{ "cells": [ { "cell_type": "markdown", "id": "e74a8aaa-e960-4d76-a52e-24e7ead28023", "metadata": {}, "source": [ "# Numerical Differentiation\n", "WHAT IS IT?\n", "Numerical Differentiation is a way we can use \n", "\n", "WHAT IS A DERIVATIVE?\n", "\n", "\n", "HOW CAN WE CALCULATE IT?\n", "\n", "\n", "We can find the derivate of both tabulated data and a continuous function using a finite difference method, which calculates rise over run of a function. To do this, we must first initalize our independant variable. Let's call this domain $x$ to be a vector such that $\\vec{x}$ =\n", "$\\pmatrix{x_0, x_1, x_2, ...}$. This domain is also known as the **numerical grid**, is either determined by our data (often time) or can be set by us if it's a continuous function. The **step size** is defined as the spacing between adjacent points on the grid ($h = x_{i+1} - x_i$). Next, let's introduce the dependent variable $y$, this can be any function of $x$.\n", "\n", "![image.png](https://pythonnumericalmethods.studentorg.berkeley.edu/_images/20.02.01-Finite-difference.png)\n", "\n", "For this tutorial let's model a falling object reaching terminal velocity using the equation below.\n", "\n", "$$ v(t) = 42.78 * (1 - e^{\\frac{-9.81*t}{42.78}}) $$\n", "\n", "Since we're starting with a continous function we can determine our step size ourselves, let's set it to `h=0.1`." ] }, { "cell_type": "code", "execution_count": 1, "id": "a97491b4-b183-4bdd-8c29-4cda0829d785", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Step size\n", "h = 4\n", "\n", "# Initiate vectors\n", "t = np.arange(0, 20, h) \n", "v = 42.78 * (1 - np.exp(-9.81 * t / 42.78))\n" ] }, { "cell_type": "markdown", "id": "9b79e5ba-4b71-4aeb-b3fb-878c2d728f7e", "metadata": {}, "source": [ "---\n", "## Forward Difference\n", "The forward difference method takes the point at which we want to find the derivative and the point *forwards* on the grid.\n", "\n", "$$ f'(x_i) = \\frac{f(x_{i+1})-f(x_i)}{h} $$ \n", "\n", "Note that $f'$ will be 1 element shorter than $f$ due we are unable to take the derivative of the last element." ] }, { "cell_type": "code", "execution_count": 2, "id": "d2fe3ad1-8af0-499a-8954-41a88a49b834", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. 25.68442511 35.94833378 40.04995649 41.68903078]\n", " [ 6.42110628 2.56597717 1.02540568 0.40976857 nan]]\n" ] } ], "source": [ "# Forward difference method\n", "dvdt = (v[1:] - v[:-1]) / h\n", "\n", "# Make a table of forward method\n", "dvdt_fd = np.append(dvdt,np.nan)\n", "table = np.vstack((v,dvdt_fd))\n", "print(table)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "4dfe5c25-f333-46bb-ab87-a7c97bb1e05f", "metadata": {}, "source": [ "## Backwards Difference\n", "\n", "Uses the point at which we want to find the derivative and the *backward* point.$$\n", "f'(x_i) = \\frac{f(x_{i})-f(x_{i-1})}{h}\n", "$$\n", "\n", "Notice that this equation is essentially the same as the forwards difference formula. Let's think about it this way - the slope between each point will remain the same. However, since we're using the previous element to calculate the gradient, the enitre array will be shifted to the right. We can therefore use the same dvdt equation." ] }, { "cell_type": "code", "execution_count": 3, "id": "415d0b3c-a70d-48ef-93ad-6e827127b222", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. 25.68442511 35.94833378 40.04995649 41.68903078]\n", " [ nan 6.42110628 2.56597717 1.02540568 0.40976857]]\n" ] } ], "source": [ "dvdt = (v[1:] - v[:-1]) / h\n", "\n", "# Output results\n", "dvdt_bd = np.insert(dvdt,0,np.nan)\n", "table = np.vstack((v,dvdt_bd))\n", "print(table)" ] }, { "cell_type": "markdown", "id": "21c87595-add2-4f7a-8d10-2da3b4284e02", "metadata": {}, "source": [ "## Central Difference\n", "Combinging the two previous techniques we get the central difference. Here we average the two to slopes to get out slope.\n", "$$\n", "f'(x_i) = \\frac{f(x_{i+1})-f(x_{i-1})}{2h}\n", "$$" ] }, { "cell_type": "code", "execution_count": 4, "id": "9d90ed83-d811-4394-b30b-ec80e7d835d4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0. 25.68442511 35.94833378 40.04995649 41.68903078]\n", " [ nan 4.49354172 1.79569142 0.71758712 nan]]\n" ] } ], "source": [ "dvdt_cd = (v[2:] - v[:-2]) / (2*h)\n", "\n", "# Output results\n", "dvdt_cd = np.pad(dvdt_cd, (1, 1), mode='constant', constant_values=np.nan)\n", "table = np.vstack((v,dvdt_cd))\n", "print(table)" ] }, { "cell_type": "markdown", "id": "213b1d8a-d92c-43f3-91d1-3c67711d0987", "metadata": {}, "source": [ "## Visualization\n", "Below we can plot $v(t)$ and $v'(t)$ using the methods above. Try decreasing step size and restart the kernel to see how `h` affects the derivative function." ] }, { "cell_type": "code", "execution_count": 5, "id": "e6a9f673-e9fc-457a-97b4-7e233f1fc280", "metadata": {}, "outputs": [ { "data": { "image/png": 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oKLNmzUqSAKTmPhPLby2LjY3l6tWrduW3rh7077//4ubmlmQCsMViITg42Hatq1evUrNmTbZt28a7777Lhg0b2L59O9999x2A7bOROAQmpRNib/2seXp62p3vfo5NjP1eP6d3kjisq1+/fkk+U6+99hpAkqV0b7dyU7Zs2ZKUeXh4JClPTOJv3Lhx1/ju9jsM8N133/Hcc8+RJ08evv76a7Zs2cL27dvp3Llziq6RHIvFQufOndm7d69tOeWZM2dSsGBB6tatC/zXdlWrVk3SdgsWLLjjEsSJ72lybZk7d27b66n9HKZU7969OXz4sG2I5uTJk6levTqVKlVy6HVE0jutCiWSCXz99dd06NCB0aNH25VfuHDhnlZOuldZs2bFYrEkO2Y+IiLirsdXrlyZrFmzsnTpUsaMGZPsXxSXLl2K1WolLCzMrvxO10zuy1SiHDlyUK5cOUaNGpXs64l/Gc6ZMye//PILVqvVYcnFoUOH+OWXX4D/kqpbrVq1iiZNmtiep+Y+k2vziIgIPDw88PPzsyu/ta2zZ89OfHw858+ft0suDMMgIiKCqlWrAmbPxunTp9mwYYOtlwJIMsE78Rx3Gsf+oCS20+3a8n56LXLkyAHAoEGDaNGiRbJ1ihcvbvc8LfdjuBdff/01BQsWZMGCBXax3Tyv5l506tSJIUOGMGPGDNzd3fn9998ZOXKk7RqJbfftt99SoECBVJ078T09c+ZMkqTh9OnTtnOn1efwiSeeoEyZMnzyySf4+fmxa9cuu3krIg8L9ViIZAIWi8X2V9lEy5cv59SpUw80Dl9fX6pUqcKSJUtsezKA+Vft5FaPupWHhwf9+/fnwIEDya6kcu7cOQYNGkRQUBBdu3a1ey0qKoqlS5falc2dOxcXFxdq1ap122s2bdqUP//8k8KFCyfpDapSpYotsWjcuDE3bty46wZZt/71904SJ2hPmzaN9evX2/2sWLECd3d3ZsyYcc/3+d1339n9hTkqKooffviBmjVrJrufwM3q1asHkOTL0aJFi4iOjra9nvil8NbP32effWb3vFixYhQuXJgZM2bc9xfU+/Xoo4/i6enJggUL7Mq3bt2aouFEd1K8eHGKFi3Knj17kv08ValSxW44YXpksVjw8PCwSyoiIiLueVWoRLlz56ZRo0bMmzePyZMn4+LiQseOHW2vN2zYEDc3N44cOXLbtrudJ554Akj6ed2+fTsHDhywfV5r1KhBYGCgbYGC1Ljb73avXr1Yvny57d+oZ599NlXnF8kM1GMhkgk0bdqUWbNmUaJECcqVK8fOnTsZP368U9ZhHzFiBE8++SQNGzakd+/eJCQkMH78ePz8/Lh48eJdjx84cCB79uyx/ff555+32yAvKiqKZcuWERgYaHdc9uzZefXVVzl+/DjFihVjxYoVTJs2jVdfffW2vQGJ8a5Zs4YaNWrQq1cvihcvzo0bNwgPD2fFihV8+umn5M2blzZt2jBz5kxeeeUVDh48SN26dbFarWzbto2SJUvSunVrAMqWLcuGDRv44YcfCAkJwd/fP8lfqMEce//ll19SsmTJJElSombNmrF06VK7XoPU3KerqythYWH07dsXq9XKe++9R2RkJMOHD7/r+xAWFkbDhg0ZOHAgkZGRPPbYY/zxxx8MHTqUihUr0r59e8D8opY1a1ZeeeUVhg4diru7O3PmzGHPnj1Jzjl58mSaNWtGtWrVeP3118mfPz/Hjx9n1apVzJkz564xOUq2bNno27cvY8aMIWvWrDzzzDOcPHmS4cOHExISct89Up999hmNGzemYcOGdOrUiTx58nDx4kUOHDjArl27WLhwoYPuJG00bdqU7777jtdee41WrVpx4sQJRo4cSUhICIcPH76vc3fp0oXly5fzxRdf0LBhQ7shjaGhoYwYMYLBgwfzzz//0KhRI7JmzcrZs2f57bff8PX1ve1nt3jx4nTr1o2PP/7YtvpZeHg477zzDvny5bOtKObn58eECRPo2rUr9evX56WXXiIoKIi///6bPXv28Mknn9w29rJlyzJ//nwWLFhAoUKF8PLyomzZsrbXX3jhBQYNGsTPP//M22+/bTfPTOSh4cyZ4yKSMokrvGzfvj3Z1y9dumR06dLFyJUrl+Hj42M8/vjjxqZNm4zatWvbrWJyv6tCde/ePcm1k1sVZvHixUbZsmUNDw8PI3/+/MbYsWONXr16GVmzZk3R/VqtVmPOnDlGnTp1jCxZshgeHh5GwYIFjVdffTXJ6k2GYa52U7p0aWPDhg1GlSpVDE9PTyMkJMR46623kqzMAxjDhg2zKzt//rzRq1cvo2DBgoa7u7uRLVs2o3LlysbgwYONq1ev2updv37dGDJkiFG0aFHDw8PDyJ49u/HEE08YmzdvttXZvXu38dhjjxk+Pj53XGFoyZIlBmBMnDjxtu2QuDLThAkTUnWfie/ze++9ZwwfPtzImzev4eHhYVSsWNFYtWqV3TUSV785f/58kutfv37dGDhwoFGgQAHD3d3dCAkJMV599VXj0qVLdvU2b95sVK9e3fDx8TFy5sxpdO3a1di1a1eSz5phmCsvNW7c2AgMDDQ8PT2NwoUL261cdrt4kvuc3m5VqIULF9odm9zn3mq1Gu+++66tbcqVK2csW7bMKF++vPHMM88kaYvbSW5VKMMwjD179hjPPfeckStXLsPd3d0IDg42nnjiCbsVz+70e534Xt+qQIECxpNPPpmk/Nbfz9utCpXcOZP7fR87dqwRGhpqeHp6GiVLljSmTZuW7EpJKV0VKlFsbKwRFBRkAMY333yTbJ0lS5YYdevWNQICAgxPT0+jQIECRqtWrYy1a9fa6iQXS0JCgvHee+8ZxYoVM9zd3Y0cOXIYL7zwgnHixIkk11ixYoVRu3Ztw9fX1/Dx8TFKlSplvPfee3c8f3h4uNGgQQPD39/fAJK0mWEYRqdOnQw3Nzfj5MmTKW4TkczEYhip7AsUEUmluLg4KlSoQJ48eVi9erXT4rhy5QpZsmTh448/zpCrtdSpU4cLFy7w559/3rFeeHg4BQsWZPz48fTr1+8BRZfxHT16lBIlSjB06FDeeustZ4cjGUxsbCyhoaE8/vjjSTZDFHlYaCiUiDhcly5dCAsLIyQkhIiICD799FMOHDjARx995LSYtm7dahtTX716dafFIenDnj17mDdvHjVq1CAgIICDBw8ybtw4AgIC6NKli7PDkwzk/PnzHDx4kJkzZ3L27FnefPNNZ4ck4jRKLETE4aKioujXrx/nz5/H3d2dSpUqsWLFCurXr++0mNq2bUtCQgITJkyw2xtAHk6+vr7s2LGD6dOnc/nyZQIDA6lTpw6jRo267yVn5eGyfPlyXnzxRUJCQpgyZYqWmJWHmoZCiYiIiIjIfdNysyIiIiIict+UWIiIiIiIyH1TYiEiIiIiIvct00/etlqtnD59Gn9/f7tdREVERERE5M4MwyAqKorcuXPfdQPRTJ9YnD592m5nTxERERERSZ0TJ06QN2/eO9bJ9ImFv78/YDZGQECAU2KIi4tj9erVNGjQAHd3d6fEkBmoHR1D7egYakfHUVs6htrRMdSOjqF2dIz00I6RkZHky5fP9p36TjJ9YpE4/CkgIMCpiYWPjw8BAQH65boPakfHUDs6htrRcdSWjqF2dAy1o2OoHR0jPbVjSqYUaPK2iIiIiIjcNyUWIiIiIiJy35RYiIiIiIjIfcv0cyxSKiEhgbi4uDQ5d1xcHG5ubty4cYOEhIQ0ucbDQO3oGIntmJCQ4PTxmiIiIpJ5PPSJhWEYREREcPny5TS9RnBwMCdOnNBeGvdB7egYie34zz//kDVrVoKDg9WeIiIict8e+sQiManIlSsXPj4+afIFy2q1cvXqVfz8/O66sYjcntrRMaxWK1FRUbi4uHDhwgUAQkJCnByViIiIZHQPdWKRkJBgSyqyZ8+eZtexWq3Exsbi5eWlL8T3Qe3oGIntGBAQgIuLC+fOnSNXrly4uro6OzQRERHJwB7qb2eJcyp8fHycHImIcyR+9tNqfpGIiIg8PB7qxCKRxpfLw0qffREREXEUJRYiIiIiInLflFg8pEJDQ5k4cWK6Pd/NDh48SHBwMFFRUWly/uScO3eOnDlzcurUqQd2TREREZGMTIlFBtOsWTPq16+f7GtbtmzBYrGwa9euBxwVbN++nW7dutmeWywWlixZ4pBzDx48mO7du+Pv7++Q89WpU4dPP/30jnVy5cpF+/btGTp0qEOuKSIiIpLZKbHIYLp06cJPP/3EsWPHkrw2Y8YMKlSoQKVKlR54XDlz5kyTSfAnT55k6dKlvPjiiw4538WLF9m8eTPNmjW7a90XX3yROXPmcOnSJYdcW0RERCQzU2KRwTRt2pRcuXIxa9Ysu/Jr166xYMECunTpAsDmzZupVasW3t7e5MuXj169ehEdHX3b8x4/fpynn34aPz8/AgICeO655zh79qxdnaVLl1KlShW8vLzIkSMHLVq0sL1281Co0NBQAJ555hksFguhoaGEh4fj4uLCjh077M758ccfU6BAAQzDSDaub775hvLly5M3b15b2axZs8iSJQvLli2jePHi+Pj40KpVK6Kjo5k9ezahoaFkzZqVnj17Jtmhe/ny5ZQvX548efJw6dIl2rVrR86cOfH29qZo0aLMnDnTVrds2bIEBwezePHi27abiIiIiJiUWNzCMCA6+sH/3OZ7dRJubm506NCBWbNm2X0ZX7hwIbGxsbRr1469e/fSsGFDWrRowR9//MGCBQv45Zdf6NGjx23u2aB58+ZcvHiRjRs3smbNGo4cOcLzzz9vq7N8+XJatGjBk08+ye+//866deuoUqVKsufbvn07ADNnzuTMmTNs376d0NBQ6tevb/fFPbFOp06dbrs60c8//5zsda5du8akSZOYP38+K1euZMOGDbRo0YIVK1awYsUKvvrqKz7//HO+/fZbu+OWLl3K008/DcA777zD/v37+fHHHzlw4ABTp04lR44cdvUfeeQRNm3alGxsIiIiImkhLg7OnIHdu+H333Ny44azI0qZh3qDvORcuwZ+fo4+qwuQ5Y41rl4FX9+Una1z586MHz+eDRs2ULduXcAcBtWiRQuyZs1K7969adu2LX369AGgaNGiTJo0idq1azN16lS8vLzszrd27Vr++OMPjh49Sr58+QD46quvKF26NNu3b6dq1aqMGjWK1q1bM3z4cNtx5cuXTza+nDlzApAlSxaCg4Nt5V27duWVV17hgw8+wNPTkz179rB7926+++67295reHg4lStXTlIeFxfH1KlTKVy4MACtWrXiq6++4uzZs/j5+VGqVCnq1q3L+vXrbQlSTEwMq1atYsiQIYDZS1OxYkVb4pLY03KzPHny8Pvvv982PhEREZGUuHYNzp2Ds2fNn+QeJ/73338Tj3IHatCyZRxlyzox+BRSYpEBlShRgho1ajBjxgzq1q3LkSNH2LRpE6tXrwZg586d/P3338yZM8d2jGEYWK1Wjh49SsmSJe3Od+DAAfLly2dLKgBKlSpFlixZOHDgAFWrVmX37t289NJL9xV38+bN6dGjB4sXL6Z169a2+JP7Qp/o+vXrSRIhMDd2S0wqAIKCgggNDcXvpqwwKCiIc+fO2Z7/9NNPZM+enbL//8189dVXadmyJbt27aJBgwY0b96cGjVq2F3H29uba9eu3esti4iISCZlGHD5cvKJQXKPr15N3fldXCBnTgNv70hiYzPGZs5KLG7h45P6N/5urFYrkZGRBAQE4OKS/Oiz1M577tKlCz169GDy5MnMnDmTAgUKUK9ePdv1Xn75ZXr16pXkuPz58ycpMwwj2aFIN5d7e3unLsBkeHh40L59e2bOnEmLFi2YO3fuXZeozZEjR7KTp93d3e2eWyyWZMusVqvt+c3DoAAaN27MsWPHWL58OWvXrqVevXp0796d999/31bn4sWLth4YERERydzi4+HChZQnC3FxqTu/pycEBf33kyuX/X9vfpw9OyQkxLNixQbKlWuSNjfsYEosbmGxpHxIUkpZrZCQYJ73NnlFqj333HP07t2buXPnMnv2bF566SVbElCpUiX27dtHkSJFUnSuUqVKcfz4cU6cOGHrtdi/fz9Xrlyx9W6UK1eOdevWpXh1Jnd39yQTp8EcDlWmTBmmTJlCXFyc3QTw5FSsWJH9+/en6Jp3YhgGP/zwA19++aVdec6cOenUqROdOnWiZs2a9O/f3y6x+PPPP6lTp859X19ERESc48aNlA0/ShyClNJ5r4kCA5NPDJIr8/c3v2umVDJfpdI1JRYZlJ+fH88//zxvvfUWV65coVOnTrbXBg4cSLVq1ejevTsvvfQSvr6+HDhwgDVr1vDxxx8nOVf9+vUpV64c7dq1Y+LEicTHx/Paa69Ru3Zt2/yDoUOHUq9ePQoXLkzr1q2Jj4/nxx9/ZMCAAcnGFxoayrp163jsscfw9PQka9asAJQsWZJq1aoxcOBAOnfufNeekIYNG9K1a1cSEhJuO8E7JXbu3El0dDS1atWylQ0ZMoTKlStTunRpYmJiWLZsmd0wsWvXrrFz505Gjx59z9cVERERxzIMiIy8c7Jw8+PU7q9rsUDOnMknBrcmDrlyQTIjth9aSiwysC5dujB9+nQaNGhgN8SpXLlybNy4kcGDB1OzZk0Mw6Bw4cJ2qzzdLHEzu549e1KrVi1cXFxo1KiRXRJSp04dFi5cyMiRIxk7diwBAQF2X9JvNWHCBPr27cu0adPIkycP4eHhdnFv3ryZzp073/UemzRpgru7O2vXriUsLCwFrZK877//nieffBI3t/8+8h4eHgwaNIjw8HC8vb2pWbMm8+fPtzsmf/781KxZ856vKyIiIneXkGD2FqQkWTh3DmJiUnd+D4/bJwi3Jgs5coCra9rcZ2ZnMW63gUAmERkZSWBgIFeuXCEgIMDutRs3bnD06FEKFiyY7ARhR0nJHIuHyahRo5g/fz579+5NUf0pU6bw/fff8+OPP95zO5YrV463336b5557LsXHPPLII/Tp04e2bdum6lrp3c2fx9jY2AfyO5AZxcXFsWLFClvyK/dObekYakfHUDs6RlxcHN9/v5KKFRtx6ZL7XZOFCxfMoeOp4e+f8mQhMDB1Q5DSi/TwebzTd+lbqcdCHpirV69y4MABPv74Y0aOHJni47p168alS5eISm1f5v/FxsbSsmVLGjdunOJjzp07R6tWrWjTps09XVNERCSzMQxzWFFK5iqcO+fGlSvNUnV+i8WcsJzSZMEB68qIgymxkAemR48ezJs3j+bNm6doGFQiNzc3Bg8ebPtLe2p5eHgwdOjQVB2TK1eu284fERERySys1v+GIN09WSAVG7WZ3QPu7ga5cllSlCzkyAFu+maaoentkwdm1qxZzJo1y9lhiIiIZGqxsSlbKvXsWTh/PvVDkPz87rzyUVAQZM0axx9/rOHZZ8Pw8NCQsoeFEgsRERGRdMwwzD22UposXL6c+mtkz373ZCFxFaSULMsfFwf//BOXIec1yL1LN4nFmDFjeOutt+jdu7dt0zTDMBg+fDiff/45ly5d4tFHH2Xy5MmULl3aucGKiIiI3AerFS5eTHmycP166s7v5vZfInC3/RVy5gTNUxdHSBeJxfbt2/n8888pV66cXfm4ceP44IMPmDVrFsWKFePdd98lLCyMgwcP4u/v76RoRURERJKKi/tvOdS7zVU4f97c5Tk1fHzuPJn55rKsWR23Ka9ISjk9sbh69Srt2rVj2rRpvPvuu7ZywzCYOHEigwcPtu3OPHv2bIKCgpg7dy4vv/yys0IWERGRh0R0dMonNl+8mPrzZ82a8mTBz8/x9yfiSE5PLLp3786TTz5J/fr17RKLo0ePEhERQYMGDWxlnp6e1K5dm82bNyuxEBEREYe4cQN27YKtW2HLFlf27q3J66+7ce6cmVikhqurObQoJclCzpzmxm0imYVTE4v58+eza9cutm/fnuS1iIgIAIKCguzKg4KCOHbs2G3PGRMTQ8xN2zEmLk8aFxdHXFycXd24uDgMw8BqtWJN7ZIIqZC4B2HiteTeqB0d49Z2NAyDuLg4XLXNaKok/nty678rknpqS8dQO6aMYcDx47Btm4Vt2yxs3Wph924LcXGJs4xdgGx2x3h5Gf9PCoybkgbj/3MYjP8nCeZ/s2VL3RCkzPp26fPoGOmhHVNzbaclFidOnKB3796sXr36jjv+Wm5ZTsAwjCRlNxszZgzDhw9PUr569Wp8fHzsytzc3AgODubq1avExsam8g5S7143eMvsxo4dy/Lly9m0aVOK6kdFRfHLL7/QrFkzwsPDCQwMZO7cuQwaNMgu6Zw1axbjx4/nzJkzjBo1ildffTXZsodVVFQUsbGxXL9+nZ9//pn41A72FQDWrFnj7BAyDbWlY6gd7cXEuHDkSBYOHszGwYNZOXgwG5cuJf3eERgYQ/HiFylW7BJ5814lS5YbBAbGkiVLDF5e8Xdc3ejaNTh2zPwRe/o8OoYz2/HatWsprmsxEv98+YAtWbKEZ555xu6vpAkJCVgsFlxcXDh48CBFihRh165dVKxY0Vbn6aefJkuWLMyePTvZ8ybXY5EvXz4uXLiQZBvyGzducOLECUJDQ++Y3NwvwzCIiorC39//jklRSr344ot8+eWXScoT2yyjGT58ON9//z27du26Y72b23Hjxo3Uq1ePf//9lyxZsnD9+nWioqLIlSsXYL7vuXLlYsKECbRo0YLAwEDi4+OTlN2abD4Mbm7HmJgYwsPDyZcvX5r+DmRGcXFxrFmzhrCwMNy1nMp9UVs6htrR7I0ID4etWy389pvZG7Fnj4X4ePv/97q5GZQrZ1CtmsEjj5j/LVjQ3PlZ7egYakfHSA/tGBkZSY4cObhy5UqS79K3clqPRb169di7d69d2YsvvkiJEiUYOHAghQoVIjg4mDVr1tgSi9jYWDZu3Mh777132/N6enri6emZpNzd3T3JG3JzIuOShksnJA7bSbzW/bJYLDRq1IiZM2falefMmfOezh8bG4vHAxjkGRcXl+wvRWKydbfYk2vHxPfO19cX35sW1j558iRxcXE0bdqUPHnyAPDnn38mKXPkfWQUt7ajxWJJ9vdDUkZt5zhqS8d4mNoxOhp27EicG2H+9+zZpPWCg6F6dahWzfxv5coWfHzu/Ie+h6kd05La0TGc2Y6pua7TFiLz9/enTJkydj++vr5kz56dMmXKYLFY6NOnD6NHj2bx4sX8+eefdOrUCR8fH9q2beussNMNT09PgoOD7X4Se382btzII488gqenJyEhIbz55pt2w1zq1KlDjx496Nu3Lzly5CAsLIw33niDZs2a2epMnDgRi8XC8uXLbWXFixfns88+A8wlgsPCwsiRIweBgYHUrl07SY+DxWLh008/5emnn8bX19c2OX/s2LEEBQXh7+9Ply5duHHjxl3vd8WKFZQoUYKQkBDq1atHeHi43euzZs0iS5Ystsdly5YFoFChQlgslmTLEs/xww8/ULlyZby8vChUqBDDhw+3a6/b3UdKjvviiy945pln8PHxoWjRoixdutQu7n379vHkk08SEBCAv78/NWvW5MiRI7bXZ86cScmSJfHy8qJEiRJMmTLlrm0lIpIZGQYcOQJffw3du0PlyhAYCHXqwJtvwvffm0mFmxtUrQq9esG8eXD0KJw+Dd99BwMGQM2a5rKtIuJ4Tl8V6k4GDBjA9evXee2112wb5K1evTpN97AwDIPrcQkOPafVauV6bAJusfG3/au8t7urQ4ZJnTp1iiZNmtCpUye+/PJL/vrrL1566SW8vLwYNmyYrd7s2bN59dVX+fXXXzEMg8OHDzN9+nSsVisuLi5s3LiRHDlysHHjRp588kkiIiI4dOgQtWvXBszx+R07dmTSpEkATJgwgSZNmnD48GG792fo0KGMGTOGDz/8EFdXV7755huGDh3K5MmTqVmzJl999RWTJk2iUKFCt72nEydO0KJFC15++WVeeOEF/vrrL/r373/b+s8//zz58uWjfv36/Pbbb+TLlw9/f/8kZTlz5mTVqlW88MILTJo0yfalvlu3brbYb3cfKT1u+PDhjBs3jvHjx/Pxxx/Trl07jh07RrZs2Th16hS1atWiTp06/PTTTwQEBPDrr7/akpNp06YxdOhQPvnkEypWrMjvv//OSy+9hK+vLx07dkzpR0JEJEO6ehW2b/+vJ2LrVnPvh1vlzm3fG1GpEnh7P/h4RSSdJRYbNmywe26xWBg2bJjdF+K0dj0ugVJDVj2w6yXaP6IhPh4pfzuWLVuG300LWjdu3JiFCxcyZcoU8uXLxyeffILFYqFEiRKcPn2agQMHMmTIEFtiU6RIEcaNG2c7PiQkhKioKH7//XcqVarEpk2b6NevH9999x0A69evJygoiBIlSgDwxBNP2MXz2WefkTVrVjZu3EjTpk1t5W3btqVz5862523atKFz58507doVgHfffZe1a9fesddi6tSpFCpUiA8++ICoqCgqV67Mvn37bjskztvbm+zZswPm8LDg4GCAZMtGjRrFm2++afuiXqhQIUaOHMmAAQPsEoRb76N9+/YpOq5Tp060adMGgNGjR/Pxxx/z22+/0ahRIyZPnkxgYCDz58+3dTMWK1bMduzIkSNt80EAChYsyP79+/nss8+UWIhIpmIYcPjwf0OatmyBvXvN3alv5uFhJg6JSUT16pA3L3ecWC0iD066Siwk5erWrcvUqVNtzxPnFxw4cIDq1avb9X489thjXL16lZMnT5I/f34AqlSpYne+wMBAKlSowIYNG3B3d8fFxYWXX36ZoUOHEhUVxYYNG2y9FQDnzp1jyJAh/PTTT5w9e5aEhASuXbvG8ePH7c5763UOHDjAK6+8YldWvXp11q9ff9t7PXDgANWqVbO7p+rVq9+xfVJq586dbN++nVGjRtnKEhISuHHjBteuXbNN7r71PlJ63M27yfv6+uLv78+5c+cA2L17NzVr1kx27OL58+c5ceIEXbp04aWXXrKVx8fHExgY6IA7FxFxnsjIpL0R//6btF6+fPZJRMWKkMw0ShFJJ5RY3MLb3ZX9Ixo69JxWq5WoyCj8A/zvOBQqNXx9fZNdASq55XgTF/66ufzmic6J6tSpw4YNG/Dw8KB27dpkzZqV0qVL8+uvv7Jhwwb69Oljq9upUyfOnz/PxIkTKVCgAJ6enlSvXj3Jsr3JXSe10nLhMqvVyvDhw229Aje7eZWkW+8jpcfdmjRYLBbb5GnvO/TVJ9aZNm0ajz76qN1r2m9CRDISqxUOHfovidiyBf780+yluJmnpzlv4uZhTfexzoaIOIESi1tYLJZUDUlKCavVSryHKz4ebmm6+hRAqVKlWLRokV2CsXnzZvz9/e+6ElKdOnWYPn06bm5u1K9fH4DatWszf/58u/kVAJs2bWLKlCk0adIEMOdBXLhw4a7xlSxZkq1bt9KhQwdb2datW+96T0uWLLEru9sxKVWpUqV7Wqb3Xo+7Wbly5Zg9e3ayq0wFBQWRJ08e/vnnH9q1a3fP1xARedCuXIFt2/5LIrZtg0uXktYrUMC+N6JCBe1CLZLRKbHIZF577TUmTpxIz5496dGjBwcPHmTo0KH07dv3rklNrVq1iIqK4ocffrCtfFSnTh1atmxJzpw5KVWqlK1ukSJF+Oqrr6hSpQqRkZH079//jn+BT9S7d286duxIlSpVePzxx5kzZw779u274+TtV155hQkTJvDGG2/Qtm1bDh48yKxZs1LWIHcxZMgQmjZtSr58+Xj22WdxcXHhjz/+YO/evbY2cORxN+vRowcff/wxrVu3ZtCgQQQGBrJ161YeeeQRihcvzrBhw+jVqxcBAQE0btyYmJgYduzYwaVLl+jbt69D7l9E5H5YrfDXX//Ni9i6FfbvT9ob4eUFVar8l0RUqwYhIc6JWUTSjhKLTCZPnjysWLGC/v37U758ebJly0aXLl14++2373psYGAgFStW5Pjx47YkombNmlitVrveCoAZM2bQrVs3KlasSP78+Rk9ejT9+vW76zWef/55jhw5wsCBA7lx4wYtW7bk1VdfZdWq20+Yz58/P4sWLeL1119n6tSpPPLII4wePdpuMvW9atiwIcuWLWPEiBGMGzcOd3d3SpQoYZtc7ujjbpY9e3Z++ukn+vfvT+3atXF1daVChQo89thjAHTt2hUfHx/Gjx/PgAED8PX1pWzZsnZD0kREHqRLl5L2Rly5krRewYL2SUT58qCtDEQyP6ftvP2gREZGEhgYmOxugTdu3ODo0aMULFgwTXcdtlqtREZGEhAQkOZDoTIztaNj3NyOsbGxD+R3IDOKi4tjxYoVNGnSRJs/3Se1pWM4uh0TEszeh5tXavrrr6T1fHzMfSMShzVVqwZBQfd9eafR59Ex1I6OkR7a8U7fpW+lHgsRERHh33/NHojEJOK33yAqKmm9woXteyPKlTM3pRMR0T8FIiIiD5mEBHNlpptXajp0KGk9X1945JH/kohq1SBnzgcfr4hkDEosREREMrnz55P2RkRHJ61XrJj9cq+lS6s3QkRSTv9ciIiIZCLx8f/1RiT2SPz9d9J6/v7/9UZUrw6PPgrZsz/4eEUk81BiISIikoGdO2cmEL/84sKPPz5G27ZuXLuWtF6JEva9EaVKgfbbFBFHUmIhIiKSQcTFwZ499is1HT2a+KorkAOAwECzByIxiXj0Ucia1VlRi8jDQomFiIhIOhURYT+kaccOuH7dvo7FYvY+PPKIFR+fPXTtWoZy5dzRqtwi8qApsRAREUkHYmNh9277lZqOHUtaL0sW+z0jHnnELIuLS2DFiuOULl1GSYWIOIUSCxERESc4dco+idi5E2Ji7OtYLFCmzH+JRPXq5spNShxEJD3SP01yW6GhoUycONHZYSSxYcMGLBYLly9fTtVxFouFJUuWABAeHo7FYmH37t2213/99VfKli2Lu7s7zZs3v22ZiEhqxcSYCcSHH8Jzz0H+/JA3Lzz7LEyYAJs3m3WyZYMmTWDkSFi7Fi5fhj/+gM8/hxdfNCdgK6kQkfRKPRYZUKdOnZg9e7btebZs2ahatSrjxo2jXLlyTows48iXLx9nzpwhR44ctrK+fftSoUIFfvzxR/z8/G5bJiJyJ4YBJ0/az43Ytcsc6nQzFxcoW9Z+paaiRc1eChGRjEiJRQbVqFEjZs6cCUBERARvv/02TZs25fjx406OzHFiY2Px8PBIk3O7uroSHBxsV3bkyBFeeeUV8ubNe8ey1ErL+xAR57txwxzGdPNKTadPJ62XI4d9ElG1KujvFSKSmahDNYPy9PQkODiY4OBgKlSowMCBAzlx4gTnz5+31Rk4cCDFihXDx8eHQoUK8c477xAXF2d3nqVLl1KlShW8vLzIkSMHLVq0uO01Z86cSWBgIGvWrOGHH34gS5YsWK1WAHbv3o3FYqF///62+i+//DJt2rQB4N9//6VNmzbkzZsXHx8fypYty7x58+zOX6dOHXr06EHfvn3JkSMHYWFhAKxYsYJixYrh6+tLs2bNCA8Pv2v7HD58mFq1auHl5UWpUqVYs2aN3es3D4VKfPzvv//SuXNnLBYLs2bNSrYMYP/+/TRp0gQ/Pz+CgoJo3749Fy5cuOt9pOS4Xr16MWDAALJly0ZwcDDDhg2zi/vy5ct069aNoKAgvLy8KFOmDMuWLbO9vnnzZmrVqoW3tzf58uWjV69eRCe3va6I3BPDgPBwmD8fevc2J04HBMDjj0O/frBokZlUuLpCxYrw2mvw1Vdw+LC538TSpfDWW1C3rpIKEcl8lFjcyjAgNtrxP3HX7vy6YdxzyFevXmXOnDkUKVKE7Ddtm+rv78+sWbPYv38/H330EdOmTePDDz+0vb58+XJatGjBk08+ye+//866deuoUqVKstd4//336devH6tWrSIsLIxatWoRFRXF77//DsDGjRvJkSMHGzdutB2zYcMGateuDcCNGzeoXLkyy5Yt488//6Rbt260b9+ebdu22V1n9uzZuLm58euvv/LZZ59x4sQJWrRoQZMmTdi1axft27fnrbfeumN7WK1WWrRogaurK1u3buXTTz9l4MCBt62fOCwqICCAiRMncubMGZ599tkkZc8//zxnzpyhdu3aVKhQgR07drBy5UrOnj3Lc889d8f7SM1xvr6+bNu2jXHjxjFixAhbUmS1WmncuDGbN2/m66+/Zv/+/YwdOxbX/+9wtXfvXho2bEiLFi34448/WLBgAb/88gs9evS4Y3uJyO1dvw6bNsG4cdCiBeTODQULQps2MGkSbN9u7i2RKxc8/TSMHQsbNsCVK+bwp8mT4YUXoEgRDXESkcxPQ6FuFXcNRud26CldgCx3q/TWafDwTfE5ly1bZhvzHx0dTUhICMuWLcPlpll9b7/9tu1xaGgob7zxBgsWLGDAgAEAjBo1itatWzN8+HBbvfLlyye51qBBg5g9ezYbNmygbNmyAAQGBlKhQgU2bNhA5cqV2bBhA6+//jrDhw8nKiqK6OhoDh06RJ06dQDIkycP/fr1s52zZ8+erFy5koULF/Loo4/ayosUKcK4ceP+a5a33qJQoUJ8+OGHGIZBSEgIR44csatzq7Vr13LgwAHCw8NtQ5hGjx5N48aNk62fOCzKYrEQGBhoGyLl6+ubpGzMmDFUqlSJ0aNH246fMWMG+fLl49ChQxQrVizZ+xgyZEiKjitXrhxDhw4FoGjRonzyySesW7eOsLAw1q5dy2+//caBAwds9QsVKmQ73/jx42nbti19+vSxHT9p0iRq167N1KlT8fLyum2biYj5952jR+1XatqzB+Lj7eu5uUGFCvYrNYWGKnEQEVFikUHVrVuXqVOnAnDx4kWmTJlC48aN+e233yhQoAAA3377LRMnTuTvv//m6tWrxMfHExAQYDvH7t27eemll+54nQkTJhAdHc2OHTvsvsSCOXRnw4YN9O3bl02bNvHuu++yaNEifvnlFy5fvkxQUBAlSpQAICEhgbFjx7JgwQJOnTpFTEwMMTEx+PraJ1O39pgcOHCAatWqYbFYMP7fq1OtWrU7xnzgwAHy589vNy+ievXqdzwmpXbu3Mn69euTnch95MgR2xf+W+8jpcfdOvk+JCSEc+fOAeb7lTdvXlvd5GL7+++/mTNnjq3MMAysVitHjx6lZMmSqbhTkcwvOtrccO7mSdb//3WzExz8XwJRvTpUqgQ+Pg8+XhGR9E6Jxa3cfczeAweyWq1ERkUR4O9v16OQ5Lqp4OvrS5EiRWzPK1euTGBgINOmTePdd99l69attt6Ihg0bEhgYyPz585kwYYLtGG9v77tep2bNmixfvpxvvvmGN9980+61OnXqMH36dPbs2YOLiwulSpWidu3abNy4kUuXLtmGQYGZoHz44YdMnDiRsmXL4uvrS58+fYi9ZZmUWxMN4x6GiCV3jMVBf0q0Wq00a9aM9957L8lrISEhtse33kdKj3N3d7d7zWKx2Oax3O39slqtvPzyy/Tq1SvJa/nz57/jsSKZnWHAkSP2ScQff0BCgn09d3dzbsTNk6zz51dvhIhISiixuJXFkqohSSlitYJ7gnneNFqA3GKx4OLiwvXr1wFz/4UCBQowePBgW51jt2zhWq5cOdatW8eLL7542/M+8sgj9OzZk4YNG+Lq6mo3OTtxnsXEiROpXbs2FouF2rVrM2bMGC5dukTv3r1tdTdt2sTTTz/NCy+8AJhfgg8fPnzXv6KXKlXKtvdEolvnZSR3zPHjxzl9+jS5c5vD2rZs2XLHY1KqUqVKLFq0iNDQUNzcUv7rc6/H3axcuXKcPHnSbujUrdfYt2+fXcIp8rC6ehV+++2/IU1bt8JNayXY5Mljn0RUqgQaNSgicm80eTuDiomJISIigoiICA4cOEDPnj25evUqzZo1A8wx/sePH2f+/PkcOXKESZMmsXjxYrtzDB06lHnz5jF06FAOHDjA3r17k527UL16dX788UdGjBhhN/k7cZ7F119/bZtLUatWLXbt2mU3vyIxnjVr1rB582YOHDjAyy+/TERExF3v85VXXuHIkSP07duXgwcPsnDhQrs9PJJTv359ihcvTocOHdizZw+bNm2yS7DuR/fu3bl48SJt2rTht99+459//mH16tV07tyZhFv/9OmA425Wu3ZtatWqRcuWLVmzZg1Hjx7lxx9/ZOXKlYC5CtiWLVvo3r07u3fv5vDhwyxdupSePXs65N5F0ivDgIMHYfZseOUVc/5DYCDUqweDB8OyZWZS4eFhJhCvvw7ffAPHj5v7TSxcCG+8ATVqKKkQEbkfSiwyqJUrVxISEkJISAiPPvoo27dvZ+HChbYv808//TSvv/46PXr0oEKFCmzevJl33nnH7hx16tRh4cKFLF26lAoVKvDEE0/ctjfgscceY/ny5bzzzjtMmjTJVl63bl0SEhJs182aNSulSpUiZ86cdr0R77zzDpUqVaJhw4bUqVOH4ODgFO1knT9/fhYtWsQPP/xAxYoVmTlzJu++++4dj3FxcWHx4sXExMTwyCOP0LVrV0aNGnXXa6VE7ty5+fXXX0lISKBhw4aUKVOG3r17ExgYePthbvdx3K0WLVpE1apVadOmDaVKlWLAgAG2xKRcuXJs3LiRw4cPU7NmTSpWrMg777xjN9RKJDOIjDR3pR45Ep580twfokQJ6NQJPvvMnHBttUK+fOYu1x9+aPZaREaa//3gA3PH63z5nH0nIiKZi8W4l0HsGUhkZCSBgYFcuXLFbuIymEugHj16lIIFC6bpijlWq5XIyEgCAgJS9SVS7KkdHePmdoyNjX0gvwOZUVxcHCtWrKBJkyZJ5sZI6typLa1Wszfi5pWa9u1LukK3pydUqfLfkKZq1cxhTg8TfSYdQ+3oGGpHx0gP7Xin79K30hwLERFJNy5fNudGJE6y3rbNLLtVaKh9ElGhgjnUSUREnEeJhYiIOM3VqzBvnoUFCyowaJAbf/2VtDfC29vsjUhMIqpVA43wExFJf5RYiIjIAxcfDzNmwJAhcPasG1DA9lqhQvYrNZUrZy4DKyIi6ZsSCxEReWAMA1asgP794cABs6xwYYMKFQ7Ttm0hHnvMjaAg58YoIiL3RjNgRUTkgfj9d6hfH5o2NZOKbNngo49gz5542rc/QLNmhpIKEZEMTD0WIiKSpk6cMPeT+Pprs8fC0xN694ZBgyBLFoiLc3aEIiLiCEosREQkTURGwtix5j4SN26YZW3bwqhR5qpOIiKSuSixEBERh4qLg88/h+HD4fx5s6x2bXj/fXN1JxERyZyUWIiIiEMYBixdCgMGwKFDZlnx4jBuHDRrBhaLc+MTEZG0pcnb8kCFhoYyceLEVB3TqVMnmjdvbnv+xBNP0KdPH9vza9eu0bJlSwICArBYLFy+fDnZMhFJO7/9ZvZKNG9uJhU5c8KUKbB3Lzz1lJIKEZGHgRKLDCoiIoKePXtSqFAhPD09yZcvH82aNWPdunUOvU6dOnXsvsSnB99++y0jR460PZ89ezabNm1i8+bNnDlzhsDAwGTLRMTxwsPNeROPPgqbNoGXF7z1Fvz9N7z6qvafEBF5mGgoVAYUHh7OY489RpYsWRg3bhzlypUjLi6OVatW0b17d/76668HGo9hGCQkJODm9mA+TtmyZcPF5b+c+MiRI5QsWZIyZcrcsSy1EhISsFgsdtcSEdOlSzB6NEyaBLGxZo9Ehw4wciTky+fs6ERExBn0jSkDeu2117BYLPz222+0atWKYsWKUbp0afr27cvWrVtt9a5cuUK3bt3IlSsXAQEBPPHEE+zZs8f2+rBhw6hQoQJfffUVoaGhBAYG0rp1a6KiogBzCNLGjRv56KOPsFgsWCwWwsPD2bBhAxaLhVWrVlGlShU8PT3ZtGkTR44c4emnnyYoKAg/Pz+qVq3K2rVrU3VvCQkJ9O3blyxZspA9e3YGDBiAYRh2dW4eClWnTh0mTJjAzz//jMVioU6dOsmWAcTGxjJgwADy5MmDr68vjz76KBs2bLCdd9asWWTJkoVly5ZRqlQpPD09OXbsWIqPW7VqFSVLlsTPz49GjRpx5swZu7hnzJhB6dKl8fT0JCQkhB49eqT4vRJJL2Jjzb0nihQxJ2PHxkK9erBrF8yapaRCRORhpsTiFoZhcC3umsN/rsdfv+Prt355vp2LFy+ycuVKunfvjq+vb5LXs2TJYruPJ598koiICFasWMHOnTupVKkS9erV4+LFi7b6R44cYcmSJSxbtoxly5axceNGxo4dC8BHH31E9erVeemllzhz5gxnzpwh303fGgYMGMCYMWM4cOAA5cqV4+rVqzRp0oS1a9fy+++/07BhQ5o1a8bx48dT3P4TJkxgxowZTJ8+nV9++YWLFy+yePHi29b/7rvveOmll6hevTpnzpzhu+++S7YM4MUXX+TXX39l/vz5/PHHHzz77LM0atSIw4cP28537do1xowZwxdffMG+ffvIlStXio97//33+eqrr/j55585fvw4/fr1s70+depUunfvTrdu3di7dy9Lly6lSJEiqXqvRJzJMODbb6FUKejTBy5ehNKlzV2016yBChWcHaGIiDibhkLd4nr8dR6d++gDv+62ttvwcfe5a72///4bwzAoUaLEHeutX7+evXv3cu7cOTw9PQF4//33WbJkCd9++y3dunUDwGq1MmvWLPz9/QFo374969atY9SoUQQGBuLh4YGPjw/BwcFJrjFixAjCwsJsz7Nnz0758uVtz999910WL17M0qVL7f46fycTJ05k0KBBtGzZEoBPP/2UVatW3bZ+tmzZ8PHxwcPDwy7GW8uOHDnCvHnzOHnyJLlz5wagX79+rFy5kpkzZzJ69GgA4uLimDJliu0+UnPcp59+SuHChQHo0aMHI0aMsGuLN954g969e9vKqlatCqT8vRJxli1b4I03zP8CBAebQ546dYIHNAJSREQyAP0vIYNJ7Nmw3GWJlZ07d3L16lWyZ89uV379+nWOHDliex4aGmpLKgBCQkI4d+5cimKpcsuC9NHR0QwfPpxly5Zx+vRp4uPjuX79eop7LK5cucKZM2eoXr26rczNzY0qVaqkuEfndnbt2oVhGBQrVsyuPCYmxq6NPDw8KFeuXKqP8/HxsSUVYN+O586d4/Tp09SrVy/Z2FL6Xok8aEeOwJtvmj0VAD4+0L8/9OsHfn7OjU1ERNIfJRa38HbzZlvbbQ49p9VqJSoqCn9//9tOBPZ2807RuYoWLYrFYuHAgQN2S7Amd82QkBC7uQCJEodLAbjfsmSLxWLBarWmKJZbh2L179+fVatW8f7771OkSBG8vb1p1aoVsbGxKTpfWrJarbi6urJz505cXV3tXvO76RuSt7e3XdKW0uOSa8fEZMjb+87vbUrfK5EH5d9/4d13YfJkc7M7Fxd48UUYMQL+33EnIiKShBKLW1gslhQNSUoNq9VKvFs8Pu4+973CULZs2WjYsCGTJ0+mV69eSb7cX758mSxZslCpUiUiIiJwc3MjNDT0nq/n4eFBQkJCiupu2rSJTp068cwzzwBw9epVwsPDU3ytwMBAQkJC2Lp1K7Vq1QIgPj7eNufgflSsWJGEhATOnTtHzZo10/y4m/n7+xMaGsq6deuoW7duktcd9V6J3K8bN+CTT8yk4soVs6xRI3ODu7JlnRubiIikf5q8nQFNmTKFhIQEHnnkERYtWsThw4c5cOAAkyZNsg0jql+/PtWrV6d58+asWrWK8PBwNm/ezNtvv82OHTtSfK3Q0FC2bdtGeHg4Fy5cuGNvRpEiRfjuu+/YvXs3e/bsoW3btinu/UjUu3dvxo4dy+LFi/nrr7947bXXHLK5XbFixWjXrh0dOnTgu+++4+jRo2zfvp333nuPFStWOPy4Ww0bNowJEyYwadIkDh8+zK5du/j4448Bx71XIvfKaoV586BkSXOo05UrUK4crF4NP/6opEJERFJGiUUGVLBgQXbt2kXdunV54403KFOmDGFhYaxbt46pU6cCZs/LihUrqFWrFp07d6ZYsWK0bt2a8PBwgoKCUnytfv364erqSqlSpciZM+cd50t8+OGHZM2alRo1atCsWTMaNmyY6p6GN954gw4dOtCpUyeqV6+Ov7+/rQfkfs2cOZMOHTrwxhtvULx4cZ566im2bdtmt9KVI4+7WceOHZk4cSJTpkyhdOnSNG3a1LaqlKPeK5F78fPPUK2aucldeLg51GnmTHP52JvWZhAREbkri3G/s2LTucjISAIDA7ly5QoBAQF2r924cYOjR49SsGBBvLy80iwGq9VKZGQkAQEB2mztPqgdHePmdoyNjX0gvwOZUVxcHCtWrKBJkyZJ5thkBAcPmhOzlywxn/v5wcCB0LevOUn7QcrobZleqB0dQ+3oGGpHx0gP7Xin79K30hwLEZGHyPnzMHw4fPopJCSAqyu89BIMGwbqIBMRkfuhxEJE5CFw/TpMnAhjxkBUlFnWrBm89545t0JEROR+KbEQEcnErFaYMwcGD4YTJ8yySpXg/fchmUXKRERE7pkSCxGRTOqnn8zN7H7/3XyePz+MGmVO1NY0JRERcTQlFiIimcz+/TBgACxfbj4PCIC33oJeveAu+zWKiIjcMyUWIiKZRESEOQl72jRzCJSbG7z6KrzzDuTM6ezoREQks1NiISKSwUVHwwcfmBOxo6PNsmeegbFjoVgx58YmIiIPDyUWIiIZVEICzJ5t9kicPm2WPfIITJgAjz/u3NhEROTho8RCRCQDWr3anJi9d6/5vGBBcynZ554Di8W5sYmIyMNJ64KIw1ksFpYkbuebQnXq1KFPnz73fe1OnTrRvHnz+z7P3cyaNYssWbKk+XVEbvXHH9Cwofmzdy9kyWL2UBw4AM8/r6RCREScR4lFBrZ582ZcXV1p1KhRqo8NDQ1l4sSJjg/KyT766CNmzZrl0HMm11bPP/88hw4dcuh1RO7k1Cno0gUqVDB7K9zd4fXX4cgR6NsXPD2dHaGIiDzslFhkYDNmzKBnz5788ssvHD9+3NnhOFVCQgJWq5XAwMAH0pPg7e1Nrly50vw6IlFRMGQIFC0KM2aAYZjDnQ4cMCdsZ8vm7AhFRERMSiwyqOjoaL755hteffVVmjZtmuxf6ZcuXUqVKlXw8vIiR44ctGjRAjCHHR07dozXX38di8WC5f9jJ4YNG0aFChXszjFx4kRCQ0Ntz7dv305YWBg5cuQgMDCQ2rVrs2vXrlTH3qFDB/z8/AgJCWHChAlJ6sTGxjJgwADy5MmDr68vjz76KBs2bLC9njgUadmyZZQqVQpPT0+OHTtmNxTqs88+I0+ePFitVrtzP/XUU3Ts2BGAI0eO8PTTTxMUFISfnx9Vq1Zl7dq1trq3a6ubh0IdPHgQi8XCX3/9ZXedDz74gNDQUAzDAGD//v00adIEPz8/goKCaN++PRcuXEhV28nDIz4ePv/cTChGjoTr16FGDdi8GRYsgMKFnR2hiIiIPSUWt2G9dg3rtWu2L4UARmysWR4bm3zdm77AGnFxZnlMzF3r3osFCxZQvHhxihcvzgsvvMDMmTPtYl2+fDktWrTgySef5Pfff2fdunVUqVIFgO+++468efMyYsQIzpw5w5kzZ1J83aioKDp27MimTZvYunUrRYsWpUmTJkRFRaX4HP3792f9+vUsXryY1atXs2HDBnbu3GlX58UXX+TXX39l/vz5/PHHHzz77LM0adKEI0eO2Opcu3aNMWPG8MUXX7Bv374kPQjPPvssFy5cYP369bayS5cusWrVKtq1awfA1atXadKkCWvXruX333+nYcOGNGvWzNYDlJK2Kl68OJUrV2bOnDl25XPnzqVt27ZYLBbOnDlD7dq1qVChAjt27GDlypWcPXuW5557LsXtJg8HwzA3titfHl5+Gc6ehSJFYNEi+OUXqF7d2RGKiIgkT6tC3cbBSpUBKLr5V9z+P9bg3xkzOD/xI7I824qQkSNtdQ899jjG9esUXrsWj7x5ALg0dy5nx4wloGlTQsa9Z6v7d736JFy6RKEfluJZtOg9xzd9+nReeOEFABo1asTVq1dZt24d9evXB2DUqFG0bt2a4cOH244pX748ANmyZcPV1RV/f3+Cg4NTdd0nnnjC7vlnn31G1qxZ2bhxI02bNr3r8VevXmX69Ol8+eWXhIWFATB79mzy5s1rq3PkyBHmzZvHyZMnyZ07NwD9+vVj5cqVzJkzh4oVKwIQFxfHlClTbPd1q2zZstGoUSPmzp1LvXr1AFi4cCHZsmWzPS9fvrzd8e+++y6LFy9m6dKl9OjRI8Vt1a5dOz755BNG/v9zcejQIXbu3MmXX34JwNSpU6lUqRKjR4+2HTNjxgzy5cvHoUOHKKbNBgT4/XdzpaeffjKfZ89uDoN65RXw8HBubCIiInejHosM6ODBg/z222+0bt0aADc3N55//nlmzJhhq7N7927bl2dHOnfuHK+88grFihUjMDCQwMBArl69muI5HkeOHCE2NpbqN/3ZNVu2bBQvXtz2fNeuXRiGQbFixfDz87P9bNy4kfDwcFs9Dw8PypUrd8frtWvXjkWLFhHz/56jOXPm0Lp1a1xdXQFzWNaAAQMoVaoUWbJkwc/Pj7/++ivVc1Zat27NsWPH2Lp1q+06FSpUoFSpUgDs3LmT9evX291PiRIlbG0iD7cTJ6BDB6hc2UwqPD1hwAD4+2/o1UtJhYiIZAzqsbiN4rvMoTkWb29bWfbOncnWoQO42TdbsV9/Met6ednKsrZtS5Znn4X/f4FNVGTd2iR1U2v69OnEx8eTJ08eW5lhGLi7u3Pp0iWyZs2K901xp5SLi4vdcCowewVu1qlTJ86fP8/EiRMpUKAAnp6eVK9endhbhofdzq3nT47VasXV1ZWdO3faEoDE8puP9/b2ts15uJ1mzZphtVpZvnw5VatWZdOmTXzwwQe21/v378+qVat4//33KVKkCN7e3rRq1SrF95MoJCSEunXrMnfuXKpVq8a8efN4+eWX7WJv1qwZ7733XrLHysMpMtLcHfvDD+HGDbOsXTsYNQoKFHBubCIiIqmlxOI2XHx8kpRZPDywJPOnw2TrurtjcXcHsJs8nFzd1IiPj+fLL79kwoQJNGjQwO61li1bMmfOHHr06EG5cuVYt24dL774YrLn8fDwICEhwa4sZ86cREREYBiG7Qv77t277eps2rSJKVOm0KRJEwBOnDiRqgnIRYoUwd3dna1bt5I/f37AnPdw6NAhateuDUDFihVJSEjg3Llz1KxZ03as1WolMjIyxdcCM/lo0aIFc+bM4e+//6ZYsWJUrlzZ7n46derEM888A5hDtW7uFYHk2yo57dq1Y+DAgbRp04YjR47YepQAKlWqxKJFiwgNDcXNTb92D7u4OHNi9vDhcP68WVa7Nrz/Pvx/KpSIiEiGo6FQGcyyZcu4dOkSXbp0oUyZMnY/rVq1Yvr06QAMHTqUefPmMXToUA4cOMDevXsZN26c7TyhoaH8/PPPnDp1ypYY1KlTh/PnzzNu3DiOHDnC5MmT+fHHH+2uX6RIEb766isOHDjAtm3baNeuXap6R/z8/OjSpQv9+/dn3bp1/Pnnn3Tq1AkXl/8+isWKFaNdu3Z06NCB7777jqNHj7J9+3bGjRvH6tWrU91m7dq1Y/ny5cyYMcM2L+Xm+/nuu+/YvXs3e/bsoW3btklWkUqurZLTokULIiMjefXVV6lbt65dj1L37t25ePEibdq04bfffuOff/5h9erVdO7cOUVJi2QOhgHffw9lykCPHmZSUby4WbZ+vZIKERHJ2JRYZDDTp0+nfv36BAYGJnmtZcuW7N69m127dlGnTh0WLlzI0qVLqVChAk888QTbtm2z1R0xYgTh4eEULlyYnDlzAlCyZEmmTJnC5MmTKV++PL/99hv9+vWzu8aMGTO4dOkSFStWpH379vTq1SvV+zmMHz+eWrVq8dRTT1G/fn0ef/xxu14EgJkzZ9KhQwfeeOMNihcvzlNPPcW2bdvsvqyn1BNPPEG2bNk4ePAgbdu2tXvtww8/JGvWrNSoUYNmzZrRsGFDKlWqZFcnubZKTkBAAM2aNWPPnj22VacS5c6dm19//ZWEhAQaNmxImTJl6N27N4GBgXZJlWRev/1m9ko0bw6HDkHOnDBlirl79lNPacdsERHJ+CxGSga9Z2CRkZEEBgZy5coVAgIC7F67ceMGR48epWDBgnjdx5yHu0kcwhMQEKAvkfdB7egYN7djbGzsA/kdyIzi4uJYsWIFTZo0wf3/wx6TEx4Ob70F8+aZz7284I03zMnZt/yT9NBKaVvKnakdHUPt6BhqR8dID+14p+/St9JgbxGRNHDpEoweDZMmQWys2SPRoQO8+y7ctLqyiIhIpqHEQkTEgWJjYepUGDECLl40y+rVMydm37KxvYiISKaixEJExAEMw9wd+803IXFrktKlYfx4aNRIcyhERCTzU2IhInKftmwx501s2WI+Dw6GkSOhU6ck296IiIhkWvpfHinbtE0kM9Jn//6cOeND69aufPed+dzHB/r3h379wM/PubGJiIg8aA91YpE4u/7atWv3tFO1SEZ37do1AK3YkUr//gsjRrgwZUo94uNdcHGBzp3NDe9y53Z2dCIiIs7xUCcWrq6uZMmShXPnzgHg4+Nj23HakaxWK7Gxsdy4cUPLpN4HtaNjWK1WYmJi+Pfff7lw4QJZsmTB1dXV2WFlCDduwCefmCs7XblitlnDhlbGj3ehbFknByciIuJkD3ViARAcHAxgSy7SgmEYXL9+HW9v7zRJXB4WakfHuLkds2bNavsdkNuzWmHBAnM/ivBws6xsWYOWLbfw1ltVcXdXoisiIvLQJxYWi4WQkBBy5cpFXFxcmlwjLi6On3/+mVq1amnIyX1QOzpGYjvWq1dPm+KlwM8/m3Mmtm83n+fJY/ZYtG4dz6pV550bnIiISDri1MRi6tSpTJ06lfD//wmwdOnSDBkyhMaNGwPmX1aHDx/O559/zqVLl3j00UeZPHkypUuXdngsrq6uaTYcxNXVlfj4eLy8vPSF+D6oHR0jsR01/OnODh40l45dssR87udnPn/9dXOSdhr9HUJERCTDcmr/fd68eRk7diw7duxgx44dPPHEEzz99NPs27cPgHHjxvHBBx/wySefsH37doKDgwkLCyMqKsqZYYtIJnb+PPToYe5BsWQJuLrCK6/A33/D4MFmUiEiIiJJOTWxaNasGU2aNKFYsWIUK1aMUaNG4efnx9atWzEMg4kTJzJ48GBatGhBmTJlmD17NteuXWPu3LnODFtEMqHr12HsWChcGCZPhoQEaNYM9u41d9IOCnJ2hCIiIulbupljkZCQwMKFC4mOjqZ69eocPXqUiIgIGjRoYKvj6elJ7dq12bx5My+//HKy54mJiSEmJsb2PDIyEjDHlafVHIq7Sbyus66fWagdHUPtaM9qhblzLQwd6sqJE+aiAJUqWXnvPSu1a5v7fCTXVGpHx1FbOoba0THUjo6hdnSM9NCOqbm2xXDyDll79+6levXq3LhxAz8/P+bOnUuTJk3YvHkzjz32GKdOnSL3TQvDd+vWjWPHjrFq1apkzzds2DCGDx+epHzu3Ln4aAyDiNzkjz9yMGtWaf75JwsAOXNe44UXDlCz5km0orGIiIi551Xbtm25cuUKAQEBd6zr9B6L4sWLs3v3bi5fvsyiRYvo2LEjGzdutL1+67KihmHccanRQYMG0bdvX9vzyMhI8uXLR4MGDe7aGGklLi6ONWvWEBYWpknH90Ht6BhqR9i/H956y5UVK8zsISDAYOBAKz16uOPtXQ4od9dzqB0dR23pGGpHx1A7Ooba0THSQzsmjv5JCacnFh4eHhQpUgSAKlWqsH37dj766CMGDhwIQEREBCEhIbb6586dI+gOg509PT3x9PRMUu7u7u70D3Z6iCEzUDs6xsPYjhERMGwYTJtmDoFyc4NXX4UhQyzkyOEKpH6lrIexHdOK2tIx1I6OoXZ0DLWjYzizHVNz3XTX2W8YBjExMRQsWJDg4GDWrFljey02NpaNGzdSo0YNJ0YoIhlNdDSMHAlFisBnn5lJRYsWsG8fTJoEOXI4O0IREZGMz6k9Fm+99RaNGzcmX758REVFMX/+fDZs2MDKlSuxWCz06dOH0aNHU7RoUYoWLcro0aPx8fGhbdu2zgxbRDKIhASYPRveeQdOnzbLHnkEJkyAxx93bmwiIiKZjVMTi7Nnz9K+fXvOnDlDYGAg5cqVY+XKlYSFhQEwYMAArl+/zmuvvWbbIG/16tX4+/s7M2wRyQBWrzZ3zN6713xesCCMGQPPPQd3mKYlIiIi98ipicX06dPv+LrFYmHYsGEMGzbswQQkIhneH39A//5mYgGQJYvZY9G9OyQz/UpEREQcxOmTt0VEHOH0aTOBmDkTDAPc3aFnT3O37GzZnB2diIhI5qfEQkQytKgoGD/enDdx7ZpZ9txzMHq0uYu2iIiIPBhKLEQkQ4qPhxkzYMgQOHvWLHvsMXj/fahWzbmxiYiIPIyUWIhIhmIYsGIFDBhgbnQH5jKy770HzzyjidkiIiLOosRCRDKM3383V3r66SfzefbsMHQovPwyeHg4NzYREZGHnRILEUn3TpwwJ2F//bXZY+HpCb17w6BB5qpPIiIi4nxKLEQk3YqMhLFj4cMP4cYNs6xdOxg1CgoUcG5sIiIiYk+JhYikO3Fx8PnnMHw4nD9vltWubU7MrlLFubGJiIhI8pRYiEi6YRiwdKk5MfvQIbOseHFzOdmmTTUxW0REJD1TYiEi6cJvv5kTszdtMp/nzGn2WHTtam52JyIiIumbEgsRcarwcHjrLZg3z3zu5QVvvGH2WgQEODU0ERERSQUlFiLiFJcumbtjT5oEsbHmMKcOHeDddyFvXmdHJyIiIqmlxEJEHqjYWJg6FUaMgIsXzbJ69cyJ2RUqODU0ERERuQ9KLETkgTAMWLQI3nwTjhwxy0qXNidmN2qkidkiIiIZnRILEUlzW7aY8ya2bDGfBwfDyJHQqRO46V8hERGRTEH/SxeRNHPkiNlD8e235nMfH+jf31z9yc/PubGJiIiIYymxEBGH+/dfcxL25MnmZncuLtC5s7l8bO7czo5ORERE0oISCxFxmBs34JNPzKTiyhWzrHFjGDcOypRxbmwiIiKStpRYiMh9s1phwQJzP4rwcLOsfHlzYnZYmFNDExERkQdEiYWI3JeffzbnTGzfbj7PkwdGjYIXXgBXV+fGJiIiIg+OEgsRuSeHDsHAgbBkifncz8+cqP366+YkbREREXm4KLEQkVQ5f96chP3ZZxAfb/ZKdOsGQ4dCUJCzoxMRERFnUWIhIily/Tp89BGMHg1RUWZZs2bw3ntQsqRzYxMRERHnU2IhIndktcKcOTB4MJw4YZZVrgzvvw916jg1NBEREUlHlFiIyG399JM5Mfv3383n+fObPRZt2ph7U4iIiIgkUmIhIkns3w8DBsDy5ebzgACzx6JXL/Dycm5sIiIikj4psRARm4gIGDYMpk0zh0C5ucGrr8KQIZAjh7OjExERkfRMiYWIEB0NH3xgTsSOjjbLWrSAsWOhaFHnxiYiIiIZgxILkYdYQgLMng3vvAOnT5tljz5qTsx+/HHnxiYiIiIZS6oSiytXrrB48WI2bdpEeHg4165dI2fOnFSsWJGGDRtSo0aNtIpTRBxszRoLb74Je/eazwsWNHsonn0WLBbnxiYiIiIZT4rWdTlz5gwvvfQSISEhjBgxgujoaCpUqEC9evXImzcv69evJywsjFKlSrFgwYK0jllE7sPBgzB8eDWefNKNvXsha1aYMAEOHIDnnlNSISIiIvcmRT0W5cuXp0OHDvz222+UKVMm2TrXr19nyZIlfPDBB5w4cYJ+/fo5NFARuX/nz0NYmBsREUG4uxv07Glh8GDIls3ZkYmIiEhGl6LEYt++feTMmfOOdby9vWnTpg1t2rTh/PnzDglORBzHMODFFyEiwkK+fJGsWeNN8eLuzg5LREREMokUDYW6W1Jxv/VFJO19/LG5L4Wnp8Ebb+ygUCFnRyQiIiKZSar3zp09ezbLE3fNAgYMGECWLFmoUaMGx44dc2hwIuIYe/ZA//7m43HjrISGRjk3IBEREcl0Up1YjB49Gm9vbwC2bNnCJ598wrhx48iRIwevv/66wwMUkftz7Rq0aQOxsfDUU/DKK1ZnhyQiIiKZUKr3sThx4gRFihQBYMmSJbRq1Ypu3brx2GOPUadOHUfHJyL3qW9fc8WnkBCYPl2rPomIiEjaSHWPhZ+fH//++y8Aq1evpn79+gB4eXlx/fp1x0YnIvflu+/gs8/MZOKrryBHDmdHJCIiIplVqnsswsLC6Nq1KxUrVuTQoUM8+eSTgLlyVGhoqKPjE5F7dOIEdO1qPh4wAOrVc248IiIikrmlusdi8uTJVK9enfPnz7No0SKyZ88OwM6dO2nTpo3DAxSR1EtIgPbt4dIlqFoVRo50dkQiIiKS2aW4x+Lzzz/nqaeeIjg4mE8++STJ68OHD3doYCJy78aOhY0bwc8P5s0Dd21XISIiImksxT0W8+bNIzQ0lEcffZTRo0ezf//+tIxLRO7Rli0wdKj5eMoUKFzYufGIiIjIwyHFicX69es5c+YMPXv2ZPfu3VSvXp3ChQvTt29fNmzYgNWqJSxFnO3KFWjb1hwK1bYtvPCCsyMSERGRh0Wq5lhkzZqVF154gW+++Ybz588zefJkbty4Qfv27cmZMycdOnTg22+/JTo6Oq3iFZHbMAx49VUID4eCBWHqVC0tKyIiIg9OqidvJ/Lw8KBRo0ZMmTKFEydOsGrVKkJDQxk5ciQffPCBI2MUkRT48ktzPoWrK8ydCwEBzo5IREREHiapXm72dqpUqUKVKlUYMWIEcXFxjjqtiKTA4cPQvbv5eMQIqFbNufGIiIjIwyfViYVhGHz77besX7+ec+fO2c2tsFgsLFq0CHctQSPywMTGmvMpoqOhTh0YONDZEYmIiMjDKNWJRe/evfn888+pW7cuQUFBWDSIW8Sp3nkHduyAbNnM3bVdXZ0dkYiIiDyMUp1YfP3113z33Xc0adIkLeIRkVRYuxbGjTMfT58OefM6Nx4RERF5eKV68nZgYCCFChVKi1hEJBXOnzd31wZ45RVo3typ4YiIiMhDLtWJxbBhwxg+fDjXr19Pi3hEJAUMA158ESIioFQpmDDB2RGJiIjIwy7VQ6GeffZZ5s2bR65cuQgNDU0yUXvXrl0OC05Ekjd5MixfDp6e5hKzPj7OjkhEREQedqlOLDp16sTOnTt54YUXNHlbxAn++AP69TMfjx8P5co5Nx4RERERuIfEYvny5axatYrHH388LeIRkTu4dg3atIGYGGjaFHr0cHZEIiIiIqZUz7HIly8fAdrSV8Qp3ngD9u+HkBCYMQPUYSgiIiLpRaoTiwkTJjBgwADCw8PTIBwRuZ3Fi+HTT81k4ssvIWdOZ0ckIiIi8p9UD4V64YUXuHbtGoULF8bHxyfJ5O2LFy86LDgRMZ08CV27mo/794f69Z0bj4iIiMitUp1YTJw4MQ3CEJHbSUgw96u4eBGqVIGRI50dkYiIiEhSqU4sOnbsmBZxiMhtvPcebNgAvr4wdy54eDg7IhEREZGkUjTHIjo6OlUnTW19EUne1q0wZIj5ePJkKFrUufGIiIiI3E6KEosiRYowevRoTp8+fds6hmGwZs0aGjduzKRJkxwWoMjD6soVaNvWHArVpg106ODsiERERERuL0VDoTZs2MDbb7/N8OHDqVChAlWqVCF37tx4eXlx6dIl9u/fz5YtW3B3d2fQoEF069YtreMWyfS6d4ejRyE0FKZO1dKyIiIikr6lKLEoXrw4Cxcu5OTJkyxcuJCff/6ZzZs3c/36dXLkyEHFihWZNm0aTZo0wcUl1SvYisgtvvoK5swBV1dzXkVgoLMjEhEREbmzVE3ezps3L6+//jqvv/56WsUj8tD7+2947TXz8bBhUL26U8MRERERSRF1L4ikI7Gx5ryKq1ehdm0YNMjZEYmIiIikjBILkXRkyBDYvh2yZjWHQ7m6OjsiERERkZRRYiGSTqxbB+PGmY+/+ALy5XNuPCIiIiKpocRCJB24cMHcXdswoFs3aNHC2RGJiIiIpI4SCxEnMwzo3BnOnIGSJeHDD50dkYiIiEjqpTqxCA0NZcSIERw/fjwt4hF56EyZAj/8AB4eMG8e+Pg4OyIRERGR1Et1YvHGG2/w/fffU6hQIcLCwpg/fz4xMTFpEZtIprd3L7zxhvl4/HgoX9658YiIiIjcq1QnFj179mTnzp3s3LmTUqVK0atXL0JCQujRowe7du1KixhFMqXr16FNG4iJgSefhJ49nR2RiIiIyL275zkW5cuX56OPPuLUqVMMHTqUL774gqpVq1K+fHlmzJiBYRiOjFMk0+nXD/btg+BgmDkTLBZnRyQiIiJy71K18/bN4uLiWLx4MTNnzmTNmjVUq1aNLl26cPr0aQYPHszatWuZO3euI2MVyTS+/96cWwEwezbkzOnceERERETuV6oTi127djFz5kzmzZuHq6sr7du358MPP6REiRK2Og0aNKBWrVoODVQkszh1ylwFCsxeiwYNnBuPiIiIiCOkOrGoWrUqYWFhTJ06lebNm+Pu7p6kTqlSpWjdurVDAhTJTBISzP0qLl6EypVh1ChnRyQiIiLiGKlOLP755x8KFChwxzq+vr7MnDnznoMSyazGj4f168HX11xa1sPD2RGJiIiIOEaqJ2/XrVuXf//9N0n55cuXKVSokEOCEsmMfvsN3nnHfPzJJ1C0qHPjEREREXGkVCcW4eHhJCQkJCmPiYnh1KlTqTrXmDFjqFq1Kv7+/uTKlYvmzZtz8OBBuzqGYTBs2DBy586Nt7c3derUYd++fakNW8SpIiPNpWXj4+H556FjR2dHJCIiIuJYKR4KtXTpUtvjVatWERgYaHuekJDAunXrCA0NTdXFN27cSPfu3alatSrx8fEMHjyYBg0asH//fnx9fQEYN24cH3zwAbNmzaJYsWK8++67hIWFcfDgQfz9/VN1PRFn6d4d/vkHChSATz/V0rIiIiKS+aQ4sWjevDkAFouFjrf8udXd3Z3Q0FAmTJiQqouvXLnS7vnMmTPJlSsXO3fupFatWhiGwcSJExk8eDAtWrQAYPbs2QQFBTF37lxefvnlVF1PxBm+/tr8cXWFuXMhSxZnRyQiIiLieClOLKxWKwAFCxZk+/bt5MiRw+HBXLlyBYBs2bIBcPToUSIiImhw03qcnp6e1K5dm82bNyebWMTExBATE2N7HhkZCZj7bsTFxTk85pRIvK6zrp9ZZMR2PHIEXn3VDbDw9tsJVK1qxdnhZ8R2TI/Ujo6jtnQMtaNjqB0dQ+3oGOmhHVNzbYuRTrbINgyDp59+mkuXLrFp0yYANm/ezGOPPcapU6fInTu3rW63bt04duwYq1atSnKeYcOGMXz48CTlc+fOxcfHJ+1uQOQW8fEWBg2qyeHDWSlV6gIjR/6Kq6uzoxIRERFJuWvXrtG2bVuuXLlCQEDAHeumqMdi0qRJdOvWDS8vLyZNmnTHur169Up5pDfp0aMHf/zxB7/88kuS1yy3DEg3DCNJWaJBgwbRt29f2/PIyEjy5ctHgwYN7toYaSUuLo41a9YQFhaW7L4fkjIZrR3fftuFw4ddyZLFYOnSQPLnb+LskICM147pldrRcdSWjqF2dAy1o2OoHR0jPbRj4uiflEhRYvHhhx/Srl07vLy8+PDDD29bz2Kx3FNi0bNnT5YuXcrPP/9M3rx5beXBwcEAREREEBISYis/d+4cQUFByZ7L09MTT0/PJOXu7u5O/2Cnhxgyg4zQjj/9ZO5ZAfDFFxYKF05/8WaEdswI1I6Oo7Z0DLWjY6gdHUPt6BjObMfUXDdFicXRo0eTfXy/DMOgZ8+eLF68mA0bNlCwYEG71wsWLEhwcDBr1qyhYsWKAMTGxrJx40bee+89h8Uh4kgXLpi7axsGvPQStGzp7IhERERE0l6qd952pO7duzN37ly+//57/P39iYiIACAwMBBvb28sFgt9+vRh9OjRFC1alKJFizJ69Gh8fHxo27atM0MXSZZhQJcucPo0lCgBd+jgExEREclUUr1BXqtWrRg7dmyS8vHjx/Pss8+m6lxTp07lypUr1KlTh5CQENvPggULbHUGDBhAnz59eO2116hSpQqnTp1i9erV2sNC0qVPP4WlS8HDA+bNg/9vxyIiIiKS6aW6x2Ljxo0MHTo0SXmjRo14//33U3WulCxIZbFYGDZsGMOGDUvVuUUetD//hMR1A957DypUcGo4IiIiIg9Uqnssrl69ioeHR5Jyd3f3VM0aF8lMrl+HNm3gxg1o3Bh693Z2RCIiIiIPVqoTizJlytgNVUo0f/58SpUq5ZCgRDKa/v3NHougIJg1C26zGrKIiIhIppXqoVDvvPMOLVu25MiRIzzxxBMArFu3jnnz5rFw4UKHByiS3i1dCpMnm4+//BJy5XJuPCIiIiLOkOrE4qmnnmLJkiWMHj2ab7/9Fm9vb8qVK8fatWupXbt2WsQokm6dPg2dO5uP33gDGjRwbjwiIiIiznJPy80++eSTPPnkk46ORSRDsVqhQwf491+oWBFGjXJ2RCIiIiLOc8/7WOzcuZMDBw5gsVgoVaqUbQM7kYfF+PGwbh34+JhLyyaz4buIiIjIQyPVicW5c+do3bo1GzZsIEuWLBiGwZUrV6hbty7z588nZ86caRGnSLry22/w9tvm448/huLFnRuPiIiIiLOlelWonj17EhkZyb59+7h48SKXLl3izz//JDIykl69eqVFjCLpSlQUtG0L8fHw3HPw4ovOjkhERETE+VLdY7Fy5UrWrl1LyZIlbWWlSpVi8uTJNNDMVXkI9OgBR45A/vzw2WdaWlZEREQE7qHHwmq14u7unqTc3d0dq9XqkKBE0qu5c80lZV1czMdZsjg7IhEREZH0IdWJxRNPPEHv3r05ffq0rezUqVO8/vrr1KtXz6HBiaQn//wDr7xiPh4yBB57zLnxiIiIiKQnqU4sPvnkE6KioggNDaVw4cIUKVKEggULEhUVxccff5wWMYo4XVycOa8iKgoefxwGD3Z2RCIiIiLpS6rnWOTLl49du3axZs0a/vrrLwzDoFSpUtSvXz8t4hNJF4YNg23bzKFPc+aA2z0v1CwiIiKSOd3z16OwsDDCwsIcGYtIurRhA4wZYz6eNs2ctC0iIiIi9lKUWEyaNCnFJ9SSs5KZ/PsvvPACGAZ06QKtWjk7IhEREZH0KUWJxYcffpiik1ksFiUWkmkYBnTtCqdOmRvgffSRsyMSERERSb9SlFgcPXo0reMQSXc++wyWLAEPD5g3D3x9nR2RiIiISPqV6lWhEsXGxnLw4EHi4+MdGY9IurBvH7z+uvl47FioWNG58YiIiIikd6lOLK5du0aXLl3w8fGhdOnSHD9+HDDnVowdO9bhAYo8aDduQJs25n8bNYLevZ0dkYiIiEj6l+rEYtCgQezZs4cNGzbg5eVlK69fvz4LFixwaHAizjBgAOzdC7lywaxZ5i7bIiIiInJnqV5udsmSJSxYsIBq1aphsVhs5aVKleLIkSMODU7kQVu2DBL3eZw9G4KCnBuPiIiISEaR6r/Fnj9/nly5ciUpj46Otks0RDKaM2fgxRfNx6+/bg6DEhEREZGUSXViUbVqVZYvX257nphMTJs2jerVqzsuMpEHyGqFDh3gwgVzonbihngiIiIikjKpHgo1ZswYGjVqxP79+4mPj+ejjz5i3759bNmyhY0bN6ZFjCJpbsIEWLsWfHzMpWU9PZ0dkYiIiEjGkuIei927dwNQo0YNfv31V65du0bhwoVZvXo1QUFBbNmyhcqVK6dVnCJpZscOeOst8/FHH5mb4YmIiIhI6qS4x6JSpUpUrFiRrl270rZtW2bPnp2WcYk8EFFR5tKy8fHQqhV06eLsiEREREQyphT3WPz6669UqlSJN998k5CQENq3b8/69evTMjaRNNezJ/z9N+TPD59/Dlp/QEREROTepDixqF69OtOmTSMiIoKpU6dy4sQJ6tevT+HChRk1ahQnT55MyzhFHG7ePHNJWRcXmDMHsmZ1dkQiIiIiGVeqV4Xy9vamY8eObNiwgUOHDtGmTRs+++wzChYsSJMmTdIiRhGHO3oUXnnFfPzOO/D4486NR0RERCSju689hQsXLsybb77J4MGDCQgIYNWqVY6KSyTNxMdDu3YQGQmPPQZvv+3siEREREQyvlQvN5to48aNzJgxg0WLFuHq6spzzz1HF818lQxg+HDYsgUCA80hUG73/FsgIiIiIolS9ZXqxIkTzJo1i1mzZnH06FFq1KjBxx9/zHPPPYevr29axSjiMBs3wqhR5uPPP4cCBZwbj4iIiEhmkeLEIiwsjPXr15MzZ046dOhA586dKa4F/yUDuXgRXngBDAM6d4bnnnN2RCIiIiKZR4oTC29vbxYtWkTTpk1xdXVNy5hEHM4woGtXOHkSihUzN8ITEREREcdJcWKxdOnStIxDJE1NmwaLF4O7u7nMrJ+fsyMSERERyVzua1UokYxg/37o08d8PGYMVKrk1HBEREREMiUlFpKp3bgBbdrA9evQoAG8/rqzIxIRERHJnJRYSKY2cCD88QfkyvXfLtsiIiIi4nj6miWZ1vLlMGmS+XjWLAgOdmo4IiIiIpmaEgvJlM6cgU6dzMd9+kDjxs6MRkRERCTzU2IhmY7VCh07woULUL48jB3r7IhEREREMj8lFpLpfPABrFkD3t7m0rKens6OSERERCTzU2IhmcrOnfDWW+bjjz6CkiWdG4+IiIjIw0KJhWQaV6+aS8vGxUHLluZO2yIiIiLyYCixkEyjVy84fBjy5TN32rZYnB2RiIiIyMNDiYVkCgsWwMyZ5j4VX38NWbM6OyIRERGRh4sSC8nwwsOhWzfz8eDBUKuWU8MREREReSgpsZAMLT4e2raFyEioUQOGDHF2RCIiIiIPJyUWkqGNGAFbtkBgIMyZA25uzo5IRERE5OGkxEIyrJ9/hlGjzMeffgqhoU4NR0REROShpsRCMqRLl+CFF8xdtjt1gtatnR2RiIiIyMNNiYVkOIYBL70EJ05A0aLw8cfOjkhERERElFhIhjNjhoVFi8DdHebNAz8/Z0ckIiIiIkosJEM5ccKPvn1dARg9GipXdnJAIiIiIgIosZAMJCYGJkyowvXrFsLCoG9fZ0ckIiIiIomUWEiGMXiwC+HhgeTIYTB7trnLtoiIiIikD/pqJhnCjz/CpEnmEKgvvkggJMTJAYmIiIiIHSUWku5FREDHjubjpk2P0KSJ4dyARERERCQJJRaSrlmtZlJx/jyUK2fQocN+Z4ckIiIiIslQYiHp2sSJsHo1eHvDl1/G4+FhdXZIIiIiIpIMJRaSbu3aBW++aT7+8EMoVcq58YiIiIjI7SmxkHTp6lVo0wbi4qBFC+jWzdkRiYiIiMidKLGQdKl3bzh0CPLmhWnTwGJxdkQiIiIicidKLCTd+eYbmDHDTCa+/hqyZXN2RCIiIiJyN0osJF05duy/YU+DB0Pt2s6NR0RERERSRomFpBvx8dCuHVy5AtWqwZAhzo5IRERERFJKiYWkG+++C7/+CgEBMHcuuLs7OyIRERERSSklFpIubNoEI0eajz/9FAoWdG48IiIiIpI6SizE6S5dModAJe6y3aaNsyMSERERkdRSYiFOZRjmZO0TJ6BIEfj4Y2dHJCIiIiL3QomFONWMGfDtt+DmZs6r8Pd3dkQiIiIici+UWIjT/PUX9OplPh41CqpWdW48IiIiInLvlFiIU8TEmHMprl2D+vWhXz9nRyQiIiIi90OJhTjFoEGwezfkyAFffgku+iSKiIiIZGj6OicP3MqV8OGH5uOZMyEkxLnxiIiIiMj9U2IhD9TZs+aSsgA9ekDTps6NR0REREQcQ4mFPDBWK3TqBOfOQdmyMH68syMSEREREUdxamLx888/06xZM3Lnzo3FYmHJkiV2rxuGwbBhw8idOzfe3t7UqVOHffv2OSdYuW8ffWQOg/Lygvnzzf+KiIiISObg1MQiOjqa8uXL88knnyT7+rhx4/jggw/45JNP2L59O8HBwYSFhREVFfWAI5X79fvvMHCg+fjDD6FUKefGIyIiIiKO5ebMizdu3JjGjRsn+5phGEycOJHBgwfTokULAGbPnk1QUBBz587l5ZdffpChyn2IjjaXlo2Lg+bNQW+diIiISOaTbudYHD16lIiICBo0aGAr8/T0pHbt2mzevNmJkUlq9ekDBw9CnjzwxRdgsTg7IhERERFxNKf2WNxJREQEAEFBQXblQUFBHDt27LbHxcTEEBMTY3seGRkJQFxcHHFxcWkQ6d0lXtdZ13emRYssfPGFGxaLwcyZCQQEGNxrMzzM7ehIakfHUDs6jtrSMdSOjqF2dAy1o2Okh3ZMzbXTbWKRyHLLn7cNw0hSdrMxY8YwfPjwJOWrV6/Gx8fH4fGliGGQffVqfj10mGuFC4Grq3PieMDOn/emT586ALRseZhr1w6wYsX9n3fNmjX3fxJROzqI2tFx1JaOoXZ0DLWjY6gdHcOZ7Xjt2rUU1023iUVwcDBg9lyE3LSD2rlz55L0Ytxs0KBB9O3b1/Y8MjKSfPny0aBBAwICAtIu4DuIPnCAMz+tB49fKfTzRlx8fYG7J0kZWXw8hIW5Eh3twiOPWJk9uyDu7gXv65xxcXGsWbOGsLAw3N3dHRTpw0ft6BhqR8dRWzqG2tEx1I6OoXZ0jPTQjomjf1Ii3SYWBQsWJDg4mDVr1lCxYkUAYmNj2bhxI++9995tj/P09MTT0zNJubu7u9PeEHdvby4/8gj58uTBM0sWW/mpvn0x4uLI0b07XiVKOCW2tDJ6NPz6K/j7w7x5Lvj4OG46jzPfy8xE7egYakfHUVs6htrRMdSOjqF2dAynfo9NxXWdmlhcvXqVv//+2/b86NGj7N69m2zZspE/f3769OnD6NGjKVq0KEWLFmX06NH4+PjQtm1bJ0adeh6hoZxr2YIqTZrYyqzR0UStXYcRG0uOnj1t5XHnzgHgnivXA4/TUX79FUaMMB9PnQqFCjk3HhERERFJe05NLHbs2EHdunVtzxOHMHXs2JFZs2YxYMAArl+/zmuvvcalS5d49NFHWb16Nf7+/s4K2WEsPj6Ezp9H9JateBYtaiu/OHs2F6fPIMdrr5KzVy8nRnhvLl+Gtm3NXbbbt4d27ZwdkYiIiIg8CE5NLOrUqYNhGLd93WKxMGzYMIYNG/bggnpALBYLXqVK4XXLTnHxEWcB8CxW/L+yS5e49NXX+DcIS9dDpgzD3KPi+HEoXBgmT3Z2RCIiIiLyoKTbfSweVnkmvE+RjRvwq1PbVnb1p5+4MGUKp996y4mR3d3MmfDNN+DmBvPmmfMrREREROThkG4nbz/M3G9Z9co9Tx786tfDp2IlW5lhtXK0VSu8S5chZ9/Xccua9UGHaefgQUicKvLuu1C1qlPDEREREZEHTIlFBuBbrRq+1arZlV3fs4eY/QeIO36C4HfetpXHHj+OW/bstiVtH4SYGGjTBq5dgyeegP79H9ilRURERCSdUGKRQXmXLk2+L74g/mwEFg8PW/mZwW9z/Y8/yDPhffzr138gsQweDL//Dtmzw1dfgYsG2ImIiIg8dJRYZFAWDw/8Hn/MrswaG0v8+fMYMTF4lihpK7++dy/X9/yBf/16uP9/40FHWbUKJkwwH8+cCblzO/T0IiIiIpJBKLHIRFw8PCj04wpij4bjkTePrfzyokVcnr+AmMOHCRk+zGHXO3cOOnY0H3fvDs2aOezUIiIiIpLBaNBKJmOxWPAsVNCuzLtMGbwrVcK/QZitLO70aY40bcr5SR/fccnf27FaoVMnOHsWypSB8ePvN3IRERERycjUY/EQyNKqFVlatbIri1q7lti/j3At63YsFoutPOaff/AoUACLq+sdz/nxx/Djj+DlZS4t6+2dJqGLiIiISAahxOIhFdi8Oa5Zs+IaEGArM2JjCX++NRY3N0IXzMcjf/5kj929GwYMMB9PmGD2WIiIiIjIw02JxUPKNSCAwFsmRcSEh2NxcQFXV9zz5rWVR65ZA3Fx+NaqzQ2LL23aQGwsPP00vPrqg45cRERERNIjJRZi41WsGEV/2UTsyZNmgvF//079lBv79xPy7kgGrG7FX3+Zqz998QXcNIpKRERERB5imrwtdizu7ngW/G/yt5GQgO9jj+FRuDDro59g2jQzmVjYbw3RfdpzZelSJ0YrIiIiIumFEgu5I4urK7ne6IvHp8vo3CcbAG++CQVOrebajh3c+Ougra5hGMT8c/SeVpkSERERkYxNQ6HkrhIS4IUX4PJleOQRGD4cjLN98C5bBp9q1Wz1Yv/+m3+aPYVniRIUXPTtXVeWEhEREZHMQ4mF3NXo0fDzz+DvD3Pngrs7kDcP2RJ3x/u/G38dxOLujntQkF1ScWn+AjxCC+BTpQoWN33kRERERDIjfcuTO9q82eyhAJgyBQoXvn3dwGZN8atbh4TLl21l1uhozo4ejREbS8Hvv8ereLE0jVdEREREnEOJhdzW5cvQtu1/Q6FeeOHux7j6+eHq52d7nhAdTUCzpsT+fQTPYkVt5ecnTybm4CGydeyAT+XKaRC9iIiIiDxISiwkWYYBr7wCx45BoUIwefK9ncc9Vy5yjxp1y7kNrixdStyx4wQ0bmQrt0ZHY71+HbccOe4ndBERERFxAq0KJcmaPRsWLAA3N3NexU0bdDtEngkfkP3ll/GtWctWFrlyFYdr1uLMO+849mIiIiIikubUYyFJHDoEPXqYj0eMgEcfdez5LRYL3mVK412mtF15zKFDYBi4BQfbygyrlYszZuBbsxYuBUMdG4iIiIiIOIx6LMRObKw5ryI6GurWhQEDHty1gwa9SZH1P5H1+edtZdf37OHc+xM41q4dxMc/uGBEREREJFXUYyF2Bg+GnTshe3b46it40FtRuIeE2D23uLnhV7curtmyYnF3t5WfeqMfLgH+ZO/SFY+8eR5skCIiIiKShBILsVmzBt5/33w8fTrkSQff173LliXf1CkYhkH8/3ssEi5eJPLHH8FqJXuXrra68f/+i4uPDy7e3s4KV0REROShpaFQAsD589Chg/n41Vfh6aedG8+tLBaL7bGLvz/5Pp1Kjh497Horzn/8MYeq1+DSvHnOCFFERETkoaYeizQWE5/As59txS/OheidJ6lYIDtFc/nh5pp+cjrDgBdfhIgIKF0aJkxwdkR3ZnF3x69WLfxq1bIrj/nrIMaNG7jnzWsrizt7lqs//YRfvXq458r1oENNl1x+7E+Vo/tw2foP5HsEQsqDp9/dDxQRERG5AyUWaeyvM1H8cTIScGHzkv0AeLu7UiZPAOXyZqFc3kDK581Cgew+dn+Vf5A+/hiWLwdPT5g3DzLqSKIC8+YSc+AAnkWK2MqiVq3i7Ogx+CxfQYGvv3JidOmHy6EV5Ll6Ftb9ZhZYXCBHcchTyfzJXQmCyoCbh3MDFRERkQxFiUUaC83uy6Tny7Fk026iPbPz56lIomMT2B5+ie3hl2z1svi4UzaPmWSUyxtI+XxZCArwSvP49uyB/v3NxxMmQNmyaX7JNGOxWPAqVcquzC1HDrzLl8e/QZitzIiN5VjHTvhWr072l7o+XHMyDIOEp6ZwaP18SvhH43JmN0SdhvMHzJ/dc8x6rh5mcpGnEuSpbCYbOYqCywOezS8iIiIZhhKLNBbo407jMsEYx600aVIVF1c3/jl/lT0nr/DHycvsOXmFA6cjuXwtjk2HL7Dp8AXbscEBXrYko1zeQMrlyUKgj/sdrpY6165B69bmErPNmsFrrzns1OlGQJMmBDRpgmEYtrLobb9x/fffiT1xghw9utvK486ewy1HdiwPeimsB8liwShYm8MHoinapAku7u4QFQGndsGpnXB6l/n4xmXz8eldsP0L81gPPwipAHkq/pdsZMkPTuppExERkfRFicUD5upioWiQP0WD/GlV2ZwLEBtv5a+ISDPZOHGZP05e4fC5KCIibxCx/war95+1HV8wh6+ZZOTNQoV8gZQKCcTb496+CPftC3/9BSEhMGNG5v5+ePMwM+/y5QgZOwbjRgwWl//mupx89VXizp0j76SP8KlUyRlhOod/MJRoYv6AOenm0tH/Jxv/Ty7O7IHYq3DsF/MnkU92M8HIU/m/YVR+OZ1zHyIiIuJUSizSAQ83l//Pt8gC1QoAEB0Tz5+nrvDHySvsOXmZPScvc+LidY5eiObohWi+330aMBOVYkH+lP9/slE+XyDFgvxxv8vk8O++g88+M5OJr76CHDnS+i7TD9eAALI0b25XlnDlCrEnT2K9ehWP0FBb+fU9e4g7E4Ffzcdx8fV9sIE6i8UC2QqZP2VbmWUJ8XDhoNmrkZhsnN0H1/6Fv9eYP4kC8/2XZOSpZPZyeAU45VZERETkwVFikU75errxaKHsPFoou63sf+3dd3yV5f3/8dd99skZ2YOEDPZegqIijoqIOGutCoq11EHROkvd1doW19dRteLXam37tY7+WkfdggNQW0T2kk12CElIzjlJzr5/f9wnZ5AAQQInCZ/n43E/zjlX7nPOdS5CznmfazU0+1lbofVorCnXhlHVeXxsqnaxqdrF68vLATAbdIzId0Z6NbRhVCWZNnQ67Vv78nK4JrL9w69+BWeeedRfXrejT01l8JdL8W7ahCEjI1re8H+v4HrvPTJmzyb3V/OSWMMk0xsgd4R2HBdZlzjghZp1seFTVSuhbgs0lWvHxncid1a0+Rltw6cKIpPDjUd+DpEQQgghjh4JFj1Ihs3E6UNyOH2ItmyqqqpUN3mjczXWlDeyrqIJty/IyrJGVpY1Ru/rsBgY3TeVUflp/OtPabiCqUw43sJvf9uLxz8dIsVkwjpmTEKZqX8/jIWFOKbE0pdv2zZqfvs7nNOnk37ZpUe7mt2H0QKFx2tHG28TVK2OCxurtJBRt0U71kT2GNEZtZAS37ORPVQmhwshhBA9mASLHkxRFPLTrOSnWZk2sg8A4bDKzvpmLWyUa8OoNlS5cHuDfLWtnq+21cMQ6DsEQlYzP381shJVYRqjC1JJt8kSo/Gy584l6+c/TyhzL1xIy7Jl6CyWhGARqK2VvTIsqdD/NO1o46mN9Wi0TRJvbYDq1drBn7XzjCmRyeHHQf447TK9X++e/COEEEL0IhIsehmdTmFAtp0B2XZ+OE6bHB4Ihdlc4+btJU384f8aMeY1Ysnx0NDqY9GmWhZtqo3evygjhTGFadE5GyMLnKSYju1fk333F3GefwGK2YKpf79oWbi5me1TzsJYWEjxK/+HIT39aFez+7LnwJBp2gHa5PDG0riwsUrr2Qg0Q9nX2tHGmh7r0Wi7dOQl53UIIYQQ4oCO7U+MxwijXkehPZWX7k6lblcRM2fCn34TYmN1E6sjq1CtrWhkV30LZQ3a8e4abXK4ToFBOQ7GFEYmh/dNY0ieA5Oh++wcfrSZ+haQOfunCWXejRtRw2HUQAB9Wlq03P3Z5+jsNlLGj+/dy9geCkWB9BLtGHmxVhYOaUOlomFjBdSsh9a9sP1T7WjjLIj1aORHejesaUl4IUIIIYSIJ8HiGKCq8POfw65d0K8fLFgAKWY9E0oymFASm6jc2OKPhoy2fTZ2u3xs3u1m8243//i2AtBWsRrWx8nYuJWo+mfZo5PDj0Upxx/P4K+/IlBREe3hUFWV3Y88TKC0jIKnnsI57ewk17Ib0+khZ5h2jLtCKwv6YPf62FyNyhWwZzO4KrXju/di988cGOvRKBgPeaPAeAxtfCiEEEJ0AxIsjgF/+xu89hro9fDqq+Dcz8qfaSkmTh2czamDY/sQ1DR5WVPRmLAalcsb1FalKm8ESgGwmw2MKkhldGFs9/CCNGu7YUS9md7pRB+387fq9ZIy7jiaW73YTjklWt70/vt4Pv2U1B/9CPukScmoas9gMEf2xxgfK/O5tT014jf0ayyD+m3ase4f2nk6gxZS4vfYyB6mrW4lhBBCiCNC3mV7ua1b4YbI5tIPPggnnnho989LtZCXmsfZI7Rx7aqqUlrfou2tUa71aqyvasLjC/KfHfX8Z0d99L5ZdlNkf45Y2Mi0m7vqpXV7OquV/IcfQg2HEzbic733Pp7PP8c0YEA0WKjhMKHGxoSlbkUHzA4oOUU72jTXxXo02oZSNe/RlsKtWQcr/6qdZ7BCn9GJYSOjv0wOF0IIIbqIBItezO+HmTOhuRlOPx3uuOPwH1NRFEqybJRk2bhwbAEAwVCYLbs9CUOovqtxU+fx89l3tXz2XWxyeN90azRkjClMY2RBKnZz7/41jA8VAFlzf4554ACc55wTLWtds4bSK67EftppFC547mhXsWezZcGgs7QDtLF/TRWxuRqVK7UlcP1uKF+mHW0sqZH5GnF7bDjzk/IyhBBCiJ6ud3+iO8bddx98+y1kZGi7ax+pucMGvY7h+U6G5zu5/AStzBsIsaHKFRtCVdHIjj3NVOxtpWJvK++vqwa0L4sHZtujczXG9E1jaB8HZkPvnehsHTUK66hRCWWtq9dAOIzOmjgvoPHtt7GOGoV5wICjWcWeTVEgrVA7hl+olYXD2lCp+LBRs07bd2PHF9rRxp4X6dEYF5scniI9SUIIIcTBSLDopRYtgkcf1a6/9BL07Xt0n99i1DO+OJ3xxbFlV5taA6yv1ELG2sgeG9VNXrbWetha6+FfK7XJ4Ua9wrA+TkZHJoePLUxjQLb96L6Aoyzzp1fjOOss1IA/Whbcu5fqu++BcJiBn32KMV++Sf/edDrIHqwdYy7XyoJ+qN0Ym6tRuQr2bAJPDWx+XzvapPeLDZ/KP04bUqXIni9CCCFEPAkWvdCePTBrlnZ9zhy46KKkVicq1Wpk0sAsJg3MipbVur2sjczVWB0ZRtXYEoisTtUElAFgM+kZnu/E7tPBuhqOK8mkb3rvmhxu6luQcDvU2IjtlEmEmpoSQsWeZ54l1NhI+ozLMQ8ceMjP88zqZ9jQsoGG7xoYkD6AIkcRBY4CjDrjYb+GHsVggvyx2sHPtDJ/c2xyeNuGfnt3xo71/9TOU3QYsocxNpSFbmWttvt47gjQH2NtKIQQQsSRYNHLqCr89KdQUwPDh8Pjjye7RgeW47AwZbiFKcNzAW1yeHlDa3QlqjXlTayvaqLZH2L5rr2Ajs//sRaADJuJUQWpCRv6ZTt6z+Rwc79+FL3wAmo4HC1Tw2H2/uMNQnvqsJ9+WjRYhFtaQKdDZ7Ec9HE/Kf2ESn8l36z8JlqmV/Tk2/MpdhZT7CymyFEUvd7H1ge9rvcOTUtgskHxydrRpqUhbiO/yFAqz26U2g0UA3y4WDtPb46bHB7p2cgcqPWWCCGEEMcACRa9zB//CO+/D2aztsRsSkqya3RoFEWhKDOFoswUzh+jfUsfCqtsq/WwsrSe975eR5M+jc273TQ0+1m8ZQ+Lt+yJ3j8/1RKZr6GFjZF9U3Faeva3yAmTv1WVPr/9LZ7Pv8A2cWK0uPGf/6L2qafInD2b7BtvOODjXT/qehatWoQpx0SZp4xydzmtwVbK3eWUu8v5svLLhPONOiN9HX0pdkRChzMWOnJSctApvfyDc0oGDJyiHaCld1cVwbLl7PjynwxMcaGrWg2+JqhYrh1tzM5Ir0hc2EjtKytRCSGE6JUkWPQia9fCL3+pXX/sMRg9Orn16Sp6ncKQPAf9My2k1Kxh+vQTCaHjuxq3NoQqsnv49j0eqpq8VDXV8NGGmuj9+2fbGBtZiWp0YRrD+zixGHvmN/CKXo/j9NNxnH56QnnLypWoLS3o7LZomer30/jOOzjOOANDVmz42Xn9z0P3nY7pk6djNBpRVZXallrK3GXscu2izFVGqauUMlcZZe4yAuEAO5t2srNpZ7v6WPQWCp2F0dARHzwyLZm9aqhalKJAagHq0Bw27VDoN306Or0eGnbEhk9VrdSGVPlcsHOJdrSx5cRCRtulLTN5r0cIIYToIhIseomWFpgxA3w+OO88uPHGZNfoyLIY9Ywt1CZ2X3WSVub2Blhf6UoYRlXZ2MqOPc3s2NPMm6sqATBEgkr8EKpBOXYM+p77zXvBk0/g/dnPMOb3iZY1f7Ocmvt+TV12NgOXLN7vh3xFUci15ZJry+X4vOMTfhYKh6hpqYkGjVJXqXbdXUaluxJvyMvWvVvZundru8e1GW3RIVXxvRzFjmLSLGld+vqTTqeDrIHaMfpSrSwUgNpNiWFj90ZoroUtH2lHm7TiuLAxHvqMAXPvXrBACCFE7yPBope4/XbYuBH69IE///nYHGnhsBg5aUAmJw2Ifftb5/FFQ0bb0rf1zX42VLnYUOXi1ciWBlajnpEFzoQN/YozU3rMN+6KomAdNTKxUA1jGTUKy/DhCa9j9113k9nsIXzqqZCezoHodXoK7AUU2As4Of/khJ8FwgGqPFUdho4qTxXNgWY2NWxiU8Omdo/rNDkTezjihlk5TI7v3xDdid6ozbnoMxrGX62V+Vu0ZW7bwkblCmjYDo2l2rHhLe08RQdZQ7Sw0RY4ckdqE86FEEKIbkqCRS/w1lvw/PPa9b/9DbKzk1uf7iTLbuYHQ3P5wdDY5PDKxtZo0FhT0ci6itjkcG2CuCYtxahNDo+EjbGFaeQ4Dz45uruwT56MffJk1FAoWhaorMT93ntkQsLGJnULFtD4z3+RfsUVZM7+abS8ZeVKjPn5GHJy2m30Z9QZo+FgX/6Qnwp3RWxolVsLH7tcu6htqcXld7Gubh3r6ta1u2+GJSPWuxE3kbzQUUiKsYdNGtqXKQWKJmpHm9a92gZ+0bCxEtxV2tK3ezbB6r9r5+lNWrgoOC62oV/WIDhWJtYLIYTo9iRY9HAVFXDNNdr1efNgypTk1qe7UxSFvukp9E1P4dzR2rChUFhlxx5PdNfwNRVNbKpy0dgSYOnWOpZurYveP89pie4aPrpvKqML0khN6d6Tw5W4AKFLTSXnwQfZ/MknCZvx+XeVEqisRA0EomUhl4vSmVcAMGTVSpTI+e7PPse3ZQu2k0/Cup+JPCa9if5p/emf1r/dz1oCLZS7yylzx/VyRHo86r31NHgbaPA2sKp2Vbv75qTkRMNGibMkOsSq0FGISd9Dv823psOAM7Sjjbsm1qPRFji8jdr1qpWw/EXtPJMd+oxN7NlIKzo2uyyFEEIknQSLHiwU0varaGiACRPgd79Ldo16Jr1OYVCug0G5Di4Zr+0k6A+G+a7GpYWNyOTwrbVualxeajZ6+WTj7uj9+2XZ4jbzS2V4n1Sspu75LbLebsf5w4vYY078EJ7zq3mkXXYphpzcaFlo716Mffui+v0JIcT9ySc0vf02QDRYhFwudl0+A2NBAYULnkMxaH9aArW1KEYj+rS06HCsFGMKQzKGMCRjSLv6efyeaO9GQuhwl9Lka6K2pZballqW1yxPuJ+CQr49nyJHUeJ8Dmcx+fb8nrdHhyMPhk7XDtBWotq7M9aj0TY53O+B0i+1o01KZmyuRlvYsEs3phBCiCNPgkUP9sgj8MUXYLPBq6+CqYd+YdsdmQy6yHyLNDhRG+rT7AuyvlLbuG9NZBhVeUMrO+ua2VnXzDurqwAtqAzOdUQnho8pTGVwrgNjN54cbsjMxJCZuDKRqbiYgYsWJuyjAZASWebWOibWWxGorMS/YwehxsZoqADY8+RTNL31Ftm33UbWddcC2p4be9/4B8a+BTimTEmY/2E32RmROYIRmSPa1bHR25gQOtqGVpW5y2gONFPpqaTSU8l/qv+T+NoUQ+IeHW1zOlKLyUvJ6xl7dCgKZPTXjlGXaGWhINRtTuzZ2L0BWuph20LtaJNamLgSVZ+xYHEm5aUIIYTovSRY9FD//S/8+tfa9T/+EQYNSm59jgU2s4GJ/TOZ2D/2Abyh2R+dFL6mXBtGVefxsanaxaZqF68vLwfAbNAxIt8Z6dXQhlGVZNrQ6br/kJV951ak/fAi0n54UUKZqaiIopf/TLi5OaE87PEAYOwTW63KX1ZG7SOPoE9Px3nWWdHyPX/8I95Nm0ifMQP7pEkAqMEgqs+HzmYjzZJGmiWNMdljEp5DVVXqvfXtJpC3hQ9vyEuZW1s6d2nl0oT7GnVGCh2FFDnjhlY5tPCRm5LbvSfv6w3abt+5I+C4WVpZwAu712tBo61no24LNJVrx8Z3IndWIGtwYtjIHQnGnjOHSAghRPcjwaIHamqCmTO1oVAzZsBVVyW7RseuDJuJ04fkcPqQHED7kFvd5I3O1VhTrk0Od/uCrCxrZGVZY/S+DoshOoRqTKRnI89p6d4fZvdDZ7NhO+mkduV9n3masM+XUKYYDDinn4NiTvwQ2/LNclqWLcM5dWq0zLd9OzsvvAhTSQkDPvowWt7832Wofh+WESMwZGaSZc0iy5rFcbnHJTxmWA1re3REhlOVNpVGez3K3eUEwgF2NO1gR9OOdnW3GqwUOgrb7URe5Cwi09JN950wWqDvBO1o421KnBxetUoLGXWbtWPNa9p5OqMWUuLDRvZQmRwuhBCi0yRY9EA33AA7d0JJCSxYIPM0uxNFUchPs5KfZmXaSO1b+nBYZWd9c3TZ2zUVjWyocuH2BvlqWz1fbauP3j/bYWZMZLnb0YVpjC5IJd3Ws8e46czmhNvmgQMpeOKJdudlzZ2Lb+pZWMeNi5YFqqu1x7DZEs6tW7CAlmXLyH/0EVIvuAAAf2kpe/7wNOYhQ8i6/jrtfoqOXGsOebY8TuhzQsJjhMIhqpur261aVeYqo9JTSWuwlS17t7Bl75Z2dbUb7RQ6CjE0GyhdW0q/tH7R4JFqTv0erXQEWVKh/2na0cZTG+vRaLtsqYfq1drBn7XzjCmxyeH547TL9H7yR0cIIUSHJFj0MP/3f/D3v2srhb76KqR2s88woj2dTmFAtp0B2XZ+OE6bHB4Ihdlc444bQtXI1loPe9w+Fm2qZdGm2uj9izJSEjbzG1ngJMXU+/7r2iaegG1i4od/x+mnM/jb5YRdroRyU78SQo2NmIpjS936tm/H9cEHWEpLo8ECoPyaa/Bt30Gf3/0W++TJAAT37sW3eQu5hX3pW3AyJ7P/PTr2XbmqurkaT8AT3Z9j3frEJXNTzakJ+3LETyS3GRMDUtLYc2DINO0AbXJ4Y2lc2FilBQy/B8q+1o421vTEXcMLjtMmmwshhDjm9b5PJ73Ytm0wd652/YEHoIORJ6KHMOp1jCxIZWRBKjMnFgHQ6g+xoaqJ1ZFVqNZWNLKrvoWyBu14d402OVynwKAcB2MKY8OohuQ5MBm67+Tww6G329HbE3eh7vPAA+3OMw8YQM6vfoXOkXiuv7yC4O7d6FJie2C0rlpNxdy5WIYPp9+b/4qW17/0EmGvl9Tzz6e4qOM9OnwhHxXuCnbs3cHH33xMSkEKFc0VlDaVUttaS5OvibW+taytW9vuvpmWzHaBo20lK6vB2u78o0ZRIL1EO0ZerJWFQ9r8jPiejZp12r4b2z/VjjbOgliPRsF47bpFvvUQQohjjQSLHsLv1+ZVeDxw2mlw113JrpHoalaTngklGUwoyYiWNbb4oyGjbZ+N3S4fm3e72bzbzT++rQC0VayG93EmrETVP8veIyaHdxVTcXHC5n5tSl5/jUBlJeYBA2KF4RCmkhJM/RP32dj7+hsEysuxTZyIqUgLfJ6lS6n57e+wTTqZPvffj1lvZkDaAPJqAvj8Y5h6wmWYIkuyte3R0TaBfFfTruhE8gZvA/Xeeuq99aysXdmunrkpue12Ii92FtPX0Tc5e3To9JAzTDvGafuZEPRFJodH5mpUroQ934GrUju+ey92/8yBsR6NgvGQNwqMSQxPQgghjjgJFj3Er38Ny5dDero2HEov8ymPCWkpJk4dnM2pg2P7ENQ0eVlT0ZiwGpXLG2R1eSOryxuBUgDsZgOjClIZXRjbPbwg7dj7YNfRUrqOKVNwdLCbZPpll+LbtSthiJV/VymBsjJCQxL33aj+xU0MKC/HO3Agpkj3oW5HBVlLl1IwbBhTJ12TcL7b746tXLXPXh0uv4vdLbvZ3bKbb2q+SbifTtHRx9an3STytj06DLqj+GfcYI7sjzE+VuZza3tqRHs2VkBjGdRv0451/4i8EIMWUuL32Mgepq1uJYQQoleQv+g9wKefwqOPatdffBEKC5NbH5FceakW8lLzOHuENq5dVVVK61u0vTXKtV6N9VVNeHxB/rOjnv/siE0Oz7KbGJnvxNCsY89/Ssl2Wsm0mcmwmciym0i3mbr1fhtHWuY117Qrc553LpahQ1AssVCmqiooCqqiYOjbN1resnw5tf/zOPYpZ0aXzAUov34OKAqD7rqTEf21Te9CnmYIBdGnpkb36Nh3Pkepq5SWYEt0j46viZvrgLZHR4GjICF0tC2dm2fLQ6cchX9LswNKTtGONs11sR6Ntj02mvdoQ6lq1sHKv0ZegBX6jEaXN4aBu5tQ1jSBMxdsWZCSpV2ausm8FCGEEAclwaKbq6vTdtdWVbjuOrj44mTXSHQ3iqJQkmWjJMvGhWMLAAiGwmzZ7UkYQvVdjZs6j58vttQBOhZVbu7w8ZwWA1l2LWxk2Exk2k3R8JFpj5TZzGTaTaSnmHrt3I42hvR0DMcfn1CmKArF77/HB+++y8Dc2G7lpuIinOefj3VMbK8NNRTC8/XXEAiQd9+90fKmd95m929/h3P6dAqeeDy6R0fjm2+hTxuB7QcTUVJSqPfWt59E7i6l3FWON+SNlu/LpDO136MjEkByUnKO7LLGtiwYdJZ2gPYHrKki1qNRuVJbAtfvhvJl6MuXMQKg6o32j2VMiYSMzMhldtz1yO22n9uyJYgIIUQSSbDoxlQVZs+G6moYNgyefDLZNRI9hUGvY3i+k+H5Ti6PLLTkDYTYUOViVWk9i1dswpHdh4aWAA3N/ugRVsHlDeLyBtlR13zgJ4lw7BNEsiLhI8NmJnOfMJJh62VBRK9P3Dl88uToylNRqkrhggUEKiowxIWQUL3Wk2TIzoqdGg5Tc//9qIEAAxYtwmSzkWXNwrRkJbkfLOEHp59O2g9vBbQ9OnY3VlDmrU7s5XCXUu4uxx/2s71pO9ubtrerttVgjU4ajx9aVeQoIsOS0fWhQ1EgrVA7hl+olYXD2lCpqpWEqtZQtWU1BekWdK31Wo9Hcx2EfBBogaYy7egMgzXS4xEJGtHr8SEk7ucmmyyfK4QQXUSCRTf23HPw7rtgMsFrr0HcojZCHDKLUc/44nRG59vJ3ruB6dPHYDQaoz8Ph1UaWwM0NPuo9/ipb9aOBo+fhmYfddHrkfJmH2EV3N4gbm+QnYcQRDJtsfARCyKmdj0lGTYTZkPPnlCkGAzYT5nUrjz7ppvIvPZaVL8/Wqa2tmI/4wwC1dUY82IhpHXtGtwff4whNwciu54rKjSdfgHpDgfHvfkvjJFNGn3btuGrrqKxj4Nya0tsInlkj44qTxWtwVY2793M5r3te63sRnvCylVFjliPR5fu0aHTQfZgyB5MePiPWOn/gLzp09G1/U6qqrbcbVvIaIlcNu/R9tyIlu2B5nrtetALwdbYTuOdYbDE9X5kdXw9vsxklyAihBD7IcGim1q3Dm6/Xbv+2GMQN7JCiCNCp1OiH+oH5hz8/HBYpak1oAUQjy8ucGi36+N6Quo8fva2+AmF1WgQ2VXf0ql6OcwGMuKHYNlMZNhNcb0hiT0jPSmI6KxWsMbmbuhsNvo+/Yd25zmnTcOYm4t56NBoWXBPHarPRygYxJARW0ms6e23qX/xJdKvmsWku+9mUsEk1HCY6rvvwdBnGKmzr6Y6vDc2tCqyalWZqyy6R8eG+g1sqN/Qrh5p5rTY0Kq4OR1HZI8ORdHmb5gdkNHv4OerKvib9xM86iJl+1wPerXDVaEdnaE372c4VmZcCIn7udkhQUQIccyQYNENtbbCjBng88H06fCLXyS7RkK0p9MppNu0Cd8Dc+wHPT8cVnF5A9R52gKHLxJKEntB2npL9jb7CYZV3L4gbl+Q0k4GEbvZEDc3pK33wxzXS5LYM2Ixdv8gYh01CuuoUQllhpxsBi/7L4Ga3SiG2J9yXWoq5kEDMcctpRusq6Pp7bdBpyN77lxKjKmUpJZQ++RTuN79nIyrrybjqln4Qj7Kmsqo+fozyuxethobKHWXUeYqo7a1lkZfI417Glm7p/0eHVnWrHarVhU5iyhyFGExWI5Y20QpCpjt2nEoQaSlLtbjEQ0edfv0lLQFkVZteNYhB5GOhmPFzxmJG5olQUQI0YNJsOiGfvlL2LABcnPh5ZflPUb0DjqdQlqKibSUzu3J0BZEYr0gfuqbfTR44npGIkGkrWckGFbx+IJ4fEHKGjoXRGwmPZmRoLFvL0jC5PVIUOkuQURRFPSpqehTE4cnZV17LVnXXpt4rtFI9u23EXa5UeKGv/nLSglUVaGGQwCY9WZKgqkEf/kUWTodM9esjp5f9+F77Nm0ipqReWzLIzq0qsxdRoO3gbrWOupa6zrcoyPPlkexY5+NAZ1FFNoLMeqN7c4/KuKDSHpJ5+7jb95P8IgbjhVfHmiJBJHIPh+doTclTkbfd07IvkOzzE55kxBCdBsSLLqZd97R5lYA/O1vkNOJISlC9EbxQWRA9sHPV1UVV2tQCx+R4Vf76xlpG7oVDKs0+0M0R3Y37wybSU+G3UR6ipGgR8cS33qyHBYtlMQFkLaeke4QRAzp6e3CBkDevfeSMesqjH3yomVhlwtjUREoJIQQ7yefwocfMfrOOzhj6tWA1hNSOusqlL4DaZl/S7R3Y0/Zd5S2VLEpXIE74KGmuYaa5hqW1SxLeP62PToK7YU0Nzez6ptVOC1OHEYHdpMduzFymOw4TA7sRu3SZrQd3f072phs2pHefkf2DiUEkX17Rerj5oxEfh5ohpAf3FXa0Rl6U7Q3RG/N5LhGH7pPvgJHzj4hJDJcy5IqQUQIccRIsOhGKiu1VaBA67WYOjW59RGiJ1EUhdQUI6kpRvp3Noh4g/uZE+JLmB/SEAkrgVBbEGmlvKEV0LFx5YE/AKaY9HG9IQfvGbGajl4Q6WjzQPPAgQz85GNtr4449kmT0FmsWEeOjJYFKirw79yJwedlZPYoRmZrw7Uq/3Ybrg/Wk3PHHehmXEipq5Tyqu8Iv/sJZU4/S/v72eXaRWuwNbpHB8C6bes6XXerwYrD6MBmsiUEkbYAEh9G2m7bTfbouQ6j48j3lhxyEGmJ9XokzAmJG44V/3O/JxJEqsFdjQ4oBFj+n/0/h84YFzg6sYSvJU2CiBCi0yRYdBOhkLZfRUMDjB8Pv/99smskRO+mKAqpViOpViP9sg4+8VhVtfke9ZGgUdvUyuL/riC//xAaW0PtekYamv34Q2Fa/CFa/K1U7G3tVL2sRn37ZXsT5osk7iuSYjoyf8b3XXI27ZJLSLvkkoQy08BBFP3lZcKtia8t3NIKioKxIB+nJZ10SzpDqmDX33/D8Lw8fvHF56iqSl1rHVWPP4Zvy1aWjsrEPGUsLaEWgnvqyF22jQZrmJUjrXgCHjwBD6Y9LgJBH002aKWV1mArdK5ZO2TWm2Ohw5gYPOJDSlsvSUIwifzMrDd33fK8phQwFUFaUefOD7QmDM0Kunbz3YovGVacjb61of1KWn4PhAPRINIpOsMBhmN1MFzLmi5BRIhjmASLbuLRR+Hzz8Fmg1df1ZaYFUJ0H4qi4LQYcVq0IBIIBPDvVJl+Wv+EZXvbtAWRhDkhcT0j+/aS1Hu0INIaCFHZ2EplY+c+MVuMuuiGhR1NTs/ap2ckxaTvsg/CersN24kntisvfH4B4bhldAEUqxXn9OnonA7ttqKQnZKNZ30p3jXfMXbwFZw66nqMRiMtK1dS+sYVGIuKmHfn29HHKLv+epoXL8F5/12Ezz0Dd8BNy9YtmO/4H/w5qXz34Ew8fi2EZH+yGmtFHRvHpLGlUEezvxmfp4mSzU00GH1sLNbhC/nwhXy4PHUEdaDqDr1dDDpD4tCtjnpODvBzh8mB1WD9fv8mRmtsfxBADQTYXuFgyA+mo+/gd5KAdz9zQvZ00CtSr21gGA6Cp0Y7OkNn0AJGZ5fwtaRpSw8LIXoFCRbdwLJlcN992vVnnoHBg5NbHyHE4YsPIiWd7BHx+IJx80AOvnKWPxjGGwh/ryCSuLN6Bz0jkdvfN4jo9vl2xDJkCAVPPN7uvJxbb6V1+3Z2xAURnd2OY9q0hGV0ARSdHsVkwpGWjdOpfZhuKfVRurseqymFK4ZdET23/E9z8Cz+lilnPEj69B8D4N2yhZ2/uxB9ejq5X3yo9YT4Pfh//QiGRf+h7voLqTxnLJ6AB1/tbkY9/QktKTr+/bNheAIe3H43xevrSKtpZlVBgB19IBgO4mppIK20gb0m2JTOIX9jr1f0Wo/IvsFjPz0nHYWWTi33a7RAal/t6IxoENnPcKz4iewt9eBzRYLIbu3oDEUft2JWB3NCEpbwlSAiRHcnwSLJXC6YOVMbCnXZZXD11cmukRAiGRRFwWEx4rAYKc7sXBBp9odiPR+R8FEXWTkrGlDiVtLyfY8gYjbo4vYOiVu2124iqy2gtF23m7AdYhCxnXgipvHjCX7wQbTMMngwfZ96st25hQuei772aP0GD6b4tVfbnes871zMQ4ZgGT48Wqbo9VjHjEHncJBqTo1u+FcesuABRhYcx+ShlwLg27qVHZtfQZ+aynNTnos+RuVXv8K18F1u/NU8LDMuxRPw4KrYSejC2ah6HaXvPoY7MnSrz18WkvvVFtadPYBvJ+fiDrjxeVxM/2cZbkOQF6eoBJQwITVEZmkTuY2NlGcrbMmKtJ+q4miFVhMEDQduUwUFm9GGLqjj5fdfjgaTaG/Jvj0nnZkUf6hBJOjbz6pZ+ynzuUANQXOtdnSGooeUjMTgsd8lfLO0oVkSRIQ4aiRYJNkNN8COHVBcDM8/L0NThRCdoygKdrMBu9nQ6SDS4g/Flu2NLuHbvmekbQK7LxjGFwxT1eSlqsnbqXqZIkGk48np7XtG7OZDfxuKDy56u42UcePanZN6/vntyswDBlDyxuvtygueepKwx4POEttvw5CbS8GTT6CGwwnnphx3HKhgGTQ4+oE9w+qnNCcHDHrO6T89em6VfjNNe1dzXuHZ/OTMnwEQ2L2bbfeeDno9c/62Fm/IiyfgYe/8xwi//R6tV55H7Wln0uxvpsVVz4QrtYD12h8voEnRzh3+2U6Gr2rg61FG3h8bIhAOoKphzlvUhNeo8MHxTfiNWhtlNamkeaDeCXsdB3+DsRqsB5xv0uF8lPi5J/YcjKkFB30eQAsiCatjdbBSVvzQLV9TJIjs0Y7OUHT7H5rV0RK+1vTOPa4QokMSLJLolVe0Q6/X5lWkpSW7RkKI3kpRFGxmAzazgaLMlIOe3xZE4pfo3d/KWW1hxRsI4w+GqW7yUt3ZIKLXkZ5iJBzQs2DH15hNBiwGHWajfp9LHRaDPvHSqMdsiF2a97nd0aVBp7TrUdGZzejM5oQyvdOJ85xz2tU3/fLLSb/88sTXUFTEoCWL252bfdttpM+6CkN2bJkyndVKzrx5qIEAOp2OFF0KKcYU9ANH4J5QTZ8RkziuZBoAgdpatvEk6HT85gcPR+tds/z37C17hfHTr+a3s27R5ok07qbu4bMBlbNvf4ZWs4rH78H51/fI/+fX7DhrGMsuH6kN6fK5uOFX/8FvVPjt3AxqTK14Q14mfhfmpO88rOnXzOdjYh/cT18bpkYP3w5S8Jm0Oli9KpYANFuIhpg2Zr15v0O29jukKzUHe3b/A0+KD/pjq2Xtb6Ws+JW0vE2ghmNBpDNZRNFhsGYwJajDUDEfDBZtLovBDIbIZfxto0U7p+041NsGs3yjKHoVCRZJsn07/Pzn2vX774eTT05ufYQQIl58ECnMOHgQAWjxBxN7QRL2DmnfM9IaCOEPhdnt9gEKe7yeI/uiAJ3CfoNHZ4LJgS7b3T8lDfPADPQGPaqqapsaOp1k/mx2u3plXn01mfuMhTXm5DB0/TrCra0JH7LTL78M24kTtf1G0D7IZ1oyCcycSdnmzZxQPBlTJCjVFdXRmL+LiSOmcu6kOQCEW1vZ7DsOsw/evvRD9HYbgVCA6qeeoHnTXzhp2NlcOXUG7oAbj8/NoEfuRgmrfPr0DOrsYTwBD4M/3MTkt3ewcpyDP1/swOP30BJs4fd/CaJTgzx+sZfS1AYAhpSrDNwaZkcfhbeHxYYljSgNE9Ip7MwlGlgUVUUFDHpjdMhWR/NNoj0nmdk48vp3PCkePUrC6lgHGZrlbQQ1jNJShw1gTyeHZx2uwwkmh3NbAo04AiRYJEEgoM2r8Hhg8mS4++5k10gIIQ5fislASsahB5E6VyufL/2ScRMmElQVfMEQ3kC4w0vffso7vAyE8Aa1XpQ2YZXIEsAhIHCEWqI9nQLmfXtc9rk88M9rYz04Rgvm3BFYwjrM2+qwRO6r/9mNbPxyCUXNAWxhnTZR/9pryLpun53YzWYGLFpEuLkZXYoVAKPeSPaUadiz+2AePARbnxMAUINBKn6gnTt30u3obNqwu7pN/8se3dOcOew8rvjxrwEIhoJsfWwsBEMsOOt5POkWPAEP+tffI2vZ+9ROHsqwkZPx+D24A24uf/ojrM0Bnrq1HztsAZr9zZyw3MU1H4X479Awf7goSKOvEYAb3g1h8cMrZ+jYnaF9IC6oUxm1S6U6HdYMiAWW3L0qIR00OXRYLB0M6TLZsduycRT013pO2oZx6a3Yw2Esvla2fruScyeegkENasv6Bn0QjFx2xW3i9okJerXjaNObj2xwwUCKbze4qsFqj5XLnJdeTYJFEtx/P3zzjTb0qW0olBBCHGvagkiew0iZE04ZmNnh0r2HKxxW8YfC+AJhvJFw0u4yEIpMbj/wpa+T57VdRuugQmsgRGvgSAcaAw+uig3LUhQO3Nvy5d7E3hbHOMx7dFg++i523ozbtcvNe7EYXVr5lB9hPvsSQnpw73ZjMeox6RUyF/wJg6+F1P7Ho4/0mjSfmoInnEP+8OGcNv68aN12DSontHcvz170MsbcXADqfH9mz4ePcUbxDzjtgpujq3Fl/PE29K5mzHNmsSfPitvvJq9yPScvXM22EWl4JxREz7339QZyG+HeWbClrxu338341WGuXhRmY6HCgvNib7qXLA1j86p8PF5HTSSwpLtVxlZaOWPg2TjjllP2bt6M6vdjKilB79CWTQ57vYSamtCZzejjxjO39VB1SFUhFOjaoNLZ22rcnKGQTzto+j6/aAdlBM4C2Dgv8Qd6U9ywsiPdQxM3bE0CzVEhweIo++wzePhh7fqLL0JRJ/dBEkII8f3odAoWnR6LUU8qR3i37TiqqkYnwB9qIPlewSYQptnnJ6gqtC2cpargDWirgR1VixbtE2SOx7xVh+WZL2Pl027TLr+oxmysxWzQkZI5Aftv/4zJbES3wYDFmInZkE34p7dibm2mqM9ZDExPxWLQYxq9HOUH7zBq2HBemnJNpNdHx45XzsPfUsEz5z2Pt1hbjcv/zkfYG/9CysBB/HLCxbj9bjwBDz948Z849jTjOnkY32UoeAIeBm2rY85bburLnk0IFlV33Invu+8ofPFF7KdMAqBl2TLKr5+DZcQI+v3rn9FzS2deQevatfR9+g84zjwTgNbVq6m49TbM/ftT9NKLYNCWZK6ZPx/vho1kzf059kna4/rLyqh98kkM2dnkxQ1raPzXm/h2bMd59g+xjh4NQHDvXlz//jc6my1hE8vWNWsI1NZiGToUU2EhqCphbwu+9WtQdGAZ0DcaPEJ7G1Bb3ehMOnT6UJcEGTXYSsjbjF4NoKih2O9GyK8dvi7+nTsYnbGD+TH7mTtzyLcPEHJ0x9a3xxIsjqK6Om13bVWFa6+FH/0o2TUSQghxpCiKgsWoBRqsRz7QBAIBPvjgA8455xxUnT4hcOw7nGz/PTYHHmJ2oKFo3mCIuJWAo6Hq+4vfCyNNO97YmHiKcxpUAg9+Ei0yjbsRy/E6zO81YzHuwmzQkxEcRf6ld6FYrTQtL4kOH9s0UcHe3ER6+jmcaMnF4tCR1WcltX3/wqAhQxKeypCdTcjVhC4lNtRPDYfBYEDZp6dNDQa1deTjviUPt7QQrK6O9na08X23mdYVKwg3xXoOgvX1uD/8CGNhYcJ4affChXi++AJz//6xYFFby+6HHkafmZkQLBr++ldcH3xI7t13k3HVLFAUgnvq2TXrZygpKQxduSLW0s/eQ9O/3iT71lvJuv467XHr6tg6+VQUk4khq1dFe2D2PP0MTe+8Q/qVV5L506u119baStnsn6EYDBS++Cd0ZjPBQIClv5/PIJcL52mnkjrtB1rg8LdQ+/TzKIpK1oxz0RlUCPpo3biZ1s07MRekYRuUGx0i5v52G6gBbAOc6JQABLwE97oJNHowmEIYU4LRYBN0eSHkRa/zoYRbtX1Vov8AAfAFkhNoDtq7sv/gotOZKNmzDZpPgLQ+R7nyh65HBIvnnnuOxx57jOrqakaMGMFTTz3F5MmTk12tQ6KqcN11eqqqYOhQeLL9Eu1CCCHEYVMUBZNBj9mgx2k5uj00gZDadXNkOtlj4w2ECMcFGn/bvBpvcJ8aZoIfaIpNyn7LMBJSgTUuwBUptZExaS7L7jo74d5Ff3qh3Wt2nHEGw9avS9hbBaDoxT8R9vrQpzqjZZbRoyn5f/8PxZT4b5J9800E99RhHTM6WmYsKCD3nnsSQgyA46yzMPXrhzluJ12dzY7z3HOj81/amEpKsI4bhyEyzAwARcFYUIASt7QyQFsDKobYx0I1EABVRQ2HE4Z1BRvqCVRWEvbEFltQ/X5aV63SHiMuTJmrqvAsWYIpL4/UCy8EswOMfhpeewuAzJvvhFRtPxnPR99R9+f3SZtxObYrYvOCKm4YDYEAA7/4HF1eHgBNL71E7Uv/Q+qFF5L/yMPRc7efMJGwK0z/DxZh7t8PQkH2vvp3ah75H5xnnkrBr2+L9qjsvPE+Qk1uCu+6GnOfVAh68azYRP2//4u1fxY5F4zSwk3Ay+631xFyt5I5OQdzKhD04q1241rvwugMkz44HO2xadoaJuwLYy/wYkwJQzhAsClEa30AvbmJlOzYZqA+lwE1BEZbCL1J+zdQQxAK6FD0Knqjih4YAwQ8syVYdIU33niDW265heeee45Jkybxv//7v5xzzjls3LiRoh40juijj0p47z0dJhO89hrYOrFJqhBCCNFTaIFGwWTQ4bAc/PyuFAh1EEQ66Jlp12PTQVBp9Qdp2lN1SM+/73wKfWoq+tTEc/R2O9ZRI9vdN2X8+HZlxpwcMmZd2a487UcXtysz9S2g4PH/aVeefdNNZN90U+K5hYUM/HRRu3PzH5pP/kPzEwKSISeHQUuXoIZCCedmXXstaRddlBBYFKuVgqf/oPXSxIUTz/DhDD5xIrZRo2IPoChkzJ6NGgwkBBzzoIE4zpmGdcSIhOezjh6NGgigxC0JrVitGPLy0Kfvs+9IZN8ZxRipg96AqioQDILeApkDoqcG9rgI1dejFk+GIVpQC2z7f7RseRNdwRD4wb3Rc91PnkWgYg/pdz4NY8cC4Hv/fer/+ktSJk4k/da/RM+tP/8CfFu3UnT9cxgnjIFAK61fLKbijt9iGTqAfvPuivbGVM17Cu/WCvreehGO0X0h6KVl/S7K/rAIc56D/rdNJOxvoaailGxrRrt/t+6o2weLJ554gp/97Gdcc801ADz11FN8/PHHLFiwgIceeijJteuc9evh5Ze1PyaPPBL9nRRCCCFEFzDqdRj1uu+14eK+tCFlFV1Qq54nPiApen3CHixtjAUFGAsSN0HUmUw4p05td663Xwlp06cnLMqgGI3k/mpeu3Od06bhnDatXXnJ319pV5YxcyYZM2e2Kx/y7XJteFrc60i75BIcU6eimEwJ5xa+8L+oPh+mwtjO8raTTqLgqScxZGUlnJv18zmEGpsw5OdHy0wlJWT85CcYixO/5LZNmoSppARDn77aLvGAPn8Q1jFjMA0aCCWTouca8t/F0OhDN/oCOOkkAFTlK2ARpPeFC54hFAiw/IMPmO7Mpyfo1sHC7/ezYsUK7rzzzoTyqVOn8vXXX3d4H5/Ph88XG0Dncmldm4FAgEDg6C0t2Ka1Fa68Uo/fr2Pq1BBz54ZJQjV6hbZ/v2T8O/Ym0o5dQ9qx60hbdg1px64h7dg1uk07Go2QmYm6T10MkeFkISAUKVdyc7FGemLiz7VdcEH0elu5YfBgMn55e7tzM26/rd25xrFjKXjl/9qdm/fsM+3ONU88gQFr10AolPDZNZnteCjPraj7DgzsRqqqqigoKOCrr77i5Lgd5ObPn89f//pXNm/e3O4+DzzwAL/5zW/alb/66qukpHRubfWu9M03eTz00Amkpvp46qnPSUvzH/xOQgghhBBCdAMtLS3MnDmTpqYmnE7nAc/t1j0WbfYdu3ig9aHvuusubrstlhZdLheFhYVMnTr1oI1xJEyfDief7GPFihX8+MenHZE12o8VgUCAhQsXctZZZ0k7HgZpx64h7dh1pC27hrRj15B27BrSjl2jO7Rj2+ifzujWwSIrKwu9Xk9NTU1CeW1tLbnxqxzEMZvNmOMm+LQxGo1J+weZOhWCwbqk1qE3kXbsGtKOXUPasetIW3YNaceuIe3YNaQdu0Yy2/FQnrdbb0NoMpkYP348CxcuTChfuHBhwtAoIYQQQgghRHJ16x4LgNtuu41Zs2YxYcIETjrpJF544QXKysqYM2dOsqsmhBBCCCGEiOj2weKyyy6jvr6eBx98kOrqakaOHMkHH3xAcXFxsqsmhBBCCCGEiOj2wQJg7ty5zJ07N9nVEEIIIYQQQuxHt55jIYQQQgghhOgZJFgIIYQQQgghDpsECyGEEEIIIcRhk2AhhBBCCCGEOGwSLIQQQgghhBCHTYKFEEIIIYQQ4rBJsBBCCCGEEEIcNgkWQgghhBBCiMMmwUIIIYQQQghx2CRYCCGEEEIIIQ6bBAshhBBCCCHEYTMkuwJHmqqqALhcrqTVIRAI0NLSgsvlwmg0Jq0ePZ20Y9eQduwa0o5dR9qya0g7dg1px64h7dg1ukM7tn2GbvtMfSC9Pli43W4ACgsLk1wTIYQQQggheia3201qauoBz1HUzsSPHiwcDlNVVYXD4UBRlKTUweVyUVhYSHl5OU6nMyl16A2kHbuGtGPXkHbsOtKWXUPasWtIO3YNaceu0R3aUVVV3G43+fn56HQHnkXR63ssdDodffv2TXY1AHA6nfKfqwtIO3YNaceuIe3YdaQtu4a0Y9eQduwa0o5dI9nteLCeijYyeVsIIYQQQghx2CRYCCGEEEIIIQ6bBIujwGw2c//992M2m5NdlR5N2rFrSDt2DWnHriNt2TWkHbuGtGPXkHbsGj2tHXv95G0hhBBCCCHEkSc9FkIIIYQQQojDJsFCCCGEEEIIcdgkWAghhBBCCCEOmwSLI+y5556jX79+WCwWxo8fz9KlS5NdpR7noYce4vjjj8fhcJCTk8NFF13E5s2bk12tHu2hhx5CURRuueWWZFelR6qsrOTKK68kMzOTlJQUxo4dy4oVK5JdrR4lGAxy77330q9fP6xWK/379+fBBx8kHA4nu2rd2pIlSzj//PPJz89HURTefvvthJ+rqsoDDzxAfn4+VquV008/nQ0bNiSnst3cgdoyEAhwxx13MGrUKGw2G/n5+Vx11VVUVVUlr8Ld1MF+J+Ndf/31KIrCU089ddTq11N0ph03bdrEBRdcQGpqKg6HgxNPPJGysrKjX9kDkGBxBL3xxhvccsst3HPPPaxatYrJkydzzjnndLtfgu5u8eLF3HDDDfz3v/9l4cKFBINBpk6dSnNzc7Kr1iMtX76cF154gdGjRye7Kj3S3r17mTRpEkajkQ8//JCNGzfy+OOPk5aWluyq9SiPPPIIzz//PM8++yybNm3i0Ucf5bHHHuOZZ55JdtW6tebmZsaMGcOzzz7b4c8fffRRnnjiCZ599lmWL19OXl4eZ511Fm63+yjXtPs7UFu2tLSwcuVK7rvvPlauXMmbb77Jli1buOCCC5JQ0+7tYL+Tbd5++22WLVtGfn7+UapZz3Kwdty+fTunnHIKQ4cO5YsvvmDNmjXcd999WCyWo1zTg1DFEXPCCSeoc+bMSSgbOnSoeueddyapRr1DbW2tCqiLFy9OdlV6HLfbrQ4aNEhduHChetppp6k333xzsqvU49xxxx3qKaeckuxq9HjnnnuuOnv27ISyiy++WL3yyiuTVKOeB1Dfeuut6O1wOKzm5eWpDz/8cLTM6/Wqqamp6vPPP5+EGvYc+7ZlR7755hsVUEtLS49OpXqg/bVjRUWFWlBQoK5fv14tLi5Wn3zyyaNet56ko3a87LLLesTfR+mxOEL8fj8rVqxg6tSpCeVTp07l66+/TlKteoempiYAMjIyklyTnueGG27g3HPPZcqUKcmuSo/173//mwkTJvDjH/+YnJwcxo0bx5/+9KdkV6vHOeWUU/j000/ZsmULAGvWrOHLL79k+vTpSa5Zz7Vz505qamoS3nfMZjOnnXaavO90gaamJhRFkd7JQxQOh5k1axbz5s1jxIgRya5OjxQOh3n//fcZPHgwZ599Njk5OUycOPGAw86SRYLFEVJXV0coFCI3NzehPDc3l5qamiTVqudTVZXbbruNU045hZEjRya7Oj3K66+/zsqVK3nooYeSXZUebceOHSxYsIBBgwbx8ccfM2fOHG666Sb+9re/JbtqPcodd9zBjBkzGDp0KEajkXHjxnHLLbcwY8aMZFetx2p7b5H3na7n9Xq58847mTlzJk6nM9nV6VEeeeQRDAYDN910U7Kr0mPV1tbi8Xh4+OGHmTZtGp988gk//OEPufjii1m8eHGyq5fAkOwK9HaKoiTcVlW1XZnovBtvvJG1a9fy5ZdfJrsqPUp5eTk333wzn3zySfcbj9nDhMNhJkyYwPz58wEYN24cGzZsYMGCBVx11VVJrl3P8cYbb/DKK6/w6quvMmLECFavXs0tt9xCfn4+P/nJT5JdvR5N3ne6ViAQ4PLLLyccDvPcc88luzo9yooVK/jDH/7AypUr5XfwMLQtanHhhRdy6623AjB27Fi+/vprnn/+eU477bRkVi+B9FgcIVlZWej1+nbfEtXW1rb7Nkl0zi9+8Qv+/e9/8/nnn9O3b99kV6dHWbFiBbW1tYwfPx6DwYDBYGDx4sU8/fTTGAwGQqFQsqvYY/Tp04fhw4cnlA0bNkwWZThE8+bN48477+Tyyy9n1KhRzJo1i1tvvVV61A5DXl4egLzvdKFAIMCll17Kzp07WbhwofRWHKKlS5dSW1tLUVFR9L2ntLSU22+/nZKSkmRXr8fIysrCYDD0iPceCRZHiMlkYvz48SxcuDChfOHChZx88slJqlXPpKoqN954I2+++SafffYZ/fr1S3aVepwzzzyTdevWsXr16ugxYcIErrjiClavXo1er092FXuMSZMmtVvueMuWLRQXFyepRj1TS0sLOl3iW5Ber5flZg9Dv379yMvLS3jf8fv9LF68WN53voe2ULF161YWLVpEZmZmsqvU48yaNYu1a9cmvPfk5+czb948Pv7442RXr8cwmUwcf/zxPeK9R4ZCHUG33XYbs2bNYsKECZx00km88MILlJWVMWfOnGRXrUe54YYbePXVV3nnnXdwOBzRb+NSU1OxWq1Jrl3P4HA42s1JsdlsZGZmylyVQ3Trrbdy8sknM3/+fC699FK++eYbXnjhBV544YVkV61HOf/88/n9739PUVERI0aMYNWqVTzxxBPMnj072VXr1jweD9u2bYve3rlzJ6tXryYjI4OioiJuueUW5s+fz6BBgxg0aBDz588nJSWFmTNnJrHW3dOB2jI/P59LLrmElStX8t577xEKhaLvPRkZGZhMpmRVu9s52O/kvoHMaDSSl5fHkCFDjnZVu7WDteO8efO47LLLOPXUUznjjDP46KOPePfdd/niiy+SV+mOJHdRqt7vj3/8o1pcXKyaTCb1uOOOkyVSvwegw+Pll19OdtV6NFlu9vt799131ZEjR6pms1kdOnSo+sILLyS7Sj2Oy+VSb775ZrWoqEi1WCxq//791XvuuUf1+XzJrlq39vnnn3f49/AnP/mJqqrakrP333+/mpeXp5rNZvXUU09V161bl9xKd1MHasudO3fu973n888/T3bVu5WD/U7uS5ab7Vhn2vGll15SBw4cqFosFnXMmDHq22+/nbwK74eiqqp65OOLEEIIIYQQojeTORZCCCGEEEKIwybBQgghhBBCCHHYJFgIIYQQQgghDpsECyGEEEIIIcRhk2AhhBBCCCGEOGwSLIQQQgghhBCHTYKFEEIIIYQQ4rBJsBBCCCGEEEIcNgkWQgghhBBCiMMmwUIIIcQhe+CBBxg7dmzSnv++++7juuuu69S5v/zlL7npppuOcI2EEEIoqqqqya6EEEKI7kNRlAP+/Cc/+QnPPvssPp+PzMzMo1SrmN27dzNo0CDWrl1LSUnJQc+vra1lwIABrF27ln79+h35CgohxDFKgoUQQogENTU10etvvPEGv/71r9m8eXO0zGq1kpqamoyqATB//nwWL17Mxx9/3On7/OhHP2LgwIE88sgjR7BmQghxbJOhUEIIIRLk5eVFj9TUVBRFaVe271Coq6++mosuuoj58+eTm5tLWloav/nNbwgGg8ybN4+MjAz69u3Ln//854Tnqqys5LLLLiM9PZ3MzEwuvPBCdu3adcD6vf7661xwwQUJZf/85z8ZNWoUVquVzMxMpkyZQnNzc/TnF1xwAa+99tpht40QQoj9k2AhhBCiS3z22WdUVVWxZMkSnnjiCR544AHOO+880tPTWbZsGXPmzGHOnDmUl5cD0NLSwhlnnIHdbmfJkiV8+eWX2O12pk2bht/v7/A59u7dy/r165kwYUK0rLq6mhkzZjB79mw2bdrEF198wcUXX0x8h/wJJ5xAeXk5paWlR7YRhBDiGCbBQgghRJfIyMjg6aefZsiQIcyePZshQ4bQ0tLC3XffzaBBg7jrrrswmUx89dVXgNbzoNPpePHFFxk1ahTDhg3j5ZdfpqysjC+++KLD5ygtLUVVVfLz86Nl1dXVBINBLr74YkpKShg1ahRz587FbrdHzykoKAA4aG+IEEKI78+Q7AoIIYToHUaMGIFOF/u+Kjc3l5EjR0Zv6/V6MjMzqa2tBWDFihVs27YNh8OR8Dher5ft27d3+Bytra0AWCyWaNmYMWM488wzGTVqFGeffTZTp07lkksuIT09PXqO1WoFtF4SIYQQR4YECyGEEF3CaDQm3FYUpcOycDgMQDgcZvz48fz9739v91jZ2dkdPkdWVhagDYlqO0ev17Nw4UK+/vprPvnkE5555hnuueceli1bFl0FqqGh4YCPK4QQ4vDJUCghhBBJcdxxx7F161ZycnIYOHBgwrG/VacGDBiA0+lk48aNCeWKojBp0iR+85vfsGrVKkwmE2+99Vb05+vXr8doNDJixIgj+pqEEOJYJsFCCCFEUlxxxRVkZWVx4YUXsnTpUnbu3MnixYu5+eabqaio6PA+Op2OKVOm8OWXX0bLli1bxvz58/n2228pKyvjzTffZM+ePQwbNix6ztKlS5k8eXJ0SJQQQoiuJ8FCCCFEUqSkpLBkyRKKioq4+OKLGTZsGLNnz6a1tRWn07nf+1133XW8/vrr0SFVTqeTJUuWMH36dAYPHsy9997L448/zjnnnBO9z2uvvca11157xF+TEEIcy2SDPCGEED2KqqqceOKJ3HLLLcyYMeOg57///vvMmzePtWvXYjDI1EIhhDhSpMdCCCFEj6IoCi+88ALBYLBT5zc3N/Pyyy9LqBBCiCNMeiyEEEIIIYQQh016LIQQQgghhBCHTYKFEEIIIYQQ4rBJsBBCCCGEEEIcNgkWQgghhBBCiMMmwUIIIYQQQghx2CRYCCGEEEIIIQ6bBAshhBBCCCHEYZNgIYQQQgghhDhsEiyEEEIIIYQQh+3/A5OeFbeYL5voAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dvdt = (v[1:] - v[:-1]) / (t[1:] - t[:-1])\n", "dvdt_cd = (v[2:] - v[:-2]) / (t[2:] - t[:-2])\n", "\n", "# Analytical derivative of v(t)\n", "dvdt_actual = 9.81 * np.exp(-9.81 * t / 42.78)\n", "\n", "# Plotting\n", "plt.figure(figsize=(8, 5))\n", "plt.plot(t, v, label='Velocity (m/s)', color='blue')\n", "plt.plot(t[:-1], dvdt, label='Forward difference')\n", "plt.plot(t[1:], dvdt, label='Backward difference')\n", "plt.plot(t[1:-1], dvdt_cd, label='Central difference')\n", "plt.plot(t, dvdt_actual, label='Actual derivative', linestyle='dotted')\n", "#plt.axhline(y=42.78, color='red', linestyle='--', label=f'Terminal velocity')\n", "plt.title('Falling Object Approaching Terminal Velocity')\n", "plt.xlabel('Time (s)')\n", "plt.ylabel('Velocity (m/s)')\n", "plt.grid(True)\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2a9c23e9-ec7a-4a8a-a189-f9d58a6d3f52", "metadata": {}, "source": [ "## Comparing Forward, Backward and Central Difference" ] }, { "cell_type": "code", "execution_count": 6, "id": "ea8d487e-96db-4347-a561-71ee4d9b1257", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "17.73%\n", "16.68%\n", "1.22%\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "## Initiate Horizontal Axis\n", "h = 0.1 # Step size\n", "t = np.arange(0, 4, h)\n", "\n", "## Initiate Vertical Axis\n", "# Wave parameters\n", "A = 1.0 # amplitude\n", "k = 0.5 # damping coefficient\n", "omega = 2.0 # angular frequency\n", "v = A * np.exp(-k * t) * np.cos(omega * t) # Velocity v(t)\n", "\n", "\n", "# Finite difference methods (forward, backwards and central)\n", "dvdt_fd = (v[1:] - v[:-1]) / h\n", "dvdt_bd = (v[1:] - v[:-1]) / h\n", "dvdt_cd = (v[2:] - v[:-2]) / (2*h)\n", "\n", "#Actual solution (Analytical)\n", "dvdt_actual=A*np.exp(-k*t)*(-k*np.cos(omega*t)-omega*np.sin(omega*t))\n", "\n", "\n", "# Plotting\n", "plt.figure(figsize=(8, 5))\n", "plt.plot(t, v, label='Velocity (m/s)', color='blue')\n", "plt.plot(t[:-1], dvdt_fd, label='Forward difference')\n", "plt.plot(t[1:], dvdt_bd, label='Backward difference')\n", "plt.plot(t[1:-1], dvdt_cd, label='Central difference')\n", "plt.plot(t, dvdt_actual, label='Analytical Solution',linestyle='dotted')\n", "plt.title('Velocity of a pendulum in a viscous fluid')\n", "plt.xlabel('Time (s)')\n", "plt.ylabel('Velocity (m/s)')\n", "plt.grid(True)\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "\n", "max_error_fd = max(abs(dvdt_fd - dvdt_actual[:-1]))\n", "max_error_bd = max(abs(dvdt_bd - dvdt_actual[1:]))\n", "max_error_cd = max(abs(dvdt_cd - dvdt_actual[1:-1]))\n", "\n", "error = [max_error_fd, max_error_bd, max_error_cd]\n", "\n", "print(f\"{error[0]*100:.2f}%\\n{error[1]*100:.2f}%\\n{error[2]*100:.2f}%\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.2" } }, "nbformat": 4, "nbformat_minor": 5 }