{ "cells": [ { "cell_type": "markdown", "source": [ "# Quantum Dropout for QAOA" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "## Overview" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "Quantum Approximation Optimization Algorithm (QAOA) is a hybrid classical-quantum algorithm used for solving the combinatorial optimization problem, which is proposed by [Farhi, Goldstone, and Gutmann (2014)](https://arxiv.org/abs/1411.4028). In the [previous tutorial](qaoa_nae3sat.ipynb), we introduced solving the [Not-all-equal 3-satisfiability (NAE3SAT)](https://en.wikipedia.org/wiki/Not-all-equal_3-satisfiability) by QAOA and the dilemma of QAOA on the hard problem. In this tutorial, we will introduce a simple trick to alleviate this dilemma, namely quantum dropout, please refer to [Wang, Zheng, Wu, and Zhang (2023)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.023171) for more details." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "## NAE3SAT and Hard Problem" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "Let's briefly review the NAE3SAT and the difference between the easy and hard problem.\n", "\n", "Let the set of clauses in the NAE3SAT be $\\mathcal{C}$. In each clause, there are three literals and each literal is represented by a spin. Spins up ($s=1$, $\\text{bit}=0$) and down ($s=-1$, $\\text{bit}=1$) represent false and true respectively. NAE3SAT requires the three spins in each clause are not all equal to each other, in other words, at least one is up, and at least one is down. The Hamiltonian of the NAE3SAT is as follows\n", "$$\n", "\\begin{split}\n", " \\hat{H}_C&=\\sum_{(i,j,k)\\in\\mathcal{C}}\\left[(s_i+s_j+s_k)^2-1\\right]/2\\\\\n", " &=\\sum_{(i,j,k)\\in\\mathcal{C}}(s_i s_j+s_j s_k+s_k s_i)+|\\mathcal{C}|,\n", "\\end{split}\n", "$$\n", "where $|\\mathcal{C}|$ is the number of clauses in $\\mathcal{C}$. When all clauses are true, $\\hat{H}_C$ takes the minimum value 0, and the corresponding bit string is the solution of the NAE3SAT.\n", "\n", "The difference between the easy and hard problem is the energy landscape, as shown in the following figure.\n", "\n", "\n", "\n", "The global minimum is located in a large and smooth neighborhood for a simpler problem and a narrow region for a harder problem. It is worth noting that when the system size is relatively small, most of the randomly generated problems are easy, and hard problems need to be constructed with special methods, please refer to [Wang, Zheng, Wu, and Zhang (2023)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.023171)." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "## Quantum Dropout" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "The algorithm is shown in the following figure.\n", "\n", "\n", "\n", "We first implement the classical algorithm that can be done in polynomial time, such as simulated annealing method (SA). If the result is satisfactory, we stop the procedure since there is no point in a quantum solver. Otherwise, these failed classical results, typically low-lying excited states (local minima), offer insights as we prepare quantum dropout for QAOA: whether a clause should be kept or available for quantum dropout to underweight the distracting local minima and enhance the chances to locate the true ground state. Specifically, the clauses violated by low-lying excited states should be all kept, and the other clauses can be randomly discarded at the ratio $R$.\n", "\n", "Finally, we optimize the PQC with respect to the original cost function $H_C$ with a complete set of clauses to ensure the uniqueness of the global minimum. The current procedure does not incur obvious overhead to the conventional QAOA since the preliminary approaches and the quantum-dropout controls are both inexpensive on a classical computer." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "### Setup" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": null, "outputs": [], "source": [ "import tensorcircuit as tc\n", "import optax\n", "import jax.numpy as jnp\n", "import tensorflow as tf\n", "import networkx as nx\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from functools import partial\n", "from IPython.display import clear_output\n", "import random\n", "\n", "K = tc.set_backend(\"jax\")\n", "\n", "nlayers = 30 # the number of layers\n", "ncircuits = 6 # six circuits with different initial parameters are going to be optimized at the same time\n", "R = 0.5 # dropout ratio, 0 means no dropout, 1 means all dropout" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "We use the same NAE3SAT as the [previous tutorial](qaoa_nae3sat.ipynb)." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 2, "outputs": [], "source": [ "# a hard graph instance\n", "hard_clauses = [\n", " [4, 1, 7],\n", " [5, 11, 8],\n", " [4, 1, 8],\n", " [4, 11, 8],\n", " [4, 1, 10],\n", " [5, 11, 8],\n", " [4, 1, 8],\n", " [1, 11, 8],\n", " [4, 1, 7],\n", " [0, 11, 8],\n", " [4, 1, 10],\n", " [4, 11, 8],\n", " [5, 0, 10],\n", " [0, 6, 7],\n", " [5, 0, 11],\n", " [0, 6, 7],\n", " [5, 0, 9],\n", " [3, 6, 7],\n", " [5, 0, 8],\n", " [5, 6, 7],\n", " [5, 0, 10],\n", " [3, 6, 7],\n", " [5, 0, 10],\n", " [1, 6, 7],\n", " [2, 4, 6],\n", " [1, 8, 11],\n", " [2, 4, 6],\n", " [2, 8, 11],\n", " [2, 4, 9],\n", " [5, 8, 11],\n", " [2, 4, 10],\n", " [2, 8, 11],\n", " [2, 4, 10],\n", " [4, 8, 11],\n", " [2, 4, 8],\n", " [4, 8, 11],\n", " [3, 0, 9],\n", " [5, 11, 7],\n", " [3, 0, 10],\n", " [2, 11, 7],\n", " [3, 0, 9],\n", " [0, 11, 7],\n", " [3, 0, 9],\n", " [5, 11, 7],\n", " [3, 0, 10],\n", " [3, 11, 7],\n", " [3, 0, 7],\n", " [4, 11, 7],\n", " [5, 0, 10],\n", " [4, 0, 10],\n", " [2, 5, 6],\n", " [2, 11, 10],\n", " [2, 6, 10],\n", " [2, 4, 9],\n", " [0, 9, 10],\n", " [3, 0, 7],\n", " [2, 5, 6],\n", " [1, 10, 9],\n", " [1, 4, 11],\n", " [5, 10, 11],\n", " [0, 4, 8],\n", " [0, 9, 8],\n", " [2, 11, 10],\n", " [2, 8, 6],\n", " [3, 6, 7],\n", " [0, 8, 10],\n", " [4, 0, 9],\n", " [3, 5, 8],\n", " [5, 11, 10],\n", " [2, 11, 10],\n", " [4, 11, 8],\n", " [1, 3, 11],\n", "]\n", "cost_factor = 1 / len(hard_clauses) / 4" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T11:45:08.202605500Z", "start_time": "2023-07-03T11:45:08.202029100Z" } } }, { "cell_type": "code", "execution_count": 3, "outputs": [], "source": [ "# convert to a NetworkX graph\n", "def construct_graph(clauses):\n", " graph = nx.Graph()\n", " for i, j, k in clauses:\n", " graph.add_edge(i, j, weight=0)\n", " graph.add_edge(j, k, weight=0)\n", " graph.add_edge(k, i, weight=0)\n", " for i, j, k in clauses:\n", " graph[i][j][\"weight\"] += 1\n", " graph[j][k][\"weight\"] += 1\n", " graph[k][i][\"weight\"] += 1\n", " return graph" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T11:45:08.206621400Z", "start_time": "2023-07-03T11:45:08.203172500Z" } } }, { "cell_type": "code", "execution_count": 4, "outputs": [ { "data": { "text/plain": "
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206dP5ObmRuLi4qSgoEBLliyhxMTEcusEBwdTmzZtiMVi0fTp0ykjI6PMsteuXSMpKSnq3LkzpaSkVGmsc+bMITU1tTKTEsnJydHGjRspNDS0wpwCXC6XevbsSfr6+pSbm1ulcTH8eRgHQgYGhjpJdnY2Xbt2rZj5X05OjgYMGECHDh0Suvn/d0JCQmj48OEkIiJCqqqqtGbNmgqffbm5ubRs2TISExMjY2PjCh0Ajx8/TqKiomRvb09ZWVlVHrOZmVmJkMKiqKur0/Llyyk/P5/ExcVp+/bt5bYXHBxMIiIitH79+iqPjeHPwogBBgaGOkNcXBwdOHCA+vbtW6r3f02sUF+9ekX9+/cnFotFWlpatG3bNsrMzKywXmBgIJmampKoqCgtXry4wkiF7du3E4vFolGjRgklyU9ZIYVF0dPTo7lz5xLRL+EwYcKECtudPHkyycnJlRr5wFB3YMQAAwNDraWo+b9NmzYEoMbM/7/z8OFDsrGxIQCkp6dH+/fv50t8ZGZm0syZM4nNZlOrVq3ozZs35Zbncrm0dOlSAkDu7u4VnjPAL2WFFBalWbNmNHnyZCIiGjRoEHXp0qXCdpOSkkhJSYlcXFyEMk6GPwMjBhgYGGoVheb/CRMmUMOGDUuY/3/8+FFjY+FyuXTr1i3q0qULASATExM6duwY3yt1f39/aty4MUlKStK6desqrMfhcGjy5MkEgDw9PYUqdBwdHalDhw7llmnXrh05OzsTEZGHhwepqKjw1faOHTuIxWLRy5cvqzxOhj8DIwYYGBj+OHFxceTl5VXM/K+rq0tTp06tMfN/UTgcDl26dIlnjWjdujVduHCB71V6SkoKubm5EQDq3LkzhYaGVlgnNzeXhgwZQiwWi/bu3VvVWyjRtpycHK1cubLccj169CAnJyci+v9TDPnxvcjPzycTExPq2LEjE2pYR2HEAAMDQ41TmvmfzWZThw4daM2aNTVq/i9KQUEBnThxgszMzAgAderUiW7cuCHQWC5fvkwNGjQgOTk52r17N18CIiMjg6ytrUlcXJzOnDlTlVsolbt37xKAClfuDg4OZGtrS0S/HCTxv/TE/ODn51ehTwJD7YURAwwMDDVCbTL//05ubi4dOHCADAwMCABZWVnR/fv3BWojISGBBg8eTACod+/eFBUVxVe9pKQksrCwIBkZGfLz86vM8CukopDCQoYMGUJdu3Ylol/viaioqECHEvXp04caNmzIl0MlQ+2CSTrEwMBQbXz//r1Y8p+srCzo6urC0dGRl/xHXFz8j40vOzsb3t7eWLduHaKiouDo6Ijjx4+jdevWfLdBRDhx4gSmTp0KADh69CiGDh3KV0rj2NhYWFlZIS4uDv7+/mjTpk2l76U8rl+/Dmtra7DZ7HLLycjIICsrCwAgLi4OAwODMtMSl8aGDRtgYmKC9evXY+nSpVUaM0MtRZjKgoGB4e+Ey+XS69evafny5aWa/0NCQmrFnnJaWhqtW7eO1NTUiM1m07Bhw+jdu3cCtxMVFUW2trYEgAYPHkzx8fF81w0PDyddXV3S0tKi9+/fC9y3IGMEQKdOnaqw7LRp08jExIT37/79+1P37t0F6m/u3LkkJSVFkZGRAo+V4c/BbBMwMDBUiezsbLp69WoJ8//AgQP/uPn/d5KSkmjZsmWkqKhIYmJiNHbsWAoPDxe4HQ6HQ3v27CE5OTlq0KABXbp0SaD6r1+/JjU1NTIyMqr2SXPfvn3EZrPLPPOgKAsWLCAdHR3evxcvXkzq6uoC9ZeWlkbq6uo0ePBggcfK8OdgxAADA4PAFHr/9+nTh6SlpYt5//v5+dW69LTfv3+nOXPmkKysLElKStLUqVP53tP/nbCwMF6ooaurK/38+VOg+gEBASQvL0+tWrWq9iyJRPyFFBaycuVKql+/Pu/fJ06cIADl5iYoDR8fHwIgsN8Fw5+DEQMMDAwVUtT8/99//9Va8//vREVF0ZQpU0hSUpLk5ORo7ty5lc6Ul5+fT+vXrydJSUlq3LhxuXn7y+Ly5cskKSlJ3bp1o7S0tEqNQxD4DSksZPPmzSQtLc37d1BQEAGghw8fCtQvh8Oh1q1bU8uWLYWWNImhemHEAAMDQ6kUmv/Hjx9PWlpaxcz/hw8frlXm/98JDw8nFxcXEhMTIyUlJfLw8ODLTF4WQUFB1Lp1a2Kz2TRjxoxyDxYqi0OHDpGIiAg5OjpSdnZ2pcciCPyGFBayb98+AsCbwLOzs4nNZtO+ffsE7vvRo0cEgA4cOCBwXYaahxEDDAwMPEoz/zdu3JimTZtWK83/vxMcHExDhw4lNptN6urqtH79+iqtwHNycmjx4sUkKipKJiYm9PTp00q1s3nzZgJALi4uQjlngF9mz55N6urqfK/Ojx07RgCKiR0DAwOaPn16pfofOnQoqaqqMnNCHYARAwwM/zBcLpdevXpVwvzfsWPHWm3+/53nz59T3759CQBpa2vTzp07q7z6fvLkCTVt2pTExMRo6dKllRJCXC6XFi5cSABo7ty5Nf5empqa0ujRo/kuf/HixRJZB/v06UOWlpaV6j86OpqkpaVp9uzZlarPUHMwYoCB4R+jLpv/fycgIIAsLS0JABkYGJC3tzfl5eVVqc2MjAyaPn06sVgs+u+//+jt27eVaqegoIDGjRtHAP7IEb+ChBQWUphF8MuXL7zX5s+fT1paWpUex/Lly0lMTIzCwsIq3QZD9cOIAQaGf4DY2Fjav38/OTg4lDD/3759u9ab/4vC5XLp+vXr1LFjRwJAzZo1o5MnT1JBQUGV2759+zbp6uqSlJQUbdiwodJt5uTk0IABA4jNZpO3t3eVx1UZBAkpLOTx48cEoFjOhSNHjlTpuZ6VlUXa2tpkb29fqfoMNQMjBhgY/kIKzf8eHh4lzP9r166tM+b/onA4HDp//jy1atWKAFCbNm3o8uXLQrmPnz9/kouLCwGgrl27Vir3QCHp6enUq1cvkpCQoAsXLlR5bJVFkJDCQgqjBwIDA3mvvXr1igBU2l+CiOj06dMEgG7cuFHpNhiqF0YMMDD8JWRlZZUw/8vLy5OTk1OdM/8XJT8/n44ePUomJia8ydrPz09oYubixYukoaFB8vLytHfv3iqFwiUmJlKbNm1ITk6O/P39hTK+ypCbm0uysrK0atUqgeqFh4cTgGJjz8zMJBaLVSULB5fLpc6dO5OxsXGVt3EYqgfmbAIGhjpMXFwcL/f/7du3kZWVhcaNG6N///6wt7dHp06d/mju/6qQm5uLw4cPY+3atfj06RN69+6Nffv2oX379kJpPz4+HlOnTsXp06dhZ2eH3bt3Q0tLq9Ltffv2DZaWlkhMTMS9e/fQsmVLoYyzMjx69AgZGRmwsbERqJ6MjAwAIDMzk/eatLQ0dHV1BTqj4HdYLBa2bt2Kli1bYs+ePZgyZUql22L4szBigIGhFkBEePPmDa5cuYIrV67gxYsXYLPZaN++PZYuXQp7e3s0adKEr0NyaitZWVnw8vLC+vXrERMTg/79++PMmTMwNzcXSvtEhKNHj2L69Olgs9k4fvw4Bg8eXKX3LDQ0FJaWlgCAhw8fwtDQUChjrSzXr1+Huro6WrRoIVC90sQAADRt2rRKYgAAWrRogbFjx2LJkiUYMmQIVFRUqtQewx9CmGYGBgYG/snKyiJfX18aN24caWpqFjP/HzlypM6a/38nNTWVVq9eTfXr1ycREREaMWKE0A/wiYyMJBsbGwJAQ4cOFUo64BcvXpCKigo1bdqUoqOjhTDKqiNoSGEhBQUFpSYKmjNnTrEzCypLfHw8ycvL08SJE6vcFoNwYXwGGBhqIaV5/+vp6dH06dPrnPd/RSQmJtKSJUtIQUGBxMXFady4cfTp0yeh9sHhcGjnzp0kKytLmpqadOXKFaG06+/vT3JyctS2bVtKTEwUSptVpTIhhUWRkJCg7du3F3vt4MGDJZIRVZaNGzcSm82udMgmQ/XAiAEGhlpAUe//1q1bl/D+f//+fZ3z/q+I2NhYmjVrFsnIyJCUlBS5u7vTt2/fhN5PaGgoderUiQDQuHHjKCUlRSjtnj9/nsTFxalXr16Unp4ulDaFwd69e0lERKTS6ZeVlJRozZo1xV579uwZAaAXL15UeXy5ublkaGhI3bp1++u+03UZRgwwMPwhKjL/15aVprD5+vUrTZw4kSQkJEheXp4WLFhQLaf35efn05o1a0hCQoL09PTo7t27Qmv7wIEDxGazycnJiXJycoTWrjDo27cvdezYsdL1GzZsSIsXLy72WlpaGgGgw4cPV3V4RER09epVAkDnz58XSnsMVYcRAwwMNUhsbCzt27eP7O3tSUpKqpj5/86dO3+V+f93QkNDafTo0SQqKkrKysq0cuVKgY//5Zc3b95Qy5Ytic1m06xZsygzM1Noba9du5YA0Pjx44WS6EiYVDaksChGRkY0Y8aMEq9ra2vTvHnzqjK8YtjY2JCurm6NHdrEUD6MGGBgqEa4XC69fPmyhPm/U6dOf635/3eCgoJo0KBBxGKxqEGDBrRp0yah7D2XRnZ2Ni1cuJBERUXJzMyMnj17JrS2uVwuzZ49mwDQokWLauXn5u/vTwDo1atXlW6jZcuWNG7cuBKvW1tbk4ODQ1WGV4wPHz6QqKgoeXp6Cq1NhsrDiAEGBiGTlZVFV65c+efM/7/z9OlTsre3JwCko6NDe/bsqVaT+qNHj6hJkyYkJiZGHh4eQrWy5Ofn8zIUbt68WWjtCptZs2aRurp6lYRKp06daPjw4SVenzFjBunr61dleCVwd3cnGRkZiomJEWq7DILDiAEGBiFQkfm/tmRdy8jJp3cxKfQqMpnexaRQRo5wj9Plcrl09+5d6tGjBwGgJk2a0KFDh6r1/tPT02nKlCnEYrGobdu2xfLqC4Ps7GxydHQkERERoe2ZVxcmJibk7OxcpTasra3J0dGxxOteXl7EYrEoKyurSu0X5efPn6SiokKjRo0SWpsMlYPJQMjAUAmICK9fv+Yl/3n58iXYbDY6dOgADw8P2Nvbw8jIqFYk/wmPT8exwCjcDU1AVHIWqMg1FgBtJWl0M1LFsLbaMFCTq1QfRITr169j1apVePz4MVq0aIEzZ87A0dERIiIiQrmP0rh16xbc3Nzw48cPbNq0CVOmTBFqf2lpaejbty+ePHmCixcvws7OTmhtC5vo6GiEhIRg6dKlVWpHRkYGGRkZJV5v2rQpiAihoaECJzMqCwUFBaxcuRLjx4/HxIkT0aZNG6G0y1B9MGKA4Z8nOzsbd+7cwZUrV+Dr64vY2FjUq1cP1tbWmD59OmxsbKCsrPynh8kjOjkLCy4E40FEIkTYLHC4VKIMAYhMzsKRwEgcfPIVnfRV4OlohoZK0nz1weVycf78eXh6euL169ewsLDA1atXYWNjU61C6OfPn5gxYwYOHjyIHj16wN/fH40bNxZqHwkJCbCxsUFERARu3bqFTp06CbV9YXP9+nWIiIigV69eVWpHRkYG8fHxJV43NjYGALx//15oYgAAxo4di127dmHq1Kl4/Pgx2Gy20NpmED6MGGD4J4mNjS2W+z87Oxt6enpwcnLi5f4XExP708MswcnnUVh6OQQF/xMApQmBohRef/w5CT03B8DDwQSD/9Mus3x+fj5OnDiB1atX4+PHj7wJuWvXrtVuDTl//jwmTZqE7OxseHl5YcyYMULvMzIyEpaWlkhNTUVAQIBQJ7/q4vr167CwsICCgkKV2pGRkSmRjhj4tYpv0KBBldMS/46IiAi2bt2Kbt264fjx4xg+fLhQ22cQLowYYPgnqEvm/7LYcTccG26FVaouh0vgcAnzzgcjMSMXk7sZFLuem5uLgwcPYs2aNfj69Svs7e3h4+ODdu3aCWPo5fL9+3dMnjwZ586dQ58+fbBr1y40aNBA6P28f/8elpaWEBcXx6NHj6Cnpyf0PoRNXl4ebt++jQULFlS5rbLEACCcMwpKo2vXrhgwYADmzp2Lvn37QlZWVuh9MAgHRgww/LWUZ/53d3eHtbV1rTL/l8fJ51F8CYHUx6eQcv8IxFS00WDsrlLLbLgVhvqyEhj0nzYyMzOxb98+bNiwAXFxcXBycsKlS5fQrFkzYd9CCYgIhw8fhru7O0RFRXHq1CkMHDiwWgRZYGAgevfuDU1NTdy8eRMaGhpC76M6ePjwYaVOKSwNaWnpcsXAzZs3q9xHaaxfvx5NmjTBmjVrsHLlymrpg6HqMGKA4a8iNjYWvr6+uHLlCu7cuYPs7Gzo6+tj0KBBsLOzq7Xm//KITs7C0sshFZYrSEtE6pPTYIlJVlh2yeUQvLpxCt7b1iElJQXDhw/HvHnzYGRkJIwhV0hkZCTGjRuHmzdvYvjw4diyZUu1CTM/Pz84OjqiefPm8PX1haKiYrX0Ux1cv34dGhoaaN68eZXbqsgysHPnTuTm5kJCQqLKfRVFR0cHs2fPxvr16+Hi4gJdXV2hts8gHBiPDoY6DRHh5cuX8PDwQOvWraGpqYkJEyYgLS0NHh4e+PDhA8LCwrBp0yZ07969zgkBAFhwIZjnI1AeP+8egEQDI4ir61dYNicvH4c/5MHJyQkRERHw8fGpESHA5XKxY8cOmJiYICQkBFevXsWRI0eqTQicOXMGtra26Ny5M/z8/OqUEAB+iQFra2uhWEsqEgMcDgfh4eFV7qc05s6dC2VlZcyZM6da2meoOowYYKhzZGVlwdfXF+PGjYOWlhZat26NzZs3Q19fH0ePHsWPHz8QEBCA2bNno0mTJrXaD6AiwuPT8SAisUJHwZyod8j6+AiKPdz4apfFFoFEoxZwX7oGjRo1EsZQK+Tjx4/o3LkzpkyZgpEjRyIkJAS9e/eutv727t2LQYMGYeDAgbh06RKkpfmLpKgtREVFISQkRChbBMAvMZCfn4/8/PwS15o2bQoA1eI3AACysrJYu3Ytzp49i3v37lVLHwxVgxEDDHWC2NhY7Nu3D/b29lBRUYG9vT38/f0xaNAg+Pv748ePHzh58iSGDRsGJSWlPz1coXEsMAoi7PLFDHE5SPbbA9nmlhBX1eG7bRE2C0efRlVxhBWTn58PT09PNG/eHAkJCQgICMCuXbsgLy9fLf0RETw9PTF+/HhMmjQJR44cqZMWIWGFFBYiIyMD4JeY/h1lZWWoqqpWmxgAgKFDh6Jdu3aYNm0aOBxOtfXDUDkYnwGGWgkR4dWrVzznv0Lv/44dO2L58uWws7Or9d7/wuBuaEKFVoGM19dRkPYDakNWCdQ2h0u4G5aAZTCpyhDL5fXr1xgzZgyCg4Mxa9YsLF26FFJSUtXWH5fLxaxZs7B582Z4eHhg8eLFdfY7cv36dbRv377KIYWFFIqBzMxM1KtXr8T16oooKITNZmPr1q1o27YtvLy8MG7cuGrri0FwGDHAUGvIysrCnTt34OvrW8z738bGBu7u7rCxsfmrVv0VkZFbgKjkkqu4onCy05Dy4BgU2g+CiHTJB3xFRCVlITO3ADISwn0U5OTkwMPDA+vXr4epqSkCAwPRqlUrofbxO/n5+XBxccHRo0exc+dOTJw4sVr7q07y8vJw584doYQUFlJUDJRG06ZNERAQILT+SqNNmzYYNWoUFi5cCCcnpzrnw/E3w2wTMPxRYmJieOZ/ZWVlODg4lDD/nzhx4q8z//NDZFImKnIbTLl/BGwpWci1tq9UHwTga1Lpk0NlefjwIZo3b45NmzbBw8MDz58/r3YhkJ2djf79++PEiRM4duxYnRYCgHBDCgsp9JkoTwyEhYWV6lMgTFavXo3c3FwsX768WvthEAzGMsBQoxQ1/1+5cgWvXr2CiIgIOnTogBUrVsDe3h6GhoZ11rQrTPIKuOVez0+OQcabm1Ds4QpOejLvdeLkg7gcFKTEgyUhDRGp8s8lqKgffklPT8f8+fOxc+dOWFhY4OLFi7xUt9VJamoq7O3t8eLFC1y5cgXW1tbV3md1I8yQwkL4sQzk5+fj06dPaNKkidD6/R0NDQ0sXLgQixcvhpubW418RxgqhhEDDNVOofn/ypUruHr1ajHz/8yZM2Ftbf3PrfpLIzc3Fx8/fkRwcDDevXuH5xFxgIFTmeU56UkAcfHz9l78vL23xPWYPS6Qa+0ApZ7lRxi8ff0KOnItq2SyvXHjBsaNG4fExERs3boVkyZNqtaDjAr5/v07rK2tERUVhTt37sDCwqLa+6wJrl27JvRzICoSAyYmv3xH3r9/X61iAACmT5+O/fv3Y8aMGbh+/Xq19sXAH4wYYKgWYmJiiiX/ycnJ4SX/sbe3R8eOHeukh7cw4HA4+PTpE969e4d3797xJv/w8HCel7W2tjaMm7UAiIAyJgSx+o1Qv9/CEq+n3D8Cbl42lHq6QVSh/Ex7RATngXag/Bzo6urC3Ny82J+Ghka5E1JSUhJmzJiBw4cPo2fPnrh3716NJZX58uULevXqhaysLNy/fx+mpqY10m91ExUVhffv38PDw0Oo7VYkBurXrw9lZWW8f/8e/fr1E2rfvyMpKYkNGzagX79+uHbtWrWGmDLwByMGGIQCl8vFq1eveAKgNPN/TWW3qy0QEWJiYniTfeHf+/fvkZOTAwBQUVGBmZkZevXqBXd3d5iamsLExITn7d1l/V1EluFEKCJdD9KGJVfCac8vAUCp135HU14c19+8xOvXr/Hq1Su8fv0aGzduREpKCgBATU2thEBo3LgxWCwWzp07h0mTJiEvLw/e3t4YPXp0jW3vBAcHw8rKCjIyMnj06NFfldWuMKSwZ8+eQm23vNBCAGCxWNUeUVCUvn37onv37nB3d0fPnj0hLi5eI/0ylA4jBhgqTVHzv6+vL+Li4v5Z839SUlKJlf67d++QmpoK4NeD2NTUFObm5hg5ciRMTU1hamoKVVXVcifQbkaqOBIYWWF4YWUgLgcf717GxFuhcHZ2xvLlyyEjIwMiQmRkZDGBcOjQIaxevRrArwQyEhISSEpKQqtWrbB27Vp07ty5xoTA48ePYWtrCx0dHdy4cQNqamo10m9NIeyQwkIkJSXBYrHKtAwAv/wGnj59KtR+y4LFYmHLli1o0aIFduzYgRkzZtRIvwylwyKiCp8yaWlpqFevHlJTU6stUQhD3aA087+BgQHs7e1hb2+PDh06/NXm/8zMTISEhBRb6QcHB+P79+8AADExMRgbG/Mme1NTU5iZmUFbW7tS57mHx6ej15b7wr4NHtP003D1xAHcuXMHsrKycHJygrOzMzp06FBico+Pj8e6deuwa9cuEBEUFRV59y0hIQEzM7NiFoRmzZoJPevf9evX0b9/f/z333+4fPlyqfHydZnc3FwoKytj4cKFmD9/vtDbl5OTw/Lly+Hu7l7q9W3btmHOnDnIzMysEZ8PAJg0aRKOHj2K8PBwqKqq1kif/xL8zt+MZYChXArN/4Xe/69fv4aIiAg6duz4V5v/8/LyEBYWVmKl//nzZwC/VjV6enowNTWFq6srb+I3MDAQqhgyUJNDJ30VPP6cJFTrgAibhfaNleHuYgt3lyGIjIzEoUOH4OPjA29vbxgYGGD06NEYOXIktLS08OXLF7i5ueH27dsYNWoUNm3aBCUlJaSlpSEoKIhnRQgMDISPjw8KCgrAZrNhZGSEli1bFhMJlXVUPHHiBEaOHAkbGxucOnWqWpMX/SkePnyIzMzMattDL+/kQuCXZSA3NxdfvnyBvn7FZ1wIg+XLl+PEiRNYtGgR9u3bVyN9MpSEsQwwlCArKwu3b9/mJf8pav63t7f/q8z/XC4XX758KbHSDw0NRUFBAQBAU1OzxErf2Ni4xnLdRydnoefmAOQKKQQQACRE2bjt3gUNlYrfA5fLRUBAAHx8fHD27Fnk5OTAyMgIX758gaqqKvbv3w8rK6ty287JyUFISEixbYagoCBkZ2cDABo1alRCIDRo0KDcbYYdO3Zg6tSpGDlyJLy8vCAq+neuY2bNmoUTJ07g27dv1bLt0rhxYwwaNIi35fM7sbGx0NTUxKVLl+Dg4CD0/sti+/btmDZtGl6+fAlzc/Ma6/dfgN/5mxEDDACAb9++4erVq3+t+Z+I8P379xIr/ZCQEJ5DlYKCAszMzGBmZsab+E1MTGqF8Dke+BULLlZ8jDG/rO1nhkH/aZdb5vnz5xgyZAg+ffoE4Nf7M2zYMDg7O6Nly5YCTVYcDgdhYWHFBMLr16/x8+dPAL882X8XCHp6emCxWFi+fDmWLVsGd3d3bNiwoVLbLXUFExMTtGvXDgcOHKiW9s3MzNCtWzds27at1OuF2z/z5s3DvHnzqmUMpZGfn48WLVpAWVkZAQEBTJ4RIcJsEzCUS3nm/5UrV/Jy/9dFUlJSiq30CwVAcvKvxDxSUlIwMTGBqakpBg0axJv8Kwqj+1MQEZ4c3YiUVz+g0HlEldsTe38dPWa2LfN6fn4+1q5dixUrVkBXVxcPHjxA/fr1cfDgQRw6dAg7d+6EmZkZnJ2dMXz4cNSvX7/CPkVERGBsbAxjY2MMHTqUd19RUVE8YfDq1SscOXIEa9asAfDLUVFOTg5xcXHo378/Ro4cCQ6H89eKgcjIyGoJKSxKeccYAzUfUVCImJgYtmzZAktLS5w5cwZOTmXn12CoHhjLwD9Eofm/MPlPXFwcFBQUYGNjAzs7uzpn/s/OzsaHDx9KrPa/ffsG4NcEZGRkxDPtF672dXV1a8w5ShisW7cOc+fOxZ49e1CvpQ2WXg5BAZcE8iEQYbMgymZhYlsVrBpji0aNGuHOnTslfs8vX77EmDFjEBISgjlz5mDJkiWQlJTkXS8oKMCtW7fg4+ODS5cugYhgb28PZ2dn2NjYCMV8/+PHDzx79gwLFy5EUFAQVFVVkZCQAAAQFxeHqalpMStCs2bNeGFzdZk9e/Zg8uTJSExMFHokQSE9evSAqqoqTpw4UWaZsWPH4s2bN3jx4kW1jKE8HBwcEBQUhI8fP/6VPiF/AmabgAHAL/N/4d5/XTX/FxQUIDw8vMRK/9OnT+Byf+2j6+rqltjXNzQ0hISExB8efdU4evQoRowYgcWLF/NyuUcnZ2HBhWA8iEiECJtVrihgswAuAfqyBfCZ0AsNlaTx+vVrdO3aFS1btsS1a9cgJSWF7OxsLFu2DBs2bECzZs1w4MABtGzZstyxJSUl4fjx4/Dx8cHr16+hpqaGESNGwNnZGU2bNq30PWdmZmLAgAHw9/fHsWPHMGDAAKSnpxdzVHz9+jVCQkJ4joqGhoYwNzcvJhLqkrAFgD59+iAlJaVaDwsq9AO4fPlymWU2bdqExYsXIz09vcatMOHh4TAxMcHixYuxePHiGu37b4URA/8oXC4XL1++5IX/FTX/FwoAQ0PDPz3MUik0G/++0v/w4QPy8vIA/EqC8/tKv2nTppCTKz//fl3Ez88PvXv3xogRI3DgwIESWxjh8enY6/8eJ+69hZiSBoD/v84CoK0sjW6Gqgg4sBKJn98hKCiI93B/+PAhLC0t0bNnT0yfPh3jx49HVFQUli5dilmzZgksEIOCguDj44OjR48iKSkJbdq0gbOzMwYPHizQKjc5ORl2dnZ4+/YtLl68WG7indzc3FIdFQt9QLS1tUsIBE1NzVq5FVQYUrho0aJq3asfMmQIEhIScOfOnTLL3LhxAzY2Nvj8+fMfSeY0Z84c7NixA6GhoWjYsGGN9/+3wff8TXyQmppKACg1NZWf4gw1TGZmJl26dInGjh1LGhoaBIAUFBRoyJAhdPz4cUpOTv7TQyxBfHw83blzh7Zu3Uqurq7Url07kpOTI/w6SI/k5eWpffv25ObmRtu2baO7d+9SQkLCnx52jfHq1SuSlZUlGxsbysvLK7Pc1atXCQCFhEaQikELmr5iC72LSaGMnHxemQcPHhAAunjxYrG6Z8+eJTabTQCoQ4cO9OHDhyqPOzc3l86ePUu2trbEZrNJUlKShg4dSn5+fsThcMqtGxMTQ6ampqSsrEyBgYGV6r+goIA+fPhAx48fp9mzZ1OPHj1ISUmJ971SUVGhXr160dy5c+nkyZMUGhpa4bhqgtu3bxMAevPmTbX2M8rFjVr2cKBXkcklvieFREZGEgDy9fWt1rGURWpqKqmqqtLQoUP/SP9/G/zO34xloI5SaP6/cuUK/P39kZOTA0NDQ9jb28POzq7WmP/T09MREhJSIiVv4R6whIQEjI2Ni630TU1N0bBhw1q5gqsJvn79CgsLC2hqauLevXuQlZUts+zq1auxZs0apKSkQFFREQsXLsTs2bNLlOvSpQuys7MRGBgIFouFa9euYfz48UhISEBubi4mTJiAnTt3CvU9j4uLw5EjR+Dj44OPHz9CW1sbo0aNwujRo9G4ceNiZSMiImBpaYn8/HzcunVLqCfZERGio6OLOSq+fv2a51siKyuL5s2bF7MgNG3atEbT41ZnSGF4fDqOBUbhbmgCIpMyi511wQKgrSSNbkaqGNZWGwZqciAiyMvLY8mSJaV+l2oCb29vuLi44OHDh+jQocMfGcPfArNN8JdRaP4vTP1baP7v1KkT7Ozs/rj5v/DEvd9T8kZGRgIA2Gw2DAwMiu3pm5qaQk9P76+NGa8MSUlJ6NChA/Lz8/H48eMKU+0OGjQIcXFxuH//frnZ5fz8/GBpaYnTp0/j8uXLOHr0KKysrLB3717cunULbm5uWLhwIVauXCn0eyIiBAYGwtvbGydPnkR6ejq6dOkCZ2dnDBgwAOHh4bC2toaCggJu3boFbe3yQx6FxY8fP/DmzZtiAiE8PBxEBHFxcZiYmBTbZmjevHm1OSo2bdoUFhYWQg0pFMS3pPB6J30VeDqaob91V5iYmMDHx0do4xEELpeLNm3aAACePXv210aQ1ASMGPgLyMzMLJb85/v37zzv/8LkP1U5drYycDgcfP78ucRKPywsjHfiXsOGDUus9I2NjYt5pTOUJDs7Gz179kRYWBgeP34MAwODCus0adIElpaW2LZtG6SkpLB27VpMnTq1RDkulwsDAwNER0dDVlYWmzdvxsiRI3mr0PXr12POnDnYsGEDZs6cKfR7KyQrKwvnz5+Hj48P/P39ISUlhYKCAjRu3Bj379//4+lo09PT8fbt2xKOivn5+WCxWKU6KiorK1epz8jISOjo6ODs2bPo37+/UO7j5POoKkWdNEp8htRX1xAYGCiU8VSGR48eoWPHjvD29oazs/MfG0ddh8kzUEcpy/w/bNgwnvd/Tayk6X8n7v2+0i964p6ysjLMzMzQo0cPTJs2DWZmZsVO3GPgHw6Hg6FDh+LNmze4e/cuX0IgMzMTYWFhPFMuh8MpNWQyNjYWEyZM4KVSPnDgABwdHYuVmT17Nn7+/IlZs2ZBQUEBLi4uQrirkkhLS2P48OEYPnw4vLy8MGHCBIiKiiI0NBSdOnXipUDW1NSslv4rQk5ODh06dChmms7LyyvhqHjlyhVevH7Dhg15wqBQJGhpafFt7r9+/TpERUWFdkrhjrvh2HArrFJ1Of8TD2EKrZElFQEi+mPbdR06dMCQIUMwf/589O/fn1mIVjOMZeAPU9T8f+XKFbx584Zn/i/c/69u83/RE/eK/hUeYysjIwMTE5MSq301NbV/dl9fmBARJk+ejL179+LSpUuwtbXlq15gYCDatWuH58+fo3Xr1hAREcGuXbswbtw4XrsHDhzArFmzICkpiR07dmDFihVQV1fHzZs3Sx3HpEmTsHfvXpw6dQoDBgwQ6n0W5fDhwxgzZgwcHBxw9OhRPH36FD4+Pjh37hxyc3NhaWkJZ2dn9OnTp1aGh3I4HERERJTIqJiUlATgl1D+XSAYGBiUau4WZkjhyedRmHc+uMrtFDK3qxYmWDUXWnuCEh0dDSMjI0ydOpWXjIpBMJhoglpMRkYGXbx4kVxcXEhdXZ0AkKKiIg0dOrRavf8zMjLo2bNn5O3tTe7u7tSrVy9e9AEAEhMTIzMzMxoyZAitWrWKLl++TJ8/f64V3tZ/M56engSA9u/fL1C9PXv2kIiICGVlZRGXyy3WxqdPn6h79+4EgJydnXnfqZMnTxIAevbsWaltcjgcGjJkCImJidGNGzeqdmNlsHnzZgJALi4ulJ9f3Js9JSWF9u3bRxYWFgSAlJSUaPLkyfTy5UvicrnVMh5hweVyKSoqii5dukRLly4lBwcHatiwIe/3JSMjQ+3bt6dJkybRgQMH6NWrV5SWlkYyMjK0evXqKvcflZRJhouuUcMZZ6hehyEkqduS2JKyBICUe0+nRvN8S/w1GLubJHVbEktMktiSsiRj0o20ph6jRvN8SXvuFdJf4EtRSZlCeHcqz7Jly0hcXJzCw8P/6DjqKv9kNEFmbgG+JmUir4ALcVE2dJRlICNRO3ZCoqOjiyX/yc3N5Xn/C9v8n5+fj9DQ0BJJer58+cIz+zVu3LjESt/Q0LBWRCD8Sxw6dAijR4/GsmXLsHTpUoHqTpw4EQEBAbzkO2JiYvDy8kJaWhoWLlwINTU17N27F5aWlrw6HA4HTZs2hbGxMS5evFhqu/n5+XB0dIS/vz/8/PyE5s1NRFi8eDFWrVqFuXPnYvXq1eValj5+/IiDBw/i8OHDiIuLQ7NmzeDs7Ixhw4bxlQK5tpCYmIg3b94UsyCEhYWBiCAiIgIOh4M+ffqgR48eaNmyJZo3b15uBElZjDgQiMefk5Cb/B0xe1wgIl8fogrqyI0KhnLv6ZBtVnwboiAtEXE+U8GWkIFca3tQXg7Snp2HiHx9aIzaBJaIGFggdNSvjyMuZaevrm6ysrLQpEkTtGzZsszvLEPZ/DMOhEXDZqKSs1D0ZkoLm6kpuFwuXrx4wdv/rw7zP5fLxdevX0sk6QkNDUV+fj4AoEGDBiU8+I2Njf+K9K11nZs3b8LOzg6jR4/Gvn37BN5y6dChA3R0dHDs2DHk5uZCUlISenp6+Pz5M6ZMmYJVq1aVOqkcPHgQzs7OePv2LczMzEptOzs7GzY2Nnjz5g3u3buHFi1aVOYWeXA4HN4WxPr16zFr1iy+6xamQPb29uZlzrOzs8OYMWNgbW1dJ6NRMjIy8PbtWyxevBhPnz6FoaFhMUdFAwODEtsMKioqZbYXHp+OXlvuAwCoIB/cnAyIyCoiNy4c3w+5lyoGkm7uQmbwHTRw3Q3Rer8cN7O/vkHCyUVQsp4MuRbWvLK33TtDX/XPJfY6deoUBg8ejFu3bqFXr15/bBx1kb9eDFQlbOb3Y1uFRaH3f2Hu/+/fv0NRUZHn/W9lZVUp738qcuJe0ZX+7yfu/Z6Zz9TUtM6lZP1XePnyJbp06YKuXbvi4sWLAk9oXC6XFws+ffp0rFixAitXrkSDBg1w5swZtG/fvsy6+fn5MDAwgIWFRbk56tPS0tC9e3dER0fjwYMHlRavubm5GDFiBM6dOwcvL68qeYYnJibyUiC/efMG6urqvBTIwsxNUFM0bdoU7du3h5eXF/Ly8vD+/fsSGRUzMjIAAFpaWsVOdWzZsiUvH8eyyyE4EhhZ4jlYnhiI3jYcktqmqN+3eMbDmH3jICqnArUhqwD8en6OaNsIyxxMqvGdKB8iQufOnZGcnIygoKA6KQD/FH+1GKhq2IyHgwkGV3B8K78Umv8Lvf9zc3NhZGTEi/0X1PyfkpJSapKeQsckSUlJ3ol7RSf/is6DZ6g9fPnyBRYWFmjUqBH8/f0rZaWJiIiAgYEBtm3bhv379+PDhw8oKCjA4cOHMWJExScb7tmzBxMnTsSHDx/KPZ0yMTERnTp1QlZWFh4+fChwetiMjAz069cP9+/fx8mTJ9G3b1+B6pfHmzdv4OPjg2PHjiEpKQlt27blpUCuCxEt/IQUcrncUh0VExMTAQBKSkowNzdHXOvxyGSVPNinLDFQkJ6ImJ2jodB1NOq1K+4omnhlI7I/vUDD6f8vFBspSyNgVjdh3HalefXqFVq3bo1t27Zh8uTJf3QsdYm/VgxUJWymKLMsDTG5W8XhW79TaP4vTP7zu/nf3t6er7CwoifuFTXzFz1xz9DQsMRKv3HjxnXqxD2G4iQmJqJDhw7gcrl49OhRpePqjx07huHDh4PNZqNFixbYvHkzunTpgjNnzvAVBZCTk4PGjRvDysqqwsQy3759Q8eOHSEpKck7zpgfkpKS0Lt3b3z48AGXLl1Ct27VM5nk5ubC19cX3t7euHHjBsTFxdGvXz+MGTMG3bp1q7UJa/bs2YMpU6YgMTFRIPFC/wv7LRQIL4Le4a3hqFIXA2WJAd7rdjMga9q9WJ2fd72RFnge2rMugCX6y4eIBeDdMqs/7oPl6uqKc+fOITw8vMr5Hf4V/so8AyefR5UpBLh52UgLPI/c2FDkxYWBm5NRqmmskA23wlBfVgKD+LAQZGZmws/PD76+viXM/3PnzuVlTyuNgoICRERElFjpR0RE8E7c09HRgampKYYPH86b/I2MjGplSBVD5cnKyoK9vT1+/vyJJ0+eVFoI3Lt3D1OmTAEAeHp6YubMmbwwUH6tUJKSkpg9ezbmzJmDpUuXQkdHp8yyWlpa8PPzQ6dOnWBtbQ1/f/8KJ69v377B0tISiYmJuHfvXoUnIFYFCQkJ9O/fH/3790dsbCwvBfLx48fRqFEjXgrkP3HoTnlcu3YN7du350sIcLlc5OXlIT8/H/n5+RATE4O5uTlMTU3R5nsGJlyOEqhvKsgFALBESjoMs0TEeWUKxQAB+JqUCZMGf9bisnLlSpw+fRrLli3D9u3b/+hY/jbqjBiITs7C0sshZV7nZqUh9dEJiMjXh5iqLnKjKo61XXI5BO31VEr1ISjL/D98+HBe7v+iD14qcuJe0ZV+0RP3VFVVYWpqChsbG95K38TE5K88cY+hOAUFBRgyZAiCg4Nx79496OnpCdxGamoq5syZg3379kFJSQkdO3bE3LlzAYCX/VEQq5Gbmxs8PT2xbt067Nq1q9yyBgYGuHnzJrp27QoHBwfcuHGjzPPmQ0NDeREMDx8+rNE02Q0aNMDcuXMxZ84cPH36FAcOHMCmTZuwfPlydOjQAU5OTrCysoKYmBhvYi38KzrZlvcnjHK5ubl49uwZ1NTUYGJiUmFbhQuH0hDXMITGqE0CvU8s0V8LDeLkl7hGnLxiZQrJKyh7DDWFmpoaFi9ejHnz5mHcuHEwNTX900P6a6gzYmDBhWAUlOckKKsErclHinnQVkQBl7DgQjCOuLQtZv6/cuUKgoKCICIigs6dO2P16tWws7Pjmf9//PiB+/fvl0jSk56eDuBXFjNTU1O0adMGY8aM4WXm+9OpVhn+DPS/ZD5Xr17FlStX0Lp1a4Hb8PX1xfjx45GamoqdO3di9erVxZwECwoKAAgmBmRkZODu7o7ly5dj0aJFaNCgAW+8HA6nxISmqKiIvXv3YtSoUbCyssKGDRtARMXKfPjwAUuXLoW8vDxmz56Nx48fIyAgoMYn28K/orugjx49wqNHjwR+74siKioKMTGxCv/ExcVLvCYhIQFZWVmIiYnhx48f4HK56NSpEzQ0NARqs6CgAImJifj+/Tvi4+PxJSUfXwW8DxHZX47MnIzkEtc4GT/BlpTjWQUKERetHdstU6dOxb59+zB9+nT4+fkxvlJCok6IgfD4dDyISCy3DEtUjPcF5xcOl/AgIhGD3abj3uWTiI+P55n/582bhw4dOvBS8u7YsaPEiXvi4uK8E/f69OnDW+1ra2szX9B/ECJCQUFBiYlq06ZN2LdvH1auXAlNTU28fPmS7wktOTkZZ86cwatXr2BoaIiBAwciIiIC3759Q3BwMCZPnoz8/Hz8/PkTALB27Vp4eXnxPZHm5eUhLy+P54tSeL0iHjx4gLZty449T0tLw7Rp03j/ruwEKiYmBikpKcjLy1dYjp82k5OTce/ePfj5+SEhIQENGzaEg4MD+vbtC01NzQrbE9bveubMmXj//j1OnjxZapvZ2dn49OkTwsPDERYWhvDwcN7/f//+nVdOWVkZek2aAkZU7DTCihCVUwFbuh7yvkeUuJYbFwZxteJbKiwAOsq1IxxZXFwcmzZtgr29PS5fvow+ffr86SH9FdQJMXAsMKrC8MHKQlwOnv+UhJWVFbS1tXnhPfPmzSt24p6+vj5MTU0xfvx43r6+vr4+E+IiBIjoj5hqhV2ucHVeFosWLcKiRYsq9R5JS0sjOTkZp0+f5m0JhIaGIjY2FmJiYjwzcnp6OqSlpSEmJgYZGRm+JtB79+7h0aNHWLRoEZSUlPiaZB88eIBFixZhwIAB8PDwwL179zB9+nS0a9cOhw4dgqKiIq+sqKhorRLHY8eOBZfLxb179+Dj44MDBw5g9+7dsLKygrOzMxwcHKrdX+fatWuwtLTkTfS/T/jfvn3jWTXk5eVhYGAAAwMDdOnSBYaGhrx/F4YOd1l/F5HJWQKNQdqoPTKD/VGQ9gOi8r+cQrO/vkFBcgzk/ys+wWorS/9x58Gi2NrawsrKCjNmzIC1tTXjXyUEas+nWw53QxOqRQgAAIstghxlPRzeuxbAL2cpMzMzODk5FTtxr6z90T8Jl8ut1ZMjv+UKJzdhwWazK7UCLfyTlJQUaAVaVrm3b9/C09MT1tbWmDlzJiQkJPhqLz4+Hu7u7rh69SqcnJywffv2YltMW7Zswfz58xEaGsoTo+Hh4TA0NMSmTZvQtWtXgd6vSZMmQUdHBzk5OZg4cSJfdTp16gR1dXW4uLggIyMDN2/exIABA3D48OE68WBms9no3r07unfvjh07duDUqVPw8fGBk5MTlJSUMHToUIwZMwbm5uZV6ofD4SAyMrLYhB8UFISPHz8iLCyMF8khJSXFm+CHDRtWbMJXVVWtUEx1M1LFkadfwfnfYzLt5RVwczJ52wDZEc9QkP7Luirfyh5sSRnUs3BC1sdHiD++AHKtHUD5v5ywxerrQNbs/xP7EJeDdg1rl18Ti8XC5s2bYWZmhi1btvB8ZxgqT60XAxm5BYgSUPEKipiiBo6fPgdjg8aQkpIqNlFlZ2cjMDDwj02k5ZUpz6moMoiIiFRq8iz8k5aWrvIEKoxytSGU7Pnz5xg9ejRsbW1x/vx5vixIXC4XXl5emD17NmRkZHDhwoVS4/LfvHkDU1PTYm1WxoGwEBUVFUyYMAHbt2/nnVrID2PGjMGFCxfg6+uLdu3a4fjx43Uy7LVevXpwc3ODm5sbPnz4wEuBvGPHDjRv3pyXArmsDIBcLhcxMTElVvjh4eH49OkTb9tFXFwcenp6EBUVBZvNxqZNm9CsWTMYGBigQYMGlf7eZmdnIyfkNjikz3stLfACOGkJvH9nhT0Gwh4DAGRNuoEtKQNR+fpQG7oaP/29kBJwECy2KKT0/4Nid5di/gIstghayKZXamzVibGxMSZPnoyVK1di5MiR0NDQ+NNDqtPU+jwDIbGpsN3+UKA65WXdKotY7ynIT/hSmSGW6lQk7MmuuifQwgcUQ9X59OkTLCws0LhxY/j7+0NauuKMlxEREXB1dcW9e/fg4uKCDRs2lDkpm5ubo1WrVvDy8uK9FhISAlNTUzx+/BgWFhYCjzkuLg66urpYvHgxFi5cWGF5IsK8efOwbt06dOzYEQ8fPsTevXvh5uYmcN+1kYKCAty8eRM+Pj64fPkyiAiWlpbo3LkzlJSUePv54eHhiIiIQHZ2NoBfYkxXV5e3qi+6wtfW1oaIiAgcHByQlpaGe/fuVWmMHA4Hhw8fxpIlSxAXFwe1wSsgqmkCFlt4gkyEBWR+eY2lnZUxYcIEobUrLH7+/AkDAwPY29tXmC/jX+WvyTNQU+Es23bsgqFyxZPo7xNtbdsPZfiz/Pjxg5d3wtfXt0IhUFBQgC1btmDx4sXQ0NDA7du30aNHjzLLF/q0uLi4FHu9KpYBANDQ0MDYsWOxefNmTJs2rdyDcgoKCjB+/HgcOHCAV37q1KkYP3486tWrh0GDBlVqDLWBpKSkYnv3oqKiMDY2RmhoKK5du4Zr164B+LWPb2Jigo4dO2LMmDG8CV9XVxdiYmUf9pWbm4s7d+5gyZIllR4jEcHX1xfz589HSEgIDAwMwOFwoBl7Hyk6zZHHEc6W6i+H2HxIBJ3HexXhHFYlbBQVFbFixQpMnDgREydOxH///fenh1RnqfVioKbCWRYtmAc9JQno6+vDwMCA919NTU0m0xUDX2RmZsLOzg7p6el4/PhxuQfLAEBwcDBcXFzw4sULTJs2DStXrqwwNfHHjx+Rl5eH5s2LnzFfmdDC35kzZw727t2LvXv3YubMmaWWycnJwdChQ3H58uViqY+3bt2KlJQUDB8+HPLy8rCxsan0OKqbtLS0YhN+UbN+cvL/h9o1aNAABgYGaNOmDW8fv6CgAP7+/jh16hSePHkCIkKLFi3QsWNHvpIH3b9/H1lZWZV+f54+fYo5c+bgwYMHaNGiBTQ0NPDt2zds3rwZU6ZMwZlXMZh3vuIcK/zAYrGgFnMfzz68xoW0BKxdu5YvK1dN4+rqit27d2PatGl49OgRszirJLVeDOgoy4AFoHrcBwshTBk9GJGffj0Y7ty5g/j4eN5VRUXFEiKh8L9KSkrMl48BBQUFGDRoEN6/f4+AgAA0bty4zLK5ubnw9PSEp6cnDA0N8fjxY7Rr146vfoKCggAAzZo1K/Z6oWWgKtEt2traGDlyJDZs2IBJkyZBUlKy2PW0tDT07dsXT548wcWLF2FnZ8e7xmaz4e3tjdTUVPTv3x83b95Ep06dKj2WqpKVlYWIiIhSJ/2iv20VFRUYGhqiSZMmsLe355n19fX1y7SODBgwAJs3b8aVK1fg4+ODCRMmYPr06ejXrx+cnZ3LTYF8/fp1aGpqlnlaZFmEhoZiwYIFOH/+PExNTWFtbY0bN26ga9eu8PLy4iWxGvyfNmKTM7Dt3heABAs3/J3ZlkaY2LU3ev/8iBs3bqBly5Y4evRopfJkVCeioqLYsmULevTogRMnTmDo0KF/ekh1klrvMwDwHzZT1IM24/U1SBu2h5jar4dyoQdtaZR2CEd6ejoiIiJ4D5Si/y0a56ugoFCqSGCEwr8DEcHNzQ0HDx7E1atXedn3SiMwMBAuLi68h/uCBQsE8r6fOXMmLly4gM+fPxd7/enTp7CwsEBwcHCVsrKFh4ejSZMm2L59e7HIgh8/fsDGxgYRERG4cuVKmRN9Tk4ObGxs8OrVK9y7d6/K3vjlkZubi8+fP5c64Ree8QH8chAsundf9P/5dZYsj5iYGF4K5LCwsHJTIBsbG6Njx47Yv38/X23HxcXBw8MDXl5e0NLSwoABA3DixAmkp6dj/fr1cHV1LSE8XF1dcT7oO5QtJ4BDqNRhbssdTHip2guPD27evDlCQkKwZMkSzJ8/v9aFVffv3x+BgYEIDQ1ljmgvwl91UFFZx3P+zrddY4p50BZFc/wBiCqolbzA5aCDGheHptrx/eVOT0/nORD9Lhb4EQr6+vpQVlZmhMJfgoeHB5YtW4ZDhw5h5MiRpZbJzMzE4sWLsWXLFrRq1QoHDhwosbrnh549e0JeXh7nz58v9vrDhw/RqVMnvH//vspH+Q4dOhSPHj1CREQExMTEEBUVhV69eiE1NRU3b94ssUXxO+np6ejRowe+fv2KBw8elHsqYkUUFBTg69evpU74kZGRvIgaaWnpYpN80UlfRUWlRn5rRIQnT57Ax8cHp06dQnp6Orp16wZnZ2f0798fCQkJ0NXVxblz59CvX79y20pLS8P69euxadMmSEpKwt3dHe/fv8eJEydgZWWFffv2QVu75LkqZ86cgZOTE7y8vGDpOEQox7wHBwejWbNmuHv3Lvz9/bFq1Sq0adMGR44cgb6+fplt1jSfP39G06ZNMWfOHCxfvvxPD6fW8FeJgfD4dPTacr/a2o/ZPx6asiKYNm0aXFxcqnSPGRkZZVoU4uLieOUUFBTK3HpghELdwcvLC66urvD09MT8+fNLLePv7w9XV1fExsZixYoVmD59eqVWVUSE+vXrY8qUKVi6dGmxawEBAejatStCQ0OrfBbAu3fvYGZmBm9vb7Rt2xaWlpYQFxeHn58f32cqJCUloXPnzkhPT8fDhw9LnbgK4XK5iI6OLrZ3Xzjpf/78mecPISEhAT09vVJX+RoaGrXqN5OZmYnz58/Dx8cHd+/ehZycHMzMzBAYGIikpKQy/Qvy8vKwZ88erFixAhkZGZg+fTqMjY0xe/Zs5OXlYcuWLRg5cmSp9xoZGYnmzZvD0tISp06d4pUJj0/HscAoXH39FQnZVKwuEaG+JGDXUhfD22lDX7VkPoHc3FxIS0tj9+7dcHNzw5MnTzBixAjExcVh8+bNcHV1rTXv/cKFC7Fp0yZ8+PCh3MO3/iX+KjEAACMOBOLx5yThJh/icmCqKo4V3dWwadMmnDx5EtLS0nB1dcXUqVPLfYBVhoyMjDItCkWFQr169cq0KNTUKoehYnx9fdG3b1+4ublh586dJT6XlJQUzJ49G15eXujSpQu8vLyqtJKKiYmBlpZWqfkH/P390aNHD3z69KlcfwV+cXR0xMuXL5GZmQlNTU3cvHlT4DjumJgYdOzYEeLi4rh//z64XG6JTHuFsfg5OTkAfu3/6urqljrha2lp1ck8Bl++fMHBgwexbt065OTkwMjICM7OzhgxYgTvPAgul4tTp05h4cKFiIyMxJgxYzBp0iSsXLkS586dQ58+fbB79+4yP4OCggJ07doV3759w5s3b0rd/vDx8YHLuIl4Ff4NxGJDXJQN2y5t4GjXG5s3by73HoyMjGBjY4MtW7YA+PUsmzlzJvbt2wc7Ozt4eXlBTa0Uy2sNk5GRAUNDQ3Ts2BGnT5/+08OpFfx1YiA6OQs9NwcgV5ihhpx8xOyfgKljhmLlypVITk7G9u3bsXfvXqSnp2PgwIGYOXNmjTjMFAqF30VCaUKhLIsCIxQqT2ZuAb4mZSKvgAtxUTZ0lGXKTb/67NkzdOvWDZaWljh79myJSerSpUuYMGECMjIyytzbFZRr167B1tYWX758KbHq8fPzg6WlJb5+/YpGjRpVqR8A2LlzJyZPngxDQ0M8ffoUiooVn/tBREhKSio24b969Qp+fn7gcrk8kz6LxUKjRo1KNes3atSo3NC8ukpOTg6UlZUxbNgwZGVl4dy5c8jLy4O1tTVatWoFX19fvH79Gn369MGqVavw+vVrTJs2DWw2Gzt27ICTk1O5v+1ly5ZhxYoVuH//Pjp0KD0McNWqVdiyZQt+/PjBe2306NF4+/YtXr16Ve74HR0dkZmZiVu3bhV7/cqVK7z0zvv37y81SVZNc+TIEYwcORL37t1Dly5d/vRw/jh/nRgAgJPPo4QWNgMAq/uaIubBGSxatAi6uro4ePAg2rZti4yMDPj4+GDLli34/PkzOnXqhJkzZ8LOzu6PrEwyMzPL3HqIjY3llWOEgmAUmk/vhiYgKjmrWMQKC4C2kjS6GaliWFttGKj9v/k0IiICFhYWMDQ0xO3bt4ulqk5ISMDUqVNx6tQp2NraYs+ePdDS0hLKeAuPG/7582eJz/L69evo3bs3oqOjq9zfmTNnMGzYMNSrVw+qqqoIDg4uJmRSUlKKmfSLrvJTUlJ45TQ1NXnfvatXr0JHRwdHjx6FiYlJnUhZLEwKxdrbt29hZmaG1NRUrF+/Hjt27EBqaipERUXRp08fjB07Fjt27MDVq1cxePBgbNu2DfXr1y+37QcPHqBr165YunRpufkLJk+ejPv37+Pt27e817y9vTF27Fj8/Pmz3NDIhQsX4tChQ8UcMwtJSEiAq6srLl++jDFjxmDLli1/9Fh2LpcLCwsL5OXl4cWLF3XSmiRM/koxAAA77oZjw62wStcn+rVnNtvSCJO6/TLZvn//HqNGjcKrV68wd+5cLF26FBISEuBwOLh06RI2btyIx48fQ19fH+7u7hg1alSt8VbNzMwsc+uhqFAoPOykNLFQv379f0ooRCdnVdqxSjw/He3bt4eYmBgePXrEy0FBRDh27BimTZsGFouFbdu2YciQIUJ9XwcNGoTv378jICCgxDVfX1/Y29sjLi4O6urqle5j7969mDBhAgYOHIhevXrB1dUVw4YNg5iYGG/CL7qyVFVVLeGhb2hoCD09vWK/kadPn6Jnz57o1KkTLl26BHFx8UqPsS4yY8YMnD59GtHR0fj69SsWLVqE48ePo0mTJpg4cSIiIyOxf/9+pKWlQVRUFKNGjcKaNWsqzFXx8+dPNG/eHDo6Orh79265E1+/fv2QmZmJmzdv8l779OkT9PX14evrC1tb2zLrHjt2DMOHD0dKSkqpooGI4OPjg2nTpqF+/fo4cuRImRaKmqAwumbfvn1wdXX9Y+OoDfy1YgD4ZSFYejkEBVwSyIeAuBywuBxk3PfB4yMbijlaFRQUYM2aNVi+fDmaNGmCw4cPo0WLFrzrT58+xaZNm3Du3DkoKChg/PjxmDx5cq3Oh10oFEqzKMTExPDKycvLl2lR+NuEQmW/O4UhV2JvLyLp2WU8efKEZ6qPjo7G+PHjce3aNb5Xc5XByMgIVlZW2LZtW4lrly5dQt++fZGQkMB33zk5Ofj8+TPCwsIQFhaGM2fO4MWLF5CRkUFmZiavnIiICFq1alXCrG9gYMBXop1Cbt++DVtbW/Tt27fOnmNQWYyNjdG6dWsoKytj165dUFFRgYeHB5ydnREdHQ1XV1fcuXMHPXv2hKSkJG/CdnBwgLOzM6ysrEo4nRIRBg4cCH9/f7x586ZCHycLCws0adKkWNpeIoKWlhaGDx+OtWvXlln39evXaNmyJZ48eVJuTozPnz9jxIgRePr0KebOnYtly5b9MeE3cuRI3LhxA2FhYUIJIa2r/NViAKjc6q6ReBYeb50CDXlxKCgo4OnTpyUyar158wajRo3C+/fvsWTJEsybN6/YHubXr1+xdetWeHl5ITc3F0OHDsWMGTMqFSb2J8nMzOTFaBf1TyhLKJSWR6GuCYWqWpUKk7gMM5PHqqGdwOVysXfvXsydOxdycnLYvXs3HBwchDfgImRmZkJOTg5eXl4YM2ZMievnzp3DgAEDkJSUxDvWFgDy8/Px9evXEpn2wsLCEBUVxTsmV0xMDPn5+TAxMUHfvn15E39sbCwGDBiAGzduwMrKqsr3cf78eQwcOBAuLi7Yu3dvnfr+VJbCcyMkJSUhLi6OuXPnYvr06ZCUlMSuXbswb948KCkpYf/+/bz3+MePHzh+/Di8vb3x9u1baGhoYMSIEXB2dkaTJk0AAPv374ebmxtfoYoAoKOjg6FDh8LT07PY60OGDMHXr1/x5MmTMutmZWVBVla2zO9fUTgcDtatW4clS5bA1NSUtzVU08TExMDIyAjjxo3Dxo0ba7z/2sJfLwYK4e37hiUgKqmUfV9laXQzVMXwdtrQVZZG+/btkZSUhJiYGAwaNAg+Pj4lHkh5eXlYvnw51qxZgxYtWuDQoUMlvsypqanYv38/tm7dim/fvqFnz56YOXMmrKys6vwDrjShUPjfokJBTk6uzK0Hfo5drUmE7W8yo6Mazq2bifv378PNzQ3r1q0TaJUsKIVmzxcvXqBVq1bFrnE4HOzevRtTpkzBhg0beGF6YWFh+PLlCy87oaSkJO8zKpzsdXV1sWfPHpw9exY7duwocYQxEaFdu3aQkJDA/fvCCe89ePAgnJ2dMWfOnHJXo3WdgoICeHt7Y/bs2UhLS8OECROwfPlyqKioICwsDC4uLnj48CEmTJiANWvWlPpsJSK8fv0aPj4+OH78OJKTk9GuXTtYW1tj7dq1GDFiBPbu3VvhWIgIkpKS2LhxIyZPnlzs2p49ezBlyhSkpKSUu/2pp6cHR0dHbNiwga/7f/XqFYYPH47Pnz9j7dq1mDJlSo0fhubp6YmlS5fi3bt3Vcp3UZfhe/4mPkhNTSUAlJqayk/xP0ZGTj69i0mhV5HJ9C4mhTJy8kuUCQoKIhEREerfvz8BoP3795fZXmBgIDVp0oTExcVp3bp1VFBQUKJMXl4eHT9+nFq1akUAqGnTpuTl5UXZ2dlCvbfaQmZmJr19+5bOnz9Pa9euJVdXV+ratStpaWkRfmWNJgAkJydH5ubm5OTkRAsWLCAfHx968OABff/+nbhcbo2OOSopkwwXXaNG83xL/WvgtpekjTuRiJwysUQlSFRJi+p1HEYNZ54to84V0p51jhqb/Uf+/v41cg+7d+8mNptNN27coL1799KsWbOoT58+ZGxsTOLi4rz3XUxMjIyMjMjOzo5mzJhBu3fvptu3b1NkZCRxOJxibWZlZZG9vT2JiorS8ePHy+z78uXLBIACAgKEdj9btmwhALR69WqhtVlb4HK5dP78eTIyMiIApKmpSe3atSMiovz8fFq3bh1JSkqSnp4e3b17l+92c3Jy6PTp02RpaUkAiMVi0eDBg+nOnTslPtvfSUxMJAB09uzZEtdCQkIIAPn5+ZXbhp2dHdnY2PA9XqJf37Fp06YRAOrRowdFR0cLVL+qZGdnk46ODvXu3btG+61N8Dt//1VigF/mzp1LEhISNGjQIJKQkKBXr16VWTYrK4tmzpxJLBaL2rdvT2FhYaWW43K5FBAQQA4ODsRisUhVVZU8PDwoISGhum6j1pGZmUnBwcF0/vx5WrduHbm6ulK3bt3KFAoDBw6kBQsWkLe3Nz148IDi4uKqRSgM93pKjRdcLXVi15zoQ2wJGRKRVyWFLqNIyXoyyZj1JAAkpd+2TAGhM/cyDdn3SKjj5HK5FB8fTw8fPiRvb2+aP38+DRgwgJo1a0aioqK894/NZlPjxo3JysqKJk+eTNu2baNZs2YRAEpPT+err5SUFOrUqRNJSUnR9evXKxxXs2bNyNLSUhi3yWPp0qUEgHbt2iXUdv8kDx48IAsLCwJAVlZW9OTJE5KWlqa1a9dScHAw/ffff8RisWjGjBmUmZlZqT6mTp1KEhISNHXqVDIwMCAApKOjQ0uXLqUvX76UWic4OJgA0KNHJb+zXC6XVFRUaNGiReX2O2fOHGrUqFGlxuzn50eampqkoKBAJ06cqFQbleXcuXMEgK5du1aj/dYWGDFQDpmZmdS4cWPq3LkzmZubU+PGjennz5/l1nnw4AHp6emRlJQUbdu2rVwlHhoaShMmTCApKSmSlJQkNzc3+vDhg5Dvom6RlZVFwcHBdOHCBVq3bh25ubmVKhRkZWWpRYsWNHDgQJo/fz55e3vT/fv3Ky0Uwr6nlTmhN5rnSwqdRxIA0nDZWex1GdPuBIC0pp8st354fJrAY0pOTqbAwEA6cuQILVmyhIYMGUKtWrUieXn5Yu9Fw4YNqXv37jRu3Dhq1KgRde7cmT58+EC5ubkl2vTx8SEAlJeXV2H/cXFx1Lx5c1JUVKTHjx/zNeZTp04RAAoMDBT4fsuCy+XS1KlTicVilWuZqAuEhISQvb09AaCWLVvS7du3iYjo1q1bBIAmTZpEYmJi1KRJE77f89K4cuUKAaBt27YR0a/38OHDh+Ti4kKysrIEgLp3705HjhwpJjZu3rxJAMoUC/369aPOnTuX2/fBgwcFEpy/k5SURIMGDSIANGTIEEpOTq5UO4LC5XKpW7duZGRkxNfv42+DEQMVUPgjXbt2LSkoKJCDg0OFk01GRgZNmjSJAFC3bt3K/GEVkpiYSCtXriR1dXUCQLa2tuTv71/jZvLaTllCoWHDhlUWCksvvSvTKtBoni/Jtxvwa9Kfeqzk6yw2NZxR1laBLzVecJWWXnpXar/p6en06tUrOnnyJK1YsYJGjhxJFhYWpKysXOye1NXVqVOnTjRmzBhas2YNnTt3jt6+fVvsQc7hcEhGRobWrVtX5nvo5eVFACo0F3/+/Jn09PRIQ0ODgoOD+fh0flFQUEBGRkbk4ODAdx1+4HA4NGrUKBIVFSVfX1+htl0TREdH05gxY3jWmhMnThT7DIYOHUpiYmLEZrNpwYIFVdo+jI2NJRUVFbKzsyv1+56RkUGHDh2irl27EgCSl5cnV1dXevz4MU8sltX/1q1bSUJCotzxPXv2jADQ8+fPK30PRETHjx+nevXqkaamJk80VTdBQUHEZrNp8+bNNdJfbYLf+bvOOxBWhREjRuDq1avYunUrRo4cibVr12LOnDkV1rtz5w7GjBmD5ORkbNq0CWPHji3XWS43NxcnTpzApk2bEBwcDHNzc8yYMQNOTk7/XLy1oGRnZ5fpzBgdHc0rJysrW2rUw7xHOYhJzSu7/c8vkXB6KaT020Kh0zCwpeSQG/MBSTd2QNasF5R6lh+jrCErijlNs0qk2S16YJWysnKpB+jo6+vz9XsKDw+HoaEhbt68WeaJiPv27cP48eN5Wf5KIzg4GFZWVpCRkcGtW7dKnKhXEYcOHcLo0aMRFBQk1OiZgoICDBw4EDdu3MCNGzfqRNa4lJQUrFmzBlu3boWsrCyWLFmCcePG8X7POTk5WL58OVavXg0lJSX4+fmhZcuWle6Py+XCysoKISEhCAoKqjB89PPnzzh06BAOHjyIqKgo1K9fn3duSmEK5KK8efMG5ubmCAgIQOfOnUttMyMjA3JycuUeyMUv0dHRGD16NPz9/TF9+nR4enoWS95VHUyYMAEnTpxAeHh4tYT+1lb+SQdCQUlISCAlJSUaNmwYzZs3j0REROjevXt81U1NTSUXFxcCQNbW1vTt27cK63C5XLp16xZZW1sTAGrQoAGtWbOmxsxlfxtZWVn07t07unjxIq1fv57GjRtH3bt3J21tbWKxWMQSlyLtuVfKNfM3mudL9ToNJ5aoRLEVu3z7QRXWazTPl7TnXiGWmCTJyclRq1ataPDgwbR48WI6cuQIPX36lJKSkqp8n2fOnCEA9P379zLL7Ny5k0RFRcu8/ujRI1JQUKAWLVqU20555OXlkY6ODg0aNKhS9csjOzubunfvTnJycvTixQuhty8ssrOzacOGDaSoqEjS0tK0ePHiEs/Fx48fU5MmTXh+HqdPn65yv2vXriUWiyXwSprD4ZCfnx8ZGhoSi8UiNptNvXv3prNnzxbbbiooKKB69erRihUrym2vUaNGNHfu3ErdQ2lj27x5M0lISFDTpk3L9d0SBgkJCaSgoEDjxo2r1n5qG8w2AZ8U7oNdvXqVunbtSurq6hQbG8t3/atXr5KGhgYpKCjQ4cOH+d4CePfuHbm4uJC4uDjJyMjQlClTKCIiorK3wfAbWVlZdPnBK74mdGW7mSSp25KUrCdTfccFJNOsFwEsUuw1jq/6999+rtatn4ULF5K6unq5ZbZt20aSkpKlXrt27RpJSUlR586dKSUlpUpj2b17N7FYLPr48WOV2imNtLQ0atOmDamoqNQ6H5uCggI6dOgQaWtrk4iICI0fP57i4uKKlcnMzCR3d3disVj033//0cKFC0lUVLTKz83AwEASFRWt0iQ8YMAA6tq1K+3Zs4fatm1LAEhZWZmmTp1Kr1+/JqJf0QI9e/Ystx0bGxuyt7ev9DhK4927d9SiRQsSExOj1atXlxq1JSy2bNlCLBaLd8//AvzO3zUb9FkLGTlyJLp3745JkybhwIEDYLFYGDJkCO/Y1Iro3bs33r17B1tbW4wcORKOjo6Ij4+vsJ6JiQm8vLwQFRWFGTNm4Pjx4zAwMED//v3x6NEjXjIYhsohJSUFLW2dCstlvg9A8o0dULaZCrkW1pA2ag+V3tMgY9YDKfcOgpOdVmEbsvUUqjWnQlBQEJo3b15uGQ6HU2pGvxMnTsDBwQE9e/bEjRs3qpwLYfTo0dDQ0MCaNWuq1E5pyMnJ4fr161BTU0OvXr0QGRkp9D4EhYhw/fp1tGzZEqNGjcJ///2H9+/fY/fu3cXSPt+7dw/NmjXD7t27sW7dOjx+/Bhv3rxBx44dq7S1mp6ejqFDh8Lc3BwrVqyodDuxsbHQ1tbGuHHj8PTpU4SEhGDMmDE4deoUzM3NYW5uDjabjcePHyM/P7/Mdpo2bYr3799XehylYWJigsDAQMycORMLFixAly5d8PnzZ6H2UcjEiRNhZGSE6dOnM8/Y3/jnxQCLxcKePXsQFxeHPXv24OTJk3j48CEWLVrEdxtKSko4evQozp8/j8ePH8PExARnzpzhq66amhqWL1+O6Oho7NmzByEhIejYsSMsLCxw5swZvkUJQ0nERSv+eqe/ugZxtcYQlS+eA15avw0oPxd58RU/lHp07QITExNYW1tj7Nix8PDwwIEDB3Dr1i28f/8e6enplb4H4JcYKJoauzQKCgpKiIEdO3Zg2LBhGDZsGM6fPy+UPVlJSUnMmjULR44cwdevX6vc3u8oKSnh1q1bEBcXR8+ePfkS1tXF8+fP0aNHD/Tu3RsKCgp48uQJzp49WyyNeXp6OiZOnIhu3bpBQ0MDQUFBmDVrFgoKCuDv7w8bG5sqjWHSpElISEjAiRMnqnSaY1xcXLHU6U2bNsW6desQHR2Ny5cvQ1dXF1evXkVWVhasrKxw7dq1Up89TZs2xefPn5GdnV3psZSGuLg4Vq9ejYCAAMTExKB58+bw9vYW+oQtJiaGLVu2ICAgAOfOnRNq23Wdf14MAICBgQGWLFmCTZs2QV5eHqtXr8batWtx+fJlgdpxdHRESEgIunbtCicnJwwePBhJSUl81ZWSkoKbmxvev38PX19fSEtLw8nJCQYGBtiyZQvS0ipeoTIUR0dZBhWt1zlZKSAq6XRH3F9Z+1D43zIhzBw3Ej169ICUlBSCgoKwe/dujB07FlZWVjAxMYG8vDzq1asHU1NTgQVDcnIyoqOj+bIMFOauJyJ4eHhgypQpcHd3h7e3d4m89lXBzc0NioqKWLdundDaLEqDBg1w+/ZtZGZmwtLSEj9//qyWfsoiIiICTk5OaNOmDX78+AFfX1/cu3evRE7+mzdvwtTUFIcPH8b27dsREBDAEwr3799HdnY2evfuXelxHD16FEeOHMGuXbugp6dX6XaICLGxsaWeoyImJgZ7e3ucP38eUVFREBcXx4cPH2BrawttbW3MmzcPoaGhvPJNmzYFERV7TZh06tQJQUFBcHJygouLC/r161fsYCxhYGVlBTs7O8yaNUvooqYuw4iB/zFr1iwYGxvD1dUV7u7u6Nu3L0aOHCmwuap+/fo4c+YMjh8/jlu3bsHExEQgUcFms2Frawt/f3+8fPkSHTt2xOzZs9GwYUPMmjULUVFRgt7aP4uMhCi0laTLLSOm2AB58Z+QnxxT7PXM9wEAiw2x+jrl1hfN/gkJkV/Hw164cAHPnz/H9+/fkZubi8+fP+P+/fs4fvw4Fi5ciO7du/MtGFxdXeHh4cEzx8vJyZVrYSjcJuByuZg6dSqWLVsGT09PbNiwQegpYGVkZDBjxgwcOHCg2MmYwkRXVxd+fn749u0bbG1tix2cVF3Ex8dj0qRJMDY2xpMnT+Dj44M3b97A1ta22DbQz58/4ezsDGtraxgYGCA4OBiTJ08u9j5fv34dWlpalc7J/+nTJ0yYMAHDhw/H8OHDq3RfKSkpyM3NLTWKoCgNGjRAly5d0LJlS7x8+RL9+/fHvn370KRJE7Rv3x779++HpqYmAAh9q6Ao8vLyOHDgAM6fP4+HDx/C1NQUV69eFWofGzduRGxsLDZt2iTUdus0wnRAqOs8fvyYWCwWbdmyhX7+/El6enpkbm5e6djgmJgYsrW1JQA0atSoChMblUV0dDTNnTuXFBQUSEREhIYMGVLlWN9/hYryDKgNXUNgsYktrUD1Og0jJcsJJNn4V2pp2eaW5ToO6sy7Qi1dV5OkpCQBIENDQ5o1axYFBARQfn7JVNi/k5ubS58/f6b79+/TsWPHaO3atTR58mTq27cvtWrVitTU1IpFOACgevXqkYmJCVlZWdHYsWNp2bJldODAARo5ciQpKyvTgAEDiMVi0d69e6v1fU1JSaF69eqRu7t7tfYTGBhIsrKyZGlpSTk5OdXSR1paGi1btoxkZWVJQUGB1q1bR1lZWaWWvXjxIqmrq5O8vDzt37+/TMdRIyMjcnV1rdR48vLyqE2bNtS4cWOhPHML0w0/ePCgwrIrV64keXl5nhNfdnY2nTp1iqytrYnNZpOUlBRJS0vTsGHDKsxpIQzi4uJ4z9Bx48ZVOuFRacycOZOkpaX5igSryzDRBJVk4sSJJCMjQ5GRkfT69WuSkJCo9I+a6Fc4obe3N8nJyZGWlhbdvHmz0m2lp6fTtm3bSFdXlwBQ586d6eLFizXyo6yrVJSBsNE8X1IfuZEkG7ciERlFAluURJU0SaHzSNKec6nCugfOXqWMjAy6dOkSjR07lpdgSklJiYYPH06nT5+u0u9m+PDhZGZmJpBgkJaWJhMTE7K2tqaxY8eSh4cHHThwgG7evEnv37+ntDTBsyaWxuLFi0laWrraU27fuXOHJCQkaMCAAUL1NM/Ly6OdO3eSqqoqSUhI0OzZs8sMBU1ISKDBgwfzkoeVl2P/06dPBIDOnz9fqXHNmzePREVFhZbt0c/PjwDQp0+fKix7//59AlBqmN+3b9/I09OTpKWleSmQly1bVmHytarC5XJpz549JC0tTfr6+vTkyROhtJuSkkL169en4cOHC6W92gojBipJSkoKNWjQgJflqzCz28GDB6vUbmRkJPXs2ZOncKvyQC4oKKBz585R+/btCQAZGBjQzp07K53r/G+nvLMJKvunO9+XDMdtIwBkYWFBt2/fJi6XSxwOhwIDA2nRokXUrFkz3uFBvXr1om3btgn84GzRogWNHTu23DJxcXGkrq5OLBaL5s+fT2vWrOHbwvC7YLh16xa9f/+erxVYYmIiycjI0IIFCwS6p8pw8eJFEhERIRcXlyqHcXK5XDp16hTp6+sTi8Wi0aNHU1RUVJllT548SSoqKqSkpERHjx6tsP8dO3ZUOqTw9u3bxGKxaM2aNQLXLYvDhw8TgDKtHUXJyckhCQmJcjP1TZ06lbS1tWnMmDHlpkAWNmFhYdS2bVtis9m0ePFioaQW3r9/PwGoUoro2g4jBqrA+fPnCQCdOXOGiIicnZ1JSkqK3r59W6V2uVwu7dq1i6SlpUlXV5fvBEfl8eTJExo4cCCx2WxSUlKihQsXCpQn4V+golMLK/NnuOgaRSZm0I0bN+i///7jWWp+P9nv69evtH37drK0tCQxMTECQGZmZrRw4UJ6+vRpuVad3NxcEhMTo+3bt5dZJiYmhkxNTUlKSooaNGhQZrmcnBz6/PkzBQQE0LFjx3iCoU+fPtSqVStSVVUtVTCYmpqWKxhmzZpF8vLyld4CE4RDhw4RAJo5c2alBYG/vz/v87K1tS33Nx0bG0t9+/YlADRgwAC+kzXZ2tpSt27dBB5bQkICaWhoUI8ePYRq7Vu7di3Vq1eP7/JdunQhR0fHMq/v3buXREREKCcnhzIyMujgwYPUpUsXXgpkNzc3evLkSbXk3sjPz6fly5eTiIgItW7dusr5LgoKCsjc3Jz++++/v9bCyoiBKtK3b19SV1ennz9/UmZmJjVr1owMDAyE8h5ERERQp06dCABNmzZNKGr6y5cvNH36dJKVlSVxcXEaPXo0BQUFVbndv4UTzyKFKgZOPovktc3lcuny5cvUokULAkA9e/Ys1ZSZmppKZ86coREjRpCSkhIBIDU1NXJxcaFLly6V+B4EBQWVu9cbHh5Ourq6pKWlRc7OzmRgYFCl9ygnJ4c+ffokkGCQl5cnFotFBgYG5OrqSh4eHuTt7U23bt2iDx8+CHWPl+hXciUAtHLlSoHqBQUFkY2NDQGgNm3alCvEuVwu+fj4kIKCAqmqqvIWBfyQnZ1NUlJS5Z4jUVaf9vb2pKysTDExMQLVrYhp06aRsbEx3+UXL15MysrKZU6ODx48IAAlzraIiIigxYsXk7a2NgGgJk2a0Nq1a6tlcfLs2TMyNDQkKSkp2rFjR5WER+HWSFWtv7UVRgxUkejoaJKTk+OlrgwLCyN5eXkaMGCAUBQvh8OhTZs2kaSkJBkaGgptH+znz5+0fv163mmAPXv2pOvXrzOHIxHRdv+wKgmAwtTGblvPldo+h8Ohc+fOkampKQGg3r17l5laNz8/n+7fv0+zZ8/mnXsvKSlJdnZ2tHfvXoqJieGthEv73b1+/ZrU1NTIyMiIIiMjyd3dXaAHfmUpKhiOHj1Ka9asITMzMxITE6MWLVqUKhgUFBR4FgZhCIbly5cTANqxY0eFZb9+/UojRozgCZazZ8+W+1uIjIwkKysrAkDDhw+nxMREgcZWeDqgIIdAERFt376dANCVK1cEqscPTk5O1L17d77L3759mwDQu3elH8KVmJhIAOjkyZOlXi9MgTx06FCSlJQkERERsrW1LZECuapkZmbyDo6zsrKqkogaNGgQqaurC82fpjbBiAEhUPgDLVyZFZ6LLcyTrz58+EBt2rQhNptNc+fOFZrHdF5eHh0/fpxatfrlGd+0aVPy8vKq0qlpfwMnnkWS3vzLpD37osA+Ag1nniND69EkLi5O9+/fL7MPDodDJ0+epCZNmhAA6tOnT4VWmtDQUNqwYQN17tyZ2Gw2z2qgqKhIr1+/LjaBBQQEkLy8PLVq1YrnvDd16lQyNTUVzpskIJGRkSQqKkobNmwgol+r498Fw6RJk6hPnz7UsmXLcgWDjY0Nubq60vLly8nb25v8/PxKCAYul0vu7u4EgI4cOVLqmBITE2nmzJkkLi5OampqtHv37nL3mDkcDu3evZtkZWVJU1Oz0icoTps2jbS0tAQS30FBQSQhIUFTpkypVJ8V0bFjR4Gc5DIyMkhUVJR27dpVZhk1NTVasmRJhW39/PmTdu/eTW3atCEApKKiQtOmTaM3b97wPZ6KuH79Oqmrq5OSkpJAVpyiREZGkqSkJM2bN09o46otMGJACBQUFFDbtm3J2NiYN0nPmDGDREVF6dGjR0LrJz8/nzw9PUlMTIxMTEyEelALl8ulgIAAcnBwIBaLRaqqquTh4VHtHuC1laSkJFLRMaIW7geo0TzfCh0LC68P93pKCz03EQBq0aIFKSoqVpg/v6CggA4fPkx6enoEgAYOHEghISEVjjExMZGOHDlCqqqqvMNuGjZsSBMnTqRly5aRpKQkde/evdgqZtKkSdS8efOqvj2VxsXFhdTV1fkWm4WC4d69e3T06FFavXo1TZo0iRwcHPgSDGPHjiVzc3NisVjk4eFBHz58oIyMDMrKyqI1a9ZQvXr1SFZWlpYvX16h5SEiIoJ37K+rq2uVzm8wNDQUKPooMzOTjI2NqVmzZtUm1PX09Gj27NkC1bGwsCj3QKpu3brRgAEDBGrz3bt3NGvWLJ5Dq7m5OW3btk1g60tp/Pjxg/r3708AaMSIEZX6DJcsWULi4uJ8RV3UJRgxICSCgoJIVFSUli9fTkS/VtwdOnQgTU1Nio+PF3pfLVq0IBEREVq6dKlQvGWLEhoaShMmTCApKSmSlJQkNze3WncgTHUzefJkkpeXp+/fv1PY9zRaeukddV7vTzolcgj4Uuf1/rT00jsKj/816XI4HOrevTupq6uTkZER6erq8uVUlpeXR15eXtSoUSNisVg0bNgwCg0NLbcOl8slZWVlWrRoEfn5+dGUKVNIRUWFAJCIiAj17duXDh48yBN148aNo5YtW1b9Daok4eHhxGazaefOnUJrsyLBUL9+/RKCgcViEQBq1KgRDR8+vISFISMjg9d+QUEBbd68maSkpEhHR4f8/PyqNN7CkMILFy7wXWfcuHEkJSXFl0isDFwul6SlpWnTpk0C1Zs7dy5paGiUaeGYNGkSNW3atFJjysvLo8uXL1Pfvn1JVFSUxMXFacCAAXTt2rUqhY5yuVw6fPgwycvLk7a2tsAO2hkZGaSlpVWu82RdhBEDQmTevHkkLi7O81z99u0bqaqqUs+ePYV+wlZubi4tWbKEREREyNzcvMoRDKWRmJhIK1eu5MXE29nZkb+//1/vV/D27Vtis9m0cePGEtcycvLpXUwKvYpMpncxKZSRU3rSoG/fvpGSkhJZWlqSuro6/ffff8UmmPLIzc2l3bt3k6amJomIiNDo0aPp8+fPZfYDgC5evEhERJs3byYA5OjoSCtWrKC2bdvyjqTt0KED/ffff2RmZvZHP8OhQ4eStra2UPeFK+Lnz5/UpEkTngho1qwZDR8+vFzBoKCgQIaGhqSgoEAAqG3btrR7927y8/Ojjx8/8v15/s6OHTtITEyM733nwm3H6kwQlZKSUu7+fllcu3aNAFBYWFip1wuPzK7qgiU+Pp42bdpEZmZmBPw61n3evHkViuXy+Pr1K3Xu3JlYLBbNmjVLoK3X48ePEwCBj4quzTBiQIhkZWWRnp4edenShfewvX37Ni/etTp4/vw5NW3alMTFxWn16tV8ZbQTlJycHPLx8eH9EM3NzenIkSM1+jCvKbhcLnXt2pWMjIyqfH8XLlwgALRw4UKSkZEhe3t7gURhdnY2bd26ldTU1EhUVJTc3NxKxLn7+voSAPr8+TMtXLiQANDcuXOLTfZxcXHk5eVFffr0IREREQJA+vr65O7uTnfv3hW6ZakigoODCQAdOHCgRvp7/PgxdezYkRfVIC8vX+oKOzs7myIiIujevXt08OBBsrKyIjabTTIyMmRgYFCqYFBUVCQzMzOysbEhNzc3Wr58Ofn4+JQrGAQJKYyKiiJFRUXq169ftQq4Dx8+EIASIa8VkZKSQmw2m7y8vEq9fvfuXQJA79+/F8Ywicvl0osXL2jSpEmkqKhIAKh9+/a0f//+Ss07BQUFtH79ehIXFyczMzO+I6u4XC516NCBTE1Nq+WZ+ydgxICQKcziVfRBt3LlSgJA165dq5Y+s7Ozac6cOcRisaht27bVcoY80a8fwK1bt3he1JqamrRmzRpKTk6ulv7+BKdPnyYAdP36daG0V2je3bNnD4mIiNCkSZMEfqhnZmbShg0bSEVFhcTFxWnSpEk8j+hVq1bxYrYB0Pr168tta8iQIdS0aVNyc3OjBg0a8FbAQ4cOpRMnTtRIHgAiIkdHR9LX16/WM+k/fvxIjo6OBICaN29ON27coKSkJDIzM6MGDRqUaW158+YNtWzZkthsNs2ZM6dYEp6iguHIkSO0evVqmjhxIjk4OJC5uXm5gqF37940ZswYEhMTIycnJ7p9+3a5FoaCggLq3LkzaWlplZnxUFjcuXOn3BV+ebRs2ZJGjBhR6rX4+HgCQGfPnq3qEEtQmALZysqKWCwWSUtL04gRI8jf31/gXABBQUFkampK4uLitH79er6+ly9evCAWiyXULa8/CSMGqoGRI0eSoqIib5+Yw+FQ7969SUlJib5+/Vpt/T569Ij09fVJUlKSNm/eXK3JMYKDg2nMmDEkLi5OMjIyNGXKlDrvUJOZmUkNGzYkBwcHobbZpEkTatGiBe3YsYMA8LzpBSU9PZ08PT1JUVGRJCUlyd3dnXr37k0qKirEZrPJ29u7wjaGDh1KXbt2JaJf38vnz5/TkiVLeLkPREVFqXv37rR58+Zq/TxfvHhBAOj48eNCbzsmJobc3NxIRESEGjVqREeOHCn2W4iLiyM9PT3S09MrFtteuPUmKipKJiYm9OzZs0r1XygY7t69S0eOHCFPT0+aOHEi2dvb85xEyxMMbm5utGLFCnJ0dCQ2m01Hjhyp9JYEvxw9epQAVCrfg7u7OzVq1KjUa4U+LYW+VNVFdHQ0rVq1ivT19QkA6erqkoeHh0DP2+zsbJo1axaxWCzq0qULX3XHjBlDSkpK1S7WagJGDFQDP378IGVlZRoyZAjvtaSkJGrUqBG1adOm2g5SIfo1+UydOpWAX5nuqnuC/v79Oy/5CJvNpn79+gk1gqImWbp0KYmLi1NERIRQ23316hWJiYnRzJkzaf78+QSATp8+Xen2UlJSaNmyZSQnJ8dzhjt06BBfdQcNGkQ9evQo9VpkZCTt3LmTrK2tSVxcnACQiYkJzZs3jx4/fiz0Vby1tTWZmpoKTbSmpKTQwoULSUpKipSUlGjTpk1l/ta+fPlCDRo0IDMzM0pKSqJnz56RqakpiYqK0pIlS6rtNzpt2jRq2LAhZWVllSkYzM3NqV69eqUKhmbNmlHv3r1p3LhxtGLFCjp48CDPwlCVpGTr168nOTm5StUt3A4ra/Ls1KkTDR48uNJjEwQul0sPHjzgpUBmsVjUo0cPOnr0KF9plol+bW1oa2uTvLw8HT58uFxLXlxcHMnJyZUa7smvf1FtgRED1URhIpii5ubnz5/zzLzVjb+/PzVq1IhkZGRo9+7d1e4wlpWVRXv27OElxmnXrh2dPn26zuynffnyhSQlJastf/7GjRt534ehQ4eShIQEPXz4sNLtJSYm8lbzYmJiJCsrS4sWLapwy2bAgAFkaWlZYftpaWl07tw5GjVqFC86oX79+uTs7Eznz58XSsbAhw8fCuxVXxo5OTm0ZcsWUlZWJikpKVqwYAFfIWMhISGkpKREGhoaxGazydzcXKhx7aVhaGhIbm5u5Zb5+fMnaWtrk4WFBX348KFMwVD4ufArGEJDQ8sUDO7u7mRkZFSpeypMLnT48OFSr48bN46aNWtWqbarQnp6Ovn4+FDnzp15/iL8pkBOSUmhESNGEPArxXR5YY3r1q0jERERevfu3f9HHq0rI/Jo3a/Io7DvtS9pESMGqgkul0s9evQgHR2dYia+Xbt2VZt59HfS0tLI1dWVAJClpWWZh6wIEw6HQ1euXKFu3boR8OvEss2bN9f6jF39+/cnTU1NoafFLYTD4fAiC6Kjo6lLly6kpKRUKW/o6OhoMjY25jlQ3b59m2bPnk1SUlJUr1498vDwKPM32LdvX+rdu7dA/RUUFNDDhw9p7ty5ZGxsTABIQkKCbGxsaPfu3eWezFcRXbp0oVatWlVKrHI4HDp27Bjp6uoSm82msWPHCnTM7IMHD3gpcfX09Krtsy8kIiKiQvHD5XLJycmJ6tWrx5eZOisri8LDw+nu3bt0+PBh8vT0pAkTJpC9vT21aNGiVMGgpKRUQjC0bduWmjdvXq5gKA9TU9MyD8raunUrSUhI/NGFQUREBC1atIgaNmxIAMjY2JjWrVtHcXFx5dY7ffo0TzCW5UeUk5NDjc3+I+MJOwXOSRKVVHsOjWPEQDUSHh5OkpKSNGvWLN5rXC6Xhg0bRjIyMkLzsK2I69evk6amJsnLy5OPj0+NhZW9fPmShg0bRqKioiQvL0+zZs2qEUEiKIVpVY8dO1at/cTGxpKKigrZ2dlRUlISGRsbU+PGjQXKQ/Hx40fS1tYmbW1t8vDwIBEREV4Smri4OJo+fTpJSEiQkpISrV69usQEZ29vT/b29lW6j/DwcNq0aRN169aNF53QsmVLWrp0Kb18+VKg71ehw+2NGzcEGsPNmzd5lpE+ffoI9FtKT0+nKVOmEIvFonbt2tHBgwdJQkKCHB0dq3XC2r59e4UhhQcOHCAAdOrUKaH1WxXBYGtrS+PGjaOVK1fSwYMH6c6dO6UKhokTJ5Z55kXhZ1wZ50RhU1BQQLdu3aIhQ4aQhIQEiYiIkJ2dHZ07d67M6KGYmBiytLQkADRp0qQS937iWSTpz78icLbSxguukuGia3SiyPklfxJGDFQznp6exGaz6eXLl7zXMjIyqGnTpmRsbFztq5FCfv78SSNHjiQAZG9vX6MnFkZHR9PcuXNJQUGBREREaMiQIULNnlgV8vLyyMTEhDp06FAjIunKlSsEgHbu3ElfvnwhNTU1atOmDV+rsRcvXlD9+vWpadOmFB0dTePHjycTE5MS5b59+0YTJ04kMTExql+/Pm3cuJG3X9q7d2/q27ev0O4nOTmZjh8/ToMHD+btc2tqatL48ePp6tWrFWbL43K51LZtW+rYsSNf/b18+ZJ3xHf79u0F3mq5ffs26ejokJSUFG3evJnnB3H58mVeTofqcrzt3bt3uSGFHz9+JGlpaXJxcamW/stDX1+fXFxcyN/fnw4fPkyrVq2iCRMmkJ2dHV+CofAz2bJlSwnBEBMTUywXRm0hOTmZdu3axTudsrwUyFwul3bs2ME7I6bQubSq55gU/m33//NCiRED1UxeXh6ZmppSq1atiq06Pnz4QDIyMjRkyJAaTQBz8eJFUlVVJSUlJTpx4kSN9p2enk7btm0jXV1dnoPjpUuX/uiRoFu3biUWi0WvXr2qsT4nTZpEkpKS9O7dO3rx4gVJS0tTnz59ynXQ8/f3Jzk5OWrbti1v/9LCwoKGDRtWZp3IyEhydXUlUVFRUldXp23btlHPnj2pf//+Qr8nol/f9Tt37tD06dOpcePGBICkpaWpb9++5O3tXaYF5PLlyxXGuH/69ImGDBlCwK9T7i5evCjQdzclJYW3Zda1a1cKDw8vUebo0aPEYrFo+vTpQv9dFJ5SWFboZ05ODrVo0YKMjIyqPXKgNGRlZSuMcim0MJQmGAoP3SpNMDRv3pxERUWpTZs2tHLlSjp06FCZFoY/xbt372jmzJm89NYtW7ak7du3l4gS+PDhA7Vu3ZpERUVp2JKd1XbC6Z+AEQM1wJMnT4jFYpU4uOjEiRO8VWJN8uPHD3JycuI5x9T0+QMFBQV09uxZat++PQEgAwMD2rVrV40/GBISEqhevXq8EydriqysLDIxMSEzMzPKzs4mX19fYrPZNGXKlFInofPnz5O4uDj16tWLZ0nicDgkIyPD1xG4nz59olGjRhGbzSYJCQlq1apVtSeM4nK5FBISQqtXr6b27dsTi8UiFotFFhYW5OnpSe/evePdK5fLpebNm1OvXr1KtJOQkEBTp04lMTExatCgAe3fv19gU76vry9pamqSrKws7d69u1zxuXPnTgJAHh4egt1wBdy4cYOAsk/4c3d3J3Fx8RoVpYWkpaUJxY+p0DkyLCyM/P396dChQzzBoKioSIqKiqSsrFymYLC1taXx48cXEwxhYWE1+lzIy8ujS5cuFUuBPHDgwGIpkPPy8mj6opXUcOY5avS/E0qL/qmP2kRyLW1JTEWbWGISJCJfn6SbdKQGbnvLFQOGi679UR8CRgzUEJMnTyYZGZkSTkGTJ08mMTExCgwMrPExnTx5kpSUlEhVVbXKHt2V5cmTJzRw4EBis9mkpKRECxcurNCpR1i4ubmRgoIC/fjxo0b6K0rhCXRTp04lIqLdu3cTgBK54Q8cOEBsNpucnJyKhbuFhYURALp16xbffX78+JG38tHR0SFvb+8ac+qKj48nHx8fcnR0JBkZGV4s+NSpU+n27dt07NgxAsD7HWRkZNCKFStITk6O5OXlydPTU+BJITExkecRbmVlRZGR/K28CpOEbd26VeD7LIupU6dSw4YNSxV7hSl9BT0XQFiEhoYSALp7926V2hk7dmyZJ2KOHTuWdyZGVlZWCcEwfvx4srOzo+bNm5cqGJSVlal58+ZkZ2dXqmDgN2xQEOLj42njxo08q0fRFMjDvZ6S7vzSJ3Vpo/YkIqNIcq3sSclmCtXrNJzYMgrEEpMkDZcd5foQDPd6KvT74BdGDNQQqamppKmpSba2tsUeCLm5udS2bVvS1tYWyqlcghIXF0cODg4E/DqX/U9lE/z8+TNNnz6dZGVlSVxcnEaPHl0t5y0U8vLlS2KxWLR9+/Zq66Mitm7dSsD/Z6acO3cusVgs3vGq69atIwA0fvz4ElsIhZkSBT0Eq1OnTmRvb08DBgwg4Fda4iNHjlRrJsDfyc7OpmvXrtGECRNIU1OTF/YlJydH5ubmtGnTJlJXVydxcXFyd3ev1O/i7NmzpKqqSgoKCgI7zXK5XJo5cyYB4Dt/Q0UYGBiUGlIYFxdH9evXJxsbmz+2XXbv3j0CUOXMpYcPHyYApYrrTZs2kZSUFN/3mJmZWWXBsGrVKjp06BD5+/tXSTBwuVx6/vw5TZw4kRQUFEhMuWG5K3y14etJe/aFYq81cNtLEBEjGZOuFW4XFB54VtPwO3+ziIhQAWlpaahXrx5SU1MhLy9fUfF/josXL8LR0RGnTp2Ck5MT7/WoqCi0bNkSbdq0ga+vL9hsdo2Oi4hw+PBhTJs2DTIyMjhw4ACsra1rdAyFpKSkwMvLC1u3bsW3b9/Qq1cvzJw5E5aWlmCxWELpg4jQsWNHpKWl4fXr1xAVFRVKu5UZh62tLV6+fIm3b9+ifv36GDZsGM6fP4+BAwfi2LFjWLx4MTw8PErc+6JFi3DgwAHExcUJ1Gf79u3RpEkTeHt7482bN1i6dCkuX74MY2NjLFu2DAMGDKjR7x8R4c2bN7h06RJ27dqFHz9+AADU1NQwduxYjBo1CgYGBny3Fx8fj8mTJ+Ps2bPo06cPdu/eDQ0NjUqNy9XVFQcPHsTZs2fRt29fgdso5NOnT9DX18eFCxeKtcPlcmFjY4OgoCC8ffsWqqqqle6jKpw4cQJDhw5FWloa5OTkKt1OVFQUGjVqVOI+AeDmzZuwtrbG58+foaurW8UR/yIrKwsxMTGIjo7Gt2/fSvz327dvSEpKKlZHWVkZWlpaaNiwYan/1dLSgpSUVJl95uTkYMzO63j8QxRgCfY7ifOZBgDQcN5aZhkRNgsj2jbCMgcTgdoWBvzO34wYEBL9+vXD48eP8eHDBygqKvJev3HjBnr37o3ly5dj0aJFf2Rs3759g4uLC27duoWxY8di48aNf+xzzM/Px9mzZ7Fx40a8fPkSJiYmmDFjBoYOHQpJSckqtX3s2DEMHz4cd+7cQffu3YU04soRHx+PZs2aoVWrVrh69SqysrKgp6eH+Ph4LFy4ECtXriy1nr29PQoKCnD9+nWB+mvbti2aNWuG/fv38157/vw5li5diuvXr8PMzAweHh7o27ev0MRXRTx48ABz5szB06dPISEhgcaNG0NXVxd37txBbm4umjRpAnt7ezg4OMDCwgIiIiIl2iAiHD9+HFOnTgWbzcaOHTvg5ORUpXvgcDgYMmQILl26hGvXrqFHjx6VamfHjh2YMWMGkpKSik22GzduxKxZs3Dz5k1YWlpWepxVZdOmTf/H3llHRdV+b/+aoLskREAQRDDARFQwEBXFxha7WxSxuwu7u/Oxuxs7MFFMQFQUEJCaud4/fJmfSA0woM/34bMWa+k5d+xzZubc++x7ByZMmIC4uLh8j2VlZYUWLVpg4cKF6Y6/f/8eFhYWOHLkCBo3bpzveeQlJ4Xh/fv3+Pr1a7o+BgYG2SoL3f95j/fffuRKDpIIW94VSoYWMG47Ndu2lgbquDiiTq6vNb/IvX4r0szwX+bDhw/U0tLK1GQ4YcIECgSCfNdLzw9SqZQrV66khoYGLS0tee7cuT8mS5o8Fy9eZNOmTSkQCFisWDFOmTIlz/v8sbGxNDU1ZevWrRUsad5J2zOeN28eW7RoQZFIRBMTE9rY2GTp3Glubs5Ro0bleq5KlSpl6TB59epV1qtXj8DPypSHDx8u0GiT4OBgNmnShABYqVIlnjlzhitXrqRAIJAV8Pnnn3/YvXt3ma+DgYEBfX19uXfvXlm8/ocPH2TjtGvXTqEOsUlJSWzQoAE1NDR440bO+7mZpaD18vJi3bp107W7ffu2LEX1n8bPz4+lSpVSyFi+vr4y34BfkUql1NTUlMvhtbCJj4/n8+fPefbsWW7cuJHTpk1jnz592LhxY1aoUIH6+vqyrQiBshotMnEazOnPoMnPbSeDRoNzbGsVcOSPpC4u2ib4AyxbtgwDBw7EpUuXUKtWLdlxiUSCRo0a4f79+7h37x6KFy/+x2QMDQ1F9+7dcfHiRQwaNAgzZ86EhobGH5MHAF68eIHAwEBs3LgRJNGlSxcMGzYMpUuXlnuM0aNHIzAwEM+ePYOlpWUBSps7+vbti9WrV0NZWRl79+6Fo6MjXFxcYG1tjXPnzqUzXUZFRcHQ0BA7duxAu3btcjWPk5MTatSogWXLlmXZ5uLFixg/fjwuX76MatWqYcqUKahfv77CLAUfPnzAhAkTsGnTJlhZWWHGjBnw8fGBUChEUlISrK2tUb9+fWzcuFHWRyqV4ubNmzh06BAOHz6M4OBgKCsrw9bWFq9evYKWlhZWr16dL3N+VsTHx6NBgwZ48uQJLl26hLJly6Y7HxL5HduC3uH880949zUBvz4oBQBSoj+iooky5vdtDltjLcTFxaFixYrQ1tbGtWvXoKysrHCZc0PHjh3x4cMHXLx4Md9jrVu3Dr1798bXr1+ho6OT7ly1atXg4OCADRs25HuewiYhIQEfPnzAtafvMOlGUq76pkS9R8RmPygbWsC442wIhBktW79zdFBNOJrp5NhOkci7fhfuJvb/OH379oWLiwt69+6NpKT/+2KJRCJs27YNKioqaNOmDVJSUv6YjGmLUGBgINasWQMnJydcu3btj8kDAHZ2dli+fDnevXuHcePG4cCBAzIT8oULF5CTvvry5UssWLAAAQEBf5Ui8PnzZ9y6dQsCgQAmJiaoV68eSpYsiaNHj+Lhw4fo2LEjJBKJrP2DBw8AABUqVMj1XBKJJEcfCXd3d1y8eBGnT5+GQCBAgwYN4ObmhgsXLuR6vl/59u0bRo0aBVtbWxw5cgSLFi3C06dP0bZtW5mfgoqKCkaOHImtW7fizZs3sr5CoRAuLi6YMWMGHj16hIsXL8LKygqPHz9GUlISPn/+jEmTJmHChAm4desWpFJpvmT9FQ0NDRw5cgQWFhbw9PREaGgoAOD91wR0XheE+oGXsCXoLd7+pggAP18nxbomCE7SR/3AS+i8Lgg9h45CeHg4duzY8ccVAQCIiIjIk19FZri7u0MqleLq1asZzjk4OODJkycKmaewUVdXh52dHSo4V8pVP0ncN3zaMxlCFQ0YNh8tlyIAAMmpivv+KpoiZUCBiEQirF69Gi9fvsTs2bPTnTMyMsLu3btx8+ZNBAQE/CEJfyIUCjFkyBA8ePAAhoaGqFmzJvz9/ZGYmPhH5TI0NMTYsWPx9u1bbNiwAW/evEGdOnVQuXJlbNu2LUslavjw4TA1NYW/v38hS5w17969Q82aNREWFobdu3cjMjISI0aMAABUrlwZO3fuxMGDB2XHgJ/KgKqqaq4c69KQSCSZ7rn/jkAggIeHB65du4ajR4/ix48fqFOnDurVq5fpgz47EhMTMW/ePNjY2GDZsmXw9/fHy5cvMXDgwEwXw169ekFfXz/DbwP4aSFYunQpvLy88OPHD5w4cQLfvn3Dzp07UbZsWSxduhRVq1aFubk5evfujSNHjuDHj9zt72aGrq4uTp48CU1NTXh4eGDl6YfwWHgR10J/OqhJpNkrommnr778jGu69dBt2to8fX4FQXh4OMzMzBQylo2NDUxNTXHp0qUM59KUATmMzH8FiYmJePToEfbs2YOpU6eiQ4cO6NK5o9z9pYnxiNw9EdLEeBRrMxliLQO5+yqL/94l9++V7F9KuXLl4O/vj+nTp+PZs2fpzlWvXh3z5s3DggULsG/fvj8k4f9hZ2eHK1euYNasWVi0aBEqVaqE27dv/2mxoKKigq5du+Lhw4c4deoUjIyM0KlTJ5QsWRJz5szBt2/fZG2PHz+Ow4cPY968edl6CxcmT548gaurK1JSUnD16lW0atUK8+fPx/Lly3H48GEAPx0FFy9ejMDAQAQGBgIA7t+/j3LlyuUpCkJeZSANgUAALy8v3Lp1CwcOHMCXL19Qs2ZNNGzYEDdv3sxxrk2bNsHOzg4BAQFo164dXr58icmTJ2drhtTQ0MCwYcOwfv16hIeHy46/ePECtWvXxqBBg+Dr64vg4GA0aNAAOjo6aNu2LbZu3YpPnz7hwoULaN++Pc6fPw9vb28YGBigWbNmWLt2LT5+/Cj3tf+OsbExTp8+jdTSHph17j2SUqU5KgG/I4UAQrEyDkdqYen5kDzLokgUaRkQCARwc3PLdMvBwcEBcXFx+PDhg0LmUhRRUVG4cuUK1q5dixEjRqBJkyawsbGBuro6ypcvjzZt2mDJkiX48OEDKpe2BDLYfzLC1GR82jsFqd/CUMxnApQNLeSWRwDAyuDPbslmR5EyUACMGzcOFhYW6N27dwaz5uDBg+Hj44Nu3bohJOTPPzREIhH8/f1x584dqKqqwsXFBePHj0dycvKfFg0CgQD169fHiRMn8OjRIzRo0ADjx49HiRIlMGTIEDx79gxDhw5FnTp10KpVqz8tLgAgKCgItWrVgr6+Pq5evQobGxsAQL9+/eDt7Y3u3bvLwgYHDBiAkSNHYvjw4di/fz8ePHiQpy0CAEhNTc2TEiEQCNCsWTPcu3cPu3fvxrt371CtWjU0bdoU9+/fT9eWJI4dOwZnZ2d07doV1apVw5MnT7B8+XKYmJjINd+AAQOgrq6OefPmQSKRYN68eahQoQLCwsJw/vx5LF++PFOFQiwWw93dHfPnz8eLFy/w9OlTTJ48GV+/fkWfPn1gamqKatWqYfr06Xj48GGu31KvfxJA6NQsV30y8P99L+adeoFdt97lb6x8Eh8fj9jYWIUpA8DPrYLbt28jPj4+3XEHBwcA+CNbBRKJBKGhoTh27Bjmz5+PXr16oVatWjAyMoKhoSFq1aqFPn364MCBAwB+Rn2tWbMGV65cwZcvX/Dp0ydcunQJ61evgKV+9gs1pRJ8PjAbSeHPYNQ8ACrFy+RKVgsDdWio/JlwZ3kociAsIM6ePQsPDw+sWbMGPXv2THcuNjYWVapUgYqKCm7cuAF1dfU/JGV6UlJSMHPmTEydOhWOjo7YvHkzypcv/6fFSkdkZCSWLVuG5cuXy0KHNm3ahM6dO/9hyYDTp0+jRYsWqFChAo4cOZIuxBT46UNQvnx5lCtXDidOnIBQKIRUKkX79u1x6NAhpKSkYNGiRRgwYECu57ayskKnTp2yDFmUF4lEgl27dmHSpEkICQlBy5YtMXnyZCQkJGDUqFG4cOEC3N3dMXv2bFSrVi1Pc0yYMAFz5syBo6Mj7t27h6FDh2Lq1Kl5dmT98uULjh07hsOHD+PEiROIi4uDpaWlLGzR3d092z38918T4LHwIpKy2M9lagqiL29F/OPzkCbGQcnICrpunaFW0jnLMVXEQpwZ5o4S+n/mt/3y5UvY2toqNMz28ePHKFu2LE6fPg0PDw/ZcalUCk1NTUybNg3Dhw9XyFy/Ex8fjxcvXuDZs2d49uwZnj59imfPnuHFixcy/yx1dXXY29vL/sqUKQN7e3uUKlVKrrDlSYceY8uNN5BksSJ+PbMa328fglqpqlC3r5XhvGbZrMMGi/IM/Mfp2rUrDh48iGfPnsHY2DjdueDgYFStWhVt2rTBhg0bCi32Wx7u3r2LLl264Pnz55g4cSJGjRr1xxL4ZMWrV6/g6OgINTU1REdHw8XFBX5+fmjevPkfkXXv3r3o0KEDPDw8sHfv3iwVvNOnT8PT0xPz58+XPTgTExPh6uqKe/fu5SmSAABKlCiB7t27Y/Lkyfm6jjRSU1OxdetWjB8/Xmb+tbW1RWBgIBo1apTn72tKSgomTJiAWbNmwcDAAIcPH0b16tUVIjMAJCUl4cKFCzh8+DAOHTqE9+/fQ0tLCw0aNEDTpk3h5eUFA4P0e7yd1wXhWmhUllsDnw/OQcLzq9Cu3AxifTPEPzqDpIgQGLefAdUSmT/cRUIBXK0NsKVH3hSm/HL58mW4ubnhyZMnKFMmd2+wWUESxYoVQ79+/TBlypR05ypVqgRnZ2esXbs2X+N/+vRJttD/uvC/e/d/lhYTExPZQv/rn7m5eZ4Ta0VHR2PUjECcFFXJss3HbQFIeh+c5XnLgCPZznFmmBtKFct78qe8Iu/6/Xc94f/HmDdvHo4ePYqhQ4dix44d6c6VLVsWq1atgq+vL2rWrJnBevAnqVixIm7fvi3z4j548CA2bdqksIeKIpg6dSo0NTXx/PlzXL9+HfPnz4ePjw+srKwwdOhQdO/ePV9Z13LDqlWr0K9fP7Rv3x4bN26EkpJSlm3r16+P4cOHIyAgAHXq1IGzszNUVVXRs2dPDBgwAGPHjoWHhwcMDQ1zJUNetwmyIioqCjdv3sTHjx+hp6cHgUCAly9fYteuXbCzs0OpUqVyPea9e/fQrVs3BAcHw8XFBY8fP1b4d0pFRQUNGjRAgwYNsGTJEjx8+FAWtujr6wuhUIgaNWqgadOm8Pb2hlDXDJdffslyvKTw50h4egm6dbpDp1pLAIBm2boIXzsA0Rc2wKTzvEz7SaTE5Zdf8PLT9z+yAKT5ZCjKgRD4uaVUq1atbJ0I5SE1NRWhoaHp3vDT/qKjowH83L4sVaoU7O3t0b59e9niX7p0aejq6irsmpKTk7FixQpMmTIFiYmJqDBkDSKhk6l1wKTjrDzNkaYY/onvQW4o8hkoQAwNDbFw4ULs3LkTx44dy3C+c+fO6N27NwYOHIh79+79AQmzRkVFBTNnzsTVq1cRExMDZ2dnzJ8/P10o3J8iKCgImzZtwowZM2BgYIAmTZrg/PnzuHPnDmrUqIERI0agRIkS8Pf3x/v37wtMDpKYMWMG+vbtiwEDBmDLli3ZKgJpzJgxA46OjujQoYNs//Xly5coUaIEvn//jqZNm+baUz63DoRZ8f37d0ycOBE2NjbYuXMnZs6cibCwMISHh2PJkiU4ffo07O3t0bNnT7x9+1auMRMTEzF27FhUqVIFJHHz5k38888/SE5OxtKlS/Mtc1YIBAJUqFAB48ePx82bNxEWFoaVK1dCR0cH48ePh729PRoOnA4Bsw73Snh+FRAIoeX0f2m8BWJlaFaoj6SwZ0iN/ZxlX5FQgK03/ozvQEREBNTU1BRuyXVzc8ONGzcyRB5lFlEQGxuLW7duYcuWLRg7dixatWoFBwcHqKuro3Tp0mjWrBmmT5+OJ0+ewM7ODv7+/ti/fz+ePn2KhIQEPHv2DAcOHMCsWbPQpUsXVKtWTWGKAEns2bMHDg4OGD58OFq2bImQkBDsGtEcYpFil0WxUIAZLcopdMyCoEgZKGA6duyI+vXro3///hkcbwBg0aJFcHR0ROvWrWVa8d+Ei4sL7t27h379+mHkyJGoXbs2Xr169cfkkUqlGDRoEJydndGjR4905ypWrIitW7fi9evX6NOnD1avXg1ra2t07NgRd+7cUbgcfn5+GDt2LCZPnozFixfLbaJUUVHBjh078PbtW9lWwYMHD1C5cmUcOXIE9+/fR+fOnXMVU59fZSBtYbaxscHs2bMxYMAAvHr1CiNGjICamhpUVFRkx+bOnYvDhw/D1tYW/fr1y9aL/MaNG6hYsSLmzp2LiRMn4tatW6hYsSJMTEzQq1cvLFy4UCHpcuXBzMwMvXr1wuHDhxEVFYWDBw9CuaQzmE0u+uTIUCjpF4dQJf22j7Kpnex8VkikxPkXnxQjfC5JiyRQ9Paju7s7kpKScOvWLQD/Px1vWBhSUlIQExOD7t27w8PDA+bm5tDR0UHVqlXh6+uLzZs3IzY2Fh4eHggMDMTZs2cRFhaGmJgYmXI/evRotGjRAvb29gWap+Hq1atwdXVFmzZtULp0aTx8+BBr1qyBmZkZSuirY7KC9/WnNHX8Y74juaFIGShgBAIBVqxYgcjISEycODHDeVVVVezduxdfv35Fly5d/spYXXV1dSxcuBAXLlxAWFgYypcvj+XLlys0AYy8bNq0Cbdu3cLixYuzXPzMzc0xe/ZsfPjwAfPnz8f169dRuXJl1K5dG4cOHcq33CkpKejWrRsCAwOxbNkyTJgwIdcPXXt7ewQGBmL16tWySAInJydUrVoVO3bswP79+zFy5Ei5x8urMiCVSrFr1y44ODhg8ODBaNKkCUJCQjB79uwMDpAAoKamhmHDhiE0NBTTpk3Dnj17UKpUKQwZMiRdeF9CQgL8/Pzg6uoKTU1N3L17F+PHj0/3kB85ciRiY2OxcuXKXMudX9TV1VG3gRcSRZrZtpPEfYVIM+N9EGnqy85nx7uoBMQnpeZd0DyiyBwDwE9l8cmTJ3j16hVUVFQwaNAgVKlSBdra2jA3N5c92y5cuABdXV107doVW7Zswe3btxEbG4v379/j9OnTWLx4Mfr374+6devCzMysUH2lXrx4gZYtW6JmzZpISkrC2bNncfToUTg6pl/821WxwAjPn8pefp/HIz1Lo20V+cMP/yRFykAhYGNjg0mTJmHhwoW4e/duhvMlS5bE5s2bcejQIcydO/cPSCgfbm5uePjwIXx9fTFgwAB4enqmc+wpaGJiYhAQEIAOHTqgZs2aObbX1NTE4MGDERISgr179yI5ORnNmjWDvb09VqxYgYSEhFzL8OPHD7Rq1Qrbt2/H9u3b0b9//7xcCoCfSXhatGiBHj16ICoqShZW2KxZMyxevBgLFizA4sWL5RorLz4D586dQ7Vq1dCuXTuUKVMGDx8+xPr161GiRIkc+2poaMDf3x+hoaEYN24cNm/eDGtra4wcORIHDx5E+fLlsWzZMsyePRvXrl3LkOoXACwsLNClSxfMnz9fIQmEcsvbqPgcI8uZmgyIMm79CMTK/3c+u/4A3kRltAgWNHnNMfDt2zdcv34dGzZswKhRo9CsWTOULl0a6urqcHR0hI+PD6RSKd68eYPy5ctjwoQJOHToEJ48eQJlZWUMGzYMe/fuxbRp09CpUydUqlSp0Hx3suLz588YOHAgHB0dcefOHZmSkl2UxYDapWAYegpITQay2UbKDJFQABWxELNblsOAOrn3rflTFCkDhcTw4cNRtmxZ9OrVC6mpGd8UvL29ERAQgDFjxigkl3hBoampiRUrVuDkyZN4/vw5ypYti/Xr1xeKRWPKlCmIj4/HnDlzctVPJBKhVatWuHbtGq5du4YKFSpg4MCBsLCwwPjx4+VOWBMTE4MGDRrg7NmzOHz4cJ68/n9FIBBgzZo1su2FX8M4Bw4cCD8/PwwdOlQWI50dubEMPHjwAI0aNUK9evUgEolk3veZLdg5oa2tjXHjxuH169cYNGgQFi1ahObNmyMpKQkXL17EyJEjs1VSAgIC8OnTJ6xfvz7Xc+cXeVLDCsTKgCRj5ss0JSBNKcjvPIomPDw8S2VAKpXi7du3OHnyJAIDA9G3b1/Url0bJiYm0NfXh6urK3r06IHdu3cjOTkZXl5eWL58OS5evIjIyEhMnToVqampWLlyJUaOHAlvb2+Zg9/flJY4ISEBM2bMgI2NDbZu3Yrp06fj+fPn6NSpU45behs3bsSd3YsRuXEQKpv/VGZEwuytGGnnXa0NcGaY+7/GIpBGkTJQSCgpKWHNmjW4d+9elm97U6dORa1atdCuXbtc17MvbDw9PfHo0SO0atUKPXr0QJMmTdJllVM0T58+xeLFizF27Nh8FXqqXr069uzZg5cvX6JTp04IDAyEpaUlunfvjkePHmXZ7+PHj3B3d0dwcDDOnDmDhg0bZtk2N6Rl0QOA3bt3pzs3Z84ctGrVCh06dEBQUFC248ijDLx58wa+vr5wdnZGaGgo9u7di+vXr8Pd3T1/F4GfTp07d+6EsrIy6tevj6ioKHh6emLSpEmIiYnJsl+pUqXQrl07zJ49u9ATXcmTGlakqQ9J3LcMx9O2B9K2C/I7j6KJiIiAkZERHj58iN27d2PKlCno0KEDnJ2doampCSsrKzRs2BCjR4/GjRs3YGJigr59+2LHjh24d+8e4uLi8Pr1axw/fhwLFy5E79694ebmhmLFiqF27dqIj4/PYOX8W2oUpGXILF26NCZOnIju3bvj5cuX8Pf3lyvfQEREBIYOHQqhUAi/Pl2xd2BtnB7qhs7VLGFpoI7fVQIBfpYn7lzNEmeGuWFLj2r/Ch+BDCiyBGIROTNo0CCqq6vz9evXmZ6PiIigqakp3d3dmZJS+OUu88KhQ4doYmJCPT09bt26VeHlcaVSKT09PWljY8MfP34odOxv375xzpw5NDc3JwB6enryxIkT6a4hNDSUNjY2NDU15aNHjxQ6P0n6+PiwRIkSFIvFvHXrVrpzCQkJdHV1pZGREV++fJnlGAKBgKtWrcr03JcvXzh8+HAqKyvT2NiYK1asYHJyskJk//r1K7t160YArFevHkNDQ0mSkZGR9PPzo6qqKnV1dTlt2jRZaeLfCQ4OJgCuW7dOITLJy7fvCTmWndWu2pIQCFli2O50x3XdfAmAxftv+ONlaz9//szLly9z9erVHD58OBs0aCArzZv2Z2RkxFq1arFXr15csGABjx07xtDQUKampuZ6vuTkZKqrq2coWzxlyhTq6+sXaHnsnDh16hQrVKhAAGzdujVDQkJyPUbLli2poqJCY2Njfv/+PcP5zMpZ/83Iu34XKQOFTGxsLM3NzdmoUaMsfzQXL16kSCRiQEBAIUuXd758+cL27dsTAFu0aMHIyEiFjX3w4EEC4KFDhxQ25u8kJydz27ZtrFixIgHQ0dGR69at4507d2hqaspSpUrJFjpFY2trywEDBrBSpUq0tbXN8AD6/PkzbW1taWtryy9fvmToL5VKCYBr165Ndzw+Pp4zZ86kjo4ONTU1OWXKlEwfbnnl4MGDNDU1pba2NtesWZPp9zk8PJyDBg2isrIyDQ0NOWfOHMbHx2do16JFC5YqVapAFeDU1FTeuXOHc+fOZaNGjaiurk6zPquzXcxNfOcTAHXrdJcdsxjxD8V6plQ2K52jMuE295zCZH/58iWPHDnCefPmsUePHqxRowYNDAxkC75QKGSpUqVYp04dAuDw4cN59erVTL8z+cXDw4ONGzdOd2zv3r0EoNDfvrw8ePBApgS5urry2rVreRpnz549svu5adMmBUv5ZyhSBv5i0ha3nTt3Ztlmzpw5BMCDBw8WomT5Z8+ePTQ0NKShoSH37t2b7/F+/PhBa2trNmjQoFDeOKRSKS9cuMCmTZsSAAUCAU1MTPj48eMCmS8uLo4CgYDr1q3j8+fPqa6uzu7du2do9/LlSxoZGbFGjRoZrCMpKSkEwA0bNsj+v3btWhYvXpxKSkocPHiwQh/Qnz59kil+Xl5efP/+fY593r17xz59+lAsFtPY2JiBgYHpruP27dsEwO3btytMTqlUyuDgYC5ZsoQtWrSgnp4eAVBJSYlGRkYUi8XU8+hNS/+D2S7o6vY1CaGI2tVaUr/hQKoUL0MIRTTuMCvbftZjjnLiweBcyRwXF8c7d+5w27ZtHD9+PH18fFi2bFmqqKjIFil1dXVWrFiRHTt25NSpU7lnzx4+evRIdj+vXLlCAAwOzt3cuWHq1KnU0dFJZ1l48uQJAfD8+fMFNu/vfPjwgd26daNAIKCtrS337duX5+dEVFQUixUrRh0dHVapUoUSiUTB0v4ZipSBv5yWLVuyWLFi/Pr1a6bnpVIpmzdvTl1dXb569aqQpcsfHz9+ZPPmzQmAHTp0YFRUVJ7Hmj59OsViMZ8+fapACXPm2LFjVFVVpampKVVVVamqqso+ffrw2bNnCp3n+vXrBMA7d+6QJNetW0cA3LNnT6ZtVVVV6ePjk+5BlZiYSADcvHkzDxw4wDJlyhAA27dvn+3WQm6RSqXcuXMnDQ0Nqa+vzy1btuT6wfv69Wt2796dIpGIZmZmXLZsGRMTE0mSjRo1oqOjY54fwlKplC9fvuTq1avZrl07GhsbEwDFYjFLly5NOzs7KikpEQCrV6/OBQsW8OL9Fzm+3VuM2E/tqi0p0tAjREpUNrVlsTaTc+xnGXCEIZEZt0akUikjIiJ4/vx5Ll++nIMHD6anpyctLCzSmfZNTU1Zp04d9uvXj4sWLeKpU6f47t27HO9P2tttfn53OXHx4kUC4N27d2XHkpOTKRaLuWzZsgKbN43Y2FiOHTuWampqNDQ05JIlS/K99dWlSxeqqakRAK9fv64gSf88RcrAX86HDx+ora3NXr16Zdnm27dvtLGxYcWKFRW+V17QSKVSbtmyhbq6ujQ1NeWRI0dyPcb79++prq5OPz+/ApAwa7Zv306xWExvb28mJCTw8+fPnDZtmmxx8fb25vnz5xViqVixYgVFIpHs85VKpWzdujV1dXX57t27DO33799PgUDAESNGyI7FxcURAO3s7GR797dv3863bL8SHh7OFi1aEABbtWrFjx8/5mu8Fy9esFOnThQIBLSwsOCaNWt44cIFAuD+/fvlHuf9+/fcvHkzu3btKltMhUIhK1asyMaNG7NatWpUVlaWmY8XLlyY4b52WnuD1mOOyrW4y/tnPeYoO6y5zmfPnvHAgQOcNWsWu3btymrVqlFHR0e24ItEIpYuXZrNmzdnQEAAN27cyBs3bjA6OjrP93bRokVUUVEpUEvajx8/qKKiwsDAwHTHHRwcOGDAgAKbNzk5mcuWLaORkRFVVVU5evTofN2rNE6cOEEA1NTUZKdOnRQg6d9DkTLwL2D58uUEwIsXL2bZ5t69e1RRUWHv3r0LUTLF8eHDBzZs2JAA2L1791z9cNu3b09jY+NC/d4tXbqUAoGAXbp0ybB/nZiYyA0bNrBs2bIEwIoVK3Lr1q35eiPp27cvy5Ytm+7Y169faW5uTjc3t0wdvBYtWkQAXLp0KZ8+fcomTZoQAK2srHjy5EmFLgJSqZQbN26krq4uixUrlqnFIj88efKEbdq0IQBaW1vT3t6eFStWzPIaIiMjuWvXLvbp00em/ABghQoV2LdvXw4ZMoQNGjSQWQBq1KjBwMDAbLcy3kXF027cMYUpAhajDtNy5D9UNSguk09bW5tVq1alr68vZ86cyX/++YdPnz5lUlKSQu8nSQYEBNDKykrh4/6Om5sbW7Zsme6Yj48P69Spo/C5pFIpDxw4wNKlS8t+n5kpy3khNjaWFhYWtLCwoJqaGj98+KCQcf8WipSBfwESiYSurq4sXbq0zFSaGWvXrv1XO7RIpVKuWbOGmpqaLFGiBE+fPp1jn8uXL6fbBy9opFIpJ02aJHO8ys4UK5VKefLkSZnDUvHixTl79mx++/Yt1/O6uLiwY8eOGY5fuHCBAoGA06dPz7Rfr169ZG/BaW/Eu3fvzvX82fH27VuZItepU6cCcURL4+HDhzLLAwCOGjWKqamp/PbtGw8ePMghQ4awXLlysvOlS5dmv379uGHDBi5evJheXl5UUlKiQCBgzZo1uWjRolw91LcHvVWoZaB4LR/Onj2bZ8+eZXh4eKF62Pv6+tLV1bXA5xk3bhwNDQ3TXdvEiRNpbGys0HmCgoJYq1YtAqCHhwfv3bun0PEHDhxINTU1isViTp06VaFj/w0UKQP/Eh49ekSxWMyJEydm265bt25UU1Pjw4cPC0ewAuD169cyT+f+/ftn6dmemppKJycnVq1atVCceCQSCQcOHEgAnDlzZq4e3I8ePWL37t2prKxMDQ0NDh48WO6og9TUVGpoaHDu3LmZnh8zZgxFIhFv3LghOxYdHc0xY8ZQTU2NysrKVFJS4uHDhwmABw4ckFvu7JBIJFy5ciW1tLRoZmbGw4cPK2Rcebh8+TI1NDQIgGpqahQIBARACwsLduvWjVu2bGFwcDDXr1/PRo0ayRSAWrVqcfHixQwLC8v1nFKplAMHDqR29TYKUQT8N56lkZERbWxsCt3XhSTr16/PVq1aFfg8p0+fJoB0zrW7du0iAIUojq9evWLbtm0JgGXLluXx48cVrlRdvnyZAoGAjo6OtLS0ZEJCgkLH/xsoUgb+RYwdO5bKysp88uRJlm3i4+NZvnx52tra/qs/B4lEwiVLllBNTY3W1ta8dOlShjYrV64kgHSLYEGRlJTE9u3bZxunLw8REREcP348DQwMKBQK2apVqxzDm54/f04APHXqVKbnk5OTWbVqVVpbW/Pz589cuHAhDQwMqKamxjFjxjAiIoIuLi40NDQkAIUs2i9fvpQpbD179syTtSM3JCYm8sKFC5wwYQJr1qwpM+8DoL6+PgHQ3t6eW7Zs4bp169ioUSOKxeJ8KwBfv37ltWvXuHbtWlaqVIkAWKxYMWo5NWQJv320GHkg1z4CduOOcefNtyR/5qZwcHCgrq4uz549q+jbli1ly5blwIEDC3yeuLg4isViLl++XHbs0aNHBMDLly/nedyoqCgOGzaMSkpKNDMz47p16/KUDyEnfvz4wdKlS9Pe3r5ALGt/C0XKwL+IHz9+0NbWlrVq1cr2TfjFixfU1tZm69at/2hiD0Xw4sULurq6UiAQcPjw4TKNPCoqigYGBuzatWuByxAXF8eGDRtSWVlZYXvh8fHxXLlypWw/28XFhXv27Mn0YbZ79+4c47JfvHhBFRUVampqUigUslevXukWvzcfImjpVIPKpnZcuGFPnhOgpKamMjAwkOrq6rSyspJrKycvpKSk8MaNG5wxYwY9PDyoqqpKANTT02PLli25dOlSPn78mOXLl6e7uztHjRolUwrS3hAXL17M8PDwHOeSSCR8/fo1jx8/zoULF7JPnz50c3NjsWLFMiTlcXR05LBhw7hq1SruPX6ebZZfki3yOSkBlgFH2GntDb6LSp8/ITo6mvXr16dYLM6QA6Ig0dfX54wZMwplLhcXF7Zr1072/8TERIpEojwp1j9+/ODcuXOpq6tLTU1NTp06lXFxcYoUNx2jR4+msrIyra2t6ebm9q9/pmZFkTLwL+PcuXMEwNWrV2fbbt++fQTAhQsXFo5gBUhqairnzp1LFRUV2tvbMygoiAMHDqSWlhYjIiIKdO6vX7/S1dWVGhoaBbLwSSQSHj58mLVr1yYAlixZkoGBgemy8I0dO5ampqaZ9k/zS3BycpItWPPmzSNJvvgYy4kHg+k25xytflucrAKO0G3OOU48GMwXHzPP+Pc7T58+ZfXq1QmAAwcOVGhiIolEwnv37nH+/Pls0qQJtbS0ZF7bjRs35rx583j37l2ZEvzlyxeuXbtWlkVOIBDQ3d2dgwYNYuXKlWVRAWfOnJE9vBMSEnj//n3u3LmTkyZNYrt27ejk5CQLEwNAVVVVVqhQgW3btuXEiRO5Y8cOdu3aVeaImRmy+zw34322GHWYlSYe4sSDwZmGD6aRnJzMPn36EAD9/f0LfNsrLcy0sHxt/P39aWpqmm4hLV26NIcMGSL3GBKJhNu2baOVlRVFIhH79euX72iVnLh79y5FIhG9vLwoEAjShUj+r1GkDPwL6dq1K3V0dHJcCIcPH06xWMyrV68WkmQFy+PHj1m5cmUKBAIKBALOmjWrQOcLCwtj2bJlaWBgwKCgoAKdiyTv3LnDjh07UiwWU0dHhyNHjuT79+/ZuHFjNmzYMEP727dvs169ejJv+CtXrrBdu3bUMy/FVkvO5/uNNY2UlBTOnDmTKioqtLW1zXTLJrdIpVI+ffqUy5YtY6tWrWQZ8lRVVVmvXj1Onz6d169fTxeB8eXLF65Zs4aenp4UiUQUCoV0d3ensbEx69evLxs3MjKS8+bNo5WVlWwbwdTUVOZXAPxMu+vm5sbevXvL0u6+fv063SIslUo5ZswYAsgQGpcVv6egNTG35NixY+W+JwsWLKBAIGDLli0zzcCoKF6/fk0APHHiRIHN8StHjhwhgHRpf1u0aCH73HLiwoULMiWvWbNmheJjkZycTCcnJ9k2Tnbh3f8LFCkD/0K+fPlCQ0NDtm3bNtt2ycnJrFGjBosXL/5HUn8WBMnJySxZsqTMZKtoj+E0QkJCWLJkSZqbm2fro1EQvH//nv7+/tTR0aFYLKaamlq67ZBXr16xXbt2BMAyZcrw4MGDsjeudRee0nLE/hyz5WW1l73j/+9lp/HgwQNWqlSJQqGQI0eOzJfj1OvXr7lu3Tp27NiRpqamskQ/NWrU4Pjx43n+/PkMeTI+f/7M1atXs379+jIFoE6dOly6dCmvX7/Ow4cPy5zHKlSokG6rQCgUytIgA6CDgwNXrVolt9PaxIkTCYDz58/P8zU3atSIXl5euepz8OBBamhosHLlynJtc+SFa9euEUChORpHR0fLMmimMXbsWBYvXjzbfk+ePKG3tzcBsEqVKtmGVyuaGTNmUCgU0sfHh9ra2v8zz9CsKFIG/qVs3bqVAHJM0vPhwwcWK1aMHh4eBeJcU9ikZU1bunQpy5cvT7FYzClTpiisoA75M2eDsbExS5cuzbdv3+bcoYCIjY3ljBkzZItb9erV2aRJE5nD1Nq1a9PlOFhyLucsefL8LTn3gklJSZw4cSLFYjEdHR3zZBkJCwvj1q1b2b17d9lbukAgYOXKlenv788TJ05kutXw6dMnrlq1ih4eHjIFwMHBgY0aNWKTJk1YtmxZWYIgANTQ0KCysjItLCxkaXeDg4NlYbgSiYT79u2T5X3w8vLKMdnSlClTCICzZ8/O9XX/ypgxY7Lc4smOu3fvsnjx4ixRogTv37+fLxkyI20b8fPnzwofOyucnZ3p6+sr+/+2bdsIINOcIhEREezTpw9FIhGtrKy4Y8eOQk37+/TpU6qoqLBr164UCoWyrbf/ZYqUgX8paRX6LCwscty7PXPmDIVCISdMmFBI0hUM8fHxtLCwoLe3N8mfHv5jx46lSCRipUqVFJJj/dKlS9TW1malSpX46dOnfI+XX86ePStbwIRCIQHQ0NCQixYtSmdG3nHzZ/x7ieF7qFOjPVVLVqRQVZMAaOA1NMOCb+I7n5rOXlQ2tiGEIgJId96uUVeKxWKOHz8+29wWv/Llyxfu3buX/fv3l3lepznzDR48mAcOHMg0rbZUKuWjR484bNgwWbIYAOny7AP/l3a3f//+XLx4sSztrlQq5cqVKykQCLI1H0skEu7YsYOlS5cmADZv3pwPHjzI0G769OkEkGXuhtyQprzmZW/7w4cPdHZ2pqamZp4yc2bHkiVLqKSkVKjOcEOHDk2X5OjevXsE0qf0jYuL4+TJk6mhoUE9PT3Onz9f7u+fopBIJKxRowZLlSrF2rVr09bWtkCSPv1tFCkD/2JevXpFNTU1Dhs2LMe206ZNo0Ag4PHjxwtBsoJh4sSJVFZWzlBuNCgoiPb29lRWVuacOXPybAE5fPgwVVVVWbdu3SzL6BYmycnJbNWqFQFQWVmZw4cP5/Hjx9m6dWsKhUIaGBhw3LhxvPPsjSwzXvG+P2sWiLSNqGJRLktlQKdGe0IoprJJKYr1i6dTBtIy4524fCtb+WJiYnjkyBEOHz6cTk5OskXc1taWffr04c6dO9MtgsnJyXz69Cn/+ecfzpw5k23atJE5g6Ut+GkFnxo1asSAgABu2rSJQUFBOWakTExMpJmZGbt06ZLjfU1JSeHmzZtpY2NDAPTx8ZHFwM+ePZsAOHny5Jw/IDl4+fIlAeT5dxcXF8emTZtSKBRy8eLFCpGJ/GmxsLCwUNh48rB//34CkFnbEhISZFsHqampXLNmDU1NTamsrEw/P78s67EUNEuXLiUATps2TWGhuP8GipSBfzmzZ8+mUCjM0ewpkUjo5eVFfX39P2r6ziuvX7+W5RjPjISEBPr5+VEgENDV1ZUvXrzI1fibNm2iSCRiy5Yt/3h9B6lUyr1798rCDg0MDPj69et0bUJDQzlkyBBqamrSuN00Wo469HMhH/EPzQdu+fn232VhlsqA+aAtLOG3j5YBR6hVsXEGy4D1mKPstDZ9/ob4+HiePn2ao0ePZrVq1WSLuLm5Obt06cJNmzbx3bt3jI6OZlBQEDdu3MiAgAA2b96c9vb2FIvFskU/ra9AIGCpUqXYr18/Xr16NV/bPYGBgRSJRHInc0pOTubatWtpaWlJgUAgK0utSAuaRCKhtrZ2vkL4UlNT6efnRwAcMGCAQso3d+vWjdWqVcv3OLnh8+fPBMAtW7bIjtnY2LBFixayLZx27doVWAlweXjz5g01NTXZq1cv2tjYFFoV1L8BeddvAUkiB2JjY6Gjo4OYmBhoa2vn1LwIBZCSkoIqVapAKBTi5s2bEIvFWbb9+vUrKlasCGNjY1y6dAkqKiqFKGn+aN26Na5fv47nz59DU1Mzy3ZXrlxB165dER4ejtmzZ2PAgAEQCoXZjh0YGIhhw4ahR48eWLVqFUQikaLFl5tLly7B398fQUFBaNiwIUJDQ+Hu7o7Vq1dn2v7Oy3C0Wncv03NJESH4uGkYDLyGQrO8R5Zzfj21At/vHoVlwJEM52a7aeL5rYs4d+4crl+/juTkZBQrVgy1a9eGs7MzTExMEBsbi+fPn+Pp06d49uwZIiIiZP1LlCiBkiVLQigUIjw8HC9fvoRAIEDdunXh4+ODFi1awNDQMJd3KXMSEhJgZWWFVq1aYcWKFXL3S05ORseOHbF3714IBAJ06dIFEyZMQMmSJRUil7u7O4yNjbF79+58jbN69Wr0798fnp6e2LlzZ76esQ0bNoS6ujr279+fL5lyS9myZeHq6orVq1fj3r178PT0xJcvX+Dm5oZ58+ahSpUqhSrPr5BEo0aN8PjxY/Tq1QtTpkzBw4cP4eDg8MdkKkzkXb+zf5oW8cdQUlLCmjVrcP/+fSxatCjbtvr6+ti7dy/u37+PESNGFJKE+efcuXPYt28f5s6dm60iAAA1a9bEgwcP0L17dwwePBgeHh548+ZNpm1JYty4cRg2bBhGjRqFNWvW/DFFIDg4GE2aNIG7uzskEgnOnj2LgwcP4vXr16hQoUKW/Q4/+QaRUFAgMlEqQb8F2zFv3jwkJCSgfv36aNy4MUqUKIGjR49i9OjR6NatG0aOHIlLly7BwMAAPXr0wNatW3Hy5EksWLAANjY2uHLlCi5fvgwrKyusWrUKHz9+xKlTp9CrVy+FKQIAoK6ujuHDh2P9+vUICwuTu9+aNWuwd+9eDB8+HAsXLsTx48dhZ2eHPn364P379/mWy9nZGffuZa6w5YbevXvj+PHjuHbtGmrWrIl3797leayIiAiYmprmW6bc4ubmhrNnz8LX1xeVKlWCVCqFkZERLly48EcVAQDYsmULTp48iZkzZ2Lu3LkYMGDAf0YRyA1FysBfTJUqVTBo0CBMmDAhy4UvjcqVKyMwMBBLly7Fzp07C0fAfJCamorBgwejRo0aaN++vVx9NDQ0sHTpUpw5cwavXr1CuXLlsGbNGvxq3JJIJOjXrx+mT5+OuXPnYtasWRAICmZRzY7379+jW7duKF++PJ49e4Zdu3YhKCgIdevWxdOnT5GSkgInJ6cs+59//gkSaY5GuzwhEIqgZl0Z379/x61bt3Dt2jV8+/YNTk5OmDRpEg4fPoyQkBDEx8fj0aNHWLJkCUxMTLBmzRo0bNgQ/v7+UFFRwerVqxEZGYmTJ0+iZ8+eClUAfqd///5QV1fHvHnz5Gq/cuVKDBw4EMOHD8e8efMwZMgQhIaGYubMmdi/fz9KlSqFgQMHIjw8PM8yOTs74+XLl4iNjc3zGGnUr18f165dQ1xcHKpWrYqbN2/maZzw8HCYmZnlW57cEBMTg7CwMISGhuLYsWNYvnw55s2bh8+fPyMuLq5QZfmdyMhIDB06FB07dsT58+ehrKyMiRMn/lGZ/loUuedQhOKJjY2lubk5GzZsmOMel1QqZceOHamhoVHoMfS5ZfHixfnK/BUTE8MePXoQABs2bMgPHz4wMTGRPj4+FAqFXL9+vYIllo+vX79y5MiRVFFRoZGREZcuXZrBY3njxo0EkKUz4/fElAwZ79JFDGTjM/DrX2Y+A//3d5inzl3kp0+fMv1ehYeHc8mSJXRzc6NAIKBYLGbDhg25bt06RkVFFci9y4kJEyZQTU0tx2iQNWvWEACHDBmS6bWlhXbq6elRVVWVw4YNy1Os+YMHDwhAIcma0oiMjGT16tWpqqqa6xTZSUlJBJAu5r8gSUpK4qJFi2hgYCBLK71x40aS5K1btwiAN2/eLBRZsqJ169Y0NDTk6dOnKRAIuGzZsj8qz59A3vW7yDLwl6OlpYXly5fjxIkT2LVrV7ZtBQIBVq1aBUtLS7Rq1eqPa+VZ8fnzZ0yYMAG9evWCs7NznsbQ1tbG2rVrceTIETx48ACOjo6oXLkyDh06hH379qFbt24Kljp7EhMTMXfuXFhbW2P58uUICAjAq1evMGDAACgrK6dr++DBA1hbW0NLSyvTsd5GxaNgbAK/IoBZ6QowMjKSWU7Cw8OxZMkSuLm5oXjx4hg2bBg0NDSwbt06REZG4vjx4+jevTv09fULXLrMGDx4MEQiERYuXJhlmw0bNqB3794YMGAAFi5cmKlVSEtLC6NHj8br168REBCAdevWoWTJkggICEBUVJTc8pQpUwYqKioK2SpIo1ixYjh37hyaN28OHx8fzJw5M53lKzsiIyMBoMC3CUhi7969cHR0xLBhw9C8eXO8evUKtra2uHXrFgDA3t4eAPDkyZMClSU79u/fj71792Lx4sWYNGkSHB0d0bt37z8mz99OkTLwL8Db2xutW7fGkCFD8PXr12zbamhoYN++fXj37h169+4t94OkMBk3bhwAYNq0afkeq3Hjxrh06RLEYjGCg4NRuXJlVK9ePd/jyotEIsHGjRthZ2eHMWPGoEOHDnj58iUmTZqU5WJ///79bLcIklOlBSRtxnnCwsKwePFi1KpVC+bm5vDz84OWlhbWr1+PT58+4dixY+jWrdsfUwB+xcDAAP369cPSpUvx7du3DOc3b96MHj16oE+fPliyZEmO20M6OjqYOHEi3rx5g2HDhmHZsmWwsrLC+PHjER0dnaM8SkpKKFu2rEKVAQBQVVXF9u3bMWHCBIwZMwbdu3dHcnJyjv3StjwKcpvg2rVrqFGjBnx8fFCqVCncv38fa9euhZmZGdzc3HDx4kUAgKamJiwtLf+YMvDt2zcMGDAA3t7eAICrV68iMDAwW0fs/zpFysC/hEWLFiExMRH+/v45trW3t8fatWuxY8eOXHlfFwZ3797FmjVrMGXKFBgZGeV7vA8fPqBp06YQCoWYO3cuXrx4AUdHR+zZs0cB0mYNSRw9ehROTk7o1q0bXFxc8OTJEyxbtgwmJibZ9nvw4EG2zoPK4sL5WXbu2AHm5uYYMWIEdHR0sGHDBkRGRuLo0aPo2rUr9PT0CkWO3DB8+HCkpKRg6dKl6Y5v27YNXbt2RY8ePbBs2bJc+Yno6elh2rRpeP36Nfr164f58+fDysoKU6dOzdEfQFFOhL8jEAgwefJkbNmyBdu3b4enp2eOLwJp0R4FYRkICQlB69atUaNGDfz48QOnT5/G8ePHUa5cOVkbNzc3BAcHy6wrDg4Of0wZ8PPzQ0JCAhYsWAB/f380b94c9erV+yOy/FsoUgb+JZiZmWH27NlYt26dTPvOjnbt2mHgwIEYOnRonp2RFA1JDBo0CA4ODujXr1++x3v+/Dlq1KiB+Ph4XLlyBSNGjMDjx49Ru3ZttGnTBu3atcuV2VdegoKCUKdOHTRp0gQGBgYICgrC7t27YWtrm2PfsLAwfP36NVvLgJWBBgra5ZEknt++jL59++L9+/c4cuQIunTp8lcqAL9iYmKCnj17IjAwULYNtmvXLvj6+qJLly5YtWpVjiGnWWFoaIg5c+YgNDQU3bp1w/Tp01GyZEnMnj0b8fHxmfZxdnbG48ePkZSUlOdryo5OnTrh7NmzCA4ORvXq1RESEpJl2/DwcIjFYoU6cn758gWDBw+Gg4MDgoKCsGnTJty5cwceHhlDWt3d3QH8DAMG/pwycPr0aWzYsAHz5s3Dtm3b8OnTJ7kdT//TKNIBoYiCRSKR0NXVlaVLl5YrgU5SUhKrVatGCwsLuYu4FCRpdRfOnj2b77Fu375NIyMjOjg48P379+nOSaVSbt++nXp6ejQ2NubBgwfzPR9JPn/+nK1btyYAlitXjkePHs114pLDhw8TAN+8eZNlm8jISJYbsz+D059e/T7UqdWJms5eBEB1O1fq1OpEnVqdWGLorp+ZCvutlx1TNvuZnjft/wZNhsvGsh2+TZYgSE1NjV5eXgwMDOTTp0//+mQsb9++pZKSEufOncs9e/ZQJBKxc+fOCq/R8eHDB/bv359KSko0MjLi/PnzMxR0SisMdOfOHYXO/TsvX75k6dKlqa+vn2VRn3HjxtHc3Fwh8yUkJHDmzJnU1tamtrY2Z86cKVcxKwsLC1nm1HXr1lEgEBRolcbf+f79O62srFinTh2+ffuWampqHDVqVKHN/zdSlIHwf5Tg4GAqKSnJnU3t7du3NDAwYKNGjQq1IMjvfP/+nWZmZmzdunW+xzp37hy1tLRYrVq1bJWcsLAwNm7806O+S5cu/PbtW57mi4iIYN++fSkSiViiRAlu2rQpzwvPtGnTqKurm2HBlUgkPHnyJFu3bk0lJSUaNugnyz6Y9ifSLpYup/+vf8X7rqNlwBEat5+RZRuVEmVlWQgnHgzm06dPqaOjQ2tra9atW1dWJMjCwoI9e/bk7t27/1jq2Jzo2bOnrPpjhw4dCrRY15s3b9izZ0+KRCKamJhw8eLFsrz6cXFxFAgEXLt2bYHNn8bXr19Zt25dKikpcdOmTRnO9+jRg1WqVMnXHBKJhJs2bWKJEiUoFos5aNCgXNXy6Ny5MytVqkSSvH79OgHkOWIoLwwZMoRqamp8+fIl27dvT2Nj478iBfmfpEgZ+B9m3LhxVFJSkuVdz4njx49TIBBw2rRpBSxZ1owePZqqqqrZvhHLw/79+6msrMz69evnWMiJ/GklWL9+PbW0tGhubs6TJ0/KPVdsbCzHjx9PdXV16unpce7cuflOady6dWu6u7vL/v/hwwdOmTKFlpaWsuI/ixYt4q3n7xVSqTCrv5DInw/Iy5cvU0VFhR06dGBcXByPHTvGoUOHskyZMrJywdWqVeOECRN45coVhaTMVQQrV64kAFasWLHQZHr58iW7dOlCoVBIc3Nzrly5kklJSbS3t+eAAQMKRYbk5GRZSO3YsWPTKfiNGjVis2bN8jz26dOn6eTkRABs1apVrlN/kz/DOoVCIaOjoxkdHU0A3Lp1a55lyg1Xr16lQCDg/PnzefnyZQL4YyHGfxNFysD/MD9+/KCtrS1r1qwp99v+hAkTKBQKeebMmQKWLiMhISFUVlbmxIkT8zXOunXrKBQK2aZNm1xXPHv79i09PDwIgH369Mn2bSEpKYmLFy+mkZERVVRU6O/vr7A3ZFtbWw4cOJAHDx5kkyZNKBQKqa6uzu7du/P69evpLAad1t6g9ZijClUCMqtNsGvXLgLgmDFj0h1/9+4d165dyzZt2lBPT48AqK2tzRYtWnDlypV/LNf84cOHqaSkRAsLC5qbmxd65blnz56xffv2FAgEtLKyYrVq1Vi9evVCm18qlcoKL7Vp00ZmvndycmLfvn1zPd6jR4/YqFEjWTntq1ev5lm258+fEwCPHTtGkixevHiG71VB8OPHD9rb27Nq1apMTk5mpUqVWKlSpT9qDf1bKFIG/sc5f/48AXDVqlVytU9NTWX9+vVpZGTEDx8+FLB06fH29qaFhUW+9g7nzJlDAOzbt2+eTcJSqZTLly+nuro6S5YsyQsXLqQ7n1YK19ramkKhkN27d+e7d+/yLPPvPHr0iACoq6tLAKxcuTJXrVqV5e/qXVS8rGqhov7sxh3ju6iMn0Pa/V29enWmsqSmpjIoKIhTpkxhzZo1Zf4Gtra2HDBgAA8dOlQo5tjjx49TWVmZLVq0kJXKLQwTfWY8evRIVn1SIBDka/soL+zbt49qamqsVq0aP378SGNj41xVZQwLC2OPHj0oFAppY2PDPXv25NtfRCqV0sTERLZPX79+fTZv3jxfY8pDmrX00aNHXL9+PQHwypUrBT7vv4EiZeA/QPfu3amjo8Pw8HC52n/69Inm5uasUaNGvqrI5YZjx44RQK6zqaUhlUrp7+9PABw/frxCnNtevnzJWrVqybLUxcfH88yZM6xUqRIB0Nvbm48ePcr3POTPEry7du2SWSXw/0vr3rt3T67+S47dVagysPNm5pUtpVIp+/fvT5FIJHury47o6Gj+888/7Nu3L0uWLEkAVFJSoru7O6dPn87bt28r/K3s1KlTVFFRYdOmTWXWgJYtW7JUqVJ/dPtixYoVss+2TJky3LVrV6G9kd66dYsmJia0sLCgQCDgmjVrcuzz6/aXgYEBFy1apFDrSps2bWSWkqFDh9LOzk5hY2fG/fv3KRaLOWnSJMbExNDY2Jjt27cv0Dn/TRQpA/8BoqKiaGRkRB8fH7n7XLt2jWKxmMOHDy9AyX6SlJREOzs71qlTJ0+LeEpKimx/NDAwUKGypaamcv78+VRSUqK6ujoB0MXFJUtP7dzy9OlT+vn50dDQkABYo0YN+vr6UiQS5eh3EBoaytmzZ7Ny5co/0w7X6iBLIZwfRWDpuZBs501JSaG3tzc1NDRy7fQVEhLCZcuWsVmzZtTS0iIAGhoasn379tywYQPDwsJyNd7vnD17lqqqqmzcuHG6LaI7d+4QALdt25av8fPDly9fCIDTpk2TmdvLlSvH/fv3F0pkxrt372Q+HtlZBlJSUrhixQoaGxtTRUWFo0aNyrNTbXYsW7aMYrGY8fHxXL16NYVCYa639eQlJSWFlSpVYtmyZZmUlMRRo0ZRTU1NoRa9fztFysB/hG3bthEADx8+LHefwMBAAuDevXsLUDJy3rx5FIlEfPjwYa77/vjxgy1atKBIJOLmzZsVLtvr16/ZqVMnCgQCqqqqUiAQ0N/fP18PrYSEBG7evFlmdTAwMODw4cNldSL69OnDsmXLZtr31atXnDVrlsw6oaamxlatWnHnzp38/v07d9x8S7txx3LtQ2A95ijtxh3L0iLwO3FxcaxcuTJNTU359q18fX4nOTmZly5d4tixY1m5cmUKBAKZc6Sfnx9PnjwpV5haGufPn6eamhobNmyYqSLVqFEjOjo6/tH94RIlStDf35/kT0e2evXqyRwcjxw5UuBKQdq2oVAo5PLly9Odk0qlPHjwIO3t7QmAnTt3zvNnKw9p22FnzpzhlStXCCBPzwB5mD17NoVCIYOCgmS+SZMmTSqQuf6tFCkD/xGkUikbNGjAEiVKyOVdn9bHx8eHWlpaefIYloeIiAhqaWlx4MCBue4bExPDOnXqUFVVNVdKjjx8/vyZQ4cOpbKyMk1MTLhy5UomJCRw+vTpVFJSoqOjI2/fvp2rMe/fv88BAwZQR0eHAFivXj3u3Lkzg2Lh4uLCTp06yf7/8uVLzpw5kxUrVpQpAK1bt+auXbsy/SzfRcWz09obPxf638IOM1MCLAOOsNPaG5n6CGTHx48faWVlRUdHR4W8OX7+/Jk7duxgt27daGZmRgBUVVWlp6cn58+fz0ePHmW5WF66dInq6uqsX79+lgrE1atXCYD79+/Pt6x5pWnTpqxfv366YxcuXJAphtWqVeOpU6cKTCk4ePAgAcgsaUOHDmVqaipv3rxJd3d32feyMML8JBIJDQwMOGHCBEZFRREAd+7cqfB5nj9/TlVVVZmVs1mzZixRokSh5jX4N1CkDPyHCA0NpZqaGocOHSp3n5iYGNrZ2bFcuXIF8uPp2rUrDQwMcl3h7tOnT6xUqRJ1dHQUWg0uPj6eM2bMoLa2NrW0tDh16lTGxcWla/PgwQM6OTlRJBJx4sSJ2fpVxMbGcvXq1axSpQoB0MTEhKNHj+bLly8zbZ+amkp1dXWOGjWKM2bMoLOzczoFYPfu3RnkyYz3799TydCCrWfuotvccxmqG1oFHKHb3HOceDBYFj6YF548eUI9PT3WqVNHofvJUqmUwcHBnD9/Phs0aCCrdmdmZsauXbtyx44d/Pz5M0nyypUr1NDQYN26dXP8jtauXZsVK1b8YwmTJk6cSENDwwzzS6VSnj59mi4uLgTAWrVq8fz58wqff+XKlRQKhUxNTeWSJUsoFAplipejoyOPHTtWqPemefPmshBaExMTufOiyItEImGtWrVobW3N+Ph4nj59mgC4Y8cOhc7zv0CRMvAfY86cORQKhbx165bcfR49ekQ1NTV26dJFoQ+KGzduEABXrlyZq35v376lnZ0djY2Nef/+fYXIkpKSwjVr1tDMzIxKSkocPHhwtklUkpKSOH78eIpEIjo7O6czb0qlUt64cYM9evSghoYGhUIhGzduzAMHDmSrOISEhHD48OEyJzN1dXX6+PjIrQD8ysyZM6mmpib7LcYlpjA4LJp3335lcFg04xIV50h38eJFKisrs3PnzgW2kCQkJPDUqVP08/NjuXLlZJ75ZcqUobKyMp2cnOQK6zxz5gwB8Pjx4wUiZ04cOHCAADJkw0xDKpXy6NGjsm2gunXr5iuE73cmTJhAMzMzfv36lX5+fhSLxRQIBCxRogRfv36tsHnkZcGCBVRRUWFiYiLr1q2rkGRjv7J8+XIC4Llz55iSkkJHR0fWqFHjr8+e+ScoUgb+Y6SkpNDJyYlOTk658qzevHkzAcjlhSwPEomEVapUoZOTU67CrB4/fszixYuzZMmSWb5d5wapVMoDBw7IHKvat2/PV69eyd3/1q1bdHBwoLKyMidMmMCFCxfKFisLCwtOnjw5WyelFy9ecPr06bIkLioqKrIwuLxaYqRSKe3t7dmhQ4c89c8LO3bskEVyFAZhYWGcMGECxWIxxWIxAVBTU5NNmzbl0qVLGRISkukDXyqV0sXFha6urn9kQXj79i0B8NChQ9m2k0ql/Oeff1i+fHkCYMOGDRkUFJTv+bt3705zc3Pq6elRQ0ODkydP5o0bN2hhYUEzM7Ncb33llzTHzsuXL3PgwIF0cHBQ2Nhv376lpqYme/XqRfKnw6JAICj0a/y3UKQM/Ae5efMmhUIh586dm6t+vXv3poqKikL2E9NifC9fvix3nxs3blBfX5/lypWTO0wyO65cuUJXV1cCoIeHR57yxkulUp46dYoODg6yt1VPT08eP348SyXn+fPnnDZtGitUqEAA1NDQYNu2bbl3716OHDmSpqam+bquoKAgAshVFkVFMGvWrEKL5799+zZ1dXXp6urK6Oho3r59mzNmzKC7u7tMOShZsiT79u3L/fv3Mzo6WtY3re5DQZjhc0IqlVJfX1/uOH+JRMLdu3fLlFVvb2+5w01/n3fHjh1UU1OTJdSKiIiQnY+IiGDVqlWprq7Of/75J9fj55XU1FRqa2tz2rRpXL58OcVisULCmaVSKRs1akQzMzNGR0czKiqK+vr67N69uwKk/t+kSBn4jzJ06FCqqanlKjvcjx8/WLFiRVpbW+fLYSw6OprGxsa5enM9deoUNTQ06Orqmu8sf0+ePGGzZs0IgM7Ozjx16lSux4iMjOScOXNoZ2cnS6rTv39/WllZUVVVlQsXLkzntf7s2TNOnTpV9qanoaHBdu3acd++feksAI0bN2ajRo3ydX39+/dn8eLFCzWxDfnzAZxWm+HEiRMFNs/du3epp6fHatWqZfqsiY2N5aFDhzhw4EDZ5yMSiVijRg1OmTKF169fZ/ny5enh4VFgMmZHvXr1cp1gJzU1lVu3bqWtrS0BsGXLlnLnuLh48aLMZ0VHRyfLEOOEhAT6+PhQIBBw3rx5hWY58fLyoqenJy9cuEAAsqia/LBly5Z0FpjBgwdTS0srnQJURHqKlIH/KN+/f2eJEiXYoEGDXP3oQ0NDqaury6ZNm+b5YeHn50cNDQ25Mxzu2bOHSkpKbNSoUb6cGD98+MCePXtSKBTSysqK27Zty1WY2e9FgtJy9Z8/f152L+Lj4zl48GBZ5sChQ4fKtg00NTXZvn177t+/P0uP9+LFizMgICDP15iYmEg9Pb0/VoEtJSWFjRs3pqamZp7eYHPi/v371NfXZ5UqVdK97WdHaGgoV65cyZYtW8oiOTQ0NGSplQs71nzEiBG0tLTMU9+UlBRu2LCBJUuWpEAgYLt27fjs2bNM2z579kym9FauXJnnz5+nqalptum+JRIJR48eTQDs1atXoSQdmzVrFjU0NBgWFqaQUObIyEjq6+uzXbt2JH9uLYpEIs6ePVsR4v7PUqQM/Ic5dOgQAXD79u156jdnzpxcz/n06VOKxWJOnz5drvYrV66kQCBgx44d8/xg+vbtG0ePHk01NTUaGBgwMDAwV3kCfi8S5OjoyMDAwEwjIJ48ecLJkyfLsu0BYJUqVbJVANL4/PlzvsOr9u7dq7C3q7zy/ft3VqpUiWZmZgpP02xoaMiKFSvm2TqUkpLCq1evcty4cbIIhbSMgEOGDOGxY8dy7ayZW9JyfuQ2guZXkpKSuGrVKpYoUYJCoZC+vr4yH5qPHz+yX79+FIlEtLS05Pbt2ymRSJiamkqhUChXavL169dTSUmJ9erVK5CEQ7+SVt45KCiIhoaGnDJlSr7Ga9u2LQ0MDPjp0ydKpVJ6enrSxsamwBIa/a9QpAz8x/Hx8aGRkVGuH0wBAQEUiUS5ysSX9sO0trbOMbueVCrl9OnTCYCDBg3KU6KYxMRELliwgPr6+lRTU+PYsWPlfptMSUmRq0gQ+fPNY9KkSXR0dCQAamlpsWPHjrKYeQD09PTMcWFM83R/+vRprq81DW9v73yXp1UEERERtLS0ZNmyZeW+59nx+PFjGhkZ0cnJKV+L6K+kOcXOmTOHPXv2ZIkSJQiAysrKrFevHmfPns379+8r3Fz+5MkTAuDZs2fzPVZiYiKXLFlCU1NTikQiVqpUierq6tTV1c1QPTM8PFwu58U0zp8/Tz09Pdrb2+fKqTa3JCUlUV1dnXPmzKGbmxvbtm2b57HSojXSMk2m+YccOHBAUeL+z1KkDPzHCQ8Pp46OTq4da1JSUli7dm2amJjIvQ+XlvDk4MGD2baTSCQcNmyYLG1qbh/GEomEW7ZsoaWlJUUiEXv37i13mtvQ0FCOHTtWFntdqVIlrly5MsN3Ojg4mBMnTpQ5Dmpra7NTp048ePBgBkXn+PHjLF68OLW1tblhw4Ysr2f+/PlUU1PL815/ZGQkxWIxly5dmqf+iubx48fU1dVlvXr18pWD4OnTpzQ2Nmb58uX55csXhcmXkpLCkiVLyvbQpVIpnz59ykWLFtHLy0uWftrY2JidO3fmli1b+PHjx3zPm5ZLYt68efkeK228FStWUFtbW5ZdsFu3bhm24dI893MTVvz8+XOWKlWKhoaGCg1x/J169eqxSZMm7Nu3L8uVK5enMb59+0ZTU1M2btyYUqmUSUlJtLW1pYeHR1EooRwUKQNFyGq+59a7OiIigqampnR3d88xTPHHjx+0trbO0UchOTmZvr6+FAgEXLZsWa7kkUqlPHHihMxLv0WLFnK9Zf9eJEhbW5v9+/fPEDURHBzMCRMmyDy70xSAQ4cO5WiC/Pr1Kzt37izzCM9MgfL19WXVqlVzdc2/snDhQiopKSl0wcwvFy5coLKyMn19ffP0QH7+/DlNTU3p6OiYbd6HvLJq1SoKBIJMvyeJiYk8e/YsR40aJQv9BEAnJyeOGjWKZ8+ezbPp2cXFhR07dsyv+Dxx4oTMJ6Vt27Z89OgRZ8+eTQMDA6qoqHDIkCGy71raW3Ju6z98+fKFbm5uVFFRyfWWorxMmTKFOjo6DAwMpLKycp4KSvXs2ZNaWloyC9y8efMoFAoVVkzsf50iZaAISiQS1qhRg3Z2djma73/n4sWLFIlEOTq9TZ8+nWKxONvFOSEhgd7e3hSLxbnOEHbr1i3WrVuXwM9iP/K8xWRWJGjjxo0yJ0WpVMpHjx5lUAA6d+4slwKQGQcOHGCxYsWor6/PHTt2pFsgy5cvL4uJzgtOTk5s2bJlnvsXFGl75Nk5rmVGSEgIzczMWKZMGYW8kWdGYmIiixcvTl9f3xzbfvz4kVu2bGHnzp1pbGwsSwzl5eXFRYsW8enTp3IrPP369ctXTP29e/dYv359WbbC33MQxMTEcOrUqdTV1aWamhpHjBjB+fPnUyAQ5GmhTUxMpK+vLwFw0qRJCn/TToskSHsxef78ea76p22xpSUwi4yMpLa2NgcMGKBQOf+XKVIGiiD506SrpKSUp6QxaTXuszL/v3//nurq6vTz88tyjOjoaNaqVYvq6uq5yg738uVLtm3blgDo4ODAQ4cOZfugyqxI0LBhw/j48WOSPxWAhw8fcvz48bKCLTo6OvT19eXhw4cV4oT0+fNn+vj4EABbt27NT58+MSkpiUpKSrm2hqTx4MEDubZg/hQzZswgAK5fv16u9q9evaK5uTlLly5d4OFggYGBFIlEuQqzlUgkvH//PmfPns169epRWVlZlmiqZ8+e3LNnT7ZOjmlV+nIbHfP+/Xt26dKFAoGApUuX5oEDB7L9vn/79o3jx4+nlpYWlZSUqKGhkWefC6lUymnTphEAO3bsmOsXh+z48eMHlZWVOWXKFALIVa6DuLg4lixZku7u7jLfol69elFPT++vspL97RQpA0XImDBhApWUlBgcHJyrflKplM2bN6eurm6mjkYdOnRgsWLFsnQki4iIYIUKFainp8dr167JNWdkZCQHDhxIsVjM4sWLc926ddm+8WRXJEgqlfLBgwccN24cS5cuLVMAunTpwiNHjhSYF/LOnTupr6/PYsWKccGCBQTAK1eu5Gms4cOH08jIqFBCwfKCVCpl7969KRaLc8zr8Pr1a1pYWNDW1jbfJY3lIT4+nkZGRuzTp0+ex4iLi+OxY8c4ZMgQmRVJKBTSxcWFEyZM4NWrV9N9P2/dukUAvHHjhlzjR0dHc/To0VRVVaWRkRGXL1+eq8/6y5cvdHJyokAgoLa2NidOnJhnx85du3ZRRUWFNWrUUOjWTa1atdiiRQvq6urKHW1EksOGDaOqqqqsmNrdu3cpEAi4ePFihcn2X6BIGShCxo8fP2hnZ0dXV9dce+9/+/aNNjY2rFixYro3hsuXL2f7RhgaGkobGxuamprKtbf3/ft3Tp48mZqamtTR0eGsWbOyfLvKrkiQVCrl/fv3OXbsWFliGl1dXXbt2pVHjx5VaNGd7IiIiGDTpk1l+9F5KRmbkpJCY2NjDhkyRPECKpCUlBR6eXlRS0uLDx48yLTN27dvaWVlRRsbG7nzUCiCmTNnUllZWWFzvn37lmvXrqWPjw/19PRkCmbLli25cuVKPnv2jCKRiCtWrMh2nOTkZC5ZsoSGhoayiJi8Pl+bNm1KDw8PDh8+nKqqqtTT0+P06dMZG5v7QlXXr19nsWLFaG1tna/ol18ZO3YsDQ0N6erqKrc/xfXr1ykQCGRhzlKplLVq1aKDg8Nfqxj/rRQpA0Wk49e9u9xy7949qqiosHfv3iR/ejk7OTmxSpUqmSoXjx49oqmpKUuVKpWjiTY5OZnLly+nsbExlZWV6efnl6kJMLsiQUlJSbx37x7HjBkjy+Smp6fHbt268dixY4WmAGQms6enp6yCXG6L6Bw5coQACqXsbH75/v07nZ2dWbx48QzFet6/f09ra2uWLFmy0BMBxcTEUFdXN1cVPeUlNTWVN27c4JQpU1ijRg2KRCJZCKOjoyMPHTqUYUGWSqXct28fbW1tKRAIMo0OyC2VK1dmz549Sf6s7TBw4EAqKyvT0NCQc+bMyfWWxevXr+no6EhdXV2eOXMmX7KRP7OMpm2dOTs759g+MTGRDg4OrFy5sszqsnv37j+Sivt/gSJloIgM9OjRg9ra2nky0a5du5YAuGnTJpkzUGam0KtXr1JXV5dOTk7ZOodJpVLu2bNH9lD09fXlmzdvMrT7+vUrFy9enKFI0Nu3b3n37l2OHj2apUqVkikA3bt35/Hjx/+YAvA7derUYcOGDenp6UkA7Nmzp9y/Ix8fH5YrV+5fEz4VFhZGCwsLlitXTmaqDgsLY6lSpWhpaZnp51sYTJw4kWpqaoyMjCzQeaKjo7l//37a2dnJfA2UlJTo7u7OGTNmcMOGDbKaGQ0aNMjSipJbihcvnsEn6N27d+zTpw/FYjGNjY0ZGBiYK1+A6Ohoenp6UiwW57uI2ffv3ykSidi6dWuqqqrmGGKbVqgq7f4kJCTQwsKC3t7e+ZLjv0qRMlBEBqKiolisWLE8lxPt1q0bVVVVZWb33zl27BjV1NTo5uaW7b7lhQsXWLVqVQJgo0aNMpQrlkqlvHDhAjt27EgVFRWKxWK2bNmSx44d461btxgQECBTAPT19dmjRw+eOHHirzMfphWvmTJlCqVSKVeuXEkNDQ1aWlry3Llz2fb9+vUrlZWVFRazXlgEBwdTR0eH9evXl5WkLlGiRK6c+BRNVFQUNTU1OXr06EKZb+HChVRVVeXTp0+5dOlS1qtXT1ZkSSQSsU6dOty4caNC/CZSU1MpEom4fPnyTM+HhoayW7duFIlENDMz47Jly+T2lUlJSWG/fv0IgCNHjsxTgrA0qlWrxtq1axNAtomOHjx4QLFYnE65mTp1KpWUlGS+A0XkjiJloIhM2b59e7bZyuISUxgcFs27b78yOCyacYn/5xwVHx9PAwMDCoXCDD/M7du3UywW09vbO8v0vA8fPmTjxo1lOdV/XxB/LxJUqlQpzpo1i6dOnWJAQABtbGxkkQI9e/bkyZMn/zoF4FfevXuXIRLg1atXdHd3l2VgzCpF7ooVKygSif6VBVjOnTtHJSUl6ujo0MzMTCElqfOLv78/tbS08l0MSx7StuQuX77MIUOGUElJicWLF+fo0aMZEBDAypUrUyAQEADLlStHPz8/njp1Kse01pnx8eNHuTLxvXjxgp06daJAIKCFhQXXrFkj129HKpVy4cKFFAgEbNGiRZ5TOo8cOVIWtnn48OFM26SkpLBy5cp0cHCQKSwfPnyguro6R4wYkad5iyhSBorIAqlUyoYNG7JEiRKy/cwXH2M58WAw3eaco1XAEVr+8mcVcIRuc85x4sFgHrl8hyKRiCoqKmzdurXMfL106VIKBAJ26dIlU8//t2/fysKmbGxsuGvXLlnfzIoEtW/fnitXrqS/vz+tra3TKQCnTp36qxWAX0lLBvO786BEImFgYCBVVVVZqlSpTHMnuLi40MvLq7BEVSiRkZGyTI+DBw/+0+KQ/Lloqqqqyl1iOL9zAaCamhq1tLQ4Y8aMDAv958+fuWPHDnbt2lV2r1RVVdmgQQPOnz+fwcHBcm0P3bt3T5b/Xx6ePHnCNm3aEACtra25adMmufITHDp0iBoaGqxUqVKeLBppvwUNDY0sCwvNmzePAoGA169flx3r1KkTjYyMFJL6+r9KkTJQRJaEhoZSXV2dPYeOYqe1N2gZcITWY46mUwJ+/0s7b9VtPpdv2kUAXLhwISdNmkQAHD58eAYzYlRUFEeMGEEVFRUWK1aMy5Ytky3kvxcJcnBw4PDhwzlo0CBZMSBDQ0P26tXrX6UA/EpacpisHurPnj2ji4sLBQIBR44cKdvTffbsGQFw165dhSmuQvj8+TPLlStHY2NjDh06lAC4cePGPy0WSXLQoEHU19fPk5e9PKSly7awsCAAVqhQQS4/hbQkWPPnz6enp6es0FLx4sXZrVs37tixg58/f86079GjRwkgg9NmTjx8+JAtWrQgAJYuXVpW9Cg77t27x+LFi9Pc3DzD1l5OfPv2jQKBgCVLlmSXLl0ynA8JCaGqqmo6R8+0Qkf59Vn4r1OkDBSRLd2mrWEJv30sOTprBSCzv5IBR2g37hib+82VmTpnzpyZbsFLSEjg7NmzqaurSw0NDU6cOJGxsbEZigSpqanR29ubHTt2TKcA9O7dm6dPn85TRrW/idatW9Pd3T3bNqmpqZw1axaVlZXp4ODAW7duccyYMdTV1VVo8pfCICoqihUqVGCxYsX4+PFjSqVS9uzZk2KxmKdPn/7T4vHdu3dUUlLKU1XOnDh79iwrVqwoS5fdoEED1q5dO09jJSQk8OTJk/Tz82PZsmUJgAKBgJUrV+bYsWN58eJFmXK8du1aCgSCPCvLd+7ckW3dOTo6cu/evdkqBWFhYaxYsSI1NTV55MiRXM3l5OREGxubDAW3JBIJ3d3dWbJkSdk2hEQiYZUqVejs7Jznmh5F/KRIGSgiS5ace/FzcR91OFeKwO9/2tXbUFdXV5agJDU1levXr6e5uTnFYjH79+/Pjx8/ZigSZG9vz/r168veoNISw5w5c+ZfrwD8SqlSpeTOEfDo0SM6OztTKBRSW1tbFir2b+Hr16+sWLEiDQ0N0+WVSE5OZsOGDamtrc2HDx/+QQl/0rNnTxobG+dpfz4zgoOD6eXlRQB0cXHh5cuXSZLTpk3L1iqUG8LCwrhhwwa2b99elmJbU1OTTZs2ZZMmTaivr5/vOa5fvy6LeHFycuLBgwezlD0uLo7NmzenUCjkokWL5L7GIUOGUF9fnxoaGun6rFq1igDShTFu2rSJAHjp0qX8XVgRcq/fQhTxn2LnrXeYd+rFz/8IBPkaS8/dF2qO9dC+fXscPHgQFSpUQPfu3eHq6or79+/D3d0dnTp1grW1NRYuXAgjIyOYmpri2bNnePDgAby8vHD27FmEh4dj5cqVqFevHsRisQKu8s8TFxeHV69eoUKFCnK1L1u2LIKCgtCpUyfExsbiwoULePjwYQFLqRiio6Ph6emJt2/f4uzZsyhbtqzsnJKSEnbv3g1ra2t4eXkhLCzsD0oKBAQE4PPnz1i3bl2+xomIiECvXr1Qvnx5PHv2DLt378a1a9dQs2ZNAICzszOio6Px5s2bfMtsZmaGrl27Yvv27YiMjMTt27cxevRoxMTE4OjRo/j69StsbGzQr18//PPPP4iJicn1HC4uLjh58iQuXboEXV1dNGvWDNWqVcOJEydAMl1bDQ0N7Nu3D8OHD8eQIUMwcOBApKam5jiHm5sbvn79ivj4eDwPfYPH4TE4efs5AmYtRZcevVGvXj0AP387AQEBaNOmDWrVqpXraykibwj4+yedCbGxsdDR0UFMTAy0tbULQ64iCoD3XxPgsfAiklKlGc4lf36LmCvbkfzxJSTx0RAoqUDJoAS0q7WEum21LMcUQ4q3K3ohNSYStWvXRv/+/REUFISNGzciKioKZmZmSEpKQlRUFIoVK4ZWrVrBx8cHbm5uEIlEBXm5f5Tr16/D1dUVd+/ehbOzs9z9fH19cfHiRWhqaiIkJAQTJ07EqFGj/lolKSYmBp6enggJCcG5c+fg5OSUabvw8HC4uLhAX18fly5d+qPPkU6dOuHixYt49eoVlJWVc9U3Li4O8+bNw9y5c6GqqooJEyagX79+GcaJiIiAmZkZ9u3bh5YtWypS/HR4e3sjPDwc1atXx6lTpxASEgKRSAQXFxc0aNAAnp6eqFy5cq5/a+fOncP48eNx7do1uLq6YsqUKahbty4Ev71ArF69Gv3790f9+vWxa9eubD/XoGfv0GjQdKjZVIaSnlm6cwIAFvrqqFO6GL7c+AfrFk7Hs2fPYGlpmSu5i8iIvOt3kWXgP8SYfx4hVZq57ieJ/QRp8g9olKsHPY9e0HFtCwD4vG8qvt8/keWYKRIpTLyHAQA+ffqENm3aYNmyZUhOTv45rkSCtm3b4vz58wgPD8fy5ctRp06d/2lFAADu378PsVgMBwcHuft8//4d+/btQ+/evXH37l34+flhwoQJcHV1xdOnTwtQ2rzx/ft3NGrUCC9evMCZM2eyVASAn2+3x44dw+vXr+Hj44OUlJTCE/Q3xowZgw8fPmDLli1y90lNTcXq1atha2uLWbNmYcCAAXj16hWGDBmSqUJhamoKY2Nj3Lt3T5GiZ+DTp09wcnLC0qVL8eLFC4SGhmLZsmUoVqwY5s2bBxcXFxQrVgxt27bFunXr8P79e7nGrVu3Lq5cuYITJ04gJSUFHh4eqFOnDi5fvpyuXe/evXHixAlcv34dNWrUwNu3bzOM9f5rAjqvC0LbTY+gXbFxBkUA+Jmz++3XBGy58QZH6AynYWsh1DLK0z0pIm8UKQP/EUIiv+Pyyy+QZKEMqNlUgXHbKdCt2QFaTg2hXaUZjDvMgFKxkoi9eSDLcQUiMUTmZSE2MMeTJ08AALq6uvD19cWFCxcQFhaGZcuWoXbt2v/zCsCvPHjwAGXKlIGKiorcffbt24cfP36gc+fOUFFRwcyZM3H16lXExMTA2dkZ8+fPh0QiKUCp5ScuLg5eXl54/PgxTp06hYoVK+bYp2zZsvjnn39w/vx59OvXL4P5ubBwcHBAq1atMHPmzBzN2yRx5MgRlC9fHn369EG9evXw/PlzzJkzB7q6utn2dXZ2LnBlICIiAqamprL/lyxZEn369MH+/fsRFRWFK1euYODAgXj79i169+4NCwsLODg4YOjQoTh+/DgSEhKyHFsgEKBBgwYICgrCoUOHEBMTAzc3N3h6euLGjRuydh4eHrh+/Tri4+NRtWpVBAUFyc7tvPUOHgsv4lpo1M8DwuyfAZL//5X4BF14LLyInbfe5eGuFJEXipSB/wjbgt5BJMydj4BAKIJYyxDSpLhs21EqQTHXVtDS0oK9vT1evXqFpUuXwt3d/T+lAPzK/fv35fYXSGPTpk2oU6cOLCwsZMdcXFxw79499OvXDyNHjkTt2rXx6tUrRYubK+Lj49G4cWM8ePAAp06dQpUqVeTuW7duXaxduxbr1q3D9OnTC1DK7Bk7dixevXqF3bt3Z9nmzp07qFu3Lry9vWFiYoLbt29j69atcpuuC1oZkEql+PjxYzpl4FfEYjFq1KiByZMn48aNG/j8+TN2796NGjVqYP/+/fDy8oKenh48PDwwd+5cPHjwIFMFTSAQwNvbG3fu3MHevXtl2xKNGzfGnTt3AABlypRBUFAQSpUqhdq1a2PPnj1Yej4EAfsfISlVmuVLSFZICCSlShGw/xGWng/J/c0pItcUKQP/Ec4//yTXD1KanAhJQgxSvkUg9uYB/Ai9A1XL7Bc1gVCEUrWa4dy5cwgNDcWoUaMUJfa/EolEgkePHuVKGXjz5g0uXLiALl26ZDinrq6OhQsXyiwt5cuXx/LlyyGVZvT9KGgSEhLg7e2Nu3fv4sSJE6hWLWt/kqzw9fXFlClTMH78+FyZ6hWJs7MzvLy8MH369Az38c2bN+jYsSMqV66MT58+4ciRIzh79iwqVaqU6znCw8Px6dMnRYouIyoqCikpKTAzy2h2zwx9fX34+PhgzZo1ePv2LZ4+fYo5c+ZARUUFkyZNgpOTE0xNTeHr64utW7ciMjIyXX+hUIhWrVrh4cOH2LFjB169eoXKlSujRYsWePjwIYyMjHD27Fm0bNkS3aet/T9H5Xwy79QL7CqyEBQ4RQ6E/wHiklJRbtJJyKObR51Yirg0HwGBEOp21aHfaBBEqprZ9hMACJ7UAJvXr0H//v2xY8cOtGvXLt+y/xt58eIFSpcujdOnT8PDw0OuPlOnTsXs2bPx8eNHaGpmfa/j4uIwcuRIWfTF+vXr01kSCpIfP36gadOmuH79Ok6cOCHznM8LJNGzZ09s2bIFJ06cQN26dRUoqXxcu3YNNWrUkDn5ffv2DTNmzMDixYuhr6+PKVOmoFu3bnl23nz58iVsbW1x4sQJNGjQQMHSAw8fPkSFChVw/fp1uLi45GuspKQkXL16FSdPnsSpU6dw//59AICTk5PMEbFGjRrptr1SU1Oxfft2TJ48GaGhofDx8cGkSZOgaWyJOvPOIZWCDA6HiW8fInLHmExlMOk8DyrF7TM9pyIW4swwd5TQV8/Xdf4XkXf9LlIG/gM8Do9B4yVX5GqbEvUeqd+jIPkehYRnVwCRGAYN+kOkoZdj30P9q6Ns8Z/+AgcOHMCtW7dQpkyZ/Ir/r2P37t1o27YtPn36BCOjnJ2gSMLOzg41atTAxo0b5Zrj1KlT6NGjB2JiYhAYGIhu3bplePAqksTERDRv3hyXLl3C8ePH4e7unu8xU1JS0KRJEwQFBeHKlSvpQhILi7p16+Lbt2/w9fXFtGnTkJiYCH9/f/j5+WWrlMmDVCqFrq4uxowZg4CAAAVJ/H+cOHECjRo1wps3bxTudf/x40ecOXNGphx8+vQJ6urqqFOnDjw9PeHp6YnSpUtDIBAgJSUFmzdvxtSpU/Hu3TuUH7Ia39VMZfv/v5KmDGhV8oayqV26c2rWFSFS18lUHpFQAFdrA2zpkXtL1H+dImWgCBn33n1DixXX8tQ3cud4SJPiYOK7IMfFJmLTcCRHvIBIJIJUKoVAIICOjg7EYjHEYjGUlJSy/Xd+zxf2WFn5Q4wdOxYbN26UO6b+6tWrqFmzJs6dO4c6derI/dlER0dj2LBh2LhxI7y8vLBmzRq5Tca5ISkpCS1btsS5c+dw9OhRhb7Fx8bGolatWvj27Rtu3LhRIPJnBUlMnDgRU6dOhVAoRI8ePTB58uQs9+DzgpubG0xNTbFr1y6FjZnGhg0b0L17dyQmJubKUTW3SKVSPHz4EKdOncLJkydx5coVJCcnw8LCAp6enmjQoAHq1asHDQ0NzF65Cesisv4M05QBw+YB0LDPvWXpzDA3lCqmlZ/L+c8h7/r9dwYvF6FQlMV5dw1Rt6+BryeWIvVrGJQMzLNtO3nieBiKEpGamooPHz5g7ty5sLS0hI+PD1JTU5GamoqUlJRs//3rsYSEhGzPyzNWQe6rCwSCTJWFmJgYCAQC2NrayqVYBAcHQ11dHatWrcL69etzpdA4OztDVVUV27Ztg62tLXx9feHm5pZhjLwqPCTRrl07nD17FocPH1a4OV9bWxvHjh2Di4sLGjdujEuXLkFLq+Af9leuXMGIESMQFBQEXV1dWFlZYdWqVQq3rjg7O+P48eMKHTONiIgIGBgYFKgiAPz0FXBycoKTkxP8/f0RHx+PixcvypSDtWvXQigUomrVqtCp2xNCASCPv6A0KQECJRUIcogwSEMkFGDrjXeY1NQxn1dURGYUKQP/AawMNCAA5PIZ+B2mJAEApEnx2bYTABjUtR00VP7vK1W2bFm0b98evXv3Rr9+/fIwe/6RSqWQSCQ5Kh6KPD979myUK1cOtWrVyrFtYmIiwsLCYGFhgc+fP+dLFgBYuXIlVq5cqfD7KBQK4e3tXWBWl5o1a2L//v0oX7482rRpAxUVlQKx9rx//x5z587FqVOnUK5cORw8eBDJycnw8fHBuXPnMk2skx+cnZ2xePFifP/+XeFKTnh4eKFaUtLQ0NCAl5cXvLy8AADv3r3DqVOncOrUKVz/JoAoc0t/OqKOLQKTfwACIVRKOEKvTneomNpm20ciJc6/+IRJKFIGCoKibYL/CO5zz+Pt16xjiiXx0RBp6KY7RkkqPm72Q0rUB5gP3gqhslqW/S0N1HFxREYT96BBg7B69WpcuXIlVyFo/1a+fPkCIyMj7Ny5E23bts2x/c6dO9G+fXu8ePECtrbZPwyzgySkUil27dqFQYMGAQDmzZuHhg0b5kmxSExMRGBgIO7evYsBAwbAwcEhz9YZec9/+/YN7969g5aWFnR0dLJU4go614Iit6S+f/+OU6dOoVGjRihevLhCFanp06cjKSkJCxcuzNNYQqFig8nkcVRO/PAU32/9AzXryhCq6yDlyzvE3vwHTEmESae5UDaxyXaONEflX186isieIp+BItIx6dBjbAl6m2V44ad908DkBKiUKAuRlgEkcd8Q/+QCUqM+QK9uD2hXbZHl2JRKoPvpIYbUMkOrVq2go/N/rwbJyclwc3NDREQE7t69CwMDA4Vf29/E2bNn4eHhgadPn8LePnPP6F9p1KgRYmNjcfXqVYXJEBkZib59++LAgQPo0KEDlixZAn19fbn7p6amomPHjvjnn3+wb98+eHt7K0y2nNi4cSO6deuG6dOnY8yYzL3OScqtjHz//h1btmzBpk2bIBAI0LFjR3h7e0MgEKRre+3aNSxZsgQBAQGwsLBQmKUoOTkZFy5cgJWVFYyMjHI1VkFnaRQIBAq1uiSrF8MDM69cy5HyLRwR6wZBpYQjjNtOybH90UE14Wgmh/mhCABFPgNF/EbHahbYeP1Nluc1ytRC3MPT+H7vGKQ/vkOorAZlk1LQq90t29oEwM88A1qR99Gz5wT0798fTZo0QceOHeHl5QUVFRXs3r0bFStWROfOnXHkyBGFv5H8TTx48ABqampyveWHh4fj1KlTWLFihUJlMDY2xv79+7Ft2zYMGjQI58+fx5o1a9C4ceMc+0okEvj6+mL//v3YvXt3oSoCANC1a1e8ffsWY8eOhaWlJTp27JihTdoipqSkBDW1zK1VEokEW7Zswbhx4/Dp0ycMGDAA48aNy1IZbdOmDc6cOYPg4GDMnDlToddUqVIlVKhQAevXr891X6lUmqWyUL16dTRp0gSDBw8ukO0uec8nJSUhPj4ecYlKQB52LZT0zKBmWw0JL66BUkmOPgTJmdRWKSL/FCkD/xFsjbVQq5QhroVGZWod0HBwh4ZD7sPFZCE/M/ciLCwMO3fuxLZt29CyZUvo6uqidevW6NChAzZv3owmTZpg5syZGDt2rCIu6a/k/v37KFeunFyZF7dt2wYlJSW0adNG4XIIBAJ06tQJderUQc+ePdGkSRN0794dCxYsSGe5+RWJRIKuXbti9+7d2LVrF1q0yNoaVJBMmDABb968Qbdu3WBmZparCAvgZ9jlyJEj8fDhQ/j4+GDmzJmwscne/CwUCjF69Gj4+vri/v372dZZyC3Ozs6yTH25RSgUQkVFJYOTIEl8/vwZjo6Ouap/UZDkJoT5d8TahoAkFUxJgkAl+1wC+XGILiJriu7qf4gZLcpBnMuUxDkhFgowo0U5AEDx4sXh5+eHu3fv4smTJxgwYADOnj2LunXronfv3nBxccH48eNx5swZhcrwN/HgwQO5FhKS2LRpE5o3b55jjvv8ULx4cRw7dgxr1qzB7t27Ua5cuUzvv1QqRY8ePbB9+3Zs374drVq1vJ2/FwAAQPRJREFUKjCZckIgEGD16tVwd3dHixYt8PjxY7n6PXz4EA0aNECDBg2gpaWF69evY/fu3TkqAmm0b98eJUuWxIwZM/IjfgacnZ3x+PFjWfEuRfD161ckJyf/EQfCrDBSA/LmpgykRn+EQKwMgbJqtu0E+OkQXYTiKVIG/kOU0FfHZAWH5Uxp6phpVrAyZcpg2rRpePXqFa5evYpmzZohJCQEJNGwYUMEBAQopNb730RSUhKePHkiVxriu3fv4vHjx5mmH1Y0AoEAPXv2xKNHj1CqVCnUr18fAwYMQFzcz5oTUqkUvXv3xpYtW7Bly5YCsVTkFiUlJezduxcWFhbw8vJCRERElm0/fPiAbt26wcnJCa9fv8b+/ftx+fLlXGflE4vFCAgIwN69exVaJdLZ2RkpKSlyKzXykHY/FJkTIS+EhIRg0aJFaNCgAUqYFEPKt6w/JwCQJMRkOJYcGYqEkJtQtXKGQJD9kmRhoF7kPFhAFCkD/zHaVbHACE+7nBvKgTD4CFxNsrc0CAQCuLq6YtmyZQgPD8f27duhrKyMuXPnomTJkqhZsyZWrFiBL1++KESmP8nTp0+Rmpoql2Vg06ZNMDExQf369QtesP+PlZUVzpw5gyVLlmDDhg2oUKECLl68iH79+mH9+vXYuHEjOnToUGjy5ISOjg6OHTsGiUSCJk2ayJSXNGJjYzF27FjY2dnhyJEjWLJkCR4/fowWLVrkOTywS5cuMDMzw6xZsxRxCQCA8uXLQyAQKLRo0Z9SBn78+IETJ05g8ODBKFWqFOzs7ODv7w+SmD17Nlq7lkF2xsfPB2bj055JiLm2C9/vn8DXM2vwcetICJRUoFe7a7Zzi4QC1LErptgLKkJGkTLwH2RgHVvMalkOKmJhrisZioQCqIiFGOFmCgafgJubG16/fi1XXyUlJbRv3x5nz56FQCBAo0aNoK2tjUGDBsHU1BRNmjTBjh07si2r+jeTls+9XLly2bZLTk7G9u3b0alTJ4jFhfuWIxQKMXDgQDx48ADGxsaoXbs2Vq9ejZUrV6Jz586FKos8mJub4+jRowgJCUHbtm1ljmvLly9HqVKlsGDBAgwbNgyvXr3CgAEDoKSklK/5VFRU4O/vj23btiE0NFQh16CpqQk7OzuFKgPh4eEACkcZeP36NZYtW4YmTZrAwMAAjRo1wsGDB1G/fn0cOnQIUVFROHXqFIYOHYoBnuWzTTikbucCSUIsYm8ewNdTK5Dw7DLU7Vxh2nUhlAxLZCuHREp0cimcOhz/RYqUgf8o7apY4Mwwd7ha//SuzkkpSDvvam2AM8PcMbBRRVy8eBEikQju7u54+fKl3HNXr14d8+fPx/Hjx9GjRw+Eh4dj4cKF+Pr1Kzp06IBixYqhc+fOOHHiBFJTs683/zfx4MED2NjY5Jhc5tixY4iKiiqULYKsKFWqlKwKn1gsxsKFC3Hz5s0/Jk92VKhQAXv37sXJkyfRuHFjODo6YuDAgWjcuDFCQkIwffp0hYY89+zZE/r6+pgzZ47CxlR0OeOIiAjo6elBVTX7Pfa8kJSUhLNnz8LPzw9lypSBtbU1hg4dioSEBEyZMgWPHz/GmzdvsGLFCnh7e6er4XDpyG78eH03y4VFu3JTmHZZgBJDd8DS/yDMB26GobcflPSy930QCQWoVcqwKBVxAVKkDPyHKaGvji09quH0UDd0rmYJSwN1/K4SCPAzoVDnapY4M8wNW3pUk/kIWFhY4NKlS1BXV4ebmxuePXsm99yDBw+Gj48PunXrhpiYGAwcOBDXrl3Dq1evEBAQgNu3b8sStQwePBhBQUGZ1lr/m5DXeXDTpk2oWLHiHynMA/x0Xhw+fDiWLl2KVatW4cGDB9DU1ET16tUxduxYJCUl/RG5skNHRwclS5bEqVOnQBL37t3Dhg0bYG6efYrsvKCurg4/Pz9s2LABHz58UMiYzs7OePDggcLSY4eHhyvUKvD+/XusXr0azZs3h4GBATw8PLBz505ZZsioqCicO3cOI0aMgIODQ6bbMGFhYfDz80NdzUgoKdjj/1dH5SIKhqKkQ0WkIz4pFW+i4pGcKoWyWAgrA40cHXYiIyNRr149fP78GWfPnpV7kYuNjUWVKlWgqqqK69evQ139/xwR0x7427Ztw44dOxAREQEbGxt07NgRHTp0QOnSpfN1nYqGJAwMDDBs2DCMHz8+y3ZfvnyBmZkZ5s2bh8GDBxeihD8hCX9/f8ybNw/Lli1D//79AfysIDh79mxMnjwZZcqUwebNmxUaXpdXQkNDMXr0aFkkRPny5bFt2zZs374d7du3L7B5Y2NjYWlpiS5duiAwMDDf450+fRqenp54/vw57Ozy77Pj4+OD6OhonD59Ok/90xItHTt2DMePH8ejR48gEong6uqKRo0awcvLS+brIA8k0bx5c9y8eRNPnjzByZffEbD/UZ5ky4zZLcuhbZWiLYK8IO/6XWQZKCIdGipiOJrpwNlCD45mOnJ57hobG+P8+fMwNTVF7dq1ZXvnOaGtrY19+/YhJCQEAwYMSPfmLxAIULFiRcyfPx/v37/HmTNn4ObmhsDAQNjb26Ny5cpYuHBhtl7mhcmHDx/w7du3HBfQHTt2gGSBLmRZQRJjxozBvHnzsGjRIpkiAPz05xg3bhxu3boFgUCAKlWqYOrUqQWeBS8roqKiMGzYMNjb2+PKlStYv3497t27hy1btsDX1xddu3bFxYsXC2x+bW1tDBkyBKtXr8anT5/yPZ6zszMAKGyrICIiIteWgYiICKxfvx4+Pj4wNDRE7dq1sXHjRlSsWBG7du3C58+fcenSJYwePRoVKlTIlRPmnj17cOjQISxbtgx6enpoV8UCXSv+/wRP+bTojfQsXaQIFAaUg5iYGAJgTEyMPM2L+I8SFRXFypUrU09Pjzdv3pS73+bNmwmAa9euzbHtjx8/uHfvXrZo0YLKysoUCoX08PDghg0b/uj389ChQwTAt2/fZtuuUqVKbNasWeEI9Rvjx48nAC5YsCDbdomJiRwzZgyFQiErVarE4ODgQpLw5+c7Z84c6urqUlNTk9OmTWN8fHy6NklJSaxbty51dXX55MmTApMlKiqKmpqaDAgIUMh45ubmHDVqlELGKlmyZI5jpaSk8MqVKxw7diydnZ0JgAKBgC4uLpwyZQpv375NiUSSb1k+f/5MIyMjtmrVSnYsKSmJFStWpHX9TrQbd4zWY47SMuCI3H/WY47Sbtwx7ryZ/e+piJyRd/0uUgaKUCjR0dGsXr06tbW1efXqVbn79e7dmyoqKrx7967cfb5+/co1a9awdu3aFAgEVFVVpY+PDw8cOMDExMS8iJ9npk6dSj09PUql0izbBAcHEwD3799fiJL9ZNKkSQTAOXPmyN0nKCiI9vb2VFZW5pw5c5iamlpg8kkkEm7bto2WlpYUiUTs378/IyMjs2wfHR3NsmXL0tLSkhEREQUml7+/P7W0tPj169d8j+Xt7U1PT898jyOVSqmqqsrAwMAM5yIjI7l582a2a9eOenp6BEADAwN26NCBW7du5efPn/M9/+906tSJenp66T6H4cOHU0lJibdv3+a7qHh2WntDtsjnpARYBhxhp7U3+C4qPptZi5CXImWgiD9GbGws3dzcqKGhwYsXL8rV58ePHz/fJKyt+e3bt1zP+f79e86ZM4cVKlQgAOrp6bFXr168cOGCQt5+cqJVq1asXbt2tm1GjhxJAwMDJiUlFbg8vzJ16lQC4MyZM3PdNyEhgX5+fhQIBHR1deWLFy8ULt/58+dZqVIlAmDz5s357Nkzufq9e/eOZmZmrFSpEuPi4hQuF0l+/PiRqqqqnDx5cr7HmjBhAo2MjLJVGOXh27dvBMBdu3ZRIpEwKCiIEydOZJUqVSgQCAiAlSpV4vjx43n9+vUCVeKOHj1KANy4caPs2LFjxzK1QL34GMuJB4PpNvccrX5TAqwCjtBt7jlOPBjMkMjYApP3v0iRMlDEHyUuLo5169almpoaz5w5I1ef0NBQ6urqslmzZvl6YAYHB3PMmDG0srIiAJYoUYL+/v588OBBnsfMiVKlSnHIkCFZnk9JSaGpqSkHDhxYYDJkxsyZMwmAU6dOzdc4ly9fpo2NDdXU1Lh48WKFKFiPHz9mkyZNCIBVq1blpUuXcj3GvXv3qKmpySZNmjAlJSXfMmXGoEGDqKenx9jY/C1S//zzDwHww4cP+Rrn6tWrBMAGDRrQyMiIAKijo8M2bdpw48aN/PjxY77Gl5eYmBiWKFGCnp6est9reHg4jYyM2KhRo2y/I3GJKQwOi+bdt18ZHBbNuMSC+eyKKFIGivgLSEhIYMOGDamqqsrjx4/L1Sdt7z035uyskEqlvHLlCvv160cDAwMCYNmyZTlz5ky+efMm3+OnERsbS4FAwA0bNmTZ5vjx4wTAW7duKWzenJg7dy4BcOLEiQoZLy4ujgMGDCAA1qlTh69fv87TOBEREezduzeFQiFLlizJnTt35kv5O378OEUiEfv165fvt+7MePfuHZWUlPL9nXzz5g0B8PDhw7nqJ5VKeffuXU6bNo2urq6yt397e3uOHj2aly9fLjBFKDv69etHDQ0N2fdAIpHQw8ODJiYm2W7xFFG4FCkDRfwVJCYm0tvbm8rKyjx06JBcfQICAigSieTeYpCHpKQkHj58mO3ataOamhoBsGbNmlyxYgW/fPmSr7HT3tSy83do164dHRwcCmSxyoyFCxcSAMeOHavwOc+cOUMLCwtqampy9erVco8fFxfHSZMmUUNDg3p6elywYIHCfDvWrFlDAJw9e7ZCxvudXr16sVixYkxISMjzGFKplHp6epwyZUqObaOjo7lnzx5269aNJiYmBEAtLS22bNmS3bt3J4AMjpWFycWLFwmAS5YskR2bNWsWBQKB3JbAIgqHImWgiL+GpKQktmrVimKxmHv37s2xfUpKCmvXrk0TE5MCcQ6LjY3l5s2b2aBBA4pEIiopKdHb25s7d+7M0wN2+fLlFIvFWS5s0dHRVFVVLbCF6ncWL15MABw1alSBKR8xMTHs0aMHAbBhw4bZmr5TUlK4evVqmpiYUFlZmSNGjFCIQ97vjBs3jgC4c+dOhY/98uVLCoVCLl68OF/j1K1bly1atMhwXCqV8uHDh5w1axbd3d0pFosJgA4ODhwxYgTPnTsn8zWZPXs2dXR08iVHfkhISKCtrS1r1Kgh2wq4ceMGxWKxwiIvilAcRcpAEX8VKSkpbN++PUUiEbdt25Zj+4iICJqamtLd3b1ATaAfP37k4sWLWa1aNQKgpqYmfX19eeLECbnn7d27N8uVK5fl+dWrV1MoFDIsLExRYmfJsmXLCIAjRowoFCvEkSNHaGpqSl1dXW7evDndnFKplEePHqWjoyMBsEOHDnneWpAHqVTKTp06UVlZOU/+BznRqVMnmpub58sB1M/Pj1ZWViR/KqX//PMPe/fuTXNzcwKguro6vb29uWLFiiy3soYOHUp7e/s8y5Bf/P39qaKiwqdPn5L8qexaWVnRxcWFycnJf0yuIjKnSBko4q8jNTWVXbp0oUAgSOd9nBUXL16kSCQqtLeNkJAQTp48mXZ2dgRAY2NjDh48mEFBQdkurNWqVWOnTp2yPF+jRg02aNCgIEROx6pVqwiAQ4cOLbTtCPJnPH7Hjh0JgM2aNePHjx95584d1q1blwBYu3btQvOVSEpKYp06dainpydbrBTF48ePKRAIuGbNmjz1l0qlnDNnDgHQzc2NSkpKBEA7OzsOHTqUJ0+e5I8fP3Icp02bNqxbt26eZMgvt27dolAo5IwZM0j+vKa2bdtSW1uboaGhf0SmIrKnSBko4q9EIpGwV69eFAgEXL16dY7t0x6eBw8eLATpfiKVSnnr1i0OHTpUtl9ra2vLiRMnZgitS01NpZqaGufNm5fpWCEhIQTA7du3F6jM69atIwAOHDiwUBWBX9m3bx/19fWprKxMACxTpgwPHz5c6PJ8+/aNDg4OtLKyUrhnfatWrWhjYyO31Sg+Pp5Hjhxh//79ZdEtadETixcvZkhISK5lqFWrFjt27JjrfvklOTmZ5cuXp5OTk8wCkPa9K4itmSIUQ5EyUMRfi0QikXmlL126NNu2UqmUzZs3p66uLl+9elVIEv4fqampPH36NLt27UotLS0CYJUqVRgYGMiIiAg+e/aMAHj69OlM+48fP57a2tr5cjzLiY0bN1IgEBSYN708fPv2TWY+VlFRIQD6+Pjk2zkzr7x9+5ampqasUqWKQnMQ3L17lwC4devWLNuEhIRw0aJFbNiwoexelCxZkgMGDOChQ4eopqbG+fPn51kGGxsbjhgxIs/988q0adMoEol4584dkuSTJ0+orq7OHj16FLosRchPkTJQxF+NVCrl8OHDCSDHB+O3b99oY2PDihUrymVGLSgSEhK4e/duNmvWjEpKShQKhSxfvjwBZKqoSCQSWlpasmfPngUm05YtWygQCNirV69CSa70O0lJSQwMDKSBgQHV1dU5YcIExsTEcNu2bdTT06OxsXGhWnV+5e7du9TQ0KC3t7dCE+94eXnRwcFBdr9//PjBkydPcsiQIbS1tSUAKikp0cPDgwsWLOCzZ8/SKWk5bStlh1Qqpbq6eo4ppRXN48ePqaysLNuy+/HjBytUqEB7e/sCS/hUhGIoUgaK+OuRSqUcPXo0Acj2ILPi3r17VFFRYe/evQtJuuyJioriqlWrWKJECQKgqqoq27Rpw4MHD8oczM6fP08AvHz5coHIsH37dgqFQnbv3r3QFQGpVMrdu3fTxsaGQqGQPXv2zOAgGRYWRi8vLwJgly5d8pRZMr8cO3aMIpGIAwYMUJjV5Nq1awTAXr16sUmTJlRXV5clt+rTpw8PHDjA79+/Z9m/b9++dHR0zNPcac/iHTt25FX8XJOamsrq1avTzs5OpowPGjSIKioqvH//fqHJUUTeKFIGivhXIJVKOXnyZFlynOwe2GvXriUAbtq0qRAlzB4vLy/WqVOHs2bNklkJ9PX12adPHzZq1IjW1tYFYrrftWsXhUIhu3TpUuiKwNWrV1m9enUCoJeXFx89epRlW6lUynXr1lFLS4vm5v+vvTuPi6rq/wD+uTMDDAwiiywKgiKiIppmaoiGCO5JiZAkST5mT1qaW26Z6eNeuVtqZqiPoeaOmSuJlmum5oqRuKCCbC7syMx8fn/4ML+QbYbNhfN+vXipd+6594yOc7/33O/5Hifu27evGnv6WEFiZUl5HfrIy8vjL7/8wrFjx9LDw0P37N/Hx4dffPEFL1y4oPe/87fffku5XF6uR0cxMTEEUKk1OMqyePHiQkFtQWGwf9YYEJ5dIhgQnisFZXMnTpxY4peqVqvloEGDaGpqyvPnz1dzD4tXr149Tpo0SffnCxcucOLEiboRg9q1a3PChAmV2t8tW7ZQLpczNDS0SuvOPyk2NpaBgYEEwNatW/OXX37Ru+3Nmzfp7+9PAPzggw8qXNrXUAUjUJs2bdK7za1bt7hy5Ur27duX5ubmBEAHBwcOHjyYU6dOJQDu3r3b4L78/vvvBMCTJ08a3PbgwYMEUCVrRBTn+vXrNDMz40cffUSSvH37Nm1sbBgQEPDU8lMEw4hgQHjuLFiwgAA4evToEr9osrKy2LJlSzZu3Pipfx5TUlJKzKRes2aNbm69tbU1AbBFixacO3dumcscl2b79u1UKBQMCQmpthK0ycnJHD58OBUKBZ2dnblu3bpyjUZotVouW7aMZmZmbNiwIQ8dOlQFvS2eRqPhgAEDaGJiUuJjm/z8fP7666+cOHGibpRHJpPR29ubs2bN4pkzZ3SfS61WSy8vL3p5eRl8UczJyaFcLueKFSsMfh8REREEUOpjiMqi1Wrp7+9PZ2dnpqenU61W08fHh46Ojk8tMVQwnAgGhOfS119/TQD86KOPSrzgxMbG0sLCgkFBQU/17iQqKooAil1lz8/Pjz4+PiQfDzFHRkayf//+VCqVunnm3377LdPS0vQ+386dO2lkZMTg4OBqCQSys7M5e/ZsWlhY0MLCgnPnzq2UWRFXr15lp06dCIAjR46strK6ubm59PHxobW1te7fLDExkatXr2ZwcDBr165NALS1tWVYWBg3bNhQ6r/Prl27CIAHDx40uC+enp784IMPDG731VdfsVatWga3K4/w8HAC0K0rMmPGDEqSxOjo6Go5v1A5RDAgPLdWrlxJSZI4ZMiQEgOCrVu3EkCxa7pXl3nz5tHU1LTIUH18fDwlSWJ4eHiRNunp6Vy7di27detGmUxGIyMjvvHGG9y0aVOpF9qff/6ZxsbGDAwMrPIqbxqNhmvWrKGTkxMVCgU//vhjpqSkVOo51Go158+fTxMTE7q7u/P48eOVevySpKSksEGDBrS0tNTd/UuSxHbt2nHatGn8/fff9R710Gq1bNWqFf38/Azux8CBA9muXTuD240ZM4bu7u4GtzNUQkICLS0tGRYWRpI8cuQI5XI5p0yZUuXnFiqXCAaE59qaNWsok8kYFhZW4nPxMWPGUKFQ8OjRo9Xcu8cGDhzI9u3bF9k+a9YsmpmZlflcPDExkYsWLWLbtm11C9G8++673L9/f6H3vHfvXpqYmPCNN96oUClcfRw4cICtWrUiAAYFBZWrKI4hYmJi2K5dO8pkMk6YMKHSFi76p5SUFP7www+FHtlIkkQbGxuuWrWKycnJ5T72li1bCMDgYGbBggVUKpUGj/CEhISwc+fOBrUxlFarZd++fWlnZ8fU1FTeu3ePzs7O9Pb2fiqrIwoVI4IB4bm3YcMGyuVyhoSEFHs3/OjRI3p7e9PR0bFCX+jl1aJFiyJTHbVaLd3d3Q2eRx4bG8tp06bp5qk7ODhw1KhR/Prrr2liYsLXX3+9SgOB8+fPs0ePHgTADh068NixY1V2rifl5+dz1qxZNDIyoqenp66oTXlpNBqeOnWK//nPf9i+fXvdkr8vv/wyP/vsMx49epQnT56kmZkZ33jjjQolYWo0GjZr1oyvv/66Qe0Kpp1evHjRoHY+Pj58++23DWpjqM2bNxMAN2/eTK1Wy379+tHS0rJSl/0Wqo8IBoQXwpYtW6hQKBgYGFjsxfD27du0s7Ojv79/tWbW5+bmUqFQcNmyZYW2Hz9+vNSKhGXRarX8/fffOXLkSFpZWREAVSoVp0yZUiV36bdv3+bgwYMpk8no5ubGLVu2PLU8jHPnzrFVq1ZUKBScOnWqQY9D7t27x40bNzIsLIx2dnYEoMsrCQ8PZ0JCQpE2u3btokwm44gRIyr0ntetW1fmEtZPun//PgFw3bp1Bp3L3d2dY8aMMbSLektLS6OdnR379u1LrVbLFStWEIBeq40KzyYRDAgvjJ07d9LY2Jh9+vQpdhg5KiqKMpmMn3/+ebX1qaAs7ZOPKIYOHUonJ6cKByaHDh2iqakpX375ZYaGhuqmtrVv356LFy+ucM399PR0fvbZZzQ1NaWNjQ2XLFlS5Y8g9JGXl8cpU6ZQLpezdevWJU7J1Gq1PHv2LGfNmsWOHTtSJpPpZmxMmDCBhw8f1iuYKLjYVaSiX35+Pl1dXRkUFGRQu4YNGxp8YTc3N69QvYSyvPvuu7S0tGRCQgIvXrxIpVJZrkRH4dkhggHhhbJnzx4qlUp279692ES7mTNnUpIkXeZzVVu9ejUBFMoLyMnJoaWlZaG6A+Xx22+/UaVS0c/PT/des7KyuHHjRgYEBNDIyIhyuZzdu3fnf//7X4Pm7Ofn53PZsmW0s7OjUqnkxIkT+eDBgwr1tyqcOnWKzZo1o7GxMefMmcP8/Hw+fPiQW7du5Xvvvcd69erpRk3efPNNrly5kvHx8eU614QJEyhJEjdv3lzu/hYkvV6+fFnvNoGBgfT19dV7//T0dALQawnw8tizZw8BMDw8nNnZ2WzevDmbN29epetqCFVPBAPCCycqKoqmpqbs0qVLkXroGo2GvXr1orW1dYXm8etr1KhRdHNzK7Rt06ZNJU411NexY8dobm7Ozp07lzjlLjU1lStWrNBNzzM1NWVISAh/+umnEu+GtVotd+zYwSZNmlCSJIaFhZX74lldsrOz+a9//UuXXKlQKHSrIY4ZM4ZRUVGVknCo0WgYEhJCExOTciej5ubm0snJiQMHDtS7zYwZM2hpaan3I4q//vqr3FMZy5Kenk5nZ2f6+/tTq9Vy2LBhVCqVpVaXFJ4PIhgQXkiHDx+mubk5O3XqVOSOOC0tjS4uLmzXrl2VD3l37tyZ/fr1K7Std+/exc4u0NeJEydYq1YtdurUSe/FX27cuME5c+bQ09OTAGhjY8Nhw4bxt99+002R+/333/naa68RAP39/Q16tl3dMjIyGBkZyQ8++IDOzs4EQBMTE5qZmVGhUPCzzz6rkvLLubm5fO2112hjY1Pu6n6LFy+mXC7Xe3XNgjoF169f12v/Q4cOVTjYLMnw4cNpZmbGa9eu6abtLl++vNLPI1Q/EQwIL6xjx47RwsKCr776apHFb06dOkVjY2MOHz68ys6v1WppZWXFGTNm6LbdvXuXcrm8SEKhvk6dOsXatWvT29u73KV6z507x/Hjx+tKITs6OrJZs2YEQE9PT+7Zs+eZKyGr1Wp55coVLly4kF27dqWxsTEB0M3NjR9//DH37t3LnJwcZmZmcsSIEbqCTVWxnHVaWhqbNm3KRo0alWt2SlZWFu3s7PReTOvOnTsEwG3btum1/4YNG6rke/i3336jJElctGgRb968SUtLSwYGBj5znxWhfEQwILzQTp06RSsrK7Zp06ZIlbhly5ZV6cpuN2/eJADu3LlTt23+/Pk0NjY2qKJggdOnT9PS0pJeXl6V8n8sJSWFb731FmUymW5a3UsvvcQvv/zymXg0kJ2dzd27d3P48OF0dXXV3f13796dixcvLvXO/ODBg3RxcaFKpeLy5csr/YJ17do12tnZsX379uWqjDh37lwaGRnx1q1bZe6r1WppZ2endyGf+fPnU6VSVep7zsnJYZMmTejl5cXc3Fx27NiR9evXL9fnWHg2iWBAeOGdPXuWderU4UsvvVToTk6r1TI0NJQqlcqghC59Faza9s8La8uWLYs8NtDH2bNnaWVlxXbt2lU4kS83N5fz5s2jlZUVzc3NOX36dKalpXHHjh0MDg6mUqmkJEn08fHhypUree/evQqdzxBxcXFcunQpe/bsqSvJ7OLiwmHDhvGnn37S+7EI+fj59vvvv08A7NatW6UHOKdOnaKZmRn79u1r8KyQhw8f0srKiiNHjtRr/+7du+tdo+CTTz4pkqdSUZMmTaKxsTEvXbrEzz//nDKZrMqW3BaeDhEMCDXChQsXaG9vz+bNmzMxMVG3PSMjgx4eHmzWrFmlL+oyffp0WllZ6e7Qzp49W2SkQB/nz5+njY0N27RpU+RxhyE0Gg3Xr1/PBg0aUC6Xc+jQocVOPXz48CFXr15Nf39/ymQyGhsb88033+TmzZt169RXltzcXO7fv5+jRo2iu7s7AdDIyIhdunThvHnzePny5Qrf4e7Zs4eOjo60sLDg6tWrK/WOeefOnZTJZBw1apTBbadNm0ZTU1MmJSWVue/EiRPp6Oio13FDQ0PZqVMng/tTkjNnzlAul3PGjBk8dOgQZTIZp0+fXmnHF54NIhgQaoyYmBjWrVuXTZo04e3bt3XbL1++TJVKxQEDBlTqhaJfv36FSsKOGjWKtra2BhXJuXjxIm1tbdm6desKDckeOnRIV844ICCAMTExerVLSEjgggUL+Morr+gK9PzrX/9iVFRUuWsk3Lx5k8uXL2dAQABVKpUub+H999/n9u3bq2TZ4nv37nHgwIEEwD59+hQKCCvqm2++IQAuXLjQoHZpaWk0NzfnxIkTy9z3xx9/JAC9chR8fX3Zv39/g/pSkkePHrFVq1Zs2bIlExMT6ejoSB8fn2ot3CVUDxEMCDXK33//zfr167NRo0aFphYWJF2VN7GvOG5ubro7xkePHtHW1tagO8jLly/Tzs6OLVu2LPdSsDExMQwICCAAtm3btkLLAV+5coWff/45GzVqRACsW7cuR48ezT/++KPUIOrRo0eMjo7muHHj2Lx5cwKgXC7na6+9xjlz5vDcuXPVloS2Y8cO2tnZ0drautglpctr3LhxlCSJW7duNajdhAkTaG5uXmagFxsbSwDct29fmcds2rRpuUYqijN79mzKZDKeOnWKAQEBtLa21ivPQXj+iGBAqHGuX7/Ohg0b0sXFpVC2+fDhw2lsbMzff/+9wucoKPyyevVqkv+fP3D27Fm92l+5coUODg709PQsV8b63bt3OXToUMrlcjZo0IAbNmyotKl2Wq2WJ06c4IgRI3QlfZs0acLp06fz6tWrJB9nwK9atYqBgYGsVasWAdDe3p6DBg3ipk2bKvS4o6JSUlIYHBxMAAwODq6U9So0Gg3feustKpVKg9ZruHv3LpVKJadNm1bm8WvVqsW5c+eWeUwLCwt++eWXevehJDExMTQxMeH48eN1S4ZHRkZW+LjCs0kEA0KNFB8fz8aNG9PJyUmXlZ6Xl8f27dvT2dm53HfiBY4ePVro4t+vXz+2bNlSr7axsbGsW7cuPTw89Hqe/E+ZmZmcPn06zc3NaWVlxfnz51fJCn8F8vPzuWfPHg4YMICmpqYEQDMzM92Kf15eXpwxYwZPnz5dJfP+K2Ljxo20tramnZ0dt2/fXuHj5eTksGPHjqxTp45B60N8/PHHtLKyKvPxSMeOHcsc/s/KyirXWgZP0mg09Pb2ZuPGjXnixAmamJhU6TRc4ekTwYBQYyUkJLBp06Z0cHDQzSa4efMmbWxs2LNnzwpdvL755hsqFArm5uYyLS2NxsbGnD9/fpntrl69SkdHRzZt2tSgdQXUajVXrVrFevXq0djYmGPGjKnyaV9JSUlcu3Yt+/fvT0tLS10FQEdHR8rlcsrlcvbs2ZM//PBDpSdnVpbExET26dOHAPjOO+9UeOZEamoq3d3d6ebmxpSUFL3a3Lp1i0ZGRvziiy9K3W/EiBF0d3cvdZ+rV68SAKOiovTuc3GWLl1KANy7dy+bNm3Kli1bVnryqPBsEcGAUKPdvXuXnp6etLW11S12s2fPHkqSxJkzZ5b7uP/+9791IwHffPMN5XJ5mRf3a9eusX79+nR3dy929bziaLVa7t69W1dZMCQkhNeuXSt3v0ujVqt54sQJfv7557qEwoJchKlTp/LEiRO6xLKUlBQuW7aM3t7eutGCt99+m7t27TIogbI6aLVarlmzhhYWFqxXr16F162Ii4ujra0tvby89K7X//7779POzq7U/cPDwylJUqmB1a+//koAFZoqe+PGDapUKg4bNoxDhgyhmZlZlUy9FZ4tIhgQaryUlBS2atWK1tbWPH36NEnq5lKX9w6rXbt2uvrz7dq1Y+/evUvd/8aNG3RxcWGjRo0KzXQozZkzZ+jn56ertlcZuQ5PSk1NZUREBENDQ2ljY0MAtLS0ZP/+/bl27Vq9Ri+uX7/OWbNm0cPDgwBYp04dfvjhhzx69OgzVb0uPj6eXbt2JQAOGTKkQt9jJ0+epKmpKfv166fXCFNcXBzlcjmXLFlS4j4FU1OPHDlS4j4Fsw7Km5Oh1WrZvXt3Ojk5MTw8nAC4atWqch1LeL6IYEAQ+HjqWdu2bWlpacmTJ09SrVaza9eutLW11fviXECtVtPU1JTz5s1jTEwMAXDTpk0l7h8fH8+GDRvS1dVVr8I48fHxDAsLoyRJbNq0KSMjIyvtoqrRaPjHH39w+vTp9PLy0i3526pVK3766ac8cuQI8/Pzy3XsguWEx40bR0dHRwJgw4YNOXny5GfmzlOr1XLFihVUqVR0cXGp0GI/kZGRlMlkei8//M4779DJyanE9TLy8vJoZGTEpUuXlniMhQsXUqlUlvvzsHbtWgLg999/TwsLC/bv3/+ZCtiEqiOCAUH4n4cPH7JDhw6sVasWjxw5wuTkZDo5OdHb29ugoe0rV67onttOnDiRlpaWJT5vvX37Nhs1asQGDRqUuYrigwcPOHHiRCqVStrZ2XH58uXlvjD/0/3797lp0yYOGjSI9vb2umf//fr14/fff887d+5U+BxP0mg0jI6O5pAhQ3T5Bq1ateJXX31lcPBVFeLi4ujj40MAHDFihEGVD/+p4Nn74sWLy9z30qVLlCSJ3333XYn7tG7dmoMHDy7x9fHjx9PV1bVcfU1MTKSVlRUHDBjAV199lQ0aNHgml60WqoYIBgThHzIyMujj40OVSsXo6GgeO3aMCoVC77s78nGWOgDevXuXjo6OHDp0aLH7JSQksHHjxnR2di51Rbq8vDwuWbKEderUoampKadMmVKhwjxarZbnzp3jnDlz2KlTJ8rlct0iRePGjWN0dHSVr+b4T7m5udy2bRuDgoJoYmJCSZLo6+vLVatWPdUpiBqNhosWLaJSqaSbm1u5ly0eO3YsJUnSa8ZCUFAQXV1dSwzyBg8ezNatW5fYfuDAgfT29i5XP4OCgmhra8uRI0dSLpfz+PHj5TqO8HwSwYAgPCErK4v+/v40NTXlgQMHuGjRIgIotaBMZm4+L955wDM373HoxJl0dHHl/v37CaDYL9XExEQ2bdqUTk5Ourn5T9JqtdyyZQvd3NwoSRIHDx5c7rvm9PR0btu2jUOGDNEN0atUKgYEBHDFihVljkpUlwcPHjA8PJx+fn6UJIkmJiYMDAzk1q1bn1o2+5UrV/jqq69SkiSOGzfO4H5oNBoGBQVRqVTyxIkTpe575syZUqcGLl26lEZGRiUGa35+fgwODjaofyR1yxFPnjyZkiRx9uzZBh9DeL6JYEAQipGTk8OePXvSxMSEu3btYnBwMC0sLAqtlBd7N51TIy/ytS8PssHEXXT558+En9hk7Aa6Bk3gX4mF/z8kJSXRw8OD9erVK3HlvWPHjrFDhw4EwB49euhmOuhLq9Xy0qVLnDdvHrt06UIjIyNdcaDRo0fzwIEDVVp/oDLcuXOH8+fP58svv0wArF27Nt977z3+8ssv1V4OV61Wc+7cuTQ2NqaHhwdPnTplUPucnBx6e3vT1ta2xOCvQO/evdmsWbNiEw+PHDlSavEqDw8Pfvzxxwb17d69e3RwcGCPHj3o4OBAPz+/Z64mhFD19L1+yyAINYhSqcT27dvRo0cP9O3bF3379oWDgwOCgoIQeycNA78/ia6LfsW6kzdx8142+OQBJAm5RrWgdeuIbot/w8DvT+LWvWykpKTAz88P9+7dw8GDB9G4ceNCza5evYqgoCB06NAB2dnZOHDgAPbs2YMWLVqU2eesrCzs2rULH374IRo2bIjmzZvjs88+g1KpxMKFCxEXF4crV65gwYIF8Pf3h4mJSeX9hVWBevXqYcyYMTh9+jRiYmIwYsQIREdHw8/PDy4uLvjkk09w9uxZkEX+9iudXC7HhAkTcPr0aZiYmODVV1/F559/jkePHunVXqlUIjIyEpaWlujZsydSU1NL3Hfy5MmIiYnB9u3bi7z20ksvQZIknD17tti2iYmJqFu3rn5v6n/Gjh2LnJwcPHr0CGq1GuvWrYNMJr7yheJJ1ON/XHp6OmrXro2HDx/CwsKiOvolCFUqPz8foaGh2L59O+bOnYtZG6Nh6fdvSHIFNFr9L0JymQSFDJCd2Yr7p3/GoUOH0LRpU93rqampmDFjBpYtWwYHBwfMmjUL77zzTplfyn///Td2796N3bt34/Dhw8jLy4Orqyt69eqFXr16oXPnzjA1NS33+3/WkMTJkycRERGBH3/8ESkpKWjWrBlCQ0MxYMAANGzYsMr7kJ+fj9mzZ2PmzJnw9PTE2rVr0bJlS73axsXFwcvLC+7u7oiKioJSqSx2Pz8/P9y/fx+nT5+GJEmFXmvSpAm6d++OJUuWFNqek5MDMzMzrF27FmFhYXr158CBA+jWrRv69++PH3/8ET///DN69eqlV1vhxaLv9VsEA0KNpVarMWjQIOy6roblawNBssgXtF5IQJIw8CVLzAjxBvD4C3zJkiWYPXs2AGDSpEkYOXJkiRfwnJwcHD58GLt378aePXtw9epVGBsbw8fHRxcANG7cuHz9e87k5+cjKioKERER2LFjB7KystChQweEhoYiODgYtra2VXr+M2fOICwsDLGxsZg6dSomTJgAhUJRZruTJ0/C19cXr7/+OjZu3FhswBcdHY0uXboUe3F+++23cfv2bfz222+Ftl+/fh2urq7Yv38/unbtWmY/MjMz0aJFC9ja2uLs2bMYMWIEFixYUGY74cUkggFB0MP6kzfw6Y5LRban7lqIrIu/lNjO8aM1UNSqU2T7nL6eUP/1KyZPnozExEQMGzYMU6ZMKfYCdv36dezZswe7d+/GwYMHkZOTA2dnZ93F39fXF+bm5hV7g8+5rKwsREZGIiIiAvv27YMkSejWrRtCQ0PxxhtvQKVSVcl58/LyMG3aNHz55Zdo06YN1q5di2bNmpXZbseOHQgMDMTYsWPx1VdfFXmdJLy9HweMR48eLRTcffnll5gxYwYePnxYKJA4evQoOnbsiIsXL6J58+Zl9mHkyJH47rvvYG9vDysrKxw/fvyZf3QkVB0RDAhCGW7dy4b/wsPIU2uLvJZ3Jwb59+8+sZW4t+8bKGrbo96QZcUfVJOPOyuHIsDPG3Pnzi2UO5CXl4cjR47ohv+vXLkChUKBTp06oWfPnujVqxc8PDxqxN1/eaSkpGDz5s2IiIjAsWPHoFKp8OabbyI0NBRdu3bV6+7dUCdOnMC7776LmzdvYtasWRg1ahTkcnmpbZYsWYKRI0di6dKlGD58eJHXd+/ejd69e+PgwYPw9fXVbS8Y2o+NjS30udmyZQuCg4ORlpYGa2vrUs997NgxdOzYEW3atEFMTAzOnDkDd3d3A9+18CIRwYAglGHg9ydx7Fqa3jkCubcuISliAixfC0PtDm8Vv5NWA087E+wa2x0AcOvWLd3d/y+//ILMzEzUq1dPd/H39/cX/6fK4fr161i/fj0iIiIQExMDW1tb9O/fH6GhoWjfvn2lBlTZ2dmYPHkyFi1ahI4dO2LNmjVo1KhRqW3GjBmDxYsXY/v27QgICCj0Gkm0adMGVlZW+OWX/x99Sk1Nha2tLX788Ue89db/f76WLl2KcePGIScnp9T3lZubi9atWyM/Px9xcXEG5RgILy59r98itVSokf5OysBvV1MNShbMunwYgASVh0/JO8nkuJiqxrCJ/0HLli3h7OyMYcOGIS0tDZ9++in+/PNP3L59G6tWrUJgYKAIBMqpYcOGmDx5Mi5duqR7xr9t2zZ4eXnBzc0NU6ZMwZUrVyrlXGZmZli4cCEOHTqEO3fuoGXLlli2bBm02qIjSgXmzZuHvn37IiQkBKdOnSr0miRJmDx5Mg4ePIjjx4/rttepUwdOTk5FZhQkJCSgbt26ZQY4s2bNQlxcHBISEhAaGoqBAweW490KNZUYGRBqpGk7L2HdyZt6BwPUqHH76zAY2TjB4Z0vS99Xq4EmJhr+1vfRq1cvdO3aFVZWVpXRbaEUGo0Ghw8fRkREBLZu3YqHDx/i5ZdfRmhoKEJCQlCvXr0KnyMzMxPjxo3DihUr4Ofnh/DwcDg7Oxe7b05ODvz8/BAXF4fjx4/D1dVV95pWq4WnpydcXV2xa9cu3faAgAA8evQIe/fu1W0bNGgQYmNjcezYsRL7de7cObzyyiuws7ODqakpzpw5I76rBQBiZEAQShX9V7JBowI5189Am5MOlUfnMveVZHI06hSANWvW4K233hKBQDWRy+Xo0qULvv/+e9y9exdbt25FgwYNMGnSJDg5OcHf3x/h4eF4+PBhuc9hbm6O5cuXY9++ffjrr7/g6emJ8PDwYmsimJqaIjIyEhYWFujVqxfS0tJ0r8lkMnz66af4+eefC40EtG7dukiNhYKRgZKo1WoMHjwYlpaWSEpKwoYNG0QgIBhMBANCjZOZp0b8vWyD2mRdPgzIFDBr1lGv/ePvZSMrT12e7gmVQKlUIjAwEFu3bkVSUhK+++47aLVaDBkyBPb29ggKCsL27duRl5dXruN369YNFy5cQL9+/fDee+/h9ddfR0JCQpH9bG1tsWfPHqSlpeHNN99Ebm6u7rWQkBC4urrqpp8Cj4OB5ORkJCYm6rYlJiaWOqqxYMEC/Pnnn0hNTcXcuXPRtm3bcr0noWYTwYBQ49xMyypaWbAU2kc5yPn7BEwbtobcVL87LgK4kZZVrv4JlcvS0hLvvfceDh48iPj4eMycORNxcXEIDAyEg4MD3n//fRw6dKjUHICSjrt69Wrs3LkTp0+fhqenJ9avX19klMDNzQ07d+7EH3/8gUGDBunOo1AoMGnSJGzduhUxMTEAHgcDAAqNFpRWfbCgFoJSqUT37t0xZswYg96DIBQQwYBQ4zwqZiphabJjT4D5eVA172xQu3ETJmH48OGYMWMGVq5cicjISBw/fhzXrl1DVpYIFJ4GJycnXbnjS5cu4aOPPkJUVBR8fX3h4uKC8ePH49y5cwaVQu7Tpw8uXbqE7t27IzQ0FEFBQUhOTi60j5eXFyIiIrBp0yZMmjRJtz0sLAyOjo6YM2cOAMDZ2RlWVla6YCAvLw9paWnFjgwUjHRIkgRzc3OsXbtWlBsWyq3yJ+YKwjPOWGHYF2bW5UOQjE1h2ri9Qe0yHz7Ar+cuIikpCampqUXuPFUqFezt7WFnZwd7e/tCP09uq127tqg/UMk8PDwwc+ZMzJgxA8ePH0dERATCw8Px1VdfwcPDQ1cKuUGDBmUey8bGBhs2bEBgYCCGDRsGT09PLF++HP369dPtExgYiAULFmD06NFwcXHBhx9+CGNjY4wfPx6jR4/G1KlT0ahRI7Ru3Rp//HkBlxIeIv52AozsGsLK1qHIOb/99ltdtcIdO3bA3t6+0v5uhJpHzCYQapysPDU8p+3T61GBJvshbn8dBlWz11Cnz1i9zyEBuDitO1Qmj+NtjUaDtLQ0JCUl6X6Sk5ML/fmf2/Lz8wsdz9jYuEiAUNKfbWxsyiyMIxQvPz8f+/fvR0REBCIjI5GdnQ1vb29dKeQ6dYpWnXxSUlIShg4dih07dmDAgAFYunRpoWJBo0aNwtKlS7Fjxw706dMHOTk5aNCgAfwC34F7z8HYfOwysmAKPBH8uVibwbeJHULbO8Mk7z6aNWuGnJwcjBs3Dl988UWl/10ILwZRdEgQSuHzVTRu6pFEmH76J9w/8C3s3voPTF3b6H18FxszHP7Et+wdi0ESDx48KDNgKPjJzi78PmQyGWxtbfUadbCzs4ORkVG5+vmiy8zMxI4dO7B+/Xrs378fkiShR48eCA0NRUBAAMzMzEpsSxI//PADRowYATMzM3z33Xfo3bs3gMeBYXBwMPbt24fDhw/D3tUDby/8CbfV5pBLgKaUb2S5TIJGS5g9vIm4H2eiuYsDTpw4AWNj48p++8ILQgQDglAKfesMJP53LNQPkuA0fC0kmX5323KZhIHtXTAtoOw68pUhMzOzSIBQUhDx4MGDIu2trKzKfExRsK20C+CLLDk5GZs2bUJERAROnDgBlUqFvn37IjQ0FP7+/iWWQr5z5w6GDBmCvXv3YvDgwViwYAFq166N7OxsdOnSBfFGTjD3GQyNlqUGAU+iRg1Qg7GdXfBxb/2DVKHmEcGAIJTi76QMdF30a5UdP2r0a3Czq1Vlxy+vvLy8QoFCaUFEampqkUQ6c3PzMgOGgt9bWFi8kHkOcXFxulLIf/31F+zs7HSlkNu1a1fkPZPEqlWrMGbMGFhZWSE8PBz+/v74Ytc5LD96W7fqpeEIQMIn3dwx3LdxmXsLNZMIBgShDIauTaAPuUxCB1cbrHvPsGTDZ5FarUZqaqpejyqSk5OhVheuq2BiYlJqbsM/f6ytrZ+7THiSOHPmDNavX48NGzYgMTERbm5uGDBgAEJDQ4ssEHTjxg0MHjwY0dHReH3kbFwwbVlpffkisAX6ty2+EqJQs4lgQBDKUNqqheVlopAharQP6lvXrOF0krh//36ZAUPB73Nycgq1l8vlujyHskYdbG1tn7k8B41Gg0OHDulKIaenp+OVV15BaGgo+vfvr6sToNVqMXvxt/guwR6S3LjEEYG8u1fx8Mh65N2+DKrzobC0h3mrHrB4JaDY/Wvq504omwgGBEEPG0/FY+K2C5V2PHGHVjaSyMzM1DtBMj09vcgxbGxs9B51UCqV1fr+cnJy8PPPPyMiIgK7d++GWq1Gly5dEBoaisDAQHy0OQbH4lJLzBHIuX4GyVumw9i+EVRNO0EyVkL94C5ALax8Bxfb5kUakRIqlwgGBEFPX0f/jXn7Yyt8nHHdmuAjX7dK6JHwT7m5uWUmSBb8OS0trUieQ61atfRKjrS3t0etWrUqNc/h/v372Lp1KyIiInD48GGY1W2EOmGLStxfm5eNOyv/DRPHZrDtOwmSZNijk2c1V0V4ekQwIAgG2HgqHlN3XoJaS4NyCOQyCQqZhOkBzcWIwDNArVYjJSVFr1GH5ORkaDSaQu2VSmWZdRwKfqysrAzKc7h16xY+/D4aF3IsgRJmpmSc3Y17+5ah3pDlMKpTH9pHuZCMjPUKCqp7FovwfND3+i0qEAoCgJC2zvBuVAefbr+A366m6uZzl6Tg9Q6uNpjdt4V4VvuMUCgUqFu3bqmr/BXQarVF8hyeDBjOnz+v+/2TixopFIpCeQ6ljTrY2tqifv36SFfVB/JKrm+Re+NPSCZmUGemIXnbTKjv3YFkpITK0xfWfu9DUpRcT0CjJaJjkzENIhgQDCdGBgThCX8nZSDiZDyiY5MRn5ZdqFKhBMDZxgy+7nZ451VnMSRbQ5BERkaGXtUjk5KSkJGRUai9JEmwcXCEKmx5qdMIE74fDvWDxysWmrfsBqVzC+TGX0DG6Z9g1uw12L4xvtR+Pln5UhDEyIAglFNj+1qYFtAc09AcWXlq3EjLwiO1FsYKGRrYqMQXbQ0kSRIsLCxgYWGBxo3LntOfk5NTJGC4nJCObTml5yMwPxfMz4N5656w7voBAMCsSQdQk4/MP/civ1MojKwdS26Px6tlNq9X26D3JwjiW00QSqEyUYgvVsFgpqamcHFxgYuLi27b2fj72Lb8WKntCh4DqJr5FNqu8uiMzD/3Iu/OlVKDAcDwVTkFARBLGAuCIFQLfVbLlJvbPP5VZVl4u+pxQKrNzayU8wjCk8SnRhAEoRo0sFGhrEmLxg6NAADqjLRC29UZ9wAAcrPSR6mk/51HEAwlggFBEIRqoDJRwLmMWSeqpp0AAJnn9xfannl+PyCTw8S5RantnW3MRE6LUC7iUyMIglBNfJvYlbpaprFDI6hadkXW+QNI0WqhdPZEbvwFZF85AguvYChq2ZR4bLlMgq+7XVV1XXjBiWBAEAShmoS2d8aa4zdK3cem+0dQWNgi83wUsmOPQ1HbFlZ+78Oi7RulttNoiXdeFYWvhPIRwYAgCEI1aWxfC53c6pS6WqYkV8Cy4wBYdhyg93EL1iYQdS+E8hI5A4IgCNVodt8WUMgqb/0DAFDIJMzuW3o+gSCURgQDgiAI1ai+tRn+U8nrB0wPaC5KYgsVIoIBQRCEahbS1hmfdHOvlGON69ZELJIlVJjIGRAEQXgKhvs2Rh1zE7FapvBMECMDgiAIT0lIW2dEjfZBB9f/VR4sI5eg4PUOrjaIGu0jAgGh0oiRAUEQhKeovrUZ1r3XXqyWKTxVYgljQRCEZ4xYLVOoLGIJY0EQhOeUWC1TqG4iZ0AQBEEQajgRDAiCIAhCDSeCAUEQBEGo4UQwIAiCIAg1nAgGBEEQBKGGE8GAIAiCINRwIhgQBEEQhBpOBAOCIAiCUMOJYEAQBEEQajgRDAiCIAhCDSeCAUEQBEGo4UQwIAiCIAg1nAgGBEEQBKGGE8GAIAiCINRwIhgQBEEQhBpOBAOCIAiCUMMp9NmJJAAgPT29SjsjCIIgCELlKbhuF1zHS6JXMJCRkQEAqF+/fgW7JQiCIAhCdcvIyEDt2rVLfF1iWeECAK1Wi4SEBNSqVQuSJFVqBwVBEARBqBokkZGRgXr16kEmKzkzQK9gQBAEQRCEF5dIIBQEQRCEGk4EA4IgCIJQw4lgQBAEQRBqOBEMCIIgCEINJ4IBQRAEQajhRDAgCIIgCDWcCAYEQRAEoYb7P1p3O/uPtXSlAAAAAElFTkSuQmCC" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot original hard graph\n", "hard_graph = construct_graph(hard_clauses)\n", "pos = nx.spring_layout(hard_graph)\n", "nx.draw_networkx(hard_graph, with_labels=True, pos=pos)\n", "ax = plt.gca()\n", "ax.set_facecolor(\"w\")" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T11:45:08.390560600Z", "start_time": "2023-07-03T11:45:08.210412300Z" } } }, { "cell_type": "markdown", "source": [ "We first use the brutal force method (BF) to obtain the true solution." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 5, "outputs": [], "source": [ "def b2s(bit):\n", " return 1 - 2 * int(bit)\n", "\n", "\n", "def energy(cfg, graph, n_cls, normalize=True):\n", " factor = 1 / n_cls / 4\n", " E = 0.25\n", " for a, b in graph.edges:\n", " E += cfg[a] * cfg[b] * graph[a][b][\"weight\"] * factor\n", " return E if normalize else E / factor\n", "\n", "\n", "def brutal_force(graph):\n", " num_nodes, n_cls = graph.number_of_nodes(), len(hard_clauses)\n", " min_cost, best_case = 1.0, []\n", " for i in range(2**num_nodes):\n", " case = f\"{bin(i)[2:]:0>{num_nodes}}\"\n", "\n", " cost = energy(list(map(b2s, case)), graph, n_cls)\n", "\n", " gap = min_cost - cost\n", " if gap > 1e-6:\n", " min_cost = cost\n", " best_case = [case]\n", " elif abs(gap) < 1e-6:\n", " best_case.append(case)\n", "\n", " return best_case, min_cost" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T11:45:08.390560600Z", "start_time": "2023-07-03T11:45:08.390046300Z" } } }, { "cell_type": "code", "execution_count": 6, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cost: 0.000\n", "bit string: ['000000111111', '111111000000']\n" ] }, { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# print BF results\n", "bf_best_cases, bf_best = brutal_force(hard_graph)\n", "print(f\"cost: {bf_best:.3f}\\nbit string: {bf_best_cases}\")\n", "\n", "# plot NetworkX graph\n", "colors = [\"r\" if bf_best_cases[0][i] == \"0\" else \"c\" for i in hard_graph.nodes]\n", "nx.draw_networkx(hard_graph, with_labels=True, node_color=colors, pos=pos)\n", "ax = plt.gca()\n", "ax.set_facecolor(\"w\")" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T11:45:08.708112400Z", "start_time": "2023-07-03T11:45:08.390560600Z" } } }, { "cell_type": "markdown", "source": [ "Then we start to execute the algorithm loop shown in the figure above. The algorithm starts from the classical method - SA." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 7, "outputs": [], "source": [ "def sim_annealing(graph, t_max: int, T: float):\n", " num_nodes, num_cls = graph.number_of_nodes(), len(hard_clauses)\n", " state = np.random.randint(0, 2, num_nodes)\n", " next_state = state.copy()\n", " E = energy(1 - 2 * state, graph, num_cls, normalize=False)\n", " t = 0\n", " while t < t_max:\n", " temper = (1 - t / t_max) * T\n", " flip_idx = np.random.randint(num_nodes)\n", " next_state[flip_idx] = 1 - next_state[flip_idx]\n", " next_E = energy(1 - 2 * next_state, graph, num_cls, normalize=False)\n", " if next_E <= E or np.exp(-(next_E - E) / temper) > np.random.rand():\n", " state[flip_idx] = 1 - state[flip_idx]\n", " E = next_E\n", " else:\n", " next_state[flip_idx] = 1 - next_state[flip_idx]\n", " t += 1\n", " return tuple(state), E" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T11:45:08.711814200Z", "start_time": "2023-07-03T11:45:08.709702400Z" } } }, { "cell_type": "code", "execution_count": 8, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of low-lying excited states: 23\n" ] } ], "source": [ "# obtain the low-lying excited states\n", "ll_excited, n_exp = set(), 100\n", "for _ in range(n_exp):\n", " sa_case, sa_cost = sim_annealing(hard_graph, 200, 1)\n", " if sa_cost > 1e-6:\n", " ll_excited.add(sa_case)\n", "print(f\"number of low-lying excited states: {len(ll_excited)}\")" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T11:45:12.123684300Z", "start_time": "2023-07-03T11:45:08.709702400Z" } } }, { "cell_type": "code", "execution_count": 9, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "number of clauses should be kept: 12\n", "number of clauses can be discarded: 60\n", "number of clauses after dropout: 42\n" ] } ], "source": [ "# obtain the clauses violated by low-lying excited states and the clauses can be discarded\n", "def get_clauses(ll_exc_st, clauses):\n", " kept, drop = [], []\n", " for cls in clauses:\n", " violated = False\n", " for state in ll_exc_st:\n", " if sum(state[i] for i in cls) in [0, 3]:\n", " kept.append(cls)\n", " violated = True\n", " break\n", " if not violated:\n", " drop.append(cls)\n", " return kept, drop\n", "\n", "\n", "kept_clauses, drop_clauses = get_clauses(ll_excited, hard_clauses)\n", "num_selected = int((1 - R) * len(drop_clauses))\n", "num_after_drop = len(kept_clauses) + num_selected\n", "driving_factor = 1 / num_after_drop / 4\n", "print(f\"number of clauses should be kept: {len(kept_clauses)}\")\n", "print(f\"number of clauses can be discarded: {len(drop_clauses)}\")\n", "print(f\"number of clauses after dropout: {num_after_drop}\")" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T11:45:12.128858800Z", "start_time": "2023-07-03T11:45:12.128083Z" } } }, { "cell_type": "markdown", "source": [ "There are two ways of quantum dropout. One isotropic or uniform, i.e., $\\hat H_{C_1} = \\hat H_{C_2} = \\cdots = \\hat H_{C_p}$. The other is random or different, i.e., $\\hat H_{C_i}\\neq\\hat H_{C_j}$ if $i\\neq j$." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "### Isotropic Quantum Dropout" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 10, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# get the graph after dropout\n", "iso_clauses = kept_clauses + random.sample(drop_clauses, num_selected)\n", "iso_graph = construct_graph(iso_clauses)\n", "nx.draw_networkx(iso_graph, with_labels=True, pos=pos)\n", "ax = plt.gca()\n", "ax.set_facecolor(\"w\")" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T11:45:12.461569500Z", "start_time": "2023-07-03T11:45:12.132507800Z" } } }, { "cell_type": "markdown", "source": [ "The PQC is similar to the regular QAOA, but the cost Hamiltonian is the original Hamiltonian but the driving Hamiltonian is the one after dropout." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 11, "outputs": [], "source": [ "def QAOAansatz_iso(params, g, each=1, return_circuit=False):\n", " n = g.number_of_nodes() # the number of nodes\n", "\n", " # PQC loop\n", " def pqc_loop(s_, params_):\n", " c_ = tc.Circuit(n, inputs=s_)\n", " for j in range(each):\n", " # driving layer\n", " for a, b in g.edges:\n", " c_.RZZ(a, b, theta=g[a][b][\"weight\"] * params_[2 * j] * driving_factor)\n", " # mixing layer\n", " for i in range(n):\n", " c_.RX(i, theta=params_[2 * j + 1])\n", " s_ = c_.state()\n", " return s_\n", "\n", " c0 = tc.Circuit(n)\n", " for i in range(n):\n", " c0.H(i)\n", " s0 = c0.state()\n", " s = K.scan(pqc_loop, K.reshape(params, [nlayers // each, 2 * each]), s0)\n", " c = tc.Circuit(n, inputs=s)\n", "\n", " # whether to return the circuit\n", " if return_circuit is True:\n", " return c\n", "\n", " # calculate the loss function\n", " loss = 0.25\n", " for a, b in hard_graph.edges:\n", " loss += c.expectation_ps(z=[a, b]) * hard_graph[a][b][\"weight\"] * cost_factor\n", "\n", " return K.real(loss)" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T11:45:12.464821600Z", "start_time": "2023-07-03T11:45:12.462095700Z" } } }, { "cell_type": "markdown", "source": [ "Here, several circuits with different initial parameters are optimized/trained at the same time." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 12, "outputs": [ { "data": { "text/plain": "
", "image/png": 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9kpIS6urqGD9+fJ9eZ+7cuVRWVibfL1q0iMmTJx/zvGXLlnHWWWeRkZFBRkYGM2fO5NNPP+3DliZIAOpnRqMmOQk6HgykuDVCCCEGO61WS35+Pjqd7oifq6pKNBrt9XXMZjO5ubndPm/VqlVcffXVvPvuu3z00UeUlJRw4YUXUlNT0+s2HY0EoH6mN2iTPUDxsKwELYQQovfi8ThLliyhoqICo9HIsGHDWLx4MXD4ENiqVatQFIU33niDKVOmYDQaWb169VHrOHCO0+lMXnPdunUoikJ1dTXQcQhs+fLl3HPPPaxfvx5FUVAUheXLlx+x7c899xy33HILkydPZvTo0fzud78jHo+zcuXKvvhRJR05Doo+YzIbUBQtAGoknOLWCCGEOBpVVQlE+7+33qwzoyhKl8svWLCAZcuW8cgjjzBjxgzq6urYtm3bUc+58847Wbp0KWVlZWRkZPSojs7MnTuXTZs2sWLFCt5++20AHA5Hl871+/1EIhEyMzN7dO2ukgDUz8xmIyjtXY0xCUBCCDGQBaIBpj8/vd+v+8k3PsGit3SprMfj4bHHHuOJJ55g3rx5AJSXlzNjxoyjnnfvvfcya9asXtXRGbPZjM1mQ6fTkZ+f361z77jjDgoLC5k5c2aPrt1VEoD6mdlsBiWUeBPv/ZirEEKIoW3r1q2EQiEuuOCCbp03derUXtdxvD3wwAO8+OKLrFq1CpPJ1KfXkgDUz8xWK4rSviFqPJbaxgghhDgqs87MJ9/4JCXX7XJZc9fLHspqtXa5Do0mMWVYVQ9u6B2JRHp03c4sXbqUBx54gLfffpuJEyce17qPRAJQP7PY0kBJ/EOjKuoxSgshhEglRVG6PBSVKiNHjsRsNrNy5UpuuOGGPqkjJycHgLq6OjIyMgCOua6QwWAgFuva/+gvWbKExYsX8+abb3bomepLEoD6mdXqAMXd/k4lFI1h1GlT2iYhhBAnLpPJxB133MHtt9+OwWDgzDPPpKmpic2bN3P99dcflzoqKiooKSlh0aJFLF68mMrKSh5++OGj1llaWkpVVRXr1q2juLiYtLQ0jEbjYeUefPBBFi5cyPPPP09paSn19fUA2Gw2bDZb938gXSSPwfczkymDePtPXdWoeIMyD0gIIUTv3HXXXfzwhz9k4cKFjBkzhrlz59LY2Hjc6tDr9bzwwgts27aNiRMn8uCDD3Lfffcdtb45c+Zw0UUXcd5555GTk8MLL7xwxHK/+c1vCIfDfO1rX6OgoCD5Wrp0abfa312KeuiAngDA7XbjcDhwuVzY7fbjWneLay/Lb38PnC+BCnN+/SKl2X2XcIUQQnRNMBikqqqKESNG9PkEXNFzR/s9defvt/QA9TOzKZOoLp54o4DLK6tBCyGEEP1NAlA/M+rNhHUHh71cbm8KWyOEEEIMTRKA+plWoyWsD0L7jvCeNmdK2yOEEEIMRRKAUiCiCyX3A/M1t6S4NUIIIcTQIwEoBeK6UHJH+ECrBCAhhBCiv0kASoH4IT1AYZcztY0RQgghhiAJQKmgDaMoicWgIh5XihsjhBBCDD0SgFJA0YWTPUAxryfFrRFCCCGGHglAKaDRRZJzgOIBX4pbI4QQQgw9EoBSQKuPJ3uA1KAshCiEEKLvVFdXoyjKMTcv7a3ly5eTnp7ep9c4niQApYBWHzsYgMLBFLdGCCHEYFZSUkJdXR3jx4/v0+vMnTuXysrK5PtFixYxefLkY573yiuvMHXqVNLT07FarUyePJk//vGPfdjSBNkNPgV0BjU5CZpoKLWNEUIIMahptVry8/M7/VxVVWKxGDpd7yKB2WzGbDZ3+7zMzEx++tOfMnr0aAwGA//85z+57rrryM3NZfbs2b1q09FID1AKGAwke4CUWCS1jRFCCHHCi8fjLFmyhIqKCoxGI8OGDWPx4sXA4UNgq1atQlEU3njjDaZMmYLRaGT16tVHrePAOU6nM3nNdevWoSgK1dXVQMchsOXLl3PPPfewfv16FEVBURSWL19+xLafe+65XHHFFYwZM4by8nK+//3vM3HiRFavXt0XP6ok6QFKAYNJk5wETVwCkBBCDFSqqqIG+n+upmI2oyhKl8svWLCAZcuW8cgjjzBjxgzq6urYtm3bUc+58847Wbp0KWVlZWRkZPSojs7MnTuXTZs2sWLFCt5++20AHA7HMc9TVZV33nmH7du38+CDD/bo2l0lASgFjCYd8QMBSI2ntjFCCCE6pQYCbD9lSr9fd9TaNSgWS5fKejweHnvsMZ544gnmzZsHQHl5OTNmzDjqeffeey+zZs3qVR2dMZvN2Gw2dDrdUYffDnC5XBQVFREKhdBqtfz6179Otq2vSABKAaPZSPDAHCAlTiQWR6+V0UghhBDdt3XrVkKhEBdccEG3zps6dWqv6zhe0tLSWLduHV6vl5UrVzJ//nzKyso499xz++yaEoBSwGIy4W+ffqUq4AtFSbcYUtwqIYQQX6SYzYxauyYl1+2qnkw8BrBarV2uQ6Np/5ulqsljkcjxm8Kh0WioqKgAYPLkyWzdupX777+/TwOQdDukgMXoIKZNfK8q4AlGU9sgIYQQR6QoChqLpd9f3Zn/M3LkSMxmMytXruzxfR6rjpycHADq6uqSx461rpDBYCAWi/WoPfF4nFCob5+Slh6gFDAbHUS1cbSAqgG3PwiZXRvrFUIIIQ5lMpm44447uP322zEYDJx55pk0NTWxefNmrr/++uNSR0VFBSUlJSxatIjFixdTWVnJww8/fNQ6S0tLqaqqYt26dRQXF5OWlobRaDys3P3338/UqVMpLy8nFArx+uuv88c//pHf/OY3Pfp5dJUEoBSwmDMI6z0c6HB0ub1AZiqbJIQQ4gR21113odPpWLhwIbW1tRQUFHDTTTcdtzr0ej0vvPACN998MxMnTmTatGncd999XHnllZ3WN2fOHF555RXOO+88nE4nzzzzDNdee+1h5Xw+H7fccgv79+/HbDYzevRo/vSnPzF37txutb+7FPXQAT0BgNvtxuFw4HK5sNvtx73+z/a8y2u/2kH6vteBKONu/QUXnTXxuF9HCCFE1wWDQaqqqhgxYgQmkynVzRGdONrvqTt/v2UOUApYzFmEdMHkYoi+5qYUt0gIIYQYWiQApYDFaCesDSUXQwy0tKS4RUIIIcTQIgEoBax6K+FDeoDCLmdqGySEEEIMMRKAUsCitxDRHgxAUQlAQgghRL+SAJQCJq2JsDaYHAKL+jwpbpEQQggxtEgASgGtRouqCSV7gOJ+X4pbJIQQQgwtEoBSRNGFUEgEIDXkT3FrhBBCiKFlQASgJ598ktLSUkwmE9OnT+fTTz/ttOyyZcs466yzyMjIICMjg5kzZx5WXlVVFi5cSEFBAWazmZkzZ7Jjx46+vo1u0egiyR4gNRRMcWuEEEKIoSXlAeill15i/vz53H333axdu5ZJkyYxe/ZsGhsbj1h+1apVXH311bz77rt89NFHlJSUcOGFF1JTU5Mss2TJEh5//HGeeuopPvnkE6xWK7NnzyYYHDhBQ6uLohzYET7at/udCCGEEKKjlAegX/7yl9x4441cd911jB07lqeeegqLxcLTTz99xPLPPfcct9xyC5MnT2b06NH87ne/Ix6PJzdwU1WVRx99lJ/97Gd85StfYeLEifzhD3+gtraWV199tR/v7Oj0+jgo+sSbaDi1jRFCCDFoVVdXoyjKMTcv7a3ly5eTnp7ep9c4nlIagMLhMGvWrGHmzJnJYxqNhpkzZ/LRRx91qQ6/308kEiEzM7GXVlVVFfX19R3qdDgcTJ8+vdM6Q6EQbre7w6uv6Q0qtPcAKarsBi+EEKJvlJSUUFdXx/jx4/v0OnPnzqWysjL5ftGiRUyePLlbdbz44osoisLll19+fBt3BCkNQM3NzcRiMfLy8jocz8vLo76+vkt13HHHHRQWFiYDz4HzulPn/fffj8PhSL5KSkq6eyvdZjAqycfgUWN9fj0hhBBDk1arJT8/H53uyPufq6pKNNr7/xE3m83k5ub2+Pzq6mp+9KMfcdZZZ/W6LV2R8iGw3njggQd48cUX+dvf/tarjesWLFiAy+VKvvbt23ccW3lkJpMuOQkaVOJx2ZNWCCFEz8TjcZYsWUJFRQVGo5Fhw4axePFi4PAhsFWrVqEoCm+88QZTpkzBaDSyevXqo9Zx4Byn05m85rp161AUherqaqDjENjy5cu55557WL9+PYqioCgKy5cv77T9sViMb37zm9xzzz2UlZUd7x/PER05DvaT7OxstFotDQ0NHY43NDSQn59/1HOXLl3KAw88wNtvv83EiQd3Uj9wXkNDAwUFBR3q7Kwrzmg0YjQae3gXPWMyG5I9QKoCvnCUNJO+X9sghBDi6FRVJRqO9/t1dQYNiqJ0ufyCBQtYtmwZjzzyCDNmzKCuro5t27Yd9Zw777yTpUuXUlZWRkZGRo/q6MzcuXPZtGkTK1as4O233wYS01E6c++995Kbm8v111/Pf/7znx5ds7tSGoAMBgNTpkxh5cqVyfG+AxOab7311k7PW7JkCYsXL+bNN99k6tSpHT4bMWIE+fn5rFy5Mhl43G43n3zyCTfffHNf3Uq3WQxWYppEr09cA75QTAKQEEIMMNFwnP/7/nv9ft1vP3YOeqO2S2U9Hg+PPfYYTzzxBPPmzQOgvLycGTNmHPW8e++9l1mzZvWqjs6YzWZsNhs6ne6YHRqrV6/m97//fZ9P0v6ilAYggPnz5zNv3jymTp3KqaeeyqOPPorP5+O6664D4JprrqGoqIj7778fgAcffJCFCxfy/PPPU1pampzXY7PZsNlsKIrCD37wA+677z5GjhzJiBEjuOuuuygsLOyXSVVdZTHY8WhVNCQCkCcYJt/R82E8IYQQQ9PWrVsJhUJccMEF3Trv0A6EntbRWx6Ph//3//4fy5YtIzs7u1+vnfIANHfuXJqamli4cCH19fVMnjyZFStWJCcx7927F43m4FSl3/zmN4TDYb72ta91qOfuu+9m0aJFANx+++34fD6+/e1v43Q6mTFjBitWrOjVPKHjzWK006KLYwJURcHd5oE8e6qbJYQQ4hA6g4ZvP3ZOSq7bVWazuUfXsFqtXa7jwN9hVT04XzUSifTouofatWsX1dXVfOlLX0oei8cTQ446nY7t27dTXl7e6+scScoDEMCtt97a6ZDXqlWrOrw/MNnqaBRF4d577+Xee+89Dq3rGxZTOiF9lAORzFPfAKOLUtomIYQQHSmK0uWhqFQZOXIkZrOZlStXcsMNN/RJHTk5OQDU1dWRkZEBcMwhK4PBQCx29KecR48ezcaNGzsc+9nPfpYckuvLp7IHRAAaiiymTCL6RsAAhPG1NKe6SUIIIU5AJpOJO+64g9tvvx2DwcCZZ55JU1MTmzdv5vrrrz8udVRUVFBSUsKiRYtYvHgxlZWVPPzww0ets7S0lKqqKtatW0dxcTFpaWmHPXBkMpkOW5/owJNkfb1ukQSgFLFasghr9yZWg1bDBFpaUt0kIYQQJ6i77roLnU7HwoULqa2tpaCggJtuuum41aHX63nhhRe4+eabmThxItOmTeO+++7jyiuv7LS+OXPm8Morr3DeeefhdDp55plnuPbaa3tzm8eVoh46oCeAxFNjDocDl8uF3d4383I+q/+MZ598ixE7t6LGWymYcgnfuP2WPrmWEEKIYwsGg1RVVTFixIgBNWdUdHS031N3/n6f0AshnshsBhthbSC5GGLE0/fbbwghhBAiQQJQitj0NsK6YHIxxKhXApAQQgjRXyQApYhN37EHKOb3pbhFQgghxNAhAShFrAYrId3BAKSG/ClukRBCCDF0SABKEb1GD9rQwf3AQsEUt0gIIYQYOiQApZBGHzm4I3w0lNrGCCGEEEOIBKAU0hviyR4gYuHUNkYIIYQYQiQApZDOoJJYCRqIRVPaFiGEEGIokQCUQmaT5mAPEPGUtkUIIYQYSiQApZDJrAclsS+KLMcthBCiL1RXV6MoyjE3L+2t5cuXJ/fxOhFIAEohq8VGXJPYZTiugVhcYpAQQojjq6SkhLq6uj7fXHTu3LlUVlYm3y9atIjJkycf87zly5ejKEqHV39sRSKboaaQzZROTJsIPTGNgjcUwWE2HOMsIYQQouu0Wi35+fmdfq6qKrFYDJ2ud5HAbDZjNpt7dK7dbmf79u3J94qi9KotXSE9QClkNWUS0ie+j2oVvE5PahskhBCiA1VViQSD/f7q7j7l8XicJUuWUFFRgdFoZNiwYSxevBg4fAhs1apVKIrCG2+8wZQpUzAajaxevfqodRw4x+l0Jq+5bt06FEWhuroa6DgEtnz5cu655x7Wr1+f7NVZvnx5p+1XFIX8/PzkKy8vr1v33xPSA5RCNnMmLfoYRkBVwFXfSFFBVqqbJYQQol00FOLxeV/r9+t+79m/oO/GMNCCBQtYtmwZjzzyCDNmzKCuro5t27Yd9Zw777yTpUuXUlZWRkZGRo/q6MzcuXPZtGkTK1as4O233wbA4XB0Wt7r9TJ8+HDi8TinnHIKv/jFLxg3blyPrt1VEoBSyGawE9Y3Awqg4qlvAMakuFVCCCFOJB6Ph8cee4wnnniCefPmAVBeXs6MGTOOet69997LrFmzelVHZ8xmMzabDZ1Od9ThN4BRo0bx9NNPM3HiRFwuF0uXLuWMM85g8+bNFBcX9+j6XSEBKIUcRgch3f7Ek2BqEE9jY6qbJIQQ4hA6o5HvPfuXlFy3q7Zu3UooFOKCCy7o1jWmTp3a6zqOh9NPP53TTz89+f6MM85gzJgx/Pa3v+XnP/95n11XAlAKpRvTCWuDKIoJVQ3ib2lOdZOEEEIcQlGUbg1FpUJPJx5brdYu16HRJKYMHzo3KRKJ9Oi6x6LX6zn55JPZuXNnn9R/gEyCTiGH0UFYF0iuBRRqbU1xi4QQQpxoRo4cidlsZuXKlX1WR05ODgB1dXXJY8daV8hgMBCLxbrdllgsxsaNGykoKOj2ud0hPUAp5DA4COn8iR4gIOx2pbpJQgghTjAmk4k77riD22+/HYPBwJlnnklTUxObN2/m+uuvPy51VFRUUFJSwqJFi1i8eDGVlZU8/PDDR62ztLSUqqoq1q1bR3FxMWlpaRiPMLR37733ctppp1FRUYHT6eShhx5iz5493HDDDT36eXSVBKAUSswB8oOS6HqM+OUxeCGEEN131113odPpWLhwIbW1tRQUFHDTTTcdtzr0ej0vvPACN998MxMnTmTatGncd999XHnllZ3WN2fOHF555RXOO+88nE4nzzzzDNdee+1h5dra2rjxxhupr68nIyODKVOm8OGHHzJ27Nhutb+7FLW7iw0MAW63G4fDgcvlwm6399l1VFXla7+8lrPWFRELbyBDl8G3nvtjn11PCCFE54LBIFVVVYwYMaJfViIWPXO031N3/n7LHKAUUhQFnTFycD+wUCDFLRJCCCGGBglAKaY3qSia9gAUC6e4NUIIIcTQIAEoxcwWLSiJLjw1Fk1xa4QQQoihQQJQilnSTCgHhsCQ6VhCCCFEf5AAlGL2tHRiGi2Q2BFeCCFEasmzQQPb8fr9SABKMYcll4gu8cuMahVioVCKWySEEEOTXq8HwO/3p7gl4mgO/H4O/L56StYBSrF0cya1hhBWIKpR8De1klbct6tfCiGEOJxWqyU9PZ3G9n0ZLRYLiiI98wOFqqr4/X4aGxtJT09Hq9X2qj4JQClmN9jZra/HCsQ14KytlwAkhBApcmDn8kbZnHrASk9PP+YO810hASjFHEYHAWN18n3b3n2UnHpy6hokhBBDmKIoFBQUkJub22ebfYqe0+v1ve75OUACUIplGDMI6v2AAQjjrq071ilCCCH6mFarPW5/aMXAJJOgUyzTlInf4EHRJPYD8zfWp7hFQgghxOAnASjFssxZ+PVuUCwABFtbUtwiIYQQYvCTAJRiDqODoMGDokkEoLDHmdoGCSGEEEOABKAU0ygadOYISnsPUMTvS3GLhBBCiMFPAtAAYE7TQnsPUDQcTHFrhBBCiMFPAtAAkOawoiiJSdBRNZ7i1gghhBCDnwSgASDLnk9En/hVRDUKalxCkBBCCNGXJAANALmWPAKGROgJ67TEXK4Ut0gIIYQY3CQADQD51nwCxigAYS3EmptT3CIhhBBicJMANADkW/PxmRK7wMc1KoE6WQ1aCCGE6EsSgAaAfGs+XpMfSCy73rRrd2obJIQQQgxyEoAGgHxLPj6jG0WTBkDLnj0pbpEQQggxuEkAGgAcRgdBkzMZgNz1MgQmhBBC9CUJQAOAoiiY0+LQHoD8ztYUt0gIIYQY3CQADRBpWZZkD5A/EEhxa4QQQojBTQLQAJGXVURcawQgKKtBCyGEEH1KAtAAkW8rwG9SAQhqNcS83hS3SAghhBi8JAANEPmWfDyWMAAhHURqa1PcIiGEEGLwkgA0QORb83FaEnN/4hoV366dKW6REEIIMXhJABoghqUNw2ltBSUxD6ht+/YUt0gIIYQYvCQADRCFtkI8lmYUTToArXtkNWghhBCir0gAGiC0Gi2WTM3BAFRfn9oGCSGEEIOYBKABpDi/EFWbWAuo1StrAQkhhBB9RQLQADIiYwQBU+JX4tVqiHk8KW6REEIIMThJABpARjhG4LJFAAjoFUKVlSlukRBCCDE4SQAaQEZnjqbF7gMgqonh3rAxxS0SQgghBicJQANImaOMVlszKDYAGjauS22DhBBCiEFKAtAAotPoiDk0aHS5ADRU70pxi4QQQojBSQLQAOPIKkTVZQLQGIyiRiIpbpEQQggx+EgAGmBGpo/GY038WtwmA6HdVSlukRBCCDH4SAAaYCbkjKcxPQhAQBfDvWFdahskhBBCDEIpD0BPPvkkpaWlmEwmpk+fzqefftpp2c2bNzNnzhxKS0tRFIVHH330sDKLFi1CUZQOr9GjR/fhHRxfk/NH0mhvRdHYQYF9H7yX6iYJIYQQg06PAtC9996L3+8/7HggEODee+/tcj0vvfQS8+fP5+6772bt2rVMmjSJ2bNn09jYeMTyfr+fsrIyHnjgAfLz8zutd9y4cdTV1SVfq1ev7nKbUq0o3UqtFjS6EgBqdslaQEIIIcTx1qMAdM899+D1eg877vf7ueeee7pczy9/+UtuvPFGrrvuOsaOHctTTz2FxWLh6aefPmL5adOm8dBDD3HVVVdhNBo7rVen05Gfn598ZWdnd7lNqWbQaQjoCogZcgCo1xiINjenuFVCCCHE4NKjAKSqKoqiHHZ8/fr1ZGZmdqmOcDjMmjVrmDlz5sHGaDTMnDmTjz76qCfNStqxYweFhYWUlZXxzW9+k7179x61fCgUwu12d3ilUoFxIo0Ziae/PEYF1wcfpLQ9QgghxGDTrQCUkZFBZmYmiqJw0kknkZmZmXw5HA5mzZrF17/+9S7V1dzcTCwWIy8vr8PxvLw86nuxE/r06dNZvnw5K1as4De/+Q1VVVWcddZZeI6yr9b999+Pw+FIvkpKSnp8/eOh1D6MveltKBoHKLBrxcspbY8QQggx2Oi6U/jRRx9FVVW+9a1vcc899+BwOJKfGQwGSktLOf300497I7vj4osvTn4/ceJEpk+fzvDhw/nzn//M9ddff8RzFixYwPz585Pv3W53SkNQcYaF9Xu0TNdXEAutYfe+OqZ10usmhBBCiO7rVgCaN28eACNGjODMM89Ep+vW6R1kZ2ej1WppaGjocLyhoeGoE5y7Kz09nZNOOomdO3d2WsZoNB51TlF/K8owUxcuJmLRoglBvdmMf9N6rBMmp7ppQgghxKDQozlAaWlpbN26Nfn+tdde4/LLL+cnP/kJ4XC4S3UYDAamTJnCypUrk8fi8TgrV648rr1IXq+XXbt2UVBQcNzq7GuFDjOx4DD25DhBsRLTQOUffpXqZgkhhBCDRo8C0He+8x0qKxOPZ+/evZu5c+disVh4+eWXuf3227tcz/z581m2bBnPPvssW7du5eabb8bn83HdddcBcM0117BgwYJk+XA4zLp161i3bh3hcJiamhrWrVvXoXfnRz/6Ee+99x7V1dV8+OGHXHHFFWi1Wq6++uqe3GpKFGWYAQ3VJhWtYRQA2yplRWghhBDieOnRGFZlZSWTJ08G4OWXX+acc87h+eef54MPPuCqq6464gKFRzJ37lyamppYuHAh9fX1TJ48mRUrViQnRu/duxeN5mBGq62t5eSTT06+X7p0KUuXLuWcc85h1apVAOzfv5+rr76alpYWcnJymDFjBh9//DE5OTk9udWUKM4wA7AtUMR5ZiC0ljqjBec7L5N+/pWpbZwQQggxCCiqqqrdPclut7NmzRpGjhzJrFmzuOyyy/j+97/P3r17GTVqFIFAoC/a2m/cbjcOhwOXy4Xdbk9JG6YtfpsmT4hv2KvJ3rQWNdbAFHOEc5e/mZL2CCGEEANdd/5+92gIbOrUqdx333388Y9/5L333uPSSy8FoKqq6rDH2kXPlGVbAbCPyUdrnADAFrdCbO+6FLZKCCGEGBx6FIAeffRR1q5dy6233spPf/pTKioqAPjLX/7CGWeccVwbOFSV5dgA0FvG4s/MAsVMQK9jw8M/SXHLhBBCiBNfj+YATZw4kY0bNx52/KGHHkKr1fa6UQLKcxI9QLubA8w4J4vGv55MNPgha/aFmbzrXZTy81LcQiGEEOLE1avd4NesWcOf/vQn/vSnP7F27VpMJhN6vf54tW1IK2sPQLuavHz14plE7MMBHS69iW1P/gxi0dQ2UAghhDiB9agHqLGxkblz5/Lee++Rnp4OgNPp5LzzzuPFF188oZ64GqjKshNDYNUtPvRaPYXnZtD42snEQv/l/T0WRn32NJrp305xK4UQQogTU496gG677Ta8Xi+bN2+mtbWV1tZWNm3ahNvt5nvf+97xbuOQVJxhxqDVEIzEqXEG+NqXZhG3jwbFhFdn5POnnwJ/a6qbKYQQQpyQehSAVqxYwa9//WvGjBmTPDZ27FiefPJJ3njjjePWuKFMp9VwUn6iF2hTjQuDQc+Er5aiM00H4MOWPMJvLU5lE4UQQogTVo8CUDweP+JcH71eTzwe73WjRMKEosRmsxtrXADMPO9U4vnFoLET1mp57+VVsO+/KWyhEEIIcWLqUQA6//zz+f73v09tbW3yWE1NDf/7v//LBRdccNwaN9SNK+wYgBRF4Us3zkBnPguADeECmp69FSIn9sKTQgghRH/rUQB64okncLvdlJaWUl5eTnl5OSNGjMDtdvOrX8mmncfLgR6gTTUuDizYXVFeQubZJWj0ZaDA3zfYUd+5L5XNFEIIIU44PXoKrKSkhLVr1/L222+zbds2AMaMGcPMmTOPa+OGulH5aeg0Cm3+CDXOAMUZFgC+8T8X88RndcSb9uJU4L9/eZVTK2aCrA0khBBCdEm3eoDeeecdxo4di9vtRlEUZs2axW233cZtt93GtGnTGDduHP/5z3/6qq1DjkmvZXRBGgBr9rQlj2t1Wi69fTY601QAVrvKcT9/C3gbU9JOIYQQ4kTTrQD06KOPcuONNx5xgzGHw8F3vvMdfvnLXx63xgk4vSwLgI92tXQ4XjFsGCVfHoOiLUBV4rywZRTqK98GmYQuhBBCHFO3AtD69eu56KKLOv38wgsvZM2aNb1ulDjo9PL2ALS75bDPvjpnDpb8YkCLNx5lxWo/fPh4P7dQCCGEOPF0KwA1NDQcdasLnU5HU1NTrxslDppWmolWo7CnxU+N8/Cnvb7xi//Foh0OwBaXhV3/eF4ejRdCCCGOoVsBqKioiE2bNnX6+YYNGygoKOh1o8RBaSY9E4sTT4P9p/LwcGk32Tn1BxejJxOI8vf9k2h97k4IOPu3oUIIIcQJpFsB6JJLLuGuu+4iGAwe9lkgEODuu+/msssuO26NEwnnj8oF4M3N9Uf8fMqpF1NcbgS0xKN1vLD9HJwv/RTaH50XQgghREeKqnb9r2RDQwOnnHIKWq2WW2+9lVGjRgGwbds2nnzySWKxGGvXriUvL6/PGtwf3G43DocDl8t1xAnf/W1no4eZv3wfvVZhzV2zsJsOH4aMBoP87auXsDfNAmhJT7+MK68yYj/vmv5vsBBCCJEC3fn73a0eoLy8PD788EPGjx/PggULuOKKK7jiiiv4yU9+wvjx41m9evUJH34GoorcNCpybURiKiu3NhyxjM5k4rQf/ZBMbwiI4fJ8wisv63FuWd+/jRVCCCFOAN1eCXr48OG8/vrrNDc388knn/Dxxx/T3NzM66+/zogRI/qijQK4dEJibtVf1uzvtEzJ+ZcyqjAHXSyOGqvH5avib7+uoqVaJqYLIYQQh+rRVhgAGRkZTJs2jVNPPZWMjIzj2SZxBFdOLUZR4IOdLVQ3+zotN+2+Rxhdn3hkPhr8CG8wyN8e/oyGand/NVUIIYQY8HocgET/Ks6wcM5JOQC88N+9nZbT5+Ux/stfJc/pBVRCgb8TDGt57eH/UrO9rdPzhBBCiKFEAtAJ5OpThwHw0n/34QtFOy2X/+3vML7VhyESRYm6iUX/QSSi8I9fraN6Y3N/NVcIIYQYsCQAnUBmjsmjNMuC0x/hhU877wXSpqdTdN11TNifmPsT8e7GqnmHWFTljd9spPLTIz9OL4QQQgwVEoBOIFqNws3nlgPwf+/vJhiJdVo283/+h4IoFLW6UVDY7/8vww3vEo+rvPXMFjau6nwytRBCCDHYSQA6wVxxcjGFDhONnhAvHq0XyG4n/etfZ2xNC7p4FHNAzzrlHSZYXgcV3n+xkv/+q4puLAMlhBBCDBoSgE4wBp2G755fAcBjK3fgCkQ6LZs57xr0Gg2nVDUCYK7PoMbyD6amvwbAp/+oYvXLO1DjEoKEEEIMLRKATkBzp5YwMtdGmz/Cr9/d2Wk5fUEB9tmzyfYGyDZpAdi5dwSZ5heYMWwlABve2c/KZ7cSi8X7pe1CCCHEQCAB6ASk02r4yaVjAHjmg+qjrguUPvfrAEzduJ9wmgZLSMfTrWMYG36CmafuQNEobP+knhW/3UQ03PmcIiGEEGIwkQB0gjr3pBzOPimHcCzOglc2djqXxzJtGoayMjR+P7PHnYGKSnZ9Go+rJYzaewcXX6Gg1Wuo3tDMP361nnCw88frhRBCiMFCAtAJSlEU7vvKeEx6DR/tbuHPn+3rtFxGey9Q+nufkHv2VAB81cW8bzAzYuMtfPk75RhMWmp3OPmnhCAhhBBDgASgE9iwLAvzZ50EwD3/2EJlg+eI5Rxf+QqKwUBo2zYuP/Ny4nYj1qCOl9pG0uyto7DyPr7yvydjtOio2+Xi9d9sJHqUR+yFEEKIE50EoBPct84cwZkVWfjDMX7yykaiR5jMrE1Px3bB+QD4X3+Dy2+5HYARe9O431CEuuFFcn3vctltk9AbtdRsb2PF/20iFpWJ0UIIIQYnCUAnOJ1WwwNfnYhJr+GzPW0s+0/VEcs5vvIVANz//BcV40+hePpUFBTMOwr5u8UG//gB+dlBLrt1Ijq9hj0bW3jr6c3E5ekwIYQQg5AEoEGgJNPCz78yHoBH3qpkW/3hO7/bzjwTbVYWsdZWvKtX86Ub/hfFYiDDa+BVdykNYRf843sUVqRz8U0T0OgUdq1t4p0/bJN1goQQQgw6EoAGia9NKWbmmFzCsTg/eHHdYdtkKHo9jssuBcD12t+x2B1ceO0tAIzZlc4vrPmolStg7R8YNi6L2TeMTz4i//5LlbJitBBCiEFFAtAgoSgK9391IllWA9vqPfzs1U2HhZYDw2Ded94h5nIx7uwLyB07Gm1cQb+jkFetVnjzJ9BaRdnkHGZdNxYU2PReDZ//u/NtN4QQQogTjQSgQSQnzcivrj4ZjQJ/WbOfF//b8dF445gxGEeORA2Hca94E0VR+PLNPwKdloJWEy+FhlMfC8Crt0A8zshpecy4ciQAH/1tl+wiL4QQYtCQADTInFGRzY9njwbg7tc2s2G/M/mZoig4Lk/0ArlefRUAR24+Z3ztGwBM2J7OvRl5qHs/hE9+A8Ck80uYNLMEgJXPbqVme1s/3YkQQgjRdyQADUI3nVPGrLF5hGNxbvrjGpo8oeRn9su+BBoNgc8/J1xdDcCpX5qDvbAAU1hLrCqP12xWWHkvNO8A4MyvVlB+Sg7xmMrrT22ktbbzrTeEEEKIE4EEoEFIURQe/vokyrKt1LqCfOePnxGKJiZF6/NysZ55JgDOv70KgFan45Kb5gNw0n4bv9cW0ahG4G83QSyKolGYed1YCsodhANR/vWbDQR9ne9CL4QQQgx0EoAGKbtJz+/mTcVu0rF2r7PDfmHpX70CSAyDqbFEMCoaNYbx588CYPKmDH6enYta8xl8+DgAOr2Wi2+aQFqWCXdTgDeXbZI1goQQQpywJAANYmU5Np785iloNQqvrK3ht+/vBsB2wQVoHQ6iDQ34PvwoWf7sb34LQ5qNdK+Bltos/mW1wKr7oWELAOY0A5fcPBGdUcv+bW188JedKbkvIYQQorckAA1yZ43MYeFlYwF4cMU2/rmhFo3BgP2yywBw/e2VZFmzLY2Z874DwKSdDn5lLaSZKLx6E8QSQ17ZxTZmXZuob8O7+9nyQW1/3o4QQghxXEgAGgKuOX0415w+HFWF+S+t56NdLTjah8E8b68k5nIly46ecS4l4yehi2sYtzmdxdl5qHXr4T+/TJYpOzmHU780AoD3XthOQ/XhK08LIYQQA5kEoCFAURTu/tI4LhqXTzgW59t//IzqzGKMo0ahhsO4/v6PDmVn3XALGp2OomYzu5wO3rRa4P0lULc+WW7qJaWMmJRNPKqy4rcbCXjCqbg1IYQQokckAA0RWo3Co1dNZlppBp5glOue+Qz1sssBaHvuOdT4wQnNGQVFnHbFXABO3ZLJkox8WonD326GaOKRekVRuODasaTnWfC2hfj37zcTlz3DhBBCnCAkAA0hJr2W310zjZG5NurdQb7TmAtWG+HqanyrV3coO+0rXyOjoAhzWEv5djv35+VD42Z478FkGaNZx0XfGY/OoGH/tjY++fvu/r4lIYQQokckAA0xDoueP90wneFZFnZ6VFaOmA5A6x/+2KGcTq9n1o3fBWDUXhtrAhZWWsyw+hHYvyZZLqvQxvn/bwwAa1fsYfe6pn66EyGEEKLnJAANQXl2E8/dMJ2idDN/LDiVuKLgW72a0I4dHcqVjJvIuHMuQEHh9E1Z3JdbiFMh8VRYJJAsN3JaHpPOb98uY/kWnA3+/rwdIYQQotskAA1RxRkWnrthOmp+IR8WjAdg/69+fVi5s//nWxhtNjI9BvKqzDyYVwDNlfDOfR3KnT6nnIIKB+FgjNef2kg4GO2X+xBCCCF6QgLQEFaabeX5G6ez4uRLAAj++032rd3UoYzF7uCc//kWAJN3OHhXNfCe2QQfPQl7Di6iqNVqmH3jeCwOA211Pt7947bkytNCCCHEQCMBaIiryE3j4QVXsmb4ZDSovPuTX1Dd3HGz0/HnzqJ4zHj0MQ3TN2dyb34xbg3w6s0QPljW6jBy0bcnoNEo7FzTyPqV+/r5boQQQoiukQAkKM22cs59dxJHYVr15/z053+issGT/FxRFGbe8F00Wh3DGi2Y6rU8lFcEbVXw9qIOdRWUOzjzypEAfPjKLmq2t/XnrQghhBBdIgFIAFAybRLmyxOrQ1/98Z/52pOr+XBXc/LzrOISpn15DgDTt2TyT52W1WYTfPp/sPu9DnVNOLeIUdPzUeMqb/5uE962YP/diBBCCNEFEoBE0rDbf4hiS6PcVctZ21cz7+lPeWXt/uTn07/6ddLzCrAGdZxSmc6iwhK8igKv3QrBg9thKIrCOd8cRVaxjYAnwor/20QsIjvHCyGEGDgkAIkkXWYmud//HgDf3vo6GZ4W5v95PY+v3IGqqugNRi64/mYAxuxJI9Km8nBBCbj2wr9/1qEuvUHLxd+ZgNGio6HKzX/+XNnv9yOEEEJ0RgKQ6CDjG1djPvlkDOEgS6v+gaLG+eVblXz/xXUEwjFKJ53C6DPPQVEVztiUyV8N8LHJCGufhR1vd6jLkWNm1rfGgQKb/1MrO8cLIYQYMCQAiQ4UrZbC+3+BYjKRs2Mj/2fZiU6j8Pf1tVzx6w/Y2+Ln3GtuwGixku0yMnpPGouKSvErCvz9Ngg4O9Q3fHwWp16W2Dn+/RcqadwjO8cLIYRIPQlA4jCG0lLy7rgdgOKXn+alMyxk2wxsq/fwpSdW81ljlLO+MQ+AqdszcHsiPFIwHDy1sGLBYfVNvbiU0onZxKJx3vjtRgJe2TleCCFEakkAEkeUftVV2C+5BKJR7Evu5u/fHMfkknRcgQjXPvMp7ynlFI+dgDamMGNDFi8Z4vzHYoH1z8O21zvUpWgUZl47BkeOGW9riH//TnaOF0IIkVoSgMQRKYpCwc/vxVBWRrSxkchdd/Dit6Zw9anDUFX45ds7WZF5DnqTmbw2E+N32/lZQSHNWg38/VZw13Woz2jRc/FNE5I7x3/4ys4U3ZkQQgghAUgchcZqpfhXj6Ox2fB/9hmtixbxiyvG89DXJmLWa3m3JsZ/smcAcPKODFSnyoKiUuL+FvjrDRDruB9YVpGN869J7By//u19MilaCCFEykgAEkdlLC+n6JFHQKvF9dprtDz1FFdOLeEft53J6Pw0/qsrZ5dlBJo4nLM+h0+J8kxmNuxZDe89eFh9I6fmMe3SUgDee347tTtkpWghhBD9TwKQOCbbWTPIvyuxzk/TY4/j+ue/qMhN49Xvnsn/nD6cd7PPxq8xke7Rc/KOdJ5w2NhgNMD7D8HuVYfVN+3SEVRMySUeU3njqU24mgL9fEdCCCGGOglAoksyrrqKzGuvBaBuwQJ8n3yKSa/lvssn8Oi1Z/Hf4pkAjN/tILvZwO3FpXgU4K83gqehQ12KRuH8eWPIHZ5G0BfhX7/eQCgQRQghhOgvKQ9ATz75JKWlpZhMJqZPn86nn37aadnNmzczZ84cSktLURSFRx99tNd1iq7L/fGPSJs1CzUSYf8ttxDcsgWA2ePyefru63CWnIICnL0uh5ZAmIWFpai+RvjLtyAW6VCX3qDl4psmYnUYaKvzyZNhQggh+lVKA9BLL73E/Pnzufvuu1m7di2TJk1i9uzZNDY2HrG83++nrKyMBx54gPz8/ONSp+g6RaulcOlDWKZNI+7zsffb3yG8dy8A2TYjd923AH1WAZawhhnrs3lbH+OZ9KzEfKAvbJUBYMswcsktE9HpNezd3MLqPye23BBCCCH6mqKm8C/O9OnTmTZtGk888QQA8XickpISbrvtNu68886jnltaWsoPfvADfvCDH/S6zlAoRCgUSr53u92UlJTgcrmw2+29uMPBKebxsOf/XUNo2zb0JSWUPv8cupwcAJr3VvOnn/wvsUiEz0a1sanMw9P19UwLhuDyp2Dy1YfVt3NNI28u2wTAGXMqOHnWsH69HyGEEIOD2+3G4XB06e93ynqAwuEwa9asYebMmQcbo9Ewc+ZMPvroo36t8/7778fhcCRfJSUlPbr+UKFNS2PYsv9DX1JCZN8+9n77O8Q8HgCyh5Vy/rXfAeCUygxynHpuySmiXqsl9vfvEd//+WH1VUzJ5Yw5FQB8+Ned7Pis4bAyQgghxPGUsgDU3NxMLBYjLy+vw/G8vDzq6+v7tc4FCxbgcrmSr3379vXo+kOJLieHYb//HdqsLEJbt7L/lu8Sb+9Fm3DBbE46/Sw0KsxcVwCxONfnDicWD9P69JVU76k+rL7JM0uYcF4xAG8v3yKPxwshhOhTKZ8EPRAYjUbsdnuHlzg2w7BhDFv2f2isVvz//S81P/hf1EgERVG48Nu3kVFYjDEAF6zLZ58hyk+zisiON9Hw9FUse3cb0Vg8WZeiKMy4ciRlk3OIR1Ve/81GWmt9Kbw7IYQQg1nKAlB2djZarZaGho7DHQ0NDZ1OcE5FneLoTGPHUvybX6MYjXjffZfaOxegxmIYLRa+8qOfYjCbyWnRc+rWTFbYtfzRnsl0ZSuOlbfz1V9/wLb6g7vDazQKs741lvwyOyF/lH88sQ6fK3SUqwshhBA9k7IAZDAYmDJlCitXrkwei8fjrFy5ktNPP33A1CmOzXrqqRQ//hjodLj/9S/q77kXVVXJKirh4u/+EIAxe9Io32/l4Sw7/zGb+bruPc6q/wOXPb6apW9uJxiJAaAzaLnklok4chMbp/7zifWE/JGjXV4IIYTotpQOgc2fP59ly5bx7LPPsnXrVm6++WZ8Ph/XXXcdANdccw0LFixIlg+Hw6xbt45169YRDoepqalh3bp17Ny5s8t1ir5hO+ccih5aAhoNzj//mcYlD6GqKhXTTuO0OYknv2ZsziHdqePHhUVU6vX8WP9nLmE1T7y7k0se+w8f724BwGwz8KXbJmFO09O8z8u/ntxAJBxL5e0JIYQYZFL6GDzAE088wUMPPUR9fT2TJ0/m8ccfZ/r06QCce+65lJaWsnz5cgCqq6sZMWLEYXWcc845rFq1qkt1dkV3HqMTHTn/+lfqfppY8yf7e7eRc8stqPE4rz70c3av/S8Ri4ZXTttLusXA89U7yFS1fEdZyFu+cgCuPrWEOy8eg8Osp2mfh1d/+TnhQJRhYzO55OaJaPUybU0IIcSRdefvd8oD0EAkAah3Wp99lob7HwAg7ycLyLzmGkJ+H8/99Ie01e7Hkw6vnbqX0XoTv6+qxGyw8/iwx3hkowGAnDQj93x5HBePz6d+t5u/P/Y50XCc8pNzuPCGcWi0EoKEEEIc7oRYB0gMXpnz5pF9260ANPzifpx//StGi5Wv3rkIs91BmhNmrS9gcyzA/GHlREMuvl97O69elUdZtpUmT4hbnlvLjX9YA9kGLrlpIhqdwq7Pm3j3ue2osmWGEEKIXpIAJPpE9i23kNk+76ruroW4V6wgPS+fK+5YiM5gJK9Bz4ytuXyghPlJSTkxXyOT372W168bwW3nV6DTKLy9tYFZv3yfd11uZn1rHIoC2z6sY/VfZMsMIYQQvSMBSPQJRVHIvf3HpF95JcTj1Pzox3jfe4+CilFc+r0fg6JQvsfM5N0ZrNBFuL+oFNW1D9Pzc/jhGZn863tncfKwdLyhKAtf28ztH+9g7OWJ+V8b3tnPBy/vlBAkhBCixyQAiT6jKAr5i+7GfumlEI2y/9bb8Lz7LhXTTuO8ed8GYPJ2O2Oq03jJEOfR/BLUlh3wpysYZY/wl5vO4J4vj8Nq0LJ2r5Mb399K5OR0ANa/s4/VL0tPkBBCiJ6RACT6lKLVUvjA/aTNmoUaibD/e9/H/dZbnHLxl5KPx0/fkkn5fitPmxUeyy1Ard8If/gy2kAr884o5a355zBzTC6RmMqjVXWszVWARE+QhCAhhBA9IQFI9DlFr6folw9jv+QSiESo+cH/4n7jDc648huccvGXAThrYw7D6yz83qrnsdzCRAhafil4GylMN7Psmqk8+Y1TyLYZWRn286Y5DCRC0HvPbycuE6OFEEJ0gwQg0S8UvZ7Ch5bg+MqXIRaj5oc/wv33v3PuNTcw7tyZoKqcty6X0loLv7fqeCyvCLVpayIEuetQFIVLJxawcv45XDWthA3GGCvMYVRUNv+nlree3kwsGj92Q4QQQggkAIl+pGi1FPziFzi+NgficWrvuJPWZ55h1rdvZexZ54Gqcu76XMpqrPzeouXB/BLizZXwzMXQsgsAh0XPA3Mm8sKNp+EtMvEPS4QYKjs/a+Rvj68jEpIVo4UQQhybBCDRrxStloJ77yVz3jUAND60lKbF93Phd25j/HkXgqpy9oZsRu6z8ZxZ4c6iYUTaquD3F0LNmmQ9p5dn8cb3z2LW7BG8ZosQRqWh0snv7/sYvyecqtsTQghxgpCVoI9AVoLuHy3Ll9P44BJQVWwXXEDhkgd598U/sP7f/wLgv2OdbC51cUZMxyP7qrDozHDlcjhpdod6ttW7uf+P65mwO4xZVfAZFS66eTwTR+ek4K6EEEKkimyF0UsSgPqPe8UKam+/AzUcxjh2DMWPP86H77zBmn+9BsC2ch8fn9TMBMXI43t2ka0qcNkvYcq1HeqJxVWWv1FJ87/2Y4sr+BUVwzm53PS1sRh12hTcmRBCiP4mW2GIE4b9oosY9szTaDMyCG3ZSvWVX2fqyAnMuHoeAKN3WblgYwGbYyGuLi1nq14D//g+vP5jiEWS9Wg1CtdfOoo5d07FZ9VgURVY1ch3fv4+Oxo8qbo9IYQQA5T0AB2B9AD1v0hNDftuu43Qlq2g1ZLz/e/TMKqMf//2ceKxGM4ceGPSPjRGDYvr65jlD8DwGfD1Z8Ga3aGucDDKnx5bS6DKC8B/TVGmf6WMG88uQycbqQohxKAlQ2C9JAEoNeLBIHULF+L++z8AsJx+GtFrr+H1Z35NOBAgYtPy+uR9tNkjfNcd4NstTWgcJXDVc1AwqUNdalxl5Z+3s31VLQB7dDG2jzCy6MoJnDwso9/vTQghRN+TANRLEoBSR1VVXH/9K/WLf4EaCKDNyMD4w//l7ff/jbOhDlWnYdWEBvYU+Dk7orC4dh/pih5mL4ZpN4CidKiv8tN63vrDVoiqeBSVv9vCnH9mMT+ePRqHWZ+iuxRCCNEXJAD1kgSg1Avt3k3ND39EaOtWAIyXXsIau4G9WzYCsLncy2cjW8jT6Fhau59JoTCMvgy+/CuwZHaoq7XWx7+e2oC7MUAMlVXmCPuydNz1pbF8aWIByhdCkxBCiBOTBKBekgA0MMTDYZoefYzW5cshHkfJzGTfReexYfM6AJxZKm9NrCFkVvlBq5P/53KisRfD134Pw07rUFc4GOXdP25j55pGAKp0Md6whDllVDY//8p4SrOt/Xx3QgghjjcJQL0kAWhgCaxfT93PfkZox04A2s44lTUxP+FggLhBw6rx9ezND3BqVOHndfspjKlw5vfhnDtBb0rWo6oqm96r4YO/7iQWiRNQVN40h9ljgdvOq+Db55TJI/NCCHECkwDUSxKABh41HKb5/5bR/NvfQiRCwGJi4+QxNPvcAOwaHuCjUU0YdRruaGrkcq8PJWc0fOXXUDylQ12tdT7eenozzfsST4ltNER51xShKM/KXZeO5bzRuf1+f0IIIXpPAlAvSQAauEK7d9Ow+Bf4PviAOLCzvJidNiMAYauGd8fVUZcd5JxQjLsb6siJA2d8D869E/TmZD2xaJxP/7Gbtf/eCyr4NSpvmyJs18c4Z1QOP7t0DCPz0lJzk0IIIXpEAlAvSQAa2FRVxfvuuzTc/wCRfftosZrYWF6Ev30uc+VwH5+OasGs0/C95iau9HjRZpTCJQ/DyJkd6qrd6WTVn7bRVu8HYLc+xr/NEfw6+J/pw/jBzJPIsBr6+Q6FEEL0hASgXpIAdGKIh0K0Ln+WlmXLCPt9bCvIYm+2A4CQReHDUY3syfczLqpyV2MD48JhGHs5zP4FOIqS9cQicdasqGbNij3EYyoxDbxviLDWGCXNoucHM0fyP6cNRy+LKAohxIAmAaiXJACdWKJtbbQs+x1tf/oTTQYtG4tzCBgTa/zU54T5cEwTHluUuW4vt7W1YdeYEpOkz/weGA4+/dVa62PVc9uo2+UCwGuAFfoQVfo45TlW7rhoNLPG5slj80IIMUBJAOolCUAnpkh9Pc1P/pqWv/2NXVlp7M5NJ67RgALry1xsLHdh1yp8t6WZr3q86NIK4YKFMHEuaBK9O2pcZetHdXz86i4CnsReY/uMKv82hGjVqkwZnsEdF43m1BGZR2uKEEKIFJAA1EsSgE5s4epqmv9vGbUrXmdLXjpN9kQvT9QQ54MxLVQV+qmIww+bGpkRCELB5MRK0qUzDtYRiPLZ69Wsf2cf8ZiKqsAWY4z/GCJ4NCrnj87lx7NHMaZA/vkQQoiBQgJQL0kAGhzC+2toXvZ/VL61gs156QQNiWGxsDHCexNaqMkNcVowwm2tLUwMhaHsXDjvZ1AyLVmHs8HPB3/dSfWGZgBUBT43RPnIGCGghcsnF3Hb+RWU5dhScYtCCCEOIQGolyQADS6R+noali3j81VvsSvDRqx9MnPYEOCdya3UZ0c51x/k1rY2RoUjcNJFcN5POmywWrfLxSev7aKm0glAXAOf6iP81xglrIUvTyrk1vMrqMiVR+eFECJVJAD1kgSgwSna1kbts8v57N//otpmRFUUUFXiOh/vT3BRXRhlts/PLW1OyiJRGPNlOPtHySCkqir7t7Xx8au7aNzjASCmgbXtQcivhUsnFHDb+SMZlS9BSAgh+psEoF6SADS4xYNB9j33HB/986/UGNofbVdVjDEvn41y8flJUS70BfiWy8WYcATKL4Cz5sPwM0FRUFWVqvXNfPrPKlr2J1aTjiuwUR/lU2MUp1blonH53HZBBeMKHSm8UyGEGFokAPWSBKChQY3Hqf7Ln/n41T9TGwu3H1RxBLxUDnPzzuQIU2Ihrne6mBYMoRRPgxnzE0NkGg2qqrJ3cytrVlRTtzPx6LwK7NTHWGOIsk8X56yTsrnhrDLOHpktj88LIUQfkwDUSxKAhp59773Lh3/8Pfs9zuSxDJ+f5nQXb04JkWeN8i2nk/P9ATQ5Y+D0W2DClcntNWp3OFmzYg97N7ckz2/UxlljiLLVEKMiP43rzxrBVyYXyoarQgjRRyQA9ZIEoKGrbuN6Pvzdb6iu2wftPTZ2fwgtTj4c56d5RJz/8bq41OvHbEqHU66BaTdA+jAgsdHqhnf3s/3jOqLhOAB+RWWjIcoGQwx9uoGvTSlmzinFVOTKk2NCCHE8SQDqJQlAoq2ulk9+9xu2bfqcWPsxczhCvtNF5TAPn05UOEvn5iq3l4K4CqMugVO/DSPOBkUh6IuwZXUtG1ftx9sWSta7VxdjgyFGpT7GuBIHV04t4etTi6VXSAghjgMJQL0kAUgc4He7WPvyC6x7501C0cTK0LpojOI2DyGjh/cnRrEVBbnK72FKMISSMwZOvREmXQUGK/FYnOoNLWz5oJa9m1s48G9bUFHZrI+x0RglZtcz7/RSrp5eQm6aKYV3K4QQJzYJQL0kAUh8USQUZPM7b/HfV17E7XYlj2d5/OR43Gwu9bN7nMp5ejeXeH2kGexw8jfh5P+BvHEAeFqDbPuoji0f1OJtPdgrVKuNs9EQZZcxzqmjsvnqKcXMGpuHSS+9QkII0R0SgHpJApDoTDweo3r9Wj7/+9+o3rIhedwYiVLS4iZkdPPJOJX0Yj9fCXuZEAqjFJ6cCELjvwbmdOJxlf1bW9nyQS1V65qJxxP/CsZQ2a2Ls9UQo8GmMHtiAV+eXMj0EZnoZCd6IYQ4JglAvSQBSHSFq7GBDW+9wca3XicQ8AOgqCq5Lh+FbW6qCoNUnRRnfLaHS4I+7BojjPkSTP4mjDgHNBr87jDbP65n+yf1tNR4k3WHUanUx9hqiOFL13HxxAIunVDA1NJMtBp5nF4IIY5EAlAvSQAS3RGLRtjxyYd8/q9Xqd21I3ncEgozrNlNesDLupFxomVBzrJ5OTkcQnEMg8nfSLwyhgPQUuOl8r8N7Pi0AU9rMFmPT1HZrk9MnA44dJw/NpcLx+YzY2S2DJMJIcQhJAD1kgQg0VPNe6tZ99YbbFn1NpFwYp6PoqrkuP0UtXlQFD+bRqmkDfdzgcFLSTSaeHLs5P8Hoy8DgwVVVanf5UqEoc8aCPmiyfp9isqO9jDUZFY4e1QOF47L4+yTcsi2GVN120IIMSBIAOolCUCit8IBP1tXv8emd/9N/SG9QrpojEKnl6I2D21pIXaPilNU7OMCvDj0aTB+DkycCyXTQaMhFouzb0sruz9vYvf6pg5hyK+o7NTH2KmPsUcXZ0yxg7NPyubskTmcMjwDvcwbEkIMMRKAekkCkDieWvbvY8v7K9ny/jt421qTx63BMEVtHgravFQVxnCWRTgpz8sZ+NHbi2H8FYlAVDAZFIVYLE7tdic7P29k9+dNBL2RZF1hVPbo4+zUxdilj6E16zijPIuzT8rhnJNyKMm0pODOhRCif0kA6iUJQKIvxOMx9m3ayOb3V7Ljkw+Ihg/uP5blDVDU5iHX5WNvgUpgeISxeR7GGYMomWWJIDR+DuSOSdQVi1O708Xuz5uoWt/UYbFFFZUabZyd+jg79THatCojsq2cXp7FaWVZnDYik1y7rDckhBh8JAD1kgQg0dfCAT+Vn3zIlvdWsm/LxuRxbSxOvstHUZuHLG+A2lyIDA8xNt/DcGsYcsfB+K8mXpllAKiqSvM+L1Ubmqla30TzPm+Ha7VqEkFoty5OjS5OXIGybCvTy7I4rSyT08qyyJNAJIQYBCQA9ZIEINGfXI0NbPnPO2x5/x2c9XXJ46ZwhMI2L4VOL2nBMM2ZKuHhYUbleym2h1CKTmnvGfoq2AuT53lag1S3h6Ga7c7kOkMAUQ1UaWPs1sWo0sfxaBKfjci2JsPQ9BFZ5DskEAkhTjwSgHpJApBIBVVVqa3cxpb3VrL9o/8Q8vuSn1mDYQqdXgqcXmyhCK60xDBZRZ6X4swQStkZiSA09nKwZifPCwWi7N3Uwp5NLezd0kLAE+lwTY8RthFhty7O/vbeIYDSLAvTSjOZMjyDKcMzKM+xoZH1h4QQA5wEoF6SACRSLRIOsXvNp2z74H2q1n1GLHIwuNgCIYraEmHIEokSMqj4i6IU5/kpzA+jG3dWIgiNvgysWcnz1LhK0z5PIgxtbqGhys2h//arWoVGC2yIhditi+PWHPzQYdZzyrD09kCUyaQSBxaDrj9+FEII0WUSgHpJApAYSEJ+Hzv/+zHbP3yfPRvXEY/Fkp/ZAkFKWhNhyBRNHPflxMjJ95NbEMY05XSU8VfA6C91CEMAQV+EfVta2bM5EYi+2DsUT9NRa4LPwn52EyN2SAeQVqMwtsCe7CGaWppBgcPcdz8EIYToAglAvSQBSAxUAY+bHZ9+yPYP32fv5o0c7MJRMYeDlDV6yXf5MLaHoYg5TlpBkKzCMNbpU9FO/kqiZygtv0O9B3qH9m5uYe/mVup3uzr0Dmn0Gsg1UWNW+cjvZ5c/yBcVOkxMHpbOxOJ0JhY7mFDkIM2k76sfhRBCHEYCUC9JABInAm9bK5Uff8D2D9+ntnJr8riKij4WZESTl5IWX7JnSNWoGHPCpBeGsJ1yEsYzv5oIQ5kjDqs76Iuwb2trMhD53eEOn9tyzJBvosao8onPx6YGD7F4x/+UKO1Pm01qD0QTS9IZW2CX7TuEEH1GAlAvSQASJxp3UyPbPnyfHZ980GHlaRUVlBBFrV5G1fkwRw6uJK2xRbHnh7CNzscy88toT5kDOaMTyeUQalyleb83OVRWv9uNekjY0eo05JbZUQpM1JsVNnh8bKhxU+MMHNZOnUZhVH4ak0rSmVTsYGJxOiNzbbLbvRDiuJAA1EsSgMSJzNXYwI5PP6Tykw+oq9zW4bOILki2x8eEPV7soYNhCEXFnB3GVmbDeva5mC78fyhFU0BzeDAJ+iLs39aW6CHa0oK3NdThc4vDwLAxmaSX2WmxKWxu8bFhv5MN+120+MKH1WfSaxhfmAhDk0oSX0uzLCiKPHUmhOgeCUC9JAFIDBaeluZEGPr4A2q2b+HQiT0BYwhL2MfoGi8jmjpOgNYaYlhLNFinTMA6+0r0078CusM3W1VVFWeDn72bW9m7pZXayjaikXiHMtklNkrGZFIyJoN4lpHNDR7W73eyYZ+LjTUuvIcGsXZ2k46JxelMKHYwtsDO2EI7pVlWtPIovhDiKCQA9ZIEIDEY+Zxt7Pj0I3Z8spp9mzehqgeDiscSRlV8DGvxMakqhPULHTX6tBjWUflYZ5yD5UvXoSsqO+I1YpE4tbuc7Nvcyr5trYetSq3TaygcmU7xmEyGjc0kPd9CVYs/2UO0fr+TzbVuwtH4YXWb9VpG5acxttDO2AI7YwrsjM5Pw2qUx/GFEAkSgHpJApAY7PxuFzv/+xGVH3/A3k3rUeMHA4fPFMVj8ZPh8zF2v5+KOtB2+K+EijHPiPXkcVgvvALLuZeisRx5s1W/O8z+ba3s29LK3q2t+F0dk5XFbkj2DhWPycTqMBKJxdle72HDfhebal1srXOzrc5DIBI7rH5FgRFZVsa0h6IDvUW5aUYZQhNiCJIA1EsSgMRQEvC42fXZJ+xa8wnV6z8nGj44pyeiU6nL9IPio6TFz8Q9MUqav1CBBixlOVjOPBvrrMsxT5yIYjAcdh1VVWmt87FvSyv7trYdcbgsq8jaHogyKRiZjt6QeGIsFlepbvGxpdbN1jo3W+rcbKl10+gJHXYdgCyrgVH5aYzMtVGRl/g6MtdGlu3wYTwhxOAhAaiXJACJoSoSDrF343p2ffYxu9Z8it/lTH4WV6A+M0Bzup+0gJ8xNRFOro6T4e7Y06LoNZhHj8Ay43wsp83APGkiGtPhe4vFInHqdrvaA1ErTfs8cMh/jbQ6DQUVjkQgGptJdpEN5QtzgJq9oUQgqj0YinY1eYl38l+1TKuBivYwNDLXxsi8NEbm2cixSY+REIOBBKBekgAkBKjxOHU7K9m15hN2ffYJLfv3dvi8LS3M3lw/PoufkqYQU6vjjNujYgp+IRDpNJjGjMJyxllYpk7DfPLJaG3Ww64X8IYTT5e1ByJvW8feHXOanuLRmckeIlvGkXtzgpEYlQ0eKhu87Gj0sLPBS2Wjh/1tATr7r53DrG8PRDYqctOS3+fbTRKMhDiBSADqJQlAQhyurb6W3Ws+ZednH1OzdUuHSdQBU5y9OT725flRCDJuf5wZVVFG7Ae9/wuP0ms0mMaOxjJtOpZpU7Gccgra9PQORZJPl21pZf/WVvZXOomGOs4ByiiwMmxMJsVjMig6KQO98egLLPrDUXY3+djR6GFHg5cdjV52NnrZ0+LrtMfIZtQd7DHKszEyN42KXBtF6WbZHFaIAUgCUC9JABLi6AIeN1Wff8auzz6hav1aIsGDix5GdSr7s/3szwlQmxUgLRTj/Koop1VFya/VoHgPDyqGESMwT56cfBkrylG0B8vFonEaqlzs3ZKYUN24t+NwmUanUFDmoGRsoncopyTtsOGyzgQjMaqafYlA1OBhR2MiHFU3+4h2kozMem0yGFW0B6ORuTZKMi3yqL4QKSQBqJckAAnRddFIhH2bNyQnUntbWzp87rRFqM0OUJMdoCEzxHBvnIt2BZm8N05mrZaY+/DH2DU2G+aJExOB6OTJmCdOROtwJD8PeiPs355YjHHfllY8rR33JjNZ9RSPyUgOl6VlHj4H6VjC0Th7WhLBaMeB4bRGL7ubfIRjhz+mD2DQaSjPsVGRa2NEtpXhmRZKsy0Mz7KSZTXIcJoQfUwCUC9JABKiZ1RVpbFqV+KJsg2fU7+jssNQWUxRacwMtQeiIK32MBPdEWZXhxi/XyWjQUO4RU88evgK1IbycsyTJ2GeNAnzhAkYKypQ9HpUVcXVGGhfmbqVmso2IsGOw2XpeZZk71DRSekYTD1fOygai7O31Z8cQtvR3mu0s9FL6AjrFx1gM+oYnmWhNMva8Wu2VR7bF+I4kQDUSxKAhDg+gl4vezevZ8/6z6nesBZ3U2PHzw0xarOC1OYEqM0OEjPGmOoLcH5tmIn74qQ1agm0GIl4Dh82U4xGTGPGYJowAfOE8ZgmTMAwfDhxFRqq3MneocZqd8ed7TUKeWV2ik7KoPCkdPLLHMnH7XsjFlepaQske4qqW/zsafGxp8VPravzCdiQ2A5keObBQHRoQCpwmGVYTYgukgDUSxKAhDj+VFXFWV9L9YbP2bPhc/Zu2tBh7hBAmy1MbXYiENVnhsgkzml+P6e1hZhYE8PSoCPgtBBsNRAPHb4woiYtDdP4cZjHj8c0diymMWOIZRdQu+Pg4/bu5o7DZRqtQu5wO4UnpVM0Mp38ckeveoiOJBiJsb/NT3Wzn+oWH3tb/cmAtL8tQKyzWdiAQauhJNPM8C/2HGVZKcowo5eNZIVIkgDUSxKAhOh7sWiUuh3b2LPh88Rw2a4dHfYqi2lUGjKCyUDUmhahKBZnasDPqYEQpzRGSGvSEvBkEPTYCdb5USOH7yumsVoxjhmdCERjxxIuOInGQBq1u9zU7nDic3Z83F7RKOQMS6NoZDqFJ6VTUJGO0dx3221EYnFq2gJUt/cWHfp1f2ug0/lGAFqNQnFGezjKtDA8KzHfqCjdTHGmGbtJ32ftFmIgkgDUSxKAhOh/Aa+HvRvXs2fDWqrXf46npanD5yF9nIaMIA2ZQeozQ7TawxTFokwLBpkWCDLVHyKjVSEQyCMYzCPYohDa14wajhx2LcVoxHjSSRjHjCU6Yhxt5mE0es3U7fYeNqFaUSC7JI2CCgd5pXbyRtixZ5v7Zc5OLK5S5wp0DEbNia97Wn0EI52HI0hsKlucYaE4w5z8WpRhTr53mCUgicHlhAtATz75JA899BD19fVMmjSJX/3qV5x66qmdln/55Ze56667qK6uZuTIkTz44INccsklyc+vvfZann322Q7nzJ49mxUrVnSpPRKAhEgtVVVpq6uhev3n7Nmwln2bNxIJdQwmEW2cxowQDZkhGjKDNDtCFMajnBwMMikUZlIwRHkoQjScQ1AZSdCbTrA+SGj3PuI+3xGvqy8pIXbSJNx5E2jRFdLkNuB2Ht6rZLLqyS21k1ealvg6wo7Zdvj2H30pHldp9IQSQ2rtAam6fUhtf1uAVl/4mHWkdQhI5kTPUfv7kgwLdrNOJmeLE8oJFYBeeuklrrnmGp566immT5/Oo48+yssvv8z27dvJzc09rPyHH37I2Wefzf33389ll13G888/z4MPPsjatWsZP348kAhADQ0NPPPMM8nzjEYjGRkZXWqTBCAhBpZYNEpj1S72b9vM/q2bqNm2mdAXQkxMo9LkOBiIGjNCGDUxJoZCTA6GmRQKMTEYwqa1ELGMJxguIugyE6z1ENxdTazpi5ucJYTScvGNPAN37mhculza/EbiR+h4sWebyBuR6CXKLbWTU2JDdxwmV/eULxSlxhlgf5s/GYpq2g6+b+lKQDLq2nuMDoakQ3uTHGa9BCQxoJxQAWj69OlMmzaNJ554AoB4PE5JSQm33XYbd95552Hl586di8/n45///Gfy2GmnncbkyZN56qmngEQAcjqdvPrqqz1qkwQgIQY2NR6ned+e9kC0mZqtm/A52zqUiaPSag/TmBmiKT1EY0YIvzFKeTTC5GCISaEwk4MhhkejKI4SohmTCMWGEfKYCTb4Ce3YRWjHDtRQxzlCcUWL11aEt3A83ryxuIz5eCLmw9qo0ShkFduSgSiv1E5GvqXLCzT2NX842h6I2kORM3BIUPLT7D12QLIZdYf0HJkpTDeT7zBR4DBT4DCRZzdh0MkkbdF/TpgAFA6HsVgs/OUvf+Hyyy9PHp83bx5Op5PXXnvtsHOGDRvG/Pnz+cEPfpA8dvfdd/Pqq6+yfv16IBGAXn31VQwGAxkZGZx//vncd999ZGVlHbEdoVCI0CH/kXO73ZSUlEgAEuIEceAJs/3bNlOzNdFL5GpsOKyc3xilMT1EU0aYpvQQLY4QacSSgWhSKMT4UBizooP88aiFUwnrygh5rYRqXQQrKwlV7iCyt+O+aBGdGU/acNxpw/Fkj8KVNoywcngo0pu05A63J+cS5ZXasaYPzB3qA+EYNU4/+5I9Rx17k5q9oWNXAmTbjBQ4TO3B6GA4OvA+z27CpE9dT5kYXLoTgPru0YYuaG5uJhaLkZeX1+F4Xl4e27ZtO+I59fX1RyxfX1+ffH/RRRfx1a9+lREjRrBr1y5+8pOfcPHFF/PRRx+h1R7+L9r999/PPffccxzuSAiRCoqikFFQREZBERPOuxAAT0szNds2U7tjG7Xbt9G0ZzeWEJQ26ChtSGzGGlNU2tLCtDjCvOEI8ydHGE9uiJHRMOND1YzdVsmYcJiKcAS7ORNOnwZXXkA8cxwhn43g3gZC2ysJ7d6FedduMvdug71vogIhYwZueynutFLc9kQ4igQN1Gxvo2b7wd4qa7qBvBEOsottZBZYySy04sgxo0nx4+1mg5aK3DQqctOO+HkiIAWSw2z7WgPUuwLUuYLUu4PUuYKEo3GavSGavSE21rg6vVam1UC+3URhuinZg5RvNx0SlMyYUzicKAanlAagvnLVVVclv58wYQITJ06kvLycVatWccEFFxxWfsGCBcyfPz/5/kAPkBDixJWWlc3oM89h9JnnABAJBWnYvZPaym3U7dhGbeU2/C4n2W4j2W4j7EucdyAU7XWE+dwRpsUexpsXojwWZkzrfxlb/wFjQ2FGRsJkpBVDxSQ4axIUzCWWVk64yU9odxXh3bvI3rWb8K61hDe8RlwFvyUfV3so8tiH47UW4nOG2f15E7s/P/jUm0YD6TkmMkvsyVCUWTAwgtEBiYCU2PbjSFRVpdUXTgQiV5A6d/BgQHIlAlKdK0AwEqfVF6bVF2ZLnbvT66Vb9IeEokRAyrMbybUbyU0zkWs3kmU1yqKRostSGoCys7PRarU0NHTsqm5oaCA/P/+I5+Tn53erPEBZWRnZ2dns3LnziAHIaDRiNA7MbmghxPGhN5ooHjOe4jGJhyVUVcXd1ED9rp00VO2kYXfiFfJ5jxiKnGlh6hxhNtnDNDvCuG1hRsTCjGn5iLG17zE2HOakcASLNRdzwSSYNB4uPA/ybiWeNozwvhrCu6sI7d5FeNduQrtfxb+lBrc+F0/acLzWAnzWAvzWAmIYaW0I0trwhUUbNSqOdB1ZJXYyh6eTVZjoNbLnDLzd6RVFIctmJMtmZHyR44hlVFXFFYh0CEWH9iLVOhPf+8MxnP4ITn+EbfWeTq+pURJDbjlpietmWw1k2Qxk2YxkWg1k2wxkWY1k2Qxk24wy9DbEDYhJ0Keeeiq/+tWvgMQk6GHDhnHrrbd2Ogna7/fzj3/8I3nsjDPOYOLEiclJ0F+0f/9+hg0bxquvvsqXv/zlY7ZJJkELMTQdCEUHwlBD1S4adu8k6D38j25cUWlLi9BiD9HiCNNqj+C2higmEYTKIxHK2r+WxDXos0+CvHGQOxbyxkPeWFRrHpG6esK7dxHavZvwnj2E9+zBvd+J06fFZ8nH1x6MfJZ84toj/4+aRoljN0fJyNaTVWwna2Qu2eU52LMHXjDqLlVV8YSihwckV5BGT4hGT5AGd4gWb4ijLKh9RFaDtj2kGciyHgxHWTZjh7CUZTOQaTGgGyC9b6JzJ8wkaEg8Bj9v3jx++9vfcuqpp/Loo4/y5z//mW3btpGXl8c111xDUVER999/P5B4DP6cc87hgQce4NJLL+XFF1/kF7/4RfIxeK/Xyz333MOcOXPIz89n165d3H777Xg8HjZu3Nilnh4JQEKIAxKhqLFDL1FD1U6CniP3RHjMUdrSwrSlRZJf/ZYwxbEo5ZEIIyIRysMRyiIRSrU2zLnjIG9sezgaB9kjwZxOPBQism9fIhRV7yFUvQfnvhbamsN4QqYvBKMjr0GkUSOkKT4c1ijpWXocBXYyRuSQOboES176oHqEPRpLDKU1uEM0+0K0eMO0eEO0+MI0e9vfJ4+Hj7rCdmfSLfpEUPpiQGo/duhndpP+hA+fJ6ITKgABPPHEE8mFECdPnszjjz/O9OnTATj33HMpLS1l+fLlyfIvv/wyP/vZz5ILIS5ZsiS5EGIgEODyyy/n888/x+l0UlhYyIUXXsjPf/7zwyZPd0YCkBDiaFRVxdPcdLCXqGonzXur8ba2HLF8TKPitEVwWSOJr+0vjzlMvhqj7JBQVBaJUKazk5Y1ErIqEq/s9u8zRoDOQDwQIFJbS6SmhtD+Glx7mmip8+N0qrhDJry6TPyWvE6DEYAuGsCierAZItjSFBzZZhwlGWSW55E+ahh6x5EnPw8GqqriDUWToai5PRQdCEwtvvbv2z9v9YW73buk0yhkWg1kWg2kW/Q4zHrSzQYc7d9/8XWgTJpJL/OYeuGEC0ADjQQgIURPBLwemvdW07SnmuZ91TTvraZ5757DVrE+II6K1xLFZYskA9KBcORQIpRFoslhtLJIhBGRGFn2YpTskw4PR2kFiX07gLjfT6imlrbt+2ne3UJrvR+3M443pMOPlZD+GH8Y4jFMESdWxYfNFCPNocORZyV9WCYZIwuxjihBa7Me95/fQBWLqzj94WRvUqvvYGBq7hCWEp97goevHt5VipJYgNJxaGgy67F/ISglPjt43GHRk2aUlbslAPWSBCAhxPGixuO4mhpp3reH1pp9tNbsp7VmHy01+wgH/J2eFzDEOvQWua0R3JYoWkOIEbEIZeFosseoPBwhT2NCk1V+MBBljYTs9pBk7NibE3J6aNu2n9Zd9ThrnHiaQ3i8Kt6wgYDGRlxz9D3C9GEPpqgbizaE1axitetIyzJjL7DjGJZD2ogCDHm5KIb+3R5koAhFY7T5IomhN18Ypz+MOxDB1f5y+g9+f+jLH4716rpajYLdpGsPRIZDeph0ySB1ICx9sefJrNcOivAkAaiXJAAJIfqaqqr4nG3JUNRSs4/W2kQ46mwoDRKTr32mKB5LFLc18dVjiRCwRLAZghTEIxRGoxRFYxRHo4nvDZlkZpajZFVAxnBIP/AaBrbcZM8RgBpX8dS20VpZQ2t1M+46N+7WMB6/Bl/MRERz+AKPX6TEoxhDTsxxDxZtGItZxebQk5ZtIa3AgX1YDtZh+ejz89HIE7hJ4Wj8C6EonPjqj+AKRHG2v3d/IUQ5AxHC0e7PaTqUXqscYVjuC71PhwSoA9/bzfoB9TSdBKBekgAkhEilcMB/WChqq6vF1VhPNHz0LSr8xgOhKIq7PRx5rFEipjDZSpiiWIzCaJTiSJSiaJRCVUuRtQC7YxhKRnsoOjQgWbM7BKRQIIpzbyuu3XW49rXgafDidYXxBRT8ET1BxQLKsZ+W0sTCGENtmOI+zNowFjNY0nRYMy1Yc9JIK8gkbVgO5uI8tOmDa8J2XwhGYp33MPnDHcLSweOJr9HuTnD6AqNO02FoznFIb1P6F+c8feG9/jg/WScBqJckAAkhBiI1HsfnbMNZX4ezoQ5nQz3Ohjra6mtx1tcS9nc+pAYQ0cbxmWL4zFF85ijeQ75XjREytCEK23uQEr1HMYpUHcW2QiwHAlEyIA0DRwlYshIrN7aLx+J4nSFce5txVzfhrnPiafbjdUXxBRQCMT0RxdTle9bGQhjCbkwEMGmjmM1gsemwpJuw5diwFWSQVpKDbXg+WnuaBKVuUlUVfzh2hOAU7hCiDnzmPiREuQORbk8OP9S3zhzBwi+NPX43wwm0FYYQQoiuUzQabJlZ2DKzKB47/rDPg15vIhjV1ybDkauhnraGWnytrehjGtJ9GtJ9nc/x8RujtJlj7DNF28NRDB9RlMgO0ts2kqtEKI5GKYhGyYvFyFMV8kzZZKYVobEXobEXYrcXYbcXwrQisI9JDLNpDg6TRMMxvM4QnppW3Hub8dQ58TT78LvDBPwqwYiWoGokpjEQ0xoJmHMIHDg5BrjaX3sAQsB+lPgeDFEPRjWASRvBbEz0KFnSTVizraQVZJBWko29NB+9/cirVw9FiqJgNeqwGnUUph97ePNQ8biKNxxN9iQdeX5T+IifeYJRHOajzzXra9IDdATSAySEGGyi4TCe1mY8zU24m5sOfm1pwtXUgKe5iVgkcux6NHF85hhecxSfKZr8PmiKYtKHsWtD5BAhNxYjPxojNxYjL6aSa8oi11aAwV4E9iKwF4C9sP37wsRTbNqOfxDDwSjeZh/evY14alvxNrjxtfrxuyMEAnECYS0h1UhYa+nWz0IX9WNS/Ri1ESxGFbNVi8VhwpZtxVaQjq04G/vwPEzpFulR6iOxuEo0HseoO77zh2QIrJckAAkhhhpVVQl43Ilg1NIekJoa8TQ30dZUj7u5kZC7820oDhXRxgkYY/iNMQLGGAFT+1djDK0+glUbxqELk6OEyI3HyIvGyI3GyDWmk2PNw24rQrHnJ0KRLS/xNa39qyW7w5AbQCwWx9foxrO3Ec/+FnyNbrzJHqVEUAqqBkIaK6qm6wMfmngEY9yPURPGpI9hNmsw2/RY7AbMmVZsOWlY8zOwFmdhyXYMmH3ahjIJQL0kAUgIIQ4XjUTwtjQne47czYmA5GpuxNlYj6+tlVjo6JO0DxVX1EQwMiRC0oHAFDbE0OvDmHUR7LoQGdowOWqUnGiM7LhKjiGdHEsOGdYCtGm5YM1NDLNZcxJfbXmJ702ODhO44/E4gWY3nup6PPtb8Da48Lf48LlC+H1xgmENwXgiKEV13RsOUtQY+pgfoxrCqI1iMsYxmzSYbTrM6WbMGVbM2TaseRlYC7Mx59jRHufeDyEBqNckAAkhRM+EgwF8zjZ8ba2Jr+3fe9tacbU14W5tJuByEfUefcL2FwX1B3uRDn1pDBGMusjBsESErHicrFiMTFVDptFBlimTTEseprS8zsOSOSMZllRVJdzixLOnAU9NC956N/5WH35XkKAvSiAEoaiOUNxASGMmqu/ZopC6WACDGsKoiWLQxzGZFExWHaY0A+Z0C5YsG5ZcB5b8TCw5Dsw2vfQyHYMEoF6SACSEEH0rFo3idzvxtbXhc7aHpbY23K3NOFsbcLe1EHA6iXh80I19u6Ka9uE3U8eg5DfGiBuiGHVhLLoIdm2YrHiMzFiczHiMrLhClsFOpimDTHMODlsBGtuBsJQLtpz2r3mJsHTIMFzE68O3vxlvbSu+xkSvkt/px++JEPTHCYVUQlEtYVVPWGMiquv5Ktq6eBCjEsagjWE0gsmkxXSglyndiiU7DWueA3OOA3OaEZNVN6RCkwSgXpIAJIQQA4OqqgR93kSPUlsbPleiR8nT1kJbSwOetmZ8zjbCbi/xYNeH3yDRqxQ0xAkaYgSNh3xvaB+G00UxayPYdGEcmkgiKMViZMYhS2cly5hOpjmTTHMuRltuYn6SNav9a3aiZ8mSfVhginr9+Gub8NW34W904W/2EHD6CXpCBLwRQkGVUEQhHNMRUoxEtGai+p4/uaaLhxKhSRfDqFcxmTWYLFpMaUbMDjPmTCuWbDuWvHQsOfYTuqdJAlAvSQASQogTTyQUxOd0tg+9tSaH4bxtbbhbm/C0NeN3OQl7fNCDP30hfYygPk7IcCAsHfwefRSDNoJZF8WqCZOmjWAnSroaIz2u4tBZcRjspJsycFiySbfkYbDlJtZRsmSBJfOQ77NAf3AOUjwYJNLcgq+2hUBDG75mN4EWH0F3gIAnQjAQO9jLFNcT1pqJ6K29DE3BxPCctn14zqhgNGsx2/SYHSbMGRbMWTasuelY8tIxZaWhGwBzmiQA9ZIEICGEGLzi8RhBr5eA24Xf5cSf/Oom4HbidbbhdrbgdzsJeb1E/QHowV/KmEYlaIgR0h/oWUp8DRnihPRxVF0UvS6KURPFrE0EJ7smSroax4EOh86Cw2Aj3ZiOw5yFw5KDw5KL7kCvkjkDLBkHvzc6QKMhHg4TczqJtjkJNLThb/bgb/UScAYIuoMEfFFCgTihMISiWkJxPRHFSFhn6V1oigUwxIMYlEhiiM6gYjAqmCw6TDY9pjQT5nQLpkwr5mw7aSW5mHMzeny9I5EA1EsSgIQQQhxwMDC5CbhdBDxu/Id89bha2gOTi5DXQ8QbgGjPNjZVUQnpEwEp3B6UQvqDoSmkj6Pooui1UYzaKBZtBKsm0h6cVBwaY3twSiPd6MBhyiDdnEOaJReNJTPR02RObw9Nme3ByZ4ITsEgkdY2Ao1t+OpdBFo8+Nv8idDkDRP0t/c0RTSEYzrCGAhrzIkn5rqw/ckXjUyr58KHvtGjn1NnZCVoIYQQ4jjRaLRY7A4sdgdQ0qVzIsFgh6AU8CTCk9/tIuD14HW34XM7CXjdhHw+Ij4/ajiKgoIposUU0UI3HpSLo+LUx2loD05BfYyw3kvI4CakryKsj6HRRhPzgLQRzNooNk0UhxLGoYJDayRdZ8FhsOMwOnCYMsnPyMFalINiyTzYy2TOaA9RieCkAjGvLxGaGpz4mzz423wEXQFCnhBBX5RQIJbobYoohOM6IhiIaEwYramNIBKAhBBCiONMbzKhN5mw5+R2+ZxoJELI5yXgcRP0egh6vQS9HgJeD0GvB7/Hjdfdis+TCFFhr4+IPxGcND0MTgBObXtw0scJ6+KE9T7Ceg9hXRVRXRyNLoZeG8WgjWJWoli0UdI0EeyaGA69jgy9hTS9DbshjTRTOkUZmdiKstGbM8CUnliPyZx+yPft4UmT2jlDEoCEEEKIAUCn16NLz8Ca3r15MccOTi48rkRwCno9hHw+ov4AajgKgD6mQR/TQLB77fW0v3brDgSnOGF9M2F9I2FdnLguhqKNtQeoRIgyaaKYNVGsmghTTjqfs65Y1r2LHkcSgIQQQogTWE+DUywaJeT3JV6+9pffS9CXOObzuHC7W/F5nQR8ieAU8fuJBkOogTBEE+szGaIaDNHuBagY8F9fM2dd0a0mH1cSgIQQQoghSKvTHTK3qfti0Qghn689MHnbA5QPv9eNx9OGx9OWHK4L+X2E/T6igSCxQAg1GKGo5OTjfEfdIwFICCGEEN2m1emxONKxONJ7dL4a7/oK333hxFzqUQghhBAnNEWT2ggiAUgIIYQQQ44EICGEEEIMORKAhBBCCDHkSAASQgghxJAjAUgIIYQQQ44EICGEEEIMORKAhBBCCDHkSAASQgghxJAjAUgIIYQQQ44EICGEEEIMORKAhBBCCDHkSAASQgghxJAjAUgIIYQQQ44u1Q0YiFRVBcDtdqe4JUIIIYToqgN/tw/8HT8aCUBH4PF4ACgpKUlxS4QQQgjRXR6PB4fDcdQyitqVmDTExONxamtrSUtLQ1GU41q32+2mpKSEffv2Ybfbj2vdA4Hc34lvsN/jYL8/GPz3KPd34uure1RVFY/HQ2FhIRrN0Wf5SA/QEWg0GoqLi/v0Gna7fdD+gw1yf4PBYL/HwX5/MPjvUe7vxNcX93isnp8DZBK0EEIIIYYcCUBCCCGEGHIkAPUzo9HI3XffjdFoTHVT+oTc34lvsN/jYL8/GPz3KPd34hsI9yiToIUQQggx5EgPkBBCCCGGHAlAQgghhBhyJAAJIYQQYsiRACSEEEKIIUcCUD968sknKS0txWQyMX36dD799NNUN6lL7r//fqZNm0ZaWhq5ublcfvnlbN++vUOZc889F0VROrxuuummDmX27t3LpZdeisViITc3lx//+MdEo9H+vJUjWrRo0WFtHz16dPLzYDDId7/7XbKysrDZbMyZM4eGhoYOdQzUezugtLT0sHtUFIXvfve7wIn3+3v//ff50pe+RGFhIYqi8Oqrr3b4XFVVFi5cSEFBAWazmZkzZ7Jjx44OZVpbW/nmN7+J3W4nPT2d66+/Hq/X26HMhg0bOOusszCZTJSUlLBkyZK+vrWko91jJBLhjjvuYMKECVitVgoLC7nmmmuora3tUMeRfu8PPPBAhzKpusdj/Q6vvfbaw9p+0UUXdSgzkH+Hx7q/I/37qCgKDz30ULLMQP79deXvwvH6b+eqVas45ZRTMBqNVFRUsHz58uNzE6roFy+++KJqMBjUp59+Wt28ebN64403qunp6WpDQ0Oqm3ZMs2fPVp955hl106ZN6rp169RLLrlEHTZsmOr1epNlzjnnHPXGG29U6+rqki+Xy5X8PBqNquPHj1dnzpypfv755+rrr7+uZmdnqwsWLEjFLXVw9913q+PGjevQ9qampuTnN910k1pSUqKuXLlS/eyzz9TTTjtNPeOMM5KfD+R7O6CxsbHD/b311lsqoL777ruqqp54v7/XX3/9/7d37zFNnW8cwL8FKYJIC4ItIFcvKIqIOEjdhkYakWyTzT9ERlCc04mYSbwRtyxzZirODHVsOv+Y4tR4WaaQsE0j1ylWRCYqgkwqiFu4BFgRgg6kz+8Pf5xw5KoitOvzSUjK+77nnPfp057zcE4PpU8//ZTOnDlDAOjs2bOi/sTERJLJZJSamko3btyghQsXkqenJz169EgYs2DBAvLz86MrV67QxYsXacKECRQZGSn0NzU1kUKhoKioKCouLqYTJ06QlZUVHTx4cNhj1Ol0pFar6dSpU3Tnzh3SaDQUGBhIAQEBonW4u7vTtm3bRHnt+r4dzhj7y+GyZctowYIFork3NjaKxhhyDvuLr2tc1dXVdOjQIZJIJKTVaoUxhpy/gRwXBmPfee/ePbK2tqb169dTSUkJJScnk7m5OZ07d+6lY+ACaIgEBgZSXFyc8HtHRwc5OzvTzp07h3FWL6auro4AUG5urtA2Z84cWrduXa/L/Prrr2RmZkY1NTVC24EDB8jW1pb+/fffVzndfn3++efk5+fXY59OpyMLCwv66aefhLbS0lICQBqNhogMO7berFu3jsaPH096vZ6IjDt/zx5c9Ho9KZVK2r17t9Cm0+nI0tKSTpw4QUREJSUlBIAKCgqEMb/99htJJBL6+++/iYho//79ZGdnJ4ovISGBvL29X3FE3fV0AH3W1atXCQDdv39faHN3d6c9e/b0uoyhxNhbARQeHt7rMsaUw4HkLzw8nObNmydqM5b8EXU/LgzWvnPz5s00depU0bYiIiIoNDT0pefMl8CGQFtbGwoLC6FWq4U2MzMzqNVqaDSaYZzZi2lqagIA2Nvbi9qPHz8OBwcHTJs2DVu2bEFra6vQp9Fo4OvrC4VCIbSFhobi4cOHuH379tBMvA93796Fs7MzvLy8EBUVhaqqKgBAYWEh2tvbRbmbPHky3NzchNwZemzPamtrw7Fjx/DBBx+IvuzXmPPXVUVFBWpqakQ5k8lkCAoKEuVMLpdj1qxZwhi1Wg0zMzPk5+cLY4KDgyGVSoUxoaGhKCsrwz///DNE0QxcU1MTJBIJ5HK5qD0xMRFjxoyBv78/du/eLbq8YOgx5uTkYOzYsfD29kZsbCwaGhqEvv9SDmtra/HLL79gxYoV3fqMJX/PHhcGa9+p0WhE6+gcMxjHTv4y1CFQX1+Pjo4OUZIBQKFQ4M6dO8M0qxej1+sRHx+P119/HdOmTRPa33//fbi7u8PZ2Rk3b95EQkICysrKcObMGQBATU1Nj/F39g2noKAgpKSkwNvbG9XV1fjiiy/w5ptvori4GDU1NZBKpd0OKgqFQpi3IcfWk9TUVOh0OsTExAhtxpy/Z3XOp6f5ds3Z2LFjRf0jRoyAvb29aIynp2e3dXT22dnZvZL5v4jHjx8jISEBkZGRoi+W/PjjjzFz5kzY29vj8uXL2LJlC6qrq5GUlATAsGNcsGABFi1aBE9PT2i1WnzyyScICwuDRqOBubn5fyqHR44cwejRo7Fo0SJRu7Hkr6fjwmDtO3sb8/DhQzx69AhWVlYvPG8ugNhziYuLQ3FxMS5duiRqX7VqlfDY19cXTk5OCAkJgVarxfjx44d6ms8lLCxMeDx9+nQEBQXB3d0dp0+ffqk3l6H64YcfEBYWBmdnZ6HNmPNn6trb27F48WIQEQ4cOCDqW79+vfB4+vTpkEql+Oijj7Bz506D/5qFJUuWCI99fX0xffp0jB8/Hjk5OQgJCRnGmQ2+Q4cOISoqCiNHjhS1G0v+ejsuGDq+BDYEHBwcYG5u3u3T77W1tVAqlcM0q+e3du1apKenIzs7G+PGjetzbFBQEACgvLwcAKBUKnuMv7PPkMjlckyaNAnl5eVQKpVoa2uDTqcTjemaO2OK7f79+8jIyMCHH37Y5zhjzl/nfPp6vymVStTV1Yn6nzx5gsbGRqPKa2fxc//+fVy4cEF09qcnQUFBePLkCSorKwEYR4ydvLy84ODgIHpN/hdyePHiRZSVlfX7ngQMM3+9HRcGa9/Z2xhbW9uX/gOVC6AhIJVKERAQgMzMTKFNr9cjMzMTKpVqGGc2MESEtWvX4uzZs8jKyup2yrUnRUVFAAAnJycAgEqlwq1bt0Q7rM4dto+PzyuZ94tqaWmBVquFk5MTAgICYGFhIcpdWVkZqqqqhNwZU2yHDx/G2LFj8dZbb/U5zpjz5+npCaVSKcrZw4cPkZ+fL8qZTqdDYWGhMCYrKwt6vV4o/lQqFX7//Xe0t7cLYy5cuABvb2+DuHTSWfzcvXsXGRkZGDNmTL/LFBUVwczMTLh0ZOgxdvXXX3+hoaFB9Jo09hwCT8/IBgQEwM/Pr9+xhpS//o4Lg7XvVKlUonV0jhmUY+dLf4yaDcjJkyfJ0tKSUlJSqKSkhFatWkVyuVz06XdDFRsbSzKZjHJyckS3Y7a2thIRUXl5OW3bto2uXbtGFRUVlJaWRl5eXhQcHCyso/N2x/nz51NRURGdO3eOHB0dDeJW8Q0bNlBOTg5VVFRQXl4eqdVqcnBwoLq6OiJ6eiunm5sbZWVl0bVr10ilUpFKpRKWN+TYuuro6CA3NzdKSEgQtRtj/pqbm+n69et0/fp1AkBJSUl0/fp14Q6oxMREksvllJaWRjdv3qTw8PAeb4P39/en/Px8unTpEk2cOFF0C7VOpyOFQkHR0dFUXFxMJ0+eJGtr6yG7Db6vGNva2mjhwoU0btw4KioqEr0vO++euXz5Mu3Zs4eKiopIq9XSsWPHyNHRkZYuXWoQMfYVX3NzM23cuJE0Gg1VVFRQRkYGzZw5kyZOnEiPHz8W1mHIOezvNUr09DZ2a2trOnDgQLflDT1//R0XiAZn39l5G/ymTZuotLSUvvvuO74N3hglJyeTm5sbSaVSCgwMpCtXrgz3lAYEQI8/hw8fJiKiqqoqCg4OJnt7e7K0tKQJEybQpk2bRP9HhoiosrKSwsLCyMrKihwcHGjDhg3U3t4+DBGJRUREkJOTE0mlUnJxcaGIiAgqLy8X+h89ekRr1qwhOzs7sra2pvfee4+qq6tF6zDU2Lo6f/48AaCysjJRuzHmLzs7u8fX5LJly4jo6a3wn332GSkUCrK0tKSQkJBucTc0NFBkZCTZ2NiQra0tLV++nJqbm0Vjbty4QW+88QZZWlqSi4sLJSYmDlWIfcZYUVHR6/uy8387FRYWUlBQEMlkMho5ciRNmTKFduzYISoghjPGvuJrbW2l+fPnk6OjI1lYWJC7uzutXLmy2x+MhpzD/l6jREQHDx4kKysr0ul03ZY39Pz1d1wgGrx9Z3Z2Ns2YMYOkUil5eXmJtvEyJP8PhDHGGGPMZPBngBhjjDFmcrgAYowxxpjJ4QKIMcYYYyaHCyDGGGOMmRwugBhjjDFmcrgAYowxxpjJ4QKIMcYYYyaHCyDGGGOMmRwugBhjrAceHh7Yu3fvcE+DMfaKcAHEGBt2MTExePfddwEAc+fORXx8/JBtOyUlBXK5vFt7QUEBVq1aNWTzYIwNrRHDPQHGGHsV2traIJVKX3h5R0fHQZwNY8zQ8BkgxpjBiImJQW5uLvbt2weJRAKJRILKykoAQHFxMcLCwmBjYwOFQoHo6GjU19cLy86dOxdr165FfHw8HBwcEBoaCgBISkqCr68vRo0aBVdXV6xZswYtLS0AgJycHCxfvhxNTU3C9rZu3Qqg+yWwqqoqhIeHw8bGBra2tli8eDFqa2uF/q1bt2LGjBk4evQoPDw8IJPJsGTJEjQ3N7/aJ40x9kK4AGKMGYx9+/ZBpVJh5cqVqK6uRnV1NVxdXaHT6TBv3jz4+/vj2rVrOHfuHGpra7F48WLR8keOHIFUKkVeXh6+//57AICZmRm++eYb3L59G0eOHEFWVhY2b94MAJg9ezb27t0LW1tbYXsbN27sNi+9Xo/w8HA0NjYiNzcXFy5cwL179xARESEap9VqkZqaivT0dKSnpyM3NxeJiYmv6NlijL0MvgTGGDMYMpkMUqkU1tbWUCqVQvu3334Lf39/7NixQ2g7dOgQXF1d8eeff2LSpEkAgIkTJ+Krr74SrbPr54k8PDzw5ZdfYvXq1di/fz+kUilkMhkkEoloe8/KzMzErVu3UFFRAVdXVwDAjz/+iKlTp6KgoACvvfYagKeFUkpKCkaPHg0AiI6ORmZmJrZv3/5yTwxjbNDxGSDGmMG7ceMGsrOzYWNjI/xMnjwZwNOzLp0CAgK6LZuRkYGQkBC4uLhg9OjRiI6ORkNDA1pbWwe8/dLSUri6ugrFDwD4+PhALpejtLRUaPPw8BCKHwBwcnJCXV3dc8XKGBsafAaIMWbwWlpa8M4772DXrl3d+pycnITHo0aNEvVVVlbi7bffRmxsLLZv3w57e3tcunQJK1asQFtbG6ytrQd1nhYWFqLfJRIJ9Hr9oG6DMTY4uABijBkUqVSKjo4OUdvMmTPx888/w8PDAyNGDHy3VVhYCL1ej6+//hpmZk9PeJ8+fbrf7T1rypQpePDgAR48eCCcBSopKYFOp4OPj8+A58MYMxx8CYwxZlA8PDyQn5+PyspK1NfXQ6/XIy4uDo2NjYiMjERBQQG0Wi3Onz+P5cuX91m8TJgwAe3t7UhOTsa9e/dw9OhR4cPRXbfX0tKCzMxM1NfX93hpTK1Ww9fXF1FRUfjjjz9w9epVLF26FHPmzMGsWbMG/TlgjL16XAAxxgzKxo0bYW5uDh8fHzg6OqKqqgrOzs7Iy8tDR0cH5s+fD19fX8THx0Mulwtndnri5+eHpKQk7Nq1C9OmTcPx48exc+dO0ZjZs2dj9erViIiIgKOjY7cPUQNPL2WlpaXBzs4OwcHBUKvV8PLywqlTpwY9fsbY0JAQEQ33JBhjjDHGhhKfAWKMMcaYyeECiDHGGGMmhwsgxhhjjJkcLoAYY4wxZnK4AGKMMcaYyeECiDHGGGMmhwsgxhhjjJkcLoAYY4wxZnK4AGKMMcaYyeECiDHGGGMmhwsgxhhjjJmc/wEX7+UBb+xwkQAAAABJRU5ErkJggg==" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# use vvag to get the losses and gradients with different random circuit instances\n", "QAOA_vvag = K.jit(\n", " K.vvag(QAOAansatz_iso, argnums=0, vectorized_argnums=0), static_argnums=(1, 2, 3)\n", ")\n", "\n", "params_iso = K.implicit_randn(\n", " shape=[ncircuits, 2 * nlayers], stddev=0.1\n", ") # initial parameters\n", "if type(K).__name__ == \"JaxBackend\":\n", " opt = K.optimizer(optax.adam(1e-2))\n", "else:\n", " opt = K.optimizer(tf.keras.optimizers.Adam(1e-2))\n", "\n", "list_of_loss = [[] for i in range(ncircuits)]\n", "\n", "for i in range(2000):\n", " loss, grads = QAOA_vvag(params_iso, iso_graph)\n", " params_iso = opt.update(grads, params_iso) # gradient descent\n", "\n", " # visualise the progress\n", " clear_output(wait=True)\n", " list_of_loss = np.hstack((list_of_loss, K.numpy(loss)[:, np.newaxis]))\n", " plt.xlabel(\"Iteration\")\n", " plt.ylabel(\"Cost\")\n", " for index in range(ncircuits):\n", " plt.plot(range(i + 1), list_of_loss[index])\n", " legend = [f\"circuit {leg}\" for leg in range(ncircuits)]\n", " plt.legend(legend)\n", " plt.show()" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "After inputting the optimized parameters back to the ansatz circuit, we can perform the projective measurement on the output quantum state to get the solution. Here we directly use the bit string with the maximum probability as the solution since we know all information of the probability distribution of the output quantum state, but which is not feasible in the experiment." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 13, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Circuit #0\n", "cost: 0.042537812143564224\n", "max prob: 0.047906018793582916\n", "bit strings: ['000000111111']\n", "\n", "Circuit #1\n", "cost: 0.033970173448324203\n", "max prob: 0.054868899285793304\n", "bit strings: ['000000111111']\n", "\n", "Circuit #2\n", "cost: 0.033648744225502014\n", "max prob: 0.055139534175395966\n", "bit strings: ['111111000000']\n", "\n", "Circuit #3\n", "cost: 0.03602508455514908\n", "max prob: 0.05475332960486412\n", "bit strings: ['111111000000']\n", "\n", "Circuit #4\n", "cost: 0.03601868823170662\n", "max prob: 0.05406792089343071\n", "bit strings: ['111111000000']\n", "\n", "Circuit #5\n", "cost: 0.03338256850838661\n", "max prob: 0.05537496879696846\n", "bit strings: ['000000111111']\n", "\n" ] } ], "source": [ "# print QAOA results\n", "for num_circuit in range(ncircuits):\n", " print(f\"Circuit #{num_circuit}\")\n", " c = QAOAansatz_iso(params=params_iso[num_circuit], g=iso_graph, return_circuit=True)\n", " loss = QAOAansatz_iso(params=params_iso[num_circuit], g=iso_graph)\n", "\n", " # find the states with max probabilities\n", " probs = K.numpy(c.probability())\n", " max_prob = max(probs)\n", " index = np.where(probs == max_prob)[0]\n", " states = []\n", " for i in index:\n", " states.append(f\"{bin(i)[2:]:0>{c._nqubits}}\")\n", " print(f\"cost: {K.numpy(loss)}\\nmax prob: {max_prob}\\nbit strings: {states}\\n\")" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T12:07:03.904854400Z", "start_time": "2023-07-03T12:06:31.721659700Z" } } }, { "cell_type": "markdown", "source": [ "On average, QAOA with isotropic quantum dropout improves the probability of correct solution (max prob) by nearly 0.015 compared to regular QAOA.\n", "\n", "It should be noted that isotropic quantum dropout will lead to more ground state degeneracy, so it does not necessarily lead to better results than conventional QAOA. However, it has a high upper limit, which means that it is possible to get much better results, please refer to [Wang, Zheng, Wu, and Zhang (2023)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.023171) for more analysis and details." ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "### Random Quantum Dropout" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "Because the dropout of each layer is different, we need to generate $\\text{nlayers}$ graphs after dropout. In order to perform just-in-time (JIT) compilation more conveniently, here we only save the weights in the order of the edges of the original hard graph, instead of saving each graph after dropout." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 21, "outputs": [], "source": [ "def graph_weights(graph):\n", " gw = []\n", " for a, b in hard_graph.edges:\n", " gw.append(graph[a].get(b, default={\"weight\": 0})[\"weight\"])\n", " return jnp.asarray(gw)" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T13:23:26.871885Z", "start_time": "2023-07-03T13:23:26.858216600Z" } } }, { "cell_type": "code", "execution_count": 22, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Here is the graph of the H_C of the last driving layer:\n" ] }, { "data": { "text/plain": "
", "image/png": 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/f19tT7CfP38me3t7EhUVJTk5OVq+fDklJCSUec67d++oU6dOxGKxyNnZmdLT00tte+3aNZKQkKBevXpRcnJylWydP38+KSkplVqUSEZGhrZu3UohISHl1hTgcrk0YMAA0tDQoJycnCrZxVD7MAGEDAwM9ZKsrCy6du1aEfe/jIwMDR8+nI4cOSJw9/+fBAcH07hx40hISIgaN25MGzZsKPfel5OTQytXriQRERHS1tYuNwDw5MmTJCwsTBYWFpSZmVllm/X19YulFBamSZMmtGrVKsrLyyNRUVHatWtXmf29e/eOhISEaPPmzVW2jaF2YcQAAwNDvSE2NpY8PDxoyJAhJUb/18QT6qtXr2jYsGHEYrFIWVmZdu7cSRkZGeWe9/TpU9LT0yNhYWFatmxZuZkKu3btIhaLRRMmTBBIkZ/SUgoLo66uTgsWLCCi38Jh+vTp5fbr6OhIMjIyJWY+MNQfGDHAwMBQZyns/u/UqRMBqDH3/588fPiQTE1NCQCpq6vToUOH+BIfGRkZNGfOHGKz2dShQwd68+ZNme25XC6tWLGCAJCLi0u5+wzwS2kphYVp27YtOTo6EhHRyJEjqXfv3uX2m5iYSPLy8mRnZycQOxlqB0YMMDAw1CkK3P/Tp0+nFi1aFHP///z5s8Zs4XK5dOvWLerduzcBIF1dXTpx4gTfT+r+/v7UqlUrEhcXp02bNpV7HofDIUdHRwJA69atE6jQsbKyou7du5fZpkuXLmRra0tERK6urqSoqMhX37t37yYWi0UvX76ssp0MtQMjBhgYGGqd2NhYcnd3L+L+V1NTIycnpxpz/xeGw+HQlStXeN6Ijh070qVLl/h+Sk9OTiZ7e3sCQL169aKQkJByz8nJyaHRo0cTi8WiAwcOVPUSivUtIyNDa9asKbNd//79ydramoj+fxdDfmIv8vLySFdXl3r06MGkGtZTGDHAwMBQ45Tk/mez2dS9e3fasGFDjbr/C5Ofn0+nTp0ifX19AkA9e/akGzduVMgWb29vatasGcnIyNC+ffv4EhDp6elkYmJCoqKidO7cuapcQoncvXuXAJT75G5paUlmZmZE9DtAEv8rT8wPfn5+5cYkMNRdGDHAwMBQI9Ql9/+f5OTkkIeHB2lqahIAMjY2pvv371eoj/j4eBo1ahQBoEGDBlFkZCRf5yUmJlLXrl1JSkqK/Pz8KmN+uZSXUljA6NGjqU+fPkT0+z0RFhau0KZEgwcPphYtWvAVUMlQt2CKDjEwMFQbP378KFL8JzMzE2pqarCysuIV/xEVFa01+7KysuDp6YlNmzYhMjISVlZWOHnyJDp27Mh3H0SEU6dOwcnJCQBw/PhxjBkzhq+SxjExMTA2NkZsbCz8/f3RqVOnSl9LWVy/fh0mJiZgs9lltpOSkkJmZiYAQFRUFJqamqWWJS6JLVu2QFdXF5s3b8aKFSuqZDNDHUWQyoKBgeHvhMvl0uvXr2nVqlUluv+Dg4PrxJpyamoqbdq0iZSUlIjNZtPYsWPp/fv3Fe4nMjKSzMzMCACNGjWK4uLi+D43LCyM1NTUSFlZmT58+FDhsStiIwA6c+ZMuW1nzZpFurq6vP8PGzaM+vXrV6HxFixYQBISEhQREVFhWxlqD2aZgIGBoUpkZWXR1atXi7n/R4wYUevu/z9JTEyklStXUsOGDUlERIQmT55MYWFhFe6Hw+HQ/v37SUZGhpo1a0ZXrlyp0PmvX78mJSUlat26dbVPmgcPHiQ2m13qngeFWbx4MamqqvL+v2zZMmrSpEmFxktNTaUmTZrQqFGjKmwrQ+3BiAEGBoYKUxD9P3jwYJKUlCwS/e/n51fnytP++PGD5s+fT9LS0iQuLk5OTk58r+n/SWhoKC/VcMqUKfTr168KnR8QEECysrLUoUOHaq+SSMRfSmEBa9asoUaNGvH+f+rUKQJQZm2CkvDy8iIAFY67YKg9GDHAwMBQLoXd///991+ddf//SWRkJM2cOZPExcVJRkaGFixYUOlKeXl5ebR582YSFxenVq1alVm3vzS8vb1JXFyc+vbtS6mpqZWyoyLwm1JYgJubG0lKSvL+HxQURADo4cOHFRqXw+FQx44dydDQUGBFkxiqF0YMMDAwlEiB+3/atGmkrKxcxP1/9OjROuX+/5OwsDCys7MjERERkpeXJ1dXV77c5KURFBREHTt2JDabTbNnzy5zY6HSOHLkCAkJCZGVlRVlZWVV2paKwG9KYQEHDx4kALwJPCsri9hsNh08eLDCYz969IgAkIeHR4XPZah5GDHAwMDAoyT3f6tWrWjWrFl10v3/J+/evaMxY8YQm82mJk2a0ObNm6v0BJ6dnU3Lli0jYWFh0tXVpSdPnlSqHzc3NwJAdnZ2AtlngF/mzZtHTZo04fvp/MSJEwSgiNjR1NQkZ2fnSo0/ZswYaty4MTMn1AMYMcDA8A/D5XLp1atXxdz/PXr0qNPu/z95/vw5DRkyhACQiooK7dmzp8pP348fPyYdHR0SERGhFStWVEoIcblcWrJkCQGgBQsW1Ph7qaenRxMnTuS7/eXLl4tVHRw8eDAZGRlVavyoqCiSlJSkefPmVep8hpqDEQMMDP8Y9dn9/ycBAQFkZGREAEhTU5M8PT0pNze3Sn2mp6eTs7MzsVgs+u+//+jt27eV6ic/P5+mTp1KAGpli9+KpBQWUFBF8OvXr7zXFi1aRMrKypW2Y9WqVSQiIkKhoaGV7oOh+mHEAAPDP0BMTAwdOnSILC0ti7n/b9++Xefd/4Xhcrl0/fp16tGjBwGgtm3b0unTpyk/P7/Kfd++fZvU1NRIQkKCtmzZUuk+s7Ozafjw4cRms8nT07PKdlWGiqQUFhAYGEgAitRcOHbsWJXu65mZmaSiokIWFhaVOp+hZmDEAAPDX0iB+9/V1bWY+3/jxo31xv1fGA6HQxcvXqQOHToQAOrUqRN5e3sL5Dp+/fpFdnZ2BID69OlTqdoDBaSlpdHAgQNJTEyMLl26VGXbKktFUgoLKMgeePr0Ke+1V69eEYBKx0sQEZ09e5YA0I0bNyrdB0P1wogBBoa/hMzMzGLuf1lZWbK2tq537v/C5OXl0fHjx0lXV5c3Wfv5+QlMzFy+fJmaNm1KsrKydODAgSqlwiUkJFCnTp1IRkaG/P39BWJfZcjJySFpaWlau3Zthc4LCwsjAEVsz8jIIBaLVSUPB5fLpV69epG2tnaVl3EYqgdmbwIGhnpMbGwsr/b/7du3kZmZiVatWmHYsGGwsLBAz549a7X2f1XIycnB0aNHsXHjRnz+/BmDBg3CwYMH0a1bN4H0HxcXBycnJ5w9exbm5ubYt28flJWVK93f9+/fYWRkhISEBNy7dw+GhoYCsbMyPHr0COnp6TA1Na3QeVJSUgCAjIwM3muSkpJQU1Or0B4Ff8JisbBjxw4YGhpi//79mDlzZqX7YqhdGDHAwFAHICK8efMGPj4+8PHxwYsXL8Bms9GtWzesWLECFhYWaNOmDV+b5NRVMjMz4e7ujs2bNyM6OhrDhg3DuXPnYGBgIJD+iQjHjx+Hs7Mz2Gw2Tp48iVGjRlXpPQsJCYGRkREA4OHDh9DS0hKIrZXl+vXraNKkCdq3b1+h80oSAwCgo6NTJTEAAO3bt8fkyZOxfPlyjB49GoqKilXqj6GWEKSbgYGBgX8yMzPJ19eXpk6dSs2bNy/i/j927Fi9df//SUpKCq1fv54aNWpEQkJCZGNjI/ANfCIiIsjU1JQA0JgxYwRSDvjFixekqKhIOjo6FBUVJQArq05FUwoLyM/PL7FQ0Pz584vsWVBZ4uLiSFZWlmbMmFHlvhgECxMzwMBQBykp+l9dXZ2cnZ3rXfR/eSQkJNDy5ctJTk6OREVFaerUqfT582eBjsHhcGjPnj0kLS1NzZs3Jx8fH4H06+/vTzIyMtS5c2dKSEgQSJ9VpTIphYURExOjXbt2FXnt8OHDxYoRVZatW7cSm82udMomQ/XAiAEGhjpA4ej/jh07Fov+//DhQ72L/i+PmJgYmjt3LklJSZGEhAS5uLjQ9+/fBT5OSEgI9ezZkwDQ1KlTKTk5WSD9Xrx4kURFRWngwIGUlpYmkD4FwYEDB0hISKjS5Zfl5eVpw4YNRV579uwZAaAXL15U2b6cnBzS0tKivn37/nWf6foMIwYYGGqJ8tz/deVJU9B8+/aNZsyYQWJiYiQrK0uLFy+ult378vLyaMOGDSQmJkbq6up09+5dgfXt4eFBbDabrK2tKTs7W2D9CoIhQ4ZQjx49Kn1+ixYtaNmyZUVeS01NJQB09OjRqppHRERXr14lAHTx4kWB9MdQdRgxwMBQg8TExNDBgwfJwsKCJCQkirj/79y581e5//8kJCSEJk6cSMLCwqSgoEBr1qyp8Pa//PLmzRsyNDQkNptNc+fOpYyMDIH1vXHjRgJA06ZNE0ihI0FS2ZTCwrRu3Zpmz55d7HUVFRVauHBhVcwrgqmpKampqdXYpk0MZcOIAQaGaoTL5dLLly+Luf979uz517r//yQoKIhGjhxJLBaLmjVrRtu2bRPI2nNJZGVl0ZIlS0hYWJj09fXp2bNnAuuby+XSvHnzCAAtXbq0Tv7d/P39CQC9evWq0n0YGhrS1KlTi71uYmJClpaWVTGvCB8/fiRhYWFat26dwPpkqDyMGGBgEDCZmZnk4+Pzz7n//+TJkydkYWFBAEhVVZX2799frS71R48eUZs2bUhERIRcXV0F6mXJy8vjVSh0c3MTWL+CZu7cudSkSZMqCZWePXvSuHHjir0+e/Zs0tDQqIp5xXBxcSEpKSmKjo4WaL8MFYcRAwwMAqA8939dqbqWnp1H76OT6VVEEr2PTqb0bMFup8vlcunu3bvUv39/AkBt2rShI0eOVOv1p6Wl0cyZM4nFYlHnzp2L1NUXBFlZWWRlZUVCQkICWzOvLnR1dcnW1rZKfZiYmJCVlVWx193d3YnFYlFmZmaV+i/Mr1+/SFFRkSZMmCCwPhkqB1OBkIGhEhARXr9+zSv+8/LlS7DZbHTv3h2urq6wsLBA69at60Txn7C4NJx4Gom7IfGITMoEFTrGAqAiL4m+rRtjbGcVaCrJVGoMIsL169exdu1aBAYGon379jh37hysrKwgJCQkkOsoiVu3bsHe3h4/f/7Etm3bMHPmTIGOl5qaiiFDhuDx48e4fPkyzM3NBda3oImKikJwcDBWrFhRpX6kpKSQnp5e7HUdHR0QEUJCQipczKg05OTksGbNGkybNg0zZsxAp06dBNIvQ/XBiAGGf56srCzcuXMHPj4+8PX1RUxMDBo0aAATExM4OzvD1NQUCgoKtW0mj6ikTCy+9A4PwhMgxGaBw6VibQhARFImjj2NwOHH39BTQxHrrPTRQl6SrzG4XC4uXryIdevW4fXr1+jatSuuXr0KU1PTahVCv379wuzZs3H48GH0798f/v7+aNWqlUDHiI+Ph6mpKcLDw3Hr1i307NlToP0LmuvXr0NISAgDBw6sUj9SUlKIi4sr9rq2tjYA4MOHDwITAwAwefJk7N27F05OTggMDASbzRZY3wyChxEDDP8kMTExRWr/Z2VlQV1dHdbW1rza/yIiIrVtZjFOP4/ECu9g5P9PAJQkBApTcDzwSyIGuAXA1VIXo/5TKbV9Xl4eTp06hfXr1+PTp0+8CblPnz7V7g25ePEiHBwckJWVBXd3d0yaNEngY0ZERMDIyAgpKSkICAgQ6ORXXVy/fh1du3aFnJxclfqRkpIqVo4Y+P0U36xZsyqXJf4TISEh7NixA3379sXJkycxbtw4gfbPIFgYMcDwT1Cf3P+lsftuGLbcCq3UuRwugcMlLLz4DgnpOXDsq1nkeE5ODg4fPowNGzbg27dvsLCwgJeXF7p06SII08vkx48fcHR0xIULFzB48GDs3bsXzZo1E/g4Hz58gJGREURFRfHo0SOoq6sLfAxBk5ubi9u3b2Px4sVV7qs0MQAIZo+CkujTpw+GDx+OBQsWYMiQIZCWlhb4GAyCgREDDH8tZbn/XVxcYGJiUqfc/2Vx+nkkX0IgJfAMku8fg4iiCppN3ltimy23QtFIWgwj/1NBRkYGDh48iC1btiA2NhbW1ta4cuUK2rZtK+hLKAYR4ejRo3BxcYGwsDDOnDmDESNGVIsge/r0KQYNGoTmzZvj5s2baNq0qcDHqA4ePnxYqV0KS0JSUrJMMXDz5s0qj1ESmzdvRps2bbBhwwasWbOmWsZgqDqMGGD4q4iJiYGvry98fHxw584dZGVlQUNDAyNHjoS5uXmddf+XRVRSJlZ4B5fbLj81ASmPz4IlIl5u2+XewXh14ww8d25CcnIyxo0bh4ULF6J169aCMLlcIiIiMHXqVNy8eRPjxo3D9u3bq02Y+fn5wcrKCu3atYOvry8aNmxYLeNUB9evX0fTpk3Rrl27KvdVnmdgz549yMnJgZiYWJXHKoyqqirmzZuHzZs3w87ODmpqagLtn0EwMBEdDPUaIsLLly/h6uqKjh07onnz5pg+fTpSU1Ph6uqKjx8/IjQ0FNu2bUO/fv3qnRAAgMWX3vFiBMri110PiDVrDdEmGuW2zc7Nw9GPubC2tkZ4eDi8vLxqRAhwuVzs3r0burq6CA4OxtWrV3Hs2LFqEwLnzp2DmZkZevXqBT8/v3olBIDfYsDExEQg3pLyxACHw0FYWFiVxymJBQsWQEFBAfPnz6+W/hmqDiMGGOodmZmZ8PX1xdSpU6GsrIyOHTvCzc0NGhoaOH78OH7+/ImAgADMmzcPbdq0qdNxAOURFpeGB+EJ5QYKZke+R+anR2jY356vfllsIYi1bA+XFRvQsmVLQZhaLp8+fUKvXr0wc+ZMjB8/HsHBwRg0aFC1jXfgwAGMHDkSI0aMwJUrVyApyV8mRV0hMjISwcHBAlkiAH6Lgby8POTl5RU7pqOjAwDVEjcAANLS0ti4cSPOnz+Pe/fuVcsYDFWDEQMM9YKYmBgcPHgQFhYWUFRUhIWFBfz9/TFy5Ej4+/vj58+fOH36NMaOHQt5efnaNldgnHgaCSF22WKGuBwk+e2HdDsjiDZW5btvITYLx59EVtHC8snLy8O6devQrl07xMfHIyAgAHv37oWsrGy1jEdEWLduHaZNmwYHBwccO3asXnqEBJVSWICUlBSA32L6TxQUFNC4ceNqEwMAMGbMGHTp0gWzZs0Ch8OptnEYKgcTM8BQJyEivHr1ihf8VxD936NHD6xatQrm5uZ1PvpfENwNiS/XK5D++jryU39CafTaCvXN4RLuhsZjJXSrYmKZvH79GpMmTcK7d+8wd+5crFixAhISEtU2HpfLxdy5c+Hm5gZXV1csW7as3n5Grl+/jm7dulU5pbCAAjGQkZGBBg0aFDteXRkFBbDZbOzYsQOdO3eGu7s7pk6dWm1jMVQcRgww1BkyMzNx584d+Pr6Fon+NzU1hYuLC0xNTf+qp/7ySM/JR2RS8ae4wnCyUpH84ATkuo2EkGTxG3x5RCZmIiMnH1Jigr0VZGdnw9XVFZs3b4aenh6ePn2KDh06CHSMP8nLy4OdnR2OHz+OPXv2YMaMGdU6XnWSm5uLO3fuCCSlsIDCYqAkdHR0EBAQILDxSqJTp06YMGEClixZAmtr63oXw/E3wywTMNQq0dHRPPe/goICLC0ti7n/T5069de5//khIjED5YUNJt8/BraENGQ6WlRqDALwLbHkyaGyPHz4EO3atcO2bdvg6uqK58+fV7sQyMrKwrBhw3Dq1CmcOHGiXgsBQLAphQUUxEyUJQZCQ0NLjCkQJOvXr0dOTg5WrVpVreMwVAzGM8BQoxR2//v4+ODVq1cQEhJC9+7dsXr1alhYWEBLS6veunYFSW4+t8zjeUnRSH9zEw37TwEnLYn3OnHyQFwO8pPjwBKThJBE2fsSlDcOv6SlpWHRokXYs2cPunbtisuXL/NK3VYnKSkpsLCwwIsXL+Dj4wMTE5NqH7O6EWRKYQH8eAby8vLw+fNntGnTRmDj/knTpk2xZMkSLFu2DPb29jXyGWEoH0YMMFQ7Be5/Hx8fXL16tYj7f86cOTAxMfnnnvpLIicnB58+fcK7d+/w/v17PA+PBTStS23PSUsEiItftw/g1+0DxY5H77eDTEdLyA8oO8Pg7etXUJUxrJLL9saNG5g6dSoSEhKwY8cOODg4VOtGRgX8+PEDJiYmiIyMxJ07d9C1a9dqH7MmuHbtmsD3gShPDOjq/o4d+fDhQ7WKAQBwdnbGoUOHMHv2bFy/fr1ax2LgD0YMMFQL0dHRRYr/ZGdn84r/WFhYoEePHvUywlsQcDgcfP78Ge/fv8f79+95k39YWBgvylpFRQXabdsDREApE4JIo5ZoNHRJsdeT7x8DNzcL8gPsISxXdqU9IoLtCHNQXjbU1NRgYGBQ5Kdp06ZlTkiJiYmYPXs2jh49igEDBuDevXs1VlTm69evGDhwIDIzM3H//n3o6enVyLjVTWRkJD58+ABXV1eB9lueGGjUqBEUFBTw4cMHDB06VKBj/4m4uDi2bNmCoUOH4tq1a9WaYsrAH4wYYBAIXC4Xr1694gmAktz/NVXdrq5ARIiOjuZN9gU/Hz58QHZ2NgBAUVER+vr6GDhwIFxcXKCnpwddXV1etHfvzXcRUUoQoZBkA0hqFX8STn1+BQBKPPYnzWVFcf3NS7x+/RqvXr3C69evsXXrViQnJwMAlJSUigmEVq1agcVi4cKFC3BwcEBubi48PT0xceLEGlveeffuHYyNjSElJYVHjx79VVXtClIKBwwYINB+y0otBAAWi1XtGQWFGTJkCPr16wcXFxcMGDAAoqKiNTIuQ8kwYoCh0hR2//v6+iI2Nvafdf8nJiYWe9J///49UlJSAPy+Eevp6cHAwADjx4+Hnp4e9PT00Lhx4zIn0L6tG+PY04hy0wsrA3E5+HTXGzNuhcDW1harVq2ClJQUiAgRERFFBMKRI0ewfv16AL8LyIiJiSExMREdOnTAxo0b0atXrxoTAoGBgTAzM4Oqqipu3LgBJSWlGhm3phB0SmEB4uLiYLFYpXoGgN9xA0+ePBHouKXBYrGwfft2tG/fHrt378bs2bNrZFyGkmERUbl3mdTUVDRo0AApKSnVViiEoX5QkvtfU1MTFhYWsLCwQPfu3f9q939GRgaCg4OLPOm/e/cOP378AACIiIhAW1ubN9nr6elBX18fKioqldrPPSwuDQO33xf0ZfCYpZGKq6c8cOfOHUhLS8Pa2hq2trbo3r17sck9Li4OmzZtwt69e0FEaNiwIe+6xcTEoK+vX8SD0LZtW4FX/bt+/TqGDRuG//77D97e3iXmy9dncnJyoKCggCVLlmDRokUC719GRgarVq2Ci4tLicd37tyJ+fPnIyMjo0ZiPgDAwcEBx48fR1hYGBo3blwjY/5L8Dt/M54BhjIpcP8XRP+/fv0aQkJC6NGjx1/t/s/NzUVoaGixJ/0vX74A+P1Uo66uDj09PUyZMoU38WtqagpUDGkqyaCnhiICvyQK1DsgxGahWysFuNiZwcVuNCIiInDkyBF4eXnB09MTmpqamDhxIsaPHw9lZWV8/foV9vb2uH37NiZMmIBt27ZBXl4eqampCAoK4nkRnj59Ci8vL+Tn54PNZqN169YwNDQsIhIqG6h46tQpjB8/Hqampjhz5ky1Fi+qLR4+fIiMjIxqW0Mva+dC4LdnICcnB1+/foWGRvl7XAiCVatW4dSpU1i6dCkOHjxYI2MyFIfxDDAUIzMzE7dv3+YV/yns/rewsPir3P9cLhdfv34t9qQfEhKC/Px8AEDz5s2LPelra2vXWK37qKRMDHALQI6AUgABQEyYjdsuvdFCvug1cLlcBAQEwMvLC+fPn0d2djZat26Nr1+/onHjxjh06BCMjY3L7Ds7OxvBwcFFlhmCgoKQlZUFAGjZsmUxgdCsWbMylxl2794NJycnjB8/Hu7u7hAW/jufY+bOnYtTp07h+/fv1bLs0qpVK4wcOZK35PMnMTExaN68Oa5cuQJLS0uBj18au3btwqxZs/Dy5UsYGBjU2Lj/AvzO34wYYAAAfP/+HVevXv1r3f9EhB8/fhR70g8ODuYFVMnJyUFfXx/6+vq8iV9XV7dOCJ+TT79h8eXytzHml41D9THyP5Uy2zx//hyjR4/G58+fAfx+f8aOHQtbW1sYGhpWaLLicDgIDQ0tIhBev36NX79+Afgdyf6nQFBXVweLxcKqVauwcuVKuLi4YMuWLZVabqkv6OrqokuXLvDw8KiW/vX19dG3b1/s3LmzxOMFyz8LFy7EwoULq8WGksjLy0P79u2hoKCAgIAAps6IAGGWCRjKpCz3/5o1a3i1/+sjycnJRZ70CwRAUtLvwjwSEhLQ1dWFnp4eRo4cyZv8y0ujqy2ICI+Pb0Xyq5+Q62VT5f5EPlxH/zmdSz2el5eHjRs3YvXq1VBTU8ODBw/QqFEjHD58GEeOHMGePXugr68PW1tbjBs3Do0aNSp3TCEhIWhra0NbWxtjxozhXVdkZCRPGLx69QrHjh3Dhg0bAPwOVJSRkUFsbCyGDRuG8ePHg8Ph/LViICIiolpSCgtT1jbGQM1nFBQgIiKC7du3w8jICOfOnYO1den1NRiqB8Yz8A9R4P4vKP4TGxsLOTk5mJqawtzcvN65/7OysvDx48diT/vfv38H8HsCat26Nc+1X/C0r6amVmPBUYJg06ZNWLBgAfbv348GhqZY4R2MfC5VKIZAiM2CMJuFGZ0VsXaSGVq2bIk7d+4U+z6/fPkSkyZNQnBwMObPn4/ly5dDXFycdzw/Px+3bt2Cl5cXrly5AiKChYUFbG1tYWpqKhD3/c+fP/Hs2TMsWbIEQUFBaNy4MeLj4wEAoqKi0NPTK+JFaNu2LS9trj6zf/9+ODo6IiEhQeCZBAX0798fjRs3xqlTp0ptM3nyZLx58wYvXryoFhvKwtLSEkFBQfj06dNfGRNSGzDLBAwAfrv/C9b+66v7Pz8/H2FhYcWe9D9//gwu9/c6upqaWrF1fS0tLYiJidWy9VXj+PHjsLGxwbJly3i13KOSMrH40js8CE+AEJtVpihgswAuARrS+fCaPhAt5CXx+vVr9OnTB4aGhrh27RokJCSQlZWFlStXYsuWLWjbti08PDxgaGhYpm2JiYk4efIkvLy88Pr1aygpKcHGxga2trbQ0dGp9DVnZGRg+PDh8Pf3x4kTJzB8+HCkpaUVCVR8/fo1goODeYGKWlpaMDAwKCIS6pOwBYDBgwcjOTm5WjcLKogD8Pb2LrXNtm3bsGzZMqSlpdW4FyYsLAy6urpYtmwZli1bVqNj/60wYuAfhcvl4uXLl7z0v8Lu/wIBoKWlVdtmlkiB2/jPJ/2PHz8iNzcXwO8iOH8+6evo6EBGpuz6+/URPz8/DBo0CDY2NvDw8Ci2hBEWl4YD/h9w6t5biMg3BfD/x1kAVBQk0VerMQI81iDhy3sEBQXxbu4PHz6EkZERBgwYAGdnZ0ybNg2RkZFYsWIF5s6dW2GBGBQUBC8vLxw/fhyJiYno1KkTbG1tMWrUqAo95SYlJcHc3Bxv377F5cuXyyy8k5OTU2KgYkEMiIqKSjGB0Lx58zq5FFSQUrh06dJqXasfPXo04uPjcefOnVLb3LhxA6ampvjy5UutFHOaP38+du/ejZCQELRo0aLGx//b4Hv+Jj5ISUkhAJSSksJPc4YaJiMjg65cuUKTJ0+mpk2bEgCSk5Oj0aNH08mTJykpKam2TSxGXFwc3blzh3bs2EFTpkyhLl26kIyMDOH3RnokKytL3bp1I3t7e9q5cyfdvXuX4uPja9vsGuPVq1ckLS1NpqamlJubW2q7q1evEgAKDgknRc325Lx6O72PTqb07DxemwcPHhAAunz5cpFzz58/T2w2mwBQ9+7d6ePHj1W2Oycnh86fP09mZmbEZrNJXFycxowZQ35+fsThcMo8Nzo6mvT09EhBQYGePn1aqfHz8/Pp48ePdPLkSZo3bx7179+f5OXleZ8rRUVFGjhwIC1YsIBOnz5NISEh5dpVE9y+fZsA0Js3b6p1nAl29mTY35JeRSQV+5wUEBERQQDI19e3Wm0pjZSUFGrcuDGNGTOmVsb/2+B3/mY8A/WUAve/j48P/P39kZ2dDS0tLVhYWMDc3LzOuP/T0tIQHBxcrCRvwRqwmJgYtLW1izzp6+npoUWLFnXyCa4m+PbtG7p27YrmzZvj3r17kJaWLrXt+vXrsWHDBiQnJ6Nhw4ZYsmQJ5s2bV6xd7969kZWVhadPn4LFYuHatWuYNm0a4uPjkZOTg+nTp2PPnj0Cfc9jY2Nx7NgxeHl54dOnT1BRUcGECRMwceJEtGrVqkjb8PBwGBkZIS8vD7du3RLoTnZEhKioqCKBiq9fv+bFlkhLS6Ndu3ZFPAg6Ojo1Wh63OlMKw+LScOJpJO6GxCMiMaPIXhcsACrykujbujHGdlaBppIMiAiysrJYvnx5iZ+lmsDT0xN2dnZ4+PAhunfvXis2/C0wywR/GQXu/4LSvwXu/549e8Lc3LzW3f8FO+79WZI3IiICAMBms6GpqVlkTV9PTw/q6up/bc54ZUhMTET37t2Rl5eHwMDAckvtjhw5ErGxsbh//36Z1eX8/PxgZGSEs2fPwtvbG8ePH4exsTEOHDiAW7duwd7eHkuWLMGaNWsEfk1EhKdPn8LT0xOnT59GWloaevfuDVtbWwwfPhxhYWEwMTGBnJwcbt26BRWVslMeBcXPnz/x5s2bIgIhLCwMRARRUVHo6uoWWWZo165dtQUq6ujooGvXrgJNKaxIbEnB8Z4ailhnpY9hJn2gq6sLLy8vgdlTEbhcLjp16gQAePbs2V+bQVITMGLgLyAjI6NI8Z8fP37wov8Liv9UZdvZysDhcPDly5diT/qhoaG8HfdatGhR7ElfW1u7SFQ6Q3GysrIwYMAAhIaGIjAwEJqamuWe06ZNGxgZGWHnzp2QkJDAxo0b4eTkVKwdl8uFpqYmoqKiIC0tDTc3N4wfP573FLp582bMnz8fW7ZswZw5cwR+bQVkZmbi4sWL8PLygr+/PyQkJJCfn49WrVrh/v37tV6ONi0tDW/fvi0WqJiXlwcWi1VioKKCgkKVxoyIiICqqirOnz+PYcOGCeQ6Tj+PrFLWScuEZ0h5dQ1Pnz4ViD2V4dGjR+jRowc8PT1ha2tba3bUd5g6A/WU0tz/Y8eO5UX/18STNP1vx70/n/QL77inoKAAfX199O/fH7NmzYK+vn6RHfcY+IfD4WDMmDF48+YN7t69y5cQyMjIQGhoKM+Vy+FwSkyZjImJwfTp03mllD08PGBlZVWkzbx58/Dr1y/MnTsXcnJysLOzE8BVFUdSUhLjxo3DuHHj4O7ujunTp0NYWBghISHo2bMnrwRy8+bNq2X88pCRkUH37t2LuKZzc3OLBSr6+Pjw8vVbtGjBEwYFIkFZWZlvd//169chLCwssF0Kd98Nw5ZboZU6l/M/8RAq1xGZEuEgolpbruvevTtGjx6NRYsWYdiwYcyDaDXDeAZqmcLufx8fH7x584bn/i9Y/69u93/hHfcK/xRsYyslJQVdXd1iT/tKSkr/7Lq+ICEiODo64sCBA7hy5QrMzMz4Ou/p06fo0qULnj9/jo4dO0JISAh79+7F1KlTef16eHhg7ty5EBcXx+7du7F69Wo0adIEN2/eLNEOBwcHHDhwAGfOnMHw4cMFep2FOXr0KCZNmgRLS0scP34cT548gZeXFy5cuICcnBwYGRnB1tYWgwcPrpPpoRwOB+Hh4cUqKiYmJgL4LZT/FAiampolursFmVJ4+nkkFl58V+V+CljQRxnTjdsJrL+KEhUVhdatW8PJyYlXjIqhYjDZBHWY9PR0unz5MtnZ2VGTJk0IADVs2JDGjBlTrdH/6enp9OzZM/L09CQXFxcaOHAgL/sAAImIiJC+vj6NHj2a1q5dS97e3vTly5c6EW39N7Nu3ToCQIcOHarQefv37ychISHKzMwkLpdbpI/Pnz9Tv379CADZ2tryPlOnT58mAPTs2bMS++RwODR69GgSERGhGzduVO3CSsHNzY0AkJ2dHeXlFY1mT05OpoMHD1LXrl0JAMnLy5OjoyO9fPmSuFxutdgjKLhcLkVGRtKVK1doxYoVZGlpSS1atOB9v6SkpKhbt27k4OBAHh4e9OrVK0pNTSUpKSlav359lcePTMwgraXXqMXsc9Sg+2gSVzMktrg0ASCFQc7UcqFvsZ9mk/eRuJohsUTEiS0uTVK6fUnZ6QS1XOhLKgt8SGOxL0UmZgjg3ak8K1euJFFRUQoLC6tVO+or/2Q2QUZOPr4lZiA3nwtRYTZUFaQgJVY3VkKioqKKFP/JycnhRf8L2v2fl5eHkJCQYkV6vn79ynP7tWrVqtiTvpaWVp3IQPiXOHLkCCZOnIiVK1dixYoVFTp3xowZCAgI4BXfERERgbu7O1JTU7FkyRIoKSnhwIEDMDIy4p3D4XCgo6MDbW1tXL58ucR+8/LyYGVlBX9/f/j5+QksmpuIsGzZMqxduxYLFizA+vXry/Qsffr0CYcPH8bRo0cRGxuLtm3bwtbWFmPHjuWrBHJdISEhAW/evCniQQgNDQURQUhICBwOB4MHD0b//v1haGiIdu3alZlBUho2Hk8R+CUROUk/EL3fDkKyjSAs1wQ5ke+gMMgZ0m2LLkPkpyYg1ssJbDEpyHS0AOVmI/XZRQjJNkLTCdvAEhIBC4QeGo1wzK708tXVTWZmJtq0aQNDQ8NSP7MMpfPPBBAWTpuJTMpE4YspKW2mpuByuXjx4gVv/b863P9cLhffvn0rVqQnJCQEeXl5AIBmzZoVi+DX1tb+K8q31ndu3rwJc3NzTJw4EQcPHqzwkkv37t2hqqqKEydOICcnB+Li4lBXV8eXL18wc+ZMrF27tsRJ5fDhw7C1tcXbt2+hr69fYt9ZWVkwNTXFmzdvcO/ePbRv374yl8iDw+HwliA2b96MuXPn8n1uQQlkT09PXuU8c3NzTJo0CSYmJvUyGyU9PR1v377FsmXL8OTJE2hpaRUJVNTU1Cy2zKCoqFhqf2FxaRi4/T4AgPLzwM1Oh5B0Q+TEhuHHEZcSxUDizb3IeHcHzabsg3CD34GbWd/eIP70UsibOEKmvQmv7W2XXtBoXHuFvc6cOYNRo0bh1q1bGDhwYK3ZUR/568VAVdJm/ty2VVAURP8X1P7/8eMHGjZsyIv+NzY2rlT0PxXaca/wk/6fO+79WZlPT0+v3pVk/Vd4+fIlevfujT59+uDy5csVntC4XC4vF9zZ2RmrV6/GmjVr0KxZM5w7dw7dunUr9dy8vDxoamqia9euZdaoT01NRb9+/RAVFYUHDx5UWrzm5OTAxsYGFy5cgLu7e5UiwxMSEnglkN+8eYMmTZrwSiALsjZBTaGjo4Nu3brB3d0dubm5+PDhQ7GKiunp6QAAZWXlIrs6Ghoa8upxrPQOxrGnEcXug2WJgaid4yCuoodGQ4pWPIw+OBXCMopQGr0WwO/7p03nllhpqVuN70TZEBF69eqFpKQkBAUF1UsBWFv81WKgqmkzrpa6GFXO9q38UuD+L4j+z8nJQevWrXm5/xV1/ycnJ5dYpKcgMElcXJy3417hyb+8/eAZ6g5fv35F165d0bJlS/j7+1fKSxMeHg5NTU3s3LkThw4dwsePH5Gfn4+jR4/Cxqb8nQ3379+PGTNm4OPHj2XuTpmQkICePXsiMzMTDx8+rHB52PT0dAwdOhT379/H6dOnMWTIkAqdXxZv3ryBl5cXTpw4gcTERHTu3JlXArk+ZLTwk1LI5XJLDFRMSEgAAMjLy8PAwACxHachg1V8Y5/SxEB+WgKi90yEXJ+JaNClaKBogs9WZH1+gRbO/y8UWypIImBuX0FcdqV59eoVOnbsiJ07d8LR0bFWbalP/LVioCppM4WZa6QFx77lp2/9SYH7v6D4z5/ufwsLC77SwgrvuFfYzV94xz0tLa1iT/qtWrWqVzvuMRQlISEB3bt3B5fLxaNHjyqdV3/ixAmMGzcObDYb7du3h5ubG3r37o1z587xlQWQnZ2NVq1awdjYuNzCMt+/f0ePHj0gLi7O286YHxITEzFo0CB8/PgRV65cQd++1TOZ5OTkwNfXF56enrhx4wZERUUxdOhQTJo0CX379q2zBWv279+PmTNnIiEhoULihf6X9lsgEF4EvcdbrQklPgyUJgZ4r5vPhrRevyLn/LrridSnF6Ey9xJYwr9jiFgA3q80rvUYrClTpuDChQsICwurcn2Hf4W/ss7A6eeRpQoBbm4WUp9eRE5MCHJjQ8HNTi/RNVbAlluhaCQthpF8eAgyMjLg5+cHX1/fYu7/BQsW8KqnlUR+fj7Cw8OLPemHh4fzdtxTVVWFnp4exo0bx5v8W7duXSdTqhgqT2ZmJiwsLPDr1y88fvy40kLg3r17mDlzJgBg3bp1mDNnDi8NlF8vlLi4OObNm4f58+djxYoVUFVVLbWtsrIy/Pz80LNnT5iYmMDf37/cyev79+8wMjJCQkIC7t27V+4OiFVBTEwMw4YNw7BhwxATE8MrgXzy5Em0bNmSVwK5NjbdKYtr166hW7dufAkBLpeL3Nxc5OXlIS8vDyIiIjAwMICenh46/UjHdO/ICo1N+TkAAJZQ8YBhlpAor02BGCAA3xIzoNusdj0ua9aswdmzZ7Fy5Urs2rWrVm3526g3YiAqKRMrvINLPc7NTEXKo1MQkm0EkcZqyIksP9d2uXcwuqkrlhhDUJr7f9y4cbza/4VvvFRox73CT/qFd9xr3Lgx9PT0YGpqynvS19XV/St33GMoSn5+PkaPHo13797h3r17UFdXr3AfKSkpmD9/Pg4ePAh5eXn06NEDCxYsAABe9ceKeI3s7e2xbt06bNq0CXv37i2zraamJm7evIk+ffrA0tISN27cKHW/+ZCQEF4Gw8OHD2u0THazZs2wYMECzJ8/H0+ePIGHhwe2bduGVatWoXv37rC2toaxsTFERER4E2vBT+HJtqwfQbTLycnBs2fPoKSkBF1d3XL7KnhwKAnRplpoOmFbhd4nlvDvBw3i5BU7RpzcIm0KyM0v3YaaQklJCcuWLcPChQsxdepU6Onp1bZJfw31RgwsvvQO+WUFCUrLQ9nxWJEI2vLI5xIWX3qHY3adi7j/fXx8EBQUBCEhIfTq1Qvr16+Hubk5z/3/8+dP3L9/v1iRnrS0NAC/q5jp6emhU6dOmDRpEq8yX22XWmWoHeh/xXyuXr0KHx8fdOzYscJ9+Pr6Ytq0aUhJScGePXuwfv36IkGC+fn5AComBqSkpODi4oJVq1Zh6dKlaNasGc9eDodTbEJr2LAhDhw4gAkTJsDY2BhbtmwBERVp8/HjR6xYsQKysrKYN28eAgMDERAQUOOTbcFP4VXQR48e4dGjRxV+7wsjLCwMERGRcn9ERUWLvSYmJgZpaWmIiIjg58+f4HK56NmzJ5o2bVqhPvPz85GQkIAfP34gLi4OX5Pz8K2C1yEk/TuQmZOeVOwYJ/0X2OIyPK9AAaLCdWO5xcnJCQcPHoSzszP8/PyYWCkBUS/EQFhcGh6EJ5TZhiUswvuA8wuHS3gQnoBR9s64530acXFxPPf/woUL0b17d15J3t27dxfbcU9UVJS3497gwYN5T/sqKirMB/QfhIiQn59fbKLatm0bDh48iDVr1qB58+Z4+fIl3xNaUlISzp07h1evXkFLSwsjRoxAeHg4vn//jnfv3sHR0RF5eXn49esXAGDjxo1wd3fneyLNzc1Fbm4uLxal4Hh5PHjwAJ07l557npqailmzZvH+X9kJVEREBBISEpCVlS23HT99JiUl4d69e/Dz80N8fDxatGgBS0tLDBkyBM2bNy+3P0F9r+fMmYMPHz7g9OnTJfaZlZWFz58/IywsDKGhoQgLC+P9+8ePH7x2CgoKUG+jA7SmIrsRloewjCLYkg2Q+yO82LGc2FCIKhVdUmEBUFWoG+nIoqKi2LZtGywsLODt7Y3BgwfXtkl/BfVCDJx4Gllu+mBlIS4Hz3+Jw9jYGCoqKrz0noULFxbZcU9DQwN6enqYNm0ab11fQ0ODSXERAERUK65aQbcreDovjaVLl2Lp0qWVeo8kJSWRlJSEs2fP8pYEQkJCEBMTAxEREZ4bOS0tDZKSkhAREYGUlBRfE+i9e/fw6NEjLF26FPLy8nxNsg8ePMDSpUsxfPhwuLq64t69e3B2dkaXLl1w5MgRNGzYkNdWWFi4TonjyZMng8vl4t69e/Dy8oKHhwf27dsHY2Nj2NrawtLSstrjda5du4aBAwfyJvo/J/zv37/zvBqysrLQ1NSEpqYmevfuDS0tLd7/C1KHe2++i4ikzArZINm6GzLe+SM/9SeEZX8HhWZ9e4P8pGjI/ld0glVRkKz14MHCmJmZwdjYGLNnz4aJiQkTXyUA6s5ftwzuhsRXixAAABZbCNkK6jh6YCOA38FS+vr6sLa2LrLjXmnro7UJl8ut05Mjv+0KJjdBwWazK/UEWvAjLi5eoSfQ0tq9ffsW69atg4mJCebMmQMxMTG++ouLi4OLiwuuXr0Ka2tr7Nq1q8gS0/bt27Fo0SKEhITwxGhYWBi0tLSwbds29OnTp0Lvl4ODA1RVVZGdnY0ZM2bwdU7Pnj3RpEkT2NnZIT09HTdv3sTw4cNx9OjRenFjZrPZ6NevH/r164fdu3fjzJkz8PLygrW1NeTl5TFmzBhMmjQJBgYGVRqHw+EgIiKiyIT/9u1bfPr0CaGhoTh8+DAAQEJCgjfBjx07tsiE37hx43LFVN/WjXHsyTdw/nebTH3pA252Bm8ZICv8GfLTfntXZTtYgC0uhQZdrZH56RHiTi6GTEdLUN7vIGyRRqqQ1v//wj7E5aBLi7oV18RiseDm5gZ9fX1s376dFzvDUHnqvBhIz8lHZAUVb0URadgUJ89egLZmK0hISBSZqLKysvD06dNam0jLalNWUFFlEBISqtTkWfAjKSlZ5QlUEO3qQirZ8+fPMXHiRJiZmeHixYt8eZC4XC7c3d0xb948SElJ4dKlSyXm5b958wZ6enpF+qxMAGEBioqKmD59Onbt2sXbtZAfJk2ahEuXLsHX1xddunTByZMn62Xaa4MGDWBvbw97e3t8/PiRVwJ59+7daNeuHa8EcmkVALlcLqKjo4s94YeFheHz58+8ZRdRUVGoq6vzlhu2bduGtm3bQlNTE82aNav05zYrKwvZwbfBIQ3ea6lPL4GTGs/7f2ZoIBAaCACQ1u0LtrgUhGUbQWnMevzyd0dywGGw2MKQ0PgPDfvZFYkXYLGF0F46rVK2VSfa2tpwdHTEmjVrMH78eDRt2rS2TarX1Pk6A8ExKTDb9bBC55RVdas0YjxnIi/+a2VMLDGoSNCTXXVPoMLCwnViEv0b+Pz5M7p27YpWrVrB398fkpLlV7wMDw/HlClTcO/ePdjZ2WHLli2lTsoGBgbo0KED3N3dea8FBwdDT08PgYGB6Nq1a4Vtjo2NhZqaGpYtW4YlS5aU256IsHDhQmzatAk9evTAw4cPceDAAdjb21d47LpIfn4+bt68CS8vL3h7e4OIYGRkhF69ekFeXp63nh8WFobw8HBkZWUB+C3G1NTUeE/1hZ/wVVRUICQkBEtLS6SmpuLevXtVspHD4eDo0aNYvnw5YmNjoTRqNYSb64LFFpwgE2IBGV9fY0UvBUyfPl1g/QqKX79+QVNTExYWFuXWy/hX+WvqDNRUOsvO3XuhpVD+JPrnRFvX1kMZapefP3/y6k74+vqWKwTy8/Oxfft2LFu2DE2bNsXt27fRv3//UtsXxLTY2dkVeb0qngEAaNq0KSZPngw3NzfMmjWrzI1y8vPzMW3aNHh4ePDaOzk5Ydq0aWjQoAFGjhxZKRvqAomJiUXW7oWFhaGtrY2QkBBcu3YN165dA/B7HV9XVxc9evTApEmTeBO+mpoaRERK3+wrJycHd+7cwfLlyyttIxHB19cXixYtQnBwMDQ1NcHhcNA85j6SVdshlyOYJdXfAbF5EAu6iA+KgtmsStA0bNgQq1evxowZMzBjxgz8999/tW1SvaXOi4GaSmdZungh1OXFoKGhAU1NTd7v5s2bM5WuGPgiIyMD5ubmSEtLQ2BgYJkbywDAu3fvYGdnhxcvXmDWrFlYs2ZNuaWJP336hNzcXLRrV3SP+cqkFv7J/PnzceDAARw4cABz5swpsU12djbGjBkDb2/vIqWPd+zYgeTkZIwbNw6ysrIwNTWttB3VTWpqapEJv7BbPynp/1PtmjVrBk1NTXTq1Im3jp+fnw9/f3+cOXMGjx8/BhGhffv26NGjB1/Fg+7fv4/MzMxKvz9PnjzB/Pnz8eDBA7Rv3x5NmzbF9+/f4ebmhpkzZ+Lcq2gsvFh+jRV+YLFYUIq+j2cfX+NSajw2btzIl5erppkyZQr27duHWbNm4dGjR8zDWSWp82JAVUEKLADVEz5YAGHmxFGI+Pz7xnDnzh3ExcXxjjZs2LCYSCj4LS8vz3z4GJCfn4+RI0fiw4cPCAgIQKtWrUptm5OTg3Xr1mHdunXQ0tJCYGAgunTpwtc4QUFBAIC2bdsWeb3AM1CV7BYVFRWMHz8eW7ZsgYODA8TFxYscT01NxZAhQ/D48WNcvnwZ5ubmvGNsNhuenp5ISUnBsGHDcPPmTfTs2bPStlSVzMxMhIeHlzjpF/5uKyoqQktLC23atIGFhQXPra+hoVGqd2T48OFwc3ODj48PvLy8MH36dDg7O2Po0KGwtbUtswTy9evX0bx581J3iyyNkJAQLF68GBcvXoSenh5MTExw48YN9OnTB+7u7rwiVqP+U0FMUjp23vsKUMXSDf9knlFrzOgzCIN+fcKNGzdgaGiI48ePV6pORnUiLCyM7du3o3///jh16hTGjBlT2ybVS+p8zADAf9pM4Qja9NfXIKnVDSJKv2/KBRG0JVHSJhxpaWkIDw/n3VAK/y6c5ysnJ1eiSGCEwr8DEcHe3h6HDx/G1atXedX3SuLp06ews7Pj3dwXL15coej7OXPm4NKlS/jy5UuR1588eYKuXbvi3bt3VarKFhYWhjZt2mDXrl1FMgt+/vwJU1NThIeHw8fHp9SJPjs7G6ampnj16hXu3btX5Wj8ssjJycGXL19KnPAL9vgAfgcIFl67L/xvfoMlyyI6OppXAjk0NLTMEsja2tro0aMHDh06xFffsbGxcHV1hbu7O5SVlTF8+HCcOnUKaWlp2Lx5M6ZMmVJMeEyZMgUXg35AwWg6OIRKbea2ylKXV6q9YPvgdu3aITg4GMuXL8eiRYvqXFr1sGHD8PTpU4SEhDBbtBfir9qoqLTtOf/k+95JRSJoC9N8mgeE5ZSKH+By0F2JiyNO5nx/uNPS0ngBRH+KBX6EgoaGBhQUFBih8Jfg6uqKlStX4siRIxg/fnyJbTIyMrBs2TJs374dHTp0gIeHR7Gne34YMGAAZGVlcfHixSKvP3z4ED179sSHDx+qvJXvmDFj8OjRI4SHh0NERASRkZEYOHAgUlJScPPmzWJLFH+SlpaG/v3749u3b3jw4EGZuyKWR35+Pr59+1bihB8REcHLqJGUlCwyyRee9BUVFWvku0ZEePz4Mby8vHDmzBmkpaWhb9++sLW1xbBhwxAfHw81NTVcuHABQ4cOLbOv1NRUbN68Gdu2bYO4uDhcXFzw4cMHnDp1CsbGxjh48CBUVIrvq3Lu3DlYW1vD3d0dRlajBbLN+7t379C2bVvcvXsX/v7+WLt2LTp16oRjx45BQ0Oj1D5rmi9fvkBHRwfz58/HqlWratucOsNfJQbC4tIwcPv9aus/+tA0NJcWwqxZs2BnZ1ela0xPTy/VoxAbG8trJycnV+rSAyMU6g/u7u6YMmUK1q1bh0WLFpXYxt/fH1OmTEFMTAxWr14NZ2fnSj1VEREaNWqEmTNnYsWKFUWOBQQEoE+fPggJCanyXgDv37+Hvr4+PD090blzZxgZGUFUVBR+fn5876mQmJiIXr16IS0tDQ8fPixx4iqAy+UiKiqqyNp9waT/5csXXjyEmJgY1NXVS3zKb9q0aZ36zmRkZODixYvw8vLC3bt3ISMjA319fTx9+hSJiYmlxhfk5uZi//79WL16NdLT0+Hs7AxtbW3MmzcPubm52L59O8aPH1/itUZERKBdu3YwMjLCmTNneG3C4tJw4mkk7obGIzIxs8iSKxGhkThgbqiGcV1UoNG4eD2BnJwcSEpKYt++fbC3t8fjx49hY2OD2NhYuLm5YcqUKXXmvV+yZAm2bduGjx8/lrn51r/EXyUGAMDG4ykCvyQKtPiQEJuFbq0UMNvwd3nL06dPQ1JSElOmTIGTk1OZN7DKkJ6eXqpHobBQaNCgQakehZp6ymEoH19fXwwZMgT29vbYs2dPsb9LcnIy5s2bB3d3d/Tu3Rvu7u5VepKKjo6GsrJyifUH/P390b9/f3z+/LnMeAV+sbKywsuXL5GRkYHmzZvj5s2bFc7jjo6ORo8ePSAqKor79++Dy+UWq7RXkIufnZ0N4Pf6r5qaWokTvrKycr2sY/D161ccPnwYmzZtQnZ2Nlq3bg1bW1vY2Njw9oPgcrk4c+YMlixZgoiICEyaNAkODg5Ys2YNLly4gMGDB2Pfvn2l/g3y8/PRp08ffP/+HW/evCl1+SMjJx/fEjOQm8+FqDAbZr07wcp8ENzc3Mq8htatW8PU1BTbt28H8PteNmfOHBw8eBDm5uZwd3eHklIJntcaJj09HVpaWujRowfOnj1b2+bUCf46MRCVlIkBbgHIEWCqoZgwG7ddevNcYtHR0di1axcOHDiAtLQ0jBgxAnPmzKmRgJkCofCnSChJKJTmUWCEQuX58yapqiBVZvnVZ8+eoW/fvjAyMsL58+eLTVJXrlzB9OnTkZ6eXurabkW5du0azMzM8PXr12JPPX5+fjAyMsK3b9/QsmXLKo0DAHv27IGjoyO0tLTw5MkTNGxY/r4fRITExMQiE/6rV6/g5+cHLpfLc+mzWCy0bNmyRLd+y5Yty0zNq69kZ2dDQUEBY8eORWZmJi5cuIDc3FyYmJigQ4cO8PX1xevXrzF48GCsXbsWr1+/xqxZs8Bms7F7925YW1uX+d1euXIlVq9ejfv376N7d/7TACdOnIi3b9/i1atXZbazsrJCRkYGbt26VeR1Hx8fXnnnQ4cOlVgkq6Y5duwYxo8fj3v37qF37961bU6t89eJAQA4/TxSYGkzALBxqD4vSKYw6enp8PLywvbt2/Hlyxf07NkTc+bMgbm5ea08mWRkZJS69BATE8NrxwiFisFzn4bEIzKpqPuUBUBFXhJ9WzfG2M4q0FT6f/dpeHg4unbtCi0tLdy+fbtIqer4+Hg4OTnhzJkzMDMzw/79+6GsrCwQewu2G/7161exv+X169cxaNAgREVFVXm8c+fOYezYsWjQoAEaN26Md+/eFREyycnJRVz6hZ/yk5OTee2aN2/O++xdvXoVqqqqOH78OHR1detFyWJBUiDW3r59C319faSkpGDz5s3YvXs3UlJSICwsjMGDB2Py5MnYvXs3rl69ilGjRmHnzp1o1KhRmX0/ePAAffr0wYoVKypcv8DT0xOTJ0/Gr1+/ykyNXLJkCY4cOVIkMLOA+Ph4TJkyBd7e3pg0aRK2b99eq9uyc7lcdO3aFbm5uXjx4kW99CYJkr9SDADA7rth2HIrtNLnExFYLBbmGbWGQ9+yXbYcDgdXrlzB1q1bERgYCA0NDbi4uGDChAl1Jlo1IyOj1KWHwkKhYLOTksRCo0aN/imhEJWUWenAKtG8NHTr1g0iIiJ49OgRrwYFEeHEiROYNWsWWCwWdu7cidGjRwv0fR05ciR+/PiBgICAYsd8fX1hYWGB2NhYNGnSpNJjHDhwANOnT8eIESMwcOBATJkyBWPHjoWIiAhvwv/58yevfePGjYtF6GtpaUFdXb3Id+TJkycYMGAAevbsiStXrkBUVLTSNtZHZs+ejbNnzyIqKgrfvn3D0qVLcfLkSbRp0wYzZsxAREQEDh06hNTUVAgLC2PChAnYsGFDubUqfv36hXbt2kFVVRV3796t8MT3+fNnaGhowNfXF2ZmZqW2O3HiBMaNG4fk5OQSRQMRwcvLC7NmzUKjRo1w7NixCnkoBE1Bds3BgwcxZcqUWrOjLvDXigHgt4dghXcw8rlUoRgC4nLA4nKQft8Lgce2VCjQ6smTJ9i2bRsuXLgAOTk5TJs2DY6OjnW6HnaBUCjJoxAdHc1rJysrW6pH4W8TCpX97BSkXIm8vYzEZ954/Pgxz1UfFRWFadOm4dq1a3w/zVWG1q1bw9jYGDt37ix27MqVKxgyZAji4+P5Hjs7OxtfvnxBaGgoQkNDce7cObx48QJSUlLIyMjgtRMSEkKHDh2KufU1NTX5KrRTwO3bt2FmZoYhQ4bU230MKou2tjY6duwIBQUF7N27F4qKinB1dYWtrS2ioqIwZcoU3LlzBwMGDIC4uDhu3rwJALC0tIStrS2MjY2LBZ0SEUaMGAF/f3+8efOmUjFORARlZWWMGzcOGzduLLXd69evYWhoiMePH5dZE+PLly+wsbHBkydPsGDBAqxcubLWhN/48eNx48YNhIaGCiSFtL7yV4sBoHJPdy1FMxG4YyaayopCTk4OT548qXBFrW/fvmHHjh1wd3dHTk4OxowZg9mzZ1cqTaw2ycjI4OVoF45PKE0olFRHob4Jhap6lQqKuIzVl8XaMT3B5XJx4MABLFiwADIyMti3bx8sLS0FZ3AhMjIyICMjA3d3d0yaNKnY8QsXLmD48OFITEzkbWsLAHl5efj27VuxSnuhoaGIjIzkbZMrIiKCvLw86OrqYsiQIbyJPyYmBsOHD8eNGzdgbGxc5eu4ePEiRowYATs7Oxw4cKBefX4qS8G+ERISEhAREcGCBQvg7OwMcXFx7N27FwsXLoS8vDwOHTrEe49//vyJkydPwtPTE2/fvkXTpk1hY2MDW1tbtGnTBgBw6NAh2Nvb85WqWBajR4/Gt2/f8Pjx41LbZGZmQlpautTPX2E4HA42bdqE5cuXQ09Pj7c0VNNER0ejdevWmDp1KrZu3Vrj49cV/noxUEBZaTMs/N6Hu69WY4zrogI1BUl069YNiYmJiI6OxsiRI+Hl5VWpG1JKSgoOHTqEHTt24Pv37xgwYADmzJkDY2Pjen+DK0koFPwuLBRkZGRKXXrgZ9vVmkTQ8SazeyjhwqY5uH//Puzt7bFp06YKPSVXlAK354sXL9ChQ4cixzgcDvbt24eZM2diy5YtvDS90NBQfP36lVedUFxcnPc3Kpjs1dTUsH//fpw/fx67d+8utoUxEaFLly4QExPD/fuCSe89fPgwbG1tMX/+/DKfRus7+fn58PT0xPz585GSkoIZM2bA1dUVioqKCA0NhZ2dHR4+fIjp06djw4YNJd5biQivX7+Gl5cXTp48iaSkJHTp0gUmJibYuHEjbGxscODAgSrZuX//fsycORPJycllLn+qq6vDysoKW7Zs4avfV69eYdy4cfjy5Qs2btyImTNn1vhmaOvWrcOKFSvw/v37KtW7qM/8M2KgMPxEhL99+xaGhoYYMmQILly4gEOHDmHy5MmVHjMvLw/nz5/H1q1b8fLlS+jo6GD27NkYO3ZssXKufwOZmZmlLj0UDi6SkZEpdemhpoVCeZkoeUnRSH5wHDnfP4CblQ4h2UaQ0ukN2c5WYIuU9DckUH4uhG9ugPuOjejbt28JbQTL/v374eDggGvXriEiIqLIE/7nz5+Rm5sL4PcTfqtWrYqt4xek5hW+GWdlZWHkyJG4fv06jh49itGjR5c4to+PDywtLREQEIBevXoJ5Hp27NgBZ2dnrF+/HgsXLhRIn3UFIsLly5exaNEihISEoHnz5lBWVsaTJ0+Qn58PNzc3LF++HM2bN4e7uzv69OnDV785OTnw9vaGu7s7bt26BRaLhZEjR2LKlCno06dPpSfaDx8+QFdXF35+fhgwoPRdXi0sLMDhcHibNfFDVlYWFi1ahB07dqB///44fPiwwAJq+SE7Oxva2trQ0dHB1atXa2zcusQ/KQb4ZeHChdi+fTuGDBmCy5cv4/Hjx1Uum0pEePDgAbZu3QofHx80atQIDg4OmD59erWsH9dFMjMzS/UolCQUShILSkpKAhcKZdWoyE/9iVgPR7DEpCBjYAq2hAxyoj8h491tSGh0RuPhy0rsk0VcdFVXwMkp3QRmJxHh58+fxSrthYaG4sOHD7ziO2w2G6qqqkUC9iIjI7FlyxakpaWVueNgASkpKbCwsMCLFy9w8eJFmJiYlGlX+/bt0aRJE95atiBYuXIlXF1dsXfv3jq5PW5lePjwIebPn4/Hjx/D2NgYK1euRP/+/bFixQoMGjQIkyZNwosXL+Di4oLVq1dXauOfWbNm4cCBA5g6dSquX7+OsLAwqKqq8kogV7TYDhGhcePGmDZtGlavXl1quwULFuDMmTP49u1bhW2+ffs2Jk6ciIyMDOzbtw+jRo2qcB+V5eLFixg2bBiuXbtWpzfQqi4YMVAGmZmZ0NfXh7KyMtLS0pCSkoKXL18KLMgkNDQU27dvx+HDh0FEGD9+PFxcXHhrff8iWVlZpdZRKCwUpKWlS/UoVEYolFe9MiXwLJLvH0VTuz0QbfT/+fkJvtuQ8d4fys6nISRe+uR626VXiVXbyuLXr18lTvhhYWFITU3ltWvRogVvwr9x4wZatmyJAwcOoFWrVsWCsgpc77m5ueXm6f/48QMmJiaIjIzE1atX0bVr13JtPnv2LEaOHImnT5+iU6dOFbre0iAiODs7Y9euXThx4kSpnon6wIcPH7Bw4UL4+PjA0NAQmzZtQv/+/XkphQ4ODjh48CDU1dXh6enJ13teEgVZIzt37sTMmTNBRAgMDOSVQE5PT0e/fv1ga2uLoUOH8i02hg0bhoSEhBIzVQo4cuQIJk6cyLfg/JOkpCTMmDEDZ86cwejRo7Fnzx6+6ldUFSJC//79ERMTg3fv3v2VdSzKghED5VDwJd24cSPWr1+PXr164fLlywJ9Kk1MTMT+/fuxe/du/PjxA2ZmZpgzZw769OlTp9bTa5vShEJ4eDiioqJ47SojFMrb1+LXvcNIfXIeyk4nICTZoOjrTy+ihctZsEVLXu4RYrNg07klVloWD45KT08vcYvc0NBQJCYm8to1adKkxA101NXVeTdyLpcLWVlZrFixAvPmzSvRFg8PD0yePBkcDqdMd/HXr18xcOBAZGZm4tatW3xvasThcKCrq4vWrVvjypUrfJ3DD1wuF5MmTcKJEydw+fLlMtPb6iLfv3/HihUrcPjwYaiqqmLt2rWwtrbm/Q3Gjh2Lc+fOgcvlYsGCBVi2bFmllw9jY2PRtm1bdOnSBd7e3sU+7xkZGbhw4QK8vLxw7949yMrKYuTIkbC1tUWXLl3KvOfs3LkT8+fPR3Jycqn2PX/+HJ06dcLz58+rVIjt1KlTmD59OqSlpXHkyBH079+/0n3xy9u3b2FgYICtW7fC2dm52serSzBigA9sbGxw9epV7NixA+PHj8fGjRsxf/58gY+Tk5ODU6dOYdu2bXj37h0MDAwwe/ZsWFtb/3P51hUlKyur1KWHkoTCnyJh4aNsRKfklt7/l5eIP7sCEhqdIddz7P+WCT4i8cZuSOsPhPyAsnOUm0oLY75OZrGn/MIbVikoKJS4gY6GhgZf36ewsDBoaWnh5s2bpe6IePDgQUybNo1X5a8k3r17B2NjY0hJSeHWrVvFdtQrj4Inw6CgIIFmz+Tn52PEiBG4ceMGbty4US+qxiUnJ2PDhg3YsWMHpKWlsXz5ckydOpX3fc7OzsaqVauwfv16yMvLw8/PD4aGhpUej8vlwtjYGMHBwQgKCip36fHLly84cuQIDh8+jMjISLRp0wYTJ04sUgK5MG/evIGBgUGZcSHp6emQkZEpc0MufomKisLEiRPh7+8PZ2dnrFu3rkjxrupg+vTpOHXqFMLCwv6ZpVuAEQN88fPnT7Rp0wampqZo0aIFNm/ejDt37lTbzYiIcPv2bWzbtg03btxAs2bN4OTkBHt7+xpxl/1tFAiFUj0KIuJo4XK2XC9M8qPTSH18DpSfw3tNtttINOxlU64NRISobSMgLS5S6ja5hVP9KsP58+cxYsQI/Pjxo9T673v37sWsWbOQl5dX4vHAwECYmZlBVVUVN27cqFQd+by8PGhpaaFz5844ffp0hc8vi+zsbJiZmeH58+e4e/dusYyJukJ2djb27NmDtWvXIicnB3PmzMHcuXOL3BcfP36MSZMm4fPnz8jLy8OZM2dgbW1dpXE3bdqEhQsXws/Pr0JP0lwuF/7+/vDy8sLFixd5JZAnTZoECwsLnnjhcDhQUFDA3LlzsXTp0lL7U1VVxahRo7Bhw4YqXU+BbTt37sTChQuhrq6O48ePV+uW1z9//oSWlhZGjhyJ/fv3V9s4dQ2+52/ig5SUFAJAKSkp/DSvVxw+fJgA0NWrV6lPnz7UpEkTiomJqfZx379/T3Z2diQqKkpSUlI0c+ZMCg8Pr/Zx/xUyMzPJ+8ErarnQt9wfBfM5JK5mSPImjtTIajFJtR1IAIsaDpzK1/n3334hLpdbbdeyZMkSatKkSZltdu7cSeLi4iUeu3btGklISFCvXr0oOTm5Srbs27ePWCwWffr0qUr9lERqaip16tSJFBUV6ePHjwLvvyrk5+fTkSNHSEVFhYSEhGjatGkUGxtbpE1GRga5uLgQi8Wi//77j5YsWULCwsJVvm8+ffqUhIWFacGCBVXq59evX7R//37q3LkzASAFBQVycnKi169fExGRubk5DRgwoMw+TE1NycLCokp2/Mn79++pffv2JCIiQuvXr6f8/HyB9l+Y7du3E4vF4l3zvwC/83fNJn3WQcaPH49+/frBwcEBHh4eYLFYGD16NC9yu7rQ1dWFu7s7IiMjMXv2bJw8eRKampoYNmwYHj16xCsGw1A5JCQkoKyiWm67jA8BSLqxGwqmTpBpbwLJ1t2gOGgWpPT7I/neYXCyUsvtQ7qBXLXGgAQFBaFdu3ZltuFwOCVW9Dt16hQsLS0xYMAA3Lhxo8q1ECZOnIimTZsK5MnwT2RkZHD9+nUoKSlh4MCBiIiIEPgYFYWIcP36dRgaGmLChAn477//8OHDB+zbt69I2ed79+6hbdu22LdvHzZt2oTAwEC8efMGPXr0qJI3NS0tDWPGjIGBgUGZkf78ICcnh6lTp+LJkycIDg7GpEmTcObMGRgYGMDAwABsNhuBgYGlepcAQEdHBx8+fKiSHX+iq6uLp0+fYs6cOVi8eDF69+6NL1++CHSMAmbMmIHWrVvD2dmZucf+wT8vBlgsFvbv34/Y2Fjs378fp0+fxsOHD8t0lQkSJSUlrFq1ClFRUdi/fz+Cg4PRo0cPdO3aFefOnat2UfI3Iypc/sc77dU1iCq1grBs0RrwkhqdQHk5yI0r/6bUv09v6OrqwsTEBJMnT4arqys8PDxw69YtfPjwAWlpaZW+BuC3GGjfvn2ZbfLz84uJgd27d2Ps2LEYO3YsLl68KJA1WXFxccydOxfHjh2rVIpZecjLy+PWrVsQFRXFgAEDEBcXJ/Ax+OX58+fo378/Bg0aBDk5OTx+/Bjnz58vUsY8LS0NM2bMQN++fdG0aVMEBQVh7ty5yM/Ph7+/f5VT2RwcHBAfH49Tp04JNApeR0cHmzZtQlRUFLy9vaGmpoarV68iMzMTxsbGuHbtWon3Hh0dHXz58gVZWVkCswUAREVFsX79egQEBCA6Ohrt2rWDp6enwCdsERERbN++HQEBAbhw4YJA+67v/PNiAAA0NTWxfPlybNu2DbKysli/fj02btwIb2/vGrNBQkIC9vb2+PDhA3x9fSEpKQlra2toampi+/btRVLOGPhDVUEK5T2vczKTQVQ86I64v6v2oeB3qRDmTB2P/v37Q0JCAkFBQdi3bx8mT54MY2Nj6OrqQlZWFg0aNICenl6FBUNSUhKioqL48gwU1K4nIri6umLmzJlwcXGBp6dnsbr2VaEgxmXTpk0C67MwzZo1w+3bt5GRkQEjIyP8+vWrWsYpjfDwcFhbW6NTp074+fMnfH19ce/evWI1+W/evAk9PT0cPXoUu3btQkBAAE8o3L9/H1lZWRg0aFCl7Th+/DiOHTuGvXv3Ql1dvUrXVBoiIiKwsLDAxYsXERkZCVFRUXz8+BFmZmZQUVHBwoULERISwmuvo6MDIirymiDp2bMngoKCYG1tDTs7OwwdOrTIxliCwNjYGObm5pg7d67ARU19hhED/2Pu3LnQ1tbGlClT4OLigiFDhmD8+PHV5q4qDTabDTMzM/j7++Ply5fo0aMH5s2bhxYtWmDu3LmIjIysUXvqM1JiwlCRLzvPWqRhM+TGfUZeUnSR1zM+BAAsNkQaqZZ5vnDWL4gJAY6Ojrh06RKeP3+OHz9+ICcnB1++fMH9+/dx8uRJLFmyBP369eNbMEyZMgWurq48d7yMjEyZHoaCZQIulwsnJyesXLkS69atw5YtWwReAlZKSgqzZ8+Gh4dHkZ0xBYmamhr8/Pzw/ft3mJmZFdk4qbqIi4uDg4MDtLW18fjxY3h5eeHNmzcwMzMrsgz069cv2NrawsTEBJqamnj37h0cHR2LvM/Xr1+HsrJypWvyf/78GdOnT8e4ceMwbty4Kl8bPzRr1gy9e/eGoaEhXr58iWHDhuHgwYNo06YNunXrhkOHDqF58+YAIPClgsLIysrCw8MDFy9exMOHD6Gnpyfw6oFbt25FTEwMtm3bJtB+6zP/dDbBnzx+/Bjdu3eHm5sbJkyYgI4dO0JWVhaBgYG1Wlr4+/fv2L17Nw4cOIC0tDRYW1tj9uzZVcr1/Vcor85AduR7xJ1aDLaELGQ6mEFIQhaZ4c+Q/eUlpNsZQcHUqdS+WSDIJ77Hh2OuyM7OhpaWFiwtLWFhYYFu3bqV+zSem5uL6OhofP/+HVFRUSX+/tNN3qBBAygrK0NZWRktWrTg/Q4ICMDVq1fRt29fXLhwAfv374e9vX3F3zA+SUlJQcuWLTFp0qRqvaE+e/YM/fv3R7du3eDt7Q0xMTGBj5GWloZt27Zhy5YtEBYWxuLFi+Ho6FjissqVK1cwbdo0ZGZmYuvWrbCzsysxXqRNmzbo1asXDh48WGF78vLy0KNHDyQkJOD169c1es9du3YtNm3ahKSkJAgJCSE7Oxve3t7w8vLCrVu3ICYmBhaLBSsrKxw9erTa9xr48eMHJk+ejKtXr2Lq1KnYsmVLpQoelcTcuXOxb98+hIaG8kTO3wiTWlhJHBwccOTIEXz48IG3Kcj48eMr9aUWNOnp6fDy8oKbmxu+fv2KXr16Yfbs2bCwsKjxDUDqC+VVIASAnJgQJD88iby4L+BkpUFYTgnSev0h22UYWOyyt9ld3pGFkSa9cefOHfj4+MDX1xc/fvyAvLw8Bg0aBEtLSxgbG1f6e2NjY4OgoCDs2bOHb8EgKSkJNTW1ImLhTwEhI1OxqoklXvvy5di6dSu+fftWrXnb/v7+GDRoECwsLHD69GmBbX2cl5eHQ4cOwdXVFSkpKXBycuLtIPgnP3/+hJOTE06fPg0zMzPs37+/1Br7X758gbq6Oi5evAgrK6sK27Vo0SJs2bIFjx49Eli1R3558OABevXqhVevXhVL84uOjsbRo0exZs0aZGZmQlVVFRMnTsSECRMqXAK5IhARDh48iNmzZ6NZs2Y4duxYmdso80tKSgo0NTVhbGyMY8eOCcDSugkjBipJSkoKdHR0YGhoCG9vb3h6emLy5Mk4fPgwJkyYUNvmAfjtEr5y5Qq2bt2KwMBAaGpqwtnZGRMnTqxUrfO/nbL2JqgsbBYgkvQFoQec0LVrV6xevRr9+vUDEeHFixfw8fGBt7c33r59CxEREfTp0wcWFhawsLCo0I3TwMAAHTt2xKFDh0pt8+PHDxgYGCAuLg4LFy5EgwYN8P37d748DH8KhsK/y3sCS0xMRMuWLTFr1iysXbuW72uqDFeuXMGwYcMwceJEHDp0qErZG0SEc+fOYcmSJfj8+TMmTJiAVatWoUWLFiW2PXv2LBwdHXl58WPGjClz/D179sDZ2RmJiYkVvl/euXMHAwcOxPr167FgwYIKX1tVycnJQYMGDbBhw4ZSK/XNmjULly9fxoABA3D27NlKl0CuKGFhYbCxscHz58+xZMkSLFu2rMpBle7u7pgyZQoCAwMrXSK6rsOIgSpw6dIlDB06FOfOncPw4cMxadIknD59Gk+fPoW+vn5tm1eEJ0+eYNu2bbhw4QLk5OQwffp0ODg4oGnTprVtWp2hvF0LK4OYMBt+zr3w8cVDLFu2DM+fP0evXr2wevXqIhXcIiIi4OPjAx8fH9y9exd5eXnQ19fnLSf8999/pXp1cnNzIS0tjW3btsHR0bHENjExMTA2Nsbnz5/RsGHDIltMFyYnJwcxMTGleheioqIQHx9f5JwGDRqU6FUo/NvV1RUHDx5ERESEwPb2KI2jR49iwoQJmDNnDjZv3lwpQXD37l0sWLAAz58/h5mZGdavX1/qdzo2NhYzZszA5cuXMXz4cOzevZuvYk3m5ubIzMyEv79/hWz7+fMn2rVrBx0dHdy6davWvH19+vSBvLw8Ll68WOLxgwcPYsaMGcjIyEB+fj7Onz8PLy8vBAQEQFZWFqNGjYKtrS06d+4s8JTb/Px8rF+/Hq6urjAwMMDx48ertDUxh8PBf//9B2FhYTx58uSv9LAyRYeqyJAhQ6hJkyb069cvysjIoLZt25KmpmadfQ++fv1Kzs7OJC0tTaKiojRx4kQKCgqqbbPqDKeeRfBVQIjfn9PPInh9c7lc8vb2pvbt2xMAGjBgAD1+/LiYDSkpKXTu3DmysbEheXl5AkBKSkpkZ2dHV65coYyMjCLtg4KCCAA9ePCgxGsKCwsjNTU1UlZWJltbW9LU1KzSe5SdnU2fP3+mgIAAOnHiBG3YsIEcHR1p8ODB1KFDB2rcuDEBKPIjKytLLBaLNDU1acqUKeTq6kqenp5069Yt+vjxI6WlpVXJpj/ZuXMnAaA1a9ZU6LygoCAyNTUlANSpUye6d+9eqW25XC55eXmRnJwcNW7cmM6dO8f3OFlZWSQhIUGbNm2qkH1cLpcsLCxIQUGBoqOjK3SuoFm2bBkpKCgQh8Mp8fiDBw8IAL17967I6+Hh4bRs2TJSUVEhANSmTRvauHFjtRRxe/bsGWlpaZGEhATt3r27SkW/7t+/TwDo8OHDArSw7sDv/M2IgVKIiooiGRkZmjp1KhERhYaGkqysLA0fPrxaq81VlV+/ftHmzZtJWVmZNzFdv369TttcU+zyD62aCFjgQy0X+tJu/7AS++dwOHThwgXS09MjADRo0CB68eJFiW3z8vLo/v37NG/ePGrdujUBIHFxcTI3N6cDBw5QdHQ0HTlypNTv3evXr0lJSYlat25NERER5OLiQtra2gJ9v0qisGA4fvw4bdiwgfT19UlERITat29fomCQk5MjPT09MjExEYhgWLVqFQGg3bt3l9v227dvZGNjwxMs58+fL/O7EBERQcbGxgSAxo0bRwkJCRWy7ebNmyVOlOWxa9cuAkA+Pj4VOq86uH37NgGg9+/fl3g8ISGBANDp06dLPM7hcMjPz4/GjBlD4uLiJCQkRGZmZnT+/HnKyckRmJ0ZGRnk4OBAAMjY2LhKImrkyJHUpEkTSk1NFZh9dQVGDAiAgi9owZPZhQsXCAC5ubnVrmF8kJubSydPnqQOHToQANLR0SF3d3fKysqqbdNqlVPPIkh9kTepzLtcISGgtsiXVOZcoOELtpU7BofDodOnT1ObNm0IAA0ePLhcL01ISAht2bKFevXqRWw2m+c1aNiwIb1+/brIBBYQEECysrLUoUMHio+PJyIiJycn0tPTq9qbU0kiIiJIWFiYtmzZQkS/n47/FAwODg40ePBgMjQ0LFMwmJqa0pQpU2jVqlXk6elJfn5+xQQDl8slFxcXAkDHjh0r0aaEhASaM2cOiYqKkpKSEu3bt49yc3NLvQYOh0P79u0jaWlpat68Ofn6+lbqvZg1axYpKytXSHwHBQWRmJgYzZw5s1JjCpr09HQSFhamvXv3ltpGSUmJli9fXm5fv379on379lGnTp0IACkqKtKsWbPozZs3ArP3+vXr1KRJE5KXl6+QF6cwERERJC4uTgsXLhSYXXUFRgwIgPz8fOrcuTNpa2tTdnY2ERHNnj2bhIWF6dGjR7VsHX9wuVwKCAggS0tLYrFY1LhxY3J1deVNIv8aiYmJpKjamtq7eFDLhb7UavHVMkVAwfFx7k9oybptxGKx6M6dO3yNlZ+fT0ePHiV1dXUCQCNGjKDg4OByz0tISKBjx45R48aNSVhYmABQixYtaMaMGbRy5UoSFxenfv36FXmKcXBwoHbt2lX2bakydnZ21KRJE77FZoFguHfvHh0/fpzWr19PDg4OZGlpyZdgmDx5MhkYGBCLxSJXV1f6+PEjpaenU2ZmJm3YsIEaNGhA0tLStGrVqnI9D+Hh4dSnTx8CQFOmTKnS/g1aWlo0ZcoUvttnZGSQtrY2tW3btk4J9a5du9LIkSNLPd63b18aPnx4hfp8//49zZ07l5SUlAgAGRgY0M6dOyvsfSmJnz9/0rBhwwgA2djYVOpvuHz5chIVFaXPnz9X2Z66BCMGBERQUBAJCwvTqlWriOj3E3f37t2pefPmFBcXV8vWVYyQkBCaPn06SUhIkLi4ONnb29e5DWGqG0dHR5KVlaUfP35Q6I9UWnHlPfXa7E+qf4gA1YW+1GuzP6248p7C4n5PuhwOh/r160fNmjWr0A0sNzeX3N3dqWXLlsRisWjs2LEUEhJS5jlcLpcUFBRo6dKl5OfnRzNnziRFRUUCQEJCQjRkyBA6fPgwT9RNnTqVDA0NK//GVJGwsDBis9m0Z88egfVZnmBo1KhRMcHAYrEIALVs2ZLGjRtXzMOQnp7O6z8/P5/c3NxIQkKCVFVVyc/Pr0r2fv78mQDQpUuX+D5n6tSpJCEhwZdIrEkWLFhATZs2LdXD4eDgQDo6OpXqOzc3l7y9vWnIkCEkLCxMoqKiNHz4cLp27VqVNinicrl09OhRkpWVJRUVlTLjQkoiPT2dlJWVycrKqtI21EUYMSBAFi5cSKKioryd2r5//06NGzemAQMGVOsOW9VFQkICrVmzhpo0aUIAyNzcnPz9/f/6uIK3b98Sm82mrVu3FjuWnp1H76OT6VVEEr2PTqb07LwS+/j+/TvJy8vTkCFDKvx+5eTk0L59+6h58+YkJCREEydOpC9fvpQ6DgC6fPkyERG5ubkRALKysqLVq1dT586dicViEZvNpu7du9N///1H+vr6tfo3HDNmDKmoqAh0Xbg8fv36RW3atOGJgLZt29K4cePKFAxycnKkpaVFcnJyBIA6d+5M+/btIz8/P/r06VMRwVARdu/eTSIiInyvOxcsOx44cKBS41Un165dIwAUGhpa4vE9e/aQsLBwmUsv/BAXF0fbtm0jfX19AkDNmjWjhQsXliuWy+Lbt2/Uq1cvYrFYNHfuXJ5Xlx9OnjxJAOj27duVHr+uwYgBAZKZmUnq6urUu3dv3s329u3bxGazadmyZbVsXeXJzs4mLy8v3hfRwMCAjh07VqM385qCy+VSnz59qHXr1lW+vkuXLlXpJp6VlUU7duwgJSUlEhYWJnt7e4qMjCzSxtfXlwDQly9faMmSJQSAFixYUGSyj42NJXd3dxo8eDAJCQkRANLQ0CAXFxe6e/dulW/UFeXdu3cEgDw8PGpkvMDAQOrRowcvq0FWVrbEJ+ysrCwKDw+ne/fu0eHDh8nY2JjYbDZJSUmRpqZmiYKhYcOGpK+vT6ampmRvb0+rVq0iLy+vMgWDmZkZ9e3bly/bIyMjqWHDhjR06NA6KcKTk5OJzWaTu7t7icfv3r1LAOjDhw8CGY/L5dKLFy/IwcGBGjZsSACoW7dudOjQoUrNO/n5+bR582YSFRUlfX19vjOruFwude/enfT09Cgvr+QHgvoGIwYEjJ+fX7Eb3Zo1awgAXbt2rRYtqzpcLpdu3brFi6Ju3rw5bdiwgZKSkmrbNIFx9uxZAkDXr18XSH8F7t2q3AwzMjJoy5YtpKioSKKiouTg4MCLiF67di3JysqSvb09AaDNmzeX2dfo0aNJR0eH7O3tqVmzZrwn4DFjxtCpU6fo169flbazIlhZWZGGhka1esw+ffpEVlZWBIDatWtHN27coMTERNLX16dmzZqV6m158+YNGRoaEpvNpvnz51NmZibvWGHBcOzYMVq/fj3NmDGDLC0tycDAoEzBMGjQILKzsyNhYWGytram27dvl+lhyM/Pp169epGysjIlJiZWy3skCAwNDcnGxqbEY3FxcQSAzp8/L/Bxs7Ky6MyZM2RsbEwsFoskJSXJxsaG/P39S013LI2goCDS09MjUVFR2rx5M1+fyxcvXhCLxRLokldtwoiBamD8+PHUsGFD+vHjBxH9XkMeNGgQycvL07dv32rZOsHw7t07mjRpEomKipKUlBTNnDmz3gfUZGRkUIsWLcjS0lKgfbZp04bat29fITdkSaSlpdG6deuoYcOGJC4uTi4uLjRo0CBSVFQkNptNnp6e5fYxZswY6tOnDxH9/lw+f/6cli9fzqt9ICwsTP369SM3N7dq/Xu+ePGCANDJkycF3nd0dDTZ29uTkJAQtWzZko4dO1ZkcoiNjSV1dXVSV1cvktuek5NDy5cvJ2FhYdLV1aVnz55VavwCwXD37l06duwYrVu3jmbMmEEWFha8INGyBIO9vT2tXr2arKysiMVi0bFjxyq9JFETuLi4UMuWLUs8VhDTUhBLVV1ERUXR2rVrSUNDgwCQmpoaubq6Vuh+m5WVRXPnziUWi0W9e/fm69xJkyaRvLx8nRZr/MKIgWrg58+fpKCgQKNHj+a9lpiYSC1btqROnTpVeVKoS/z48YNXfITNZtPQoUPrTQbFn6xYsYJERUUpPDxcoP2+evWKREREaM6cOQLpLzk5mVauXEkyMjK8YLgjR47wde7IkSOpf//+JR6LiIigPXv2kImJCYmKihIA0tXVpYULF1JgYKDAn+JNTExIT0+vwk9xpZGcnExLliwhCQkJkpeXp23btpX6Xfv69Ss1a9aM9PX1KTExkZ49e0Z6enokLCxMy5cvr7bv6KxZs6hFixaUmZlZqmAwMDDgxSn8KRjatm1LgwYNoqlTp9Lq1avp8OHDPA/Dn8WoaoqC5bDSJs+ePXvSqFGjasQWLpdLDx48oEmTJpG0tDSxWCzq378/HT9+vIiHpyzu3r1LKioqJCsrS0ePHi1zeSY2NpZkZGRKTPfkN76orsCIgWqioBBMYXfz8+fPeW7ev43MzEzav38/rzBOly5d6OzZs/VmPe3r168kLi5Oixcvrpb+t27dSgDo5s2bAukvISGB9zQvIiJC0tLStHTp0nKXbIYPH05GRkbl9p+amkoXLlygCRMm8LITGjVqRLa2tnTx4kWBVAx8+PBhhaPqSyI7O5u2b99OCgoKJCEhQYsXL+YrZSw4OJjk5eWpadOmxGazycDAQKB57SWhpaVF9vb2Zbb59esXqaioUNeuXenjx4+lCoaCvwu/giEkJKRaBENBcaGjR4+WeHzq1KnUtm1bgY9bHmlpaeTl5UW9evXixYvY29vT48ePy42/SE5OJhsbGwJAw4cPLzMraNOmTSQkJETv37///8yjTaVkHm36nXkU+qPuFS1ixEA1weVyqX///qSqqlrExbd3795qc4/WBTgcDvn4+FDfvn0JAKmqqpKbm1udr9g1bNgwat68ucDL4hbA4XDIyMiImjRpUuXaDVFRUaStrc0LoLp9+zbNmzePJCQkqEGDBuTq6lrqd3DIkCE0aNCgCo2Xn59PDx8+pAULFpC2tjYBIDExMTI1NaV9+/ZRVFRUpa+ld+/e1KFDh0oFx3E4HDpx4gSpqakRm82myZMn0/fv3/k+/8GDB7ySuOrq6tX2ty8gPDy8XPHD5XLJ2tqaGjRowJebOjMzk8LCwuju3bt09OhRWrduHU2fPp0sLCyoffv2JQoGeXl5gQsGPT09mjx5conHduzYQWJiYrX6YBAeHk5Lly6lFi1aEADS1tamTZs2UWxsbJnnnT17licYS4sjys7Oplb6/5H29D0VrkkSmVg73pySYMRANRIWFkbi4uI0d+5c3mtcLpfGjh1LUlJSAouwrau8fPmSxo4dS8LCwiQrK0tz584tFg1fFygoq3rixIlqHScmJoYUFRXJ3Ny80pHhnz59IhUVFVJRUSFXV1cSEhLiFaGJjY0lZ2dnEhMTI3l5eVq/fn2xCc7CwoIsLCyqdB1hYWG0bds26tu3Ly87wdDQkFasWEEvX76s0LUVBNzeuHGjQjbcvHmT5xkZPHhwhb5LaWlpNHPmTGKxWNSlSxc6fPgwiYmJkZWVVbVOWLt27So3pdDDw4MA0JkzZwQ2blUEg5mZGU2dOpXWrFlDhw8fpjt37pQoGGbMmFHqnhcFf+PS0g9rkvz8fLp16xaNHj2axMTESEhIiMzNzenChQulZg9FR0eTkZERASAHB4di137qWQRpLPKpcLXSVouvktbSa3Sq0P4ltQkjBqqZdevWEZvNppcvX/JeS09PJx0dHdLW1q72p5G6QFRUFC1YsIDk5ORISEiIRo8eXWot/pomNzeXdHV1qXv37jWSuuXj40MAKhWB/OLFC2rUqBHp6OhQVFQUTZs2jXR1dYu1+/79O82YMYNERESoUaNGtHXrVt566aBBg2jIkCFVvo4CkpKS6OTJkzRq1Chq0KABL8tk2rRpdPXq1XKr5XG5XOrcuTP16NGDr/FevnxJAwYM4KWUPXz4sEL23r59m1RVVUlCQoLc3Nx4cRDe3t68mg6CimH4k0GDBpWZUvjp0yeSlJQkOzu7ahm/LAoEg7+/Px09epTWrl1L06dPJ3Nzc74EQ8HfZPv27cUEQ3R0dJFaGHWFpKQk2rt3L/33338ElF0Cmcvl0u7du0lcXJy0tLR4waVV3sfkfz+7/GtfKPE7fzNbGFeSvLw8GBoaQkxMDE+ePIGwsDAA4NOnT+jYsSMsLS1x4sQJgW/hWRdJT0+Hl5cX3Nzc8PXrV/Tq1Qtz5syBubl5rW0JunPnTjg7O+Ply5cwMDCokTEdHR3h4eGBFy9eQFdXl69z7t69i8GDB0NHRwdXr16FgoICunXrhlatWuH48eMlnhMZGYk1a9bAy8sLioqKWLx4Mby9vdGgQQOcP39ekJcE4Pdn/cGDB/Dx8YG3tze+fPkCSUlJGBkZwdLSEmZmZmjcuHGx83x8fGBpaYmAgIAi2zoX5suXL1i6dClOnTqFNm3aYMOGDbC0tOT7e5OSkoJ58+bh0KFD6NOnDw4dOgQNDY0ibU6cOAEbGxvMmjUL27ZtE+h3Mjs7G/Ly8li1ahXmzp1b7HhOTg66dOmCrKwsvHz5ElJSUgIbW1BkZWUhOjq6xG2tv337hvfv3xc7R15eHi1atEBwcDAMDQ1haWlZZLtrZWVlSEpK1sLVFCU4OBheXl44duwY4uPjYWhoCFtbW4wZMwby8vK8dp8+fYKNjQ3evHmDkYt34GFuS4HZsHGoPkb+pyKw/ioKs4VxDfD48WNisVjFNi46depUpZ8S6zP5+fl0/vx56tatGwEgTU1N2rt3b41HQ8fHx1ODBg14O07WFJmZmaSrq0v6+vp81Zm/ePEiiYqK0sCBA3meJA6HQ1JSUnxtgfv582eaMGECsdlsEhMTow4dOlR7wSgul0vBwcG0fv166tatG7FYLGKxWNS1a1dat24dvX//nueJ4XK51K5dOxo4cGCxfuLj48nJyYlERESoWbNmdOjQoQq78n19fal58+YkLS1N+/btK/PJf8+ePQSAXF1dK3bB5XDjxg0CSt/hz8XFhURFRenVq1cCHbcmKQiODA0NJX9/fzpy5AjPw9CwYUNq2LAhKSgolOhhaNeuHZmZmdG0adNozZo1dOTIEbpz5w6FhobW6H0hNzeXrly5UqQE8ogRI4qUQM7NzSXnpWuoxZwLvB1KC/80mbCNZAzNSERRhVgiYiQk24gk2/SgZvYHyvQOaC29VqsxBMwyQQ3h6OhIUlJSxYKCHB0dSUREhJ4+fVpLltUujx8/phEjRhCbzSZ5eXlasmRJuUE9gsLe3p7k5OTo58+fNTJeYQp2oHNyciqznYeHB7HZbLK2ti6S7hYaGkoA6NatW3yP+enTJ97GPqqqquTp6VljQV1xcXHk5eVFVlZWJCUlxcsFd3Jyotu3b9OJEycIAO97kJ6eTqtXryYZGRmSlZWldevWVXhSSEhI4EWEGxsbU0QEf2uzBUXCduzYUeHrLA0nJydq0aJFiUtRBSV9t20rf6fLuszkyZNL3RFz8uTJvD0xMjMziwmGadOmkbm5ObVr165EwaCgoEDt2rUjc3PzEgUDv2mDFSEuLo62bt3K22q8cAnkce5PSG1RyZO6ZOtuJCTVkGQ6WJC86Uxq0HMcsaXkiCUiTk3tdpcZQzDO/YnAr4NfmGWCGiI1NRU6Ojpo3749fHx8eC7I3Nxc9OrVC7GxsXj16hUUFBRq2dLa4evXr9i5cyfc3d2Rm5uLMWPGYPbs2dDX16+W8V69eoWOHTti586dcHR0rJYxymPnzp2YNWsWrl27BlNT02LHN2/ejPnz52PatGnYvXs3hISEeMfOnTsHa2trxMXFleh6L41evXpBTk4OYmJiOH/+PDQ0NLBixQqMHj26SP/VSXZ2Nu7evctbToiOjoasrCyICBoaGrCxscGmTZuQlJQEBwcHLFmypMLfiwsXLmDGjBnIzc2Fm5sbJkyYwLfbn4gwb948bN26FUeOHMH48eMrc5lF0NLSQt++fXHgwIEir//48QNt27ZFx44d4evrW2vLZYLg2LFjGD9+PH7+/AlFRcUix9zc3LBkyRKkp6fzdY2ZmZmIjo4uthxR+HdiYmKRcxQUFKCsrMxbhvjzt7KyMiQkJCp8XUSEly9fwsvLCydPnkSGkAyaTdlXavvs7x8h1lQDLCER3mt5SdGI8XCEVJvuULQovkxUmNsuvaDRWKbCdlYVfudvRgwIgMuXL8PKygpnzpyBtbU17/XIyEgYGhqiU6dO9f6GUFWSk5Ph7u6OHTt24Pv37xg4cCDmzJkDIyMjga3hEhF69OiB1NRUvH79mhfHUdMQEczMzPDy5Uu8ffsWSkpKvNcXLlyITZs2YdmyZXB1dS127UuXLoWHhwdiY2MrNGa3bt3Qpk0beHp64s2bN1ixYgW8vb2hra2NlStXYvjw4TX6+SMivHnzBleuXMHevXvx8+dPAICSkhImT56MCRMmQFNTk+/+4uLi4OjoiPPnz2Pw4MHYt28fmjZtWim7pkyZgsOHD+P8+fMYMmRIhfso4PPnz9DQ0MClS5eK9MPlcmFqaoqgoCC8ffu2QqKuLhIZGYmWLVsWu04AuHnzJkxMTPDlyxeoqakJZLwCwVCaWKgOwZCdnY1Je64j8KcwwKrY9yTWaxYAoKntjlLbCLFZsOncEist+YslEiT8zt+1c7f8yxgyZAisrKzg5OSEgQMHomHDhgAAFRUVHD9+HIMGDcK6deuwdOnSWra09pCTk8PcuXMxa9YsnD9/Hlu3boWJiQl0dXUxe/ZsjBkzBuLi4lUa4+TJkwgMDMSdO3dqTQgAAIvFgpeXF9q2bQtbW1tcvXoVHA4H06ZNg4eHB7Zv345Zs2aVeG5QUBDat29f4TE5HA7PA9C+fXtcuXIFz58/x4oVKzBy5Ejo6+vD1dUVQ4YMqZGgVhaLhfT0dNy8eRM/f/6EmJgYWrVqBTU1NWzZsgVr165FmzZtYGFhAUtLS3Tt2rVEDwYR4eTJk3BycgKbzcbp06dhbW1d6WtgsVg4cOAAUlNTMXLkSFy7dg39+/evVF/Xr1+HiIhIsfPd3Nxw69Yt3Lx5s94LAeD3faxly5YICAgoJgZ0dHQAAB8+fBCYGJCUlISmpmaZYrEswfD48WOcPXsWSUlJRc5RUFAoUyxEcRoArKwK2UpE4GQmQ0Sx7ABBDpdwNzQeK1HzYoBfGM+AgIiOjoa2tjZGjx5dzGW4YsUKrF69Grdu3cKAAQNqycK6BRHhwYMH2Lp1K3x8fNCoUSM4Ojpi+vTpxVyR/JCWlobWrVuje/fuOHfuXDVYXHGuX7+OQYMGYcuWLXj06BG8vb3h5eUFGxubUs9p0aIFxo4diw0bNlRorI4dO6Jjx47Yv39/sWOBgYFYvnw57ty5AwMDA6xatQpmZmbVJgqCg4OxcOFC+Pr6okOHDti4cSPCw8Mxffp0fPz4EcrKyvDz84OPjw98fX0RHx8PBQUFmJmZwdLSEkZGRpCRkUF0dDSmTZsGX19fjBo1Cjt37kSjRo0EYmNubi4sLS3x8OFD3LlzB507dy6zfUZOPr4lZiA3nwtRYTZUFaRgPXQwsrOzcefOHV67ly9fomvXrnBycsKWLVsEYmtdYMKECXj//j1evnxZ5HUigqysLJYvX4558+bVknUlk5mZyfMklORdiIqK4gkGlqgEWricrfB3Iv39XST6boWCqROk2xmV2ZYF4P1KY0iJ1eyDCrNMUAvs2bPn/9g766got7aNXxN0CCICIqigoFjYgYqNhYFii92NiljYgXHE7u48dmB3JygoimIhIoJIw8z1/eHHvHKoAYZQ57cWa+k8O+4Zhmdfz953YMSIEbh69Srq168ve10ikaBly5Z4/PgxHj16BFNT03y0suDx8uVLeHl5YevWrSCJ3r17Y+zYsbC2tpZ7jEmTJsHLywv+/v4oUUJxYUE5ZciQIVi/fj1UVVVx8OBBtGnTJt22YWFhKFKkCPbs2YOuXbtmaR5bW1vY2dlh1apV6ba5cuUKpk2bhmvXrqFWrVqYNWsWmjVrpjBR8OHDB3h4eGDbtm0oWbIk5s2bB2dnZwiFQsTHx8PCwgLNmjXD1q1bZX2kUinu3r2LY8eO4fjx4/D19YWKigqsrKzw+vVr6OjoYP369Tnazk+P6OhoODg44Pnz57h69SoqVKiQ4npAyA/suvMOl158wbtvMfj1RikAkBjxGVWNVbFkSHuUMdJBVFQUqlatCl1dXdy8eROqqqoKtzm/2LRpEwYNGoRv376hUKFCKa7VqlULNjY22LJlSz5Zl32SBcNNv3eYcTs+S30Tw94jePs4qBYxh1EPTwiEmfvmnBxZD+WLFcq0nSKRd/3+ew+xc4EhQ4agdu3aGDRoEOLj//fFEolE2LVrF9TU1NC5c2ckJibmo5UFDysrK6xevRrv3r3D1KlTceTIEdkW8uXLl5GZXn316hX++ecfuLu7FyghEBoainv37kEgEMDY2DjT7egnT54AACpXrpzluSQSSaZHI/b29rhy5QrOnTsHgUAABwcHNGjQAJcvX87yfL8SHh6OiRMnokyZMjhx4gSWLVsGPz8/dOnSReanoKamhgkTJmDnzp14+/atrK9QKETt2rUxb948+Pj44MqVKyhVqhSePXuG+Ph4hIaGYsaMGfDw8MC9e/cglUpzZOuvaGlp4cSJEzA3N0fz5s0RGBgIAHj/LQa9Nt1BM6+r2HEnCEH/EQLAT1d4sZ4xfOMLo5nXVfTadAcDxkzEp0+fsGfPnj9KCAA/vztSqRQ3btxIdc3GxgbPnz/PB6tyjqamJqysrFC5SrUs9ZNEhePLgZkQqmmhSPtJcgkBAEhIUtz3V9EoxYACEYlEWL9+PV69egVPT88U1wwNDbF//37cvXsX7u7u+WRhwaZIkSKYMmUKgoKCsGXLFrx9+xaNGjVC9erVsWvXrnRFlKurK0xMTODm5pbHFqfPu3fvUK9ePXz8+BH79+9HSEhImklpfuXJkydQV1fPkmNdMr/6DGSEQCBA06ZNcfPmTZw8eRKxsbFo1KgRmjRpkuaNPiPi4uKwePFiWFpaYtWqVXBzc8OrV68wYsSINBfDgQMHonDhwqn+NoCfOwQrV65Eq1atEBsbizNnziA8PBx79+5FhQoVsHLlStSsWRPFixfHoEGDcOLECcTGZu18Ny309PRw9uxZaGtro2nTplh77imaLr2Cm4E/HdQk0oyFaPLlG69CcVOvCfrO2Zit319Bx9LSEiYmJrh69Wqqa8liQI5N5gJBXFwcfHx8cODAAcyePRvdu3dH71495O4vjYtGyP7pkMZFo2jnmRDryB8RoyouuEtuwbXsN6VixYpwc3PD3Llz4e/vn+JanTp1sHjxYvzzzz84dOhQPllY8FFTU0OfPn3w9OlTeHt7w9DQED179kSpUqWwcOFChIeHy9qePn0ax48fx+LFi7MVXpQbPH/+HHXr1kViYiJu3LiBjh07YsmSJVi9ejWOHz+ebr/Hjx+jYsWK2XJ+lFcMJCMQCNCqVSvcu3cPR44cwdevX1GvXj20aNECd+/ezXSubdu2wcrKCu7u7ujatStevXqFmTNnZrgNqaWlhbFjx2Lz5s349OmT7PWXL1+iYcOGGDlyJFxcXODr6wsHBwcUKlQIXbp0wc6dO/HlyxdcvnwZ3bp1w6VLl+Do6AgDAwO0a9cOGzduxOfPn+V+7//FyMgI586dQ5J1Uyy4+B7xSdJMRcB/kUIAoVgVx0N0sPJSQLZtKagIBAI0aNAAV65cSXXNxsYGUVFR+PDhQz5Ylj5hYWG4fv06Nm7ciPHjx6NNmzawtLSEpqYmKlWqhM6dO2PFihX48OEDqluXAFLt/6SGSQn4cnAWksI/oqizB1QzcRz8FQGAkgYFLwNlMkqfgVwgNjYWlSpVgomJCS5fvpwipIskunTpgjNnzuDBgwd/5FNEbuDr64ulS5di586dUFFRQf/+/TF06FC0a9cOpqamuHDhQoFI/Xznzh20atUKpqamOHv2rCz8jSTatWuHW7du4enTp2mGxdna2qJGjRrYsGFDlue1tLRE586dMX/+/GzZLZVKcejQIUyfPh1+fn5wdHTErFmzUkQ2kMTp06fh7u4OHx8fdOrUCXPnzoWVlZXc80RGRqJEiRLo27cvFi1ahKVLl2LatGkoVqwYNm3ahIYNG2Y6Bkm8ePFCls/g5s2bkEqlqFmzJtq2bQtHR0dUrFgxS9+Hvffewf2wj9ztMyO/U9DmBmvWrMGoUaMQERGRIq3ymzdvYGFhgTNnzsDBwSFPbZJIJAgKCoK/vz/8/Pzg7+8v+/n69SuAn0dRpUqVQtmyZVGuXDmULVtW9vNrngv7RZcQ9C0m3bkolSD08DzEBt5H0Y5ToWFZI0u2ljDQxJXxjbL3RnOA0oEwn7lw4QKaNm2KDRs2YMCAASmuRUZGokaNGrK6BgUhh/fvQkhICFatWoXVq1fLPIG3bduWoYd+XnHu3Dl06NABlStXxokTJ2QhpsmEhoaiUqVKqFixIs6cOZNCJCYkJEBbWxtLly7F8OHDszx3yZIl0bNnT8yZMydH70EikWDfvn2YMWMGAgIC4OTkhJkzZyImJgYTJ07E5cuXYW9vD09Pz0w98NPDw8MDCxcuRPny5fHo0SOMGTMGs2fPznbe/q9fv+LUqVM4fvw4zpw5g6ioKJQoUUIWtmhvb5/hGf77bzFouvQK4tM5z2VSIiKu7UT0s0uQxkVBxbAk9Br0gkap9GteqImFOD/WHmaF/5y/7WfPnqFChQo4d+5ciqgoqVQKbW1tzJkzB66urrkyd3R0NF6+fClb6JMX/pcvX8r8szQ1NVMs9MkLf+nSpeUKW55x7Bl23H4LSTor4rfz6/Hj/jFolK4JzbL1U13XrpD+Qv875BlQioFcpE+fPjh69Cj8/f1liWeS8fX1Rc2aNdG5c2ds2bKlQDzV/k68fv0a5cuXh4aGBiIiIlC7dm2MGzcO7du3z5ccAwcPHkT37t3RtGlTHDx4MF2Bd+7cOTRv3hxLlixJceNMzi9w7do11KtXL8vzm5mZoV+/fpg5c2a238OvJCUlYefOnZg2bZps+7dMmTLw8vJCy5Yts/19TUxMhIeHBxYsWAADAwMcP34cderUUYjNwM/CQJcvX5btGrx//x46OjpwcHBA27Zt0apVq1RZD3ttuoObgWHpHg2EHl2ImBc3oFu9HcSFiyHa5zzigwNg1G0e1M3SvrmLhALUtTDAjv7ZE0wFEZIoWrQohg4dilmzZqW4Vq1aNVSpUgUbN27M0fhfvnxJ9YTv5+eHd+/eydoZGxunesIvW7Ysihcvnu3EWhEREZg4zwtnRek/7X/e5Y7496mLNiVTwv1EhnMU9AyEyqRDucjixYtx8uRJjBkzBnv27ElxrUKFCli3bh1cXFxQr169VLsHSjJm9uzZ0NbWxosXL3Dr1i0sWbIEzs7OKFmyJMaMGYN+/fpBRydv/vDWrVuHoUOHolu3bti6dStUVFTSbdusWTO4urrC3d0djRo1klVUTI4kqFSpUrZsSEpKUqgICgsLw927d/H582fo6+tDIBDg1atX2LdvH6ysrFJVBpSHR48eoW/fvvD19UXt2rXx7NkzlCtXTmE2Az/9TRwcHODg4IAVK1bg6dOnsrBFFxcXCIVC2NnZyY4ThHrFcO3V13THi//0AjF+V6HXqB8K1XICAGhXaIxPG4cj4vIWGPdKO5eAREpce/UVr778yJcFIDcQCASoX79+hk6E8pCUlITAwMA0t/YjIiIA/HTGLl26NMqWLYtu3brJFn9ra2vo6ekp7D0lJCRgzZo1mDVrFuLi4lB59AaEoFCauwPGPbKW+yOZZGFY0L8HSgfCXKRIkSJYunQp9u7di1OnTqW63qtXLwwaNAgjRozAo0eP8sHC35M7d+5g27ZtmDdvHgwMDNCmTRtcunQJDx48gJ2dHcaPHw8zMzO4ubnh/fv3uWYHScybNw9DhgzB8OHDsWPHjgyFQDLz5s1D+fLl0b17d0RHRwP46TxoYWGR7Z23rDoQpsePHz8wffp0WFpaYu/evZg/fz4+fvyIT58+YcWKFTh37hzKli2LAQMGICgoSK4x4+LiMGXKFNSoUQMkcffuXfz7779ISEjAypUrc2xzeggEAlSuXBnTpk3D3bt38fHjR6xduxaFChXCtGnTULZsWbQYMRcCph/uFfPiBiAQQse2xf/GFatCu3IzxH/0R1JkaLp9RUIBdt5+l+7135EGDRrg9u3biIuLS/F6WhEFkZGRuHfvHnbs2IEpU6agY8eOsLGxgaamJqytrdGuXTvMnTsXz58/h5WVFdzc3HD48GH4+fkhJiYG/v7+OHLkCBYsWIDevXujVq1aChMCJHHgwAHY2NjA1dUVTk5OCAgIwL7x7SEWKXZZFAsFmNchd2qxKBLlMUEuQxIODg54+fIlnj17lupcNC4uDnZ2doiIiMCDBw8Uqnr/RKRSKWrXro2kpCTcu3cvzQXww4cPWLFiBdatW4fo6Gh07twZrq6uqFYta7HEmdkxfvx4LF26FDNnzsS0adOytHXu7++PqlWrolevXli3bh2aNGmCQoUK4fDhw9myx8DAAG5ubpg4cWK2+ickJGD9+vWYNWsWIiMjMXr0aLi7u6fye4iNjcXatWuxYMEChIeHo3///pgyZQqKFy+e5ri3b99Gv3798OrVK0ybNg0TJ06Und+PHDkSu3fvRlBQELS1tbNld3aJiYnB+fPnMfF6LGJF6c8dsncqJD/CUhWwiX37GF/2ToVhx2nQLJP+UUB+OY3lFo8ePULVqlVlidVI4tOnT9i0aROmT5+OPn364P379/D398fHjx9l/YoXL56mA5+JiUmeH5HeuHED48ePx+3bt9GqVSuZ/0oyf5ozqTLpUAFBIBBgzZo1CAkJwfTp01NdV1dXx8GDB/Ht2zf07t37t4nVzS+2bduGe/fuYfny5ek+CRcvXhyenp748OEDlixZglu3bqF69epo2LAhjh07luPENYmJiejbty+8vLywatUqeHh4ZPmGVrZsWXh5eWH9+vU4fPhwtmsSJJPdnQGpVIp9+/bBxsYGo0aNQps2bRAQEABPT89UQgAANDQ0MHbsWAQGBmLOnDk4cOAASpcujdGjR6cI74uJicG4ceNQt25daGtr4+HDh5g2bVoKR74JEyYgMjIyzRTKuY2mpiYaO7RCXAZCAAAkUd8g0k79OYi0C8uuZ8S7sBhExydl39ACQkJCAp4/f47Xr19DTU0NI0eORI0aNaCrq4vixYvL7m2XL1+Gnp4e+vTpgx07duD+/fuIjIzE+/fvce7cOSxfvhzDhg1D48aNUaxYsTwVAi9fvoSTkxPq1auH+Ph4XLhwASdPnkwhBACgaw1zjG/+M0Imp/fjCc2tf5uoEqUYyAMsLS0xY8YMLF26FA8fPkx1vVSpUti+fTuOHTuGRYsW5YOFvwffv3+Hu7s7unfvLpeTnba2NkaNGoWAgAAcPHgQCQkJaNeuHcqWLYs1a9YgJib9MKL0iI2NRceOHbF7927s3r0bw4YNy85bAfAzCU+HDh3Qv39/hIWFZSvzYDLZ8Rm4ePEiatWqha5du6JcuXJ4+vQpNm/eDDMzs0z7amlpwc3NDYGBgZg6dSq2b98OCwsLTJgwAUePHkWlSpWwatUqeHp64ubNm6lS/QI/C+D07t0bS5YsUUgCoawSFBadaWQ5kxIAUeqjH4FY9X/XM+oP4G1YdDYtzHvCw8Nx69YtbNmyBRMnTkS7du1gbW0NTU1NlC9fHs7OzpBKpXj79i0qVaoEDw8PHDt2DM+fP4eqqirGjh2LgwcPYs6cOejZsyeqVauWZ7476REaGooRI0agfPnyePDggUykNG7cON0+wxuWRtG35wBJIkRZ1CsioQBqYiE8nSpieKOs+9bkF0oxkEe4urqiQoUKGDhwIJKSUj8pODo6wt3dHZMnT04zsYcSYNasWYiOjsbChQuz1E8kEqFjx464efMmbt68icqVK2PEiBEwNzfHtGnT5E5Y8/37dzg4OODChQs4fvx4lusH/BeBQIANGzbIPKCz6zwIZG1n4MmTJ2jZsiWaNGkCkUgk875Pa8HODF1dXUydOhVv3rzByJEjsWzZMrRv3x7x8fG4cuUKJkyYkKFIcXd3x5cvX7B58+Ysz51T5EkNKxCrApLUmS+TRUCyKMjpPHmJVCpFUFAQzp49Cy8vLwwZMgQNGzaEsbExChcujLp166J///7Yv38/EhIS0KpVK6xevRpXrlxBSEgIZs+ejaSkJKxduxYTJkyAo6OjbPu/IKUljomJwbx582BpaYmdO3di7ty5ePHiBXr27Jlp1MHWrVtxb+8yzKmjhrqWPwuniYQZq4Lk63UtDHB+rP1vsyOQjDKaII9QUVHBhg0bULt2bSxfvjzNeNzZs2fj9u3b6Nq1Kx4+fJiteu1/Kn5+fli+fDlmzZqVo0JPderUwYEDB/DmzRssW7YMXl5eWLhwIXr06IGxY8eiYsW0HX0+f/6MFi1a4N27dzh//rzCwuGSs+ht2bIF+/fvz/aZvzxi4O3bt/Dw8MDOnTtRpkwZHDx4EE5OTgrZqr1z5w727t0LVVVVNGzYENevX0fz5s0xduxYjB07NlVxm2RKly6Nrl27wtPTEwMHDszTnP7ypIYVaReG5EdYqteTjweSjwtyOk9uEBsbi4CAgFRhei9evJDtxKirq8Pa2hply5ZFw4YNZWf5VlZW6YbHNmzYEO7u7nj48GGKXBMFpUaBRCLBzp07MXXqVHz+/BnDhw/H1KlT5a6GGhwcDFdXV/Tq1Qu9nFqhF34pWvXyC96FpS5aZW6giUZWRdGztnmBjxpIF8rB9+/fCYDfv3+Xp7mSDBg5ciQ1NTX55s2bNK8HBwfTxMSE9vb2TExMzFvjCihSqZTNmzenpaUlY2NjFTp2eHg4Fy5cyOLFixMAmzdvzjNnzlAqlcraBAYG0tLSkiYmJvTx8VHo/CTp7OxMMzMzisVi3rt3L1tjCAQCrlu3Ls1rX79+paurK1VVVWlkZMQ1a9YwISEhJybL+PbtG/v27UsAbNKkCQMDA0mSISEhHDduHNXV1amnp8c5c+YwMjIyzTF8fX0JgJs2bVKITfIS/iOGJdxPZPijW9OJEAhpNnZ/itf1GrgQAE2Hbcmwf0n3E4yKy92/49DQUF67do3r16+nq6srW7VqRQsLCwoEAuLnSQUNDQ1Zv359Dhw4kP/88w9PnTrFwMBAJiUlZXm+hIQEampqcuHChSlenzVrFgsXLpzibyev8fb2ZuXKlQmAnTp1YkBAQJbHcHJyYtGiRfn169c0r0fFJdL3YwQfBn2j78eIXP/95hR5129lNEEe8+PHD9jY2KBixYo4efJkmk9lV69eRePGjTFhwoRsp5f9kzh27BjatWuHY8eOwdHRMVfmSExMxIEDB7BkyRI8fPgQ5cuXh6urK2xtbdGmTRtoaWnB29sbpUqVUvjcVlZWaN68OW7fvo3IyEg8fPgwS971JCEUCrFx40b0799f9npMTAyWL1+OBQsWQCKRwM3NDWPHjlWY5/6xY8cwZMgQREdHY8mSJejfv3+q73NwcDDmz5+PdevWQVdXF25ubhg+fHiqp04nJyf4+PjAz88v15JGSSQSPHnyBBcvXsTFixdx5coV6PXygop+sXT7xH96gc/bx6XIM8CkRHzaNAxCDV2YuCzJcE5FRRNIJBK8ffs2VQY+f39/hIX93LkQCoWwsLBIlYXP2to6VaKlnNKsWTOoqanhxIn/Jdo5dOgQOnXqhJCQEBQtWlSh82XG06dP4ebmhrNnz6Ju3bpYvHhxtnbvDh48CGdnZ+zfvx/Ozs65YGneI/f6rUhloUQ+jh49SgDcu3dvum0WLlxIADx69GgeWlbwiI2NpYWFBR0cHPLkiUMqlfLy5cts27YtAVAgENDY2JjPnj3LlfmioqIoEAi4adMmvnjxgpqamuzXr1+WxkhMTCQAbtmyRfb/jRs30tTUlCoqKhw1ahRDQkIUZvOXL1/YrVs3AmCrVq34/v37TPu8e/eOgwcPplgsppGREb28vFLs8ty/f58AuHv3boXZKZVK6evryxUrVrBDhw7U19cnAKqoqNDQ0JBisZj6TQexhNvRDJ/uNcvWI4Qi6tZyYuEWI6hmWo4QimjUfUGG/Swmn+T0o75ZsjkqKooPHjzgrl27OG3aNDo7O7NChQpUU1OTPeVramqyatWq7NGjB2fPns0DBw7Qx8dH4btmGTF79mwWKlQoxc7C8+fPCYCXLl3KMzs+fPjAvn37UiAQsEyZMjx06FC27xNhYWEsWrQo27dvn6+7G4pGuTNQwOnYsSOuX78Of3//NEO4SMLJyQmXL1/GgwcPYGFhkQ9W5j/z5s3D9OnT4ePjg7Jly+bZvKdPn4aTkxP09fVlVRJ79+6NsWPHwtraWmHz3L59G3Xq1MGDBw9QtWpVbN68Gf3798eBAwfQqVMnucaIj4+Huro6tm/fDl1dXUyaNAl+fn7o1q0bZs+eDUtLS4XYShL79+/HiBEjIJVKsWzZMvTo0SNLPgdv377F7NmzsW3bNhgZGWHKlCno378/1NTU0KpVK7x79w5Pnz7NVlpZkggMDJQ9+V+6dAkhISEQi8WwtLQESbx58waJiYmoU6cOnJ2dUa1xG7jsfZnxuEkJiLj6szaBJC4KqkVLQq9+T2hYZJ63Iq0UtCQREhKSZga+X9PumpiYpJlr39TUNNtpdxXF1atXYW9vj4cPH8qyaCYmJkJTUxPLli3LUZSNPPz48QOenp74559/oKWlhenTp2Pw4MFyJf1Kjz59+uDIkSN4/vw5ihVLf7fod0NZm6CA8/HjR9jY2KBLly5Yv359mm0iIiJQvXp1FCpUCDdu3JCr2MafxIcPH2BtbY2hQ4di8eK0077mBnv27IGLiwtatmyJffv2ITo6GuvWrcOKFSsQEhICR0dHuLq6wt7ePsfOd2vXrsWIESMQFRUFdXV1kETnzp1x/vx5PH36VK4wv+joaGhra8PKygovX75EkyZN4OnpqdAkS8HBwRg+fDj+/fdfdOzYEatWrUpVbyMrBAQEYNasWdi1axfMzMwwbdo0lClTBg0bNsThw4fRoUMHucb58OEDLl26JBMA7969g1AohK2tLUxMTPD161c8evQICQkJqFu3LpydndGxY8cUn2tmtQmyg0goQO1SheFRXz+VA5+/vz++f//+s93/p91NK9d+ek6XBYG4uDjo6enB09MTo0ePlr1evnx5NGrUKNcySyYmJmLDhg2YMWMGfvz4gbFjx2LixIk5/qzOnj2LFi1apDpq+xNQioHfgDVr1mDYsGG4cuUKGjRokGabx48fo3bt2ujduzfWrVuXxxbmL927d8fFixfx8uXLPPverVq1CiNHjoSLiws2btyY4vw6Pj4ee/bswZIlS+Dr64uqVavC1dUVnTt3zvYTydChQ3H9+nX4+Pwv41l4eDgqVaoECwsLXLx4McMoAX9/f0yYMAEnTpxAyZIlsW7dOjRr1kxhyVxIYvv27RgzZgxUVVWxatUquXcs5MHPzw8zZszA/v37YWFhAVVVVWhqauL+/ftpvocvX77g8uXLsif/ly9/PtVXrlwZderUgZqaGvz9/XHx4kUkJibCzs5OJgDSy5KYWdXCrEISAmkSQjaPQFzYzyx8urq6qZ7wy5YtK3vPvyP29vYoUqQIDh06JHutc+fO+Pr1Ky5evKjQuUji2LFjmDhxIl6+fAkXFxfMnj1bLrGcGT9+/ECFChVQpkwZnDt37o8rGqf0GfgNkEgkrFu3Lq2trRkXF5duu40bNxIAt23blofW5S/Xrl1LcQ6e20ilUs6YMYMA6OrqSolEkmHbs2fP0sHB4adHuakpPT09GR4enuV5a9euzR49eqR6/fLlyxQIBJw7d26a/T5+/MiBAwdSKBTS3NycALh///4sz58RQUFBbNGiBQGwZ8+e6XpXK4KnT5+yQ4cOsnPxiRMnMikpieHh4Tx69ChHjx7NihUryq5bW1tz6NCh3LJlC5cvX85WrVpRRUWFAoGA9erV47Jly/jhwwe55999JyjTyIKs/JjWd6anpycvXLjAT58+/VFn0MlMnTqVRYoUSfHepk+fTiMjI4XOc+fOHdavX58A2LRpUz569Eih448YMYKampp8/fq1QsctKMi7fivFQD7j4+NDsVjM6dOnZ9iub9++1NDQ4NOnT/PGsHwkKSmJtra2rFmzZoaLsqKQSCQcMWIEAXD+/PlZunH7+PiwX79+VFVVpZaWFkeNGiULr8uMpKQkamlpcdGiRWlenzx5MkUiEW/fvi17LSIigpMnT6aGhgYNDAy4dOlSvn//ngB45MgRue3OCIlEwrVr11JHR4fFihXj8ePHFTKuPFy7do1aWloEQA0NDVl4nLm5Ofv27csdO3bQ19eXmzdvZsuWLWUCoH79+ly+fDk/fvyY5TmlUilHjBhB3TqdFSIE3LZeoKGhIS0tLenn55cLn1LB4Ny5cwSQwrl23759BKAQ4fj69Wt26dKFAFihQgWePn1a4aLq2rVrFAgEXLp0qULHLUgoxcBvxJQpU6iqqsrnz5+n2yY6OpqVKlVimTJl/vjfw9q1awkgxSKYW8THx7Nbt24ZxunLQ3BwMKdNm0YDAwMKhUJ27NiRN2/ezLDPixcvCIDe3t5pXk9ISGDNmjVpYWHB0NBQLl26lAYGBtTQ0ODkyZMZEREhmxuAQhbtV69esVGjRgTAAQMGZGu3IyvExcXx8uXL9PDwYL169aiioiJ7+i9cuDABsGzZstyxYwc3bdrEli1bUiwW51gAfPv2jTdv3uTGjRtZrVo1AmDRokWpY9uCZuMO0XzCkSwJAIvJJ2k19RT33g0i+TM3hY2NDfX09HjhwgVFf2wFgqioKIrFYq5evVr2mo+PDwHw2rVr2R43LCyMY8eOpYqKCosVK8ZNmzZlKx9CZsTGxtLa2pq1a9fOlfELCkox8BsRGxvLMmXKsH79+hk+Cb98+ZK6urrs1KnTH7ntSP68ERgYGLBPnz65PldUVBRbtGhBVVVVHjhwQCFjRkdHc+3atbSysiIA1q5dmwcOHEjzZrN//34CyDDs7+XLl1RTU6O2tjaFQiEHDhyYYvGLikvkxUcvqWpixXX7T2Y7AUpSUhK9vLyoqanJkiVL8ty5c9kaJzMSExN5+/Ztzps3j02bNqW6ujoBUF9fn05OTly5ciWfPXvGSpUq0d7enhMnTpSJguQnxOXLl/PTp0+ZziWRSPjmzRuePn2aS5cu5eDBg9mgQQMWLVpUNl7yT/ny5Tl27FiuW7eOB09fYufVV2WLfGYioIT7CfbceJvvwqJTzB8REcFmzZpRLBZz48aNufJ55je1a9dm165dZf+Pi4ujSCTKlrCOjY3lokWLqKenR21tbc6ePZtRUVGKNDcFkyZNoqqqaq6FDRcUlGLgN+PixYsEwPXr12fY7tChQwTwx25rjRgxgjo6OgwODs7Veb59+8a6detSS0srVxY+iUTC48ePs2HDhgTAUqVK0cvLK0UWvilTptDExCTN/sl+Cba2trIFa/HixSTJl58jOf2oLxssvMiSaWS8a7DwIqcf9eXLz2ln/Psvfn5+rFOnDgFwxIgR/PHjR84/gP9HIpHw0aNHXLJkCdu0aUMdHR0CoLa2Nlu3bs3Fixfz4cOHMhH89etXbty4UZZFTiAQ0N7eniNHjmT16tUJgHXr1uX58+dlgjgmJoaPHz/m3r17OWPGDHbt2pW2trbU0NCQfXbq6uqsXLkyu3TpwunTp3PPnj3s06cPAXDlypVp2i77nBel/pzNJx5ntenHOP2oLwNC0v+cExISOHjwYAKgm5tbnhx75SVubm40MTFJ8XBibW3N0aNHyz2GRCLhrl27WLJkSYpEIg4dOpSfP3/OBWv/x8OHDykSiThr1qxcnacgoBQDvyF9+vRhoUKFMl0IXV1dKRaLeePGjTyyLG94+vQphUKhbNHLLT5+/MgKFSrQwMCAd+7cydW5SPLBgwfs0aMHxWIxCxUqxAkTJvD9+/ds3bo1W7Rokar9/fv32aRJEwKgnZ0dr1+/zq5du1K/eGl2XHEpx0+sySQmJnL+/PlUU1NjmTJlePXq1Ry/V6lUSj8/P65atYodO3akgYGBbDFu0qQJ586dy1u3bqVIh/z161du2LCBzZs3p0gkolAopL29PY2MjNisWTPZuCEhIVy8eDFLliwpO0YwMTFJlXa3QYMGHDRokCzt7ps3b1IswlKplJMnTyYAenl5yfW+/puC1rh4CU6ZMkXuz+Sff/6hQCCgk5MTo6PT/n38jpw4cYIAUqT97dChg+z3lhmXL1+Wibx27drliY9FQkICbW1tWbFiRcbHx+f6fPmNUgz8hnz9+pVFihRhly5dMmyXkJBAOzs7mpqaKjSzXH4ilUrZsGFDWltb5+ofaEBAAEuVKsXixYtn6KORG7x//55ubm4sVKgQxWIxNTQ0UhyHvH79ml27diUAlitXjkePHpU9cW267McS4w9nmi0vvbPsPf9/lp3MkydPWK1aNQqFQk6YMIExMTHZfl9v3rzhpk2b2KNHD5qYmBAAxWIx7ezsOG3aNF66dClVdrzQ0FCuX7+ezZo1kwmARo0aceXKlbx16xaPHz8ucx6rXLlyiqMCoVBIExMT6urqEgBtbGy4bt06uZ3Wpk+fTgBcsmRJtt9zy5Yt2apVqyz1OXr0KLW0tFi9enW5jjl+ByIiImQZNJOZMmUKTU1NM+z3/PlzOjo6EgBr1KjBK1eu5LapMubNm0ehUJjtOiC/G0ox8Juyc+dOAuCJEycybPfhwwcWLVqUTZs2/SOcXw4cOEAAPH36dK7N8ejRIxoZGdHa2ppBQUGZd8glIiMjOW/ePNniVqdOHbZp00bmMLVx48YURapWXHypEC/3FRdfMj4+ntOnT6dYLGb58uWztTPy8eNH7ty5k/369ZM9pQsEAlavXp1ubm48c+ZMmkcNX7584bp169i0aVMKhUIKBALa2NiwZcuWbNOmDStUqEBVVVXZ56KlpUVVVVWam5vL0u76+vrKwnAlEgkPHTrEChUqyFIj379/P0PbZ82aRQD09PTM8vv+lcmTJ6d7xJMRDx8+pKmpKc3MzPj48eMc2VBQqFKlCl1cXGT/37VrFwHIHFx/JTg4mIMHD6ZIJGLJkiW5Z8+ePD068fPzo5qaGidMmJBnc+Y3SjHwm5Jcoc/c3DzTs9vz589TKBTSw8Mjj6zLHaKjo2lubk5HR8dcm+Pq1avU1dVltWrV+OXLl1ybR14uXLggW8CEQiEBsEiRIly2bFmKbeQ9d3/Gv5u5HmAhu25UL1WVQnVtAqBBqzGpFnxjlyXUrtKKqkaWhFBEACmuW7XsQ7FYzGnTpmWY2+JXvn79yoMHD3LYsGEsW7ZsCme+UaNG8ciRI/z27VuqflKplD4+Phw7diytra1l2/m/5tkHQBMTEzZq1IjDhg3j8uXL6e3tzXfv3lEqlXLt2rUUCAQZbh9LJBLu2bOH1tbWBMD27dvzyZMnqdrNnTuXANLN3ZAVksVrds62P3z4wCpVqlBbWztT0f87MGbMGJYsWVL2/0ePHhEAb926JXstKiqKM2fOpJaWFvX19blkyRK5v3+KQiKR0M7OjqVLl/6jjmoyQykGfmNev35NDQ0Njh07NtO2c+bMoUAgyNUn6txm+vTpVFVVzVa5UXk4fvw41dXV2bhx43TL6OYlCQkJ7NixIwFQVVWVrq6uPH36NDt16kShUEgDAwNOnTqVD/zf0mrqqZ9JbIZsIgCKdA2pZl4xXTFQyK4bIRRT1bg0xYVNU4gB84nHWWLCvzxzLePt0e/fv/PEiRN0dXWlra2tbBEvU6YMBw8ezL1796ZYBBMSEujn58d///2X8+fPZ5cuXWTOYMkLfnLBp5YtW9Ld3Z3btm3jnTt30nx6/JW4uDgWK1aMvXv3zvRzTUxM5Pbt22lpaUkAdHZ2lnmKe3p6EgBnzpyZ+S9IDl69epWjnayoqCi2bduWQqGQy5cvV4hN+cXhw4cJQLbbFhMTIzs6SEpK4oYNG2hiYkJVVVWOGzcuTeGYF6xcuZIAePny5XyZP79QioHfHE9PTwqFwky3PSUSCVu1asXChQvn69Z3dnnz5g3V1dU5adKkXBl/27ZtFIlEdHJyytOqbmkhlUp58OBBWdihgYEB37x5k6JNYGAgR48eTW1tbRp1ncMSE4/9XMjH/8viI3b8fPrvvTRdMVB85A6ajTvEEu4nqFO1daqdAYvJJ9lzY8r8DdHR0Tx37hwnTZrEWrVqyRbx4sWLs3fv3ty2bRvfvXvHiIgI3rlzh1u3bqW7uzvbt2/PsmXLUiwWyxb95L4CgYClS5fm0KFDeePGjRQOg1nFy8uLIpFI7mROCQkJ3LhxI0uUKEGBQMCqVasSgEJ30CQSCXV1dTlv3rxsj5GUlMRx48YRAIcPH57iaOh3IjQ0lAC4Y8cO2WuWlpbs0KGD7Aina9eucv/+coO3b99SW1ubQ4YMyTcb8gtl1cLfnMTERNSoUQNCoRB3797NsMb7t2/fULVqVRgZGeHq1atQU1PLQ0tzRqdOnXDr1i28ePEC2traCh3by8sLY8eORf/+/bFu3boMc/znNlevXoWbmxvu3LmDFi1aIDAwEPb29ukWqXrw6hM6bnqU5rX44AB83jYWBq3GQLtS03Tn/Oa9Bj8enkQJ9xOprnk20MaLe1dw8eJF3Lp1CwkJCShatCgaNmyIKlWqwNjYGJGRkXjx4oWsuE5wcLCsv5mZGSwsLCAQCPDp0ycEBARAIBCgcePG6Ny5Mzp06IAiRYpk8VNKm5iYGJQsWRIdO3bEmjVr5O6XkJCAHj164ODBgxAIBOjduzc8PDxQqlQphdhlb28PIyMj7N+/P0fjrF+/HsOGDUPz5s2xd+/e3/IeW6FCBdStWxfr16/Ho0eP0Lx5c3z9+hUNGjTA4sWLUaNGjXyzjSRatmyJZ8+e4dmzZ7/l55sT5F2/87cOppJ0UVFRwYYNG/D48WMsW7Ysw7aFCxfGwYMH8fjxY4wfPz6PLMw5Fy9exKFDh7Bo0SKFCgGSmDp1qqyi2YYNG/JNCPj6+qJNmzawt7eHRCLBhQsXcPToUbx58waVK1dOt9/x5+EQCXOnYAqlEgz9ZzcWL16MmJgYNGvWDK1bt4aZmRlOnjyJSZMmoW/fvpgwYQKuXr0KAwMD9O/fHzt37sTZs2exZMkSWFpa4tq1a7h27RpKliyJ9evXIyQkBOfOncPAgQMVJgQAQFNTE66urti8eTM+fvwod78NGzbg4MGDcHV1xdKlS3H69GlYWVlh8ODBeP/+fY7tqlKlCh49SluwZYVBgwbh9OnTuHnzJurVq5eijPHvQoMGDXDhwgW4uLigWrVqkEqlMDQ0xOXLl/NVCADAjh07cPbsWaxdu/avEwJZQSkGCjA1atTAyJEj4eHhgbdv32bYtnr16vDy8sLKlSuxd+/evDEwByQlJWHUqFGws7NDt27dFDauRCLB0KFDMXfuXCxatAgLFizIlypk79+/R9++fVGpUiX4+/tj3759uHPnDho3bgw/Pz8kJibC1tY23f6XXnxRaEndXxEIRdCwqI4fP37g3r17uHnzJsLDw2Fra4sZM2bg+PHjCAgIQHR0NHx8fLBixQoYGxtjw4YNaNGiBSZOnAg1NTWZADh79iwGDBigUAHwX4YNGwZNTU25S1knl4Z2dXXF4sWLMXr0aAQGBmL+/Pk4fPgwSpcujREjRuDTp0/ZtqlKlSp49eoVIiMjsz1GMs2aNcPNmzcRFRWFmjVr4u7duzkeM6/4/v07Pn78iMDAQJw6dQqrV6/G4sWLERoaiqioqHy1LSQkBGPGjEGPHj3QunXrfLWlwKPIMwcliicyMpLFixdnixYtMk1BLJVK2aNHD2ppaeV5DH1WWb58OQUCAR8+fKiwMePi4ujs7EyhUMjNmzcrbNys8O3bN06YMIFqamo0NDTkypUrU+VN2Lp1KwGk68z4Iy4xVca7FBEDGfgM/PqTls/A/36O0/viFX758iXN79WnT5+4YsUKNmjQgAKBgGKxmC1atOCmTZsYFhaWK59dZnh4eFBDQyPTaJANGzYQAEePHp3me0sO7dTX16e6ujrHjh2brXwdT548IQCFJGtKJiQkhHXq1KG6urrCUmTnFvHx8Vy2bBkNDAxkaaW3bt1Kkrx37x4B8O7du/lqY6dOnVikSBGGhobmqx35ibzrt3JnoICjo6OD1atX48yZM9i3b1+GbQUCAdatW4cSJUqgY8eO+a7K0yM0NBQeHh4YOHAgqlSpopAxo6Ki4OjoiGPHjuHQoUPo27evQsaVl7i4OCxatAgWFhZYvXo13N3d8fr1awwfPjxVvfonT57AwsICOjo6aY4VFBaN3NkT+BUBillXhqGhoWzn5NOnT1ixYgUaNGgAU1NTjB07FlpaWti0aRNCQkJw+vRp9OvXD4ULF85169Ji1KhREIlEWLp0abpttmzZgkGDBmH48OFYunRpmrtCOjo6mDRpEt68eQN3d3ds2rQJpUqVgru7O8LCwuS2p1y5clBTU1PIUUEyRYsWxcWLF9G+fXs4Oztj/vz5YOZuXXkKSRw8eBDly5fH2LFj0b59e7x+/RplypTBvXv3AABly5YFADx//jzf7Dx8+DAOHjyIFStW5Oqu1Z+CUgz8Bjg6OqJTp04YPXo0vn37lmFbLS0tHDp0CO/evcOgQYMK3I0EAKZOnQoAmDNnjkLGCwsLQ5MmTXD79m2cOXMG7du3V8i48iCRSLB161ZYWVlh8uTJ6N69O169eoUZM2aku9g/fvw4wyOChCRpLlmbep6PHz9i+fLlqF+/PooXL45x48ZBR0cHmzdvxpcvX3Dq1Cn07ds33wTArxgYGGDo0KFYuXIlwsPDU13fvn07+vfvj8GDB2PFihWZHg8VKlQI06dPx9u3bzF27FisWrUKJUuWxLRp0xAREZGpPSoqKqhQoYJCxQAAqKurY/fu3fDw8MDkyZPRr18/JCQkKHSO7HLz5k3Y2dnB2dkZpUuXxuPHj7Fx40YUK1YMDRo0wJUrVwAA2traKFGiRL6JgfDwcAwfPhyOjo7o0qVLvtjwu6EUA78Jy5YtQ1xcHNzc3DJtW7ZsWWzcuBF79uzJkvd1XvDw4UNs2LABs2bNgqGhYY7H+/DhA+rXr483b97g8uXLaNiwYc6NlAOSOHnyJGxtbdG3b1/Url0bz58/x6pVq2BsbJxhvydPnmToPKgqzps/y8ED+6N48eIYP348ChUqhC1btiAkJAQnT55Enz59oK+vnyd2ZAVXV1ckJiZi5cqVKV7ftWsX+vTpg/79+2PVqlVZ8hPR19fHnDlz8ObNGwwdOhRLlixByZIlMXv27Ez9ARTlRPhfBAIBZs6ciR07dmD37t1o3rx5pg8CuUlAQAA6deoEOzs7xMbG4ty5czh9+jQqVqwoa9OgQQP4+vrKdldsbGzyTQyMGzcOMTExWLNmTb74DP2OKMXAb0KxYsXg6emJTZs2ydR3RnTt2hUjRozAmDFjCowzEkmMHDkSNjY2GDp0aI7He/HiBezs7BAdHY3r16+jatWqCrAyc+7cuYNGjRqhTZs2MDAwwJ07d7B//36UKVMm074fP37Et2/fMtwZKGmghdy+fZFE2Ft/TJw4Ee/fv8eJEyfQu3fvAikAfsXY2BgDBgyAl5eX7Bhs3759cHFxQe/evbFu3ToIhdm7rRUpUgQLFy5EYGAg+vbti7lz56JUqVLw9PREdHR0mn2qVKmCZ8+eIT4+PtvvKSN69uyJCxcuwNfXF3Xq1EFAQECuzJMeX79+xahRo2BjY4M7d+5g27ZtePDgAZo2TR3Sam9vDwC4fv06gPwTA+fOncOWLVuwePFimJqa5vn8vy2KdEBQkrtIJBLWrVuX1tbWciXQiY+PZ61atWhubi53EZfcJLnuwoULF3I81v3792loaEgbGxu+f/9eAdZlzosXL9ipUycCYMWKFXny5MlMnTr/y/HjxwmAb9++TbdNSEgIK04+nMrpT7/ZYBaq35PaVVoRADWt6rJQ/Z4sVL8nzcbs+5mpcOhm2WuqxX6m503+v0Eb1/+lJR63m0ZGRj/H0dRkq1at6OXlRT8/vyy/p7wmKCiIKioqXLRoEQ8cOECRSMRevXopvEbHhw8fOGzYMKqoqNDQ0JBLlixJVdDp5s2bBMAHDx4odO7/8urVK1pbW7Nw4cJ5UtQnJiaG8+fPp66uLnV1dTl//ny5ilmZm5vLMqdu2rSJAoEgT1P//vjxgyVLlmSjRo0K/Pc4r1BmIPxD8fX1pYqKitzZ1IKCgmhgYMCWLVvmay31Hz9+sFixYuzUqVOOx7p48SJ1dHRYq1atPBE5wcHBHDJkCEUiEc3MzLht27ZsLzxz5syhnp5eqhuVRCLh2bNn2alTJ6qoqLCIw1BZ9sHkH5Fu0RQ5/X/9MR2yiSXcT9Co27x026iZVZBlIZx+1JdSqZSPHz/mwoUL2bRpU1mRIHNzcw4YMID79+/Pt9SxmTFgwABZ9cfu3bvnarGut2/fcsCAARSJRDQ2Nuby5ctlefWjoqIoEAi4cePGXJs/mW/fvrFx48ZUUVHhtm3bcmUOiUTCbdu20czMjGKxmCNHjsxSLY9evXqxWrVqJMlbt24RgEIjhjJj9OjR1NDQ4KtXr/JszoKOUgz8wUydOpUqKiqyvOuZcfr0aQoEAs6ZMyeXLUufSZMmUV1dPcMnYnk4fPgwVVVV2axZs0wLOeWUyMhITps2jZqamtTX1+eiRYtynNK4U6dOtLe3l/3/w4cPnDVrFkuUKCEr/rNs2TLee/FeIZUK0/sJCEkd1hgdHc1Tp05xzJgxLFeunKxccK1atejh4cHr168XmJS5a9euJQBWrVo1z2x69eoVe/fuTaFQyOLFi3Pt2rWMj49n2bJlOXz48DyxISEhgf379ycATpkyRaEC/9y5c7S1tSUAduzYkS9fvszyGBs2bKBQKGRERAQjIiIIgDt37lSYjRlx48YNCgSCHJWm/hNRpiP+g4mLi0OlSpVgZGSEK1euyHVGOn36dMyZMwfe3t5o0qRJHlj5P169eoXy5ctj0qRJmDFjRrbH2bx5MwYOHIhOnTph+/btuZZ2OSEhAevWrZM5kI0ePRru7u4KOU+3srKCg4MDmjVrhg0bNuDUqVNQV1dH165dMXDgQNSqVUvm8NRr0x3cDAxTaPIhkVCAuhYG2NG/VqZt379/D29vb3h7e+PcuXMIDw+Hrq4umjRpAgcHBzRv3lxhqX2zwokTJ+Dk5AQTExNIpVK8fv06VfhmbvLixQvMnDkTe/fuRYkSJWBkZAShUIibN2/myfwksWjRIkycOBGdO3fG1q1boaGhke3xfH194ebmhtOnT6NOnTpYvHgx6tatm62xXr58CWtra5w6dQotW7ZE8eLF0bt3b8ydOzfb9slDXFwcqlSpAl1dXdy8eTNfU48XNORevxWpLJTkHZcuXSIArlu3Tq72SUlJbNasGQ0NDfnhw4dcti4ljo6ONDc3z9HZ4cKFCwmAQ4YMybUt4eRSuBYWFhQKhezXrx/fvXunsPF9fHwIgHp6egTA6tWrc926den+Xb0Li5ZVLVTUj9XUU3wXlvXfQ1JSEu/cucNZs2axXr16soJEZcqU4fDhw3ns2LE8qQh5+vRpqqqqskOHDrJSuXmxRZ8WPj4+suqTAoEgR8dH2eHQoUPU0NBgrVq1slVK+ePHj+zfvz+FQiEtLS154MCBHJ+zS6VSGhsbc+LEiSTJZs2asX379jkaUx6Sd0t9fHxyfa7fDeUxwV9Av379WKhQIX769Emu9l++fGHx4sVpZ2eXoypyWeHUqVMEkO1salKplG5ubgTAadOm5ZpT0Pnz51mtWjUCoKOjo8JuKnFxcdy3bx+bNm0qO7t3dnbmo0eP5Oq/4tRDhYqBvXcVU9kyIiKC//77L4cMGcJSpUoRAFVUVGhvb8+5c+fy/v37CvdR8fb2ppqaGtu2bSvL6ujk5MTSpUvn6/HFmjVrZL/bcuXKcd++fXnmn3Pv3j0aGxuzRIkS9PX1lavPr8dfBgYGXLZsWaosmTmhc+fOrFOnDklyzJgxtLKyUtjYafH48WOKxWLOmDEjV+f5XVGKgb+AsLAwGhoa0tnZWe4+N2/epFgspquray5a9pP4+HhaWVll27M3MTFRdj7q5eWVCxaSjx49ooODAwGwdu3aCvPU9vPz47hx41ikSBECoJ2dHV1cXCgSiTL1OwgMDKSnpyerV6/+M+1w/e6yFMI5EQIrLwYo5L2lRUBAAFetWsV27dpRR0eHAFikSBF269aNW7Zs4cePH3M0/oULF6iurs7WrVvLnPdI8sGDBwTAXbt25fQtZJuvX78SAOfMmcOWLVvKok0OHz6cJx7t7969Y6VKlairq8szZ86k2y4xMZFr1qyhkZER1dTUOHHiRIaHhyvcnlWrVlEsFjM6Oprr16+nUChM8TtTJImJiaxWrRorVKigUEHzJ6EUA38Ju3btIgAeP35c7j5eXl4EwIMHD+aiZeTixYspEon49OnTLPeNjY1lhw4dKBKJuH37doXb9ubNG/bs2ZMCgYBWVlY8dOhQjm/cMTEx3L59O+vXr/9zETcwoKurq6xOxODBg1mhQoU0+75+/ZoLFiyQ7U5oaGiwY8eO3Lt3L3/8+ME9d4NoNfUULSafzJIAsJh8klZTTylsR0AeEhISePXqVU6ZMoXVq1enQCCQOUeOGzeOZ8+elStMLZlLly5RQ0ODLVq0SFNItWzZkuXLl8/XaBkzMzO6ubmR/OnI1qRJE5mD44kTJ3JdFERGRrJ169YUiURcvXp1imtSqZRHjx5l2bJlCYC9evViUFDufR+Sj8POnz/P69evE0C27gHy4OnpSaFQyDt37uTK+H8CSjHwlyCVSung4EAzMzO5veulUimdnZ2po6OTLY9heQgODqaOjg5HjBiR5b7fv39no0aNqK6uniWRIw+hoaEcM2YMVVVVaWxszLVr1+b4yOTx48ccPnw4CxUqRABs0qQJ9+7dm+ppqHbt2uzZs6fs/69eveL8+fNZtWpVmQDo1KkT9+3bl+bv8l1YNHtuvP1zof9P2GFaIqCE+wn23Hg7Wz4CiiQ0NJR79uxh3759WaxYMQKguro6mzdvziVLltDHxyfdxfLq1avU1NRks2bN0hUQN27cIAAePnw4N99GhrRt25bNmjVL8drly5dlwrBWrVr09vbOVVGQlJTEUaNGEQDHjBnDpKQk3r17l/b29rLvZV6E+UkkEhoYGNDDw4NhYWEEwL179yp8nhcvXlBdXT1Pdjl/Z5Ri4C8iMDCQGhoaHDNmjNx9vn//TisrK1asWDFXkoL06dOHBgYGWa5w9+XLF1arVo2FChVSaDW46Ohozps3j7q6utTR0eHs2bMZFRWV7fEiIyO5fv161qhRgwBobGzMSZMmpRvfnJSURE1NTU6cOJHz5s1jlSpVUgiA/fv3y2XP+/fvqVLEnJ3m72ODRRdTVTcs6X6CDRZd5PSjvmmGD+Y3UqmUvr6+XLJkCR0cHGTV7ooVK8Y+ffpwz549sgpz169fp5aWFhs3bpzpd7Rhw4asWrVqviWamT59OosUKZJqfqlUynPnzrF27doEwPr16/PSpUu5asuKFSsoFAplwqt8+fI8depUnn427du3l4XQGhsby50XRV4kEgnr169PCwuLPE1q9DuiFAN/GQsXLqRQKOS9e/fk7uPj40MNDQ327t1boTeK27dvEwDXrl2bpX5BQUG0srKikZERHz9+rBBbEhMTuWHDBhYrVowqKiocNWpUlpKo/IpUKuXt27fZv39/amlpUSgUsnXr1jxy5EiGuwsBAQF0dXWVOZlpamrS2dlZbgHwK/Pnz6eGhobsbzEqLpG+HyP4MOgbfT9GMCquYOQBkJeYmBh6e3tz3LhxrFixoswzv1y5clRVVaWtra1ciY/Onz9PADx9+nQeWJ2aI0eOEEC62TClUilPnjwpOwZq3Lgxb9y4oXA7vn37xnHjxlEsFlMgENDMzIxv3rxR+DyZ8c8//1BNTY1xcXFs3LixQpKN/crq1asJgBcvXlTouH8iSjHwl5GYmEhbW1va2tpmybN6+/btBMANGzYoxA6JRMIaNWrQ1tY2S2FWz549o6mpKUuVKqWQ7GFSqZRHjhyRJc/p1q0bX79+na2xvn37xuXLl8sWK3Nzc86cOTPDsMOXL19y7ty5siQuampqsjC47D7JSKVSli1blt27d89W/9+Bjx8/0sPDg2KxmGKxmACora3Ntm3bcuXKlQwICEhTuEqlUtauXZt169bNl92BoKAgAuCxY8cybCeVSvnvv/+yUqVKBMAWLVoo5Lw7Li6OS5Ysob6+PrW0tDhz5kzevn2b5ubmLFasGO/fv5/jObJCsmPntWvXOGLECNrY2Chs7KCgIGpra3PgwIEKG/NPRikG/kLu3r1LoVDIRYsWZanfoEGDqKamppDzxM2bN8tuAvJy+/ZtFi5cmBUrVpQ7TDIjrl+/zrp16xIAmzZtmq288VKplJcvX2aPHj2opqZGsVjMjh078vTp0+mKnBcvXnDOnDmsXLkyAVBLS4tdunThwYMHOWHCBJqYmOTofd25c4cAePbs2RyNU5C5f/8+9fT0WLduXUZERPD+/fucN28e7e3tZeKgVKlSHDJkCA8fPsyIiAhZ3+S6D7m9DZ8WUqmUhQsX5syZM+VqL5FIuH//fplYdXR0lDvc9L/z7tmzh6VKlaJIJOLgwYMZHBwsux4cHMyaNWtSU1OT//77b5bHzy5JSUnU1dXlnDlzuHr1aorFYoWEM0ulUrZs2ZLFihVL8btXkj5KMfCXMmbMGGpoaDAwMFDuPrGxsaxatSotLCxyFGoUERFBIyOjLD25ent7U0tLi3Xr1s1xHvznz5+zXbt2BMAqVarQ29s7y2OEhIRw4cKFtLKykiXV8fT0TDepi7+/P2fPni170tPS0mLXrl156NChFDsArVu3ZsuWLbP93khy2LBhNDU1zdPENnnJw4cPqa+vz1q1aqV5r4mMjOSxY8c4YsQI2e9HJBLRzs6Os2bN4q1bt1ipUiU2bdo0H6wnmzRpkuUEO0lJSdy5cyfLlClDAHRycpI7x8WVK1dkPiuOjo6yqJX/EhMTQ2dnZwoEAi5evDjPdk5atWrF5s2b8/LlywSQrn1ZYceOHXLtwCj5H0ox8Jfy48cPmpmZ0cHBIUt/9IGBgdTT02Pbtm2zfbMYN24ctbS05M5weODAAaqoqLBly5Y5cgL68OEDBwwYQKFQyJIlS3LXrl1ZCjP7b5EgNTU1du/enZcuXUrzs/Dz8+OsWbNkxwba2trs1q0bDx8+nK7Hu6mpKd3d3bP9HuPi4qivry/L7Pan8fjxYxYuXJg1atSQ+4kvMDCQa9eupZOTkyySQ0tLiwA4efJkhWaPlIfx48ezRIkS2eqbmJjILVu2sFSpUhQIBOzatSv9/f3TbOvv7y8TvdWrV5drJ0QikXDSpEkEwIEDB+ZJ0rEFCxZQS0uLHz9+VEgoc0hICAsXLsyuXbsqyMK/A6UY+Is5duwYAXD37t3Z6rdw4cIsz+nn50exWMy5c+fK1X7t2rUUCATs0aNHtm9M4eHhnDRpEjU0NGhgYEAvL68sJTf5b5Gg8uXL08vLK80IiOfPn3PmzJmsUKGCTAB0796d//77b6Yx86GhoTkOrzp48KDCnq4KGj4+PixSpAirVq2a7d2hxMRE3rhxg1OnTpVFKCRnBBw9ejRPnTqVo+gReUjO+ZHVCJpfiY+P57p162hmZkahUEgXFxeZD83nz585dOhQikQilihRgrt3785yboXNmzdTRUWFTZo0yZWEQ7+SXN75zp07LFKkCGfNmpWj8bp06UIDA4NsOwD/rSjFwF+Os7MzDQ0Ns3xjcnd3p0gkylImPqlUyubNm9PCwiLT7HpSqZRz584lAI4cOTJbiWLi4uL4zz//sHDhwtTQ0OCUKVPkfppMTEzk0aNH2aZNGwqFQmpqarJfv368detWql2AZ8+eccaMGSxfvjwBUEdHhz169OCRI0eyVL0w2dPdz88vS+/zVxwdHVmjRo1s9y+oPHv2jIaGhrS1tc3RIvoryU6xCxcu5IABA2hmZkYAVFVVZZMmTejp6cnHjx8rfLv8+fPnBMALFy7keKy4uDiuWLGCJiYmFIlErFatGjU1Namnp5fj6pmXLl2ivr4+y5Ytm22nWnmIj4+npqYmFy5cyAYNGrBLly7ZHis5WiM/M03+rijFwF/Op0+fWKhQIfbr1y9L/RITE9mwYUMaGxuncETKiKNHjxIAjx49mmE7iUTCsWPHEgBnzpyZ5ZuxRCLhjh07WKJECYpEIg4aNEjuNLeBgYGcMmWKLPa6WrVqXLt2barvtK+vL6dPn04bGxsCoK6uLnv27MmjR49m+wa8ZMkSamhoZPusPyQkhGKxmCtXrsxW/4KKn58fjYyMWKlSJX79+lVh4yYmJrJUqVKyNN1SqZR+fn5ctmwZW7VqRU1NTQKgkZERe/XqxR07dmSr0M9/Sc4lsXjx4hyPlTzemjVrqKurS+BnOem+ffsqpNDYixcvWLp0aRYpUiRXQhyTadKkCdu0acMhQ4awYsWK2RojPDycJiYmbN26db7lkfidUYoBJbKa71n1rg4ODqaJiQnt7e0zDVOMjY2lhYVFpj4KCQkJdHFxoUAg4KpVq7Jkj1Qq5ZkzZ2Re+h06dJDrKfu/RYJ0dXU5bNiwVFETvr6+9PDwkHl2JwuAY8eOKSSnuouLC2vWrJnt/kuXLqWKiopCF8z85sWLFzQxMWH58uVzZdt33bp1FAgEaX5P4uLieOHCBU6cOFEW+gmAtra2nDhxIi9cuJDt33vt2rXZo0ePnJrPM2fOyHxSunTpQh8fH3p6etLAwIBqamocPXq03GI9Pb5+/coGDRpQTU0ty0eK8jJr1iwWKlSIXl5eVFVVzVZBqQEDBlBHRyfPfUD+FJRiQAklEgnt7OxoZWWV5afaK1euUCQSZer0NnfuXIrF4gwX55iYGDo6OlIsFnPPnj1ZsuPevXts3LixrNiPPE8xaRUJ2rp1q8xJUSqV0sfHJ5UA6NWrl8IEwK9UqlQpRzHRtra2dHJyUqBF+UtAQACLFSvGcuXKKeSJPC3i4uJoampKFxeXTNt+/vyZO3bsYK9evWhkZCRLDNWqVSsuW7aMfn5+cj+RDh06NEcx9Y8ePWKzZs1k2Qr/m4Pg+/fvnD17NvX09KihocHx48fnSEzFxcXRxcWFADhjxgyFP3knRxIkP5i8ePEiS/2Tj9iymsBMyf9QigElJH+eyaqoqHDatGlZ7rtw4cIMt//fv39PTU1Njhs3Lt0xIiIiWL9+fWpqamYpO9yrV6/YpUsXAqCNjQ2PHTuW4Y0qrSJBY8eO5bNnz0j+FABPnz7ltGnTZAVbChUqRBcXFx4/fjzXqqrFx8dTRUUly7shyTx58kSuI5jfhdevX7N48eK0trbO8ZNtZnh5eVEkEmUpzFYikfDx48f09PRkkyZNqKqqKks0NWDAAB44cCBDJ8fkKn1ZjY55//49e/fuTYFAQGtrax45ciTD73t4eDinTZtGHR0damlpcfLkydn2uZBKpZwzZw4BsEePHjnyR/gvsbGxVFVV5axZswggS7kOoqKiWKpUKdrb2+drEarfHaUYUCLDw8ODKioqctc7T0YqlbJ9+/bU09NL09Goe/fuLFq0aLrOe8HBwaxcuTL19fV58+ZNueYMCQnhiBEjKBaLaWpqyk2bNmW4tZhRkSCpVMonT55w6tSptLa2lgmA3r1788SJE7kmAH7l0aNHBMDr169nq7+rqysNDQ3zJBQst3nz5g3Nzc1ZpkyZHJc0lofo6GgaGhpy8ODB2R4jKiqKp06d4ujRo2W7SEKhkLVr16aHhwdv3LiR4vt57949AuDt27flGj8iIoKTJk2iuro6DQ0NuXr16iz9rr9+/Up3d3dqampSV1eX06dPz3Yynn379lFNTY12dnYKPbqpX78+O3ToQD09PbmjjUhy7NixVFdXz7Vian8LSjGgREZsbCytrKxYt27dLCvs8PBwWlpasmrVqimeGK5du0YA3Lx5c5r9AgMDaWlpSRMTE7mSqPz48YMzZ86ktrY2CxUqxAULFqT7dJVRkSCpVMrHjx9zypQpssQ0enp67NOnD0+ePJnnNc+3bt1KAIyMzHrRoMTERBoZGXH06NGKNyyPCQoKYsmSJWlpaakQBzh5mT9/PlVVVRU2Z1BQEDdu3EhnZ2fq6+vLBKaTkxPXrl1Lf39/ikQirlmzJsNxEhISuGLFChYpUkQWEZOT+2tISAhdXV2prq5OfX19zp07N1vfuVu3brFo0aK0sLDIUfTLr0yZMoVFihRh3bp15fanuHXrFgUCQbbCnJWkRCkGlKTg17O7rPLo0SOqqalx0KBBJH96Odva2rJGjRppigsfHx+amJiwdOnSmW7RJiQkcPXq1TQyMqKqqirHjRuXpqNcRkWC4uPj+ejRI06ePFmWyU1fX599+/blqVOn8lwA/MqYMWNoaWmZrb4nTpwggDwpO5ubvH//nhYWFixVqlSeO4F9//6denp6WaroKS9JSUm8ffs2Z82aRTs7O4pEIlkIY/ny5Xns2LFUC7JUKuWhQ4dYpkwZCgQChUUHJPPx40eOGDGCqqqqLFKkCBcuXJjlI4s3b96wfPny1NPT4/nz53Nsk7e3NwGwU6dOrFKlSqbt4+LiaGNjw+rVq2fL4VBJSpRiQEkq+vfvT11d3Wxt0W7cuJEAuG3bNpkzUFpboTdu3KCenh5tbW0zdA6TSqU8cOCA7Kbo4uLCt2/fpmqXXpGgoKAgPnz4kJMmTWLp0qVlAqBfv348ffp0vgqAX2nUqFG2nf+cnZ1ZsWLF3zqc6uPHjyxdujRLlCiR5u83L5g+fTo1NDQYEhKSq/NERETw8OHDtLKykvkaqKio0N7envPmzeOWLVtkNTMcHBz45MmTXLPl3bt3HDx4MMViMY2MjOjl5ZUlX4CIiAg2b96cYrE4x0XMfvz4QZFIxE6dOlFdXT3TENvkQlW5+fn8TSjFgJJUhIWFsWjRotkuJ9q3b1+qq6vLtt3/y6lTp6ihocEGDRpkeG55+fJl1qxZkwDYsmXLVOWK0yoS5OTkxFOnTvHevXt0d3eXCYDChQuzf//+PHPmTIE7V08uXpOdzGvfvn2jqqqqwmLW84NPnz7RysqKZmZmWXLiUzRhYWHU1tbmpEmT8mS+pUuXUl1dnX5+fly5ciWbNGkiK7IkEonYqFEjbt26NU/8JgIDA9m3b1+KRCIWK1aMq1atkttXJjExkUOHDiUATpgwIUdOfLVq1WLDhg0JIMNER0+ePKFYLM6Ww7OStFGKASVpsnv37gwLfUTFJdL3YwQfBn2j78cIRsX9b5suOjqaBgYGFAqFqZx6du/eTbFYTEdHx3TT8z59+pStW7eW5VT/by3y/xYJKl26NBcsWEBvb2+6u7vT0tJSFikwYMAAnj17tsAJgF959+5dtiMB1qxZQ5FIlOse97nF58+fWbZsWZqamiqkJHVOcXNzo46OTo6LYclD8pHctWvXOHr0aKqoqNDU1JSTJk2iu7s7q1evToFAQACsWLEix40bR29v70zTWueEly9fsmfPnhQIBDQ3N+eGDRvk+tuRSqVcunQpBQIBO3TokO2UzhMmTJCFbR4/fjzNNomJiaxevTptbGzyxLn3b0EpBpSkiVQqZYsWLWhmZiY7z3z5OZLTj/qywcKLLOl+giV++SnpfoINFl7k9KO+PHHtAUUiEdXU1NipUyfZ9vXKlSspEAjYu3fvNM/4goKCZGFTlpaW3Ldvn6xvekWC1q5dSzc3N1pYWKQQAN7e3gVaAPxKckndoKCgLPetXbs2W7VqlQtW5T4hISG0sbGhiYlJgfEE//z5M9XV1eUuMZzTuQBQQ0ODOjo6nDdvXqqFPjQ0lHv27GGfPn1kWTHV1dXp4ODAJUuW0NfXN1eOh54/f87OnTsTAC0sLLht2za5zuWPHTtGLS0tVqtWLVs7Gsl/C1paWvT09EyzzeLFiykQCHjr1q0sj68kfZRiQEm6BAYGUlNTkwPGTGTPjbdZwv0ELSafTCEC/vuTfL1k3yVcvW0fAXDp0qWcMWMGAdDV1TXVNmJYWBjHjx9PNTU1Fi1alKtWrZIt5GkVCXJ1deXIkSNZqlQpAmCRIkU4cODA30oA/Epycpis3tT9/f0JgPv27csly3KP0NBQVqxYkUZGRulW3csvRo4cycKFC2fLy14ektNlm5ubEwArV64sl59CchKsJUuWsHnz5rJCS6ampuzbty/37NnD0NBQhdr69OlTdujQgQBobW0tV9GjR48e0dTUlMWLF091tJcZ4eHhFAgELFWqFHv37p3qekBAANXV1XPF0fNvR971W0CSyITIyEgUKlQI379/h66ubmbNlfwG9Ju7EefDC0OsqgZppt+A/yEEoCIWwib2GY7+4waSmD9/PiZOnAiBQAAAiI2NxYoVKzB//nwkJiZi/PjxGDduHDQ0NHDq1Cls2LABp06dgrq6Opo0aQIdHR3cvHkTb9++RZEiReDk5ARnZ2c0bNgQYrE4dz6APMDZ2RmhoaG4fPlylvpNmTIFq1evRnBwMNTV1XPHuFzg27dvaNy4MYKDg3Hp0iXY2Njkt0kpeP/+PSwtLTF37lxMmDBBoWNfvHgREyZMwMOHD9GhQwfExMQgPj4ely5dyvJYsbGxuHbtGry9vXH27Fn4+vpCIBCgWrVqcHBwQPPmzVGnTh2oqKjk2O6HDx/Cw8MDJ0+eRPny5TFz5kx06NABQqEwzfafPn2Co6MjXr58ib1796J169Zyz1WlShX8+PEDhQsXxt27d2WvS6VSNG7cGO/evYOPjw+0tLRy/L6U/A951++0f+NK/mhWXgrAxSgTCMWqWRICACAFEJ8kxSOVctCp7Qw9PT30798fAoEAEokEW7ZsgZWVFaZMmYLu3bvj9evX6N27Nzw9PVGiRAm0a9cOr169QpMmTVCkSBEcP34c586dg4ODA86fP4/g4GCsW7cOTZs2/a2FAAA8fvwYtra2WeojlUqxY8cOdOnS5bcSAuHh4WjWrBk+fvyICxcuFDghAABmZmbo3bs3lixZgtjYWIWM+ezZM7Ru3RpNmjSBqqoqrl27hsOHD6N+/fp4/Pgx5HjWSoWGhgaaN2+OxYsXw8fHBx8/fsTmzZtRpkwZrFu3Dvb29ihcuDDatWuH1atX49WrV9m2v2rVqjhx4gRu3boFU1NTdOrUCdWqVcOxY8fStL1YsWK4evUqmjZtirZt22L58uVyv0d7e3uEh4fj+fPnKfps3LgRV65cwYYNG5RCIB9RioG/jL333mGx98uf//n/J/nsom/vAo3yTdCtWzccPXoUlStXRr9+/VC3bl08fvwY9vb26NmzJywsLODl5QVDQ0OYmJjA398fT548QatWrXDhwgV8+vQJa9euRZMmTX57AZBMVFQUXr9+jcqVK2ep36VLl/D+/Xv07t07lyxTPBEREWjevDmCgoJw4cIFVKhQIb9NShd3d3eEhoZi06ZNORonODgYAwcORKVKleDv74/9+/fj5s2bqFevHoCfT8ERERF4+/Ztjm0uVqwY+vTpg927dyMkJAT379/HpEmT8P37d4wePRplypSBpaUlhg4din///Rffv3/P8hy1a9fG2bNncfXqVejp6aFdu3aoVasWzpw5k2qx19LSwqFDh+Dq6orRo0djxIgRSEpKynSOBg0a4Nu3b4iOjsaLwLd49uk7zt5/AfcFK9G7/yA0adIky3YrURzKY4K/iPffYtB06RXEJ0lTXUsIDcL367uR8PkVJNEREKioQcXADLq1nKBZpla6Y4ohRdCagUj6HoKGDRti2LBhuHPnDrZt24avX7+iWLFiiIuLw7dv31C0aFF07NgRzs7OaNCgAUQiUW6+3Xzl1q1bqFu3Lh4+fIgqVarI3c/FxQW3b9/GixcvZMcuBZnv37+jefPmCAgIwMWLF7O8E5If9OzZE1euXMHr16+hqqqapb5RUVFYvHgxFi1aBHV1dXh4eGDo0KGpxgkODkaxYsVw6NAhODk5KdL8FPz48QOXL1/G2bNn4e3tjYCAAIhEItSuXVt2pFC9evUs/61dvHgR06ZNw82bN1G3bl3MmjULjRs3TvWdXL9+PYYNG4ZmzZph3759Ga4Pd/zfoeXIudCwrA4V/WIprgkAmBfWRCProuhRyxxljHSyZK+S9JF3/VaKgb+IXpvu4GZgGCRpnA3Evr6HyPvHoWZaFiLtwmBiPGJe3ET8h2co3GIEdGxbpDkmJUmQBvvjw0532NjY4Pnz51BXV4dYLEZUVBSMjIxkAqB+/fp/tAD4lTVr1mDUqFGIioqCmpqaXH1+/PgBY2NjTJ48GVOmTMllC3POjx8/4ODgAD8/P1y4cAFVq1bNb5Pk4vnz5yhfvjw2btyI/v37y9UnKSkJmzdvxvTp0xEeHo5Ro0Zh8uTJ0NPTS7ePsbExBg4ciNmzZyvI8sx58+aNzNfgwoULiIyMROHChdG0aVM0b94czZs3h5mZmVxjkYS3tzemTZuGe/fuwd7eHrNnz0b9+vVTtDt//jw6deoEMzMznDhxAiVKlEhx/f23GEz+1wfXXn0FpBJAmP49QCQUQCIl6pcugnkdKsKssGbWPwQlKVCKASUpCAj5gWZeV7PUh1IJgreOAZMSYTpobYZtP24YgqSwDwAAIyMjdOrUCc7OzqhXr95fIwB+ZciQIbh58yaePn0qd5+tW7eiX79+ePv2LczNzXPRupwTFRWFli1b4unTpzh//jxq1KiR3yZliU6dOuHx48fw9/fP8GiKJE6ePAk3Nzf4+fmhR48emDt3bqoFLy1atmwJkUiEEydOKNJ0uUlKSsKdO3dk4uDevXuQSqUoV64cmjdvDgcHB9jb20NTM+MFlyROnDgBDw8PPH78GM2aNcOsWbNQu3ZtWRs/Pz+0bt0a0dHROHbsGGrV+rmbuPfeO0w/9gxJUqb5EJIeIqEAYqEAM9uWR9caBftvoaCjdCBUkoJdd95BJMzatrNAKIJYpwik8VEZtqNUAsM6TtDR0UHZsmURGBiIlStXwt7e/q8UAsBP58Gs+gts27YNjRo1KvBCIDo6Gq1bt8aTJ0/g7e392wkB4GfExuvXr7F///502zx48ACNGzeGo6MjjI2Ncf/+fezcuVMuIQD89Bt49OiRokzOMmKxGHZ2dpg5cyZu376N0NBQ7N+/H3Z2djh8+DBatWoFfX19NG3aFIsWLcKTJ0/SdAYUCARwdHTEgwcPcPDgQXz69Al16tRB69at8eDBAwBAuXLlcOfOHZQuXRoNGzbEgQMHsPJSANwP+yA+SZolIQAAEikRnySF+2EfrLwUoJDPQ0nGKMXAX8KlF1/k+oOUJsRBEvMdieHBiLx7BLGBD6BeIuNFTSAUoUyD9rh48SICAwMxceJERZn9WyKRSODj45MlMfD27Vtcvny5wDsOxsTEwNHREQ8fPsSZM2dkT4C/G1WqVEGrVq0wd+5cSKUpfWjevn2LHj16oHr16vjy5QtOnDiBCxcuoFq1alme49OnT/jy5YsiTc82hQsXhrOzMzZs2ICgoCD4+flh4cKFUFNTw4wZM2BrawsTExO4uLhg586dCAkJSdFfKBSiY8eOePr0Kfbs2YPXr1+jevXq6NChA54+fQpDQ0NcuHABTk5O6Ddn4/8clXPIYu+X2HfvnULGUpI+ymOCv4Co+CRUnHEW8mjzsDMrEfX4zM//CITQtKqDwi1HQqSunWE/AQDfGQ7YvnkDhg0bhj179qBr1645tv135OXLl7C2tsa5c+fQtGlTufrMnj0bnp6e+Pz5M7S1M/6s84vY2Fi0bdsWt27dwpkzZ2Se878rN2/ehJ2dnczJLzw8HPPmzcPy5ctRuHBhzJo1C3379s12hMurV69QpkwZnDlzBg4ODgq2XrHEx8fjxo0bMkfEx48fAwBsbW1ljoh2dnYp/F+SkpKwe/duzJw5E4GBgXB2dsaMGTOgbVQCjRZfRBIFqRwO44KeImTP5DRtMO61GGqmZdO8piYW4vxYe6UPQTZQ+gwokfHs03e0XnFdrraJYe+R9CMMkh9hiPG/DojEMHAYBpGWfqZ9jw2rgwqmenBxccGRI0dw7949lCtXLqfm/3bs378fXbp0wZcvX2BoaJhpe5KwsrKCnZ0dtm7dmvsGZoO4uDi0b98eV69exenTp2Fvb5/fJimExo0bIzw8HC4uLpgzZw7i4uLg5uaGcePG5ViUSaVS6OnpYfLkyXB3d1eQxXnD58+fcf78eZk4+PLlCzQ1NdGoUSOZI6K1tTUEAgESExOxfft2zJ49G+/evUOl0evxQ8MEkjRWlmQxoFPNEaomVimuaVhUhUizUJr2iIQC1LUwwI7+v+dOVH4i7/r9ZwR1K8mQhDRCCdNDxcAMKgY/vY21KzZByN5p+HJwFoxd/sk01K1GrTpICH4JkUgEqVSKChUqoFChQhCLxRCLxVBRUcnw3zm9ntdjpecP8eTJExQrVkwuIQD8fEJ99eoV1q9fL/fvKS+Jj49Hx44dceXKFZw8efKPEQIkUa9ePcyePRtPnz5F//79MXPmTJiYmChkfKFQCFtb23z1G8guxsbG6NmzJ3r27AmpVIqnT5/KHBEnTJiA0aNHw9zcXOaI6OTkhF69esFz7TZsCjZBZtuQambloVVW/p0liZS49uorXn35gdJFlWGHuYFSDPwFqIqz7xqiWdYO386sRNK3j1AxKJ5h25nTp6GIKA5JSUn48OEDFi1ahBIlSsDZ2RlJSUlISkpCYmJihv/+9bWYmJgMr8sz1n/PgxWJQCBIUyx8//4dAoEAZcqUkUtY+Pr6QlNTE+vWrcPmzZsLlDgiia5du+LChQs4fvw4GjdunGufZ15y/fp1jB8/Hnfu3IGenh5KliyJdevWKTy3Q5UqVXD69GmFjpnXJIsaW1tbuLm5ITo6GleuXJGJg40bN0IoFKJmzZoo1HgAhALIldlUGh8DgYoaBBmEGv6KSCjAztvvMKNt+Ry+IyVpoRQDfwElDbQgQKZiPU2YGA8AkMZHZ9hOAGBkn67QUvvfV6pChQro1q0bBg0ahKFDh2Zj9pwjlUohkUgyFR6KvO7p6YmKFSuifv36mbaNi4vDx48fYW5ujtDQ0BzZkpsIhUI4OjrmuUhR9G7P+/fvsWjRInh7e6NixYo4evQoEhIS4OzsjIsXL6aZWCcnVKlSBcuXL8ePHz+go/NnPNFqaWmhVatWaNWqFQDg3bt38Pb2hre3N26FCyBKe6c/BWGnloEJsYBACDWz8tBv1A9qJmUy7COREpdefsEMKMVAbqD0GfhLsF90CUHfYtK9LomOgEhLL8VrlCTh8/ZxSAz7gOKjdkKoqpFu/xIGmrgyvlGq10eOHIn169fj+vXrv2UIWlb5+vUrDA0NsXfvXnTp0iXT9nv37kW3bt3w8uVLlCmT8c0wI0hCKpUqTOTExcXBy8sLDx8+xPDhw2FjY5Pt3RlFX5dIJNn+nORBkSLlx48f8Pb2RsuWLWFqalqgxFF6xYiyizyOynEf/PDj3r/QsKgOoWYhJH59h8i7/4KJcTDuuQiqxpYZzpHsqPzrQ4eSjFH6DChJQSProthxJyjd8MKwMyvBhBiomVWASMcAkqhwRD+/jKSwD9Bv3D9DIUCpBBHPbmDz5jfo2LEjChX636PBkiVLcO/ePXTq1AkPHz6EgYGBwt9bQeLJkycAIHdY4bZt21C3bt0cCQHg55GFSCSCSCSSO+NheiQlJaFHjx54/Pgx/v33Xzg6OuZoPEVDUm4x8uPHD+zYsQPbtm2DQCBAjx494OjoCIFAkKLtzZs3sWLFCri7u8Pc3FwhwiU+Ph6JiYkQCATw9/dHWFhYlsbK7d0egUCg0F2XBM2iYLFWGc6pXrwc1Iv/4lRcphY0y9oheNNIhF/ZBqMuszLsTwBvw6JRvpgc2w9KsoRSDPwl9Khljq233qZ7XatcfUQ9PYcfj05BGvsDQlUNqBqXhn7DvhnWJgB+5hnQCXmMAQM8MGzYMLRp0wY9evRAq1atoKamhv3796Nq1aro1asXTpw4ofAnkoLEkydPoKGhIdfi/unTJ3h7e2PNmjV5YJl8SCQSuLi44PDhw9i/f3+BEwLA/xYxFRUVaGikLVIlEgl27NiBqVOn4suXLxg+fDimTp2arhjt3Lkzzp8/D19fX8yfP1+h9larVg2VK1fG5s2bs9xXKpVmS5jkxXFY8r/j4+MRHR2NqDgVoFjm7+m/qOgXg0aZWoh5eROUSjL1IciKQ7QS+VGKgb+EMkY6qF+6SLq1CbRs7KFlk3UvcVnIz/yD+PjxI/bu3Ytdu3bByckJenp66NSpE7p3747t27ejTZs2mD9//m+Rdz+7PH78GBUrVpQr8+KuXbugoqKCzp0754FlmSORSNCnTx/s378f+/btQ4cOHfLbpGzh7e2NCRMm4OnTp3B2dsb8+fNhaZnx9rNQKMSkSZPg4uKSrdLTGVGlShVZpr6sIhQKoaamluPdnrwgKyHM/0WsWwSQJIGJ8RCoZZxLICcO0UrSR/mp/kXM61AR4iymJM4MsVCAeR0qAgBMTU0xbtw4PHz4EM+fP8fw4cNx4cIFNG7cGIMGDULt2rUxbdo0nD9/XqE2FCSePHki10JCEtu2bUP79u0zLHaTV0ilUvTv3x+7d+/G7t270bFjx/w2Kcs8ffoUDg4OcHBwgI6ODm7duoX9+/dnKgSS6datG0qVKoV58+Yp1K4qVarg2bNnSEhIUOi4BQ1DDSB7bspAUsRnCMSqEKiqZ9hOgJ8O0UoUj1IM/EWYFdbETAWH5cxqWz7NrGDlypXDnDlz8Pr1a9y4cQPt2rVDQEAASKJFixZwd3dXSK33gkR8fDyeP38ul7/Aw4cP8ezZswKRflgqlWLQoEHYsWMHduzYUWB2KuTlw4cP6Nu3L2xtbfHmzRscPnwY165dS1FIRx7EYjHc3d1x8OBB+Pn5Kcy+KlWqIDExEc+ePVPYmAWFgIAALFu2DA4ODjAzLorE8OAM20tivqd6LSEkEDEBd6FesgoEgoyXJHMDTaXzYC6hFAN/GV1rmGN8c6vMG8qB0PcE6hpnvNMgEAhQt25drFq1Cp8+fcLu3buhqqqKRYsWoVSpUqhXrx7WrFmDr1+/KsSm/MTPzw9JSUly7Qxs27YNxsbGaNasWe4blgFSqRRDhw7F5s2bsXXrVnTv3j1f7ckKkZGRmDJlCqysrHDixAmsWLECz549Q4cOHbIdHti7d28UK1YMCxYsUJidlSpVgkAg+C2TD/2X2NhYnDlzBqNGjULp0qVhZWUFNzc3kISnpyc61S2HjDYfQ4944suBGfh+cx9+PD6Db+c34PPOCRCoqEG/YZ8M5xYJBWhkVVSxb0iJDKUY+AsZ0agMFjhVhJpYmOVKhiKhAGpiIcY3MAF9z6BBgwZ48+aNXH1VVFTQrVs3XLhwAQKBAC1btoSuri5GjhwJExMTtGnTBnv27EFMTPohkAWZ5HzuFStWzLBdQkICdu/ejZ49e0Iszr+nHJIYOXIkNmzYgM2bN6NXr175ZktWSExMxOrVq1G6dGn8888/GDt2LF6/fo3hw4dDRUUlR2OrqanBzc0Nu3btQmBgoELs1dbWhpWV1W8rBt68eYNVq1ahTZs2MDAwQMuWLXH06FE0a9YMx44dQ1hYGLy9vTFmzBgMb14pw4RDmla1IYmJROTdI/jmvQYx/tegaVUXJn2WQqWIWYZ2SKREz9oFu6Ln74wyz8BfzPtvMZj8rw+uvfoKkVCQYVXD5Ov1SxfBvA4VYVZYE+/evUPjxo2RkJCAixcvonTp0nLPvWzZMowZMwYHDx5E/fr1sX//fuzevRu3bt2ClpYWOnTogB49eqBp06b5umBmhbFjx+L48eN49epVhu2OHDmCDh06wMfHBxUqVMgj61JCEqNHj8aKFSuwceNG9O/fP1/syAokcfToUUycOBEBAQHo3bs3Zs+ejeLFM86MmVViYmJQsmRJODk5Ye3atQoZs1u3bnj//j2uX8+eg11eEh8fj+vXr+PUqVM4deoU/P39IRaLUb9+fVmyoXLlyqW5+7Jx40ZMOR8MrVJVoUiff2VtguyjLFSkRG4CQn5g1513uPTyC96FxaRwARLg5zldI6ui6FnbPFVe8E+fPqFx48aIjIzExYsXUbZs2lXH/gtJdOnSBWfOnMGDBw9koXiBgYHYvXs3du3aBX9/fxQtWhRdunRBjx49ULNmTYWni1UkjRs3RuHChXHw4MEM23Xo0AHv3r3Ltod5TiEJV1dXeHl5Yd26dRg0aFC+2JEV7ty5g/Hjx+P69eto1qwZFi1alKUS0VnF09MTHh4eeP36tULExsKFCzF79mx8//69QIbWvn//HqdPn8apU6dw/vx5REdHo1ixYrLFv0mTJpne+z9+/AgbGxu0cu6FhyatEa/AEEBl1cLsoxQDSrJFdHwS3oZFIyFJClWxECUNtDJ12AkJCUGTJk0QGhqKCxcuyP20GxkZiRo1akBdXR23bt2Cpub//tBJ4tGjR9i1axf27NmD4OBgWFpaokePHujevTusra1z9D4VDUkYGBhg7NixmDZtWrrtvn79imLFimHx4sUYNWpUHlr4E5Jwc3PD4sWLsWrVKgwbNizPbcgKgYGBmDRpEvbv34+KFSti0aJFeVIOODIyEiVKlEDv3r3h5eWV4/HOnTuH5s2b48WLF7CyUozPTk5ITrR06tQpnD59Gj4+PhCJRKhbty5atmyJVq1ayXwd5IEk2rdvj7t37+L58+c4++oH3A/7KMxeT6eK6FJDeUSQHeRdvwueRFWSr2ipiVG+WCFUMddH+WKF5PLcNTIywqVLl2BiYoKGDRvKzs4zQ1dXF4cOHUJAQACGDx+OX3WpQCBA1apVsWTJErx//x7nz59HgwYN4OXlhbJly6J69epYunQpgoMz9l7OKz58+IDw8PBMnQf37NkDkujWrVveGPYLJDF58mQsXrwYy5YtK9BCICwsDGPHjkXZsmVx/fp1bN68GY8ePcoTIQD8/G6OHj0a69evx5cvX3I8XpUqVQAgX/0GgoODsXnzZjg7O6NIkSJo2LAhtm7diqpVq2Lfvn0IDQ3F1atXMWnSJFSuXDlLu3AHDhzAsWPHsGrVKujr66NrDXP0qfr/CZ4yf97MkAnNrZVCIA9Q7gwoURjfvn2Dg4MDXr9+jbNnz8pdi2DHjh1wcXGR6+w6Li4OJ0+exK5du3Dy5EkkJSWhcePG6NGjB5ycnPLt+3n8+HG0bdsWQUFBMDdP/8ZVvXp1FC9eHEeOHMk74/4fDw8PzJ49W+Z0VxCJi4vDihUrMG/ePCQlJcHd3R1jx45NsWuUV3z79g0lSpTAiBEjFJKV0MzMDD169FBopEJGJCUl4c6dO7Lt/0ePHkEgEKBWrVqy7f8qVark+Nji69evsLGxQYMGDWRHZAkJCahTpw4iDGwgrtUdSVJm6JP0X0RCAcRCAWa1La8UAjlE7vWbcvD9+3cC4Pfv3+VpruQvJiIignXq1KGuri5v3Lghd79BgwZRTU2NDx8+lLvPt2/fuGHDBjZs2JACgYDq6up0dnbmkSNHGBcXlx3zs83s2bOpr69PqVSabhtfX18C4OHDh/PQsp/MmDGDALhw4cI8n1seJBIJd+3axRIlSlAkEnHYsGEMCQnJb7Po5uZGHR0dfvv2LcdjOTo6snnz5gqwKn1CQkK4fft2du3alfr6+gRAAwMDdu/enTt37mRoaKjC5+zZsyf19fUZHBwse83V1ZUqKiq8f/8+34VFs+fG2yzhfoIWk0+yhPuJdH+Sr/fceJvvwqIVbuvfiLzrt1IMKFE4kZGRbNCgAbW0tHjlyhW5+sTGxrJq1aq0sLBgeHh4lud8//49Fy5cyMqVKxMA9fX1OXDgQF6+fJkSiSTL42WVjh07smHDhhm2mTBhAg0MDBgfH5/r9vzK7NmzCYDz58/P03nl5dKlS6xWrRoBsH379vT3989vk2R8/vyZ6urqnDlzZo7H8vDwoKGhYYaCMatIJBLeuXOH06dPZ40aNSgQCAiA1apV47Rp03jr1i0mJSUpbL7/cvLkSQLg1q1bZa+dOnWKAPjPP/+kaPvycySnH/Vlg0UXWfI/IqCk+wk2WHSR04/6MiAkMtfs/RtRigEl+UpUVBQbN25MDQ0Nnj9/Xq4+gYGB1NPTY7t27XJ0w/T19eXkyZNZsmRJAqCZmRnd3Nz45MmTbI+ZGaVLl+bo0aPTvZ6YmEgTExOOGDEi12xIi/nz5xMAZ8+enafzysOzZ8/Ypk0bAmDNmjV59erV/DYpTUaOHEl9fX1GRuZskfr3338JgB8+fMjROGFhYdy9ezd79epFQ0NDAmChQoXYuXNnbt26lZ8/f87R+PLy/ft3mpmZsXnz5rK/10+fPtHQ0JAtW7bMUIRHxSXS92MEHwZ9o+/HCEbFJeaJzX8jSjGgJN+JiYlhixYtqK6uztOnT8vV59ixYwrbzpZKpbx+/TqHDh1KAwMDAmCFChU4f/58vn37NsfjJxMZGUmBQMAtW7ak2+b06dMEwHv37ils3sxYtGgRAXD69Ol5Nqc8BAcHc9CgQRQKhSxVqhT37t2r0KdlRfPu3TuqqKjk+Dv59u1bAuDx48ez1E8qlfLhw4ecM2cO69atS6FQSACsXLkyJ02axGvXrjExMe8X06FDh1JLS4tv3rwh+XOXomnTpjQ2Ni4QRzxKfqIUA0oKBHFxcXR0dKSqqiqPHTsmVx93d3eKRCK5jxjkIT4+nsePH2fXrl2poaFBAKxXrx7XrFnDr1+/5mjsGzduEECG/g5du3aljY1Nni16S5cuJQBOmTKlwCy0UVFRnDFjBrW0tKivr89//vknz307ssvAgQNZtGhRxsTEZHsMqVRKfX19zpo1K9O2ERERPHDgAPv27UtjY2MCoI6ODp2cnLhhw4Yc7y7klCtXrhAAV6xYIXttwYIFFAgEcu8EKskblGJASYEhPj6eHTt2pFgs5sGDBzNtn5iYyIYNG9LY2DiFU5KiiIyM5Pbt2+ng4ECRSEQVFRU6Ojpy7969jI7OutPS6tWrKRaL013YIiIiqK6uTk9Pz5yaLhfLly8nAE6cOLFACIHExESuX7+exsbGVFVV5fjx4xXikJeXvHr1ikKhkMuXL8/ROI0bN2aHDh1SvS6VSvn06VMuWLCA9vb2FIvFBEAbGxuOHz+eFy9ezHNfk/SIiYlhmTJlaGdnJzsKuH37NsViMd3d3fPZOiX/RSkGlBQoEhMT2a1bN4pEIu7atSvT9sHBwTQxMaG9vX2uboF+/vyZy5cvZ61atQiA2tradHFxzKW5OAAAKaBJREFU4ZkzZ+Sed9CgQaxYsWK619evX0+hUMiPHz8qyux0WbVqFQFw/Pjx+S4EpFIpT548yfLlyxMAu3fvLttS/h3p2bMnixcvnqNFedy4cSxZsiTJn6L033//5aBBg1i8eHECoKamJh0dHblmzRqFHmUpEjc3N6qpqdHPz4/kT7FbsmRJ1q5dmwkJCflsnZL/ohQDSgocSUlJ7N27NwUCQQrv4/S4cuUKRSJRnj1tBAQEcObMmbSysiIAGhkZcdSoUbxz506GC2utWrXYs2fPdK/b2dnRwcEhN0xOwbp16wiAY8aMyXch8ODBAzZu3JgA2LBhwzz1lcgtnj17RoFAwA0bNmSrv1Qq5cKFCwmADRo0oIqKCgHQysqKY8aM4dmzZxkbG6tgqxXLvXv3KBQKOW/ePJI/31OXLl2oq6vLwMDAfLZOSVooxYCSAolEIuHAgQMpEAi4fv36TNsn3zyPHj2aB9b9RCqV8t69exwzZozsvLZMmTKcPn06X758maJtUlISNTQ0uHjx4jTHCggIIADu3r07V23etGkTAXDEiBH5KgSCgoLYs2dPAmC5cuV4/PjxfBcmiqRjx460tLSUe9coOjqaJ06c4LBhw2TRLcnRE8uXL2dAQEAuW6w4EhISWKlSJdra2sp2AJK/d3v37s1n65Skh1IMKCmwSCQSDh8+nAC4cuXKDNtKpVK2b9+eenp6fP36dR5Z+D+SkpJ47tw59unThzo6OgTAGjVq0MvLi8HBwfT39ycAnjt3Ls3+06ZNo66ubo4czzJj69atFAgEHDp0aL4tvOHh4bLtYyMjI65duzZfPNxzm4cPHxIAd+7cmW6bgIAALlu2jC1atKCamhoBsFSpUhw+fDiPHTtGDQ0NLlmyJA+tVgxz5syhSCTigwcPSJLPnz+npqYm+/fvn8+WKckIpRhQUqCRSqV0dXUlgExvjOHh4bS0tGTVqlXzdRs1JiaG+/fvZ7t27aiiokKhUMhKlSoRQJpCRSKRsESJEhwwYECu2bRjxw4KBAIOHDgwT5Ir/Zf4+Hh6eXnRwMCAmpqa9PDwyHE8fkGnVatWtLGxkX3esbGxPHv2LEePHs0yZcoQAFVUVNi0aVP+888/9Pf3TyHSMjtWKog8e/aMqqqqsiO72NhYVq5cmWXLlmVUVFQ+W6ckI5RiQEmBRyqVctKkSQQgO4NMj0ePHlFNTY2DBg3KI+syJiwsjOvWraOZmRkBUF1dnZ07d+bRo0dlDmaXLl0iAF67di1XbNi9ezeFQiH79euX50JAKpVy//79tLS0pFAo5IABA/LEQbIgcPPmTQLgwIED2aZNG2pqasqSWw0ePJhHjhzhjx8/0u0/ZMgQli9fPg8tzhlJSUmsU6cOraysZGJ85MiRVFNT4+PHj/PZOiWZoRQDSn4LpFIpZ86cKUuOk9E298aNGwmA27Zty0MLM6ZVq1Zs1KgRFyxYINslKFy4MAcPHsyWLVvSwsIiV7bu9+3bR6FQyN69e+e5ELhx4wbr1KlDAGzVqhV9fHzydP78ID4+nhcuXOC4ceNoY2MjO/u3t7enp6cnfXx85P49r1u3jiKRKFePjhTJsmXLUoja5MRgv+YYUFJwUYoBJb8VyWlz3d3d072pSqVS9unThxoaGnz69GkeW5g2xYoV46RJk2T/9/Hxobu7u2zHoFChQpw4caJC7T148CBFIhF79OiRq3nn/8vLly/p5OREAKxSpQovXLiQZ3PnB+/fv+f69evZoUMHamtrEwCNjY3Zr18/Tp8+nQB46tSpLI979+5dAuCdO3dywWrF8ubNG2pqanL48OEkyQ8fPtDAwIBt27b9oxxD/2SUYkDJb8c///xDABw7dmy6N5ro6GhWqlSJZcqUyffvY2hoaLqe1Fu3bpXF1hcuXJgAWLFiRS5YsIBBQUHZnvPff/+lWCxm165d88xB78uXLxwxYgTFYjHNzc25Y8eOfPFPyG0SExN59epVuru7y3Z5hEIh7ezsOHfuXD58+FD2vZRKpaxTpw7r1KmT5UUxNjaWIpGIa9euzY23oTCkUimbNm1Kc3NzRkZGMikpifb29jQ1Nc1x1k4leYdSDCj5LVm5ciUBcPjw4ekuOC9fvqSuri47deqUr08n58+fJ4A0q+w1adKE9vb2JH9uMR89epRdunShurq6LM583bp1DAsLk3u+Y8eOUUVFhc7OznkiBGJiYjhv3jzq6upSV1eXCxYs+G22tuUlODiYW7ZsobOzMwsVKkQANDQ0pIuLC/fs2ZPh7+fEiRMEwIsXL2Z53goVKnDw4ME5MT3X2bx5MwHI6orMnj2bAoGAly5dyl/DlGQJpRhQ8tuyfv16CgQCDhgwIF1BcOjQIQKgl5dXHlv3PxYvXkwNDY1UW/Xv3r2jQCDg5s2bU/WJjIzktm3b2Lx5cwqFQqqoqLBdu3bcv39/hgvtyZMnqaqqSicnp1zP8iaRSLh161YWL16cYrGYo0aNYmhoaK7OmVckJSXx5s2bnDp1qqxsskAgYM2aNTljxgzevXtX7l0PqVRKW1tbNmnSJMt29OrVizVr1sxyv7zi06dP1NPTo4uLC0ny+vXrFIlEnDZtWj5bpiSrKMWAkt+arVu3UigU0sXFJd1zcVdXV4rFYt64cSOPrftJr169WKtWrVSvz507l5qampmG2AUHB9PLy4s1atSQFaLp3bs3vb29U7znM2fOUE1Nje3atcv1/PTnzp2jra0tAbBTp06/VVKc9AgNDeXOnTtTHNno6+uzW7du3LFjB798+ZLtsQ8ePEgAvHXrVpb6/fPPP1RXVy+QuRikUik7dOjAokWL8uvXr/z27RvNzc1pZ2dXIO1VkjFKMaDkt2fPnj0UiUTs2rVrmk/DCQkJtLOzo6mpaY5u6NmlYsWKqUIdpVIpraysshxH/vLlS86YMUMWp25sbMwxY8Zw5cqVVFNTY5s2bXJVCDx9+pQtWrQgANatW5c3b97MtblyG4lEwnv37nHmzJmsVasWBQIBAbBq1aqcOnUqb9y4oTDHS4lEwnLlyrFNmzZZ6pccdurr66sQOxTJgQMHCIAHDhygVCplx44dqaenV2BrJSjJGKUYUPJHcPDgQYrFYjo5OaW5GH748IFFixZl06ZN89SzPi4ujmKxmKtXr07x+q1btzLMSJgZUqmUd+/e5ejRo6mvr08A1NLS4rRp03LlKf3Dhw/s168fhUIhS5cuzYMHD/6WXuLfvn3j3r176eLiwqJFixKAzK9k8+bN/PTpU67NvWPHjkxLWP+X8PBwAuCOHTtyza7sEBYWxqJFi7JDhw6USqVcu3YtAchVbVRJwUQpBpT8MRw7doyqqqp0dHRMs0zw+fPnKRQK6eHhkWc2Jael/e8RxZAhQ1i8ePEcC5PLly9TQ0ODVatWZY8ePWShbbVq1eKyZcv4+fPnHI0fGRnJqVOnUkNDgwYGBly+fHmBKZErD1KplI8ePeLcuXNZr149CoVCWcTGxIkTeeXKlTyroJeYmEgLCwt26tQpS/1KlSpFV1fXXLIqe/Tu3Zt6enr89OkTfX19qa6uXuAdHZVkjFIMKPmjOH36NNXV1eng4JCmo92cOXMoEAhkns+5zZYtWwgghV9AbGws9fT0UuQdyA7Xrl2jlpYWmzRpInuv0dHR3Lt3L9u2bUsVFRWKRCI6ODhw+/btWUr/m5iYyNWrV7No0aJUV1enu7s7IyIicmRvXvH9+3ceOnSI/fv3Z7FixWS7Ju3bt+f69ev57t27fLMt2en1+fPncvdxcnJio0aNctGqrHH69GkC4ObNmxkTE8Py5cuzfPnyf1wEyd+GUgwo+eM4f/48NTQ02Lhx41T50CUSCVu1asXChQvnKI5fXsaMGcPSpUuneG3//v3phhrKy82bN6mtrc2GDRsyOjo6zTZfv37l2rVrWb9+fQKghoYGu3btyuPHj6f7NCyVSnnkyBFaW1tTIBDQxcUlXxdPeZBKpfT19eXChQvZsGFDisViWTVEV1dXnj9/Ps2dovwgLi6OxYsXZ69eveTuM3v2bOrp6RWIY5nIyEiam5uzadOmlEqlHDp0KNXV1f+K7JJ/OkoxoOSP5MqVK9TW1mb9+vVTPRGHhYWxRIkSrFmzZq5veTds2JAdO3ZM8Vrr1q3TjC6Ql9u3b1NHR4f169eXu/jL27dvOX/+fFaoUIEAaGBgwKFDh/LatWuyELm7d++yQYMGBMCmTZtm6Ww7r/nx4wePHj3KwYMH09zcXCZ2WrduzVWrVjEwMDC/TUyXZcuWUSQSyV1dMzlPwZs3b3LXMDkYMWIENTU1GRgYKAvbXbNmTX6bpUQBKMWAkj+WmzdvUldXl7Vr12Z4eHiKa/fu3aOqqipHjBiRa/NLpVLq6+tz9uzZstc+f/5MkUiUyqFQXu7du8dChQrRzs4u21X/njx5Qjc3N1kqZFNTU5YrV44AWKFCBZ4+fbpAPIX+ilQqpb+/P5cuXcpmzZpRVVWVAFi6dGmOGjWKZ86cyddKlVkhOjqaRYsWlbuY1sePHwmAhw8fzmXLMubatWsUCAT08vJiUFAQ9fT06OTkVOC+K0qyh1IMKPmjuXfvHvX19VmtWrVUWeJWr15NANyzZ0+uzB0UFEQAPHbsmOy1JUuWUFVVNUsZBZN58OAB9fT0WKdOHYX8jYWGhrJz584UCoWysLrKlStz4cKFBeJoICYmhqdOneKIESNoYWFBAFRTU6ODgwOXLVvGly9f5reJ2WbBggVUUVHh+/fvM20rlUpZtGjRfE3kExsbS2tra9apU4dxcXGsV68ezczMsvU9VlIwUYoBJX88jx49YpEiRVi5cuUUeQakUil79OhBLS2tLDl0yUty1bZfF9ZKlSqlOjaQh0ePHlFfX581a9bMsSNfXFwcFy9eTH19fWpra3PWrFkMCwvjkSNH6OzsTHV1dQoEAtrb23P9+vX89u1bjubLCq9fv+aKFSvYsmVLWUrmEiVKcOjQoTx+/LjcxyIFne/fv1NfX5+jR4+Wq72Dg0OWcxQokkmTJlFVVZXPnj2jh4cHhUJhrpXcVpI/KMWAkr8CHx8fGhkZsXz58gwODpa9/uPHD9rY2LBcuXIZ1pbPDrNmzaK+vr5sG/XRo0epdgrk4enTpzQwMGC1atVSHXdkBYlEwt27d7NkyZIUiUQcMmRImqGH379/55YtW9i0aVMKhUKqqqqyffv2PHDggMK34uPi4ujt7c0xY8bQysqKAKiiosLGjRtz8eLFfP78+R+7DT1jxgxqaGgwJCQk07bu7u40NTXNA6tS8/DhQ4pEIs6ePZuXL1+mUCjkrFmz8sUWJbmHUgwo+Wvw8/OjiYkJra2t+eHDB9nrz58/p5aWFrt3767Qhadjx45s2LCh7P9jxoyhoaFhluLafX19aWhoyCpVquRoS/by5cuydMZt27aln5+fXP0+ffrEf/75h9WrV5cl6Onbty/Pnz+f7RwJQUFBXLNmDdu2bUstLS2Z38LAgQP577//ZtsX4ncjLCyM2tradHd3z7Ttvn37CCDPM2gmJCTQ1taWlSpVYnBwME1NTWlvb5+nibuU5A1KMaDkryIgIIBmZma0tLRMEVq4Z88eAsi2Y19alC5dmmPGjCH586ZqaGgo+788PH/+nEWLFmWlSpWyXQrWz8+Pbdu2JQDWqFGDly9fztY4JOnv708PDw9aWloSAE1MTDh27Fjev38/QxGVkJDAS5cuccKECSxfvjwBUCQSsUGDBpw/fz6fPHnyxz79Z8bEiROpra2dqdB7+fIlAfDs2bN5ZNlP5s2bR6FQyHv37rFt27YsXLiwXH4OSn4/lGJAyV/HmzdvWKpUKZYoUSJFeNeIESOoqqrKu3fv5niOyMhIAuCWLVtI/s9/4NGjR3L19/f3p7GxMStUqJCtp8HPnz9zyJAhFIlELFmyJPfs2SN3lb3MkEqlvH37NkeOHClL6Wttbc1Zs2bx1atXJH96wG/cuJFOTk7U0dEhABoZGbFPnz7cv39/jo47/iQ+f/5MdXV1zpgxI8N2EomEOjo6XLBgQR5Z9lNIqqmp0c3NTVYy/OjRo3k2v5K8RSkGlPyVvHv3jmXKlGHx4sVlXunx8fGsVasWzc3Ns/0knsyNGzdSLP4dO3ZkpUqV5Or78uVLmpiY0MbGRq7z5F+JiorirFmzqK2tTX19fS5ZsiRXE+4kJiby9OnT7N69OzU0NAiAmpqaspK/derU4ezZs/ngwQOFiZE/jVGjRlFfXz/T45F69eqxS5cueWKTRCKhnZ0dy5Qpw9u3b1NNTS1Xw3CV5D9KMaDkr+XTp08sW7YsjY2NZdEEQUFBNDAwYMuWLXO0eK1atYpisZhxcXEMCwujqqoqlyxZkmm/V69e0dTUlGXLls1SXYGkpCRu3LiRxYoVo6qqKl1dXXM97CskJITbtm1jly5dqKenJyuvbGpqSpFIRJFIxJYtW3Lnzp0Kd878k3j//j1VVFTo6emZYbuRI0fSysoqT2xasWIFAfDMmTMsW7YsK1Wq9NvkcVCSPZRiQMlfzefPn1mhQgUaGhry6dOnJH/mXhcIBJwzZ062xx00aJBsJ2DVqlUUiUSZLu6BgYE0MzOjlZWV3NXzpFIpT506Jcss2LVr11zLvpeUlMTbt2/Tw8ND5lCY7Iswffp03r59W+ZYFhoaytWrV9POzk62W9CtWzeeOHEizwoD/U4MHDiQRYsWzTC//+bNmykQCHJdWL19+5ZaWlocOnQoBwwYQE1NzVwJvVVSsFCKASV/PaGhobS1tWXhwoX54MEDkpTFUp8/fz5bY9asWVOWf75mzZps3bp1hu3fvn3LEiVK0NLSMkWkQ0Y8fPiQTZo0IQA2aNBAIb4O/+Xr16/ctWsXe/ToQQMDAwKgnp4eu3Tpwm3btsm1e/HmzRvOnTuXNjY2BMAiRYpw2LBhvHHjxl/rOPhfXr9+TZFIxOXLl6fbJjk09fr167lmh1QqpYODA4sXL87NmzcT+L/27j2qqSvfA/j3JAECkZcQUEHkKYqPC6OOFaUI4ovOpZVaQaKsDrVz623nurS1V2VcOvVRq51Ol85tp6O4SrtC1RrUqWJFy2O0oGssIFWhKj4QQSLIKxBiHvv+4ZARkCRAeOb3WSvLcHLOPjuuJOd79tlnb7ADBw702f7I4EFhgBD2dJ77GTNmMCcnJ3bp0iWm0WjY/PnzmVgsNvng3Eaj0TBbW1v28ccfs5KSEgaAHTlypMv1y8vLmY+PD/P19TVp5L/y8nKWmJjIOI5jEyZMYCdOnDDbQVWr1bLLly+zDz74gM2aNUs/5W9wcDDbtGkTu3DhAlOr1T0qu2064fXr1zMPDw8GgPn4+LDk5GQ682SMrVixgnl6enY5X4ZKpWJWVlZs3759fVaH1NRUBoClpKQwBwcHFhcXR4HNQlAYIORfGhoaWGhoKLO3t2cXLlxgcrmceXp6stmzZ3erabu0tJQBYOfOnWMbNmxgTk5OXV5vraioYH5+fszb29voLIr19fVsw4YNTCgUMjc3N/b555/3+MD8rLq6OnbkyBH2+uuvM3d3d/21/1dffZWlpKSwBw8e9HofHWm1Wpadnc1WrVql728QHBzM9uzZ0+3wNVxcu3aNcRzH9u/f3+U6ISEhLCkpqU/2X1VVxZydnVlCQgJ74YUXmLe395CZtpr0HoUBQp7R1NTEwsPDmUgkYtnZ2SwvL48JBAK2bt06k8s4dOgQA8AePnzIPDw82FtvvfXc9SorK1lAQADz8vIyOCOdSqVie/fuZa6urszW1pZt3ry5VwPz6HQ6duXKFfbhhx+ysLAwxufz9ZMUrV+/nmVnZ/f5bI7Pam1tZenp6Wzp0qXMxsaGcRzHIiIi2IEDByzuFsSlS5cyX1/fLkNeUlISCwkJ6bN9i8VitmbNGsbn81l+fn6f7IcMThQGCOmgubmZRUVFMVtbW3b27Fn26aefMgBMJpN1uY2iVc2uPqhnBfces7c2bGce43xZZmYmA/DcH9Wqqio2YcIE5unpqb83vyOdTseOHj3K/P39GcdxLCkpqcdnzY2NjSw9PZ2tWrVK30QvEolYTEwM++tf/2q0VaK/1NfXs4MHD7J58+YxjuOYjY0Ni42NZTKZzCJ6sxcUFDAA7Ouvv37u6/v27WNWVlZmD2tt0xEnJyczjuPYzp07zVo+GfxMPX5zjDEGIxobG+Ho6IiGhgY4ODgYW52QQau1tRWxsbHIysqCTCZDamoqzpw5g8uXLyMgIAAAcLO6CdJL5cj+RY7yxy1o9wVhDEKNAup7RTi9bxPGj/r390EulyMiIgL19fXIycnRl/es/Px8vPfee8jLy8OiRYuwe/duTJkyxeT6M8ZQUlKC06dPIyMjA+fPn4darUZgYCCio6MRHR2NsLAw2NjY9PS/qM9VVlbi0KFDkEqlKCgogKOjI5YuXYqEhASEh4eDz+cPdBX7xG9+8xvcvn0bV69eBY/Ha/fajz/+iDlz5qCwsBDBwcFm2V9dXR2CgoIQHByMoqIiTJo0CZmZmZ32TYY3U4/fFAaIxVGpVIiLi0NGRgZSU1OxdetWCIVCfJuRhW3f38L5WzXg8zhodV1/NTgwMHAI83fFziVTINQ2IzIyEjU1NcjJyUFgYGC79W/duoUNGzZAJpMhODgYe/bsQVRUlEn1bW5uRnZ2NjIyMpCRkYF79+5BKBQiMjIS0dHRWLx4MXx9fXv1fzJQSktLIZVKkZaWhtu3b8PDwwPx8fGQSCQIDg4Gx3EDXUWzyc/PR2hoKI4ePYpXX3213WsKhQIODg5ISUnBb3/7W7PsLykpCenp6Zg2bRqKi4tRXFyM0aNHm6VsMnRQGCDEALVaDYlEgmPHjmHXrl3YcSgbTvN+B44vMBgCOuLzOAh4AK9AhrqfTiEnJwcTJkzQv15TU4Nt27bhs88+w6hRo7Bjxw6sWLHC6NnZzZs39Qf/3NxcqFQq+Pr66s/+586dC1tb2x6//8GGMYZLly5BKpXi8OHDePToESZOnAiJRIKEhAT4+PgMdBXNYt68eairq8NPP/3UKegEBgZi4cKF2Lt3b6/3c/bsWSxYsABxcXE4fPgwTp06hejo6F6XS4YeCgOEGKHRaPD666/j5B0NnF5cCcZYz85EGQM4Div/wwnb4mcDAJRKJfbu3YudO3cCADZu3Ig1a9Z0eQBXKpXIzc1FRkYGTp8+jVu3bsHa2hrh4eH6ABAQEDCszpS7olarce7cOUilUhw/fhzNzc0IDQ2FRCLBa6+9BrFYPNBV7LHs7GxERkY+9+C8fPlyVFRU4Pz5873ah0KhwJQpUyAWi1FYWIjf//73+OSTT3pVJhm6KAwQYoK0S3ex6fi1TstrTv4ZzVd/6HI7j7e/hMDetdPyD5dMhuaXfyA5ORlVVVVYvXo1Nm/e/NwD2J07d/TX/rOysqBUKuHl5aU/+EdERGDEiBG9e4NDXHNzM06cOAGpVIozZ86A4zgsWLAAEokEL7/8MkQi0UBXsVsYY5g9+2lg/PHHH9uFu927d2Pbtm1oaGjo1XX9NWvWYP/+/XB3d4ezszPy8/MHdR8S0rcoDBBixP3HLYj6cy5UGl2n11QPSqCue9hhKcPjM/8HgaM7xqz67PmFatV48Le3EDNvNnbt2tWuE6FKpcKFCxf0zf+lpaUQCAQICwvD4sWLER0djaCgIIs4+++JR48e4dtvv4VUKkVeXh5EIhFeeeUVSCQSzJ8/HwKBYKCraJKMjAy89NJLyMrKQkREhH55W9P+jRs3ntv51BR5eXmYM2cOpk2bhpKSEhQUFGD8+PHmqjoZgigMEGLEypRLyLtda3Ifgdb711At/V84vZgIx9Blz19Jp8VkNxucfHchAOD+/fv6s/8ffvgBCoUCY8aM0R/8o6Ki6DvVA3fu3EFaWhqkUilKSkogFosRFxcHiUSCmTNnDupAxRjDtGnT4OzsjB9++HfrU01NDcRiMQ4fPoxly7r4fBnQ2tqKkJAQqNVqlJWVITU1FYmJieasOhmCTD1+0z0mxCLdrG7C+Vs13eos2Hw9FwAHUVB41yvx+Lhao8HqDX/E1KlT4eXlhdWrV6O2thabNm1CUVERKioqcODAAcTGxlIQ6CEfHx8kJyfj2rVrKCgoQGJiItLT0zFr1iz4+/tj8+bNKC0tHehqPhfHcUhOTkZWVhby8/P1y11dXeHp6YnCwsIelbtjxw6UlZWhsrISEokEK1euNFeViQWglgFikbb+/Rq+vnTP5DDAtBpU/CURVi6eGLVit+F1dVpoS7IRNbIO0dHRmD9/Ppydnc1RbWKAVqtFbm4upFIpZDIZGhoa8Ktf/QoSiQTx8fEYM2bMQFdRT6fTYfLkyfD19cXJkyf1y2NiYvDkyRN8//333SrvypUrmD59Otzc3GBra4uCggL6rSYAqGWAEIOyf5F3q1VAeacAOmUjREFzja7L8fjwC4vBl19+iWXLllEQ6Cd8Ph+RkZFISUnBw4cPIZPJ4O3tjY0bN8LT0xNRUVE4ePAgGhoaBrqq4PF42LRpE06dOtWuJSAkJASFhYUw4RxNT6PRICkpCU5OTqiursY333xDQYB0G4UBYnEUKg3KH7d0a5vm67kATwC7iXNMWr/8cQuaVZqeVI+YgVAoRGxsLGQyGaqrq7F//37odDqsWrUK7u7uWLp0KY4dOwaVSjVgdYyPj4evr6/+9lPgaRiQy+WoqqoyuZxPPvkERUVFqKmpwa5duzBjxoy+qC4Z5igMEItzr7YZpp93AbonSihvXoStTwj4tqadcTEAd2ube1Q/Yl5OTk544403kJWVhfLycmzfvh1lZWWIjY3FqFGj8OabbyInJwc6Xee7SvqSQCDAxo0bIZPJUFJSAuBpGABgcr+BGzduYMuWLRAKhVi4cCHWrVvXZ/Ulwxv1GSAWp7C8Dks+zzN5fcXVbNSe/BNcY9Yb7jzYQVDFKfg68uDu7q5/uLm56Z8PtXvkh5vr16/r70i4e/cuPD09sXz5ckgkEkydOrVf7kh48uQJ/Pz8EBERga+++gqMMbi4uGDdunX4wx/+YHBbnU6HuXPn4vLly7C3t0dxcTHc3d37vM5kaDH1+D00bswlxIysBd1rEGu+ngPO2ha2ATO7tZ2ioR7/uHIV1dXVqKmp6XTmKRKJOgWE54UGd3d3ODo6Durb5YaioKAgbN++Hdu2bUN+fj6kUikOHjyIPXv2ICgoSD8Usre3d5/VwdraGu+//z7Wrl2LLVu2wM/PDyEhIbhc9DOuVTbgiUYHawEP3i4iiGza/1x/8cUX+tEKjx8/TkGA9Aq1DBCL06zSYPLWMyZdKtC2NKDiL4kQTXwRrv/5rsn74ABc3bpQ/wOu1WpRW1uL6upq/UMul7f7+9llarW6XXnW1tadAkJXf7u4uAzbmf/6mlqtRmZmJqRSKU6cOIGWlhbMnj1bPxSyq2vnUSd7S6lUwtvbG/NiV2D84iR8m3cdzbAFngl/HACvkXaICHSDZKYXbFR1mDhxIpRKJdavX4+PPvrI7PUiwwMNOkSIAeF7snHPhE6EjT99h7qzX8Bt2R9h6zvN5PLHudgh970I4ys+B2MM9fX1RgND26Olpf374PF4EIvFJrU6uLm5wcrKqkf1HO4UCgWOHz+OtLQ0ZGZmguM4LFq0CBKJBDExMbCzszPLfu4/bsHyP3+HCs0I8DlAa+AXuW02TbuGeyg7vB2Txo3CxYsXYW1tbZa6kOGHwgAhBpg6zkDVV+9CU18Nz3dSwfFMO9vm8zisnDkOW2MmmaOqRikUik4BoasQUV9f32l7Z2dno5cp2paZ6wA41Mjlchw5cgRSqRQXL16ESCTCkiVLIJFIEBUV1eOhkA/9sxxb/n4NGq3OYAjoiGk1ANPi3bnj8D8vmR5SieWhMECIATermzD/03/0Wfnn1r4Ifzf7Piu/p1QqVbugYChE1NTUdLrffcSIEUYDQ9tzBweHYdnPoaysTN/x8JdffoGbm5t+KORf//rXJr/nv2TfxMeZN3pREwaAw3sLxuOdiJ7NZUCGPwoDhBjR3bkJTMHncQj1dcHXb3Svs+FgpNFoUFNTY9KlCrlcDo2m/bgKNjY2Bvs2PPsYOXJkr2bqGwiMMRQUFCAtLQ3ffPMNqqqq4O/vj4SEBEgkEoMTBB36Zzk2pP9strp8FDsFcTO8zFYeGT4oDBBihKFZC3vKRsDDubXhGDvSsprTGWOoq6szGhjaniuVynbb8/l8fT8HY60OYrF40PVz0Gq1yMnJ0Q+F3NjYiOnTp0MikSAuLg6jR4/Wr2vK50718BYaLqRBVXEdTKOGwMkdI4IXwWF6zHPXt9TPHTGOwgAhJqAztP7HGINCoTC5g2RjY2OnMlxcXExudRAKhf36/pRKJU6dOgWpVIqMjAxoNBpERkZCIpEgNjYWb39bYrBFSnmnAPKjH8Da3Q+iCWHgrIXQ1D8EmA7OEUnP3WY4tUgR86IwQIiJen/t9qn1CwLxdoS/GWpEntXa2mq0g2Tb37W1tZ36Odjb25vUOdLd3R329vZm7edQV1cHmUwGqVSK3Nxc2I32g2vip12ur1O14MHffgcbj4kQL9kIjuvepZPB2leFDBwKA4R0g75Xt451qw8Bn8dBwOPwQcwkahEYBDQaDR49emRSq4NcLodWq223vVAoNDqOQ9vD2dm5W/0c7t+/j/9OycbPSiegiztTmgoz8PjMZxiz6nNYuY6F7kkrOCtrk0JBf9/FQoYGGoGQkG6In+GF2X6u2HTsZ5y/VaO/n7srba+H+rpg55IpdK12kBAIBBg9enS7a/Rd0el0nfo5dAwMxcXF+ucdJzUSCATt+jkYanUQi8UYO3YsGkVjAVXX41u03i0CZ2MHjaIW8vTt0Dx+AM5KCNHkCIyc9yY4QdfjCWh1DNk35NgKCgOk+6hlgJAOblY3QXqpHNk35CivbWk3UiEHwMvFDhHj3bDiBS9qkrUQjDE0NTWZNHpkdXU1mpqa2m3PcRxcRnlAlPh5u5EFO6pMeQea+qczFo6YugBCryloLf8ZTT99B7uJL0L88vsG69lx5EtCqGWAkB4KcLfH1phJ2IpJaFZpcLe22eAY8WT44zgODg4OcHBwQECA8Xv6lUplp8BwvbIR6UrD/RGYuhVMrcKIkMUYOf+/AAB2gaFgWjUURd9DHSaB1UiPrrfH09kyJ41x7Nb7I4R+1QgxQGQjoB9W0m22trYYN24cxo0bp19WWF6HdCOzZbZdBhBNbD87pihoLhRF30P1oNRgGACAJ2a8VZZYjqE1ygchhAxRpsyWyR/h8vRfkVP75aKngVTXqjDLfgjpiD41hBDSD7xdRDB206L1KD8AgKaptt1yTdNjAADfznArFfev/RDSXRQGCCGkH4hsBPAycteJaEIYAEBRnNluuaI4E+DxYeM1xeD2Xi521KeF9Ah9agghpJ9EBLoZnC3TepQfRFPno7n4LB7pdBB6TUZr+c9oKb0Ah1mvQWDv0mXZfB6HiPFufVV1MsxRGCCEkH4imemFL/PvGlzHZeHbEDiIoSg+h5Yb+RA4iuE87004zHjZ4HZaHcOKF2jgK9IzFAYIIaSfBLjbI8zf1eDcBBxfAKc5CXCak2ByuW1zE9C4F6SnqM8AIYT0o51LpkDAM9/8BwAg4HHYucRwfwJCDKEwQAgh/WjsSDv80czzB3wQM4mGxCa9QmGAEEL6WfwML7y3YLxZylq/IJAmySK9Rn0GCCFkALwTEQDXETY0WyYZFKhlgBBCBkj8DC+cWxuOUN9/jTxopC9B2+uhvi44tzacggAxG2oZIISQATR2pB2+fmMmzZZJBhRNYUwIIYMMzZZJzIWmMCaEkCGKZssk/Y36DBBCCCEWjsIAIYQQYuEoDBBCCCEWjsIAIYQQYuEoDBBCCCEWjsIAIYQQYuEoDBBCCCEWjsIAIYQQYuEoDBBCCCEWjsIAIYQQYuEoDBBCCCEWjsIAIYQQYuEoDBBCCCEWjsIAIYQQYuEoDBBCCCEWjsIAIYQQYuEEpqzEGAMANDY29mllCCGEEGI+bcfttuN4V0wKA01NTQCAsWPH9rJahBBCCOlvTU1NcHR07PJ1jhmLCwB0Oh0qKythb28PjuPMWkFCCCGE9A3GGJqamjBmzBjweF33DDApDBBCCCFk+KIOhIQQQoiFozBACCGEWDgKA4QQQoiFozBACCGEWDgKA4QQQoiFozBACCGEWDgKA4QQQoiF+3+p92uyR1vOpAAAAABJRU5ErkJggg==" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# get the graph after dropout\n", "rnd_graphs_w = []\n", "for _ in range(nlayers):\n", " rnd_clauses = kept_clauses + random.sample(drop_clauses, num_selected)\n", " rnd_graph = construct_graph(rnd_clauses)\n", " rnd_graphs_w.append(graph_weights(rnd_graph))\n", "print(\"Here is the graph of the H_C of the last driving layer:\")\n", "rnd_graphs_w = jnp.stack(rnd_graphs_w, axis=0)\n", "nx.draw_networkx(rnd_graph, with_labels=True, pos=pos)\n", "ax = plt.gca()\n", "ax.set_facecolor(\"w\")" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T13:23:28.437985100Z", "start_time": "2023-07-03T13:23:28.262064700Z" } } }, { "cell_type": "markdown", "source": [ "The ansatz needs to accept $\\text{nlayers}$ weights of graphs as inputs." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 23, "outputs": [], "source": [ "def QAOAansatz_rnd(params, g, each=1, return_circuit=False):\n", " n = hard_graph.number_of_nodes() # the number of nodes\n", " rep = nlayers // each\n", " g = g.reshape(rep, each, g.shape[-1]) * driving_factor\n", "\n", " # PQC loop\n", " def pqc_loop(s_, pkg):\n", " params_, g_ = pkg\n", " c_ = tc.Circuit(n, inputs=s_)\n", " for j in range(each):\n", " # driving layer\n", " for i, (a, b) in enumerate(hard_graph.edges):\n", " c_.RZZ(a, b, theta=g_[j][i] * params_[2 * j])\n", " # mixing layer\n", " for i in range(n):\n", " c_.RX(i, theta=params_[2 * j + 1])\n", " s_ = c_.state()\n", " return s_\n", "\n", " c0 = tc.Circuit(n)\n", " for i in range(n):\n", " c0.H(i)\n", " s0 = c0.state()\n", " s = K.scan(pqc_loop, [K.reshape(params, [rep, 2 * each]), g], s0)\n", " c = tc.Circuit(n, inputs=s)\n", "\n", " # whether to return the circuit\n", " if return_circuit is True:\n", " return c\n", "\n", " # calculate the loss function\n", " loss = 0.25\n", " for a, b in hard_graph.edges:\n", " loss += c.expectation_ps(z=[a, b]) * hard_graph[a][b][\"weight\"] * cost_factor\n", "\n", " return K.real(loss)" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-03T13:23:41.855222600Z", "start_time": "2023-07-03T13:23:41.802298100Z" } } }, { "cell_type": "markdown", "source": [ "Then, we perform the optimization step, and also optimize several circuits in parallel. Since graph weights Jax arrays are non-hashable static arguments and not supported when using vmap, we use $\\text{partial}$ to wrap the ansatz and accept the graph weights input." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 28, "outputs": [ { "data": { "text/plain": "
", "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# use vvag to get the losses and gradients with different random circuit instances\n", "QAOA_vvag = K.jit(\n", " K.vvag(partial(QAOAansatz_rnd, g=rnd_graphs_w), argnums=0, vectorized_argnums=0)\n", ")\n", "\n", "params_rnd = K.implicit_randn(\n", " shape=[ncircuits, 2 * nlayers], stddev=0.1\n", ") # initial parameters\n", "if type(K).__name__ == \"JaxBackend\":\n", " opt = K.optimizer(optax.adam(1e-2))\n", "else:\n", " opt = K.optimizer(tf.keras.optimizers.Adam(1e-2))\n", "\n", "list_of_loss = [[] for i in range(ncircuits)]\n", "\n", "for i in range(2000):\n", " loss, grads = QAOA_vvag(params_rnd)\n", " params_rnd = opt.update(grads, params_rnd) # gradient descent\n", "\n", " # visualise the progress\n", " clear_output(wait=True)\n", " list_of_loss = np.hstack((list_of_loss, K.numpy(loss)[:, np.newaxis]))\n", " plt.xlabel(\"Iteration\")\n", " plt.ylabel(\"Cost\")\n", " for index in range(ncircuits):\n", " plt.plot(range(i + 1), list_of_loss[index])\n", " legend = [f\"circuit {leg}\" for leg in range(ncircuits)]\n", " plt.legend(legend)\n", " plt.show()" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 29, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Circuit #0\n", "cost: 0.034298673272132874\n", "max prob: 0.061373475939035416\n", "bit strings: ['000000111111']\n", "\n", "Circuit #1\n", "cost: 0.034172173589468\n", "max prob: 0.06166590005159378\n", "bit strings: ['000000111111', '111111000000']\n", "\n", "Circuit #2\n", "cost: 0.03370116278529167\n", "max prob: 0.06229700148105621\n", "bit strings: ['000000111111']\n", "\n", "Circuit #3\n", "cost: 0.035995520651340485\n", "max prob: 0.0600101463496685\n", "bit strings: ['111111000000']\n", "\n", "Circuit #4\n", "cost: 0.03770057111978531\n", "max prob: 0.05639055743813515\n", "bit strings: ['000000111111']\n", "\n", "Circuit #5\n", "cost: 0.042536795139312744\n", "max prob: 0.047668762505054474\n", "bit strings: ['111111000000']\n", "\n" ] } ], "source": [ "# print QAOA results\n", "for num_circuit in range(ncircuits):\n", " print(f\"Circuit #{num_circuit}\")\n", " c = QAOAansatz_rnd(\n", " params=params_rnd[num_circuit], g=rnd_graphs_w, return_circuit=True\n", " )\n", " loss = QAOAansatz_rnd(params=params_rnd[num_circuit], g=rnd_graphs_w)\n", "\n", " # find the states with max probabilities\n", " probs = K.numpy(c.probability())\n", " max_prob = max(probs)\n", " index = np.where(probs == max_prob)[0]\n", " states = []\n", " for i in index:\n", " states.append(f\"{bin(i)[2:]:0>{c._nqubits}}\")\n", " print(f\"cost: {K.numpy(loss)}\\nmax prob: {max_prob}\\nbit strings: {states}\\n\")" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-04T01:38:27.853435600Z", "start_time": "2023-07-04T01:37:48.381823700Z" } } }, { "cell_type": "markdown", "source": [ "On average, QAOA with random quantum dropout improves the probability of correct solution (max prob) by nearly 0.02 compared to regular QAOA.\n", "\n", "Compared with isotropic quantum dropout, the standard deviation of the probability of correct solution obtained by random quantum dropout is smaller, but the upper limit is lower. From the physical picture, QAOA after random quantum dropout works like a quantum interferometer. QAOA circuits with different dropouts over driving layers may work through a focusing effect on the true ground state: different clause sets lead to different energy landscapes and minima, whose configurations receive constructive interference and enhanced amplitudes. Being the only common minimum of all $\\hat{H}_{C_i}$ irrespective of the dropouts, the true ground state remains stand-out through all driving layers. Please refer to [Wang, Zheng, Wu, and Zhang (2023)](https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.5.023171) for more analysis and details." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 30, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OS info: Linux-5.4.119-1-tlinux4-0010.2-x86_64-with-glibc2.28\n", "Python version: 3.10.11\n", "Numpy version: 1.23.5\n", "Scipy version: 1.11.0\n", "Pandas version: 2.0.2\n", "TensorNetwork version: 0.4.6\n", "Cotengra is not installed\n", "TensorFlow version: 2.12.0\n", "TensorFlow GPU: []\n", "TensorFlow CUDA infos: {'cpu_compiler': '/dt9/usr/bin/gcc', 'cuda_compute_capabilities': ['sm_35', 'sm_50', 'sm_60', 'sm_70', 'sm_75', 'compute_80'], 'cuda_version': '11.8', 'cudnn_version': '8', 'is_cuda_build': True, 'is_rocm_build': False, 'is_tensorrt_build': True}\n", "Jax version: 0.4.13\n", "Jax installation doesn't support GPU\n", "JaxLib version: 0.4.13\n", "PyTorch version: 2.0.1\n", "PyTorch GPU support: False\n", "PyTorch GPUs: []\n", "Cupy is not installed\n", "Qiskit version: 0.24.1\n", "Cirq version: 1.1.0\n", "TensorCircuit version 0.10.0\n" ] } ], "source": [ "tc.about()" ], "metadata": { "collapsed": false, "ExecuteTime": { "end_time": "2023-07-04T01:40:31.531945400Z", "start_time": "2023-07-04T01:40:31.478214100Z" } } } ], "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": "3.10.10" } }, "nbformat": 4, "nbformat_minor": 5 }