{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Hartree-Fock 交换算符\n", "\n", "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/bud-primordium/AtomSCF/blob/main/docs/source/tutorials/04-hartree-fock.ipynb)\n", "\n", "## 学习目标\n", "\n", "- 理解 Hartree-Fock 方法的交换积分\n", "- 掌握 Slater 径向积分的物理意义\n", "- 对比 HF 交换与 DFT 交换的核心差异\n", "\n", "## HF 交换的物理图像\n", "\n", "Hartree-Fock 方法通过反对称化波函数自然引入交换项:\n", "\n", "$$\\hat{K}[u_i](r) = -\\sum_{j \\text{ occ}} \\int_0^\\infty \\frac{u_j(r) u_j(r') u_i(r')}{|r - r'|} dr'$$\n", "\n", "对球对称原子,交换算符通过 Slater 径向积分实现:\n", "\n", "$$R^k_{ij}(r) = \\int_0^\\infty \\frac{r_<^k}{r_>^{k+1}} u_i(r') u_j(r') dr'$$\n", "\n", "角动量选择规则限制 $k$ 的取值:$|l_i - l_j| \\leq k \\leq l_i + l_j$,且 $k$ 与 $l_i + l_j$ 同奇偶。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 理论基础:Hartree-Fock 交换\n", "\n", "Hartree-Fock 方法显式处理交换积分(反对称性)。\n", "\n", "### Fock 算符\n", "\n", "$$\\hat{F} = \\hat{h} + \\hat{J} - \\hat{K}$$\n", "\n", "其中:\n", "- $\\hat{h}$:单电子 Hamiltonian(动能 + 核势)\n", "- $\\hat{J}$:Coulomb 算符(Hartree 势)\n", "- $\\hat{K}$:交换算符\n", "\n", "### 交换势(Slater 积分)\n", "\n", "对于原子轨道 $\\psi_i = u_i(r)Y_{lm}$,交换算符矩阵元:\n", "\n", "$$K_{ij} = \\sum_k f_k \\int\\int \\frac{\\psi_i^*(r)\\psi_k^*(r')\\psi_k(r')\\psi_j(r)}{|r-r'|}d^3r d^3r'$$\n", "\n", "球对称简化为 Slater 积分:\n", "\n", "$$R^k(r) = \\int_0^\\infty \\frac{r_<^k}{r_>^{k+1}}|u_j(r')|^2 dr'$$\n", "\n", "**代码实现**:`exchange_operator_general()` 构造交换矩阵\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:13:48.864615Z", "iopub.status.busy": "2025-12-04T04:13:48.864447Z", "iopub.status.idle": "2025-12-04T04:13:48.868943Z", "shell.execute_reply": "2025-12-04T04:13:48.868870Z" } }, "outputs": [], "source": [ "# 环境配置\n", "import sys\n", "\n", "if \"google.colab\" in sys.modules:\n", " !pip install -q git+https://github.com/bud-primordium/AtomSCF.git" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:13:48.874318Z", "iopub.status.busy": "2025-12-04T04:13:48.874198Z", "iopub.status.idle": "2025-12-04T04:14:07.209756Z", "shell.execute_reply": "2025-12-04T04:14:07.209635Z" } }, "outputs": [], "source": [ "# 配置中文字体(避免乱码)\n", "import matplotlib.pyplot as plt\n", "import matplotlib\n", "\n", "# 跨平台中文字体配置\n", "matplotlib.rcParams['font.sans-serif'] = [\n", " 'Arial Unicode MS', # macOS\n", " 'WenQuanYi Micro Hei', # Linux\n", " 'SimHei', # Windows\n", " 'DejaVu Sans' # Fallback\n", "]\n", "matplotlib.rcParams['axes.unicode_minus'] = False\n", "\n", "# 清除字体缓存(重要!)\n", "try:\n", " import matplotlib.font_manager as fm\n", " fm._load_fontmanager(try_read_cache=False)\n", "except Exception:\n", " pass\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:14:07.214838Z", "iopub.status.busy": "2025-12-04T04:14:07.214752Z", "iopub.status.idle": "2025-12-04T04:14:07.838093Z", "shell.execute_reply": "2025-12-04T04:14:07.837959Z" } }, "outputs": [], "source": [ "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from atomscf.grid import radial_grid_linear\n", "from atomscf.scf_hf import HFSCFGeneralConfig, run_hf_scf\n", "from atomscf.hf.slater import slater_integral_radial\n", "\n", "plt.style.use('seaborn-v0_8-darkgrid')\n", "plt.rcParams['figure.figsize'] = (12, 5)\n", "\n", "\n", "def get_hf_energy(result):\n", " return getattr(result, 'E_total', 0.0)\n", "\n", "\n", "def get_hf_eps(result, l, idx=0):\n", " values = result.eigenvalues_by_l.get(l)\n", " if values is None or idx >= len(values):\n", " return 0.0\n", " return float(values[idx])\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## He 原子 HF 计算\n", "\n", "氦(Z=2)闭壳层 1s²,是最简单的多电子体系:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:14:07.843780Z", "iopub.status.busy": "2025-12-04T04:14:07.843653Z", "iopub.status.idle": "2025-12-04T04:15:41.610790Z", "shell.execute_reply": "2025-12-04T04:15:41.610506Z" } }, "outputs": [], "source": [ "\n", "# 生成网格\n", "r, w = radial_grid_linear(n=1000, rmin=1e-5, rmax=30.0)\n", "\n", "# 配置 He 原子 HF(Z=2 会自动使用 RHF,1s²)\n", "cfg_he = HFSCFGeneralConfig(\n", " Z=2,\n", " r=r,\n", " w=w,\n", " occ_by_l={0: [2.0]}, # He: 1s^2\n", " eigs_per_l={0: 1}, # 只需求解 1 个 s 态\n", " maxiter=50,\n", " tol=1e-6, # 参数名是 tol 而不是 conv_tol\n", ")\n", "\n", "# 运行 HF 自洽\n", "result_he = run_hf_scf(cfg_he)\n", "\n", "hf_total = get_hf_energy(result_he)\n", "hf_eps_1s = get_hf_eps(result_he, l=0, idx=0)\n", "\n", "print('He 原子 HF 结果:')\n", "print(f' 收敛: {result_he.converged}')\n", "print(f' 迭代次数: {result_he.iterations}')\n", "print(f' 总能量: {hf_total:.6f} Hartree')\n", "print(f' 总能量: {hf_total * 27.211:.3f} eV')\n", "print(f' 1s 轨道能量: {hf_eps_1s:.6f} Hartree')\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Slater 积分可视化\n", "\n", "对 He 的 1s 轨道,计算 Slater 径向积分 $R^0_{1s,1s}(r)$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:15:41.698842Z", "iopub.status.busy": "2025-12-04T04:15:41.697720Z", "iopub.status.idle": "2025-12-04T04:15:42.057833Z", "shell.execute_reply": "2025-12-04T04:15:42.057711Z" } }, "outputs": [ { "data": { "image/png": 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+RXHLv5aCgi5xT+QnPgMDD2MeeBjzwMOYBx7aIxRyHo80aFCQr2Bbr0GqHnsm/wu2knfdi4e7JGv4xFjZbN66/2ef2fXYYyEKkMUGAQAACjRPkaKKn79YmWWvliTZt29T2IihJqcCAACARNG2QFm82KbPPrNLkooUdWvwyLjLWTQ4T9zdLFVjJsfIEeQt3K5ZY1PHjhRuAQAACgJ32asVP3ehPP/Mrg19b7ocn31qcioAAABQtC0g/vrL0Isvnulj239YnEpE+cfqX/UbpmnSu6cUGubN8+OPNj35ZIjS000OBgAAgEvKrHGzksZM9G1H9O0py4H/mZgIAAAAFG0LAI9H6ts3WAkJ3mm1Te9z6u5mqSanyqpmdLreeO9M4XbNGpueey5YLpfJwQAAAHBJqV26KvXBdpIkS2KCijzdVUpLMzcUAABAAKNoWwCsXGnV2rU2SVJUqUz1eTHe5ETnd2P1DI2feqZVwmef2TVgQLAusAgfAAAA/IVhKGnS23JdX1GSZP95u8JGDTc5FAAAQOCiaOvnMjOlMWPOrODbe0i8Iop6TEx0cTWj0zX6rRjf4mTz59s1YgQrEAMAAPg7T3iEEt6bc6a/7Yz/yP7DOpNTAQAABCaKtn5u8WKbdu2ySpKq3ZyuRvf4V1uE86nXIE3DJsTKYvEWbv/zH4fef99ucioAAABcSmb1GkoeNsK3HdGnp5SUZGIiAACAwETR1o+lpUkTJ56Zpdq9b4IMw8RAl+Gue1PVb+iZNg4vvRSklSutJiYCAABAdqQ89azS698uSbL+eUDho18xOREAAEDgoWjrx2bPtuvQIe8Q3XpHqmrXTTc50eVp/bBTjz6RKElyuw09/XSIduzgVw4AAMCvWSxKfOsdeUJDJUkh78+Ufd1ak0MBAAAEFipofioxUXrrLYdvu3vfBBPT5Fz3vom6694USZLTaahTpxAdOVJApgsDAAAEKPf1FZU09FXfdkS/XrRJAAAAyEcUbf3UtGkOnTrlHZ57WjpVuarL5EQ5Y7FIL42J1U01vbOEjx616IknQpTq/615AQAAAlrqk92VfnsDSZL1z4MKGzviEvcAAABAbqFo64ecTmnWLO8sW5vNo269Ek1OdGWCgqWxk2NU5mpv4Xn7dqsGDw6Wx2NyMAAAAFzYedok2H7aZnIoAACAwEDR1g/93//ZFRfnbSFwT8sUlS2faXKiKxdZ3K0xb8coKNgtSZo/367337ebnAoAAAAX465wnZIHDJEkGW63wl/oJ2UW/HNTAAAAf0fR1s94PNJ7750pZj7YMdnENLmrUhWXBo2I920PGxakDRusJiYCAADApaQ821OuG6tJkuw/b1fwBzNNTgQAAFD4UbT1Mz/+aNWuXd5CZvVa6apyU4bJiXLXPS1T1OFx7yIWLpehJ58M1t9/szAZAACA37LblTjxLd9m2NhRshz927w8AAAAAYCirZ+ZOfPsWbaFc4Xe7n0TVKdemiTp5EmLnnkmWK6Cuc4aAABAQHDVq6+Uzo9LkixJiQob9qLJiQAAAAo3irZ+5NAhQ199ZZMklSyVqTvvSTU5Ud6w2aThr8UqqrS3H9qGDTZNmOAwORUAAAAuJnnoq3KXKCFJCv50iezfrjY5EQAAQOFF0daPfPCBXW63t1VA64eTZSvE63RFFnPr1Ukxsto8kqS33w7SmjX0twUAAPBXnuIllPTKaN92+NDBUkbhauUFAADgLyja+gmnU5o3zzvb1G73qFU7p8mJ8l71Whnq3ifBt92jR7COHKG/LQAAgL9Ka/+oMqJvlSTZ9vyhkFnTTU4EAABQOFG09RNLl9oVG+stWN7dPEXFS7pNTpQ/OjyerNvv8raBiImxqHt3+tsCAAD4LYtFSWMnymN4z1tDXxsv48QJk0MBAAAUPhRt/cQnn9h8///go8kmJslfhiG9ODpWZcp6K7WbNtn05pv0twUAAPBXrlq3KLVjF0mSJTFBYWNHmJwIAACg8KFo6weOHDG0fr23n+s1FTJUtXpg9QYrUtSjYRNiZbV6+9u+/rpDGzfS3xYAAMBfJb/0itwRRSRJwR/Ple2nbSYnAgAAKFwo2vqBZcts8ni8l5g1aZkiIwDbulavlaGuzyVKktxuQz16BCs+3uRQAAAAOC9PVJScLwyRJBkej8JffEHyeExOBQAAUHhQtPUDS5bYff9/T8sUE5OYq9NTSbr5ljRJ0qFDFg0aFMy5PwAAgJ9K6faMXDdUkSTZt25W0KdLTE4EAABQeFC0NdnevYZ++cXbCqBKtXSVuzbT5ETmsVqloePjFB7hXYRt6VK7Fi2yXeJeAAAAMIXdrqSRY32bYaNfldLSzMsDAABQiFC0NdnZs2ybBPAs29NKX5WpAcPjfNsvvRSsw4cDsF8EAABAAZBx9z1Kv/NuSZL1z4MKmTXD5EQAAACFA0VbE3k83tmkkmQYHjVuTtFWkho3T1Xz1k5JUmKiob59g+V2mxwKAAAA5zIMJb0yWp5/FmUIffM1GTGnTA4FAABQ8FG0NdGOHRbt2+cdgpp10hVVmsrkab2HxCuqtLdVxPff2zR7tv0S9wAAAIAZMqvXUOojnSRJlvg4hb75msmJAAAACj6Ktib6v/+jNcKFhEd4NHhknG975Mgg7d9PmwQAAOBfYmJi1LRpU23cuPGCxzz11FOqUaOGateu7fvz/fff+26fOXOmGjVqpFq1aqlLly7av39/fkTPVc4hQ+UJCZEkhbw/U5b9+0xOBAAAULBRtDWJ2y0tW+ZdZMtq8+jOphRt/63u7Wlq0yFZkuR0GurTJ1iZgbtOGwAA8DNbt25Vhw4d9Oeff170uF9//VWzZs3S9u3bfX8aNWokSVq6dKnmzp2rWbNmaePGjbrpppv0/PPPy+Px5MePkGvcV5WV87nekiQjI0PhY0aYnAgAAKBgo2hrkk2brPr7b+/Lf+vtaSoaWbBOzPPLs/0TVLacS5K0caNN06fTJgEAAJhv6dKlGjhwoPr163fR4w4dOqT4+HhVq1btvLcvWrRIHTt2VOXKlRUUFKQBAwboyJEjF525669SevWRO6qUJCnos2WybSp4PwMAAIC/oGhrkm++sfr+/65mzLK9kNBQj4aMjpNheIva48YF6fff+bUFAADmatCggVauXKmWLVte9LgdO3YoLCxM/fr1U/369XX//fdr8eLFvtv37t2rG264wbdtt9tVoUIF7d69O8+y5xVPeISSB7/s2w5/5SXvyrsAAAC4bDazAwSq1au9L71heFS/QZrJafxbzTrperhLshbNCVdamqHevYO1YoVTNn57AQCASaKiorJ1XHp6umrVqqV+/fqpcuXK2rhxo3r37q2wsDC1aNFCycnJCvmnF+xpwcHBcjqd5308m82/v7x2d+2qzJn/kfX33bJv3azQL5fL1fZBs2MVaDab9dIHoVBhzAMPYx54GHNkB2UvExw+bGjXLu8b9MYaGYos7jY5kf97qneCNqwL0p//s+unn6yaPNmh/v3TzY4FAABwUW3btlXbtm192w0aNFDbtm315ZdfqkWLFgoJCVFqamqW+6SmpiosLOy8j+dyuZWe7s9N/g0lDR+pop3aS5KCXxmmmCbNpaAgk3MVbP495sgLjHngYcwDD2OOS/Hvr+oLqVWrztTK6zdMvciROC0oWHppTJysVu8ldpMmObRjB7++AADAvy1evFhffvllln3p6ekK+qeIWblyZe3Zs8d3W0ZGhg4cOJClZUJBk35PM6U3vFOSZD14QCEfzDQ5EQAAQMFjetXr1KlT6tGjh6Kjo1WvXj2NGTNGLpfrvMd++OGHaty4sW655Ra1atVKX3/9dT6nzR2nWyNIUv2GtEbIrhtrZKhTtyRJkstlqFevYKXx8gEAAD+WlJSkUaNGaefOnXK73fruu+/0+eefq0OHDpKkhx56SB999JF2796ttLQ0vf766ypZsqSio6NNTn4FDEPJr46WxzAkSaFvTJQRG2NyKAAAgILF9KJt3759FRoaqnXr1mnx4sVav369Zs+efc5xa9eu1fTp0/Xee+9p27Zt6tWrl/r27avDhw/nf+grkJoqrVvnbY1QvESmKt+YYXKiguWxZxNVqYr3Ndu1y6q333aYnAgAACCr2rVra/ny5ZKkxx9/XJ07d1avXr1Uu3ZtTZo0SRMmTPAVZdu1a6euXbuqZ8+eql+/vnbu3Knp06fLbreb+SNcMVeNmkp7+BFJkiUuTqFvTjI5EQAAQMFieDzmLel68OBB3Xvvvfr+++9VunRpSdKKFSv02muv6dtvv81y7AcffKAZM2boo48+0vXXX6/Vq1erf//++uabb1SmTJnzPn58vNPveoSsWWPVI4+ESpJatHVqyKg4cwMVQHt/t6n7I1HKdBmy2z1avdqpqlW9fYEdDqvfjTnyFmMeeBjzwMOYB56oqAizI/gtfzy/vRDLX4dV/LZbZKSmyuNwKGb9NrnLX2N2rAKHz8DAw5gHHsY88DDmgScn57emzrTds2ePIiMjfQVbSapYsaKOHDmihISELMfed999KlmypFq2bKmbbrpJffr00fjx4y9YsPVXWVsj0M82JypVcenRJ7xtEjIyDPXrF6xMPusAAAD8ivvqckp5+jlJkpGerrDxo01OBAAAUHCYWrRNTk5WSEhIln2nt51OZ5b9GRkZqlq1qj755BP99NNPGjlypF5++WX9/vvv+Zb3Snk80sqV3qKt1eZR9G00ZM2px55J1DUVvG0Stm61atasgn0JIQAAQGHkfL6f3JGRkqSgxQtl/XWHuYEAAAAKCNulD8k7oaGhSklJybLv9HZYWFiW/aNGjdItt9yim2++WZJ30YbPP/9cS5cu1ZAhQ877+Dab6S17s9i719CBA95MNW/JULFi/pWvILHbpCGjEtWjS3FJ0tixQWrVyqOKFXlNA43NZjU7AvIZYx54GHOg4PIUjZSz7wsKf/VlGR6Pwke/ovgFS8yOBQAA4PdMLdpWrlxZcXFxOnnypEqWLClJ2rdvn8qUKaOIiKy9Ho4cOaLq1atn2Wez2S66SIPL5farHiErVpzJemuDFGW4/CdbQXRTrUy16ZCsTxeGyek01KePXUuXpisjg9c10PjT+xz5gzEPPIw5UHClPPm0Qt57V9bDh+RYs0r2dWuV0fBOs2MBAAD4NVOnJVaoUEF16tTR2LFjlZSUpEOHDmnatGlq167dOcc2btxYH330kX777Te53W599dVX2rhxo1q2bGlC8pxZtersfra0RsgNz/RNUFRp7z/kv/vOpoULmY0FAADgV4KDlTxkqG8zbORwye02MRAAAID/M/1a8smTJ8vlcqlJkyZq3769GjZsqB49ekiSateureXLl0uSevXqpU6dOql3796qW7euZsyYoXfeeUc33nijmfGzLTlZ2rDBW1AsU9alChVdJicqHMLCPeo/LM63/eKLDp04YZgXCAAAAOdIe6i9XNW8V83Zf96uoOVLTU4EAADg3wyPx+MxO0ReiY93+s3llGvXWvXww6GSpPsfStYLr8abnKhwGTEoUmu+9L6+DzyQoenTU01OhPzicFj95n2O/MGYBx7GPPBERUVc+qAA5U/nt5fLvmalIh95SJKUeW0FxfywRXI4TE7l//gMDDyMeeBhzAMPYx54cnJ+a/pM20Cxfv2Zy/ZrRaebmKRwen5wgooU9V5mt3SpXd98Q5sEAAAAf5Jx9z1K/6eXrfXgAQXPed/kRAAAAP6Lom0+ObtoWzOafra5rVgJt3oOOjN7edCgYCUmmhgIAAAAWRmGkoeN8G2GvT5BRmKCiYEAAAD8F0XbfJCaKm3b5i3aXnW1S6XKsPBCXmjWKkW33uEtiB85YtHo0UEmJwIAAMDZXLVuUWrbByVJllOnFPLOZJMTAQAA+CeKtvlg+3ar0tK8i2PVpDVCnjEMafCIBIWEeIvis2fbtXUrv+IAAAD+JPnF4fLYbJKk0Henyjh2zOREAAAA/oeKVj748cezWiPUoTVCXrrqaree6Onti+DxGBo4MFgul8mhAAAA4OO+7nqlPv6kJMlwOhU2abzJiQAAAPwPRdt8wCJk+euhTsmqVCVDkvTbb1bNnGk3OREAAADOltx/sNxh4ZKk4I9my7p3j8mJAAAA/AtF2zyWkSFt2eIt2kaVytRV5TJNTlT42WzSgOFxMgyPJGnChCAdPmyYnAoAAACneaKilNKrjyTJyMxU2NiRJicCAADwLxRt89jPP1vkdJ7uZ5smg9phvqh2c4Zat3dKkpxOQy+9xKJkAAAA/sT5TE+5o0pJkoI+/1S2LZtMTgQAAOA/KNrmsR9/tPn+n0XI8tfTzyeoeAnvzOavvrLryy9tl7gHAAAA8k14uJJfeNG3GTZyuOTxmBgIAADAf1C0zWMbNpy9CBlF2/wUUcSjnoMSfNsvvRSkpCQTAwEAACCL1E6PyVWxkiTJseFHOVZ+ZXIiAAAA/0DRNg9lZkobN3qLtsWKZ+qa61wmJwo8TVqkKPq2VEnSX39Z9NprtEkAAADwG3a7kl96xbcZNvpV70k0AABAgKNom4d++82ixERvE9ub66TTz9YEhiH1Gxovh8N7qd2MGXb9+iu/9gAAAP4i/f7WyqgTLUmy7d6l4IUfm5wIAADAfFSv8tCPP55pjVArOs3EJIGt3DWZ6tI9UZKUmWnohReC5XabHAoAAABehqHk4aN8m6ETxkgpKSYGAgAAMB9F2zy0fj39bP3FI08k6ZoKGZKkrVutmjPHbnIiAAAAnJZx2x1Ku7e5JMn69xGFzHzX5EQAAADmomibRzweacsWb9E2PMKt6yrTz9ZMDofUf3i8b3v06CAdO0a/CgAAAH+R/PKr8li8/zwJnfyGjJhTJicCAAAwD0XbPPLXX4ZOnPC+vFWrp8vCK2262nXT1by1U5KUkGDolVdYlAwAAMBfZN5YTakdOkqSLAnxCn37DZMTAQAAmIdSYh7Zvv1Ma4Sq1TNMTIKzPTcgQUWKehvaLlli13ffWS9xDwAAAOQX5+CX5QkOliSFzJouy6E/TU4EAABgDoq2eeSnn868tDdStPUbkcXderZ/gm978OBgpaaaGAgAAAA+7rJXK+Xp5yRJRnq6wsaPNjkRAACAOSja5pGffjp7pi2LkPmTFm2dqnFLmiTpf/+z6K23HCYnAgAAwGnO3n3ljoyUJAUtXijrrzvMDQQAAGACirZ5wO0+U7QtWSpTJUu5TU6Es1ks0oBh8bLaPJKkKVMc2rOHtwIAAIA/8EQWk7PvC5Ikw+NR+OhXTE4EAACQ/6hU5YH9+w0lJhqSpKo3McvWH11XyaVHHk+SJGVkGBo0KEgej8mhAAAAIElKefJpZZYrL0lyrFkl+7q1JicCAADIXxRt88C2bWe1RqhBP1t/9dgzSSpztUuS9MMPNi1ebDM5EQAAACRJwcFKHvyybzNs5HDv5WwAAAABgqJtHsjSz/Ymirb+KjjEo34vxfu2X3klSHFx5uUBAADAGWntOshVrbokyf7zdgUtX2pyIgAAgPxD0TYPbN9+dtGW9gj+rH6jNDVskiJJOnnSorFjg0xOBAAAAEmS1arkYa/6NsPGjpTSObcGAACBgaJtLsvIkH77zfuyXn2NSxFFaZTq754fEq+QEO/ldh9+aNf27bwtAAAA/EF646ZKb9BIkmQ98D8Fz/3A5EQAAAD5g+pULtu926LUVBYhK0hKlXGra49ESZLHY2jQoGBlZpocCgAAAJJhKHnYCN9m2OsTZCQmmBgIAAAgf1C0zWVnt0a4kUXICox2nZJ1XSXveP38s1WzZ9tNTgQAAABJctWuo9Q2D0qSLCdPKmTaFJMTAQAA5D2Ktrns7Evrq1anaFtQ2OxS/2FnFiUbOzZIx44ZJiYCAADAackvDpPHZpMkhf5nqoxjx0xOBAAAkLco2uay0zNtrVaPKlelaFuQ3HxLulq0dUqSEhMNvfIKi5IBAAD4A/f1FZX6+JOSJMOZrLBJ401OBAAAkLco2uYip1P6/XfvS1qhokvBISxCVtA82z9BRYp6FyVbssSu77+3XuIeAAAAyA/J/QfLHRYuSQr+aLas+/aYnAgAACDvULTNRTt2WJWZ+c8iZNVZhKwgiizm1jP9zixuMXhwsNLSTAwEAAAASZInKkopPZ+XJBmZmQobM9LkRAAAAHmHom0u+ukn+tkWBi0fcOqmmt6i+759Fr3zjsPkRAAAAJAk57O95I4qJUkK+vxT2bZsMjkRAABA3qBom4t++eXMpfRVb6JoW1BZLFL/YXGyWr3tLd56y6EDB1iUDAAAwHTh4UoeOMS3GTZyuOShJRkAACh8KNrmol27vC+n1erRtRUp2hZklaq49GDHZElSaqqhl14K5t8DAAAAfiC18+NyVawkSXJs+FGOlV+ZnAgAACD3UbTNJRkZ0h9/eF/Octe6FBRkciBcsSd7JiqqVKYkadUqm774wmZyIgAAAMhuV/JLr/g2w0a/KmVmmpcHAAAgD1C0zSX791uUnu69hL7iDS6T0yA3hIZ51GtwvG976NAgJSWZGAgAAACSpPT7WyujTrQkybZ7l4IWzTc5EQAAQO6iaJtLdu4881JefwOtEQqLO5um6tY7UiVJR45Y9NprTKEGAAAwnWEoefgo32bYhDFSSoqJgQAAAHIXRdtckqVoW5mibWFhGFKfl+LlcHgb2s6YYc8y1gAAADBHxm13KO3e5pIk65G/FDLzXZMTAQAA5B6qT7lk1y6r7/9pj1C4lLsmU52eSpQkZWYaGjQoSG63yaEAAACg5Jdflcfi/SdN6OQ3ZMTGmJwIAAAgd1C0zSWnZ1+GhbtV+ioWQihsOnZLUrlrvcX4TZtsWrCARckAAIAUExOjpk2bauPGjRc8Zv78+WrWrJlq166tZs2aad68eb7b3G63ateurVq1aql27dq+P06nMz/iF3iZN1ZTaoeOkiRLQrxC33rd5EQAAAC5g6JtLoiPlw4f9r6U11fOkGGYHAi5zuGQ+r0c59seOTJIMUzkAAAgoG3dulUdOnTQn3/+ecFjVq1apTfeeEMTJkzQtm3bNH78eL311lv6+uuvJUl79+5VRkaGNm3apO3bt/v+hIaG5tePUeA5B70kT3CwJCnkvXdl2b/P5EQAAABXjqJtLji7NcL1tEYotKJvS1fjFt5ZLzExFo0ezaJkAAAEqqVLl2rgwIHq16/fRY87duyYnn76adWqVUuGYah27dqqV6+eNm/eLEnasWOHqlSpIofDkR+xCyX31eWU8kxPSZKRkaHwEcNMTgQAAHDlKNrmAhYhCxw9ByYoNMzb0PajjxzatIm3EAAAgahBgwZauXKlWrZsedHjOnXqpO7du/u2T506pc2bN6t69eqSvEXbtLQ0PfTQQ6pfv746deqkbdu25Wn2wsjZp78yS5WWJAV9+bns69aanAgAAODKUHHKBWcXbVmErHArWcqtbr0TfduDBgXLxZADABBwoqKiZLNdXo/7EydO6Omnn1b16tV1//33S5KCg4N18803a9q0afruu+/UuHFjdevWTYcOHcqL2IWWJzxCyS+/4tsOHzpEymSdCQAAUHCxmlIuOLs9wnWVmGlb2LXtkKyvPg3Rnl0O7dxp1cyZdj33HOMOAAAu7KefflKfPn0UHR2tcePG+Qq+Q4YMyXJct27dtGTJEq1du1adO3c+53FsNuZcXIinSxe5Ppgp20/bZdv1m8IXzFX6E93MjnXFbDbrpQ9CocKYBx7GPPAw5sgOirZXyOORdu3ynjyXKetSeITH5ETIazab1H9ovHp0LimPx9DEiUFq08alsmUZewAAcK7Fixdr9OjRev755/Xkk09mue3NN99Us2bNVK1aNd++9PR0BQWdv3e+y+VWejozSC/EPXK8irVuJkkKGj1Cyfe3ladopLmhcgFjHngY88DDmAcexhyXwlf1V+jQIUNJSYYk6brKXCcfKKrdnKFW7byLkiUnGxo2jEXJAADAub7++mu9+uqrmjJlyjkFW0n6448/NGbMGJ04cULp6emaOnWqkpKS1LRpUxPSFnyu+rcptc2DkiTLqVMKfeM1kxMBAADkDEXbK5S1ny2XyAeS7n0SFFnc+83YZ5/ZtWYNlzcAAACpdu3aWr58uSRp6tSpyszM1PPPP6/atWv7/gwfPlySNG7cOF1zzTVq06aN6tWrp02bNumDDz5QZGSkiT9BwZY8fKQ8wcGSpJD33pV1/16TEwEAAFw+w+PxFNpruuPjnXk+3fyNNxwaP947y/KV12LUuHlqnj4fLs5usyrDlX+XGHy1PETjXi4mSbr2Wre+/z5ZISH59vSQ5HBYuawkwDDmgYcxDzxRURFmR/Bb+XF+WxiEjh+lsH9m2aY1b6mEOQtMTpRzfAYGHsY88DDmgYcxDzw5Ob9lpu0VOt3PVpKupz1CwGnWKkW1otMkSQcPWvT22w6TEwEAAMDZq58yS5eRJAV9tUL2td+anAgAAODyULS9QqfbI9jtHpW7lqJtoDEMqd/QeFlt3gnrU6c6tG+fYXIqAACAABceruShr57ZHDZEcnGuDgAACg6KtlcgJUXat8/7El5b0SWbzeRAMEWFii51eCxJkpSebmjw4GAV3qYjAAAABUPaw48oo/YtkiTb7l0Knjvb3EAAAACXgaLtFdizxyK32zurkkXIAttjzySpTFnv7I3vv7dp2TIq+AAAAKayWJQ0aoJvM2zCaBlxsSYGAgAAyD6Ktldg9+4zL991lSjaBrKQUI+eHxLv2x42LEgJCSYGAgAAgFy31lPqg+0kSZaYGIVNGGNyIgAAgOyhaHsF9u498/Jdez09sgLdHXen6Y67UiRJx49bNGFCkMmJAAAAkDxspDyhoZKk4A/ek3XHLyYnAgAAuDSKtlfg7KLtNddRtIXUe0iCgoLdkqRZs+z65RfeYgAAAGZyX11Oyf0HSZIMt1sRQwZIbrfJqQAAAC6OitIVOF20tdk8KlM20+Q08AdXXZ2px5/xLkrmdhsaNChYmfxqAAAAmCrl2V5yVawkSbJv3qigRfNNTgQAAHBxFG1zKDNT+t//vC/f1de4ZGPdKfyj/eNJqlDR2+N42zar5s61m5wIAAAgwDkcShr7mm8zfORwGfFx5uUBAAC4BIq2OXTokKG0NEMSrRGQld0u9Xv5zKJkY8YE6fhxw8REAAAAyLi7idLubyNJspw8oVAWJQMAAH6Mom0OZelnW4GiLbKqVTddzVo7JUnx8YZGjmRRMgAAALMljRzrW5Qs5P2Zsv66w+REAAAA50fRNodYhAyX8lz/BIVHeBe5WLTIrh9/tJqcCAAAILC5y5VXcr8XJJ21KJnHY3IqAACAc1G0zaGzi7blmWmL8yhWwq3ufRN824MGBSk93cRAAAAA8C5Kdn1FSZJ90wYWJQMAAH6Jom0O0R4B2dGqnVM31vBWav/4w6p333WYnAgAACDABQVlXZRsxDAWJQMAAH6Hom0OnS7aFiueqYiiXFKF87NYpP5D42WxeH9HXn/doUOHWJQMAADATBmN71Hafa0l/bMo2cSxJicCAADIiqJtDiQkSMePe186WiPgUm6olqG2jyRLklJSDL38MouSAQAAmC1p1Dh5QkIkSSGzZsj6268mJwIAADiDom0OZOlnyyJkyIZuvRJVvGSmJOmrr+z66isWJQMAADCTu1x5Oc9elGxwf8ntNjkVAACAF0XbHDi7aHstRVtkQ3iER70Gxfu2X3opWMnJJgYCAACAnM/1zrIoWfBHH5qcCAAAwIuibQ5kmWlLewRkU+PmqapTP02SdPiwRW+8waJkAAAApgoKUtLEN32bYSOHyzh2zMRAAAAAXhRtc+Dsou01zLRFNhmG1O/lONnt3kXJ/vMfh37/nbcgAACAmTIa3aXU9o9KkiwJ8QofNtjkRAAAABRtc2TfPu/LZrN5VKZspslpUJCUr5CpR59MkiS5XIYGDQqSx2NyKAAAgACXNGKs3MWLS5KCly2RY9XXJicCAACBjqLtZcrMlPbv975sV1/jks1mciAUOJ2fSlTZct4Z2uvX2/Txx3aTEwEAAAQ2T4kSShox1rcdPniAWIAAAACYyfSi7alTp9SjRw9FR0erXr16GjNmjFyu87cc2LRpkx5++GHVrl1bd955p6ZPn57PaaVDhwylpRmSaI2AnAkKlvoPO7Mo2auvBun4ccPERAAAAEhr/6jSG94lSbIe+lNhE8de/A4AAAB5yPSibd++fRUaGqp169Zp8eLFWr9+vWbPnn3Ocfv27VP37t3VsWNHbdu2TdOnT9f777+vr776Kl/znm6NIEnXsAgZcqju7Wlqer9TkhQfb2jo0CCTEwEAAAQ4w1DSa2/IE+Q9LwuZ/o5sv/xkbiYAABCwTC3aHjx4UJs2bdILL7ygkJAQlS9fXj169NC8efPOOfbjjz9WkyZN9MADD8gwDFWtWlULFixQnTp18jXznj1nXrLyFG1xBXq9kKCikd6eyMuW2bVypdXkRAAAAIEt8/pKcvYfJEky3G6FD+gjXeAqQAAAgLxkatF2z549ioyMVOnSpX37KlasqCNHjighISHLsb/88ovKlSun/v37q169emrRooU2bdqkqKiofM28d+9ZM21pj4ArEFncrR4vnPk9HzQoWElJJgYCAACAnD37yFX1RkmS/eftCpmV/y3ZAAAATC3aJicnKyQkJMu+09tOpzPL/vj4eM2ZM0etW7fWDz/8oJEjR2rChAm0R0CB1qxViurUT5Mk/fWXRePH0yYBAADAVA6HEidN9m2GjRsty+FDJgYCAACByGbmk4eGhiolJSXLvtPbYWFhWfY7HA41adJEd911lySpbt26atOmjb788ks1b978vI9vs+V+TXrvXu8l7MVKZKp4CdNbAuNfrHkw5nlt8IhEdWnjUFqqoZkz7erQwa06ddxmxyowbDbaSgQaxjzwMOYA8pvr1npKebybQj6cJcOZrPAhA5Qwd6FksHgsAADIH6YWbStXrqy4uDidPHlSJUuWlORdcKxMmTKKiIjIcmzFihWVnp6eZV9mZqY8Hs8FH9/lcis9PTPX8iYmSseOeU/Uyl/rUoYr9x4buaegjUvpspnq+lyipr9ZRB6PoV697Fq1yim73exkBUduvs9RMDDmgYcxB5Dfkoe+IsdXX8h67KiCvvlKQZ8uUVrbh8yOBQAAAoSp0xIrVKigOnXqaOzYsUpKStKhQ4c0bdo0tWvX7pxjH3nkEa1evVqffvqpPB6PNm/erM8++0xt2rTJt7wHDpx5ucpdS2sE5J72jyWpUtUMSdKuXVb95z8OkxMBAAAENk/RSCWNnejbDn9xoIwTJ0xMBAAAAonp15JPnjxZLpdLTZo0Ufv27dWwYUP16NFDklS7dm0tX75cknTbbbdp2rRpmjNnjurUqaMXX3xRgwcPVpMmTfIt68GDZ16usuWY8YPcY7NJL7waJ4vFO3N80iSH9u/n8jsAAAAzpd/fRmn3eyeJWE6dUsSQASYnAgAAgcLwXKy/QAEXH+/M1cspp061a+TIYEnSsAmxuqdlyiXugfxmt1kLXHuEs02dWESfzA2XJDVs6NLixSm0TrsEh8PKZdMBhjEPPIx54ImKirj0QQEqt89vcWnGiRMq3rCuLDExkqSEmbOV1ubBfHt+PgMDD2MeeBjzwMOYB56cnN+aPtO2IMk605b2CMh9T/ZKVJmy3t+tdetsWrjQ1LbTAAAAAc8TFaWk8a/7tsOHDKBNAgAAyHMUbS8D7RGQ10JDPeo3NN63/corwTpxgqm2AAAAZkpr82CWNgnhLw40OREAACjsKNpehtNF29Awt4oWc5ucBoVV/YZpatLCKUmKjTU0bFiQyYkAAAACnGEocfzrchcvLkkKXr5UjuVLTQ4FAAAKM4q22ZSZKR065J3xWLZcJn1Gkad6D05QkaLeLwaWLLFr9WqryYkAAAACm6dUqSxtEiIG95dx8qSJiQAAQGFG0Tabjhwx5HJ5K7VX0c8WeaxYCbd6DDzTJmHQoGAlJZkYCAAAAN42Cfe1lvRPm4QhA0xOBAAACiuKttlEP1vkt+ZtUnRLvTRJ0qFDFk2YQJsEAAAAUxmGEie8QZsEAACQ5yjaZtOBA2deKmbaIj8YhjRgeJwcQR5J0syZdm3fzlsWAADATJ5SpZQ0bpJvO2LIANokAACAXEcFKJsOHjzTxJaZtsgv5a7JVNdnEyVJbrehPn2ClZZmcigAAIAAl9b2oTNtEk6eVMTg/pLHY3IqAABQmFC0zaaz2yNcXZ6Ztsg/HR5PUuUb0yVJu3db9dZbDpMTAQAABLh/tUkI+myZghbNNzkUAAAoTCjaZtPpoq1heFS6LDNtkX9sdmnwyDhZbd7ZG2+/7dCvv/LWBQAAMJOnVCklvvaWbzv8xRdkOXjAtDwAAKBwofKTTafbI5Qqkym73eQwCDiVq7rUqVuSJMnlMtS3b7BcTPgGAAAwVXqrtkp9pJMkyZKUqCI9nhYnaQAAIDdQtM2GhAQpJsb7Ul1FP1uYpEv3RF1XKUOS9MsvVk2bRpsEAAAAsyWNnajMaytIkuybNyp08hvmBgIAAIUCRdtsOLufbdlyfHMOczgc3jYJFou3TcJrrzn0xx+8hQEAAMzkCY9QwrSZ8li852Whr42TbdsWk1MBAICCjopPNhw4cHbRlpm2MM+NNTLU/vFkSVJamrdNQia/kgAAAKZy1a0nZ78XJElGZqYinntKSkoyORUAACjIKNpmw+l+tpJUtjwzbWGuJ3skqNy13t/DLVuseu89miwDAACYzTlgsDLqREuSbP/br/DhL5qcCAAAFGQUbbMha3sEpjXCXEHB0qARcb7tsWOD9L//GRe+AwAAyDMxMTFq2rSpNm7ceMFj1q5dq1atWqlWrVpq0aKFvv322yy3z5w5U40aNVKtWrXUpUsX7d+/P69jIy/YbEp4Z6Y8oWGSpJCPPpTji89MDgUAAAoqirbZcHbRloXI4A9q1knXA496L7lLSTHUv3+w3G6TQwEAEGC2bt2qDh066M8//7zgMQcOHFDv3r3Vp08fbdmyRb1791bfvn117NgxSdLSpUs1d+5czZo1Sxs3btRNN92k559/Xh6PJ79+DOQi9/UVlTR2om87YkBvWY4dNTERAAAoqCjaZsPpom1omFtFI6mMwT9075uoMmW9bRJ++MGmDz+kTQIAAPll6dKlGjhwoPr163fJ46Kjo3XPPffIZrOpZcuWqlu3rhYuXChJWrRokTp27KjKlSsrKChIAwYM0JEjRy46cxf+LfXRzkq7r7UkyRITo4jnnxPfrgMAgMtF0fYSMjOlQ4e8l56XLZcpg6vQ4SdCQz164dU43/aIEUFZ+i8DAIC806BBA61cuVItW7a86HF79+7VDTfckGVfpUqVtHv37vPebrfbVaFCBd/tKIAMQ4mvv63M0mUkSY5vVyvk3XdMDgUAAAoam9kB/N2RI4ZcLm8h7KpyLEIG/xJ9W7rufyhZn/9fmJxOQ336BGvJkhRZ+DoGAIA8FRUVla3jkpOTFRISkmVfcHCwnE5ntm7/N5uNv+QLhDKllPruDIU94J1xGzb6FemO25VZ99bLfiibzZrb6eDnGPPAw5gHHsYc2UHR9hIOHDhzYnx1efrZwv/0GJigzT8G6djfNv34o03vv2/XU09lmB0LAABICgkJUWpqapZ9qampCgsLy9bt/+ZyuZWezjlpQZB+x10y+gxQ6Nuvy3C5FPLEY4pdvU6eYsUv/7EY84DDmAcexjzwMOa4FL6qv4Ssi5Ax0xb+JyzcoyGj4nzbo0YFaf9+2iQAAOAPbrjhBu3ZsyfLvr1796py5cqSpMqVK2e5PSMjQwcOHDinpQIKpuTBLyuj3m2SJOvhQ4ro/azEInMAACAbKNpewtk9QsuW41sQ+Kdb6qXrgUeSJUkpKYZ69w5RJr+uAACYrnXr1tq0aZNWrFghl8ulFStWaNOmTWrTpo0k6aGHHtJHH32k3bt3Ky0tTa+//rpKliyp6Ohok5MjV9hsSpj+vtwlSkiSgr75SiH/mWpyKAAAUBBQtL2Es2falmWmLfzYM/0SdHV57+/o5s1Wvfuu3eREAAAEptq1a2v58uWSpIoVK+qdd97R9OnTVbduXU2bNk1TpkzRddddJ0lq166dunbtqp49e6p+/frauXOnpk+fLrudv8cLC3fZq5XwzgzfdtjoV2TbvNHERAAAoCAwPJ7Ce31OfLzzinuENGsWqu3brTIMj1Zu/VucP/s3u82qDFfgTjH9ZZtDz3ctIY/HUFCQR6tWOVWlitvsWHnK4bDSCyjAMOaBhzEPPFFREWZH8Fu5cX4Lc4SOHamwtyZJkjKvLqfYNf/NVn9bPgMDD2MeeBjzwMOYB56cnN8y0/YSDh3ytkcoWcpNwRZ+7+Zb0vVwF2+bhLQ0Q88/HywXE8QBAABM5xz0ktLr3y5Jsv51mP62AADgoijaXkRKinTypPclKn0V34CgYHiqd4KuqZAhSdq+3aopUxwmJwIAAIBsNiXS3xYAAGQTRduL+PvvM4uQlbqK6YooGIKCpRfHxMli8c7cmDTJoV9/5a0OAABgNvdVZZXwzkzfNv1tAQDAhVDJuYi//jrz8pQuw0xbFBzVbs7Qo08kSZIyMgz17h2s9HSTQwEAAEAZje9Rct+BkiTD5VKRpx6Xcfy4yakAAIC/oWh7EX/9dWamLe0RUNB07ZGo6yp52yT89ptVkybRJgEAAMAfOAe9pPTb7pAkWf8+oiJPPy5lZJicCgAA+BOKthdx+PCZl6cUM21RwDgc0ktj4mS1edskTJ7s0MaNVpNTAQAAQDabEmbMVuZVZSVJjvU/KHz4iyaHAgAA/oSi7UWcPdO2FDNtUQDdUC1DT/RIlCS53YZ69gxWYqLJoQAAACBP6dJKeH+uPA7v1VAhs2YoaME8k1MBAAB/QdH2Is6eaUt7BBRUHZ9MUvVa3oa2f/5p0bBhQSYnAgAAgCS56tRV0oQ3fNsRL/SVbftWExMBAAB/YTM7gD87csQ70zYkxK2IIh6T0wA5Y7VKL4+N1ZPtopTitOjjjx26995MtWzpMjsaAAD57uDBg1q/fr0OHz6sxMREFStWTFdffbUaNGigq666yux4CECpnR6T7eftCpk9S0Zamoo80VmxK7+XJyrK7GgAAMBEFG0vwOOR/vrLO9O21FWZMoxL3AHwY2XLZ6r3kHhNHF5MkjRgQJDq1MlU6dJ8GQEACAyrVq3SjBkztGPHDnk8HhUpUkQhISFKSEhQSkqKDMPQzTffrGeeeUaNGzc2Oy4CTNLoCbLt/E32TRtkPfKXijz1mOIXL5fsdrOjAQAAk9Ae4QJiYyWn01upZREyFAYt26aoQeMUSdKpUxb16xcsDzVbAEAh99dff+mxxx7Tyy+/rKpVq+r999/Xli1btGnTJq1du1bbt2/Xxo0bNXXqVFWtWlUvvPCCHn30UR06dMjs6AgkDofiZ81VZhnvbG/H+h8U9spLJocCAABmomh7Aadn2UosQobCwTCkF16JV/ES3t/nVats+vBDZm8AAAq3Tp06qXHjxlq3bp1Gjhyp2267TeHh4VmOKVq0qJo0aaIRI0Zo3bp1aty4sTp37mxSYgQq38Jk/8yuDX1vOguTAQAQwCjaXkCWRciYaYtCIrK4W4NHxvm2X301SPv20fsDAFB4LVmyRF27dpXD4cjW8aGhoXr66ae1dOnSPE4GnMsVfauSxr/u2454oa+sW7eYmAgAAJiFou0F/PXXmUJWaWbaohCp3yhNrdsnS/K2AOnZM0QZGSaHAgAgjxQvXtz3/6+++qq2b99+2fcD8lNql65KeexJSZKRlqbQRx+W5TDtOgAACDQUbS+A9ggozHoMSFC5a12SpG3brHrzzezNPgIAoCD77LPPlJqaanYM4JKSxk5U+m13SJIsx4+raKf2MhITTE4FAADyE0XbCzh7pi0LkaGwCQn1aOi4WFmt3pXI3njDoQ0brCanAgAgb9WoUUPff/+92TGAS3M4lPDBR3Jdd70kybbrN0V0f0JyuUwOBgAA8ostp3dMSUnRli1bdPjwYSUmJqpYsWK6+uqrFR0dne2eYf7s7J62UaUp2qLwubFGhh5/NlHvv1NEbrehHj2CtWZNsiIjzU4GAEDeqFKliubOnauvv/5alSpVUokSJbLcbhiGxo4da1I6ICtP8RJK+PgTRba4R5a4WAWtXqnwYUOUNG6S2dEAAEA+uOyi7a5duzRjxgytWrVKGedphBkSEqK7775b3bt3V9WqVXMlpBlOz7QtXiJTQUEmhwHySOenk7R1Q5B+3hqkw4ctGjgwWDNnpspgbTIAQCG0cuVKlSpVSpK0d+9e7d27N8vtBn8Bws9kVqws50fzFfZAKxkZGQqZNUOuipWU+tSzZkcDAAB5zPB4PJ7sHJiUlKTRo0frs88+U/369dW8eXPVqFFD5cqVU0hIiOLj43X06FFt2bJF69at048//qgWLVpo2LBhKlq0aF7/HOcVH+9Uevrlz5LNyJDKlQuXx2OoavV0TZ9/Mg/SIS/YbVZluJgZfTmOH7XoyYdKKTHBO7v8zTdT1alTwVmZzOGw5uh9joKLMQ88jHngiYqKMDuC38rp+S0KLofDKmPOHBV5/jlJksdiUcLcBUpv2tzkZMgr/L0XeBjzwMOYB56cnN9mu6dtmzZtFBERoe+++06zZs3Sww8/rKpVqyo8PFxWq1XFixdXtWrV9Nhjj2nmzJn6+uuvFR4ergceeOCyQ5nt6FFDHo93pkVpFiFDIVeqjFuDRsT5tl9+OUh79tDuGgBQOOzfvz9H99u3b18uJwFyLu2RTkruO1CSZLjdiuj+pKy/7jA5FQAAyEvZrszMmDFDL7/8sqKiorJ1fLly5fTqq69q5syZOQ5nlr/+OvOylKKfLQJAo3tS1frhZEmS02nomWeClZZmcigAAHJB9+7dNXbsWJ08mb0rp/7++2+NHDlS3bt3z+NkwOVxDhmq1NbeCTGW5CQV7dxelmNHTU4FAADySraLthUrVvT9/7vvvqs9e/Zc9v0KisOHz/QzK8VMWwSIni8kqEJFb1uEX3+1avRomjkDAAq+ZcuWKSEhQXfddZe6deumTz75RLt371ZSUpLcbrfi4uK0e/duzZs3T88884yaNm2q+Ph4LVmyxOzoQFYWixKnvKuMOtGSJOuRv1SkU3sZSYkmBwMAAHkh2z1tzxYdHa033nhDjRo1yotMuSanPb/eftuhMWO8BauRb8TozqapuR0NeYSetldm3+82PdsxSunp3i8u5s93qkkT/3496QUUeBjzwMOYB5686Gn722+/afr06VqzZo0yM8/9fQoKClKjRo3UvXt3Va9ePdefP7fQ0zbw/Psz0Dh+XMVaNJb10J+SpPSGdyn+40/E6smFB3/vBR7GPPAw5oEnJ+e3tpw8UYUKFbRnzx6/L9rmFDNtEagqVnHp2f4Jmjzeu3hg797B+vZbp0qXvuzvdgAA8Cs33XSTJk+eLKfTqS1btujQoUNKSkpSsWLFVLZsWUVHRys4ONjsmMAleUqVUvz8/1Nkq3tliY2VY913iuj1jBKnvy9ZWJcAAIDCIkdF27vuuktvvvmmvv32W1WuXFklSpTIcrthGOrZs2euBDTD2T1tS5ehaIvA8mDHZG1eH6T1a4N18qRFvXsHa8GCFP4NAAAoFEJDQwvtxAMEjswbqij+o0WKbNdaRkqKgj9dIk/Jkkoa+5pkGJd+AAAA4Pdy1B6hatWqF39Qw9CuXbtyHCq35PTysTvvDNWuXVbZ7R59s+VvilUFCO0RckdcjEVPtovSqRNWSdLQoWl6/vl0k1OdH5eVBB7GPPAw5oEnL9ojFBa0Rwg8F/sMdKz8SkUee1TGPy0/kocMlbP/oPyMhzzA33uBhzEPPIx54MnJ+W2OirYFRU5PaitVCldCgqGry7v08YrjeZAMeYWibe7ZusGhAd1LyOMxZLV6tHRpiurX97/Xlr/sAg9jHngY88CT20XbH374QZZsfAv/119/qV27drn63LmNom3gudRnYNDCj1Wk97O+7cTXJyu1S9d8SIa8wt97gYcxDzyMeeDJ0562sbGxKlas2GU/QU7vZ5aEBCkhwXtJEf1sEcjq1E9Xl+5JmjM9QpmZhp55Jlhr1jhVokSh/Z4HAFBI/fDDDxo06NKzDydOnJgPaYDcldaho5JOnFD4yGGSpPAX+spdvITS72tlcjIAAHAlsn3h/4MPPqgPP/xQ6enZu0Q6NTVVs2bN0gMPPJDjcGagny1wRtfnElWrbpok6e+/LerZM1hut8mhAAC4TIX4wjJAkpTSq4+cz/WWJBlut4o8+6TsP/7X5FQAAOBKZLtoO3fuXK1Zs0YNGzbU8OHDtX79eiUlJWU5JjExUWvXrtXIkSPVsGFDrVq1SnPnzs310Hnpr7/ONO5npi0CndUqDZ8Qq2LFve+FNWtsmjrVYXIqAAAuj8HCTAgAya+MUmq7DpIkIy1NRbo8ItuOn01OBQAAcirb7RHKlSunDz/8UN98841mzJihRYsWyTAMFSlSRCEhIUpISFBKSoo8Ho+qVaumMWPG6N57783L7Hni7Jm2pZhpC6hElFtDx8dq4DPe/rbjxjl0662ZftnfFgAAIGBZLEp8e5qM2BgFrV4pS2KCij7cRnFLVyjzxmpmpwMAAJcp20Xb0+69917de++92r9/vzZs2KDDhw8rKSlJxYoVU9myZXXHHXeoXLlyeZE1X5w907Y0M20BSVL0bel67Jkkffiut79t9+7e/rYlS3K5KQAAgN+w25Xw3hxFtm8r++aNssTEKPKhVor79EtlVr7B7HQAAOAyXHbRVpKOHDmi4OBg3XXXXRe8vWzZsleSyzRHjpyZaRtVmqItcNrjzybql20Obd8UpKNHvf1t589PUTYW4wYAAEB+CQtT/PzFKvpwG9m3b5Pl5AkV/adw677uerPTAQCAbMpR0bZx48aX7A22a9euHAUy29GjZ36ukqUo2gKnWa3SsAmxeqpdlGJOWfXttzZNnuxQ377ZW5wQAAAA+cNTpKjiFy5V0Qdbyf7rL7Ie/ds349Zd/hqz4wEAgGzIUdF27Nix5xRtnU6ntm7dqg0bNmjs2LG5Es4Mx455f66gYLfCI7j0GzhbiZJuDZsQq/5Pe/vbjh/v7W97++18wQEA8F/h4eFav379JY9LTEzMhzRA/vBEFlP8omWKfPA+2XbvkvXwoTOF26sK5lWRAAAEEsPj8eRqZXLChAk6fvy4Xn/99dx82ByJj3cqPf3yikmVK4crPt7Q1eVd+njF8TxKhrxit1mV4aKAmNdm/ydcH0wrIkkqVcqt1audKl3anC85HA7rZb/PUbAx5oGHMQ88UVERZkfwWzk5v0XBdqWfgcaxY4ps20K2fXslSa5KlRW37Et5SpXKrYjIZfy9F3gY88DDmAeenJzf5no3yrvuukvfffddbj9svnA6pfh470xbWiMAF9ale5Lq1E+TJB0/btFTTwUrI8PkUAAAXAG32605c+aYHQPIdZ7SpRW/5HNlXltBkmTbu0eRD7eWceqUucEAAMBF5XrR9qeffpLNlqOuC6Y7u59tCYq2wAVZrdLwCbG+xfo2brRpxIggk1MBAHB+//3vf9WvXz/169dPa9euPef2zZs3q23btho3bpwJ6YC8576qrOKWfK7McuUlSbZdOxXZrrWMkydNTgYAAC4kR9XVF1988Zx9brdbf//9t7Zs2aJ27dpdcTAzHDt2poZdMsptYhLA/0UWd2vUmzHq/XhJZWQYmjHDoVtuydSDD7rMjgYAgM+KFSvUv39/ORwO2e12ffXVV5o8ebKaNm2q2NhYjRkzRl988YWsVqueeOIJs+MCecZd/hrFLV6uyLYtZT36t2y/7VDkAy0Vv3i53KXLmB0PAAD8S46Kths3bjxnn2EYCg8P19NPP61nn332ioOZ4eyZtrRHAC7txhoZen5IvF4fFSlJ6t8/WFWrOlWtGl96AAD8w+zZs1WzZk3NmjVLDodDQ4cO1TvvvKOKFSvqySef1NGjR9WwYUO99NJLuu6668yOC+Qp9/UVFb/0cxV9sJWsfx+R7ffdKtqmheKXfC532avNjgcAAM6So6LtmjVrcjuHX8jSHoGZtkC2tHrYqZ07HPpyWaicTkNPPBGilSuTVaSI2ckAAJD279+vkSNHKjw8XJLUq1cvNWvWTL169ZLL5dKUKVPUtGlTk1MC+SezYmXFffqlItu1lvXPg7Lt36fI1i0Ut+Qzua+51ux4AADgH7ne07YgO3r07PYIzLQFssMwpH4vx6nyjemSpP/9z6JevYLl5nsPAIAfSE5O1lVXXeXbLlOmjDwej2w2m5YvX07BFgHJXeE6xS1bIdd110uSrH8eUGTr5rLu32tyMgAAcBpF27McO0Z7BCAngoKlUW/EKqKIt1L71Vd2TZ7sMDkVAACSx+OR1Wr1bZ/+/z59+qh48eJmxQJM5y5XXvGffilX5RskSdYjf6lo6xay/r7b5GQAAECiaJvF2e0RitMeAbgsV5XL1LAJsTIMjyRp3DiHvv3Weol7AQBgjjJlWHgJcJe5SnHLvpSrWnVJkvX4MUU+0FLWX3eYnAwAAFC0Pcvp9ghh4W6FhnpMTgMUPPUapOmJHomSJI/H0LPPhujPP41L3AsAgPxnGPz9BEiSJypKcUs+U0bN2pIky8mTinzwPtm2bjY5GQAAgc3weDyFtjoZH+9Uenr22hx4PNJ114XL6TR0zXUZmrv8RB6nQ16w26zKcNHawkxut/TS88W1fm2wJKlatUx9/rlT/6z/kuscDmu23+coHBjzwMOYB56oqIhce6yqVauqWrVqvoXIPB6PNm/erJtuuklhYWFZjjUMQx9++GGuPXdeuJzzWxQO+fUZaMTHqeij7WTfskmS5AkNVcKsOUpvcm+ePzey4u+9wMOYBx7GPPDk5PzW9Jm2p06dUo8ePRQdHa169eppzJgxcrlcF73PH3/8oZo1a2rjxo25liMpSXI6vTMuSpaiNQKQUxaL9PLYWJW71vs+3rnTquefZ2EyAIA56tatq7CwMHk8Hp2eq1C3bl2Fhob69p3+476Mv6yyew771FNPqXbt2ln+VKlSRcOHD5ckud1u1a5dW7Vq1cpyjNPpzJ0XAMgmT9FIxS9aqvQGjSRJhtOpIl0eUdCi+SYnAwAgMNnMDtC3b1+VLl1a69at08mTJ/Xcc89p9uzZeuqpp857fEpKigYMGKDU1NRczfH332fq1yxCBlyZiCIejZkco+c6lpQz2aLPP7frjTfcGjgw3exoAIAAM3fu3Dx53Oyew7733ntZthcvXqypU6eqV69ekqS9e/cqIyND27Ztk8PBIp4wlyc8QvHz/09FejytoM+WyXC5VKTXM0o6eVIpPXqbHQ8AgIBi6kzbgwcPatOmTXrhhRcUEhKi8uXLq0ePHpo3b94F7zNixAjdc889uZ7l7EXISkZRtAWuVIXrXRo+8czCZBMnBumLL0z/nggAgCuWk3NYSdq/f79GjRqlSZMmqVSpUpKkHTt2qEqVKhRs4T+CgpQw4wOlPPm0b1f4qy8r7NWh4tIpAADyj6lF2z179igyMlKlS5f27atYsaKOHDmihISEc45ftmyZDh486JuZkJvOLtqWoD0CkCtua5Sm7n0Sfds9ewZr507Tu7IAAHBFLvcc9rQRI0aobdu2io6O9u3bsWOH0tLS9NBDD6l+/frq1KmTtm3blqf5gUuyWpU0bpKShwz17QqdNlkRvZ+VMjJMDAYAQOAwddpbcnKyQkJCsuw7ve10OlWkSBHf/n379unNN9/U/PnzZbVas/X4Nlv2i0MnT555zNJlPLLbsvcc8C/Wyxhz5I/Huqfof3vt+ubzEDmdhh5/PERr1qSqRInceXwb79WAw5gHHsYc/uZyzmFP27Jli37++WdNmjQpy/7g4GDdfPPN6tOnj4oWLap58+apW7duWr58ucqXL3/O41zO+S0KBzM/A11DXpTzqjIK6fe8DLdbwZ8skDUuRs7ZH0n/WsgPuYe/9wIPYx54GHNkh6lF29DQUKWkpGTZd3r77NV809LS1K9fP7300ksqW7Zsth/f5XJnezW+v/4681IUK5GhDBctEgoqxs7/DHwlVgf3W/X7TocOHrTo8ccdWrgwRXZ77jw+q24GHsY88DDm8CfZPYc928KFC9WiRQtFRUVl2T9kyJAs2926ddOSJUu0du1ade7c+ZzHuZzzWxQeZo55+qOPKaNocRV55gkZaWmyr/xGofc3V/ychfKcNdscuYv3eeBhzAMPY45LMfWr+sqVKysuLk4nT5707du3b5/KlCmjiIgI374dO3bowIEDevnllxUdHe27pOzZZ5/Vq6++mitZsrRHiKI9ApCbgoKl0W/HqHgJ719K//2vTcOHB5mcCgCAnMnuOexpLpdLq1evVuvWrc+57c0339TOnTuz7EtPT1dQEH9Pwn+kt7xf8YuWyV2kqCTJvn2birVoLOvO30xOBgBA4WVq0bZChQqqU6eOxo4dq6SkJB06dEjTpk1Tu3btshwXHR2tX375RVu2bPH9kaR33303F4u2Z16KEixEBuS6UmXcGvVWjOx278Jks2Y5NGdOLk21BQAgH2X3HPa033//XWlpabrlllvOue2PP/7QmDFjdOLECaWnp2vq1KlKSkpS06ZN8/rHAC5Lxm13KG75V8os523bYT18SJH3NZVj1dcmJwMAoHAyvSnW5MmT5XK51KRJE7Vv314NGzZUjx49JEm1a9fW8uXL8yXHsWPembZFIzPF4r1A3qheK0P9hsX5tocMCdL339PLBwBQ8FzOOeyhQ4dUtGjR886eHTdunK655hq1adNG9erV06ZNm/TBBx8oMjIyv34UINsyq92k2C/XKKO29wsIS3KSinTuoOD33jU5GQAAhY/h8Xg8ZofIK/Hxzmz1CPF4pPLlw5Webuj6yhn6YMmJfEiHvGC3WelpWwBMnVBEn3wULkkqUsSjFSucuuGGnLUlcTis9AIKMIx54GHMA09U1LktBuCV3fNbFB5++RnodKpI72cV9Nky366Ubt2VNGq8ZDN12ZRCwS/HHHmKMQ88jHngycn5rekzbf1BbKyUnu6daVuyFG8aIK89NzBBt92ZKklKSDDUsWOITp40LnEvAAAA+IXQUCXMnC1nnwG+XSGzZqhIlw4yEhNMDAYAQOFB0VbS33+feRko2gJ5z2qVhk+MVaWqGZKkP/+06PHHQ5SaanIwAAAAZI/FouSXX1HC5P/IY/euUxC0eqUi728my8ED5mYDAKAQoGirM/1sJalkVM4u0QZweUJDPRo35ZTvi5LNm63q2zdYhbdhCwAAQOGT9kgnxX/yqdz/9GG27fpNxe69U/bv1pgbDACAAo6iraSjR88UbUsw0xbIN6XKuDVuSoyCQ7xflixZYtfEiawECAAAUJBk3N5AcV+ulqtiJUmSJTZWRR95UCFT3xbfyAMAkDMUbSUdPXpWewRm2gL56oZqGRo2Pk6G4T2hf/31IC1axAIWAAAABUlmxcqK+/pbpd3bXJJkuN0KHzlMEd2fkJKTTU4HAEDBQ9FWzLQFzNagcap6DDyzaEW/fsFav95qYiIAAABcLk+RokqYs0DJA4f49gV/ukTFWt4jy//2m5gMAICCh6KtshZtS0ZRtAXM8HCXZLVu752FkZFhqGvXEO3bZ1ziXgAAAPArFoucg15S/JwFcodHSPqnz22zu2Rfs8rkcAAAFBwUbSUdO+Z9GQzDo2IlaI8AmMEwpD4vxuvWO1IlSbGxhjp0CM2yUCAAAAAKhvTmLRX39bdyVb5BkmSJi1PRRx9S6JuvSW7+zQUAwKVQtNWZmbbFSrhlo5UmYBqbTXp1Uqwq3pAhSfrzT4s6dgxRUpLJwQAAAHDZMivfoLiv1iit+X2SJMPjUdi4USr66EMyTp40OR0AAP4t4Iu2mZnS8ePeoi2tEQDzhYV7NPE/p1T6KpckaccOq554IkTp6SYHAwAAwGXzRBRRwux5Sh78sjyG999djm9Xq1jjO2Rf/4PJ6QAA8F8BX7Q9edJQZqb35KFEKS7TAfxByVJuTXw3RhFFvO/JtWtt6ts3mCvpAAAACiKLRc4BgxX/yadyR5WSJFmP/q2iD9xHuwQAAC4g4Iu2LEIG+KcK17s0/p1TcgR5JEmLF9s1erTD5FQAAADIqYxGdylmzQ9Kb3inJMlwu73tEh55UMaJEyanAwDAv1C0PbtoW4qiLeBPqtfK0PAJsbJYvIXbqVODNHOm3eRUAAAAyClP6dKKX7RMyS+8eKZdwndrvO0SfvyvyekAAPAfAV+0PX78zEtQvCSX5QD+pmGTVPV9Od63PXRokJYvZ8VAAACAAstqlfOFF7O2Szh2VEUfvF+h40dJGRkmBwQAwHwBX7Q9ceLMTNviJSjaAv6oTXunHuueKEnyeAz16BGsH3+0mpwKAAAAV+K87RLeeE2R9zeVdd8ek9MBAGAuirZnFW2LlaA9AuCvnuyVqJYPJEuS0tMNdekSol9+CfiPMAAAgALN1y7hxWHy2LxXU9m3b1OxJg0VPOcDyeMxOSEAAOYI+IoHM22BgsEwpAHD4lW/YaokKTHRUIcOIfrjD+MS9wQAAIBfs1rl7PeC4r5YKVfFSpIkw+lUxMA+KvLYIyxSBgAISBRts8y0pWgL+DObXRrxeqxq3JImSTp1yqK2bYP0558UbgEAAAo6V+06il21TimPd/PtC/r6SxW/s74cK78yMRkAAPmPou0/RduQULeCQ7j0BvB3wSEejZ8ao8o3pkuSjhyx6OGHQ3XsGIVbAACAAi8sTEmvvan4uQvlLllSkmQ5eUJFO7VX+MC+MpISTQ4IAED+oGh7wvsS0BoBKDjCIzya9G6MrrnOu7Lw//5nUfv2IYqLMzcXAAAAckd6sxaK+W6D0po28+0LmfO+ijWqL/u3q01MBgBA/gjoom1amhQf752dR2sEoGCJLO7W6zNOqUxZ7wKCu3ZZ9eijoUpKMjkYAAAAcoWnVCklfLRIiRPflCc0TJJkPXxIkR0eUHi/XjIS4k1OCABA3gnoou3Jk2f3s800MQmAnChVxq23Z8Wq+D/v361brXr88RClppocDAAAALnDMJTatZti1q5XeoNGvt0h8+aoWKP6cqz+xsRwAADknYAu2rIIGVDwla+QqUnTTyk8wvseXrfOpmeeCZbLZXIwAAAA5Br3tRUUv3i5Eie+KXdYuCTJeuQvFX20nSJ6PysjLtbkhAAA5C6Ktv+gpy1QcFWs4tLE/5xSSIj3ffzll3b17EnhFgAAoFCxWJTatZtiv9+g9Dvv9u0OXvixijWsJ8dnyyQPi0sDAAoHirb/iCxOewSgILupZoZGvx0ju917or50qV29ewcrk7c2AABAoeIuf43iFy1T4htT5I4oIkmyHjuqot0eU5HO7WX586DJCQEAuHIBXrQ98+Mz0xYo+KJvS9fot2Jks3kLt//3f3b16UPhFgAAoNAxDKV2flyx329QWtNmvt1BK79W8Ub1FDLlLSkjw7x8AABcoQAv2tLTFihs6jdK08g3zxRuFy2ya8CAILl5iwMAABQ67qvLKeGjRYqfNUeZpctIkgynU+GjhqvYPY1k27zR5IQAAOQMRdt/nF59HkDBd8ddaXplUqysVm/h9uOPHXrhBQq3AAAAhZJhKL1VW8X+sFkp3brLY3j/nWfb9Zsi779X4QP7slAZAKDACeii7cmTzLQFCqtGTVI1bMKZwu3cuQ4NGRLE2hQAAACFlKdIUSWNm6S4r9Yoo0ZNSZLh8ShkzvsqfnsdBX/0oeibBQAoKAK6aHt6pq0jyKPQMCo5QGFzd7NUvTwuVhaL9/09e7ZDL79M4RYAAKAwc9Wuo7ivv1XSyLHyhIZJkiwnTyqif29FNm9MywQAQIFA0Vbe1giGcYmDARRITVqk6qUxcTIMb6X2vfccGjaMwi0AAEChZrMp5dleivlhs1LbPOjbbf95u4rd11QRPbvLcuyoiQEBALi4gC3aulxSTIy3UktrBKBwa3p/ioaMOlO4nTHDoUGD6HELAABQ2LmvLqfEmbMVt/QLuW68ybc/+JMFKlb/FoVMeUtKSzMvIAAAFxCwRdtTpwx5PBRtgUDRvE2KBo04U7j98EOH+vYNpq0ZAABAAMi4o6FiV69T4rhJckdGSpIsyUkKHzVcxe6sL8eKz8WlWAAAfxKwRdvjx89ehIyqDRAIWj6QopfHxfkWJ1uwwK6ePYOVkWFyMAAAAOQ9m02p3borZv12pTzeTZ5/euTZ9u9T0a4dFdm6uWxbN5scEgAAr4At2p7uZytJxYsz0xYIFE3vS9Err8XKZvMWbpcssevpp4OVnm5yMAAAAOQLT4kSSnrtTcWuWqf02+7w7bdvXK9iLZooontXWQ4eMC8gAACiaCuJ9ghAoLmzaapGvRUju91buF2xwq4nnghRaqrJwQAAAJBvMmvcrPhlKxT/4Xy5Klby7Q9etkTF74hW2PCXZMTGmJgQABDIKNqK9ghAILr9zjSNmxqjoGDvlzYrV9rUuXOIkpNNDgYAAID8YxhKb3GfYr/fqMTxr8tdsqR3d3q6Qt+dquL1ainknclSSorJQQEAgSaAi7ZnfvTizLQFAlLd29M0cVqMQkK9nwHff2/To4+GKDHR5GAAAADIX3a7Up98WjEbf1Jy34HyBAdLkixxcQofMVTF69VS8AfviZ5aAID8EsBFW9ojAJBq1U3XpOmnFBbu/RzYsMGmBx4IzfIZAQAAgMDgiSgi50vDFbN+m1I7dPQtVmY9+rciBvdX8dujFbTwYymTqzUBAHmLoq2k4rRHAAJa9VoZevO9Uyoa6f0s+OUXq1q1CtWff1K4BQAACETuq8spccq7iv1uvdJatvLtt/55QEV6P6tid9aX47NPJY/HxJQAgMIs4Iu2drtH4UX4ixYIdFVuytDkD08pqrS3cLt/v0X33x+qXbsC9mMSAAAg4GXeWE0Js+cp9utvlX5XY99+2x+/q2i3LopseqccX62geAsAyHUBW404XbSNLO6WwWQ6AJIqXO/SO3NP6poKGZKko0ctatMmVJs2BexHJQAAACS5atdR/KJlilu2Qhm31vftt//yk4o+9ogimzSU4/PlkpvWewCA3BGQlYjMTOnUKW+lltYIAM5W+qpMTZlzSlWrexeZiIsz9PDDoVq92mpyMgAAAJgt4/YGivvsa8V//IkyatT07bf/+ouKPtlZxe6+XUGfLqHnLQDgigVk0TYmxpDb7S3asggZgH+LLObWm++dUp36aZKklBRDXbqEaPFim8nJAAAAYDrDUPo9zRS36nvFz12ojFq1fTfZdu1Ukae7qtid9RW05BOKtwCAHAvIou3Zi5BRtAVwPqFhHo1/55TuujdFkuRyGerRI0TTp9tNTgYAAAC/YBhKb9ZCcV9/p/j5i5VRJ9p3k+2P31Xk2W4qdnsdBc/5QEpNNTEoAKAgCviiLe0RAFyIwyENnxir1u2TffuGDQvW0KFBTJoAAACAl2Eovcm9iluxWnGLlmXpeWv7335FDOyjEnWqK2TyGzIS4k0MCgAoSAK+aMtMWwAXY7VK/YfG6/FnE337ZsxwqFu3YDmdJgYDAJjq1KlT6tGjh6Kjo1WvXj2NGTNGLpfrvMc+9dRTqlGjhmrXru378/333/tunzlzpho1aqRatWqpS5cu2r9/f379GAByk2Eo467Givvsa8Ut+VzpDe/y3WQ5cVzho19V8VrVFDZimCxH/zYvJwCgQKBoS9EWwCUYhvRkz0QNGhEnq9UjSVqxwq6HHgrN8nkCAAgcffv2VWhoqNatW6fFixdr/fr1mj179nmP/fXXXzVr1ixt377d96dRo0aSpKVLl2ru3LmaNWuWNm7cqJtuuknPP/+8PB5PPv40AHKVYSijQSPF/99yxX7znVJbPyCP4T1ntCQlKvSdt1U8uobC+/WSdfcuk8MCAPxVwBdtaY8AILvue9CpCdNiFBrm/bJn61arWrYM1d69FG4BIJAcPHhQmzZt0gsvvKCQkBCVL19ePXr00Lx588459tChQ4qPj1e1atXO+1iLFi1Sx44dVblyZQUFBWnAgAE6cuSINm7cmNc/BoB84Kp1ixLf+1Cx67cqpcsT8gQFSZKM9HSFzJuj4o3qqWj7trKvWSnxZQ0A4CwBWrQ982Mz0xbA5ah7e5qmfHhSUaW8X/gcPGjRffeFacMGq8nJAAD5Zc+ePYqMjFTp0qV9+ypWrKgjR44oISEhy7E7duxQWFiY+vXrp/r16+v+++/X4sWLfbfv3btXN9xwg2/bbrerQoUK2r17d97/IADyTeb1lZT0+ts6teVXOZ/vL3dEEd9tju/WKPKRh1Ss4a3eRctSUkxMCgDwFwFatD2rPUJxirYALk+lKi5Nm3dCFW/IkCTFxhpq1y5Ey5bZTE4GAMgPycnJCgkJybLv9LbzXw3P09PTVatWLfXr10/r1q3TkCFDNGbMGH355ZcXfKzg4OBzHgdA4eApXVrJQ19VzE87lTR6vDKvqeC7zfbH74oY2EcRN1VR6NiR9L0FgAAXkBWG00Vbq9WjIpEUbQFcvlJl3Jry4Um9MqCYNv8YrPR0Q927h2jv3jQNGJAug44JAFBohYaGKuVfM+FOb4eFhWXZ37ZtW7Vt29a33aBBA7Vt21ZffvmlWrRooZCQEKWmpma5T2pq6jmPc5rNFpBzLgKazcbVPIVSiWLK7NVbSc/1kG3FFwqaNlW29T9IkiwxpxT21iSFTnlTrvtbK+2p7sps0FCcYBZevM8DD2OO7Ajoom3RYm5ZOO8FkENh4R6NnxqjN0YX1RdLvP+4njgxSL//btHbb6cqNNTkgACAPFG5cmXFxcXp5MmTKlmypCRp3759KlOmjCIiIrIcu3jxYoWFhalFixa+fenp6Qr6p69l5cqVtWfPHt19992SpIyMDB04cCBLy4SzuVxupaezJkOgYcwLt/Rm98nZ7D7Zft6ukOnTFLTs/2S4XDIyM2X/dKnsny6Vq0pVpXR9SmntH5HnrNYKKDx4nwcexhyXEnAlS7dbOnnSW7QtTj9bAFfIZpdeeDVez/RNkGF4F4/49FO7WrcO1ZEjzIYAgMKoQoUKqlOnjsaOHaukpCQdOnRI06ZNU7t27c45NikpSaNGjdLOnTvldrv13Xff6fPPP1eHDh0kSQ899JA++ugj7d69W2lpaXr99ddVsmRJRUdH5/ePBcBkrpq1lThtphJ37FZy/0FyR5Xy3Wb7fbciXhyo4jdXVfjg/rLu2mliUgBAfjA8nsK7RGV8vPOcby5iY6UqVbwzIOrenqpJ02PMiIY8YrdZleHi26pA4k9j/sN3QRo1uJhSnN7vw0qVcmv27BRFR/MFUW5yOKx8Kx1gGPPAExUVcemDTHby5EmNHDlSGzdulMViUdu2bTVw4EBZrVbVrl1bI0aMUOvWreXxePSf//xHixcv1qlTp1S+fHn16tVLzZs3lyR5PB598MEHmjdvnmJiYlSjRg2NGDFC11133Xmf93zntyjc+AwMPL4xT09X0BfLFfL+TNk3rj/nuIy69ZTS+XGltWorhYfnf1DkGt7ngYcxDzw5Ob8NuKLt3r2Gbr/d+xda0/udGjouzoRkyCv+VMBD/vC3Md+/x6aXehfX3395u88EBXn0+uupat/eZXKywoMTnMDDmAeeglC0NQtF28DDZ2DgOd+YW3/7VSEfvKfgxQtk/GuhQnd4hNIeaKfUzo/JVesWet8WQLzPAw9jHnhycn4bcO0RTp068yNHsggZgFx2fWWX3p1/UrWi0yRJaWmGevUK0YgRQcrk72QAAADkQOZN1ZU06S2d+uV3JY2ZINeN1Xy3WZISFTL3AxVrdreK3X2Hgt97V0YsV5QCQEEXgEXbM986Fi1O0RZA7oss5takGafU+uFk37533nGoc+cQxcaaGAwAAAAFmqdIUaU8/Zxiv1uv2C9XK6Xz4/KEhvlut+38VREvDVKJm6so4tlusv/3e+/CLgCAAifgirYxMWcVbZlpCyCP2O3SgOHx6vtynKxWbxea1attato0TDt2BNxHLwAAAHKTYchVp66S3piiU7/+ocQ3pyqjTt0zN6elKXjJJ4p88H4Vr19boZPGy3LgfyYGBgBcroCrHJxdtI0sRtEWQN564BGnJk0/paLFvL0R/vzTovvuC9XChTaTkwEAAKAw8IRHKLXTY4r7crVi1m6Q85kechcr5rvdeuB/Cps4ViVuranI+5oqePYsGTGnTEwMAMiOgCvaZmmPwExbAPnglnrpmrnwpKpWT5ckpaYa6t07RIMGBSktzeRwAAAAKDQyb6ym5FHjdeqXP5Qw4wOlN7pbnrMWJrNv3qiIQf1UosYNKvJ4Rzk++1SckAKAfwrsoi09bQHkk9JXZWry7JNq1e5Mn9vZsx1q2zZUR46wwi8AAAByUVCQ0to+pPjFnypm229KGjpCrqo3+m42MjIU9OXnKtqti0pUr6zwAc/LvuFH+t8CgB8JuKJtlvYIzLQFkI+CgqSBr8Rr8MhYORzePrdbt1p1zz2h+u9/rSanAwAAQGHkvrqcUp7vp9i1GxSz+r9yPttLmaVK+263xMcpZO5sRbZuruK31lTYmBGy7fhZ8nhMTA0ACNiirWF4FF6Eoi2A/NfygRS9M/ekypR1SZJOnrSoXbsQvfGGQ5mZJocDAABA4WQYyqxxs5JHjlXMz7sVt3CpUh9+RJ7QMN8h1j8PKvTt11WsSUMVq19boWNHyvrrDgq4AGACw+MpvJ++8fFOpadnrYDUrRumgwctKlLUrc/+e9SkZMgrdptVGS6qXoGkII95fJyh0UOKadMPwb59DRu6NG1aqkqXLrQfzVfM4bCe89mOwo0xDzxRURFmR/Bb5zu/ReHGZ2DgyfcxT0pS0FdfKPiTBbKv/VbGeVokuCpWUlqbB5TW6gFlVrtJMmjvlZt4nwcexjzw5OT8NuCKthUrhisx0dA1FTI097MTJiVDXinIBTzkTEEf88xMae6McH34boTcbu/Jb8mSbk2blqq77iq4P1de4gQn8DDmgYei7YVRtA08fAYGHjPH3Dh+XEErPlPQ8qWy//jf8xdwK1VWWusHlNbmQWVWvZECbi7gfR54GPPAQ9H2X/59UpuWJpUv732RatRO09Q5p8yKhjxS0At4uHyFZcy3b3Zo1OBiOnXC29vWMDx6/vl0DR6cLpvN5HB+hhOcwMOYBx6KthdG0Tbw8BkYePxlzI1jxxT0xXJvAXf9DzLOUzpwVb5B6S3uV1qL++SqXUeyBFwHxlzhL2OO/MOYBx6Ktv/y75Pao0cN3XxzuCSpwd0pGjM51qxoyCOFpYCH7CtMYx4XY9HYlyO18b9n2iXUrZup6dNTVK5cof2ovmyc4AQexjzwULS9MIq2gYfPwMDjj2NuOXZUjs//KeBu+PG8BdzM0mWU3qyl0lrep4w7GnlX4UW2+OOYI28x5oEnJ+e3AfU12KlTZy7bKFqMRcgA+JfI4m6NfydGz/aPl9XmPRHevNmqxo3DtGIF020BAABgDnfpMkrt1l3xn36pmJ93K3HsRKXXv12es1ojWI8dVcic9xX5yEMqceP1iujeVUFLPpGREG9icgAouAKqaBsTc+YvlEiKtgD8kMUiPfpEsqbMPqkyZV2SpLg4Q127hqhfvyAlJZkcEAAAAAHNXeYqpT71rOKXf6VTv+5V4lvvKK1ZC3mCz1wtZklKVPCyJSrybDeVuPF6FW3fVsHvz5Tl0J8mJgeAgiWgirbMtAVQUNxUM0PvLTqhRvek+PbNm+dQ48Zh2rw5oD66AQAA4Kc8UVFK7dhFCXMX6uSu/yn+g3lKbf+o3JGRvmOMjAw5vlujiCEDVKJOdRVreKvCRgyT/Yd1UkaGeeEBwM+Z/i//U6dOqUePHoqOjla9evU0ZswYuVyu8x47f/58NWvWTLVr11azZs00b968y3yus4q2kRRtAfi3iKIejXwjVoNGxCkkxPuZ9f/t3Xl8E2X+B/DPzCRpk9705Ch3y42UFioiKouIooAH4i6K4ooHuAor4vnTVVyvH+d64AL6k90Vr2VhVxEVdRFRseUU5JCWoy0tbelNz2Qm8/tjeqWlnE2T5vm8X6+80kwmyRO+dPrtp0+eOXZMxoQJNrzyioU9LhERERF5j4AA2K+fgFNvLEfh/iMoWfcZKu+bCS22q8tupl8PwvbmXxB60/UI79sDwffcCb8P3oOUl+ehgRMReSePh7Zz5syBzWbDli1bsGbNGmzduhWrVq1qtt/XX3+NxYsX49VXX8XOnTvxyiuvYOnSpfjyyy/P+bUaL4/AmbZE1B5IEnD9zZV4518nMeASOwDA6ZSweLEfbrjBhsOHpbM8AxERERFRGzOZ4Bg5ChV/fhVF2/ei6JvvUfHE/8CRNNxlHVz5VBn8Pv03gmfPQsSgOISOvRK2V/4M0/ZUQONJmohIbB4NbTMyMpCamop58+bBarUiNjYWs2bNOu0M2ry8PNx7770YMmQIJElCQkICkpOTsW3btnN+Pa5pS0TtVedYDa+tKsA9fyiDohgnKdu1yzhJ2bvvmnGaE/gSEREREXmeJEEbNBiVjzyGkg1fo3D/EZQtW4nqm2+FMyzMZVfzz7sQsPh/ETb+aoT3M2bh+v/9XciZGR4aPBGR53j0dORpaWkIDQ1FdHR0/bZevXohJycHZWVlCA4Ort9+++23uzy2sLAQ27Ztw5NPPnnOr8flEYioPTOZgDvvL8ewkTV48ckwZB0zoapKwuOP+2PDBhMWL65GbCzTWyIiIiLyXnp4OGom34aaybcBmgbTju2wfPMlLF9thPmXPfX7ySUl8Pv03/D79N8AALVHTziuHA37VWPguHwU9OAQD70DIqK24dHQtqKiAlar1WVb3e3KykqX0LaxkydP4v7778fAgQNxww03tPj8JpPrROLi4obbEZESzCblQodOXkoxeXzFD2pjItZ88BAnVv2rEG8sCMK6D20AgM2bTbjyygA8/7wDd9+tQvbhfxYTj93CYc2JiIh8lKJAHZ4MdXgyKp98FvKJHFj++zUs33wF85bNkEtL6nc1HT0C09EjsK56B7qiQB2aBPuVo2G/8jdQhyYCZrPn3gcRkRt4NLS12Wyoqqpy2VZ3OyAg4LSP2b17N2bPno2kpCS8/PLLMJlafguq6oTd3rAOTkGBcW0y6TD7qXCc/nxn1M45VK59JBoRa26yAHOeLsGIK6uw4LlQnMxTUF4uYe5cC9aulbFkSTW6d/fdWbeNj+0kBtaciIjI9zk7dkL17Xei+vY7jVm4u3fCsnkTzJs3wbwtBVLtScslTYN5WwrM21IQsPAVOAMC4bh0BByXjYLj8lFQBw8BFP7Rl4jaN4/OxYqLi0NJSQkK6tJUAIcPH0ZMTAyCgoKa7b9mzRpMnz4dd911FxYtWgSLxXJer1e3pm1oBycknruHiHxA8uU1WLUuHzfcUlG/7YcfTLjqqgC8/bYZTq4EQ0RERETtkaJATRyGykceQ+l/PkfhoQyUvvcRKu99AGpcvMuuckU5/L75CoEvPIuwcaMRHt8NwXdMgfWtN2Da+zPYFBNReyTpumdPXzN16lTExMRg/vz5KC4uxsyZMzFu3Dg89NBDLvt9+eWXmDt3Lt566y2MGjXqnJ67tLSyfmaOrgOxsYGw2yX0infg//51stXfC3me2aQIOetSZKx5g+1bLVjwXChycxo+gXDppSqWLq1Gz56+M+vWYlE461IwrLl4IiOb//GeDI37WxIDj4HiYc3PjZx9HObvvoVl839h/n4LlPy8Fvd1hobCMeJyOEZeDvtlo6D16+9VM3FZc/Gw5uK5kP7W46FtQUEB5s+fj5SUFMiyjBtvvBGPPvooFEVBQkICnn/+eUycOBETJkxAeno6/P39XR4/YcIEzJ8//7TP3bipLS8HevY0/oGGJtdgyduF7n1j5BEM8MTDmruqrJCwfEkw/v1RwxIzfn465syx4w9/sMPPz4ODayVscMTDmouHoW3LGNqKh8dA8bDmF0DXoaSnwfz9dzD/sAWWH7dAbvSJ3qacwSFwDBsONXkEHMkj4BgyFGhyvp22xJqLhzUXT7sMbd2pcVObkSFh2LBAAMDocVV4bmGxJ4dGbsIATzys+ent2mbB/z4bipzjDbNu4+I0LFxYgxEj2ve/Fxsc8bDm4mFo2zKGtuLhMVA8rHkr0HUovx6E+YfvYPl+C8w/boFc3HIGoFssUC9JMALc5BFwDBsOvUN4mw2XNRcPay4ehrZNNG5qd+2SMW6cMfPspt9WYM7TpZ4cGrkJAzzxsOYtq6qU8Le/BuLjvwdC0xoW8v7d7xz405+q0aGDBwd3EdjgiIc1Fw9D25YxtBUPj4HiYc3dwOmEcmA/LD98B/NPW2FO2Qr5ZP4ZH6L26QvH8BFwJF8KR/IIOLt2g7tOjsOai4c1Fw9D2yYaN7Vff61g6lQbAGD6zFO4e9YpTw6N3IQBnnhY87NL/9WERfNDsX9Pw8kbw8OdeO65GkyZora7EzOywREPay4ehrYtY2grHh4DxcOatwFdh3z0CMypP8GcshXmn36E6XD6GR+ixXSEY/ilUIcmwZE4DOrgS1ptSQXWXDysuXgY2jbRuKn96CMTHnrIOKDOfrIEN0+t9OTQyE0Y4ImHNT83mgZ8usaGFUuDUVEu12+//HIVL79cgz592s8ZddngiIc1Fw9D25YxtBUPj4HiYc09Qzp5siHETd0K056fIalqi/vrJhPU/gOhJibBMTQJauIwaD17AbLc4mNawpqLhzUXD0PbJho3tW+9Zcaf/mScxOzZ/y3CmOuqPTk0chMGeOJhzc9P4UkZr78agk1fNswKMJl03HOPA/Pm1SA42IODO0dscMTDmouHoW3LGNqKh8dA8bDmXqKiAuad240QN2UrTNu3Qa4oP+NDnKGhUBMSjRA3aRgcCYnntDYuay4e1lw8DG2baNzUvviiBX/5i3Ha9MUrC5B4qd2TQyM3YYAnHtb8wvy0xQ9LXgxBbnbDicoiIpx45pka3HabeiETBNoMGxzxsObiYWjbMoa24uExUDysuZdSVSgHD8C8cztMO7fDvGMblEO/QjpLpKL26Fm7pEIS1MEJUAcOAmw2l31Yc/Gw5uJhaNtE46b2kUf88N57xnqO76zJR+8+LX/MgdovBnjiYc0vXE018MG7gVj9ThDsNQ0L2yYmanjppWokJHjnkglscMTDmouHoW3LGNqKh8dA8bDm7YdUVgrT7l0w79hWG+Ruh1xw8oyP0WUZWnwfqIOHQL1kCByDEyAPHQK72b+NRk3egN/n4mFo20Tjpvauu/zx+edmAMCar3MRGe2dYQRdHAZ44mHNL15ujoJlC4Ox+auGJRMkScfUqQ489ZQdkZHe9WOCDY54WHPxMLRtGUNb8fAYKB7WvB3TdciZGQ2zcbdvg+mXPZBqas78sNMEuerAQUBAQBsNnNoav8/Fw9C2icZN7YQJVqSkGB8D/mpHDiyWMz2S2isGeOJhzVvP9q0WvPZKCDKOmOu3BQbqmD3bjvvus7fWyXEvGhsc8bDm4mFo2zKGtuLhMVA8rLmPsdth2rcXpt27YNqzG6afd8N0cP8ZT3IG1Aa5cfFGkDv4EqgDBkEdMBB6WIc2Gji5E7/PxcPQtonGTe3IkTakpSmwBTjx+U+5Hh4ZuQsDPPGw5q1LdQDrPgzAu8uCUFHesLBt585OPPVUDW65xfPr3bLBEQ9rLh6Gti1jaCseHgPFw5oLoLoapgP7jAB3z25Yft4F+cDZg1wA0Dp3gTpgoHEZOBjagIHQuveEx5t0Oi/8PhcPQ9smGje1/foFoLBQRsfOKj78It/DIyN3YYAnHtbcPYoKZLy7LAjr/2WD09mw3u3gwRqee64Gl1/uuX9zNjjiYc3Fw9C2ZQxtxcNjoHhYc/FYLArsZRUuQW79jFyH46yP120BUPv1N2bjDjRm5Kr9BgCBgW0weroQ/D4XD0PbJuqaWk0DOnUKhK5L6DvQjuUfFHh6aOQmDPDEw5q719F0E/66OBg/bXE9McK4cSqeeaYG8fFtvz44GxzxsObiYWjbMoa24uExUDysuXharHlNjRHk/rIXpn17oez7BaZ9v0A+VXbW59QlCVr3HtAGDILatx/Ufv2h9e0PrUdPwGRyw7ug88Hvc/EwtG2irqktLJTQr5/xF6bky6vxv28VeXhk5C4M8MTDmreN7VsteGtRCNJ/bVjvVlF0/Pa3Dsyda0eXLm33o4QNjnhYc/EwtG0ZQ1vx8BgoHtZcPOdV89qTnZn2/WKslbvvF5h+2Qsl89i5PdxigdY73iXIVfv0hbNrNy6x0Ib4fS4ehrZN1DW1aWkyRo40zro4bmIlnnqxxLMDI7dhgCce1rztaBrw1Xor3n4tGCfzlfrtFouO6dMdmD3bjshI9/9IYYMjHtZcPAxtW8bQVjw8BoqHNRdPa9RcOlUGZd8+I8jd/wtMv+yB6eABSFVV5/R43WaD2qcv1L4NQa7Wtx+cHTsBknT2J6Dzwu9z8TC0baKuqf3pJwUTJ9oAAFPuLMeD887+UQJqnxjgiYc1b3vVVRL++V4APnw3EOWnGv4ab7PpuP9+O2bNsiMkxH2vzwZHPKy5eBjatoyhrXh4DBQPay4et9Vc06BkHIVy4ABMB/dDOVh7nZ4GSTu313MGBEKLi4MW1wdaXDzU3vHQ4vtA694DsFhaf8yC4Pe5eBjaNlHX1H72mQl3320FANw7uwx3zCj38MjIXRjgiYc195yyUgkfvhuINasDUFPdEN6GhOh46CE77rnHjoCA1n9dNjjiYc3Fw9C2ZQxtxcNjoHhYc/G0ec1raqAcTofp1wNQDu6HqTbUlTOOQTrHiEg3mYw1c2tDXLV3HLS4eGhx8dCD3TiDw0fw+1w8DG2bqGtq//EPM+bONU6i8+ifSjBhcqWHR0buwgBPPKy55xUWyPjHikB8+s8AqGrDR6ciIpyYOdOBu++2t+qJa9ngiIc1Fw9D25YxtBUPj4HiYc3F4zU1r6iAKe1XY0bugf1Q0n6FKe0Q5MyMcw5zAUCLjjFm4/aOgxrfxwh2e8cZSy1w3VwAXlRzajMMbZuoa2r/8hcLXnzRDwDw56VFGDWm2sMjI3dhgCce1tx7nMhWsOqtIGz81AqnsyG87dDBCG9//3s7glohh2GDIx7WXDwMbVvG0FY8PAaKhzUXj9fXvKoKypHDRqCbdghK+iGYDh2CcjgNUvW55yu6vz+0Hj2h9egFrafrxRkdI9TauV5fc2p1DG2bqGtqn33WD3/9q7HWyut/K8DgoXYPj4zchQGeeFhz73PsiAl/+2sgNn1hha43NF6hocaatzNmXNyat2xwxMOai4ehbcsY2oqHx0DxsObiabc1dzohZ2XClH7ICHNrL6a0XyEXFp7XU+m2ACPQrQ1x1Z696sNdPTLS5wLddltzumAMbZuoa2offNAf//ynGQDw9//ko1tP1cMjI3dhgCce1tx7ZRwx4R8rA/HNBteZt8HBOmbMsOPeex0IDz//H0FscMTDmouHoW3LGNqKh8dA8bDm4vHFmkuFhVDS04zZuYd+hXL0MJQjh6EcOwrJ4Tiv53IGBdeGubWzdLv3gLN7D2jduhszdNvhkgu+WHM6M4a2TdQ1tb/7nRXffGMCAPznu1yEhjk9PDJyFwZ44mHNvd/xDAX/WBmEr9ZboWkN4a3NpmPqVAceeMCOrl3P/UcRGxzxsObiYWjbMoa24uExUDysuXiEqrmmQT6eZQS4Rw43hLlHDkPJzICknt8kO93fH1rXbtC6dTdC3G7doXUzAl2taze45czIrUComhMAhrbN1DW148bZsGuXAlnW8fXOE1AUT4+M3IUBnnhY8/YjO0vB6rcD8cUnNmiNTlimKDomTVLxhz/YMXDg2f+oxgZHPKy5eBjatoyhrXh4DBQPay4e1ryWw2Est3D0MJTD6Q1h7pEjkI9nQnKe/wQ8LSq6NshtuHjDLF3WXDwMbZuoa2qHDQtARoaMkFANn2zJ8/SwyI0Y4ImHNW9/cnMUfPz3AHy21obqKtcm6Te/UfHQQ3ZcdpnW4rJVbHDEw5qLh6FtyxjaiofHQPGw5uJhzc9BTQ2UzIzaGbnHIGccg5JxDMqxo1Ayjp3XCdHq6H5+0Dp3gTO2K7TYrnB2iYXWJRbOrt2M65iOgMnkhjfDmouIoW0TdU1tXFwgSkslxHZX8d6n+Z4eFrkRAzzxsObtV2mJhHUfBGDt+wEoLXH9CMQll2i47z47Jk1SYbG4Po4NjnhYc/G0h9C2sLAQzzzzDFJTU6EoCiZOnIjHH38cptP8cvfBBx9g1apVyM/PR1RUFO68807cfvvtAACn04nExEToug6p0V+rfvjhB9hstmbPxdBWPDwGioc1Fw9rfpF0HXJ+HuRjx6BkGCFuXaArZxyDkpd7YU+rKHB26uwa6MZ2hdYl1tjWuQvg53dBz82ai+dC+lv3/MnAi2gaUFpqNMBBwVzLlojIW4SE6pg+sxy33VWBz/9txUd/D0RutvFj6eefFTz4oBXPP+/E73/vwJ13OhAR4bN/YySidmjOnDmIjo7Gli1bUFBQgJkzZ2LVqlWYMWOGy35ff/01Fi9ejJUrV+KSSy7B7t27cd999yEiIgLjxo1Deno6HA4Hdu7cCUvTv1IRERHR2UkSnNExcEbHQE2+tPn9lZVQsjLrA936WboZxyBnZUGuKD/902qa8biszNPer0sSnFHRRqDbtSucXbrWBrux0DrHwtm5M/TgkNZ8pyQYnw9tS0sbvmZoS0Tkfaw2HTdPrcTEKZXY9KUVH/0tAGkHjOAiP1/GK6/4YckSC265xYF773UgIcHDAyYi4WVkZCA1NRXfffcdrFYrYmNjMWvWLCxYsKBZaJuXl4d7770XQ4YMAQAkJCQgOTkZ27Ztw7hx47B371706dOHgS0REZG72GzQ+vSF1qdv8/t0HVJJMZSsTMhZWVCOZxonSsusvT6eCbm4+LRPK+k6lLxcKHm5MO/Ydtp9nIFBcHbqZMzY7dQZztqL3C0WWmRHI9gNCm7Nd0s+xOdD25KSho+ZBYcwtCUi8lYmEzD2+ipcPb4Ke3ZasOa9AHz/X384nRJqaiS8/74F779vwahRGqZPt+Paa1WYzZ4eNRGJKC0tDaGhoYiOjq7f1qtXL+Tk5KCsrAzBwQ2/fNUtg1CnsLAQ27Ztw5NPPgkA2Lt3L2pqanDLLbcgOzsbvXr1wty5czF06NC2eTNEREQikyToYR2ghnUABg85/S7lpxoC3awsKMezIGdlNtzOb/ncSXL5KciHfgUO/drsvoDaa2dgEJydO8PZsZOxxm7HTnB27gKt9trZqRODXUH5fGhbXNwQ2gYxtCUi8nqSBFySaMcliXacyFaw7oMArP+XDRXlxknLtmxRsGWLFdHRTtxxhwPTpjnQqROXTiCitlNRUQGr1eqyre52ZWWlS2jb2MmTJ3H//fdj4MCBuOGGGwAA/v7+GDx4MGbPno2QkBCsXr0a99xzDz755BPExsY2ew6TyTNnuSbPMZmUs+9EPoU1Fw9r7uU6hBqXSwbBCaBZslRdDTn7OOTMDEhZWZAzM43b2cch5eQY11VVLT69XH4K8q8HgV8PtriPHhxszNLt3Bl6TEc4O3aE3rETnDEdoXfsaFxHRbntxGnkGT5fTdeZtvylnoioPenYWcOsR8swfeYpfPEfK/71fiCOZxg/uvLyZCxa5IelSy245hoV06c7cOWVGmTmGUTkZjabDVVNfvmqux0QEHC6h2D37t2YPXs2kpKS8PLLL9efsOyJJ55w2e+ee+7B2rVrsXnzZtxxxx3NnkdVnTxxiYBYc/Gw5uJhzdsx2QzE9jAup1O7BIOcnQ3lRDbk7GyY83KArOOQc7Ih52RDycmGVF3d4ktIZWVQysqgHDzQ4j66JMEZGQVnTEc4Y2LgjOlUe23c1qJrw93wcPCXpvbB50NbzrQlImr/bAHGurc3/rYSu7dZsfYDf/z4rT80TYKmSfj8czM+/9yM7t2N2be33eZAdDT/UEdE7hEXF4eSkhIUFBQgIiICAHD48GHExMQgKKj5mYHXrFmDP//5z3j44Yfx+9//3uW+JUuWYNy4cejfv3/9NrvdDr8LPBs1EREReZnaJRi0sA7QBg4CADgtimtQr+uQiotcgl35RA6U7OOQTxizdZUTOWcOdnUdSn6esVzDnpaHo5tMxonbYjo2BLoxHY1tUVFwRkbDGRUNPSICUDgL3JN8PrR1mWnLE5EREbVrsgwkj7RjaHIV8nNlfLbWWDqhIN9oJo4dk/HnP/vh5ZctGDtWxdSpDlx9tcZPCRFRq+revTsSExPx0ksvYf78+SguLsayZcswefLkZvt++eWXeO655/DWW29h1KhRze4/dOgQtm/fjqVLlyIkJAQrVqxAeXk5xo4d2xZvhYiIiLyBJEHvEA6tQzi0QYNPv4+uQyoqgpyXCzn3BOS8XCi5J4xQNzcXct4J4zo/D5LW8sxtSVWhZB+Hkn38jEPSJQl6eAScUdFGmBtlhLnOyCjX21FR0EPDjHXuqFVJuq777FSk0tJKvPiiggULjJkKr75ZiEuvqPHwqMidzCYFDpUfKxEJay6epjVXHcCPm/3x748CsOOn5jPToqKcmDLFgalTHejd22d/5Pk0S9OZCOTzIiObz1b1NgUFBZg/fz5SUlIgyzJuvPFGPProo1AUBQkJCXj++ecxceJETJgwAenp6fD393d5/IQJEzB//nyUlJTg1VdfxebNm1FVVYVBgwbhqaeeQt++pznDNYz+lt8PYuExUDysuXhYc/G4teaaBqmgAEreCSPcza0NeXMbbiu5JyAXnGy1l9TN5tOGucas3UbXUdFAYGCrvW57ciH9rc+Hto89ZsKKFRYAwLL3TmLAJQ4Pj4rciQGeeFhz8Zyp5sczFXz+bxu++E/D7NvGkpNVTJmiYsIEB0JD3TxQajX8RUY87SG09RSGtuLhMVA8rLl4WHPxeEXN7XbIJ/ONIPfECcj5ecbl5EnIJ2u/zs83Zu7a7a32srrNBmdEJJwREcZ1eAT0iMiGbeER0CMj6++DxdJqr+1JDG2bKC2txL33mvHPf5oBAP/4JA9de/BA6MsY4ImHNRfPudRcVYHtP/rhs3U2/PCtPzTV9aM6FouOa65RceutKsaMUX2lD/BZXtHUUptiaNsyhrbi4TFQPKy5eFhz8bSrmus6pNKS+gDXCHbzXW/XhbsFJyG1cszoDA6BM6JRsBseAWekEfjqdbdr79M7dPDadXgvpL/1+VX+XNa0DfHZfJqIiBoxmYBLr6jBpVfUoLhQxsb1VmxYZ8Oxw8Yf8ex2CevXm7F+vRlhYTomTXLg1lsdSEpycikmIiIiIiKiOpIEPTQMWmgYtPg+Z95XVSEVFjYKdmsD3SYzd+XCAkjFxecU8MplpZDLSoEjh8+6ry5J0Dt0aJjBGx4BZ1gHOMM7QO8QDmeHcOP+uq/Dw6EHBHrterw+P9P26qv9sH27kbJ/syuHJ6PxcZx1KR7WXDwXWnNdBw7tN2Pjeiu+2WBFcVHzv8B26+bEpEkOTJqkYuBABrjeol3NRKBWwZm2LeNMW/HwGCge1lw8rLl4WHMYAW9REeSCk8alsABywUlIBSchFxTUXmpvFxYawa0b6GZzbZgbDmd4OPSw2lC3LugN62BsbxT6XkjQy+URmigtrURSkh/S0xUEBDqxYWuup4dEbsYATzysuXhao+Z1yydsXG/F95v8UVMtN9und28NkyapuPFGFX36OC/q9ejisKkVD0PbljG0FQ+PgeJhzcXDmouHNb8ANTWNgt2C2rC39nZhQaPwtxDyyXxIVVVuG4pusTQEvbUzd/XG12EdoIeFNVyHhiGiT/fzfh2fD2179/ZHQYGMmM4qPvoi39NDIjdjgCce1lw8rV3zinIJ333tj68+s2FXqgVOZ/O/mPbrZwS411+vIj6eM3DbGpta8TC0bRlDW/HwGCge1lw8rLl4WPM2UFEBubgIclGhsWRDcRGkokIj1C0qhFRcBLmw9v6i2m01Ne4bzwXErz4d2paUVCIiwgpNkxDfz46VHxd4ekjkZgzwxMOai8edNS8ulLH5a3/893Mr9uy0QNebp7M9ezoxfrwD112nIjHRCbn5JF1qZWxqxcPQtmUMbcXDY6B4WHPxsObiYc29kK4DlZWQ6wLcoqKGr+tD39pthXWhbwEku/3cn/88+XRom5VVia5dbQCAxEtrsHhloYdHRO7GAE88rLl42qrmBfkyvt1oxX+/sGLfz5bT7hMV5cS116oYP17F5ZdrsJx+N7pIbGrFw9C2ZQxtxcNjoHhYc/Gw5uJhzX2ErhszeotqQ926WbwlxZCLi41gt7gYcnERLN98dd5P79Oh7Z49VbjkEisAYPS4Kjy3sNjDIyJ3Y4AnHtZcPJ6oeW6Ogu//648t3/hjz87TL6EQFKRj7FgV112nYswYFYGBbTpEn8amVjwMbVvG0FY8PAaKhzUXD2suHtZcPBfS35rcMA6vUdwoow0K4UlkiIjowsR00jD5jgpMvqMCJcUyfvzWD1v+a8X2H/1gtxsB7qlTEtauNWPtWjMsFh0jRmgYM0bFmDEaevfmOrhERERERER07nw6tC0tbfgNOZihLRERtYLQMCfG31SF8TdVobJSwrYf/LDlv/7Yutkf5aeMBW7tdgmbN5uwebMJzz4LdO3qrA1wVYwcqSEgwMNvgoiIiIiIiLyaT4e2xcUNoW1QMENbIiJqXTabjivHVuPKsdVQHcDu7RZs+caKHzf7IT+34UdsZqaMd9+14N13LfDzazwLV0WvXjpn4RIREREREZELcUJbzrQlIiI3MpmBpBF2JI2wY87TwLHDJvy0xQ8p3/tj704LVNX4mVRTI+Hbb0349lsTnnnGmIU7erSKUaM0jBypITzcZ5eaJyIiIiIionPk46Ftw9fBwfwlmIiI2oYkAT16q+jRW8Xv7q5AZYWEHT/5IeV749J0Fu7f/mbB3/5m3B4wQMOoURpGjVIxYoTGE5oREREREREJyMdDW65pS0REnmcL0DFqTDVGjamGrhuzcI0A1x97djTMwgWAffsU7Nun4K9/tUBRdCQkOHHFFcZM3MREDf7+HnwjRERERERE1CaECW25PAIREXmDxrNwfzu9ApWVEvbutGBnqh92/mRB2kEzdN34+aVpErZvV7B9u4LFiwF/fx3DhmlITjYuiYmciUtEREREROSLfDy0bfiaM22JiMgb2Ww6ki+vQfLlNQCAslIJu7f5YWeKH3akWJB51Fy/b3W1hC1bTNiyxfjxrSg6Bg1yIjlZw/DhRpAbFcXlgIiIiIiIiNo7Hw9tG820DWZoS0RE3i84RMcVV1fjiqurAQAF+TJ2pvgZM3FTLMg70fCjW9Mk7N6tYPduBcuXG9t69nTWzsRVMXy4hl69dEjS6V6JiIiIiIiIvJWk67rPTskZMMCJ/ftl+Pk7sXFbrqeHQ23AbFLgUDVPD4PaEGsuHtFrnndCwZ6dFuzZacHenRYcTTefcf/QUB0JCRoSEozlFBISnIiIaF8/+i0WBXa7uDUXUWRkkKeH4LVKSyv5/SAYHgPFw5qLhzUXD2sungvpb316pm1JiXEdHNy+fjklIiJqSXRHDWOvr8LY66sAGMsp7PvZgj07LNi7y4KDv1jgcDRMrS0pkbBpkwmbNjX8yO/WzYmhQ7X6y6BBTp7gjIiIiIiIyIv4dGhbtzxCIJdGICIiHxUcomPEFTUYcYWxJm5NDXDwF2Mm7v49FhzYY0ZxkeLymIwMGRkZMtatM2bpms06BgxwYtAgDYMHG9f9+jlhtbb52yEiIiIiIiL4eGhbVWWEtjwJGRERicLPD7gk0Y5LEu0AAF03llTYv8eMA3stOLDXjF/3W2CvaZiN63A0rI1bR1F0xMc7MWhQQ5g7cKCGIH5qnYiIiIiIyO18OrStE8TQloiIBCVJQEwnDTGdNPzmWuPkZqoDOJJuqg1xjSA344gJut4Q5GqahAMHFBw4oODjjxvWze3RwwhxBwxwol8/Y0ZubKwOWW7zt0ZEREREROSzhAhtOdOWiIiogckMxPdTEd9PxaQplQCAygoJ6b+akXbAjEMHzEg/aMbRwyZoquTy2KNHZRw9KuOTTxq2BQTo6NvXif79jRDXuGjo0KEt3xUREREREZHvECS05YnIiIiIzsQWoGPwUDsGD7XXb6upAY6muwa56b+aXZZWAICKCgk7dijYscN17dzoaCPA7dPHifh4J+LinIiPZ5hLRERERER0NkKEtlwegYiI6Pz5+QF9BzjQd4CjfpuqAplHTTiSZsbRdOP6SJoJudnNW4q8PBl5eTK+/dZ1e3i4EeDWXeoC3c6ducwCERERERERIEhoGxzM0JaIiKg1mExAzzgVPeNUl+0V5ZJLiHs03YyjaSaUlijNnqOwUEZhoYyffnLdbrPp6NnTiZ49nejRw7j07KkjPh4ICzPW5yUiIiIiIhKBEKEtZ9oSERG5V0CgjoFDHBg4pGFWrq4DRQUyjh02IfOoCRlHzMg4anxdkN88zK2slPDLLwp++aX5fTabju7dG8LcHj30+nA3JoYzdImIiIiIyLcIEdryRGRERERtT5KA8EgnwiPtSLzU7nJf+SkJmUfrwlzjknnMjJwsBZrWfEptZaWE/fsV7N/fPND19zcC3e7dnYiN1REb60SXLjq6dnUiNtaJ0FDO0iUiIiIiovZFiNA2KJgnIiMiIvImgUE6+g92oP9gh8t21QHknlCQnWlCdqaC45km5GSZcTxTQc5xBZraPH2trpZw8KCCgwebB7oAEBBgBLhdutQFuk507doQ7kZE6Ax1iYiIiIjIq4gR2nKmLRERUbtgMgNdumro0lWr32Y2KXCoGlQVOJlrBLnHM2uD3Swj3M3JMsHhOH3yWlEh4cABBQcOnP41rVYdXbo40bGjjo4ddXTqZCy50KmTE5066YiJ0REeziUYiIiIiIio7QgR2nJ5BCIiovbPZAI6dtHQsYuGYZe53qdpQOFJGbk5JuRmK8jNUZB7QkFutgl5JxTk5SgthrpVVRLS0hSkpbX82haLEd527NgQ5HbqZAS9MTFOREfriIrSYbW24hsmIiIiIiJh+Xxoqyg6bAFcHoGIiMiXKQoQFeNEVIwdg4c2v9/pBIoLZZzIVpCbY0JeTm2wW3vJO6GgprrlqbR2u4TMTAmZmWeebhsUZIS3UVFOREXp9WFu3e3ISON2RIQO5fSrORAREREREfl+aBsU4uQ6dURERIKT5bqTojkxcIij2f26DpSXSTiZr+BknnEpyJeRn6egIK9h26myM4e2p05JOHVKwuHDZ95Plo0lFyIjjeuICOO6Q4eG23Vf121nyEtEREREJA6fD22Dg7k0AhEREZ2ZJAFBITqCQlT0jFNb3K+6SkJBvmyEu7m1YW6+jOJCBUUFMopqrysrzhzaOp0STp6UcPLkuY5PR2goEB7urA9xmwa94eE6QkJ0hIXpCAkBQkJ0mHy+0yMiIiIi8k0+38oHhXBpBCIiImod/lYdXbpp6NJNO+N+VZUSigtlFBXKKCpQUHiy9rr2dlGBcV1cKENVz/6RIF2XUFwMFBcrSE8/9/EGBekIDW0c5jZch4YCoaG6y6Xu/sBA8MRrREREREQe5POhLU9CRkRERG3NatNhtWnoFKsBaL4cQx1dByrKJZQUyygtllFSeyktVupvN70+2yzexuqWa8jKOr/xS5IR3AYH6wgK0hEU1PjrhtvBwToCA3UEBxsBcdP9/fzO73WJiIiIiMjg86FtEENbIiIi8lKSBAQG6QgM0tCl65ln79apqQHKSmoD3iIFpbVfl5XIOFUm4VSpjFNltZdSqf7rc5nRW0fXJZw6ZYS+F8NiMULdgAAgIKDx9Zm3zZx5US9LRERERNTu+X5oyzVtiYiIyIf4+QGR0U5ERjsBtLz+bmO6DlRVSSgvk1DmEurWBr1lMspKZZSXySgrlVBRLqOivOG6uurC1kqw2yUUFUkoKjq/xzG0JSIiIiLReTy0LSwsxDPPPIPU1FQoioKJEyfi8ccfh+k0Z87YvHkzFi5ciKysLHTs2BGPPfYYRo8efcbn5/IIREREJDpJAmw2HTabjqiY8++NVBWorJBQcUpGRZPr8nIJlbXhbnm5jMra64pTEiorZFRVSg2XCwx/iYiIiIhE4/HQds6cOYiOjsaWLVtQUFCAmTNnYtWqVZgxY4bLfseOHcNDDz2ExYsX46qrrsLGjRsxZ84cbNy4EdHR0S0+f1AwT0RGREREdDFMJiA4REdwyLkt4dASpxOorpZcg9xK12DXWLM3pHUGTkRERETUTnk0tM3IyEBqaiq+++47WK1WxMbGYtasWViwYEGz0HbdunVISkrC1VdfDQAYP3481q5di48++ggPP/xwi6/BmbZERERE3kGWG2b8nhlDWyIiIiISm0c/o5aWlobQ0FCXmbK9evVCTk4OysrKXPZNT09HfHy8y7bevXvj4MGDZ3wNnoiMiIiIiIiIiIiI2hOPzrStqKiA1Wp12VZ3u7KyEsHBwWfc19/fH5WVlWd8jZBQHbJ0cWc+pvZDlsF6C4Y1Fw9rLh7WnIiIiIiIROPR0NZms6GqqsplW93tgIAAl+1WqxXV1dUu26qrq5vt11hkpI6JV9lgs7XSgMnrmUwKVPXi1tuj9oU1Fw9rLh7WnIiIiIiIROPR0DYuLg4lJSUoKChAREQEAODw4cOIiYlBUFCQy77x8fHYt2+fy7b09HQMHDiwxedPSamCyaTBbm/9sZP3stv5i71oWHPxsObiYc2JiIiIiEgkHl3Ttnv37khMTMRLL72E8vJyZGVlYdmyZZg8eXKzfSdOnIjU1FRs2LABqqpiw4YNSE1NxaRJk1p8/g4d3Dl6IiIiIiIiIiIiotbn0dAWAF577TWoqooxY8ZgypQpGDVqFGbNmgUASEhIwCeffALAOEHZm2++ieXLl2PYsGFYtmwZXn/9dfTo0cOTwyciIiIiARUWFmLWrFlISkpCcnIyXnzxRaiqetp9N2/ejAkTJmDIkCG47rrrsGnTJpf7V65ciSuuuAJDhgzBtGnTcOTIkbZ4C0RERETkxSRd13VPD8JdSksr+XFKwVgsCmsuGNZcPKy5eFhz8URGBp19Jw+bNm0aoqOj8cILL6CgoAAzZ87EjTfeiBkzZrjsd+zYMUycOBGLFy/GVVddhY0bN+LJJ5/Exo0bER0djXXr1mHJkiV455130LVrVyxZsgTff/89Pv30U0inOQEf+1vx8BgoHtZcPKy5eFhz8VxIf+vxmbZERERERO1JRkYGUlNTMW/ePFitVsTGxmLWrFlYvXp1s33XrVuHpKQkXH311TCZTBg/fjyGDRuGjz76CADw8ccfY+rUqYiLi4Ofnx/mzp2LnJwcpKSktPXbIiIiIiIvwtCWiIiIiOg8pKWlITQ0FNHR0fXbevXqhZycHJSVlbnsm56ejvj4eJdtvXv3xsGDB097v9lsRvfu3evvJyIiIiIxmTw9ACIiIiKi9qSiogJWq9VlW93tyspKBAcHn3Fff39/VFZWntP9TZlMnHMhGpNJ8fQQqI2x5uJhzcXDmtO5YGhLRERERHQebDYbqqqqXLbV3Q4ICHDZbrVaUV1d7bKturq6fr+z3d+Uqjq5Bp6AWHPxsObiYc3Fw5rT2fBP9URERERE5yEuLg4lJSUoKCio33b48GHExMQgKMj1JBPx8fFIS0tz2Zaeno64uLj652p8v8PhwLFjx5otqUBEREREYmFoS0RERER0Hrp3747ExES89NJLKC8vR1ZWFpYtW4bJkyc323fixIlITU3Fhg0boKoqNmzYgNTUVEyaNAkAcMstt+C9997DwYMHUVNTg0WLFiEiIgJJSUlt/baIiIiIyIswtCUiIiIiOk+vvfYaVFXFmDFjMGXKFIwaNQqzZs0CACQkJOCTTz4BYJyg7M0338Ty5csxbNgwLFu2DK+//jp69OgBAJg8eTKmT5+OBx98EJdeein279+P5cuXw2w2e+y9EREREZHnSbqu654ehLuUllZyjRDBWCwKay4Y1lw8rLl4WHPxREYGnX0nQbG/FQ+PgeJhzcXDmouHNRfPhfS3nGlLRERERERERERE5EUY2hIRERERERERERF5EYa2RERERERERERERF6EoS0RERERERERERGRF2FoS0RERERERERERORFGNoSEREREREREREReRFJ13Xd04MgIiIiIiIiIiIiIgNn2hIRERERERERERF5EYa2RERERERERERERF6EoS0RERERERERERGRF/HJ0LawsBCzZs1CUlISkpOT8eKLL0JVVU8Pi9ysqKgIY8eORUpKiqeHQm528OBB3H333Rg+fDhGjhyJxx57DEVFRZ4eFrnZ1q1bceutt2Lo0KEYOXIkXnjhBVRXV3t6WORmmqZh2rRpeOKJJzw9FHKzDRs2oH///khISKi/zJs3z9PD8hrsb8XFHlcc7HHFw/5WTOxvxXIxPa5PhrZz5syBzWbDli1bsGbNGmzduhWrVq3y9LDIjXbs2IHbbrsNmZmZnh4KuVl1dTVmzJiBhIQEfP/991i/fj1KSkrw1FNPeXpo5EZFRUW4//778bvf/Q7bt2/HunXrkJqaihUrVnh6aORmb7zxBrZv3+7pYVAb2Lt3LyZNmoRdu3bVXxYsWODpYXkN9rdiYo8rDva44mF/Ky72t2K5mB7X50LbjIwMpKamYt68ebBarYiNjcWsWbOwevVqTw+N3GTdunV49NFH8cc//tHTQ6E2kJOTg759++LBBx+ExWJBWFgYbrvtNmzbts3TQyM36tChA3788UfcfPPNkCQJJSUlqKmpQYcOHTw9NHKjrVu3YuPGjbjmmms8PRRqA3v37sXAgQM9PQyvxP5WTOxxxcIeVzzsb8XE/lY8F9Pj+lxom5aWhtDQUERHR9dv69WrF3JyclBWVubBkZG7XH755fjqq68wfvx4Tw+F2kDPnj3x9ttvQ1GU+m1ffvklBgwY4MFRUVsIDAwEAFx55ZWYMGECIiMjcfPNN3t4VOQuhYWFePrpp7Fo0SJYrVZPD4fczOl0Yt++ffj2228xevRoXHHFFXjmmWdQWlrq6aF5Bfa3YmKPKxb2uGJifysW9rfiudge1+dC24qKimb/+etuV1ZWemJI5GaRkZEwmUyeHgZ5gK7rWLJkCTZt2oSnn37a08OhNrJx40Z89913kGUZDz/8sKeHQ27gdDoxb9483H333ejbt6+nh0NtoKioCP3798e4ceOwYcMGfPjhhzh27BjXtK3F/lZM7HHFxR5XPOxvfR/7WzFdbI/rc12AzWZDVVWVy7a62wEBAZ4YEhG5QXl5OZ588kns27cP7733Hvr06ePpIVEb8ff3h7+/P+bNm4dbb70VpaWlCAkJ8fSwqBUtX74cFosF06ZN8/RQqI1ERES4fNTfarVi3rx5mDJlCsrLy+tnIomK/S2RONjjion9re9jfyumi+1xfW6mbVxcHEpKSlBQUFC/7fDhw4iJiUFQUJAHR0ZErSUzMxO33HILysvLsWbNGjazAti5cyeuvfZa2O32+m12ux1ms5kfLfJB//nPf5CamoqkpCQkJSVh/fr1WL9+PZKSkjw9NHKTgwcPYuHChdB1vX6b3W6HLMuwWCweHJl3YH9LJAb2uGJhfysW9rdiutge1+dC2+7duyMxMREvvfQSysvLkZWVhWXLlmHy5MmeHhoRtYLS0lLcddddGDp0KN555x0u1C+IPn36oLq6GosWLYLdbkd2djZeffVVTJ48mYGOD/riiy+wc+dObN++Hdu3b8cNN9yAG264gWfZ9WGhoaFYvXo13n77baiqipycHCxYsAA33XQTv8fB/pZIBOxxxcP+Vizsb8V0sT2uz4W2APDaa69BVVWMGTMGU6ZMwahRozBr1ixPD4uIWsHatWuRk5ODzz//HImJiUhISKi/kO8KCAjA22+/jbS0NIwcORLTpk3DZZddhqeeesrTQyOiVhATE4Ply5fjm2++wfDhw3HLLbdg0KBBePbZZz09NK/B/pbIt7HHFQ/7WyLfd7E9rqQ3nqNLRERERERERERERB7lkzNtiYiIiIiIiIiIiNorhrZEREREREREREREXoShLREREREREREREZEXYWhLRERERERERERE5EUY2hIRERERERERERF5EYa2RERERERERERERF6EoS0RERERERERERGRF2FoS0RERERERERERORFGNoSEXnInj17MG7cONjtdgBAnz59XC79+/fHZZddhkceeQTZ2dnn/fzTpk3DtGnTLmhsc+fOxdtvv31BjyUiIiIiMbG/JSJqPSZPD4CISEQ1NTV4/PHHMXfuXFgslvrtkydPxq233goAcDgcyM7OxltvvYXp06fjs88+c9nXnR577DFMmDABo0ePRq9evdrkNYmIiIio/WJ/S0TUujjTlojIA95//31IkoRrrrnGZXtMTAyGDBmCIUOGYNiwYbjxxhvx/PPPIzMzEz/++GObjS86Ohrjx4/HwoUL2+w1iYiIiKj9Yn9LRNS6GNoSEbWS3/zmN3jppZdw1113YejQoXj22WdPu5/dbse7776LCRMmnNPzhoaGAgAkSarfVlNTgzfffBPXXnstBg0ahGuuuQYrVqyA0+l0eayu61i5ciWuuuoqDB48GLfddhv27t1bf//rr7+OsWPH4o033kBycjKuvvpqFBcXAwAmTpyITZs24dChQ+fzz0BEREREPoL9LRGR53B5BCKiVrR69WrcfvvtuO++++Dv73/afVJSUpCXl4drr7222X1OpxOqqtZ/nZ2djUWLFqFnz54YMWIEAKNRfeCBB7B79248+OCD6NevH1JSUrB06VJkZWXhhRdeqH++HTt2wG6345lnnoHdbserr76KBx54AJs3b4bJZPwIyMnJwVdffYXFixejuLgYYWFhAICEhARER0dj/fr1eOSRR1r134mIiIiI2gf2t0REnsHQloioFUVFReGJJ56ALLf8QYaffvoJwcHB6NGjR7P7li1bhmXLlrlss1gsWLlyZf16X9999x1+/PFHLFiwABMnTgQAjBw5Ev7+/vjLX/6Cu+66C717965/7IoVK+pnM5SXl+N//ud/kJ6ejr59+wIAVFXF448/jssuu8zldSVJwsCBA7F169YL+8cgIiIionaP/S0RkWdweQQiolbUq1evMza0AJCVlYXOnTuf9r4pU6ZgzZo1WLNmDT7++GO8+eabuOyyyzBjxgxs3rwZAJCamgpFUTB+/HiXx9Y1uCkpKfXbevfuXd/QAkCXLl0AAKdOnXJ5bHx8/GnH07lzZxw/fvyM74eIiIiIfBf7WyIiz+BMWyKiVhQREXHWfcrLy2G1Wk97X1RUFAYNGuSybfTo0bj++uuxcOFCXHnllSgtLUVYWFj9x7/qREZGAnBtWG02m8s+dQ1307XBWhq31Wpt1gATERERkTjY3xIReQZn2hIRtbGwsLDzahQVRUF8fDwyMjIAACEhISguLq5fG6xOfn5+/fO3lrKyslZ9PiIiIiLyPexviYhaH0NbIqI21qlTJ+Tm5kLX9XPa3+FwYN++fejWrRsAYPjw4dA0DRs2bHDZ75NPPgEAJCYmttpYT5w40eJH3YiIiIiIAPa3RETuwOURiIja2MiRI7FixQqkpaU1W2srNzcXu3fvrr9dVlaG1atX4/jx41i4cCEA4IorrkBycjL+9Kc/IT8/H/3790dqaipWrlyJm266qf4kDRdL13Xs2rUL06ZNa5XnIyIiIiLfxP6WiKj1MbQlImpjSUlJCA8Px+bNm5s1tXUnaQCMs9sGBAQgPj4eS5cuxXXXXVe/ffny5Xjttdfw97//HUVFRejSpQv++Mc/4u677261ce7ZswclJSW49tprW+05iYiIiMj3sL8lImp9kn6un18gIqJW83//93/48MMP8eWXX0KSJE8P57SefPJJlJaWYtmyZZ4eChERERF5Ofa3RESti2vaEhF5wNSpU6FpGr744gtPD+W0cnJysHHjRsyePdvTQyEiIiKidoD9LRFR62JoS0TkAf7+/liwYAGWLFkCu93u6eE0s3DhQtx3333o06ePp4dCRERERO0A+1siotbF5RGIiIiIiIiIiIiIvAhn2hIRERERERERERF5EYa2RERERERERERERF6EoS0RERERERERERGRF2FoS0RERERERERERORFGNoSEREREREREREReRGGtkRERERERERERERehKEtERERERERERERkRdhaEtERERERERERETkRRjaEhEREREREREREXmR/wfQVtdjrUhpBQAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 提取 1s 波函数\n", "u_1s = result_he.orbitals_by_l[0][0]\n", "\n", "# 计算 R^0 Slater 积分\n", "R0_1s1s = slater_integral_radial(r, w, u_1s, u_1s, k=0)\n", "\n", "# 可视化\n", "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))\n", "\n", "# 左图:波函数\n", "ax1.plot(r, u_1s, 'b-', linewidth=2, label='1s 波函数')\n", "ax1.fill_between(r, 0, u_1s, alpha=0.2)\n", "ax1.set_xlabel('r (Bohr)', fontsize=12)\n", "ax1.set_ylabel('u(r)', fontsize=12)\n", "ax1.set_title('He 1s 轨道波函数', fontsize=14)\n", "ax1.set_xlim(0, 5)\n", "ax1.legend(fontsize=11)\n", "ax1.grid(alpha=0.3)\n", "\n", "# 右图:Slater 积分\n", "ax2.plot(r, R0_1s1s, 'r-', linewidth=2, label='R⁰₁ₛ₁ₛ(r)')\n", "ax2.set_xlabel('r (Bohr)', fontsize=12)\n", "ax2.set_ylabel('R⁰(r)', fontsize=12)\n", "ax2.set_title('Slater 径向积分 (k=0)', fontsize=14)\n", "ax2.set_xlim(0, 5)\n", "ax2.legend(fontsize=11)\n", "ax2.grid(alpha=0.3)\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "print(f\"\\nR⁰ 积分在 r=0 处的值: {R0_1s1s[0]:.6f}\")\n", "print(f\"R⁰ 积分在 r→∞ 处的渐近值: {R0_1s1s[-100]:.6f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## HF vs DFT 比较\n", "\n", "对比 He 原子的 HF 和 LDA 结果:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:15:42.095567Z", "iopub.status.busy": "2025-12-04T04:15:42.095444Z", "iopub.status.idle": "2025-12-04T04:15:47.097050Z", "shell.execute_reply": "2025-12-04T04:15:47.096909Z" } }, "outputs": [], "source": [ "\n", "from atomscf.scf import SCFConfig, run_lsda_pz81\n", "\n", "# He 原子 LDA 计算(Z=2 会自动使用 default_occupations)\n", "cfg_lda = SCFConfig(\n", " Z=2,\n", " r=r,\n", " w=w,\n", " maxiter=50,\n", " tol=1e-6,\n", ")\n", "\n", "result_lda = run_lsda_pz81(cfg_lda)\n", "\n", "hf_total = get_hf_energy(result_he)\n", "hf_eps_1s = get_hf_eps(result_he, l=0, idx=0)\n", "lsda_total = result_lda.energies.get('E_total', 0.0) if result_lda.energies else 0.0\n", "lsda_1s_energy = result_lda.eps_by_l_sigma.get((0, 'up'), [0.0])[0]\n", "\n", "print('方法比较 (He 原子):')\n", "print('\\n 方法 总能量 (Ha) 1s 能量 (Ha)')\n", "print(' ' + '-' * 48)\n", "print(f' HF {hf_total:>12.6f} {hf_eps_1s:>12.6f}')\n", "print(f' LSDA-PZ81 {lsda_total:>12.6f} {lsda_1s_energy:>12.6f}')\n", "\n", "delta = abs(hf_total - lsda_total)\n", "print(f'\\n 能量差: {delta:.6f} Ha')\n", "print(f' 能量差: {delta * 27.211:.3f} eV')\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 核心差异\n", "\n", "| 特性 | Hartree-Fock | DFT-LDA |\n", "|------|--------------|----------|\n", "| 交换处理 | 非局域(Slater 积分) | 局域近似(Dirac 泛函) |\n", "| 计算复杂度 | O(N⁴) | O(N²) |\n", "| 自洽难度 | 较高(交换矩阵构造) | 较低(密度泛函) |\n", "| 物理图像 | 波函数反对称化 | 均匀电子气模型 |\n", "\n", "**关键洞察**:\n", "- HF 交换是精确的,但不包含关联\n", "- LDA 同时近似交换和关联,误差相互抵消\n", "- 对小原子,HF 通常更接近实验能量\n", "\n", "## 下一步\n", "\n", "在 **[05-dft-xc.ipynb](05-dft-xc.ipynb)** 中,深入理解 DFT 的交换关联泛函实现细节。" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.2" } }, "nbformat": 4, "nbformat_minor": 4 }