Class_Work/ME_2016/.ipynb_checkpoints/LinstedtPoincareExampleNB-checkpoint.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6945cd62",
   "metadata": {},
   "source": [
    "## Example Problem - Linstedt Poincare Procedure"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "797e4d60",
   "metadata": {},
   "source": [
    "In this problem, we will apply Lindstedt's method to $\\ddot{x} + \\epsilon x \\dot{x} + x = 0$, for $0 < \\epsilon << 1$, where $x(0) = a_0$, and $\\dot{x}(0) = 0$. We will show that the frequency-amplitude relation for periodic solutions is given by $\\omega = 1 - \\frac{1}{24}a_0^2 \\epsilon^2 + O(\\epsilon^3)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f25ba29d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7f1e21b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = Function('x')\n",
    "x0 = Function('x_0')\n",
    "x1 = Function('x_1')\n",
    "x2 = Function('x_2')\n",
    "t = Symbol('t')\n",
    "eps = Symbol('epsilon')\n",
    "w1 = Symbol('w_1')\n",
    "w2 = Symbol('w_2')\n",
    "w = Symbol('w')\n",
    "a0 = Symbol('a_0')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6364f15",
   "metadata": {},
   "source": [
    "Note that to a second order expansion in the frequency due to Lindstedt method, $\\tau = \\omega t$, with $\\omega = 1 + \\epsilon \\omega_1  + \\epsilon^2 \\omega_2$. In addtion, we use the expansion in the solution, $x = x_0(t) + \\epsilon  x_1(t) + \\epsilon^2  x_2(t)$, and substitute both into the differential equation we are trying to solve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "989d7206",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\epsilon^{2} x_{2}{\\left(t \\right)} + \\epsilon \\left(\\epsilon^{2} w_{2} + \\epsilon w_{1} + 1\\right) \\left(\\epsilon^{2} x_{2}{\\left(t \\right)} + \\epsilon x_{1}{\\left(t \\right)} + x_{0}{\\left(t \\right)}\\right) \\left(\\epsilon^{2} \\frac{d}{d t} x_{2}{\\left(t \\right)} + \\epsilon \\frac{d}{d t} x_{1}{\\left(t \\right)} + \\frac{d}{d t} x_{0}{\\left(t \\right)}\\right) + \\epsilon x_{1}{\\left(t \\right)} + \\left(\\epsilon^{2} w_{2} + \\epsilon w_{1} + 1\\right)^{2} \\left(\\epsilon^{2} \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} + \\epsilon \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)}\\right) + x_{0}{\\left(t \\right)}$"
      ],
      "text/plain": [
       "epsilon**2*x_2(t) + epsilon*(epsilon**2*w_2 + epsilon*w_1 + 1)*(epsilon**2*x_2(t) + epsilon*x_1(t) + x_0(t))*(epsilon**2*Derivative(x_2(t), t) + epsilon*Derivative(x_1(t), t) + Derivative(x_0(t), t)) + epsilon*x_1(t) + (epsilon**2*w_2 + epsilon*w_1 + 1)**2*(epsilon**2*Derivative(x_2(t), (t, 2)) + epsilon*Derivative(x_1(t), (t, 2)) + Derivative(x_0(t), (t, 2))) + x_0(t)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "w = 1 + eps * w1 + eps**2 * w2\n",
    "x = x0(t) + eps * x1(t) + eps**2 * x2(t)\n",
    "expr = w**2 * x.diff(t,t) + w*eps*x*x.diff(t) + x\n",
    "display(expr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71535ff6",
   "metadata": {},
   "source": [
    "Next, we expand and collect like terms of $\\epsilon$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a1762f64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\epsilon^{7} w_{2} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + \\epsilon^{6} \\left(w_{1} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + w_{2}^{2} \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} + w_{2} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + w_{2} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)}\\right) + \\epsilon^{5} \\cdot \\left(2 w_{1} w_{2} \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} + w_{1} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + w_{1} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + w_{2}^{2} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + w_{2} x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + w_{2} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + w_{2} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)}\\right) + \\epsilon^{4} \\left(w_{1}^{2} \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} + 2 w_{1} w_{2} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + w_{1} x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + w_{1} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + w_{1} x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + w_{2}^{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + w_{2} x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + w_{2} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + 2 w_{2} \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} + x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)}\\right) + \\epsilon^{3} \\left(w_{1}^{2} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + 2 w_{1} w_{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + w_{1} x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + w_{1} x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + 2 w_{1} \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} + w_{2} x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + 2 w_{2} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{2}{\\left(t \\right)} + x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + x_{2}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)}\\right) + \\epsilon^{2} \\left(w_{1}^{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + w_{1} x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + 2 w_{1} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + 2 w_{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + x_{2}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)}\\right) + \\epsilon \\left(2 w_{1} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + x_{1}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)}\\right) + x_{0}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)}$"
      ],
      "text/plain": [
       "epsilon**7*w_2*x_2(t)*Derivative(x_2(t), t) + epsilon**6*(w_1*x_2(t)*Derivative(x_2(t), t) + w_2**2*Derivative(x_2(t), (t, 2)) + w_2*x_1(t)*Derivative(x_2(t), t) + w_2*x_2(t)*Derivative(x_1(t), t)) + epsilon**5*(2*w_1*w_2*Derivative(x_2(t), (t, 2)) + w_1*x_1(t)*Derivative(x_2(t), t) + w_1*x_2(t)*Derivative(x_1(t), t) + w_2**2*Derivative(x_1(t), (t, 2)) + w_2*x_0(t)*Derivative(x_2(t), t) + w_2*x_1(t)*Derivative(x_1(t), t) + w_2*x_2(t)*Derivative(x_0(t), t) + x_2(t)*Derivative(x_2(t), t)) + epsilon**4*(w_1**2*Derivative(x_2(t), (t, 2)) + 2*w_1*w_2*Derivative(x_1(t), (t, 2)) + w_1*x_0(t)*Derivative(x_2(t), t) + w_1*x_1(t)*Derivative(x_1(t), t) + w_1*x_2(t)*Derivative(x_0(t), t) + w_2**2*Derivative(x_0(t), (t, 2)) + w_2*x_0(t)*Derivative(x_1(t), t) + w_2*x_1(t)*Derivative(x_0(t), t) + 2*w_2*Derivative(x_2(t), (t, 2)) + x_1(t)*Derivative(x_2(t), t) + x_2(t)*Derivative(x_1(t), t)) + epsilon**3*(w_1**2*Derivative(x_1(t), (t, 2)) + 2*w_1*w_2*Derivative(x_0(t), (t, 2)) + w_1*x_0(t)*Derivative(x_1(t), t) + w_1*x_1(t)*Derivative(x_0(t), t) + 2*w_1*Derivative(x_2(t), (t, 2)) + w_2*x_0(t)*Derivative(x_0(t), t) + 2*w_2*Derivative(x_1(t), (t, 2)) + x_0(t)*Derivative(x_2(t), t) + x_1(t)*Derivative(x_1(t), t) + x_2(t)*Derivative(x_0(t), t)) + epsilon**2*(w_1**2*Derivative(x_0(t), (t, 2)) + w_1*x_0(t)*Derivative(x_0(t), t) + 2*w_1*Derivative(x_1(t), (t, 2)) + 2*w_2*Derivative(x_0(t), (t, 2)) + x_0(t)*Derivative(x_1(t), t) + x_1(t)*Derivative(x_0(t), t) + x_2(t) + Derivative(x_2(t), (t, 2))) + epsilon*(2*w_1*Derivative(x_0(t), (t, 2)) + x_0(t)*Derivative(x_0(t), t) + x_1(t) + Derivative(x_1(t), (t, 2))) + x_0(t) + Derivative(x_0(t), (t, 2))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expr = expand(expr)\n",
    "expr = collect(expr,eps)\n",
    "display(expr)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7961634",
   "metadata": {},
   "source": [
    "We can clean this up a bit more. We can create a list of the equations! Let's do this for terms 0, 1, 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1e1f6897",
   "metadata": {},
   "outputs": [],
   "source": [
    "eqLHS = collect(expr,eps,evaluate=False)\n",
    "LHSlist = []\n",
    "for k in [0,1,2]:\n",
    "    LHSlist.append(eqLHS[eps**k])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a63234af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x_{0}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)}$"
      ],
      "text/plain": [
       "x_0(t) + Derivative(x_0(t), (t, 2))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 w_{1} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + x_{1}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)}$"
      ],
      "text/plain": [
       "2*w_1*Derivative(x_0(t), (t, 2)) + x_0(t)*Derivative(x_0(t), t) + x_1(t) + Derivative(x_1(t), (t, 2))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle w_{1}^{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + w_{1} x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + 2 w_{1} \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} + 2 w_{2} \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} + x_{0}{\\left(t \\right)} \\frac{d}{d t} x_{1}{\\left(t \\right)} + x_{1}{\\left(t \\right)} \\frac{d}{d t} x_{0}{\\left(t \\right)} + x_{2}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)}$"
      ],
      "text/plain": [
       "w_1**2*Derivative(x_0(t), (t, 2)) + w_1*x_0(t)*Derivative(x_0(t), t) + 2*w_1*Derivative(x_1(t), (t, 2)) + 2*w_2*Derivative(x_0(t), (t, 2)) + x_0(t)*Derivative(x_1(t), t) + x_1(t)*Derivative(x_0(t), t) + x_2(t) + Derivative(x_2(t), (t, 2))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for k in [0,1,2]:\n",
    "    display(LHSlist[k])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f53aed26",
   "metadata": {},
   "source": [
    "We know that each of these is equal to zero! Let's solve the first one (order $O(\\epsilon^0))$. First we define it as an equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b295ad34",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x_{0}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{0}{\\left(t \\right)} = 0$"
      ],
      "text/plain": [
       "Eq(x_0(t) + Derivative(x_0(t), (t, 2)), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ODE class  nth_linear_constant_coeff_homogeneous\n"
     ]
    }
   ],
   "source": [
    "eq0 = Eq(LHSlist[0],0)\n",
    "display(eq0)\n",
    "print('ODE class ', classify_ode(eq0)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eac29466",
   "metadata": {},
   "source": [
    "Now we solve, including initial conditions. Note that there is some funny syntax that has to be used to specify the initial condition of the derivative. This is a quirk of SymPy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f2ee72c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a_{0} \\cos{\\left(t \\right)}$"
      ],
      "text/plain": [
       "a_0*cos(t)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0sol = dsolve(eq0, ics={x0(0): a0, x0(t).diff(t).subs(t, 0): 0}).rhs\n",
    "display(x0sol)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77e50b75",
   "metadata": {},
   "source": [
    "Great, so now we have a solution for $x_0$. Let's go look at our order $O(\\epsilon^1)$ equation and substitute in the order $O(\\epsilon^0)$ solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "984909c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - a_{0}^{2} \\sin{\\left(t \\right)} \\cos{\\left(t \\right)} - 2 a_{0} w_{1} \\cos{\\left(t \\right)} + x_{1}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{1}{\\left(t \\right)} = 0$"
      ],
      "text/plain": [
       "Eq(-a_0**2*sin(t)*cos(t) - 2*a_0*w_1*cos(t) + x_1(t) + Derivative(x_1(t), (t, 2)), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ODE class  nth_linear_constant_coeff_variation_of_parameters\n"
     ]
    }
   ],
   "source": [
    "eq1 = Eq(simplify(LHSlist[1].subs(x0(t),x0sol)),0)\n",
    "display(eq1)\n",
    "print('ODE class ', classify_ode(eq1)[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7d280ace",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{a_{0}^{2} \\sin{\\left(2 t \\right)}}{6} + \\left(\\frac{a_{0}^{2}}{3} + a_{0} t w_{1}\\right) \\sin{\\left(t \\right)}$"
      ],
      "text/plain": [
       "-a_0**2*sin(2*t)/6 + (a_0**2/3 + a_0*t*w_1)*sin(t)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1sol = dsolve(eq1, ics={x1(0): 0, x1(t).diff(t).subs(t, 0): 0}).rhs\n",
    "display(x1sol)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73f19ac6",
   "metadata": {},
   "source": [
    "Periodicity requires that $w_1 = 0$ (to remove the secular term)!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4d3609b3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a_{0}^{2} \\sin{\\left(t \\right)}}{3} - \\frac{a_{0}^{2} \\sin{\\left(2 t \\right)}}{6}$"
      ],
      "text/plain": [
       "a_0**2*sin(t)/3 - a_0**2*sin(2*t)/6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1sol_nonsec = x1sol.subs(w1, 0)\n",
    "display(x1sol_nonsec)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3de59464",
   "metadata": {},
   "source": [
    "Great, so now we have a solution for $x_0$ and $x_1$. Let's go look at our order $O(\\epsilon^2)$ equation and substitute in the order $O(\\epsilon^1)$ and $O(\\epsilon^0)$ solutions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a183bb78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{a_{0}^{3} \\cdot \\left(2 \\sin{\\left(t \\right)} - \\sin{\\left(2 t \\right)}\\right) \\sin{\\left(t \\right)}}{6} + \\frac{a_{0}^{3} \\cdot \\left(2 \\cos{\\left(t \\right)} - 2 \\cos{\\left(2 t \\right)}\\right) \\cos{\\left(t \\right)}}{6} - 2 a_{0} w_{2} \\cos{\\left(t \\right)} + x_{2}{\\left(t \\right)} + \\frac{d^{2}}{d t^{2}} x_{2}{\\left(t \\right)} = 0$"
      ],
      "text/plain": [
       "Eq(-a_0**3*(2*sin(t) - sin(2*t))*sin(t)/6 + a_0**3*(2*cos(t) - 2*cos(2*t))*cos(t)/6 - 2*a_0*w_2*cos(t) + x_2(t) + Derivative(x_2(t), (t, 2)), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ODE class  nth_linear_constant_coeff_variation_of_parameters\n"
     ]
    }
   ],
   "source": [
    "eq2 = Eq(simplify(LHSlist[2].subs({x0(t):x0sol, x1(t):x1sol_nonsec, w1:0})),0)\n",
    "display(eq2)\n",
    "print('ODE class ', classify_ode(eq1)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d42ed9bd",
   "metadata": {},
   "source": [
    "Now, we solve it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f210aadc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a_{0}^{3} \\left(- 9 \\cos{\\left(t \\right)} - 8\\right) \\sin^{4}{\\left(t \\right)}}{36} + \\frac{a_{0}^{3} \\cdot \\left(45 \\cos{\\left(t \\right)} - 4\\right) \\sin^{2}{\\left(t \\right)}}{72} + \\frac{a_{0}^{3} \\cos^{5}{\\left(t \\right)}}{4} - \\frac{13 a_{0}^{3} \\cos{\\left(t \\right)}}{36} + \\frac{a_{0}^{3}}{9} + \\left(\\frac{a_{0}^{3} t}{24} - \\frac{a_{0}^{3} \\sin{\\left(3 t \\right)}}{18} + a_{0} t w_{2}\\right) \\sin{\\left(t \\right)}$"
      ],
      "text/plain": [
       "a_0**3*(-9*cos(t) - 8)*sin(t)**4/36 + a_0**3*(45*cos(t) - 4)*sin(t)**2/72 + a_0**3*cos(t)**5/4 - 13*a_0**3*cos(t)/36 + a_0**3/9 + (a_0**3*t/24 - a_0**3*sin(3*t)/18 + a_0*t*w_2)*sin(t)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x2sol = dsolve(eq2, ics={x2(0): 0, x2(t).diff(t).subs(t, 0): 0}).rhs\n",
    "display(x2sol)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc0a815e",
   "metadata": {},
   "source": [
    "Lots of terms. But! We need to figure out what will give us secular behavior. So we can just collect with respect to $t$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "cbcb696c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{t: a_0**3*sin(t)/24 + a_0*w_2*sin(t),\n",
       " 1: -a_0**3*sin(t)**4*cos(t)/4 - 2*a_0**3*sin(t)**4/9 + 5*a_0**3*sin(t)**2*cos(t)/8 - a_0**3*sin(t)**2/18 - a_0**3*sin(t)*sin(3*t)/18 + a_0**3*cos(t)**5/4 - 13*a_0**3*cos(t)/36 + a_0**3/9}"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x2solterms = collect(expand(x2sol),t,evaluate=False)\n",
    "display(x2solterms)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "14144cab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{a_{0}^{3} \\sin{\\left(t \\right)}}{24} + a_{0} w_{2} \\sin{\\left(t \\right)} = 0$"
      ],
      "text/plain": [
       "Eq(a_0**3*sin(t)/24 + a_0*w_2*sin(t), 0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "[-a_0**2/24]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "testeqn=Eq(x2solterms[t],0)\n",
    "display(testeqn)\n",
    "w2sol = solve(Eq(x2solterms[t],0),w2)\n",
    "display(w2sol)\n",
    "w2sol = list(w2sol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d2344049",
   "metadata": {},
   "outputs": [],
   "source": [
    "w2val = w2sol[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3087dbb",
   "metadata": {},
   "source": [
    "Therefore, we can get the expression for $w$ that..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a9f106f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{a_{0}^{2} \\epsilon^{2}}{24} + 1$"
      ],
      "text/plain": [
       "-a_0**2*epsilon**2/24 + 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "- \\frac{a_{0}^{2} \\epsilon^{2}}{24} + 1\n"
     ]
    }
   ],
   "source": [
    "wsol = Symbol('w_sol')\n",
    "wsol = w.subs(w2,w2val).subs(w1,0)\n",
    "display(wsol)\n",
    "print(latex(wsol))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fc92804",
   "metadata": {},
   "source": [
    "Therefore, our answer is that $\\omega =  - \\frac{a_{0}^{2} \\epsilon^{2}}{24} + 1 + O(\\epsilon^3)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b038975f",
   "metadata": {},
   "source": [
    "Okay, but what if we want to plot our solution?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "256fe342",
   "metadata": {},
   "outputs": [],
   "source": [
    "xsol = x.subs(x0(t),x0sol).subs(x1(t),x1sol).subs(w1,0).subs(x2(t),x2sol).subs(w2,w2val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9767609f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a_{0} \\cos{\\left(t \\right)} + \\epsilon^{2} \\left(\\frac{a_{0}^{3} \\left(- 9 \\cos{\\left(t \\right)} - 8\\right) \\sin^{4}{\\left(t \\right)}}{36} + \\frac{a_{0}^{3} \\cdot \\left(45 \\cos{\\left(t \\right)} - 4\\right) \\sin^{2}{\\left(t \\right)}}{72} - \\frac{a_{0}^{3} \\sin{\\left(t \\right)} \\sin{\\left(3 t \\right)}}{18} + \\frac{a_{0}^{3} \\cos^{5}{\\left(t \\right)}}{4} - \\frac{13 a_{0}^{3} \\cos{\\left(t \\right)}}{36} + \\frac{a_{0}^{3}}{9}\\right) + \\epsilon \\left(\\frac{a_{0}^{2} \\sin{\\left(t \\right)}}{3} - \\frac{a_{0}^{2} \\sin{\\left(2 t \\right)}}{6}\\right)$"
      ],
      "text/plain": [
       "a_0*cos(t) + epsilon**2*(a_0**3*(-9*cos(t) - 8)*sin(t)**4/36 + a_0**3*(45*cos(t) - 4)*sin(t)**2/72 - a_0**3*sin(t)*sin(3*t)/18 + a_0**3*cos(t)**5/4 - 13*a_0**3*cos(t)/36 + a_0**3/9) + epsilon*(a_0**2*sin(t)/3 - a_0**2*sin(2*t)/6)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a_{0} \\cos{\\left(t \\right)} + \\epsilon^{2} \\left(\\frac{a_{0}^{3} \\left(- 9 \\cos{\\left(t \\right)} - 8\\right) \\sin^{4}{\\left(t \\right)}}{36} + \\frac{a_{0}^{3} \\cdot \\left(45 \\cos{\\left(t \\right)} - 4\\right) \\sin^{2}{\\left(t \\right)}}{72} - \\frac{a_{0}^{3} \\sin{\\left(t \\right)} \\sin{\\left(3 t \\right)}}{18} + \\frac{a_{0}^{3} \\cos^{5}{\\left(t \\right)}}{4} - \\frac{13 a_{0}^{3} \\cos{\\left(t \\right)}}{36} + \\frac{a_{0}^{3}}{9}\\right) + \\epsilon \\left(\\frac{a_{0}^{2} \\sin{\\left(t \\right)}}{3} - \\frac{a_{0}^{2} \\sin{\\left(2 t \\right)}}{6}\\right)\n"
     ]
    }
   ],
   "source": [
    "display(xsol)\n",
    "print(latex(xsol))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8be665e",
   "metadata": {},
   "source": [
    "#### Let $a_0 = 4$. And let's plot for a few values of epsilon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e4707cdc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\epsilon^{2} \\cdot \\left(\\frac{16 \\left(- 9 \\cos{\\left(t \\right)} - 8\\right) \\sin^{4}{\\left(t \\right)}}{9} + \\frac{8 \\cdot \\left(45 \\cos{\\left(t \\right)} - 4\\right) \\sin^{2}{\\left(t \\right)}}{9} - \\frac{32 \\sin{\\left(t \\right)} \\sin{\\left(3 t \\right)}}{9} + 16 \\cos^{5}{\\left(t \\right)} - \\frac{208 \\cos{\\left(t \\right)}}{9} + \\frac{64}{9}\\right) + \\epsilon \\left(\\frac{16 \\sin{\\left(t \\right)}}{3} - \\frac{8 \\sin{\\left(2 t \\right)}}{3}\\right) + 4 \\cos{\\left(t \\right)}$"
      ],
      "text/plain": [
       "epsilon**2*(16*(-9*cos(t) - 8)*sin(t)**4/9 + 8*(45*cos(t) - 4)*sin(t)**2/9 - 32*sin(t)*sin(3*t)/9 + 16*cos(t)**5 - 208*cos(t)/9 + 64/9) + epsilon*(16*sin(t)/3 - 8*sin(2*t)/3) + 4*cos(t)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xsol_sub_a0 = xsol.subs(a0,4)\n",
    "display(xsol_sub_a0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a8b671ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "epslist = [0.25,0.1,0.05,0.005]\n",
    "a = plot(xsol_sub_a0.subs(eps,.4),(t,0,20),show=False)\n",
    "a.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "28c9e769",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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w0f/wir12uSAduRfgws2NmDLilhnqrwFdL7FFknLHf2KWhCrSqt7mZ3g0u4Mrelb2Jvjyl2/BlJ5CUy1M/Da6oq8tWZ+cfGYITbVhS8zR3XKQp7iYy89itupy+P23vhhTJkTG4ub5+/as6GtL1ifHHjwIioondIJL60Y4ZLt0xcpQDG54z++jaBkSzlYe+9+vr+hrlwPSkVsGardP/F+7mOmB6hjCKzl3nr/vGUCkVS9xhhh2bKe3YflDn5eD2aSi1YQBUBKXkPDL8UiSM/P8r54DwBbbR6/ZgrX1wvOWHVmM12EBS647cK6XbCq+oq8vWX/0PS0CJZp2ADXbTHdP74qVoRh0t9Zgyg4BkDjeAJq2oq9faqQjtwyu+8NXABDxbODJ73+txNZIyp2Tx0RjTNyyl4n0Zi7taVjxjQlg++vEuoy5t/LkTz+z4q8vWT9oms7MtJjRG/PuY1fmYnZ2r069UOO1lwOQsV3E3se/vCrvIVkfZFJZAhEhAqzV7OdJ7aIVz14YWDaJma0KlzL2/A9W5T1KhXTklsH2LQ2Y0uOgqASPOGV6VXJa5iaixKlF0TI4GnfxlLZ9xevjDK6/vhdTJoBmsjH45NyqvIdkfTB5dJqs6sScjlHTeogntIvZ2b066/KGWy5H0dIkHA0c+fljq/IekvXB8J4RdNWCLTFHZ9MxfqtdzBWrtC6vv/XloGtEPD387kffWZX3KBXSkVsmSotw3kypi0kMP1NiayTlyvFHhFivN9jPRb4Znta2r1rkw2RSURzz4tfh7aTnh1blfSSVz7EHxagiZ+QwV9giPKVduGqOXI3HhoJIr+oTXZBJrcr7SCqfQw8a6f6DXGZOs0/dzsUdNavyXpt7ajFlRId/eLAJ1tHILunILZNr3ijSWGHvBTx533+V2BpJuTKwZwSAFIfpTZsYMPVyUbt31d5v48suAyBtv4hdj31x1d5HUtkMHgsBELUewpyqw+prpaXGvmrv59wqZgqrysUM77931d5HUrnous5krpwy6jrAQHYTm9ubsZlXtm6zGLVFjEi0pi5gbuChVXuftUY6csvk4svaUDMBNJOV0eeTMr0qOYVMKst8RDQ1JGoPsk/bysWddau6MV3/mktQtBRJez2HH1mfquWS8yMaSBLN+kDXUOueY5++edWicQYveeM1AIS8vez6yf+t6ntJKhP/UICU4kHNprC0HGC3tmXV1+WO17wIgKh7C88++D+r+l5riXTklomiKOAIAKDHtqGP7y+pPZLyY/TAJLpiwZacx9d0gj3a6h+YNrsZFSGmqU5vQo/Nr+r7SSqPE0+eAMATHqanYYq92mYu6/Kt6ntu6PGhZqdBUQmfrJfpVckpDDx0CABPuI+tNUH2aZtWLa1qcMXVnSjZGFmzg8l90XUTkJGO3Fmw4eptAGjmCzi8539LbI2k3Dj+6BEAHJEj7LDH2adv5uL21d2YAGovFEPPLWznxF65LiULGcg5ckrqEDv1BHu1zVzYtvrrUhVNgpjSFxPp/9Wqv5+ksjhxyA9ATDnEZckk+7VNXLTK69JkUsGaqysObkWfXB9ZDOnInQXXvW4n6BoxVyt7fyfFLiULGT4eAWDefpgtyQzPa71sb129+jiDa19/BQARdw/7Hrpv1d9PUjloWY2pWZHan/cexJG1cFTvYlurZ9Xf+9JXi3UZc1/A7x5ffyKsknMnEU0zHxNlKOHa55nNNpKy1dNV51z19+64YjMAimkbR55aH+tSOnJngdtrw5QVMy7jkz0QmiitQZKyITyXIKZ5QddINxxkQO8Aq3ttNqbuGhQtgmayEj1hh3Ri1d9TUhlMnwySxYo5HUVvGeA5bSPtdR68dsuqv/fO6zagaEkyFjeDB8LrToRVcu6MHZ4BRcUZm8TVNMk+fRPb27yo6srrbS7mxTdfDEDIu4GDj/921d9vLZCO3FnibrECYE1tZ/bwj0tsjaRcGNor2q+8oUFa6+fZp23igta12ZgURcHkEs6bJbKF7IlHV/09JZXB0JP9AHhC/XT64uzVN61JlBjAbDZhUkT6TAlsJTu+d03eV1L+DD81AIAj0s8F9jj7tLUpQwGoa3aiaEF01Ux6ogvmB9fkfVcT6cidJVf83k4AUo5tPLrnhyW2RlIuDD4rNNys8aNcpoj6uO1ta3NgAmy6eov4hXkTzz/zrTV7X0l5M3poBoCEOsBl6SR7tbVdly2bGwFwZLbw3EEpQyIRjB4PAhCwDXBZKsk+bRMXrZEjpygKzhZRbmBJXUDk8E/W5H1XE+nInSWbr+pBySZJWz1MHNUgLWcJVju6rjMxlgQgaD/G5nSafdraRT4Adly3CYBQzUaO79on01gSslmN6YAZgOmaPnrSGfZpm7lgDdflFb8vdA6j7s08ve/xNXtfSfmSiKYJJUTJSbD+KLasmSN696rqbS7miht2ABB3beWpp6QjV3WYzCoWk7hNmOc3kTzxSIktkpSa4EycVNaGoqVJ1w4Qw8lxvW1NIx/1bS7QE2RNNhIznTD5/Jq9t6Q8mR4MoSkWLOkIWuMwQ3oLc3jXdF22bmlEzSbImh2khnwQk6Pkqp3xw9OgKDhjUzibZzigb8BssbGhwb1mNmy8TAhWR9wdjA8EKl4eRzpy50Db5gYAapIb2XfguyW2RlJqxo6KOiBvaAhvY5R92V5U1cSW5tXvDDRQVAVXnRg544huIdYn5R6qneGnTwJiXFxbbZw92iZqHBbaVnGiw2JUVcHpEN3crtA2olKGpOoZelLUx9lj/Wy3JtinbWJLsxvTGtQTGzg8VsyKkCHR57fDSGWP3ZSO3Dlw4SsuBCDu3MDhI7tKbI2k1IzuGQbAFelnsyPOAb2XjY0u7JbVm+iwFBdeK3QO07bN7N51/5q+t6T8GD0oOuxT9HNpOslBbQPbW71C3HwN2XKZ0Dm0a1t48oCsK652xk6IcXEB6wBX5PTjNjWt3aXXoG2TqMmzZy5g4FBlNy5KR+4caNvWCLpOwtFIfNQJclh5VTN2MgxA0Hqci1MpDmvda1ofZ9B9SbOww7eRqeMTkIquuQ2S8iCb0ZieF9v7RE0/25MpDms9a5pWNdicu/hGPBs5cfTIulHTl5w9yXiGYMIBQKi2jxpN44C+gc3Na5dWNbj4BiFDEvFsZde+R9f8/VcS6cidA1aHGatFHJLOuc2kTjxWYoskpSLkjxNPWVH0LMG6E7h0nUN6aQ7Mhg43CikyZiepuW4Y/N2a2yApD6YHQ2iYsaTCxJpGsAJH9K6SXDDqO72oWgzNZCM92Q2TB9bcBkl5MH5sDhQVR2wae8M0MRyM6I1salx7R679ggbQsyTtdQRH7RCdXXMbVgrpyJ0jXVvE/Blvspddh35RYmskpWK8PwCIOZaWxhBx7AzpzWxtWfsDUzWp1DaKtJk9voXpw3JdVisje0cAqAn201CfYIxGQrjWtGPVQFEVvB7R1e0KbSR4VKb9q5WRZwcBcIf76XAlOap3oKOWJCJnsZqwWkT9pnW+l/TAw2tuw0ohHblzpOeqXgBi7o0MHpEdgtXK6P6cEHBwgI6aBEe0TjRUehtcJbFn0xUbAMjaNrH3qOyorlYmjkwDoGVPsCOb5GC2G5OqsLGpROvy8h4AHFoPTx/5ZUlskJSesWOiwSCuDnBhJsXhbBdWs0pH7epPwFmKjk2icdGb7OGZQ5VbvykduXOkdZMPgLC7k8SkAsGx0hokKQnj+Y2pn0sySQ5p3VhNKm0+R0ns6bhI1MkFajYxORaG4GhJ7JCUltlpIafgdw6zIynqNjtrHdjMa9uAY9Bxpbj4hj0bGD05BolgSeyQlI5UPMNcWOgaTtQMsDGV5ojezcbGte1YLWZDLiATd/ZwtO/5iq3flI7cOeKpt2M2JdFVE9ZAL+mTUuyy2oiHU4Rj4mCcqh2kO5PhsN5Nd72zZBtTU7cHhQxpq4fUXBccl1G5aiMaTJLI2kDXCDWMU6NpHM4dmKWiqUfMIU7ZfKRnmkDWFVcdEyeCgII9PkusZR4LcETrYnNT6dZly8ZaACKeTmJTCkwfLpkt54N05M4RRVFo6xYL0JPsZfchWfdRbUwNijZ6Z3SSdHMUBTisdbOhRGlVEILVdbViqoMnupnRo7JOrtqYHhLr0hWbwl4rfn1Y62ZjCQ9Mi9WEyymihDXzvcz3yXVZbUwcFnI4vuBxvL4YGgpH9S42lXBd1jQ5MClpNNWCfa6LZP+vS2bL+SAdufOg89JOABKuXo6deK7E1kjWmsmjYo6lNzyIuy6Khkqf3llSRw6gZ0c7AGZlE3tGngUtW1J7JGvL1EFR5uGKDNPkThBV3IzRwMbG0q7Lrm1NADiyPewafKKktkjWnolDkwDo2UE2qykmTa3EsJc0IqcoCo3NFgDqYz3sr9ALhnTkzoPWLXUABL29RCZTEJ4ssUWStWTy8AQAemaQjaYUE+YOEthK7sh15gRYA77NjMwCE/tLao9kbZk6Ji4YaYbZmE3Rp/QACr0lTK0CtF4iLhgRzwZO+mMQmiipPZK1Q9d1ZqYzAEy7hrgwmeJQRuxTpYzIAbRfJMZ1Ye7hyHR/Rc5Pl47cedDQ6UYhQ8biwuRvJ3Pyt6U2SbJG6LrOzJTYmKbcw2zNFe4C9JTYkWve4AU9S8rmIzXbhl7BbfWSs2d2RkRgZ1wjbE6l2ZcSmYNS1sgBtPYKJf2wu5OQ3w7DT5bUHsnaEZyOk9bMqNkUg80TbEinOZDpwqwqdNeXdr9s2doIQMjbw+ycGYYqb11KR+48MJlUGhvER1gf7WX/kZ+X2CLJWhGciZPSzKhamsGWSToyGQ4mReqoVNIjBmariVpvGoD60GYGjsn5ltWCaHSwgq4x2ThOvaZxVO+k1mmhzmUtqW01TQ7MahrNZMU138VUv2zEqRYmjgcA8ERG0Fp1TAiB6p4GF1Zzad2Q5g1CWzHmbEab9ZLpf6ik9pwL0pE7T9ovagFANW3kwOieElsjWSumTgr5BHd4hEy7ggqc0FpwWU00emylNQ7oukDcMh3aJvYEKzNdIDl7pgfFunTFJtEaEyjAgNZe8mgciHqkpiZRj9QQ62HX2FMltkiyVkweHAfAFRmk2SFGGh7Ru0sy0WExDrcVl11kV1rmN3D0eOVlMKQjd54Y+fWgt5fAVBSi/hJbJFkLJg/kNqboEA2uBACDegs9Da41H0q+FO07RZo35upkMGSBMXnJqAYmnhO6ga7IMD5nDIATeiu9JW50MGi9QEStVXUDRxJ+iM+X2CLJWjB5Qlww0gyyPZUgrroZ1RtKMtFhKVpyChQ16W4OJypP51A6cueJEZaNO5vIzNahyW6sqmAylypIMcTmuJB4GNRbSt7oYNDYlUsXuFrQpp3oFVj3ITl7pgfEvMikMsymbIqwqYYg7rKIyAG05S6+IW8Ps0ErDD9TYoskq00mlWU+IH494xzkwmSKIVMXoJS80cGg9WLRiBN39nA8boeRZ0ts0dkhHbnzxO6y4HWKeqTmwEYOyPmW655sRmMuIBTA/c4htqVSREw+QrjKxpFz+WxYTRl0xUTTbDsTA4+W2iTJGuD3Cw3BabdodBhWxAFVLo5cU0/h4mubqcF/7NHSGiRZdWaGw+goWJNBputDdGUyHM2IkqRyWZfNG32AuGDEZqxkTlbWxVc6ciuA0Y3lTveyb2JXia2RrDb+sQiarmJORxmun2VTKs2Y2gZQNo6coig0tNgBaA63c8x/ELKZElslWU2igUKjw/HGMTam0hxNiZFtpRQDLsbusuCxCWHgzrluDgzLiTjrncmTImPhDZ1EbXGgAkdy67KzrjQzVhfT2OFBRSNtcdPob+TE8cqaPCIduRWg/XLR3h919zI5H5J1H+ucKWNjCg+RaHPh1HUGsmJjKhdHDqBpq7Apa+1gMA5MStHq9czUyQAArugEoXYFj65zLNuCSVXorC3N7N+laOoQh7cv2cPx1CikYiW2SLKaTA2I89AbHqTeJ6RxTuotuG1mvHZzKU3LY7Ko1NaK2ubWYDfHov2QSZbYquUjHbkVoG2zmNcW9nQSn3GiDf6uxBZJVpPJgTkAvKFBXM0i6nU4KbpEy8mRa9xQ0O0K+23ocl2uayafGwHAGRvGKzKYnNRbaPHaMZvKZ6tv2yGEYNO2DQxkLTC2u8QWSVaTyePCkTMnB9mcEXvnCb2VNp+9LBrDDFq21ANgoYcDqgnG95fWoLOgfH66KxhvgwOrmkFXLbTMtnP08C9LbZJkFZnKOXKkB9mgivrIQb2FWqcFn7O0Wl3FNHR4AIi621H8FiIDshFnPTM1IDrmE8oIGxNC4uG43ka7r3yicQCt28SlJ+ztJuK3EZfrct0SC6WIRjTQNfzOYbbGQmioDOvNtJXbutwu6vbC3h5m521kK6hBTDpyK4CiKNTn9JGawu08NyE7sdYryXiGYECkB+acw2wNiS5BQ3qknPA1OzGpOlmTjYZAI/MTz4KmldosySqg6zr+OdGAM+0ZZnM8WnRg2kts3ULq212YyJIxO2mZbubk8UdLbZJklZgdFRcKZ3yG8YYMHZkMIXsrKSxl58gZChRhdweOGRsTFdSIIx25FaJpq9BHMqmdjEVmIREqsUWS1WB6KAQo2OOzjDRE2BoWUZBBvbms0qoAqqpQ1yQihLXxDvqVJMwcLbFVktUgGkiS1KwoepbjjeNsTqcJ2FpJY6a1zA5M1aRS5xWNN22hDRyPHJONOOsU/2gUAHdkjHirCzMwaRap9XKLFNc0OrCasuiqhQ0zbfTNP18xF1/pyK0QTZtEfj3s7iAyZ0UffrrEFklWg+nBQqPDbKuDpmyWkLmOKA42lHhm4FIY6zJl7+R4yoZWQekCyfKZPhEARKPDibYsG9JpRlVxYJZb5AOgJSf34Mr0cMiiyEacdYp/LAKAKzqGqUU0uZxEaAmWW6RYURQaW8XFtz7WwyFzFmb7SmzV8pCO3ArR2CnqkSLudhzTFvxH5BzB9Ui+YzU0iLmzAQUYUXLSI2Winl9MY7doeIi4OwgErIT7KqutXrI8Jp4bBsARG8HW4MKmw3FN1Py0l9mBCdB2uZg8Enf1MJS0kj4pG3HWIzNDAQBckTFqfeLP+tKim76tpvwuGK0XCiczY+thOGVFH6qMMXLSkVshappEPZJmstE520TfsDww1xu6rjOV68ByRIdoahDO+7FM+UmPGBgND2F3J8qcGfPo06DrJbZKstJMHRcNODHTMJt0sa0fzml1lWNErnWziBRHXG2YZpz4+x4trUGSFSeb0QhMi/GFcfMYPckAAPtjDUB5rsuW3LoMebtJ+y2Ej1WGzqF05FYIVVWoL6pHGk6OQCpaYqskK0kslCIWyYKuEbSPsDUrOlb7UqILr6cMU6v17S4UdNJWD82zPmazczA/WGqzJCuIruvM5Rqpp92i0QHgYE4SpxwPTJfPhl1NgqLSM9POoH9fxdQjSZZHYCqGpoE5E2PcN8/GgJhP3ZduQVGgpab8IsXN+ckjzbRPuJiqkMZF6citII2bxE0jY+tkMGWGkcpYBJLlYdR7OOPTjDSm2RIWp+dJvYVmrw2XrTzELYsxW03U1JoAaIy1c9BmBVknt66IzCdJ6lYULUt/8wSbQzMAHNfacqKrlhJbuDR1deL4aQ61c9SchtljJbZIspLMjubq4yLjjDWpdCcTaCY7k9TS7LFjKSNtQwO724LHKVQJOgLdnNTmIThaYqtemPL7JCuYpp6cAKunk3DASujoo6U1SLKi+MdEpMMVGWek2USvfwjISY+UYTTOoHGDEKzG1MGxrJXYQGWkCyTLYzqXVnXFJjjemmFTMknG7GIaX9kVlBfTuFGksRzZDp63ykac9YY/58i5o2NE271YgIi7Gx21rNelMQ/Yk+7hkNkGFdC4KB25FaShU8wzDLs7cPhNBCpsXpvkzMyNGRvTBNkNrVgSQQCG9GZ6y7DRwcBw5MLuDgJBG9qgPDDXExMHxgBRtxnymenMZAi5ugGlLNOqBs0Xia7auKud6bCV4FG5X64nDA05d2QMa5twjmZtXUB5pvsNjIaHqLuHmYiV2MBvS2zRCyMduRWkvs2NouhkLC66ZmsZj/dDOl5qsyQrxOyI6Fh1Rcdw9YhDaN7cSAIbXXXl68gZF4yIpxN1zow9OgzhyRJbJVkpZnIzVlPKCL1WHyZg2iLmP5fzgdlgdPq72qmfMuGfKP/Ih2T5zA6L/dKaGKPBI8pOxkztQPlpyBXT0usDRMODMm0hVQGjDaUjt4KIwbuiHqk+1sERqwqju0pslWQl0DSd+Ukx3DvDOL0ekUYfU4X0SHsZDSVfTGOuczXuaKR9xs5xi0XWya0Tiic6BOzDbNbF/jOck8RpK8OCcoOaJicmRUMzWdk43cCAEoLAcKnNkqwAsVCKeFQ0hs05JtiYFGUpx7NCEqecLxj17S5AJ21x0zFdQyB6EuKBUpt1RqQjt8I09tYBoJg6OabZCPfJeqT1QGgmTjYLajbFhNfP1rRQoh/IComHctTqMrC7LbiEFifNoTYO26ykTpR/ukDywoTnEiSzZhQty6hvgk0JIffQVwEHpqoq1PrE0PSWUDsHbFZ0ecFYFxiNYY74LKONKTYGRAbgUBl3UhuYrSa8HrEu2wKtHLZZYOTZElt1ZqQjt8I09op6pIi7g3DASkIWlq8LCgrlE4w06WyNBAA4UgEbE0BDl6hRsemdHFWkI7demBkWdUiu6BijjRk2h6YBeD4uRgaW/brM1W/atQ4GVCuRY0+U2CLJSuAfKzQ6DDcq9AQnANgTEQ0urWUcKQZo6PEBYNfbOKZbSZW5YLV05FYYY8JD2N2Jd1YlO/8cZJIltkpyvhQ2pnECnbXUzIuO1eNaCyZVoclT3htT40YRKY64O/CHrLgCxyA2V2KrJOeLMZrLEx5htEFhU2727+6wcJDKuRYJoGmLcDhjrg5i8xa0ofI+MCXLw5AecUfGiHfUYtd1dGc9J6JCa7Xc12VDTy4g42onOGcjXuYND9KRW2EaOkRhedJeS8+0kz4rMLa3tEZJzptCRG4c25ZN4D8OCA25Fq8dk6qU0rwXpHDB6MA0ZyaNLnUO1wFT/bMA2OPDpGodNGezZN2tzGesKAo0e8v7gtGQX5fttE0qhBLDEJ0tsVWS88Wfa3RwR8awdYooXLKmFwCHxYTPWZ7ahgb17bkGMVebaBCbfQ7SiRJbdXqkI7fCWB1mPGIN0BTp4IDNRuTYoyW1SXL+zA4LqRF7fJzG3i2QiqCjMqI3lbUmkoHRuRp1tdI1ZaLPaiU7WN63TMmZ0XWdmTHRFR81D7PZLmb/xr0bAGh027Cay3uLNwrLUzYfvZMujlqtMFwZ8y0lS5PNaswZjWH6GG1OsT8GnWK+bpvPjqKU98XXcOSirhZaZ1TGzDpM7C+tUWegvH/KK5TG7lw9ktbJUdVKvF/WyVUymVSW0FwKgIBtnF6LkBoJ21tIYSn7OiQAT50dq0VHV820Blo4aLOSGJBprEom7E+QSisoWoZpzwSbEGmrObtxYJb/urTazXiMwvJQG0dsVmIDsk6ukglMitFcpkycyZp5epMikjVlEZJNlbAuvfV2zGbQVQttgUYO2axky1iGRDpyq0DTZjGqK+LpIBS04JndB7m5nJLKY24iCihYUmFG68P0pMW/5YxFaCK11pT/xqQoCvVtonXVk+7gsNmKY/aAnAdcwUwP5QRXo+OMNWTZlBS1uOPm8tfqKqYxV1hupYMTmpXUifI9MCUvTHE98WijzsZc3eYwlbMuFVWhrlXsl45MG0cVG5H+8s1gSEduFcgLXbo7aZxRmVHTML6/tEZJzpn8aK7oOCNNCt3RAADDilAAL2fpkWKaNolalZirg8mIA1XPlH1bveT0GB2rnvAwIw2wOTf7d1DPachVyLrMTx5xdZCYs+CZPwLJSImtkpwreUcuMsZQk5IfZXgsI6SaKiEiB9DQ7QMg6m5nNmzFPrELNK20Rp0G6citAkZheczRSM+0hQM2K4njMr1aqfjHiztWfbjnhWhpf4VtTMUd1Q6/QlRR0KUjV7FMD4q6TU94WHSs5g7Mw+nKWpcNHcbFt52mKRW/CRiV67JSmR0pOHKxznpciRCgcDAhOucrZV0W6uTa0OfMmDJhmDlSYquWRjpyq4DTa8Vh10FRaQ22c9BmJdon5whWKv5co4MrOo66aQPMnQDgQKIyNOQMCpHidnqm4LDNSuKkHItUiei6zsyQ6Ay0xYdRG+rwpRNgsnIwImp0KyHlD1Cf6/SPOVvYOGHiqNVC8nj5prEkZ8YYZeiIjeHoEJcKfF0MBrNA5USKRSOO2C87ZuCExYI+VJ6NONKRWyUacovAle7ksNmKe3o3ZDMltkpyLvhzw581bZzmtk0FRy4uUpVtFXJg+lqcqKpO1uygfa6Ow1YrpvHdZZsukJye0GyCZEJD0dLM28fZ6BKXCup6GQ2KxpxKqEUCcNfasNkUdNVEe6CZw1YrcdnwUJHEIyliYXHORazjdNvEOajXb2I8IDqsK2VdGhG5hL2ezhkbh2zWsq2Tk47cKtG0RWyscVcHgYgVNRuFqQMltkpytsQjKeIxMctyxj1Jj7UO0jF0xcSo3ojLasLrMJfYyuVhMqnUNYrOxtpEJ89Z7VjTIfAPlNgyydli1Me5I+OMNWpsVsThqNVtYiYimh4qJfKhKAr1uWixYupgJGXFNSuF1CsR/6gxmmuG0YYUGzMiCpes2UAiLS6MLWU+1cHA7rLgdIvZxXWxNg5ZrKgjMiJXVTR2FQRY26fhuNVC9mR5evOS0zOXa3Swx2cZaUzSg/jBTrg7yGCmzecoe02kYhp7RRQxZW9nLJ67GY/uKqFFknNhOpdW9URy9XG52b8Rdw+6DjazSp3LWkoTz4rG7hpApLHiczYsWlI2iFUgRmOYOzLGUKPCxqhYp3P2LgAaPTZsZlPJ7DtbjNGGaXsbkzEbrsQkBEZKbNWpSEdulTAKy6OuNjZMqRy0WYnIOrmKo7jRYbBJoTsn8RDIbUyVUh9nYGgcRtydeP0aAVUlOSjr5CoNIyLnDQ8zWg+bI/Piz22dgEhfVdIFw5iIE3F3UONXCKgqmTLW7ZIszexoYfbvcBP0zo8DMG4S0iOVtl/WG404rja0eTNpgOHy2y+lI7dKeOrtWM0aumqmfb6FgzYbtvFnZD1ShWGkClzRMcaazLRHxPigSbMh8VBZG1ND0aiuDVM6h2xWUoNyVFelUZB4GGWsQaV3ThyYI4pYl60VklY1MCaPRFwddM3oHLVaiByTdXKVhrFfeiJjhDrqqMlFrwY1MVO3UqSaDAqjutrpmNEZsFrKUrBaOnKrhKIo1DbZAKiNt3DEbMOeCcHssRJbJjkbZgdFpMMen0Dt6cQyNwjAEC0AtFVIvYdB8Uikrhk3B21W3MFjkAiV2jTJMklE0sTDQpTanJzC1t6BMzQGwMmMECOvlAYcg9oWF6oKGYuT1vlajtisOCafBS1batMky0TLaszlMhim5Bi1nT2QEQ0OAwmRCai0dZmXIHG30TVFbsLDkyW26lSkI7eK1PeIeqSMtYVA3EwG0KU+UsWg6zpzU2IjiljG6ardAHPHAeirMK0uA6vdTI1P1Kg0RtvZbfWgoMP43hJbJlkuYtII2BN+JuuSbPR2gJ4Fk5WBuOgSrLR1aTKr1DaJS5Ej284RxYEtE4HpwyW2TLJcAlNxslkwZRJMe/302sX5h7uFkZDIRFXauqxtcaKokDE7aQ/4OGS14gn1Q3y+1KYtoOIcuU996lNceeWVeDwempqauOWWW+jr6yu1WUtS156rk3O20jGjM2wxEzlefvl1ydKE/QkyGTHLctw3Tbe3C+ZOAvB8LCc9UmEbExSU9HVzJ6Np0XGbHpLp1UrBcORc0UlG6xU2W4XQKjUdjAVFDWelSDwU05Ab1RV1dzAbFk6dVobRD8nSGOl+MQEHNprEiCtqOhjLSY9U2n4pLhjCZjNt9GXFRancJuJUnCP32GOPcfvtt/P000/z4IMPkk6nufHGG4lGy29mZF2r+EePuVrZMKnTZ7WSHZYdgpWCfzx3YMYmGW7S6bHUQDaJrlrYGxJOeiUemMZsy7CngwZ/limTiejx8myrl5yK4cg5YxOMNihsJtedWtOZ1+qqtAMTihse2nHPacQUhbBclxXD7KjRGDbGcKNCr5EV93VWnIZcMfWdRoNYG+o8JBVInSgvBYqKc+QeeOABbrvtNi688EJ27NjBN7/5TYaHh9mzZ0+pTTuFuracI+dopHvKTJ/VgjfcD8lwiS2TLIfiG+ZwI3Tn+lQ0Xw/xnLZzc42tRNadO8Udghum4KDNin1yL+h6iS2TLIf5fERugtEG2JTT6tJrOhmbFwdmpTU7wMJ12TWj02e1oIyV374uWZriGavDjQq9iQQAGU870+HK0jYsxpjwEHW10zUN/RYr8ePl1VFdcY7cYoJBMT6prq6uxJacirPGitWKGNUVauQ5qxsVHcb3ldo0yTLwDxVGcw02K2xIxACIuruBytNEMmjIzwJuonvawnNWB/ZMEPzHS2yZZDkUp1Ynmsx0RwMAJN0dRFO5MUgVVlQOhZmrcUcjHbN2DtuseGPDEPWX2DLJcjBGc7kjYwQ6vNSHJgEIWVuBytM2NCh0rrbRM6XzgLWNo7aLS2zVQirakdM0jQ984AO8+MUv5qKLLjrtc8lkklAotOC/tUBRFGpbxSIw08JErh4pfkLWyVUC/uGA+EVmHK3GTX1QbExzdqHVVYnpKxCzgJ0OQFFpCbbxrE2kDrQRWSdX7iSiaWK5EVyW5CSu7l4swVEA5iyiAafOZcVhrbwLht1twekSR1JjtJlnzUIkWJeC1WVPIpImGhSd1EllnNaWzSi5TuppVUw5qjRtQwPDkYs5W+iaUfma5XI+p91aYqsWUtGO3O23387Bgwe59957z/jcpz71KWpqavL/dXZ2rpGFUNdhCAO30uDPMqeqsuGhAshmNALzIn/qd07Q4+1Byc1YHVeFVlelaSIVYyiWW+lgHNCBcL8sLC93jLSqLTHHtC/BxrrNEBRaXZOKODArMX1lUJtrEMPUwnBWlC2EBmSdXLljpFXt8VnGGpJsqNmQX5ejWuU2hoGYBWy1q+iqCV+8GbdllPba8vpeKtaRu+OOO7j//vt55JFH6OjoOOOzf/M3f0MwGMz/NzKydiM2jIaHqKuVninos1pwTst6pHInMBVD1xXMmRhTvnm6vd156ZFB3dCQK68f5rOhsVd0robdnbTMZhk1m9FGZOSj3MmnVWOTjDYobKnZDLmI3GBWaMi1VvC6NDr9Y84W3IE0KSAxWF4dgpJTWdjoABvdnRATKfETKbHXVOoFQ1EU6nPrMu5qpzs8xT++YUuJrVpIxTlyuq5zxx138OMf/5jf/OY3bNiw4QW/xmaz4fV6F/y3VuQdOWcLG6Z0DlvtuDLzEBheMxskZ0+h0WGC8TqFHk8XzA8CcDglIh+tFXrDhEI9UsTdQc+UzkGblRrZiFP2zE+IOk3R6KCwyV4P2RQoJgYSldtJbVDXIiQros4WOmZ0+q0WavzPyYk4Zc7iRoeN5lxk1erhZFSUFFVqRA6gvqNQJ9cxlaVvrrwkzyrOkbv99tu55557+M53voPH42FycpLJyUni8XipTVuS2pwjF3c00T2lssvqAyAldbvKmsLw53HG66HH7AItA2Y7hyPih7qSU6uNXQXF8p4phaetNahoMCaFgcuZuclCRG6kATYpua5pbztjuRqlSo18gJjwABB1tdA9rfOc1YVdi8qJOGXObJEjN9Sk0KvnajSLtA0r2pEzJjy42umZ0jnkP1RiixZScY7cl7/8ZYLBIC972ctobW3N//fd73631KYtibvWhsUq8uveRCPDiujame+T9UjljH9UNMS4ouOM1yl0Z3Kp8LredbExeesdWMw6mmqhPdDEXps4QCPH5bosZ4wRSK7oBP5mB225Tmp8nUwEhNxDJa9L4+KbsNfTPmvmqZzYcUQ2iJUtWlZjLufIOWJjBFtcNMdzDYUVriFnUJ+TEou4RefqYX95TRypOEdO1/Ul/7vttttKbdqSKIpCbZvw5uOuVlzzSdIAshOrrPHnWuktyXHmPNCTEBuVVttbpIlUuRuToirUt4o0ljvVzqQpQxaIyUacsiUZzxANiI5VW3wS94bNqLmCcmo6K1Y9vxiHx4LNroKiUhdrYsCWu/gekxeMciU4Eyeb0VGzSeZcs3TXbcx3rOrejooWqTaoy0XkkrZa2uecHJ4+WGKLFlJxjlwlUtdaqPvontI4YbVQF+6DTLLElkmWIhXPEAkJPa6QdYwmZzPOeVHTGHF3o+tgNavUV6AmUjF13T4AEo5mWueynLBYcM3ul404ZYrRsWpNBpj2xemp6813Bmo1nUyGchG5Cm52UBSF2tyhmba3oIYTZADrhBQGLlcKjQ5COL23phcCYl0mXG3EctqGrTWVm/K3Ocx46kQZQ9bSxsc2vL/EFi1EOnJrQF2rkV9vZcOUzm6LFwtptPHnS2yZZCmM0Vy25DzTvgQ9NT2Qkx6ZtYoO6bYae0VqIhVj1CPFnC30TOnstzpwZQL571VSXswVTXQYaVDo9HTmm6ZC9laymo5ZVWj0VN60kWLqWgoNYu0zGQYtFhriJyAZKbFlkqXwjxY1OjQpbPRtzHdS+81NADS4rdgtladtWEy9ISXmbmfjTHm5TuVlzTqltigi1zOl87RV6Or4+8prXptEkO9YzTU6dHu7IShSBRPkOlYrOOphkC8sdzazYVLnCZtYlzE537IsKUiPiI5V4ciJyIchutpSY8ekVvgFo6jTv2tG53fWOkxoJIZ3l9gyyVIs7Fgl58iJC8Y4hrZh5e+X+To5VxvJo0dLbM1CpCO3BhgSJDFnM+2zKsN2cWOOnZCdq+WIUbjrzjU69Hh7IFfzMaoJTaRmb2VHPQBqc1IPMWcT3VPQbxepD3nBKE/mi0ZzjTZAl6czn1od0dbPgZmPFLta6JqBXXZxwZg8JNdlObJAQ65JYYOnG0LjAAxlRLNKJaf7DYolSBJHpfxI1eGps2O2quiqmYy1AS2aQAfcs3LmajlipFZd0XHG6xV6HE2QFM0PwxnhyDW4K9+R89TZMZkVdNVCa6ieGXMSHTCPy8hHObJYDLjL7Ia06Fo9kfIBld0ZaJC/YDia6JpWGMrVomaHpTBwuZGIponMi1pvJT1G1GenTVeEVJNi4nhcOD/r4YJR32aUSLWRPFFe5SfSkVsDFFUpumW20jgbZ1I1U5+ehMh0ia2TFKPrOv4xIYorInLQY2h12WuYiIk6j0qvQwKxLn3N4tDMWFuoC6QZN5toih+X9UhlRiqRITInDkxbfIJos4eaWED8paeV0VDlF5QbeOrsmC3i4utJNRDIRtCAusAB2YhTZuRHcyX8TNYm2ODrxRSaEH/pbWc0Nxe4krUNDXzNDlSTQtZsp+Gb3yu1OQuQjtwaUddWqPvonIVHrWLMU0DOtywrYsEUyVgWRc+SUCfJ2i20ZcRmhLedmYg4TNdDRA4K9UgxZ7Oo37TUY0IjckJGP8oJY6KDNRlk1huj3dddmA5T08nYOtCQM1BUZUGdXNN0kkGTlVptjvTcUImtkxQzZ2QvIuNM1CkLZqyuFw05A9Wk5s/xuclEia1ZiHTk1ojimaudMzp7naKbx3/0d6U0S7IIf17YcobJ2iydnk7M4Snxl952ZnIacg3rICIHxQ0PYoTcbnszAOOHniilWZJFLE6rdhbVx+HrZCK4fg5MKKRXoy7R8PCIrQ2AsYNyXZYT81O5kXGxSSaMeuK8tmEH4+voggGF9KpxTpQL0pFbI2qLHLmOWZ1Rj9io1HGpj1RO5Edz5dKqxR2r1LQzGxHRuQZ3ZWvIGRQaHprpmYJhj9io9BEZkSsn5oukR0brWdCxiq9rXYiuFlMsjdM9rXPQI5o5wgOyo7qcCORGxjljU0zUQoenI78us94OpsLrzJFrNxy5aIktWYh05NYIQxQ45mymdU5h1iI23pbIYdCypTRNUkRhBNIY4/UKG7wb8h2rmqeNuaiIyDWul9RqUUSuZ0pn2iYc1ebQ87IeqYxYLD3S5e3Kp1ZT7nbmY5U/Z7WYYsmmzhmdUbcFAOe0bBArJ+YnF0bkRKRYaMgFrc3rRjzdoL49l1odlxG5qsRT78BkUdFUCxlrA+bpWWZw4NDjxMfLawBvNWN0rLqjE4WIXM6Ri9pb0HRQFKhbJxuTr8kBCmQsLpxpN+mAnxBmfHqIwJgcVF4uGI6cMzrJaOPC1OqsSaTDPTYzHrulZDauJMWSTV3TMK4E0IGOZD+6nIhTFqQSmXzHqjM2zWQtC9bltCLKh9pq7KgVrm1o0NTj5cY/uZCb//TiUpuyAOnIrRGqqhTqPpwttM9kecTWA8DYwcdLaJnEQNP0IvX8nPRITU9eE2nO1ABAndOK2bQ+fnTMVhPeehHFiTpb6JrM8IR9AwBDzz1aQsskBulklrBfpKgcsQkmaqHLU4jIja0j0VUDb6MDVRUdgmZ8WObD9KtebKQZPSLT/uVAcFpklSypMCFHFJPTRZ29Lh+RG9VzGnLraF3aXRY2X9Gcz2SUC+vjNKoQCg0PLXTMwhGfKOBNnJTCwOVAcDpGNq2hZpOYUrPMehfWyM2owpFbLx2rBsX1SB2zcLRWjCFLnny6lGZJcszn6pAsqTB+TxSL3UkD5ry24VBO23C9pFUBTCaVmibhAESdrXRN6zzh7gFg6rAUBi4H5hfUx4l0v5II5tfl8dT6c+TKFenIrSGFlvo2Omd1pmrF72v8+0tolcTAKGB1RSeYqtNx27zUY4GU0JUbz011aPCsj7SqQXHDQ8eszlStT/z53P7SGSXJUzxjdbRBocPTgRISUQ+c9QxHxDa+3g7MvDRObsLDcZ+4SCljUrC6HFhYH8eC+jgcdQyJbXPdrctyRDpya0hd0cbUMaMzaxP1Be3pERLh+VKaJgH84wtHc3V7u1HCIq2K3cdU3Aysn0YHg3zDg6uFzlmdGadovtmQHWR2bq6Upkko6liNTTDaAJ3uzoKG3DrsWDUoLkXpntYZd4ufv5bwgVKaJclhOHLO2BSTdeKCsbSG3PqJFJcr0pFbQ+qKRC5b5xTGIkMM04yq6Bx/TtbJlZq5BaO5yNXH5aRH1qEYsIFvQUQOTkaGmVHqMSsa/fukblepmcuJAYsZq0bHqqHV1VnkyK2vA7N4v+ya0RlDXHbb9SmmJkZKaZoECEwVUqvjiyNyC9bl+rpglCPSkVtDvA12TGYVzWQlY63DMx3lkG8rAIFjcsJDqZlb0LGqnKoht87EgA3qchG5hL0eS9aKMu2n37cdgPCAXJelJi+Jk5MeWSgGXBSRWweDyYspjDVsoc0PM5FJDlg6ATgpL74lRdN0AlNi3blik0zW5tZlLlKs13QwNi8dubVCOnJriGpS87Mto84WOmZ1RprFxmSf2ltK06qebFYjNCM2HmdskvG6hR2reNvWbUTO7rZgz+l0xZxNdMzqjLVuBMA9I9dlKUmnsoRyHauunCSOODDFqCq9ppPx4PoSXTXwtThBgbTFjWZy0+6H52t7AdkgVmrC/jjZjIaqpbEm55jyLYzIJZxtRFOiRGO9XTDKEenIrTGGMLAY1QXz9V4ANiQOE09mSmlaVROaiaNpOqZsElsyIFKr3h4wisq9HetuqkMxxfVInbMQbK4HYHP6KDOh8porWE0EJmOggyUdIeiIkrYsTK2G7a2kMhqKAi016yu1arGa8NQVSeNM64w3CG0yr/+5UppW9Rj1cY7YNLM1OlgttDhb8pFiv1loG9a5rDisppLZWS1IR26NKR7V1TmrM2aKkMRCnRLh0KH9pTWuiglMGRvTFEEnxOyK0OoqisjN5iJyjesstQrFEiSic3VITZDGTKMS4vmD8tAsFcVCwJO1YFbN4sDMpbCmc2LA9S4blnWibVjMglFdMzp+r/jZ25zuIxiRF4xSUehYFdIj7e52TKopH5GbVESHcYt3fV0uypX195Nf5hQX8HbM6hwLDDDu2ALApNRHKhnG8GdnbJrxemh2NuO0OPM1cllPO/7I+hrPVUxxRK5jRudY8DhTLlG/6T8q12WpMBw5d3SCyTrocHdgyiQgLrqJp3Lq+esxSgzFGYxmOqdhODNHHDseJc6Rg1KGpFQUZqwK6ZEOTwdkUhCeBGBcF47cerz0liPSkVtjCtpIrbTMwWRwlEDLJQCoUh+pZASKb5hGfRzkI3Iha+O6G89VzIKInB+Ozw+Qat0JgHVCrstSYUiPOGMTTOQLynONDrYaplJiLa63uk2DgvZmK90zOgPB44w6cxeMPtmIUyoKF9/cjFV3Z67DXweznbGUGC5fv04vGOWGdOTWmJomB6pJIWuykbXU0joH851iJFJH9BBRWSdXEozUqjM+JUZzeXsgEcyLAU8romasdh2N5yqmWBTYnlJwzydJ9l4AQG/yCNOyTq4kFMSAi0RXizTkZvMNOOvzwCxOrdaHQQ3HGGsVHdXmiT2lNK2qWZhaRdRt5qVHOvBHRT3xesxelCPr70Qqc0zFnau5OrlJn7i9XKAMsff4RCnNq1oKN0yhiSQaHQpiwDMJIUa6Xg9MT50dk0VFV83EHQ2io9onJllcoAzz7LHREltYfWTS2XwntSs2wWRuDBJBw5HrxJ9vwFmfB6ZxwUjaa8mYbHTNQLBDdPp3xw4RjKVLaV5VEo+kSETE5+6MTTNZt0gSp6aj6IKxPtdluSEduRKQV9J3top6pPg0IXMdFiXL4EGZLlhrEpH0go3pVA25DmZyhdXrteZDUZX8BSPmbKZzFo4l/YQsDViULGOHnyqxhdVHYCqGroM5HcWcDhUkHgIFDbm8JM46XZd2lwWHV1yejEacCZf4XrcoozxzdLCE1lUnRhmKLTGHToqZmlPFgI0Of5laXRukI1cCCgW8Qurh6Hwf4YbLAEgPPVtK06oSIxpnbEzTvsVTHdqYDa/vyAdAXctCjcP++X7izaJOjtFdJbSsOsmnVWOTzNUoZMwLRVcXHJjrsG7TIL9fGusyNkHAKibiDMmL75pj7Jeu2CRTPtBU0bW6cF3KiNxaIh25ElC7qHN1IDCAvfcqAJpDB4jIOrk1pXjUzJQPFLOFVlfrgvFc1bAx+RZJkBybP4Z30zUA9MQPMRmUdXJryXx+NNcEEz5QFVUcmEXzLP3rPCIHxbOAW2n3Q3+gn2TugpEdfhZd10tpXtVRPGN1ok6hydmE3WwvROR8nUWam+t3XZYT0pErAXVthY2pZQ4yqQTBdqFYfqk6wK6TclD5WlJodJhmvF6hzd2GWTUXUqvreM5qMQskSGZhNDyC1iUixZer/Tx9fLaU5lUdxRG5iVpocbZgNVmXbHZYz0XlxQ0PHbM6w6FhnJvFxXdj8ghD/lgpzas6CtIjU4UGHMhfMLKeduai67sJp9yQjlwJ8DU5UVSFrNlB1lJD2xz0WSxoqLQrfp47fKTUJlYVCzqwDE0kKETkatrzN8z1WiMHCyVIHCmoD8OAw0lWMdOoBOnrO1hiC6uL+WIx4DqFTm8nZJIQmQJA8xaaHdZzLVJtPrXaTF0E7LEMo/XiZ/RSdYAnjk2X0ryqo7Bf5qRHPJ2g6/mIXMjWsq6lmsoR6ciVAJNZxdck5s9FXaLhoS88RLhGCAMH+mVh+VoSWNCxqtDhXuTIeduZCa//G6avyQEKZCwu0haPSK+Gh4jWChmS5KCcb7lWaFmNoDH7Ny4kHjo9nYVOarOdIB4ymkgr1rvW7wWjLnfBiDsa0RQz7X4YsKj5C8ahI4dKbGH1kE1rhGaNmdRF6zI6C5kEoDCdm+qwXqWayhH5KZeIxaO6+ub7sPdcDUBL+CAjczJdsBZkiw/MmNCQ6/B05G6Y1VUjZ7aa8NYbsy2b6ZiF/vl+7BtEnVxn9BDjgXgpTawawnMJtKyOqqWxJ+aZqMuNjAvn5Ik8rfhjIhpX47BgNa/frdxZY8XqMIOiEnM2ioaH0BDJhgsBUSeXzmoltrI6CMyITmpTJo41FSpE5Iy6TU8Ls3HjcrF+L73lxvr96S9zikd1dc5C31wfth5R93GZ2s+jfTJdsBaEZ3MHZjaJLRlg3EitJoKQFqktzdPKXHT9p1bh1HqkY/PHsOYuGJer/Tx9wl9K86qG4qHkuqIz7VsUkfO2MRNe/2lVAEVRiuo3W3OjDY9h3yDW5QXZPp4bCZTQwuoh34ATmyJtgXkP4oIhNeRKinTkSkRdUUSuY0ZnJj7DXKNIrV6inOCxo5OlNK9qKJ6xGrNDyCnmWeYPTEct82kz2VwKa73XfOQPTFcznTPCkdM7rgRguzLE7oHxUppXNRSn+2d9KlmTcoojV00HZn60Ya4Rp3++H7VDXHwvV/t5ol824qwFhQ7/ScZrQVdyGYwlNOTWcyd1uSEduRJRLEHSHABzRqdPyZC1enEoKfwn9pJIZ0trZBVgiFs641OM1YkK3Q5PR1F9XEd+Y6pzWbGs85qPBRE5P4STIaYsVpL2RixKlsBxqXO4FizopPaJS0Snp3NharUKOlYNii8YHX6d6dg0wWZRu7ldGeQZOXlkTSiWHpmsVfBavdTYagoi1UUROZlaXTvW96lUxviaHSi5wvKs2UvbHBwL9KN2XgHAdk2msdaCYg25iTqFGlsNHqtngRhwNTQ6GBRLkDiTUBcW69LUJaIfHZGDjM7L+s3VpjgiN1kLDY4GnBbnooicodW1/tdlXdEFoyEEjqROvx4n62zEqmTRxvYRjMtxXavN4g7/xdIj+LoKFwwZkVszpCNXIswWE97GXOeqs4XOGZ2+uT6UXBrrMnWAR/tmSmliVbBgxmp9UcdqsFh6pIpSWLkDM2mvI6ta8xMezN1GnZxcl2tBoCjln290gCVTq/XVsC6LUqs6Cm1+6A8MYOoS6/JSpZ+njsuL72qi63rRflkkPQKLauSq54JRLkhHroQsqJPLda7SLiJylyn9/ObotFQtX2UC+XEz04VGB6jaWiS724LDYwGKZq7OH4OieqSHD8v6zdUklcgQDYrD0BkXEbn8usynVqtrXXrq7ZgsKppqJu5oyF8wyF18L1cHeOyYvGCsJtFAkkwyi6JrOOKzixy54ho5I7W6/tdluSAduRJSl79lttI5CycCJ0i1XgLARnWC0NwUJ2ajpTRxXZOIpomHRTrGkZvqUNCQy21M3o6qmOpQjK+5IMBqdK7Sdim6aqZJCXDyRB+xlBwjt1oYlwtLKowlEy9E5DSt4Mh5W6sq8qGqSn5dGiPk+uf7obNwwXjw0GS+KUmy8uQ7qeMzqHq2oCGXikIsFw2t6ciLVMtmh7VDOnIlxEgXRFytdM0qZPQMJ9IBqN8MiPTqI0elDMlqYRyYtsQ8Ji25MPKxQOahumo+FkuQDAYHSatmaLkYgIu1Pn4ruwRXjeL6OE2FmRro8nZBdAa0DCgquJurKrUKULdohNxAYAC9tXDBsMfG2Ds8X2Ir1y/FjQ5xuyo6/D0dhTIUmxfdXlN08V3/F4xyQTpyJcQoLI85m2ia17BkRJ0cnaLuY6d6TNYjrSLzRR2rgRozafMSYsBVWPNRaHhopnNWIaOlORE8gVKUXn3oyFQpTVzXFDpWp5j1mQrSI+Hc5cLVhK6aq2LOajHFnf6dfoikI0ykAii5C8blSj+/PCDT/qtFYcbqJOO1osNfiAHnZv/WdBBOZkhlhDhztWQwygHpyJUQI1WQtnrJmhyigLc4XaD088xJP9GkTGOtBgtGc/nE5tPhXigGjKeVWaNrtdoicq4WnEmd2gj0Bwr1SJepA/zm6AyaTGOtCsWNDqO5dSk05App1VgqSyKdOzA91XLBMNZlKw1BHVvKqJMrCKn/6tCkrCteJeanCh2r47VgVa00OZsW1McZaVW3zYzdYiqVqVWHdORKiNVuxlUjNuGYQ9R9DAQG8hG5y0zH0bIZKXa5SsxPFqRHxmt1TIqJFldLQXrEUQdWZ/VFPooixZqiFurkOoUjd6EySDgS5rnRQAmtXL8Ud1JP1lHQ6jLWZVGjg8Niwmk1l8rUNaW21dCSa0HRoW0ud8HIXXyvMPUzFohzYCxYSjPXLYXU6iSTOekRVVGX1JCrluxFuSAduRLjKzo0O2d1sTE1bAF7DQ6SbFOG+dUhmS5YDRZqdSm0uloxq+ai+rh2NE3HXyXjuQw8dXbMFhVdMZOw19M5k+tc9XWDqwmLkuUi5SQPyHW54ui6TmA6N/s3Ps1kbZH0SL7RoahjtUqicQC+JieKqpA12UlZa4ouGMKR264MYSPFAwflulxpUokM0YBYc87YFONLdaz6OvPZi2qp2ywXpCNXYnzNRmF5E50zCMXydDifLtipHuOhw1MkM3LKw0qiZTWCM7kDMza9sNEhnypoZz6WqprxXAaKqhRdMISSfv98PyjKgi7Bnz8/IdNYK0w0kFoo8VBbJLoaWqpjtXoOTJNZpcbQ3nS1FDpXazrB3YKJLJcoJ3jgoEyvrjTGpdeaFp3Uk7VK0X5pROQ6mY1WVz1xuSAduRJTa7TUO5rpmRM1BSK9Kg7MF9tOEE5meOKYTK+uJCF/Ai2ro2op7Mn5hRvTEur5tU7Luh/PVUxtc3GHYG4kUjIIHULn8ArzcUbn4zw3KtNYK4kxacSemEXVs0zWKXR6DUfu1NRqNTlysHDySMcsoqNay+TT/leaBzgxG+XYVKSUZq478mnVqLhMLDnVoaYQkau2dVlqqudkKlOKtZEa5jJY0joD8wVH7mpzPwC/ODBRMhvXI/kZq7FpFHSmfBRpyBnjuaprqkMxviIJkq5ZFXR9gTDw1ZbjgM79z42X0Mr1Rz7dH50iqypCemSp1Gq4OiMftcXam34h2XQydDK/Lm/wDAHI9OoKU1xPHHGZiNlzqVUtW7j4Fs9ZrbL9stRIR67E+JpFqiDubAJdod2fK+Bt3wmKii81STNzPCjTqytKcUF5qMZCylIckZOOXLEEiTOh4Yvm6uTaLgPFhC8zSxt+fn5gQnavriD5dRmfxl9nQlOVJVKr1RuRy2vJuZrzkk3Fnf7bs0cBnV8elBfflaR4xup4nfgzIYkzKbQNVTN4WvJdq41VdsEoNdKRKzGeegeqWUFTLSTstaLhYb4fbB5ovhCAV7gHCSczPCY15VaMxUPJobhGrjBntdrEgA3yUg/uNnSgcya3Lq1OaLkIgGttJ5gIJqQI6woSmDLqNqcY9YmLW5e3CxIhSIXFQ55W/NHqdOTyETlXG6oOrXM5yabWS0G1YE/66VFnOToZZlBOxVkxisWAx3waqqLS7m4v1BN720A1Ve0Fo9RIR67EqKpCTWOhTq4j17mq63pehuSWevHD8qO9YyWzc71RnCoYqRE6fR3unBhwUddqtY3nMvA1O0CBjMlO2uKhYzZ3YEI+jfXaerEefybTqyuGUSPnjE0xUQsOs4N6e30hrWqrAZs7n1qtr7LIh1GKkrK4SZud+f0Six1y4w3f0iI+q5/LcpQVQctqBKcL0iMTdQotzhYsJsuC7AUgU6slQjpyZUBtUZ1c16xCOBVmOjadd+Qu0fsAePjoFPO5riDJ+bFYesRj8QitrkSgIAZcXItURTIPAGaLCW+9HSjMXO0P9KPpWj6NdalyDICfPjcu0/4rQDatEfYnAJFanagVaVVFUYouF60AVRv5sNrNuGvF9xx1ttBuZDAgf8F4lUdMGvjh3lHZvboChGZzjWF6BntifmGjg3HB8Ih16a+yKTjlgnTkyoBCw0MT3Ut0rjpmD7KjxU46q/Oz52X043xJRNPEw2nA0OpaIq3qqAOLo2oPTChOY7XQ5VeIZ+KMhcfyEx6884fp9CjMx9I8dFjOBD5fAjMxdB3MWhJrKsRkbVGjg+HIearbkQOoM0Z1uVro8MNEdIJwKpzvXO1NHsJhMXFiJsq+kUAJLV0fFNdtKuhMLOikLnT4J9JZwrkpRNUyBadckI5cGZB35BxN1M+lsaZzt0xfN7ibQUvzJ5uEzMMP94yW0tR1gRGNs6WCmLPJpaVHahamCqplqkMxBQkSMXM137la2wPOBhQtzZ9uFTIP9+4aLqGl6wNjXTqiUyggDsx85KOQ7k9msoQSuQOzCiMftUUd1T3+ootvLiJnmjrI6y+sAeD7u+V+eb7ky1AiYg1O1i4dkTP2SqtJxWOrjmkj5YJ05MoAw5GLu1tRdAqdq4qSj368wnkSs6rw3GiQQ+NSu+t8KEg8CImCydpi6RGjeFf8vlqbHaD4wGzFGc9SE4VjgWMLhIFv9onP67cDs4zOx0pm63qgkO6fJGtWmPVSFPkoiAEb6SuLSaHGYSmFqSUlP6rL2UKTP4spawgDd4iIpZ7l7V1zANz/3DixlJxVfT4Uz/41OvzPLFJtFeUAkjVDOnJlgBH5SFh9ZFUrHTO5mauQr5NzTe/l1Re1AHDP00MlsXO9UCw9EvVaSVqXFgMuHs9VjSms/MxVbxtAoaMa8heMurn9XLuxHl2X0Y/zpbhuc7bWjF4sPVIU+TAcuXqXrSoPzEJHdSsmTadlnsLkkdy63J7po6feSTiZ4cf7ZJPY+VC8LsdzHf6nRIo9bfjzY+Oqb68sNdKRKwPsbgt2l7hZGzNXjweOk9WyeUeOkWd4x9WiXua+feME4+lSmVvxFG9MM3UiNZOPyBVJjwTi6fx4rmrrDoTCgZkw15Ax2eiYzWnJQT4ix8gu3nql2NS/t3uEdFYrhanrguLIR156JF8jt4S2YZU14Bj48hffWrKqpdC5Cvl1qY7t4h3X9ABw95ODsunhPCjeL0dqRXSz09OZ6/AvjsjlOlarZJRhOSEduTKhuE6u26+SzCYZjYxC6w4wWSE6w1W+EFua3cTTWVkrdx4UayINe4VDfCYxYF+VjecysLstODzighF3iAvGcGiYeCaeFwYmPM5NnRka3FYmggk5geQ8KC4qH6/VMatmmp3N4i+LDsyZ/IFZnZEPh8eC1WEGRSHuaMxL4+i6nq+TY+RZ3nR5O06riWNTEZ4+MVdaoyuUZKy4MWyGiVqFOnsdLosL4vOQFWsRd0tVzv8tF6rvdCpTioeU5wt45wdy+kiXAqCMPss7XtQNwNd/e1JGP84BTdMJzhgHZkHcstUlugEXOHLh6m10MPAVzVztmTOjI6LFWF15wWr75F7elYt+fPXxEzL6cQ4kImmSURHtcMamRQOOuwOTaoJMCqI5MfAqnrNqoCjKgtGGnX4IpUJCsql1B6gWiM1SkxjlDZeJpqVvPnmylCZXLIFpIVBty0YxZxNM1HFqGYqjDiz2okhxda7LUiIduTKhWEuudi6FNa2LwnIoSmM9w5t2dtLgtjEWiPNjKRB81oT9cbRMQRNpspaCuOUCMeC2qhUDLqYw27KZjhkd9KI6uaL06ttf1I3donJoPMRTx/0lsrZyMaJx9kwIk5ZaeGBGJgFdOCjO+oJWV5WmVqFov3Q00TMnOiQLwsA7xEMju7jt2h4Afn14iuMzkVKYWtEUOqlFY9jCTurcPNtcDe1svnazetdlqZCOXJmQ71zN6US1+XMROSiqk3sWh9XE/3tJLwBffHSAjIzKnRX5tGpiFgV9ofRIfB7Suc5Lb2E8VzXfMPMSJK4WHLEMNbGiOrlcYTmjz1LrsvKWK8QG/9+PnyiFqRWNMdHBEREpVCMiByxIq6KqhchHlaZWYaH2ZtNsBlVb4oIx+iybmz3ccEEzug5feuR4iaytXPL1cZEJNEVhyrdUo0NO27CKO/xLjXTkygRfU+GGqQPt/uLO1dzGNHUIEiHe9qIu6lxWhvwxfirHI50V+Y0pXNBEOiVV4KzPpQqkSrkRkYvXiM+oY0Y/1ZGbeA4ySf74ug2oCjx2bIZ9cv7qWVEsiZMxq/i9ReuyqDMQqPpmByhy5FytmDMaTQFO6ahm5FkA7njFJgDu2z/GyJyUyDkbAtOFus1QnZWsaWnpEaBq5/+WA9KRKxNqGh0oCmQUKymrl45ZnaHQEKlsCjwt4OsCdBjbjdNq5r3Xi6jcF34zkO+slLwwxdIjCY+NuL048rH03MBq3pjyKSxrHZqi0uEXETld16GuVzi92RRMPE93vYs/uFx8lp/+5VFZK3cWBKZELZIzNs1cvRVdKV6XC8dz+WVReZEj14wOS3auMnUIUlEu7fRx/eYGsprO5x/uL43BFUo+tRqbZqJOSN3kO6lPuWBU5/zfckA6cmWCyaLiaXAAoh6pe95MVs9yMpgr0i1KrwK845pufE4LJ2aj3C/Hdi2bQFHH6my96MhcqmMVqlsM2MBTZ8dsUdEwkbDX0+GHQDKAP+HP6XYV0lgAH3zVFqxmlWdOzvHosZkSWl5ZFF8wxn2iXKLdI9ZhwZFbNJi8mlOrTQ5QIKPaSVvcdMzCicAJMlomJwzcBnoWxvYCYl0C/GDvKEcmQqU0vWLQdT3f7OCMTzPoFY5aYb8sROQyWY35mLxglArpyJURhQLeZrqLC3jhFEfObTPzJ9dtAOBff9VHIi2Hli+HgsTDFGM14jNbSkMOqns8l4GiKgs6qnsD4rMopLGuEP/Prct2n4N3XSM6qz/zQB+ajBa/IIs7qYd9Qu6h3Z1z5IrEgLOazlxUNjuYrSY8tXYgd/GdU0lpKYZDuVFxnQsvGJd31fKaS1rRdfjnXxwphckVRyyYIpPMoqDhiM8yUQcOs4N6e714oCgiNxdLoeugKlDrrN51WSqkI1dGFBfw1s8mCqNnoGhj2gWauLG/57oNtNbYGZ2P8zVZYP6CJOMZ4iFxCDpj0wx6haO21FQHkKlVg9oiCZK2WbH2TqnfHN2df/7PXrYJj83MkYkQ9+4aWVNbK5FCJ3UWe2KeiVoFn82Hx+oRDxSlVueiKTRdBEPrqvzAzF8wHE30zono+qmd/rvyz3/kpm1YTSpP9M/ym6NTa2prJWJceh3pIKqezXdS56eJFIsBh8W+WueyYlKrb9pIqZGOXBmRd+Q8bahZneZA0YHZdCFYXJAMwcxRAJxWM3998zYAvvDIACdke/0ZMdKqNi2GOZtgshZcFhc+m088UDRnVdN0KfOQoyBB0oIrmMSZKGrEabscFFV8djmHo9Zl5QO5VNanfnmE6VCiJHZXCvn6uPSc6KSuK4rGwYLUqlFQXue0Yq5Ckepi8g1izmYaZ1IoxdI4xSn/XK1mV72T217cA8Df3XeISFLOYD0T+fq4XCf1RK1SWJeZJMRmxa+ltmHJqe6doMyozUuQiIhQe/FsS5MZOnaKX488k/+a1+1o4/rNDSQzGn/1g+dlKusMGBIPzri4jRsSD4UbZiEiF4ynyRjjuaq4FgmKLhg1olutfbZIGsfmFpcMyKdXAW67todLOmoIJzL8/f2H19TeSiN/YOZqNCeKJXF0fUFq1Yh8yILy4oaHFsypLA3BopR/6yViIk7MD3OFbMUHbthMR62DsUCcf/tVXynMrhjyHauRSTSTymxNURmKoSFnsoKzTnaslhjpyJUR+Y3J5EVTTHT4YSI6QSSVi7QtqpMDoXL+qT+4GJfVxO6heb755OAaW105GIW7jqCIvC2QHtH1BTVyM0Xjuazm6v4xqTMico5G0SGYk8bR9JyGYaehJ1dIY5lUhX9+w8WYVIWfPz/Bz6RMzmmZL5IeyVpMzHuKInIxv+gKBuHIychHnvzFN1cK0e7PTR0BMNvyE3GK16XTaubTf3AJAHc/NcgzJ6R49ekIGheM+DShBgeaWnTByF8uWkBR5AWjxFT3CVVmOGusWGwmQCHuaGBjrrC8UI9kOHLPLPi6jlonf/17FwBC9kFqeC1NYcbqNCm3jaijSOIhPg8Z4ejhacuLW8oDE2pyHYJpxUba4qFzTiWWiTEeyTlnHUX1m0Vc1F7Dn71sIwB/+6MDDPulhtdS5CPFsSnmG+xCemRx3aarEcxW6cgVka+Rs9SiKSrtfhgJj4hZwLBgIk4x121u4C1XdKDr8Bf37s83j0gWku9YjU0xVSdchUJEznDkZD1xOSAduTJi8QzB7jkxczXfuWp0CM4dh+jsgq9921Vd3Li9mVRW40/v2cN0WNYlLSafKohNMd8gNpxTpEecDWCxF43nkjdMs8WEt150CEadzWwOiF+f0vAwvl/MBS3iL165mSu6awknM/z5vftIZeQkksUEii4YkzmtrqU6VkFqdRXj9tkwW1R0VBL2ejbOW9HRORHMpVKNdTn8zClf+/HXXkhvg4vJUIIPff85WZKyiGxWIzRTkB4ZykmP5NflIjHgWaltWFKkI1dm+IokSOqnEyi6XqhHctRCw1bx66L0KoCqKnz2rZeyqcnNVCjJn92zVx6aReiaTrBIpXzCJ/789B2rcmMqxtdcmLna5l/UuVrXKwZnZ5Mw+fyCrzObVP7z1svw2s08NxLgn34u6+WKSSUyRIO5Tur4VL6TutNtqOcb2oYy8rEYRVWoKZqI0zMvOlfzdXJd14j/Tx8WEfciXDYzX/ijy7GaVX5zdJovPybHdxUTnk2gaTomMtiSQUZqcpI4hrbhaaaNyAtGaZCOXJlRa6QL3C2YkxnqQkUHJpw2XQBCW+6r79iJx25m99A8f/+zQ2thckUQDSbJpDQUNOwJP4MeEbEsaMjlOlZzo6ikGPBCaosixe7ZGJZ0USOOopwyFqmYdp+Df3/LpQDc/dQQ//fs8FqYXBEEc+krq57Akokz6suiKiot7hbxQGhhRM4vtQ0XUJzBaJpOQvHF190E9ZsAfcmo3PY2L3//OtGo82+/7uPBw1KSxCA/Mi6V66SuhXp7PQ6zEK0/NSIn12UpkY5cmWFsTHGfuJF3+MWBmR93tETDQzG9jW4+/4eXoSjw7WeG5aGZI19QroVRdY2RmgwKCm1ucaOUGnJnxqhHinvbUXRom1t8wTi14aGYV21v5i9zkiQf+8lBnj05t6r2VgrzRn1cQkzBmKhTaHG2YFFFdCkf+chPdZCp1WJqi8SqrdEU3tiidWlE5YafXPLrb72qi3e8qBtdhw/cu4++yfBqm1wRGGUojpAxk7qobhNOSfnLsXGlRTpyZUb+hmlrAKBjFuaT82IkEhQcufG9p9QjGbx8W9OCQ3PPkGx+CBaNQAKxMTW7mrGacgfiaeasyhumIL8u3WLjbvfrnAyeJK2JlMvpGh6KueMVm3jNxa2kszrvv2cPo/Oy+cGoj3MEhHDygk5qOGXOqrxgLMTXJCJE8Vox/7PdX1RTDNB9rfj/0FOnfY2PvXY71/TWE01l+ZNv7WJeNj8UInKRCTSTykzN6bQN29B1PS8/Ii8YpUE6cmWGIXKZwkba7GJr2A0U3TLrN4lauUwCpg6c9nVuf/kmbr6oJX9oTlW5KKshumqfFxHKybqitCqc1pGrdjFgg7zUg8mDppjomTOT1tKFkUjtOWHg4Egh7bIIRVH41zdfwoVtXvzRFO/91h5iqeoWZS3uDMzazMy7Fx+YhciHrheLVEtHDopqN+2NAHTM6kzHpgkmg+IBIyI3vhdSS18cLCaVL73tcjrrHIzMxfmzb+8lna3u+uJAkfRItN65UHpkkbZhMJ4mnc1pbkpHriRIR67MsNhMuGvFJh1zNhU6V416JFUtRD9Ok14FcWj+25t3sKXZzXQ4yZ/es4dkpnrnsRaGkk+TcVgJOxYdmIvnrIZlqqAYQxpHRyXuaGBLSDh2+eiHzQNN28WvzxCVc1rNfPWdV9DgtnJkIsRffq+6OwYDResy1OgCZXEKq5BaDSUypHIORr1LHphQSPknFQcZk50tQfH7vJ5cbY9I/2kZGNt9mlcR00i+/q4rcVlNPHXCzz/8rLqbcorX5WyDSPMvlGrKBQY8rfl0v9duxmY2rbmtEunIlSXFBbz1k+LGvtyGh2JcNjNffccVeO1m9g0H+MRPq7f5oVh6JNTkXHhg6vqCiJym6YXUqox8AKdK47QbM1fni9ZlvuHhzOuy3efgK2/ficWk8MuDk/zXbwbO+Px6Rdf1woEZn2I6p9WVv2CkopDIRZa8BTFgj82M3SIPTACbw4zDK5zamLOJDbnO1fx+qSiFqNwZ0qsAW5o9/Geuvvh/nx7inqeHVs3ucmZxJ/VojQgAnCIG7KgFi12m+8sA6ciVIcUHpjWSwBPTFx6YL9DwUExPg4vP3yo2p/97doRvP1N9m1M2oxGeLWgiTdWJQzC/MRXfMOV4rtNSLI3jmYqgavqiwvIXif8Pn/nABLiip45/uuViAP7joWP86tDkittb7kQDKdLJLAo6jvgsw15Rb1iQxMkdmBYX2LwFkWp5uVhAbdG6bJoWDkg+gwGFOrnTNDwUc8P2Zj50o5B4+sRPD7F7sPqacvKd1CSxZOKc8IjLxikaclIMuGyoWEfui1/8Ij09Pdjtdq6++mqeffaFnZpKId+5WtcNiIaH/kB/YSRS++WgmEQUKVckfSZetrWJD98kNqd/+Nlh+qeqqzMrNBtH18GsZLCmQgznxC1PkR5xNYLZlt+YahxyPFcxeUfO04qa0WieXxQpNg7M8f2QjLzg673lyk5uu7YHgI/88Pmqq+PMR4n1CKqe5YRHHKAFMeCiTmpFwR810v0yrVqM0fAQczZhn4/iSC6+YOQiciO7IPvCNZl/9rKNvHZHGxlN5wPf3U8okV4Ns8sWY126UqLBbrxGw6yYaXY2iweMiJx3UceqrCcuGRV5Sn33u9/lzjvv5OMf/zh79+5lx44d3HTTTUxPT5fatBWhtmgYNEDXnEo8Ey+MRLK6oEVEMxh+elmv+f6XbuSlWxpJZjQ++L39VSUWbIzmcmWDKMBxt/j96cSA5VSHpTHWZSInjdPu1xkODZMwopm+LqjpAj0Lo8u7WP3t713ARe1eArE0H/7B8wWZnSqgkFYV+9ZkrY7D7KDeXi8eOI1Wl4wSL8RoeIjXinXZ5hcXjPxaatoO9hpIR2HyuRd8PUVR+Oc3XERnnYPR+Tif+El1laQY69IeMGZSC5kmk5pL558ybUSuy1JTkY7cZz/7Wd773vfy7ne/m+3bt/OVr3wFp9PJXXfdVWrTVoR85EPxoKNwQdgDLI5+vFj8f+i3y3pNRVH4zJsuwee0cHAsxBd+0//CX7ROyGsiRUX6bqKWRQdmLiLnFY6dUbwr6+MWYqzLqFVI42wKONDROR4sUsXPyz28cBoLwGpW+dxbL8VmVnn82Az3PFM9uoeG9IjRST1Rq9DubkdRxJiufN2mkcIKy07qpchrHOamDnT6IZAMFCSbVHXZdXIGHruFz731UlQFfrRvjAcOVk/qP9+xGhlHV1WmfaeXHgGZWi0HKs6RS6VS7NmzhxtuuCH/Z6qqcsMNN/DUU8v7IS133HV2TGYVDZW4vf7UzlWAHsORW96BCdDstefrkr7y2AmG/NEVs7mcMTTk7HOiPnCylkUH5qKIXFhuTEthOHIprKTNTrbmOlcX1G8ajtzg75b9upuaPPz1zdsA+Mwvj1bNnOD5Yq0uq5l5zyJJnHwKK3dg5lOrcl0WY0SKo6aaBRffY/PHCg/lhYGXf0bs7K7jT1+6EYC//9khosnqkMop7liNN7jJms4sBjwrU6slx1xqAwx0XSccfuHarYmJCbLZLG63m1AolP9zn8/HoUOHFvyZQTKZJJlM5n9vvM9Sz5YLFq9GZDLKrLUW19gY2XiWg2MHCfXkbPZdCEkdxvpg/Di4G5f1utd1O7m6w8FTx/38/Q9387k/vGwVv4vyYGxomngqih4cIWhRmVOzXKg2Ff79J06Kz9JcD6EQo1N+tGQMj5ou6zVSCkzODJFAkhlbHTWTYbEuRw/y8qaXiwfqLhGf5fFnwT8NFvuyXveWC+v43pNmDo2H+Psf7OZTb7xkFb+L8mBieJp4KoEeHmWqzkEmEaFBaSisuckh8VmqtRAKMT4t1qVTScl1WYRu1UhmYmiajt/sonlaJRvPcmDkABe5LxIPGevy2O8gGBTdrMvgXVc086Nn+hmbnuMz9+/jL1+1dRW/k9Kj6zoTI7OkUhm08DijXSay8Sx11BXW3NRwbl3WQCjExMwcWjKGXZfrcjXweDyFoMNpUPQyKUoJhULU1NSU2gyJRCKRSCSSsiAYDOL1es/4TNk4csuNyKVSKZqbm/nf//1ffv/3fz//5//v//0/gsEg99577ylfszgiNzExwVVXXcXhw4dpb28/5flyYNf9J9j30Ajtc3vZdOjbfPxtJkZbLTzylkewmHJzGH/9UdjzTdh5G9z4ybN6/U/ef5h7d42Qmj7Jrk/fum6d6GQ8w91/I9J8L37y/2P0Ii8fv2GOD+78IG/d+lYAsl+6FlNwmOgb7sa17ZW8/57dPNHv5+9ft5037uwspflrSigUorOzk5GRkdNuHL/9fj+HfzdO1+gjbDh5Px98rwlzczM/fcNPCw/9+E/h6P1w/Yfhur84Kxs+/P3n+OXBSa7bXM9X3n7F+Xw758xyPofzZW4iyg/+ZTdmJcu1j/8Vz7y4ni+/KMi/vuRfub7jevHQf+2EyBS862fQdhmv/tzjjM7H+dZ7ruTy7rpVsauYtfgcVopffe0gQ4f8bBr4IW1TT/HeP1fZ0nwRX7/p64WHvv1mkVq96dNw+duX/drBYJCdd34de8eF3HJpG598w8Wr8B2UBxPHA/zsv57DqcS58vGPct8NHn68I843bvoG7ZZ2NnR14v+ISF3z/3sOXPVc+U8PEk9p/OIvrqOrzlXab2ANWOufi+VE5MomtaooyrI/lCuuuIKnnnqKP/qjPwJA0zSeeOIJ7rjjjrP6YD0eT9luUO29zRy1zqE0bsJtMrE14WDEnmaeeTZ5N4mHLng5HLwbpnfDWX4ff/36y7n/aICY7UL2TWd4XWd5fg7ny/R8CIfVhV1N4SPNgUYFk8PE1tat4t9e19HT0yg2BaVlIx6vl2DWgmpz0t3aULbrYzXxer2n/b7bNzRxclcQtWUr7uFf0h1VeR4/2MFrzX3NBS+Hkz+H2T1nvS7/5vWX8/Dxx3hyOM7xQJbLumrP99s5Z870OZwvs8eTOKwufMzhMZkYr09hcpjY0rpFvGc2A5lZsCnQvhU8XoIZM6rNSU9rI17v2h2Yq/k5rBRtPU1M9ydQ63vxTD9De9zEUGoIt8eNquRKwbe+BKaehrn94P2zs3r94JP34nzHv/PzviAfSpvpqneu/DdRBozGIjisLuqTftwmE6P1CUwOE9vatqEkFdq8Cl6bAqoFWnqIpbMkFTuqDXpaG3HbysalWHXK6eei4podAO68806+9rWvcffdd3PkyBHe//73E41Gefe7311q01aMfIegRdy8LwyLiNnCgdC5hofpQxA7O+HKOpeVt14uilW/9ruRdSv7YEiPOLMBAAbcosGjeNyMkhXRWt0t5F7keK7TU1skVg0UOqqXangYeRayZ6fB1dPg4pbLRJT8K48df4GnK5f5KbEOjU7qIY9o8Mh3B0amQNeEXqSrkXgqSzQlFPblPMtTMbTkEjntze7Fkk0A3WfXuVpMaryPazf4yGo6//34+l2X+Y7VgDGTWsFtcecvae2enMvgaQVFye+VdouKyyqnjZSKinTk3vrWt/Jv//ZvfOxjH+PSSy9l//79PPDAAzQ3N5fatBXD15TT7NJsZEy2pTtX3U3QsEX8+iy6sQzeeVU7WjrJgfEwz5xcnwrmedHVnLjqYE4MuM0tOgGNjtWZqAZmuxhMHpVdq6cjf8FQ3OgobAmKyNACaZzGC8T4nnQUJl5Yt2sxf/rSXgB+dWiKgekXFhauRAI59Xy7X3RST9Qp1NnrcFpykZ58Z2ALqKa8xIPNrFZV1GO51OYkSKI2IY1zUcQHLFqXHVcJxzg4vCwh9cX8ybWizOL7e0bz/x7rjbwjFxpHVxSma4TeppHaa/PkUnyGtmHRXvlC6T/J6lGRjhzAHXfcwdDQEMlkkmeeeYarr7562V9rs9kW/L8csbssODyiFi7maKJhaomZq3DWul3FtNV72GYXsxz/96n1OborLz3iHwSE9EiTowm7OddNmTsws65mbDYbwXiadDY3nqvKIh82m42Pf/zjZ/y5yEvj6EIap90vhKUXXDBUFbqMdbl8GRKDTU0ebrhAXMq+UwJdueV8DueLoSHnDI+jW0z4PSyUeDiDVtdaHZhr8TmsFIYocEyzk1XNbAiIn90F+6XNDa25buizuPgan8O1m5vY0ekjldH47q6zdwQrAeOC4YhNkWrwkjEr+SixzWbjj99ys3jQkB7JSTXVV9Gltxx/LirWkTsfKsGRg+KZq03YJgOYsvrCAxOg+zrx/8HlCQMXY7PZ+NztbwTgV4cmmV6HI5Lm8+KWk2g2CwH34gNTiK62bL4cm60wnstrN2MzV1eqwGaz8YlPfOKMPxeqqlCTS2PFnU14J0SD0kpeMADednUXAD/aN0oinT2n1zhXlvM5nC/FUx0STTXoqrK06Opira41vFysxeewUjg8FqwOM6AQdzQuPXMVioTUl78ujc/BbrfzrmtE6vaep4fIZNfXdBxN0wnOFNZlqFGcP0YZis1m4+Zrd4iH8xeMnHh6FV16y/HnoioduUohP3O1phNF02idg9HIKLF0rPCQcWBOPg+J4Fm/x/Y2Lzu7a8lo+rq7Zeq6nr9hOuPTxJtq0JVF4paLxiBN526YcqrD6SmukzMHo7hj+sKRSFDkyD0F2tk7Yi/Z0khbjZ1ALM2vDq0vVf1EJE0iKmoHnbFp5htEdHihGLBUzz8bFEUpXHwdzTjH51E0/dQLxjkIAxfzmktaqXNZmQgmeLx/5nxMLjvC/gRaRkdVNOyJeabrhHvQ7im6YCwSA/bLdVkWSEeujDE2pkTDBgC2hdwAnAieKDxU0w61PaIwemR58y0X8/YXiejHd3evr6aHWDBFJplFQccRn2W+QWw2Sx+YYrMqRD7kxnQ68heM3LrsnFMWjkQCaLkErG5IBmHq7GdVmlSFN18hapLW2wUjPzLOlMSkpZiqFanSTk+R1E3+grFoPJdcl6fF15yLFHvaUNIZmoJwMniStFbUcGM4cjNHz7pBDMBmNnHLpWKv+MGe0fO2uZww1qWbCAo6QzXic1uwXy5el8ac1SqKyJUj0pErY2qLUqsAF0ZynaunSxecQ3oV4NUXtuKymhidj7N3eP7cjC1D8ukrcwJVzzJRK5zUJWuRFtV8NMiI3GnJz7bMzaa9OCIkQhaMRDKZoTNXt3qO6dW3XNmJosCTx/3rapyc0UntyooI+qBXrLmlU6viwPTnxnPJA/P0GPtlolFcMHrnraS1NCOhoouAqx4actMZzjEq96adYt0/dHia+dy/y3og3+iQEJHGfpcom1gYkTtdyl/ul6VEOnJlTL5DUHejQ6FzNXD+dR/FOKwmbrpISG/8ZP/4CzxdORj1ca60cE5P5iQezpRaNW6YjXJjOi0FaRzhwG01OlfnF6Wx8vOAz77hAaDd5+Alm8XouR/uHTun1yhH8heMnDRGn1M4dAvnWRqRYrEuZ2QK6wXJNzy4xWd2iXHBCBxb+GBehuTc9svtbV62t3pJZTXuPzBxbsaWIUZjmGNONBgN5Tr88xcMXT/tfinXZWlZt47cF7/4RXp6erDb7Vx99dU8++yZ047f//732bZtG3a7nYsvvphf/OIXa2Tp6fE2OFBUhYymkrT5aJgWjshpD8zxvZASkYtPfepTXHnllXg8Hpqamrjlllvo6+s77Xu9Ppcu+MZDz6GYzCiKgqIo2O3Lm5VZjhipgsTQQQCO2AMA3HrzrYWHcs0ORmp1JheRu+d/vlRWa+F86enpyf+bFv93++23L/n8N7/5zVOeNdZCPvKRtZIx2WjLda6e2vBQdME4x5T9LZeJiNQvDkycU9r/8ccf57WvfS1tbW0oisJ999234O91XedjH/sYra2tOBwObrjhBvr7+5d+sSLOdn8pxnDk7DMnARjzaZgVM805bb6FB+ai1Oo5RorP9Dmk02k+8pGPcPHFF+NyuWhra+Od73wn4+NnvtR94hOfOGWNbNu27ZzsWwkK0jhedCh0rhbtl48//jj//gMRiXvm+/95ynq47bbbTvmeXv3qV5/yXq+/NLcunxf/TuezHkrBUuvBuPjagyJlPOWD9Fwau9mOoijUOlXIiJrjQkSukFott/XwQiznjEwkEtx+++3U19fjdrt54xvfyNTU1Blf91z3lPNhXTpy3/3ud7nzzjv5+Mc/zt69e9mxYwc33XQT09PTSz7/5JNPcuutt/LHf/zH7Nu3j1tuuYVbbrmFgwcPrrHlCzGZVby5QuiYoxnbmB9F10+NyPm6hSOiZWB0FwCPPfYYt99+O08//TQPPvgg6XSaG2+8kWh06RTVizfW4zRpmFw+fvy7Q0xMTDAxMcHQUOXKkhg3zKaUqN2arFewqlaeeOAJ8UA6DomA+HVuY+ofEYX11195aVmthfNl165d+X/TiYkJHnzwQQDe/OY3n/ZrvF7vgq8x1oLNuVAap+Z0nattl4HZDrFZmD23jeyVFzRjNakMTEc4NnX2mnLRaJQdO3bwxS9+ccm//8xnPsPnP/95vvKVr/DMM8/gcrm46aabSCRO38F9tvvLYvI1cqExdJOJmRpodbdiUnNd0vH5Uw5MI7V6rl2rZ/ocYrEYe/fu5e/+7u/Yu3cvP/rRj+jr6+N1r3vdC77uhRdeuGCN/Pa351besRIY3dSprIm0xZ3vXC1el9FoFL3zRQBc3qpiyp6qB/fqV796wff0f//3f6c883sXi3+XZ076+Z97vnde66EULLUejHXpik2RqvOStihc1nsZExMT3HXXXXR4c+vTUQsW8VkXulbFBaOc1sMLsZwz8oMf/CA/+9nP+P73v89jjz3G+Pg4f/AHf3DG1z2XPeV8WZfKkp/97Gd573vfm5/08JWvfIWf//zn3HXXXfz1X//1Kc//53/+J69+9av58Ic/DMA//uM/8uCDD/KFL3yBr3zlK2tq+2Jqm50Ep+PEvW3UBfpoCJqYUWaZT8xTa8+NL1IUEf048D0Y/B30vowHHnhgwet885vfpKmpiT179vCSl7zklPcxm1Qu8CTZE3CwezLFLS9qWYtvb1UxOlbdsWl0i5k5r06vp5PGRpGuy9chWVxgz9UfjkyCrYG3v+l1XHBBc1mthfMh/z3n+PSnP83GjRt56UtfetqvURSFlpal14Gv2Uk8HCTmbMY7PYItZWIgMICma4WRSGYbdFwJg0/A0G+hcctZ2+21W3jJlkYeOjLFLw5MsLXFc1Zff/PNN3PzzTcv+Xe6rvO5z32Oj370o7z+9a8H4Fvf+hbNzc3cd999/OEf/uGSX3e2+0sxmqYTLOqkTjf70NTgwvo4ozNwwYF5fimsM30ONTU1ecfe4Atf+AJXXXUVw8PDdHV1nfZ1zWbzadfIWmOxmnDX2YjMJcUFY3wC9IWdq/nP4bMPYwmNUhsbOOV1bDbbC35PnXVOdnTU8NxokP/84SPnvB5KxeL1oGchMifWmCM+TWxLHRCjt76XlpYWfvKTn/B7110K9OcvF6mMRjAuGiKMdVlO6+GFeKEzMhgM8vWvf53vfOc7vOIVrwDgG9/4BhdccAFPP/00L3rRi055zXPdU86XdReRS6VS7NmzhxtuuCH/Z6qqcsMNN/DUU0sXtz711FMLnge46aabTvv8WpLvXG3aCMCOaD1wJt2upeuRgkFRh1NXd/ph21vd4nb1vw/vp7Ozk9e//vUcOnT2HYflQDarEZopHJgjSkoolfdPMzycE5kNFdUh5URWIxnxI1F8YJbLWlgpUqkU99xzD+95z3vOKC4biUTo7u5eci3k06v1PQB0zZtPHYkE512/CXDjdpFyfLRvZSMcJ0+eZHJycsHPfk1NDVdfffVp/73PZX8pJuxPkM1oqKqOPTFHqEnUdS1dtymcu3RWIxBbeGCuNsFgUEh6+HxnfK6/v5+2tjZ6e3t529veVvjZKhH5BjFXC0o0Tm0EhkPDJDKLoiG5OrmGyLHFL8Gjjz5KU1MTW7du5f3vfz9+v/+UZwBuvFA4LNNqwzmvh3IhExP7ntWUxZKO4q8XEfd2dztTU1P8/Oc/5w035ByXnCM3l4sSm1SFGod4vtzWw9mw+Izcs2cP6XR6wb/ttm3b6OrqOu2/7bnsKSvBunPkZmdnyWazp4zram5uZnJyaT2qycnJs3p+LclLPeQ29fzM1cWdqz05YeDR3ZBeuGlpmsYHPvABXvziF3PRRRed9r1uurQHi6KjuOr4py/djaZpXHvttYyOVl6bfXg2gabpqGSxJQOwWWw+iakE119/PeFw+BRNJF3XwS4iPsW1SOWyFlaK++67j0AgwG233XbaZ7Zu3cpdd93FT37yE+65555T1oJRWG7MtrwsJkYjndpRnbtgDP7unOvkXrpVRBOfHwvmdatWAuPf9Gx+9s9lfynGqI9zmxMo6MzUiaTIQomHXN3mEgemL3dgriaJRIKPfOQj3HrrrWccCn711VfzzW9+kwceeIAvf/nLnDx5svCzVSLy67JZXHy3hdzo6AslmyAvQ1IfXVgT9epXv5pvfetbPPzww/zLv/wLjz32GDfffDPZ7KlaiC/dItalresS6hubFvxdpe0ZmahwBVx6GAUY84nvt8PTwd13343H42HnltxYw0WNDvUuK6qqlOV6WC5LnZGTk5NYrdZTLjMv5EsYzyz3a1aCdefIrTfyMwRNPgC650WdwikRufpN4GqCbBLG9iz4q9tvv52DBw9y7733nvG9XnrdtbzsAnHLnHd08qMf/YjGxkb++7//ewW+k7XFODC91gQKEGgRtYZ/9kd/RiAQ4Hvf+94pjQ7BeBrFJA7KtVTQX2u+/vWvc/PNN9PW1nbaZ6655hre+c53cumll/LSl770lLVgSJBEHeIw2xJaYuYqiNSqahZdmIFzq7ds9trZ3upF16l4EdZAvpNaaJiNeEWkbUnRVaNjNdfoUJc7MFeTdDrNW97yFnRd58tf/vIZn7355pt585vfzCWXXMJNN93EL37xi8LPVokwtOQSPpEOvjgqyk9O14hTGz0OmcLl4A//8A953etex8UXX8wtt9zC/fffz65du3j00UdPea/trV7qnGZUm5Oj/swqfDdrh+HIOeMi6j3gFuu03d3OXXfdxdve9jYs8dzPnmdpkepyXA/LZblnZLmy7hy5hoYGTCbTKZ0lU1NTp83dt7S0nNXza4lxw4ymLWRVc37m6imRD0VZcizSHXfcwf33388jjzxCR0cHL8SrcjMuHz46hcVi4bLLLmNg4NQ6knLH6MBypsSBOegRm86Wpi1s2bJFfE+naaW3KdkF47nKZS2sBENDQzz00EP8yZ/8yVl93eK14MsVlkc1FzrQPiuibac04lid0HZ57s3PPb36slxU7tG+lXPkjH/Ts/nZP5f9pZi89EhOXmTALRo4Ot3FYsALNeTWSuLBcOKGhoZ48MEHzxiNWwqfz1f42SoR+c5Vq3DgepfoXAWgcSvTUQ2znoKxvad9vd7eXhoaGpb8nlRVyUflnjwZWPB3lbZnGI6cMZO6zxkAYPzwOH19fWK/OGW/PLO2YTmsh+VwujOypaWFVCpFIBBY8PwL+RLGM8v9mpVg3TlyVquVnTt38vDDD+f/TNM0Hn74Ya655polv+aaa65Z8DzAgw8+eNrn15LFMwTto7P5At5T5BiM9OrQb9F1nTvuuIMf//jH/OY3v2HDhg3Ler+XbRMb04GxILPhOAcOHKC1tXUFv6O1obgzEApaXXVqHcePHxff06KpDjPhnLhnIrTgtcplLawE3/jGN2hqauI1r3nNWX1dNptdsBa8jQ7UImmcmsnTdK7CwvTqOfKyrSJ19fixGbLaykwf2bBhAy0tLQt+9kOhEM8888xp/73PZX8pxrhg2KaOA9DnFGttyWaHRfMsVzNKbDhx/f39PPTQQ9TX15/1a0QikcLPVonIO3JpO5qi0jQtIp6nXDAUhUcHc+nSMwipj46O4vf7T/s9vSKXwdg9VhibeDbroVwwauQc86KmbbxGw6pa+cHdP2Dnzp3s2LGjSAx44QXjdJqb5bAezsQLnZE7d+7EYrEs+Fnv6+tjeHj4tP+257KnrATn5cil02lGRkbo6+tjbu7sx52sFnfeeSdf+9rXuPvuuzly5Ajvf//7iUaj+a6i973vfQue/4u/+AseeOAB/v3f/52jR4/yiU98gt27d3PHHXeUwvwFKIqST6/GXK0QjlIfMxNJR5iKLdKzMQ7MkWf589vfzz333MN3vvMdPB4Pk5OTTE5OEo/H84+/853v5G/+5m/yv/+Hf/gH9j/1OD21NnQd/ugDn2BoaOisozflgCE9Yh4XNTBD3hQKCh949wcwmUzceuut+cjH//7kIaCwMYWmx8pyLZwvmqbxjW98g3e9612YzQsb1pdaC7/+9a85ceIEe/fu5e1vf/uCtWAyqXgbRVQu5mjGPDaNKaufOhIJii4Y5+7IXd7lw2M3Mx9L89xoYNlfF4lE2L9/P/v37wdEMfL+/fsZHh5GURQ+8IEP8MlPfpKf/vSnHDhwgHe+8520tbVxyy235F/jla98JV/4whfyv3+h/eVM5NXzgyOgqkz7wG1xU2OrKTyUb8LJTXVYgYjcmT6HdDrNm970Jnbv3s23v/1tstlsfr9IpQqTCxZ/Dh/60Id47LHHGBwc5Mknn+QNb3hD4WerRHhq7ZgsKpqukLDX4xoTYuDGBaP4c3h0UKRDwwd/yfDwMJFIhA9/+MM8/fTTDA4O8vDDD/P617+eTZs2cdNNN+Xfo/hzuH5zAwo6YdXD5//nf896PZSKxeshmStjc8Sm0Rp8JK0KLc4WfvD9HxT2/0URuS9/4x6gUE9cjuvhTNx+++1nPCNramr44z/+Y+68804eeeQR9uzZw7vf/W6uueaaBR2r27Zt48c//jHAsveUleas5UfC4TD33HMP9957L88++yypVApd11EUhY6ODm688Ube9773ceWVV66GvcvirW99KzMzM3zsYx9jcnKSSy+9lAceeCBfgLi4eP/aa6/lO9/5Dh/96Ef527/9WzZv3sx99913xsaAtaS22cnUyRDxli0wvZediSZ+7Zrg2PwxWlxF4drGC4RkQXye3T/9H4LBLC972csWvNY3vvGNfJH78PAwqlrw5efn53nve99LbNvv4brs95lR63jyySfZvn37GnyXK4txYHqiU2TQma2BbCBLQ20DTz/9tJDjyG1MJ2ZEc4hRi3TlJdv46lf/qizXwvnw0EMPMTw8zHve855T/u50a2FycpLa2lp27tx5ylrwNTsJTMWI+zog0MeGkIuB2iTDoWE2+jYWXrzzKlBUmD8pnBTv6WvzTofZpHL95gZ+cWCSR/tmuLyrdllft3v3bl7+8pfnf3/nnXcC8K53vYtvfvOb/NVf/RXRaJT3ve99BAIBrrvuOh544IEFQtjHjx9ndnY2//sX2l9ORyqRIRoQa8wZmyLbXEfWFKDd3b6we3jx2Li8I3fuEbkzfQ6f+MQn+OlPfwrApZdeuuDrHnnkkfwesvhzGB0d5dZbb8Xv99PY2Mh1111X+NkqEYqq4Gty4B+LEnM04Zw7hCtuYpJJwqkwe3bvyX8OFzSI9W4a380/fOz/47++/FWef/557r77bgKBAG1tbdx444384z/+IzZbwYku/hx8TiuXd9exZ2ief//OL/nw7X+y7PVQSorXg8vmRckKV8AZnyHe0wZEICSiVrfeeitk0xBdWCMXTAgh8HqXWJfluB7OhFEDeqYz8j/+4z9QVZU3vvGNJJNJbrrpJr70pS8teL6vry/f8Qosa09ZaRT9LOTSP/vZz/JP//RPbNy4kde+9rVcddVVtLW14XA4mJub4+DBgzzxxBPcd999XH311fzXf/0XmzdvXjXjz5VQKERNTQ3BYPCs60BKwd5fDfHUj4/TzjBbH/0Xnrz1Ij7Xc5QP7vwg77lo0aF879vg6P1wwyfgug+e0/s9dHiKP/nWbnrqnTz64Ze/8BeUGalEhq994HEArv/th9CbXbz9nQGubLmSu266SzyUzcAnG0HX4C/7wNPCZx44ypcePc5t1/bwidddWMLvoDL43Q8H2P/gMD3x5+l95r/5wbs28L22Ef71Jf/KqzcsUsP/75fAxHPwxq/DxW86p/f73q4R/uqHz3N5l48f/dmLV+A7WFtmhsN87593YbNovPjBPyd0aS9/cvMwr+x6JZ97+efEQ+kE/FPOAfirk+Cs487v7udH+8b465u38acv3Xja15cIHvjqAY7vnWHr1K9oP/JTPvveBp5uCPCtm7/FZU2XFR7UdfjXTUKw+t0PFEZ3nSX/9XA///7gMV59YQtfecfOFfou1o7JE0F++Jk9OCxprnnwA4y+bBt3XjPAW7e+lY++6KPiocAIfO4iUC3w0WlQVd7x9Wd4on+Wf3/zDt6484XrryWrx1mlVnft2sXjjz/Os88+y9/93d9x0003cfHFF7Np0yauuuoq3vOe9/CNb3yDiYkJbrnlFp544onVsruqyHeuWoXEQ09u5uopBbywZMPD2XJ1bx0mVWHQH2N0PvbCX1BmGIKrdouGJRMn3OQGFkk8RKeFE6eYwCVujCsR+agm8ppduRv61lzn6in1SLAienIv6hV1WwfGgiTSp8pBlDsF6RGxPv31Yp0trI/LRePMdhFdB2bzUx3kPMvlkNfebBA1T5dEhS7Ykg1iRXXF58q1m8S6fHZw7pzGyJWa+UkxycCti6jSpE/8+YL9sliqKRe5f6FmB8nacVaO3P/93/9x4YUiUnHttdcSCoWWfM5ut/Onf/qnS6ZwJGdPbYs4IMMZBzoK9ZO5ztUzHZjDT4N2boedx27hkg5Rs/Pk8aXFMMuZvMSDSWxQM7XC8e30FHcGFm9M4u8LReXywFwO+cJyVayVdr84xJa+YBiO3LnXyXXWOWjy2EhndZ4bCZzz65QKo9HBlRsZN+4TqaklxYA9BZHquWhBr0vywuQvGLnZtb0B8fO8ZCOO4cidoeHhhbi43YfNrDIXTXF85uzHyJWafCd1VNRcD3pFqcnCdVkknp5jJWo3JSvDOTc7PP3000vODguFQnzkIx85L6MkC/E22FHNCllNIWGvwz4itH5OBE6Q0RbpF7VcDDYvJEMweeCc3/PqDeKWuXuwfJpYlkv+wEyKA3PYJ4rvFzpyhobcqRtTvdyYlkXekUuZyaoWaibEIbbkgZkTYGXmKERnT/37ZaAoClf2iOjK7qH5c3qNUlJodBA1uic84kK2ZOSjqI7Qn7tg1ElHblkYkk0RXUTim3Odq0s7cteL/w8/A5nUqX+/DKxmlcu6fAA8e7Ly1uX8pFiX9tmTABzNdfgvcOTCOTFbj6jJ1nWd+Zhcl+XCWTtyb3rTm/j0pz+NoihLDgWORqP827/924oYJxGoJhVfU+7QdLagzwVoTNlIaSlGwiOLH4auXEfNeUQ/ruwRaZ1KPjDt8+Kz6XOLlqyFG9MSB2ZUpgrOBofHgs1ZkMYxjUyi6Doj4RHimfjCh131ohkHYPjcR9VckVuXuyrwgmGsS9uEGAt12C6+hwViwItEqnVdl+vyLDFEgeMpExmTHee4+Jz75/tPTX02bgVnA2TiMH56PbkX4qrcBaOS16Uj58gdW1ISZ6H0SCiRIZ0Vn6V05ErPWTtyXV1d3H///ei6zo4dO2hqauJVr3oVH/rQh7jnnnv40pe+VLa6MZWMkV5Ntm0F4KqY+IxPqfuAQhrrPHS7dnaLA/PETHRFxyKtBcGchpw9d2AedYmNacmInOfUyEeDS0bkloOiKPmoXMzTBokkmxK+pUciwYroyRkRuT1D8yumJ7cW6LpeODDnh0FRGPaIjMaCA3NRCiuSzJDKGN2Bcl0uB5vTgsMjJrTEHI0oEzNY0xBIBvAnFpWKFNfJDZ57TfeVG8S6fPZkZTly2ayWryl2xiahzkfCplBjq/n/t/ffYZJlV50u/J4T3mVGem+qsrzvat+tbmRbjRpJSIAQSDDiA10Bd8QFNMNg7h3GaHDDnbnA5QPBDIJBGEkISTjZbpn2tqqrunxWVXrvIsO7c+4f+5wTkZVh01RGZO33efqpVGXEyejWzr3XXuu3fouAM5B74S3WI+bYOL/LjtthQ7KzVB3I/bf/9t945plnsNvtvPDCC/zpn/4pDz/8MMPDw/z6r/86n/nMZ/id3/md7fisdzRNXcbM1RYh4D0cFr9khQ1YTZ3cc6BpG/p5Qa+TfUaTwKt1lJVbc2CGp8DpYKEBAs7ALV5dazemWCpD3BDQy8xH5ZiBXKpLdKefjgnj3oIXjC0Qlh/qDOBz2ggnMlydrf0ZjiaxUIp0MouigCe+gN7RStqu0O5px2XLC9BuyciZB6bXacPjlAdmpaxpeNB17k6KkuB26eRO9zdhUxUmV+J11SC2Oh9H03TsNh1XMkSqSwSkay4XkNfsIC6+pm5TZuNqg6p95Eyi0SgOh7j1vPe9792yDyQpTLORkYt6xEE5sKBAX5GNqfsUOLwQX4b5S9CxMSuNewaaGJ6L8OroMo8drY9xM7HVFKmECMg88QXS/W3o6vxaHRLklVbFhmVm49wOFa88MCvGPDDjTQMAHFz1QkuRhgfzwJx5A2JL4G2u+ufZbSqnB5p4+toCr4wscbir9u2DIKfb9HuyqHqWeGcQWF5b7oe8C8baqQ7ywKyOpg4v08Mhkl0HYOS7nAw38bx/hmvL13ig64G1L75VJ2ev/r+1z2XnWHcDr0+EeHlkid4m7xb8W2w/Vie1M4mCzmqbOGfW7Ze3ZIqlbrO22HCzgxnESW4PZkYunBWzLZuNlvGCmQ+bQ5iwwqbsHszyaj3p5Myyqs+VQdUzRDpF5nJNWRXySqtrTVdbfK615qySkpgdglGXaI4xZ64WvGD426H1IKBvTic3YOqR6mddWgemKn5vQ8ZUjHWZj1umOixZ+jhZVq2GRvOCYVzUhpZFwHF1+er6F2+RTu60sV++Ph4q88rawWx08GdWAJhrEZfYNbpNXV9rP0KenlgGcjVBVYHc2NhYVQ+fnJys6vWS4gTbvaBAKq2QdgRwjopW8bHwGInM+u5hBjZfLrjH0COdnwhZOp1aZ2VW6D38iLLbXItIOq8J5HR9XeZjSQrKN4SZkYtkPOhA45TQIxa0xoEtKWNZjTjbJCz/hV/4Bd7//vdv6TMti4eE6NidaRKXhTUZuWwGIkZ3oFValdYjG8G6YNiDALTPiv+OBQO5LdLJnewVP6uaEXI7jSVDiYgLxFij6PBdk5FLhCBtlItv2S9lRq42qCqQu/fee/nYxz7Gyy+/XPQ1oVCIP/3TP+XYsWN84Qtf2PQHlAjsThsNLWLER9Tbgb68Qm+mAU3XCgvLB/N8uzZoUjnY4iXgtpPKalybqw89klnC8sZER/V4UNizrDkw48vi9g25G2ZE3jA3QmObJ++C4cc2Og26zlxsjlCyQGZiCw7MU/1BVAWmQglmVwtcYjbJSy+9xD333LOlz7QOzBXRST3aIAKLNRm5yKwwqVbteSbV8sDcCJb3ZtKJjoJ3XDQ5DC8Pr7dsgi25YJjemxenVkln6+Pia1mPzIoM+jWvsBAqaInjDoJDZJKt0qq8+NYEVQVyTzzxBH6/n3e84x10dnbyxBNP8NGPfpSPf/zjfPjDH+b06dO0t7fzZ3/2Z/zO7/wOP/dzP7ddn/uOxOpc7RE2DvfGSwh4e+4W7vDReVgocAutAEVRONYtNqc3JuujXGBZjyyOAHDVL0pZazJy5sbkaQaHCI4XotJDbiPYnTYCzeK/YSzQjR6NcjgjdJzXV66vf8OtOrkN4HXaGWoTjTgXpwqbkm+EVCqFw+Hgueee49d+7ddQFGXNcOzNYF4wnGYndSGvLrOs6u+0TKplpnhjNLS6UW0KmQwkXE3oUzM06m5SWoqx1QKVpS3wkxts8RFw20lmtLppxLH2yznxu3rBLTLGhc2Acx3+MlNcW1QVyH3mM5/hl37pl5iamiIcDtPV1cXCwgLXrokyyoc+9CFeffVVnn/+ed71rndtywe+kzFHdcXbxbzFwyER2BUUlttd0Huv+HozruXGLfN8nQRypkbO9Oo65xEbU8GpDg25bMiiHDezYcwyVrJXXDBOx0Q2qaB+M18ntwn95pFu0eRwcXrrAjm73c6zzwprlLNnzzI9Pc1Xv/rVTT83m9YIL4gMsGdeZM8vukSGaK31iNmxmm+JIw/MjaDaVBoN781Exz7Qde5PiuBku3RyqqpYWblzE7W/X8YjKRJRUUr1xmZRgo0sOZIoKHT58izEbtHHQU4j1ywtcWqCqgK57u5uzp49i9frJR6P8xu/8Rt88Ytf5Ktf/Sqf+cxn+MQnPsGxY8e267Pe8TR1icAt5hGjZ/oMg/yrK0UybuYtcxOB3LEeM5DbugNzu9CyGqF50xNpFnw+ljwZ7KqdDmNcD1B6qoM8MKvG1Mkl2/YCcCAkyi/bqZM70rX1gZyqqkxNTdHS0sLJkyfp7OwkGAxu+rmhhTi6Dg6HgjO1itLeStyu4VSdtHvbcy8sZVItD8yqaTYuvmYF43hY7GVXlq+sf7Gi5OQomyj7H+8JAnCuDnRyZlnV59GxaWmyPWItdvo6cdjymhkLBHIyU1xbVBXIfeITn+Dd7343jzzyCIqi8Fd/9Ve8/PLLxOPx8m+WbBpL92GMngkanasFM3Kw9sDcoE7uuBHIXZqufd3H6mICLatjU3VcyRWyve2gKPT4e7CpeZYi8sDcUixTYMMap2dOrJOCGTnYmkDOyMhd2sLSKsCZM2c4efLklj7TLF8FvBkUINUlOnz7An2oSt4WfIuHHOSJyuWBWTVBs4LRJLLxexbFHlAwIwdbcvE9WUcZOWtd2sX5HekQHf79gf61L7zFcxPyAjl58a0JqgrkPv7xj/PKK6/w+OOPo+s6f/iHf8iDDz5IQ0MDhw8f5oMf/CC/9Vu/xVe+8pXt+rx3NGZpNZZQydhcOEbEL9hsbJbVVIEDzdLJzcFCkUO1DAPNXgIuO6mMxvBcbQ+EtiweXCkUdGtjWu/VVXyqg7xhVo95YJqzLRumxCFWcCQS5AK52Y3r5Ez/uJuLUaLJAuL1DXL27NltC+T8iN+f1XZxIVtvibNeiySbcDaOefGN2EXg3GJkoIoHcsa63IRO7kRfEIArM2EShsF4rWJl5NKizL/QLDr81+2Xt2Tk8sfGySac2qBqH7kTJ07wa7/2awwNDfHCCy8QDod55pln+Pmf/3mampr48pe/zAc+8IHt+Kx3PG6fA0+D+MWJ+TrRlpfZh9AjFczKOdx5OrmNlQtUVbGyH7Wuk1ueNg7M7AoA862iPNDnv/XAXH/DXDTEu62y2aFqTI1cOK6iKSrKyCR2xUY4HWY6Or3+DVugk2v1u+hocKHrcHlm64Tl58+f59SpU1v2PMjrpE6ITuq5ZrHt9jWUDuR0XZc+cpug2ZCirKbEnmlaNs1EZwp3VLcdAm/LpnRy3Y1uWv1OMpq+pWX/7SDXST0BwHijuBD1N9yakVu7LuXYuNpjw4bA165do7W1FY/Hw/3338/HPvYx/uiP/ojnn3+e1dXaXsD1jKn7SBi6j7ujopxVsHMVtqRcYJZXa71zddkoNXsNT6SC1iOwrrSq67rMyG0CX9CF3WVD1yDh60CPRrkLcRiUzX7UmE5O0zSuXLnC1NQUodDWrPeQeWAujgIw1iDWWlGTamNdhpMZUlnzwJTrslos7WYCUg4f2alp9jjE5W27/OQUReGE4Sd3bnxlQ8+4XZj7pWtG/LcY9ouM8brS6i0ZOfNy4XHIsXG1woYDuVJIZ/ztI2iUCxId+wA4tCrKWRXpkTaqk6uTztWcJ5L4b3EtUMB6BNaVVlfjGTLGAHZZKqgeRVEItosGh9SAaHa6K9oKwJWlAsJy2FKd3FZakHzyk5/kz//8z+np6eGTn/zkljzTzMi5Ji8DcMUrPu+aA1PT1ptUG5cLn9MmB5NvAIfLhr9ZZIwSnQcAuDchLJu2UydnNojVckYum9FYXRAejO4p8Tt63l2gwz+bhojIJJvrUpZVa49tCeQk24elkzPaw3vmDWF5sQ7BLdDJHctreMjUaMODruvWDdM9I7KT5wptTOm4MASG3DxLo6wacNlx2eWBuREsC5LO/QDsXxHecmUzcpvQyR3p2voD88Mf/jCTk5Pous5//a//ddPPS0TTJCLC4sE1K7y6zrnEwbhmXcYWQUsDivCRI1ful40OG8ecUZ3sE/OmD68K3ex26uQOGtrcq7O1qykOzcfRNd3opA6hNDYwpYrfozXrMjIL6KA6hD0LuQuGrF7UDjKQqzPMjSmC2CyCRjZieGW4sLA8Xyc3urFb5p4WH36XnURa4/p8dEPP2G7i4TTJmCileuNzqC3NzKliI13r1WXoPRxecItAQLbSbx6rc9XIcnbOiuCl6IG5BTo5MyN3uYYvGKYOyedXsWkplJZmVm0pbIqNLn+eV5eZJfa3W0Pbc40OUoe0UcyGh3jTAAB98+Lvry4VWZdboJM70GFUSWbDhffkGmDFqF4EfBoKoHULiU6LuwWvw5t7oZklDnSCKsIFOZ6r9pCBXJ3R1GUIy2M2NMWGOjqFqqiEkiEW4guF37TJMlY9NDyY2Ti/V1vjidTqaV27MeXrPQwJgOUhJwXlG8YM5KI2ERz7JkWWbSw8RjxTxJ5ok+tyoNmL12kjmdEYWazNC4Zl8eAWgW2mW2Q1unxdONQ8r66C7vmyY3WzmPtl1CU6V/MvvlmtQFfpFujkBlt9OGwK0VSWyZXatOZanhW/LwHjshvrEPv7+kYHU4ay3gxYXjBqBxnI1Rm+oAuH24auQ9zbjra0zGFFZJy2UydnCstrdfSMqY8LqOLPaKcIKCqxeFiQFg+bxgzkVuPCwkC7MUqzqwlN1wqP6oItuWCYNiQXtthPbqsw9XE+TVyAwp1lDsz8aSMy87FpTClKOCVK/erIJG6bm0Q2wVi4wKgu2LROzmFT2dtqZuVqs7xqZuS8CXH5XzA7/Ivtl4353obmxVeuy1pBBnJ1hqIolh4pYeg+7jZHIhXVyd0DNpfQOywW6W4tw55WUaK4uVCbmQ+rYzUpaiem9cia4c9Q2qtLZuQ2jBnIJWIaaVcALRrltDIIVNDwsCmd3NZ3rm4lZkbOG5kBYK5VBLpFD8z8zIdcl5vG8pKL6mRVB5npaY56xASSsjq58Zc2rJPbb5RXr9TqxdfspF4WwexkUEgTindSywtGLSMDuTrEHNVlCssPrBgjkYpl5Bxu6LtPfL2JcgHAaI2WsMyMnHdZWDxMNBXZmApOdZDjuTaL023HFxQBR3qvMNQ9GWkGbo9Obis7V7eSW4eSjwZFibUiM2C5LjeNJ+DE7XOADomegwCcjgnZRdF1aerk0jGYOrOhn5treKi9QE7XdWtduqZEJ/WwT+zr66xHQsJjrtBcahnI1Q4ykKtDrM5VQ1jevSCClqIbE2y6jDXYIn7m6GIMTas9Aa/liTRxCchZj1Q01UE2O2wJzd2GNU7PIQD2Lovs03auSysjN7Vac8JyTdMJzQmNlHPkPACX/QU6AwHCZiC3fjyXXJebw9TJpfqFNc6BFXHhKNrwsAU6uf1GIFeLpVWrMUwB57jYLy+4xXSHykqrUopSa8hArg6xZq4qQgfWYDQgDK8Mk9bShd+0SZ1cT9CDXVVIZjSmVxPVf+htJJXIEFkS2QvPwk1QFN5wFbAegcJTHWSzw5ZgdlTHjIkFbTNinVxZvlI8yNpkIHewM4CqiGB8Ppzc0DO2i8hSgmxGw2ZXcK5Mgc3Geaco/a+fZ1lcuykzH5vD6lxt2QNA95xocih9wdicTs7qXJ0L19zFd8VsdGiwYdPSKAE/NxWxXxbXbuYuxLJrtfaQgVwdYmbkVmM2dBSUm+P4HX7SWpqboZuF37RGJ1dEfF4Cu02lv1n83JEa08lZ5Su3giMTxd7VxWRKeHWtz8gV18i1yo1pU5iZj4hdlFRd4/PYFTvhVJjZ2GzhN21SJ+d22BhqE4fmhRrTyZk6pIAfFHRsPd2saCJDs2Zd6nqRrlWztCovGJvB3C+jLqEl9k8IH8mp6BThVJHSp6WT25if3ECLD6ddJZHWGF+OVf+htxGrMcwlLv16n+jgDzgDNLoacy/MZspIUeS6rBVkIFeHNLZ5UG0K2Qwk3M1kl5e5yyEEvJeXLhd+0xbMXTV1crVm9WBtTIbFg9bbgY6Ox+6hxd2Se6GWNQwuKVJalRvTZrBmW8ZFo0n6+g0GG4R/152ok7O8uuyivJruEYFEu7cdt92de2FiReixoMicVXnB2AxWBSMjtMTZGyN0+spMeNikTs6mKuwzLhhXtnAW8FaQ66ReASDWIy5e67LEkVnQNVDt4vcUiKUyJNJCyiONqmsHGcjVIapNpbHdcNLvF52rdxmdq0UDOdi8b1dLbWbkTH1cwNiYol0565E14+Iic6BnQbFZG1NW01mOyVLBVmA24UTCWTIuH1okwl2KCOSKdq7C1unkaiwjZ3WspoT+aLVTHOxFy6qeJnCIYGM1kSGdlWPjtgKrgrGqoykqmdlZjrvKdK5ugU7uYKehk5urLZ2cZT1irLuFdnGpWL8u8/TEqph4Y1YvXHYVn5yzWjPIQK5OaTY2p2S3EJbvWxabfcUH5gZ0cjkLktoqFVgbU0SUARZaxX+LotYjgU5rY1qOpdB1sW83eR1INo7b58DbIP7bm52rR8OG/+B2NjwYGblLtRbIzRkWDyvjAMyWsx4p0Ojgd9nlnNVNEmh2Y3eoaFmdtNG5ejIqMvXbqZMzLUhqrXPVmv07I1wOxlvEWbBOhmJ1rBY2qZYz1WsHGcjVKWb2I2Zs/p2z4hfs8tLl4sLy3nsNndzMhnRygy21WVpdmjEtHoRHXnHrkeL6uCavE7tN/jpsFnNdJnqOADC4IP6bXlmu4IKxQZ3cAaNDcHQxRipTO6O6LIuHaXFgjjSK0v96QXmhdWnMWZXZuE2jqApB4+KbGjwOwNCSuLQV7VyFTevkDrSLdVlLpdVMOkt4weikvvk6AFcaDOuRYuuyQMeqLKvWFvLkqlPMckHEFgTAPb6AXbGzmlplJjpT+E2b1MmZGbmxxRjZGunE0rIaISPz4RwVFg/XA+J/V2a6Kr26thLTgiTWKP7bN02LstLo6iiJTJFuZ3+70CRtUCfXHnDhc9rIajpjS7WRLU4ns0SWxdpyjr4B5KxHKmrAkfq4LcXqXG0VJdX2WfH/zbWVa2h6keB/kzo5s7R6Yz5aM7OAQ3NxdB0cLhVHeB7F4eCC0UldiRnwgnXBkHriWkIGcnWKuTHlC8v3Bss0PMCmyljdQQ8Om0IqqzEdqo0ZgqsLCbSsjt2h4ArPgcPBJbtopa/kwFyQB+aWYjY8ROxNACgjkzSZo7pCJbLAm1iXiqKw1xCW35ivDT2S1UntUXGkIqg+H5cQ66+oFqmQh5y8YGwJlvemR2hjnWOzuGwu4pk4E+GJwm9ao5P7btU/syfoweOwkcpqjCzWxgXDXJeNfg0FcAwOMJkQF/9KzIDluqxNZCBXpwQ7vaBAMqGTcgbILi9z0j4IwOXlCgK50Wer1snZVIU+y4KkNjampWlRFmgICIsHZ18fY3FxMFY01SEiW+m3kmbDgmQ1ITb61PXrHGgSE0gqKmNtUI+0t00EkDdqpBHH1McFvMKzzD44wFJS2F5UNNVBlla3FKtzNSvWZ3r4OkPBIaBM2X/gYfHn6PNV/0xVVXJ+cjWikzM7/P2K+D3J9HWi6Roeu4dWT+vaF5cqrcp1WVPIQK5OcThtBJpFt1FyQOg+ToSDQJmGB1MnF56GpRtV/9w9hk7uZo3o5MwbZsAm/tT7ukhmk6iKSpe/a+2LrdJqoTmrcmPaCkyNXHg1S9bpRYtEOKGLg6CksHxgczo5s+xfaxk5P+IAT/WIQ7LJ1UTAGVj74kIlf2mJs6WYGbnQKuhAZn6eY05hEFxyXfY/KP4cf0nYF1XJfmtUV22tS6/h6xjpFh3+vYHe9c0Lcs5q3SADuTrGvGUmjZFIg4uiu61kadXhht57xNcb0MlZXnI1kvlYNjJyvpQop8YM65EuXxcO9ZYu1FJaJJmR2xI8fieegJhtmTI6Vw+HDNF3qcyHv21TOrlcabVG1qXZSR0TxtQhw3pkXTYOCnatWhcMeWBuCcF2L4oCqUSWbK/IEB8Li72iZKa44yi4GiAVFpeMKjlQY52rplWTe0EYx8+2iz1yXVk1m4awobWWpdWaRwZydYx5y4wHxS9hk/FLOhmZZDVVwophE2UsM5AbrZGMnNmx6lkeFf+7VWQp1+nj1rjnFxrPJTemrcK6YPSKztXevFnAJeehbsK3a29rjZVWTY2ccWDONIuttq/hlkAuGYGkGLFX0OZBrsstweZQaWgTHn3pPSeACjuqVRv03S++3kB59YCVkdv5QE7X9VwntdEYNtoksozrZSgzgA6qA3xt1l/LjFxtIgO5OsbqXDWE5dwYo9snDoPt8pMbNEyBb9bAganrOitG8OqaFP++Ra1HEiuQMRo0CpSwWuWBuWWYDQ9m52pgcgWbYiOUDDFnZKgKYumRnq36Z5oauaVoipVY9VYRW4mu65ZGzjl2AYCRoPhMRXWbzgC4G6y/lt2BW4/VudoutHHNeRffSKpE6bP/AfHnWPWZYjOQu7kQ3XFrnNhqilQii6KAa07MpL5kdFIX71jtBjUXJlhj42TJv6aQgVwdY+qRVpMiCEkOD3Ow6QBQiU7OuSGdnOklN74U33ELklgotzE5R0TZY7io9YhxYHqaLfd8yBeVy41pqzAtSCIOMfonc/0mexqFHqm0sPwh8efMG5AIVfUzvU47XY0iG3t9h8urkeUk6UQWVQXXnPj9uuwV/z7FO1a71/y1LGFtPVbnqleM5+LmOO1e0cV6beVa8Tea63Lshaovvl2NbgIuOxlN3/HLr9Xo4FdQ9QyOnh5uJsT6W+chV6BjFWBJlvxrEhnI1THNxg0zGtbI2FxkV1Y4bhcjkUrr5Dwb9pPrDnpw2lRSWY2plZ21ILFGczXaUbMpFK+Xa6rwRCo61eGWA1M2O2w91gUjIYLj5PXr7A/uA8oIywOd0LwX0GHsxap/rtW5usMND1YndaOKqmexd3VxIyXWXyUdq3LO6vZgda5qQreWHB7mgHHxLamT6z4tLr6R2aovvoqi1MyEB6sxzCH8HJ179zAZKdLhX6BjNZHOEk2JUqw0BK4tZCBXx7j9DiEsB1KG7uNQSGxWJTMfkFdera6MZVMV+s2ZqzuskzNvmA3eDADOwQEmosWsR9YfmMlMlnBSvLdVZuS2DLO0Gg5lyDo9aJEIxyvpXAXoN7MfG2h4aBUH5k5nPpamjEDOKQ5Mx+CAZdJdsoRl/lU8Q0aTc1a3mibTGseIp7ILCxwzLr4l16XDLYI5gLHqdXL7jQkPwzs8c9W8+PrSYvZvur+TtJbGrtrpNLOUJgXWpSlDcdgUAi779n9gScXIQK7OWScsnxc6jOGVYdLZdPE3boFObqc7V61SgS7KVrb+XpYSwrqiqBlwnj7OzHrYVYUGj9yYtgpPwIHLZ0fXIb1XXDD2L4uyZ8nMB8CAYfewAWF5LiO3w4GckZHzGwdmsrsFHR2v3Uuzu3ntiwt2Uotyf8Blx2WXc1a3CnOvjK6moVeU+g9XevHdxLo0G8R2euqImZHzLIvZv2Ynda+/F5t6yzqzSqu5fdQsqzbLOas1hwzk6hyrc7VJaBzcY/MEnAEyWoYboRJlgJ57REdSeApWxqr6maZO7uYOmwKbN0xvROjfYl1BAIKuYHGvrgJzVlv8cmPaShRFsbJyyd6jAHTOiUvFyOoIyWyy+JtNPdLkq5CurnRveckt7HBpdVL8fF9I/F6FOsTn6m/oL+DVVcCkWs6z3BZcHju+RsOoekhY4/QsiEvsteUSo7ogL1O8gUCuxioYzikRtE63Gp3UpSxx8kqr5gVD6olrDxnI1TnWLdMpDEdT169zqFn4ypXUyTm90H1KfF3l5mR5ye30xmRkPjzzYvTTkmEvUHBjKjDVYUFOddg2TJ1czLDGcY7NEnQFyepZrq+UGNXVtAf8naClRTBXBUOGl9zIDs4C1jXdssRxTV4EYKal1IFZwHRVCsq3jaCxXybahZdcYHIZh+oglolZerGC9N0HKLB0HcKzVf3MgRbTsmnnLr6ZVJbwkij1u8dFJ/WNJrHO1jU6QMHSqmzAqV1kIFfnWLqPlCEsHx7mYFAIeEsGcpDXVl9dILenBgK5VDxDNCQ2FnMo+VRQ3KjXlVVBTnW4zZiNOGbnaipfWF5Kj6QoGy5jdQc9OO0qqYzG5PLONOKElxJkkllUu4LjuvDqutEoLgylzYDXH5gy87H1NJudq8bUl/TwDfaZjTilyv6eoDAHhqr3ywEjI7cUTRGKl5C7bCMrc3HQwelScKQj2FpauKGJxrB16zKTgohhE5RfWpUecjWLDOTqHKsTK6ShqTayKyscVcUvX/lAbmMHprkxjS/FyGR3xhvJcs4POFCmRQnLtB5Z17EKJQ9MecPcepoLdK4eCBozV8s1PJh+clU2PNhUxRohd32HyqumPi7Y7EBJJ1GcTq44hW5z3YGZTkBMTCRZm5EzM8VyXW41ZqY4ogvpRXJ4mP1NFa5Lc78ce6Gqn+lz2WkLiN+DsR3KypkylAZPBgVw7d3LWFjsm4W9DXXRqevLzV9dlJ3UNYsM5Oocf5MLu8uGpumWY/m+ZbFpXFm6UtpJv8/IyC1cgehixT+zu1FkPtJZnamVxIY/+2ZYnhUbU2Oj0BzZmpq4qRe5YabjEDfmd+ZNdViQ5pbbhukltxrKoDlcaJEIRzIdQAUND/nzLbOZqn7uTjc8WB2rHpF5cQ4MMB4VwvF1HnJmud/mAk+T9dfywNw+rJmrURUUhezSEkeMi2/5QG7jxsA7rZMzGx18mmgMc+7dy3hYND2U7KTO03RKD7naRQZydY6iKDR1iE0i1S9S/y0zceyqnXA6zFR0qvibfS3QelB8PV65b5eqKgw0GxMedmhjWp42PJHsooTmHBwsvjGZB6bdA+6g9deytLp9eBudOD12dA0y++4CYO9ibiRSyQtG+xFwN0IqAjPnqvq5O+0lZ2bkAtoKAI49g5b2ap0WKT9LnHdgyjFI24dZwVhdSGDrFdYjB0JCW1u+c9U0rD4PiRIjEAu91dLJ7dB+aVYwjMawdH8n8UwcVVHp8a81/SVkBnJrKxuLsuRfs8hAbhdg6uTizYMAZG7kdB9ly6umHqnKW6bV8LBDFiSWJ1JKlKbsA/1MR8Umtd56JK/RIf/ANEpY0kNu6xGdq2JdJgeOA9AyEUZVVFaSK8zH54u/WVVz2eIq9Uiml9xOZ+S8YZGFS/W0ktEyOFWnNUXAwmrAucU938gUt8pM8ZbjbXTidNuENY7Rudo1KwKU8fA4sXSJ0mdDNwQHQNdg4uWqfm4uI7czpdWlKXGx8cyIrOOykZns8nXhtN1yYTAzco1r12Wua1VeMGoNGcjtAqzOVZfQM4hRXSLTVnJUF2xY97HTDQ/WDXNFZOGS3c1k9WzhA7PYVAeZ+dhWrM5V84JxZZjBBvF1eZ2ckf0Yre6CYWXkdkAjp2t6rpN6Vox8Wjay5b2BXlTllu22yHiuxYhcl9uFoijWukx2Cm2cbWSKVo/YO0uO6oK8/bJaXfHOZeSyWc3aL12jIsM90Swy4oUbw8qMjZMVjJpDBnK7ALNDMJwRJYLUtWEOGYFcxZ2rU2cgVfltcWAHTYGzGY3QvCipugxPpKV2YThb8MAsMNUBZGl1uzEbHiJ20bmavHzZumBUHMiNPV+VYbWZkZtdTRJJVqev2yyri3EyaQ2bQ8VxQ3SsTjeLDHClHasgLxjbjamTixod7FVdfDfYUW16b+5ERm5lNoaW1XE4FNzROVSvl5suURpep9uEvHVZeM6qXJe1hwzkdgFmaXVlRUNXVLKhEIcUsUmV3ZiCA8KSQ8tU5du1Zwc3ptB8HF3TcbhsqDeFJ9K0oRUveWDmTXXQdd0qFcgS1vaQm7lqjJEbG+OQZxCoYF12nRKaxtgiLJQJ+vJo9DosMfbN21xeNcuqTW1usrNiJFdp65H1HnKaprNsBHJyXW4PZgUjojQC4uJbcUe1aQw8+Yqw6agQc6zhfDhJ9DZfMMx12RjQUBCNDmORInpiyE11aMxl6/LHGcpmh9pDBnK7gIY2D6qqkElpZAcPAzBguBpMRacIJUPF36woed1YlZdXTY3cTliQmPq4YKsLLST+3a75RCmt0sxHLJUlkRafW2bktgczIxdaSKG2dYCuc2hFZI3LHph2J/TeI74erW4e8E6VV81Gh8aAWFe25mZuZIV5bOl1mbtgrCbS1pzVJp9jGz/tnYuZkVuN2kA1Lr6I/w+uLZcprbbuB28LZBIwfbbin9nocViZrNttDLxoTBppUMRe6Rray/iqCOQKZ+TWl1aXo6IL26YqNLjluqw1ZCC3C7DZVBrbxQGZ3nsKAPX6uNWNVL5cUP2g8s4GNy67SkbTmVy5vearZsdqg1fcEO1dXVyLC0+kvcG9699QYKqDWVb1OGx4nXLO6nbgb3LhMKxxModFUNYzbYzqCo2QypbJaFg6ufpoeDAzHwFFTGV37tnDuJH5KOyeX2jOqvhvEnDLOavbhZmRW5mLY+8TWaehZRGcXF2+WrqjWlHy/Der02+acpTbrZMz16XP6Fh17h2y1mVfw61mwEmIGo1IeV2r+Y0OqirHGdYaMpDbJZhlrHiH6FZNXLhQ2aguyGXkqvDtUlXF2phu3madnOkh50foPJyDA9Zc2aHGofVvKDDVYUF2YG07a4Tl3SJT7LwxSYOzgYyeKT2qCzYuLG/NGVbfThbNAzMmyqrOwUEmjO7VdRm5bAYixqgnOZ7rttLQ6ka1K2TSGprRudo8HcWu2omkI6Utm2DDDWI7pZMz16VnVmTBM/2dVpVmnXm6uVfa3eBttv5amqfXNjKQ2yWYXnIxrzBdTVy8yMFmQ8Bbzh+p/Qi4GoRv1+wbFf9Ma2O63YGckZEzD0y1v9eyHtnbeEtGTstCWLyuUEauVZZVtxXTgiRq6G2Sl69wuFkEdZeWLpV+c999oNohNA4rYxX/zN4m8TMnbuOYLk3TWTE7qY3Zv+meNuKZODbFRrdvbUMDkVlhY6Hawddm/fWSNKnedlSbSrBdrJFEl9gjM9dvWntHxYbVY8+DVrmsZCcyculkltUFozHsxhkAFjtEY1ibpw2vw7v2DcXMgGUDTk0jA7ldgiUsTxvmwDdvctg9CFSQkVNt0He/+LqKW2bOguT23TB1XWfZcCl3z98EYLVDlNKa3c0E8wx/ATEzUM+CYgN/zpZEHpi3B2skkhIEIHH1KkeMTPHFxYul3+z0QZfImFRTXu1rEjKDieXbty5X5+NkMxp2h4p9VDTgLHeIz9Hp68Rhu0VXlN+Ao+ZKqLJj9fZglldjRjY0ee1arnO13MW36wQ4vJBYgfkye2seuYzc7QvklqajoIPHZ8OxOg92O2MBscZK6zbXdqwuyI7VmkYGcrsEa/TMUgp7ezvoOkPzQvt1Y+VGeT1Sf/UGrIM74CUXWU6KoeSqgmNMBAIzTeLmuKdxz/o3mNYjgc41B+aCLGHdFsyGh5VVUNxu9HicE0kRUF9YuFD+AVb2o3I9kpmRm15NkMrcnkYcq2O1y0d6ZASAKaMyVamgHGRp9XbR0mNcfI0LRvLKFQ40Vti5anNA773i6yr2y5xl0+27YJhGwI1+8XvgHBhgLCbWXsmO1SIm1XJd1iYykNslmDfMeDiNeuQUAN6bM5XrkTbg27UTXnLW8Oc2N5lRkZG70SBKB4X1cUajQ571COR7yMmM3HZiBXJzMRwHRMZjaF4E1FeWr5DOpks/YOBh8WcVGblWvxO3Q0XXYTp0e8qrS9PiwAw2qWixGNhsDFfSSX3LupSmq7eH1r4AAMshBcXlQovFOBQXdiRlKxiwIf2mmZGbWU0QT2Wr+8AbZHHS2C8VoSd25c1YLdyAU3iqw5Icz1XTyEBul+Bw2fA3i1+y5OAJ8efFS5Yeqezm1H0abE6h3Vm+WdHPNEur48tx0rfJgsTUxzU2qujxOIrTyQWn8Fop2LFawOIBcl1Y8oa5vQSa3didKlpGJ2sIy30jczQ4G0hraYZXhks/wMwUL1yB6EJFP1NRFCsrN750mwI5IyPXYBfr09Hbw/XIKFBsXa73kANYiJhNOPLA3E5ae4UcY3k6hv2g2CMHZ8QeNh4eL23ZBBsyBg56HTS4RZVk7DY14pgZOZ/RwOEc2svI6ghQnRmwNW1EXjBqEhnI7SLMCQ/xFlFirKrhweGGbjHcvNLNqSPgxu1QyWr6bROWLxieSI028adz3xDXIyNAmdJqkY1JZj62F0VVrGxxwhiJlLx8hSMtRwC4sFimvOpthjZx0FaT/bjdOjmzM9CfEtYNrsE9uU7qYIFMcQFLHMhlPmQTzvbib3Lh8tnRNJ30vtMAqMOjDDQMAPDGQpmmr957he52dQKMMYHlUBTltstRbu1Yde7dy42VEuuyaGlVlvxrGRnI7SKsmasOYyTS8DCHfeKXdTvKBaqq3PbO1YVx4dHlN3Qezn37rFJBaeuRWzNysrR6uzDLq1G/CFoSly9ztOUoUEEgBxvyk7MycrchkMtmNVaMBhzvkshm2wb7GQuLTtuS61LOWd0RFEWxsnLRNnHBSFy8xLHWYwCcXzhf+gH5jThV6eRu38zVRCRNLCTWk+u66FiN9TQTToexKTYraF1DmdKqDORqk7oK5EZGRvjJn/xJ9uzZg8fjYWhoiF//9V8nlap8VMpuxhzVFVoVrvJks+xfEr94V5auoOllyp8b0H1YOrnbsDFlM1rO3HJaBKbR/layehafw0e7t339m4qWCmRp9XZhrstwVhximdlZjjsHgQo6VyEvkKt8wkOvlZHb/kxxaC6OltWxu2zYxkXme7UzgKZrBJwBayD7GoqUVmXX6u2jtVfo5MIusW8kLl3ieIsI5Mpm5CBvXVbeiDNo7Zfbf8FYNMqqgSYnyqLwLBwJCk1qX6APp+2WNZZOiJF4UHRdygpGbVJXgdzly5fRNI1PfepTXLhwgf/+3/87f/zHf8yv/uqv7vRHqwnMjNzyTAz3EVG6ahkL4VAdRNIRJiOTpR/Qb1iQLA5DZL6in2mVCm5DRm5pKoqW1XF57ajDrwMw2ykyansb96IoBRzHrRJWLiOnaXpeCUtm5LYbMyO3PJ/E0S90OfsWhFbo6vLVCjqqjQvGzDlIhiv6mX3Nt88U2LxcNHf5SN8cAWC6WazFocah9etS03JNOHkZOU3TWY7JdXm7aO0TGbmVqBNsNrJLSxxDBDDnF86XnvAAG7z43r6MnLkug8bIOEd3NzeS4gzYF9y3/g3m5cLuAU+T9dfprEYoLgJAqd2sTeoqkHv88cf59Kc/zWOPPcbevXt5z3vew7/5N/+Gv//7v9/pj1YTmBYk4aUE9kPiZpm+dMX6pS07qsvTJMyBAcYr85PbY2xMN2/DDXPeKKu29PhIjwoh+XCL2GAK6uN0vWBpNX+epcx8bD+ml9zyTAyX0bnqH5kn6AqS0TLl51s29kCwXxjoTrxc0c+8nRk5c8Zqc7uL9ITQGF1rNDqpC+mQYgugpQFF2OIYhOJpsuacVa9cl9uNmZFbmIrh3Cv2j77pDHbFzlJiqYIJD0YjzvxliC1V9DMHb6MFiTljNWB0rDr37uV6SLgXlGzAaexZYwa8bFx6VQWCHjlntRapq0CuEKFQiObm5pKvSSaTrK6urvlnN+IJOHEbg7aTvcJ0NXHxYuWjuiC3OVWoR7qdGbmFcbExNfvTkM1ia2zksiJKBgUPzEQI0saGmZf5MD3kAm47Tnvd/wrUPA2tHmx2lWxaIzN0HBAND1Xp5EzD6vHKArk+QyM3F06SSG+v1YM1Y9UeA13H1tLCZYpMGoHcgelvF55kBmb5qkGuy9tCU6cX1aaQimfIHhQND9kr1zjQfACoQCfna4VW8dpKjdTNjNxUKE4yc3vWpd+YeuMa2mvZUJXWbRYuqzZ55ZzVWqWud4vh4WH+4A/+gI997GMlX/ebv/mbNDY2Wv/09RXwddolmHqkmDHwOHn1KocCFWbkAPrz/OQqwGx2mFiObbv5qtno0JAVOg7XgQPcWBXi8sIHprExeZrA4bH+2tTHyfLV7UFVFYJGtjjeJg6QxOXLVudqRTo5K5B7saKfGfQ68DmFX93kyvZm5UyLB78xMs598IDVGVg481G4Y9XSbcp1eVuw2VWau41O/y6xFpOXLnO8VVw23pivQCdXpWF1q9+Jz2lD17fXGkfX9YIdq1Ygt4GOVVm9qF1qIpD75V/+ZRRFKfnP5ctrs0mTk5M8/vjj/NAP/RAf/ehHSz7/V37lVwiFQtY/4+OVtYvXIy09hu4j7kRtaEBPpzm8Kv7u8nIVGbnp1yEZKfvyjgYXHocNTd9eqwdd01mYMDyRlsQh6dy/3/JEKhjIFbEekR1Ytx+rc9UphP/JGzc42iDKrBVl5Ewn/YlXKppvqSjKbdHJZTMaoTlxILtnRYnYsX8/o6ui9F8481G40UGuy9uP2bkaMWbhJi5V0bkKeYFcZRk5RVFui04uspwkFc+gqgrO62cBiPe2sppaRVVUBhsH17+pSMeqbMCpfWoikPvEJz7BpUuXSv6zd2/uoJ6amuItb3kLDz30EH/yJ39S9vkul4uGhoY1/+xWzI1pcTJqNTx0TSYAmInOsJJYKf2AYB809on5pJOvlP15YmPa/s7V0HycdDKLzaHiHBEbbHygjWQ2iVN10uPvWf+mIlMdFmQH1m3HDORCUTtqQwOk0xxcFX83vDxMMpss/YCOY2K+ZTIkzIEr4Hbo5FZmY2iajtNtQ70u1mWkv4WMnsFr99Lp61z/piLWIwvywLztmDq5lZTYw9ITExxzCb3cpaVLZLRM6QeYxsBTZyBV2YVhsHX7O1fNsmpjm5vslMi0jbeIC1BfoA+XrUDWt0hpdcnKFMt1WavURCDX1tbGoUOHSv7jdIpFNDk5yZvf/GbuvvtuPv3pT6OqNfGvUDO0GIHcwnjYCuS4MmyNCSprDAx5c1crbHgwdHI3t1HAm2t08JO+Kv4dpo2O1cHGQWx5c1Qtik11kCWs244ZyC1NR3EfNBoeRudpdjeT0TNcXSo339IOPXeLr8dfquhn3g4vObPRoanLR+qKWJdTnUL3VrSTukggtyRNqm871sV3NomjW/z/0TEZw+fwEc/Ey482DA5AoBu0TEUXX7g9HdWm9YjZsWpramJYnwOKVC8AQqUzxfKCUbvUVRRkBnH9/f387u/+LvPz88zMzDAzM7PTH61maOnxoyhi5qq+VwRyiQsbbXioTPdhNjxsZ6nA1Me1tDvJzIkNabhZBGRFN6ZyUx3kxnTbMLWbyzNRnIfEWqxqwgNA333iz4oDue3PyJmZj6YmlWwoBDYbVxrEAV1QHwe5Elbg1qkOprehvGDcLsyLb3gxgXpYjDZM5TXilPWTU5SqL77mBeN2rMsGVeybzqHcRIeC1iMgplRA0dKqXJe1S10Fct/4xjcYHh7mySefpLe3l66uLusficDhtNHYLjaKaNMgAIkrVzjYINzLKwvkjIaHiVeg3FBzci31N7exc3Xe6FhttIuNydHTw3BKHIjFD8xiUx2kGfDtprHNg92hkklppPuMC0a1DQ+9RiA3UVkgZ2Y+JrYx82Fm5AIYFg97BhmOG/q4QoJykKXVGsLtcxBodgOQGDA6qqvVyVVpDGxeMLazCce0HvHFjI7VvUPWXOOC+2UqBvFl8XUx7abMFNcsdRXIfeQjH0HX9YL/SHKY5YJQ2ofq9aInEhyNBoEKA7m2Q+AOQjoqTFjLYI3p2qaMnK7rVkYuEBXBm+tAXmdgsYycOQPx1humVcKSN8zbhWpTrezHasDoqL58maPNVWTkzIaHhasV+XbdzoycNyyyGe4DB3OzLAs1Ouh68TmrsrS6I5jGwJGGQUCM6rI6VyuZ8GA2PEy8DNkymjqgN7i9c4A1TWd5WjzbYzTgOPfssTzkSlqPOHzgblzzLTk2rvapq0BOUhmWTm4yiuuwGDjeNy0yazdDN8sLy1U1r4xV3rfL1MhNLse3xYIkupIiHk6jKOCZugSA68B+ayh5wUBO12F5RHzdtNYsWI6b2Rna+g1hedoPdjvZUIjDWTEe6frKdRKZROkH+FqgxSgLTZTXI5klrMVoiliq/AFbLZl0ltCcODDdU0If5zywn5shwxKnUOYjsVLQ21B8Tlla3QnM/TJEEDA6qv2igjG8MkwsXSbgaj8MrkZIRWC2fAavx7hghBMZa2LCVrI6Hyeb0bA7VOw3xUU82ddGKBlCQSlsnp5fVr1F12muSxnI1S4ykNuFmBm5hYkI7qMi4+EaniToCpLVs1aKvSSW3UP5MlZbwIXXKSxIxrahjGVm44KdPrLXREYxOdhJJB1BVdTCw58js5CJg2ITUwHykD5yO4MZyC1MxnHtEYeJf2SBFncLWT1bWSNOFeXVRo+DBrcYBbYdWbmV2Ri6Di6vHeWaODDD/S2ktBRum5tuX/f6N1nehs1rvA1Bisp3ijajc3VpMYOtqQmyWRonQ7R52sjq2fJVDNWWG29YgZG612m3ZB3bkZUzy6pNXV7So2MATLaI4Kw30Ivb7l7/piIdq5AzUG+T+2XNIgO5XYjVUj8bw3HQMLrMn/CwWEF51QzkKsjIbbc3ktmx2trnJ3lNlAqmO8RG2B/oXz/8GWBJZEVo7F3jnp/JaizHzLmB8sC8nbT1GYHceDjX8HD1CkdbjQkPC9U0PFRmDGzp5LbhwLQaHTq9pG6I7PB4u9hSy3dSrz0w187/levydmKWVpemozgP54yBN+YnV51ObjsuGKYRcLABSKdRPB6GXStAkbIqFO1YTWayVtawLSADuVpFBnK7EF9QjOrSNZ14uyhFJS5d4miT2KQq2ph67gYUCI1BuHxX8J7W7Wt4sEZzNWho0Sg4HFwLiJ9TsEwAsGwEcs1rv79kDCVXFDnP8nbT3O1DtSskYxmye8Qhmbh0ucpRXUYgN/laZXok48DcDhd9y6vLl4FMBrWhgWtOod0rqtu0zIDXNuCsxNMYY1ZpkheM20qgxY3TbUPL6KSHTgGQuHyJE22ii7Uqndzo80LWUYbt7Fw1J400qqIBx7VnD9dXDd1m0QacIh2rRjbOYVNolHNWaxYZyO1CFEXJ6T70RhSXCy0a5XRaHB5n586Wf4i7AdoNH7oKBpVvZ8ODmZFrSM8DYmO6GRUlg6IHppmRMzp3rb82y1deJzY5N/C2YrOrtHQbwvLgICAaHqrqXG07BK4GoUeaK//6vqZtzMiZHatZ0e0ndJti3RU9MK3MR2HrkUaPA4dNbsu3E0VRaDWyxRFDg5m8WGXnas9psDkhtgDG5JlS5DJy21FaFevSZ8xYdQ4NWXriajup58NiXbb5XYU9ESU1gdwxdilmuWBxOo7rkDBg3Tcn/u++HrrOamq1/EP6zPJqeT2S6SU3ssWmwIlomvCiEMH7FkXXlevAgfIbk5mRu7XRQXYG7ihWw4PSDEBqbIzDnkEAboRulBeWq7acMXAFOrntzMiZJSzvsrAbcR84WLozEPLW5eCav16Q3oY7itVRbRcj5BJXr3IkKMr/k5FJlhJluqTtLug6Kb6u4OJrWZBscUYuvwHHOydMtl1DuRmrRa2arAtG75q/tgI5WVataWQgt0uxHMsnItaEB9u1UfoDQvh/br68rUhOWL5zGTlzvmqg2Q03hLbPdeBAbmMql5G7pbS6EJGdgTuJGcgtzWewt7WBrhMYX6bd046ma5U1PPQZwvIKLhiWRm5lay8Y6VSW1QVjxuq4KAk7D5bpWIW8dbn2+9Kra2cx98vlVRXF60WPx3FNLVrSjYrKq1Wsy55t0sgtzxgNOD47jIjfpVRvmxWI7mkoIkUpUlqdj8hArh6QgdwuJb9z1WUIeBMXL3KyTdwaX59/vfxDTD3S1BnIpEq+1JwfOLUSJ5nJbvBTr2ehQKNDdk9PbmMqp5ErkpFrlgfmjmA2PMyPh3EeNhoeruRNeKio4aHyTLE1pmuLM3JLU1HQwe13oF8Rv0uR/lbimTh21W6NxFv/RqPstm5dSouHncRcl4uTUVwHDgAb8JOrotO/d5tK/ktGx2pLt4+00YAz3So6t3v8PXgd3vVvSkYgERJfFyutykCuppGB3C6lqdOHalNIxTNk+kRpNXHxEqeMQK4inVzLPvA0QSZR1h+pze/CZ1iQbOUMQbPRobXbS/KmCM7MWZadvs7CG1NiFWKL4uvmWz3kDOsReWDuCC09PhRVMUbIiUMycekyR1qr0Mn13AMoIliPzJd8qVnCCsXTrCa2zrPLumB0ucnOi88w2ipE7oMNg9hV+/o3JUIQN0p069alaT0iD8ydoKnLi6oqJKJp9INij0xUO+HBvPjOXhDBUQl6DFPg1S32krM6VoOqaAyz2bjuE5+lrD7OGVhnBmwGctKqqbaRgdwuxWZXaTIGlUccbeBwoIVCnMiKhofzC+fJamUyZ4pSsQ2JoiiWTu7mFurkzEaHoCMqOgMDAW44xe2xuA5pRPzpbQVXYM235FSHncXutNFsrMtouzBdTV6usnPVExRND1A2++Fz2a0s18QWZuXmx4x16RLPdPT3cyMlDsSiB6ZZVvW1rVuX0npkZ7E7bAQ7xaUw1inWVuLSxTUZubIThBq6hcZM12Dy1ZIvzV+XW6mTWzdjtb+f4ZgxMq7YflmkrAoyI1cvyEBuF2Pp5GYTuPeLQ7NzIobX7iWajlZoDFy5AevgFnvJZVJZlmdEUOiPiM3GtX+/1Upfvqw6uO5bcqrDztPWb3RU29sAISw/HBRZ45uhm0TTFawfq7xa3k+ubxs6BM1ArjEprHncB3O6zaIHZpGyKsgxSLWA2SAWdovLbvLiJfYH9+NQHawkV5gw9qCS9FVTXt36dWmaAfutjtW9uZFxVXasQp5GTl58axoZyO1iCk14SF28zPE2ccusSCfXe4/4swJj4MEt9pJbnIqiazpuvwPbmBDurhnNVVZQXujAlM0OO43V8LBqQ3G70eNxGuZjdHg70NErmwdsCcsr6RA0dHJblPnIZjXL4sHqDMzrWN0TrM7bEPLGc8kDc8ewjNSTbmuEnDq3aBmpn5+voLxqXnwrWpdb2/CQjGeILIt15DbX5d4h68Je3hKn0FQHmZGrB2Qgt4uxArnxsNW5mrh4kVNtp4AKA7kqjIG3unPV1CG19flJXTMPzAPcXDG8uspaPBQ6MGUJa6fJTXiIWMLy5JUrufJqJQ0P5oE59RpkS2uMepu3NvOxMhMjm9FwuG3Yh88ChiWOmfkompEr3LEKeSV/mZHbMSzLpskYriHx/+GGdXITL5c1BjYvGJMrWxPImY0O/iYX3BSNYZn+ThYTQi9c3KTaLK32rvuWLK3WBzKQ28WYN8zVhQTqPkP3ceECJ1uFY3lFgVy+MXCZLsE9W+wlN282OvQFSBiBHHsHmIqKUkC11iMgS1i1QEuvHxSIhlKwP6/hwexcrUQnl9+IM1PaSmerO1fNsmpbr5/UsMh2RAZaiKQj2BRb4dm/kGdSvX5dyjmrO4958Q3Nx7EdMiaPVNu52nkCbC7R1GL4XhbDbHjYqguGuV+29PpJGh2rs22iMazb1124MQyKllajyQyxlNBRy2aH2kYGcrsYt9+BLyh+ASO+HrDZyC4tcVQXGpDR1dHyRpeQp/soXS4wmx2mQnES6c1bkJgZuZY2O5kpofmY7hDdgM3uZoLuYOE3ms0OtxyYiXSWSFKMdZIlrJ3D6bbT1CEOlWiXccG4fMmauVpR56qqVtyIs9VaJLMBp6lRQ08mUTweRvwiSOwL9BWe/QtFS6tZTWc5JrWbO43H77T2y0SfEchdzs1cvbR0ibRWpsPU7oTuU+LrMjq5rS6tzo8Jk/fWdgfZRZGFu94gnl1UhgJFS6tmNs7ntOFzFejCltQMMpDb5Zi3zKW5FK694pfZMTxhZbO20hi4xefE77Kjb4EFiabpLBpmwOZoLntnJze0OaBEo0M2DSGjVFBkPJfDptDglhvTTmLq5MJecXgkzp3ncPNhAEZWR4ikSts3ALkyVpmGh768uZZlOw8rwGp00PNGc62OACV0SOl4bs7qLaXVlVgqN2dVzv/dUczyasTwAUxcushAwwABR4BkNsnwciUNYpX5HG71vNW5UaOT2i7+tHd2MpwWa65ouR9y6/KW0qo0A64fZCC3y1nb8CAyHomLFznVfgqo0E+uQmNgYUGyNQ0PKzMxMmkNu8uGa9YczZVzzi+6Ma2MgZ4FuwcCnWu+ldMhybmBO40ZyC0nvChOJ9nlZQKzYbp8Ilt8aelS+YdUeMEwMx+R5OY9u3RNt7wN/cuifJU/mqtoud8Y44UzAN6WNd8yLxhBr5yzutNY5VWtAYDM1DTaSsjKFlemkzMaccqsy54t9DhMp7IsG7N/zXXpOrA/10ld7IIRX4akMa6xSEZOllVrH7lr7HJa8gO5vIaHqiY8VGEM3N+8NbdMs3zV2pNrdHDnzVgtWirItx65JVhbsDoDZdZjp7EaHiaiuI+J0lXszFmr4aEyY+C7QVEhNJ7T+RTA7bBZWYXN6uRC83HSySw2h4pzRGim1jQ6lJv92zy4fl1K3WbNYOqKF2cSOPrFOMPk5cvV6eTMi+/cRWFOXgS/y06TV2jYNusltzgRQdfB2+BEHRaf0XPsWPlAzvI2bAeXf823ZKND/SADuV2OVVqdjOA8LEpX+Z2rbyy8UV73UYUx8FaVC/I7VhNXcx2r5sZUtLQqGx3qAsuzaymBeuJuAOJnzliZj4oOTJcfOsTry5extkYnZ14wWnr8pK/mzf4NVXhgFuhYtcyApSXOjmN5b05FcR4yL75Vdq4GOqGxvyJjYKtzdZP75dyoCBjbBwIkLohmoeyBPczHhSyleKZ4RPxZYL+UgVz9IAO5XU5juxeHy0YmrREPDoCikJmZoTcTIOAMkMgmuLp8tfyDKjQGNg/M8U0fmEYHVp+f5FXRSm8b2st4eByoYKpDQdNVWSqoFVxeBw1tYq3E+0QXdfzMGevArEi7CXm+XaXXZd8WXzBaO12kJ4W2KDbQRigZQkFhsGGw8BtLmQFH5ZzVWqGxzYPdZSOb1shYI+RynavXV65XZ1hdrry6RZ2r84Y+rrXbQ9LopJ7pFWu+w9uB3+kv/MYSVk0L0gy4bpCB3C5HVRXaB41B5bNpnIODAKQuXeZEm2FDMldBebWvsozcVhyYuq5bB2azN4W2ugo2GzNtdrJ6Fp/DR7u3vfCbS9wwzcyH9OqqDdqthgdhe5AcHuaYcw82xcZUdIqZaGnfQiBPj3SbLhjmaC6HuGjYOzsZYQEQQ8nddnfhNy6X95BrliX/HUdRFVp7jIYHI7hJXLxIm7eNTl8nOnplZf8KLxhb1bk6Z65LZQWyWWwtLVx3iGacfcF9xd+4VHwKjszI1Q8ykLsD6BgUg5Bnb4ZyOrkLufLq2fmz5R9SoTHwVpSwwksJkrEMqqrgDY0B4NwzyI2Y+Hpv497izQolNqYFOWe1pjAbHhYXNKFH0nW4eM1y0j8zd6b8Q8wLxtRZSCeKv2wLtJu6rjM/JgK4QNQYGZc/mqtYWRVKlvxzpVUZyNUCZnl11SFGyKVu3CAbClWpk8vLyGla0ZdtRSCXTuYaHXxLYi26jx5h2GzAKWU9Uqq0KrtW6wYZyN0BdOwRHVgzN1cLNjxUVMZyBSoyBjY7scKJjXcIml2BTd0+MtdFWXVNo0MxvYeuly6tymaHmsJseJgfC+O96xQgyqt3td8FwGuzr5V/SNMeMYReS8N08cyylZHbhC1OZDlJIppGVRXckyIr4z5w0Arkih6Y2QysjOY+7y3I0mptYeo3lxYyOAZEw0P83LnqdHIdx8HuhsQKLBa3LLE0xSsbX5cLZqNDY67RwX30qLVflrQesfbLwXXfkhm5+kEGcncAZiC3NB3FdiDX8HC89TiqojIZmWQ+Nl/+QRUMhPY67VbpcqNZufkijQ5lO1Yjc5COik7GYP+6b8sxSLVFa3+ek/7x0wDEz57hdIf4uqKMnKJUpN/cCi85s6za1OUjc9WY/XvwYPkDc3UCtIxw/C8wz3JRZoprCrNzdWE8jPfUKQDiZ85Wl5GzO6FbXEhKrcvc+LiNZ+SsRof+XKOD5+jR8pniTCrPc3PtBUPTdDlntY6QgdwdgK/Rhb/ZBTqs+oTRZXpiAk88a+knKrIhsQ7MV0q/zMp+bGxzWsgbzWU2OrgOHLA85Ip3YBnlq4ZesZHegtnsIA/M2sDjd4p1CcS6xAUjfvZ1TrUI7ebV5auEU+HyD6rAGLgr6EZRIJ7OWvN2qyX/gpE0LhjuSkqrVrl/QEykuIVFqd2sKZp7fGKthNNwxOioPnuGIy1HUFCYjk6zEF8o/6AKjIHNZoeVWNqaOlMt5gWjtcdrNTpkDgwyG5sFSlx8V8YAHRxe8K/VHIfiadJZceFpkd3UNY8M5O4QOvcIndz8XAZHn+lafimnk9tCY+BeS4+0sYyc1RnY5SF1XRySjn1D5QO5pTyvrlvQdZ0FeWDWHO39Ilsc0hpRfT60WIzAxDL9gX509MouGH15wvIi2TaX3UZng2hE2Gj2wyr5N2bRolEUh4NYZ5M1lLy4JU7xjlXIm7MqS/41gcNpI2iMkIt1HAAg/vo5vKrbCtar8pMr0bkacDsIbtJLbv7WRofmZsbcYq22e9ppcDYUfmN+WfUWzbGpjwt6HTjtMkyodeT/Q3cIZnl1Nl8nd+ECJ9u33hh4MwLeeCRFZFlsIg3aEno6jer1MtcIyWwSp+qkx7++PAWUbKWPprKkMkJ0LDVytUObUV6dH4/gOSnWYvzs2ep0ct13gWqHyKyRZSjMZnVy5oHZkBJj4pz79nHTaMDp8nXhc/gKv7FEx+qaOasy81EzWBMe9EZUrxctGiU5fL06nZxZwZi7BIlQ0ZdtxoIkv9HBbzY6HDvKDXMCTqkGnBL7paWPk9WLukAGcncIHUZGbubmKq7D6ztXLyxeIJUtU3Kq0Bh4M6bAC0ZXYEObB31UlAlc+/czEhZi8cHGQWyqrfCbSwh3zbKq12nD65RzVmuF1ryGB89dIniLn6lSJ+fwQKcox5bKfmzGGicaShJdSYIC3rlcA871SjoDS3SsLsdSVhLRdPmX7DzmulyYjOI+mfM5rEonF+iA4ACgl5SjbObiuzAeRtfB1+hEGRbBpfvoUYZXxN5ZOpAbEX8W7PCX+rh6QgZydwhtfX5UVSG+miI7kGt46Av00eRqIq2lq5xvWULAuwkLkmKNDqZpcckOrBIHphyDVJtYM1dnY9iPnwLEqC4zI3d+4Xz5CwZUpJPbjJfc7A0hKG/p9qENGxMdDh60hqhXtC4LZD7MsmqT14FdzlmtGawJDxMRPGbDw9mzazJyFTXNVFBezV18q1+Xpn9c20ADiTfyGh02ecGQHav1hdw57hDsTps1dzXkEQasqZERtGjUKq9WppMrn5Hry7thVtshaOnj+gIkLgqLB9fBg1xYEJuUOcKpICVKBbLRoTbxNbrwNjpBh1jLXlAU0mNj9Kb8NLmaSGaTlRmw5uvkitC7CS+56esrAHTubbQaHVwHD1if7XDL4cJvzLfEKVBalYPJaxNzr1yejeEwLhjxM2fY37Qfp+oknAozFi5exreowBh4Mxm5QhMd3EePWrN/S5oBy9LqrkEGcncQnYZObn5ew97ZCYiB0KafXEU6OWtQeXFjYPOGGUlW7yVnjuZq7fURf13423lOnuSNRVHKMIeqryMZhqhhoVJozqo0Xa1Z2vOMgV379wOQeP11KytXUXnVPDBnzkOq8Agl68DcgEZu5obQOHX0eUmNijK/ff8Ql5dEdq7ouixjiTMXFibG7Q3ywKwl8i8YkSaRbU2NjqKEIlbQXpFOzrJseqWoMfBmpChmRq5JXbEaHZItAaaj00ClnpuD674tM3L1hQzk7iDWNDwcFQdP4mJOJ/f63OvlM2gVGAO7HTYrw1DN5pROZlmZE4dso76CFgqhuFxEBlqZic6goBTPfJibkqcZ3I3rvm2N55KNDjVHqxHIzY/ndHKxPJ3ca3MVNDw09kKgG/Ss6KougKWRW4mjaZVnijPprHVgNrMAmoatuZlRe4hENoHP4WOgYaDwm82O1SKWOHOrMvNRq3QNiX1kbjaDc68IiOJnc35y5+crMQY+BnYPJEOwUHim9UalKOlklpWZWyc6HLUkMh3eDhpd6/dCwLhgxACl4AVDTnWoL2QgdwdhNjzMj4VxHDJ8u14/x9HWo9gVO3PxucrmW/aWNwbeyOa0OBkBHbwNThTTofzYMS6tig1wb+Pe4p2BJfQekBPvytJq7WFNeBgN5/RIeTq5s3Nn0fTiY44A0Yhjlf0L6+S6Gt3YVIVURrMOqkqYH4ugZXQ8AQf2m4YO6fhxq6x6pOUIqlJkK10uvS7njMxHe0ORGa2SHaNrKAjA9HAIjzV5JKeTq6jhweaAHnEhKbZfmtNwlmNpolV4yc2OrKLr4G9yoVwzGx2OWJlCc5Z2QcyLb2PhC4Ys+dcXMpC7g2hs9+Dy2clmNJJ7TgEQe+UV3DY3B5sPAhXOXa2oc7V63YdlbNkXIH5WfA7PqZPWhllaHzci/ixQJgA51aGWMRselqajOI+Lwyfxxhsc8g/htrlZSa4wEhop/6C++8WfRdal3abS1Wh6yVV+wcjXxyVePwuIdXlh0dBtFiurQi4jVy6Qk5mPmqNrn9HpfyOE++QpYG1G7tLSJdLZCqQjZYyBG9wOGtyik35ypfL9csZYl11DjSQuGCPjjh619ksz4CyIpY8bLPhtWVqtL2QgdwehKAodg4YBq6sbHA4ys7Okx8er08mZB+bUGcgUzmyYuo9qPLsW8jpW46+Lz+E5WeGBWUK4C3LOai3jb3Lh9jvQNZ1VWwu2pib0VIrslWscbxOHZkXl1fyO6iISgY1MHZm5LvRxXUPBteuykgacEh2rAHOrQiMnD8zao7XXj91lIxnLkOwTcpL4+fP0eroIuoKktbSl3S3JNnWuTg8bus0Bv9Xo4Dl2zMrImQFnQUpcfNNZjSXD21Cuy/pABnJ3GGZ5dXYihueEyH7EXnrJCuQq6lxtGQJvK2STRQeV921ghqDZ6NDc5iB5TXh1eU6eqiwjV6a0msvIyY2p1si/YMzeWM3TyZ2truGh6wTYnBBbzGXCbqGvygNT13Wr0aGtRSM9OQmKgv3oYa4si3mrFV0wCnSsQi7z0R6QpdVaQ7WpVoPYQrIBNRBAj8dJXr3KfZ0iOHth6oXyDzIvGPOXIb5c+CVVVjA0LbcuW9QlyGSwNTez3GBjJjqDqqhlMsXF98ulqPA2tKkKTV558a0HZCB3h5Hf8OC99x4AYi+/zKn2UwBcWbpCPFNmM1EU6H9AfD32fMGXVNuJlc1qLE6JQC4QGQdNw9HdzaJfYymxhF2xc7DpYPEHlMnILURks0Mt070/CMDk1eU8PdIZTrcbDQ+VTHiwu3KDyouUsapdl6sLceLhNKpdwb9gGFTv28dwZoq0lqbB2UCvv7f4Ayotrcqu1ZrEbHiYubG6ZvLIg90PAvDCdAWBnL8tty9NvFrwJdWuy6WpKKlEFofLhmdWXCjcR49aGcKh4BBeh7f4A6yMXHHrkRafE5uqrPu+pPaQgdwdhlVanYujnhCBXPTll+n0dtLmaSOjZ6ySUUn6xUbGWOGNLL/ZoRIvueXpGFpGx+m2Yb8hSgP5+rh9Tftw24tkLbJpWBkXXxc4MLW8MUhSvFubmIHc9HDIaniInXmNE60nUBWVicgEc7G58g/qLd3wYGaKKzUFnjbKqu39AVJvGGXVU3ll1ZajKEqRwy6+ksvAFDgwY6mMNShdauRqk659QUCsg/yGhwe6xEX23Pw5ounCdjdr6Msr+xeg2uYwUx/XsaeB5AWjMSyv0aFkWRVKauRkx2r9IQO5Owy3z2ENhA437gG7nczUNJmpKSsrV5FOLj+QK+CPZM4PjKayLMfKC4Jnb4oDs7UvQMJqdDhVmT4uNC5sJ+xu8Heu/3Y8Tdawm5ClgtqkbSCA3amSiKaJte4Fu53s/AKu+VUONInB5RWVV039ZhE9UrWZD1Mf17m3kfhZM5A7ZXWsViQo97WDy7/u22bmw+Ow4XfJsXG1SMeeBhQFwosJtP25jFxvoJdefy8ZPcMrM8XHb1mUaXiotrQ6ZejjuvYF1zQ6mIFcyXWZioq5xCCnOuwSZCB3B2Jm5eankniOiV/42Esv53RylXSudp0Q/kjxJVi8tu7bbofN2ggquWVOXl0BoHt/Y05QfqpKfVxwANT1S9psdGhw23Ha5ZKvRWw2lc69RhlrNI77iCEuP3OmOp2cmfmYvQCJ1XXfNg/MqZW4FdyXwtQhde4JEH9DrEXPybxO6q3oWG1wFc/qSXYUp9tuzV1d8faJySMTE2Tm56srr5rrcvLVghdf84IxWe0Foy830cF15LCVKT7RWsp6RBha424ET9O6b8upDvWHPNXuQNbq5MRNMb/h4dz8ufLlUJsDekVptphOrq/CW6au60xeFSWojsYU2ZUVFKdTjOYyMnLHWkplPkbEn0U95GRZtR4wy6tTwyt4C+jkXp4p3vVnEeg0DE51cWjeQkeDG4dNIZ3VmTU6RouRjGdYnBJlsyZtHj0eR/X70fq7raHklTXgFG50kGbA9YGpk5udTOI6dAiA6IsvWeXVigK59qPg8EFyVTQ93ILpJbcYTRFLlfaSiywnCS8lUBRoiIxCJoO9vZ0Jb5JIOoLb5mYoWGL2bxk9seUhJzNydYMM5O5ArEBuZBWPGci9/DJHWo7gtrlZSixZB1VJyurkKusQXJmNEQulsNlVAgs54e5EcpZwKoxTdbKvaWMzAyGvY1U2OtQ0ViB3dQX3KaNz9ewZ7uu6DwWFq8tXK9TJFZ9vaVMVuoOmBUnpdTl7IwQ6NLS6LYNqz4kTXA1dI6tnaXY30+HtKP6AMutSjueqDzqNQG56eAXfAyJ4i77wPPd33Y+CwvDKcPl1abOXNAZu9DgImF5yZS6+pq9hS6+fzHmRpfbcfdpqdDjScgS7WqJUX+bia2nk5AWjbpCB3B1IS68fm0MV/ki9h8FmIz05iTIzb41Fen6qcJZtDWU7VyvLyJll1Y49DaTOnwXWllUPNR/CoTqKP6CM9ciS6SEnrUdqmo49Dah2hdhqinS/mDySvHyFYNZllTCfm3qu/IMsnVxhPVJfhTq5abOsOtSYZ1B9qrJGByi7Luek9UhdYE54WJyI4LhX7Hmx556nwdnAkRYhAXhxunBzzRrKGKlXqt/M9zWMvSq6ub2n76680WGpeKMDSI1cPSIDuTsQm021dHIzE0ncx8QhGX35ZR7qfgiA56crCOR67xXDwJdHYHV6/bcrNAU2y6o9B5tygvJ8I+BS5Sso2UoP0nqkXrA7bNa6nFt2YO/uAk0jfv4NHu55GIBnJ58t/6C+vAOzoB6pss7VNUbAVqNDbl2WFJRD5aVVeWDWNP4mFw2tbnQdwk37wOEgPTVFeny8uvLqFnWump3UnXsCxM+IjJz37tO5Roe2Muuy3H4pA7m6QwZydyg9B4XIdfLqMr688qq5Mb06+yqpbKr0Q9wNYig0wPj6jaySjJzQx60A0N3vJnlVzFX13HWqMkG5rpc3A7YycjKQq3Ws8uq1FbxGeTV+9owVyD039RxZLVv6IWUGlfc1l898aJrO7E3RLNHWqpAaFQJxz4kTazJyRUnHITwlvi5XWpUHZs1jZuVmJhJ4DT+56HPPWw0Pz089X15XbGbkFq5CbGn9tyvYL1OJDAsTwm+zRVlEi0RQfT7YN8jVJbHWSzY6QK45rZhJtbQfqTtkIHeH0msGcleW8dxjGgO/woGmA7S4W4hn4tXbkNxC/oFZbJNbno4RX01hc6g0hEdB07B3dqK2tXJp6RJQJvMRnYd0FFAMkft6cho5uTHVOj37xbqcuraSN+HhDMdbjxNwBFhNrVoZsaLYHNBzt/i6gJ9cbkxX8czH4mSEdDKLw23DPSN0m849e0j6nNwIiW5Us6xWEDPr4WoAb3PBl1hTHRpkabXWyenkQngfNHVyL3Cq/RQum4v5+Ly1Loria4VmowlhYr1lSSWl1dmRVXRNx9/sQrlqZInvuovLK1fJ6Bma3c10+bqKf4ZUNLc22w+v+3YinSWcEM0WMpCrH2Qgd4fSMdiA3aESD6dJ9B4BVSU9NkZmdpYHusVGtVmdXHdQHFDxdJalaOHsnllW7dzbSOp8znbkZugm8Uwcj93DYMNg8Z9vbkoNPcLZvwCy2aF+6NjbgKIqhJcSZIdEZiH+6mvYsrq1LqsqrxYoY1VyYFr2DnsaSLwknuExylc6Oh3eDtq8bcV/fn6WuIiOLqeRkwdmrdO1z+hcvRnCc7+4vMZeeAGn4rC6qjdbXrUycivF16U5X7VrKEj8NdGV7b37tFW9ON56vLRu0+yY9bWLwPLWbxtr0mVXCUhvw7pBBnJ3KDaHmrtljqcs367Yyy/zYJfYqCoSlpuB3Mx5SIbXfMtlt9HRYHrJFd6czECu92DeQPJTJzm3cA4QWQ+baiv+88uUVSG/tCoPzFrH6bbTPiB8uxZpxRYMokUixM+d4009bwLgmalnyj/IbHgo0Llq2uJMh+Kks+s1dCA6FEFcMKLPid8D/0MP8eqsODzNpqCilOlYTWU063IjA7nap7nTh8trJ5PSiAQHUb1esisrJC9fXlNeLUsJY2DTRH2yhEZu4rIoyXbvDxJ7RaxFz913W/tl2UaHOVHlKJSNg7VlVeltWD/IQO4OpvdQrrya85PL6eQuLl5kJbFS+iEN3cKIV9cKuulbDQ8FNiddy9PH7Q9awl3PyZOWW7p52y1KiVEzJotR00dOZuTqgW5jLNLU9RC+h4U2LvL001YjzhsLb5RflyX0SG0BFy67iqbDTGi9l5yu6UxcMTLFnaql2/Q+8IAVyN3TcU/pn1/GDHjBODDtcjB5XaCoijWua3I4578Zff55a798eeZl0lqZKTZrjIHXaj3NbuqFSIp4ar0ONJXIWLrNzmCSzNwcOBx4jh9fk5ErSblAzvSQkzKUukIGcncwPQdyDQ+ee425qy+9SIevg6HGIXR0XpypoK2+hE6ulIB3aTpKIpLG7lRpTE4LI2CvF8/Ro7wyKwK5ezrLHZilM3LprMaKMSKsWTY71AX5DQ/+Rx8BIPrdp+n0dbIvuA9N18qXsfL1SLcYAyuKYhmwFtLJLU5FiIfT2F02/FPigHQdOYzeGODcvMh83N1xd+mfX6ZjNf/AVOVg8rqg/4jQOo5dWML3kNjzos+/wMHmgzS5mohlYlZAVZT2I+D0QyqSC6oMGjx2q5w5ubJ+XU4Ph9CyOoEWN7brYh16jhxhVUkyHhazpst2+FcYyEl9XH0hA7k7mLaBAA6XjWQsQ7z7CNjtpEfHSI2NVVcuKKGT6ythCmyWVbuGGkm8JAJG7733MJWaZzo6jV2xc6rtVOmfXSYjZ+rjbKpCUGY+6oKufY2gQGguDidEBiNx8SKZhQUe7jZsSKYq0cmZxsDrLyPmuhwrEMiNXzLscPYHSbwgyqq+Bx/kwuIFEtkETa4m9jYWDtAsypoB58ZzSeqDgWMtgLD/sN8lSvexV1+FdIb7u8T/LrtfqracMfAt63LNBaPAxdcsq/YeaiL+gvg53vvus2xHBhsGaXQ1lv75ViBXuFFHBnL1iQzk7mBsNjWX/RhL4T0tNpjId75r2T08PfE0ml5YR2RhZuQmXoHs2tJCqYzc5JUVQFihRI2NyffAg1ZZ9UjrEbwOb+mfvVT6wJwOiZ/bEXBhk5mPusDlddDaK4bMz8wpln4z+uyza/zkyto99BWf8DDYItbVaIFALv/AjD5vrMsH1+rjSuqHshlYGRNfFzUDltYj9UZDq4dghxdd05nLNGNraUGPx4mfPVuln1zxi2+pRhyz3N97sInoc8a6fPghXp4VkhZzxGJR4ss5S5y2QwVfIqc61CcykLvD6TssygWjFxbxf8+jAES+8x3u67wPr93LXHyOi4sXSz+k9YAYvpyOwcy5Nd8qtjHpms7kNbExde/xE3tZBG++Bx/IlVXL6ZBSUYgao3GKHJimBqqzUVo81BP9R0T2Y+zCIr5HRHk18vQznO44jcfuYT4+z9Xl9R5xazBHdU28IoKrPAZafACMLkbX/H02rTFlThoJxMnMzKA4nXjvudsK5MqWVUPjoGXA5oJAd8GX5MyA5bqsJ/qPiv1y/MKiNa4r9sILVgXj3Pw5IqlI6YcMissII88KH8w8ipkCx8MpFsbFc9ucy2Tm51HcbjynT/PytAjkzKxgUeaMjtXGPuEBWgBpBlyfyEDuDscqFwyv4HxAHJixl17CnsxY2Y9vjX+r9ENUNe+WufZGmr8x5WdQFqciJKMZ7C4bgdBN9HgcW3MzrgMHrIxc2UDOtB5xB0UgWYCZVRnI1SMDx3J6JK/R8BB95hmc2Lm3UwjNy5ZX2w+Du1H4DM6s9UQcbBUXjJGFtQfmzI0QmbSGp8GJ85pYh57Tp9GdDs7MiWacyjtWB8XvRgGk9Uh9MnBU7JejF5bwPiiCt8izz9Lt76Y/0E9Wz1oBf1F67wPVIbJjS2u958z98tZ5q2Y2rqXHj3bWkKHccw9RklxcEhdt8/eiKPNGWbVINg6kGXC9IgO5O5xgh5fGdg9aVmc2GcTR04OeShF94UXe0vcWAL49/u3yDyqik+sKulEUSKQ1a1QW5Mqq3fsaib8oNibfA/czG59jIjKBqqjc1X5X6Z9ZgfWIlZFr8JT/d5DUDB17G3F67CSiaSLNQ6iBANmVFRIXLljdq2X95FRbruw/utZKJz8jl3/BGLu4CEDfoSZiVln1Qa4uXyWSjuBz+DjYdLD0zy3TsQowb5ZWpUaurujeH8TmUImuJEkdEIFT4tx5MvPzVnn16cmnSz/E6c0ZVo+uXcPFpCij58W67D/SbNnh+Aw7HE3XGGgYoNPXWfrnlml0AKmRq1dkICexsnJj+eXV736HR3oewabYuLp8lYnwROmH5Heu5h2MLruNTsO5Pr9cMHZBbExCHyeyeN4HH7TKqoebD+N3+kv/zDKCcshl5LpkRq6usNlU+g6LLOvopRV8Zvbj6actP7nX5l4jli49l5IBEfTdGsj1NnlQFYimsmsuGDfPiXU5cKSJmHnBeOghXpoROrtT7aewq2WMUst0rEJ+Rk6uy3rC7rTluv1ndNzHj4OuE/7Wt3hz35sBeGrsqfK64kGxhhlZ64lYSIqiaTqjb5iBXGNOhvLwQ7w4LdbofZ33lf/wZRoddF3PBXJSI1dXyEBOYgVyo28s4nvU1Ml9l0ZXo5UV+87Ed0o/pPuU0ARF54uWC8zNKRXPWKWC/kEX8bNnASEof2laHJhly6qQ1+gwWPQl00ZGrkMGcnWHdcF4YxHfI+Lgiz79DP2Bfnr9vWS0jHWQFX+IoUcafQ603OHqstvoNgxYTZ1caD7O8nQUVVVoV2bEHMvGRtxHDlvm2KZZdknKDCWHnEZOllbrj1zZf5HA294KQOTJp3ig6wH8Dj/z8XnLpqYoViC3Vidn7pULkSSJtPCSm70RIhFN4/LaaVy5IWQora24DhywLhiVBXKG1rlIRi6czJDMiN8RmZGrL2QgJ6F7fxC7UyUWShHvPY7icpGZniZ59Zp1yyyrk7O7cuWCW8qrt94yxy4uoWV1Gts92C+/DNksrv37cfR088ykuKE+1PNQ+Q9eZvgz5EqrMiNXf/QbeqS50TC2u0QAFX/9dbILC1ZWruy67DoJDh8kVnIaIYNBo7w6siiyeiPnFsRb9jeSec3Ixt1/Pwk9Zek2zZ9bksVh8WeRdalpumUILEur9YfZiDM9HML5pjcDwhjYlkjxPX3fA8A3R79Z+iF994Fqh9UJWBm1/rrR48BveMmZ++WIWVY92kL8ebOs+iAryRWr4aes32ZkHmKLgCKa0wpgZuMCLjtuR4lpOpKaQwZyEuwOG72HjFvm1bBVxgp/8xtWIPfqzKusplZLP6iITs4aUr689sDcc6KVyLeeAsD/1rdyZfkK8/F5PHZP+YycrsOMYb7ZeazIS/Rcs4McTF53+BpdtPaJ8vrknA33iROijPXkk7xj4B0APDn2ZGk3fZsjZ0MyslaPNGBakBgZuZHzYl0OHm8l+mxOh/TKzCuktBSdvs7y/nHpBCwYF4wimY+lWIqMJrIwcmxc/RHs8NLQJnTFC5lmHH196KkUkWef5R39Yl1+c+ybpe1xnL7cxTevvKooyrrOVWtdnmgh8u1vA+B/5BHr0nug6QCtnvVzU9dgZuOa9wiNXgGkPq5+kYGcBMiVsW6eWyDwzncCEP7qVxloGGBv414yeobvTny39EOKTHjIL61qWY2RN4yN6UiQ6HeFMDjw1rfw9IT4+v6u+3Haypj3rk5BfAkUG7QVPjCXY2lSRqlAZj7qkz0nxAF14+w8DY+JQzL89a9zd8fdNLubWU2tVlFeXRvI5WfkkvGMZTsysN9HzJj763voQaus+nD3w+XnT85fAj0ruqgbSluPNPucOO1yC65HzO7VsQtLBN6aK68+1PMQbpubycgkl5cul3lIng1JHlbn6kqc1YU4S1NRMSIsmBTj4mw2/I88Yu3H39P7PeU/cBl9HORNG5GBXN0hdxEJAHtOtoICcyOrcPphcDhIXhsmOTxsZT++cvMrpR/Sdy+giNJSZD7313nTHWZurJKMZnD57AQWr6BFo9haW3EfP25tTI/0PFL+A88IN3PaDoKjcLbNLKu2+p247LJUUI8MnW4HYPziEq7veTsA0RdfQg+tWuvy6yNfL/2Q/IaHvCxJfkZu7MIimqbT1OnFdvElSKdx9Pfj6OuzMh+mHU9JZi+IPzuOQZGgT5oB1z/5F1/vW0R3f+Tb38at263y+zdGv1H6IUUaHnqCuYuvmY3rGmok/bzYH72nT6M1+KyubbOcW5Iy+jjIzf+VGbn6QwZyEkCUscxh5SPX4vgfEoff6le/xrv2vguA5yafYzmxXPwhnqbcjW88l5UzNXKTy3FunBUGvoPHWokZZYLAW95MKLXKuQUhEH6099HyH9gM5DqLD4meWTWmOsiyat3S3O0j2OElm9GYWnHjOnwYslkiTz7JYwOPAfDU+FOly6s9dxuNOHOweN3668FWkZG7uRDlxllx8Rg80crq10Vg2PDOx5iMTDKyOoJNsZU3XIW8cn/xdSlLWPVP76EmnB47sVCK1eAQtpYWsqEQ0eee4+0D4sLxzbFyOrn7RUUhNAbLOZ1cvqZ4+BWxX+452Uo4T4ZyZvYM4XSYZnczx1oKS0vWUI31iOxYrTtkICexMLMfw6/OEXj8cQBWv/oV9jbu5XDzYTJ6pnz2o3+9MXBnoxtVgVRa48rLxsZ0Km9jestbeW7qOTRdY3/T/vJ+SJCbIFHiwJyWjQ51j6Io7L2rDYAbr83T8E4RvK1+9WtWeTWUDJUurzrc0GtoLvPKq/3N4sBMxDPcfN3QbR5tJPIdkfkIPPaY1a19su0kDc7CbvhrmDUCuY7ih6u0Hql/bHaVvadE2f/6mUUa3iUuu6F//Cce7X0Uh+rgZuhm6fKqy5+bu5q3LvuaRUZubibK9PUQKLBnn4vYS2KCQ+Ctb7HW5Zt63oRNLVNt0HWYNz5HERkKyAtGPSMDOYnF0Ok2UGD25irK3W8Ch4PU8HWS167xxN4nAPjnm/9c+iGWTi7X8OC0q3Q2uOnNqCRWU7i8djpt82SmplHcbnwPPmCZaFZUVoWKMnKzpvWIzMjVNUNGIDf6xiLuN4tyavT559GXlq2s3D8M/0Pph1jl1dyB6XbY6Gp0sz9tI5vWCHZ48Y29jh6LYe/uwn3smHVxeVv/28p/UF3PW5fFAznzwJS6zfpm390dAAyfmSfwhNgfw08+iS+tWmbqXx7+cumHFNDJmWbVrilRUejZH0R78TuQzeI+cgTnwEB1+rjVSUiuii7Zln1FXyanOtQvMpCTWPgaXXQNNQJw43IM/5uEhiP0D//A44OPo6BwZu4Mk5HJ4g8xM3LTr4tZqAa9TV4Op8XNceiuNiJf/RdAdF9lnXbrhllRIJdYzZkBd8iM3G6nrT9AQ5uHTFpjMuTDffIEZLOE/vGf+P593w+I7tVQMlT8IWYgd4tv10CLlyMpsS4P3NdB2CyrvuMx5mJz1liuxwYfK/9BVyeFzYlqLzkGSWrkdge9h5pwee3EV1MsufpwDgygx+OEn3yS9+57LwD/cvNfSpf9B439biQ3DcLUbu6JCo3l/ns7WP2q0CcHvvdxRkIjjKyOYFft1pSTkphl1Zb9YC/eRCZLq/WLDOQkazh4vyhrXnpuiob3vQ+AlS9+iXZns2U6+S83/qX4A4J90NArhoZP5mYO9gbdHDACuf33tLH6T/8EQON738Pz088TToVp9bSWH8sFOUF5Qw/4Woq+LDdnVY7nqmcUReHgfSL7ceXFGYLf//0AhL74RQ43H2Z/035SWoqv3vxq8YeY8y1XJ9YYVu/1exjIiG1w34kgkW8JX7rAOx/jG6PfQEfnVNupCsv9Rlm19YDwVSxCzgxYXjDqGZtdteQoV1+coeHd7wYg9A//yEPdD9HibmEpscQzE88Uf0i/oZNbGYWVcQC8TjsHPC7aNRVFhYFBO7EXhfFvw/d+L18fFZeN+zrvKz/9BipqdABZWq1nZCAnWcP+ezqwO1WWZ2LEBk8LEe/CApHvfMcqr35x+IulR9CYWbnRXHm1P6ni0RWyLpXGpatk5uZQGxvxPfooXxv5GgDvGHhHeb0HVFRWhfw5q/LArHcOGBeMiUtL2N70dhSHg+TVq6QuX+b7h74fgC8Nf6n4A1z+3Lq8/pT1171hHRWFeIMd9bXvokUiOHp78Zw6Za3Lx/c8XtmHnDXWZQl9HORp5GRpte45/FAXAMOvzeF5TOjkos89h76wxPft/T4Avny9RHnVFRBTcWBN2f+ULjJnzl4fqae+CpqG+/hxnL29lnvA44MVrss5Qx9XIpDLajqLUTGqTgZy9YcM5CRrcHrs7DNumZdenCP4vu8HYOXzf8c7B9+J3+FnPDxeWlw+aOg+8g5M36QIqmaDKmEjG9fw+OOkVI2nxsTr3jn4zso+ZAWNDpAXyMnSat0TbPfSNdSIrsPV81H8bxeatZUv/D3fN/R92BU7byy+wbXla8UfMiR0Sww/af2VY0LokEb94lkAje9/H7PxOc7On0VB4e39b6/sQ06b67J4IKfrulValSWs+qdjTwNNnV4yKY3RWSee06dB01j57Od4z773APCd8e+wEF8o/hBLJycyd1pWo2dZXJQjHc7cunzf93Nt+RrDK8PYVTtvG6hAtwkVZeSWYymymo6iCH9DSX0hAznJOg4/LIxMh1+Zw/tuUV6NPP00jsVVKyv3+aufL/6AfcbBN/ESxJcJLyVIjQu93FUlyurXRKaj8T3v5smxJ4mkI/T4eyorq0JFGblIMkM4mREvk4HcruDoI2JdXnhmkob3/wAgyquNaYflpVVyXQ4ZB9/I05BJMT8eJjWfIIvOSGiS2EsvgaIQfN/7rCaHu9rvosPXUdkHnBBjvCzH/gKEkxkSaWlSvVtQFIXDD4l1eem5aZo//CEAlj/7Wfb5BjnRdoKMnuGzVz5b/CGWTk4EciPnF7EnNWKKzurSDZJXr6I4nTQ+8QT/eP0fAdGtWlEXtZaF+Svi6xJmwKaHXLPXicMmw4J6Q/4/JllH175Ggh1e0sksY/MevPfcA5rG8mc/yw8d+CEAnhp7iunIdOEHBPuF2FvX4PpTXHx2CnQYs2UZuPBt9FgM1/79eE6ftrq63jP0HlSlguWYTefEu6U85IxsXMBlt2YXSuqbobvbcfnsRJaSLDYexLlvCC0WY+ULX+ADBz8AiPJq0VFynSfA2wqpCIy/yPlvTwBw1ZHlrmuirOV7+GHsnZ186fqXgCrKqqFJCE+BokJ38QuJqY/zu+x4nXJd7gYOPtCJalOYvblKbP/92Ds6yC4sEP7KV/jxIz8OwGcvf5ZEJlH4Af0PiHWzfBNCk9a6PO/MMPC8uPQG3v52tICXf7guurPNJp+yzF2ETBycAWgaLPoyqY+rb2QgJ1mHoigceZO4ZZ795hjBD/8YAMt/9dfsc/Zwf+f9ZPUsn7n0meIP2S9sIjKXn+LCd0WX6xvuDO+6Lm6dTT/2YaaiU7wwLfzm3j307so+3PxlyCbFxhQcLPqy2VVZVt1t2B02Dj8oNEmvPzlO84+LQ3L5Lz/DA+33MdQ4RDwT54vXvlj4AaoKQ2KcUuLid7j60iwAYw0a7xwVYvLgD/4A5xbOcW35Gi6bi3fteVdlH27SyMa1HxVzNIsgO1Z3H94GJweMZpyzT03R9CM/AsDS//pL3tr3Vrp93Swnl/nHG/9Y+AHuBug6CcDymeeZuCxM14cJc+qK2B+bPvSjPD3xNIuJRZrdzZWZpgOMGxKY3nughP5YBnL1b1N1QQAAIUZJREFUjQzkJAU5+qZunG4byzMxlrpO4dy7F211lZW//Vv+1dF/BcAXrn2BcCpc+AH7RCB35fUY8XAaf7OLgdgVumJL6P4Aje9+N5+9/Fl0dB7oeoC+QF9lH2xcHLj03i0O5iJMS33cruTEW/tQbQqTV1aIH38ztmCQ9OQkkSef4sNHPgzAZy59hnS2iOXDPlFePfdykmxao7XPz/2hczQnw6SbWwm87W187srnAKHZbHQ1VvbBzLJqb/GyKsgDc7dy6h39AFw/O4/ytveiOJ0kLlwg/fp5PnRYlFv/8uJfFm8S2yOkAeeeEVq6vmMtvGn8OZzZNPZDh/GcPs1fX/prAN677704VEdlH8zcL/tKTyWR1iP1jQzkJAVxeuwcfbQHgNe+Nk7zT30UgMU//wsearmHocYhoukof3nxLws/oP9Bso5GziyJg/PU2/r5vmvCK27pLe8iYdf5wrUvAFgbXUVYB+a9JV82ExIidtmxursINLs59IDoYH3tyWmCH/xhABb+6I94YvBdtHnamInOFO8U3PsWUpqbc7Ni0sNd7+jjLa8LPdzIo08wn17mX24Ke50fPvjDlX8w02qnzLrMmQHLdbmbaOn2i/mrOpx/OUTDe0SFYeFTn+L9+9+P3+HnZugmT088XfgB+x8jmm3i0uQeAO56tJ333xDVi+j3/SDDK8O8OPMiqqLywYMfrPyDmRm5vvtKvsxcl63yglGXyEBOUpSTb+3DZleZuRFieeABHN3dZBcWCP3dF/jZUz8LwJ9f+PPCHVl2J1e8P0ko243blWbAOcmeicukFRuX7n+Mz1/9PKupVfoCfZVPcwDRQAHCF6wEpoecNAPefZx+fABFEZMesm//IVS/n+Tly6S+9iQ/cewnAPjTc39KKpta/+ZAB+fUnyKpB2hszNI69hxN85OEHR6eP/won7n0GTJahtPtpznRdqKyD5TNwJQwDqbnnpIvzY3nkgfmbuMuIyt3+blpnD/4EbDZiH7nu6hvXLO0xb9/5vfJatn1b+67n1cTP0pWd9DVZ8Pz0ldoTISZ9jZz/fhD/NkbfwaICSPd/u7KPlB4FpZHAKX8BSMiM3L1jAzkJEXxBV2cfLsoeT735ZsEjazcwh/+IW8N3sfx1uPEM3E+9fqn1r03nczy8oQY13W67Tus/OHvAfDVwfu5ioNPv/FpAH7q+E9V5h0HEFuCxWHxdW/pA9NsduiQgdyuo7HNy/57hSbppW/O0fyTPwXA/O/9Pj8w+B7aPG1MRaf4m8t/s+698XCK1xZEGeve7hdY/IM/AOBvD7yNS7FV/vby3wJYAWFFzF2EdAxcDcIMuNRLV6VGbrfSfSBI76EmshmNl1+ME3y/6Pif/a3f4ieOfISAM8DV5atWw0I+KwspLkSEfvOe3ldZ+p//A4C/PvgOzi2OWFninzz+k5V/IPPS23FU6PBKkMvISeuRekQGcpKS3P3OATwBB6G5OBNtD+DcN0R2ZYWF3/99fuHuXwDg767+HTdCN9a875WvjBCJ2gnYZukf/gzxs2fRnC7+9sDbOLP6JRYTi3T5unj33gqbHAAmxNBoWvaBt7nkS2VGbndz37v3YrOrTFxeZuXku7C1tZKemCD66c/w8bs+DsCnXv8U87H5Ne977gvDpDN22uzXaX75M2RmZ9HbO/nHvQ9zM/tl4pk4J1pPVDbD0sRclz2nS+o2ASZXRMm/Kyinjew2FEXhTT+0H0VVuHFmnuQTP4Hq9ZI4dw7++Uk+duJjAPy/Z/5fYumY9T5d0/n2X11G01X6na/h/Mpfkl1eJtbRw1N9p/nuwl+g6RqP9j7K0ZajlX+gCsuqkKcpbpDrsh6RgZykJE6PnfvfsxeAF/9pFM/HfxWA5b/+Gw5fS/Bo76Nk9Ay//uyvWyWD+bEwZ78+BsBDbV9n8YwIplI/+hGWAxqzqnAm/8W7fxGHrULRLuTmEfY/WPalVkZOapF2JY1tHk6/U5Synv7SKA0//8sALPzxp3hcO8zRlqOE02H+/XP/Ht2YrTp6YZHLL8yAAg+6/pJFoxra/HMfJ+tdIOt/DoCfO/1zKIpS+YexArnSWWKA8SURyPU1yQNzN9LS4+eYoS1+5l9mafwZcamY/c3f4gc9D9Pj72EuPsfvvfZ71nsuPD3J5NUV7A6F+7RPs3xWrJHIz/wiiv8mC/or2BQbP3/656v7MBU2Omiabl0weuW6rEvqNpBLJpOcOnUKRVE4e/bsTn+cXc3hh7vpORgkk8zyzKsOAj8qbB+mfvVX+dU9H8Pn8HF2/ix/cv5PiIdTfOWPz6NpOntPtuJ4/SbZpA1Xh5emn/hx3N2fByXN3R33VD7JweSmEcjtKd16n8xkWYgIfVSXnLO6azn9+ADN3T7iqylemujG+5a3QTrN1M/9PJ889as4VSfPTD7D5658jvBSgm/+mXC4P/6mTjKvRdCzKt5DXQTf+734ez+Homjc1/493N9V+uBbg67n1uVA6QHmyUyWWcN+pLfJu6F/Z0ntc9+79+BvchGai3MmexrPvfeix2LM/btf5d/f/SsA/PXlv+apsadYnIzw7N9fB+D+x3sIvwSg0PCmYzS86S7c3X8HwAcOfID9Tfsr/xCZZE63WSYjtxBNkspoqIrs8q9X6jaQ+6Vf+iW6uysUfUo2haoqvP0jR3H57MyPhTkTfCf2/QfJzi+Q/D/+T37t4L8G4H+88mn++v95mvBSgoY2N4dH/o7YpVkUm073Qyt8afx/YffdQNec/Oyxf1dd1iO+khvNNfimki81TVeddpUmbxUZP0ldYXfYeOynjmJzqIxfWubqXT+Fraub1Ogo9l/+HT5x5H8H4A+e+WM+93+/QCKapq3PT/9zf0xiOo7NmaXroRj/5aXfQHdOo2V8PNbxs9V9iOWbsDoBqiM3y7UIUysJdB08DhutfqlF2q24fQ7e+b8dQ7Up3Di7wOhbfxGloZHE+fP0/c7n+PCQ6Ib+L1//r3zx918lk8zSsy9A41//J9KrGg5/htYH4U8u/WdUxwpaqpkfO/Qz1X2IqbOQTYGvDZr2lHzp5LLIxnU0uOVUhzqlLv9f+8pXvsLXv/51fvd3f3enP8odg7/JxRM/cwK7Q2Xs4gqv3fNvifUdJ3ntGof/3V/w8dAP8r7zv0BiUkFxZDk990XiX/482Gx0fU+C/9GR5n9e+J8AJKbfh5Jpr+4DjD0vJkU0D0FD6QDe1Md1NrirCxYldUdLt5/HfvIoigJXX1viwtv/I/GWQeKvvMp9v/5FPrz0Hr7v3P9OYlHD4cty7PKfEX/yGygOB52PhPhtzwxfGv4SoJCY+gCLq1UGWMZYJXrvKWkEDDC+JHRRvU0euS53OZ17GvmeHzkIwBsvLnHt+3+bpL+NyFNP8YO/d44fnHs333v2Z0iGsrgDGQ49/V9JvPoqqtdD+yPL/FryLM9MPQ26g/jkjzC7olf3AW4KqycxNaL0WjPLqj1St1m31N2MmNnZWT760Y/ypS99Ca+3svJEMpkkmUxa/3t1tcgIH0lJuvYFeeJfn+Rrf/IGC9NJFoZ+Gk//ClpWI32xmSbAll7m1Cv/f9TIFJrTztjH38MnXd/knC4OsY7M+xlevYuJ5Rj3DpZuWFiDVVYtb1UyI82A7yj2nmrjnR89xjc/fZGp8RRTx/8t3uQCGez4rwQBcCTnueeF30dJLJH1OLn+b3+AX0l/mWFECf6R4M/yL5f6GF2IlfhJBbjxbfHnYPl1ObEsdUh3Ekfe1I3NofLU/7rE2FiW8Xv/A97YHCmbh9brAQBcsTHufu6P0FOrZIJ+Lvzq+/j5hb9hwgZ2RaUn81HeSPRxcyHKPdXsl8NPij/N+cIlMDNyPXJd1i11Fcjpus5HPvIRfvqnf5p77rmHkZGRit73m7/5m/zH//gft/fD3SH0HmziA792L89/8TrDr8wSdwTBAYqWoWvmBfbe/Eec6QhvDCj8xdt0Rp3/ADp4NY1fjqk81/Y+hplkwhB9V8zwN8Sfe99c9qVWICcbHe4Yhk6309zt47m/v87I+QVirlYAbNkk3VPPsmfkn7Bnk7w6pPDn78gym/48AA3ZLJ/MBFgdeDf/8vxZRhajlf/QbCZ3YO57e9mXjy+LILGvWerj7hQO3t9JU6eXZ/9umKlrK0Q9ohJhT0fpnfwOg6NfQyfDd44p/NVb4qws/w3YoD2T4Tc9B/ly4E28wVh16zIRyjXgGCPpSiEzcvVPTQRyv/zLv8xv//Zvl3zNpUuX+PrXv044HOZXfuVXqnr+r/zKr/CLv/iL1v9eXV2lr6/CkVCSdQSa3Tz2k0d59IMHWJyMoCgKTUHQrjegJR5lqSfAdPhZ+pYuMaCoHG86xPu//tu0J8Kkum7weVzWoVYRSzdg4Sqo9oo2JrOVXlqP3Fk0dfp44mdPEA+nWJiMYHfYaGrIkh0OomceZ6rbxfzKM+xfvsph1c7dTYd53z//exozk1yyzQAwuljFupx8BRIr4Gkq62sIudJqn2x0uKNoH2jgfZ84TXgpwcpcDJfHToMjTuZ6EJT3MdptJ7z4XQ4tXyXgDHC3u5Pv/9pv4LMtcelhMdJrpJpM8c3vgp4VNk1NA2VfLjNy9U9NBHKf+MQn+MhHPlLyNXv37uWpp57i+eefx+Vaa6Z5zz338KEPfYi/+Iu/KPhel8u17j2SzeP2Oeg50JT7izYh9g4AP8ctMydvnoPzn+Pu8JPAu6wyU0VcFSOU6H8Q3OVnX86uytLqnYwn4KTvUF4Zqk3Y1RwADnCLw/2FJ2H4mwzOfh04wcxqgngqi8dZgUn11a+JP4feVnIguYksrd7ZBJrdBJrNPakBuoWp9VHg6N68Tmldh1f+DhaucG/0u8De6jJyl4V5sDnvuhwyI1f/1EQg19bWRltbW9nX/f7v/z6f/OQnrf89NTXFO9/5Tj772c9y//1VWAZIbj/HfwjOf46BqX/GyTuqC+Qu/5P4c/9jFb18Ws5ZlVTK0ffB8DfxXPw8QfddrCSyjC3FONgZKP0+Xa96XU7I0qqkEhQFTv0IfPM/sGfyH4CfZ2Qhiq7r5Ztksmm4YgRyhyszW5+UF4y6p666Vvv7+zl27Jj1z4EDYhzO0NAQvb29O/zpJCUZeisEunEkl3mH+ipTK3GyWgWdWOGZXGfgkfdW9KNmDfsRmZGTlOXI94MzAEvXeU/DNYDKsh+zF0S53+aEg4+XfXkslbG8DWVpVVKWEz8Miopn+iX2KDNEU1lrHmpJbn5XlPt9bWXtcABC8TThZAaAbpmRq1vqKpCT1DE2O5z6UQA+ZH+KjKZbN8GSXPgioEPvfRXpPbKaLkurkspx+UX2A/gBTZRKRysJ5C78vfhz3zsqKvebaz3gstPgqYlCiKSWaei29MAf9QkrkYp0cua6PPREReV+c102+5x4nXJd1it1HcgNDg6i6zqnTp3a6Y8iqYTTPw6KykPqGxxQxrk+Hyn/nnOfE38e/8GKfsRiJElG01EVaPNLXaSkAu4Rg8iPR56lk0VGyjU8aFl4/bPi62Pvr+hHmM09vc1e6SEnqYx7fwqA92afxEOCkYUyF4xkGN74ovj6+Acq+hFSH7c7qOtATlJnNA1Yuo2fsv1L+UBu6gxMvSZc849WdmCaZsDtATd26VIuqYT2QzD4CCoaP2b/RvmM3LVviGkOniY49H0V/Qg5Y1VSNfsfg6ZBfHqED9q+xc1y6/LCFyEdFabpZcbFmUwaFwwZyNU38qST3F4eFEOk3297mtDYhdKvfelPxZ9H3wf+8s0wkLMe6ZBlVUk13P/TAHzE9jVW5ydLv/alT4k/T30IHJWtM9noIKka1QYP/zwAP2v/B6bmFoq/VtfhhT8WX5/+sbLTHEysjJy8YNQ1MpCT3F767mW68y3YFY3vGfuD4q9bvA7njPLV/R+r+PGmPq5LdqxKquHQE6Q7T+NTknwg9jckM9nCrxt7Ea4/BYrNKn1VgpmRk52Bkqq468PEfb20KSFOTH+++Ouufg3mLoDTD3d/pOLHy9Lq7kAGcpLbTviRf09GV7kn+WJuxNGtfOu/gJYR5YUKzFZNpuV4LslGUBTs7/xPAHxQfYrZa2fWv0bX4an/LL6+60PQXHoYeT4TK9IMWLIBbA7C9wsz+x+OfRZ9ZWz9azIp+Mb/Jb6+5/8nSv4VIs2AdwcykJPcdnr3n+AzWTHSSPv7n4boLSWDy/8Mb3wBUOCt/1dVz5ZzViUbRdnzCC847sehZGn66s9C6hZN0qufhpGnweaCR/5NVc+2NHKytCqpkuADP84r2gH8Spz0F35aeMXl8+z/I6xwvK3wyCeqevbkitgvZUauvpGBnOS243Xa+Svfv+K61oUamYa/+iEIz4pvjr0IXxR6JR7619B1oqpnm6UCOZ5LshG+3PtLLOoBAqEr8Lc/CvFl8Y1r34Cv/LL4+u3/oSIrHJPVRJpQXBy+srQqqRan08F/8/4fxHQXzvFn4Ysfg7Rh3XT2r+FbvyG+fud/AU+w4ucm0lkWDG86uS7rG2kcI9kROtvb+NjwL/DP/v+Ca+o1+IPT0HoAps+CrsHAw1Vn4wDGDOuIfpn5kGyApo5ePnr5E/yt57dw3vg2/N4paBoU6xLg4LusxohKmVjKeXX5XHLLlVSPvf0A/3r44/wP139HfeMLcP1bEOiEuYviBff8JJz8YFXPnDIuvT6njUaPY6s/suQ2IjNykh1hX7ufYb2XPzv4Keg8AamIsBrRNTj2A/CjnwN7dT5wiXTWsh8ZaPFtx8eW7HIGW3y8ph/gk22/Cy37hUv+9FlAEYflD/0FqNVtm6aHnLQekWyUPS1entJO89mD/w0a+yC+JII41Q6P/lt41+9W/cz8jlXpbVjfyOuhZEcYavMD8HKklZ/5374jPONCY9BxHFr3beiZ40viwAy47DR55Q1TUj0DLSKT++1wL/ybF2HsBYjOQ/ddVZVT8zHXZa9sdJBskMFWcTH9Tvo4P/JzZ2DseUisQu+9EOjY0DOtRgepj6t7ZCAn2RHMQG54LiIyHL13i382wahZVm2R7vmSjWEemBPLMVKagnPw4U0/c8IcSt4sD0zJxhg0Kgwji1GwOWDPo5t+pvSQ2z3I0qpkR9jXLgK58eUYiXQRz64qGTUyH2ZWRSKplvaAC7dDRdNzB91mscyAZUZOskHMC8bIYhRN07fkmbmMnFyX9Y4M5CQ7QqvfSYPbjq4bt8wtYMx4Tn+z1MdJNoaiKGuzH1uANAOWbJbeJg82VSGR1pgNJ7bkmRMyI7drkIGcZEdQFIWh9rzy6hYgM3KSrcBcP6PlhpRXgK7rcjyXZNM4bKrVLHNzC9YlSI3cbkIGcpIdY5+hk7s+t1UZORnISTZPLiMX2/SzlmNpoikhHZAHpmQzWOXVhc2vy0xWszr85bqsf2QgJ9kxzIzc9fnNZ+Symm7ZPEjrEclmMNfP6BaUVs2OVaG9s236eZI7l8GtXJfLcbKajsdhoz1Qnc2TpPaQgZxkxzA7V7cikJtaiZPO6jhtKp0NcqqDZOMMmqXVLcjImR2rsqwq2SzmutyK0urNBbHnDrb6UFXZ4V/vyEBOsmPsy8vIbbYTa8z06moWomCJZKMMGCWs8eUYmay2qWdJM2DJVpHfubpZbsyLZ+xtldWL3YAM5CQ7Rl+TB4dNdGJNhTZn9WBmTwZk5kOySboa3DjtKumsznRocx2C0gxYslXsaTVLq7FNX3xvGFm9vW0ykNsNyEBOsmPYbaql+7g+v7lb5uiSeL/Ux0k2i6oq1qzezWY/cqVVmZGTbI6eoAe7qpDMaEyvbu6CcdPYb/fIjNyuQAZykh3FKq9u0oLE7Fjtlxk5yRZg6pE227k6Ls2AJVuE3abmLhib1MndMDRyMpDbHchATrKjWKO6NtnwYAqApfWIZCuwOlc3cWBqmi6bHSRbiqmT20zDQzSZYXY1CcDeVv+WfC7JziIDOcmOMtRulFY3kZHLZDVLvHugI7Aln0tyZ7MVGbmFSJJURkNVoLNRdlJLNs9WWJCYQWCLz0mj17Eln0uys8hATrKj5CxINr4xjS7FSGU1PA6bNLeUbAlb4SVnllW7Gj04bHKrlWyewVbTgmTjFwzZ6LD7kLuLZEcxA7mFSJJQLL2hZ1ydCQOwv8MvPZEkW4KV+VjaeIfgtVmRZZYHpmSr2Io5wLLRYfchAznJjuJz2ekyyk4b1cldNQ5MWVaVbBXdQTd2VSGVyY0yqpbLxgXjUKdcl5KtwQy+xhZjZDd4wcg1Okh93G5BBnKSHWezEx6uzooD80CH3JgkW4PdploNChvtELw8swrAwc6GLftckjub7qAHl10lldU2XPY3M8VDMlO8a5CBnGTH2bfJmau5QE5mPiRbh7kuL06vVv1eXde5IjNyki3Gpioc7hIXg/OToarfn85qDBuNZeZzJPWPDOQkO85+I5N2car6AzOV0awuLBnISbaSk72NAJybqP7AnA8nWY6lUZVcQCiRbAXHe8S6fGMDgdzNhSiprIbfZadXjo3bNchATrLjnOwNAuLA1PXqdB83F6JkNJ1AntZOItkKThjr8vWJlarfa+rjBlt9uB22LfxUkjsdM5DbSEbu0rRZ7g+gKLIxbLcgAznJjnOwM4DTrhKKp6v27boym+tYlRuTZCs5YWTkRhdjrMRSVb1XllUl28UxI5C7MLladUf1pWm5LncjMpCT7DgOm8qxbqHXeH18par3XjMCuYNyY5JsMUGv0zIGrra8eslodDgkGx0kW8z+Dj9Ou0o4mWF0qbqLr9mAc0jq43YVMpCT1ASn+poAOFtlIGdmPva3y0BOsvVY5dUNrkt5wZBsNQ6buuGGh8tGRu6wXJe7ChnISWqCk32iXFBtIGcKfmUHlmQ7MMurr1eRkctkNa4ZnYGyhCXZDo73iP2umoaH5WjK8kQ8INflrkIGcpKa4FRfEBCdq6mMVtF75lYTTIUSqEruwJVIthJzXZ6rouHh+nyUVEbD57TR1+Tdng8muaMxGx6qWZdm9m6gxUuDW85Y3U3IQE5SE/Q3e2nyOkhlNUvHUQ4zS7K/PYDPZd/Ojye5Qzna3YhNVZgLJ5kJVTbh4ez4MgDHexvlyDjJtmBKUc5NhEhnK7v4mtUO83Ii2T3IQE5SEyiKwkljg6m0vGrqlsyyrESy1XicNsufsNJ1eXZcXDDMw1Yi2Wr2t/tpcNuJpbKWpUg5rP3S0H1Kdg8ykJPUDOYGc3ZspaLXm/5eJ+UNU7KNmMbAlQdy4nWn5AVDsk2oqsI9g80AvDyyXPb1uq7L/XIXIwM5Sc1wekBkMF64sVjWGFjTdOvAlDdMyXZyt7EuX7y5WPa1q4k0VwxpwF39MiMn2T7uNQO5m0tlX3tzIcpCJIXTrnK0WzaG7TZkICepGe7f04zLrjIVSljzAItxaWaVcCKDz2mTnYGSbeWhfa2A0COFE+mSr311ZBlNh8EWLx0NctKIZPu4f68I5J67vkCmjE7uRSPYO9UXlJNGdiEykJPUDG6Hjfv3tgDwnavzJV/7wg2xMd0z2IzdJpexZPvoCXoYbPGS1XRevFE6+/GCkbW7b0/z7fhokjuYk71Bgl4Hq4kMZ8qU/V+8IdblA3Jd7krkCSipKR7dL7If5QK5Z66J7z9gBH4SyXbysJGV+/bVuZKve3Z4AYD798h1KdlebKrC9xxoA+Bbl4uvS13Xed4I5O6X++WuRAZykprizQfFxvTizSXiqWzB18RSGZ69Ljamtx5qv22fTXLn8o4jHQB87cJs0fmWs6sJ3phcRVHgUeOAlUi2E3O//PaV4hffi9OrzK4m8Thslt5TsruQgZykphhq89MT9JDKaLxwo7C4/JlrC6QyGr1NHg50+G/zJ5TciTw01ErAbWc+nOTVscJdgmZW5ERvkLaA63Z+PMkdyqP721AUEawV8zl86pJYlw/va5X6uF2KDOQkNYWiKFaW7UtnJwu+5kljY3r74Q4URRquSrYfp13lHYdFVu5fzk8XfM3XL84C8DaZJZbcJlr8Lsvgt9y6fPthuS53KzKQk9QcP3B3LwBffWOGUHxtl2AineWrF2aAXLlLIrkdPH6sE4CvnJ9Z1yU4F05Yus53He+87Z9Ncufy/rt6APjcK+PrbJuuzoY5PxnCriq8Xe6XuxYZyElqjpO9jRzo8JPMaPzD61Nrvve1CyK46250y0YHyW3l0QNtNHkdzKwm+NqF2TXf++Jrk2Q1ndP9Qfa1Szscye3jPad6cNlVLs+E15lWf/6VcQDecqidVr8s9+9WZCAnqTkUReGD9/YD8Mffvk4yI5oeNE3nU9+5AcAP39uPTc6xlNxG3A4bP/bgIAB/8t3rVvYjkc7y58+NAPCBe/p26NNJ7lQaPQ6eONEFwO8/ec36++Voir9+cQyAH7lPrsvdjAzkJDXJj97fT0eDi8mVOH/8bRG8/e3L41ycXsXrtPHjDw7s8CeU3In8+IMDuB0qr0+E+CvjkPzUd24wHUrQ3ejmfad7dvgTSu5EPv7W/dhUhW9dmeepyyJb/H9/4wrRVJaj3Q285aDUx+1mFL3cLKRdyOrqKo2NjYRCIRoa5LiSWuXvX5vgFz/3OooCTxzv4msXZkhndf7PJw7zU4/s3emPJ7lD+Z/P3OQ//9NFnDaVdxzt4Cvnp9F0+L0PnuK9p2QgJ9kZ/tM/XuTPnr2Jz2nj0QNtfOUNoSX+q5+63/JBlOxOZEZOUrO8/3QvH3loEF2Hfzo3TTqr88SJLn7i4T07/dEkdzA/8dAgTxzvIpXV+OdzIoj7Vw8OyCBOsqP8u+89yENDLURTWSuI+8Q7Dsgg7g5AZuRkRq6m0XWdb16a48UbixztaeA9J3ukNk6y42iazj+em+L8RIj79jTzjiPSCkey82SyGn/36gTDcxHefLCdN+2XQdydgAzkZCAnkUgkEomkTpGlVYlEIpFIJJI6RQZyEolEIpFIJHWKDOQkEolEIpFI6hQZyEkkEolEIpHUKTKQk0gkEolEIqlTZCAnkUgkEolEUqfIQE4ikUgkEomkTpGBnEQikUgkEkmdIgM5iUQikUgkkjpFBnISiUQikUgkdYoM5CQSiUQikUjqFBnISSQSiUQikdQpMpCTSCQSiUQiqVNkICeRSCQSiURSp8hATiKRSCQSiaROkYGcRCKRSCQSSZ0iAzmJRCKRSCSSOkUGchKJRCKRSCR1igzkJBKJRCKRSOoURdd1fac/xO1G13XC4TCBQABFUXb640gkEolEIpFsiDsykJNIJBKJRCLZDcjSqkQikUgkEkmdIgM5iUQikUgkkjpFBnISiUQikUgkdYoM5CQSiUQikUjqFBnISSQSiUQikdQpMpCTSCQSiUQiqVNkICeRSCQSiURSp/x/p3q/lazZ104AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for k in epslist:\n",
    "    p2 = plot(xsol_sub_a0.subs(eps,k),(t,0,20),show=False)\n",
    "    a.extend(p2)\n",
    "a.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0b202aa0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}