBnPvQ7s2PJSXB27ow1Pp5gcTHuDRuJ7N/P7EgicgJUOB2BzWZrlDcXNpsNv99PRESE3niGgfo3vNS/4aX+bd3eXfsu/9n4b24r/SM+F7R3riau3eVmx5KTUHUh3FMon/cdlT/9pMJJpJnRSQkiIiJNzPe7v+fZpc+StXoAPlcqDl8Zw+/9tdmxpAGEruekmfVEmh0VTiIiIk3ItuJt3DP3HoKBAL0KswBItywnsUs3k5NJQ4gcMBBQ4STSHKlwEhERaSKKPcXc/s3tlPpK+dXmkbgjO2Dzuxl6+1izo0kDiTyl6iLGvpwc/EVFJqcRkROhwklERKQJ8Af93DP3HnaU7CAtIpUuO4cB0C6wlLQBg0xOJw3FFheHs2tXQEedRJobFU4iIiJNwLNLnmVh7kIi7ZHctvtySqMysQZ9DBo/yuxo0sB0npNI86TCSURExGSLchfx3rr3AHjsjMcoX17157mdeymdzjjLzGgSBpGnnAKAWxfCFWlWVDiJiIiYKGgEeXbJswCM6zmOuDkVHIjugcUI0GfcKSank3CIHFh9xGklRiBgchoROV4qnEREREz05bYvWVe0jmhHNBMHTmTr7J0ApFYsp8fFl5icTsLB1a0blqgoguXleLduNTuOiBwnFU4iIiIm8Qa8vLDsBQDG9xvPjpkrKIruA0aQXhe1NzmdhIvFbieyX9XFb3Wek0jzocJJRETEJB+u/5A95XtIiUzh2j7XsvHTqnNe2laspO/VuuBtS6YJIkSaHxVOIiIiJij2FPPqylcBmDRoEtvmraYgsuooRI8zY8BiMTOehFnoPKcVKpxEmgsVTiIiIiZ4ffXrlHhL6JbQjbFdx7L6nXlgsZJUvoaBN99sdjwJs+qZ9TybNxMoKzM5jYgcDxVOIiIijSy3LJf3174PwN1D7mbnyk0UOKuONnUZGACr/jy3dPa2bXG0bw+GgXvVKrPjiMhx0G9mERGRRvbiihfxBr2cmnYqZ7Y/kxV//w+G1UF8xVZOu2uS2fGkkeg8J5HmRYWTiIhII1pftJ7/bPkPAJOHTCbgC1BYmQFAWvIesNnNjCeNKHJA1XC9yp90IVyR5kCFk4iISCN6funzGBiM6TyGfsn9mD91Gu6IZOz+Ck69UzPptSaHH3EyDMPkNCJyLCqcREREGsmC3QtYsGcBdqud2wffDkDesgIAUr0ric/oZmY8aWSuPn2wOBwEiorw7dpldhwROQYVTiIiIo0gaAR5bulzAFzd82o6xnZk55otFEX0BiBzVJqZ8cQEVqcTV5+qn7+mJRdp+lQ4iYiINIL/bv0vG/ZvINYRy62n3ArAsqnTMax24iq2M+C3N5icUMygCSJEmg8VTiIiImHmCXj42/K/AXBT/5tIiEggEAhQWN4BgNSEHLDazIwoJlHhJNJ8qHASEREJsw/XfUhueS6pUalc2/taABa8+gmVEanYAm6GTrrS5IRilsgBAwFwr1tH0O02N4yIHJUKJxERkTAq9hTz6qpXAZg0aBIR9ggA9izcA0CKZyWJPfqalk/M5Wifji05Gfx+3GvXmR1HRI5ChZOIiEgY/WPlPyj1ltK9TXcu7XIpAHs376LIVTUpQKdhCSamE7NZLBYN1xNpJlQ4iYiIhMnust18sP4DoOpit7aD5zEtemEaQZuTmMqdDPrdb82MKE1AqHBaqcJJpClT4SQiIhImf1v+N3xBH8PaDeP09NMBCAQCFBWnApAWsw2bw2VmRGkCIk85BdARJ5GmToWTiIhIGKwtXMt/t/4XqDraZLFYAFj0zueUR6ZjDXgZNGGsmRGliYjo1w+sVvx7cvHtzTc7jogcgQonERGRBmYYRuhitxd3uZg+SX1Cy3bN2QZAinslKf0Hm5JPmhZbTDSu7t0BDdcTacpUOImIiDSwBXsWsCh3EQ6rg9sH3R5q35eTR6GzalKIDoMjzYonTVD1eU5uDdcTabJUOImIiDSgQDAQOtp0Ta9raB/TPrRs0ZQPCdpcRFfmMvS2m82KKE1QaIKIFSqcRJoqFU4iIiIN6IutX7Bx/0ZinbH87pTf1VhWWNAGgLTITdicOuIkh0QOPFg4rV6N4febnEZE6qLCSUREpIG4/W7+tvxvANzS/xbiXfGhZT9+8F/KojphCfoYMP5CsyJKE+XMzMQaG4vhduPZuNHsOCJSBxVOIiIiDeSfG/7J3oq9tItux697/7rGsh2z1gGQUrmKdqcONyOeNGEWq5WIvn0BcK/fYHIaEamLCicREZEG8sXWLwAY3288Ltuh6zPt31tIob1qUoj2fW2mZJOmz9WtGwCeLZtNTiIidVHhJCIi0gB2le5iXdE6rBYrozuPrrFswbPvEbBHEunO59Q7bjEpoTR1rm5dAfBu3mJyEhGpiwonERGRBjB7x2wATk09lcSIxBrLivJiAEhzrsceFdPo2aR5cHbpAoBniwonkaZIhZOIiEgDyM7JBuD8jPNrtC+b/jUlUZlYggH6X3+2CcmkuagequfbvZtgRYXJaUTk51Q4iYiInKS88jxW7luJBQvndTqvxrKt/1kGQHLlajqecbYJ6aS5sCcmYmvTBgwDz7ZtZscRkZ9R4SQiInKSvs75GoBBKYNoG9U21F5SVEKhtRcA6T10bR45NlfXg+c5abieSJOjwklEROQkZe+oe5je98+8g98RTYSnkNPu0qQQcmzOgxNEeDRBhEiTo8JJRETkJBRUFrBsb9VwvPM71SycCndWTUmeZluDMzahsaNJM+TqWj0luQonkaZGhZOIiMhJ+CbnGwwM+if3p11Mu1D7qq++ozi6KxhBel89wsSE0pwcmpJc13ISaWpUOImIiJyEIw3T2/jPhQAkV6yly/kXNHouaZ6c1ec47dxJ0OMxOY2IHE6Fk4iISD0dcB9gcd5iAEZ3OnTR24qSCgotPQFol6lppeX42du2xRoXB8Eg3u3bzY4jIodR4SQiIlJP3+78loARoFdiLzrGdQy1f/fc2/gcsbi8Bxh2980mJpTmxmKxaGY9kSZKhZOIiEg9hYbp/WxSiIItFgBSWYWrTXKj55LmzaWZ9USaJBVOIiIi9VDiLWFhbtV5TKMzDg3TW//tYg5E9wAjSK/LB5kVT5qx6vOcNLOeSNOiwklERKQe5u6ciz/op2t8V7okdAm1r33/WwCSKjbQ/eJLzYonzdihKck1s55IU6LCSUREpB5m75gN1JxNz1PupjBY9aY3tcMBsFjMiCbNXGhK8u07MHw+k9OISDUVTiIiIieowlfB93u+B2oO05s35V28zgSc3hKG3X2TWfGkmbOnpWGNigK/H29OjtlxROQgFU4iIiInaN7ueXgCHjrFdqJHmx6h9oL1bgBSjVVEpbQ70uYiR2WxWHB2OzhcTxNEiDQZKpxEREROUPb2Qxe9tRwcjrd32272R1YVUZ3PyTAtm7QMrtAEETrPSaSpUOEkIiJyAtx+N9/t/g6ArIysUPvSqf/EsDqIqdzNKdf+xqx40kKEznPSESeRJkOFk4iIyAn4fs/3VPorSY9Op09Sn1D7/rxIAJJdW8FqMyuetBCaklyk6VHhJCIicgKqL3p7XsZ5oWF625eu4UBU1Tkp3S8bYlo2aTmqh+p5t23D8PtNTiMioMJJRETkuHkDXubunAvUHKa36q0ZYLESX76FHhddbFY8aUEc6elYIiIwvF58u3aZHUdEUOEkIiJy3H7I/YEyXxkpkSmc0vaUUPv+4mQAkuNyde0maRAWmw1nl0xAw/VEmgoVTiIiIsepepjeuZ3OxWqp+hO6ZuZ8SqMysBgB+l57/tE2Fzkhrq6aklykKVHhJCIichx8QR/f7vwWgKzOh4bpbfp0PgBtKjbSccRIU7JJy6QpyUWaFhVOIiIix2FJ3hKKPcUkRiQyOGUwAIFAgP3eTgAkpxwwMZ20RJqSXKRpUeEkIiJyHKqH6Z3T8RxsB6cbX/7PGVREpGENeBl06+VmxpMWKDQl+datGMGgyWlERIWTiIjIMQSCAb7O+RqoOZteTvZaAJLc60ju0duUbNJyOTt2xOJwYLjd+PbsMTuOSKunwklEROQYlucvp8hdRJwzjlPbnQqA3+OjyKg6eb9tZ11nRxqexW7HmXlwZr3NOs9JxGwqnERERI6hepje2R3PxmF1ALDwH9PwuNpg91cw5LbfmBlPWrDQeU6aklzEdCqcREREjiJoBJmdMxuoOUxv7+JcAJK9a4lLSzclm7R8ofOcNEGEiOlUOImIiBzFyn0rya/IJ9oRzYj0EQBUFJdRaO8JQGrfKDPjSQsXupbTVhVOImZT4SQiInIUs3dUHW06q8NZOG1OAH6Y+h5+RwxObzGnTbrRxHTS0h0+JblhGCanEWndTC+cpk6dSmZmJhEREQwZMoTvvvvuqOt7PB4eeOABMjIycLlcdO3alTfeeKOR0oqISGtiGEadw/T2rasEIDm4Dmd0jCnZpHVwduoEdjvB8nL8e/eaHUekVbOb+eTTpk3jrrvuYurUqZx++un8/e9/Z8yYMaxdu5ZOnTrVuc1VV13F3r17ef311+nWrRv5+fn4/ZrNSEREGt7aorXsLttNpD2S09ufDsD+3HyKXL0A6DBC5zZJeFmcTpwZGXi3bMGzeQuOtDSzI4m0WqYWTs899xzjx4/n5ptvBmDKlCnMnDmTl19+mSeeeKLW+l999RVz585l69atJCYmAtC5c+fGjCwiIq1I9TC9M9qfQaQ9EoDFL35A0HYKke58Bo/XbHoSfq6uXfFu2YJ3y2Y443Sz44i0WqYVTl6vl6VLl3LffffVaM/KymLBggV1bvP5558zdOhQnn76ad59912io6MZO3Ys/+///T8iIyPr3Mbj8eDxeEL3S0pKAPD5fPh8vgZ6NfVXnaEpZGmJ1L/hpf4NL/VveB2rfw3DYNb2WQCc2/7c0HqFOTaIhiTbZoIGBPXzqZP234ZjP3gtp8qNm2r1q/o3PNS/4dWU+vdEMphWOBUUFBAIBEhNTa3RnpqaSl5eXp3bbN26lfnz5xMREcFnn31GQUEBEydOpKio6IjnOT3xxBM88sgjtdpnzZpFVFTTmQkpOzvb7Agtmvo3vNS/4aX+Da8j9W9eII+c0hzs2KlYU8GMtTPw7t3P/siqYXr+Lg5mzJjRmFGbJe2/Jy+2pIR2wN6lS1jys31O/Rte6t/wagr9W1FRcdzrmjpUD8BisdS4bxhGrbZqwWAQi8XC+++/T3x8PFA13O+KK67gpZdeqvOo0/3338/kyZND90tKSujYsSNZWVnExcU14CupH5/PR3Z2NqNHj8bhcJgdp8VR/4aX+je81L/hdaz+fWXlK7AaTm9/Or8c9UsAsu95jnxrJ2IqdzL2nrvhCH+vRPtvQ/J07cbODz8kumg/Y8aMwWKxqH/DTP0bXk2pf6tHox0P0wqn5ORkbDZbraNL+fn5tY5CVWvXrh3t27cPFU0AvXv3xjAMdu3aRffu3Wtt43K5cLlctdodDofpP6jDNbU8LY36N7zUv+Gl/g2vI/XvN7u+ASArMyu0vKiwTdUwvcidOJzORs3ZXGn/PXm27t3AaiVYUoK1uBh727ahZerf8FL/hldT6N8TeX7TpiN3Op0MGTKk1iG67OxsRo4cWec2p59+Onv27KGsrCzUtnHjRqxWKx06dAhrXhERaT22FW9j84HN2C12RnUYBcCW73+kOKoLAL3GnWVmPGllrC4Xjo5V73M8W3QhXBGzmHodp8mTJ/Paa6/xxhtvsG7dOu6++25ycnKYMGECUDXM7vrrrw+t/+tf/5qkpCR++9vfsnbtWubNm8c999zDTTfddMTJIURERE5U9Wx6w9KHEe+qGuWw9v2vwWIlvnwz3c5R4SSNy9W1GwCezSqcRMxi6jlO48aNo7CwkEcffZTc3Fz69evHjBkzyMjIACA3N5ecnJzQ+jExMWRnZ3P77bczdOhQkpKSuOqqq/jzn/9s1ksQEZEWKHtH1WiI0Z1Gh9r2l7WDKEhKLDArlrRirq5dKfvmGzxbNpsdRaTVMn1yiIkTJzJx4sQ6l7311lu12nr16tUkZuAQEZGWqdRbyrqidQCM6lg1TG/Vv76iNKoTlmCAATddamY8aaVc3boC4NURJxHTmDpUT0REpKlZX7QegPTodJIjkwHY+sUyANpUbiB9QH/Tsknr5aweqqdznERMo8JJRETkMGsK1gDQJ6kPAAG/n0J/1QVIk9IrTcslrZurS9U+GCgqwl9UZHIakdZJhZOIiMhh1hRWFU59k/sCsOydj6mMSMUa8DJ04tVmRpNWzBoVhaN9ewC8OuokYgoVTiIiIoepLpyqjzjt+m47AEnudSRmdDQrlgjOg+c5abieiDlUOImIiBxU7ClmZ+lOAPom9cVb6abA0hOAtt1tZkYT0ZTkIiZT4SQiInJQ9Wx67WPaE++K58epb+N1JmD3lTPsjhtMTietnatr9REnTUkuYgYVTiIiIgdVTwzRN6nq/Ka9PxUDkORfR1RCvGm5REBTkouYTYWTiIjIQWsL1wJVE0OUFxVS4Kw6zyltUJKZsUQAcB484uTft49ASYnJaURaHxVOIiIiBx0+McSPL7yL3x6Fy3uA0yZca3IyEbDFxGBPSwPAu3WbyWlEWh8VTiIiIsAB9wF2l+0GoHdib/ZtMQBINDbijHCZGU0kpPo8J99WDdcTaWwqnERERIC1RVXD9DrFdsK/5wCFEb2r7o/qamYskRpC5zlt2WpyEpHWR4WTiIgIh85v6pPUh2Uvf0TQ5iTKvZdB1/7S5GQih1Sf56SL4Io0PhVOIiIi1JxRryA3GoA2ju3Y7HYzY4nU4OpWdS0n71YdcRJpbCqcREREODQxRIfCaPZHVV30tuvYoWZGEqnF1aULAP7cXCwej8lpRFoXFU4iItLqFbmLyC3PBcDz2UYMi42Yyp30v3S0yclEarIlJGBLTgbAmZ9vchqR1kWFk4iItHrV5zd1jutMcWEiAG0i95gZSeSIqmfWc6lwEmlUKpxERKTVqz6/6RR3JvujugPQ/RfDzYwkckTVhZNzrwonkcakwklERFq96iNO3RZGgcVKbEUOvS88x+RUInVzHpyS3Jm/1+QkIq2LCicREWn1qieGsB/IAKBNdK6ZcUSOytW1amY9HXESaVwqnEREpFUrqCxgb8VeUg/EUhJZNUyvx69ONzmVyJFVXwTXsX8/wcpKk9OItB4qnEREpFVbV7QOgNGbBh8cpreDnuefZXIqkSOzJSZiTUjAYhj4tm83O45Iq6HCSUREWrXqwqltSX8A2sRomJ40bRaLBefB6zl5t+hCuCKNRYWTiIi0amuL1pK2P5bKyKrhT72uGGVyIpFjcx6cWc+7dYvJSURaDxVOIiLSqq0tWssZGweAxUpcxTa6n6vzm6Tpc3bVESeRxmY/0Q0Mw2Du3Ll89913bN++nYqKCtq2bcugQYM4//zz6dixYzhyioiINLiSYAkFlQWklw/CGwltYjW9szQPzi464iTS2I77iFNlZSWPP/44HTt2ZMyYMfz3v//lwIED2Gw2Nm/ezEMPPURmZiYXXXQRP/zwQzgzi4iINIg9gT2kF8Xhjaj69L7XOF27SZqH6iNOvpydBL1ek9OItA7HfcSpR48eDBs2jFdeeYULLrgAh8NRa50dO3bwwQcfMG7cOB588EFuueWWBg0rIiLSkHb7d3PGpuphelvpdtbNZkcSOS62tm0JRERgc7vxbttORM8eZkcSafGOu3D68ssv6dev31HXycjI4P777+cPf/gDO3bsOOlwIiIi4bQnsId+5Rfgi4Q2sfvMjiNy3CwWC96UFCJzcvBu3aLCSaQRHPdQvWMVTYdzOp107969XoFEREQag2EYBPcewBfZFYwgfa453+xIIifEm5oCgGezznMSaQz1mlXv//7v/wgEArXai4uLueaaa046lIiISLjlV+YzeFMvAOIrttLljFNNTiRyYjwpqVVft6hwEmkM9Sqc3nnnHU4//XS2HPYPdc6cOfTv35/tuoK1iIg0A2sL15JaMRCANgmF5oYRqYfqI07eLZtNTiLSOtSrcFq5ciWdO3dm4MCB/OMf/+Cee+4hKyuLG2+8kfnz5zd0RhERkQa3Zv48vJFdwAjS99oss+OInDBv9RGn7TswfD6T04i0fCd8HSeA+Ph4PvroIx544AFuvfVW7HY7X375Jeedd15D5xMREQkL20I3ANGVW+g87FaT04icOH9CPJbISIzKSrw7d+Lq0sXsSCItWr2OOAH87W9/4/nnn+eaa66hS5cu3HHHHfz0008NmU1ERCQsDMMgsqIPAFHxe0xOI1JPFgvOg8WSZ7OG64mEW70KpzFjxvDII4/wzjvv8P7777N8+XLOOusshg8fztNPP93QGUVERBrUov/+G29kZzCCDLxmjNlxROqt+kK4Xk0QIRJ29Sqc/H4/K1eu5IorrgAgMjKSl19+mU8++YTnn3++QQOKiIg0tC1fLAPAVbmJzFOHmJxGpP6cXboCmpJcpDHU6xyn7OzsOtsvvvhiVq1adVKBREREws1T2QUioTx6vdlRRE5K9REnTUkuEn71PsfpSJKTk4Gq8eMiIiJNzboZX1MZ2QmMIPv72cyOI3JSnF2rjjh5t27FqOMamyLScI67cOrduzcffPABXq/3qOtt2rSJ3//+9zz11FMnHU5ERKShbfr3IgAc7o2kpHUzOY3IybGnp2NxuTC8Xny7dpkdR6RFO+6hei+99BL/+7//y2233UZWVhZDhw4lPT2diIgI9u/fz9q1a5k/fz5r165l0qRJTJw4MZy5RURE6qXI3R4iYXfcck6xXWh2HJGTYrHZcHbpgmfdOjxbtuDMyDA7kkiLddyF07nnnsvixYtZsGAB06ZN44MPPmD79u1UVlaSnJzMoEGDuP7667n22mtJSEgIY2QREZH6Wf35TMojO4IRYMfgYgZb6nWqr0iT4uratapw2ryF2HPPNTuOSIt1wn8xRo4cyebNm7nrrrvIzMwMRyYREZGw2PrFUrAOx+HeQOcefaDA7EQiJ8/VrXpmvU0mJxFp2er1Udtvf/tbXnzxRbxeLytXrsRms9GnTx9uuukm4uLiGjqjiIhIgyjydIRIyIlfTv/ELBVO0iK4uncHwLNJF8EVCad6zapnGAaTJk3imWee4cCBA+Tn5/PMM8/QtWtXli9f3tAZRURETtqqz76kPLI9lmCAeT1W0Sexj9mRRBqEq2dPALybN2P4fCanEWm56j0d+c0338z27dv59NNP+de//sX27du5+OKLufPOOxsyn4iISIPYOqPqgz2bZz3l8QG6xnc1OZFIw3Ckp2ONjsbw+fBu3252HJEWq96F0+TJk7HZDl3/wm63c++997JkyZIGCSYiItKQ9ns7AZATv4webXrgsDlMTiTSMCxWa2i4nnvDRpPTiLRc9SqcEhIS2FXHtQJ27typc5xERKTJWfHJF5RHpmMJ+pnbczV9k/uaHUmkQVUP1/Ns2GByEpGWq16FU1ZWFuPHj+eTTz5h9+7d5OTk8OGHH3LzzTfzm9/8pqEzioiInJQdM1cB4PKsozjGTd8kFU7Ssrh69gDAs1FHnETCpV6z6k2dOpU777yTcePGhdpcLheTJk3isccea7BwIiIiJysQCFDkywAbbE/4CYA+SZoYQlqWiINHnNwqnETCpl6FU2JiIu+++y5Tp05ly5YtOBwOunbtSkREREPnExEROSkrP/kvFRFpWII+vum5EpfNRdeErhgBw+xoIg3G1aPqiJM/N5dAcTG2+HiTE4m0PPWeHAIgNjaWgQMH0rdvXxVNIiLSJO3IXgNArHs9JdEeeib2xG6t1+eGIk2WLTYWR3o6oOF6IuFyUoWTiIhIUxYIBNjv7wxAadsdADq/SVqs6gkiNLOeSHiocBIRkRZrxUefUxGRijXoY/mpBYDOb5KWKzRBhGbWEwkLFU4iItJi5XyzHoDEyvWsDFS9mdQRJ2mpIg6e5+TeqMJJJBxUOImISIsUCATYH+gCQET7Eir8FUTaI8mMzzQ5mUh4hK7ltGkzRjBochqRlkeFk4iItEjL3/8XlRFtsQa8+MZ2BqBXYi9NDCEtljMjA4vTiVFRgW/XLrPjiLQ4KpxERKRFypmzCYBE93q22PcAOr9JWjaL3Y6rWzcA3DrPSaTBqXASEZEWx+/xUUR3ANpmBllTWDUluc5vkpYuNFxPM+uJNDgVTiIi0uL88Pf38DjbYPNXMuS2a1hfVDVJhAonaek0s55I+KhwEhGRFidv6T4Akr1r2ecsp9JfSaQ9koy4DJOTiYRXRPW1nDSznkiDU+EkIiItSsWBEgrtvQBI7R8TGqbXO7E3NqvNzGgiYec6OCW5L2cnwYoKk9OItCwqnEREpEVZ9OI7+B0xOL3FDJt0I2sL1wLQN1nD9KTlsyclYUtOBsPAs3mz2XFEWhQVTiIi0qLs2+ADICm4AWdkZOiIk2bUk9YidCFcneck0qBUOImISIuxf/ceCiOqhum1H9kef9DPhqKqN4+aGEJaC82sJxIeKpxERKTFWPzihwRtLiLd+xh60zVsLd6KO+Am2hGtiSGk1dDMeiLhocJJRERajMJdLgCS7Jux2e2sKTg0TM9q0Z88aR0Ozay3EcMwTE4j0nLor4iIiLQIuavXsj+y6g1jlzEDAA6d35So85uk9XB27Qo2G8HiYvx795odR6TFUOEkIiItworX/o1htRFTuYv+v7oEQDPqSatkdTpxdckENFxPpCGpcBIRkRahqDARgMSoXQD4gj5NDCGtlqt79cx6miBCpKGocBIRkWZv85zvORDVFYBeV48CYMuBLXiDXmIdsXSM7WhmPJFGF5pZb6MKJ5GGosJJRESavfXT5oDFSnz5ZrqPOh2ARbmLgKphehaLxcR0Io1PM+uJNDwVTiIi0uwVlbcHoE1iUaht9o7ZAJzT8RxTMomYqXpmPc+2bQS9XpPTiLQMKpxERKRZW/3pfyiN6oQlGGDQzZcBsLd8Lyv2rQDgvE7nmZhOxBz2tDSscXHg9+PdutXsOCItgumF09SpU8nMzCQiIoIhQ4bw3XffHdd233//PXa7nYEDB4Y3oIiINGlbv1wJQJvKjaT37w3A1zlfAzCw7UBSo1NNyyZiFovFQkQPDdcTaUimFk7Tpk3jrrvu4oEHHmD58uWceeaZjBkzhpycnKNuV1xczPXXX8955+lTRBGR1izg91Hgr5oUIrG9O9Q+O6dqmN75GeebkkukKaieIEIz64k0DFMLp+eee47x48dz880307t3b6ZMmULHjh15+eWXj7rdrbfeyq9//WtGjBjRSElFRKQpWvbWR1RGpGANeDn1tmsAKKwsZOnepYAKJ2ndXDriJNKg7GY9sdfrZenSpdx333012rOysliwYMERt3vzzTfZsmUL7733Hn/+85+P+TwejwePxxO6X1JSAoDP58Pn89UzfcOpztAUsrRE6t/wUv+Gl/r32HbN3wkR7Ul0ryc27Tx8Ph/Z27MJGkH6JPYhxZVyxP5T/4aX+je8jqd/7V27AODeuFE/hxOk/Te8mlL/nkgG0wqngoICAoEAqak1x56npqaSl5dX5zabNm3ivvvu47vvvsNuP77oTzzxBI888kit9lmzZhEVFXXiwcMkOzvb7Agtmvo3vNS/4aX+rVvQ56XA2gsAS1IJM2bMAGBa2TQA2le0D7Udjfo3vNS/4XW0/rV4PHQHAvv2MfOf/yQQE9N4wVoI7b/h1RT6t6Ki4rjXNa1wqvbza2sYhlHn9TYCgQC//vWveeSRR+hx8NDz8bj//vuZPHly6H5JSQkdO3YkKyuLuLi4+gdvID6fj+zsbEaPHo3D4TA7Touj/g0v9W94qX+P7ofnX2WPszd2XzkX/HkSUfGxFHuKeXj6wwDcdv5tdIrrdMTt1b/hpf4Nr+Pt3x3/eA3fzp2cmZFB1LBhjZiwedP+G15NqX+rR6MdD9MKp+TkZGw2W62jS/n5+bWOQgGUlpayZMkSli9fzqRJkwAIBoMYhoHdbmfWrFmce+65tbZzuVy4XK5a7Q6Hw/Qf1OGaWp6WRv0bXurf8FL/1i1/dRlEQZJ/PfHJlwIwf8d8/IafHm160DWp63E9jvo3vNS/4XWs/o3o1RPfzp0EtmzBccYZjZisZdD+G15NoX9P5PlNmxzC6XQyZMiQWofosrOzGTlyZK314+LiWLVqFStWrAjdJkyYQM+ePVmxYgXD9CmKiEirUV6QT4GzLwCpg9qG2qsveqtJIUSquHpoZj2RhmLqUL3Jkydz3XXXMXToUEaMGMGrr75KTk4OEyZMAKqG2e3evZt33nkHq9VKv379amyfkpJCRERErXYREWnZfvzbO/jtg3F5DzBswq8BKPOWsWBP1eRCozuNNjOeSJPh6qmZ9UQaiqmF07hx4ygsLOTRRx8lNzeXfv36MWPGDDIyMgDIzc095jWdRESk9dm31QrRkGhswhnhBGDurrn4gj4y4zPpmnB8w/REWrqIg9dy8mzejBEIYLHZTE4k0nyZPjnExIkTmThxYp3L3nrrraNu+/DDD/Pwww83fCgREWmyCrdsoTCiDwAdzzk0WVBomF6n8+ucZEikNXJ07IglMhKjshLvjhxcXTLNjiTSbJl6AVwREZETtfyVaQRtTqLcexn8m7EAVPgqmL97PgBZnbPMjCfSpFisVlzduwPg2ajheiInQ4WTiIg0KwV5VZeSaOPYge3gsKP5u+fjDrjpENOBnm16mhlPpMmJOHiek1vnOYmcFBVOIiLSbOxe8iNFUVWFUZdfnBZqz95RNUPr6IzRGqYn8jPVM+t5NLOeyElR4SQiIs3GqrdnYlhsxFTkcMrFVdfu8wQ8zNs1D6gqnESkJs2sJ9IwVDiJiEizUXig6gLpbWL3htoW7F5Ahb+CtOg0+iXr8hQiPxfRo6pw8u3eTaC01OQ0Is2XCicREWkWNn/1FQeiu4ERpN91F4baq4fpaTY9kbrZEhKwp6UB4Nm0yeQ0Is2XCicREWkWNkz/EYD4iq10GT4AAF/Ax5ydcwAN0xM5mtBwvY06z0mkvlQ4iYhI0xcMUuDpDECbtoeGGi3KW0Spr5TkyGQGpgw0J5tIM1A9XE8z64nUnwonERFp8lZ9OI2yyA5Ygn4G33p5qL16mN55nc7DatGfNJEj0cx6IidPf2VERKTJ2/b1ZgDaVG6kXc9MAPxBP9/kfANomJ7IsRw+s55hGCanEWmeVDiJiEiTFvBWUhCs+rQ8MeNQ+9K9SzngOUCCK4EhqUNMSifSPLgyM8HhIFhejm/3HrPjiDRLKpxERKRJW/rqO1RGJGMLuDnt9mtC7YcP07Nb7WbFE2kWLA4Hrq5dAfBs1HlOIvWhwklERJq0PYsLAGjj2UCb1CQAgkaQr3O+BuD8jPNNyybSnEToQrgiJ0WFk4iINFklu3eQb+8PQHK/NqH2FfkrKKgsINYRy7C0YWbFE2lWqieIcGuCCJF6UeEkIiJN1pIp7+BzxODyFHHmnb8JtVcP0zun0zk4bA6z4ok0K64eupaTyMlQ4SQiIk2TYZCX1xaAJMdWnC7HwWaD2TmzATi/k4bpiRyv6pn1vNu3E3S7TU4j0vyocBIRkSZp3fRP2B/dA4wgfW/ICrWvLlhNXnkeUfYoRrYfaWJCkebF3rYttjZtIBjEs3mL2XFEmh0VTiIi0iRt+mI9AG0qNtLj9IGh9upheqM6jMJlc5kRTaRZslgsuHpWXwhXE0SInCgVTiIi0uRU5Oey13JwUoieh6YaNwwjVDhpNj2RExeaWU9TkoucMBVOIiLS5Cx6/g28zjic3mLOuuvaUPuG/RvYVbaLCFsEZ7Q/w8SEIs2TZtYTqT8VTiIi0rQYBnt3JQCQZN1ERExUaNGs7bMAOKP9GUQ5ouraWkSO4vCheoZhmJxGpHlR4SQiIk3Kpv/+h8Koqjd3va8ZVWNZaDY9DdMTqRdXt65gtRLYv59AQYHZcUSaFRVOIiLSpKyfvhwsVhLKN9L7vEMXt91yYAvbirfhsDoY1WHUUR5BRI7EGhGBMyMD0HA9kROlwklERJoMz/4C9lI1KURSl2CNZbN2VA3TG5k+khhnTKNnE2kpNLOeSP2ocBIRkSZj0fOv4XEm4PCVcubk62ssm71Dw/REGoJm1hOpHxVOIiLSZORuq5rwIcnYQHT8oaNKO0p2sHH/RuwWO+d0PMeseCItQvURJw3VEzkxKpxERKRJ2Dr7Kwqi+gDQ7YoRNZZVX7vptHanEe+Kb/RsIi1J9ZTkni1bMHw+k9OINB8qnEREpElY99EPYLESV76FARedWWOZhumJNBxH+3Ss0dHg8+HZts3sOCLNhgonERExnbf0AHmBvgAkdXDXWLa7bDdrCtdgtVg5t+O5ZsQTaVEsFsuhCSI2bjI5jUjzocJJRERM9+OUf+B2JWH3V3DG/9Q9KcSQ1CEkRSaZEU+kxXFVTxChmfVEjpsKJxERMd2ejXYAkgLriEs6dA6TL+jj440fA3B+Jw3TE2koET2qCie3ZtYTOW4qnERExFQ758+hILIfAF0uHVxj2acbP2VHyQ4SIxK5rNtlZsQTaZEOXctJM+uJHC8VTiIiYqpV78zBsNqIrdjO4MvPC7WX+8p5+aeXAfj9gN8T7Yg2K6JIi+Pq3h0Af14egQMHzA0j0kyocBIREdP4K8rI8/YCICm1tMayt9a8RZG7iIy4DH7V41dmxBNpsWyxsTjatwfAvVFHnUSOhwonERExzeIX/kFlRAo2fyUj/+faUPu+in28veZtAO4cfCcOq8OsiCItlobriZwYFU4iImKa3WsCACT519Em9dCMeVN/mkqlv5JT2p6iSSFEwiQ0s56OOIkcFxVOIiJiitzFP5Af2R+AjKzeofatB7YyfdN0AP4w5A9YLBZT8om0dBEHjzhpZj2R46PCSURETPHT619hWB3EVOzktF9fHGp/ftnzBI0g53Y8l8Gpg4/yCCJyMlw9qo84bcIIBExOI9L0qXASEZFGF/BWkueumtUrMbkw1L4kbwlzds7BZrFx55A7TUon0jo4MzKwRkdjVFbiXr/e7DgiTZ4KJxERaXRLXnqN8oh2WAMeht95DQCGYfDc0ucA+FX3X9ElvouZEUVaPIvNRtSppwJQ8cMPJqcRafpUOImISKPbtawSgCTvOtpmtANg1o5ZrCpYRaQ9kt8P/L2Z8URajegRwwEoX6jCSeRYVDiJiEijyl+1jPyIUwDoMCoTAF/AxwvLXgDgxr43khyZbFo+kdYkavgIACqWLsXwek1OI9K0qXASEZFGtfyVzwnanERX7mHYDWMB+Hjjx+SU5pAUkcQNfW8wOaFI6+Hq0R1bUhJGZSWVP/1kdhyRJk2Fk4iINJqAz0NeWdW5S4nxe7HZbJR5y3jlp1cAmDhwItGOaDMjirQqFouF6OHVw/UWmpxGpGlT4SQiIo1m+atvUhbZAWvAy6m3XwnAG6vfYL9nP53jOvPL7r80OaFI66PznESOjwonERFpNDmLDgCQ6FlHu+6d2Fu+l3fXvgvAXUPuwmF1mJhOpHWqPs+pctUqAmXlJqcRabpUOImISKMo2riGfFfVpBDpw9MBmPrTVNwBN4NSBnFux3PNjCfSajk7tMfRsSP4/VQsWWx2HJEmS4WTiIg0iiUvfkLAFkGUey8jb72CTfs38a/N/wJg8pDJWCwWcwOKtGLV5zlVaLieyBGpcBIRkfALBth7oCMAidG7sNlsTFk2haARZHTGaAamDDQ3n0grFzrPSRfCFTkiFU4iIhJ2i194iZKozliCfgZPvJzFeYuZt2seNouNOwbdYXY8kVYv6uARJ8+GDfgLC01OI9I0qXASEZHwMgy2Lq36NtmzmvZ9Mnl2ybMAXNHjCjrHdzYvm4gAYE9MxNWrF6CjTiJHosJJRETC6qfXX6cguh8YQfr8Zjizts9iTeEaouxRTBgwwex4InJQ6DwnFU4idVLhJCIiYbVxbjEASZVr6HHeUKYsmwLAb/v9luTIZBOTicjhdD0nkaNT4SQiImGz7uNp5EcNAKD72N78c8M/2V22m+TIZK7vc73J6UTkcFFDh4Ldjm/XLry7dpkdR6TJUeEkIiJhs+7zbWCx0qZ8Ld3HDufvK/8OwG0DbyPKEWVyOhE5nDU6mshTqq61Vr5woclpRJoeFU4iIhIWW2Z9SV7kEAA6n9OeN1a9wQHPAbrEd+EX3X5hbjgRqVP0iBEAVKhwEqlFhZOIiITFqveXYVhtxJdvJuGynry79l0A7h5yN3ar3eR0IlKXQ9dzWoQRDJqcRqRpUeEkIiINbtfCBeQ6q442JQ+2csc3d+ANejmrw1mM6jDK5HQiciSRp5yCJTKSQFERnk2bzI4j0qSocBIRkQa37NWvCdqcxFbs4L3u37K3Yi+d4zrz5JlPYrFYzI4nIkdgcTqrJolA5zmJ/JwKJxERaVD5q1exxza46vsOP/FT4UpinbG8eN6LxDpjTU4nIscSup6TpiUXqUGFk4iINKjFf51OwB5JROUe3un+NTaLjWdGPUNGXIbZ0UTkOFSf51SxeDGGz2dyGpGmQ4WTiIg0mP07trI7OAiATYnZGFa459R7GJk+0uRkInK8XL16YUtIIFhRQeWqVWbHEWkyVDiJiEiD+eHJd/E5YnB49vFV/+Vc3v1yft3r12bHEpETYLFaiTo4XE/nOYkcosJJREQaRPm+XHZ7+gGwK3o2A9oN4sFhD2oyCJFmSOc5idSmwklERBrEd3/+Bx5nGxzeAywdkcNzZz+Hw+YwO5aI1EPoPKeffiJYUWFyGpGmQYWTiIicNE9JMbuKewBQ4PqWZ8f8laTIJJNTiUh9OTp1wp7eDnw+KpYuMzuOSJOgwklERE7aR48+jiciBbuvjFNuOYdeib3MjiQiJ8FisRA9fASg85xEqqlwEhGRk7J450K8BVXnNtlti7lk8OUmJxKRhhA94mDh9IMKJxFQ4SQiIidhT9kePnnhJbwR7bH5K7noD781O5KINJDo4cMA8Kxbj3//fpPTiJhPhZOIiNRLha+C22dPolv+uQC0NVbRrmcXk1OJSEOxt22Lq3s3MAwqFv1odhwR06lwEhGRExY0gjww/wHa/mjgjeyMNeDl1NsuNTuWiDSwqOEaridSTYWTiIicsJd/epnZObMZvDsLgBTfSjoN7mtyKhFpaNXTkmuCCBEVTiIicoJmbp/JKz+9wpCtGfgie2IJBjjlprPNjiUiYRB16qlgs+HbkYNvzx6z44iYyvTCaerUqWRmZhIREcGQIUP47rvvjrju9OnTGT16NG3btiUuLo4RI0Ywc+bMRkwrItK6rchfwYPzHwTg7G2jAWjrXkn3s04zM5aIhIktNpbIflWzZpYv/MHkNCLmMrVwmjZtGnfddRcPPPAAy5cv58wzz2TMmDHk5OTUuf68efMYPXo0M2bMYOnSpZxzzjlceumlLF++vJGTi4i0PjO3z2T8zPG4A24u2TeU8qj+YATpdeVAs6OJSBhFVQ/X+0GFk7RuphZOzz33HOPHj+fmm2+md+/eTJkyhY4dO/Lyyy/Xuf6UKVO49957OfXUU+nevTuPP/443bt35z//+U8jJxcRaT0Mw+CN1W/wP3P/B2/Qy9kdzmbQT/0BSK5YTf9LzzM5oYiEU/RhE0QYhmFyGhHz2M16Yq/Xy9KlS7nvvvtqtGdlZbFgwYLjeoxgMEhpaSmJiYlHXMfj8eDxeEL3S0pKAPD5fPh8vnokb1jVGZpClpZI/Rte6t/wagr96w/6eXrJ03yy+RMAru5xNZfk9md+VBQAmRd0bLY//6bQvy2Z+je8GrN/7f36YnG5COwroGLDBpxdu4b9Oc2m/Te8mlL/nkgGi2HSRwd79uyhffv2fP/994wcOTLU/vjjj/P222+zYcOGYz7GX/7yF5588knWrVtHSkpKnes8/PDDPPLII7XaP/jgA6IO/uEXEZHaPIaHaeXT2OjfiAULYyLHMNI1Eu/H68iPOY02ZWuJvrKj2TFFpBG0/8drRG/eTP7YSzlw+ulmxxFpMBUVFfz617+muLiYuLi4o65r2hGnahaLpcZ9wzBqtdXlww8/5OGHH+bf//73EYsmgPvvv5/JkyeH7peUlNCxY0eysrKO2TmNwefzkZ2dzejRo3E4HGbHaXHUv+Gl/g0vM/s3vyKfO+bcwUb/RiJsETw28jHO6XgO2+YtYHbUYAA6jYhj2EUXNWquhqT9N7zUv+HV2P27PzePwilTyCwppV0z/nd/vLT/hldT6t/q0WjHw7TCKTk5GZvNRl5eXo32/Px8UlNTj7rttGnTGD9+PB9//DHnn3/+Udd1uVy4XK5a7Q6Hw/Qf1OGaWp6WRv0bXurf8Grs/t1QtIGJX08kvyKfxIhEXjrvJfolV82qtfLtHzGihhBfvpkzbvtdo2UKJ+2/4aX+Da/G6t/Y00+ncMoUKpcswW6xYLGb/tl7o9D+G15NoX9P5PlNmxzC6XQyZMgQsrOza7RnZ2fXGLr3cx9++CE33ngjH3zwARdffHG4Y4qItCrzd8/n+i+vJ78iny7xXXj/ovdDRdOCKa+yN2oIGEG6nRljclIRaUwRfXpjjYsjWFaGe80as+OImMLUWfUmT57Ma6+9xhtvvMG6deu4++67ycnJYcKECUDVMLvrr78+tP6HH37I9ddfz7PPPsvw4cPJy8sjLy+P4uJis16CiEiL8fHGj5n09SQq/BWclnYa74x5hw6xHQCo2L+fjcujAUh1L2f4735tZlQRaWQWm43oYVXXa9P1nKS1MrVwGjduHFOmTOHRRx9l4MCBzJs3jxkzZpCRkQFAbm5ujWs6/f3vf8fv93PbbbfRrl270O3OO+806yWIiDR7QSPI80uf59GFjxIwAoztOpZXzn+FeFd8aJ1v7n+J8sh2OHylnH7fL8wLKyKmiRqu6zlJ62b6ANWJEycyceLEOpe99dZbNe7PmTMn/IFERFoRT8DDA/MfYOb2mQBMHDiRCadMqDFJz6bZ37IzMARs0ClxM+16X2ZWXBExUfSIqus5VS5bRtDtxhoRYXIikcZl6hEnERExz373fm6eeTMzt8/EbrXz+BmP8/sBv685s6lhsOztVQRtLuLLNzP6CR3hF2mtnJmZ2FNTMbxeKpctMzuOSKNT4SQi0gptL97OtTOuZcW+FcQ6Y3l19Ktc2vXSWuvNeXQKBdH9sAQD9PtFe2ytZCYtEanNYrEQXT1cT+c5SSukwklEpBUJBAO8u/ZdrvriKnJKc2gf0573xrzHqWmn1lp3/66dbNleNTlEO/9SBv5KM5mKtHZRI3Sek7Re+uhQRKSV2Lx/Mw8teIiVBSsBODXtVJ4+62mSI5PrXH/en97G7RpJhKeQsx//bWNGFZEmqvo8J/eaNQSKi7HFxx9jC5GWQ4WTiEgL5wv4eG3Va7y66lX8QT8xjhgmD53Mr7r/Cqul7oEHq6ZNZ7d9GACdM/Np0+7oFyYXkdbBkZqKMzMT77ZtlP/4I3GjR5sdSaTRaKieiEgLtmrfKq764iqm/jQVf9DPqA6j+Oyyz7iyx5VHLJoCPi8rv9iHYbWRWL6W8/50WyOnFpGmLPrgcL0KneckrYyOOImItEAVvgpeWvES7617j6ARJDEikftOu48LO19Yc9a8Onzzx2c5ED0Ma8DL4BsHNVJiEWkuokaMYP8HH+o8J2l1VDiJiLQwP+T+wMMLHmZ32W4ALulyCfeeei9tItocc9u9a9eyragPOCDdtoKe590X7rgi0sxEn3YaWK14t27Ft3cvjlQN5ZXWQYWTiEgLUeIt4dklzzJ903QA0qLT+L/h/8dZHc467sf4/snP8UWdRlRlLqNf0BA9EanNFh9PRJ8+uFevpvy770i44gqzI4k0Cp3jJCLSAnyd8zW/+NcvQkXTuJ7j+GzsZydUNC3++1vkRg4FoNtgP1HxsWHJKiLNX+z55wNQ9N77GIZhchqRxqHCSUSkGSuoLGDynMnc9e1d7KvcR+e4zrx14Vs8OPxBYpwxx/043opy1n0PWKy0rVjBmXfeEL7QItLsJYy7CktkJJ716ylfsMDsOCKNQoWTiEgzVOYt45WfXmHsZ2PJ3pGNzWLj5v4388nYTxiSOuSEH+/re5+jNKoTdn8FIyZfGIbEItKS2Nu0IeFXvwKg6PU3TE4j0jh0jpOISDNS5i3jg/Uf8PaatynxlgDQO7E3j4x8hN5Jvev1mNu/X8AO92CwQ4eYdXQceElDRhaRFirxxhvY/8EHlC9YgHvdOiJ61+93kEhzocJJRKQZKPeV88G6D3h77dsUe4oByIzP5PcDfk9WRhY2q61+D2wYLH5lIYHoQcRW7GD0lDsbMLWItGTODh2Iu/ACSmZ8SeEbb9L+L0+bHUkkrFQ4iYg0YR7Dw5tr3uTd9e9ywHMAgM5xnZkwYAIXdr6w/gXTQd8//TfyoweBEaR3VgLOCGcDpBaR1iLxpvGUzPiSkhkzSJl8N4527cyOJBI2KpxERJqgCl8F7699n9dKXqPipwqgqmC6dcCtjOk85qQLJoDygr1sXNcWIiDVu5xTr73npB9TRFqXyH59iRo2jIpFiyh6+x1S7/tfsyOJhI0KJxGRJqTCV8G0DdN4c/Wb7PfsB6BTbCcmDJjAmMwx2K0N92v72/v+TkXEGTi9xZz1p6sb7HFFpHVJGn8TFYsWceCf/yR54u+xxcWZHUkkLFQ4iYg0AZX+Sv654Z+8sfoNitxFAHSM6chpwdP434v/l0hXZIM+3/r//Jed1mEAdErfSUrmLxv08UWk9Yg+80xc3bvh2bSZ/dOmkXzLLWZHEgkLTUcuImKivPI8Xl7xMmM+HcMzS56hyF1Ex9iO/Pn0P/PpJZ8yyDmoQY8yAXhKSlj2zxyCVgcJ5Rs5/5HbGvTxRaR1sVgsJP72JgD2v/MuQa/X5EQi4aEjTiIijSwQDPD9nu/5eOPHzNs1j6ARBKB9THtuPeVWLul6CQ6rA5/PF5bn//KOF9kfPRxrwMMpV/fAZjv586VEpHWLv+Ri9k2Zgj8/n5L/fEHCry43O5JIg1PhJCLSSPIr8pm+aTrTN00ntzw31D40dShX9riS0Z1H47A6wpph5h+eZHfEcAC6pW+h/8WTwvp8ItI6WJxOEq+/jvxnnqXwzTeI/+UvsFg1sElaFhVOIiJhFDSCLNizgI83fMzcXXMJGAEA4l3xjO06lit6XEGX+C6NkuWHl99hS+kgsEL7wCJGP3J/ozyviLQOCePGUfDyK3g3b6H8u++IGTXK7EgiDUqFk4hIGBRUFvDZps/4dNOn7C7bHWofnDKYK3pcQVbnLFw2V6Pl2TRvESsXx2E4HSSXr+SS1/6n0Z5bRFoHW2wsCVddRdGbb1L4+hsqnKTFUeEkItJAgkaQH/b8wMcbP2bOzjn4DT8Asc5YLut6GVf0uIKuCV0bPVdxXgELXluPL6ojMZW7yHriCuyu8A4JFJHWKfH66yh6910qfvyRylWriezfz+xIIg1GhZOIyEkIGkFW7lvJrB2zyN6RTV55XmjZwLYDubLnlWRlZBFhjzAlXyAQ4Mt736csqj8OXykjr21Pmw4dTMkiIi2fo1074i4aQ8nn/6Hwjdfp8PzzZkcSaTAqnERETlAgGGB5/nKyd2Qze8ds8ivzQ8tiHbFc0vUSruxxJd3bdDcxZZXPb3uewqjBWIJ+Tum3m+6jJ5odSURauKSbbqLk8/9QOnMW3p07cXbsaHYkkQahwklE5Dj4g36W7l0aKpYK3YWhZTGOGM7ueDajM0YzMn2kaUeXfm7m/3uNPQwGoHvE9wy/+xGTE4lIaxDRqxfRp59O+fffU/TW26T934NmRxJpECqcRESOwBf0sThvMdk7svkm5xuK3EWhZbHOWM7teC5ZnbMY3m44TpvTxKS1Lfn0G7blpIMNOlQsYPTUh8yOJCKtSNL4myj//nsOTJ9O8qTbsLdpY3YkkZOmwklE5DCV/koW5y1m9o7ZfLPzG4o9xaFlCa4Ezut0HqMzRnNa2mk4bE1zgoWd67az4otCAq4kEsvXceFffwe6noqINKKoESNw9e6NZ906Dnz0Ecm//73ZkUROmgonEWnVgkaQjfs3smDPAhbsWcCyvcvwBX2h5YkRiaFi6dS0U7Fbm/avzYrSCr59YjaeqC5EuvM5986BuBJTzI4lIq2MxWIh6abfsueeeyl6730Sb7oJq6vxLsEgEg5N+x2AiEgY7KvYx8LchSzYs4CFexbWGIIHkBadxtkdziarcxaDUwZjs9pMSnpiAoEA/77jNUqj+mHzVzJ8VDGpQ682O5aItFJxF15I/nPP48/Npfhf/6bNuKvMjiRyUlQ4iUiL5/a7WbZ3WdVRpdwFbNq/qcbySHskp6Wdxoj0EYxMH0nnuM5YLBaT0tbfv+/9B0WufmAEGZg6nz6/fcLsSCLSilkcDhJvuJ78J5+i6M03SbjyCiwaNizNmAonEWlxfEEfG4s2sjhvMQv2LGDp3qV4g97QcgsW+iT1YWT6SEakj2Bg24FN9nyl4/XNy/8mr6wrWKCHfxbD/5+KJhExX8IVV1Lw0lS827dT9s03xJ5/vtmRROpNhZOINHul3lJ+2vcTy/OXsyJ/BasKVlHpr6yxTmpUKiPTRzIyfSTD2g2jTUTLmeFp9dyVbFpixXDYSC9bxLkv3wPNZHihiLRstpho2lx9NYX/+AeFr7+hwkmaNRVOItKsGIbBnvI9oSJpef5yNu3fhIFRY71YZyyDUgYxol3V8LvM+MxmOfzuWPbtKuDHN1bjj0wjvmIb5//fudhi25odS0QkpM1111L01ltULl9OxbLlRA0eZHYkkXpR4SQiTZo/6GfD/g2hIml5/nLyK/JrrdchpgODUwczMGUgg9oOoktCF6yWlj2W3lPh4cs/Tqcyqhsu7wHO/mWA2J7DzI4lIlKDIyWFuLGXUvzpdIrefIOowX8zO5JIvahwEpEmwxf0sfXAVtYWrq26Fa1lY9FG3AF3jfXsFju9EnsxKHUQg1IGMbDtQNpGta6jLIW5RXzxv9Mpi+qGNehjRLeFdPjlX8yOJSJSp6Tf/pbiT6dTOvtrPNu24crMNDuSyAlT4SQipvAFfGw+sJm1hWtZV7SOtYVr2bh/I56Ap9a6sY5YTkk5hcEpgxmUMoh+yf2ItEeakLpp2PbTVuY89z0VUV2wBrycFv0Jff/3ZbNjiYgckatbN2JGjaJs7lyK3nqbdo88bHYkkROmwklEws7td7OleEvoSNK6wnVs3L+xxoVmq8U4YuiV2Is+SX3ok9SH3km96RzXucUPuztey7/4nqWf5uKJbI/DV8Lpmd/S976XoJnPCigiLV/i+JsomzuX4s8+o+0dt2NPSjI7ksgJUeEkIg3GF/SRU5LDpgOb2Lx/M5sPVN12lu4kaARrrR/rjKVP4qECqU9SHzrGdlSRdARzX5rG+uXR+F2JRLn3MurcfLpc/1ezY4mIHJeoU08lon9/3KtWUfTuu6TcdZfZkUROiAonETlhQSPI7rLdbCjYwBz3HOZ/P58tJVvYVrwNf9Bf5zYJrgR6J/YOFUh9kvrQIaZDi5zpLhxm/vGvbCnojWG3k1C+hfNu7UTaGdeYHUtE5LhZLBaSxo9n9113Ufja60QPH0H0cE1oI82HCicROaJKfyU5JTnsKNnB9pLt7CjZwdYDW9lSvKXmdZJ2HPo2yh5Ftzbd6J7QnW4J3ejWphvdErqRFJGkIqkegv4AX932FDnWkWCFlPIVXPDYZcR16mp2NBGRExZ7QRZxF42hZMaX7LrjDjp/9BGuLpooQpoHFU4irVwgGGBP+R52lOxgR8kOthVvC32fW557xO2cVidd4rsQURbBWX3PomdST7oldKNddDsVSA3Es7+A4GfryIkZCUB7zw9c8upd2COjTE4mIlI/FouFdk88gW9PLpUrVrBzwgQ6T/sIe5uWc1FyablUOIm0Ar6gj7yyPHaW7WRX6S52le0ipySH7cXbySnNqXOShmpxzjg6x3emc9zBW3xnuid0p0NsB4yAwYwZM7ioz0U4HJqcoCHtX7eEWY8toCBmBBhBMpzLuOSVP5odS0TkpFldLjpMfYntV43Dl5PDrtsm0enNN7C6XGZHEzkqFU4iLYBhGBzwHGBX6S52l+1mV9muqgLpYJGUW55b5+QM1ZxWJ53iOtE5rjMZcRk1CqWEiIQjbucLHLngkvrbNeM9vv3IR0lMP6wBL5kdd3Dhn+41O5aISIOxJybS8e+vsP3qa6hctozcBx4k/S9Pa8SCNGkqnESaAcMwKHQXkleeR255LrlluVVfy3NDxVG5r/yoj+GyuegQ04EOsR1oH9M+VCh1ju9MWlQaNqutkV6NHFEwyOaX/sTcZafgjkrH4Sslsn0O590/wexkIiINztW1Kx1e+Cs5t/yOki++wJmRQdvbJ5kdS+SIVDiJNAFuvztUFIWKo4O3vPI8csty8Qa9x3yclKiUUHEU+nrw++TIZH2S15RVHmD1o3/g+32/xO+KIsK9j6HXdWd7mdnBRETCJ3rECNo9/BC5D/4fBS+9hDOjE/Fjx5odS6ROKpxEwqh6CF1+RT57K/aSX5Efuh1+/4DnwDEfy4KFtlFtaRfdLnRLi04LFUftY9rjsml8eLO0ZwVLHn2OH4O/wbA7iK7IYfSDo0nJTGH7jJ1mpxMRCauEK67Au2MHhf94jdwHHsSRnk7U0KFmxxKpRYWTSD0YhkGJt4SCyoIat58XRvsq9h3XkSKASHsk6dHppMWk1SiO2kW3o11MO1IiU3DYNAFDi1J5gLJ/P8qCL+xsirkRrBBTuYVfTrmauMRYfD6dQyYirUPbu+/GuyOH0lmz2HXbJDr/cxrOjAyzY4nUoMJJ5DBuv5sidxEFlQXsq9xHYWVhqCj6+f2jzUT3c4kRiaREpdS4pUal0jayLSlRKaRFpxHnjNNQutbCMAgs/4A1r37Gj56r8cQkAhAb2MzVr/4Wp0sFsoi0LharlfSnnmRHXh7ulSvZeesEOn/0IbaEBLOjiYSocJIWzR/0UxYsY9OBTZT4SyiqLKLIfehW6C6s+v5ge4W/4oQeP9YZS9vItiRHJpMUkXSoMIquKoxSolJoG9kWp80Zplcozc7eNeS9/gDz157F3piJ4AKnp5AOg6IYc8fvzE4nImIaa2QkHV96kW3jxuHdvp1dt99Bp9dfw+LU31BpGlQ4SbNhGAZlvjIOuA9wwHOA/Z79VV/ddX8tchdR7CnGwIAZx/88DquD5MjkqmIoMilUGP38flJkks4pkuPnLsHz1WMsmn6ANa4JBGOcWIJ+Yu07Gfv0FcS3jTc7oYiI6ext29LxlVfYcc2vqVi8mNw/PUS7Jx7XiAxpElQ4iSncfjfFnmKKvcVVX6tvh90v8ZbUKIQOuA/gN/wn/FwWLMS74kmKSCIxMpHEiJq3w9vbRLQh1hGrX9DScAwDVn3CxtfeZGHxrymLSgcgsiKHQdeewqCsLJMDiog0LRE9etB+yhR2TphA8b/+hbNzBskTdFkGMZ8KJ6k3T8BDiaeEEm8Jpd5SSrwlFHuKQ9+XeEso8RxadsBzgBJPCcXeYjwBT72fN9IeSYIrgQRXAm0i2tT86mpDQkTVssSIROLscSz4egGXXHwJDofOG5FGlr+eovfu5/ulA8mJ/R+IBLuvlOQMD7944DpsNl07S0SkLjFnnkHa/z1I3sOPsG/KX3F26kTcRReZHUtaORVOrVTQCFLhq6DMV0aJt4Qyb9mRv/eWUeorpdRbeqgo8pQc92xxR2Kz2Ih3xVfdnPGh7+OccTXaEyKqCqI2EW2Id8UTaY887ufw+XxYLdaTyilywjxlBL5+kmUfb2W59bf4YmPACBLt386YBy8lNTPV7IQiIk1em6uvxrt9B0VvvcWe++7HntaOqMGDzI4lrZgKp2YmEAxQ4a+g3FceKnyqC51yX3nVfV8Z5d7yUFupr7TG/er1DYyTzmO1WIl1xhLriCXOFUecs+oW66x5v0YxdLAginZEa0ictCyGAWv/xc63XuC7vGvYH30uABGVeXS/sANnXXOzyQFFRJqXlHv+B29ODmXffMOuSZPoPO0jnB07mh1LWikVTibacmALS3KXsNS9lJ2rduIOuCn3l4eKonJfeY1bhb+CSn9lg2ZwWB3EOmOJccRUfXXGEOuIrfF9jDMmVBwdXhDFOmOJdkTriI6IYcC2uVTMeI7vf+jBpug/YkTbsPndxCcUcvlzV+GK0kQiIiInymKz0f6Zv7Dj2utwr13Lzlt+R/spzxPRq5fZ0aQVUuFkokW5i3jixyeq7qw6sW3tFjtRjqhQ8RLjiKn66owhxhFT4360I5pYRyzRzkPrxTqriiDNCidyEoJB2DCD/OlTWbWuB1tcN+GLiQMgyr2NM+84m26Du5ocUkSkebNGRdHh5ZfZfnCa8m2/uoLEa68l+fbbscVEmx1PWhEVTibKiMvgzPQzKd5XTLeMbsS54ohyRBFtjybaUXWLckSFvo+2RxPtrPreaXVqmJuIWQI+Aj/9k03vTmftvmHkRd+NEVM10YPTU0SHwZGMuX28ySFFRFoOR2oKnadNY++TT1D65VcUvf02JV99Reof/0hs1mi9J5JGocLJRKe3P53TUk5jxowZXHTaRZr1TaSp81VS+u1rrJ62gk3+UZRG3gYxVYsiK3aSfEoCF0y8VMPyRETCwJGaQofnn6fs8svJ+39/xpeTw+477yT6rDNJ+7//07lPEnYqnEREjsVdzPb3XmD93HJ2uM7A7+gLDrAGPEQFd9PnioGcOuYGs1OKiLQKMWeeSZfP/03hq69S+I/XKJ/3HVsvuZTk308g8aabsDqdZkeUFkqFk4jIEfj357L02RfI2Z5CfvQIiK6aCMXlKSQ6sYJzb7+Q1M5jTE4pItL6WCMiaHvHHcRdcil5/+9RKhb+wL4pf6X435+T9tBDRA8fZnZEaYFUOImI/EzB2p9Y9sLH7K7sQ0Xk6NBwvNiKLSQPTeX8Cb/E6dSvTxERs7m6ZNLpjTco+eK/7H3qKbzbtpFz443Ejb2U1HvvxZ6cbHZEaUH0l19EBNi8aA3rP/qKsgIHByK6EbCdC5Fg81eSYGyh929GMeDcc82OKSIiP2OxWIi/9BJiRp3FvilT2P/hR5R8/h/K5swlZfLdJFx1FRarLp0iJ0+Fk4i0Sp5yNwv+OZ+8hRtwe+KpiEwHBsHBmW2j3Hm0SSzkzHt+Q1K7i03NKiIix2aLiyPtT38i/pe/JO+hh3GvXUvew49wYPpntHv4ISL69DE7ojRzKpxEpNXYvmobSz9ZROn2MjyONPz2KLD2hkjACJJQuY24iDzSzjqFwdeMw2azmR1ZREROUGT//nT++J/s/+BD9k2ZgnvlSrZdcSXRI0cSmzWa2PPPx56YaHZMaYZUOIlIi+X3+Phh+gK2z9+Cp9SJOyodSIHIFAAcvjJSPatITsyn2y/OIHXUb8GmX4siIs2dxWYj8bprib0gi/wnn6RkxpeUz59P+fz55D38CFGnnkrsBVnEnn8+jpQUs+NKM6F3CCLSIhiGwbYVW1g/dw1FmwvxlYLXnozfEQN0hqiq9eIqdtCe5XRM3UXnS8/BMeRWiNbJwyIiLZEjJYX2zz1H8u23Uzorm9KZM3GvXUvFokVULFrE3v/3ZyIHDyYuazSxo0fjSE83O7I0YSqcRKTZCQQCbP5xAxvnr6d463685Rb89kR8zjggtuoWWbWuzV9Jqns1Gc5ldGm3loRLRsOgGyF9EOhK8yIirYIrMxPXrb8j+dbf4d21i9KZsyidNYvKn36iculSKpcuZe8TTxJxyinEZY0mUpMBSR1UOIlIkxbw+Vg3fw3bvl9LWU4R3koXbmfqwSNJCVW3g0eTMILEuPNoE9hOsn0L7aI30aHtOhzdz4BB10Gvi8ERadprERER8zk7dCBp/E0kjb8JX15e1ZGoWbOoWLoU98qVuFeuhGeepVN6O4p27iLurDNxde+ONVJ/P1o7FU4iYi7D4MDWLexYtIKiTbsp31uBp8KK1x+Nx5ZApTOJoM0FpIE1LTTrnSUYIMazh8TANto6tpIWvYnUpD1EtE2B+A4Q3xGSroK+v4CETma+QhERaaIcaWkkXn8diddfh3/fPkq//pqSmTOp+HExEXtyKXrxRYpefBEsFhydOhLRoyeuHj0O3rrj7NQJiyYSajVUOIlIeBgGeEowSvMp372NfRu2U7Apj9I8N5Vldtz+GCotbah0JON1xgOJB29ARM2HsgZ9xLp30cbIISE6n7btfXTs14bI1AxIGATxY6uKo6gkDb8TEZF6sbdtS5urr6bN1Vfjzs9n4V9foMu+fXjWrCFQWIhvRw6+HTmUZmeHtrFERODq1g1Xjx5E9OwRKqrsSUkmvhIJFxVOInL8gkFwHyCwfw/F27aQvzGHyNWbWTTvBzzlQbxuGz6/C68RhdcSi8cWh9ceh98RBXQ7eKNWYQRg91cQ6SvAZRwgwl5ORGyAmLQo2vZIp9PQvkSkjQRXbGO+WhERaaVsbdpQctqppF90EQ6HA39BAZ6NG3Fv3Ihn4yY8Gzfi2bwZw+3GvXo17tWrKT58+6QkXF27Yk9Nxd62be1bSgq2mGjTXp/Uj+mF09SpU/nLX/5Cbm4uffv2ZcqUKZx55plHXH/u3LlMnjyZNWvWkJ6ezr333suECRMaMbFI82YYBgGPh7L8/ezP2UXZnjzK9+7De6AEX2kF/go/AU+AgM9CMGDHbzgIGE78lgj81kh81mi8jliCtlig78HbQXUURNUsQT8u735cwWIctnKcMRCVGkNCtw50Hj6I1M5p4X7pIiIi9WJPTsaenEz0yJGhNiMQwJuTc6iQ2rgR98YN+HJ2EigspKKw8KiPaYmKwt42uc7CyhYXjy02BmvMoZstJgaLwxHulypHYWrhNG3aNO666y6mTp3K6aefzt///nfGjBnD2rVr6dSp9jkJ27Zt46KLLuKWW27hvffe4/vvv2fixIm0bduWX/3qVya8ApETYxgG+P0YgQB+rw+/z0fA68Pn9uJxu/G5vfjcHnyVHnxuD363B7/Hi9/twVvhw1vpx+sO4PcYVTcfBL1+LD4/hj8AAQPDsBy82TEsNoI4CFocBK0OglYnAauDoM2JYakekx1N6MSharaDt2OwBdw4/GXYg+XYcWOz+bC6wB7twJkUT2R6KokZabTrmkZK+zZYrdYG7lERERFzWGy2qtn6MjPhgqxQe7CiAs+WLXi3b8efvw//voO3/PzQ98HycoyKitDwv+N+TpcLa2wstujoqoIqNhZrTDS2mNiq+1FRWFxOrC4XFldE1fcREVicrkPfu1xYnC6sEa5D37ucYHdgcdix2O06b+sITC2cnnvuOcaPH8/NN98MwJQpU5g5cyYvv/wyTzzxRK31X3nlFTp16sSUKVMA6N27N0uWLOGZZ55ploXTuv9ms+v7n/AXlzJn0SYsFitgHP8DBI+8rnHY/3/+7aHvay83oOrcFKD6TBHDMGptZsGomdQ4/AHqeC7DOLSFcfB/Vf9hqd7cMA5tZPzsCaszhNYzDm+u0RbaJli1QsDjYeanC7Actq0RPOxxD38M41Cbpcb9updZarQFDz5HEEuw6n6oHbAEDax1/HwNIGh14nNEH3aLwWc/9L3fEX9YoVMHK+A88uIjMoLYA27sgUrswUpshgcbHqxWH1ZrEKsDrC4r1kgX9tgonAlxRKamkJSZTrtuaURHO5gxYwYXXfRLHPoUTEREBGtUFJH9+xPZv/8R1wlWVBwqqGoVVgUESksJlpURKCslWFaOUVkJgOHxEPB4CBQUhPdFWCxY7HZwOKoKqcNuOOxY7IfasduwWG1gs9b9tY7lBhZS9+zB178/ji5dwvtaGpBphZPX62Xp0qXcd999NdqzsrJYsGBBndssXLiQrKysGm0XXHABr7/+Oj6fr843bh6PB4/HE7pfUlICgM/nw+fznezLOClbv1rMdt9wAPKKTI3SfFg4VNEdrxY0e6gt6MEZKMUZLMcZLMMZLMOBG5vFh9Xiryp27AYWO1gdVqwuG7YIJ9YoF/aYaOxxsbgSEnC2aUNshw7Ep6Zhdda/g6r/DZn9b6mlUv+Gl/o3vNS/4aX+Da+w96/DgSU9HUd6OsfzsaPh9xMsLydYVkawrJxgWWnV/dLSw9rLCFZWYni8GB73wa8egh4PhseD4fViuN1VXw9v93iqzmGu8YQGhs8HPt+JfKR/QuIBz759ODp2DNMzHJ8T+RmbVjgVFBQQCARITU2t0Z6amkpeXl6d2+Tl5dW5vt/vp6CggHbt2tXa5oknnuCRRx6p1T5r1iyioqJqtTcmr8VLQvlGUzPUcDKTkTXItsd4kGM9x5GW19VuqaPZcpQVLLXXsfx8m4PfW+pa12L52f2a69isARx2Nw67F7vdh93hx+oIYHMEsTkMcILFacWwOwjYXPitLgJWF35rGj5bNB6r88Rmk9tfCvvXwap1x7/NUWQfNsOQNDz1b3ipf8NL/Rte6t/wavL9a7FATEzV7WQEAlgCASyBIAQPfW8JBg4uq/reEgjAYd9bAsGDI22CEDSqvhpBCAaxBI2Dy4w617EEDbZs3EjgCO/7G0tFRcVxr2v65BCWn73ZMwyjVtux1q+rvdr999/P5MmTQ/dLSkro2LEjWVlZxMXF1Td2w7joInw+H9nZ2YwePVpDncJA/Rte6t/wUv+Gl/o3vNS/4aX+DS/1b3g1pf6tHo12PEwrnJKTk7HZbLWOLuXn59c6qlQtLS2tzvXtdjtJR5gv3+Vy4XK5arU7HA7Tf1CHa2p5Whr1b3ipf8NL/Rte6t/wUv+Gl/o3vNS/4dUU+vdEnt+0Ka6cTidDhgypdQg0OzubkYdN9Xi4ESNG1Fp/1qxZDB061PROFxERERGRlsvUuYEnT57Ma6+9xhtvvMG6deu4++67ycnJCV2X6f777+f6668PrT9hwgR27NjB5MmTWbduHW+88Qavv/46//M//2PWSxARERERkVbA1HOcxo0bR2FhIY8++ii5ubn069ePGTNmkJGRAUBubi45OYfmts/MzGTGjBncfffdvPTSS6Snp/PCCy80y6nIRURERESk+TB9coiJEycyceLEOpe99dZbtdpGjRrFsmXLwpxKRERERETkEFOH6omIiIiIiDQHKpxERERERESOQYWTiIiIiIjIMahwEhEREREROQYVTiIiIiIiIsegwklEREREROQYVDiJiIiIiIgcgwonERERERGRY1DhJCIiIiIicgwqnERERERERI5BhZOIiIiIiMgxqHASERERERE5BhVOIiIiIiIix2A3O0BjMwwDgJKSEpOTVPH5fFRUVFBSUoLD4TA7Touj/g0v9W94qX/DS/0bXurf8FL/hpf6N7yaUv9W1wTVNcLRtLrCqbS0FICOHTuanERERERERJqC0tJS4uPjj7qOxTie8qoFCQaD7Nmzh9jYWCwWi9lxKCkpoWPHjuzcuZO4uDiz47Q46t/wUv+Gl/o3vNS/4aX+DS/1b3ipf8OrKfWvYRiUlpaSnp6O1Xr0s5ha3REnq9VKhw4dzI5RS1xcnOk7Tkum/g0v9W94qX/DS/0bXurf8FL/hpf6N7yaSv8e60hTNU0OISIiIiIicgwqnERERERERI5BhZPJXC4XDz30EC6Xy+woLZL6N7zUv+Gl/g0v9W94qX/DS/0bXurf8Gqu/dvqJocQERERERE5UTriJCIiIiIicgwqnERERERERI5BhZOIiIiIiMgxqHASERERERE5BhVOYfbYY48xcuRIoqKiSEhIqHOdnJwcLr30UqKjo0lOTuaOO+7A6/Ue9XE9Hg+33347ycnJREdHM3bsWHbt2hWGV9B8zJkzB4vFUudt8eLFR9zuxhtvrLX+8OHDGzF589G5c+dafXXfffcddRvDMHj44YdJT08nMjKSs88+mzVr1jRS4uZj+/btjB8/nszMTCIjI+natSsPPfTQMX8XaP89uqlTp5KZmUlERARDhgzhu+++O+r6c+fOZciQIURERNClSxdeeeWVRkravDzxxBOceuqpxMbGkpKSwi9+8Qs2bNhw1G2O9Dt6/fr1jZS6+Xj44Ydr9VNaWtpRt9G+e/zq+ltmsVi47bbb6lxf++7RzZs3j0svvZT09HQsFgv/+te/aiyv7/uATz/9lD59+uByuejTpw+fffZZmF7B8VPhFGZer5crr7yS3//+93UuDwQCXHzxxZSXlzN//nw++ugjPv30U/7whz8c9XHvuusuPvvsMz766CPmz59PWVkZl1xyCYFAIBwvo1kYOXIkubm5NW4333wznTt3ZujQoUfd9sILL6yx3YwZMxopdfPz6KOP1uirBx988KjrP/300zz33HO8+OKLLF68mLS0NEaPHk1paWkjJW4e1q9fTzAY5O9//ztr1qzh+eef55VXXuGPf/zjMbfV/lu3adOmcdddd/HAAw+wfPlyzjzzTMaMGUNOTk6d62/bto2LLrqIM888k+XLl/PHP/6RO+64g08//bSRkzd9c+fO5bbbbuOHH34gOzsbv99PVlYW5eXlx9x2w4YNNfbX7t27N0Li5qdv3741+mnVqlVHXFf77olZvHhxjb7Nzs4G4Morrzzqdtp361ZeXs6AAQN48cUX61xen/cBCxcuZNy4cVx33XX89NNPXHfddVx11VUsWrQoXC/j+BjSKN58800jPj6+VvuMGTMMq9Vq7N69O9T24YcfGi6XyyguLq7zsQ4cOGA4HA7jo48+CrXt3r3bsFqtxldffdXg2Zsrr9drpKSkGI8++uhR17vhhhuMyy67rHFCNXMZGRnG888/f9zrB4NBIy0tzXjyySdDbW6324iPjzdeeeWVMCRsWZ5++mkjMzPzqOto/z2y0047zZgwYUKNtl69ehn33Xdfnevfe++9Rq9evWq03Xrrrcbw4cPDlrGlyM/PNwBj7ty5R1zn22+/NQBj//79jResmXrooYeMAQMGHPf62ndPzp133ml07drVCAaDdS7Xvnv8AOOzzz4L3a/v+4CrrrrKuPDCC2u0XXDBBcbVV1/d4JlPhI44mWzhwoX069eP9PT0UNsFF1yAx+Nh6dKldW6zdOlSfD4fWVlZobb09HT69evHggULwp65ufj8888pKCjgxhtvPOa6c+bMISUlhR49enDLLbeQn58f/oDN1FNPPUVSUhIDBw7kscceO+pQsm3btpGXl1djX3W5XIwaNUr76nEoLi4mMTHxmOtp/63N6/WydOnSGvseQFZW1hH3vYULF9Za/4ILLmDJkiX4fL6wZW0JiouLAY5rfx00aBDt2rXjvPPO49tvvw13tGZr06ZNpKenk5mZydVXX83WrVuPuK723frzer2899573HTTTVgslqOuq333xNX3fcCR9mmz3zuocDJZXl4eqampNdratGmD0+kkLy/viNs4nU7atGlToz01NfWI27RGr7/+OhdccAEdO3Y86npjxozh/fff55tvvuHZZ59l8eLFnHvuuXg8nkZK2nzceeedfPTRR3z77bdMmjSJKVOmMHHixCOuX70//nwf1756bFu2bOFvf/sbEyZMOOp62n/rVlBQQCAQOKF9r67fx6mpqfj9fgoKCsKWtbkzDIPJkydzxhln0K9fvyOu165dO1599VU+/fRTpk+fTs+ePTnvvPOYN29eI6ZtHoYNG8Y777zDzJkz+cc//kFeXh4jR46ksLCwzvW179bfv/71Lw4cOHDUD1m179Zffd8HHGmfNvu9g93UZ2+mHn74YR555JGjrrN48eJjnldTra5POAzDOOYnHw2xTXNQn/7etWsXM2fO5J///OcxH3/cuHGh7/v168fQoUPJyMjgv//9L5dffnn9gzcTJ9K/d999d6jtlFNOoU2bNlxxxRWho1BH8vP9sqXuq3Wpz/67Z88eLrzwQq688kpuvvnmo27b2vffYznRfa+u9etql0MmTZrEypUrmT9//lHX69mzJz179gzdHzFiBDt37uSZZ57hrLPOCnfMZmXMmDGh7/v378+IESPo2rUrb7/9NpMnT65zG+279fP6668zZsyYGiN/fk777smrz/uApvjeQYVTPUyaNImrr776qOt07tz5uB4rLS2t1olu+/fvx+fz1aq0D9/G6/Wyf//+Gked8vPzGTly5HE9b3NSn/5+8803SUpKYuzYsSf8fO3atSMjI4NNmzad8LbN0cnsz9Wzt23evLnOwql6Fqi8vDzatWsXas/Pzz/i/t3SnGj/7tmzh3POOYcRI0bw6quvnvDztbb990iSk5Ox2Wy1Pp082r6XlpZW5/p2u/2oHwy0Zrfffjuff/458+bNo0OHDie8/fDhw3nvvffCkKxliY6Opn///kf8d619t3527NjB7NmzmT59+glvq333+NT3fcCR9mmz3zuocKqH5ORkkpOTG+SxRowYwWOPPUZubm5oh5o1axYul4shQ4bUuc2QIUNwOBxkZ2dz1VVXAZCbm8vq1at5+umnGyRXU3Ki/W0YBm+++SbXX389DofjhJ+vsLCQnTt31vgH3pKdzP68fPlygCP2VWZmJmlpaWRnZzNo0CCgajz53Llzeeqpp+oXuJk5kf7dvXs355xzDkOGDOHNN9/Eaj3x0dStbf89EqfTyZAhQ8jOzuaXv/xlqD07O5vLLruszm1GjBjBf/7znxpts2bNYujQofX6XdKSGYbB7bffzmeffcacOXPIzMys1+MsX7681e+rx8Pj8bBu3TrOPPPMOpdr362fN998k5SUFC6++OIT3lb77vGp7/uAESNGkJ2dXWOky6xZs8w/QGDSpBStxo4dO4zly5cbjzzyiBETE2MsX77cWL58uVFaWmoYhmH4/X6jX79+xnnnnWcsW7bMmD17ttGhQwdj0qRJocfYtWuX0bNnT2PRokWhtgkTJhgdOnQwZs+ebSxbtsw499xzjQEDBhh+v7/RX2NTM3v2bAMw1q5dW+fynj17GtOnTzcMwzBKS0uNP/zhD8aCBQuMbdu2Gd9++60xYsQIo3379kZJSUljxm7yFixYYDz33HPG8uXLja1btxrTpk0z0tPTjbFjx9ZY7/D+NQzDePLJJ434+Hhj+vTpxqpVq4xrrrnGaNeunfr3Z3bv3m1069bNOPfcc41du3YZubm5odvhtP8ev48++shwOBzG66+/bqxdu9a46667jOjoaGP79u2GYRjGfffdZ1x33XWh9bdu3WpERUUZd999t7F27Vrj9ddfNxwOh/HJJ5+Y9RKarN///vdGfHy8MWfOnBr7akVFRWidn/fv888/b3z22WfGxo0bjdWrVxv33XefARiffvqpGS+hSfvDH/5gzJkzx9i6davxww8/GJdccokRGxurfbcBBQIBo1OnTsb//u//1lqmfffElJaWht7fAqH3Cjt27DAM4/jeB1x33XU1Zjz9/vvvDZvNZjz55JPGunXrjCeffNKw2+3GDz/80Oiv73AqnMLshhtuMIBat2+//Ta0zo4dO4yLL77YiIyMNBITE41JkyYZbrc7tHzbtm21tqmsrDQmTZpkJCYmGpGRkcYll1xi5OTkNOIra7quueYaY+TIkUdcDhhvvvmmYRiGUVFRYWRlZRlt27Y1HA6H0alTJ+OGG25QX9Zh6dKlxrBhw4z4+HgjIiLC6Nmzp/HQQw8Z5eXlNdY7vH8No2oq0oceeshIS0szXC6XcdZZZxmrVq1q5PRN35tvvlnn74qff76l/ffEvPTSS0ZGRobhdDqNwYMH15gu+4YbbjBGjRpVY/05c+YYgwYNMpxOp9G5c2fj5ZdfbuTEzcOR9tXD/+3/vH+feuopo2vXrkZERITRpk0b44wzzjD++9//Nn74ZmDcuHFGu3btDIfDYaSnpxuXX365sWbNmtBy7bsnb+bMmQZgbNiwodYy7bsnpnq69p/fbrjhBsMwju99wKhRo0LrV/v444+Nnj17Gg6Hw+jVq1eTKFQthnHw7EERERERERGpk6YjFxEREREROQYVTiIiIiIiIsegwklEREREROQYVDiJiIiIiIgcgwonERERERGRY1DhJCIiIiIicgwqnERERERERI5BhZOIiIiIiMgxqHASERERERE5BhVOIiIiIiIix6DCSURERERE5BhUOImISKuxb98+0tLSePzxx0NtixYtwul0MmvWLBOTiYhIU2cxDMMwO4SIiEhjmTFjBr/4xS9YsGABvXr1YtCgQVx88cVMmTLF7GgiItKEqXASEZFW57bbbmP27Nmceuqp/PTTTyxevJiIiAizY4mISBOmwklERFqdyspK+vXrx86dO1myZAmnnHKK2ZFERKSJ0zlOIiLS6mzdupU9e/YQDAbZsWOH2XFERKQZ0BEnERFpVbxeL6eddhoDBw6kV69ePPfcc6xatYrU1FSzo4mISBOmwklERFqVe+65h08++YSffvqJ8HzyzwAAALlJREFUmJgYzjnnHGJjY/niiy/MjiYiIk2YhuqJiEirMWfOHKZMmcK7775LXFwcVquVd999l/nz5/Pyyy+bHU9ERJowHXESERERERE5Bh1xEhEREREROQYVTiIiIiIiIsegwklEREREROQYVDiJiIiIiIgcgwonERERERGRY1DhJCIiIiIicgwqnERERERERI5BhZOIiIiIiMgxqHASERERERE5BhVOIiIiIiIix6DCSURERERE5Bj+P2lZ2gXhm1GgAAAAAElFTkSuQmCC", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.figure(figsize = (10, 6))\n", | |
| "\n", | |
| "y = 1.0 / (1.0 + np.exp(-x))\n", | |
| "plt.plot(x, y, label = \"Standard Sigmoid, Numpy\")\n", | |
| "\n", | |
| "y = fast_sigmoid_branching(x)\n", | |
| "plt.plot(x, y, label = \"Exponential-less Sigmoid, Branching\")\n", | |
| "\n", | |
| "y = fast_sigmoid(x)\n", | |
| "plt.plot(x, y, label = \"Exponential-less Sigmoid, Branchless\")\n", | |
| "\n", | |
| "order = 10\n", | |
| "y = sigmoid_f32_taylor_exp(x, order = order, inverseDefinition = False)\n", | |
| "plt.plot(x, y, label = f\"Standard Sigmoid (Taylor, order = {order})\")\n", | |
| "\n", | |
| "y = sigmoid_lut_based(x, lut, lutSize)\n", | |
| "plt.plot(x, y, label = f\"LUT-based Sigmoid, {lutSize} points\")\n", | |
| "\n", | |
| "plt.xlabel(\"x\")\n", | |
| "plt.ylabel(\"σ(x)\")\n", | |
| "plt.title(\"Exponential-less, Branching Sigmoid Approximation, f32\")\n", | |
| "plt.grid(True)\n", | |
| "plt.legend()\n", | |
| "plt.show()\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "id": "fddfe617", | |
| "metadata": {}, | |
| "source": [ | |
| "Squared error in LUT vs Exponential-less, branching algorithm:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 396, | |
| "id": "af636ff0", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", 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| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "y = 1.0 / (1.0 + np.exp(-x))\n", | |
| "\n", | |
| "error_lut = np.square(y - sigmoid_lut_based(x, lut, lutSize))\n", | |
| "error_fast_branching = np.square(y - fast_sigmoid_branching(x))\n", | |
| "\n", | |
| "plt.figure(figsize = (10, 6))\n", | |
| "plt.plot(x, error_lut, label = f\"LUT-based ({lutSize} points)\")\n", | |
| "plt.plot(x, error_fast_branching, label = \"Exponential-less, Branching\")\n", | |
| "\n", | |
| "plt.xlabel(\"x\")\n", | |
| "plt.ylabel(\"$|y_{pred} - y_{true}|^2$\")\n", | |
| "plt.title(\"Squared Error Comparison, LUT vs Exponential-less Branching algorithm, f32\")\n", | |
| "plt.grid(True)\n", | |
| "plt.legend()\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 399, | |
| "id": "0253c08f", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "def polynomial_sigmoid(x, coefficients, offset):\n", | |
| " y = coefficients[0]\n", | |
| " x_power = np.ones_like(x)\n", | |
| " x_multiplier = x - np.broadcast_to(offset, x.shape)\n", | |
| "\n", | |
| " for i in range(1, len(coefficients)):\n", | |
| " x_power *= x_multiplier\n", | |
| " y = y + x_power * coefficients[i]\n", | |
| " return y\n", | |
| "\n", | |
| "# Exponential-less, branchful approximation of sigmoid function\n", | |
| "def sigmoid_branching_polynomial(x_vec):\n", | |
| " output = np.empty_like(x_vec)\n", | |
| " \n", | |
| " for i, x in enumerate(x_vec):\n", | |
| " # Sigmoid is symmetrical around 0. Calculate sigmoid on abs(x), then flip it accordingly if it was negaitve\n", | |
| " x_abs = np.abs(x)\n", | |
| " y = 0\n", | |
| "\n", | |
| " if x_abs < 1:\n", | |
| " y = polynomial_sigmoid(x_abs, [0.5010008, 0.22136687, 0.19342738, -0.5231247, 0.5537795, -0.21612851], 0)\n", | |
| " elif x_abs < 2:\n", | |
| " y = polynomial_sigmoid(x_abs, [0.7320988, 0.16688538, 0.15533534, -0.5270234, 0.57939947, -0.22665948], 1)\n", | |
| " elif x_abs < 3:\n", | |
| " y = polynomial_sigmoid(x_abs, [0.88158137, 0.08256347, 0.11147195, -0.3865234, 0.433558, -0.17065544], 2)\n", | |
| " elif x_abs < 4:\n", | |
| " y = polynomial_sigmoid(x_abs, [0.95209116, 0.05905316, -0.1141415, 0.24869199, -0.26870516, 0.10539465], 3)\n", | |
| " elif x_abs < 5:\n", | |
| " y = polynomial_sigmoid(x_abs, [0.9812842, 0.04014706, -0.1599278, 0.3958077, -0.43351972, 0.17042148], 4)\n", | |
| " elif x_abs < 6:\n", | |
| " y = polynomial_sigmoid(x_abs, [0.99375355, -0.0061026, 0.08283123, -0.2224306, 0.24593456, -0.09678433], 5)\n", | |
| " else:\n", | |
| " y = 0.9999\n", | |
| "\n", | |
| " # If x < 0, σ(x) = 1 - σ(|x|) due to sigmoid symmetry\n", | |
| " if x < 0:\n", | |
| " y = 1 - y\n", | |
| " output[i] = y\n", | |
| " return output\n", | |
| "\n", | |
| "plt.figure(figsize = (10, 6))\n", | |
| "\n", | |
| "y = 1.0 / (1.0 + np.exp(-x))\n", | |
| "plt.plot(x, y, label = \"Standard Sigmoid, Numpy\")\n", | |
| "\n", | |
| "y = sigmoid_branching_polynomial(x)\n", | |
| "plt.plot(x, y, label = \"Exponential-less Sigmoid, Polynomial\")\n", | |
| "\n", | |
| "plt.xlabel(\"x\")\n", | |
| "plt.ylabel(\"σ(x)\")\n", | |
| "plt.title(\"Exponential-less, Branching Sigmoid Approximation with 5th Order Polynomial, f32\")\n", | |
| "plt.grid(True)\n", | |
| "plt.legend()\n", | |
| "plt.show()\n" | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "base", | |
| "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": "3.12.7" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 5 | |
| } |
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