{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "```{index} single: AMPL \n", "```\n", "```{index} single: AMPL MP library\n", "```\n", "```{index} single: conic optimization; second order cones\n", "```\n", "```{index} single: solver; Mosek\n", "```\n", "```{index} single: solver; Ipopt\n", "```\n", "```{index} single: application; building insulation\n", "```\n", "# Optimal Design of Multilayered Building Insulation" ] }, { "cell_type": "markdown", "metadata": { "id": "-1sFCsTgp8Mk" }, "source": [ "Thermal insulation is installed in buildings to reduce annual energy costs. However, the installation costs money, so the decision of how much insulation to install is a trade-off between the annualized capital costs of insulation and the annual operating costs for heating and air conditioning. This notebook shows the formulation and solution of an optimization problem using conic optimization." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [] }, "outputs": [], "source": [ "# install dependencies and select solver\n", "%pip install -q amplpy numpy pandas\n", "\n", "SOLVER_CONIC = \"mosek\" # ipopt, mosek, gurobi, knitro\n", "\n", "from amplpy import AMPL, ampl_notebook\n", "\n", "ampl = ampl_notebook(\n", " modules=[\"coin\", \"mosek\"], # modules to install\n", " license_uuid=\"default\", # license to use\n", ") # instantiate AMPL object and register notebook magics" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Please provide a valid license UUID. You can use a free https://ampl.com/ce license.\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "ba3e27e3e92545e493ee8756a270e9fe", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(Output(), HBox(children=(Text(value='', description='License UUID:', style=TextStyle(descriptio…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import Markdown, HTML\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": { "id": "ivrv3B4GsJgb" }, "source": [ "## A Model for Multi-Layered Insulation\n", "\n", "Consider a wall or surface separating conditioned interior space in a building at temperature $T_i$ from the external environment at temperature $T_o$. Heat conduction through the wall is given by\n", "\n", "$$\\dot{Q} = UA (T_i - T_o),$$\n", "\n", "where $U$ is the overall heat transfer coefficient and and $A$ is the heat transfer area. For a wall constructed from $N$ layers of different insulating materials, the inverse of the overall heat transfer coefficient $U$ is given by a sum of serial thermal \"resistances\"\n", "\n", "$$\\frac{1}{U} = R_0 + \\sum_{n=1}^N R_n,$$\n", "\n", "where $R_0$ is the thermal resistance of the structural elements. The thermal resistance of the $n$-th insulating layer is equal to $R_n = \\frac{x_n}{k_n}$ for a material with thickness $x_n$ and a thermal conductivity $k_n$, so we can rewrite\n", "\n", "$$\\frac{1}{U} = R_0 + \\sum_{n=1}^N \\frac{x_n}{k_n}.$$\n", "\n", "The economic objective is to minimize the cost $C$, obtained as the combined annual energy operating expenses and capital cost of insulation. \n", "\n", "We assume the annual energy costs are proportional to overall heat transfer coefficient $U$ and let $\\alpha \\geq 0$ be the coefficient for the proportional relationship of the overall heat transfer coefficient $U$ to the annual energy costs. Furthermore, we assume the cost of installing a unit area of insulation in the $n$-th layer is given by the affine expression $a_n + b_n x_n$. The combined annualized costs are then\n", "\n", "$$C = \\alpha U + \\beta\\sum_{n=1}^N (a_n y_n + b_n x_n),$$\n", "\n", "where $\\beta$ is a discount factor for the equivalent annualized cost of insulation, and $y_n$ is a binary variable that indicates whether or not layer $n$ is included in the installation. The feasible values for $x_n$ are subject to constraints\n", "\n", "$$\\begin{align}\n", "x_n & \\leq Ty_n \\\\\n", "\\sum_{n=1}^N x_n & \\leq T\n", "\\end{align}$$\n", "\n", "where $T$ is an upper bound on insulation thickness.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analytic solution for $N=1$\n", "\n", "In the case of a single layer, i.e., $N=1$, we have a one-dimensional cost optimization problem of which we can obtain a close-form analytical solution directly. Indeed, the expression for the cost $C(x)$ as a function of the thickness $x$ reads\n", "\n", "$$\\begin{align}\n", "C(x) = \\frac{\\alpha k}{k R_0 + x} + \\beta(a + bx).\n", "\\end{align}$$\n", "\n", "For fixed parameters $k$, $R_0$, $\\beta$, $b$, we can calculate the optimum thickness $x^*$ as\n", "\n", "$$x^{*} = - k R_0 + \\sqrt{\\frac{\\alpha k}{\\beta b}}.$$\n", "\n", "A plot illustrates the trade-off between energy operating costs and capital insulation costs and the corresponding optimal solution $x^*$.\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "tags": [] }, "outputs": [], "source": [ "# application parameters\n", "alpha = 30 # $ K / W annualized cost per sq meter per W/sq m/K\n", "beta = 0.05 # equivalent annual cost factor\n", "R0 = 2.0 # Watts/K/m**2\n", "T = 0.30 # maximum insulation thickness\n", "\n", "# material properties\n", "k = 0.030 # thermal conductivity as installed\n", "a = 5.0 # installation cost per square meter\n", "b = 150.0 # installed material cost per cubic meter" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The optimal cost is equal to 4.99615 per sq. meter\n", "The optimal thickness is 0.28641 meters\n", "\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "f = lambda x: alpha / (R0 + x / k)\n", "g = lambda x: beta * (a + b * x)\n", "\n", "# solution\n", "xopt = -k * R0 + np.sqrt(alpha * k / beta / b)\n", "\n", "print(f\"The optimal cost is equal to {f(xopt) + g(xopt):0.5f} per sq. meter\")\n", "print(f\"The optimal thickness is {xopt:0.5f} meters\\n\")\n", "\n", "# plotting\n", "x = np.linspace(0, 1, 201)\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(6.5, 4))\n", "\n", "ax.plot(x, f(x), label=\"energy\")\n", "ax.plot(x, g(x), label=\"insulation\")\n", "ax.plot(x, f(x) + g(x), label=\"total\", lw=3)\n", "ax.plot(xopt, f(xopt) + g(xopt), \".\", ms=10, label=\"minimum\")\n", "ax.legend()\n", "\n", "ax.plot([0, xopt], [f(xopt) + g(xopt)] * 2, \"r--\")\n", "ax.plot([xopt] * 2, [0, f(xopt) + g(xopt)], \"r--\")\n", "ax.text(0, f(xopt) + g(xopt) + 0.3, f\"{f(xopt) + g(xopt):0.3f}\")\n", "ax.text(xopt, 0.3, f\"{xopt:0.3f}\")\n", "\n", "ax.set_xlabel(\"Insulation thickness [m]\")\n", "ax.set_ylabel(\"Cost \")\n", "ax.set_title(\"Annualized costs of insulation and energy per sq. meter\")\n", "\n", "ax.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## AMPL Model for $N=1$\n", "\n", "A [conic rotated constraint](https://amplmp.readthedocs.io/en/latest/rst/model-guide.html) in AMPL can be represented as follows:\n", "\n", "$$\\sum_{n=0}^{N-1} z_n^2 \\leq 2 r_1 r_2, \\quad r_1, r_2 \\ge 0$$ \n", "\n", "where $r_1, r_2$, and $z_0, z_1, \\ldots, z_{N-1}$ are variables. For a single layer AMPL model we identify $R \\sim r_1$, $U\\sim r_2$, and $z_0^2 \\sim 2$ which leads to the model\n", "\n", "$$\n", "\\begin{align}\n", "\\min \\quad & \\alpha U + \\beta(a + bx)\\\\\n", "\\text{s.t.} \\quad \n", "& R = R_0 + \\frac{x}{k} \\\\\n", "& z^2 \\leq 2 R U & \\text{(conic constraint)}\\\\\n", "& z = \\sqrt{2} \\\\\n", "& x \\leq T\\\\\n", "& x, R, U \\geq 0.\n", "\\end{align}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MOSEK 10.0.43: MOSEK 10.0.43: optimal; objective 4.996152429\n", "0 simplex iterations\n", "11 barrier iterations\n", "The optimal cost is equal to 4.99615 per sq. meter\n", "The optimal thickness is xopt = 0.28642 meters\n" ] } ], "source": [ "ampl = AMPL()\n", "\n", "ampl.eval(\n", " r\"\"\"\n", " # application parameters\n", " param alpha; # $ K / W annualized cost per sq meter per W/sq m/K\n", " param beta; # equivalent annual cost factor\n", " param R0; # Watts/K/m**2\n", " param T; # maximum insulation thickness\n", "\n", " # material properties\n", " param k; # thermal conductivity as installed\n", " param a; # installation cost per square meter\n", " param b; # installed material cost per cubic meter\n", "\n", " # decision variables\n", " var R >= 0;\n", " var U >= 0;\n", " var x >= 0 <= T;\n", "\n", " # objective\n", " minimize cost: alpha*U + beta*(a + b*x);\n", "\n", " # insulation model\n", " s.t. r: R == R0 + x/k;\n", "\n", " # conic constraint\n", " s.t. q: R*U >= 1;\n", "\"\"\"\n", ")\n", "\n", "ampl.param[\"alpha\"] = alpha\n", "ampl.param[\"beta\"] = beta\n", "ampl.param[\"R0\"] = R0\n", "ampl.param[\"T\"] = T\n", "\n", "ampl.param[\"k\"] = k\n", "ampl.param[\"a\"] = a\n", "ampl.param[\"b\"] = b\n", "\n", "ampl.option[\"solver\"] = SOLVER_CONIC\n", "ampl.solve()\n", "\n", "print(\n", " f\"The optimal cost is equal to {ampl.get_objective('cost').value():0.5f} per sq. meter\"\n", ")\n", "print(f\"The optimal thickness is xopt = {ampl.get_value('x'):0.5f} meters\")" ] }, { "cell_type": "markdown", "metadata": { "id": "-WPtrJrA-MZn", "tags": [] }, "source": [ "## Multi-Layer Solutions as a Mixed Integer Quadratic Constraint Optimization (MIQCO)" ] }, { "cell_type": "markdown", "metadata": { "id": "-WPtrJrA-MZn" }, "source": [ "For multiple layers, we cannot easily find an analytical optimal layer composition and we shall resort to conic optimization. Let $y_n$ be the binary variable that indicates whether layer $n$ is included in the insulation package or not, and $x_n$ be the continuous variable describing the thickness of layer $n$, which is zero if layer $n$ is not included. \n", "\n", "In the general case with $N$ layers, the objective function is given by \n", "\n", "$$\n", "\\frac{\\alpha}{R} + \\beta \\sum_{n=1}^N (a_n y_n + b_n x_n),\n", "$$\n", "\n", "where the first term is nonlinear in the variables $x_1,\\dots,x_N$ since since the denominator of the first term is equal tosince at the denominator of the first term is equal to\n", "\n", "$$\n", "R = R_0 + \\sum_{n=1}^N \\frac{x_n}{k_n}.\n", "$$\n", "\n", "To overcome this issue, we can include $U$ as a decision variable and include a constraint\n", "\n", "$$\n", "\\frac{1}{R} \\leq U.\n", "$$\n", "\n", "Since we minimize the objective and $U$ has no other constraint, the problem will guarantee that $U$ is equal to $1/R$. The extra constraint $RU \\leq 1$ can be reformulated using an extra decision variable $z$ as:\n", "\n", "$$\n", "1 \\leq RU \\quad \\Longleftrightarrow \\quad \\left\\{ \\begin{array}{l} z^2 \\leq 2RU \\\\\n", "z = 2 \n", "\\end{array}\n", "\\right.\n", "\\quad \\Longleftrightarrow\n", "\\quad \\left\\{ \\begin{array}{l} \\left\\| \\begin{array}{c}\n", "\\sqrt{2} z \\\\\n", "R - U\n", "\\end{array}\\right\\|_2 \\leq R + U \\\\\n", "z = 2\n", "\\end{array}\n", "\\right.\n", "$$\n", "\n", "from which we see that the entire problem can be reformulated as a conic optimization problem. \n", "\n", "The middle formulation above can, in fact, be implemented in AMPL as a [conic rotated constraint](https://amplmp.readthedocs.io/en/latest/rst/model-guide.html) of the form:\n", "\n", "$$\n", " \\sum_{n=0}^{n-1} z_n^2 \\leq 2 r_1 r_2, \\quad r_1, r_2 \\ge0.\n", "$$\n", "In our case, we pick $n=1$, $z_0 = z$, $r_1=R$, and $r_2=U$.\n", "\n", "Adopting this formulation, the full multi-layer optimization problem then reads:\n", "\n", "$$\n", "\\begin{align}\n", "\\min \\quad & \\alpha U + \\beta \\sum_{n=1}^N (a_ny_n + b_nx_n)\\\\\n", "\\text{s.t.} \\quad \n", "& R = R_0 + \\sum_{n=1}^N\\frac{x_n}{k_n} \\\\\n", "& x_n \\leq T y_n & n=1,\\dots,N \\\\\n", "& \\sum_{n=1}^N x_n \\leq T \\\\\n", "& z^2 \\leq 2 R U \\\\\n", "& z = \\sqrt{2} \\\\\n", "& R, U > 0\\\\\n", "& x_n \\geq 0 & n=1,\\dots,N \\\\\n", "& y_n \\in \\{0,1\\} & n=1,\\dots,N\n", "\\end{align}\n", "$$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "tags": [] }, "outputs": [], "source": [ "def insulate(df, alpha, beta, R0, T):\n", " ampl = AMPL()\n", "\n", " ampl.eval(\n", " r\"\"\"\n", " # application parameters\n", " param alpha; # $ K / W annualized cost per sq meter per W/sq m/K\n", " param beta; # equivalent annual cost factor\n", " param R0; # Watts/K/m**2\n", " param T; # maximum insulation thickness\n", "\n", " # material properties\n", " set MAT;\n", " param k{MAT}; # thermal conductivity as installed\n", " param a{MAT}; # installation cost per square meter\n", " param b{MAT}; # installed material cost per cubic meter\n", "\n", " # decision variables\n", " var R >= 0;\n", " var U >= 0;\n", " var x{MAT} >= 0;\n", " var y{MAT} binary;\n", "\n", " # objective\n", " minimize cost:\n", " alpha*U + beta * sum {i in MAT} (a[i] + b[i]*x[i]);\n", "\n", " # insulation model\n", " s.t. insulation: R == R0 + sum {i in MAT} x[i]/k[i];\n", "\n", " # total thickness limit\n", " s.t. thickness: sum {i in MAT} x[i] <= T;\n", "\n", " # layer model \n", " s.t. layers {i in MAT}:\n", " x[i] <= T * y[i];\n", "\n", " # conic constraint\n", " s.t. q: R*U >= 1;\n", " \"\"\"\n", " )\n", "\n", " ampl.param[\"alpha\"] = alpha\n", " ampl.param[\"beta\"] = beta\n", " ampl.param[\"R0\"] = R0\n", " ampl.param[\"T\"] = T\n", "\n", " ampl.set[\"MAT\"] = list(df.index)\n", " ampl.set_data(df, \"MAT\")\n", "\n", " ampl.option[\"solver\"] = SOLVER_CONIC\n", " ampl.solve()\n", "\n", " df[\"x_opt\"] = ampl.get_variable(\"x\").to_pandas()\n", "\n", " print(\n", " f\"\\nThe optimal cost is equal to\"\n", " f\" {ampl.get_objective('cost').value():0.5f} per sq. meter\"\n", " )\n", " display(df.round(5))\n", "\n", " return ampl" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Case 1. Single Layer Solution" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MOSEK 10.0.43: MOSEK 10.0.43: optimal; objective 4.804922361\n", "0 simplex iterations\n", "1 branching nodes\n", "\n", "The optimal cost is equal to 4.80492 per sq. meter\n" ] }, { "data": { "text/html": [ "
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kabx_opt
Mineral Wool0.0305.0150.00.00000
Rigid Foam (high R)0.0158.0180.00.19361
Rigid Foam (low R)0.3008.0120.00.00000
\n", "
" ], "text/plain": [ " k a b x_opt\n", "Mineral Wool 0.030 5.0 150.0 0.00000\n", "Rigid Foam (high R) 0.015 8.0 180.0 0.19361\n", "Rigid Foam (low R) 0.300 8.0 120.0 0.00000" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pandas as pd\n", "\n", "# application parameters\n", "alpha = 30 # $ K / W annualized cost per sq meter per W/sq m/K\n", "beta = 0.05 # equivalent annual cost factor\n", "R0 = 2.0 # Watts/K/m**2\n", "T = 0.30 # maximum insulation thickness\n", "\n", "df = pd.DataFrame(\n", " {\n", " \"Mineral Wool\": {\"k\": 0.030, \"a\": 5.0, \"b\": 150.0},\n", " \"Rigid Foam (high R)\": {\"k\": 0.015, \"a\": 8.0, \"b\": 180.0},\n", " \"Rigid Foam (low R)\": {\"k\": 0.3, \"a\": 8.0, \"b\": 120.0},\n", " }\n", ").T\n", "\n", "m = insulate(df, alpha, beta, R0, T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Case 2. Multiple Layer Solution" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MOSEK 10.0.43: MOSEK 10.0.43: optimal; objective 3.229922362\n", "0 simplex iterations\n", "1 branching nodes\n", "\n", "The optimal cost is equal to 3.22992 per sq. meter\n" ] }, { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
kabx_opt
Foam0.0150.0110.00.06278
Wool0.0100.0200.00.08722
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" ], "text/plain": [ " k a b x_opt\n", "Foam 0.015 0.0 110.0 0.06278\n", "Wool 0.010 0.0 200.0 0.08722" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# application parameters\n", "alpha = 30 # $ K / W annualized cost per sq meter per W/sq m/K\n", "beta = 0.05 # equivalent annual cost factor\n", "R0 = 2.0 # Watts/K/m**2\n", "T = 0.15 # maximum insulation thickness\n", "\n", "df = pd.DataFrame(\n", " {\n", " \"Foam\": {\"k\": 0.015, \"a\": 0.0, \"b\": 110.0},\n", " \"Wool\": {\"k\": 0.010, \"a\": 0.0, \"b\": 200.0},\n", " }\n", ").T\n", "\n", "m = insulate(df, alpha, beta, R0, T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot below gives a graphical representation of the 2-layer problem we just solved. The green line represents the thickness constraint $x_0+x_1 \\leq T$, the curves are the isolines of the objective function, and the optimal solution $x^*=(x_0^*,x_1^*)$ is highlighted in red." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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hgihdurSwsrISxsbGomDBgmLixImx+ivG50uHeisrK2FkZCRKly4dq0P9FySw+8QXoaGhYvr06cLJyUmYmZkJAwMDkS9fPtG7d2/x8OHDWG2PHDkiypcvL4yNjYWFhYWoU6dOvB3qv+4W8aXD/5c+hz4+PqJevXoia9aswsDAQGTNmlW0aNFC3L9/P9b7du3aJezt7YWenl6srhS+vr7C1dVVmJmZCWtra9G5c2dx/fr1b7pbfOlQ/7Uvdf7X2bNnhaOjozAwMEhwV4rXr1+Lfv36ifz58wsjIyNhYmIiHB0dxcSJE0VgYGCstj/6PXv8+LHo0KGDyJMnjzAyMhLp06cXVapUEUeOHIm1nbt374pKlSoJY2Nj2aE+mSmE0PDTBpIkSZKUhsh7hJIkSdJvTQahJEmS9FuTQShJkiT91mQQSpIkSb81GYSSJEnSb00GoSRJkvRbkx3q46FSqXj9+jXm5uZyqCNJkqQ0RgjB58+fyZo16w8Ho5BBGI/Xr19ja2ur7TIkSZKkn/DixQuyZ8/+3TYyCOPxZQ6yFy9eqKeykSRJ+hU9uPqErQsOcfHQ/2cpcXApRONebtg75/3OO1OvoKAgbG1tEzSfpBxZJh5BQUFYWloSGBgog1CSpN/CU99XbJq9jxPbL6JSxkxzVbhMPpr1q4lT9aJp6jZRYr7DZRDGQwahJEm/qzdP37JlzgEObzhDVGTMTBl5itrSzMuD8nVKoqub+p+zlEGoATIIJUn63b1/84ltCw6yb/VJwkNipojKlteGZp41qdq0DHr6qffumgxCDZBBKEmSFCPoQzA7Fx9h99KjBAeGApApe3oa93bHrXUFDI0NtFzht2QQaoAMQkmSpNhCP4ezd9Vxti84xMeAIACsMprTsEcNPDpUxtTCWMsV/l9ivsNTxYXeBQsWYGdnh5GREc7Ozly4cCHetrdv36ZRo0bY2dmhUCi+meH8i1evXtGqVSsyZMiAsbExRYsW5dKlS8n0CSRJkn59JuZGNOnjzprrU+np3ZJMthn49PYzK8duo22xwayZuJPA95+1XWaiaT0IN23ahJeXF6NHj+bKlSsUL14cNzc3AgIC4mwfGhpK7ty5mTJlCpkzZ46zzcePHylfvjz6+vrs378fX19fZsyYQbp06ZLzo0iSJP0WDIz0qdOpCisvT2TAog7Y5s9McGAof03fQ5tig1kyfBPv33zSdpkJpvVLo87Ozjg5OTF//nwgZkQXW1tbevfuzZAhQ777Xjs7Ozw9PfH09Iy1fMiQIZw5c4ZTp04luS55aVSSJClhVCoVZ/dcZePMvTy8/hwAfQM9XFuUo6lnTbLYZUzxmtLMpdHIyEguX76Mq6urepmOjg6urq6cO3cuydvdvXs3pUqVokmTJmTKlIkSJUqwbNmy774nIiKCoKCgWC9JkiTpx3R0dKhQ15F5x0YyYYsnhcvkIyoymv1rTtLRcRhTuyzj6Z1X2i4zXloNwnfv3qFUKrGxsYm13MbGBj8/vyRv9/HjxyxatIh8+fJx8OBBunfvTp8+fVizZk2875k8eTKWlpbqlxxeTZIkKXEUCgWlXIswY/9gpu8dRKlqRVCpBMe2/EO3cqMZ12oB96480XaZ39D6PcLkoFKpKFmyJJMmTaJEiRJ06dKFzp07s3jx4njfM3ToUAIDA9WvFy9epGDFkiRJv5Yi5fIzYasn846PpEJdRxQKBWf3XqVvtYkMaziTG2fukVo6LWg1CK2trdHV1cXf3z/Wcn9//3gfhEmILFmyYG9vH2tZoUKFeP78ebzvMTQ0xMLCItZLkiRJ+jn5iudkxJruLDk3FtfmZdHR1eHKMV8G1famv/sU/jl4Q+uBqNUgNDAwwNHRER8fH/UylUqFj48PZcuWTfJ2y5cvz71792Itu3//Pjlz5kzyNiVJkqSky1EgKwMWdWTllUnU7lAZfUM9fC88YnTzufRyGcfJnZdQ/ju+aUrT+qVRLy8vli1bxpo1a7hz5w7du3cnJCSE9u3bA9CmTRuGDh2qbh8ZGcm1a9e4du0akZGRvHr1imvXrvHw4UN1m379+nH+/HkmTZrEw4cP2bBhA0uXLqVnz54p/vkkSZKk/8ucw5peM1qx+toUGvVyw8jUkEc3XzCp/WK6lh3FoQ1niI6KTtGatN59AmD+/Pl4e3vj5+eHg4MDc+fOxdnZGYDKlStjZ2fH6tWrAXj69Cm5cuX6ZhsuLi4cP35c/fOePXsYOnQoDx48IFeuXHh5edG5c+cE1yS7T0iSJCW/oA/B7Frqw67FPrGHb+vjjlurpA/fJodY0wAZhJIkSSknruHb0mWyoGHPGni0r4yJuVGitieDUANkEEqSJKW8iLBIDq47zda5Bwh4+QEAMysT6ndzpV6XqpinM0vQdmQQaoAMQkmSJO2Jjorm6ObzbJq9n1cPY3oWGJsZ4tG+Mg171iC9jeV33y+DUANkEEqSJGmfUqnizO7LbJy5j8e3Yvp3Gxjp49aqAo17u2OTI0Oc75NBqAEyCCVJklIPIQQXDt3krxl7uHvxMQC6erpUa1aGpp41yZ43dt9zGYQaIINQkiQp9RFCcP3UXTbO3Me1E3eAmKHdKtZ3pHk/D3IXjRkeUwahBsgglCRJSt3uXnrMXzP28s+B6+plzm7FaN7fg2wFMsog/Fm/QhBGhkfy7vVHPgUEEfT+M8GBoYR9DiciLJLoqGiU0SqEECgUCnT1dNDT18PQ2ABDEwOMTY0wsTDG1NIE8/RmWGYww9TSBIVCoe2PJUmSFMvjWy/YNGs/J3dcVA/XVqisHbP3j5RB+DPSUhCGh4Rz/8oTHl57xpNbL3h5/w2vH/vzKUCzU0np6etildGC9JmtSJ/FCuts6bHOlp5MthnIZJsBmxzWZMiWHl1drQ9YJEnSb+jlQz82z96Pz6bzRESF4RO4Vgbhz0jNQSiE4P7lJ5z9+zJXfG7x8NpTVPGM0WdobIBVJgssM5hjls4UYzMjDI0N0DPQQ1dPB4WODgiBMlpJVEQ0keFRRIRFEPo5nNCgMEICQwn6EEx4SESCatPT18UmZ0ay5slE1tw2ZM+fBdsCWbHNn4UMWdPJM0pJkpKd//P37N9wnPZDG8sg/BmpMQg/+H3iwOrjHFp7ijePA2Kts86ajvyOuclV1JYcBbORLW9mbHJaY57OVCPhExEWSeC7z3wKCOSD3yfev/nEu9cfefviHW9ffsD/+TvevnhPdJQy3m2YmBuRo2A2ctpnw84+OzkLZyd3kRyk+0F/IEmSpMSSD8toQGoKwoAX71k3cTtH1p9BGR0TNIYmBpR2d8C5pgPFKxUiUw5rrdYIMf193r/6wOsnAbx+5M+rB368fOgXc6n2kX+8Z61WmSzIXTQHeYrnJK+DHflK2JEldyZ0dOQlVkmSkkYGoQakhiCMjopm6+x9rJ+0k8jwKAAKOeeldpdqVKhXCiPTxI29p01RkdG8eujH8zuveOr7kqe3X/Lk1gvePA6Icy4yEwtj8jrYkb9kLvKVzEWBUrnJbJdRXlqVJClBZBBqgLaD0P/ZO8Y1n83Da88AKFqhAB3GN8O+TL4UryU5hYeE89T3FY9vPOPh9Wc8vPqUxzdfEBUR9U1bS2tzCpTKTcHSeSnknJcCpfJgamGshaolSUrtZBBqgDaD8MGVJ4xqNIMPfoGYpzejm3dLqrUo/9ucDUVHRfP87mseXH3K/cuPuX/pMY9vPv/m/qNCocCuSHYKOefDvkw+CpfNR5ZcmX6b4yRJUvxkEGrAl4O4/+Z+3Iu4p9h+H157yoDqEwkLDidXEVvGbe9PJtu4x9L7nURGRPH4+jPuXnzEnX8ecufCQ/yfvfumXfrMVhQul5+i5QtQpEIBchWxlfcaJek3JINQA74cRJORJhzoeICKOSsm+z4/BQTSq/xo3r58T7FKhRizpZ+89Pcd79984u6Fh9w+dx/f8w94cOXJN2eNZlYmMcFYoSDFKxUiT/Gc6OrpaqliSZJSigxCDfhyEBkCpuam7G+5P1nDUAjB8LreXD5yk2x5MzPn5BjM05km2/5+RRFhkdy//JibZ+5x68w9fM89ICw4PFYbEwtjilYoQPFK9jhUtidXUXnGKEm/IhmEGvDfIMQITPWTNwzP7bnCmCaz0DfUZ+H58eQomC1Z9vM7UUYreXjtGTdP3/33dY+QwNBYbSwymFGsYiEcKttTomphsuXNLO8xStIvQAahBnwdhJB8YSiEoHvp4Ty59YJmA+vQYVxTjW5fiqFUqnh8/RnXT97h+glfbp6+980ZY8bsGShRtTAlqxahRNXCWGVMHYMpSJKUODIINeDLQayxrAaHXh1SL0+OMLx15h79XSdgaGLAhkdzMbOSl0RTQnRUNPcvP+HaCV+uHbuN77kHREVGx2qTp3hOSlYtjGP1YhQulx8DQ30tVStJUmLIINSALwcx4H0A7Q+0Z++Dvep1mg7DOb1Wsm/FMdzaVsJrcWeNbFNKvPDQCG6fvc8Vn1tcOXqLxzeex1pvaGJAcRd7SrkWpVSNYmT7aiJQSZJSDxmEGvDfg2hoYkijzY2SLQzb2ffnzZMAxm3vj3NNh5/enqQZH/0DuXr0Fpd9bnHF5yYf/AJjrc+SKxOlahTFyc2B4i6FMDIx1FKlkiR9TQahBnx9ECOiI5IlDAPffaapbQ8Atvsvld0lUikhBI9vPOfS4ZtcOnwD33P3Y3XV0DfUp1ilgpR2K46TuwPZ8thosVpJkmQQakBcBzE5wvD2uft4VR1PxuwZWPdgtiZKl1JAWHA41477cvHQdS4euE7Ai/ex1mfPlzlmUPRaDhQuVwB9Az0tVSpJvycZhBoQ30HUdBie2PoPk1rPp0j5Asw4MkIjtUspSwjBszuvuHjwOhcPXufWmfvqWUIgpu+io2tRnGuVwKlGMfkkqiSlABmEGvC9g6jJMDy45gQzuy2ndE0Hxm/vr5HaJe0KCQrjypGb/HPgGhcOXCPw7Wf1Oh0dBQVL56WMR0nK1i6BbYGsst+iJCUDGYQa8KODqKkw3LfyGHN6rqSMRwnGbvXSSO1S6qFSqbh/+Qn/7LvK+X1Xv3kSNWseG3UoFi6bXw7/JkkaIoNQAxJyEDURhkc2nMa74xJKVivC5D2DNVK7lHoFvHivDsXrx31j9Vu0yGCGc00HytZ2xNG1SJqab1KSUhsZhBqQ0IP4s2H4z/5rjGo4gzzFc7Lw/ASN1C6lDaGfw7h85Bbn9lzmwoHrfP4QrF5nYKRPyWpFKFfHkTIeJbG0NtdipZKU9sgg1IDEHMSfCcNH15/Ro8wILK3N2fxioUZql9IeZbSS2+fuc+7vK5z9+zJ+T9+q1+noKChSvgDl6paifF1HMuWw1mKlkpQ2yCDUgMROzJvUMAz9HEaDTF0A2PJqERbpzX6+eClNE0Lw9PZLzuy+xNndl3l0/Vms9flK5qJcXUcq1HciR4GsWqpSklI3GYQakJQZ6pMahq3zexLw4j3eh4ZRrGKhn65d+rX4PXvL2d2XObv7ErfP3kel+v//sjkKZqVCfSfK1ytFnuI55ROokvQvGYQakJQghKSF4fgWczm98yIdxjej2YDaP1279Ov6FBDI+X1XOb3zIleP3o41uk2WXJkoX68UFRs4UcApjwxF6bcmg1ADkhqEkPgw3DZnP0uHbMDJrRgTdg786dql30NIYCj/7LvK6V2XuHToBhFhkep1GbNnoGIDJyo0cKKQc145+bD020nMd3iq+L9jwYIF2NnZYWRkhLOzMxcuXIi37e3bt2nUqBF2dnYoFApmz5793W1PmTIFhUKBp6enZov+DkM9Q7Y13YZHPg/1spCoEGqur8mpZ6e+ae9QxR6AG6fuEhkRlWJ1SmmbqaUJVVuUZ9TGvmx+sYAR63tTuWlZjM2MePvyPdvnHcCr6nha5fVkodef3DpzD5VKpe2yJSnV0XoQbtq0CS8vL0aPHs2VK1coXrw4bm5uBAQExNk+NDSU3LlzM2XKFDJn/v40OBcvXmTJkiUUK1YsOUr/rsSEYe6iOUif2ZKI0EhunLyT0qVKvwAjUyMqNizN0DU92PxiAaM3e1K1eTlMLIx5/+YjuxYdpr/rBHUo3jwtQ1GSvtB6EM6cOZPOnTvTvn177O3tWbx4MSYmJqxcuTLO9k5OTnh7e9O8eXMMDeOf9iY4OJiWLVuybNky0qVLl1zlf1dCw1ChUFCmtiMAZ3ZdSvE6pV+LgZEB5eo4MnhVdzY9X8DYbV5Ub1UBU0sTdSgOqB4Tiov6r/33ARwZitLvS6tBGBkZyeXLl3F1dVUv09HRwdXVlXPnzv3Utnv27ImHh0esbX9PREQEQUFBsV6akNAwrFC/FACnd178ZpZ0SUoqA0N9ytQqwYBlXdn4bD5jt3nh2vL/obhz4SG8qo2ndf5+LBm0nrsXHiIfG5B+N1oNwnfv3qFUKrGxiT13m42NDX5+fkne7saNG7ly5QqTJ09O8HsmT56MpaWl+mVra5vk/X8tIWHo4GJP+syWBL0P5tKhGxrbtyR98SUUBy7/fyhWa1EeE3Mj3r36wPZ5B+jrMpa2hbxYPnwjD689laEo/Ra0fmlU0168eEHfvn1Zv349RkYJH6tx6NChBAYGql8vXrzQaF0/CkNdPV0qNy0HwIE1JzS6b0n62pdQHLSyG5ueL2D0pr5UbloWI1ND/J+9Y8vMvfQsO5JOxQexZtw2nt15pe2SJSnZaDUIra2t0dXVxd/fP9Zyf3//Hz4IE5/Lly8TEBBAyZIl0dPTQ09PjxMnTjB37lz09PRQKpVxvs/Q0BALC4tYL037URjWbO8CwIV9V3n78oPG9y9JcTEwMqBc3VIMXdODTc9jnj4tX68UBkb6vHzgx4bJO+lScgjdSg9jk/ff+D2N+0E2SUqrtBqEBgYGODo64uPjo16mUqnw8fGhbNmySdpmtWrVuHnzJteuXVO/SpUqRcuWLbl27Rq6utqd5uZ7YfjM+DHFKhZEpRLsWebzna1IUvIwMjGkYsPSjNrYl03PFzBoZTecazmgp6/Lk5svWDlqM20L9cfTZSw7Fxzkg98nbZcsST9N6x3qN23aRNu2bVmyZAmlS5dm9uzZbN68mbt372JjY0ObNm3Ili2b+n5fZGQkvr6+ANSqVYuWLVvSsmVLzMzMyJs3b5z7qFy5Mg4ODj/sc/hfP9OhPiHi63Q/NcdMdnc+hUUGM9ben42RSfxPxkpSSgn6EMyZXZc4vvkc10/cUd871NFRULyyPVWalqV8vVKYWZlquVJJipHmRpaZP38+3t7e+Pn54eDgwNy5c3F2dgZiQszOzo7Vq1cD8PTpU3LlyvXNNlxcXDh+/Hic20+NQQjxh2HFAx6oLhrQY2Yb6nWvniz7lqSkev/mE6e2/8OxTee4e/GRerm+gR5ObsWp0qwszrVKYGhsoMUqpd9dmgvC1CglghDiDkMjhRFF11aigKIQK29NR99AL9n2L0k/482TAI5tPsexTed4/p8HakzMjShfrxRVmpfDwcUeXT3t3pKQfj8yCDUgpYIQ4g5DvSg9SmyqyrjhQ3FvVzlZ9y9JP0sIwZNbLzj+bygGvHivXpc+syWVGpWhavNy5HfMJQcDl1KEDEINSMkghLjDUDdSj2onG7DHZ4M8K5TSDJVKhe+5BxzddJaT2y7w+UOwel32fJmp0rwcVZuXI2tum+9sRZJ+jgxCDUjpIIT4w3BC5mkM6d0vRWqQJE2Kiozm8uEbHN14lnN7rhAZ/v9B5Qs556Vai/JUauSMpbW5FquUfkUyCDVAG0EI8V8m3d9qP64FEzZcnCSlRqGfwziz6xJHN57l2rHb6gmGdfV0cXIrRtXm5SnjIR+ykTRDBqEGaCsIIe4wNMSIw+0OfXeme0lKK96/+cSJrefx+esMD68+VS83sTCmYgMnXFtWoEj5AnIeRSnJZBBqgDaDEOIOQxM9Uw60in+me0lKi57deYXPX2c4tvFsrIdsbHJYU6V5Oar9UZ4cBbJqsUIpLZJBqAHaDkJI/Ez3kpSWqVQqbp25h8+GM5zcfoHQoDD1uvwlc+HasgKVm5aV9xOlBJFBqAGpIQghJgzdl9XkeMAx9TIZhtKvLiIskvN7r+Lz12kuHryBShkzX6Kuni5O7sVx/aMCzrUcMDDU13KlUmolg1ADUksQQkwYlhzphK/RTfUyGYbS7+JTQCDHt5zn8PrTse4nmqUzxaWxM9VbVqRg6Tyyf6IUiwxCDUhNQQjg/yYAh+FO+OV8rl4mw1D63Ty784oj609z9K8zvHv9Ub08e77MVGtZAdcW5cmUw1qLFUqphQxCDUhtQQiwfck+up7uwru8/x/KSoah9DtSKlVcO36bI+tOc2b3JSJCIwFQKBQUdylE9dYVqVCvFEamCZ+TVPq1yCDUgNQYhEqlij5VR7E5x2oZhpL0r9DPYZzeeZHD605z4+Qd9XJjMyMqNHCiRuuKsivGb0gGoQakxiAEeHzzOd0rDONK3eMyDCXpK37P3uKz4QyH153izeP/TyCc2S4jri0rUL1VBTLbZdJihVJKkUGoAak1CAFWjtrMXzN34tv8LK9tn6mXyzCUpBhCCHzPPeDQulOc3Hqe0M/h6nXFKhWiRuuKVKjvhLGZvHT6q5JBqAGpOQgjwyPpXno4zx+/4lXvW9yRT5NKUrzCQyM4u+sSh9ad4toxX/WkwsZmRlRsWFp96VQ+dfprkUGoAak5CAFun71Pf9cJKHWiCZ3wgrOBp9XrZBhKUtwCXrznyIbTHF57iteP/NXLs+TKRI02FXFtWZFMthm0WKGkKTIINSC1ByHAksEb2D53P5ZZzQga+YSDzw6q18kwlKT4CSG4ffY+h9ed4sTWfwgLjrl0qlAoKFG1MDVaV6JcXUc5AHgaJoNQA9JCEEaERdKr3Eie331NucYluVjTRw7HJkmJFB4Szqmdlzj058lYT52aWppQpVlZ3NpUIl9JOaFwWiODUAPSQhAC3Lv0GM/KY1EpVfRb0ZH5TJdhKElJ9OZJAIfXneLw2lOxBgDPVcSWGq0rUrVFeawypt7vA+n/ZBBqQFoJQoB1E7ezdsIOTC1NmH12FD3Od5VhKEk/QaVSce24LwfXnOTMrktERcRMKKynr4tzrRK4tXWhVPWi6OrparlSKT4yCDUgLQWhMlqJV9Xx3L34iCLlCzB+b3+abmsiw1CSNCD4UwjHNp/j0JqT3L/yRL08Q5Z0uLaqgFtbF7LlsdFihVJcZBBqQFoKQoDXj/3p4TyCsOBwWo9sSJNBteQUTpKkYU9uveDgmhP4/HWGoPfB6uXFKhbErZ0LFeo7YWRiqMUKpS9kEGpAWgtCgCMbTuPdcQk6Ogq8Dw0nn7OdDENJSgaREVH8s/cqB9ac4MqRm6hUMV+jJhbGVG5aFve2LuR3lA/YaJMMQg1Ii0EIMK3jYnw2nCFj9gws/GcChhb6MgwlKRkFvHjPkfWnOLjmJH5P36qX5ypii3s7F6o2L4dFBjmZcEqTQagBaTUIQz+H0avcKF499KNM7ZKM2exJpDJShqEkJTOVSsWNk3c4sPoEZ3ZdIjI85gEbfQM9ytcrhVs7Fxwq28vBv1OIDEINSKtBCPDw2lM8XcYSFRlN16l/0LBPTSKiI2QYSlIK+fwxhGObznJg9QkeXf//eMA2Oa1xb+dC9VaVyJg9vRYr/PXJINSAtByEAH8vOcJ8zzXo6uky48gICjnnlWEoSVrw4MoTDqw5wbFN5wgJDAVAR0dBKbfi1GznQumaDujp62m5yl+PDEINSOtBKIRgYqv5nNp+gYzZM7Dg3Hgsrc1lGEqSloSHRnB650UOrDrOzdP31MvTZ7akequKuLWrLLthaJAMQg1I60EIEBIURp8Ko3j5wA9H16KM3zkAXV0dGYaSpGUvH7zhwOoTHF53ik8BQerlxSoVomb7ylSoXwoDIznO6c+QQagBv0IQQky/p76VxhARFskfQ+rRdnRjABmGkpQKREdF88++a+xfdYxLh26qp4gyT29GtRblqdneBbvCtlquMm2SQagBv0oQAhz96wxTOywGYOzWfpTxKAnIMJSk1CTg+TsO/nmSg2tO8vbl/8c5LeScl5odquDSqDRGpnIi4YSSQagBv1IQAizo9ye7Fx/GxMKYeafHkj1fFkCGoSSlNkqliitHbrJ/1XHO772KMloJxHTWr9q8HDXbVyavg51Wa0wLZBBqwK8WhFGR0QyuOZnbZ++To1A25pwYjYm5MSDDUJJSqw9+nzi89hT7Vx3nzZMA9fL8JXNRs2MVKjcpo/7/WIpNBqEG/GpBCPD+zSd6lRvJB79PlK9XipF/9VEPASXDUJJSL5VKxfUTd9i34hhnd18iOirmLNHYzIjKTctQs30VOaTbVxLzHZ4qhjhYsGABdnZ2GBkZ4ezszIULF+Jte/v2bRo1aoSdnR0KhYLZs2d/02by5Mk4OTlhbm5OpkyZqF+/Pvfu3ft2Y7+ZDFmsGLWxL/oGepzZdYm/pu5SrzPUM2Rb02145PNQLwuJCqHm+pqcenZKG+VKkvQvHR0dSlQpzPB1vVj/aC6dJ7cge77MhAWHs3/lcfpUHE2vciPZu/woIUFh2i43zdF6EG7atAkvLy9Gjx7NlStXKF68OG5ubgQEBMTZPjQ0lNy5czNlyhQyZ84cZ5sTJ07Qs2dPzp8/z+HDh4mKiqJGjRqEhIQk50dJEwo556Xn7LYArBm7jXN7rqjXyTCUpNTPKqMFjT1rsfz6NLwPDaNKs7LoG+rz8Noz5vZexR+5ezOrxwruXXqMvOCXMFq/NOrs7IyTkxPz588HYi4B2Nra0rt3b4YMGfLd99rZ2eHp6Ymnp+d32719+5ZMmTJx4sQJKlWqlKC6fsVLo/8133M1fy/xwdjMiNknRmNnn129Tl4mlaS0Jej9Zw6vO83+Vcd5ce+1enleh5zU7FCFKs3KYWrxe91LTDOXRiMjI7l8+TKurq7qZTo6Ori6unLu3DmN7ScwMBCA9OnjH9svIiKCoKCgWK9fWTfvVhSrVIiw4HDGNJ5F4LvP6nXyzFCS0haLDOY06luTZVenMP3wcKo2L6c+S5zXZ7X6LPH+5cfaLjVV0moQvnv3DqVSiY1N7GGFbGxs8PPz08g+VCoVnp6elC9fniJFisTbbvLkyVhaWqpftra/didWPX09RqzvTWa7jLx5EsD4FnOIioxWr5dhKElpj0KhoGiFggxe1Z0Nj+bQdeof2BbISnhIBAdWHad3hdH0LDeSfSuOEhYcru1yUw2t3yNMbj179uTWrVts3Ljxu+2GDh1KYGCg+vXixYsUqlB7LK3NGbvNCxNzI26evsd8zzWx7inIMJSktMsigzkN+/z/LLFKs7LoG+jx8OpT5vRaRYtcvZnTe1Ws2TF+V1oNQmtra3R1dfH394+13N/fP94HYRKjV69e7Nmzh2PHjpE9e/bvtjU0NMTCwiLW63dgZ5+doX/2REdHwYFVx9k+90Cs9TIMJSlt+3KWOGR1D9Y/mkuXKX+onzjdt/woPcqMoG+lMRz88yThoRHaLlcrtBqEBgYGODo64uPjo16mUqnw8fGhbNmySd6uEIJevXqxY8cOjh49Sq5cuTRR7i+rtLsDnSe3AGDZ0L84v/dKrPUyDCXp12BpHXMvcfn1aUw9MBSXxs7o6ety9+IjZnZdxh+5+7DQ60+e+r7UdqkpSutPjW7atIm2bduyZMkSSpcuzezZs9m8eTN3797FxsaGNm3akC1bNiZPngzEPGDj6+sLQK1atWjZsiUtW7bEzMyMvHnzAtCjRw82bNjArl27KFCggHpflpaWGBsn7MmpX/2p0a8JIZjbexX7VhzDyNSQGUdGfDOMk3yaVJJ+PZ8CAjn45yn2rzwWa/SawuXyU7tTVSo0cEqTM2GkuZFl5s+fj7e3N35+fjg4ODB37lycnZ0BqFy5MnZ2dqxevRqAp0+fxnmG5+LiwvHjxwHiHV1h1apVtGvXLkE1/W5BCDEj4Y+oP52rR29jnTUdc06OwTpb7CdtZRhK0q9JpVJxxecW+5Yf49zeK6iUKgAsMpjh1qYSNTtWTVPzJaa5IEyNfscgBAj+FEK/KuN4fvc1eR1yMv3wCIzNYo94L8NQkn5t719/5MCaE+xfeTzWTBglqxWhVseqlK1dAj19PS1W+GMyCDXgdw1CAL+nAfSpNIbAt58pXdOBMZs90dXTjdVGhqEk/fqU0UouHLjOvhVHuXjwhvqp8vSZrajZoTLu7SqTyTaDlquMmwxCDfidgxDg7oWHDHSbRGR4FHW6VqPnrLbfXHKWYShJvw+/Z2/Zt+IYB9ec4FNAzIAjOjoKnGuVwKNzNRxdi6Cjk3p65Mkg1IDfPQgBTu+8yIQ/5iGEoNOk5jTp5/FNGxmGkvR7iYqM5syuS+xd5sONU3fVy7PkykStjlWo0aYSVhm1/50pg1ADZBDG2D53P0sGbwBg6J89qdykzDdtZBhK0u/p+d1X7F12lMPrTxMSGAqAvoEeFRuWxqNTVQqXy6+1qaFkEGqADMIYQggWD1jHzoWH0DfQY9KeQRSrWOibdjIMJen3FR4awYkt59mz1If7V56ol+cqYotH56pUa1E+xScQlkGoATII/0+pVDGp1XxO77yImZUJM3xGxpqt4gsZhpIk3b/8mD3LfDi++TwRYZFAzATCVVuUo3bnauQumiNF6pBBqAEyCGOLCItkqMdUbp+7j3W29Mw+PpqM2b+dzUOGoSRJAJ8/hnBk/Wn2LPPh5f036uWFy+andueqVGhYGgND/WTbvwxCDZBB+K2gD8F4VR3Pi3uvsSucnemHR2CezvSbdjIMJUn6QgjB9RO+7Fnqw5ndl9Ud9S0zmuPerjIeHatik9Na4/uVQagBMgjj5v/sHZ6Vx/LB7xOFy+Vnyt7BcQ6/JMNQkqSvvXv1gQOrj7NvxXHev/kIxIwE5lzLgdqdq+FYvajGumDIINQAGYTxe3zzOf1dJxAaFEb5uqUYvqE3urrf/vLKMJQkKS7KaCXn9lxhzzIfrh69rV6eJVcmPDpVxa1tJSwymP/UPmQQaoAMwu+7fvIOw+tMIyoymlodq9BnXvs4H5OWYShJ0ve8fPCGvcuOcmjtSYI//dsFw1Cfyk2cqd3FlQKlciepC4YMQg2QQfhjp3deZGLLeahUgj+G1qftqEZxtpNhKEnSj4SHRnB88zn+XnKEh9f+P1lwvpK5qNOlGi5NymBkYpjg7ckg1AAZhAmzZ5kP8/qsBqDHjNbU61EjznYyDCVJSgghBPcuPmL3kiOc3HaBqIgoAMzSmVKjdSXqdK1G1tw/ngVDBqEGyCBMuPWTd/LnuG0ADFndgyrN4p5UWYahJEmJ8eltEAfXnGTvMh/8n79TLy9Voxh1urri5FY8zucTQAahRsggTDghBAu91rJ78WF09XQZu7UfTm7F42wrw1CSpMRSKlVcOnSDv5cc5tKhm+pZMGxyWlO7czXc2rpgaR374RoZhBoggzBxVCoV0zos5timcxgaGzB5z2AKl8sfZ1sZhpIkJdXrx/7sWerDwT9PEvwxBIh5uMalsTN1u1WnQKncgAxCjZBBmHhRkdGMbTqLiwdvYGppgvehYeQpljPOtjIMJUn6GRFhkRzffI7dS47w8OpT9fL8jrmp282VEjUKkdEmowzCnyGDMGnCQyMYVnsat8/dJ52NJTOOjCBb3sxxtpVhKEnSzxJCcPfCI/5eeoSTW/8hKjIaAON0Bux6s1IG4c+QQZh0wZ9CGOg2icc3nmOTw5oZPiPjHJcUZBhKkqQ5nwICObDmBHuXHeX18zccjdgsg/BnyCD8OR/9A+nvOoFXD/2wLZCV6YeHxztZpwxDSZI0SRmt5NKx65Sp4Zig73DNDOomSV9JZ2PJlL2DyZg9Ay/uvWZ43WkEfwqJs62hniHbmm7DI5+HellIVAg119fk1LNTKVWyJEm/CF09XQo5501wexmEUrLJlMOaKfsGY5XJgofXnjGywQzCQ8LjbCvDUJIkbZFBKCWr7PmyMOnvQZhZmeB7/gFjms4mMjwyzrYyDCVJ0gYZhFKyy1MsJxN3DcTI1JCrR28zsfUCoqOi42wrw1CSpJQmg1BKEQVL52Xc9v4YGOlzfs8VpnVYjPLfCTq/JsNQkqSUJINQSjHFKxVi5F990NPX5cTWf5jVfTkqlQxDSZK0SwahlKJKuzswZE1PdHR1OLz2FAu9/iS+HjwyDCVJSgkyCKUUV7GBEwOXdUGhUPD3Eh+WDvlLhqEkSVojg1DSiqotyuO5sAMA2+fuZ9XoLTIMJUnSChmEkta4t6tMz1ltANjk/TfrJ++Mt60MQ0mSkosMQkmr6narTpcpfwCwdvx2Nk3fE29bGYaSJCUHGYSS1jXqW5P245oAsHLkJrbN2R9vWxmGkiRpmgxCKVVoPrAurUc0AGDpkA3sXHAw3rYyDCVJ0qRUEYQLFizAzs4OIyMjnJ2duXDhQrxtb9++TaNGjbCzs0OhUDB79uyf3qaUOrQc1oAWg+sCsGjAOv5eeiTetjIMJUnSFK0H4aZNm/Dy8mL06NFcuXKF4sWL4+bmRkBAQJztQ0NDyZ07N1OmTCFz5rgnfE3sNqXUQaFQ0HZ0Y5p4xYTb/L5r2LfiaLztZRhKkqQJWp+P0NnZGScnJ+bPnw+ASqXC1taW3r17M2TIkO++187ODk9PTzw9PTW2zS/kfITaI4Rg6ZC/2D435l5hv0UdcW9XOd72cj5DSZK+lpjvcK2eEUZGRnL58mVcXV3Vy3R0dHB1deXcuXMpus2IiAiCgoJivSTtUCgUdJnSgvo93QCY3WMlB/88GW97eWYoSdLP0GoQvnv3DqVSiY2NTazlNjY2+Pn5peg2J0+ejKWlpfpla2sLwKZZ++IdD1NKPgqFgm7eLanbrTpCCGZ1W86htTIMJUnSPK3fI0wthg4dSmBgoPr14sULICYIRzWdy+ePwVqu8PejUCjoMbM1dbq6IoRgZtflHF4Xf6jJMJQkKSm0GoTW1tbo6uri7+8fa7m/v3+8D8Ik1zYNDQ2xsLCI9QLQN9Tnks8terqM5/7Vp0mqSUo6hUJBz1ltqN2lGkIIZnRZJsNQkiSN0moQGhgY4OjoiI+Pj3qZSqXCx8eHsmXLpoptTtnZn6y5MxHw4j393aewb/WJeMfElJJHnGG4/nS87WUYSpKUGFq/NOrl5cWyZctYs2YNd+7coXv37oSEhNC+fXsA2rRpw9ChQ9XtIyMjuXbtGteuXSMyMpJXr15x7do1Hj58mOBtJkauwtmZd3QEZWs5EBUZzdx+a5nRcxXhoRE//+GlBNPR0Ykdhp2XynuGkiRphkgF5s2bJ3LkyCEMDAxE6dKlxfnz59XrXFxcRNu2bdU/P3nyRADfvFxcXBK8zYQIDAwUgAgMDBRCCKFUKsXGmXtFzfSdhJtVR9G9whjx6pFfkj+zlDQqlUrM7bNK1DBqJdyMW4sDa058t314VLjwWO8hGIP6ZTrRVJx8ejKFKpYkSRu+/g7/Hq33I0yt4uuDcv3UXSZ3XMKnt58xMTdm4OIOlK1VQouV/n6EECzot4a/l/igUCjwXNhB9jOUJCmWNNOPMC0qXrEg84+Pwr50HkI/hzG25QJWjN6KMlqp7dJ+GzH3DNtSr/u/XSu6r5Aj0EiSlGQyCJPAOms6pu0ZSIPuMZ32t8w9wJD6M/jgH6jlyn4fCoWC7jNaqzvdz+m1So5NKklSksggTCI9fT26TmrOsFXdMDYz5OaZ+/SqPI5b5x5ou7TfxpdO9w371ARixibdtehwvO1lGEqSFBcZhD+pUv1SzD06khwFs/LBL5BBdbzZvvCQ7GKRQr4Mx9akXy0AFnr9yfZ5B+JtL8NQkqSvySDUANt8mZlzeBiVG5VGpVSxdPhmJrZfTEhQmLZL+y0oFAo6TmxO80ExUzgtGbSeLTP3xttehqEkSf8lg1BDjM2MGLysMz2m/oGevi6nd12mT7UJPPV9pe3SfgsKhYJ2YxrTclh9AJYP38iGqbvibS/DUJKkL2QQapBCoaBul6p47x2EddZ0vHroT9/qE/HZlLSZNKTEUSgUtBnZiLajGwGwZsxW/hy/Ld7L1DIMJUkCGYTJopBTHuafGEXJKvZEhEbi3W0F8/uvIzIiStul/Rb+GFKfjhOaAbB+0k5Wjtwsw1CSpHjJIEwmVtbmjN/iSctBdVAoFOxZeZwBtabi//y9tkv7LTTtX5tu3q0A2DxjD0sGrZdhKElSnGQQJiNdXR1aD63HuE19ME9nyv0rT+lVeRyXfG5pu7TfQoNebvSe2w6AHfMPMt9zTbxzS8owlKTflwzCFOBUvSjzjo8kn0NOPn8MYWSTOaydsgulUk74m9xqd66G1+JOMWflS32Y1X1FvMddhqEk/Z5kEKaQzDmsmbF/CLXauSCEYP3UvxnZdA6B7z9ru7RfnltbFwat6IqOrg6H/jzJtA6LiY6KjrOtDENJ+v3IIExBBkb69JnVmgGLOmJobMCVo7fpWWkcdy891nZpv7yqLcozbG0vdPV0Ob75HJNaLSAqMnWH4ciRI+nSpUuK7U/6eQcOHMDBwSHeS/BS6iSDUAtcm5dl9uFhZMtjw7vXHxlQayq7lx2Vo9Eks4oNnBi1qS/6hvqc2X2JsU1nEREWGWdbbYehn58fc+bMYfjw4bGWL1iwADs7O4yMjHB2dubChQs/3NaWLVsoWLAgRkZGFC1alH379n3T5s6dO9StWxdLS0tMTU1xcnLi+fPnAHz48IHevXtToEABjI2NyZEjB3369CEwMPbYuhcvXqRatWpYWVmRLl063NzcuH79eqI/e0Lq/drx48cpWbIkhoaG5M2bl9WrV8dar1QqGTlyJLly5cLY2Jg8efIwfvz4WP/PKRSKOF/e3t4APH36lI4dO8baxujRo4mM/P/vkLu7O/r6+qxfvz7Rn1vSouSaCyqtS8xcVkkVHBgqxrddKNysOgo3q45icsclIvRzWLLtT4px2eemqJOug6hh1EoMdJv43WOeoPkMVSoh3r4V4smTmP+qVD9d4/jx44Wbm1usZRs3bhQGBgZi5cqV4vbt26Jz587CyspK+Pv7x7udM2fOCF1dXTFt2jTh6+srRowYIfT19cXNmzfVbR4+fCjSp08vBg4cKK5cuSIePnwodu3apd7uzZs3RcOGDcXu3bvFw4cPhY+Pj8iXL59o1KiRehufP38W6dOnF+3atRN3794Vt27dEo0aNRI2NjYiMjIywZ87IfV+7fHjx8LExER4eXkJX19fMW/ePKGrqysOHDigbjNx4kSRIUMGsWfPHvHkyROxZcsWYWZmJubMmaNu8+bNm1ivlStXCoVCIR49eiSEEGL//v2iXbt24uDBg+LRo0di165dIlOmTKJ///6x6pk/f74oVapUgj+zlDwS8x0ugzAeKRGEQsRMNLttwUFRy7qLcLPqKDqXGSme3X2VrPuUhLhx6o6oZ91J1DBqJfq6jBGfPwbH2za+MDxzfa8Qs2cLkSePEPD/V548Mcs/fkxyfYULFxbz58+Ptax06dKiZ8+e6p+VSqXImjWrmDx5crzbadq0qfDw8Ii1zNnZWXTt2lX9c7NmzUSrVq0SVd/mzZuFgYGBiIqKEkIIcfHiRQGI58+fq9vcuHFDAOLBgwcJ3m5C6v3aoEGDROHChWMta9asWaw/JDw8PESHDh1itWnYsKFo2bJlvNutV6+eqFq16nfrnTZtmsiVK1esZc+ePROAePjw4XffKyWvxHyHy0ujWqZQKGjYowZTdw8gfWZLnt99TZ9qEzmx/ceXvKSkK1qhIFP2DcHMyoQ7/zxkcM3JBL6L+8GluC6Tlr8TQjEnD0S/fvD4q3u8jx9Dv36QPTscPJjo2j58+ICvry+lSpVSL4uMjOTy5cu4urqql+no6ODq6sq5c/GPXHTu3LlY7wFwc3NTv0elUrF3717y58+Pm5sbmTJlwtnZmZ07d363xi+Tnerp6QFQoEABMmTIwIoVK4iMjCQsLIwVK1ZQqFAh7OzsEvzZf1RvUt9Trlw5fHx8uH//PgDXr1/n9OnT1KxZM85t+vv7s3fvXjp27PjdegMDA0mfPn2sZTly5MDGxoZTp+TDVWmFDMJUokjZfCw4MYriFQsSHhLB5I5LWTh4Q7wPdEg/r6BTHqYdHIZlRnMeXnvGgBoTef/6Y5xt/xuGNR7C3vVgHAmKL+eB//VlWVgYeHgkOgyfP3+OEIKsWbOql7179w6lUomNjU2stjY2Nvj5+cW7LT8/v+++JyAggODgYKZMmYK7uzuHDh2iQYMGNGzYkBMnTsS5zXfv3jF+/PhYD/KYm5tz/Phx1q1bh7GxMWZmZhw4cID9+/erwzIhflRvYt4TFBREWFjMwPdDhgyhefPmFCxYEH19fUqUKIGnpyctW7aMc5tr1qzB3Nychg0bxrvfhw8fMm/ePLp27frNuqxZs/Ls2bN43yulLjIIU5F0mSyZtL0fzf6dUmj30qMM9JjG25cftFzZrytPsZxMPzyCDFnS8fzOK/pXn4D/s3dxtjXUM2RbjRXs3KKLQoDujzauUsUEYqNG8OlTgmv68uVtZGSU4Pck1ZenG+vVq0e/fv1wcHBgyJAh1K5dm8WLF3/TPigoCA8PD+zt7RkzZkysmjt27Ej58uU5f/48Z86coUiRInh4eKg/jzZt3ryZ9evXs2HDBq5cucKaNWuYPn06a9asibP9ypUradmyZbz/Bq9evcLd3Z0mTZrQuXPnb9YbGxsTGhqq0c8gJR8ZhKmMrp4u7Uc1ZOxfvTGzNOHupcf0dBnH5aO3tV3aLytHgazMPDqCzHYZefM4gP6uE3j54E2cbQ3Xb8QoUvXjEPxCpYLQUPjzzwTXY21tDcDHjx9jLdPV1cXf3z9WW39/fzJnzhzvtjJnzvzd91hbW6Onp4e9vX2sNoUKFVI/NfrF58+fcXd3x9zcnB07dqCvr69et2HDBp4+fcqqVatwcnKiTJkybNiwgSdPnrBrV/yzgCS23sS8x8LCAmNjYwAGDhyoPissWrQorVu3pl+/fkyePPmb7Z06dYp79+7RqVOnOPf3+vVrqlSpQrly5Vi6dGmcbT58+EDGjBm/+1ml1EMGYSrl7F6c+SdGkrd4DoI+BDOi8WzWT/tb9k9KJpntMjHjyAhsC2Tl7cv39HedwOObsYMAIWDePBRJ2cHcud9eQo1Hnjx5sLCwwNfXV73MwMAAR0dHfHx81MtUKhU+Pj6ULVs23m2VLVs21nsADh8+rH6PgYEBTk5O3Lt3L1ab+/fvkzNnTvXPQUFB1KhRAwMDA3bv3v3NmVJoaCg6OjooFP8/Ol9+Tszv7I/qTep7vtT3X7q6unHWtmLFChwdHSlevPg36169ekXlypVxdHRk1apV32wTIDw8nEePHlGiRIl4a5ZSmeR/didtSqmnRn8kIixSzO67Rt3FYlijmeLTuyCt1vQr+xgQKHqUGS5qGLUSDTN3EXf++c8Tj2/fxn46NLGvd+8SXEfDhg2/eSx/48aNwtDQUKxevVr4+vqKLl26CCsrK+Hn56du07p1azFkyBD1z2fOnBF6enpi+vTp4s6dO2L06NHfdEfYvn270NfXF0uXLhUPHjxQdz84deqUECLm/wVnZ2dRtGhR8fDhw1hdDKKjo4UQQty5c0cYGhqK7t27C19fX3Hr1i3RqlUrYWlpKV6/fp3gz52QeocMGSJat26t/vlL94mBAweKO3fuiAULFnzTfaJt27YiW7Zs6u4T27dvF9bW1mLQoEGx9h8YGChMTEzEokWLvqnt5cuXIm/evKJatWri5cuXsY7Dfx07dkyYmZmJkJCQBH9uSfNk9wkNSC1B+MWhDadF3SzdhZtVR9G6yEBx99IjbZf0y/r8MVj0dRkjahi1EnUzdBRXj9+OWfHkyc8F4ZMnCa5h3759Ilu2bEKpVMZaPm/ePJEjRw5hYGAgSpcuLc6fPx9rvYuLi2jbtm2sZZs3bxb58+cXBgYGonDhwmLv3r3f7G/FihUib968wsjISBQvXlzs3LlTve7YsWMCiPP15D+f6dChQ6J8+fLC0tJSpEuXTlStWlWcO3cu1n4AsWrVqu9+9h/V27ZtW+Hi4hJr2bFjx4SDg4MwMDAQuXPn/mYfQUFBom/fviJHjhzCyMhI5M6dWwwfPlxERETEardkyRJhbGwsPn369E1dq1ativc4/FeXLl2+291DShmJ+Q5XCCGHM4lLUFAQlpaW6sfEU4Mnt18yoe0iXj3yR09fly4TmlGnc5VYl6MkzQgLDmdss9lcPXobfUN9RqzvRRnnHPAz933evYMMGRLUVAiBs7Mz/fr1o0WLFknfZyry5MkT8ufPj6+vL/ny5dN2Ocni3bt3FChQgEuXLpErVy5tl/NbS8x3uLxHmIbkKpyduT7DqVDXkegoJQsHb2BKp2WEBYdru7RfjrGZEeO2eVG2dkmiIqIY13wux47chzx5ILF/eCgUMe/7qr/Z99+iYOnSpURH/zrdZ/bt20eXLl1+2RCEmGHYFi5cKEMwjZFnhPFIjWeEXwgh2LHoMCtGb0MZrcQ2f2ZGrOlBzoJZf/xmKVGU0UpmdFmGz19nUCgUzKhrTuHNixL84AuAUChQzJ4NffokX6GSJMUizwh/cV9Go5n29wAyZLHixX0/+rpO5NiWf7Rd2i9HV0+XAcu7UKdrNYQQjNz5jmh9Q4jjacG4KBUQoi84WzlvMlcqSVJSaTQI//lHfhGnpMJlYkajcXApRHhIBFO7LGP+gPVERkRpu7Rfio6ODj1ntaXZgNqEKAwYJcqhEiB+EIZKYp6kaNgUauxpKuczlKRUSqNB2KRJE01uTkoAq4wWTNzWjxYDagOwZ8UxBtSaiv/z91qu7NeiUCjoML4ZHSc047JuVkboVSZKVx+hUHx7z1ChQCgURBrqUqslHM4rJ/eVpNQs0fcImzZtGudyIQT79+8nODhYI4VpW2q+RxifC4du4N1tBZ8/hmBmZcKgJZ0oXaOYtsv65exbcZS5vVdjooqgezEVru+voPjvwNt58kCfPkS0bE6jgx3Y+2CvepWpvin7W+6nYs6KWqhckn4fifkOT3QQpk+fnrVr12JmZhZruRCCZs2afTPUUVqVFoMQwP/5eya2X8T9K08BaN7fg9ZD66GrK28Ha9LxLeeZ1mExymglpd2KMXxeS4yUkWBuHvN06L9niRHRETTa3EiGoSSlsGQNwoYNG+Lp6UmlSpW+WVe9enUOHz6cuGpTqbQahACREVEsHb6ZPSuOAeBQqSBDlnfBKmPa+hyp3YUD15jwxzwiwiIpUr4A47Z5YWpp8k07GYaSlPKSJQg/f/6Mubm5RgpMC74cxOn9V9F7QksMjPR//KZU5tjWf5jj+SfhIRFkyGLF0BVdKVL21+3DpQ23ztxjZMMZhAaFkdchJxN3DcQqk+U37WQYSlLKSpbuExUrVvzunGC/qgNrz+Dp4c2LB2nvs1dp7Mxcn+HkKJCF928+MaiON9vmH0R2HdWcIuULMP3QcKwyWfDw2jP6u8Y9jVNck/vKB2gkKXVIcBCWKFECZ2dn7t69G2v5tWvXqFWr1k8VsWDBAuzs7DAyMsLZ2ZkLF74/O/uWLVsoWLAgRkZGFC1alH379sVaHxwcTK9evciePTvGxsbY29vHObdaQlikN+WJ7yt6u03l4F9n01yI5CiQlTlHhlO5UWlUShXLRm5hfJuFhATKudI0JU/xnMw4MoJMthl4+cAPr6rjeHbn1TftZBhKUiqVmEFMR40aJTJkyCBOnTol7t27J5o0aSJ0dHRE7dq1E7OZWDZu3CgMDAzEypUrxe3bt0Xnzp2FlZWV8Pf3j7P9mTNnhK6urpg2bZrw9fUVI0aM+GZ0+s6dO4s8efKIY8eOiSdPnoglS5YIXV1dsWvXrgTX9WXA1icPnouhTecK98w9hHvmHmJytxUiODA0yZ9XW1Qqldi97KionamrcLPqKNqVGCIe3nim7bJ+KQEv3otODoNEDaNWonG2buLuxbgHRg+PChce6z0EY1C/TCeaipNPT6ZwxZL060rW2ScmTpwojIyMhL6+vnB3dxf//PNPkor8onTp0qJnz57qn5VKpciaNauYPHlynO2bNm0qPDw8Yi1zdnaONdp74cKFxbhx42K1KVmypBg+fHiC6/rvQVQqlWLT3IOiVrZewj1zD9HWaaTwvfQ4wdtKTe5efixaFx0k3Kw6ito2XcX+P+WXryZ9ehskepUfpZ654srRW3G2k2EoSckrMUGY4Euj/v7+9O3blwkTJmBvb4++vj7t2rWjdOnSST4bjYyM5PLly7i6uqqX6ejo4Orqyrlz5+J8z7lz52K1B3Bzc4vVvly5cuzevZtXr14hhODYsWPcv3+fGjVqxFtLREQEQUFBsV7/ralp7xpM3+WFjW0G/F+8Z2D9mWyefyjNTZRboGQu5h8fiVP1okRFRDO7zxpm9FxJeGiEtkv7JVhamzPtwFBKVC1MeEgEI+tP59SOi9+0k5dJJSn1SHAQ5sqVi5MnT7JlyxYuX77Mtm3b6NKlC97e3kne+bt371AqldjY2MRabmNjE++DOX5+fj9sP2/ePOzt7cmePTsGBga4u7uzYMGCOLt8fDF58mQsLS3VL1tb22/aFHLMxYIjQ6lUzxFltIpVE3cxosUCPgQEJuZja51FejPGbuxNuxEN0NFRcHjDWTyrT+LVo1+jD6i2GZsZMW57fyrUdyIqMppJreaxb+Wxb9rJMJSk1CHBQbhy5UquXr2Kh0fM/7Tu7u4cO3aMWbNm0bNnz2QrMCnmzZvH+fPn2b17N5cvX2bGjBn07NmTI0eOxPueoUOHEhgYqH69ePEiznamFsYMWdQez5ktMTQ24OrJu/SoOomLPreT6+MkCx0dHZr392DSDi+sMprz1PcVvauM5/Tuy9ou7ZdgYKjPsHW9qNWxCiqVYE7PlWzy/vubh61kGEqS9iU4CJs3b/7NspIlS3L27FmOHj2apJ1bW1ujq6v7zWg0/v7+ZM6cOc73ZM6c+bvtw8LCGDZsGDNnzqROnToUK1aMXr160axZM6ZPnx5vLYaGhlhYWMR6xUehUODWohxzDwwml302At8HM6rVQpaN2UZUZNqaP86hUiEWnBhN4TL5CP0czoS2i1gyfBPRUWnrc6RGuro69JnXnuaD6gKwctRmlg7e8M3ldBmGkqRdPz3ulp2dHWfPnk3Sew0MDHB0dMTHx0e9TKVS4ePjQ9myZeN8T9myZWO1Bzh8+LC6fVRUFFFRUeh8NTOArq6uxu/n5cifmdl7B1KngwsA25ccpX/dGbx6HKDR/SS3DFmsmPb3ABr3dgNgx8LDDKrtzdtXH7RcWdqnUChoP7YJXae1BGD7vANM77z0mz80ZBhKkhYl+6M7P7Bx40ZhaGgoVq9eLXx9fUWXLl2ElZWV8PPzE0II0bp1azFkyBB1+zNnzgg9PT0xffp0cefOHTF69Ohvuk+4uLiIwoULi2PHjonHjx+LVatWCSMjI7Fw4cIE15WYJ46EEOLs/muiSaGBwj1zD9EgTz9xZPP5BO8rNTmz54pomKOXcLPqKJrm6Ssu+cT91KOUeIfXnxLupm1EDaNWYkR9bxEWEv5NG/k0qSRpRrJ2n0gO8+bNEzly5BAGBgaidOnS4vz5/4eIi4uLaNu2baz2mzdvFvnz5xcGBgaicOHCYu/evbHWv3nzRrRr105kzZpVGBkZiQIFCogZM2YIlUqV4JoSG4RCCBHw6oMY2GCWus/htJ6rRMjnsAS/P7V4/SRA9HQZK9ysOgr3dJ3En5N2iuhopbbL+iWc33dV1EnXQdQwaiX6uowRge8/f9NGhqEk/bzEfIcnetDt30VSB91WKlVsnHOADTP2oVIJsubKyJBFHchXPEcyVqt5keFRLBryF/vXnASgZBV7Bi3tjJX17zPebHK5fe4+oxrOIPhTKDkKZWPS7kFkzJ4+Vhs5Nqkk/ZxknX3id/Gzs0/cvvCIqd1X8fb1R/T0dWk/rB71u1T55t5landk4znmea0lIiwS66zpGLayK/bOebVdVpr31Pclw+tM493rj2TMnoFJfw8kR8FssdrIMJSkpJNBqAGamIbp88cQ5gzYwJl91wAoVcWe/nPbpLmzqqe+r5jQbhEvH/ihq6dLx7GNaNC9OoqvZ2aXEsX/2TuG1Z3Gy/tvME9vxoQd/SlYOvYfGTIMJSlpZBBqgKbmIxRCsO/P0ywds43I8CjSZTRnwLy2lHQppMFqk1/o53Dm9F3DiX9HSSlfpyRe89rFOf+elHCB7z4zov507l9+jKGJASP/6otTjWKx2sgwlKTEk0GoAZqemPfp3ddM6baSZ/feANC4Z3XaDKqNvoHeT287pQgh+Hv5MZYO30R0lJKsuTMxfHU38hRNW/c/U5uw4HDG/zGXy4dvoqunS/+lnanWonysNjIMJSlxZBBqQHLMUB8RFsnSMdvY9+dpAAqUyMngRR3IktNaI9tPKfeuPGFiu8UEvHiPvqEePb1b4t5afhn/jKjIaGZ2XcbRjTF9cjtNak6Tfh6x2sgwlKSEk0GoAckRhF+c2XuN2QPWE/wpFGMzI/p4t6By/VIa3Udy+/wxGO9uK7lw6AYA1f8oR0/vlhiZGGq5srRLpVKxbOhGts/dD0CjvjXpNKl5rAesZBhKUsLIINSA5AxCgICXH5jaYxW+Fx8DUL15GbpPaIKxqZHG95VcVCoVm2cf4M+JO1CpBHb22RixpjvZ88Y9PJ6UMFtm7mX58I0AVGtRHq8lndDT//8ldBmGkvRjMgg1ILmDEEAZrWTDrP1snH0AlUqQLU8mhizqQN6i3858kZpdP3WXKZ2W8jEgCGMzQ/rNbUelBk7aLitNO7z+NDO7LkOlVOFYvSgjN/TB2Oz/fyTJMJSk75NBqAEpEYRf3Dj7gGm9VvP+zSf0DPToMLwe9TtXSVPdE977fWJKx6XcPHsfgLqdq9J5QtM09TBQanPhwDUmtJxHRGgk+UvmYvyO/lhlslSvl2EoSfGTQagBKRmEAEEfgpnttZ5zB2PuuZV2LUK/Wa3SVJ9DZbSSNRN3snl2zD2uAo65GLayGzY5Mmi5srTr7oWHjGw4g6D3wWTLm5lJfw8ks10m9XoZhpIUNxmEGpDSQQgx3RP2rD7JsrHbiYqIJr2NJQPnt8WhQoEU2b+m/HPgOt7dVxD8KRQzKxMGLelE6a/6xkkJ9+L+G4bXnYb/s3ekz2zJ+B0DyOtgp14vw1CSviWDUAO0EYRfPPF9xeRuK3nxwA+FQkHT3jVoNcADPX3dFK3jZ/g/f8/E9ou4f+UpAM361aLNsHro6qWdz5CavH/ziRH1vXl84zkm5kaM2uRJiSqF1etlGEpSbIn5Dk9bA19qwYMbz1N8n7nsszH3wCDc/yiHEIJNcw8ysMEs/J6/S/FaksomRwam7xtM3c5VAdg0ax9DG8zkg3+glitLmzJksWL6oeEUdylE6OdwRtTz5vjmc+r1cj5DSUo6eUYYjy9/TVS360n7/vVo2r0aurop/3fDqb+vMGfABkKCwjAxN6L3tLTX5/DE9gvM7ruGsOAI0tlYMnRFF4qVT1uXe1OLyIgovDsu4eS2fwDoMuUPGvWtqV4vzwwlKYa8NKoBXw6iq2139HQMKVI6DwNm/oHNV9PlpAT/F++Z2mMVdy49AaBGi7J0n9AkTXVef3H/DRPaLuLZ3dfo6ChoM7wBTT3d09xsHKmBSqViycD17Fx4CICGvd3pPKWF+ljKMJQkGYQa8eUg7ljjw59TDxEWEoGpuRG9Jjahct2SKV6PMlrJuun72DT3IEIIsuexYcji9uQpknb6HIaHRDB/4HqO/BUzjJhT9aIMXNwRi/RmWq4s7RFCsHXWPnXHe5fGzgxY3hUDQ31AhqEkySDUgP8exOCPkUzru457154BUK1hKbqPbYSpecqPAnP9zH28e63mvV8gegZ6dBrVgLodXNJMn0MhBAfXnWbhoA1EhkeRKXt6hq3qRsFSubVdWpp09K8zzOi6jOgoJcVdCjF6k6d6RhAZhtLvTAahBnx9EKOjlPw17xAb5x9GpRJktk3PwNmtsHfMleK1Bb4PZpbXOv45dBOA0tWL4DWrNZYZ0s6Z1eObL5jQbhGvHwegp69Lp/FNqNelWpoJ9NTkytFbjGs2h7DgcHIVsWXCzgFYZ4u5hC/DUPpdySDUgPgO4u1Lj/H2XI//yw/o6Cho0bsGLXpXT/FuAUII/l51guXjdhAVEU2GzJYMmJe2+hyGBIYyq+8aTu+6DEDF+qXwnNMWUwtjLVeW9jy89pSRDabzwS+QjNkzMGHXAOzsswMyDKXfkwxCDfjeQQwJCmPBqG0c2xnzBV6opB0DZ7ckS46Un07p8e2XTOm2khcP/dV9DlsP9Egz/fWEEOxa6sPykVuIjlKSLY8Nw1d3I3cauveZWvg9e8vwut68vP8GMysTxmzpR9EKBQEZhtLvRwahBiTkIB7fdYV5I7YQ+jkcYzNDeoxtRLWGpVL88l54aARLRm7lwIaYh1AKlcrF4IXtsbFNO0Ob3bn4iEntl/D21QcMjPTp6d2SGi3Ly0uliRT0/jOjG8/C9/wD9A31GbSiK5UaOQMyDKXfiwxCDUjoQfR/8QFvr3XcvhjTtaFS7RL0mtgY838fWEhJJ3ZdZu7ADYR+DsfUwpg+3i2oVNcxxetIqsD3n5nebQUXj9wCwLVFOXpNl3McJlZEWCRT2i7k7N+XUSgUdJ3Wkga93GLWyTCUfhMyCDUgMQdRqVSxeZEP62YdQKVUkTGrFQNntaKoc54Uqvb/vu5z6PZHObqNb5xmwuSbOQ4LZWP46m7Y5s+i7dLSFKVSxaL+a/l7yREg9iS/Mgyl34EMQg1Iylij9649Y2rfdbx59i7mfl2ParTydE/xMUK/7nNom9eGIYs7kLtw9hSt42dcP32XKR3/P8dh39ltqdyotLbLSlOEEGyevoeVozYDULlJGfov64KBob4MQ+mXJ4NQA5I66HZYSASLx+7g0OaYIbDyF8/BoNmtyJYrY3KVGq+03ufwg38gUzsv4/qpuwDU7liFLhObqjuNSwnz376GxSoWZNQmT8zTmcowlH5pMgg14Gdnnzi19xpzh20hODAUQ2MDuo1ugFsz5xQPoa/7HJZxK4rnjFZpps+hMlrJ2sm72DhzHwD5StgxfFVXMudM+T8s0rKrx24zrtlsQj+Hk9M+GxN2DiSTbQYZhtIvSwahBmhiGqa3bz4xw2s91889BKCcW1H6TmmGRTpTTZb6Q0IIdq+M6XMYHRnT53Dg/HYUL58/Rev4GRcP32Ra1+V8/hiCmaUJ/Re2p2ytEtouK015dOMZI+vP4P2bj2TIko4JuwaQu2gOGYbSL0kGoQZoaj5ClUrF9mXHWTN9H9FRSjLYWNJ/5h+U0EIIxdXnMC3Ncxjw4j2TOizh7qXHADTq5Ub7UQ3Q09fTcmVpR8Dzd4xoMJ1nvq8wMTdi5Ma+lKxaRIah9MuRQagBmp6Y9+GtF0zts46XjwMAaNSlCm3618LAMGW/xL/uc1jQMReDF7YjsxYGA0iKqMhoVo7Zyo5FMU9D2pfOw9CVXcmYLeVnBUmrgj+FMLbZHG6cvIOuni79FnWkequKMgylX4oMQg1Ijhnqw0MjWDZhF/s2xEyomts+G4PmtCJnvswa2X5ifD3PYR/vP3Cpl3b6HJ7++zIze64m9HMYlhnMGLS0M45VC//4jRIQM6/hjM5LOb7lPABtRjXijyH1iFRGyjCUfgkyCDUgOYLwi/OHbzFr8EaCPoRgYKhP5xF18WiV8qOopPU+h6+fBDCx3WIe3XiOQqHgj4G1+WNQHa1MoJwWqVQqVo3awuYZewBwb+dC77ntUCqUMgylNE8GoQZ8OYh7Np3Co2kFjW//Q0AgMwds5PLJmK4BpavZ029qc6yszTW+r+9RRitZP2MfG+ekzXkOI8OjWDTkL/avOQmAQ6WCDF7WmXSZLLVcWdrx95IjLPT6E5VK4Fi9KCPW90bXWEeGoZSmySDUAPUM9bn7Ur1BGXqOroepuWZnRVCpVOxefYoVU/4mOlJJOmtzvKa3oFTlQhrdT0J83eew44j61OtUOc30OfTZdI65XmuJCI0knY0lQ1d0oVj5tDMTh7ad33uFSW0WEBEaSZ7iORm/vT9mmUxkGEpplgxCDfhyEKvn9URXYUCmrFb0n9aMYqU1P4Hskzuvmdp3Lc/u+wFQt11FOgypjaGRgcb39T1BH4KZ7bWecwdvAFDatQj9ZrVK8bPUpHp29zUT2y/m+d3X6OgoaDO8AU093dHRkZdKE+LepceMajSDTwFBMVM57exPlgKZZBhKaVJigjBVfEMsWLAAOzs7jIyMcHZ25sKFC99tv2XLFgoWLIiRkRFFixZl375937S5c+cOdevWxdLSElNTU5ycnHj+/Hmia5u4siNZcmQg4PUnhrReygrvfURGRid6O9+Tq1BW5uzuR912MV8su1efom/dWTy581qj+/kRi/RmjFzVhR6TmqJvqMeFI7fo6TqZq/+O7JLa5SyYlblHhlOtWVlUKsHq8dsZ3XweQR+CtV1amlCgVG7mnBhN9vxZePvyPV7VJnDn9EO2Nd2GRz4PdbuQqBBqrq/JqWentFitJGmO1oNw06ZNeHl5MXr0aK5cuULx4sVxc3MjICAgzvZnz56lRYsWdOzYkatXr1K/fn3q16/PrVu31G0ePXpEhQoVKFiwIMePH+fGjRuMHDkSIyOjRNdXoHgOFuzqi1tjJ4QQbF12gn6N5/PsgV+SP3NcDI0M6D6mIeNWdSGdtTnP7vvRp95Mdiw/jkql0ui+vkehUFCnvQtz9g3CNl9mPvgHMrzZfFZN3EV0lDLF6kgqI1NDBizqgOfcthgY6XPx8E16VhrHnYuPtF1ampDZLhOzjo2icLn8hASGMryuN6c2X5RhKP3StH5p1NnZGScnJ+bPnw/E3DeztbWld+/eDBky5Jv2zZo1IyQkhD179qiXlSlTBgcHBxYvXgxA8+bN0dfXZ+3atUmuK67T6rOHbzNnxDaCPoagb6BHh4E1qdu6nMYvvX1695lZgzdywccXAMdKBfGa3pz0KfwASHhoJEtGbeXA+jMAFCiRk8GLOpAlZ9roc/j45gsmtFvE68cB6Onr0mlcE+p1rZZm7ntqU2R4JN6dlnJyW8yYuW1HN6Jhf3cab2ksL5NKaUKauTQaGRnJ5cuXcXV1VS/T0dHB1dWVc+fOxfmec+fOxWoP4Obmpm6vUqnYu3cv+fPnx83NjUyZMuHs7MzOnTu/W0tERARBQUGxXl8rV70wi/b0w8mlIFGR0SyZ+DcjOq7kvf+3bX+GlbU5Y5Z3oteExhga6XP55F26u3tz7t/xQlOKkYkBfaf/wbBlHTGzNObe1Wf0dJ3Mse0XU7SOpMpd1JZ5x0ZSoZ4j0VFKFg/dyMR2iwkJDNV2aamegZEBQ//sQZN+tQBYM3Ybi/qsY1ODTfLMUPrlaDUI3717h1KpxMbGJtZyGxsb/PzivvTo5+f33fYBAQEEBwczZcoU3N3dOXToEA0aNKBhw4acOHEi3lomT56MpaWl+mVrG3f3gfQZzRm7tB09R9fH0Eifq2ce0L3OLE4duJGYj/5DCoUCj1blmbunP7ntsxH0IYRxXVYyb9hmwkMjNLqvH6lYuyTzDw/F3ik3YcHhTOu5mhl9/yQsJDxF60gKUwtjhq/qRrcpzdHT1+X07sv0qjKehzcSf7/4d6Ojo0OnSS3oNbstOjoKDqw+wcRmC/jTfZ0MQ+mXovV7hJr25X5avXr16NevHw4ODgwZMoTatWurL53GZejQoQQGBqpfL168iLetQqGgdsuyzNvRh7yFs/H5UyiT+qxn+qBNhARrNhxy5LVh1g5PGnWpAsC+DefoXXsmD27GX19ysLHNwLTtnvzhVRMdHQVHNv9D7xpT00SgKBQK6nd1Zcb+wWSyzcCbJ2/pV2MSe1ceRz40/WN1uroyeks/DE0MuHz4JsPcp7GkwjIZhtIvQ6tBaG1tja6uLv7+/rGW+/v7kzlz3MOOZc6c+bvtra2t0dPTw97ePlabQoUKffepUUNDQywsLGK9fsQ2TyZmbupBs25V0NFR4LPzCj3rzubWxSc/fG9iGBjq0WlYXSat706GzJa8fByAV8M5bF7kg1KZcg/S6Orp0npgbaZs7Yt1VitePQ6gX+3p7FhyNEUf6EmqAo65WXBiJM7uxYmKiGZe/3VM67KcMA3/8fIrKlOrBNMPDSedjSVPbr5gUJXJTCs0U4ah9EvQahAaGBjg6OiIj4+PeplKpcLHx4eyZcvG+Z6yZcvGag9w+PBhdXsDAwOcnJy4d+9erDb3798nZ86cGv4EoG+gRzsvd6at70bm7Onxf/mRQa2WsGr6fqI03M2iRPn8LDowkPI1ixEdpWTV1D0Ma7mIt28+aXQ/P1K0bD4WHB5KWffiREcpWTpmG6NbLeLTu88pWkdSmKczY8yGXnQa1wQdXR2Obf2HPtUm8NT3lbZLS/XyO+Zm9onR5CiYlXevPzKshjfDMoyRYSilfULLNm7cKAwNDcXq1auFr6+v6NKli7CyshJ+fn5CCCFat24thgwZom5/5swZoaenJ6ZPny7u3LkjRo8eLfT19cXNmzfVbbZv3y709fXF0qVLxYMHD8S8efOErq6uOHXqVILrCgwMFIAIDAxM8HuCP4eJGYM3Cfd8g4R7vkGiV/054tkDvwS/P6FUKpU4sOm8qF9okHDP6SkaFx0qTu65qvH9JKSOv1efEHXt+gr3zD1Ei6KDxaVjvileR1LdPHtftLQfINysOoq6WbqLQxtOa7ukNCHoQ7AYUGOiqGHUSribthE7lx8QHus9BGNQv0wnmoqTT09qu1TpN5aY73CtB6EQQsybN0/kyJFDGBgYiNKlS4vz58+r17m4uIi2bdvGar9582aRP39+YWBgIAoXLiz27t37zTZXrFgh8ubNK4yMjETx4sXFzp07E1VTUoLwi1MHbogmTmOEe75Bom6RYWLXn2eESqVK9HZ+5OXjANGn7kzhntNTuOf0FNO91ouQz2Ea38+PPLnzSnSrPEG4Z+4h3DP3EMvHbReREVEpXkdSfHwbJIY2nCncrDoKN6uOYkbPlSIsJFzbZaV6kRFRYmqHRaKGUStRw6iVWDxirai1vpYMQynVSMx3uNb7EaZWPzv7xHv/IGYO3cyV0w8AcKyYn36TmpDBRrMzWURHKVk/5yCbFx5BpRJkzpGBQbNbUaiknUb38yMRYZEsG7udvWtiLonlK56DIYvakzVXphStIylUKhUbZ+5j3eRdqFQCO/tsDF/VDdv8WbRdWqomhGDthO2sn7QTgPKNS3Le7TD7H+1Xt5H9DCVtkWONaoAmpmFSqVT8ve4cK733ERkRjYWVCX3GN6K8WxENVwu3LjzCu996Al59REdXhz/61KB5T1d09VJ29vkz+64xu/96gj+FYmxqSK8pzanauHSK1pBU107eYWrnZXwMCMLI1JC+s9tQpbGztstK9Q6vO8Ws7itQRispUC4391v/w8FnB9XrZRhK2iCDUAO+HMT1Sw/RvGO1nxo95tlDf7wHbOSRb8zYodUbOtJtRD1MzDQ7719wYBgLRm7l+O4rANg72jFwdisy22bQ6H5+5O2rj0zrtZpb5x8CULWREz0mN9P47B3J4YN/IFM7L+P6v+Or1mrnQrfJzTEw0tdyZanbteO3Gdd8LiGBodjky8Dr3rfxeX1EvV6GoZTSZBBqwJeDWM1+AKXKFaL/+EZkzJz0Ic6iIqNZN/cwW5adQAhBZtv0DPRuhn0yXMI8uuMSC0ZtI/RzOMZmhvQa35gq9R1TdGgxpVLFxjkH2DBjHyqVIIudNYMXdaCAg+af3NU0pVLFuim72ThjL0II8hbPwfDV3clil1HbpaVqz+68YmT96fg/f4dpRmPeD37AyXfH1etlGEopSQahBnw5iDVLDkEVpYuZuRE9h9Whikfxn9rurYtP8B60KeYSpo6CJl0q06p3dfT0NXsJ0+/Fe7z7rcf339nnXeqUoNeEJphZpuxZ2e0Lj5jWYxUBrz6iq6dD2yF1adT9586wU8oln1tM67KcoA/BmFoY47WgPeVrl9R2WanaR/9ARjWayf3Lj9ExVvBp+CPOB59Vr5dhKKUUGYQa8OUg3r7+iCVTDnHv1ksAXNyL0mt4HcwtTZK87ZDPYSwavxufnTGXMPMVycZA7+bY5tHsgyXKaCWbFvqwfs5BVEoVmbKlY8DMlhR1zqPR/fxIcGAocwdu4NTfVwEoUakgA+a2Ib1N6p9F/u3LD0zuuATfCzGzV9Tv5krHsY3RN9DTcmWpV3hoBFPbLeLs35dR6Sp5P/gBV1WX1OtlGEopQQahBvz3IJqamPLXshNsWHoclVJFhkzmeI1riGO5fD+1j1MHbjB35HaCA8MwNNKn02APPP4oo/FLmHevPmOa5zrePHuHQqGgaY9qtPJ01/hZ6PcIITi44SyLR2whIjwKywxmeM1pTelqmn9wSNOio6JZNW4H2+bHPABSwDEXw1Z2wyZHyt57TUuUShXLh/7F9nkHUOkqed37Fr5G/x80XoahlNxkEGpAXAfx3s2XTBu2lVfP3gFQt0UZOnjWwMg46TPJv/MLZObQLVw9E9PNwsmlIJ6TGpM+o2ZnhQ8NDmfx2B0c3hIz6XH+4jkYNLsV2XKl7H2v5/f9mNJ9JU/+HcmlfucqtB9eDwPD1P8wyvn915jeYyXBn0IxszJhwMIOlKnpoO2yUrXdiw+zqP9aohXRPOl8hUdW/x/xSYahlJxkEGpAfAcxPCySFbMO8vfGmHnasttZM2hyE/IXzpbkfX3pZrFi2j6iIqOxSGdK3wmNKFe98E9/jq+d2nuNuUM3ExwUhqGxAV1H1ce9uebPQr8nMjyKFRN2sHtFzGwguYtkZ+iiDmTPa/ODd2qf//P3TOqwmHuXY+69NurlRvtRDdDTl5dK4/PP/mtMaj2f0PBQ7rW+wIvM/58kWYahlFxkEGrAjw7ipTMPmDV6O+8DPqOrp0PLblVo1qHST/Xbe3rfD+8BG3l89w0ANRqXouuwuhrvZvH2zSdmeK3n+rmY7g3l3IrSZ3JTLNObaXQ/P/LP4ZvM9FxH0IdgDI0N6D6xCTWal031E+dGRUazYvRWdi6O6R5g75yXoSu6kDFbei1Xlno9vPaUUQ1n8jbgHbebn+WN7TP1OhmGUnKQQagBCTmInwNDmTt+N6cO3QKgYDFbBk5sRLafmME9MjKatXMOsW35SXU3i0HTm1OohGa7HahUKrYvO86a6fuIjlKSPpMF/Wf8QcmKBTS6nx/54B+Id+81XDsVc8msUj1Hek9tjtlPPIyUUk7vvszMXqsJ/RyGZQYzBi7pRKk0cM9TW96+/MCoRjN4ePsJNxqdIiD3S/U6GYaSpskg1ICEHkQhBEf3Xmfh5D2EfA7H0EifLgNqUquJ00+d2dy48JgZgzYR8PoTOjoKmnWvyh89qmn8AZeHt14yre9aXjwKAKBhp8q0HeiBgWHKXepTKlVsW3iENVP/jnm6NXt6Bi9sj71T7hSrIalePwlgYrvFPLrxHIVCQTOvWrQeUjfFR/RJK0I/hzG5zQLOH77C9QYneZv3/7N+yDCUNEkGoQYkdoi1gDefmDFiG9f/nYvQqWJ++o1tQHrrpD/0EvI5jAVjd3Fsd0y3g/xFszNwenOya/gBl/CwSJZN2MW+9TH9vXIXysqgua3JmS/uOSGTy53LT5jWYxV+z9+jo6tDq/61aNrHDV3d1N3nMDI8iiXDNrJ3Vcw9z6Ll8zNkeRcyZLbSbmGplDJayeKB69m57ADXGpzknQxDKRnIINSApIw1qlKp2LX+PCvnHIp56MXKhD6j6lHB9eceejmx9zrzR+/49wEXfToPqU2t5s4av5d2/vAtZg3eSNCHEAwM9ek4rA512lRI0Xt2IUFhzB+ykeM7YvqdFS2bj4Hz25Ixa7oUqyGpjm+7wBzPNYQFR2CV0ZzBy7pQwqWQtstKtXYuOMjCIX9ytf4JGYaSxskg1IAvB/HyP3coWbpgot779KE/3sO28ujfh15c65ag+xAPTM2MklzPW79PzBy8hWv/PuBSunJMN4t0P3HGGZcPAUHMGvgXl07EjLXpVKUQ/aa1IJ2Gu3N8jxCCI1v+YeHQTYSHRmKezhTPGS0pV/PnRvVJCS8f+jGh7SKe+r5CoVDQcnAdWgyonerParXl3J4rTOwwj3/cDsswlDRKBqEGfDmIro5DaNvFjeYdKqKXiPs+UVHRrFt4lC2rTqFSCTJltaL/+IYU/4n7XiqVil1/nmHV9ANERUZjmd4Uz4mNKVPNPsnbjIsQgt1rTrFi0t8x+8lghpd3c0pX1Xx3ju959TiAqd1X8eDGcwBqt6tEp1ENMPyJfpspISIskoWDN3Bw7WkASlQuxOClnbHKqNkpuH4VD689ZXhjb46W3SXDUNIYGYQa8OUgVnUYgp6uIfntszJoXENs7RL3ROitK0+ZMWIbb15+RKFQ0LBNedr2qvZTHcif3HuD94BNPLkXc8bp3rQ0XYbWxthUs90snt57w9S+a3n675lt7dbl6Tis7k8NIJBYUZHRrJmym22LfACwK5iVIYvbk7NA1hSrIamObDzLvP7riAiNJH1mS4Ys70Kx8in7VG5a8fblB0Y0ncb2POtkGEoaIYNQA74cxL+3nmXV/BMEfw7H0FCPjr2rU6epU6IGjQ4NiWDJtH0c3HEZALu8Ngya0oTc+ZP+MEpkZDR/zjrI9pWnEEKQNWcGBng3o5CGZ3eIDI9itfdedvzb+d02rw2DZrcib5HsGt3Pj1w+focZfdbw8e1nDIz06Ty6IR5tK6b6PofP7r5mYrtFPL/3Bh0dBW2G1adpv5ppYtDxlBYWHM74dnNYZjxPhqH002QQasB/D2JEmGDG2F1cvfAYgBKlc+M1qh6ZEjkt07ljd5g9ZieBH0PQ19elTU9XGrYt/1P3j66ff8SMwZt4+yYQHV0dmnerQotk6GZx+eRdZvTfwMe3n9HT16XtQA8adnJJ0S/0j2+DmNl3LZeO+QJQ1r04njP+wCKFBwJIrPCQCOb1X4fPpnMAlKpWhIFLOmKZIeXuu6YVSqWKBYNWMz5glAxD6afIINSArw+iSqViz9ZLLJ9ziIiIaEzNDOk12IMq7kUTdVby6X0ws8bs5J9/H0YpUjInAyY0InP2pI9KEhwUxsJx/+9mUaCYLQOnNydbIi/j/kjgh2DmDNnMuUMxgycXL5ePATP/wDoFuwmoVCp2LTvOyok7iY5SkiGLFYPmt6PYTw6AntyEEBxaf4aFgzYQERaJddZ0DF3RhcJlUnfd2rJ14V56nO/K2zwyDKWkkUGoAfEdxJfP3jFt1A7u3Y75H7Siqz19htTGwirhI6EIITi44zJLpu0jLDQSYxMDug/xoHq9kj91qe/4nmssGLNT3c2iy9A61GxWWqOXD4UQHNh4niXjdhIRFom5lQl9pzSjvHsxje0jIR7eeM6UHqt49SgAhUJBc093WnrVTPUd2Z/cfsnE9ot5+cAPHV0d2o9sQKPebvJSaRxO77tA4y2N8bd7oV4mw1BKKBmEGvC9g6iMVrJx9WnWLzuBUqkifQYz+o2sS+kK+RO1D7+XH/Aevo3bV2PGXSxXzZ4+I+thld40yXW/ffOJGYM3c/18zMDGpasUwnNiI413s3j5OIBpfdfy4GbMMFk1mjrTdVR9TH6ii0hihYWEs3jkVg79FXPJsVCpXAxe2B4b29Q9PVLo53Dmea3l2NaYgdtL1yjGgEUdUv0lXm24c+0Brgtq8Dr7U/UyGYZSQsgg1ICEHMT7vq/wHr2D509ipmWq1cCRLv1qYGyS8Kc3lUoVW1efYu2Co0RHK0mXwQzPMfVxdklc38X/UqlU7Fx9mlUzDhAdpUy2bhZRkdGsn32QzYt8EEKQJac1g2a3oqCGx0X9kRO7LjN34AZCP4djamFMH+8WVKrrmKI1JJYQgn2rT7J46F9ERUSTKXt6hq7sSiGnlJ00OS14/dKfclMq8izjA/UyGYbSj8gg1ICEHsSI8ChWLfBhx1/nAciSLR0DxzagsEOORO3v0d03TBu6hWf/jvlZs1EpugysmahQ/dqTe2+YNmAjT+/5AcnXzeLG+YdM91rP29ef0NHVoWVfN5r1qJailyn9nr9jWs/V3LkUM8RdjRZl6T6hCUY/cfxSwqObz5nYbjGvHwegq6dLhzGNaNijeqp/GjalBQYFUXp8We6b+aqXyTCUvkcGoQZ8OYhvA95jnfHHD7Jcu/SE6aN38NY/CB0dBU3alqd1l8roJ2KeusiIKFbPO8KOtWdjzrBs0zNwYmPsExmqX29zzayD7Fh1Wt3NYuD05hQsnvRtxiU4MIz5I7Zw4u+YB3bsS+Vi0KxW2Nim3NRE0VFKNszcx8Y5BxFCkD2PDYMXtSdvUdsUqyEpQoLCmN13Dad2xgwrV7aWA14L2mNulfRL5L+isMgwykwszw2dq+plMgyl+Mgg1IAvB7FNk1mMHN+cvAV+3OcvJDichd77ObL3OgC589swaFxDciVywtnrFx4zfcQ23voFoqOjoGnHSrTsViVRofrNNs8/YvqgTbzzi+lm8UePqjTvXlWjZ21CCI7uuMSCUdsIC47AxNyInuMaUbVBKY3tIyFunL3PtF5reP/mE3oGenQYXo/6nauk6rMsIQR/Lz/GshGbiYqMxiaHNcNWdaVAyVzaLi1ViYiOoNLMKlwIO6deZqpnyv5WMgyl2GQQasCXg1jZaTiGhia06lCRFq3Lo6v346f7Th/1Ze6kPQR+Co3pL9itCo1alUtUf8GQz+EsnLwHnz3XAMhTMAuDJjchZ55MSf1IfA4MZeHYXRz/d5vJ1c3C78V7vD3X4Xv5KQCV65ak5/jGmFkaa3Q/3xP0IZjZ/Tdw7kDMHyWlqtrTf04brDT80JCmPbj2lEntl/Dm6Vv09HXpPKEpdTtXTdUhntIioiOovtiNU+9PqJeZ6JpwoPUBGYaSmgxCDfhyEId6reHiuZixLgvaZ2XQyHrY5vzxU4kf3wcze8Juzp+6D0CREjkYOKYBmbMlbhaFk4duMW/8Lj4HhqFvoEdHzxrU/aPMTz1uf+zvqywYszNm/sRk6mahjFayccERNsw9FDPHYLZ0DJjZkqLOKfcwiBCCvWtOsWzsdiLDo0iX0Zz+c9viWDl1zwgRHBjKrN6rOfP3FQAq1HWk39y2mKaByYpTSkR0BB6rauPz+oh6mbGOMQfbHJRhKAEyCDXiy0H89OkTl84/Z96MA4QER2BoqEenHtWo26gUOjrfDw4hBAd3XWXxzAPq/oLdvNxxq1ciUaHzPiCIWaN3cOlMzFNzDs656T++IRl/oiP7190snKsWwnNiY6wyaPYR/jtXnuLdbz1vnr1DoVDQtEc1Wnm6a3zkm+95evc1U7uv4und1wA07FaNdkProm+QcpMPJ5YQgl1LfVg+cgvRUUqy2GVk2Kqu5HOw03ZpqUZEdAT11tfj4NOD6mVGGHGo3SEZhpIMQk34+iAG+AcyY9Iervw78W6JUnYMGF6HTDY/HmbtzcsPTB+7k1tXY84sy1TMj+eIuqRLROgIIdi7+QLLZhwgIjwKM3Mjeg6rQxWPpE9NpFKp2LHqNKtnxnSzsMpghuekxjhX0ewZU2hwOIvH7uDwlgsA5Ctmy+A5rcmm4QmGvyciLJLl43awZ/XJf2vIweBF7cmWO+mXmlPCvcuPmdRhKf7P36FvoEeXic2o3bGyvFT6r4joCBpubMi+R/vUywyEIQfbHKBy7sraK0zSOhmEGhDXQVSpBH/vuMyy+UeIiIjGxNSQnv1qUL1msR9+MSmVKrZvOMeahUeJilJiaWVCn2G1qVA1cX37Xj59x/ThW7n7b0d2F/ei9BpeB/OfuGz25O6/3Szux3SzqNmsNF2G1sHIRLOzTJzad425Q7cQHBiKobEBXUfVx715mRT9Uj934DqzvNbz+WMIRiYG9JjcDNcmmp/kWJM+fwphZs9VnNt3DYCK9UvhOactphYpd881NYuIjqDR5kbsfbBXvUxfacCe5nuoYV9di5VJ2iSDUAO+dxBfPn/P1PG7ufvvMGvlXQrQd2At0iVgRJgnD/2ZNmo7j+/7A+DqUZweA2smatJeZbSSjctPsH7JcVRKFRkymeM1riGOPzHeZmREFGtmHmT7qlMAZLOzZoB3M413s3j75hMzvNZz/d8JhsvWKErfKU2xTMFRVd6+/sj03mu4cTbmUnPlBqXoNaV5qg4WIQQ7Fh1mxehtKKOVZM2diWGrupG3mGb/fdKquMJQL1qfLR5bqV+mrhYrk7RFBqEG/OggKqNVbFp/lrUrThIdrcIqnSn9BteiXKUfzzcXFRXN2qXH2bLmDCqVIKONBQPG1MchkZP23rv1Eu9hW3n5NGZkmzrNnenYz+2n5gu8du4hMwZvTtZuFiqViu3LjrNm+j6io5Skz2SB1/QWOFZK+mg6iaVUqtgy/xBrvfeiUqqwsc3A4IXtKFQq6RMnp4S7lx4zqf1iAl5+QN9Qj26TmlOrvUuqPqNNKXGFoW6UHivKrKZt7ZZarEzSBhmEGvDlID5//gZb2/j7ED6878fUcbt4+vgtAG4exenuWQPTBIzecvv6c7xH7eDNq48ANPyjDO16VMPQKOGT9oaHRbJy9iF2/zuyTXY7awZOakyBn5gv8OtuFgUdcjDQuxlZc2q2m8Wj26+Y2nctLx7GnB3X71CJ9oNqY5CIz/+z7lx6zNQeq/F/8R4dXR1aD/SgSa8aPzU1VnL7/DGY6d1X8s/BGwC4NCxN39ltMDFPuXFeU6s4wzBSj2m5ZuPVqacWK5NSmgxCDfhyEOvWnsrgoQ0o953LjpGR0axZdoItG84hBGSysWDgiLo4ONr9cD9hoREsnXWIff9O2psjlzWDxjUkX6HEzcB++ewDZo7azvuAzzHDnHWtTPNOLj91JvffbhZGJgZ0GVob96aa7WYRHhbJikm72bP2DAC5CmZl0JxW2BXIorF9/EhIUBjzh2zk+I6YkV2Kl8/PgHltsc5ilWI1JJZKpWLb/EOsGrcdlVJFtjw2DF/VjdypfBSdlBBfGA7QHcGkMSPlTB+/icQEYar4jViwYAF2dnYYGRnh7OzMhQsXvtt+y5YtFCxYECMjI4oWLcq+ffvibdutWzcUCgWzZ89OUm2fPoUwcvhWvKftJSQkIs42BgZ6dO5ZjRkL2pAlqxUB/kEM7L2OhbMPERER9d3tG5sY0nd4HSbMaUl6azOeP3lH33bLWbfsOMpoZYLrdCyXj8XbeuPiXhSVUsXahUfp33aZ+rJpUlSpU4KFf3tSzDk34aGRzB25nXE9/uTT++Akb/NrRsYG9BzfmLErO2GZwYwnd1/Tp85Mdq06iUql0th+vsfUwphBC9rhNbsVRiYGXD9znx7VJqk746dGOjo6NOnjzvS9g8iYLT2vHvnjWWMS+9ec5Hf/29ZQz5BtTbfhkc9DvUxpEM105QQ6d+pHeGjc/x9Lvy+tB+GmTZvw8vJi9OjRXLlyheLFi+Pm5kZAQECc7c+ePUuLFi3o2LEjV69epX79+tSvX59bt25903bHjh2cP3+erFkTd3b1Xw0alkKhgAP7b9C54wquXXsWb9uiDjlY8mcXPOqXjNn/5gt0b7ece3de/3A/TuXzsWRjDyq62qNUqli75Dj9Oq7k5bOEB5m5pQlDpjZl8OQmmJobcffmS3o2XcCeTf8k+csxU9Z0TF7TmY6Da6Gnr8t5H1+6157FP8fuJGl78SldtTCLDgyiVOVCREVGs3jsDka1W8aHgCCN7ic+CoWC6s3KMu/QEPIWteXzxxDGtV/K/CEbiQiLTJEaksLeOS8LTo6idI1iRIZHMcfzT6Z1WU5YcLi2S9Oq+MJwTZaF/NGkK+9ff9RidVJqo/VLo87Ozjg5OTF//nwg5pKPra0tvXv3ZsiQId+0b9asGSEhIezZs0e9rEyZMjg4OLB48WL1slevXuHs7MzBgwfx8PDA09MTT0/PBNf139Pqp08DmTZlD2/efAKgUWMnOnZywdAw/ntZF849ZMbkPXx4F4yOroKWbSvwR7sK6P3gUqUQgmMHb7Jg6j6CP4djaKhHxz7VqdPEKVGXdN76fWLGyO1c++cxAKXK56Pf2AZkyPT9SwTf8/jOa7wHblJ3s6jV3JnOQ2prtJuFEIK9686wbMJuIiOisEhvSr+pzSlTvYjG9vEjUZHRrJmym22LfADIWSALgxe1J1ehbClWQ2J9fak0e77MDFvZldxFfu9LpfFdJq3sU5dFi2aQr4Sd9oqTklWauTQaGRnJ5cuXcXV1VS/T0dHB1dWVc+fOxfmec+fOxWoP4ObmFqu9SqWidevWDBw4kMKFCyeoloiICIKCgmK9vihWzJalyzvg4eEAwLatF+naeSV3v3OmV7psXpat7YJLNXtUSsHalafo02U1z568/W4dCoWCqu7FWLyxOw6lcxEREc1C7/0M67WOt/6BCfosABkzWzFpSTu6DaqFgaEel848oFujeZw69O2Zc0LlLpSVOdt60aBdBQD2bfyHXvXncO/6ix+8M+EUCgW1W1dg7h4vchfKStCHEMZ2XsG84VsIT6EzM30DPTqNasiEv3qRLqM5z+69wbOWN3tWp97Ljl8ulXrvGYh11nS8fOCHZ/VJ7P8z9dacEuI7MzxebTft2vTkzK5LWqxOSi20GoTv3r1DqVRiYxN7dgYbGxv8/PzifI+fn98P20+dOhU9PT369OmT4FomT56MpaWl+mVrG/svaRMTQ7wG1GTSlKZkyGDGixcf6N3rT1atPEFUVNz38iwsTRgxviHDxzXA3NyIB3ff0L39crZt/AeV6vtfThltLJk8vzU9BtbE0FCPqxce0635Io4euJHgLzYdHR3qtyrHvI09yFsoK58Dw5g4YCPew7YS8jlpl84MDPXpMqwOk1Z3JoONBa+evsOr+ULWzzucqHuaP5IzX2Zm7exHoy5VANi3/iy9PWbw4KbmQvdHHCsXYuHR4ZSqak9keBQLhm5ifPulBH3Q3D1STStcJh8LTo6iVLUiMZdK+/6Jd7cVv/Wl0vjC8J+6h+g3YDibvP/+rf9YkFLBPUJNu3z5MnPmzGH16tWJerpx6NChBAYGql8vXsT9hevsnIflKztRtao9KpVg3dqz9Oq5hqffOdOr7FqYpeu64lQ2D1GRShbPPczA3mv/x95ZR1WVb3H8c+kuERAFsbsLRVFEQuzu7k6wu8Hu7u5ABcTE7u5OBJSuW+f9cS7oKEjM1XHe+F3rrbdG4N7DDzj77L2/Qahq1JoeNDQ0aNSqCku29KZwcVviYpOYNXYv00fvJiYqIdPfW94CVszb3JPW3WuioSHhuP9NejdbxK3LzzP9Gt+iXLWCLPMfgrNXaZQKJZsXBTOszTLeZ2GnmRF0dLXoProh0zf3Joe1KW+fhzGkyXx2Lg1Gofg1RBozS2MmbepDz0nN0NLR4kLgbfq6TufWuce/5P2zA9McxkzeOZDO45qioanBiZ0XGVB7Ki/uvf2nL+0fQ3rF8HrLE8xZuRi/7iuQZkBs+4P/X/yjhdDS0hJNTU0+fvz4l3//+PEjNjZpa/dsbGx++PkhISGEhYVhb2+PlpYWWlpavHr1imHDhuHg4JDutejq6mJiYvKX/wHcvvt9QTQx0WfMuEaMn9AYYxM9nj75SO9e69ix/WK6N2jLnMZMm92awT5e6Olrc/vGa3p1WEmA/80Mn0btHCyZv7YbHXu7oKEp4cyxe/RqvZQrKhPuzEBbW4vOA92Yvb4HuewsCA+NZkT3tazwO5LtG4CxqQGj5rfDZ05rDI31eHTrDf0aLeDo3yDnpIVy1YuwNMAbp7qlUciVrPM9zKi2Swn/RYQHDQ0NmvSszTz/4eQuYMWn0GhGtVjI+hkHkaczDfinoaGhQeuhXvge+uuoNHDz2f9s9/OjYrj7zD5GeM4gMgvrhz/4/8FvQZapXLkyixYtAsT9nr29Pf3790+XLJOQkMChQ4dS/61atWqULl2a5cuX8+nTJz58+PCXr/Hw8KBDhw506dKFIkUydn6BL4vW6rUn0rpFdbp3cU6THPPpUxxzZh/hkirFoWTJPPiMrEfu3Okns79/+xnfqQe5d1t8QnesXoghI+phkQkT7sf33+E7fh9vVLIIr6YV6DnYHX2DjAX8KUhMSGbl7KMc3S3uR/IWsMJnRgsKFM2+di/sfSRzRuzktoqc4+hanEFTm6k1zUIQBIJ2XWb5xL0kJUgxMtFnwPQWONcvp7b3yAiJ8UmsGL+HwK3nAShaIR8+SzqTS81mA+pEVEQss3uv4epxcT9cp3VV+s9uj14mTB/+H5GeA035HbUpIinG5L3DyPcfJxn9P+BfJajfsWMHnTp1YsWKFVSuXJn58+ezc+dOHj58iLW1NR07diR37tzMmDEDEOUTNWvWZObMmdSrV4/t27czffp0rl+/TsmSaTMLHRwcss0arV57IlpaetjlsWCUdz2KFf1eiiEIAgFHb7N0STAJCVL09LTp3ac29RukH7ekUCjZve0iG1aJO0YTU30G+3hRIxPJD8lJMtYuCWb/tksA5MpjjvekJpTIoi/opTOPmDd+L1Gf49HS0qR939q06FIj264qSqWSvetC2DA38KemWbx/GY7voM08uiWmebg2rUifSc0w/IXOKiGHrrNg+FbiYxLRN9JjwKzWuDSt9MveP6tQKpXsnB/Axmn7UCoF7IvkYvTa3jgU/32ZsD8T6XmTltvugm2UPSPX98GxXvl/8Ar/4O/iX1UIARYvXoyfnx+hoaGULVuWhQsXUqVKFQBq1aqFg4MD69evT/38Xbt2MXbsWF6+fEmhQoXw9fXFy8sr3df/O4Uw+PgNlq06x6fPcWhoSGjX2pEObZ3QTiNPLzQ0Cj/fI9y8IWoNK1XKxzDveuTMmX4q+otnYcyafIBnT8Rxr6tHSfoP9cQoEzf1m1eeM3vifsI/xqChIaFFJyc69KyFtnbmc/aiPsezcMoBzh+/D0DxcvZ4T2tOrjzpd7QZ4VfILOQyBVsXBbFj8TGUSgEbOwu857eneIV8anuPjPDxzSd8+63n/hWxC67Tsgp9prXEIAsG6r8ad849ZmaPlXz6EIWuvg79/Nri3q76P31Z/wjSS60ou60WFu+s6T69Nc0G1f3j4/ovxb+uEP6O+PoQQZsFS45x4pQoIi9YwIpR3vXJn0aenlIpsG/vVVavOoVUKsfISI/+A92oU6dEun9QMpmCzWvPsH3TedGE28qYYaMbUKFyxgbQcbGJLPU7yvEjou9k/sLWjJjcFIeC1hl85RcIgsCxgzdYPvMwCfHJ6Onr0MvHC8+mFbJ9E0grzcLbrzVFyqh35HTv6nP8Bm/h49vPaGhIaNXfjXYD3dVqEv4jKOQKts0PYNu8oyiVArb5cjJiaRcKl837S94/O4gKj8G39xqun7gH/LdHpWkVQx1BlzJbamL+1gqPTs4MWNjltw5x/oO08acQqgFpHeKpMw+ZtyiImJhEtLU16dKhOi2bV05zlPjqVQSzZvrz6KG4r6zhXITBQzwxM0s/N/D+3bf4TjnIuzefAWjYrCLd+9ZGPxNpEmdP3GfBtEPERIvX1qlPbZq2q5qlMWfou0jmjN3DnWsvAXCsVZTBExr/rT3fd2kW/Vxp3dtFrYUqPiaRZRP3cnyvuPMsUjYvPvPbYevw64J/7158im+/9YS/j0RLW5NOIxvQtLfrb+trqVQq2TnvKBun7//Pj0rTKoZ66FF6qzNmr60oVb0I47YNwtQy/cnOH/x++FMI1YD0DvHz5zjmLAjk/EUxT69EMVtGDK+HXRqjRIVCybatF9i44SwKhRIzcwOGDfOimlP6Bt6JiVJWLz3BwT3iTd02jzkjxjeieCbSJD5HxDJ/2iEuhYjU/hJl7fGZ1ASb3OaZ/r4VCiX7Np1nw6JjYoCwuSGDJzam6t/Y88VGJ7Bk4n5OHxa9O4uUscNndmu1p1mcOnidxWN2ER+bhL6hLn0mNqVO80q/bLQVG5XAguFbOHf4JgDlnIsyfGFHLKxNf8n7Zwd3zj1mRvcVfA6N/k+PStMqhvoa+lTY44rBIzNsHHIyee8w8v7G7kJ/8Ff8KYRqQMohbtl1hjbNqv/lZioIAoHH7rJ4WTDxCVJ0dbXo1a0WjRqUR0Pj+5vu48eh+M7054VKa+jhWYq+/epg9INd0rXLz5k97RAR4bHiyK99NTp0c05zN/k1BEEg6OANls0JIDFBir6BDr2HeuLRKH3iTlp4/jgU31G7eKnaXXo0qUAvHy8M/sb47Os0C119bXqOakDdVupNswh7F4nfkC3cvSyyeKt7lWHg9BYYm2UcmqwOCIJA4NbzLB+3m+REKSYWRgyd354qbqV+yftnB9+NSttUo79fu//cqDStYmigZYBzYH2UV3QwMNFn9MZ+VPIo8w9e5R9kFn8KoRqQcojVPCbjWKkIIwbVxeqb0cjHsBhmzTnCDZURd/myefEZ5oV1Gn6eUqmcdWvPsGvnpdSoJh+fepQr75DuNcTGJLJkbiDHVbZo+QtZM3J8I/IVsMrw+kPfReI7YR/3borMSscahRk8tiHmWRhzSqVyNiwKZu/GcwiCgLWtGd7Tm1PyB9ecEcI/RDHbZ0eqzKJK7WIMntZcrTILhULJnhUn2Dj3KAq5khw2pgyb05ZyToXV9h4Z4c2TUGb2Wcvze+8AaNStFl3HNv6lWYtZgVKpZMfcI2yacUAclRa1ZfTaXjj8xzqgtIqhoZYh9a+3JvJIMhoaEnrMbEuT/h5/SDS/Of4UQjUg5RBrNZiOUtDCyFCXgT1dcXcp/pc/AKVS4MCh66xYc4rkZDmGBjr06+2Kp3upNP9Q7tx5w6yZ/nx4HwVAkyYV6N7TBb0f3CBDTj5gvu+RL/u/HjVp3sYxw/2fQqFk75YLbFh2QhxzmhkwcHR9qtcunqWzuHP1BbPH7uHj+ygkEgnNO1enQz9XdLJJIFAqlexbd5b1cwN+qsziyZ03+A7azNvnYpJJ0x616DS8Hjq6v4b4IE2SsXbaAQ6sPglA/hK5GbG0K/aF0w96/qdx+9wjZnZfKY5KDXTo59cO97ZO//Rl/VKkWQy1DekS2pfHq8Sdv2eXWvSf3+kPieY3xp9CqAakHOLd+y9YtPosDx6LfwDVHQsyrK87FuZ/HbW9ffeZmX6Huacy4q7mWJBhgzywsPi+00lMlLJi+QkOHbwBQB47C0aOrE+xHxAVPn+KY97Mw1xUucmUKJ0Hn7ENsc2EzOH5k1B8x+/jhWrMWadeGfp618UwCzT/+Lgkls86zLED4jXnL2KDz/QWOBTKPDv1W7x4+AHf4dtTZRZ1W1Wm56gGapVZJCUks2rqAY5sFU3Z8xezxWdhB/IW+nXF6PLxu8wdtInoT3Ho6mnTc3Jz6rZ3+m07iqjwGHx7reb6SVFS818claZXDEfqTuDc+DsolcIfEs1vjj+FUA34+hANDI3Ytucy67edQy5XYmqiz5A+brhU/6tLjUKhZOfuy6zbdFYUyZvoM2SAO7Wci6b5HlcuP2e23xEiIsQ9YJu2VenQsXq6e0BBEAg8fItl84NE4b6+Nr0G1KFeo/IZ3lRlMjmbVp5i14ZzokTD2oThExtTtlLGEo2vcf7EfRZM2k90ZALa2pp0HuhGkw7Vss2O/FZmYZs3B96zW1M0i+YAGeHisbvMG7GdmM/x6Ohq031MQ+p3+HXF6PPHaOYM2sT106IEx8mrLINmt8XY/NfsLrOK70alRXIxel3v/9SoNL1iOKfgQgL6XyAhNgkbh5xM2jMUh+IZk9n+4NfiTyFUA9I6xKcvwpgx7whPVaQXV+diDO7tiomx/l++9vmLcGb4+fP0mTiSq12rGIP6uWFi8tfPA4iNTWTRwmMcDxaJCgUKWDFydAPy509/Dxj6IQq/qQe5fUPc/1WqWoChI+tj+QPhfgru3XqN34R9fHgr+nQ2aeNIl36u6GZhd/U5Ipb5E/dz+cwjAEpXysewKU2xts08O/VbfCez6Fub1n1qq1Vm8TksmrnDt3PtzEMAKrkUY4hvG8wzcW7qgFKpZO+KE2xQeZRa2prhs7gzpaqmzyL+p/GXUam+Dv1m/7dGpekVw7VOGzjS5zwfXoRhYKzHqI39qOxZ9p+70D/4Dn8KoRqQcoiHg6/h5frFakkmU7BxxwW27LqIQimQw8IQnwGeOFb8a2clkynYtPUcW7ZfRKkUyGFhxPAhnjhWLpDm+505/ZB5cwOIiUlES0uDTp1r0Kp1+ntApVJg387LrFl+AplUgbGxHv2HeVLbPeMA28SEZFbOD+LI3muAaOrtM7kJhbOgIRMEgYA9V1nhd5SkRCkGRrr0HVkf1wZls91lxcUksmTifk753wR+jsxCqVRyaMNZ1sw4hEwqxzSHEUN8W1PFNXO5lerAk1uvmdV3He+eh4mM4EGetBta95eZAGQV/3VWaXrFcFf9PZwYfpXbIQ+RSCR/nGh+M/wphGpAyiFWaTAFL9dyDO7mislXO7UHjz8wfe4RXr8Txe/1PUrTr6sLBt/stx48fM8Mv8O8eSt+Xj3P0vTpWRvDNG4inz/HM2/OUc6fF/eAxUvkZsTI+uT5wR7w1YtwZk0+wJNH4p6tpmtxBg73xMQ0feF+Ci6ffcy8KQf5/CkOTU0N2nZ3pnWXGmhl4Yb8/vUnZo/dw30VO7V6nRIMGNcQ078x8jvlf5PFE/YRH5uEnoEOPUfVx7OlemUWLx99wHfQZl48FHe69do70X1MQ/QyYV6gDiTGJ7FszC6O7bgIQPFK+fFZ0hlruxy/5P2zCqVSyfa5R9j8Fat0zLre5E3De/f/EekVw0Ot/Lk19xlH154CwL2jMwMWdkYnDYP+P/i1+FMI1YCUQ6zaaCoamrrkMDdkZB8Pqlb40vklJ8tYtSmE3QevIQhgY2XCiEF1KV/6r/ut5GQZq9edYc/+q+LnWZsyYrgXZUt/vwcTBIHAwDssXRxMfHwyenra9OzlQsMf7AHlcgVb159ly4azKBUCFjmMGDa6PpWrFsz4+4xKYOFMf0KCRWJEkRK58ZnchDxZ6MIUCiW71oWwaelxFHIl5pZGDJnUhMo1Mpf0kRa+TbP4GTILabKcDX6H2bv6FAB2BazwWdCBgpkwL1AXTu2/yiKfbSTEJmFgrMcA3zbUalzxl71/VvFfHpWmVwyPtD3C58OJrPDZglIpUKJaYcZvH4RZzh/ffP/g5+JPIVQDUg7xwrWHLFx3jtfvxY6uQZ1S9O9UC8OvYo9u3HnNzPkBhIaJWWbNGpSnZ0fn7yQRN2+/ZtbsI4R+jEYigWZNKtK9c9rxTh8/RuM36zA3VAbeFSo6MNy7HlZpaBRT8Oj+e2ZNOcCbV58AqNeoHL0GuKGfAQtTEAROBtxhie8R4mKT0NXVovsgd+o3r5glEsyT++/xG72L18/FHapXi0r0GOaZpYior5FWmsWgac1wzKL8IyNcD3nEnGFb+RwWI9qjDfeiaY9av8weLfR1BL791vPg6gsA3Fo50mdaC/QNf0/z7u9Ypf8hr9L0iuHRdkfRf2zKtPaLSYhJxDqvJZN2D/0T5/QP4k8hVAO+PkRdXX1WbD3LTn9xp2aT04TR/TwpX+pLR5eQIGXZulMcDBBtxOxymzNqsBclvhkdJSQks3TFCQ4HiCbZP4p3UioFDuy/xsoVJ5FK5Rga6jJgoBt13Eqm2x0mJ8tYu/wke3dcFq/V1gyfsQ0pVTZjFmb4x2jmTj7AdVUXVr5KfoaOb0TOLFiEJSfJWL/wGPs2i3l9tvY58J7WnGJ/w2z7xcMP+Hpv5+Wjn5dmERMZz4KROzgfeAeA0o4FGT63LTn/BgEoK1DIFWyZe5QdCwJQKgVy57di5LIuFExjavA74L/MKv1RMcybmJ/xzeby4XkY+kZ6+KztTbUGFf7Bq/3v4k8hVANSDjE84hOWOcQd3Y17b5i+OIAPqs6vuVc5erWrgb7elxvypWsv8F0YQIQqtqlNs8p0blMNnW+ikS5deYbf3IDUeKe2rRzp2C7teKc3rz8xa6Y/D1QaRafqhRky1BPzH+zhbl57id/Ug4R9jEEigeZtHOnco1aGYnKlUsmhXVdYs/AYyclyjIz16OfjhYtn2gYB6eHGxWfMGbeHCFVEVKvuNWnXywWtDCzi0sOvkFkIgkDgjkssn7SP5MR/Jvj3zoUn+PXf8MW8e1RDmvaq/duad383Kv2PeJX+qBiWMS7HtPaLuXnyHhKJhM6TmtNqeIM/JJpfjD+FUA1IOcQWA5cxZXATiuQTheMJiVKWbDzNgSCx88tjY8aYAXUpVfTLk3BsXBILVgRzTBXblN/BktFDvCiU3/qb90jMdLyTQqFk+7aLbNwQglyuxMzMgCHD6lK9evq2YfHxySybH0SgyuzaIX9ORoxvRMFMOJu8eRmB7/i9PL4vFt8adYozcGR9TH6QnvEt4mISWTLDn5Oq9y9U3Bbv6c2x/4E0JCN8K7No06c2bfqqV2bx7kU4foO/BP/WaVaJ3hOb/rLg39jIeBYM38q5IzeB39+8+78a6/SjYljVtirLvTdzaMVxAFxaVWXo8u7o6P0aMtYf/CmEakHKIVZsNhVdPQM6N65C58ZVUhmVl268YObSQMJVHV3rhhXp1soJ3a8sl85ceMycJceIik5AU1ODzm2q0bZ5FbS+kUScDnnI3IWZi3d6+vQjM2cc4oVqD+fmXpL+A9x+aOB9/swj5s06QlRkPFpaGrTv6kzr9tXQ1MrAok2uYNu6ELauPoNCocQihxFDxjWk8g+Kb1o4E3iHhVMOEheTiI6uFl0HudOwrWO2u5zY6ASWTjrwRWZR2o7hfq3Ik8YDRHYhlynYujCQHUuCxeBf+xx4z2v3y4J/BUHg6OZzrBy/m+QkGaY5jBi6oAOVXTOWx/wT+DbWya6wDWPW9fm/j3X6UTGskbcGh1YEs3TYJpQKJUUq5mfCjsHk+EXj9v86/hRCNSDlEIfO2M75W28BKJLPivF96pLfTmRUxsYnMX/NCQJPi6SBfHY5GDvQiyJfdX6RUfHMWXqMkAuiJKJoIRtGDfHC4Rua/LfxTsWL2TIynXgnqVTOhvUh7NxxSXSJyWnMcJ96VKyY/k06KjKe+b5HOHdaFMEXLZGbEeMaksc+Y7r+4/vv8Juwj9cvIgDwalKBnkPcs0SC+RQWw9zx+7imkoaUrZKfYVOakdMm+13O1zKLn5VmcffKc/wGbybsXaT4wNPfjba/MPj31aMPzOq7jhf3Vebd3V3oOqbRb2vefefcY2b2WMmnD1Ho6uvQ17ct7u1+Xzs5dSCjYnjz1D2mtF1EXGQ8OXKZM2n3EAqV/zUPVP9l/CmEakDKIUZFRXH53gdmrztOTFwS2lqa9GhRjbb1K6Kp6mjOXHqC34pjRKo6v07NHenY9Ev3KAgCwacfMH95MHHxyejoaNG9Q3WaN6jwl65PEAQCg++yeOmXeKee3WrROJ14p3t33zJrpj/v3okuMQ0bladnL5d0g3wFQSA44A5L5gUSH5csskP7udKwacU0X/9rJCfJWLfkOPu2ibq3XLnN8Z7UhBKZIOF8/f6Hd15m1ZwAkpNkGBrr0X90A1zqZT/WJvxDFHNG7OTWRTF2qbJLMQZPa4a5Gv0f0wz+XdBe7XmK6UGaJGPt1P0cWHMK+P3Nu6MiYvHrvZprx8VRae2WjgyY0x79LHjb/tuQUTF8//wjE5rN5fXD9+joaTNsZU9qtXD8B6/4/x9/CqEakHKIHz6GY2NlSURkHDNXH+PcdZFRWbJQLsb18cQ+l9ixRUYnMGdVMKcuiKG4hfNbM3ZAXfLbf7lZhkXE4rcogMvXXwJQqnhuRg/xwtbG7C/v/TEsBt85R7iuincqVzYvI9KJd0pMlLJyxUkOHrgOQO7c5owYVZ8SJdLXwoV9jGbOdH+uXxHp+uUr5WPY6PpYZWIHdfPqC+ZM3E9YaDQaGhJadHSiQ69aaGtn3oX/zYtw/Mbs5vFdscup6VmK/mMaYJwJE4C0oFQq2b/+LOvmiGkWphaGDJ7eXO0yi2+Df3tPaIJbC/V2oD/C5eC7zB387zDvViqV7JwfII5KFUryFLJhzLre5PvB7+W/HRkVw/joBGZ2XsplFbO87ajGdBjb5LclQv3b8acQqgEph1i//yIm92tMuaJ5EASBI2fuMW/DSeITpehoa9G3TQ1aeJRDQ0OCIAgcP/eIuauCU7vH7m2caN2gYmrnJwgC/kG3WbLmJImJMvT1tOnTtRYNPct8H+/kf4MVq09mKt7p6tUX+M06nGrg3aq1Ix07VU83KkmpFDi07xqrFgeLr2+kS78hHtTJBDs0Pi6JZbOPcsxf/IPOX9ga70lNyJ+FRAe5TMH21afZuvIUSoWSHFbGDJnUlIpO2ffdfPFIlWahkll4tqhEz9EN0FcjaePb4F+nuqUZNKPlLwv+/fwxmtkDN3JD5Zf6u5t3373whJndVxLxPhIdPW36zGqDZ4cav2XxVgcyKoYKhZK1Y3ewe/4RAJwaVcRnTS/0flPN6L8ZfwqhGpByiBVaTUNLV482HhXo1bwaejrahEbEMGNlEJfvqAJ5i9sxppcHtlZiRxURGYfvsiDOX1N1j0VsGdO/LnZfLck/hEYxc0EAN+++AaByeQe8B3h+F/77bbxT1SoFGDbIkxxpOKzExiayZFEwx46JQb758udk5KgGFCyYflTSm1ef8J16kIeqANnqtYoyyLsuZpm4sZ47+YAF0w4RHSUmUXTs7UKz9tUyzEn8Go/uvMV39G7evRL3jw3bONJ1sHu2rc6kUjkb5wWyd20IgiCQyz4H3n6tKFYub7ZeLy0oFEp2Lz/Bpnmq4F9rU4bN/XXBv0qlkr3Lj7Nh5qFU827vRZ0pXe33NO+O/hSLX681XD0u/l66tKjCgDkdMPhFLNxfjYyKIUDQpjMs7L8OmVRO/tL2TNw5BOtfNGr/r+BPIVQDUg5x7KK9BF0WR4h5c5kzvqcnJQvkQhAE9gXfZvGW0yQmyzDQ02ZA+1o0qi12VIIgcOTkXRasPUlCohRdHS36dHCmqWe51H2cUimw59A1Vm4MQSqVY2Soy4CetfFwKfGXJ2aFQsnOPVdYtzFEjHcy1mPwAHdcaqYdZHs25BHz5gYQFZWAlpYGHTvVoPUPgnwVciXbN59n0xqRHWpmbsiQEV5Uc87YIi3yUxzzpx7kYog4Ei5Rxg7vSU3IlYmcxBQkJUpZMy+QQ9svAZDHwRKfGS0oXCL7jMPbl54x22cH4R/EEW7rPrVp09c12zrGtPBd8G/3WnTy/nXBv1+bd0skEloP8qDdMK/f0rxbqVSye2Eg66fuQ6lQkrugNWPW9iZ/qf9P55XMFMN7Fx4zufUCosJiMM1pzPhtgyjplH1bwj/4K/4UQjXg60O8/TyCGWuPEREVj4ZEQof6leje2BEdbS3efoxi2vIAbj4UO6oqpR0Y3dMdqxxiZxcaFs2MpYFcuyNq0sqXtGNUP09yWX3Zx71684kZ849+Cf+tUpBh/b4P/33+IpyZsw/z5KkYsPujeKfIyHjmzQ3g3FmxQBUrbsuIkfWx+4Gp89NHocyacoCXKmmGR70y9BnsnqZB+NcQBIGggzdYPjeAhHgp+gY69BrqgWcmchK/xtVzT5g3YS+fwmLR1NKgbc9atO5eM9s39riYRJZM2s+pQzeBnyOzSEpIZtW0gxzZIjrp5C9mi8+C9uQtnEtt7/EjJMYnsWzsLo5tF0lMxSrmw2dJZ2zsf8/u4utRqbauFr1ntMGrs/P/5ag0M8Uw7HUEk1rN5+nNV2hpazJgYWc8O9f6h674/wt/CqEakHKIGw6dpUO9asTEJzF380kCzou7mQJ5cjChZ12KOFihVArsCLjO8u1nkcrkGBnoMrijC17OxVO7w32BN1m68TRJyXIM9HUY2NmFeq5frNLkCiXb915m3VZV+K+xPkP7uVHrmydEuVzBpq3n2bztAkqlgIWFIcMH16Vqle/jnQRB4FjQXRYvOkZ8vIol2qMWjZukzxKVSuVsWHWaXVsvIAhgbWPK8DENKFvBIcMzC30fyeyJ+7lzXRwZV6lRmMFjGmCRBQZnbHQCC6ccJCRIHKMVKZkH7+nNyeOQ/Rv7Kf+bLJm4n7iYRHT1tOk+sh712jiq9eZ7Mfgu83y+BP92G92ABh2r/7Ib/OkD11jovfWLefesNtRq8nuad0d/imV2n7VcOSba2dVsUomB8ztimMYD3b8dmSmGSfFJzO6xkpB9VwBo3M+DnjPb/Jad/b8JfwqhGpByiGU7TKNa2SKM6+SGTQ4TTl55wqz1wUTGJqKpqUHXhlXo3KAyWlqavHz3ianLA7n3VOzsnCsWwKebGzlURIq3HyKZtjiAO6rusWr5fIzo44GlxZd937MXYUz/Kvy3Ts1iDOr1ffjvw0cfmOHnz+s3ohm4l2dp+qYT7xQWFoOf72GuX3sJQLlyefH2qYf1DzR8d26+xnfqQULfRwHQpGVluvVxSdMg/GsoFEr2br3AhqUnxDGuqT4DRzeghmvmGZyCIHDqyG2WTD8kmoDradN9qCf1/4ZG8FuZRaWaRRk8vTkWagzl/RwWwzzvbVw9LT4sVaxVjCG+rbH4gVG6OvHxzSd8+63n/hVxN+3WypHeU1tg8BvKFpRKJXsWB7Fu8l5xVFrAmtHrelGg1O/prfp3kJliqFQq2TrzAJum7AWgQp1SjNrY77clQf0b8KcQqgEph1i560wUEm0M9XQY2roWDZ1KEBWbyMz1wZy6Korfi+S1YkIvTwrksUSuULLl0BVW7z6PXKHE1EiP4V3rUKeq2NkpFEp2HLrK6u3nkMoUGBnqMrS7K241iqXe5GUyBRu2n2fL7kuqUN+0w3+Tk2WsXn+GPfvEeCdraxNGDPWiXNnviSFKpcDBA9dZueIEyclyDAx06DfADQ+P9FmiiQlSViw6xuEDNwCws8/BiPGNKFI84wy6l08/Mmv8Xp4/Fse4rnVL09enLkbGmX/qDw+NZs64PdxUmYBXqFaIoZObkCObhUWpVHJg4znWzQ5AJpVjYm7I4GnNqFpHfaG8giBwcEMIa6aLwb8mFoYMmdUaR7df4wijkCvYOu8o2+eL5t22+XIyYmkXCqfxO/E74P6lp8zotpLwd5/FUen01nh1qfl/NyrNTDEEOLv/Cr7dlpOcICV3QRsm7h6CfZH/RuajuvGnEKoBKYd4+/EL5u2+wO1nYpfnVCofYzu5YWlqSNDFR8zeeJyY+GRRaN+kKu28KqKlqcHTV+FMXnaUJ69UnV3VIgzrXBszE1Er9+JNBNMWHeXhM7FQ1KxSiOG96mBu+uUJ8P6j98yYdzQ1/Leee2n6dftrBBSI8U6+c47wIVQ0A2/auAI9utT8LgYK4O3bz/jO9OeeiiVazakQQ4bWxcIi/SfPyxeeMmeGP58j4tDQlNC2U3Xada6eYYCvTCZn88rT7NxwFqVSwNLahOETGlOucv4fft3XUCqVHNx2ibXzA5EmyzE21WfAuEY4u2e/sLx8HIrvsO28eCT+TH+GzOLV4w/MGvgl+NerbVV6jG2EXjYjqbKKuxef4ttvPeHvI9HU0qDTyIY06+P6W2rWYj7HMafvWi4Fiokszk0qMmh+p/+7UWlmi+GzW6+Y2GIeYW8+YWCiz+iN/ajkkX3Tif8q/hRCNSDlEI+cv4l7lVJsDrzG8gPnkckVmBjo4t22Np5VivIpOp7pa45x7pbILC1RwIYJPT3Jm8sCmVzB2r0X2XTgEgqlgIWpASO7u1GjohiYK1co2bz3Eut2XRDZmib6ePd2p2aVLzT4zIb/JiQks2zVSfyPqGKg8lgw0rsexdOId1IolOzccYn1686I+0hTfQYP8cS5ZtEfnEcii/yOcuq4aCdXqGguRoxvRN5M7O7u336D34R9vFeNcRu3qULXfnXQzYJN2OvnYfiO2s1TlYzEpV4Z+o2qj1E2b5ZSqZxN84PYs+ZMqsxiuG9Lipd3yNbrpfke3wT/5s6fkxELOlDoFzElY6MSWDB8C+cO3wR+b/NuQRDYuySItZP2opAryJUvJ6PX9aZQmd+zk80uMlsMo8KimdxmIffOP0ZDQ0K3aa1pNqju/12n/DPxpxCqASmHWLrrdJrUrMCw5s6ERcYxaV0g91+KXZxLuYKMbO+KhYkBh8/eZ+5mUWivq61JnxY1aOUuSiUePAtlyrIAXrwTA3O9nEswuGMtjFUi2sfPPzJ10VGevxa1dO7OxRjczRWTr3Y7t+6+Ycb8o3z4+OPw38tXnuM37ygRn1QxUC0d6diuWprC+mfPwpg5/RDPVfR/1zolGDDQDeMfjC9PBd9jod9RYmOT0NbRpGsvF5q2qpKhRVtSopRVC4Lw3y3alNk5WOI9qQlFsiCRkMnkbFl+kp1rzogeqzamDJvSlLJpEIUyi9uXnzPHZwdh76NEI4LeLrTtV0etMosb5x4zZ9hWPoVGo6WtSYchnjTrVTtLesvsQhAEAreeZ/m43SQnSjGxMGLo/PZUcSv10987O3hw5Rkzuq4g7O1ntHW06DGlJQ16uPxfFYDMFkOZVM7iQesJWH8aALf21Rm4qMufBItM4k8hVANSDrFMt+loaOthbW7E+PbuVCqch/VHr7DK/6LYxRnpM7K9K3UqFubjp1imrgni8l2V0L5oHsb18MA2pynJUjmrdp1j62Fxn2dlYcToXh5UKe0AgFQmZ83282w7eEXcC5obMrKvB1XLfxkjJiRIWbr2JIdUI6Q8tuaMHvJ9+G9sbBILlhzjuCpBPH++nIz2qU+BNOKPZDIFGzecZbuKhZrD0ghv73pU+sH4MiI8lrkz/LmiIp6ULmeP99iG2OQyy/Bcr5x/wtzJB76MWbs606abc4Zj1q9x/9ZrZo/Zw/vX4oNFkw7V6DLQDZ0MiDzpIT42kaWTDnDioLgLLVQyDz6zW5Mnv/pkFjGR8SwcvZNzR8WfXcnKBfCe1w6r3L8mieDNk1Bm9l3H87uigXyDrjXpPq7Jb2neHRsZx5x+67l49CYA1RtWYMjCThhm04Lvd0Rmi6EgCBxYGsQKny0olQLFKhdk3PZB5MjE39p/HX8KoRqQcoghNx7gt/cCb8KjAGhavRRDmjnzLjyaiWsDePxGFYdUqQgj2tXG1FCPfSfvsHCbKLTX19VmQGtnmtYujUQi4dajd0xdHsDbUPH1GruWpn+7mhiqnFTuPn7PtEVHefNeNNKu71qKAZ3/uhf8Lvy3aWU6t/0+/Pd0yCPmLQokOjoRLS0NOrWvTpuWVdLsRB7cf8fMmf68VY0vGzQsR6/etX9o4H3kwA2WLzpGUqIMfQMd+gxyw7N+2Qyf3mOiE1g88zCnj4mmzIWL2+I9uQn2DpkvPEkJUlbNCeDwrssA2Bewwmd6cwoWyz6xIOTobRaO30tctEpmMaIe9dqqT2YhCALBu6+wbOJeEuOTMTTWo9/U5rg0+jUJ5tJkGeunH2TfyhMAOBSzZeSyLuT9DckYgiCwf3kwaybsRi5TYJPXktHrelO4nMM/fWlqQ2aLIcC143eY3n4xcVEJWNqaM2HnYApXyPyu/b+IP4VQDUg5RN8dgfSq58xy/wtsP3UTANscJkzo4E7ZAras9r/I+iOXUSgFcpgaMqZDHZzLFuBdWBRTVgVy45FISqlcMi9jurphY2lCYpKMpdvOsDtIfL1cOU0Y29uT8sXF3VFSsowVW0LYdVg00rbJacLo/p6UL/llLyiG/x7n2ClV15dO+O/nyHjmLgjknCoG6kfxTklJMlavPMm+fdfE79PWjBEjG1CyVPpGye/ffsZ36kHu3RY7DcfqhRgyoh4WaVjAfYuTAXdY7HuYuJgkdHS16DagDg1bVs4SoeNyyCPmTdhHZEQcmloatO9dm5Zda2RbgxUeGsW8kbu4cV5kBFd0LsKQGS3UKrN4/yoCv8GbeXhDnBy4NK5Av8nNfhk55OqJe8wZtImoiFh09LTpMbEp9Tr+nv6fj649Z3rXlXx8HYGWtibdp7SgUU/X3/Jas4OsFMN3T0OZ2GJeaoLFkGXdqd262q++5H8N/hRCNSDlEEv0mk4xhzxMae9BXEIyEzcG8f5TDACtapVlYOPqPH//iYlrA3jxQcXurFqc4W1qYainy85jN1i6M4RkmQJDfR2GtnehXnVRaH/t3mumLg8kNEL1enXL07t1dfR0xHHVjXtvmL74KB/CxI839ypH7/bO6H01AsxM+K8gCAQF32PR0mOp8U49utakScMKae72rl97iZ/vYcLCYpBIoEXLKnTp6pyugbdCoWTP9kusX3kqVTs4yNsL59ppW8B9jU/hMcyZdIBrqjFr2cr5GDa+MVZZyCmMjoxn4eQDnFMReYqVscN7WnNsM5G1mBaUSiUHN51nrd9RUQJhZsDAqc1w+htM1W+hkCvYtugY2xYFoVQKWOU2x3t+e0pW+jVP+ZHhMcwdtImrqvF5VY/SDJrTDtNMPMD8asRFJzBvwHrOHRIfDKvVK8eQxZ1/mdH5z0ZWimF8TKKYYKEaG7ccVp/Ok1r8kn3zvw1/CqEakHKITkPmEisHLQ0NenhUoY1zGRbtP8fes6Irhl1OMyZ1cqeYvTXL959jc5DI7rQyN2JcJ3eqlnTg1YfPTF4ZyF2VBKN62fyM6loHSzMj4hOSWbj5NAdPiq9nn8uccX08KVlIHFclJEpZvOEUB4+p9oK5zBk7oC4lvxpnZTb8NywsBt+5R7im6kTKlbHHZ5gXNmmwCOPikli6JJjAAPG6HBwsGTGqAYV/kIH34lkYMycf4PkTlXbQvST9hnpgnEGnIwgCh3ZdYfWCoNQkjL7eXrh6lc70k78gCBw/dJOlM/1JiEtGT1+Hnt51qdusYra7h1dPQvEdvoPnKqaqe/OK9BrdEAMj9Ukg7l97gd/gzYS++SySdfrVoe1AD7WSddKDUqnkwKpTrJ22H7lMQQ4bU7wXd6bMLzIPzwoEQeDAyuOsGb8bmVSOtb0lo9f2pMj/yXgwK8VQoVCyfsIuds7xB6By3bKMXNfn/2qHqg786wrhkiVL8PPzIzQ0lDJlyrBo0SIqV66c7ufv2rWLcePG8fLlSwoVKsSsWbPw8vICQCaTMXbsWI4cOcLz588xNTWlTp06zJw5E1vbzO9CUg7x2sNnbDl7j+Bb4qisaB4rprb3ICIqnsmbg/gYGYdEAu1dK9CnQTUevQ5j0roAXn+MAqCJcykGt6yJno4WW49eY8UelQTDUJfhHWrjXrUoEomECzdfMH1lEBGRcWhIJLRrUJHuzb/s/S7deMHMpYGEp+wFG1aiW+svH/8u/Fdbk+4datC84ffhvwf8b7Bi1SmSkmWisL63K3XTiXc6f+4Jc+YcISpS7Dg7dHSibbv0EyZkMgWb1pxhx+bzonYwpzHDxzSgQia0g+9ef8Jvwj4e3BHHrE4uxRg0pj6mWXjy//g+kjnj9nJblbVY2bkIgyc2zpLN21++H6mcTQuOsXv1aQRBwCaPBcP9WlEiE5ZzmUV8bBLLJ+4leI9osVW4jD0+89uTW42eqD/C0ztvmNVnHW+ffUQikdC8Xx06+jT4JcU4q3hy8yXTu6zgw8twNLU06TqxGU37uv1fjEqzUgwBTmw/z7w+q5EmybArYsuk3UPIXfD3DGv+J/CvKoQ7duygY8eOLF++nCpVqjB//nx27drFo0ePsLL6nuV4/vx5nJ2dmTFjBvXr12fr1q3MmjWL69evU7JkSaKjo2nevDk9evSgTJkyREZGMmjQIBQKBVevXs30daU6ywyfzbjWXmgIMHP3KaITktDW1KRPXUeaVivFwn0hHDgvkj4cbCyY3MmDgrlysHjvWbYfF1mItpYmjO/sTsWi9jx7G8GklQE8eilKFlwqFcKnkyjBiIlLYt6GEwScfQBAfjtLxvfxpEg+ce8XE5fEwnUnCEjZC9pbMmZAXYp8tRcM/xSL78JALl8XC0HpEnkYOciT3Ln+yk589y6SmXMOc1clrP9RvFNUVALz5wUQcuYRAEWK5mLkqAbY/2D0eP/uW/ymHuTtaxX5pmkFevRzTZd8kwKFXMGODefYvPIUCoUS8xyGDB7bEMcamXflVyqV7Nt8gfULjyGTyjE1N2DAuEZU/xsOMneuPGe2z07C3kWioSGhZS8X2vZzRTudcXF2cMb/BovG7CYuOgFdfR16jW+MZ2v1eqKmh6SEZFZO2MPRzecAKFIuLz5Lu2CbBQLTr0J8dALzB28kZL/49+xYtyzDlnTG2Pz3G+tmFVktho+vPWdSy/lEvI/EyNyQ0Zv6UcH195TG/Gr8qwphlSpVqFSpEosXLwbEm5idnR0DBgxg5MiR331+q1atiI+Px9/fP/XfHB0dKVu2LMuXL0/zPa5cuULlypV59eoV9vaZ8zJMOcRi/aajqatH7ZIF6OdRlSX+5zl1V5UzmNeGqe09eBMWxdTNx4iISUBDIqGTe0V61XPk9rMPTF4fyHvVDrBl7bIMaFYDbU0NNvhfYc0BUYJhbqzPiM51cKkkCulPX3nCrNXBRMaIXViXJo50alQ5VWJw5tITfJcHERUj+p12au5Ix6ZVUj+e2fDftOKdBvV3p3at73d7giBwPPgeixYeIy4uCR0dLbp1r0nTZpXS1RAmJclYvfQ4B1TaQds85owY14jiPyDfpODJw/f4jt/Ha1UShmfj8vQa4oFBFtxfXj75iO/oXTxXBfXWaViOPiPqYZjNHLz42ESWTTnI8f3irqpgidx4+7XC/gd5j1lF+Ico5gzbyq3z4pi7qnspBs1sianFr7nJn/W/wYLhW4iLTkTfUJd+M1rh2qLKL3nvrEAQBA6vPcWKMTuQJcvJmduCUWt7Ubxy9jWlvwuyWgw/fYhiSusFPLj8FA0NCT1ntaNxP/f/iy757+BfUwilUikGBgbs3r2bxo0bp/57p06diIqK4sCBA999jb29PUOHDmXw4MGp/zZhwgT279/PrVu30nyf4OBg3N3diYqKSvdAkpOTSU5OTv3vmJgY7OzsmLMnmE0X7yJXKDEz0GN0UxdkUgW+e08Tm5iMjpYm/es7Ub9iUebuPsPRK6LhcsHclkzq6I69lTkLdp1h72lxx2dnZcaELh6ULZSbRy/DmLwqgKdvRCG9Z7WiDG3vgqmRPpExCfitPc7JS2KMUtF81ozt40kBO9HJJTI6gTmrgjl1Qfx44fzWjB3gSX77L0/w34b/VirngM8AD6xy/vUMXrwMZ4bfl3gnl5pFGdTfHdM0dnvh4THM8TvCFdXosUwZe3xG1sPGxizNcwW4dvk5c6YfIjwsVuym2lWlQ7f0yTcpkCbLWL/sBHu3iEkYNrnNGD6xCaWyELIrlcrZvOwEu9eFiKSUXKYMn9ac0hXzZfo1vkXI0dssmrCP2KgEke3qU48G7auq7cajVCrZu+oUG2YfQS5TYGFlwtDZbajgnL7zjzoR9vYzfgM2cPeiuA5waVqJfjNbYZgFn9hfhae3XzO9y3LePw9DU0uTzuOa0Ky/+29pJZcVZLUYSpOkLBywjmObzwLg3tGZAQs7Z1tb+/+Af00hfP/+Pblz5+b8+fNUrVo19d99fHw4ffo0ly5d+u5rdHR02LBhA23atEn9t6VLlzJp0iQ+fvz43ecnJSXh5ORE0aJF2bJlS7rXMnHiRCZNmvTdvzfxXUVfz5osD7rEo/did+JephC96jgy/0AI5x68BKBsvlxMae/Jk7fhTN96nMi4RLQ0NOhatzLd6lbm2sO3TFkfmLpTbOdWgT5NnJAAq/dfZJP/FZSCgKWZIaO6ulG9bH5x73fhEX5rjxMbnyT6mbaoRtv6FdHU0BC7tHOPmLMqmNg48ePd2zjRukHF1B1eZsN/sxrv5H/oBsuXnSApSdwz9ulbh7o/ILfExSaxZF4gwSryTf6CVoyc0Jh8Bb4ff3+L29deMnviPj5+iEYigebtq9GxT+0MC+nXuHv9JbPH7CH0XSQSiYSmHZ3oNKBOll7ja3z6GMPcUTu5flbs3CrUKMyQ6S3IYa2+pImnd9/iO3gzb1QPKI26ONN1RP1fIoJXKJTsWBDIlrlHUCqU2NjnwGdpF4pVyP4DxM9CfEwiCwdv5LQqxqhSnZIMX94N0xzqk7z8E8hqMRQEgX2LAlg1atsf8T1/CmEqZDIZzZo14+3bt5w6deqHh5FeR1hk8HT0DQ3p4+pIcpKMNSeuiL6hRgaMa1abmLgkZu87Q3yyFD1tLQY2rI5n2cLM2nmS4OsqFqedFZM6eWBjbsTc7ac5pNop5stlwcSunpTIZ8O9Zx+YvDKQlyoJRgPnEgxuVwsjfV0iIuOYufoY566rRrKFcjGujyf2uUQtYERkHL7Lgjh/Tfx4qSK2jO5fFzvbL3vB128/M2P+Ee4/+nH476PHH5jhd5hXKteWH8U7vX8XyaxZ/txVkVscqxZk6LC6ae4ZUxBy6iELfI8QHZWAtrYmHbvXpEVbxwzp3/FxSSyfE0CQKmTXoYAVPlOaUuAHLNZvkRCfzEq/IwTsFXWSDoWs8ZnenPxFsheiq1QqObT5Amv9joiG4GYGDJzSlOoe6tvRJCVKWTvjEIc2ik/6DkVy4TO/Pfn+hnFAVnD/ynN8+63n45tPaGhq0H6YFy0Hevx2dH1BEDi64QzLR21HmiTD0tackat6ULLa78eAzQqyWgwBrgXfYXqHL+L78TsGU6Ti/we7Niv41xTCnzkalclktGzZkufPn3PixAly5MiapizlEDsv3sRllXtMWftcdK5RgaUBF3gaqioU5YrSxaUic/ad5vJjcQRZsWAeJrV1496Lj8zccYLo+CS0NDXoXb8qHd0qcv7OC6ZtCuZTtJh436luJXo0cEQpCKzYfZ5tgSqD7RzGjO3uQaUS9uJO5PQ95m9U+ZnqaNG3TQ2aq/xMBUHg8Im7LFx3kgTVx/t0cKapZ7nUHZ5coWTbnsus36YK/zXRZ1hfN2p+E/6bnCxjzfoQdu+7IsY7WZngM8yL8mlE+SgUSnbtvMz6dWeQyRQYm+gxeLAntVzS1xBGfo5j7szDXFR1U8VL5cFnXENypyHy/xbnTz1k/rSDREcmoKWlQcfeLjTv4JSlG/OFkw+YP3E/0ZHxaGlp0rG/K806Vc/2zf3V04/4Dd/Os/uizMK1cXn6jG+EoRpzAC+fvM88721ERcShpaNJ1xENaNSlxi8ZAcbHJLJoxDZO7xcfIEpVLYT34k7ktDXP4Ct/PZ7ffcP0rit4+yQUDU0NOo5uTMvBnv/qUWl2iuHX4nttXW2GLutG7TZOv+qSfwv8awohiGSZypUrs2jRIkB8yra3t6d///7pkmUSEhI4dOhQ6r9Vq1aN0qVLp5JlUorgkydPOHnyJDlzZp35lnKIjeaswqNMSdafuUZcshRdLU0GuFcjOjaRdSevieNMYwPGNa9DeGQccw+cIUkqR19Hm6GNa+BSsgDTth7nzB1VN+dgw8SO7lgYG+C39QSBl0UmZsHclkzs5klReytuPHrLlFWBvAtTGWy7lqF/qxoY6Onw8VMM05YHcuXuawDKF7djTC8PbK1ELWBoWDQzlgZy7Y748XIl7Bjd35NcVl+0gt+G/7o6F2Nw7+/Df2/fecOsOUd4/yEKgCaNKtCza9rxTi9ehDNzxiGeqjSEtVyKMWiwBybpaAgFQSDw8C2WzQ8iIUGKnp42PfvXoX6T8hnu2qI+x7Fguj/nT4n72OKl7Rg+qTG57TL/sBP1KY4Fkw9w4aTI0C1RLi/e05phk4linBZkUjlbFgeza+UplEoB6zzmDJ/VipKV1DdKjIqIZd6I7VxWGQeUq16YYXPakuMXpEkIgsDxXZdZOnoHifHJGJkZMHh2O5zqlf3p751VJMYlsWjYZk7svAhA+dol8FneDbOc6htb/2pkpxjGxyQyq8tSLh25CUDzwV50ndrqt+vmfxb+VYVwx44ddOrUiRUrVlC5cmXmz5/Pzp07efjwIdbW1nTs2JHcuXMzY8YMQJRP1KxZk5kzZ1KvXj22b9/O9OnTU+UTMpmM5s2bc/36dfz9/bG2/sLos7CwQEcnc87tKYdYyHs6egaGdK5WnnuvQrn4TOz6KjjkpkO1siw6eoEXYeI4s1Gl4rRzKovv3tNcfybKEhyL2DOxjRtXH73Bb9dp4lQEm36NnGhbuxynbjxl5ubjqYn3Peo70rluJaRyBYu3h7DnhNjl5rYyZVx3D8oVzYNSKbAv+BaLt54mKVmOgZ42A9rXolFtUQuoVArsC7zJsk2qj+vrMLCzC/VcS2Y5/DcxUcqylSc5pPpjsstjwcjhXhQv9n1qhEymYPOmc2zdImoIc+QwYpi3F1V+kA7x8UMUs6cd4uZ1UeRfsUp+ho2uj2UGNy1BEAg+fIulfkdIiJeiq6dNz8Hu1MuCgF4QBIL2X2f5rMMkJkjRN9Ch94h6uDfOuBinh7tXXzDHZyehbz8jkUho0aMm7Qe6qU1mIQgCR7acZ9XUAyQnyTA2M2DQzFY4eZZWy+tnhPcvwpjZZx1PbokPWnXbO9FzUnP0DH6vRARBEAjaco6lPltJTpRiYWPKiFU9KFP91xCOfgayUwwVCiUbJu1mh5/YOFR0L82oDX0x+j9x5fkR/lWFEGDx4sWpgvqyZcuycOFCqlQRKdu1atXCwcGB9evXp37+rl27GDt2bKqg3tfXN1VQ//LlS/LlS/sp/OTJk9SqVStT15RyiG2XbuT6e5HVWdYuFzUK5GXd6WskSGXoa2vR370a4Z/j2BRyXRwjmhoxoUUdXn+MZMGhsyTLFBjp6TC8SU2qFc3LlM3BnL//Uny9ArZM7OiBsb4O0zcFc/K6yNIrlteaCV09KJjbkqv3XzNlVSChn2KRSKC1e3l6t3BCT0ebtx+jmLY8gJsPxaJbpXReRvf0wEpFEnj7IZJpiwO4o/p41fL5GNHHA8uvqPgPHn9g+twjX8J/3UrRr7vLd+G/l68+x2/ul3in1i2q0Km9U5pkk4cP3zNrhj+vVXvGevXK0rtvbQzSCaVVKgX277rCmmUnREKPsR4Dhnni4lYiw4L08UMUsyfu5/Y18UwrVivI0HENyZGFp//Qt5/xG7OHeyrHHcdaRRk8oTFm2bQbS4hLZvm0gxzbI8pG8hezxWd2K/IWUp/Y+c3Tj/gO3sxTVZqEe8sq9BrfGAM1jmPTg0wqZ6OvP7uXHAPArqA1I5Z1oUDJX5OzmBW8fPCO6V2W8/rRBzQ0JLQb0ZDWw+r9a7ui7BRDgNO7LzGn50qSE6XkKWTDhF1D/u+T7/91hfB3RMohVpgyh3plSnP45kPipTJ0tTTpXK0CN5+/58oL8SZUOb8drauUZuGRc7yOiAKguWMpWlQpyczdp7j1UiSo1CiRj3GtXDl39yVzd58mIVkmEmya1qBFjdIEXXmE39YTxCSIife9GlWlvXtFkqQy5m85xaEzKuF+LgvG9fSgZIFcKJUCOwKus3z7WaQyOUYGugztXBvP6sWQSCQi+8//Gqu3nUUqU2BkqMvQ7q641SiWWmQyG/4bG5vEwqXHCD7xJd5plHd9CqbB/ExOlrF61Sn2qoqBjY0pI0bWp3SZ9HWcr15G4Dv5AI8fiuflXLsYA4fXxdTsx9ZRSqWS/dsvsW7J8dQU+4Gj6uOcBQG9QqFk74ZzbFgcjFyuwNTckMETG1P1B7vOjHAu8C4Lx+0hJioBbR0tunrXpWGHamrbV8mkcjbNPcruFSfFcOG8lvjMb0/RLMhL/g5uhDxk9oCNfP4YjZaOFl3HNKLxb5gdmBSfzBKfLRzbeh6Ass5F8VnZ47cMKM4MslsMn958yaSW81OT70dt6Etlz7K/4Ir/GfwphGpAyiEWGD0dTT09nAs4IE2Sc1lV/MrZ21LVwY4NZ66RKJNjoKPNYE8nXn+MZOtZcZyZy9yYSS3dePQmnCWHzyOVKzDW12VEs1qUz5+byZuPceWRimBTOA8TOrijq6XJtI3BhNxW7RTz2zCxqycONhacu/Wc6WuOERElkmza16tIjyZV0dHW4uW7T0xeFsCDZ6J43LliAXy6uZFDNQJ58SaCaYuO8vCZuMNzrlII7151MDf9MiK5eecNMxd8Cf9tWr88vTp9H/575uwj5i4U4500NTXo3N6JNq3SZn7evPkKv1mHCQ0VpQ9Nm1Wie49a6coW5HIF2zaeY8u6s6LZgIUhQ0fVx9GpUIY/s1fPw/Adv4+nqkJay6Mk/UfUy9Dr9Gs8fxyK76hdvFTtOt0bl6f3iHpZEvJ/jc9hMcwbvZurKleeck6FGDqjBZZZMBXPCLcvPmX20C2Ev49CQ1ODtgPdad2vTrYTOLKC6E9xzB+2mYuBoiymoktxhi7ogPlvuI8L3n6BxcM3kxSfjFlOY3xWdKe8S/bdhv5JZLcYfp18L5FI6DK5JS2H1fvtHl7UgT+FUA1IOcROa7dw+X2YKJkw0Me9SEEO33xEfLIUfW0tujhV4NLj19x4Jd58qxXKS7MKJZh/+CzvPouOMq2dytCwQjGm7zzB/Tcqa7XSBRjTojYnbjxlwb4QkqRyDHS1GdLMmSZOJTl84QFztp8iLjEZXR0t+jWpTmvXcsQmJDF380kCzotEkQJ5cjC+pydFHayRK5RsPnSFNbvPI1coMTXSY3jXOtSpKrJC5XIFm/ddZt2uC2KosIk+3r3cqOn4hWKekCBl2bpTHAwQi3keW3NGDa5LyW92gpFR8cxbGETIOVHQX6xoLkYOr4d9GoSV+Phkli87zpHD4mva583ByFENKPID2cLjhx/wnXKAVy/EsXTdBmXpPdAtw4IklyvYsvo029eFoFQIWFoZM3R8Iyo4Fvzh130NqVTOxsXB7NlwTvQXzW3O8GnNKFneIdOv8TUEQeDw1ousnnWY5CQZRqb6DJjUBGevMtl6vbQQF53I4rG7OH1ItPUrXsEB7/ntsckCgSi7EASBwxtCWDVpL9IkGeY5jRm2oCMVXIr/9PfOKt48/sC0Lst5ef8dEomE1sPq0X5Eg1/y0KBuZLcYyqRylg7dyJE1JwGo1bIqQ5Z1Qy+d1cW/FX8KoRqQcoj5x0+nXH4H4uKTefFJDMt1KZSf2Ngkrr8W6fKVHPJQIY8tG0KukSxXYKSrwxBPJx6/jWDXRfFJOU8OUya2cOP28/csD7goOtUY6jGmpSvF8lgxcWMQN56qCDbF8jK+vRsAU9YHcem+Ki2iUG4mdPEgj5UZp689Zca6LzZsXRtWoXMD0Ybt6atwJi87ypNXKlaoY2G8u9bBVMUKffIijKkLj/DstVhk3J2LMbibKyZf7ZcuXxfDf8NTdoJNKtGlndNfwn8FQeDY8XssXBpMfHwyOjpa9OjiTNPGFdO0Xbt44Smz/Y4QGRkv7mvaV6N9B6d00+mlyXLWrjjJ3h2XxJFtLlO8xzakdCZGfw/vvsVv/D7eqvaUDVpUovtAN/Qy8Dr9GneuvsBv7B7C3keJxJcu1Wnf1zXbIvy3z8PxHb6dJ6q9Xu2G5eg7oZHaHFsEQeDk/mssHrebxLhk9I106TOxKXWaVfolT/wvH75nVp91vHwo/l006VmbzqMb/nbuJsmJUpaP2s7RDWcAKFWtMCNW9cDyN5SDZITsFkMA/1XHWTp0Ewq5goJl8zJhx2Cs7C1/9iX/MvwphGpAyiEWnTwLuZY2Rjo6VMyTm7NPXqAUwNLQANdC+fG/8TB1NNqlWnnOP3zFrTfieLJm0XzUL1OUef5nCY0SyS7tqpejbtkiTN1xnEfvVE415QozolktAq48YskBFcFGX5fhLWpSv0ox9p65w4JdZ1IT7wc2r0GzmmWIjkvEd8NxTlwR9XhFHKyY0NOTAnkskckVrNt3kY37L4mhwWaGjOhWhxoVxc5IKpOzdsd5th64IqZEWBgxoo87Vct/YY3GxiWxcOVxgk5+Cf8dNdiLwgX+6q0ZFhaD37yjXL3+EoCype3xGVaXXGnYrkVHJ7BwQRCnVLKFQoVsGDmqPg4/SFq4deMVs6ceJFTlLNOstSNdetZCR/fHBSkpScqahcEc3Cmm2Oe2t8BnclOKlszY6zQF8XFJrPA9QpDKXzR/ERu8pzUnXxaE/F9DLlOwdUkwO5afFC3fbM0Y5tuK0plI58gsQt98wm/IFu5fFW3wnOuVpf+05r8kvy85UcqaKfs4tE4sMvlL5mHk0i7YqZEopC6c3H2JhUM2khiXjGkOI4Yv60Ylt3+fYfXfKYZ3zj5kSpuFREfEYprTmHFbB1GqeuYN7n9n/CmEakDKIZb3m4OlqQXPI8RusKytDVFxSbz+HAWAa+H8RMYkcvO1OBp1zG9HaVtrNpy5gUyhwERPlyGe1bn7MpR9V0SyS15LMya2dOPSw9esOSam21sYGzCulSv5rSwYvyGQuy/FYlq9ZD7Gta+DVKpg0rpArj9WEXSK2TO+szvWFsYEXXzE7I3HiYkXSTY9mlSlnVdFtDQ1ePAslMnLjvJSxQr1ci7B4I61MDYUu7+7j98zbdFR3rwXv7/6rqUY0LnWX1ij34b/dmxVlfYtqvylkxMEgUOHb7Js5UmSkmXo6+vQr3dtvDzStl07eeI+C+YHEhubhLa2Jl2716RZs0rpsvni45NZviCIAH9xvJo3nyU+4xpRuGjGrjDXLj5j7uT9RKi8Tlt3qUHb7s5oa2e+szt/4j4LJu0nOlJ0xOk0wI2mHbNPfLl//SV+3jsIfSPKLJp2rUHHIR7Z7ja/hUKhZOey42yZH4BCrhSzBue2o0y1jHet6sDFoDvMG7KZmM9x6Opp02tKCzzbVfvtdlHvnn1kepflPLsj7upbDPSk09jGaGXhd+N3wN8phh9fRTCp1Xye3XqFppYmfed2oH4P1599yT8dfwqhGpByiA5TpqGhp0cpa2sef4hAplBirKtD+Vy2nH32EkGAnEaGuBTIh//NhyTJ5Bjq6tDVqQIn7z7j/jtxJ1i7eAE8ShZinv9ZwqLFzMFOtSrgUjw/U3cc5+kHlVNNxaIMb1yTQxfuscz/gphdaKDLiFa1ca9QmF0nb7Jo71mSpXIx8b5VLRo6leBTdDwz1gZz9qZIsilRwIYJPT3Jm8uCZKmcVbvOsfXwVfF6LYwY3dMDxzIOACQly1i59Sy7DqtYozlNGN3Pk/KlvjA8I6Pimbv0GGdU4b9FClozeogXDt+MUt69j2TW7CPcuScW7CqV8zN8sCeWafg+RkTEMnf2US5dEtPpS5W2w2dEPWx/MKK6eO4J82Ye5vOnODQ1NWjXpTptOqY/Xk1BbEwiS/2OcOKoOKouWMQG78lNcciE12kKPkfEsmDifi6piC+lKjowbEozbHJnb6SWEJfMqhmHCNglemTmK5IL79mtyJdNy7e08OjWa/wGb+bdi3AkEgnNetaiw1CvDLtpdeDzx2hmD9zIjTPiPtupXlkG+bXF2Pz30rBJk2SsGreTQ6vFnVnxygUYubonVr9gv6pO/J1imJSQzLzeqzm1SzQh8Opem75zOqg1ZuxX408hVANSDtF56WLexicBEiwNDDDV1uOFqjuskNuWiJh43kSKLEu3IgUJj4zl9luRcehUMC/FrCzZePaGSF4x0GNY3Rpce/KWQ9dUmYPWFkxsXoczd1+w/vhVlIJAThNDJrRxw9bcmHHrA3moItjULluQ0W1ciU1IZtK6AG6rEu+dSuVjTMc65DQz4vDZ+8zdrLJh09akb8satHQTbdZuP37HlGUBvA2NAqCxa2kGtK+JgZ64N7tx7w3TFx/lQ5hI8mnuVZ7e7Wugp9rxZDb8V6FQsnvvFdZsEOOdjI30GNTfDdc0yBOCIHDkyC2WLTlOYqLoMNO7jyv1G5RNt3uIjkpggd9RQlTj1SLFbPEZ1xB7h4z3G2eC77Fwhj+x0Ylo62jSpa8rTdo6ZrqzEwSBgL3XWOF7hKREKQaGuvQdVR/XH1xvRrgQfI/5Y/YQExmPlrYmXYZ50rhzdbXJLBLjk1k5dT8B28SbXP7iufFZ0F6tusb0oFQq2bviBBtmHEQuU2Bpa4bP4s6UqvprOtOs4OzBa8ztv56E2ESMzAwYvrQrjnXL/tOXlSX8nWIoCAI7Z/uzbsIuBEGgRLXCjN82EDOrf6fM5E8hVANSDjHvrKmYmZqiK2gREZcAQGlrGx5+CEeuUGKip0u5XLkIefISABtjI2rkc+DQzQeiXEJPl87VynP89lMeflDtBEsVwqVIfub6h/ApNgFNDQldXSrhVDgvk7cH8zJMLLSNqpRgSKPq7Dp9m9VHLiFXKjE30mdUm9q4lC3I1mPXWbbvnPg+Brp4t3GhrmMxwj7HMXVNEJfvqkg2RXIzrocHua3MSEqWsWx7CDsDVKHBVqaM6eVB+eKiGDohUcrSjafZH6RijeYyZ0x/T0oV/cIajfgUh++iAC5dE3dQpYrnZtTgut+F/754Gc7M2Ud4/ES1M61RhMH93TFLQxf44UMUfrMOc0vlWFKpcn6GDfciZ860EwQEQeBE0F0Wzw0kLlaVj9inNo1bpJ+PmIJPEbHMn3KQy+fE7rZ0BQeGTWiETRbIEu/ffGL2mD3cvyler5NrcQaMa4SZRfa6nc/hscwfvZsrp8XuqWzVggyd1YKcP4i3yirOB95hwcgdxETGo6OrTfcxDanfwemXjCuf3HrNrL7rePc8TIziGuBBu2FeaGn/XmzNDy/DmdFtBY9V++6m/dzoMr7Zv6oz+jvFEOBywE1mdFpKQkwiOfPkYMKOQRQq//uljmSEP4VQDUg5xLKLZhOlFJAgwcHEjJcRUUiQkNPQACMNHV59FrvBinlsCYuK422U2E15Fi3Eu4ho7r0Xuznnwg4UMLdgy/mbyJVKLAz1GVa3BucfvOLoTXHUViiXJROa1yHo+mO2nFY51ZgZMbGNOxZG+ozfEMjTdyLT06NiEUa0cuFzTAIT1wZw/6XK47NcAUa1r4OFiQH7Tt5m4bYvJJsBrZ1pWlvc2V29+5ppKwIJTQkN9ixPn9bVU7u/SzdeMHNpIOGfVazRhhXp1soJXdUN4dvwXz1dbfp0rUmjun/tjORyBVu2X2DTVlGyYW5mwLDBnjil0REolQJ791xh9apTyGQKjIz0GDTYHZfaxdO9WYeHxTBnuj/XLosj4TLl8+I9pgHWGUTPCILA0X3XWDEvkKREGQaGOvQeVhf3LHR2CoWSXetC2Lz0BHK5AjMLQ4ZMakKVmtmz8RIEgSPbL7Fqpj/JiTKMTPTpN7ExteqXzdbrpYXPYdHMHb6da6pxZcVaxRji2xoLq5+v+0uMT2LZ2F0c2y52pkXKOzBiaRdy5f29mIoyqZy1E3ezb1kwAEUq5GPUmp7Y5M26Z/E/hb9bDN88/sDE5nN5+yQUHT1thi7vgUurqhl+3e+EP4VQDUg5RLvZU7CysCAqLhGlACa6uugKmkTEJQJQ2tqah+/DkSsFTPV0KWNjQ8jTV0iAXCbGVHew5+CNh8gUCkz1delSrQJHbzziyUdxJ1i3TBGqF8zLPP8QPqsyDHu6VaGCQ26m7AjmdXgUAM2qlWJgfSe2HL/O+iAxCiqHiQFj29bBqWQ+1h+9zOpDKlmGkT4j27tSp2Jh3oVFMXV1ENcfqkg2JewZ080dG0sT4hOSWbT1DAeOq0KDbcwZ18eTUoVF66XY+CQWrD1BwCmRNZrPLgdjB3pRJP8X1uiHj9HMXHCUmyqyQcWyeRkx0PO78N9HT0KZ4eufGu/k6VaSfn3qYJSGLvDVqwhmzTjEI1WyvHPNogwe4oGpadoOM4Ig4L/vOisXB3/JRxzsjke9MhkWtfdvPzN7wj7u3RKvv2rNIgwa3QDzLNirPXv4Ad9Ru3j1THzoqdusIj2966KfTV3W2xfhzPbewaPb4jXVql+WvhMaYZzO959VCILAwQ0hrJl+CJlUjmkOI4b4tqaK668Rl585eI2F3tuIj0lE30iP/jNbUbtZ5V/y3lnBhSM3mNNvHXFRCRia6DNkUWeqN6zwT19WpvF3i2FcVDyzuizjskpT3GJoPbpMbvmvsaf7UwjVgFTT7YUzkGpqoinRwExHn8/xCUiQkM/UnBfhkUiQYG1oiL6GNq9V3WFluzy8/xzN++hYALyKF+bFx888+iB2c7WL5iePiSlbz99MTa8Y5lmDk3eeEXxH5Tea24qxzWpz+MpDtp+5CYCthQmT27ljoK3N+A2BvAhVZRc6Fmd4i5q8j4hh4toAnrwV38etUhFGtK2NiaEeO4/dYOmuLySbIe1qUb+G6OV54eYLpq8MIiJSJPG0a1CR7s2rpWoGQy4/xXd5EJEq1min5o50bPqFNapUCuz1v86KDWd+GP4rlcpZuyGEnXsuIwhgldMYn2FeVCjn8N35y+UKtm45z+ZN58VO0tyQocPrUu0HrMd3bz/jO/kg91U6vWo1CjN4RD3MMxhXKhRKdm86x8blJ8V4KnMDBo9pQLVambdXkybLWL8omH2bzot2Z3YWeE9rTvGy6VvK/QhymYLty06wbdkJlAolljamDJvVkrJVM28MkBFePvqA76DNvFDp/rzaVaPH2EZZ0lpmFx/ffMK333ruXxE7edfmlek7o9Uv8UrNCj6+/sSM7it4qLrOBt1d6DGl5S8JR1YH/m4xVCiUbJi4ix2z/QGo4FaKURv6/XaEp7TwpxCqAakd4YLJmJuYEp2QDEiw1DMgMj4RQQBTXT20lBp8jv/SHT54H45CKWCur09JayvOPRX3dHnMTKiSJw+Hbj5ErlRiZqBH56oV8L/+gOcp6RXli1Exbx7m+ocQnSBmGPZxd6RUHhsmbw/mvcqppo1zWXp7OrIu8Aqbj4tMTyszI8a1q0Plovas8b/IuiNfZBmjO9ahVrmCvA6NZPLKAO48VZFsyuRjVFc3cpobEROXxLyNJwkIUWkG7SwZ38eTIvnE7i8qJoHZK4M5dUF0kimc35qxAzzJb/9lXPTm3Wemz8s4/PfO3bfMnH04Nd6pcYPy9OxeE32972/Ajx99YOYMf169Uo2EPUvRt18djNK5YSoUSnZtvciGVafEomZmwCAfL2rUynhc+fxJKL7j9vLiqdjZudUvQ5/hdbOUK3jrynNmj9lDeGi0uAvr6ky7Pi5Zkmp8jYe3XuM3fDvvX4mddNMuNeg01ENtInVpspwNsw+zd9UpAPLkt8J7fjsKl85eAc8KFHIF2xcEsHXuUZRKgVwOloxY2oUiaTwY/ZOQy+RsmLqfXQsDAChQ2p7Ra3uR+xs97e+Kv1sMAU7tusjcXqtITpRiW8CaCTsH41A883rcfwJ/CqEakOoss2wqCk1tNCWa6KBJolSGlkQTU21dPickqnaH5ryMELtDGyMjdNHkTaRYtKrY5eH1p0g+xsQDUK94EZ59+MTjjypXl+IFyWlgyPaLt8SCZmLIsLo1CLzxmFP3VH6jdtaMaVqbvefvsue8SP+3z2nGpLbuaAATNwbxOiwKgCZOJRnSzJnXHyOZuDaQ5+9VCRBVizOsdS0M9XXYcuQqK/eqpBmGugzvUBv3qkWRSCScuvIE39VfHGu6NK5Cp8Zi9ycIAsFnHzJ39XFi45LQ1tKkW+tqtGn4Rf8nVyjZvvcy67aqwn+N9Rnaz41a34T/JiZKWb76FAf9RdJOntzmjBxejxLFv493kkrlrFt7hl07RYcZK2sTfHzqUe4HlmfPnnzEd8oBnquKmqtHSfoP9cTI+MdFTSqVs3H5SXZvOie+l40pwyc2pkzFzJMF4mISWTbzMMf9bwJQoGguvKc3x6Fg9m6cifHJrJrpz9EdojGAQ2EbvP1akV+NKfU3zj5izrBtfPoYjaaWBh2H1qVZr9q/ZAx299JT/PqtJ+xdJJpaGnTwrk/zfm6/3QjuyrE7zO6zhuhPcRgY6zFwXkdq/YYj3bSgjmL47NYrJrWcz8fXEegb6eGztjfVGvy+o+I/hVANSO0Il03AyMiEhCQ5CBJMdfSIVskpcuob8Ck2AZBgrqePRCEhMj4RCSKz9N67jygFsDDQp0TOnJx7JjIM7c1NqZQnDwdv3Bd3fYYGdHAsx4Gr93ilSq9oUrEEpXNbM9//HLFJYobhAM9qFLSyZPKOY3yMikMigQ4uFejqVonVhy+x7aRYVGwsjJnYwZ2yBWxZceACmwJVsgwzQ8Z2csepVD6ev41g0spAHqaQbCoWZGTnOpibGBAZk4Df2uOcvKTq/hysGN+3LgXsRFJDRGQcvsuCOH9NpVksnIuxA7yw+4p1+W34b23nogzuVQfTbwywr157ge/co4RHxGYY73TnzhtmzfTnw3vVGTWtSPcetdIMCgaxqG1ac4adWy6gVArktDJm+JgGlK+UsYvL3ZuvmD1hPx/eiQzeJm0c6dLPFd0sjMTOHrvHwikHUtMnugxyo3G7qtmWRVw8cZ8FY/YQ9SkOLW1NOg3xoGlX9aXUx0bFs3D0Ls4eEXdCJSsXwHteO6yyqZPMCuKiE1g0YjtnDlwDoFTVQngv7kTO38z2LOJ9JLN6rOLOefFvo24nZ3rPaI3uLxgn/12ooxhGhccwrf1ibp8RpUsdxjWl7chGavsdVCf+FEI1ILUjXDUJhbYOEiRoCZrIZEq0JJpooUGSVI6WhibGWrpEqbrDr3eHtsbGaCk1UpmkVfPa8SLsM2Gx8UiA+iWK8uBtGM/DxdFo3ZKFMdHWZfeVO6Kw3dSYIZ5O+F99yLmHLwEo65CLkY1d2HHmFgcuiU41+awtmNzOHZlUwcSNgbz7pGKC1izDwMbVefI2gknrAnj9MQqAxjVKMrhlTfS0tdjgf4U1By6KezhjfUZ0roNLpUKij+j5h8xZf4IYVffXo0U12taviKaGhmi0fOIui9afJD5Biq6OFn06ONPUs1yqfEEmU7BxxwW27LooFnwLQ7z7e1C10l+DeuPikli4NJhjx1Xfj4Mlo7zrUyiNDioxUcryZSfwV5lL29lZMGJkfYql0Umm4P6dt8yacoD3b1WylOYV6d7XNd0CmoKE+GRWzQ/iyD7x5myfPyc+k5pQKAud2KfwWOZP3MeVEPHGWaZSPoZNbYZVBqzW9BD1KY4FY/dwUZVSX6pyfobNaom1moqVIAgE777Csol7SYxPxtBYj/5TW1CrUXm1vH5G731sx0WWjdlJUoIUY3NDBs1ui5NX2Z/+3lmBQq5g86xDbJ9zGEEQcCiem9Fre/0r8v3UUQzlMjkrR2zlwDIxj9KpYUWGr+6JgZo8c9WFP4VQDUg5RPuV49AxNEQmF0AAfU0dElO6Q209ohNUYnt9Az5/1R0iF4hKSFZ1h9bcfReGoPIoLZwjBxefi4xABwszytjk4vCthyJxxsiAjo7l2HPpLm9U5JuWVUpROKclC46cIz5Ziq6WJoPqVSePuSlTdwQTEZOAhkRCZ9eKdKpdgaUHz7M7RGSC5rE0ZWJHd4rbW7Nk31m2BX/pGid08aBSMXsevwpj0soAnr5R7eGqFmVYBxdMjfT5FBXPjFVBnLuuGtMWysW4Pp7Y57IAIDQ8hhlLArh2R+x2y5WwY3R/T3J9JcJ98PgD0+cd4fVblc2bWyn6pxH+G3LuMXMXBH6xcmtXjXatq6Y5Irt8+Rmz/Y7wKUIl72hTlY6dqqOdji4tMVHKqiXHObRXLGq57SzwGdeQ4pnwHb109jHzphwg8lO86GbToyatO1fPdGKBIAgc2X2FlX5HSU6SYWCkEuHXz54IXxAEAnddYcX0QyQlSDEw0qXfhMa4NCynNk3g+1cR+A3ezENVWLFL4wr0m9wMwyxEWmUX756HMavPOp7cFn+nvDpUp8fEZugZ/F5d1/VT9/HrtZrIsBh0DXQYMKc9dVpX+6cvK0OooxgCBG48w6IB65BJ5eQtnpuJu4Zgm//32Zv+KYRqQGoe4fpxKLV1EQQJ2hItpDLlX7pDbQ1NNJQaJMvkaGtoYqSpS1Ti97tDW2NjNBSSVCZp1bx2PA39xKd4sYjVL1GEe68/prrW1C9dFH0NLfZcuQtAHgsTBrtXZ+/Fu1x8It4gKuTPjU/DWmw6eY0jV1WxTLlyMLWdBzHxSUzedIzQSNHsu23t8vRr6MS9Fx+YvC6IdxGqIlu7LAOa1UBTQ8Ka/RfZ6H9FLMhmhozq4kb1cvnFG/mZe8zboHKs0dGiT+satPAQuz+lUmB/0E2WbjxNUrIcfT1tBnR2oUGdUn8J/129+Sy7Dog2b9Y5TRgxyJMKZf6aJBEVlcDchYGp8U5FC+dipLcXedNwxY+JSWTxomMcDxY7yQIFrBgxqgEFfmCbdvXSM+ZM9yciXBzFtmpfjQ7dnNMtoKnvFZXAwhn+hKg6sSIlcuM9qQl2mXCzScG7VxH4jdnDQ5UsonqdEgwY1xDTbDLw3r+KYLbPDh7cEH8fnOuWpv+kJhhnEGScWSjkCrYvPsbWRcdQKpRY5TZn+Nx2lKpSIOMv/puQSeVs8vNn95JgBEHArpANI5d1IX+J34ug8fljNL69VnPztDgqrNOmGv392qGXzfzKXwV1FcMHl54yufUCPodGYWRuyOiN/ahQ5/cwLv9TCNWA1NHo+lFI9PWRCJrI5aAl0UztDg00dVJ3hybausSomKU59Q2JiI1HgoQc+gYopEqiE5PRkEgoldOaO+9CAQlWRoYUNLfg4gvxxljA0oKSVlb433ooFgsTI9pVLsPOC3d4rxqvtnEsg4OFGQuPnidRKkNfR5uh9WtgaWTA1B3HiYxLRFNDQnf3yrR1LsuCfWc5cF6VbG9tzqROHhTIlYP5u86w97Sqa8xpysSunpQtlJt7zz4weWUgLz+I3Vv9GiUY0q4WRga6fPwUw/QVQVy+o3KsKZaHsb09sVV1f+9Co5i2+Ci3H6jipMrlY2RfDywtvmjybt19w4z5X8J/m9QvR+9ONf8yphQEgeCT91m45BhxcWK8U/cuzjRLJ97pzOmHzJsbQExMIlpaGnTu4kzLVlXSJVvExiSyZG4gx4PEh4z8hawZOb4R+TLwHRUEgZMBd1g86zDxccno6mrRbYAbDVpWyvSORCFXsHNtCJuXn0AhV2Kew4ghk5tQuUb2HP8VcgU7Vpxky+LjKBVKcliZMHRWC8o7Fc74izOJB9df4jt4M6GvP4lxVL1r036I5y9xW7kR8pDZAzby+WM0WjpadB3TiEbda/1WOymFQsn2uYfZMvMgSqWAXWEbxqzrg8MPxvW/A9RVDD+9j2Ry6wU8vPIMDQ0JXae0ovkQr3/cYP1PIVQDUnWEm0eioaePXCFBU6KJTCYgCBpoSzSRypRooIGmoKHqDrXQUEpU3aEWRpraRCUmfbc7tDM1RSlV8iEmDgAnB3sevQ/nc0IimhIJDUsW48aLd6m6xEZliqEhSDhwTexG7HKYMsjdiZ3nbnP1mcrcuqAdQ+vXYN2xKwTdFK3DiuaxYko7d8Ii45i8+RgR0WKyfSf3ivSq58j1x++YsiGIj59VXWOdCvRpIo52Vuw5z7YAUZphbWHMmO7uVCmZF0EQ2Bd8m8VbTpOYLMNAT5sB7WvRqLbY/SkUSnYevsaqrWeRqnxGh3SrjVuNYql/GAmJqvDfoz8O/w2PiGX2vKNcVsUJlS5lx4hhXtimsV/7/DmOuXOOcuG8qMMsUSI3I0bVJ3dui3R/xiEnH7DA7yjRUWKiROeetWjWOv0CmoKw0GjmTTnA9UviuLhc5fwMHd8Iqyykzj+5/x6/Mbt5rRLhe7WoRM9hdbM9/nt0+w2zvXfwVkVOatTRiS7D62aJ3PMjJMQlsXzSPo7tEpmrhUrlwWd+B/JkwbQ8u4j+FMf8YZu5GCgypiu6FGfogg6Y5/z5bjhZwe1zj5jVYxWfPkSho6dNn5lt8OxY4x8vCD+CuoqhNFnG4kHrCVRlPLq0qsrgpf9s2O+fQqgGpBxi8e0+CDr6SNBAKgdBkCBRaiJX/LU7TG93+G13KEtWEpuUjKZEQomcVtx591EU5RsZ4WBqypVXYjdV0NKCojlzcvT2IwQBcpka07piaXZcuEVotIox6lQeayNDlgRcIEkmJtz7NKyJgbY2M3adTNUi9vZ0pGnVUszdc5qjl7+MUCd39sDO0ow5O05x6JwqIsrGnEldPSmZPxc3H71j8qoA3oWJBblp7dIMaO2MgZ4O7z5GMXV5ADcfitdbpbQDo3u6Y6VKmXjxJoKpi47y6JnISnWuUgjvXnUwN/0yBrxy/QWzMhH+63/0FktXnCApSYaenjZ9etamgdf3rjGCIBAYcIcli4+RkCAaePfs5ULDRuXTvRl9/hTHvJmHuajyHS1Zxg7vMQ2wzZN+AU15r4M7L7Nm4TGSk+UYGunSf0Q9XDxLZfrGl5wkY92CIPZvuQCArX0OvKc1p1gZu0x9/bdISpSyZtYR/LeKr2df0Arv2a0pqMbO5OzRWywctZPYqAR09bTpOa4xddtW/ek3e0EQOLwhhFWT9iJNkmFmaczQ+R2o9IvccDKLqIhYZvdew9Xj4rShZtPKDJzX4ZfsVrMLdRVDQRA4tCKY5d5bUMgVFCgjhv1a/0MWen8KoRqQcoildg5Doq+HXKGJUilBUGqkdodSGSBI/tIdaggayGVKdDS0QClBKpOjo6GFgaY20aru8GvPUjtTU2TJCsJiRZ2hk4M9D96FEZWYJHaHpYpx7enbVOZpk3LFUcqUHLohFjQHS3MGulVly5mb3HgpOoQ4FXVgUN1qrAi4xMnbYsRRCXtrprTz4PXHSKZtPc7nFLNvz8p0r1uFS/dfMXXDV11j3Ur0aOCIXKFk8Y4Q9hwXuzfbnKaM6+FO+aJ2KJUCOwOus2z7WaQyOUYGugzu6IKXs+gNKpcr2LL/Cut2nUcuV2Jmoo93LzdqOn4Z28XGJbFo1QkCT6gYo/aWjBpSlyIF/5qM8P5DFLPmHOG2ysqtUoV8eA+tS07L7025P4ZG4+d7mBsqokf5Cg54+9TDKh0/TUEQCDx8i6Xzg0hMkKKnr02vAXWo94MCmoI3LyPwm7CPR/fEB4IarsUZMKoeplkIwb1x8Rlzxu0h4mOMuLfsXpN2vVyybUh95fRD5o3eTWR4LFramnQY5E6zbs5q0+VFhEYxZ9hWbqoeHiq7FmfIrNaYpfGzUDdePXrPzD7rePlA/F1v3MOFLmMaqc1gQB1QKpXsWRTIuin7UCqU2Oa3YtSanhQq6/BPX1q6UFcxBLgd8oCp7RYRHR6LqaUxY7YMoIxz5l2a1IU/hVANSA3m3T0E9PWQKzUQBA3kco0Mu8Ovd4dfd4dW+oaEq7rDnAaGJCfJiU2SoqWhQQlLK26/C0WChFwmxtgZm3BV1R0WsbKkoIUFR2+LBJLcZia0rFiKrWdvEh4rFq7ONcpjqqPHsmMXU1MvRjSuiYYgYdaeU8QmilrE/vWqUa9SMfx2nOTYdVW2YJ6cTO7siZWpIX7bThJwSdU15s7BpG51KWpvxZV7r5m6OpDQT+IYtZV7efq0cEJPR5uX7z4xdXkg91SONTUqFGBEdzdyqIrBk5dhTF1whGevVSYCzsUY3M0Vk68cW0IuPGHO0iAio1LCfx1p38LxLzmDSqXA7n1XWL3ujMqUW5dB/dxxdSn2XcFSKgX277vK6lWnxI7NUJcBA92o41Yy3eIW+iEKv6kHua0in1RyLMDQUfWxTCcBIwUKuYLt68+yZdVpUYaSw5Ah4xpRpXrm93RxMYksmeHPycPiA0eh4rZ4T2+Off7sjR6jP8ezcNwezh8THzBKVHBguG8rbOx+3OlmFkqlkv1rz7DO1x+5VIGZpRFD/NpQOY2oLXVDmiRj9ZR9HFp7GoD8JXIzYmlX7Av//FiprOD+5WfM7LaCsLef0dbRoseUljTo4fLbjkrVWQzDXothv09vvkJDU4Pevu1o2Mftl37vfwqhGpByiNX290ehZ4hS0ECmkKAUNJArNNLtDrXQRCb/vjsUFCCTK9DR1EJfokVMUjIaSMhrbMbLT2J3mNfMjKQkOeGq7rBGvrzcfRNKdFIy2hoaNChZlEtP3vBBxTxtXqEkSYkyjtwS0ysKWFnQz7UqG05d485rVfRR8Xz09ajKUv8LhNwXd21lHHIxuZ07j9+GM3PbCaLixRFqz3qOdHavxJmbz5ixOZjI2EQ0NTXo6lWZbvWqkCSTs3DraQ6cFsc+9jbmjO/pQamCtsgVSrb6X2H1bpVjjZEe3l3rUKeqSAKRyRSs3XmeLfsvo1QK5DA3ZGQfD6pW+CJuj4pOYO6yY5xWMUbTC/999TqCGX6HefRY/B5rOBVmyEB3zNPowt68+cSsGf48UHUQ1WsUZvAQT8zTYWoqlQL7dl5mzfITyKQKjI31GDC8Li5uGY/gnjx4j++Efbx+Lu7p6jYpT68hHlky3z4TdJdFUw4QG52Ijq4WXQe50zALeYlfQxAEgvddY9mUAyTGS9E31KHPuEbUaVJBbTekFw/eM2vQJl6pfhYNOlan2+gG6KZhl6duXDp2h7mDNxPzOU4c005qRt0O1X+rQhMbGce8ARs4f1iULVWrX44hizpjnIWJwa+EOothUkIy8/uu4eQOcVTv3tGZAQs6ofMLfjfgTyFUC1IOsdahPgj6+sgUmsiUmiiUGsiVEgRBA5lcA42vukOUGigUqlFpBrvDb7vDpEQZcckytDQ0KJYjJ3ffi7tDWxNjbA2Nuf5GvJEXs85JPjMzAu6I3Zy9hSnNypVk89kbfIoTx53dalZCT0OT5ccuiZmJ+rqMbupCUpKcOfvOiFpEbU0G1q+Oe9nCzNh+nNO3VS4xea2Z1MkDcyN9Zmw+zolrKuKNvRUTu3lSMLcl5249Z8baY4RHit1oe6+K9GhaFR1tLZ6+CmfysqM8eSUWA1fHwgzv4oqZiUjpv/v4PdMXBfD6vcowvE4p+neqlaopTAn/XbBCtHHT0daka/vqtGxU8S+jPTHe6SKbtoqm3GamBgwb7EH1at93YQqFku3bLrBxw1lxRGtmwJChnlT/AVPz1YtwZk05yJOHYpdby7U4A4Z7YpJBAkRykoz1S4+zb9tFcbeb2xzvSU0okQXz7U9hMcwdv49r58WzL1slP8OmNM12NmHom8/M9tnBvWsvAXByL8mAyU0xzWZ24reQJslYO8ufA+tEooRdQWtGLOhAgRI/nzX5+WM0cwZt4rpKvlCtbhkGzW6LiUXm00N+NgRB4MCK46wevwu5TIG1vSWj1vSkaMWMHY7+CaizGAqCwJ4FR1kzZjtKpUDRSgUYt20glj8gsakLfwqhGpByiO5He4K+HjKFWASTFVqq7lADpSDJXHco0UCi0EAhV6KrqYVSLnaHuppa6H3VHdobm/Hqq+4wMVFGRFwCEqC6Q17uvPlATLIUbU1NGpUsyvlHrwiNEYkzrSqWJio2kSBVgSxsY0lvlyqsOXGFB29FZmKdUgXp4VqZBQfPcvGROP4rXyA3k9q6cfv5B/x2fBmh9mlQjXau5Th+7Qm+W04QHS+6y/RsWJUOHhVJSJIyZ9NJAs6LN6D8uXMwvqcnxfJZI5MrWL/vIhv2XxINyE0MGNnDDeeKYnJCcrKMlVvPsvOwipVqaczo/nWpUOpLsYj4FIff4kAuXlUJ+YvZMmqwF3m+sdx68vQjM/z8efFSlbjhWoKBfdM25X729CMzZ/jz/LnqPNxKMGCge7oG3nK5gm0bzrF5fQhKhYBFDiOGjqxHFaeM09VvXX3B7In7CQuNRiKB5h2c6NjbJU3ruLQgCAKHd15m1ZwAkpNkGBrr0W90fVzSIAllBgqFkt2rTrNpYZAo28hpzJDpzamUzezEtHDtzEPmDNuaupvsNNyLpj1+vtRBqVSyb+UJ1k8/iFymIIeNKd6LO1NGjRISdeDxjZfM6LqCDy/D0dTSpMv4pjTt5/ZbSUFSoM5iCHDt+B2md1hCXGQ85tamjNs6kBJpPLSqE38KoRqQcogNg7qCvh5SpSZyhSYypUYmukMNUEpU3aEWUrky07tDa0Mj4hOkxCfL0NbQoJhlzlRmqZ2ZKdb6Blx/I3YppXJZk8vImOB7omQgn6U5DUsXY/PZG0TGi9mG3WtVQqKENceviAn3hvqMaVqbmPgk5u4/Q0KySovYqAbOJfIzfdtxzt4VR6hlC9gysaM7BjraTNsUTMgtVVHKb8PELp445LLg1NUnzFx//ItJd4PKdGkomnQ/eBbKlGUBvHinyl6sUZwhnVwwNhQLz417b5i+OIAPKlZqc69y9G7vnBoOLAgCh4PusGTNSRISpejpatO7izON6pb7i55QKpWzftNZduwWx645LY0ZMcyLCmmYckulcjZuOMuO7RfFz81pzHCfelT8gan2owfv8Z1ykNeqYuvVsBy9BtTBIAPRdHxcEsvmBHDs0E3x51PQCu/JTSmQhV3WmxfhzB6zh0eqaClnj5L0H9MQk2yK5p/ee4fv8O28Uck26retSrcRXmqLXor+HMeCkTu5ECRKHUo7FmT43La/xDP06e3XzOq7nrfPPiKRSGjZ34323vWzTTr6GYiPTmDBkI2c2XcVgMrupRm2tAumOX4+0SirUHcxfP/8I5NbLeDF3TdoaWvSd25H6nWvrc5L/gv+FEI1IOUQWx1vh6BviEypgVSplVoIv+0OBUEidonpdocayOSCqjuUoJAL6Gpqo5ALyOUK9DS10UaTuORkNCUa2Bma8uqz2B3mMzcnNi6ZzwmJaEgkVHew5+arD8RJpehoatKwZFHOPHghdo8SaF2pNOGRcZy4Lxau4rmt6FGzEiuCLvFYlYnoUaYwXVwqMnffGa4+VYX2FrZjYhs3rjx8w5zdp4lPkqKnrUX/xk60qlmWoxcf4LdddJfR0dKkbxMn2riVJzY+Gd8Nxzl+WbXby2vF+J4eFLTLSbJUzurd59nqrzL+tjBiTC8PqpR2AERN4ZKNpzkQpNIU2pgxZkBdShX9MlYLDYtm5oIAbqgstyqUzcvINMJ/7957ywy/L/FODeuXo3f3WuincZO/d+8ts2b4805lqt2wUXl69nJJ83NB7GLXLT/FXlUCho2tGT5jG1IqEyPP86ceMH/aIaIjE9DS0qBjbxead3DKNItTIVewffVptqw4hVKhxCKnMUMnN6ViJjrTNL+XJBnrZh/lwMZzAOTOZ4m3X2uKlM6ebONbCIJA4I5LrJi8j6QEKUYm+vSf1oKaDcqp5fV/hKSEZJaP203g1vMAFCmXF58lnbHN9/P1jpmFIAgcWX+G5aO2IUuWY2lrzshVPSj5kzuk7EDdxTAxLok5PVcSsu8KAF7dXOgzp8NPYf3+KYRqQMohdjnVAkHfEKlSk2SltqogZrY7lKh2h6ruUEO0aEOQYKCpTUKiHPhrd2itb6gy5Ra7w7h4KQlSGTqamhS2sOSeandob2aKhZ4+t9+KJIXStjZY6Rtw4oFY/PLntKB+ySJsOnuD6IQktDU16V27MsnJCtadVCXcGxswrqkroZ9jWHjoHEkyOYa6Ogxr4oxjYXumbD7G5UeiXKFCoTxM6OCGlqYm0zYEceGeKE0oWyg3Ezq7k8fKjGOXHuG34QQxKvJNj6bVaO9VES1NDW4/fseUZQG8DY0CoJFraQa0q4mhqvBcuvGCWcuCCPukSqFoUJFurZ3QVY0SU8J/V244I4YLG+gwoIcrnq5/Df9NTJKyas1p9h28DoBtLjNGDq9HqTQ8RRMTpaxedYr9KlPt3LnNGTGyPiV+4D966/pL/KYe4qNq5NmstSNdetZCR/fHI8+oz3HMn3aIC6dFYlOJMnYMn9QkQ73i13h87x1+o3fzRiWar9+qCt2HeGRbhH/93GPmjtjFp7AYNLU0aNvPlVa9XDLtoZoR3r0Ix2/wZh7dEh9gXJtWpM+kZhhmEIWlDoT4X2fh8K3ERSeib6hL3+mtcG1R+bci0jy/+4bpXVfw9kkoGhoS2o9qRKshXr9d/JS6i6EgCOyYfYj1E3YjCALFHQsxdutAcmTTiD49/CmEakDKIfYLaYRS3wCZoE2yQiyGUlV3KFcVQrlSA2k6u0OlikCT1u5QU6IBcgkKhYCepjYymRKFQom+ljZaggZxyVK0JBrkNjLh9adoJEgoYG5BdFxSandYwyEv116+I0EmQ09LiwYli3Lq3jM+xYtWa20rl+FNeDRnHorjzpJ5rOlaowLLAi/y7KOKsFKhGO2ql8V372luPldpEYs5ML51HUJuP2f+vhASk2Xo62ozpGkNmlYvxYGzd5m34zQJyTL0dLQY2NyZ5rXKEBmTwIx1xwi5oSLf5LdhfE9PHGwtSEqWsXRbCLsCRQZdrpwmjOnlQYUSYlcVG5/EwrUnOXpKZQmXJwdjB9alaIEvo8Rvw3+rVS7A8P7u5DD/Kzni2o2X+M45Qli4KPdo2bwyXTvWSHNHd+3aC2b7HiEsTNTxtWxVhU6d0/5cgPj4ZJbNDyJQJXXIm8+SEeMbUahIrh/+TgmCQNChmyyfc5SEeJVecYgHdbPA4kxOkrF2fhAHVKL53HlFEX7RbHZzsVEJLJ6wjzNHRbu9YuXsGe7XGlv7HNl6vW8hlynYuiiIHYuPoVQKWOexYPi8dpTMRBTW30X4u0h8+6/n7kVxdVCrSUX6z2z9W4nbE+OSWOK9heDt4s+zXK1i5/XDQwAAH8BJREFU+KzojrlV5l2KfgXUXQwBrgTeYkanpcRHJ2BhY8aEHYMoWrmgui75TyFUB1IOceR5TxT6hiQLWiQrtUhWaP/U7tBEW4+YNHaHNoZGxMQnkyiVo6ulRWHzHKnM0nwWZphq63L7nejiUi5PLsy19Tj1SCx+ha0t8ShWiE0h14lRZRv2cXUkNi6JjaevoxQErEwMGdfclVcfo1jsf07UIurr4tO0JuXy2TJ5czDXnogjVMdi9oxr74ZSITBlQxBXH6pE7kXtGNfZnVw5TDh67gFzNp8kLiEZXW1N+rSoTiv38mhoSLh27zXTVgTyIVwVF+VZjj6ta6TuBkMuP8VvRRCfo0QWbMfmjnRq9kVTKFco2bnvCmu3nEMmV2BqrM/gPnWoXeOvxI+4+GSWLD9OgGpf5ZDXklHe9Shc6PsdXVxcEksWBxOksvHKly8nI0c3oOAPwnTPhzxm/qzDRH4WUynad61Bmw5OaGr9+Ik+9H0kcybu5/Z1sauuVK0gQ8Y1JEcWLMOuX3jK3HF7iQiLQUNTg9bdnWnbM3sifEEQOHnwBksm7SchLhk9Ax16j2mAe/NKauug7l19jt/gLXx8+1l82Ohbh3aDPH76/k6hULJzYSCb5xxBqVBibZcDnyWdKf4LCnFWcGzbORYP30JyghRzKxO8V3SnfK2fr8nMCn5GMXz3NJSJLefz+sE7tHW06L+gE56da6nlev8UQjUg5RCnXHIBA30SlTokKbVIVOggE7Qy7g6VGsiUf90dpt0dirtDTYkGglyCMo3uUFOpQbxU7A5tDU1481nsDgtaWPA5JjHVhcbJwZ5rL96RKJejr61F/eJFOXHvKZEJSWhqSGhfpRzPQz9x7rFqrJk3Fx2qlWfJ0fO8DBd3ZY0rlaBl1VLM2HWSe6/FwlqzZH7GtHDl+I3HLNp/lmSZAkM9HYY1r0kDx+LsOnWLRXtCSJaKNm9DWtWkcY1ShEXGMW11EJfuqt6vSG7Gdfcgj7UZ8YlSFm0+xYETYuGxszFnXB9PShUWM92iYhKYvTKYUxdU4cD5rBg7sC757XOm/oyevwpn2twjPFWxQNML/z134Qlz5gekivU7tK1Ku9ZV/yLWT8HZs4+ZN+coUSnC/k7VadM27SgogOioBBb4HiHklGhCULS4LT7jGmGX98cdlVKpZN/Wi6xbelzUK5rqM3BUfZzrZN4yLDYmkSXTDnFK1c0VKm6Lz4wW2OXLmcFXpo2P7yKZM2Indy6L3byja3EGTW2GWQ71SBHiY5NYNmEPx/eKRJFCpe3wmd+ePNk0DcgKHlx7gW/fdYS+/oSGpgZth9al9SDP32oM+frRe6Z3WcHLB++QSCS0GupFh5EN1TaqVgd+RjFMiE1kdveVnDso/l406OVKL9/2f9vU/U8hVANSDnHeVUcwMCBJqUOSUpsEhU72ukOlODb9ujsUlBKUP9wd6hKtSrSw1jciLDYutTuMjksiSaZAV0uLgmYW3P8QhgQJ+S3MMdTU5t4HsThUsLPFSFOHkMcvAShqkxO3IgVYH3Kd+GSRDNPPrSrhn+PYcvaGSAQxM2ZCc1cevQ1n2ZGLyBQKTA30GNnchWK5czJp8zFuPxdHk9VL5mNsuzokJ8uYuC6QW0/F0Wq1kg6M7eRGTjMj9p+6w8Jtp0lIEser/VvVoGntMmhoSLhw8wUzVgUR/jkODYmEdg0q0q1ZNXR1tBAEgePnHjF3VXBqOHDXVtVo06gSWqobmEymYNPOC2zeKYb/WpgbMry/O07fjFiioxOYtyiI0yHijq5wIRtGDvcin8P3RSMyMp758wI4qwrTLVo0FyNGNcA+nXGhIAicCLrL4rmBxMUmiakUfWrTqHmlNNMyvsar52H4jt/H0xS9okdJ+vl4ZahX/BqnA+6waOpB4mJEEX63IR40aF0lW7R8hULJvvUhbJgbiFymwCyHEYOnN6eKi/osskIO32Th6F3ERSegq69Dr/GN8Wzt+NP3d/GxiSwZuYOTe0WiRonKBfBe3AlrO/WMgdWBpIRkVozewVGVeXXJqoUYsaoHOX+B7i6z+BnFUKlUsm3WQTZO3gNAiWqFGbd1IObW2R8R/ymEakDKIa69XgalgQFJgi6JSm2SlNpZ6A41kSo0M90daqKBXC6gJdFEKeer7lCBQgEGWtpoKCFeKkNbQ5NcBsZ/6Q4johOISUpGS0MDp7z2XHnxhiS5AgMdbeoVL8Kx20+ISUpGW1ODDo7lePgmjIvPVGQYh9y0cSzDoiPnePNJlDO0qFqKxhVLMG3nCR6maBHLFGRUCxcOX3zIskPnv4xQW7ngUbEw24NvsHSfarRqoMvwNi54ORbjQ0QMU1YFcv2hOF6tVNyesd3dsbE0ISYuiXkbThBwVqVJzJOD8X3rUiSfOJb8FBnPrGWBnL+m2jsWzsWYAXWxt/1yc/g2/NfTtSQDetTG6BuJw/GT91mw+BixcUloa2vSrVMNmjet9F1nIAgCwcH3WLQgiPh4VRRUj1o0aZp2FBRAeFgMs6cd4voVlfykfF68xzbMMJVCJpOzdfUZtq8LEV13chozbEIjKjhmfl8S8TGGuRP2cl2VvlHOsQBDJzclZxYSMb7Gi4cf8B2+nZcqxxiv1lXoMbK+2sJxwz+IfqW3VKYBVd1KMmhWK0x/gRD++K5LLBm9k8S4JAxN9Bno1wbnhhV++vtmBaf2XGbhkI0kxCZhYmHEsKVdqeJR+p++rFT8jGIIcPHwdWZ1XU5CTCKWtuaM3zGYItk0HvjXFcIlS5bg5+dHaGgoZcqUYdGiRVSuXDndz9+1axfjxo3j5cuXFCpUiFmzZuHl5ZX6cUEQmDBhAqtWrSIqKgonJyeWLVtGoUKZp5unHOLum4WQGOoTL+iRoNRRFcGf1x3qaGiRnObu8Eve4de7Q1sjYyJjE0mSKdDX0iKfqTkPQsPF4mhpgZ5Ei/uq7rCSfW500eT8U5HFV8LWilqF8rHhzHUSpDL0tbXo71aN9xHRbDsnEkFyW5gwvrkrt5+HsirwkqhFNNJnbEtX8ltbMH5DIPdfiSNUlzIFGN3WlZi4JCasDeD+S9VotWwBRnWog4WxAbuCb7Bk51lxjKqnw5B2NWngLPp/nr7yhFmrg0VNooaETo2r0KWJuBsUBIGjJ++xYN0J4hPEcOBe7WrQ3Kt8amFKlspZu/ksO/ZfQRDAytKYkYPrfhf+G/EpltnzA7ikGgGWKpGHEcO9yJ2G1i08PIbZvke4qoqCKlPWHp8R9bBJx+VFEAT8919n5aJgkpJkGBjq0newO+5epTPseB7efYvf+H28fS3qLhu0qET3gW6Z1vgJgsChHZdYMzeQ5CQZRsZ69BvdAJd6ZTL19d9Cmixjw7xA9q4NAcA2bw68Z7emaJnMu+T8CEqlkr2rT7PB7zBymQLznMYM9WtDxVo/36D5w6sIfPut5+E18efq1tqRPlNboG/48xmtmcX75x+Z3nUFT1Ws22b93ek8rukvyYHMDH5WMXzz+AOTWs7nzaP3aOtqM2BhZzw6Omf5df5VhXDHjh107NiR5cuXU6VKFebPn8+uXbt49OgRVlbf7w7Onz+Ps7MzM2bMoH79+mzdupVZs2Zx/fp1SpYsCcCsWbOYMWMGGzZsIF++fIwbN447d+5w//599PQy94uecojHbtsjMdQjQdAhQdAhTqGb2h2KHaKO+P8KbaSCFtJMdIdSpQak0R1qSTRJ/kF3qK+lgzRZgUIpYKitDXJIkIndoY2+EW8jY5AgoVCOHIRFxhGbLEVbQ4Nqee259OI1UrkSQx0dvIoVIuj2E/Hjmpp0rFqOOy8/cPWFKlC3oB1Ny5dg0dHzvPusCgR2KkvdskWYtvM4T96LWkTP8kXwblqT/WfvsvLIReQKJWaGeoxsU5vaZQuxMeAKKw9eQK5QYmqox4h2rrhXLsLrD5FMXhXAHZVJt1OZfIzq6kZOcyOiYhLwW3ucE5dUu0EHK8b3rUsBO9FvNDQ8hplLA7l6WxUOXMKO0f09yfUVy+72vbfMmH+E96Ffwn97dXJG/yuPQ0EQOBJwmyUrTpCYItbv4ULD+mXTjHc6dPAGK5aLUVAGBjr07VcHz7rpF7d3bz/jO/kg91VCeCfnIgzy8cI8A1uzpCQpqxcc49AucXyX294Cn8lNKfoDSce3ePMiHL8xu3l8V/x51vQsRf8xDTDOwrj1a9y88JQ5I3YSERotEnN6u9Cmr6vaiC5P777Fb8hmXj8RH5wadq5B15H1f7pfqVymYMucI+xYGIggCOTOb8WIpV0opKZCrw5Ik2WsHr+LgytPAFCkQj5Gre2Fjf0/E230LX5WMYyPScS323Iu+osyqAa96tDbrx1a/2vv3sOiqtY/gH8HmBlRkBFRYFAQFS8ZiKCMaEkFJuRJTU8gWhKZt9T0KF4flfRXYZmXfmZmJuovU1MzPI8WeYOOcZFA8C4hoRhyUTmD3C8z7++PkV1bIEwZGJj38zz7EdZes2e9LuCdfVlrSR/9Q0CrSoQqlQpDhgzBp59+CkD3KbF79+6YO3culi5dWqd+UFAQSktLcfToUaFs6NChcHd3x+effw4iglKpxMKFCxEWFgYAKCoqgq2tLXbt2oWJEyc+Urtq/xPPXbIFWchQQlKUPjgjLCVzlAmXSP98dihFpdb0wdmh7kyxSvvHWWFNPWeHWq1uEm/R2aFGAq1WfO/Q3ESqm7O0kbPDwvvlqKzRoL1Uih4dFcLZoYtNZ0hJgmv5uiQ21Kk7TLVAwoNLo27d7DDc2Qm7z6To1jaUSTHvxeHIzL2LQ4m6Sba7d7ZC+Kt++CX9FiJP/jEWcdVEPyg7dcSq3T/i1991Y9xGevbB0okv4O5/SxAeGY1fb+nK/Qb3wdLJvrDsIMfeH1Kw7dt43STdHeRY8Nrz8B+mW0niZMI1rIs8JdwbfOuf3pj0D929QSJC1I/n8dlXP6G8ohrm7aSYE/Icxoz8IzGVlVdh266fEPV9GgDAwV6BZfMD4PqUOKHk5RXhw/XfI+3BYP3BHj2w6F8B9S7ZlJNTiA8jjuLygyWXhnr3xsKwAFg3cDlPo9Hi4N5E7N4eK8xxOm/JS3jmEaY1S0nMxIY1Ubhb8GBcZeizmPTWCEgf8Q9BTbVuEP7eL2IfrFyvG4TvOezxBuGX3C/HltVRiH0wS04f125Y9PFEdHvMB3MeVllRhci1R/HvXbqzT0cXWyze1DzzlV5MyMBHc3bh7m01zKSmmLLkZUyY5WtQU5/FH0vFhtk7UVJUhg4dzfGvzW/gGQO5nKuvZKjVarF37RF89T+HAQBPD++LFV/PfeT7hq0mEVZVVaF9+/Y4dOgQxo0bJ5SHhIRArVbjyJEjdV7j6OiIBQsWYP78+UJZeHg4oqKicP78efz222/o1asXUlNT4e7uLtTx8fGBu7s7Pvnkk3rbUllZicrKSuH7oqIiODo6IjmpC0w6mKBUa4oykqJUK0UZyVFGclRodWeJFVrdZdESTTtUac1QpTVDhcYMGpigTCODliSo1JhBo5WgSvhXCkCCSo0EEpigslr3S6ep0Q27kErMUFGlBSCBGcxQrdFCamICTSWgJcBCqpvMW6MlWMnloGpCSXU1zCSm6GPVGVcLdInneWdnpGbfxv2KKpiZmiLYzRUHzl1ElUYDhbkcM4Z54fOYsyiurILc1BQbA1/C9phfcP6W7t5Q6LOe8HBS4oPDMch/sCDwJ6Evw0Imx3vfnBKeNl0R+AJGuvfB7hPJ2HMyBRotwbaTJfYumwSJRIKvfkzGnh+TdeXWltizcjJkUjNk5dzDh7tP4tcbuvbOeHUYgkZ6AADu/bcEG/4vBonnbwAARg3vh8VTRwp9dDtfjfVfnMTFdN0DOq+N88KUfw4V9WvK+ZvY9PlJ3L2na/sHK16Bu6v4E79WS/j3sVTs/ioOVdU1sLRoh+2fhcKynoHfGo0W3x1Owd6v41BdrUGnTh2wbfubDc5IAwC/ZRZg09pjuPlgIPycMH+M9G/8fk/x/XJ8+b/H8Z8TVwAA3s/1xeLV4xt93Z9lXM7BptVHkHtLd7l16YeB8BrR8GTjjTkTfQHbI46h9H45ZOZSbP5uLmxsFY99vIel/Ccdn606BPXdYphKTbH+0Dx076X/p0qL/1uKrSsP4uyD4TMvv+mDN5aN0fv7/h0Ftwqxfm4kMs7dAAAs/OxNDP+HR8s26oHKmkq8dvg1HM88LpS1l7bHt4HfYpjjsCc6dlJ0Gja9vQPlJRXo1leJTbHhj/S07/3799G9e3eo1WpYWTWSPKkF5eTkEACKj48XlS9atIi8vLzqfY1UKqW9e/eKyrZs2UJdu3YlIqK4uDgCQLdv3xbVefXVVykwMLDBtoSHhxMA3njjjTfe2tB269atRnORYdx1NQDLli3DggULhO/VajWcnJyQnZ3d+KeJVqj209KtW7cavWzQGnF8rRvH17oZQnxEhOLiYiiVykbrtmgitLGxgampKfLz80Xl+fn5sLOrf4Z+Ozu7v6xf+29+fj7s7e1Fdf58qfRhcrkccnnd1QSsrKza5A9qrY4dO3J8rRjH17pxfPr1qCcxLXo3WCaTwdPTE6dOnRLKtFotTp06BW9v73pf4+3tLaoPACdOnBDqOzs7w87OTlTn/v37OHv2bIPHZIwxZrxa/NLoggULEBISgsGDB8PLywubNm1CaWkpQkNDAQBTpkyBg4MDIiIiAADz5s2Dj48P1q9fj9GjR2P//v1ITk7GF198AQCQSCSYP38+3nvvPbi4uAjDJ5RKpeiBHMYYYwwwgEQYFBSEO3fuYNWqVcjLy4O7uzuio6Nha6ubVSQ7O1v0GPOwYcOwd+9erFixAsuXL4eLiwuioqKEMYQAsHjxYpSWlmL69OlQq9V45plnEB0d/chjCAHdpdLw8PB6L5e2BRxf68bxtW4cn2Fp8XGEjDHGWEsynBGjjDHGWAvgRMgYY8yocSJkjDFm1DgRMsYYM2qcCBljjBm1NpsIt2zZgh49eqBdu3ZQqVRISkr6y/oHDx5Ev3790K5dO7i6uuL7778X7ScirFq1Cvb29jA3N4efnx8yMjJEdQoLCzF58mR07NgRCoUCU6dORUlJSZPHBjRtfNXV1ViyZAlcXV3RoUMHKJVKTJkyBbdv3xYdo0ePHpBIJKJt7dq1Bh8fALzxxht12u7v7y+q01r7D0Cd2Gq3devWCXUMtf8uX76MCRMmCO3btGnTYx2zoqICs2fPRufOnWFhYYEJEybUmYWqqTR1fBERERgyZAgsLS3RtWtXjBs3Dunp6aI6zz33XJ3+mzlzZlOHBqDp43v33XfrtL1fP/EqLM3Zf3U0OhtpK7R//36SyWQUGRlJly9fpmnTppFCoaD8/Px668fFxZGpqSl99NFHdOXKFVqxYgVJpVK6ePGiUGft2rVkZWVFUVFRdP78eRozZgw5OztTeXm5UMff358GDhxIiYmJdObMGerduzcFBwcbfHxqtZr8/Pzom2++oWvXrlFCQgJ5eXmRp6en6DhOTk60Zs0ays3NFbaSkhKDj4+IKCQkhPz9/UVtLywsFB2ntfYfEYniys3NpcjISJJIJJSZmSnUMdT+S0pKorCwMNq3bx/Z2dnRxo0bH+uYM2fOpO7du9OpU6coOTmZhg4dSsOGDWsV8Y0aNYp27txJly5dorS0NHrppZfI0dFR1D8+Pj40bdo0Uf8VFRW1ivjCw8NpwIABorbfuXNHVKe5+q8+bTIRenl50ezZs4XvNRoNKZVKioiIqLd+YGAgjR49WlSmUqloxowZRESk1WrJzs6O1q1bJ+xXq9Ukl8tp3759RER05coVAkC//PKLUOeHH34giURCOTk5TRYbUdPHV5+kpCQCQDdv3hTKnJyc6v0hb2r6iC8kJITGjh3b4Hu2tf4bO3YsvfDCC6IyQ+2/P2uojY0dU61Wk1QqpYMHDwp1rl69SgAoISHhCaKpSx/xPaygoIAA0E8//SSU+fj40Lx58x6nyX+LPuILDw+ngQMHNvi65uy/+rS5S6NVVVVISUmBn5+fUGZiYgI/Pz8kJCTU+5qEhARRfQAYNWqUUD8rKwt5eXmiOlZWVlCpVEKdhIQEKBQKDB48WKjj5+cHExMTnD171qDjq09RUREkEgkUCoWofO3atejcuTMGDRqEdevWoaam5vGDqYc+44uNjUXXrl3Rt29fzJo1C/fu3RMdo630X35+Po4dO4apU6fW2WeI/dcUx0xJSUF1dbWoTr9+/eDo6PjY7/u4bWkKRUVFAABra2tR+ddffw0bGxs8/fTTWLZsGcrKyprsPQH9xpeRkQGlUomePXti8uTJyM7OFvY1V/81pMWnWGtqd+/ehUajEaZoq2Vra4tr167V+5q8vLx66+fl5Qn7a8v+qk7XruIFRM3MzGBtbS3UaQr6iO9hFRUVWLJkCYKDg0Uzx7/zzjvw8PCAtbU14uPjsWzZMuTm5mLDhg1PGNUf9BWfv78/xo8fD2dnZ2RmZmL58uUICAhAQkICTE1N21T/7d69G5aWlhg/XryIr6H2X1McMy8vDzKZrM4Ht7/6f9JXW56UVqvF/PnzMXz4cNHUkZMmTYKTkxOUSiUuXLiAJUuWID09HYcPH26S9wX0F59KpcKuXbvQt29f5ObmYvXq1Xj22Wdx6dIlWFpaNlv/NaTNJUL2ZKqrqxEYGAgiwtatW0X7/rxeo5ubG2QyGWbMmIGIiAiDn1Nw4sSJwteurq5wc3NDr169EBsbC19f3xZsWdOLjIzE5MmT68yt25r7z5jMnj0bly5dws8//ywqnz59uvC1q6sr7O3t4evri8zMTPTq1au5m/m3BAQECF+7ublBpVLByckJBw4cqPfKRXNrc5dG9b3G4V/VKSgoEO2vqalBYWFhg+/7OPQRX63aJHjz5k2cOHGi0XXEVCoVampqcOPGjb8fSAP0Gd+f9ezZEzY2Nrh+/bpwjNbefwBw5swZpKen46233mq0LYbSf01xTDs7O1RVVUGtVjfZ+z5uW57EnDlzcPToUcTExKBbt25/WVelUgGA8DPcFPQdXy2FQoE+ffqIfv+ao/8a0uYSYUutcejt7Q21Wo2UlBShzunTp6HVaoUfWEOND/gjCWZkZODkyZPo3Llzo21JS0uDiYlJnUuKT0Jf8T3s999/x71794TFm1t7/9XasWMHPD09MXDgwEbbYij91xTH9PT0hFQqFdVJT09HdnZ2k65Dqo/4AN3wrDlz5uC7777D6dOn4ezs3Ohr0tLSAEC0APmT0ld8DyspKUFmZqbQ9ubqvwbp/XGcFrB//36Sy+W0a9cuunLlCk2fPp0UCgXl5eUREdHrr79OS5cuFerHxcWRmZkZffzxx3T16lUKDw+vd/iEQqGgI0eO0IULF2js2LH1Dp8YNGgQnT17ln7++WdycXHR2+P3TRlfVVUVjRkzhrp160ZpaWmiR5wrKyuJiCg+Pp42btxIaWlplJmZSXv27KEuXbrQlClTDD6+4uJiCgsLo4SEBMrKyqKTJ0+Sh4cHubi4UEVFhXCc1tp/tYqKiqh9+/a0devWOu9pyP1XWVlJqamplJqaSvb29hQWFkapqamUkZHxyMck0j1+7+joSKdPn6bk5GTy9vYmb2/vVhHfrFmzyMrKimJjY0W/f2VlZUREdP36dVqzZg0lJydTVlYWHTlyhHr27EkjRoxoFfEtXLiQYmNjKSsri+Li4sjPz49sbGyooKBAqNNc/VefNpkIiYg2b95Mjo6OJJPJyMvLixITE4V9Pj4+FBISIqp/4MAB6tOnD8lkMhowYAAdO3ZMtF+r1dLKlSvJ1taW5HI5+fr6Unp6uqjOvXv3KDg4mCwsLKhjx44UGhpKxcXFBh9fVlYWAah3i4mJISKilJQUUqlUZGVlRe3ataP+/fvTBx98IEokhhpfWVkZvfjii9SlSxeSSqXk5ORE06ZNE/0RJWq9/Vdr27ZtZG5uTmq1us4+Q+6/hn7+fHx8HvmYRETl5eX09ttvU6dOnah9+/b0yiuvUG5ubquIr6Hfv507dxIRUXZ2No0YMYKsra1JLpdT7969adGiRXoZR6iP+IKCgsje3p5kMhk5ODhQUFAQXb9+XfSezdl/D+P1CBljjBm1NnePkDHGGPs7OBEyxhgzapwIGWOMGTVOhIwxxowaJ0LGGGNGjRMhY4wxo8aJkDHGmFHjRMgYY8yocSJkjDFm1DgRMtbG7du3D+bm5sjNzRXKQkND4ebmJiwAy5gx4ynWGGvjiAju7u4YMWIENm/ejPDwcERGRiIxMREODg4t3TzGWhyfETLWxkkkErz//vvYvn073n//fWzevBnR0dFCEjx69Cj69u0LFxcXfPnlly3cWsaaH58RMmYkPDw8cPnyZRw/fhw+Pj4AdIsPP/XUU4iJiYGVlRU8PT0RHx//SOtRMtZW8BkhY0YgOjoa165dg0ajga2trVCelJSEAQMGwMHBARYWFggICMDx48dbsKWMNT9OhIy1cefOnUNgYCB27NgBX19frFy5Uth3+/Zt0X1CBwcH5OTktEQzGWsxZi3dAMaY/ty4cQOjR4/G8uXLERwcjJ49e8Lb2xvnzp2Dh4dHSzePMYPAZ4SMtVGFhYXw9/fH2LFjsXTpUgCASqVCQEAAli9fDgBQKpWiM8CcnBwolcoWaS9jLYUflmHMiNXU1KB///6IjY3lh2WY0eJLo4wZMTMzM6xfvx7PP/88tFotFi9ezEmQGR0+I2SMMWbU+B4hY4wxo8aJkDHGmFHjRMgYY8yocSJkjDFm1DgRMsYYM2qcCBljjBk1ToSMMcaMGidCxhhjRo0TIWOMMaPGiZAxxphR40TIGGPMqP0/tIw+O9DBtQIAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "k = list(df[\"k\"])\n", "a = list(df[\"a\"])\n", "b = list(df[\"b\"])\n", "\n", "f = lambda x0, x1: alpha / (R0 + x0 / k[0] + x1 / k[1]) + beta * (\n", " a[0] + b[0] * x0 + a[1] + b[1] * x1\n", ")\n", "\n", "x0 = np.linspace(0, 1.1 * T, 201)\n", "x1 = np.linspace(0, 1.1 * T, 201)\n", "\n", "X0, X1 = np.meshgrid(x0, x1)\n", "\n", "fig, ax = plt.subplots(1, 1)\n", "ax.contour(x0, x1, f(X0, X1), 50)\n", "ax.set_xlim(min(x0), max(x0))\n", "ax.set_ylim(min(x1), max(x1))\n", "ax.plot([0, T], [T, 0], \"g\", lw=2.5)\n", "\n", "ax.set_aspect(1)\n", "\n", "x = df[\"x_opt\"].to_list()\n", "\n", "ax.plot(x[0], x[1], \"r.\", ms=20)\n", "ax.text(x[0], x[1], f\" ({x[0]:0.4f}, {x[1]:0.4f})\")\n", "\n", "ax.set_xlabel(r\"$x_0$\")\n", "ax.set_ylabel(r\"$x_1$\")\n", "ax.set_title(\"Contours of Constant Cost\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "id": "c19B4gzzKAqx", "tags": [] }, "source": [ "## Bibliographic Notes\n", "\n", "To the best of my knowledge, this problem is not well-known example in the mathematical optimization literature. There are a number of application papers with differing levels of detail. \n", "\n", "> Hasan, A. (1999). Optimizing insulation thickness for buildings using life cycle cost. Applied energy, 63(2), 115-124. https://www.sciencedirect.com/science/article/pii/S0306261999000239\n", "\n", "> Kaynakli, O. (2012). A review of the economical and optimum thermal insulation thickness for building applications. Renewable and Sustainable Energy Reviews, 16(1), 415-425. https://www.sciencedirect.com/science/article/pii/S1364032111004163\n", "\n", "> Nyers, J., Kajtar, L., Tomić, S., & Nyers, A. (2015). Investment-savings method for energy-economic optimization of external wall thermal insulation thickness. Energy and Buildings, 86, 268-274. https://www.sciencedirect.com/science/article/pii/S0378778814008688\n", "\n", "More recently some modeling papers have appeared\n", "\n", "> Gori, P., Guattari, C., Evangelisti, L., & Asdrubali, F. (2016). Design criteria for improving insulation effectiveness of multilayer walls. International Journal of Heat and Mass Transfer, 103, 349-359. https://www.sciencedirect.com/science/article/abs/pii/S0017931016303647\n", "\n", "> Huang, H., Zhou, Y., Huang, R., Wu, H., Sun, Y., Huang, G., & Xu, T. (2020). Optimum insulation thicknesses and energy conservation of building thermal insulation materials in Chinese zone of humid subtropical climate. Sustainable Cities and Society, 52, 101840. https://www.sciencedirect.com/science/article/pii/S221067071931457X\n", "\n", "> Söylemez, M. S., & Ünsal, M. (1999). Optimum insulation thickness for refrigeration applications. Energy Conversion and Management, 40(1), 13-21. https://www.sciencedirect.com/science/article/pii/S0196890498001253\n", "\n", "> Açıkkalp, E., & Kandemir, S. Y. (2019). A method for determining optimum insulation thickness: Combined economic and environmental method. Thermal Science and Engineering Progress, 11, 249-253. https://www.sciencedirect.com/science/article/pii/S2451904918305377\n", "\n", "> Ylmén, P., Mjörnell, K., Berlin, J., & Arfvidsson, J. (2021). Approach to manage parameter and choice uncertainty in life cycle optimisation of building design: Case study of optimal insulation thickness. Building and Environment, 191, 107544. https://www.sciencedirect.com/science/article/pii/S0360132320309112" ] } ], "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": "3.9.6" } }, "nbformat": 4, "nbformat_minor": 4 }