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@caryan
Last active August 29, 2015 14:14
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Stochastic Differential Equations by Code Snippet
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Introduction\n",
"\n",
"I had to figure out stochastic differntial equations to simulate thermal fluctuation in the switching of MRAM elements at low temperature. Here are some simple notes and examples for reference when I need to figure out what I've done. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Wiener Processes or Brownian Motion\n",
"\n",
"A common first assumption is that the motion of interest is on a much faster timescale than the process that generates the noise so that the noise looks essentially white. The strength of the noise diverges as the time step goes to zero but the definite integral of white noise over any time period is well-behaved and gives a Wiener process. In particular a Wiener process $W(t)$ has three properties:\n",
"\n",
"1. W(0) = 0\n",
"2. The difference between any two points $W(t+\\Delta t) - W(t)$ is a Gaussian random variable zero mean and a variance equal to $\\Delta t$. In other words $W(t+\\Delta t) - W(t) = \\sqrt{\\Delta t}N(0,1)$\n",
"3. Increments between non-overlapping times are independent.\n",
"\n",
"We can get the required plot for any stochastic calculus discussion."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"using PyPlot"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": [
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"
],
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f9f132cfc10>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.text.Text object at 0x7f9f13118fd0>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Brownian Motion\n",
"Δt = 0.001 #arbitrary time step\n",
"dW = √Δt * randn(int(1/Δt)) #increments are normal random number scaled by \\sqrt(\\Delta t)\n",
"W = [0, cumsum(dW)] # Wiener process is sum of increments\n",
"\n",
"plot(0:Δt:1, W)\n",
"xlabel(\"Time\")\n",
"ylabel(\"W(t)\")\n",
"title(\"Required Brownian Motion Plot\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Functions of Wiener Processes\n",
"\n",
"Many of the differential equation will have functions of Wiener processes. Certain functions of Wiener processes may be well-behaved. Consider for example:\n",
"\n",
"$$ f\\left(W(t)\\right) = \\exp\\left(t + \\frac{1}{2}W(t)\\right) $$\n",
"\n",
"\n",
"\n",
"The probability distribution function for $W(t)$ is a Gaussian with variance $t$, the expectation value of f, $\\langle f \\rangle$, is given by:\n",
"\n",
"$$ \\langle f(t) \\rangle = \\int_{-\\infty}^\\infty dx f\\left(x\\right)Prob(W(t)=x) = \\int_{-\\infty}^\\infty dx f\\left(x\\right) \\frac{1}{\\sqrt{2\\pi t}} \\exp\\left(-\\frac{x^2}{2t}\\right) \\\\ = \\frac{1}{\\sqrt{2\\pi t}} \\int_{-\\infty}^\\infty dx \\exp\\left(t + \\frac{1}{2}x - \\frac{1}{2t}x^2\\right)$$\n",
"\n",
"The final expression is standard [Gaussian integral](http://en.wikipedia.org/wiki/Gaussian_function#Integral_of_a_Gaussian_function) so using \n",
"\n",
"$$ \\int_{-\\infty}^\\infty dx \\exp\\left(-ax^2 + bx + c\\right) = \\sqrt{\\frac{\\pi}{a}}\\exp\\left(\\frac{b^2}{4a} + c\\right)$$\n",
"\n",
"with $a = \\frac{1}{2t}; b = \\frac{1}{2}; c = t$\n",
"\n",
"$$ \\langle f(t) \\rangle = \\exp\\left(\\frac{9}{8}t\\right) $$"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": [
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"
],
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f9f117e6e90>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.text.Text object at 0x7f9f1264a250>"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Function of Brownian Motion\n",
"\n",
"# Consider the average of a thousand traces\n",
"numTraces = 1000\n",
"\n",
"# Create dW and W(t) along columns\n",
"Δt = 0.001\n",
"timeSteps = [0:Δt:1]\n",
"dW = √Δt * randn(int(1/Δt), numTraces)\n",
"W = cat(1, zeros(1, numTraces), cumsum(dW, 1))\n",
"\n",
"U = exp(timeSteps .+ 0.5*W)\n",
"\n",
"Uavg = mean(U,2)\n",
"Uideal = exp((9/8)*timeSteps)\n",
"\n",
"subplot2grid((4, 1), (0, 0), rowspan=3)\n",
"plot(timeSteps, mean(U,2))\n",
"plot(timeSteps, Uideal)\n",
"for ct in 1:5\n",
" plot(timeSteps, U[:, rand(1:int(1/Δt))], \"r--\")\n",
"end\n",
"legend([\"Sample Mean\", \"True Average\", \"Random Traces\"], loc=\"best\")\n",
"subplot2grid((4, 1), (3, 0))\n",
"\n",
"plot(timeSteps, Uavg - Uideal)\n",
"legend([\"Residuals\"], loc=\"best\")\n",
"xlabel(\"Time\")\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Stochastic Integrals\n",
"\n",
"## Reimann Sums\n",
"\n",
"Integrals of functions are usually introduced as the limit of a Riemann sum. So for some function f(t) we consider the approximation to $\\int_0^Tdt h(t)$\n",
"\n",
"$$ \\sum_{k=0}^{N-1}h(t_k)(t_{k+1} - t_k) $$ \n",
"\n",
"But the choice of where we evaluate the the function in the interval $[t_k, t_{k+1}]$ is arbitrary. We could just as well have written down\n",
"\n",
"$$ \\sum_{k=0}^{N-1}h(t_{k+1})(t_{k+1} - t_k) $$ \n",
"\n",
"or\n",
"\n",
"$$ \\sum_{k=0}^{N-1}h(\\frac{t_k + t_{k+1}}{2})(t_{k+1} - t_k) $$ \n",
"\n",
"However in the stochastic world life is not so simple. If we consider approximations to the stochastic integral, $\\int_0^T h(t)dW(t)$ then where we evaluate the function in the increment matters and leads to different calculus rules and differential equations. \n",
"\n",
"These stochastic sums are usually actually Reimann-Stieltges sums that summed with respect to a function $t$ rather than $t$ itself. A common example might be the expectation value of a random variable $X$ following a distribution $P(x)$. It can be defined as $\\langle x \\rangle = \\int_{-\\infty}^\\infty x P(x) dx$ but it can also be defined with respect to the cummulative distribution function $C$ so that $\\langle x \\rangle = \\int_{-\\infty}^\\infty x dC(x)$\n",
"\n",
"Let us consider a stochastic integral where the function being integrated depends on the stochastic variable and take it as the limit of a sum:\n",
"\n",
"$$ \\int_a^b f(t, W)dW = \\lim_{n\\rightarrow\\infty}\\sum_{k=1}^n f\\left(\\xi_k, W(\\xi_k)\\right)\\left[W(t_{k}) - W(t_{k-1})\\right], \\quad \\xi_k \\in \\left[t_{k-1}, t_k\\right] $$\n",
"\n",
"where we have been explicit that the sampling point can lie anywhere in the step. Above for determistic functions this didn't matter - all the integrals converged to the same sum. Here, where the integrand also depends on the stochastic function this is no longer true.\n",
"\n",
"## A simple example\n",
"\n",
"Most texts start with this deceptively simple example where $f(t,W) = W$:\n",
"\n",
"$$ \\int_a^b WdW $$\n",
"\n",
"We paramterize the choice of of sample point in the interval by $\\lambda$: $\\xi_k = t_{k-1} + \\lambda\\left(t_k - t_{k-1}\\right)$. Then we shorten notation with $W_k = W(t_k)$ so that $W(\\xi_k) = W_{k-1+\\lambda}$ then \n",
"\n",
"$$ \\int_a^b WdW = \\lim_{n\\rightarrow\\infty}\\sum_{k=1}^n W_{k-1+\\lambda}\\left[W_k - W_{k-1}\\right] $$\n",
"\n",
"by completing some squares and letting intermediate terms in the sum cancel:\n",
"\n",
"\\begin{align} \\sum_{k=1}^n W_{k-1+\\lambda}\\left[W_k - W_{k-1}\\right] &= \\sum_{k=1}^n\\frac{1}{2}\\left[W_k^2 - W_{k-1}^2 - \\left(W_k - W_{k-1+\\lambda}\\right)^2 + \\left(W_{k-1+\\lambda} - W_{k-1}\\right)^2 \\right] \\\\ &= \\frac{1}{2}\\left[W_n^2 - W_0^2\\right] + \\sum_{k=1}^n\\frac{1}{2}\\left[\\left(W_k - W_{k-1+\\lambda}\\right)^2 + \\left(W_{k-1+\\lambda} - W_{k-1}\\right)^2 \\right]\\end{align}\n",
"\n",
"Then the Weiner increments have a variance proportional to the timestep so\n",
"\n",
"$$ \\langle \\left(W_k - W_{k-1+\\lambda}\\right)^2 \\rangle = \\left(1-\\lambda\\right)\\left(t_k - t_{k-1}\\right) \\quad ; \\quad \\langle \\left(W_{k-1+\\lambda} - W_{k-1}\\right)^2 \\rangle = \\lambda\\left(t_k - t_{k-1}\\right) $$\n",
"\n",
"Putting this back into an expecation value of the sum approximation to the integral \n",
"\n",
"$$ \\mathbb{E}\\left[ \\sum_{k=1}^n W_{k-1+\\lambda}\\left[W_k - W_{k-1}\\right] \\right] = \\frac{b-a}{2} + \\frac{1}{2}\\sum_{k=1}^n \\left(2\\lambda - 1\\right)(t_k-t_{k-1}) = \\lambda\\left(b-a\\right)$$\n",
"\n",
"Which is a bit of a shocker. The value the sum converges to depends on the evalutation point chosen! "
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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rK4uWLVuWSFslrWXLliil2LVrV55lZ86c4dKlS7i6uub6gGFnZ5fv1arMzEyOHDmSJ2nNbmPv3r15tjlw4IDe9rUglpaWecr+7XE4c+YMDg4O+d78KL/zJLvNx51jQL7H6c6dOxw5cgRzc3MaN25crHj/TRsPd3O5efMmmzdvpnnz5jRr1uwf26xatSpNmzbl2rVrJdoNrDCKc4yKqlWrViil8q1v7969ZGVllUg72bK7haiHZnlp164dCQkJnDx5skh1DRkyhKpVq7Js2TK+//57EhMTGT58eL6vbyjdczN7Fp/82jh79qxcPRclShJ0IcqJ7K99z58/n+/y119/HYApU6aQkpKSU56cnMzkyZMB8kzXVpDs7h4FtVXSsmOfNWtWrqt5mZmZTJo0CaVUntiffvppzp8/n3PFNNusWbPyzH8O8NprrwHw8ccf55oT+cGDB0ydOrXE9qUgX3zxRYG3QI+Ojmbt2rVoNJpcidq/PQ6urq7cunWL48eP5yr/5ptv2LZtW77bODg4cOPGDVJTU/Ms8/X1xcTEhEWLFhEbG5tr2QcffMC9e/dy1imu4rbh5eWFu7s769evZ+nSpWRkZOQk7YUxfvx4QNd14tE5s7Oyskrt6mhxjlFRZT8PH3/8ca4+1ampqUyZMqXY9ap8pln8448/2LNnT54+79nTdo4YMSLfq9xJSUn5vj6srKwYPHgwUVFRfPDBBxgbGzNixIg86+nj3Bw8eHBOGw+/JrOysnjnnXfkhmKiREkfdCHKCUtLS9q2bcuePXvw9fXF3d0dIyMjevXqxZNPPsnAgQNZv349P/zwA02aNKFXr15oNBrWrVtHXFwc//nPf3K6UfyT5557jrlz5zJixAj69u2LlZUVdnZ2jBkzJmedkvxn1K5dO959910CAwNp2rQp/fr1w8LCgs2bN3PixAk6duzIO++8k2ubSZMmsXXrVnr16sUrr7yCnZ0dv/32G3FxcXTq1CnPVa5nnnmGkSNHsmzZMpo0aULfvn0xMTFhw4YN2NnZ4eTkVKzBcoW1detW/Pz8cHFxoX379jg7O5OWlsbp06fZunUrmZmZjB8/Ptdc2507d0ar1TJlyhSOHz+e8yHt/fffL1Sb/v7+bN26lQ4dOjBgwACsra05ePAg+/bto1+/fvz44495tnnuuec4ePAg3bp1o2PHjpiamtKiRQt69OhBvXr1WLhwIWPGjKFly5YMGDAAR0dHdu/ezYEDB2jcuDGffPJJnjqLcq4Utw3QfQj74IMP+OijjzAxMWHw4MGFbveNN95gz549BAcH4+7uTs+ePXPmJN+5cyfDhw/PM7d4SSjOMSoqLy8vxo0bx6JFi2jatCkvv/wyJiYmrF+/HgcHB2rVqlXk17NSioULF+Z0+0hNTeXMmTP88ssvZGVlMXbs2Fzz53fu3Jk5c+YwZcoU3N3d6d69Oy4uLty/f5/z588TERFBx44d2bRpU562Ro8ezbJly7h8+TI9e/bEyckpzzr6OjfnzJnDxIkT8fT05JVXXsHa2pqtW7dy9+5dmjVrxrFjxwpdnxCPZZjJY8qX+/fvq+nTp6uuXbsqOzu7AqerKsjt27fViBEjlKOjo6patary9vZWhw8fLsWIRXlX0Hy6Z86cUS+99JJycHDImdJr1apVOcuzsrLUkiVLVOvWrZWFhYWqWrWqat26tVqyZEmRY5g/f75q3LixMjU1zTMNW6dOnQqcTmzlypV54srep4KmRcz23XffqQ4dOigrKytlZmammjZtqmbPnp1rarSH/fLLL6p169bKzMxMOTo6qoEDB6oLFy6ooUOHKq1Wm2eayKysLLVgwQLl4eGhTE1NVe3atdXYsWNVYmKisrS0VJ6enoXal6LsU7aYmBg1b9489cILL6gGDRqoqlWrKlNTU1WvXj318ssv55mWMltISIhq0aKFMjc3z3NeFLSfD9u4caNq27atsrKyUnZ2dqpr165qz549Be5bUlKSGj16tHJ2dlbGxsZKq9Xmmdpz27ZtysfHR9nZ2SlTU1Pl7u6u3nvvvTzzWytVvHOlqG1ku3DhgjIyMlJarVb17NmzwPVcXFwKnFZw9erV6tlnn1U2NjbKzMxMubm5KV9fXxUVFVWouJUq2nmhVNGP0ePinzFjhtJqtflOzfn555/nvKYfPvcfV19+XFxclFarzTW9opGRkapevbrq2rWrWrt2bYHb7t27Vw0YMEA5OTmpKlWqqOrVqytPT081ceLEPNMpPszT01NpNBq1adOmx8amj3NzzZo1qmXLlsrMzExVr15dvfrqq+rq1auPrU+IotIoJd/J/JO4uDjc3NyoV68erq6u7Nq1i5UrV+Z8Zf44WVlZdOzYkWPHjvHuu+/i4ODAkiVLuHjxIocOHaJBgwZ62AMhxOOcPn2aRo0aMXDgQFavXm3ocIQQD7l79y61a9fG0dGRc+fOGTocIfRC+qAXgpOTE9euXePcuXP873//K9K2P/74I/v372fVqlV88MEH+Pn5sWvXLoyMjIo957EQoniuX7+eZ0BccnIy/v7+gG66PiFE2bJ06VKSkpJy5kUXojKQPuiFUKVKFapXrw4Uvd/tjz/+SM2aNenbt29OmaOjIwMGDCAkJIT09PR/NWhFCFF4CxYsYM2aNXh7e1OzZk2uXbtGWFgYly9fpnv37vTr18/QIQoh0F01X7JkCZcvX+arr77CyclJEnRRqUiCXsqioqLyndruqaeeYtmyZcTExNCkSRMDRCZE5ePj48OxY8fYtm0bCQkJmJiY0LBhQ/z9/XOuogshDC8hIYGpU6diZmbGU089xaJFi6hataqhwxJCbyRBL2VXr17N99br2Xc1u3LliiToQuhJ586d870VuBCibHFxcSnx+dmFKE+kD3opS01NxdTUNE+5mZkZQK75qh+WnJzM4cOHSU5OLtX4hBBCCCFE8ZRWviZX0EuZubk5aWlpecqzbwJibm6e73ZRUVF06NABT09PrKysci3r2rUr3bp1K/lghRBCCCFEvrZs2cLWrVtzld27d4+oqCj27t1L+/btS6wtSdBLWa1atbhy5Uqe8uw7qeV3wwXQTe0IukT9UREREUybNq3kghRCCCGEEMUWFxcnCXp50qJFC/bs2YNSCo1Gk1MeGRlJ1apVadiwYb7bubi4ABASEkLjxo31EaowsAkTJrBgwQJDhyH0RI535SLHu3KR410xnU1JYchff5GclYWRRkNdU1OGPHjAjBEjcvK2kiIJegm6du0ad+7coUGDBhgb657a7Fs1h4aG8vLLLwNw8+ZN1q5dy0svvVTgFIvZXV8aN26c7ywwouKxsbGRY12JyPGuXOR4Vy5yvCuWlMxMgq5f573YWFybNWPjk09SvUoVLIyMOHz4MDMouMtycUmCXkiff/45d+7cyemu8ssvv3DhwgUAxo8fj7W1NZMnTyYoKIi4uDjq1q0L6BL0tm3bMmzYME6ePJlzJ1GlFDNnzjTY/gghhBBCiMdLSE/n+aNHOXz/Pq9Uq8aXjRphY1z66bMk6IU0b948zp8/D4BGo+Hnn38mNDQUjUbDa6+9hrW1NRqNJlc3FgCtVsumTZt45513+Oyzz0hJSaFNmzYEBQXh7u5uiF0RQgghhBCFMDQ6mvOpqRxq1YqWj0zaUZokQS+kc+fO/eM6K1asYMWKFXnKbW1t+eqrr/jqq69KIzQhhBBCCFGClFL898IFNty6xY9Nmug1OQdJ0IUoMwYOHGjoEIQeyfGuXOR4Vy5yvMu3LKV468wZPr98mYB69ejr6Kj3GCRBF6KMkDf0ykWOd+Uix7tykeNdPj3IyuLgvXsEXrjAL7du8WXDhowsYDrs0iYJuhBCCCGEqLSUUqy+fp1Xo6NzyoI8PHi1Zk2DxSQJejmXnJxM9EMnlBD58fDwwMLCwtBhCCGEEGXCg6wsLqSmYmtszKC//mL77dsAdLK1JcjDgzpmZgaNTxL0ci46OppWrVoZOgxRxh06dEjm5BVCCFHpKaX4KT6ed86eJS41FQA7Y2OWuLvTr1o1qlWpYuAIdSRBryDkjqMiP3/99Re+vr6GDkMIIYQwuJNJSbwZE8OexES629szr359LqSm0rdaNeoa+Ir5oyRBryDkjqNCCCGEEPm7m5HBS8ePY6zRsLVZM3zs7Q0d0mNJgi6EEEIIISqsW+nptDt8mOsPHnCodWsalYMxWZKgCyGEEEKICmdbQgKv/vUXCRkZWBoZcbh1axqWg+QcJEEXQgghhBAVhFIK/zNnSMjIIPz2beqZmfF+jRr0dHSkXhnrZ/44kqALIYQQQohy72RSEvMvXuSba9doXrUqNatU4ZtGjXjS0tLQoRWZJOhCCCGEEKJcu5SaSoeoKG5nZDCvfn3erlPH0CH9K5KgCyGEEEKIcitTKXz/+ouqRkacefpp7E1MDB3Sv6Y1dABClKTw8HBatmzJyJEjycjI0Hv7ly5d4vXXX8fJyQkzMzNcXV2ZMGECd+7cMWhdQgghREU158IFIhITCWncuEIk5yBX0EUF07lzZ+bNm0eXLl1o164dw4YN01vbsbGxeHl5ER8fT+/evfHw8CAyMpJPP/2ULVu2sG/fPuwLOe9qSdYlhBBCVDSbb91iZEwMxhoNcampTKtbl2dtbQ0dVomRK+iiwvH29sbNzY2goCC9tuvn50d8fDyLFi0iNDSU2bNnExYWxoQJEzh16hTTpk0zSF1CCCFERRJ++zYvHj+OFmhlacnXjRoxw8XF0GGVKEnQRYU0ePBgIiIiuHjxol7ai42NZfv27bi6ujJmzJhcy2bOnImFhQUhISEkJyfrtS4hhBCiIlFK8WFcHK2srDjXti0/Nm3K8Fq1MNZWrJS2Yu2NEH/z9fVFKcXq1av10t7OnTsB8PHxybPM0tKS9u3bk5SUxIEDB/RalxBCCFERKKXYcPMmb8bEsDsxkRkuLmg1GkOHVWokQRcVkru7O23atCEkJEQv7Z06dQqAhg0bFhgPwOnTp/ValxBCCFERLLp8mZ5//knQ9etMr1ePFx0cDB1SqZJBopVUcjJER+u/XQ8P0Ndddn19fRk/fjxRUVF4enoWuN7o0aM5cuRIkeoODAykY8eOOY8TExMBsLGxyXf97PLCzMBSknUJIYQQ5d3uO3d4/9w5RtWqxReNGhk6HL2QBL2Sio6GVq303+6hQ9CypX7acvl7wEhwcPBjE/SlS5fqJyAhhBBCFNq9jAx237lD3xMneMbGhk/q1zd0SHojCXol5eGhS5YN0a4+hIeH8/XXX+Pj48N3333H3Llz0ZbiAJLsq9rZV78flV1uW4gpoEqyLiGEEKI82nzrFn3+/JM0pehsa8vmZs0wqWADQR9HEvRKysJCf1ey9W3z5s1Mnz6dsLAwNm3axKBBg9ixY0e+gy5Lisffnzyy+48/Kru/eEH9ykurLiGEEKK8Sc7M5PVTp/C2s+Ot2rV5xta2UiXnIAm6qGDWrVuHv78/ERERWFtb06tXLywtLQkODi4wQR85ciRRUVFFamfBggV06NAh57G3tzcA27dvRymF5qGR5ffu3WPfvn1UrVqVtm3b/mPdJVmXEEIIUR4kZ2ZyPCmJtTdusCkhgYT0dBa7u+Nmbm7o0AxCEnRRYXz//feMGjWKsLAw6tatC4C5uTl9+vQhNDSU5ORkLPIZobps2bJ/3babmxs+Pj5s27aNxYsXM3bs2JxlAQEBJCcn8+abb2L+0BtNbGws6enpNGjQAGNj439VlxBCCFFe7blzh9ExMZxITsZcq6WPoyPLGjastMk5SIIuKoigoCBGjBjB2rVrafXI6NfBgwcTHBxMaGgovr6+pRbDkiVL8PLyYvz48YSFheHh4UFkZCS7du2iUaNGfPzxx7nW79KlCxcuXCAuLi7nA0Vx6xJCCCHKg0ylWHblCkHXr2Oh1dK0alWCrl+njqkpM11c6F+tGo2rVjV0mAZXuTr0iAorMDCQ+fPn07NnzzzLnnvuOby8vFi8eHGpxuDm5sbBgwcZOnQokZGRzJ8/n3PnzuG7Wl6bAAAgAElEQVTv78+BAwews7PLtb5Go8nVfeXf1CWEEEKUdUopXjlxAr/Tp8lQCisjI5ZeuYK1kRHbmzdnuouLJOd/kyvookL4888/C1ym1WrZu3evXuJwdnZm+fLlhVr33LlzJVaXEEIIUVZFJyVxOiWFTQkJ/HTzJqs8PHitZk0AbqenU9XIiCqVbBDoP5EEXQghhBBClLjlV68y5exZbqSnA2Ci0fB+vXo5yTmAnYmJocIr0yRBF0IIIYQQJWrTrVuMPHWKPtWq0d3enrbW1jS0sMCogK6dIjdJ0IUQQgghRLGkZmay/tYtWlla0sDCAqUU406fZvGVKzxnZ8eaxo0xlu4rRSYJuhBCCCGEKLLopCRGxcQQkZiIpZERHW1sSFeKHbdvE+jmxrjatSU5LyZJ0IUQQgghRKGdTUlBCzxz5AgAPzZpwuF79ziWlERiRgYhjRszuEYNwwZZzkmCLoQQQggh/lGWUrwbG8u8S5cAqGdqysFWrXCsUoWXq1UzcHQGkJEBv/5aKlVLgi6EEEIIIR7rcloafjExbLx1i9dq1KCemRmv1qiBY5Uqhg5NvyIiYNcuiI/X/X38eKk0Iwm6EEIIIYQokFKKvn/+yemUFH5u2pSejo6GDskwQkOhf3/d31ZW4OYGX38Nw4eXeFPSc18IIYQQQuTr6P37vHLyJL/fu8dPTZpUzuT899/hpZfg5Zehb19IS4Pbt+HwYWjRolSalCvoQgghhBAiR5ZSKODd2FjmX7qEo4kJ3z3xBN52doYOTf+2b4cePaBBA/jmGxg2DPQwl7sk6EIIIYQQAoDTycmMPX2abbdvAzC/fn1GOzlhZmRk4MgMID4ehgyBTp1gwwbQY397SdCFEEIIISo5pRTfXL3K2NOneaAU3eztGe3kVDm7tACcOAE9e+pmavn6a70m5yAJuhBCCCFEpfXJhQt8f+MGdUxN+eXWLYbVrEmgm1vlm53lYbt36/qcu7hAWBjUqaP3EGSQqBBCCCFEJXQiKYkPzp3jQVYW++/eZVGDBiz38KicyXlMDDz5pK5/eadO0KYN7NunS9INQBJ0UaGEh4fTsmVLRo4cSUZGht7bv3TpEq+//jpOTk6YmZnh6urKhAkTuHPnTpHq+fHHHxk3bhwdO3bE2toarVbLq6++WkpRCyGEqExikpPxPnIEr8OHcTUz41Dr1txo356xzs6GDk1/kpPh1Cndbz8/aNQI/vxTtywgADZu1E2laCDSxUVUKJ07d2bevHl06dKFdu3aMWzYML21HRsbi5eXF/Hx8fTu3RsPDw8iIyP59NNP2bJlC/v27cPe3r5Qdc2aNYtjx45hZWWFs7Mz0dHRaPQwalwIIUTFdjktjU5HjmBtZMSkOnUYVKMGptpKdL02ORmWLoXAQLhxQ1dmagqjR8OgQeDuDjVqGDZGJEEXFZC3tzdubm4EBQXpNUH38/MjPj6eRYsWMWbMmJzyiRMnsmDBAqZNm8bSpUsLVdfChQupU6cO9evXZ/fu3Xh7e5dW2EIIISoBpRRbEhIYc/o0ALtatKCmqamBo9Kz0FBdIp6QoJsusUcPOHYMeveGpk0NHV0ulegjk6hMBg8eTEREBBcvXtRLe7GxsWzfvh1XV9dcyTnAzJkzsbCwICQkhOTk5ELV16lTJ+rXrw/o3lSFEEKI4opNSaHloUN0P34cayMj1jZpUvmS81274LXXdH3LT5+GZct0s7S8/36ZS85BEnRRQfn6+qKUYvXq1Xppb+fOnQD4+PjkWWZpaUn79u1JSkriwIEDeolHCCGEADhy7x7djh3jXkYGPzzxBAdbtaK9jY2hw9KPu3dh5UpYsAB8fHSDQENCDDbwsygkQRcVkru7O23atCEkJEQv7Z06dQqAhg0bFhgPwOm/v1oUQgghSotSih9u3GDAiRO0OXwYC62Wzc2a0b96dYwrQ3/z/ft1M7BMnKjryvL22/DCC7rpE8vJhxPpg15JJacnE30zWu/tejh6YGFioZe2fH19GT9+PFFRUXh6eha43ujRozly5EiR6g4MDKRjx445jxMTEwGwKeCFn11e1NlchBBCiKI4n5rK4JMn2Xf3Lm5mZkxwduZDV9fKMRA0LQ02bYJXXoH0dF3ZrFm6RN3MzLCxFZEk6JVU9M1oWi1rpfd2D408RMtaLfXSlsvfX2EFBwc/NkEv7MBNIYQQoixSShF68ybRycksv3qVTKXY0bw5XezsDB2a/iQlQbt2cPy4bh7zjz7Szdjy3HNQDj+cSIJeSXk4enBo5CGDtKsP4eHhfP311/j4+PDdd98xd+5ctKX4As2+Qp59Jf1R2eW2tralFoMQQojK50xyMv85eZJD9+8D8IK9PZ81aEADC/18W10mKKWbnSU2FlavhgEDwLh8p7jlO3pRbBYmFnq7kq1vmzdvZvr06YSFhbFp0yYGDRrEjh078h3AWVI8PHQfPLL7oj8qu+95QX3UhRBCiKJ4kJXFr7duMTImBgdjY7Y1a0YHGxvMjYwMHZr+KKW78+c330BwsO5n0CBDR1UiJEEXFcq6devw9/cnIiICa2trevXqhaWlJcHBwQUm6CNHjiQqKqpI7SxYsIAOHTrkPM6ep3z79u0opXLdVOjevXvs27ePqlWr0rZt22LslRBCCPH/bqen8/zRoxy6f58ONjasb9oUexMTQ4elX8HB4O8PDg66aRNHjgRfX0NHVWIkQRcVxvfff8+oUaMICwujbt26AJibm9OnTx9CQ0NJTk7GIp+v/JYtW/av23Zzc8PHx4dt27axePFixo4dm7MsICCA5ORk3nzzTczNzXPKY2NjSU9Pp0GDBhiX86/ihBBC6MfBu3fpf/IkiRkZ/Prkk/jY2VWOmVke9tNPujnNmzaFBg1gxAgYN87QUZUoyQpEhRAUFMSIESNYu3YtrVrlHvw6ePBggoODCQ0NxbcUP10vWbIELy8vxo8fT1hYGB4eHkRGRrJr1y4aNWrExx9/nGv9Ll26cOHCBeLi4nI+UGRbt24d69atA+DatWsA/PbbbwwdOhSAatWq8b///a/U9kUIIUTZk6UUw0+doopGQ1jz5nhaWRk6JP1LT4cZM+D552HbNkNHU2okQRcVQmBgIPPnz6dnz555lj333HN4eXmxePHiUk3Q3dzcOHjwINOnT2fLli1s2rQJJycn/P39CQgIyDMFo0ajydUV5mFHjx4lKCgoZ7lGo+HcuXOcPXsW0M1QIwm6EEJUHmlZWfwUH8+xpCQiWrSofMn57dswdapujvPoaN0NiCowSdBFhfDnn38WuEyr1bJ37169xOHs7Mzy5csLte65c+cKXBYQEEBAQEBJhSWEEKIce5CVRcuDBzmZnMxTVlZ0KCc32ykxSsHYsbBuHTzzjO4Keiv9TxWtT5KgCyGEEEKUYd9ev87J5GR+bNIEHzu7Ar99rZDS0nQDQL/9VnfVfMgQQ0ekF5KgCyGEEEKUUQ+ysphz4QI9HRx4uVo1Q4ejP3fuQEAAHDkCBw5ASAgMHmzoqPRGEnQhhBBCiDJoXXw8w06dIjkzk9VPPGHocPRr4EBdf/MnntBNqThggKEj0itJ0IUQQgghyphfbt5k0F9/0cbKivkNGtCyog8KVQoePIDwcAgLgy1b4OefoXdvQ0dmEJKgCyGEEEKUEZF37/LW6dP8fu8efR0dCWncGLOKfnfQP/+Ed97RJeUAlpYwYQL06mXYuAxIEnQhhBBCCAO5nZ7OpbQ0fr11i3Opqay7eRMnU1NWeXgwqEYNjCragNBr13R9y3/6CZycwMtLd6XcyEiXkA8aBP37Q0Xb7yKSBF0IIYQQwgBup6fT5I8/uPrgAQCNzM3pZm/Pf93ccDI1NXB0pSAlBTp3hrg46NsXTE1hxQpwcIDffwdnZ0NHWGZIgi6EEEIIoWdX0tLocfw4SZmZBHt44GFhQWtra0OHVbJu3NBNj3jkiO7vY8cgIUGXjDdtqltn7lywsNAl6yKHJOhCCCGEEHo2JDqaGw8esNfTkyctLQ0dTsm7fRs6doSzZ6F6dWjQQHf1/I03/j85B7CzM1yMZZjW0AGUF2lpabz33ns4OTlhYWFB27Zt2bFjR6G23bFjB126dKF69epYWVnRvHlzFi1aRFZWVilHLYQQQoiyQinFjoQEFl++zI7bt5lbv375T87T0uCXX+Dixf8v27gRWraEmzfhr7/g8mXYvRuCgnR3AhX/SK6gF9LQoUP56aefmDBhAu7u7qxYsYLu3buzc+dO2rdvX+B2W7ZsoXv37jRt2pRp06ZhYWHBpk2beOutt4iNjWXhwoV63AshhBBCGMKl1FTeOnOG0Js3Aejr6Fj+bzx06BCMHw+//QbVqsErr4C1NXzyiW7w5/z5uivnosgkQS+E33//ne+//565c+fy9ttvA/Dqq6/StGlT3n33Xfbt21fgtsHBwZiamhIREYGtrS0AI0aMoFOnTqxcuVISdCGEEKKCO5+aiveRIyRnZvJlw4a8XK0aDiYmhg6reFJSIDRUN6DzpZfAxgZWr4YdO2DbNjh/HkaMgEWLwFjSzOKSZ64QfvzxR4yNjRk5cmROmampKcOHD2fq1KlcvnyZ2rVr57utubk5pqam2NjY5CqvWbMmFhYWpRq3EEIIIQxHKaVLzo8eRQNEtmpFPTMzQ4dVfNevwwsvQFSU7nHz5rBnD1hZ6aZHFCVG+qAXQlRUFA0bNsTykX5iTz31FABHjhwpcNtx48aRlZXFqFGjiI6O5vz583zxxRf8/PPPTJkypVTjFkIIIYR+KaX4+soV2h46hMnu3TT8/Xe0wO4WLcp3cv7999CkCVy9Cps26WZnCQvTJeeixEmCXghXr16lVq1aecqzy65cuVLgts2bNyc8PJwNGzbwxBNP4Orqyrhx41i0aBHjxo0rtZgrq/DwcFq2bMnIkSPJyMjQe/uXLl3i9ddfx8nJCTMzM1xdXZkwYQJ37twp1PYJCQl8/fXX9OnThwYNGmBhYYGtrS0dO3Zk+fLlKKVKeQ+EEEIUVUJ6OhPPnCHg3DncIyMZERMDwH/d3AhwceG3li2pU56T81OnYNQoaN1ad/X8hRdg4EDd/OWiVEgXl0JISUnBNJ/5Oc3+frGlpKQUuG10dDQvvvgi9erV43//+x9mZmZ8++23jB07lho1atCrEt/GtjR07tyZefPm0aVLF9q1a8ewYcP01nZsbCxeXl7Ex8fTu3dvPDw8iIyM5NNPP2XLli3s27cPe3v7x9bxww8/4Ofnh5OTE97e3tStW5dr164RGhrKG2+8webNm1m7dq2e9kgIIcQ/OXb/Pr3//JNzqakAdLe3Z0nDhvj8w/t9uXD4MEydCuHhULcuBAfrBoOKUicJeiGYm5uTlpaWpzz17xejubl5gdtOmjQJY2Njdu3aldPnvF+/fnTu3JkxY8bQo0cPjIyMSifwSsrb2xs3NzeCgoL0mqD7+fkRHx/PokWLGDNmTE75xIkTWbBgAdOmTWPp0qWPraNRo0Zs2LCBF198MVf57NmzadOmDT/99BOhoaH07du3VPZBCCFE4fxx9y4LLl1i3c2bNLKw4HSbNpgbGVG7vN9wJy0NPv8cdu3S/bi6wn//C35+8Jh8pzJSSnH46uFSqVu6uBRCrVq18u3GcvXqVQCcnJwK3Hbv3r107tw5z4DQl156iStXrnD+/PnHtj1hwgR69uyZ62fNmjXF2IvKZfDgwURERHDx4XlZS1FsbCzbt2/H1dU1V3IOMHPmTCwsLAgJCSE5Ofmx9Xh7e+dJzgFq1KjBm2++CcDu3btLLnAhhBD/SCnFhdRUfrl5k/fPnsVl/37aHD7M73fvMqJWLfZ5etLAwqL8J+dhYeDmBpMm6eYy79FDN4XixImSnANr1qyhVadWuLV1w/VpVxxbOjLCb0SptCVX0AvB09OTXbt2ce/ePaweGgwRGRkJQIsWLQrcNiMjg8zMzDzl6enpOcsfZ8GCBbRs2bI4YVdqvr6+fPTRR6xevZrJkyeXens7d+4EwMfHJ88yS0tL2rdvz/bt2zlw4ACdO3cuVhvGf09XZSzTVgkhRKk7n5pKwLlzbL19m5TMTBL//l/uaGJCDwcHXrS3p0+1ahhpNAaO9F/68ENYuxY8PXVdWDp0gG++ga5dobzvWwl6kPmAmFoxHPY+jJ2ZHRqNBkcLR6bUmsI7/d4p8fbkCnoh9OvXj8zMTJYtW5ZTlpaWxooVK2jbtm3OFIvXrl0jOjo6V9Lt6enJtm3bSEhIyCnLzMzkhx9+wNramvr16+tvRyoRd3d32rRpQ0hIiF7aO3XqFAANGzYsMB6A06dPF6v+jIwMgoKCAOjWrVux6hBCCPF41x88YOSpUzzx+++4HTjAL7duMaxmTSbXrcuGpk252LYtN7y8WOHhQb/q1ct3cq4UREbCzJm6v3/8ET74ACIioFs3Sc7/lqWymLFrBtX/V52PIj5i+jPTufXuLW69e4tTY0/R2bV4F93+iVyKK4Q2bdrQv39/pkyZwo0bN6hfvz6rVq3iwoULrFixIme9yZMnExQURFxcHHXr1gVg2rRpvPjiizz99NOMHDkSMzMz1qxZw+HDh/n4448N1/88ORmio/XfrocH6Gn+d19fX8aPH09UVBSenp4Frjd69OjHTpWZn8DAQDp27JjzODExESDPfPfZsssLO5vLoyZPnsyJEyd48cUXef7554tVhxBCiILdfPAA/zNn+O7GDUbWqsWkOnV4pXp1qlbEcWK//grDhkF8vO7KeWQklNcbJ5Wyd7e/y/z98/Fv68/rnq/TtHpTvbQrCXohBQUF8cEHHxAcHMzt27dp3rw5GzdupEOHDjnraDQaNI984uzWrRubNm3i448/ZubMmWRkZODh4cGXX37JiBGl02+pUKKjoVUr/bd76BDoqcuOi4sLoLub6+MS9H8auGlon332GfPnz6dx48YEBwcbOhwhhKhwVl69yoiYGDKUYqm7O28WcPPBCmHvXujTR9eF5T//0f2W5Dxfy6OWM3//fAKfD2SS1yS9ti0JeiGZmpoSGBhIYGBggeusWLEi1xX1bF27dqVr166lGV7ReXjokmVDtKsH4eHhfP311/j4+PDdd98xd+5ctNrS69GVfYU8+0r6o7LLbW1ti1Tv559/jr+/P02aNCEsLKzI2wshhMjf6eRkwu/coZG5OSNiYni1Rg0+dHHBuTzPV/44e/boZmf54Qdo3x5CQyUxL0BaRhp+v/qx/MhyRrQcwYS2E/QegyTolZWFhd6uZOvb5s2bmT59OmFhYWzatIlBgwaxY8eOfAdwlhSPvz94ZPdFf1R23/OC+qjnZ+HChbz99ts8+eSThIWF4ejo+O8DFUKISk4pRdD16/jFxJCclQVABxsbvmjYkCqleCHHYJSCOXN085nb2cFHH+mmTJTkPJfE1EQW/b6IC4kX2HF2B1fuXWFlr5UMaTHEIPFIgi4qlHXr1uHv709ERATW1tb06tULS0tLgoODC0zQR44cSVRUVJHaWbBgQa7uTd7e3gBs374dpVSurk737t1j3759VK1albZt2xaq/k8++YQpU6bg6enJ9u3b//EGR0IIIQrnw/PnmREXx8uOjkyoU4ezKSn0q1at4iXnN2/qpkhcsgS2boVp03TJuQz+BOBm8k2u3b+Gh6MHi39fzHs73iMtU3fPG0cLR8KHhONVx8tg8UmCLiqM77//nlGjRhEWFpYzSNfc3Jw+ffoQGhpKcnJynvnogVyz8xSXm5sbPj4+bNu2jcWLFzN27NicZQEBASQnJ/Pmm2/muqlVbGws6enpNGjQINfUiR999BEBAQG0bt2abdu2SbcWIYQoIcuvXmVGXBwfu7oytV49ANoXMLi/3EpKglmzYNEi3d/OzrBhg25Oc8Hx68cJ/C2QNcfXkKkyMTc2JyUjhXbO7ehQtwNedbzo7dHb0GFKgi4qhqCgIEaMGMHatWtp9cjg18GDBxMcHExoaCi+vr6lFsOSJUvw8vJi/PjxhIWF4eHhQWRkJLt27aJRo0Z8/PHHudbv0qULFy5cyDXrz6pVqwgICMDIyIgOHTqwcOHCPO24uroyZIhhvnITQojyatmVK4yOieFNJyem/P2eW2EoBVu2wJUrsGoVHDwIb72lGwz6xBNgaWnoCMuEyTsm88m+T6hrU5d5PvNwd3Bn57md9GjYg2ddnjV0eLlIgi4qhMDAQObPn0/Pnj3zLHvuuefw8vJi8eLFpZqgu7m5cfDgQaZPn86WLVvYtGkTTk5O+Pv7ExAQkGcKxvxm/YmLiwMgKysr3+QcoFOnTpKgCyFEEey6fZs3Y2IY7eTEInf3PO+95VpUFPj6wsmTusfu7rBpE3TqZNCwyhKlFO9uf5e5++cy49kZTO04FRMjXR/87u7dDRxd/iRBFxXCn3/+WeAyrVbL3r179RKHs7Mzy5cvL9S6586dy1MWEBBAQEBASYclhBCVVkZWFqNiYuhgY8Mid3e0FSU5v3BBd7X8v/+Fxo1h+3Zdcl63bqXvZ56lstCgYfvZ7fj96odWo+V0wmlmdprJ+8+8j1ZT9scbSIIuhBBCiAop/e/kPCYlhTVPPFFxkvP9+3V9yhMSYOhQ3UDQh8Y4VWYJKQm0+6YdWSqLm8k3qWNdB686Xsx5bg59G/c1dHiFJgm6EEIIISqUO+np7E5MJDQ+ntXXrxPo5kZLKytDh1Uyli7VTZPo6QkxMeDgYOiIyoQslcWw9cNYc3wN1qbWvNjwRW4k3WC+z3waV2ts6PCKTBJ0IYQQQlQYp5KTeeHYMc6lpgKwsEED3nJ2NnBUJeTOHXjvPRgwAJYvh6pVDR1RmRGwM4Cgo0GMajWKyR0m42LrYuiQ/hVJ0IUQQghR7iml+PbGDcadPk2tKlWIaNGC6w8e8HK1aoYOrWR8+y0EB0NqKixcKMk5ujt+mhqbEvpXKLP2zOK/Xf7L5A6TDR1WiZAEXQghhBDlVlpWFi8eO0bYnTsA9HJwYKWHB7YV6U6Z0dG6mVoaNtTdcKhWLUNHZFCZWZl8su8TZu6eibO1M2dvn6XfE/14r/17hg6txEiCLoQQQohy6a+kJLodO8aVBw/oYmtLk6pVWdigQcWaRhFg9mxwcoKjR8HU1NDRGNyXh77k/fD36eTSCQcLB15r9hoTvSZWqOMuCboQQgghypVLqansSUxk/Jkz2Bkbs61ZM7zt7AwdVsm7eBHmzNF1b5k/v9In51kqi1vJt5gVMYuBTw5kdd/Vhg6p1EiCLoQQQohyQSnFx+fP88HfN3UbUK0an7u7U61KFcMGVhrOn4cXXoCzZ2HcOBg92tARGdSBSwfo830frt2/hp2ZHXO6zDF0SKVKEnQhhBBClHlZSjEsOpqg69fpamfHpDp1eM7e3tBhlbyzZ3U3HwoNBWtrXbeWRo0MHZVBnb9zniHrhlC9anXe8XqH3h69qWNTx9BhlSpJ0IUQQghR5hy8e5fZFy5wJiWF5paW3E5P59eEBEIaN2ZwjRqGDq/kHD0KN25AZCTcvAkbNuhmahk8GKZPB0dHQ0doMGcSznAm4QwDfxqItak16/+zHg9HD0OHpReSoAshhBCiTDly7x5PHT6MBuhub8/R+/dJzMjgIxeXipWcx8ZC+/aQlKR7XK8ePPEELFhQ6a+aL4pcxPgt4wFo69yWzYM3Y2tma+Co9EcSdCGEEEKUGYkZGYw+fZrqJiYce+opalTE/uUA+/dDr15Qo4bupkMWFvDUU4aOyuASUxM5cu0I7+54lzdbvcmAJgN4qvZTWFaxNHRoeiUJuhBCCCHKDL+YGE4mJbG1WbOKm5xnZcHw4eDqCr/+Wum6sWRmZZKQkkC1qrqbSJ2/c57AfYGEHA/hbtpdABo6NCTw+UCsTK0MGarBSIIuhBBCiDLhhxs3+PbGDYI9PGhrY2PocEre6dPw/vtw6xb89Rfs2VPpkvM95/cwcdtE/rjyB44WjnR3786OsztISEnAycqJ4Z7D6ePRh9ZOrTE3MTd0uAajNXQAQpSk8PBwWrZsyciRI8nIyNB7+5cuXeL111/HyckJMzMzXF1dmTBhAnf+vsNdYb333nt06dKFOnXqYGFhgb29Pc2bN+f999/n+vXrpRS9EEIYRpZSRN27x+iYGPpVq1ax+pkDKAWzZun6lW/dChoNfPMNdOhg6MhKXXpmOlfuXeFMwhnCz4XTY00PktKT+Mj7I4Z7DueHEz+QnpnOSb+TxI6PZX7X+XSs17FSJ+cgV9BFBdO5c2fmzZtHly5daNeuHcOGDdNb27GxsXh5eREfH0/v3r3x8PAgMjKSTz/9lC1btrBv3z7sCzkl2MKFC2nVqhVdu3alevXqJCUlsX//fmbPns2yZcvYt28f7u7upbxHQghR+hLS0xl7+jRrbtzAwdiYLxo2rFB3hCQrCyZMgM8+gylT4N13wbbiD3ZUSjFp2yQ+jfyUTJWZU96kWhP2vb4PGzPdNyRTOkzB1NgUM2MzQ4VaJkmCLiocb29v3NzcCAoK0muC7ufnR3x8PIsWLWLMmDE55RMnTmTBggVMmzaNpUuXFqque/fuUSWfvpfvv/8+s2fPZs6cOXzzzTclFrsQQhjC/YwMOkRFEZ2cTDd7ez5yccHBxMTQYf17ERHw448QHQ0PHugeL10Kb75p6MhK3P0H99kYs5F2zu2oZ1sPgLg7cUzfOZ3gY8G81/49Gtg3wN7cHmtTa9rUboO1qXXO9tmJushNEnRRIQ0ePJhZs2Zx8eJF6tQp/ZsZxMbGsn37dlxdXXMl5wAzZ87kyy+/JCQkhHnz5mFhYfGP9eWXnAP079+f2bNnc+XKlRKJWwghDCX+wQOGRkdzMS2No61b86RlOZ6l4/x5mDkT6tSBzZvhjz+galXdFIr378PatfDyy4aOssRtjNnIezve42T8SWpUrYHfU37Ut6vPhK0TSEpPYu7zc5noNdHQYZZL0shdcGQAACAASURBVAddVEi+vr4opVi9erVe2tu5cycAPj4+eZZZWlrSvn17kpKSOHDgwL9qZ8OGDQB06tTpX9UjhBCGsi4+noBz5/A+coTf7t5ldePG5Ts5/+knaNECVqyADz/UTZf4zTeQmKjrb37wYIVKzg9dOcTg0MFMDZtK7+96Y2ZsxoaBG3im3jPM2z8P3599qW9fn/P+5yU5/xfkCrqokNzd3WnTpg0hISFMnjy51Ns7deoUAA0bNiwwnu3bt3P69Gk6d+5c6Hrnzp3L/fv3SUxM5ODBg0RGRvLGG2/w9ttvl0jcQgihL2lZWXx7/TqvnzpFrSpVqGdmxu4nnqBZeUvO09MhPFz38803uhlZXn4ZvvhCt6xWLUNHWCpSM1JZEbWCt7e9TWpGKgC9PXqztv9ajLXG9GjYg/TMdC7fu0xdm7poNXIN+N+QBL2SSs7MJDo5We/telhYYGFkpJe2fH19GT9+PFFRUXh6eha43ujRozly5EiR6g4MDKRjx445jxMTEwGwKWBasOzyos7mMm/evFyztrRv357//Oc/mFSEPppCiErjVno6bQ8f5kxKCi87OrK2SZOyPxA0LQ1WroTffgNTU4iLg7Nndd1ZMjJ0XViGDYNnn9Ul6GV9f/6l/mv7szFmI8M9h/N598+5kXSDOtZ1ch1HEyMTXGxdDBdkBSIJeiUVnZxMq0OH9N7uoVataGmln5sOuLi4ABAcHPzYBL2wAzcN4erVqwDEx8ezb98+Jk+ejI+PDytXrsTX19fA0QkhxONlKsWSy5f58Px5lFLsaN6czra2ZTc5v3FD103l2DE4fhzu3NHd3TMzE+rVgz59oH59aNMGnnwSKvjFkvTMdNafWs8PJ35gY8xGVvddzaAnBwFQ16augaOr2CRBr6Q8LCw41KqVQdrVh/DwcL7++mt8fHz47rvvmDt3Llpt6X3dln2F/P/Yu++4quo3gOMfhmxwgAsnOMAtbtEsFz/3qNRScovbcKGpgeZKBHHkyBwJak4kc5AIGoqKCzUHiowQB7Knsu75/XHSUlEx5d4LfN+vV6/k3HvPeVDGc7/n+T7Ps5X0lz07XuY/ttYqX748/fr1o1mzZtStW5fp06eLBF0QBLWWo1DgFBHBqpgYhleqxHc1a1JVT41b6d26JQ8R8vaGQYPgk0/gyy+hXj1VR6Z0Z+6d4VzMOXbf2M35++epUboGW/tu5cuGX6o6tBJDJOgllIGWltJWspXt6NGjODs74+/vz5EjRxg8eDDHjx/PdwPnh2JtbQ38U4v+srCwMOD1NeoFVb16derVq8e1a9eIjY2lYnEb5iEIQrFwITWVT2/cICYrC7datZiuhG5a78XFRV45fzZAaORIVUekNJIkAaChocH1x9eZcHgCp6JPAVDeoDznRp2jddXWqgyxRBIJulCs+Pj44OjoSGBgICYmJvTt2xcjIyO8vLxem6A7ODgQEhLyTtfx8PCg/b8mwHXs2BEAPz8/JEl64fZtWloaQUFBGBoa0qZNm//wWb3owYMHaGhoYFTUNlYJglAirL9/nwlhYTQ3MuJQo0Y0UcefVZIEy5fLXVaaNQM3NzlB//prMDF5++uLkWm/T8M71Bs7Szu2XtlKtdLVWNJpCQMaDKCKcZUSP9FTVUSCLhQbu3fvZuzYsfj7+1O9ulwbp6+vT//+/fH29iYzMzPfHuQbN25872tbWlpiZ2fHsWPHWLt2LZMmTXr+mIuLC5mZmYwbNw59/X9+0IWHh5OTk0Pt2rXR1v7nWzEsLIwKFSq8suFUoVDw7bffEhcXh52dHYaGhu8dtyAIwodyPjWV1TEx7ImLw75iRTbUrYuhkpoCvJN792DAAAgOBi0tuRvLxIlyeYu61sYXgrCEMM7GnGVl8EpamLfA85onk1pNwrWrKzpa+c/iEJRHJOhCseDp6cmYMWPYu3cvzV+qrR8yZAheXl54e3sXat32unXrsLW1ZcqUKfj7+2NtbU1wcDAnT57EysqKxYsXv/D8zp07Ex0dTVRU1PM3FACHDx/mm2++4aOPPqJmzZqYmpoSGxvLH3/8QWRkJDVq1GDDhg2F9nkIgiAUVFhmJqdTUghITmZnbCyW+vostrBgStWq6Bbivp//LC4OunaFJ0/kgUKdOkF8PJibqzoypZEkiVnHZ7H8zHIAulp2xdfeFw001HfzbgkkEnShWHB1dWXFihX06dPnlce6dOmCra0ta9euLdQE3dLSkosXL+Ls7Iyvry9HjhzB3NwcR0dHXFxcXlkR19DI/4dh165dCQ8P5/Tp04SEhJCcnIyxsTHW1taMHj2ayZMni/IWQRBUbt39+0wOC0MCGhsassTSkhnVqqGlrkne/fvQq5fcmeX0aahdWz5egpLzmNQY5gbMxfOqJ8u7LqerZVfql68vepb/RwoF/PFH4ZxbJOhCsXD9+vXXPqapqcnp06eVEkfVqlXZsmVLgZ4bGRmZ7/EGDRqwZs2aDxmWIAjCB3UxNZWv795lnLk531taYqyt5ulEfLzcrzwrC/z8/knOS4io5CjGHRpHQGQAOYocXD52YYbtDFWHVeQ8eQKjRskdOMuUgYcPITy8cK4l3jIJgiAIglBgGXl5DLl1iyaGhnjUrq3+yTnAhAnyyvmpU3L/8hJCkiS8b3nTYWsHbifcxvljZx7PeMz8T+arOrQiJT4efvwRWrQAHx+oWxd0dMDKCjZtKpxrFoHvKkEQBEEQ1EFiTg49rl3jXlYWIS1aoKOOdeYv274d9u4FT0/4e4BdcaaQFBy4dYCVwSs5c+8MCklBt9rd2NBzAzXK1FB1eEXO+fPQowckJEDHjvKX079nH16+XDjXFQm6IAiCIAhvFZqRQf8bN4jLziagSROslDR47j/JzobQULlTi4ODvBl08GBVR1VoJEnC964v6dnpHAg9wC/Xf6FDjQ7MbjebdtXb0aNOD1WHWCQ9egSffQZ16sDNm1ChgvKuLRJ0QRAEQRDeKEuhwP7WLbIVCvyaNMFGnQfdRURAv35yoTDIRcM//VRsWygeCz/GqIOjiEmNAaC0bmk8+3nyVZOvVBxZ0XbwIIweDZqasGuXcpNzEAm6IAiCIAhvMSs8nOsZGQQ1a6aeyXlmJiQlwW+/wZw5UK4cbN0qJ+tz5xbL5Py327+xKWQTB28fpKtlV3Z+upPSeqWxNrMWfcz/gydPYPduyMkBf3/5z717yzXmyk7OQSTogiAIgiC8wZ3MTNY+eMBiCwuaq2Nyfv06dOsmt1EEGDQI1q+HsmVVG1chSXmawqLARbiddcOijAXLuy5nWttpolXiO5Akufrpr7/gf/+DzZvB2Vl+n/eMmxtMm6a693YiQRcEQRAEIV+nkpPp/eefmOvoMKVKFVWH8yJJkktXxo6F8uXlWnMLC5g9W9WRFSqHQw7subGHmbYzWdZlmRgu9A4eP5a/ZLZtg7Cwf45raMgbP6tXh3bt4MsvQdVf7iJBFwRBEAThFYHJyQy6eRN9LS1+qV8fPS0tVYcki4qC776TN4GePQtDh8KKFWBqqurIClV2XjaXH15mz409/Nz3Z4Y1HabqkIqU+Hh5r3BUlLzxc8MGOSH/9Vf45BN4aQi5yokEXRAEQRCEF+x+/JjBN2/SzNiYvfXrU1NfX9UhyQIDwd4e7t2D+vXh8GG5B14xl5WbRYN1DQhPCqd66eoMaTxE1SEVCY8eyavlpqbyVoSMDDhzBho3/uc506erLr43EQm6IAiCIAgA5EkS30ZG8n10NEMqVuRna2u0VFVC8ddfci35gwfyFFBtbbmMpU0beeBQjZLT03tLyBYikiLY0HMD7au3R1tTpG+vk50NI0aAnh7cuiXfZAF5PtXRo6ovXSko8S8sCIIgCAK7YmOZHxXFnSdPWGppyYxq1VSXnN+8CQ0ayH+uXBm8vOQ/N2sGx46Brq5q4lKyPEUeZ+6dYfGpxXzZ6EvGthir6pDUliSBkxP88otca16xovzezstL7sZiYlK0mvmILb+CIAiCUIJJksSG+/f58tYtrAwMCLKxYVb16qpLzlNT5Y2fhoZw9SrExMgFxBcuyCvnJSQ5z87LZpjPMDr83AGFpOC7T75TdUhqbfFiufNKo0YQECDXmqekyBVRpUsXreQcxAq6IAiCIJRY0U+fMv7OHY4kJjLe3Jy1deqotiuIJMGYMXDtmlyP8KxY2NS02G8CfSYuI47NIZvZc2MP1x9fZ1W3VYy0GYmRjpGqQ1MrkiS/f2vQAA4cgG+/hQUL5HaJzxgV4b8ykaALgiAIQgmSrVCw5v59jiYkEJSaiqm2Nr82bEgfMzNVhyYPF9qzR/7vo49UHY1SHLh1gOiUaO4m3gUgICqAv5L/olWVVpwddZbm5mrWXkQNJCXBkCHyezgdHbnu/Msv5SS9uBAlLkKxEhAQQLNmzXBwcCA3N1fp14+JiWHkyJGYm5ujp6eHhYUFU6dOJTk5+b3Ou337djQ1NdHU1GTz5s0fKFpBEEoShSRxMimJphcvMjsiAgMtLRZZWHCjVSvVJ+cpKbBuHUyaBKNGwYABqo1HSQ7fOcynez7F8XdHfrjwA77hvpgZmHF65GkChgWI5Pw1vvsOTp+GWbPg66/hhx9gy5aiV8byJmIFXShWOnXqhLu7O507d6Zt27aMGDFCadcODw/H1taWuLg4+vXrh7W1NcHBwaxatQpfX1+CgoIoV67cO5/33r17TJo0CSMjI9LT08VQCkEQ3km2QsGO2Fim3L1Lel4eH5Uuzc569WiqLlNBg4JgwgS5rMXCAlatUnVESrHuwjomHplIr7q92NBzA09zn1KrXC1Vh6W2cnNh716IjJQTchcXmDdP1VEVHrGCLhQ7HTt2xNLSEk9PT6Ved8KECcTFxbFmzRq8vb1ZsmQJ/v7+TJ06ldu3bzN37tx3PqckSYwYMYLy5cszbty4QohaEITizDsujupnzzLy9m3aly7N7vr1Odm0qfok59evy7PW09LAwwNOnpQ3hxZj91PvE5EUwRz/OYxsOpJfv/iVKiZVRHL+FnPmwODBcj/zrl3l1fPiTCToQrE0ZMgQAgMDuXfvnlKuFx4ejp+fHxYWFkycOPGFxxYsWICBgQHbt28nMzPznc67evVqTpw4wdatWzEwMPiQIQuCUMw9yspi1O3bNDM25nrLlhxt3JiBFSqgqS534by95f7mtWrBn3+Co6M82rGYikyKZJjPMKp6VKXWajkZX9BxAZoaIhV7k8xMGD0ali+HpUvl93JHjkCpUqqOrHCJrwqhWLK3t0eSJHbs2KGU6504cQIAOzu7Vx4zMjKiXbt2ZGRkcO7cuQKf89atW8yePRtHR0fat2//wWIVBKH4y1UoGHfnDtoaGnjVq0cDdVmVjo2FOnXkKTKffQbt2sk7/dQlvkJyLuYcrTe15ve7vzOr3Sx2f76bWxNvUdWkqqpDU1tnzkDDhvLA2F9+gY0b5VXzotyZ5V2IGnShWKpTpw6tWrVi+/btzJ49u9Cvd/v2bQDq1q372nj8/PwICwujU6dObz1fbm4uX331FTVr1mTJkiUfNFZBEIq3+OxsRt++zeHERPbWr4+pOiw1KhQwYwbs3Cn/2dUVzMzkzaDqEN8HFpkUyYmoE0SnRGOsY8y8E/NoXrk5Pl/4YGagBt1y1JgkQXIyfP45VK0qD44dMgQ6dlR1ZMolEvQSKi8zj8zQdyu3+BAMrA3QMtBSyrXs7e2ZMmUKISEh2NjYvPZ548eP58qVK+90bldXVz76VwuwlJQUAEqXLp3v858dL2g3l++++44rV64QFBSEbgkZyiEIwvvb+vAhI/9eMDjcqBE91KF3eFCQ3Hbj2DG5VmHGDLCyUnVUH9SlB5eY/8d8GldozPkH5wmIDEAhKTDWMSYtO43BjQazuc9m9LT1VB2qWoiIkL8s2raVK5zu3JH3Bvv4yCUs6enyTZU9e6BmTVVHqxoiQS+hMkMzudT8ktKv2/xSc4ybKWdzUs2/v6u9vLzemKCvX79eKfEUVHBwMEuXLmXmzJm0bt1a1eEIglAEBCYnMycigjOpqVTS0WGrlRXdVJ2cS5KcdU2dKk+T8faG/v1VG9MHpJAUXHl0hX039+Ea5EqelMehO4doU7UN333yHYMbDaaqSVUSnyRS0aiiqsNVG9OmyV8WCoX8ccuWcPcuPH0KxsbQpw906ABdupTc5BxEgl5iGVgb0PyS8vurGlgrZ6NjQEAAmzZtws7Ojl27duHm5oamZuFtuXi2Qv5sJf1lz46XKVPmjefJzc1l6NChWFlZsWDBgnyfI0nSe0QqCEJx4/XoEcNDQ6mpp8fkKlVYammJgZZy7lS+1rlzMGyYvDQ6eTKsXAmF+DO4sNyMu8mfsX9ibmxO8tNkEp4kEJcRx8WHFwl5GEJYYhjamto4f+zM7PazSc9Op5z+i+10S3JyfuQIbN4MGRmgqyuvjAcEyB1ZRo6Ey5fl92+VKsnHK1VSdcTqQyToJZSWgZbSVrKV7ejRozg7O+Pv78+RI0cYPHgwx48fz3cD54dibW0N/FOL/rKwsDDg9TXqz6Snpz9/rp5e/rdCx4wZw5gxY/j666/x8PD4ryELglAM+CYkMPL2bYZXqsSPdeuirQ5J8PLl4OQENjbg5wedOhWZ5Dw+M55lp5fxOPMxdxLuEBwTjMSLiyImuiZYm1nTtlpbVnZbScMKDaleWu4+83JyXhLExICXF/ToAU2ayMfS0+WhsNOmydVMJibyDRWFQu6m6egoP69WLbnWHIrXkKEPQSToQrHi4+ODo6MjgYGBmJiY0LdvX4yMjPDy8nptgu7g4EBISMg7XcfDw+OFziod/9694ufnhyRJLwwTSktLIygoCENDQ9q0afPG8+rp6TFq1Kh8hxFdunSJkJAQPvroI6ysrLC1tX2nmAVBKF72x8Ux8MYNupcrxwZVJ+cKBaxfL2dlly6Bg4OciRWR9rCSJHE25izLzyzHL9yPppWaUs2kGuP7jadb7W4kZCZQVr8s5fTLoaOlo+pwVS4zE/T15UFBq1fLCbmrq3yzpE0bmDkTbt6UG/Xs2gXab8g2RWKeP5GgC8XG7t27GTt2LP7+/lT/u5euvr4+/fv3x9vbm8zMzHx7iW/cuPG9r21paYmdnR3Hjh1j7dq1TJo06fljLi4uZGZmMm7cOPT19Z8fDw8PJycnh9q1a6P9908vPT09fvrpp3yvMX/+fEJCQhg2bBgjR45875gFQSh6/khOxjU6Gg3gcGIiA8uXZ0e9eqpJzhMSYPFiuHJFngKamCjXmDs5yZmZqsts3kKSJHIVuWhrajPq4Ci2XtmKpoYmm3pvYoTNi1OoKxhWUFGU6uXpU7kk5ccf5W6Zd+7A2LHw9dfg5ibXli9cCLVrw/nz0KKFSMD/K5GgC8WCp6cnY8aMYe/evTRv/mJt/ZAhQ/Dy8sLb2xt7e/tCi2HdunXY2toyZcoU/P39sba2Jjg4mJMnT2JlZcXixYtfeH7nzp2Jjo4mKirq+RsKQRCE/JxMSsIzNpYdsbHU0dfHWFubDXXrMrpyZbRUkQFlZckTQCMi5N18kyZB9+5QRDa2/xn7J6N/G83VR1dpW60tJ6NOsqn3JoY0HiI6rbzGnj3yynhsrPz+Kzpa7k0+Zoz8+ObNsHYthIbKZS3/Wo8S/gORoAvFgqurKytWrKBPnz6vPNalSxdsbW1Zu3ZtoSbolpaWXLx4EWdnZ3x9fTly5Ajm5uY4Ojri4uLySgtGDQ2NfEtZXuddny8IQtGXo1Cw8K+/WPLXX9TW12dOjRo4VauGvqpXp2fNkqd/nj0LzZqpNpZ39NOln3A45EBVk6q0r96esMQw1vdcz6hmo1QdmlpKT4fAQBg1Sl4R9/WFevXyf66eHjRtqtz4iiuRoAvFwvXr11/7mKamJqdPn1ZKHFWrVmXLli0Fem5kZOQ7ndvFxQUXF5f/EpYgCEXQg6wsxty+zdHERL6qWJFNVlaUUvVmy2etE1etkouPi1hyvvnyZhwOOTCu+Tg8unmI1fLXiIiAv/6Cw4flBjx5eWBrK3fKLFtW1dGVDCJBFwRBEAQ145uQwKCbN9HX1OSQugwcSkuTaxx+/FHeDfivvTbqTpIk5gbMZenppYxrPo51PdeJO5J/y86W2yCWLQu3b8Ps2fLAIJDrx11c5Gqm1q1FPbkyiQRdEARBENTI07w8xt65QwtjY/Y2aEC5UqVUHZK8cj56tJy5rVgh7xQsQjZe2sjS00tx7eLKDNsZIjn/myTJbQ79/aFnT3mF3MwMJk6UV8wbNZL/E5SvaDQmVQNZWVnMmjULc3NzDAwMaNOmDcePHy/w648fP06nTp0oU6YMJiYmtGjRgj179hRixIIgCEJR8yQvj4lhYTzKzmZ93brqkZyDnJTv2SM3vC5iyfmDtAfM9JvJmGZjmNlupkjOgdRUcHeXu2H+9pu8vzcwUO5b/tdf8MMPMHiwSM5VSaygF9Dw4cPZv38/U6dOpU6dOmzdupUePXpw4sQJ2rVr98bXbt26ldGjR2NnZ8fSpUvR0tIiNDSUmJgYJUUvCIIgqLubGRkMunmT25mZrK5dm7rq0kP8wQNwdpZ76Q0cqOpoCuxp7lNuxt3kk58/QVNDkyWdl6g6JLXw8CF88olcZ25iIpe0LF2q6qiEl4kEvQDOnz/P7t27cXNzY9q0aQB89dVXNGzYECcnJ4KCgl772qioKCZOnMiUKVPE1EdBEAThFbkKBcvu3WPxX39hoafH5ebNaWhkpOqwZKdPy73NDQ1hwQJVR1MgD9MeMsxnGH4RfgA0q9yMvQP2YmZgpuLIVEeS4Pff4ddfYdMmKF9eHiRUp46qIxNeRyToBbBv3z60tbVxcHB4fkxXV5dRo0YxZ84c7t+/T5UqVfJ97YYNG5Akie+++w6QR7kbGhqKW2yCIAgCSTk59L1+nTMpKUytVo0FNWtioOoWis8cOwbDh8OTJ+DpCS+1ilUnkUmRPEh7QMijEBYGLkRTQ5NZ7WYR8iiEbf22UcmokqpDVJmEBJg+HbZtkwe7DhkifyySc/UmEvQCCAkJoW7duhi9tKLRsmVLAK5cufLaBP348eNYW1tz6NAhZs6cyYMHDyhbtiwTJ05kwYIFIlEXBEEooS6lpTHk5k3icnI42bQp7cuUUXVIMkkCDw85i2vTBnbuBAsLVUeVrzxFHltCtjDFdwpPc58CMLDBQNZ0X1Oip39evAhbtsgDXq9dg5wc+eMRI97+WkE9iAS9AB4+fEjlypVfOf7s2IMHD1772rCwMLS1tRk5ciSzZs2iSZMm7N+/n0WLFpGbm8uSJaImThAEoSSRJInNDx/iePcu1gYG7GvQQH1KWqKjYcIEuQH2jBng6qqWvfUysjNIfJLI9GPT2XtzL62rtKavVV/K6pdlXItxqg5P6VJS5M2eGhoQFATr10OVKlC3rtx8Z/ZsqFBy368USSJBL4AnT56gq6v7ynE9Pb3nj79Oeno6kiSxbNkyZs6cCUD//v1JTExk1apVzJkz55WVeUEQBKF4SsjJYVRoKL8mJDCqUiVW1q6NkbYa/Cp+8gSGDoV9+8DUVM72evVSdVSvyFXksuz0MuadmAeAmYEZv3z2C180/ELFkalGXp58s2PePMjKko/p68tNd6ZMAXWplhLenRr8VFB/+vr6ZD37yv+Xp0+fPn/8Ta998uQJX3755QvHv/jiC3x9fbly5Qrt27f/sAELgiAIaictN5fef/7J7cxMDjRoQL/y5VUdkuzqVbnx9eXLsHEjDBgAalBuk5WbxW93fuNR+iMG1B+Asa4xvX/pTUBkAC3NWzKwwUDGNh+Lsa6xqkNVusxM+UbH3r3yeytHR/njvDyoWRPyWVMUPhCFQkFubi46OjooFIpCm1QuEvQCqFy5cr5lLA8fPgTA3Nz8ta81NzcnPDycihUrvnC8wt/3mpKSkt547alTp1L6pY05X3755SsJvyAIgqB+zqaksComhhxJIjQzk5isLI41aUJrExPVBhYRAefPg58f/PyzvGPw6FH4+GPVxvW3yKRIrNdak52XDcDko5PR1NBEV0uXgKEBdLToqOIIVcfPD+ztIT0dRo6EL7+UhwoJhc/d3R1nZ2eePHmCnp4eCoUi3wXcD0Ek6AVgY2PDyZMnSUtLw9j4n3fqwcHBADRt2vS1r23RogV3794lJiYGi39tsnmW8Jd/ywqKh4cHzZo1e5/wBUEQBCXLVSiYEBbGTw8fUk1Xl5TcXDSA402a0FKVyfnDh7BwIfz4IygUULWqPLFm4kRQk6FIaVlpOBxyIDsvm30D9tGscjMC/wrk8sPL9Krbq0Qn55mZMGwYVK4sb/oU6UHhkySJzZs3s3PnTgIDA6lZsyaDBw8mOjqanJwcunTpwsiRIz/4dUWCXgCff/45bm5ubNy4kenTpwPyZNGtW7fSpk2b5x1cHj16RHJyMrVr10b775rCQYMGsWvXLjZv3syiRYsA+fbI1q1bMTU1pXnz5qr5pARBEIQPzi8xkYMJCVxKS+N8aiob69ZlVOXKSECuJKGrqYIB3nl5cOiQvFPw7l15Os3338OoUVCunPLjeQNJkhh1cBTnYs7xu/3v2NWyA8CirAXDmg5TcXSqtXKlXFv+8CGcOgW1aqk6opLByckJNzc37OzscHd3Z8yYMRj8a4jY5cuXC+W6IkEvgFatWjFgwAC++eYbHj9+TK1atdi2bRvR0dFs3br1+fNmz56Np6cnUVFRVK9eHYC+ffvSuXNnli5dSnx8PI0bN8bHx4egoCA2btxIKTVZsRAEQRDez/64OD6/cYNaenpU1tXlWJMmdCpb9vnjWqrohrJzJ0ydCo8fQ9Om8O23MHky/CsudfLD+R/Ye3Mv+wbse56cC3DunPzPWK2a3FxHJOeFLyUlheHDh+Pj44O7u/vzQZXKIhL0AvL09OTbb7/Fy8uLpKQkmjRpvcsvAQAAIABJREFUwqFDh17Y4KmhoZFvX3MfHx/mzZvH7t27+fnnn7G2tmbHjh2ijrwQBAQEMGPGDFq0aMG6deue38lQlpiYGJydnfH19SUxMZHKlSvTr18/XFxcKPMOm65q1qxJdHR0vo9VrFjx+f4HQRBUR5IkVsTEcCIpieisLG5kZDCwfHl21a+vHjMuIiNhzBjo2lVePW/dWi1bJgLcTbzL3IC57Lmxh69bf81n9T9TdUhqQ5Jgzhxo2BCuXBGdWQqLQqEgJCSEcuXKERMTw/Dhw0lISGDjxo2MGjVK6fGIBL2AdHV1cXV1xdXV9bXP2bp16wsr6s8YGhri4eGBh4dHYYYoAJ06dcLd3Z3OnTvTtm1bRihxKkN4eDi2trbExcXRr18/rK2tCQ4OZtWqVfj6+hIUFES5d7idXKZMGRwdHV85LtpyCoLq5SgUjLtzhy2PHtG9XDk6lC7NpCpVGFmpknok58nJ8shIMzPw8gJj9e104nbGjfkn55ORk0HrKq1x7fr637MliSTBmjUwaxY8fSpXKYnk/MNISUl5vpA2cOBADh06xIIFC4iMjHz+nNatW3Ps2DFqqeh2hUjQhWKnY8eOWFpa4unpqdQEfcKECcTFxbFmzRomTpz4/Pj06dPx8PBg7ty5rF+/vsDnK1OmDM7OzoURqiAI7+FBVhajbt8mICmJrVZWDM9nkJ3KZGbKXVnc3SEpSR44pKbJeZ4ij9XBq5npN5NBDQYx03YmVmZW6GjpqDo0lUpMhN27wdcXDh6Ezz6Te5p36KDqyIq+48ePs3TpUgIDA8nNzUVDQ4MJEyYAYGZmhpaWFk2bNmXkyJGMHj0aHR3VfS2KBF0oloYMGcKiRYu4d+8e1apVK/TrhYeH4+fnh4WFxQvJOcCCBQv48ccf2b59O+7u7i9sLhEEoWi5mJpKt2vXKKWpycFGjfifumyylCS4cweWLoVt2+SV8zNnwNpa1ZG9QJIk1l1YR9LTJPwj/TkZdZJJLSexuvtq9bjzoGSSJFcfZWTI00Dz8uS29HfugKUl7Nkjt6UX/juFQoGmpiZeXl6MGzeOhg0bsmrVKnr16oWmpia7d+/G1taWtm3bqjrUF4gEXSiW7O3tWbhwITt27GD27NmFfr0TJ04AYGf36qYmIyMj2rVrh5+fH+fOnaNTp04FOufTp0/Zvn070dHRGBoa0qRJEzp06ICmKrpACEIJ5/XoER4xMYSkp9PAwICTTZtipsLVtRckJMgdWX79Vf7422/l2nMlLE68iz+i/mDb1W1svbKV8gbl0dHSwXugN/2s+5XI5DwzE5ycYO1a+f1URgY0aiS3UNy+HWxsVB1h0fXLL79QpkwZYmNjGT16NJaWloSFhdGrVy927tz5QsvsZ9351I1I0IViqU6dOrRq1Yrt27crJUG/ffs2AHXr1n1tPH5+foSFhRUoQdfQ0ODRo0cMHTr0heMWFhZs3bqVDuJepyAoRZ4kseLePZwiIuhtasq8GjXoaWqqmnaJ+UlLg27d5A2h7u5yHUSLFqqO6gXxmfH8dOkn5gbMxVjXmGVdluHUzknVYanc0KFyBdIPP4CDA2hqihrz97Vjxw7279/PgQMHnh/r2LEjdevWZcaMGYwZM6bIvBkUCXoJlZeXSWZmqNKva2BgjZaWcko87O3tmTJlCiEhIdi8YSli/PjxXLly5Z3O7erqykcfffT845SUFIBXpr4+8+x4cnJygc4/YsQIOnToQIMGDTA2NiY8PJwffviBjRs30r17d86ePUvjxo3fKWZBEAruano6++Pi8IqNJerpU6ZWrcqK2rVVHdaL7t+H3r0hPBxOnlTLJddfQ39l0L5BSEiMazGONd3XoKVZMrNQSYLLl+UVcz092L9fHjakxK1Sxdq2bdsYPnw4ZcuWZenSpbRq1Yo///yTYcOGvVMXNXUhEvQSKjMzlEuXlD8kqXnzSxgbK2f0Wc2aNQHw8vJ6Y4L+Lhs3leXlzaENGjRg/fr1GBkZ4e7uzvz58/H29lZRdIJQfMVmZ9P84kXuZ8sj5odWrMie+vVVO/3z3+7c+afGfPVqyM1Vy+T8XMw5vvb9mvP3z9PHqg+bem+ivOGbJ2cXZ+npchXSnj2grw/ly8uJub29qiMrunJzcwkICKBdu3acPn2a0aNHM3r0aDZu3Ph8lbygJaXqSCToJZSBgTXNm19SyXWVISAggE2bNmFnZ8euXbtwc3Mr1NrtZyvkz1bSX/bs+Pu+ix83bhzu7u6cOnXqvc4jCIIsT5I4mZxMUk4OcTk5eMXGcj87mxW1ajG6cmWMlTxL4bVOnQIfHzk5f/pULlju1Qs8PECNVvYVkoL5J+ezMHAhDSs0xLOfJwMbDERXW1fVoSnVo0dw7ZrckcXSUk7OIyPlFfOBA8HQUNURFm2RkZH06NGD0NBQtLS0yMvLo2fPnqxfv77IlLC8jZr85BGUTUvLQGkr2cp29OhRnJ2d8ff358iRIwwePJjjx4/nu4HzQ7H+u1PCs1r0l4WFhQGvr1EvKDMzMwAyMjLe6zyCUJJJkkRcTg4nkpNZGRPDudTU5481NDQkoEkTOqrLpM3MTLnNx9q1UKWK3HNv8WK5daKu6pPenLwckp8mE50SzYaLGzgQeoCEJwl83fprlnRegkGp4t+1SqGQO1suWSJvAYiIgNOn5Y4sz9SpA8HB0KCBysIsVpycnEhLS2Pz5s1ERkZStmxZxo4dq/ThhIWp+HwmgoA8tdXR0ZHAwEBMTEzo27cvRkZGeHl5vTZBd3BwICQk5J2u4+Hh8cIU2Y4dOwLg5+eHJEkvvINPS0sjKCgIQ0ND2rRp8x8+q3+cO3cOAEtLy/c6jyCUVCFpafzv2jXicnIAKKOtjW/jxlQoVYr6hobqs/kT5Cxv8mS4eVPuyrJmDZQqpeqonttxbQfjD48nLTsNgLJ6ZZnQcgL/q/U/2ldvXyxWMlNTIT4eLCz+GcIqSRAVJa+I+/rCiRNw8SKUKwe7dkG7dnIjne7doWJFuW1ix45q246+yAgPD2fq1KkkJCRw5swZtm/fzpAhQ1QdVqERCbpQbOzevZuxY8fi7+9P9erVAdDX16d///54e3uTmZmZbw/yjRs3vve1LS0tsbOz49ixY6xdu5ZJkyY9f8zFxYXMzEzGjRuHvr7+8+Ph4eHk5ORQu3btF971h4aGUq1aNQxfugcaFRX1/Lz2onBREN6JQpJY/+ABsyMiKF+qFN9bWtLMyAjTUqWopqen6vBe5e4OM2bIHVnOnIHmyt8z9CbnYs4x4tcRfFrvU75o+AXmxubUL18fI52iPen44UNYtAiysuTEPCBAbpSjry8n6Hl5ctn/s9XxcuWgVi15G8DHH8vJ+8vvS2rUUPqnUexERUUxYMAA7t+/j5WVFa6ursU6OQeRoAvFhKenJ2PGjGHv3r00f+kX2ZAhQ/Dy8sLb27tQE9t169Zha2vLlClT8Pf3x9ramuDgYE6ePImVlRWLFy9+4fmdO3cmOjqaqKio528oAHbt2oW7uzsff/wx1atXf97F5fDhw2RlZdGzZ09mzJhRaJ+HIBQ3B+LiWBYdTXBaGmMrV2ZZrVqUVudb4dHR4OwMEyfKG0HVaVUfeJD2gM/3fE7LKi3x7O9ZLCZ/PnkCO3bI/4WEyPOdDA1h+nRo0kReMdfQkNsgammBubncr7xFixf/eYrBTQO1kZ6ezoYNG8jLy2P+/PmUK1eOI0eOvPI7vrhS459QglBwrq6urFixgj59+rzyWJcuXbC1tWXt2rWFmqBbWlpy8eJFnJ2d8fX15ciRI5ibm+Po6IiLi8srLRg1NDTyvQXcqVMn7ty5Q0hICEFBQWRkZFC2bFk6dOjAV199JVbPBaGAknNy6Hv9OoEpKbQ2NuaPpk3poO7t1gIDYexYMDWVa83VLDkPiAzg092fol9Knz2f7ynSyfnFixAaCv36QefO8seVKsn15P36qTq6kk2SJPr27UtgYCC5ubn06dOHHTt2YGRUtO/QvAuRoAvFwvXr11/7mKamJqdPn1ZKHFWrVmXLli0Fem5kZGS+xzt06CAGEQnCe7qUlsaXN28Sk5XFZisrRlSqpN410UlJMH++vGLepo1czPyauQqqsvLcSqb+PpW2Vdvi84UPFQwrqDqk/yQuDqZOhZ075ZIUbW25tP/cOWjZUtXRFX8pKSns2bOHixcv0r17d3r06EF0dDRbtmzh+PHjaGtrk5qayo0bN/j9999p06YNxsbG6v39WwhEgi4IgiAUK4v/+otvIyNpaGjI0caN+VjdV81/+UUuZ3n6VG6bOHmy2o2UPBJ2hBnHZjChxQQ8unkU2ZXzBw+gSxd4/Bi+/14uZfn9dxg9Wu1ayRcLycnJnDlzBm1tbSpUqICpqSndunXj5s2blCpVio0bN1KzZk2SkpKetyNu1qwZNjY2ODk5FWr3NXUnEnRBEASh2Fh7/z7zIiOZXKUKiy0s1KePeX4yMuRVczc3GDQIVq2S236omdSsVEYfHM3/av+P1d1XF9lJoOfOwRdfyBs8z5yBZ11v86mMFN7BrVu3+Pnnn/nss89o1arV8+MRERHY2dkRHh7+wvPLlSvHhQsXaN68OVeuXGHYsGGYmZlx6NAhypUrh7a2dolbLc+PGv/kEgRBEISCyVEoWBETw5yICCZVqcKq2rXV+5f89eswdKjcQnHpUrnXuRoKeRjCgL0DSMlKYX3P9UU2Ob94Ua4zb9xYrh4SnVX+u+TkZE6ePEn79u0ZOXIkv/32GwA//vgjc+fOpVevXjg7O7Nv3z5q1KjBuXPn0NDQIDExkfj4eNq3b/980reNjQ3Xrl1T4WejvkSCLgiCIBRpM8PDcbt3D4D+Zma41aqlvsl5Vpbcx+/77+UJoOfOQdOmqo4qX7/f/Z0xv43hXuo91vZYS/XS1d/+IjWUnQ1ffikPCQoIkFsmCu8uMzOTAwcOMHPmTB4+fAiAoaEhK1asYMCAAcyZM4dvv/0WJycnTExMWL58Ofb29lSqVEnFkRdNIkEXBEEQiqw9jx/jdu8eU6pUYWCFCrRTs42VL8jKgs8/l4ue586Fb75Ri2mgL8vJy2HxqcUs+GMBLcxbcHzoceqavt8UZFV58AB69IDwcLh2TSTn/5VCoaBXr16cOHGCHj164OXlRUBAAP369aPl3ztrPT098fDw4NSpUzRv3pxq1aqpOOqiTSTogiAIQpFzJzOTpdHReD16xKDy5VmpjiUtWVlyPcW2bXKrkLg4uaTl11/lMZNq5mnuU45HHMflpAuXH15m/sfzcf7YWf3+Xt/i3j1wcAA/P7ne3NwcvL2hYUNVR1Z0ZGRkkJmZyZ9//skPP/zA1atXiYiIYP/+/Xz66aeAPMvjZaampvQTPSo/CJGgC4IgCEVGWGYmO2JjWRIdTRltbb63tGRSlSrql0Q+fAj9+0NwsDznPTRUbqV4/Dh89JGqo3tFeGI4nT0781fKXzSs0JALYy7QwryFqsMqsL17ISICHj2CLVvA2FjuzPLHH3JyXq+eqiNUXykpKcTHx1OrVi3u3bvHsmXL2LFjBykpKUiSRNOmTfnkk0/Yvn07bdu2VXW4JYZI0AVBEAS1JkkSCTk57IuLY3p4OFoaGoypXBm3WrXQV6d2hOnpMHy4vHT75AmYmckJeqtWoFBATo7albTEZcThGuTK2gtrqWpSlavjrtKoQiP1e8PzGjEx8lynI0f+OTZlCixYAOreXVMd5OTk0L17d86fP0/Pnj05evQoOjo6tGzZksqVK2Nra8v48ePRUqfvsxJCJOiCIAiCWop5+pRPb9zgQlra82O19PQIbt4c01KlVBjZv9y5I3dkSUuD7dvlTZ9OTnKx8/DhcpIO8kRQNUnOL9y/wOJTi/nz8Z/cS7mHnrYeM2xnMK3tNMroqX9WGxkJ7u7ykKEdO+SW8QsWwMcfQ26u3K1FeLOgoCCWLFlCQkICly5dYvTo0Rw9epTJkyfj7Oz8yuRrQflEgi4IgiConYupqQwPDSUpN5fVtWuTmpfHqEqVKK+jg5a6rO7u2iUn4VlZ8sdVqoCPj1pmiHcT77L01FJuxt/kXMw56prW5bN6n1GzTE0GNRiEqYGpqkN8RU4OBAVBcrLcq1xTEzZuhFmz5GNGRvLq+YwZIBqFFExycjI//fQTc+bMoV69elSuXJnNmzczdOhQVYcmvEQk6IIgCILayFIo+CYiglUxMTQyNOT3xo1paGSk6rBe9PSpPGBo2TJ58s3q1VC6NOio33TN327/hvNJZ64+uoqOlg4tq7Rk/8D99LXqq9Y9zSMjoX59+a8a5PlNtWvLCfvIkfDdd2BqCnp6qo2zqAgODmbSpElcuXKF3NxcevXqhbe3N6XU5U6U8AqRoAuCIAhqIT03l5G3b3MwPp7vLS1xrFqVUpqaqg7rRRERct++iAg5QXdyUnVErxWVHMUQ7yE0N2/Otn7b6F+vP0Y6avZmJx/x8fKNiadPwdMTqlWD/fvlHuazZskt5IU3S05O5vDhw0RERHD9+nX279+PjY0Nzs7O2NnZ0bJlSzTV7XtLeIFI0AVBEASVC3/yhOGhoVxOS2N7vXp8XqGCqkP6hyTB2rVye5CQEKhaFa5ckZd41dTjjMcM2jeIsvpl8RnkQ2m9olFTnJQk76lNS4MTJ+CTT+Tjz/4v5C8qKoqAgACMjIy4e/cu8+fPJycnBwALCwvc3d0ZM2YMBgYGKo5UKCiRoAuCIAgqte/xY0bcvk2WQoFPw4b0MFWjeuj4eFi4UC5jGTAAHB2hd28oW1bVkeXrUfoj5gXMY/+t/ehq6XLwy4NFJjmXJBg3Tk7SL18GCwtVR6Tenj59SmhoKGvXrmXTpk0vPDZ58mScnJwoX7482traogtLESTubwjFSkBAAM2aNcPBwYHc3FylXz8mJoaRI0dibm6Onp4eFhYWTJ06leTk5P90Pn9/f/r370+lSpXQ09OjSpUqdOvWjaNHj37gyAVBNVbFxDDg5k26li3LI1tb9UjOjx6VS1fatYPy5eGnn8DNDfbsgaFD1TI5j02PZXnQcnru7MnmkM2YGZhx0eEiraq0UnVob5WbK9+cKFVK/iv+8UeRnL+JQqHg8OHD1KtXDxsbG/bu3cuqVat48OABISEhJCQksHr1aqpWrYqurq5IzososYIuFCudOnXC3d2dzp0707ZtW0aMGKG0a4eHh2Nra0tcXBz9+vXD2tqa4OBgVq1aha+vL0FBQZQrV67A53NycsLNzY1q1arRr18/zMzMePz4MZcvX+aPP/6guxpOIhSEgjoUH8/q+/fxS0rCqVo1vre0VI/e2z4+8oAhgLZtYf16+PRTUKeSm5ccunOIId5DSM1KpbRuaQ4PPszHNT7GUMdQ1aG9VVoadOkC58/LH48fDwMHqjYmdTd9+nRWrlyJjY0Nrq6ufPzxx1T4++uzcuXKKo5O+FBEgi4UOx07dsTS0hJPT0+lJugTJkwgLi6ONWvWMHHixOfHp0+fjoeHB3PnzmX9+vUFOtdPP/2Em5sbw4cPZ+PGjWhrv/itqoq7A4LwIVxPT2dmRAS+iYm0NTHB09oa+4oVlZ+cKxQQFwfbtoGrq7yMm5sLGRlyQ21vb3iHN9Sq4hPqw6B9g+hWuxsbe22krH5ZdLTUr5vMvyUmyi0Tb92SE/LISNi3D/r1k48L+UtKSuLs2bOsXLmS2bNn891334kuLMWY+FYQiqUhQ4YQGBjIvXv3lHK98PBw/Pz8sLCweCE5B1iwYAEGBgZs376dzMzMt54rKyuLuXPnUqNGjXyTcyDfY4Kg7k4nJ9Pp6lWupaezunZtgmxs+KpSJeUm5zdvyps7TU3l5tmzZsFnn4G9PcyeLWeKx4+rbXKenZdNyMMQUrNSWXByAf1396dnnZ7sHbCXikYV1To5T02F336T28WXLQu2tvJxX1/5n0BLC9ThJoo6io+Px9ramp49e2JmZsb8+fNFcl7Mid/yQrFkb2/PwoUL2bFjB7Nnzy706504cQIAOzu7Vx4zMjKiXbt2+Pn5ce7cOTp16vTGc/n5+REfH89XX32FhoYGhw8f5vr16+jp6dG6dWvatGlTKJ+DIBSWXIWCM6mpDL55k7r6+vg0bIiZsnuGZ2fDqlXyhk99fZg8GapXl5P0Xr2UG8t/EJ0STVB0EOsvrudU9CkANNDAuYMz8z+Zrx7lQa+Rmyu/5xk6VL5p0bo1TJkit1H84gsQjUXebuHChWRkZODp6UmTJk3QVZOptELhEQm6UCzVqVOHVq1asX37dqUk6Ldv3wagbt26r43Hz8+PsLCwtyboFy5cAEBXV5emTZty48aNFx7v0KED+/btw+zZCHFBUGN5ksTnN27wa0IC1XR12VG/vnKT84wMWLkSNm+G6Gi5pmLBArVdIX9ZVm4W35/+HtczrmTmZGJlasXOT3eS+CQRu1p21DGto+oQ3+jkSRg0CB4/hmbNYO9eee+tuAlYMFevXsXDw4MdO3Ywb948vvrqK1WHJCiJ+BYpoTIzMwkNDVX6da2trZXWh9Xe3p4pU6YQEhKCjY3Na583fvx4rly58k7ndnV15aOPPnr+cUpKCgClS+ffzuzZ8YJ0c3n8+DEAy5cvp0GDBpw+fZqmTZsSERHBjBkzOHbsGAMGDHi+ai8I6up4YiIzIyK4lp7Ohrp1+apiRQyU2VHi0iXo3FmurfjiCzh4EBo2VN7134MkSfje9WVuwFxCHoXQu25vNvfZTHnD8qoO7a0kCY4dA2dn+Z+gfXs4fBiaNxclLAWRlZVFUFAQFy5cYNGiRWhqamJvb8/06dNVHZoAZGbeJjs7DhOT1khSLklJhfO7WCToJVRoaCjNmzdX+nUvXbpEs2bNlHKtmjVrAuDl5fXGBL2gGzeVRaFQAFCqVCkOHjxI9erVAWjYsCEHDhzAysqKP/74g3PnzolyF0EtPcjKYtrdu+yOi6OtiQneDRvSV5l3fOLj5XGT7u5Qsyb4+8vZYRHyjf83LAtaRrtq7QgeHVwk2iVKEty7J9+g2LIFbGxg3ToYPBiM1H+AqUpkZ2fz6aefkp6ejqamJhUrViQyMpLg4GA0NTUZP348S5YswcTERNWhlmiSlEdm5h3i438lKupbJOmfRg3h4YVzTZGgl1DW1tZcunRJJddVhoCAADZt2oSdnR27du3Czc2tUMcaP1shf7aS/rJnx8uUKfPWcz17jo2NzfPk/Bl9fX3+97//sXnzZi5cuCASdEHteMfF8dWtW5TW1mZD3bqMqVwZTWUum8bHy6vm167BzJnyxs8iUs7yzJVHV3A/647Lxy64fOyitvXlmZnwyy+QkADp6bB7N9y5I6+SL10K06fLvc2F/N26dYvhw4cTEhJCvXr1ePz4Menp6SgUCg4dOsRHH30kEnM1kJ5+nRs3PuPJkztoaOhQubIDpqa9SU8PITc3mVKlWgGff/DrigS9hDIwMFDaSrayHT16FGdnZ/z9/Tly5AiDBw/m+PHj+W7g/FCevfF4Vov+srCwMOD1Ner5net1yfyz40+ePHnnOAWhsORJEqtjYpgTGYld2bJstrJS/kbQxER5JnxsrJygN2qk3Ou/p6zcLNzOuPF90Pc0rNCQb9p/o7bJeVYWdO0KZ8+CiQkYG0PTprB8ObRsCaId9+ulpaVhaGjIwIEDyc7O5uTJk9g+a2kjqJXExGOEhg6nVKnyNGp0GGPjFujoyD3nTU27AZCScrlQri0SdKFY8fHxwdHRkcDAQExMTOjbty9GRkZ4eXm9NkF3cHAgJCTkna7j4eFB+/btn3/csWNHQO7AIknSC79U09LSCAoKwtDQsEAr3p07d0ZDQ4ObN2++ci6A69evA2AhRu0JauJGRgajQkM5n5bG5CpVWGppqdxacz8/WLMGjhyRl2/Pny9SyblCUuB51ZPFpxYTlRzFpJaT+Oajb9DVVs9OHZIk77W9dAmCguR5TsLbnT9/nu+//54DBw5gaGhIRkYGp0+fFsm5GsnOjqdUKVMUikwiIuZy//4qDAwa0KjRb+jpVX/7CT4gkaALxcbu3bsZO3Ys/v7+z0tD9PX16d+/P97e3mRmZua7QXXjxo3vfW1LS0vs7Ow4duwYa9euZdKkSc8fc3FxITMzk3HjxqGvr//8eHh4ODk5OdSuXfuFvubVq1end+/eHDx4kFWrVuHo6Pj8sWPHjvH7779TtmxZunXr9t5xC8L7Wnf/Po5371JLX5/TNjbYvmajdKG5fl1uk1i5MgwbBk5OYGWl3Bjew/3U+3y25zOC7wfTu25vfv3iV+qXr6/qsF4rPR3GjoWdO8HTUyTnryNJEikpKWRlZVG+fHnc3d2ZM2cOFhYWODo6YmJiQps2bWjXrp2qQy1xcnISSUkJIiXlFApFFlWqTCI1NZiYmBWkp/+zWKepqU+tWiuoWtVRJXeyRIIuFAuenp6MGTOGvXv3vrL5dciQIXh5eeHt7Y29vX2hxbBu3TpsbW2ZMmUK/v7+WFtbExwczMmTJ7GysmLx4sUvPL9z585ER0cTFRX1Sq352rVrCQkJYdq0aRw+fJimTZsSGRmJj48PpUqVYtOmTRgbGxfa5yIIbyJJEgCHEhKYEhaGg7k5K2rVQk+Zq+bx8fDzz+DmBnXqwMWLoKenvOu/J0mS2HBxA07HnSijV4ZTI07Rvnr7t79QhU6fljd8JiXBjz+C6PgnS05OZt68eezcuZPPPvuMlJQU/P39SUxMBORFl+joaJycnFi0aJEYMKQikiQRFjaBBw82AKCjY44k5XD//moANDSe/btoYGbWD0vLZRgYqK6NaaEm6LNnzyY2Nva9zlGpUiWWLl36gSISiitXV1dWrFhBnz59XnmsS5cu2Nrasnbt2kJN0C0tLbl48SLOzs74+vpy5MgRzM3NcXR0xMXF5ZUWjBoaGq99V16lShUuXbrEd999x8GDBwkMDKRaBQXAAAAgAElEQVR06dL07duXb775hhYtWhTa5yEIb3IiKYlRt2+TnJtLUm4ufUxNWV27NtrKmtEeFgbe3rBokVwI/fnn4OpapJLzM/fOMO33aQTfD2a0zWgWdlpIJaNKqg7rjUJD5Wmf1arBr7/KHVqKo0ePHuHm5kapUqXQ0tIiKCiI2NhYOnTogJmZGUZGRhgbG5OQkEBKSgpnzpzh1q1bKBQKGjVqxLZt22jUqBG9e/emTZs2SJLE2bNnsbe3L9R9UMKLMjJCKVWqHDk5icTErMTEpCX3768lPT0EC4tFVKjwJXp6FuTlpRIf74OhYSOMjJ59USvQ0FDiYsNrFGqCfvXqVaZPn06XLl3+8zm6d+/+ASMSiqtnddn50dTU5PTp00qJo2rVqmzZsqVAz42MjHzj42ZmZqxevZrVq1d/iNAE4T/LkyRuZGSw6/Fjvo+Opn3p0gyrVIlqurqMqFSpcG//Pn4Md++Cjo5cY754sTwT/tNP5dXzSuqd2P6bJEksDFyIy0kXbCrZcGLYCT6p+Ymqw3qrnBwYOBDMzODoUSiv/q3Y31l8fDybNm3iyJEjnDp1iho1apCVlUXjxo1p2bIlZ86cITU1lbS0tOebPPX19WndujU2NjbMmzcPc3NzFArFKx3Dxo8fr6LPquSJjz9ISsppYmJWo6GhjYaGJpKUw8OHP6KjU4XGjX0pV+5/z5+vrV2aSpWGvXQW1SfnUMgJepcuXZg5c+Y7b8D7t65du37AiARBEIR3cSMjg8lhYZxITkYLWGxhgVP16mgpoybz2DG5vjwnR/5YR0dewr1wAcqWLfzrv6fUrFS8rnrhc9sHYx1jJCR8Qn1Y8MkC5nWYh6aGku46vIewMLmU5cYN+a+9uCTniYmJuLm5ER4ezsyZMxk0aBCPHj2iUqVKHDhwgH79+r3x9flt4AcKtZ2v8GaPH+/h5s1BAFSo8AW6utVITT33d6lKXbS0jNDUVM+N1/kp1AR9+vTpzJw5EwcHB5YuXYqpqek7n2PatGmFEJkgCILwJv5JSSyIiuJUSgpltLXZU78+H5cpQwVltE6MjwcXF7nQuWNHual2TAz06CEn6Wos5WkKYYlhpGWl4XDIgajkKDrW7MjJqJMkP01mS58tjLAZoeowC+T332HCBIiIkNvJF5fOvF5eXowePRpJksjNzWXPnj1UrlyZ69evF7g7lrq2vyxJsrLuExu7kwoVBpGefo1bt4ZQsaI91tbb0CgCb37fptA3iXbs2JE1a9awefNmtLS0GDlypNggIQiCoKYkScIjJoY5ERE0MzZmR716DChfnlLKWhk8dQr69JF7+S1bBpMmga4uFIF9F1ceXaGLZxcSniQAYFPJhtCJodQqV4v07HRSs1IxNzZXcZRvl5Iivz9atQoaNy6SLeXzlZeXx9KlS/n2228ZOnQoCxYsQENDg1OnTtG9e/f/tIgoqEZS0kmuXfsfkpRNRIQTAGZm/bGy2losknNQQoL+22+/oaury4QJE4iNjWXFihVYW1vTt2/fwr60IAiC8A7is7OZFh6OV2wsDpUrs6p2beV2ZtmxA0aPhjZtYM8eta+nSHmagsMhB27G3UQDDcKTwqlnVo8Dgw4gIdGuWju0NOW/PyMdI4x01Hve/fXrsG8fbN4sl/67u8PUqXJr+aIuMzOTfv364efnx/z583F2dn6+Cl6jRg0VRycUVGbmXTQ0tAgLm4SxcXOsrX8mOTkQTU0dKlQYhKZm8WlOWOifyb/7TlesWJFZs2bx559/smjRInr27IlNcd0KLgiCUERIksTxpCSG3LpFel4e2+vVY0jFisoLIDYWhg6Va86/+AI2bQJDQ+Vd/z84F3OOz/d8Tnp2Ol81lvsNfl7/c75u/TWl9ZTcC/49ZWfDli3wf/bOOzyK8mvD9242vRdSIIFQAkkooQuhSf+UjqKIKCodlR8IgoIEVFBAEJGOSEcBBRFBSoBQgogYegtJSEJ6T0iyKVve74+RaKQImt0lYe7rygWZmZ1zdll2n3nnnOe8/bb0svfsKU0ErWncuSwGZezYsfzyyy8cOnSIrl27mjodmX9BQsIiYmKksmel0pbmzX/BxqY+Njb/PKG7MmJwgX7gwAF69uxZblvjxo1p3Lgx+/fvZ968ebz66qt4yXOBZWRkZIyKTggWJSSwJiWFyKIiujo5sSUwEA9j1nmHh0OfPpIzy+LFMGrUY22ZWKItYezesaw7v4423m3Y+txWajlVrhVYIeDQIbh1C+LjpeuhlBR4/XVYufKxL/N/JEpKSggJCWHjxo2sXbtWFueVjMLCa5iZ2XLz5lTS07fi6fk6Tk5PY2/fGltbf1OnZ1AMLtAXLlxYJtBLSkrIysoiOzubrKwsioqKcHBwoFevXgwYMIB3330Xq8f4g1lGRkamqlCs09Hr0iWO5ubysocHC+vV4/9cXIzjzgLw66+webNUT9GmDezYAS4uxon9iAgh2HhhI99d/Y5TiadQa9Ss7LWSN5q9gblZ5eipKiiQXu60NKmSKCpK2m5vL920mDgRAgJMm2NFkZ6eztSpUwkPDyc6OhozMzNee+01hg37u52ezONMTMx7JCTMA0ClcqV+/dV4eb3xWHiUGwODC/RDhw7h7e1NTk4ORUVF9z3u6tWrHD58mKNHjxo6JRkZGZknnpC4OMLz8jgUFERnY1oWXrgA06ZJnuY+PlIT6McfP5ar5nqh50bWDZb+tpRlZ5bR2bcz41qO47nA52jq2dTU6T0UBw9KvbZnzkB+Ppibw4svwldfQfv20o2Lyo4Qgjlz5nDr1i10Oh07d+5EqVQSFBREfHw8e/bskYcEmRAhdOVEdUbGThITv0Ctvka1ai/i4/MOWm0uaWmbuH37DBYW7oCSzMwd1Ko1A0vLGjg5da6ypSz3w+AC3dHRkW7duhEZGYm9vT19+/bFxcUFNzc3XF1dy37kseUyMjIyhiWppIT1qalcKyxkS3o6n9WpY1xxvnevNCvezk5SjZMnw2PmG63RaZgSOoVzqee4lnmN9MJ07Czs+Kz7Z0wOnmzq9B6JuDgYNAj8/SWbxBdeAC+vx768/6EoLS1FpVLx448/MnLkSLKyssr2jR8/nhkzZuDq6srt27fvmuIsU3GUlmaQkfEdmZm7qV59JNWqPVe2T6vN59q1IWRl7UGlcsXauh6WljXIzPwRO7smODk9TWbmDlJS1iCEFoVChRAlWFnVQaVypkaN/+HrO/OJWTH/OwYX6C+88AKrVq0C4JtvvuH06dNMnDgRX19fQ4eWkZGRkQGKdDo+iI3ly6QkAOpYWbGkXj3erFHDOAmkpUmuLLNmQbt28O238JiIpvjceDZf3IydhR0Olg4cjT/Kxgsb8XPxo2/9vvRp0IenfZ/GwdLB1Kk+EjdvwoABUtXQwYOPzcv9yKSnp6PX6/H8Y2JsXl4en376KZ999hmOjo7k5OTQrl07pkyZQs2aNdFoNLRq1ars8bI4r1j0eg2JiYvJzNyFs3NnkpNXo9Gko1I5c/VqGD4+k/DyGk5S0gqSkpaiVFpSu/YnlJamUlQUTWHhZapXH0O9el+gVKrQavO4cWMMAPXrr0KhMEOptHpiRflfMbhAvyPOAYYMGUKfPn2YO3cuAFOnTsXBoXJ96MnIyMhUJo7l5jLg8mXUOh0f+voytnp1nI05iyIuDp55Bq5fh+Bg2LjRpGoxrSCN0XtGoxd6IrMiuZF1A0szS0p0JQA4Wjqy+P8WM/6p8SbL8b9w8aLkVHnmDNSpAz/+WDnFeWpqKh06dCA6OhqlUsmwYcPo2LEjISEhpKWl0bBhQ9q0acOwYcMIDg6WBwcZgaSkZcTFfYRGk4mlpTfx8bOxt29NUNBhbGz8iI0NISlpCbdufYpCYYGn52tUrz4Ge/v7u/WpVI4EBn5rxGdReTC4QI+NjS03mcve3p45c+Zw5coVRowYQadOnRg7dqw8HldGRkamgkkrLWXw1av429iw3t+f+n+xvTU4ycnwwQewbh14eEBkJNQ3XQ2pVq9l88XNzDo6i/i8eLrU7kID1wa0rtGa5c8up0hbhLXKGmtza1SVzEtZp4NNmySrxAsX4PZt6NSp8orznJwchg8fTnR0NBMnTkSlUvHtt9+ybt06ateuzY0bN2TvcgOj15ei1xej0WSRkbGd4uIEUlJW4eLyDLVrz8bWtjHFxbFYWnqjVEq2P3XrzqNmzank5BzCzq7pE1czXtEY/FNozJgxHDhw4K7tDRs2ZPv27WzdupUePXowYcIEevfubeh0ZGRkZJ4IYouK6Hz+PEIIdjZsiKelpXEC5+TA7NmSZaKdHXz+udSVWN00EzQT8hJYdmYZ31/9npicGAYGDCT0lVD8XP3KHWdvWTn7oDQayUJ+61Zo1EgS5l9+CbVqVc4BQ1lZWbRu3ZqsrCx2795Nnz59AJg7dy5nz56lbt26OBuzb+IJ4Pbt3yksvICn5+sUFFwgKWkJmZm70OtLAT0gMDd3x9t7ArVrzykT5NbWde46l7m5C+7uLxj3CVRRDC7QQ0NDy5WxCCHuOkar1XLkyBGeeeYZ9u7da+iUZGRkZKo0+Vot/S9fxkyh4NfmzY0nzhMSJM++8+dh+nSYMAFMJKZ0eh0bLmxg9J7RALzU6CW2Pb+NFtVbmCQfQ5CYKPXcnjolTQB97rl/fszjjF6vZ9iwYeTm5nLu3Llyd9+VSiUtW7Y0YXZVD7U6GiFKuHTpGTSaTOLjZ1NcHIdK5YKtbROUSktsbRvj6zsTlapyXsBWZgwu0FUqFf7+/jg7O+Pi4nLXj6ura9nf3d3dDZ2OTBXnyJEjTJ48mZYtW7J8+XJUKuPeqk5MTCQkJIT9+/eTnZ2Nl5cX/fv3Z+bMmTg5OT3wsevXr+eNN9544DFKpRKtVluRKctUMfZkZjIuKoocrZZfmjXD19ra8EGLiqTRk3PnSjUVhw5B27aGj3sfjsYdZUroFM4kn6GNdxu2Pb+Nmo6VeyxmSYl0/bNlC6xfDy1bQliY5Mhy8CB07mzqDP890dHRLFy4kJUrVwKwZ8+ecuJcpmKR3FWGkpW1GwBLSx8CAraQnr4VH58peHmNQKmsHP7+VRmDq5fevXuzc+dOQ4eRkQGgS5cuLFy4kK5du9K2bVtef/11o8WOiYkhODiYjIwM+vfvj7+/P6dPn2bx4sXs37+fkydP4vKAQSzNmjVj1qxZ99x3/Phxjhw5wrPPPmug7GUqOzfUaqbevMmuzEz+z8WFpX5+1DWGOA8NhZEjpZrziROllXMTNv/vjtzNkB1DqOlYkx9e/IE+9ftgpqy8jhAFBVIZ//z50oq5UgnPPw8xMVJpy+TJJqseqhDOnDlDjx49yM3NxdLSkpCQEHr16mXqtKocWm0eyckryc8/S2bmDyiVVjRosA6l0hx7+5bY2DTAw2OIqdOU+QsGF+hbtmwxdAgZmXJ07tyZOnXqsHHjRqMK9HHjxpGRkcGSJUt48803y7ZPmjSJRYsWMX36dFasWHHfxwcFBREUFHTPfW3/WI0cNWpUxSYtUyX4ISODUTduYKtUssnfn5c9PAzraqHXSwXOZ85IXn5PPSUt45qoCVSr13Iu5Ry7I3fzafin9Krfi28GfoOtReU1/NZqJWEeEgKpqdCkiTR0tWFDMJY7piEoLi5m7NixODg4kJKSwnfffUerVq3Yt28frq6upk6vyqDV5pOXd4LS0nQ0mjSSk1dRWpqCpaU31aq9QI0a43B0DDZ1mjIPwKACfcqUKdjY2NChQweCg4Oxvs9qzpkzZ2jatCnmxrT+kqnSvPzyy8yePZuEhAR8fHwMHi8mJobQ0FBq165dTpwDfPjhh6xatYrNmzezcOFCbB7RSePSpUucPn0ab29veWVJphwlej2vXLvGdxkZ9HZ1ZV2DBrhZWBguoBBSfcW0aZKCzM2FZs0kuxA7O8PFfQBFmiI6rOtAREoEChRVQpwDjBsnTft8+WWYM0dq+qzMqNVqRo4cybFjx8jKyqJGjRpkZmYyb948xo0bh52J3j9VAZ2umIyMbdy+fQYrK180mkwSExcihFQOqVBY4ubWD1/fD7G19TdxtjIPi0EFekFBAcuXL2flypVkZ2fTokULOnToQMeOHWnfvn1ZTa5Wq2XBggVUq1aNESNGGDIlmSeEoUOH8vHHH7Nlyxbee+89g8cLCwsDuOc4aTs7O9q1a0doaCi//vorXbp0eaRzr169GoDhw4fLXr8yZeiF4PXr1/kxM5OtgYG8UK2a4d4fCQmwZw/8/LP05+DBUK+e1AD69tvS/HgTcCX9CjPCZnA5/TKbBmyirXdb6rrUNUkuFcmPP0rifOlS+Nv1fqXj2rVrTJw4kYiICAoKChg6dCjDhg2jffv2pk6tUiOEICNjO7m5x8jK2ktJyS3MzOzR6fJRKCzx9n4HL6/hKBQWqFT2mJvLdycqGwYV6BMnTuT27dts3ryZq1evEhYWxpEjR1iwYAEKhYJGjRrRsWNHOnbsyIABA1i0aJEs0GUqBD8/P1q3bs3mzZuNItAjIyMBqH+fW/x+fn6EhoYSFRX1SAK9qKiIzZs3o1Kp5P8bMmUU6XS8ExPD1vR0tgUGMsgQDfZCwKVL0gTQVask+8Tq1WH3bvjD+s4UZKozCb8VzsfHP+ZsylnsLOzYNGATgxoOMllOFUVEBHz8sSTQn30Wxo41dUb/Dp1OR2hoKAsXLuT06dNli2+vvfYaDRo0MHV6lZ68vF+Jjn6b/PzfUamccHLqSlBQKDY29dFq8zAzs5MncVYBDCrQ/fz82Lx5MwCBgYEEBgaSkZHBrFmzMDc3Jzw8nPDwcKZNm0ZiYiLTp083ZDoyf0Gtlgb7GRt/fzDWrJShQ4cyfvx4zp07R7Nm959kNnbsWM6fP/9I554/fz4dOnQo+z0vLw+4/1jpO9tzc3MfKc727dvJy8ujd+/e1KjMhacy/xm9EITn5WGhUPB5YiI7MzJY7udnGHGemwuvvCKtljs6SoJ8/nzw8qr4WP/ALwm/EJ8bj7O1MxHJEXwa/imFmkIauzdmxws76F2/NxZmBizrMQK//Sb11h46BHXrSsNWBw+WGkIrE+np6Vy6dIkVK1awY8cOGjVqxOTJkxk1ahSenp6mTq9KoNMVcfXqCwihJyDgWzw8Bpfbr1JVwslUMvfE6OPSbGxsaNy4MQD+/v5lq4JffvkljRo1MnY6TyzXr0MLE9gBR0RA8+bGieXr6wvApk2bHijQH9S4aWrulLeMHj3axJnImAohBNNjY1mQkIDmL3MkZteuzRhDXLSdOAEDB0J+PnzzjfR3Y/mo/wWtXsu88Hl8EPZB2TalQomHrQdnR5/Fz8Wv0pd8ZWdLzpQLFkhDhjZtkoS5kd1h/zV79+5l5syZ6HQ6zMzMuHjxIhqNBgsLC7788kvGjBkj95ZVEELouHz5ObKyfgSgdesobGzqmTgrGUNi9I+BmJgYfvnlF4KDy3cPjx8/nlmzZj1yfa7Mv8PfXxLLpohrDI4cOcKaNWvo0aMHW7duZcGCBSgNuBx1Z4X8zkr637mz/Z+80P/KlStXOHXqFD4+PrK94hNKckkJ46Oi2JGZybs+PnR1dsZVpSJDo6FrRQ8AysuD//1PUomdOkl/muCujV7o2XJxCx8d/4jo7GjeDX6XycGTuZpxlfY12yOEwNyscou+0lLJoeXjj6WbFR98ADNnglklqkoIDw9n4MCBtG3bloCAAHQ6HS+88AIDBgzA19dXFuYVTFLSCrKyfsTJqQtOTp1kcf4EYJRJot27dy/7fcaMGXTp0oXmzZszYMAAOnbsiJeXFxqNhtTUVEOnI/MHNjbGW8k2Nvv27SMkJITDhw/z888/M2TIEA4dOnTPBs6Kwv+PK487teh/JyoqCrh/jfq9kJtDn2x+zMzkxStXcFKpWO/vzzBDlQgcPizVmf/0ExQWwhdfwOjRYEg3mPtwu+Q2E/dPZO35tfRr0I/vBn1HU8+mALjbVo1BdocOwfDhfw5dnTsXalayGUonTpygf//+BAcHc+DAASxM8F55UigpSSI9fSvx8Z/i4TGMgID1pk5JxkgYXKC/++675ep7vb29CQ8PZ/LkybzyyitotVrs7e1RKBQsXLjQ0On8a0pKSggJCWHTpk3k5ubSpEkTZs+eTbdu3R7pPCNHjuTrr7+mV69e/PTTTwbK9sll165dTJgwgePHj+Pg4EC/fv2ws7Nj06ZN9xXoo0aN4ty5c48UZ9GiReVcCDr/McYvNDQUIUQ5QZ2fn8/JkyextbWlTZs2D3X+4uJiNm3ahEqlYvjw4Y+Um0zlRi8EnyUkMCM2lt6urqxt0AAnQ6xGarUwapS0lFu/vjQnfuJEqFOn4mM9BAeiDzDxwERic2P5qs9XjGhe+ZuiMzKkKqGjR8HTU3ppZ8yA9u1h/34ICDB1ho9GRkYGM2fOZMWKFQQFBbFz505ZnFcAJSXJKJVWmJtLg+x0OjV5eScoKoohPn42paUp2Ng0pHbtD02cqYxREQZGoVCIkSNHiszMzLv2ZWZmij179ojvv/9eJCQkGDqV/8TgwYOFubm5mDJlivjqq69EcHCwMDc3F+Hh4Q99jjNnzghzc3NhbW0t+vTp88BjIyIiBCAiIiIq5Lgnga1btwpHR0fx+++/l9v+6quvCjs7O1FYWGjQ+D179hQKhUIsWbKk3PaJEycKhUIhxo4dW257dHS0uHbtmtBoNHeda+PGjUKhUIi+ffv+p5zk90flIqW4WPS/dEkow8LEpKgoUarTGS7Yxx8LoVQK8fXXQuj1hovzD9wuvi2G7hwqmIVw/8xdhMWGmSyXiuD4cSGWLBFixQohnJyEsLAQokMHIczNhQAhxo0ToqjI1Fk+Onl5eaJNmzbCyspKzJw5U+gM+d58grh9+3dx4oSLOHrUUhw/bifOnGkqTp8OEGFhiLAwxJUrg0VxcaKp05R5AIb6njW4QO/SpYsoLi4Wy5YtEytXrhSlpaWGDlnhnD59WigUCrFw4cKybcXFxaJevXoiODj4oc6h1+tF27ZtxYgRI4Svr68s0CuYDRs2CAsLC/Hjjz/ete/AgQNCoVCITZs2GTSHmJgY4eHhIRQKhejfv7947733ROfOnYVCoRD+/v4iOzu73PG1atUSCoVCxMfH33Wu9u3bC4VCIfbs2fOfcpLfH5UDnV4vdqSni7qnTolq4eFiW1paxQfR64U4eVKIt94SYvBgSS3OmFHxcR6SzMJMsf3ydhG0Ikg4fOogVv++WuhNeKHwbzl7VoiffhIiPFyITz6RXtY7P/36CZGRIR1386YQR4+a9FroX6PX60WvXr2Eo6Oj+O2330ydTpUhPn6+CAtTiN9+CxJRURPE+fM9xJUrQ8TFi71FdnaYKC29e2FT5vGj0gr0v65apqamirlz54pdu3YZOmyF8u677wpzc3ORn59fbvunn34qFAqFSEz856vbDRs2CEdHR5Gamipq1aolC/QKpmHDhmLp0qX33KfT6US7du1EmzZtDJ5HQkKCeP3114WXl5ewsLAQvr6+YuLEiSI3N/euY319fYVSqbxLoF+9elUoFApRs2bN/yxY5PfH402xTidO5OSIbufPC8LCRMezZ0W0Wl2xQfR6IQ4fFqJFC0k1OjsLERQkxKJFJlGLNzJviFG7Rwm7T+wEsxCNljcSl9IuGT2P/0pxsRDvvSeEQlFelE+eLERJiRCpqabOsGJITk4WgwYNEoDYvXu3qdOp1Gi1hSItbbu4cuVlcfPmTHH0qIWIjHxT6HSVb+FS5k8M9T1r8Br0v4419/DwYOrUqVy6dInZs2fTq1evB9rfPS6cO3eO+vXr3zWKuFWrVgCcP3/+gR7V+fn5TJ06lWnTpuHh4WHQXJ9ULl++fN99SqWS8PBwo+Th7e3N2rVrH+rY2NjYe24PCAhAr9dXZFoyjxlCCDalpfHezZuklJZSw8KCg02a0N3FpeKDffyxZBHSqBEcOABdupjMx+/nqJ955YdXKNYWM7TxUD7o+AHeDt6Vrgl6+3b48EOIjoZZs2DkSGmOk6Wl5GMOUNk/6oUQHDx4kIkTJ3Lt2jWGDBlCHxMOqKoMFBfHY2lZE4VCgRB6hNAghMDMzIq8vJNcv/4aRUXRmJk5oNeXYGcXRO3as1EqZccbmbsx+Kf0gQMH6NmzZ7ltjRs3pnHjxuzfv5958+bx6quv4mWCARgPS0pKyj3zu7MtOTn5gY//6KOPsLW1ZeLEiQbJT0ZGpvJQrNMxLiqKdampvFCtGlNq1iTI1hZVRduACgEbNkgKcto0+Ogjk/n4RWZGsvHCRpaeWUqwTzCbB2zG1aZyjR7ft0+6vrl4EcLC4JlnJCfKO25Yj/FX2COTkJBASEgI69evx9/fn9DQUDp16mTqtIyCWh1FbOwMLCzcMTd3Q62+hk5XiJtbP6yt62Fp6Y2lpXeZGYBafYOSkiQSEj4jN/cIDg7tUChUFBScQ6fLR6GwwMmpIzk5h3BwaENg4HfY2TUBFJXuwlTGuBhcoC9cuLBMoJeUlJCVlUV2djZZWVkUFRXh4OBAr169GDBgAO+++y5WVlaGTumRKSoqwvIegzru5FpUVHTfx964cYMvv/ySrVu3yr6wMjJPMOmlpXybns5nt26RpdWywd+fVw05XXHJEsnX/NVXpVV0E4ylLNGW8MP1Hxi/bzwZ6gx61u3JNwO/wdm6gj3cDURREVy+DN9+C4sWSS4sgYHw1VcwovKbzJRDCMGKFSvYs2cPR48exdLSktWrVzNixIgqKyQ1mhx0uttYWdUiJ+coCQmfoVZfp7j4JjY2AWg0GVhZ+QJmREbe6x9cAUjDw+zsmlGz5vtkZu7GysoXD48hWFvXR6PJJCfnMHXqzMfHZyIKRSUyu5cxKQYX6IcOHcLb25ucnJwHCtmrV69y+PBhjh49auiUHhlra2tKSkru2l5cXFrfjYQAACAASURBVFy2/37873//o127dgwYMMBg+cnIyDy+ZJSWMj8hgWVJSRTp9Tzn5sYMX1+C/lYyV2EkJcGqVTBnDkyeDJ99Zpg4D0CtUfNVxFd8+duX3My5SVPPplx789pju2qu1/95/ZKRAT17QmysNEQIwN5eusb54IP7n6OyotFo2LNnD8uXL+fQoUN069aNadOmMX78eBwcHEydnkEoLU0nLm4mqakb0evVeHq+RlraN9jaNsTOLojAwG9wcHiq3GN0ukJKShIpKUmkuDgBITTo9SXY2PihVNrg6NgehUJBnTqf3CPiHOM8MRmjkLknE222FpeeLqhcVORfyDdIHIMLdEdHR7p160ZkZCT29vb07dsXFxcX3NzccHV1Lfuxt7c3dCr/Gi8vr3uWsaSkpABQvXr1ez7uyJEjHDhwgJ07dxIXF1e2XavVolariY+Px8XF5YHPfeLEiWVTKu/w0ksv8dJLL/2LZyIjI2MsMkpL+eTWLb5KTkahUDDZx4c3PD3xfcAF/X+ipAS2bIF33pFGVU6cKE3BMTI7r+1kxO4RFJQW0Kt+L7Y/v50gzyBUysdjfn1JCSxeLInu9HQ4dw727pV8ymvWhORkiIuThgg1aQIdOkhlLH9pp6qUCCG4cOECCoWCXbt2lc30KCkpoaCggJYtW7Jz584qv5iUn3+ey5f7odPl4+U1nJKSJNLSvsHdfTANGnyFUnlvX3czM1tsbBpgY9PAyBnLPA7cPn2b3GO5fLvtW3af3V1uXwEFBolp8E/MF154gVWrVgHwzTffcPr0aSZOnIivr6+hQ1cYzZo14+jRo+Tn55cT06dPnwagadOm93zcrVu3ABg4cOBd+5KTk6lduzZffPEF48ePv2/sRYsW0byqjvyUkamCFOt0HM7N5ZP4eC4WFvJmjRq86+ODmyEHusTEwLBhcPIkvPgirFgBzsYtI4nPjeejYx+x4cIGnvF7hi96fkFdl7pGzeFBCAFHjkgl+Xd6xpVKsLWVhgfduAFqNTRoAOPGQcuWJk23wjh27BjLli3j8uXLXLt2DaBsiFtgYCAKhYJnnnmGJk2amDhTwyKE4NatecTFzcLWtiHNmoVjZeVTtq+qlvHI/Hfi58YT+34sSislXQO78uq6V3Fo40Du4VyKE4pJCkyi07CK79EwuEC/I86Bsi7wuX+s6kydOrVS3EJ7/vnnWbBgAatXr2bSpEmAVE+/bt062rRpU+bgkpqaSm5uLvXq1UOlUtG1a1d27dpV7lxCCEaNGoWvry/Tp0+nUaNGRn8+MjIyhiE8N5fXrl8nprgYRzMz9jdpQru/3QGrUPR6CAmRylg8PODECWlMpRFJLUhl9vHZrI5YjbO1Mwt7LGRcq3GYmz0ePTeXLsH69XDwoFRP3qwZHDoEHTtCQQEUF1etBs+/cvPmTfr164e3tzft27dnwoQJeHt706VLl8ey38uQ3Lo1j9jY9/HxmYKv70zMzP68JSKLc5l7URRTxPU3rpN3PI+a02pS++PaKJR/vlds/W0ByDubZ5D4jyTQs7KyWLBgAT4+PowbN+6hHhMbG0vt2rXLfre3t2fOnDlcuXKFESNG0KlTJ8aOHYvSBA1MD0vr1q0ZNGgQ77//Punp6dStW5cNGzZw69Yt1q1bV3bce++9x8aNG4mLi6NmzZr4+Pjg4+Nz1/n+97//4eHhQd++fY35NGRkZAzI3qwsnr9yhZb29qz196eJrS1OhmwMFwLGj4flyyWRPmWK0eswMtWZtFvbjuyibD58+kPefupt7CwMVFv/iOTlwaefwrx5kqvk889LjZ5du8IdPWbkmwxG5ezZswwZMgRXV1dOnjx5V6nkk4IQelJSviY2djo1a75/nxpxmScFXbGO26duU3i5kMJLhShUCmpOrUlJcglpG9PI3p+NZS1LzF3Myfo5C0svS/w3+OMx1KOcODcGjyTQ+/Tpg6WlJaGhoQ8t0MeMGcOBAwfu2t6wYUO2b9/O1q1b6dGjBxMmTKB3796Pko5R2bhxIzNmzGDTpk3k5OQQFBTEnj17aP+X1SqF4uFsk+SrdRmZqsMNtZqlSUmsSE6mt6sr3wYEYGVoO0O1WhLky5ZJDaGjRhk23h/ohZ7NFzczN3wulipLkvOT0eq1RIyKoI5zHaPk8DDMnSs1darVkjBftQoMYTH/uJGdnc2JEycYNGgQGo2Gpk2bsmvXridOnBcWXic2dhoFBecoLk4AdNjbP0WtWiGmTk3GyAgh0BXqUNmpUEerufriVQrOFqCwUGATYENpainJK8r3GBbHSQYgNafVpNa0WpjZmsZ555EEelxcHLNnz+bVV1996MeEhoaWK2MRQtx1jFar5ciRIzzzzDPs3bv3UVIyGpaWlsyfP5/58+ff95h169aVW1G/H/cbUCMjI1N5yNVoGH3jBtszMnAzN+eDWrWYXrNmxfuZA2i1cOYM/P67tOy7Zo1USL14sVHE+amEU2y/sp2IlAhO3DpBf//+2Jrb0sKrBR93/hgv+8ejRkQIqX585UrJXXLGDKhXz9RZGZ6rV6/y5ptvlnNBGzNmDIsXL8bCkL0PjwFC6MnK+onY2BkUFUWjUjlSWpqOlVVNrKxqU1wcR2DgNtzdXzB1qjJGoCSphJKkEmKnx2LpbYm5mzkJCxNwaOtA/u/5KC2VBB0OwrGjI0qVEk2WhrTNaVjXs8a2kS1CJ9AX67GqZWUyYX6HRxLo27dvZ8iQIbz33ns8++yzdO/enXbt2j2w4VOlUtGgQQNcXFzu+ePq6lr2d3d39//6fGRkZGQMznfp6YyMjEQPrGnQgJfd3Q23ap6ZKU3F+f338tvnz5dKXAxEZGYkWy5tIfRmKL8m/koN+xrUcKjBoVcO0bVOV4PF/Tds2yYNDTp1CrKzpR7ZMWNMnZVxCA0N5cUXX8TDw4MPP/wQV1dXhg8fXmVqzDWabECJublT2bbCwiskJS3Dzq456elbyM09ikrljFJphV5fjJ/fMry8XkehsECjScfCopKPdZV5KAouFnCh6wU0mRoAFOYKhEbg8n8uKFQKqo+qTu05tVE5/Cl9zV3N8f6ft6lSfiCPJNDbt29PZGQkGzduZP369WzatAkhBG5ubgQFBREUFESzZs0ICgrC398flUpFnz592LFjh6Hyl5GRkTEaFwoKeDcmhtCcHAZVq8YX9epR/R5DzCqEoiKp+fOzzyS7kf37JWsRISTXFgPZjOiFnmW/LWNG2AzMlGY87fs0y55dxhvN3sBK9fiJvp9/hpdegtq1oV07yczmuedMnZXhOHz4MNu2baN79+4cOnSI1atX07lzZ3bu3ImTk9M/n6CSUFycyNmzbSgtTUKhsKRWrffx8HiVuLgPSUvbyJ0BQQ4O7QgI+AY3t34IoQP0qFR/lvTI4rzqor6hJmNHBh6veKDJ1HCh2wUsvSypt7gezj2cUSgV5Efk49jeETPryjcg6pFdXKytrRk9ejSjR48mNTWVI0eOEBYWxvHjxzl8+PCfJ1apqFevHoGBgcyaNYuGDRvSqFEjGjRo8Fg3hMrIyMj8nZ8yM9mQmsr+7GxqWVmxLTCQQdWqGa6fJDMThgyBY8dg9GiYNk0y6r6Dm5tBwkYkRzD9yHQOxhzkxUYvsqLXCpysHi/Rp9VKXuXLl8OePXDlCvTuDT/+aJJhqQYnPz+frVu3snTpUi5dulRWJvrVV1/h7OzM4sWLefvtt6tUb5NaHcX1669RWpqEt/ckNJoM4uNnExc3C4XCgnr1vsTd/UVAYGEh33l/Esncncnl/pdBQOw0qWzYroUdQaFBmDv/2Zzv0r3yNp/8J5tFT09PhgwZwpAhQwBIT0/nl19+4eTJk5w6dYqzZ89y/fp1du7cWfYYS0tL/P39adq0Kc2bN6dFixY0a9bsgdM4ZWRkZEyBEIIvEhN5JyaGIFtbxtaowcxatbBTGcihVgjYvRteeUWyHtm/Hzp3NkysP8gpyuHXxF/ZF72PZWeW4ePgw94he3nG7xmDxn0Y9Hr44QfpeqVOHYiOlpxZEhIkw5rnn4fp06UV86omzgsKCvjiiy9YtGgR2dnZ1KxZkyVLllC7dm169OhBXFwctWrVwtyQTkEmQK2+QUREK8zNXWja9BhOTh0BqFfvC9LSNmNr2whnZ8P+n5B5PNEV6kjdmIrSWklcSBzOPZypv6w+mbsz0RfrqT62OuZOVef/Q4V+y7i7u9O/f3/69+8PSCOEL168yK+//srp06c5c+YMN27c4MKFC1y4cIENGzYAYGZmRkBAAC1btqRVq1YEBwfTpEmTKrUiICMjU7nQ6PVMiI5meXIyk318mF+njmE/kzIz4d13JdPunj2loupq1QwWTgjBsjPLmHZ4Gvml+ThbOTO782zebffuYzH1MylJavJct04S33q9tN3eHnbsgDZt4D5DnCs9QggGDx7MoUOHGDlyJFOmTKFGjRrl7j7Xq2LdrzqdmoKCc0RGjsLCwosWLU6XK1UxN3fG2/ttE2YoY0pKM0uJfD2SrD1ZAFjUsKDB6gZY1bTCZ+LddtZVAYN+Cpubm9OiRQtatGjBm2++CUirAufPn+fs2bOcP3+e8+fPc/XqVS5fvszly5dZv349IPmlP/XUUwQHB9OuXTvatm2Lnd3j4a8r8/hy5MgRJk+eTMuWLVm+fDkqQ6103ofExERCQkLYv38/2dnZeHl50b9/f2bOnPnQ9aFCCLZv387KlSu5ceMGOTk5eHl50aJFC9555x3atGlj4Gch83VKCosTE7laWMiq+vUZZSglqNdDYqJUr7FgAVhawtdfw+uv/2nWbSA2XNjA2/veZkyLMUwOnkwdZwNfgDwkGRkwcaLU+GltLVkkvvginD0LzZtDaalBr1tMTn5+Pp988gl79+5l165d9OvXz9QpGZQ7Ez4TExei0WQC0KrV1XLiXKbqIXR/2B863P87uuBCAXEfxWFZ3ZKUtSkgoNHuRlj7WWPpbYnKzvQLCYbE6M/Ozs6O9u3bl/MP1+l0REdHc/XqVa5evcq1a9e4du0aJ0+e5NChQ4C0yt68eXO6dOnC//3f/9G+fXvMDO01LFPp6NKlCwsXLqRr1660bduW119/3WixY2JiCA4OJiMjg/79++Pv78/p06dZvHgx+/fv5+TJk7g8hBnzyJEjWbt2LW5ubvTv3x83NzeioqL48ccf2bFjBxs3buTll182wjN68jiWm8vwPyaBdnZy4pfmzWltqGnHmzfDhx9KdRuWljBzpmQ9YiD1WaIt4UjsEfbc2INO6Fh7bi2vN32dFb1XGCTevyEsTLo2Uaul3tg33oA7L7+BK31MzrVr11izZg3r168nLy+P6dOnV1lxnpW1HwsLdxQKc+LiZpGZuRMXl//D0rIm7u6DsbUNMHWKMv+AXqNHaa6kOL6YjJ0Z5IblUn1sdVyfcS13XPbBbHKO5GDTwAb7VvbYNrQldkYsKWtS0GZpcR/iTq0ZtVBaKcnen01pUilWta1Q2iiJeisKoZVsD117u+K3zA8Lt6ptG/pXHovLDzMzMxo0aECDBg0YMGBA2Xa9Xl+uJCYiIoIVK1Ywb948PDw8GDlyJFOnTsXW1taE2cs8bnTu3Jk6deqwceNGowr0cePGkZGRwZIlS8ruGAFMmjSJRYsWMX36dFaseLAYio+PZ+3atXh6enLx4kXc/tIMePToUbp06UJISIgs0CuY21otr1y7xu6sLDo5OrLUz4//c3X95wf+G7KyYMIESaAPGACffy45shho3nxhaSErf1/JwlMLSSlIwdXaFWdrZya1ncRHnT8ySMxH5eJF6SUJC5OcWNatAz8/U2dlHJKSknjzzTf58ccfcXBwYNSoUYwfP/6eU6grM0IIkpKWcfv2SdLTt5ZtNzf3oEGDNXh5DTdhdjIPg65YR97xPBI+SyAnLAfX3q7kHslFl6/DzNGMnCM51Pu8Hp5veJJ3Io+kZUlk7sjEzN4MXb5OOokZoAOPVz1QOanI/CGTjB0ZAOgL9eXimbub0/J8Syw8LFCoHm4QZJVCVDJ0Op04c+aMCAkJEb6+vsLb21ucO3fO1GlVOBEREQIQERERFXLck0ZISIhQKpXi1q1bRokXHR0tFAqFqFOnzl378vPzha2trbCzsxOFhYUPPM+ZM2eEQqEQ/fv3v+d+e3t74eDg8NB5ye+PfyartFS0/P134Xj8uPj81i1RotNVfJC8PCEOHRJi7FghlEohXFyEWLu24uP8DZ1eJ/pv7S+YhXh++/PifMp5odfrDR73YdFohPjsM+kl8fUV4pNPpJfqSSAhIUG89dZbwszMTHh5eYkNGzaI4uJiU6dV4ajVN8XVq6+KM2eai7AwxK+/1hM3b4aI7OzDIjl5ndBo8k2dosw/oCvVCU2eRpztcFaEESZ+rf+ruPLSFXHM+pi4NOCSKLpVJDT5GnFlyBURRpg44XxC+tP1hLgZclPodXpRnFIs0r5LE9HvRouMXRll5y7NKRUX+14U57ufF+oYtcj7LU+oY9Si8Eah0BZqTfisHx5Dfc9WOoH+VzQajZg+fbpo0qSJqVOpcGSB/t+4ceOGUCgU4tNPPzVKvK+++kooFAoxZsyYe+7v0aOHUCgU4vDhww88T1FRkfDy8hJeXl4iMzOz3L5jx44JhUIhBg4c+NB5ye+P+1Ok1YpvUlNF4OnTwi08XJy9fbvig9y+LcSHHwphaysECOHgIMTMmUIkJVV8rL+RV5wnBm4bKBSzFOKnyJ8MHu9hyckRYuVKITp0kF4SEGLKFCFKS02dmXGIiYkRgwcPFiqVStjb24s5c+aIjIyMf35gJUKrLRDJyevE2bPtxfHjjiI83ENcvjxIZGbuMXVqMvcg70yeSF6bLPR6vdDkakTS6iRx6blL4tKAS+LSwEsiTBkmwggTR1VHRdrWNKHXSRf5d/78K7fP3RZRk6JEyoaUe+6vihjqe/axKHH5t5w6dYqmTZuydOlSU6ci85jh5+dH69at2bx5M++9957B40VGRgJQv379++YTGhpKVFQUXbp0ue95rKys2LVrF0OHDiUwMJB+/frh6upKTEwMP/30Ez169GDVqlUGeQ5PCl+npPBlYiLxxcXk6XQE2NhwtGlTGlZ0qdzGjTBypPT3t9+G4cOhQQOj+AGqNWoGbhvIb0m/8e1z39K7fm+Dx3wYTp+WHCSjoqBRI1i6FNq2lZo/qyLXr19n69atnDt3Dl9fX7p06cKYMWOwsLDg888/57XXXsPe3t7Uaf5r9PoScnIOoVRaY2HhQUHBRYqKosjK+pn8/NM4OLTB23sCXl4jsLJ6PKc1Pqno1DqyD2ZjZm3G1SFX0WZrSV6eTOHlQvTFf5aamLuZU2duHcxdzHHq4oR17T8tsRXKu0tO7JvaY9+08r6nHycqtUCfPXs2R48eZe7cuaZOpdKh1qi5nnnd6HH93fyxMbcxSqyhQ4cyfvx4zp07R7Nmze573NixYzl//vwjnXv+/Pl06NCh7Pe8vDwAHB3v7TxwZ3tubu4/nrtJkya89tprzJs3jzVr1pRtr1evHsOGDStXly7z8AghmBQTw6LERJ5zc2NQtWq86O6On00Fvh9zc2HRIli7VnJnGTQIFi4EI9UTF5QWMOPIDDZc2IBao2b/0P087fu0UWI/iKtX4dtvJUcWHx9puFBAgMGNaoyOWq3mgw8+4MaNG3h6erJhwwbs7e1p1qwZy5Yt48svv6Rnz55s2LABD4/KPeFSpyvkwoXu3L59qtx2CwtPzM09aNz4Z1xc/u/Jqxt+zNEV6cgLz+PGmBsU3ywGwNrPmrrz65K8Opkab9eg+rjqWNWyAj2gRP43NBEGFehXr14lMDDQYOfYt28fhYWFlXoFwlRcz7xOi9UtjB43YlQEzb2Ms1zm6+sLwKZNmx4o0P+pcdOYaLVaunbtyqlTp3jnnXd466238PT05Nq1a7z//vu8/PLLnD9/nnnz5pk61UrH1ykpLEpMZEm9erzlbYDVvJs34dlnIT4e+vSB4GB4800wwiAZvdCz+NfFfHz8Y0p0Jbzd+m3eaPYG9V3vfUfHWKSlSXbuc+ZI1y7t2sH335cfilqZuXTpEm+++SZZWVnUrVuXuLg4oqOjad26NYcPH+a9997jgw8+wNLSkgsXLnD9+nWef/75Su9ApteXcuXKIAoLLxEUFIalZXU0mkzMzathY/OEdPdWAoReILQCoRGkfZNG/MfxlCSVgB5sAm1oebEl2hwt1vWssaxuidfwvzWqV+63aaXHoAJ90qRJ7Nu3z2DnUCqVsjj/l/i7+RMxKsIkcY3BkSNHWLNmDT169GDr1q0sWLCg3JCPiubOCvmdlfS/c2f7P3mhb968mVOnTjFw4EAWLFhQtr1Zs2b88MMP1K9fn4ULFzJmzBhq165dQdlXfTalpjI+OprXPD0rXpxnZkqm3R9+CI6OkiWJES1IdkfuZtrhaVzJuMLI5iN5v/371HY23XtDr4fDh6XV8p9/hqIi6NpVGi50nxtMlY6YmBiWLl3K4sWL8fPzo2fPnsTExODl5cXq1avvOasgKCiIoKAgE2RbcQihIytrD1FR/6O0NJnGjffi7Pz0H3tNezH4JKMt0JK5IxN1lBq7xnYoVAoSv0gk/1w+olSgMFOgL9bjNtANr1Fe2AbY4tTFCXPnqjN1sypiUIGelpb2n23u0tPTKygbmb9iY25jtJVsY7Nv3z5CQkI4fPgwP//8M0OGDOHQoUP06NHDYDH9/aULjzu16H8nKioKuH+N+h1+//13QLKK/DvW1ta0atWKXbt2cf78eVmgPwTFOh0ToqNZlZLCa56eLK9I4ZyZCZMmwTffSL/37SupUiOWIC05vYTx+8fTrU431vRdQxtv0w6xSk+H8eOl65WAAHj/fXjrLXB2NmlaFUJoaCinTp0iISGBjRs3Ymtry8cff8yUKVMwN8JdElMjhI7IyBGkpq7H3r4VjRrtwN7e+HdhZSS0+VriZ8eTH5FPwbkCtNnacvsd2jngO8MXTbYGlZMKtwFu2PrLltSVCYMK9LNnzxry9DIyd7Fr1y4mTJjA8ePHcXBwoF+/ftjZ2bFp06b7CvRRo0Zx7ty5R4qzaNGicsO27gjq0NBQhBDlavby8/M5efIktra2/zgF1MJCGsJwvwvTjIyMcsfJ3J8cjYaeFy9ysaCAr+rXZ7iXV8XUUup0sGIFTJkCKhXMnw8vvwzu7v/93A9Jqa6UeeHzCDkawuS2k5nffb5J60QjIyU79w0bwMwM1q+XmkGN0A9rEOLj49FoNKSnp5OYmMjBgwf5+uuvqVatGp6enowePZp58+ZhbW39zyerIkRFvUVq6kbq11+Jl9cIFAq5/sFUJH6ZSPT/olFaK7FtYovHUA98Jvlg6WNJwYUClJZKbBrY3LOJU6byYPAm0WHDhuHh4UGNGjUIDAyke/fuhg4p84Sybds2Ro8ezeHDh6lZsyYgrToPGDCAnTt3olarsblHQ+Dq1av/c+w6derQo0cPDh48yLJly3jrrbfK9s2cORO1Ws2YMWPKfaHHxMSg0WioV68eKpX0X7Fbt2588cUXrF69mtGjR1P9LyPm9+3bx8mTJ7G2tiY4OPg/51xVEUJwJj+f165fJ620lPBmzWhZEdNAhYAtW2DaNEhIgHHjpOmfRhDmCXkJ/Bz1MzE5MdR0rMkP13/gSOwR3m//PnO6zDGZOBdCMqhZtkyqK585E0aPhocYmGsyhBDs3r2bGjVqYGFhQXZ2Nrt27cLf358mTZqQlpbGwIEDyz2mevXqLFiwgHfeeeeJa5grLc0kPv4jkpNX4ue3nOrVR5s6pSeWggsFqCPVxEyKwbWvK3U/q4tN/fLfabKDStXB4AJ969atfPvtt3Tq1AmttvwtmK+//pqCggJeeukl3I24+iRT9di4cSMjR47ku+++o0WL8rddX375ZTZt2sTOnTsZOnSowXJYvnw5wcHBjB8/nsOHD+Pv78/p06c5evQoDRo0YM6cOeWO79q1K7du3SIuLq7sguLZZ5+lf//+7Nq1i4CAAAYMGICHhwfXrl1jz549KBQK5s6di3NVqBkwADkaDf+LjmZTWhpNbG0Jb9aMgP9qn6hWw6hR8N13UFoKzz8PP/wALQx/e18v9Oy6vouRP40kuygbK5UVJdoSBII5XeYwrcM0g+fwd44dg5UrpXryrCyp6XPBAqmUxdLS6Ok8NEIIfvnlFxYtWsSOHTvK7fPw8CAtLa3sdy8vL+bOnYunpydNmjTBw8PjiRPmQujJyNhBXNxM1OprODv3oHr1MaZO64lFfUNNROsIRKnAzN6MwG8DMbOR72JUZQwu0Nu1a3fXasQdhg8fTnp6OvPnzycmJoYRI0bQq1cvQ6ckUwWZP38+n3/+OX379r1rX7du3QgODmbZsmUGFeh16tTh999/JyQkhP379/Pzzz9TvXp1JkyYwMyZM++yYFQo7j26+Pvvv2f16tVs2rSJH374AbVajaurK71792b8+PF069bNYM+hshKlVnMoJ4eZcXHc1mpZ4efHG15eWPzXGovoaHjuOYiJkVbOn3oKevY0ij/g6cTTvLrrVW5k3aBDzQ7sfHEnrtauFGmLOJ96nqdqPGXwHEBaJT94EHbvhthY2LcPAgMhP1+q9tmyBYYMMUoqj4wQgu3bt/PDDz/w22+/ERsbS+3atVm2bBnNmjUjMTGRwsJChg0bRmxsLKmpqSiVSlq0aPFE1JXfCyEEeXnHiY+fQ05OKLa2jQkM3Iara68n7iLlcUGn1hE9MRoLdwvqr66PhaeFLM6fAAwu0L28/rTt+emnn3B0dKRNmzZlNbTu7u4sWLCAr7/+mr59+6LT6QydkkwV5PLly/fdp1QqCQ8PN0oe3t7erF279qGOjY2Nved2pVLJmDFjGDNGXq16GDampjLsuuTpP9DNjSV+flT/r0u5mZmwaxe89x64YLFPbgAAIABJREFUusKJE/AAq86KpERbwicnPuGzXz6jsUdjTrx+gvY1/+x3sDG3IdjH8CVOW7dKteQREdLL4esrrZpv2ybZu9/hcdRsxcXFHDhwgAULFhAeHk61atV47rnneO655+jSpcs9HZ3q1KlDnTp1TJDt40FxcSI3bowiN/cYer0aG5tAGjXajZtbH1OnVuUpuFyAma1ZuSFAmiwNmhwNcTPiSN8q9SQFfBOA6zOupkpTxsgYXKD/9YOwa9euLFmyhB49etCzZ086duzIpEmTAGk1ffbs2YZOR0ZGpgqxKCGBd2JiGOLuzhI/P1z+66pnRobU9LlmjWTc/cIL0rjLatUqJuF/4Hj8ccbsGUNMTgxvt36bjzp/ZLTBXneIioIRI+D4cejcGcaOla5N+vSRemIfd+Lj4xk0aBBnzpyhbt26LFmyhDfffFNe/QV0uiKUSksKCs6Tmbkb0KFUWpGdfZC8vHAsLDzw9Q3B1jYIF5ceKBSVtMu3kiB0gvRt6USOiERfrMfM1gy7pnYorZXkhOYAoHJV4TPFB+fuzrh0e4ybO2QqHKN+3NrY2DB16lR27NjB999/f9ctxMruESsjI2MctHo9c2/dYlZcHBO8vVlYty7K/yLAdDppms7y5VBSAv36Savn/sbx7T8QfYB5J+dxNO4obX3acrzfcZ7yNk4Jyx2SkyVjmu+/l6Z9fvstvPji47lC/nfy8vI4e/YskZGRTJ8+HWtra3bv3s0zzzxT1oD9pJKbe4yUlK8pKUkmN/cICoU5QpRiZmaPSuWEVpuHo2M76tdfSbVqz2FuLotAQ6Mr1mFmZcb116+TtikNt/5u2DS0If9MPgqlguKEYuouqotVLStcerrI5SxPKAb/5Lp48SIRERE0b968bAUjICDgnvV9dnZ2hk5HRkamEiOEYGdmJnNv3eJsfj7TatViZq1a/02cFxVJRdS7d8PAgZJfoI9PxSV9H3ZH7ubzU58TkRJBQWkBwT7BrOq9imFNh2FhZhwbzevXpflKp07BrVvSjYKPPpIMairLx3FaWhotWrQgKSkJgLp163Ls2DFq1Khh4sxMT2HhdS5d6oOFRXVsbBrg7T0RMzMbnJ27YW//FGZmVqZO8bGjKK6IW5/cwrqeNdb1rdGka0CA+2B3VI73l0xCCIpiirCuY31Pe0OhF6SuSyVlTQq3f72NTaAN6qtq/Jb7UWOs/F6VuRuDC/RLly7RqlUrnJycaN++PU8//TS5ubl3eUUD8i1IGRmZe5Kv1bI9I4N1KSmcvH2bjo6OnGjWjOD/MpoyPx/27IFFi+DKFUmgG7hJXQjBjawbfHT8I7659A0da3VkZqeZNHZvTI+6PYz6GXjmDLRvD9Wrw+DB0vDTgQMrx1AhjUbDtm3bOH78OHv37kWv17N3715q165NQECAqdMzKUIIiovjKCg4R1TUW1ha+tC8+a+oVLL93l/Rl+rJ2JGBNkeL1ygvMr7LIPGLRErTSimJL8HM3gxd/p89cVFvRWHjb4NtE1tsG9ti7myOubs5pWml6Iv1pK5PpfBCIc7dnbHwsKA4rhihFahcVLi/4E7yqmRun7qNc09nvCd5U5JYQrXnq+E10usBWco8yRhcoHfq1IlZs2Zx/PhxTpw4waxZsygoKMDBwYGnnnqKtm3bEhwcTJs2bdDr9YZOR0ZGppKRUFzMs5cucaWwkM5OTuxt3JhnXf9lo1RpqTT9c/16aeVcp5O6H8PCoHXriky7DL3QExoTyu/Jv3Mk7ghHYo/gYevBmj5reKPZG0YT5cXF0kp5eLjU7PnppxAUJNWaWz2mC6n5+fnMmzcPtVpNkyZNuH37NkuXLi2bzBsQEED37t2ZPn06fhU5JbYSolZHkpW1j/z8M6SnS9NtXV37Ur/+clmc/wUhBMkrk4l5JwZ9saQ5klcmU3ipEOduzlh6WxKwKQDHYEdKM0pROarQ5mjJ/DGTwouFFFwqIOunrHLiHSW49nLFra8bqRtT0WRoMHMww8LLgqLoIq6/dh2bQBuaHm2KUycnEz1zmcqGwQX64MGD6dSpE506dQJAp9Nx7tw5wsPDOXHiBKtXry7zh1apVGzZssXQKcnIyFQCinQ61qamMiUmBkeViostW9Lov9RdFBbCgAGSkfeUKVCjBjz7LPzhQV/R3C65zfrz61kdsZorGVdwsXahgWsDvu77NQP8B+BsbZyl6vR0mDdPuibJzpa2KZXQvTts3Ph4ivOcnBy2bdvG8uXLuX79Ou7u7ixatAiQeplWrFhBq1at7pp58CQihI6bN98jIWFB2TZb20bUqDH+j4mf8p3pOxTFFREzOYbMHZl4Dvek+qjqqK+pSfk6hTrz6+Az2afc62XpKblBmVmblStDEUIgNILStFLMXczRqXVYVJPK0mp/VLtcTKETFMcVY1nLEqVKbrqVeXgMLtBHjy4/dczMzIyWLVvSsmVLJkyYAEBkZCTHjx9nxowZhk5HRkamEhCWk8Mr166R9P/snXd0FIXXhp8t2bTd9IQkJIE0EnoVFAQpiooFUFGqgjRFQFREBAUR/KlUEQULUgIoiFKkEylBqrRIDSVACulls5vdzdb5/hjgEwUJkArznJNDMjM7c5dsZt65c+97LRYGBQUxIzISj7tp9nM44M03Yc8e2LxZtCcpJ1K0KaxOWs3PJ39mX/o+nop+im+e/uY6q8SKwmiEp5+G48fh5ZdFR5b69cV1VdHm22az8cMPPzBq1CgsFgtPPvkk8+fPp2nTppw7d47atWtTVFR0nX3v/YbZnIlWm4Cv71OUlFzgzJkh6PWHiIiYSmBgfxwOEy4u5XPTWZ3R/anjr85/oXBVUO/negT0EIcjerT0IPCVwNval0wmQ6aS4RIq3t0q3G/exClTyHCNdL3pegmJm1El2ttjYmKIiYkhPj6+skORkJCoJOyCQIJWy+KsLJZkZ9Pey4tVDRrwgEZzd1nAzEzo31+ctvPdd+Umzi12C6O3jubrg1/jEBwEuAewq/8u2tZqWy7HuxVJSWJJfVaWWNZS1ZPNa9as4eOPP+bo0aO88sorfPrpp9cJ8Xr16gFiBv1+wmrVkpe3muzspZSUXMJiycLhMCKTOSMIZtzc6tO48e94e5ffTWd1x3TRxPFnj+Nez51Gmxr9Z7OnhERVoUp9St99993KDkFCQqICyTKbWZGby6WSElbm5HDZYiHSxYWZkZGMCAlBcbeP5zdsEMW5QgFbtkDnzmUS99+xOWzsTdvL+O3jOZB+gM86fcagZoPQOGtQyiv+FKvTwe+/w4gRYsPn/v3QsGGFh1FqTpw4wYABAzh06BBeXl6sXLmSF154obLDqnRKStJJSZlCdvYSHA4jTk5+BAb2R6n0wcfncQoKtuLmFo2PTxcUCilDa9VawQFOPk4YkgykfpqK6bwJVYCKvDV5yN3l1FteTxLnEtWGKvVJfeCBByo7BAkJiQriqF7P08ePk2u1EuDkRDc/P/rWqEErD4+7r5sVBHHA0JtvinXmCxZAQEDZBH6FXEMukxIm8ePxHyksKSTMM4yE/gk8FPpQmR6n1PHkwuLFYr15Xh60aAHr1kHg7T29L3dMJhPbt29n48aNHDx4kL/++os6deqwefNmHn/88coOr0rgcFg5caIrZnMaYWHvERQ0ECenAOTy/69L0miaVWKEFcs/Xd8EQcCab0Xlp8KcYSblkxQyf8hEMAvXtnEOcUbhoUC3V0fNN2sS+nYoLmFVsOFCQuImVCmBLiEhcW9TaLWyMjeXJdnZ7C4qoolazaHmzQlydi67g2zYAB9+CEePigJ95kyxK7KMKDQVMvvAbD7d/SlKuZK3HnyLZ2OepUVwC+SVMHlRp4MffoBp08SG0N694YMPRNvEqtYfePDgQQYOHMjx48fx9fWlS5cu9OjRg+HDh+PqKmWBHQ4LhYXbSE39HIPhOE2b7sHD4/5MXFlyLBx74piYBQ9UUefbOni190K3X0fq56nkr81H3URN8bFikIF3R2+sBVYcJgdh74cR0CMAwSGgP6jHs62n1CwrUe2QBLqEhESFcNJgoENiIvlWK495e7MkNpbn/f1xVZTBlDyTSfQy//hjMW388MMQHw+PPnr3+0YU5QczDrL+7HrmHZqHDBnvtn6XNx98kwD3ss3M3w6HDokPCAoLxamfn38umtNUNXbu3MmPP/7IqlWrqFmzJps2baJNmzZoNJL9H4Bef5SMjHnk56/DYsnC3b0h9eqtuG/FuSHJwNnXzlJ8tBi/5/wwnTfxV8e/cA5xxpxuxjXaFc9HPHEOdiZ4WDB+3f1Q+akQ7GIGXab4fzHu1U6yNZSonkgCXUJColzJtVh4OzmZn3NyiHFz40jz5oSUpbffpk3w/POiSK9VS/QT7NtXrDsvA36/8Dsv/fISBaYCVAoVHz3yEa82fZUgTeU5iQiC2PPao4foyrJyJYSEVFo4N8RisbB582aWLVvGqlWrUCgUdOjQgcWLFxNQxuVG1RWd7hBpadPIzf0ZZ+cwAgJ6EhDQB42m+X2b8S3+q5gjbY6g8lfRaGsjfB7zwWF2kL8pn/QZ6fg+60v0l9HXifCr3GiZhER1RRLoEhIS5cbWggJGnDtHgc3GlPBwhtWsiXsZCWcAvvlGnEvfsSOMHw8PPghlVCpRYithwo4JTNs7jQ61OzDz8ZmEe4Xj6XIX00vvkCNHxMqdwkJRkJ88KQ5AffRRWL0a7sYevqw5deoUH3/8MWvWrMFsNlOnTh2GDx/O1KlTcaqK3o4VjN1uJCsrjqysRej1B3B1jSIqajbBwcOQV0JTcVXBdNFE3qo80men41bHjaZ/NL1mXyh3luPfzR//bv6VHKXE/U6xzcaES5cwORy86O9Pc42Go3p9uRzr/j0bSNyTbN++ndGjR9OiRQvmzp2L8m68s++A9PR0JkyYwObNmykoKCAoKIhu3boxceJEvLxK/6hVEATmz5/P/PnzOXnyJCBOTRw0aBBDhgyp8tk1g93OkDNn+DEnhzYeHqxp0IC67u5ldwCTSSxnmTYNBg+GOXNApbrr3QqCwL70fXx/5Hs2nN1AYUkhUx+dyjut36mU+vKLF0VnyFmzxAcCCgVcvRYMHgzz5pXZg4K75tixYyxYsIBFixbh6enJuHHjePLJJ++75n9BcCAINuRyFYWF28jNXU1JyUXc3GKoUaMvZ84Mprg4ER+fJ6lX72f8/Lpd1/x5v2EtsHLy+ZNod2oBkLvKabq36X96i0tIVCSXzWZGJydzUKfjssWCQxBwVyj4JiND3ODs2XI5riTQJe4pOnbsyIwZM+jUqRMPPfQQAwYMqLBjJycn07p1a3Jzc+nWrRuxsbEcOHCA2bNns3nzZvbs2YOPj0+p9tW3b19++uknatSoQZ8+fXBzc2Pr1q28/vrr7N27l8WLF5fzu7lzMs1mnjl+nDMmE/NjYhgQGIi8rG4odDpRrf7wA2Rnw8SJ8P77UAY3YhvObmDOn3PYkrwFjUrDK41f4Y2WbxDrF1sGgd8eNhtMmQKTJoGnJwwaBDNmgLOz+LZ37IBnnqka4vy3337j448/5vDhwwQEBDB48GDef//9Un/WqzOCIJCXtwq73YRG0wybTcfp072xWDJxdY3BYPgLV9coXF2jSU+fTXr6LNzcYmne/BAaTdPKDr/CKUkpwZhk5Pyo87iEu+Dk50TuL7ko3BVEfB6BS4QL6oZqXEIktxWJykcQBFbn5fHW+fPYBIHn/f2p5eLC835++Dk5sbuoiFNGI0EKBb3L4fiSQJe45+jQoQMRERHExcVVqEAfNmwYubm5zJkzhzfeeOPa8nfeeYdZs2Yxfvx45s2bd8v9rF69mp9++omIiAj+/PPPa0LHarXy/PPPs2TJErp160b37t3L7b3cKRdMJjokJmITBP5o0oQmZdUEmJAAX3whNn4KAvTqBaNHQ+zdi2e7w86Y+DHM3D+TYE0wK3us5Ok6T+OirHiRYLfD2rUwciRkZIhmNO++C3//b6xRA3r2rPDQrnHgwAGWLVtGUFAQKpWKsWPH0q5dO9asWUOXLl3uizIWQXCg1SZw4cJ76PUHr1un0bQgMPBVDIYThIWNJSDgJWQyGUVFe9DrjxAUNBiF4v4RoDadjazFWZjTzaTPTkcwC7jUdsGms6HbpyN4aDA1R9bENVxy8ZEofw7qdPycm0u62cxlsxkvpZLPIiKwCwK7iopI0Gp5yMODcBcX5mZkEF9YSH03N9Y0aEDUP4akPeHryxO+vhzJzS2XWCWBLnFP0qdPH6ZMmUJaWhqhoaHlfrzk5GTi4+MJDw+/TpwDTJo0iW+//ZalS5cyY8aMW05CXL16NSAK+79nIZ2cnJg8eTLr16/nq6++qnIC3eZw0PvUKZQyGbubNiW0LBpBi4vFjPmUKVCvHowbJzaAht35KHNBEMgqzsIu2Em4lMCCxAXsvLSTL5/4kuEth1dK+ZDRCL/9Jpaz7NghltRv3AiNGlV4KNdhtVq5ePEi69evJyEhAb1ez44dO6hZsyb5+flYrVYGDRrEnDlz7nlhXlS0H4PhGHZ7MZcvz6WkJBm1uimNGsWj0TSnuDgRm02Lr28X5PJ/24Z6erbB07NNJURe8dgNdvLW5pG7MpfiY8WUXChB6ask8OVAAl8NRN1QLZWwSJQLNocDB/BlejoRrq7EurnxZXo6PQIC2FZYyKz0dHyUSqJdXQl1duaQXk/9g9ffZK+8IrjrXhHmXf38KuGdSAJd4h6lb9++TJ48mWXLljF27NhyP96OHTsA6HyDSZVqtZo2bdoQHx/P/v376dix43/uKysrC4CIiIh/rQsPDwdg9+7d2Gy2Cq+xvxnHiot549w5Dun1ZSPOzWaYPl0sZcnIgOHD4dNP77rO/GLhRfqv7c+ulF3XltVwr8GmPpvoHFn2U0b/i8REiIuD8+fh4EHIyoK6dcVm0CefrFwP81OnTvHhhx+yevVqBEG0rmvdujVKpZJffvmF7t27o9VqMZvNBAVVnpvNnVJSkoqzc01kMgWC4Lj2s1zuhCAIZGZ+h8NhQS53xm43UlycSHa2WFYmk6nQaB4gNnYhnp5tkF3pTfD27lCZb6lS0CZouTzvMip/Fa4xrpjTzVhzregP6zH8ZcCtvhuebT2pv7I+mmaSpaZE+bK/qIiuJ06QY7Vet1wBfJuZiVIm4+UaNfgiKgrNlWunzmbjx+xsgp2d8VEqKbTZyLJYCFSpeNLHB2UZztC4XarG1V1CooyJjo6mZcuWLF26tEIE+pkzZwCoU6fOTeOJj4/n3LlztxToflfu1i9cuPCvdVeX2Ww2kpOTiYmJuZuwy4QlWVkMOnOGSFdXfqxXjwc978LlpLgYtmwRazvOnxdNvtetE61L7pJz+edos6AN7ip3lnZfirvKndahrSvUx1wQ4MwZ+PJL+PZbcbhpixbw3HPw9tsQGVlhodyQEydO8M033zB37lzUajUzZ86kQYMGhIeHE/mP4KpjjbnReI6srAWkpn6GQqFBoXDH4TBjsxWiUgXh4fEQICMv79e/vUqBq2sUERFTCQ19G5lMyvwCFPxewPGnj+Ma4Uqxo5iSb0tQqBW41nFF6aWk4aaG+HT2QSav2g3tEtUThyDwS24uWwoKGFGzJi5yOS+cPEmwszOvBwfTwdubbIuFNXl5jA4NxeJw4O3kRMw/nmB7KJW8VhWHRyAJ9PsXoxGSkir+uLGxcIsSj7Kib9++jBw5kqNHj9K06c0bsl5//XUSExNva99Tp06lbdu2134uKioCwPMm4vTqcq1We8t9P/300yxfvpyZM2fSs2dPvL29AbHcYOLEiYBYplGafZUnl0wmhpw9S3xhIQMCA5lXpw7Ot5ttyMkRBbhOJxp7b98OFgu0bi16CzZoUCaxns0/S4+VPfBy8WLvwL34uVXcI8vLl0Vr9nPn4Phx8W35+sInn4hl9JX5EMRsNrN8+XJOnTpFcnIyq1atQq1W8/nnnzNixAhcytKvvhJwOGxkZMylsHAbRmMSJtNZ5HJ3/P1fQK1uSnFxIlZrAUFBgygo2IDRmITdXkxExGfUqPEKACpVjSrvmlSROGwOMr7O4MK4C3h38KbBmgbIneUIDgEEyYtcomKYkZbGmAsX8FIqWXDlqXN9Nzc2NGxI8N8mU79YjWcuSAL9fiUpCZo3r/jjHj4MzZpVyKFq164NwJIlS/5ToJemcbMi6dmzJ0uWLGHLli3Uq1ePZ599FhcXF37//XeysrIICwsjNTUVeSU+eks2mXji2DGsDgc/1a3LiwEBt+fUIghi42fv3pCZKarURx4RR2E+/TRERZVJnDaHjVn7ZjFh5wRqamry64u/Vpg437dPLJn/4w9wcYHGjcU5Su+8I5awXLnvqjRSU1Np164dqamphIeH4+fnx5w5cxgyZEi1ryc3GE6SmbmArKzF2Gz5uLpG4eXViYiIT/HxeRKF4t8NiTVqVGLnbTUhb10eZ4eexZJlwf9Ff2IXxiJ3Fs9DUqZcorzZpdUy6vx5/JycSNBqGRUSwsRatfgtP58si4XBQUF4V/Nz19+RBPr9SmysKJYr47gVwPbt25k/fz6dO3dm+fLlTJ8+vVwF7dUM+dVM+j+5urw0XuhyuZx169Yxc+ZMli5dSlxcHK6urrRv357Vq1fz3HPPIZPJKmUa4/HiYkacO0dCURHBKhW7mzYl/HYGA+3YAcuWiR2QmZnQqpU4rz4goMxTydnF2XRd3pWDGQcZ1WoUkztOxs2pfJ/eHD8u9rTGx4t2iFFRMHs29OsHHh7leuhbkpeXx/79+zl+/Djh4eH873//QxAETp48Sd26dSs3uDIkK2sx586NxOEw4uv7DEFBA/H1faqyw6r2ZP+YTVL/JDwe8qDez/Xwerj0cx0k7i0umkz8qdfzrK8v+3U61uTlcViv553QULr7Xz9MymC3k1ZSQh03t2tJHIvDwXGDgUKrlU7e3jd9QlVit/Nbfj513dxYmJXFD5mZBDs7k2Ox0DMggM8iInCWy3k5MLDc33NlIAn0+xU3twrLZFc0mzZtYsKECWzbto2NGzfSu3dvfv/99xs2cJYVsVduPK7Wov+Tc+fOATevUf8nSqWSMWPGMGbMmOuWl5SUcO7cOfz8/KhVq9ZdRHx75FkszM3IYNKlS9R0duanunV50tcXz9KK6vx8mD9f9CyvU0fMnHfpAu3albkwzzHksChxEdP2TsNJ7sSeV/fwYMiDZXqMf2KziUOD3n0XAgPFtxUaKr7duynJLwuOHTvGu+++y44dO7D+rXkqOjqajRs3VntxLggCKSlTKCjYhNWah8l0joCA3tSp8w1KpdSYeLc4rA60O7WcGXQG/x5Xsuaqynt6J1F5rM7NZV5GBju1WqyCgJdSidZmQyWTEaRS0e/0ab5zOOgVEEC2xcLqvDw+SUnhssWCj1JJey8vHvX2Zm5GBicMBgCaq9V8GR1NLRcXdmm1lDgcNFGrCXZ25sWTJ9l1JbnloVAwJDiYcWFh91SW/L+QBLrEPcWaNWsYNWoUu3btwsPDg65du6JWq1myZMlNBfqQIUM4evTobR1n1qxZPPzww9d+7tBBdHCIj49HEITrMgJ6vZ49e/bg7u7Ogw/enVBcvnw5VquVXr163dV+SoMgCJwyGpmelsZP2dkAvB0ayv/Cw3Eq7dMIh0MswB4xQpz+OXo0fPYZlMPTDKPVyNyDc5m5bybZhmx6N+zN1EenEqQpH5cRs1m0RVy7FvbvB4NB9C///HOxpKUqcOTIEbp06YKLiwuTJ0/mpZdeIjg4GK1Wi7+/f7WurS4pScdoPEle3loyMuah0TyAi0stgoIGEho6WmrmvEsEQUC7Q0vK5BS0O7W4RrsS812MJM7vQTbl53NIr+f9sDDswLbCQvbrdLjJ5QSqVGwpLMRZJmNFbi7hLi5MjYigkVrNzLQ0Onh783ZICAa7nf5JSfQ5fZrPUlO5YDJhcDhoqdEwMyqK3UVFbMzPZ1VeHqHOzqysVw+VXM6nqak8kpiIAjBfcYy6igxY16ABeVYrD3p4EFuW06irAZJAl7hnWLFiBUOHDmXbtm2EXfHJdnV1pXv37qxatQqj0XhDD/Lvvvvuro8dERFB586d2bp1K19//TXDhw+/tm7ixIkYjUZee+01XP9WDpKcnIzVaiUqKupfdok6nQ6Pf9REJCYm8u677+Lj41PuzjR7iooYfu4cicXFBKpUfBwezquBgfjdjs1hQoKYUj54UKzx+OwzCA4u81j3pu2l16+9SC1KRSlX0rNBTz7t9CkhHiFlfiwQ7RAXLhTfjl4PTz0lDjTt1KlqPZSaN28ew4YNIzY2loSEhOtKoiqjPOpOMJszuHBhLCDHy6s9crmKnJwVlJRcwGA4DdiRyZREREwlLOzdyg632iPYBSzZFvSH9Vz++jKFWwpReikJGhRE2Ngwybv8HmJvURFLs7MJVKn4X0oKZkFgZW7uNWH9d5qq1ciAQUFBfB4RgduVEcYd/9ZIo1Yq+aVBA7YWFDAvI4MnfHx4JTCQGFdXlHI5LwYE8GV0NBdNJgJUKtyv7KOztzfDzp1Da7PxaUQEZ4xG5ECBzUaMmxutKrs2sBKRBLrEPUFcXByDBw9m5cqVNP9H82ufPn1YsmQJq1atom/fvuUWw9y5c2ndujUjR45k27ZtxMbGcuDAAXbu3ElMTAyffPLJddt36tSJ1NRULl26dO2G4iqPPfYYbm5u1K9fH41Gw+nTp9mwYQPu7u6sW7eOwHKqubM5HDx/8iS/5efTTK1mXYMGPOLldc0ztlQ4HDB5Mnz0ETRpIhZkd+pULsbe3x3+jmEbhtEksAnvtXmPxyMfJ9Kn7L0K//gDdu8Wy+VXrRKrcl5/HYYOLRMHyDLDYDAwZ84cNmzYwO7duxkxYgTTp09HdZf+8RWJINjJzf2VvLzV5OdvRCZT4OTkf82HHCD13mCZAAAgAElEQVQoaCiBgQPx9X0aF5fayOXSpex2seZbkbvJUbgqMGeaKYwv5MLYC1gyLQC4N3an3op6+Peo3k9aJER0NhsrcnLIs1rFbHZBATVVKrKtVtp4ePBWaCjT09IYEhxMnxo18HdyQmezYREEmt3GROjOPj50/g8L1n/2LLkoFCz4W2/aP20Q72eks5rEPcHUqVOZOXMmzz777L/WPfroo7Ru3Zqvv/66XAV6REQEhw4dYsKECWzevJmNGzcSHBzMqFGjmDhx4r8sGGUy2U0vfD169GD58uUsW7YMk8lESEgIr732Gu+//z7B5ZCFBjA7HPQ7fZoN+fl35swCoo95377iWMwpU8Qi7HIoZ8kz5jFhxwS+PfwtA5oM4MsnvyyXBlCdTrRk//JLUZQHBYn+5d26iX2tVYUTJ04we/Zs4uLiEASBp556ih9++IEBAwZUK3Gl1x/h3LmR6HR7UKubEhr6NoGBA1GpAjGZzqJQaLDZClGrK3nEajWi+K9iclbm4ChxoNujQxWswnjGiPGkEWTgFOCENVvsTfDu7E3019G4hLugbqyuVp+d+5lLJhM/5+aSa7XS2sODEGdnFmVlkWwyoZDJ8FYqiS8svDbAR6NQ8HZICFMjIzHY7bjI5ajk8kqbmClxYySBLnFPcOLEiZuuk8vl7N69u0LiCAkJYcGCBaXa9uLFizddN3r0aEaPHl1WYZWKYWfP8lteHsvr1eOFO1GfggCDB8O2baJAf/rpMo3PYDGwN20vc/6cw9bkrbgoXZjReQYjWo5AIS/bR+8XLsDOnWI9eUYGTJsm2iNWNb2Sk5NDv3792Lp1K97e3owfP55+/fpdmzhbHRAEO9nZS0lLm47BcAJX1zo0arQFH5/re0bc3etd+S604oOsphjPG0nsKM54UHorcfJ1ouRiCZ4PexIyKgSZTEbJpRLcG7rj2c4T50DnW+xRoipQZLOxPCeHbzIyOGM0UuJw4CyX4xAEpl+p4w5xdqa5Ws1Zk4nLMhm9a9RgeM2a1FSpcFH8//nSo4pMo5b4N9JvRkLiPkYQBPbrdKzNy2NBVhbzY2LuTJxfugTjx8Py5eJXGYpzk9XEyE0jWZi4ELtgp75/ff7X6X/0a9QPf3f/W++glOj14sykWbPEYUIOBzz2GKxZA1XR6OT48eN069YNg8FAXFwcPXv2rBb+5YLgwGQ6j063D6PxLFrtDnS6fXh5dSAi4nOCggbj5FTJJvHVGHuJHe0OLZYMCxc/uIiTnxPN9jfDybvqfzYkbo1DEHjuxAm2a7W00GgYGhxMfTc3etWogZtczu6iIiyCwEMeHtdqxSWqJ5JAl5C4TxEEgXEXL/JZaipucjnjwsJ49U5q23/8UcycazTwv//BSy+VSXyZ+kx+OfULU/6YQoGpgE87fcrjUY9T379+mWfM166FV16BoiJRlE+dCi++KFolVgXi4uLYtGkTdrudVq1aUVRUxOTJk6lfvz7btm27NpSrqlNcfIxz50ZQVLQLkKFSBeLiUosmTRLw8mpX2eFVW2xFNjK+yUD7hxbLZQvFicUABPQKIGJqhCTO7wFsDgcvnjrF1oICDA4H6xs2pIuPz7/KkNqWYtaGRPVAEugSEvchqSUldExMJLmkhOmRkbxZsybK260VP34cBg4UXVr69oW5c0WRfpfkG/OZfWA20/ZOo8RWQp+GfZjUflKZNX9arWLC39NTfAurV8PXX0PXrqILZJs2VaOURafTMW/ePH7++WeOHDlC48aNsVgs/PrrrzgcDnr27Mn8+fNxrwbWY7m5q8nNXUlhYTxKpTfR0V/j5dURd/eKGVx2LyEIAoJdQK4U/16L9haR1D8Jc5oZVU0VjhIHIW+F4P2YN75P+lZytBJlxcz0dFbn5RHt6koLjYanfKXf7b2OJNAlJO4zThQX0+3ECUocDjY1bMgTt3uiLywUJ4K+9po4lWf1anj22TtqBs0qzmLz+c3IkHHg8gESUhI4lXsKlULFOw+9w4AmA4jyiSqzZrV9+2DQIDh16v+XKRQwYwa89VbVEOY2m424uDg+//xzUlJSePLJJxk7diw9evQAoLCwkHXr1tG9e/cqK87t9hK02m1otX+Qn/8bRuNplEovNJpWxMYuxNm5fLzp70XsBjuFOwop2FyArcCGJdOC9g8tga8EYiuwkbcmD/fG7jxw4gFcI29jqq9ElWFzfj6eSiUP/cNIwC4ILM/JYUlWFju0WobXrMmc6OhKilKiopEEuoTEfcSG/HxeOnmSSFdXtjZuTITrbVzQrVZRyU6dKor0Fi1g82a4g0xOvjGf+AvxjNg0gjxjHgDRPtG0r92esW3G0r52e0I9y7a+ZOdOePxxaNpULGmxWESLxMBA8K4CJc8mk4nVq1czceJEkpOTefzxx1m7du21KbVX8fb25uWXX66kKP8bq7WA9PRZpKZ+hiDYUCq98PbuTM2abxAcPExyBbkNjGeMpExJIXd1Lg6DA5lKhkcrD5BDjT41KNhSgCpQRcz8GAL7ByJTSP+3ZUF6SQlfpKfTVKOhpUaDALjI5YSVw/SxbIuFaampzEhPB0ABtPPyoraLC+vy85EDOVYrES4uvODvz0fVpJRNomyQBLqExH3CSYOBHidP8pi3Nz/Wq3dtUMQtSUuDZctg8WI4f14cOvThh1C79m2lnK12Kx9s/4Dfzv5GUl4SAJ0jO7O422JclC54uZRP7aTdDgsWwNix0Lo1bNkCVcEW/MKFC2zYsIHs7GxOnz7NmjVrcDgcdOnShUWLFtGmTZvKDrFUWCy55OSsIC9vNVptAuCgZs2RBAUNws0tVvIovwNsehvHnzmOo8RB2Ngw/J7xQxWoQlWjCnxw7wHMDgcrcnJYn59PicPBDzExLMrK4vvMTEwOB+lm83Xby4Hufn484ePDI15eRLm6/utmU2ezcd5koolafVN7WrPDwX6djqN6PY/7+NDn9GkulpTwQa1aeCuV7NJqKbTZ+C0vj54BAWiUSrr6+tLKw0O6ub0Pkc6cEhL3AVvy8/nm2DFqubiwvF49XG8lzq1WcY79+vWwdSs4O4vm34sWQatWt3Vso9XIt4e+5ccTP5KYlcjApgMZ33Y8rUNbE+4VXq4XngMHYPhwccBQv34wc2blinOLxcKhQ4dYunQp33//PXK5nMDAQLy9vZk5cyYPP/wwzZo1q9IXY6PxPPn563B1jcTZOZQTJ7phsWTg5dWR6Oiv8PPrKpWw3AEOq4PiI8Xkb8wna1EWNq2N5n82xy1GGtxSlhwrLqbf6dMcMxgIc3Ym22IhbP9+ShwOegcEYBEE3ggOpoG7O0eLxWbbM0Yji7KyGHr2LA4gUKUiytWVaFdXzA4HcpmMNXl5FNvtdPb2pr67OzqbDXeFgtouLgwOCuK3/HzGXbhAylXxn5wMQEKTJrS70tj5dlXpSpeoEkgCXULiPmDcxYs8+9BDzIqKurU4nzdPnGN/+TJ07CiWtQwceNsNoA7BwS+nfmHyrsmcyTtDx/CObH95O21rtb2Ld1I6TCbRLvHDD6FxY9izR8yeVzRpaWls2bKFn3/+mczMTHJycsjJySEgIIAPP/yQd955p8rWkVuthRQXJ2K15lJUtIfi4iPI5S4UFv6OTOaEIIhDT1xcImnV6jwuLrUqOeLqhyAImM6bSJuWRs6KHOw6OwqNAr/ufoSMDJHEeRlitNsZdvYscdnZ1Hd352jz5jTRaDis17M0O5tOXl48/Y9BPY9dmYj5mI8Pw0NCKLLZ2FtURIJWS3JJCUf0egRAZ7fzdkgIznI5X1++zEmDAQGQy2RkWyy8m5yMHejq68vSunWJdXNjV1ERNZ2d7+tR9hL/jSTQJSTuA2ZFRjKqYcP/3kgQYPp0GDMGevcW/23c+I6Ot/7seoZvHE5KUQrta7dn4cCFtAhucUf7uh2Sk8Us+fz5oo/56NGi82NF2QELgkBSUhJ79+5lz549LFy4ELlcTocOHejYsSOurq507tyZVq1aVVlhXlKSxuXLX5GVtQirNQcAmUyJj88T2O0GYmMX4e/fg+Lio1itefj4PCWVsdwmlmwLeWvzyP4xm6KEIpwCnAh5MwTvR73xbOMp1ZOXMYIg0PvUKeILC/kqOpqBQUE4X2lqb67R0LyUyQdPpZInfX158j/6bsbVuv5GNclg4Ne8PB7x9OThv1kgPudfdjMcJO5NpLOqhMR9QLvSdEF+8omYcn73XXGE5h2UWQiCwLeHv+WtLW/xSK1HWPrcUh4Oe/gOIi49Fy7AqFGQnS06Prq4iMJ8wACIiirXQ19HUlISvXr1IjFRnNyoUCiYNGkSgwcPJiio6pZ8WCx5WK052O16MjK+ITt7KQqFBh+fLoSFjcHZOQSFQoNcfr2Xtqdn9aiRr2hMySashVY0zTTkrc1Du10r/txUQ9DgIC5+eJHLcy6DDLzaeVF3WV18uvjg5CV5ld8NfxUXIwcaqtWklZTwTUYGGRYL7b28+Cw1lSSjkbUNGvBsBY+zj3V3Z3wVvRmXqNpIAl1C4n5GEODPP2H3bpg4Ufz66KM73t2khElMSpjE0OZD+eKJL3BRlr3zwd9ZuVK0TVSroW1bePVVsdbcrQIqAwRBYNOmTWzfvp0TJ06wa9cuateuzbp162jSpAlKpZLAOxn8VEHY7QbOnBlMbu5KBMEGgEoVTETEZwQFDUGpvHtP+3sZh81Bzk85pE1NA8CrkxcyhYz0WekggEKjwK634xbrhtJbSc6yHJJHJyNzkhHxWQSBrwai8pOaPm9Gkc1Gv9OnybFYiHR1ZU50ND5XJuWeMhhYnpPDC/7+HNbr+SI9nWMGw3Wv91AoUMpkLMrKooVGw/yYmAoX5xISd4Mk0CUk7ldMJrGM5auvxGz5K6/ABx/c0a7yjHnM2DuDz/d8zsftP+bDRz4s42CvJy1NLJP/7jt4+mmxbL4itLAgCFy4cIG1a9cya9Ys0tPTqV27Ng0bNmTcuHG8+eabaMpgWFN5YDSexWA4TklJKhpNM1JTp6HV7iQycgYaTQtAjkbTFLncubJDrZIYzxsxp5iRu8rJ+SmHvDV5mC+b8XrEC+dazuStycOSZSFsbBiebT3R7dXh/ag3Xo+IZQ1ZS7Io+qOIWuNr4VKrfG9cqzunDQZGnT/P1sJC6ru5sSE/n/jCQgYFBbFTq2WfTgfA5JQUAJqp1YwPC+OEwUCO1crgoCB6+PtTZLfzc04Ow2rWvFbSIiFRXZAEuoTE/ciRI9ChA+j1MGeO2AR6O57oVxAEgZ9O/MSwDcMw280MaDKA8e3Gl3m4RUXwxx9w7Jjo+HjqFPj4wOTJ8Pbb5evMYrVamTFjBocPHyYtLY0DBw6gUCh4+eWX6dOnDx07dqzSriu5uas4f/5NzOb065YrFGrq11+Jr++TlRRZxSM4BAo2F3B22Fk8HvDAJdwFpZcS42kjXp288H3SF7m7nLOvnUXuIkdVQ4VcJcecbibzh0wQxP0oNAoCXw2kRt8aeLT4/yY/h81xbcLnP6d4BvYLJLBf1X2iUlU4oNPRITERPycn1jRoQFc/P84YjXyWmsqnqakEq1T8WLcuTdRq0sxmmqnV+F05AQiCcN3folqp5C3JGUWimiIJdAmJ+42lS+H11yEyEn74AZo3v6Pd7Ly0k0G/DSK5MJmeDXry5RNf4u9eto1PViusWQPvvQcXL4qlLE88AePHi5nz8jZA2LZtG2+88QbJyck0adIEtVrNL7/8Qvv27fGt4qO2HQ4LaWnTuHTpIzw92xIZORMvr/bI5a6UlCTj4hKJUqmu7DDLFbvBTsqnKRQfLsaSa8GYZMRhcKAKUmG+bKZgcwH2Yjtu9dzIXpoNClBqlNi0NuTucgSzgEKjQFVDRa0PaxH4ciA2vQ3nms6o/P99V3hVnEvcHrkWC7/l57PxSqa8qVrN740bX3OcinFzY2FsLOPDwlArFAQ6i0956v6jtrsq3yhLSNwukkCXuKfYvn07o0ePpkWLFsydOxelsuI+4r/88gsJCQkkJiby119/UVxcTJ8+fViyZMkd7S89PZ0JEyawefNmCgoKCAoKolu3bkycOBEvrzsY6iMI4rSeqVPFQu2vv75t60QQhfnW5K3M2j+LB0Me5Junv6FTeKcyvTimpYlhbtggCvO2bcXvY2PvqHe11Oh0OlavXs3OnTs5dOgQJ06coF27dixbtozmd3gjU9HY7SaMxiQuXBiDVruToKDBREXNvq7JU62+M3ee6oAgCGQtzCJzfia6fWIphHtjd9SN1QS8GIBHKw8823kik8kwZ5ix6Wy4xbhRfLSYor1FWDIs+HX1w6OVx78yshJ3j0MQ+C4jg3ru7jRWq9mQn8/b58+TbRVtO2uqVPzWsOEN7WCjKqK5REKiiiAJdIl7io4dOzJjxgw6derEQw89xIABAyrs2FOmTOHYsWNoNBpCQkJISkq644t7cnIyrVu3Jjc3l27duhEbG8uBAweYPXs2mzdvZs+ePfhc8egtFYIgFmxPnSr6EL711m3FY3fY+SP1D96Nf5dDGYcIVAfSs0FP5j01764aQYuKYO9e8PISh5QmJsLx45CQIN47dOwIy5dDy5Z3fIhScenSJd5880127tyJTqfDz8+Pjh07MmnSJLp27Yqionwa7xBBENDpDpCT8xPZ2cuw2fJRKDxp1Cgeb+/2lR1euWPJs2A6a0KmkJH8XjJFCUVoHtBQa2It/Lr5oWly4xtR52BnnIPFbKymmQZNs+u3k8T53WN1ONip1WKw2/k0NZWLJSXkXhHjV3nY05OV4eHUUKnwUSrxdZIcbSQkJIEucc/RoUMHIiIiiIuLq1CB/sUXXxAaGkpkZCQJCQl06NDhjvc1bNgwcnNzmTNnDm+88ca15e+88w6zZs1i/PjxzJs3r/Q7HDBAVL6vvlpqcZ5ryOXPy3+y6vQqfjv7G3nGPBoGNOTXF3+le2z3OxYvNptojXjwoNijmpHx/+siIqBhQ7G2/PXX7yjBf0sMBgOnT5+mVq1apKens2fPHsaNG4enpyevvPIKb7/9NrVq1aoW4szhsJGePoPMzIWYTGdQqQIJCHiJgICeqNVN7nknFkEQMJ4xcvTho9jyRScaFFBvRT38e/hXi99hdSfXYsHHyQnF3/6vC61WVuXlsbWggPMmE0euTOSMcHHhRX9/Onl7465QcECn41k/Pxq5u0u/KwmJfyAJ9FJiNpuZMGECS5YsQavV0qhRI6ZMmcKjjz76n6/btm0by5YtY/fu3Vy+fJnAwEA6duzI5MmTq7QFW3WnT58+TJkyhbS0NEIrqEmoffv2174XBOGO95OcnEx8fDzh4eHXiXOASZMm8e2337J06VJmzJiBW2kf+dpssHGjWMB9Cw5nHOb7I9+zKHERZruZMM8wBjUdxDMxz9CqZisU8jvLJmdmwssvw65dYLGIyx59FDZtgpISiIkBT8872nWpWbZsGe+88w7Z2dnXLe/fvz+zZ8/GoxpN9bNY8jh9ug+FhdsICOhBZOQ0fHyevGeGBgmCgP5PPcljklF6KvF/3h9VkIqivUWYzpswHDNQklKCXSfWkMfMj0GmkKFppsG5puREU96YHQ56nTrF6rw8vJRKWmo0mB0OTA4HWRYLqWYzdd3ciHBxYVX9+jRRq6nl4oL8b0K88+08BZSQuM+4N87kFUD//v359ddfeeutt4iOjmbhwoV06dKFHTt20KbNzQd2vPfee2i1Wnr06EF0dDTJycl89dVXrF+/nsTERGrUqFGB7+L+oW/fvkyePJlly5YxduzYyg7nttixYwcAnTt3/tc6tVpNmzZtiI+PZ//+/XTs2LF0O/3hB3jooVtutuX8Frou70qgOpBxbcfRp2EfannVQnmHok8QYOdOsanz0CHw9YVp06BBA6hbV7RGrKjE2ffff8+QIUN46aWXeOONN8jKyiIkJAQPDw/q169fMUHcAXa7gYsXP0CrTUCh0ODt3QmFQs3Fix+gULjTuPEWvL07VXaYZYbxjJFLH19Cu0OLJdOCa5Qrdp2dpP5J17bRtNTgGulKjT41cApwwv8Ff5Qa6XJWURRarfQ+fZqdWi1zoqIosNk4rNfjJJMR6epKjJsbb4aE0EytljLjEhJ3iHRGKwV//vknK1asYPr06bz99tsA9OvXjwYNGjBmzBj27Nlz09d+8cUXPPzw9ZMUn3jiCR555BG++uorJk+eXK6x369ER0fTsmVLli5dWu0E+pkzZwCoU6fODddHR0cTHx/PuXPnSi/QnW+dUVyUuIgBawfwaMSjrOu17q5ry5cuhQULREfHli3F0vfevUV7xIrk5MmTfPDBB6xZs4ahQ4cyb968aiEa8vM3cfHihxgMxwDw83sOiyWLlJQpCIIVb+/OxMYuwNm5ZiVHevc4LA7y1uSRuSCTwi2FuNR2oUa/Gng94oVXBy9kTjJMZ0wINgFLlgWfx6XMa2WQWlLCtLQ05mdmIgPWN2xIp9JMKZaQkLhtJIFeCn755ReUSiVDhgy5tszZ2ZmBAwcybtw4Ll++TM2aN75I/lOcA7Rt2xYfHx+SkpJu8IqKwWi3k2Q0VvhxY93ccKughru+ffsycuRIjh49StOmTW+63euvv35tPHtpmTp1Km3btr3bEG9IUVERAJ43qfe4ulyr1d71sQRBICElgRM5Jxi9dTQDmw7k+2e+vysBm5oKzz0Hf/0F7dvDqlXw1FPl61V+I4qLixk1ahQLFy4kLCyMuLg4evfuXaXFuc1WTE7OT6SlzcBkOoOnZzuior7Ax+dxXF0jAbBateTmrsDf/yWcnO7AzacKIDgETOdNmC+bMZw0cGniJWwFYg157Y9qE/J2yL8y4u71r1jq3bsGNFWao3o93U6cIMdqZUBgIGNCQ6l9B7MTJCQkSock0EvB0aNHqVOnDmr19Z7BDzzwAACJiYk3Feg3ori4GL1ej18ljh1OMhppfvhwhR/3cPPmNKugSYu1a9cGYMmSJf8p0G+r2fIe4nzBecZvH8/PJ38GoGtMV77q8tVdCdj4eOjeXawl//NP+I//9nLjyJEjxMXFsWLFCoqLi/niiy8YOnQoqoq+Q7gFNpsOne5PHA4jVmsu+fkb0OkOYLFk4O39OFFRs/DxeRyZ7HpvbScnL4KDh1ZS1HeH8YyRix9cJPeX3OuWBw4IpObImrjXc0eukrzEqxKCIHDZbOaZ48cJUKnY3bQpoS7SJFQJifJGEuilIDMzk6CgoH8tv7os4+82FKXgiy++wGq18tJLL5VJfHdCrJsbhyvB1zm2gnxst2/fzvz58+ncuTPLly9n+vTpyKvJqOerGfKrmfR/cnX5HXmhX2HZsWX0W90PlULFj8/9SNfYrrg53fnvxmYTBwoNGiR6lq9YUf5DhK5SWFjIzJkzMZlMbN++naNHj+Lv70/37t157733iIiIqJhA/gNBsAMy7HYDOt0+Cgo2k5n5PXZ78ZUtZHh6tsXPrzshISNxc7txeVN1RBAEMuZlkL8+H/1BPTKVjNDRoWhaanCv547CU4FLiCT4qhqCILCrqIjZ6emszsvDW6lkXcOG1CxFuZyEhMTdIwn0UmAymXC+wUnJ5UoWwWQylXpfu3btYtKkSbz00kvXuX5UNG4KRYVlsiuaTZs2MWHCBLZt28bGjRvp3bs3v//++w2bLqsisbGxwP/Xov+Tc+fOATevUf8vCk2FjNg0gmXHl/Fi/Rf58okvqaG+u0bl+HjREjE5WbRIXL684sT577//zsCBA8nMzCQgIIAHHniA0aNH88ILL1R6xrykJJ3s7MXo9YcoKIjH4TBcW+fk5E9Q0GCCg4eiUIhDc1Sqe6Nh3FpgJfeXXHQHdBiTjOj2isOCnGs5o2mlIea7mGve4xJVi5MGA8kmEyklJfyUk8M+nQ4nmYwOXl5MDg+XxLmEBEBhIcjl5W47Jgn0UuDq6orZbP7X8pKSkmvrS0NSUhLdu3enUaNGzJ8/v0xjlBBZs2YNo0aNYteuXXh4eNC1a1fUajVLliy5qUAfMmQIR48eva3jzJo164b9BWXBVf/0+Pj4f00y1Ov17NmzB3d3dx588MHb2m9RSRHtFrUjXZdOXLc4+jbqe1flLFu2wBtviMK8Y0f48UexpKW8Z4w4HA5OnTrFN998ww8//MADDzzApk2bqFevXvke+JZx2cjImEt+/noMhlM4HAZsNj2eng9Rq9Y4VKoaOBwWPDxa4eZWF4Xi3qnfteZb0e7Sot2pJW91HuY0M2513XCLcSP8f+Fommmkxs5KIslgYFNBAW4KBacMBuq7u5NvtXLCYCBQpaKxWk1KSQmH9XrW5ucDoAA6eXvzW4MGdPH1vc7jXELivsPhgNWr4dQpKCiAb78Fux169YLWreHkyXI5rCTQS0FQUNANy1gyMzMBCA4OvuU+0tLS6Ny5M97e3mzcuBF3d/dSHfutt976V7Ngr1696NWrV6lefz+xYsUKhg4dyrZt2wgLCwPEm6fu3buzatUqjEbjDX3Dv/vuu4oOFRD9zq1WK1FRUSiV//+nGBERQefOndm6dStff/01w4cPv7Zu4sSJGI1GXnvttVLfGALsS9vHyMSRpBalsn/gfur6172jmHNzYfFiccjQqlXQoQPMmCE2gSrL8WySkJDA2rVruXz5Mps3b0an0+Hv7897773HmDFjSu8HX8YYDKfR6w9iNqeRn78ene4gPj6d8fJqj0ymJDx8Mi4uFePDX1GYs8wU/VGEez13XKNcSeqfRM6KHBDAJdwF78e8qTWuFq6R984NSHXlnNFI28REimw2rIKAArADXkolkS4u7CkqYmZ6Ot5KJU3UamZHRdHdzw9PpRKP8vyDlpCoLBwO8UJWXAwGA/j7ww1KmK9x/jyMHCkO7NBo+MnJiZ8CAsQM+vLlsHgxReVkfCH9BZaCpk2bsnPnTvR6PZq/lYUcOHAAgCZNmvzn65e8G9wAACAASURBVPPz8+ncuTNWq5UdO3bclvf5rFmzaNas2Z0Ffh8RFxfH4MGDWblyJc3/UVvfp08flixZwqpVq+jbt2+5xbBmzRrWrFkDQFZWFgB79+6lf//+APj7+zNt2rRr23fq1InU1FQuXbp07YbiKnPnzqV169aMHDmSbdu2ERsby4EDB9i5cycxMTF88skntxXb8I3DadS0EateXHXb4jwvD/74Q/Qz/+Yb8fzWpo04BXTSpPIT5snJyRw5coSFCxeyZcsWQkNDCQsLY/jw4bRv356HH374tm5SygKHw4xef4Siot1kZS3GaBQzJ0qlL+7udWnSZCdeXuXzZKUiEQSBgs0FFP1RhGATMJ42YjxjRBWsomhXEQiADJSeSuzFdqLnROP7tC8utaRa8srE4nCQa7XybUYGFoeD7zMz8XdyIqllS3yUSgSgwGrF18np2tMzvc2GWqGo0u5GEhKlprBQHK6xZIk4/a5JEzGb1KsXXLoEI0aIF7SrODnBhx+KIj0+Hi5ehK5dxYvcihXw/ffi/latgu7d6QVcS4+azXD5MkcKC2neokXZvxdB4pYcOHBAkMlkwvTp068tKykpEaKiooSHHnro2rLMzEzh9OnTgtVqvbasuLhYaNmypeDp6SkcOXKk1Mc8fPiwAAiHDx8uk+3uderXry989dVXN1xnt9uFNm3aCA8++GC5xvDRRx8JMplMkMvl133JZDJBJpMJ4eHh121fu3ZtQS6XCykpKTfcX1pamjBgwAAhKChIUKlUQu3atYW33npL0Gq1pY7p6udjzpo5gsPhKNVrzGZBSEgQhJdfFoRGjQRBLhcEEIRatQRhzBhBSEsr9eFvidFoFI4cOSLodDrhwoULwrZt24SFCxcKjz32mIAoA4UWLVoI8+bNE2w2W9kd+DbQ6Y4KiYmdhb17Q4U9e4KFHTsQdu50Ek6e7C1kZsYJNltxpcRVHhgvGIXz750XdvvvFnawQ9gTvEfYF7lP2B+9Xzg98LTw1xN/CZe/uyyUpJcIl7+5LFz44IJgSDJUdtj3PSuys4V6Bw4I7NghOO3cKbBjh8COHcKIs2eFzJKSyg5PQqL8+Pt1be1aQXB2Fi9YV7+uXsBcXMR/1WpBWLhQELZvF4T9+wVh1Kjrt//7l7+/IHz6qSDk5v5nCOWlw6QMeilo2bIlPXr04P333ycnJ4fIyEgWL15MamoqCxcuvLbd2LFjiYuLuy4j2qdPHw4ePMirr77KyZMnOfm3WiWNRkPXrl0r/P3ci5w4ceKm6+RyObt37y73GCZOnMjEiRNLvf3Fixf/c31ISAgLFiy427AAaB3aulQZsowMsWzl7FmoXRs6d4bXXoOnn4bQMqjUMJlMpKSkkJWVxcWLF/n444+5dOnSv7arW7cuP/30E7GxsTRq1KhCHXgEwUFJySWMxiSys5eSk/MTrq5R+Po+A0Bg4Mu4uzdAoShdmVpVRXAIZHybQc6POdh0NuQqOfrDepSeSmq8XAOfx33wedLnpp+b4KG3Lu2TuHv0NhsHdDoO6PVYHA5sgsBBvZ63QkJQyeV8mpLCNq2WZ319eTEggAsmEz0DAqjt4kLdUpZSSkjcFXY75ORU7Gjo8+ehf384ehSGDYOwMHj/fWjXDrp0gRYtxCl5y5aJWfNLl0CthqFD4e9PXlu1glGjwN0drFZIT4czZ8RHw88+C5VUPglSiUupiYuL48MPP2TJkiUUFhbSuHFj1q9ff12joEwm+9fF7K+//kImk7FgwYJ/ia3atWtLAl2iyrBrFzzzjHg+2rtXPG+VlS5OSUlh9+7dvPnmm+RfaUQDscznu+++4/LlywQHBxMeHk5oaOg1h6SKwuGwkpW1AK02gby8NTgcojOTs3MIdep8S2Bgf+TyquWjfjtYC60U/1WMOdWMXW/Hq5MXmd9lkj4rHd9nfHFv7I5dbyf49WACegagcKuYYWISN2dfURETLl1il1aLRRCQAX5OThjtdtwVCrocPw5AQ3d3fqpbl5cCAqQyFYny5fx5WLcOfvtNnEQ3apQ48GLnTrGee/hwmDPn+tc4HGIpSFmUIxYUwKJFEBEBU6dCZib06AHTp4vrn3sO4uJEsQ3w8MNi/fitqFXr/78PCoIrM24qG0mglxJnZ2emTp3K1KlTb7rNwoULr8uow62zpBISlYkgiGI8PV20SmzeHFauBF/fu9+31Wpl+/btLFiwgJ9/FochdenShTFjxhAUFERgYCAeFeXH+DcslhwMhuOo1U1xOEyYTMmcOzccg+E4KlUwoaHv4uoaiVrdFHf3eshk1VesCoLApQmXSJmS8u+VMoj6IoqQN0MqPjCJ/+S80Ui3EycIUqmYFhlJaw8PPJVKoq9k8xyCwJ6iItwVChq5u6OsJjMeJKoYeXng7S3ace3fD+vXg14P27aJjiX+/qJ37r59UKMGzJ4tPmZt0waaNYOJE0VB++qrYvb5q6/+j73zDI+iXMPwvb2k956QBAgl9CZ6OCqg6FGaghUFRbEromA5eqwI2BVEEQEbKFJUVDSAoiBI752QXjY9m8323Znz46MLSAl97uvKlWTL7CxkZ555v+d9XrHdMWOEmP7pJyHYd+wQS7P9+sHgwcIf/t13Qri/+qqoeh8JSRIXAJmZ8Ntv8MorsGaNuM9kgkWLRIrKO++Ii4cOHRquqnQOoAh0BYWLlGXL4I034Pvvxe8dOsDs2RB+iml4siwzY8YMRo4cSWlpKSkpKYwfP54+ffr8rRn2TCLLfvLyXqKw8A0kyXXIfUFBHenQYR1BQWdh9Olpwr7Nzs6hO6lbUUfi8ESib48moGUAklPCtsaGMdWIucnZW75VOECx2838qio21tfzV10d6+rrSTUayWrThpgj5PmrVSq6ncKgMoWLlIIC8T07W3T4L1kCkZFCqEdHC1+j3//358XFgdUKrVsLwZyQIKo7W7YI72NoqPi9WTNhM/nqK6irE6K9dWshwn/4QVSz91W0O3USaSqXXy4q7716iSZNs1nclpkp/JU//XRgPzIzxYWE2w2JiaKSDuIi4xypejckikBXULjI8Hhg9Gh4+WVhyZs5U6wExsWdun2wqKiI22+/nSVLljBgwABGjBjBJZdcctaX3v1+O9nZT1BaOpnk5GeIjh6I3b4NjSYQgIiI/5zXlXIQnnJXgYvKuZXUb6yn8ttKDIkGWs5pSdQNUfsfpzFpCL9aySQ/25S63fxcXc3sigqyqqtRAWkmE5cEB/NwQgK9IyKIPMvDthTOYWRZWE0KC0WFevlykUjSs6eoKs+aJYR3aKhIM/n9d1GF3kdKisjzXrlSVMSvvho+/FCI4GuuAaMRcnJERb1Ll7+fHFQqUV0/+PfHHhOZuxMmCAHduzekpoJeD88+C7t3izSU5s2Fv1uSRDTYQw+J5xiN4HLB2LEHtvvOO+I9Xn65eM5FhCLQFRQuIlatEiuMu3fDc8+JY2ZDJRXm5ubSu3dvrFYrWVlZ58TkVq+3iqKi8RQXj8fns9KkyQQSEh4AIDCwzVneu4ahbmUdFd9WUPVDFY5tDlR6FYFtA4kZFEPa2DS0wcph/nRR6/XyWVkZZrWavpGRBGo0vFtUhFOSuDEykqyaGlbV1aECuoWG8khCAp9ZLIwrKGDn3gnU3UJCeDM9nSGxsYSd7ilfChcGEybAE0+IaguICnK/fpCfD6+9Jm5r2lRUtBctEtXrNm3gk0/EAV+vF1WZ2FgYNuzAdg+P723Z8sT3rXFjePfdI9/XpAk89dSB39Vq0eCZng5lZTBokGj69PtFlT85WeznRYpy5FZQuEjYsEHYADMzxTHw4OLHqbBq1SpGjRrFH3/8QWhoKMuXL6d585MbhNQQyLKMx1NKZeW35OQ8iyx7iYu7l6SkERiNKf+8gfMEySOR+99cCt8sRBumJbxXOI1ebETo5aHoo5XK65GQZZl19fU8tWcPPcPC6BIcTKuAALKdTtoGBmLcO3DEK0noDvOyFrhcVHm9JBgM/Fxdza81NcwsL8cjywDcv2sXwVotDr8fnUrFq/n5GNVqLgsOxifLDM/O5umcHFx7xftLqalcERp6RAuLgsIReecd4Q3/5BPo0UNUWZo3h6CgA2kjJSXC/928OWg0QuyqVOe2N7tXrwM/75tj0rnz2dmXcwhFoCsoXAQMHy6se5mZsHhxwyRHzZ49m5EjR5KXl0e7du2YNm0a3bt3P+M+c0nyUV39EyqVnvr6jVRWzsVmWw2oiYm5nfT0t9Dro/5xO+cirnwX9m12CsYVYFttw5BkILJvJOamZnL/l4u3wkvaG2kkPZ6ESqMkeByMzedjUU0NH5aUUOrx4JEkSj0ebHs9tkusVrx7xTVAisHATdHRtAoI4OHduwnRamlmNhOr1+OWJGZVVCAftP32gYH8NyWFoXFx6FUq5lVVsdPhYHBsLMkGA8usVtoEBhJnMAAwoaiIbysrebFRI8U/fi4gy6JqAdCunfg9Jwdqa0Xz45VXCuEYHi5SQQ6b6H3GmTULRowQPycnC2/23r+tQ4iPF1/7OE1TLhVOP4pAV1C4CCgvF0lUd9xx8uLc7/czZ84cvvnmG3bu3MmWLVvo168fY8eOpV+/fhiOdLI4zdhsa9m16yFsNjHVV602ExJyGRkZ0wgL64HR2ADh7WcYWZKp+qmKss/LqJhdAYAh2UDSiCQcOxwUv1+M5JII6hJEq59aEdQ26B+2eHGx3W7n0exsFtXUAKABro+IINloJMlgIMNs5prwcDQqFbMrKtjjdNI1OJh3i4r4qKRkv4C/IjSUUo+Haq8Xo1rNy40acXV4OEVuN0kGA50OSyAaeti48GsOi0J6ODGRhxOVxJyzjscjuuNHj4a9NiPGjoVvvxV+7H389hs8+aT4OSBANDfefju0aNGwWd/19XDPPaJZ8667hEUkJETsp0Yj7Clz54qElX79hE9cko4szhUuKBSBrqBwEfD55ye2YijLMn/99Rc5OTls27aN/Px85s+fT21tLc2aNaN79+488sgj3HvvvWe8AdTrrcLh2ElFxSxKS6diMCTQqtVPmEzpGAxJaDTnRzKJ5JNw57tRaVWgBusyK/ZNdkqnlOIt92JMNdL0o6aEXRWGMdW4/9/ZW+vF8qmFmEEx6CMVe4RXknho925W22wEazQssVpJ0Ot5NTWVrsHBdAwKIlh75FPdzdHR+3++MiwMh9+PxeMhyWD4m8VlH8rC+3mKLMOUKSI/OydHJIT07AlTp8LTT4su+RkzRObsDTeIWME1a0RFfdkyERc4ZozwS/ftKxonO3QQnu6wMCGkd+4Unu6YmGPvR1mZeMxHH8GoUUKkA3zwgci4zcgQTZ9BQaJJMzhYWFbeflv4xhUuChSBrqBwEXAUffI3fD4fjz/+OLNnz8ZisQAQFRVFamoqw4YN44YbbqBLly6ncU//jsdTQVHRO1RX/4IkOXE4dgCg00UTF3cvKSnPodOdu5YByS1Rv7Ee1CJBxb7Vjm21DcunFryV3kMeqzarib0zlpg7Ygi59MhL6rpQHUnDz7+VgRPB4fez1W5nqdXKa/n5JBgM3BMXR3OzmTyXiwK3m2K3mxqfj10OBzudTi4JDsbm99MvMpLPmjU7qig/FmaNhrSG6ppWOLcYORLeegtuvFHYRdrsbRLv2/dAQ+LhVekrrhDf+/UTGdyLF4tc2hkzhFg+ElOmHGiujIsTzT733SeSVl59VVTC3W4RC7hmDdx2m2jsdDhg6VLRwb9ypbhNkqB7d7jkkjM3oVPhnEER6BcI27dvP9u7oHAOciJ/F7m5uQwYMICNGzcyYsQIrrnmGjp16oTZbEZzmnyMsizh81nRakP3V4hlWaa29jcsli9wufZgtf6JSqUlJmYQGk0wSUkjCQxsQ0BAa9Tqcyv1wlvlxbbGhqvQha/aR+mUUtwFbiSXdMjjdNE6IvtHEjUgCtknIzklQi4PQRemu2i95H5ZZo/TyTtFRXxSWopv7/TM3hEROCSJR7Oz9z82QqslSKslw2QizWTi/SZN6B4WdvZ2XqHhKSsTsXpOpxDTEyYc8IFLEuzaJVJKJEnkec+cKfzi99wjKtlffSWq3wMHiqbKP/4QTZbDhx/6OiqVSBf5J4xGuPZa8TVxIlgsYpR8dbWYaNm/v5im+fLLIgPcahVi+7PPhLivqhK53c88I1JUFi2CAQOEZSVor02tWbOG/TdUOK9RBPoFwqBBg872Liich8iyzPr166mvr+euu+5CpVKxePFiunXrdlpez27fgcu1B0ly4fPVUVT0Lnb7JgwGka7i89Xg99cBYDa3QKeLomnTj4iI6IPBEHesTZ8VvNVeXHku/DY/1mVW8l7OQ3YfaCUMvyac+PvjCbksBJVWhbfCi7mZGX28HrXuHE5VOAN4JQmXJFHp9fJmYSGzKyoo93oJ1Wp5JjmZ3hERtAwIwKzRIMky+S4X5V4veS7XIdYUhQuQuXNFo+aWLcKb9913osv9jTdEBNWMGaLq/a9/iYzs/IMm5R4cM+hwiKzwjAx4/nmR090QqNV/b8bcx7ffHvr7unViPH3nznDLLQeWM595pmH2ReGCRRHo5znNmjVj7dq1Z3s3zmtkWWZDfT2fWSwstVrpGhzMC40aEXW0+DObTZi6p00To5B79hRfrVodNcrK6XXy/Y7v+XLzl5TaSgFICU2hX7N+XNfkOiLMEUd83pEoKhKFoN9/FxOS77wT2rY99gpos8MqM7Is8+OPPzJp0iR+2jupLS4ujmXLlpGamnrc+3I8eDyVlJV9ht2+DYvlU+BANTk4+FKaNv0Yu30LGk0gWm0YWm0QJlNjQkO7n/UBR/vwO/z4anyoDCrq/qrDsc1B5feV2NbZ9gtylVZF/EPxJD6SiMqgwlfjI7BV4Fne83OL3Q4H4woK+LGqilqfD48sIwMxOh19IiNJNhh4ID7+bwN61CoVqSYTqSYTXQ5rzlS4gJAkYREZNkzECE6ZIoTt+vXCotK/v3jc4MGiqu7xCKvIJZeI4TxZWWJa5oABIrKqtFRU1h94QFTAzwbt24svBYUTRBHo5zlms5n2yof/pJBlmeV1dbyUl8dCWaZFaipTk5IYEht7ZGFotYrly7ffFlWQV14RQxeO4nXdVbWLD1d/yPc7v6fAKkYs33zpzTzZ9Ulax7RGrVKfsAD96SdxbgoIgC+/FKECJ0ppaSlPPfUUX3zxBeHh4Xz11VdkZGTQvHlzjA10EnM4dlJW9hVW61Ks1iWoVFqMxkakpr5CbOwQ1GoTarXhnG/o9FZ7KXqviKJ3i/DX+UUkiB9UBhUR10WQ+koqoVeGog3WoovSoQs7yHKjBHZQ6fGQ43LxTXk5i2tryXW50KpUXB0Wtj/CUKtSMTA6mgAlDu7iYedOMSLebAafTzRfzpkDGzeK+x9+GN5//0DVoV07WLBA+L/j4oQgPxJDhx76e3w8PP746XsfCgqnEUWgK1yU1Hi93Lh1K4tra2lqMjG3ZUv6REaiOZJgdjhEB/+4ccIP+cwzYuJZixZH3LYsy0zbMI2H5z9MiDGEKxpdwX0d7uPmzJtpFNropPZ35Uphe/z8c7j+evjiCzHB+USZOHEiI0eOxGg0MnXqVO68884G9ZfLsp/CwjfJzX0BjSaAoKD2pKaOISbm9nPSonIw7hI39i12ahbW4Cp04S33YlttQ5ZlYu+MJbhLMP56PxHXRygWlaNgcbv5oaqKyaWl7HA4qPf7kQGtSkW7wECuCgvjvcaNiVUi4i4evF6RgqLTweTJwru9YAFER0PXrvDXX1BRIVYgTSZxbH3vvb8vCarVByroCgoXAYpAV7io8EoSbxUW8nJ+PhqViu8zM7k+IgL1kYR5drbIyp03T9ha7rlHTG47ku9wL5Z6C0O+G0LWnizubns34/8zHrPu5KvEq1fDSy+JynliokjlGjbsxBv6LRYLU6ZM4bnnnuPBBx9k9OjRhDbwsBRZltm58x4sls9JShpBo0Yvo9Gce4kYzj1O7FvthF4ZiiZAg7fKS95LeZR8VAJ+0Mfq0YZqMTYykvRUEnFD4zDEKYLSL8toVCqqvF622O00M5uJ0ev5wmLhy7IyNtbXU+YVqTQ9QkN5MimJBIOBdKORBIOBJg0xHUvh3CIrS/jB27aF664TcYBqtRDcU6aIykJNDexrVg8IEEJ8+HARLbhokag4DB0qxLqCgsJ+FIGucNGw3mbjzh072G6380hiIo8kJBw5Us3jEVN9XnlFeMyHDRNf/+DN/iPvDwbOGohWreXHW3/kuqbXndR+er2iH+rDD0UQQUYGfP21sFWeaLHbarVyzz33MHv2bFQqFcOHD+edd945qf06Gk5nLoWFr1NePgufr4rmzacTE3Nbg75GQ+Cr97Hr/l2UzyjnkJGQgCZEQ+rLqQRfGkxot9CLNkkFDvRkvF9czMq6OkK1Wso8HiweDy0CAlhrsyEDQRoNHYOCWFxbS4/QUIbFx9M2MJC2gYFKVOHFwD6veGqqOEDtm3J5MFddBSkponEzIUFkeQcqfRkKCseDItAVLgoWVldzy7ZtJBuNrO7QgXZBR5m+uHy5OOns2CFOOC+8IKo+x6DOXceinEU8PP9hMiIzmDVwFrGBJzZMIjdXFKNmzhQ2zJoaMfti2jQx/fN4hXlVVRUrV67EbrezefNmvvzyS6qrq/n444/p168fUVENN/K+rGw6eXkv4nLlodNFERNzG2FhPYmM7NNgr9EQyLJM3V915P43F9saG00/bEroFaFYl1uRPTI+q4/Yu2MvyqE/62025ldXCxuPXs8qm435VVUUezyEabXcEh2Nw+8nTq8nxWik2O3mvrg4OgYFMc1iYZfTydSMjKP3bShcWNjtIqVk6lSRCX7//SL+0G4Xx866OhEhWFUl8sYbeJVOQeFiQhHoChc01V4vL+TlMaG4mCtCQ5nbsiVhusOysz0e4SGZPBl+/vnAAIm2bY+6XZ/k48PVHzJz60xWFK3AL/vpmtiVmQNmHrc4l2WRIjZtmkhlUatFcMFDD4lV344dT6xiPmfOHO6//34qKysBCA8Pp1WrVixcuJD09PTj39Df9tOPJHmxWv+ksnIuNTULcbtLkSQ7kZE3kpj4BDExt6LVHnmwztlC9suUflJK8QfF2DfbMaYZafltS8J7hgNgzrg4LBdeSWJFXR2Fbje1Ph8alYobIyP5vqqKe3buJFijQa9WU+n10sRk4qboaK6LiKBbSAj6o6QSAbx3tItchQuT/Hy46SZYtUpUwj/+WNj+VCphbbnmmrO9hwoKFxSKQFe4YFlmtXLDli3Y/H7GN27MQwkJh1b5Kith+nThJdm5UwjzSZOEH/IoyrjSUckXG7/gs42fsbl8M30y+jDhPxO4Ku0q0sOPLYIlCX79VbxEXp4oNu3eLc5tL78Mjz56YA7H8eLz+fj555/54IMPyMrKon///rz++utERkYSHByM+hgC62hUVf1MTc1Camp+w+utwOutQJaFt1iniyY8vBeBgW0wGtOIjOx3TlRO3cVutGFaPOUean+rpXZxLdZlVlx5LiL7R5L+ZjphPcNQqc/+vp5JLG43Q3bsIKumBhDNmj5Z5v5duwC4Ny6OiU2aoFWrcUsShpP4e1G4wJFlKC+Hq68Gl0vku3brdtRIWQUFhYZBEegKFyRzKiq4Y/t2OgUFMbNFi0NTI5xOWLgQ7r5bqOTrrxdCvUOHo26vylHFB6s/YPyq8VQ6Kumc0JmV96ykY3zHoz5HkkR875IlUFIiUsRyc8WwuPh4EeP77ruian6ioRZut5tx48YxefJkioqK6NChA9988w0DBgw4acHs89WTk/MUJSUTMRrTCA6+BKMxFZ0uHK02lMDAdgQEtECtPncaJp05TnL/l0v59HJQsd9bbm5pJqxnGHH3xhHc6eLKzfZKEnV+P5+UlvLfnBzMGg1fNm/OVWFhROp0WDweFtfWEqPT0SMsbP/fiyLOFQ7B7RZ2ls8+g19+EVa/DRugceOzvWcKChcFikBXuKBw+f08kp3NJ6Wl9I+MZHrz5pj2VcNlWZi8H39cRH116SJydWNijrgtn+Rj3s55ZGVn8cWmLwC4u93dPNvtWeKDjp7kAsK6MniwGCK3bwW4Xz+RXd6164mnsBzM/PnzeeKJJ8jNzWXw4MEMGzaMDse4uDgWsixjt29CpdKyc+e92O2bSU0dQ3LyU+dEZXwfsizjr/ejNqlx7HDgsXioWVSDZZoFJEh5IQVdhA5DkoGgDkEYk87SUJKzgMvvZ119PX/U1vKn1cryujpqfT4AnkhM5ImkJOIOugKMNxi4/Sh/8woXIBs3iljDuDhx3LvySmHrKyoSI+7btBHHxuJisZpYViaKGL/+Kirn4eHiOf/7nyLOFRTOIIpAV7hgcPj9DNi6ld9qapiSkcFdBzeueb0wZIiIBOvfXyS0tGhxRKUsyRJZ2Vk8v/h51pauJS0sjacue4qHOj9EpDnymPtgt4vz2Pjx4ty3YIHwkoeFnfr7q6ysZPjw4UyfPp0rr7ySqVOn0vUko8kkyUdp6WQqKmZRW7sYALXaTNu2vxEc3OXUd/YEkGX5bxcDsizjzHbir/NT+0ctls8t2DfaD3mMLlJHZL9IGr3c6IKPQXT6/VT7fCQcJLRlWebr8nIe3L2bWp8PrUrFv0NCeDA+njaBgTQ2mWiv+MQvbtasEUt0LpcQ5UciLEwcuDweUSVv2lRY/IYMER3qmZlndJcVFBQEikBXuCDYardz+7Zt7HI6+aFVK64KDz9w57Jlws6SnS0E+q23HnU7BdYC7vr+Ln7L/Y22sW1ZMXQFXRKPT7CuXi02XVoqwl+eeKJhpkuvX7+et956ix9++AGtVsuUKVMYMmTISfnLZVmmpmYBeXkvUVf3FyZTY1q0+AadLpyAgEz0+tNXWZUlmbIZZXiKPajNalRaFWVflGFbayP08lB0OWTAMgAAIABJREFUEXubd1VQv74exw4HAGqTmuAuwTT7rBmyT8aYYsSQbMCYakStvXBtGeUeD1+UlVHidjOjvByLx0O4VsttMTFcHhLC2IIC1tbXc1NUFI8nJtIxKAitYlO5OPF4RDUgN1cI7jffFL65NWtEhWDRIlGM8HrFsl5MjKiMb98ujo9hYdCoEXTufNQVRQUFhTOLItAVzmtkWeaD4mJG5uSQajTyV/v2tNmXs2uxwH33iUFDl1wiTkxt2vxtGzXOGmZtm8Wc7XP4Lfc3woxhZA3K4qq0q/7R5iFJotFz9Wp46ilxbvvxR+EzP9X39euvv/LSSy/x559/kp6ezogRI7j33nuJP8agpGPh9zvZtu0WqqrmERTUmTZtFhMWdsWp7eixXs/lx77FTu3iWiq+qcBd6sZT7EEbpkVySkguieBLgkl5LgXrn1Y8FaLCJ/tkAtoEkP6maLoNuTwEbeCFeajyyzIqQK1S4ZdlLB4PsysqmFtRwWqbDb8sk2w0ckVoKNeEh7Oiro6ppaVMKC6micnEd5mZ9I089qqOwnmMLAvRvWED7NolRPc+YT18OERGwg8/wPPPw9atQoTLexsxkpLE+OE77oCDh0T16HHg5/j4Q39XUFA4Z7gwz3oKFwVOv59bt23j+6oqHk5I4PW0tAN+840bhenb5YIvvhCl7cOSWbKys/hs42f8uOtH7F47l6dczltXv8Xd7e4mUH/sYRrbt4uhogsXiiGjAJddJgYLJSWd+HupqKhgzZo1/PLLL2RnZ7N8+XJqa2vp2rUrs2fPpm/fvmi1J/dxtdu3UV7+FVVV83E4ttOy5bdERvY9bR5zZ46T7MezqZpXtf+2iD4RhFweQmS/SEL/JbKRj2RtuZDwSBIb6uup8HrZbrcTptORoNdT4vGwx+lkbmUluxwOgrVaonU6djmdAKiBf4eG8kpqKoNjYojUH8hnHxwby+jUVD4sKWFobOyhzc8KFxZTp8IzzwgfOAjxbTCIYxoIv7jJJDzjHTuKanlMjGiA+fe/QasVmeQKCgrnJYpAVzgv+dxi4eW8PEo8HuZlZtJ7XxXR6xWZha+9Jjzmf/wBycn7nyfLMr/n/c67K99l3s55tIpuxYiuI7ivw33EBcUd8zXr6sTwvEmTRNU8JUWcPzt2hPbtISLi+Pbd6/Xi9XpRq9WsWLGC7777jvHjxyNJEklJSTRp0oThw4fTuXNnevXqdUJWFlmWkSQHsiwhy34slmnk5DyNVhtMcHBX0tLGER7e87i3d6KUzyxn++Dt6KP0NJnQhIBWAQR1CkJj+nts5YUgzmVZRkZUwLMdDl7Iy2OT3U6tz4dJrWb3XtFtVqtxSRLS3udF6nR0Dw3l8cRELB4PZR4PjycmEqDR0DsigtDDs/oPIlyn478pKaf/zSmceZxOcXBZsACefVYUGQYPPuALT0gAq1VEHL7/vljC691bNLzvIzHx7O2/goJCg6EIdIXzCkmWGZGdzXvFxfSNiOC7zEwy91laHA647TbhMXnxReE5OaiCtLp4NSMWjODPgj9pFd2KcT3HMfLSkccUivX1sHYtfP65CIBxOuG668QwoWHDji8e0e/3I8syS5YsYebMmcyZM4fa2lq0Wi1ut5uIiAiee+457rjjDtLT009auNpsG9i1635stpWH3J6Y+DhpaWNOWzyit9ZL2Zdl1GTVUPVTFdG3RZMxKQNNwAlMWTqHkWWZ5XV1VHg8pJpMbKqvx+Lx8HttLevr6yn1ePYnPCYZDPSOiKDS66XS62V0aiqdg4NJNhhwSRK5LhcJBgMBarXiFz9TyLIQsiqV+Nq+XVzA9+0r0klO1SJUUABBQYd2gsvy8UU1VVYKf/j334s81rIy8PvFfTffLA48h1fBo6PF95dfPrX9VlBQOKdRBLrCeYNPknhw924+KS3lgyZNeDAh4cCdf/4pptoVFIiT3XXX7b/L4/cwcfVEnl/8PI3DG/PjrT/ynyb/OaYQLiiAt96CDz4Q58vkZBg1SvSaHk+Byuv1MnHiRGbMmMHWrVtxOp1IkkRqaip33XUXOp2OyMhIunfvTuvWrU+q4RNAktxUVy+gvHwG5eXfEBDQgoyMaWg0ZkCNyZRKUNDJRTAeDZ/Nh+yTqZpXReFbhbjyXUhOiaAOQSQ+nkj66+moNOdndVySZfY4nTglCbcksa6+nonFxWyyH5ogY1CpuDw0lAFRUbQJDMQvywRpNPSNjMR8lCFXJo2GFgEBZ+JtKGzfLoTvxo3iytrlEh3bLhfsjaBk+nTxPSVFCOo77hCj6xMS4JtvRNU6I+OAf3vDBtGM2aKF2O7q1TB7thhxr9eL0fbt2sF77wlxPmyY6HvZsUMsr11zjaiK//GH8IZv2CAa12VZvM6dd4p9adFCLMkFHttmp6CgcGGjCHSF84I8p5Pbt29nRV0d05o1Y3BsrLijrk74TCZOFAHj334rxlADfsnPJ+s+4e0Vb7Oneg93trmT9699/5j+8upqGDkSpk0TiWMvvyzOq23aHHW46CHIssx3333H//73P7Zt28aNN95Iz549CQoKokePHnTs2LFBrB0eTzk5OU9TUTEHv78Os7kljRu/Q3z8A6jVR7dHHA9+lx93gRvbWhuSS0L2yKAGxzYHtb/XYt9uR3aLRrTIGyKJGhhF7F2xGBPP/exxSZZZUlvLHpeLvhERROr1+CSJGeXlvFNURJ7LtT9DfB+9IyJ4NTWVdJOJQrebS4ODCdBoUF8AFp1zHlmGTZtEY8fByUyHs3ChmAbcrJmoOn/9tbC7mc1C/F53nfg5JETkgffqJaaHvfuuEPNpaTB6NLz+utjG5s1iuwaDuDo3m4UoPxi9Hi6/HCZMEEttU6eKlKg+fYQ3/IUXoFUr0YRZWiqaVt55B6qqxAHlP/+Btm2hZ09xUaD8PSkoKByEItAVznkKXC46rl1LoEbD0nbtuDQkRNyxaZOoWpWWCj/mgw/uV9E1zhpum3sbWdlZ9G/en1kDZ9E6pvURt5+TIwphixbB0qXC3jlhgnDLhIYe/37m5ORw//33s3DhQnr06MGnn3560gOEjobPZyM//xWKit5Bqw0jMfFxoqMHEhDQ8pS3Lcsy1b9Us/PenXiKD8pMVgMS+4cARd8ejSHRgD5aT1j3Bgh4P0PkOp3csHUrG+rrAbgHhNVEpcLq93N1WBjdQkK4eu90zSCNhhZm8yFNmkoF/AxQXCxEdl6eEM9LlwqhPGwYXHqpuCivrRWTLv1+0UT54YeHbuPFF+HRR8UH+GjCt3Fj8UHfx//+JwT2mjXiw5+aKoR6TY0Q+48/LgT3pk0QFQXXXnvouPuRI0We+L7K94wZh97//vsHBqX17398V/wKCgoXLSpZ3pfJpHAusW7dOjp06MDatWtp37792d6ds8Yyq5UhO3bgkSTWdexIhE4nfJqDB0NWllgOnjcP0kUknyzLfLz2Y55a9BRqlZqZA2ZyVfpVf9uu2y2q43PnihVos1kEH1x5pZjPsc/m+U84nU4sFgs7d+7ksccew+l0MmHCBPr06dOA/wrgdhdTWfkDeXn/w+erIynpSRISHsBgSPjnJ//Tti1udOE69jyxh+IJxQR1CiJtbBrmFmY0gRpUWhUqjUp8P8+qfLIss6G+npnl5XxWVoZZrWZKRgYtAgKYX1VFuddLkdvN3bGxtFWG+pwd/H7RFLnva9s2IXKbNhWV5V69YM8eIXD3+bONRiF+Q0KEKH74YSHgc3KEKG/X7uy+JwUFhYuG06XXlAq6wjlJhcfDqJwcPrVY6BQUxFctWghxvm0bXH218JF+8QUMHLi/U9PhdXDPvHv4astXDG03lJevfJn4oEMzw1etEkWzGTNEYe2uu0ThrG/fQ6OCj4Ysy+zZs4fly5czbtw4tm3btv++5s2bs2DBApqdagj6Xvx+J5WV31NW9gXV1fMBiIq6mfT01zEak//h2f+wbZefkokl1Cyqofrn6v23N5nYhPj74887IX4wdr+fHQ4HW+123igsZIvdToRWy4CoKJ5JSSFl7/SoIXHHTu1ROA1s3gxvvw2//y6q0rIsKsmFhRAcLIT52LEwdOjfmzffeENkge/YAddfL557eAOlkm6joKBwgaAIdIVzjuVWK703b0YGJjVtytC4ODQAs2YdaOL65RcxZAMhmudun8uTC5+krL6MbwZ8w8CWAw/ZZk2NmFk0a5ZYuX7lFbFC3bbt8e1TbW0tb7/9NnPnzmXr1q0A9O7dm1GjRhEfH09ycjJNmzY9aWHr89XhdO7Gav0Lr7cCh2M7dXUrcLsLCQ6+hKZNJxMZ2Re9Puqktr//dep8lH5SSsmHJTiznRjTjTSd1BRkMLc0788oP1+o8HiYUFzMhyUlJBkMeGSZPJeL+r2V1h6hobzRqhU9wsLQKakpZwaHQ0ynLCsT3myLRQjyVatEBTwyUgwNiI8X4tztFstWHToc24et0Yj+kr09JgoKCgoXMopAVzinmFJayojsbFoHBjKnZUui9XpRaRs0SCQr9O8vwsj3RpptKd/Coz8/yuK8xVzX5DoWDFpAk4gm+7eXlycaPt9+W2zmKDOLjsiyZcuYPHky27dvZ926dRgMBvr27cuIESPo3LkzmZmZJ/z+JMmHzbYSWZbR62Oor19Hbe0SSkomAX5UKh1qtZnAwDaEh/ciMXEEAQENI0gc2Q42Xb0Jd5GbqAFRtPimBUHtzg9bR7bDwTaHgxi9ngqPB5cksb6+nullZRS63fSLjEQGonU6bomO5tLgYJqbzcogn1PBYoH8fNE0KUlQUSFsJ8XFYrply5bic7h5s7Cm5OWJx69fD0VFYhsajVjhiogQ/SJRUWLqZdj507ugoKCgsA9Jlpi5ZSZGrZF+zfqd1tVmRaArnBM4/X4e2b2bKRYLd8XG8lZ6OmE6nQgeHzYM5swRyQw33wxAbk0u0zdPZ/TS0SSHJDP/tvlc2+Ta/dvz+2HMGHjpJTFQ76GH4MknYV/4y9GQJIkpU6bw9ttvs2PHDpo2bUrHjh2566676NOnD/Hx8cfewEG4XAXU1PyK212EWm3E6dxDVdU8PJ7SQx5nMCSTkvIMERHXExDQam9EYsPgq/OR+99cKuZW4CnxYGpsovPOzphSTQ32Gv+EJMvscDhwShJTSkux+f0k6PXE6vX8XF3NDoeDfpGRpJtMhGi1hGm1FLrd/F5bC8A2u51dTie+w9plovYO+/ktLY0005l7PxcUFRUiLjAoSKSdrFolBPfMmWJ0/GGJNsTGCuEOQmz37SviClUqsTSVkiJuu/lmyMwEne6AX1xZwVBQOCexuW3UuGpIDjm2dVKWZWpdtSwrXEZ2dTZ3t7sbu8fOtoptVDoq+U+T/xBkOLtFH7vHjkatYWn+UpJCksiIyKDKWUWkWVjmVhatZMGeBeg1evQaPc2jmtMrvdcxhfbCPQt57JfHKLAWoFVrsbqtADSNaErvpr2pyK44Le9FEegKZ52tdju3btvGbqeTaRkZwhvs98NXX4k0hsJC+OwzuPlmZFnmozUf8cSCJ/DLfu5tfy9vXPUGJt0BgTZ/Pjz9tJh4/eyzIoXxaOEbkiSxZcsWsrKyWLNmDX/99ReFhYXccsstjBkzhj59+pxwRrnLVUhR0TsUF3+ALHtQqfTIsg+zuTmRkTcQG3sHXm81KpWGwMB2p2xb2YenwkP+q/nY1tjQx+iRnBK2dTYkh0T8A/EEtgkkrFcY+sjTP/57SW0tn1osVHi97HY42Ll3omaEVkvzgACWWa2UuN1kBgRwTXg4sysqqPb5cEli1qYG6BoSQpXXy79CQngkIYHrIyKo8HoJ02oJ1GiI0OnOa6/8GaOgQKSi1NWJz1VEhGi+WLsWBgwQFpOD0evFdMpBg0R0aX6+SEoKCxM9IF27QqNGIpLwzz+Fd2zMGCHEFRQUzjg+yUeNs4YIcwRq1fGdr5YXLicrO4vOCZ15+tenya3J5ftbvkeSJdaUrKHYVkxaWBpXp1/NutJ1ZERk8OrSV/lx14/7tzFu2TisLitOnzi+90zryYJBC87YcbnSUUlOTQ7t49qjVWuZt3Met8y+Bb/sx+MXSWTdU7uzOHcxd7S5g0pHJfN3zyfUGIpapcbtc2P32rmj9R20i23H2tK1lNvLeajTQ1zR6AqWFS7j9WWv80f+H3RP7c5trW5DrVLTI7UH5fZyxq8az/sr3yemLua0vD8lxeUc5WJJcfmouJgHd++mqcnErJYtaRUYKCp4N90kmsH+8x8hBFq2xOVz8UTWE0xcM5H7O9zPG1e/cUimudMJjz0GkydD9+4ipeWyy/7+mh6PhyVLlvDuu++yePFiHA4HJpOJ9u3b07ZtWwYNGsQll1xywu/F4yknP/8VSko+Qq0OIClpBImJj6PRBAAyKlXDx6r56n1Y/7BS9XMVZZ+XgRoirovAW+VFpVahDdeSNjoNY8qZEU9b7XaG7dzJ8ro6mpnNNDGZiNbp6BcZSahWS9vAQAK1oi4gy/LfDuQeSaLS68WgVoumYIWTx+GASZNE02V5ucgSNxiE4PZ6xWP69BHZ3Ha7EN+tWyseb4ULnj3Ve/hozUdsLt+MWWdmat+pWOotLNyzEI1aw+vLXqdfs37c1uo20sLSCNIHYdCeO3a5AmsB09ZPY1HuIqqd1VhdVoptxQD0yejDDc1uYGHOQnySj9TQVP6V/C82WDYwe/tsTFoTxbZiCqwFmLQmnD4nUeYomkU2Y2nB0mO+rlat5dl/PcsNzW/A4/cwatEo2sS0oU9GH6ocVdw0+yaua3Id0/pOQ5IlVhSt4PNNn5Ndnc1tmbcxoMUA0sPTcXqd5Fvz0aq1NA5vfFL/BnO3z+WmWTfhl/30TOtJ6+jWTFwzkX8l/4sOcR1oGtGU3Jpcxi4by7WNr2V1yWq0ai1D2w3lqcue2l/Um7x2Mg///DAqVLj9B4oVapUaSZboENeBm1vezKNdHj3i34Bf8rNxw8bTotcUgX6OcqEL9Fqvl7EFBYwrLOThhATeTE/HoFKJYR9PPSUaQSdPhs6dAfhp10888vMjFNYVMuHaCdzX8b792/J6hc/8lVeEDvngAxECcfhF/Pbt23n33XeZNWsWNTU1REVFMWrUKNq0acO///1vDCfoV/b56nC7i5AkJ15vJTk5T+N05pCUNJLExOFotadnEqDsl6ldWkv+q/lYl1iRvTKGZAPRt0STPCoZXcSZFbZ2v5+fq6pYUVfHFIuFeL2e51JSGBgVpYyzP1N4vWIq5aZN4quqChYvFrGD11wjPldRe1dqKiqEZzwgQAh05f9I4SJhW8U2PlrzEZPWTsKkNdEsshnrLetpHN6YnJocXD4XAK2iW2Gpt1DhENaFKHMUY3qM4fbWt2PUnr2Voq3lW1Gr1PT9ui+7q3dzSeIlhBhCSAhKoFfjXmywbOCD1R9Q566jZVRLYgJjWFG0AofXgUaloXdGb+weO/Weega0GMBjXR5jcd5iUkNTiQ+KZ97OeTQKbUT7uPb4ZT+rildRVl/GlalXklebR1JwEjGBR68Wz989nyHfDcHpc+L2ufFKXuKD4mkX246fdv+EWWfmuibXsbpkNXm1eahQ8ViXx3il+ytHHSC4r5Djl/xMWjuJUQtH0SqmFdsrttMtpRt9mvbhpT9eothWzL3t7+X9a98/5P/I6rISbAje//uRqvtOrxOVSkW5vZyt5Vv5JfsXtGotN2feTKf4Tv+4InC69Joi0M9RLlSB7pYk3igo4K2iItySxDPJyTyXkoKqqkoktMyZI5bW33wTYsSBYNbWWdw8+2Z6pvXk/Wvfp1nkgRjDWbOEnSU3F265RXjOmzQ59DUtFgvjx49n/PjxhISEMGjQIAYOHEizZs0wH0+24l4kyUN9/Xpqan7D6dxFefnXSJJr//0GQwqZmXMICmrY4UT7kGWZmoU15P4vF9tKG+YWZuIfiCf86nBMTUwNvqx4pAp3sdtNttOJJMusqKvj49JSarxerH4/EXsr5N+0bEm4Uv1uWNauFU2Y//73AaENsHIljBghxsY7HOK2yEgxLTM2VoydVyriCuchBdYCrvnyGnQaHZcmXsrbvd4+xMp4OPukzNGOg59t+Iyh84YSbgrn4c4P8+SlT2LWmcnKzuKN5W/QNrYtL1z+AhssG2gb2xaD1sD60vXkW/OZu30uM7fOJMwYxq2ZtzKk7RA6xjfMVGiAKkcVJp0Js+7o56NNZZvo8HEHfJLoC9nx0A4yIjP+9rh9dpdIcyQqlYoKewUun4uE4ITjtr+cCqW2UiasmkCoMZTOCZ1pFdOKcFM4Nc4a3v7rbSavm0xqWCqPdn6UzeWbeX/l+zSPas71Ta5ne+V2YgNjGdBiAK1jWvPW8rcYvXQ0mdGZFFgLqHHV0Cu9F+X2chKDE/m8/+eEGkORZZkKRwXRAcc5wKSBUQT6RcaFKNDX2mwM2bGDnQ4H98fH83RyMvE6nWj+HDFCNKRNmiTSHhAJLeOWjePLTV9yc8ubmXHjDNQqNT4ffPSRCHVZulQUAV99VQz5O5jVq1czatQoli5ditls5o477mDMmDEEBwcfYe/+jt/vwmpdisdjob5+PRbLp/h8NQAYDInExz9AaOgVqNUmtNpgjMZUVA18AJT9MnWr6qiYXYF1qRXbahtBnYJo9GIjwnqGodY37OuVeTyM3LOHdTYbOS4XOpVqv9+71OOhcp81AuETvysujiSDgVuio2l6Ahc7CsfA7RaxhCtXis+GwyF85PsO1f37iybMTz4R42/bthUXtc2bQ/v2QsArUyoVzlMkWWLcn+OYsHoCJbYSOsV3EuI0vgOTe0/G6rLyw64fWJy3mFGXjsLhdfDtjm/5NfdX4gLjeLTLo7h9brL2ZOHxe3ig4wN8u+Nbpm+ezt1t7+bD6z9ErznxPpwdlTv4bMNnfL7pc0psJUSZo7gq/SriAuNoEt6EPwv/pLiumDeueoMO8cdXpKlz1zFzy0ye+fUZgg3B3NnmTm5sfiOZ0ZnYvXYC9YGsL11P1p4svtj0BU6vk4c6PUSkOZLBbQef8Hs4F1lXuo5/Tf0XTp+TRqGNyKvNA0Cj0uCX/dzY/EY2lW2iS2IXHuj4AF0Tu55zvUeKQL/IuJAEer3Px6v5+bxZWEirwEA+a9aM1oGBYll+8GDRDNqnj1DdcXHk1ORw34/3sShnEfFB8bx0xUsMbTcUlUpFYaHoa1u9WswruuceoecP/rzu2rWL119/nU8//ZRWrVrx4IMPMnDgQEJDjy/j22pdRmnpFKqrf8bjEYkVRmMjIiJ6ExV1E0FBHdFoGnaZU/JIeKu9OLY5kNwSHouH+o31lM8ox1vhRR+nJ+SyEGLujCHi+ogGPUCVeTxE6XR8VFLC8OxsDGo1Q2JjSTQY8EoSTkmiyuslSq+niclEC7MZk0aDSa1W0lMOxueD778XyzkAycnw889gMokGCZ9PNFfq9SKYf/FiKCkR3vDMTBFN6PGIq04Qk7P69xfJKE2bQpcu8OOPoiejogISE+G558SHQBHkCucxbp+boroiCqwFzNw6k4/Xfsy97e9lRNcRZERm8GvOrzzw0wPsrt4NQLAhmDp33f7nR5mjSAxOZL1lPSC80t2Su5FvzSenJococxRdk7oya+CskxLnB+OX/CzKWcSinEUszltMUV0RZfYyWse0pspRRaWjkrSwNMJN4TSLbMZlSZdxZ5s7cfvdzNg8gz/y/6DaWc2gVoN466+3WG9ZT/PI5ljdVorqilChIswURrWzmuiAaMrt5QCYtCZ+GfQL/0759ynt/7lIcV0xFY4K2sa2ZU3JGmxuGyuLVxIdEM1dbe865wT54SgC/SLjQhHoK6xWBmzdSpXPx7PJyTydnIxOkkRl8LXXhG92+nQYOBBZlpm6fir//e2/mHVmRncfzYAWA9BpdHi9YtL3mDFi2ODXX8PhfZwej4fRo0czevRoYmNjeeSRRxgxYgS6o9gtJMmHx1OMw7GTurqVOJ27cTi2Y7OtwWTKIDz8KmJjh2IypaPVnlx0lCzLSG4JtV6N7JOxLrdSs6gGjVlDQGYArlwX9m12LJ9akD2HfhQ1IRri7okjsl8kwZcEo9Y2XLW80uNhTEEBq202llqtmNVqHJLEQ/HxPN+oETGHT2i8WJFlYR+ZMUNUsrt0EalCXq/I+87JEekoERFCdOfliT/Q+nrx/NhYYTcxm8VV5KpVwvMdEwOdOkGbNiLOcM8eIbj9frjySmFlad1aZIQejs0mGi2GDPnn3FAFhdOI1+8lpyaHtLA0dJqjHGdliS3lW4gyR/Htjm+pc9cxY/MMLku6jCFth7CmZA1jl42lqK5o/3Om9Z3GkLZDDtmOzW3j1SWvEhckquQ+yUeBtYBIcyQhhhBUKhXrS9dj99rpFN8Jg9ZAUV0RX276kkc6P0KA/ihRXqeI2+fG6rYSHRBNWX0ZE1dPpLCukHxrPnm1eeTU5NAmpg0F1gJqXbX7q+M5NTkALLpjET3SeuD2ual0VPJz9s8szFlI18SuVNgr6JTQiR6pPdCqtce0+CicPRSBfpFxvgv0Gq+XNwsLebeoiLaBgUxv3pxGOp3o5hw7Vgib668XMYodOrC7ajcP/PQAv+b+yi2Zt/B6z9dJCkkCxEDCK64QU76HDoXRow+14dpsNj755BPee+89CgsLef7553n66acxHiH2ze93Ulv7GzU1v1FePmN/hVyrDcdkaoLJlEZERG+io28+abuKLMnULq6lYGwBtb/XIvtltKFa/DY/sk9GF63DV+tD9sioDCqMjYxE3RBF8CXBwkuuFrepDQ3vF/zLauWNwkLmV1XhlWU6BgUxLD6eCo+HNJOJgVFR53y14pSorobvvhOV68GDRfUaYONG0UhZWSnEssEgYgMLCkSaUHi4qFJXVIi4QY0G2rUT4jsxUWwX4O67hfAuKhJ/45dddmh1W5KUpkwz2XV0AAAgAElEQVSFC4JCayG9v+rNxrKNxAXGcUvmLaSEpOz3Ps/aNoudlTuRkdlRueOQ55p1ZjQqDTaPDYDLUy7n1sxb2V29m84Jnbmp5U1n4y2dFrKys3hv5XtkRmfyQMcHSA1LBYS1w6Ax0DK65VneQ4VT5XTpNSUHXaHB+aqsjAd378YjSTyWmMgzyckEbdwopgWtWiU8KXPmQNu21DhreG3BSMavGk98UDxZg7K4Ov1qAFwu8bCnnhKFxTVrhCbah8vlYty4cbzzzjvY7XZuvfVWRo0adcQJn15vFfn5r1JS8hGS5EKvjyMwsAMJCQ9jNDbCbM44ZWHqd/ixfGqh8K1CXDkuAtsFkvZ6GqjAW+7FkGwgqF0QQZ2D8FZ4kX0y+lg9KvXpFcQlbjd/Wq1ss9t5JT+flgEBjE5L4/bo6Itn0qYsQ1aW6CSuqxO2k+efFw2VERGwc6f4HhoKHTtCba0Q05ddBm+9Ja4Q91lToo4jtz4xUXwdjiLOFc5jZFmmsK6Q2dtm88byN9Br9MwcMJMl+UuYuXUmZfVl+GU/ADEBMfRI6wHA05c9jUlnonVMa9LC0tCqtdS561iav5TOCZ2JDoi+YAsDvRr3olfjXn+7vX3c+Vd4UzizKAJdocFwSxKv5efzcn4+t0ZH83Z6OrG1taKBbeZM4bNdunR/OPn60vXcOudWSmwlPHnpkzzb7VnMOjMVFfDCC8KaXlsrZqaMHy+suABbtmzhiSee4I8//sDv9/PYY48xfPhwEg8TRH6/HYvlM2pqFlFV9SOyLJGS8l+io289ZUEuyzK2tTY8Fo+odEuQPzof61IrUQOiaDatGSHdQo76GvrohreQeCWJGeXl7HA4aGY2Y1ar2WS381ZhIU5JQq9SMSw+nglNmqC5QE+GhyDL8Msv8MMPQpzn5ECvXvDppyJicN48Icy3bxddxn37ismXx+J4xLmCwgWI1WXlofkPMX3zdLRqLT1Se/Bpv0+JDYzlppY3Mf7a8fhlP/WeevJq82gV3QqN+ui9EaHGUHpn9D6D70BB4fxCEegKDcLG+npu27aNXU4nLzVqxPOxsahmzBDh5HY7fPwx3HUXHpXE3C1f88HqD/iz4E8yIjJYO2wtTSKaIEli4OGLL4oi5wMPwJ13QrO9qYo+n48JEyYwatQoGjVqxCuvvELfvn1p2rTpIfvi89VRVjadgoKxeDwlBAV1IS3tdaKjB2IwJJzwe5NlGW+Vl8o5ldjW2ahfV4+32osrx3XI43RROtr82oaw7mEn+894wpS43ay22VhZV8f0sjIK3G4S9HqKPWKKmlalYnhiIiOTkog6FyZvyvLfA+pPhaoqMWV2+nRo2RJCQoQnaudOYVcpKYH0dLj2WiHOr7nmgAi//faG2w8FhQuUfePde33Zi+2V23n1yle5rdVt+60a+1CpVGhVWkKNobSNbXuW9lZB4cJBEegKp0Sp280ju3czp7KSZmYz6zt0IHPBAnjkESGOeveGd97Bn9qILzZ9wbO/PktpfSlXNLqC2QNn0yejDzqNjhUr4PHHYcUKYU1/803I2BvxKssykydP5rXXXiM/P5/HH3+cMWPG/G2wkCz7KSn5iNzc5/D5bEREXE/jxr9hMqWf0HvylHmoml9F7e+1VP9cjeSS8Nv8oAFzUzPGFCMBrQKInhRNQMsAJLcEMhiSDA3ayHk0St1uviwr44PiYvL3jmmP0em4JjycJ5OSyAwMpN7no97vR61SEX02Gj7r62HdOuFTKigQ1iaDAebOFX6lVq2EoF63Tvi177xTDKVKThZJJ06nuC8qSty/erUYwBMRIWwpoaFiIubPP4umza5dYfly4Rs3m0WDZWKimETbrduZf/8KCucIywqWsShnEc2jmuP2uemd0ZsQQwhOnxOT9sjzE2RZpqiuiG+2fsO8XfNYkr8ErVrLiqErjjtCUEFB4dRQBLrCSSHLMl+WlfFodjYGlYppGRncbjSie/FF4dnt1w9Gj8bfLIOZW2cyZlI/tpRv4ZbMW/hvt/+SGS184lu2wMiRwonQpo1InrviigOvk5uby5tvvsnEiRO59dZb+f7772nTps0h++JyFWGxfIrFMgWXK4+4uHtp1OiFf6yWuwpcOLOdeMo9OHY48FZ48Vg81Cyowe/wY0o3EXt3LLpIHcZkI8GXBmNMPDtT5Ox+PzscDj4sLuar8nKckkT/yEjeadyYTkFBJBgMh5xoA7VaAo+UAHK6qa4WTcAzZkBx8YHbMzKEML/8clHR3rpViOuUFJFYMmaMiBg8GkajsEaVlYmqeU2NmDbbo4eIGkw/sYswBYULFVmWqXRUEm4KZ/a22Qz+bjBatRa71w4cyJcGyIjIYGCLgRi0BmqcNXy99WvsHjsB+gBKbCWYtCZiA2PpltyNZ7s9q4hzBYUziCLQFU6YYreb+3bu5KfqagbFxPBuYiIR338PTz4pvCljxyKPHMmqktW8/HUf5u+ezzWNr+GT3p/QJbELINLopk8XSYvJySLc5Y47ROCF0+nkk08+YcaMGaxYsYLAwEDee+89Hn300f374PXWYLdvobh4AhUVs1GrjURH30JCwoNHneTpKfNQOa8S6zIr9evqsW+xw94MI120Dn2MHl2EjsQnEkl8JBFdxJmbhumVJDyyjMXjwaRW45QkSt1ufqquZpnVynKrFT+QoNfzdHIyDyckEHYuTOuUZVHt/u034eX++GMoL4eBA+G++0TiSXi4+H4sa8uUKVBaKqri2dnitq5dYfduUQ2PiRFNmgoKJ8i60nXoNXoiTBGYdWZKbCWMXzWe21vdzqVJl55929dRkGUZS72FHZU7yKvNo8pZRaQ5kqYRTSm0FnJD8xvQaXRIssTnGz9n0tpJ/2fvvsOjqNY/gH+3Zftukk1PCKTSAqHXgPSOSBHRH3bAiooKdu8Vy7Wggl5RQS8CCkpHeq+ihA4RQ4D03pPd7Gbr/P54TUKkGEhhkffzPHmU2Z3ZM3Nmzrxz5hQUVBQgUBuIg+kHq7dzV6u78OP4H1Fhr0BBRQF2JO+AXEJvHw+kH8D8o/MhFUuhl+vRv0V/RHlHodJRiY6BHTEofBC8ld436xAwdlvjAJ3VmSAIWJybi+cuXIBSIsH6tm1x5+7d1K43PZ3apnz1FTabT+Glr2ORkJ+AUH0oNty7AaOiR8FiAb78Evj+e2qNoFJRy4Y5c6jPniAI2LhxE9566y2cPHkSw4cPx7Jly3DnnXdCraYxbF0uK9LS3kNm5idwOk3w8AhAVNQX8Pe/D1Lp5TOEWnOtMJ0woWhTEfJ/zIejxAFNrAbarlr4TfKD3z1+kHpKGzwYr3A68WN+Po4ajRADiFAqIRGJcMZkwhGjEQaZDP09PVHicCDHZsPqggLYrzDiqb9Mhji9Hp9HRSFGrUYXrRbKxpyUxmYDPv2U2nCXl1NzkhYtqIbaaqV8Liigsb4zM+kpSxBoEh4ACA+n5ih/6RfwtySSmpFP/uxEDOD6t8P+EQRBgM1pQ7YxG8vOLEOHgA4YETXiqsG0yWZCha0C/hp/JJck4+NDH2N/+n5klmeitLL0iut8efRLBGoCMSxyGHRyHR7p+Aja+7dvzN2qM0EQ8OSmJ/HVsa+u+p0eIT3Qwb8D1iauRV5FHu5seScCNAE4mH4Qerkeo6JHYXq36egW3A0ikQhyqRzeSu9a08NP7Ty1KXaHMXYDOEBndXJprfkD/v741GaD97hxwMGD1M532zZkBmnwnwPvYf7R+RgUPghzBs/BoPBBKCmW4MMPgXnzqIXCkCEUpI8ZQ3GeIAjYuXMX/vWvf+HQoUPo1q0b9u7di96XBGpOZwXy839CRsbHsFjOIyRkBnx974ZG0x5ice2aVUEQYIw3InNeJvJ/zKf24aFy+I73RdjsMHj4N05NrFMQsKukBN/m5GBLcTFMTifaqFQodzqRYbVCLhIhQqlEH70eh8rL8UVWFrxkMnhJpXg1NBRRKhX8ZDKUOhzwkkrhIRajt17fuCOuOJ3U3CQ6Gli5EnjmGZoIp0sXemo6dQrIza2ZeEeppHbgZjMNGfjmm9T8ZNQoCuIlEh5KkF23cms5TuaexNmCs9ibuhfrz61HpaN2J+y40DgMixgGsUgMsUgMvUIPnVwHl+DC89ueR4G5AIGaQOSYcqDx0CAuNA4dAzrCR+WD/i36w+KwAKAxuONC4xCfFY9/7/03Vp1dBY2HBvOPzMeYVmMwud1kfHjoQ7TxaYOhkUPRM6QnArWB2H5xO2RiGXqE9ECOKQcXiy9ib+pebE/ejma6Znih5wvo2awn1ieuh0qmwrDIYQAAm9MGufTqw5m6BBcOph/EmbwzKLeWI8eUg6PZR/Fr5q94f+D7uKvVXfBR+aDcWg6VTIWU0hSY7Wa8susV7Endg7GtxmJy+8noHdr7qr/BGLv18ERFbspdJioyOhz4MCMDH2dkQC+VYkGzZhj96ac0rWdUFPDFFzjXPhiLTy3GvMPzIJfI8Xrf1/Fcj+dQVirGggU0ZKIg0GiLL79Mq1VZt24dXnnlFSQmJqJr1654++23MWTIkFo1ZUbjcZw+PQJ2ez68vAYjImIONJp2l6VVcAnI/ykfqf9KheW8BR5BHmj+enN4DfaCMuLKnaGul1MQkGm1QioSYVtxMUocDuglEuikUizJzcWm4mK0Vqlwr58fJvv7I0xJM79VOp2Qi8Xu8TrdbAZ27gQ++oimpc/KopFN7HYa2WTmTOoQcKnc3JoOmB4eNEa4IPAU86xOCs2FOFd4DlanFZ/8+gmO5RyDTq6DxkODAE0Atl/cDoeL3sKEeYbh/9r9H6IN0VB7qNG7WW/sT9uPdw68g7MFZ+FwOaCUKqsDbgDoGdITQyKGILEwER4SD3w+/HPoFfq/TZfD5YDD5YDT5cScQ3Ow4PgCZBuzAdRuqy0Ty2B32QEAIogg/Nk2zlfli27B3ZBckow/Cv+A1kNbPflOrH8ssoxZKDQXIkgbhPGtx2PesHn4veB3/HD6B6SWpeJ80XkcyzlW/RtKmRJB2iCEe4VjUttJuD/2/gbKAcZYY+GZRG8zNztAFwQBKwoK8Mz58yh3OjEjOBgvHT8O/XPP0eDkb76JCw+Oxuxf38fyhOXQemjxQOwDmN1/Nk4e1uHdd6lZssMBPPss9ePz8QFcLhcOHjyI3bt3Y/fu3Thw4ACGDx+OZ555BkOHDoVIJIIgCCgr24+ioi0oKdkGk+kkNJoOaNt2DZTK2kN7CS4B5b+Vo2BVAQpWF8CaboXhTgNCnguBPk4Psez6a3OdgoA/KipwpqICe0tL4SEWI62yEqdNJmRarXD++T0xAJVEApOTlmglEnwdHY17/PwgdodA/K8sFuD556nBv9VKT0pxcTRx1IULNG38xIkNOwwic2sWuwXJJcnwU/vBV+2LSkcl8ivysf3idhzPOY5cUy66B3eHt9IbZrsZY1uPRXJJMkosJegR0gOB2kDkGHNwJPsICioKYLKZkGXMwoakDbA5bdWBdI4xpzqgjvGLQax/LDQeGhRbilFoLsSYlmPQNbgrKh2V6BPa56rTxucYc5BUlITuId1hd9ohQECOMQdRhiiIb3Dm30s5XA5klGXAX+MPpVSJ+Kx4pJSmoKCiALEBsfBR+WB/2n6oZWrEhcYhRBdS3Q5864Wt2J+2H3e1ugullaVYeHwhwj3D0dq3Nc7kncHcw3NhUBpQZCmCv9ofrXxaoYVnC3QK7IQuQV3QLbgbpGJ+qc3YrYYD9NvMzQzQUy0WPHPhAjYUFWG8jw8+zcpCs3feoeYsd92Fov+8idkp3+HLo1/CX+OP53s8jye7PomUC3J8+imwcCHQuTPNpD52LA22UVRUhKVLl+LLL79EUlISvLy80LdvX9x999247777qmuWy8p+QXr6Bygq2gCZzA/e3kPg7T0Cvr7jq5uyuBwuFK4pRMWZCuSvyIclyQKPAA/4jPOB/33+0Pe+ds2Zw+VCrs2G38rLkWWzwSEIyLZaYRcE2FwubCspQWolvV5vq1JBABCqUKCdWo0QuRwaiQRqiQSDvbzgLZPBKQgwOhxQSSTwuJnNO1wuYMcOaiferRuNkJKfD7z1FjX6Ly2lwPyNNyhjWrbkYPwfThAELDq5CF8c+QJSsRQaDw3CPcPxXI/nkFGegbtX3g2TjZovhXuFI7M8EzanDSKIYFAZEG2Ixum809XfuZSXwgv3t78f35/5HsWWYgCAXCKHVCzF6Jaj4afyg9VphdVphUamQcfAjhAEAffH3g8Pye3X4XfhsYVYcnoJpnScgkkxk67Z7IUxdutorHiNH9dZNavLhXfS0vB+ejp8ZDKsEYkw9pFHqNNf166w/rwWn3j+gffX9QMAvN3/bTzV5RlsWq/E/30MrFtHteRz5lCtuUQCHD16FI8++jp27doFAJgwYQIWLlyIuLg4iP8MZl0uBwoL1yMj41OUl/8ChaIFWrdeBj+/eyC6pFZMcArI/zEfya8lw5pmhdQghb63Hi0XtoS+tx4iyZWDTUEQkFxZiR/y8rAiPx/nLRbY/nwuVf2ZhiC5HB4iEWQiEe7Q6/G/li0RpVQiRPH3wypKRCJ43owRVbKyaOSU8+epU+emTVQTLhJR85MqISHAvfdSg//Ro4GOHZs+razRCYKASkclMsszYXVaq9tYZ5RnoFezXojyjkK5tRwbkjbgmxPfAACGRgzFa31eQ2Z5Jg5nHUaYZxhC9aGIC42Dr5pmTXW6nMgx5UAmlmFf2j609W0LrVyLWTtmYf259RgeORzvDngXwbpgSEQSCBAapDb7n2Zq56ncKZMxVmccoDMAwIHSUkxLSsIFiwWvajSY+ckn0CxbBnTtioqNa7HYNwv/+WU68kx5eKrrU5jR5TWsXuqDlvfQfETdu1OT5qeeAk6fPoqpU+dj7969SElJQbt27fDZZ59h/Pjx8PPzq/5Np9OCjIyPkJ7+IVyuCuj1fRATsw4Gw+hagbnL5kLKGynIW5IHW64NPuN80G59O2hiNVfdnzybDWsKCrCyoABnKyqQZ7dDDODBgAA8HhSEZgoF/GUy9ND/fTtVt2IyAStW0Ogpu3fTMqkUCAuj0U+WLKFhCY8epZp0h4OC8zo8aLCrEwShToFnjjEHxZZi6OQ6BGgCkFqaCq1ciwpbBZrpm11XzXFpZSl2Ju+EVCzFL+m/VI/UMSxyGDQedO7/nv87Zu+fjaSiJGSVZ6HAXFBrG3e3uRtfdfgKI6JGVC8z2UzYk7IHIpEII6JGVO/Tve3uvWI6JGIJQnQhAICJbSdWL/9xwo9X/L4I/FaGMcbqiwP025zJ4cDLycn4IjsbvZRKnPj5Z8R88gkQGIi8Lz7C7GYXseT0/bDYLZjQZgJe7fEuti6LQNcHaU6a++8HnnySBv04dOgQpk1bgKVLlyI8PByjR49Gv379MGLECMjlcrhcVhQWbkRBwU8wGk/AbE4EAISEPAt//8nQamtqdq1ZVpT/Vo7yw+Uo3lIM8zkzgp8Khu89vtB1112xs6XD5cLW4mJ8mpmJvaWlEAEY6OWFaUFB6KbVoqtOB/+mHEs7LY1qtr29qTmJRkMT7OTl0UyYgYE137VYqKOm1UrBtERCwfX580BSEv2dOQOsWkXf7duXOuoOH05NWf5ag3/HHU23n7eQ3Sm7seaPNSizluHZ7s+ic2BniEQiFFQUYP259bA6rCg0F8Jf449ATSDMdjM2nd+ELRe2AABGRI1AubUcerkeySXJKLYUwyW4qqc933pha/Vv+av9kVeRV/1vnVyHuNA4SMVSiEVinM47DaPViLZ+bdE3tC8sDgs0HhrEZ8XjeM5x5FfkV3dSVMvU8FP7YenppWjr2xb3tbsPWy9sxcH0g2ju2RyDwwdjZNRItPBsgWa6ZlBIFdDKtegUePnrVo2HBqNbjm7Mw8wYY6yeuA26m2qKNug7i4sx5dw5FNjteD8tDU9Nnw6xRILcmU/itRYXsThpBQwqAx7v/DjGh03F2sUh+PxzGh774YdpRJbKyj/w9ddfY9euXUhISEBYWBimT5+O6dOnQyqVwuk0Iz//J5SUbEdR0SY4nUaoVG3h6XkHNJr28PTsD5WKxrquGh4x+6ts5H6XCwCQN5ND11OHkGdDoO91eW13vs2GjUVF2FpcjB0lJSh1ONBbp8NDAQEY6+sLQ1M2PREE4ORJms5+1y7g119rPpPJao8XrlTWBNFmM3DgQE2zFI2GgnSXi56CqpZFRQF33kmN+8Nqd5Z1dxW2CqhkKhzJPgKlVIm2fm2brBlEha0Cx3KO4ceEH/Hl0S8R4UWzjl4suQiNhwbRhmicyj1VHQzr5XqUWcuq12/n1w6DwgfBaDXiWM4x+Kp9UW4tR7hXOFRSFTQeGqSUpsBoM2JC6wlo598OB9IO4HT+aQwKGwQ/tR8UUgV+y/wNu1N3w+60QyFVIMo7CsG6YOxL24fTeaehlCpRUlmCToGd0MG/A1r7tsbg8MHQeGiglWvhIfHAb5m/YfqW6TiecxzhXuF4seeLeLTTo7dlm27GGHMH3En0NtOYAXqZw4EXL17ENzk56G+345s330R4fDxKHrwHL/YxY1H6zwjWBePFHi8hIOdRrPhBic2bqWnzo48CM2bYcezYOsyfT81Y/Pz8MGbMGAwbNgxjx46FxXIB+fnLYTKdRnn5r7DZcqDRdIKPz53w9R0PtbptdVoEQYDlggXFW4qRuygXppMmyHxlCH0pFH73+UEeWLsjlVMQsK24GP/LyUGa1YqEigpYXS5002oxzNsbw7y90V135Rr26+JyUQfL48dpFkuFgoLvwkL6MxiAY8foey1aUC32li3UEN/LCxgwALjrLuqsmZ5O39VqaVteXtRePC2t5ve6dgV8fWkIw5QUOthmMzB4MNCqFY2wcgt06HS6nNh8fjNW/bEK2y9uh9ZDCwA4X3weKpkKZrsZAHUw7B3aG1nlWSitLMX0btMxLHIYog3RkIgvH7qxajg8hbR2U50SSwlWnl2JDUkb0D24OyK9I+FwOZBjzIHD5cD6c+txNPsonIITapkab/V7C8/3fB5OwYkdF3fgSPYRHMk+ghGRI3B327sBAAalASabCbmmXHgqPKvbYrsLu9OOZWeWYUyrMfBUeN7s5DDG2G2NA/TbTGNl+JaiIkxLSkKZzYaPNm7E1I8/RuWAPvjPaC+8V7YBIboQPBXzOowHH8T/FnogO5tGZLn7bmD48GysWvUVFi5ciNzcXPTp0wdPPvkkxo0bB5lMiuLircjPX4H8/GWQSNTQaDpCrW6PoKDHoFa3rk6Dy+aC5aIF5kQzsr/KRsn2EoikIhhGGRA4JRDew7wv6/B5wWzGxqIiLM3Lw3GTCe3VarTXaNBercbDAQHwqUvTlcJCqtXOywOKioCLFykI1unov2o1jfN95AiNWON0Xr4NiYRqusVi6mypVAKpqTSrplpNPWQfeOCWbvN9MP0gssqzIBaJEe4VjtiA2CsO/yYIAkorSyGXyvFb5m/INmbju5PfYVfKLoToQnBvzL0QBAEmmwmdAjuh0FyINr5toJVrcSDtAA5mHISPygciiLA8YTkAQCFVoL1/e6hlapwvPo/m+uawu+w01bm5CB0COsCgMiBAEwCj1YjfMn9DjikHYZ5hyCzPrB6rWiwSQ+uhRe/Q3hjTcgy6B3dHW7+2PIwdY4yxBsWjuLB6MToceP7PWvMh5eVYOGMGAm2V+OT1AXhZuhc+dh88Gz0PF1dOxSsvyKFU0sRCQ4emIi1tHbZu3YrXXtsJpVKJBx54AE888QQiI3UoKFiFs2eHobz8MFwuM1SqVmjRYjZCQp6FREKT9NgKbCjaV4SSXSUo3lwMywULBAc9FyojlWi9vDW8B3tDZqhpjuL6c+jDJIsFv5SVYXZaGiQA+np6Yl+HDuij11+7ltzlAk6coKYmGRk02kl8PM2SKRJRAK1QADExQFkZBdpmM7XvDgsD5s4F/PyoZruoiNqGR0bSMqeTmqpcGoTb7RS032IT99iddhzLOYb2/u1xKOMQXtn1Co5mH73se1VBs8lmgt1lR4AmAA6XAwfTD9b6nl6ux+b7NmN41PBr/u6AsAG1/v358M9xKu8UTuWewpHsI6iwV+DemHsRnxWPSO9I9AzpiXCvcBzNPgqTzYTzReeh8dDgrlZ34Znuz6CVTyuUVVKzFJvTBoPKABFE7jExFGOMMXaduAbdTTXkE9nekhI8fO4cCi0WfPLdd3h02TKcGNoOwzokwMPLF0PUL+GPH6bi8EElWrYEHnnECIViNX744UvEx8dDLpfjjjvuwJgxY3DPPSNhtW5HXt4PKCvbB7FYAb0+Dl5eQ6HX94Ze3xPWLCuKNhXBmmGF6bQJRT8XAQA8gjxgGGmAtrMWqlYqqFqpIPOTVQdRgiDglMmEnwoK8N+srOoJgOQiEaYGBeGD8HCorhUAu1w0Q+a331JgXlREtdrNm1MnzVatgKlTgWbNKJi+DWfCNNvN2JOyBwfSD2DBsQWwu+ww2UxQSBWodFSib/O+mNJxCka3HA2Hy4FTuadwvvg84rPiUemohIfEA3KJHGllabA4LHgw9kGY7Wb0bd4XPiofqGQqbnbBGGPstsE16Oy6WZxOvJqSgrmZmeibmYndM2dCaKZF9xlqnNImoI/4Jfwx71V8l6FEnz4uzJx5AMePv42XXtoBsViMYcOGYeXKFejXLxoOx2kUFq5HQsIMCIIDXl6D0KrVYvj4jIXYqUZlRiVKV5Yic+fvKFxbCMEhwCPQA4pQBaK+iIL3UG8owhWX1WhWOJ3YXlyMw+XlWFdYiHMWCxRiMaYFBmKwlxeiVSq0UCgunwCorIyGHDx9moLxY8eovXh5OU1T/8QT1H67Rw9q132bSMhPQLGlGD1DelbPxngy9yTO5J2B1WnFm3veRI4pB35qPwwMH4jWPq3RPbh79TTlUzpNqfwWL5gAACAASURBVNUGfGD4QAwMH4jHuzx+s3aJMcYYu+1wgP4PJAgC1hYWYubFi8gym/Hxd99h2tYNeGG4GIsiUtBN+jgMy57B/nNRGDOmBMo7/ostWz7AgQNFiIuLw4IFn6NnTzWk0v0oLHwCCQlUA67RdEB4+H/g6zsJjiQdihYV4cy2CzAeNcJV4QLEgK6bDi3eaoHgp4Ih1UprpSnTasUvZWXIttmQ9+ff1uJi5Nnt8JHJMNpgwCeRkRjs5QXZlWbkrKwEtm0DvvySgvKqEVFCQ6kpyssv0/CDvXrdEh0q68PutGPz+c3IKM9AQUUB8irycCjjEM7knwFAQ/rF+MXA4XIgPiu+er07mt+B3Q/uRktDy1oPSyOjRzb5PjDGGGPsyjhA/4fJqKzE0+fP4+eiIow4cwabPvoIF/xK0fxhI/xkkyD9+l0cLQpDbGwKAttNxOrVK+Hj44P775+AO+80wNNzP8rKnkFhoQCVqjWCgqZBr7sD0vy2qDwhQ9m3ZTixKQ3WDCskGgm8BnmhxRstoO2ihbKlEooQBQpsNmwsK4Gpwoksmw2rCwpw0WJB8Z8BtVoshr+HB/w9PDDW1xczQkIQqVRCfKWg2maj9uMzZtBQhA4HBeCffkrjiIeFAY00DCVAo5JcaVSRKxEEAWlladiTsgcnc09i28VtyCjPQLhXOPqG9kWAJgAWhwUWuwUtfVrisc6PVQfJBRUF0Cv0Vx0ur6CiACabCTuSd2Bd4rrqcbllYhl81b7wVfmivX97vDPgHQRrg7H5/Gaczj+NYksxfprwE0ZFj4LD5YDWQ8vtshljjDE3xwH6P4RTEDA/KwuvXrgArdGIVXPmICj3GCaNqEChbiTKlr0FW2kHtIrajqSygYiPT8XAgX3x5ZcPoWPHJFgsCyASSSGRDEZE0JeQZnSEeY0BZb+UI+ukCU7TBQDUqdNnrA8Mowzw7OsJk8SFRLMZx6xWnKnIRfzpcuwsKYH1z64NUpEIow0GjPHxQYxajV46HXyv1uREEKhj57ZtNCNmTg41ZQEoEJ83j6Ys7dSpTjXkVocVZwvOwmgzIs+Uh/iseOxP349CcyHkEjnMdjNEIhGa6ZpBJpEhVB+KZrpmSC5JxvGc46h0VCK1NBUR3hEI1AQirSwNNqcNDpcD0YZopJSkQClTomNAR3QM6Ijjucex5o81EEGEcK9w9GvRDxFeETiTfwar/1hNx0+mhEKqwNzDc/Hs1mfhqfCEUqpEWlkaRBBBKpYiwjsCzXTNoFfocbbgLLKN2SitLAUASEQSdA/pjg8HfYjBEYMR6x97xYC7c1Dn6z2FGGOMMeYmOED/B8i32XD3iRM4YDbjsZ9/xuPrFuO1niU41GEQSta8DYOlLUI0/0OaqT/y89WYMiUWgwb5QKM5AJHoVygkg+Btmgdhfy+UbXHhYkIFADNkfnZ49vNE89HNqWNnRzWS5XZsLSnB9pIsnD95HuctFrj+TIdOIkEvvR6zw8Jwn58ffGQyyMXia9fYHj9OY4cnJQF799IQiGIxMHEi8MgjNGpKUBAQF0cjrVyD0WrE0eyjWJu4FoezDuNEzonqYfcAGsJvQpsJ6Ne8H4osRTDbzWima4ZMYyYsdgt+z/8dOy7ugEFlwMCwgZBJZIj0jsSF4gvIr8hH9+Du8JB4oMBcgJLKEgwMGwij1YiTeSfx0aGPIBKJ8OnQTzG5/WT4qHyumdb9aftxJu8MSitLUVpZimhDNMQiMcx2M47lHEOZtQzpZeno36I/QnQhiPCKgNpDjc6BneGv8a/bicEYY7cwl4tuBw1NEGiS5/R0mtKi81/qM8rKAP3l8+Ix1qQ4QK8jq9WKN998E0uXLkVpaSnat2+Pd955B4MGDfrbdUtLSzFr1iysXbsWFosF3bp1w8cff4yOHTv+7brXUu5w4IOUFMzLyIC8woQN7/wbm31OoO+Qvijf+g58zMGQG99CkXUZ2rQJx9NPB6Njx0RIpUXQCv0hPvwfWL7vhJIEGUoAyJvb4NXfC14vBqGgjRQpIQJ2WSuRXmlGhrUE8WeNKHU4IBOJ0EevxwiDAW1UKrTXaBCuUEAnlVJnTqORasJlMmo3vmcPjUGemgr8/jsNZ2i1UvMVkwnw9safw8cAgwZRMH6VWnZBEPBH4R/Ym7q3ekKa+Ox4JBYmItuYDQBorm+OPs37YHK7yegc1BleCi/4qf2gV+gbbRzsqsGQ6tp8pG/zvujbvG+jpIUxxm51Z85QlyIvL2DIEBr5tr7TS1RWArt3A++9B/zyS83ylSuBCxdoEDB/f2D5cmD0aODpp2muOa22cR4UGLsWDtDr6KGHHsLq1asxY8YMREVFYdGiRRgxYgT27NmD3r17X3U9l8uFkSNH4vTp05g1axYMBgPmz5+Pfv364dixY4iMjLzutAiCgLUFBZh+5gxKHA48s3o12h77CY+0i0L+/p1Q73MCFa9AEXIWEyaocMcdDgQGpEBZ2hfYeB/MizuivEQDeXM5MEyP4qdlOBMj4JDGguOmIhTac4EKAOcAX5kMzRUKBHp4YEZICHrpdOih00FjtVKt9x9/AOfP0+gpOTn0/7/9RuOJV9HrgeBgGt5wzBj6t1xOQXhYGDBqFCC9+qnoElxYfHIxjmQfwaGMQziVdwoSEbUL1yv0GBA2AA93eBgtDS3RyqcVOgd1brJp5Ktwu27GGKu/0lKa623TJqpB79QJ+O47qt/59lu6fZw8SS9fH3uMbiWFhUBCAgXzsbFX3u7Bg8A99wDZ2TSmwPLlNLXFzJk0EZ9YDPTpA6xaBYwdCyQm0oMBAEREAN98A/Tr10QHgTHwOOh1Eh8fjx49emDOnDl4/vnnAVCNekxMDPz8/PDLpY/if7FixQpMmjQJq1atwrhx4wAAhYWFiI6OxvDhw/HDDz9ccb2rjauZXlmJp+IPY6NLwKhDhzDu58/waXMdzlx8HjjugtzjcwwYkIkhQ0yIjVFBkdYHjq3d4dzSFSKnFrY4NVJ7yHAi0oklzY2oAGV/sIcHOmm16KRWo63LhUiHAxE5OdBlZ9dMb19YCGRlUS14Sgq9JwSo6YmnJ5Wc7dvTDJtDh1I7cYcDaNeOStG/YXfacSL3BH7L/A3rz62H2W6GzWlDobkQGWUZaOffDtGGaDzQ/gEMCBsAmUQGmVjGwXEDKy+nbPP0vLFao8JCYN8+ek5r1oxeIScn080wIQHw8QHuvJNueoyxW5PLBXzwAbB9OzB8ODBlCr0MvZTTSd87fhyIiqJ+/gCwYwcwYAAFwi4XBd6HDgG5uVRWFBVRLffEiRR0b9gATJsGFBfTNqsmeQ4NpaksUlJqfrNHD6BNG5oQWioF3ngD2L8f+Owzejk7dy7QoUNNN6bKSmDrViqfYmLo33I53d4SEoBTp4AFCyjA79uXxisYPfrmTqEhCFROHztGx8/Xl0YcDgigblo6Xd2243TSfuzZQ01+HnusbgOgOZ10nNTq+u3HP0VjjYPOAXodzJo1C3PnzkVxcTE0Gk318vfffx+vvvoqMjIyEBwcfMV1J06ciIMHDyI7O7vW8scffxzff/89SkpKIJPJLlvvrxnucLkw78wZvJmXC8+ycryw5HNsspixO2UGkJwIb+81ePjhsxjU3QDVyTi4dvaEcLojjC01SOokwb4YO3a0ccCqAPxlMkQDGJmbiz4XL6LNhQvwTE2lkjE9nWbFvJRCQSWAjw+9/2vblkqy1q2phPTzq1VaVToqkVmeCV+VL5QyJU7knIDVaYXJZkKxpRh5pjxoPDTwU/vhQvEF7ErZhQJzARLyE2Bz2gAAg8IHIVQXCg+JB9QeaoxpOQZ9mve5sQz8U0kJVfg7HFSQVVXke96m8+rk59Oz1ZEjVKgnJwNz5gBr1lDLI4CyecAAqjkKDaWXHmo1nQZyOb0wCQmh42qzAWvX0g3Q5aLvlJVRQa7VUssnpZIKd5uNbqJ2O/29/jrVbl1yeTU4kwl4/30aodPlohv3sGF0E3c6qVZOq6UWWG3aUAstkYiChUOHAJWKjsWt9jzocNDN18eHAqhLixunk2osPT1rBxwuF+230QiEhzdNOp1OOhcOH6aAweWic2fzZqB3bwrYDIa6bSsri85JQaDgzGCgACwoiLa5ZAnNWfbXtsfs7wkCXQ/vvkuBbf/+FLwKAp0rYWF0S9i2DSgooAC7qOjK2woJoXLIZqPrShCojIiPp7LnUllZNL2Ftzf9t6iIfkMiobImMBCYP5/Ks5gYoEsXqiQ4e5ZuYS1b0rlQ1+D1Uk4nlW2ffkr7HhEB/N//Uc17VBSVhU4ntdxUqa5/+3UlCHScnnkG+PzzK38nOhoYP56aCCmVVD82fjyQlkbHy9+froEdO+j49O9PD052Oz18BAdTeWE00nGcPJma/3TvDixcSG8Yzp+n++knn9CDQmIirT9rVqMOqua2OEC/iQYPHoycnBwkJCTUWr5r1y4MHjwYGzZswMiRVx5HOioqCi1btsTGjRtrLf/2228xdepUnDlzBm3btr1svUsz3BEQgAd//QXnvAx4eNM6WE/uw/ILk6Er345Ro3bhjvYGhJW1g+jnCcgUt0V8DBDfXkBCDKBWuBBrNKJDbi56nD6NHnv3IuTsWfoRkYiqOIOC6C88HI7QEJh9PQGtFpUBPij31UOu94bGQ4PSylKcKzqHC8UXUGguRImlBMWVxSixlEAulaPSUYlCcyF+z/8dFfaKqx5PtUwNi8MCl+CCh8QDA8IGIEgThNiAWHQL7ob2/u2hkl1/KWe3U43Hjh1UwCQl0WtRiYQ+KyykG8FfNW9ON/CYGHoBYDRSgaRU0k2ga1cK2MrLaZlWS69C8/NpPa22ZltWK9VkpKfTjaK4mGprhg1rmkCnvJz20ecqfVR37gR+/pluWrt21SzXaKhVUvPmVDvUsycVwLt2Ue1XcnLt7Wi1dKPLyrr8N95+Gxg3jp7fBIGOgcFAx8vLi9K3fTu9wpbLafnq1RQod+lCQXCzZrQ8NpZ+q7SU8qJLF8qnqiCztJS2s28fzUvVvTsFm0Yj/XffPuoOkZhYU0M3diyQmUmfqdXUxvT06cuDiNBQyu9z52qWBQXR+RQWRueTy0Xb6NiRjvn69bR/ISH0evz33+nc8fenZT173ljns6oh/6/REuwyFgu1rZ0/n4JegNLarh09ENntwMMP0zE0GOgcLSurqZmr+PMSjoigIEQsrvm+00n7FxZG+5udTWmUSOiz3bvp2EVGUnCUk0PnkUoFLF1KN/iwMDombdvSeZmcTPkG0DHS6SiNrVpRLaZEQmnUaCgfIiJofT8/4IUX6DcGDqQHrf37r3yt/1XXrsCDD9I2Ro5s3ODqVmc2A7NnU5Bqs9G1vHw5vSzNywN++omuleRkyq8uXeh6LC2l/5pMFCSrVHQ9HD4MLFtG58ioUXRtJCZS3gcG3ngaBaGmZjc7G/j+e+DJJxvu4T8+niohtmyhfZNK6fo/d46uma+/pu5U1/Mg/+OPdE73vUa3pMJCOkYXaEA1TJ5MD5lOJ6WhXTu6bt96i+6DMTFUobJ/f02dm78/5RVA193//R89rHbqRIH9v/9NZbK3N11PV9KlC11n587R+A5iMV2HFRV0zR4/fvtVenGAfhPFxMQgMDAQO3bsqLX87NmziImJwddff42pU6decV2NRoN7770XCxcurLV88+bNGDVqFLZt24bBgwdftl5Vhvd/7VXsHTAQ7S9eQNcN3+OnhE5oF7gHE9vZEF0wAheNnZHgHYSMZkBGbBFa5yQjNiEBHc6dQ+zFiwgqLIRLrYI52BeFzXyQHaxDhp8C2VoBx5pJkS2mWu1iCwXa1wqsq1SNve2t9Ia30hteCi+Y7WZIxBKEaEMQ4R2BLkFdUGwpRqG5EB0DOsJbSUG+t9IbSpkSDpcDJZYSKKQKaOXav/1Nq5UCtnPnqEbt5Em68TscFIgXF9fc3DUauqlHRVFQ7HRSQaVSUVChUlHtWkEBBREJCRS4JSTQDUIqpcLNYqGCJj6+pkb5ryQSusn37083g8WLaz4LCqKbzR9/UCGmUlHhJ5dTzd1bb1GQotdTYejnV7cArKyMaj5+/ZX22eGgG2ZiItVkuVwUrA4cSDfR1avppqnRUOEZEUGFeWws3QhbtqQaFKmUalCu1BHr4kUq2C0WugkePUoB7ciRFOxWtfvUaikwv17nztEgPnv3UrBWXEzHpaTk8u8qFPR7EgkFelX5eGm3h0t5eVGaWrUCpk+nByZBoGO4fTvV1sbFAXfcQcGptzedX0lJ9CDQpQvlcXIypU8sBjIy6Ht2Ox37EycoD4cMoZvgzz9T2po1o3QVFlJaZDI6LwwGengEKHgZO5Y+CwmhY5GSQvt16BC9vEpKou3cdx/w3HN0c63Kl3nz6LdNJjpeFgttKy+P8qZ1a+D55+k4XLhANWBHj9L6Q4dS04Tjx+lY+PjQedKxI/2utzcF20ePUp5cvFgTeOh01Inuxx9peV0NH04PglXnbGoqPZSFhtI1PnEiBSqXtoo7dw748EOqsc3OpgCs4pKiymCgY3fqFK33xhv0EO100vEODaU8Mxopz9q0oXLk9ddr0t6mDfDOO8Bdd9E+d+16Y7Wt7uabb+hBu1cvytuxY68vgHI6qXycNImC6smT6RgNGnR7P9CYzRT8xsfT9dO1K5W/W7fS9RceTg//Q4cC995L5cb58xRECwI9lGzdSm8iTp2ibfbtS8H9pElUZgQH03l76BCwaBGVjTExdD6vX1+3h4ALF6gs0OupLLBa6d8BAZcPjJadTWV4VaXT/v10fcbEUI28ry9dv1VvO/btA1q0oL+kJCrLDAZ6C6vX03HZtIl+74kn6J5Uh9au9ZKZSeXD2bNUJjRvXvtzQaAyoCEnGOcA/SaKiIhA69atL6sFT05ORmRkJObOnYtnnnnmiutKpVI8/vjj+O9//1tr+e7duzFo0CCsW7cOd95552XrVWW44rPPcOcfx3H6FxPuCMpCm6DeOOXREyWeJfC1nkX7lGREZKXD21iEQo8CJOucOK+1IVUvIE0PpHkCpQoAf17IBqUBXgpveCm84anwgrfCG15Kb3jKvaqX6RU6SKUuKKQKqGQqVDoqUWGvgNZDi5Y+LdFM1+yak/fc6AXgctFFlZxMwYJUSjcAu51erVUNiR4aSgFuWRkFa+3bU6FgMNDFeI1BYG6Iy0UFjFZLv3nxIgVQAQH03z176IZuNlOAO2oUBcE+PlSQGY1Uu1ReToWj2Qx88UVN8FkVXMrltM1OnSgAjYigG2NVMxCzmW4AR4/SdnQ6Cj6kUvpr1oxqGCUSqpk6epTW6dWLCs7CQgqEHnzQvZtpOJ300CGT0VsILy9Kb3AwBcLx8RRAi0R0jO+/nx44jh6lfczPr8n/du3o5tLU++t00gOMnx/9226nG91PP9FN0G6nz9RqenVeFTBXCQykvO3Uib5b9XC3ZAlte8AAOg9Pn6bzvn17+lyvpz+zmfb51VfpAexSVW2CTSYKCOraz8DlotfkwcF0vk6ZQud9bCzVYKvVtNxopAcVQaA3Sbm5lJeRkZQ3nTvfeH4YjbTNsDD6/6qH9v796Tg4HHSN1rUpTGEh5ZPZTNfFmTNUvqSn0+ejRgEjRtDx/e03OheHD6ffKSig43/kCB3jadPqP8rIpQoKKLjJz6d9cjqpfOvdm2pu+/SpOY4lJfTAYTbT56tW0TW/ahUF6DExdJzsdirHDAY6p/r1Ax5/nAIZl4sCLkGg3zl3jppE/PorBXliMZU/PXs23D7+0zgclGdnztC5ceIEHbvBg6n8r3qTBdD1nZ1NQetjj9GxXbq0dqWEnx/lf5WlS+kByV0lJ9Pb06oHDqCmZezvv9MDwnvvUWXY4cNUAfDxx1d/43stRiP1K8jKogqIyEi6rz79NJ2rLhfdBx55hOKJN9+kcmjePLqHeHnR/bZr179PQ14evYksLqY8WbmS1v/Pf+h6OHGCA/Sbpj416FqtFpMmTbrhGvRu3QZgQEQYHCI1bM4zEJdmw2QxI9NDj3QPAzIkfjDKRRBJXBAKWgKVesCqB6y6P/9fB5FND1R6QjD6A67L27tfiUpFQZ+HB9W2VPUBraykm0NODgWCYjEFBl5eVPDb7XQTz8ujp+qQELpoFQraXlW70pAQuljLy+li8fSkG3lVYRQaWtMeuOp1+vjxdKHHxrrfkFdVV1FdA4+yspraw/R0CsiKi6nA3rGDjmFRER0DubwmLzp3pqCqf396JXmtoeErKmgboaH13j3WyOx2eujKyKAHs6r2739VWkqv65cvp6Br+nR6QPmbKQJYHW3ZQkFp1du5tWvpWqzqTCcIVIZVEYnohl1QQAHXxInUodFgoA6UDgcFEp06UZl3rfLBaqVyzWajMnPSJKqwqKrtLi2t/f377qM3WPv2AStWXP45QOXlK68Azz5L51hyMr1RMxqpbPj555omD1fSti3VmiqVVPlwhVsV+xs//US15C1a0LUaF0f3uQ8/pPNh/vzab2p++43Ou2bNKPhs1aqmr8Rf2+W7I7OZHiQUCgqaW7akc3j3bnpjdeQIfa9jR3q7rFLRMarDiNVITKSgvE8fOo83baK3Qi4X/VZ8PD1oR0TQefvbb/RWu0WLmjeWzZoBL75I6czNpSZQPj41TR1FIuC11+hBPDubOgh/911Nsy6zmSp+UlLoLzoaUKmO4+RJDtBvisGDByM7Oxu///57reV1aYMeHR2NqKgobNq0qdbyurZBj4ntAZ3GABEoIhUEYMCAe9G//71wuejGkZ9PT90+PnSiXulPEGoCvb/eJP76b4eDCu+qznylpfRXVlYzYIuvb813rVaqiTKZ6HM/P6rhunCBavkiImoGdJFIKPhITaXXfSIRFVg2GwWjgwfTjSwiwv2C8KYkCHRMq44zY1WqOj726NH4r4sZPTinp9cE2Js3U5napg2Vcz4+VNv8739TcN+/P5V7l9YiAlRbvX07ffbzzzX9Ki5coEA8N7f29/396e1c69ZUdprN9IYiIYHKzpkzqcytGqn2lVfoQWH3bgoaZDKqnb1WOWq10m9UVNTsk1pN95TwcHrQcOe3bezWIgj0psDHh87r3FwKqA8epLdUOTlUoTRtGr0N/v576ojasyedowcO0DnvclEs8eOP1ATxvfeo+eELL9C6l56zJ07QeV01QESXLrXTdOYMVXSYzdRMp+pNvU5HFYh6PT0Q/Pe/9GZp+fLlWL58OZxOCuBzcwGXqwz5+fs5QL8ZZs2ahU8//RTFxcXQXtIj8L333sPrr7/+t6O4HDhwANnZ2bWGA5w2bRqWL1+O4uLiOo3iwhhj7NZgt1PNtp8f1brt20cdbEUi+kyjoSBFr6cAOzKSaqsdDqp59PamV+/XekB3OCjI9/a+vSsz2K2tooKmR/n9d3qIXbeO3rJXNVOJi6N2+xER1Hzm6acp2Pb0pKC+IZlM9GC9YgVVUPbvTzXpf9fXorHiNZ6oqA4mTJiAOXPmYMGCBXjhhRcA0DjoixYtQo8ePaqD89zcXJSWliIyMhLSP3v7TZgwAatWrcKaNWswfvx4ADQO+sqVKzF69OgrBueMMcZuXTJZ7Vf2kydTQPHtt8CECdRcr77t1aXSG2u7y5g7Uaup82uVzEyqud64kd6qP/44PYhqtTWDKDTWm2WNhvpwXGPuySbFAXoddOvWDXfffTdeeeUV5OfnIyIiAosXL0Z6ejoWLVpU/b2XX34ZS5YsQWpqKkL/bPg7YcIE9OjRAw8//DDOnj1bPZOoIAh46623btYuMcYYa0KjRtEfY+zqQkLov23a1Czz8ro5abnZOECvoyVLluCNN97A0qVLUVJSgtjYWGzcuBFxcXHV3xGJRJfNaikWi7F582bMnDkTn332GSwWC7p164YlS5YgKiqqqXeDMcYYY4y5OW6D7qa4DTpjjDHGmHtrrHiNu5YwxhhjjDHmRjhAZ4wxxhhjzI1wgM4YY4wxxpgb4QCdMcYYY4wxN8IBOmOMMcYYY26EA3TGGGOMMcbcCAfojDHGGGOMuREO0BljjDHGGHMjHKAzxhhjjDHmRjhAZ4wxxhhjzI1wgM4YY4wxxpgb4QCdMcYYY4wxN8IBOmOMMcYYY26EA3TGGGOMMcbcCAfojDHGGGOMuREO0BljjDHGGHMjHKAzxhhjjDHmRjhAZ4wxxhhjzI1wgM4YY4wxxpgb4QCdMcYYY4wxN8IBOmOMMcYYY26EA3TGGGOMMcbcCAfojDHGGGOMuREO0BljjDHGGHMjHKAzxhhjjDHmRjhAZ4wxxhhjzI1wgM4YY4wxxpgb4QCdMcYYY4wxN8IBOmOMMcYYY26EA3TGGGOMMcbcCAfojDHGGGOMuREO0BljjDHGGHMjHKAzxhhjjDHmRjhAZ4wxxhhjzI1wgM4YY4wxxpgb4QCdMcYYY4wxN8IBOmOMMcYYY26EA3TGGGOMMcbcCAfojDHGGGOMuREO0BljjDHGGHMjHKAzxhhjjDHmRjhAZ4wxxhhjzI1wgM4YY4wxxpgb4QCdMcYYY4wxN8IBOmOMMcYYY26EA3TGGGOMMcbcCAfojDHGGGOMuREO0BljjDHGGHMjHKAzxhhjjDHmRjhAZ4wxxhhjzI1wgM4YY4wxxpgb4QCdMcYYY4wxN8IBOmOMMcYYY26EA3TGGGOMMcbcCAfojDHGGGOMuREO0BljjDHGGHMjHKAzxhhjjDHmRjhAZ4wxxhhjzI1wgM4YY4wxxpgb4QCdMcYYY4wxN8IBOmOMMcYYY26EA3TGGGOMMcbcCAfojDHGGGOMuREO0BljjDHGGHMjHKAzxhhjjDHmRjhAZ4wxxhhjzI1wgF5HpaWlmDZtGnx9faHRaDBgwACcOHGiTuuuWbMG99xzD8LDw6FWq9GqVSu8+OKLKCsra+RUM8YYY4yxW430ZifgVuByuTBy5EicJJAgjwAAD+JJREFUPn0as2bNgsFgwPz589GvXz8cO3YMkZGR11z/scceQ3BwMB544AGEhobi9OnT+O9//4vNmzfj+PHjUCgUTbQnjDHGGGPM3XENeh2sWrUKv/76KxYvXow33ngDTz75JPbu3QuJRIJ//etff7v+6tWrcfLkSfz73//GI488grlz52LhwoVITEzEDz/80AR7wG4Fy5cvv9lJYE2I8/v2wvl9e+H8ZvXFAXodrFq1CgEBARg3blz1Mh8fH0ycOBHr16+H3W6/5vp9+/a9bNldd90FAEhMTGzYxLJbFhfotxfO79sL5/fthfOb1RcH6HVw4sQJdOrU6bLlXbt2hdlsRlJS0nVvMzc3FwAF+owxxhhjjFXhAL0OcnJyEBgYeNnyqmXZ2dnXvc0PPvgAUqkUEyZMqHf6GGOMMcbYP8dt10lUEARYrdY6fbeq82ZlZSXkcvlVP7dYLNeVhmXLluF///sfXnrpJURERFzXuowxxhhj7J/ttgvQ9+3bhwEDBtTpu4mJiYiOjoZSqbxiUF9ZWQkAUCqVdf79AwcO4NFHH8WwYcPw7rvvXvV7VUH/H3/8Uedts1tbWVkZjh8/frOTwZoI5/fthfP79sL5ffuoitOut7L279x2AXrr1q3x3Xff1em7AQEBAKgpy5WaseTk5AAAgoKC6rS9U6dO4c4770T79u2xatUqiMVXb2GUmpoKAJg8eXKdts3+GTp37nyzk8CaEOf37YXz+/bC+X17SU1NRe/evRtseyJBEIQG29o/1MSJE3HgwAFkZ2dDJBJVL582bRqWL1+O4uJiyGSya27j4sWLiIuLg6enJw4ePAiDwXDN7xcWFmLbtm1o0aLFddXQM8YYY4yxpmGxWJCamoqhQ4c26MAfHKDXwYoVKzBp0iSsXLkS48ePB0ABdFRUFIYPH45ly5ZVfzc9PR1msxmtWrWqXpabm4vevXvDZrPhl19+QWhoaJPvA2OMMcYYuzVwgF4HLpcLcXFxSEhIwMyZM6tnEs3MzMSRI0cQFRVV/d1+/fph//79cLlc1cs6dOhQPQtpTExMrW0HBARg0KBBTbYvjDHGGGPMvXGAXkelpaWYOXMm1q1bB4vFgm7dumHOnDmXjY/ev39/7N+/H06ns3qZWCyGSCTClQ51v379sHv37kZPP2OMMcYYuzVwgM4YY4wxxpgb4YmKGGOMMcYYcyMcoDchq9WKl156CUFBQVCpVOjRowd27txZp3VLS0sxbdo0+Pr6QqPRYMCAAThx4kQjp5jV143m+a5du/DII48gOjoaarUaERERmDp1KnJzc5sg1exG1Of6vtTUqVMhFosxevToRkglayj1ze+dO3diwIAB8PT0hE6nQ5cuXbBixYpGTDGrj/rk986dOzFw4ED4+flBq9UiNjYWn3/+ea2+asy9VFRU4F//+heGDRsGb29viMViLF68uM7rN0jMJrAmM2nSJEEmkwmzZs0SFi5cKPTq1UuQyWTCwYMHr7me0+kUevXqJWg0GmH27NnCF198IbRt21bQ6XTC+fPnmyj17EbcaJ537txZiIiIEF5++WXh22+/FV599VVBp9MJAQEBQm5ubhOlnl2PG83rSx05ckSQyWSCUqkURo8e3YipZfVVn/z+3//+J4jFYmHYsGHC/Pnzha+//lqYMWOG8PHHHzdBytmNuNH83rJliyASiYR27doJc+fOFRYsWCDcddddgkgkEp599tkmSj27XikpKYJIJBJatGgh9O/fXxCJRMLixYvrtG5DxWwcoDeRw4cPCyKRqFYBXFlZKURGRgq9evW65ro//fSTIBKJhNWrV1cvKygoELy8vIT77ruv0dLM6qc+eX7gwIHLlu3fv18QiUTC66+/3uBpZfVTn7yu4nK5hJ49ewpTpkwRWrRowQG6G6tPfqekpAhKpVJ47rnnGjuZrIHUJ7/vu+8+QaFQCCUlJbWW33HHHYJer2+U9LL6s1qtQl5eniAIgnD06NHrCtAbKmbjJi5NZNWqVZBKpZg2bVr1MrlcjkcffRS//vorsrKyrrluQEAAxo0bV73Mx8cHEydOxPr162G32xs17ezG1CfP4+LiLlvWp08feHt7IzExsVHSy25cffK6ytKlS3H27Fm88847VxzxibmP+uT3V199BUEQMHv2bACAyWTi/HZz9clvpVIJuVwOvV5fa3lAQABUKlWjpZnVj4eHB/z8/ADguq/PhorZOEBvIidOnEB0dDQ0Gk2t5V27dgUAnDx58prr/nU4x6p1zWYzkpKSGjaxrEHUJ8+vxGQywWg0NuhMZaxh1DevjUYjXnrpJbz66qvw9/dvtHSyhlGf/N65cydatWqFjRs3IiQkBDqdDj4+PnjzzTc5UHdT9cnv6dOnw+Vy4bHHHkNiYiLS0tLw1VdfYe3atXjllVcaNd3s5miomI0D9CaSk5ODwMDAy5ZXLcvOzm6UddnN09D5NnfuXNjtdtxzzz0Nkj7WcOqb17Nnz4ZarcaMGTMaJX2sYdUnv8+fP4/09HQ88sgjmDJlClavXo3hw4fjnXfewWuvvdZoaWY3rj75HRsbi927d2PDhg1o06YNwsLCMH36dHz++eeYPn16o6WZ3TwNde+XNmiq2FVZLBbI5fLLlisUiurPr6aysvKG12U3T33y/K/279+Pt956C/fccw/69evXUElkDaQ+eZ2UlITPPvsMP/74I2QyWaOlkTWc+uR3VZOWDz74ADNnzgQAjB07FsXFxZg3bx5effXVy2pq2c1Vn/xOTEzEyJEj0bx5c3z00UdQKBRYtmwZnn76afj7+2PMmDGNlm52czRUzMY16E1EqVTCarVetryysrL688ZYl908DZVviYmJGDt2LNq3b49vvvmmQdPIGkZ98vrZZ59F7969MXbs2EZLH2tY9S3PRSIR7r333lrLJ02aBIvFct1N31jjq09+v/jii5BKpdi7dy8mT56MCRMmYM2aNYiLi8NTTz1Va9Zx9s/QUPd+DtCbSGBg4BVfa+Tk5AAAgoKCGmVddvM0RL5lZGRgyJAh8PLywubNm6FWqxs8naz+bjSvd+/ejW3btuGZZ55Bampq9Z/D4YDZbEZaWhqMRmOjpp1dv/pc21Wf/bWvQVWHtJKSkoZKJmsg9cnvgwcPYsCAAZd1CB09ejSys7ORlpbWsIllN11DxWwcoDeRjh07Iikp6bKb7eHDhwEAHTp0uOq6HTp0wPHjxy/rQHT48GGo1WpER0c3fIJZvdUnzwGgqKgIQ4YMgd1ux7Zt27jzoBu70bxOT08HAIwbNw7h4eHVf9nZ2di9ezfCwsKwaNGixk08u271uba7dOkCQRCQmZlZa3nVDd3X17eBU8vqqz757XA4rlhLXjWSh8PhaMCUMnfQUDEbB+hNZMKECXA6nViwYEH1MqvVikWLFqFHjx4IDg4GAOTm5iIxMbHWRTthwgTk5eVhzZo11csKCwuxcuVKjB49mtutuqn65HlFRQVGjBiBnJwcbN68GREREU2eflZ3N5rXAwcOxLp162r9rV27Fr6+vujatSvWrVuHUaNG3ZR9YldXn2u7qpP3t99+W73M5XJh0aJFMBgM6Ny5cxPtBaur+uR3x44dsX37dhQXF1cvczqdWLFiBXQ6HZftt7hGjdn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"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f77c83ae910>)"
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"# We'll try and demonstrate this by looking at ten different sampling points of \\int WdW\n",
"# and then averaging over 1000 noise realizations.\n",
"Δt = 0.0001\n",
"\n",
"avgSums = zeros(1001, 11)\n",
"numAvgs = 1000\n",
"for avgct = 1:numAvgs\n",
" sums = zeros(1001, 11) \n",
" dW = √Δt*randn(10000)\n",
" W = [0, cumsum(dW)]\n",
" for (ct, λ) in enumerate(0:0.1:1)\n",
" for ct2 = 1:1000\n",
" W₂ = W[10*ct2+1]\n",
" W₁ = W[10*(ct2-1)+1]\n",
" W₃ = W[10*(ct2-1) + int(10*λ) + 1]\n",
" sums[ct2+1,ct] = sums[ct2,ct] + W₃*(W₂ - W₁)\n",
" end\n",
" end\n",
" avgSums += sums\n",
"end\n",
"avgSums /= numAvgs\n",
"\n",
"plot(0:Δt*10:1, avgSums)\n",
"xlabel(\"Time\")\n",
"ylabel(L\"E[\\int WdW]\")\n",
"legend([L\"\\lambda = \" * string(x) for x in 0:0.1:1], loc=\"best\")\n",
"title(\"Ito through Stratonovich and Beyond\")\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The integral with $\\lambda = 0$ is known as Ito calculus and with $\\lambda = 0.5$, Stratonovich. When one defines a stochastic equation one has to be explicit about how the integral is interpreted. An attraction to Ito is that it is not forward looking and so makes sense for finance. For Stratonovich the chain rule for differentiation follow the normal rules for caculus and for some physical systems it gives something consistent with physical expecations - e.g. in the stochastic LLG equation for magnetic particles the Statonovich interpretation conserves the magnitude of the magnitization. To distinguish the Stratonovich interpretation the $\\circ$ operator is used so that $\\int W\\circ dW$ implies Stratonovich integration.\n",
"\n",
"## Conversion between Ito and Stratonovich\n",
"\n",
"For convenience, say perhaps to use a solver or obtain physically consistent results it may be more convenient to work in one representation or the other. Fortunately there is a straightforward relationship between the two forms:\n",
"\n",
"$$ \\int_a^b f(t,W_t) \\circ dW_t = \\int_a^b f(t, W_t)dW_t + \\frac{1}{2}\\int_a^b\\frac{\\partial f(t, W_t)}{\\partial W}dt $$\n",
"\n",
"Note they are only different if the noise is mulitplicative i.e. f depends on W.\n",
"\n",
"We can also write the relationship down in terms of the differential equation with a correction to the drift term. If $X$ is a one-dimensional function of time with an Ito equation of motion\n",
"\n",
"$$ dX_t = A(x,t) + B(x,t)dW_t $$ \n",
"\n",
"then the solution X_t will be the same as that for the Stratonivich equation with a modified drift term:\n",
"\n",
"$$ \\begin{align} dX_t &= \\underline{A}(x,t) + B(x,t)dW_t \\\\ \\underline{A} &= A(x,t) - \\frac{1}{2}b(x,t)\\frac{\\partial b(x,t)}{\\partial x} \\end{align} $$\n",
"\n",
"Notice again that only if the noise is multiplicative is there a difference. \n",
"\n",
"For a multi-dimensional SDE the conversion generalizes to a double sum. In particular, if we have an Ito equation of motion for an $N$ dimensional system where the diffusion matrix potenially couples to $M$ noise sources then the equation of motion for each dimension follows:\n",
"\n",
"$$ dX_i = A(X,t)dt + \\sum_{j=1}^MB_{ij}(X,t)dW_j $$\n",
"\n",
"Then the equivalent Stratonvich equation is\n",
"\n",
"\\begin{align} dX_i &= \\underline{A}(X,t)dt + \\sum_{j=1}^MB_{ij}(X,t)\\circ dW_j \\\\ \\underline{A}(X,t)dt &= A(X,t) - \\frac{1}{2}\\sum_{k=1}^N\\sum_{j=1}^MB_{kj}(X,t)\\frac{\\partial B_{ij}(X,t)}{\\partial x_k} \\end{align}\n",
"\n",
"## Choosing between Ito and Stratonovich\n",
"\n",
"TODO: references or justification\n",
"\n",
"White noise is an idealization of a real physical process. \n",
"\n",
"* If white noise is approximation to continuously fluctuating noise with finite memory (much shorter than dynamical timescales), appropriate representation is Stratonovich (Wong-Zakai Theorem)\n",
"* If white noise approximates set of discrete pulses with finite separation to which system responds, or SDE continuous approximation to discrete system, then Ito representation appropriate\n",
"\n",
"Generically finance prefers Ito and physics Stratonovich. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Numerical Solutions\n",
"\n",
"It is difficult to get robust solvers for stochastic differential equations. \n",
"\n",
" Intuition is a bad guide in the development of simulation algorithms for stochastic differential equations so we develop the formal theoretical basis for them immediately, with no further preliminaries. \n",
"\n",
"## Convergence Criteria\n",
"\n",
"Discuss strong and weak convergence.\n",
"\n",
"## Stability\n",
"\n",
"## Euler Scheme\n",
"\n",
"The Euler (sometimes Euler-Maruyama) approximation is the simplest approach one could take. Given an Ito differential equation:\n",
"\n",
"$$ dX_t = A(X_t,t)dt + b(X_t,t)dW $$ \n",
"\n",
"Then we discritize time into time steps and propagate the an approximation to the solution according to:\n",
"\n",
"$$ Y_{k+1} = Y_k + A(Y_k, t)(t_{k+1}-t_k) + B(Y_n, t)(W_{k+1} - W_k) $$\n",
"\n",
"If the noise is additive then this has a strong convergence of order 1 but if the noise is multiplicative then the strong order of convergence is only 0.5. \n",
"\n",
"Consider a linear SDE which is excatly solvable and a reasonable model of a stock price. \n",
"\n",
"$$ dX_t = \\lambda X(t)dt + \\mu X(t) dW, \\quad X(0) = X_0 $$\n",
"\n",
"We can use the analytical solution to test the convergence. \n",
"\n",
"$$ X(t) = X_0\\exp\\left(\\left(\\lambda - \\frac{1}{2}\\mu^2\\right)t + \\mu W(t)\\right) $$"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning: redefining constant Δt\n"
]
},
{
"data": {
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s1BnW1fcJDw/Xe+4RERFQqVSa9mU1HTlyBNXV1Yi457vKL7/8ErGxsRgyZAhSUlLg5eWF5557rkEdRoiIyHIw9FKD/fOf/4SrqyvefPNNneEpJCQEbdu2xZ49ezT1s4C0M9iiRYuMPr/evXtj0KBB2LVrl86XqQDg3LlztebWGDKZDAsWLIBSqcRzzz2HioqKWucrKio0P5L39vaGo6MjTp8+XetzVllZicWLFzd54w+lUom4uDhYW1sjLi4OGzdu1PoVGxuL8ePHo7S0FAkJCVr3+OCDD2p9o1JdXY3/+Z//gSiKmrZn91qxYkWtj7ugoACrVq2CIAh1XqPL7NmzNfdTKpWa4wqFAsuXLwcAzJkzR3P86tWriImJgaenJ+Lj4+Hn54etW7eirKwMkydP1vpa5OfnIy0tzeI3WCEismQMvdRgbm5ueOWVV3D79m3k5+dr9ci1trbG4sWLUVRUhPDwcCxcuBDPPfccwsLCUFZWhvbt22tdY2jx8fHo3Lkz5syZg/DwcMybNw8vv/wypk6dirCwMPTs2RPp6elNfs7KlSsxfPhw7N27F0FBQViwYAGWL1+OqVOnws/PD99//z0AKSAvWrQImZmZCAsLw5IlSzB//nz06NED33//PYYOHdqkz8mOHTtQVFSEJ5544r51yXPnzgWgu2fvwIED0atXLzz//PN4+eWXERERgd27dyMyMhIvvfSS1nhfX1/cuXMHoaGhWLZsGRYtWoTQ0FBcvXoV8+fPx8CBA/Wef3R0NCZNmoRTp06he/fuWLp0KV544QWEhobi9OnTePrppzWdOyorK/H000+jtLQUmzdv1rzoOHLkSLz44os4c+YMli1bVuv+H374Ibp164aPPvpI7zkREVHrwtBLjbJo0SIEBgZCEASdP5Z//fXXsXr1atjb2yM2NhaJiYmYMGECEhMTYWNjo3VNXfdprA4dOiA5ORlvvvkmrKysEB8fjw8//BC//vorAgMDsXHjRoSGhjb5+TY2NkhMTMSHH36Idu3a4fPPP8dHH32E06dP46mnnqoV/N544w288847cHBwwMaNG/HNN9+gb9++OHnyJPz9/Zv08X/66acQBEETausyePBgBAUFITk5WWszjPfeew//+7//i8OHD2Pt2rXIz8/HkiVLcPDgQdja2mrdy87ODgcOHMBjjz2G7du3Y+PGjXBzc8PatWvrLH25n4SEBHz88cfw8PDQrE57eHjg448/Rnx8vGbc8uXLkZycjEWLFmHUqFG17vHWW2+hb9+++Pjjj7Fnzx7NcfXX15D/GyMiopZFEI295GYmUlJS0Lt3byQnJ2vVBjZmHFFrMXPmTHz++efIyMiAv7+/XtcEBgZCJpPh6tWrRp5d8+LffyIi0zLmv8Nc6SUiIiKiVo+hl4iIiIhaPYZeIgvXmFpX1sYSEVFLw9BLZOE2b94MlUqldz0vAKSnp7e6el4iImrdGHqJiIiIGuD9X9/HksQlpp4GNRBDLxEREZGePjvzGZYmLcWHJz/EbeVtU0+HGoChl4iIiEgP+y7tw7N7n8WEbhNQLVZj/9X9pp4SNQBDLxEREVE9km8mY+JXE/FE1yeQMD4Bod6h2Hd5n6mnRQ3A0EtERER0H+m30zEqfhRCvUOxfcJ2WMusEdUlComXE1EtVpt6eqQnhl4iIiKiOsgVcoyMGwlnO2fsjd4LRxtHAEBUlyjklOYgNSfVxDMkfTH0EhEREemgqFRgbMJY3FbeRuLURHi18dKcG+A/AE62TixxaEEYeomIiIjuoapWYequqUjNTcV/p/wXnd071zpva2WL4Z2GM/S2IAy9RERERDWIoojFiYvx7Z/f4ssJX6JPhz46x0V1icLxa8dRWF7YzDOkxmDopRZly5YtkMlk2Lp1q9GekZGRAZlMhlmzZhntGfc6fPgwZDIZXn/99WZ7JhER6favX/6Fj099jPWj1mNU0Kg6x0V1jYJKVGH/lca3LqtUVWJj8kZUqiobfQ/SD0Mv6eXNN9+ETCaDTCbDxYsXTT0dCILQpOtlMhmGDh1q1Gc0himeSUREd8WdjcPyA8vx6uBXEdM75r5j/V380c2rW5NKHL78/UvM+24efs76udH3IP0w9FK9RFHEp59+qvlzbGysCWdjOHUFTD8/P6SlpWH16tXNPCMiIjKlKwVXMGvPLMzsNROvP6LfT97UrctEUWzUM2NTpP9PzSzKbNT1pD+GXqrXDz/8gMzMTEyfPh1eXl7YunUrKitb749hrK2tERQUhHbt2pl6KkRE1Iz+yPsDldWVeGvYW3r/5C2qSxSyS7ORmtvw1mUX8y/ip8yfAACZhQy9xsbQS/VSr+w+++yzmDp1KuRyOXbv3q017rXXXoNMJsNPP/2EnTt3om/fvmjTpg08PDwQHR2Nmzdval2TnJyMxYsXo2fPnvDw8ICDgwOCgoKwbNkyFBbW/2KASqVCx44d4eLigrKyMp1j/v73v0Mmk2HXrl2ammDgbh2t+pe6nvZ+Nb0KhQJr1qxBZGQk2rZtC2dnZ3Tr1g2LFy/GrVu3NOMuXryI5cuXIzIyEl5eXrC3t0dgYCDmzZuHGzdu1PtxERFR85Mr5AAAT0dPva8Z6D8QbWzaIPFyYoOftyllE9zs3dCjXQ+u9DYDhl66r9zcXHz77bcICgpC//79NUFw48aNdV6zbt06PPPMM3jggQewcOFChIaGYseOHXj00UdRUVFRa2xsbCx27NiBkJAQzJ49G/Pnz4evry/effddDBgwAKWlpfedn5WVFZ599lmUlJQgISFB67xSqcS2bdvg6+uLcePGITw8HCtXrgQABAYG4rXXXtP8urfG997v8m/fvo3+/ftjxYoVUCgUmDNnDubPn4+QkBBs2bIFaWlpmrG7du3Chg0bEBAQgKlTp2LRokXo1q0bPv30U/Tp00fnNwBERGRacoUcLnYusLGy0fsaO2s7DH+g4a3LKlQV2JK6Bc/0eAZBHkHIKspq6HSpgaxNPQEyb5s3b0ZVVRVmzpwJAAgLC0N4eDgOHTqEK1euoHPnzlrXJCUl4fTp0+jevbvm2NSpU5GQkIA9e/Zg4sSJmuOvvPIKPvnkE62A+dlnn2Hu3LlYt24dXnrppfvOMSYmBqtWrcKGDRswd+7cWud27NiBoqIiLFy4EFZWVujZsyd69uyJ119/HYGBgfjnP/+p9+diwYIFOHv2LJ5//nl8/PHHtc4pFApUVVVp/jx9+nS8+OKLsLGp/Q/n/v37ERUVhVWrVmHdunV6P5uIiIxPrpA3aJVXLapLFBZ+vxBF5UVwsXfR65rvLn6HW2W3MDdiLrambsVvOb81+LnUMAy9BqKoVCBNnlb/QAML9gzWbIloaOoX2KysrDB9+nTN8VmzZmHRokWIjY3F22+/rXXdokWLagVeQAqmCQkJOHXqVK3Q6+/vr/PZs2bNwtKlS/HDDz/UG3p9fHzwt7/9DV999RVSUlIQERGhObdhwwZYWVkhJub+b+DW59atW9ixYwfat2+P//znP1rnHR1rfw3at2+v8z4jRoxAt27dkJSU1KT5EBGR4eUr8xsdelWiCj9e/RHju43X65rYlFg81OEhhLULQ4BLALKKslAtVkMm8IfwxsLQayBp8jT03ti72Z+b/GwyInwj6h/YCAcPHsTVq1cxcuTIWiFuypQpWLZsGbZs2YJVq1bB2rr2/4wiIyO17uXn5wdAKhGoqbKyEhs2bMD27dvxxx9/oLi4GNXV1Zrz+ta/zp8/H1999RU2bNiADRs2AADOnTuHEydO4IknnqgzXOvr1KlTEEURgwcPhoODg17XbNu2DVu2bEFqaioKCwuhUqk05+zs7Jo0HyIiMjy5Qg4PR48GXxfgGoAQzxDsu7xPr9CbVZSFpMtJiB0Tq7m+QlWB3NJc+Dr7Nvj5pB+GXgMJ9gxG8rPJJnmusajrdmfMmFHruLu7O0aPHo1du3Zhz549GD++9l9wV1dXrXupg3HN4AcAkydPxjfffIPOnTvjySefhI+PD+zs7CCKIt5//33cuXNHr7kOGTIEISEhSEhIwDvvvAMnJyfN/OfNm6ffB3wf6pfqOnTooNf4pUuX4oMPPkD79u0RFRWFDh06aMLy5s2bkZXF2i0iInMjV8i1thvW18guI/Hl719CFMV6Oz98duYztLFtg8mhkwFI/X4BqW0ZQ6/xMPQaiKONo9FWXE0hLy8P33zzDQAgOjoa0dHROsdt3LhRK/Tq6/Tp0/jmm28wYsQI7Nu3T9NVAZBKK9asWdOg+z3//PNYtGgR4uLiMH36dGzbtg1+fn4YPXp0o+ZXk5ubGwD9Vp5v3bqFtWvXIiwsDMeOHUObNm1qnY+Li2vyfIiIyPDkCjke6vBQo66N6hKF9359D+dunUOPdj3qHKeqVuGzM58hOjQaTrZOAIAAlwAA0grww34PN+r5VD+GXtJJ3Ys3MjISvXr10jlmz549+PHHH5GRkYHAwMAGP+Py5csAgLFjx9YKvABw4sQJlJeXN+h+M2bMwIoVK7Bx40bY2dmhqKgIS5Ys0fkdtyAIWqvO99O3b18IgoAjR45AoVBo1fDWdPXqVYiiiMcee0wr8F6/fh1Xr17V/4MiIqJm09gX2QBgcMBgONo4Yt+lffcNvT9c+QHXiq8hJuLuuyau9q5wtnVmr14jY7U06RQbGwtBELBu3Tps3LhR56958+Zp7dbWEJ06dQIAHDp0qNbxW7duYcGCBQ2+n7OzM6ZOnYozZ87g1VdfhbW1dZ0vsHl4eODatWt639vT01PTa3jZsmVaO++UlpaiuLgYADTfABw9erRWfXJpaSliYmIaFLaJiKh5qKpVKFAWNDr02lnbYVinYfW2LotNiUWPdj0Q2f7u+y+CICDANYC9eo2MoZe0HD58GJcuXUJYWJjOl9LU5syZA0CqUW1MkOvTpw8GDBiAXbt2YcCAAXjppZcwY8YMhIWFwcnJCe3bt2/wto7PP/88AKkM4Yknnqizi8Kjjz6KjIwMjB07FitXrsSqVatw9OjR+977o48+Qo8ePbB+/Xp0794dS5YswUsvvYSJEyeiQ4cO+O03qd2Mj48Pnn76aZw8eRK9evXCiy++iLlz56J79+7IyMhAr169Gr1dJRERGUdheSFEiI0OvYBU4vDLtV9QfKdY5/mc0hzsvbgXMRExWj+FDHBh6DU2hl7S8umnn0IQBK2et/cKCAjAiBEjkJOTg71790IQBL23bQQAmUyGb7/9Fs8//zxu3ryJDz/8EMeOHUNMTAwSExNhY2Ojdb/6ntGzZ09NOcb9XmD74IMPEB0djZMnT+LNN9/EypUrtVac7+Xq6opjx45h1apVsLGxQWxsLNavX48LFy5gzpw5CAkJ0YzdtGkTXnnlFSiVSqxbtw779+/H2LFj8csvv8DFxaVBnyciIjI+9W5sjeneoBbVJQpV1VX48eqPOs9v/W0rrGXWmBo2Veucv4s/yxuMTBAtZMkpJSUFvXv3RnJycq0+ro0dR+apuLgYHTp0gKenJ9LT0009HWph+PefyHL9kvULBm4eiN/n/45uXt0afZ/gj4IxyH8QYsfG1jouiiKCPgrCw34P44snv9C6bs3Pa7D659UoXF7Y6Ge3Bsb8d5grvdSqfPLJJygrK8P8+fNNPRUiImpB1Cu9TSlvAKTV3n2X92mVsf2U+RMuF1yu9QJbTQGuASi6U4Si8qImPZ/qxtBLLV5xcTHefvtt/P3vf8fKlSvRvn17hl4iImoQdeh1d3DXa3yNnedrieoahRslN3D+1vlax2NTYhHkEYRB/oN0XqduW8a6XuNh6KUWr6CgAK+88go2bdqEPn364LvvvtNqFUZERHQ/coUcbvZusJbdv5urKAKzZwODB+s+r2ldVqOLQ4GyAF//8TXmhs+t852OANe/Qi/reo2GfXqpxQsMDKzVGoyIiKih8pX5epU2bNkCbN4s/feFC0CNd5gBAPbW9hgaOBSJlxPx0oCXAADbzm6DSlRhes/pdd7Xx8kHNjIbrvQaEVd6iYiIyOLJFfIYkaWKAAAgAElEQVR6OzdcuAAsXAg88wzg5ATs2qV73MguI/Fz1s8ouVMCURQRmxKLcQ+OQzundnXeWybI0NGlI7KKuE29sTD0EhERkcWrbzc2pRJ4+mkgIABYvx4YNQr4+mvdY6O6RKGyuhIH0g/g5I2TOH/rfJ0vsNXEXr3GxdBLREREFq++0LtsGfDnn8COHYCjIzB+PHDmDKBrZ/nO7p3R1b0r9l3ah9iUWPi7+OPRBx7Ved+SEmDxYun3ANcA1vQaEUMvERERWTy5Qg5PB92hd9cuYN064P33gbAw6VhUFGBvD+zerft+UV2isPfiXmw/vx1zwufASmalc9wXXwBr1wLHj3Ol19gYeomIiMji1bXSm5kJzJkjrezW3OjTyQl4/PH7lDh0jUJ2aTaUVUrM6jWrzueqX4rLzJR2ZcspzUF5VXlTPhSqA0MvERERWbSq6ioUlhdqhd7KSiA6GnBxAWJjgXu7jY0fL63Q3rihfc8hAUNgb22PkV1GoqNLR53PPX8eOH1a+u+srLu9eq8XX2/yx0Ta2LKsDhcuXDD1FIiomfHvPZFluq28DRGiVveG114DTp4Ejh4F3Ny0rxszBrC2Br75BliwoPY5BxsHxD0VhxDPEO0L/7J5M+DpCQQG/hV6a/Tq7eLepYkfFd2LobcO06ZNM/UUiIiIqBno2oL4wAFg9WrgrbeAfv10X+fqCgwfLpU43Bt6AeCpkKfqfGZlJbBtGzBtGpCTI5U3dGwrrQizrtc4GHrvERwcjOTkZFNPg4hMKDg42NRTIKJmdG/ovXVLCqPDhwMvvXT/a8ePB557DpDLpVVbfX3/vfScWbOAuDjgxAnAztoOvk6+7OBgJAy993B0dERERISpp0FERETNpGbora4GZswAqqulzgqyet5+GjdOCr179kgvvOlr82YgIgLo0QP4+Wfg2jVApZJeZuNKr3HwRTYiIiKyaHKFHAIEuNm74d13gcREKfD6+NR/rbc3MGhQ3V0cdLl1C/jvf6VVXgDw9weqqqQyhwDXAO7KZiQMvURERGTR8pX5cHdwR0a6FVaskEoaHntM/+vHjwd+/BEoKtJvfFyctIIcHS39OUB6fw2ZmezVa0wMvURERGTR5Ao5PBw9cO6ctOL64osNu/7JJ6UX0777rv6xoiiVNowdC3j81SzC31/6Xd227FrRNVSL1Q2bBNWLoZeIiIgsmnpjipwcwMqqYS+kAYCfH/DQQ/qVOKSkAOfO3S1tAKQ+wG3b/rXS6xqAyupKZJdkN2wSVC+GXiIiIrJo6tCbmyvV6Nb38pou48dLtcBlZfcft3kz4OurXT4RECCt9Pq7SMu+LHEwPIZeIiIismhyhRyeDtJKrz4vr+ny1FOAUikF37qUlwPx8cD06dKmFjX5+9+t6QXAl9mMgKGXiIiILFrN8obGht7OnYGePe9f4vDtt8Dt27VLG9TUK70u9i5wsXNhr14jYOglIiIii5avzG9y6AWk1d7vvgPu3NF9fvNmaXe3Bx/UPqde6QWkul6WNxgeQy8RERFZrEpVJQrLC+Hh6IHc3KaF3vHjgZISqX3ZvW7cAH74QfcqLyCt9BYXS23P2LbMOBh6iYiIyGIVKAsAAB5/1fS2a9f4e3XrJq3i7tqlfe7zzwE7O2DSJN3XqtuWZWb+tSsbyxsMjqGXiIiILJZ6C2JHeEKpbNpKryBIJQ579kj9ftVEEdiyRTrn4qL7WvUGFepevZlFmRBFsfGTIS1mFXpPnTqFhQsXonv37nByckJAQAAmT56MS5cuaY29cOECRo4cCWdnZ3h4eGD69OmQy+UmmDURERG1VOrQW10qNedtSugFpBKH/Hzgp5/uHjt+HLh4se7SBvVzra3/Cr2uASitKEVheWHTJkO1WNc/pPmsWbMGx48fx8SJE9GjRw9kZ2fjo48+QkREBH799Vd0794dAHD9+nUMHjwYbm5uWL16NUpKSvCf//wH586dw8mTJ2FjY2Pij4SIiIhaAnXorSwyTOiNiJBWbXftAoYPl45t3iwdGzq07uusrICOHaXyht5/tS3LLMqEm4Nb0yZEGmYVel988UX06dMH1jWa102ePBlhYWF4++238cUXXwAA3nrrLSiVSpw5cwZ+fn4AgL59+2LEiBHYsmULYmJiTDJ/IiIialnylfmQCTKU5bsCaHroVZc4bN8OfPih1Lt3xw5g6dL6N73w97+70gsAmYWZ6OXTq2kTIg2zKm/o169frcALAF26dEG3bt2QlpamOfb1119j9OjRmsALAMOHD0dQUBC+/PLLZpsvERERtWxyhRzuDu64lSuDnZ20HXBTjR8PZGdLZQ27dkkdHWbOrP+6gABppde7jTdsrWzZwcHAzCr06iKKInJzc+H510bYN27cQF5eHiIjI7XG9unTB2fOnGnuKRIREVELde/GFILQ9Hv26yfda9cuqbThkUeATp3qv0690isTZPB38eeubAZm9qE3Li4ON2/exOTJkwEA2dnZAABfX1+tsb6+vigoKEBlZWWzzpGIiIhaJkPsxnYvmQx48kmpTdmhQ/d/ga2mgADg5k2gooK9eo3BrENvWloaFixYgP79+2PGjBkAAKVSCQCws7PTGm9vb19rDBEREdH9GCP0AlKJg1wOODlJ/60Pf3+pvdmNG3+FXvbqNSizDb05OTkYNWoU3NzcsHPnTgh//bzBwcEBAHBHxx5/5eXltcYQERER3Y9cIYengydyc5u2McW9Bg8GvLyAyZOBNm30u6bmBhXcitjwzKp7g1pRURGioqJQXFyMo0ePwqfGt17qsgZ1mUNN2dnZ8PDwuG/LsqVLl8Llns7Q0dHRiI6ONtDsiYiIqKXIV+YbZaXXxgY4dgzw9tb/GnXozcoC/Hv441bZLSgrlXCwaZ2LeQkJCUhISKh1rKioyGjPM7vQW15ejjFjxuDy5cv48ccfERwcXOt8hw4d4OXlhVOnTmlde/LkSfTqdf/WHu+99x4iIiIMOmciIiJqmeQKOTz+Wuk1ZOgFgC5dGjbe0RHw9JRWegcOktqWXSu+hiCPIMNOzEzoWnRMSUlB7969jfI8sypvUKlUmDx5Mk6cOIGvvvoKDz30kM5x48ePx3fffYfr169rjh04cACXLl3CxIkTm2u6RERE1IJVqCpQfKcYdtUeqKoyfOhtjIAA7V69ZBhmtdL74osvYu/evRgzZgzkcjm2bdtW6/y0adMAAK+88gq++uorDB06FIsXL0ZJSQn+/e9/o0ePHpil7yuSREREZNHyFfkAAFm5YXZjMwR/f2ml16+tHwQIrOs1ILMKvampqRAEAXv37sXevXtrnRMEQRN6/fz88NNPP+GFF17A8uXLYWdnh9GjR+Odd97hFsRERESkF/UWxNWlUug15ItsjRUQAOzbB9ha2aK9c3uu9BqQWYXeQ4cO6T22W7duSExMNOJsiIiIqDVTh96KQvMJveoNKkQR8Hfx50qvAZlVTS8RERFRc8lXSuUNynxPODvr31rMmAICAKVS6vHLtmWGxdBLREREFkmukMNKsEJhrotZ1PMCtduWBbgEcCtiA2LoJSIiIoskV8jh4eiB3BzBLEobAGmlF/hrgwqXAFwvvg5Vtcq0k2olGHqJiIjIIqm3IDZGj97G8vQEHBzuti2rqq7CzZKbpp5Wq8DQS0RERBZJHXoNvRtbUwjC3bZl/i5SrQPreg2DoZeIiIgskjmGXuBuB4cAF25QYUgMvURERGSR8pX5cLf3hFxuXqE3IEBa6XW2c4abvRtfZjMQhl4iIiKySHKFHI6iJ0TRPHr0qqlXegG2LTMkhl4iIiKySHKFHNaVHgDMa6XX3x/IywMUCm5QYUgMvURERGRxyqvKUVpRCkEp7cZmTqFX3bbs2jWprpc1vYbB0EtEREQWJ18h7camKpFCr7e3KWdTm3qDCnWv3syiTIiiaNpJtQIMvURERGRx5Ao5AODObU94eAC2tiaeUA1+flLrMnWvXkWlAgXKAlNPq8Vj6CUiIiKLk6+UVnqV+Z5m9RIbIAVwX9+7K70Ae/UaAkMvERERWRz1Sm9xjqdZ1fOqBQRIK72aDSpY19tkDL1ERERkceQKOaxl1pDfdDbL0KtuW+bdxhv21vZc6TUAhl4iIiKyOOrd2HJzBLMMveoNKgRBkNqWcaW3yRh6iYiIyOLU3ILY3Gp6AWml9/p1QKWS6nqzirkrW1Mx9BIREZHFkSvkcLf3RFGRefXoVQsIACorgZwc9uo1FIZeIiIisjj5ynw4Cea3MYWaulev+mU21vQ2HUMvERERWRy5Qg67avMNvepd2TIzpV69coUcZRVlpp1UC8fQS0RERBZHrpDDusIDgHmGXhcXoG3bvzao+KtXb1YR63qbgqGXiIiILI5cIQcUnpDJAA8PU89GN3UHhwBXhl5DsDb1BIiIiIiak6JSAUWlAqpKT3h7A1ZWpp6RbupevR2cO0AmyFjX20Rc6SUiIiKLkq+QtiC+c9s8d2NT8/eXVnptrGzQ3rk9Ozg0EUMvERERWRT1FsRleeYdetVbEQN/tS3jSm+TMPQSERGRRclXSiu9RdmeZrkxhZq/P1BUJP0KcGXobSqGXiIiIrIo6pXeguseZr/SC9zt4JBRmGHS+bR0DL1ERERkUeQKOWytbHHrhpNZh96aG1SEeofievF1FCgLTDupFoyhl4iIiCyKXCGHh70nlArBrEOvry9gbS29zBbhGwEAOJN9xsSzarkYeomIiMiiyBVytLUx393Y1KysAD8/aaW3q3tXtLFpg5TsFFNPq8Vi6CUiIiKLIlfI0UaQQq85v8gG3N2gwkpmhZ4+PZGSw9DbWAy9REREZFHylfmwU5n/Si9wd4MKAIjwiWB5QxMw9BIREZFFkSvksLrjAVtbwNXV1LO5P/VKLyDV9V7Mv4iSOyWmnVQLxdBLREREFkWukAMKaWMKQTD1bO7P3x+4eROorJRCrwgRqbmpzfLsnX/shP97/vj2z2+b5XnGxtBLREREFkMURcgVclQVm/dubGoBAYAoAtevA928usHWyrbZXmbb8fsO5JTmYNz2cZi3dx7KKsqa5bnGwtBLREREFkNRqUB5VTnKC8x7Nza1mr16baxsEOYdhjM5xq/rrRarcSj9EJYPXI71o9bji7NfIGJjBE7fPG30ZxsLQy8RERFZDPVubGV5LWOlVx16a9b1NsdK79ncs8hX5mN4p+GYFzkPZ+adgbOtM/pt6oe3jr4FVbXK6HMwNIZeIiIishj5ynwAQFF2ywi9jo6Ap2eNDg6+Efj91u8oryo36nMPXD0AB2sHPOz3MADgQc8HcWzOMfxP///B/x78XwzdOhSZhZlGnYOhMfQSERGRxVCv9BZcbxmhF5BWe9UrveE+4VCJKpzLPWfUZx5IP4CB/gNhZ22nOWZrZYu3hr+FwzMPI7MoEz3W90Dc2TijzsOQGHqJiIjIYqhDb1WxR4uo6QWkl9nUK7092vWAlWBl1LreSlUljmQewfBOw3WeHxwwGKnPpWJ00GhM2z0NU76egsLyQqPNx1AYeomIiMhiyBVy2MnsgUrHFrnS62DjgBCvEKPW9Z68cRJllWUY1mlYnWNc7V0R91Qc4p6Kw3cXv8MLSS8YbT6GYm3qCRARERE1F7lCjrbWnsiD0GJCr3qlVxSlvsLGfpntYPpBuNi5IMI3ot6xU8Km4Oesn3E066jR5mMoXOklIiIiiyFXyOEoSFsQt5TyBn9/QKkE8qV38BDuE46zuWdRqao0yvMOpB/AI4GPwEpmpdf4UO9QpMnTUKGqMMp8DIWhl4iIiCxGvjIftlWecHICnJxMPRv9BARIv9dsW3ZHdQdp8jSDP0tRqcDx68frrOfVJdQ7FFXVVbiUf8ng8zEkhl4iIiKyGHKFHFZ3WsbGFGo1N6gAgF4+vQDAKCUOv2T9ggpVBYY/0LDQCwDnbhm3o0RTMfQSERGRxZAr5BDLPFpMPS8AeHkB9vZ3V3rb2rVFV/euRgm9B9IPwMfJByGeIXpf4+7gjvbO7XH+1nmDz8eQGHqJiIjIYsgVclQWt5wevYD08pq//92VXgAI9w1HSo7hQ+/B9IMY1mkYBEFo0HWh3qEMvURERETmQBRFyBVylOe3rNALSHW9mTU2QIvwicBvOb+hWqw22DMKywuRnJ2MYYF1tyqrS6hXKMsbiIiIiMxBaUUpKlQVKL3Vsmp6Ae2V3gjfCJRWlOJywWWDPeNwxmFUi9UNqudVC2sXhqu3r6Ksosxg8zE0hl4iIiKyCPlKqedXcU7LW+nt1Am4fFnq1QtI5Q2AYV9mO5h+EJ1cOyHQNbDB16pfZvsj7w+DzcfQGHqJiIjIIqi3IIai5YXe8HCgsBBIT5f+7OnoiY5tOxo09B5IP9CgVmU1hXiGQIBg1nW9DL1ERERkEe6G3pbVvQEAeveWfj99+u6xCN8InMk5Y5D755Tm4I+8PxpV2gAAbWzb4AG3B8y6rpehl4iIiCyCJvQqW17obdcO6NhRO/SmZKdAVNc8NMHB9IMAgKGBQxt9j7B2YVzpJSIiIjI1uUIOW8ERqHSEt7epZ9NwkZHaobdAWYCsoqy6L9LTwfSDCPUORTunu2/4qVRAXp7+9wj1Mu+2ZQy9REREZBHkCjkcRU+4uQF2dqaeTcNFRgLJyUD1X13Kwn0M9zLbgfQDWq3KPvkE8PYGHnsM2L0bqKq6/z1CvUORXZqNfEV+k+djDAy9REREZBHyFfmwrWp5L7GpRUYCxcVSFwcAaO/cHt5tvJtc13v19lVkFGZo1fN++y3QvTtQWgo89RQQGAi8/jpw44bu+6g7OJjrai9DLxEREVkEuVIOWXnLDb33vswmCIKmrrcpDqYfhEyQYUjAEM0xpRI4cgSYOxc4dgw4cwYYPRr497+ljTLGjwd+/PHuqjMABHkEwUZmw9BLREREZEpyhRzVZS3vJTY1Dw+pX29y8t1jET5ND70H0g8gsn0kXOxdNMeOHAHu3JFKGwCgVy9g/Xrg5k1g7Vrg4kVgxAggOBh4912gpASwsbJBsGcwQy8RERGRKckVclQWtbzd2Gq692W2cN9wZJdmI6c0p1H3E0URB9MPavXn/eEHwM8PCAmpPb5tW2D+fODsWeDoUaBPH2DFCmDJEul8qLf5bkfM0EtEREQWQa6QQ5nfcssbACn0pqRInRUAqYMDAJzJblxd7+95v+NW2S0M61T7JbYffpBWeQVB93WCAAwcCMTFATExwK+/SsfDvKW2ZYZoo2ZoDL1ERETU6omiCLlCjvKClh96S0ul8gIA6OTaCS52Lo0ucThw9QDsrOwwoOMAzbEbN4Dz5++WNtQnLAz480+pHCLUOxRFd4pwo6SOt91MiKGXiIiIWr2SihJUVVe1yC2Ia4qQFna1X2bLaVzoPZhxEP079oeDjYPm2P790kruo4/qd4/QUGnlOS3NvDs4MPQSERFRq3d3C+KWXdPr6gp07XpPXa9PeKNWequqq3A447BWaUNSkrSi7OGh331CpZyL8+eBANcAtLFpg3O55lfXy9BLRERErd7d0Ntyuzeo6dqZLaMwA7eVtxt0n5TsFBTfKa71Elt1tbTSq29pAwC4uAD+/sC5c4BMkCHUOxTn87jSS0RERNTs1KFXKPeEl5eJJ9NEkZFS31z1Dmmal9kauEnFgasH4GTrhMj2kZpjZ84A+fnA4483bE6hoVLoBaQSB5Y3EBEREZmAOvR6tfGAlZWJJ9NEkZHS5hEXLkh/DvIIgqONY4NLHA6kH8CQgCGwsbLRHEtKApydgYcfbticwsKk8gZACr1/5P0BVbWqYTcxMoZeIiIiavXkCjlsqp3g62Vv6qk0WXi49KKZusTBSmaFnu16Nij0lleV45drv+jszztsGGBjU8eFdQgLA7KygKIiKfSWV5Xjyu0rDbuJkTH0EhERUauXr8iHTVXLfolNzdlZ2gnt3rrehpQ3HL92HOVV5bVeYispAX75pWH1vGo1X2YL8w6T/tvMShwYeomIiKjVkyvkEJQtu11ZTbpeZvtT/idKK0r1uv5g+kF4OnoirF2Y5tjhw1KdcGNCb3AwYGUlhV7vNt7wdPRk6CUiIiJqbnKlHNWlLb9zg1pkJJCaClRUSH+O8I2ACBGpOal6XX8g/QCGBg6FTLgbBX/4AXjgAaBLl4bPx84OePBB6WU2QRDMcjtihl4iIiJq9eQKOSqKWtdK7507wO+/S3/u5tUNtla2etX17r+yHydvnNSq501Katwqr1rNDg7q7YjNCUMvERERtXq3SuVQFbeOml4A6NULkMnuljjYWtki1Dv0vnW9Vwqu4G/b/4bHtj2Gfh37YVL3SZpz6enApUsNb1VWk7qDgyhKL7Ndyr+E8qryxt/QwKxNPQEiIiKixjpx/QS2n98OZZUS5VXlUFYpoaxU1vq9vKoclwr+BBTRrWal19ER6N5dCr0xMdKxCJ8InLp5SmtsyZ0SvHX0Lbz767to16Ydto/fjkndJ0EQBM2Y/fulmtyhQxs/p7AwoKAAyM6WQq9KVOFP+Z/o6dOz8Tc1IIZeIiKiVqasogwX8y8iwDUA7g7upp6OUS1OXIzLBZcR4BoAB2sHONg4wMHaAe4O7nBwdtAci2zzJD5Pnd5qQi+g+2W2LalbUF5VDntre1SL1dh2dhuW/7gct8tvY8XAFXhpwEtwtHHUuldSktSb18Wl8fMJ++uduHPngIeHdJf++9Y5hl4iIiJqPFEUkVuWizR5Gi7kXUCaPA1p+WlIk6chqygLADCyy0jsm7rPxDM1nisFV3DixgkkjE/A06FP33fs118Dnxeh1YXebduA8nLA3l4KvVXVVTh/6zyqxWos2rcIJ26cwKTuk/CvR/+FANcAnfepqgIOHABefLFp8wkMBNq0kULv44+7wN/F36zqehl6iYiIWpCTN05iceJiXMi7gKI7RQAAa5k1urh3QbBnMKaGTUWwZzCuFFzBG0feQFZRFvxd/E08a+NIOJ+ANjZtMCZoTL1jc3KkDRfc3JphYs0kMhKorJRCZp8+QFi7MMgEGWbvmS2tsLbriZ9m/oTBAYPve5+TJ6VNJZryEhsg1Rh37157ZzaGXiIiImqUjckbkVWUheUDlyPYMxghniF4wO2BWlvJAlId5zvH38GW37bgn0P+2aRnXsq/hPd+fQ/zes8zmx9Vi6KI+HPx+Fvw39DGtk2943NygHbtpJ3MWosePQBra6nEoU8fwNHGEeE+4cgsysSG0RswJ3wOrGT177n8ww/SNwORkU2fU1gYcOavd+lCvUKx/fftTb+pgbB7AxERUQshiiKSriRhcvfJWD5wOf4W/Dc86PmgVuAFAGc7Z0zuPhmbf9uMarG6Sc/9vyP/h09Of4JeG3ph/Jfj9e4Fa0xnc8/igvwCpoRN0Wt8Tk7rKm0ApJKGsLDadb1J05JwddFVPNv7Wb0CLyCF3kcflV5ka6rQUOCPPwCVSlrpzSrKQvGd4qbf2AAYeomIiFqIP/L+wPXi6xjZZaRe4+dEzEFGYQYOph9s9DNzSnOw4/wO/OvRf2HzuM34Lec3Tfg9m3u20fdtqvhz8fBw8MCIB0boNb41hl5A+2U2D0cPONs563397dvAiRNNL21QCwuTaoyvXIFmt7ffb/1umJs3EUMvERFRC5F0JQn21vYY5D9Ir/H9/Poh2DMYn535rNHP3HB6A2ytbBHTOwYze81E2oI0fDb2M/yW8xt6ru+JCV9OaPbwWy1WI+F8AiZ1n6RzlVuX3NzWG3p//x1QKBp3/cGDQHW1YUMvINUZB3sGQybIzKaul6GXiIiohUi8nIhHAh+Bg42DXuMFQcDsXrOx68Iu3FbebvDzKlQV+OT0J5jRcwZc7V0BADZWNpgVPksTflOyU9BzfU9M/GoizuU2z7azv2T9gmvF1xAdGl3v2MJCYNcuaeWxtYZelUrakrgxkpKA4GDA30DvOnp7A15eUui1t7ZHV/euZrMdMUMvERFRC6CoVOBI5hE83rn+LbNu3AD+/W+pDdX0ntOhElWIOxfX4Gd+9ftXyC3LxRNeC/HMM8CHH0r1mqJ4N/z+ufBPbBq7Cck3k9FjfQ+s+XlNYz68Bok/F4+ObTtigP8ArXOVlcDRo8Crr0p9Zz08gPHjpd9H6lcV0qKEhgK2trVLHPQlilI9b1N2YdNFvTMbIJU4cKW3DmVlZVi5ciVGjhwJd3d3yGQybN26VWvczJkzIZPJtH6FhISYYNZERETG9VPGT7ijulNnPW9lJbB7NzB6tLRq99JL0k5dng7tMDpoNDad2dTgZ649uRaPdX4M2z8Mwa5dUh/X7t0BX19gyhTg00+B61k2mB0+G38u/BNPhTyF+PPxTf1Q76tSVYmv/vgK0aHRkAkyiCJw4QKwdi0wZgzg7g4MHgysWwcEBAAbNgAZGcDFi8AA7Yzc4tnaAj17Ni70XroEZGYarrRBLSxMWukFpA4O5hJ6za5lWV5eHt544w0EBASgV69eOHz4cK1t8mqys7PDpk21/xK7NGUrESIiIjOVeDkR/i7+eNDjwVrH09KATZuAzz8Hbt2SWletWwd06iSt4CUlAbN7zcbY7WNxJvsMwn3D9XreiesncPLGScQ98R1mzQHefBOYPx/4+WepDvTgQWDHDqkeNDAQGDbMBo4Rg3Dx9vdQVav07hzQUPuv7ke+Ml/TteEf/wBWr5bC34ABwCuvACNGAOHhhulG0BJERgI//dTw65KSpM/bkCGGnU9oqPRTAaVS6uCQp8hDbmku2jm1M+yDGsjsQm/79u2Rk5MDb29vJCcno0+fPnWOtbGxwZQp+rUqISIiasmSriRhZOeREAQBpaXAl19KYffYMWl185lngDlz7r5IJIpARATw8cfAnr1R8HXyxaYzm/CR70d6Pe+DEx+gs1tnZB6IgiAAs2YBjo7SqqB6ZbCwUApb6hB8/kgwMK0cWUVZ6MulGHQAACAASURBVOTWySifh/hz8ejm1Q092vVARQWwfj0wbx7wzjvSbmCWKDJS+jyUlgJOTvpf98MPwMCBhv+8hYVJ3wxduACE+ocCAM7fOm/y0Gt25Q22trbw9vYGIPUjvB9RFFFdXY3iYvPo/0ZERGQMGYUZ+DP/Tzze5XEcPiyVF8ydKwWcHTuAmzeB99+/G3gBaROGBQuAffuArAxrzOg5A3Hn4qCsVNb7vJslN/HVH19hQZ+/Y+MGGZ5+WqqJvZerKzBuHPDBB9KPs+eMCwYApMnTDPSR11ZWUYZv0r7BlNApEAQBiYlSy62FCy038AJS6BXFu5tC6KOiAjh0yPClDYBUAgNI/5vo4t4FdlZ2ZlHiYHahtyEUCgXatm0LV1dXeHh4YOHChSgrKzP1tIiIiAwq6XISrAQrDO80HBs3Ah07Aunp0o+nJ00C7Ox0X/f001IwXb8emB0+G4Xlhdidtrve560/vR721vZof2smMjKk8KyPyK7+QKU9zucaJ/TuvbgXZZVliA6TujbExUlBPzTUKI9rMbp1kzaqaEhd77FjQFmZ4V9iA6Rvxjp1kkKvlcwK3by6MfQ2Rfv27fHyyy9jy5Yt2L59O8aOHYt169Zh5MiRUKlUpp4eERGRwSReSUT/jv3hZOOCxERgwgTpJa36ODpKZQmbNgF+jl0xyH9QvT1771TdwfrT6zGz50xs3eCCyEipTlgfDwbJgPwHcTrDOKE3/lw8HurwEB5wewAlJcC33wJTpxrlUS2KtbVUw9yQ0PvDD1J7sR49jDOnmh0cQr1DzaJtWYsNvW+99RbeeustTJgwAZMmTcLmzZvx5ptv4pdffsHOnTtNPT0iIiKDqFRV4sDVA3i88+M4cUL6cf4TT+h//fPPAwUFUhnEnPA5OJB+AOm30+scv+P3HchT5GGsz0IkJkovr+mra1cA8mD8boSV3gJlARIvJ2peYNu9W9r56+mnDf6oFunendnqk5QkvfAnM1ISrNnBIcw7DL/n/d7k7bCbqsWGXl2WLl0KmUyGAwcOmHoqREREBnH8+nGUVJRgZJeR+P57qbZW35VXAOjSRepPu24dMKHbBDjbOmPzb5t1jhVFEWtPrMXILiOxf/uDcHUFJk/W/1nt2wPWhcHILDN86P36j6+hElWY1H0SACA+Hhg0SL8Vb0sQGSm1ZSsqqn/snj1ASopxShvUQkOlWvOCAmmlt7SiFFlFWcZ7oB7MrntDU9jb28Pd3R0FBQV1jlm6dKlWW7Po6GhER9e/qwsREVFzS7ycCC9HL4T7hiPmeynANrQV1/z5wNixwB+pbRAdGo3Nv23GyiErtdqKHb9+HMnZydg94XvMWQTMni2VSOhLJgN8bYJxTbyFAmUB3B3cGzbR+4g/H4/hnYbDx8kHubnAjz8CH+nXiMIiREZKv6ekAEOH6h5TWQmsWCF1unjySWDiROPNp+Z2xKG97nZwCHQN1IxJSEhAQkJCreuK9EntjdSqQm9JSQnkcjm8vLzqHPPee+8hIiKiGWdFRETUeElXkvBY58eQky3DmTPAsmUNv8cTT0groh9/DDy/ajY2pmzEj1d/xONdai/1rT2xFl3du+L2qcdRUAA891zDnxXkHoxrAP6U/4l+Hfs1/AY6XC++jp8y/p+9O4+Lqt7/OP4ahl0BEcF9AUQRl1xRvO6Sktot0yzNXOq2L2b7vd32n9W9LbbfVpdS08o0NZeU3AEXRHPPRAXEDUUE2YZhfn9MVqYWCsMZmPfz8fChMmfOedOty5vD53y/q5lynX0e+csv7atTOLK0VTUtW9pXsNi8+eKl9/Bh+137DRvgjTfgoYfs/wwdpUUL8PCwz/X26tWIAK8Ath/bzpAWQ3495mI3Hbds2UKnTp0ckqlKjjcUFRWRm5t7wcdffPFFAOKq4z6DIiLico7lHWPLkS0MDB/I0qX2knIlP5I2m+2zvbNnQ7h3NK2DW1+wQ1vGmQy+3vU1D0Q/wAf/c2PgQPtoxOVq37gFULHLls3ZMQdPsydDI4cC9tGGuLiLL6Pmqsxm+7rMF5vrXb4c2re37762ejVMnOjYwgv2whsZab/TazKZaBPShh0njF3BwSnv9L777rucPn2azMxMABYsWEBamn0O5MEHH+TUqVN06NCBUaNG0bKlfWeaZcuWsWTJEq655hquu+46w7KLiIhUlOWpywEYED6A+16Ebt2uvOjddhs88wxMnWri9h6388SKJ8jKz6KObx3AvkyZr4cvbUvHsnGjfe7zSkRF+ML2phW6bNmsHbMY3GIwAd4B7N8PSUnwh5+KC/YRh9//72a1wosvwgsv2NfjnTED6tSpvDznbUcc0obEjMTKu/hFOGXpff311zl06BBg/+5g3rx5fPPNN5hMJsaMGUNgYCDXXnsty5cvZ/r06VitViIiInj55Zd59Ep+7iMiIuKElv68lA71OlDbqy7ffw+PP37l5woOtv94+3//g4S7RvPEiieY+eNMJnSbQGFJIR8mf8j49uP5/BN/mjSBwYOv7DoREcDKSFLSKqb07s3ay5YjW/hXj38B9rJbowZce22FnL5a6dwZJk+2PzxWUmJfzi0+Hp5/3r5ds6NWariUtm1h0SL7xhltQtowJWUKFqsFD7NH5Qb5hVOW3gMHLr2UyjmfffZZJSQRERExRqmtlGX7l3FHxztYvx5ycy9vqbKLue8++PxzSF4bzN9b/p1PUz7lwa4PMnvHbLLys7g18n56zrLfEb7ch+XOObds2d6TS8oX9hdf7PgCfy9/BkUMwmazb0hx/fWuvQPbpZx7mO2dd+Cjj+zFd/ly6N/fmDxt2sCZM5Cebi+9llIL+07tIyo4ypA8VXKmV0REpLpLOZJCVn4WA8MHsngx1Ktnn8ssj+ho+9zn++/b1+zdfnw7mzM38/aGtxkUMYi18yOwWuH226/8GnXrglduJEeL91NsLS5XXpvNxqzts7ih1Q34ePiwdSvs2aMNKS6leXPw94fnnoPwcPu2xEYVXjh/BYe2Ifa/pBy5jL2SK5hKr4iIiBNa+vNS/Dz9iGkcw+LFcM015f/xtMlkv9u7ZAk0Nw2goV9D7l18LylHU7i/y4O8/759RYSQkPJdo4lvJKVY2X9qf7nyJh9JZt+pfYxqY9+QYuZM+0xqbGy5TlttubnZH1J7+mn44Qf7uslGatIE/PzsKzgE+QbROrg1Kw+uNCyPSq+IiIgTWrZ/Gf1C+3Ekw5OdO8s/2nDOzTdDrVrw0YdmxrUfx+bMzbQMaokp9Wp+/vnydmC7lFbBkUD5V3CYtX0WdWvUpW9oX6xW+zzvTTfZVwaQi3vuOfuDa+5OMMBqMtlHHM49zBYbFsvy1OXYbDZD8qj0ioiIOJmcwhwS0hOIax7HkiX2+dqrr66Yc/v6wvjxMGUKjGp1G2aTmQldJ/DB/9xo1w66dy//NdqG1cVUFFCu0msttTJ7x2xuan0T7m7urFlj3+Fr1Kjy55PK8/sVHGLDYknLSWN/dvl+AnClVHpFRESczA8HfsBqs/46z9ujB/xhM9Fyuece+xP+G5eFsef+PVwTchcLF9pHHypi/dYWESZsJyLZfvTKS+/69PUcyTvCyLb2zQtmzYJmzSCmYva7kErStq19Dttigd5Ne2M2mVmRusKQLCq9IiIiTmbpz0tpEdSCBr6hxMdX3GjDOc2b2ze5eO89aF67OZ987EbNmhV3F/XcCg7bM6+89K4+uJpa3rWIbhhNURF8/bU9n6M3VZCK1aYNFBfDvn3g5+VHt0bdVHpFRETEvmLB0v1LGRg+kDVrID/f/hBbRbvvPvvuXevWwccfw9ixULNmxZy7RQsgK5LUM3uveH4zMSORmEYxuJncWLIETp/Wqg1V0e9XcAD7iMMPB37AWmqt9CwqvSIiIk5k78m9pOWkEdc8jsWLoVEj+92yijZoEDRtar97evy4feShogQFQY2CSPJLczh29thlv7/UVkpiRiLdG9sHjGfNgquugihjlneVcggKgvr1zy+92YXZpByt/KXLVHpFREScyNKfl+Jl9qJ3094sXmwvp474kb7ZDHffbd84oF8/aNWqYs8f5n/lKzjszdrL6cLTxDSK4cwZWLhQd3mrsjZt7MuWAXRt2JWanjUNGXFQ6RUREXEiy/Yvo2fTnhxJq8FPP1X8PO/v3X67fXviRx6p+HO3aRCOqdT9ikpvQnoCbiY3ohtGM28eFBbal1qTqun3Kzh4mD3o3bS3Sq+IiIgrK7AUsOrgKuLC7UuVeXg4dket4GD7aIMjinXLCA/ccsKvqPQmZiTSNqQtfl5+zJwJvXpB48YVn1EqR9u2kJoKeXn2v8eGxbIubR0FloJKzaHSKyIi4iTWpq2lsKSQgc3tS5X17l1xD5dVthYtwHoskh1XsGxZQnoC3Rt35+hRiI/XaENVd+5htl277L/HhsVSZC1iffr6Ss2h0isiIuIklv68lIZ+DQmt0ZqVKx072uBo55Yt23X88kpvdkE2u7N2E9Mohjlz7LPHw4c7JqNUjlat7HPp50YcWge3pm6NupU+4qDSKyIi4iSW/mxfqmzVKhNFRdWj9B4pOES+Jb/M70vKSAKge+PuzJplX66tdm0HhZRK4etrXxv6XOk1mUzEhsWq9IqIiLii9Jx0dmft/nW0ISzsl/Vuq6iAAKhVYl/B4aeTP5X5fQnpCQT7BlN6MoyNG7XtcHXRtu1vKziAfcRhy5EtnMw/WWkZVHpFREScQPyBeEyY6Nesv0OXKqtMLWq3BC5v2bJz6/MuXWrCwwOGDHFUOqlMbdr8dqcXoH9of2zYWHlwZaVlUOkVERFxAitSV9C+XntOpAVx8GDVHm04p1VoIB5Fdctceq2lVjYc3kBMoxjWroXoaKhRw8EhpVK0bWtfKeT4cfvfGwc0pmVQy0odcVDpFRERMZjNZiP+QDyxYbEsXgze3tCnj9Gpyq9FC7CdiCxz6d1xfAd5xXnENOrOmjX2pcqkevjjdsRApc/1qvSKiIgYbHfWbo7mHaV/qH20oV8/8PExOlX5RURAydFIdh4rW+lNSE/A3c2dWvmdOXZMpbc6ad4cAgNhzZrfPhYbFsv+7P0cyD5QKRlUekVERAwWnxqPh5sH7QJ7sHZt9RhtgN9WcPjp1F5KbaV/eXxiRiId6nVgY4IPbm7QvbvjM0rlMJshNhaWLfvtY32a9cHN5Eb8gfhKyaDSKyIiYrAVB1bQvXF3ktbUwGKxL9NVHTRvDmRFUlxaSFpO2l8en5CeQEyjGNasgfbtwd/f8Rml8sTFwcaNcPKXBRtqedeiS4MulTbioNIrIiJioJLSElYdXPXraENkpH25suqgZk0INtmXLfurud7jZ4+zP3s/3Rtrnre6GjgQbDZYvvy3j8WGxRJ/IL5MPwkoL5VeERERAyVnJnOm6Az9Qn9bqqw6adWgCeZS778svYnpiQA0cYvh0CGV3uqoYUP7A22/H3GIDYslKz+LH4/96PDrq/SKiIgYaEXqCvw8/fA+1YXMzOoz2nBOiwg3PHNb/nXpzUikoV9D9m9pDECPHpWRTirbwIGwdKn9ji9ATKMYfNx9KmXEQaVXRETEQPEH4undrDc/LPfAx6f6lb2ICLAc+etlyxLSE4hpHMPatSaioiA4uJICSqWKi4OjR+HHX27serl70atpL5VeERGR6qzAUkBCegL9Q/uzbJl9bV5vb6NTVaxzy5btOn7p0muxWtiUuYnuv6zP27NnJQaUStWjB/j6XjjisObQGopKihx6bZVeERERg6xPX0+RtYiYev1Zu9b+o9/q5tyyZScKjpFdkH3RY7Ye3UphSSEta8SwZ4/measzLy/o29c+4nBObFgsBSUFJGYkOvTaKr0iIiIGWZG6gpAaIWTtbENxcfUsveHhQJZ9BYe9J/de9JjEjES8zF7k/tQB0J3e6i4uDtatg7w8+9/b1W1HHd86Dh9xuOLSm5eXx+bNm1m6dCnLli0jOTmZ3NzciswmIiJSrcUfiKd/aH++/95EkybQsqXRiSqejw808mkBXHrZsoT0BDo16ETiOi9CQ6Fx48pMKJUtLg4sFli50v53N5Mb/UP7O1fpTU1N5dlnn6V9+/bUqlWL6OhoBg0axDXXXEOXLl0IDAykffv2PPvss6Smpjoqs4iISJWXXZBNcmbyr/O8AweCyWR0KsdoGeaLb3HTS5bexIzEX+d5NdpQ/TVvbl+L+o8jDpsyN5Fb5LgbqO5lOWjnzp0888wzzJs3j8DAQPr06cONN95IWFgYgYGB2Gw2srOzOXDgAMnJybz77ru8+OKLDB06lBdffJGoqCiHfQIiIiJV0aqDq7BhI9Irlr17YdIkoxM5TkQEbMi++AoOGWcySMtJo11QDK9vhfvvNyCgVLq4OFiyxL50mclkL72ltlI2Z2522DXLVHrbt2/P4MGDWbx4Mf3798fDw+NPj7dYLMTHx/PBBx/Qvn17iouLKySsiIhIdbEidQXhgeHsXN8Usxn69zc6keNEREDBykj2ZC294LVzm1KY0mOw2XSn11XExcH778PPP9v//WhWqxnhgeFsPLzRYdcsU+ndtm3bZd2t9fDwIC4ujri4OHbv3n3F4URERKqrc/O8y6ZBt25Qq5bRiRwnIgKsX0Sy/9R7WKwWPMy/3TxLzEikWa1m7EiqT716vzz4JtVe377g4WFfuiwiwv6x2LBYlq698BujilKmmd7yjCe0atXqit8rIiJSHWWcyWDvyb30adqf+PjquWrD751btqzEVsL+7P3nvZaQnkD3xt1Zu9Z+l7e6zjXL+WrWtK/Z+8e53kOnDznsmle0ekNoaCgLFiy45OsLFy4kLCzsikOJiIhUZ/Gp8QD4n+xHTk71L71hYWA6aV+27PdzvYUlhWw5soVOITFs2qTRBlcTF2dfwaHolz0p+jbr69DrXVHpPXToEHnnFle7iLy8PA4ePHilmURERKq1+APxtK/Xng0r61C7NnTqZHQix/L0hGbBdfGyBZxXepMzk7GUWqhxqjsWi0qvq4mLg/x8+5q9AEG+QbQKdtyEgEM2p9i8eTO1qvNwkoiIyBWy2Wy/zfMug6uvBrPZ6FSO1yLChG/++Ss4JGYk4uvhy+GUdgQGQuvWBgaUSte2LdSvf/6IQ3TDaIddr8yl96233iI0NPTXsYWHHnqIsLCwC37Vrl2byZMnM2jQIIeFFhERqar2ntxLZm4m0XVi2bSp+o82nBMRAaXHzy+9CekJRDeMZv0ad3r2BDftE+tSTCb7v/+/L71/a/w3h12vTKs3AAQHB9P6l2/BDh48SKNGjWjQoMF5x5hMJmrUqEHnzp259957KzapiIhINbAidQUebh4U7O2JzQYDBhidqHJEREDeN5HsiZyPzWYD7Hd6x7QdzzuJ8MILBgcUQ8TFwbRpcPgwNGwInRo4btanzKV31KhRjBo1CoA+ffrw73//m9jYWIcFExERqY7iD8TTrVE3Vn1fgzZt7F/oXUGLFmA9FklOUQ7Hzh6jwFLA0byjBBd2p6BA87yuKjbWfsd32TK47TbHXuuKfpCwatUqFV4REZHLZC21surgKvqF9uf7711ntAF+W7YM7Cs4JGbYN6XI3d2NGjWgQwcDw4lhgoIgOvr8EQdHKVPpTUxMvOILlOe9IiIi1cmWI1s4XXiaMGLJzHSt0tu0KZjPhOOGO3uy9pCQnkCLoBYkr61D9+72jQrENcXFwYoVUFLi2OuUqfT27duXvn37MmfOHPLz8//y+NzcXGbOnEmvXr3o169fuUOKiIhUBytSV1DTsyZHNkXj4wM9exqdqPK4u0N4Mw8CrOG/3unt1jCGdes02uDq4uIgOxs2bXLsdco007tv3z5eeOEFxowZg7u7O926daNjx46EhoYSGBiIzWYjOzubAwcOsGnTJjZu3IjVamXMmDHMnDnTsZ+BiIhIFRF/IJ5eTXuxYqoHvXuDt7fRiSpXRATknIkk+Ugy245uY1DIXeTkqPS6ui5dIDDQPuJw3XWOu06ZSm/jxo35+OOPeemll5gxYwbz58/nvffeo7Cw8LzjfHx86Ny5M5MmTWL06NGEhIQ4JLSIiEhVU2ApYF3aOp7v9TLProVXXjE6UeWLiICEw5GsC/wPACUHYvD0tM90iusym+3rVS9b5gSl95zg4GAmTpzIxIkTsVgspKWlcfLkSQCCgoJo0qQJHhrKERERuUBCegJF1iL8TvSnqMi15nnPadECctZEQmvw9/JnX0IU0dGud8dbLhQXB7ffDqdPO+4aZV69YfHixef93cPDg/DwcKKjo4mOjiY8PPzXwpuXl8fEiRMrNqmIiEgVFn8gnmDfYPaubUPjxhAZaXSiyndugwqAbg27sXaNWaMNAtjXq7bZYMMGx12jzKV3yJAhjBgxgiNHjvzpcV9//TWRkZG888475Q4nIiJSXcQfiKd/WH++X+bGwIH2tUldjX3Zspb2P/vEcPy45nnFrmFD+7bEjlz0q8yl96WXXmLRokVERUXx3nvvXfD6gQMHGDRoECNGjKBevXokJSVVaFAREZGq6nThaTZnbqZ9QH/27HHN0QaAxo3ByxbIcJ/3aZJ1B25u0L270anEWcTFQUKC485f5tL75JNPsnPnTrp168YDDzxA165d2bp1KxaLhUmTJtG6dWsSEhJ466232LhxI507d3ZcahERkSpk1cFVlNpKKd3XHzc36N/f6ETGcHOD8HCom3YP29c3pGNH8PMzOpU4i4ED4ZdHxRzish5kCw0NZcmSJcyePZuJEycSHR1NgwYNSEtL48Ybb+TNN9+kfv36jsoqIiJSJcWnxhNaK5Tk+FC6drUvz+SqWrSAfftg714YNszoNOJMevSwP9T4h8XBKswVbUM8YMAAevXqRUlJCWlpabRt25bJkyer8IqIiFzEyoMr6dusPytWuO5owzkREfa5zUOHXGtzDvlrXl72NXsd5bJL72effUZkZCTz58/nn//8J6+99hqpqam0atWKt99+G5vN5oicIiIiVVJOYQ67TuyinuVv5OSo9EZEQG6u/c89ehibRZyPI2e8y1x69+3bR//+/Rk3bhwtW7YkJSWFSZMm8fDDD7Nr1y769OnDQw89RJcuXUhOTnZcYhERkSpk4+GN2LBxens3AgMdeyerKoiIsP/eujXUqWNsFnE+/fo57txlLr3t2rVj69atfPTRR6xdu5aoqKhfX2vcuDHffvstc+fO5dixY3Tt2pUJEyY4JLCIiEhVkpiRSKB3IJuXtSA21r77lCs7V3q1VJlcjCO/ESpz6R02bBh79uzhH//4xyWPGTp0KLt27eK+++7j/fffr5CAIiIiVVliRiKd6nZj8yY3lx9tAGjQwL4Rwc03G51EXE2ZS++MGTMIDg7+y+P8/Px46623tE6viIi4vFJbKRsyNhB4thulpZrnBfumHMuW6U6vVL7LWrLscnTq1MlRpxYREakSfjr5E9mF2ZxJiyEqCho1MjqRiOu6oiXLRERE5K8lpidiwsSu76MZMMDoNCKuTaVXRETEQZIykoioFUX6zwH07m10GhHXptIrIiLiIIkZiTSwxgBak1bEaCq9IiIiDnCm6Aw7ju/AmtZNa9KKOAGVXhEREQfYdHgTNmxkJMZopQIRJ6DSKyIi4gCJGYn4ewZwYFOkSq+IE1DpFRERcYDEjERCPbuCzY2ePY1OIyIqvSIiIhXMZrORlJGE14kYwsKgYUOjE4mISq+IiEgF23dqH6cKTpGVonleEWeh0isiIlLBkjKSAEhdG63SK+IkVHpFREQqWGJ6Io29W0FBoEqviJNwNzqAiIhIdZOYkUitvBisDSAszOg0IgK60ysiIlKh8orz2H58O2f3dqNnTzCZjE4kIqDSKyIiUqE2Hd5Eqa2UQ+v0EJuIM1HpFRERqUCJGYn4mv2wHm2l0iviRDTTKyIiUoGSMpKoV9KV04FmoqKMTiMi5+hOr4iISAWx2WwkZiRiTYuhZ09w01dZEaeh/xxFREQqyP7s/WTlZ3FkYzeNNog4GZVeERGRCnJuU4riVPvKDSLiPDTTKyIiUkES0xMJNrUk3602HToYnUZEfk+lV0REpIIkHU7C83g3OvwN3PUVVsSpaLxBRESkApwtPsu2o9s4uVXr84o4I30fKiIiUgE2Z27GarNi/VkPsYk4I5VeERGRCpCUkYQXNbHltKFLF6PTiMgfOd14w9mzZ3n22WeJi4ujdu3auLm5MX369Iseu3v3buLi4vDz8yMoKIgxY8aQlZVVyYlFRETsO7H550XTtYsZb2+j04jIHzld6T1x4gQvvvgie/fupX379gCYTKYLjsvIyKBXr16kpqby8ssv8+ijj/Ldd99x9dVXY7FYKju2iIi4sHObUpzdo9EGEWfldOMNDRo04OjRo4SEhJCcnEyXS/yM6KWXXqKgoICUlBQaNWoEQHR0NFdffTXTpk3jjjvuqMzYIiLiwg6ePsjxs8fhpxh6PWB0GhG5GKe70+vp6UlISAhg/875UubOncuQIUN+LbwA/fv3p0WLFnz55ZcOzykiInJOYkYiAG6Z3YiJMTiMiFyU05Xesjh8+DAnTpygc+fOF7zWpUsXUlJSDEglIiKuKjE9Eb/i5nRqVQc/P6PTiMjFVMnSe+TIEQDq169/wWv169fn1KlTmusVEZFKk3Q4Ceshrc8r4syqZOktKCgAwMvL64LXvH95ZPbcMSIiIo5UYClg65Gt5P/UjZ49jU4jIpdSJUuvj48PAEVFRRe8VlhYeN4xIiIijrQ5czMlthJIj6FHD6PTiMilON3qDWVxbqzh3JjD7x05coSgoCA8PDwu+t6JEycSEBBw3sdGjhzJyJEjKz6oiIhUe0kZSbiX+tIyuC1BQUanEak6vvjiC7744ovzPpaTk+Ow61XJ0tuwYUOCg4PZtGnTBa9t3Ljx1/V9L2by5Ml07NjRkfFERMSF0eBJ8AAAIABJREFUJGYk4nGiC717VskvqSKGudhNxy1bttCpUyeHXK9KjjcADBs2jEWLFpGRkfHrx+Lj49m3bx833nijgclERMRV2Gw21qclUvCTHmITcXZO+W3pu+++y+nTp8nMzARgwYIFpKWlAfDggw/i7+/Pv/71L7766iv69u3LhAkTyM3N5dVXX6Vdu3aMHz/eyPgiIuIi0nLSOJ5/FDJi9BCbiJNzytL7+uuvc+jQIcC+BfG8efP45ptvMJlMjBkzBn9/fxo1asTq1at5+OGHefLJJ/Hy8mLIkCG8/vrrl5znFRERqUjnNqVo6t6NBg0MDiMif8opS++BAwfKdFxUVBRLly51cBoREZELHTx9kCdWPIFPdif6RYcYHUdE/kKVnekVERExyqHTh+g7vS9mPCiY+q3meUWqAJVeERGRy5Cek07f6X0xYeLpJivhTEOVXpEqwCnHG0RERJxRxpkM+k7vS6mtlMUjVjPu+saEhUFoqNHJROSvqPSKiIiUQWZuJv2m98NSauH7Uat48Nam7NkDq1eDyWR0OhH5Kyq9IiIif+FI7hH6Te9HQUkBK8es5rkJoaxaBUuWQIcORqcTkbJQ6RUREfkTx/KO0f+z/uQW57Jq7GrenxTGrFkwezb062d0OhEpK5VeERGRSzh+9jj9P+vP6cLTrBq3ivlTmjN5Mrz7LowYYXQ6EbkcKr0iIiIXkZWfRexnsWTlZ7Fq3CoSF7Xg8cfh6afhvvuMTicil0ulV0RE5A/yLfnEfhbLsbPHWDl2Jfs3RHL77XDHHfD880anE5ErodIrIiLyB1/t/Iptx7ax9a6tnNkfxY03wrXXwvvva6UGkapKpVdEROQPZm6fSe+mvfHMvop+g6FzZ5g1C9z1VVOkytKObCIiIr9zJPcI8QfiGdx4NAMHQsOGsGAB+PgYnUxEykOlV0RE5Hdm75iNu5s7Ux4djpsbLF0KtWoZnUpEyks/qBEREfmdmdtn0tpjMFu31WLHDmjQwOhEIlIRdKdXRETkF3uy9pB8JJn8DbcwYABERRmdSEQqikqviIjIL2b+OBM/jwD2LhzMuHFGpxGRiqTSKyIiAthsNmbtmEVY4XACanhz/fVGJxKRiqTSKyIiAiRlJJGancrhpbcwciR4exudSEQqkkqviIgIMOPHGdTxbETW5t6MH290GhGpaFq9QUREXJ7FauHLXV9S58h4giPd6NLF6EQiUtF0p1dERFze9/u/Jys/i/3zb2H8eG01LFIdqfSKiIjLm7F9BvXNrbFmtmP0aKPTiIgjqPSKiIhLyy3K5ds93+K+azTXxJmoX9/oRCLiCCq9IiLi0ubvmU9BSQHpi0dqbV6RakwPsomIiEubsX0Gjaw9yTc35dprjU4jIo6iO70iIuKyjuYdZUXqCs6sG80tt4CXl9GJRMRRVHpFRMRlzdkxBzfMnEkartEGkWpO4w0iIuKyZmyfQUjOIOpE1KZDB6PTiIgj6U6viIi4pJ9O/sTmzM0cXzGaceO0Nq9IdafSKyIiLmnmjzPxNvlj2zuEW24xOo2IOJrGG0RExOXYbDZmbp9JjUPD6BHnTUiI0YlExNF0p1dERFzOhsMb2J+9n5Mr7dsOi0j1pzu9IiLicmb+OJMapQ3wOduHQYOMTiMilUF3ekVExKVYrBbm7JxD6baR3HqLGQ8PoxOJSGVQ6RUREZeyPHU5J/JPULDhFq3NK+JCNN4gIiIuZeb2mfgVRNG8QXvatTM6jYhUFt3pFRERl3Gm6Azzds/jbNItjB+nhXlFXInu9IqIiMuYs2MOhSVFmLePYdRco9OISGVS6RUREZcxJWUKNY4MZGDfRgQFGZ1GRCqTSq+IiLiEXSd2kXQ4CdZ+xT9eNzqNiFQ2lV4REXEJU1Om4mUNon7RtQwYYHQaEalsepBNRESqPYvVwmfbPqdkyy3cfYcXbvrqJ+Jy9J+9iIhUe0t+XsLx/GOYtt6mbYdFXJTGG0REpNqbkjIFr5MdGdrzKkJCjE4jIkbQnV4REanWjuYdZeHeRRQl3cbddxudRkSMotIrIiLV2owfZ0CpOxFFI+nVy+g0ImIUlV4REXFqBZYCvtz5JSWlJZf9XpvNxkebpmDbPZT7bquNSZuwibgslV4REXFqT654kpu+volX17962e/deHgj+07vxn37eMaMcUA4EakyVHpFRMRprUtbxzsb38Gc1ZZnVj7L9mPbL+v9n26ZgjmvMSO79Scw0EEhRaRKUOkVERGnlG/JZ9y82/A41g3rh0m4Zbfg1m/GYrFayvz+Gdu+wJo8jnvvNjs4rYg4O5VeERFxSs+sfIaD2Wm4L57C8sW+mOZP58djP/LS2pfK9P65u+ZSUJpLq6JxREc7OKyIOD2VXhERcTpJGUlMTpyMdcXzTP5XJLGxMPnxTthWP8WLa/6PlCMpf3mO95OmwIG+TBgTpgfYRESlV0REnEthSSFj543H/UQn+no/wh132D9+990wwOcpTCfaMHruWIpKii55jtTsVJKOrsJr122MGlVJwUXEqan0ioiIU3l+1fP8fHI/5kVTmPKJ+693aU0mmPqJJ77fT2P3iT28sPrFS57j0+RpmIr8Gd3pBvz8Kim4iDg1lV4REXEamzM389/1r1K68hlefawNzZqd/3qDBvDppKuwrXqGV9a9wqbDmy44h7XUykcbp2HbfjMP3O1bOcFFxOmp9IqIiFMoKimyjzWcbEdPtye4556LHzd8OIxq8iQcbc+or8ZSWFJ43uvxB+LJsqTT2nIbV11VCcFFpEpQ6RUREacwae0k9pzYg+nbqUz9xAO3P/kK9d477oSsn87+7P08/cMz57329topcDyKR2/Wkg0i8huVXhERMdzWo1t5ae3LlK5+iv88fBXh4X9+fK1aMOut1tjiX+T1xNdISE8A4FTBKZYenIfPntu46SYt2SAiv1HpFRERQ1msFsbOG4/5VBQxJf/igQfK9r6+fWFC9CNwuCujvhxHviWfz1JmYS0t5db2o/HxcWxuEala3I0OICIiru2Vda+w/dh2POZvZNr3nn861nDBe18ys6jPNFLrtefJ759i4fY1sG8wDz9X13GBRaRKUukVERHDbD+2nRdWv4ht3RNMur8jLVpc3vu9veGr/7Wk8wMv8Y75YQDaljxLy5YOCCsiVZrGG0RExBD5lnzGzBuH2+kIuuQ/w8SJV3aeDh3gxcET4FBPyK3Pk8OvqdigIlIt6E6viIhUOovVwoivRrDz6F6Yu4bpS70wm6/8fE887sbCvkvZn3mK4S95VFxQEak2VHpFRASA5Mxk2oS0wcvdy6HXsdls3LXoLpbuW4Z1xiL+c19HWrUq3znNZlixxJfsbF88PSsmp4hULxpvEBERpiYsoPPHnRn58dMOv9ZTPzzF1K1T4dup3Np9II89VjHnrVEDGjWqmHOJSPWj0isi4uL2ZR3gjsVjoTCAbw9/SE7hGYdd650N7/DyupfxXvMafWqP5pNPwKTldEWkEqj0ioi4sMKSQnq+Mxxrbm3u9kig1K2Af839yCHX+nLnl0xYOgG/7Y/QIusR5s5FowgiUmlUekVEXNgNH07kWOlOJjT4mveei8L/0C1M3f0mxdbiCr1OfGo8o78ZTUDaKPw3/JfFiyEgoEIvISLyp1R6RURc1Js/zGBJ1ge0y3iXyY93wM0NHuj0CAUeh3lv9ZwKu07KkRSGzhmK38m+lM6bwtIlbjRsWGGnFxEpE5VeEREXtPXwTh5ZeRc1fh7Lytdv/3Wu9snb2uB+4BpeWv0qNput3NdJzU7lmpnX4HkmktxP5vLtN560aVPu04qIXDaVXhERF5NXnEe/D4dTeiqMJfe9T+3avz1JVrMm3FDvMbLctrNg5/flus7xs8cZOGMgljx/Tr79HdM/rkmfPuUMLyJyhVR6RURciM1mI+69O8guyeDfLb6mZzffC475z919ILMTTyx89Yqvk1uUy6CZgzh+Oo9Tby3jv88FM3JkOYKLiJSTSq+IiAt5Ycn/WH9mNjEnPuWFB1te9JhmzUxEWx5jb3E8WzJTLvsaNpuN0fNGs+vYT+T+bwkP3BrKo4+WN7mISPmo9IqIuIg1qRt5fsND1NrzIEtfH/Gn6+O+PGYYZDfj0XmvXfZ1JidNZsHeBZR+NYvru7Vn8mStxSsixlPpFRFxASfzTzJ46o1wpCPLH38Vf/8/P75vb3capk9k1Yk5HDp9qMzX2ZCxgSdWPEHNbY/SocYQZs60bxEsImI0lV4RkWqu1FZK/3fHkFd8llc6fUnnDn+9I4TJBP8efBu2Qn+eXfpmma5zquAUN319EzVyOuO1/iW+/hp8fMqbXkSkYqj0iohUc0/On8y2/CXEnpnBY3c2KfP7xo2qie/Oe5m152OyC7L/9Fibzcb4b8dzPOcMOZ/MYdbnHlqLV0ScikqviEg1Vmor5e2Nb1Er9XbmvxZ3WbO13t5wV4f7sVgtvLX+wz899q0Nb7Fg7wIKZ0/nmQlNGDCgnMFFRCqYSq+ISDU2f/MGirzTuedvt1KjxuW//7F76mHaPoY3Et6iqKToosdsPLyRx5c/ju/WR+jX8FqeeaacoUVEHEClV0SkGnt18RxMefV5clSPK3p//fowOPARcm1H+XzbzAtezy7I5qavbsI7uyP+m17Wg2si4rRUekVEqilraSmb8r8i0noj/n5X/n/3z9wbCXv+zvPLX6PUVvrrx202G7ctuI2jp0+TN20Oc2Z5ULduRSQXEal4Kr0iItXUh4sTsPpmck/vEeU6T5cu0DrnMTKKdrNk35JfP/72hreZv2c+hbOn8dLjTenVq7yJRUQcp8qW3lWrVuHm5nbRXxs3bjQ6noiI4d5bNQfz2UbcMySm3Of695i/QUZXnltu35p40+FNPLb8MbxSJjK4+XU8/ni5LyEi4lDuRgcorwkTJtClS5fzPhYeHm5QGhER53Am18pu09d09R2Ju7n89zeGDTNR+93H2NxoOMv3L+eOhXfieaoDtbe9wvTN4FZlb6GIiKuo8qW3Z8+e3HDDDUbHEBFxKv+ZvQ5bzaM8Gle+0YZzPDzg4UHX8/Sx5gyZNQST1RfrjJV8tciToKAKuYSIiENV+e/NbTYbubm5lJSUGB1FRMRpfJY8B6/CJtwQ3bXCznn3XWbMGx+luLSYojlTee3fzehacacXEXGoKl96x48fT0BAAD4+PvTr14/k5GSjI4mIGCr1YAkZfnPpGzwC0+XsRvEXgoJgbJs74c1UhrW+ngcfrLBTi4g4XJUdb/Dy8mL48OEMGjSIOnXqsHPnTl577TV69uxJQkIC7du3NzqiiIgh/u/z1VDzOE9ee1OFn/vfT5lwN4fyn/9wWbu7iYgYrcqW3piYGGJifnsieciQIQwfPpx27drxz3/+kyVLlvzJu0VEqiebDebu/ZKazULp1bxThZ+/WTP44IMKP62IiMNV+fGG3wsPD+e6665j5cqV2Gw2o+OIiFS6tetLONNwLkNCK3a0QUSkqquyd3ovpVGjRhQXF3P27Flq1qx5wesTJ04kICDgvI+NHDmSkSNHVlZEERGHeWXOD1DnJI/GVfxog4hIRfriiy/44osvzvtYTk6Ow65X7UpvamoqPj4+Fy28AJMnT6Zjx46VnEpExPHy82HFkS+pHdScjg30XIOIOLeL3XTcsmULnTpV/GgWVOHxhhMnTlzwsW3btrFgwQIGDBhgQCIREWN9Pc+Cpfk33Nz2Jo02iIj8QZW903vTTTfh6+tLTEwMISEh7Nq1i48++oiaNWvyyiuvGB1PRKTSvfntCmidzV09KmZDChGR6qTKlt6hQ4cyc+ZMJk+ezJkzZwgJCWH48OE8++yzhIWFGR1PRKRSZWRASvGX1HNvSduQtkbHERFxOlW29D7wwAM88MADRscQEXEKUz8rglbzGNtpgkYbREQuosrO9IqIiJ3NBh8sXw7eOdzaUaMNIiIXo9IrIlLFJSVBZuCXNPWJonVIa6PjiIg4JZVeEZEq7pNphZhazWdcF63NKyJyKSq9IiJVWEEBzN60DJtnLje31WiDiMilqPSKiFRh334L+WFzaFmrHZF1Io2OIyLitFR6RUSqsE8/K8Ct1QJu7aC7vCIif0alV0SkCrLZICUF4g8todT9LCNaq/SKiPyZKrtOr4iIq0lLgx9+gJUr7b9nZIDX6Dm0DO5ARFCE0fFERJyaSq+IiJM6evS3grtyJezfDyYTXHUVjBgB3XufZcz2RYxs97TRUUVEnJ5Kr4hIJTl71l5WV68Gsxnc3Oy/X+yX1QqHDtnfFxUF11wDnXpm4d9iK/vPppByNIV/HtpMfkm+RhtERMpApVdEpBLk58Pgv1tYX+tegh5PpIapDr4E4UMQ3rZffpUG4WUNwqs0CC+bP7XCfsZWL4V9eSnMP7qVd3dnwG6o6VmTq+pexcDwgUweOJmwwDCjPz0REaen0isi4mCFhfD3oRbWhYzC1OpbruswnjxLHifzT5KVf4j0gpOczD9JbnHu+Y8XZ0JITggd6nVgdNvRdKjfgfb12tO8dnPcTHoOWUTkcqj0iog4UFERXDe0hFWBo6HVfL4e8TXXRV530WOLrcWcKjjFyfyTnC48TVhgGPX96ldyYhGR6kmlV0TEQYqL4YZhVlb4jYFWc/n6xq8uWXgBPM2e1KtZj3o161ViShER16Cfj4mIOIDFAjeOsLLUexy0/pI5N85maKuhRscSEXFZKr0iIhXMYoGbR5ay0O12aDuLWcNmMjxquNGxRERcmkqviEgFKimB0beWMs96B6arPufzGz7npjY3GR1LRMTlqfSKiFQQqxXGjC3lq4K7of1Upg+dzqi2o4yOJSIiqPSKiFQIqxXG32bjizP3QcdPmHrdVEa3G210LBER+YVKr4hIOSUnQ6/eNj7PegA6f8Anf/+Ese3HGh1LRER+R6VXROQKHTsG//gHdL42hW3tBkD0e3w05CNu63Cb0dFEROQPVHpFxCUdPVZK6Nj/o/7NL/Dv/2aQmVn29xYXw+uvQ/POB/j87C1wV0caRaWzcORC7uh0h+NCi4jIFVPpFRGXc/CQlZaP3snB0Gc40fI/TDrblIaPXEeHEYuZNt1Kbu6l3/vdd9CqUxaPrZhI/u2RBHZcyYdDPmTHvTsY0mJI5X0SIiJyWVR6RcSl7N1XQuunx3AmbCqvdp/OqX8d4fX+79G4bRpbWw9m/NYwal//f1x/ayZLltiXIAPYswcGDslnyH9e4tD14fj2+JQX+j3D/gn7uLPTnbi7aYNLERFnpv+XFhGXsXV7MTGvjaQwdAH/i53N3T1vBODhXnczseddbMrcxOurP2RerZf5tvQ5vp1+LQFP30Wfpv1YmPYZpn7P4l7jBPd0uYene/2b4BrBBn9GIiJSViq9IuIS1m8opO//hlPSdDmfDf6GW6OvPe91k8lEdMNo5oyKJqfwDWb8OJO3an3IvlbXsKDEB1u7Aka0GsnLV/8fYYFhBn0WIiJypVR6RaTa+37VWQZ9dj22Juv5etgibrjq6j89PsA7gPui7+XeLvew4fAGvvvpO66PvJ5ODTpVUmIREaloKr0iUq19890Zbpw3BFPDFBbdvIRronqX+b0mk4lujbrRrVE3ByYUEZHKoNIrItXWZ19lM255HOb6e1kxbjm9w1VeRURclUqviFRL7007wf0bBuBZN521d/5AdOOORkcSEREDqfSKSLVis8HT/81kUtrV+ASfJPGeVVxVv43RsURExGAqvSJSbZw5A9fet441dUfgF+zGhntX0yqkpdGxRETECWhzChGpFrZvtxF+y1usCe1LVL0Ifnp0swqviIj8SqVXRKq8Tz/Po8OkkWR1fojbWk9g68QV1KtZz+hYIiLiRDTeICJVVlER3Pb4HmaVDMO9ZRoz/v4Vt3QYbnQsERFxQiq9IuIUiovtD6F5eZXt+PR06H//XPa1Hkc938b8cNcmWgVHOjakiIhUWSq9ImK4nT+focOb/bC45VIrN4aWvt3p2SyGAR2j6NjeTFDQ+ccvW17C0Hf/SUHH14itN4J54z+lpmdNY8KLiEiVoNIrIobKybHR/b/jKQneR0//W9h9ZgMb3GewId/Ka/F+ML0b/jkxtPKLoWdoN/KLC3n/+M2YOqzjxb+9wVP9H8JkMhn9aYiIiJNT6RURw5SUQPTD/+VMk294p/t87r/6OgDOFp8lKX0Ti7YlsKZ2Irvz3mOD6QU2AJT6UrOpPwvHrqRPaE9D84uISNWh0isihrDZ4IZHV/BTo38xqtFTvxZegBqeNegf3of+4X1+OdbGvlP7SExPZO+J/TzQ7R7q+9U3KLmIiFRFKr0iYojn3jzEQq+bae1zNZ+Nf/5PjzWZTLQIakGLoBaVlE5ERKobrdMrIpXu628LeGHPDQR4+7H6wZmY3cxGRxIRkWpOd3pFpFKlpNgY+fl9uLXeRfydCQT5Bv31m0RERMpJd3pFnFxODpw5A1ar0UnK7/Bh6PfYR5S0ncr/Bn9Ap4YdjI4kIiIuQnd6RZzE6dOwcyek7MgnaW8q2zNSOXA6lVzzQSjxhrPBeFiC8SWYmqZg/NyCCfAIplYNX2rWhPr14bHHoEmT8uXIyoI33oCQELj5ZqhXQbv55uVBvzFJnP7bA4yLuo87o8dWzIlFRETKQKVXxCCzvkvjs9Wr2XcylSOF+ynwToXA/eB3FAKAAHC3+dDAsylWiskpOUGhLZccIOd35zGX+uJRHIz1ZCgfD3iW58f3YeJE8PS8vDylpfDppzYmTp9Ofsy/sO2ty8NDx9G79ihuuzmYoUOh5hXu/2C1wrCxx9jXYRjtg7vw4Q1vXNmJRERErpBKr0gl27b7LDe+9TL7gl+DGkV4edaljjmM0IBwWjfsT5fwcFqGhBEeGE69mvXO23ihsKSQE2dPcCL/xAW/r9i/kk0N+/Jk8gg+7f4aH7/emN69y5hpG4x9dCfbGt8DV6/luuY3UVJazNJ6j7G69FFWLR6E5+tjuT5qCGNHe3L11eDhUfbP+ZHHLXzvfxO1Aq18N+4rPM2X2chFRETKSaVXpJLk5NgY/cpsFhU/BsFZDKv3GB/f9giBPrXKfA5vd28aBzSmcUDjC16b1M/GjB9n8LDX4+xvGUmfp59iVLNHeONVL+rWvfj5cnPhX8/m896OF7F1f43GNcKYOnwF/cP6A5CVn8XsHbP5KHga2yOHMbcoiC/fHUnAY2MZ3a8TNww1YTLZ545Pn7b//sdfWVmwyusJ3GLWs2D0DzTwa3BF//xERETKw2Sz2WxGh6gMW7ZsoVOnTiQnJ9OxY0ej44gLsVrhhY9SeHnrg1garKMVQ/n6zteIqh/mkOudKTrDC6tf5M3EN7Gdbor3qjd59Y4h3HUXmH9ZGcxmg7lz4a43FpHd7X7MAUd5qudT/LPX43i5e130vDuP72Ta1ulM2zKDrKIjuJ+KomTbCLD4gnsRmItw9yrG07cID58iPLyL8fAuwuSVS6b/At6Ke4sHuz7okM9ZRESqB0f2NZVeEQda9EMW4z//N1lNPyKguBX/u+4tRnaNrZRr78nawz0LHmRV+nL4aRCtM95k2usRBAbC7Q+nsdpnArSaT68GA/l02Ls0r928TOctKS1hReoKpqVMZ/G+pZhM4GX2wtvDEy93LzzNnniZvc77898a/41nej9z3qiGiIjIHzmyr2m8QcQBUg+WcON//8cW/2cwN7QxIXIyr954Lx7myxiELafIOpH8MH4Z8/fM594FE9kV3oYuTz6Cubg2pb2eI9DHnw+v/5LhUcMvq4y6u7kT1zyOuOZxDkwvIiJSsVR6RYDdx/ZzKj+bLk3aXfFDVj/tszJt2Va+27Ga7e5TsYXspLffP5hz5yTq+gVXcOKyMZlMDG01lLjmcby89j+8Yv4PJRRzT8cHeHnAC/h7+RuSS0REpLKp9IpLO3z6ODd/+Czr8j8Ct1JMVi+CLB2I9IumV1hXbujalY7Nwi56J/TocQtTlmzh222r2Z67moI668D7DG4h3jR378PHI6fRO6KTAZ/VhXw8fHih33Pc1fkOCksKCa8dbnQkERGRSqXSKy6pwFLIHZ++xRcZkygtMdMl/3X6RnRj/cGN7M3byPqCxayzvM1Le8GtMIg6RdG08utKx4btSE7bw9bs1ZwJWA9eeZhq+NLI52/0avo4o3v0pm+LLpd8GMxoDf0bGh1BRETEECq94lJsNhvPz/2Slzc/QbHnYZpm3cdntz9Nry5BvxzRDbCvuLBxx0m+3bSRtQc3sLd0A2uK32b1kVOYbDWpV6MHA+o+xS09ejO4fedKndUVERGRy6fSKy5j9rok7v12Itk1kwjIuY6PBn/P2CEtLnqs2QwxVwURc9U1wDUAlJba2Jl+mMhG9fAw6z8dERGRqkRfuaXa27D3IKOm/JNU39l4FrXnqcgfeOHpvri5Xd553NxMtG3ayDEhRURExKFUeqVaOnj8JJMXLuHb3Ys45DMfU2ltRvpM5ZP/3Iqvj9noeCIiIlLJVHqlWrDZbKzauZu3ly1kdeYismsmgFspPpbOxPo9x7TH76dhcE2jY4qIiIhBVHqlyiq0FDF99Rqmrl9IytlFFNc4AMW+1Cm+mptqfMhDgwbTrU19o2OKiIiIE1DplSpnw76feXj2uyQWTsXmeQbTmSaElQzhhoghTLy+L/WDvY2OKCIiIk5GpVeqBGtpKW9/t5zX1r5Dpu9iKAiineV+7u18M+MGtcHLq+zb6IqIiIjrUekVp3bsdC4PT/uMuRnvUOS3F8+i9txUewpv3HszDUJ0R1dERETKRqVXnFL8lv089vW7pDAFPM5SzzKUh1t9zMPDemA2666uiIiIXB6VXnEap3KKeO6LhczaPZWTgUswlQbS1f1eXht+Dz3aNjE6noiIiFRhKr1iqNJS+OS7FN5cNZXd7rPA9yR+5mjG1/mI18feQqCTTPoNAAATdUlEQVSfj9ERRUREpBpQ6ZUrcir3LEs272Llzh2kZG4ns+AAwZ5NiAyKIrpZFP3aRnFViyDMl9gHIunHLJ7+aiarc6ZiCdqG2aMuf/MZz9N/H8fADq0r95MRERGRak+lV/6UxWoh4ad9LEvZzsYDO9h7ejvH2UFxjVQw2cBmwr0ojADC2FuyjO1n3+Or3VbYDZwNxvdsFHXdomgeEEWHRlHk5J/ly33TyA5eCCYI9b2We9r/HxMGD8TT3cPoT1dERESqKZVeAx1Is/DU9AXMT/8YqzmPgfXG8sb4m2nexM+QPDabjX3HMvhiXRLxezew83QSp7yTwb0QAFNeffwL2xDpfR1X+behd6s2DIqOon5QjV/PUWgpZs2OfazevYst6bv42byLo9Z1HHD7lOXHigHw97+KcQ1e5YURo2hcO9iQz1VERERci8uV3m/WbSewXjihDQIMuX5REXzy9UHeWP0xqf5TwO8owUExeFOLhaV3s/CDhwkvGMk/B97B+AGdcXNz3EoFeUVnWbA5mQVbktiUuYF0WxIWn0wATDlNCS7qRj+vYfQO7cg1ndrQqVUQbm5/fk5vD08GdGjNgD+MKJSUlrDjcCqFxSV0C49y1KckIiIiclEuV3on7RzHpGww5TXAv6gVDT2jaFG7FZ2atKJvmyi6RAXj6flb0bTZwGKxl9Xi4vN/BQRAUBCXnFv9veSUEp6d+R3fn/wAS9NlmEP86FvrVibdcBcxYW0B2JGezqMzpxBf8in/2PAxD3x/FcOa3cmrY26hXq3yl3RrqZVvN21m6rqlJBxbyimfTeBmheIa+OR0oaXXGHrU78bwbl3p3ake7hX4b4e7mzvtG7eouBOKiIiIXAaTzWazGR2iMmzZsoVOnTrx8kczyQR+zNxNat4uTth2U+i7D8wl9gPza+NWGIINKzZKwWQFU6m9HP7+z9igMBBy6+NpqUdNW30CzPWo41WfejXr0zCgHqF16pNXVMjHm6dwtP6n4H+Y+tZo7u16FxOvvokanjUumtVSYuXlr77n/aSPOFZrIVg9aWMawXPX3sHfO0XjYS777Ouew0d4b+kylv68lFTTckq9TkFBLYJyYokOjmXIVTEM6xVF3WCX+/5HREREnMy5vpacnEzHjh0r9NwuV3ov9g+xuMRC0k8/s2rnbpLTdnOq4CQe7mY8zGbczW64m814mN3sH3M34+HuhtnNRNbZUxzJPcKJwqOcLjlCru0oxe4nL7i22VqT2JBbeOG6u4hu3OGycidsP8JjM6eRWPwxtoAD9vMVBeFtrUsNQggw16W2V11CfOtSzy+ExrXr4mn2YMH2lWzNXUa+/zawmfA62Zm2PnEMuyqOOwZFExSokivy/+3de0xTdx8G8OdUaoFCmQ6UMh0wDNvcBW8wRNgmKjIncTgvaDQSRX2Xec1UhrtlYrxgzJxERRwjROam87Zs06kMjXMzuCkmb+II/CHgoOKtc4DQSfm9fyw0w6Iv9JxeeT5J//BXTnlOvmn7eHIOh4iIXIs9Sy+bD4C+Xmq8PPRZvDz0WdmvZWoz4UbzDRiaDKj7y4DmVhOmDH0N/hrbLk6Le0GPnzdl4a/GTGz84hz+W1eFG6YGGP++gb/MDaiXGnDV679oa74BNN8GGv75P4x0bwAGmydiwmNr8J+kCRj1LC8YIyIiot6LpVdhGi8NBgcMxuCAwcATyr2uzl+Fjf95GcDLXT4vBPDnX22o/OMmbjc2YcKoCKi9/s9VZ0RERES9BEuvh5AkoF+AF14K0Ds7ChEREZHL4aFAIiIiIvJ4LL1ERERE5PFYeomIiIjI47H0EhEREZHHY+klIiIiIo/H0ktEREREHs9tS6/JZEJmZiZCQkLg6+uL2NhYlJSUODsWEREREbkgty296enp+OSTTzB37lxs374dffr0waRJk/Dzzz87OxoRERERuRi3LL0XLlzA/v37sWnTJmzevBkZGRkoLS1FaGgo1qxZ4+x45CK+/PJLZ0cgB+K8exfOu3fhvEkJbll6Dx48CC8vLyxatMiyptFosGDBApw/fx51dXVOTEeugh+SvQvn3btw3r0L501KcMvSW15ejsjISPj5+XVaj46OBgBcvnzZGbGIiIiIyEW5Zek1GAzQ6/VW6x1r9fX1jo5ERERERC7MLUtvS0sLNBqN1bq3t7fleSIiIiKiDl7ODmALHx8fmEwmq/XW1lbL8w/qKMK///67fcORy7h79y4uXbrk7BjkIJx378J59y6cd+/R0dPscQDTLUuvXq/v8hQGg8EAAAgJCbF6rrq6GgAwZ84cu2Yj1zJy5EhnRyAH4rx7F867d+G8e5fq6mqMGTNG0dd0y9I7fPhwnDlzBo2NjfD397esl5WVAQCGDRtmtc3EiRNRXFyMsLCwLo8EExEREZFztbS0oLq6GhMnTlT8tSUhhFD8Ve3swoULiI2NxZYtW/DOO+8A+OcObc8//zyCgoLwyy+/ODkhEREREbkStzzSGxMTg+nTpyMrKws3btxAREQEioqKUFtbi8LCQmfHIyIiIiIX45ZHeoF/jux+8MEHKC4uhtFoRFRUFLKzszFhwgRnRyMiIiIiF+O2pZeIiIiIqLvc8u/0EhERERH1hNuXXpPJhMzMTISEhMDX1xexsbEoKSnp1rZ//vknFi1ahKCgIPj5+SExMRHl5eV2Tkxy2DrvH3/8EfPnz0dkZCS0Wi0iIiKwcOFCXL9+3QGpyVZy3t//tnDhQqhUKqSkpNghJSlF7rxLSkqQmJiIxx57DDqdDqNGjcKBAwfsmJjkkDPvkpISjBs3DgMGDIC/vz+ioqKQm5uL9vZ2O6cmWzU3N+Ojjz5CcnIy+vfvD5VKhaKiom5vr0hnE24uLS1NqNVqsWbNGrFnzx4RFxcn1Gq1OHfu3CO3M5vNIi4uTvj5+Yl169aJHTt2iOeee07odDpRVVXloPTUU7bOe+TIkSIiIkK8++67oqCgQKxdu1bodDoRHBwsrl+/7qD01FO2zvvffv31V6FWq4WPj49ISUmxY1qSS868P//8c6FSqURycrLYuXOn2L17t1i5cqXYunWrA5KTLWyd9/Hjx4UkSeKFF14Q27ZtE/n5+eKNN94QkiSJ5cuXOyg99dTVq1eFJEkiLCxMjB07VkiSJIqKirq1rVKdza1Lb1lZmZAkqdOHWmtrqxgyZIiIi4t75Lb79+8XkiSJQ4cOWdZu3rwp+vXrJ2bPnm23zGQ7OfP+6aefrNbOnj0rJEkS77//vuJZST458+7Q3t4uRo8eLTIyMkRYWBhLrwuTM++rV68KHx8fsWLFCnvHJIXImffs2bOFt7e3MBqNndZfeeUVERAQYJe8JJ/JZBINDQ1CCCF+++23HpVepTqbW5/ecPDgQXh5eWHRokWWNY1GgwULFuD8+fOoq6t75LbBwcGYOnWqZS0wMBAzZszAN998g/v379s1O/WcnHnHx8dbrSUkJKB///6oqKiwS16SR868O+zduxdXrlzB+vXrIXjNrkuTM++8vDwIIbBu3ToAQFNTE+ft4uTM28fHBxqNBgEBAZ3Wg4OD4evra7fMJE/fvn0xYMAAAOjx+1OpzubWpbe8vByRkZHw8/PrtB4dHQ0AuHz58iO3HTFihNV6dHQ07t27h8rKSmXDkmxy5t2VpqYmNDY2IjAwULGMpBy5825sbERmZibWrl2LgQMH2i0nKUPOvEtKSvDMM8/gu+++w6BBg6DT6RAYGIgPP/yQ5ddFyZn30qVL0d7ejsWLF6OiogI1NTXIy8vDkSNHkJWVZdfc5BxKdTa3Lr0GgwF6vd5qvWOtvr7eLtuScyg9s23btuH+/fuYOXOmIvlIWXLnvW7dOmi1WqxcudIu+UhZcuZdVVWF2tpazJ8/HxkZGTh06BBee+01rF+/Hu+9957dMpPt5Mw7KioKpaWl+PbbbzF06FCEh4dj6dKlyM3NxdKlS+2WmZxHqe9/t7wjW4eWlhZoNBqrdW9vb8vzD9Pa2mrztuQccub9oLNnz+Ljjz/GzJkz8eqrryoVkRQkZ96VlZXYvn07vvrqK6jVartlJOXImXfH6QybN2/G6tWrAQCpqam4c+cOPv30U6xdu9bqiCI5l5x5V1RU4PXXX0doaCi2bNkCb29v7Nu3D0uWLMHAgQMxZcoUu+Um51Cqs7n1kV4fHx+YTCar9dbWVsvz9tiWnEOpmVVUVCA1NRUvvvgiPvvsM0UzknLkzHv58uUYM2YMUlNT7ZaPlCX381ySJMyaNavTelpaGlpaWnp86hPZn5x5r1q1Cl5eXjhz5gzmzJmDadOm4fDhw4iPj8fbb78Ns9lst9zkHEp9/7t16dXr9V0e0jYYDACAkJAQu2xLzqHEzK5du4akpCT069cPx44dg1arVTwnKcPWeZeWluLEiRNYtmwZqqurLY+2tjbcu3cPNTU1aGxstGt26jk57++O5x48d7vjohmj0ahUTFKInHmfO3cOiYmJVhetpaSkoL6+HjU1NcqGJadTqrO5dekdPnw4Kisrrb7AysrKAADDhg176LbDhg3DpUuXrC5yKCsrg1arRWRkpPKBSRY58waA27dvIykpCffv38eJEyd4cZOLs3XetbW1AICpU6fiqaeesjzq6+tRWlqK8PBwFBYW2jc89Zic9/eoUaMghMAff/zRab3jSzIoKEjhtCSXnHm3tbV1eTS34wr+trY2BZOSK1Cqs7l16Z02bRrMZjPy8/MtayaTCYWFhYiNjcUTTzwBALh+/ToqKio6vRGmTZuGhoYGHD582LJ269YtfP3110hJSeF5gC5Izrybm5sxadIkGAwGHDt2DBEREQ7PTz1j67zHjRuHo0ePdnocOXIEQUFBiI6OxtGjRzF58mSn7BM9nJz3d8fFqAUFBZa19vZ2FBYW4vHHH8fIkSMdtBfUXXLmPXz4cJw8eRJ37tyxrJnNZhw4cAA6nY6f727Orp2t23/R10XNmDHDckeX3bt3i7i4ONG3b99ONyOYN2+ekCRJ1NTUWNbMZrMYPXq08Pf373R3j4CAAFFZWemMXaFusHXeU6ZMEZIkiQULFoi9e/d2ehw9etQZu0LdYOu8uxIaGsqbU7g4OfMeP368UKlUYvHixWLHjh1iwoQJQpIksWfPHkfvBnWTrfM+fvy4UKlUYsiQISInJ0ds375djB49WkiSJDZs2OCMXaFuys3NFdnZ2eKtt94SkiSJN998U2RnZ4vs7Gxx9+5dIYR9O5vbl97W1laxevVqodfrhbe3t3jppZfEyZMnO/1Menq6UKlUVh+SRqNRZGRkiMDAQKHVasXYsWPFxYsXHRmfesjWeYeFhQmVSiUkSbJ6hIeHO3o3qJvkvL8fxDuyuT45825qahIrVqwQer1eaDQaERUVJfbt2+fI+NRDcub9ww8/iISEBKHVai3zzs/Pd2R8skFYWJjlu1elUlm+l/89Y3t2NkkI/uVuIiIiIvJsbn1OLxERERFRd7D0EhEREZHHY+klIiIiIo/H0ktEREREHo+ll4iIiIg8HksvEREREXk8ll4iIiIi8ngsvURERETk8Vh6iYiIiMjjsfQSERERkcdj6SUiclHp6ekIDw93dgwiIo/g5ewARES9iUrVvWMNp0+fhiRJkCTJzomIiHoHSQghnB2CiKi32LdvX6d/FxUV4dSpUyguLu60Pn78ePTv3x9CCKjVakdGJCLySCy9REROtGTJEuzcuRPt7e3OjkJE5NF4Ti8RkYt68Jze6upqqFQqbN26Fbm5uQgPD4dWq0VSUhKuXbuG9vZ2ZGdnY9CgQfD19UVqaiqMRqPV6x4/fhwJCQnw8/ODTqfD5MmTceXKFUfuGhGRw/GcXiIiF9bVOb3FxcVoa2vDihUrcPv2beTk5GDmzJkYM2YMzp8/j6ysLFRVVSE3NxerVq1CQUGBZdu9e/ciPT0dycnJyMnJQXNzM3bt2oX4+HiUl5cjNDTUkbtHROQwLL1ERC6sqzPQDAYDqqqq4O/vDwAwm83YuHEjWlpacPHiRcvFcjdv3sQXX3yBvLw8qNVqNDU1YdmyZVi4cCHy8vIsrzdv3jw8/fTT2LBhA3bv3u2YHSMicjCe3kBE5GamT59uKbwAEBMTAwCYO3dup78OERMTg7///ht1dXUAgFOnTuHu3btIS0vDrVu3LA+VSoWYmBicPn3asTtCRORAPNJLRORmnnzyyU7/DggIAAAMHjy4y3Wj0YiwsDBUVVUBABITE7t83Y6fJyLyRCy9RERupk+fPj1a7zhFouMvRBQXFyM4ONjq57y8+JVARJ6Ln3BERL1EREQEACAoKOihR3uJiDwVz+klInJhSt6RLTk5GTqdDhs2bEBbW5vV87du3VLsdxERuRoe6SUicmFK3j/I398fu3btwty5czFixAikpaUhMDAQtbW1+P777xEfH4/c3FzFfh8RkSth6SUiciJJkh56NPdRz3X1s91ZnzVrFkJCQrBp0yZs2bIFJpMJgwYNQkJCAubPn9+z8EREboS3ISYiIiIij8dzeomIiIjI47H0EhEREZHHY+klIiIiIo/H0ktEREREHo+ll4iIiIg8HksvEREREXk8ll4iIiIi8ngsvURERETk8Vh6iYiIiMjjsfQSERERkcdj6SUiIiIij8fSS0REREQe73/Zpgm/VKzVxAAAAABJRU5ErkJggg=="
],
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7fdcf3dcdfd0>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.legend.Legend object at 0x7fdcf3a40e50>"
]
},
"execution_count": 71,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"function prop_euler(A, B, X₀, Δt; T=1.0, dW=nothing)\n",
" #Propagates a stochastic differential equation using a simple Euler stepping scheme\n",
" numSteps = int(T/Δt)\n",
" Y = zeros(Float64, numSteps+1)\n",
" Y[1] = X₀\n",
" \n",
" if dW == nothing\n",
" dW = √Δt*randn(numSteps)\n",
" end\n",
" \n",
" timeSteps = 0:Δt:T\n",
" \n",
" for ct = 1:numSteps\n",
" Y[ct+1] = Y[ct] + A(Y[ct],timeSteps[ct])*Δt + B(Y[ct], timeSteps[ct])*dW[ct]\n",
" end\n",
" \n",
" return Y, dW\n",
"end\n",
"\n",
"#Specific linear SDE\n",
"const T = 1 # final time\n",
"const λ = 2.0\n",
"const μ = 1.0\n",
"const X₀ = 1.0\n",
"const Δt = 2.0^-6\n",
"\n",
"A(x,t) = λ*x\n",
"B(x,t) = μ*x\n",
"\n",
"#Approximate numerical solution\n",
"(Y, dW) = prop_euler(A, B, X₀, Δt; T=T)\n",
"W = [0.0, cumsum(dW)]\n",
"timeSteps = [0:Δt:T]\n",
"#Analytical solution\n",
"X = X₀*exp((λ - 0.5*μ^2)*timeSteps + μ*W)\n",
"\n",
"plot(timeSteps, Y)\n",
"plot(timeSteps, X)\n",
"xlabel(\"Time\")\n",
"ylabel(\"X(t)\")\n",
"legend([\"Numerical Approx.\", \"Analytical\"], loc=\"best\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looking at a single trace we can see the error grow as expected. We can quantify this by looking at multiple traces and estimating the average error as the step size changes. By plotting the error vs step and performing linear regression we can estimate the convergence constant. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"ename": "LoadError",
"evalue": "prop_euler not defined\nwhile loading In[12], in expression starting on line 15",
"output_type": "error",
"traceback": [
"prop_euler not defined\nwhile loading In[12], in expression starting on line 15",
"",
" in anonymous at no file:29"
]
}
],
"source": [
"const T = 1 # final time\n",
"const λ = 2.0\n",
"const μ = 1.0\n",
"const X₀ = 1.0\n",
"const Δt = 2.0^-10\n",
"const numTraces = 1000\n",
"numSteps = int(T/Δt)\n",
"A(x,t) = λ*x\n",
"B(x,t) = μ*x\n",
"\n",
"#Store error at T\n",
"timeSteps = Δt*(2.^[0:6])\n",
"Xerr = zeros(Float64, (length(timeSteps), numTraces))\n",
"\n",
"for ct = 1:numTraces\n",
"\n",
" #Create Wiener process for finest discritization\n",
" dW = √Δt*randn(numSteps)\n",
" W = cumsum(dW)\n",
" \n",
" #Analytical solution at T\n",
" Xtrue = X₀*exp((λ - 0.5*μ^2)*1.0 + μ*W[end])\n",
" \n",
" #Loop over different discritization steps\n",
" for (ct2, δt) in enumerate(timeSteps)\n",
" Xtemp = X₀\n",
" R = 2^(ct2-1)\n",
" dWtemp = sum(reshape(dW, (R, int(numSteps/R))), 1)\n",
" (Xtemp, _) = prop_euler(A, B, X₀, δt; dW=dWtemp)\n",
" Xerr[ct2, ct] = abs(Xtemp[end] - Xtrue)\n",
" end\n",
"end\n",
"\n",
"#Linear regression to get convergence power estimate\n",
"meanErr = mean(Xerr,2)\n",
"\n",
"Amat = cat(2, ones(length(timeSteps)), log(timeSteps))\n",
"rhs = log(meanErr)\n",
"fitResult = Amat\\rhs\n",
"\n",
"\n",
"#Plotting\n",
"loglog(timeSteps, mean(Xerr,2), \"b-*\")\n",
"loglog(timeSteps, (exp(fitResult[1]))*(timeSteps.^fitResult[2]), \"r--\")\n",
"xlabel(\"Time Step\")\n",
"ylabel(\"Mean Error at T=1\")\n",
"legend([\"Numerical Estimate\", @sprintf(\"Linear fit with slope = %.2f\", fitResult[2])], loc=\"best\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Higher - Order Integrators\n",
"\n",
"The order 0.5 is lousy compared to most integrators available for deterministic differential equations and this forces a small step size. \n",
"\n",
"### Platen Order 1.0\n",
"\n",
"In the one dimensional case and explicit order 1.0 strong scheme is given by the following update rule. Using the notation $A(X,t) = a$ and $B(X,t) = b$ then:\n",
"\n",
"$$ Y_{n+1} = Y_n + a\\Delta t + b\\Delta W + \\frac{1}{2\\sqrt{\\Delta t}}\\left(b(t,\\overline{Y_n}) - b\\right) \\left((\\Delta W)^2 - \\Delta t\\right) $$\n",
"\n",
"with the supporting value \n",
"\n",
"$$ \\overline{Y_n} = Y_n + a\\Delta t + b\\sqrt{\\Delta t} $$"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"
],
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f7bdf3c4d90>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.legend.Legend object at 0x7f7bded9ccd0>"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#Platen 10 method plus convergence testing\n",
"\n",
"function platen_10(A, B, X₀, Δt; T=1.0, dW=nothing)\n",
"\n",
" numSteps = int(T/Δt)\n",
" Y = zeros(Float64, numSteps+1)\n",
" Y[1] = X₀\n",
" \n",
" if dW == nothing\n",
" dW = √Δt*randn(numSteps)\n",
" end\n",
" \n",
" times = 0:Δt:T\n",
" \n",
" for ct = 1:numSteps\n",
" a = A(Y[ct], times[ct])\n",
" b = B(Y[ct], times[ct])\n",
" #Supporting value\n",
" Ȳ = Y[ct] + a*Δt + b*√Δt\n",
" Y[ct+1] = Y[ct] + a*Δt + b*dW[ct] + (1.0/2/√Δt)*(B(Ȳ, times[ct]) - b)*(dW[ct]^2 - Δt) \n",
" end\n",
" \n",
" return Y, dW\n",
" \n",
"end\n",
"\n",
"#Store error at T\n",
"timeSteps = Δt*(2.^[0:6])\n",
"Xerr = zeros(Float64, (length(timeSteps), numTraces))\n",
"\n",
"for ct = 1:numTraces\n",
"\n",
" #Create Wiener process for finest discritization\n",
" dW = √Δt*randn(numSteps)\n",
" W = cumsum(dW)\n",
" \n",
" #Analytical solution at T\n",
" Xtrue = X₀*exp((λ - 0.5*μ^2)*1.0 + μ*W[end])\n",
" \n",
" #Loop over different discritization steps\n",
" for (ct2, δt) in enumerate(timeSteps)\n",
" Xtemp = X₀\n",
" R = 2^(ct2-1)\n",
" dWtemp = sum(reshape(dW, (R, int(numSteps/R))), 1)\n",
" (Xtemp, _) = platen_10(A, B, X₀, δt; dW=dWtemp)\n",
" Xerr[ct2, ct] = abs(Xtemp[end] - Xtrue)\n",
" end\n",
"end\n",
"\n",
"#Linear regression to get convergence power estimate\n",
"meanErr = mean(Xerr,2)\n",
"\n",
"Amat = cat(2, ones(length(timeSteps)), log(timeSteps))\n",
"rhs = log(meanErr)\n",
"fitResult = Amat\\rhs\n",
"\n",
"\n",
"#Plotting\n",
"loglog(timeSteps, mean(Xerr,2), \"b-*\")\n",
"loglog(timeSteps, (exp(fitResult[1]))*(timeSteps.^fitResult[2]), \"r--\")\n",
"xlabel(\"Time Step\")\n",
"ylabel(\"Mean Error at T=1\")\n",
"legend([\"Numerical Estimate\", @sprintf(\"Linear fit with slope = %.2f\", fitResult[2])], loc=\"best\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And we get the expected slope of 1.0 and also notice that at the smallest step size the mean error is an order of magnitude smaller.\n",
"\n",
"## Platen Order 1.5 Scheme\n",
"\n",
"To step up even half an order more is subtantially more complex. There is an explicit strong order 1.5 scheme from Platen. For 1 dimensional problems the steps are given by:\n",
"\n",
"\\begin{align} Y_{n+1} = Y_n &+ b\\Delta W + \\frac{1}{2\\sqrt{\\Delta t}}\\left(A(\\bar{\\Upsilon}_+) - A(\\bar{\\Upsilon}_-) \\right)\\Delta Z \\\\ &+ \\frac{1}{4}\\left(A(\\bar{\\Upsilon}_+) + 2a + A(\\bar{\\Upsilon}_-) \\right)\\Delta t \\\\ &+ \\frac{1}{4\\sqrt{\\Delta t}}\\left(B(\\bar{\\Upsilon}_+) - B(\\bar{\\Upsilon}_-) \\right)\\left((\\Delta W)^2 - \\Delta t \\right) \\\\ &+ \\frac{1}{2\\Delta t}\\left(B(\\bar{\\Upsilon}_+) -2B + B(\\bar{\\Upsilon}_- \\right)\\left(\\Delta W \\Delta t - \\Delta Z \\right) \\\\ &+ \\frac{1}{4\\Delta t}\\left[B(\\bar{\\Phi}_+) - B(\\bar{\\Phi}_-) -B(\\bar{\\Upsilon}_+) +B(\\bar{\\Upsilon}_-) \\right]\\left[\\frac{1}{3}(\\Delta W)^2 - \\Delta t \\right]\\Delta W\\end{align}\n",
"\n",
"with multiple supporting values:\n",
"\n",
"$$ \\bar{\\Upsilon}_\\pm = Y_n + a\\Delta t \\pm b\\sqrt{\\Delta t} \\quad ; \\quad \\bar{\\Phi}_\\pm = \\bar{\\Upsilon}_+ \\pm B(\\bar{\\Upsilon}_+)\\sqrt{\\Delta t}$$\n",
"\n",
"and $\\Delta Z$ is the multiple Ito integral $I_{(1,0)}$ (not really sure what this integral is)\n",
"\n",
"$$ \\Delta Z = I_{(1,0)} = \\int_{t_k}^{t_{k+1}} \\int_{t_k}^{s_2}dW_{s_1}ds_2$$\n",
"\n",
"However, numerically the pair of correlated random variables $(\\Delta W, \\Delta Z)$ can be calculated from two independent $N(0,1)$ variables $(U_1, U_2)$ as:\n",
"\n",
"$$ \\Delta W = U_1\\sqrt{\\Delta t} \\quad ; \\quad \\Delta Z = \\frac{1}{2}\\Delta t ^{\\frac{3}{2}}\\left(U_1 + \\frac{1}{\\sqrt{3}} U_2 \\right) $$"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"platen_15 (generic function with 1 method)"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Platen 15 scheme plus convergence testing\n",
"\n",
"function platen_15(A, B, X₀, Δt; T=1.0, dW=nothing)\n",
"\n",
" numSteps = int(T/Δt)\n",
" Y = zeros(Float64, numSteps+1)\n",
" Y[1] = X₀\n",
" \n",
" if dW == nothing\n",
" U₁ = randn(numSteps)\n",
" dW = √Δt*U₁\n",
" else\n",
" U₁ = dW/√Δt\n",
" end\n",
" U₂ = randn(numSteps)\n",
" \n",
" t = 0:Δt:T\n",
" \n",
" for ct = 1:numSteps\n",
" #Inital evaluation of A and B\n",
" a = A(Y[ct], t[ct])\n",
" b = B(Y[ct], t[ct])\n",
" \n",
" #Supporting values\n",
" Ῡ₊ = Y[ct] + a*Δt + b*√Δt\n",
" Ῡ₋ = Y[ct] + a*Δt - b*√Δt\n",
" \n",
" Φ₊ = Ῡ₊ + B(Ῡ₊, t[ct])*√Δt\n",
" Φ₋ = Ῡ₊ - B(Ῡ₊, t[ct])*√Δt\n",
" \n",
" #A,B evaluated at supporting values\n",
" aΥ₊ = A(Ῡ₊, t[ct])\n",
" aΥ₋ = A(Ῡ₋, t[ct])\n",
" bΥ₊ = B(Ῡ₊, t[ct])\n",
" bΥ₋ = B(Ῡ₋, t[ct])\n",
" \n",
" bΦ₊ = B(Φ₊, t[ct])\n",
" bΦ₋ = B(Φ₋, t[ct])\n",
" \n",
" #correlated double Ito\n",
" ΔW = dW[ct]\n",
" ΔZ = 0.5*(Δt)^(1.5)*(U₁[ct] + U₂[ct]/√3)\n",
"\n",
" #Finally put the whole step together\n",
" Y[ct+1] = Y[ct] + b*ΔW +\n",
" (1.0/2/√Δt) * (aΥ₊ - aΥ₋)*ΔZ + \n",
" 0.25 * (aΥ₊ + 2*a + aΥ₋) * Δt + \n",
" (0.25/√Δt) * (bΥ₊ - bΥ₋) * (ΔW^2 - Δt) + \n",
" (0.5/Δt) * (bΥ₊ - 2*b + bΥ₋) * (ΔW*Δt - ΔZ) + \n",
" (0.25/Δt) * (bΦ₊ - bΦ₋ - bΥ₊ + bΥ₋) * ((1/3)*ΔW^2 - Δt)*ΔW\n",
" end\n",
" \n",
" return Y, dW\n",
" \n",
"end\n"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"
],
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f7bde7e9cd0>)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"PyObject <matplotlib.legend.Legend object at 0x7f7bde758ed0>"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"const T = 1 # final time\n",
"const λ = 2.0\n",
"const μ = 1.0\n",
"const X₀ = 1.0\n",
"const Δt = 2.0^-10\n",
"const numTraces = 1000\n",
"numSteps = int(T/Δt)\n",
"A(x,t) = λ*x\n",
"B(x,t) = μ*x\n",
"\n",
"#Store error at T\n",
"timeSteps = Δt*(2.^[0:6])\n",
"Xerr = zeros(Float64, (length(timeSteps), numTraces))\n",
"\n",
"for ct = 1:numTraces\n",
"\n",
" #Create Wiener process for finest discritization\n",
" dW = √Δt*randn(numSteps)\n",
" W = cumsum(dW)\n",
" \n",
" #Analytical solution at T\n",
" Xtrue = X₀*exp((λ - 0.5*μ^2)*1.0 + μ*W[end])\n",
" \n",
" #Loop over different discritization steps\n",
" for (ct2, δt) in enumerate(timeSteps)\n",
" Xtemp = X₀\n",
" R = 2^(ct2-1)\n",
" dWtemp = sum(reshape(dW, (R, int(numSteps/R))), 1)\n",
" (Xtemp, _) = platen_15(A, B, X₀, δt; dW=dWtemp)\n",
" Xerr[ct2, ct] = abs(Xtemp[end] - Xtrue)\n",
" end\n",
"end\n",
"\n",
"#Linear regression to get convergence power estimate\n",
"meanErr = mean(Xerr,2)\n",
"\n",
"Amat = cat(2, ones(length(timeSteps)), log(timeSteps))\n",
"rhs = log(meanErr)\n",
"fitResult = Amat\\rhs\n",
"\n",
"\n",
"#Plotting\n",
"loglog(timeSteps, mean(Xerr,2), \"b-*\")\n",
"loglog(timeSteps, (exp(fitResult[1]))*(timeSteps.^fitResult[2]), \"r--\")\n",
"xlabel(\"Time Step\")\n",
"ylabel(\"Mean Error at T=1\")\n",
"legend([\"Numerical Estimate\", @sprintf(\"Linear fit with slope = %.2f\", fitResult[2])], loc=\"best\")"
]
},
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"# References\n",
"\n",
"1. [Stochastic Differential Equations with Applications (2012)](http://www.ncer.edu.au/papers/documents/SDE.pdf) - quite nice authorless introduction from an Australian economics group. There are a few typos though. \n",
"2. [Handbook of Stochastic Methods](http://books.google.com/books/about/Handbook_of_Stochastic_Methods_for_Physi.html?id=wLm7QgAACAAJ). C.W. Gardiner. Third Edition (2004).\n",
"3. [Numerical Solution of Stochastic Differential Equations](http://www.springer.com/us/book/9783540540625) Peter Kloeden and Eckhar Platen. Authorative text for numerical approaches.\n",
"4. Higham., D. J. (2001). [An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations](http://epubs.siam.org/doi/abs/10.1137/S0036144500378302). SIAM Review, 43(3), 525–546."
]
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