Optimization_HW2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "fc3be30e",
   "metadata": {},
   "source": [
    "# Optimization Methods MA060002\n",
    "## Homework 2\n",
    "By: Darío Slaifstein, PhD-2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e4819305",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.patches import Polygon\n",
    "from matplotlib.lines import Line2D\n",
    "from matplotlib import cm\n",
    "\n",
    "from numpy import linalg as LNG\n",
    "from scipy.optimize import minimize_scalar\n",
    "from scipy.optimize import minimize\n",
    "from scipy import optimize"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "d68065e7",
   "metadata": {},
   "source": [
    "### 1. \n",
    "_Find minimum (i.e. both point $x^∗$ and function value $f^∗ = f(x^∗)$) of function with\n",
    "respect to parameters $a$, $b$, $c$ :\n",
    "\\begin{equation}\n",
    "f(x) = a.x^2 + b.x + c\n",
    "\\end{equation}_\n",
    "\n",
    "To find the minimum value of $f(x)$ we need to assure the optimally conditions:\n",
    "\\begin{equation}\n",
    " \\nabla f(x^*) = 0 \\rightarrow f'(x^*)=0\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    " det(\\nabla^{2} f(x^*)) > 0 \\rightarrow f''(x^*)=0\n",
    "\\end{equation}\n",
    "\n",
    "Hence the first derivative $f'(x)$ is:\n",
    "\\begin{equation}\n",
    "f'(x^*) = 2.a.x^* + b \\rightarrow 2.a.x+b=0\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    " x^*=-b/2a\n",
    "\\end{equation}\n",
    "\n",
    "for the second derivative $f''(x)$\n",
    "\\begin{equation}\n",
    "f''(x^*) = 2.a >0 \\rightarrow a>0\n",
    "\\end{equation}\n",
    "\n",
    "The minimum function value $f^*$ is:\n",
    "\\begin{equation}\n",
    "f(x^*) = a.(\\frac{-b}{2a})^2 + b.\\frac{-b}{2a} + c\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "f(x^*) = \\frac{b^2}{4a} -\\frac{b^2}{2a} + c\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "f(x^*) = \\frac{-b^2}{4a}+ c\n",
    "\\end{equation}\n",
    "\n",
    "### 2.\n",
    "The gradient $\\nabla h(x): \\mathbb{R}^m \\rightarrow \\mathbb{R}^k$ due to the composition rule. Because:\n",
    "\\begin{equation}\n",
    "\\nabla h = A^T.\\nabla f(A.x)\n",
    "\\end{equation}\n",
    "\n",
    "Since $\\nabla f(A.x): \\mathbb{R}^m \\rightarrow \\mathbb{R}^m$ and $A^T\\ \\in \\mathbb{R}^{k\\ x\\ m}$ their product has to be a function $\\mathbb{R}^m \\rightarrow \\mathbb{R}^k$.\n",
    "\n",
    "### 3.\n",
    "The gradient of $f$ is:\n",
    "\\begin{equation}\n",
    "\\nabla f = 2.(x.c^T).c\n",
    "\\end{equation}\n",
    "And the Hessian is\n",
    "\\begin{equation}\n",
    "\\nabla^2 f = 2.c.c^T\n",
    "\\end{equation}\n",
    "\n",
    "### 4.\n",
    "\\begin{equation}\n",
    "\\nabla f = A^T.\\nabla_y g(Ax+b)\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "\\nabla^2_x f = A^{T}.\\nabla^2_y g(Ax+b).A\n",
    "\\end{equation}\n",
    "\n",
    "### 5.\n",
    "Given that $A\\succ 0 \\in \\mathbb{R}^{n \\times n}$ and $x,\\ b,\\ d \\in \\mathbb{R}^n$ we need to find the optimal $\\gamma^*$ so that:\n",
    "\\begin{equation}\n",
    "f(\\gamma)=(A(x+\\gamma d),x+\\gamma d)+(b, x+\\gamma d) \\rightarrow \\min_{f \\in \\mathbb{R}}\n",
    "\\end{equation}\n",
    "The optimal-step size method can be summed up as:\n",
    "\\begin{equation}\n",
    "x^{k+1}=x^k - \\gamma.\\nabla f^k\n",
    "\\end{equation}\n",
    "from our initial $f(\\gamma)$ we can assume a generic quadratic $f(x)$ as:\n",
    "\\begin{equation}\n",
    "f(x)=x^T A x+b^T x\n",
    "\\end{equation}\n",
    "the gradient of this function is:\n",
    "\\begin{equation}\n",
    "\\nabla f(x)= g = 2A x+ b\n",
    "\\end{equation}\n",
    "From now on, just for the sake of clarity, we will explicitly write the superscripts $k$ indicating the number of the iteration.\n",
    "Now, to find $\\gamma^*$ we need to find the optimal $f(x^{k+1})$ with respect to our step-size. Hence:\n",
    "\\begin{equation}\n",
    "0 = \\frac{\\partial f^{k+1}}{\\partial \\gamma}=\\frac{\\partial f(x^{k+1})}{\\partial \\gamma}\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "0 = \\frac{\\partial f(x^k - \\gamma^* g^k)}{\\partial \\gamma}\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "0 = \\frac{\\partial f(x^k - \\gamma^* (2A x^k+ b))}{\\partial \\gamma}\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "\\frac{\\partial}{\\partial \\gamma}(f(x^k - \\gamma^* g^k)) = \\frac{\\partial}{\\partial \\gamma}((x^k - \\gamma^* g^k)^T.A.(x^k - \\gamma^* g^k)+b^T.(x^k - \\gamma^* g^k))\n",
    "\\end{equation}\n",
    "\n",
    "Which, if we looks closely its actually an inner product with gradient in this iteration $g^k$\n",
    "\\begin{equation}\n",
    "0=(2A(x^k-\\gamma.g^k)+b,-g^k)\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "0=-(g^k,g^k)+\\gamma(2A.g^k,g^k)\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "(g^k,g^k)=\\gamma(2A.g^k,g^k)\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "\\gamma=\\frac{(g^k,g^k)}{(2A.g^k,g^k)}\n",
    "\\end{equation}\n",
    "\n",
    "### 6. \n",
    "The specified $f(x)$ can also be expressed as:\n",
    "\n",
    "\\begin{equation}\n",
    "f(x)=\\max\\{0,x^2-1\\}\n",
    "\\end{equation}\n",
    "\n",
    "Hence we can use 2 auxilliary functions $h$ and $g$, to derive the subgradients.\n",
    "\\begin{equation}\n",
    "h(x)=0 \n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "g(x)=x^2-1\n",
    "\\end{equation}\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "Hence we can see that the frontiers are at $x=1$ and $x=-1$, so the subgradients of $f$ come as:\n",
    "\\begin{equation}\n",
    "\\partial f(x) = 0, -1<x<1 \n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "\\partial f(x)=2x, -1\\geq x\\ \\vee\\ x\\geq 1\n",
    "\\end{equation}\n",
    "Finally we join both of them accordingly\n",
    "\\begin{equation}\n",
    "\\partial f(x)=\\text{conv} ({\\nabla h(x),\\nabla g(x)})\n",
    "\\end{equation}\n",
    "\n",
    "### 7. \n",
    "Our objective function is:\n",
    "\\begin{equation}\n",
    "f(x)=x^T Q x -x^T b\n",
    "\\end{equation}\n",
    "Whose gradient comes as:\n",
    "\\begin{equation}\n",
    "\\nabla f(x)=Q x - b\n",
    "\\end{equation}\n",
    "The gradient descent method is:\n",
    "\\begin{equation}\n",
    "x^{k+1}=x^k - \\gamma \\nabla f^k\n",
    "\\end{equation}\n",
    "\n",
    "We need to show that if for the first step we reach the minimum, so $\\nabla f(x^1)=0$:\n",
    "\\begin{equation}\n",
    "\\nabla f(x^1)=0=Q x^1 - b = Q.(x^0 - \\gamma \\nabla f^0) - b\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "\\nabla f(x^1)=0=Q x^1 - b = Q.(x^0 - \\gamma (Q.x^0-b)) - b\n",
    "\\end{equation}\n",
    "So, we take the left side and solve it in terms of x^0:\n",
    "\\begin{equation}\n",
    "0 = Q.(x^0 - \\gamma (Q.x^0-b)) - b\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "0 = (Q.x^0 - \\gamma Q.(Q.x^0-b)) - b = Q.x^0 - \\gamma Q.x^0 - Q \\gamma.b - b\n",
    "\\end{equation}\n",
    "\\begin{equation}\n",
    "0=(I-\\gamma.Q)(Q.x^0-b)\n",
    "\\end{equation}\n",
    "\n",
    "Hence, $g^0=Q.x^0-b$ is an eigenvector of $Q$.\n",
    "\n",
    "### 8. \n",
    "Find the minimizer of,\n",
    "\\begin{equation}\n",
    "f(x, y) = x^2 + xy + 10y^2 − 22y − 5x\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c8f27c39",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x,y): # Function for Q.8.\n",
    "    return x**2 + x*y + 10*y**2 - 22*y - 5*x;\n",
    "def gradF(x,y): # its gradient\n",
    "    return np.array([[2*x+y-5, x+5*y-22]]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "06977559",
   "metadata": {},
   "source": [
    "the contour and surface plots for $f(x,y)$ look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "33f805d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+erwDlX3B62c58/QZAEq6xHwhRjw/Syw/TSw/TTw/Qyw/w2hmmIvzL1OszGNMysK3tSx63e20ujpodXXQ4mrDYduOxJ6CIDzoaK3TSqnfB/6rtesu8IVVLqnmtzEF2ButeNB3WPtrrbXAOpIVUDdeeFhrvX+1a7TWnwE+o5TqB96CmbX4NdbhdwCrCdu1shpfWON4Nf8N04q9EuU3mOUcBLerRG010XWMq2WN44KwI4iwFQRBuI+xK3vFEnuQY8uOG9ogUZw3RW/OFL6zlgC+lxni/PyLlHSpcr5CEXZGaXV30OrqpM1tCt5Wqw06wphhdIIgCMuYqlpvrT1oxXv+n1W7Bqzt9bjw/gWm23InpkttK2YW4nqZl8v3nlxHv+tGKRUsJ1LSWt8DPqaU+p/AgnVKtQDMY7oWV7vI7F/jFtkNDOedVnsR+Lta63tKqZ8BfqPmvGnMkkQHlFKOOuWX4oCBme35L7XWtXG75dhpQdh1RNgKgiA8wNiUjbAzStgZZdB/ZNlxQxssFOLM5qeZzU1a7RSz+SmuJc7zQiy+5HyXzU2rq4M2d6e5uDor61FXG3YlZRYF4QFmGDPeswV4pM7x/xeIYArgLwHvAX5RKfV5rfVFgJXid62Mxx8Ffh54vXX861rregnkyvd+abXBaq3PrOdDVfF5pdR14E+svkvAj1cdv1a1PgIcAF6rlApiZnV+3wbvtxrlZAoFIKWUOkr9WOW/Av450AX8pvV8c5gxzue11peUUt/AjB3+IaXUP8F8ieAE3gD8a8y6xF9v4NgFYVOIsBUEQRBWxKZsRFxm5uWDgeUW37yRN628uUlm81PM5CaZyU0xnRvn6sI5ClWebTbstLjaaHN30u7usgRvF+3uLlpdHThs8pMkCPczWmutlPpbzHI1r60+ppT65yzGe/7vmILrTZgZfD+mlHpNHWtiLb+LGadrs7b/sPYEq/7rY9bmVzbzOVbBg5mc6V/UOZYCfqtq+88xrdEDmJZjF6YVt1H8L+CfYJb7KccU36pz3i9githeTLfpn6w69ozV/nvgG4Af07W71r37vzRmyIKwNWQW0YQY2iBvlEjrAtPZBfJGkZxRIF8qkjdK5I0CBaNE3iiSN4qV9YJRpKBLFIwSRaNUWS8YJUp6cV/RMMxtbVA0SpS0QUkbFK22vBjaoKQ1JV3C0NpcMPdprTGobg0MbVbm1Nb+8jqwdklyRaU+p83yaFEobMrcq5SNQi7P/+/sd7FZ+21KYcOGXSlsyoZNmev2yrq5OKrXbXZrnx2Hrbp14LDZcCo7Tpsdh9U6bY7FVtlxWesua7/b7sRps+OyOXFb+112B26bA4eyi0umcN/jsrno8vTSVSfBlWntnWMmN8FMfpLp3CSzObMdSt0gW5XRWaFocbVXRG+7u9tqu2h1t2NX8nMlCPcJv48pbN+glGrXWk8rpfowM+8CfF5r/SkApdRPYlpuTwI/h1nupuxGPMZi1l4AtNbDSqm/Av4+kMEUj7X8XUwBmmH1eNfN8EHgH2BajLsxrc9x4FvAr2itqy22vwy0YcbdKsyEV5dZ7iq8Wf41Zmzs3wWKmM/9OqabdgWt9ahS6ikW69j2YtaxfRmz7i1a65eVUqeA/4hZrqkFszbwVeCz1rmCsOsorddSHDvH0aNH9bVr19Y+cZcpaYNMKU+mmCddzJEu5c3tkrmdLRUq29lSnkypUGlzpTzZUoFsqUDOqGlLBXKWWG0ECmWKMmXHbok4Zx1hVxZ95jk27NY+myUSy+umoDRFY1lcKmv/YmveV1Wtl3M0rCTx9JL/mgK6el1j1v0cHR+jq6urIrBNsW0K7fL2oijXFfFeMowq8V4W9ta6Je6LRomi9SLAWFOFrw8byhK5Ttx2U/i67U48NiduuwOP3VU55rH2ex0us7W7cNvN1utw4bE78dndeO1OvHY3L3/3Rb7/jc/gtjlEPLP36thuN3vheWitSRUTTOcnmM5awjc7znR+kpncxJIavjbstLrbaXd30+Hupt3TRYe7mw53D2FndNW/AaXUS1rrp1Y8QRCEHUUpZcNMgvQw8O+01r+6wesvAw8B79Baf67mmB1TRD4N/KHW+j11rv8cZsmc39Za//TmPoUgCM3IA/UKvGiUSBaz5lLIkihmSRVzJItZUtb+VDFnLVnSxbzZWoI1VcyRLpnCdb0oFG67A6/dFCweS7i47U6CTi/tnhBumylsagXQ3dtDHD9yDJe9yhpYsRY6llgPXTY7Dpu9Ykk0hev9Fct2duYsZ06c2fb7lLRRZfUuVqzeBcO0mBeqLOU5y1JuWtWL5EuFynqusl4gVzK3s9Z61sgzm0suvuiwXm5kS4VFK/ca/PKXz2JXNjx2J367G6/Dhc/uxudw47O78Dnc+B3mtt9urvsdHqtduh5wePDaXSKShR1DKUXAGSLgDC2L7dVakywuMJ2bYDo3wVRunJncBFPZcW4kLlHQi956LpvbErnddHh6lrRStkgQmg+ttaGU+gDwGeDfKKV+Yx0uxgAopXowRe0n64jar2K6GLdiWij/W53rj7Jozf2VLX0QQRCajj0nbPNGkYV8mvlChoVCmkQxy0I+zUIxQ6KQYaGQIVHIkrC2ExURm1mXIHXZHEsm/j67i3Z3CJ/fhd8SDV67C7/VlrfLoqJsUfM6LKubzblpsXD2rubMwNObulbYPHZlw263gX3nS5porckbxSor/1LLf9lT4PzVS/QODljeAjnSxTzpUo5MMU+qlGMiO295E+RIF3Pk1uEFYEOZItfpJeDwEHC4CTq9+B0egg4PQaeHgMNL0Okh6PQSdHgIOb3Wuhe/wy3CWGgISimCzjBBZ5gDgaNLjhnaYL4QZyo7xlRunKncONPZcYbTt3hl7jtLXgxFnFKBQhCaEa31X7LOkjs1142tct1BzNI0t4APaK2XlcaxXIFttfsFQbg/aCphm6XInw59i7l8ivlC2lyqROx8Ib2qOFWoymQ8ZE3O9/vbCTgWJ+IBh4eA02zLlqrqbackLxF2EaWUabW3OwHfiucFbyY4c/DMuvstGqVFb4TSomdCslD2VljquZAsmO1YJk6qyrthNWuyDVX52ysL3pDTS9jps/b5Kuthl69q24NNyTxDWB82ZSPqaiXqauUoJ5YcKxh5pnOTlugdYzI7tkujFARhp1mrvqwgCPc/TaXiUjrPr179X9hQlclv2OmjyxPmSLDbmgwvnyyXJ9EBh1smyIJQB4fNbv49uVYWy2thaINUMUeikCVZLHtHmF4RZW+J8r4F6/hIerbiRbGSKFblv3enj4j1Nx9x+Qm7fEScfiIuH1GXn7DTT9RlLmIdFurhtLno8fbT4+2v7HsPP7OLIxIEQRAEYadoKmEbVV6+/OYPEhQLjiA0HTZlMz0fnF5Mb6/1U9IGyUKW+UKahUKmyhsjvWR9Lp9iPDvHtYUx5grpFROpOZSdqMtPxOWnxeUnl0/y8pUULS4/UXfAbF0BWlwBWtx+PHZX3X4EQVgXzZNlUhAEQbgf2BbrRFMJWxtqSxYlQRCaE7uybdhirLUmU8oTt0IT4vkUc9YSr1rm8inG9DzXR14kXapfAtBnd9HiLgtds211ByttqztAq8ts3bsQWy0IgiAIgiBsjaYStoIgCGWUUmaGZ4ebXlZPAlQub5MtFYjnk8TzKWZzSeL5JLFcklg+RSyfIJZLMpya4ZXYEPOFdN2+gg6PJXaDtFW15aXdHaLVE8RvF3doQRAEQRCEZkGErSAI9w0eu5Nub5Ru79qu0kWjRCyfZDaXZDaXYDZvtZUlycW5e8zkEuSM5UnrvHZXRei2e0KVts0dpMMTtraDkpBOEARBEARhB5AZlyAIDyQOm50OT5gOT3jV87TWpIo5pnMLzOQSzFjtdNZcn84tcGHuLjO5RN2Y4BaXn3ZPmA53yBS8nhCd1n07PGE6PSGJARYEQRAEQdgiImwFQRBWQSlllgRzehgMdKx4ntaa+ULGFLvZBaZyC0xl55nOmuJ3PDvHublhFgqZZdeGnF46PRE6PWE6PWG6vIvrnZ4IHZ4QDpt9Oz+mIAiCIAjCnkaErSAIQgNQShFxmSWLDgW7VjwvWyowlZ23lgUms/NMZucq6+friF+Fot0dpNMbodsTMVtvhC5PhC6vuQQcnu3+iIIgCIIgCE2LCFtBEIQdxGN3MuBvY8DftuI5mWKeyewcE9l5JrPzTGTiTGTmmcjOcXlhhK9NXqKgS0uuCTm9dHkidHujlApJxofMeOMeawk4RfgKgiAIgnD/IsJWEAShyfA6XOwPdLB/BddnQxvEcknGs3NMZOYYz8wxnokzkZ3jbnqG0dIsz129u+SaoMNDj6+lInR7vNHKdrc3ikfKHAmCIAiCsIcRYSsIgrDHsCkbbZ4QbZ4QJyIDy45/7Wtf44nXn2YsE2csE2fcWsbSce4kp/j29DVyNYmu2t0henxRer0t9Ppa6PW20OdrocfXQqsrIKWNBEEQBEFoakTYCoIg3GeY8b5+Ii4/D4f7lh3XWjObSzCWiTOaiTGWNtvRdIzvxW7zxbFX0ejK+V67qyJ4+32tS9oubwS7su3kxxMEQRAEQViGCFtBEIQHDKVUxeL7aHTfsuO5UoHxTJzRTJyR9Cyj6Rgj6Rh3U9M8P3N9SVkjh7LT64vS52ulv7z42+j3tYroFQRBEARhxxBhKwiCICzBbXeuGONraIPp7AIj6Rj30rOMWMvd9Cwvx+6QKeUr5zqUnT7Lujtgid1y4qx2d0jcmwVBEARBaBgibAVBEIR1Y1M2Or1myaGTrQeWHNNaM5NLcC89ay6pGe6mZ7iXmuWF2ZtL4nq9dpcpcn2t7PO3M+Bvq7R+h3unP5YgCIIgCHscEbaCIAhCQ1BK0e4J0e4J8WTL4JJjhjaYyi5w1xK7w6lp7qZmuTw/ylcnLmJUxfS2u0MM+NvY729nv7+dfQGz7fCEsIlrsyAIgiAIdRBhe59jaE2+VCRXKpGravNGiXypRMFq86UiecOgYJj7CqUSBWu7aBgUDIOiUaKgDUqGQdEwKJbXtUHJ0JS0QUlrDKstGQaG1hhaU9Iaja5sa0zrjkajNZUWWJK0ppr5uTl+90sTACgUNsuNUSmFDYVNgU0plFLYlQ2bMs+xV23blcJus+FQNmzKhsOmcNjsOJQNu03htNlx2Gw4bDacylx32u24bDYcNjtOm7nusjtwWq3Lbsdls+O22611B267Hbfdgd0mk3BBANPS2+WN0OWNcJpDS47ljSL3UrPcTU0znJphKDXN3dQMfz1+jmQxWznPY3daYreDfYE2Bv0d7A+00+9rxWmTnzNBEARBeJCRmcAuorUmUyyQKhZIF/JL2kyhwEuJGUauvkKmWCBdLJAuFMiWimSKBWspki0VyBaLZEvFxbZUJFcskCuVyBulho+7LA6dyobdZsNutY4aAWmz2cwWc90GFbGJJUwVpjCtbleipDUFw7AEMZZAXhTGZdG8dLFEdo3gLlavW9uGri+ot4JD2Soi12134HEsth67A4/dicfhwOsw170OB16HE6/D3O+z1r0OJ77y4nQxWcgylU7id7rwOpwVkS8IexGXzcHBYCcHg51L9mutmc0nGU5OM5SaZjg1zZ3kNK/Gh/jS+KuV8+zKRr+vlcFAh7n4zXafv22HP4kgCIIgCLuFCNtNoLUmXSywkM+xkM+SyOdI5HMsFHLWep5kIUeykCeRN9tkIUeqkCdZyJMqL8XC2mJq5nZl1WWzWyLHYQkfJx67KYpCLndle6mIWhRVpkXR2mczLY1Om31J67LZcVpWSqfNZlkwzXWHZencrYQvZ8+e5cyZM9vWv6G1KXIN01pd1OZ6vrRoua62dC9au0vkjOLiumURzy2xlJsvHnKlxZcQuVKRWC5NJmW+nMiUimStlxal9YjsPztfWS0LXr/Did/pIuB04beWQFUbdLoJuFwEnO7KdtBVXlz4HS5J6CM0DUop2txB2tzBZfG86WLOsu5OcSc5xZ3kNLcSk3xj6golbQBgW/VVmSAIgiAI9xMPtLDNFgvEc1nmchniuQzzuSzz+SxzOXOZz2VZyJv7zPVcRcyuJTzsSuF3ugi63AQcLgIuNxG3l75AeIng8Dms1unE7zDbski58NLLPPP6N1Qsdg5xa91WbEqZ4t5u3+2hkC+VKpb5dFWbLlvzL5xn4PDBpZb+QoFUMU/aeoEyk0kxvBAnYb1ISRcLa95XQUXohlwegk4XIZeHkLUddluttW62nkrrdTi3/+EIAuBzuHko3MtD4d4l+/NGkbupGUvsTvFd/usujVAQBEEQhJ3kvhG2+VKJeC7NbDZDLJtmNpsmns0Qy2XMNpsmnsuYQjZrCtlsqbhif06bjbDLQ8iatLd6/AyGW8x9Ljeh6sm/y03QWd5nWsG8DueWLV9TTg8dvsCW+hD2JmWBHXZ76h73DI1x5tgTG+qzZBikigWS+UVvgkSVZ0F5e6HsgWC9xBlJzlvbWRKF/Kr3cNntRFweIm4vEbcpdiNuL9FKay4Rj6eyHvV4cdp2/2WCcH/gsjk4FOziULALgJ/c5fEIgiAIgrAzNK2w1VpXrE7TmRQz2TSzmTTT2RQzmRSzGVO8lpeFfK5uPwoIuz20uL1EPT56/UGOt3RYk+vFCXek3FqWJ18DhKkgNBN2m63yUmazlAyDRCFX8WAoeziUvR3mLQ+IuVyWuXyWe4l5LsxMEM9lya3yIinoclt/o15a3F5aPD5aPOXWR5vVtnq8tHp8+JyuTX8GQRAEQRAE4f6jqYTtXKnAj37hj5i2xGw9i6oCom4vbV4/rR4fD7d0VNZbrElv9aQ44vJIZlpBaBB2m816EeTd8LWZYoG45S0xl8sSy6bNNrfUu2IyneRKbJrZXJp8qX7yM6/DSavHR6vHR5vXRyG+wIsv2axtP21eHx3eAG1eH2GXR15SCYIgCIIg3Oc0lbDVaDwOByc7emnz+mj3+mm3JqdtXn/FaiOxpoKw9/A6nHgDTnoCoXWdr7UmVcwTy2aYzabNEIOMGW4wm00xm00zk0kzlkownpnjWxe+Wzf23WmzWd8lNYsvQIc3QIfPT4c3QLvX3xTx1YIgCIIgCMLGaSphG7W7+JO3vXu3hyEIQhOglLKyN7sZCEZWPffs2bO88U1vYi6XYSaTNkMYsqbnx3TaDGWYzqQYTSV4dXqc2Wy6brXkFreXDl+ADl+ATl+ATq/V+gJ0+c22zeMXLxBBEARBEIQmo6mErSAIwmaxKVWJyT0SXb1+adEwmM2mmEqnmMokK+1kenH9Wnya6UxqWUkuu1K0e/10+YN0+cyl2x+gyx+k2xek2x+k0xcU668gCIIgCMIOIsJWEIQHDofNRqfPFKCrUTIMZrIpJtNJJlJJJjNJJlNJxtMJJtMJbs7N8tzYEMk62aLbvH56KmI3RI8/SE8gRLc/SK8/RLtXLL+CIAiCIAiNQoStIAjCCtirBPCjqxiBE/kcE+kE46kEE6kEY6kEE2mzvb0Q41vjw8vEr0PZ6PIH6Q2E6PWHzDYQotcfpjcQoscfwuOQr2hBEARBEIT1ILMmQRCELRK06lofjqysfhfyOcaSC4ylFhhNLVTWx1IJvjNxl4l0cpnbc7vXT28gRF8gbC0h+oMR+iwBLMJXEARBEATBRGZFgiAIO0DI5SbU0s6xlva6x4uGwUQ6wWhygZHkPKPJBUaT84wkF7gwM8FfD1+nYBhLrun0BegPhOkPhukPRugPhBkIRogV8xhaY5MyR4IgCIIgPCCIsBUEQWgCHDZbxTL7NP3LjpcMg6lMinuJOUaSC9xLznEvMc+95DwvTIzw2dtXllh83/+HF+gLhNkXjDBgLfuCEfaHovQFxNorCIIgCML9hcxsBEEQ9gB2m41uv5l1+XSd4/lSidGkKXS/8tKLeLrbuZuY525ijhcnR5bE+CqgyxdkX8gUuvuCUfZX1iP4nK4d+1yCIAiCIAiNQIStIAjCfYDLbmcw3MJguAXjxjBnTp2pHNNaE8tlGF6Y424iznBijuGFOYYW4nz57k1ms+klfXX6AuwPRRkMRa22hQPhKP2BiFh6BUHYFQzDIJfL4XQ6sdvtKAm1EAShBpmhCIIg3OcopWj1+Gj1+Hiyo2fZ8UQ+x/BCnDsLpui9sxCvK3oV0BsIcyDcwoFQlAPhFkv0ttDtD0pMryAIDUdrTbFYpFAokMvlyOVyANjtdpxOJw6HQ4SuIAiACFtBEIQHnqDLzSNtXTzS1rXs2Hwuy9BCnDsLMW4vxLkzH+POQpyXJkdIFQuV87wOJ4OW2D0YbuFguJWDYVP0eh3Onfw4giDcJxiGQaFQwDAMlFIVAau1xjAMMplMRdCK0BUEQYStIAiCsCJht4fH2rt5rL17yX6tNVOZJLfmY9yuLHHOTY/zv+5cpZzGSgE9gRCHwq0cirQuaaMe745/HkEQmh+tNaVSiULBfHlWFrNllFIopbDZbJXzRegKgiDCVhAEQdgwSik6fUE6fUFe171vybFsscjQQpyb87Pcmp/l1nyMm3OzfHfiHtlSsXJem8dnitxIK4fDbRyOtnI40kabxyeTUEF4QNFaUygUKJVKFQFb3r8SqwndkZEROjs78fl8OBwOEbqCcB8jwlYQBEFoKB6Hg2N1avYaWjOanOfm3Cw352e5MWcun719hUQ+Vzkv6vZyONLKkWgbRyJtHI60cTTaRovHt9MfRRCEHcQwDPL5PFrrJaK2THn/WlQL3WQySXt7O6VSiWJx8cWaw+GoWHRtNpsIXUG4DxBhKwiCIOwINqXoD0boD0Z4pv9gZb/Wmsl00hK6M9yYm+F6HcHb5vVzJNLK0Wg7R6NtHI22cyTShl/KEwnCnkZrTSaToVQq4XQ6K5bXWjYrPqutueX7VQtdpVTFmitCVxD2LiJsBUEQhF1FKUWXP0iXP8j39e6v7C8L3mtzM1yPT3N9bpZr8Wk+ef08marEVQPBCEejbRyLtnMs2s7RaDuDoSj2FSbHgiA0D1pr8vk8t2/fJhQK0dnZWfe8rYjaWjfmWmtwdebl8nERuoKw9xBhK6yK1pp8qUSuWCRXNNt8sWQupRL5UpFCySBfLFEomfsKJYOCUaJYMiiUShQNg0LJoGQYFK2lZBiUDE3RMDC01RoGJa3NN6mGxrDWDWuZmprmf04n0Bo0mvLvlKbmBwvzx0cpc91srTe21lK9brMp7NbbXLtS2G027DaFXdlwWOsOux2HTeGw2XHYzf1Oux1nubWXWzsuh7ntstvNxeHA7Vi67rTbd/hfUhD2HtWC9029g5X9htbcTcxxLW4K3qvW8tV7tzCsLwa33cHRaNtuDV0QhHVQ63q8WhztdiJCVxDuD0TY3gfki0WS+QKpXJ50vkAqb7Zpq00VCmSs7UyhSKZQsBZzPVsoWkuBbLFItlgkV7DaYqnh47VZ4tFhs0RklZi0KVtFbFZEKGabyWRJzMZN2apURawClH9eyj+JWlty12pNgYw16dWU9KJwNkW0URHTpsjWiwJ8G35obUrhcThwOex4nA48Dgduh8NcdzrxWOtea9vndFrbTnwuJ8MTs6QvXcPvcuFzOa3FXPdb61JTVLhfsSnF/lCU/aEoP7jvcGV/tljk5twMV8piNza9i6MUBGElysKxWCxW3IRtNtu2CNvNCOZ6QrdQKCwTuk6nE7vdLkJXEJoEEba7TL5UYiGTZT6bI5HNsVBuc1nO3Zvkpa8+RyKXI5nLk8zlSOTylfVkLk8qX6BQWr/49DgceF2LQqkslkJeN53BAG5LZHmcpmXR7VgUXS6HaY102831suXRVbZS2pZaLh32Raumw27DbrPh3MKX/9mzZzlz5symrt0KWpdFrqZomBZp0wq9aJUulAzyhmW1LlrbpRL5YtFqLWt3qVSxfJet4NmCuV5uM4UCM9mc+ZKhUCRdKJC1XkRU84kbd1cdt8/pxO924ne5zMXtIlBZ3ARc1rrHTdDtIuh2E/S4CLo9BD0uQh43fpdLfqyFPYPH4VhWj/dPePcujkgQhFrKrsfl2rSVF9S7aLFdi3IN3TL1hG45EZXD4aib+EoQhO1HhG2DKBoG85ks8XSGeDrDXCbLXCZDPG2285kc85ks89ksc5ks85ksC9nsMrFSi+PuBAG3i6DHTdDtJuB20R0KEnC3VkRKWbSYAsa01vndTvxO04LntSx6XqdTrHibQClliXXYzT8ZrTXZYpFMvsDffvObPPrkSTKFgmWlr7LQV7Up60VIytoem09UXookc3mKhrHqPW1KEXS7CHk9hNxuQl43IY+HsMdqvR7CXjdhaz3i9RDxegl7PXidDvlhFwRBEID6tWmrfyPWI2zXmxW5mu0QzPWEbj6fJ5czk93ZbDacTmfFoitCVxB2BhG2K1AyDOLpDLOpDLOplNmm08StNpbKEEunK0J2PptbsS+X3V6Z9Ie9HvojYR7p7iRcIxJCHjdBj7vSnnvhBX7gzc/Il6EAmD+kXqf5gqLN4+ZIx9biB7XW5IolkjnTUyCZy5OorJvtQpUngblkmVyYZSFrehms5i3gstuJ+EyhG/V5iXg9RH1eol4vUZ+53uLzEfV5aPH5aPF7cTvkK0kQBOF+o9b1uN68Zj0CtFnnQ9VCt/wZ8vk8c3NzxGIxBgYGlrkuC4LQeB6oWaTWmlQ+z1QixXRy6TKTTDOTKremYDXqfMHalTIn5H4fLT4vD3V10OIzJ+7Vk/aI11uZ1G/WcuWyS8yGsH0opSru6G0B/4av11qTKRRZqPJCmM9kLW8F01NhLpNlLp0lnslwY2qWeCbDfCZb928LwOdy0mr9bbX4fLT6fbT6zb+3Nr+53eb30RrwE/F6xANBEAShyTEMg0KhsMz1uJbtckXeaRfn8ucrC91UKgWYQjefzwOmRVeEriA0nvtG2OZLJaYTKSYSCSYXkkwlUkwmkkwlkmabTDGVSNZ1/XXZ7bQFfLT5/fRGQjzW20Wr309boDyx9tFqidmwTKYFATB/vMuJq7pCwXVfZ2hdcduPpTPMWW0snWE2lTbXU2nG5he4OD5JPJ2p6zLtsNlo8Xtp8/ux5bL89UKe9oCP9oCftoCf9oCfjoCf9qAfr9PZyI8uCIIgrEGt6/Fa4u1+Ebb17r+SRVeEriA0lj0hbEuGwXQyxdh8gomFRKUdX0gwsZBkYiHBbCpN7deW22GnIxigMxjgeFcHzxw+QHt5whv0V9ZDHrdYRgVhh7BZXg9Rn5cD6zi/LIRnU+nKMpNKM5NMWW2aO8kEz90eYjaZrpvFOuh2V/7uO4J+OgIBOkMBOgJ+OkPmd0R7wC9lmARBEBpAOblSqVRad3ypUgpjjbwP9wO1Fl1tVWioFbrlZFQidAVh/TSVsM0ZBp9+5SKjcwuMzZeXBJOJ5DKLjd/lojsUoCsc5FhnO12hAF2hAJ3BIJ1Bc9IaFsEqCHueaiF8qL217jnljNmG1sTTmaWhBokUU8kU05bnxkt3x5hKppbFByug1e+rCN2uUJCuchsK0G21LokDFgRBWJHa2rTrnYfdrxbbtahXWkhrTS6XW5aMqjrrsiAIy2mqGdpCvsAHv/BlbErRGQzQEw7yZH8PPeEg3eEgPeEQ3aEg3aEgQY97t4crCEKTYVOqEj5wrLN9xfO0JYDLIQvVy8RCkpH4PN+7O8pCnaRwrX4fXaEAPaEQXWGzNb+fzO+mtoBfwhUEQXjgqFebdiM0uwDdKdYjdO12+xKLrghdQTBpKmEbdbn46v/+z+gMBsQlUBCEbUMpZSaA8/s41rWyAE7nC0wsmF4j4wsJxithEEnuzMb49p27pCzXsTJOu50eS+j2hEP0lpeIuXQGA9jFrUwQhPuIlWrTboTtEmd7XTDXE7qGYZDNZiv7ROgKgklTCVuHTdEXCe/2MARBEAAzS/OBthYOtLWseM58Jsv4QoKx+QXG5xOMWiEUY/MLfOPmHaaT6SXnO2w2usNBesMh+iJh+iJm2x8111v9PpmUCIKwZyhbaTfqelzLgxJju1VE6ArCyjSVsBUEQdhrhK361Cu5PueKRcbmE4zOLTA6P8/o3AIjcwuMzi1w9sZtZlJLha/X6aA/EqYvaordgWik0vZGQrjEm0UQhCZAa00ikahk9N1qgiOx2G6OlYRuJpMhk8mQTCbp7u4WoSs8EIiwFQRB2EbcDgeDrVEGW6N1j2cKBUbnFrgXn2dkbp57c/Pci5vL83fuLilRZlOK7nCQAUvo7muJsM9q+6MRPE75ShcEYfsp16a9du0a+/fvJxQKbblPsdg2hrLQtdlsFItFkslkRehWZ2QWoSvcj8gsSBAEYRfxOp0cam+tm/FZa810MsXd+Dz34nPcjc+bS2yOv75yg7nMouuZArpCQfa1RHBlM9zxvMT+lij7W6P0RUKSt0AQhC1TrzZto6yhYrFtPGX3cJvNVrGoV1t0y8+8nG1ZhK6w1xFhKwiC0KQopegIBugIBnhqoHfZ8flMluH4HMOzc2YbizMcm+P8TJxvfPkblfMcNht9kZBlOW5hf2uEA60tDLZGJaZXEIR1Ua82baNFo1hst59qiy4sfVlRLXTLFl2bzSa/EcKeYcvCVinVD3wC6AIM4He11v9DKdUC/BmwHxgCntVax7d6P0EQBMEk7PXwqLeLR3u6luw/e/Ysj51+mqFYnKHZOEOzc9yZjXEnNse379wlV1ys4RvyuBlsjXKgtaWSKOtgWwv90TAOyd4sCAIr16ZtpMV2qzG6KyEW29VF6UpCt1gsVo5Xuy6L0BWamUZYbIvAv9dav6yUCgIvKaW+DLwP+KrW+sNKqfcD7wd+tgH3EwRBENYg6vMS9Xl5oq9nyX5Da8bmF7gzG+fObJzbMzFuz8Z57vYwnzl/uXKe02Zjf2u0InQPtbVysN208rod4uwjCA8Ca9WmbXRcrFhsd596yahqhW6167IIXaGZ2PLsRGs9Doxb6wml1BWgF3gHcMY67ePAWUTYCoIg7Co2pawyQ2G+7+D+JccS2Ry3Z2PcnolxaybGzekYVyen+fLVmxiWxcOmFAPRCIfaWzjU3sphKz74QGsUlwheQbhvWE9t2kZaQ9ey2E5NTXHz5k2CwSDRaJRoNIrL5VqzX7HYbk101hO6xWKxEmctQldoJho6C1FK7QeeAL4LdFqiF631uFKqY4VrfgL4CYD29nbOnj3byCHtaZLJpDyPKuR5LCLPYinyPJay1ecRBZ6yw1NdYegKUzAMJjM5xlNZxtNZxtIZLtwd4W+v3aJsX7EBnV4P3X4PPT4PvX4vvT4P7V43NpnkCMKeohxzuVZtWpvN1lAraz0BahgG169fJ5VKceLECbLZLPF4nNHRUUqlEpFIhGg0SiQSwSEv17adekK3UCgsE7pOpxO73S5CV9hRGvYNoJQKAP8T+Dda64X1/k+stf5d4HcBjh49qs+cOdOoIe15zp49izyPReR5LCLPYinyPJayU88jXyxyZ3aOG9Mz3Jie5cbULDemZ3jl7gTl6anH4eBgewtHO9o52tHG0c42jna00eL3bfv4BEHYGGu5HtfSaIttbV/pdJoLFy7Q0dHBkSNHKBaLeDweIpEIg4ODlEol5ufnicViDA0NoZSqCN1wOFzJ8CsW2+2jHINbfc9qoTs7O0t3d3cl47IIXWE7aYiwVUo5MUXtH2ut/8LaPamU6rastd3AVCPuJQiCIDQHLofDFKqdbUv2ZwoFbk7Pcm1qhhtTs1yfmuHrN+/wF+cuVc5pD/hMsdvZxrHOdo51tjPYGpWyRIKwS5Rr067melxLo0VjdV+Tk5PcvHmT48ePE4lE6t7HbrfT0tJCS0sLAIVCgbm5OWZmZrh169YSC65hGNuWoEpYpFboDg0N0draSi6XA8wXGOVEVA6HY93/rwnCemhEVmQFfBS4orX+71WHPge8F/iw1X52q/cSBEEQmh+v08mJni5O1GRrnk2luTY5zbWpGa5NznB1cppPvPAqhZKZpdlpt3OkvZWjne081NXOw12m4A243bvxMQThgaC2Nu1GhEYjXZHLFlvDMLh27RqZTIbTp0/jdDrX3YfT6aS9vZ329nYA8vk8169fJxaLMTU1hdvtrsTnBgKB+15Q7YTFdi3qWXTz+Ty5XK7iFVDtuixCV9gKjbDYvh74J8AFpdSr1r6fxxS0n1JK/XPgLvDOBtxLEARB2KO0+n287sA+XndgX2VfoVTizmycq5PTXJmc5trkNGdv3F5i3R2Ihnmoq4OHuzp4qKud410dtAX8u/ERBOG+otb1eKOCotEW20KhwAsvvEBXVxfHjh3bssBxuVyEQiFcLhddXV1kMhni8Th3794llUrh8/kqQtfr9Yqg2gGqhW75/518Pk8+nwdYJnTFyi5shEZkRX4OWOmb4C1b7V8QBEG4f3Ha7RzpaONIRxtvP/EQYE52ppIprk5Mc3liiisTU1yemOKvr9yoXNcR9HPcErvHuzt5pLuTjqBfJqaCsE5Wqk27ERopbGdnZ4nFYpw6dYpwOFz3nK1aIL1eL16vl56eHrTWpNNp4vE4t27dIpPJEAgEKkLX4/Fs+j7NQjNYbFejPDYRukKjkPRxgiAIQlOhlKIzGKAzGOBNhwcr+xPZHFcmp7k8PsWliUkuj0/x9ZtDlVJEbX6fJXJNsXuip3O3PoIgNC3VrsfrSRC1Go2oY1sqlbh27RqpVIqWlpYVRe1mWUl8K6Xw+/34/X76+vrQWpNIJIjH41y9epV8Pk84HK5kXF5PaSFha9QTumXX5WqhW47RFaEr1CLCVhAEQdgTBD1uTu/r4/S+vsq+dL7A1clpLo1Pcml8iovjk3zz1qLYFQRhkfXUpt0INpuNkhUjvxlSqRQXLlygu7ubffv2cf369S2NZysopQiFQoRCIfbt24dhGCwsLBCPxxkZGdmTpYWa3WK7FvVKC2mtyeVydZNRidAVmv+vUhAEQRBWwOdy8mR/D0/291T2pfMFrkxOcXFskvf9p10cnCA0EYZhMDU1xczMDIcOHWqI4NmKK/L4+Dh37tzh+PHjhMNhMpnMuvraqFjb7BhtNhuRSGRJaaG5uTni8fiKpYWE7WUtoau1XuK2XM66LDw4iLAV9hwlw6BUMigZmqK1bhiakrZaw8yqaOjFL72y9cbcXrlvpRa/OBVgs5nrNqWw2RR2mw2lwGGzYbPZsNsUdrsNh82G3WbDZpMvUEHYbXwuJyf7eznZ38v7dnswgrDLVCeIAiouyI1gM6KxVCpx9epVCoUCp06dqmQ9Xquv8m/zbtWktdvttLa20traCtQvLVSOzw0Gg01hOdzrFtu1qCd0DcMgm81W9pWtuG63u5J1Wbh/EWErbArD0GTzBdI5c8nmC2RyBTJWm80XyebNNlcokskXyBWK5Aol8oUi2UKRvLVdKJbIFxfbfLFEsViiUCpRKBoUiiWKhkG+UMT41CurCtPdxqYUDrutsjgddrO123E47LisxVnVup12XA4HbqcDl9OO2+lYXFwOPC4HHqfVupx4XU7uzqa4PT5rbrud+NxOXA75whYEQRAWqXU9bmR5Hth4uZ9UKsX58+fp7e2lv79/yW/WdonW7eq3trRQLpcjHo8zNjZGIpHA7Xbj8/koFAr3vcBsFlYSui+88AInT54ETKFb7bos/y73FyJsHzC01uQKJRLpLIlMjkQ6V2mTmRzJbI5kJm8u2RypTJ50ztxO5/Kks3lSOVO8bpSKgHM5cDvsuF0OXA5TzLkcdjw+d0X4ORx2nHY7ToclCu02xkZHODA4iMNuWkftdrXEUmq3mT/aNpvCrhTKZlpaFWaLsiyyKOp9j2kNGtOiW7bsGlUWX8Mw21LJoGR9WZYMc7tsOS5a60VrvVAsmW3JFO7VIj6TLzCfypIvFskXSuQKRfLFErl8kVyxuKaA/7WvLI1FstsUXpcTn8eFz13Vul34vS785dbjIuBxEfC6zXWvm4DXRdDrttbdOOy7/6ZZEARB2Bwr1aZttLDdiGgcGxtjaGiIRx55hFAotKW+mhG3201XVxddXWb97kwmw/j4OMlkkhdeeAG/37/jpYUedEFd8cCzSgytZNEVoXv/IMJ2D1MsGcynMsQTGeZSGeaTWeJWO5/KMJ/OMp/MspC2llSWhXSOfHH1RA8Om42AJYD8lvhpC/vxuSP4Pa4lgsnnNi2GlcXlxONyWK25bgpZx5bddM+ePcuZM6/bUh97Ba01haIpdrP5Ipmy5duyjr/40iscOnrMtJBnTUt5Olcgk8tXrOjpbJ5UNs9EPEF6PE/S2i6s8e8P4HM7CfrcBH0eQj43Qa+bkN9DyOch7PMQ8le1fjdhv5ew34Pf45IfBUEQhF1ktdq0NputoeJxPf2VSiWuXLlCqVTi9OnTKyZd2k6LbSPF/Hrxer20t7eTy+U4duxYpbTQzZs3yWaz911poXo0w4uK6jGsZNHNZDJLMjKL0N27iLBtIrTWpLJ5ZhfSzC6kOHcvzuTZV4kl0taSIZ5IE09kiCfTLKRzK/blcTkI+z2E/V5CPg+DXS2EfB6CPjehiljxEPS7CXjcpojxuvF7XXicEmy/2yilcDkduJwOgr7lx9MTtznz1NFN9Z0vFEllTaGbzJQt9KbFfokVv7yezjE2u8DVe1MspHOrWusddhsRv4dIwEvY7yUa9BKpaluCPiJBL9GAtR7winVYEAShQRiGQaFQWDHrcaNF3lr9JZNJLly4QF9fH319favOLfa6xbYe5c+7W6WFdttiu9v3X2sM1Z4M5XNrha7D4agsInSbHxG2O4DWmmQmx9Rckun5FNPldj7FzHySmfkUswtpZuZTZAvFmquHUIqKOGgJ+jjS3040YIqDSGBRNESs7bDfg9sp/7RCfcqCOVpPMa+DQrHEQjrLfMpcFlJZ5lKml8BcMsN8KstcMkM8meHm2Ky1L1PXtVopCPs8tIR8tATNpTXkozXkpyXkoy3kpzXkoy3sJxrwiQgWBEGoQ63r8UqJi3bSFXl0dJTh4WFOnDhBMBjcUl9boRkF81qlhQzDWCJ0N1taaLeF5W7ff6NjqCd0q2s+A5Wsyw6HA5vNtuufT1iKqJ8torUmkc4xEU8wEU8wGTPbqbkkk/EkU3PmejZfK1gh4HXTFvbTFvJzYrC7MqFvDftoDfq5c/0yb33mjWLVEpoKp8Nu/n8a8q/7mpJhsJDKEk+arvOxRJp40mxjC+mKV8KVu1PEEmlS2fyyPpSClqApdtvCftrDAav1Mzk6R8fwBO3hAC0hH/YmyEYpCIKwE2itKRQKlEqlNWvTbocrcq1QLpVKXL58Ga31qq7HtTSjAN0p1lNaqOy2HAqFNlRa6EEXtoZhbDpD9UpCt1gsVj6bCN3mQoTtGhiGZjaRYmx2gfHZBcZjC4zNLjARSzAeM9t0jWumw2ajLeKnMxLgaF8733fiAB2RAB3hAG0Rc0LeHvHjdTlXvXdu6g5t4fWLB0FoVuw2G9Ggz7QSd699fiZfILaQZmbB9GaYnU8xs5BipuLpkOLavSliiUyllNPvP3fHupeiNeQ3/+YiATqjAToiQbqiQTqiATqjQdojfpxSc1AQhD2OYRjk8/nKJHutSfV2W2zLrsf9/f309vbuSL3Z3ep3O1mptND09DQ3b95cd2mh3RaWu31/2JqwraVejG5Z6JaPV7sui9DdeUTYAulsnpGZeUZm5hmdmWdkep6xWXN9PLZArrA02U7E76GrJcS+jihPH9tHV4s5ae6MBulqCdIqFiNB2BJel5PetjC9beFVzyuWDOKJNF/622/Qf/AoU3NJ0+Xfam9PxPjOleFlL5+UgraQn85okO7WEF3RIN0tQbpaQnS3BOluCRH0ueUHSRCEpqQ2QdR6J+7bEWNbFo0jIyPcvXt33a7H9fq6H2mEqF5PaaGWlhai0Sh+v79pnmUzCNvtHEM9oVssFpdkIxehu7M8MMI2mclxd2qOe1Nz3Jue4+5UnJGZee5NzzG7kF5ybsDrpq8tzIHuVr7vxAF6WkOVpbslhM/TmKB+QRC2hsNuoz0SoL/Fx5nHDq54XjKTYzKeYHIuWQkXKIcOXLs3xTfO31r2AsvvcZkitzVET2vY/A5oCdHTFqK3NUzIf39msRQEobmprU27kYnydrgiF4tFzp8/D7Ah1+OdYi9abNeiXmmheDzO8PAwyWSyUlool8vt6r9HMwjbRlps16Ke0C0UChQKBaanpwkEAoRCIZxOJ3a7XYTuNtBc3z5bpFgyGJud585EjOHJuLlMxbk7GWemRrx2RAL0t0d4wyOD9LdH6GsP09cWpq8tIhNWQbjPKNfnPdjTVve41pp4IlMJLyiHHJTbV26MkqyJ+w143fS2hiqW5b62ML3t5ndId2tQXJ0FQWg4ZSvtel2Pa2m0yEun08zOznL06FH6+voa1m8juR+FbS1erxev10tPTw9aa9LpNLFYjNnZWSYnJ4nH40SjUVpaWnC73Ts2rmYRtrs1hnL9XID5+Xk8Hk9F6JaPV5cWEqG7dfaksM3miwxPxrg9HuPORIzb47MMTca4OzVHsbToYhMNeNnXGeV1xwfZ1xlhoCPKQEeUvvbwmvGtgiA8OCilzMzMIR/H93fVPWchlWUstsDozDxjs4vt7YkYz128s6Q+tE0puluC9LVHKi/O+tsjDHRE6G2L4HHtya9eQRB2ic26Hm/neEZHRxkaGiIcDu+YqH0QROpWqS4tZBgGbrcbn89HPB7nypUrS0oLRaNRnM7tmw83g7DVWu/63wuYSdXKArZM2fsilzPLd9pstorQdTgcm3p59aDT1LOrQrHE0GScW2Mz3Byb5fb4LLfGZhmZmauUDrHbFH1tEfZ3RXnjiQPs72phX2eUwc4WsbwKgtAwQn4PIb+HY/0dy44ZhmZmIcXI9JwZrz89z8i0Gfbw5ZevM5/KVs5VCjojQfo7IuzriDLQEWGgM8q+jig9bSGx9AqCsIS1atPuNMVikUuXLmGz2Xjssce4efPmro5nLR50MVyvtND8/HzDSwvVoxmE7U66Im90HNUWXVgqdMt/606ns+K63Ax//81OUwnbXNHgD/76BW6MzHBzbIahiThFK8mB3aYY6IhytL+dv3P6GAe6WzjQ1cpARwSX1GwVBGEXsdlUJQvzk4eXWy4WUlkrtn8xxv/u1Bx/89I1FtK5ynkOm43etjD7OqPmC7quFvZ3RdnX2UI04N3JjyQIwi6jtSabzZLP53G5XE0xOU8kEly4cIF9+/bR29tLNpttaDIqobHUE5Y2m61irQUaWlpoPfffaXbTFbl2HGv9DVcL3fLLmHw+Tz5vhkLZbLZKeaGy67KwlKZShMlsgd/4y2/R1RLkcG8b33fiAId62jjU28b+zihOh1gyBEHYe4T8Ho77u+q6Oc8lMwxPxRfzAljLd64ML3FvjgS87O+MMtjdwmBXK4NdLQx2tdAVDWKz7f6PtiAIjaOcdGZsbIxCocDg4OCuj2dkZISRkREeffRRAoEAsDesoXthjLtJo0oL1aMZhG2zuCJv1HJcfm4idDdGUwnbiM/F1/+vf0nQJy7EgiA8GEQCXiIBL48d6Fmyv2QYjM8uMDQZZ2gixp3JGHfGY3ztlZt8JnWxcp7X7WSwq4WD3a0MdpttLJXDMLQIXkHYg1TXprXb7ZVJ7G5Rdj222+2cPn16iQVPRGNzsxlhuVZpIY/HUxG6a5UWagZraTO7Im+EekK37LpcLXRrk1E9aDSVsLXblIhaQRAEwG6z0dceoc/K3l5NPJHm9oSZPO/O+Cy3x2M8f2WYz3/ncuWc//7lGxzobuVgTysHe9o4bLWtId+uTzQEQVhOvQRRdrudUqm09sXbxMLCAhcvXmT//v309PQsO26z2ZreFVnE99ZYb2mhaDSK1+tdVu5mt8VVM1iNofECu15pIa01uVyubjKqB0XoNpWwFQRBENYmGvRxMujjZE0870Iqy+2JWb549nnsgVZujs3yjfO3+ey3L1XOiQS8HO5t41BPG4f72jjS28aB7jbJ1CwIu8hKtWmVUrsiHLXW3Lt3j9HRUR577DH8fn/d83ZSNGqtGRsbw2az0dLSsq3ZfO8XtkPU1ZYWSqVSxONxbt68STabJRAI0NLSQjQabQpR2SwW2+0W+WsJXa11Jdtyddbl+w2ZyQiCINwnhPweHj/Yy9y9Ns6cOVPZH1tIc3PMTMp3c3SWG6PTfOZbF8jmi4BZnmigM8qR3jaO9LVztK+dI/3ttIVWdzMTBGHrlEolCoVC3dq0drt9W4TtaoKjUChw6dIlnE7nMtfjWmw2244I23w+z4ULF3C73TgcDkZGRtBaE4lEaGlpIRwOrzhOsdhuH0opAoEAgUCA/v5+tNYkEgni8TiXL18mm81it9uZmpra9tJCK9EswnanqSd0DcPgpZde4uDBg3i9Xux2+xKL7v3wey/CVhAE4T6nJeTjdGiA08cGKvtKhsHozDw3Rma4PjrN9ZFpLtyZ4G9eur54XdDHkb52jvW3c7S/g2P9HfS3RyR2VxAawHpq026Hq29ZjNabxM7Pz3Pp0iUGBwfp7u5eV3/bLRrn5+e5ePEihw4doqWlBcMwOHDgAMVikbm5OWZmZrh161YlyVFLSwvBYPC+mKRvlZ22mNaWFpqZmWFiYoJkMlkpLRSJRIhGo4TD4YaWFlqJZrAaNwNloVuubVz+bslmF8sR3g9CV4StIAjCA4jdZmOgI8pAR5S3PHm4sj+RznJ9dIbr96a5NjLNtXtT/NFXX6ZYMifXPreTI33tPDTQwUMDnRzr72B/VwsO+4P3RlwQNst6a9Nuh7AtT26rhbTWmrt37zI+Pr6q63G9vraLanfoJ554Ap/PR6FQqBx3OBy0tbXR1tYGLCY5GhkZIZFI4PP5aGlp2Tart7A2Sim8Xi8HDhwAzERk5Rq6d+7cWVJaKBwOb4tl9UG12K5EqVTCZrOtaNHd60JXhK0gCIJQIejzcPJw35L43UKxxK3xWa7em+Lq3Smu3ZviM9+6yJ9+7VUAPE4HR/vbeWigk4f3mcu+zih2mUwIwhK01hXXY1juLljLdllsq/ssFApcvHgRt9vNqVOntlS3tFGslom5lvdd+Nkl2x878RG01qTTaWKxGBMTE6TTaUqlUiX20+VybfdHaAp221pZe3+Hw7GstFA8HmdqampJaaGWlhYCgUBDBOluP4NmYyWhv5LQzWQylf2/8zu/w0/91E8RDod3bLwbRYStIAiCsCpOh51jlisyrzP3lQyD4ck4l+9OcmV4iit3J/ns85f45NlXAdOye2ygg+P7uji+v5Pj+7roaQ3JBEN4YKl1PV7P38J2uiLDopvvwYMHK1lvd5tEIsGFCxfYt28fvb29S46t53m85/z7AfjEox/G7/cTDAaZnJykq6uLWCzG6OgopVKpEp8biUSaQszfj6wlKp1OJx0dHXR0dACLVvfR0dENlxZaCbHYLmc9z7H8HVV+dlprPve5z/FTP/VT2z28LSHCVhAEQdgwdpuNA92tHOhu5e8//TBgit2hiRiXhye5NDzJ5eFJ/uzsq+SLZrmSaMDL8f1dPLK/i0cGu3hkXxchv5R4E+5/qmvTrlfUwvYJ21KpxNDQEBMTExU332agUChw/vx5Hn30UYLB4LLjG4nnLQtcgA96/hnhcJhwOMzg4GDFJTYWi3H79m3sdnvFmhsMBu8bIbTb1sqN3r+6tJDWmmw2SywWY2hoiFQqtWppoZVoBmHbDPV8y2x2HEop0ul003xXrIQIW0EQBKEh2G02Dva0cbCnjR967XHAdGO+MTrDpaEJLg5PcGlogm9dukN5frq/M8qJwW5ODHZxYrCbgz1tEq8r3DdUux6vlCBqNbZD2GqtuXTpEoFAgNOnT+/6pB/Mif/Vq1cpFou89rWvbairsKEVv5z5AzgHf/TYh4DlLrH5fJ54PM7Y2FjFUlgWuj6f1P7eLFsR1uX43N7eXnp7e+uWFgoGgxWh63a7Gz6GRtEM4rrMVpK9lUsGNTPNPTpBEARhT+N02Ctxt+/kMQCSmRyXhie5eGeCC3fGee7iHT7/ncsAeN1Oju/r4rED3Tx2sIcTg92Exaor7EFWqk27ERotbOfm5ojFYhw6dIj9+/c3rN+tkE6nOX/+PN3d3fj9/m0VAP/43M9V1ssiF8DlctHZ2UlnZydaazKZTMWam06nCQaDFaG7koBqRnZb1DXy/rWlhQzDIJlMEovFuHz5MsVikVAoVBG65dJCzSAqm2EMW6VcF7fZEWErCIIg7CgBr5unjw3wtFV+SGvN6Mw85++Mc/62uXzsb16kZJg/ooNdLTx+sIfHDvbw+MEe+tsju/4GXhBWY7Oux7U0SthqrRkaGmJqaoq2tjZaWlq23GcjmJqa4saNGxw/fpxIJMLk5OSa11SLpdrEUYZWq25XUxa51QIXTAHl8/nw+Xz09fVVarNWC6hwOFyJz212C9b9ImxrsdlsldJC+/fvxzCMSsble/fuVeocp1IpIpHItoxhvTSLsG3EOJr9t7e5/xoFQRCE+x6lFH3tEfraI/zd0w8BkMkVuDQ8wblb45y7PcZXX7nBZ751ETDr6z5+sIcnDvXyxKEejvR1iPuy0BSspzbtRqhO9LRZ8vk8Fy9exOfzcerUKa5cubLr5W8Mw+DmzZssLCxw6tSpiutxuRTRjo1DK/7Rqz9f2f6Tx//rsnOqa7Pu37+fUqlUic8dGhrCZrNVrIShUKgpBEyZ3baw7aTFuPrfAVgSR33r1i2Gh4e3vbTQSpRKpaZIULaVcey29X+9iLAVBEEQmg6v28lTR/p56kg/AIahuTMxyyu3xjh3a4xXbo7yt6/eBMwMzI8e6OHJQ708cbiXR/Z34XbKz5uws5RdI51O55astI0kHo9z+fJlDh8+XMk8ux1xuxshl8tx/vx5otEoJ0+eXPKcdvuZvfuVD1TWP/nEf6l7TjnRVNnqXS5ZMzExwfXr13G73RW35d0WlnD/WmzXohxHPTU1RV9fHx6PZ8XSQsFgcFvH2SwW260I23w+vyfKZMkvvyAIgtD02Gyqkpjqx77vUQCm5pK8cmOUl2+O8srNEX7r898GwOWwc2KwmycP967WpSA0jGKxSC6X46WXXuK1r33trgs0rTV37txhenqaJ598Eq/XWznWCCvwZonFYly5coWjR4/S1ta27PhOW2xXoyxyVxK4ZWpL1pTjc4eGhkgkEmitGR8fJxqN4vHsbL6A3RbWhmHsuqt2OcZ9J0oLrTaGZhC2WxlHMpnE7/c3eESNR4StIAiCsCfpiAT4wVNH+cFTRwGYT2V55eYoL98Y4aUbI3z0iy/s8giF+51q1+OyJWS3RW0+n+fChQsEAgFOnTq1bCK7HeJxLctctdA+efLkigJvt59dPdZjxa2mOpNvIpHg9u3b5PN5rl69SqFQIBwOVwTUdou+3XYf3e37l8dQT8zVlhbKZDLE4/FlpYVaWlrweDxb+hzNImy3YrFNJpMEAoEGj6jxiLAVBEEQ7gvCfg9nHjvImccOAmb25eBv/9tdHpVwv2IYBoVCYUtZjxtNPdfjWhrtilzub6UJc6FQ4MKFC5UY39Um+BsR3VtJHLVZnn3lg5X1Tz3xn9c8v2wp3LdvH/v27aNUKrGwsEAsFmN4eBil1K7Ffe4EzSBs1yMqqxOG1ZYWunHjxrpLC21lDDvBVoRtOp0WYSsIgiAIu0XAu3fKcgh7h+ratEBTTFi11ty+fZuZmZllrse1NNoVWSm1Yn/z8/NcvHiRgwcP0tXVta6+1stYMgRAT2Bh3ddUs1EhbLD0+EZFLpjxudUJjgqFAnNzc5Xs0C6XqxKfGwgEtiwKd1tY7vb9NzuG9ZYWKmfGLpcWWon7QdimUil8Pl+DR9R4RNgKgiAIgiCsA601hUKBUqnUNFbaXC7HhQsXCAaDa1pEofGuyPWErdaakZERRkZGePzxxzcUm7ea6K73vMsCt8ufWPc9Gs2zr3ywIoz//MlfWfd1TqeT9vZ22tvbAchms8RiMe7evVuJaSwL3dVeVjQrzSBsGyEqa0sLlS3v8Xicu3fvVkoLRaNRIpHIMvHYLFmRtxpjKxZbQRAEQRCE+4BG1abdKGUhWm9CWk7GdOTIkYo4WovtckUuUywWuXz5MjabjdOnT29oQr8Va/K4JXABujdpxW0EP/byf6ysf+zIz65y5nI8Hg89PT309PRU3GFjsRjXr18nl8stic9dy0oIuy8sd/v+sD3W0lrLe7FYZG5ujlgsxp07d7DZbBWhGw6H7wuLrQhbQRAEQRCEPc5Ga9M2ejJfFo7V9y27Hs/Ozq6ajGm1/hpFtcU2mUxy4cIF+vv76evr21R/jXCTHk+GMLTaVYEL8L7rHzFXXjabjVhzq91hBwYGMAyjEp977949tNZL4nObwSJYSzMI250Yg8PhoK2trZLpu1wCquxibhgGfr+fUCi07aWFVmOrMbaSFVkQBEEQBGGPorUmn8+vO0FUWeRth7AtU64DG4lEeOqppzZsCWq0K3J5fOPj49y5c4cTJ04QDAY33dd6hO1bn1+anVivEC9btuLutsAtU23N3YjIBSpWwEgkAixaCWdmZrh16xYOh6PitlwWT7stLHf7/rBY7mcnqS0tVM6MPTIyQjKZ3NbSQqtRKpXWZemvRyqVEoutIOxltNaUDI1hGBgljaE1Wmu0Bm2YP7yaxR9gVU4socyam0opbEqhbAq7zXzLb7PtfjyWIAiCsDZlK+1GXI/tdjulUqmhbofVwnZ2dparV6+uWAd2vf2VE181irJV6tSpU5ueOJfZjtqrY4lFN+We4MKWE0ctO76JDMxbEbmw3EqYy+WIxWKMjIyQSCTw+Xxks1my2Sxer3dXBGYzCNtmiIVXStHa2kp7e3vd0kKBQKAidLczlrpUKm26lnIymaSnp6fBI2o8ImyFpkdrTTZXIJHMc28kRjqTJ5PNk8kUyGTyZHIFsllryRXI5Yrmki+SyxfI54rkCyXyhSL5fIlCoUixaJAvFCkWDIqlEsWiQbFYolTSFEslDENjGNtT2Nxut2G323CUW4cNh8OO02HH4bThdNhxOu04nQ5cTru5uBxLlqnJce6MPIfb7cTrceJ2O/F4zHWv14nX46q0Pp8Lr8cloloQBGEdbNT1uJpGu/mW+yyVSty8eZN4PL5h1+N6/TVqjJlMhlgsRl9fH0eOHNmygGh0xuZ6jCVCFaG62YzKjaZa5MLmhK7b7aa7u5vu7m601qTTaS5dusTw8DA3b94kGAxWLLoul6tRQ1+VZhC2zUB1KMF2lxZaaxybdUXOZDJisRWEMqWSQSKZZSGRYWHBapNZEoksiaS5JJM5EsksqVSOZCpHKpUjlcmRTuerROara97L7XbgcTtxuRy4K2LQjsvpwOd14Qx5q8SjHbvdFJMOh60iOu02G3a7ZWW1K+w2G8qyxIIy18tf1kqBLltwsay6pjDWGkskGxiGpmQYlEqaUsmgVCpRLGmKxUVhXSiUKBZL5Avmei5XJJHMks+bojyXL5DLF8lm8nzrhfEN/Rt4vU58Xhd+n9tc/G78PhcBv5tAwFNpgwE3wYCHQMBDKOghFPQSCHhw2Hc/8YEgCMJ2stXatGWLbSPRWnPhwgVaW1t56qmnmkY8Tk9Pc/36dcLhMD09PQ0TMNstbKtphozK9fjRl/7Tku2/OPnLG7peKYXf78fr9XLo0CHcbjeJRIJYLMbo6CiGYayaxbdRiLA1WS15VL3SQolEolKTulgsVpKGrae00GpsNXmUxNgK9y1aa9KZPLFYithcilg8xdxcmtic2cbn08zNZ5ifTzO/kGEhkWGl3yqlwO+rFlduerrCpvDyu/F73fh8LkZGhnji8UdMK6TXhdfrqlgpPR4nHrcTt9vxQHyJnj17lje+8U2WhbpANlckmzUt2NlsgUw2T9qyaKfLSzpPOp0jlTa3k6kc0zMJkqksqVSebG511zS/z0Uo5CUc8hIKmm0k7CUc9hEJ+4iEfETCXqIRH5GIH7/P9UD8WwiCsPdpVG3aRltsZ2ZmiMfjHD58mIGBgYb0udUYW601N2/eZH5+nlOnTnH9+vWGfebVauKWedt3P9SQe1UzkVqMCW42kQtLhe5GRG5ZWNpsNsLhMOFwmMHBQYrFIvPz88RiMW7fvo3dbl8Sn9soV3oRtiYbyYpc/W+1mdJCq7HVOrZisRX2JPlCkdnZJFMzCaZnEszMJpmZtdpYilgsyWwsVVcIKQVhS+BEwj4G97eb4ifkJRzyEQ6ZFsBQ0EswaFoE/T439nVYA8+ezXDmzPHt+Mh7EptN4fOaIr8RFAolkqlF6/lCIksimSGRzLGwkGEhYVra5xfM5e5IjPmFNJlMfUHsctqJRHy0RP1EI35aon5ao1bbEqClxU+b1bqc8lUkCMLu0MjatI2y2JbF49zcHO3t7YRCobUvWidbEd/lxFXRaJSTJ09WnlejrKyb6WulxFGLx5eev1a87EQqWOmzWZJOVfOjL/0nbGrxQ63ltlzv/2eHw0Frayutra0A5PN5YrEYY2NjJBIJPB5PRej6fL5N/02IsDXZSrmf9ZYWamlpIRQKrXqfrcT/i7AVmhKtNYlklonJeSamFpicWmByap7JqQST0wtMzySIxVPLrvN6nLS2BGhrDXD0SBet0QCtLX5aogFaon5aoj6iET/hkHddIlVoPpxOO9GIKUI3Qi5fZH4+zdx8mnjZWj9nrc+liM+lmZ5JcO3GBHPz6bqxy+GQl7bWAG2tQdpaA7S3BmhvC1aWjvYQAX/j4kwEQRCg8bVpG2GxzWazXLhwgWg0ylNPPcXVq1cbnsV4M0K07BpZm7hqp4VtLOmjJZBuyP3qUS2Uq2vjdgbqW3I3kziqkdTG58Ki2F3vv4vL5aKrq4uurq5KcqOyNTedTi+Jz91IzOduZCRuRhpZx7Y2aVg+n2dubo7JyUmuX7+Oy+WqCOHa0kJbibEt/3/Q7IiwvQ8pFktMTC0wNj7H6PgcY+NxxifnGZ+YZ3xijlQ6v+R8j9tJZ0eIjvYghw500NFuiQlLVLS1BsWtVFgRt8tBR3uIjva1LQqlksHcfJrZuGn5n5k1rf8zswlmrO0btyaJz6WWvWX3eV10doRobwvS1RGioyNEV0eIzo4w8ws5SiVDXqoIgrAutpIgajW2arEtx60eO3asYk1rtHvzRvvTWjM0NMTU1BRPPvnksqytjRzfWsK2PA+JJX2VfVF/piH3XovJpDmpX0ngNoq1hHK1tXYllojdSxuvn1tObtTX12caRKz43HLMZ7UrrMOxspTQWjc0Q/heZSsuwGvhcrmWlBbKZrPE4/FlpYVaWlooFosSYys0J4ahmZ5JcHckxshojHujce6NxhgdizMxOU+pyirmcjno7gzT0xXmxPE+ujtDdHdG6OwI0dkRIhzanTTwwoOH3W6jtSVAa0sADnaueF6hUGI2lmR6JsHUTIKp6QWrNdev3ZhgfmHpZObXf+8CHW0hurvCdHWG6e4KW//fR+jpjsj/54IgAOZkOx6PE4/H6e3t3daas+vFMAxu3rzJwsICTz311BKrWKOF7UZibAuFAhcuXMDr9XLq1Km6ImUnLbazs7PL9pVF7nZacasZryod1B1sPlflelQL3bIw/tQT/3ld1yqlCIVChEKhSsxnOT53aGgIm81WsRDWusLutivyTiYiW41GWmzXwuPxLMmOXS4tdOfOHRYWFrh27VrF+r6R0kKpVEostsLWKRZLjIzNMXx3hqG7swzfM5eR0fiSGFev10lfT5Qjhzp55o3H6O2O0tsTobc7Qks0IKVehD2F02mnq9MUqCuRzRYsd/p5vvHc9wiHOxmfmmdiYp5vf/cm8bmlkxyf10VPt/k30dsTrbR9PVHaWgMiegXhAaCcIKpQKDA3N0dfX19D+9+MCM1ms5w/f57W1tZK3OpW+1xrjOuZ8C8sLHDx4kUOHDhAV1fXiufthLDVWnP79m1+5Oqf1+xffFZlgRvZIQsuLBW5223JbTTPvvLBZfvWI3bLiaZaWlqARVfYiYkJrl+/jtvtrgin3XZF3u37V49jNyzXtaWFXnjhBfbt20c8Huf69evkcrl1lxYq10NudkTYNglaayYm57k9NM3toRluD09z8dIwv/Lfv0exuPiD1tURYqC/lSce7Wegr5X+vhb6e6O0tsjEXHiw8Hic7B9oZf9AK5nkXc6cedOS45lsvuJ+PzYxb7nlz3F7aJpvfffmkr8rj9tJb0+Evl7z76m/r4WB3hb6+1oIBjZfL1IQhOag1vXY4XA0vCwPbNwVuex6/NBDD1WEQr0+d9IVWWvNyMgIIyMjPPbYY2u6H263K3LZarwuN0gNc8nFyXe4RuSulTiqNhHVRii7KmsNXcG9JXLLbEbs1rrCluNzh4aGmJub48aNG7S1tRGNRrdUf3kzNIsr9G4J21qUUgSDQYLBIAMDAxsqLVQvPvef/bN/xhe+8AU6Ojq4ePEiALFYjHe9610MDQ2xf/9+PvWpT1USX33oQx/iox/9KHa7nevXr/+g1vqvrXGdBD4GeIG/Av611lorpdzAJ4CTwCzwLq310GqfUYTtLpDLF7k9NM3N21PcvDXFrTtT3LozTTqzGPva1RkmEnbz/c88yv6BNvYPtDLQ34LXszNFtQVhr+P1uDiwv50D+9uXHSuVDKamFxgZm2NkLM7oWIyR0Ti3bk/x3LevL3Hlj0Z8DPS1sK+/lYH+Vvb1m2K6vS0oL5MEYQ9QrzbtdtSbBVPkradfwzC4ceMGyWSSU6dO4XKt/Nu+3j7Xy2quyKVSiUuXLqGU4vTp0+uKx9tOi20ikeDChQuLVuObG+tvrmzFbZCb8lrxr+WhTySWumzuVaEL8O5XPrBku+zK/CeP/9e653u9Xnp7e+nt7eWVV16ht7eXRCLB1atXyefzlfjcaDS6anxuI2gWQdksArv277ReaaH5+fklpYW+9rWvcejQobrjf9/73sfP/MzP8J73vKey78Mf/jBvectbeP/738+HP/xhPvzhD/ORj3yEy5cv88lPfpJLly4xNjbGgQMHfkspdURrXQJ+G/gJ4DuYwvZtwBeBfw7EtdaHlFLvBj4CvGu1zyjCdpvJ5QrcuD3FtRsTXL85yfWbkwzfnalMnH1eFwcPdPDWNx/n4AFzEn5gXxs+n5uzZ88us0IJgrB17HYb3V0RursinHpy/5JjxWKJsYk57o3EuFte7sU4+9w1FhLZynler5P9/W3sG2hlcF8b+wfaOLC/TQSvIDQJtbVpq7Meb5ewtdvtlfutRCaT4fz587S3t/Pkk0+u+X3RaGG7kityKpXi/Pnz9Pf3b8hFe7uE7djYGENDQzz66KNbLjMyV5VsKhTYOVflMtVCdzWR24jEUY283kaNEKq6/h+9+vN1r6kVvOWMyvv27avUZI3FYgwPD6OUqojccDjccPG32zG+e41aN/Nisci9e/f4m7/5G+7du8czzzzDM888w5vf/Gaefvpp3vjGNzI0NLSkj89+9rOcPXsWgPe+972cOXOGj3zkI3z2s5/l3e9+N263m8HBQTBfU51WSg0BIa318wBKqU8AP4wpbN8B/KLV9Z8Dv6mUUnqVLxwRtg2kVDIYujvD5WvjXLk2zrUbE9wZmq6I2GjEx5FDXbzu6YMcOdjJoYMddHdGJP5VEJoIh8POQF8rA32tvL5qv9aaufk0w/dmGbprLsN3Z3jhpTt86SsXK+f5faaleHBfGwcGOziwv40D+9vFpVkQdpBa1+PayW2j3XvLrOWWOzU1xY0bN3j44Ycr7nnr6XMtsbwR6o1xYmKC27dv88gjj2y4Zm6jXZENw+DKlStks1lOnz5dseo9+r8+0pB7LFiuyrshcGH9IncvYlOaf3zu5xa37Rqu/Fll+xOPfnhJTdZyrHv578LlclXicwOBrYfYNYvFthnYjMh3OBz8yI/8CO94xzt405vexJ//+Z/zta99jT/5kz/hG9/4Bh/4wAeWXTM5OUl3dzcA3d3dTE1NATA6OsprXvOa6lNHgF6gYK3X7sdq71njLyql5oFWYGbFMW/oEwpLmF/IcOnKKJeujnHpyhhXb4yTyZg/PsGAh2NHunjtO1/D0cNdHD3SRbskqBGEPYtSqlLn9/ETA0uOzS9kGBqe4fbwDHeGzTj5v/3mVT73xXOVc7o6Qhw80MHBwXYODXbIiy1B2CbWU5u20VbQMitZgg3D4Pr166RSqTVdj2vZzqzIhmFw7do1stksp06dWhJTt5H+GmWxLVuI+vr6OHbs2KpzpmXxsHqN4zUsJL0V1+FwcPdFLkBHILkr49gp3nfhZ5dsL7EIe+G3Dv8ysViMu3fvVsrLbCaDbxkRtotsJZFWNpvF4/HQ1tbGO9/5Tt75znduuI8VviM01A18L5+82rG6iLBdJ+XkTucujXD+4ggXL48yfM9MO2+3KQ4d6OBtb3mEh4/18PDRbnp7oiJiBeEBIRzy8tiJfh470V/Zp7VZksuMp5/m1tAUt25P8/wLtzAsLw6/z8XBwQ6OHOrk8EFz2TfQikPq8QrChql2PV6rNu12/T7XE6Fl1+OOjg6OHj264XtvVx3b6nGtJSJXYyPlg1YjHo9z7949uru7y66K20r1PHs+4a0I4d0SuQBTyUWX6/td5NbjZ25W1d/1g00ZEMdcWOoK/f88/N/X7O9+dkX+s/G/C4BTLX+R9qNdf71sX73kT+tlIzVsOzs7GR8fp7u7m/Hx8UpSsb6+Pu7du1d9ah8whmmh7auzH+tYPzCilHIAYSC22v1F2K6A1prR8TleOX+Xcxfu8eqFe0zPmC4jgYCbRx7q5a1vPs4jD/dw7HA3Hs/G33IKgnD/opSioz1ER3uI15w6WNmfyxW4PTxTSR534/YkX/jS+Ur5LpfLwaHBdo4e7uLIoS6OHelioF/EriCshtaafD6/JEHUblBrsZ2cnOTmzZsbcj2uZTsstoVCgZdffnlL4yqzVeu31prh4WEmJyfZt2/figmFckmzFIk7kNv0vdbDfKIqq3KVyF1v4qhGUS1y4cEUuqvxU5f/3aoxwABOWwnswDXreNX5/9fR39zuIa7Ir9/9h8ByUeq2LQ05qD3uUsVVj69GqVTakrBdb5z729/+dj7+8Y/z/ve/n49//OO84x3vqOz/R//oH/Hv/t2/Y2xsDOAw8ILWuqSUSiilXgN8F3gP8BtWd58D3gs8D/wY8LerxdeCCNslTM0kePnVYV4+N8zL5+5WhGxL1M9jj/Tx2CP9PPpIH4P72sV9UBCETeF2O3noSDcPHemu7CuVDO6Nxrl+s5xkboIvffUin/nCK4BZjujwoU6OHe7ioaPmtd1d4fv2TbQgbIT1uB7vFGURWnbxzWQyG3Y9XqnPRqC15ubNm+RyOd74xjeuWrdyvWzFFblYLHLp0iUcDgenTp1ibGxsTZFcFrguf37V8xpBWeTuphW3TK3QhY3F6DYycVQj+t9t/v21nzEtwlU4a7YdtqX/L9prPqOjRljWCs3Kdgc8Nwx21fi4/lrqWWtha8I2nU7Xtdj+w3/4Dzl79iwzMzP09fXxS7/0S7z//e/n2Wef5aMf/SgDAwN8+tOfBuD48eM8++yzPPzww+WXV//KyogM8C9ZLPfzRWsB+Cjwh0qpm5iW2nevNdYHWthmsnlePX+PF18e4sVX7nD3nmndDoe8PPHoAE88NsATjw4w0NciE0hBELYNu91Wqcn71jcfB8AwNPdGY1y7McHV6xNcvTHOZ//qVT79l98DzO+ph492m+EPx3o4dqSbgH/rk1RB2CvUJohqhlg6u91OLpfjhRdeoKura0suvmUaJWzz+Tznzp0jEong8/kaImph88K2Xhbmlfo6+me/tnSHhnzSfFngCuyQwLUstsEmELllmjkRVa3QXba9hnCuFZ0bvd5ZI0prz3/QKJVKm/6OTKVSdYXtn/7pn9Y9/6tf/Wrd/R/4wAeqE06VxSta6+8Bj9Ser7XOAhsK6H2ghK3WmuF7s3z3e7f57vfucP7iCIViCbfbwWOP9PP3f/BRTj6+nwP7xSIrCMLuYrMp9ll1c8tit1gscXtomivXxivZ159/8TYASsH+gTaOP9SDQyU4eChGX6/E+gv3J41yPW50DF4sFiMej/PUU08RiUQa0mcjhG08Hufy5cscOXKE9vZ2pqenGzI22Nz4yllwT5w4sSQL82ZEcj7pqqSTKYvctRJHbYVElatys4pcaD6h22xst7W22dhqjO1WS27tFPe9sM0Xirx6/h7ffuEWz79wi4nJeQAG97Xxo29/ktMnBzlxvA+3675/FIIg7HEcDjtHDpmxt+/4e08AkEhmuXp9vJKd/exz10gmc/zlF3+PSNjHIw/1cOJ4HyeO93HkYCdO5+Z+2AShWSgWi3Vr026UcsmfzU72qjEMg6tXr5JOpwmHww0TtbA1YVsdv/rkk09uKrPsWmxEjJZdoRcWFuq6aG81w3LZiuv0r14eqfYWawrhFY5Xi9zALpUPWolaoasUdAcXdmk0Dx61QrfWDXmj8bVbZauuyCJsd5FEMst3XrzFc8/f5Lsv3SaTKeB2Ozj5+D5+/J1P8/RTB+js2FidNkEQhGYkGPBw6slBTj1pZhE1DM2f/8UX8QZ6uXh5lAuXR3juOzcBcLsdPHy0h0etnAHHj/VI4jthz7BWbdqNUk70tFVhm06nOX/+PF1dXRw6dIhXX311S/3VsllhWygUuHjxIh6Ph1OnTm2bq/Z6xWg+n+f8+fOEw2GefPLJuv9+jSodVEguCmbnDrgqa71U5EJzWXPLjCeWz31F7O4NtpI4CraePGq9WZF3m/tG2M7Np/nm8zf4xreu89Krw5RKBi1RP29500O8/ulDnHx8H263TOAEQbi/sdkUHW0+zpx5jB9622MAzMaSXLw8yvlLI5y/NMIffvJ5Pm58G4fDxrHD3Tx2op8nHu3nkYd78Xo2n+RGELYLwzAoFAoNzXq8Us3ZjTAxMcHt27c5fvw44XAYwzAaXh93M8J2YWGBixcvMjg4SHd399oXbIH1jG9+fp6LFy9y+PDhSvmPetQTtsviazdIIelCa3AFt1/gVlMWus0gcFf7c6kndm1K0x1YWLK9GmvF0wo7w0qJo2BrwjaVSonFdieYm0/zjW9f5+w3r/HK+bsYhqa3O8I7f/gpvu91h3n4aI/EygqC8MDT2hLgTW84ypvecBSAVDrHhUujnLtoljL75P98gT/+1Hew2208fLS7kjzv+EO9EqYh7CrVtWmBhlodt1KmplQqce3aNXK5HKdOncLpNF+cN8riWE3ZZXq9jIyMcO/ePR599NEdmYyu9ZnL43n88cfXtPqs6/nVHl62XX/el0/srBW3zF6w5NZjPLlU8PYG5zfdV7Mljqrt/0HAMIwtJY/q7+9v8Ii2h4bMWJRSvw/8fWBKa/2Ita8F+DNgPzAEPKu1jm/1XulMnueev8FXzl7hey/foWRo+nqi/Pg7X8Ob3nCEQwc6JFmKIAjCKvh9bl5z6gCvOXUAML9XL14e5ZXzd3nl3F3+6FPf4ROffB6Xy8GJh3s5+fg+nnpiP4cOdGCXerrCDlFOEHXx4kWOHz/e8N/2zVpsy9l8e3p6eOihh5aMazvmH+sV4KVSicuXL6O15vTp0w2JHV4PK4lRwzC4fPkypVJp3ePZjhcD9boruyo7A3kKCReOwOoxuY2kWZNPrcVoIlxZV1VCsiew912Zt63MTxNRKpU2XXZspXI/zUijXsV/DPhN4BNV+94PfFVr/WGl1Put7Z/dTOelksFLrw7z11+9yHPP3ySbK9DZHuJd/+A0z7zxGIdFzAqCIGwan9fF6ZODnD5pxukmUznOXbzHy68O89Krw/zux77B737sG4SCHp58bB+nntzPqScHJVeBsG1U16ZdWFjYlt/4zQjb8fFx7ty5U3E93gnW4+pbFtt9fX309fWt+bzKArIRz7Xe+DKZDOfOnaO7u5uBgYF136eusE3aIbA9QqEscItJ58rido3EUlvR4RWRqyEY2jsit5qxZGiZRbT8z70VK+/9xG4njoKtx9g+UK7IWutvKKX21+x+B3DGWv84cJYNCtu7I7N88csX+Zu/vcTMbJJgwMNb3/wwP/Dm4zzyUK+4GQuCIGwDAb+b1z99iNc/fQgwY3RfPjfM914Z5nuvDHH2uWsADPS38PTJQU6fPMBjj/RJHgNhy+xkbdqNCNtSqcTVq1cpFAqcPn0ah2PnXPTXEoXlON9HHnlkSemc1SiL0UZYdWvF6OzsLFevXuXhhx8mGo1uqa+jH/0NcyVpjXObBC6Y4hYArXDsZDyu9XETCzUuy5bQTSx496zorbbyVmNTmv7g3M4OZg+z1cRRIDG2jaBTaz0OoLUeV0qtnC2gilyuwNeeu8YXvnSeC5dGsNsUp586wP/xk2/htU8fxOWUeC9BEISdpLUlwA88c5wfeOY4WmuG7s7ywkt3ePHlO3z2r87x6b98CZfLwROPDpguzk8doKc7stvDFvYYjapNu17WK2yTySQXLlygt7eX/v7+pvEQMwyDa9eukclklsT5rgelVMOFrdaaO3fuMDMzw1NPPYXb7d50XyuSqJoDBorL42sbRNGKx91RgVtDtdDdirjd6P+uayV+UmvEu673fvcSkZX7tLYHgluOYHxgWC1xFGwtxlbK/WwApdRPAD8BEG3p4u3v/nWyuRKtUTff/6Y+Hj/eRjDgQhfH+fa3xnd5tDtLMpnk7Nmzuz2MpkGexyLyLJYiz2MpO/E8Olvg739/Bz/4pjaG7i1w4848N26O8t3v3eZ/AG0tHo4cjHD0YIT+viB28bARVqFspS27x+6EeFxPUqaxsTGGhoY2ZA3dCbLZLOfOnaOjo4Njx45t+HltpTZuvb6KxSKvvvoqHo+Hp556atMT6A3F2CYdKA06UGXNqnEb3mq4brEq4dROxuHWYyWL7l6jVjivJGoB7iaiy447atx6q48PBOYYSYUZDMYq+4aTUQYDi9v30hH2+WPsNa5meirrtTG+60EstltnUinVbVlru4GpeidprX8X+F2Aru5B/brXHOaH3vYYTzy6/piM+5WzZ89y5syZ3R5G0yDPYxF5FkuR57GU3XweI2NxvvPCLZ5/8TYvvHKXb784QSDg5jVPHeD1Tx/i9FMHCPg3bskR7k/W43pcti422i15taRMpVKJK1euVBIfbcT1eLvGW2ZmZoZr167x0EMP0dLSsqk+bDZbw5I0pdNpZmdnOX78+JZLC20meZRKmv82SwTuellnRmVYdFVWGuzB3RW5UCV0rSHvpURU28XdZASb0txJLP5d2JTmTnJx22EzGE5VHa/5n8Bhq00kVZOhedn5S79DaoV3vXPWSla1LBmVbesvoUTYbp3PAe8FPmy1n13rgnDIxS/87Nu3cUiCIAjCdtLXE+XHfvgpfuyHnyKdzvG9V4b51ndv8vwLt/jK2Ss4HDYePzHAG157mDe85hDtbcHdHrKwS6y3Nq3D4aBUKjVcKNrt9koZoWrKrsfrTcRUS9ka2ujxaq25desW8Xh8066+Zcrie6tMTExw8+ZNwuFwQ+rlbiUrsko6KkJVb1Msbtk4WEosun3bdtmSW2avlhW639mqqG0UW00eFQzujd/qRpX7+VPMRFFtSqkR4BcwBe2nlFL/HLgLvLMR9xIEQRD2Bj6fmze+/ghvfP0RSiWDy1fHeO47N/nWd27wa7/1ZX7tt77Mw0e7+b7Xmef09Wws0YywtzEMY10CsBwLu5EYUgBn/AQAheiFFfvNZrNL9o2OjjI8PMyJEyc2PZErj7eRCaYMw+Cll14iHA7z1FNPbdmjbauuyIZhcP36ddLpNI8//jjXrl3b0njKVAvbSuKoMmtkJ17Sj5VsSvu3v+yKkdyCyN2q0XyVR1IrdEN71HX5QafWWrsZN2RgSy8Hc7kcHo9nU9fuNI3KivwPVzj0lkb0LwiCIOxt7HYbJ473ceJ4Hz/1z97E8L1Zvvn8Db75rev8zh98nd/5g69zcLCdN73+KG96w1H2D7Tu9pCFbcZms61romW32ykWN+FmauGMn6grbquTRxWLRa5cuVKpAbsVUdrI+FWAeDxOOp3myJEjdHSsKw/nmmzFFTmXy3Hu3Dna2to4evRopSxTI9iIxXZZjqM6l9lSixYqo9lF7jazUBOjC2aip2rL7nYnjlorvlbYHB8Y/IM1z9lKsjit9bZmqG8ku548ShAEQXiwUEqxf6CN/QNt/JN3vZaJyXm+8e3rfONb1/mDP36O3/+j5xjc18Yz33eMZ954lIE+EbkPMpupNwumpbZsta0nbsv9JhIJLl68SH9/P729vQ2xhm5mvLVorRkeHmZiYgK/309bW9uW+yyzWVfkeDzO5cuXOXr0aGU8W3EfrjeuRvVVi92y4pbKbsobiK/dDEbSWbmHrQliclei1rIbDqV3aSRrC9/VEkfVu752e6142b3KetyMNxsesV1/j9uFCFtBEARhV+nqDPPsj5zi2R85xcxsgq9/6zpf++a1isg9dKCDt7zpId78xmN0ddaviyjcv5RjbLdM7CGzbbkCmAJ0YWGBCxcubMn1uJb1ZFtei2KxyIULF3C73Zw+fZoXX3yxoXG7G7Uqa625d+8eY2NjPPnkk3i9i2KokRbqamHrSNko+htn+S5TFrhoRWkDCae2Ylw0Ekvd6JtZ6M4v+BY3rA8dfkDidRudOKr2+Hbx8ssv43A4aGlpIRqNEgwGG56Ad68k9BVhKwiCIDQNba1B/sHbT/IP3n6S6ZkEZ5+7xt9+/UrFXfmRh3r5/mce5pnvO0ok7Fu7Q6FpWe9EaauuyGWcykFBFyH2EMXQBW7dukU2m+X1r399Q+NhN2thLpNIJLhw4QKDg4OVhEyNdm/eSH+lUolLly5hs9k4derUMsvQdlhsj//6/w2Y4hYArbZJ5Jr/7hsRuOtmlUdi1Ek+ZSSdTee+XGY+sdyNGaAllNrhkexttisb8qlTp8jlcsRiMUZGRkgkEvh8vorQ9Xq9mxam25nhfTsQYSsIgiA0Je1tQd75w0/xzh9+ivGJOb7y9St89ewVfu23vsxv/M5XOX1ykLe++Tivf/ogbvfGEgsJe4etCMVqd+RqHAsnODkIrwz/SUNFLWxNhI6MjHD37l0effTRJeU1Gi1s1ytG0+k0586do6+vj/7+/i31td5xrUS1BXc98bUboSxwAUo7EItbTXVc7obYogGtEQa4eGLpy8Vyn9Hg7rkz38/USxxVjq91u910d3fT3d2N1pp0Ok0sFuPmzZtks1lyuRyTk5NEo1FcLteyflYik8ks8dBodkTYCoIgCE1Pd1eEf/Ku1/KPn30Nt+5M8+WvXearZy/z/Au3CPjdnPm+o7ztLY/wyMNbj5EUmouGuSLXUKTEiX3vAq43tN/NiNBy3VzDMOomr2qEe/NGxzg9Pc3169d55JFHCIdXDgHYyRjbRQsulDZgwV0uhFf+jrCXE07pqnjcHaJW5O6qBXeDiaSqv3bjCd/yxFBVx1sCaWJJH63BRYtvLOmjrWpbEkttHqUUfr8fv99Pf38/pVKJF198kXQ6zejoKIZhEIlEiEajRCKRVeNzk8kkfr9/B0e/NUTYCoIgCHsGpRSHDnRw6EAHP/G+N/LK+bv89Vcv8ZWvXeELXzpPX0+Ut/3AI7ztLY9IjdwmZyOuyPXqzW4VB3aKlCjGjpjbLY0RuBu1MKdSKc6fP79q3dxGJaSq7m8lYau15ubNm8zPz3Pq1Kk1rTuNfJG0EZFst0TuRgTuurGGUInHZWeyKtfSVEK3gcSSpqV3NrEomJTSzFjb1QK3zHYnjlorvnav43Q6GRwcZHBwkGKxyPz8PLFYjNu3b2O325fE51a7HqfT6SXeI82OCFtBEARhT2K323jqif089cR+/u1Pfz9f/9Z1vvjlC/zex7/J7//hc5w+ObjbQxQaQL16sxth1v4tWkuvB6ribOtQjB1piLjdiMV2cnKSmzdvrmkV3Y4Y23oCMp/Pc+HCBYLBICdPntxx7welFO/51neW7lwjW7E9ZUNptiUGt5py6aB1CdxtMjYuE7pNnIRqK8wk/GtmSC7/r9kRTOzImLaaOKo2vnYnqa1h63A4aG1tpbXVrDiQz+eJxWKMjY2RSCTweDxEIhHi8Thaa3y+1fNZ/Oqv/iq/93u/h1KKEydO8Ad/8Aek02ne9a53MTQ0xP79+/nUpz5FNGrWqv/Qhz7Ez//8z98ESsD/obX+awCl1EngY4AX+CvgX+sNuoOIsBUEQRD2PD6fm7/zAyf4Oz9wgpGxOF/88gW+/LeXd3tYwhqsx0K32Rjbcibf0dFR3nhs7fOzugSzBwEItN7a8P3KrGe8hmFw/fp10uk0p0+fxulcPc5yO2Jsa/srZ4g+dOgQnZ2dDbvXRse1JrUertZ2xU2Z7RW5tpS9MgZjh12Va9lL2Za3i6mE6ZmzlhC22Va26HYHFrZpdCtzLx1Zsl0rjF321YXzRlirHJDL5aKrq4uuri601mQyGe7cucMHP/hBhoaG8Pl8/PEf/zFvectb6OrqWnLt6Ogov/7rv87ly5fxer08++yzfPKTn+Ty5cu85S1v4f3vfz8f/vCH+fCHP8xHPvIRLl++zCc/+UmA40AP8BWl1BGtdQn4beAngO9gCtu3AV/cyGcVYSsIgiDcV/T1RPkX730j/9t7vo9Pf+Jf7vZwhC2ymRjbYrHIxYsXcTqdnD59GlaYt5bdkQE8ym6KWyA5e3DT4nYtt+FsNsu5c+dob2/n6NGj6xJz250VeXR0lLt37/L444/vajxdLpfbeicaHElT5BYDBs6EjWKg6tk1sF6trdpVeZdFLqxf6K75v9wG42v3OuPJEPZlrs5Lz7HXuCbXbq/lKr0drs6/98h/W9d5hmGsWee2jFIKn8/H8ePH+fznP8+XvvQl/vIv/5K7d+/y4z/+48zPz/M7v/M7nDx5snJNsVgkk8ngdDpJp9P09PTwoQ99iLNnzwLw3ve+lzNnzvCRj3yEz372s7z73e/m3LlzOeCOUuomcFopNQSEtNbPW+P4BPDDiLAVBEEQhL1Td09YnY2W+1lYWODixYtLyuUUohe4PnWQ407fqu7I1SRnD1LQBtG2Oxsebz6fr3tsZmaGa9eu8dBDD9HS0rLuPrdL2BqGwdWrV8nn85w6darhGaI3Qjwe59KlSw3tsyxwHckacbsam9Rstl2Ox61HRehaX4XbFaNb+1W7WuKo+tevHh+7WqKqeucLS1nLYrsauVyOQ4cO8XM/93P83M/9HOl0eslva29vL//hP/wHBgYG8Hq9vPWtb+Wtb30rk5OTle/f7u5upqamAPMl2mte85rqW4wAvUDBWq/dvyFE2AqCIAiCsCs00hVZa83du3cZGxvjscceq2t5vFRIc9y5sfrH8ZnBDYnbeiJUa82tW7eIx+M89dRTuN3uDY1hO1yRc7kcL774Ip2dnTz00EO7+iKo/O/2r547j8NSQUWfbqh1tWLF9W9RBK1xudJLk07tdGbl1ahXWsh+H7ovb8QNGdiwtXavsRVhW5sVuTbeNh6P89nPfpY7d+4QiUR45zvfyR/90R+t2N8K3/ea+q8/NvzHuncq7gqCIAiC8MCxHmFbKBR49dVXSaVSnD59elV32kuFpTU2HSxO+Dyq/uQvPjNIfGZ9ychqXZHz+TwvvfQShmFw8uTJDYvacp+NFLbpdJqRkREOHz7M/v37d03UGobBxYsXmZub49SpU0uOOdIKR2051BXiazeCI6kqy05gT9orS3m7mSglnMsWYXWawQ15I9Qmj9oIqVRq1azIX/nKVxgcHKS9vR2n08mP/uiP8u1vf5vOzk7Gx8cBGB8fp6OjA4C+vj7u3btX3UUfMIZpoe2rs39DiLAVBEEQBKFpcTgcq7oiz8/P8+KLL9Ld3c3DDz+8omXiSMdizOz1Yp5LhfW7N5eZmtm/5jnVNWfn5uZ48cUXGRgY4MiRI5ueXDZK2GqtuXPnDpOTk/T09GzIHbrRZLNZXnzxRQKBACdOnFjx382RZrnAXYkNCt+dFLjAEnG7YwJ3Ex+vmHAtXepYeoXGsZ2Jo2BjMba1pNNpgsGVS+cNDAzwne98h3Q6jdaar371qzz00EO8/e1v5+Mf/zgAH//4x3nHO94BwNvf/nY++clPopRyK6UGgcPAC1rrcSChlHqNMt+0vQf47EbHK67IgiAIgiDsCuuxFFYLxWq01gwPDzMxMcHjjz++ZkmKelwqFDnuXHkq5FQ2CnrpvcvitqNtaMXxFotFhoeHGR8f54knntjU2KpphLAtJ9RyuVwcOnSIRGJnyqTUIx6Pc/nyZY4dO1YpOfLYh39r1WscaSrCtbjZx7mC0K2IWw3FwM7Fazajy/Iy72/r7cCK4laBK7gYU15IunAFc0uOC41nvYmjYGuuyKlUatXvr6effpof+7Ef48knn8ThcPDEE0/wEz/xEySTSZ599lk++tGPMjAwwKc//WkAjh8/zrPPPsv58+cvA0XgX1kZkQH+JYvlfr7IBhNHgQhbQRAEQRCamHpxuIVCgYsXL+J2uzl9+vSmLaFAxXJ71GnOwKuzI6/G1Mz+uuLWMAxmZ2ex2+1bHluZtTItr0UymeT8+fPs37+fnp4eZmZmGuravBHKJZiefPJJvF7vyieuoi/LFtzSKpdvlmoL7jKRu42at9aC2yxCdz3kE67KulKQT5ju9ksE7go0OnHUWvG1DyJbFbarWWwBfumXfolf+qVfWrLP7Xbz1a9+te75H/jAB/jABz5wsHa/1vp7wCObGqiFCFtBEARBEPYMc3NzXLp0iYMHDy6rqbgWRzpucX3KnE85lUFBL4rOc3k7j7k2JibuTptxtwPtZnKpRCLBpUuXcLvdPPzwwxvqazVsNhuFwuaS/ExMTHD79m1OnDhRmaA2OmYXTAv6ahZ4wzC4fPkyhmFw6tSpjU+067gZlwXupi24a7CqyK1DI5PzNqM1d6OUBe4SrIdUbeXdSbaaOGqt+NpmpFQqbTrjeTKZXDXGttkQYSsIgiAIQtNT7XrcCPfeepzLm2LiqHNRSFS7IztRFOqY7coCd+TGH/PQQw8xNDTU0HFtRogahsGNGzdIJpOcOnUKp3PRldRms62ZjXoz41tJrJZr93Z2drJv376GJ6uq56bc6AowjqRCaSjsoKtymZWsufakfQ+LXsvKu8z12Wy8weyOjqdRbDRx1FrxtY1gqzG2ImwFQRAEQRDWYL0CR2vNK6+8gtfrbZh7Lyy12npUkaw2p0XXCi6OOjduUeo89I8JBq823Bq6UpzxSuTzec6dO0dLSwtPPvnksueslGp4+aCVhHK9eNpaTv7H34KVE1lviBXdlNfSo+vUq84qK+5uiFxYKnRXFbcbfH+wUnztbpBJeKy1GlfjWtdiBYE9KoLXQz2L8Ebia2HrrsgibAVBEARBEBpAPB4nlUptyvW4Hkc6bvGX997Aw+7xVc+7mDdNf4+4Vk7J61GabI0auDd3jJZ9ALe3OtQKG7HYll21jxw5Qnt7+5b7Ww8rCdt79+4xMjKydjwt4EhBsSxua7vaTFmfBrsp19N4zSByYRfjc2uE8JrvqWof4grW2kXW90yTFRFcJya39h3YGjG5LaH1puDeGpNJMyyg1hXaXiPcG1FDV4StIAiCIAjCLqK1ZmhoiKmpKUKh0IrWvs1yOde9prgFU+AedSYr2yu5I9dya+oABzsaI27XkzxKa83IyAijo6NrumpvlytyGcMwuHLlCqVSidOnT697Uu1IWSu6SuTWYZnIXEeiKfT2xeLCUpFb9GscKUXRv7sW3ep3LsYedVmupp61dsnmFkWtzaaZSy59AVN7z1rtbVsWg1vb5+rHd4LtTh7VTEgdW0EQBEEQdoWVXJHz+Twvv/wyuVyOU6dO4XK5Vq1lu1F+uP85wBS3N/Kdlf0etXgPZ9X6tUKAC/nwhu9zdfIQVycPbWGkJmtZWEulEhcvXmRubo5Tp06tGX+8na7I5fq0fr9/1fq0a+FIVQndjY5nBeG7oZq4W8CRUkvaZsCWtC9ZhLVptKjdLQzD2HT4Rj6fx+VyrX1ikyAWW0EQBEEQmoZyTObhw4fp6OgAzBjTrZS7WYsLuT5OuEfWPi8f5oRrfsXjTqUpLAtUpCJuj3Xe3NT4VhO26XSa8+fP09PTQ39//7rilrfLFbnsBr1aPG0tJ/9jTf3aGlHqSJlCtdCgGNxyn2WKfssNersyK9eI252y4tb533AJ9cRtKbj3rbrNzDI34x1wQ4atWWy11g3LabATiLAVBEEQBGHX0Vpz584dpqenl8VkOhyObRW2YIpbgMOuibrHXapEXtsrlttjrjmgfpztSpyfPMqjndc2PLaVhOj09DTXr1/n+PHjRCKRDfXXaFfksbExpqamGp6xumx9dVpitJECFxZFriO9srhtZA6laqG7W67KdVHLY3UBSsEVPCW2Gl8rbIovveaDG75ms8K2kd8RO8XekeCCIAiCINxXlK2LZdfjQqHAqVOnliUastvtDXVFhkV3ZACPWqwReyO/mKCq2h25lldz7byaq5+cafH65WL0/ORRzk8e3chQlwlbrTW3bt1iaGiIp556akOitl5/W8EwDBYWFpibm+P06dPbUoapGmeyxk25kaJzh1yVK/dLqcrSrNgTDnNJLl22zAYTR205vvYBplQqbdrqqpRqeHmu7UQstoIgCIIg7BqxWIwrV66smsV3u12Ra7mc6wXgYffomue+mmvnmGumsr2SO3ItZXG7HgtutRAtFApcuHABv9/PyZMnNzVhbVSMbS6X49VXX8XhcPD/Z++8w+M4z2t/ZnYW2Iq2BR0gSJBgJwpBVatYli25yLIlU7JclMQlsWVHjkuiXDmJ4zix5Ju4y7FvrBspdnJlyZLVLVmWTdmyJZESSQBEI4hC9N62Yst894/ZmZ2Zne27KOL3e559COzOfjO7AJZz5rzveXfu3Jm2KxRThpwmnAcxQVPpBEvFQy8rVc61QxwPhbglQGgDU5ZTQcvdBQB+s5YzpxAcpXg8zf7azUym5cThcHhLiVqAOrYUCoVCoVA2iEAggOHhYbS1tcUVtcD6lCJrIQpckQImegxyl7cvYEfXWjnSJUhYvDG9J+l2orB1uVw4ceIEqqqq0NTUlLELk4tS5OXlZbz++utobGxEUVFRRutxPtUdGR5SWkFTae5D71l/JxcAODcTvaXp6KZYGZ8XWJcOrEsHxq26ud7cXlq6acjJ+mtzSabi1Ov1wmxepys7OYIKWwqFQqFQKBtCYWEh2traYDAYEm6XL8f26qJnpK/lQlUvE7ADgXJ0+WtSWk9L3MrLkQug/RremN6TUOCyLAu/34+uri4cPHgw63m+8ebOpsr4+Dh6e3vR0tICm82W1XqcT0PgiseZpvvK5UCEJmoFFdfONK05G/Jatpy0P1b9fWY/a8bFxb1RlGgFR2XSX5sNbrd7ywlb+ptEoVAoFAplU6PT6RAMBpNvmCYsy6LXXwUA2GOYTLhtl78GBwwpJCdHxO3ugtm0j+fVqQMAgIsru6T7eJ5Hf38/AoEALr30UnDcxp268TyPvr4+BINBxXzabIUyEBG3BAgZk24aJUHbpShu01ovjX2qk5XXk41KWk6VpI6x6nHCAJCLW7VwZqI/asaa+8+BrcLg4CDKyspQXFy8LknFXq8XFosl7/vJJVTYUigUCoVC2TBSEUU6nQ5+vz/n+5b3hPb6q9BQOJdwe9G5bSqcAiC4vH6iByC4vEESXa9rTRDMBwrjC2Y9wyNIYk9QX506gIsru+D3+9HR0QGn0wmj0bihonZtbQ0dHR1wOBzYs2ePorwxk57di76oPeZHdG9zIkiJ0r3N30gf2T42wOBSC93gJu/PzQbi0ms0vBLlNQ4N4cxZA9L3IY8eeov8+wIUWNdyfqy5pqioCLOzsxgYGEBhYSHKyspQVlYGk8kUt9w4mwtO1LGlUCgUCoVCyTH5KkXW6XS4duWv8ULxNwAAw2sO+Hk99hgnFULVwAbh5/XS8874a7HfMJbSPrrWqnCgcFISsAUII4DkIUuvTh1AGAx2N/4WNpsNU1NT6b68nCHOp21qaoLdbo95PNfjgwBAnwfHNW8urnwf7ujXoUzMLvXbmEHlsd4d+6Q3s9hNhZCrIPoNSxB0R79nGCDgKlQ8rkDDQVZ8myx4SqN/NllYFatR7u1wOKQsAp/Ph8XFRQwNDcHr9aKoqAilpaUoKytDQUH0tfE8n7G7S4UthUKhUCgUSo7hOC7n435EVldXgWLlfb2+KuwxJi5NPuOvBQA0FmrPvdUzIQSJcJrVtVaFANHhYJKUZflzRPoCVwNTAIMfJnxuvhgfH8fY2FjC+bS5KEWOh9R/qy5TzmJ34poMAYKyl5S0dTTNfWYtcnOIWuyKQlfvZhC0Xtiid73JRNSqMRqNqK6uRnV1NQghWF1dxeLiIs6cOQOe51FSUiK5uZnMsAW2ZikyDY+iUCgUCoWyYaSS2JkPx9br9eLUqVNgWRZ3Nf5Mut/ACj18vb4qnPOXx9wPKOfbnluTz71NfIydqpRl4TmplfCShr/AH6YOprRtLuB5Hj09PZifn0d7e3vC+bTpzsWNKUNOkYRBUxmtKDjD+lwlHicKnnJHb5sBvZuRxK7exUDvivMOphkclW5/LSU1Tlz7V3EfYxgGxcXFaGhoQGtrK5qbm1FSUoL5+Xl0dHTA5XJhdHQUbrc7rQtQHo8HVqs1F4e/blDHlkKhUCgUyqYm18JW7FPbt28fenp6EorrPl8Vdidxb3v9gmDdY4jvyBYwYQSIThK3u+M4vXJ0IAjLlECQ6HBssgVXVZ1K+txsSNRPq0W6ji3ni24bMjLpO6G+iNuaqKQ43bE+3uhz8tWLK7KZnFw5ehcTI0xDeXZzY4RwkrJfrf7aRI9v5OijjYLjONjtdtjtdrjdbgwNDYHjOIyMjEhiVezPlZctq/F4PAkvaG1GqGNLoVAoFAplU5OrObZiwvDY2Bja29tRUlKS0vP6fFXo81Ul3a7XX61ycOOXT3f5azTHCCV6jsixyRYcm2xJul0mrKys4PXXX8f27dvR0NCQkqOe3bif2OelOuZH7xNumZBoH9JYn3WYXSt3cmPc3E0gyjgXo7qx4FxbWD6oy4CTCuX0+ms3GzzPo6CgAFVVVdi/fz+OHDmCmpoa+P1+nDlzBidOnMC5c+ewuLgY8xnrdruTliIvLy/j5ptvxu7du7Fnzx688sorWFxcxLXXXoudO3fi2muvxdLSkrT917/+dTQ2NoJhmH6GYd4h3s8wTBvDMF0Mw5xjGOa7TIbDd7fwbyaFQqFQKJStTqqlyNn22Pr9frz++uvgOA6tra0xTsXf7nxY+lpedszJyotH1hzS13IBqi5BFh3cVOjy16Rcjqzez68m2vGrifaU96VGLUYnJibQ09ODlpYWzZCoeKRTinzZHffF3Mf5iHRLBbXW0PvyJ0TXe3Yt54neNjOiwOXcytuFTrLgqGT9tbkmHA4remwZhkFRURG2bduG1tZWtLS0SGXLJ0+exKlTp3DixAm89tprKZUi33nnnbjuuuvQ19eHjo4O7NmzB/fccw+uueYaDAwM4JprrsE999wDAOjp6cFDDz2E7u5uALgOwA8YhhEP7t8BfBLAzsjtukxeLy1FplAoFAqFsqnJthR5YWEBfX192L17N2w2W9ztBj2CcN1hjj/2Z8An9N3uNM4k3KcobhsLo9uJ5ciAKlzKX4Mg0eGARtKyuhxZC1Hcvr36RMLt5IhJxuKonr6+PgQCAbS3t6c9Viir8CjV0zgfAUMiJcoZrMFFSorzUU4spSprrZ0HfaJ2cPNdtpx2f6zG9nqZmytfL2RJbxzUhYpWcFSi/tpkqIWtGnnZMiBcAPzjH/+I++67D729vdixYwfC4TCuvfZaVFZWKp67urqK3/3ud3jggQcAAAUFBSgoKMATTzyBY8eOAQBuv/12XHXVVbj33nvxxBNP4NZbb0VhYSEIIcMMw5wDcIRhmBEARYSQVwCAYZj/AnAjgF+m+3rppRUKhUKhUCibmgyr0kAIwdDQEAYHB9HW1hZX1Iqi7MfNgpsoCtxEiAJXC7mzem4t/nZquvy16PLXplSOrMVzExfhuYmLUtpWFLRra2t4/fXXYTAYcOjQoYxm5eYyFVk8r0/HwdUiUTlxCqGzGa+dTxKWLW9yODcLzqN0d3UepdPLeVSyJN3+WkoM4XA4rXE/BoMBb33rW/Hoo4/iPe95D2699VZMTU3hIx/5CC655BJF5czQ0BAcDgf+9E//FC0tLfj4xz8Oj8eDmZkZSQRXVlZidnYWgFARUltbK9/dOIDqyG1c4/60oY4thUKhUCiUDSNT0ZqMQCCArq4uWCwWHD58OO7Jndy5lDPhK0GA59BgngfHhBESnVaWR5AX1hrx27DGc2gyzSjm3qrp9Qv9uXsM8UOo5M/v8tdGHNzxuNsDQAETQoDEnsqJ4va66tfiPpdlWSwvL6O/vz/ufNpUYVk2L3OGAYDzCuJFdHAzEaUJnVYgu9FBMnGbz/m4mvteZ0c3n3BuFmAAzi37G1L9sEPWJK5vsuCobPtrtyDJHNtEeL1eNDc34+KLL8bf/M3fYG1tTXHhKxQK4eTJk/je976Hiy66CHfeeadUdqxFnItfBNrd5Bm9+dSxpVAoFAqF8qZiZWUFJ06cQE1NDZqamhI6FsnKnIc9yQVfvzc1V7bXX4VBmYObzJnVDpdKXUA+OX5p3McCgQD6+/vT7qfVIlXHNqa/No1T17gObjprZOq0prgPcRxRvJFE+Ubh6G7yHt1M0LlZ1U2nuLGqW85JEhyV7PuQR5/7Y0oCz/MZC1uPx6MIjyosLFQ8XlNTg5qaGlx0kXAh7eabb8bJkydRXl6OqakpAMDU1BScTqe0/diYot2iBsAkBIe2RuP+tKHClkKhUCgUypsCQghGR0elAKTy8uSCUy1sxXJkAChgBeE57LFjzFsq3a9no85RYWSbfm85hnxRgSgXoGoxmkrCsvicLn8NelIMo2IR62g9OX6pQuDyPI/e3l4EAgEcOnQoJ+M8UhW2nD9601wnBQGZNGgqVRGax1JihkTn4+ZsRm4GyIOokgndXPTXbjbUwld9Y9Q3F6e4waVX3tyc4kbcesWNV91CqhsABFwF0i3o1SPgLojePHr43QUxt2zIxrFVC1s1FRUVqK2tRX9/PwDgxRdfxN69e3HDDTfgwQcfBAA8+OCDeO973wsAuOGGG/DQQw9hbW0NDMM0QAiJOk4ImQLgYhjm4kga8kcBPJHJMdNSZAqFQqFQKBtGqqXIYk9oPPc1FAqhu7sbOp0OR44cSflkLp0y2mGPDQ3mhYTbnI24t7tMicOlRHG7wzAr3ZeonLnLL/SmqQOm4pUjC49Fw6pEcVsx+W3Y7XaUlJTkrAw8nVRkEc4PhAqTbJREpHI+IgRFpRE0pRbPYtgUkL/5tXJxGzQJ3wc3YDyolrgNmfOzr9j5tOk9/mYoA84FXe+7I6vn51PYAsD3vvc9fOhDH0IgEMD27dvxn//5n+B5HkePHsX999+Puro6PPLIIwCAffv24ejRo9i7dy8APAfgDkKI+OH7KQAPADBCCI1KOzgKoMKWQqFQKBTKFoDjOIRCoZgxPYAwb7GzsxP19fWork4vc0SrFPnHzffh46e1TyiHPUIAVY1xSfNxkbPecjQY5zUf07NhBHnhZHPQ70SQ6LDbOJXS8YoCd3dh+pV6QcJhrPKLGAOwU/f9tMVoPFJxbK/8mMaYH3/0OSFDCvNy48yelbu3qayjtQaQQi9uDhBFrvjvRghcOZLYlb1twTyJ3WyI7ZdN8niS/tmkDvWbhHTDo+R4vd6kwra5uRmvv/56zP0vvvii5vZ333037r77bgBokt9PCHkdwP6MDlQGLUWmUCgUCoWy6YnXCzs5OYnOzk4cOHAgbVGbaN0xdwmAaDkyAHCyebPjvmhpcqFim+hawz47znoEBzdZb2yfrzLmPvlzdKoyY1HgqtEqR46uFz3OgdLP4FfL70p4TKmSUSqyanu9N7sUZCBSAuwj0Ge5jqIXN8/GYV5KlrMUbXpP7O1NT5rBUzEKSi2cN0liczY9toFAIKavdrNDHVsKhUKhUCibHrUAlc9ePXLkSEZjarTWlSOK23KT9myVkYh7uy1ZebKnHLvMiUuTgai4lZcnJ0JenhyvHDkRYcLg4dErAQBH615K+/kiYpl4PJaXl1NeSxS3aTuvKvSRMuWgKbpOJtWtem/0SfK14pFNBa1a3K6bm5vkZRFGVcYsn0+7Cd3dTYk6eEq3PgnM2ZQib0WoY0uhUCgUCmXDSLXPk+M4SYB6vV4cP34cZrM549mrIvGE7fOX/7P09Yw3cTneiMeG856yhNuc9ZRj2CsLl2IThUtVajq4cuTP6fLX4oxGgjIg9NnGQyc7mX549EpJ5KaLODJJi4mJCbz3C/+d9pp6L1GIykzP+8V15GtJpLlmwrXywGYIoEqGOqCK82iEctH+2ozItr8WyFzY5mou9XpDHVsKhUKhUCibHp1Oh1AohNnZWQwMDGDfvn0oKSnJybqphEdNeIoAANXmVYSI4AtwLI9QZKZtARvGeU8Z6s2Lqrm30X5aABjwCKMvdpqTu7J9vkrsNk5JgVI68Agn8CREcbvfMA4+A++CB4uHRq8GANxa99uUn6dViszzPM6ePQu/3w/OxyNklB2PalsmQauvXjXHNrqG6hhSOA8X10rFeRXWjL+oJG4JEDTnv2Fzw9zcDJGXL6uFbDDNebu57q+9kMjGsWUYJm9zxvMFdWwpFAqFQqFseliWxejoKEZHR9He3p4TUQsIwjZeGa3ctRURBW48znvKkrq3QFTgisQbD9Tnq0S/N7F7q37OGX8Nzvi0HdxEs3Pl/bkPjV4tidxkqFORg8EgTp48Cb1ej0OHDgEAOB8PzpdaWJWW0OW8RLqlRILNJOc1y15ccR96D5Fu64XczVWI3i2gQ9T9u+mMJcoFaSc2p9lfu5lIlCSfiFAolHHo1Eay9Y6YQqFQKBTKm4ZUHIG1tTVMT0+DYRi0tbVpJiNnSqrjfuTBUTNeCyZcxcL9spm2BbLy4glvsfS1vOxYvs6Iz4ZzKoEbj35vrMBNFkglittUy5HVBIkOPzn/Nvzk/NsS7kfu2Lrdbpw4cQK1tbXYsWMH3vah7yu2FQRuukFTym+5DMqB473MXIRNyZEL8JRFeA6QRG66YU8p9Nems30u4DyM4qZX3Tj35lbvMcFRG9RfC2Tu2KYy6mczQkuRKRQKhUKhbCiJUnUXFxfR29sLu90Oq9Wa89I4nU6HQCAQ9/E5twUOi3Z41ISrGNXWlbjPPe8WkpPrLYlHA4nitt6kHULFsWGEIuXM57zlCBIWe8yJxwOxDA+esJK43WVIbZyQHPlcXVHcfqT+1zHbiT+/ubk5DAwM4MCBA7BardqLqkb0hAvT/3mKOiDd0uJE6L0yx9mUO99HFLehHBxjOojiVhSm+RxhpCDNftpMx+4oxG3SfUbvCFlzM+Iq3+Siv1Ykk89Mt9sNs3nrJYNRYUuhUCgUCmXTQQjB8PAw5ubm0NbWhoWFBQSDwZzvJ1mP7cnr/hatz30dDosbHMNH+2t1YYTCOky4ihHmGVRZV+Oucd5diipT/Mel7bw2SdzKRaUWvZ7KGHGb6DndEYG7zzgOPRNCME6KMgs+YX/uAyNvBwD8ybZfSfcxDIPV1VX4/X4cPnxYctSvue17cdcREWfZiinIifpt46H3CE8KiYI0SwNMLnJjenszRO7errfIFfYfe9+6id10SFcIp/k452JB1L/e6jXUPbxJHNiY9dJ+fv4c20xDoFKZYbsZocKWQtkiEEIwP72C0aFZnHxpFIOv/xILs6tYXnDDteyFx+2H3xtAYC2EUCgs/MfOABynQ0Ehh0JjAUyWQliLTSguMaHUYUWZowjOqmJU1JShqs6GotKtd3WOQqG8+QgGg+jq6oLJZEJ7eztYloVOp4Pf78/5vlINj5pzCyd5peZYhaBjCSZdRaiyrqKADSMQcVfl4VKT3iKEeBZ1lmWlQJa5sQAw6HEAAHaY5+Iei57hESQsej1CaXKjKXkQlSh6uyUHdzrpcxIhCtyP1P4SAwMDCIfDaGtrS9yXl+AcWxS44YLEIVGJ4CKCVBFUhewqPaXxQ0nCq9JaMyJymTwHTyVzQzXF7pv8NCDXovbNCnVsKRRKTgkGQug9PYqO1wbRe2oUA93jcK9GT+o4/VnYnEUosVlQ5rCiZrsDRlMhCgo56DgdWIYBTwjCoTACayH4fQF4XH64V3wY7J3E4u/d8HnWFPssLjOjvrEc23dXYuf+auw+WIvKOtuWS8WjUChbl5WVFZw5cwY7duxARUWFdD/HcQiF4gcfZUoqwlZ0bQFgyWPSFLcAMOkSgqXs5vhNjqOR2bhV5sQO7qDHgRDPYrtlHkCsAJZz1iO8T7vMSrEqliNr0eurAgDsMU5CxxCE46igZM7xA2PvAsqAVubraYfNaAlOzi9zSw2x66UiUuUhVWqRq0kKrla682xTRR04tR4Jy3FhVGI3cihiArPeCwS3ntbJK5vZrQUyK0MGqLClUCg5gBCCjteG8OtfvIFXftMDr3sNLMtgW1MF3nLdQWzfXYm6HU6cnzyLd93w9qwT67yeNcxNLmNqfBETI/MYG5zFyMA0fvnwcTz+X0LJX6ndgoNHtqP1sp04/JYmlDni9E1RKBRKhjAMA57nMT4+jvHxcTQ3N8ecVKXqrKZLsnUJITh37pzivgWXcGw2qwehcGQUD0sQ5oWTyHmPOaG4BYBJT5EkbuWiVenm8hhy2yVxmwxR4DaY4ru9IjqGR5iwksCV9+AmK0fW4mTp3+LkiPD1x7Y9h7e//zuQy+GwhkhVw/DKk3zOzwNEW+BKJBGlnI+XxHBKIjcFFCI3w1LluGFWMqG7oSJXhjx1Wezd1RS469Rf+2an6yN/npN1splFS0uRKRRKxhBC8PKvzuC/v/8izp+bgdlqwGVv34+Lr96DQxftgNlqUGy/eGw0JzHsJnMh6neWo35nueL+cCiM0cFZ9J4eRdfrw+h4dQgvPdsJhmGwp7kOV77rIK585yEU09JlCoWSA0KhEM6cOQOWZXHkyBHNFM98Ctt4434CgQC6urpgtVrxxjvuQtvz9ygeX3CZUWzSLo+ecQsXAcstLqkcWV6aDABjEfe21rKc8BiH3HYAQJ0pGkIlliMDsc7sWY/wmb7LPKNYJ9Ue3ESIgjgePGHwH8PX4wP/Bjzyheuiz4u4qKkIXAkxaCri4iYUuHGQC0jRyU1X4CZyiaVEZZJbJxfYZG6uCr1HW7hm1beb6/7aLcrQ0BDKyspQVFSU1bleNjNsaSoyhULJiOUFN/71rofxxssDqNvhxBe+/gFccf0BFBTqN+yYdJwODU2VaGiqxDtvuUgIcemfxqu/6cHvnz+Df//aU/iPe5/FW647gPfffjka91Vv2LFSKJStT39/P8rKylBToz17FRBKkfMhbOON+1ldXcWZM2fQ2NgIp9Opeg4BH3FnV7wGhHkWZRbt8uQZtxVhnoEzTrIyIAjcMM+ixhKbsCwXw6PeUvCEwTbzYkqvTRS4jSk4uOoe3D3GyZjHtNCBRziOu/uBf3sOgErgRkQqX5j+Cbvel7nAlSDRXlxAFjiVDXlIadZCLnQJkziEaqNEnlbfrkhwvXVSspCndPtr1wmLxYLp6Wn09/fDZDKhrKwMZWVlMBqNaa2T6QxbQBC2tBSZQqGkxcLsKr744R9hcXYVn/rye/CuWy+GTrf5xkszDIPtuyuxfXclbvv0NRjun8JzPz+BF35xEr996jQuunoP/uwL16FuR2rzGCkUCkXOvn374rqmIvlybLUE88TEBEZHR3Ho0CHFyZ2811bNotuEMotXKkeWO5s6lmDWbYHT4lYIVeU2PMbdxaixrCjKkbUY8ZQBAKpNy5qPy91cQBC4avdWvX813V7hguU+00Tc40iFMFi8/9+EBOXHPv/26L59wnseNgqCWV2GnAjJwc1gVJAaMVE5p32zqvm16rVzNbZUPSc3q7TlNOfVZiKcOfW1Hdka6y56MyHHacjxcDqdcDqdIITA6/VicXER/f39CAQCKCkpgc1mQ0lJSVI3NhvH1u12o7S0NKPnbiRU2FIoGwQhBP/6Nw9jecGNex/8BHYfqtvoQ0qZhqZKfOruG/DRv3w7nvzvV/Do//0dPn3jd/DBv3grbv2LqzelOKdQKJuXVAJOdDpdXsKj5I4tz/Po7e1FKBRCe3s7OC72NMnrLgQAmCxrkmsrsug2gfAMSuK4t7ORZOUyU3xba9xdDACoMLuSHvuEt0QSt4mCogBleXKiMCgRliHgCSMJ3F3GaDBVIkEsPk+L93/zV+AJi8e/8LboWhGBG+Pg5iAkKh0BGc9tzYUIzVfwlBq10F3X0uVkQjjJ9np37H3qX6PgmyziQ8sRlvfXMgwDs9kMs9mM2tpahMNhrKysYGFhAUNDQ+A4DjabDWVlZTCbzTGfo9kIW6/Xi7q6rXNeKkKFLYWyQQz3T+P0q4P4879995YStXLMVgM++BdX4/qj7fjR15/GT7//a/SePo8vf+fDMJgKNvrwKBTKm4h8ObYsy4IQAr/fj46ODpSXl6O+vj6p2Pa6C2EwBYRjY3mEIy4swxIsu00osXhjXFspXMptgT1BaTIATHusCPMsqq0rCpdXLRzPR9zb+gTlyXLRe9ZTjhBhsdMcOyIoUcnxWV8FeLDYLStRTgWtUuUb/+3X0tdP/NU1wnb+xD24yQQm54sETSUqLU5BpKrd1qRzbNMUvnovyXo2bqpu6Wbu0Y0hiaglLMDJ89hScJi3hAucBjqdTipLBgC/34/FxUWMjIzA4/HAarVKQlev12fdY0tLkSkUSsqMDgonFS2XNG7wkWRPSZkFf/O/b8XB9u34/j8+jn/+3H/jK/9+O3VuKRRKSqTi2OZz7FgoFMIbb7yBPXv2SCeN8ei7+fPY/fNvAgD83gKQMAOjdS1mu2W3kKJjNceGS7Esj/mIe2u3uBXlyGFe+bk54SpGtTW291aNKHBrIw6uuhxZzYBHaB3ZaZ5NGAalpi+SorxTNgc3UZ9tMt79rd8AAJ753FuFtUSBm6wHN07psrx/NpwkJCql0UHibNxc9OKKa8abjZtnJKErjfERvtB7yeYWvRlAWO3RRdLjKZUVKzcSnxMyZ2bj6zyqnWTZw2swGFBVVYWqqioQQrC6uorFxUWMj49LjxNCMuq1peFRFAolLWxOYd7h6NBsTCrxVuX6o0fA8wTf/8fH8fyjr+OdR49s9CFRKBRKXAghGBkZwdraGt7ylrfAYDAkf5IGPlchjNY1hWtLxHAplxD4Umz1aT533m1BmGdgt8YfDzThKgZPGFRahPFActdW3Y877BYEboMlvoMrf86AxwmeMGg0xwZMJSorHvBXIEwY7DZOxTyW6HnxSqbf9W2ZwCXJHdwYNDSClMSc6Zgf2biUnAdOISpwgajI5XzZO7qpInenRdEbNDPp99e+uTSxJvLXzHli36PY4ClAvlEa144ygmEYFBcXo7i4GA0NDQgGgzh//jwWFxdx4sSJtEOotuq4H2qnUCgbxN6WOlTUlOIn330BPk/s1f6tyjtvOYKd+6vxy5+9ttGHQqFQKHEJhUI4ffo0/H4/TCZTWqK27+bPS18zOkEQ+FyFCLhjWzDYiCuz4jJCJ3NoWDYqlHQswXxkNq5OcX/0a5YhmHIXYcpdlNIxDrvLMOqOhr+wTOJwrnMeB855HNAz8cu9WcSu0eerRJ+vMqVj0kKnUqTXf+sYrv+2cAMEgcv5sitB1/l4cF5e0ZObDZxXWC/dMuSEa/qIJHTlgldNvtOO9R4CzgPFLVuS9ddeCMI4Bg239tRffCJny+v1elitVpSXl+PIkSPYvn07wuEw+vv7cfz4cZw9exYLCwtx2zvcbveWLEWmwpZC2SB0nA5/+dX3Y2JkHl/59H/Bvap9NX+rIc66nRxd2OhDoVAoW4R0yowJyV5NuN1uHD9+HOXl5dizZw8Yhkl7XeLWGMnGEE1xK7LiMsLliu+WzLvMksBNxJS7CJNxBC6nEsOj7lKFwNWCldXknvM4MOh2JD0GNQO+cvR7K9DvrYh5TKchiFNBKXDD0i1eGXIqcD5B4OYmFIpX3HKJKHQTidz1Qi109ZFbvkhaJpxsni1VNwCi4VFiCFVdXR2am5vR1tYGm82GxcVFnDx5EqdOncLo6Cjcbrf0OSj27CZbv6WlBe9+97sBAIuLi7j22muxc+dOXHvttVhais7d/vrXv47GxkY0NTXh+eefl+5nGKaNYZguhmHOMQzzXSbLnhP6o6dQNpCWSxrxxXuPovvkCD578/dx5vXhjT6krCGEYODMBJxVWy8mnkKhbG7EoKdsmJ6eRmdnJw4cOICqKqFfNBNh2/8nnwVx6zUFbsBdgKA3ej8rc2cYlkjiVu7ayllwmbGgIXDlAlTHEEncckncWAAx4jbZcwbdgsBlEyhAXZzH+r0VGPDFb7FJ5B5rPXbdd16SboDg4oqlygAyck51vrB00ySD37P1ELnqcKu0SVpmnLquEAVurh3enJNRf2387bcK4XBYs7dWp9PBZrNh586daG9vx549e8BxHEZGRnDnnXfitttug9vtRjAYTLj+d77zHezZs0f6/p577sE111yDgYEBXHPNNbjnnnsAAD09PXjooYfQ3d2N5557Dp/+9KfBMIyYavXvAD4JYGfkdh2ygApbCmWDufrdzbj3wU+A8ARf+sj/wb1feggTI/MbfVgZ8+RP/4je06O0v5ZCoeScbEb+8DyP/v5+TE5Oor29XeFGZJ247JNFlsjEXtBdgGAcB9elcm+1ypQXXGZFObIWkwncW0Aphsc9xTjvSn7RkWOj78Wg24FBT/oOLgD0eyvR7828TFmL677zEq793u8AaAjcOCRzZxMK3AzJl8gV1iaK27qSRCSCEUKb5De9T7i9aUipvzb+9+tFqqnIYgjV/v378c1vfhOf+MQnsLi4iNtvvx2XX345/uEf/gFvvPGG4jnj4+N45pln8PGPf1y674knnsDtt98OALj99tvx+OOPS/ffeuutKCwsRENDAxobGwHgCMMwlQCKCCGvEOHK4n8BuDGb15z3t5phmOsYhumPWMx35Xt/FMpWZF/rNvzwyc/hlj+/Cq/8ugeffNc38bU7/xunXx0Ez+f+P8V8sOYP4j/ufQY//Jencck1e/HOWy/a6EOiUChbhFSrzzIVoGtra3jjjTfAcRxaWlqg1ytd1kzX7f+Tz0a/8XDCTU5ErAbdBQrXVo7bZYDbFb+/d8FlxmIkYTkRsx4LplwRBzeJGD7vKo0RuImcWQAY9AgCV6vPNtka/d5KnPPGd3DVfbapcO33fifdOH9YuqVEHDc2qYsrI70ZufkTucL6Gyh0kyH70xYFrt4bvXG+qAAGAF1siPibjzz314rwPJ/2uB+O43D11VdDr9fj97//PZ566ikcOHAAXV1diu0+97nP4Rvf+IbCEZ6ZmUFlpXAhq7KyErOzwvSPiYkJ1NbWStvV1NQAQHXkNi5bdjxyX8bkNRU5YjPfB+BaCAd7gmGYJwkhPfncL4WyFTGYCvAnn3sHbvjQpXjiJ3/Asw8fxx9+dQbOqhJc+c5DuPRte7HrQE3ake35xu8L4DdPnsLPfnQMs1PLePcHL8Yn73oXHfVDoVByDsdxaQvQ5eVldHd3Y9euXXA4tJ3HnMzIZQHwEMStORRjZQXdBSA8wFmCitRk8Wu3ywCL1S/NumVZHrxsdq0obsssXilxWMcQhFX7EcWtw6w9J1c+UmjCXQweDGoty0leGgEfUSiDHgd4wmCHZT7uMcRD7L9tMk3HTUcG4icnx+Ot3/sDAOA3n71MCpoKGTOb3wkIolUMmgplmqgcB7m4DeZwhJByH6r5teJYHx+Rvt6McN7ImB65u6vhEIdk13k4n/L7pP24FxCZzrGVt2WUlpbi5ptvVjz+9NNPw+l0oq2tDceOHUtrPfnd0P7pZHVlJt/jfo4AOEcIGQIAhmEeAvBeAFTYUihxKHNY8aefvw63ffoa/OGFM/jtU6fx2AO/xyM/fgnFZWa0XNKIwpIgttfOoqbBviFCd80fRNeJIfzhhW78/rkueFx+NB2swRfu+QAOHtm+7sdDoVAuDNIpRSaEYGxsDJOTk2hpaYHJFN/1zEbY9v/JZ9H0wPeUd3o4gGcAS0hwZyQRC4TcenAW7d41t8sAwjMwWePbVotuEwjPoNTqjbsNAMy4hFLrcqsr4fgdABhzlwAAqs3RebkcG0aIj39SPOi2A4AkcLWIJ1BFgcsTBk2mmfgvIk1EgQsAv/nMZQCAsCFzgQtAkaS8FUWusJ/o/Fq9N764Tae/diNRz6eNN682qJHDdqH01wKZC1uReJU0f/jDH/Dkk0/i2Wefhd/vx+rqKj784Q+jvLwcU1NTqKysxNTUFJxOYVZ2TU0NxsbGpOdH5uxOQjA9a2RL10Tuz/yYc5EuGHdxhrkZwHWEkI9Hvv8IgIsIIZ+RbfNJCE3DcDgcbQ8//HDejmer4Xa7t+QMqXxxIb8fPk8AQ93zGOqex/m+BXhWAwCAAgOHijorHNVW2KsssJVbUOo0wVxUkFbKaCLCIR5Lc17MTboxM7qKyeFlTA6vIBziUVCow85DThy6vAY1jaU522e6XMi/G1rQ9yPK1Vdf/QYh5PBGH8cWJ++1jYQQBAKBpNv19fXB4XDAZrMl3C4cDqOnR7iGvnfv3qQndz09PaisrERpaWahd3vvu0/Yr5mHolJXFLe8bJ6l7HGdKSS7n4n52mT1S64tAIU4lYtbuWMalm8fWafc6lI8V74NAMmNFR+rswpppnJhy6vMFfl6PGGwXSZwlY8p9xUGo7ldk2lG9VhioZfqtr+549Loc4xcSqFQycqMU56tmwV5EboJ/osOmpjkwjaF/tpU9xdvjWSOa7r7jOl3VR9AEiEbT/iKLrHOH+sgywW11vdanPjCx7UfyILu7m7U19enfT5ACMEVV1yB06dPJ9322LFj+Nd//Vc8/fTT+NKXvgSbzYa77roL99xzDxYXF/GNb3wD3d3duO2223D8+HFMTk7immuuwfDwMEcICTMMcwLAZwG8BuBZAN8jhDybwcsFkH/HNqnFTAj5PwD+DwA0NTWRq666Ks+HtHU4duwY6PsR5YJ/P94l/EMIwWM/exbWgnL0d45jsHcCZ16dwpov6gDoCzg4KopR5ixCic2MohIzLEUGGM2FMBgLwOl1UqkwIQTBQAhr/hC8Hj/cKz6sLHmwOOfC/NQK5mdWwEdGK3B6HRqaKnDDh/ai5dKdOHTRdhQUaoy8WGcu+N8NFfT9oGw1ctlj6/V60dHRgZqaGtTU1KS0tk6nyyrPoOeOO7D3vvug87AIG1XruCOnWqbY4+YjicpsHAfX6zLAYI4v+Jdcwhl1kSVxMs+MywpCGDitLgDKcmQtRiP9t1XmVek+eTmyGpYhGIo4uNsTOLiJ6PeWgycsdpmnI2umV44cj7fe90eEI+u89JmLASR2cVPpndWp5uGGc+zkAojpx82noyvsj4Aw6hLm/O4z7bE+mwjRJSZsrGMsH4VE2Njv1eRD1AKZ9dgCQCAQAMelLxHvuusuHD16FPfffz/q6urwyCOPAAD27duHo0ePYu/eveA4Dvfddx+uv/568QPxUwAeAGAE8MvILWPyLWzHAdTKvs/aYqZQLnQYhoGtwoyrrjqMt79fMKJ4nsfs5DLGh+cwNbqImcklzE2tYHHOhZGzM1hd9sLj8iEcSnzixrIMLEVGFJWaUWq3YP/hbSivKUPNNjvqdjhRt7McBQX5/tigUCgXIqmM3OE4LmEp8tzcHM6ePYt9+/ahpKQk5X2zLJt9j20EnY8F+Ih7Ky9DdutALGEwbNS1JSwBwzPg3XqwlqDCtRXxuwsBAAbLWtx9rkTSlYutPoVoZVkiubYMQzAbKU8WBa7m8cueP+kpAk8Y1FhWYraLV9485LZL92+3zCfppY1d46wnOge30TQb9ziV66Qmgq/8/qvS16mI3FSRC918iFwgB2XLScf8JN6nsAazoT26OXdr3+RkWors8XhgNiefpw0AV111lXQh3Waz4cUXX9Tc7u6778bdd98dcz8h5HUA+9M+yDjk+wz1BICdDMM0AJgAcCuA2/K8TwrlgoNlWVTUlKGipizuNpIz6wsiGAghHHFhWZYBp9eh0KBHoUG/YeXEFAqFkox4ji0hBENDQ1hcXER7ezsKCrRH7KS7bjqIrq20pocVxK14jKwgbgGAxHNveQaMKlwKDAEIIwncgoiDqwigYoQKW1HgWszxRTAAzLqsCPMMnFYhYCqRGwsA4+5iAECVZTXuNnJEwSq6uNvMi9JjOhBFGbHyeUqBejaSpLwrh324InKR+7s7Lk49bCrp6KD1FblA/p1VAMIvGaL9umqRuZlDqeKSYRnyViEbYbtV25nyKmwJISGGYT4D4HkAOgD/lxDSnc99UigUbRiGQUGhflOUDlMoFEom6HQ6BIPKst1gMIjOzk5YLBa0tbVlFKiXk1RkyMRtJCFZ5xGOJWxUqiHWqwPDMwhbQpJrK0Ii5ckwaTvTAVcBCqyJ+5HF+bhWq7JEmWEIiJiozBLMuoSTV1HgaiF3VSfdRSCEQbU1dQcXAIbcQk/0dstCwuOOWTMiuEWBGyYM9kRKlRMJZDU6hpfKkbW44j5B5P7ujty5uEBU5DKEIGTKzZpabIjQjTkGleKP/GiCZuELzksQ2oriNwFJ+4E3eJ4tz/MZfR6m49huNvJeUxhpAM64CZhCoVAoFMqbn1RLkf3+aGKwy+VCV1cXtm/fjoqKigTPTEyuhG0wGATnYRAyk+j4HwCch0XIzAuurTw8ys0hbJEJWFnpMrxcVNxGXFthG0HcAkCBNRDj2gIAw/IgPAuXywir1SeVI8dj1mUBIQwcRYLATdaDO+ESHNxq60rCtGXpZUkOriBw6y2LMY+lSm+kVFkUuNF1su/JFQUuIIjcXAhcJvJD4byRMUR5FLgiMULXvHFWo94TdXg5ufhllC5v1qFRW5R89deKZFKFR4UthUKhUCgUSp6Rj/uZnJzEyMgIDh48mHXZnE6nSymVORGiyH7h9ptw7YOPAgBCEaeWsASc5N7y0n0Mz0AXCZfiNcqTpeApS3z3FoSB3hL/2F0uIwgPWDRGCOlYIs3NZRiCuVXhfRQFrhZy13fCVQw+Awf3vLsMPBg0aDi4iQSqfGZur6wXd5c596XKl9/3mvT1y58+EklUzn5dUeCKrIfQ5VRCN6RydDdqpI3c5dUSrqLbmxJZpiFTomzlyQpU2FIoFAqFQtkSiMK2p6cHgUAAR44cySi9U2vdbBzb6elpDA0NxYhszsdI4lbal08jORkAG+m/5S3hqGsrur6iwDVrH2PQLTi4nCxBWXRtha+FGbmAIHBJEiUztyo4uDarEOeazFVN18EVGY44uDzRFrmpctYjlCo3mubibpOsHDkRl//guPT1y58+grAhd6fPm0HoAklcXZXrt15CWHR7tfZJWOGOUPzx1GmR9nzbN7Ewpj22FAqFQqFQKHkmHA5jZmYGDQ0N2LNnT87C7jId90MIwcDAAFwuF9rb26HXC/2xnX/9aRz8xg8AAJxXPAGP9tKK7m3IzEf7ayMilnXrwJviHIuLA6whRZmzvEw55CkA4QF9gh5ct8sAQhhNB1cOwxAsuIRyRFHgaiEXvROuYhACVFljQ6YSiWOWIZLIVQvcZMFWcs55HZLbmw8XF1CKXAB46fOXxtkyWoacDnKhux4iV0Tvkf3ORf6uMg6ESrOMOBuhLI3aSbamSogGc11pu8n6a7OBliJTKBQKhUKhZEEykbq4uIje3l6YzWY0NDTkdN+ZjPsRQ6uKiorQ2toac/ycN+ImMQCIIHDDgmkq9dpyHhYMD6EnV348XuH+sIVXilhAELcAYI4/9ijoKkgobhmGKBxceTmylpu74DKDlzm48bYTmXQVSV9XWLRHC8UTrKLArTcvaT5PXo6cCNHFzZfAFbnym3+Uvk4kcjMhF25uNqIxmoAc/f1UlzHnhSQiVXRr422fCorZs8g+CCqZkNYStq/8Xf76a7OZy00dWwqFQqFQKJQ8QAjB+fPnMTMzg4MHD2JgYCDn+0i3FNntdqOzszNhaNXrf/8XOPzVHypKJXV+gAkDIZkZQlhoBk4BgM4d6csVHVx5uJSHA8MDxBpSuLbinNygSyxPDinuj3ktLgMIz8CUxMFlU3Rw5SFWgJCkDKQ+Kkhk2B0dX1dv0Ra5qSAKXEAQuamWI6fjFIvkU+QC6+TmJik7TruMeQNIKjKTlR2/CeB5PqNRP4AgbB0OR46PaH2gwpZCoVAoFMqmJBQK4cyZMygoKEB7ezt4ns9JerGadITtzMwMBgcHceDAAVit1rjbsSyL77+9GZ/51WkAQMgYfYzzCOJWnpDMeSLlxFLgVPRxnZeNilsVTMTBJRbt4w+7hPJonTWo+biIN+LgmmQ9uIkcXBCgzCrYXqkkG4sCt8Icx8FNGDZVKvThWhc1H1euEz986qynXNrHTvNs0rWyQS5yf/dXl+R8/Y3ozdWEUaYwx8y33WSiNyVy7NbGI9NxPKmQ6QxbQBC2ua6KWS+osKVQKBQKhbLhqEt5PR4POjs7UVdXh+rqammbjRK2hBCcO3cOq6urin7aVOF8grglOsG15TyIlCErRSznYwCN8mRpJq6Zl1xb+fMYt04St3J3VkxfFgUuaxYErly0MiyRxgZ5XQaAAEbrWuIXxACLLsGOFgWuFmrncyoicCstqwldUS2hO+yKurh1Wbi4ADDgcUpf51vkXvGtVxTf50voEtnfUNjIbljasRz1fFvxmMSZtvnsv90saF1n+c8PXI7XX38dJpMJZWVlsNlsKCwszNk+sxW2tMeWQqFQKBQKJQeIruj+/ftRVBTt18xVWJSaZMJW7Ke1Wq2a/bSJOPmVT6P1K5EgqUgFb8gsiFuhDFl2n8rBDZlJ9L5Ir67Ow4LhGYTMsQ4uE0lWjufeAgDvjghcS2IH1+cSTrKN1jVJAMdzVRddJhDCoDQicNXlyIpjjAhqUeCWx+nBTcaouxRA9gIXiIpctcDNpBw5FeRCNx8iFwB0vsQjfjRZx/RjaaZtHHc0ZNTeebL+2kzd0/Vm9+7dIITA4/FgcXERPT09CIVCKC0thc1mQ3FxcVZubjZuMO2xpVAoFAqFQsmSeCnD+SaRsE2lnzYZJ7/yaRz5mx8I5ci8zK01yYOkgLBYrsyK2zFgiJCoLEecixsy8wrXVoRx68AgzmzciEAWBS4j9eBGXVtxG0AUuAwMFg0HV7YdwxAsRRzc0gQOrpopWdBUpXU1YXKy1mOiwOUJg20plSrHL3ke8DglIduU59ApkVy5uSTJxRat3tisg6Dy6K5yPuEXK+Nk5jgk7a9dx/5bhmFgsVhgsVhQV1eHUCiEpaUlzM7OYmBgAEajUXJzDQZDWmtn49h6vV4qbCkUCoVCoVAyJRAI4OTJkygpKUnbFc0WhmFANCzGVPtpU4XzAaFItSFhZcnJEXS+aHmyCGGUI4MgO0xxbJDWXFwA0EXm34YtoehYIRXEpQeTpP8WAPxu4cANlrWk/bRLLhMIiQrcVEuOp1xFIASosLpiHkuFkUip8jbrYtw+21Tpl4VO5btUWc56lC2LcDGubo77dJM5wCn8aPU+dSlz9PvgeiQ0q8hFGnI8OI6Dw+GAw+EAIQRerxcLCwvo6+tDMBhEaWkpysrKUFJSktSNpaXIFAqFQqFQKBtEIBBAXV0dnE5n0m0JITkVvuq1xH7alZWVrJ1j8ViP3yu4ttwahB7aiDsrjh0JywwZqTzZqFgKnJeRhUtF5+LqfOLYoAQClwf4OCXKJNJ/y1iDmq6t8IVwv99dCPBAgcY4IUXfLoO4Dm6ycUHTLuEigihwU0EugkcUvbjLKa8BaIvw9ezHVZM3oavx9qsDqQizvqFUSd1T1fdq0au1hvw5oRy7v5mSypgfhmFgNpthNptRV1eHcDiMpaUlzM3N4dy5czAYDLDZbCgrK4PRaIx5fjbC1u125+RC3kZAhS2FQqFQKJQNx2q1plRux7JsVqMskhEMBtHV1QWLxYK2trasBLToBItriOIWbDRMSgqN8ipLkwFA7wGCZuHkXDSqOB8DhgeC5tiTetHBFQWuXPyCBVi3ThC3ctEqGyFEXHrhfkv8Gbkigcg4oQJrQOEiayEKXEIYlBQlLlOW9+dOu6ySAC63utJ2cAFg1F0i7bveKvTjZrKOyEaKXAC46lt/VHx/7K9yP1YIiApCtdgFImJ3c2hEBcncVE7t/mqYnrFrMAkfT+bQ5qqUWafTwW63w263A4Dk5p49exaBQAAlJSVSb67YWpFNjy0VthQKhUKhUCgZkqqAFE/a8iFsc9FPK0en08WEuOh80V5azif8Gy6MliYDUfeWsIK4BZQlywCgl8YDRbeVBLGLRdCq7d6ykYAp3pwgBTpSwgyzXOBGXVv5vN2AqwAgDAo0UpS1QqSWV4UXUmz1RY8pgdAU3d2ZiIvrsLjjH3cSzruEflxR4GaLXOQCm0Po/vbzl+V9n5w3HFNmHDPWZx2DqHJFtqJ2PTGZTDCZTKitrUU4HMby8jLm5+dx7tw5FBYWguM4TSc3FXw+H0wmU/INNyFU2FIoFAqFQtkycByXl5E/YvJxrvppAcFdDofD4Ljo6dYr3/00LvlLISU5HOm3lUYBRcSpzi84tIrZt14ARGM8kEfZkwtEBLFLOOsOWnmFaysKUtajA0OAsCWscG0Vbq6HS8PBFV5MgSxFORErLiNAGBRrOLiJUpVnXdGfjVNVqpyKQAaiAhcAajVKlTNNQ95oNxcArv7mH2LuixG7eRCZMeFUihJgjYtQaYY4bQXy5dYmQ6fTwWazwWazARCE6blz5zA/P4/5+XnJzS0pKUnpgqD6M2srsTWPmkKhUCgUygWJTqdDKJRcaKWK2E8bDAZx8cUX53SWZLy0ZVHc6tYiYVFGpXsLREKjVOXKYDSEbIKRQUBE4BIgZNFWirqIgxs2aTu8AKIOrrxHVyaSwRDJkgu4CkFI8h5ckZWIg2uVObiJkK8hily1wE2HsUipMg8G9TkYHSSyGUQuAOgYHm/71u8V9/36829J+Jxcu6ucNwyw2g5uyJia+osNnkrspm5Wh/j3/5K8vzZbjEYjrFYrysvLYbPZsLKygoWFBQwNDUGv10si2Gg0auYLbGWosKVQKBQKhbLhpFuKnAtCoRA6OzthNpthtVpzXt4s9gNrIYpbouq3lYtdIFbwAlEhG1aHS4ljhFSuLhiAc0dKly1EEqTy3l2dVxDAYTOvdG3lX7t1YHgGpCi9HtxUzpVdLqO0XVGRUuQmC5uSu7j2DEuVWRCcdyd2cjMllyXLPBiwyZqaZYQJC53qasfbv/VSzHa/+qsrUz+IHKQdi0jJzHGCorIeSRTnmJK5q8nGJ212xB5bnU6HsrIylJUJgWo+nw+Li4s4d+4c/H4/iouLYbPZUFpaKn3+MQwT9/N4bGwMH/3oRzE9PQ2WZfHJT34Sd955JxYXF3HLLbdgZGQE27Ztw8MPP4zSUuHv6etf/zruv/9+6HQ6fPe738U73vEOcT9tAB4AYATwLIA7SZbKmgpbCoVCoVAoW4ZcCVuxn7ahoQGVlZV44403EAqFclqCJ/bYxuOV734aV3ziPoQKGXA+gOEJQkZGKXal0Cjh35ARktCUO7WSWGXjC19AELgMDwTjObjiCKEEDi6zKrxHRF6iLHNt5aXEQg8uoNdwcOXPkbO6Khx4PBc3kdCdd1vAE0bTxU0mkOWITi6QW5ELbB43V45a7D7/+TSEbjLiuLUSCX4kUolzjJiO/v7mTPwmYKNCozIlXsCe0WhEdXU1qqurwfO85OYODw/jBz/4AbZv3w6dThc3eZ7jOPzbv/0bWltb4XK50NbWhmuvvRYPPPAArrnmGtx111245557cM899+Dee+9FT08PHnroIXR3d2NychJve9vbcPbsWfHY/h3AJwG8CkHYXgfgl9m87g1+2ykUCoVCoVAEUnFtc9FjOzs7i46ODhw4cACVlZUAkovQTBB7bONBCMGPv3QtuDUCvY+AsIwiuZXzCf22QPREmZNpPek+DzTP6HS+aCCVXDwQFtC7GejdjFJkyL7WeVlwblbjudHjY9wcGFcKFwIYIOgqQNBVAIaJb8iof/yuVSNcq5kF4My6rNItW8bcJdIt1wx4nIrbZuEd34x1ddeLpGXHMWnHPPQe1c1LFDdOddsI1qMMWSSVgD2WZVFaWorGxka0t7fjy1/+MkwmE6amptDc3IxPfepTePLJJ+F2R6sgKisr0draCkBIst+zZw8mJibwxBNP4PbbbwcA3H777Xj88ccBAE888QRuvfVWFBYWoqGhAY2NjTh+/DgYhqkEUEQIeSXi0v4XgBuzfd3UsaVQKBQKhbJlyKbHlhCCwcFBLC8vo729HQUFBdJjyURoJiQqRQ6FQujo6EBRURE4n+DU6n0EQWNU3IYLhTN4UZyGTEJ5MeeHMAtXNh5ILEMOqsuQER0lpIXezSCkMTpIeq5bOUJIC1HcElkPbrwAqGAkRRkAOGsgrmsrRy5uLVZ/wm21kIvbRKnKqYRG5dPJBdYnaZknLFh1M7YGnE/59xAy6nJahpwvSBKHmOhUo380jjl5qXJ62683mSTH79ixA7fffjteeukl/OpXv8Irr7yCX/5SMFBvuOGGmO1HRkZw6tQpXHTRRZiZmZEuElZWVmJ2Vvi9nZiYwMUXXyw9p6amBhMTEwBQDWBcttx45L6soMKWQqFQKBTKliHTUmR5P63WfNpc9u4mW9Pj8aCjo0Mqg/7NT3firR/+vvJ4CwHdGon02wrlw5w3OgoIycYDiWOAIn20kjjWGA/EiaODEglcDwsQBiFLWDkfV9aDy0SCqOQCV5OImA1F+nA5SzDOdtG1Rdwu4cVarP64ZcWJ0pHn3BYQAjitmY8NEsm3yAWiQlfsq91hnstJn20mcL5wjKALmZJIiSzKkDeKGGGcpqjdDGQ6x9bj8cBisUCv1+OKK67AFVdcobmd2+3GTTfdhG9/+9soKiqKu55Wy2zks1frJ5+1lU6FLYVCoVAolE0BwzBJUzk5jkMgoNGvmQB1P60W+RC2Wo7t/Pw8+vv7ceDAAcUJ4W9++hlc+4HvAmARLmTArQniVui3JZK41fkjAVEyB1bnlwneCJwPgqtrVoZEKfpyVUgC1yRsrHZ+AYBLIUVZFLgMZPNyNUSqSNilF16HNZhw1I8ct8sgCdvMXFyL9PVWEbkAMOhxKL7f6B5dtasrypWQMbMgtnTLkDcjWkL3t9/+xLoeQ6azvj0eD8xmjQ8HGcFgEDfddBM+9KEP4f3vfz8AoLy8HFNTU6isrMTU1BScTuGCTE1NDcbGxqTnjo+Po6qqChAc2hrZsjUAJtM+YBWb8BoDhUKhUCgUijbpClCxn3b//v1xRW0m66aCfE1CCEZGRjA4OIjDhw9ruhwvPPKX+M1PPwPdGgHn48GtAfpIySTnI1L5JIm4tZxMz3Fe4aY+qeY8UTELQDrz4zxCD64WYv9twtfmYaWgqUSum86tk0YKxUMUK2GXXhK56eB2GSQnNxNmXRbplo4TGg+xH/e8q1QxMzcf5LNH95p/f1nxfTLRKYfzhYWbJ6S65XgGdYx7uvWEcD6IFx6VjGTClhCCj33sY9izZw8+//nPS/ffcMMNePDBBwEADz74IN773vdK9z/00ENYW1vD8PAwBgYGcOTIERBCpgC4GIa5mBEs3I8CeCLtA1ZBHVsKhUKhUChbhlR7bMV+2qWlpZh+2njr5sux5Xke3d3dYBgG7e3tSUsERfeWAx9xbwmYMBA0afTf+oGQQdZr6xXc2ZARilmzOi8Q1uizlffviohrieJWdHAV/bARBzaVFGVANi9XcnDj99byMnHLWoNxnV51yrF7NSpuLUX+uOXIiVzhWZdFWtNRlJ2TK5ZEi+KWZUjGbm6q5cdyccsyBDtMcwBiy5FT7bNNiyQiUhyhoxC3qj+FoDm3I7dijkG9fDJhvEUtQJ7nsypFjscf/vAH/OQnP8GBAwfQ3NwMAPiXf/kX3HXXXTh69Cjuv/9+1NXV4ZFHHgEA7Nu3D0ePHsXevXvBcRzuu+8+ueD+FKLjfn6JLBORASpsKRQKhUKhbBJSSUVORYCGQiF0dXXBZDKhra0tpRO8fDm2Pp8PJ06cQEVFBerq6lKe1/vCI38ZKU2G1Ger9xIETZGS5DUiiVt9JOVVfIwwqvFAYi+tXMSqZtlqCVyRlHpwxZApi1IsycugAUDnFk49w5ZQ/O1kZcuiyGXj9eHKkT1PFLkm61ry58VhbjV6gp+tyAUAnjDrVrIsMuh1xNy3yzyT9/2mhMbsWGm8D+KISoZByLhxanOzh0bJSfWzRo7b7U4obC+//PK47SIvvvii5v1333037r777pj7CSGvA9if9kEmgApbCoVCoVAoW4Zk437UwUypko9xP36/H2NjYzh48CBsNlvaz3/hkb8EALz9/d8Bp1IBIQOjCpcSxpqACN9LgtUXSUs2CpqPgUzEalTvcm4gZFH110YEY7QHV3k/IHOM4whcNZLANad2MYF3pyFwZXhdhdLXqYpcrXm3uRa5AGLGB62H0AWAs55yAFA4tvHE7jX//jJe/NTlaZUh5w3R8fUJx50siCrf7m+qrHd/bTak0mO7maHClkKhUCgUypYhUSny7OwsBgYGYoKZUoFlWQSD6YmmRExNTWFiYgLl5eUZiVo5v3rsTlz/zm+BL2ABsAgXMOD8gqhVlicDYKKjTMIG4UyfsIDeJ4hbOfqIwA2aZG4pK4hbQLt0GUgcQCVt42bBECBo5VVurLIEWd5/y8tFbpywKd6tl57PWgOaIjQeHlmpsrnIn1JIlRb5ELlAcqGbbhpyOohiVyez13eYhGAq1if8vYUTJSCnWIa8nnB+1cWVlPpxle9v0LKJLNh1IFkp8maHClsKhUKhUChbBq2SYUIIhoaGsLi4mFI/barrZgIhBAMDA3C73WhqasLy8nLWawLAL5/9KwCCewuwYHiCkIGF3ksQMohOlnBSHjIyQv+rn0jiFhDErfB45FjFXlovBKdXJWR1Yr+uGUqhKTm4kfVMyvXk6F1JHFzZuqxHBxCAT3FcEB8ZF8TIXdwE6ctyEeyRSpXTT1SWk0zkqkcP8YQBy6QmTrN1dJPtK1mf7aBXGUal88ouKMn0XtiYfuCXVhmy4vtNoCeFkDZ5abRKGWvMx93qeDyetCpdNhub4NcmysrqGr7x7V9iamZlow+FQqFQKBTKOpNJj20oFMLp06cRDAbR1taWkajVWjcTQqEQTp06BQBoaWlBQUFBzvt2v/LFdvz6oc+CDRBwfj5yI9B7eenEWxS4gCBuOS9RCAXOp0pKBgSnN5KsrD47jElWVqH3ROfnxoNzs+BcYopyYmHHunVg3bqUZ5wStx7EJdzSxesySDc5TIriU87cqkW65YMxdwnOu0ul24ah+v3Q+YLQ+UKKW85JNvZnk6Yf/+pHn1z3ffI8n1F/LQB4vd4tXYq8qYQtwzB44bc9+PAn/gP/+r3nMU0FLoVCoVAoFBlyAerxeHD8+HGUl5dj9+7dGaWAaq2bCV6vF8ePH0dlZSV27doFhmE059jmiucfvxP61RDYgCBuCctA7xVELgBB7MoELucl0PmVYi1m5A8jbhstU5YLCM4rE7iy+8Vt9J5oaJX6udIaLjZyi3PiLbubTTQqKI7wJC49iDsDBxHxRW4m5FvkAsB5d6k0Wkjt7uaSuh8MJd4gRnQyYP3h6G0tDJ0/JN3WA6JL4q6+iccChcPhjD8Lk4VHbXY2VSlykbUA/33/J/HTn72CZ5/vwrO/6sJ1b9uPDx+9GFWVJRt9eBQKhUKhUDYY0YmYm5vD2bNnM+qn1SIbYbuwsIC+vj7s378fxcXFijXzJWwB4NnnhDmS193wbemETuy/FUOkRHEbEscDRRKUQyZGOy05AmEFcRs0xSYbq0uQ1YjubTCR8cNAErchK4lbPgwo+3DDycqUI8jFrbxUOdWeXK/LIB2TMYtkZQBYcCnfCJvVk3I5cjLkfbdapcvpliOHCaPos80HujVVK4G8rNnAbZoyZOX3W6cMOdMZtgDtsc05TrsVn7/j7fjw0YvxP4+8hmee78RzL3ThrVfuwYeOXoyGevtGHyKFQqFQKJQ8kEr5HCEEa2trGBkZybifVotMhC0hBKOjo5iensbhw4dRWFioeJxl2ZyXImvxXz++DefOncNX7zkOgAV4grCBBecjQmIygWIWrjDvNiJwDUzsyB9ZyJRefZ+sh5XzRhKXLUrxK/XuqgVwnP5XzsVEgqZiH4wZF+SKzMO1qt7XBL21xK2XHmOsaQSERdb0yZKVsxW5gFLo5jJ8So0odOVl1XXZJi+rRWeOQ6F0/lDCsuOwkdsyZcj/9+/eCZ/PB6PRmHzjHBIOhzMWtl6vlwrbfOB0FOFzn74WH77lYvzssRN48tkOvPDbHlx2cSNu+8BF2L+neqMPkUKhUCgUyjoizqclhKQ8nzZV0nVXeZ5HT08PCCFob2/XPJZ8lCIzDAOe58GyLAghGBkZwfz8PA4fPoxfPnEJ3v2Ob0bSk6WjACAkJBMdFLNwAUiObjAigAFBsIZMyjAozodowJRKROoj2ixeSrK8P1fh8srHBTGAPuLgBpM4uEBU4AJAOMloITlSH64ls5LYXItcdalyPoUuAIyqXN1UhW7dD4Yw+untSbeLST/OsejU+WKFb6x7GqkEMOq0H1e7r3nk7NmzCAQCKC0thc1mQ3FxcU4/t7TIRthSxzbP2G1W3PGJt+LDt1yCx558A489dRJ3vHoOB/bV4Nb3t+PSixrBruMvKIVCoVAolPXH4/Ggs7MT9fX18Pl8GYejxCMdd3VtbQ2nT59GeXk56uvr4x5LrpKW5cjFcnd3N1iWRVtbmyR4H3/mL8EwDN5z4/fAhMUxQKyU7houFJKUAaVbq/dF05XFIClAEKLy4Fy1q6sQvx4I4jfOHFzp+STxqCC9rP82aCGqcUGIEb26yOzcsIVPKogl3LJT4EQiN4ETnGuRC2QmdJONASKEiRuGJQpddblyg3UxZlt2TXC7+UxSkEWSpR/n8O+a8wl/e0kTl1WPB83KDZKVIcejpqYGNTU1CIfDWFpaksaRGY1G2Gw22Gy2mCqPXJCNsKU9tutEcZERf/rhy3HrzUfwzHOdeOTx13H3P/0CtdWluPnGw7jumv0wGLL4Q6NQKBQKhbKhxBOIYj+t2MM6OjqaVR+ZFhzHpSRCV1dX0dXVhaamJtjtiduj8tFjy7Is/H4/enp6UF5ejrq6OgCCgyymoTIMg6ef+EsAwHve/R0AgsgMFzLQrfFgeCBkjArcoClSriybjSuN9PFCGC0kuw8QHFyGCD24asQ5uAzi9+Fq9emqy44BQO+OuG/m5IpV52al44txcRMIVLi56GPWzeHkiohCl2EI7NYk0dM5RCt1WfxrY32Rcm7Z32tWYjcBsWXH+XWEAYDzKX930g2iAoAn/+/HpMoKnU4Hu90Ou90OQgi8Xi8WFhbQ09ODcDiMsrIy2Gw2FBUV5eSCnbjfTPB6vbBarVkfw0axZYStiNFQgJtvPIwb39OKl17ux8O/OIFv3fcCfvzg7/Ge6w/hfe9ugdORfYgEhUKhUCiUjSXefFrRCc2lsBUdz0RMTU1heHgYzc3NKY3ESGXNdOF5HqdPn0ZTUxMcDgcIIQiHwyCESKJWzlNP3wlAFLg6QaQaWenkXXJwCUHIxEZCo6LlyYBw4i715BqV60s9uGKQsLy8GKpgKg3XlYvMyk0YNAWA88gEbiKRGkHh4qaDS3ZqvIlELiEM5lUhVOspdJPB+oIgDKPUfCzAy02nHFdZaKEWoRs1H5dhGITDYelvU6fTSUnpZrMZZrMZdXV1CIVCWFxcxOTkJPr6+mCxWCQ3V6/P7GJBtj22690TnEu2nLAV4XQsrrlyD956xW509UzgkV+8jocePY6fPXocl1+6Cze9pxUH99fkvFSJQqFQKBRK/hH7aQ0GQ0w/LcdxCIVCOQuOAhIHVxFCMDAwAJfLhSNHjoDjUjt9yvU5yNzcHFwuF5qbmyX3JxQSxFcyh+app+/Ee6/9JvgCXTRBuZCFbo1HuJAFGCZarmwQ1tL7BMEbNMneex+JOLWMwmHl/IgkMWvvXypBTiFJOVEoryhwhXJmjQ1VolcUuECSUmUtsexKsVw5AXKRC+TWzVULXQBwWrVLlxOVI6dK+Dtu6O5Mr0yV9cvCulR/D2GTSrhtxDl7EuGbzK2NR0FBAXiely48iRe4QqEQWJaVbhzHwel0wul0ghACt9uNhYUFdHZ2AgDKyspgt9thsVhS/jzJRtiKInyrsmWFrQjDMDi4rwYH99VgamYFjz99Cs8834mXXu7H9m0O3PiuZlx79V6YTLmvYadQKBQKhZI7xBM3r9eLjo4O1NXVobo6NiwyH72r8QiFQujs7ITFYkFra+uGXDAnhOD8+fOYnZ2FzWaDwWCQTpa1XNp4PPGCMB7oxmv+DXxB5ORVTAsmQMjAAoRA54+UK5sEwauPCF6xB5cwUVdX7eCKc2xFB5dApgUYbQdXLpD1nuj9ifpwwahc3BTQuVlpP6F0ndxUe3KTkK+SZZFZV1R4MgzgsKQWRqUeC5RsTJDW7Np00fmU7yNRlDZrpR/nvww5XRIFUYkXm0ShyPO89HcrurnidqKba7VaYbVasW3bNgSDQSwsLGB0dBRutxtFRUWw2WwoKytLeHEtU2FLSH7HPK0HW17YyqksL8anPnYV/vRDl+HFl3rxi6dP4pv3vYAf/t+XcO1b9+K972zGjgbnRh8mhUKhUCiUOKj7abVYL2ErCuz6+npUVVXlfX9aiOnLAHD48GF0d3cjFAqlLWrlPP7iFwAA73nXd8DwkYApAwvOHxGwhQwIC8nBFcUr54+4tTIxy/kiM3PVPbj+aHiUlksrlSBrObhif6/Yh5tCmbKowYKW1EqVuYiTm7bABfIicoHkQjcT13XOrXRYnVZXWs/PmCxDoVhfKOkaYaNSxmyWMuTn//vTmveLLi0Q7YkXb2IrgVzk6vV6VFRUoKKiAoQQrK6uSkKXZVnY7XbYbDaYTCbF5wDP8ylXlajJ9DNls/CmErYiBoMe73rHQbzz7QfQ0z+FJ545hV/+qgtPPHMae5sq8e7rD+GtV+yG0ZC7EiYKhUKhUCjZwfM8ZmZmks6nTTXoKRsWFhbQ19eXUGDnm0AggI6ODjgcDtTX1wMQXvvIyAiqqqpQWlqa8Uno1NQU/u4fLsHBgwdx9H0/lO7nC1lwawQICz23DB9bfiyOCFKmKGs7uIAqCVk94ifi4AZN8UuQ4wpc1VoMiYZNBeO4uOqAKk5WqhxKJ1VZRBS5hAHSmZGrQa7dXEJi9eSsKxoMJDqy9hRdXSCzcmRNkjm+KYhQ1q/6DGDjC9mwQUPy5KkMORXUIpcQohC6oVAIDMNAp9NJYre4uBjFxcXYvn071tbWsLCwgKGhIfh8PhQXF8Nms6G0tBThcDijtGVCyJZ3bd+UwlaEYRjs212Ffbur8JlPvhXP/foMnn6uE9/49nP4/o9+g7deuRvvevtB7Gmq3NJXJygUCoVCeTPAsiwOHDiQ9OQqX46tGPgyPj6O6elpHD58OC/jOFLB7Xajs7MTjY2NUv9dOBzG9u3bsby8LDnbFosFDocDdrs9JZeGEILBwUG43W60traC4zg8+cvPCeXJehYAByZMEDbpFD23Yvlx0CRza/0ETBgImpUOLsML96lH/mglIYvoI+JXelzDdZXm4UZGCiVC74keUzyRq4Zzs1IMb8iSwe+XS9YzmkORC+SnbFksN553y8uXhffKYXHHLUdmAkqXml8PoyipEE58Hq/zx86/VZcRx5QVq4Wu7PGwgc3ZPFytkmV5ubJWyXJhYSGqqqpQVVUFnuexsrKChYUFDA8PIxgMoqysDBaLBSZTnKZ2Dfx+/5YOjgLe5MJWTpHViKPva8cHbjyMrp4JPPN8J3792148/VwnGurtuO5t+3Ht1XthK9u6s5soFAqFQrkQ0Ol0UmhSLmEYRir7bW9vz3hkhnrNdMdvzM/Po7+/HwcPHoTValWERHEcpxgd4nK5MDc3h9HRUXAcB4fDAYfDAYPBELNuOBxGd3c3DAYDDh06pLioL5Yn3/jWfxX6byNOariQFXpuiXJEkNyZ1XuiY4MAwfkS74vn4IpJyFozatWzcrUQRwqFLNDs1ZWj9zAAiZQpJ9hOOAYCEAacO9qjmJLIjTxPIociF1AJXQYwWf1Zr5kIdQmzSLlGKTPrDyjviPxeSSOAYnpj1yEdOUkZc7aiVOfnNdd49tHPZLUuAEWwlNzNFQVuOByWBK54Ky0tRWmpMKKpp6cHOp0OAwMDWFtbQ2lpKWw2G0pKShJ+Drnd7pTS3jczF4ywFZGHTf3lX1yDF1/qxS9fOIN/v/8Y/s9/voQjbQ14x9v249KLGlFYcMG9PRQKhUKhbCgMw2yIY7u2tgaPxwO73Y4dO3bkrJKLZdm0hO358+cV5diJQqIYhkFRURGKioqwY8cO+Hw+zM3Nobu7G+FwGDabDU6nExaLBYFAAJ2dnaisrERNTU3c/T/+my8CAN535f+OBExxYAhBuFAXHRFkYCO9tZFy5ciPQhgbpOHgiv2vJkZZhqyVhCzv0/VBO0lZvo0bsv7aBG8sEy1TBlIPnBL2kabIVZNjkQsAXpfywkU8oatVjpwNMy4r8A2g+q+Tvw5x3m1Mr6tJ6fBmUoaca9Jxa9cTuZur1+slgStWcGiNE2IYBuXl5SgqKkI4HMby8jLm5+dx7tw5GAwGaZyQ+uKXx+OBxbK1Db4LWrmZTYW44fpm3HB9M86PLeC5X5/BC7/pxitffxIWcyGuvLwJb3/rXhzcVwt2g36hKRQKhUKhKOE4DoFAIPmGKbK6uoquri6YzWZUVVXltD1JFLbJ4Hkevb29CIfDOHz4sFQWnU5IlNFoRF1dHerq6qRE1eHhYbhcLgSDwbRCsH7x0pcAAO+74hvgCyOnizxB2MhB54s4R0ZZuXJhVAmo3Vqp/1UUviblaxGTkOOFRCmSlBOgF13cFEwnzpMHkat2bbVwqUbcrLPQVaMuN856LFAKv6eMyuFVBB9plTVnWYacD7SE7t99sQ1nzpyBw+FAWVlZxnNoE6HVmysfJxQOh6X+XEAQxKKQJYTA5/NhYWEBvb29CIVCKCsrg81mg8VigcfjyYlj+9xzz+HOO+9EOBzGxz/+cdx1111Zr5kqF7SwlVNfa8Of/+mV+PhH34JTnaN4/sVu/OalXjzzfCecDiuuuXIP3nbVXuxocNB+XAqFQqFQNpBcliJPT09jaGgIzc3NGBwczLkTnIq7HAwGcfr0adjtdmzbtg1AdDSI6MCki5ioynEcBgYGsHPnTrhcLrz22mtSX67NZkt68v2L3/01AOC9134z4pIK73vYoIPOF5bGAunWIiOCjKzMcY2GTknIRgUFTYzCqZV6aCETsXJ31itzZ82IW4KsWEd+nh4nLZmLlCqHLLLZR8kEKnLg5AJRocuQ1BOWFTOUtJELXVGomvLQp5uMpG6s6nHWH0hYuiyVNyfaZ57LkONx8cUXY3V1FfPz8zh//ryUXGy322E2m3OuH7R6c5eXl+H1esFxHILBoLSd6OaaTCaYTCbU1tYiFAphaWkJIyMj+JM/+RNUV1ejsLAQs7OzcDozmyITDodxxx134IUXXkBNTQ3a29txww03YO/evbl50UmgwlaFTsficMs2HG7ZBp//Wrz8yjn8+lgPHv7F6/h/Pz+O+lob3nrlbrz1it2oq7Ft9OFSKBQKhfKmIpWTv1yUIhNCcO7cOayurqK9vR16vT4vJc7JHFuPx4OOjo6YkChCSMaiVmR0dBSzs7Noa2uTUqbT7csVEWfgvvdt35TuE/pulSFTYrlyyCBzcNV9uRGBqfdqCF/xOWLfrln79UtlzElcXE50g5NVWDIApyhVTrK9ej9ykWvOYIQQYZRjhICsRgkplo64sF6xT1f2lposmYndiW/oUypHTpsk/bisL6iRVhz7vXoUUCLSLUOOJ4zlycU7duzA2toa5ufnMTg4CK/Xi9LSUtjtdpSWlmY0ZzYZHo8H/f39aG5uhsFgiHFzQ6GQomRZ/rd/8uRJPPDAA/j5z3+Oo0ePIhgM4u1vfzvuuOMO2O32lI/h+PHjaGxsxPbt2wEAt956K5544gkqbDcDRkMBrr16L669ei+WV7w49nI/fvNSLx747z/gP3/6BzRud+KqtzTh6subUFNdttGHS6FQKBTKBUG2AjQUCqGzsxNmsxmtra2Ksr31dGzFkULykChR1GYzT5LneZw9exahUAitra2K/t50+nK19v/Er6MCl+F56UQyXKiLhEwRQexGAqeAqMiV9+WKiGnLgLoHlwFDSGwwlcqdFccFAamFTQGpliqnt73yubIRQpmIXJE8CV254+t1K9OXLVZ/6uXIaxFhW6gdEhXj1uaAVEQtAOh80fcq2XPUQjVsSl8eaYVGFRYWorq6GtXV1eB5HktLS1Kva2FhIex2e9ILSqnidrtx5swZHDx4UJGELHdzRZErD6ISH2dZFg6HA1deeSW+9rWvYWlpCS+88ELaAnxiYgK1tbXS9zU1NXjttdeyfXkpQ4VtipQUm3Dju1pw47taMDfvwrGX+/Hb3/fhxw/+Hj9+8Pdo3O7ElZftwhWXNWFbHXVyKRQKhULJFxzHZVyK7PV60dHRodlvqtPpUuqHTYd4ju3o6CimpqakkULyftps0phDoRC6urpQXFyMpqampOI4Xl+ux+NBaWkpHA4HSktLY45JFLg3vvVfAfHlEYKwgQMn9uAahJNizs8DPEHIFPk+4vCGjMKayh5cgqAp9vWL4ld4nvZrituLqypBTmUurmLd9RK5CeOaESt0rblPBndHSpjVwtaSqGdXFLhqJ7NQ1S+bpEQ4H2nJ6YpaAFIPebw1MillZllW6nUFhM+h+fl59PT0SON57HY7iouL0/77d7vd6OrqwsGDB+P2yKp7c+UCV7yQtry8LI37KS0txdGjR9N+nVrBf+vZwkmFbQY47FZ84MbD+MCNhzE7t4pjL/fjpZfP4v6fvIz7f/Iy6mtteMulO3HFpbuwq7Gc9uRSKBQKhZIi+SxFFh3S/fv3o7i4OOZxlmXz7tjyPI++vj6EQiEcPnxY2mc6IVHx8Pl86OzsRH19PSoqKtJ+vtiXW1FRITlM6nm56r5cMUVZIXAB8IU66PxhgAfCJh3AMuC8wvsgClrOJ3N1I/eBYaD3RhfSHBfkI5G0ZLVogWJcEJA4cEoUrAxJkqis8RwgO5ErPD/Liyiu1IVujAubQp+uHLc71lXs/2cDmu5eFL7REHtMQLtUmRhSDFVSi1C1SM0HSfaZq/5ck8kkXVAKhUJYXFzE1NQU+vr6YLFYYLfbYbPZpBaCeKQiatVoBVAFAgH813/9Fy677LKsXldNTQ3Gxsak78fHx1MOrMsFVNhmidNRhKPva8fR97Vjbt6F378ygN/94Sz+3yOv4ac/exVOhxWXXbwTl1/ciOYDteC43NfUUygUCoVyIZGusCWEYGxsDFNTU2hra4tb+pfvHttgMIiOjg6UlpZiz549AKLuSbaidmVlBT09Pdi7d6+maM/kuOVpqm63G7OzsxgdHYVOp5N680SHRxK4V/0rmIhrw/BCcrLOKzq4UUErCNOo0FPcxzDCnBpERCzizcONPKYKp1K4s3IXN4EZqpeVKgdTFKzZiFzh+TkqWRbJYelytkI4kfvK+IPaj+siDn6q4zaTOL7rIoQBPPXMnVk9n+M4OJ1Oqcfe7XZjbm4OHR0dACAFUKnbAzweD7q6unDgwIGM04xZlkUoFMKnP/1pvOtd78KXv/zlrF5Le3s7BgYGMDw8jOrqajz00EP4n//5n6zWTAcqbHOIw27F+9/Tive/pxUrqz788bVzePmVATz7q0784qmTsJgLceRwAy490oiLDjegyJqgGYRCoVAoFIomHMelLEB5nkdPTw8IITh8+HDCnrF89tiKIVHbt29HRUVFzvppASHZ+fz582hubpaEZi5hGAZWqxVWq1Xqy52fn5dGhthsNjgcDlitVjx+LFbgArE9uGCiJclhya2Vlykr348YgatIS5bNyo0TNqVIVFa5uDF9uzLBuhEiF8gwZVktPmNKl/MQ9gTkZtyOTtYHHghpC9/IfcSQoXxJVoa8CSos5X9r27dvRyAQULQHFBcXw263w2AwoLu7GwcOHMhq9qyYYrxz5058+ctfzrrKlOM4fP/738c73vEOhMNh/Nmf/Rn27duX1Zpp7X/d9nSBUVxkxPXXHsD11x6A3x/E66dG8IfXzuGV44P4zUt90LEM9u+txsXtO3DJkR3YVmejJcsUCoVCueBJ5f/CVEuG19bW0NHRAafTifr6+qRr63Q6rK3ldiQKy7JYXV3F4OAgDhw4gKKiopyJWkIIhoeHsbKygra2NnDc+pzWGY1G1NbWora2VurLPX/+PNxut9SX+9hvPg+WZfG+K/+35L6qe3BDRh1AAF2kJFnp4GonJov3A+qwqUifripsSk60l1d8fvLXuhEiF8jRKCEVxKWPcV2ZLMVu/z+XoenvllSL5qFXVrYm4w/F9utq7JeYEpfxJt1nnsqQ06GgoACVlZWorKwEz/NYWVnB1NQUpqamYLVasbi4KI3xSRee5/G5z30OlZWV+OpXv5ozHfLOd74T73znO3OyVrpQYbsOGAx6XH7JTlx+yU7wPEHv2Sm88togXjkxiB/950v40X++hApnEY4c3o6LDzeg5VA9TMbs/hgpFAqFQnmzksoJ2OrqKrq6utDU1JTyuIp8OLarq6tYWVnBkSNHYDAYchYSJTrRHMfh0KFDWa2VDYn6cs1mM/79Zx/B2toaPvfRh6MCF0IPLucLC+XHRh2Iwq2NhkrJQ6PUYlUIm4ozLijB86LbQLZN4twmQCZy16knV1rDrawyyJXQBSJiVw4DMBZB7KZcjrwWiH6tDozSQv33q8vB727MvFwWrF+WjKzxmcHECZbiC1OXR9mWIacDy7IoLCyUPk84jsP8/Dz6+/uxtrYmXVQqKSlJ+nnA8zy++MUvwmKx4J577tmwz49cQ4XtOsOyDPbtrsK+3VX4+O1vwey8C6+eGMRrJ4bwwm+68eSzp8FxLA7uq4GthKCmbhY7GhzUzaVQKBQKJUWmp6cxNDSE5ubmtHrPcilsCSHo6+uD1+tFbW1tTPJxNv+vBwIBdHZ2wul0oq6uLifHmwvUfbkulwv9/f3weDy4+9+uhtPpxJ0ffkjm4AK8QadwcBki9tuK/bM6SXDqPZFeZTMbFaGqcUFa4lQSwGYmbvCw3gvJ/U0UOCVtL+/JzUDkAlkI3UQhVMl6YVPolSXuqNglkTeLtaTo7MpFrgjDpCZ45dvLjycf58AJ0pLZtRCIjgEja1EmLJtWi3E+EMPh9u3bB6vVCgBS5UQ4HMbS0hJmZ2fR398Pk8kk9eYWFipHOvE8j//1v/4XGIbBt771rTeNqAWosN1wnHYrbri+GTdc34xgMIyu7nG89sYQXnt9GCc75vHCSw+grNSMtuZ6HG7dhsPN9bDbrBt92BQKhUKhbDoIITh37hxWV1fR3t6uSO9NhVyN+wmFQujo6EBxcTHq6+vh9/tzFhIlBsY0Njam7ERvBIQQjIyMoKSkBIcPH8ba2hrm5ubwd99+G0KhEO757AuKkKCogysIqbCRAwgB5w1HypR1UqiUKHCl0uVIv63eS8BEfnxavbZimbLwXK0eTqSWqqwKqMpE5AJZuLkqdR7bn5vF77Ba+Eb2xYtiV22MWoLo/fsa7PnquPZ64u+6KHjV5bxJUn81STY2aJ2Emjjyaj3w+Xzo6OjA3r17UVRUFPO4TqeThCwhBB6PB/Pz8+jq6gLP82BZFm63G5dddhm+9rWvwePx4D/+4z/eVKIWoMJ2U6HX69DaXI/W5np86mNX48mnfgW9oRInTo7gxMkRvPDbHgDAtjob2pq3oa25DocO1MFiLkyyMoVCoVAoW4N0RJ/YowpE57eaTCa0trZmJB5zMe5HnJPb0NCAiooKTE9PIxAI5ETULiwsYGBgAPv3788qMCbfiOnP5eXlqK2tBQAYDAZFX+4PnqjD3Nwc/uHPnpTCgMSwqXChDjqfYJeFDWKZcsTVNekk8SsKXADS7FvCCmnMUq+tKHBj0pKTiFxpO8i2S/7acyFygczdXADg3EqxQhggnIvUZSBG+PLu9C4exRAMAnIzmFEJLUP2rXkxjm+S2babDVHU7tmzR1PUqmEYBhaLBRaLBdu2bUMwGMQbb7yB++67D3/+53+OgoIC/Mu//AtcLldOEtQ3E1TYbmKKrAW46iohgIrnCc4Nz+KNUyN44/R5PP18Bx598g2wLINdjeVoPVSPloN12L+3mvbnUigUCuVNjzhGR6fTSWKyvr4+q5mJ2ZYiLy4uore3V5qTSwiBxWLB+Pg4jh8/DrvdDofDgaKiorQF7vj4OKamptDS0hJTWriZ8Hq96OzsxI4dO+BwODS3kffl/vy1fVhaWsInrvshSAEHYuCgWwtLQVM6f8SxFcuUvdGfT8gYLUkWZ98GTawkbgGlSxs0M9Aa+SOmKgfNTIwAVm4X2a8JCbeTXmeGIhdIQejGq6nWgCGATuXqhrNxdVMlF4IxGFKaxOoy5VRn4qZBbGjUxrmafr9fErWZilC9Xo+LLroIR44cgdVqxWc/+1k8//zz+Na3voXi4mI8++yzCdPitxJU2G4RWJbBrh3l2LWjHB+8+SIEgiF0907iZMd5nOoYxcO/OIH/eeQ16HQsmnZWoOVALQ7ur8WBfdUwmzbvf4AUCoVCoWSCOPJneXkZfX19kpjMhmyE7fj4OMbHx6U5uYQQhEIhGAwGtLS0IBQKYWFhAWNjY3C5XFLQS2lpacJyQEIIBgYG4Pf70drauqlPQMVZuvv27UvJWQKifbmPnbgbhBDcdORfQAo45aggWZIyCBHKlBHpxUV0Pi4QFbhCKJXyfdV7iCRGk5UqxwucAqICV0htTullZiVygdyEUMnRqVxdyF3dOOXI0e8RU5KcsBxZJNl4HbVbmwLMmmpWr44FEBXthGGULyXVGblJWI8yZL/fj9OnT2P37t1ZfbYRQvDd734XnZ2deOihh6DX63HZZZfhq1/9KhYXFzf1Z0q6UGG7RSnQc2g5WIeWg3XARwCfP4AzPRM41TmG012jeOixE/jvR14DyzLYud2Jg/trcXB/DQ7srUZpSQ4+ESkUCoVCyQOpOpk6nQ6jo6NYWFiQxGS2ZCJsCSE4e/YsfD4f2tvbpXJmdekxx3EoLy9HeXl5THqwxWKB0+mEzWZTjOwJhUI4c+YMLBYLDhw4sKmDJGdnZzE8PJzVLF2GYfDYibsBADft/3uwUKpGvpADGCZaphwRuDo/DxDZPFxAmInrU6Ysi/eDxJYqx8yyTSFVWUhthmy71F6nXOQCWbi5Yhm+OblzyxDheBOhcHUj26ZVwhyU1RTLf1fT7HWPHpBafGf/+8+EQoBcC6suKhGWVYRGAQDDKj8T+MLcu8Rq5KK2pKQk43UIIfjhD3+IV155BT//+c9jcgfKysqyPNLNBRW2bxKMhgK0tzagvbUBgCB0u3sn0XFmDJ1nxvHEs6fxyOOvAwBqq0txYF8N9u+txoG91aitLtvU/1lSKBQKhSKH53m4XC7wPI/Dhw/nzHFIV9iGQiF0dnbCarXi0KFD0rEl66fVSg+enZ3FyMgICgoK4HQ6YbVa0dfXh5qamqzKq9eD0dFRzM3NobW1Ne3Arng8euar0tfvv/SeaJJyRGfxBp1S4DLCPFxA6NUVwqYghEH5ouIsZGQVZcTqUuW4qcriNgmcXLnIFbZN8iLF52Xq5kacU86jPKZUhG68tdTfi2JXLop5s/bfSO8/NWDP3w3HPhAMCgJS/rSCHPye5GNskBqNJfPt1q6treH06dNoamrKWtTef//9ePHFF/HYY4+hIJOgri0GFbZvUoyGAhxu2YbDLdsAAIFgCGcHZtDZPY7O7nG8/MoAnv1VFwCguMiIvbursG+PMIZo965K2qdLoVC2LKEwj96+SZw4NbLRh0LJEIZhQIj2yXkgEMDp06dRUFCA7du357SMTuzbTQWfz4fTp09Lfb2EkIySjxmGQVFREYqKitDY2Aiv14uxsTH09fXBZDIhEAjA6/XCZEpRJa0jolsdDAbR0tKSt4TVx/54FwDgppavghj04Av1YP1hMJGyZFHgMjwQMnEgDKMKm4quJbm4hthj1XuIJGy1SpUBmchNMj5I2Db69Xq5uUCs0AUEsZuKaxsP+XNZT5K/uVR+94NqW5SBQvkasm+jiwmNUv/IN2EisChqd+3ahdLS0qzW+slPfoKnnnoKTz75ZE4qWrYCVNheIBToOezfW439e6tx2wcuAiEE58cWcaZnHN19kzjTO4FXjg8CEPp5G+rt2Lu7CnuaKrFnVyXqa23Q5eNKGIVCoWQJIQQTk0t4/fR5vH5qBKc6RuH2rIFV93NRtjyrq6vo6urCrl27sLi4mJPRPHJSFaNLS0tSL2lJSQkIIQiHw1JKczZVUG63G0tLS7jkkkug0+kwNzeH/v5+BAIB2Gw2yc3d6EqrcDiMM2fOwGw2Y9euXetyPI+e+nsAEYFbGClDFo/HyIGwAOcVBFPIJPTpKsOmooKM8/NRESsrVRaFakyqsgZJxwfJt81A5AIyocsAQa1OshTm0gIysRv5J6jl6qa4VtqoBWQqvyvqebjqz3N1gFoOzlFjQqLW+bRXvGi3c+fOrEuE/+d//gc/+9nP8PTTT2fcGrAVocL2AoVhGGyrs2FbnQ3vvk4on1p1+dDTN4We/kn09E3it7/vw1O/7AAAGI16NDVWYPeuSjTtrMCeXRWoKC/e8P9YKRTKhcnsvAunOkalAL2ZuVUAQLmjCFde3oT21m043LwNRUV/vcFHSskV09PTGBoaQnNzM8xmM1ZWVhAKhZI/McdMTExgdHQUra2tMBqNUkgUgKwcS0IIzp8/j8XFRbS1tUklvTU1NaipqZHCp86fPw+3251y+FQ+CAQC6OjoQFVVFaqrq9d130BU4ALA+y/+F4AQQeBGXH7eoJcELghB2CSGTUVc3IjAlUSsrFQ5aGQVLmxMqrJIhuODgCxEriopWVPoprxWtLdYJGRSiV2V0E3F8e3/m0Y0fWMwvYOJCZHKwPENx64h3kMK9DkTqff97CMIBAI5L+sNBAI4deoUGhsbsxa1P//5z/GTn/wETz/9NMzmCytXhwpbikSR1YiL27fj4vbtAACeJxifXERP/xT6+qfQd3Yajz7xBoKhcGR7A5p2VmBXYwWaGsuxq7Gcil0KhZJzCCGYnl1Fx5kxdHQJt4mpZQDC51DzgTrcdvQitB2qR011Kf0MehMgL0UmhODcuXNYXV1Fe3u7JPiyHc2TLmI6scfjQXt7u7T/XMyn5Xkevb29YBgGzc3NmkI1UfiU1WqFw+GA3W7Pe8Kpx+NBV1cXdu7cCZvNltd9pcJjr/4vAMBNzf8oubjiu8cb9ELYVETkKgRuRMuGTcr3S5+kVFkk0WigTEUukEDoaripMUI3lbLlBGKV82qUMFvS79clshAphmEBhKM9tZn8najdWja933EmEIx1jVkGivRklgUj+14uhOVJymtra+joEEwfu90Ou90Oi8WS1d+/XNRm+zf15JNP4kc/+hGeeeYZWK3WrNbaimQlbBmG+QCArwDYA+AIIeR12WN/C+BjEArm/5IQ8nw2+6KsPyzLoK7GhroaG667Zj8AIBgMY2hkDn1np9A/MI3+czN46NHjCIeFDwOLpRA7twsit3G7Ezt3lKO2pgwcLWOmUCgpEgrzGBqZQ3fPBDp7xtHVPYG5eRcAwGox4OD+Gtz47ha0HKzDjgYnLTl+ExMKhdDV1QWTyYTW1lbFyeN6ClvxOMxmM5qbmwGkFhKVCsFgEJ2dnbDb7airq0tpLXX41OrqKubm5jA8PIzCwkI4nU44HI6cu0rLy8vSnN7NdtL86Ol/AADcdOgr0n3yMw++kJMELhARuTygk5Uqy0Uu5+cBXhB1IVOskEp9NFDqIhfI3M0FlP25hMnNWCDOzcQI6mASsXv27t3Y9c99yjsDEbGr/rxW/47mQvjG9NZmdw7KBITfm8deExK7GxoaEAgEsLCwgOHhYXg8HpSUlEgVFOlcXAoGgzh9+jR27NiRtaj95S9/ie985zt45plnsgqd2spk69ieAfB+AD+S38kwzF4AtwLYB6AKwK8ZhtlFCFm/S6uUvKDX69C0swJNOyuk+9YCIQyNzGHg3AzODs5gYHAGv3jqJAJB4cddoNehod6OHdud2NHgxI4GB3Y0OFBkvXBqsa/eZQAAoYdJREFU/ikUSnyWlj3o6Z9CT5/QBtF7dgo+n3AS5LBZcGBfDQ7sq8Gh/TVoqHdQIXuB4PV60dHRIYUzqeE4Dmtra3nZt9grC0RDourq6lBdXZ1xSJQWXq8XnZ2d2L59O5xOZ0ZrMAyD4uJiFBcXo7GxER6PB3Nzc+jo6ADDMHA4HHA4HFmHT83MzOD8+fNoaWnZ1EE0j5z6e/T19YFlWdx9y0MgBj1IoR7sWgggRHBxAUHkkujIIOE+4bxFErgsA/CqPl0tkZtianImIldRKmxEWj2wnCf2vpAZWffS6t3KJ4vHqE5jZtRzabU+u+UjgoQnKb8vVAnfNN1aTVTHkUlvbUFBASorK1FZWQme57G8vIz5+XmcO3cOBoNBcnMT/a0Eg0GcOnUKDQ0NsNvtmbwSiRdeeAH33nsvnn322TfdCJ90yErYEkJ6Ac2whfcCeIgQsgZgmGGYcwCOAHglm/1RNieFBRz27BJCpkRCYR6jYws4NzQr3f7w6jkpiRkQTlgbtjmwfZsDDdvs2F5vR32tDYXrMB+MQqFsDF7vGs4OzqB/YBq9/VPoPTuN6ZkVAICOZbBjuxPXXbMf+/YIYXcVziJaWnwBsri4iO7ubimcSYt8ObbiuhzHYXl5Gd3d3di7dy9KS0tzGhK1tLSEvr4+7Nu3D0VFRTk7frPZDLPZjG3btmFtbU0RPmW32+FwONIKn5L3/ra2tirm7G42wuEwurq6UFxcjG3btuHRjq8AEFxcEimFVbi4Br2UqAzI5uJ6hcRlQBk4BSAvIldYS3tbRamwT/lYKMG1inj9sNEZuJE1zCn0zqYbUAVg6HN7sOM7/YmfkEpvrbqXllUFxqmFb57+vxDdWi1YlkVZWZkkKD0eD+bn59Hd3Y1wOAybzQa73Y6iouj/Z3JR63A4sjq2Y8eO4Z/+6Z/wzDPPZC2Qtzr5+nSqBvCq7PvxyH2UCwROx2J7RLS+/a37AAj/OS4ueXBuaBZDI3MYHJ7D8Pl5nOoYlfp2GQaoqixBQ50d9XV2NNTbUF8rlENTKJSthcvlx8DQDAYGZ3H23DTODs5gbHxRGkdZ7ijC7qZK3PiuZuzdXYWmxgoYDPTCFkXoOWtra0voduRb2M7OzuL8+fM5D4kCgMnJSYyPj+fd/SwsLEwYPuV0OlFSUhL39fA8j/7+fvA8H7f3d7MgBlpVV1fHOPyiwAWAmw7+Q8wMVT5yQV0tchlCpMApIH8iV1grPTdXeI7y+0RCNwZpBm7sQ+mOGEppjFAmlTYxTqrG719A5fhq9eNG2uWg55K7tTlAvLhUX1+PYDCIxcVFjI2NweVyoaioCKWlpRgfH8e2bduyFrUvv/wyvvzlL+OZZ55BeXl5jl7B1oWJNydO2oBhfg2gQuOhuwkhT0S2OQbgi2KPLcMw9wF4hRDy08j39wN4lhDyqMb6nwTwSQBwOBxtDz/8cOav5k2G2+2GxZLBALMtRpgnWFzyY3bOh9l5L2YXfJib92FhaQ08H/39LLbq4bCbYC8zwG4zwlFmgK3MAItZf8E5OhfK70aq0PdDyXq/HzwhWFpaw8ycF9NzXszMejE968XyanRcQ5FFj8oKM6rKzaiqEG4Wc/5F7NVXX/0GIeRw3nf05ib99JgsCYVCSUXr8vIyJicnsXfv3pzu++TJkzAYDPD7/Th48CA4jstZSBQhBIODg/B4PNi/f3/eg57iIYZPzc7OYnl5GVarFU6nEzabTTqmcDiMzs5OFBcXo6GhYVP/P+vz+dDR0YHGxsaUHSu5wOWNkc8iXvZ1BN6g/TNSi1zFYxoiV00yoatcj0l9/qyqdDnh85KsqSiDTvJfitZ+tv9bt2xf0Q0YPZeaW5tM2Mb00mqtoUu8TQqjiEiBLqFjmyqEEKkahWVZmEwmKfQtk5E8r776Kr7whS/gqaeeQk1NTdbH5/f7ccUVV2BtbQ2hUAg333wz/vEf/xGLi4u45ZZbMDIygm3btuHhhx/OesYu8jNYKrmwTWmRWGH7twBACPl65PvnAXyFEJKwFLmpqYn09ycpW7iAOHbsGK666qqNPowNIxgMY3xyCefHFjAyOo/X3+iFb43D2MQi1taiV1XNpgLUVJehtroUtdVlqK4qRU11KWqqSmG1bN4+oGy40H831ND3Q0m+3g9CCGbnXBgZncfI6DyGRuYxfF74WvybZFkGNdWlaGxwSgFyO3c4UVqyMSMHGIahwjZ71l3YhsPhpKN8XC4XhoeHcfDgwZzu9/e//z1sNhv27xdCE3PVTxsOh9Hd3Q2j0YjGxsZNIxTF8KnZ2VksLCzAYDCgtLQUU1NTqK+vR2VlZfJFNhCXy4UzZ85g7969KC4uzmgNhciVtUNtKpEr2yTp9nEe1gyjSrBUjFjV+F7uEscVt5qiVXmf1I/Lif3NKbi1yYRtuqJWa00ox0tlQygUwqlTp1BXV4fy8nL4fD7Mz89jbm4OwWAQZWVlcDgcKC5OPmHkjTfewGc+8xk8+eSTqK+vz8nxEULg8XhgsVgQDAZx+eWX4zvf+Q4ee+wxlJWV4a677sI999yDpaUl3HvvvdnuLi8fgPkqRX4SwP8wDPNNCOFROwEcz9O+KG9S9JHQqYZ6O4AmbKsK4qqrrgLPE8zOrWJsYhGj44sYG1/E2MQSzvRM4MWXeiG/VlNcZER1ZQmqq0pRVVki3CpKUFVRjLJSCw2hoVA0CARDmJxaxuj4IkbHFnF+bAGj4ws4P7YghToBQFmpGQ31dtxw/SE0bHNgxzYHGurttE+esi7kuhTZ7/fj9OnTMBqNqKurA5A7Ubu2tobOzs4Nm/uaCHn41M6dOzE3N4eenh4UFBRgYmICgUAATqczI0cp3ywuLuLs2bM4ePBgVvM6H+38RwCCwJVGBRXqwUY+7xhCEDYVgPVHe2/loVPZlCsDypJlII5wlfW5plPirNxPZCnF7Nr426dSYiwvh0513biiFgAirWkxvbTi358+ztigXJzP5fFiUygUwunTp1FbWyuVDBuNRtTW1qK2thahUAiLi4uYnJxEb28vrFYr7HY7bDabNOJMpKOjA3fccQcee+yxnIlaQPgsEKu9gsEggsEgGIbBE088gWPHjgEAbr/9dlx11VW5ELZ5IdtxP+8D8D0ADgDPMAxzmhDyDkJIN8MwDwPoARACcAdNRKbkCpZlUFFejIryYrS3NigeWwsIJ+TjE0sYn1zExNQyJiaX0NU9jhdf6lWUNhcUcKgsL0ZlRTEqnJF/y4tR4SxCRXkxiouMm+aKOoWSa4LBMKZnVoS/kakljE8uCX83E0uYnl1R/K04bBbU1dpw/bUHUF9rQ0OdHdvq7Sgu2nwnupQLB7FEOBesrKxIrt/09LRUCp2LkCjRUWxqatr0aaWLi4sYHBxEW1sbLBaLFD7V29uLYDAIu90Op9OZ9dzOXDA9PY3R0VG0tLSgsLAwJ2uKAhcAbtr/94ChIJKkXADWF5QELkOIZugUEBG5kY9PtZBNReQC6QlXTVGcRuqxuk8XTCR9WQv1ugn2I647+ql9qPthT/SBVARoovE9Yoqyuoyfl23D6TJzazXIhVsbDodx+vRp1NTUoKJCq7tT+DxzOp1wOp0ghMDlcmFubg6jo6PQ6XTo7u5GS0sLGIbBn//5n+ORRx5BY2Nj1semdaxtbW04d+4c7rjjDlx00UWYmZmRKjcqKysxOzub8/3mimxTkX8B4BdxHvtnAP+czfoUSroUFnAyl1eJeCI/Ob2MyallTEW+nppewZmeCbg9yrERhYUcyp1FKHcUwekQ/7XC6SiC026Fw26lQTeUTQvPEywtezA1s4Kp6RVMz65gSvy9n1rG7LxLIV5NxgJUV5Vg964KvO3qPairKUNtdRnqaspgMuXmpJFCSZVURJNOp0tarpwK09PTGB4eRktLC0wmE+bm5uDz+VBUVJR1WNLc3BwGBwezdhTXg6mpKYyNjSmEojp8an5+XprbKZZNJgqfyhejo6OYn5/Pa0rzo2e+Kn190/6/B8SAKdk2YqlyjMhlAJDEQlb+mNbjIjHC1Zya0FW6pyqHNJETS2LTl0kisZvKuuq/U1l4V0ojgdSoRa368yLMRwOjpOck6aXN8cxn6VAiora6ujquqFXDMAyKiopQVFSEHTt2wO/348SJE/irv/or9Pf34z3veQ8mJyexffv2GDc3W3Q6HU6fPo3l5WW8733vw5kzZ3K6fr7ZvJntFEqO0et1qK0pQ22N9hVzl9uP6ZkVTM+sYmZ2BdOzq5idW8X07CrODc1iaVl9WROwWgxw2K2w2yxw2Cyw262wl1lgs1mEf8vMKCkxg1N/oFIoWUAIgccbwNy8C3PzLszOrWJ23oWZ2VXMzbswPDKNr33zDSltXKS0xITKihLs31uNqsoSVFcKJfo1VaUoLTFtuANDoaQDy7LgeT75hnEQg5xWVlbQ3t4uOcB2ux1DQ0MYHR3N2KEkhGBsbAxzc3NobW1FQZ5OmnMBIQTDw8NYWVlBW1tb3EArjuNQUVGBiooK8DyPxcVFzMzMoL+/H0VFRXA4HIrwqXwd67lz5+D3+9c1pVkhcvd9GTAIwl8xOkhL5BpkTm4StzZlN9eTmtBVjAlKcbRQIhRiVxwVZERK7vDoZw6i7vudUTEpG+EjTyVmtC5SqP/uMvn9SiZqAUCj+kPu4GeCKGrFebeZYjAYcM011+CBBx7As88+i8XFRfz85z/H5z73OXzuc5/Dn/7pn2Z1nFqUlJTgqquuwnPPPYfy8nJMTU2hsrISU1NTGc/cXg+osKVQIlgtBlgtBuzcoR2XvhYISSJibt6N2flVzM+7Mbfgwvy8KyJ+PVDnsbEsg5JiE8pKzdKttMSE0hIzykqFf0tLTCgpNqG4yAiOy99JAWVzQwiB272GhSUPFpfcWFzyYGFR+Hp+wY2FRQ/mF1yYX3DD51eOOGAYwFZmgdNRhMpyM95+TaNUVi/cimA0bN6TawolXbINcjpz5gwKCgrQ2toq3cfzPIqKitDS0qLpUJaXlycNdpGPyGlpadnUI3J4nkdfXx8YhsGhQ4dSPlaWZWG322G320EIwcrKCubm5jA0NASDwQCn0wm73Z5TQc/zvNT7u3///g27EPdo99cACAKX8a8lFrn+5CIXyNzNBQShKwrYVJ1ZSeiKOlMtdFViNe46vtj7ACCYanGC6veNhMOASl8yciGrZRKkkq6cjDxcjAmHw+jo6EBlZWXM+Kl0GRkZwUc+8hE88MAD0ufV9ddfD0II/H5/Lg4XgFBhotfrUVJSAp/Ph1//+tf4m7/5G9xwww148MEHcdddd+HBBx/Ee9/73pztM9dQYUuhpEhhAYeaKiFtOR6hUBiLy14sLESEyJIbC4vuiDgRbsPn57G87I1x00SsFgOKi4yC0C02orjIiCKr+K8BRUVGjIyuYnB4DlarAUUWAwoLOeq2bUKCwTBcbj9WXT6srPqwuurHyqoXK6s+LK94sbwi/uvF0pIHSytehEKxDlSBXidVAexocOLi9u2w24RyeOlms0gXRWhKNGWrk8/PM7/fj46ODlRVVaG2thaEEPA8j3A4DJZlpX3LHcpwOIzFxUVMTEygt7cXxcXFKC8vR2lpqUIMBoNBdHV1obS0FNu2bdvUn8uhUAidnZ0oKytDfX19xsfKMAxKSkpQUlKCnTt3wuPxYHZ2Fh0dHWAYBk6nEw6HI6vwKfFYbTZbTsNyskEUuEB2IhfInZurdmaB5KXLQGy5MxARuwnKlRO5tPrYAjdM/dlBVP5nV/SOFC6iMGrBSUhsWbP691ZdmpvMrY0jarNxa0VRW15enrWoHRsbw2233YYf//jHkqgVYRgmp6FuU1NTuP3226WLfEePHsW73/1uXHLJJTh69Cjuv/9+1NXV4ZFHHsnZPnMNFbYUSg7hOB2cdiucdmvC7URnbnHZg+VlL5ZWvFha9mIlInKWVwTxMz2zgv6Baayu+hAIKoXwfz7UJ32t53SwWAphMRfCYjbAYimE2VQIs1m4z2QqgNkk/GsyRm9GYwGMRj2MhgIYDHoYCvU0KRrCzycQCMHnD8LnC8DrC8DrFf71eAPwetfg8Qbg8a7B41mDW7y5/XB71rDq8sHl9isShNUYCvUoKTaiOOLmb9/mULj5tlIzysrMsJVaYLEUbuoTZAplq7C6uoquri7s3r0bNpsNhBApJEouatXodDo4HA44HA7wPI/l5WXMzs7i7NmzsFqtcDgcMJvN6O7uxrZt26TU082K3+9HZ2cn6uvrc36sZrMZDQ0NaGhogN/vzzp8am1tDR0dHairq0u5R3G9EUVuMBjErc3/GFfkAoLQlYtcQMPNlUp9E4tcQBC6iXpmE5YuJxCoei+JWTMVkZxoXSIr92WSzI+NEbVaaIlUeXsCw0RTlhM9J4fwPI/Ozk44nc6sE9AnJydxyy234Pvf/z6OHDmSoyOMz8GDB3Hq1KmY+202G1588cW87z8XUGFLoWwADMPAajXAajWgvtaWdHtCCHz+IFwuP1ZcPrz88qto2N4El9sPt3sNLrc/8rUgrDyeNczMrkaEVwD+tfgCS01hIQdDoSByCws54VYgfF2g16GgUC/8q9dBr+egj3zN6XXQczrodCz0eh04HQudjoWOi/zLMmBZFizLQBc5gWRZSImjwv81jPR/jlDSTUCI8PoFV0X4Oszz4HnRZSHo7pnDqvc0QmEeoVAYoRCPYDCMUCiMYCiMYDCMQDCMQCCEQDCEQCDydSAE/1oQa2shrK0JX/v8AaythRTBSokwGQsiFxUMsJgLUe4sQuN2J6yWQlgtUZddcN0NKC4SSs5p8BiFkhvE5OJkzMzMYHBwEM3NzTCbzQpRm07yMcuyKCsrQ1lZmTQDdmxsDGfOnEFxcTHC4TCCwWDOQ11yhcvlQnd3N3bv3o2SkpK87stgMEjjTILBYExpt9PpRElJSdz33uv1orOzE7t27dr0idJiJcAPj90Jh8MBQObkRkqyibFAGiEEJHBzI8JQPkYISEHosgyCxsROqN5DlDNxE4hVtWBWO7sk8nPTHO2jIW6nP96Mih+fFkStvKdVp4OijyuFubcZlRzHiFo21gEG8GhPZtm3PM+jo6MDdrsdNTU1Ga0hMj09jaNHj+Lb3/42Lr/88qzWupDYVMI2zBP4AyEYCjbVYVEoGw7DMJLLWu4swuRYMa56y+6Unx8K8/BFHEZvxIH0+QLw+YLw+oV/fb5AROQF4fMLYs/vD2ItIgDX1kJYdfkEURgMIRgUBWMoIiIzD3HJDcMx9zCM4GbrIyK8oED4urBAj4ICHQoLOBRZjSi0c5KQNxr0MBQKTrbBoJecbcnpVrnfOhoMRqFsGDqdDjzPJwwsIoRgaGgIS0tLaG9vh16vl0rthAtsmf8NMwwDr9cLj8eDSy+9FOFwGHNzczh16hR0Op00viNX42iyZWFhAQMDAzhw4MC6pzTr9XopREcMn5qamkJfX59m+NTKygp6enqwf/9+WK2Jq6A2Go/Hg66uLjQ1NaG0NNquFFOuHAikJXKB+PNyAW2hq/cp/y/WFLrymbgeAqLaJGSMIxpjem8JCMNERwapnqYleGOc2jjI3V2wjKL3VtPNTZaUnCLZiNrOzk7Y7XbU1tZmtIbI7OwsPvCBD+Dee++lbUVpsqkU5JI3gKu/+AMc3lWLy/Ztw6X7tqHWEf9KHoVCSQ1Ox0oOcb4ghAhOaSiMcIhHKBxGOMwjFOIFhzVMEI64rDxPwBMCEvkXoiurWpNBpNeOAViGAcMyYBkGbMT91bEMdDoWx0+8hssvuxSc6BhzOnARp5h+flAoW49U/251Oh3C4XBcYRsOh9Hd3Q2O49Da2gqGYRSiNpvPB1Ewr66uoq2tTRo7Y7FY0NDQAJ/Ph7m5OXR1dYEQAofDAafTCZNJy97KPxMTE5icnNwUKc2JwqeMRiOMRiMWFhbQ3Nyc0x7CfLC6uoru7u6kAlwucoFIunJBgeREapUsAxqjhGRoCl2VsykXulLIlEG5N4aHQtxyPtX/xgwQFMVuov5a1WOcN7ZEevaDB+H8f53ROzIRpDwB5GcMLBPrvLKscm0ttzZHiKK2rKwsa1G7sLCAD3zgA/inf/onXHvttTk6wguHTSVsrQY93n/5AfyhewTfePgYAKDGXoxL9m7DpXvrcbipFmaa6kmhbEoYhok4o+uf6lxSVAi7bXNf0adQKOnBMAyIOmZehTjLVkuora2tSaM26urqpJCoXIjacDgsJfQ2NzdrrmU0GlFXV4e6ujoEAgHMzc2hv78fgUAg4zFCmSCONfJ4PGhtbc3rOJ5MkIdPNTY2YmRkBOPj4ygoKEBPT4/U27wZBe7S0hL6+/tx6NChtC9YxLi5ssdIoV7bzfXFd3OBqNAVS4TDqqApsbSY8ytd3VCS8mUQQC8Tu5JANjKSayvfNtn4n9kPHoTjv+OUJKtRCfWYubdaiK6wuDbLImZkhQaP9n89+doqeJ6XAuPq6urSfr6cpaUlfOADH8Df/d3f4Z3vfGdWa12obCphW8ix+NLRq/ElAGNzy/hj9wj+2DOCp17txiO/6wCnY3FoexUu3lOPS/bWoanWCd0mjtGnUCgUCoWSP0THVo3L5UJnZ6dmSFS2ojYQCKCjowMVFRUpuzMFBQWorq5GdXV1zBghm80Gp9OZdIxQJogjcvR6PQ4ePLipK1gIIRgZGcHy8jIuvfRS6HQ6KXyqp6dHmjHscDjW5YJAMkSHuaWlJetS80QJy2qRCyiFrlxU8gZBGIpiU6cKmlILXRFOdHXlvbem+OfXkkAWxa46ZEo2PihesJVmSbJ6LjXLAuHIPuI5rOre21R0QY60A8/zUm99tmndKysrOHr0KL74xS/ihhtuyMnxXYhsKmErp9ZRgluuasYtVzUjEAzh9OAkXuk9j1d7zuO+J/+A+578A4rNBhxpqsVFe+px0e46VNuLN/qwKRQKhUKhrBMcx8UI29nZWZw7dy7rkCgt3G43zpw5g507d8JmSx78F++Y440RKikpgdPpjBkjlAnBYBCdnZ1wOBxZO0n5hhCC/v5+hMNhxTzdeOFTXq8XZWVlcDgcCcOn8sXk5CQmJibQ2tqa85AwzZJlQ1Q4i0JXErQGTvqa9auErMrRlYRu5FcrpkdX3nvr5WMEaUgmdhWClRBFqa9WorKinBnA0o0HUPq4bPyP+meo/v0P84COBSG87ClspCxZfI5W6BSb+PsId/30/Thx4oR08cRsNiedV33mzBkUFRVh27ZtcbdLBZfLhVtuuQWf+cxncPPNN2e11oXOphW2cgr0HI7srsOR3XW4831vwcKqB6/1jeK13lG81jeKF04OABDKltt31+JIUx2ONNWi1LoxfSwUCoVCoVCyI51SZCDq+M3Pz0shUeJ8WgBZC0UxeGn//v2wWCxZrSWSbIyQ0+lUBCqlis/nQ2dnJxoaGuB0OnNyrPlC7IM2mUxoamqKKybk4VPiBQF5+JTT6URZWVneS63Pnz+PxcXFdSvrjufmiu8SD6VhKrq5QILSZR4AG9ujC0TEbmRBtdvKeVWOKsNE3VmVuNVCr+rdlcRtKhcmVI5t3JJkuevLsvG/l30eiCXIgUAA8/PzGBwchNfrRWlpKRwOR8yFJkIIuru7YbVasxa1Ho8HH/zgB/Hxj38cH/zgB7Nai7JFhK0aW5EZ7zyyB+88sgeEEAxPL+J4X0Tkvn4Wv3j5DACgsdqOI021aN9Vi9ad1bCa8hecQ6FQKBQKZX0RS5F5nkd3dzdYlkVbW1tOQ6IAYGxsDNPT03kNXtIaIzQ7OysFKjmdTtjt9qQOoRhmtHfvXhQXb+5KNtFVdjqdaYXuyC8IiOFTs7OzGBwcTOu9SgexV9nn8ylc5fUkxs3d//dg14JAYeR1avyexwhd2SZhU6wMUPfpAkqnVgEh0HsVd0T7b02s0rWN13urOdon8YxbTdItSdYQuAUFBaiqqkJVVRV4nsfS0hLm5uZw9uxZmM1mKblb/L6hoSH5cSXA5/Phtttuw2233YaPfvSjWa1FEdiSwlYOwzDYXmnD9kobbr26BaEwj97RGRzvG8OJ/lE8+vtO/M9vToFlGDTVOnB4Vy0O76pBc2M1rMbNEb9PoVAoFAolfXQ6HdbW1vD666+jvLwc9fX1OQ2JIoTg7NmzCAQC6xq8xDAMiouLUVxcjMbGRng8HszOzuLUqVPgOE5KWFb3ds7NzWFwcDCjMKP1Rpz7mq2rLA+fIoQo3itRADudThgMmZsbhBD09fWBYRjs379/w/t7RR4981XF9zft/3uw8ZxTmc7jI3PUdd5QzLZhzVm5vEKUEgYIi8nKcfYnubvq/luzUnAuvXc/Sp84IzvOOKJWVXKsKElO5e8yjtCNFxjFsixsNpvUo+92uzE3N4c//vGP0Ol0sFgs8Hg8GY/NWltbw4c//GG8733vw8c+9rGM1lAzNjaGj370o5iengbLsvjkJz+JO++8E4uLi7jlllswMjKCbdu24eGHH1aMpXozwSQr81lPmpqaSH9/f07XDARD6BqexvH+UbwxMI6u4WkEQ2FJ6LbtrEHbzhq0NFajyLy5HN1jx47R+VUy6PsRhb4XSuj7oYS+H1EYhnmDEHJ4o49ji7MhJwrBYBC8OkxGxcDAACYmJrB//35pdEyuRG0oFEJXVxeKioqwffv2TSNmfD4fZmdnMTc3pxgjtLCwgJmZGRw6dCjnfZ+5RuxVVs99zTV+v196r8TwKafTmbR/Uo7YS2k2mzfV70E8pqamMD4+jubmZtza8k+AapqI3MGN3qddhSCOAAobIj6YStwqYBhJ7Gr118Z9XgTrCz2pObXqlGQtUat+XhxX+NGBe7UPRgNCCHp6elBYWIja2lrMzc1hfn4efr9f6vcuLi5OyckPBAL4yEc+gmuuuQZ33nlnzn6npqamMDU1hdbWVrhcLrS1teHxxx/HAw88gLKyMtx111245557sLS0hHvvTf2154m8/CFtecc2GQV6Dm27atC2qwYA4A+E0Dk0iTcGxvHGwDgefqkDP33xJBgGaKyyo3VnDVoaq9DSWA1HcW56aCgUCoVCoaRHspO9ubk5TE5OoqKiQhK1uQqJ8vv96OzsRG1tLSorKzNeJx8YjUbU19ejvr4egUAAs7OzOHnyJILBIGpra+H3+8Fx3KYVYMvLy+jr68tpr3I8DAaDNHJJDJ8Sy4nLysqSplGHQiF0dnbCbrdv+gAuABgfH8fMzAxaWlrAcVyso3vwH8AGgiCFUSFLDBxYX0Ap/hgGfCEHJnJdSecPKR4DgLBBFyNSdX7tC1FxQ6dkuK7dC+uLfTH7UZArUQukLWp7e3tRWFiIHTt2gGEY1NTUoKamJqbf22q1SiXL4mxrOcFgEH/2Z3+Gt7zlLTkVtQCkHnQAsFqt2LNnDyYmJvDEE0/g2LFjAIDbb78dV1111WYQtnnhTS9s1RgKokFUALAWDOHM8DROnhvHyYEJPPlKN3527DQAoMZRjJYd1WjeUYXmxmpsKy/dtP9RUCgUCoVyIUAIwfnz5zE3N4fGxkb4fD4QQqQQqWx7H1dWVtDT04M9e/agpKQkB0ecP3Q6HRYXF1FeXo5t27bFpAbna4xQpszOzmJ4eBjNzc1ZlQZnglb4lJhGXVxcDIfDoQifEsc61dTUbLqLG1qIoVbNzc1xS+Yf7fxHxfc3HfwHMGsBhdAFG0le9gc1ypQ5qfRY59cIntLo2QWEsuQYMasT7ggVas0CSkHUqhORgdiRQPFE7eD/1rxfC1HU6vV6SdQqdqnq915dXcXc3BxGRkag1+tht9thNpths9kQCoXwyU9+Eq2trfjSl76U17/LkZERnDp1ChdddBFmZmak3+HKykrMzs7mbb8bzQUnbNUUqhzdYDiM/rE5nDo3gdPnJvD7M8N46tUeAECJ2YCD26vQvKMKB7dXYm99BQwFF/xbSKFQKBTKuiDOZQWAtrY2LC4uYnV1FaFQKCchUTMzMxgZGUFzczOMRmMuDjlvBAIBdHZ2oqKiAjU1wjlMPOGWyzFCmTI+Pi4FcG10qbRajCwvL2Nubg7nzp2D2WxGSUkJJicnsWPHDjgcjg091mQQQjA8PAy32512qJVa6ALATYe+AsYfBDEoA6lIoV6RsiyGS/GykUKcNxSnRFkX69SGCaBjwK1Fxanv8iYYXxmIOSYxAVnsq9VMRE5R1KaD2FvNcRwaGxuTfr6oe+N9Ph/m5+fx13/91zh16hTKysqwe/du/O3f/m1eRa3b7cZNN92Eb3/72ygqKsrbfjYjVJWp0Ot02L+tAvu3VeAjb2sTrgzPLOH04CROD06iY3ASv+saAgBwOha7a5040FCJQzsqcaChEhWl1k1zZZRCoVAolK2K+v/SQCCA06dPw+l0or6+HgBQWFgouQ/l5eUoKirK6P9gcVTQ0tLSphBeyfB6vejs7ERjYyPsdnvM4/kaI5QJhBAMDQ3B7XajpaVl3QK4UoVhGJSWlqK0tBSEEMzNzUkO3ejoKPx+PxwOx7o7zKlACMG5c+cQCARw4MCBnJx/PtrxFcX3N+29GygoUIpdCA2SvKEArCh21WNnxb5cQpTurno2rlkpRXyX7JTErVrAMgyrPas2xfJjIHW3VpytzLIsdu7cmdF7azQaUVtbi//4j//AZz7zGbjdboTDYbS0tODIkSP4yEc+giuvvDLtdRMRDAZx00034UMf+hDe//73AxA+G6emplBZWYmpqalNPwIsG6iwTQLDMNhWUYZtFWW48bL9AIAllxedQ1PoGJpEx9AUfvFyF/7fb08BABzFZhxoEETu/oYK7K0rh7Fwc/8HSaFQKBTKZsbtdqOzsxM7d+6UXDae52EwGHDxxRdjcXERo6OjcLvdUgluSUlJSiejPM+jt7cXLMuiubl5wxzNVBFLpfft25eSG5OrMUKZwPM8+vr6wLIsDh48uOkv/LtcLgwODqK1tRVWqxU+nw9zc3Po7u5GOByWLhakEz6VL+RJzXv37s3b8Tza888x992078uAXg/dWgikkFMISTGcSudXJi5LDm+hTiFuOU9IMVoIAAKHtqPwzPnYg2EYoRRafZ+ceBdOeD4tUXv27Nn/396dB7ZxF3j/f480uiVL1uk7dpz7TksvKG1o04MesUtpmrbQQttdug8FlhZooMC2QC/YfZbtrzzb3YcCZVno0ySF9KJsWxpuCLS5D+dyDp/ybeuWZub3x0iynTiJE9/x91WG72gkS19PZFuf+V5IksScOXNGdG5VVeXBBx/E4/Hwgx/8AIPBgKIo/PnPfyYWi53+Cc6Apmncc889zJ8/nwceeCB/fNWqVTz//POsXbuW559/npqamlF93cnknJ8VeTykFYX9DW1sP9TMjvoWdtQ309DeA4DRIFFd4s+3Ai+sLGJmsRfjMP5wiplNBxPno584F4OJ8zGYOB/9xKzIo2JCPigoikImk6GtrY39+/ezePFiXC7XKSeJUlWVjo4OwuEwvb29p+2Cm+vOm1tHdaLDyunkxqguWbJkxF2lBy6N097ejizLBINBAoHACcsInQ1FUdixYwdut5vKyspJf267urqoq6tjyZIlQy6VlE6naWtro62tjXg8js/ny8+EO97fW65LvtVqHXLc50S5+fxvAqCZ+8NuLrRqVvmEADuo9VaSUCyDQ6kxqSDvbxi6BXaoYwND7YB8c6YTRe3btw9N05g7d+6IQ+1XvvIVMpkMzzzzzJhfNPv973/PBz/4QRYvXpx/rccff5yLLrqI1atXc/ToUSoqKli3bh1er3dM6zIMYlbkycpkNLJgRhELZhSx5kP6sa6+GDsOt7CzvoWdh5t58919vPT7HQDYLCbmlQdZOCPEwhlFzJ8RojwweSZ3EARBEITJ4MiRI7S2tvK+970Ps9l82kmiDAbDCV1wW1tb2bdvHwUFBfkuuAaDgWg0yo4dO6bEOEqAo0eP0tbWNmpdpSVJwul04nQ6mTlzZn4ZoR07dqBpGsFgkGAweFYBOjfxUmlpKSUlJSOu61jLXTBYvnz5SUO9yWSipKSEkpKSISefCgaDeL3eMQ8vqqrml6Gqqqoa09c6Uxve/doJx3p6erj7yv8Pkmk0SdJD78BTlJ2BGU3DmBxiQqrZZcj1LYMePyzZx23Y9+Sw669pGvv370dVVebNmzfiUPvII48Qi8X4z//8z3HpCXLppZdysgbLt99+e8xffzIQwXaMFLrsXLZ4JpctngmAqmocDXex60gruw63sOtIK+t+u42fpN8DwGWzML8iyIIZIeZXhJhfETzpm1MQBEEQznW5iaHe9773IUkSiqKc0fq0x3fB7enpobW1lQMHDmA2m4nFYixevHjSz3yca0FKp9MsX758zD4gD1xGKJlM5seaptNp/H4/oVBoWF1w4/E427ZtO+n438mmqamJpqamM7pgcPwY5p6eHsLhMPv378fhcBAIBMake7eiKGzfvh2fzzcllh/q6elhz549/NdvH8i3gicSCdrb2wmHw3zrU78EAxiTabSBw/aOe4+pJfr7yNDWPfgFJAmUk6x1rapnHGoPHDhAJpNh/vz5Iwq1mqbx+OOPEw6H+eEPfzjphzecS0SwHScGQ/9Y3esvmg/oXZgPNnWw+0hrfvvJ2++Ryf6Q2kxGFm3rYF55kPkVQeaWB6kIeobVjVkQBEEQpjKfz4fL5QL01o8zCbXHkyQJj8eDx+OhoaGBY8eOEQgE2Lt3LzabjVAohN/vH3LdyYmkKAo7d+7E6XSOeKzfmbBYLPl1Oo9f//VUXXD7+vrYuXMnCxYswO12j0tdRyK3RM5IJrUyGAyDJp+KRCKEw2G2bNmCLMv5ADzSyacymQzbtm2jqKiI0tLSET3XeMitV7x06dJBrf5WqzX/3nrxT0vo6Oigra2Nvr6+QS3fH33/k4PH6JplNLe+7rGUzrbspjN6kskMWGdXUdmw9/EzqqumaRw8eJB0Oj0qofY73/kO9fX1/Nd//dekmyztXDe5foNPMyajkXnlQeaVB/nIpYsBSKUzHGjqYM/RVt7+81Z6Eyn+36atpDL6D7HNYmJ2qZ+5ZUHmlgeYWxagusQvlh0SBEEQzim5D5cjDbU5uRaZWCzGhRdeiNFoHBREjhw5gtlsJhQKEQgEJnxm5MnSnff49V87OjpoaGg4YRmh7u5u9u3bx5IlS3A4HBNW3+HIBZl4PH7GS+SciiRJuFwuXC4X1dXV+cmndu7ciaqqBAIBgsHgGZ+fdDrN1q1bKS8vp6ioaFTqOpZyofZ06xXLskwoFCIUCuWHDuTG1P/Tf1yfvyhwsp/Fm5c+AsCGXd8aUX0PHTpEMpkc8SRcmqbx9NNPs3PnTn72s59Nugtl04E445OM2SSzYEaIBTNC+JROVqxYQVpRqG/uZO+xMHXHwuw91sbrm/ew7rfbADBIEpVFhcwpDTCnLMDsUj9zygL43RM/a58gCIIgnI3m5mZUVc3PbjySv2e5lk+73T5odt7jg0huMqVca9toTqZ0JnLjf2fPno3P5xvX1z4Vo9GYH3urqipdXV20tbWxe/duFEVh9uzZk3JZnIE0TcvPgr1o0aIx/Zxks9moqKigoqKCVCpFe3s7+/fvJ5FIDHvyqdwyV1VVVVNiLHhnZyf79u07bag93vFDBwb+LBqNRvx+/wljvo9fmuhs5C5wLFy4cMSh9tlnn+XPf/4z69atm/ALY9OVCLZTgMloZE6ZHlq5ZCGgj9lt7Ohh37E26hra2NfQxtZDTbzxt/5ZpT0OK7NK/cwu9TOrxM+sUj/VxT7sVvNEfSuCIAiCMCzbtm3j61//Ol6vl5qaGm644YazGrOZSCTYvn07ZWVlp235dDgcVFVVUVVVlZ9Mafv27UiSlA90Yx3ccrPzLly4MN8VezIyGAz4fD6i0Sh2u53Kyko6Ozv561//OubLCJ0tVVXZuXMnDoeDmTNnjuvFf7PZPGjyqY6OjvzkUx6Ph0AgcMLkU4lEgq1bt066Cxwn09HRwYEDB045CddwHD+xWW5c7t69e0mlUvmLAme7bnXOoUOHRi3UPvfcc7z99tv8/Oc/x2wWn7Mnigi2U5TBIFEe8FAe8HDlebPzx3ujCfY3trO/sS1btvOLP+4inkznH1PqK6C6xE91iY9Z2XJGqBCLSbwdBEEQhMnhwx/+MNdeey379+9n/fr13HrrrdhsNmpqarjxxhsJhUKn/TDa29vLrl27mDt37hkvbzFwMqVEIpFfz3Rgl9KhloUZiZaWFo4ePXrGrV0TIde1O5FI5Ce18vl8zJo1i2g0SmtrK++99x4mk2nCWr4HymQybN++nUAgQHl5+YTVA05s+R7YBdfhcOTfW7t372bevHmTfoIzID8Oe9myZaP+7zxwXG4mk6Gjo4Njx46dMC73TLqU19fXE41GR6XV/sc//jGvvvoqGzdunND3uCCC7TmnwGHl/DllnD+nLH8s17p7oLGdA03tHGjq4GBTO3/cdZiMqk9UZZD0oDyzxMfMIi8zi31UFXuZESrEZp48V1sFQRCE6UOSJObMmcNXvvIVvvzlL1NfX8+GDRv4+Mc/jizL3HjjjdTW1lJcXHzCh9NwOMyhQ4dGZcyn1WqlvLyc8vJyUqkUbW1t7N27l3Q6nQ+5TqfzrJ9f07T8REbnnXfepB+bl1tH1Ww2nxAMBra25caZ5lq+gREtI3S2cuOVy8rKKC4uHrfXHY7ju+BGIhEaGhrYtWsXLpeLSCSCzWab1IGpra0tv1zSWLdWnmpcrt1uP+24XIDDhw/T19c3KqH2pz/9KevWrePVV18d1/e0MLTJ/ZtTGBUDW3c/tGxW/ng6o3CktYuDTR0caunQy+YOfrv9IIqqLzUkSVDiLaCq2EdVkZfKUGF+dudCp/gBFgRBEMaHJEnMnDmTL37xi3zhC1+goaGBDRs2cM8995DJZLjxxhtZtWoV5eXlfPOb36S6upo1a9aMeldYs9lMaWkppaWl+RmDcy2XuWVxnE7nsD8wq6pKXV0dmqaxbNmySb80SK7l0+fzMWPGjNM+/mTLCGUymfy4yeEsI3S2EokE27Zto7q6etIvPyRJEpqm0d3dzUUXXYTRaBy0tvDA8zVZhMNhDh8+zPLly8e92/lQ43Lb2trYsmXLoDWtB/asOHLkCL29vSxatGjEP2vr16/nv/7rv3jttddGvfeGcHZEsJ3GTLKRWaX62NuBcoH3UEsH9c2d1Lfo21/rjpJM9y+e7XFYmREqZEZID7wzsluZ341ZdGsWBEEQxogkSZSXl/OP//iPfO5zn6OlpYWXXnqJT3/60xw9epTS0lJWr1495i2fA2cMznWRzHVx9Pl8hEKhU44DzGQy7NixA4/HQ2Vl5aSf8DGZTLJt2zYqKirOanbe0y0jFAwGRzxucqDcJFxTpTvvwCVyckEpd1Eg11Ng4ORTo32+zlRraytHjx6dkFB7vIE9BaqqqvLjcuvq6vLjcjOZDIlEgiVLlow41G7cuJH//M//5LXXXhtRbw1hdIn0IZzgZIFXUVWaO3o53NrF4ZZOvWzt5A+76nn5T7vyjzNIEsVeF+VBPehWBDxUBD2UBz0U+wowiTW9BEEQhFEiSRLFxcXccccdvPzyy3zsYx+jpKSEr371q3R0dHDdddexatUq5s2bN6YBYGAXydzkQLlxgIWFhfllcXJ1yIXE8vLySdc9diixWIzt27czZ86cMx6vPJShlhE6/nx5PJ6zDiC58dWLFi2a1JNw5ZxuNuGBPQWOP18Dl10arxb/lpYWjh07xrJlyyY81A7l+HG5dXV1dHR0YDKZ2Lt3b/58nc06s6+//jpPP/00r7322qiu13z33Xfz6quvEgwG2blzJ6C/L2699VYOHz5MZWUlL774IoWFhaP2mucaEWyFYTMaDJQFPJQFPFy6qGrQfX3xJEdbuzgS7uJIaxdHw90cae1iR30z0URqwHNIFPsKKPN7st2j3fpz+t2U+t3YLJPvl6MgCIIwuaXTaT784Q/z0EMPUVtbC8CnPvUpOjs7efnll3nkkUdobGzk6quv5qabbmLhwoVjGgCOnxyos7OTlpYW6urqcLvdFBQUcOzYMebNmzclPqT29PSwe/fuMQuJQy0j1NraSl1dHQUFBQQCAXw+37BDSC4kDmz5nMxyY1TPO++8YY1RHWryqXA4zL59+3A6nQQCAfx+/5j1WGhubqaxsZHly5dP+vHgoNc3nU5z6aWXAgw5Ltfv9w/r3L/55pt8+9vf5vXXXx+VCzwDfeITn+D+++/nzjvvzB978sknufLKK1m7di1PPvkkTz75JE899dSovu65ZPK/G4UpwWWzsLCyiIWVg7smaZpGZ1+MY23dHA13cyzczbE2fdt5uIVIPDno8f4CO6XZkJvffG6KfQWo2XG/giAIgjCQyWTi9ddfPyEker1ePvGJT/CJT3yCnp4eXn31VZ566ikOHTrEypUrqa2tHfNxrQaDAb/fj9/vR9M0jh49yoEDBzCZTDQ2NpLJZPB6vWfVcjQecmOIly1bNi6T4+RmV/b5fGiaRk9PT34isOEsIxQOh/MTGU3mCZdyci2fZ9ud9/hxpn19fbS1tXHkyBHMZnN+nOlonYumpiaam5tZtmzZlAi1DQ0NtLe3s3Tp0vzP+VDjcrdu3XrScbk5mzZt4pvf/Cavv/76mIzXvuyyyzh8+PCgYxs3bmTTpk0A3HXXXaxYsUIE21OY/O9IYUqTJAlfgQNfgYNl1aUn3N8didPQ3kNDWzcN7T00Zrf3DjTyxl/rULX+MGuQoPjXhyj2uSnxFVDiK6DY66LYV0Cxt4BgoVN0cxaEaUpVNdp7oxxr66ahrSd/AU2YPk7X8ul2u7njjju44447iEQi+e6Ee/fu5UMf+hA1NTVccMEFYxowW1paCIfDXHLJJZjN5nxoO3DgAA6Hg1AohN/vnzQht6mpicbGxmG3JI42SZLweDx4PJ78jMHhcHjQMkLBYDBft6amJpqamjjvvPMmZffY4zU2NtLS0jJqLZ+SJFFQUEBBQQHV1dXEYjHa2tryk0/lQtvZTj7V2NhIa2sry5YtmzTv0VNpaGigra3tpGNqjx+Xm5vcrK6ujmQyidfrpbm5mUsvvZQ//vGPfPWrX+W1114jGAyO2/fQ2tqaH6pQXFxMOBwet9eeikSwFSaUx2nD47SxqPLESSjSGYXmzj6aOvSw++ctOzE5PDR19vLH3Ydp74kOerxBkvC7HRR7XYQKXRR5XRQVuijyFhD0OCkqdFHosk36yTkEQTiRpmn0xpI0dfTQ1NFLU0cvje36fkN7D03tPaQy/ZPb5YY9CMJQnE4nq1evZvXq1cTjcX71q1/xwx/+kM9+9rNcdtll1NTUcMkll4xai5SmadTX19Pb28t5552XDwUDQ1tfX1++tXE4LZNjSdM0Dh8+THd396D6TiRJknC5XLhcrnxoC4fDbNu2DUmSkGWZTCbD8uXLJ0V9T+fo0aN0dHSMaUi02+0nTD61b98+kskkfr+fQCAw7Mmnjh07RltbG0uXLp0S57exsZFwOHxG9R04uVkmk6G+vp5nnnmGf/iHfyCdTvPEE09MiaED05kItsKkZZKNVAT1iacAfEonK1asyN+fTGdo7eqjuaOX5s4+mjt7aenso7mzj91HW3ln20HSAz7oAphlI0GPk2Chk5DHRcDjIORxEfQ48XscelngwCRP/l/agnAuySgq7T1RWrv6sj/HA3+u9f2B4/UBnDYLpb4CZhZ5+eCiKsr82TH7ATdFXhcmoxHpm/dM0HckTBU2m43a2lpqa2tJJpO89dZbvPDCCzz44IO8//3vp6amhksvvfSsA6aqquzZswej0cjSpUuHDBEDW9pmzZo1qGXSbDYTDAYJBALj0mqqaRp1dXUoijKo++ZkY7fbqaysZMaMGezdu5fe3l5kWebdd98dl2WERiJ3kWM8z+/AyadyM3gPd/KpXAifKqG2qamJ1tbWEdVXlmVmz57NQw89xOc+9znWrl3L5s2b+dd//Veqq6v5xje+wYIFC0a55icKhUI0NzdTXFxMc3PzuLYWT0Ui2ApTlsUkUxEspCI49NUzVdXoisT0D8pdEVo7+2jt7iPcFaG1O8L2Q02Ee6InhF+AQqeNgMdJwO3A73YQcDvxFdjxZ2/7s92rrWbxIyQIp5NIZWjviRDujtDWHSXcE6G1q49wd4TWrgjh7j7auqODhh6APna/2FdAqd/N++aU68MPssMQSn1uChwnzhwqCCNhsVi4/vrruf7660mn07zzzjts2LCBhx56iAsuuICamhpWrFgx7IA5cM3XioqKYYesXPfImTNn5lsmt27dOmjSoLEYP6ooCrt27cLhcDB37txJGQoH0jSNPXv2YDAYuPDCC5EkaVyWERpJfQ8cOEAymWTx4sUTdtFg4Azeucm6cq25TqeTYDCIz+dDlmWOHDlCV1fXpL7IMdDAMcAjDeFbt27l/vvv5+c//znV1dXceuut+fdcIBAYpRqf2qpVq3j++edZu3Ytzz//PDU1NePyulOV+FQunLMMhv7xvQtOsoa8pml0R+KEu7MfunuitOXKHv1DeF1DG529sRM+dAM4rWa8Bfbs69gpdNrxFdjxumwUuuz5Y16XDafNMuF/VAVhtOS6Bnf0RunojdHZG6OtN0pHb5T2nv6trSdCbyx5wtfbLCaCbr33xIVzKwgVuggVOrPDB/QhBA7r+I/pE4Qck8nE1VdfzdVXX00mk+H3v/8969at46tf/SpLly6ltraWK6+8csilWQASiQTbt29nxowZhEKhs65HrmWysrKSRCJBOBxmx44dAAQCAYLB4KhM6pROp9m+fTuhUIiysrIRP99YU1WVHTt24HK5qKqqyv99HetlhM5WriVc0zQWLlw4aT4PHD9ZV65L/OHDh8lkMvmeBlMh1DY3N49aqN25cyf33Xcf69ato7q6On9ckqQxa6m97bbb2LRpE+3t7ZSVlfHoo4+ydu1aVq9ezXPPPUdFRQXr1q0bk9c+V0yqYJvRNLrjCTw2cRVeGB+SJFHoslPosjO3/OTdOxRVpasvTntvlI6eqP4BvidGZ1+U9uyH+gNNHXT2Hh3yQzyAbDTgcdoozI4rzu27HdZsqR9zO6z5zWE1T5o/fsK5TVU1IvEk3dEEXZEY3ZE4XZE43X162dkXo6tPL3NbRlFPeB6TbNR7NxQ4qAh6OG92GQGP3ush6HESzHb5Fxd6hKlElmVWrFjBihUrUBSFP/3pT6xfv55vfOMbzJ8/n9raWq666qr8pDzvvvsu0WiUJUuW4PF4Rq0eVquViooKKioqSCaThMNhdu/ejaIo+ZB7NhMDJRIJtm3bRlVV1ZTo6phrCQ8EApSXl5/0cadbRigYDI7LjNSaprF7927MZjOzZs2atL/7BnaJNxgMdHd3U1hYmF9TNfcem4xLKLW0tOSXIBrpv+eePXu49957eeGFF5g7d+4o1fD0fvaznw15/O233x63Okx1kyrYdiVSXPTP/84sv5fl5SWcV17C8rISKr2eSftLQJgejAZDvhsyJ/8bCuiTXuWCQG7LhYOuvng+NNQdC9MdiZ80CAPIBgMuuwW3w4rLbs2WFvo629nd+0cK7BacdgsumwWnbUBpt+C0msVY4WlG0zRSGYXeeJr6lk76Ykn6Ygn64kl6ogn6Ykl6Ywl6Ygl6Igl6Ywm6owl6InF6YwmUkyypZTXJeFw2vC69O/7sMj8+lx1vgQNftmeC3633jiiwi8AqnNuMRiOXXnopl156Kaqq8re//Y1169bx1FNPUV1dzaxZs/jFL37Biy++OKqh9ngWi4Xy8nLKy8sHTQyUSqXw+/2EQqFhjTGNRCLs3LmTefPmjWl9R0sqlWLbtm2UlZXlZ4sdjpMtI3Tw4EHsdnt+sq7RXsJGVVV27tyZn3l3sv9+1DSNQ4cOEYvF8kthHT9jcCqVynfxdrlcE/49tba20tDQMCottfv37+eTn/wkP/nJT8ZlDK0wuiRtiO6VE6Vy1mztoR/+hPcamtja0ExvQv/A77FZWV5WzPKyEpaVFbO4pAi7efJP4z5SmzZtGjRZ0nR3rp6PjKLSlw0Y3ZE4PdFEdtP3e2MJeqMJerOhpDeaoLMvSiKtcLofX4vJiMNqwWE147CacdrM2C36vt1q6t+3mLBZ9Nt2iwmrxYTNrB+zmWWs2X2rWcY4CbsjTeX3RlpRSCTTxFMZ4sk08VSaeDJNLJkmnkwRS6aJJVJEE2liyRTRhL7FEikiiRSReJJIPFsmUkOOGR/IZjFRYLfgdtgosFvxOHM9BGx4HNZBvQlypX0KdwmWJOldTdPeN9H1mOImzweFSUxVVR599FGef/55gsEgoVCIVatWcf31149rYMxkMrS1tREOh/NjTEOh0JABpLu7m71797Jo0SKcTue41fFs5VqWq6urR20d0YHLCLW3t4/qZF2KorB9+3a8Xi8zZpxkTNQkomkaBw8eJJlMsmDBgpMG1tzkU+FwmEgkQmFhIYFA4KSTT42l1tZWjh49OipLJtXX13Pbbbfxox/9iPPOO2+UaiicxJhcDZlULbYWo4F/+OBFAKiaxsG2DrY0NGe3Jt7ZXw+AUZKYE/SzrKyYZaXFLCktospXOOFXjAThbMhGQ7479HBt2rSJyy67nGgyRV8sQSSe0lvn4sls0MmGnYRe5sJQNJGipasvG5RSxJIpkulTB6HjmWQjFpOM1WTEajZhNum3c5vZZMQsGzGbZL2UjZgGlCajEVk26KXRkN0G7BsMGI0GjAYJg8GAnC0NBgmDJPWXkoQkSUgSNHTFqDsWHvQ7QJIkBl640zQNLVdqGqqmd7/VNA1FVVE1DUXVUFUNVVXJqCqKqpFRFBRFLzOKmt/SikI6kyv1LZUtk+kMqVyZ1sv8lsqQyJWpDBn1xO68JyMbDNitJv1ihc2M02rGV+CgIliI02bGabPgtFpoaTjCeUsX47LrrfcFdisF2VK04gvC6NM0ja9//evU1dWxZ88erFYru3btYv369axatQq/309NTQ033HADPp9vTOsiy/KgMabt7e0cOXKESCSC1+slFArhdrtpa2ujvr6eZcuWnXSc8GQSjUbZsWPHqLcsn24ZoVzIPdNxzJlMhm3btk2ZMcuaprF//34ymcwpQy2cevIpl8tFIBAYl/WYw+HwqIXao0ePcvvtt/P9739fhNopbFK12M6dO1erq6s76f3d8QTbskF3W2Mz2xpbiKb05R/cVguLS4tYWlLE0tJiFpcW4bWPfDKFiTSVW6HGgjgf/UbzXGQUNd8ymG8pzLYaxpNpEim9NTGRSpPIlsm0HspyAS2VUUikMqQy/UEuF/RSx4W+c5FsNAwK7xbZiMkkY5GNWMwyZlnGapax5C4CmGWsJr0F3GbWW8hz+3rL+eAWdLvFhN1qxmIa3h9u8bPST7TYjorJ80FhkorFYjz77LP84z/+4wktVpqmsW/fPtavX88rr7yCw+GgpqaGG2+8kWAwOG4X5VVVzbeydXR0ADBv3jz8fv+knxiot7eXXbt2sWjRIlwu17i9biKRyLd+K4qSX0bodK3b6XSarVu3nnF36YmSe4+qqsq8efPO+j2paRq9vb20tbXR3t6OxWIZs6WqwuEwR44cYdmyZSNe67mxsZHVq1fzzDPP8IEPfGCUaiicxpj84ptSwfZ4iqpysL2TbY0t+aB7oK0jP3tteaGbJSVFLC4JsbikiAVFwSnVhVl8OB1MnI9+U/VcaJpGRlXJZFTSmWwLqKrvK2p/a6iSbS1VVBVF6W9N1QaUqqahqXor7I4dO1i4aFF/C+3AX2vZX52SJCHlSon+Vl+DhFHqbxU2GiQMkgHZKGE0GDAaDEO2LOutz/oxg2Fy9RaZqu+PsSCC7aiYPB8Uprjc+MUNGzbwi1/8ArPZzI033khNTQ3FxcVjHnJzr9/X10dpaSnt7e10d3fjdrvzEylNtpDb2dnJvn37WLp06ajM/ny20ul0PuQmEomTLiOUSqXYunUrlZWVU2IirtxszcCoL/EUjUZpa2ujra0NSZIIBAIEAoERTz6V622wfPnyEYfalpYWPvrRj/K///f/Fn83x9e53xX5TBkNBuYE/cwJ+rll+SIAoqkUO5ta2d7Uwo7GFt471sRru/QfWIMkMSvgywbdEIuKQ8wN+jGP8kQBgiAMTZIkTEa9O7LNMooXmbqOsWLZrNF7PkEQhDEgSRLV1dV86Utf4otf/CINDQ2sX7+ee+65h0wmw4033khtbS3l5eWjHnJVVWXv3r0YDAaWLl2aDxqaptHd3U04HGb//v24XK78OqZj3ZX0dHLLzixfvnxM1u09EyaTiZKSEkpKSvJdvI9fRshms7F9+3ZmzZo15l3OR0NuTVZZlpk9e/aov+ccDgcOh4PKyspRm3xqNENtOBzmlltu4dvf/rYIteeIcy7ROcxmLqos56LK/qlr2yJRdjS1sKOplR1Nrbxdd5ANW3cBYDIYmBPys6g4xMLiIIuKQ8wO+jFP8C9zQRAEQRDOXZIkUV5ezuc//3n+8R//kebmZl566SU+/elPE41Guf7666mpqaG6unrEgUNRFHbs2IHb7aaysvKE+QgKCwspLCzMdyUNh8McOnRoTGcLPp3Gxkaam5tHJcCMNqPReMIY08bGRsLhMF6vF1VVURRlwi8MnMp4L0FksVgoKyujrKwsP/lUbuz3cNcXbm9vz48LH+l7oqOjg1tuuYVvfetbrFy5ckTPJUwe51ywHUrA6eCKOdVcMUdfYFnTNBp7etnR1MrOplZ2tbTyy937+H/v6Quem7ItwQuKgywoCrKwOMjcYADrMMe3CYIgCIIw+r72ta+xceNGDAYDwWCQH/3oR5SUlADwxBNP8Nxzz2E0Gnn66ae55pprJri2wydJEiUlJdx///3cf//9hMNhfvGLX/DFL36Rzs5OrrvuOmpqas6qq2hueZzS0tL8uTpVPdxuN263m1mzZhGJRGhtbeXw4cNYrdb8eMmxDpqHDx+mq6trVNYkHWsGgwGr1UokEuF973sfmqYRDoc5cOAADodjwi4MnIqmaezatQur1ToqF07O1FCTT+XWFz5Zj4GOjg4OHjzI8uXLRzxet6uri1tuuYWvfe1rfPjDHx7ptyNMIlN6jO1o0jSNY1097GxuZVdzmN0t+tYdTwD6TMwz/V7mFwVYUBRkflGQ+aEAbtvYzSQoxskNJs5HP3EuBhPnYzBxPvqJMbajYtJ8UOjt7aWgoACAp59+mt27d/Pss8+ye/dubrvtNjZv3kxTUxMrV65k3759kz4UDUdnZycbN25kw4YNNDU1cc0113DTTTexYMGC046HjcfjbNu2jVmzZo14eZxoNEprayvt7e3IskwwGCQYDI7qpECapnHgwIH8cjOTbbzvUPr6+ti5cyeLFy8eNKnUWC4jNBKqqrJr1y4cDgczZ86csHoMZWCPgY6ODqxWK4FAAFmW813SR3ruenp6uPnmm3nwwQe5+eabR6nmwlkQY2zHkiRJVHg9VHg9XLdwLqD/gDX19LG7Jcyu5jB7WsP8+fAxXt6xN/91pe4C5ob8zA8FmF8UZF7IT6nHjUEsPSQIgiAIoyoXakEPWrmWpo0bN7JmzRosFgtVVVXMmjWLzZs3c8kll0xUVUeN1+vlk5/8JJ/85Cfp6enhlVde4YknnqC+vp6rrrqK2tpali5dekIIzAWuBQsW4Ha7R1yPXBCaOXPmoCVxDAYDgUCAYDA4omWDcuM9jUYjCxcunBJLOPb09LBnzx6WLl16woRIw1lGaKTn7EypqsrOnTtxuVxUVVWN2+sO18AeA7NnzyYajXLkyBFaWlpwOp00NzfnxzKfjb6+Pm699VY++9nPjmmofeONN/jc5z6Hoijce++9rF27dsxeSxhMBNtTkCSJUk8BpZ4CrprXPzFNRzTG7pYwe1ra2Nvaxp6WNjbtr8/Pxuwwm5kb8jM36GdeKMDckJ/ZAT9Oy8RdoRMEQRCEc8HDDz/Mj3/8Y9xuN++88w6gj8e8+OKL848pKyujsbFxoqo4ZtxuNx/72Mf42Mc+Rl9fH6+//jrf/e53qaur44orrqCmpoYLLriA119/nd/+9rc88sgjI56Bdih2u53KykoqKytJJBKEw2F27tyJpmkEAgFCodAZhQ9VVdmxY0c+cE2FUHumszUff87a2trYtWsXiqLkLww4HI4xq2/uHOfGWU8FyWSS3t7e/BI8bW1t7Nmzh3Q6PWjppeG8X6LRKLfddhv33nsva9asGbM6K4rCpz/9ad58803Kysq44IILWLVqFQsWLBiz1xT6iWB7FnwOOx+sruSD1ZX5Y/F0mv3hDva2tuW3V3bu5Wfvbs8/przQzZyAPzuTs4+5QT8zfIXIU6CrjSAIgiCMh5UrV9LS0nLC8ccee4yamhoee+wxHnvsMZ544gmeeeYZHn30UYYaVjUVwtFIuFwubr31Vm699Vbi8ThvvPEGzz33HHfffTdGo5Fvfetb4zKTsNVqpaKigoqKClKpFOFwmD179pDJZIYV2DKZDNu3bycQCFBeXn7Sx00m7e3t+fGeZ3OOrVYr5eXllJeX55cR2r9/P4lEIh/YznS24FNRVZXt27fj9XqpqKgYlecca11dXezbt2/QOR44+VRuIqloNIrX6yUQCJx08ql4PM5tt93GHXfcwZ133jmm9d68eTOzZs3Kd/Nes2YNGzduFMF2nIhgO0psJhNLSotYUlqUP5abpKqutZ26cDv7wu3Utbbzzv5D+dZdk9FItd/L7ICPOUEfswI+Zgf8lHoKTvZSgiAIgnDOeuutt4b1uNtvv53rr7+eRx99lLKyMo4dO5a/r6Gh4bQTJZ1LbDYbN910E0ePHiUcDnPPPffwy1/+km9961tccskl3HTTTXzgAx8Y80mfzGZzPnwMDGzJZHLIFrbcxFbl5eUUFRWd5tknh9bWVo4ePToq4z1h6GWEcrMF5wJbYWHhWYdcRVHYvn07fr9/ylw46O7upq6ujmXLlg154UCWZYqKiigqKkJVVTo7O0+YfMrtdmOxWEgkEnzsYx/j5ptv5u677x7zujc2Ng46z2VlZfzlL38Z89cVdCLYjiFJkijzuCnzuLlybnX+eDKT4WBbJ/vC7exra2d/Wwd/PdrAKzv7x+7aTSYCFhNv9CSpDujBt9rvo9RTIMbvCoIgCNPS/v37mT17NgAvv/wy8+bNA2DVqlXcfvvtPPDAAzQ1NbF//34uvPDCiazquPv2t7/Njh07ePXVVzGbzdx6662k02neeecd1q9fz5e+9CUuuOACamtrufzyy8d8AqOBgW1gC1ssFsPn8+HxeDh48OCoTGw1XpqammhqamL58uVjMsvx8csIdXZ20tLSQl1dHQUFBfnZgoc7qZaiKGzbto1gMEhZWdmo13csdHd3s3fvXpYtWzas8ccGgwG/34/f70fTNHp6egiHw9x00024XC5UVeW6667jvvvuG5deHNOx98hkIoLtBLDIsr6UUHFw0PG+RJL9bR0caOvQw+6+A/z+0BF+vn13/jFWWaba72Wm30v1gK3C68F0Dsz+KAiCIAgns3btWurq6jAYDMyYMYNnn30WgIULF7J69WoWLFiALMt873vfOydmRD4TH//4xwmFQoNCj8lk4uqrr+bqq68mk8nwu9/9jnXr1vHwww+zbNkyamtrueKKK8Z8AqOBLWyKotDY2MjOnTsxmUx0dHRgNBrxeDyTOgAcO3aMtra2cVuC6PjA1t3dfUbLCCmKwtatWykqKqK0tHTM6zsaenp6zijUHk+SJDweDx6Ph02bNvGJT3yCdDrN66+/zltvvUVNTQ0f+chHxrTlerr3HploYrmfSSy3ZEdPPMGB9g4OtnXmy4PtnTT39uUfKxsMlBe6menzMtNfyEy/l5k+L1W+wjFdkmg8iSVM+olzMZg4H4OJ89FPLPczKibPBwVhVCiKwh//+EfWr1/Pr3/9axYsWEBtbS1XXXXVmEw2NVBvby+7du1i8eLF2O32fDfS3t5ePB4PwWCQwsLCSbXUz+HDh+np6WHx4sUTXq/hLCOUyWTYunUrpaWlFBcXT2h9h2vgDNNnO+txTiaT4e/+7u9YvHgxDz/8MJIk0dTUxMsvv0wwGOQjH/nIKNV66NeeM2cOb7/9NqWlpVxwwQX89Kc/ZeHChWP2mlOUWO5nunLbrJxfXsr55YOvuEVTKQ616yG3vr2Lg+2dHOro5LcH6kmrav5xXruNKl8hVT4vlT4PVd5CKn2FVBS6MU+iBcMFQRAEQRh7RqORD37wg3zwgx9EVVX++te/sm7dOp588klmzZrFqlWruPbaa3G5XKP6urmZhJctW5YPL7lWSVVV6e7uprW1lX379p1V19vRpmkaBw8eJB6PT4pQCycuIxSNRmlra8svveTz+QiHw1RUVEyZccu9vb2jFmoVReF//a//xdy5c/OhFqCkpIT77rtvNKp7SrIs88wzz3DNNdegKAp33323CLXjSKSaKcxhNrO4pIjFJYN/cWVUlWNdPdR3dFLf0ZXf3tl/iI6tsfzjDJJEidtFpa+QSm8hM7wefSv0UOopEF2bBUEQBGGAL37xi7zyyiuYzWaqq6v54Q9/iMfjAeCJJ57gueeew2g08vTTT3PNNddMbGWHyWAwcNFFF3HRRRehqipbt25l/fr1fPe736W8vJxVq1Zx3XXX5b/PsxUOhzl8+PBJZxI2GAx4vV68Xm9+rGRraysHDhzA6XTmu96OVxdzTdPYt28fiqKwaNGiSdtN2uFw4HA4qKysJBKJsHXrVoxGI0ePHiUej4/5MkIj1dvby+7du0cl1Kqqyuc+9zlKS0t55JFHJuzf7LrrruO6666bkNee7kSwPQfJBkO2hbbwhPt6EwkOd3RT39HFkc4uDnd2c7iji60NzUSSqfzjjNk1fCuyQbei0EOF101FoYcyjxurSbx1BEEQhOnlqquu4oknnkCWZR566CGeeOIJnnrqKXbv3s0LL7zArl27aGpqYuXKlezbt2/KjfM1GAycd955nHfeeTz22GPs3LmT9evXs2rVKvx+P7W1tVx//fX4fL4zet7Gxkaam5tZvnz5sGZmHjhWUtM0ent7CYfD1NfXY7PZ8l1vx2ICJ9BD7Z49e5Blmfnz50/aUDtQOp1m9+7dzJkzh2AwSCqVor29fUyXERqpvr4+du3aNWqh9sEHH8TtdvPEE09MitZ1YfyJdDLNFFitJyxLBPov8Y5ojCNd3Rzp7N+OdnazraGFvmRy0OODLgcVhR7KPW7KC/WtLLvvd9gnzS9NQRAEQRgtV199dX7/4osvZv369QBs3LiRNWvWYLFYqKqqYtasWWzevJlLLrlkoqo6YpIksXjxYhYvXswjjzxCXV0d69ev55ZbbsHlcrFq1SpuvPFGAoHAKf/mHz58mO7u7rOedEmSJNxuN263m1mzZhGNRmltbeXdd9/FbDYTCoUIBAKjtpSRqqrs2rULu93OzJkzp8TnmVQqxdatW6mqqiIQCAD60ksDZ6Xu6OgYtIxQMBic0Am7+vr62LlzJ0uXLh3xuG5VVfnyl7+MLMv8y7/8iwi105gItgKg/+HwOx34nY4TxvJqmkZXPMGxrm6OdvZwtKubY116+Yf6I4S3Rwc93irLlHoKsksd6WWpp0Df3AV4bNYp8YdCEARBEE7mBz/4Abfeeiugt0hefPHF+fvKyspobGycqKqNOkmSmDdvHl/96ld5+OGHOXToEOvXr+f222/HbDazatUqampqKCoqyv99V1WVvXv3oqoqS5YsGZWwIUkSTqcTp9OZH18aDofZsmULsiznW3KH6uo8HIqisGPHDjweD5WVlSOu73hIpVJs2bKF6urqky6bJMvyCcsINTc3s3fvXtxuN8FgEK/XO26BMBKJsHPnTpYsWTIqofaRRx4hkUjwH//xHyLUTnMi2AqnJUkSXrsNr93G0tITZ9dLpDM0dvdwrLuHhu5eGrp7ONbVQ2N3L+8dazqhtdduNlHq1oNuibuAEreLUncBxW4XJe4CAk6HWKtXEARBmBArV66kpaXlhOOPPfYYNTU1+X1ZlrnjjjuA6bV2pSRJVFdX89BDD/GlL32Jo0ePsmHDBj75yU+iqio33ngjN9xwAw8//DDnn38+DzzwwJidC4fDQVVVFVVVVcTjccLhMNu3b0eSJILBIMFgcNjLxkzFNV+TySRbt25l1qxZw+4efrJlhPbv358fy+zz+casm3ckEmHHjh0sWbJkxGN/NU3j8ccfp62tjR/84Aci1Aoi2AojZzXJVAd8VAeG/qXaE0/Q2N1LY08vjd29NPT00NTdR2OPHnx7E4ODr8lgIFTgpMRdQFGBk5KCAorcTto7eyhqbaOowIXbajlnPzQIgiAIE+ett9465f3PP/88r776Km+//Xb+79B0XbtSkiRmzJjBAw88wOc//3mam5t54YUXWLlyZb7F89ChQ+PSpddmszFjxgxmzJhBMpkkHA6za9cuFEXJh9yTtQ6m02m2bds2pZbHSSQSbN26lTlz5uD1es/qOSRJorCwkMLCQjRNo6+vLz/JV66bt9/vzy8jNFLRaJQdO3awePHiUQm13/nOdzh8+DA//vGPp9x4dmFsiGArjDm3zYrbZmVBcXDI+yPJJE09fTT19ObL5t4IzT29vHu0idf79pHJLl/0zK5DANhMMiGXi6ICJ0UFTkIuJ6ECl166HIRcTnwOO0Zx9U4QBEEYJW+88QZPPfUUv/nNbwaFpFWrVnH77bfzwAMP0NTUxP79+7nwwgsnsKbjL7cMzRtvvME//dM/8ZGPfISf//znfOELX6Czs5PrrruO2tpa5syZM+Yh12KxUF5eTnl5OalUira2Nvbu3Us6nSYQCBAMBnE6nUD/+NTKykqCwaE/p0w2uVA7d+5cCgtPnCj0bEiSREFBAQUFBfmxzOFwOL+MUO68DbcF/HjRaJTt27ezePHi/Lk/W5qm8W//9m/s2rWLn/70p2PWuixMPeKdIEw4p8XCnKCFOcGhx4Yoqkp7JMZrm35D8azZtPT20dIboaW3j9a+CH853EBbJJoPvznG7LjhYDboBl1OAtnbAaeDoFMvC+02EYAFQRCE07r//vtJJpNcddVVgD6B1LPPPsvChQtZvXo1CxYsQJZlvve9703LFqQvfelL3HvvvaxevRqAT33qU3zqU5+io6ODjRs38tWvfpWWlhauueYabrrpJubPnz/m3UfNZjOlpaWUlpaSTqdpb2/nwIEDJBIJPB4PnZ2dzJ49Oz/p0mQXj8fZtm0b8+bNG/ESTKcysJt3IpGgra0t3wKeC7nDbXXNhdpFixaNSqj993//dzZv3syLL744apOGCecGaahxIcP+Ykn6DnAjkAIOAp/UNK07e9+XgXsABfispmm/Ot3zzZ07V6urqzvr+pxrNm3axIoVKya6GpPGqc6Hoqp0RGO09kVo7YvS2hch3BshHIkQzt5ui0TpjidO+FqjJOF12AlmJ8/yO+0EHHrpc9jxOx166bBTMEm6QIv3xmDifAwmzof+4SeaSuOyWt7VNO19E12fKe7sPygI04qqqqcNqt3d3bzyyiu89NJL1NfXc9VVV1FbW8vSpUvHdYxkJBJhy5Yt2Gw20uk0Pp+PYDCI2+2eFH/nh5ILtfPnz8ftdk9IHXLLCIXD4WEtIxSLxdi2bRuLFi3C5XKN6LU1TeO5557jV7/6FS+99NJZTxImTApj8kM20hbbN4Eva5qWkSTpKeDLwEOSJC0A1gALgRLgLUmS5miappzqybqUNP/w61+w2F/EYl8Ri/0hPJaRrWslTA9Gg4FgtlV28Skel8xkCPdFaYsM2PqitEX7b+9uCdMZjaEMcdHHZDDgdeiBV99seO12vLnSbsvu2yi023GYTZP2D6QgTEXRVIrOaIyOaJz2aIyOaJT2SEzfj0Rpi8Zoz/4sx9OZia6uIEwrwwmmHo+Hj3/843z84x+nr6+P1157je9+97vU1dVxxRVXUFtby/ve974xDbnRaDQ/K6/b7UZRFDo7O2loaGDPnj0UFhYSDAYpLCycNH/DcwFx4cKFFBQUTFg9zmQZoVgslm+pHWmoBfjxj3/Mq6++ysaNG0WoFYY0omCradr/DLj5Z+Cj2f0a4AVN05JAvSRJB4ALgT+d5hnZ1Rnml0f25Y+UOd0s9oVY5C9ikS/EIl8In3VkU4ML05dFlvPr7p6Kqml0x+K0RbIfnKMxOgZtcTqiMQ62d9ARjZHMDH3NxmQ0Umi3UmizUWjXN4/Nmi89tmxpt+K26mORC6wW0TVamBZUTaMnnqA7nqArFte3uF52xuJ0RfWyMxajM6qXJwurbqslv2TZkpIi/NmhBn/39XH+pgRBGDaXy8WaNWtYs2YNsViMX/7yl/zf//t/+cxnPsNll11GbW0tF1988ah2686tnzowbBmNRgKBAIFAAFVV6erqoqWlhbq6OtxuN6FQiMLCwgmbdXdgV97RCIij5VTLCDkcDnp7e0etzv/93//NunXrePXVV7HZRr/Ra926dTzyyCPs2bOHzZs387739Xf0eeKJJ3juuecwGo08/fTTXHPNNaP++sLoGFFX5EFPJEmvAP9P07SfSJL0DPBnTdN+kr3vOeCXmqatH+Lr/h74e4BAIHD+iy++SFTJcDgV5XAyyuFUjCPJKOFM/8y5XqOZGRY7FWY7lWYHFRY7XqN50lxVGy2RSGTEYxHOJZP1fGiaRlJViaQz9KUy9KUzRDLZMp0hms4QSStEMvrtSDpDLKOctG+fBNhkI/bs5pDl/H5uMyoKHocdu2zEZtSP2bL7JoN0zv0snM5kfW9MlPE8H5qmkVY1YhmFWCaTLZX87Wh2P5rJEE1ny4xC9DQ/ByaDhFOWcZpkXGYZlym3mXCZZArM+n6BWabAJCOf5APnhz70IdEVeeREV+RJYrp8+E4kErz55pusX7+ed999l/e///3cdNNNfOADHxjRREE9PT3s2bNn2LPyappGV1cX4XCYrq4uXC4XoVAIr9c7bmOoc8vjTLZQeyqxWIz33nuPgoICotHoiJcRWrduHT/4wQ947bXXxuxv2549ezAYDHzqU5/in//5n/M/W7t37+a2225j8+bNNDU1sXLlSvbt2zctx9CPsonpiixJ0ltA0RB3Paxp2sbsYx4GMsB/575siMcP+YdR07T/BP4T9DG2JxsX1pNMsKuzlV0drezMbi93N+WftNBiY4E3yEJfkAXeIAu8IWa6vSf9sDMViHFyg51L52NgS5VexvP7PfEEPYkk3fEEvYkEvfEknYkEh/vi9MYTpI+bJOt4JoMBp9WC02LGaTbjslpwmM04LWYc2WMOixmH2ZQtzdjNJhxm/Zg9e9tmMmE3m6bEmsLn0ntjNAznfCiqSjydJppKE0uliaZSRJOpbJkmkkrqZTKV3U/Rl0jRl0zSl0wSSaboSyTpSyRP+550Wsy4bVY8VivFHiue7EzpHpuNQnuu1PdzPRvsJtGNXxCOt2jRIl566SU+9alPDTq+e/duXnjhBXbt2nVOfPi2Wq3ceOON3HjjjaRSKd555x3Wr1/PF7/4RS688EJqa2u57LLLzmgZmq6uLurq6li6dOmwW/wkScLr9eL1etE0jZ6eHsLhMAcOHMDhcOSXwxmr85wLtaMxk/B4icfj+dmP3W73oGWE6uvrsVqtBINBAoHAsCZ+2rhxI9///vd59dVXx/QczJ8//6Svv2bNGiwWC1VVVcyaNYvNmzdzySWXjFldhLN32mCradrKU90vSdJdwA3AlVp/828DUD7gYWVA09lWEsBtsfL+4hm8v3hG/lgsnWJPZ1s+8O7uDPOjPe+RUvRuoRajzNxCP/MLAyzwhpjvDTDPG6TALPrlCxPLIEn5D/BnKp5O86tfb2Lh8uX0ZcNFbyIXNpIDwkeKaDaAtPT2EUmliCT18JL7GRkOqyxjM5uwm0zYTDLWbOC1mmRssn7bapL1TZaxyPq+Rc5txkGlyWjEIhsxG2XMshGz0YjJaMBkNGKWjZiMRkwGw7QKNaqmkVEUUopKSlFIKwqpjKLvZxSSSoZURiGZUUhmMgM2hUQmQzKdIZ7Wj8XTaQ4fa+Dn7a+SyGSIpdIk0vrxWFoPsfFUmkRmeONPDZKUvzDisphxWi34HHYqvYW4rBZcFjMFVgsuqwW31ZovC6wWCrJd66fyBUZBmEym44dvs9nMNddcwzXXXEMmk+G3v/0t69at4ytf+QrLly+ntraWD33oQ6dchqa9vZ2DBw+yfPnysx6bKUkSHo8Hj8czZFjLhdzRmqU312V6yZIlI17zdbwkEon8jM25ya1OtozQli1bMBqN+ZA71L/f66+/ztNPP83rr78+YZNlNTY2cvHFF+dvl5WV0djYOCF1EU5vRGNsJUm6FngIuFzTtNiAu14GfipJ0v9GnzxqNrB5JK81FLvJzPmhUs4PleaPpVWFg92d7O4Ms7uzlT2dbfzP0QP8v/078o8pdRYwvzCoB93CAPO8ASpdhWJcozAl2EwmPBYTs0+yPNJwpBQl3zqXa62LDWi5y+3Hs0Eols6GoXSaWDpDIp2mMxonkU4TPy5YHb/s0tmSDQZMRgOywYhsNORvGw0GjNLAfYloNMKz9S0YJAmjwZAt9S7ZRsmAJIGEhEGSkCQ9rEkAuRIGBencNTpNv4GmF6iahoaGpmmo2duqpqJqGoqqZUsVRc2W2dtpRUXR1Px+RlXJKCppRdH3R+GcSZC9wGBCUjK4FQ179qJDgc1CUYETm8mkX6TIXqjItdQPKge06jstZtFyKghTwHT58C3LMldccQVXXHEFiqLwhz/8gQ0bNvDII4+wcOFCampquOqqqwatMXzgwAE6OztZvnz5GbXwnsrxYS0SiRAOh3nvvfcwmUyEQiECgcBZv15vby+7du1i6dKlg76XySy3tu7pliE6fhmhcDjMrl27UFUVu92OqqosXryYN998k+985zu89tpro7ZW78qVK2lpaTnh+GOPPUZNTc2QXzPUkE3xN3HyGumsyM8AFuDN7D/ynzVNu0/TtF2SJL0I7Ebvovzp082IPFpMBiPzvHpY/QgLAf1N2RqLsKczzO6uNvZ0htnb2cavGw6iZt+wVqPMbI+Ped4gcwv9zCsMMMfjJ2BziDewcM4xG42Yz7LF+HQyqkoiPbhVMZnJtThmSCn9t1OKMqiFMp0Ne7nAl1ZU0qpCZkAYzAVBJVuqmoaWjGMzmVA0DVVVSakqajobNDUV8iE0F1L1cJr7czXUVAO5H3sJ/Y9YvpQGB+RccM4FapNJzodvo0FCNugBXM5txv4y1zptMmZbqo2GbAu2Md+abTbqLd1mWT9mkWUsRiNWk4xZ1lvJrSYZs9GY/10lumYLwtQlPnwPj9Fo5LLLLuOyyy5DVVU2b97M+vXreeKJJ5g9eza1tbU0Njby8ssv8/rrr49aqB2K0+nE6XQyc+ZMYrEY4XCYrVu35lskg8HgsFuKc+OAp1KoTSaTbN26lblz557R2rpWq5WKigoqKipIpVK89957fP3rX6elpYVUKsUPf/hDfD7fqNXzrbfeOuOvKSsr49ixY/nbDQ0NlJSUjFqdhNE10lmRZ53ivseAx0by/KNFkiSKHC6KHC4+VF6dP57IZDjQ3c6erjb2drVR19XGO8cOsm5A667XYmNuYYA5hX7mFvqZ4/Ez2+PHbTl5lxdBmM5kg0Ef32sZuw8RxxNBThCEc4X48H3mDAYDF198MRdffDGqqrJlyxa++tWvsn37ds4//3w2bNjAddddNy7dWe12O5WVlVRWVuZbJHfs2IGmafmQe7Ixvt3d3ezdu/eMxgFPtGQyyZYtW5g7d+6IWlbNZjMXX3wxX/va1/jqV7/Kvffey/e//30eeOABrrzySj7/+c9TXl5++icaZatWreL222/ngQceoKmpif3793PhhReOez2E4Rlpi+2UZpVlfRkh/+C5sdrjUeq62qnLht267nbW799BNJPOP6bI7mS2x8+cAWF3tseHS4zfFQRBEARhHIkP3/0MBgObNm3CYrFw4MABDhw4wLp167jxxhsJBALU1NRwww034PV6x7wuA1skk8kkbW1t7Nmzh0wmQyAQIBgM5sfP5ia3WrZs2SnHC08muZbaOXPmjEp34T/96U+sXbuWV155hbKyMj71qU+RTCZ5++23x3witJ///Od85jOfoa2tjeuvv55ly5bxq1/9ioULF7J69WoWLFiALMt873vfm7KTsk0H0zrYnozf5sBvc/CBkv6JqlRNozHSy77uNvZ1dWTLdn6ydytJpX8SlmK7i1keH7M9vmzpZ5bbR6F1alx5EwRBEARhchIfvk9vy5YtvPvuu6xbtw6TycTixYtZvHgxjz76KHv37mX9+vXcfPPNuN1uVq1axQ033EAgEBjzrtsWi4WysjLKyspIp9O0tbWxb98+UqkUDoeDnp4ezjvvvCkTalOpFFu3bmXWrFmjcpHgb3/7Gw8++CAbN26krKwsf9xisXDdddeN+PlP56abbuKmm24a8r6HH36Yhx9+eMzrIIzcqK1jOxrmzp2r1dXVTXQ1zoiiqhyL9LC/u5393R358mBPJ/EBLbw+q51qt5dZHh/Vbl+29FLiKDjpciqie+Vg4nz0E+diMHE+BhPno58kSWId25GbPB8UBGEYNE07ZVDVNI2DBw+yfv16Xn75ZSwWCzfeeCM1NTUUFRWN6/jkcDjMvn37cDgcJJNJfD4fwWCQgoKCSTtOOpVKsWXLFmbNmjUqY2C3bt3KP/zDP/DSSy9RXV19+i8QzgUTs46tcGpGg4HKgkIqCwq5qmJ2/niuhfdAdzsHejo40N3BgZ5OXquvoyeVyD/OapSZ6fYy0+2lOlcWeKlyj30XGUEQBEEQhHPN6QKhJEnMmjWLtWvX8tBDD3HkyBFeeuklPvGJTwBwww03UFtbS1lZ2ZiGy/b2durr67nwwgsxm80oikJ7eztHjx4lEong9XoJhUK43e5JE3Jzoba6unpUQu3OnTu57777WL9+vQi1woiJYDtGDJJEuctNucs9aMIqTdPoSMQ42NPJge4ODvZ0cKini21tzbxWv3fQZfFCo4l5v2xhpttLlbuQmQVeqgoKKXO5MRmmZxcjQRAEQRCE0SJJEpWVlTzwwAN8/vOfp7m5mQ0bNnDfffeRSCS44YYbqKmpoaqqalTDZVtbG/X19YOWITIajYRCIUKhEKqq0tHRQWNjI3v27MHj8RAKhfB4PBgmaHnKdDrN1q1bqa6uxu8/+yUHc/bs2cO9997LCy+8wJw5c0ahhsJ0J4LtOJMkKT+G96KiwbO7JTIZDvd2cai3k/qeTv64bzdRJc2r9XsHtfLKkoFylzvfUlyVLSsLCilxFCCL9XgFQRAEQRgjb7zxBp/73OdQFIV7772XtWvXTnSVRoUkSZSUlPCZz3yG+++/n3A4zM9//nMeeOABuru7ue6666ipqWHOnDkjCrnhcJjDhw+zfPlyTCbTkI8xGAwEAgECgQCqqtLV1UVrayt1dXUUFBQQCoXwer3jFnLT6TRbtmyhqqpqVELtvn37+OQnP8lPfvITFixYMAo1FAQRbCcVqyzn1+AFWNiVzI+T60zEqO/RQ+/h3i7qs9ufW44NGstrMhgod7qZUVDIDFchMwo8VLo8VBR4KHO6sRjFP7kgCIIgCGdHURQ+/elP8+abb1JWVsYFF1zAqlWrzrlwIkkSoVCI++67j/vuu4+Ojg5+8Ytf8PDDDxMOh7nmmmu46aabmD9//hmF3NbWVo4ePXrKUHs8g8GAz+fD5/OhaRrd3d2Ew2H279+Py+UiGAzi8/nGbMKwXKitrKwkEAiM+Pnq6+u56667+NGPfsSSJUtGoYaCoBMpZ4rwWu14rXbOD5UOOq5pGuF4hPreLo70dmfLLg73dbO55digJYokoMRRQIXLw4wCD+UuDxVOt77v9OCxWCfNGA5BEARBECafzZs3M2vWLGbOnAnAmjVr2Lhx4zkXbI/n8/m45557uOeee+ju7ubll1/mW9/6FkeOHOGqq66itraWJUuWnLIFtaWlhWPHjrFs2bJhh9rjSZJEYWEhhYWFaJpGb28v4XCYQ4cOYbfbCQaD+P1+ZHl0PuLnuh9XVlYSDAZH/HxHjx7l9ttv5/vf/z7nnXfeKNRQEPqJYDvFSZJEyO4iZHdxcVHFoPs0TaM9EeNIbxdH+ro50tfN0V69fOvoAdoTsUGPd5nMlLs8lDv1scHlTk9+nHCZ041NPrtfwoIgCIIgnBsaGxspL+8fSlVWVsZf/vKXCazR+PN4PNx5553ceeed9Pb28tprr/Gv//qv7Nu3jyuuuILa2lrOP//8QSG3vr6ejo4Oli9fPmqhU5Ik3G43brebWbNmEYlECIfDHDlyBIvFQjAYJBAInHWIzmQybN26lYqKilEJtY2NjaxZs4b/83/+DxdccMGIn08QjieC7TlMkiQCNgcBm4P3hcpOuD+aTnG0r5ujfT0c6+vmaF83xyI9HOzpZFNj/aD1eQH8VjulTjdlzgLKnO7sVkCp002pswCHyTxe35ogCIIgCBNgqGUip3Nvr4KCAm677TZuu+02YrEYv/zlL/mP//gPduzYweWXX05tbS3vvvsumzZt4sUXXxyz7sKSJOFyuXC5XFRXVxONRgmHw2zZsgVZlgkGgwSDwfxEVaczMNSGQqER16+lpYVbb72Vf/u3f+MDH/jAiJ9PEIYigu005jCZme8NMt974lU4TdNoi0c5Fumhoa9HL7Pbro5W3jx6gJSqDPoaj8VKqUMPuiWOAsqcBRQ7XNnbLvw2x0nX7BUEQRAEYfIrKyvj2LFj+dsNDQ2UlJRMYI0mD7vdzs0338zNN99MIpHgzTff5Gtf+xqNjY1cffXV/OEPf+D973//qLXYnorD4aCqqoqqqiri8Titra1s27YNSZLyIddqtQ75tblQW1ZWNiqhNhwOc8stt/Dtb3+byy+/fMTPJwgnI4KtMCRJkgjanQTtTs4Plp5wv6pptMUjNPT10hDtoTHSm98O93bxh6bDg8b3gj6xVZHdRYmzgBKHi2JHAcV2F8UOF0UOFyUOF4UW27S+8isIgiAIk9kFF1zA/v37qa+vp7S0lBdeeIGf/vSnE12tScdqtdLQ0IDP5+NXv/oVf/zjH1m/fj0PPvggF198MbW1tXzwgx8cdgvqSNhsNiorK6msrCSRSBAOh9m1axeqqhIIBAiFQthsNkCfHGzbtm2UlpZSVFQ04tdub2/nlltu4bHHHmPlypUjfj5BOBURbIWzYhgwtvd8Tgy+mqbRm0rSGO2lKdJLc7RP34/q+5tbG2iNRsho6qCvMxuNFNtdhOxOPfDa9dBbZHfSmIgwO9JL0O4Q6/gKgiAIwgSQZZlnnnmGa665BkVRuPvuu1m4cOFEV2vS+d3vfscbb7zBhg0bsFgsXHvttVx77bVkMhl+85vfsG7dOr785S9z3nnnUVNTwxVXXIHFYhnzelmtVioqKqioqCCVShEOh9mzZw+ZTAafz0dHRwfl5eUUFxeP+LW6urq45ZZb+PrXv8611147CrU/0Re/+EVeeeUVzGYz1dXV/PCHP8Tj8QDwxBNP8Nxzz2E0Gnn66ae55pprxqQOwuQhDTVWYqLMnTtXq6urm+hqTBqbNm3KL/dzLlJUlfZElOZohOZs4G2J9WXLCC3RPlpjkRO6PEuAz2onaHdSlG1VDtqdhGxOgnYHQZuTkN2Jz2Y/ZwPwuf7eOFPifAwmzkc/SZLe1TTtfRNdjylu8nxQEIQpQtM0MpnMKSduUhSF3//+92zYsIF33nmHRYsWUVNTw8qVK7Hb7eNYW0gkErz33nv5Ca/8fj+hUAin03lWPel6enq4+eab+cIXvsBHPvKR0a5u3v/8z/9wxRVXIMsyDz30EABPPfUUu3fv5rbbbmPz5s00NTWxcuVK9u3bN2ZjnIUzNibdMydVi62KRkrNYDZMqmoJY8RoMORbfZcFhr4yqGkanck4LdE+3vzLnwhVV9ES6yMci9Aai9ASi7C9o5WOePSET14S+jJJuQm08pvdccIxt1ksdSQIgiAIwuiQJOm0sxEbjUYuv/xyLr/8clRV5S9/+Qvr16/n8ccfZ/bs2dx0001cffXVOJ3OMa2roijs3r2bGTNmUFpaSiaTob29nfr6emKxGD6fj2AwSEFBwbA+K/X19XHrrbfy2c9+dkxDLcDVV1+d37/44otZv349ABs3bmTNmjVYLBaqqqqYNWsWmzdv5pJLLhnT+ggTa1IlyC4tzuVvPkKVI8jsgiJmu4qZ5SpilqsIv8U10dUTJoAkSfisdnxWO212DyvmLh3ycWlVoT0eIxyLEI5HCMei+bItHqEtHuVgTwdt8ShpVT3h62XJgN+mv47f5tC37Ov6bPoawrnbXqsd6zhM/CAIgiAIwvRgMBi45JJLuOSSS1BVlS1btrBu3Tr++Z//mRkzZlBTU8OHP/xh3G73qL5ubkxtMBiktFQfWibLMkVFRRQVFaEoCh0dHRw7doy+vj68Xi/BYBCPxzNkyI1Go6xZs4Z7772XNWvWjGpdT+cHP/gBt956K6AvLXTxxRfn7ysrK6OxsXFc6yOMv0n16dwhmflY5QfZ39fMux2H+GXT1vx9hWaHHnKdRcx2FVHtKqLKGcRqFGurCmAyGCl26BNRnYqmafSkErTFo/mtPR6jPR6lPaGXHYkY+7vbaU/ESCnKkM/jkE14syHXa7XppcVGodWG12qj0GLPlvoxt9mKfIpF2wVBEARBOLW7776bV199lWAwyM6dOwHo7Ozk1ltv5fDhw1RWVvLiiy9SWFg4wTUdGYPBwPnnn8/555/P448/zs6dO1m3bh033HADoVCImpoarr/+erxe74heR1VVtm/fTjAYpKzsxGUhQW9Vzs2irKoqnZ2dNDc3s3fvXjweD8FgELfbjSzLxONxbrvtNj72sY9x5513jqhuA61cuZKWlpYTjj/22GPU1NTk92VZ5o477gDEslTT1aQKtlZkPj23f2B3dyrGgb5mDvS1sL+vhQN9Lbx07C8kVX19VQMSZXYfs1whql1FVDv1sszuxSiJECGcSJIkPBYbHouN2R7/KR+raRqRdIqORIyOeIz2RIzO7NaRiNGZiNOR0FuJ67ra6EzESRy39u9ABWYLhRYbHos1WwcrhRYb7uxtt9mKx2LFbbbituhbgdmCxTipfkwFYVJSNY2+VJLuZJzuZIKuZJyeZGKiqyUIwij6xCc+wf333z8oND355JNceeWVrF27lieffJInn3ySp556agJrOboMBgNLlixhyZIlfOMb32DPnj2sX7+ej3zkI3g8Hmpqarjhhhvw+/1nFNxUVWXbtm34/f6Thtqh6uL3+/H7/aiqSnd3N8eOHeNDH/oQ8+bNo6enh1tuuYW77777bL/dIb311lunvP/555/n1Vdf5e23386fA7Es1fQ05SaPUjSVhmgHByItHOxrzZcNsU607ChLi0Gm0hlkpjPETGeQameImc4QRTY3hikUeMUEMINNhfMRS6foTMbpTsTpTMbpSsTpSupb7sN2VyJOTyqRv92XSp7yOa1GOR9y3Wa9jHf1MKu8ggKzhQKzBZfZgsuULbPHnCYLTpMZh8l8zq8fPBXeG+NpKp4PTdNIKgq9qQR96SR9qRS9qQS9qeSAMklPMkFPKkFPMkFvtuzO3q8O8ffsyN0PicmjRm7yfFAQpr3Dhw9zww035Fts586dy6ZNmyguLqa5uZkVK1YwHSYi1TSNAwcOsH79el555RWsVis33ngjNTU1hEKhU4bcXEut1+uloqJixHWJx+PcddddxGIxOjo6WLhwITfffDPXXnstDodjxM9/Km+88QYPPPAAv/nNbwgEAvnju3bt4vbbb89PHnXllVeyf/9+MXnU5HHuTx41HEbJwAxngBnOAFcWLc4fTygpDkXCHOpr5WBE397tOMgvm7bkH2MzmqlyBpmZDb1VziBVjuCUC7zC5GU3mbGbzJQ5hz8GRlHV/Af17mzZk0rQm0zmj/cM+IAfjkdpTUbYU7+HvlQS5TQXpyTIB1ynyYLTbNZvy7ljepnfZBP2AaVdNmE3mbDL+r5NNmEWfxgE9PduLJMmnkkTTaeIZtLEsmU0nSKWThFJp4hmy/79JH3pFJFUfxlJp06YAf14smTQL/BYrBSYrbgtNipcnnwPCLfFisc8uDfE7LsfGqezIQjCRGhtbc0vTVNcXEw4HJ7gGo0PSZKYPXs2X/7yl1m7di1Hjhxhw4YN3HnnnRgMBm644QZqa2spLS0dFHJVVWXHjh2jFmrT6TR/93d/x+WXX84XvvAFALZs2cKGDRvo6ekZ9dbb491///0kk0muuuoqQJ9A6tlnn2XhwoWsXr2aBQsWIMsy3/ve90SonQamXIvtmepLx/XAG2nlYF8r9dEwhyJhOpJ9+cfYjGZmOAL50FvpCFDpDFJqK0SewOVipmKry1gS56Nf7lxomkYsk6Y3laQvlcy2dPXvR1IDQsSAABE9LnDEMqkhJ9U6GVkyYJNlbNmga5NNWGUZm9GETZaxyiasRhmrLGdLExajEatRxpLdrLKM2WDM3zYbjfqWPWY2GjEZjP2lwYDJYMQ4xFjl6f7eUDWNtKqQUhTSqsJvfv973nfRhSQVhVT2eFLJ5Et90/cT2duJjL6fyKRJKBnimTSJTIZ49lg8kyaWPRbL7idP0fX+eGajEadsxmnWexI4TWZc+f0BvQ1MFlxmMwVma773QUG2p4JdNp3xGCmx3M+omDwfFIRp7/gWW4/HQ3d3d/7+wsJCurq6Jqh2E0/TNJqamtiwYQM///nPSSaT3HDDDdTU1FBcXMzHPvYxvvCFLwyaWOlsZTIZ7r33XpYuXcpXvvIVMYZVOBOixfZsuEw2lhbOYGnhjEHHe1Ix6qNh6rOh93Ck7YQWXpNkpMLhz4beQD78Vtj92GTzeH8rgnACSZLyLa2nmzjrdJJKhlg6TTSTGlymU/lQExsQcGLpNAml/1gio4ehvnhSv61kSObDUoaMNvzgfCoGSUI2GDAbjMgGA7LBiJpK41hXh8lgwGgwYJQMyINKKb9vkCSMkoRBkjBI/bel3DEkJAkk9GNS9jxL9P8WPv6Pd+4CoZbbNG1AqaFq/ZuG3tKpZo8rqoaiqfq+pqJoGhlVRdFUvVRV0ppeZlSVtKropaaSzgbZIVvtj20943NrNhixyDK27MWIfCnL+G0O7LIJq2zSW/GzFzRyLfoOkxmbbMJpMmOXzTiyx3I9As7VNaUFQZhYoVCI5ubmfFfkYDA40VWaUJIkUVpaymc/+1k+85nPEA6Heemll/jsZz/LwYMHWb58OV6vF03TRhREFUXhf/2v/8X8+fNFqBUmjXM+2J6M22xnmbmSZYWVg45HMgkOR9o4HAlTH9XL/X3NbGrdhTrgonWR1cOMbOitdAbyAThoGd4aX4Iw2eRaTguxjcnzZ1Q131qYyPS3GqbUbKkopJQMSTW3r9+XVvQwl1L1EJe7nQ94qkpDUyP+UJB0NghmckFQ0/K3M5pKIp1BzYbHgWFT0VS03G30QKqiof9PQ8uWcPKmq3zoHSIYG7KhWcoG51yQNkoSxnzY1gO4LBmwmuRsEO8P5LkQb8rtS0bMxv5jZkN/C3f9gYMsmj8fs9GIxaC3fudawS3G/lZyi1HOtqIbscqmc34stiAI555Vq1bx/PPPs3btWp5//vn8LLmCHnJDoRB/93d/x+9+9zs+8IEPUFFRwVe+8hXC4TDXXnsttbW1zJ8//4w+uyqKwmc/+1nKysp45JFHxOdeYdKYtsH2ZJyylUWechZ5ygcdT6kZjkXbORxt43C0jSMRff/VxneJKan842xGMxUOPxV2HzMceuDVb/txmqzj/e0IwqShBzO99W60bdq0iRWXrRj1552qNoX7WDF78ekfKAiCMIXcdtttbNq0ifb2dsrKynj00UdZu3Ytq1ev5rnnnqOiooJ169ZNdDUnnXvuuYdFixbxla98BYB7772Xrq4uXn75Zb75zW9y9OhRrr76ampra1m8eDGGUyxPqKoqDz74IIWFhTz++OMi1AqTigi2w2Q2yPqSQq6iQcc1TaMt2cuRaDtHom0cjbZzJNrOrp4G3m7ZOaiV12t2UJ4NuRUOP+V2H+UOH2U2n+jaLAiCIAiCcAo/+9nPhjz+9ttvj3NNppYHH3yQJUuWDDpWWFjIXXfdxV133UVvby+vvvoq//Iv/8L+/fu58sorqa2t5bzzzhsUclVV5ctf/jJms5l//ud/PmUAFoSJIILtCEmSRNDqJmh1c4GvetB9KTVDQ6yDo9EOjkbbORpr52i0nT+27+OVxncHPTZgKaDc7qPM4dNLu5dWtZdYJoldtozntyQIgiAIgiCcI44PtccrKCjg9ttv5/bbbycWi/H666/z7//+7+zcuZMVK1ZQW1vLBRdcwKOPPkoymeTZZ58VoVaYlESwHUNmg5xdSzd0wn3RTJJj0XaOxTr0LdrBsVg7vw/voTMVzT/uu2/9Ga/ZSZndS6ndR7ndS5ndR4nNS5ndS6HZIbqBCIIgCIIgCCNmt9v56Ec/ykc/+lESiQT/8z//w49+9CPuvPNOli1bxssvvyxCrTBpiWA7QRyyhXnuUua5S0+4L5JJ0Bjr5Fd//S0FlUU0xDtpiHbwbuch3mjamp/EBsBuNFNi91Jq81Jq91JqK8zeLqTYVojFaBrPb0sQBEEQBOGcdezYMe68805aWlowGAz8/d//PZ/73Ofo7Ozk1ltv5fDhw1RWVvLiiy9SWFg40dUdEavVyqpVq1i1ahVdXV2YzWaxFqwwqYlgOwk5ZStzC0poNhaxonrFoPuSSpqmeBcNsU6aYp00xDtojHVxNNbOn9v3k1TTgx4fsBRQYiukxK4H3RJbfxmyuid0nV5BEARBEISpRJZl/uVf/oXzzjuPvr4+zj//fK666ip+9KMfceWVV7J27VqefPJJnnzySZ566qmJru6omeohXZgeRLCdYixGE1XOIFXOE9dp0zSNjmQfjfEumuKdNMY6aYp30RTrYkvnYX6V2DZoMisD+vjgYpuHIlshJdmy2OqhyKZvZoN4iwiCIAiCIAAUFxdTXFwMgMvlYv78+TQ2NrJx40Y2bdoEwF133cWKFSvOqWArCFOBSC3nEEmS8FsL8FsLWFo444T7M6pCa6JHD7vxLpqzW1O8i/c6D/GrRO+g4Avgs7gotnoI2dwUW/VW3lzoDVnduE12McZXEARBEIRp5/Dhw2zZsoWLLrqI1tbWfOAtLi4mHA5PcO0EYfoRwXYakQ1GfRyu3Tvk/bng2xLvpjnRTUu8i+Z4N62JHvb1NvP78F6SambQ11gMJkJWNyGbWy+tbkJWPfQGrQWErB4cskWEX0EQBEEQzhmRSISbb76Z7373uxQUFEx0dQRBQARbYYDTBV9N0+hMRWhN9NAa76Yl0aPvJ7ppjffwl/YDtCf7Bk1uBfoEV7klkQKWAoLWAgLWAkLZ2wFrAYVmBwZJzLInCIIgCMLklk6nufnmm7njjjv4yEc+AkAoFKK5uZni4mKam5sJBk8cMib0+9rXvsbGjRsxGAwEg0F+9KMfUVJSAsATTzzBc889h9Fo5Omnn+aaa66Z4NoKU4UItsKwSZKEz+LCZ3GxwF025GMyqkJbspdwopfWRDfhRC/hRE926+WvkQN0pCIomjro64ySAb/FlQ+6udJvcWW3AmJaGk3TROuvIAiCIAgTQtM07rnnHubPn88DDzyQP75q1Sqef/551q5dy/PPP09NTc0E1nLy++IXv8g3v/lNAJ5++mm+8Y1v8Oyzz7J7925eeOEFdu3aRVNTEytXrmTfvn1iNmZhWESwFUaVbDBSnJ15GU4c5wugaCodyT7aEr2Ek720JbJbUt8OR8L8teMgkUzihK99/M3f4cuHXX3zWpz4LQX4zM5s8HbiNTvFjM+CIAiCIIyqP/zhD/zXf/0XixcvZtmyZQA8/vjjrF27ltWrV/Pcc89RUVHBunXrJraik9zA7tvRaDTfaLFx40bWrFmDxWKhqqqKWbNmsXnzZi655JKJqqowhUyqYBsz9PHkni9RbC2j2FZOkbWMImsZfktIdFM9hxglQ75r8sJTPC6eSdGe7KMt2Ut7spc/79qKpyxIe7KP9mwAfrfzEL3p+JBf7zHZ8Vr0sOs162HXa3Hiy5aFZides4NCi1PM/iwIgiAIwmldeumlaJo25H1vv/32ONdmanv44Yf58Y9/jNvt5p133gGgsbGRiy++OP+YsrIyGhsbJ6qKwhQzqT7NGzWZQrOfw7H9vNf9p/xxk2QiZC0lZC2lOBt2i2xl+MxBEXjPYTbZTLnso9zhA8Bc18WKeStOeFxSSdOZitCe7KMjGaEj2UdHso/OVISOZITOVIQd3UfpTEVIKOkTvh70tYMLzQ68ZiceswOv2YHH7KDQ7KDQ7MRjtlOYPeYxO0QQFgRBEARBOIWVK1fS0tJywvHHHnuMmpoaHnvsMR577DGeeOIJnnnmGR599NEhLxqIIWjCcE2qT+cWzcanqr8EQEKJ05JopCVxjOZ4Ay2JBg5G9vBu1x/yj5clEyFrCSFrKUXZ4FtkKcVvKUIWwWPasBhNA7o/n1osk6QrFc0H3q5UtkxGs/tRjsXa2dF9hO5U7ITlj3IcRgtus10PuiY7brMDt8mOx2zHbbLjzpUD9q1G02h/64IgCIIgCJPSW2+9NazH3X777Vx//fU8+uijlJWVcezYsfx9DQ0N+UmlBOF0Jm36sxptVDpmUemYNeh4QollA29DtmzkcHQf73X9Mf8YA0b8ltCg0Bu0lBCylmA12sb7WxEmEbtswS5bTjrz80CqptKbjtOVitKVitKd3brSUXpSMbpTMbrTUTpTUeojYXrSMWJK6qTPZzHIFGTDboHJhstko8Bkw22y5/cHHnfK1nwpxgsLgiAIgnCu2L9/P7Nnzwbg5ZdfZt68eYA+Cdftt9/OAw88QFNTE/v37+fCCy+cyKoKU8ikDbYnYzXaqXTMptIxe9DxpJIgnGyiJdFIa6KJ1kQjrYlGdvVsQUXJP85t8hLKhtygtZigpYSgtQSPySu6NQuDGCRDvutx1TC/JqVm6EnF6EnH+svsfm86nr/dm47TEOugNx2nNx07YX3g49mNZpwmGy7ZitNkJZmK8uttYZwmC07ZhkO25O9zylYcshWHbMnu62HeKN7fwjShaCrRTJJI+sQJ6ARBEM4ViUSCyy67jGQySSaT4aMf/SiPPvoonZ2d3HrrrRw+fJjKykpefPFFCgtP36ttPK1du5a6ujoMBgMzZszg2WefBWDhwoWsXr2aBQsWIMsy3/ve98SMyMKwTblgezIWo5Vy+0zK7TMHHVe0DG3JVloTTYQTjbQmmwgnmvhr5+9IqP2TDpkNFgKWomzQLSZoKc6XVqN9vL8dYYoyG2R9uSLrmS3WnlTS9KXj9KTj9GXi9KUT9KXj+pa7nS0jmQRtWpId3Ufpy8SJZpInLJ80FKvRpAdeox50HbIZh2zFZjTrt40W7LIZW77Uj9uMZuxGM1ajOX/cajRjMchi3IswKjRNI6mmiWVSxBV9i2WSxJQU8UySaLaMKSmimSTRTIJYJkVUyZaZhB5ks2X8FD0nBEEQzhUWi4Vf//rXOJ1O0uk0l156KR/+8Id56aWXuPLKK1m7di1PPvkkTz75JE899dREV3eQDRs2nPS+hx9+mIcffngcayOcK86ZYHsyRkmmKNsdGS7IH9c0jd5MN+FEM63JRsKJZsLJZo7GDrK1+89oA8ZWumQ3QUsxAWsxQUsRAUsxAUsRfksIk8E8Ad+VcK6xGE1YjCb8wwzEmzZtYsXlKwD9vRzPfuCPZPTgG0kniCrJfAjQy1wgyO4rSZrj3dkAkSSWSZFUh55caygSEjajCavRhNVoxmo0YTOasRhM2GQ9+FqMZqy50ihjMejfp8UgY86WA/fNuc2ol6bs/SaDjNlgRJaMIkyPA03TSGsKKTVDSsmQVjMk1f4ypWZIKmm9zO4nlXT/vpomMaDMbXElRTJbxpUUCSVFPHufdpLx7MczSgbsRv2ijD17ccZlslFk8+Qv3PT3XLBQwxNjfLYEQRAmhiRJOJ1OANLpNOl0GkmS2LhxI5s2bQLgrrvuYsWKFZMu2ArCWDjng+3JSJKE21SI21TIbNeCQfdl1DTtyVZak820JZvzoXdnz7tEMr39z4FEodmH31JEYMDmtxThNweRDWKyIGHsSZKUHzsc4Mxaio+XURUSSpqoksy3kCWU1KCWND2QZMNJRr8/oabzxxNKmo5khKSSIqFmSCopkkqGhJoeVsvy6ZgkI2aDjGwwYjIYMUlG0skUz/5+K7KkH5MlI7LBkC2NGCUDsqTfNhoMGKUTN0N+X0JCyh6TkCQJIwYkScIgSRjQj0no+/r/JCQGz9yoHzlRLsBpmr6noaH/T0NFQ8vtaxoaGoqmoml6qaKhaiqK1l8qmoKavV/RVDKaSlOqmTe2NJHRFP2YqpLRMtlSIa0q/aWq5ENsRlVIZe8bCQkJS/ZChnXgxQ+D3mvAZ3FhM5qzF0bM2LI9AXK9A2yyGbvRki/t+dIiegoIgiAMoCgK559/PgcOHODTn/40F110Ea2trRQXFwNQXFxMOBye4FoKwviYtsH2VGSDiSKbvqTQ8eJKjHCimbZkC23JXNnCe11/Iq5E84/Lh16z3rIbsBThs4TwW4L4zSEsRut4fkuCMCyywYjTYMRpGpv3Z0ZVBrXqpZQMSVVv6UspekvgUFtaVbJlbl8ho+n7aVWhsaUZr8OXD2kZVSGjqSSVJBlNHRDwlHwAPH4bGA5zoXKykdDDdS50GzFgNBgwIGHMBnijZCCtJemNKBhzIV/SH2cyGLEZzJiygT9f5i8S5FrKjflWclO2Fd1i7G9BN+ePZVvdjabBrfEifAqCIIwLo9HI1q1b6e7u5qabbmLnzp0TXSVBmDAi2J4hm9HODEc1MxzVJ9wXzfTlg25bsoX2ZCvtyRa2dv+FmBIZ9NgC2TMo6PosQfyWED5zEJfsFh8KhXOSbNCDlEO2jOrzburcxIrlK0b1OTUt14KabTXNtqLmjmmAquXaXPtbWoHBkTi3Jt+g1txsK6+Ua9nV/9+QbQmWBrQMD2xBHu7vhU2bNrHigytGfA4EQRCEqcHj8bBixQreeOMNQqEQzc3NFBcX09zcTDAYnOjqCcK4EMF2FDlkFw7ZdcKMzQCxTJT2VAvtyXA+8LanWtnft4u/pX8/qHXIbLDgMwfR7AY6G47iMwfxWYL4zAG85oBo7RWEcaB3Qda7GsuIGRkFQRCEyaWtrQ2TyYTH4yEej/PWW2/x0EMPsWrVKp5//nnWrl3L888/T01NzURXVRDGhQi248QuO6iQq6mwn9jSm1ZTdKTa6Ei20pEK054M05EKczRaz586fk1KTQ56vFMu0MOuOYDXEsBnDuLNht5Cs09MaCUIgiAIgnCOa25u5q677kJRFFRVZfXq1dxwww1ccsklrF69mueee46KigrWrVs30VUVhHEhgu0kYDKYB8zc3G/T0U1cfvnlRDK9dKTCdCTDdKTa6EyF6Ui2cSR2kK3dmwet0wt6N2evJYDX5MdrCVBo9uM1BfCa/RSa/aLFVxAEQRAEYYpbsmQJW7ZsOeG4z+fj7bffnoAaCcLEEsF2kpMkCZfJjcvkHrKLs6qpdKc76Uy10Zls08vsdiR2kG09m1GOm+HUYXRSmA25hWY/hSYfXnMAj9lHodmHS3ZjkAzj9S0KgiAIgiAIgiCMiAi2U5xBMuA1+/Ga/eCcf8L9qqbSm+6iM9VOZ6qdrlSbXqY7aEs2s69vJ0k1MehrjJIRj0kPuR6TTw+82dJj8lJo9mE3OsUEV4IgCIIgCIIgTAoi2J7jDJJBD6RmHzOZe8L9mqYRV6J0pTroSrfrZTb4dqc6OBTdS3dX1wndnU2SGY/Zi8fkxWPy4c7ve3GbC/GYfDjlAtHyKwiCIAiCIAjCmBPBdpqTJAm77MQuOyllxpCPUTWVvkw3XalOulMddKc76Ep10JPupDvdyYHIHnrSJ4ZfA0YKTB48Ji8FpkI85kLcJi9uUyEFpkLc2c1qsInWX0EQBEEQBEEQzpoItsJpGSRDNpB6wTFryMfo4bdHD7upTnrSXXSnO+lJd9KT6qI10cC+vh0k1PgJX2s2WPSgK3soMHmyoVcvC2QPLpMHt8kzaEkkQRAEYdyIK4+CIAjCpDepgq1miHKo54c4TTNxmmZik0uRRFfWKUEPv3oL7FBLGuUklQQ96a781jtwP9NFQ/wwPb1bTljiCEAqMLBp5wY9/MpuXCY9CLtkfXItl+zO37YYrKIVWBAEQRAEQRCmiUkVbDHE2dv5L/03JQsOU2U26FbhNM3EYa7CIc/AaBBL1kxFFqOVoLGYoLX4lI9LKHF60930prvozfTQm+5i58EdeHwu+tI9dKbaORw7QDTTN2RLrkky4zIV6KFXduPMBl+nXIBLLsBpcuOUXbhkNw7ZhVEyjtW3LAiCIAiCIAjCGJtUwVbK+FlZ8Qci6YNE04eIpOqJpA/RndxBc/QNyAcYCZtcitNUhcNUhdNUmS2rMBt9oqXuHGA12rAabYMD8G47K2asGPQ4VVOJZHrpS/fQm+mmL91DXya7Zfe70h0cjR0ikulFRR3y9exGJ065AKfsypb6viN7Wy/12w6jC7PBIt5ngiAIgiAIgjBJTKpgC2A2uvEaz8NrPW/QcUVNEE0fJpI+RCRdTzRdTzR9mI7EX1G1/uVqZMmJw1SZbemtwmGagcNUid1UgWywj/e3I4wxg2TIjsv1nHTyqxxVU4krUfoyvUTSPXp5wtZHONnMoWgdsUzkpEHYJJmwZ8OuHopd2GUnDmOudOLITsplz+7bjA7RMiwIgiAIgiAIY2DSBduTMRqsFFjmUWCZN+i4pqkkMi3ZsHs4G37r6Uz8jaboq4MeazWGsqG3P+w6TJXY5VIMkmk8vx1hAhgkg97iKrvAWnrax+tBOEYk00s000c000dE6evfz/QRy/QRVSI0xo8QzfQRU6KnnOTKZrRjN+oh1y47sBsdJ9y2GR3642R93250YDXaRSgWBEEQBEEQhJOYMsH2ZCTJgM1Ugs1UQoAPDLpPUeNE00eygfcI0YxeNkffIK329j8HRmxyCQ7TDD3syjPy+za5BIM05U+TcBb0IKy3tg6XqqkklBhRJUI0EyGWiRBV+ohlosSUiL7l96N0pzqJKRHiShRFU0753BaDFavRjs1oJ+XIUHfwL/nbVoMdm9HWf9tow2rQb+e6dVsNdmSDeC8LgiAIgiAI555z+lOu0WAbspUXIKV0ZUOvvsUyetmZeA9Fi+UfJyFnQ28FdlMFdrlc35crsJlKMUrm8fyWhEnOIBny6wIHLMP/Ok3TSKlJ4kqUmBIlrsT0wJuJEVdixLPHcmVzpJHedA/hRDNxNUZCiZ02GAMYJXlA6LVhMVixGG1YDVbMBitWoxWLwYbFaNXvM1gw5/etmA0WLMZsabBgNlgxiJnLhQmmaRqKppBUEyTVBCklkd8XBEEQBGF6OKeD7amYjYWYjYUUWpcNOq5pGimlg2jmCNH0UWLpI0Qzx4ilj9KV2EJGiw54tITVWJQNveXY5XLspjK9lMswGQvG9XsSpi5JkvQwabTiwXfax286uokVF6wYdCytpogrMRJKXC/VOAklTnLAfkKJ9x9XEySVOJFMLx1KmKQaJ6EkSKmJM1ozWJZMmA2W4zYzZoMFU7Y0G8yYDGZMkgWTwZS9bckeM2VLMyaDCdlgwiSZkLP39d82IUsmEaSniFzYzGhpMmqatJYmrabIZMv8bTVNWkuRUlP6cTWVvZ3MHtNL/XZuPzHgdpKkkkTl9Bd2BEEQBEE4d03bYHsykiRhkf1YZD9e6/mD7tNb1TqJpY8SSx8jmtHLWKaB1uivSamdgx5vMrixy2XYTWXY5LIBwbcMq1wkujgLo8qUDY8FJs+InkfTNNJaioQSz4aGbCuYmuwvlcG3BwcOPYzElRg96S7S2VCSCy+KlhlR/QwYkQ0ysmRClmRkg0zKmebPe15HlmSMBlkvJRmjZMQo6bcN2X39mDF/n0Ey6CWG7GP00oARg2TQNwxI2TJ3TMKAJEnZ+yT9NhKG7D7oQyUkQBrw/0hSbu/U/w65iwuavqeh6kc0jfx/mpY9rqFq/WWD6QB/6zShoaJqKioqqqbo+5qKioKqKSha9jgqipZB1fRS0ZQBW2bAsQyZ7O2MmsnfzmgZMmqajJbO3pcmo2XO6ALJ8YySUb84Ih1/kcSC3eTL71uMes+BXA8CS75Xgd7L4GleOOs6CIIgCIIwdYhkdQb0VjUfFqOPQuvyE+7PqNFs4D1GPBt4Y+lj9CR30xJ9G43+D/QSRqxyEXa5DJtcit1UqpdyKTa5DIvx9K12gjAWJEnCLOmhYSyomppvmUtpqUGtdmk1TUZLkVLTZLKterkWv4yWybb46cFJD1X68aZIEz6LN39b0TIklcSAIKbkw5k6YF/RFFSUYXXjnlLs8Ncjb5/RlxizYX5w6Nf3B10oyF44sBptyJJJv3Aw6EJDtpRMyAYZk2Qe1Oqevz2wtX5Ai30uxIrJ0gRBEARBOBMjCraSJH0TqAFUIAx8QtO0pux9XwbuARTgs5qm/WqEdZ30ZIPjpGN6VS1DItNKPNNILHOMWLqRWKaBeKaRcPw3pCIdgx5vkMxoJR42t/wMm1ySDbwl+c1i9COJLpnCFGSQDPlu16NlU/0mVsxcMaLnULOtl0q2BTPfwomCqmn5fU3TsveremtpvqU0146qZltS9f9yLa70H9Fpp2nNlPrbdaXsf7nW3vx/Un9pINeKbOBvf/0bF1140aDWZmO2ldkoGbMt0v37uecQBEEQBEGYqkbaYvsdTdO+BiBJ0meBrwP3SZK0AFgDLARKgLckSZqjaedas8jwGSQZu0lvmfVx4Qn3K2qcWKYpG3wbiWcaOdq0jZTSRU9yF2m1e/DzYcIqF2eDbvGA0FuMTS7OdnUWSxgJwnDluhjLTP2fmwL1ICFryURXQxAEQRAEYdyMKNhqmtY74KYD8o0RNcALmqYlgXpJkg4AFwJ/GsnrncuMBhsuczUuc3X+WOv2TVy6aAUAGTVGPBt845nmbNlEPNNMW/x3JJX2455RwmIMYJOL9KBrLMoHXr0sxmwoFK00giAIgiAIgiBMeSMeYytJ0mPAnUAP8KHs4VLgzwMe1pA9Jpwl2WDHZZ6FyzxryPsVLUUi05INu3rgTWSaiWda6EnupVXZhKolB31NieN6lgWfGo/qC4IgCIIgCIIgjJnTBltJkt4Cioa462FN0zZqmvYw8HB2TO39wD/BkFN+DjmgTJKkvwf+PnszKUnSzmHVfHrwA8c3xY6iXcC3x+7pR98Yn48pRZyLwcT5GEycj34zJroCgiAIgiCMPUk73QQmw30iSZoBvKZp2qJsyEXTtCey9/0KeETTtFN2RZYk6W+apr1vVCp0DhDnYzBxPvqJczGYOB+DifMhCIIgCMJ0M6JpdSVJmj3g5ipgb3b/ZWCNJEkWSZKqgNnA5pG8liAIgiAIgiAIgiAMZaRjbJ+UJGku+nI/R4D7ADRN2yVJ0ovAbiADfHo6z4gsCIIgCIIgCIIgjJ2Rzop88ynuewx47Ayf8j9HUp9zkDgfg4nz0U+ci8HE+RhMnA9BEARBEKaVURtjKwiCIAiCIAiCIAgTYURjbAVBEARBEARBEARhok2KYCtJ0jclSdouSdJWSZL+R5KkkgH3fVmSpAOSJNVJknTNRNZzvEiS9B1JkvZmz8nPJUnyDLhvWp0PSZJukSRplyRJqiRJ7zvuvml1LnIkSbo2+z0fkCRp7UTXZ7xJkvQDSZLCA5cGkyTJK0nSm5Ik7c+WhRNZx/EiSVK5JEnvSJK0J/tz8rns8Wl5PgRBEARBmL4mRbAFvqNp2hJN05YBrwJfB5AkaQGwBlgIXAv8H0mSjBNWy/HzJrBI07QlwD7gyzBtz8dO4CPAbwcenKbnguz3+D3gw8AC4LbsuZhOfoT+bz7QWuBtTdNmA29nb08HGeBBTdPmAxcDn86+H6br+RAEQRAEYZqaFMFW07TeATcdQG7gbw3wgqZpSU3T6oEDwIXjXb/xpmna/2ialsne/DNQlt2fdudD07Q9mqbVDXHXtDsXWRcCBzRNO6RpWgp4Af1cTBuapv0W6DzucA3wfHb/eaB2POs0UTRNa9Y07b3sfh+wByhlmp4PQRAEQRCmr0kRbAEkSXpMkqRjwB1kW2zRP6AdG/Cwhuyx6eRu4JfZfXE++k3XczFdv+/TCWma1gx62AOCE1yfcSdJUiWwHPgL4nwIgiAIgjDNjHQd22GTJOktoGiIux7WNG2jpmkPAw9LkvRl4H7gnwBpiMefE9M4n+58ZB/zMHpXw//OfdkQj5/y52M452KoLxvi2JQ/F8MwXb9v4RQkSXICG4B/1DStV5KGepsIgiAIgiCcu8Yt2GqatnKYD/0p8Bp6sG0AygfcVwY0jXLVJsTpzockSXcBNwBXav1rMp2T5+MM3hsDnZPnYhim6/d9Oq2SJBVrmtYsSVIxEJ7oCo0XSZJM6KH2vzVNeyl7eNqeD0EQBEEQpqdJ0RVZkqTZA26uAvZm918G1kiSZJEkqQqYDWwe7/qNN0mSrgUeAlZpmhYbcNe0PB8nMV3PxV+B2ZIkVUmSZEafQOvlCa7TZPAycFd2/y7gZC395xRJb5p9Dtijadr/HnDXtDwfgiAIgiBMX1J/Y+AEVkKSNgBzARU4AtynaVpj9r6H0ceZZtC72f3ypE90jpAk6QBgATqyh/6sadp92fum1fmQJOkm4P8DAkA3sFXTtGuy902rc5EjSdJ1wHcBI/ADTdMem9gajS9Jkn4GrAD8QCt6745fAC8CFcBR4BZN046fYOqcI0nSpcDvgB3ovz8BvoI+znbanQ9BEARBEKavSRFsBUEQBEEQBEEQBOFsTYquyIIgCIIgCIIgCIJwtkSwFQRBEARBEARBEKY0EWwFQRAEQRAEQRCEKU0EW0EQBEEQBEEQBGFKE8FWEARBEARBEARBmNJEsBUEQRAEQRAEQRCmNBFsBUEQBEEQBEEQhClNBFtBEARBEARBEARhSvv/AX7khKwneeTyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dx=0.01\n",
    "x=np.arange(-30,30,dx) # x array for grid\n",
    "y=np.arange(-30,30,dx) # y array for grid\n",
    "X, Y = np.meshgrid(x, y) # grid\n",
    "\n",
    "# Min. function\n",
    "Z=f(X,Y)\n",
    "\n",
    "# set up a figure twice as wide as it is tall\n",
    "fig = plt.figure(figsize=(16,8))\n",
    "\n",
    "# =============\n",
    "# First subplot: contour\n",
    "# =============\n",
    "# set up the axes for the first plot\n",
    "ax1 = fig.add_subplot(1, 2, 1)\n",
    "\n",
    "# contour plot\n",
    "ax1.contour(X, Y, Z)\n",
    "ax1.set_title('f(x,y) - Contour plot',fontweight='bold', fontsize=15)\n",
    "plt.grid()\n",
    "\n",
    "# =============\n",
    "# Second subplot: surface\n",
    "# =============\n",
    "# set up the axes for the second plot\n",
    "ax2 = fig.add_subplot(1, 2, 2, projection='3d')\n",
    "surf = ax2.plot_surface(X, Y, Z, cmap=cm.viridis,\n",
    "                       linewidth=0, antialiased=False)\n",
    "ax2.set_title('f(x,y) - Surface',fontweight='bold', fontsize=15)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22862e8e",
   "metadata": {},
   "source": [
    "The gradient descent method has the following function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "1b473abe",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bisection(f,x,grad,a,b,N):\n",
    "    # initial values\n",
    "    an = a; bn = b;\n",
    "    cn = (an + bn)/2\n",
    "    # evaluate first set\n",
    "    fa=f(x[0]-an*grad[0],x[1]-an*grad[1]);\n",
    "    fb=f(x[0]-bn*grad[0],x[1]-bn*grad[1]);\n",
    "    fc=f(x[0]-cn*grad[0],x[1]-cn*grad[1]);\n",
    "    for n in range(1,N+1): # loop through maxIter\n",
    "        # mid points\n",
    "        dn=(an+cn)/2; en=(bn+cn)/2;\n",
    "        fd=f(x[0]-dn*grad[0],x[1]-dn*grad[1]);\n",
    "        fe=f(x[0]-en*grad[0],x[1]-en*grad[1]);\n",
    "        \n",
    "        if fd < fc: # move to the right\n",
    "            an = an; bn = cn; cn = dn;\n",
    "        elif fe > fc: # move to the left\n",
    "            an = cn; cn = en; bn = bn;\n",
    "        elif fc < np.minimum(fd, fe): # shrink interval\n",
    "            an = dn; cn = cn; bn = en;\n",
    "    return (an + bn)/2;\n",
    "\n",
    "def gradDescent(x0,f,gradF,alpha0,steep, maxIter=50): # main function\n",
    "    ## Initial values\n",
    "    x=x0 #seed\n",
    "    grad=gradF(x[0][0],x[0][1])\n",
    "    alpha=alpha0\n",
    "    \n",
    "    # Parameters\n",
    "    err=1\n",
    "    tol=1e-5\n",
    "    k=0\n",
    "\n",
    "    while err > tol and k < maxIter: # iterations\n",
    "        k=k+1 \n",
    "\n",
    "        # Step 1: pick alpha\n",
    "        if steep == 1: # check for scalar step-size\n",
    "            # Steepest descent\n",
    "            a = 0.005 #lower bound for alpha\n",
    "            b = 5 #upper bound \n",
    "            N = 100 # number of iterations\n",
    "            alphak = bisection(f,x[k-1],grad[k-1],a,b,N) # doesn't work\n",
    "            alpha = np.append(alpha, [alphak]) # find the optimum alpha\n",
    "        else:\n",
    "            alpha = np.append(alpha, alpha0)\n",
    "        \n",
    "        # Step 3: calculate x for k+1\n",
    "        x = np.append(x, [x[k-1] - alpha[k-1]*grad[k-1]],axis=0) # x^k+1\n",
    "        # Step 1: Calculate gradient\n",
    "        grad = np.append(grad,gradF(x[k][0],x[k][1]),axis=0)\n",
    "        # Step 4: convergence\n",
    "        err=np.abs(f(x[k][0],x[k][1])-f(x[k-1][0],x[k-1][1])) # f[k]-f[k-1]\n",
    "    return x,k;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05ed1000",
   "metadata": {},
   "source": [
    "Just as a proof of concept we try to minimize the function for a given seed $x_0=(1,10)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "f9c9fb62",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'k - number of iterations')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0du1apdNdvyc0NTUpFov1Yu/QlWKOhed56tevn0aOHKmKioqCzhWYUGVmSkQ81lQBQMBVVFRo+PDhGj58+E7bzZ49W8ccc0wv9Qo7s6eMRWCm/yQpFvW4+w8AABRFoEJVIkqlCgAAFEegQlU84rGjOgAAKIpghaqox0J1AABQFMEKVVSqAABAkQQqVLGmCgAAFEugQlUswvQfAAAojpKGKjM7x8werqmp6ZXrJaJM/wEAgOIoaahyzj3vnJtaWVnZK9eLRzw18JgaAABQBIGa/otHw2pqyZS6GwAAYC8UrFAV8ZRMZ5RKE6wAAIC/AhWqElFPklisDgAAfBeoUBVrDVUsVgcAAD4LVKhKRKhUAQCA4ghUqIrnKlVsAAoAAPwWyFBFpQoAAPgtWKEqwpoqAABQHIEKVQkWqgMAgCIJVKhqrVQ1MP0HAAB8FqxQlatUNVGpAgAAPgtUqEpEw5LE8/8AAIDvAhWq2haq8/w/AADgs0CFqlgk++02UqkCAAA+C1SoMjPFIx77VAEAAN8FKlRJ2W0V2FEdAAD4LXChKkalCgAAFEHgQlUi6rH5JwAA8F3gQlU8SqUKAAD4L3ihKsKaKgAA4L/ghaqopyYqVQAAwGeBC1Xc/QcAAIohcKEqFmGhOgAA8F9JQ5WZnWNmD9fU1PTaNRMsVAcAAEVQ0lDlnHveOTe1srKy164Zp1IFAACKIHDTf/FoWI0taWUyrtRdAQAAe5HghaqIJ0lqTmVK3BMAALA3CVyoSkSzoaohmSpxTwAAwN4kcKGqtVLFYnUAAOCn4IWqXKWKxeoAAMBPwQtVVKoAAEARBC5UfbqmilAFAAD8E7hQFYtSqQIAAP4LXKhKsKYKAAAUQeBCVduaKkIVAADwUfBCVeuaKqb/AACAj4IXqnKVqiYqVQAAwEeBDVXc/QcAAPwUuFAV9kKKeiHu/gMAAL4KXKiSsuuqGnn2HwAA8FEwQ1XEo1IFAAB8FchQlYh6rKkCAAC+CmSoikU8NVGpAgAAPgpkqKJSBQAA/BbIUBUnVAEAAJ8FM1Qx/QcAAHwWzFBFpQoAAPgskKEqEWVLBQAA4K9AhqpYxFMjlSoAAOCjQIaq1kqVc67UXQEAAHuJQIaqeMRTOuOUTGdK3RUAALCXCGaoioYlSU1JQhUAAPBHMENVxJMkNbTwUGUAAOCPQIaqRDQbqlisDgAA/BLIUBVrrVQRqgAAgE9KGqrM7Bwze7impqZXr9taqWJXdQAA4JeShirn3PPOuamVlZW9et14lEoVAADwVyCn/1oXqrOrOgAA8EsgQxUL1QEAgN8CGapap/+oVAEAAL8EMlQlItnNP1lTBQAA/BLIUBWLZr9t7v4DAAB+CWSoinoheSFTQ5Id1QEAgD8CGarMTPGIp0ae/QcAAHwSyFAlZRerN/LsPwAA4JPghqqIx5YKAADAN4ENVYmox91/AADAN4ENVbGIxz5VAADAN4ENVYko038AAMA/gQ1VcSpVAADAR8ENVVSqAACAj4IbqqhUAQAAHwU2VHH3HwAA8FNgQ1UsSqUKAAD4J7ChKhEJK5nKKJ1xpe4KAADYCwQ2VMWj2W+dahUAAPBDgENVWJLUkOT5fwAAoHDBDVURT5LUlMyUuCcAAGBvENhQlYhmQ1VDC5UqAABQuMCGqtZKFRuAAgAAPwQ3VEUJVQAAwD/BDVWtlSru/gMAAD4IbKhqW1NFpQoAAPggsKEqRqUKAAD4KLChKsGaKgAA4KPAhqq2hepUqgAAgA8CG6piYdZUAQAA/wQ2VIVCplgkpCYqVQAAwAeBDVWSlIiGefYfAADwRaBDVTziqZFn/wEAAB8EO1RFPTXy7D8AAOCDYIeqiMdCdQAA4Itgh6qoxz5VAADAF8EOVRGPfaoAAIAvAh2qElSqAACATwIdqlhTBQAA/BLsUBX12PwTAAD4ItihikoVAADwSaBDVSKaXajunCt1VwAAwB4u0KEqFs0+VLmphV3VAQBAYUoaqszsHDN7uKampiTXT0SyoYptFQAAQKFKGqqcc88756ZWVlaW5PrxXKWKhyoDAIBCBXr6Lx4NSxJ3AAIAgIIFO1RFWitVhCoAAFCYQIeqRG76j13VAQBAoQIdqtrWVDH9BwAAChTsUJWb/muiUgUAAAoU6FCViLKmCgAA+CPQoSrOPlUAAMAnwQ5VLFQHAAA+CXaoolIFAAB8EuhQFfZCinoh1lQBAICCBTpUSVIsEmJHdQAAULDAh6pENMyz/wAAQMECH6riUU+NLZlSdwMAAOzhCFURT41UqgAAQIEIVVGPu/8AAEDBAh+qElGPu/8AAEDBAh+qYhGPzT8BAEDBAh+qEkz/AQAAHwQ+VMWpVAEAAB8QqqKEKgAAUDhCVYTpPwAAULjAh6pE1FMq45RMsQEoAADoucCHqljEkySqVQAAoCCBD1WJaFiSWFcFAAAKEvhQFY9mfwRUqgAAQCEIVZFspaqB5/8BAIACEKqi2TVVTVSqAABAAQIfqhK5UMXz/wAAQCECH6rirXf/EaoAAEABCFVRtlQAAACFI1RRqQIAAD4IfKhiTRUAAPBD4EMVO6oDAAA/BD5UVYRDChnTfwAAoDCBD1VmpnjEo1IFAAAKEvhQJUnxaJg1VQAAoCCEKmWf/9fIY2oAAEABCFWSEpEw038AAKAghCpJsajH9B8AACgIoUpSIuLxQGUAAFAQQpWyj6qhUgUAAApBqFI2VLGmCgAAFIJQpezz/9j8EwAAFIJQpezz/6hUAQCAQhCqlK1UsaYKAAAUglCl7JqqZCqjdMaVuisAAGAPRahStlIliSlAAADQY4QqZddUSWKxOgAA6DFClbIPVJYIVQAAoOcIVWL6DwAAFI5QpU+n/xqSqRL3BAAA7KkIVZJiVKoAAECBCFVioToAACgcoUrZfaokKlUAAKDnCFX6dKE6u6oDAICeIlTp00pVE5UqAADQQ4Qqtb/7j1AFAAB6hlAlKRZmoToAACgMoUpSKGSKRUIsVAcAAD1GqMqJRzwqVQAAoMcIVTmJaJg1VQAAoMcIVTmxSIi7/wAAQI8RqnKylSqe/QcAAHqGUJUTj3gsVAcAAD1GqMqJR1moDgAAeo5QlUOlCgAAFIJQlZOIetz9BwAAeoxQlROLetz9BwAAeoxQlZOIUKkCAAA9R6jKiUeza6qcc6XuCgAA2AMRqnLiUU/OSc2pTKm7AgAA9kC+hyozO9/M/sfMfmdmX/D7/MUSj3iSxLYKAACgR7oVqszsETOrMrMlOxw/08xWmtkaM7tZkpxzzzrnvirpakmX+t7jIklEs6GqgcXqAACgB7pbqXpM0pntD5iZJ+khSV+UdJikL5vZYe2a3Jb7+h4hRqUKAAAUoFuhyjn3R0lbdjh8nKQ1zrn3nXNJSb+SdJ5l/VDSS865+f52t3gS0bAkQhUAAOiZcAGv3U/S+nafb5D0WUnXSTpNUqWZHeKc+698LzazqZKmStKwYcM0e/bsArqya9u3b9/pNVZVZ8PUW3+eq0/WeEXtC3Y9Hug9jEX5YCzKC+NRPvaUsSgkVFmeY84596CkB3f1Yufcw5IelqSJEye6k046qYCu7Nrs2bO1s2v0+2CrNPctjTn8SJ00ZmhR+4Jdjwd6D2NRPhiL8sJ4lIdVm+t0zf+8rke/OkGjh/Xbabt//OV8/eQrx+60XTEVcvffBkkj2n2+v6SPCutO6bTe/ceu6gCAXVm1uU5f+LfXtGpz3R7drtz72JBM6ZpH/6yPtjtd8+gcNSRTO223umr7TtsVWyGhao6kQ83sQDOLSrpM0nP+dKv3td39x5oqANgt5fymXIxzdvcNvNzb7Ql9vPGZRarenpSTVL29Wd99ZtHO27mdtyu27m6p8JSkP0kaY2YbzOxvnXMpSf8oabqk5ZKeds4tLV5XiyueC1WNVKoA9IJyDw7dbVfub8qFnLM5lf8JG919Ay/3doWc89tPL1R9c0p1TS2qaWjRlvqkqrc36xtPvauPc+0+3t6sr/9ivt7/eLvWVNVp5aY6Ld9YqyUf1mjq43P1cV2znJOq6pr0t4/N0Z/e+0RvrqnW66s/1uyVVbr7+aWasWxz26bczamMXl66SbdMW6Rn3/1Q0+Zv0K/nrtd3fr1QLy/d1KHdK8ur9PSc9Xm/l2Kycngsy8SJE93cuXOLeo1dzY3XNrXoqLte1m1fGqe/+/xBRe0LWKtQTvbWseju+opStGtIpnT6A6/po5om7VsZ14xvTVEiGu40Fl21251zFrvd1385XzNzb3wV4ZBOP2yYfvKVY8umXb62p40bqn+9ZLzSGae0c0qns3/e/JtF+uPqaiVTGUU905gBIf3oislKZTLZthmnGcs26WdvrO3w9I2oF9Jlx43Q8QcNamv31nvVevbdj5RMf9ou4pnOOHyYjtxvH6UyTpmM06IN2zRr5cdKZT59Lw6HTMeNGqCDhvZVOiNlMk5rquq0YEON0u3ahUwaM6yfhlXGlM44ZZzTxm2NWvtJg9o1k0ka1r9ClfGo0i573bRzqmlIqqYxpR1TQEXYFA6Fcm2llnSmU5s9waA+Uc27/fSinNvM5jnnJnY6TqjKaklndOj3XtK3Tx+t6049tKh9wd77Rr4n6slYlCqwdLdtqQJGoUFkx7EoJDh0N4ycNm6YHrj0aKUzTi1pp1Q6o1TG6ZZpi/XG6o+VTDtFPdNnDxqk73xhjFKZjFJpp1TG6dUVVXri7Q+U7BAwTOeO30/HjhygdCajlrTT/A+2aPqyzWpJdwwOJxw8UAcN6ad0Jnu+NZtrNX995+Bw6NC+Gto/plQ6G1g21TZqw9bGTsFhn0RYiWikLQSlMk6NzSk1p0v/Pre7TNKAPlGFzBQOmarqmjp8v628kOnwffsrZCYvZFq4fluHgNYq6plOGTtMoZDa2v5hyaa8j2aLRUK6/LMHyAuZQmb6+Vtr887iJKKevnX6aJmZPJPun75S9XmW0PStCOv7Fxwpz0xeKFv1qmvqXC3sHwvrf66cKC9kMjPNWlml//nj+x36WBEO6bpTDtGXjtpXIct+L79fslH/NmOVmlo+bRePeLrnvMN18cQRna7jh65CVSF3/+1VIl5IEc/YUR17lFJVWa559M/6qKZJ1zw6Z6cBw892u9M235RGvoBRSLv/+PIxSmWcWtLZ4NCSzuimZxZ9OvVR16S/f2KevnX66Gy7VEYtGadZKzZrxrLNbUGkOZXR9KWb9I2n5ivR1KLlek+pdEYL12/V7FXVbW+QzamMXlqySRf+9E3tPzChVNopmc4olc5ow9YGvfdxfdubbnMqoxcXbdQ7789QoiKcC0EZbW9KdXjTa05l9OLijXpx8ca8P+9WybTT66ur9frq6p22a237zLwNembehp22S2Wc/rj6E727vkbhkCnshfTJ9uZOwSHjpDUf1ytREVY4lA0DG2s6BwwnqSGZ0anjBrW1C4dM/zd3vZQnVCWinq4/9VB5ubY/6iIQ9KsI60eXHJ0NBJ7pzTXVeuJPH3R6o7/2pIN15hGfUTgXRKYv3aR/f2V1hzf6WCSkW88ap4sm7N8WbKbN26C7nl/WIbTkCwRPz1mvO59b6lu73Wl70OA+edvdfW7HdoloOG+7O885TOcevW/bsdrGVN52t599mD570KC2YxMOGKC/VNd3+sfCP57SsfDx91MO1qINNR3anTpuaNEC1c4QqtqJRTw2/8RuK2U1phThpjcCywOXjM+FlYySqYySuT/vem5ph3UY1zw6R1OnHJRtl84Gl7feq9bLSze1VUWaUxn9YckmXfXIOzp4SL+2867aXKeF7aZTmlMZ/X7xRp1436uqTESVTGXbba1PamtDS9v0R3MqoxcWbdQLi/wLIi1pp+cW5s63ckWX7dIZp3fXb1N1fVLhkCnihRT2TH+pbsgbMmoaUzrhkMEKh7L/aHz23Q/znrc1YIS9kMIh033TV6i+OU/AiIX1k68cq0guiLy26mP97I2/dAgYsXBI3/zCaJ0/fr+2YPP8wo/0/d+vKElwOHzfym4Fgj55AkE0JN1xzmE64/DPtB07ecxQbaxp6vRGf8Npoztc99qTDtGSj2o7VQWv/KtRHdpdetxI/XFN9S4DwSWTRui11R/71q4Y5yxGH++/6Cid/sBr+nBbkwb3rdB9Fx3VqU37dh/tol2xMf3Xzme/P1MnjR6qH5ZoMIKkGNN/5bQ2pqftdqetX2tPXp01S381eYqu/9W7mr3q47b1JJ89aJC+dfroDqFm1soqPT1nQ8d1IiHTSWOGavRn+mbbpjJavqlW8z7Y1mkaZ+TAuCrjUTXnAsuW+mZta+i8pqNY+sXCinohRbxQl9MpEc/0uUMGZ6vX4VDbz25H8YinfzjpYEXC2fM98HL+Skf/WFg/vXyCwl42BM1eWaWHd5jSiEVCuvnMsRrasFYnnzhFYc80bf4G3fXcrisYkv9hZHdCy564pqq75zx6sOnpG87s1K7td3Rbk/bdpxu/92Xabk/p46f7VH2+bPapYk1VN97ET7p/lo7cfx/9x5ePKWpfkB2PfcdNKNtw01vBxrnsFE5zKqOmlrSaWzK67dkl+tN71UqmnSKe6ZgRA/Q3nztQzam0mlPZtu+8X63pSzuuUfFCpvH7V2r4PnElc+3Wb6nvtGhVkuKRkMxMyVQm7/qLnvBCpqgXUjQcUm1Ti/L91RIJmU7IBZaKcEgzl+cPLImopxtOO1SR3PkiXkj3PL9M25s7r8OojEf0q6nHZ9t6IU1fukn/OmPlLtdXlGMQKcWaqkLb7Qlvyj095x0TTWecdnLec5bzjRC7025P6WO5rcMty1BlZudIOueQQw756urVq4t6re4MyBf//XXtt09c/3tVp5/TXqtUvyTTZ87SPXMzZRNupOwdNk2ptJpaMvrOrxe2LdKNeKYJBwzQ3085WE0t6bY2f3qvWi8t2dQp2By9XzbYNLWk24LNuq2NnUJGOJRd6uHnr2DIpFGD+yjqhVQR8bT0w5q8oSkWCemKzx6gikhIH61fp+nrMnn3aOsfC+s/r5igaDgbWGavqtJ/zn5vh8AS0l3nHK5LjxvZdqyU6z+k8q+edPUm3+Xdf2VccZD2jDflnpzzo+XzyuqNPMgIVbuhXCpVF/z0TcWjnn7xd8cXtS+FKOepq92Z4rr4x3/Qomq36zepX8xvq2ZEwyFNPniQbjxjrBpb0mpqSasxmdarKzbrmXkfdpiSCodMnz1woEYOSqgxmQ1B71dv15qq7Z2qNrGwKSPrcAdTIUImHTi4j2IRTxXhkBZ/WNMheLVdNxLS1M8fpIpcu1jE0w9eWq7tedayVMYjmvYPJ6giHFJF2NPvF2/UD17yZ43K7NmzVdXn4LIPLLvTdk+onuT7Hc3399SeUHHYW5XbG3mQldtYEKq6MSBX/O87akimNO0fJvt23XIOQX686aUzTo0taTUkU7rpmUV6c82n01bjR+yjv/6rUWpKZr/e0JJWUzKtd9dt1ZvvfdIh3IRM2rcypng03BaYahpb8oaR7jJJQ/pVKBbxFI94eu/j7V1Wba46YZTiEU+xiKf/eGV13rUxrdNMrWFp+tJNuu8PK/f4akzr70a5B5bdbbsnVE92VG5vHEHHeJSPchsLQlU3BuSyh9/W/A+26oVvfM6XvzTLKQT96OKj1ZBMq745pYZkWs8t/FD/+3rHu3YinumUMUN14JC+akxm263cXKslH9Z22g8mFgkp45R3PczOmHU93RXxTKcfNqwtBP1m/oYO00ytWu9AioVDikc9vbbyYz00e02vr6GR9o5qTOvvxp4QWHa37Z6m3N44go7xKB/lNhaEql0MSEMypQn/NFONLWnt1503qG5McfX0DfeUsUP1T+cfofrmlOqb06pPpvTS4o168u11eae49hsQV30yrYbmlNZW12vtloaC1ulEvWxYSUQ9VdU25dviRbFwrrqTa/fvM/NXd/ZJRPTiNz6vRMRTPJqt8Px67gbd9uwitW9ebuGmVFWb3W3rR2hp/7uxNweWPUG5vXEEHeNRPsptLNj8cxdufGaRkqnsm3dP9tSpb05pe3NK9cmUtjel9PvFGzVj6ea2ENS6V85l//0nfaYypu3N2arR+i31+nBbU4c9cF5askkvLdm0yz6nMk5vvfeJPlMZUyLqqU9FWOvzLIiWsndT3XTmWMWjnvpEw5r7wRb98p11nW7rvuucw3VZDxYc7xOP5m33vbPGab994h36csmkEfr1m0s7rKnyay+TXe1R4ne7RDSsR685ri2IdBV+uttud9uOHtZPL3/zxC6/Xqx2AIDOCFXKBodXl1e1VWRadzj++8fnatTgPqprzgal1ZvrtHJzXYddi7uzCWCrVMbpnb9s0f4D4+oTDatvRVib65rz7tHTJ+rp7vOOUN8KT4loWG+//4keeeMvakr1bIprx43uvnTUcFXVNXfamK59oJKKs5mbJP3dERXZu//KNNyUMtjsblsAQHkgVEn64R863kUlZXc4nr5ssyrCIfWLZQPQ+h2eNdUqEfV04xlj1Kci265vReEh6K5zD9dFE/ZvOzZl9BB9sKWhKDvV9nZ1R8o+sLPcww3BBgCwO0Kl7kA5uOnMsYpHvA7HYpGQfnDBkVr5z1/U3NtO1+wbT9a//L8jO7VrrQJdM/lAXTJxhM46crimjB6i7545VqceNkwV4eyPeGch6JRxQ3fZTsqGlsF9ozJpl+GmO+1aA8uhw/rq0Wsm7TLY+NWuVWto2dXane62AwCglAhVyh9supoK624Akso/BEn+BxsCEAAgqAhVOX4HIGnPCEEAAMAfhKocprgAAEAhWKjeDguYAQBAT5W0UmVm55jZwzU1NaXsBgAAQMFKGqqcc88756ZWVlaWshsAAAAFY00VAACADwhVAAAAPiBUAQAA+IBQBQAA4ANCFQAAgA/MuTxPCO7tTph9LOmDIl9msKTqIl8D3cd4lA/GonwwFuWF8Sgf5TYWBzjnhux4sCxCVW8ws7nOuYml7geyGI/ywViUD8aivDAe5WNPGQum/wAAAHxAqAIAAPBBkELVw6XuADpgPMoHY1E+GIvywniUjz1iLAKzpgoAAKCYglSpAgAAKJpAhCozO9PMVprZGjO7udT9CRIze8TMqsxsSbtjA81shpmtzv05oJR9DAozG2Fms8xsuZktNbPrc8cZjxIws5iZ/dnMFubG4+7cccajRMzMM7N3zeyF3OeMRYmY2VozW2xmC8xsbu5Y2Y/HXh+qzMyT9JCkL0o6TNKXzeyw0vYqUB6TdOYOx26W9Ipz7lBJr+Q+R/GlJH3bOTdO0vGSvp77XWA8SqNZ0inOuaMljZd0ppkdL8ajlK6XtLzd54xFaZ3snBvfbiuFsh+PvT5USTpO0hrn3PvOuaSkX0k6r8R9Cgzn3B8lbdnh8HmSfp77+OeSzu/NPgWVc26jc25+7uM6Zd889hPjURIua3vu00juPyfGoyTMbH9JX5L0v+0OMxblpezHIwihaj9J69t9viF3DKUzzDm3Ucq+0UsaWuL+BI6ZjZJ0jKR3xHiUTG66aYGkKkkznHOMR+n8WNJ3JWXaHWMsSsdJetnM5pnZ1Nyxsh+PcKk70AsszzFueURgmVlfSb+RdINzrtYs368IeoNzLi1pvJntI+m3ZnZEibsUSGZ2tqQq59w8MzupxN1B1mTn3EdmNlTSDDNbUeoOdUcQKlUbJI1o9/n+kj4qUV+QtdnMhktS7s+qEvcnMMwsomyg+oVzblruMONRYs65bZJmK7v+kPHofZMlnWtma5VdInKKmT0pxqJknHMf5f6skvRbZZfylP14BCFUzZF0qJkdaGZRSZdJeq7EfQq65yRdlfv4Kkm/K2FfAsOyJamfSVrunHug3ZcYjxIwsyG5CpXMLC7pNEkrxHj0OufcLc65/Z1zo5R9j3jVOXeFGIuSMLM+Ztav9WNJX5C0RHvAeARi808zO0vZ+XJP0iPOuXtL26PgMLOnJJ2k7BPGN0u6U9Kzkp6WNFLSOkkXO+d2XMwOn5nZ5yS9LmmxPl03cquy66oYj15mZkcpu9jWU/YfuE875+4xs0FiPEomN/33Hefc2YxFaZjZQcpWp6TsMqVfOufu3RPGIxChCgAAoNiCMP0HAABQdIQqAAAAHxCqAAAAfECoAgAA8AGhCgAAwAeEKiBgzGyUmS0pdT921Fv9MrMKM5tpZgvM7NIdvnaPmZ2W+/gGM0v4eN3z2z/Mvf21AOwdgvCYGgABYGZh51yqG02PkRRxzo3f8QvOuTvafXqDpCclNexGH7zco2fyOV/SC5KW5bkWgL0AlSogwMzsIDN718wm7cZr7jKzR8xstpm9b2bfyB3vUGkys++Y2V25j2eb2b+Z2R/NbLmZTTKzaWa22sz+ud3pw2b2czNbZGbPtFaKzGyCmb2We7jq9HaPqphtZt83s9ckXb9DPwea2bO5c71tZkflniP2pLLP21tgZgfv8JrHzOyi3Pe0r6RZZjYr97UvmNmfzGy+mf069wxFmdlaM7vDzN6QdLGZfdXM5pjZQjP7jZklzOwESedKur/1uq3Xyp3j1Nw4LM79bCvanfvu3DUXm9nY3PETc+dZkHtdv+6OH4DiIVQBAWVmY5R9DuA1zrk5u/nysZLOUPZ5XHda9pmCu5J0zk2R9F/KPl7i65KOkHR1bqdkSRoj6WHn3FGSaiX9Q+7c/yHpIufcBEmPSGr/VIR9nHMnOuf+dYfr3S3p3dy5bpX0eO45Yn8n6XXn3Hjn3Hv5Ouqce1DZZ4Se7Jw72cwGS7pN0mnOuWMlzZX0rXYvaXLOfc459ytJ05xzk5xzR0taLulvnXNvKfuIjRt3vK6ZxSQ9JulS59yRys4gXNvu3NW5a/6npO/kjn1H0tdz1bbPS2rM930A6F2EKiCYhigbbK5wzi3owetfdM41O+eqlX2o6bBuvKb1mZuLJS11zm10zjVLel+fPvR8vXPuzdzHT0r6nLJB6whln1S/QNlws3+78/5fF9f7nKQnJMk596qkQWZW2Z1vLo/jJR0m6c1cH66SdEAXfTjCzF43s8WSLpd0+C7OPUbSX5xzq3Kf/1zSlHZfb33w9TxJo3IfvynpgVxFbZ9uTnsCKDLWVAHBVCNpvaTJkpbu+EUzu1fSlyQp39ojSc3tPk4r+3dJSh3/oRbr4jWZHV6f0ad/F+343CwnyZQNYX+V/1tRfRfHLc+xnj6XyyTNcM59uRt9eEzS+c65hWZ2tbLPvtzVuXem9WfV+nOWc+4HZvaipLMkvW1mpznnVuziPACKjEoVEExJZRdOX2lmX9nxi8657+Wmqcbvxjk3SxpqZoNya4LO7kG/RppZa3j6sqQ3JK2UNKT1uJlFzGxX1R9J+qOylaLWh+RWO+dqd6MvdZJa1yq9LWmymR2SO1/CzEZ38bp+kjbmpi0v7+J87a2QNKr13JL+WtJrO+uYmR3snFvsnPuhslORY7vzDQEoLkIVEFDOuXplg883zew8H87XIukeSe8oe5dbTyonyyVdZWaLJA2U9J/OuaSkiyT90MwWSlog6YRunOsuSRNz5/qBslN2u+NhSS+Z2Szn3MeSrpb0VO58b6vrIHO7sj+DGer4M/iVpBtzC8vbFsg755okXSPp17kpw4yy68525gYzW5L7eTRKemk3vzcARWDO9bQaDgAAgFZUqgAAAHxAqAIAAPABoQoAAMAHhCoAAAAfEKoAAAB8QKgCAADwAaEKAADAB4QqAAAAH/x/tAi7W3HARzQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0=np.array([[1, 10]])\n",
    "alpha0=np.array([0.2])\n",
    "[xRes,k]=gradDescent(x0,f,gradF,alpha0,1)\n",
    "fRes=f(xRes[:,0],xRes[:,1])\n",
    "\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.semilogy(np.linspace(0,k+1,k+1),np.array(fRes),'-d',label='$log(f^k)$')\n",
    "plt.grid()\n",
    "plt.legend(fontsize=20,loc='upper right')\n",
    "plt.xlabel('k - number of iterations')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "144a69fd",
   "metadata": {},
   "source": [
    "Having checked that the code works we proceed to minimize $f(x)$ with several different seeds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "f23c020b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set up a figure twice as wide as it is tall\n",
    "fig = plt.figure(figsize=(12,6))\n",
    "\n",
    "# =============\n",
    "# First subplot: contour\n",
    "# =============\n",
    "# set up the axes for the first plot\n",
    "\n",
    "# contour plot\n",
    "plt.contour(X, Y, Z)\n",
    "plt.grid()\n",
    "\n",
    "seeds=np.array([[1, 10],[10,10],[10,1]]) \n",
    "for i in range(len(seeds)):\n",
    "    # pick seed\n",
    "    x0=[seeds[i]]\n",
    "    alpha0=np.array([0.2])\n",
    "    # minimize\n",
    "    [xRes,k]=gradDescent(x0,f,gradF,alpha0,1)\n",
    "    fRes=f(xRes[:,0],xRes[:,1])\n",
    "    \n",
    "    # Plot results\n",
    "    legLabel= f'$x_0=[{x0[0][0]}, {x0[0][1]}]$'\n",
    "    plt.plot(xRes[:,0],xRes[:,1],'-o',label=legLabel)\n",
    "    plt.legend(fontsize=15)\n",
    "    plt.xlim(-5, 15)\n",
    "    plt.ylim(-10, 15)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ecbcd5e",
   "metadata": {},
   "source": [
    "We can see how the convergence of the algorithm changes depending on the seed chosen. This is of course sensitive to the limits imposed to $\\alpha$ during the bisection method.\n",
    "\n",
    "### 9. \n",
    "The cost function of interest is:\n",
    "\\begin{equation}\n",
    "f(x)=\\frac{1}{4}(x_1-1)^2+\\sum_{i=2}^{n} (2.x_{i-1}^2-x_i-1)^2 \n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a3961c0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    n=np.shape(x)\n",
    "    secondTerm=0\n",
    "    for i in range(n,2):\n",
    "        sumTerm = 2*x[i-1]**2-x[i]-1\n",
    "        secondTerm = secondTerm+(sumTerm)**2\n",
    "    return ((x[0]-1)**2)/4+secondTerm;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b863b889",
   "metadata": {},
   "source": [
    "Its gradient is:\n",
    "\\begin{equation}\n",
    "\\frac{\\partial f}{\\partial x_n}=-2.(2x_{n-1}^2-x_n-1)+8.x_n.(2x_n^2-x_{n+1}-1)\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b37e0912",
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradF(x):\n",
    "    n=np.shape(x);\n",
    "    parDevF=np.zeros(n)\n",
    "    for i in range(n[0]):\n",
    "        if i == (n[0]-1):\n",
    "            parDevF[i]=np.array(-2*(2*x[i-1]**2-x[i]-1)+8*x[i]*(2*x[i]**2-1))\n",
    "        else:\n",
    "            parDevF[i]=np.array(-2*(2*x[i-1]**2-x[i]-1)+8*x[i]*(2*x[i]**2-x[i+1]-1))\n",
    "    return parDevF;"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d9cc87e",
   "metadata": {},
   "source": [
    "Having defined our functions we can get our first required iteration for $n=3$ and $n=10$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0196c1ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "def bisection(f,x,grad,a,b,N):\n",
    "    # initial values\n",
    "    an = a; bn = b;\n",
    "    cn = (an + bn)/2\n",
    "    # evaluate first set\n",
    "    fa=f(x-an*grad); fb=f(x-bn*grad); fc=f(x-cn*grad);\n",
    "    for n in range(1,N+1): # loop through maxIter\n",
    "        # mid points\n",
    "        dn=(an+cn)/2; en=(bn+cn)/2;\n",
    "        fd=f(x-dn*grad); fe=f(x-en*grad);\n",
    "        \n",
    "        if fd < fc: # move to the right\n",
    "            an = an; bn = cn; cn = dn;\n",
    "        elif fe > fc: # move to the left\n",
    "            an = cn; cn = en; bn = bn;\n",
    "        elif fc < np.minimum(fd, fe): # shrink interval\n",
    "            an = dn; cn = cn; bn = en;\n",
    "    return (an + bn)/2;\n",
    "\n",
    "def gradDescent(x0,f,gradF,alpha0,steep, maxIter=50): # main function\n",
    "    ## Initial values\n",
    "    x=x0 #seed\n",
    "    grad=np.array([gradF(x)])\n",
    "    alpha=alpha0\n",
    "    \n",
    "    # Parameters\n",
    "    err=1\n",
    "    tol=1e-3\n",
    "    k=0\n",
    "    while err > tol and k < maxIter: # iterations\n",
    "        k=k+1 \n",
    "\n",
    "        # Step 1: pick alpha\n",
    "        if steep == 1: # check for scalar step-size\n",
    "            # Steepest descent\n",
    "            a = 0 #lower bound for alpha\n",
    "            b = 1 #upper bound \n",
    "            N = 100 # number of iterations\n",
    "            alphak = bisection(f,x[k-1],grad[k-1],a,b,N) # doesn't work\n",
    "            alpha = np.append(alpha, [alphak]) # find the optimum alpha\n",
    "        else:\n",
    "            alpha = np.append(alpha, alpha0)\n",
    "            \n",
    "        # Step 3: calculate x for k+1\n",
    "        print(x)\n",
    "        x = np.append(x, [x[k-1] - alpha[k-1]*grad[k-1]],axis=0) # x^k+1\n",
    "        # Step 4: Calculate gradient\n",
    "        print(x)\n",
    "        grad = np.append(grad,gradF(x[k]),axis=0)\n",
    "        # Step 5: convergence\n",
    "        err=np.abs(f(x[k])-f(x[k-1]))\n",
    "    return x,k;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "33f4e5ac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.5  1.   1. ]]\n"
     ]
    },
    {
     "ename": "ValueError",
     "evalue": "all the input arrays must have same number of dimensions, but the array at index 0 has 2 dimension(s) and the array at index 1 has 3 dimension(s)",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_13284/858304206.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mx0\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1.5\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0malpha0\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0.1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[1;33m[\u001b[0m\u001b[0mxRes\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mgradDescent\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mgradF\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0malpha0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# maxIter=1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_13284/1349975566.py\u001b[0m in \u001b[0;36mgradDescent\u001b[1;34m(x0, f, gradF, alpha0, steep, maxIter)\u001b[0m\n\u001b[0;32m     44\u001b[0m         \u001b[1;31m# Step 3: calculate x for k+1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     45\u001b[0m         \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 46\u001b[1;33m         \u001b[0mx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0malpha\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mgrad\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;31m# x^k+1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     47\u001b[0m         \u001b[1;31m# Step 4: Calculate gradient\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     48\u001b[0m         \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<__array_function__ internals>\u001b[0m in \u001b[0;36mappend\u001b[1;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\numpy\\lib\\function_base.py\u001b[0m in \u001b[0;36mappend\u001b[1;34m(arr, values, axis)\u001b[0m\n\u001b[0;32m   4743\u001b[0m         \u001b[0mvalues\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mravel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvalues\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4744\u001b[0m         \u001b[0maxis\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0marr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 4745\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mconcatenate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marr\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalues\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0maxis\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   4746\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   4747\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<__array_function__ internals>\u001b[0m in \u001b[0;36mconcatenate\u001b[1;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[1;31mValueError\u001b[0m: all the input arrays must have same number of dimensions, but the array at index 0 has 2 dimension(s) and the array at index 1 has 3 dimension(s)"
     ]
    }
   ],
   "source": [
    "x0=np.array([[-1.5,1,1]])\n",
    "alpha0=np.array([0.1])\n",
    "[xRes,k]=gradDescent(x0,f,gradF,alpha0,0,1) # maxIter=1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62ffa4d3",
   "metadata": {},
   "source": [
    "**COMMENT FOR MILE/ELENA**\n",
    "\n",
    "*The algo seems to be okay but just can't around python/numpy's indexing, the np.array and [ ] confuse me and I can't get them straight through all the functions and variable definitions.*\n",
    "\n",
    "*The rest of the pseudo code below should work once the function is corrected*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "19e5d36e",
   "metadata": {},
   "outputs": [],
   "source": [
    "x0=np.ones(10)\n",
    "x0[0]=-1.5\n",
    "x0=np.array([x0])\n",
    "alpha0=np.array([0.1])\n",
    "[xRes,k]=gradDescent(x0,f,gradF,alpha0,0,1) # maxIter=1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a5b7296",
   "metadata": {},
   "source": [
    "First we will solve for n=3 with steepest descent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "90451048",
   "metadata": {},
   "outputs": [],
   "source": [
    "x0=np.array([[-1.5,1,1]])\n",
    "alpha0=np.array([0.1])\n",
    "[xRes,k]=gradDescent(x0,f,gradF,alpha0,1) # steep=1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26c343e4",
   "metadata": {},
   "source": [
    "Then for all the constant step sizes required:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5669d2f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "x0=np.array([[-1.5,1,1]])\n",
    "alpha0=np.array([0.1,0.5,1])\n",
    "for aa in range(len(alpha0)):\n",
    "    [xRes,k]=gradDescent(x0,f,gradF,alpha0[aa],1) # steep=1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7fda1c0",
   "metadata": {},
   "source": [
    "We can see that the number of iterations for each method increases a"
   ]
  }
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