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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# CompMech04-Linear Algebra Project\n",
"# Practical Linear Algebra for Finite Element Analysis\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this project we will perform a linear-elastic finite element analysis (FEA) on a support structure made of 11 beams that are riveted in 7 locations to create a truss as shown in the image below. \n",
"\n",
"![Mesh image of truss](../images/mesh.png)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The triangular truss shown above can be modeled using a [direct stiffness method [1]](https://en.wikipedia.org/wiki/Direct_stiffness_method), that is detailed in the [extra-FEA_material](./extra-FEA_material.ipynb) notebook. The end result of converting this structure to a FE model. Is that each joint, labeled $n~1-7$, short for _node 1-7_ can move in the x- and y-directions, but causes a force modeled with Hooke's law. Each beam labeled $el~1-11$, short for _element 1-11_, contributes to the stiffness of the structure. We have 14 equations where the sum of the components of forces = 0, represented by the equation\n",
"\n",
"$\\mathbf{F-Ku}=\\mathbf{0}$\n",
"\n",
"Where, $\\mathbf{F}$ are externally applied forces, $\\mathbf{u}$ are x- and y- displacements of nodes, and $\\mathbf{K}$ is the stiffness matrix given in `fea_arrays.npz` as `K`, shown below\n",
"\n",
"_note: the array shown is 1000x(`K`). You can use units of MPa (N/mm^2), N, and mm. The array `K` is in 1/mm_\n",
"\n",
"$\\mathbf{K}=EA*$\n",
"\n",
"$ \\left[ \\begin{array}{cccccccccccccc}\n",
" 4.2 & 1.4 & -0.8 & -1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
" 1.4 & 2.5 & -1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
" -0.8 & -1.4 & 5.0 & 0.0 & -0.8 & 1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
" -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
" -3.3 & 0.0 & -0.8 & 1.4 & 8.3 & 0.0 & -0.8 & -1.4 & -3.3 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
" 0.0 & 0.0 & 1.4 & -2.5 & 0.0 & 5.0 & -1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
" 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & -1.4 & 8.3 & 0.0 & -0.8 & 1.4 & -3.3 & 0.0 & 0.0 & 0.0 \\\\\n",
" 0.0 & 0.0 & 0.0 & 0.0 & -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 & 0.0 & 0.0 & 0.0 & 0.0 \\\\\n",
" 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & 1.4 & 8.3 & 0.0 & -0.8 & -1.4 & -3.3 & 0.0 \\\\\n",
" 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.4 & -2.5 & 0.0 & 5.0 & -1.4 & -2.5 & 0.0 & 0.0 \\\\\n",
" 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & -1.4 & 5.0 & 0.0 & -0.8 & 1.4 \\\\\n",
" 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -1.4 & -2.5 & 0.0 & 5.0 & 1.4 & -2.5 \\\\\n",
" 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & -3.3 & 0.0 & -0.8 & 1.4 & 4.2 & -1.4 \\\\\n",
" 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.4 & -2.5 & -1.4 & 2.5 \\\\\n",
"\\end{array}\\right]~\\frac{1}{m}$"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fea_arrays = np.load('./fea_arrays.npz')\n",
"K=fea_arrays['K']*1000\n",
"\n",
"def LUNaive(A):\n",
" '''LUNaive: naive LU decomposition\n",
" L,U = LUNaive(A): LU decomposition without pivoting.\n",
" solution method requires floating point numbers, \n",
" as such the dtype is changed to float\n",
" \n",
" Arguments:\n",
" ----------\n",
" A = coefficient matrix\n",
" returns:\n",
" ---------\n",
" L = Lower triangular matrix\n",
" U = Upper triangular matrix\n",
" '''\n",
" [m,n] = np.shape(A)\n",
" if m!=n: error('Matrix A must be square')\n",
" nb = n+1\n",
" # Gauss Elimination\n",
" U = A.astype(float)\n",
" L = np.eye(n)\n",
"\n",
" for k in range(0,n-1):\n",
" for i in range(k+1,n):\n",
" if U[k,k] != 0.0:\n",
" factor = U[i,k]/U[k,k]\n",
" L[i,k]=factor\n",
" U[i,:] = U[i,:] - factor*U[k,:]\n",
" return L,U\n",
"\n",
"def solveLU(L,U,b):\n",
" '''solveLU: solve for x when LUx = b\n",
" x = solveLU(L,U,b): solves for x given the lower and upper \n",
" triangular matrix storage\n",
" uses forward substitution for \n",
" 1. Ly = b\n",
" then backward substitution for\n",
" 2. Ux = y\n",
" \n",
" Arguments:\n",
" ----------\n",
" L = Lower triangular matrix\n",
" U = Upper triangular matrix\n",
" b = output vector\n",
" \n",
" returns:\n",
" ---------\n",
" x = solution of LUx=b '''\n",
" n=len(b)\n",
" x=np.zeros(n)\n",
" y=np.zeros(n)\n",
" \n",
" # forward substitution\n",
" for k in range(0,n):\n",
" y[k] = b[k] - L[k,0:k]@y[0:k]\n",
" # backward substitution\n",
" for k in range(n-1,-1,-1):\n",
" x[k] = (y[k] - U[k,k+1:n]@x[k+1:n])/U[k,k]\n",
" return x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this project we are solving the problem, $\\mathbf{F}=\\mathbf{Ku}$, where $\\mathbf{F}$ is measured in Newtons, $\\mathbf{K}$ `=E*A*K` is the stiffness in N/mm, `E` is Young's modulus measured in MPa (N/mm^2), and `A` is the cross-sectional area of the beam measured in mm^2. \n",
"\n",
"There are three constraints on the motion of the joints:\n",
"\n",
"i. node 1 displacement in the x-direction is 0 = `u[0]`\n",
"\n",
"ii. node 1 displacement in the y-direction is 0 = `u[1]`\n",
"\n",
"iii. node 7 displacement in the y-direction is 0 = `u[13]`\n",
"\n",
"We can satisfy these constraints by leaving out the first, second, and last rows and columns from our linear algebra description. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1. Calculate the condition of `K` and the condition of `K[2:13,2:13]`. \n",
"\n",
"a. What error would you expect when you solve for `u` in `K*u = F`? \n",
"\n",
"b. Why is the condition of `K` so large?\n",
"\n",
"c. What error would you expect when you solve for `u[2:13]` in `K[2:13,2:13]*u=F[2:13]`"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The condition of K is 6.640986594413607e+16\n",
"The condition of K[2:13,2:13] is 52.23542514351013\n",
"\n",
"\n",
"The expected error of u is 6.640986594413607\n",
"The expected error of u[2:13] is 5.223542514351013e-15\n"
]
}
],
"source": [
"cond1 = np.linalg.cond(K)\n",
"cond2 = np.linalg.cond(K[2:13,2:13])\n",
"\n",
"error1 = cond1*1e-16\n",
"error2 = cond2*1e-16\n",
"\n",
"print('The condition of K is',cond1)\n",
"print('The condition of K[2:13,2:13] is',cond2)\n",
"print('\\n')\n",
"print('The expected error of u is',error1)\n",
"print('The expected error of u[2:13] is',error2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_The condition of K is so large because it's easily affected by the input. It can be described as \"ill-conditioned\"._"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2. Apply a 100-N downward force to the central top node (n 4)\n",
"\n",
"a. Create the LU matrix for K[2:13,2:13]\n",
"\n",
"b. Use cross-sectional area of $0.1~mm^2$ and steel and almuminum moduli, $E=200~GPa~and~E=70~GPa,$ respectively. Solve the forward and backward substitution methods for \n",
"\n",
"* $\\mathbf{Ly}=\\mathbf{F}\\frac{1}{EA}$\n",
"\n",
"* $\\mathbf{Uu}=\\mathbf{y}$\n",
"\n",
"_your array `F` is zeros, except for `F[5]=-100`, to create a -100 N load at node 4._\n",
"\n",
"c. Plug in the values for $\\mathbf{u}$ into the full equation, $\\mathbf{Ku}=\\mathbf{F}$, to solve for the reaction forces\n",
"\n",
"d. Create a plot of the undeformed and deformed structure with the displacements and forces plotted as vectors (via `quiver`). Your result for aluminum should match the following result from [extra-FEA_material](./extra-FEA_material.ipynb). _note: The scale factor is applied to displacements $\\mathbf{u}$, not forces._\n",
"\n",
"![Deformed structure with loads applied](../images/deformed_truss.png)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"L,U = LUNaive(K[2:13,2:13])\n",
"\n",
"A = 1e-7\n",
"E_steel = 200e9\n",
"E_aluminum = 70e9\n",
"F = np.zeros(11)\n",
"F[5] = -100\n",
"\n",
"u_steel = solveLU(L,U,F/E_steel/A)\n",
"u_aluminum = solveLU(L,U,F/E_aluminum/A)\n",
"\n",
"u_1 = np.zeros(14)\n",
"for i in range(len(u_steel)):\n",
" u_1[i+2] = u_steel[i]\n",
" \n",
"u_2 = np.zeros(14)\n",
"for i in range(len(u_aluminum)):\n",
" u_2[i+2] = u_aluminum[i]\n",
"\n",
"F_steel = K*E_steel*A@u_1\n",
"F_aluminum = K*E_aluminum*A@u_2"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\tSTEEL\n",
"----------------------\n",
"\n",
"\n",
"Force:\n",
"F_1x = 0.00 Newtons\n",
"F_1y = 50.00 Newtons\n",
"F_2x = 0.00 Newtons\n",
"F_2y = 0.00 Newtons\n",
"F_3x = -0.00 Newtons\n",
"F_3y = -0.00 Newtons\n",
"F_4x = -0.00 Newtons\n",
"F_4y = -100.00 Newtons\n",
"F_5x = 0.00 Newtons\n",
"F_5y = 0.00 Newtons\n",
"F_6x = -0.00 Newtons\n",
"F_6y = 0.00 Newtons\n",
"F_7x = -0.00 Newtons\n",
"F_7y = 50.00 Newtons\n",
"\n",
"\n",
"Displacement:\n",
"u_1x = 0.00 millimeters\n",
"u_1y = 0.00 millimeters\n",
"u_2x = 1.95 millimeters\n",
"u_2y = -2.12 millimeters\n",
"u_3x = 0.43 millimeters\n",
"u_3y = -4.00 millimeters\n",
"u_4x = 1.08 millimeters\n",
"u_4y = -5.37 millimeters\n",
"u_5x = 1.73 millimeters\n",
"u_5y = -4.00 millimeters\n",
"u_6x = 0.22 millimeters\n",
"u_6y = -2.12 millimeters\n",
"u_7x = 2.17 millimeters\n",
"u_7y = 0.00 millimeters\n"
]
},
{
"data": {
"image/png": 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887UaqBXJ82Tp0E6iao+tDMMwDONQx8YQGIZhGIZhgsAwDMMwDBMEhmEYhmFggsAwDMMwDA7RaYd16tTR5s2bR9oMwzCMSsWCBQu2qGrdkmsalZFDUhA0b96c9PRg6+oYhmEYRSEiayJtg1F+2CMDwzAMwzBMEBiGYRiGYYLAMAzDMAxMEBiGYRiGgQkCwzAMwzAwQWAYhmEYBiYIDMMwDMPABIFhGIZhGJggMAzDMAwDEwSGYRiGYRClgkBEYkVkoYi8571PE5FPRGSFt60dUHekiPwqIstE5PTIWW0YhmEYlZeoFATATcAvAe//DsxS1TbALO89ItIBuAjoCJwBTBCR2Aq21TAMwzAqPVEnCESkCXA2MCkg+xzgRe/1i8C5AfkzVDVbVX8DfgV6VZSthmEYhlFViDpBADwB3An4AvLqq+oGAG9bz8tvDKwNqLfOyyuEiAwXkXQRSd+8eXP4rTYMwzCMSkxUCQIR6Q9sUtUFoe4SJE+DVVTV51W1h6r2qFvXlvM2DMMwjEDiIm1AAY4HBojIWUASkCoirwAbRaShqm4QkYbAJq/+OuDwgP2bAOsr1GLDMAzDqAJElYdAVUeqahNVbY4bLPiZql4CvAtc5lW7DJjpvX4XuEhEEkWkBdAGmFfBZhuGYRhGpSfaPARF8TDwuohcBfwOXAigqotF5HVgCZALXK+qeZEz0zAMwzAqJ6Ia9JF7laZHjx6anp4eaTMMwzAqFSKyQFV7RNoOo3yIqkcGhmEYhmFEBhMEhmEYhmGYIDAMwzAMwwSBYRiGYRiYIDAMwzAMAxMEhmEYhmFggsAwDMMwDEwQGIZhGIaBCQLDMAzDMDBBYBiGYRgGJggMwzAMw8AEgWEYhmEYmCAwDMMwDAMTBIZhGIZhYILAMAzDMAxMEBiGYRiGgQkCwzAMwzAwQWAYhmEYBiYIDMMwDMPABIFhGIZhGESZIBCRJBGZJyKLRGSxiIzx8tNE5BMRWeFtawfsM1JEfhWRZSJyeuSsNwzDMIzKS1QJAiAb6KuqXYCuwBkicgzwd2CWqrYBZnnvEZEOwEVAR+AMYIKIxEbEcsMwDMOoxESVIFBHpvc23ksKnAO86OW/CJzrvT4HmKGq2ar6G/Ar0KsCTTYMwzCMKkFUCQIAEYkVkR+ATcAnqvodUF9VNwB423pe9cbA2oDd13l5wdodLiLpIpK+efPm8jsAwzAMw6iERJ0gUNU8Ve0KNAF6iUinYqpLsCaKaPd5Ve2hqj3q1q0bDlMNwzAMo8oQdYLAj6ruAGbjxgZsFJGGAN52k1dtHXB4wG5NgPUVaKZhGIZhVAmiShCISF0RqeW9Tgb6AUuBd4HLvGqXATO91+8CF4lIooi0ANoA8yrWasMwDMOo/ESVIAAaAp+LyI/AfNwYgveAh4FTRWQFcKr3HlVdDLwOLAE+Aq5X1byIWF4Jeewx6NABOneGU06BNWsibVHl5803QQTS0yNtSeXn9dfd9dmxIwwZEmlrDKPqExdpAwJR1R+BbkHytwKnFLHPWGBsOZtWJenWzf1xVasGzz4Ld94Jr70WaasqLxkZ8NRTcPTRkbak8rNiBTz0EHz1FdSuDZs2lbyPYRgHR7R5CIwwsHo1tG8Pw4a5u6vTToO9ewvXO/lkJwYAjjkG1q2rUDMrBaGeS4B77nGiKimpQk2sVIR6PidOhOuvd2IAoF69wnUMwwgvJgiqKCtWuB/UxYuhVi14663i60+eDGeeWTG2VTZCOZcLF8LatdC/f8XbV9kI5XwuX+7S8cc7sfrRRxVvp2EcakTVIwMjfLRoAV27utfdu7s7s6J45RX36GDOnAoxrdJR0rn0+eCWW2Dq1Iq2rHISyrWZm+uEw+zZznN1wgnw889OQBiGUT6Yh6CKkph44HVsrPuBDcann8LYsfDuu/n3KYl+/dzgOX/q1+/g7I1mSjqXGRnuz+qkk6B5c/j2WxgwoHQDCzt2zH8+O3YMh+XRSSjXZpMmcM45EB/vBMQRRziBECojRkBcnDuXcXHuvWEYxWMegkOYhQvhmmucO7Y0z2j79YNZs/LnzZqldO++jfHjfwLcD31V4M8/k9i9+0hmz54PwMqVh7N3byyzZ6/OV+/NNw+8vvnmrlx33UoyMzOYPbvkPi6/vDtr1qQQGGdryRKlefNMpk5dcPAHEUWEej5btkxj+vR6NG++lJ074/npp+6sX5/O7NlFKNsAnniiNTNnNsZ/PvPy3KBZgAkTwnk0hlG1ENWggf2qND169ND0KjwvbPVq9yz755/d+0cfhcxMGD06f71+/eCnn6BhQ/e+aVPnKSgJCRYfEnBBIqua06kZ8B5wpPf+NiAFGFPMPp8DtwOh/pn7KDro5qF8Pv+Ji0uWh5tIFOoUmByC3esU5ykzQkNEFqhqj0jbYZQPJgiMUlOcIEhMnENOTmEPglE0J598IkUJgs8/t4EdpWHqVHjxxaLOJxyCP3dhxQRB1cYeGRhhoR1L6Ml8Ps4+nV2k8uEHyYwbX6RyMPJR1L+UcNJJJ1WkIZWe446DaS9mUZMM0tjKFuqwjTpA1XmMZRjlhQkCo9Qce2wm33xTnQN3Ycov5B8Fl/NIHEypCampUDNgW9TrovIOgV/xlJQ1ZGY2I/9drdKhwyEmqHw+92xr507YtSv/tqQ873X8zp3sI3t/k3tIpj4bySSF4cMPsfNpGKXEBIFRaho0uBSREaieAggX8Mb+sg004AlupiY7Ob3NLrq3DvjhXrvWDWzw/4iH8kC3evXSiYhg5cnJxT3niChr1qxh9+6WCItQOuFEgQI/MmrUUmBQZA0MlezsUv95F8rLyCjZpx8T4z7XwM+4fn1o2xZSU/lm8WLe+/JLjqYX5zCPauxlNKMYGX8UTzwxCEiokNNhGJURG0NglIq5c+fSp08fxo4dS/fud3HZwF18v7cdG9hEK/KogVCHLewgjaSkoqP6oeoKy/LHEfh69+6SjY6LOzhBUbMm1Kjh2gkzRx99NPPmzWPG+eeT/lZPHuVvwBqgBbVr12LLli3ExJTjwMJgd+Wl+Qz82+zskvtKSiq9l6hgeUpKkeIuKyuLWrVqkZeXx0ZfKrV823mNv3Ahb9ADH1c88QQ33XRTmE/goYWNIajamCAwQsbn83HMMcewYcMGli1bRrVq1eCmm/A99TRH8wTHcBNPA+9wDgN5B4Cnn4YbbihHo3Jz3Z1lWe9KS+utKMujjyK8FV9++SUnnHACrVq14tehQ9kx+lFqswsQRC5A9S1Gjx7NvffeG9ye7OyDP+7S3JWXVUz57+gTyvfu/NJLL+Xll1/mzVNO4fxZs3iPs7mUl1hKO7am7uOE2BhWrFxJbX88ZKPUmCCo2pggMEJm+vTpDBkyhJdeeomhQ4fCggXQqxdcdx2ZDz9D3bpdWJf1I7UQGvAnW6hH9eruBjSqKeitKOufbCm9FYvXrWNLTg5devem1s6d8NNPPMO1XMMkpnEhGTGvUQsYfPbZxGZmFu4/lLvy5OSD945Urx61j1z8bNiwgSZNmlC9enV2xsXBzp0cHr+RP7LrMDz5Zf6991KuBVJuu41HH3000uZWWkwQVG1MEBghkZWVRbt27UhLSyM9PZ0Y1QMrIi1dCjVrsnTpUv7Zvj0Tgfc5k/58AMDLL8Mll0TW/gqhFN6KX7//niXffkvT1FS6tmzpgkfs2IGPA5EH9iQmsik7m5hatWjaqVPpB2RWwF15tNCnTx/mzp3L13/5C8e+/jqcey6Xpb7NSy9Bt67K97X6svvrr2mnypylS2nZsmWkTa6UmCCo4qjqIZe6d++uRukYP368Ajpr1iyX8a9/qYLq9On56p155pm6ETQPtCF/KKjWrBkBg6OYvLw8TU1N1ZiYGP3jjz9c5ujRqt5583lpSr9XCtczCjF//nwF9PDGjVVTU1VjYlS3btWNG90les01qvrLL+qLj9dXY2N10KBBkTa50gKkaxT8hlsqn1TVwqAZ5cCWLVsYO3Ys/fv3p2/fvvDnnzByJJx6KgzKPwp+2rRp/E2EGOD3ky6le3d3U/z225GxPRoZOXIku3btYvDgwTRq1ChfmQC38iiKcMGs63jiscfw+XwMGlRJZhtEgCFDhgAwu39/54U5/3xIS6NePbeI0umnA+3aIX/7G0Py8tj42mt8++23kTXaMKKRSCuSSCTzEJSOG2+8UWNjY3XJkiUuY/Bg1cRE1eXLg9a//vrrdYN3l6tr1ug336jeeWcFGhzFZGRkaHx8vCYmJurevXsPFFx8sToPgSj4dCqXqoLqDTdos2bNFNB58+ZFzvAo5bXXXlNAu3frppqSohobq7pz5/7yTz9V3X+a9+zRvBYtdEVsrJ54zDHq8/kiY3QlBvMQVOkUcQMikUwQhM6yZcs0Li5Or7vuOpfx8cfushkzpsh9cnJy9LKEBFXQ7OOOqyBLKwfnn3++Ajp69OgDmXl5qtWqufMKCj6NI1szSVaNidFvZs5UQFu3bh05w6OQvLw8TUtLUxHRrbfc4s7fxRcXv9OHH6qC3g365ptvVoyhVQgTBFU7RdyASCQTBKEzcOBArVGjhm7cuNHdarVurdq2rWpWVrH7PfXUU7rO7yX49dcKsja6Wb16tYqIpqWlaV5e3oGCe+5RvxhQ0CTZ6559M8HlHX+89urVSwGdMWNG5A4gyrjvvvsU0IHnnOMEVVycakZGifvlXXihZolo36ZNNTs7uwIsrTqYIKjaKeIGRCKZIAiNOXPmKKBjx451Gffe6y6ZTz8Naf8ra9VSH2hm167lZ2QlomfPnoX/1HfuVI2Pd65uTxC0T/h1vz7YXKO5KuiGGTNURLR27dr5xcQhyt69ezUxMVHj4uI064473Mm6/PLQdv7jD81JTtaPQJ94/PHyNbSKYYKgaqeIG5DPGDgct3bsL8Bi4CYvPw34BFjhbWsH7DMS+BVYBpweSj8mCEomLy9Pe/bsqU2aNNHdu3erLlummpCgOmRIyG189NFHutrvJVi6tBytjX7mzp2rgLZq1Sp/wZlnuq9h377qVwH31PnXfkFwdoP5qqC59RvqwIFBHjccogwdOlQBvePWW1WTkpx3YM+ekPf3PfGEKugV1avrtm3bytHSqoUJgqqdIm5APmOgIXCU97oGsBzoAIwH/u7l/x0Y573uACwCEoEWwEogtqR+TBCUzLRp0xTQl156SdXnUz3lFDd/cMOGUrVzfbNm6gPd2rZtOVlaOWjatGnhgYHff+++gg0a7J92qKAZR3TfLwji41XXdTxVFXTPmAeCD0g8xFi/fr3GxMRojRo1NO/22/XA3MJSkJOju9u31z9A777hhvIxtApigqBqp4gbUKxxMBM41bv7b+jlNQSWea9HAiMD6v8POLakdk0QFM/evXu1WbNm2q1bN+eefvVVd6lMmFDqtpYuXaqr/F6Cn34qB2ujn8mTJyugvXv3zl/QsqU7r7NmqY4erS8wVGuxVYemvh04pEBT2a77iFNNTNS7b7lFAb24pMFzVZgTTjhBAZ303HNutktCgmpZxgLMm6d5oM/ExOjKlSvDb2gVxARB1U4RN6BIw6A58DuQCuwoULbd2z4DXBKQPxm4oIj2hgPpQHrTpk3VKJp8QYi2bVOtV0+1Vy/V3NwytTeyZ0/1gW5o3DjMlkY/QYMQqapOmuS+fscc4957HgIhL58Y8KcHGKkKmjdwoKampqqIHJLBivYHITr8cNWbbnIn58Yby9xexmWXaS7oyFNPDaOVVRcTBFU7RdyAoEZBCrAAOM97X5Qg+FcQQXB+Se2bh6BoNm/erDVr1tT+/fu7jOuuc5Hfvv++zG1u375dl3tegpxDbC79nXfeWfiOPidHtXp1d17Xr3d5niD4K48FFQQx5KmmpamK6JsPPBDc43AI0KZNGwV0ziefOM9AYmLZvAN+duzQXSkpOh/0my+/DJ+hVRQTBFU7RV2kQhGJB94CXlXV/3jZG0WkoVfeENjk5a/DDUT00wRYX1G2VkXuu+8+MjMzGT9+PHz3HTz3HPz1r9CtW5nbrFWrFu+fcw4AG844I1ymRj2ZmZk8/vjjJCYmMmnSpAMFw4e7hZCGD4eGDfPt8yS3EkvhlRfjE2PghRdAlfNffZVmzZrx5fZUj+EAACAASURBVJdfMn/+/PI+jKjh9ddfZ8WKFfTo0YM+b70F+/bB9dcf3HoNNWsS//TT9AC+HjoU959nGIcokVYkgQkXufUl4IkC+Y+Qf1DheO91R/IPKlyFDSosM/mCEOXkqHbtqtq4sequXQfddk5Oji4VUR/o9o8+CoO10U/QIES//+48AykpLiCRn4BBhY/We7iQh6BWLa9e166qoL+MGnVIBSsKDEK0askSN9oyKcldpweLz6drO3TQnaDvPf/8wbdXhcE8BFU6RdyAfMZAb0CBH4EfvHQWcBgwCzftcBaQFrDP3bjZBcuAM0PpxwRBcPIFIfKmZWkYo7m9fvPN6gP9rXr1sLUZrRQZhKhHD3deX3wx/w4BgkA7dtTERM0nCJo339+wqohqaqr26tHjkAlWtD8I0cCBqlde6U7KyJFhaz/3l180S0T/m5JiwYqKwQRB1U4RNyASyQRBYfIFIVq3zt3BnnWWm3IYRpbExakP9NepU8PabrQRNAjRBx+4r1ywKZgFBMEbb2g+QZAvAvTQoaqgOy+77JAIVhQYhChj40YXc6BatfweljCw/JJLVEH/c+21YW23KmGCoGqniBsQiWSCID+FghBdcIFzx65aFfa+vn7ySfWBrkpICHvb0ULQIEQ+n2qdOu4rF2z6ZQFBoOpW8vVnXXFFQN3sbNXkZNXYWL3i7LOrfLAifxCi22+/fb8Y0nI4Xt/evfp7tWq6MiZGtx2CMzhCwQRB1U4RNyASyQRBfvIFIXr/fXdZPPhgufX3S1KS+kC/vP/+cusjkgQNQjRqlDuvAwYE3ymIIPj66wNZ//53gfoT3DoHucceW6WDFeULQrR9uwvxXL162L0DflY+/7wq6P/800GNfJggqNop4gZEIpkgOEC+IEQZGaotWqi2b39wU7lKYNXbbzsvQUxMufURKYIGIdq1yw2CS0goevGdIIJAVbV+fZe1dm2QfZo1UwV9dvDgKhusaH8QokmTVAcN0vIWq6qqX7dqpVmgv3/ySbn2UxkxQVC1U8QNiEQyQXCAcePGHQhCdNdd7pKYM6fc+12Wmqo+0Deuuqrc+6ooigxCdNZZ7rw+8EDROxchCH77zfuWBmPePFVQX6NGVTJYUb4gRNu3u9kZqanl5h3ws37hQt0O+lO9emEfQ1PZMUFQtVPUxSEwKo4tW7YwduxY+vfvT98GDeCRR+Dyy6FPn3Lvu8H//gdAjylTyM0tPO++MjJy5Eh27drF4MGDadSokcv84Qf44AOoXx/uvrvUbTZvDkOGFFHYsyf064esX8+nZ5yBqjJo0KAy2x9tDPEO/JVXXoErrwSfD+69F2LK92erYdeuzD3rLDpt2sSK++4r174MI6oojXoAEoDGQCsCVhysbMk8BI4bb7xRY2Njdcnixap9+rhIeJs2VVj/K+vXVx/o01UgbGxGRkbwZ/mtWqlCyUtGF+EhKJHt292o+8REbXP44YXHLlRSZsyYoYD26NFDdfNm5x3YH4yh/MnYuVMXxMfr1vh49W3dWmH9RjuYh6BKpxKltoh0FJFxIrIAyMStL7Ac2CIim0TkHRG5RESSy0u0GOFn+fLlPPvsswwfPpz28+fDF1/AuHFQt26F2dD0888BOOeTT9iyZUuF9VseXH755eTk5DBy5EiSkpJc5uTJsHIlHHMMnHJK+XRcqxbcfjtkZ/NVy5YADB48uHz6qiB8Ph8jRoxARHj99dfhiiucd+D++yvMhpTUVNb8/e/UzMnht0p+Pg0jZIpSCsDxwOdAHvAt8BhwGXA20A+4ALgdmAFsBrYD9wApkVY5JSXzEKiee+65WqNGDd30yy9uOtxxx5X7s9lgrPNW/Bt95JEV3ne4CBqEKHC9glCe65fVQ6DqPjdvnYPzjzxSAZ0+fXrpDyRKGDNmzIEgRBs2uEBMaWkVbkdubq6+dNhhmge674svKrz/aATzEFTpVHQBbMRFAWxSYiMQC5wOfAjcE+mDKikd6oIgXxCiq692U7l+/DEyxqxapT7QP0B/qqTLIwcNQuSPpnfNNaE1cjCCQFV15kxV0OzWrSt1sCJ/EKL4+HjNyMhQPeMMd04mToyIPR+/9ZauBd3UqFF4wiRXckwQVO1UdAEklanBMu5XkelQFgSBQYiyZs1yl8Add0TUpi1duqiC3tGoUUTtKAv+IET51hRYu/bAegWh/okcrCBQ3b/OwT979aq0wYr8QYjuuOMOdx5FVOvWjZg9Pp9Px3TurAq6u7hZIocIJgiqdoq4AZFIh7Ig8AchennKFNVOnVSbNlXNzIysUWvWaB7oBtCZM2dG1pZSEjQIUc+e7qtVmvDM4RAE3joHvtRUjY+NrXTBivIFIcrLU+3bV4Ou+1DBLPrhB30PNCs+3i1OdQhjgqBqp1LN3xGRI0Skr4icVTCVbuSCEQmysrIYOXIk3bp1Y8iWLfDzz/D001C9emQNa9qUPccfTwPgs0suiawtpWDKlCn8/vvv9O7dm549e7rMjz6C+fOhTRu47LKKNahZMxgyBNm1i8+6dCE7O5urrrqqYm04CAYNGoTP5+Pxxx8nZu1a+OwzaNAALr00onZ17tKFLy68EF9ODruHDYuoLYZRroSiGoAjgZ9xAwx9QVJepJVNadKh6iHwByH6cto0tzjMOedE2qQDrF+veaCbQMePHx9pa0qkyCBEdetqkesVFEc4PASq+9c58MXGaouUlEoTrChfECJVNw0WVKNkJcd169bpqPh4Z9N770XanIiBeQiqdArVQzAFyAH6A0cALQqkluESKEb5EBiE6PjXXnOZTz0VWaMCadiQvNNOoy7w+113RX2woqBBiEaPhs2boX9/6NQpMoYlJMCjjyJ5eXzdqBGqlSNYUb4gRL/+6qbBNm4MUWJ748aNib3zTpYAWcOGwZ49kTbJMMJPKKoBF3/g9Eirl3ClQ9FD4A9C9PvTT6uC6iOPRNqkwmzerHmgW0GHDRsWaWuKJGgQooyMktcrKI5weQj8eOscnF+vXtQHK8oXhEjVTYEF1f/8J7KGFSAjI0PPTUtTBfX9/e+RNiciYB6CKp1C9RDMA5qWjyQxyht/EKIbr7iCw8ePhyOPhJtuirRZhalTBwYMIA2oPnFi1AYr8gchuuuuuw4EIRo0CHJy4J57ICUlsgYCvPEGAK/6fED0BisqFITol1/g66+haVMYODDS5uUjJSWFs8eN4wVAH3kEFi+OtEmGEV5CUQ1Aa2A+cDHQCKhWMEVa2ZQmHWoeAn8Qoszrr1cF1a++irRJRbN1q+aJ6HbQfn37RtqaQgQNQvTDD+681qtX9obD7SFQVe3XTxX0cS+k8bRp08LTbhjJF4RI9cAMjfffj6xhRZCbm6sntGun22JiNK9370Nu8SPMQ1ClU2iVoBbwBm5QYdAU6QMpTTqUBIE/CNHzN97oAhBFsSt+PxdeqAp6RxQGKwoahMi/XsHHH5e94fIQBN46B3kJCZoIUResqFAQoh9/dMffokWkTSuWDz/8UK/0f1YvvBBpcyoUEwRVO4X6yOAVoC/wKHAtcGWQZISTe+456CZ8Ph+33347hzduzJXz50Pt2vDww2EwrpyZNAlfTAz/AAZdeGGkrdnPl19+yfz582nduvWBgXpTprj1Co4+Gk49NbIGFqRWLbj1VmL27eOzxo3Zvn0791fgegAlMXz4cLKzs7n55ptJSUk5ME3z3/+OrGElcPrpp7OuXz++jY3Fd9ttsHXrwTX43/+GxzDDOFhCUQ3AbmBIpNVLuFLUewhyctwKdps3H1Qz/iBEX/vD6EY4wEupuPhiVdC7oyhYUaEgRKVdr6A4ysNDoLp/nQOfiLaPjdWEhISoCFZUKAhRero79jZtIm1aSCxatEiPBM0VUb3qqoNr7KijDv76qSAwD0GVTqF6CFYDFTLPRkSmeKso/hyQlyYin4jICm9bO6BspIj8KiLLROT0irCx3JkxA3JzD2paoD8I0cmdOnHM22/DiSfC0KFhNLKcee45NDaWkcCwKAiuEzQI0bXXwu7dcNVV4J96GG3ExMALLyCqfFa7Nvv27YuKYEX5ghDFxLgVDQEmTYqsYSHSuXNnel55JU+IuFUtv/yybA398Qd8/z289154DTSMshCKagDOwg0qbF7eCgXoAxwF/ByQNx74u/f678A473UHYBGQiIuHsBKILamPqPcQnHiiKqi2a1fmJvxBiNaffrqbDrdkSfjsqyguv1wVdEyEgxUFDULkX6+gevXwLHpTXh4CP126qA/00qSkiAcrKhSE6OuvD/p6jwTr1q3TOsnJuqlaNfeZ7dtX+kaee84de//+4TewHMA8BFU6hVbJiYGNwD5gOW4aYr4UVqOgeQFBsAxo6L1uCCzzXo8ERgbU+x9wbEntR70gSE52H01MTJmWJN68ebOmpqbqyGOPde3cdVc5GFkB7Nmjvrg43Q1aLTFRcyK02tydd96pgF588cUHMv2j4cM1qKy8BcGqVaoimp2crID27t07/H2ESJs2bRTQOXPmuIz27d1xf/11xGwqK6NGjdL/839u48aVvoGzz3b7JiWp7t4dfgPDjAmCqp1CqwQvlJTCalRhQbCjQPl2b/sMcElA/mTggiLaHA6kA+lNmzbVqGX+fN3/xwCqL79c6iZuvPFGTYqJ0ayWLd2I7UrwQ1Mk11yjCvpwhIIVBQ1C9NFHGvbn3eUtCFT3j8uYVKNGxIIVFQpC9MUX7pg7dapwW8JBRkaGNmjQQOekpakvOVn1t99C33n3bicE/J/7f/9bbnaGCxMEVTtF3ICgRoUuCP4VRBCcX1L7Ue0hGDJE8wmCE08s1e7Lli3TuLg4fadXL43m+dwhk5WlvoQE3QsaB7r5IAdalpbzzjtPAR0zZsyBTP96BYsWha+jihAE/nUOYmI0DbRVq1bl008R5OXlaVpamoqIrlq1ymW2aeOOef78CrUlnEycOFEPB81JTHSu/1BjE8ycmf+7Pnx4+RoaBkwQVO1UqtUOI8hGEWkI4G03efnrgMMD6jUB1lewbeHl00/zv58/v1S7/+1vf6N9YiIDfvwRLrgAzqrkC1EmJiLDh5OEG0hSkRH31qxZw9tvv01aWhr/+Mc/XOaYMW69grPPhs6dK8yWsJCQAOPHIz4fn6SksHLlSqZPn15h3T/wwANs27aNc889lxYtWsCsWbBiBXTtCj16VJgd4eaKK66gZqdOPJKS4gYHzpwZ2o4FBxK+956TBoYRKUJVDkAv4CHgJeD1gimcKoXCHoJHyD+ocLz3uiP5BxWuojIPKty8WfPdMfjTggUh7e4PQrSibVvVlBTVdevK2eAKYt8+1cREzfK8BBUVrKhQECL/egXx8WVbr6A4KsJD4KdpU/WBHl+BwYoKBSFSVW3ZUsPuaYkQH374ocaBbmrYUPXww0u+PvLyVBs2LPxdT0+vGIPLCOYhqNIpJA+BiNwCfAtcDrQC6gZJYUFEpgPfAEeIyDoRuQp4GDhVRFYAp3rvUdXFOEGyBPgIuF5V88JlS4Xz5JPB8x97rMRd/UGIhqWl0Xr5cnjgAbdaXFUgPh5uuIFE4AmokNX75s6dWzgI0UUXufUK/vGP6FivoKy8/joCzExKqrBgRcOGDcsfhOiDD2DVKucZqGyeliCcccYZ9D3tNIZmZsLatc6TVBzffw8bNhTOtyBFRiQJRTXgXPOPAxJpBROOFLUegnbtNKiHIIQY+dOmTdMU0N21a6t26xaeqXDRRE6OalKS7gNNqIBgRYWCEC1aFPJnUSYq0kOgqnrKKaqgt8XElHuwokJBiFRVmzZ1x1oZp8MWwaJFi1RE9Jsjj3RhwovzfIwaFfy7Hq2/TR6Yh6BKp1DHECQC73sXhFEe+HywfDnUqwf+FfRiY92qb5s2QTEr//mDED1Xty7JO3bAc89BXFwFGV5BxMXBLbcQjxtJOmzYsHLrKmgQovPPd9tXXim3fiuU11+HuDgeEoFyDlZUKAjRO+/A77/DscdC+/bl1m9F07lzZ6644grOXbqUvJo1XeAqb7XJQrz3HvTpA8cf797XrAnDhsGPP8L6yj0MyqjEhKIacM/wJ0RavYQrRaWHYPVq1alT3Wv/KPbkZPd+5sxiR2GPGzdOu4L6YmJUR4yoAGMjRF6earVqmiOiSeUUrChoEKIpU9zn0atX2PvbT0V7CFRV77xTFfStuLhyC1bkD0KUb6pv48buOJcvD3t/kWbdunVarVo1fcY/y+f55wtX2rdPdfZs9/rqq129+vXd+99+i+rzgnkIqnQKrRLEABOAT4G7gBEF0nWRPpDSpKgUBIEUFATFsHnzZq1Vo4Yuq1XL/ahs314BBkYQ74/zRdDk5OSwBysqFIQocL2C8hik+dBDqnv3BhcE990X/v4CyctTrV1bfaCtyilYUaEgRDNmuGM84YSw9xUtjBo1SgHd2a2bau3aqhs3Fl25oCCIckwQVO0UWiXoB+wEfEUkW/44nJRCENx44406QsTVj8L17sNOXp5q9eqaK6IpoFdffXXYmg4ahGjYMHduw9hPPlq0cO2npel+QZCUpCqimpBQPn0G8s47qqBL4+LCHqyoUBAiVdUGDdwxliaATyXDH6xocNeu6ouPV7300qIrmyCwFEUptEouXPHHQHsgPtJGH2yqKoJg2bJl2jg2VncnJKj26xd6QJTKzoMPqoK+HhurMTExYQtWVCgI0bp14V2vIBivvqpBB5eBap8+5dNnQTp3Vh/oBWEMVhQ0CNHLL7vj6ts3LH1EMxMnTlRAfznvPHfMn30WvKIJAktRlEKrBJlAv0gbG65UVQTBueeeq6/FxakvMTGqnzuGnbw81dRUzRPRVNB+/foddJOrV69WEdG0tLQDI+H9z4GnTDno9oulKEGwYkX59uvHW+dgV2ysAjotDJ6mMWPGKKADBw48kFm3rvN8rF170O1HO7m5udqpUyft2KKF+po3Vz3iCNWsrMIVTRBYiqIU6lD0T4Eu3taIAr744gsy3nmHvwDcfTe0aRNpkyqOmBi4915ibruNaYmJ9P/0U37++Wc6depU5iYvvPBCVJUJEya4kfAffwzz5kHr1geW5i0vatWCHTvy58XEuL4rghYtYPBgakybxmPA9ddfz6BBg9x5KANZWVk8+OCDxMfH89JLL7nMSZNchMfTT4cmTcJne5QSGxvLI488wplnnsnMYcM4d+JEePRR912tYixYsKBeXFzcJKATVJrot4ciPuDn3Nzcq7t3774pWAVxoq94RKQv8BwuSuFnwI6CdVR1ycHZWnH06NFD09PTI21G0dSr5348k5Nhz55CxT6fjz69evHSokU0b9aMmJ9/PjBV8VCidm10507qqNKgQwcWL15cpmbmzp1Lnz59aN26NStWrHCZ9eu76Z6LFpV/4JwRI+DZZ/PntWwJK1eWb7+B7NsHtWqRl5VFPVVuvPdeRo8eXaamhg4dyiuvvMIdd9zB+PHjXWadOrBtm5tS16BB+OyOck4//XTmz5/PnyecQMLHH8PPP0OrVgcqDBvmxFL9+vDnn5EzNEREZIGq5oszvWjRoncbNGjQvm7durtiYmJsanqU4vP5ZPPmzTX//PPPJV26dBkQrE6oau5ToDVwHzAX+Ckg/extjQpixowZnLJgAS1zc4l59tlDUwwA3H8/ospbNWqwZMkS3n333TI1c8kllwAwbdo0l3HffU4MVNR6BU89VThv7Njy7zcQb52DWFX+Azz00ENkZWWVupn169czbdo0atSowcMPP+wyJ0yArVvduhqHkBgAeOSRR9ixYwcPN2jgYmnccENVXK+gk4mB6CcmJkbr1q27E+fJCV4nxLZODkh9CyR/nlEBZGVl8e/bb+cuEfSii+DUUyNtUuS44QZIS+PEzEzqUbZgRZMnT84fhCgz04V9jo+HGTPCb3Mw4uLcH3IgF11UMX0HcsMN0LQpfYDuZQxWdNFFF+UPQgTOTR4TA1OnhtXcyoA/WNHYqVPZcvPN8NFH8OabkTYr3MSYGKgceJ9Tkf/7IQkCVZ1TUgqbxUaxPPXkk9y9YQMx1aohjz8eaXMiz7hxiCrv16nDpk2beOSRR0Le1efzceuttxITE8Nrr73mMgcPdusV3H13xa5XcMwxB17XqlVx/Rbk9dcBeEOE6dOns74UUfPS09OZO3cuTZs2PSAmHnvMjY845xz32OAQ5L777iMuLo6/LlsG3brBTTfBrl2RNsswClGkIBCRMv0aikiNsptjFMeWLVtYOmYMpwHx48cfcu7XoFx9NdStS/etWzlchHvvvZecnJyQdh05ciS7du1i8ODBNGrUyIWNfe89qFsX7r23nA0vwOTJB157jzAiwtFHI3370liVm1T5y1/+EvKuQ4YMAeDll192GT6fW+QnJib/8R1iNG7cmNtvv53pb7zBT9df78YKjBoVabPKD5HuYU0VxFNPPXXYpZde2hRg/PjxdZ955pnDSrN/tWrVugXLf+CBB+q1bNmy44ABA1qEw87ypDgPwe8i8oCItCqmDgAikigi54vIF8DN4TPPCOSRu+9m7N697D3ySLjmmkibEz3885+IKh83bszevXsZMWJEibtkZmby+OOPk5iYyKRJk1zmBRe4rf8PrSJp3RpE3OtIe37eeMOtcwDM/+or5s+fX+Iur732GitWrKBHjx706dPHZY4f7+6EL7gAatcuX5ujnDvuuIMGDRpw7ZQp6LXXwtNPuxUPjajkzjvv3HzDDTdsDUdbkydPrvvBBx+sePfdd38LpX6oNzTlQXGC4FTgKGCFiCwUkX+JyHUicqGIDBCRS0XkXhF5F9iEW3PmXdy6B0YxdOvWjREjRrAh2PKngWRl7R95vHz5cppNnEh9EZKnTnULHxmOoUOhQQOO+OMP2iUnM2XKFLYUsxgUwGWXXUZOTg533XUXSUlJ7vn2ihXQs6ebGhcJmjd3YwkivTBVWhrccgtJwIvA4MGDi63u8/kYMWIEIsLr3iMHfD43MDI2FiZOLHeTo52UlBTuv/9+vv76a/57zDHOCxW4+NG2bZVilkE00q9fv1YdO3Zs37p1646PPvro/udS1apV6zZs2LAmHTp0aH/ssce2Xb9+fRxAr169jrjyyisP79atW7s2bdp0/Pzzz6sVbPPWW29tNGrUqPoAixcvTjzhhBPadOzYsX337t2PWLhwYRLA0qVLE7p27dquU6dO7W+66aZGwWwbMmRI03Xr1iUOGDCg9ZgxY+pt3Lgxtl+/fq3atm3boUuXLu2+++67ZH9/gwcPbnb88ce3Oe+881rk5uYyfPjwJm3btu3Qtm3bDmPHjq0HMHfu3Go9e/Y8omPHju179+7dZs2aNfHgvBCtWrXq2LZt2w79+/dvWeaTWVKgAqANcD/wNbCX/CGLVwOvAudTiSIYRjowEaAJCQmalJSk1113na5fvz5/BX9gIti/WNHtJ56oeaC7hw2LgMWVAC9G/rpWrZQSghUVCkKUk6OakuKiEkYyaM706aonnhi5/gPx1jnI89Y5KC5YUdAgRGPGuOvXvyaEsT9YUatWrTTnpZfc+TnuuELf9WiGIIGJfvjhh9Wqmr4/FRVoq6wpsO0g6c8//1yoqukZGRkLWrduvXfDhg0LVTUd0AkTJqxS1fTbbrvtj6FDh25S1fSePXtmDBo0aLOqpn/wwQdLW7duvVdV05988snf/HVuueWW9ffcc89aVU0/5phjdv34448/qWr6rFmzfjn66KN3qWr6ySefvOPpp5/+TVXTH3zwwTXJycl5wexr1KhR9vr1639Q1fRLL71046233vqHqqbPnDlz2RFHHLHH31+HDh12Z2RkLFDV9IcffnjNaaedtn3fvn37jzErK2tB165dM//4448fVDX9+eefX3nBBRdsUdX0unXr7tuzZ88CVU3fvHnzwuLOl/d5Bf1vLHFQoaquUNV7VPU4VU0GDgMaA0mq2lxVL1bVt1Q1cn6OSsi+ffvIyspi8uTJtGzZMr/HIC/vQMUXXuCbN99k8Jw57E5Npdqjj0bG4Ghn0CBo3JjGK1dybN26fPrpp/z0U/DZsIWCEI0Y4WYXXHFFZIPmXHSRG4UeDXjP/QV4GxesyBdkKd+gQYh8Phg3znk6/v3vCjU7mvEHK1q5ciXPbNkC/fpB4OOYF14wL0EZGDduXP0jjjiiQ/fu3dv/+eef8YsXL04CiImJ4eqrr94GcOWVV26dN2/e/nFxQ4YM2QZw5plnZmZmZsZs2bIlqMt1586dMQsXLky58MILW7Vr167DiBEjmm3atCke4Pvvv08ZNmzYNoBrrrkmpMcL8+bNq3HVVVdtBRgwYEDGjh074rZu3RoLcMYZZ+xISUlRgM8++yz12muv3RwfHw9A/fr183788cfEFStWJPft27dtu3btOjzyyCMN169fHw9wxBFH7B04cGCLCRMmpMXHx5d5xkepo0qp6nZV3aCq+8raqXGAoMJg9+795ZqXR9Lll3MUkPDss5CaGjljo52nnwbgfW80+6BBgwpVmTt3LvPnz6d169aufP16N+CtenV47rkKNTco0RRTYuBApHNnOgF9t2/nvvvuK1Rl2LBhZGdnc/PNN5Pin5Vxzz0uoNbQoe68Gvs544wzOO2007jv/vvZ+dBDkJt7oDAvD+6/P3LGVULee++9GnPmzKmRnp6+dNmyZUvat2+/d+/evUH/18Q/RqfA62Dv/eTl5VGjRo3cpUuXLvGnVatW7Y+AVtrplhokBoWIKED16tV9gfX8+QF50rp1671+O5YvX77kq6++WgHw+eefr7j++us3L1iwoHqXLl06lHUcgoWZjBLyCYPsbEYAGwDZt4+uu3ezoUMHEkt4lnvIM3AgNG1K7V9+4ZwjjuCXX34pFKyoUBCi885zd7RPPhn5Z/fRyNtvgwiTgIfGjs0XrMgfhCg1NfVAEKLcXDfVMD7eBSQyCuEPVvSEfzCrn337BZAe5QAAHxpJREFUzEtQSnbs2BFbs2bNvBo1avgWLlyYtGjRov0K1Ofz8cILL9QGmDp16mG9evXK8JdNnz69NsD//ve/lBo1auQddthheYVbh7S0NF+TJk32TZkypba/zW+++SYZ4KijjsqcOHFiGsDEiRNDmpFwzDHHZLzwwguHgRMztWvXzk1LSyvkeuvXr9+u5557rq7/j33jxo2xnTt3ztq2bVvcp59+Wh0gOztb0tPTk/Ly8li5cmXC//3f/2VMmDBhXUZGRuzOnTvLNMjMfgGjjH37nONlMvAC8CXQDWjQrduBUehG0Tz7LJx9NtMTEqiGu4MdMMBF6SwUhOiTT+C771wo2TIE4TkkaNkSuegiak2fzoO5uVx11VW8+uqrwIEgRI899tiBIEQjR7rBsNdcE13ejijCH6yo/sSJ+ChwV+b3EvzrXxGyLgyoLqiors4///ydzz//fN22bdt2aNWqVVaXLl32u1eTk5N9ixcvTu7YsWODGjVq5P3nP/9Z5S+rXbt2Xrdu3dplZmbGPv/888WO/p8+ffqqYcOGNRs3blzD3NxcGThw4LZjjz1274QJE36/6KKLWk6YMKH+gAEDtodi77hx49YPGTKkedu2bTskJyf7pk6dGrTvW265ZfPy5csT27Vr1zEuLk4vu+yyzXfdddfmGTNmrPzrX//aNCMjIzYvL0+uu+66jUceeWT2kCFDWmRkZMSqqlxzzTUb69SpE1TglERIaxlUNSK9lkFR7qmCnAF8CIwCtsTGcs+CBTTs0qU8TasatGwJv/3GiN69efbLLxk/fjy33XYbtWvXJjMzk7Vr17q4A/71ChYuhK5dI2119LJvH1qzJnlZWTQAfvzjD9avX0/Pnj1p2rQpa9ascfVyc10wJ1XIyCgcfdHYz4bvv6dW9+4kBytMToZVq6IyzkgRaxms7tKlS/HTeiJAtWrVuu3Zs2dhwfxevXod8eijj67t06dP4YViDgEWLVpUp0uXLs2DlVWJRwYicoaILBORX0Xk75G2Jxwk4eZxLgEeBibn5dGye/fQpise6jz/PABP7doFLOLOO28nNlbYtWsHKSm/OTFw//1ODJx1lomBkkhIQMaPJw54g+40btyQnj27Az5iYgIWlLrtNsjOdt4BEwPF0nDSJOKLmDqcuy+PHbfZWAKj4gl1tcP+wAeqWniYcYQRkVhgOS5uwjpgPjBYi1l9sTJ4CO4H/gGcBATGhU5ISCAmJoYrrriCe+65h4YNG5aPkZWdtm3RFSvoznwWEnhDo3Rvt5v0lWnu7datUMOCa4bC+vimNMxdy3F8xbcctz+/QwdYvHCfO48ibsaGjccomg0bnBermMWj9pDMqS1XcezABvTvD717R8cprUweAiM4xXkIQhUEebjgQy8BU1X1l7BaeBCIyLHAaFU93Xs/EkBVHypqn2gXBBcCXngX0oFtwPYCW//rzPh49iQlsSs2lu0i7HUdlJPllYdjcnJ4LyODnziSLvyYr+wd/o9zeI9xSUmMr1YoJolRBK22vc93HMtamtCMtQElypTEZK7IzuaZpCTutXMKQIIqtVSprUpNn4/a3uuhWVn0yMsrdgBXFglM5mpuwI0lqFULzjzTza4dMCByX3ETBJWf4gRBqJqzFXAFcClwu4jMA6YAr6lqpFfpaAz5fp3WAUcXrCQiw4HhAE2bNq0Yy8rIOm/7PyAXSAOaets0CnxoOTku+d/GxLAnKcmlxMQDKSmJ3UlJ7E1MZLf3fk/Adm9iIr6YKvEEaT+/PPMpR/ITR/MN33EsAB35iQG8R0ZSEuuuvpohEbaxMvH/7d17lFTVmffx79MXumlRaRCDNATIAEYUEOnwSsZEBJYyAiKDLPESUUCWCjGRiTKKJiujTmIUwwAqogaiMeIFBAQiSsSlM8GBNqNAgwgiBBAVucqlm276ef84p6Voq7uroC9V1b/PWrXq1D7nVO9dXZfn7HP2s6dN+3+8xSX0ZRk/YzL/FWYpb0QRPykp4Uh6OhtGjuTaFHofmTvZR46QU1RETnHxsfviYk4pKqJxeF9xXU5REVmRQwrjlM0RbmIm93MfGXlBL8GgQdCnj+J9qT1xX1RoZn0IgoMhgAFzgT+4+7Kar15M9RkGXObuo8PHPwF6uvtPK9sn0XsIqtMEaJmZSfO0NK657DJuGDSIXPcg/enu3bBnz/H35ctff131E59+epBzvlmzY/eVLUeW5eQk5LfUhbac5fyQdZzDuQRnkNbTiY5swBYvDg65JGZm0JTdfMmZlJJJU/ZwhGyeZiSjmAn33BOkK05ERUXf/jxE+4xUXN6791h64WgaN47tM1K+/PvfB3NFxDBOvDS9EXv+dTRnvPhYwny81EOQ/Gqih+Ab7v4W8JaZtQJmA9cB15rZP4ApwFR3P/HQOH7bgDYRj1sDsc/ZmmQaAUeBS6+9lvt++1taxnMlcklJ8AUX65fi9u3Hyqr6AsvMjD+IyM0NbrV4YvTrzr1YvfY8urCGi3iH9nxKJzawOjufLgoG4ta5M6xd24zJ3MGdPMIsbmQUzzCC54KgsLaT6pSVwb59sf2QVyw7fLjy501LO/Z+LH9/duhQ/Y97bm58Qyt37IC5c2MKBgAyjh6hxcKZ8MV9CTniQFJP3N/GZnYxQQ/BUKCE4GL4ecBlwK+BH0Cd9sSuBDqaWXtgOzC8jv9+nWgEpBO88PdlZtLylFPi/5LIzAwmVWnRIr793OHgwdiPrLZvhzVrgsfVzft+6qnxBRHl902aVNsrUVgIV31vFi9/ms8zjOIsPqeMNLpseDW+9gsQvJ7nngt3rX2I0TzN1bxEEw6QQSlMuC/4YY3F4cOx/5BXPFqvqkczJ+f490rHjrG9l047Lfa6n4z776+6tyGaJMxLYEaNTlnsTlx5DcaPH9+qSZMmR/fv35/eu3fvr6+88spqukaPt3DhwlMnTZr0nWXLlm2Mr6Z177nnnmvauXPnoh49elR+hWocYgoIzKwtMCK8tQPeJjgfP9fdi8PN/mpmy4E/1UTFYuXupWY2juCUezrB6YvCanZLGscFAkBLCI4wZs4MUsTWxZGDWfAD3KQJxHv9RWnpsV6JWH4ACguPPa7qSCojI6Yg4pWpuWwZ1I5OHny2D/cbROOSEvg0pplIpYLChcH9r/L/g1/vvp1BLMIB+8EP4IUXYvtxr+LqetLTjz9ab9ECOnWKrbcpK6tOXoMTsmNH8Jk9EmfG9/LshXX1WU8hkydPTtme4nLz5s1rWlpauq9OAwJgE0E3/CyCH9zKvk0LgRU1UK+4uPtiYHFd/93aFDUQiJQsRw4ZGXDGGcEtHu5BPvxYjyJ37IC1a4PlffuOe6q2EcuNl74G33vt5NvVwP06YtkgyOcQqUmT43+0zz47tl6g8qGLqeZEegfKJctnvR5NmDCh5YsvvnhGq1atjjRv3ryke/fuh4YOHdpu4MCB+2666aY9t912W96SJUuapqene+/evffPmDFj29ChQ9tlZWWVrV+/vvGuXbsyf/Ob32y95pprjvvyWLZsWc748eO/W1RUlJadnV02a9asT7t161ZcWlrKbbfd1vrtt98+DWDEiBFfTZw48ct33303Z/z48W0OHTqUlpubW/r8889vbtu2bUnPnj3P7tKly6EPP/wwZ/fu3RkzZ8789MEHHzxr/fr1jQcPHrx7ypQpnwE8/vjjzZ544onvlJSU2AUXXHDw2Wef3ZKRkUFOTk73UaNGffnGG2+cnp2dXbZw4cKNH330UdbSpUubvvfee6c+9NBDZ82ZM+eTV1999fSZM2e2SE9P906dOhUtXLhwU7TXqzKxBgSDgNery0Pg7h8Dl8RTATletYFAuVQ/cjALJsY55ZT4ZyA8evS4Xok7R+3mqjW/5CO+z4GefRl7W+1UuaH53aj1DDv6Aj9lCr0ub87ESRFH60pMdMyJ9g6US/XP+kl69913c1599dVmq1evXltSUsL555/fuXv37t9kIfziiy/SFy9enLtp06Y1aWlpRM5suHXr1qwVK1asX7t2bVa/fv3OHjx48HFTpHbr1q1oxYoVH2VmZjJv3rxT77rrrtZLliz5ZNKkSS22bNmSVVhYuDYzM5Mvvvgivbi42G6//fbvLlq0aGOrVq1Kn3rqqdxf/OIXeS+//PJmgEaNGpUVFBSsv//++88cNmxYh5UrV64788wzS9u1a9flnnvu+eKzzz7LfOWVV5oVFBR8lJWV5ddff/13p0+f3nzcuHG7Dh8+nNarV68DU6dO3X7LLbe0njp1aovf/e53O/r167e3POgBuOSSS1pu2bJldePGjb2yGRyrElNAEB6BSy2KORCIpCOH6NLToXnz4AaU9IUL1/QHoGsRjB1Rn5VLHc1L4Xuj/xOA15fAxEVBeVFRkGlTQifTO1BOn/VKLVu2rMnll1++99RTTy0DuPTSS/dGrm/WrNnRrKyssuHDh7cdMGDAvquvvvqbXoChQ4fuTk9Pp0uXLsVt2rQp/uCDD4576+7evTv96quvbr958+ZsM/OSkhKD6NMTr1y5Mrt8emIIJkJq0aLFN+c9hwwZshegW7duhzt06HC4bdu2JQBt2rQp3rRpU6O33367yZo1a3K6det2DkBRUVHamWeeWQqQmZnpw4cP3wfQo0ePg0uXLo067W35NMhXXHHF3uuuu25vtG2qkjoDhpNUI6AxMJrgvMxjxBgMgGZHq8bmzcH9gAHHynbsCGY7btIk6i4Sh1GjgtgLgt+rP/8Z5s8HJc+McLK9A+X0Wa9SVUO5MzMz+eCDD9YNHTp077x585r27t27Y2X7VXw8YcKEvIsvvvjrDRs2FL722msbjxw5kgbxT08MkJ2d7QBpaWlkZWV9s29aWhqlpaXm7jZs2LBd5ftv3rx5zaOPPvoZQEZGhpdPIJaRkUFpaWnUBp/sNMgKCOrJSQUCkTSHeqVGjgzOPIwZc6xs504YPbrq69okdsOGHVseMwauvPJbl3A0bDXRO1BOn/Wo+vTpc2DRokVNDxw4YHv27El78803m0au37dvX1p4pL9v+vTpW9etW/dNKs25c+fmHj16lMLCwqytW7dmdevW7bhvhv3796e3bt36CMCTTz75zYVQ8UxPHGs7+vfvv3/hwoW527dvzyh/zo8//rjKc2/haIo0gJqYBjkBsmOnnnfegZ//HFatgtmz4aqrjl9/fnY2Pywqiv3UQFWOHIG//e1knyVhTZ8e9JKmpwdH9TNmBOPhY7F4cZA3prynIFJubo1WM2nMmgV33gl5ecHjceOCACleGzcGB6tPPRW8xyEYmQpVjwxMNXfcAcvClGyHDgXzZe2N7KhdvvzkewfKJclnPd5hgifroosuOjRkyJDd55133rl5eXnFPXv2PBC5fu/evekDBw7sUFxcbAAPPPDAN5ltO3ToUNyzZ8+zd+3alTl58uQtOTk5x717J0yY8Pno0aPbT5kypeWPfvSjb8ZQxzM9cX5+fkyHHz169Ci69957t/ft27dTWVkZmZmZPmXKlH906tSp0jfQddddt/vWW29tN3369O/Mnj37k5EjR7Y7mWmQNf1xLdi8ORh+/8gjQd7xigGBxG7//mCYOMCCBfD44/D667Hvf9ZZ0XtZ+/aFpUtrpo7JZNYsKCiAadNO7nlWrYKqZuI+fDi+nD2pYOrUYCbtP/yhvmtSe1IpU2HkKIT6rktdSvnpj+vK5s1wzjlw881BgpZLL42eAK1dO+jatW5ynSSrWF/L0yIunTl4MP4RaS++GL38llvie55EF+vrWVO6dg1OaVdmcZJfhnwir+cLL8A119RJ9URqhX6y4rRhA4wdG+TPadoU5syp7xolr1hfy8ceg3/6J7jrLpgyJb6/8eMfRx8Bl4q9NrG+nnPmBD/oV10FW7dG3yYWN94YXFgYTbIHBBDfZ33LliDXVZ8+dVc/OTlz5szZ3NB6B6qjgCBO7dvD+ecHyz16RD8/LbGJ9bUcOxY++QQeeggeeCD+vzNu3PGPUzHvDcT2eg4aFJSvWgX9+sGIkxyC+fTTcMEF3y7/8MOTe95EEM9nvfxaofS4R36nhLKysrIU/VSllvD/VOlVrgoI4hSZHTU9PcjMKycm3tdy+HCYNy/+vzNp0vGPc3Kib5fsYnk9mzc/tt3NN8P7NXD51/vvf/sizW3bom+bTOJ5f86e3aBPF6zZuXPn6QoKEltZWZnt3LnzdGBNZdtolIEktA0bgjlqABYtOrYcrwsugL//PVhu165GqpaUduw4lidgwYLgPHlN+PLL4CLCo+E1zXvjTomSvNavDzJo9+pV3zWpH6WlpaM///zzpz///PPz0EFmIisD1pSWllY6rkgBQS1YuRKGDAm+JF57DX71q+A8pMRv2rRgNEBmZnAU+sc/ntjzLFlybJLHK66oufolmylTgkCgfG6oWbNq5nkzMoKhiO3bB49raqRdMnjhhaD3KlVPRVWnR48eXwIN+FOVOjTsUBqM3NzgyHXPnuAiMal58+cHyYmgYeUjaCiiDTuU1KHuHWkwnnoquFcwUHsGDw5Gg4hI8lFAIA3GVVfBwIH1XYvU99BDQeKnVLiwUKQh0TUE0qC89lp916BhaIhZIEWSnXoIRERERAGBiIiIKCAQERERFBCIiIgICRQQmNkwMys0szIzy6+w7m4z22hm683ssojyHma2Olw3xayhpgYRERE5OQkTEBDkV/5X4J3IQjPrDAwHzgX6A4+bWfkUIk8AY4CO4a1/ndVWREQkhSRMQODu69x9fZRVg4HZ7l7s7p8CG4GeZnYWcJq7L/cg3eKzwJV1WGUREZGUkTABQRXygMhZ27eFZXnhcsXyqMxsjJkVmFnBzp07a6WiIiIiyapOExOZ2VKgZZRVE919fmW7RSnzKsqjcvcZwAwI5jKopqoiIiINSp0GBO7e7wR22wa0iXjcGvgsLG8dpVxERETilAynDBYAw80sy8zaE1w8uMLddwBfm9mF4eiCG4DKehlERESkCgkTEJjZEDPbBvQCFpnZEgB3LwReAtYCrwNj3f1ouNutwNMEFxp+AvylzisuIiKSAswb4KTl+fn5XlBQUN/VEBFJKmb2vrvnV7+lJKOE6SEQERGR+qOAQERERBQQiIiIiAICERERQQGBiIiIoIBAREREUEAgIiIiKCAQERERFBCIiIgICghEREQEBQQiIiKCAgIRERFBAYGIiIiggEBERERQQCAiIiIoIBAREREUEIiIiAgKCERERAQFBCIiIoICAhERESGBAgIze9jMPjKzVWb2qpk1jVh3t5ltNLP1ZnZZRHkPM1sdrptiZlY/tRcREUluCRMQAG8C57l7V+Bj4G4AM+sMDAfOBfoDj5tZerjPE8AYoGN461/XlRYREUkFCRMQuPsb7l4aPnwPaB0uDwZmu3uxu38KbAR6mtlZwGnuvtzdHXgWuLLOKy4iIpICEiYgqGAk8JdwOQ/YGrFuW1iWFy5XLI/KzMaYWYGZFezcubOGqysiIpLcMuryj5nZUqBllFUT3X1+uM1EoBR4vny3KNt7FeVRufsMYAZAfn5+pduJiIg0RHUaELh7v6rWm9kIYCDQNzwNAMGRf5uIzVoDn4XlraOUi4iISJwS5pSBmfUHJgBXuPuhiFULgOFmlmVm7QkuHlzh7juAr83swnB0wQ3A/DqvuIiISAqo0x6CakwDsoA3w9GD77n7Le5eaGYvAWsJTiWMdfej4T63ArOAxgTXHPzlW88qIiIi1UqYgMDdO1Sx7kHgwSjlBcB5tVkvERGRhiBhThmIiIhI/VFAICIiIgoIRERERAGBiIiIoIBAREREUEAgIiIiKCAQERERFBCIiIgICghEREQEBQQiIiKCAgIRERFBAYGIiIiggEBERERQQCAiIiIoIBAREREUEIiIiAgKCERERAQFBCIiIoICAhEREUEBgYiIiJBAAYGZ3W9mq8zsAzN7w8xaRay728w2mtl6M7ssoryHma0O100xM6uf2ouIiCS3hAkIgIfdvau7nw8sBH4JYGadgeHAuUB/4HEzSw/3eQIYA3QMb/3rvNYiIiIpIGECAnffH/HwFMDD5cHAbHcvdvdPgY1ATzM7CzjN3Ze7uwPPAlfWaaVFRERSREZ9VyCSmT0I3ADsAy4Ji/OA9yI22xaWlYTLFcsre+4xBL0JAAfMbH0NVbs2nQF8Vd+VqCWp3DZQ+5Kd2hdd25quiCSOOg0IzGwp0DLKqonuPt/dJwITzexuYBzwKyDadQFeRXlU7j4DmBF/reuPmRW4e35916M2pHLbQO1LdmqfNER1GhC4e78YN/0zsIggINgGtIlY1xr4LCxvHaVcRERE4pQw1xCYWceIh1cAH4XLC4DhZpZlZu0JLh5c4e47gK/N7MJwdMENwPw6rbSIiEiKSKRrCH5rZmcDZcAW4BYAdy80s5eAtUApMNbdj4b73ArMAhoDfwlvqSSpTnHEKZXbBmpfslP7pMGx4AJ9ERERacgS5pSBiIiI1B8FBCIiIqKAIBGZWf8wTfNGM/v3+q7PiTCzNma2zMzWmVmhmf0sLG9mZm+a2YbwPjdin6gpqhOVmaWb2f+Z2cLwcSq1ramZvWJmH4X/w14p1r47wvflGjN7wcyyk7l9ZvYHM/vSzNZElMXdHqWDb9gUECSYMC3zY8C/AJ2Ba8L0zcmmFPg3dz8HuBAYG7bj34G/untH4K/h4+pSVCeqnwHrIh6nUtv+C3jd3b8PdCNoZ0q0z8zygNuBfHc/D0gnqH8yt28W307dfiLtUTr4BkwBQeLpCWx0903ufgSYTZC+Oam4+w53/3u4/DXBD0oeQVv+GG72R46lm46aorpuax07M2sNDACejihOlbadBvwYeAbA3Y+4+15SpH2hDKCxmWUAOQQ5TJK2fe7+DrC7QnFc7VE6eFFAkHjygK0Rj6tMyZwMzKwd0B34X+A7YQ4Jwvszw82Srd2TgbsIhsmWS5W2fQ/YCcwMT4k8bWankCLtc/ftwCPAP4AdwD53f4MUaV+EeNuTRxzp4CX1KCBIPHGlZE50ZtYEmAP8vMIEVt/aNEpZQrbbzAYCX7r7+7HuEqUsIdsWygAuAJ5w9+7AQcLu5kokVfvCc+mDgfZAK+AUM7u+ql2ilCVs+2JQI+ngJfUoIEg8laVqTjpmlkkQDDzv7nPD4i/CrknC+y/D8mRq9z8DV5jZZoJTOn3M7E+kRtsgqO82d//f8PErBAFCqrSvH/Cpu+909xJgLvBDUqd95eJtj9LBN3AKCBLPSqCjmbU3s0YEF/8sqOc6xS28OvkZYJ27PxqxagEwIlwewbF001FTVNdVfePh7ne7e2t3b0fw/3nL3a8nBdoG4O6fA1vDzKEAfQkyhaZE+whOFVxoZjnh+7QvwTUuqdK+cnG1R+ngBXfXLcFuwOXAx8AnBDNB1nudTqANFxF0N64CPghvlwPNCa543hDeN4vYZ2LY5vXAv9R3G2JsZ29gYbicMm0DzgcKwv/fPCA3xdr3a4L5UtYAzwFZydw+4AWC6yHKp4UfdSLtAfLD1+QTYBphNlvdGsZNqYtFREREpwxEREREAYGIiIiggEBERERQQCAiIiIoIBAREREUEIjUunAGuT3hHAH1VYfG4Wx4P6qvOohIYlNAIFL7HgCme9Wpm2uVux8GpgL311cdRCSxKQ+BSC0ys44ESaY6ufuGeq5LG2AL0M3dV9dnXUQk8aiHQKQaZtbUzLaZ2bMVyheY2cdmllPF7iOAVZHBgJn1NjM3s75mNt/MDprZBjO71MzSzexhM/vKzLab2fgKf3OWmRWY2QAzW2tmh8xskZk1M7MOZrYsfL4CM+saua+7byVIjX3Dyb8qIpJqFBCIVMPd9xKkgv2JmV0JYGY3AQOAG939UBW79wX+Vsm6J4H/BoYQHLm/QpAu9lTg2vDxJDO7sMJ+3wX+A7gXGEMwMc8MgomWZgNXEcxYODvMSR/pbwST+4iIHCejvisgkgzcfYmZzQCeNLMtwO+BR9y9sh/78gmeugN/qmST59z94XDbbUAhcLa79wnLlgJXEwQM70Xs1wzo5e6fhNt1Be4ERrj7sxF/exHwfYKJe8p9CPzUzLLdvSie10BEUpt6CERi92/AQWA5wQQyv6xm+1yCSXO+qmT9XyOWN4b3b5UXuHsZsAnIq7Df5vJgoLJ9I8oq7vsVkA60qLLmItLgKCAQiZG7HwAWEvzIP+PuxdXskh3eV7bd3ojnPlKxLHQk4nm+tV/ENhXLy8sq7ltcSbmINHAKCERiZGb5wK3A/wH3mlnLanbZFd43rdWKxae8LrvrtRYiknAUEIjEwMyygWeBJcBFBD+oM6raJ+xB+AfQvtYrGLt2wC5331XdhiLSsCggEInNA0BL4OZwVMEIYICZ3VjNfv8D9KjlusUjn8pHPYhIA6aAQKQaZvbPwB3AOHffARCOLngUmGxmravYfS5wsZk1rv2aVs3MMgiGQc6p77qISOJRpkKRWmRmjQhGJIx195fruS6XAS8Brdz9YH3WRUQSj3oIRGpROHrgYeBn9V0Xgl6O3ysYEJFolJhIpPZNA3LM7HR331cfFQhPWSwnSKgkIvItOmUgIiIiOmUgIiIiCghEREQEBQQiIiKCAgIRERFBAYGIiIgA/x+lplBu8t1I2AAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"u_1 = u_1*1000\n",
"print('\\tSTEEL')\n",
"print('----------------------')\n",
"print('\\n')\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print('Force:')\n",
"for i in range(len(F_steel)):\n",
" print('F_{}{} = {:.2f} Newtons'.format(int(i/2)+1,xy[i%2],F_steel[i]))\n",
"\n",
"print('\\n')\n",
"\n",
"print('Displacement:')\n",
"for i in range(len(u_1)):\n",
" print('u_{}{} = {:.2f} millimeters'.format(int(i/2)+1,xy[i%2],u_1[i]))\n",
"\n",
"l = 300\n",
"s = 5\n",
"num_nodes = np.array([[1,0,0],[2,0.5,3**0.5/2],[3,1,0],[4,1.5,3**0.5/2],[5,2,0],[6,2.5,3**0.5/2],[7,3,0]])\n",
"num_nodes[:,1:3]*=l\n",
"elems = np.array([[1,1,2],[2,2,3],[3,1,3],[4,2,4],[5,3,4],[6,3,5],[7,4,5],[8,4,6],[9,5,6],[10,5,7],[11,6,7]])\n",
"ix = 2*np.block([[np.arange(0,5)],[np.arange(1,6)],[np.arange(2,7)],[np.arange(0,5)]])\n",
"iy = ix + 1\n",
"r = np.block([n[1:3] for n in num_nodes]);\n",
"plt.plot(r[ix],r[iy],'k-');\n",
"plt.plot(r[ix],r[iy],'bo');\n",
"plt.plot(r[0],r[1],'r^',markersize=20);\n",
"plt.plot(r[0],r[1],'k>',markersize=20);\n",
"plt.plot(r[-2],r[-1],'r^',markersize=20);\n",
"for n in num_nodes:\n",
" if n[2]>0.8*l: offset=0.1\n",
" else: offset=-l/5\n",
" plt.text(n[1]-l/3,n[2]+offset,'n {}'.format(int(n[0])),color='b'); \n",
"\n",
"plt.plot(r[ix]+u_1[ix]*s,r[iy]+u_1[iy]*s,'-',color=(1,0,0,1));\n",
"plt.quiver(r[ix],r[iy],F_steel[ix],F_steel[iy],color=(1,0,0,1),label='applied forces');\n",
"plt.quiver(r[ix],r[iy],u_1[ix],u_1[iy],color=(0,0,1,1),label='displacements');\n",
"plt.axis(l*np.array([-0.5,3.5,-1,1.5]));\n",
"plt.legend(bbox_to_anchor=(1,0.5));\n",
"plt.title('STEEL\\nDeformation scale = {:.1f}x'.format(s),size=20);\n",
"plt.xlabel('x (mm)',size=15);\n",
"plt.ylabel('y (mm)',size=15);"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\tALUMINUM\n",
"------------------------\n",
"\n",
"\n",
"Force:\n",
"F_1x = 0.00 Newtons\n",
"F_1y = 50.00 Newtons\n",
"F_2x = 0.00 Newtons\n",
"F_2y = 0.00 Newtons\n",
"F_3x = -0.00 Newtons\n",
"F_3y = 0.00 Newtons\n",
"F_4x = 0.00 Newtons\n",
"F_4y = -100.00 Newtons\n",
"F_5x = 0.00 Newtons\n",
"F_5y = 0.00 Newtons\n",
"F_6x = 0.00 Newtons\n",
"F_6y = 0.00 Newtons\n",
"F_7x = -0.00 Newtons\n",
"F_7y = 50.00 Newtons\n",
"\n",
"\n",
"Displacement:\n",
"u_1x = 0.00 millimeters\n",
"u_1y = 0.00 millimeters\n",
"u_2x = 5.57 millimeters\n",
"u_2y = -6.07 millimeters\n",
"u_3x = 1.24 millimeters\n",
"u_3y = -11.43 millimeters\n",
"u_4x = 3.09 millimeters\n",
"u_4y = -15.36 millimeters\n",
"u_5x = 4.95 millimeters\n",
"u_5y = -11.43 millimeters\n",
"u_6x = 0.62 millimeters\n",
"u_6y = -6.07 millimeters\n",
"u_7x = 6.19 millimeters\n",
"u_7y = 0.00 millimeters\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"u_2 = u_2*1000\n",
"print('\\tALUMINUM')\n",
"print('------------------------')\n",
"print('\\n')\n",
"\n",
"xy={0:'x',1:'y'}\n",
"print('Force:')\n",
"for i in range(len(F_aluminum)):\n",
" print('F_{}{} = {:.2f} Newtons'.format(int(i/2)+1,xy[i%2],F_aluminum[i]))\n",
"\n",
"print('\\n')\n",
"\n",
"print('Displacement:')\n",
"for i in range(len(u_2)):\n",
" print('u_{}{} = {:.2f} millimeters'.format(int(i/2)+1,xy[i%2],u_2[i]))\n",
"\n",
"l = 300\n",
"s = 5\n",
"num_nodes = np.array([[1,0,0],[2,0.5,3**0.5/2],[3,1,0],[4,1.5,3**0.5/2],[5,2,0],[6,2.5,3**0.5/2],[7,3,0]])\n",
"num_nodes[:,1:3]*=l\n",
"elems = np.array([[1,1,2],[2,2,3],[3,1,3],[4,2,4],[5,3,4],[6,3,5],[7,4,5],[8,4,6],[9,5,6],[10,5,7],[11,6,7]])\n",
"ix = 2*np.block([[np.arange(0,5)],[np.arange(1,6)],[np.arange(2,7)],[np.arange(0,5)]])\n",
"iy = ix + 1\n",
"r = np.block([n[1:3] for n in num_nodes]);\n",
"plt.plot(r[ix],r[iy],'k-');\n",
"plt.plot(r[ix],r[iy],'bo');\n",
"plt.plot(r[0],r[1],'r^',markersize=20);\n",
"plt.plot(r[0],r[1],'k>',markersize=20);\n",
"plt.plot(r[-2],r[-1],'r^',markersize=20);\n",
"for n in num_nodes:\n",
" if n[2]>0.8*l: offset=0.1\n",
" else: offset=-l/5\n",
" plt.text(n[1]-l/3,n[2]+offset,'n {}'.format(int(n[0])),color='b'); \n",
"\n",
"plt.plot(r[ix]+u_2[ix]*s,r[iy]+u_2[iy]*s,'-',color=(1,0,0,1));\n",
"plt.quiver(r[ix],r[iy],F_aluminum[ix],F_aluminum[iy],color=(1,0,0,1),label='applied forces');\n",
"plt.quiver(r[ix],r[iy],u_2[ix],u_2[iy],color=(0,0,1,1),label='displacements');\n",
"plt.axis(l*np.array([-0.5,3.5,-1,1.5]));\n",
"plt.legend(bbox_to_anchor=(1,0.5));\n",
"plt.title('ALUMINUM\\nDeformation scale = {:.1f}x'.format(s),size=20);\n",
"plt.xlabel('x (mm)',size=15);\n",
"plt.ylabel('y (mm)',size=15);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3. Determine cross-sectional area\n",
"\n",
"a. Using aluminum, what is the minimum cross-sectional area to keep total y-deflections $<0.2~mm$?\n",
"\n",
"b. Using steel, what is the minimum cross-sectional area to keep total y-deflections $<0.2~mm$?\n",
"\n",
"c. What are the weights of the aluminum and steel trusses with the chosed cross-sectional areas?\n",
"\n",
"d. The current price (2020/03) of [aluminum](https://tradingeconomics.com/commodity/aluminum) is 1545 dollars/Tonne and [steel](https://tradingeconomics.com/commodity/steel) is 476 dollars/Tonne [2]. Which material is cheaper to create the truss?"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The minimum cross-sectional area for aluminum is 7.9e-06 m^2\n",
"The minimum cross-sectional area for steel is 2.8e-06 m^2\n",
"\n",
"\n",
"The weight of an aluminum truss is 761.413 Newtowns\n",
"The weight of a steel truss is 756.0802 Newtons\n",
"\n",
"\n",
"The cost of steel is $ 36.95\n",
"The cost of aluminum is $ 119.08\n"
]
}
],
"source": [
"A_aluminum = 0.0000079\n",
"A_steel = 0.0000028\n",
"\n",
"u_aluminum = solveLU(L,U,F/E_aluminum/A_aluminum)\n",
"u_2 = np.zeros(14)\n",
"u_steel = solveLU(L,U,F/E_steel/A_steel)\n",
"u_1 = np.zeros(14)\n",
"\n",
"for i in range(len(u_aluminum)):\n",
" u_2[i+2] = u_aluminum[i]\n",
"F_aluminum = K*E_aluminum*A_aluminum@u_2\n",
"\n",
"for i in range(len(u_steel)):\n",
" u_1[i+2] = u_steel[i]\n",
"F_steel = K*E_steel*A_steel@u_1\n",
"\n",
"print('The minimum cross-sectional area for aluminum is', A_aluminum,'m^2')\n",
"print('The minimum cross-sectional area for steel is', A_steel,'m^2')\n",
"print('\\n')\n",
"\n",
"density_aluminum = 2710\n",
"density_steel = 7700\n",
"\n",
"num_nodes = np.array([[1,0,0],[2,0.5,3**0.5/2],[3,1,0],[4,1.5,3**0.5/2],[5,2,0],[6,2.5,3**0.5/2],[7,3,0]])\n",
"num_nodes[:,1:3]*=l\n",
"elems = np.array([[1,1,2],[2,2,3],[3,1,3],[4,2,4],[5,3,4],[6,3,5],[7,4,5],[8,4,6],[9,5,6],[10,5,7],[11,6,7]])\n",
"for i in range(0,len(elems)):\n",
" n1 = elems[i][1] - 1\n",
" n2 = elems[i][2] - 1 \n",
" ix1 = num_nodes[n1][1]\n",
" iy1 = num_nodes[n1][2] \n",
" ix2 = num_nodes[n2][1]\n",
" iy2 = num_nodes[n2][2]\n",
" l += ((iy2-iy1)**2 + (ix2-ix1)**2)**0.5\n",
"\n",
"m_aluminum = A_aluminum*density_aluminum*l\n",
"m_steel = A_steel*density_steel*l\n",
"\n",
"g = 9.81\n",
"w_aluminum = m_aluminum*g\n",
"w_steel = m_steel*g\n",
"\n",
"print('The weight of an aluminum truss is', round(w_steel,4),'Newtowns')\n",
"print('The weight of a steel truss is', round(w_aluminum,4),'Newtons')\n",
"print('\\n')\n",
"\n",
"pr_steel = 476/1000\n",
"pr_aluminum = 1545/1000\n",
"\n",
"cost_steel = m_steel*pr_steel\n",
"cost_aluminum = m_aluminum*pr_aluminum\n",
"\n",
"print('The cost of steel is $',round(cost_steel,2))\n",
"print('The cost of aluminum is $',round(cost_aluminum,2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_Steal is the cheaper material to make the truss._"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 4. Future Predictions using past data\n",
"\n",
"The data from the price of aluminum and steel are in the data files `../data/al_prices.csv` and `../data/steel_price.csv`. If you're going to produce these supports for 5 years, how would you use the price history of steel and aluminum to compare how much manufacturing will cost?\n",
"\n",
"a. Separate the aluminum and steel data points into training and testing data (70-30%-split)\n",
"\n",
"b. Fit the training data to polynomial functions of order n. _Choose the highest order._\n",
"\n",
"c. Plot the error between your model and the training data and the error between your model and you testing data as a function of the polynomial function order, n. [Create the training-testing curves](../notebooks/03_Linear-regression-algebra.ipynb)\n",
"\n",
"d. Choose a polynomial function to predict the price of aluminum and steel in the year 2025. \n",
"\n",
"e. Based upon your price model would you change your answer in __3.b__?"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import random\n",
"\n",
"steel = pd.read_csv('../data/steel_price.csv')\n",
"aluminum = pd.read_csv('../data/al_price.csv')\n",
"t_steel = steel['Year']\n",
"P_steel = steel['dollars/MT']\n",
"t_aluminum = aluminum['Year']\n",
"P_aluminum = aluminum['dollars/MT']\n",
"train_per=0.7\n",
"\n",
"np.random.seed(100)\n",
"\n",
"steel_rand = random.sample(range(0,len(t_steel)),len(t_steel))\n",
"aluminum_rand = random.sample(range(0,len(t_aluminum)),len(t_aluminum))\n",
"\n",
"t_steel_train = np.sort(t_steel[steel_rand[:int(len(t_steel)*train_per)]])\n",
"P_steel_train = np.sort(P_steel[steel_rand[:int(len(t_steel)*train_per)]])\n",
"t_steel_test = np.sort(t_steel[steel_rand[int(len(t_steel)*train_per):]])\n",
"P_steel_test = np.sort(P_steel[steel_rand[int(len(t_steel)*train_per):]])\n",
"\n",
"t_aluminum_train = np.sort(t_aluminum[steel_rand[:int(len(t_aluminum)*train_per)]])\n",
"P_aluminum_train = np.sort(P_aluminum[steel_rand[:int(len(t_aluminum)*train_per)]])\n",
"t_aluminum_test = np.sort(t_aluminum[aluminum_rand[int(len(t_aluminum)*train_per):]])\n",
"P_aluminum_test = np.sort(P_aluminum[aluminum_rand[int(len(t_aluminum)*train_per):]])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
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UFPCHP/whoO9NN93EnXfeyRNPPEHPnj0xxnDVVVeRn5/P66+/TkREBE888QSFhYUMGzbMd9/u3bs5++yzSUtL46233sLlcvH4449zxRVXsG7dOt8eOoDZs2dz2223MXfu3KAzhOPHj2f16tVMmjSJBx54gOuuuy7o0unjjz9OVlYWRUVF/P73vwdgwIABgCdgve2229i7dy8pKSn1/rcxxnDPPffw0EMPkZiYGLTP2rVrGTNmDAsWLOCll16ipKSEc889lxdffJGRI0fW/x9eKaVUk1WfOuHIclA51Ma3P4liRWk+haWBWbHhlXDhxjAuWxNOTIXQMyq8/mPFBM7JP6dtfoAOqkMGeP5EJAUYB6wFtgJXAu8B1wMDvd0SgTV+tx30tnVp8+fPZ/LkySxZsgSASy+9FPAsSz722GO+oAjgvvvu4/777/d9v3LlSr777jvWrFnDGWecAcCECRMYMmRIQIC3cOFCEhIS+OCDDwgPDwdg7NixjBgxgpUrVzJt2jRf3+uvv54nn3yy3vHGxMRw5plnAp4Zu+rPtQ0ZMoTevXvjdrvr9LFYLFit1oDAMpg33niDnJycgMSN2nJyctiwYQMZGRm8+uqrhIWF8dhjj3HppZeyc+fOVl/GVkqpzix3WS677t+Fq8DFkRg3H11YxZdjS6nMKwro170MpmywMWW9je4Vnj/b7cme/dn2JDuO/XWDvM5y3FhLdOgAT0S6AyuAucaYYhGZBfxOROYD7wOV1V2D3B50zlZE5gBzAJKSkk5oPCk///cJ9W8N+56Z1ngnwOVysWHDBn77298GtN944408/PDDrF69muuvv97X7h+IAaxbt474+HhfcAeQnJzMhAkTAvp98sknzJw5E4vF4lv6HTRoECkpKaSnpwc8t/Y7WsMtt9zCLbfc0mCfY8eO8eijj/K73/2u3n2AAG63m9LSUlasWOGbsRs9ejSpqaksW7aM2bNnh3TsSinVVeQuy2XHnB1s6+Pk4/Oq2DjUham1aSyxZyTTI/swYv5RbMU1f6X7168bvGgwO+fsxF3mDnq9K+uwAZ6I2PAEd8uMMe8AGGN2AJd4r6cC1RHDQWpm8wAGAIeCPdcYsxhYDJCWlhZ84b4TyM/Pp6qqivj4wL0H1d8XFhYGba+Wk5NDXFxcnefGxcVRUlIS8J5f/epX/OpXv6rTt3biQu13tJenn36agQMHcskll1BU5PmXotPppKqqiqKiIqKjo7FarfTu3Zvjx48HLMcOHjyYlJQUtm/f3l7DV0qpk1pZpZPFf9rOh9PLye5b96/hAXnCZevC+X+bJmOzWsjtU7OEW7t+XfXX+q53ZR0ywBPP+trrQIYx5jd+7XHGmDwRsQCP4cmoBc9s3l9E5DdAf2AYsK6Nh92h9OnTB5vNRl5eXkB7bm4uAL179w5or72kmZCQUOde8JQV8Z/16t27N9dccw2333570DE09I72snPnTtLT0+nVq1eda7169eKrr77inHPOYeTIkWRlZdXpY4zBYumo+UlKKdUxHSgsY+nqffzt2wMUn+6sc330XgtT022MybQSkRyBzer5czZ+RnyDAVtj17uqDhngAWcDNwNbRGSjt+1RYJiI3O39/h3gDQBjzDYRWQ5sx5OBe7cxxkWINXV5tCOwWq1MmDCBv//979x5552+9uXLl2OxWJg0qeGz904//XQWLlzI2rVrfcu0WVlZbNiwgbPPPtvX76KLLmLr1q1MmDChTQO48PBwKioqmnXvU089xdy5cwPa5s6dS48ePVi4cCFjxowB4PLLL2fJkiVs376dUaNGAbBnzx7279/Pqaee2rIfQCmluoAql5tPM/L427dZfLHrCKbWhJ29Es7eGsaUDTb6F3gCOl1iDY0OGeAZY74m+L46gBfquWcRsKjVBnUSWrhwIVOnTuW2225j+vTpbNmyhccff5wf//jHAQkWwVx22WWceuqpXH/99fzqV78iIiKC+fPn11m2XbBgARMnTmTatGnMmjWLPn36kJ2dzccff8ytt97aaqdejBgxgvfee493332XAQMG0L9/f/r378/SpUuZNWsWe/bsITk5Oei9p5xySp22nj170qdPn4DxXnPNNYwfP54f/vCHPPXUU1itVubPn09qaqqeZqGUUg3Ym1/K299msWL9QfKPV9a53t9t44KvLZy93kpUZc1f92GxYQx7YZjOyIVAhwzwVGhccsklvP322zz11FMsW7aMuLg4HnjgARYuXNjovSLC+++/z5w5c5g1axZxcXE8+uijfPzxx+Tn5/v6paamsmbNGh577DHmzJlDeXk5iYmJXHTRRQwdOrTVfra77rqL7777jlmzZnH06FGeeOIJFixYgNvtxuVyYWr/M7EZrFYrK1euZO7cucyePRu3282UKVN44YUXsNlsIfgplFKq86iocvHB1sO8ve4Aa/cWBu1zSqaVi9eHcWqOjf4z+1FwqOucDdvWJBR/EZ6s0tLSTHp6etBrGRkZWutMNZv+/lFKdSb+ter8gzG327A+6yh/Wb6bj3LyKQ2vG1P0KhXO2RTGuZvDiDtWs3/Znmxn0r6GtwupQCKy3hiT1pS+OoOnlFJKqXrlLssNKEXi2O/gs4e3szPnIJ84j3HwaLmnY3jNPRY3nN2jJ1f37kPPuw9hNXV3XdVbpFiFhAZ4SimllKpX5rxM3GVuirq5WTPKxepRTvYnuOFIWZ2+fY8K528O4+ytYSTEWoBCHEGCO9BixK1NAzyllFKqi6tvCTa3uIJ/xx4nfZKTnQPddYoRA3Qrh9N3hDFpexjDDlqweHMkHaUNz9Bppmzr0gBPKaWU6kJ8wdx+B1iBWkXFso+W88/fb2Hrngw2l5XCxXWfEeaECYdszJo3lsgrMnHvrZspWz1DF+woMWusVRMqWpkGeEoppVQXUXs/XXVwd7i3mw3DnKSnutjb33utLDAwEwPDsyxM2h5G2q4w0l4bRfzoeHKflAaPCwt2LfWF1Nb7IRWgAV6DjDEd5vQFdfLoypnpSqmOrXo/ndNi+H6Am02DXWwc6iQnNvifWxY3jMiykLYzjPHfW+lZWrNGeyLHhelRYm1PA7x62Gw2ysvLiYqKau+hqJNMeXm51slTSrWpYMuu9mS7bxYtc14mB46Vs2WQi60TXGxPduEID/4sqwtG7bcyKT+CCQdt2L+vqtPHnhyYINHQcWF6lFj70ACvHnFxcWRnZ5OYmEhkZKTO5KlGGWMoLy8nOzub+Hj9w0wp1TbqW3Ytzq7g7V9sYWuKm82XOMntXf/qQngljNlrZfz3Vk7bHUa3SmHkW55ang0tv6qOSwO8esTExABw6NAhqqrq/utFqWBsNhvx8fG+3z9KKRVKucty2XX/LlwF3ijOAnhjLzeGA3Futie72TrIk/XqbOBv+b5FwphMK2P3WBm130q4yzuRIdD/J/11ifUkpwFeA2JiYvQvaqWUUh1C7rJcMm7LAO+cgxvDgT5udiS52THQxa6BLkoj678/vBJGZlkZs9fKKXutxB8VxCqeGT+rp0/1sq5/AKdLrCcnDfCUUkqpdlZfHTr/ayXZFexNcLOnv4vvE92NBnQAiUeEMXutjMn01KirnqWzJ9uZVKjHhHVmGuAppZRS7SjYUWA75uzgcKWDLWWlfPXPA3x/nouseDcua8PP6nFcGJFlYdR+z0xd7woLIoKprNl/p3vougYN8JRSSql2lDkvk/JKF1mJbnYnutnd38We/m6Kdm7xdDit/ntjjgsjsyyMyLIy4oCVhMKaZdfaWbS6h65r0QBPKaWUaoGGlleDXY+6rBcb1+bxPQ4ODIE9F1WRHWuCHgNWW78CYWi2lSGHLKQetNKvQBDv0WCWKAvD/zw8aPCmAV3XowGeUkqpLs8/CLP2tiIIzkKnL2CD4LNgwZZXd87ZCUDfm+LY8GYWX/52N1kDXBwc5+ZAXBl5MYVBj/+qLaIKhhaEMShTGJZtYfAhK90rapXs8mbRBkuOUF2bBnhKKaW6tNpBmq8ECZ6ALeO2jIB9bP5BXPXJEMcjDAf7ujnQ182BODeHPv+O7B1QXuWCyxofgxhIKBQGH7IyNNvC0MNWLnp+FFYJfgzY8MXBZ+qUqqYBnlJKqS6tOkirVxUYDG4MhTGGw7FuDsUalvxjCwfPquLwFW6KuwW/LxiL27PUmpRnISXHSkqOhaQ8C5GVgbNz/f8nIWCMuodOnQgN8JRSSnUatQsBh8WGMeyFYQ3uiXPsd/iuucRQ0MOQ19NNXk9Dbi/P17xebo70NFSe4CmEPcqFATnCwCMWBuZZGHDEQv8CCzZXw6cj+R8FpnXoVHNogKeUUqpTqF0IGMBZ4GTHrB0Avj1zG+/ewRGbiyND3OT1rCI3tSaIK4gxjZYiCcZWBf0LLJ5ArsjKWbckc+aPknC/X1RnibUxWsZEhYIGeEoppdpdsExUaHhpsnZihOuoCyeGohhDgfdXYYybwmjD0Q83UX4kgqys45T9pP4zWRvTvcwTyPU/ZuXUKfGc9oN+9PxvBWW/OEjV/sq64/R+9f85Yi+LpWBlQb3f6xKsCgUxpvm/0VuLiAwElgIJeE7ZW2yMeUFETgP+AEQATuAuY8w67z2PALPxHLpynzFmVWPvSUtLM+np6a30UyillGqK2kkOANgISGxwWgzHY4VeTydhzu1O5sdH2Pm3QxTZ3ByN9uyNK4gxFHVrWrmRhvQqFeKKLcQdEfphY8y0fgwMt1P168PY9lRpEKbajYisN8akNaVvR53BcwIPGGM2iEg0sF5EPgZ+DSw0xnwgIpd5v58sIqOA6cBooD/wiYikGmNc9b1AKaVU62isLly1/W8dYuMzmRwpclDS33Csm6E4yvO1xPu12NvmO5Jrdwbs9n4+u3njs1VBbLHQp9hC3FEhrshCoi2cS1aMJ6l3FJHh9azR/liXTdXJo0MGeMaYw8Bh7+cSEckAEgEDxHi79QAOeT9fBbxtjHEAe0VkNzARWN2mA1dKqS7MGMOetw6x/pHvKbK4OJZqKI6qouT1zUh2DGUJVvKPO8g/XsmRogrK3W64IrRjEOM5rqt3iRBb7P1VamHszIGMurIftk9LyL1rD6Ys8Oiu4YuHE58QHdrBKNWOOmSA509EUoBxwFpgLrBKRJ7DU97xLG+3RGCN320HvW1KKaVawOU2HC2r9ARmJd6v3iAt/7iDgoDPlVS63HBzkAcV5kNh88chboguhx5VVpLTemE+Kab7ETcxpULP40JssYXYYqFXiRDmrslQrZNFO7MHvcJsWnZEdXodOsATke7ACmCuMaZYRJ4CfmqMWSEiNwCvA1OAYPnmQTcXisgcYA5AUlJS6wxcKaU6sANvHWbT05nkF1VQlhJG+I/6UDUmgvzjDg5uOUb2zmKKLC6KY+B4hKHp+Z8nJswJMWVCTKkQUyb0KBWivV9jHEKPMiH6mOdr93IIi7T6CvzmRgbZt+enoWLAWnZEdQUdMskCQERswL+AVcaY33jbjgE9jTFGRAQ4ZoyJ8SZYYIz5pbffKmCBMabBJVpNslBKnYxq73GLvSyWrBU5FDqcFHczHE+wYJ/Zl8OZJWRnFHMssmYvW3F3Q5m98Xc0V4TDG7RVB26lngCtt93G6f87gj7d7cR2D2fvWZuw7q70naPqr/rYLTixLNrax4tpEKc6mxNJsuiQAZ43eFsCFBpj5vq1ZwB3GmO+EJGLgF8bYyaIyGjgL3j23fUHPgWGNZZkoQGeUqojc7kNhaWVHClxcOS4g7ziCvZ+VcDuVXkU2d0c6+ZJRDjW3VDeikFbd4eQMLAb4Vsq6F5ofDNu1bNu1YFcTJlgd9YN2ILNpgXLnNUjuJRqWGfIoj0bzy6OLSKy0dv2KPBj4AURCQMq8C61GmO2ichyYDueDNy7NYNWKdVRGWMoKqvi8LEKcosrOHysgpziCnKPVZBbUuEJ6EocFJRW4nIH+Uf4aS17v8UN0WU1s2ue4Mwz89bjuN8yaZnnc5gRJrvP5wvLF/VsfqmHUO9sWnyQ+nA666ZU6HTIAM8Y8zXB99UBTKjnnkXAolYblFJK1aP2UmGlFXJdVRQPtcKMWHIqHXz/bSH5VidHexiORhmqQvynb5iTmtk0vwAt2PfdysFS63cEOcgAACAASURBVI/Y6qOx/I/tqn2t9rFeDbEn25m0b1KDfXQvnFKtp0MGeEop1ZFVVLnYV1BKVkEZOz7JY/vKHPLHuSk435Af46bE/+D57OOerynNe1cPaxjd89z0KPEEcD2OWzxfS4WepZ4Ztx6lQrcKgu5nawr/o7GCLZtWXxu8aHCjBYlr36OUah8a4CmlVBAOp4sDhWXszS9jX34pewtK2Zfv+XXoWEVg53En/vxIB/QqEXodF3qVWDyfvd9XB219+0Rgc0uTZ80CCPUvp9ogLCas3oSE+pZN61tWbegepVT76JBJFm1FkyyU6tqcLjcHj5azN7+Uvfml7Cuo+Zp9tJxg29+awurCU2j3mKc+W5/ims/VQVxkZRNm26q71DcO7x632MtiyV2ei6vAs/W4uvbbsW+OcWjxIc8Bjl7VGaoagCl18jnps2jbigZ4Sp2cGjoKa9ddu2qCGiv0n9OfwS8OZX9hGbtyStiVe5zN3x5hR9Yxcrq7cdVzKlVDLG7oc0yIO2qhzzHxBnDeQK7YU3jXYpq3XOqvsX1xje1xU0p1Lp0hi1YppYKqXV7Dsd/Bzjk7ASj6poiMpdnsT3ZzoK+b7L5ussv3cPjR3VRJrX/M9mj4PYLnvNL4QiG+0EL8UQvxR4WEQk9Q539aQoOC7FFriqbui1NKqWA0wFNKnVQy52XiLnPjxpDXy7A/3s3+eDcHP9rEvpgqiu85sef1LBHijwqJVTbOuGcQKX26MahPNw5P2oLZW9n0B1kBN0EL7laPu3ZB3vo+n8i+OKWUCibkS7QiEg70AcqNMUdD+vAQ0yVapTq26qXYiqwKCpMs7OvrZnf3KvYmuNiX4KbiBIr7xsfYSY2PJuovRQw4YiEx30L/fAsRVd6ZOIHJ7sm+/idS800L9Cql2kKbLtGKSDQwHbgYOA/o63fNCWwGPgPeMcasben7lFIdR7D9bj3O7hF0tsm3b26/IyDDszohAGpmqRgUTv5lUazddIRdaS4yr3RREtW0MdkrYWCehaQ8CwOOeH4lHrUwrfQCAFY/uTr4nrYke53vG8xe9c7Y6YyaUqojavYMnogkAo8DM4Dqqk9FQA5QCEQCsUAinj8KDbAReM4Y89eWDTs0dAZPqebbddcuDr1yqE67hAnGGVgTLWFmAjlLcuo9GP5ojJs9Aw274p18n+gmK75pyQ8xpZCcayWl0MqZ1wygf4YL8/KROkV8+9/Zn9TfpwJNPyIrWL+G+iulVGtr9Rk8EVkIPADYgY+Bt4FvjDF7gvSNwnNG7FQ8weAyEbkfmGOM2dyc9yul2t+hxXWDOyAguANwl7kDSnUYDHk9DRnJLnYMdLE70U1+z8b/oRlZAYNyLAw6bPV+tdC7RIhIjgjMonXXnVWsDu6g6UdkBfTb7/D8M9WlZUaUUieHZs3giUgZ8AfgWWPM4RO4T4DLgQXAe8aYX5zwy0NIZ/BUV1O7vEjsZbEUrCyos/m/KQVsv5Avmvzegmg3O5JcbE92k5HsojCm8T93+ucLQ7OtDMu2MCTbSkKhBD1eS0uFKKW6irbYgzfUGBP8n+8NMJ5o8p/AP0UkoZnvVko1Q7DyIv5LrNVFcquvZdyWEVDew78cSfyMeN+MVjAlkYbtyS4ykl1kJLnI7d1wQGergsGHLQzLtjI028LQbCvdK6TB0xi0VIhSStWvWQFec4K7IM/IaekzlFLB5S7LZdf9uwJONgDq3QMXVJVnOdWfu8xN5rxM4mfE039Of1+AaDAc6Otm0xAXm4a62NPPjbHU/+gIBww/YGVElpXhBy0k5VuwiaXOeaYJMxManGHUZVKllApO6+Ap1cnkLssl47YMqKppcxY4Q/Z8R5Yns3Tgb4ewOuw4n+86wubBDS+72sMsnBrRjUH/dTJskyEl10KYy7PcGhYbxrA3ArNoNYBTSqmWabUAT0QswDXAUGA/njIpJ1A1VCl1onKX5ZIxM6PepdOWOhLjZvvpwptvrGP1ngIcUW44rW4/EThtYE/OHdaXs4bEMi6pJ/awxtNiNaBTSqnQaFGAJyJW4DVgmzHmuVrtHwGTqdlFkyEi5xhjilryTqVUcNV77EIW3NnACOzp42LDMBebhjjJ7uudpdtZVqd7dEQY56f25cIRcZyf2pfY7idQhVgppVRItXQGLw2YCdxVq/124ALgAzzZthcB9wEPA4+08J1KqSCqj/BqiDXWSlj3sAazaCsLqzgwzkrG9Eg+Kz5KXlVVvc8bFtedC0fEccGIOCYk98JmbWDjnVJKqTbT0gBvFJ7Zuc9qtf8IT7HjG4wxpXiyZkcCV6IBnlIhFXBCRAMkXEh9ITXoMqjbbdiQdZR/bznMh1tzOHysDApK6vQLD7MwaXAsF46I48IRcQzs3cTjJZRSSrWp5hY6Ps/78Qzv10G1yp6cDqwHJnhK3wGQCZwjIufiWbbFGPOf5rxfqa4qWB27hk6IqFZ9HFjt4C7jcDHvbDjIPzcdJqe4Iui9PSJtTB0dz8WjEjh7aCxR4ZqbpZRSHV1z/6Re6P2a5P36c79rMUAE0MevH0Cct30hNfvyLmzm+5XqcoLWsfvDoXrrxEHwI7XySip4f+MhVmzIJuNwcdD7ekbZmDoqgcvG9uOsIbG69KqUUieZ5tbBuwBAROYArwCzjDF7vW23Aq8Dd/jP0InIj4FFxhgN6pRqhqB77BoI7vyP1KqocvHR9lze2XCQ/+w6gjvIfb2ibFx6SgI/OKUfkzSoU0qpk1pL11o245mNe1JEbga640mmKAL+W6vvKOBAUx4qIgOBpUAC4AYWG2NeEJG/AcO93XoCRcaY07z3PALMxpNDeJ8xZlVLfjClOprG9tj5syfbOSPzTL7dV8hv/m8zK7ccpsRRtxaePczC1NEJXDM+kXOH9iFMgzqllOoUWhTgGWPWiMhneJIqrgBseJZhHzHG+P428Z5BezXwjyY+2gk8YIzZICLRwHoR+dgYc6PfM58Hjnk/jwKmA6OB/sAnIpJqjGmlamBKta1dd+2q/2Kt47yOx0L63Egeef4L9hXULWcCcMag3lw7fgA/GJNAdIQttINVSinV7kKxW/pa4Ck8ZVGOAn82xvyxVp+p3q9/b8oDjTGHgcPezyUikgEkAtvBFzDeQM0evquAt40xDmCviOwGJgKrm/tDKdXe/BMqGlqK7f+T/hxZmc8myvnPWW7Sk6tw5pTW6TeoTzd+OC6Rq8clavarUkp1ci0O8Iwxx4B7G+nzITCoOc8XkRRgHLDWr/lcINcY8733+0Rgjd/1g942pU5KtRMq6lNqN3w5PYxlgxzsK/BmwfoFg9ERYVx5an+unTCAcQN74pfVrpRSqhPr0PUORKQ7sAKYa4zxT/e7Cfirf9cgtwed8/AmhswBSEpKCtZFqTYVUMfOimcXaa1l19oO9HHzyYQqVo92Urkyo871Ccm9uGliEtPG9CMyvPEjwpRSSnUuHTbAExEbnuBumTHmHb/2MOCHwAS/7geBgX7fDwAOBXuuMWYxsBggLS2tgb9ClWp9dWbqqneNBvmd6RLDhmEuPplQxc6kujN70RFhXDt+ANMnDmREQkzrDVoppVSH19xCxy/iKXmS08z7rwEijDF/ree64Cm1kmGM+U2ty1OAHcaYg35t7wN/EZHf4EmyGAasa87YlGpLTTlezGEz/GeMk1WnV5Hfs27kN7JfDLeelcyVpybqbJ1SSimg+TN4M4BZIrIUeNMYs7axG0SkB55M1zuAU4H7G+h+NnAzsEVENnrbHjXGrPQ+IyAwNMZsE5HleJIwnMDdmkGrTgaOrPpLnxRHGT6eUMVn46oojQy8ZrUIl45OYOZZKZye0kv31imllArQ3ABvCPAknr1sc0TkAPANkI4n+/UonnIpscAI4Ew8x5fZgQzgcmPMB/U93BjzNcH31WGMubWe9kXAoub9OEq1D3uSvU59u5xebj6cWMXXpzhx1vp/aM8oGzPOSOJ/zkymX49aUZ9SSinlJcY0fxuatyDxT4BbgX7e5toPFDw7iz4Ffg/8yxjT8JpUG0lLSzPp6entPQzVhfnvwctMcPHvM6vYkOrC1PrnTd8i4QZ7H+5+dryeBauUUl2UiKw3xqQ1pW9LCx0fAOYB80RkNHAOnvNpY4FyIA/PaRdf1cqCVUoB8TPi2VJ6nBe/3sOm/lV1rg86bOEH6TauOH8gI18YHuQJSimlVF0hmwowxmwDtoXqeUqdjPyLE1t7WxEEZ6ETe5LnXFjAd333SMO74yvZmuj0pAb5uWB4X+acN4QzB/fW/XVKKaVOmK71KBUitUueuApq8nwc+x1k3JYBAhkJLt67sZIdyYE7FcQNF/fqzQO3ncLwhOg2HbtSSqnORQM8pUKksZInu/u6+L/z6gZ2FjdM2hbG5WtspETD8Ec0uFNKKdUyGuApFSL1lTzJ7uPm/86t5LvUwMo9VhectS2My1fbiC+yeJ5xtP6yKUoppVRTaYCnVIjULnlyJMbNu+dU8d9TnAFZsRY3nLvZM2PX95ilzjOUUkqpltIAT6kQGbxoMDvn7OQoLv45qZLPxzlx1TpY4swdYVzzZc2MnT9LlMWXiKGUUkq1hAZ4SoVIzPV9+Cr3EEuzD+GwBV477ZCNB84bRuqYKDI3ZuI4FjzLNn5GfPsMXimlVKeiAZ5SLXT4zzn8+dUd/HV0GYUxBvyCuwnJvXho6nDOGBzra9MgTimlVGtrlQBPRHoB3b2FkJXqNPzr3NmT7ORdEcXvSg6xZ1JgZuzQiEgeuXE0F46I0zp2Siml2lzIAjwR6Q4sBGYAffEcWRbmvXYG8ATwmDFmQ6jeqVRb8q9zVxDt5u9jjrGmWyF0q+kTUwrX/iecKcURnL1AZ+qUUkq1j5AEeCLSA/gaGA1sBPKBkX5dtgDnAjcBGuCpk1LmvEzKK12sPKeKDyZWUem3FBvmhEvSbVyx2kZkpVAlle03UKWUUl1eqGbw5uEJ7m41xiwVkSeA+dUXjTFlIvIlcFGI3qdUm1sTXsqfb6+koIcJaE/baeWGz8OJ8yt5ouVOlFJKtadQBXg/BFYZY5Y20Gc/cHqI3qdUm8kuKmfB+9v4+IeBRYiTcyzc9Fk4Iw5aPRsSvLTciVJKqfYWqgBvALCikT7HgR4hep9Sra7K5eb1r/fywiffU15VcwpF9zK4/stwzt0SRliklYSfJFCwssCXeKHlTpRSSrW3UAV4JUBcI30G4dmbp1SHtzazgMfe3cr3eccD2q/q1Ydp7zgJ312lwZxSSqkOK1QB3rfA5SISbYwpqX1RRPoBlwH/CtH7lAoZ/9InZf2Ev57h4KvUqoA+IxKiWXTNKUxI7g0Pt9NAlVJKqSYKVYD3AvABsFJE5vhfEJGRwKtABPC7EL1PqZCoLn3iKnPx7QgXb01xUOJX9sReCT9JGsC9944hzFr3eDGllFKqIwpJgGeMWSUiC4AFwFagCkBE8oFegAAPG2P+G4r3KRUqmfMyKRQnb11dyfrhroBraTut/OjTcPr1LiNsrgZ3SimlTh4hK3RsjPmFiHwF3AecCcTiyS1cCfyvMeazUL1LqebyX44NTwrn8+6l/OWqSkoja/r0LhZuWRXOaZme/3s4jjvqeZpSSinVMYX0qDJjzOfA56F8plKh4n8SRWG0myVpxWwaGjhrN3ljGDd8Hk5UZc3xYlrTTiml1MmmVc6ibSkRGQgsBRIAN7DYGPOC99q9wD2AE/i3MeYhb/sjwGzABdxnjFnVHmNXHVfmvExcZS7+M9bJ2xdWUu4Xt/UpEmZ9aGfUfmvAPVrTTiml1MkoVEeVXYTnDNrHjDGHglzvDzwFLDXGfNGERzqBB4wxG0QkGlgvIh8D8cBVwFhjjENE4rzPHwVMx3OaRn/gExFJNca46nm+6oJyC8r503WVbB4S+NtiSnoYM/ZFI1mVWGOtCIKz0KllUJRSSp20QjWDdy8wIlhwB2CMOSQik/AUOv6isYcZYw4Dh72fS0QkA0gEfgw8Y4xxeK/leW+5Cnjb275XRHYDE4HVLfqpVKexalsOj8+uoCSi5siJ+EJh1gd2xlqjmLRvUjuOTimllAqtUKUGjgcay5D9Gkg70QeLSAowDlgLpALnishaEflSRKqPPksEDvjddtDbprq4UoeTn6/YzB1vrQ8I7qZ+G8Yv3ohkZKFNl2CVUkp1OqGawYsDgs7e+cml8dMuAohIdzxHoM01xhSLSBiesitn4jnXdrmIDMZThqU2E6QNb52+OQBJSUknMhx1ktmQdZSf/m0j+wvKfG19w2zM+SiCYeluXYJVSinVaYUqwDsGDGykz0CgtKkPFBEbnuBumTHmHW/zQeAdY4wB1omIG+jjbfd//wDqCTiNMYuBxQBpaWlBg0B1cnO63Lz0+W5e/Gw3LnfN/8TTxvbj6avH0OMpWzuOTimllGp9oQrw1gFXi0iCMSan9kVvksXVwDdNeZiICPA6kGGM+Y3fpXeBC4EvRCQVCMdzvu37wF9E5Dd4kiyGecekupisgjLu/9t3fJdV5GuLtofxi6tHc/VpiXh+aymllFKdW6gCvBeBacBXIvIAsMqb5WoHLgWeB7rT9KPKzgZuBraIyEZv26PAn4A/ichWoBKY6Z3N2yYiy4HteDJw79YM2q7nX5sP8ciKLZQ4nL62iSm9ef6GUxnYO6odR6aUUkq1LfHERyF4kMhC4HE8e98McJSaY8oE+IUxZkFIXhYiaWlpJj09vb2HoVqoosrFk//azrK1Wb62MIvws0tSueO8IVgtOmunlFLq5Cci640xTUpYDeVRZU+IyDd4SqacAfQECoE1wIvGmI9D9S6lqu3OO849f9nAjpwSX9vA3pG8dNN4Th3Ysx1HppRSSrWfUB9V9hHwUSifqVR93tuYzSPvbKGssmY1ftqYfvzy2jHERNQkUvifP6uZs0oppbqCDnlUmVINqXS6eerf21m6er+vLTzMwhNXjOJHE5MCEin8z58FcOx3sHPOTgAN8pRSSnVaGuCpk8rhY+XctWxDQJbs4D7deOlH4xnVP6ZO/8x5mb7grpq7zE3mvEwN8JRSSnVazQrwvPXn3MAoY8wu7/dNydYwxhgNKlWzfLM7n3v/+h2FpZW+th+cksCvrxtLtHdJtvZyrGO/I+izHFnB25VSSqnOoLnB1n/wBHRltb5XKuTcbsMrX+7h+Y92Ul232GoRfn7pCG4/d5BvSTbYcixC0N+Z9iR7G41eKaWUanvNCvCMMZMb+l6pUCmrdPLA8k18sLWmfnbfaDsv3TSOMwbHBvQNthyLoU6QZ4my6PmzSimlOrWQLJeKyHlAsTFmY6OdlWqiQ0Xl/HhpOtsOFfvaTk/pxcs/Gk9cTESd/vUuuxqwJ9s1i1YppVSXEar9cJ8DfwTuCtHzVBe3Iesoc5auJ/94TdB261kpzJs2EpvVEvSe+vbc2ZPtTNo3qdXGqpRSSnU0wf+mPHH5QHmInqW6uH98d5Dpi9f4grswi/D0NWNYcOXoeoM7gMGLBmOJCryuy7FKKaW6olDN4H0BnBWiZ6kuyu02PPvRTl75Yo+vrVeUjVf+ZwJn1tpvF0z1sqsWNVZKKdXVhSrAewxYKyJP4jlztipEz1VdxHGHk7lvb+STjFxf27C47rw+83SSYqOa/Jz4GfEa0CmllOryQhXgPQJsBR4FZovIJiCHugUqjDFmdojeqTqJA4Vl/HhpesB5sheOiOOF6af56tsFo0eQKaWUUsGFKsC71e9zgvdXMAbQAE/5fLuvkJ+8tZ4Cv+LFc84bzMOXjsBqkXrv0yPIlFJKqfqFKsAbFKLnqC7k7+kHePQfW6hyeSZ6w60WFl1zCtenDWz0Xj2CTCmllKpfSAI8Y8z+xnsp5WGM4derApMpYruF88ebJ5CW0rtJz6iv5p0eQaaUUkqFIMATkSTgdDzLr98aYw60eFSq06p0uvn5is288122r21EQjSvzUxjQK+mJ1PUW/NOjyBTSimlWlYHT0SeAzKB5cDfgb0i8mwoBqY6n5KKKma9+W1AcHfRiDhW3HlWg8Fd7rJcVqes5gvLF6xOWU3uslyteaeUUko1oNkBnoj8CPgZnpM+dwA7vZ9/JiI3hWZ4qrPIK67gxj+u4evd+b62myYm8cebJ9DNXv9EcnUyhWO/A0xgMsXwxcOxJ9tBPKdVDF88XPffKaWUUrRsiXY24ASmGmM+BxCRKcAH3mt/bfnwVGewO6+EmX/6luyimsNOHrg4lXsuHIpI/Zmy0HAyxaR9kzSgU0oppYJoSYA3Fni3OrgDMMZ8IiLvAZNbOjDVOaTvK2T2knSOlXtqX1stwi9/OIYbmpApC5pMoZRSSjVHS/bg9cKzLFvbDqBnC56LiAwUkc9FJENEtonI/d72BSKSLSIbvb8u87vnERHZLSI7RWRqS96vQuOjbTnMeG2tL7iLCrfy2sy0Jgd3UH/ShCZTKKWUUvVryQyeBQh2JFkVnr14LeEEHjDGbBCRaGC9iHzsvfa/xpjn/DuLyChgOjAa6A98IiKpxhhXC8ehmml5+gF+vmIzbu9ZJn26h/OnW09n7IATi/0HLxocUNAYNJlCKaWUakxLy6TUPoosJIwxh4HD3s8lIpIBJDZwy1XA28YYB55M3t3ARGB1a4xPNWzxf/bw9Modvu9TYqNYMmsiybHdfG2NHTPmf93a20pYZBjOQqceSaaUUko1QUsDvAUisiDYBREJNntmjDEn9E4RSQHGAWuBs4F7ROQWIB3PLN9RPMHfGr/bDtJwQKhagTGG5z/axUuf7/a1jeoXw5JZE+kbXbOk2tgxY7WvuwpcWKIsjHxrpAZ2SimlVBO0qA4enqXYE/l1Qu8Tke7ACmCuMaYYeAUYApyGZ4bveb9x1BZ0dlFE5ohIuoikHzly5ESGoxpgjOHJf2UEBHcTB/Xm7TvODAjuoOHM2KZcV0oppVTDmh3gGWMszfnV1OeLiA1PcLfMGPOO9525xhiXMcYNvIpnGRY8M3b+O/cHAIfqGfdiY0yaMSatb9++zfnRVS1ut2Heu1v50zd7fW0XDO/L0lkTiYmw1enfWGasZs4qpZRSLdPSGbxWIZ7iaK8DGcaY3/i19/Prdg2w1fv5fWC6iNhFZBAwDFjXVuPtypwuNw/+fRN/WZvla/vBKQn88eY0ImzWoPeE9Q6+Sl/drpmzSimlVMt0yAAPz167m4ELa5VE+bWIbBGRzcAFwE8BjDHb8ByXth34ELhbM2hbX6XTzf1vbww4euyacYm8eNM4wsMsQY8YAzD15OZUt+sxZEoppVTLtDTJolUYY74m+L66lQ3cswhY1GqDUgEqqlzcvWwDn+7I87XdNHEgi64eg8UiDSZSuAqDx97V7dWJFA1l2SqllFKqfh0ywFMdW1mlkzlL1wecK3vrWSk8ccUo39FjDSVK2JPsnrNla/Ffgo2fEa8BnVJKKdVMHXWJVnVQJRVV3PqnbwOCuzsnDwkI7qDhRAldglVKKaValwZ4qslKHU5ue+Nb1u0r9LU9cHEqD00dHhDcQcOJEvEz4hm+eDj2ZDsI2JPtDF88XGfslFJKqRDRJVrVJGWVTm5781vS9x/1td2XMIC02fl8mZWNPclO7GWx5C7PxVUQfI+d/yydLsEqpZRSrUcDPNWoiioXty9JZ93empm7uf0GMv7RIhx+SRSHXglaehDwzNJpooRSSinVNjTAUw2qqHLx46Xp/HdPga/tkR+MYOzMPF9w1xh7sp1J+ya11hCVUkopVYvuwVP1cjhd3Pnn9Xz1fU1Cxf+bOpw7zh9yQqdK6AkUSimlVNvSAE8FVel0c/ey7/h8Z815vXOnDOO6Q9GsTlldz0m/wekJFEoppVTb0iVaVUeVy819f/2OTzJyfW33XDCU6Tkx7LxjZ536dg2RcNHyJ0oppVQb0xk8FcDpcjP3bxv5cFuOr+3mPgmcdUcBO27eUW9wZ0+20//O/lhja86fDYsNY8SfRmhihVJKKdXGdAZP+bjchgf+vol/bz7sa7spNp4pTxynsqyBNVnBl0SR+vvU1h6mUkoppRqhAZ4CwBjDT59dx/tHaxIqboiN44qXKxsO7tA9dkoppVRHowGewhjDI8+lBwR3F3wXxrSvyxoN7vSIMaWUUqrj0T14ihc/283bBXm+78/eEsbNH4VjygxY679PjxhTSimlOiadweticpflkjkvE0eWA3uSnY0/685vDmX5rqfttDLrg3AseM+WdXlm6fyTKyxRFg3slFJKqQ5MZ/C6kNxlueycsxPHfgcY+Npeyq+za4K70fss3PFPO1YjvrbqWTp7sh1EZ+2UUkqpk4HO4HUBvlm7/TUnSmQkufjjFQ6qY7lBhy3c848IbK6a4K56f138jHgN6JRSSqmTiAZ4nVz1rJ3/Euv+OBcv/LACp/d//YQC4ad/jyCyUgLu1Zk6pZRS6uSkS7SdXOa8zIDgLrenm+dvqKDCW9mkZ4nwwPIIYsoDgzt7sl2DO6WUUuokpQFeJ+e/LFvUzc1zN1RQ3M3zfVQFPPCPCOIqAlNltfSJUkopdXLTAK+z88ZuZeGG5693cKSXp66drQr+39fRXPLsaEb8aYQmUSillFKdiO7B6+xcUGk1vHBtBQfiPUu1Fjfc9Z6d23af5+umAZ1SSinVeXTIGTwRGSgin4tIhohsE5H7a11/UESMiPTxa3tERHaLyE4Rmdr2o+5Ycpfl8lWfr3BjeG2ag51JNfvwbvsgnDOd3dpxdEoppZRqTR11Bs8JPGCM2SAi0cB6EfnYGLNdRAYCFwO+Am4iMgqYDowG+gOfiEiqMcbVHoNvb7nLcsm4LQOqYMV5VawbWfOf4YbPbZyfaWfwYt1jp5RSSnVWHXIGzxhz2Bizwfu5BMgAEr2X/xd4CPA/JPUq4G1jjMMYsxfYDUxswyF3KJnzMqEKvji1in9PqvK1X7Q+jB+st+keO6WUUqqT66gzeD4ikgKMa+NiuQAAIABJREFUA9aKyJVAtjFmk0hAWY9EYI3f9wepCQg7vdrHjzn2O9ia4mTpJZW+PqfutvKjT8MRRIO7/8/enYdHWd39H39/Z5IMhEX2IAQIYUcQgbjVpah1xbWK4s9WrfbB1ro9bZ9Wi1rbSqu1tdrajW5qH8RirdWnxV2wLiACIsoSlsgOYd9Dlpnv74+ZhCyTkECSmQyf13VxZebc577nzN0UP5z7LCIiIikuqQOembUFngfuIvrYdiJwXryqcco8ThlmNgGYANC7d+/GaWgCVV/IuHh1MWu7Rnji8mIisf7ZPpsCfP2l6BZkoT6hBLZWREREmkNSPqIFMLN0ouFuirv/A+gH9AU+NrNVQDYw38y6E+2x61Xp9GxgQ7zruvtkd89z97yuXbs25VdoFtUXMt7RNsIvrjq4kHGn3cZdz4doVWpYhml9OxERkaNAUgY8iz5//ROwxN0fBXD3T9y9m7vnuHsO0VA3yt03AS8B480sZGZ9gQHAnAQ1v1kVrzm4kPGBdOexK4vZ3j7aedmqBP77uVZ03BsgrXMag/88WI9nRUREjgLJ+oj2NODLwCdmtiBW9j13nx6vsrsvMrNpwGKij3K/cbTMoC0fcxcx53eXFLO6+8G17iZ/7STOfLTl91KKiIhIwyRlwHP3d4k/rq5ynZxq7ycBk5qwWUkpd1IuSycsZcrnilkw4GCm/W6vPpw5UOFORETkaJSUAU/qL+u6LJ6es5o3W++tKLumuCO33D4sga0SERGRRErKMXhSf//+/XJ+G9pS8f6kJUEunFxK4ZTCBLZKREREEkkBL4kVTilkVs4sZgZmMitnVpXQVjilkBePe5fvLlpWsRxK3w0Bvjo9BPs9utixiIiIHJX0iDZJxVvfLn9CfsXxj7+xlEe+uI+9mdH3x+w17nghREZZdOhi5dm1IiIicnRRwEtS1de3A4jsj0TLcX5/VhHrukWXQ0krg9tfCNFx78EO2VBvLWgsIiJytNIj2iRT/li2eHX8HrjiNcU8l72XeYMOzpi94bUM+m8IVrwPZAa0oLGIiMhRTD14SaT6Y9l4Fp5q/PP00or3585N44xP0iveh/qEyJ2UqwWNRUREjmIKeEkk3mPZytb3cn77+SKIVRm6KsD4tzKAaK/doMmDFOxEREREj2iTSV0TI0oGpPPrG8ooikTTXc+MEHfNb08QI9QnpHAnIiIiFdSDl0TKtx2rLpiTwZP/E2DDyhIA2mQE+fOtJzPoh+2au4kiIiLSAqgHL4nkTsolkFn1f5JAZoD/uzWd91duqyh79JoTGNRd4U5ERETiU8BLIlnXZTFo8iBCfUJg0QkT+Q91Ztq2zRV1/vsLAzn/uO4JbKWIiIgkOz2iTTJZ12VVjKWbv2YHP/39rIpjFw7rzu1n909U00RERKSFUA9eAtW1Fdm2vcV8Y8p8SsPRxYwHd2/Hz8aNIBCwRDVXREREWgj14CVIXVuRdbm2G3f9bQEbdx0A4JjW6Uz+ch5tQvqfS0RERA5NiSFB6tqKbEq3XbyzfGtF+S+uGUHvzpnN3UQRERFpoRTwEqS2Ne8+DO7jV29tr3j/jbP6cfZgrW8nIiIi9acxeAkS6h2qUba1fYTJl5bg0WF3fK5fZ7557qBmbpmIiIi0dAp4zax8YkXx6mKoNF+iNOj85opi9oai6S6rfYhfXjuSoCZViIiISAPpEW0zqj6xAica8hyeuzRMQfdoeVrA+PX/G0WXtjV7+UREREQORT14zWj5nctrTKzAYe6Z8NrAg2Py7r5wMHk5nZq5dSIiIpIqkjLgmVkvM5thZkvMbJGZ3Rkr/5GZLTSzBWb2mpn1qHTOPWa2wszyzez8xLU+vsIphZRtK6tRvr5zhMmj91W8v2h4d24+vW9zNk1ERERSTLI+oi0DvuXu882sHTDPzF4HHnH3+wDM7A7gfuBrZjYUGA8cB/QA3jCzge4eTlD7KZxSSMHEAorXFBPqHSK8t2ZTDqQ7T1xxgJKM6PvcLm14+MrjMdO4OxERETl8SdmD5+4b3X1+7PUeYAnQ0913V6rWhugoNoDLgGfdvdjdPwNWACc1Z5srKx9rV7y6GDy6iHG83ru/nlvCxs7Rr9AqPcBvvjSKdq3Sm7u5IiIikmKStQevgpnlACOBD2LvJwHXA7uAs2LVegKzK522LlaWEPEWMa7u/aFlvDf8YOibdPlwBndv39RNExERkaNAUvbglTOztsDzwF3lvXfuPtHdewFTgNvKq8Y53eOUYWYTzGyumc3dsmVLUzS71kWMy23qGOHp8w7WuXJUNleOzm6StoiIiMjRJ2kDnpmlEw13U9z9H3GqPANcGXu9DuhV6Vg2sCHedd19srvnuXte165dG7PJFeItYgwQ7Bwk2DeD311azIFYlb5d2vDDy45rknaIiIjI0SkpA55FZxn8CVji7o9WKh9QqdqlwNLY65eA8WYWMrO+wABgTnO1t7rcSbkEMqve2kBmgIGPD+TtX3ZgVWy9u/Sg8atrR9ImlPRPykVERKQFSdZkcRrwZeATM1sQK/secLOZDQIiwGrgawDuvsjMpgGLic7A/UYiZ9BmXRfdO7byLNrcSbkszjP++JfPKurdfeEQhvU8JlHNFBERkRRl7nGHqh0V8vLyfO7cuc3yWZt3H+DCx99h274SAM4e3I0/3ZCnJVFERESkXsxsnrvn1aduUj6iTTWRiPPNaR9XhLtu7UI8cpXWuxMREZGmoYDXDH73n5W8u2IrAGbw2DUn0Fn7zIqIiEgTUcBrYvPX7ODnry2reH/rmH58rn+XBLZIREREUp0CXhPaVVTKHVM/IhyJjnMc1bsDd31hYIJbJSIiIqlOAa+JuDsTX/iEdTuKAGjXKo3Hx48kPahbLiIiIk1LaaOJTJu7ln8t3Fjx/uErj6dXp8wEtkhERESOFgp4TcDd+fcnmyreX3tSby4afmwCWyQiIiJHEwW8JmBm/PmGPO44uz+Du7fj/ouHJrpJIiIichTRQsdNvNBxcVmYUFqwST9DREREUp8WOk4iCnciIiLS3BTwRERERFKMAp6IiIhIilHAExEREUkxCngiIiIiKUYBT0RERCTFKOCJiIiIpBgFPBEREZEUc1QvdGxmW4DViW5HA3QBtia6EUch3ffmp3ueGLrviaH73vxa6j3v4+5d61PxqA54LY2Zza3vCtbSeHTfm5/ueWLovieG7nvzOxruuR7RioiIiKQYBTwRERGRFKOA17JMTnQDjlK6781P9zwxdN8TQ/e9+aX8PdcYPBEREZEUox48ERERkRSjgJdAZtbLzGaY2RIzW2Rmd8bKO5nZ62a2PPazY6y8c6z+XjN7otq1ZppZvpktiP3plojv1BI08n3PMLPJZrbMzJaa2ZWJ+E7JrrHuuZm1q/Q7vsDMtprZY4n6XsmukX/XrzWzT8xsoZm9YmZdEvGdWoJGvu/XxO75IjP7aSK+T0twGPf8XDObF/udnmdmZ1e61uhY+Qoz+6WZWaK+15HQI9oEMrNjgWPdfb6ZtQPmAZcDNwLb3f0hM7sb6Oju3zWzNsBIYBgwzN1vq3StmcC33X1uc3+PlqaR7/sPgKC732tmAaCTu7fEtZWaVGPe82rXnQf8t7v/p1m+SAvTWPfdzNKADcBQd98aCxr73f2B5v9Wya8R73tn4CNgtLtvMbOngKfd/c0EfK2kdhj3fCRQ6O4bzGwY8Kq794xdaw5wJzAbmA780t1fTsDXOiLqwUsgd9/o7vNjr/cAS4CewGXAU7FqTxH9JcXd97n7u8CBBDQ3ZTTyfb8J+EmsXkThLr6m+F03swFAN+CdJmx6i9aI991if9rEejPaEw18Ekcj3vdcYJm7b4m9fwPQU4I4DuOef+Tu5b/Di4BWZhaKBcX27j7Loz1gT5ef09Io4CUJM8sh+i+4D4Asd98I0V9aov8Rq4+/xB5b3ddSu5Sb25HcdzPrEHv5IzObb2bPmVlWEzY3JTTS7zrAtcDfXI8h6uVI7ru7lwJfBz4h1pMH/KkJm5syjvD3fQUw2MxyYr2olwO9mq61qeEw7vmVwEfuXkw0FK6rdGxdrKzFUcBLAmbWFngeuMvddx/mZa5z9+HAGbE/X26s9qWqRrjvaUA28J67jwJmAT9rxCamnEb6XS83Hph65K1KfUd6380snWjAGwn0ABYC9zRqI1PQkd53d99B9L7/jWhP9SqgrDHbmGoaes/N7DjgYeCW8qI41VrkPyIV8BIs9hfn88AUd/9HrLgw1k1cPq5g86Gu4+7rYz/3AM8AJzVNi1NDI933bcB+4IXY++eAUU3Q3JTQWL/rsbojgDR3n9ckjU0hjXTfTwBw95WxHtNpwOeaqMkpoRH/bv8/dz/Z3U8F8oHlTdXmlq6h99zMson+/X29u6+MFa8j+g/3ctm00OEICngJFHuM+idgibs/WunQS8ANsdc3AC8e4jpp5TPaYr/gFwOfNn6LU0Nj3ffYf+j+DxgTKzoHWNyojU0RjXXPK7kW9d4dUiPe9/XAUDMr3+T8XKJjnCSOxvx9t9iKCLHZn7cCf2zc1qaGht7z2BCbfwP3uPt75ZVjj3H3mNkpsWteT/3/XkoqmkWbQGZ2OtFu90+ASKz4e0THDUwDegNrgHHuvj12ziqiA5wzgJ3AecBq4D9AOhAkOhD3m+4ebq7v0pI01n1398Vm1gf4K9AB2AJ8xd3XNN+3aRka857HjhUAF7n70mb8Gi1OI/+uf43ozMJSon/n3Oju25rv27QcjXzfpwIjYtf4obs/21zfoyVp6D03s3uJDjOo3CN6nrtvNrM84EmgNfAycHtLHOurgCciIiKSYvSIVkRERCTFKOCJiIiIpBgFPBEREZEUo4AnIiIikmIU8ERERERSjAKeiIiISIpRwBMRERFJMQp4IiIiIilGAU9EREQkxSjgiYiIiKQYBTwRERGRFKOAJyIiIpJiFPBEREREUowCnoiIiEiKUcATERERSTEKeCIiIiIpRgFPREREJMUo4ImIiIikGAU8ERERkRSjgCciIiKSYhTwRERERFKMAp6IiIhIilHAExEREUkxCngiIiIiKUYBT0RERCTFKOCJiIiIpBgFPBEREZEUo4AnIiIikmIU8ERERERSjAKeiIiISIpRwBMRERFJMQp4IiIiIilGAU9EREQkxSjgiYiIiKSYtEQ3IJG6dOniOTk5iW6GiIiIyCHNmzdvq7t3rU/dozrg5eTkMHfu3EQ3Q0REROSQzGx1fevqEa2IiIhIilHAExEREUkxCngiIiIiKUYBT0RERCTFKOCJiIiIpJijehbtoezevZvNmzdTWlqa6KZIC5Genk63bt1o3759opsiIiJHMQW8WuzevZvCwkJ69uxJ69atMbNEN0mSnLtTVFTE+vXrARTyRERSXOGUQgomFlC8pphQ7xC5k3LJui4r0c0C9Ii2Vps3b6Znz55kZmYq3Em9mBmZmZn07NmTzZs3J7o5IiLShAqnFJI/IZ/i1cXgULy6mPwJ+RROKUx004AEBzwzG2RmCyr92W1md5lZJzN73cyWx352rHTOPWa2wszyzez8SuWjzeyT2LFf2hGmstLSUlq3bn0kl5CjVOvWrfVYX0QkxRVMLCCyP1KlLLI/QsHEggS1qKqEBjx3z3f3E9z9BGA0sB94AbgbeNPdBwBvxt5jZkOB8cBxwAXAb8wsGLvcb4EJwIDYnwuOtH3quZPDod8bEZHUV7ymuEHlzS2ZHtGeA6x099XAZcBTsfKngMtjry8DnnX3Ynf/DFgBnGRmxwLt3X2WuzvwdKVzRERERBpVqHeoQeXNLZkC3nhgaux1lrtvBIj97BYr7wmsrXTOulhZz9jr6uVCdPB/3759MTNWrFhR5diTTz6JmbF3795ma4+Z8cQTTzTb54mIiDS23Em5BDKrxqhAZoDcSbkJalFVSRHwzCwDuBR47lBV45R5HeXxPmuCmc01s7lbtmxpWENbqFmzZrFq1SoAnn322cQ2hmh7xo0bl+hmiIiIHLas67IYNHkQoT4hMAj1CTFo8qCkmUWbLMukXAjMd/fyqSeFZnasu2+MPX4tn5K4DuhV6bxsYEOsPDtOeQ3uPhmYDJCXlxc3BKaaqVOn0qZNG4YNG8bUqVO59957E9qeU045JaGfLyIi0hiyrstKmkBXXVL04AHXcvDxLMBLwA2x1zcAL1YqH29mITPrS3QyxZzYY9w9ZnZKbPbs9ZXOOaqFw2Gee+45Lr30Um666SYWL17MwoULa60/c+ZMzIxPP/20SvmYMWO46qqrKt7feOON5OXl8e9//5uhQ4eSmZnJ2LFj2b59OytWrOCss86iTZs25OXl1fi86o9oy6/9zDPP0L9/f9q3b8+FF17IunUHn7o3R7tERERSRcIDnpllAucC/6hU/BBwrpktjx17CMDdFwHTgMXAK8A33D0cO+frwB+JTrxYCbzcLF+gHgqnFDIrZxYzAzOZlTOrWdfIeeuttygsLGT8+PFcddVVpKenM3Xq1EOfWA9r1qzh/vvv58EHH2Ty5Mm8//77TJgwgfHjxzN+/Hj+/ve/U1ZWxvjx44nOfandBx98wBNPPMHPf/5zJk+ezPz585kwYULC2yUiItISJfwRrbvvBzpXK9tGdFZtvPqTgElxyucCw5qijUeifCHE8rVyyhdCBJqlW3fq1Kl06NCBCy64gIyMDM4991yeffZZfvzjHx/xch7bt29n1qxZ9OvXD4CFCxfyyCOP8NRTT3H99dcD0QkeY8eOZenSpQwZMqTWa+3evZt///vfdOwYXfJw06ZN/Pd//zdFRUUNXo+wMdslIiLSEiW8By/VJXIhxOLiYl544QWuuOIKMjIyALj22mtZtWoVs2fPPuLr5+TkVIQogP79+wNw9tln1ygr376rNieeeGJFuAMYOnRovc5r6naJiIi0RAp4TSyRCyG+/PLL7Ny5k4suuoidO3eyc+dOxowZQygUapTHtB06dKjyvjxEVi4vLztw4MBhXetQ5zV1u0RERFoiBbwmlsiFEMtD3Lhx4+jYsSMdO3akV69eFBcXM23aNMLhcI1zWrVqBUBJSUmV8u3btzd5e+uSrO0SERFJRgp4TSxRCyHu3buXf/3rX1x77bXMmDGjyp9HH32UwsJCZsyYUeO87OzoajNLliypKFu7di35+flN2t5DSdZ2iYiIJKOET7JIdeUTKQomFlC8pphQ7xC5k3KbfILFiy++yP79+7nzzjs5+eSTqxw77bTTmDRpElOnTuWMM86ociw7O5sTTzyR++67j8zMTCKRCD/+8Y/p1KlTk7b3UJK1XSIiIslIAa8ZJGIhxKlTpzJgwIAa4Q4gPT2dq6++mqlTp3LSSSfVOP7MM8/w1a9+lS996UtkZ2fz05/+lF/84hfN0ew6JWu7REREko0dzeuA5eXl+dy5c+MeW7JkiZbPkMOm3x8REWlsZjbP3fPqU1dj8ERERERSjAKeiIiISIpRwBMRERFJMQp4IiIiIilGAU9EREQkxSjgiYiIiKQYBTwRERGRFKOAJyIiIpJiFPBEREREUowCnoiIiMgRWLB2Z6KbUIMCnjTIVVddxZgxY5r0M9577z1GjRpFq1atMDMAcnJy+Pa3v11RZ9q0aTz55JON8nmPPfYYZsZVV10V9/jkyZMZNmwYrVq1Iisri2uuuaZRPldERFq2A6Vh7vnHQi7/9Xu8uGB9optTRVqiGyBS3S233EK3bt149dVXCYVCALzwwgt07ty5os60adPYunUrN9544xF91ubNm/nhD39I165d4x6/9957eeKJJ7j33ns58cQTKSws5O233z6izxQRkZZvxea93PbMfJZu2gPA9/7xCcN7HkNu17YJblmUAp7UcODAAVq1atWkn1FUVETr1q3jHlu6dCkTJkzg85//fEXZyJEjm6Qd99xzD2PHjmXt2rU1ji1atIif/OQnvPLKK5x77rkV5VdffXWTtEVERFqGf8xfx73//JT9JeGKsrMGd6Nru1ACW1WVHtGmuGnTpjF8+HBCoRC9evVi4sSJlJWVVRx/8sknMTPmzJnDmDFjaN26NY888ggAa9eu5aKLLqJ169bk5OTwxz/+Me5nfPrpp4wdO5Z27drRrl07xo0bx6ZNmyqOz5w5EzPj1Vdf5dJLL6Vt27bcdtttNa5TXi8cDnPnnXdiZhU9dJUf0d544408//zzvP3225gZZsYDDzzQ4Hvz4YcfMm3aNB566KG4x5966in69etXJdyJiMjRq6gkzP889zHfnPZxRbjLSAsw6Yph/OrakbRrlZ7gFh6kgJfCXnvtNa655hpGjRrFiy++yO23387PfvazuOHq2muv5eKLL2b69OlcfPHFuDuXXXYZn376KX/605949NFHefzxx5k1a1aV81asWMFpp53GgQMH+Otf/8qTTz7JokWLuOSSS3D3KnVvvvlmRowYwUsvvcTNN99cow2jRo2quP63vvUtZs2axX333Vej3n333cdZZ53FyJEjmTVrFrNmzeKrX/0qcDCwrlq1qs574+7cdtttfOc736Fnz55x63zwwQcMHz6cBx54gC5duhAKhfjCF77AkiVL6ry2iIiknuWFe7j0iXd5bt66irLcLm34562ncd3JfSrGjCcLPaJtgJy7/53oJrDqobH1rnv//fczZswYnnrqKQAuuOACIPpY8t577yU7O7ui7h133MGdd95Z8X769Ol89NFHzJ49m5NPPhmA0aNH069fPwYMGFBR7wc/+AHdu3fn5ZdfJiMjA4Djjz+ewYMHM336dMaOPdjecePG8aMf/ajW9rZv355TTjkFiPbYlb+url+/fnTq1IlIJFKjTiAQIBgMHvL/aH/5y1/YtGlTlYkb1W3atIn58+ezZMkS/vCHP5CWlsa9997LBRdcQH5+fpM/xhYRkeTw3Ny13PfipxwojVSUXX5CDx68YjhtQ8kZpdSDl6LC4TDz589n3LhxVcqvueYaIpFIjZ64ykEMYM6cOWRlZVWEO4A+ffowevToKvXeeOMNrrjiCgKBAGVlZZSVldG3b19ycnKYO3dunZ/RFK6//nrKysro06dPrXV27drF9773PR555JFaxwECRCIR9u3bx/PPP88VV1zBJZdcwgsvvMD69euZMmVKUzRfRESSyJ4DpXzzbwv4n78vrAh3obQAD185nF9cc0LShjtQD17K2rp1K6WlpWRlZVUpL3+/ffv2uOXlNm3aRLdu3Wpct1u3buzZs6fK5zz88MM8/PDDNepWn7hQ/TMS5cc//jG9evXivPPOY+fO6NpFZWVllJaWsnPnTtq1a0cwGKRTp07s3buXIUOGVJybm5tLTk4OixcvTlTzRUSkGcxbvZ27/raAtduLKsr6dW3Db64bzaDu7RLYsvpJeMAzsw7AH4FhgAM3AfnA34AcYBVwtbvviNW/B7gZCAN3uPursfLRwJNAa2A6cKdXHwR2hBryeDTRunTpQnp6Ops3b65SXlhYCECnTp2qlFd/pNm9e/ca50J0WZHKvV6dOnXiiiuuqBgDV70NdX1GouTn5zN37lw6duxY41jHjh155513OP300xkyZAhr1qypUcfdCQTU+S0ikopKwxF+9eZynpixgkilFPHFUT350WXDaJPEvXaVJcN/pR4HXnH3wcAIYAlwN/Cmuw8A3oy9x8yGAuOB44ALgN+YWTB2nd8CE4ABsT8XNOeXSDbBYJDRo0fz3HPPVSmfNm0agUCAU089tc7zy9d8++CDDyrK1qxZw/z586vUO+ecc/j0008ZPXo0eXl5Vf7k5OQ02vepLiMjgwMHDhzWuQ8++CAzZsyo8mfEiBGceeaZzJgxg+HDhwNw8cUXs2nTpiq9dStXrmT16tWMGDGiUb6HiIgkj1Vb9zHud7P45VsHw127Vmn88tqRPHr1CS0m3EGCe/DMrD1wJnAjgLuXACVmdhkwJlbtKWAm8F3gMuBZdy8GPjOzFcBJZrYKaO/us2LXfRq4HHi5ub5LMvrBD37A+eefz1e+8hXGjx/PJ598wn333cd//dd/VZlgEc9FF13EiBEjGDduHA8//DCtWrXi/vvvr/HY9oEHHuCkk05i7Nix3HTTTXTp0oX169fz+uuvc+ONNzbZrheDBw/mxRdf5J///CfZ2dn06NGDHj168PTTT3PTTTexcuXKWsfhDRs2rEZZhw4d6NKlS5X2XnHFFYwaNYovfvGLPPjggwSDQe6//34GDhyo3SxERFKIu/PcvHU88NKiKmvbndS3E7+45gR6dqh9vHaySnQPXi6wBfiLmX1kZn80szZAlrtvBIj9LE8VPYHKA7vWxcp6xl5XLz+qnXfeeTz77LPMnTuXSy65hMcee4xvfetbPPHEE4c818x46aWXGDp0KDfddBN33XUXt912W42ev4EDBzJ79mwyMzOZMGECF154Id///vcJhUL079+/qb4at956K+eddx433XQTJ554IpMnTwaiEyPC4XCNJVoORzAYZPr06YwcOZKbb76Z66+/nv79+/PKK6+Qnp48ax2JiEj9FU4pZFbOLGYGZjIrZxbLnlrPrVPm852/L6wId2kB4zsXDOKxNn1Zc8KCirqFUwoT3Pr6s0YeptawDzfLA2YDp7n7B2b2OLAbuN3dO1Sqt8PdO5rZr4FZ7v6/sfI/ER1vtwb4ibt/IVZ+BvAdd78kzmdOIPool969e49evXp13LYtWbKkyuB6kYbQ74+ISPIpnFJI/oR8IvujM2IX9wnzh4uL2dH2YBbK7dKGx8ePpNvbB6rUBQhkBhg0eRBZ1yVm0qCZzXP3vPrUTXQP3jpgnbuXD/T6OzAKKDSzYwFiPzdXqt+r0vnZwIZYeXac8hrcfbK757l7Xm37j4qIiEjqKZhYQGR/hNKg8+xZxfx0/IEq4e7/ndybf91xOsOzj6moW1lkf4SCiQXN3ezDktCA5+6bgLVmNijWn0IDAAAgAElEQVRWdA6wGHgJuCFWdgPwYuz1S8B4MwuZWV+ikynmxB7j7jGzUyw6VfP6SueIiIiIULymmPVdIvzwywd45aSD23a22w9/uD6PH18xnMyMtIq6tV2jJUiG6SC3A1PMLAMoAL5CNHhOM7ObiT5+HQfg7ovMbBrREFgGfMPdy0dDfp2Dy6S8zFE+wUJEREQOKgtHePW8CM8NK6KsUvoZXhDk1oXtOPeXVR+7hnqHKF5dM8yFeoeauqmNIuEBz90XAPGeJ59TS/1JwKQ45XOJrqUnIiIiUmHF5j1867mFfHzCwUWL08rgmhkZnLc0g8GTa04KzJ2UG3cMXu6k3GZp85FKeMATERERaQrhiPPHdwr4+evLKCk7GNT6bg/y1RcyyG3TmtzJuXEnTZSXFUwsoHhNMaHeIXInxa+bjBTw6uDuSbP7grQciZyZLiIiUSu37OV/nvuY+Wt2VpSlB427vjCQW87MJW3yoachZF2X1WICXXUKeLVIT0+nqKiIzMzMRDdFWpiioiKtkycikiDhiPOX9z7jkVfzKa7Ua3dcj/b8/OoRDO7ePoGtaz4KeLXo1q0b69evp2fPnrRu3Vo9eXJI7k5RURHr168nK6tl/otPRKQly9+0h7v/sZCPKvXapQWM288ewFWb2rLmlEXMbIGPWw+HAl4t2rePJvwNGzZQWlqa4NZIS5Genk5WVlbF74+IiDS9A6VhnnhrBb97eyVlkYPDZPrsCPLgiYMYWJhJ/i0HJ0wUry4mf0I+QMqGPAW8OrRv317/oRYREUliswu28b1/fELB1n0VZcEwXDw7nUveT8f/dy3LWwdqXbRYAU9EREQkSezaX8pPXl7Csx+urVLef12Ar7waoufW6CSKyP5IjXBXrqUsWnw4FPBERESkxXB3pn+yie+/tIitew8GtFbFcPXMDMYsSCNA/cbNt5RFiw+HAp6IiIgkrcIphRVr0e0dnMaz18G7e3ZVqTNqWZAvv55Bx73xlz4Jdg7iRd5iFy0+HAp4IiIikpQKpxSSPyGfsqIwb44s4/kz93Fgz8Hj3dqFuOZpGL2s9jgTyAww8PGBQMtdtPhwKOCJiIhIUiqYWMBnbUt56soSCnpUHUd33cm9+e6Fg1n0h7kUE38sXahP1SCXyoGuOgU8ERERSTo795fwh0G7mXFCGV5pSF2PrcaNr4aY8NBwoPY9YwdNHnRUBbrqFPBEREQkaUQizt/mruWnryxlx8iyivJgGC6Zlc7Y2em0zW5VUd7S94xtKgp4IiIikhQ+XruT+1/8lI/XVZ1EMawgyJfeyKD7jkDcyREtec/YpqKAJyIiIgm1fV8JP31lKX+buxY/uBEFPTu05s72Pch+djslO0tqjKmT2ingiYiISEKEI84zc9bws1fz2VV0cFvQjLQAX/t8P77++X60zgjCrQlsZAulgCciIiLNbt7qHdz/4qcs2rC7SvkXhnTjvouH0qdzmwS1LDUo4ImIiEiz2biriJ++ks8LH62vUt67UyYPXDqUswfr8WtjUMATERGRJrevuIzfv72Sye8UcKD04JImobQA3zirPxPOzKVVehCounuFZsUeHgU8ERERaTKRiPP8/HU88mo+m/dUXZD4guO6M3HsEHp1yqwoK9+9onxdu+LVxeRPyAeOroWKj5QCnoiIiDSJ2QXb+NG/FtcYZ3dcj/bcO3Yop/brXKW8cEohS25YAuGq14nsj1AwsUABrwEU8ERERKRRrdyyl4dfXspriwurlHdtF+J/zh/E6UvTWX3OMmZWegQLRHvqwvGuCMVr4m9HJvEp4ImIiEij2LznAI+9sZy/fbCmSk4LmXHLWf245fP92Pv3beTfUvMRbKB1oMp2Y9WFeoeauPWpRQFPREREjsje4jIm/6eAP75TwP6Sql1wpywKcs2cVnxuWAfahNJYOLGgRpCL7I/UGe7i7V4hdVPAExERkcNSUhbh2Q/X8Ms3l7N1b0mVY0NWBbj67Qz6borOjC0fQ9fgR61BGDR5kMbfNZACnoiIiDRIOOK8uGA9v3hjGWu3F1U5lr3ZuHpmBsM/C2JYRXl5sAv1DlG8umbIC3YO4kVepScvkBlQuDtMgUQ3wMxWmdknZrbAzObGyjqZ2etmtjz2s2Ol+veY2Qozyzez8yuVj45dZ4WZ/dLMLN7niYiIyOFxd175dBMXPPYfvjnt4yrhrvO+APdn5/DwjA4c/1lalXAHB8fQ5U7KJZBZNX4EMgMMfHwggyYPItQnBAahPiGFuyOQLD14Z7n71krv7wbedPeHzOzu2PvvmtlQYDxwHNADeMPMBrp7GPgtMAGYDUwHLgBebs4vISIikorcnXdXbOVnr+bz8bpdVY613Q9jZ2dwzkdptMrYRtcburPpqU01euLKx9CVB7baFjJWoGscyRLwqrsMGBN7/RQwE/hurPxZdy8GPjOzFcBJZrYKaO/uswDM7GngchTwREREjsicz7bz6Ov5zC7YXqW8VQmcPyedCz5Mp3VJtLcuUhZh2/RtDJo8qM6dKLKuy1KQa2LJEPAceM3MHPi9u08Gstx9I4C7bzSzbrG6PYn20JVbFysrjb2uXi4iIiINUL5N2Cfh/bz4hTIWZZVVOZ4egbPnpXHxrAzaFdUcDVW8plgBLgkcVsAzswygC1Dk7juOsA2nufuGWIh73cyW1vXRccq8jvKaFzCbQPRRLr17925oW0VERFJW4ZRC/u/7i/jHKcUszqm6bEkgAmcsTOOy99PptKf2Ifxary451CvgmVk7omPfzgXOBLpWOlYGLATeAv7h7h80pAHuviH2c7OZvQCcBBSa2bGx3rtjgc2x6uuAXpVOzwY2xMqz45TH+7zJwGSAvLy8uCFQRETkaDNv9Xa+//oCPr2qao9dIAKnfZrGJbPS6baz7rmZWq8uedQZ8MysJ3AfcB3QJla8E8gHtgOtgc7ACcBo4NtmtgD4mbtPPdSHm1kbIODue2KvzwN+CLwE3AA8FPv5YuyUl4BnzOxRopMsBgBz3D1sZnvM7BTgA+B64Ff1uwUiIiJHJ3fnlckr+c2slXzSvQy6HzwWiMDnFqVxyfvpZB0i2AFary7J1BrwzOwHwLeAEPA68CzwnruvjFM3k2jP2/lEw+AUM7sTmODuC+v4/CzghdiKJmnAM+7+ipl9CEwzs5uBNcA4AHdfZGbTgMVAGfCN2AxagK8DTxINnS+jCRYiIiJxuTtvLtnMo3/+lMVpB6oEO4sFu0vrG+wADIY8NUThLomYe/ynlGa2H/gd8Ej5hId6XTCa1i4GHgBedPcfNkI7m0ReXp7PnTs30c0QERFpFmXhCP/+ZCO/mbGS/MI9VY6VB7tLZqXTfUcDlsk16PG1Hgz8zcBGbq1UZ2bz3D2vPnXrekTbv3x8XEN4NDH+H/B/Ztb9UPVFRESkcZTPgK2+PMmB0jC/+fY8phZvZUuHqh07aWXRMXYXzqkj2AWBSHQCReeLOrNt+rZal0CR5FBrwDuccBfnGpuO9BoiIiJyaMtuXcaG322oWEOieHUxC76xlE+2bOSZDZvY3jocHcQUEyqBsxakcf6H6XTcW3uPnbYLa5mSYR08EREROQKFUwqrhLvdrZ3X80p5c1Qp+zftrbIxaZsiOHdeOl+Yl07bA/F39UzrnEbZ9jL10LVgRxTwzCwAXAH0B1YTXSalpDEaJiIiInWreCS7uhiATR0jvD66lHeOL6MkvWrdjnuMC+ak8/mP02hVWst27RpPlzIOGfDMLAj8EVjk7j+rVv4a0S3FjOi/G5aY2enuvrNpmisiIiIQDXf5E/IJ7w+zuE+E1/JK+bh/uEa97nsCXPheGp/7NI30cLVgZ9FxdRpPl3rq04OXR3QtulurlX8VOIvociS/A84B7iC6Z+w9jdhGERGRlFR9UkTnizpTOK2Q8LZoUEvrnMaAxwfEDV1L71/JjAHFvD66lPVda66I0bswwMWz0/nSxGHs9d1s+Ljm0Hr11qWu+gS8oUR7596qVv7/iC52fLW77yM6a3YIcCkKeCIiInUq74GL7I9uCVa8upgNv60awsq2lbH0pugOnuUhb9OuA/x19iqeGruDvZlVr2kOI1YEOW9eOkNWBzCMHl/qDl+KLmqxYfIGCANB6DFB4S6V1bXQ8ZmxlyfHfvattuzJicA8YHRsoWKAAuB0MzuD2P6w7v6fRm2xiIhICxBvyZJd7+2qMhmiPrzEKZhYwMYzQ/zlvc/498KNlEUcKoW7UEl0n9gvzK+61Emoz8F9YQf+ZqAC3VGkrh68H8R+9o79vLvSsfZAK6BLpXoA3WLlP+DguLyzG6WlIiIiLUS83rkl1y+BSMOuEzZn3qAwr+UVseLX79U43mWX8YV56ZyxMI02xVXH12lf2KNbXevgnQVgZhOA3wI3uftnsbIbgT8Bt1TuoTOz/wImubtCnYiIHDWq99aF94Yrwl2FBoS7fSHn7RGlvDG6jO3ta3b3ndS3Ezed1pfjF8Dqlz+juKSYYOcghml5EwHqNwZvIdHeuB+Z2ZeBtkQnU+wE3q9WdyiwtlFbKCIiksTi9dYdrlVZYd4aWcbsIWWUZFQ9lh40LhnRg5tO68uwnsdEC4cRHWMnUs0hA567zzazt4hOqrgESCf6GPYedy8rrxfbg/Zy4IUmaquIiEjSKZhYULO3rgFK0pwPBpcx85QwKzvXXOakYzCNL4/py5dO6U23dq2OpKlyFKnvQsdXAg8SXRZlB/C/7v77anXOj/18rpHaJiIikvSK19Szxy5Alce067tEmDmilPePK2Nf65rVhxzbnq+clsOlI3rQKj3YKG2Vo0e9Ap677wJuP0SdV4C+jdEoERGRZBNvzbpt07fVOiM22DlIWtu0KrNoC9/bwYvvruXt48tYkV2z1y8jGGDs8cfypVN6M6p3RyqtUiHSINqLVkRE5BDqs2ZdZYHMAAMfH1gxyWHRhl08MWct/+y6nj0XldWo36tTa647uQ/jRmfTuW2oxnGRhlLAExEROYSGjLML9Yn21mVe2YlnPljDsx+uYeG6XTXqpQWMc4dmce1JvTm9fxcCAfXWSeOpa6HjXxFd8mTT4VzYzK4AWrn71MNtnIiISDKo7zi7SMApe70/P5m3jlcmzedAac1QmNM5k/En9ebKUdl0bafeOmkadfXgXQfcZGZPA0+6+weHupiZHQOMB24BRgB3NkorRUREEijUO1Tn8iebOkZ4d1gZ758QZvuf5tQ4nhEMcOHw7ow/sTen5HbS2DppcnUFvH7Aj4AJwAQzWwu8B8wFNhKdTdsK6AwMBk4hun1ZCFgCXOzuLzdd00VERJpG5QkVwU5BIgdq9sTtCzkfDi7j3eFlrOgZ//Ht4O7tGJfXiy+O7EnHNhlx64g0hbp2stgB3GZmDwNfA24Ero39qT5nyIhuX/wm8BvgX+5++IsCiYiINJGK8La6GIJA+OC4uazrsmpMqAhvO7g2XcScRTlh3h8VYV6/Mkqs5hTaTm0yuOyEHlw1OpvjehzTXF9LpIr6LHS8FpgITDSz44DTie5P2xkoAjYT3e3iHXff3YRtFREROSLVwxux7Fa8upj8CflAzQkVjvNZ9wizh5YxZ3CYne1qhrq0gHH24G5cNTqbMYO6kZEWaPLvIlKXBs2idfdFwKImaouIiEiTqms2bGR/pOKxLMCGzhFmDynjgyFlFHaKv9jdcT3ac9XobC4d0UPLm0hS0TIpIiJy1DjUbNgNO4qYdx68172Y1d3jB8H2++D0ta24/bcnMuTY9k3RTJEjpoAnIiJHhcIphdHtwqpt97q3lfPhoDJmDy0jv3f8UNe6GEYvS+OUxWkctyWNob8fTJbCnSQxBTwREUl55WPvysPdvpAzf0AZHw4OsygnTDjOVq/pYRixIsjn1mZwwtp0AlvC0S3Hfp9bsUOFSLJKioBnZkGiy6+sd/eLzawT8DcgB1gFXB2b1YuZ3QPcTPT/pne4+6ux8tHAk0BrYDpwp7vXskOgiIikuspLnRCAfWnO/OFlfDio9lAXMDitfxcuHdGD84d1p32r9OZvuEgjSIqAR3RB5CVAeX/33cCb7v6Qmd0de/9dMxtKdCHl44AewBtmNtDdw8Bvia7ZN5towLsA0Dp8IiJHkSpLoBjsDTkfDas71AGM7N2By0b0YOzxPbS7hKSEhAc8M8sGxgKTgG/Gii8DxsRePwXMBL4bK3/W3YuBz8xsBXCSma0C2rv7rNg1nwYuRwFPRCTlVQ9129pG+GhUmHkDomPqIrWsWNJ3Q4BTN4f4+jOn0KtTZvM2WqSJJTzgAY8B3wHaVSrLcveNAO6+0cy6xcp7Eu2hK7cuVlYae129XEREUlDhlEKW3bmM8LYwjrOhizPv1DLmDwiz6tja19nP3RDgxPw08pYGySpLY9DkQWQp3EkKOuyAZ2YdgbaxhZAP9xoXA5vdfZ6ZjanPKXHKvI7yeJ85geijXHr37l3PloqISLIonFLIoq8sZmW3CPPHhJk/oPZ16gD6rQ+Ql5/GiflBuuwLQCS6t2z5zhUiqahBAc/M2gI/AK4DuhINUWmxYycD3wfudff59bzkacClZnYR0X1t25vZ/wKFZnZsrPfuWKK7ZUC0Z65XpfOzgQ2x8uw45TW4+2RgMkBeXp4mYYiItBDFZWHeX7mN/33hEz6cUMLutvH/Cg+GYcjqIKOWBxm5IkjHvdFntIHMAIOeGqRQJ0eFegc8MzsGeJfoBIcFwFZgSKUqnwBnEN2rtl4Bz93vAe6JXX8M8G13/5KZPQLcADwU+/li7JSXgGfM7FGikywGAHPcPWxme8zsFOAD4HrgV/X9biIikpx27Cvhpb+s4JX31vNR9xIOhID+Neu1KobjC4KMWp7G8SuDZJbEHuzEflTea1bkaNCQHryJRMPdje7+tJl9H7i//KC77zezt4FzGqFdDwHTzOxmYA0wLvYZi8xsGrAYKAO+EZtBC/B1Di6T8jKaYCEi0uK4O/mFe3hpagFvflrIss5leADoU7Nu+31wwoo0Ri8LMmR1kIywQp1IuYYEvC8Cr7r703XUWQ2ceDgNcfeZRGfL4u7bqCUouvskojNuq5fPBYYdzmeLiEjiHCgNM2vlNv710ireXruNrW1ikyS61qzbdYcxenmQ0cvS6LchQMCrDsFO65zGgMcHKNTJUa8hAS8beP4QdfYCxxx+c0RE5Giwdvt+3l62hZn5m3l3xVYOlMZCXZuq9cyh34YAI1YEOWFFGtlbDYt10QU7Bwlviz7EUbATqaohAW8P0O0QdfoSHZsnIiJSoagkzOyCbby9bAv/WbaFgq37aq3b+gAM/yzIiJVBhhek0b6o5kIJoT4hTl11alM2WaRFa0jA+xC42Mzaufue6gdjs10vAv7VWI0TEZGWyd1Zvnkvb+dv4e1lW5izajslZbWvT3fsNmPEijRGrAwyYH2AtEi81a+iApkBciflNkWzRVJGQwLe40QnLkyPrSVXwcyGAH8gutTJLxuveSIi0lLs2l/Kuyu28p9lW3hrwSa2lJXWWjfkxpCNaQxdYpxY1Jqum6BsW1ntFzfANXFCpL7qHfDc/VUzewB4APiU6O4RmNlWoCPR//t9193fb/xmiohIsikNR1iwdifvLt/Kuyu28tGaHUTqWF205xZj+GdBhn2WxsC1gYOzXimjLB0sw/CSShdQqBM5bA1a6Njdf2hm7wB3AKcAnYkudjwd+IW7v9X4TRQRkWTg7iwr3Mu7K7by3oqtfFCwjX0l4VrrZx6AoauCsVAXpPOeWjaFBSiFQOcAaW3TKF5TrJ0mRI5Qg7cqc/cZwIwmaIuIiCSZDTuLeHfFVt5fsZV3V2xj697iWuuaQ9+NAYZ9Fg11uRsCBL32sXTVhbeHOWPrGY3RbJGj3mHvRSsiIqln1/5SZhVs471YL11ds10BOu8yjlsVZOjqIMetCtIuzozX+gr1Dh32uSJSVUO2KjuH6B6097p7jX1ezawH8CDwdGzRYhERSXK7D5Ty4WfbmbVyG7M/28aiDbvxOsbRtQ8GGbzUGLoywNDVQbruPLgu3ZHQzFiRxtWQHrzbgcHxwh2Au28ws1OJLnQ8sxHaJiIijWz3gVLmrtrO7IJoqFu0YVedEyPSS2HQxiBjTurOBeP6suu0RZSuLmnYhwahx4QebJu+rWJ8XeeLOld5r/F2Io2rIQFvFPDGIeq8C5x3+M0REZHGtOdAKXNX7WB2wTZmF2zjk/V1BzqLQM6mAMetCnLc6iD91kdnu4beL2LYXccwc03Dwl0gM8CgyYMU3kSaWUMCXjcgbu9dJYUcercLERFpInuLy/hw1fZYoNvOp+t3Ea4j0VkE+hQGGLwmyOA1AQatC9K6pOYj1+I10ckVod4hilfHn2gR6qOeOZFk0ZCAtwvodYg6vYC6R+SKiEij2bW/lHlrtjPnsx0VPXR1Bjqgz+YAg1YFGLImyIB1QdoUH3oMXfkEiNxJueRPyCey/+CuFOqlE0k+DQl4c4DLzay7u2+qfjA2yeJy4L3GapyIiMCyW5exYfIGCMO2DhG2fLk9684OMXvBFlYWFVHXSiQG5IZD9J8fZvCaIAPX1i/QVVZ5AkR5iCuYWKBeOpEk1pCA9ytgLPCOmX0LeNXdi80sBFwA/Bxoi7YqExFpFBv/dxNvTlzMsk5hll0YZnl2hG3HOFAEs2OV4mS1XoUBBq+NPnYdtD5I2/3G4a6KldY5jQGPD6gS4LKuy1KgE0lyDdmq7DUz+xFwH/AC4Ga2g4PblBnwQ3d/pUlaKiKS4orLwixct4sPV23nvfc28dGWXey/tu5zArExdAPWBRi4LsjgNUHaHjjyZUsw6PG1Hgz8zcAjv5aINLuGblX2fTN7j+iSKScDHYDtRP8t+St3f73xmygikpp2FZXy5pMFzHx5HUvblfBZjwilwUoVWtU8J6ME+m8IMGBdkIHrgvTbEKBVaSMEOtDeryIp5HC2KnsNeK0J2iIiktI27Cziw1Xbo7NcK4+fG1r7Oe33URHmBqwL0HtzgLRIIwU6gCAQVqgTSTXaqkxEpAlEIs7yzXsrAt3cVTtYv7OoaqU4OS1ruzF4ZzqDtqST+3GErB3xd4rocE4Hds/aXWU2a1wBIE4VSzMGPzlYgU4kRSngiYg0guKyMG//+TNm/GMNi9uVsKJXhH0ZdawoTNXxc+W9dMfsNzAY8tch0eVIqqezAPS4JTo2rnBKYXQ26+riip64YOcghlG2vaxihuuu93ax4XcbINacYNsgA383UOFOJIWZ17LpoJlFiP67b6i7L4u9r/tvqyh39xYRHPPy8nzu3LmJboaItEC7ikqZv3pHRe/cgtU7KKlrE1egdXqQUX060OXJ3XWOnwv1CXHqqlMPBjgtRyIigJnNc/e8+tStK4j9h2ig21/tvYhISorXI1Y+Ni08tn1FmPtw1XbyC/dwiDxH+30weHs6532tPyfmdGJoj/akBwPM/NpMCMc/p/qacwp0InI4ag147j6mrvciIqmkcEphxQ4NEZwNHZ1l2WGWZx9g+Xvz2PrJof99m7XdKiZDDFwXjI6fM2PMlNyqFWsJd4B2hBCRRlHvR6lmdiaw290XNGF7REQaVZVeudgyIBBdwLfb1d3YNn0be9cfYNWxEZYND7MsO8KKnmH2ta77usGA0WdLgP4FVnX8XDXlW3xVKesTfz/XUJ+Qwp2INIqGjJWbAfweuLWJ2iIiclhqG6tWOKWQpTctxUtiqS72Y1/IWXnMAZYtWsWy08IUHBuh7BB/G2aUwIlDO5PXpxMn5nRiZO8OfNj63ToHrlR+3FpZbfu5xqsrInI4GhLwtgJFh6wlItJMCqcUsuzOZYS3HXzmWby6mPwJ+QAsv3M5XuJsbxdhWXYk9sg1wrqukTr3bwVotw8GVlp/bkCr1pzx6ClV6oR6x++Jg7rXldN+riLS1BoS8GYCn2vMDzezVkQnb4Ribfl7bLeMTsDfgBxgFXC1u++InXMPcDPRUSx3uPursfLRwJNAa2A6cKfXNkVYRFqUeD10QI1eMADHWde6jP/8eTGLTilmWa/y/VvrFnf8XGz9uUBmgIE/61fjnNp64uozjk4TKESkKdW6TEqNimYDgA+AXxPdc7b0iD/czIA27r7XzNKBd4E7gS8C2939ITO7G+jo7t81s6HAVOAkoAfwBjDQ3cNmNid27myiAe+X7v5yXZ+vZVJEEqdyaAt2iq3dtq2sxuxVqBnkApkBAq0DlG0royzgrMmKkF/RQxdmb2bdn119/bkB6wN02BeIHox9fn13eNBSJiLSXBqyTEpDAt6fgf7AaUAh8DGwiZojUNzdb65/cyuun0k04H0deBoY4+4bzexYYKa7D4r13uHuP4md8yrwANFevhnuPjhWfm3s/Fvq+kwFPJHmVduEh9pUDnLlDqQ7K3tEw9yy7DAre0Qoyaj7Ohkl0G9DoOKRa+7GAK1Laj6jrW/vm4hIIjTWOnjV3VjpdffYn3ic6CPUejGzIDCPaHj8tbt/YGZZ7r4RIBbyusWq9yTaQ1duXaysNPa6ermIJInaJjzUJbI/wk4Ps3xAOBboIqzuHiESqPu8dkXGqKxjGJHZlg6PbqX3+pr7t1aeRaveNxFJNQ0JeH2bogHuHgZOMLMOwAtmNqyO6vGGRXsd5TUvYDYBmADQu3fvBrZWRA5X+YSHujjO1mO8Iswt6xVmY+dDJ8EuOy3WOxdgyN4MPv/AILp/Kfpv0MKueoQqIkefegc8d1/dlA1x951mNhO4ACg0s2MrPaLdHKu2DuhV6bRsYEOsPDtOebzPmQxMhugj2kb9EiJSQ/lj2cqPWcs5zqZOztJeYfJ7h/9/e3ceHXdd73/8+Z6ZpE26QJvSvemedAFqVwg7FgQRLyDqD0RF4Zzen3i8uByveLn3d9F7uRc9irtgFQWkrIICatnKVqCl0FK6ZWmTNmmbNl1tm6aZZGY+v66d/VwAAB6CSURBVD++3yQzk8kGWaaT1+OcnJl8vp/vd77fTz5p3/mslE6IcXhI+7+W5mD8wQCLCvKYM2gww395mMGljW0Gb5rMICL9UacCPDPLBxbitYq945zb2R0fbmanAY1+cJcDXAL8AHgGuBG4y3992j/lGeBhM7sbb5LFdGCNP8nimJmdjTcR5IvAL7rjHkUkUXtrznU009Xh2DPcUZIfpXRClJL8GEcGtx/QhcyYlZPLpHejTCl2zCaHM++Y1hK0fbVHH1dE5KTUYYBnZj8Cvk5LN6gzs584577dDZ8/BnjAH4cXAB53zv3VzFYBj5vZzUAV8BkA59xmM3sc2AJEgK/6XbzgTc64H2+ZlOX+l4h0o/jtvKBlzbkjbx5h7wN7W6VbjrErJ0JJQZSS/CglE2Ic7SCgGxiGabuDzKrN5uKr8rn4pskMzAr2+LOJiGSSdmfRmtnngIfwWu5K8IK8Qv/w551zj/T4HfYgzaIV6ZpVk1alXtjXX1LE4ajOc37rnPd1dFD71xwSCHJW4QjOnjKcs6fkMWP0EELBDmZRiIj0Q905i/ZmvJayy5xzr/gXvwSvdexmvDXpRCQDdGZduuTgzuGoHuGNoWvqdu0ooBt0Agp2Bjm9dgAf++wkzrlpEsFAB9tKiIhIl3QU4J0J/KUpuANwzr1kZk8DF/XkjYlI70nueo3f+gv/bbgyjDNHzamOzZOiFPsB3bGOArp6KKwKMqMqyIyqAPnHQ8xcOkMTH0REelBHAd4woDRFeglwdfffjoj0prJbyqheWt0cxKVyeHCMLROjbJkYo3hilEND2x9DN+gEzKgKMnNviMtunsq0gTns+Mv2lskXP9EyJSIiPa2jAC+At4hwskZSrz0nIieJslvKqL6n9WpCxwd4s1y3TIxSPDFK9Yj2A7pTgiGKZoxg1qEsRv7+CCM3RsjJH5iwZMmYz7e1LrqIiPSEziyTorXiRDJIwnZhQEPQsW18UytdlO2jY7h25jjkNBjnzhnJudPyKJqaR8HIIQSaxtDd2gsPICIiHepMgHeHmd2R6oCZperYcc65ruyQISK9pGZZDSVLStiVE2XTgigbJ3vj6Bqz2j4nFIHpuwPMrAxy+t4sLvv+TMapRU5EJK11JhDralesum5F+kjNshrKbi1rniQRygsx/WfTGfip4by57QBP/GUz79/Y0O44OnMw6UCA2dVZzCgxpu8JMCBsDJiobb5ERE4W7QZ4zrXXUSMifSl554i8K/Ko/l01NELMHNtHx9g0uYGNz6+jYmOMGMDU1NcafdCYVRlkVmWQixaPY8F9M3vzUUREpJupK1XkJJIwfs5oHiEbrgyz+aFdbCqMsnFKlM2TohzPafs6OWGYtSPIGduDnFERJO9YAIIwdslYCn5d0CvPIiIiPUcBnshJInmtuog5tk6IsWFKlI2TI+wa2X6365kTTmFeOJdx9/yDyRVG0HmjKQK5AQofKlTXq4hIBlGAJ3ISqFlWQ/GNxRzLdmyYHeH9qV5L3YkBbZ9zSq1x+navlW5uJIfLys71rjU6sWtX4+pERDKPAjyRNOac4837dvCXP25j/XURysfFcG1MYwpGoWBXwAvqKoJM2B/AMCzbmPH7ac35Rt0wSgGdiEiGU4An0kdSTZI4+PeDHKuuZ9v8AFuKgqxqPMbBQTEoSn2NvCPGnHIvoJt9IItJnxtDzYs1rWbRKqATEelfFOCJ9IHk8XQHa+pZsbKStfOibL42SkPTunTZiedZDKZWB/hIeZA520KMP2iY85cw+ZXX1apJEiIiogBPpA9svXUrBwMR1s6NsrYgQml+jFgbixLl1MMZ24N8ZFuIM7YHGXLC76MNwsw/zlTrnIiItKIAT6QXVeyv5cll21h+xTEqxsbazDf6oDW30k3fHSAUSxx4F8gNULhUM19FRCQ1BXgi3SR5TN2UO6cw8nMj2Vx9lOc27eX5zXvZuq/Wyzy29flTqgPMLwsyvyzE6MNtrzGuHSVERKQjCvBEukH8mLqYOTZE6/jDH99nY4mxp7Eh5TmBGMyoCjC/LMS8rUGG1ba/cYxa7UREpLMU4Il0UXxLXXB4EMOoP9xI8cQo7xRGeW9ahGOD/MyNiecOCAU4Y0eQueuNOeUhBte3dL3aICN7RHarWbVar05ERLpKAZ5IFyS31G0Z1MCamRHeLYhQm5v6nCEDQ1wycxSXzR7FBQWnceyJg5T+uZRYfcsYvEBugMLfqHVORES6hwI8kS7Ydns5xcMbWXNOhHcKoxwdnHp7sFNqjXlbg5x9JIcvv3Ee2aGW7tdcP4jTbhIiItJTFOCJ+FJNkgAov72cLY0nWLvIsfoTDRwekjqoG3bMWFQSZGFJiCnVAUK5QQqXFiYEd020m4SIiPQkBXgitF54OFwZZsU3N7N6ZoRVl0fYf2rqoG5orbGwNMhZxSGm7Q4QwBtTp5muIiLSlxTgieB1l8bqYhzJdbw9M8Kq2RG2j0m9Tt2QOphfGuKskhCFOwME4jaH1UxXERFJBwrwpN+ra4jwyuDjrPpMhM2Toil3lMith/llIc4qDjKzMkhu/kDCO1tm0UYORTSWTkRE0oYCPOlXmsbZ1e2sZ9vCIO9dncXrdUeouzLaKm8oAnPKg5yzOcSZFUGyoi3dr0U7inr71kVERDqtTwM8M5sAPAiMBmLAUufcz8xsOPAYMAnYAXzWOXfYP+e7wM1AFPgX59zzfvp84H4gB/g7cKtzLvXAKemXapbV8PJ3tvBaQQOrroxyZLCDf7TOV1gVoGhLiIXlIQY3BHANLdUokBtonnwhIiKSrvq6BS8CfMs5t87MhgBrzexF4EvACufcXWZ2G3Ab8B0zmwVcB8zG2+zpJTMrcM5FgXuAJcBqvADvcmB5rz+RpI2m1rrDe+tZdy68MjFM+edbt9QBTD1tEB8LnMrM39YytMTvbr3XC+S0nImIiJxs+jTAc87tAfb474+ZWTEwDrgKuMjP9gDwKvAdP/1R51wY2G5m24BFZrYDGOqcWwVgZg8CV6MAr9/a89Benv7+Fl47vYG110ZpyGqdZ2itUVQcpGhLiBurL8TM4But8ymgExGRk01ft+A1M7NJwFzgbWCUH/zhnNtjZiP9bOPwWuia7PLTGv33yenSz+z+xwke+H0Jfy7bw/5Pte6hD0Zh7tYgF2wMMXt7kKAzBkwc4AV3IiIiGSItAjwzGww8CXzdOXe0nf9sUx1w7aSn+qwleF255Ofnd/1mJe00RmM88ZtSHn27io2jIzgDTk3MM2FfgPM3hCjaEmLIicRlTTSmTkREMk2fB3hmloUX3C1zzj3lJ9eY2Ri/9W4MsM9P3wVMiDt9PFDtp49Pkd6Kc24psBRgwYIFmoRxEqv+xwkeXVPFw69XciDSCGMSj+fWQ9HmEOdvDDGxJoBhBPOChEaGNKZOREQyWl/PojXgPqDYOXd33KFngBuBu/zXp+PSHzazu/EmWUwH1jjnomZ2zMzOxuvi/SLwi156DOlFsZjj9a37eWh1FS8X15C8FLE5mLUjwPkbs5hXFiQ7mthaV/CzAgV0IiKS8fq6Be9c4AvARjNb76f9G15g97iZ3QxUAZ8BcM5tNrPHgS14M3C/6s+gBfgKLcukLEcTLDLKwdowj7+7i4fXVLLz0IlWx0+pNS7YEOLC90OMOJpipeIg2mFCRET6DevPS8UtWLDAvfvuu319G/1K09Il8V2k4C9FUhmGIBD1FhOe/N+T2XleNg+trmT5xr00RFtvHTZzR4CPrs9i7tYgoVjqsZvaPkxERDKBma11zi3oTN6+bsGTfqRmWQ2lS0qJ1XmBWrgyTPGXizGzlsWEo3Ai2/HS8FpeffU9dm1qHdQNqofzNoa4aH0WYw6laK0Db9qN8wJFjbMTEZH+RgGe9JqK2yuag7tmjeD8Cc/VeTFenN/IW7MjhLNbnz9nwqkU/amReW84siNtL2uioE5ERPo7BXjSa8JV4VZpMRybpkR5YX6ETVNa7zKR3QDXnjeBG86ayOnjTuHVr72Ktw5Ka+qKFRER8SjAk14zIH+AN84OqM9yvHl6hBfnN7I3r/U40HH7jYvfy+LiY7ksvvvMlNdIoEkUIiIizRTgSa+ZcucU3vxWMS/MbOC1OY2cGJh43Bx8ZGuQj63NYkZVgGBukMKl01pdI34cH6jlTkREJJkCPOkVm6uP8JtANX/70nGSO2IHBYJcuCXERa8GGFkbaJ5Fm2ocXdP3yTNxFdyJiIi0UIAnPcY5x6ryg9zzWjkrtx5odXxSXi5fOmcSn14wgcEDOl8VR90wSgGdiIhIOxTgSbeLxhzLN+3hN69VsHH3kVbHZ1YGuLIyl0/dUsiYc0f3wR2KiIhkNgV40m3qG6M8sXYXv329gqpDdQnHLAYLy4JcsTqLSTVBwLH1/TICZmqNExER6WYK8KTLknejyPtePs+Pr+P+t3Zw8HhDQt6sRjh/Y4jL38li5D8SFyWO1cWouL1CAZ6IiEg3U4AnndIc1MUtUXJwSIznpx7ltffXEy5OzD/oBCxel8Ul67IYWtf2osSp1sYTERGRD0cBnnSoZlkNJTeVNG8ntmd4jL+e3ciq2RFiSTuFjTs1hwufjHLB+yEGNrYd2DUZkD+gJ25ZRESkX1OAJx3aeutWXINj94gYzxY18PaMKC4psBu/z/jW187kyjPH8u69bxNu7LhlLpAbYMqdU3rorkVERPovBXjSoe2BBp6+qoG1hdFWu4TNqAxwxdtZnLE9yMW/Hw+kXoy4mQFO+8WKiIj0JAV40qZNu4/w8xVbeeGmE62OnVke5J/eymJadRCAYF6w+VjCYsSVYQjS7uLFIiIi0r0U4Ekrr/9uOz99bSvrxjW2OjZ3a5BPvpXFlL0tAR1ZUPCzgoR8WoxYRESk7yjAk2bb9h3jf363kZePHoZxicfml3otdhP3BRPS1SonIiKSfhTgCVUH6/jpijL+8t5uYq4l3RwsLAnyybeymXCgZVaFgjoREZH0pgCvH9tz5AS/eHkbj7+zk0h8ZIfXYnfNG9mMP5A0XdagaEdRL96liIiIdJUCvH7oQG2Ye14t54+rK2mIJM50PaMiyKdWZjF5bzDluVq3TkREJP0pwOtHjtQ1snRlOX94cwd1DdGEY4VVAT61MpvCXakDO9C6dSIiIicLBXgZrGl7saO763lxYSN/W9TIiYGJeSbvCXDt69nM3hHASLHzhJY4EREROekowMtQNctqKP7nElZObuCpJY0cHpI4xm5iXYirlgeZuy2YOrDDC+o03k5EROTkowAvQz31wy08/Jl6do5KHGM36pBxzRvZLCoOEmgjsAN1x4qIiJzMFOBlmOI9R/nefe+z+uN1CelDa41r3sjigg0hgsn7jSVRd6yIiMjJrU8DPDP7PXAlsM85d7qfNhx4DJgE7AA+65w77B/7LnAzEAX+xTn3vJ8+H7gfyAH+DtzqnEvsk8xwe4/U8+MXSvnTul3EP3l2A3z8nSwuX5NFTkP7gR0AQS2DIiIicrILdJylR90PXJ6Udhuwwjk3HVjhf4+ZzQKuA2b75/zazJqmfN4DLAGm+1/J18xYteEIP36hlIt+9ApPrG0J7iwGF7wf4ge/zeGaN7ITgrtAboBTF5+a8npjl4ztjdsWERGRHtSnLXjOudfNbFJS8lXARf77B4BXge/46Y8658LAdjPbBiwysx3AUOfcKgAzexC4Gljew7ffp6Ixx6PvVPGTF8s4UNuQcGxOdRafXh5K2H2iSXz3a9ktZVQvrfbaQ4NecFfw64JW54iIiMjJJR3H4I1yzu0BcM7tMbORfvo4YHVcvl1+WqP/Pjk9Y71VfoDvP7uFkr3HEtJnjRnKv10xk+lropQ+WUqMlgkWgdwAhUsLE8bVFfy6QAGdiIhIBkrHAK8tqQaQuXbSU1/EbAledy75+fndc2c9rGk9u11HTvDEFRHWTGhMOD68LsDXCvK58ZZZBALmdVIDFbdXEK4KMyBfkyZERET6k3QM8GrMbIzfejcG2Oen7wImxOUbD1T76eNTpKfknFsKLAVYsGBB2k/EqFlWw4ZbSnh6TpjnFjUSifuJZTfAlauzuPydLAZmH2T/sH3NQdyoG0YpoBMREemn0jHAewa4EbjLf306Lv1hM7sbGIvXTrXGORc1s2NmdjbwNvBF4Be9f9vdq2ZZDeW3l/PmwDoeuaGBQ0MTY9GiTUE++1o2w2q9cXaxSIyK2ysU1ImIiEifL5PyCN6EihFmtgv4T7zA7nEzuxmoAj4D4JzbbGaPA1uACPBV51zThqpfoWWZlOWc5BMsapbV8Oq/FvPgeSfYPDlxoeIp1QE+tyKbadWt94wNV4V76xZFREQkjfX1LNrr2zi0uI38dwJ3pkh/Fzi9G2+tRzSNpQtXhQkO97YIixyKJIyRq2uI8D+PbeKvn6snGhfDDT0On301m3M2hdrcgWJA/oBeehIRERFJZ+nYRZuRapbVULqklFid1yIXPRhtPhauDFOypIRXjhzm50d2Uz2rvvmYxWDxuhDXvJHNoLAf2GWBmeEaWrpttbWYiIiINFGA18OaW+0q2+4+3TssxkOXNLCpqjwhfdruAF94IZuJ+1qa8prWsQPNkhUREZHUFOD1oORWu2ThkOOvRY0sT5odOywY4tPPhShaF2jujk21jp0COhEREUlFAV4Pqri9os3gbsPkCA9+rIEDp7Z0s1oMvnDuRL51aSH1sw6phU5EREQ+EAV4PSjVrNYjuY5HFodZPSuakD51T4D/d34hF17ldb+eonXsRERE5ANSgNdDapbVQABvn1fA4Vh5RoTHLm7geE5LvkEn4IaNg/jyTTMY8/nRfXKvIiIiklkU4PWAprF3TcHd3mEx7r8sTMnExO7aa+aO498/MZO8wVreRERERLqPArwe0DT2LhJw/P2sRp45J3ESRf7wXO685nTOn35a392kiIiIZCwFeD0gXBVm67gof7g8TPWIuLXqYrDk4qncung6Odmtd6IQERER6Q4K8HpAdn42TxYdSQjuJlcHWLJhMNf/cEYf3pmIiIj0B4G+voFMNPXOqXxp5UBCERjQADe8lM1/PpXLR79d0Ne3JiIiIv2AWvB6wKgbRnExcMu9xUzcEGPssBym/Ebr2ImIiEjvUIDXQ0bdMIpvKqATERGRPqAuWhEREZEMowBPREREJMMowBMRERHJMArwRERERDKMAjwRERGRDKMAT0RERCTDKMATERERyTAK8EREREQyjDnnOs6VocxsP1DZgx8xAjjQg9c/GagMVAagMgCVAagMQGUAKgP44GUw0Tl3Wmcy9usAr6eZ2bvOuQV9fR99SWWgMgCVAagMQGUAKgNQGUDvlIG6aEVEREQyjAI8ERERkQyjAK9nLe3rG0gDKgOVAagMQGUAKgNQGYDKAHqhDDQGT0RERCTDqAVPREREJMMowGuDmU0ws1fMrNjMNpvZrX76cDN70cy2+q/D/PQ8P3+tmf0y6VrZZrbUzMrMrMTMrm3jM79rZtvMrNTMLuv5p2xfb5eBmU0ysxNmtt7/urd3nrRt3VUGZjYk7rnWm9kBM/tpG5+ZkfWgs2WQyfXAP3a9mW00sw1m9pyZjWjjMzOyHvjHOiyDdKwH0O3l8H/8MthsZj9s5zMzuS50WAbpWBc+QBlcamZr/Xq/1sw+Gnet+X76NjP7uZlZG5/ZtXrgnNNXii9gDDDPfz8EKANmAT8EbvPTbwN+4L8fBJwH/F/gl0nX+h7w3/77ADAixefNAt4HBgCTgXIg2M/KYBKwqa9/9j1VBknXXQtc0N/qQSfLIGPrARAC9jXVf//8O/pTPehCGaRdPejmcsgDqoDT/O8fABb3s7rQ2TJIu7rwAcpgLjDWf386sDvuWmuAIsCA5cDHu6MeqAWvDc65Pc65df77Y0AxMA64Cq8S4r9e7ec57px7A6hPcbmbgP/188Wcc6kWN7wKeNQ5F3bObQe2AYu68ZG6rA/KIO10cxkAYGbTgZHAyhSHM70eAB2WQdrpxjIw/2uQ/1f6UKA6xUdmcj3obBmkpW4shylAmXNuv//9S0Cq3p1MrgudLYO08wHK4D3nXFM93wwMNLMBZjYGGOqcW+W8SO7BpnOSdLkeKMDrBDObhBd9vw2Mcs7tAe8HjPefVHvnnuq//S8zW2dmT5jZqBRZxwE7477f5aelhV4qA4DJZvaemb1mZud3z913jw9TBkmuBx7zf5mTZWw9SNJeGUCG1gPnXCPwFWAjXlAzC7gvRdaMrQddKANI43oAH/r3YRsww+9+DOH9pz4hRb6MrQt0vgwgjevCByiDa4H3nHNhvJ/lrrhjbf18u1wPFOB1wMwGA08CX3fOHf0AlwgB44E3nXPzgFXAj1J9VIq0tJji3ItlsAfId87NBb4JPGxmQz/gbXerbiiDeNcBj7T1USnSMqUexGuvDDK2HphZFl5wMxcYC2wAvpsqa4q0jKgHXSiDtK0H8OHLwTl3GK8cHsNryd4BRFJ9VKrTu/p5PaEXyyBt60JXy8DMZgM/AP65KSlFtlQ/3y7XAwV47fD/IXoSWOace8pPrvGbVPFf93VwmYNAHfBn//sngHkp8u0i8S+X8aRBt0VvloHf9HzQf78Wb4xBwYd+iA+pm8qg6VpzgJD/fKlkcj1oula7ZZDh9eAjAM65cr/18nHgnBT5MrkedKoM0rUeQPf9PjjnnnXOneWcKwJKga0psmVyXehUGaRrXehqGZjZeLz/B7/onCv3k3fh/UybtPXz7XI9UIDXBn9syH1AsXPu7rhDzwA3+u9vBJ5u7zr+P2DPAhf5SYuBLSmyPgNc5/fJTwam4w287DO9XQZmdpqZBf33U/DKoOJDPMKH1l1lEOd62m65arpuRtaDOO2WQYbXg93ALDNr2iz8UryxO8kyuR50qgzSsR7499Jtvw9mNtJ/HQbcAvwuRbZMrgudKoN0rAtdLQPzhir9Dfiuc+7Npsx+N+4xMzvbv+YXSV1uXa8HLg1mo6TjF96MH4fXfbDe/7oCb9bPCry/MlYAw+PO2QEcAmrxou1ZfvpE4HX/WivwmpoB/gn4ftz5t+P9ZVJKilk0mV4GeOMSNuPNFFoHfDKTysA/VgHMSPqMflMPOlMGmV4P8GYSFvvXehbI62/1oDNlkI71oAfK4RG8P3a3ANel+n3oB3WhwzJIx7rQ1TIA/h04Hpd3PTDSP7YA2OT/jH8JzZtQfKh6oJ0sRERERDKMumhFREREMowCPBEREZEMowBPREREJMMowBMRERHJMArwRERERDKMAjwRERGRDKMAT0T6LTN7ysycmX2jnTwLzazRzLany/ZIIiId0Tp4ItJvmVke3qb3w4GFzrmNScdzgfeAacCFzrk3ev8uRUS6Ti14ItJvOW9/yy8D2cAyMxuQlOXHeHte3qXgTkROJgrwRKRfc849j7c90BnA/zalm9kVeFtqrQXuiD/HzCaa2b1+t23YzA6Y2Z/NbG7y9c1sgpl9z8xWmdleM2sws91m9pCZtdow3cxm+N3G95rZTDP7k5ntN7OYmZ3dzY8vIhlKXbQi0u+Z2UC8QG4mcCnenpebgCHAPOdcaVzes4DngKH+6xZgJHANXkvgJ5xzK+Lyfwn4FfAyUAnU4bUKfsJ/f7Zzrjgu/wy8fVpfA+b597EaGAz83Dm3qdsLQEQyjgI8ERHAzD4CvA3sx9tA/OPALc65e+LyDADKgNOAxc65VXHH8oF3gDAw1TnX6KePAmqdc8eTPm8BsBJ4zjl3TVx6U4AHcIdz7nvd/awikvnURSsiAjjn1gP/AYzDC+7+Fh/c+a4G8oEfxwd3/vlVwN3ABOD8uPSa5ODOT38XL8C71MxS/Vu8E7jzgz+RiPRnob6+ARGRNPIj4BvAaODbKY4X+a9TzeyOFMdnxr2+3JRoZlcDS/C6XPNo/W/vKcDhpLT3nHORrty8iEgTBXgiIj7nXMzMwv63J1JkyfNfr+/gUoOb3pjZd4C7gIPAS0CVf20HfBqYDSTP3gXY2/k7FxFJpABPRKTzjvivlznnXugosz9m7z/wulvnO+f2Jx2/uJ3TNUBaRD4wjcETEem81f7r+e3majEGGASsTBHcnQLM6cZ7ExFppgBPRKTz/oTXGvd1M7s0+aB5zjOzbD9pN9AILPJ3xWjKl423dMopvXDPItIPqYtWRKSTnHP1ZnYNsBx4wczewFszrx5v9uwiYBIwDGhwzjWa2a+ArwMbzOxZYCCwGG+c3ko63xooItJpasETEekC59xa4Ey8Gbd5wM14O17MA9YANwBH4075V+A2IAJ8BW+plbeAhUB1r924iPQrWuhYREREJMOoBU9EREQkwyjAExEREckwCvBEREREMowCPBEREZEMowBPREREJMMowBMRERHJMArwRERERDKMAjwRERGRDKMAT0RERCTDKMATERERyTD/H1f5RHl95JfdAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 720x720 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"max_N = 46\n",
"\n",
"Z_steel_train = np.block([[t_steel_train**0]]).T\n",
"for i in range(1,max_N+1):\n",
" Z_steel_train = np.hstack((Z_steel_train,t_steel_train.reshape(-1,1)**i))\n",
"a_steel_train = np.linalg.solve(Z_steel_train.T@Z_steel_train,Z_steel_train.T@P_steel_train)\n",
"\n",
"Z_aluminum_train = np.block([[t_aluminum_train**0]]).T\n",
"for i in range(1,max_N+1):\n",
" Z_aluminum_train = np.hstack((Z_aluminum_train,t_aluminum_train.reshape(-1,1)**i))\n",
"a_aluminum_train = np.linalg.solve(Z_aluminum_train.T@Z_aluminum_train,Z_aluminum_train.T@P_aluminum_train)\n",
"\n",
"f,axes = plt.subplots(2,1,figsize=(10,10));\n",
"axes[0].plot(t_steel_train,P_steel_train,'mo',label='Steel');\n",
"axes[0].set_ylabel('Price ($)',size=20);\n",
"axes[0].plot(t_steel_train,Z_steel_train@a_steel_train,label='order fit: {}'.format(max_N),lw=3);\n",
"axes[0].legend(prop={'size':15});\n",
"\n",
"axes[1].plot(t_aluminum_train,P_aluminum_train,'mo',label='Aluminum');\n",
"axes[1].set_ylabel('Price ($)',size=20);\n",
"axes[1].plot(t_aluminum_train,Z_aluminum_train@a_aluminum_train,label='order fit: {}'.format(max_N),lw=3);\n",
"axes[1].legend(prop={'size':15});\n",
"\n",
"plt.xlabel('Year',size=20);"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Z_steel = np.block([[t_steel_train**0]]).T\n",
"Z_steel_test = np.block([[t_steel_test**0]]).T\n",
"Z_steel_train = np.block([[t_steel_train**0]]).T\n",
"\n",
"max_N = 20\n",
"\n",
"SSE_steel_train=np.zeros(max_N)\n",
"SSE_steel_test=np.zeros(max_N)\n",
"for i in range(1,max_N):\n",
" Z_steel = np.hstack((Z_steel,t_steel_train.reshape(-1,1)**i))\n",
" Z_steel_test=np.hstack((Z_steel_test,t_steel_test.reshape(-1,1)**i))\n",
" A_steel = np.linalg.solve(Z_steel.T@Z_steel,Z_steel.T@P_steel_train)\n",
" plt.plot(t_steel_train,P_steel_train-Z_steel@A_steel,'-',label='order {:d}'.format(i))\n",
" SSE_steel_train[i]=np.sum((P_steel_train-Z_steel@A_steel)**2)/len(P_steel_train)\n",
" SSE_steel_test[i]=np.sum((P_steel_test-Z_steel_test@A_steel)**2)/len(P_steel_test)\n",
" \n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
"plt.title('Error in Predicted Values',size=20);\n",
"plt.xlabel('Year',size=20);\n",
"plt.ylabel('Y Error',size=20);"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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pUPsBjDHxdbyG8Rxfax94HZ9PZ6zBfAlY86zXYDVvd8aaR52CNZ3ue8/x/lhBv3we+OdYAe+nWH25V1W+nlhrmP8M6F5xhTjPPPD/wwrkH2LNA4/CqjnmG2PGVTh2NTAUeAvrQ5cL+Kh8+VIReRD4C1AMfOq57xCsWvAY4DtjzKQK56tuHngK1jzw0ZXLWxci8md+DN5HgS5V1XJF5AKsZ+0GFnmun4IV/N/Fep5/NMY8XuE13wHDjDGVg+mbwPVYH1aXYr0fl2MNNpsGfGWMuaTC8b7A+1hTGzOx3v8jWF0KCVhN5A8aY/6f5/gCrFr7d1gfPHywWm0GYfXjj6hvTb650XSi5666dKLahN561TR4Zj8VFuhoKGPMGs9iLg9hzX2djLUQxVtYU5i8sYBKi2WMyRSRVOCXWNPFZmD9gT6KtejNv4DNFY4v9cw5fwQryNyD9Z49jhUUrqrHtV8QkS1Y/cFjsT5U/YAVQCv3G8/EqmlPwgpWghV80j3nelJEVmK1AozEmiqWizVIbh7wZqVrLxKRSVj/FqdhLWSyAmtE+2+xAvi5eBHr35oNeKW6wGaM+a+IXAw8hhVIfbA+EE3BqtH+tB7XnI31AWA61noCB4CnsOZ5n9XP7Zn9cBXWM/0Z1v+JECAb2Ospf8VphQ8AE4BUT1lLsN7zB4DnWnrwVo1Da+BKKaUandbAz111NXDtA1dKKaVaIA3gSimlVAukAVwppZRqgTSAK6WUUi2QBnCllFKqGnPnzo266aabqlsfoVYZGRl+ycnJffv06ZPUq1ev5L/+9a+1zh2vK51GVoPo6GgTHx/f1MVQSqkWZf369T8YY7wWqM6Xxkgn2rVrV0daWtqOwMBAk5uba0tKSkqeNm3aqfj4+LMyz9WXBvAaxMfHk5Z2VoIrpZRSNRCRqpa2bXKPPPJI+zfeeCMaYObMmdkPP/zw8Z07d/pddtllCcOHD89fv359yIcffrh76dKlof/4xz86xsTEOHr27Fni5+dnwEonOmvWrG6HDx/2A3jqqacOTpgwofDee++Ny8rK8j148KBfZGSkc8mSJfvKrxkQEHB6rnZxcbG43dUumV5vGsCVUkq1ek2ZTnT37t2+l19+ecKhQ4f8H3744Uxv1L5BA7hSSqnz7I8r/9hl98ndXk0n2iuiV9FjIx5rlulEe/Xq5cjIyNi2f/9+38mTJ/e68cYbT3bp0qXBq+tpAFdKKdXqNWU60XLx8fGO3r17Fy9btix01qxZDc5MpgFcKaXUeVVTTbmxNFU60T179vi2b9/eGRISYrKzs33S0tJCHnjggWPeuCcN4EoppVq9iulEwRrENmLEiOKdO3f6VTyuYjrRmJgYR//+/YtcLpeAlU70lltu6ZqYmJjkcrlk6NCh+cOHDz9Y03XT09MDH3zwwc4igjGGX/ziF0eHDBlSY9CvK01mUoNBgwYZHYWulFL1IyLrjTFn5IHXZCbnrkUmMxGRLiKyXES2i8hWEbnHsz1SRL4UkV2e7xEVXvM7EdktIjtFZGKF7akistmzb65U18mhlFJKtQDNOoADTuA+Y0xfYBhwl4gkYeUS/soYkwB85fkdz77pQDJWTuNnRaR8Rv5zwG1Agudr0vm8EaWUagnKysr46quvOHz4cFMXRdWiWQdwY0yWMWaD5+d8YDvQCbgaeM1z2GvAFM/PVwNvG2NKjTH7gN3AEBHpCIQZY1Ybq89gfoXXKKWU8iguLubbb7/l6NGjTV0UVYtmHcArEpF44AJgDdDeGJMFVpAHYj2HdQIqjm7M9Gzr5Pm58nallFIVlJSUABAQENDEJVG1aREBXERCgMXAr4wxeTUdWsU2U8P2qq51m4ikiUhadnZ2/QurlFItmAbwlqPZB3AR8cUK3m8YY97zbD7maRbH8/24Z3sm0KXCyzsDRzzbO1ex/SzGmHnGmEHGmEExMS1uLX6llGoQDeAtR7MO4J6R4i8B240xT1XY9RHwM8/PPwM+rLB9uoj4i0h3rMFqaz3N7PkiMsxzzpsqvEYppZSHBvAzNTSdaLmcnBxbbGxsf2+cq1xzX8hlBDAT2CwiGz3bfg/MAd4Vkf8BDgLXARhjtorIu8A2rBHsdxljXJ7X3Qm8CgQCSz1fSimlKmjLAbwx0omWu++++zoNHTo0vyHlq6xZB3BjzHdU3X8NML6a1zwBPFHF9jQgxXulU0qp1qc8gPv7+zdxSbyvKdKJgpUJLTs723fChAm5aWlpwd66n2YdwJVSSp1fJSUl+Pr6Yre3rvDQVOlEXS4X9913X5c333xz76effhrmzXtqXe+QUkqpBikpKWn02veR3/+hS+muXV5NJ+qfkFAU979PNLt0ok8++WTMhAkTTvXq1csrOcAr0gCulFLqtJKSklbZ/91U6US///77kHXr1oW88sorsUVFRTaHw2ELCQlxPfvssw1e6k4DuFJKqdPORwCvqabcWJoqnehHH310uj987ty5UWlpacHeCN6gAVwppVQFJSUlBAd7bZxVs9FU6UQbk6YTrYGmE1VKtTVz584lLi6On/zkJ+d8Dk0n6l0tMp2oUkqp86u19oG3RhrAlVJKAdYgLQ3gLYcGcKWUUoC1ipjb7dYA3kJoAFdKKQW07WVUWyIN4EoppQAN4C2NBnCllFKABvCWRgO4UkopQAN4VbyRTtTHxye1T58+SX369Em6+OKLe3mrbLqQi1JKKUADeGOlE/X393fv2LFjW0PLV5nWwJVSSgGtP4A/8sgj7RMSEpITEhKSH3300ViAnTt3+vXo0SP5xhtv7JqcnJy0Z88ev6effjoqPj4+ZfDgwb1XrVoVUv76I0eO2CdOnNgzJSWlb0pKSt8vvvgiGODee++Nu/7667uNGDEiYerUqd3P1/1oDVwppRTQunOBN1U6UYCysjJbSkpKXx8fH3P//fcfnTlz5ilv3JMGcKWUUoAVwH18fM5qAva2r+Zv75JzuMCr6UQjO4UUjb+pb7NLJwqwe/fu9Pj4eMe2bdv8Lr300t4XXnhhcXJycmlD71kDuFJKKaB1L6PaVOlEAeLj4x0ASUlJZcOGDctfu3ZtkAZwpZRSXlNaWnpeAnhNNeXG0lTpRLOzs31CQkLcgYGBJisry56Wlhby+9///qg37kkDuFJKKaB118CbKp3oxo0bA+66665uIoIxhl/96ldHU1NTS7xxT5pOtAaaTlQp1Za88MILBAQEMHPmzAadR9OJepemE1VKKVWj1lwDb400gCullAI0gLc0GsCVUkppLvAWSAO4UkopnE4nLpdLA3gL0uwDuIi8LCLHRWRLhW2PiMhhEdno+bq8wr7fichuEdkpIhMrbE8Vkc2efXOluol+SinVBrX2ZVRbo2YfwIFXgUlVbP+HMWag5+tTABFJAqYDyZ7XPCsi5avSPwfcBiR4vqo6p1JKtUkawFueZh/AjTErgJw6Hn418LYxptQYsw/YDQwRkY5AmDFmtbHmzc0HpjROiZVSquXRAF41b6QT3bVrl9+IESMSevTokdyzZ8/kynPPz1WzD+A1+IWIpHua2CM82zoBFVf4yfRs6+T5ufJ2pZRStO5EJnXldrtxuVwNOofD4Thr24wZM7rff//9x/bu3bt1w4YN28vXWW+olhrAnwN6AgOBLODvnu1V9WubGrafRURuE5E0EUnLzs72RlmVUqrZaws18KZIJ7p+/foAl8vFNddckwcQHh7uDg0NrXbd9PpokUupGmOOlf8sIi8AH3t+zQS6VDi0M3DEs71zFdurOvc8YB5YK7F5r9RKKdV8tfYA3lTpRLdt2xYQFhbmmjBhQs9Dhw75jx49Ou/f//53pt3e8PDbIgO4iHQ0xmR5fr0GKB+h/hHwpog8BcRhDVZba4xxiUi+iAwD1gA3Af863+VWSqnmqrTUSo51PgL458/9s8sPhw54NZ1odJduRRPv/FWzSyfqdDolLS0tZM2aNdsSEhLKrrzyyp7/+te/on/96183eFnZZh/AReQtYCwQLSKZwJ+AsSIyEKsZfD9wO4AxZquIvAtsA5zAXcaY8g6NO7FGtAcCSz1fSimlsGrgNput0XOBN5WmSifatWvXsr59+xYnJSWVAVx11VUnv//++5Cqjq2vZh/AjTHXV7H5pRqOfwJ4oortaUCKF4umlFKtRvkqbKeKinj47WeYeMF4rrxwUO0vPAc11ZQbS1OlEx0zZkxhbm6uz5EjR+xxcXHO5cuXh6WmphZ6456afQBXSinV+MoDeE7+caZ0n0dhSSjQOAG8KTRVOlG73c6cOXMyx44dmwjQr1+/Im80n4OmE62RphNVSrUVr7/+OkVFRQwan8rJA9Mw4Y9xSeoN53QuTSfqXZpOVCmlVLXKa+B5Rda6WcGBEbW8QjU1DeBKKaVOB/CikpMAhAVFNnGJVG00gCullPoxgOdbS2SE5R+r5RWqqWkAV0opdTqAu7M2ALBu0YtNXCJVGw3gSinVxjmdTpxOp7WIS2k2uMFxyKvrrKhGoAFcKaXauIrLqPpSjMsRRIF/UhOXStVGA7hSSrVxFTOR+djLcDmCyQ8oauJSNQ8NTSe6ZMmS0D59+iSVf/n7+1+4YMGCdt4omy7kopRSbVzFGrjN7sRVFkJx8NlpMVs7t9uNMQYfH59zPofD4ThjOdrJkyfnT548eRvAsWPHfBITE/tNmTIlr+Gl1Rq4Ukq1eRUTmdjsTtxlwQRFeaWS2Kw0RTrRihYsWBAxZsyY3DadTlQppZT3nFED93PgKgqiW0rr6gNvqnSiFS1atCjynnvu8dr8PA3gSinVxp0RwH2duMqC6dOnb6NdL2dRRhfH0UKvDnP37RBcFPmTxGaXTrTcgQMHfHfu3Bk4depUrzSfgwZwpZRq88oDuM3uh83fgasskOh2rWsltqZKJ1pu/vz5EZMmTTrl7+/vtQQkGsCVUqqNKykpQUQoKCtCbAZT6ke7wMbrA6+pptxYmiqdaLlFixZFPv7444e9eU8awJVSqo0rX4Utt9BKZOIusRNgD2jiUnlXU6UTBWugXFZWlt/ll1+e78170nSiNdB0okqptmDx4sVkZmZy0WVDyc+cQdY313Ljo3895/NpOlHv0nSiSimlqlReA88vtmrgrrKq+4BV86IBXCml2rjyAF6QfxwApwbwFkEDuFJKtXHlAbz0+FYAxoQOpnDt0SYulaqNBnCllGrjygO4yd0HgJ8zFPHV8NDc6TuklFJtXHkA93HnYdw+iCsACdJJSs2dBnCllGrDXC4XDofDykQmpZiyIATBFqgBvLnTAK6UUm1YxWVUfexl4AgGwBbkW9PL2oyGphMFuOOOOzr36tUruUePHsk333xzF7fbK7lMNIArpVRbVjkTGQ5rifK2WAN3u924XK4GncPhODMN65dffhm8du3akB07dmzNyMjYunHjxuBPP/00tEEX8ahzABeRh0VkpjcuWh8i8rKIHBeRLRW2RYrIlyKyy/M9osK+34nIbhHZKSITK2xPFZHNnn1zpbrFbpVSqg05owbu60TKa+CtMIA3RTpREaG0tFRKSkqkuLjY5nQ6JS4uzivJ1utTA38I6OeNi9bTq8CkStt+C3xljEkAvvL8jogkAdOBZM9rnhWR8szszwG3AQmer8rnVEqpNufMVKJObI5gXL4gttZVx6mYTjQtLW37/PnzY1auXBkIsH///oBZs2ad2L59+zZ/f38zZ86cuFWrVu349ttvMzIyMk5nHytPJ7ply5bt77///p477rgjvnxfenp60Oeff757yZIl+ype95JLLikcMWJEfseOHQfExcX1HzduXN6FF15Y4o17qs9HrMNAmDcuWh/GmBUiEl9p89XAWM/PrwHfAA96tr9tjCkF9onIbmCIiOwHwowxqwFEZD4wBVjayMVXSqlmrXIucB9HMLbgxq19f/DBB12OHz/u1XSisbGxRVOmTGl26US3bNnin5GREZCZmZkOMGbMmMSlS5eGXHbZZQUNvef6vEvvA1eJSKAxpk7ZVxpRe2NMFoAxJktEYj3bOwHfVzgu07PN4fm58vaziMhtWDV1unZt0LgFpZRq9soDuLH5IH4OfByB+AS3vgFsTZVO9J133mk3ePDgwvDwcDfAJZdckrty5crg8wEWkuYAACAASURBVB3A/wSMAj4QkfuMMVtqe0ETqOqpmxq2n73RmHnAPLCSmXivaEop1fyUB/AiVzEi4OsIxjfIv1GvWVNNubE0VTrRrl27lr3yyisxDocjy+12y8qVK0N/+ctfHvPGPdUngG8C/IALgU0iUgIc5+xAaIwxPb1RuBocE5GOntp3R085wKpZd6lwXGfgiGd75yq2K6VUm3Y6gJdZmS59nYGcyD6Ec7cfHXv1bsqieVVTpROdNWvWyeXLl4f17t07WUQYN25c7g033JDrjXuqczpRTz9ynQ42xnSv/ai68/SBf2yMSfH8/jfghDFmjoj8Fog0xjwgIsnAm8AQIA5rgFuCMcYlIuuAXwJrgE+BfxljPq3puppOVCnV2n366aekp6cz6uqRlGT9jNj1v+CHfULUtX3pP35i7SeogqYT9a7q0onWuQZujDnrxeeDiLyFNWAtWkQysZry5wDvisj/AAeB6zxl3Coi7wLbACdwlzGmfFLfnVgj2gOxBq/pADalVJtXvoxqYXEOPoC/M5Qy1w8EhnplqrJqRM1+op8x5vpqdo2v5vgngCeq2J4GpHixaEop1eKdzgV+6iDtAB9nCGXuTAJCNIA3d+e8EpuIhIlIFxE571PLlFJKeUd5AHce3QyAjzOIUncxgRrAm716BXAR8RGR33rmV58E9gMnPaub/VZEmn2NXimllKWsrIzCwkICAgKQYmtcr80RTJmrmIBQrZs1d3UOuCLiB3wGjMEazHYIyAI6AvFYzdaTRGSCMabM+0VVSinVEC6Xi8OHD7N371727t1LZmYmbrebXr16UVRQhHH5YnP7UeYu0Sb0FqA+NeZ7sQaTfQzcZ4zZVb5DRHoCfwcme46b48UyKqWUaoDNmzeTnp7OgQMHKCuz6lcdO3bkoosuokePHnTr1o0lC/4XU2Ytjub2cWP3bX2LubQ29QngNwBbgCnGmDNWnDHG7BGRqcBGYAYawJVSqlkwxvDBBx8QFBRE//796dGjB/Hx8QQFnbmSqY/doalEqzB37tyotLS04Pnz59c437smd955Z6dly5a1A3jggQeO3HrrrSe9Ubb6BPBeWHOnq1wuzhjjFpGlWHOtlVJKNQMOhwOXy8XQoUMZOXJktcf52J2Io531c4hftce1Zm63G2MMPj4+tR9cDYfDgW+F1ou33347fNOmTUHbtm3bWlxcbBs+fHjva6+9NjcyMrLBScHrM4itDAip5ZhgrHXHlVJKNQMVk5XUxObrxOYIwmHKCAip7U99y9QU6US3bt0aMHLkyAJfX1/CwsLcSUlJRe+99164N+6nPgE8HfiJiMRUtVNEooGfYC25qpRSqhmocwD3c2JzhOAwpa1yAFtTpRO94IILipctWxaen59vy8rKsq9atSrs0KFDXmniqE8T+jPA28BaEXkcWI41Cr0D1uC2h4AY4G5vFEwppVTD1SWAu93Gk0o0iFJXcaOvwrZt+4NdCgsyvJpONDgksSip75PNLp3o1KlT89asWRM0ePDgPpGRkY4LL7ywwG63eyVRVn2WUn1XRAYCv8WTrasSAf5qjHnXGwVTSinVcHUJ4LnFxdj8nNgdQZQ6iwgIaX1zwJsqnSjAk08+efTJJ588CjB58uTuiYmJpXUtd03qtfCKMeb3IvIR8D/ABUA4kAv8F3jZGLPaG4VSSinlHXUJ4KcKcwDwdQZZi7iEVNlT6jU11ZQbS1OlE3U6nfzwww8+HTp0cK1ZsyZwx44dQVOnTt1X02vqqt4rpxljvge+98bFlVJKNa46BfCC8gAeTIG7mPBWuApbU6UTLSsrkxEjRvQBCAkJcb322mt7fb00x74+6UT3AkuNMXd55cotgKYTVUq1dCtWrODrr7/moYcewm6vus62Yss3OI7/D3Hrf8XBPUX0unUcPVOHnPM1NZ2od1WXTrQ+o9BjsJrLlVJKtRAlJSXY7fZqgzdAQfEJAOzOEMpcuoxqS1GfAL4V6NlYBVFKKeV95dnGalJ4dCsAPo5gytyNPwpdeUd9AvhcYLKI9G+swiillPKuugRw14mdANicwZrIpAWpzyC2TGAZsFJEngfWAUexMpOdwRizwjvFU0op1RB1CeA+jhzPd88o9ODWuRJba1OfAP4NVrAWrIxjNY1+O/eFZJVSSnlNSUnJWYlLKvOREozDHzF2jL9ga8Ba4Or8qU8Af5Sag7ZSSqlmpqSkhMjIyBqPsflUyEQWWO/ZxaqJ1GcltkcasRxKKaUaQZ2a0H1/DOD24LaZiaw63kgnOmrUqISNGzcGDxo0qGD58uW7y7fv2LHDb9q0aT1yc3PtKSkpRYsXL94XEBBQ54pynQexicjDIjKzvgVXSinVNIwxdQrgNrsTcQThcJfhH9Z2B7C53W5cLleDzuFwnJ2Q8/777z/6/PPPn7X62r333tv5F7/4xbEDBw5sCQ8Pdz799NPR9blWfUahPwT0q8/JlVJKNR2Hw4Hb7a5DKlEXNkewlYmsFQ9ga4p0ogBXX311fnkSlXJut5vVq1eHzpo16yTA7NmzTyxZsqRdfe6nPp0dh4HWt76eUkq1Uhs2bAAgODi4xuN8/B345FtTyAJb4TKqcGY6UWMMqampfcePH58fHR3t2r9/f8ALL7yw//XXXz944MAB3zlz5sStX79+e2RkpGv48OG9U1JSiuDHdKITJ04s2LVrl9/EiRMT9u7duxWsdKJr1qzZUVWik6ocO3bMHhoa6ipfVjU+Pr7s2LFj9eq/qE8Afx+4SkQCjTE1Lt6ulFKq6bhcLj7//HPWrl1LYmIiycnJ1R7rcLkRP4cnE1nheZkD/qvtB7vsKCzxajrRPsEBRf/s27XZpROtTlXLmItIvQaK1yeA/wkYBXwgIvcZY7bU50KNQUT2A/mAC3AaYwaJSCTwDhAP7AemGWNOeo7/HVYmNRdwtzHm8yYotlJKNZqSkhIWLlzInj17uOiii7j00kux2arvLT1VWIDN7sLuDKTUVUJASIfzWNrzpynTiValQ4cOzvz8fB+Hw4Gvry/79+/3i42NPbsDvQb1CeCbAD/gQmCTiJQAxzl7apkxxpzPJVfHGWMqLpD/W+ArY8wcEfmt5/cHRSQJmA4kA3HAMhFJNMY0bMSCUko1I0uWLGHfvn1MnjyZ1NTUWo/PKbDWQfd1hFDkLibiPCyjWlNNubE0VTrR6thsNoYNG5b/yiuvRNx2220nX3755agrr7zyVL3OUc9jHcBBz9dxz3ap9FWfczaGq4HXPD+/BkypsP1tY0ypMWYfsBs493Q7SinVzBQVFbF9+3aGDBlSp+ANkFdkrcLm5wqx+sBb6TKqFdOJpqam9i1PJ1r5uIrpREeOHJnYv3//ovJ98+bNO7Rhw4bgxMTEpJ49eyY/88wzdUqcnpqa2nvmzJk9Vq9eHda+ffv+ixcvDgP4+9//nvmvf/2rQ9euXVNOnjxpv+eee+qVra3O6USbIxHZB5zEagV43hgzT0ROGWPaVTjmpDEmQkSeAb43xrzu2f4SVnrURdWdX9OJNm8ulwuHw1HrCFul2op169bxySefcPvtt9OxY8fT240x1TYLf73pS8yJO+i8/n52ZWQz6MHpdOiV2KByaDpR76ounWhLX3JnhDHmiIjEAl+KyI4ajq3qX+9Zn15E5DbgNoCuXbt6p5SqUSxfvpxVq1bRr18/hgwZQseOHWvs61OqtUtPTycmJoYOHc7sx77qmZWkdovgT5OTzgrkebmHCaU8E9lBAlrpKPTWqEUHcGPMEc/34yLyPlaT+DER6WiMyRKRjvzY1J8JdKnw8s7AkSrOOQ+YB1YNvDHLr+DIkSOUlpbSrVu3s4Jvbm4u8+fPZ/To0QwYMOCs127bto3g4GC2bdvGpk2b8PPzo1OnTiQlJTF48OCzji8uLmbfvn3k5eURGxtLjx49Gu2+lDqfHA4HX331FYcOHeKSSy45I0g7XG56BrzJf3d15YlPhD9c0feM/WVZGyEGbI7yTGStdx54a1NjABeRvcA/jTFzK2ybCEw0xtxbxfF/Av5ojGn0DwYiEgzYjDH5np8nYK3X/hHwM2CO5/uHnpd8BLwpIk9hDWJLANY2djnbsry8PEJDQ8/6xF9cXExRUREnT57k7bffxul0Eh4eTv/+/Rk4cCBRUVEAZGRkcOLECT744ANsNhv9+v24jtCJEyfIycnhsssuo1+/fmRkZJCZmcmBAwf45JNPOHToEElJSXTv3h1/f38Avvzyy9PzYkWEG264gYSEhNPnLCgoIC8vj7i4uMZ+NEp5TWZmJu+//z4nTpxg8ODBDB069Iz9uUWlXNHjCwzCi5vL+MeXP+XeCb1P73fnH4IYTw3clOIfVPOccdV81BZo44HKK8MMA+7BykhWlao7WryvPfC+JzjYgTeNMZ+JyDrgXRH5H6zBdtcBGGO2isi7wDbACdylI9AbT3p6Ou+99x5JSUlcffXVp4Po7t27WbRoESUlJQDExMQwYsQINm/ezHfffce3335Lly5dGDBgALt27SIkJISoqCjee+89bDbb6fmsu3btAiAhIYGgoCAGDhzIwIEDcbvdLF26lE2bNpGeno7NZqNr165ERESwdetWOnbsyPTp03nrrbdYtGgRkydPJj8/nx07dnDw4EGMMfzkJz8hJSWlaR6cUnXkdDr55ptvWLlyJaGhocycOZOePc+eAJRTeBKbGAx+3NZvAS9ucfOs3438fGwvAOzuAowRbM5AJMBWbV+5an5abBO6MWYvcFa7qjHmBDC+mtc8ATzRyEVr844fP86SJUuIiIhg+/btZGdnM336dDIyMvjiiy+IiYlhwoQJlJaW0q9fP0JCQhg4cCB5eXmkp6ezadMmPv74YwD69evHlVdeyRtvvMHixYux2WxERkayatUqoqOjz8qyZLPZuOKKK5g4cSKHDh1i9+7d7N69m8zMTPr06cPw4cMJDw9n+vTpvPjiiyxaZI1hjI2NZfTo0ezdu5cPP/yQmJgY2rdvf96fnVJ1kZ2dzcKFCzl+/DgDBw5k0qRJ1Q7mzC20RpnL0QG062PjlpTXeSXdTaDvLGaN6I7YSsERiGBDNBNZi6LvlvKqkpIS3nnnHfz8/Jg9ezbHjx9n0aJFPPvss7hcLvr06cM111xzukZeUVhYGCNHjmTEiBEcOXKE7du3k5KSgr+/PzNmzGDBggUsXLgQu92On58fU6dOrbYcdrud7t270717dy699NKz9rdr145f/vKXZGdnExQUdPqDwKBBg3j++ed55513uPXWWwkMDDzrtSUlJeTk5BATE0P5MohKnU/Lli0jLy+P66+/nt69e9d47KlTWdiADhvTIPBuIuJ9mJX8Jq9tcBHkdzv+9oqZyM7+f6maLx2yq7zGGMNHH31ETk4O1113HaGhofTs2ZPbbruNbt26MXbsWKZNm1Zl8K5IROjUqROXXHLJ6dG0/v7+3HjjjXTq1Ino6GhuvfXWBvdV+/v707lz5zNq8aGhoUybNo1Tp07x/vvv43afubjSZ599xpw5c5g3bx4LFy6scXUnpRpLbm4uXbp0qTV4A+QeWA/A1rJp+H34bzrZfkZk5EhuTn6bpWufw8eTiczpduAfpv3flc2dOzfqpptuatCUpFGjRiWEhoYOHDduXK+K2//3f/83pmvXrikikpqVlVXvCrUGcOU1q1evZtu2bYwfP574+PjT2yMiIrjpppsYO3Zsg6Z5BQQEMHv2bG699VbCw8O9UOKqde3alYkTJ5KRkcGyZcvOCNJZWVlERkZy0UUXkZGRwerVqxutHEpVp7CwsNYEJeXKju0EIM+/N1tO3kDOvHvo0/FhIiLGMrPvuwTEnLRGoJvWu4hLXZ3vdKJjxowp+PLLLzPi4uLKzuVaGsBVg2VlZfHGG2/wxRdf0Lt3b0aMGNFo1xKR8zLIZsiQIQwaNIhVq1bx3nvv4XQ6AWvxmHbt2jFhwgT69u3LsmXLOHTovK8Kqdowt9tNYWEhIXWc7iWukwAUlxVzpONIDu8exc6/T6N/0tNERI4/nUq0zFVyXhKZNKXmlE4UYMSIEcW9e/c+p+ANdesDnyIi8RV+HwggIi9XcewF51oQ1fI4HA4++ugjNm/eTEBAAJdccglDhw5tFaNYRYQrrriCsLAwvv76a3Jzc4mIiCAzM5PU1FREhKuuuornn3+ehQsXcscddxAU5NXkSkpVqaSkBLfbXecauJW2Ag77rsRmL4T4awnZcJR1j17B0Ee/5KNnJ9OxeAilrqJWm0oUml86UW+oSwAf6Pmq7OZqjtdOwTZi/fr1bN68mREjRjBy5MgqB3y1ZCLC6NGjiYiI4IMPPiAzM5NRo0YxevRoAAIDA5k2bRovvfQS77zzDjfccEOt/ftKNVRBQQFAnWvgPj4O3C47kbZ27B61k7DPo9nU/RZGfP8Xvn10Cnl7hpHYYSC57r0EhUTWfkIv+M2iTV0yjuZ79RNvYofQor/9ZECLSSfqDbUF8FnnpRSqxXE6naxatYpu3bpVOcq7NenXrx/t27fHZrMRHR19xr64uDiuueYaFi9ezIIFC7jxxht1bXbVqOodwO0O3GXB+IUG8+T4P3PzyVu5eOWNrO18N+PWPMqhqFH4CZS5S4gMab018OaWTtQbagzgxpjXatqv2q5169aRl5fH5MmTm7oo50VsbGy1+1JSUvDx8WHhwoW89tprzJw5U5vTVaMpLCwEqHMTut3uwlUWRGy3eCICInjy8sf5df7vuGLTHaxqdzc2pwNfmw9lrmICz0MqUYCaasqNpbmlE/UGHcSm6qWsrIwlS5bw+eef0717d3r16lX7i9qAvn37Mn36dI4fP86rr77KDz9o0iXVOOpbA7f5OrE7gxjQZxgAfSL7cPek21jW63Vy2/UiL6IvPmKjzF3cqgexNcd0oo8//nhs+/bt+x87dsxvwIABST/96U+71eeeWnQ60cam6UTPtnjx4tP93uPGjcNub7q1gByOXIqK9hAWNhCRun0WNcZQULADuz2MwMBOZ+xzOvMpKtpHWFj/cy7T3r17WbhwIQ6HgwkTJjB48OBWMahPNR/Lli1j1apVPPTQQ3Walrl0YSrtXN3odvBBOv56EOLrA8BTaU+x5dMsRmRdxsRwX9ZlL2X8k78mLLpOMalGmk7Uu6pLJ6o18Dbs2LFj/POf/2Tp0qWcOHGi1uMzMjLYvHkzY8aM4dJLL23S4A2we8+TpK2/jlWrx7J795McObKQnJxVOBynqjz+6NGP+G7lMNauu5Lv11xKzklrDrfLVcyBA/NYtXoc69Ku4eChV6q9pjGGkyfXsm37g5w4seKs/T169ODOO+8kPj6eTz/9lAULFpCXl+edG1YKqwYeHBxcbfAucbg4WfjjzCSbvxO7Mxh3Thl5X/3Ycn3PhffgOyyPPe2t/welbp0H3tLoUqpt2LFjxzh16hRr1qxhzZo1JCYmMnToUHr06HFWrbG0tJSPP/6YmJgYRo0aVeu5i4sPsWv3HLp1vYXw8KpnFxpjOHjwBZzOPOLiphMY2LnSNY+xKf1W4rv9nNjYSWe9NivzE0xBIL4B0Rw89BLluWns9nB6J/6JkJA+BAXFY7P543aXcfjwW5QV5UF6JK6EAtI33UbHjtdyPPszysqycR8Pxl4SyC4ex8cWSKdO088q886MRzh8+HUAsg6/zwWprxEZcdEZx4SFhTFjxgzS0tL44osvmDt3LsnJyUycOFH7xlWDFRYW4vLx53fvpTMppSMjekZh97GCuTGGWa+s4/t9J0jtGsElSe3p6VeGzRGMLcSX/BWHCOwfjV9cCD42H/465q88lvUH2A4umwO7zqJoUTSAt2FlZdan9Ntuu42dO3eSlpbGggUL6NSpExdffPEZgXzjxo3k5eUxe/bsWmvepaXZ/HfjTRQXHyQn51sG9H+RiIghnmvmsGfP33A4ToL4kJ39GQD7DzxPdPTFdO50I5GRIxCx8cMPy8nP38qWrXeTwtwzgnhB4U6MrYDCdeMI3pxHeFQohe39KY2240w5ydZt5cnybAQGdsbtLqO09Cil6Ukc3joLv13ZdJ7wNEdYhCPbB//lfdhd+DNKgtvR2/yBHeYhfHyC6NDhqjPu7cCmDxDTjoOr7qPrqL+zYf3NDB78DuHhZ860FBEGDx5Mjx49WL16NRs2bKCkpITp06drk7pqkIKCAo4Xw6K1h3hr7SGigv24vF9HrhoYx8ETRRTlf8MDw4+yJbsnT3/ZkWcuLsPHGUT4pHhyP9vPyfd2EfvzgYhNCPcP588XPszJ7TsRfx/9t9nC1JYPPMQYU3C+CqPOr/IAHhkZybhx4xg1ahSbNm1ixYoVLFiwgPj4eC6++GK6du3K5s2biY2NpWvXmpcEdjjy2LhpFkX5mfh91ouyMQfZuGkWA/rPw+0uZfuO3+Fw5BEQ0JHi4kP47AghcJsvBcPCyfX9Lz/8sIygoO506jSDXRsXINhwlfqxZes9niA+EYCjh63Af7TwcjLj2iFuJ/5Zp/Dff4rIldsJTl5NWXt//KL98e8SRd6pTHL+M4ns3MmcDNlGRElvDnz4RxLzPiEzaBx5Yd1x+h/G5dpLxro/k+jzEFvlPoxx0aHDlNN/2FzuUJzucAqLC9j73R/oMebPpK29gSHDFhEamnTW84iKiuLKK68kKiqKzz//nHXr1jFkyBAvvouqrSkoKKBzh8387YL3CW83hv8c7Mu7aQ4WfH+AUL98nhz1Ov4+xSQGw9R4q7/bxxGCPSqQdpN7kPPWTgpWHSF0pDUGxBRbLVe2IK3PtTS1vWObRORGY4wu+NwKlQdwPz8/wMrglZqayoABA1i/fj0rVqzg5ZdfpkePHmRmZjJ+fJVZWk9zuYrZlH4L+Xk7yPvsCrKKrib8wy10mPx/bNw0G2OcmOIwIj4Ow37MTYC9IxuC7sZpDyRu4Sq6BSzn+Ig4ZFAAu3Y9DsFw6sAQnMsGEjF1gVUTl7n4+8Wyf///UZbflbySjXzd4yi9T0YRXtyO0NIocs1k/DNHEJRxjKDSbMrc2ZT4xPND7Fhc7t280zGGLs7PuDzzMjYFzca4T7G+/Yd869Mdcftz59F97FrzKAm2P7KN+zl+/FN69/4zOTmr8Is+StmeKN6IDuPKwv9i++73dB/zOGvXTiEx8fd07nxTlQPqhg4dyp49e/j888+x2Wxs3LiRadOmERbWeufdKu8zxlBYWEif7jtpZz+BrWgBF0e7mTipPYUyjJy8I/j7lDGo72u4/IWcnJXsXfs1gTl9sAXZ8YsPI2DDcfK+2E9gchT2iADcRdYywT4hfk18d6q+agvgXYEVIvIX4M+mvJNRtQqHT2QT23EX32RkcnGfH2vWdrudoUOHcsEFF7BmzRpWrlyJiJCSklLleUrLfuBkzioOH3mLU6fWU/jlOLKKriY7YA2YQfDRnXS45AUkL5iyL8ewJuZyTKxVM8CVT3bQNlw+Yzgk44n6dgvtln2JfUA0eTHh5GRNoDS0G7yHFcS33I2IHXeJncPf386p9v/ltTvm8vmOfWw7fojVJw4QsP89EnO6ERIYhb/7AkRCwbjJDkjj+57Cf++8g2e/HsQ8/1cJlGJynDEkhE7ljeSuBGYWMouV3Jh1kJ3fzSEx7h9kX/QNOScvwe0upexoTzrsvIHFfnFsCoxhS9F3uL9+lG4DniZDHiM7exlJSX8lIODMTGk2m40pU6bw3HPPnc51/v777zNz5swGJXhRbUtxcTFut5twez62ndGEbHZxamAE0Rd1w3XyCzr4F+O/w5/8f9/EocSOBMePxJX+KwJCgylxFBIqwbS7phfHnlrPqQ92E3VzMu4iJy7jxD+0btPSVPNRWwAfDrwO/AGYKCIzjDG7G79Y6nwoylpC76Tvyd8ylVU+ixmecOYURD8/P0aNGsWgQYNOrwVeUWlpNumbbycvbxMAboedkm8vIjP3Bg6Gf8Fdf/g5f3vhH/TZeRnuT3+Ny+ZLUWwcRwO/Z3/nI0ScCCZwUCg3jbmG5759C5NWRh8znBPya4IOHMN90IbTp5gtcUtIYTK8Z4iY8gbGx8apD6/B5h/OlZOvJybYn5lD+gJ9AXjvv/tZsm0ze08e5GjRWvwkDx8gxfdi/hWRyLG/rOVau43uF93O9rIyUiNDGJCRT/EXmQC8FXkBMzps5KfHd5Fx5AHCF6XTadBrlBTHE33gPjr42gm+IJb+G48TEDSKNaXf4Fr9eyKzvsakLmblyouJ63QtnTpdT1jojx96QkJCmDp1KgsWLABg3759rF69ulGTv6jWxVrExWALcHDCNoDdzivo8vFyfL/5mrLe8bgCS8jeeDlbIxLptOlbojd8jk9vq9vpi1f/zbUP/Rl7uwDCJsST+/Feijdl4y5y4DClBNRxXnlbM3fu3Ki0tLTg+fPnHzzXc4waNSph48aNwYMGDSpYvnz56Rh61VVXdU9PTw/29fU1AwcOLHz99dcP+Pv713lud20rsa0TkYHAU8DtwH9F5D5jzLxzvRHVjLhLAQiJPEnO1qtZZ1vI4J4JZx0WGBhY5Trnu/f8ndxT6fhsCScgox1Z2aPJihrNkZDl3P27XxKxz5c5tz/Kg8//ib4ZkzAmn40pH/LAjLtIaJdAgaOAUD9r2sozUx4nZ1IOz659k62rt5G6P5VA050cvxXcffeveXruU/TjKsxCX/yc+fwQO5rE0Gy6LA0h69s1BPSOxCfMD1uIL1d0iWTqDGuFuDKnm/0nCskvcRD//XGK03/APyWa0j2nuHDlcUb2j6FwyUGK3YawS7thjw2Ed3byRlB/bojayQD7R1x4eBS56/8OQGxYPvsCw2jXbjcdL+9JwtJsAvwv5q3Yb+m7pzf5Jx4nLmEBh13vcOTI24QEJ9Oh41UEBXYjKmocPXv2ZOzYsWzfvp2oqCi++uor4uPj6dSp01nPV3mHo7SEj//5JOGxHeg9CpmBDwAAIABJREFUfDRxCb2RFtrqUVBQgI+PA5vdiavAxbHgDJydr+Cg6xI6rV9BAHmc6DyQPN/9OLpcykEznr42cLrL2L95PYe2ptMluT8hw+Mo2pTNqSV7sccGUuosIqAVJzKpK7fbjTEGHx+fcz6Hw+HA19f3jG3333//0cLCQtsLL7xwxiT7GTNm5HzwwQf7AK6++uru//znP6MffPDB7Lpeq9ZRC8aYYuBOEVkCvAw8JyJXAA8AVS4hZ4w5508q6vzx9bz7p9bcStiFr/LDtmvYaHuHgd2Ta31tQcFOsrIWUrQ1lcxtt2BsdoiCo0H/4fbf3YL/h6fI2Z6DX/cwnrzjUf7yn3/QvUNn/m/g37HbrAuH2EPI/Ww/7lInIcPjiIyJ5KHRv8Ax0sE7W5fy2epPuL94Mt3zw7jrF7/m38/8g35Yo8L3hn3JxKDL8IsNxSfcn5KdObgLHVYqHYGgC2LxiQjAJ9SXLqF+OE+UkLc1B//u4URd3wdHdhE/vLKVgrVHCUiMoN0V3TGhNnIOZxJ9czIn5m/j7YDe3OXsyOpum7kybx3FPiX0d19OaP4xvnr5dXwDArlqxm/ovKKMe3LH8G7HXMqKV+JcfxuyVYjo/B+cPZdTUPgXAPzNIEZc/BZjx45lzJgxlJSUkJmZyeLFi7n99ts1EUojOZKxg70b1oEI//1sCWExsUy4/W669asqR1PzVlBQgJ+f9WfXVfz/2TvP6Kiqtg1fZ/qk995Ir5QAAUKHgHSkF1+agg0VK68Ve31V7NhQBJEmSO+9hhoDIUBIQnogvU6fOd+PQZSPIi2KMtdaWStz6t6TyXlm7/08920g5b/t+XbHPHwOhWCW9ABBilY4jWHMWVaeXEbkmbYkNCRhsFhluncvnMfo195DkAi4DYvg3CdpGM7UoTdr74ga8FdeecV7/vz5HgDjxo0rnzFjRtmpU6cUffv2jUhOTq4/fPiww4oVK7LXrVvnOHPmTF9PT09jWFiYTqFQiGC1E500aVJwcXGxAuDDDz8s6N27d+OTTz7pV1paKi8oKFC4ubmZVq1adZH39+DBg+tXr159yRs8atSo2t9+b9OmTWNRUdF1JSJcc9qhKIprBUGIA+YCA87/XPbQ67mujb8Pqcz6T51Q24KDO5/Es+PHnDsxnGPCjySEtL7sOTpdCbm5Myk9uwrRoKD49BgKnHeii7DgF+nB/S3uRb28Ht2pauxae6M5cg5hUR6vj38BQSZBl11NxapcRIMZiYMCY2E9SAUa95WiinbDoZMfyjAX/pMwiCGGdlQvyaJyznEiJsTxwEPTeGfO/xCA+3tMQbWiAfu2Pti39QFAtIhYGo3UrMpBl1X9e0A/jzLSFZfBYRRlZgDg/7RVKEqQCBSdPM7G1z+murSEdkNG0ubewVTOOc5skx1HnDsxo6GCCYKKZoKCE8ZiBjz+X/YvX8Ky79+g1+iHcS73Y2K2wDlZX7bG1NKgO4gm14uq7NeR2BlxDd+GR9wq9u98gOjmD5N59BUS23/F0KFDmTNnDuvXr2fw4MFN98e+gzmbnQXAlE9nU3Qig/2/LGbVh28z9s0PcPML+JOzby/q6upQKK3Kns4WLzr4dqDD6A5s77idb/fORXnanbAOnryc/DJ1beqYf2I+DSuLca1yJaRla/J+PcyZXw8R2qotch97HLsGUL+tEINFh73DzSuw3c7cznaier1eWLRokfuHH354XRrx1xtom5//EYCzgP46z7dxGyGRGhEtEpSCmpbmAA5tm45Pl5mUnhqLTJhNTHCni443meo5eHgcek0BQpYTeWeeoFZM5/V3XkYulSMazVTMzUR3ugaXIeE4tPNFGeJE9dLTVP50EolSiiatDJm7CrmvA8aSBpwHhmLXwpPG1FIaUkup+DYDuY89Dp380J2uQWInQ+KooPKH48RMiOWzae8iIqA+XEMtDZj/4DEiSASkjgrcx1rXwkWzNaCb663Z9qUVp1n1xhNUlxSBINBj4v3Ed+vF7kXzOLJuJc6eXkR16Mz+XxZTX1lBj4en0Li9hMS0MlZJnBEsIiWSM9R4VNKrQ2eatWzN6o/fY+NPnxHbpQethw5CtaWCMWWuWEgh112kxluPVlGDeCKSalkKRG0mdWcqckcN29f1omf/nXTp0oWdO3ei1+tJSEggPDz8kik4G9dH3tE0nL28cfXx42xOFkF+cdjbuRLbpQcBMfH8+PwTLH/vdca+8QEqBweMBj2CIEF2m7/vOTk5qOTWyt44SRuq5p/AdXgk3YO60zWwK+nl6cS7W/MunBROPNTiIQo376WsIpc2A4ZQXVrM7oXzaNaiNYJEglOPIOqPllJdfQ73y5RBNhnLpwZSlnlrVY28YjXc/fk/0k50woQJQe3bt2/o06fPdZVtX1MAFwRBDrwNPA6YgP8C74s2IfV/NBKZEYtZzq7Sn+nqN4p4wcivW57Fv+sHFGVNQhA/JTrEKp4iimYOpT2MXptH9ZpRlGl7IFg0dBvXE/2hChortOhzajCWNuI6PAJziISNX39KmwFDcB4YSu2qXJAKOPYIxKl74AU95t9wSgnGsWsgmvQy6ncVU/3zaQDU8e643B1O+TfHqJiTicfEWCRqORW7itCrdHwzfTJeIWGEtExE7eiE0s4er5BQvEPDEaQCUicFUifrrFT6wnVoa2u466HHyTmUytbvv2LHvNmYTSZa3tWfzmMnIleq8AgMZs/iH2msqWbgE8/h2C2Q+m2FCE4yMjbMw9nBOuJXqO24+5mX2LNoHkfWruTEru1EdehM8059OVcAsuwaWpaqkBEIdoGUZvtSpNDg1GwvAFJ7A5tW9qDngO0YjUbS09PJzMzEw8ODKVOm2KbUbxBRFFn14dvIVSrGvvEBdbmldHMaRekbqSiCnVDHuDPokWdZ8u5L/PD0wzh7+3A2OwtXX3/GvP4/FOrbUy1Pr9eTl5dHkKf1GW/QqdBmVmL87Ffcx8Ug97anldelqoeizmwdYbu4kjziHtZ99gFZ+/cQ1aEzglyCubeKzEN7SXAYdMm5/yZuVzvRp556yreiokK2YcOGnOs9908D+Plp8/lYR96ZwD2iKKZffzNt3G4IMiOYFRjdzOyvXE17twFE2ZWSufU5Ajt/QFH2I2B5h+jQ4eQXLaWxfi8VB4dT1dCWAvctdGzbioC1UEM2yARk7mrcRkehddfz84yXaKisIO/XI4x5/X+4u8chc1Mh9/r94SiKIr9uXINBq6V5Sh/UDo7Yt/HBrrU3+uwaGg6WkqfLJFzjhueUBCq+tQZxQSogUck4WLEeN/9ApHIZB5Yv+b1fEgkxHbuidnJGaWeP0s6OsrwznD6wl6gOnYnvlkJs5+4cXLkUbUM9EUnJ+EfFXDi//bDROLh7sOnrT/nu8ftpddcAmvfpw9bvv6K6tIT2w8ZcOFYildJ57EQS+w3m8Jrl/LpxLSf37kCmVOIZGEKNfwh6kwO6s2Y6ySKRnxxBhVKP3C0XSfpohLZfsXlFCn2H7yYlJYUTJ06wdOlS1q1bx9133/3XfBD+Zega6jFoNRi0Gpa8/jzOOlcEJwH7JB8MBfXUrjuDopkTPSc9xKZvP6WhuormKX04tmUj62d9xMAnnrutFMlEUaS+vp6MjAwsFgtqqQbBpKRMXkezCV2o/OkkZZ/9iuuwCNTNPalafApTuRa3MdHIPdSgt2Cw6FA5OBLdsQsHli9hz+L5RCQlI5FK0TbWA/y1TmRXGSk3FbejneiHH37osXXrVuddu3adupHEuT9TYpuGdeStBD4FpouiaJs2/5cgkZoQzQrunv4SC158mpOmg0RL26JxOkPO9v8SlPwRxZL/IlpqOHP0cwQ8qc5NRhxSzJs9X6X8o1+R+EhxnxiH1EmJIBE4m53F0ldeQSKR0Hfqk2z5bhZL35rBqFffRe5gR176EXb+NAez0YiThyd56UcASF22kITuvWndfzDOXj6oIlwprDrB9g/ncPjQGka+/DYekxOomJ0Booi8vxfFL56ix6QHaNVnIBaLGYNWi66hgV0/zaEgIx29RoNRrwOsQb3t4OF0GD7mfN+ltBsy8orvTXy3FNz8/Nm3dCF7Fv/I3iU/IYoWutwzidjO3S853t7FlS73TKLt4OHkHEylPP8M5flnyE/bg07TiEQqZbddFMlu/XA9NhVBakRiUZKfrkVoNYc1C7vTY/CPhIW50qlze3bt3EdQUBCJiYlN8Jf/Z2MNzloc3Nwvu7+uvAyAFr36cXTLepq5xIJMwGVwOIJEQPNrGVULTxHgEkL7oWMw6DR0nzAFVx8/dvz4Hdt/+IawNu0Jir9xV7qbQRRFSkpKyMzM5MyZM1RUVFwQXbK3t0ctMyDTu2AxNyILssf7sVZU/nSSqoWnkO8uxljUgCCXUPZpGm6johCMAgaz1SpUIpHScfQ4Vr7/Jpk7txLfvRe6emsAV//Ls9D/aCcK1iS2jh07ak+dOnVR4tgf7UQ9PT2NzZs315jNZgGsdqKTJ08OioyMjDWbzUK7du3qk5OT/zRpu3Xr1lG5ubkqrVYr9fb2bv7FF1/kDRs2rG769OnBvr6++jZt2sQADBgwoPr9998vvdY+XdVOVBAEC1AKTBJFceO1XvTfwj/RTlRnNDNzUxbjOgQT4Hr1qcCff+6Mg9RCnyF7KMhI5+c3XqJL7Gh8NIHsl2dSVh5AQNLn2IWcAuDcryMplKp4qPm91qm7wno8piQg9VehbajnXO5p1n32IXbOzgx/4Q1cfHwpPH6UpW/NwKtZGHbOruQcSsXFxxcnT2/OZmeR2Hcgke07cWj1L5zcswPRIhLZviNtBw0jY/tmMrZtQqZQIFMqGTXjbZy9rNPX6ZvWsuW7Wdz70Ve4+l65BMtiNqPXNCJIJKjsb6zOtaIwn7T1q3Dx8aPtwKHXda4oiljMZmrLzrHsnVdQ1Cnp5DUUmSAhrWo7rd17Uui/Dk3cogvnmBpUnKueTF5+PePHjyckJOSG2v1vZcOXH5OVupuRL7+Dd7OwS/af3r+X4h8OEdmvK9WOFbCugVqphYVBqYQnBNG+WVuiMr2p31SAQ2d/sIhoMyuRuig5qN3IyX07AOtMTPKIe/6y0XhZWRlpaWlkZmZSW1uLRCIhKCgILy8vPDw8cHd3x9fXlx0reuEsd6ZkbTzKeFf6T5uOgEDtujwadhdjn+SDY/dAKn88gbHYOt2eUbeHPl88C1g/kz+98CSNtTXc+9HXHFq5lD2Lf+Tx+b8gld2aHACbneit5Up2on8WwJcCU0RRrGrCtv1lCILQB/gYkALfiqL4ztWO/ycG8KNFNYz/cDU1chfUChmTOobwULcwJGYDhYWFlJeXExQUhFarJfPEJOxMKvqM2AbAgRU/s+unOQxs+xh2FWq2qo7QUBqFf4tvUQWfpnjNJPqFdcJUrkXuY48lXM6KVe/RWFN94f4eQSEMe/41HFzdLmw7vX8vq2a+g0yhoP2w0ST2G4xMLkcUxYsejvWVFRxZt5Kjm9dh0GqRSGUExiXQ5Z5JLHnjRWRyOSNffhu5UsWS157HbDZx38ff3FbTnVdDW1/H8vffRJNbjovCi3Jv8Dwn0tajH+WOJ6hRVCFXaDHE/IJJIyW3dCT19TKmTJmCm5vbn9/gDmHef6dRlpeDnbMLfR5+gpAWiRd9Bg6vXo7nLlckggTXEZFULDlJrk4kU2cB0YKRIiqScnnS8R40R6yjdWW4C/rsGlQJbhyoWk/xqUzqys8R3703vaZMRXITdcHXQmNjI5988glGo5GwsDBiY2OJioq6xL1OZzSza007nBsjyNsTSGFlJnFde3LXg9MQJBJMlVqkrioEiYBoNFO9PAfN4XOka3fS/+MXLlwn72gaS998iR6THqDm3FmObd3IYz8s+f/NumFsAfzWckMB/N+EIAhSIAvoBRQBB4ExoihmXumcmw3g9VUVHN28npqzpdz14DRkiqbXGl4xbzEB5cdIz9exWB2Kq8yCn6wBx8uU7Ce2WoO9xoOeY9YB1m/mqz96l+z9+xjWbjqScgurVPsQi1oilUpo56zFQ+aGx6Q4lM2cWPDydGpKS2gzcCgqB0fUjo4EJ7S8bBLQudxs7F3dLgrsV0KvaeTo5vUc27qRdkNGEte1J+X5Z1jy+gtIZTKkcjma2loGP/PiP66W12wysunbWZTmZjPhnZnM/uBjHDILaO81GJkgRS/qsLgWUZj4Pia9lMzs3sjlzZg8eTIqlervbv7fjmix8MmEEQTFN6eisIC68nP4RkaTPOIeghNaIggCO7+ZTWhOJIJCimiwqj8fUZ7CuXA12spgil2S0SscaEw5wfjynghyCW5T4mjYXkTDxkLsWnmhCHMmPXsTqb8sIjSxLQMe/y9y5cXvv6auFjsn51vSr7Vr13Lw4EHunXw/gf6+VzyuoFJD1qHWuJV0Q2/pCC5S9i6eT4ve/el574OXfJkVRZHNb3/M2ZozjHvv44u2L3nteSqLC/GPjuVcbjZTPvvulvQFbAH8VnOlAH4n1WsnAdmiKOYCCIKwEBiMNTHvllNZXMi8/z6G2WQCUcQjMPiqa663ivrsLdR03UxwS3gGaKh352xhGBvKOqFX+TGuWzzxTnqUSiVFJ9YiM/6usCYIAn0eepwFpcWsPTaLgbGPMqiuI4vDdxB6NgAPmuEwNIjMrJ0UrcigNOskfR5+griuVzc5AfAODb/mPijt7Gk7aBhtBw27sM0zuBkjZrzFkteex2Q0MmLGm/iGR13Xe3M7IJXJ6fPgYxdeT3nmSb75+keWbf0YiyhSrnAjuSqYONPzFCXOJD5mLcdPdmHJkiWMHTv2phSi/g3UVZRjLzoSHZhM5FPPk7FtM6m/LGLpmy/hHx1Lj0kPYii31kkLAzyR7q5F03AG+05vYwIUnCG4aAfFR6bApjCWjEyl0aSh+r+LMSr0PNNiApq0MjRpZUTFtsZhgjub585iyesvcPf0GRcC9m+zVT3ufZBWd11JEuPaqKys5OChQ+SKXgycfYzx7esYnxyCh8OlVQhnaysR5NY1cMHfiZYDBmLQajm0ahkKlYrOYyeiqa3BqNPh4uOLIAhU6EpQOdpfdB1BEOg4ejwLZzxD9oFUPIOb3VQfbPw93EkB3B/4Y+ZjEdCuqW5WmHEUs9HIf975mNSlC0n9ZRExnbvj5NG0Ygnm//d8d3CsJDy2ktCINBpKPPhq2wDaJwzk5YHhFJ02gPHij4BcpWLw0y8y//kn2FG8kG5eoxll6AHuILjJWfrDa9ScLUXt6ESLXn2J7dKjSfvzRzyDQpjw/ueANWns38KU+/9DRkoK1QawSKTMnL+R/rlpdNI9SUXbr4mP30rWaQ0bNrjTr1+/v7u5fytVJUXEu3bG8agKXVQVLXr1Ja5bChlbN7Jv6QJ+fuNFguxjQQ1zly5hwhPjOfn9LyiBZs2modUWUCnbhr/7xxRsehbtsigcgN+yIz5On8fTHacgaCxo0svw9vBm8P3Psvq791k4YzrDnn+Nxppqdv00BwcHN3bMm01AdNxNBcDV6zZgtEC+3Ie2AU58ui2br3bmMqx1AFM6h9LM4/fgW5qfbm2r1h4HLw8EQaDLPZMw6nQcXLkUg1ZD1v69mAwGRs54C5+wCHQN9XgEXGoD7B8VQ2hiW3KPHETl+O9XYfs38s8UBL4xLrdQesn6gSAI9wuCcEgQhEPl5dcsSXsJFUUFKNR2eIWE0m38ZLCI7Jg3+6q1iDeLKIrIRWs3K060RZeTiG71vfimPo3zuXY4+lXxTIdviC57lClzDyLKDFhMlyatOHt5M/DJ5zh3Lpd0cadVEKXeyIGTq9DW1THq1Xd56Jv5pEye+pevP9u7uP6rgvdvxIf60Dnah66Rnnz2+BCWRPfik/Is5DtGY18dQ1TUXs6e/YYDBw7c0PUNOi0VhflYLP9sQ8Gq4kKc5Nbs8+qlWdSsyUXQibS8qz+jX30XEZDqrJ9J59r2fPTRF2jczmIxSmkWMpW42Pdp3XoxckdHgru/h0xdjdK5iNjmTxIY9hUB1b144cBMXin/EUb5YGkwoN4pYfikGWjqaljw0tMUHj9KmGNL+ntOIdqtHas/fu9CtcP/p/BcNY8++Aw/b/v1svszs3I5k51FiUzF8y2fZ4THJH66+yCjWjvy8+Eien24gy+2Z2O2WJ8bVSesy11mjeJCFr4gCPS890Fiu/QgfdM65EolakdHlr3zClUlxega6q9YItZx1DiAO0JG9d/InTQCLwIC//A6ACj5/wedN2r5Gqxr4Dd6s8qifNwDgxAEAWcvb9oNGcmexT+SuiyYDn+oI74WCjKOcnjNL/SfNh2F6lJTkd84da4ed3frg0RUxNN/youIFgup8xcgPdiNSMdxFIYtxDN0G8Mb7kWU6RFNl5+SDYxNoPuE+9ny3SzcegeirlKSm/YrY994/7qmw21cPwGudix5tAeP/OTCtGPHeW5bIr7tnQkO2Ut2zvMcP+CFoyCir/bhnhdnXvYalUUF5B9L51zuac7lZlNZXIgMGUGJrRjw2HTkt/l6ekNVJWX5uXiFhNFYU01J1gkaq6s4k3aYrvKhOCT7YdGZaNhdTGNqKfbtfHHqGsCQ6S+R/clWygLX4Ch1IqgyBZXbWxiqHbGmwYC9fRitWs7h8OExhA+cDoAoSLEXD+EvlUPWvVAOC46vJmhEON2O+mPc3MDwu19k6cq3Ob58Ayk+49ELFuLsO1JWUsD2ud/Sa8ojF9qv1zQiCAK5R07yhGNvNi5YznoPL/ok/G4zqzWYmLNkBXKpiZHx80AiQ1cdjFQ9jy4O8xk0bDBLsjrz3vpT7Mwq54ORLUFrfWQZNfKLyugEiYS7HpxGQGw8zVq2waDVsnDGMyx966XzAfzyFRheIaH0vO9h3AMCL7vfxu3NnRTADwIRgiA0A4qB0cDYpriRKIpUFBYQkdThwrZ2Q0ZSc66UvYvno1Tbkdjv2nWvs1J3k3vkIDt//I6UyVMv2W+xiGw7XsKRX0/Ryi+fhno3UoY8CFj/sTuMu4fM4G0cmreJVsYxlNUFctY9HTVnMVd6X/G+LXr3oyw/l90bf0QqkxGV3NkWvP8inNVyvp/YljfWOPDkHg+mpsvp0GiPd9Qm8Lb6JBj1dix86UlGv/7hRefmp6fx6+e/4Cb3wVflR4QyDmUzNYIocOLMfha/+hxDnn0ZO2eXv6NrVyVt/SoOLF+CrqEBk9Fw0T5BIsHDKRCJq4SfslYy9pFJeHe3quQ17CmmIbUUlwHNUNl7Uh35CT6RZpQbq1G6FNJQdLHmuZNTAi1bfsuRtHsA6NxpPzk5H1DMApo5lmGs8aT0zEgqfzLwVsQSnosZi2lvDQNaT+XgwRVIBAn7q0qId3Ggc8AI1m37mpDmiUS0SwZg0ZuvU3u2CGc3d2TJx+mcNYhPv1yAetp4ukZ6ojGYePKr1fiZK2gVuwGZvRH/g09hqQ4gTVKOXdhGEFfQy2M5nQaM47lNbUj5YAev+NWDKKBvFC6ZiZJIpSR072194QpDn3uVxa89j8VsvqrTWMved/ayzJ/RlHaiI0eODE5PT7cXRZHQ0FDdokWL8pydna9Z0e2OCeCiKJoEQXgE2IC1jOw7URSPN8W9NLU16OrrLlp3EiQSej/wGAatlm0/fINCbUd8917XdL3ygjwEQUL6pnWEJyUT0vxiucR5yzZR88scgly9YUgh1XkJuLtfLHIR26U7zt4+7PtgDu2E/tgVt8FZ4sBJ/ZVF9X6bmqssKqTkVCatr+NLh42bRyaV8MqgOCK9HZmxQsau4jDG5zqjlxqpd9AQ1HYH7u128vOz/2XY2+8gCAINVZVkf72N+MBYGuXlGEyVlJmq0RulqCz2xDi3Q17/Kz+99DRDn30VN7/bx8b0yLpVbJvzFWCdAUoaPJzK4iLsnJ3xj4rF0cMTbUYlVfNP4HSmBa+9/xrPP/U8HiOjcOoRRPXKHGqW5+CmkFMvNYFFwPWuZQgSCE+8NIHU1bU9iYkLMZvqkctdiYp6FaOpjjLWoCSH8OhDlO0dS2RuT2aVLKFf+774p5to7pWCUVWJY4efyTjRl3bmELoGjmbDF5+QsX0Tjh5eRNVH4erahdPSdeicz3AucRZTDJN47NtNfPDgXczbfRrnymPExu5E7VqD/6+PYKn2xF6mpKMkiAO/9iL7+Ah84+biED6XL3rt5/uTE3D2KcGuIo5Go/lPS9t8wiIY/NQLLP/f61fVSrDxO3+1neiXX35Z6ObmZgGYPHlywLvvvuv11ltvnb3We90xARysjmrA2qa+T2WR9Yuae0Dwb/dFEAQkUin9HnuG5e+9xsavPkWhVuPi40dBRjqxXXpctiRFFEVUZUoGh0zjkGEDG7/8hAnvf4bSzprYotXqMG/YwbDAh6jw2UKlINJYG3DZtWn/qBjiJ/Zn7zcrSPTrjcQswSvk6m5MUpmcoc++THlBnm30/Tcxtl0QIR52PDz/CDOkPVDJpVQ26nki3UJ0q+24t9/H8mdeYuDbL3Niw268oxvJi30RhItXgDRAVlZfIvNGIdcpWTBjOkOmv4hfZMzlb/wXcnTzerbN+Yrwth3odf8jqB2dEASBkJYXu+IZyxqxCEY0Eg1hhX157+WP8ejnwoS2/8FrXCzls4+hrbYOcPQVPXAJykKnKyQ8su9l7+vq0vbC74IgJS72feztI1ApfSko/Bah11xcTuxBcvIxDm45xelQBV3qfShs8Rl2zmdQep4iY8dTtJaEkhw8nOKKU1Tm5NHMrw0WaTUR8pYUshaLKFLb7gfe2DWEyd+70JwsOsdtw9WjBO/MCZTnysmWrsVQ0kjPZuPo6BTKAftTlBwYj2NJIj5t5/Kf0BcAEZes7tSprm2QFty8JVO/W3jbm7T8VdxudqK/BW+LxYJWq5Vcb07RHRXA/yoqCq0B3M03gOplp9FlVeP5QHNkriojwXbXAAAgAElEQVRkcjmDn3qBn9+awaqZv+vIZO3fw8iX3rqkVrzgWDruUh+UKIhW92Vn6edsn/stdz04DYD5X31Pe7c4zsZ8j8YxH73ejnZdJlyxbdHJXagtO8fqxbNwlroT0yrlT/ujtLMnIPrPPcJtNB3JYR6smNqRmZuyUMqkGM0WPkvrzyPHzcTG78Cz/WHWPf0mOvsK3FLWoS/xwSXxVUxmAyazHpNZj/bkLBwi13FK70BUaX/kMiU/v/YifR97ioik5Kve32wykX80DW19Hf5Rsbj4XLlWGcBo0CNXXNmMRa/RkH1wH7lHDmIxm8k+lEqzVm3oN/VpJCYBzeFz6PPqUAQ4YGk0YSisx9xgwFihoSTqJ5p57qVh6QCo7Q0/mfho9Swc+tpx/8gJlH2bB0BitwdwcfahunoPavWlWdiXQyJRENrsUQB8fAZy5syn5IlfEhH0NKUHJ1CX15KC0FT0zmeoyo3D2T8LVeePydr1FJGGILyk3uAGeS1eQe+cB7XWkW9WdluaBWWg7LScV3fUYYg9hadXPu6nhpN73ELQ4BAm9n6QtHWrWDPvK3pGjyepMYryBC37jgXRWP0moQnvY3ZV4FDeApXrqWvqD2AL3ue5Xe1Ehw8fHrJt2zbn8PBw7Zdffll0PefaAngT4NUslKT+w9EsLLRKGcokVC04iecDzRGkEuQqFUP+O4M9i37EMygEiVTKhi8/ZuNXn9D3kacQBAGDTsvuhXNJW7+ann4TKBN0uJmVtAoex/5t31jX2mRK3DKKMbU7TW2gVf6xqiSSdklXL2lpd/cIIpKSObJ2OeHt2/8Vb4mNW0Cwuz0fjbYun4iiiLezih939GKC3Eh0zB682jtgyQ9HA+Tmx7PqRCH5Zld0KAAFAk8zU3gbx4QlnNA7EFPVlc6BI1j94bt0nTCZxL4DL9xL19DA+lkfkdCjF2Gt23Fi93Y2zProwv6ghJa0SOlDWJv2SGUyLBYzFQX5uPkFUFGYz6JXnyU6uSu97p+KRHLxdGRVSRELZkxHV1+Hg5s7UpmMyPaduOveR6n+/gSGAqs2t6CQojl0DgCZlxqpi4oSSRl1jrlI1Xrshq2i9aadlBT0R6Aj4mIL7257nyTnctwBT48oZDIH1Oob01+QSJSEhT2Np+ddHM98Br9u39KY3Zz86lb4AHXVfvQZ9S6pe+5G3/ETdm1+CPQyZB71uDnnoSt3QeFyDglg0dlz7HgKcQnrceiyBUFqwlAcT5UhlJR3R1+YfWvd/24sZjMb58+mS4sx+JYGkdI+lJWHDpN16C28ZAKCgwyZ6+2dhPhnvLTnpcDs6uxbavsW7hqueb3j6/84O9Gff/45z2QyMXHixKDvvvvOddq0aZXXeq4tgDcBAdFxuOk9qVpwCrfRUSAIVC04Sd3GfJz7WoOryt6Bnvc+eOGcxppqdi+ci5tfAL4R0Wz8+lPqys/Rsnd/nLPcKdBaOOZyjJ665tR592bjl59i1Av09h5GceBLaM+602hxoLKi+TXJbrr5+V82Ic7GPwNBEJh+VxRag5nNB2qRy/WEhR9C5mD9Aq+Rq+kgz6eDogAPnwCCwiIpk3rw9MbpfCR7A1XiD2TusyO2sS29Iiax6Ydvqasoo+s9kxAkEg6t/oWcQ6nkHj5Ax9HjOJdzGoXajjGv/4/TB/ZybMtGVs18B3sXVyLaJZOXfoSas6XIVWqkcjkSiYSMbRsxGfT0efgJpDLro0bX0MDy915DEARGvfou/lGxCIKARW+iYnYGhoJ6BIUU5/7NsG/rg7lah8ROjkRtPf+7J78h0eEsmnI3nPwEGgeVo6peRmLqavLzR4LQF0ngXMx6JTLZjWnf/3+cnBJol7SSvLwvyLV8isqUBYBKrsbRMYakDgs5kDoSt94fIZEakKj0iGYJ4ZEvIXcOZe3aD+kz6CkCAgL54RMzwQkbkUlNaMrc6PvUA5fcr+2gYVjMZnYunEvXlvfgkx3A8B6d+ObgMrz1kUAzlO62sq/r5Xa1EwWQyWSMGTOm6v333/exBfDbAGOZFgRQx3kgyCXoc2qo31GEucGIy+AwJIqLRyVJd4+gqriQPYt/BMDV149Rr7yDo9yf2txDNNqfprEolAyvfJrbtaK2IZ9Axxj0gYcQFQ3oGUxesT3h4eH/GG1wGzeHIAjMGBDL8wYj6UfrkMt0BIVkAOAoCkx46CGOHz/O8ePHObJ7CxKJhMfbdObpI8/yYZvXkbf7mmO7VMQb4+kX+yDr1nxNfWUF3cdPJn39WrpH/4cyWTG7F/yAu9KP/v5TMHxfQlRUIokv9qeo9CRHN68jfeM6vEPDSJk8lbK8HEpPnyJlylSKMjPY9dMcTAY9KZOnonZ0YvXH71JbVsaIGW/iHxmLqUwDEoHqn09jKKrH/T8xqOM9aDQ2kl2bTahrKAaLkazyTKp0VahFMxK5HkNDPJ2S51Bcsoj8/G9o7HsOl5o5CNuqkNvXYG64crnljSCRKAgNfRw7u1Ayjj8BQIv2HQFwdm5F66S5nMp4Cye3WNzckqip8SY7t5a6k8epqAhBIpGiUql4YPqHLHrpUXzi8tDrrlwB0m7ISMwmIzt+ns+ATo9hfwQe7zWBhpPn0BbUo/a+/SoIroerjZSbitvNTtRisZCZmamMj4/XWywWVqxY4RIREXF5QYErYAvgTYSpXIPUTYUgl2C2iLgMDkfiIKd+WyGGwnrc74lG7m2PaLagO1WNMsyFXg88hiiKOHp40n7YaCwlOkpmH6MycB3KyBX4ZyWS9+sEPFyrae85CJnEwqngb9BWunIsSwC0RERE/N1dt/EXIpEIvDm0BU9r6snO0SCX6/H2zSEguj3e3t54e3vTvXt3zp07x6pVq6jISuXhjn15NvVZ3mvzBtLkWaRvf5wWmggGJTzCqtTPyT96hFBlc7z0/ngTROITA2nMPIf8NKii3dBmVKBJK8M52o1+ox5H+oQawSxgyK8noWMK5joD5d8cJapta2QTFGyb+w25Rw7hERhMWV4Ovac8hkOuHaXLDmCpO18qJgG3MdGsMG9j5Q9rcc91w7vKjxKPEhR6GT61ASjNjrh6WhNDI9uPRSq1IyhwEgH+YyktXUbumc+QDliMaFBgqrqls7MX8PEZhNmsoaDwO2La9r+w3c21Ax06r7rw+uefP6WmpgalUomrq+tFs2KjXv8UbX096j9RP+swfCzl+WdYu+9zRvR4Af3Ws8iB47UHSfAYdMv79m/ndrMTvfvuu+vGjx/frKGhQSKKohATE6OZM2dO/vX06Y4xM7kRbsbM5NxHh5E4K/nWR8qSQ0V8P7EtLQJd0J2upmrRKUS9GccegWiPVmAsbUQe4IDHxDikDtbPkvZkFeXzMik2m6iI/gy1fzqC1IKuNITyfY/QwcGBGr/tNMQvpLRgMGVVATz44IOo1WrbCPwOxGS28PSXy3EpT0cmMzB4zFQSwi6uMKiurubLL7/E09OTqoBkFu8/yFtt38FitsOw7VFaKUOxOMPGzNn08p9ImbwOL7U7sloRUYAqWQMrQtPp1DaJ1mfDaNxbgkVjQu5rj6lCi2i0gFRAopRi0ZvBLOLYLRBTgpSjm9eTuWML8d1709yxC42ppahi3VHHuCFaROQ+9vxYtAztD3YIEg8AFPoaDEoXEC04NJag1NdgF3cQ+y576dQxFaXyYllina6Eg4dGYjCUIqEn3Xt8DYDZbGbDhg2YzWbs7e1xcHAgPj7+Eqev68FgMHDw4EFiYmIuWbKqr6/ngw8+oFevXnTs2PGG7wGga2zgx2enIZpFBrd9HF1+Db+cnMm4Dz/Fze/qFSR/JzYzk1vLlcxM7iQp1b8M0SJirNCSaTDw1Y5cNAYT4787wInSOlQRrnhPS0QR7ETdhnzMDUacUoIwntVQPisdU5WOxrQyKn44zmmLiZ/sdiJxKkNb6klszP9Qeufj0/Nt9lFETfhqtGWu5BY4ExcXh52dnS1436HIpBLeuX8QjWofTCYlrv/PvALA1dWVAQMGUFRURBvFWQYmtuG1I08gldcj6/wNhxrzkdRB36ApSC1STlXL2ZSTS10nBXnGQvJqVLjvT+Lkx3W8teNzisZJcBkYChIBu5ZeuE+Mw6GDH1JnJaoJzbBL8qF+eyGy42a6jZ/Mw7MXkNjsLhpTS3HoEoDH+Fjs2/rg0M6X7/MXo5ujRhDccGjIp4XpfUIT3qaN7DlaOT6Lb7tZON61CEWLdExGBQqFxyX9U6n8SGz1AypVILHxd1/YXlJSwoEDB8jIyGDXrl2sXbuWb7/9lqoqq0uyxWIhLS2NI0eOXLPU8a5du9i0aRNffPEFu3fvxmy2StRWV1ezaJHV2z0s7FKv8utFZe/AwCeeo7G2it1nl3Hc/RCiDBzdL+2/jTsP2xR6E2Cu0oFJZPGZCjrF1+IfcIodqUmM/HIfY9sHMSm5Gd73xqM7VUWuUuDhdScYl+RO+7Rqzn2ahqg1cUxq4X3nUgZnu6PocI7Gcj98fYeiUgVw6MB4Anq9gSCAo8vrWE5mERdnK/O601HJZbz86CT2Z2QR4HV5vfiEhARycnLYtWsXEyZMQGdsz//SH2Z64mdYOv1A6vaJtHMNolCVhU/K/6jO6sH2XwRUbvn49vyEaK2G2tMdEEuHc/CtPJZG/MLo8aMorsvi6OlTtI9viSxazs6P56GNbeCpNuOo31qILrMSVaw79dsKUcW6cyAmm+3L51F7ohaLWiD+eBIyQUFkm6exhNWjP9/ehvNusdLzPyDDy2vgFb+o2tuH0TF5+0XbSkqs8qNTp07FwcGBwsJCFi5cyOzZsxk8eDC7d++moMA6C1pYWEhKSgo1NTX4+voikVw6xqmpqWHv3r1ER0cDsHnzZo4ePUqLFi3YuXMnAMOGDcPHx+da/3RXxTs0nG7jp7Dlu1kAtBk49BJrUxt3JrYA3gQYz9sZFijOItauwel0LBEtf8FeM5lvduYye9cZBrXwo0OYO68uzMRksfBUYQ19fJx5ViPjkEXkLaGcoYW52LsGIpGaSOhulXx0dU2iY+f1HNh3D3aKGLJyLbi4uODvb1NasgEOdip6JjW/6jF9+/aloKCAZcuW8cIDD/Kiwcznv9YztdUczMmL2bRrEl7dl6IWTLjHbESmM2C2lyF3qKBYGoR/p804V+6hbP8IyO3NnpcyEQRnnCUtObG8CgsNuEqTcEvT80nSAp4Z8SD1O4up31qI3N+BdSHpVL8N/pJO/PaplQvVhCfPwBLUCICz+2iiw8ZTV5eOTOaEo2M8SqU3Esn11zSXlJTg4OCAo6MjgiAQHBzMfffdx48//shPP/0EwKBBg6itrWXHjh2kpaUB4OTkRFxcHPHx8fj5+V340lBSUoLZbKZz5874+/tz8uRJ1q5dy6ZNmwgMDGTo0KG4ut5aw50WvftRcvokhRnptLu76W2JbfwzsAXwJsBUZk1KNLqvpv+xCUhQU709l7xe3/PtlPvZdVzFooOFLEsrJtxbTr+OeThaWjBrUyPdGg3IZUbuNqfiau5NUMvnEUQV/sG/ew7b2YXQrece6urqWLdlJh07drRNndu4ZpRKJcOGDWP27NmsWb2K/w0fzmMLLcw9XseEhGVIe32K2i2fNRk98XSvIKnVdgCMtfbsrn+XquyNjIxcjle/uXjlrOHsoZHYcQRn9+OcK+1BrWMYYa2eozKnF+xvz6dOc5k+7WmMBfXsrD1A7acWFLgQUz0beWAOkkYFmm6VWLz1eAe8TELk+AttdXC4Mc/3tLQ03NzcCA4OpqSk5KIADODh4cF9993H7NmzcXV1JTExEQBPT09WrFhBbGwsWq2W/fv3s2/fPtzc3IiPjyc+Pv7CdLnivOhSdHQ0zZo1Iy8vj/Dw8CbxbBcEgb5Tn8RkNFxVIMfGnYUtgDcB6nh3Pjm8g7tOjkKl1xNSsILTYSOQbVDyUdZM3KPlvDduLJVVAew68SWWOe1I81jB2D4B1JZ3ovr0XEJO9yco6kuk3tXEx3+OSnnpdNyxY8cQRZGWLVv+Db208U/G39+fnj17smnTJo6m/8rHo1vxwDwza7Jq6B+5FX29Ha6hj3L8bCNbDhygnc9hNCTw9cS2ZJdF89GmHohFCxgQuhGfMOvUrgh4WrLx0krA3oxHwEJMW+xgYyxPFj5Lm14tqPiiAZXSi4ikF9D7N2CSWNecLaKAT9CbJESMuum+iaLImjVrEEWRoUOHUl5eftklJkdHR6ZNm4bF8nv5bnx8PFFRUchkMgRBQKvVcuLEiQvr5zt37sTDw7r+/MdArVQqiYq6sS8b14ogCLbgbeMibAG8CZC5qymsPEWC2I1WJf/DObEA+yOVZAaO4a6sezGdrmO5z2aqHEvpeXIUMrNIXNldmH6opDRkDom5vXBz34ldyzT8/e/By6vPJfcQRZG0tDSCgoIuPFBs2LgeOnToQE5ODuvWrSMoKIhZ/2nNvXPMzM7wpcoQzuJHolHLpezODmXbyR70CrUa5IR7OfLZPR3IKI7l8y39UOpX0mDyxNkpDgfzOlp4ppFZOZ4g5S/4dfseYe19RJzuQ+0pDQq5O+EdnsXs04hOOZrY4M7ojVV4ukTg5d7mT1p8bTQ2NmIymZBKpSxZsgQAPz+/yx4rCMIlI+Y/GlGo1WoSExNJTEykoaGB1NRU9uzZA3DZ9XEbNv5KbAG8CTCYLITUmEG00NDcQpt3j1H5Ug8GZj5BTn5bCty7IrP0AkGCne4s7bQz0Wo9OOb6H1rlD0apKMKjy0Ic7KOICH/+svcoKiqioqKCQYNs9aA2bgyJRMKQIUOYNWsWS5cuZfLkyXwzvi0v/KLiP3E+OKmsgax7lBfdo7wuOT/e35lZ4/tQWNUFLyclSpmUOt0QDuRWMT3Sk1/zBpB36h68+n6H/5atFJQMx7f7d+Bbj8ztDQa1GtMk/aqtrQVg4MCBHDhwgLNnz14xgF8PDg4OpKSkEBUVRV5eHs7Ol5oP2fj30ZR2or8xYcKEwCVLlnhoNJq067muLYA3AQVVjdjpnVGaqnHo05r9hwYRM/0j7HROFHzzBG1KZiGeUZNvaotn8CE0D8WiloQQufAzTNlhWEamIdrJiY//BKlURU1NDQcPHsRoNCKRSJBIJBQWFiKXy23Z5zZuCkdHRwYPHsyCBQvYvHkzffr0uaC3fq0Euv1eT+2kkpMSa1UYSwqPRG/8irzsafj1zcFX/wESpYka+aMMu4ngnZmZSVFRESkpKVfMEgfw8fFh4sSJVFdX4+Bwa2RVAQIDAwkMDLxl17Nx+/BX24kC7Ny50662tvaGYrEtgDcB2WUNyC0e2Dscp176C5YGE4ePjCEs7EninvwItTqYmhOpVK58h8ZOHuh0B6gV9yEZrEItq6bRoCMm8h3s7a32nUeOHGHPnj0olUpEUcRisWA2m2nfvj1KpW1NzMbNERUVRVJSEqmpqYSFhREREYHZbObw4cPExMTg+CeKYVejc0wizUM2sXLf98jMP2I0pTC+x+M31d5Dhw6Rm5uLXq9nwIABlyRw/jYCd3Z2RqFQ4O19ZclSG3cWt5udqMlk4plnnglYvHjxmZiYmOvWx7UF8CYg42w+DgpX3Lp/ikzmTGKr+WSdfp3s7HfIzn4HmcwRJ8fmSFPkNNadoEXzr1EqvSkqmsfZcyvx8b4bX9/hF65XVVWFq6sr06ZN+xt7ZePfTK9evcjLy2P58uU89NBDHD58mG3btpGRkcGECVZ72oKCAvz9/S9kX18rzmoV43o8BDx0S9paUVGBUqnk8OHDFBYW0qFDBxISEpCdN0ypqalBoVCgUtlqpW38zu1oJ/r222979evXryY4ONh4I32yBfAmINxVQ61fLjLXOqKjvsLePoyWLb6nofEU9XVHqTv/o9UVEh31Oh4e3QGIiXmbyMhXkEjkF40qqqqqrslhzIaNG0UulzN8+HC+/vprFixYQGlpKZ6enhQUFLB161bc3NxYtWoVCoWCHj160K5du7+ldFGv11NXV0ePHj1wcnJi7969rFixgi1btpCUlERSUhK1tbW4uLjYSitvY0qefyFQf/r0LRWsV0ZEaPzeevMfYyeal5cnX758uWtqauq1m7v/P2wBvAk4vWcPAY5WT2MXlyTAmu3q6BCNo0M0fn5WIQZRFC95yEill06JV1VVkZCQ0MSttnGn4+XlxV133cWaNWuwt7dn4sSJbN68mT179iCXy1Gr1QQEBLB+/XpKS0sZMGDAJWt9TU1FhVVK29PTk5iYGFq0aEFOTg779u1j69atZGRkYDKZcHd3/0vbZeP253azE01NTbXLz89XhYSEJADodDpJUFBQfEFBQca1XsMWwJsAyRkjirgyLHo5crnTFY+7lhGCRqNBp9PdcmUnGzYuR5s2bdDr9QQFBWFvb8/AgQPx8/Nj8+bNhIWFMXToUHbu3Mn27dspLy9n1KhRf2k29m8B/LfSSUEQCA8PJzw8nOzsbBYsWIDZbL4lOuQ2mo6rjZSbitvNTnT06NG1o0ePTv/ttZ2dXavrCd5gC+BNgkedHrU6D4vh5jNfCwutn3NbrbeNvwJBEOjUqdOF1xKJhLZt29KiRQsEQUAikdCtWzd8fHxYtmwZX3/9NaNGjSIoKAiLxXJLaqNFUUSr1VJXV4eXlxcSiQSDwYBer6ekpASJRHLZJaXw8HBGjx7NwoUL8fK6tOzNxp3N7WYnOmzYsLqb7ZPNTvQq3Kid6OppfXHseQoHzx607vDtTbVh7ty5lJeX8/jjjzeJRKMNGzdKWVkZCxcupLq6GrlcjslkIjk5mcTERDZs2EBSUtJ1jYSNRiMrV67k2LFjSKVSzGbzBf3yurrfn3Wenp5MnTr1itfRarUolUqb0MrfiM1O9NZyJTtR2wi8Cejz0kx2HO2Pu2/iTV2nrKyM3NxcevToYQveNm47vLy8mDJlCrt27cJisdDQ0MDu3bvZs2cPoiiSn5/P/ffff00JmI2NjSxcuPDCjFNYWBhRUVHk5OQgk8lwd3fHzs4OqVT6p8Y9arX6qvtt2Pi3YAvgTYBWac1lUNuF3NR19u/fj1QqpXXr1regVTZs3HrUajW9e/e+8LpFixbs27ePVq1asWbNGhYtWsR99913UemZKIocPXqUkpIS6uvr8fLy4ujRo9TW1jJixAhiY2Mv5IfYPvs2bFwZWwBvAjTaPADs1M1u/BoaDenp6TRv3hx7e/tb1DIbNpqWiIgIIiIiAFCpVMyfP5/Vq1czZMgQBEHAYrGwbt06Dh48iEKhwN7enszMTNRqNRMmTCAoKOhv7oENG/8cbAG8CdBorCI8dnbBN3yNI0eOYDKZaNeu3a1qlg0bfykRERF069aN7du3YzAYGDBgAFu2bCEtLY3k5GR69eqFIAg0NjYik8lsqoI2bFwn/8gALgjCK8AUoPz8pudFUVx7ft9zwH2AGXhMFMUN57e3BuYAamAtME1sogy+AP9xuLt1Riq9MZ0Cs9nMgQMHCAkJwcfnUhtRGzb+KXTp0gW5XM7WrVuZOXMmZrOZrl270q1btwvT5LYZJhs2box/ZAA/z0xRFN//4wZBEGKB0UAc4AdsFgQhUhRFMzALuB9IxRrA+wDrmqJhcrkTcnnzGz7/5MmT1NXV0bdv31vYKhs2/nokEgkdO3YkLCyM9evXExkZSXJy8t/dLBs2/hX82+osBgMLRVHUi6J4BsgGkgRB8AWcRFHcd37UPRe4++9s6NXYv38/Li4uREVF/d1NsWHjlvCbM5gteNv4p/HJJ5+4jx8//qaSMzp37hzh6OjYsnv37uF/3D5s2LAQf3//hOjo6Njo6OjYvXv3XlcJxT85gD8iCMJRQRC+EwThN5kyf+CPCj9F57f5n//9/2+/BEEQ7hcE4ZAgCIfKy8svd0iTUlJSQkFBAUlJSbY6Vhs2bNj4C/nN6fFmMBov9SV5+umnz3711VdnLnM4b7zxRtHJkyczT548mXm9qm63bYQQBGGzIAgZl/kZjHU6PAxoCZQCH/x22mUuJV5l+6UbRfFrURTbiKLYxtPzEuvWJkUURfbu3YtcLqdVq+vzZLZhw4YNG1fnlVde8Y6IiIiLiIiIe+2117z4v/buPTyq+kzg+PcFEm5yS4SAEAgokFujNuha1LYCGpGncimiqFChXQtVHy/laZd1WRXblVbFslKr4l6MWIFVrEClsGCfldtaibohJiGAhEsAoZAgt4Yk8+4f54yOw8xkJmRu+n6eJw+Zc36/c975MfDOuf1eYPv27amDBg3Ku/POO/vn5eXl7tq1K3XBggXpWVlZ+VdcccXQzZs3fz6l5oEDB9oVFRVdnJ+fn5Ofn5+zdu3azgAPPfTQRZMnTx5w9dVXD54wYcI5jx+NHTv2hLeISmtK2GvgqjoqnHYisghY5b7cD2T6rO4HHHCX9wuwPGEcPnyYt99+m+rqar71rW/ZZBTGGNOKErGcKMBjjz3W94knnuhz7bXXnli4cOH+jh07ht0/YRN4KCLSR1UPui/HA94J4FcAvxeR+Tg3sQ0G/qKqTSJyQkSuAt4DpgLPxjruQDweD+vXr2fLli2kpqYyZswYm7zCGPOVtr64IvNYzclWLSea1veC0yOn5iRNOVGA+fPn12RmZjbU19fLHXfcMWDOnDm9n3rqqYPN93QkZQIHfi0il+GcBq8Gfgygqh+LyDKgHGgE7nHvQAeYyRePka0mSnegR6qiooJNmzZx6aWXcsMNN9gjNcYYEwWJVk4UnMIpAB07dtTp06cfffrppzMi6Z+UCVxVp4RY90vglwGWbwXyoxlXpLzXvHv06MHYsWPtpjVjzNdCqCPlaEm0cqIAe/bsSRkwYECDx+Nh+fLl3XNyciLaVlIm8K+Kffv2UVNTw0033WTJ2xhjoigRy4neeuutA48dO9ZOVSU3N/d0cXHxnkjek5UTDaGl5UTDtWTJEvbs2cODDz74pfbt2NMAABI1SURBVGIPxhiTzKycaOsKVk7UDvvipLy8nMrKSoYNG2bJ2xhjTMTsFHoclJSUsGrVKjIzM7n66qvjHY4xxpgkZAk8xjZu3Mi6deu45JJLmDRpkh19G2OMaRFL4DGiqqxbt45NmzaRl5fH+PHjadfOht8YY0zLWAaJMo/Hw7Zt23j//ffZv38/w4YNs7vOjTHGnDdL4FG2ceNG3nnnHdLT0xkzZgzDhg0LOkmAMcYYEy47DIwij8dDSUkJAwcO5J577uGKK66w5G2MMUkkmuVEPR4P9913X9+srKz8QYMG5f3iF7/oFcl27Qg8inbv3s3x48cZNWqUnTI3xpgE5/F4UFXatm3b4m00NDSQkpLypWWzZs06dOrUqTaLFi36UonLZ599Nn3//v0pu3btKmvbti01NTUR5WTLKlH04Ycf0qFDB7Kzs+MdijHGfO0lWjnRl156qdfjjz9+0PuFoW/fvo2RvB9L4FFy+vRpKioqKCgoOOfbmDHGmNjyLSe6devWiuLi4p6bNm3qCFBdXd1h2rRpRysqKsrbt2+v8+bNu2jz5s2VGzZsqKqqqvq8+pi3nGhZWVnFm2++uWvGjBlZ3nWlpaWd1qxZs3PlypW7w41p37597V955ZUe+fn5Od/+9rcHb9u2rX0k78lOoUfJ3r17aWpqIj8/oeqnGGNM3K353W8y/7pvT6uWE70wc8DpopkPJFU50bNnz0qHDh20rKys4uWXX+5+1113ZZWUlGwPt78l8Cipq6sDID09Pc6RGGOMScRyohkZGWdvv/32WoApU6bU3XvvvVmR9LcEHiV1dXWkpKTQqVOrfsk0xpikF+pIOVoSsZzo6NGj61avXt1l6NChR99+++0uAwYMqI+kvyXwKKmrq6Nbt2722JgxxiSARCwnOnfu3EMTJ04c+Nxzz2V06tTJs2jRoupI3pOVEw3hfMqJvvDCC3Tu3Jk777yzlaMyxpjEZuVEW5eVE42xuro6unfvHu8wjDHGfEVZAo+C+vp6zpw5YwncGGNM1FgCj4Ljx48D0K1btzhHYowx5qvKEngUeB8hsyNwY4wx0WIJPAosgRtjjIk2S+BR0KVLF4YOHUrnzp3jHYoxxpivKEvgUZCTk8PkyZOtApkxxiS5aJYTLSwsHJqdnZ2bnZ2d26tXr4JRo0ZdHMl2EzbDiMgtIvKxiHhEZJjfutkislNEtotIkc/yQhHZ5q77V3FnURGR9iKy1F3+nohkxfbdGGOMSXQej4empqbz2kZDQ8M5y2bNmnXohRdeOKfISUlJyfbKysryysrK8ssvv/zUuHHj6iLZV8ImcKAMmAC867tQRHKB24A84EbgORHxFm/9HXA3MNj9udFd/kOgVlUvAZ4BfhX16I0xxiSURCsn6lVbW9tmy5YtXbzzoocrYadSVdUKCDip/FhgiarWA7tFZCdwpYhUA11VdYvbrxgYB6x2+zzq9n8dWCgiojYNnTHGfC34lhNVVQoLC3NGjhx54sILL2yqrq7usGjRourFixfv3bNnT8q8efMuKikpqUhLS2saPnz40Pz8/NPwRTnRoqKikzt27EgtKioa/Mknn3wMTjnR9957rzLSimQAr776ao/hw4d/lpaWFlFBlIRN4CH0Bf7X5/V+d1mD+7v/cm+ffQCq2igix4F0wKb1M8aYGDv2elVmw6FTrVrpKaV359NpE4ckVTlRr2XLlqVNnz79SKT94prARWQd0DvAqodV9a1g3QIs0xDLQ/UJFNPdOKfh6d//vO5bMMYYkyASsZwowKFDh9qWlpZ2njRp0s5I+8Y1gavqqBZ02w9k+rzuBxxwl/cLsNy3z34RaQd0A44FielF4EVwipm0ID5jjDEhhDpSjpZELCcKUFxcnDZixIi6Tp06RZxvEvkmtmBWALe5d5YPxLlZ7S+qehA4ISJXuXefTwXe8unzA/f3icA7dv3bGGO+PnzLiRYWFuZ4y4n6t/MtJ3rNNdcMKSgoOO1d9+KLL+774IMPOg8ZMiT34osvzlu4cGHPcPZdWFg4dMqUKYO2bNnSNSMjo+CNN97o6l33+uuvp91+++0BDyibk7DlREVkPPAs0BOoAz5S1SJ33cPAdKAReEBVV7vLhwH/CXTEuXntPlVVEekAvAJcjnPkfZuqnvPNy9/5lBM1xpivKysn2rqClRNN2ASeCETkCLCnhd0vJHFvkrPYWsZiaxmLrWWSObYBqvqlo1NL4C0XLIEn413oMeP/AYyEiGz1/waaKCy2lrHYWsZiaxmLzTQnGa+BG2OMMV97lsCNMcaYJGQJPHpejHcAIVhsLWOxtYzF1jIWmwnJbmIzxhgTdXYTW8sFu4nNjsCNMcaYIKJZTvStt97qkpubm5OdnZ1bWFg4tKysrH0k27UEHoCIZIrIn0Wkwi1per+7PE1E/ltEdrh/9nCXp7vtT4rIQr9tpYrIiyJSJSKVIvL9IPsMWCI13rGJSJaInBGRj9yf56Mdm4h08dnfRyLyVxH5TSKMW7ixxWPc3HWTxSmpWyoifxKRCxNh3MKNLY7jdqsb18ci8usQ+4zHuDUbW5TH7XoRKXH/7kpEZITPtgKWcA40bocPH+5bWlqaX1tb2zVQm0QQ63Ki999//4DFixfvrqysLL/llluOPfLII30i2Zcl8MAagZ+qag5wFXCPOGVM/wFYr6qDgfXua4C/AXOAWQG29TBwWFWHALnA//g3kNAlUuMam2uXql7m/swI0qbVYlPVEz77uwznWfzl/juLx7iFG5srpuMmzjTBC4DrVLUAKAXu9d9ZPMYt3NhcsR63dOBJYKSq5gEZIjLSf2dxGrewYnNFa9z+CnxPVb+BM6PlKz7bClbC2fc95AK39ezZ88DgwYOr9u3b1z9el24TsZxoXV1dW4Djx4+37dOnz7nZPwRL4AGo6kFV/cD9/QRQgVPRbCzwstvsZZxypajqKVXdiPOP0N904Am3nUdVA10D+rxEqqruBnYCVyZIbGFr5dgAEJHBQC9gQ4DV8Rq3cGILWyvGJu5PZ/dIqCtf1APwFY9xCze2sLVibIOAKlX1VoNaBwQ6UxaPcQs3trC1ILYPVdX7d/Ux0EGcqaz74JZwVicje0s4+xsLLBER7dix49nU1NT6EydOdD6f99ASvuVEt27dWlFcXNxz06ZNHQGqq6s7TJs27WhFRUV5+/btdd68eRdt3ry5csOGDVVVVVWfVx/zlhMtKyurePPNN3fNmDEjy7uutLS005o1a3auXLnynCPtYJ5//vnqCRMmDM7IyChYtmxZ+ty5cw9G8p5sIpdmiEgWzhSs7wEZ6sy5jqoeFJFezfTt7v76uIh8F9gF3Kuqn/o1DVYiNRFiAxgoIh8CnwH/pKrNJqzzic3PZGCpBv7KHvNxiyA2iPG4qWqDiMwEtgGngB3APQGaxnzcIogNYv952wlku9vYj5OEUgO0i8fnLdzYIDbj9n3gQ1WtF5G+BC/h7OtL45aSknJ2zZo1fWpra4OdvWiRXr16nR43blxSlROdP39+xvLly3eMGDHi1Jw5czJmzpyZuXTp0rBn/7Qj8BBE5ALgDZz51j9rwSba4VRF26Sq3wS2AE8F2lWAZSE/CDGM7SDQX1UvBx4Cfi8iIa9htUJsvm4DXgu2qwDLoj1u4cYW83ETkRRgJs5/yBfhnKaeHahpgGVRHbcIYov5uKlqrRvbUpyzKdU4p5nP2VWg7gkSW9THTUTygF8BP/YuChRyoK7NbTsWQp22j7ScaGVlZXllZWX54cOHS3v06OGByMuJHjhwoF1FRUXHESNGnAKYOnVq7datWy9orp8vOwIPwv0P5w3gVVX1XuP8VET6uN9O+wCHm9nMUeA08Kb7+r+AHwZoF6xEatxjU9V6oN79vUREdgFDgIBVXlopNu+2LgXaqWpJkCbxGLewYovTuF3m7m+Xu81lfHEd01c8xi2s2OL1eVPVlcBKd5t3A4HuZIrL5y2c2KI9biLSD+f/iqnev0NCl3D29aVxa2hoSC0qKjrQtWvXU82999aUaOVEe/bs2Xjy5Mm2paWl7QsKCupXrVrV9ZJLLgl6yS4QOwIPwL1G929AharO91nlW5b0B3xRrjQg99TqSuC77qKRQHmApgFLpCZCbCLS03ujjogMcmMLWMmttWLzMZngR7je7cZ03MKNLU7jVgPkioh3Dv/rca5v+ovHuIUVW7w+b97TxeLcef0T4KUAzeLyeQsntmiOmziX2/4IzFbVTd7GGrqEs68VOBUg5cyZM6n19fUdunTpEtPkDYlXTjQlJYUFCxbsmThx4sVDhw7Nfe2119KfeeaZiOqk20QuAYjINTinq7YB3tMi/4hznWgZ0B/YC9yiqsfcPtU4N+ak4pQ/vUFVy0VkAM5dm92BI8A0Vd0rIjcDw1T1n93+AUukxjs2cR4tm+vG1QQ84h4RRDU2d90nwE2qWumzj7iPWzixxWvcRGQGcD/QgHOH/F2qejQRxi2c2OI4bq8Bl7rbmKuqS9z2iTBuzcYWzXETkX/Cudyxw2czN6jqYQlewvmccVu7du2jGRkZTf369dublpZ2vpevvlasnKgxxpi4sZnYWs5mYjPGGGO+QiyBG2OMMUnIErgxxhiThCyBG2OMMUnIErgxxhiThCyBG2OMMUFEs5zoihUruuTm5uYMHjw4b8KECVmBKpmFYgncmCgTkeUioiLyYIg2V4hIg4jslmamwDTGREcsy4k2NTVx9913D1yyZMknO3bs+Lh///5nFy5cGLD8bzCWwI2Jvr/Hmav6CRH5hv9KEekELMb59zilFeZoN8YEkEjlRD/99NN2qampnoKCgnqAG2+88bM//OEP3f37hmIJ3JgoU9WjwDScGbZeFZH2fk2expm3ep46JSWNMa0s0cqJ9u7du7GxsVHefffdTgBLly7tcfDgwWCV5gKyYibGxICqrhGRhcB9ODXYHwIQkZuAGUAJ8KhvH3eq29lAEU4FrxM4U2DOVdUP/dpmAj8CbgAGAmk40+P+2W1f5dc+G2cu8heABcDjwHeAdGC4qvqWzTSmVZVX/Dzz1MmqTq25zc4XDDmdm/OrpCkn2qZNG4qLiz958MEHM8+ePdvmuuuuO962bWQVVi2BGxM7P8MpGvOAiPwR+D/g33Gqwt2hqp9fPBORvwP+hDM39p+A14FewHhgtIiMUdX1PtseCcwC3sH5MnAa56j+VuB7InKVqgYqbJKNMwd2Gc68+BcAJ1vtHRuTIFqznGigRB1pOVGAUaNGnSopKdkOsHz58q47d+7sEEl/S+DGxIiq/k1E7sBJmC/j1MTOAH6iqtu97dxT7MuA9sA1qrrFZ90c4H3gP0TkYp+kvxropapfqvLkFpvYAPwLTvL39x3gUVV9rJXepjHNCnWkHC2JVk4UoKampl3fvn0bz5w5I08++WTv2bNnH4ykv10DNyaGVPUjYA7QFxgN/FFVf+fXbBxORainfZO3238vMB+nvvK1Pss/9U/e7vKtOAn8ehEJ9O99H/DLlr8jY5JDopUTBZg7d27vQYMG5eXk5OSNHj267uabbz4RyXuyamTGxJibSGuA3kCu/6ltEfkNTtnN14Cqc7dADjAJuFdVf+vTbxxwN/BNnGvZ/mfY0lS11m3rvQa+QlXHtsb7MiYUq0bWcsGqkdkpdGNiTFU9IlLvvgx0+i3d/XNyM5v6/PEWEfk5MA84CqzDqed8BlBgIpCHc0re36HwIzfGJBJL4MYknuPun0Wqura5xu418zk4p8MLVfWI3/rrQnS3U3DGJCm7Bm5M4vE+wnVtyFZf6AN0BjYESN7dgEtbMTZjTIKwBG5M4nkd52j6ARG53n+lOK4REe+kDzVAA3ClO6ubt10q8FugWwxiNqY5Ho/HE/j5LBOUO2YBH1GzU+jGJBj3cbPxOI+GrRWRjTjPjP8N5+7zK4EsoAdwVlUbROS3wANAqYisBDrgPBt+Ac5d6OEezRsTLWVHjhzJ7dmz5/E2bdrYpZsweDweOXLkSDeceRrOYQncmASkqiUiUgD8FBgD/BBowplT/S/Aw4DvnOk/w7khbRowE6gF1rjtno5d5MYE1tjY+KNDhw69dOjQoXzs7G+4PEBZY2PjjwKttMfIjDHGmCRk34KMMcaYJGQJ3BhjjElClsCNMcaYJGQJ3BhjjElClsCNMcaYJGQJ3BhjjElClsCNMcaYJGQJ3BhjjElClsCNMcaYJGQJ3BhjjElC/w8JYB27q0tYhgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Z_aluminum = np.block([[t_aluminum_train**0]]).T\n",
"Z_aluminum_test = np.block([[t_aluminum_test**0]]).T\n",
"Z_aluminum_train = np.block([[t_aluminum_train**0]]).T\n",
"\n",
"max_N = 20\n",
"\n",
"SSE_aluminum_train=np.zeros(max_N)\n",
"SSE_aluminum_test=np.zeros(max_N)\n",
"for i in range(1,max_N):\n",
" Z_aluminum = np.hstack((Z_aluminum,t_aluminum_train.reshape(-1,1)**i))\n",
" Z_aluminum_test = np.hstack((Z_aluminum_test,t_aluminum_test.reshape(-1,1)**i))\n",
" A_aluminum = np.linalg.solve(Z_aluminum.T@Z_aluminum,Z_aluminum.T@P_aluminum_train)\n",
" plt.plot(t_aluminum_train,P_aluminum_train-Z_aluminum@A_aluminum,'-',label='order {:d}'.format(i))\n",
" SSE_aluminum_train[i]=np.sum((P_aluminum_train-Z_aluminum@A_aluminum)**2)/len(P_aluminum_train)\n",
" SSE_aluminum_test[i]=np.sum((P_aluminum_test-Z_aluminum_test@A_aluminum)**2)/len(P_aluminum_test)\n",
"\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5));\n",
"plt.title('Error in Predicted Values',size=20);\n",
"plt.xlabel('Year',size=20);\n",
"plt.ylabel('Y Error',size=20);"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The predicted cost of steel in 2025 is $ -22020853.67\n",
"The predicted cost of aluminum in 2025 is $ 699083539.99\n"
]
}
],
"source": [
"for i in range(0,47):\n",
" cost_steel = a_steel_train[i]*2025**i\n",
"print('The predicted cost of steel in 2025 is $',round(cost_steel,2))\n",
"\n",
"for i in range(0,47):\n",
" cost_aluminum = a_aluminum_train[i]*2025**i\n",
"print('The predicted cost of aluminum in 2025 is $',round(cost_aluminum,2))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_I would change my answer from 3b._"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# References\n",
"\n",
"1. <https://en.wikipedia.org/wiki/Direct_stiffness_method>\n",
"\n",
"2. Aluminum and steel price history on <https://tradingeconomics.com>"
]
}
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