Local_Search/n_queens_fast_conflict_calculation_with_numba.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Speeding up the objective function calculation using numba\n",
    "\n",
    "The objective function is evaluated over and over again and it makes sense to spent some time to make it faster. Here we use the just-in-time compilation option from `numba`.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The n-Queens Problem\n",
    "\n",
    "* __Goal:__ Find an arrangement of $n$ queens on a $n \\times n$ chess board so that no queen is on the same row, column or diagonal as any other queen.\n",
    "\n",
    "* __State space:__ An arrangement of the queens on the board. We restrict the state space to arrangements where there is only a single queen per column. We represent a state as an integer vector $\\mathbf{q} = \\{q_1, q_2, \\dots, q_n\\}$, each number representing the row positions of the queens from left to right. We will call a state a \"board.\"\n",
    "\n",
    "* __Objective function:__ The number of pairwise conflicts (i.e., two queens in the same row/column/diagonal).\n",
    "The optimization problem is to find the optimal arrangement $\\mathbf{q}^*$ of $n$ queens on the board can be written as:\n",
    "\n",
    "  > minimize: $\\mathrm{conflicts}(\\mathbf{q})$\n",
    "  >\n",
    "  > subject to: $\\mathbf{q} \\ \\text{contains only one queen per column}$\n",
    "\n",
    "  Note: the constraint (subject to) is enforced by the definition of the state space.\n",
    "\n",
    "* __Local improvement move:__ Move one queen to a different row in its column.\n",
    "\n",
    "* __Termination:__ For this problem there is always an arrangement $\\mathbf{q}^*$ with $\\mathrm{conflicts}(\\mathbf{q}^*) = 0$, however, the local improvement moves might end up in a local minimum. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objective function calculation\n",
    "\n",
    "### Naive $O(n^2)$ Implementation\n",
    "Naive implementation with nested loops. This is $O(n^2)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import colors\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [],
   "source": [
    "def conflicts_naive(board):\n",
    "    \"\"\"Calculate the number of conflicts, i.e., the objective function.\"\"\"\n",
    "    \n",
    "    board = np.array(board)\n",
    "    \n",
    "    n = len(board)\n",
    "    val = 0\n",
    "\n",
    "    # check horizontal (we do not check vertical since the state space is restricted to one queen per col)\n",
    "    for i in range(n): val += math.comb(np.sum(board == i), 2)\n",
    "    #print(f\"Horizontal value: {val}\")\n",
    "    \n",
    "    # check for each queen diagonally up and down (only to the right side of the queen)\n",
    "    for j in range(n):\n",
    "        q_up = board[j]\n",
    "        q_down = board[j]\n",
    "     \n",
    "        for jj in range(j+1, n):\n",
    "            q_up -= 1\n",
    "            q_down += 1\n",
    "            if board[jj] == q_up: val += 1\n",
    "            if board[jj] == q_down: val += 1\n",
    "        #print(f\"Value after queen {j}: {val}\")\n",
    "       \n",
    "    return(val)    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $O(n)$ Implementation\n",
    "\n",
    "A better implementation that should be $O(n)$. Idea: \n",
    "\n",
    "1. Count how many queens are in each row (no need to check columns) and how many are in each diagonal.\n",
    "2. Convert the number of $n$ queens in a row (diagonal) into the numbner of pariwise conflicts in $n$ choose 2. We use a faster special case for the `comb()` function to calcualte the conflicts given the number of queens.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "def comb2(n): return n*(n-1)//2 # this is n choose 2 equivalent to math.comb(n, 2); // is int division\n",
    "\n",
    "def conflicts(board):\n",
    "    \"\"\"Calculate the number of conflicts, i.e., the objective function.\"\"\"\n",
    "\n",
    "    n = len(board)\n",
    "    \n",
    "    horizontal_cnt = [0] * n\n",
    "    # we have double the diagonals compared to columns!\n",
    "    diagonal1_cnt = [0] * 2 * n\n",
    "    diagonal2_cnt = [0] * 2 * n\n",
    "    \n",
    "    for i in range(n):\n",
    "        horizontal_cnt[board[i]] += 1\n",
    "        diagonal1_cnt[i + board[i]] += 1\n",
    "        diagonal2_cnt[i - board[i] + n] += 1\n",
    "    \n",
    "    return sum(map(comb2, horizontal_cnt + diagonal1_cnt + diagonal2_cnt))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Compiled $O(n)$ Implementation\n",
    "We can use just-in-time compilation for the conflicts function. Code provided by Troy McNitt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numba import njit\n",
    "\n",
    "# with jit (cannot use some Python functions like sum and map)\n",
    "@njit()\n",
    "def comb2_jit(n): return n*(n-1)//2 # this is n choose 2 equivalent to math.comb(n, 2); // is int division\n",
    "\n",
    "@njit()\n",
    "def conflicts_jit(board):\n",
    "    \"\"\"Calculate the number of conflicts, i.e., the objective function.\"\"\"\n",
    "\n",
    "    n = len(board)\n",
    " \n",
    "    cnt = [0] * (5 * n)\n",
    " \n",
    "    for i in range(n):\n",
    "        cnt[board[i]] += 1\n",
    "        cnt[(n) + (i + board[i])] += 1\n",
    "        cnt[(3 * n) + (i - board[i] + n)] += 1\n",
    " \n",
    "    conflicts = 0\n",
    "    for x in cnt:\n",
    "        conflicts += comb2_jit(x)\n",
    " \n",
    "    return conflicts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compare Timing\n",
    "\n",
    "Compare runtime on 50 random boards of different sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(1234)\n",
    "def random_board(n):\n",
    "    \"\"\"Creates a random board of size n x n. Note that only a single queen is placed in each column!\"\"\"\n",
    "    \n",
    "    return(np.random.randint(0,n, size = n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Times for 8x8 board in microseconds\n",
      "naive: 26.115750006283633, linear: 5.600849908660166, jit: 0.5632500688079745\n"
     ]
    }
   ],
   "source": [
    "import timeit\n",
    " \n",
    "# run it once to force compilation\n",
    "conflicts_jit(random_board(4))\n",
    "    \n",
    "reps = 20\n",
    "x = []\n",
    "naive_times = []\n",
    "linear_times = []\n",
    "jit_times = []\n",
    " \n",
    " \n",
    "for i in [8] + list(range(50, 500, 50)):\n",
    "    # do reps replications on random boards\n",
    "    boards = [random_board(i) for _ in range(reps)]\n",
    " \n",
    "    #print(f\"Doing: {i}\")\n",
    "\n",
    "    # number = 1 means we only run it once in timeit \n",
    "    naive = timeit.timeit(\n",
    "        lambda: [conflicts_naive(board) for board in boards], number=1\n",
    "    )\n",
    "    linear = timeit.timeit(\n",
    "        lambda: [conflicts(board) for board in boards], number=1\n",
    "    )\n",
    "    jit = timeit.timeit(\n",
    "        lambda: [conflicts_jit(board) for board in boards], number=1\n",
    "    )\n",
    "\n",
    " \n",
    "    x.append(i)\n",
    "    naive_times.append(naive)\n",
    "    linear_times.append(linear)\n",
    "    jit_times.append(jit)\n",
    "\n",
    "# average time per board in microseconds\n",
    "naive_times = np.array(naive_times) / reps * 1e6\n",
    "linear_times = np.array(linear_times) / reps * 1e6\n",
    "jit_times = np.array(jit_times) / reps * 1e6\n",
    "\n",
    "print(\"Times for 8x8 board in microseconds\")\n",
    "print(f'naive: {naive_times[0]}, linear: {linear_times[0]}, jit: {jit_times[0]}')\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
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aoXHjxlixYgXOnTuH7du3Izw8XO6yiYioBsSnZCAqIRUKBRDRz0fuch4KQxPVGBcXF+zZswcajQZ9+vSBn58fJk2aBBsbGxgYGMDAwADr1q1DXFwcfH19MXnyZMyfP1/usomIqJoJITBnU0lHloPbuaK1i5XMFT0chRDV/B30BkqtVsPa2hqZmZmwstL9ZcjPz0dSUhI8PDxgYmIiU4VE9Rv/zoj0V/TJdIxbfQgqIwPsmNoTLjamcpckud/79914pomIiIhqTLFGi7l3hksZ/biHXgWmqmJoIiIiohqz7mAKzl/Pga25Eq/2bCF3OY+EoYmIiIhqRHZBMRZtPQMAeOPJlrAyqdvjhjI0ERERUY1YEXMeN7IL4d7YDC8GNpO7nEfG0ERERETVLl2dj6/+TQIAzOjrDaVR3Y8cdX8PiIiISO98Gn0GeUUatG9qg76+TnKXUy0YmoiIiKhanUnPwvpDKQCAd0J8oFDUreFS7oWhiYiIiKpV5OZT0AqgbxsndGhmK3c51YahiYiIiKrN3nM3sCPxOowMFJjRz1vucqoVQxPd16hRozBo0CAAQM+ePTFp0iRZ66lOs2fPRtu2baXnZff1Ye3cuRMKhQIZGRmPtJ6q1FTd26xpFy9ehEKhQHx8vNylEFE102oFPt5c0pHlsMCm8LCrXwPTlx96nqiMxYsXo3Sknd9++w3Gxv/1seHu7o5JkybV2SA1depUvP7663KXcV9lX3+gJLi2bdsWixYtkq8oIqJ7+OPoVZy4qoalyghv9GoldznVjqGJ7sva2lr62da2/lyXBgALCwtYWFjIXcZ9lX39iYj0WX6RBvP/TgQATOjZAo0tVDJXVP1kvTy3a9cuDBw4EC4uLlAoFNi4caPOfIVCUeFj/vz5Uht3d/dy8+fOnauznoSEBHTr1g0mJiZwc3PDvHnzytXy888/w9vbGyYmJvDz88PmzZtrZJ/rmntdnuvZsycuXbqEyZMnS6/7vWRkZOCVV16Bo6MjTExM4Ovri6ioKGn+r7/+ijZt2kClUsHd3R0LFizQWd7d3R0fffQRRowYAQsLCzRr1gx//PEHrl+/jqeffhoWFhbw9/fHoUOHpGVWrVoFGxsbbNy4Ea1atYKJiQmCg4ORkpIitbn78tzdtFotIiMj4eHhAVNTUwQEBOCXX37RabN582Z4enrC1NQUTzzxBC5evHjf13Pq1KkYMGCA9HzRokVQKBTYsmWLNK1ly5b4+uuvAei+/qNGjUJMTAwWL14sveZltxcXF4eOHTvCzMwMjz32GBITE+9ZR+klst9++w1PPPEEzMzMEBAQgNjY2Pu+PosWLYK7u7v0vLS+OXPmwNHRETY2Nvjggw9QXFyMadOmwdbWFq6urli5cmW5Gk6fPo3HHntM+p2IiYmR5mk0GowZM0Z67b28vLB48eL7vrZEJK/v9l7ElYw8OFmZYHRXD7nLqRGyhqacnBwEBARg6dKlFc5PTU3VeXz77bdQKBQYMmSITrsPPvhAp13ZSy5qtRp9+vRBs2bNEBcXh/nz52P27NlYsWKF1Gbv3r0IDQ3FmDFjcOTIEQwaNAiDBg3C8ePHa2bHAQghkFuUW+uPspd6HsVvv/0GV1dXnde+IlqtFv369cOePXvwww8/4OTJk5g7dy4MDQ0BlLzRP//88xg6dCiOHTuG2bNnY+bMmVi1apXOej799FN07doVR44cQUhICIYPH44RI0bgpZdewuHDh9GiRQuMGDFCZ/9yc3Px8ccfY/Xq1dizZw8yMjIwdOjQSu9jZGQkVq9ejeXLl+PEiROYPHkyXnrpJenNPSUlBYMHD8bAgQMRHx+PsWPH4q233rrvOnv06IHdu3dDo9EAAGJiYmBnZ4edO3cCAK5cuYLz58+jZ8+e5ZZdvHgxgoKCMG7cOOk1d3Nzk+a/8847WLBgAQ4dOgQjIyOMHj36gfv4zjvvYOrUqYiPj4enpydCQ0NRXFxcyVeoxPbt23H16lXs2rULCxcuxHvvvYcBAwagUaNG2L9/PyZMmIBXXnkFly9f1llu2rRpmDJlCo4cOYKgoCAMHDgQN2/eBFDye+Pq6oqff/4ZJ0+exKxZs/D2229j/fr1VaqNiGrH7ZxCLNlxDgAwpY8nTJWGMldUM2S9PNevXz/069fvnvOdnHQ7w/r999/xxBNPoHnz5jrTLS0ty7UttWbNGhQWFuLbb7+FUqlEmzZtEB8fj4ULF2L8+PEASt6M+vbti2nTpgEAPvzwQ0RHR2PJkiVYvnz5o+ziPeUV5yFwbWCNrPt+9r+4H2bGZo+8HltbWxgaGt73tQeArVu34sCBAzh16hQ8PT0BQOf4LVy4EL169cLMmTMBAJ6enjh58iTmz5+PUaNGSe369++PV155BQAwa9YsLFu2DJ06dcJzzz0HAJgxYwaCgoKQnp4u1VNUVIQlS5YgMLDkdf7uu+/g4+ODAwcOoHPnzvfdv4KCAsyZMwdbt25FUFCQVPfu3bvx5ZdfokePHli2bBlatGghnRnz8vLCsWPH8Mknn9xzvd26dUNWVhaOHDmCDh06YNeuXZg2bZp0lnXnzp1o0qQJWrZsWW5Za2trKJVKmJmZVfiaf/zxx+jRowcA4K233kJISAjy8/NhYmJyz3qmTp2KkJAQAMD777+PNm3a4Ny5c/D2rvw3XmxtbfHZZ5/BwMAAXl5emDdvHnJzc/H2228DACIiIjB37lzs3r1bJ7ROnDhR+gC0bNkybNmyBd988w2mT58OY2NjvP/++1JbDw8PxMbGYv369Xj++ecrXRsR1Y7Pt59DVn4xvJ0sMbi9q9zl1Jg68+259PR0bNq0CWPGjCk3b+7cuWjcuDHatWuH+fPn63xSjo2NRffu3aFUKqVpwcHBSExMxO3bt6U2vXv31llncHCwzqWKuxUUFECtVus8qLz4+Hi4urpKgelup06dQteuXXWmde3aFWfPnpXOxgCAv7+/9LOjoyMAwM/Pr9y0a9euSdOMjIzQqVMn6bm3tzdsbGxw6tSpB9Z97tw55Obm4qmnnpLufbKwsMDq1atx/vx5qfbSQFaqNGDdi42NDQICArBz504cO3YMSqUS48ePx5EjR5CdnY2YmBgp+FRV2dfI2dkZgO7rUV3L3K1NmzYwMPjvnxJHR0edY2NoaIjGjRuXW2/Z18rIyAgdO3bUOTZLly5Fhw4dYG9vDwsLC6xYsQLJyclVqo2Ial7yzVx8v+8iAODt/j4wNKgfHVlWpM7cCP7dd9/B0tISgwcP1pn+xhtvoH379rC1tcXevXsRERGB1NRULFy4EACQlpYGDw/da6ulb7BpaWlo1KgR0tLSpGll26Slpd2znsjISJ1PwlVlamSK/S/uf+jlH2W7tbo90+rZXtlv7ZXeP1XRNK1WWy3by87OBgBs2rQJTZo00ZmnUj3azY09e/bEzp07oVKp0KNHD9ja2sLHxwe7d+9GTEwMpkyZ8lDrfZjX437LGBgYlLucW1RUdN91lK6nomlVOTbr1q3D1KlTsWDBAgQFBcHS0hLz58/H/v21/zdDRPc37+/TKNIIdGtlh+6e9nKXU6PqTGj69ttvMWzYsHKXGsLDw6Wf/f39oVQq8corryAyMvKR39zuJyIiQmfbarVa5/6SB1EoFNVymUxOSqVS52xQRfz9/XH58mWcOXOmwrNNPj4+2LNnj860PXv2wNPTU7rv6WEVFxfj0KFD0qW4xMREZGRkwMfH54HLtm7dGiqVCsnJyfc88+Pj44M//vhDZ9q+ffseuO4ePXrg22+/hZGREfr27QugJEj9+OOPOHPmTIX3M5WqzGteXezt7ZGWlgYhhBSoqrNvpX379qF79+4ASo5VXFwcJk6cCKDkd+Cxxx7Da6+9JrUvPcNHRPojPiUDUQmpUCiAiH4P/re1rqsTl+f+/fdfJCYmYuzYsQ9sGxgYiOLiYulbRU5OTkhPT9dpU/q89L6Qe7W53706KpUKVlZWOo+Gxt3dHbt27cKVK1dw48aNCtv06NED3bt3x5AhQxAdHY2kpCT89ddf0rfFpkyZgm3btuHDDz/EmTNn8N1332HJkiWYOnXqI9dnbGyM119/Hfv370dcXBxGjRqFLl26PPB+JqDkPrmpU6di8uTJ+O6773D+/HkcPnwYn3/+Ob777jsAwIQJE3D27FlMmzYNiYmJWLt2bbkb2CvSvXt3ZGVlISoqSgpIPXv2xJo1a+Ds7HzPS5lAyWu+f/9+XLx4ETdu3Ki2M2sV6dmzJ65fv4558+bh/PnzWLp0Kf76669qW//SpUuxYcMGnD59GmFhYbh9+7Z083qrVq1w6NAh/P333zhz5gxmzpyJgwcPVtu2iejRCSEwZ1PJJfXB7VzR2qX+vw/WidD0zTffoEOHDggICHhg2/j4eBgYGMDBwQFAyX0Tu3bt0rmsEB0dDS8vLzRq1Ehqs23bNp31REdHP/D+lIbugw8+wMWLF9GiRQvY29/7lOyvv/6KTp06ITQ0FK1bt8b06dOlsyXt27fH+vXrsW7dOvj6+mLWrFn44IMPdG4Cf1hmZmaYMWMGXnzxRXTt2hUWFhb46aefKr38hx9+iJkzZyIyMhI+Pj7o27cvNm3aJF3ubdq0KX799Vds3LgRAQEBWL58OebMmfPA9TZq1Ah+fn6wt7eXbrju3r07tFrtA+9nmjp1KgwNDdG6dWvY29vX6D0+Pj4++OKLL7B06VIEBATgwIED1RJmS82dOxdz585FQEAAdu/ejT/++AN2dnYAgFdeeQWDBw/GCy+8gMDAQNy8eVPnrBMRyS/6ZDoOXLwFlZEBpgbf+8NevSJklJWVJY4cOSKOHDkiAIiFCxeKI0eOiEuXLkltMjMzhZmZmVi2bFm55ffu3Ss+/fRTER8fL86fPy9++OEHYW9vL0aMGCG1ycjIEI6OjmL48OHi+PHjYt26dcLMzEx8+eWXUps9e/YIIyMj8X//93/i1KlT4r333hPGxsbi2LFjld6XzMxMAUBkZmaWm5eXlydOnjwp8vLyKr0+fTF06FAxbNgwucuospUrVwpra2u5y6BaVJf/zojqmsJijXji/3aIZjOixCd/nZK7nEdyv/fvu8l6punQoUNo164d2rVrB6Dk/qR27dph1qxZUpt169ZBCIHQ0NByy6tUKqxbtw49evRAmzZt8PHHH2Py5Mk6fTBZW1vjn3/+QVJSEjp06IApU6Zg1qxZUncDAPDYY49h7dq1WLFihdSB4caNG+Hr61uDe6/fiouLcfLkScTGxqJNmzZyl0NERHrkp4MpuHA9B7bmSkzo2ULucmqNQohq6u2wgVOr1bC2tkZmZma5+5vy8/ORlJQEDw+P+/aZo0/i4+Px2GOP4YknnsAPP/wgXcqsK1atWoVJkybVmUFs6dHVxb8zoroou6AYPefvwI3sQrz/vzYY+Zi73CU9kvu9f9+tznx7jmpX27ZtkZubK3cZD23UqFHVcl8UERHpWhFzHjeyC+FhZ44XA5vKXU6tqhM3ghMREZH80tX5+OrfJADA9GAvGBs2rBjRsPZWZrwSSlRz+PdFVPMW/nMGeUUadGjWCH19790tT33F0FQLSntHrsuXu4j0Xenf1929kRNR9UhMy8LPcSkAgLf7e0ud3jYkvKepFhgaGsLGxkYae8vMzKxB/rIR1QQhBHJzc3Ht2jXY2Ng8ck/yRFSxuX+dglYA/Xyd0KGZrdzlyIKhqZaU9i5e1cFQiahybGxs7tuLPxE9vL3nbmBH4nUYGSgwva+33OXIhqGpligUCjg7O8PBwaHCQU+J6OEZGxvzDBNRDdFqBT7eXDJcyrDApvCwM5e5IvkwNNUyQ0ND/uNORER1xu9Hr+DEVTUsVUZ4o1crucuRFW8EJyIiogrlF2nwf3+fAQBM6NkCjS1UMlckL4YmIiIiqtB3ey/iSkYenK1NMOZxD7nLkR1DExEREZVzO6cQS3acAwBM6eMFE2PeWsLQREREROV8vv0csvKL4eNshWfaNZG7HL3A0EREREQ6Lt3Mwff7LgIAIvp5w9CAfQsCDE1ERER0l3l/J6JII9CtlR26e9rLXY7eYGgiIiIiyZHk29iUkAqFAni7v4/c5egVhiYiIiICUDIsUeTm0wCAIe1d4eNsJXNF+oWhiYiIiAAA0SfTceDiLZgYG2BKH0+5y9E7DE1ERESEIo0Wc7eUnGUa87gHnK1NZa5I/zA0EREREdYdTMGF6zmwNVfilR4t5C5HLzE0ERERNXDZBcVYvLVkuJQ3e7WClYmxzBXpJ4YmIiKiBm5FzHncyC6Eh505XgxsKnc5eouhiYiIqAFLV+fjq3+TAAAz+nrB2JDR4F74yhARETVgC/85g7wiDTo2a4TgNk5yl6PXGJqIiIgaqMS0LPwclwIAiOjvA4WCw6XcD0MTERFRAxX51yloBdDP1wkdmjWSuxy9x9BERETUAO05dwM7E6/DyECB6X295S6nTmBoIiIiamC0WoE5m08BAF7q0gweduYyV1Q3MDQRERE1ML8fvYITV9WwVBnhjV6t5C6nzmBoIiIiakDyizT4v79LOrJ89YkWsDVXylxR3cHQRERE1ICs2nsRVzLy4GxtgtFdPeQup05haCIiImogbucUYumOcwCAKX28YGJsKHNFdYusoWnXrl0YOHAgXFxcoFAosHHjRp35o0aNgkKh0Hn07dtXp82tW7cwbNgwWFlZwcbGBmPGjEF2drZOm4SEBHTr1g0mJiZwc3PDvHnzytXy888/w9vbGyYmJvDz88PmzZurfX+JiIjk9Pn2c8jKL4aPsxWeaddE7nLqHFlDU05ODgICArB06dJ7tunbty9SU1Olx48//qgzf9iwYThx4gSio6MRFRWFXbt2Yfz48dJ8tVqNPn36oFmzZoiLi8P8+fMxe/ZsrFixQmqzd+9ehIaGYsyYMThy5AgGDRqEQYMG4fjx49W/00RERDK4dDMH3++7CAB4u783DA3YkWVVKYQQQu4iAEChUGDDhg0YNGiQNG3UqFHIyMgodwaq1KlTp9C6dWscPHgQHTt2BABs2bIF/fv3x+XLl+Hi4oJly5bhnXfeQVpaGpTKkpvd3nrrLWzcuBGnT58GALzwwgvIyclBVFSUtO4uXbqgbdu2WL58eYXbLigoQEFBgfRcrVbDzc0NmZmZsLKyepSXgoiIqNqFrT2MTQmp6O5pj9WjO8tdjt5Qq9Wwtrau1Pu33t/TtHPnTjg4OMDLywuvvvoqbt68Kc2LjY2FjY2NFJgAoHfv3jAwMMD+/fulNt27d5cCEwAEBwcjMTERt2/fltr07t1bZ7vBwcGIjY29Z12RkZGwtraWHm5ubtWyv0RERNXtSPJtbEpIhUIBRPRjR5YPS69DU9++fbF69Wps27YNn3zyCWJiYtCvXz9oNBoAQFpaGhwcHHSWMTIygq2tLdLS0qQ2jo6OOm1Knz+oTen8ikRERCAzM1N6pKSkPNrOEhER1QAh/uvI8tn2rvBx5tWQh2UkdwH3M3ToUOlnPz8/+Pv7o0WLFti5cyd69eolY2WASqWCSqWStQYiIqIHiT6ZjoMXb8PE2ADhfTzlLqdO0+szTXdr3rw57OzscO5cydclnZyccO3aNZ02xcXFuHXrFpycnKQ26enpOm1Knz+oTel8IiKiuqhIo8XcLSX374553APO1qYyV1S31anQdPnyZdy8eRPOzs4AgKCgIGRkZCAuLk5qs337dmi1WgQGBkptdu3ahaKiIqlNdHQ0vLy80KhRI6nNtm3bdLYVHR2NoKCgmt4lIiKiGrPuYAouXM9BY3MlJvRoIXc5dZ6soSk7Oxvx8fGIj48HACQlJSE+Ph7JycnIzs7GtGnTsG/fPly8eBHbtm3D008/jZYtWyI4OBgA4OPjg759+2LcuHE4cOAA9uzZg4kTJ2Lo0KFwcXEBALz44otQKpUYM2YMTpw4gZ9++gmLFy9GeHi4VMebb76JLVu2YMGCBTh9+jRmz56NQ4cOYeLEibX+mhAREVWH7IJiLN5aMlzKm71bwdLEWOaK6gEhox07dggA5R4jR44Uubm5ok+fPsLe3l4YGxuLZs2aiXHjxom0tDSdddy8eVOEhoYKCwsLYWVlJV5++WWRlZWl0+bo0aPi8ccfFyqVSjRp0kTMnTu3XC3r168Xnp6eQqlUijZt2ohNmzZVaV8yMzMFAJGZmVn1F4KIiKgaaTRaMXHtYdFsRpR4Yv4OUViskbskvVWV92+96aeprqtKPw9EREQ1ae5fp7E85jyMDRVYPToQQS0ay12S3qpX/TQRERFR5X2/7xKWx5wHAHwyxJ+BqRoxNBEREdUT206l473fS4YAm/KUJwa3d5W5ovqFoYmIiKgeSLicgYlrj0ArgBc6umHiky3lLqneYWgiIiKq41Ju5WL0qoPIK9Kgu6c9PnrGFwoFB+StbgxNREREdVhGbiFGrTyAG9mFaO1shS+GtYexId/eawJfVSIiojqqoFiD8d/H4fz1HLhYm2Dly51godLrEdLqNIYmIiKiOkirFZj6cwIOJN2CpcoIK1/uDEcrE7nLqtcYmoiIiOqgeX8n4s+jV2FsqMCXwzvAy8lS7pLqPYYmIiKiOubuvpgea2knc0UNA0MTERFRHcK+mOTD0ERERFRHsC8meTE0ERER1QHsi0l+DE1ERER6jn0x6Qe+4kRERHqMfTHpD4YmIiIiPcW+mPQLQxMREZGeYl9M+oWhiYiISA+V7Ytp3rPsi0kfMDQRERHpmbJ9MU3t44ln2rEvJn3A0ERERKRHyvbFNLSTG8KeYF9M+oKhiYiISE+U7Yuph6c9PhzEvpj0CUMTERGRHsjILcTIMn0xLWVfTHqHR4OIiEhm+UUajFt9CBfYF5NeY2giIiKSUUlfTEdx8OJtWJoYYdVo9sWkrxiaiIiIZPTJ36cRlZBa0hfTSx3g6ci+mPQVQxMREZFMvo+9iC9jLgBgX0x1AUMTERGRDLaeTMd7f5wAwL6Y6gqGJiIiolp2NCUDr//IvpjqGoYmIiKiWpRyKxdjvmNfTHURQxMREVEtYV9MdRuPFBERUS1gX0x1n6yhadeuXRg4cCBcXFygUCiwceNGaV5RURFmzJgBPz8/mJubw8XFBSNGjMDVq1d11uHu7g6FQqHzmDt3rk6bhIQEdOvWDSYmJnBzc8O8efPK1fLzzz/D29sbJiYm8PPzw+bNm2tkn4mIqOFhX0z1Q6Ui7meffVblFb/88suwtLx/XxM5OTkICAjA6NGjMXjwYJ15ubm5OHz4MGbOnImAgADcvn0bb775Jv73v//h0KFDOm0/+OADjBs3TnpedrtqtRp9+vRB7969sXz5chw7dgyjR4+GjY0Nxo8fDwDYu3cvQkNDERkZiQEDBmDt2rUYNGgQDh8+DF9f3yrvOxERUVnsi6l+UAghxIMaGRgYwNXVFYaGhpVaaUpKCs6cOYPmzZtXvhCFAhs2bMCgQYPu2ebgwYPo3LkzLl26hKZNmwIoOdM0adIkTJo0qcJlli1bhnfeeQdpaWlQKpUAgLfeegsbN27E6dOnAQAvvPACcnJyEBUVJS3XpUsXtG3bFsuXL69U/Wq1GtbW1sjMzISVlVWlliEiovrv+9iLmPl7SdcCn74QwK4F9ExV3r8rfXnu0KFDSEpKqtTD1NT0kXeiIpmZmVAoFLCxsdGZPnfuXDRu3Bjt2rXD/PnzUVxcLM2LjY1F9+7dpcAEAMHBwUhMTMTt27elNr1799ZZZ3BwMGJjY+9ZS0FBAdRqtc6DiIioLPbFVL9U6vLce++9BwsLi0qv9O2334atre1DF1WR/Px8zJgxA6GhoTpJ8I033kD79u1ha2uLvXv3IiIiAqmpqVi4cCEAIC0tDR4eHjrrcnR0lOY1atQIaWlp0rSybdLS0u5ZT2RkJN5///3q2j0iIqpn2BdT/VPp0FQVERERD1XMvRQVFeH555+HEALLli3TmRceHi797O/vD6VSiVdeeQWRkZFQqVTVWkdZEREROttWq9Vwc3Orse0REVHdwb6Y6qcqf9cxLy8PQgiYmZkBAC5duoQNGzagdevW6NOnT7UXWBqYLl26hO3btz/wemNgYCCKi4tx8eJFeHl5wcnJCenp6TptSp87OTlJ/6+oTen8iqhUqhoNZUREVDexL6b6q8pH8emnn8bq1asBABkZGQgMDMSCBQvw9NNPlzsL9KhKA9PZs2exdetWNG7c+IHLxMfHw8DAAA4ODgCAoKAg7Nq1C0VFRVKb6OhoeHl5oVGjRlKbbdu26awnOjoaQUFB1bg3RERU37EvpvqtyqHp8OHD6NatGwDgl19+gaOjIy5duoTVq1dXuWuC7OxsxMfHIz4+HgCQlJSE+Ph4JCcno6ioCM8++ywOHTqENWvWQKPRIC0tDWlpaSgsLARQcgP3okWLcPToUVy4cAFr1qzB5MmT8dJLL0mB6MUXX4RSqcSYMWNw4sQJ/PTTT1i8eLHOpbU333wTW7ZswYIFC3D69GnMnj0bhw4dwsSJE6v68hARUQPFvpgaAFFFpqam4tKlS0IIIZ577jkxe/ZsIYQQycnJwtTUtErr2rFjhwBQ7jFy5EiRlJRU4TwAYseOHUIIIeLi4kRgYKCwtrYWJiYmwsfHR8yZM0fk5+frbOfo0aPi8ccfFyqVSjRp0kTMnTu3XC3r168Xnp6eQqlUijZt2ohNmzZVaV8yMzMFAJGZmVml5YiIqH6Ys/mkaDYjSrR8e5PYc/a63OVQJVXl/btS/TSV5e/vj7Fjx+KZZ56Br68vtmzZgqCgIMTFxSEkJOS+3zirz9hPExFRw8W+mOquGumnqdSsWbMwdepUuLu7IzAwULrv559//kG7du0ermIiIqI6in0xNRxVPtMElPRvlJqaioCAABgYlOSuAwcOwMrKCt7e3tVeZF3AM01ERA3P0ZQMDF2xD3lFGgzt5IbIwX7sWqCOqcr790Pd0u/k5FTu6/idO3d+mFURERHVSeyLqeGpcmjKz8/H559/jh07duDatWvQarU68w8fPlxtxREREekj9sXUMFU5NI0ZMwb//PMPnn32WXTu3JmpmoiIGhT2xdRwVfkoR0VFYfPmzejatWtN1ENERKS32BdTw1blc4lNmjSBpaVlTdRCRESk1z75+zSiElJhbKjAly91gKcj3w8bkiqHpgULFmDGjBm4dOlSTdRDRESkl76PvYgvYy4AAOY964/HWtrJXBHVtipfnuvYsSPy8/PRvHlzmJmZwdjYWGf+rVu3qq04IiIifcC+mAh4iNAUGhqKK1euYM6cOXB0dOSN4EREVK8dTcnA6z8egVYAQzu5IeyJlnKXRDKpcmjau3cvYmNjERAQUBP1EBER6Q32xURlVfmeJm9vb+Tl5dVELURERHqDfTHR3ap89OfOnYspU6Zg586duHnzJtRqtc6DiIiormNfTFSRKv8G9O3bFwDQq1cvnelCCCgUCmg0muqpjIiISAbsi4nupcqhaceOHTVRBxERkV5gX0x0L1UOTT169KiJOoiIiGS3bOd59sVE91Spe5oSEhLKDcx7PydOnEBxcfFDF0VERFSbhBBYGH0Gn2w5DQCYFuzFvpionEqFpnbt2uHmzZuVXmlQUBCSk5MfuigiIqLaIoTAnM2n8Nm2swCAGX292RcTVahSl+eEEJg5cybMzMwqtdLCwsJHKoqIiKg2aLUCM38/jjX7Sz7ozx7YGqO6eshcFemrSoWm7t27IzExsdIrDQoKgqmp6UMXRUREVNOKNVrM+PUYfj18GQoF8MlgfzzfyU3uskiPVSo07dy5s4bLICIiqj1FGi0m/RSPTQmpMDRQYOHzAXi6bRO5yyI9x566iIioQckv0mDi2sPYeuoajA0V+Dy0Pfr6OsldFtUBDE1ERNRg5BVqMP77Q/j37A2ojAzw5fAO6OnlIHdZVEcwNBERUYOQlV+EMasO4cDFWzBTGuKbkZ0Q1KKx3GVRHcLQRERE9V5GbiFGfnsARy9nlgyN8nJndGjWSO6yqI5haCIionrtRnYBXvp6P06nZaGRmTG+HxMI3ybWcpdFdVClOre82/fff4+uXbvCxcUFly5dAgAsWrQIv//+e7UWR0RE9CjSMvPxwpexOJ2WBXtLFX56JYiBiR5alUPTsmXLEB4ejv79+yMjIwMajQYAYGNjg0WLFlV3fURERA8l5VYunv8yFuev58DF2gTrXwni4Lv0SKocmj7//HN89dVXeOedd2BoaChN79ixI44dO1atxRERET2MpBs5eOHLWCTfykVTWzOsnxAEDztzucuiOq7K9zQlJSWhXbt25aarVCrk5ORUS1FEREQPKzEtC8O+3o8b2QVoYW+ONWO7wMnaRO6yqB6o8pkmDw8PxMfHl5u+ZcsW+Pj4VEdNRERED+X4lUwMXRGLG9kF8HG2wk+vBDEwUbWpcmgKDw9HWFgYfvrpJwghcODAAXz88ceIiIjA9OnTq7SuXbt2YeDAgXBxcYFCocDGjRt15gshMGvWLDg7O8PU1BS9e/fG2bNnddrcunULw4YNg5WVFWxsbDBmzBhkZ2frtElISEC3bt1gYmICNzc3zJs3r1wtP//8M7y9vWFiYgI/Pz9s3ry5SvtCRETyirt0G6Ff7cPt3CIEuFrjx3GBsLNQyV0W1SNVDk1jx47FJ598gnfffRe5ubl48cUXsWzZMixevBhDhw6t0rpycnIQEBCApUuXVjh/3rx5+Oyzz7B8+XLs378f5ubmCA4ORn5+vtRm2LBhOHHiBKKjoxEVFYVdu3Zh/Pjx0ny1Wo0+ffqgWbNmiIuLw/z58zF79mysWLFCarN3716EhoZizJgxOHLkCAYNGoRBgwbh+PHjVXx1iIhIDnvP38Dwb/YjK78Ynd1t8cPYQNiYKeUui+ob8QhycnJEenr6o6xCAkBs2LBBeq7VaoWTk5OYP3++NC0jI0OoVCrx448/CiGEOHnypAAgDh48KLX566+/hEKhEFeuXBFCCPHFF1+IRo0aiYKCAqnNjBkzhJeXl/T8+eefFyEhITr1BAYGildeeaXS9WdmZgoAIjMzs9LLEBHRo9txOl14vrNZNJsRJV76ep/ILSiWuySqQ6ry/v1Q/TSVMjMzg4NDzYzZk5SUhLS0NPTu3VuaZm1tjcDAQMTGxgIAYmNjYWNjg44dO0ptevfuDQMDA+zfv19q0717dyiV/33iCA4ORmJiIm7fvi21Kbud0jal26lIQUEB1Gq1zoOIiGrXluNpGLf6EAqKtejt44CvRnSEqdLwwQsSPYQqh6abN28iLCwMrVu3hp2dHWxtbXUe1SUtLQ0A4OjoqDPd0dFRmpeWllYutBkZGcHW1lanTUXrKLuNe7UpnV+RyMhIWFtbSw83N7eq7iIRET2C3+OvIGztYRRpBEL8nbHspQ4wMWZgoppT5S4Hhg8fjnPnzmHMmDFwdHSEQqGoibr0XkREBMLDw6XnarWawYmIqJasO5CMiA3HIAQwpL0r5j3rD0ODhvl+RLWnyqHp33//xe7duxEQEFAT9UicnJwAAOnp6XB2dpamp6eno23btlKba9eu6SxXXFyMW7duScs7OTkhPT1dp03p8we1KZ1fEZVKBZWK38ogIqptK/ck4f0/TwIAXurSFB/8zxcGDExUC6p8ec7b2xt5eXk1UYsODw8PODk5Ydu2bdI0tVqN/fv3IygoCAAQFBSEjIwMxMXFSW22b98OrVaLwMBAqc2uXbtQVFQktYmOjoaXlxcaNWoktSm7ndI2pdshIiL98MXOc1JgGtfNAx8+zcBEtafKoemLL77AO++8g5iYGNy8efORbobOzs5GfHy81FlmUlIS4uPjkZycDIVCgUmTJuGjjz7CH3/8gWPHjmHEiBFwcXHBoEGDAAA+Pj7o27cvxo0bhwMHDmDPnj2YOHEihg4dChcXFwDAiy++CKVSiTFjxuDEiRP46aefsHjxYp1La2+++Sa2bNmCBQsW4PTp05g9ezYOHTqEiRMnVvXlISKiGiCEwMJ/EjFvSyIA4I1erfB2f58Ge4sIyaSqX807c+aM6NixozAwMNB5KBQKYWBgUKV17dixQwAo9xg5cqQQoqTbgZkzZwpHR0ehUqlEr169RGJios46bt68KUJDQ4WFhYWwsrISL7/8ssjKytJpc/ToUfH4448LlUolmjRpIubOnVuulvXr1wtPT0+hVCpFmzZtxKZNm6q0L+xygIioZmi1WvHhnydEsxlRotmMKPHFjnNyl0T1SFXevxVCCFGVkNW5c2cYGRnhzTffrPBG8B49elRPmqtj1Go1rK2tkZmZCSsrK7nLISKqF7RagZm/H8ea/ckAgPf/1wYjH3OXtyiqV6ry/l3lG8GPHz+OI0eOwMvL66ELJCIiepBijRbTf03Ab4evQKEAPhnsj+c78VvKJJ8q39PUsWNHpKSk1EQtREREAIDCYi3eXBeP3w5fgaGBAoteaMvARLKr8pmm119/HW+++SamTZsGPz8/GBsb68z39/evtuKIiKjhyS/SIGzNYWw7fQ3Ghgp8HtoefX3v3QUMUW2p8j1NBgblT04pFAoIIaBQKKDRaKqtuLqE9zQRET263MJijF8dh93nbkBlZIAvh3dAT6+aGa6LCKjhe5qSkpIeujAiIqJ7ycovwuhVB3Hw4m2YKQ3xzchOCGrRWO6yiCRVDk3NmjWriTqIiKgBy8gtxMhvD+Do5UxYmhhh1cud0aFZI7nLItJRqdD0xx9/oF+/fjA2NsYff/xx37b/+9//qqUwIiJqGG5kF+Clr/fjdFoWGpkZ4/sxgfBtYi13WUTlVOqeJgMDA6SlpcHBwaHCe5qklfGeJt7TRERUBWmZ+Xjx6324cD0H9pYqrBkbCE9HS7nLogak2u9p0mq1Ff5MRET0sFJu5WLY1/uRfCsXLtYmWDOuCzzszOUui+ieqtxP0+rVq1FQUFBuemFhIVavXl0tRRERUf124Xo2nv8yFsm3ctHU1gzrJwQxMJHeq3KXA4aGhkhNTYWDg+5XQG/evAkHBwdenuPlOSKi+0pMy8Kwr/fjRnYBWtibY83YLnCyNpG7LGqgarTLgdL+mO52+fJlWFvzxj0iIrq3Y5czMeLb/bidWwQfZyt8P6Yz7CxUcpdFVCmVDk3t2rWDQqGAQqFAr169YGT036IajQZJSUno27dvjRRJRER1X9ylWxj17UFkFRQjwNUa343uDBszpdxlEVVapUPToEGDAADx8fEIDg6GhYWFNE+pVMLd3R1Dhgyp9gKJiKju23vuBsauPoTcQg06u9vim1EdYWli/OAFifRIpUPTe++9BwBwd3fHCy+8ABMTXn8mIqIH25F4DRO+j0NBsRbdWtlhxfCOMFUayl0WUZVV+Z6mkSNHAij5tty1a9fKdUHQtGnT6qmMiIjqvC3HU/H6j0dQpBHo7eOAJS+2h4kxAxPVTVUOTWfPnsXo0aOxd+9enekNfcBeIiLS9Xv8FYSvPwqNViDE3xmLXmgLY8Mq93RDpDeqHJpGjRoFIyMjREVFwdnZucJv0hERUcO27kAyIjYcgxDAkPaumPesPwwN+H5BdVuVQ1N8fDzi4uLg7e1dE/UQEVEdt3JPEt7/8yQA4KUuTfHB/3xhwMBE9UCVQ1Pr1q1x48aNmqiFiIjquKU7zmH+34kAgHHdPPB2fx9ekaB6o8oXlz/55BNMnz4dO3fuxM2bN6FWq3UeRETU8AghsOCfRCkwvdGrFQMT1TtVHkbFwKAkZ939h9DQbwTnMCpE1FAJIfDRplP4ZncSAOCtft6Y0KOFzFURVU6NDqOyY8eOhy6MiIjql9zCYsz49Rj+PHoVAPD+/9pg5GPu8hZFVEOqHJp69OhRE3UQEVEdk3IrF+O/j8OpVDWMDBSY84wfnu/kJndZRDWmyqFp165d953fvXv3hy6GiIjqhr3nbiBs7WHczi1CY3MlvhjWHoHNG8tdFlGNqnJo6tmzZ7lpZe9vaqj3NBERNQRCCHy75yLmbD4FjVbAr4k1vhzeAS42pnKXRlTjqhyabt++rfO8qKgIR44cwcyZM/Hxxx9XW2FERKRf8os0eHvDMfx2+AoAYHC7Jpgz2I/DolCDUeXQZG1tXW7aU089BaVSifDwcMTFxVVLYUREpD+uZuRhwg9xSLicCUMDBd7p74OXu7qzSwFqUKocmu7F0dERiYmJ1bU6IiLSEweSbuG1NXG4kV2IRmbGWPJie3RtaSd3WUS1rsqhKSEhQee5EAKpqamYO3cu2rZtW111ERGRzIQQ+GF/Mt7/4wSKtQI+zlZYMbwD3GzN5C6NSBZVDk1t27aFQqHA3X1idunSBd9++221FUZERPIpKNbgvd9PYN3BFADAAH9nzHvWH2bKartAQVTnVHkYlaSkJFy4cAFJSUlISkrCpUuXkJubi71799bIIL7u7iXXzO9+hIWFASj5Nt/d8yZMmKCzjuTkZISEhMDMzAwODg6YNm0aiouLddrs3LkT7du3h0qlQsuWLbFq1apq3xciorogXZ2PoSv2Yd3BFCgUJT18fx7ajoGJGrwq/QUUFRVh9OjRWL58OVq1alVTNek4ePCgTjcGx48fx1NPPYXnnntOmjZu3Dh88MEH0nMzs/9OHWs0GoSEhMDJyQl79+5FamoqRowYAWNjY8yZMwdASRAMCQnBhAkTsGbNGmzbtg1jx46Fs7MzgoODa2EviYj0w+Hk25jwfRyuZRXAysQIn4W2Q08vB7nLItILVQpNxsbG5e5pqmn29vY6z+fOnYsWLVro9ExuZmYGJyenCpf/559/cPLkSWzduhWOjo5o27YtPvzwQ8yYMQOzZ8+GUqnE8uXL4eHhgQULFgAAfHx8sHv3bnz66af3DE0FBQUoKCiQnnOwYiKq6346mIyZG0+gUKOFp6MFVgzvCHc7c7nLItIbVb4899JLL+Gbb76piVoeqLCwED/88ANGjx6t8zXXNWvWwM7ODr6+voiIiEBubq40LzY2Fn5+fnB0dJSmBQcHQ61W48SJE1Kb3r1762wrODgYsbGx96wlMjIS1tbW0sPNjUMHEFHdVFisxcyNxzHj12Mo1GgR3MYRv73WlYGJ6C5VvkBdXFyMb7/9Flu3bkWHDh1gbq77R7Vw4cJqK+5uGzduREZGBkaNGiVNe/HFF9GsWTO4uLggISEBM2bMQGJiIn777TcAQFpamk5gAiA9T0tLu28btVqNvLw8mJqW7+k2IiIC4eHh0nO1Ws3gRER1zo3sArz2w2EcuHgLADDlKU+EPdESBgbsf4noblUOTcePH0f79u0BAGfOnNGZV9OdnH3zzTfo168fXFxcpGnjx4+Xfvbz84OzszN69eqF8+fPo0WLFjVWi0qlgkqlqrH1ExHVtGOXMzH++0NIzcyHhcoIi15oi96tHR+8IFEDVeXQtGPHjpqo44EuXbqErVu3SmeQ7iUwMBAAcO7cObRo0QJOTk44cOCATpv09HQAkO6DcnJykqaVbWNlZVXhWSYiorrut8OXEfHbMRQUa9HczhwrRnRESwcLucsi0mtVvqdJLitXroSDgwNCQkLu2y4+Ph4A4OzsDAAICgrCsWPHcO3aNalNdHQ0rKys0Lp1a6nNtm3bdNYTHR2NoKCgatwDIiL5FWu0+DDqJMLXH0VBsRZPejtg48SuDExElVAnOt3QarVYuXIlRo4cCSOj/0o+f/481q5di/79+6Nx48ZISEjA5MmT0b17d/j7+wMA+vTpg9atW2P48OGYN28e0tLS8O677yIsLEy6vDZhwgQsWbIE06dPx+jRo7F9+3asX78emzZtkmV/iYhqwq2cQkxcexh7z98EALz+ZEtM7u3J+5eIKqlOhKatW7ciOTkZo0eP1pmuVCqxdetWLFq0CDk5OXBzc8OQIUPw7rvvSm0MDQ0RFRWFV199FUFBQTA3N8fIkSN1+nXy8PDApk2bMHnyZCxevBiurq74+uuv2UcTEdUbJ6+qMf77Q7h8Ow9mSkMseC4A/fyc5S6LqE5RiLvHQ6GHolarYW1tjczMTFhZWcldDhGR5M+jVzHtl6PIL9Kiqa0ZvhrREV5OlnKXRaQXqvL+XSfONBERUdVptALz/07E8pjzAIBurezweWg72JgpZa6MqG5iaCIiqocyc4vw+roj2HXmOgDglR7NMT3YG4a8f4nooTE0ERHVM2fSszBu9SFcupkLE2MDzHs2AP8LcHnwgkR0XwxNRET1yJbjqQhffxS5hRo0sTHFihEd0MbFWu6yiOoFhiYionpAqxVYtPUMPtt+DgAQ1Lwxlg5rD1tz3r9EVF0YmoiI6jh1fhEmr4vHttMlnfi+3NUdb/f3gbFhnem/mKhOYGgiIqrDzl/PxrjVh3Dheg6URgaY84wfnu3gKndZRPUSQxMRUR217VQ6Jq2LR1ZBMZysTPDl8A4IcLORuyyieouhiYiojtFqBZbuOIeFW89ACKCTeyN8MawD7C1VcpdGVK8xNBER1SHZBcWYuv4otpxIAwC81KUpZg1oA6UR718iqmkMTUREdcSlmzkYt/oQzqRnw9hQgQ+e9kVo56Zyl0XUYDA0ERHVATFnruP1tYehzi+GvaUKy19qjw7NbOUui6hBYWgiItJjQgis2HUBn2w5Da0A2rrZ4MvhHeBoZSJ3aUQNDkMTEZGeyivUYPqvCfjz6FUAwPMdXfHhIF+ojAxlroyoYWJoIiLSQym3cvHK93E4maqGkYECswa2xvAuzaBQcMBdIrkwNBER6Zm9524gbO1h3M4tQmNzJZYOa48uzRvLXRZRg8fQRESkJ4QQWLnnIj7efAoarYBvEyt8ObwjmtiYyl0aEYGhiYhIL+QXafD2hmP47fAVAMAz7ZogcrAfTIx5/xKRvmBoIiKS2dWMPEz4IQ4JlzNhoADe7u+DMY978P4lIj3D0EREJKODF2/h1R/icCO7EDZmxlgS2h6Pt7KTuywiqgBDExGRDIQQWLM/GbP/OIFirYC3kyW+GtERbrZmcpdGRPfA0EREVMtu5xTi3d+PY1NCKgAgxN8Z85/1h5mS/yQT6TP+hRIR1aIdp69h+q8JuJ5VAEMDBab28cKEHs15/xJRHcDQRERUC7ILivFR1EmsO5gCAGhhb46Fz7dFgJuNvIURUaUxNBER1bB9F25i6s9Hcfl2HhQKYHRXD0wL9mJ3AkR1DEMTEVENyS/S4P/+TsQ3e5IgBNDExhT/91wAglqwd2+iuoihiYioBiRczkD4+qM4dy0bAPBCRze8O8AHlibGMldGRA+LoYmIqBoVabRYsv0cluw4B41WwM5ChU+G+KGXj6PcpRHRI2JoIiKqJmfTsxC+/iiOXckEAIT4OePDQb6wNVfKXBkRVQeGJiKiR6TVCny7Jwnz/k5EYbEW1qbG+ODpNvhfgAu7EiCqRwzkLuB+Zs+eDYVCofPw9vaW5ufn5yMsLAyNGzeGhYUFhgwZgvT0dJ11JCcnIyQkBGZmZnBwcMC0adNQXFys02bnzp1o3749VCoVWrZsiVWrVtXG7hFRPZByKxdDv9qHjzadQmGxFj087fHP5O54um0TBiaiekbvzzS1adMGW7dulZ4bGf1X8uTJk7Fp0yb8/PPPsLa2xsSJEzF48GDs2bMHAKDRaBASEgInJyfs3bsXqampGDFiBIyNjTFnzhwAQFJSEkJCQjBhwgSsWbMG27Ztw9ixY+Hs7Izg4ODa3VkiqjOEEPjpYAo+jDqJnEINzJSGeCfEBy92bsqwRFRPKYQQQu4i7mX27NnYuHEj4uPjy83LzMyEvb091q5di2effRYAcPr0afj4+CA2NhZdunTBX3/9hQEDBuDq1atwdCy5CXP58uWYMWMGrl+/DqVSiRkzZmDTpk04fvy4tO6hQ4ciIyMDW7ZsqXStarUa1tbWyMzMhJWV1aPtOBHptWvqfLz12zFsP30NANDJvRH+77kANGtsLnNlRFRVVXn/1uvLcwBw9uxZuLi4oHnz5hg2bBiSk5MBAHFxcSgqKkLv3r2ltt7e3mjatCliY2MBALGxsfDz85MCEwAEBwdDrVbjxIkTUpuy6yhtU7qOeykoKIBardZ5EFH9F5VwFX0W7cL209egNDTA2/29sW58EAMTUQOg15fnAgMDsWrVKnh5eSE1NRXvv/8+unXrhuPHjyMtLQ1KpRI2NjY6yzg6OiItLQ0AkJaWphOYSueXzrtfG7Vajby8PJiamlZYW2RkJN5///3q2E0iqgMycgsx8/cT+PPoVQBAGxcrLHy+LbycLGWujIhqi16Hpn79+kk/+/v7IzAwEM2aNcP69evvGWZqS0REBMLDw6XnarUabm5uMlZERDVlR+I1zPglAdfuDLIb1rMFJj7ZCkojvT9ZT0TVSK9D091sbGzg6emJc+fO4amnnkJhYSEyMjJ0zjalp6fDyckJAODk5IQDBw7orKP023Vl29z9jbv09HRYWVndN5ipVCqoVKrq2C0i0lPZBcX4eNNJ/HigZJDd5ncG2W3LQXaJGqQ69TEpOzsb58+fh7OzMzp06ABjY2Ns27ZNmp+YmIjk5GQEBQUBAIKCgnDs2DFcu3ZNahMdHQ0rKyu0bt1aalN2HaVtStdBRA3TgaRb6Ld4lxSYXu7qjs1vdGNgImrA9PpM09SpUzFw4EA0a9YMV69exXvvvQdDQ0OEhobC2toaY8aMQXh4OGxtbWFlZYXXX38dQUFB6NKlCwCgT58+aN26NYYPH4558+YhLS0N7777LsLCwqSzRBMmTMCSJUswffp0jB49Gtu3b8f69euxadMmOXediGSSX6TBgn8S8fXu/wbZnf+cPx5rYSd3aUQkM70OTZcvX0ZoaChu3rwJe3t7PP7449i3bx/s7e0BAJ9++ikMDAwwZMgQFBQUIDg4GF988YW0vKGhIaKiovDqq68iKCgI5ubmGDlyJD744AOpjYeHBzZt2oTJkydj8eLFcHV1xddff80+mogaoGOXMxG+Ph5n7wyy+3xHV8wc0JqD7BIRAD3vp6kuYT9NRHVXkUaLL3acx+fbz6L4ziC7cwf7oXdrDrJLVN9V5f1br880ERHVtHPXSgbZTbhcMshufz8nfDTIj4PsElE5DE1E1CBptQIr917EvC2nUVCshZWJET4c5MtBdononhiaiKjBSbmVi2m/HMW+C7cAAN097TFviD+crE1kroyI9BlDExE1GEIIrD+Ugg+jTiG7oJiD7BJRlTA0EVGDcC0rHxG/HsO2O4PsdmzWCAue5yC7RFR5DE1EVO9tSkjFuxuP4XZuEZSGBpjSxxNjuzWHoQHPLhFR5TE0EVG9lZFbiFm/n8AfHGSXiKoBQxMR1Us7E69hxq8JSFeXDLL7Ws8WeJ2D7BLRI2BoIqJ6JaegGB9vPoW1+5MBcJBdIqo+DE1EVG8cvHgLU9YfRfKtXAAlg+xOD/aGqdJQ5sqIqD5gaCKiOi+/SINPo89gxb8X/htk91l/PNaSg+wSUfVhaCKiOu34lZJBds+klwyy+1wHV8wc2BpWHGSXiKoZQxMR1UnFGi2+2Hken20rHWRXicjB/niKg+wSUQ1haCKiOufctWxMWR+Po3cG2e3n64SPBvmisYVK5sqIqD5jaCKiOkOjFfhu70V8UmaQ3Q+e9sXTbTnILhHVPIYmItJ7Qgj8fSIdC6MTpXuXurWyw7xn/eFsbSpzdUTUUDA0EZHeEkJg19kbWPBPIhLuXIqzMjHCtL7eeCmQg+wSUe1iaCIivXTw4i3M/zsRB5JuAQDMlIYY3dUD47o3h7UpvxlHRLWPoYmI9Mqxy5n4v38SEXPmOgBAaWSA4V2a4dWeLWDHG72JSEYMTUSkF86mZ2HBP2ew5UQaAMDIQIHnOrrhjV4ted8SEekFhiYiklXyzVws2noGG+KvQAhAoQAGtW2CSb1boVljc7nLIyKSMDQRkSzSMvPx2fazWH8wBcVaAQAIbuOI8Ke84OVkKXN1RETlMTQRUa26mV2AZTvPY/W+Sygs1gIAunvaY2ofT/i72shbHBHRfTA0EVGtyMwrwtf/XsC3u5OQU6gBAHRyb4SpfbwQ2LyxzNURET0YQxMR1ajcwmKs3HMRK3ZdQGZeEQDAr4k1pvTxRA9Pe/a1RER1BkMTEdWIgmIN1u5PxtId53EjuwAA0MrBAlP6eCK4jRPDEhHVOQxNRFStijVa/BJ3GZ9tO4urmfkAgKa2ZpjUuxWebtsEhgYMS0RUNzE0EVG10GoF/ky4ik+jz+DizVwAgJOVCV7v1RLPd3SDsaGBzBUSET0ahiYieiRCCESfTMfC6DM4nZYFALA1V+K1ni3wUpdmMDE2lLlCIqLqwdBERA9FCIHd527g//45g6MpGQAASxMjjO/WHC8/7gELFf95IaL6hf+qEVGVxV0qGUx334WSwXRNjQ3xcld3jO/eHDZmSpmrIyKqGXp9k0FkZCQ6deoES0tLODg4YNCgQUhMTNRp07NnTygUCp3HhAkTdNokJycjJCQEZmZmcHBwwLRp01BcXKzTZufOnWjfvj1UKhVatmyJVatW1fTuEdU5x69k4uWVBzBkWSz2XbgFpaEBRj3mjl3Tn8D0vt4MTERUr+n1maaYmBiEhYWhU6dOKC4uxttvv40+ffrg5MmTMDf/b0yqcePG4YMPPpCem5mZST9rNBqEhITAyckJe/fuRWpqKkaMGAFjY2PMmTMHAJCUlISQkBBMmDABa9aswbZt2zB27Fg4OzsjODi49naYSE+du5aFhdFnsPlYyWC6hgYKPNfBFa/3aoUmNhxMl4gaBoUQQshdRGVdv34dDg4OiImJQffu3QGUnGlq27YtFi1aVOEyf/31FwYMGICrV6/C0dERALB8+XLMmDED169fh1KpxIwZM7Bp0yYcP35cWm7o0KHIyMjAli1bKlxvQUEBCgoKpOdqtRpubm7IzMyElZVVNe0xkbxSbuVi0daz2HDkMrR3BtP9X4ALJvX2hIcdB9MlorpPrVbD2tq6Uu/fen157m6ZmZkAAFtbW53pa9asgZ2dHXx9fREREYHc3FxpXmxsLPz8/KTABADBwcFQq9U4ceKE1KZ379466wwODkZsbOw9a4mMjIS1tbX0cHNze+T9I9IX6ep8vLvxGJ5csBO/Hi4JTE+1dsRfb3bD4qHtGJiIqEHS68tzZWm1WkyaNAldu3aFr6+vNP3FF19Es2bN4OLigoSEBMyYMQOJiYn47bffAABpaWk6gQmA9DwtLe2+bdRqNfLy8mBqWv7yQ0REBMLDw6XnpWeaiOqyWzmFWB5zHt/tvYiCO4Ppdmtlhyl9vNDWzUbe4oiIZFZnQlNYWBiOHz+O3bt360wfP3689LOfnx+cnZ3Rq1cvnD9/Hi1atKixelQqFVQqVY2tn6g2qfOL8PW/Sfh2dxKyC0q+JNGhWclgukEtOJguERFQR0LTxIkTERUVhV27dsHV1fW+bQMDAwEA586dQ4sWLeDk5IQDBw7otElPTwcAODk5Sf8vnVa2jZWVVYVnmYjqi7xCDb6LvYjlMeeRkVsymG4bFytM7eOFnl4cTJeIqCy9Dk1CCLz++uvYsGEDdu7cCQ8PjwcuEx8fDwBwdnYGAAQFBeHjjz/GtWvX4ODgAACIjo6GlZUVWrduLbXZvHmzznqio6MRFBRUjXtDpD8KijVYdyAFS3acw/Wski80tLA3x5Q+XujbxgkGHB+OiKgcvf723GuvvYa1a9fi999/h5eXlzTd2toapqamOH/+PNauXYv+/fujcePGSEhIwOTJk+Hq6oqYmBgAJV0OtG3bFi4uLpg3bx7S0tIwfPhwjB07VqfLAV9fX4SFhWH06NHYvn073njjDWzatKnSXQ5U5e57IrkUa7T47fAVLN52Flcy8gAAro1MMam3J55px8F0iajhqcr7t16HpntdGli5ciVGjRqFlJQUvPTSSzh+/DhycnLg5uaGZ555Bu+++67Ojl+6dAmvvvoqdu7cCXNzc4wcORJz586FkdF/J9p27tyJyZMn4+TJk3B1dcXMmTMxatSoStfK0ET6TKsV2HQsFZ9Gn8GFGzkAAAdLFV7v1QovdHSD0qhOfZGWiKja1JvQVJcwNJE+up5VgL+Op2Lt/mRpMN1GZsZ4rWdLDA/iYLpERFV5/9bre5qIqOpu5RRiy/E0RCVcxb4LN6G987HIUmWEsd2aY/Tj7rA0MZa3SCKiOoihiageyMwrwt8n0hCVkIo9525Ao/3vBHKAmw0G+jtjSHtXNDLn2HBERA+LoYmojsrKL8LWU+mIOpqKXWevo0jzX1Bq42KFAf4uGODvDDdbs/ushYiIKouhiagOyS0sxrZT1xCVcBU7Eq+j8E6v3QDg5WiJAf7OCPF3RnN7CxmrJCKqnxiaiPRcfpEGOxOv4c+EVGw/dQ15RRppXnM7cwzwd8aAABd4OlrKWCURUf3H0ESkhwqLtfj37HVEJaQi+mS6NLQJALjZmkqX3lo7W7HXbiKiWsLQRKQnijRa7D1/E1FHr+LvE2lQ5/8XlFysTRDi74wB/i7wd7VmUCIikgFDE5GMNFqB/Rdu4s+EVGw5norbd8Z/A0o6nywNSu3cbDi0CRGRzBiaiGqZVitw6NJtRCVcxeZjabiRXSDNa2yuRD8/Jwzwd0End1sOa0JEpEcYmohqgRACR1IyEHU0FZuPpSJNnS/NszEzRt82JUGpS3NbGBlySBMiIn3E0ERUQ4QQOH5FjaiEq4hKSJUGyAUASxMj9GnthAEBzni8pR2MGZSIiPQeQxNRNRJC4HRalhSULt3MleaZKw3Ru7UjBvi7oLunHVRGHPeNiKguYWgiqgbnrmXhz6OpiEq4ivPXc6TpJsYG6OXtiAH+znjC24ED5BIR1WEMTUQP6eKNHOmM0um0LGm60sgAPT3tMSDABb28HWCu4p8ZEVF9wH/Niaog5VYuNh0rOaN0/Ipamm5sqEC3VvYY4O+Mp1o7wtLEWMYqiYioJjA0ET1AamYeNiWkIiohFfEpGdJ0QwMFHmvRGAP9XRDcxgnWZgxKRET1GUMT0V00WoFz17IRe/4GNh1LxcGLt6V5CgXQxaMxBgQ4o28bJzS2UMlYKRER1SaGJmrwbmYXID4lA0eSM3Ak5TaOpmTqjPUGAJ3cG2GAvwv6+TnBwdJEpkqJiEhODE3UoBRptDidmoUjKbdxJDkDh5Nv63QLUMpMaYgAVxv08nFAfz9nuNiYylAtERHpE4YmqtfSMvNxJPk2jqRk4EjybSRczkRBsbZcuxb25mjftBHaNW2Edk1t4OloySFMiIhIB0MT1Rv5RRqcuJpZcpntzlmk1Mz8cu2sTIykcNSuaSO0dbXhTdxERPRADE1UJwkhkHIrT7rMdiT5Nk6mqlGkETrtDBSAl5MV2t8JSO2a2sCjsTkMeBaJiIiqiKGJ6oTsgmIkXM6QziLFp9zGjezCcu3sLJT/nUVyawR/V2t2LklERNWC7yakd7RagQs3snE4OUM6i3QmPQta3ZNIMDZUoLWL9X9nkdxs4NrIFAoFzyIREVH1Y2gi2WXkFpb5yn8G4pNvQ51fXK5dExtTtG1qg3ZuJSGpjYsVx3IjIqJaw9BEtapYo0ViepZ0me1Iym1cKDPAbSkTYwP4N7FBu2Yll9naNbWBoxX7RyIiIvkwNFGNupaVj/g7Z5BKv/KfW6gp187DzvzOGaSSs0heTpYwNjSQoWIiIqKKMTRRtdBqBW7mFCL5Vi6OpvwXki7fzivX1kJlhLZuNtK9SAFuNrA1V8pQNRERUeUxNNEDFWu0uJZVgNTMfKRl5iM1Mw/p6vwyz/NxLSu/3Nf9gZKx2jwdLO+cQSoJSS3sLdhxJBHRgwgBaDWA0JT5fzGg1Zb5ucx8nTalP2sBUcEDosxzcdf8u5/fmYaKpt+9jLjPdsq2vc+6cK/5AnBpB7QfLtshYWhq4PKLNDoBKE39XzAqDUQ3sgvKfXOtIgoF4GCpQpsy32jzd7WGpQk7jiRqUErf8Mq94WuqOF1bQbuann5XHdriu9o+KKho72pTrLudsuuTftZUvE1RfvSCBs/3WYYmfbJ06VLMnz8faWlpCAgIwOeff47OnTvLXdZDyS4oRlpm3n+BKDMfqer/zg6lq/NxK6d8X0cVMTZUwNHKBM7WJtL/naxN7/y/5Lm9hQpGvA+JHpX0hltc5qHR/flBn4rLfbqt5CfpSn1Cvt86KvupvILly+1XRdM1/y0rTdfc1VbcY3rpNiuaXma5B27v7nWXmVb6xs83+9phYAQoDEv+b2AIKAzK/GxYZtqd/5c+oCjzXKE7r9zzO9NQ0fSy7SuYX26Z+7SVlsH9t+PgI+MLztCk46effkJ4eDiWL1+OwMBALFq0CMHBwUhMTISDg4Pc5UmEEMjILSoJQ+o8pGUW/BeO7pw1Ss/MR1ZB+a/tV8TE2AAu1qZwsjaBk9V/IcjJ2lR63thcyV60y7rvG2Zl3lQraFPhm2Z1bUd7V/C4+5Pw3cGk9HlVltHcez33Xeau9qL8FwWovlHc9cZuCBgY3PX8ftMNKmh3r+mPul6jMm3vCiQ6be4RWnR+NnrAdAPdNvfczp22VOsUQohKXHhpGAIDA9GpUycsWbIEAKDVauHm5obXX38db7311n2XVavVsLa2RmZmJqysrKqtpiNnErHryG5k5uYjI6cA6rwCZOYUQqPVwgBaGEBAcef//z20UEDAEFqYKhWwNjGCtYkBrFVGsDIxhLWJASxUBrBUGcJSaQiVIaBA2U+gd/98jzdgoNynUVHuk/rd16bv+gQOAQjc9bzMdqXnuOu59r91o+y6y6yrdDmUrQmVqEeU2Rehu3zZ7VST2vgDrK0/clHTuVphCCG9oSju+jSr0P1ZYQCg9FMq7vrEqigzT6H7yRe4a15FyynKz0PZ7Zbd3t2fuCEtI+7skzTPwLDMsmX2UfpZcdf0ij7Fl58voLjzxl9aa5k2BoYlNaHMsqWvrzQNZeqr+OyBkGorDRhl25QJKVIN5Ylq+E3Vl7c0fdmX6qhDn1gpreBq6Vqt66zK+zfPNN1RWFiIuLg4RERESNMMDAzQu3dvxMbGlmtfUFCAgoIC6blara6RuvYe+wpf5/8NGACwvPN4FFoAuXcedcWd98LqXaHhnQc1HNo7j2pwJ2sTUe3q59EP87rPk237DE133LhxAxqNBo6OjjrTHR0dcfr06XLtIyMj8f7779d4XbZW1lCpRZnQoKhkflD899/7LvCgtSnu+7Siifd79uBNVjUdVaa+h1+/7pAslVlW8TCbqfRRfRTVso1qWcWjr6S2hsqpM8elMtupR8ML1cpxeYjX62HqqvIyD7HrtfU7Vhusldaybp+h6SFFREQgPDxceq5Wq+Hm5lbt2wl9aiZCMbPa10tERERVw9B0h52dHQwNDZGenq4zPT09HU5OTuXaq1QqqFSq2iqPiIiIZMbb7+9QKpXo0KEDtm3bJk3TarXYtm0bgoKCZKyMiIiI9AHPNJURHh6OkSNHomPHjujcuTMWLVqEnJwcvPzyy3KXRkRERDJjaCrjhRdewPXr1zFr1iykpaWhbdu22LJlS7mbw4mIiKjhYT9N1aSm+mkiIiKimlOV92/e00RERERUCQxNRERERJXA0ERERERUCQxNRERERJXA0ERERERUCQxNRERERJXA0ERERERUCQxNRERERJXA0ERERERUCRxGpZqUdqyuVqtlroSIiIgqq/R9uzIDpDA0VZOsrCwAgJubm8yVEBERUVVlZWXB2tr6vm049lw10Wq1uHr1KiwtLaFQKKq0rFqthpubG1JSUjhunR7hcdFPPC76icdFP/G4PJgQAllZWXBxcYGBwf3vWuKZpmpiYGAAV1fXR1qHlZUVf6n1EI+LfuJx0U88LvqJx+X+HnSGqRRvBCciIiKqBIYmIiIiokpgaNIDKpUK7733HlQqldylUBk8LvqJx0U/8bjoJx6X6sUbwYmIiIgqgWeaiIiIiCqBoYmIiIioEhiaiIiIiCqBoYmIiIioEhiaZLZ06VK4u7vDxMQEgYGBOHDggNwl1Wu7du3CwIED4eLiAoVCgY0bN+rMF0Jg1qxZcHZ2hqmpKXr37o2zZ8/qtLl16xaGDRsGKysr2NjYYMyYMcjOzq7FvahfIiMj0alTJ1haWsLBwQGDBg1CYmKiTpv8/HyEhYWhcePGsLCwwJAhQ5Cenq7TJjk5GSEhITAzM4ODgwOmTZuG4uLi2tyVemfZsmXw9/eXOkYMCgrCX3/9Jc3ncZHf3LlzoVAoMGnSJGkaj0vNYWiS0U8//YTw8HC89957OHz4MAICAhAcHIxr167JXVq9lZOTg4CAACxdurTC+fPmzcNnn32G5cuXY//+/TA3N0dwcDDy8/OlNsOGDcOJEycQHR2NqKgo7Nq1C+PHj6+tXah3YmJiEBYWhn379iE6OhpFRUXo06cPcnJypDaTJ0/Gn3/+iZ9//hkxMTG4evUqBg8eLM3XaDQICQlBYWEh9u7di++++w6rVq3CrFmz5NilesPV1RVz585FXFwcDh06hCeffBJPP/00Tpw4AYDHRW4HDx7El19+CX9/f53pPC41SJBsOnfuLMLCwqTnGo1GuLi4iMjISBmrajgAiA0bNkjPtVqtcHJyEvPnz5emZWRkCJVKJX788UchhBAnT54UAMTBgwelNn/99ZdQKBTiypUrtVZ7fXbt2jUBQMTExAghSo6BsbGx+Pnnn6U2p06dEgBEbGysEEKIzZs3CwMDA5GWlia1WbZsmbCyshIFBQW1uwP1XKNGjcTXX3/N4yKzrKws0apVKxEdHS169Ogh3nzzTSEE/15qGs80yaSwsBBxcXHo3bu3NM3AwAC9e/dGbGysjJU1XElJSUhLS9M5JtbW1ggMDJSOSWxsLGxsbNCxY0epTe/evWFgYID9+/fXes31UWZmJgDA1tYWABAXF4eioiKd4+Lt7Y2mTZvqHBc/Pz84OjpKbYKDg6FWq6WzIvRoNBoN1q1bh5ycHAQFBfG4yCwsLAwhISE6rz/Av5eaxgF7ZXLjxg1oNBqdX1oAcHR0xOnTp2WqqmFLS0sDgAqPSem8tLQ0ODg46Mw3MjKCra2t1IYenlarxaRJk9C1a1f4+voCKHnNlUolbGxsdNrefVwqOm6l8+jhHTt2DEFBQcjPz4eFhQU2bNiA1q1bIz4+nsdFJuvWrcPhw4dx8ODBcvP491KzGJqISG+EhYXh+PHj2L17t9yl0B1eXl6Ij49HZmYmfvnlF4wcORIxMTFyl9VgpaSk4M0330R0dDRMTEzkLqfB4eU5mdjZ2cHQ0LDcNxrS09Ph5OQkU1UNW+nrfr9j4uTkVO5G/eLiYty6dYvH7RFNnDgRUVFR2LFjB1xdXaXpTk5OKCwsREZGhk77u49LRcetdB49PKVSiZYtW6JDhw6IjIxEQEAAFi9ezOMik7i4OFy7dg3t27eHkZERjIyMEBMTg88++wxGRkZwdHTkcalBDE0yUSqV6NChA7Zt2yZN02q12LZtG4KCgmSsrOHy8PCAk5OTzjFRq9XYv3+/dEyCgoKQkZGBuLg4qc327duh1WoRGBhY6zXXB0IITJw4ERs2bMD27dvh4eGhM79Dhw4wNjbWOS6JiYlITk7WOS7Hjh3TCbTR0dGwsrJC69ata2dHGgitVouCggIeF5n06tULx44dQ3x8vPTo2LEjhg0bJv3M41KD5L4TvSFbt26dUKlUYtWqVeLkyZNi/PjxwsbGRucbDVS9srKyxJEjR8SRI0cEALFw4UJx5MgRcenSJSGEEHPnzhU2Njbi999/FwkJCeLpp58WHh4eIi8vT1pH3759Rbt27cT+/fvF7t27RatWrURoaKhcu1Tnvfrqq8La2lrs3LlTpKamSo/c3FypzYQJE0TTpk3F9u3bxaFDh0RQUJAICgqS5hcXFwtfX1/Rp08fER8fL7Zs2SLs7e1FRESEHLtUb7z11lsiJiZGJCUliYSEBPHWW28JhUIh/vnnHyEEj4u+KPvtOSF4XGoSQ5PMPv/8c9G0aVOhVCpF586dxb59++QuqV7bsWOHAFDuMXLkSCFESbcDM2fOFI6OjkKlUolevXqJxMREnXXcvHlThIaGCgsLC2FlZSVefvllkZWVJcPe1A8VHQ8AYuXKlVKbvLw88dprr4lGjRoJMzMz8cwzz4jU1FSd9Vy8eFH069dPmJqaCjs7OzFlyhRRVFRUy3tTv4wePVo0a9ZMKJVKYW9vL3r16iUFJiF4XPTF3aGJx6XmKIQQQp5zXERERER1B+9pIiIiIqoEhiYiIiKiSmBoIiIiIqoEhiYiIiKiSmBoIiIiIqoEhiYiIiKiSmBoIiIiIqoEhiYiIiKiSmBoIiK91bNnT0yaNEnuMiQ7d+6EQqEoNxhqZbm7u2PRokXVWhMR1R4juQsgImooDh48CHNzc7nLIKKHxNBERHSXwsJCKJXKal+vvb19ta+TiGoPL88RkV4rLi7GxIkTYW1tDTs7O8ycORNlh8y8ffs2RowYgUaNGsHMzAz9+vXD2bNnpfk3b95EaGgomjRpAjMzM/j5+eHHH3/U2UbPnj0xceJETJo0CXZ2dggODgYAbN68GZ6enjA1NcUTTzyBixcv3rdWIQRmz56Npk2bQqVSwcXFBW+88YY0v+zluVWrVkGhUJR7zJ49W2r/9ddfw8fHByYmJvD29sYXX3zxkK8iEVUHhiYi0mvfffcdjIyMcODAASxevBgLFy7E119/Lc0fNWoUDh06hD/++AOxsbEQQqB///4oKioCAOTn56NDhw7YtGkTjh8/jvHjx2P48OE4cOBAue0olUrs2bMHy5cvR0pKCgYPHoyBAwciPj4eY8eOxVtvvXXfWn/99Vd8+umn+PLLL3H27Fls3LgRfn5+FbZ94YUXkJqaKj1+/PFHGBkZoWvXrgCANWvWYNasWfj4449x6tQpzJkzBzNnzsR33333KC8nET0KQUSkp3r06CF8fHyEVquVps2YMUP4+PgIIYQ4c+aMACD27Nkjzb9x44YwNTUV69evv+d6Q0JCxJQpU3S2065dO502ERERonXr1jrTZsyYIQCI27dvV7jeBQsWCE9PT1FYWFjh/GbNmolPP/203PRz584JW1tbMW/ePGlaixYtxNq1a3XaffjhhyIoKOie+0VENYtnmohIr3Xp0gUKhUJ6HhQUhLNnz0Kj0eDUqVMwMjJCYGCgNL9x48bw8vLCqVOnAAAajQYffvgh/Pz8YGtrCwsLC/z9999ITk7W2U6HDh10np86dUpnvaXbvp/nnnsOeXl5aN68OcaNG4cNGzaguLj4vstkZmZiwIABCAkJwbRp0wAAOTk5OH/+PMaMGQMLCwvp8dFHH+H8+fP3XR8R1RzeCE5E9dr8+fOxePFiLFq0CH5+fjA3N8ekSZNQWFio0646vtXm5uaGxMREbN26FdHR0Xjttdcwf/58xMTEwNjYuFx7jUaDF154AVZWVlixYoU0PTs7GwDw1VdflQtuhoaGj1wnET0chiYi0mv79+/Xeb5v3z60atUKhoaG8PHxQXFxMfbv34/HHnsMQMmN34mJiWjdujUAYM+ePXj66afx0ksvAQC0Wi3OnDkjzb8XHx8f/PHHH+W2/SCmpqYYOHAgBg4ciLCwMHh7e+PYsWNo3759ubaTJ0/GsWPHcOjQIZiYmEjTHR0d4eLiggsXLmDYsGEP3CYR1Q6GJiLSa8nJyQgPD8crr7yCw4cP4/PPP8eCBQsAAK1atcLTTz+NcePG4csvv4SlpSXeeustNGnSBE8//bTU5pdffsHevXvRqFEjLFy4EOnp6Q8MTRMmTMCCBQswbdo0jB07FnFxcVi1atV9l1m1ahU0Gg0CAwNhZmaGH374AaampmjWrFm5titXrsQXX3yBDRs2QKFQIC0tDQCkS3Hvv/8+3njjDVhbW6Nv374oKCjAoUOHcPv2bYSHhz/EK0lEj4r3NBGRXhsxYgTy8vLQuXNnhIWF4c0338T48eOl+StXrkSHDh0wYMAABAUFQQiBzZs3S5fD3n33XbRv3x7BwcHo2bMnnJycMGjQoAdut2nTpvj111+xceNGBAQEYPny5ZgzZ859l7GxscFXX32Frl27wt/fH1u3bsWff/6Jxo0bl2sbExMDjUaD//3vf3B2dpYe//d//wcAGDt2LL7++musXLkSfn5+6NGjB1atWgUPD48qvHpEVJ0UQpTp8ISIiIiIKsQzTURERESVwNBEREREVAkMTURERESVwNBEREREVAkMTURERESVwNBEREREVAkMTURERESVwNBEREREVAkMTURERESVwNBEREREVAkMTURERESV8P/+lFd5ElGzcAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, naive_times)\n",
    "plt.plot(x, linear_times)\n",
    "plt.plot(x, jit_times)\n",
    "plt.xlabel(\"board size\")\n",
    "plt.ylabel(\"runtime [ms]\")\n",
    "plt.legend([\"naive\", \"linear\", \"jit compiled with numba\"])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, linear_times)\n",
    "plt.plot(x, jit_times)\n",
    "plt.xlabel(\"board size\")\n",
    "plt.ylabel(\"runtime [ms]\")\n",
    "plt.legend([\"linear\", \"jit compiled with numba\"])\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}