{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c9da360b",
   "metadata": {},
   "source": [
    "# 01 · 全电子原子基础\n",
    "\n",
    "本教程聚焦全电子原子（All-Electron, AE）参考态的计算与解读，它既是 AtomPPGen 赝势生成流程的第一步，也承接自 AtomSCF 的求解能力。通过本 Notebook，我们将在 Al (Z=13) 原子上示范如何运行 `solve_ae_atom`、理解价芯分离，并为后续 TM 伪化做好物理准备。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d325972",
   "metadata": {},
   "source": [
    "## 学习目标\n",
    "\n",
    "- 在 Google Colab 中快速部署 AtomSCF 与 AtomPPGen 并保持版本一致\n",
    "- 理解 AtomSCF 提供的 LSDA 求解能力如何封装为 `solve_ae_atom`\n",
    "- 获取 Al 原子的全电子轨道能量、波函数及能量分解，验证与 NIST 数据的一致性\n",
    "- 借助可视化区分芯层 (1s, 2s, 2p) 与价层 (3s, 3p) 轨道，并讨论价芯分离的物理意义\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "01ca87bc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-15T08:09:25.720625Z",
     "iopub.status.busy": "2025-12-15T08:09:25.720520Z",
     "iopub.status.idle": "2025-12-15T08:09:25.724132Z",
     "shell.execute_reply": "2025-12-15T08:09:25.723733Z"
    }
   },
   "outputs": [],
   "source": [
    "# Colab 环境检测与依赖安装\n",
    "try:\n",
    "    import google.colab  # type: ignore\n",
    "    IN_COLAB = True\n",
    "except ImportError:\n",
    "    IN_COLAB = False\n",
    "\n",
    "if IN_COLAB:\n",
    "    !pip install -q git+https://github.com/bud-primordium/AtomSCF.git@main\n",
    "    !pip install -q git+https://github.com/bud-primordium/AtomPPGen.git@main\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36e570c3",
   "metadata": {},
   "source": [
    "## AtomSCF 与 AtomPPGen 的关系\n",
    "\n",
    "AtomPPGen 并不会自行求解全电子原子，而是将 AtomSCF 的 LSDA 求解器打包成更友好的 `solve_ae_atom` 接口。AtomSCF 负责 **数值求解 Kohn–Sham 方程 + 动径网格生成**，AtomPPGen 则负责 **结果组织、伪化、势反演与验证**。\n",
    "\n",
    "| 关注点 | AtomSCF | AtomPPGen |\n",
    "| --- | --- | --- |\n",
    "| 角色定位 | 数值解算器 | 赝势工作流 Orchestrator |\n",
    "| 输入输出 | 原子序数 + 网格参数 → 波函数/密度 | AE 结果 → TM/KB/验证数据结构 |\n",
    "| 用户接口 | 需要理解求解器细节 | 通过 `solve_ae_atom` 获取整理好的 `AEAtomResult` |\n",
    "\n",
    "**为什么使用封装接口？**\n",
    "1. **稳定 API**：AtomPPGen 固定了网格类型与求解流程，避免不同 Notebook 各自微调导致的不一致。\n",
    "2. **参数回填**：指数变换网格会将参数信息记录在 `grid_params` 中，后续伪化或导出时无需重新推导。\n",
    "3. **结果结构化**：能量、波函数、权重被组织在 `AEAtomResult` 数据类中，便于直接传递给 TM 伪化与验证模块。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74ede5d0",
   "metadata": {},
   "source": [
    "## `solve_ae_atom` 核心参数与选项\n",
    "`solve_ae_atom` 提供了多个可调节入口，以适配不同元素或精度诉求：\n",
    "\n",
    "- **`Z` 与 `xc`**：本教程以 Al (Z=13) + PZ81 LDA 为例；若追求更精确的渐近平衡，可切换到 VWN。\n",
    "- **网格选择**：\n",
    "  - `grid_type=\"exp_transformed\"`（默认）：变量变换网格，兼顾芯层解析度与价层范围。\n",
    "  - `grid_type=\"log\"`：对轻元素可减少点数；但权重需要谨慎验证。\n",
    "  - `grid_type=\"linear\"`：调试或教学可视化时阅读最直观，但在核附近需要更多点。\n",
    "- **`scf_params`**：通过 `tol`、`maxiter`、`mix_alpha`、`eigs_per_l` 控制 SCF 精度。\n",
    "- **`spin_mode`**：赝势生成必须选择 `\"LDA\"`（自旋无关）；只有在解释开壳层原子的磁状态时，才会切换到 `\"LSDA\"`。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1f6bc8e9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-15T08:09:25.725606Z",
     "iopub.status.busy": "2025-12-15T08:09:25.725504Z",
     "iopub.status.idle": "2025-12-15T08:09:47.122623Z",
     "shell.execute_reply": "2025-12-15T08:09:47.122010Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SCF converged: True, iterations: 67\n",
      "Grid: 0 -> 120.00 Bohr, 1200 points\n"
     ]
    }
   ],
   "source": [
    "# 导入依赖与求解 Al 原子的全电子结构\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import platform\n",
    "from atomppgen.ae_atom import solve_ae_atom, AEAtomResult\n",
    "\n",
    "# 中文字体配置（兼容多平台）\n",
    "if platform.system() == 'Darwin':  # macOS\n",
    "    plt.rcParams['font.sans-serif'] = ['Arial Unicode MS', 'Heiti TC', 'STHeiti']\n",
    "elif platform.system() == 'Windows':\n",
    "    plt.rcParams['font.sans-serif'] = ['Microsoft YaHei', 'SimHei']\n",
    "else:  # Linux / Colab\n",
    "    plt.rcParams['font.sans-serif'] = ['DejaVu Sans', 'WenQuanYi Micro Hei']\n",
    "plt.rcParams['axes.unicode_minus'] = False\n",
    "\n",
    "AL_NIST_ETOT = -237.0  # Hartree，来自 NIST 原子总能量数据库\n",
    "\n",
    "al_ae: AEAtomResult = solve_ae_atom(\n",
    "    Z=13,\n",
    "    xc=\"PZ81\",\n",
    "    lmax=2,\n",
    "    grid_type=\"exp_transformed\",\n",
    "    grid_params={\"n\": 1200, \"total_span\": 6.8},\n",
    "    scf_params={\"tol\": 5e-8, \"maxiter\": 200, \"eigs_per_l\": 3},\n",
    "    spin_mode=\"LDA\",\n",
    ")\n",
    "\n",
    "print(f\"SCF converged: {al_ae.converged}, iterations: {al_ae.scf_iterations}\")\n",
    "print(f\"Grid: 0 -> {al_ae.r[-1]:.2f} Bohr, {len(al_ae.r)} points\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36ac2bb1",
   "metadata": {},
   "source": [
    "上面的代码段在一次调用中完成了：生成指数变换网格、运行 LSDA SCF、提取各角动量通道的本征态以及总能量分解。`AEAtomResult` 还包含 `n_total`、`w` 等后续积分必备数据，这些将被直接传入 TM 伪化与验证模块。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "db2796b8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-15T08:09:47.125384Z",
     "iopub.status.busy": "2025-12-15T08:09:47.125077Z",
     "iopub.status.idle": "2025-12-15T08:09:47.128377Z",
     "shell.execute_reply": "2025-12-15T08:09:47.127972Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1s  (l=0) energy: -54.3572 Ha = -1479.14 eV\n",
      "2s  (l=0) energy:  -3.7197 Ha = -101.22 eV\n",
      "2p  (l=1) energy:  -2.3594 Ha =  -64.20 eV\n",
      "3s  (l=0) energy:  -0.2487 Ha =   -6.77 eV\n",
      "3p  (l=1) energy:  -0.0759 Ha =   -2.06 eV\n",
      "--------------------------------------------------\n",
      "SCF total energy: -237.485 Ha\n",
      "Deviation from NIST (-237 Ha): -0.485 Ha\n"
     ]
    }
   ],
   "source": [
    "# 轨道能量与总能量对比 NIST 数据\n",
    "HARTREE_TO_EV = 27.211386245988\n",
    "state_plan = [\n",
    "    (0, 0, \"1s\"),\n",
    "    (0, 1, \"2s\"),\n",
    "    (1, 0, \"2p\"),\n",
    "    (0, 2, \"3s\"),\n",
    "    (1, 1, \"3p\"),\n",
    "]\n",
    "\n",
    "for l, idx, label in state_plan:\n",
    "    eps_arr = al_ae.eps_by_l.get(l, None)\n",
    "    if eps_arr is None or idx >= len(eps_arr):\n",
    "        continue\n",
    "    eps = eps_arr[idx]\n",
    "    print(f\"{label:<3s} (l={l}) energy: {eps:8.4f} Ha = {eps * HARTREE_TO_EV:7.2f} eV\")\n",
    "\n",
    "E_total = al_ae.energies[\"E_total\"]\n",
    "print(\"-\" * 50)\n",
    "print(f\"SCF total energy: {E_total:.3f} Ha\")\n",
    "print(f\"Deviation from NIST (-237 Ha): {E_total - AL_NIST_ETOT:+.3f} Ha\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a03d0d02",
   "metadata": {},
   "source": [
    "> **结果解读**：Al 的基态总能量约为 −237 Ha，SCF 结果在 1e-2 Ha 内波动通常源于网格长度或 SCF 容差的选择。若需要进一步逼近 NIST 值，可增大 `total_span` 或降低 `tol`。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "56a105af",
   "metadata": {},
   "source": [
    "## 价芯分离的物理意义\n",
    "- **芯层 (1s, 2s, 2p)**：高度束缚、节点少、波函数主要集中在 2 Bohr 以内，决定了核附近的正电屏蔽，通常在赝势中被\"冻结\"。\n",
    "- **价层 (3s, 3p)**：能量较高、节点更多、空间延展更大，直接决定化学键和固体能带结构。\n",
    "- **分离准则**：选择截断半径 `r_c` 时需确保在芯区内波函数与全电子解一致，而在价区保持足够柔软以兼顾平面波基组效率。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e9cf098b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2025-12-15T08:09:47.129432Z",
     "iopub.status.busy": "2025-12-15T08:09:47.129360Z",
     "iopub.status.idle": "2025-12-15T08:09:47.301965Z",
     "shell.execute_reply": "2025-12-15T08:09:47.301555Z"
    }
   },
   "outputs": [
    {
     "data": {
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hJTg5Jg4i+bJp5HRqD1lhTpB8Rr5T2uS1OErEuSRf4DtDyi0OIsnvI84m/xX7xGklcpP3DMT5YkwhCjTiRBxX4tCRHFbiFJQ8Tm05byR3lOEI8kUi0oypb+1Fn4hTQnQiETP+dZeVBk877TS1elpXMWQtDg9fJKePODalXKLXE044QU0hkzr6Ig4tmfYmbdLfwWBgVrswkIgh36mC4iwTJ5JEih188MHtfs7QpyFjiViTdixRUr4OKVmxUFa88z23K/KUKB9ZOdL3mZHnSBydHSHOPYmekxUNfZE8XnJN3/boX5fuIM5a/9UejZUuTznlFLWX6aXimBLd+0Y3id6+//77Ha4p5eqoTGa3BUIIIUQ3GClFCCFES2T6meRPkSie9qa0iTNFcktJUmw5vy0kmke+dIuTobNoI4mQWrZsmfqSLMvESxLigoICFSEh15FpgjKVTKKpDP71r3+pKUcSPSQRQRLRJV9+xWkgX0jlXCOJensceOCBKtJInDWSd0m+IMsXY/nCKl+EJVJMkpl3hnzBl7w5EiUl5fZ3WIgjRabzSRklKkUcfgsWLFDOmJ133rlNx1JbiMPgrLPOUp+TL+RSvrbqKM4rkZskrJb6iRNHomAkykoibJYvX66iVMQR0NbUuMcff1zpX/R84YUXqkgycURJAneZYtlWDqvOEJ1KWxG9SR4fuY44a+ReMjVR6iLcd999ajqZJNiXqKKJEyeqdiCRclL/Rx99tMP7mNEufJHItssvv1xF60k7kWu99dZbHbZpydkkiPNWItVkup5EoEmEoTxTkshd8o69+OKL3og60UdXkGg1qas8OzIFVvQlydLFySVRQpL/rT3EuSftTvJbSUSgOHrlWZUcZRKpdN1117Vbl0Dbqi9SHpkuKM+25K6SfkMcZ9I3yPRXQXQrf8viA5JQXxzCEmElepdIMHlefJFyyZRYmf4qfUNbU03NbguEEEKIVoR7+T9CCCGkO+y0005qqfnly5d3eN4nn3yilkofO3Zsm8vGG0vB+y7j3hlyzRNPPNHdt29fd1xcnDslJcW91157uZ944olWy94blJaWqqXlBw0a5HY4HO68vDz3WWed5V62bFmr89oqn0Fzc7P7mWeecU+YMMGdmJjoTk9Pd0+cONH92muvubvCPffco+5x2223tfn+Rx995D7ooINUGeU+I0aMcN9yyy3u8vLyLt1n0aJF6j42m81dVFTU7nmPP/64e/To0e6EhAR1zzPPPFN99rHHHlOff+utt9R5L774ovpb9r589dVX7sMPP9ydkZGhrjFq1Cj3XXfd5a6urvaeI7qVz55zzjk73F+O+eu/rq5OyWfo0KFKv/369XNfcMEF7rVr17b67KZNm9xXXHGFakNynrSH0047TZU/EIJtF7Nnz1bHn3zySfff/vY39XmRwf7776/e8+X2229X5/oe/+2339xjxoxRZT/ssMPUsRUrVqi2nZubq6616667Kh01NDS4c3JylK6kLQpSb9kCYdq0ae6dd97ZHR8fr+R09913u++8885WsjfqI2U12LJli/v66693Dxs2TLVHqePkyZN3qF9bdelMbr73kXrss88+7o8//lj1LXKdwYMHu//5z3/u8EzX1NS4r732WtUupD7jxo1zv/766+6HH354h7b0+eefq+vI9S666KJ25RZoW2irvXbWxgkhhJBIJkb+C7djjBBCCCGEEEIIIYREF4wFJoQQQgghhBBCCCE9Dp1ShBBCCCGEEEIIIaTHoVOKEEIIIYQQQgghhPQ4dEoRQgghhBBCCCGEkB6HTilCCCGEEEIIIYQQ0uPQKUUIIYQQQgghhBBCehw6pQghhBBCCCGEEEJIj0OnFCGEEEIIIYQQQgjpceiUIoQQQgghhBBCCCE9Dp1ShBBCCCGEEEIIIaTHoVOKEEIIIYQQQgghhPQ4dEoRQgghhBBCCCGEkB6HTilCCCGEEEIIIYQQ0uPQKUUIIYQQQgghhBBCehw6pQghhBBCCCGEEEJIj0OnFCGEEEIIIYQQQgjpceiUIoQQQgghhBBCCCE9Dp1ShBBCCCGEEEIIIaTHoVOKEEIIIYQQQgghhPQ4dEoRQgghhBBCCCGEkB6HTilCCCGEEEIIIYQQ0uPQKUUIIYQQQgghhBBCehw6pQghpIdxu92UOSGEEEII7SRCoh46pQghIefHH3/EySefjN69eyMhIQFDhgzBpZdeinXr1mkr/ZdeegkxMTFYu3Ztu+fIe3KOnCuUl5fjrLPOwpw5c7p0rzvuuENdhxBCCCE9wxFHHIGMjAzU19e3e84uu+yCvffeO+BrRtN4Hkhdv/76a3WO7IX169cruXfVPjz33HMxcODAoMpLCAkfdEoRQkLKo48+in322QdOp1O9njlzJm644QZ8/vnnmDBhAv744w/LakCccHPnzsVRRx2l/l6wYAFee+01RkoRQgghEc7555+PiooKfPzxx22+v3DhQjWu/9///V+Pl80q7LrrrspOkr0wa9YsfPbZZ+EuFiGkh6FTihASMuSXr2uuuQZXX301PvjgA5xyyik44IADcPHFF+OHH36A3W7HRRddZFkNxMfHY88990Rubm64i0IIIYSQLnDcccchOzsbr7/+epvvv/zyy0hJSVG2DekeaWlpyk6SPSEkeqFTihASMu69914V+n777bfv8F5+fj7+/e9/qzBt39D45557DjvttJNy6Eik0SWXXIKysrJWIdoHH3wwLrvsMiQlJWGPPfZAU1OT2qZOnYpBgwapz44dOxYvvvhip2UsLS1VTrJevXqpz8m9X3jhhVbnSGj5XXfdpcL0xQB94IEHvO99//33GDdunPrsmDFjMH369Dan74mD7sADD1THZT9p0iRvfqmHH35YXUOuLYaZTAX46quv2i3z6tWrccIJJyhjWc6XSLQvv/yy07oSQgghJDDi4uJw5pln4pNPPlHT730Rm+ONN97Aqaeeqsbu7o7nwttvv63sC0lv0K9fP9x0001oaGhoZfccfvjheOWVVzB8+HBlb4wfPx4zZsxodZ2lS5fi+OOPV3ZXZmYmjjnmGCxevNj7fk1NjfqhsG/fvupeEq3+0UcfdSoHmUp3xhlnKJsjMTEREydOxIcffriDrfPII49g6NChSE9Px7Rp07zvy4+Sclzuufvuu2P27NltTt8TW+m8885Tx8WWk3oLIovbbrsNI0aMUHaf1O2QQw7B77//3m6Zf/vtN3WOlCUrKwuTJ0/G/PnzO60rISRMuAkhJAQ4nU53fHy8+4QTTgj4M7feeqtkAHdffvnl7s8++8z95JNPurOzs91jxoxx19TUqHPOOeccd1xcnPvggw92z5w50/3ee++p4xdddJHbbre7b7nlFvfnn3/uvuOOO9T9H3300XbvV11d7R41apQ7NzfX/dRTT6l7XnLJJaoMU6dO9Z4nf8s97777bvdHH33kXrhwofvFF19Ux5OTk9333HOP+9NPP3Wfeuqp7piYGHV/Yc2aNeocObeiosL9xBNPqL9lv2jRInXOP/7xD3WN//znP+5vvvnG/c4776j6pqamuquqqtQ5t99+u/qcwciRI90HHnige8aMGe4vvvjCffTRR7sTEhLU/QghhBBiDr///rsaf5999tlWxz/++GN1fO7cud5j3RnPX3/9dfX3ySef7P7kk0/Uffr06dPKdhK7JzMz0z127Fj3W2+9pe49btw4ZeOsX79enVNYWKjsJTnnzTffVOdMmDDBnZ+f7966dau7ubnZfdhhh7mTkpLc999/v7JTrr76arfNZnN/8MEH7da/uLjY3atXL/fgwYPdr7zyirruSSedpMr80ksvtbJ1pO5iS0m9161b562rlEvsHrFZxHYTe8qwgWbPnq3Okf3mzZuVDOVvse1WrlypzjnzzDNVPZ5//nn3nDlz3K+++qq7X79+7kGDBrWS0YABA9RrkXVOTo6SqdRTyrzXXnupcojdRwiJPOiUIoSEhI0bNyrD4tprrw3ofDGaxFC58MILWx0Xw06uI0aeYXjI36tXr/aes3z5cuUMuu2221p9VpxFYgwaDi1/HnvsMXWt7777rtXx888/Xxl7W7ZsUX/LOQcccECrcwyn1L333us9Jkbfzjvv7N5jjz12cEr5G18GZ5xxhvuRRx5pdW0xxuS8n3/+eQcjVuQkr8XoNCgvL3dfc8017j///LMDCRNCCCGkq+y+++7uSZMmtTomP0KNHj261bGujudiM/Tv338H++KHH35Q53z77bet7B7DSSPIj2hyTBxAwnXXXad+nNq0aZP3HHFUFRQUqB/N5AcsOf+FF15odS/5QW/IkCHt1l2uK7aZr80lHHTQQe68vDy3y+Xy2jpSTl+Muk6bNs17rK6uTjmYTjnllDbtIsO2Mn5ka2xsdB966KHKGefLQw89pM4z7DRfp9Qvv/yi3vvxxx+954vs/va3v7mLiorarSshJHxw+h4hJCTYbJ7uxeFwBLxCX2NjowoR92X//ffHgAED8M0333iPSei2hHYbSGi8+I7ksy6Xy7tJ6HZVVRV++eWXNu8p15Rry/Q3X2SFPAkXlzIZGEk4/Tn99NO9ryUE/S9/+YsKEZf7B4LkqrjqqqtUMlW5n4Tny5QAI9TeHwmflzB/Sawq5ZTE6VLWhx56SE0fJIQQQoi5Cc9l1dzi4mL1t4zX//vf/3DBBRcENZ4vX74cRUVFO9guMq0uNTW11bQ/yU0pKxcbGK+N60oqAZkqKKkRDPr376+m3snUP5niL/bYSSedtIOdtGrVKhQWFrZrJ+21116tbC5B7I/NmzdjyZIlHdpJxj0NZAqfLP4yb968DiTe+vOyMI7k7dqyZQu+++47PP/8897k823JddSoUWqKotxH0jO8++67yMnJwf3336+mRxJCIg86pQghIUEMAMmp0NGyvtXV1di2bZt6beSNktxO/sgxMfIM/BNibt26Ve1HjhypDBhjk3xTwoYNG9q8v9yzvfsJHd3ToE+fPq3+zsvLU4aeGE+BIKvOSJJPcbRJrqnHH38czc3N6j1PkNaOyMo0YiR/8cUXyjCUMkgeiUDvSQghhJDAkB+fJL+UkSdJckDJOH322WcHNZ4btos4TnxtF9nkBzVf20VyKfkiC8UIxvXlWmJ/tIe8L6sgiy3jex8jSXuo7CRxphllNZBybty4EYEiea8k36d8TvKQSu4p45ptyVVkJU5EyakluhKnmDjrxG6qra0N+L6EkJ6DTilCSGg6F5tNJSSXX+ckAqotnn76aeW8kmSVYsQJmzZt2uE8MZbkvPaQpJ6C/Kr4888/77AdeuihbX5O7tne/YSO7mlQWVnZ6m+5XmxsrLdMHSFGpxhNYsjJstLipPvpp59w2mmndfg5McweffRRZdTJktT/+Mc/VMJT2RNCCCHEPGQ8P/HEE72r8EkE1LHHHtvKRujOeG7YCbJ4Slu2y9///veAyyj2TFs/TM2aNQtr1qxR95IfCtu6j2yyOEwo7CSRi7/jSK4XiH0lSNlPPvlkldhdIsvE5vr222+VfdkRgwcPVovdiDNOorIuvPBC9bfYToSQyINOKUJIyLjuuuuUkdSWs6SkpEStUiNT0cTYkNVc5JdII9TdQIwPCW/fb7/92r3PAQccoPZifMjKLsYmv+DdcccdbYZ3G1MDJZLrhx9+aHVcDE9Z3UZC6DvDdwUa+cVSfpWTUHdZoaa9KY2GgSYGlqz+d+WVV6rVesSZZaxUY1zPH5kaKL/4ibEr0wXl10Opo4Sri0wJIYQQYi4SZSPOJvmhTabK+U/d6854LtHdMp6L48XXdpG0AmI3+U6N6wyxg6Rcvo4pmV4nkUWyeqC8L44ysT9877Vs2TL885//bPe6YidJBJiU0Rex1aTsw4YN69QpJSvrGYg9JpFPBx10UJvn+9tJYvNIioIbb7xR3UvsHpGlsWpgW3KV98TpZfxIKFHzjz32mJoSSTuJkMikdTwlIYSYiDiSbr31Vtx1113K8DnnnHPUr25//vknHnzwQRVKboTDiwFxww034O6771Yh5ccdd5xaZlgMs9GjR6vPtof8wifLNssvYfIZMbTEQJTPSp6lgoKCNj8nSw8/+eSTaurbnXfeqX5Zk4ijF154AbfffrtaRrgzxFASo0uWaZbIrxUrViijtaNfRSUXgryWJZLlV1WpsxhOYly9+eabKn+C0FaYuTihZIljWSpZyihRUzNnzlQy7cqvqoQQQggJDJmOJ3mVLr/8cpWXaPLkya3e7854LueJQ+iiiy5SzhiJtBJ7Qo5JJJL8aBcoV199tbJdDjvsMNxyyy3qh7V77rlH5VaS6Ydic4iDSWwrscvkh6xff/1VvZYpfBJF1RbXXnut+qFOIpOmTp2qbLVXX31V2TlyP8OJ1B5SjilTpqg6GXmdJHpe7tuRnfTee+8ph5o4+GSqntg3UkdxrD3zzDNeh11bcpUfBqVckuNTbDSpm9RBHGJyjBASgYQxyTohJEr48MMP1VLEshyvrGo3dOhQ9+WXX+5dytiX5557zr3TTju5HQ6HWob4iiuucG/bts37vu8KK77ICi2y0ossESwrxciKNrLccWVlZYdlKy0tdV966aVqNRi55/jx473LHBtIVynX9sVYIUaWG5YVeOSeskLPV1995T3Hf/U9WWlHVudJTExUyzYLsuKMfE6OyTLQV111lXvDhg3qb1kaua0lpOW6p512miqznCfy8i8zIYQQQszjzjvvVGOx/0q/Bt0ZzwVZnW6XXXZR9lFOTo77pJNOci9btqxDu8ffvhBkBd4jjjjCnZKS4s7KylLXWbVqlff9qqoqVaa+ffsqm0VW3bvjjjuU/dQR69atc0+ZMkVdU8q41157uT/66KMOy2LUVe4lK+cNHDhQfVZWMVywYEErmfmuvierJU+ePFmde/TRR6tj06dPd48ZM0Ydk+uI/EU+8jmxGduSkdzjqKOOUvJMTk5WqyL7lpkQElnEyH/hdowRQgghhBBCCCGEkOiCOaUIIYQQQgghhBBCSI9DpxQhhBBCCCGEEEII6XEi1in10ksvqRUW/LfOEuoRQgghhBBCCCGEkMgnYnNKyfKfsgKFQVNTk1rO9NBDD1XLehJCCCGEEEIIIYQQfbEjQpElRGUzeOihh9QSovfdd19Yy0UIIYQQQgghhBBCLBwp5UtZWRkKCgrwxBNP4Oyzzw53cQghhBBCCCGEEEKIVSOlfHnhhReQmZmJ008/vcPpfrIZNDc3Y9u2bcjOzla5qAghhBBCQo381ifpB/r06ROyPJi0eQghhBBiFZvHrkNFn3rqKVx++eVwOBztnnfvvfdi6tSpPVo2QgghhJC2KCoqQr9+/UIiHNo8hBBCCLGKzRPx0/fmz5+P3XbbDcuWLcPw4cMD/tWwoqJCTflbs2YNMjIyvMfFgydRVL4YK/uF6rjcU8TsL2ozj3dWFtlLYxGZxMbGWqJOwRyX+61btw79+/f3enV1r1MwepLPrV+/XrUPQz661ymY4y6XSz0vRvuwQp2CKaNv+/BH1zp157hRFll4w7d9WKFOwZRdrllcXKyMEf/IZF3r1NnxjspSXl6OQYMGqX16ejpCAW0e/duUYZdJP2K326PuOdGxTkJhYaHq6wzbUfc6WVFPvnUy+/tPJNTJ7LJHUp3kHLE3+/bt2yrqRuc6WVFPMSGweSI+UuqLL77AyJEjO3RItZUY3UAcUr5OqWhFGk1lZaVqLKGaTqCbPEQW0jYoj+3tIy0tjfLwkQfbx/bnhe2jdf/B9rGjPDi+tMbfQWcmtHn0h/2InjoTO4m2gT5wfNJPXxJYwmcs+myeiPdOfP311zjggAMi0ijUCZGDPOCUB+XB9sHnhf0H+1OOL6Edb8MFx3h9oF2mH9SZflBnekF96YdZdkfEO6XWrl3baZRUR9BA2y4HOqVatwvKg/LoqN9g+6A82D4CH2f5vESG3UGbRx/43OgHdaYf1JleUF/6ETVOqY0bN2Lo0KHd/rz/HMhoReRQUlJCeVAebB98Xth/sD/l+BLi8TZc0ObRB9pl+kGd6Qd1phfUl36YZXdEfE4pSZpFzKGuro6ipDzYPvi8sP9gf2oKkvDd6XQqg6S6uhqpqalRkZNOVgKWhLmEBAvtMv2gzvSDOtOLSNaXYfdEG3FxcSG37yLeKUUIIYSQyEFWZtm0aZP3RyNjRUKZbh8t08dkumKvXr2ipr6EEEJItOJv90QbNptNrbAnzqlQQacUIYQQQgLGMMzy8vKQlJSkjskvhxJBZHUnjRimtbW12Lx5s/q7d+/e4S4SIYQQQnrQ7rG6reOLRMNv2LBBpVQqKCgIWd0t75SKpkbTmRyys7MpD8qD7YPPC/sP9qfdRiKiDMNMxhTDUWOEdkfDmJuYmKj24pgSOfhP5WOicxIItMv0gzrTD+pMLyJRX23ZPdFGbm6ucky5XC71A6QvZumKTqkoQRqM5PsglAfbB58X9h/sT7uLkUvBiJAyxpdoy7HkGyFGpxTpDrTL9IM60w/qTC8iUV9t2T3RRlzLtD1x0IXKKWX5jKRciWa7HIqLiykPyqPd54Ttg/LoqB9l+6A82jNCJFKqsbFR7aOFjowwrr5HAoH9qn5QZ/pBnelFJOsrkqK3rGjzWN4pRbYTjasFdATlQXmwffB5Yf9hDtHkkCLELGiH6Ad1ph/UmV5QX9EJnVKEEEIIiRokqmv06NH4+uuvw10UQgghhJCQsGLFChx22GFqSuTw4cPx+uuvI1KxfE4pQgghhBChoaEBZ555JpYsWUKBEEIIIcSSNDc345hjjsHEiROxcOFCLF26FGeccQb69euHAw44AJGG5SOlonn+p78c8vPzKQ/Kg+2Dzwv7D/anpuOf+DISWbx4Mfbcc0+sXLkypPfh6nsk0HZCu0wvqDP9oM70gvoyj5KSEowdOxaPP/44Bg0ahCOOOAKTJk3CBx98YOJdmOjcNEHNXrYZ17y1AMs2VcHqcpBlrOmkozzYPvi8sP9gf2r2+GKz2SJ+fJkzZw4OPPBAfPfddztM57vkkkuQk5ODjIwMHH/88di8eXO370OnFAm0ndAu0wvqTD+oM72gvsyjd+/eeOedd7yrGf7000/45ptvkJ6ebqrdw9X3AqSjjPC1jS5cNe03vP9bMa5+awGsLod169ZF5GoG4YDyoDzYPvi8sP8wrz8tq6pFTYNTjas9uXUlwboYYA899BCSk5NbHX/ssccwe/ZsfPnll5g/fz7q6+tx7bXXBiWPcMExXh9oh+gHdaYf1Jle6KAvsTt62tap7YbN48uwYcPUNL7BgwfjyiuvNNXuMUtXUZ1T6rfCclTWu9TrJRsrsa60BgOyWxurVoKrI1EebB98Xth/sD81mzpnE3b552yEg8V3HoakuOBMmaKiIuWo6tWrl5pO9eyzz6K0tNS0MhLSHrTL9IM60w/qTC8iXV9i84y+baZWNs/06dNVJNTdd9+NP/74IyLtHsvnlOqI+evKWv9d2PpvQgghhFibiy66COvXr0ffvn1VvgUJdx8xYkS4i0UIIYQQEjQ777wzJk+ejKuvvhrnnXceLrzwwoize6I6UmppSes8Uks2VuGEXcJWHEIIIUQ7Eh2x+O2WAxEX5+jxfEpy72AZPXo01qxZo5J/fv7555g6dSqmTZuGefPmRXyeLEIIIYT0rN0hEUvhILELNo8kOp87d67KF2UwcuRIrF27Fnl5eRFn91jeKdWRYIu21ar9gSNyMXvZFjWFz8py6NOnDw1syoPtg88L+w/2p6aPL+nJCWqvoxNHwtYl8eeUKVPUJonQ99tvP2zduhW5ubldvh4TnZNA2wntMr2gzvSDOtMLHfQlZQs2bUBPsHbtWpx44okoLi5W0/SEX375BUlJSXjvvfeQmZlpit3DROcmOqUOGpmn9utKPX9bVQ52uz2iH/KehPKgPNg++Lyw/zCvP9XVISVs2rQJ11xzDb799lsUFhbi7bffVslAu+OQEuiUIoG2E9plekGd6Qd1phfUl3lMmDBBbTJVb/ny5Zg5cyZuvPFGXHXVVSq/lFl2D51SQWaEr25woazWqV7vOThb7TeU16GpObKTqwUjB2l0kbyaQU9CeVAebB98Xth/mJeUVJYXjvTkpO3x97//Xf2aeMopp6ipfH/++Sc+/PDDbl+Pq++RQNsJ7TK9oM70gzrTC+rLPGw2G95//33ExcVhjz32wKWXXqpW3rvzzjtNtXu4+l6QbKlqUPuUeDsG56bAbouBq9mNksp69MlIDPbyhBBCCIlQfB1oDocD//nPf9RGCCGEEGIFevfujXfffbfN9yLN7ona1fdKqz1OqeyUOMTaYryOqPVldWEuGSGEEEIIIYQQQoj1iVqn1NbqRrXPTo5T+36ZhlPKunmlCCGEEEIIIYQQQiIFWzTMp2yL0hojUipe7fu2REoVWzRSSuRQUFDQrjyiDcqD8mD74PPC/sMcJMml5CzQNdG52YRznOUYrw+0Q/SDOtMP6kwvqC/9MMvusLyHor3Eq1urPJFSOSmeSKm8NI9zakvLtD4rysHlcmmbiNZsKA/Kg+2Dzwv7D/P6U2Mj7dsdPQF1oA+0Q/SDOtMP6kwvqC/9MMvuiFqnlDdSKtnjjMptiZjaamGn1IYNG2iwUh5sH3xe2H+wPzUdp9Ozmi2hU4oEBu0y/aDO9IM60wvqSz/olAqSUiOnVEukVE5qfKtV+QghhBBCCCGEEEJI6LB8pFR7lNd5nFKZSXGtIqXolCKEEEIIIYQQQggJPVHrlKqqd6l9aoJd7XNbIqWMVfmsCJPQUh5sH3xe2H+wPyWERAa0y/SDOtMP6kwvqK/oxOORicKM8NudUo5W0/eqG1yoa2xCYlwsrCaHAQMGhLsYEQPlQXmwffB5Yf9hngEZH+8ZQwlX3yO0Q6wKbUf9oM70gvrSD66+F2Tyrap6Z6tIqdR4O+LtNssmOxc51NXVMdE55cH2weeF/Qf7U9PHl+bm5ogfX9asWYNjjjkG6enpGDRoEO69915VbrPh6nsk0HZCu0wvqDP9oM70gvoylxUrVuCwww5Damoqhg8fjtdff93kOzDRedCCqvSbvie/9Oa05JXabMFk5yKHkpKSiP/S0FNQHpQH2wefF/Yf0bP6XmNjo3JIZWRkYP78+Xj66afx8MMP47///a/p96JTigTaTmiX6QV1ph/UmV5QX+YhP7qJ3dOrVy8sXLgQjz76KK644gp88803Jt6FTqmgaHA1odHV3Gr6nm9eKSY7J4QQQqzDvHnzsHLlSjzzzDMYMmSI+uXw6quvDsmvhoQQQggh4aSkpARjx47F448/rqLDjzjiCEyaNAkffPBBRComKhOdG/mkhJT47Wm1clI8K/GV1lgvUooQQgiJVkaOHImPPvoIiYmJ3mMSIV1TU4OysjKceuqpalpfTk4Ozj33XNTW1oa1vIQQQggh3aV3795455131NQ94aefflJRUmLrfP311xg4cCAefPBBZGVlKdvntttuQzixfKLzjpxS4pCKtcV4j2ckeZxS5bWRPQ2huzgc26PCCOXB9sHnhf0H+1NTcLsR4xQnjlM8PT07vDiSArpnbm4uDj30UO/fDQ0NeOGFF3DssccqQ2zDhg3KYJNw9ylTpuCee+7B3XffHeLCk2iHdpl+UGf6QZ3pRcTrS1LhKJsnDDgCs3n8GTZsmIoW32233XDllVfijz/+UHaPRE3NmTMH69atU7bP0KFDcfbZZyMc2KMxI7x/knODzCTPQ1Be2wgryqFv377hLkbEQHlQHmwffF7Yf5hDjKsOcQ8ORFi4eQMQl9yljzQ1NSnjq7S0FNdffz0uvfRS9Uui5F2QXxCnTZsWESvR6HZv0jVoh+gHdaYf1JleaKEvcUjd00cbm0eYPn06Nm/erH5sE4eUkQv0+eefx4gRI9Q0v6uuugpPPPFEl51SXH0viISjlXWtk5z7R0qVWTBSSuRQVVXFROeUB9sHnxf2H+xPTR9fdEEioc4//3w1lU+MNAlvF0Ps22+/RX5+Po488kj1Wn4t7C5MdE4CbSe0y/SCOtMP6kwvqK/QsPPOO2Py5Mkql+Z5552n5CxT9sQhZbD77rtj2bJlYbN5LB8p1ZagtkdKtQ4PzPRO32u0pBzkV+Hk5GSVRyPaoTwoD7YPPi/sP0zCkYSG69YgLi6u58cXCWXvQoTUWWedhffffx/vvvsuDj74YHX8wAMPxNq1a/Hee+/hiy++UKHtn332mcrF0B3olCKBthPaZXpBnekHdaYXWuhL7A6JWArXvbuQ6Hzu3Lk4/vjjW+XXFHtn69atsNvtO/xo538sEOiUMiGnVHvT96wYKUUIIYSEBDEcJZw8Lq7nc0p1AYmIkvwJM2bM8DqkhPvuuw8TJkzAhRdeqLbXXnsNF198cVjLSgghhJAItnkinLVr1+LEE09EcXGxSk8g/PLLL0hKSkJ2drZyWkleqT59PFMRf/75Z4wePTps5Y3K5ANVDa42I6W2T9+zXqQUIYQQEq3MmzdP5Up44IEHMH78ePUroWyy8t6KFStUSPv8+fOxevVqfPjhh5g4cWK4i0wIIYQQ0i3kxzbjB7fly5dj5syZuPHGG9UPdJIHSiKc5Ac4mbInP9g99thj+Nvf/oZwYfnpe21R2+KUSo6LbXU8M9lIdG7NSCnfpbAJ5cH2weeF/Qf702hJsG1MxbviiivUZjBgwAD8/vvv6pjkW5DEn5MmTcIrr7wSxtKSaIF2mX5QZ/pBnekF9WWeXSbpCsS+2WOPPZCVlaXSE9xwww347rvv1DkHHHAA9t9/f3XuXXfdhWOOOQbhwh6NhnKts0ntE/2dUj45pZqb3bDZIncaQnfkIElcCeXB9sHnhf0H+1MzkbwPkb6Es0RIydYer776qmn34up7JNB2QrtML6gz/aDO9IL6MhdZzEVyaLaHrEAsWzBExep7ElZ2++23q3mQmZmZuOiii1BfX9/la/hT1+hxSiX5OaXSEz1GdbN7+xQ/qyByKC8v12qVpFBCeVAebB98Xth/mNefulwuji8+8ggXHOP1gXaIflBn+kGd6QX1pR9m2R0R7ZSSXzWffvppvPnmm/j666/xzTff4I477jDRKdU6UCzBEYtER6wlV+DjQ055sH3weWH/wf40VMjKdmT7eBsu6JTSB9pl+kGd6Qd1phfUl35Y3iklyxI++OCDeOihh1R+B0lMetttt6ms8cFiTN8TJ5Q/XIGPEEIIIYQQQgghVmPSpEkR9yNWxDqlFi1apFbGOfbYY73HpkyZglmzZgV97bpGV5vT9wSuwEcIIYQQQgghhBASxYnOV61ahdzcXHz77be45ZZbVD6kv/zlL7j33nsRF+dJSO5LQ0OD2gwqKyu9EVey+SbjqmloiZSy29R7kqRVNnmdkeTJK1VW3aA8iMZxX3zPD+S4seyiv0fSzOOdlUX2SUlJ3s9aoU7BHBdEHv5tQ+c6BaMno30IVqlTMMcNeRj3tkqdultGeZ2cnOx9bYU6dee4URb/9mGFOgVaRgP/94xEl/7nyz3bukYoj/fUPY224G9H+Ms4FHTF5on0NmXF5ySQ4779iFXq5H/canUSZCz0va/udbKinnzrZPb3n0iok9llj6Q6yTkpKSkRWSff98Nh21jd5olYp1R1dbXabr75ZjzyyCPq2P/93/+pvBXG376Is2rq1Kk7HC8uLvYaa9LIc3JyUF3nMeRqKrahsNCFjIwMtW3ZsgXxcKr31mzYjOrhGUhNTcXGjRvVMtEGslqKLFdZVFTUSnl9+vSB3W5HYWFhqzIUFBSoJLAbNmzwHhNFylLUkri9pKTEe1xWMOrbt6+qe2lpqfe43E/uW1FRoRx0Bkadtm3bpj5j4Funurq6VtexWp2ys7O7Vafa2lq1WalOwepJOt+qqipL1ak7epJjvu3DCnUyQ0/SPtatW2epOgWjJ2kfVqtTZ3qS+4oBIvc0HFGyl/fkOr65pXyP+xotsbGxqiz+x+WYvCfX9i27XEPK1NjYOtejseKf/3H54Uo+7ysXIT4+fofjcl05X8oh5fEvu9SnvTrJcZG/lNlXT5s3b0ao6YrNE+ltyorPSVfqJG3KanWyop6MOsn11q9fb6k6WVFP/nWSft5qdbKinqQ+clyuHSl1EltPxnv5IUj660DsA6vZPE6nM+Q2T4y7vZ9Bw4wkNz/99NMxe/ZsNe9ReP/993HGGWegpqZmh+UH2/rVsH///urBEKEZyOcOe2QOlm2qwsvnTcB+w3Jaefv+8cGfeOOnIlx50FBce+jwsHtlzYyUkgdfHmppTFaoUzDH5X4yPTQrK6vVFyud6xSMnoz2YRhcVqhTMMeloxZ5GO3DCnUKNlKqrKxM9R/+6Fqn7hw3yiIDs2/7sEKdAi2jGENr1qzBwIEDkZCQ4D0uz4wYWNHyq6EYy75y8JWvGN7yrIgRnpaWhlDQFZsn0ttUNEdKGf2IPDtWqJP/cavVSZBnTFYEN2xH3esUDZFSZn7/iYQ6mV32SKqTnCP2poxjvt/1w1knsflWrFih+mmZxWX8iN/Ttk24bB5BnE/inBsyZIh6jkJh80RspFSvXr3UfsSIEd5jI0eOVF5MGRCkUfh7A2Xzx/jC0NbqeykJ9lbvyWsjp1R1g0sJ2zjeFl05bigvVMcDKYs0JnE6dLXskVyn7h6Xh86QR1udno51au94oGU0ooKsVKfuHpd7ttU+dK9TMGWUHwNk0LFSnbpzXMrRVvvQvU5dKaP/e8YXbON4W+e2d41QHe+Jexptwb+PaE/2ZtIVm0eHNmXF5ySQ42bbZV09Tj11TQbSz7U3FlJPkdv2euo54/MUfF8uz5hETvkGDYRbT+KEGTx4sIoS8o2wiiZiYmLQr18/b7RWKGyeiHVK7bzzzqri8+fPx1FHHaWOLVmyRIXuGR1Ld6ltcUolOnasflqiR9iVddtD2gghhBBCCCGEEBJdyJQ3Y+qf7/S2aMHhcCjnXCiJWKeUhO2dd955uPrqq5W3VIRx00034dJLL233l8tAqXc2tbv6XlpCi1OqvvW8TEIIIYToi0y3++tf/4o5c+You+Kiiy7CjTfe2CORTYQQQgjRF/E/iD/CP1qIWNwpJTz22GPKYDz66KNVgq3TTjsNd955Z5eu4e/AUtO2Gj1RUIltOaUSPSKprLOWU0rkII6+YB16VoHyoDzYPvi8sP8wj1D/ghYskgvrmGOOwS677KIisFeuXImzzjpLjYvyY5eZhHOc5RivD7RD9IM60w/qTC+oL/0wy+6wR3qo3MMPP6w2swTV4GpGc0sOr8QOI6VclnzICeXB9sHnhf0H+1Ozx5e2kpxHEvPmzVOOqJ9//lmt1CPJOiUS+/XXX6dTioQF2mX6QZ3pB3WmF9RX9DqlLB+z7p9135i6JyQ5YjvIKeW0nBxkmUt/eUQrlAflwfbB54X9hzlIBLL/ksaRhiyU8tFHHymHlK8hJUmLX3rpJbXK73XXXafyVsoS0E8++WS37xXOcZZjvD7QDtEP6kw/qDO9oL70wyy7I7J/2gwBRpLzuFgb7LE7+uTSEuyWzSklS1gTyoPtg88L+w/2p2Yizqiaxho43I4enz6WaE8M6J6yYu+hhx7q/buhoQEvvPACjj32WPX33LlzVZ6pX375RUVVXXjhhRg7diz233//kJafRDe0y/SDOtMP6kwvqK/oJGqdUgmOtoPEjEip6gYXmpvdsNmYg4kQQghpjzpXHfZ7Z7+wCGjeGfOQ5Ejq0mdk5ZwpU6agtLQU119/PWbOnKlyYj3//PPIzMzEiBEj8OWXX+KJJ56gU4oQQgghJMRYfvqeP3UtTqmkuLb9caktkVIyC6GqwVp5pQghhJBoDzM///zz1VS+6dOno3fv3ur4mDFjlEPKYPfdd8eyZcvCWFJCCCGEkOjA8pFS/mH9dS05pZLaSHIuxNtjEW+3qYToklcqvSVyygpyyM7O5so8lAfbB58X9h/sT02fQjf3tLlqfAnH9L2uREjJinvvv/8+3n33XRx88MHe9/wTtYvzqrvJ27n6Hgm0ndAu0wvqTD+oM72gvvQjKlbfC4Wgahtd7a685zuFb0tVg6XySokcJIEroTzYPvi8sP9gf2omNpsNKfEpET+8XHXVVfjggw8wY8aMVg4pYenSpaivr0dCQoL6W1bpGz16dLfuQ6cUCbSd0C7TC+pMP6gzvaC+9IOr7wW5+l5iGyvv7ZDsvM5lKTkUFxdzZR7Kg+2Dzwv7D/anpic6b2xsjOjV9yR5ueSIeuCBBzB+/Hhs3bpVbWVlZer98vJyXHnllVi5cqVKgP7OO++o1fi6A1ffI4G2E9plekGd6Qd1phfUl36YZfNEXU6peqdHcAkdOaVapuxZKVJKkCW7CeXB9sHnhf0H+1OziWSHlCBOJuGKK65QK/EZ2y677KKO9+/fH+np6dhjjz1w99134+WXX1bOK0JCCe0y/aDO9IM60wvqKzqJOqdUg8sTKSV5o9ojLaHFKVVHJw4hhBCiOxIhJY4z/23t2rXeKYgPPvggtm3bhtWrV+PUU08Nd5EJIYQQQqKCKHRKeSKl4h22ACKlrDN9jxBCCCGEEEIIISSSsEVb8q2Glul7sspeZzmlqiw0fU/kkJ+fz9X3KA+2Dz4v7D/Yn5qOw2GNlWrNgInOSaDthHaZXlBn+kGd6QX1pR9MdN5NQQU0fc+IlLJQonORQ2JiIp1SlAfbB58X9h/sT00fX2T6WzidMcFw7rnneqfxmQGdUiTQdkK7TC+oM/2gzvSC+tIPOqW6mRHeO30vkJxSFoqUEjmsW7eOq+9RHmwffF7Yf7A/NRXJzdTQ0BDxyc57Cq6+RwJtJ7TL9II60w/qTC+oL/3g6ntB55TqaPU9uyUTnfMLA+XB9sHnhf0H+1OOJxxPSWRAu0w/qDP9oM70gvqKTiyfU8qfBmdTVEZKEUIIIWbljqqtrY1qYRr1Zy4tQgghhJDg8IQERREBTd+zYE4pQgghJFhiY2ORkZGBzZs3q7+TkpLU3ul0qhBuXfNKdeUXXHFISf1FDiIPQgghhBDSfezRl+g88NX3rBQpJXLo06eP5b8wBArlQXmwffB5Yf/RPXr16qX2hmPKcNZE0/giDilDDv4w0TkJBNoh+kGd6Qd1phfUl36YZfNEoVOqZfqeI5BIKWs5pex2e1R9aegIyoPyYPvg88L+o/v9Z+/evZGXl6cipASJkpIV+KIBmbLXUYQUnVIkEGiH6Ad1ph/UmV5QX/pBp1R3V99zBr76XlWDC83NbthsMZaQQ2FhIQoKCqLmi0NHUB6UB9sHnxf2H8EhjhnZ2J/u2J9G471J1+Bzox/UmX5QZ3pBfekHV9/rJoFM30ttmb4nq1vXNDKvFCGEEEIIIYQQQojZRF3IjHf6XgeRUvKeI9YTHVVVT6cUIYQQQgghhBBCiNlEb6RUBzmlZG5kassUvuoGOqUIIYQQQgghhBBCzMbyTin//Enbc0p1vIxzSrxnCl+VRVbgEzkwnxTlwfbB54X9B/tTji+hH2/DBXNG6gPtMv2gzvSDOtML6ks/zLI7LO+UkmWquzp9zzevlFWm74kcXC7XDvKIVigPyoPtg88L+w/2p6EaX8IFx3h9oB2iH9SZflBnekF96YdZdkcUOqW6GillHafUhg0baLBSHmwffF7Yf7A/5fgS4vE2XNAppQ+0y/SDOtMP6kwvqC/9oFMqhDmlBOaUIoQQQgghhBBCCAkdlo+U8qfB2dXpe9bIKUUIIYQQQgghhBASSUSfUyrA6XuGU6raItP3jFUFCeXB9sHnhf0H+1OOL4SEH9pl+kGd6Qd1phfUV3Ti8bxESUb4pmY3XM3ugCKljJxSlRZxSokcBgwYEO5iRAyUB+XB9sHnhf0H+9NQjS/hgqvv6QPtEP2gzvSDOtML6ks/uPpeN5JvNbZESUVjTimRQ11dHZOgUh5sH3xe2H+wP+X4EuLxNlww0bk+0C7TD+pMP6gzvaC+9IOJzrshqAaXJ5+UEBfbSaSUxXJKiRxKSkposFIebB98Xth/sD/l+BLi8TZc0CmlD7TL9IM60w/qTC+oL/2gUyqIfFJ2WwzsnTilUlum71klUooQQgghhBBCCCEkkoiqROcNTiPJeefVtmKic0IIIYQQQgghhJBIIbqcUi3T9+IdHa+855vovMpCTimHw5Mni1AebB98Xth/sD/l+EJIeKFdph/UmX5QZ3pBfUUnUbX6njF9L7BIKY8Dp8oi0/dEDn379g13MSIGyoPyYPvg88L+g/1pqMaXcMHV9/SBdoh+UGf6QZ3pBfWlH1x9L4hE512ZvmelROdVVVVMgkp5sH3weWH/wf6U40uIx9twwUTn+kC7TD+oM/2gzvSC+tIPJjrvhqC255SKDdgpVe9shrPJ8znd5VBaWkqDlfJg++Dzwv6D/SnHlxCPt+GCTil9oF2mH9SZflBnekF96QedUt3AO33P0XmkVHJLTimByc4JIYQQQgghhBBCzCUqE53HxXZebUesDYktCdGrLZJXihBCCCGEEEIIISRSiGin1EcffYSYmJhW20knndTt6zU2eULq4wLIKSWktEzhq7RIXqnExMRwFyGioDwoD7YPPi/sP9ifEhIuaIfoB3WmH9SZXlBf0UlEr763ePFiHHXUUXjppZe8x+Lj47udEd7ZMn1PoqACQfJKbalqsMT0PZFDfn5+uIsRMVAelAfbB58X9h/sT0M1voQLrr6nD7RD9IM60w/qTC+oL/2IitX3lixZgtGjRyMnJ8e7paamdjv5VmNTF51SLXmlqizglBI5lJeXMwkq5cH2weeF/Qf7U44vIR5vwwUTnesD7TL9oM70gzrTC+pLP6Ii0blESg0bNsw0QRmr6MXZYwL6bGqCwzI5pfiQUx5sH3xe2H+wP+X40jPjbbigU0ofaJfpB3WmH9SZXlBf+mGW3RHR0/eWLl2KH374Af/5z3/Q0NCA0047DbfeeiscDo+zyBd5XzaDyspKtW9ublabOsfZ5I2UMo4JRr4q32NCSrwn0XlFXWNA57d3XMLaRGH+SjPzeGdlMeRgfDbQskdynYI57isTq9QpGD35tg2r1CmY40bbMO5tlTp1t4zd6TsivU7dOW6Uxb99WKFOwZTduKYhGyvUqbPjHZXF/71QEIjNE0hZrSh/Xerk249YpU7+x61Wp7b6Od3rZEU9+dbJ7O8/kVAns8seSXWinhC1Nk/EOqWKi4tRVVWlBCE5pTZu3IjLLrtMGV6PPPLIDuffe++9mDp16g7H169f7zXWKqpq1L7Z5URhYaH3nIyMDLVt2bIFdXV13uMtPils3FKGwsLt0VWSm0mSsBUVFbVSXJ8+fWC321tdWygoKIDL5cKGDRu8x0SRAwYMQH19PUpKSrzHxeHWt29fVFdXo7S01Htc7if3raioUNPwDFJSUtS0xm3btqnPtFcnKWdZWRmys7ORnp6u5Ol0OrWuk4HUSaZ1dqVO0q5EHsZDZYU6BaMnuZaUWbBKnYLRk7QN3/ZhhToFoyepg/HaKnUKRk8yPhntQ/oSK9QpGD0ZuR6lTsZ4q3udgtGT7/VDRSA2T7TKX5c6GXaZlC83N9cSdbKinnzrlJWVhZqaGlUew3bUvU5W1JNvnYznTOoj+rNCnayoJ4O0tDS1lzr5/vCic52sqKeMENg8Me62fgaIEMQp5ZtD6r333sOUKVOUUGJjWzxGHfxq2L9/fyVwEZrwny9X4JEvV+L0Pfrjn8eP7dTzeNeMJXjxh7W45IDBuOGwEdp6MAXZS4OSB0BkF+2/CMj9tm7dqgYoI0Gb7nUKRk9G+5COx5CP7nUK5rh07iIPo31YoU7BRkoZTm1/dK1Td44bZWlqamrVPqxQp2DKLtcUIyYzM9P7RU33OnV2vKOyiCzkWRHjzjCwzSYQmyeQslpR/rrUyRh3pR+RLxpWqJP/cavVSZBnTPo6w3bUvU7RECll5vefSKiT2WWPpDr5OhGNZ0z3OllRTzEhsHkiNlJK8E9qPnLkSOXxk8YqX559kV9q21qZTwZ6o1G3LL6HeHtsq4Zu4H9MVt8TahqaAjq/o+OG8kJ1vLOyyD4vL69bZY/UOgVbdl95WKFO7R0PpIz+7cMKdQrmuPQbbbUPnesUTBnltfyS3xG61am7x6UcbbUP3esUTNnlmv5jck+VPRLbnrSPUBOIzeNbpmiSvy51CoVd1tXj1FPXZdDeWEg9RWbb68nnjM+TOX15qO0J6gkRafNEbKLz2bNnq2lmvqFiv/32m3cVvkDx9extT3Ru61Ki86r67SF1uiJykMggs+Z96g7lQXmwffB5Yf/B/jRU40u44BivD7RD9IM60w/qTC+oL/0wy+6IWKfUHnvsoZxSF110EVatWoVZs2bhxhtvxE033dTtaza2OKUcsYGtvpfSEillhdX3BF8HH6E82D74vLD/YH/K8YWQ8EG7TD+oM/2gzvSC+opOItYplZycjM8++0zN3d55551x1llnKQfVNddc0+1rNrbM35PV9wLBmL5XWW8NpxQhhBBCCCGEEEJIpBDROaVGjx6NmTNnmnY9Y/peoE6plPiWSCk6pQghhBBCCCGEEEKiI1LKLHyTdTmbPNnk47uaU6rBaQk5yEoGbSUvi0YoD8qD7YPPC/sP9qehGl/CBcd4faAdoh/UmX5QZ3pBfemHWXZHREdKmS2o7TmlujZ9zwqRUsZDTigPtg8+L+w/2J9yfAnteBsu6JTSB9pl+kGd6Qd1phfUl36YZXdYPlLKNyN8d3NKSaJzt9sTZaWzHEpKSrgyD+XB9sHnhf0H+1OOLyEeb8MFV9/TB9pl+kGd6Qd1phfUl35YfvW9UODs6up7LTmlZNpfQ4tDS2fq6urCXYSIgvKgPNg++Lyw/2B/Ski4oB2iH9SZflBnekF9RSdR6ZSKCzCnVHKcHUZEWpUFpvARQgghhBBCCCGERArR5ZRyeabgxQU4fc9mi0FKnCdaqqpe/2TnhBBCCCGEEEIIIZGCLZqSbzV0MdG5kOKTV0p3OWRnZzMJKuXB9sHnhf0H+1OOLyEeb8MFE53rA+0y/aDO9IM60wvqSz+Y6LwbgnIaic4DnL7nm+xc9+l7IofU1FQarJQH2wefF/Yf7E85voR4vA0XdErpA+0y/aDO9IM60wvqSz/olOpGRnhvTqmuRErFW8MpJXIoLi7myjyUB9sHnxf2H+xPOb6EeLwNF1x9Tx9ol+kHdaYf1JleUF/6wdX3gkp0HvivmKkJDsvklHI69a+DmVAelAfbB58X9h/sTwkJF7RD9IM60w/qTC+or+jE8jmlfGl0RW9OKUIIIYQQQgghhJBIIrqcUk3uLjul0iySU4oQQgghhBBCCCEkkoiuROfe6Xtdzymle6SUyCE/P59JUCkPtg8+L+w/2J9yfAnxeBsumOhcH2iX6Qd1ph/UmV5QX/phlt3h8bhEm1OqC5FSVskpJXJITEwMdzEiBsqD8mD74PPC/oP9aajGl3BBp5Q+0A7RD+pMP6gzvaC+9IOr73UjI3y3ckpZaPW9devWcWUeyoPtg88L+w/2pxxfQjzehguuvqcPtMv0gzrTD+pML6gv/eDqe10WmBuuZiOnVFdW37OGU0pwuz31J5QH2wefF/Yf7E85vhASXmiX6Qd1ph/UmV5QX9GJ5XNKGTh9frnsSk4pwymle04pQgghhBBCCCGEkEgiepxSLSvvdX36njVyShFCCCGEEEIIIYREErZoSb5l5JPqqlPKKtP3RA59+vRhElTKg+2Dzwv7D/anHF9CPN6GCyY61wfaZfpBnekHdaYX1Jd+MNF5FwVlrLwXa4tRW5en71nAKWW322mwUh5sH3xe2H+wP+X4EuLxNlzQKaUPtMv0gzrTD+pML6gv/aBTqosZ4Y1IqbguREkJqQme6XvVjS6VLF1nORQWFnJlHsqD7YPPC/sP9qccX0I83oYLrr6nD7TL9IM60w/qTC+oL/3g6ntdxIiU6srKe76RUrJwnTimCCGEEEIIIYQQQkjwWD6nlEFji1OqKyvvCfF2m9eRpXteKUIIIYQQQgghhJBIIWqcUk6Xu8tJzo15ksYUPq7ARwghhBBCCCGEEGIOlndK2Wy2oCKlrLICn8ihoKDAK49oh/KgPNg++Lyw/2B/GqrxJVxwjNcH2iH6QZ3pB3WmF9SXfphld1jeQ+GWZFCtckoF45RyQmc5uFwurzyiHcqD8mD74PPC/oP9aajGl3DBMV4faIfoB3WmH9SZXlBf+mGW3RE1Tilj9b1uOaXiHdpHSokcNmzYQIOV8mD74PPC/oP9KceXEI+34YJOKX2gXaYf1Jl+UGd6QX3pB51SXcSIlIrr4up7Vpm+RwghhBBCCCGEEBJJWD5SagenVLdySukfKUUIIYQQQgghhBASSUSNU6qxqXur71klp5SxkiChPNg++Lyw/2B/yvGFkPBDu0w/qDP9oM70gvqKTjzelmhYfS+InFJpFpi+J3IYMGBAuIsRMVAelAfbB58X9h/sT0M1voQLrr6nD7RD9IM60w/qTC+oL/3g6nvdXn2v69FCKRaIlBI51NXVMQkq5cH2weeF/Qf7U44vIR5vwwUTnesD7TL9oM70gzrTC+pLP5jovIuCcnmdUtGZU0rkUFJSQoOV8mD74PPC/oP9KceXEI+34YJOKX2gXaYf1Jl+UGd6QX3pB51SXcTZklPKHlROKX2dUoQQQgghhBBCCCGRRNQkOnc1t0RK2WK6HSlVqfH0PUIIIYQQQgghhJBIIgojpWK6HSlV3aB3pJTD4XGuEcqD7YPPC/sP9qccXwgJL7TL9IM60w/qTC+or+gkalbfcwUxfc8qq+/17ds33MWIGCgPyoPtg88L+w/2p6EaX8IFV9/TB9oh+kGd6Qd1phfUl35w9b2uJjo3YfqeRErpmkRUyl1VVaVt+c2G8qA82D74vLD/YH8aqvElXHCM1wfaIfpBnekHdaYX1Jd+MNF5FwVlRqLzpmY3ahuboKscSktLabBSHmwffF7Yf7A/5fgS4vE2XNAppQ+0y/SDOtMP6kwvqC/9iCqn1MUXX4xJkyYFdQ1XU3O3c0olOmIR2xJhpfMUPkIIIYQQQgghhJBIIeKdUt999x2effbZoK/javZ48RzdyPUQExPjjZaq4gp8hBBCCCGEEEIIIdZ2SjU2NqooqX333TfoazmDiJQSUuI9TqlKjSOlEhMTw12EiILyoDzYPvi8sP9gf0pIuKAdoh/UmX5QZ3pBfUUnEe2Uuvfee7HLLrvgoIMOMm31PUc3ckr5JjvXNVJK5JCfn8+VeSgPtg8+L+w/2J9yfAnxeBsuuPqePtAu0w/qTD+oM72gvvTDLLvDE/4TgSxduhRPP/00fv/9dzz55JOdnt/Q0KA2g8rKSrVvampCc3Pz9kgpW4z62396nmwdHU+Nj1XHquqcKqFXZ+f7K0s+458IzMzjnZVFPlNRUYGMjIyAztehTsEcF8rKypCenu79W/c6BaMno31kZmZ6/9a9TsEcl35D5GG0DyvUKZgyyvWkT5X+w//autapO8eNsshx3/ZhhToFU3ZjtZy0tLRW5+pcp86Od1QW6T9CTWc2T6BltaL8damTMe5KPxIbG2uJOvkft1qd5J7l5eWqrzNsR93rZEU9+dbJ7O8/kVAns8seSXUyxrPU1FTvM6Z7nayop5gQ2DwR6ZQSYci0vTvuuAN5eXkBR1VNnTp1h+NFRUWqM6qoqvauvrdt2zZUV3v+FqSjkm3Lli2oq6vzHs/OzlYPxcaNG2F3e6btrdtQgvoRWSq0UK7tq7g+ffrAbrejsLCwVRkKCgrgcrmwYcMG7zFR5IABA1BfX4+SkhLvcYfDgb59+6ryyWp5BnI/iXSSusiAaJCSkoKcnJxO6yTllHOGDh2qDCCpk9O5PepLrq1bndrSU6B1kgdszZo1yMrK8nZ6utcpGD35Dto1NTWWqFOwepL7Gu3DKnXqrp6kDvJa+g6r1CkYPRUXF6t7S/uQvsQKdQpGT/Hx8cpBIsaJ4RzRvU7B6Mn3+qGiM5snmuWvS50Mu0yunZuba4k6WVFPvnWSPl/6fzlu2I6618mKevKtk/GcDRo0SOnPCnWyop4MxOErdoTUx/eHF53rZEU9ZYTA5olx+7vDIgBJbP7iiy/i+++/V0IV59TXX3+ttq78ati/f38lcBHa5W/8hk//3IQ7jxuDMycWdNkjee3bv+ODBRtw0xEjcNH+Q7TyYAqyl0YsDdSMX+QioU7BHJf7rV27Vj3IRtih7nUKRk/yOen8pH0Y8tG9TsEcl85dnhejfVihTsGU0bd9+KNrnbpz3CiL/Crk2z6sUKdgyi7XXL9+vRpzfX/Z1LlOnR3vqCxi0ImxKcZdW9FjZtCZzRNoWa0of13qZNhl0o/IFw0r1Mn/uNXqJKxbt049a4btqHudrKgn3zqZ/f0nEupkdtkjqU5yjtib/fr18z5jutfJinqKCYHNE5GRUm+88QZ+++0371Qi8fLJl0QxtBYuXKgGcH/kl1rZ/DG+MBir79lb/m6Ljo6nJXpySlU3NHmN7q5cx1BeqI4HUhbjy3VXyx7JderucXngjLbRVqenY53aOx5oGY3XVqpTd4/7tg3/ZyjYsrd3PNLbnq79ntnHpRxttQ/d62SWntq6vu516qqe2nvPTDqzefyPRZP8daqTr76sUqeeKns46iRfwHzHALPL3t5x6im4tmf29x/qKXR9hOH8aG8spZ5gWZsnIp1S06ZNU44og0ceeQQ//vgj3nzzTRW61h1cQa6+l5rgEVWVxqvvSQgeoTzYPvi8sP9gf8rxhZDwQ7tMP6gz/aDO9IL6ik4i0inVq1evVn9LhFRCQgIGDhzY5WsZ3jsjUsrRbaeUJ1KqUuPV92ROKKE82D74vLD/YH/K8SW042003pt0Ddpl+kGd6Qd1phfUl36YZXdY3noxwgC3r75ni8pIKZHD1q1b21zlIBqhPCgPtg8+L+w/2J+GanwJFxzj9YF2iH5QZ/pBnekF9aUfZtkdWjiljETnweBqMidSqkrTSCnBN2s+oTzYPvi8sP9gf8rxhZDwQbtMP6gz/aDO9IL6ik60cEqZgdMn0Xl3SI33REpVN+gZKUUIIYQQQgghhBASSUSNU4qJzgkhhBBCCCGEEEIiB8s7pYxlDbdP37MFOX3Ppa0cJGF8W8s8RiOUB+XB9sHnhf0H+9NQjS/hgmO8PtAO0Q/qTD+oM72gvvTDLLsjIlffC4WgnC1JuOy2mCATnTvhdru1M/yMh5xQHmwffF7Yf7A/5fgS2vE2XOhmm0QztMv0gzrTD+pML6gv/TDL7rBFS0Z4I1LK3u1IKY9TytnkRoOrWUs5lJSUcGUeyoPtg88L+w/2pxxfQjzehguuvqcPtMv0gzrTD+pML6gv/Yiq1ffMzCnV3dX3kuPsMByBlZquwFdXVxfuIkQUlAflwfbB54X9B/tTQsIF7RD9oM70gzrTC+orOokap1Swq+/ZbDFIaVmBT9e8UoQQQgghhBBCCCGRgq073svi4uIdji9atAhWjpQS0jRPdk4IIYQQQgghhBCipVPqnXfewbBhw3DUUUdh3LhxmDdvnve9s846CzqsvtfdnFL+yc51Q+SQnZ3NJKiUB9sHnxf2H+xPOb6EeLwNF0x0rg+0y/SDOtMP6kwvqC/9CEui87vvvhu//vorFixYgBdffBEXXHAB3njjDfWerEhn5dX3fJ1S1RpGSokcUlNTabBSHmwffF7Yf7A/5fgS4vE2XNAppQ+0y/SDOtMP6kwvqC/9CItTyul0Ij8/X73ebbfdMGfOHPz3v//FnXfeGbGGkP/qe44gIqV0ziklcpBpl1yZh/Jg++Dzwv6D/SnHl9COt+GCY7w+0C7TD+pMP6gzvaC+9CMsq+/l5eVh4cKF3r+zsrLwxRdfYMmSJa2ORxoSxeUyEp0HkVMqtSWnlK6r74lTkVAebB98Xth/sD/l+EJI+KFdph/UmX5QZ3pBfUUnXXJKvfrqq8ox5UtcXBymTZuGb775BpGK4ZASHN1cfa91Tin9IqUIIYQQQgghhBBCIgmPlyVA+vXr1+57++yzDyIVY+qeWZFSdEoRQgghhBBCCCGE9KBTymDQoEHdyiF19dVX469//St6EimnkeQ8eKeU3qvvST6wSM391dNQHpQH2wefF/Yf7E9DNb6EC47x+kA7RD+oM/2gzvSC+tIPs+yObjmlXnrppW7dbODAgQiHoHwjpYKZvpem8fQ9kUNiYmK4ixExUB6UB9sHnxf2H+xPQzW+hAs6pfSBdoh+UGf6QZ3pBfWlH2F1Sh1wwAHQKSO8C55IKVsMYJP/gp2+16BfpJTIoaioCP3794ctCMecVaA8KA+2Dz4v7D/Yn4ZqfAkXXH1PH2iH6Ad1ph/UmV5QX/oRltX3dMXpXXkvuOqmJ7asvlenX6SUsQohoTzYPvi8sP9gf8rxhZDwQ7tMP6gz/aDO9IL6ik66FSnV1tKNmzZtQm1tLXJzc5GVlYVIwtXk8eA5goiSEtISPeKqqNMvUooQQgghhBBCCCEkkuh26FBVVRWeeuopNZUvLS1N5YsaNWqUckoNGDAAF154IX7++WdEAs4mcyOl6JQihBBCCCGEEEIICY5ueWkeeugh5YR68cUXccghh+CDDz7AggULsHz5csydOxe33347XC4XJk+ejMMPPxwrVqxAuFCJzlvmOjqCWHlPSGtxSsnqe80tUwJ1QeTQp08fJkGlPNg++Lyw/2B/yvElxONtuGCic32gXaYf1Jl+UGd6QX3pR1gTnUsE1Jw5czBmzJg2399jjz1w/vnn4+mnn1aOq2+//RbDhg1DOPBdfc8eZILvtJZE5+KPqm50ef/WAZGD3W6nwUp5sH3weWH/wf6U40uIx9twQaeUPtAu0w/qTD+oM72gvvTDLLujW16aadOmKYdUU1OTipKSqXxtER8fj0suuUQ5qMKZEb6xJaeUPchIqQRHLOLtHpFV1OqVV0rkUFhYyJV5KA+2Dz4v7D/Yn3J8CfF4Gy64+p4+0C7TD+pMP6gzvaC+9CMiVt+LjY3F6aefji1btiCSMSKlHEHmlPKdwldZr5dTihBCCCGEEEIIISSSCNpLM2HCBKxZswaRjLH6nj3I1fcEJjsnhBBCCCGEEEIIiQCn1JVXXombb74ZRUVFiFSczeasvufrlKqsY6QUIYQQQgghhBBCSI8mOvfl1FNPVXvJMXXsscdi0qRJ2GWXXbDTTjshLi4O4cZms3kjpYJdfU9IS/CIrLLOBZ0QORQUFKg9oTzYPvi8sP9gf8rxJXTjbbjgGK8PtMv0gzrTD+pML6gv/TDL7gj6KjJ1T5KdX3/99airq8O9996rVt9LTU3FuHHjEG7cbjec3tX3onf6nsjB5XKpPaE82D74vLD/YH/K8SV042244BivD7TL9IM60w/qTC+oL/0wy+4I2ik1YMAAFSF122234d1338WqVatQXl6OWbNm4eKLL0ZENO6WrPBmTt/T0Sm1YcMGGqyUB9sHnxf2H+xPOb6EeLwNF3RK6QPtMv2gzvSDOtML6ks/wuqUKiws7PB9iZLab7/9cPnll6u/i4uLERmr75kwfY+r7xFCCCGEEEIIIYSExyklK+5JFNTPP//c7jkVFRV49tlnMXbsWBVBFU6c3tX3ojdSihBCCCGEEEIIIUT7ROeLFy/GP//5Txx66KFISEjAbrvthj59+qjXZWVl6v1FixZh1113xf33348jjzwS4cTVbH6klI5OqZiY4OtvJSgPyoPtg88L+w/2p4SEC9oh+kGd6Qd1phfUV3TSrdCh7OxsPPTQQ9i4cSMef/xxDBs2DFu3bsWKFSvU+1OmTMGvv/6KuXPnht0h5bv6nhmRUmkJHqdUpWZOKZGD5P/iyjyUB9sHnxf2H+xPOb6EdrwNFxzj9YF2mX5QZ/pBnekF9aUfZtkd3YqUMkhMTMRJJ52ktkil1ep7JkRK6Tp9T+RQX1+votnogaY82D74vLD/YH/K8SV04224YKJzfaBdph/UmX5QZ3pBfelHxKy+58s111yDF198UUVJNTQ0IBLwXX3PYerqey7ohMihpKSEBivlwfbB54X9B/tTji8hHm/DBZ1S+kC7TD+oM/2gzvSC+tIPs+yOoCKl/DnwwAOxcOFCfPrppyqnlETkjBkzBuPGjVPbMcccg3DgjZSymZFTyiOyynq9IqUIIYQQQgghhBBCIglTnVLHHnus2gxkutiff/6pHFVfffVV2JxSLu/0PfMipRpdzah3NiHBERv0NQkhhBBCCCGEEEKijaCdUtu2bUNWVlab70n+ot13311t4WT79L3gI6VS4u2QgCtZ0E/ySunklHI4PA41QnmwffB5Yf/B/pTjCyHhhXaZflBn+kGd6QX1FZ0E7ZTKyclB3759MX78+Fbb8OHDIyKhtmSE3z59L/hIKalTWqID5bVOtQJffloCdEDkIHoilAfbB58X9h/sTzm+hHa8DRdcfU8faJfpB3WmH9SZXlBf+mGW3RH0Vf744w/cd999GD16NH7++Wdcfvnl6nVKSgomTpwY1LVXrFiBww47DKmpqcrJ9frrr3cv0XmTeZFSuq7AJ3KoqqpiElTKg+2Dzwv7D/anHF9CPN6GCyY61wfaZfpBnekHdaYX1Jd+RMzqe5LIfMqUKbj//vvx+eefY/PmzZgxYwZ69+6Ngw8+uNvXbW5uVjmoevXqpXJSPfroo7jiiivwzTffdGP1PSOnVHQ7pUpLS2mwUh5sH3xe2H+wP+X4EuLxNlzQKaUPtMv0gzrTD+pML6gv/YgYp1Rb09uOOOIIvPbaa9i0aVO3r1NSUoKxY8fi8ccfx6BBg9Q1J02ahA8++KDL13K2REqZMX1PSEvwOKW4Ah8hhBBCCCGEEEJI9whZ4oM999wTs2fP7vbnJdLqnXfeUVP3hJ9++klFSaWnp3d79T3Tp+/V6hMpRQghhBBCCCGEEGKpROeSO2qnnXZSyc3HjRun9iNHjlT5pSSHkRkMGzYMK1euxG677YYrr7yyzXMaGhrUZlBZWemdBmhESsXKsnktx/yju2QL9Hhaokds5bWNrd5r73xJACahbf7hbWYe76zsso+Pj/d+NlgZREKdgjkuiDx839O9TsHoyWgfglXqFMxxQx7Gva1Sp+6WUV7LaqrGayvUqTvHjbL4tw8r1CmYsss1ExMTvbKxQp06O95RWfzfCwUd2Tz+41q0yV+XOvn2I1apk/9xq9VJkLEwENtflzpZUU++dTL7+08k1MnsskdSneQcsSesVCcr6ikmBDZP0E4piWZasGCB2iTv06pVq1RlpKB33XWXKYWcPn26ylV19913q8TqMo3Pn3vvvRdTp07d4XhxcTEqqqrV68b6OrXftm0bqqs9x4SMjAy1bdmyBXV1nnOE7OxsFam1ceNGOJ3bo6KS7B6nRvGWMhQWFnqP9+nTB3a7vdUxoaCgAC6XCxs2bPAeE/kMGDAA9fX1aqqi7zKYskqelE9yQBnIA5qfn4+KigqUl5e3cgrKCoiB1qm2trbNOsm15R5FRUWtGqMOdWpPT53VSQz69evXW6pOwepJOh5xJlupTt3RkxzzbR9WqJMZepL2sW7dOkvVKRg9SfuwWp2C0ZPUx2p16o6exF4JNR3ZPIaDKlrlr1ud5LXV6mRFPRl1kvv62o5WqJMV9eRfJ7FtrVYnK+pJ6iPny7WtVCcr6inDZJsnxt3WzwBBIE6PNWvWKEFLknIzee+993Dddddh9erVStid/WrYv39/JcSbP16NT//chDuOGY1z9xkUtEfy6W9W4/6Zy3Dirn3xwEnjIt6DKchnpKFJAzLDixsJdQrmuFBWVqamgxp/616nYPRktI/MzEzv37rXKZjjTU1NSh5G+7BCnYIpo1xP+lTpP/yvrWudgo2U8m0fVqhTMGWX12Lwp6WltTpX5zp1dryjskjbyMrKUvu2ZGIGHdk8vmkOolH+utTJGHdFX7GxsZaok/9xq9VJ7ilf2OS5NmxH3etkRT351sns7z+RUCezyx5JdTLGM3HWGM+Y7nWyop5iQmDzBB0p5U9SUpJakS9YxKs3d+5cHH/88d5jMi1w7dq12Lp1K3Jzc1udL6GZxvQjX0Rgxup7DrvNK9y2CPR4epKR6NzV5mfaOmYoL1THOyu7NBrjS2Ug5+tQp2CO+8rD932d69Te8UDK6C8PK9Qp2ONttQ+d6xRMGX2dMFapU3ePG2Xxbx9WqFN3j0v7ML6oBTomhvp4ONteW+ebTUc2j3/Zok3+utQpFHZZV49TT12TQUdjIfUUmW2vJ58zPk/B9+U9YU9QT4hIm6dbTilZDa87Bbj66qvx17/+NaBzxfl04oknqlB0I+Lql19+UU4vicLqCq6WnFIOs1ffq2Oic0IIIYQQQgghhJAec0q99NJL3brZwIEDAz53woQJarvwwgvx73//W00JvPHGG3HVVVe1661rDyNSym726nt0ShFCCCGEEEIIIYT0nFPqgAMOQKgRx9P777+PK664AnvssYeaqygr791www1dvpax+p491pxIqYwkPZ1SkqyMUB5sH3xe2H+wP+X4Qkj4oV2mH9SZflBnekF9RSem55Qyk969e+Pdd98N2rnlamrJKWUzJ1IqIzFO7ctqG6ELIgfJnk8oD7YPPi/sP9ifcnwJ7XgbjfcmXYN2mX5QZ/pBnekF9aUfZtkdlrdeJGGa0zt9z6RIqWRPpFS9sxn1ziboIgdJEN/WKgfRCOVBebB98Hlh/8H+NFTjS7jgGK8PtEP0gzrTD+pML6gv/TDL7rC8U8o30blZOaVS4+2wt0Rd6RQtVV1dHe4iRBSUB+XB9sHnhf0H+1NCwgXtEP2gzvSDOtML6is6iRKnlDF9z5zqysqDRl6p8lq98koRQgghhBBCCCGERAJR4ZRyNpsbKSVkJOmXV4oQQgghhBBCCCEkUrC8U0qimryRUmY6pRL1ipRS0V0ZGWpPKA+2Dz4v7D/Yn3J8Cd14Gy44xusD7TL9oM70gzrTC+pLP8yyOyJ69T3znFItkVImrkqjW6SU8ZATyoPtg88L+w/2pxxfQjvehgs6pfSBdpl+UGf6QZ3pBfWlH2bZHVG2+p55hmKmZjmlRA4lJSVcmYfyYPvg88L+g/0px5cQj7fhgqvv6QPtMv2gzvSDOtML6ks/uPpeFzAipRyx5vngMpNbIqVq9IiUEurq6sJdhIiC8qA82D74vLD/YH9KSLigHaIf1Jl+UGd6QX1FJ5aPlBKMnFJ2m5mJzlsiper0iJQihBBCCCGEEEIIiSSiavU9UyOlWnJKlWuSU4oQQgghhBBCCCEkkoiq1ffsIVh9r0yTnFIih+zsbCZBpTzYPvi8sP9gf8rxJcTjbbhgonN9oF2mH9SZflBnekF96QdX3+sCLiPReZSvvpeamhruYkQMlAflwfbB54X9B/vTUI0v4YJOKX2gHaIf1Jl+UGd6QX3pB1ffC5BGV5P3tcPM1feS9Vt9r7i4mCvzUB5sH3xe2H+wP+X4EuLxNlxw9T19oF2mH9SZflBnekF96QdX3wsQY+qeYA9RTqnmlkisSMfp1MOB1lNQHpQH2wefF/Yf7E8JCRe0Q/SDOtMP6kwvqK/oxBYtSc7NXn0vvSWnlPijqhpcpl2XEEIIIYQQQgghJBqwvFOqySdSyszV9xIcsUh0xKrXXIGPEEIIIYQQQgghpGtY3ynVMrVO8o7GmhgpJWQm6bMCnyQhy8/PZxJUyoPtg88L+w/2pxxfQjzehgsmOtcH2mX6QZ3pB3WmF9SXfjDReYC4WgKlHCauvKfjCnzSYBITE2mwUh5sH3xe2H+wP+X4EuLxNlzQKaUPtMv0gzrTD+pML6gv/aBTKkAaXZ58T3YTV97bcQW+Ri0y469bt44r81AebB98Xth/sD/l+BLi8TZccPU9faBdph/UmX5QZ3pBfekHV9/rYk4pM5Oc+0dKlWswfU9wu/VYJbCnoDwoD7YPPi/sP9ifEhIuaIfoB3WmH9SZXlBf0Ynlc0o5W3JKmZnk3CAjUZ+cUoQQQgghhBBCCCGRhOWdUq6m5pBN38tKbskpVRP50/cIIYQQQgghhBBCIgnrO6VaUjvYQ5DoPLvFKbVNA6eUJCHr06cPk6BSHmwffF7Yf7A/5fgS4vE2XDDRuT7QLtMP6kw/qDO9oL70g4nOA6SpJY+SIxSRUinxar+1ugE6NBi73U6DlfJg++Dzwv6D/SnHlxCPt+GCTil9oF2mH9SZflBnekF96QedUgHibAmVsocgp1ROS6RUqQaRUpIZv7CwkCvzUB5sH3xe2H+wP+X4EuLxNlxw9T19oF2mH9SZflBnekF96QdX3wsQV4txGIrV97JS9Jm+RwghhBBCCCGEEBJJWD6nlLMpdKvvZSd7pu+V1TaiqWWVP0IIIYQQQgghhBDSOZZ3SrlanEWhWH0vM8mh9pK2ShxThBBCCCGEEEIIISQwLO+UMlI7OEKw+p7kqTIcU6XVke2UstlsKCgoUHtCebB98Hlh/8H+lONL6MbbcMExXh9ol+kHdaYf1JleUF/6YZbdYXkPhbOpKWSRUkKWN9l5ZK/A53a74XK51J5QHmwffF7Yf7A/5fgSuvE2XHCM1wfaZfpBnekHdaYX1Jd+mGV3RIFTKnSr7wnZKfFaREpJg9mwYQMNVsqD7YPPC/sP9qccX0I83oYLOqX0gXaZflBn+kGd6QX1pR90SnUxp5QjBKvvCdktkVJcgY8QQgghhBBCCCEkcCwfKeXyRkqFyCmV0jJ9rzqyp+8RQgghhBBCCCGERBJRtPpeaKqaldwyfa8msqfvCTExoXHM6QrlQXmwffB5Yf/B/pSQcEE7RD+oM/2gzvSC+opO7LA4LYFSIZu+l+ONlGqM+Mz4AwYMCHcxIgbKg/Jg++Dzwv6D/WmoxpdwwdX39IF2iH5QZ/pBnekF9aUfXH0vUhKdt0RKRXpOKUlCVldXxySolAfbB58X9h/sTzm+hHi8DRdMdK4PtMv0gzrTD+pML6gv/WCi8wBxNbUkOg9RTqmslkTnW2saIr7BlJSU0GClPNg++Lyw/2B/yvElxONtuKBTSh9ol+kHdaYf1JleUF/6QadUVxOdhyic3pi+F+mRUoQQQgghhBBCCCGRREQnOl+zZg2OOeYYpKenY9CgQbj33nvR3NySJCpAnC2/WNpDHClVXuv0ThUkhBBCCCGEEEIIIZomOm9sbFQOqV122QXz58/HypUrcdZZZyEjIwOXXnppN6bvhcb/lpEUB8mhLov8ldU2Ii81AZGKw+EIdxEiCsqD8mD74PPC/oP9KSHhgnaIflBn+kGd6QX1FZ1ErFNq3rx5yhH1888/IzExEUOGDMHVV1+N119/vUtOqSbxFqnpe6GJlIq1xSAzKQ6lNY1qBb5IdUpJZvy+ffuGuxgRA+VBebB98Hlh/8H+NFTjS7jg6nv6QDtEP6gz/aDO9IL60g/Lr743cuRIfPTRR8ohZRATE4Oampru5ZQKUaSUkK1BXilJQlZVVcUkqJQH2wefF/Yf7E85voR4vA0XTHSuD7TL9IM60w/qTC+oL/2wfKLz3NxcHHrood6/Gxoa8MILL+Cggw7q0nWMPE+OEEVKCdnJ8Wq/tbohohtMaWkpDVbKg+2Dzwv7D/anHF9CPN6GCzql9IF2mX5QZ/pBnekF9aUfZtkdETt9z5empiZMmTJFOVWuv/76Ns8Rp5VsBpWVla2cUhIoJUnSJcTMP1m6RGDJ1t3jxgp8myvr1d7/fLmnKMxfaWYe76yMspfN+GywMoiEOgVz3FcmVqlTMHrybRtWqVMwx422YdzbKnXqbhm703dEep26c9woi3/7sEKdgim7cU1DNlaoU2fHOypLVxdk6Q7t2TxtjWvRJn9d6uTbj1ilTv7HrVantvo53etkRT351sns7z+RUCezyx5JdaKeELU2T8Q7paSi559/vprK98knn6B3795tnicr802dOnWH45XVnul+1ZUV2LZtG3JyctS+urrae44kT5dty5YtqKur8x7Pzs5GamoqNm7cCKfT6T2en5+vphUWFRUpxSXCM21vU0WdKm9hYWGrMhQUFMDlcmHDhg3eY6LIAQMGoL6+HiUlJa2Su0nuJymfOOEM5H5y34qKCpSXl3uPp6SkBFQnKWdZWZmqk6xm2FmdDPr06QO73R6RdeqqnnzrJA+YyMN4qKxQp2D0JNeSMgtWqVMwepK24ds+rFCnYPQkdTBeW6VOweipuLjY2z6kL7FCnYLRU3y8J1pY6mQ4R3SvUzB68r1+qGjP5lm/fr1XB9Eqf13qZNhlUj6ZHWCFOllRT751ysrKUmlEpDyG7ah7nayoJ986Gc+Z1Ef0Z4U6WVFPBmlpaWovdfL94UXnOllRTxkhsHli3G39DBBBEVKy4t7777+P6dOn4+ijj+7Sr4b9+/fH+c/MxperanD70aNwzt4DQ+JpfmbOatz32TIct3MfPHraLhHnwRRkLw0nLy8PsbGxiPZfBOR+8hCJIWgkaNO9TsHoyWgf0iEZ8tG9TsEcl85d5GG0DyvUKdhIqa1bt6r+wx9d69Sd40ZZZGzybR9WqFMwZZdrinEjhovxRU33OnV2vKOyiEEnxqYYd4aBbTbt2TyiBzEUAy2rFeWvS52McVf6EfmiYYU6+R+3Wp2EzZs3q77OsB11r1M0REqZ+f0nEupkdtkjqU5yjtibMoYaz5judbKinmJCYPNEdKTUVVddhQ8++AAzZszAwQcf3OG58kut8WutLy2z9+Cwx7ZyPrRFd4/np3tW3NtS1dDu+YbyQnW8szLK3jfKzAwZhLtOwZa9rag7nevU3vFAyujfPqxQp2COyxeEttqHznUKpozyulevXm2ep2uduntcytFW+9C9TsGUXa4pDu320LFOnR3vqCzSPkJNezaP3Nu/bNEmf13qFAq7rKvHqaeuy6C9sZB6isy215PPGZ8nc/ryUNsT1BMi0uaJ2ETn8+bNwxNPPIEHHngA48ePV15T2SQEszur7zliQ5foPC/V45Ta3OKUikTE62mEixPKg+2Dzwv7D/anHF9CN96GC47x+kC7TD+oM/2gzvSC+tIPs+yOiHVKvfPOO2p/xRVXqNBmY9tll126dB1nS6SUvR0Pnxnkpca3ipSKRPiQUx5sH3xe2H+wP+X40jPjbbigU0ofaJfpB3WmH9SZXlBf+mF5p5RESBnzGn23tWvXduk6TS2RUvYQRkrltjilKuqcqHc2hew+hBBCCCGEEEIIIVYhYp1SZuFs8njvHLGhq2p6ogNxdlvER0sRQgghhBBCCCGERAqWd0q5WrLF222hi5SShGC5KfERn1dKlnUklAfbB58X9h/sTzm+EBJ+aJfpB3WmH9SZXlBf0UlEr75nBq7m0EdKCXlp8Sgur8OWqnpEIpIdX5awJZQH2wefF/Yf7E85voR2vI3Ge5OuQbtMP6gz/aDO9IL60g+z7A5btDilQplTSodk583NzWr1QtkTyoPtg88L+w/2pxxfQjfehguO8fpAu0w/qDP9oM70gvrSD7PsDus7pYxE5yH+9dBIdh7J0/eqq6vDXYSIgvKgPNg++Lyw/2B/Ski4oB2iH9SZflBnekF9RSdR4JQypu+FOlIqQe03V0auU4oQQgghhBBCCCEkUrC8U8ppJDoPdU4pb6RUZOaUIoQQQgghhBBCCIkkLO+UamqJlArl6ntGovNInr4nKwRmZGSoPaE82D74vLD/YH/K8SV042244BivD7TL9IM60w/qTC+oL/0wy+7g6nsmkZuSoIVTilAebB98Xth/sD/l+BLa8TZc0CmlD7TL9IM60w/qTC+oL/0wy+6Ioul7oTUS89M9kVJbqxvgbEmuHhE0OYGSRWhe/gXK5k1D87ofgZpSRDuyUkBJSQlXKqI82D74vLD/YH9q+vgSLrj6nj7QDtEP6kw/qDO9oL70wyy7w/qRUjJ9zwY4Qrz6Xk5yvEqm7mxyo6SyHv0ykxA23G5gxefA/FeAlbMAV73yPmb6npM9FBh5NDD+dCBvJKKRurq6cBchoqA8KA+2Dz4v7D8I4bhLaCtZCdq3ekF9RSeWd0o1NXucUqGOlLLZYtArPQFF2+qwsSKMTqkNvwEzrvHsDeLT4M4oQGOTG3HOSsRUFAGlK4HvH/Fs4pza/29An53DU2ZCCCGEEEIIIYREHZZ3Sknkks0eeqeU0Ds9UTmlNpTXhSc66ruHga/uBtxNgCMZ2P08YNypQK+d4Ha7sbGwEAUFBYhpqABWfwMsfBtY9gmwdIZn2/184ODbgUTmniKEEEIIIYQQQkhosbxTyiDU0/eE3umeZOebKurRozS5gP9dBix8y/P3mBOAI+4HUvK8p4hLLjs725OMLDETGHO8Z9uyDJjzAPDHdOCXF4AlM4ATngaGHgwrI3LwyoNQHmwffF7Yf7A/NXF8CRcc0/SBdoh+UGf6QZ3pBfWlH0x03kV6KlJKkOl7PUZzE/D+xR6HlISEHf0wcPJLrRxSRoNJTU3dseHkjgBOfA4492MgexhQsxl47UTgy7s8zi6L0q48ohTKg/Jg++Dzwv7DvP40XHBM0weOu/pBnekHdaYX1Jd+0CnVRRyxoY+U6pPhiZTqsel7MmXv42uBP9/xOKROedUzBa+dzPjFxcXtZ8gfuC9wyXctn3cD3z4ITDsNaKiCFelUHlEG5UF5sH3weWH/YV5/Gi44pukDx139oM70gzrTC+pLP8yyO0LvqYkQ7DYLRkr98jzw60tAjA046QVg5JEdnu50Oju+niPBE2l14vOAPRFY+QXw4hFA5UZYkU7lEWVQHpQH2wefF/YfhHDcJbSVrATtW72gvqKTqHFKxfaIU8oTKbWxogcipYp+Aj690fNakpOPPs68a+90EnDex0ByLrDpD+C5gz25pwghhBBCCCGEEEJMIiqcUo7YmB7Js2A4pbZWN6LB1RS6GzXWAO9dBDS7gNHHA/tcZf49+u4G/N8sIGc4UFkMvHQUULLY/PsQQgghhBBCCCEkKomK1ffsPbDynpCVHId4uw0NrmaUVDSgIDspJPfZOPNGzG8sQWF+P5T07gvX97ciLjYOuYm5KEgrwJjsMRiQNqCVI05e5+fnd805lzkQOH8m8MpxwKaFHsfU2f8Deo+D7nRLHhaG8qA82D74vLD/MK8/DRcc0/SB465+UGf6QZ3pBfWlH2bZHdHhlOqBlfcMpUi01NrSWmyoqDPVKVVeX473V76PD5e+hZU1xUBejueN1R+1eX6v5F44qP9BmDxwMnbN21WVLTHRk/OqSyRlAed8CLz6F2DDfODlY4BzZwC9doLOdFseFoXyoDzYPvi8sP8wrz8NF3RK6QPHXf2gzvSDOtML6ks/6JSKsJX3fJOdi1PKrLxS9a56vPDnC3hl8SuocdaoY7FuN0bb0zB88GTkJ+cjzhaHhqYGbK7djBXlK7C0dCk21WzCG0vfUNuwzGE4fcTp2NmxM4YMHAJbVyPHEjOBsz8AXjsJWP8T8OoJngiq7CHQeaWAoqIi9O/fv+vysCCUB+XB9sHnhf2Hef1puODqe/rAcVc/qDP9oM70gvrSD7PsjuiIlOqBJOc7JjsPfgW+3zb/htu+vw1rK9eqv0ck5OG09UtwWKMNqVd8CaTmt+vI+nHjj5i1bhY+X/c5VpStwJ0/3omc+Bxc4boCxw09DnZbF1WfkA5MmQ68fLQn+blM6Tv/MyC9H3TF7XaHuwgRBeVBebB98Hlh/0EIx11CW8lK0L7VC+orOomKEJGejJTqk+GZErahvC6oh/HVxa/i3M/OVQ4pyRX1wN534e2iIpxUVYPU/f/WrkNKSLAnYFL/Sbh737sx6+RZuH7365GXlIetDVtxx9w7cPJHJ2N+yfyuFywxAzjzfSB7KFBRBLxyPFCztdv1JIQQQgghhBBCSPQSJU6pnouU6pfpcUoVbeueU6qpuQlT507F/T/fj2Z3M44efDQ+OP4DHL5pNWzVJUDmIGDiJQFfLy0uDeeMOQczjp+BCwZfgIz4DKwsX4lzPjsHd/xwByoaKrpWwJRc4KwPgLR+QOkK4LUTgYbqrleUEEIIIYQQQgghUU1UOKXsPRgpVZDlSW5etK22Ww6pf3z/D7y74l3YYmz42+5/wz373oM0dwzww2OekybdBNjju3xtiZ66bOJl+Oj4j3DisBPVMbnPcR8ch2/Xf9u1i2X096zCl5QNbFwAvHM+0OSCbknZ+vTpw6SwlAfbB58X9h/sT00fX8IFE53rA+0Q/aDO9IM60wvqSz/MsjuiwynVgzml+rc4pdaX1aG52d2lKXu3/XAbZqyeAXuMHQ8e8CDOHnO2R9E/PQvUbQOyhgBjPQ6lriLXsdvtyEjIwB1734GXD38Zg9MHo7S+FJd9eRnunXevykUVMDlDgdPfAuwJwIqZwKd/k0pAFwx50ICnPNg++Lyw/2B/avb4Ei44pukD7RD9oM70gzrTC+pLP+iUitjV9xIQa4tBY1MzNlc1BPy5pxc+jQ9XfYjYmFg8cMADOHTAoZ43ZGqcESV1wA1ArL3bmfELCwu9GfJ3zd8Vbx39FqaMmqL+llX6Tv/4dKyuWB34RftPAE58Tpoj8MsLwPePQhf85RHtUB6UB9sHnxf2H+b1p+GCY5o+cNzVD+pMP6gzvaC+9MMsuyM6IqV6MKeUTBXsk+FZga8wwCl8n6z+BE8ueFK9/see/8AhAw7Z/uZvr7VESQ0Gxp5kalllSt/f9/g7njz4SWQnZKtcU2d8fAa+XPdl4BcZdQxw+H2e17NuB/54x9QyEkIIIYQQQgghxJpEhVPKYevZanYlr9SKshVq2p5wzuhzcNJwH8dTcxMw7ynP670u73aUVGfs128/vHPsO9gtfzfUOGtw9ddX49H5j6ocVwGx5yXAnpd7Xn9wKbD2+5CUkxBCCCGEEEIIIdYhKpxSPRkpJfTPTAooUkpyON0w5wY0NDVgnz774Jrdrml9wrJPgLK1QGImMP70UBYZOYk5eHbyszhr9Fnq7+f+eA6Xzro08NX5Jt8NjDoWaGoE3jwD2LoipOUlhBBCCCGEEEKI3kSJU6pnq2kkOy8q69gp9eAvD6opczJ17u5970asLbb1CXM9U/qw23lAXHJQZbLZbCgoKFD79nDYHLhhwg34137/QqI9EXM3zsVZn56FosqiQG4A/OUZoN8EoL4ceP1koGYrIpVA5BFNUB6UB9sHnxf2H+b1p+GCY5o+cNzVD+pMP6gzvaC+9MMsuyMqvpE7enD1vVYr8G2ra/ecHzf+iLeWvaVe37PvPSpSqRUbFwKFPwA2B7DHRUGXSVb3c7lcat8ZRw4+Eq8e8Sryk/KxpmINpnwyBb9t/q3zmzgSgdOmARkDgLI1nogpZxdW9OtBuiKPaIDyoDzYPvi8sP8wrz8NFxzT9IHjrn5QZ/pBnekF9aUfZtkdUeGU6unpe0ZOqfam78m0vTvn3qlenzbiNOzdd+8dT/r1Jc9+1NFAWm9TGsyGDRsCbjgjskZg2lHTMDp7NMoaynDBzAswY/WMzj+YkgtMeQdISAeK5nlyTEXgCnddlYfVoTwoD7YPPi/sP8zrT8MFxzR94LirH9SZflBnekF96QedUhE8fc9wSm2qrEe9c8dk4U///jSKqoqQl5SHq3a9ascLNNYAC9/ePnUvTOQm5eLFw17EwQUHw9nsxE3f3oQnFjzReePLHQ6c+ronymvRe8Dsu3uqyIQQQgghhBBCCNGEqIiU6unpe5lJDqQnOtTrNVtrWr23vGw5XlrkiYK6ZeItSIlL2fECf74HNFYBWYOBgfshnCQ5kvDQpIdw/tjzvQ61f3z/D+Wk6pBB+wHH/sfz+tt/A/Nf7YHSEkIIIYQQQgghRBeiwinV05FSMTExGJSTvINTSiKM7v/pfjS5m3BIwSE4qOCgti9gTN3b7VxPAnETy9UdbDE2tTLg1L2nIjYmFh+u+hBXfnklapytHW47sPMZwP43eF7PuBpYNRuRRHflYVUoD8qD7YPPC/sPQjjuEtpKVoL2rV5QX9FJVDilHD2cU0oYnOtxSq3eUu09Nmf9HMzbNA9xtjhcP+H6tj+46Q+g+BfP1LfxZ5iaGX/AgAFBZcj/y7C/4D8H/UetzPf9hu9x/szzsbWukxX2DrwZ2OlkoNkFvH02sHkJIgEz5GElKA/Kg+2Dzwv7D/P603DBMU0fOO7qB3WmH9SZXlBf+sHV97qAPQwG4uCWSKnVWzzRRDLd7cFfHlSvzxx9Jvqm9G37gwve8OxHHuVJGm4SEqVVV1cXdDKy/fvtj+cnP4/M+EwsLl2MMz85E+sq17X/AYlGOu4JoGAvoKESeP0UoHozwo1Z8rAKlAflwfbB54X9h3n9abjgmKYPHHf1gzrTD+pML6gv/YiqROeNjY0YPXo0vv76ay1W3xMG53pyRa1umb43fdl0rK1ci6yELFy404Vtf6jJBfzxzvapbyY3mJKSElMazk65O+G1I19Dv5R+KK4uxlmfnIWFWxa2/wF7PHDaG0DWEKCiEHjjVKCx7ZUJewoz5WEFKA/Kg+2Dzwv7D/P603DBMU0fOO7qB3WmH9SZXlBf+hE1TqmGhgZMmTIFS5Z0f9qXo4dzSvlP36t11uKZhc+ovy8bf1nbyc2FNV8DNZuBpGxgSDv5piKEgrQCvHrkqxiTPQZlDWW4YOYF+Kbom/Y/kJQFTJkOJGYBG+YD710INDf3ZJEJIYQQQgghhBASQUS0U2rx4sXYc889sXLlyqCuY+/h1feEgdnJauZaZb0LL/0xDaX1pWrKnuRlapeFb3v2Y08EYj2r90UyOYk5eOGwF7Bv331R31SPv87+K95d/m77H8ge4omYio0Dls4AZt3Wk8UlhBBCCCGEEEJIBBHRTqk5c+bgwAMPxHfffafV6ntCgiMWfdITgZgGvLbUs5rexeMuhqM9Z1NDNbDkI8/rcaeGpEwOh/mOriRHkkp+fvzQ49HsbsYdc+/AUwueaj+Ub8BewPFPeV7/8Bjw8/MIF6GQh85QHpQH2wefF/YfhHDcJbSVrATtW72gvqITOyKYSy65xJTrOMIQKWVM4dsS+ymqnOXon9ofxww5pv2Tl34MOGuBrMFA391Ckhm/b992kqsHicPmwJ1734m8pDw1TfHJ359ESW0JbtnzFvXeDux0ErBtDTD7buCT64GMAmDYoehJQikPHaE8KA+2Dz4v7D/M60/DBVff0weOu/pBnekHdaYX1Jd+mGV3RLRTqqu5p2QzqKys9L6WQKnmlvxFIjjjtUFMTIzazD4+IDsWv2GOen3JuEtgQ+t7S1kkoki2mIVvQVxnzTudAltMjPe4L77n+x/vrCzymerqaqSmppoig7bKcvn4y5GflI9/zvsn3l3xLjbVbMID+z+AZEfyjufvey1itq1GzO9vwD39XLjP/QTotVOX6hTMcaONpKSkeP/uSL5mHe+pttfVMhrtIy0tzfu37nUK5nhTU5OSh9E+rFCnYMoo16upqVH9h/+1da1Td44bZZHjvu3DCnUKpuzyura2FsnJnlyKVqhTZ8c7Kov0H+GyeeTe/nZGtMlflzoZ4670I7GxsZaok/9xq9VJ7ulvO+peJyvqybdOZn//iYQ6mV32SKqTIPZmUlKS9xnTvU5W1FNMCGweyzil7r33XkydOrXN96orK1BYWKgGkZycHGzbtk11UAYZGRlq27JlC+rq6rzHs7OzVSe2ceNGOJ1O7/H8/HwkJiaiqKioleL69OkDu92u7iVsbvoCMfZaxLnzcGi/Q73HBVHkgAEDUF9fj61rFqHf6tmez+QfgF5S5upqlJaWes+X+8l9KyoqUF5e7j0eaJ2knHLO0KFDkZ6e3u06GRQUFMDlcmHDhg2t6nTKiFOQHpuOm+fejO83fI8zZ5yJu3a5C+MGj9uxThNvRn5FEWLWfoum107CxqNeQ1Nyfo/oSR4wyVWWlZXl7fTaq5OhJ1mtzze0VCKtzNZTMHXqip786yTXkjKPGzdODQZWqFOwepL7Gu3DKnXqrp6kDvJarmWVOgWjp+LiYnVvaR/Sl1ihTsHoKT4+XjlIpBy+PwjpXKdg9OR7/Z62eURGUuZolr8udTLsMrl2bm6uJepkRT351kn6fCmLOOAN21H3OllRT751Mp6zQYMGKf1ZoU5W1JOB/DgudoQc8/3hRec6WVFPGSGweWLc/u6wCEWEO3v2bEyaNCngXw379++P/le/jakn7oZz9h7Yox5MZ5MTk989AtsatsC+7RTMv/of7Xsk5/0Xts9uhLvv7nBf8EVIvLKyl0YsDdSMX+Q6K+PCLQtV4vNt9dvQK6kXnjrkKQzJGLLj+Q0VcD8/GTFbl8Pdaxzc534MxKWEXE9SjrVr16oH2Qg7DLenORTHAy2jfE46P2kfhnx0r1Mwx6Vzl+fFaB9WqFMwZfRtH/7oWqfuHDfKIr8K+bYPK9QpmLLLNdevX6/GXN9fNnWuU2fHOyqLGHRibIpxZ0Sfmk17No8YmWIoBlpWK8pflzoZdpn0I/JFwwp18j9utToJ69atU8+aYTvqXicr6sm3TmZ//4mEOpld9kiqk5wj9ma/fv28z5judbKinmJCYPNYJlJKfqmVrS0c9thWDdv3tS9mHv9s9WfKIdXsSkXZ5p1QWtOInJQdy6eU2pLgPGbsXxDjN8i1eX4bxwMpo/Hl2qy6dlTG8Xnj8dqRr+GyWZdhbeVanP3p2Xj4wIcxsffE1icnZiLmjLeB5w5BzKaFiHnnfM8Kfba4kOpJHjjjy2RbnV5X6mq2nsw+HmgZjddWqlN3j/u2jZ7qOyK97XWn74j0OnXnuJSjrfahe53M0lNb19e9Tl3VU3vv9YTN09b9o03+OtXJV19WqVNPlT0cdZIvYL5jgNllb+849RRc2zP7+w/1FLo+wnB+tDeWUk+wrM0T0avvmUVcD6++J6vQvfDnC+p1cv2BgNuBZZuq2j65qgRY973n9ahjQ1ouCc3rSSS5uzimds3bFVXOKlwy6xJ8tKplhUFfsgYBp78J2BOBlV8AH1wCNIc+J0dPyyPSoTwoD7YPPi/sPwjhuEtoK1kJ2rd6QX1FJ1HhlHLYe3b1vW+KvsHqitVIcaRgbMph6tjS9pxSS8VJ4/asuJfRP2RlEi+mzBXtiV9wfUmPT8czk5/B4QMPh6vZhZu/uxn//f2/O4ZE958AnPoqYLMDf77rWZUvhDNLwyWPSIXyoDzYPvi8sP8wrz8NFxzT9IHjrn5QZ/pBnekF9aUfURcpJU6M9vJJdYajhyOljCgpSfo9tne+er1s0/bkr61Y/D/PfvTxIZefkVizp4mPjce/9v8Xzht7nvr78QWP4465d6i8W60Ydijwl2ckeBD45QXgyzstKY9IhPKgPNg++Lyw/zCvPw0XHNP0geOuflBn+kGd6QX1pR9m2R3aOKV0mb73x5Y/sGDLAthtdpw56kyM6OVJ+NXm9L3qLcDa7zyvRx9r6YfcFmPDtbtdi39M/Id6/d6K93DRFxehrL6s9YljTwSOftjz+ruHgO8ftaQ8Ig3Kg/Jg++Dzwv7DvP40XHBM0weOu/pBnekHdaYX1Jd+0CnVBRz2nnNKvbH0DbU/YuARyE3KxcjeqervZSVVcDW1zlyPpTMAdzPQe2cg07M6oNU5deSpeOygx5DsSMYvJb/g9I9Px8qyla1P2v084JA7PK+/uA349aWwlJUQQgghhBBCCCGhg5FSJrK1bis+W/uZen3GqDPUflB2MlLj7ah3NmN5SXXbU/fGhHbqXqSxf7/98fqRr6NfSj8UVxdjyidTVB6uVux7DbDP1Z7XH10N/PZ6WMpKCCGEEEIIIYSQ0BAVTqmeyik1fdl0lcx7fO54jM0Zq47ZbDEY2zddvV64vnz7yTWlwJo5PbLqnkFKSgoihSEZQzDtqGmY0GsCal21uPKrK1UurlYhgBItNeFCTyL4/11uumMqkuQRCVAelAfbB58X9h+EcNwltJWsBO1bvaC+opOocErF9cD0PUna/dayt9TrKaOmtHpvXH+PU+r39RXbDy77GHA3Ab12ArKH9Ehm/JycnIhamScjIQP/PfS/OHn4yXDDjYd/fRg3fXcTap21nhNiYoAjHwAm/J/pjqlIlEc4oTwoD7YPPi/sP8zrT8MFxzR94LirH9SZflBnekF96UfUrb4XDI7YmJDfY+a6mSitL0VeYh4OGXBIq/d27pexY6SUd9W949ATNDc3Y+vWrWofSThsDty65624eeLNiI2JxcerP8aZn56JdZXrfBxTD5rumIpUeYQLyoPyYPvg88L+w7z+NFxwTNMHjrv6QZ3pB3WmF9SXfphld0SFU6onVt97Y4knwfkpI05RjhZfxvX3OKWWbqpCvbMJqN0GrP7a8+boE9BTVFf75bSKEGJiYnD6yNPx3OTnkJ2QjRVlK3DajNPwVeFX7Tumfn3ZsvIIF5QH5cH2weeF/QchHHcJbSUrQftWL6iv6CQqnFKhzim1cMtC/LH1D+WMOmn4STu83yc9ATkpcWhqdmPRhkpg2adAswvIGwPkDA1p2XRi91674+1j3sYuebug2lmNq2ZfhUd+fUTl6drumGrJMfXRX4Hv/xPuIhNCCCGEEEIIIaSbRIVTKtQ5pV5f4plOduSgI5GdmN1mJND4lil8C4rKe3zqnk7kJeXh+cOex5mjzlR/P//n87j4i4uxuXbz9hxTxqp8X9wKzJoK+CZHJ4QQQgghhBBCiBZEhVMqlJFS4iz5fO3n6vUZo85o97xdB2Sq/R8rC4FVX/W4U0ocYxkZGWof6UjE2Y173Ij7978fifZE/LTpJ5z44Yn4uuhrj2Pq0KmelfmE7x4CPr4WaG6yrDx6AsqD8mD74PPC/sO8/jRccEzTB467+kGd6Qd1phfUl36YZXdEhVMqlDmlpi+fDpfbhV3zdsXo7NHtnrfn4Cy1T143C2h2AjnDgbyR6Cl0fMiPGHQE3jr6LYzKGoXyhnJc+dWVuGfePWhoagD2vQY4+hGpGfDLC8D0c4DGllX7LCqPUEJ5UB5sH3xe2H+Y15+GC45p+sBxVz+oM/2gzvSC+tIPOqW6gMMeGgOxsakRby97u9MoKWGnvhlIdMRiP9dcz4FRx6KnM+OXlJRotzLPoPRBeO3I13DW6LPU39OWTsPpH5+OVeWrgN3PA056AYiNA5Z8BLx8NFC92dLyCBWUB+XB9sHnhf2Hef1puOCYpg8cd/WDOtMP6kwvqC/94Op7ERApNXPtTGyr36byIB1UcFDHZbDbsHf/BBxg+91zYHTPOqWEuro66EhcbBxumHADnjrkKWQlZKnV+U6dcSpeXfwqmsccD5z9PyAxEyj+FXjuYGDLMkvLI1RQHpQH2wefF/YfhHDcJbSVrATtW72gvqITy0/fkyj6WJv5kVJut9ub4Py0EaepPEidcWLaEiTGNGKrvTfQa5zpZbI6+/bdF+8e+y726bOPmsJ3/8/347zPzkNhZj/ggllA1mCgvBB47tDtebsIIYQQQgghhBASkVjeKWWPtYUkx8LCrQuxqHQR4mxxOHH4iQF9ZmLD92r/SdMEcL247pGTmKMipm7d81Yk2ZMwf/N8lQT99S3z0Hz+50D/iUBDBfDaicB3j3BlPkIIIYQQQgghJEKxvFMqLjY0+aTeWPKGNxm3TCnrFGc9sopnq5fv1++GxRsr0ZOIYy47O9sSSVClDqeMOAXvHfceJvaaiPqmetz3030479vrsfq4R4GdzwTczcCs24F3zgMaqi0tDzOgPCgPtg8+L+w/zOtPwwXHNH3guKsf1Jl+UGd6QX3pBxOdhzGf1JbaLfh87ecBJTj3sno2YhqrsS02BwvcQzB7aWAJuc1sMKmpqZYyWPum9MUzk5/BLRNvQaI90RM19ekZ+E/BcNQdcR8gUyoXvQ88fyhQusry8ggGyoPyYPvg88L+w7z+NFxwTNMHjrv6QZ3pB3WmF9SXftApFSCOEERKTV8+HS63Czvn7ozR2aMD+9DiD9Vuc7/JcMOGr3rYKSWZ8YuLiy23Mo8txobTRp6G9497Hwf0OwCuZhee/eM5nLD+f5hzzL1ASj6weTHw3/2BBdO80/msKo/uQnlQHmwffF7Yf5jXn4YLjmn6wHFXP6gz/aDO9IL60g+uvteFnFJm4mxy4u1lb6vXU0ZNCexDTU5g2SfqZc6Ek9T+t6JybKtpRE/idDphVSRq6rGDHsMjBz6C/KR8FFcX4/KF/8HV4w5C0YCJQGM18MElwHsXAvWVlpdHd6A8KA+2Dz4v7D8I4bhLaCtZCdq3ekF9RSeWzynlMNkpNXPdTJTWlyIvMQ8HDzg4sA+tmQPUlwPJucgZPQkje6WqgJ2ejpaKhvDBgwsOxofHf4hzRp+D2JhYfLnxexxn34p/jz8clbF24I/pwNP7Aut/DndxCSGEEEIIIYSQqMbyTqk4u7lVnLZkmtqfPOJkOCRnUSAs8Uzdw8ijAFssjhjbW/358cINppaNeEhyJOH6Cdfj7WPexl6994Kz2YmXKhfjqCHDMS2vAM7ydYh58XBk/vIw4Kyj2AghhBBCCCGEkDBgh8Vx2MzLKfXHlj+wcOtC5Yw6abhnGl6nNLmAJTM8r0cdq3ZHj++Nh2ctx7crtqKsphGZyXHoiSii/Pz8qEqCOjxzOP576H/xXfF3ePCXB7G6YjXuSQbeGDwcl5Wsx2F/voSYDd8Cxz0ODNgb0Uw0to+OoDwoD7YPPi/B9B/hgn14ZON2u7G1uhFbqxuU/be5IgbflxShrrEJziY3Gl3NcDY1Q5qQ3WaDwx6jFuyx22KQHG9HRlIc0hMdyEhyqH1mUpzpP76S9qFtoB/UmV5QX/phlt1hfaeUidP3Xl78stofMegI5CTmBPahNV8DtVuBpGxg0P7q0JDcFIzqnYYlGysxc9EmnLZHAXqiwSQmJiLakHrv128/7NVnL7y7/F08seAJrG0oww15OXjG5cZlpRtw8ItHwDbhQuDg24CENEQj0do+2oPyoDzYPvi8BNN/hAs6pSKD6gYXlm2qatkqsba0FuvLZKtDg8vcRPg5KfHonZ6A/LQEte+dkYCB2ckYkJ2k9uLMIuZA20A/qDO9oL70g06pHnZKFVUV4Yt1X6jXZ48+O/AP/vGuZz/6eCB2+3S/Y8b3Vk6p9+YX94hTSjLjFxUVoX///rDZou9XNbvNjlNHnoqjBh+F15a8hlcWvYKVqMK1+bkY2dCIyxa9hkmL/4eYQ+4Axp8ORJmMor19+EN5UB5sH3xeguk/wgVX3wtP9JM4m35euw0/ry3DL2u3YcXm6nbPF59ldnIcMhIdSIx1Iz8zBUlxdhXxpLYWu7WxqRlOVzNczZ4IKnF0ldc5UVnnRHltIyrqnGh2Q0VdyfZHcUWb98tLjVfOqYE5SRiWl4rhvVIxIj8V+WnxdGJ2EdoG+kGd6QX1pR9m2R2W//nEYVJY86uLX0Wzuxn79NkHI7JGBPYhZz2wtGXq3k6tp/v9ZZd+eHDmMvy0dhtWbq7C0LxU9IThFO2kxKXgkvGX4LQRp+GJH5/ARxs+wlIAf83PxdDGRpzz5d9w1C/PwXHEg0C/3RBNsH1QHmwffF7YfxDSOfXOJsxdXYrZSzerRWvEKeWPOH1G9EpTi9sMzU1Bv8xE9MtMQq/0BOV8EkO+sLAQBQUF3foxqLnZjbLaRmysqMcm2So9e4nIksisdaU1KKt1YnNVg9rE3vQlLcGOEeKganFSSVlH90lDCiOrOBZaDNq3ekF9RSeWd0ol2NsJo5cE181NQHxKp9cory/HBys/UK/PHXtu4Ddf8TnQUAmk9QX679nqLTFKDhqZj1lLSjDtpyLcevTowK9LgiYtLg1TBk7BpRMvxSuLX8GbS9/ESgC35mbjMdcmTJl+HE4ecDhSD7wVyBxAiRNCCCFR7oj6etlm/G/BBsxethn1zu2/DjtiYzC2bzomDMzC7gMyseuATDWtLpTYbDHITolXm9y7LSpqnVhbWqO21VtqsHJzNZaVVGHN1hpU1rtUZJdsvgzOScaYvukY2ydNXXdMnzSVy4oQQggJFZZ3SsXbY3dMPP7FbcBPzwDuJmDUMcBRDwPJ2e1e481lb6LOVYdRWaMwsdfEwG/+5zue/di/tDkdbMrEAuWUenf+elw3ebgK3yY9S0Z8Bq7e7WpcsNMFmL58Ol5f9Ao215fi4axMPFMxF8e/diBOKZiMwQfdAaT2onoIIYSQKPrFXpw2038pwmd/bkJVg8v7Xq+0BBw4Mg8HjczDPkOzI9KGS09yYHxSBsb3z9jBwSZOquUlVVi6qUrtF2+oVNFWq7fWqO2j37evEC1RXmP7pGNs37QWh1U6clND63QjhBASPcS4LRojV1lZifT0dFzx0rd47Jx9t7/x6Y3AvKdbn5y/E3Dex0DCjr801TprccR7R2Bb/Tbct999KidRQDRUAQ8MBVz1wEXfAH123uGUpmY3DnzwaxRuq8Xtx4zGefsMQqgQNTudTjgcDuYQ6EAeziYnPl7zMV5e8DRW1hR7j0+ob8QpvfbGwQfdA0dqb1gNtg/Kg+2Dzwv7D3OoqKhARkaG2qelpfWozVNeXq72JDgkX9P789fj9XmFrfJD9UlPwDHj+6hNIoiCSfAaieOu5KZatKESfxZXYNGGCvxZXKls1LaQ6Yk7qUiqdLXfqV+6SrZuZSJRZ6RjqDO9oL6i1+aJvJ91TCbB4RMpVfjjdofUX54DcocDr50ElPwBzLgGOOmFHT7/9rK3lUOqb0pfTB44OfAbL/rA45DKHgr0Ht/mKbG2GFx8wGDc8v6feGbOakyZOCBkS/vK4Gm32zmIdiIPR6wDxw89HscNOQ7fb/geb//2FL7ZuhA/J8Th5/JfkDX9EByfPBjH7fk3DB7gWU3RCrB9UB5sH3xe2H+Y15+GC35RDo7VW6rx7Ldr8P5v673T8xIdsTh2fB+cuFs/NTVPps1Z1S6TKYcHDM9Vm+8UwEUbK1QklTir/txQiVVbqlFS2YCSys2YtWSz91yJnpJpf8pZJY6qvulqRcBIqqPVdEY6hjrTC+pLP7j6XoC0cvJ88y/PfpczgXEne16f/ibw/KHAn+8Co44FxhzfKkrqxUUvqtcXj7sYDtv21fM65bdXPfudp3iWWmmHE3fth0dmrVCJKt/5dT3OmBialfiCTahpNTqThzxg+/bdV22bqjfivXkP4N2iWdgca8ML9WvxwteXY1RMIo4eejyO2PlC5CZtN+B0hO2D8mD74PPC/sO8/jRccPW97vFbYRn++81qzFy8Ccb8AUn+feaeBThul75IS+iC/Rep465UTH4slU0W4nHVtd43NQLuZs95au/Z0t3N2Fu2rGYgC8B4O+qbYlBY3ojV2+qxurQBK7fWYW1ZA5zVsShZbsO65XGY7o5HPRxISkrB0L65GNsvwxtZJdMBdXTs0FbSD+pML6gv/eDqewGSENsSKbXpD2DVV0CMDdj/b9tPkBXW9rsWmPMA8PmtwPDDAEeieuutZW+pKKl+Kf1w9JCjA9fOlmVA0TwgJhbY+YyOy+eIxaUHDMGdMxbjoS+W49id+3DlkwijV0pvXHbwQ7ioyYlv5j+N9xe/ju/d1ViCOixZMQ3/Xj4Ne6QOwFFjzsKBgw5HejynThBCCCGRPk3k2xVb8fjslfhpzfaV6Q4ZlYcL9xuMPQZlRabjRJxGsohO9eaWrcSzry0F6iuA+vKWfQVQ5/PaWWNaEWSS3vCWzUt7udDFR1sENBQ6lJOqHnEoiolHjCMRsXHJcCSnIzk1A4mpGYiJTwPiU302/79TPak2xM7iD6yEEGIZLD99L96IlPr9Tc9eEptnDmx90r7XAgveACoKgblPAPtfj+rGarz4Z0uU1PhuRkkNmxxQcuwz9xyAV39cp1ZDeXL2Stxw+MjA70V6DHusAwdPuFJtZUVzMfOH+/Bx+VIsSIjDj9Xr8OO8uxE775/YPWs0Dhx6DA7qfxB6p1gv/xQhhBCiM+KEenDmMvy0dpt39bzjd+6Li/YfjGH5qeEtXEM1UFEElBd57NLywpbX64HqTR4HlEQ7BYP8aCo/wNoTPJsjAYiN9zh6YjrYVBRVE9Dsatl8X7f8LRFXKhqrzvO6hfgYJ+LhRDpaclQ5WzbxlW3ucgU8zqnETCAxo2WfCST4vG7vuNSVEEJIRGF9p5SjZRBd+rHnwJi/7HhSXBJwyB3AexcC3z0C7HYunl/2OsoayjAgbQCOHtyFKKkm53YH2K5nBTzF8KYjRuKiV39VuaWOGtdbhTeTyCWz/1447dT/4bTqLSj6+Sl8suwdzIxtwIq4OMzbtgjzflqE+366D6PSh+DAQYdhnz77YEz2GMTa/FaDJIQQQkiP8HtROR78fJmKkDLsrzMnDsCF+w9C73RPlHyP4GoESlchad1coLAM2LYK2LrCs5eIp0CQKKKUPCAlH0jOBZKyPY4YccCIw0Y5bXxex6W0OKASgVjzpyO2iTipDAdVy9bYUIOikm1Yu2krNmwpxZatW1FZUYbE5lqkxNQiBXVIialDKuqQZqtHjqMB6bZ6JKMO8U3ViG1qkHCxloiwcqCsi2USGSgHVRaQlNXivDJeZ7b/uqdkRgghUYjlV9/77xcLcdFONuCpvT2/At2wGohP2fEDkgPi2QOBjQtQvNtZOLZ8LhqbG/GfA/+DAwsODPzGkpvqnfOB5Dzg2sUBD2Kihkte+xUzF5VgVO80/O/yfUxPei5zPplPKkTykPazdg6KfnoaszfNxVcJcfgtIR7NPqH/qY4UTOy9J/bqs5fa+qf2RyTB9kF5sH3weWH/YZ79EY7V93rynjqxdFMl/v35cnyxuET9bbfF4NQJ/XHlQcPQKz2EkTNiG5StAUr+BEoWAZv+BLYsAcrWeSKO2kOmp2UUABn9Pft02fcHZPVfcUSJjSk/qFoEZ1MzlpdUeRKpF1fij+IKLNlYiQbXjvnZ4uDEwKRGjMt2Y1RmM4alOlGQ1IDecQ2Id7ZMX6wra9l8XstxyZPVXeJSgaRMuBOzECNOKuWsanFY7fC6Zc9phhEB7Vu9oL70wiz7w/KRUnGxNmDJDM8fQw5q2yEliHPi0KnAK8fh4aLP0JiciD167YFJ/ScFfjPx78n0P2H387v0q4rkLbj7+J1USLkMxFM/WoR/nrBT4PfutGhuuFwuLmMbKnlI+xk8Cf0HT8LZdWU4e8lH2PbHW/hm6wLMSUzAvIQEVKEaswpnqU2QXGW799odu+Ttgp3zdsagtEFhy1/B9kF5sH3weWH/YV5/Gi4s+jtjUKvpPTxrBWYs3KBMNFk474Rd+uGqg4ehIDvJ/OgnyV+68TeP80k5oha3m8vJHZcCd9YQxOQOR0z2MCBnqGfF5owBnuidKMIRa1MzBGQ7dYLnWFOzG2tLa7BsU9X2raRKHVte68BymQVY1Po6fdITMCQvBYNzkjF4cAqG5KZgcG6yZwVAaQCNVS2Oqm0eR1Vty977epvPsZbXko8LLZ9trEKMTKcMFJnyKJFr7UZhZfodb3kvLrnDRZJI4NC+1QvqSz/MsjssHyn1+pzFOGPRhR5D4bgnPCvvdcA3r0zGFe6NkPiZt46ZjpFZXcjvVDgPeGGyJyLrmj89v2Z1kdlLN+P8l39WxtNdx43BWXv55b/qJlzNIEzyqCoBFr0P1+IPsLjkN8xNjMPchAT8nhAPl5/BkRmfifF54z1OqtydVdtLcvTML6FsH5QH2wefF/Yf5lBeXo7MzMywREqVlZUhIyO6HBptsb6sFv/5cgXenV+snBuCpEa45pBhGJpnQs4oMdIk79P6n4H1v3j2GxcCamqZH2IT5o0Ceo0F8scCeaOBnOFoTs5DYVERV0XuInWNTVi5uVpFvxmOKtlvrmpD9i0kOmKVc2pwrjiqkjEoJxkFWUkYkJ2MzKROfpyUKYjimKrdhubaUmxZtwy5KXbY6v2cWb5OLtkHk1g+Nm7HyKv2orN8nVz29rLNRy+0b/WC+opem8fykVIZzk0eh5T8WjH8iA7PleTmd8bVAw3AOeWVGFnXkowxUOY+5tmPO6VbDinhwJF5uH7yCDwwcxlu+3AREuPsOGm3ft26FokAUvOBPS+Bfc9LMK52G8at+AIXL/8Utau+xC8xjViQEI/58fH4Mz5O5TD7uuhrtQkxiMHA9IEYlTUKo7NHq00cVakSQk4IIYSQVmyqqMcTs1fizZ8L4WzyOKMOHpmHaycPDy5XZ2MNsOG31k4oWfXOH3EM9N1tuwOq105A1hAg1t721D7SZRLjYrFTv3S1+VJW04jVW6uxanMNVm2txuotNVi1pRqFpbWoczZh0YZKtfmTEm9H/6wkFGQlKkdVQbbHYSVb34xExNljPY4f2ZoHo645Hygo6Hz1P1eDXzRWG1FYbUVpNTs9CeJVUvtNXROO5A1r5cBqL0eWj2NL8o0x3ykhJMxY3inVZ/Mcz4sB+wDJ2e2eJwFj/5z3T2xuKENBTAIulZVOZt0OnP1hYCG04vha8pHn9V6XB1XmyyYNQUllPV6Zuw5/e+d3lNc24oJ9wze1i5iEDP7jT1VbUpMT+xf+iP3XzAHWfgtn0c9Y4rDht/h4lYtKnFQldjvWVKxR2ydrPvFepm9KXwxOH4whGUM8W/oQDM4YjGRHMlVFCCEk6thS1YCnvl6F1+atQ2NLHqJ9hmbjuskjsGtBZtcuJs6i0pUtDqgWJ9TmRTvmI7LZPU6nfhNatt2BzEGcdhUmMpPjsFtyFnYbkLVDvqrCbbXKSSXTOcVRtXZrrTq2qbIe1Q0ulTZDNn9kumevtAT0zkhUUwBlS2iuw6jKOPTNTELvjATkJMfDJif6Y4/3rMAdwCrcXtQUwxq/yCvDgVXejmOr5T01xbDas0kUX1dXMuwoR5Yk1U9IA+JTPa9lL5+RPRPAE0JMwPJOqbwNsz0vRna8gt47K97BjNUzEBsTi7v2norEdecA4jBY9SUw9JDOb/TlXZ792BM9YdpBIM6nqceOUa/FMXX3x0uweEMl7jhuDNISur/6B51aESQPGcQH7efZJJ9CYw3GFf6IcWvm4Jyin9QvslubG7A0Pg5L4uKwuGVf7LCjuLpYbd8Wf9vqkr2Te6MgrUAlUDc2yVsl+xT59awT2D4oD7aPwOHzQnmQ8FNa3YBnv12Dl39Yq6JhhAkDM3HtoSOw15D2f4hshXyxL/51ewRU8S8teYT8SOvncTypbQLQe7xnJbsgYD/SM/mqJLeUbEB+q/fqnU1YX1aHom0eJ9W6Us/e+Fva1IaKerW14vtNrXLX5qfHq9UbJadVfloCclLikZu6fZO/MxIdbTuvfBG7VHLfyiYJ7rviSPVN8L7DlEJ/Z1bLeZIny3clQ6xGl7EntjisDGeV4bxKb8ORZZxnHE/x5M8SGzWEzi0+Z3pBfUUnEZ1Tqq6uDpdffjmmT5+OpKQkXHXVVbj55pu7lF+h/O9pSI8HcPWfnpVL2mDexnm4dNalcDY7ce1u1+K8secBn90M/PgEkL8TcPE3HYe2rpoNvHo8EBMLXPEzkD0EZiCqeeH7tfjnx4shKRFksLvpyFE4aqfenQ9sRG+anMDmxS1G8i/AhvlqueiKGDdWOhxYFefAaocDK9Xeji32jv3Lkq9KnFMSZZWfnI/8pHy1z0vKU69zEnNgl199CSGERPXqe5KDadGGCvy4ulRNhZJoEjkmKwLLSnWSRHrn/hkY2zcdCY4ObKMQIlOynv12Nd7+pci7Qtv4/hm47tDh2G9YTvtfaiQZuUQ9ybiqHFE/e6Ki2vqi3WeX7Q4o2af1CXGtSCQhNvjW6kaVn2yjOKbK69R+Y0UdNpR79pLHKtBvUbLio+GsykmJ8zqsspLjVV6rzKQ4ZCQ5kJUs+zikJdhD/+VcngfDUdWeM0utXFgJNFQBDS17+dtVZ25ZJI+W4aBSW7LP38mt//Z1ZrV5XgogOVklWo2zTAjRwv6IaKfUFVdcgR9//BGvvvoqiouLcfLJJ+PJJ5/E6aefHriA/p6KtIG7eBxLbTC/ZL5ySNW6anHogEPx7wP+7RkEpDN+dGegoQI49C5gn7+2faPGWuDJPYHydcAeFwFHPgCz+XntNlz39u/qVxthbN80XLjfYBw+thfiZa57AIia6+vrkZCQQA+0rvJw1gNbl3mWlfbdajajwmZTzqlChwNFdjvWO+ze/bbYztuILcaGnIQc5CXnITcxF1kJWWrLTMj07rMTstVeHFwOi4dra9k+QgjlQXmwfQSOGGaSbDwcTilJOCr77iDTmN7+uQjPf7cGxeWdf+GUCJGJg7NUzqaDR+WrvDyh7ofmrdmGV39ch0//2Kh+rBPG9UvHXw8ahoNH5bXur8W83bba43wytvaSkcuqd4bzSfaSjDzE4xz7Vf3w15lMDRTH1MbyOhVNJXuZSrqlukHtt7bsy2qdXb5XrC1GRVdleB1WcR7nVXIc0hMdSE2we7Z447VnLzMqUhLs6vMh//FUOagqtjusWjmv/P5u6z1nrSd/VsiIgdtwTsUlIUa9TvA4rCTKsdXW3nvG8ZbXxnFxoslxubZssqBBW7njSJdgvxi9Nk/EOqUkSiorKwuffvopJk2apI7deeedmDVrFubMackTFahT6sg7gP2ubfW+VPuj1R9h6g9T0djciIm9J+LJg59EnHQyBr++BHx0FWBzABfM9CSvbH0R4KO/AvNf8YR1X/6jJxw1BNQ2uvDsnDV4Zs4q1DR6QtTl15TDxvTCoaPzMHFQNpLj2+8MuZqBheUhDtTSVcA22Va3vF7t+bu+AtUxMWranzipiu12bLbHoiQ2VuWs2hwbq/72XwmwM1IdKchMyEJaXJpKvG5s8ndafBpSHduPGVuiPRFJ9iS1oqDD1slqN2HGUu3DBCgPyoPtw7qr723etB4ff/8rfvpjKRIbtyEhxolEewwG5yQgLzMdyWlZcMenocqWirUN6Zhfasf8okr1hduXkb1ScciofBwyOh/j+qabFtEtycv/t6AYb/1chNVbt69odsDwXFxywBDsOTgLMfIF2fujzZ/Apj89icnVlCQ/JE+O2HOyiQNK9pI3p4dhv6of3dWZ5DkrrfE4qHydVeLQ2lbTiPJaJ8pqt+9rW+z8YEiOi/U6qmRLSXAgyRGLpPhYJMXJZm/Zx6pFlZL9Xif6n+OIhT3WFppoLZULq8Znq27jdXXn5zW0/N2W47knkBkzvk4q47X3b3Fi+TizOjtHOb7keJwnh53sxVmuNjnm8Pvb7xz1fsvfEWxz+8J+UT8sv/reggUL4HQ6sffee3uP7bPPPrj33nuVQ6lLX2jHnNDqz6XbluLx3x7HN+s90VMH9j8Q/9r/X60dUsKu5wArvgCWzgBePwU4d8b2fFHikPrmfo9DSlb2O+6xkDmkBBkYrjpkGM7cs0DlmRLjTELqp/1UqDax/Ub0SsPO/dPVvHlZ7nZgTrJK0CiDCbEwxqow/Se0Pi5ttK4MKRXrMaKyGCMq1gOVxUDlBqBC9uuBqhI0u+qwLdamHFWb7HaUxsaiLNaGbbaWfWwsSmNtKGv5uzkmBlXOarV1l1jYkBQbj0R7PJJiE5XDKtGegCRHMhKV4yoZCY4kxNsTEW9PUM9mfGy82vu+jrfFq9cSuSV747g4vWQ6omy+ryVnnGyR7BAjhJDuIjlyJIpIIquzU+JVXiVZQUwhX9bEabPxdzU9vKZ4EdyblyKvqQLnAWqDrxlU2rL5Y3PAndYb9bm9UdyciT+r0/BbeRKKN2fjq5JsvDY7G3Ep2Th4dC8VRbXbgEwV3REorqZmtUra3NWlmLloE34rNBxLbhTEVeP0YU04tn8D+rp/B377LzBzicch1eza8WLyJU9yPxlOqL67AlmDtfmCRqyBTH2VnFOyBfocGw4qX2eV2tc0orLeiap6V8vmeV3Z8tqYzio/YMu2acf87d1Goq/i7baWLRbxDp/Xsnf4vG7nHJGF5PlyxMYoJ5f3tdhrsRlwxGbBLn87bIhLlOM29bdEZsr5Mg1SriF7z+dj1DXkb69tJ05qZ53amhtrsLFwNXrnZMDWVO+ZdSARWur9WsDl+7fPJtMTjXPUZ4zXLe+JM00+6/ZxIMprdU4XV2/vCcRh5XVS2dtwavk5sSRtjfqMsbX8LY43379bvd/GMe/5/p9p5zqIQcJWWYWy0FNO+bx8zxYnsOy9f8f6/B3TxjHfv322Hc7hD8+RQsQ6pdavX4+cnBzExW03ZPr06aPCZktLS9V7gTCz/1g4tv2OmpIfsK5yHX4p+QUrylao96QDvHjcxbhwpwsR21bOKGnkxz8FvFQIbFoIPHcIsOdlQO4IYOHbwIqZnvNket+Qg9ATiJF5zaHDceVBQ/H9qlLMWlyCr5ZuVqH27a0ekuCwqXnsqQ4gN73E88uHzy8l8uuHdPAy2Einvn1v2/53rKejNzp8+d/o+2Pkn/e1r63nf7yNz4bJLmxudmPLliqsrN0cBfm5JLFnPpC2K9CGA9vmqoW9ditqN61CXlIz+jRsQ1xDKeLqS+GQzVkBe30V7M5K2BqrUNtUhQq4lJOqymZDVWwMKmXfxuY5HoNqmw11MTFoaOn8m9CMqqY6tQFt/JIdYuyIQSxivHtxknle22CP8exjmt1wiDMrxqbauPzveRUDW0zr1/KX+jtG9jD+UtMiW+2957R8xvtZm3o+1LOB7c+JPCAxPke2vzaeJ9/P+H9eBunWn9p+zOd6nhu1OqvVteQEyYNaV4ek32V6ThvPyw4Psk8dfM/36TPaCtHdXrvAaO/89q/SzvntfqCdN9xAbW0Nkv5IbvXZrpS/62UPltBdWX4oqqmtRfIfSXT4SvBqjcm5VrrAPQ89qNpkXIwLm1CHsphSjEoow0h7MbLri1o9ecZ6rc3uGFTEZiA2NR+pWb0QI/laDCNfvowZU21qS4HqErVkfUx5IRLLCzEUUNvxfjPdap3x2LggCxt+y8YsdxbcCRlITs9CfEomElOzEJeQBIc9Fs2wodbpRnWDE+XlFaisLEdZeTnsTXXIiqnCBTEVyI0rRz9HFfKwDQ4ZM1ZJLs82Ki+rgeWPBfLHePa9xwF5YzxRB4RohORq65UuW0KXPytRWVV+TitxWMn03LpGl3JUSSSWvJa9Z/N93eQ9r67lPWOqrOSWM84Buj4lMdRItxUr9pnxPabltayc6bCXqe8znmMpiLWlev+Wvc3Yq2PwHpPvP+q9hBjEJhrve2wnjy3YhDg44XA7EeduhAMuONAAh9vV8re816j+9hx3wu42jsnrBtibPX/Lcbuxb5Z9o9rb4EKsuwmxzU7Y3PLaiVi3q+W1Czaf47Zmz34HxGkvm9m5wExGbOgurFdpCm7Y4I7xbDLuqdfqmMfhJXv1noygfsc8x2XvsZrVe2ov1zCOee6x/X25j9xZrrP9uOC9T8s1PMdiWt9DMK7vfc/ver73bfmc7722f9b3ve332v4Zn3u2+tu4fgyqahus7ZQS51N8vGQo347xt0zt86ehoUFtvqHswu22csR+f2urcyVSQvJHXbTTRRiSMcRrREvIoC/qS2JCGprPfA8x089FzLrvgDn3e9932+xwT/6nJ5fU/7d3J0BSVPcDx3+zs/eyB9cuh7AgyqX8/ygGkgieoUyiWFawtExQi3jEqCSUGCMaD5J/YowxiaLGsoIkATWJSRmDMaiJckREMYjKoVE5Fl2OhUXZe673r9+bnWFm9mCH3Z2d7vl+rHFm3/Q03a9fv/7169evQ6Hw9B5Pm/loF18N2hPvlOxOutaxM04YaF8/uuhkqT7UKJt2fyqbqw/LzgMNsuNgg32KiB44mv0h+3QRtW1/eldGqVfV1wuQRiI9/XQ8ktGdTpknPimWJinxNEiJNNp3/bvQ0ywF0iLl4pNRnhb7uVCapcDjs5/zpFm8WS2SldUskuWTkCcoAW9Q/J6Q+LNC4vOExJdlpCnLI02eLPF5PK0vkZbWz4nvbdPEftZbEju6LTEgxr7arUYju52n9XNa3uDcR3pz6AcnSnggU8YjP6xgU/dvvTmajmKe/5OHpSQ3od7TDkStnYj2mTLZGqqUbaZSPpIRMnj0/8p5Z02X/x09tMMYJi5deyDU77W9bT111eI5XC1Ge+FGe+J+Ip6GGin0tMgYzx4ZI3uOLENHPa8ShWP8eK1ZqgGwp3SEmP6jRAaMFtN/tMjg8eIZcrJ4So+TUELcFGns73SdupDeG3Gc/hter9e+a3p3lzEd1ikx3W3rpLKzs+P+3XRbJ73IrMN76PhTXZ1PZ8ui02tDV6M/KP6gfjbS5Av3yIq89HtfMGR7eNm01ndNawkYafYHxOcPT9scCIp25tLxuLRXpL7rfO3nUOt75O+gEX9IpzNHpmv9OxBpKYuhqxbQ/4VMO+FK79fLR+S0vrr3dM5jZ0Sb/MMNZEH7nq2NZ57Akc/2Pfx3jufINJHfeCUo2XrZwBOy6Tq/7Jh0byTNE4pLi0wbfgVjvo+dR8z3+u6J/z7Lvoe/16YXTfd4wu9Z0Zc58l3re1bcZz1X7loA79HfmRDx/jE63GLc3Silgwhqw1SsSABWUNB2J9fb+hYtWtQm/eTSk6WgqMDe1jOyZKScMvwUmZA/QbJ8WSKHRaoOV9nxF/RVU1MT1+A1cOBAKS4ulj2f+cR/5oNStPNFKdz1kuQH6sQ77H+k+rhZ4i8dJVJVFe3JpQcrvd88lt57HggEpLq6OpqmlX1lZaVdx3379kXTc3JyZPjw4VJfX297hEXoOldUVNj7NfXezYh+/fqFe5QFG2ViiU8mluhVlXwpKxtjx5fY+fEe2XOoXg41BqS2KSCe3AIJZeXI3ppaadCrJnqA8IckNy/ftvoerquzFX3QhK+I5OTm2c8NjeF80breiJH8vHwb/EW2iYlpOAwGQ+Lz+8MTh1dWcnJzJRgMit8fiMsDXd9AMCjBwJGDRZZ2x83OFn8gIKHgkQOlN1vvZ/fa2zq1p1OE5rnXmyU+nz/uYJuTk20Pti0+X1xFk5MbHs/I1xJ/yMrNy7W/9/tirjDo03lzc+2BOXHZc3Nz7Lrqto0ue1amrFOBZHn723XyBQKyXwf77KF10gNDdjAoBTnhq/2mpbH1SpPfHkA1ziowPjF+f+sBK3wgy8v22CtFoUCg9WAZPrDlZBsxIV0Wv3gkIB5PQDz6nTckIRMQYzQ9KCFPSIwewLK0/Ot3mmYkpAer1osLNs3ePqzp+q5XFTTI07+O/GevHuhL59PasmXnHe50ZOdpg0P7d/hdS4X9bXR/0unD/RpsfrX+NrINI/tibFrkt63/YvjvuPTY+cfOJ5wavdLSOm1kOvseOc9NDNJtw190JtHpo+2Bsemx58ox89H0SM+hmDWKX7GEZY+0GSamxS5De9rMPS4PYlapnVWN5nE7WdBe+6UnieXo6Lt2sjHpdLf3BU03vhaPbOvlf6OjmGdPv5Mke1CxvQXDm18spqxSNh8ulNc/LZUNvkqp9ZTKsP6FcvrYIXJVuVcKs7Su99u4JRrz7Nlj6+8IjT00Btm9e3dM3T1Mho07rf2YZ1i5BGqrpHbHO+Jt2CeBw3ts7GL8TeJv+FRM0yHJCml9ryc8OmB6uMeB3mrnzSuU/IJ+UlxSKkUDhkpjdqnUS6EECwbZV/6QE2VQxXA5eOCAjZMiyqRYyjweqdm/v/04rkvr1DdxnH7WOK62tjZ+nY4Wm6bxOkViUzeuk56f6N0cmbqdhgwstg+fytMGaj245IhUHBdep127drWuk37hlWHDRiS9TvrvtbdOdXV1ceuUl58vAweVy8HaQ3Lg0Kf2nCVojBQUFElp//5Sc+Cg1Nc32HMYjduK+hVLYVE/OXDgoDQ2N9veX/qbfsUlkpdfIPtrasTnD/cK0/mUlJSKNydH9u2vCc87ZOx3xfZBEh6prT0UjpNa44fSsjIbP3+qdZ2mtWZDSWmZjXvr6uvDcZ9d1yxbNppaWqSpsSkc/xmxjdSFRUXS1NQszS0t4UZ2Tc/JseWusbHJnl+F292MvZsoOydXGpuabH5GSlNubp7NN+3BbBsczZE8y/J6paGhIa7s5RcU2BissbHRXlvSl35bWFBg/x3tKR8bbxUWFNpzOl3GmA0oBfn59rzC5/dF4yT99/ScQ/M2oMveOrmuq54b+ny+6DmH/iY7J9uWGT2fCbY2lmq6PVfweqWlxRfXiKrz0LsRmlvi2ww0b7QU+luaoo1V+tIx07QjScDXbBuutEFKvy/Iy7E9yQI+35HGLY+R/FyvPa8IBf06ELedPjsr/KAPPbcwQe2xFl4efa5UTpZXgkFN13m0zser50UeCdptF24wi6TrMG2aL2LnHW5o09tS9dwr4PdFl1tfOV4dfkQkENB0OzB4OF0feqYXOnQZY6fP9ooJhSQUDMaki73d1ej5jF4QsaUvfB1Il9GEgvY3kem116BHG7RDQXvMjsSTeuzWZdT0Bvuwgqelu9J2oPN169bJGWecYSsn3bGUDnI+a9Ysu9MkjgnT3lXDESNG2Io29kk0brxy05V10t/oAUcrwZ7Ig3RYp+6kR8qIHpAjfzt9nbqznSLlIzJAnRvWqTvperDV/IiUDzesU3eW0d6e1dBg64/EeTt1nY4lPbIsmh5bPtywTt1Zdv2sx+WiosgNYc5fp6Old7YseuKnD2rpzYHOiXmcX6Yix12tRyI9ppy+Tonpblsn/TcTY0enr5Mbt1PsOvX0+U86rFNPL3s6rZPSeLOwMH44ACevkxu3k6cXYp607Sk1efJk21KqjVNnnnmmTVu7dq1MnTo1rpBKTA+dxNv9VOSEIVZHT8zozfTIxuut9KMtixYafSqPVspuWafupMfmR+z3Tl6njtK7soyJ+eGGdepuenvlw8nr1J1l1PKhDfwaiLtlnY41PbIsieXDDet0rOlaPvQKtjZKtTd/J67T0dI7W5b2pu9pxDzOL1O9EZclm+7mOro30juKHXtq2TtKZzsde9lL5X7Gdup+HZGKeILtJGkZ86TtkPPaQnrllVfKggULZMuWLfLKK6/Igw8+KDfccENfLxoAAAAAAAC6KW17Sqn7779frr/+epk2bZq9Qn/bbbfJJZdc0teLBQAAAAAAADc3SmlD1O9//3v7Qve1N0B8JiM/yA/KB/sL9Qf1KdBXiEOch23mPGwzZ2F7Zaa0Hei8u3QgQh3gvDcHGgUAAOjr+IOYBwAApFpPxR9pO6ZUT3Fpm9sx5YM+Bpb8ID8oH+wv1B/Upxxfevd421c4xjsHcZnzsM2ch23mLGwv5+mpuINGqQzBTk5+UD7YX6g/qE85vqTmeNtXaJRyDuIy52GbOQ/bzFnYXs5DoxQAAAAAAAAcy/U9pQAAAAAAAJB+aJTKIPo0Q5AflA/2F+oP6lOOL0DfIy5zHraZ87DNnIXtlZl4+h4AAEAP4el7AAAgExzm6XtdEwqFenlTOCcfDhw4QH6QH5QP9hfqD+pTji+9fLztK8Q8zkFc5jxsM+dhmzkL28t5eiru4Pa9DFJfX9/Xi5BWyA/yg/LB/kL9QX0K9BXiEOdhmzkP28xZ2F6ZiUYpAAAAAAAApFy2uJQxJnqfY1YWbW/ata6uro78aEV+xCM/yI/OUD7ID8pH12ncERuHpAIxj/NQrzoP28x52GbOwvbK3JjHtY1SBw8etO+VlZV9vSgAACDDaBxSWlqasn9LEfMAAACnxTyubZQaMGCAfa+qqkpZUJjurZgjRoyQ3bt3S0lJiWQ68oP8oHywv1B/UJ/2hs8++0xGjhwZjUNSgZjHeYhDnIdt5jxsM2dhe2VuzOPaRqnILXvaIEUjzBGaF+QH+dERygf50RnKB/lB+Ug+DkkFYh7nol51HraZ87DNnIXtlXkxD4MtAQAAAAAAIOVolAIAAAAAAEDKubZRKi8vT+666y77DvKD8sH+Qv1BfcrxheOtW+MPYh7nYZs5D9vMedhmzsL2ytxt5jGpfGYxAAAAAAAA4OaeUgAAAAAAAEhfNEoBAAAAAAAg5RzdKNXU1CTf/OY3pbi4WCoqKuQnP/lJh9Nu3LhRTjvtNMnPz5dTTjlFXn/9dXGbZPJj9uzZ4vF44l7PPfecuJHP55OJEyfKqlWrMrp8JJMfbi8fO3bskFmzZklpaamMHj1a7rnnHgmFQu1O++KLL8qECROkoKBAzjjjDPnvf/8rbpNMfkyZMqVN2di8ebO4zQcffCDnnXeerU/Hjh0rTzzxREbXH8nkh9vrj1jf+ta35KyzzurTspHMsR/Oq3PhrH0e6UFHp9FxboYMGSL9+/eXa6+9Vpqbm/t6sdCJvXv32vihrKxMRo4caetFOOdccvv27XL22WfbeGfcuHHJx33GwW644QYzZcoUs3XrVvPSSy+ZsrIy8+STT7aZrq6uzlRUVJjbb7/d7Ny509x6661m0KBB5vDhw8ZNupofavz48WbZsmWmpqYm+vL5fMZtmpubzcUXX6zjpplXXnml3WkypXx0NT/cXj5aWlrMSSedZObMmWM+/PBDs3LlSjN48GDzyCOPtJl2165dprCw0Pz61782O3bsMFdccYWZMGGCCQaDxi2SyY9QKGTzY/Xq1XFlIxAIGDfR7Ttu3Di7vbdv326ef/55W5+uWrUqI+uPZPLD7fVHrLVr1xqPx2POPPPMdr9PVdlI5tgPZ9W5cNY+j/Rx7733mvLychvrbtq0yYwdO9Z8//vf7+vFQie+/OUvm7PPPtts27bNrFmzxgwdOtQsXbqUPHPAuaTGiZMmTTJz58618c7ixYtNfn6+jRm7yrGNUo2NjXZlY0+sFy1aZGbMmNFm2scff9yMGjXKnlApfT/++OPNkiVLjFskkx96cpCdnW22bNli3EzXb/LkyfbVWSNMJpSPZPLD7eVDD3R5eXl2n4n48Y9/bE4//fQ20955551xwWdDQ4MpKioy//rXv0wm5oc2zGnZqa+vN25WXV1tZs+eHdd4cNFFF5n58+dnZP2RTH64vf6IbViYOHGiPcZ2dIKairKRzLEfzqtz4ax9HulBT5C1oXf58uXRNP187rnn9ulyoXN60XPFihXRv2+66SYbayD9zyVffvllu/1izw+0gfGOO+7o8rwde/vepk2bxO/3yxe/+MVo2umnny4bNmywXTZjrV+/XqZPn25vIVD6rr9z0y0WyeSH3oah3cTHjBkjbrZmzRrbjfDf//53p9NlQvlIJj/cXj7Gjx8vK1assLfjReg2b2hoaLdszJgxI/p3YWGh627PSiY/tm7dKsOGDZOioiJxs6FDh8qf//xnezuUeuONN2T16tX2VptMrD+SyQ+31x8ReluB1gXnnHNOh9Okomwkc+yH8+pcOGufR3rYsmWLHDhwQC688MJo2je+8Q355z//2afLhc7p/vXUU09JS0uL7Nu3T1544YV24wyk37mkxjunnnpq3PmBxiLJxDuObZT6+OOPZdCgQZKbmxtN05MlvV/44MGDbaYdPnx4XJpO+8knn4hbJJMf27Zts/fr3njjjfaeXQ1mX3rpJXGb6667Tn7xi18c9QQ6E8pHMvnh9vIxePBgmTlzZvRvPfg9/vjj7QaamVA2kskPLRv9+vWTSy+9VEaMGCFf+tKX5D//+Y+42YknnijTpk2T448/XubNm5eRZSSZ/HB7/aHee+89efTRR2192plUlI1kjv1wXp0LZ+3zSA8fffSR3c/Wrl1rGzp03LYFCxbYcXCQvpYvX24bOzTO1IthwWBQfvCDH/T1YqEL55I9Ee84tlFKA668vLy4tMjfOuhnV6ZNnM7JkskPPbjq9F/4whfk73//u5x//vny1a9+Vd58803JRJlQPpKRSeVDD3h69UxP3m6++WbJ9LJxtPzQsnHo0CG55JJL7ACGOgC8XjHZvXu3uNXTTz9tr9ZpL7l3331XMr2MHC0/3F5/aO8jHej47rvvlvLy8k6nTUXZSObYD+fVuXDWPo/0UF9fb1+33Xab/PKXv5SlS5fKs88+K7fccktfLxo6ccUVV9gGxHXr1slf//pXO0B9TU0NeeYAPRHvZItD6cjuiU9R0KtNKrZLdGfTJk7nZMnkh1bS3/3ud21LtJo0aZLtXvfYY4/ZpwRlmkwoH8nIlPKhtxjpE6v0Nornn3/eXpXpatkoKSkRt+lKfuiV4l/96lfRKySLFy+2XXmXLVtmy40bTZ482b5rgDt37lz7dJHI7ViZWH8cLT/cXn/85je/sbfL6ZOcjiYVZSOZYz+cV+fCWfs80kN2drY0NjbaeCXypMT77rtPvv71r9teHllZju2T4VqvvfaavPrqq7bHTaQurKurs4322vMtNs5A+tFYRG+Z7U6849i9UruI6ZUlPVBEaBcxzZSBAwe2mXbPnj1xaTptYjczJ0smP3THjpwwxI5xUF1dLZkoE8pHMjKhfOjV6Tlz5sif/vQn+ctf/iLnnntuRpeNruaH1+tt02VXH/vqprKhdCwDvUqXuA/s3LmzzUE3E8pIMvnh9vrjySeflLfeestewdXbFH/605/a2w30c1VVVcrLRjLHfjivzoWz9nmkhyFDhkTjk9jjELc1py/tca+3osc2zuutlzt27GgTZyD99ES8k+Xkq7XaEq5d/CL03uGpU6e2aU39/Oc/bw8gkUE/9V1bYzXdLZLJj6uvvlouv/zyuDQ94OqtOJkoE8pHMjKhfGhPDj3J1lvQLrjggg6n0zKg+1GEDkSreeG2stHV/NBxUGLv79cr/W+//baryobSxpbZs2fL3r17o2l6+5nespZ4op8J9Ucy+eH2+kMHYdVxs3SAcX3p+AraA0w/6/gJqS4byRz74bw6F87a55EetF7MycmRjRs3RtN0G+rDOrThA+lHH46ijU96ESx2OAAdL1EbhJHeNK7R/S32gR0aiyQV7xgHu/baa82UKVPM5s2b7aMIy8rKzB//+Ef7XU1NjWlubrafP/vsMzNo0CBz++23m127dtn38vJyU1dXZ9ykq/nx7LPP2kd2L1u2zD7iXR9FrI+5r6qqMm4V+9jKTC0fXc0Pt5eP9evX2/V/6KGH7HpHXrW1tfYxwvpZH2uvtm/fbh+3/vDDD5udO3eauXPnmpN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      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 芯层 vs 价层轨道的径向概率密度对比\n",
    "core_specs = [\n",
    "    (0, 0, \"1s\"),\n",
    "    (0, 1, \"2s\"),\n",
    "    (1, 0, \"2p\"),\n",
    "]\n",
    "valence_specs = [\n",
    "    (0, 2, \"3s\"),\n",
    "    (1, 1, \"3p\"),\n",
    "]\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(12, 5), sharey=True)\n",
    "for ax, specs, title, rmax in [\n",
    "    (axes[0], core_specs, \"Core orbitals\", 4.0),\n",
    "    (axes[1], valence_specs, \"Valence orbitals\", 10.0),\n",
    "]:\n",
    "    for l, idx, label in specs:\n",
    "        u_array = al_ae.u_by_l[l][idx]\n",
    "        prob = np.abs(u_array) ** 2\n",
    "        ax.plot(al_ae.r, prob, label=label)\n",
    "    ax.set_xlim(0.0, rmax)\n",
    "    ax.set_xlabel(\"r (Bohr)\")\n",
    "    ax.set_title(title)\n",
    "    ax.grid(alpha=0.4, linestyle=\"--\")\n",
    "    ax.legend()\n",
    "axes[0].set_ylabel(r\"$|u_l(r)|^2$\")\n",
    "fig.suptitle(\"Al: Core vs Valence orbital distribution\", fontsize=14)\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b8ac1ba",
   "metadata": {},
   "source": [
    "图中可以看到芯层轨道近似全部密集在 2 Bohr 内，而价层轨道在 5–10 Bohr 仍有显著概率。赝势设计的关键就是在 `r < r_c` 范围保持与该图相同的芯层行为，同时在 `r > r_c` 让波函数较为平滑、易于被平面波展开。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2e78ca9",
   "metadata": {},
   "source": [
    "## 小结与下一步\n",
    "- `solve_ae_atom` 将 AtomSCF 的基础求解封装为一个稳定的 API，直接产出后续步骤需要的径向网格、波函数与能量分解。\n",
    "- 通过对比芯层/价层波函数与能量，我们获得了选择截断半径、确定价芯分离策略的定量依据。\n",
    "- 在进入 02-TM 伪化教程前，建议尝试不同的 `grid_params` 和 `scf_params` 组合，体会它们对总能量与轨道柔软度的影响。\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "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": 5
 },
 "nbformat": 4,
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}