{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# DFT 交换关联泛函\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/05-dft-xc.ipynb)\n", "\n", "## 学习目标\n", "\n", "- 理解局域密度近似(LDA)的物理基础\n", "- 掌握 Dirac 交换和 PZ81/VWN 关联泛函\n", "- 对比不同 XC 泛函对计算结果的影响\n", "\n", "## LDA 的物理图像\n", "\n", "局域密度近似假设交换关联能量密度仅依赖局域电子密度:\n", "\n", "$$E_{\\mathrm{xc}}[n] = \\int \\epsilon_{\\mathrm{xc}}(n(r)) n(r) dr$$\n", "\n", "其中 $\\epsilon_{\\mathrm{xc}}(n)$ 由均匀电子气模型确定。\n", "\n", "### Dirac 交换\n", "\n", "$$\\epsilon_x(n_\\sigma) = -\\frac{3}{4}\\left(\\frac{3}{\\pi}\\right)^{1/3} n_\\sigma^{1/3}$$\n", "\n", "$$v_x^\\sigma = \\frac{\\delta E_x}{\\delta n_\\sigma} = -\\left(\\frac{3}{\\pi}\\right)^{1/3} n_\\sigma^{1/3}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 理论基础:LDA 交换关联泛函\n", "\n", "密度泛函理论(DFT)将多体问题简化为单粒子 Kohn-Sham 方程。\n", "\n", "### 局域密度近似(LDA)\n", "\n", "交换关联能密度:\n", "\n", "$$\\varepsilon_{xc}[n(r)] \\approx \\varepsilon_{xc}^{\\text{hom}}(n(r))$$\n", "\n", "使用均匀电子气结果:\n", "\n", "#### Dirac 交换\n", "\n", "$$\\varepsilon_x(n) = -\\frac{3}{4}\\left(\\frac{3}{\\pi}\\right)^{1/3} n^{1/3}$$\n", "\n", "$$v_x(n) = \\frac{\\delta E_x}{\\delta n} = -\\left(\\frac{3}{\\pi}\\right)^{1/3} n^{1/3}$$\n", "\n", "#### PZ81 关联\n", "\n", "Perdew-Zunger 1981 参数化 Ceperley-Alder QMC 结果:\n", "\n", "$$\\varepsilon_c(r_s, \\zeta) = \\begin{cases}\n", "A\\ln r_s + B + Cr_s\\ln r_s + Dr_s & r_s \\geq 1 \\\\\n", "\\gamma/(1+\\beta_1\\sqrt{r_s}+\\beta_2 r_s) & r_s < 1\n", "\\end{cases}$$\n", "\n", "其中 $r_s = (3/(4\\pi n))^{1/3}$ 为 Wigner-Seitz 半径。\n", "\n", "**代码实现**:\n", "- `vx_dirac(n)` → 交换势\n", "- `lda_c_pz81(n_up, n_dn)` → 关联势与能量\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:15:50.483554Z", "iopub.status.busy": "2025-12-04T04:15:50.483050Z", "iopub.status.idle": "2025-12-04T04:15:50.489276Z", "shell.execute_reply": "2025-12-04T04:15:50.489185Z" } }, "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": "2025-12-04T04:15:50.494733Z", "iopub.status.busy": "2025-12-04T04:15:50.494545Z", "iopub.status.idle": "2025-12-04T04:16:09.446964Z", "shell.execute_reply": "2025-12-04T04:16:09.446666Z" } }, "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": "2025-12-04T04:16:09.451650Z", "iopub.status.busy": "2025-12-04T04:16:09.451554Z", "iopub.status.idle": "2025-12-04T04:16:09.639090Z", "shell.execute_reply": "2025-12-04T04:16:09.638952Z" } }, "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 import SCFConfig, run_lsda_pz81, run_lsda_vwn\n", "from atomscf.xc.lda import vx_dirac, ex_dirac_density, lda_c_pz81\n", "from atomscf.xc.vwn import lda_c_vwn\n", "\n", "plt.style.use('seaborn-v0_8-darkgrid')\n", "plt.rcParams['figure.figsize'] = (12, 5)\n", "\n", "\n", "def safe_energy(result, key):\n", " return result.energies.get(key, 0.0) if result.energies else 0.0\n", "\n", "\n", "def get_eps(result, l, spin='up', idx=0):\n", " eps_list = result.eps_by_l_sigma.get((l, spin), [])\n", " return eps_list[idx] if idx < len(eps_list) else 0.0\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## XC 势与能量密度\n", "\n", "可视化交换和关联势对密度的依赖:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:16:09.643490Z", "iopub.status.busy": "2025-12-04T04:16:09.643377Z", "iopub.status.idle": "2025-12-04T04:16:10.371683Z", "shell.execute_reply": "2025-12-04T04:16:10.371590Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# 测试密度范围\n", "n_test = np.logspace(-4, 1, 200) # 10⁻⁴ 到 10 Bohr⁻³\n", "\n", "# 计算 Dirac 交换势\n", "vx_test = vx_dirac(n_test)\n", "\n", "# 计算 PZ81 关联\n", "eps_c_pz81, vc_up_pz81, vc_dn_pz81, ec_pz81 = lda_c_pz81(n_test / 2, n_test / 2)\n", "\n", "# 计算 VWN 关联\n", "eps_c_vwn, vc_up_vwn, vc_dn_vwn, ec_vwn = lda_c_vwn(n_test / 2, n_test / 2)\n", "\n", "# 可视化\n", "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))\n", "\n", "# 左图:交换关联势\n", "ax1.loglog(n_test, -vx_test, 'b-', linewidth=2, label='|Dirac 交换势|')\n", "ax1.loglog(n_test, -vc_up_pz81, 'r--', linewidth=2, label='|PZ81 关联势|')\n", "ax1.loglog(n_test, -vc_up_vwn, 'g:', linewidth=2, label='|VWN 关联势|')\n", "ax1.set_xlabel('电子密度 n (Bohr⁻³)', fontsize=12)\n", "ax1.set_ylabel('|势| (Hartree)', fontsize=12)\n", "ax1.set_title('XC 势随密度变化', fontsize=14)\n", "ax1.legend(fontsize=11)\n", "ax1.grid(alpha=0.3, which='both')\n", "\n", "# 右图:关联能量密度\n", "ax2.semilogx(n_test, eps_c_pz81, 'r-', linewidth=2, label='PZ81')\n", "ax2.semilogx(n_test, eps_c_vwn, 'g--', linewidth=2, label='VWN')\n", "ax2.set_xlabel('电子密度 n (Bohr⁻³)', fontsize=12)\n", "ax2.set_ylabel('ε_c (Hartree)', fontsize=12)\n", "ax2.set_title('关联能量密度', fontsize=14)\n", "ax2.legend(fontsize=11)\n", "ax2.grid(alpha=0.3)\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "print(\"关键观察:\")\n", "print(\" • 交换势 ∝ n^(1/3),关联势在低密度区增强\")\n", "print(\" • PZ81 和 VWN 在中等密度区非常接近\")\n", "print(\" • 高密度极限:交换占主导\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Al 原子:PZ81 vs VWN\n", "\n", "对比两种关联泛函的计算结果:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:16:10.407706Z", "iopub.status.busy": "2025-12-04T04:16:10.407589Z", "iopub.status.idle": "2025-12-04T04:16:24.569011Z", "shell.execute_reply": "2025-12-04T04:16:24.568879Z" } }, "outputs": [], "source": [ "\n", "# 生成网格\n", "r, w = radial_grid_linear(n=800, rmin=1e-5, rmax=30.0)\n", "\n", "# Al 原子配置(Z=13 会自动使用 default_occupations)\n", "\n", "# PZ81 计算\n", "cfg_pz81 = SCFConfig(Z=13, r=r, w=w, maxiter=50, tol=1e-6)\n", "result_pz81 = run_lsda_pz81(cfg_pz81)\n", "\n", "# VWN 计算\n", "cfg_vwn = SCFConfig(Z=13, r=r, w=w, maxiter=50, tol=1e-6)\n", "result_vwn = run_lsda_vwn(cfg_vwn)\n", "\n", "print('Al 原子泛函比较:')\n", "print(' 泛函 总能量 (Ha) E_xc (Ha) 3s 能量 (eV)')\n", "print(' ' + '-' * 58)\n", "\n", "E_total_pz81 = safe_energy(result_pz81, 'E_total')\n", "E_xc_pz81 = safe_energy(result_pz81, 'E_xc')\n", "eps_3s_pz81 = get_eps(result_pz81, l=0, spin='up', idx=2)\n", "\n", "E_total_vwn = safe_energy(result_vwn, 'E_total')\n", "E_xc_vwn = safe_energy(result_vwn, 'E_xc')\n", "eps_3s_vwn = get_eps(result_vwn, l=0, spin='up', idx=2)\n", "\n", "print(f\" PZ81 {E_total_pz81:>12.6f} {E_xc_pz81:>10.6f} {eps_3s_pz81*27.211:>12.3f}\")\n", "print(f\" VWN {E_total_vwn:>12.6f} {E_xc_vwn:>10.6f} {eps_3s_vwn*27.211:>12.3f}\")\n", "print(f\"\\n 能量差: {abs(E_total_pz81 - E_total_vwn):.6f} Ha\")\n", "print(f\" 能量差: {abs(E_total_pz81 - E_total_vwn) * 27.211:.3f} eV\")\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## XC 势空间分布\n", "\n", "可视化 Al 原子的交换关联势:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2025-12-04T04:16:24.575040Z", "iopub.status.busy": "2025-12-04T04:16:24.574945Z", "iopub.status.idle": "2025-12-04T04:16:24.814410Z", "shell.execute_reply": "2025-12-04T04:16:24.814302Z" } }, "outputs": [ { "data": { "image/png": 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9icUoIuJlGJkvt9vnZTI870ZYOGSt0W23Y46P8+2X27LJhLtBQ5/TmY8cxhQX59PORLZ+hoERHY2rUROfvtZ1azClpeWMOWMZA5PbjbNla9y163j7mRITCPp1eZZ+bkx5HCOt/0AID/f2tWzdQtBf63Ke68xxMAxMhoE7uiJpN9zkE2/Qgi+x7N571vPhdpPe5ULSe/fzuSbhE5/O2R7D95oB9tvvwtWseWa827cR+s7/zrTxbQuGz3rSqzN84g3+8jNsy37K+d9Ftv7OVm1IHfOgT9/w8Y9iOXQoR3zeuDPivfk2HFdelXltTp4k6t67c/bxnjLzcye+OgN3vfrevrbF3xM64/XM7zZ73GdidlepSsLceb7xTniKoOXLvH1M2fuf6ZvWfyApj47z6RvdrwempESfc3r7A7jPfL+TX8bR93LvZuvG9UTdfnO27yaXdyB21V8YEZHe9dAZrxM26/U822csO9t3JP6zr3zirTD4aqwb/sq1fdZtifc8QNyohzL/84xPoOHFTfM8V9Zt2+d8T1KbLt6cZvTSr2j29B052vp8T4AzLJKlXx7xntPtNtFu+ijqL3mf/Ozvci2/jf4Qt9vk/Wfyfw92IDz2cL59l944k80XDvH2q3RkJ0Omdsq3H8BLo3cRH1nHG/PkyQXqli8lbvNh+2YB4S8+jykpyS/nNyIiSH5sPI6B1xSq39y57/Lppx8Cnhq0DoeDBg0aMmHCC9SokVnS4Ndff2HevI8YNmwkMTFdfI5x+vQpjh07xl13Dadr10vYsWM7M2a8xrvvvsmQIXef92cTERERCSRhYWGkpqb6bMtYD8+SDMhwjBocm9cA26t/Qy4Tw0r5Y7Va/B2CRx7JOkwmyPbHB9PpU54RSu5s7Q03pizrRpUqGJUqZ3Z0OLBs+TvnObKe98wxnJ0vhIiIzHPu349l08Zcz+PzCg0l/fobfOK1LvkR8+7dPufAnXGMzHO72rbD2f8qn77Bz0/EZE/Ndh7De4yM4zjuvAtXxwu8/cy7dhL8wnPgNnKN1YRBmMsFhkHK3E8gLMzbN2ju+9g+mpuzT7bv2tW6DalvvecTb9jNN2LZtCGX78bIPIbhJu3+B0l74OHMjvHxRDWonSORkpukJctwdc78PTLoux8Iu/O2fPsZkZEkHDjqsy305UnYPvwg377pV19Lyvsf+myLHHob5sP5J2VSps0k/bY7vOvmY4eJvPOWfPsBJPy9HaNi5h/YbL8tI/TJJ/Lt52rREuMW33PYPvwA609L8+2bNupeTFdckbnBMAib8VqB4jUuvxxnm1bedevxw4S++1aB+jpmzPL5/07wpvUEf/ZJvv3S42JxPfyIz7bg5cuwbN+Wb19390sxgizeAZXulHRsP+f/HQEc2JZGUqrV089tovqfp2i1amW+/ZIr1uarr2zeAZxuN1z+278027wx375/Wbowzwjx/rNyueDlrbsITU/Mt+8709L5/ctQ7zmbnjIx5fChAn3WGwaHkmgKO3NeE3cfTmfUyZP59tv0ewpXtYnI/H7dsDgplS6u+Hz7vvqSiWdfykwWR2KQQOpZemQaMiSUVWT+/B5MMJ/jyrdfSgpceaXvvdGbWCnIjABr1li49dYwn239MJHzTiunT+fZeHteiHe9FcEMOUv7rKZPt3GQYO+6ErclJGzm61h37vB7DIVN3F5zzfUMHuz5q57ZbCYqqgIRWW52AA4dOsikSc9w8cXdfEbRZpg8eSI1atTg9tvvAqBZsxaAwZQpk7nuuv8jOjr6XD6OiIiISEBq2rQpcXFxnDx5kipVqgCwe/duatSoQWRkZK59qqfu4/T2HTlGl0kRMAxwOjGl2SHNgREdDZbMxKn50EEse3ZjcqSBI93T1ul5x+XClO5ZNqKiSLv+/3wOHfzpR1h37TzzGGc6JqcTnC5wOTFlyRA4evf1HYlnGITcdIMnqZbxm7XrTHLR5cqSrHORNHEyziwDL6yrVxH54OjMxN6ZRKD3N/SM/oabU1v3+CRlwp99ktA33/C2zSth5+jZO8eIrYpX9MO6Y3u+X3fSs5NIHXlv5vd7+CgVenXPtx/A6V9X42rR0rse8vPPhN9/71l6eLhq1iJ54HU+20I++IDghV/l2zf15ltx9L3CZ1vk7FmYE3OWNcnO3r0njtaZI+Wtx04Q+eUX+fYDSE+xY1gzf/G3/nsA66o/8u3nDgvH4fBNhoQdO4b54MF8+7qSU336mlxGgZK2AOlpTpxZz+sqWD/DbeSI11awrrhd7hx9DQr2xy1XusunryX//JFXusOJO2vfAsZruFw5r00Bz5mS7OLoYTcul+fvI04ndC5g35UrTfwbZ/I+TV57i5lrCtj3kUesOF2Zff+zzkpBpiFft87M3d2CM35M4nKZ+P6AmWYF6Pvkk1ZeGZ/5zdQmjPz/6/W45b8hbCXzj0pDsPF2AfrFxsLddwf7bPsYGw2x4hnv7fnvKmM56/qff4cw9W/fMpSPEE0U5lzbZ13/ZVUY32RJx3UknEPUyvNcWd/X/WUlicz/V22nErtp5F3P3j5jeU96XY4f9/13sof6RBKXa/us7yeo6tPPjZmNtMvRPre+Kdn+a4+lImuJyTfe7P0AdtGE37k4135Z3/+hZY6+K7mYqpzIt+9hfEuAJhLJD2SOjs4rXgA7IRSHUpm4PXXqFE8++SRr1qzBYrEwaNAgHn30UW/t1ayWL1/OlClTOHDgADVr1uSRRx6hV69eRRZLyr1jCZ/8nF9H3KbcM6bQ/SIjo6hTp26e+9PS0njyyUeJjIxi/PgJmHIZxbFp0wbuvXesz7ZWrdridDo5cuSQErciIiIihdCgQQM6derEpEmTmDBhArGxscyaNYvBg89eeipo2c+Bkbg1DE8NOrfb53FkgKDff8MUH48pNQWT3Q6pKZhSUj3rqZnv9ptvJf2ii739LHt2EXXX7ZBmx+RwgN2OyZHmeaQ6Lc2TyDzj1KbtuGvU9K4HfzWfiGfH5xu2s1nzHInbkAVfZD5WfBbuypV9E7cmE8E/fp9vP8DzOHoWptSUAiVQATIeVc8MxO35fvLjziVTZS7gtCnZa/8VZhR5tr7GuZ4TMCwF62vKpe85f9aC9sutb7bvyTCbPcfL8jJMZowQ35HQAO6qVXHVqOnb3mTyPYbJhLtyZd9zWKykX9DJc27TmXP49DGD2eTZnq3Ei7tGLdKuHODpm3E+k+nM+pl3TBghORMc6Rd2PXNOTxufPmdehtmMq3XbHH1T7xyKOSEhS7vM47gNE063GZfbRGztjsTvN+FwmEhLA05Vp8YdE3C5TWdeZpxuM253Zh+ny7Pvry+qkmy2ectpVjl6OXV7VCTdbcblMuF0mUl3gcttJt1p8r4nmCqw/KownE5P+U2nE9olPkVU5ZFn2plwOM2e/k7Ped1nkn/736/Pjvd9B2Bdyi8+yb3cXgDbpzYnPksyM5IeNOFPzzXOpX3W9a1v2jzX4IwlPEFFRubaNuu21MRQjv3t++TApfyEFWee58rYlmT4fs7D1KIip3O0z61/9oTZe9zBXG49a+I16+fL6mY+4WbyH12cm/r8e0791nMBdSjYiFsAk8nw/nOcY76Ptyz3ef/Jmc1gsRgZ//yybIN6Zrd3m8Vi8LT5I287iyXHjwrvccxm6GZ2ZtkXwkOWP7P8M/f8vyHrOTPeG5ugiSk9y/YeTDWvPLNuZP3nnaP/3WaHz/4k8wN8aro/R7vs/U0meMKc5rNvq/mDXM+RvW9fM/Qz2bPEVpVdpgW5frbs/V8xgdmckvljrMB/ojm7Upm4HTt2LNWrV+e3337j5MmTjBw5kvfee4+hQ30HRe/bt4/Ro0czdepUevbsyeLFixk7diyLFy/2mfThfDgGXlPo0a5lwWuvTWHfvr3MmvV2jnpqGapVq86uXbt8tu3ZswuTyUTt2nknhUVEREQkd9OmTWPChAn06dMHs9nMNddcw6hRo87ax/bLT9jvKiVlqux2zCeOe5KlKcned1KyrqeAy0Xq6LE+XUPemk3wj99jSk2FjGSr3Z6ZfE1J8Zxi0LUkvuVbwy7ynruxFOAx0vSYLj6JW9wG1i2bC/zZsjKCbQXr53Tm2GTkMuAkV7kmFi2e0bKF7RsUhDsi8sxv5JkJNiPrb+MWi+e3SbfbJ5norlmT9Lbtz7Qzgdni/U0+a8LO2SZnwszR7VJcDRtnJhEzjmHyTS66WrTw/Zzh4aTedXfm8TH5tPccy3Mcd+UqPn2d7TuSNP7ZLG1NWc6d+XmNsJy/NKcOGY7jiqsy25uyZTfOHMtVs3aOvvEffZ753Zl94zWyfF53Ld8RW87WbTm1bnOe7W3BFhxOw7M90vd3s5T7Hybl/oczswSFkPDBp4Vq7xUaStwPy86pq7PLhcR3/pgzfyfBbjd539PSIDXV5J0/KG2RZzktDRwOEw7HHaQ1ucObVPW0O7OcBmlpZ/r+ayLtqzPHyNjmeDLLcsbxPMc2jCzf2/TsEYcDTxbswy3MvuGCM6/C207BRpvn5ld6nFO/RKJYf47xnqAaJ6iWbzuLxSDYamCx4H25rNUwzJnrZu+ygdWadR0sFpc3qehZj/Q5ltnse+zMlzPbcTzHtVrduZw3M3Fptebcl5GstFjItj/z3JnJz7wTndkTosHBZlwuV/Yfc979WROqWftnP885/CiQMq7UJW7379/PmjVr+PXXXwkNDaVu3bqMGjWKl19+OUfidsGCBcTExNC3b18A+vfvz/z585k3bx733XefP8IvExYv/oGFCxcwYsS9VK1alVOnctZDqVy5Cjfd9F9eeWUy9es34JJLurN7906mT5/KNdcMzjPZKyIiIiJ5q1KlCtOmTStQ22NUozrHCVrxmycTYStgIjE5GfPxY5hPnMCUlIi7Tl2fCWpITyfslclnRqyeSaCmpJwZxZriXTelppIw5x2fx/FtPy2hQgHqQRo2W47ErXXnDmzL808GmVJTch4vNOdowoL0NYKDPS9bMAQHY4SEYNhsEBziScwGh2BkLGf7fp0dLiBlzIMYNpunjzUIrBZPUtYaBFYrhsWCUSE6RxzJjz1J6sjRGGf6YLV6ljMyAWYThtmCEVUhR99Tm3ZkJl4tFk+CL7fka7bf3NMv6c6pPQUfsZVV6oh7SR2Rf+mB3CRPevmc+hlRFUh6Yco59XW1ak1qq9bn1Nd5UVdyptoL2LfLhefWMSTEZ+Kk7AybBcORR7I+S/mOc5ExkD0lxURqat7JVLvdkwT1bPdtk7WtZ2L2jOW8+/skSwXwjEq02SAoKONl5LHsWbdaPT+WPMlDz3rmy/D+OAny/mjxbZPbtox+QUG+bYKCfBOVGefP2JbbsXO2UULxbGw2Ew5HAetriGRR6hK3O3fuJDo62mfEbOPGjTl8+DAJCQk+CcNdu3bRrJlvtZQmTZqwbVveha9NR45A5fz/UlSerV27CoDZs2cwe/aMXNusWLGOQYOuJSgoiHnzPmbOnBlUqVKNa6+9gf/+944SjFZEREQkMC3mMm7lQ8zJSQStW0P6xd189lu2/I1180asW/7GunUL5oP/Yj5+HHOyb4mvlJGjSX72+cwNZjPhUwuWbDMlJPis5zaCMdd+Gc8DZxl5aoRm9jWCgjBCwzwJ2dBQz3KY593VMmdCLnXYSM9M3Rlts71zpq+7mu99vrtuPU4eOFGgmLNzxnTxSVoXhqttuwJMvZI7o2rV/BtJueFyQUICxMebSEnxJEHzek9O9iRfz9Ym63tGsra8J1Ezkp7BwWCzGd53m41clz3vmdvzSpxmJE1tNt8kqs129oRrUBC59s2ag7fZLDnq3oqI5KbUJW6Tk5MJzfYX9Yz1lJQUn8Rtbm1DQkJIScn5V/oMQZf3xL5qE6aCPr5UBn3xRY5nOHyMG/cM48Y9U6BjXXnlAK68siBlyGHGjP8VqJ2IiIiI5C8jcQsQ/PX8HInbyEcfIGjNqnyPY7Jnm/nZYsEIDvbUec2FYTJhhIVDaCjgOzrIXas29quv8yRQw8Iyk6dh4Z738HDvvuxDr5IfeoyUBx/x1OIM8p3QJT/2IcMK1V6kOKSnQ3IyJCV5kqhZl5OSyPbuSZ5m35+czJkErGe/w1F2k6pms0FICISGepKhISEQEmJ43z3bDEJD8S5nvGdNtOZMquadaM1YDg42zmwrXAlhEZGyptRlL8PCwkhN9b25zFgPzzZJQWhoKPZstajsdnuOdj7HH3KQXad2U6VuqyKKWEo7q/X8Hi+SskfXPPDomgceXXMJBEvo510Offctkl6c6rPf2aq1T+LWHVUBd/XquKtVx12tGu6q1TAio3B2iiG7+I+/8JQPCAvFCMlIwnoSsAQH5/m8q6t5CxLffO/cPlBEBHpIVEpSRpmAhAQTiYmed8+yZz1n0tWUIzGbdX9aWulOsppMBmFhEBbmSZaGh3veM9ZDQzOTqp5kqpEt2Zq5LTMZm7kvI/GacRw9Gi8iUvxKXeK2adOmxMXFcfLkSapU8RSh3717NzVq1CAyMtKnbbNmzdiyZYvPtl27dtGmTZuznsPhcOuxhACj6x14dM0Dj6554NE1l/LuGDXYGdGepkkbATAfPYK7Rk3v/rSB1+Bq0Ahnq9Y4W7XBqFbwcmDp3c9tchuRkmIYkJoKiYmmMwlXvEnXvNYzlzMTtenppSezaDYbRER4EqphYZ4EaFiYQXi4iZAQtzfJmrkv73dPO9/E7Fn+5iIiImVUqUvcNmjQgE6dOjFp0iQmTJhAbGwss2bNYvDgwTnaDho0iHfffZdFixZx2WWXsXjxYtasWcO4cePOeg7D0N/6RURERKT0m95oKq+YH8KIrIApPh6yJG7Tu/dQAlZKJcOAlJSzJ12zJlnzSro6nf7NQoaGGoSHG4SHQ0SEZzkj8Zr57rs/PDy37Z5tISG5J1ZV71RERPJS6hK3ANOmTWPChAn06dMHs9nMNddcw6hRowDo2LEjzz77LIMGDaJx48bMnDmTKVOmMG7cOGrXrs306dNp2LChnz+BiIiIiOTLMDDS03GkJuJMS8ZhTyKaUKxOF6Q5MKU7OJp4mH9TDpLuSGXAHeP9HXGJ21DhUuK+XO7vMCSAGIanjmthk6xZyxAkJIDL5Z+kq8ViEBUFkZEGUVGZr8hIsix71iMjsydjM5OtYWG+k0mJiIj4Q6lM3FapUoVp06blum/9+vU+6927d6d79+4lEZaIiIhI+WAYuNPsOFLiSUtJJM2eiCM1AXtqEo60RBxpyUQ5rbSgGqY0O9jtmNLS+Dh1JXHpCaS57KQ50zzvbgd2t8PzbqSTRjoj9teg79EwSEvD5HCwIySJa3seIs1s4DC5SbMYOMyQZoX0bImRg69AtcTM9Xe6wkOXnwmbwEvc6kExKYyMpGteSdbcar1mHw2bmOi/pKvVmnuSNSoq9/XM5Gzmei7z4omIiJRZpTJxW9wMw+3vEEREREQ8DANnajJpSaexp8RjT4olNSUBe2ocdnsi9tQELjDVoaLdhMlux5Sawnb7Aea7N2J32kl12bG707AbDtKMdOw4sePEgROLy2DpktqY0tK8ydfRlybyVnsXjnzuAq/fCl985rtt0lj4NxowA0F5971q5XGC/sxct1SGHRUK9nU4siVybQH+9LBbt60BxeWCuDiIj/ckUTPeExI82zLXTcTHk62Np53b7Z+sZVDQ2ZOuuSVZs6+HhirpKiIiklVAJm5FRERECsJwuXAkxZGacJLUxFMYqcnUc0VhSknGlJKCKSWZHxLWcDDtGKnpKaQ6U0l1pmJ320l1pZFqOM680hl8qAJ37IzElJqCyW4nJT2ZukNiSQnKOeo0u1/fgfr/Zq4faAGTbso/fpsTrDt3+G50kW/SFiAtl5iCC5hEtZ85vmE2Q3AwttAgKtoTCXabsLlNBLvNBBlmbIaZYCzYDAs2rNiw4O7bCbupAobNBjYbLcNPMTp1PzbzWTLF5ZgSt2VTejrExpqIjTVx+rSJU6c877GxmctxcZkJ2YwEbFKSf7KWNtu5Jl0z++RVv1VERETOXWAmbjXiVkREpPwwDEhLw5UYz8m4A6QmniI1OZbklFhSU+JISU0gOS2B1LREUhxJJKenMDauFRFJDm8C9rPIfcypeYBkUzrJFpfnZTVIsoHLnHmqDkdg/Rzf079xO/zSEM9d1VnurNruOE3Q35nrYSaIDynYR0zJlrMMTS9Yv3QLOKOiMAeHYAQHYwQHUzc4kQ5xCYQYVoKxEGwKIhgrIaYggk02Qsw2gs02WtWrQfITXTDO9CUkhGeMrditEGwLJdgWTnBwBMEh4QQHRxIcEkFwaCS20Cgib6nCifBosHq+kAhge8FCBiBLpQTan3kFKpVKKH0SEmDfPjOHD5s4csTMsWOe9yNHTBw9auLoUTNxcSWXwbRaDaKjfZOu+SVZc0u6ioiISOkTmIlbERER8S/DIC0xFldiLJF2N6akJEyJiZiSklh06jdOpZ4kyR5PkiORJGcSic5kktx2kgw7SaSRaE5n3J8RXLvF5enndLK5GrQblc95zyRXR7yxkqoJmZtPXQS/t8k/7CRbzm0RjoJ95FQrGDYbRkgoRmgohITQOu4IVsyEGVZCCCKMIEJMNkLNwYSabYRaQgmxhlD1vzEkhtTFCAuD0FCaBqUzzzhAaEgUoWFRnsRpaJTnFRZJcFgFgkMisVptxN7jm0C668yrIFKyrfcrYD8pOv567D3QGQYcOmRiyxYzW7ZY2LXLzN69ZvbtM3HqlDn/AxRCaGhmIjU62jNhVoUKhve9QoXMZGuFChnvmdtUXkBERKT8UuJWRERECsWZkkTiqUMkxh4iMf4oyQkn6eaqizk+HlNCAqaEOL5w/sUy8z6S3KkkGmkkmtNINKWTZHGRGOQmwWaQboFr/oEF83yP/8QY2FcRTx3Vs4wCO+ywY47NXC9oAhVyJmDDz/QNckFEuolwp5lwt4Uwt5UII4gwbISZbNS2RJEyvBdGWBhGWDiEhTHMdoCBVjshwRGeV0gkoWEVCAmJIiQ8mpCwCoSEVyRsaGVO2kJ9zrus4CFjz7IcCfQqRF8puzTitmTExsLq1RZWrbKyfr2ZrVstxMcXPhsaHGxQo4ZB1aoGlSrl/apc2TNKNirKIDg4s7/NZsHhCPDCziIiIuIVcInbZe9BxasLODtGGTR69HASExN5772Pc93/8suT+OmnJaSkJPPDD78QFhbm3fe//83igw/eYciQuxky5G7v9ri4OAYO7Mf48c9StWo17rtvBDfc8B/GjHkwx/G7dYvhiSeepn//gUX/4URE5LwZTicpsUdIPH2YhLijJMYfJSHpBIlJJ+meVpPaCZxJvsaz3rmfCVU3E29OI8HsIM7qIt7mJjlb0tPihvQJkDXF8dcV8P5F+ceTGJxzW2QBErBWF6RFheNqUA13RCRGRAShFYIZFLeNcFMwYZZQwi1hhFlDCbNFEBYUQXhwJGGhFQgNiSL8nU6cjqyKER6OERbOVSFBHAoNIygol4CySc623jX/cEXOmRK3xSM1FX77zcLSpVZWrbKwbVs+habPqFnTTcOGbho0cFOnjkHNmgY1a7qpUcOgRg03FStq9KuIiIgUnYBL3PbcB6csNsprldsBA65m4sSn2LNnN40aNfbZ53A4+Pnnpfzf//2Hd975H1u3/k1MTBfv/tWr/6BateqsWrXSJ3G7ceNfGIZBTEwX9u/fB8AXX3xKz569ad++Y4l8LhER8ZWemkT88X9JOHWAuNMHiU84QlzicRok27gkoQLm2FhMcbEQe5pebddw2uogNsjJ6RDDp2ZrVgs/hmZZ5rFKawA/3pF/LC4zJNt8R7xG23O2C0mHSKeZKKeFCJeVSCOI1qGVsQ/ughERgRERiREZyQNhu0gINhERGk14aEUiIyoTHlGF8ApVCa9QjYgKNYiMqkB6upvTWY5vAd7KP9zMuLMsB+a0V1IWaHKyonPqlIklSyx8/72V5cutpKTknWGtWdNN69ZuWrd20aqVmxYtPMna0NA8u4iIiIgUuYBL3JZ3PXv25tVXX2LJkh8YPvwen30rVvxKcnISV101iK+/ns/mzRu9idu4uDh27NjGgw8+xtSpLxIfH0eFCtEAbNiwnsaNm1K5chVv4rZmzVpMmvQs77//KSGazUBE5Jy5nenEHd1D7PG9xJ7az+nYQzgT47g+uYE3+WqOjeWZKhv4oeIJYq3pnLa5ch2pCjD0T7hsoe+2rRdBQgF+VMdla5M1+RrhgArpFqKdVqLcNioQQpQplChrOBWCokh6/DKMCtVwR0VhRFXgxhAHlwW7CY+qSkR0DcKiquU5mjUx2/pV+YeKSUPaJEBoxO35cbngl18szJ0bxOLFVpzOnD87LBaDtm3dXHihi4suctGli4uqVfXFi4iIiP8FZuK2HN8BBweH0LfvFSxZ8gN33z3K5xfbH374js6dL6J69Rp06tSZzZs3evetWfMHlStXYcCAq3njjWmsWbOKfv2uADwjbrt08X3e9aGHHufxxx9k9uwZjB37UMl8OBGRUs5wu0mJO8rpo7uJPbGPFvZIImOTMZ8+jfnUSX5P2crM8A2cMlI4abVz8swIWHe2EbBVkuH2l323Hb4GNjTKP4bTuYwGq5zqSXRWclio6LJRwQimAqFEWcKJskZQwRZFZHA0Le66gPjKLTCiKuCOqkDNiFB2hFmIiK6J1ZrLrFzZZB1kW/XMS0TOj0bcnpvDh018+GEQn3wSxKFDOR8zqFLFzeWXO7niCieXXOIiIsIPQYqIiIjkI+ASt980hwtcdvKvYJfpjQ0zmL1xRr7t2lVtz9z+vjOs3LroRjad2JhHj0wj2t/LyA73eteTHIlc8knnHNsLYsCAq/nqqy/YtGkj7dt3ACA29jSrV6/k2WcnARAT04XXX5+C2+3GbDazevUfdOlyEVarlQsuiGH16j/o1+8KkpOT2LVrJyNHjvY5R9269Rg2bCQzZ75Oz5696dDhgkLFKCJSVhh2O5ZTJzGfOI75xHHSjh/ijdPfciL1BCfSYzlhJHLKZOdUkIOTIW7SsvyfdeVb0PVg5npiS/j6xvzPGRsKBr41Yyuleuq6VkozUyndSkV3MNGEUNEcQbQ1iorB0VQIrUSzbo2Iu74bRsWKuKMrYlSsyB8REZgtBftfftbyshYgukC9RKS4lOPxBsVi3z4T06bZmDcviPR039G11aq5GTzYSf/+6XTq5MZSsLK2IiIiIn4TcInbq/8Dm9JiqVGIPomOBI4kH863Xa2I2jm2nUw9WaC+iY4En3UDgyPJh3NsL4gWLVrSpEkzliz53pu4XbLkByIjo+jWrQfgSdwmJyezZ89uGjduwtq1qxkzxjNytkuXrrz77psAbNq0Aas1iHbtctay/b//u5nly3/mhRcmqGSCiJQtqakc+3czh4/8w8lT+zkVd5ATSUc4YT/JcWccJ4xEjltSORbsZORag0k/ZXZNN8MzTwEFGJ11Msx3vUpK5nJkGlRxWKnstFHZCKOKOZJKtmgqBVeiUnhVTr/TH0ulKt7k68OR4TweFonJnEeB2izSs63n30NESiuNuC2YXbtMvPZaMF9+acXlykzYms0Gffu6uOWWdPr2dRKkgtYiIiJShgRc4vZcRNqiqBleK992VUKr5LqtIH0jbVE+6yZM1AyvlWN7QQ0YMIh33nmTsWMfxmq18v3333LFFVdhtXouebVq1albtx6bN2/E7XYRFxdL586eerddulzEK69MZu/ePWzYsJ727TsQHJxzjLLZbObxx5/mzjtvVskEEfE7wzBIij3MsX+3cPzINo6f2svRuAMcTT1KUHIqL/1VFfOxo5hPnMCclMgdN8OiZlkOEESuM1QdC/ddD3JDpRQ4nSUpG+SCqnYzldNtVHaHUNkcQRVLFJWvvZDE6NYYVargrlSZJtERbI60EF29McGhkWf9PO4zr6zhiUjgUeL27E6cMPHcc8F8+qkVw8hM2EZGGgwd6uD229OpVUvDlkVERKRsCsjErVHIZ85Gdih8uYIM2UsnFFSELZKNt287p74Al112JbNmTWPVqt+pVas2O3fu4JlnJvm0iYm5kL//3kRychItWrQiKqoCALVr16F27Tps3PgXmzatp3v3Xnmep169+j4lE0REikNS3DGO/7uZegkmwo+fxnz0KOZjR1mWvIEXozdyxJrK4ZB0UrKXYTUD4VDZBK+t2umzq3ry2c8Z4YDqdivRFaqS1j8Gd9VquKtWxV21Gm9FHCOkUnUqV2tElVrNiKhYK8+RsFnrvgYB1Qv74UVEJAenE959N4gXXwwmISEzYVuxosHddzsYOtRBhQp+DFBERESkCARk4tZTObB8i4qqQPfuPVm2bClVq1anbdv21K/fwKdNTEwX/ve/mcTGxnLhhV199nXp0pXNmzexbds/PPjg42c9l6dkwjJeeGFCUX8MEQkA7qREdu9cwZFDWzlyYieH4vdzKPUoh1ynOWRJ5lCog6QzCdnf34aLD2T2dTaH3/6T/zlOhUGaBYIior3J1x7RaQQnplI1pApVI2pSJboOVao0oHL1xlSu1ZywqMynKLIXrel2/h9bRKRANOI2p5UrLTz+eDD//JNZpDYqyuC++xwMGeLQRGMiIiJSbgRk4rawI27LqgEDrubJJx+jQoUK3HbbkBz7L7gghoMHD3Ds2FHuvHOoz74LL7yIZ58dT1RUFE2aND3reTwlE57izjtvLtL4RaTsS0mO5cie9Rw99DeHj+/gcNx+2p6ycs0uK5ZDhzAfPogzMY5u48H7hKvtzCsXh7NVF6iV6HmPtkPNNBs1XGHUNFWgRnBVqkfUoHp0fapVbUK1ms2Iu+MCzGGZdQ/6n3mJiJRmStxmSkqCp58OZu5c3/9J3Hyzg3HjHFStGhj3+CIiIhI4AjJxGyjT88bEdCEyMpLY2Fh69+6XY39kZCTNmjXnwIEDtGrVxmffBRfEkJ6eTkzMhQU6V7169bn77lFMn/5qkcQuImVEUhKWA/9iObCfb/d9x+8JGzmYdoz9pngOhtg5HZLt560VbjsCNy7J3GQDqifB0VxKvoY5oG5qEDVdYdQwVaBi384k3dgJd40auGvUpF7VKuyrWonoqjVwOFzF+lFFRPwhQG5b8/XHHxZGjw7h338zy9K0b+9i8mQ7nTopuy0iIiLlk8kIlOGnZ5ieNbGh7xJqNStYQlLKPpvNooROgNE1LzrxsYc5tHsdBw9u5MCx7RxI/JcDjqMkpifx06fBmE+d8rYdOgjeviD/Y/baCz+/D0ZQEO6atXHVqsWEjnGkR0ZQM6oOtao0oVatltSo35Go6g3yrB2bla554NE1D0xVq559Ur/yxmSCRo3crFqVT1HucszlgqlTbbzyig232/NoRliYwdNPp3HbbelYLPkcoIzRz7bApOseeHTNA4+ueeApqvvWgBxxG1CZahGRszEMzMeOYtm3F/PePWzdv4oX3EvZTyz7Q+zEZR8xG3bmBdgTkjIWAWgQl7lsdUGdZAt10sOobYqmVnBVakfWoWalxjRo35aTD3XHqFoVziRlxxTnZxQRKcMCa4iFrxMnTAwfHsKKFZm/snTt6uT11+00aBDAX4yIiIgEjIBM3Ab0HbCIBBy7PYmDu9awf9869h35m/3xe9jjOMJeSzxTFsOgzQ5vW2st+Obu/I9pdcG/TarTKLoJ7rr1cNWtx8Da4XSqGkyd+h2p2rADluCQPPvrp7CISMEEao3bjRvN3HFHKIcOef7AZzYbPPKIgzFjHOVulK2IiIhIXgIucWtz+jsCEZFi4HJhPngAy+6dWHftZPzpj9ngPsCeoEQOhjkzJ/4Cn1GzO7I9vdH4tOfd6oJ6yRbqO8KpZ6lM3dDa1K3UiDo1WlGnfkeqNeyAZXQo8Vn61jrzEhGRohOI4w0WLLAyZkwIdrvnf17Vq7v53//sdO2qR0xFREQksARc4jbtOTh1bS0CdPCCiJRhhmFw/NhO9v7zK7v//ZPdp7exy36QWifTeOuzVExpad62K4fB2tpnP16YA5KqVyKtbwyuho1wNWyEuUFD1tcIoUbjzlhCw85+ABERKXaBlLg1DHj9dRuTJgV7t8XEuHj33VSqVw+gL0JERETkjIBL3AKBdQcsImWPy4X53/1s27qUH//9gV0Je9npPsaOkGQSgrP8/Ar2vBq6wZTme4gmpz2J28op0Cg1lIZUolFIbepXbEKD2u2o1+QiqjRsh8lqJSHb6fPJ94qISAkKlFIJLhc8/HAwH35o82675RYHkyenERx8lo4iIiIi5VhgJm5FREqBFHsCe7b+wo6dK9hxdCP3ba9I7S37sOzehcnhYEcHmHgNkM9klKdCIaV5UywNm+Fq2gxnk6Y8WSea5xo0I7JOU8+05CIiUiYFwniDtDQYOTKEb78N8m4bPz6N0aMd+l+YiIiIBLTATNwGwh2wiJQaqWlJ7PnnF3bsWMGOoxvYlrKXbaZT7IlwZNaeDYLL1kP93Zn9mp/KXDYZUD/RTNO0KJoG1aRJhSY0rt2ehs0uoXrTLiQ/EORzzirF/7FERKQElPcRtykpcPvtoSxf7vm1JCjIYPp0O9ddp4kpRERERAIucXtPfxjjiKUiDfwdioiUMy6Xk+RDu6iy818sW/7G+s9WTNv/ocGgzaRkPPlpBaJy77+lGlz2bxCuRo1xNWlG4yb1eT/CTuOGXajX8lJCqtQsqY8iIiKlRHlO3KakwH//G8qKFZ5fSUJDDd59N5XevTUJmYiIiAgEYOJ2VhcY4kymor8DEZEyLS7+KNs3/cA/u1ew5eRmtqQfZEtYIv13whef+bZt2g021vDdFu6AlokhtDSq0SKyMU1rdaTdc5dxskVnCPKMnjUDV5bMxxERkVKqvD4olj1pGxlp8PHHqVx4oZK2IiIiIhkCLnELYJTnoQsiUrQMA/Oxo2z+cwHf7f2OLUk7+dtykgPhWR7hDMtc3Fg9W3eLhYHHK9DWGk6LiMY0q9WBps0upWbrbpiDQ0rmM4iISJlVHhO3aWlwxx2+SdvPPkuhUyfdo4uIiIhkFZCJWxGR3KQ7Hezc9gubN//A9XtDqbxxK9bNGzGfPMk/MTBlAHmWOTAZ0CTeQntXZZLuuQl367Y4W7bG1aQp92k6bBEROUflLXHrdHomIvvlFyVtRURERPKjxK2IBKQ0p53tm5ew5Z8lbDryJxvT97E5LJG0Mz8V23wFPfdltm93LHO5gh3aJobR2lyb1pVb07LBxTTteCVhNesDkFpin0JERMo7t9uUf6MywjDgoYeC+fZbT0mg0FBPeQQlbUVERERyF5CJW8PQzaFIQHG7sezdjWXDeh7c+xp/OvexJTyJdMuZ/aFnXln8WdOTuHVXqoSzbXuatW7BJ1EmWrbsQ802l2LSKFoRESkB5anC18sv2/j4Y89snUFBnonIVNNWREREJG8BmbgVkfLLbbjZvWcda1d9iXX/Pm5dnYp1/V+Y4+MA+GMUbK2We99msRY6pFelfVRzLr6zP6dmDsBduw6YPKOd+pTQZxAREclQXkolfPyxlSlTPH/0NJkM3njDTu/eStqKiIiInE1gJm7Lyx2wiHDi9L9sWreA9bt+5q+ELawLPklcsGd4UqtEuOsX3/adjsC2KtAyzkp7VzXaR7WkbcPutLxgAOF1m3qTtADlaJCTiIiUUeVhxO2KFRYefDBzQs5nn01j0CDnWXqIiIiICARo4tZAiVuRMsntxrJ7FxtXf87MI5/xJ4fYF+7I3J9t4rB/qkJCMEREViW9UwzODhcwvnV9Jra9kLDaDUs2dhERkXNQ1hO3Bw6YGDYsBJfL84fRYcMcDB+e7ueoRERERMqGgEzcikjZcPz0ftavnkfMjiQarvmHoHVrMMfGQgP48o7c+1RLhi7JFekU1pwO9buR9NvNpNVv7B1JW7HEohcREQlsqalw552hnDplBqB3bycTJqRlfbhFRERERM4i4BK3A7dDWM+Q/BuKSIlyG2527PydP//8grWHVrLa2Mfu8DQAZi6GUWsz28YcBpMBIU7oFBtKJ2tDLqjZhfbtBlCzQy+Cw0NwOFQ3T0REyr6yOuLWMOChh0LYtMkzE2iDBm5mz07FYsmno4iIiIh4BVzi9ptP4PSYaiilI+Jnbjd/rf6MFX8vYM3p9ay2HSM++EwZkzDfpr/X9SRu3ZUqkd7lIkwxXfijeXXqd74SS4VKJR+7iIhICSmrUzO89VYQn38eBEBYmMH776cSHe3fmERERETKmoBL3AJl9w5YpAxLtScSuXU7QSt/J+iPFQStXsX/rohnfisgMmf7YCd0Oh3CRdbG9Li4D6cfuh1X4ybekgeNSjZ8ERERvyiLI25XrrTw1FPB3vVp0+y0bFkGP4iIiIiInwVm4lZEil1swjHW/vERq3Z8z+8pW9kZnMipF8GWZbj7JQfwJG7x1KbtmliJLlFt6Ny0H60uvgFb1VretholLyIigaisJW6PHTMxdGjmZGT33ZfGoEFOP0clIiIiUjYpcSsiReJE7AHW/vERf+z8kd/t2/g7Mtmzw4J3RO3aWp5kLYC7ShWuqNGOCCrRqd1A6nbujyk4ONdji4iIBKqy9KCYYcCYMSGcPOmZjKxXLyePP+7wc1QiIiIiZVfAJW4b3wefJx+kLk39HYpI2Wa3E7RuDfYVS+hl/h/bIlI924POvLJpd9JKbM+LSGx7PekXd8PVtBlVTSauLdGgRUREyha32+TvEArsrbeC+Plnz68X1aq5mTnTrsnIRERERM5DwCVu91SCdEOPa4kUVlJqHGtWfghbNnHtr8cIWvMHJrsdAMd9vm3NbuhwKohLTA25uG4POne9majmF4DJhN0PsYuIiJRlhuEt8V5qbd1qZsKEzCdnpk+3U6VKGRouLCIiIlIKBVziFsBAN5Ei+Ulz2vlr7Rf8vvELfo3/i7XhcbjM0PEE3Pirb9u+e2CD00Y3SxO61u9Fp4tvJqJxm9L/W6aIiEgZUNoTt6mpMHJkCGlpniCHD3fQq5eq04uIiIicr1KXuF2+fDlTpkzhwIED1KxZk0ceeYRevXrl2jY2NpYXX3yR3377DYfDQatWrXjsscdo2bLl2U+ivK1IDi63i81//8DKtZ/w28nVrAw5RmpGyYPIzHYbasCpUIiuVIf07j1wdLuU5y/uhlGnrl/iFhERKe/cbjCb/R1F3iZODOaffzw1EVq1cjF+fJqfIxIREREpH0pV4nbfvn2MHj2aqVOn0rNnTxYvXszYsWNZvHgx1atXz9F+3LhxuFwuvv32W8LDw3njjTcYOnQoS5YsISwszA+fQKRsMSUlErTiN2w/LWHJroVc3e+4Z0dkzrbNT5vp6apP9zo9sS8dxukmrUv38B8REZFyojRPULZ0qYW33rIBEBJiMGeOHc01KiIiIlI0SlXidsGCBcTExNC3b18A+vfvz/z585k3bx733edbRNMwDEwmE2PGjKFixYoA3HXXXcyaNYt9+/bRqlWrPM9jGO7i+xAipVia087aVZ/yy4Z59N0Yz4BF2zGlpwPQMxgsfcB1ZkRPnQQTPVNrcmn1S+h64S1U79izdA/3ERERKafcpfTWNT4e7r8/xLv+zDNpNG9eSoMVERERKYNKVeJ2165dNGvWzGdbkyZN2LZtW462JpOJmTNn+mz74YcfCAsLo2HDhsUap0hZsv/gRpb/+iY/HfyJ5cGHSQkywAyxZhiYntku0h3EQ/uqU7NOGy654EbqXTQQk83mv8BFRETKsR9//JGXXnqJn376Kd+2pTVxO2FCMMeOef6o26ePkzvvTM+nh4iIiIgURqlK3CYnJxMaGuqzLSQkhJSUlHz7/vTTTzz33HM888wzOY6RndViwmaznFesUnZYrYF1rVPSkvjjtw9YuvEzlto3szPc7tkR4dtuSSNwNmiAq9/lOPv0w9mtO49HROQ8YBkUaNdcdM0Dka65lFXp6em89957vPbaa7mWAstNaSyVsGKFhblzPX/gjYgwmDLFrgpKIiIiIkXMr4nb2bNnM2fOHO96u3btsNvtPm3sdjvh4eF5HsMwDN544w3efPNNJk2aRP/+/fM9b3q6C4dDM90GkvJ+vU0nTmD75SdsPy9lWtJCnuqaChYg2z+d6knQL7kWvWv1pPvVQ4l9pJNvndpy9D2V92suOemaBx5dcymLhgwZQnBwMMOGDeObb74pUJ/SNuI2JQUeeCCzRML48WnUrl0Ks8siIiIiZZxfE7cjRoxgxIgR3vVXX32VLVu2+LTZtWsXbdq0ybV/amoq999/Pzt37uSjjz46a11bkfIkKSWWlb+9y8//LOC+X9NovyKznMiVteCprp5lixsuPhFKn9D29Gp/A8173oI5VBP3iYiI+MvLL79MjRo1mD9/vr9DOWcvvxzMvn2eEgkXXujkjjtUIkFERESkOJSqUgmDBg3i3XffZdGiRVx22WUsXryYNWvWMG7cuFzb33///Rw9epQvv/yS6OjoAp1jxndQvXulIoxapPgZhsE/25exfOW7/HTid1aGncRpAWzQzID2Wdp2iA/n3iPV6NqwF117DiOiUWt/hS0iIiLZ1KhRo9B9StOI2w0bzLzxRhAAwcEGr75q19ylIiIiIsWkVCVuGzduzMyZM5kyZQrjxo2jdu3aTJ8+3TvZ2DfffMPTTz/N+vXr2bJlC8uWLcNms9GrVy+f47z55pvExMTkeo571sLpoAro4Uop7WITjvL78rdYtuNblrKDI6FOz45I33ZLGsMD8e1I790XR+++pMd04SlNKiYiIuJ32cuCne0e9WysVgul4X/t6elw//0huN2eMkuPPJJOq1bK2hYl1e8OTLrugUfXPPDomsu5MhlGaZzuoBiZTJz+dTWuFi39HYmUEJvNUmbqIJr378P281Jsy5ZyZ9SPfNIq97gbx5npl96A3g2v4MI+dxNau1EJR1q6laVrLkVD1zzw6JoHpqpVI/NvVEbMnz+fGTNm8PPPP+fZJqMM/fbtiVSsWEKBncW0aTaeey4YgNatXSxenEJQkJ+DKmf0sy0w6boHHl3zwKNrHniK6r61VI24LTEBlquW0uvE6X/5dfkclu/+gTe+dhG9fY933xXt4ZMzZZtD06Hn6Sj6RF9Iz87/pV7XQWDRX+xEREQCgWeEq3/vXw8dMjF1qmfYr9nsKZGgpK2IiIhI8Qq4xO2uShDudgTeB5dSwelKZ/2fC/jlz4/4KWEdf0UmenaEwS0GDMjStt/pyow+VYXeTa4ips/dBFer5ZeYRURExL9Kw5iDp58OJiXFMwT4jjvS6dChFBXeFRERESmnAi5/2fQ++C3lX5rTwd+hSIA4cmw7y5e/ybL9i/nZup/44DO/fWUbNb+4sYnLKnX11qq1tmnHk5rtQ0REpFy67rrruO666wrU1t+Tky1fbuGbbzzDa6tUcfPYY2n+DUhEREQkQARc4hYoHcMWpPwyDCxbt3hq1f68hD7tfmNzdSA8Z9MOJ4Poa2lOz+ZX0/G1IcRXrFri4YqIiEjp5s9bV4cDHn882Lv+5JNpREf7Lx4RERGRQBKQiVulbaWo/XtwI8uXv8k/+/9g9ieJWI4d9e67IgxP4haomAp9E6rRp3p3ul8yhKrtumXOPCIiIiKSC38mbufMsbFrl6eufqdOLm680em/YEREREQCTEAmbjXiVs5XqiOZ1Ss+YNnfX7DUvpmdEXbPjmh4Ig0aZml7/amaBMXXpFfra2nT8w4sURX8EbKIiIiUUf4qlXD4sIlXXsmckOzFF+2oipOIiIhIyQnIxK2hMbdSSIZhsGfvGn757U1+Prqc30KPYbfi+RcU4dt2SYsgbo/ohaN3X9J796VRoyaM9UPMIiIiUj74K3GbdUKy229Pp107TUgmIiIiUpICMnErUiBOJ9Y/12H7eTHuX5bQu/9GUoPIMamYxQ1dT4bSN7Q9PdvdQIt5t5AQGuaXkEVERKT88cfDYr//buHrrz0TklWu7ObxxzUhmYiIiEhJC8zErUolSC4Mw2D37lUs++1/OHb/w1PzDmOOj/Pu79USFjXzLNdJMNHPXpfe9fpwSc+7iWjU2j9Bi4iISLlX0iNuXS548snMCcnGjXNoQjIRERERPwjIxK1KJUiGFHsiq357l5+2fMnS9C3sDXcAEFUJxiVC1jJuQ07U55I69enZ8SaadP8/TDabf4IWERGRgFLSYw4+/TSIv//2TEjWtq2L//wnvWQDEBEREREgQBO3Etj27l3HL7/OYenRX/g19BhpVsB25nVGQgj80TyCLs0uw9GnH+m9+nBp9Rpc6q+gRUREJGCV5IjbxESYNCnzpmjixDQslpI7v4iIiIhkCszErQbcBha3G+v6P7EtXczeVd9wYZ8tnu3ZatUGuaDbqQj6RXai1wX/pdHS60gMCir5eEVERESyKMkRt6+/buPECc8zRwMGpHPxxa6SO7mIiIiI+Ai4xO3OaRA+r76/w5BiFp9wnF9+nkHkX5u54astmI8eBaA1UL8T7I/2tKuTaOIyez361r+crn2GE163qd9iFhEREclNSSVu9+83MXu2Z7StzWbw1FOakExERETEnwIucdvkNMSag3D6OxApckeO/MOSpdP4/tASlocfx2mBLk648WhmGxNw394aJDdrQu9ON9O0m2rVioiISOnmdpsoiUfGJkwIxuEwATB8uIMGDfSYmoiIiIg/BVziVsqXkyf28t33L/Dl4R9YFRXn2RiVuX9NHThUJZgqMX1w9LsCR59+3Fqrtl9iFRERETkXJTHi9o8/LCxc6CkRVbWqm7FjHcV/UhERERE5KyVupexJT2f/ond5/J+XWBZxHJcZn2QtQP0EMwOcTbmi5WBC1t9DQnCEX0IVEREROV/FPTmZywXjxwd71594wkFk5Fk6iIiIiEiJCLjE7czOcJkjlmh/ByKFZt63l9CPPiDk47mYko/zy4N4krZntDpt5ZqgDlzR6Taa97gF05mJxaw2Cw6HJtYQERGRsqm4E7effWZl82YLAG3auLjppvTiPaGIiIiIFEjAJW7vvQqWpR1T4raMSE9P45sFT+L8/Wfu/WSHd3sVoN8e+KeamcFGG66+aATNevwHk8Xiv2BFREREikFxlkpISoLnn88cbTtxYhq6nRIREREpHQIucQuUxNwOcp5SUxP4/LOHmHb8C/4Nd1KlDgyzQLALDKsVxxVXMevKawjrOVCTi4mIiEi5VpyJ22nTbBw/7nmE6aqr0rnkEj2lJCIiIlJaBGTi1lDmttRKSjzJh5/cx8yERRwLc0O4Z/vJcPjhomr06TUK+423YFSvnrFLREREpFwrrsTtgQMm3njD8wdwm83gqafSiudEIiIiInJOAjJxK6WP0+ngs0/u54VjH3kStmGZ+644Hs2YTg9wwRejSdWzeyIiIhJgiqvG7fPPB5OWZgJg2LB0GjbU4AYRERGR0iQgE7eGUcwzPEih/PX7xzz86/1srpDqTdiaDLjuZDXu6/4ULUfd5t8ARURERPyoOBK3f/1lZv58z0SulSu7uf9+jbYVERERKW0CMnErpURKCuEvTeLDo9PZ3C5zhMe1J6rx6OWv0Oiiq/0YnIiIiEjpUNSlEgwDnnkmc0Kyhx5yEBVVtOcQERERkfOnxK34hXXzRiJH3IV15w5eCYdFTaCePZhJHZ4iZtRof4cnIiIiUmoU9YjbRYusrFrl+TWgSRMXt92WXrQnEBEREZEiEZCJW6M4p+aVs3K7XcTPnkzT56diSvf8klDVGcz3ltup+9AErCFh+RxBREREJLC43aYiO5bDARMmZI62feqpNIKCiuzwIiIiIlKEAjJxK/6RFH+c+2f14C8Osc4G1dIhvV0HEme9ScNmzf0dnoiIiEipVJRjDj74IIi9e80AXHyxk8svdxXdwUVERESkSAVc4rbRaQgOvI/td0f2/MXN865gSwU7ADcNhoWRY0h57Emw2fwcnYiIiEjpVVSJ2/h4mDIl877rmWfSMBXdYF4RERERKWIBl8HcPQ1i+zfG6e9AAsiujYv5vx9v5GAFz4iOCnYYeeHDpAx+0s+RiYiIiJR+RZW4fe21YE6f9oy2HTw4nQ4dirh4roiIiIgUqYBL3ErJ2vz7p9ywajinIzy/cTSJt/LRFZ/QsOPlfo5MREREpGwoisnJjh0z8fbbnmK2wcEGTzyRdv4HFREREZFiFZiJW01OViK2rp7P9auHExfq+b47ng7h41uXUbl+az9HJiIiIlJ2FEXidtYsG3a7py7CkCHp1Kmj+2ERERGR0i4wE7dS7Hb+tYjBK+70Jm27n4rk/ZGriKhS18+RiYiIiJQt5zvm4ORJE++/7xltGxJiMGqUowiiEhEREZHiZvZ3ACVt0H9gZ+oBf4dRrh3fu4EbfrqZk2eStl1Ph/PBPeuUtBURERE5B+c74nbOnCBSUjyjbf/733SqV9doWxEREZGyIOAStwubQ5wzwd9hlF9JSTQYdg/9dnp+w+gUG8qHw1cTXqmmnwMTERERKZvOZ8RtXBy8/bYNgKAgg3vv1WhbERERkbIiIEslqMRtMXG5iBp5F8GbNvPuJuiYWonLX/iByKr1/B2ZiIiISJl1PveuX34ZRFKSZ7TtTTelU6uWboRFREREyoqATNyCbliLQ9iUyQT/+D0ARlQFbn3yR1x1mvs5KhEREZGy7XxKJXz2WZB3eejQ9CKIRkRERERKSsCVSpDi8dd3Mzn+9osAGGYzCW9/gKuZkrYiIiIi5+tcR9zu3Glm/XoLAG3bumjZ8jyL5YqIiIhIiQrIxK2hWglF6vjeDdz2zxNcMBy+bg7JTzxFeo9e/g5LREREpFw41xG3n3+e+XDd//2fRtuKiIiIlDUBmbiVomO4XIz58GqOhxnEhcIbl1ch5Z4x/g5LREREpNxwu03n0Ac+/9xTJsFiMbj2WmdRhyUiIiIixUyJWzkvn749jJ8qxwJQK9nM63f9iMli8XNUIiIiIuXHuTwstnKlhUOHPLf6vXq5qFZNT5yJiIiIlDUBmbhVqYSicXDrCsalfOFdn9bqSSrVbOrHiERERETKn3MplbBggcokiIiIiJR1AZm4lfNnuFw8+OV/SLJ51u9IbMalVz3o36BEREREBIA//vA8ARUUZHDZZSqTICIiIlIWlbrE7fLlyxk4cCAdOnTgyiuvZNmyZQXq9+qrr9K7d+98241cC9WDKp5vmAFv4YcPsKxyPAB1kyw8NewbP0ckIiIiUj4VdsTtqVMmdu3yJG7btXMTFlYMQYmIiIhIsStVidt9+/YxevRoxowZw7p16xg9ejRjx47l2LFjZ+33xx9/8PbbbxfoHLO+g4a2mkURbsBKOnmAJ4+/711/ucVjRFSq5ceIRERERMqvwiZu163LvMXv3NlVxNGIiIiISEkpVYnbBQsWEBMTQ9++fbFarfTv35/OnTszb968PPucPHmS8ePHc+utt5ZgpIHttbf/w5Fwz28QA2Jr0HvQo36OSERERKT8Kuz0DGvXZk4Uq8StiIiISNlVqhK3u3btolmzZj7bmjRpwrZt23Jt73a7eeihhxg2bBhNm2pSrJJg2fI3nZZupmoyBDvhmcHv+TskERERkXKtsCNu16zJTNx26aLErYiIiEhZVaoSt8nJyYSGhvpsCwkJISUlJdf2b7zxBpGRkdx0002FOo+JQg5bEK+IiU9x20aDHdPhY26mXvOL/R2SiIiISLlWmBG3Dgds2OBJ3Nar56Z6dd33ioiIiJRVVn+efPbs2cyZM8e73q5dO+x2u08bu91OeHh4jr5r165l/vz5zJ8/v1DnDB4P36Ru4SJb93MLOoBZlv+C7eelAERVrUef0TPAZsmnl/9ZraU/RilauuaBR9c88OiaSyApzIjbzZvN2O0mQKNtRURERMo6vyZuR4wYwYgRI7zrr776Klu2bPFps2vXLtq0aZOj7zfffMPp06fp06cPAOnp6aSlpRETE8Ps2bOJiYnJ9ZwOKzidLhwO3cgWittN9FPjvatJj43HYbJCGfkedb0Dj6554NE1Dzy65hIoCjPiVmUSRERERMqPUlUqYdCgQaxZs4ZFixbhdDpZtGgRa9as4eqrr87RduLEiaxfv55169axbt06nn76aWrVqsW6devyTNp6FXaGB+GXz59hZP31HIwCZ+u2pF3/f/4OSURERCQgFObWVROTiYiIiJQfpSpx27hxY2bOnMmcOXPo3Lkzs2bNYvr06TRs2BDwjLLt2LGjn6MMPIbTyXM7Z/H2BdB0NKx9ZAiYS9V/OiIiIiLlltttKlA7w8hM3EZGGrRoUchZzURERESkVPFrqYTcdO/ene7dc68/O2jQIAYNGpTrvuuuu47rrruuOEMLWMu+eJZNlRwAtE4Jp/Hld/o5IhEREZHAUdAat3FxcOyY54/r7du7sKgUtIiIiEiZFpDDJg2VSigww+XilZ3/864/0GYMJo22FRERESkxBb11/fffzHu0Bg002lZERESkrAvQDJwStwX1x9cvs7ZyKgBt40Ppc9XDfo5IREREJLAUdMTt/v2Zt/b16+t+V0RERKSsC8jEraHEbcEYBlP/nuZdfaDZcMxmPXMnIiIiUpIKOuLWN3GrEbciIiIiZV1AJm6lYDYteYtfqyQB0CwhmCuuecrPEYmIiIgEnoKPuM2cxKxePSVuRURERMq6wEzcasBtgcxZNcW7PLruf7BYSt1cdiIiIiJlyieffMLll19Ox44dufzyy/noo4/y7XNuI251wysiIiJS1gVcJu6rT6DVxPr+DqPUO7r1d+ZXOgJAlVQzV9/5vJ8jEhERESnbli5dytSpU3nzzTdp3749GzZs4O6776ZKlSpcfvnlefYr7ORk4eEGlSopcSsiIiJS1gXciNurt0NlawV/h1HqHfpsJtWSPct3BXcnJDTSvwGJiIiIlHHHjh1j2LBhdOjQAZPJRMeOHbnwwgtZu3btWfsVpFSCywUHD3pKJdSv78ZkyqeDiIiIiJR6ATfiFij4sIUAZYqP4/L3lrEvDT7vYKPDO1Py7yQiIiIiZ3XLLbf4rJ86dYq1a9fy+OOPn7VfQW5djxwxkZ7uydaqvq2IiIhI+RCYiVs5q5CPP8SUkowNuK797STVbO7vkERERETKlRMnTjB8+HDatGnDgAEDztq2ICNuVd9WREREpPwJuMTtLw2ggTORcH8HUloZBiEfvONdTR06wo/BiIiIiJRds2fPZs6cOd71N998k5iYGDZs2MCYMWOIiYnhhRdewGo9+y252WzGZrOctc3Bg5n7Gzcm3/ZSOlmtum6BSNc98OiaBx5dczlXhU7cOp1O1qxZwx9//MHBgwdJTEykYsWK1KpVi0svvZQLLrgAUykuqtXrDvgqdTcX+zuQUurYsvk4ju+iNuDodimuJk39HZKIiIhImTRixAhGjPD9I/gXX3zBc889x3333ceQIUMKdJz0dAOHw3XWNnv3Zv5CWLu2M9/2Unrp2gUmXffAo2seeHTN5VwUOHHrcDj45JNPePfddzl69CgVKlSgVq1ahIaGcvToUX755RfmzJlDtWrVGDZsGDfeeCM2m604Y5di8NqKZ3nvfrhqB0y6dBDV/B2QiIiISDnx448/8swzz/DGG2/QvXv3AvcrSI3bfftUKkFERESkvClQ4nbTpk08+uijWCwW/vOf/3DllVdSr169HO22b9/O8uXLmTt3Lh988AEvvfQSHTt2LPKgz5dhaMKG3CQf2ce8yH24zPBzIxNhVw72d0giIiIi5caMGTNwuVzcd999PtsHDhzIhAkT8uxXkMTtv/9mJm7r1tW9roiIiEh5UKDE7cMPP8xDDz1Ev379ztquefPmNG/enLvvvptFixbx2GOP8eOPPxZJoFL8Fn75JEnBnuUbXa2JCK/k34BEREREypGFCxeeU7+CTU7mKVVWvbqb0NBzOo2IiIiIlDIFStwuXLiw0GUP+vfvT9++fc8pqOKmh8dyYRh8cPoHqOJZvbn3E/6NR0RERESA/BO3yclw4oRnxG29errTFRERESkvzPk34axJ27S0NIw8nt8qtTVuC/K8WYDZ/fuXrKuSBkCHhHDadhzg54hEREREBPK/dT1wIGt9W5VJEBERESkvCpS4zW7Pnj2MHTuWLl260LFjR7Zu3cozzzzD3Llzizo+KSFf/va6d/nG6lf6MRIRERERySq/EbcZZRJAiVsRERGR8qTQidt//vmHwYMHs2XLFgYOHOgdbRsUFMSkSZNYsGBBkQdZ1PIaIRyo3PZU5pk3AWBxw6Crxvk5IhERERHJkF/i9tixzFv6WrV0nysiIiJSXhSoxm1WL774Im3atOGdd94B4KOPPgJg3Lhx2O12PvjgA6699tqijVKK1ZrvXudApOcmv19STapWa+zniERERESkoE6fzhxxW7myErciIiIi5UWhR9xu2LCBO+64A6vVislk8tnXv39/9u3bV1SxSQn5YnNmiYsbWt7sx0hEREREJLv8RtyeOpV5T16pkhK3IiIiIuVFoRO3wcHB2O32XPfFxcWV3gnJzrBPhJ5hbf0dRqlhOn2KXqsO0/UARKWZ6HvFg/4OSURERESyyK/Kl0bcioiIiJRPhU7cXnLJJUybNo2jR496t5lMJpKTk3nnnXe4+OKLizTAohbsArPpnOZkK5eCv1vIHX+5WPk2bI6/i9DgCH+HJCIiIiJZ5DfiNmviViNuRURERMqPQte4ffjhh7nxxhu54ooraNGiBSaTicmTJ7N3714Mw2Dq1KnFEWcR0w1thuCv5nuXI6/5L04/xiIiIiIiObndprPuz0jcmkwG0dG6zxUREREpLwo99LRmzZp8/fXX3H777RiGQb169UhJSWHAgAHMnz+funXrFkecUgxMJ04Q9PuvALjqN8DZvqOfIxIRERGR7PIrlZBR47ZiRQOLpQQCEhEREZESUegRtwAVK1bk/vvvL+pYSsTjfeC6tEM08HcgpcC2b2YSVNNNl0OQdvV1YDr7aA4RERERKXn5lUqIjfXcw6lMgoiIiEj5ck6JW4fDwRdffMHKlSs5ceIEkyZNYs2aNbRu3Zp27doVdYxFanJ36OQ4qsQtMPXf91kwDOrHwZd9L6SevwMSERERkRzONuLW4YDERCVuRURERMqjQpdKOH36NNdffz3PP/88+/fvZ9OmTdjtdpYvX86tt97K+vXriyNOKWIph3bzfaVTAKQGW6jVqa+fIxIRERGR3JwtcZsx2haUuBUREREpbwqduH3ppZdITk5m0aJFLFiwAOPMneTrr79O27ZtmTZtWpEHWdR0Sws/fzcFe5BneZClLVZLkH8DEhEREZFcna1UQkZ9W4DKlXWXKyIiIlKeFDpxu2zZMsaMGUP9+vUxZamJGhwczJAhQ9iyZUuRBlgs8pvhIQB8d2ixd3lAzF1+jEREREREzuZst66nT2vErYiIiEh5VejEbVpaGtHR0bnus1gspKenn29Mxc4I8DG3jpNH+DH6BACV7Wa6dL3ZzxGJiIiISF7ONuJWiVsRERGR8qvQk5O1bduWjz/+mB49euTYt3DhQtq0aVMkgUnxWfXDDJKCPctXGM1UJkFEREQkiz179nDw4EGSkpKoWLEitWrVon79+n6LR6USRERERAJToRO3Y8aM4Y477uDqq6+mR48emEwmvv32W6ZPn86KFSt46623iiNOKUI/7FoI1TzLV7S+wb/BiIiIiJQCJ0+e5L333uObb77hxIkT3nkcAEwmE3Xq1OHKK6/ktttuo0qVKiUam0oliIiIiASmQiduY2JiePfdd3nllVd46623MAyD9957j1atWjFnzhwuuuii4oizSBkBXOPWnZLMt2H7AQhxQreew/0ckYiIiIj/uFwuZs2axZtvvknNmjW57rrraNu2LbVr1yYsLIz4+HiOHj3Kn3/+yU8//cQHH3zA7bffzr333ktQUMk8taTErYiIiEhgKnTiduXKlXTo0IFPP/0Uu91OfHw8ERERhIeHF0d8xSRwb2r/Xvo2RyM8n7+3vQ7hIVF+jkhERETEfwYPHkzNmjX58MMPadeuXa5t2rZtS79+/XjsscdYs2YNb731FoMHD+brr78ukRjPlrjNWipBiVsRERGR8qXQidtHHnmERx99lIEDBxISEkJISEhxxFVseuyDirUj/B2G30T9vppb4+DbZnBFw6v8HY6IiIiIXz388MNcfPHFBW7fpUsXunTpwooVK4oxKl8FnZxMNW5FREREypdCJ25tNhvBwcHFEUuJ+OU9iO/bHIe/A/EHt5tO367mgxOQHh7Ksc3j/B2RiIiIiF8VJmmbVbdu3Yo4kry53aY892Ukbi0Wgyg9SCUiIiJSrhQ6cTt8+HCeeuoptm3bRtOmTXOdnKFz585FElyxCdDBCNbNGzGfOA6Au3svgiOi/RuQiIiISCm0fPlyVq5cyfHjx3nggQf4559/aN26NbVr1/ZLPAWpcVupkoEp7/yuiIiIiJRBhU7cPv300wDMmjUL8Myym8EwDEwmE//8808RhSdFyfbTEu+yo3c/P0YiIiIiUvqkpqZyzz33sHLlSiIiIkhOTmbo0KF88sknbN26lQ8//JCmTZuWeFwFKZWgMgkiIiIi5U+hE7cffPBBccRRss42bKEcW79uPu1tEOkARx8lbkVERESymjp1Klu2bOG9994jJiaGNm3aAPDSSy9x11138frrrzNjxowSjyuvW9eUFEhJyRxxKyIiIiLlS6ETtyaTiVatWhEeHp5jX0JCAr/99luRBFZcLhgOE1K3cCH9/R1KiXKcOMzlXbaS3hWuOxjJ9Lr1/B2SiIiISKny/fff88ADD3DRRRfhcrm826tWrcrIkSOZMGGCX+LKa8RtbGzmk29K3IqIiIiUP+bCdrjtttvYvXt3rvu2bt3K448/ft5BFaf1NSHBnervMErc2qX/I8UG6RawVqvj73BERERESp2EhIQ869hWqFCBlJSUEo7II68RtxllEkCJWxEREZHyqEAjbh999FGOHDkCeOrYPvPMM0RERORot2/fvlwnKyuM5cuXM2XKFA4cOEDNmjV55JFH6NWrV65t3W43s2bN4vPPPychIYEmTZrwxBNP0LFjx7OfJABLJfy88zs4c2l6Nxvo32BERERESqGmTZuycOFCunXrlmPfzz//7Jf6tpD3reupU5mJW9W4FRERESl/CjTi9vLLL8cwDIwsd40Z6xkvs9lMhw4deOGFF845mH379jF69GjGjBnDunXrGD16NGPHjuXYsWO5tp81axbffvst7733HuvWraNfv36MGDECh8Nx1vMYBNiNrdvNYssuAMxu6N7zbj8HJCIiIlL6jBw5kq+//prhw4fz+eefYzKZWLt2LRMnTuSTTz5h6NChfokrr1IJGnErIiIiUr4VaMRt79696d27NwADBw7k5ZdfpnHjxkUezIIFC4iJiaFv374A9O/fn/nz5zNv3jzuu+8+n7Yul4v333+f1157jYYNGwJw11130bVr1/xPFGAjbg+t+Z7tFT112i5Mrkh0ZDU/RyQiIiJS+vTt25eXX36ZV155heXLlwMwefJkKleuzDPPPMMVV1zhl7iUuBUREREJTIWenMxut7N9+/ZiSdzu2rWLZs2a+Wxr0qQJ27Zty9F23759JCQkkJCQwHXXXcehQ4do1aoVjz/+ODabrchjK8t+XfOR90r3qXSRf4MRERERKcUGDhzIwIED2bNnD3FxcURFRdGoUSPM5kJPDVFkVCpBREREJDAV+g40ISGBihUrFkcsJCcnExoa6rMtJCQk14kg4uLiAJg7dy7Tp09n+fLltG7dmrvuuovExMRiia+s+vXUau/ypTE3+zESERERkdIvPj6evXv3sn37dipVqsS+fft8SoaVNI24FREREQlMhR5xe9ttt/HSSy/x6KOP0qxZMypVqnTOJ589ezZz5szxrrdr1w673e7Txm63Ex4enqNvxqjae++91zv77wMPPMBHH33EX3/9RY8ePfI8r9lswmaznHPcZYkrKZFlkScAiE4z0ylmEBZLYHz2DFZrYH1e0TUPRLrmgUfXXIrLG2+8wZw5c7Db7ZhMJtq1a8err75KXFwc77zzDlFRUSUeU145YyVuRURERMq3Qiduv/76aw4fPsydd96Z636TycTWrVsLdKwRI0YwYsQI7/qrr77Kli1bfNrs2rWLNm3a5OjbsGFDrFarz0RkWSdLOxuX243D4SpQjGXdlqUfcjrMs9wjvS4ulwmXKzA+e1aBcr0lk6554NE1Dzy65lLUPvzwQ6ZPn87w4cPp1asX//d//wfA7bffzkMPPcTrr7/Ok08+WeJxGYYp1+1xcZnbo6OVuBUREREpbwqduB00aFBxxOE99rvvvsuiRYu47LLLWLx4MWvWrGHcuHE52kZERDBgwABeeOEFmjRpQrVq1Xj11VeJioriootUxzVDyvrfaZ8GG2vApbXzHoUsIiIiEujmzp3L3XffzZgxY3z+0N29e3fGjh3L//73P78kbvMqlZCUlJm4zeUBNREREREp4wqduL333nuLIw4AGjduzMyZM5kyZQrjxo2jdu3aTJ8+nYYNGwLwzTff8PTTT7N+/XoAJk6cyPTp07ntttuIjY2lTZs2vP3224SEhOR5jklLocWttYrtM5Q2/X7aTf+/4Vg4JK180N/hiIiIiJRahw8fpkuXLrnua9SoESdPnizhiDzyepgsOdnzHhZmEGCVsEREREQCQqETt+CpO7t9+3bS09O9ZQncbjepqamsW7eOhx566JwD6t69O927d89136BBg3xG/NpsNh588EEefLDgCcnHV0D8kFo48m9a5plOniTo700AVGrcAXPNhn6OSERERKT0qlmzJuvXr+fiiy/Ose/vv/+mZs2afogq7xG3ycmeEbfh4SqTICIiIlIeFTpxu2rVKsaMGUNCQkKu+8PDw88rcVsi/DgrcEmy/faLdzn90p7+CkNERESkTBg8eDDTp08nJCSEnj17ApCSksKPP/7InDlz8pzjobjldeuaUSohIqIEgxERERGRElPoxO1rr71GdHQ0zz33HN988w1ms5nrrruOX3/9lU8++YQ333yzOOKUc5C+4ifvsqO76tuKiIiInM2wYcM4ePAgU6ZMYcqUKQDcdtttAAwcOJDhw4f7Ja68a9x63iMiAmNQgoiIiEigKXTidvv27UycOJF+/fqRlJTExx9/TI8ePejRowfp6em88cYb/O9//yuOWIvEiTAwjHRyn5u3fOkf9QWxo6HHvyYmdu6CSp+JiIiI5M0wDCZMmMCQIUNYtWoVcXFxREZG0qVLF5o2beq3uHJL3KalQXp6xohbJW5FREREyqNCJ27dbjc1atQAoGHDhuzatcu77/LLL+fRRx8tuuiKQbVH4P3Uv7iSwf4OpVilHNjJn5XTcJnBYgvBEhHp75BERERESrXBgwdzzz330KdPHxo0aODvcM4qo0wCqFSCiIiISHllLmyHevXqsX37dgDq169Pamoqu3fvBsDpdJKcMb2t+NWfv83FdebqdrM1828wIiIiImXAgQMHiCiFWdDcRtxmlEkAjbgVERERKa8KnbgdOHAgU6ZMYe7cuVSsWJE2bdrw3HPP8fPPPzNz5kyaNGlSHHEWKSMAJif7Y29mfduujfv5MRIRERGRsuGqq65izpw5HDhwwN+h+Mjt1tV3xG35v7cVERERCUSFLpUwdOhQYmNj2bRpEwBPP/00w4YNY9SoUURERPDGG28UeZBSeCvSd3qXu1x8qx8jERERESkb9u3bx7p167jssssICQmhUqVKPvtNJhNLly4t8bhyH3GbmbgNCyvBYERERESkxBQ6cWs2m33q2LZt25alS5eyZ88eGjVqVCofLws0qYf2sK6yHYBmSSFUr9LQzxGJiIiIlH41a9Zk4MCB/g4jh9wSt1mrk2nErYiIiEj5VOjEbW4iIiJo165dURyqRJT3Ugl//TYXp8Wz3D1I9W1FRERECuKFF144636n01lCkfgyDFOObcnJKpUgIiIiUt4VKHF72223FfiAJpOJ999//5wDkvO3cvcSqOhZvqhhX/8GIyIiIlJG9OnTh5kzZ9KiRYsc+zZt2sSwYcNYvXp1iceV/+RkJReLiIiIiJScAiVucxuhunbtWlq1akV4eHi+bUsbg9If4/lY4dzhXb7w4v/6MRIRERGR0u3bb7/1jqQ9dOgQixcvZtu2bTna/fHHH6Snp5d0eIAmJxMREREJVAVK3M6dO9dn3el00qZNGyZOnEjr1q2LJbDiVX5vbtOPHWZzlKe+bZOkYGpUa+LniERERERKr7///pv33nsP8Dw5NmvWrDzb3nnnnSUUlYfZbOB2m5S4FREREQlQ51Tj1mTKWWdLSofwv9Zz/GVYWxtOXtPP3+GIiIiIlGoPPPAAt956K4Zh0LdvX2bMmEHLli192lgsFiIiIkp8El6z2VMmQaUSRERERAJTkUxOVpb8OQcqPdXK32EUm6DVfxDqhEv3Q3zHm3H4OyARERGRUsxms1G7dm0AunXrRnR0tHfd3zLGSmjErYiIiEhgMvs7gJJ2wRGoZC6/wxKC1qzyLqd3vtCPkYiIiIiULevXr/dbHdvcmM/cqec+4laJWxEREZHyLuASt+VaairWjesBcDZuglG1qp8DEhERESk72rZty6+//lpsx3e73UyfPp0ePXrQsWNHBg4cyKJFi/JsnzHiNr9SCdnmChYRERGRcuK8SiWU2Vq3uT1vVg7sW/0N91yTziX/Qq/mrajp74BEREREypDmzZszd+5cfvzxR5o0aULlypV99ptMJiZNmnTOx//oo4/46quvmDt3LvXq1WPZsmWMGjWKNm3aUK9evRztM0bcqlSCiIiISGAqUOK2d+/euSZpR4wYQVBQkM82k8nE0qVLiya6YjC3HbR3niiXSc0/Nn/F563h89bwXIiFu/0dkIiIiEgZsmTJEqpVqwbArl272LVrl8/+8x20cMstt3D99dcTFhaGw+Hg9OnThIaGEhISkmv7syVuU1IyYwkLO6+wRERERKSUKlDitkuXLmV3dG02t10Hb6XvZpC/AykGq0+tB8/vGsS0u9q/wYiIiIiUMT///HOxHt9sNhMWFsaKFSsYNmwYhmHw+OOPe5PF2Z19cjLPe3i44U3wioiIiEj5UqDE7eTJk4s7jpJVHp8mc7v5I/goACFOaNPhKj8HJCIiIlK+7N69m8aNG5/3cbp06cLmzZtZu3Yto0aNomrVqvTv3z9Hu7PXuPXsVJkEERERkfKrQInbPXv20KhRo0IfvKhubouaUQ4zt8c3r2BvBc9dfUxKJWzWYD9HJCIiIlK2xMXFMXXqVNauXUt6ejrGmaGuhmGQkpJCfHw8//zzT4GPN3v2bObMmeNdf/PNN4mJicFmswHQtWtXrr76ahYuXJhr4jazVIIJm83isy8jcRsZSY59UnZZrbqWgUjXPfDomgceXXM5VwVK3N5999307t2bYcOGUbVq1XzbHzlyhDfffJPly5fz008/nXeQRa/8JW7X/7XAu3xhZBs/RiIiIiJSNr3wwgt8++23XHrppezZs4fQ0FAaNGjAn3/+SUJCAhMmTCjU8UaMGMGIESO865MnT2bp0qU89thj3m0Oh4Po6Ohc+2cdcetwuLzbDcO3VELWfVL26XoGJl33wKNrHnh0zeVcFKgi1ldffUVCQgK9evXirrvu4vPPP2fbtm0kJSXhdruJi4tj27ZtfPTRRwwfPpx+/foRHx/P/Pnzizv+c1L+0rbw5+FV3uVOjXv7MRIRERGRsum3337j3nvv5Y033uCmm26iRo0avPbaa/zwww80b948x2RlhRUTE8Onn37K2rVrcbvd/PzzzyxatIgbbrgh1/YZI26zl0qw28HlUqkEERERkfKuQCNuIyIimDx5Mrfeeitz5szh2WefxeXK+ZeC4OBgLr30Uj799FPatNGoz5K01rnHu9y+8/V+jERERESkbEpISKBTp04ANG3alLfffhuA8PBwhgwZwowZM3j88cfP+fh9+/Zl/PjxjB8/npMnT9KgQQOmT5/OBRdckGv7vGrcZpRJAIiIOOdwRERERKSUK1DiNkPr1q2ZNm0aKSkprFu3jgMHDpCUlETFihWpVasWMTExhISEFFesRSe3qXnLMGf8Kf6KTgWgYbKNqpXr+zkiERERkbKnYsWKJCYmAlC/fn1OnTpFbGwsFStWpHr16hw7duy8zzF48GAGDx5coLbmPJ6NyyiTAJ5SCSIiIiJSPhUqcZshLCyMSy+9tKhjKTHlbXKyHau/IjXIs9zZqOPfYERERETKqK5duzJ79myaN29OnTp1iI6OZv78+dx1110sW7aMihUrlmg8ZrMBmM464laJWxEREZHyq0A1bsudcnZ/W2frv7z+PfxnM/SpUXYT6iIiIiL+NGbMGE6dOsVjjz2GyWTi7rvv5uWXX6ZLly689957XH99yZajyiiVkP1hseRklUoQERERCQTnNOK2LKuSDLbI8vWx6/y1nftWw32r4fRDo9E8hSIiIiKFV7t2bRYtWsS+ffsAuPPOO6lSpQp//fUX7dq149prry3RePKanCw5OXNZk5OJiIiIlF/lK4NZACdehoQZMaT5O5CiYhgErVsLgDs6GlejJn4OSERERKTsCgkJoUWLFt71gQMHMnDgQL/EUrDJyZS4FRERESmvAi5xC5SrycnM/+7HfPIEAM4LYjLv8EVEREQkX1999VWh2l9zzTXFEkdu8iqV4Ju4LbFwRERERKSEnXPiNiUlhSNHjpCUlOSdaTc4OLgoY5MCOLhmEVvrQacjYHTq7O9wRERERMqUxx57LMc2k8mEkcsf+k0mU4kmbvMqlZCUlLmsEbciIiIi5VehErcOh4Mvv/ySb775hs2bN+NyZVZTtVgsxMTEcOWVV3Lttddis9mKPFjJ6fPdX/D8ELC44ZN6Znr6OyARERGRMuSnn37yWXe5XFx22WXMnj2bpk2b+ikqj7wepFKpBBEREZHAUODE7YIFC3jllVew2+306tWLK6+8ktq1axMWFkZ8fDxHjx7lzz//ZOrUqcyYMYP77ruPG264oThjPyf/vQ7+69hBJ38HUkT+su+CKHCZoVHHK/wdjoiIiEiZUrt2bZ/1jIEJVatWzbGvpOU94jYzcRseXoIBiYiIiEiJKlDidsSIERw7doxx48bRp0+fPEfT3nHHHTgcDr777jveffddFi9ezJtvvlmkAZ+vj9pBN/fJcpG4NdLTWRceB0Blu5m6ddr5NyARERERKTKZk5P5Dr1VqQQRERGRwFCgxG2fPn0YPHgwpgJMfGWz2bj22mu5+uqr+fzzz887wOJQXm5vj27+lRNnRll0clQt0PURERERkbIhY8Tt2ScnKy93tiIiIiKSnbkgjW644QZvUnDlypWkpKTkf2CzmRtvvPH8opOz2rxpkXe5Q2RLP0YiIiIiIkUtr1IJycmZyyqVICIiIlJ+FShxm9UjjzySYxIH8Y8Nh9d4l9s37ObHSERERESkqGWWSvDdnpysEbciIiIigaDAk5NlsNlsBAcHF0csJcbI/rxZGbXesce73K7TNf4LRERERKSMmjFjhs+6YRiYTCbmzZtHtWrVfPaZTCbuueeeEostv1IJZrNBWFiJhSMiIiIiJazQidvhw4fz1FNPsW3bNpo2bUqVKlVytOncuXORBCd5M9LS+DMyEYCaKRaqV2/m54hEREREyp7sidsMn332WY5tJZ24zRhxmzNx63kPD89sIyIiIiLlT6ETt08//TQAs2bNAvCZECtjhMI///xTROFJXg6uX0JcqGf5Amd1/wYjIiIiUkZt27bN3yHkKe/ErWeHyiSIiIiIlG+FTtx+8MEHxRFHyTLc+bcp5U5vXU2zk7CjCnSIbuXvcERERESkiOU1OZkStyIiIiKBodCJ2y5duhRHHFJIl2yOZftHEBcCpz4Z4e9wRERERMqkW265hfHjx9OyZcsC99m8eTOTJk3ik08+KcbIcp+czDAgOdmzHB5erKcXERERET8zF6TRLbfcUujyB5s3b+Y///lPoQNavnw5AwcOpEOHDlx55ZUsW7Ysz7anT5/m/vvv58ILL+TCCy9k1KhRHD58+KzHv2UTNDTnrMtb1gRtWA9ABYeZqI7d/ByNiIiISNl02223MXToUIYPH853331Hampqru2SkpL44YcfuPPOOxk6dCi33nprscdmNntG1GYtlZCSAm63RtyKiIiIBIICjbjNuKFt06YNgwYNonfv3oSGhuZol5SUxIoVK5g3bx5bt2711sMtqH379jF69GimTp1Kz549Wbx4MWPHjmXx4sVUr56zjuuECROwWCze5O64ceN4/PHHef/99/M8x4fzIbF7U+yFiqyUsduxbNsKgKt5CzSdsIiIiMi5ufzyy+ncuTOzZs1i/PjxOJ1OmjRpQp06dQgNDSUhIYGjR4+yc+dOrFYrN9xwAy+//HKuE/QWtdxKJaSmZs4voVtAERERkfKtQInbkrqhXbBgATExMfTt2xeA/v37M3/+fObNm8d9992Xo/3u3btp2rQpxplhCGazOdeEcnlj/WcLJpcLAGfb9n6ORkRERKRsq1SpEuPHj+eee+7hxx9/ZPXq1Rw4cIDExEQqVqxI48aNue222+jVqxcVK1YssbgyJyfLTNampWXuDwnRiFsRERGR8qzANW5L4oZ2165dNGvWzGdbkyZN8pztd+TIkYwbN45OnToBUL9+fT788MP8T5R9at4yZtH6ubw8AjoegdvbVqK1vwMSERERKQcqVqzITTfdxE033eTvUIDMEbfguX01mcCe5bGx4OCSj0lERERESk6hJycrzhva5OTkHCNmQ0JCSElJybW92+3mxhtvZOTIkbhcLsaNG8fYsWP56KOPznoei9WMzWYpsrhL2oZj69hYAzbWgP6NqpXpz1ISrFZ9P4FG1zzw6JoHHl1zCQSmzIG2uN1gsfiWStCIWxEREZHyrdCJW4BvvvmG1atX8/zzzwOwbt06nn/+eUaNGkW/fv0KfJzZs2czZ84c73q7du2w232rz9rtdsJzmTL3xIkTPPbYYyxbtowKFSoA8Mwzz3DppZeyfft2mjdvnus5qz4Mz6f8wbWO4p9QorhscOzzLrdo1x+Hw+W/YMoIfUeBR9c88OiaBx5dcynvso+4Bd8RtwFQIUxEREQkoJnzb+Jr/vz5PPLIIz4z7lauXJk6deowZswYlixZUuBjjRgxgvXr13tfHTp0YOfOnT5tdu3aRdOmTXP0PXHiBOnp6TgcDu82q9WThw4KCsrznCfDIc1wFjjG0sZIT2dDeAIAVVPNVK/WLJ8eIiIiIlIWZR9xC2C3a8StiIiISKAodOL2nXfeYejQoUydOtW7rWHDhkyfPp0777yTWbNmnXMwgwYNYs2aNSxatAin08miRYtYs2YNV199dY62TZo0oW7dujz//PMkJSWRlJTEpEmTaNeuHQ0aNDjreQzK7k3usS2/c/LMDMIdHFUwZb2jFxEREZFyI/fEbea2kJCSjUdERERESlahE7cHDhygW7duue7r1q0be/fuPedgGjduzMyZM5kzZw6dO3dm1qxZTJ8+nYYNGwKeEg0dO3YEwGaz8fbbbwPQt29fLrvsMgzDYObMmZjNhf5YZcbWv3/0LreNyDkSWURERETKh9xKJajGrYiIiEjgKHSN22rVqrFp0yYuuuiiHPu2bt1KxYoVzyug7t27071791z3DRo0iEGDBnnX69evf14jfMuizYfWQqRnuU3dC/0bjIiIiIgUm9xG3KalZW7TiFsRERGR8q3QidtrrrmGN954g/DwcPr27UulSpU4ffo0S5cuZcaMGdx2223FEWeRKsulEjal7vYmblu17e/fYERERETKgd9//71AT2wdOnSIwYMHl0BEHrlPTpZ1xG2JhSIiIiIiflDoxO3w4cPZvXs3EydO5LnnnvNuNwyDK664gtGjRxdpgMXCKKOJW8NgY8hpACIdJho0ivFzQCIiIiJl3++//84jjzySb7uXXnqpBKLJlHviNnObSiWIiIiIlG+FTtxarVamTp3KqFGjWLduHXFxcURGRtKpUydatGhRHDEWubJ6ixu3exP/Rnmib5daAbOp/NbyFRERESkpRin9o35upRJ8a9yWcEAiIiIiUqIKnbjdvXs3jRs3pkmTJjRp0iTH/gULFnDttdcWSXDFppTenOcnatsufpwL62tAxUty1hgWERERkcIzZc2QliL5jbgNDS2b97QiIiIiUjCFHrJ5/fXX89FHH+XYfvLkSUaMGMETTzxRJIFJThFbt3PZbnj0d7ix+S3+DkdEREREilHWxG3GiFvfUgklG4+IiIiIlKxCJ26vuuoqJk6cyPDhwzl16hQA3333HQMGDODPP//kqaeeKvIgi9IH8+FSS1N/h3FOrFu3eJddrVv7MRIRERERKUmG4RkV7Ds5mUbcioiIiJRnhS6V8Pzzz9OvXz+efPJJBg4cSJs2bfjtt9/o168f48ePp1q1asURZ5G5dRMk3lIVe/5NSx3rls0AGGFhuOo39HM0IiIiIlKczObMxGxuI26Dg0s4IBEREREpUec0u1XPnj15+umniYuL49dff6Vly5ZMmDCh1CdtyzJnwmneq7SPtbUgoU1zsFj8HZKIiIiIFKPcJifLOuJWNW5FREREyrdCj7iNi4vjxRdf5KuvvqJjx44MGjSI119/nf79+zN+/Hj69+9fHHEWrTI4Odme9YsZerVn+YbEOGb6NxwRERGRciMiIoI//vgj33aJiYklEE0mcy5DLFTjVkRERCRwFDpxe+WVV5KSksLDDz/MnXfeiclkol+/fjz11FM88MADfPPNN8yePbs4Yi0Sf9WEikYSEf4OpJC27fzVu9w6uqUfIxEREREpX0aNGlWgdl27di3mSHzlPjlZ1hq3JRqOiIiIiJSwQpdKqFOnDvPnz2fIkCGYzjy/VblyZWbOnMnkyZP566+/ijzIotRpOMx3bfB3GIW29fhG73LLBhf5MRIRERERKQlZSyVkPDDmO+K27D1FJiIiIiIFV+jE7bx582jcuHGu+6655hq+/fZbAAzD4PHHH+fw4cPnF6EA8LfjX+9yy/ZX+DESERERESkJuY24TU3NWuO2hAMSERERkRJV6MStObdiW1lkTFDmdrv56quviI2NPbfIJJPbzeawBAAq2c1Ur97czwGJiIiISHHLfXIyz7vNZuRaA1dEREREyo9ivd0zSukkYAalM668nN65niMRnpjbpEV7S1SIiIiISPmVNTGbcVudluZ5Dw4u+XhEREREpGTp7/RlwPa/l3iX24Q09GMkIiIiIlJSzjY5merbioiIiJR/StyWAVv/Xe1dblmjg/8CERERERG/yBhxm5rqeVd9WxEREZHyLyATt6W1hENetiTu8C63bNbTf4GIiIiISInJrVSCRtyKiIiIBI6ATNyWNZVOJFAvDsxuaNK6t7/DEREREZES4FsqwZOwzZicLCTEDwGJiIiISIlS4ra0S03ltc8T2f8anFzYlrCQSH9HJCIiIiIlIOt8tIYBTic4nRpxKyIiIhIoAjJxaypDpRKsu3ZgOjMbRWjTNn6ORkRERERKSvbJyTJG2wIEB5d8PCIiIiJSsgIucXvsZbjd3MXfYRSY5Z+t3mVni1Z+jERERERESlLWEbduN6SmZm7Q5GQiIiIi5V+BErc33ngjn3/+OSkpKQU+sMVi4aeffqJZs2bnHFxxqJYMoaYgf4dRYNZt/3iXXS1b+jESERERESlJZnPmU2KGAWlpmftUKkFERESk/CtQ4tZut/Pkk0/SrVs3xo8fz4YNGwp08Nq1axMUVAqTpGWoVMIo5+dcOBTuGgQnG9X2dzgiIiIiUkLOVipBk5OJiIiIlH/WgjT6+uuv2bZtG1999RXffvstX375JY0bN2bw4MEMGjSISpUqFXecAWud7RhbasD6mjCxblN/hyMiIiIiJSRrqQTwLZWgEbciIiIi5V+Ba9y2aNGCxx57jF9//ZXZs2fTpEkTXn31VXr06MGYMWP4/fffizPOIvNCN/jT/a+/wyiQ9LiTbK/gBKB5cihBVpufIxIRERGRknK2EbeqcSsiIiJS/hV6cjKz2UyPHj147bXX+P333xk/fjwnTpxg6NCh9O7dmxkzZhRHnEXmib6wytjv7zAKZO+mn3BaPMutTDX9G4yIiIiIFJkdO3bQvn17Vq9eXaD2nsStRtyKiIiIBJJCJ26zioiI4MYbb+Tjjz/mgw8+wGazMXPmzKKKLeDt2J05irlFdOma5E1EREREzk1qaioPPvgg9qxDaHORdcStYfiOuA0OLqbgRET+v717j46qOvs4/puZZHIHAgHCPYFwEbSABqlAQQVFaYlIURBEEEEjeANRUUC0KJUCQpFbxFttEWspVcBXkFqKIhjAiigKQiDcr2ICIfeZef8Ah8QkEDEzZ5L9/azlWvuc2eecJzld+vTJnmcDAAJGuXrcluXo0aN6//33tXz5cm3fvl0NGjTQgw8+WFGx+YxHlWOFwvZjW6Wos+OWDTtYGwwAAAAqxLPPPqsePXrou+++u+C8kq0SWHELAABgkp9duM3KytKqVau0fPlybdq0SUFBQerRo4cef/xxXXPNNb6I0Vjf5u71Fm5btOlubTAAAAD4xd59913t3btXzz//vObNm3fBuUU3J6PHLQAAgHnKVbgtLCzU2rVrtWzZMv33v/9VXl6eWrduraeeekpJSUmKiorydZwVylNJFih848yQJIUXSI2atLM0FgAAAPwyaWlpmjlzphYvXiyHw3HR+cVbJdh+suLWFxECAAAgkJSrcNu5c2edOnVK1apV02233aZ+/fqpVatWvo7NaDlHD2h3NZck6bLsSNltv6gdMQAAAPxswYIFSklJkSTl5eXJ4/Fo1qxZql+/frmuDwo6X6h1OOwqKDifD0ZG2uR0Xrz4i8olKIh3aiLeu3l45+bhneNSlatw26ZNG/Xr1089evSQ0+n0dUyQlL7tP/Kcy9UvCypfcg8AAIDAkZycrOTkZEnS5s2bNWzYMI0fP17jx48vNueWW27RM888U+J6T5GviRUUuJWVdb6QGxTkVn6+y3fBwzK8VzPx3s3DOzcP7xyXolyF29dee83XcfhVZdicrOm+03pvsfRNbalZr65WhwMAAIBfIDExUVu3bi12rmXLllqwYIE6duxY6jUlNyc7f8zmZAAAAFXfz96cDP5Rc+deJe2QknZIGY/eqgKrAwIAAIBfXWhzMnrcAgAAVH3GFW7bHZZq14uwOoyLCvpuh3dc2IJ+wgAAAFXNjh07Lvh58c3J9JPNyVhxCwAAUNUZt+PVFynSHZ52VodxUY5zhVt3zZryxMRYHA0AAAD87acrbvPyzh+z4hYAAKDqM27FbWVQ8MNxvR1zSK09UtP4hOJZOwAAAIxQNAX0eKScnPMnwsJYcQsAAFDVmVm49QR2orvn6zW68/dnx7efPqE51oYDAAAAC9jt53PWs60Szn/GilsAAICqz7hWCZXBrt2fecetqidYGAkAAACsUnJzMnrcAgAAmMS4wu21Q6V/aKvVYVzQzqNfeccJ9dtbGAkAAACsUnJzsvPHISH+jwcAAAD+ZVzhdm2cdEAZVodxQTty0r3j5i27WhcIAAAALFO0cOt2/7THrQUBAQAAwK8CtnC7atUqde/e/YJzXC6Xpk6dqk6dOql9+/a6//77dezYsYveO9C/WLbdcVKSFOySGjfraHE0AAAAsELxVgk274pbp9NTrKgLAACAqingUr6CggItXLhQY8aMkecim4jNnz9fn376qf75z3/qk08+UWhoqCZMmOCnSH2j8HSmvqtWIElqfiZUwUFOiyMCAACAFX7aKiEv7+yYjckAAADMEHCF22HDhik1NVUjRoy46Nx//OMfGjFihOrVq6fIyEiNHz9eH3/8sfbv33/hCy9SELbSgW8+Vn7Q2XEr1bE2GAAAAFimrM3J2JgMAADADAFXuJ02bZpeeeUVNW7c+ILzTp8+rSNHjqhFixbeczExMapevbp27NhxwWsDOdXduetT77hFVFMLIwEAAICVytqcjBW3AAAAZgiyOoCfio2NLde8M2fOSJLCw8OLnQ8NDfV+Vha7XXI6HZcWoI+lHdsmndsluGX9dgEbZ2USFMTv0DS8c/Pwzs3DO4cJiq649XjOb04WFhbIyxAAAABQUSwt3C5YsEApKSne44ULFyoxMbFc14ad20o3Jyen2Pnc3FxFRERc8FqX26P8fNfPjNZPThxXvWrS4SgpLq5D4MZZyfB7NA/v3Dy8c/PwzlHVlWyVcHYcEmJNPAAAAPAvSwu3ycnJSk5OvqRrq1evrrp162rXrl3edgnHjx9XRkZGsfYJlc2Tn9o18RspM9yh7B09rA4HAAAAFinaKiE/X3K56HELAABgkoDrcftz9O3bV/Pnz9f+/fuVlZWlKVOm6Oqrr75of9yA7XLrdsuxJ02SFFG/qYJCwiwOCAAAAFYpWrj9sU2CRI9bAAAAU1Sqwu2yZcvUvn177/GoUaPUrVs3DRo0SN26dVNeXp5mzZp1wXs8sU662tPQx5FeGvvBA7Kda/3gSmhucTQAAACwUtFWCUW7g4Xxt30AAAAjBNzmZD/q27ev+vbtW+xcUlKSkpKSvMfBwcEaO3asxo4dW+77vvBv6czVccqusEgrjiNtl3fsakbhFgAAwGRFV9xmZxddcRug3x4DAABAhapUK26ruve+W6Lf3C0NT5I+j+c7cAAAACYra8UtrRIAAADMQOE2gGw9+ZXWNZFevVI6GlvN6nAAAABgobJW3IaEsOIWAADABMYVbvMcUqHHZXUYpdqZd9A7btryNxZGAgAAAKvZ7ecLtPS4BQAAMI9xhdvQidKLjk+tDqNUO4MzJEmhhVKDRldYGwwAAAAsVbRVAj1uAQAAzGNc4TZQFWadUlpUoSQpITtMdrvD4ogAAABgpeKF2/NjetwCAACYwcjCrccTeKsUDny7TgXnarXNFWNtMAAAALAcK24BAADMZmThNhDtSfvMO24W0cTCSAAAABAIim5OlpNTtHBrQTAAAADwOwq3ASLt6FfecbPabSyMBAAAAIGgaOGWVgkAAADmMbJw61Hgfb1s1+k93nHTuA4WRgIAAIBAULRVQl7e+XFISODlsgAAAKh4RhZuA9FO9zHvuOll3SyMBAAAAIGg6IrbvLzzVVyn04JgAAAA4HdBVgdghYDbnMzj0diPXbqhhnSwXpSqV69rdUQAAACwWNHCbW7u+XFwsP9jAQAAgP8ZWbgNNPZjR5W0NUdJkvKv76hMqwMCAACA5Yq3Sjh/QKsEAAAAM9AqIQA40nZ5x4UJzS2MBAAAAIGieKuE82NW3AIAAJjBuMLtmjekgYWXWx1GMY5dO71jVzMKtwAAACh7xS2FWwAAADMY1yrh2nTpjKeGsq0OpIjv9qTKWUdqflJyseIWAAAAKl64LcrppFUCAACACYwr3EqSAmxzsj/aPtI/R0o2j7SpXqgaWx0QAAAALGcv47txTqd/4wAAAIA1jGuVEIi+s/8gSXK4pXpx7S2OBgAAAIGg7BW3/o0DAAAA1jCucLuspbTD9r3VYXi583K1KypfktQ0O0TBQWTiAAAAKHvFbXBwYH17DAAAAL5hXOH2ljukfwRtszoMryPbP1POuQ0mWrhrWhsMAAAAAobNVnqBlhW3AAAAZjCucBtodu9a7x0nhNHdFgAAAGfR4xYAAMBsRhZuPQqcr5elHfrSO24Wc5mFkQAAACCQlF24DZxcFgAAAL5jZOE2kOw6leYdN2uSaGEkAAAACCRlbU4WHOzfOAAAAGANIwu3gbRGYVfhEe847rJuFkYCAACAQEKrBAAAALMZWbgNJDtDsiRJ0bk21apFj1sAAACcVVrh1m73KCjI/7EAAADA/yjcWqjgxBGdCXJLklrkRcpW1vfhAAAAALHaFgAAwCRG/r0+UDYnC9t3QCf+JJ0Mk44MvMnqcAAAABBASltxS39bAAAAcxhZuA2Quq0ce3ZLkmrmSM5G7ZRjcTwAAAAIHKV9GSskJEASWQAAAPicca0SnIWSQ4HRksCxO807dsU3tTASAAAABBpW3AIAAJjNuMJt3nPShNzOVoch6fyKW4nCLQAAAIqjcAsAAGA2M1slBIgJoWuV00tKOCkNbNzYvCo6AAAAylRaqwSnk1YJAAAApqBwa6F36h7T/gSpVq5dd4ZHWB0OAAAAAkhpK26dTv/HAQAAAGsYucjT5rF+pULu90e0P8otSWqWS9EWAAAAxZW+4tb/cQAAAMAaxhVuR/5WWh680+owdOC7Dd5xU0dtCyMBAABAIKLHLQAAgNmMK9zO7yBtchy2OgztTd/sHcdHNLYwEgAAAAQiu73kt8TocQsAAGAO4wq3khQI6W76sW+947jarSyMBAAAAJUFrRIAAADMYWThNhDszkr3jps0vtK6QAAAABCQ2JwMAADAbEFWB2AN69fc7nYd947jWnS2MBIAAAD4y/Dhw5WamqqgoPNp+J///Gd17dq1xNzSNicLDrY+jwUAAIB/GFm4DYR0N815WpJUI8+m6JoNLY4GAAAA/vD111/r1Vdf1dVXX33Ruay4BQAAMButEiyQn3lC+yLdkqRmueGylbacAgAAAFXK/v37lZmZqdatW5drPoVbAAAAsxm54lYea9fcunbv1JPrpF01pcb14i2NBQAAAP7x1VdfKSIiQqNHj9ZXX32lmJgYDR06VP369St1Pq0SAAAAzGZk4dbqdLf6/iN67j9nx2ee6qtsa8MBAACAH+Tn56tdu3YaPXq0mjdvrtTUVD344IOKiIjQzTffXGI+K24BAADMFrCF21WrVulPf/qTPvroozLn/PDDD5o6dao++eQT5efnq3Xr1ho3bpwuu+wyP0b68zn27PaOC5s2szASAAAA+MqCBQuUkpLiPV64cKFeeeUV73GXLl3Up08fffDBB6UWboODS1ZuQ0NtcjodvgkYlgsK4t2aiPduHt65eXjnuFQBV7gtKCjQG2+8oVmzZqlu3boXnDt+/Hi5XC6tWLFCERERmj9/voYPH67Vq1crPDy81Gt675Ba1ov2RejlVrRw645vamEkAAAA8JXk5GQlJyd7j5csWaLjx48XK9Lm5+crJCSk1OvdbneJc0FBbuXnuyo+WAQM3q+ZeO/m4Z2bh3eOSxFwm5MNGzZMqampGjFixAXneTwe2Ww2Pfzww4qOjpbT6dQ999yjEydOKD09vczrli2W7sprU8FR/zzHD25X4bnfvCuOHrcAAAAmyMrK0uTJk/XNN9/I7Xbrv//9r1asWKH+/fuXOr+0VgnBwT4OEgAAAAEj4FbcTps2TbGxsVq6dOkF59lsNs2dO7fYuZUrVyo8PFzx8Rcphlq8Odn1V/5Pe7tKV3wfpFVR1SyNBQAAAP4xZMgQZWdn64EHHtD333+vRo0aaerUqUpMTCx1fmmbk9HjFgAAwBwBV7iNjY29pOs++ugjPffcc3rmmWcUFhZWwVFVnILTGUqPcslllzwhZN4AAACmsNlsGjlypEaOHFnO+SXPBQdbvc0uAAAA/MXSwm1pGzaUteKgLB6PR/Pnz9fChQs1ZcoU9erV66LXOBzWbepwMC1VrnNfe2tmi2FzCT+gCbh5eOfm4Z2bh3cOE5TWKqGMdrgAAACogiwt3P50w4afKycnR6NHj9bOnTu1aNEitW7d+qLXNHtIuit4o0Za1BQ6bedG7zg+rCHNqf2E37N5eOfm4Z2bh3eOqq70Fbf+jwMAAADWCLhWCT/H6NGjdeTIEf3zn/9UjRo1ynXN7prSyTO5vg3sAvYc3ebdEi6uVgvL4gAAAEBgK23FrdNJqwQAAABTlJIOBq5ly5apffv2kqRt27ZpzZo1SktL03XXXaf27dt7/9m8efMF7+ORdQnvnlN7vOP4xldaFgcAAAACGytuAQAAzBawK2779u2rvn37FjuXlJSkpKQkSVKbNm20Y8cOK0L7RXYXHvWOGzf/tYWRAAAAIJDZ7SUXG9DjFgAAwByVasVtVbA76JQkKbxAqhPb0uJoAAAAEKhKa5UQHEyrBAAAAFMYWbj1eKxJeAvPnNaeqEJJUrPsMNlK+/4bAAAAoNJbJTid/o8DAAAA1jCycGuVI99tVIHj7LipalobDAAAAAJa6Stu/R8HAAAArBGwPW59yarNyeIP5+jgDGlXTUn9e1gSAwAAACqH0gq3rLgFAAAwh5GFW6sEpe9R/dNS/dPSqSadlWd1QAAAAKhUnE563AIAAJiCVgl+5Niz2zt2xTe1MBIAAAAEOlolAAAAmM24wu2c96U+udYUTYsVbps2syQGAAAAVA6lbU4WEuL/OAAAAGAN41oljNokZbevpzMWPPvFqC9UPVFqnhOhttFsTgYAAICylb7illYJAAAApjCucGsVd36enm2Xodxg6bJTLq0tbQkFAAAAcA6bkwEAAJjNuFYJkiSP/1cqHN/1P+We60kW767u9+cDAACgcint7/z0uAUAADCHcStud9WUgu05Cvfzc/fu2eQdx4XU9/PTAQAAUNmUtuI2JIRWCQAAAKYwbsVt84ekqZGf+/25+w997R3HVbdmczQAAABUHqy4BQAAMJtxhVurpGekeceN67W2MBIAAABUBvS4BQAAMJuRhVuPzf9fMduTe8g7bhKX6PfnAwAAoHL5aeHWbvfI4bAmFgAAAPifkYVbWdAaLF0nJUk2j9SgWQf/BwAAAIBK5aetEkJCrIkDAAAA1jCycOvxd+XW49HusBxJUoNsh0JDI/37fAAAAFRKtiLfFKO/LQAAgFmMLNz6W9bhPToRfnYcXxBlbTAAAACoNIq2S3A6LfjaGAAAACwTZHUAJshJ366k7dLuaKl1WD2rwwEAAEAlUbRdAituAQAAzGJk4dbfaxUaHjqt994+O86aNEg5fn4+AAAAKqfiK26tiwMAAAD+Z2irBP+Wbh17071jV1y8X58NAACAyqvoiltaJQAAAJjF0MKtfznS93jHriZx1gUCAACASqXoiltaJQAAAJjFuFYJO2dLzluv9Osz7UVW3Lrj4vz6bAAAAFRexVfcWhcHAAAA/M+4wm3CSSnHFaosPz6zQ+JGudtLv8oI0azIKD8+GQAAAJWZCa0S+vXrrSNHDnuPg4ODFR1dU126dNU999yn6tVreD/r0iVRTz01Sb169bYgUgAAAP8yrnDrb4VnTmtbzUK57JIj1GF1OAAAAKhETNmcbMCAO3XHHXdKkvLy8rR79y7NmzdbW7b8T/Pnv6qIiEhJ0nvvrVRkZKRfY0tP36MPPlhR5uedOv1Gbdu28x4vWfK2jh8/Xupcp9Ope+65r6JDBAAAVZSZhVs/LlY4vHOjXOcS7njV9N+DAQAAUOkVXXFblXvchoWFqVatGO9x/foNlJDQUoMH367Fi/+m4cOTJanYHH/JzMzU/fc/WObnX365pdhx8+at1K/fgHLNBQAAuBDjCrdzO0gJoYflry63+/Zs9o7jQuv76akAAACoCkxZcVua2NhYde16rVavXukt3BZtlfD888/ozJkzysnJ1rZtX2vw4KG6886hWrz4r3r//WU6dOignE6n2rZtr0ceeUz16zeQJOXk5CglZa7WrPm3srPPqEWLVho16mG1bn25lT8uAABACfaLT6laHvittCRit9+et+/oN95xk+gEvz0XAAAAlZ/dfv6rYlW1x+2FNGuWoIMHDyg7O7vUzz/+eI06dOioV155UzfeeLPeeectvfnm67r//oe0ePFS/fGPM7Rv31699NJM7zWTJj2pTz/9RE8++bRef/0tNW7cRGPGPKiMjAw//VQAAADlY9yKW3/bk7lbOrcfWZP6/BUfAAAA5fdzWyUsWxakqVOdysqyXXyyD0RGejRuXL569y6soPudTaTPnMlSeHh4ic+joqpp4MC7vMcNGjTShAnPqEuXrpKk2Nh6uu66Hvroow8lSfv27dX69es0Y8ZL6tjxGknS6NGPKzw8XKdOZahGjRoVEjcAAEBFMLJw6/Fjk9u9eUe8hdvGza7223MBAABQ+RUt3JanVcLcuU7t3Gnthrhz5zorrHCblZUlSd7NyX6qYcNGxY67dOmqbdu+1quvpmj//n3au3ePdu9OU+3adSRJaWk7JUlt2lzhvcbpdOrBB8dUSLwAAAAVycjCrT/ttmdIkhxuqV7jttYGAwAAgEql+Irbiy8+eOCBfL3wgrUrbkeNyq+w++3Y8a0aNmxc6mpbSQoJCSl2vGjRX/Tqqy+rV6/eat/+KvXrN0Dr1q3Vv/+9SpIUFHT2//7YrPn1AAAA/CxGFm49Hv+suPW4XNoTnidJanImWMHBIRe5AgAAADiv6OZkIeVIJXv3Lqyw1a5WO3bsqNatW6tBg4aU+5q//OU1DRs2QnfeOdR7bvHiN735f5Mm8ZKkb7/9RomJZ78NV1hYqNtvv0UjRz6kHj16VtwPAAAA8AsZWbj1l4x93+pU6NlxvKuatcEAAACg0ilauC1Pj9vKKicnR99/f0KSlJeXp7S0nXr55XmqV6+BBgy4s9z3qVOnrjZtSlXnzl3lcNi1cuX/ae3aNapZs5YkqXHjJurW7Tq9+OJUPfroONWuXUeLFv1FBQUFuuoq2poBAIDAQuHWh6odPKaVf5V2R0vVO11ldTgAAACoZIr3uPXfPg3+9vbbf9Pbb/9NkhQWFqY6deqqa9frdMcdg8tsk1CaiRP/oBdfnKrhwwcrPDxCbdpcrrFjn9SMGS/o8OFDqlevvp56apLmzv2zJk16Unl5eWrd+grNnDlX0dHRZd53/vyXyvzs8suvKHa8eXOq1q//pNS5ubk5atu2Xbl/HgAAYDabx199AwKE7Vmb7j7VQlPHbfb5s0IW/03VHh4pSTo95U/KHZ7s82eiJKfTofx8l9VhwI945+bhnZuHd26m2rWjrA7BrzIzs3X55aE6cODsstvHHsvTY49VXP9YBB7+3WYm3rt5eOfm4Z2bp6LyVvvFp+BSOdJ3e8fuJnHWBQIAAIBKqWirBKfTujgAAADgf8a1Smh6UoqRfzYJc+xN945dcU398kwAAABUTcHBRn1RDgAAwHjGFW7TZks5d16pLD88a3X2FtVoLMVnSCGNGvvhiQAAAKhKWHELAABgLuMKt5IkP7X1Hdlmtw78WqqdY9e20FC/PBMAAABVR/HNyayLAwAAAP5Hj1sfycs4poORbklSfF6ExdEAAACgMiq+4pZWCQAAACahcOsjB3ZskOfcCol4ey1rgwEAAEClZLefL9YGB1sYCAAAAPzOuMJt0h3SvOrf+Pw5+/Zu8Y6bhDf0+fMAAABQ9dAqAQAAwFwBW7hdtWqVunfvXu75M2fO1PXXX3/RectbSltDfvgloZXL3mPfesdxNZv7/HkAAACoemiVAAAAYK6AK9wWFBRo4cKFGjNmjDzl3ERsw4YNevXVV8v9DH+kvOmn073jJg3b+uGJAAAAqGqKrrilVQIAAIBZAq5wO2zYMKWmpmrEiBHlmn/ixAlNmDBBgwcP9nFkP096wVHvuFGzjhZGAgAAgMqKVgkAAADmCrI6gJ+aNm2aYmNjtXTp0ovOdbvdGjt2rEaMGCGn06lVq1b5IcLy2RN0SpIUWiDVadDK4mgAAABQGRVtlVBVV9z269dbR44c9h7b7XaFh4erefOWGj48WW3btpckdemSWOY9YmPracmS5ZKkjRs/U0rKXO3du0c1a9bSLbf01cCBd8lWtAp+zgsvTJbL5dL48c9U7A8FAABQAQKucBsbG1vuufPnz1dUVJQGDBhQrkKvVzlbMFwqd36edkcWSJLickJktzt8+jwAAABUTUVrjSEhVbfH7YABd+qOO+6UdDZVP3UqQykpc/Xoow/qrbf+qTp16uq991aWuO7rr7/S00+PU7du10mS9u5N17hxYzR48N36wx/+qO3bv9WUKc8oNDRUv/99f+91LpdL8+e/pBUr3tPNN//uovGtX79OX375RamfuVwuDRp0l6Kja3rPzZ4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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 5))\n", "\n", "# 左图:总 XC 势\n", "v_xc_pz81 = result_pz81.v_x_up + (result_pz81.v_c_up if result_pz81.v_c_up is not None else 0.0) # 自旋向上分量\n", "v_xc_vwn = result_vwn.v_x_up + (result_vwn.v_c_up if result_vwn.v_c_up is not None else 0.0)\n", "\n", "ax1.plot(r, v_xc_pz81, 'r-', linewidth=2, label='PZ81')\n", "ax1.plot(r, v_xc_vwn, 'g--', linewidth=2, label='VWN')\n", "ax1.set_xlabel('r (Bohr)', fontsize=12)\n", "ax1.set_ylabel('V_xc(r) (Hartree)', fontsize=12)\n", "ax1.set_title('总 XC 势', fontsize=14)\n", "ax1.set_xlim(0, 10)\n", "ax1.set_ylim(-1.5, 0.1)\n", "ax1.legend(fontsize=11)\n", "ax1.grid(alpha=0.3)\n", "\n", "# 右图:交换与关联分量\n", "ax2.plot(r, result_pz81.v_x_up, 'b-', linewidth=2, label='Dirac 交换')\n", "ax2.plot(r, result_pz81.v_c_up, 'r--', linewidth=2, label='PZ81 关联')\n", "ax2.set_xlabel('r (Bohr)', fontsize=12)\n", "ax2.set_ylabel('势 (Hartree)', fontsize=12)\n", "ax2.set_title('XC 势分量(PZ81)', fontsize=14)\n", "ax2.set_xlim(0, 10)\n", "ax2.legend(fontsize=11)\n", "ax2.grid(alpha=0.3)\n", "\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "print(\"\\nXC 势特征:\")\n", "print(f\" 核附近(r=0.1): V_xc = {v_xc_pz81[np.argmin(np.abs(r-0.1))]:.4f} Ha\")\n", "print(f\" 远区(r=5.0): V_xc = {v_xc_pz81[np.argmin(np.abs(r-5.0))]:.4f} Ha\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## LDA 泛函对比总结\n", "\n", "| 泛函 | 适用场景 | 优点 | 缺点 |\n", "|------|---------|------|------|\n", "| PZ81 | 标准基准 | 参数简单、收敛稳定 | 高密度区略欠精确 |\n", "| VWN | 高精度计算 | 低密度区更准确 | 参数复杂 |\n", "\n", "**实际应用建议**:\n", "- 教学演示:优先 PZ81(参数少、公式简洁)\n", "- 高精度计算:使用 VWN(低密度区更准确)\n", "- 对大多数原子,两者差异 < 0.1 eV\n", "\n", "## 关键概念\n", "\n", "- **局域近似**:$\\epsilon_{\\mathrm{xc}}(n(r))$ 仅依赖 $n(r)$,忽略梯度\n", "- **势的导出**:$v_{\\mathrm{xc}} = \\delta E_{\\mathrm{xc}} / \\delta n$\n", "- **自旋极化**:$\\epsilon_c(n, \\zeta)$ 依赖自旋极化度 $\\zeta = (n_\\uparrow - n_\\downarrow) / n$\n", "\n", "## 下一步\n", "\n", "在 **[06-spin.ipynb](06-spin.ipynb)** 中,学习如何处理开壳层体系的自旋问题。" ] } ], "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 }