{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "peripheral-pontiac",
   "metadata": {},
   "source": [
    "# Initial Value Problems for Ordinary Differential Equations, Part 4: Systems of ODEs and Higher Order ODEs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "vietnamese-rental",
   "metadata": {},
   "source": [
    "**Last updated on March 31, 2021** (after class, adding the Runge-Kutta, Explicit Trapezoid and Explicit Midpoint method for systems)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "meaningful-saturday",
   "metadata": {},
   "source": [
    "**References:**\n",
    "\n",
    "- Section 6.3 *Systems of Ordinary Differential Equations* in [Sauer](../references.html#Sauer),\n",
    "just to Sub-section 6.3.1 *Higher order equations*.\n",
    "- Section 5.9 *Higher Order Equations and Systems of Differential Equations* in [Burden&Faires](../references.html#Burden-Faires)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "parental-crash",
   "metadata": {},
   "source": [
    "The short version of this section is that the numerical methods and algorithms developed so for for the initial value problem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "flexible-cycling",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{split}\n",
    "\\frac{d u}{d t} &= f(t, u(t)), \\quad a \\leq t \\leq b\n",
    "\\\\\n",
    "u(a) &= u_0\n",
    "\\end{split}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "african-large",
   "metadata": {},
   "source": [
    "all also work for system of first order ODEs by simply letting $u$ and $f$ be vector-valued,\n",
    "and the Python code requires only one very small change.\n",
    "\n",
    "Also, higher order ODE's (and syrem of them) can be converted into system of first order ODEs.\n",
    "\n",
    "The second point is seen in a typical first course in differential equations, so I will just illutrate the procedure for a single famous example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dominant-compensation",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "# Shortcuts for some favorite commands:\n",
    "from numpy import linspace"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "annual-complex",
   "metadata": {},
   "source": [
    "## Motion of a Damped Mass-Spring System in One Dimension\n",
    "\n",
    "A simple mathematical model of a damped mass-spring system is\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "M \\frac{d^2 y}{d t^2} &= -k u - D \\frac{d y}{d t}\n",
    "\\\\\n",
    "& \\text{with initial conditions}\n",
    "\\\\\n",
    "y(a) &= y_0\n",
    "\\\\\n",
    "\\left. \\frac{dy}{dt} \\right|_{t=a} &= v_0\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "where $k$ is the spring constant and $D$ is the coefficient of friction, or drag."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "rocky-belfast",
   "metadata": {},
   "source": [
    "To convert to a first order system, introduction the two functions\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "u_0(t) &= y(t)\n",
    "\\\\\n",
    "u_1(t) &= \\frac{d y}{d t}\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "(Aside: this is one of many places where the Pythonic system of counting from $0$ fits the mathematics better!)\n",
    "\n",
    "Then with $d^2 y/dt^2 = d u_1/dt$ the above equation becomes\n",
    "\n",
    "$$\n",
    "\\frac{d u_1}{d t} = -\\frac{k}{M} u_0 - \\frac{D}{M} u_1\n",
    "$$\n",
    "\n",
    "Combined with the definition of $u_1$ give the system\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "\\frac{d u_0}{d t} &= u_1\n",
    "\\\\\n",
    "\\frac{d u_1}{d t} &= -\\frac{k}{M} u_0 - \\frac{D}{M} u_1\n",
    "\\\\\n",
    "&\\text{with initial conditions}\n",
    "\\\\\n",
    "u_0(a) &= y_0\n",
    "\\\\\n",
    "u_1(a) &= v_0\n",
    "\\end{split}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "integrated-drain",
   "metadata": {},
   "source": [
    "Next this can be put into vector form.\n",
    "Defining the vector-valued functions\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "\\tilde{u}(t) &= \\langle u_0(t), u_1(t) \\rangle\n",
    "\\\\\n",
    "\\tilde{f}(t, \\tilde{u}(t)) &= \\left\\langle u_1(t), -\\frac{k}{M} u_0(t) - \\frac{D}{M} u_1(t) \\right\\rangle\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "and initial data vector\n",
    "\n",
    "$$\\tilde{u}_0 = \\langle u_{0,0}, u_{0,1} \\rangle = \\langle y_0, v_0 \\rangle$$\n",
    "\n",
    "puts the ODE IVP into the form"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "worse-decision",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{split}\n",
    "\\frac{d \\tilde{u}}{d t} &= \\tilde{f}(t, \\tilde{u}(t)), \\quad a \\leq t \\leq b\n",
    "\\\\\n",
    "\\tilde{u}(a) &= \\tilde{u}_0\n",
    "\\end{split}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fundamental-relations",
   "metadata": {},
   "source": [
    "The Euler's method code from before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "absolute-atlanta",
   "metadata": {},
   "outputs": [],
   "source": [
    "def euler(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use Euler's Method to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "    U = np.empty_like(t)\n",
    "    U[0] = u_0\n",
    "    for i in range(n):\n",
    "        U[i+1] = U[i] + f(t[i], U[i])*h\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "genetic-stadium",
   "metadata": {},
   "source": [
    "does not quite work, but only slgiht modificsit is needed: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "advisory-commonwealth",
   "metadata": {},
   "outputs": [],
   "source": [
    "def euler_system(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use Euler's Method to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\n",
    "    Modified from function euler to handle systems.\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "    \n",
    "    # Only the following three lines change for the systems version\n",
    "    n_unknowns = len(u_0)\n",
    "    U = np.zeros([n+1, n_unknowns])\n",
    "    U[0] = np.array(u_0)\n",
    "\n",
    "    for i in range(n):\n",
    "        U[i+1] = U[i] + f(t[i], U[i])*h\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "local-congress",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(t, u):\n",
    "    return np.array([ u[1], -(k/M)*u[0] - (D/M)*u[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cutting-hacker",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = 1.0\n",
    "k = 1.0\n",
    "D = 0.0\n",
    "u_0 = [1.0, 0.0]\n",
    "a = 0.0\n",
    "b = 8 * np.pi # Four periods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "flexible-portrait",
   "metadata": {},
   "outputs": [],
   "source": [
    "n=400\n",
    "(t, U) = euler_system(f, a, b, u_0, n)\n",
    "y = U[:,0]\n",
    "Dy = U[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fuzzy-stress",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[12,6])\n",
    "plt.title(f\"U_0, = y with {k=}, {D=} — by Euler with {n} steps\")\n",
    "plt.plot(t, y)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('y')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.figure(figsize=[12,6])\n",
    "plt.title(f\"U_1, = dy/dt with {k=}, {D=} — by Euler with {n} steps\")\n",
    "plt.plot(t, Dy)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('dy/dt')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "adult-violin",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[12,6])\n",
    "plt.title(f\"U_0=y and U_1=dy/dt with {k=}, {D=} — by Euler with {n} steps\")\n",
    "plt.plot(t, U)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('y and dy/dt')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "foster-windows",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhQAAAHwCAYAAAD+R/bsAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAADe90lEQVR4nOydZXQcR9aGnxqNRsyMlmTJIDNzYscBBxx0mBzmDSdfdrMb2uxudsPkMJMDDqMDMjtGmVlgMTMO1PejR47sSLZsa6ZbUj3nzNFouqfq9jS9fe+tW0JKiUKhUCgUCsXRYNLbAIVCoVAoFD0fJSgUCoVCoVAcNUpQKBQKhUKhOGqUoFAoFAqFQnHUKEGhUCgUCoXiqFGCQqFQKBQKxVFjGEEhhHhQCPGeTn3PFUIsPcjy74UQl7vBjrOEEHlCiHohxKgurD9dCJHvaruOBCFEjhDieL3tOBRCCCmESNXbDncjhLhYCPGT3nYYHT2vS+5ACJEhhLjaAHa4/TwUQvxVCPHaQZYf9L6g+DNuExTOm2TbyyGEaGr3/8XusuNIkFKeLKV8G1x+kD0O3Cyl9JdSrj9wYV+9+Sm6Hynl+1LKE/W2oyv09ONeCDFUCPGjEKJcCHHIwj9CiJFCiLVCiEbn35FuMPOoEEIkOfdT/QGv8/W2rTOklP+SUl4N+9lvPtp2hRBpQojmA4WoEGKmEGK7c7/+JoTo126ZEEI8JoSocL7+K4QQR9C3rgLRbYLCeZP0l1L6A3uB2e0+e99ddhxIdxxA3Ug/YIveRih6NwY75vsCVuBj4KpDrSiEsABfAu8BIcDbwJfOz3sCwe2v9VLK+a7szKDH8gvA6vYfCCHCgQXA34FQYA3Q/re5FjgTGAEMB04DrnODrd2KYUIeTixCiHeEEHVCiC1CiLFtC4QQsUKIz4QQZUKIbCHEXzprRAgR5GynTAiRK4S4Xwhhci6bK4RYJoR4SghRCTz4x9fEc0KIGqeKnNmuvQwhxNVCiMHAS8Akp/qudi4/RQix1Wl3gRDirk7sMjltyRVClDptDBJCeAkh6gEPYIMQYk8H313sfLvhQOUvhLjT2V6REOKKdp97CSEeF0LsFUKUCCFeEkL4dGLbfq7dAxW78zd4xPnb1QkhfnKeJG3rX+rcrgohxN8OaHu8EGKFEKLaaePz7S+Qzn5uFELscrb9iBCiv/M7tUKIj9vWF84wj9DcleVCC61c3K6tg26zEOJupw2FQogrO/ot2q2bIYT4pxBiufM3/1oIESaEeN9p12ohRFK79Z8RWsiqVmhPltMO+A3WOJeVCCGedH7uLYR4z/m7VTvbjOrEnlQhxCLnMVouhJjfbpkUQvxFCJHlXPY/cZBjXhzgaXN+/3rnPqgSQrwghPaEJITwEEI84Ww3WwhxszjI05wQ4l6hnQd1QogdQnsyixbak1lYu/XGCO0c9exs20Qnx70Q4jQhRKbzN1suhBjert0c537eKIRoEEK8LoSIElrosk4I8bMQIuRg+76T7fIUQnwotOtQl2/wUsodUsrX6drDwnTADDwtpWyRUj4LCOC4w7X3MOgvhFjl/O2/FEKEAgghvhVC3NJ+RedveubhdiAOeHI+8Pg7YN1Oz2Hxx/l/rxCiGHizg+/nCiHGON9f4jxW053/Xy2E+ML5vv01r+04q3YeZ5Patfe485zIFkKcfIjtvACoBn45YNHZwBYp5SdSyma0+84IIcQg5/LLgSeklPlSygLgCWBuJ310eM0QQjwKTAOed27D8871BwkhFgohKp3n43nt2nrL+fsudJ4bi4TTcyI0nhLavaXGue+HHmz7kVK6/QXkAMcf8NmDQDNwCtqN9d/ASucyE7AW+AdgAVKALOCkTtp/B03lBwBJwE7gKueyuYANuAXtxPVp99ntgCdwPlADhDq/kwFc3e77Sw/orwiY5nwfAozuxK4rgd1O+/3RFOu77ZZLIPUgv9t+y9EuPjbgYafdpwCNQIhz+dPAV2iKOAD4Gvh3J20/CLzX7v8kZ3/mdr/BHmCA8zfLAP7jXJYO1APHAF7Ak067jncuHwNMdP7eScA24LYDtusrIBAYArSgnZApQBCwFbj8gG1+0tnXsUADMPBQ2wzMAkqAoYAf8MHBfnPnNu4G+rezYydwvHNb3gHebLf+JUCYc9mdQDHg7Vy2ArjU+d4fmOh8f53TRl+0434MENiJPR8Cf0M7H7yBqQf8hr85tzvRaWf7Y7ajY37pAd//Bgh2fr8MmOVcdr1z2+PRju+faXdsHGDjQCAPiG13HPV3vv8OuKHduk8Bz3Vx29of96OBUmCC8ze7HO2a4tXu+rISiALinOuuA0ahHTO/Ag908Vr1IJq3wAf4FngL8HAuuwjt5tHZK/GAtlIBeYj+bge+P+Czb4A7u/MafMAxXsAf58RnOK8DwHnA7+3WHQFUAJYO2knq7Jho18/V7f7v6PhL7cI5PB3tWH7MuS99OujrnbbfC3gF7bp1Q7tltx94zevIfqeNVuAa53F2A1AIiE62MRDtvEvgz9fTZ4B5B6y/GTjH+b4GmNBu2VigrpN+Or1mdPA7+6Gdj1egnfujgXJgiHP5W0Adf1y7n2nbL8BJaPfdYDRROxiIOdjxZDQPxVIp5XdSSjvwLtoBDDAOiJBSPiylbJVSZgGvAhcc2IAQwgNNENwnpayTUuagqb1L261WKKV8Tkppk1I2OT8rRXsqsErNTbcDOLWLdluBdCFEoJSySkq5rpP1LgaelFJmSSnrgfuACzp70juMvh922v0d2o19oPPp8hq0k6dSSlkH/IsOfrPD4E0p5U7nb/YxMNL5+RzgGynlYillC5pbz9H2JSnlWinlSufvnQO8jCYE2vOYlLJWSrkF7UT7yfk71QDfo90M2vN3qT3BLUK70J/XhW0+z7kNm6WUDfzhnTrUNu9pZ8ceKeXPUkob8El7u6SU70kpK5zb+QTaCTrQudgKpAohwqWU9VLKle0+D0O7mNqdv1VtJ7ZY0cJisVLKZinlgU94jzm3ey/aRfnCdss6OuYP5D9Symrn93/jj/17HvCM1J6eqoD/dP5zYXdud7oQwlNKmSOlbPO4vY0mutrO0wvRzvOubFt7rgFellL+7vzN3kYToRPbrfOclLJEak97S9BujOudx+fn/Pl4OhiBwA9oN6YrnNcnpJQfSCmDD/Laexh9tOGPdnNpTw3ajdVVvNvunPg72rnkgfZQliaESHOudykwX0rZepC2yp1PzW2vwYdjSBevWw40QdjSybG8iD+uL9PQHk7b/j/Wubyr5EopX3Xu87eBGDSh2hGPAK9LKfM6WHao/Xrg8hrA3/l7HMjhXDNOA3KklG86z/11aKJxTrt1vm137f4bmgc+wdlPADAITURtk1IWddIPYLyQR3G7942At/Nm2w+IbX+gAn+l4x0bjubFyG33WS7ak0obHe3wAumUZe2+E9tFu89B8w7kOl1GkzpZL7YDu8x0foB2hQrnza2NRrSDMwJNwa5t95v94Pz8SDlw//g738fS7jd1Xpgq2v4XQgwQQnwjhCgWQtSiXSDC2Z+Sdu+bOvjfv93/Vc4+2mjbV4fa5v3sZP990RldtktooadtTvdgNZpXo207r0Lz7mx3uihPc37+LvAj8JHQwjD/dbrWp4k/EtvaXOX3oD0prBJaSPDAkM2B2xbbybLO6NL+PVhbUsrdwG1oYq1UCPGREKLNji/RhEYKcAJQI6Vc5Vx2qG1rTz/gzgOuBwnsv72Hczwdioloce3/HHCNcAX1aAKmPYFoT5H74TyvDkyC7Oz17oHfb8eBx40nEO68wXwMXCK08Fl7AdgZ4QeIqm2H2uAD6Mp1q0xqYYPOWARME0JEoz3BzwemCC08GQRkHoY9+84JKWWj8+2fjh2hJc4ej+Z164hD7dcDlwcC9Z0cbx1eMzrptx8w4YBz5WIgut067a/d9UAlmrD/FXgeLSekRAjxihDiwG3YD6MJis7IA7IPOFADpJSndLBuOX887bSRiObWa6OjnRR3gBpMRHNvHcifviulXC2lPAOIBL5AOwk7orADu2zsf7HrLsrRLpxD2v1mQVJLiu2IBrQTuY3oTtbriCK0CzoAQghfNAXdxjxgO5AmpQxEE4OHncHcjhAhhF+7/9v21aG2eT87nd/rFoSWL3Ev2tN8iJQyGO0pQwBIKXdJKS9EO0YeAz4VQvhJzbP0kJQyHZiM9kRxmZRyifwjsW2Is41iKeU1UspYNLfni2L/0Q8Hblv74/doboRFaOGOjvr5E84n96lox7pE216cN4GP0S5ol9Lu5tSFbWtPHvDoAdcDXynlh0e4fYfiJ7Sn3F9Eu/wWoQ29PdhN/EiOry3A8AOuRcPpIP9Cat5C/y6+Lj3w++048Lixop1LoD2VXwzMBBqllCuOYJug69eXrly3DnosO0VtI/AXYLHTy1GMlvi4VErp6OhrXdyOzpiOFjbZK7TcjruAc4QQbd7qLfzhccd5/erPH/t1v+XO9x3m3HR2zehkO/KARQecK/5SyhvardP+2u2PFmoqdPb1rJRyDFooegBw98F+hJ4iKFYBtUJLxPERWpLYUCHEuANXdLqmPgYeFUIECC3B5A60OOjBiAT+4nw6PBctXvRdB+uVAPHijyRBi/PCEiSltAK1aG7fjvgQuF0Ikezccf9CcyHaOlm/o75TurKi86R5FXhKCBHptDVOCHFSJ1/JBI4RQiQKIYLQwjFd5VPgNCHEVOfv8jD7H1sBaL9LvdCSkG7ooI3D5SHnbz8N7YT6pAvb/DEwVwiR7hQ9D3SDHW0EoInDMsAshPgH7Z44hJYcFuG0sdr5sV0IMUMIMUxoLuZatIt5h8ePEOJcIUTbjb0K7eLRft27hRAhQnNX3sr+WeRHw8fArc7fMhhNOHWIEGKgEOI4IYQXWk5U0wE2voMWmz6ddufkIbbtwOP+VeB6IcQEoeEnhDhVCHFEYQGhJXHOPdg6Usr/ouXc/CKcychSG3p7sJv4Xmf7QgjhjeY5bUuq8+qkqwzndv9FaMmJNzs///VItq2LXNLunHgY+FT+EdZZgRZieIJDeycORiZwthDC1ykUOxzxcgTXrc5YBNzMH+GNjAP+P5AytO3s0vW1A15BEwgjna+X0EKxbXZ/DgwVQpzjPBb+AWyUUm53Ln8HuMO5rbFoOVhvddTRIa4ZB54r3wADhJY07+l8jRP7h6JOaXftfgQtPJjnXG+C0/vRgHY+d3ZvA3qIoHAe3LPRdlQ2mop9Dc191RG3oP0AWcBStAvBG4fo5ncgzdn2o8AcKWVFB+v9iqYci4UQbSr+UiBHaO7863HGiTvgDbSTcrFzO5qdtnaVB4G3hea6Ou9QK6Nd+HcDK522/cwfMf39kFIuRLsBbURLxPmmq0ZJLe/hJrTfuQjthtC+4NZdaAlsdWgXi6O90RU7+ygE3geub3didrrNUsrv0XILfnWu050X6R/Rcix2ormNm9nflTwL2CK00TzPABc4n9ij0QRZLVqy6iI6F7/jgN+dbXwF3CqlzG63/Eu0fZeJdjF7vVu2TNtnP6EdG+vRhLaNji8uXmg5FuVo+ykSzSMFgJRyGdqFe53U8mnaONi2PUi7415KuQYtzv482nGwm04y4g+F8yIahpbEeVCklI+geSB/Fs6REF2kH5qwanvibELL0Wqz4XshxF+dfbSiDR+8DE14XgmcKQ+et3C0vIt28ypGS4g9cATdO8AwDv1QBn+Mkmh73eH8/CmgFe2G9zbaedsZXb5uHYRFaCJ/cSf/74cznPEosMx5nE3saL3OkFI2Or1sxVLKYrQQRrOUssy5vAwtNP4o2jE7gf3zQl5GS7TchJZD9q3zs4442DXjGWCO0EalPOv0zpzo7KsQbR+3JbS28QHaw1UlWoJn26i5QLRzvwrtmlaBViupU0THIRqFwpgIIaajZU/HH2LVPoXQCialOd29ru7rZOAlKWW/Q67c8fd/BT6QUnZapdBdCCGmAjc5w1GKDhBCXAZc6wxjKXoRQoi3gHwp5f3d0V6P8FAoFAr9EFqY8RQhhFkIEYf2NPP5EbY1Dm3omksLHnUVKeVSJSY6xxkGuRHNpa9QHBQlKBQKxaEQwENors/1aG7Wfxx2I0K8jea+vs3pilUYGGfeQhlamOIDnc1R9ABUyEOhUCgUCsVRozwUCoVCoVAojholKBQKhUKhUBw1Rpyp7agJDw+XSUlJ3dJWQ0MDfn5+h15R4TLUPtAftQ/0R+0D/THyPli7dm25lPJoKiEfNb1SUCQlJbFmzZpuaSsjI4Pp06d3S1uKI0PtA/1R+0B/1D7QHyPvAyFEV6YScCkq5KFQKBQKheKoUYJCoVAoFArFUaMEhUKhUCgUiqOmV+ZQKBQKhaJvYbVayc/Pp7n5YDObHx1BQUFs23a4M7J3L97e3sTHx+Pp2dmM5fqhBIVCoVAoejz5+fkEBASQlJSE2G/29+6jrq6OgIAjmtS2W5BSUlFRQX5+PsnJybrZ0Rkq5KFQKBSKHk9zczNhYWEuExNGQAhBWFiYS70wR4MSFAqFQqHoFfRmMdGGkbdRCQqFQqFQKFzA008/TWNj42F/76233qKwsNAFFrkWJSgUCoVC0Scpqivi2LeOpbi+2CXtH4mgsNvtSlAoFAqFQtGTeGTxIyzdu5SHFz181G01NDRw6qmnMmLECIYOHcpDDz1EYWEhM2bMYMaMGQDccMMNjB07liFDhvDAAw/s+25SUhIPP/wwU6dO5cMPP2TNmjVcfPHFjBw5kqampqO2zV2oUR4KhUKh6FP4POpDs+2PxMZ5a+Yxb808vM3eNP3tyG7gP/zwA7GxsXz77bcA1NTU8Oabb/Lbb78RHh4OwKOPPkpoaCh2u52ZM2eyceNGhg8fDmjDQZcuXQrAa6+9xuOPP87YsWOPZjPdjvJQKBQKhaJPkfWXLC4aehG+Zl8AfM2+XDzsYrJvzT7iNocNG8bPP//Mvffey5IlSwgKCvrTOh9//DGjR49m1KhRbNmyha1bt+5bdv755x9x30ZBeSgUCoVC0aeICYgh0CuQZnsz3mZvmu3NBHoFEu0ffcRtDhgwgLVr1/Ldd99x3333ceKJJ+63PDs7m8cff5zVq1cTEhLC3Llz9xv+adRZTA8H5aFQKBQKRZ+jpKGE68dcz8qrVnL9mOuPOjGzsLAQX19fLrnkEu666y7WrVtHQEAAdXV1ANTW1uLn50dQUBAlJSV8//33nbbV/ns9CeWhUCgUCkWfY8H5C/a9f+HUF466vU2bNnH33XdjMpnw9PRk3rx5rFixgpNPPpmYmBh+++03Ro0axZAhQ0hJSWHKlCmdtjV37lyuv/56fHx8WLFiBT4+PkdtnztQgkKhUCgUiqPkpJNO4qSTTtrvs7Fjx3LLLbfs+/+tt97q8Ls5OTn7/X/OOedwzjnndLeJLkcJCoVCcdg4HJJWu4NWuwOLhwkvs8nQFfwUCoXrUYJCoehDSCmpabJSWtdCWV0LpXXN2t/aFsrqW2hstdNic9Bidf51vq+pb0QsXUiLVfus1e74U9teZk1YeHl64O1pwsvsse8zb8+29x74eZmJCPAiMsCLyEAvIgO89733tahLkkLRU1Fnr0LRi6hvsbGntJ7dpfXkVTU6RYMmHtpeHYkBb08TEQFe+FnM+27+gT6e+wRBVXkL/RKi/yQOPD3EH8LDZncKDu1v877/HTRb7dQ122ixaX/L6lqwOeSf7PCzeBAZ6P2H4AjQ3ieG+pIa6U9SuC9eZg93/JQKheIwUYJCoeiBVDa0stspHHaV1rG7tJ49pfUU1uw/C2GIr+e+m3JKuB8RAV7azTrQmwh/zSsQEeBFgJf5oCGLjIwMpk8f1m32OxyS6iYrpXXNlNa27OcxKa1roay2hc0FNZTVldLQat/3PQ+ToJ9TXKRG+pMW5U9qRAD9I/2Ud0Oh0Bl1BioUBqbV5mBrUS2Ze6vY6RQQu0vrqWxo3beOt6eJ1Eh/xieH7rvRpkYGkBDqY9ineZNJEOpnIdTPwqBDDP2vb7GRW9Hwh4AqqWd3WT2/bi/dz8sRF+zjFBia0BiZEEJapD8mk8rtUCjcgRIUCoWBqGpoZW1uFWv3VrE2t4oNedW02LQQRaC3mbSoAE4YHKWJBufNMy7Yp1ffNP29zAyJDWJI7P6VB612B7kVDZrAKK1nl1NwrNhTse83C/A2MzoxhLH9QhjTL4SRicHKk6FQuAh1ZikUOuFwSLLK61mbW8WaHE1EZJU1AGA2CYbEBXHxhH6M6RfC6H7BRAd6q5EU7fD0MJEaGUBqZMB+n9sdktyKBtbtrdbEWW4lTywsA7SQyeCYAMb2C2WMU2TEBveMMf6K3o2/vz/19fV6m3FUKEGhULiR7PIGftlWwvI9FazNraKmyQpouQ5j+oUwZ0w8YxJDGB4fjI/FmOEKo+NhEqRE+JMS4c+cMfEA1DRaWZdXxdoczfMzf3Ueby3PASA2yJvR/UKYkBLGcYMiiVMCo+9QVAQXXADz50P0kZfdVmjoJiiEEAnAO0A04ABekVI+c8A6AngGOAVoBOZKKde521aF4khptTlYk1PJL9tL+XV7KdnlmgciJcKPWUOiGZOkPSWnhPsp74MLCfL1ZMbASGYMjAS0cMn2ojrW5Fayxukh+mZjEX8HBkUHMHNwJMcNimJkQjAevTic1Od55BFYuhQefhhefPGom3vvvfd49tlnaW1tZcKECbz44osEBQVx66238s033+Dj48OXX35JVFQU2dnZXHTRRdhsNmbNmtUNG6M/enoobMCdUsp1QogAYK0QYqGUcmu7dU4G0pyvCcA851+FwrBU1LeQsaOMX7eXsnhnGXUtNiweJib1D+OKKUnMGBhJQqiv3mb2aTw9TAyLD2JYfBBXTElGSsmesgZ+3V7CL9tKeWlRFi/8todQPwvTB0Ywc1AU0waEE+jtqbfpiu7AxwfaTczFvHnay9sbmo5s+vJt27Yxf/58li1bhqenJzfeeCPvv/8+DQ0NTJw4kUcffZR77rmHV199lfvvv59bb72VG264gcsuu4wXXjj60t9GQDdBIaUsAoqc7+uEENuAOKC9oDgDeEdKKYGVQohgIUSM87sKhSGQUrKtqE67GW0vJTOvGikhMsCLU4fHcNygSKakhuPnpSKMRkUIsW+EzLXH9Kem0cqiXWX8uk0TGAvWFWA2CcYnhzJzcBQzB0WSFN7zZ4fss2RlwV13wRdfQGMj+PrCWWfB448fcZO//PILa9euZdy4cQA0NTURGRmJxWLhtNNOA2DMmDEsXLgQgGXLlvHZZ58BcOmll3Lvvfce3TYZAENc4YQQScAo4PcDFsUBee3+z3d+9idBIYS4FrgWICoqioyMjG6xrb6+vtvaUhwZRt0HpY0OlhfaWFZgo6xJG76YHGTizP6ejIjwIDHQhElUQlklq8t0NvYoMeo+cCWBwJnRMDvSkz01HmSW2tlQUskjeyp45JutRPsJJsWYmRxrJsLX9RM398V9cDgEBQV1fYZOf3+8vL3xbG7WvBLNzVi9vWnx84ODtGG32zvto6mpiQsvvJAHH3xwv88ff/zxfcmWra2tNDU1UVdXh5SS+vp6zGbzvja7an9zc7MhjwXdBYUQwh/4DLhNSll74OIOvvLn8nqAlPIV4BWAsWPHyunTp3eLfVpBn+5pS3FkGGkf1DRZ+XZjEQvW5bMmtwohYHL/MO4aEcuMQZFEBnjrbaJLMNI+0IOZ7d7nVTby6/ZSvt9cxOe7K/l8t5XxyaHMGR3PycOiCXBRWKSv74NDsW3bNgICAg69YhtVVXD99XDttfDKK1iKirAc4vt1dXWd9nHqqadyxhlncO+99xIZGUllZeU+gdD2HR8fHzw9PQkICGDq1Kl8++23XHLJJbz33nv7rXcovL29GTVqVFe31G3oKiiEEJ5oYuJ9KeWCDlbJBxLa/R8PFLrDNoWiDavdweKdZSxYV8DCbSW02hykRvpz76xBnDkqlpggNSqgL5EQ6svlk5O4fHIS+VWNfLG+gAXrCrjns438/cvNnDQkmnPGxDM1NVwldBqZBe1uOd2Qw5Cens4///lPTjzxRBwOB56engfNjXjmmWe46KKLeOaZZ3rkzKIdoecoDwG8DmyTUj7ZyWpfATcLIT5CS8asUfkTCncgpWRLYS2frcvnq8xCKhpaCfWzcNH4RM4ZHc/QuEA1KkNBfIgvNx+Xxk0zUsnMq+azdfl8vaGIrzYUEhngxZmj4jhndDwDow/jyVnRYzn//PM5//zz9/usfW2JOXPmMGfOHACSk5NZsWLFvmX/93//5x4jXYieHoopwKXAJiFEpvOzvwKJAFLKl4Dv0IaM7kYbNnqF+81U9CXqW2x8siaPD1ftZWdJPRYPE8enR3L2qHiOHRiBp4frY+WKnocQglGJIYxKDOHvp6Xz2/ZSPltXwBtLs3llcRZDYgM5e3Q8c0bHE+SrRoooeid6jvJYSsc5Eu3XkcBN7rFI0ZfJr2rk7eU5fLQqj7oWGyMTgnn0rKGcNixW3QAUh4WX2YNZQ2OYNTSGivoWvt5QyIL1BTzyzVYe/3EH546N54opySSrUSKKXobuSZkKhZ6sza3ijaXZfL+5CCEEpwyL4aqpyYxMCNbbNEUvIMzfi7lTkpk7JZmthbW8sSybj1bl8e7KXGYOiuKqqclMTAlV4TNFr0AJCkWfw2p38P3mYt5Ymk1mXjWB3mauOSaFyyclqXkdFC4jPTaQx88dwT2zBvLeilze+30vP79aQnpMIFdNTWb2iFgsZhVSOxqklL1enGmOe2OiBIWiz1DTaOXD1Xt5Z3kOhTXNJIX58vAZQzhndLwqOqVwG5EB3txx4kBunJHKF+sLeH1pNnd+soH//LCdyyf146IJ/Qj1s+htZo/D29ubiooKwsLCeq2okFJSUVGBt7cxh6erq6ii11Nc08xLi/bw8Zo8GlvtTEoJ4+EzhnLcoMhePe23wth4e3pwwfhEzh+XwOJd5by+NJvHf9rJc7/u5uzR8Vw1NelPM6kqOic+Pp78/HzKylxXRa65uVn3m7m3tzfx8fG62tAZSlAoei0V9S3My9jDuytzsTskZ4yM48qpSQyJDdLbNIViH0IIjh0QwbEDIthVUscby7JZsC6fj1bvZfbwWG4/YYBK4OwCnp6eJCcnu7SPjIwMQxaUMgpKUCh6HTVNVl5bksUbS7Npsto5e3Q8t85MUxNyKQxPWlQA/z57OHedOJDXl2bz5rIcvt1UxJzR8Yz3c+htnkJxUJSgUPQaGlttvLksh5cX7aG22capw2K4/YQBpEb6622aQnFYhPl7cc+sQVwxJZkXM3bz/sq9fOZwsMm6hRtn9O+1Jd4VPRslKBQ9nmarnQ9+38uLGbspr2/luEGR3HHCAIbGqdCGomcTEeDFA7OHcM20FO57bzHvrsxl/uo85k5J4rpjUgj2VcmbCuOgBIWix2K1O/h0bT7P/rKLoppmJqWE8fKlAxnTL0Rv0xSKbiU22Icrhnrx4AXjePrnnby0aA/vrcjlmmNSuHJqMv5qlJLCAKijUNHjkFLy87ZSHv12KzkVjYxKDOaJc0cwOTVcb9MUCpeSHO7HMxeM4obp/Xnip508uXAnby3P4cbp/blkYj+8PT30NlHRh1GCQtGj2FvRyINfb+HX7aWkRfrz+uVjOW5QZK8dd65QdMSg6EBevWwsmXnVPPHTDv757TbeWp7Dg7OHcHx6lN7mKfooSlAoegTNVjsvLdrDixl78DQJ/nbKYOZOSVKTdSn6NCMTgnn3qgks313OA19t4ep31jBzUCQPnj5EjWpSuB0lKBSGJ7PUxj+eWszeykZmj4jlb6cMJjpIZbkrFG1MTg3nu1un8eaybJ7+eRfHP7mIm2akcu0xKSoMonAb6vFOYVjyKhu55p01PL2uBU8PwftXT+C5C0cpMaFQdICnh4lrj+nPL3cey/HpUTy5cCeznl5Mxo5SvU1T9BGUoFAYjhabned/3cUJTy1i6a5yzh3gyfe3HsMUlXSpUBySmCAfXrhoNO9eNR6TEMx9czXXv7uWguomvU1T9HKUoFAYisU7yzjpqcU8/tNOjhsUyS93HsupKRY1C6NCcZhMS4vg+9umcfdJA8nYWcrxTyzixYzdtNpUxU2Fa1BXaYUhqG+x8X+fbeSyN1YhhODtK8fz4sVj1HTiCsVR4GX24KYZqfx8x7FMSwvnvz/sYNYzi1m+p1xv0xS9ECUoFLqzJqeSk59ZzPw1eVx/bH9+uG0axw6I0NsshaLXEB/iyyuXjeXNueOwOyQXvfo7D329hWarXW/TFL0INcpDoRutNgdP/byTlxftITbYh/nXTmJ8cqjeZikUvZYZgyKZmBLGYz9s581lOSzZVc7T549UZeoV3YLyUCh0YUdxHWe8sIx5GXs4d0wCP9x2jBITCoUb8LF48ODpQ3j3qvHUNVs584VlvPDbbmx2lVuhODqUoFC4FYdD8uriLGY/t5TS2mZevWwsj80ZruYiUCjczLS0CH687RhmDY3mfz/u4LyXV5Bb0aC3WYoejLqKK9xGflUjd368gd+zKzkhPYp/nz2McH8vvc3qk1jtDqoaWimrb6GivpWKhhbK61opd/6tbbZitTu0l01SXtXE/zYucX4mabU59i23mE34Wsx4e3rga/HAx9MDH+dfX4vHvs8DfTyJDvQmKtCb6CBvogO98bGookt6Euxr4fmLRnNCegF//2IzJz+zhL+fls4F4xJUOXvFYaMEhcLlSCn5bF0BD321BYeU/HfOcM4dE68uWC7E4ZAUVDeRVd5AVlk9WWUNZJc3UFzbTEV9C1WN1g6/ZzGbCPezEOSrDdW1eAjMJhO+noLoIG88PUz7XhazwMMkaLU5aLI6aGq102S10dhqo7y+hWarncZWO01WO02tdmwO+af+Ar3NRAc5RYZTaEQFepMa6c+AqABC/dT03O7gjJFxjE8O5a5PNnDfgk38vLWE/5wznIgAJfgVXUcJCoVLaWq189fPN/H5+gLGJ4XyxHkj1BwD3UiLzc6O4jp2l2qiIav8D/HQ0q7eQIC3mZQIfwZE+ROWEkaYv4Vwfy/CnX/DnO/9vcwdCr2MjAymTx93VLbWt9goqW2mpKaZ4lrt9cf7FnaVlFNW34K9nfAI9/diYLQ/aZEBDIwOYEBUAAOi/Anw9jwqWxR/JibIh3evnMDbK3L4z/fbOenpxfz77GGcNCRab9MUPQQlKBQuY29FI9e9t5btxbXcfvwAbj4uFQ+T8kocKVJqXof1e6u1V14VWwpqaXUm03mYBAkhPqRE+DMtLZyUCH9Swv1IifAn3N+iu0fI38uMf4Q//SP8O13H7pCU1Dazu7SenSV17CiuY2dpPR+vyaOx9Y8hjrFB3gyIDmBobBDjkkMZ0y9E5eF0AyaT4IopyUxNDef2jzO57t21XDwhkX/MTsfLrMJTioOjzkCFS8jYUcqtH2UipeSNy8cxY1Ck3ib1OBpbbWzMr3EKiCrW51VTVtcCgLenieFxwVwxJYkRCcEMiPInMdSvx1cU9TAJYoN9iA324Zh2tUjaQjiawKhjZ3Ed24vrWLKrnOd/241JQHpsIOOSQve9lLv+yEmLCmDBDVN4YuEOXl6UxdaiWuZdPEbNo6M4KEpQKLoVKSUvZuzh8Z92MDAqgJcvHUO/MD+9zeoRSCnZWlRLxo4yMnaUsm5v9T73f3K4H9NSwxmVGMyoxBAGRgf0qanbTSZBQqgvCaG+HJ8ete/z+hYb6/dWsTq7klU5lXy4ai9vLssBtN9sXFII45JCmZgSpkJth4nFbOK+kwczMj6YOz/ZwGnPLeXFi0er4d2KTlGCQtFt1DVbueuTDfy4pYTTR8Tyn3OG4WtRh9jBqG22snRXORk7SsnYUUap0wMxLC6I649NYWy/UEYkBKvkxE7w9zIzLS2CaWmaN6PV5mBzYQ2rsytZnVPJj1tK+HhNPgADowI4IT2K49OjGB4XhEmF37rEycNiSI3059p313LRqyu5/9TBXD45SfcQmsJ4qKu9olvYXVrHte+uJbeikb+fls6VU9QFpyOklGwvriNjRxm/7ShlbW4VdockwNvMMQMimDEwkmMGhBMZoFzLR4LFbGJ0YgijE0O47tj+OByS3WX1LN5Zxs/bSpi3aA/P/7abyAAvZg6O4oT0SCb3D8fbU+UHHIy0qAC+vHkKd8zP5MGvt7Ixv4ZHzxqmhv0q9kMJCsVR88PmYu78OBNvTw/eu2oCk/qH6W2S4citaOCL9YV8mVlAVrlWPCg9JpDrjklhxqBIRiUEY+5DIQx3YTIJ58iQAK6elkJ1Yyu/7Sjl562lfJVZwIer9uJr8WBaWjgnpEdz3KBI5Q3qhEBvT165dCzP/bqbp3/ZyfbiOl6+dIwKJSn2oQSF4oixOyRPLtzBC7/tYURCMC9dMpqYIDU7aBsV9S18u6mIL9YXsG5vNQATkkO5eloKMwdHEhWovBDuJtjXwlmj4jlrVDwtNjsrsyr5eWsJP28r4cctJZhNgukDIzl3bDwzBkb2+CTX7sZkEtx6fBrD4gO59aNMZj+/lOcuHLUv5KTo2yhBoTgimq12bp+fyfebi7lwfAIPnj5EDStDq7vx09ZivswsZPHOMmwOycCoAO6dNYjTR8YSp6ZjNwxeZg+OHRDBsQMiePiMIWwprOXrjYV8vq6An7eVEOpn4cyRccwZE096bKDe5hqK4wZF8fXNU7nu3bVc/sYq7j5pENcfm6LCnH0cJSgUh01Nk5Vr3lnDquxK7j91MFdPS9HbJN3JzKvm3RW5/LC5iIZWOzFB3lw1LZkzR8YxOEbdjIyOEIKhcUEMjQvi7hMHsmRXOZ+szeO9lbm8sSybIbGBzBkTzxkj41RIxElSuB8LbpzMPZ9t5LEftrO5sIYnzh2h8lH6MEpQKA6L4ppmLn9jFVnl9Tx74ShOHxGrt0m60Wpz8P3mIt5clkNmXjX+XmZOGx7LmaPimJAcqkYR9FDMHiZmDIpkxqBIqhpa+WpDIZ+szeOhr7fyr++2cfzgKM4bm8CxAyL6/D728zLz/IWjGBYXxH++3055XQuvXDaWIB9VybQvogSFosvsLq3jstdXUdts460rxjMlNVxvk3ShvL6FD37fy3srcymtayE53I8HZ6czZ2yCqtbYywjxs3D55CQun5zEtqJaPl2bzxfrC/h+czH9I/y4ZloKZ46K69NP5UIIrj+2PzFB3tz1yQbOf3kFb10xXhXB6oOoq5+iS6zNreKqt1djNpn46NqJDI0L0tskt7O5oIY3l+Xw9YZCWu0OjhkQwWPnJKkn1T7C4JhA/n5aOvfOGsT3m4t4ZXEW/7dgE4//tIPLJyVxycR+hPThcMgZI+MI8/PiunfXcM685bx95XhSIzsvs67ofShBoTgkP28t4eYP1xET5MM7V47vU8PEpJT8vK2UVxbvYXVOFb4WD84fl8Dlk5PUxbKPYjGbOGNkHKePiGXFngpeXZLFEwt38kLGbs4dk8BVU5NJCu+b1WGnpoUz/7pJzH1zFXNeWs4bc8cxOjFEb7MUbkIJCsVB+WjVXv76+SaGxQXxxtxxhPn3jfkRpJRk7CjjyYU72VRQQ3yID/efOphzxyao+LAC0Fz9k1PDmZwazs6SOl5bksX81Xm893suJ6VHc80xKYzp1/dupkPjgvjshslc9sYqLnp1JS9ePJrjBkUd+ouKHo8SFIoOkVLy3K+7eXLhTqYPjOCFi0bj1wfyA6SULNlVzpMLd5KZV01CqA//mzOcs0bFqcJTik4ZEBXAf+eM4K4TB/L2ihzeW7mXH7YUMyE5lHtmDepzwqJfmB+f3TCZK95czTXvrOXfZw3jvHEJepulcDG9/w6hOGyklDz09VbeWp7DOaPj+c85w/rERFTL95Tz1MKdrM6pIjbIm3+fPYw5Y+L7xLYruofIQG/uPmkQN81IZf7qPF74bQ/nzFvOCelR3H3SQAZEBehtotsI9/fio2sncv17a7nns42U1jVz04xUVauiF6OroBBCvAGcBpRKKYd2sHw68CWQ7fxogZTyYbcZ2AeRUvLIN9t4a3kOV09N5m+nDu71F4BV2ZU8uXAHK7MqiQr04pEzhnDeuARVqEtxxPhazFwxJZnzxyXw5rIcXsrYw0lPL+bsUfHcfkIa8SF9Iw/Jz8vM65eP455PN/D4TzsprWvhgdlD8FBJzL0SvT0UbwHPA+8cZJ0lUsrT3GNO30ZKyb+/384by7K5ckrvFxO7S+t5+JutLN5ZRri/Fw/MTufC8Yl9egigonvxtZi5aUYqF41P5KVFe3hruTZK6OKJidw0I5XwPpCTZDGbePK8kUQGevPK4ixqmqw8ed5IJSp6IboKCinlYiFEkp42KDSklPzvxx28sjiLyyf14++n9V4xUdds5dlfdvHmshx8LB789ZRBXDoxSc2cqHAZIX4W7jtlMHOnJPHsL7t4Z0UuH6/O4+ppKVw9LZkA796d6GsyCf56ymCCfT357w878DAJ/jdnhBIVvQy9PRRdYZIQYgNQCNwlpdyit0G9kad+3sWLGXu4aEIiD54+pFeKCSklX2QW8K/vtlNe38J5YxK4e9bAPvGUqDAGMUE+/Pvs4Vw9LYUnf9rJM7/s4r2VufzfyYOYMya+V5537blxeip2u+SJhTsxmwT/OXu4quHSixBSSn0N0DwU33SSQxEIOKSU9UKIU4BnpJRpnbRzLXAtQFRU1JiPPvqoW+yrr6/H37931xv4ak8rC3ZZOSbezNwhFkwGu6h1xz7IrbXz3tZWdlU7SA4ycelgCynByiPRVfrCeaAH2TV23t/Wyu5qBwNDTFw2xIs4/46TgHvTPliwq5Wv9liZnmDm8nRLjxFSRt4HM2bMWCulHKunDYYWFB2smwOMlVKWH2y9sWPHyjVr1nSLfRkZGUyfPr1b2jIi8zL28NgP2zl7dByPzxlhyKeFo9kHVQ2tPLFwBx/8vpcQXwv3ztKeBI24nUamt58HeuJwSD5Zm8e/v99OfbONa49J4Zbj0v4UgutN+0BKyX9/3MG8jD1cPqlfj/GKGnkfCCF0FxSGDnkIIaKBEimlFEKMB0xAhc5m9RpeW5LFYz9s54yRsfzPoGLiSJFSMn91Hv/5YTt1zTYum5TE7ScMUEWpFIbDZBKcPy6R4wdH8e/vt/Nixh6+2lDIw2cM6bUFoYQQ3HPSQGx2B68uycbsYeL+Xp4E3hfQe9joh8B0IFwIkQ88AHgCSClfAuYANwghbEATcIHU26XSS3hzWTb//HYbpw6P4Ylze1dyVHFNM/d+tpFFO8sYnxzKw2cMYVC0mkJcYWzC/L14/NwRzBkTz/1fbObKt9Zw0pAoHpg9hNhgH73N63aE0BI1rXbJ60uz8fQwce+sgUpU9GD0HuVx4SGWP482rFTRjcxfvZeHvt7KrCHRPH3+yF5TAVJKyZeZhfzjy81Y7ZKHzxjCJRP69SrPi6L3MzEljO/+Mo3Xlmbx7C+7OP7JRdxxwgBSeuGzlBCCB2anY3M4eGnRHjw9BHeeOFBvsxRHiKFDHoruZ/HOMv76+WaOHRDBsxeO6jVVICvqW/jb55v5YUsxY/qF8Pi5I0juoxM0KXo+FrOJG6enMnt4LP/4cjP//HYbacEm0kY09rrJ+YQQPHz6UGx2rdy/p4eJv8zsMPdeYXB6x91E0SW2FdVy4/vrGBAVwAsXj8Zi7h27/8ctxZz41GJ+3V7KfScP4uPrJikxoegVJIT68sbccTx1/gjy6x2c/MwSFqzLp7dFfk0mwb/O0krdP7lwJ/My9uhtkuIIUB6KPkJJbTNXvrUafy8zb8wdi38vmOirpsnKQ19tYcH6AobEBvLBNSMZGN135kpwBS02O1UNViobWqlqbKWhxYZDSjYW2ajJLMBml9gdEptDYpcSh0Pi7WnCz8usvSxm/Lw88Pcy42sx4+9lxtvTpOLiR4EQgrNGxWMr2snHe7254+MN/Lq9lEfPHEaQb+9JMjaZBI+dMxyr3cFjP2wnOsiLs0bF622W4jDo+XcVxSFpaLFx5VurqW2y8sn1k4kJ6vkJXr9nVXDrR5mU1bdw68w0bj4utdeEb1xFTZOVnPIGcioayC5vYG9loyYcGlqpbGylqsFKfYut8wY2ZB5RvxYPEzHB3sQEeRMb5ENssA8xwdr7mGBvYoN9COzllSK7gwhfEx9dO4mXFu3hqYU7WZtbxRPnjWBy/3C9Tes22ipolta2cM+nG4kJ8mFiSpjeZim6iBIUvRyb3cEtH65ne3Edr10+lvTYnj3aQUrJa0uy+c8P2+kX6svnN05meHyw3mYZBiklxbXNbMirYWdJHTnlDWRXNJBT3kBVo3XfekJAdKA3EQFehPhaSInwJ8TXQqifJ6F+XoT6eRLia8HPy4zZQ7BuzRomThiP2WTCw0NgNglMQmAS0Gxz0NBio77FRmOLnfoWGw0tNhpbbdS32KlubKWwppmi6iZWZlVQUteC3bG/yz4iwItB0QEMjglkUHQAg6ID6R/ppyZoOwAPk+CmGalMTQ3ntvmZXPza71x7TAp3njCw14QwLWYTL10yhrPnLeO6d9ey4MbJ9I8wZjEpxf4oQdGLaZuG/NftpTx61lBmDIzU26Sjor7Fxj2fbuC7TcXMGhLN/84d3uvnQDgUNY1WNhZUszG/hsy8ajbkVVNa17JveXSgN0nhvswaGk1SmB9J4X4kh/uRGOp7WJOgFfubSOmmi7rN7qCsvoXC6maKapooqGpiV2k924treWt5Dq02BwBmk6B/hD+DYgJIjwlkfHIoQ+OClCcKGJEQzLd/mcoj32zj5UVZLNlZzrMXjiQ1sneE/IJ8PXnrivGc9eIyrnhzNZ/fOJkwVSLf8ChB0Yt5fWk2767M5bpjUrh4Qj+9zTkqdpXUcd17a8mtaOSvpwzimmkpfTIuX1bXwpJdZSzdXU7m3mqyyhv2LUsJ92NKajjD44MYkRDMoOgAfC3GO8XNHiZignycobeQ/ZbZ7A5yKhrYXlzH9qI6thfXsianii8zCwHwtXgwpl8IE1PCmJAcyvD44F7zZH64+FrM/PvsYcwYGMH/LdjEac8t5X9zRjB7RKzepnULCaG+vHb5OC54ZQVXv7OGD6+ZqGYCNjjGu9oouoXvNxXx6HfbOGVYNPfOGqS3OUfF70U23v51Gb4WM+9fPaFPxVRbbQ7W5laxaGcZi3eWsbWoFoBQPwtj+oVwzph4hscHMTwuuFck6Jk9TKRGBpAaGcBpw//4vLy+hVXZlfyeVcHKrEr+9+MOALw9TYxODGFCchgzBkUwLC6ozwnNE4dEMzIhmBvfX8ctH65nS2Etd580sFcUqxuZEMzT54/ihvfXcsfHmTx/4WhVV8bAKEHRC1m/t4rb5mcyKiGYJ88b2WNPQKvdwb++28abG1oY2y+EFy4eTVSgt95muZyS2mZ+2lLMop1lrNhTQUOrHbNJMLpfCHefNJBj0iIYEhvYY/frkRDu78Upw2I4ZVgMAJUNrZrAyK7g96xKnv5lJ0/9vJPYIG9OHBLNielRjE8O7TVF2w5FZKA3H1wzkQe/3sJLi/awraiWZy8Y1StE5qyh0fztlMH889ttPBa6nftOHqy3SYpOUIKil1Fe38L1760lKtCbVy8b22NdhKW1zdz4/jrW5FZxQj8zL147sVfHzqsbW/l+czFfZRayMrsCKSEh1IezRsdxTFoEk/qH9fl8kfaE+lmYNTSaWUOjAU1g/LKthJ+2lvDhqr28tTyHYF9PZg6K4qQhURwzIKLHngtdxWI28a+zhjEkNpAHv9rCGS8s5dXLxpIW1fPzKq6amkxuRSMvL8oiMdS3x4dweytKUPQi7A7JrR+tp7rRyuc3ju+xSUy7SuqY++ZqqhpbefbCUQRW7eyVYqKhxcbP20r4KrOQxbvKsNolyeF+3HJcGqePiKF/hH+fc98fKaF+Fs4dm8C5YxNobLWxeGcZP24pYeHWYj5bl4+PpwczB0dy/rgEpvQP79XenYsn9GNgVADXv7eOM19YxpPnj+SkIdF6m3VUtJXozq9q5B9fbiEu2IfpPTzJvDeiBEUv4plfdrFsdwWPnTOsxw4PXZVdydVvr8bL04OPr5vE0LggMjJ26m1WtyGlZPmeCj5ancfPW0tostqJDvRm7uQkTh8Rx9C4QCUijhJfi5lZQ2OYNTQGq93B71mV/LCliG82aq+4YB/OHRvPuWMTiOuFk24BjE0K5etbpnD9u2u57t213DozjVtnpvVoIWX2MPH8RaM596UV3PT+Oj69YTKDY3rmda63ogRFL2HxzjKe+3UX54yO57yxCXqbc0R8u7GI2+dnkhDqw1tXjO9VcxbUt9hYsC6fd1bksru0nmBfT84eHcfpI2IZlxTaoy/0RsbTw8TUtHCmpoVz/6npLNxawvzVeTz98y6e+WUXU1PDOX9cAiekR/W6mhcxQT7Mv24Sf/t8M8/8soutRbU8df7IHl0l18/LzBtzx3HGC0u5/r21fH3LVFUUzUD03CNLsY+imiZum5/JgMgA/nnm0B75hPvakiwe/W4bY/uF8OplYwn2tehtUrewu7Sed1fk8Nm6AupbbAyPD+Lxc0dw2vCYXh/TNxrenh7MHhHL7BGx5FU28snafD5dk8fNH6wnxNeTOWPiuWJKcq+aKtzb04PHzx3OsLhAHvl2Gxe9upI3547rseFQgOggb164aDTnv7KSez/dyIsXj+6R17zeiBIUPRyr3cHNH6ynxWrnxUtG42PpWTcph0Pyz2+38caybE4eGs1T54/s8Tdah0Py87YS3lmRy9Ld5Vg8TJw2PIbLJicxMiFYb/MUaDUO7jhhALfOTGPp7nLmr97LG8tyeHNZDmeMjOO6Y1MY0AuSGUHLP5g7JZmEUF9ufH8d5760gneuGk98SM/1AI5NCuX/Zg3i0e+28eayHK6cmqy3SQqUoOjxPPb9dtbmVvHchaN6XHnaZqudOz7O5LtNxVw5JZn7Tx3co13/Dofk+83FPPPLTnaW1BMT5M3dJw3k/HEJhPfgJ8LejIdJcOyACI4dEEFeZSOvL83mo9V7+WxdPjMHRXLdsf0ZlxTSK56AZw6O4r2rJ3DVW6s5Z95y3r1qQo8WTVdPS2ZVTiX/+m4bIxODGZ0YcugvKVxK70ud70P8sLmY15Zmc9mkfj2uOl5Nk5XLXl/Fd5uKuf/UwfxjdnqPFRMOh+SbjYXMemYxN32wDoeEZy4YyZJ7ZnDTjFQlJnoICaG+PHj6EJb/30xuOz6NdXurOO/lFZwzbzk/binG4ej5U4aPSwrl4+snISWc+9IK1uZW6W3SESOE4PE5I4gJ9ubm99dR1dCqt0l9HiUoeii5FQ3c/ckGRsQH8bdTe1ahl5omK5e9sYr1eVU8f9Eorp6WordJR4TdIfl6gyYkbv5gPQ4Jz144ih9vO4YzRsb1maJKvY1QPwu3HT+A5f83k4dOH0JpXQvXvbuWWc8s5pdtJUjZs4XFoOhAPrthMiG+nlz82kp+21Gqt0lHTJCvJy9eNIby+lbu+DizV4i+noy64vVAmq12bnx/HSaT4PmLRveo7PTaZk1MbC2sYd7FYzhteM/yrIA29PO7TUXMenoxt3yoCYnnnELi9BGxvaLksQJ8LB5cPjmJjLum88wFI2m1Objq7TWc/8pK1u/tuU/2oHljPr1hMqmR/lzz9ho+X5+vt0lHzLD4IP4+O53fdpTx0uI9epvTp1E5FD2QpxbuZEthLa9dNrZHDa2sbbZy6euamHjx4jEcnx6lt0mHzZbCGh76eiursitJjfTnuQtHccqwGCUiejFmDxNnjIzjlGExfLhqL8/8vIuzXlzOKcOiufukQSSH++lt4hER7u/Fh9dM5Np31nL7/A1UNli5qocmN14yIZFV2ZU8/uMORieG9Kn5foyE8lD0MNbtreLVJVlcOD6xR92QDxQTJ/Qg2wEq6lv46+ebmP3cUnaV1PHoWUP58bZjmK08En0GTw8Tl01KYtE9M7h1ZhoZO8o44clF3P/FJsraTRnfkwjw9uTNK8Yxa0g0j3yzlRd+2623SUeEEIJ/nz2MpHA/bvlwfY/dHz0dJSh6EM1WO3d9soGYIB/+ekrPmUG0tllLwNxaWMMLF43uUWLCanfwxtJsZjyewfzVeU4X+AwuntBPCYk+ir+XmdtPGEDG3dO5YHwCH67K49j//ca8jD1Y7Q69zTtsvD09eOHi0Zw5Mpb//biD15dm623SEeHvZWbexWOoa7Zy60frsat8CrejBEUP4smFO8kqa+A/5wzrMRNFtYmJzQWamDixB80psGRXGac8s4SHv9nKiIRgfrh1Gg/MHtIrZnBUHD2RAd7888xhLLz9GKakhvPYD9uZ/dxS1vXA/AoPk+Dxc0dw8lDNU/Heyly9TToiBkYH8M8zh7F8TwXP/9ozvS09GSUoeghrc6t4zRnqmJYWobc5XaKu2crlbzjFxMU9R0zUNFq54+NMLn19Fa12B69eNpZ3rhzfK2ZtVHQ/KRH+vHrZWF6+dAw1TVbOmbecv3+xmdpmq96mHRZmDxPPXDCK4wZFcv8Xm/l0bc9M1JwzJp6zRsXx3K+72FJYo7c5fQolKHoAzVY7d3/as0IdLTY717yzhk35NTx/0egeM9vhL9tKOOGpRXyZWchfjkvlp9uP4YT0qF5R2EjhWk4aEs3CO45l7uQk3v89l+OfWMR3m4p61DBTi9nEixePZmpqOPd8uoGvNxTqbdIR8cDsdEL8LNz1yUZabT0vDNVTUYKiB9AW6njsnOE9ItThcEju/mQjK7MqefzcEcwaanwx0eaVuOrtNYT6WfjypincceLAHjUkV6E//l5mHpg9hC9umkJEgBc3vr+Oq99eQ35Vo96mdRlvTw9euWwMY/uFctv8TH7cUqy3SYdNsK+Ff501jG1FtbyYoUIf7kIJCoOzNvePUR1T08L1NqdL/PfHHXy1oZC7TxrImaPi9DbnkPy6vYQTn9a8Erccl8pXN09laFyQ3mYpejDD44P58qYp3H/qYJbvqWDW00t6VK0HX4uZN64Yx7C4IG75YD0ZPbD41QnpUZw1Ko7nf92tQh9uQtWhMDBtoY7YHhTqeHdlLi8t2sNFExK5cXp/vc05KPUtNh78agufrs1nYFQAr102jmHxfVtI2B2S2iYr1U1WqhtbqW6yUt9sY0uhjZrMAhxS4nCAQ0okIIAAbzMB3p4EeJvx9/rjfU+f5O1oMXuYuHpaCicNieaOjzO5ff4GFu0o45Ezh/YIT6O/l5m3rxjPha+u5Lp31/LmFeOY3L9nPNS08cDsdJbuLueuTzby1c1T8FTVa12KEhQGpi3U8d5VE3rEBWjh1hIe+HIzMwdF8vDpQwydd7C9uJYb31tHTkUDN89I5ZaZqb0+vCGlpKbJSm5FI7mVjeRVNpJb0UBuRSNFNc1UN7ZS22zrvIGNmYfVn5fZRFywD3EhPsSH+LR770tCiC9RgV6GPka6i4RQXz68ZiIvZuzhmV92sXZvFc9cMKpHTGYV5OvJe1dP4IJXVnDtO2v59IZJDIoO1NusLtMW+rjmnTW88Ntubjt+gN4m9WqUoDAoG/KqeW1JFhdN6Bmhjsy8am75cB1D44J47qJRhp7H4rO1+fzti00EeHvywTUTe2VVPYdDkl3RwOaCGjbm17CpoIbtRbV/EgwRAV70C/VlZEIwoX4Wgnw8CfZ1vnwsBPl64u9lZs3q1UycMB6TEJiEQAgQAhwOzdNT12ylrtlGXYvzb7ONqoZWCmuaKKhqYmFRLeX1+0/eFOzrSXpMIENiA0mPDSQ9Joj+EX6GPnaOFLOHib/MTGNKahi3fpTJuS+t4Pbj07hheqrh65mE+ll4+8rxnPnCMq56aw2f3zSZyABvvc3qMiekR3HmyFie/3U3J6RHMSS2b3shXYkSFAbE4ZA88NUWQv28uO9k44c6cisauOqt1UQEePH65ePwtRjzsGq22nno6y18uCqPiSmhPHvhqB51YTwYDS02fs+uYGVWJRvzq9lcUEt9iyYevMwm0mMDmT0iluRwPxJDfUkM8yUx1LfL+6rQ30RKhP9R2djUaqeguon8qkb2VjayraiWrYW1vLMilxZnJr7FbGJwdAATUsKYlBLGuORQ/L2MeTwdCWP6hfLdrdP42+ebefynnSzeVc7T548kNthHb9MOSkyQD69dNo7zXl7BNe+sZf61E3tUSOuB2UNYurtChT5cTO85U3sRX2QWkJlXzf/mGH9UR1VDK3PfXI1dSt66YjwRAcacqju3ooEb31/HlsJabprRn9uPH9Cjn4RtdgcbC2pYuqucpbvLWb+3CqtdajfkmEDOGhXHsLgghsUHkRbpb4ht9bF4kBrpT2rk/sLEZneQVd7A1sJathbVkplXzVvLcnhlcRYeJsHw+CAmpYQxqX8YY/uF4mPpOTeyjgj09uTZC0YyfUAE//hyMyc/s4QXLhpteE/ksPggnr5gJNe/t5Y7P97AcxeOwmRw70obIX4W/nXWUK59d60KfbgQJSgMRn2Ljf98v50RCcGcMzpeb3MOit0h+ctH6ymoauKDaybQ/yifYF3FT1uKufOTDZiE4I25YzluUM8p/d2ehhYbv2wv5ftNRSzdXU5dsw0hYEhsIFdNTWFaWjhj+oX0qCdH0MIBA6ICGBAVsG9UUFOrnXV7q1i+p5wVeyp4ZXEWL2bswcts4pgBEZw8NJqZg6MI8jG24O4MIQTnjIlndL8Qrn93LZe/uYr7Tx3M3MlJhs4rOWlINPedPIh/fbed5HA/7jppoN4mdZkTh0Rzhgp9uBQlKAzGi7/tprSuhZcuHWN49f/ML7tYsqucf589jLFJoXqb8yeklLy8OEsTaPFBPH/R6B41OytoN9bfdpTyzcZCft1eSrPVQVSgF6cOi2FqWjiT+4cT6mfR28xux8fiwZTUcKakak/tDS02VudUkrGjjB82F7NwawmeHoLJ/cM5ZVg0J6RH98jfITncj89unMzt8zN56OutbC+q4+Ezhxg6QfiaaSlklTXw/G+7SQr3Y84YYz/4tOfB2UNYtruCu52hDyN47noTSlAYiNyKBl5bks3Zo+IMnwH+2/ZSnv1lF3PGxHPBuAS9zfkTNruDB77awvu/72X2iFj+N2d4j3lytzski3eWsWB9Ab9sK6Gx1U64vxfnjU3gtOGxjO0XYnix2d34eZmZPjCS6QMj+cdp6WTmV/PD5mK+31zEvZ9t4q+fb2Zy/zBtFt7BUVjMPedG4e9l5uVLxvDUzzt57tfd7CmrZ94lYwwbPhRC8MiZQ9lb2ch9CzaSEOLDhB6S2BziZ+Gh04dw0wfr+HB1HpdO7Ke3Sb0KJSgMxD+/3YbZQ3CvwRMx8yobuW1+JoNjAvnnmUMN56JtaLFx8wfr+G1HGTdM78/dJw7sETfg8voWPl6Txwe/7yW/qokQX0/OGBnH7OExTEgJM/xoAHdhMglGJ4YwOjGE+04exJbCWr7fXMTn6wq48f11hPtbOGdMPBeMSyQ53E9vc7uEySS488SBDIwO4K5PNnDG80t55bKxhi2w5ulhYt7FYzhr3jKue28tn984pcf81qcMi2ZCcihP/rSD2cNjCPbteZ4to9JzZHwvZ8muMhZuLeHm41KJCjTuyINmq50b31+HQ0peumS04Z76S2qbOe/lFSzeVc6/zhrGvbMGGVpMSClZnVPJrR+tZ/K/f+W/P+wgPsSHFy4azaq/Hc+/zx7G5NRwJSY6QQjB0Lgg7j5pEEvuPY43545jVGIIry3Rppy/8JWVfLWhsMfM53Da8Fg+vX4yAHNeWs43G407l0aQrydvzh2HAK56e/W+UUVGRwjBA7OHUNNk5emfd+ltTq9CeSgMgNXu4OGvt5IY6suVU5L1NuegPPT1FjYV1PDaZWPpF2asJ5LtxbVc+eZqapqsvHb5WGYMjNTbpE6xOyTfbCxkXsYethfXEeBt5qIJiVwyMZHUSDWr6ZHgYRLMGBTJjEGRlNQ288maPD5clcdfPlxPTJA3V09L4cLxCYYd1tzG0Lggvrx5Kje8t5abP1hPZUMrl01K0tusDukX5seLF4/h4tdW8rfPN/H0+SMN57HsiPTYQC4cn8i7K3O5aEIiA9RMwt2C8lAYgPdW5rKrtJ77Tx1suCf+9nzsvEDfNKM/x6cba6TE71kVnDtvBXYp+fj6SYYVE1a7g0/W5HH8k4u49aNMHFLyn7OH8ftfZ/Lg6UOUmOgmogK9ufm4NJbcM4M3544jIdSXR77ZypT//MozP++iurH10I3oSESAF+9dPYET0qP4x5dbeO6XXYadtXRS/zBuO34AX2YWMn91nt7mdJk7TxyIn8WDR77ZatjftqdhbKneB6hsaOWphTuZlhbOCQa7SbdnS2ENf/9iM1NSw7jjBGMNFVu+p5yr3lpDbLA37141wZBFglpsdj5bW8CLGbvJr2oiPSaQly4ZzYnp0YYOyfR0TO28FmtzK3nxtz089fNOXlmszTdz1dQUooOMGWL09vRg3sWjueezjTyxcCcn9TNz7LHSkMfLTTNSWZVdyQNfbWFkYnCPKM8d6mfh9hMG8NDXW1m4tYQThxh/VmSjo6uHQgjxhhCiVAixuZPlQgjxrBBitxBioxBitLttdDXP/rKLhlY7/zgt3bCuwmarnVs+XE+Ir4VnLhhlqHj+0l3lXPnWahJCffjo2kmGExN2h2T+6r1M/18Gf/18E2H+Xrx++Vi+/ctUZg2NMeTNobcypl8or88dxw+3TeOE9CjeWJbDsf/7jcd+2E5ts1Vv8zrE7GHi8TkjmDs5iR9zbdzz2UZsduPlg3iYBE+dP5JAH09uen8dDT0kn+KSif1Ii/Tnn99uo8Vm19ucHo/eIY+3gFkHWX4ykOZ8XQvMc4NNbqO4ppkPVu3l3DHxpBk4hve/H3eQVdbA4+eOINzfOEPZFu0s46q3V5MU5seH10w03DC7lVkVzH5uKfd+tonoIG/euXI8X9w4mZmDowwrHvsCg6IDefqCUfx253ROGRbDvIw9TP9fBu+syMFqwJu1ySR4YHY6Z6V68unafG76YB3NVuPd/CICvHjm/JFklTfw9y8294gwgqeHiX/MTmdvZSOvL83W25wej66CQkq5GKg8yCpnAO9IjZVAsBAixj3WuZ6XFu3B4ZDcNCNVb1M6ZWVWBW8sy+aySf0MVRr4tx2lXPPOGvpH+PPBNRMJM5DQya1o4Pp313LBKyupabLy7IWjWHDDZI4ZEKGEhIFIDPPlqfNH8vXNUxkQ5c8/vtzCSU8t5sctxYa7GQohOCPVwoOz0/lxSwlXvb3akF6Ayanh/OW4NBasL+CTtfl6m9MlpqVFcPzgKJ7/dTcltc16m9Oj0dtDcSjigPZZPvnOz3o8bd6JOWPiDVu9saHFxt2fbiAx1Jf/M1BtjF+2lXDdO2sZEOXPB9dMMEyFxLpmK//+fhsnPLmYxbvKuOvEAfxy57GcPiJWCQkDMyw+iA+vmcjrl49FCLju3bWc//JKthfX6m3an5g7JZmnzh/ByqxKrn57jSE9FX+ZmcaklDD+8eVmdpbU6W1Ol7j/1MHY7JL//rBDb1N6NEJvJS6ESAK+kVIO7WDZt8C/pZRLnf//AtwjpVzbwbrXooVFiIqKGvPRRx91i3319fX4+3f/HBXvbm0hI8/Gf6b5EOFrTF339hbNxr9O8CYtRL/RJ+33wcYyG8+sayExwMRd47zx8zTGjXpjmY23trRS2SyZGmfmnDRPQryNuV+PBFedB0bD7pAszrexYFcrjTY4JdmT2f09sXjof5y13wcrCm28srGF4REe3DLKC7PBcnGqmx38Y3kT/hbBAxN98DIby76O+HhHK99lW/n7RG/6B3d8vTPyeTBjxoy1Usqxetpg9FEe+UD7us7xQIeVXqSUrwCvAIwdO1ZOnz69WwzIyMigu9pqo7immSULf+O8cQmce8rwbm27u1i0s4zffljFtcekcM0pg3W1pW0fZOZVM++XlQyODeT9qycaYmKomkYrj3y7lU/X5pMa6c9rVw43fNn0I8EV54FRmQnc2tDKP7/dyoJ1BWyptfDvs4fpXl66/T6YDvTrv5e/fr6Jz4uDeNZgydIAYf3LuOyNVSytj+CRM//0vGg4xk6ysfrxDH4s9mX+GRM79Cr2pfPgSDD6I9RXwGXO0R4TgRopZZHeRh0t8zJ245CSG6cbM3eipsnKvZ9uJDXSnztOMMY0v9nlDVz51moiArx4c+54Q4iJn7YUc/xTi/h8fQG3HJfKt3+Z2ivFRF8k1M/Ck+eN5N2rxmN1ODj/lZXct2ATNU3GGQ1y0YRE7j91MN9uLOL/PtuIw2GsvI9paRHMnZzEuytz+T2rQm9zDom/l5mbpvdnVU4lK3qAvUZE72GjHwIrgIFCiHwhxFVCiOuFENc7V/kOyAJ2A68CN+pkardRXNPMh6vyOHescXMnHvp6C2X1LTx53ghDFNqqaZFc9sbvALx95XjdR3NUN7Zyy4frufbdtYT7e/HlTVO488SBhp4hUnFkTEuL4MfbjuGaacnMX72XE55cRMaOUr3N2sfV01K4dWYan6zN52EDFmi6+6SBJIT6cO9nG2lqNV6+x4FcMD6RyAAvnv7ZuIXEjIzeozwulFLGSCk9pZTxUsrXpZQvSSlfci6XUsqbpJT9pZTDpJRr9LS3O3jR4N6Jn7eWsGBdATfNSGV4fLDe5lDfYuPJtc2U17Xyxtxxuk9AtG5vFac+u5QfNhdx5wkD+OrmKYadwEnRPfhazPzt1HS+uGkKIb4W5r65mn99t80w84PcdnwaV09N5q3lOTzx0069zdkPX4uZ/5w9nJyKRp762Vi2dYS3pwc3Tu/PqmzlpTgSjB7y6FUU1TTxkYG9E81WOw9+vYUBUf7cbIChrK02Bze8t5a8OgcvXjyakQnButkipeTVxVmc99IKTCb47IbJ3DIzDU8PdQr1FYbHB/PlzVO4eEIiryzO4tyXlrO3olFvsxBC8LdTB3Ph+ASe/203ry3J0tuk/ZiSGs6F4xN5bUkWmXnVeptzSJSX4shRV0M3Mi9jDw5p3LoTLy/KIr+qiYdOH4rFrO+hIaXk/z7byJJd5VwxxMKMQfrNzVHd2Mo176zh0e+2MXNwJN/cMs0Q3huF+/H29ODRs4Yx7+LRZJc3cMqzS/gys0BvsxBC8M8zh3Hy0Gge/W4bv2wr0duk/bjvlEFEBnhzz6cbDF+RUnkpjhwlKNxESW2z0zuRQHyI8bwTeZWNvJixm9OGxzCpv77Z7ACvLsliwfoC7jhhANPi9UvAXO8McSzaWcYDs9N56ZIxhkgIVejLycNi+O7WaQyMDuDWjzK559MNuteE8DAJnjxvJENjg/jLh+vZUWycGhCB3p786+yh7Cyp54Xf9uhtziFRXoojQwkKN/H+ylysDgfXH5uitykd8ui32zA5Xad6s3x3Of/5fjunDIvmluP08+Z8sb6A819eiRDw6fWTuWJKsipQpdhHfIgv86+dyM0zUvlkbT7nv7yCUp0rLfpYPHj1srH4eZm56u3VlNe36GpPe44bFMVZo+J48bfdbC00XtGw9igvxZGhBIUbaLHZ+WDVXo4bGEm/MH2TCjtiya4yfthSzM3HpRITpO/kWoXVTdz84XpSIvz575wRutzApZQ8tXAnt83PZHS/YL65ZSojdMzfUBgXs4eJu04ayMuXjGFXaT2nP7+MzQU1utoUHeTNq5eNpayuhevfXWuoEMM/Tksn2NeTez7bYMhJztrT3kuh6BpKULiB7zYVUV7fyuWTk/Q25U+02hw8+NUWksJ8uXpasq62NFvt3PDeWlptDl6+dAz+Xu6vu9Zis3PHxxt45pddnDM6nneunECwrzFKeyuMy4lDovn0+sl4mARzXlrOd5v0LZczIiGYJ84bwZrcKu5bsMkwbvsQPwsPnzGUzQW1vLksR29zDsp+Xoo9ykvRFZSgcANvLc8lJcKPqanGmVyrjbeWZ7OnrIF/zE7XvY7CQ19vYUN+DY+fO4L+Ee4vb1vZ0Molr/3O5+sLuOvEATx+7nDdk1MVPYf02EC+uGkK6TGB3Pj+Op79Rd/4+2nDY7nt+DQWrCvg5cXGGflxyrAYZgyM4NlfdlFhoJBMR/zhpTD+kFcjoK6WLiYzr5oNedVcPikJk8FK45bWNvPMz7uYOSiS4wZF6WrLR6v28uGqPG6c3p9ZQ6Pd3n9eZSNnv7iMDfk1PHfhKG4+Lk3lSygOm4gALz64ZiJnj4rjyYU7uX1+pq5Tot86M43Thsfw2A/bDVWQ62+nDqbRaufJhca+Ubd5KX5XXoouoQSFi3l7eQ7+XmbOGROvtyl/4r8/7sBql/z9tHRd7dhcUMM/vtzCtLRw7jxxoNv7zy5v4LyXV1DVaOXDayYwe0Ss221Q9B68PT144rwR3HXiAL7ILOSG99bqNgJECMH/5oxgQGQAd368Qfek0TZSIwO4dGI/Ply111CjUTqizUvxYsZuvU0xPEpQuJCyuha+2VjInDHxuuQDHIzdpfUsWJfP5ZP7kaRj9clmq53b52cS4ufJMzpMcLSrpI7zXl5Bi83Bh9dMZEy/ULf2r+idCCG4+bg0HjljCD9vK+Wqt1fT0GLTxRYfiwfPXzSKhlYbt83PxG6QOT9unZlGgLcn//zWeCXD2+Pt6cFlk/qxZFc5hfXGTiTVGyUoXMiHq/ZitUsum9RPb1P+xDO/7MLb04Prj+2vqx3/+3EHu0rr+e+cEYT6uTf5cVtRLRe8shKA+ddOJD020K39K3o/l05K4olzR7BiTwWXvv67bpOLpUUF8NDpQ1i+p4KXFhmjDkSIn4VbZ6axZFc5vxkoHNMRF4xPxOJh4pe9xpkczogoQeEirHYH7/+eyzEDIkjRIcHwYOworuObjYXMnZxEmL9+E20t31PO60uzuXRiP44dEOHWvjfl13Dhqyvx9DAx/9qJpEUFuLV/Rd/hnDHxvHjxaDYV1HDBKyt1qw1x3tgEZo+I5cmFO1mTU6mLDQdy6aR+pET48c9vtumaa3Iowv29OG14DMsKbNQ1K1HRGUpQuIgfNhdTUtvC5Qb0Tjy1cCf+FjPXHqNfka3aZit3fbyB5HA/7jtlkFv73lxQw0WvrcTPYubj6yYZTvApeh+zhsbw2uXjyC6v57yXV1BW535RIYTg0bOGEhfsw60fZVLd2Op2Gw7E08PE304ZTFZ5A++uyNXbnINy+eQkmu3w2dp8vU0xLEpQuIi3l+eQGOrL9IH6zUHREZsLavhhSzFXTk3Wtb7Cg19toaROmyLd1+K+/JLcigbmvrmaAC8z86+bSGKY8cqgK3onxw6I4O0rxlNY3cTlb6zSJfwR6O3JcxeOoqS2mXs/22iI3IXjBkUyLS2cZ37ZRVWD/iKnM0YkBJMSZOKdFbk4DJKHYjSUoHABu0vrWJNbxaUT+7k9yfBQPP3zTgK9zVw5Vb8iVj9sLtKmSJ/en1GJIW7rt7SumUtfX4XN4eCdq8Ybck4VRe9mQkoYL186ll2ldVz99mqaWt0/+mNEQjD3zhrEj1tKeP/3vW7v/0CEENx/ajp1zVae+cXYVSmP7+dJVnkDS3eX622KIVGCwgV8mVmIScAZo4w1/DAzr5qft5Vy7TEpuk1wVdnQyl8/38zQuEBumZnmtn7rmq3MfWM1ZXUtvDl3HKmRKmdCoQ/HDojg6fNHsSa3ihve1yrDupurpiYzNTWcf3+3jcLqJrf3fyADowO4YHwi7/+eS4EB7OmMcdEehPtbeHt5jt6mGBIlKLoZKSVfZhYyJTWcyABvvc3ZjycX7iTE15O5U/TzTvz3h+3UNFl54tyReHq45/Brttq59p217CypY94lo93qFVEoOuLU4TH866xhZOwo446P3T+U02QS/PvsYTgk3P/FZkOEPm6aoU0E+FKGMUahdISnSXDR+ER+3VHK3opGvc0xHEpQdDPr9lazt7KRM0bG6W3KfqzNrWTxzjKuP7a/bjUx1u2t4qPVeVw5JYmB0e7xEEgpufOTDazIquDxc0cYLqdF0Xe5cHwi9508iG82FvGPL91/U08I9eXOEwfw6/ZSvt6o79wjAHHBPswZE8/8NXmUGKQAV0dcNKEfHkLw7socvU0xHEpQdDNfZhbgZTZx0hB9S1kfyKuLswny8eRSnUad2B2Sv3+xmahAL249foDb+n3ht918u7GI+04exJmjjCXyFIrrju3P9cf25/3f9/L60my393/FlGRGxAfx0FdbDJEQecOxqdgdkpcXGWfukQOJDvLmpKHRzF+dR2OrPsXKjIoSFN2I1e7g241FHD84igBvfXIUOiKvspGfthZz4fhEt46oaM8Hv+eypbCW+09Nd5uH5NftJTyxcCdnjozVdYisQnEw7jlpICcPjeZf321ze4EnD5PgP+cMp6bJyiPfbnVr3x2RGObLmSPjeP/3XF2G1naVuZOTqG228WVmod6mGAolKLqRpbvLqWho5YyRxkrGfGdFDkII3Sp2lte38L8fdzC5fxinDY9xS5/Z5Q3c+lEmg6MD+ffZw9VEXwrDYjIJnjhvBAOjA/nLB+vZXVrv1v4HxwRy/bH9WbCugMU7y9zad0fcNKM/VruD15YY10sxtl8Ig2MCeXt5jiHyT4yCEhTdyJfrCwjy8TRUnL6hxcZHq/OYNTSa2GAfXWx47PvtNFntPHzGULfc2OtbbFz7zhrMJsHLl47Bx6LvtOwKxaHwtZh59bIxWMwmrn1nDTWN7q1RcfNxqaRE+PHXzzfpNudIGykR/sweEcu7K3OpNEAYpiOEEFw0IZHtxXVsKzL25GbuRAmKbqKx1cZPW0s4ZVg0FrNxftYF6/Kpa7ZxpU4jO9bmVvHJ2nyumppCaqTrK1I6HJI7P84kq7yBFy4aTUKoqjWh6BnEh/jy0qVjyKtq5JaP1mNzYylqb08PHjtnOPlVTTz/m/6zat48I5Umq53XlxrXS3HqsBjMJsGXGwr0NsUwGOfO18NZuLWExla7oUZ3OBySN5flMCI+iNGJwW7vX0rJf77fRmSAF7ccl+qWPt9ekcOPW0q47+RBTE4Nd0ufCkV3MS4plEfOGMrinWX898cdbu/7rFFxvL40m/wqfYdEpkUFcPLQaN5enut2b01XCfWzcMyACL7OLFSVM50oQdFNfJlZSEyQN+OTjDP99aJdZWSVN3Dl1GRdcggydpaxOqeKW2am4eeGRMydJXX8+/vtzBwUyVU6VgJVKI6GC8YncsnERF5ZnEWGm5M07z5pIAJtFmC9uXlGGvUtNt5c7v7RL13ljJGxFNY0s9ogk63pjRIU3UBlQyuLd5Zx+ohYTAYqtf3mshwiA7w4eah7EiHb43BIHv9xB/EhPpw/NsHl/bXY7Nz6USaB3mYem6OSMBU9m/tPTWdgVAB3fbLBraMdYoN9uHpaMl9mFrIhr9pt/XZEemwgMwdF8t7KXFps7i9R3hVOSI/Cx9ODL9RoD0AJim7h1+2l2ByS04YbZ3TH7tI6Fu8s47JJ/XTJ6fhhSzFbCmu5/fgBbun/yZ92sq2olsfOGU64jlOyKxTdgbenB89dNIq6Zht3fbLBrS71G6anEu5v4dFvt+k+guHyyUmU17fyw+ZiXe3oDF+LmROHRPHdpiJdSqgbDSUouoGMHaVEBHgxNC5Qb1P28f7ve7F4mLhwfKLb+7Y7JE/8tIPUSH+3FJNavqecV5ZkcfGERGYONlZBMYXiSBkQFcD9p6WzaGcZbyxzn9vf38vM7ScMYFVOJT9uKXFbvx0xNTWcpDBfQ09tfubIOGqarCwywJBbvVGC4iix2R0s3lnG9AERhnGz2+wOvt5QyMzBkYTp8LT++foC9pQ1cOcJA1w+22pts5U7P95Acpgffzt1sEv7UijczSUTEjkxPYrHfthObq373P7nj00gLdKf/3y/Tdcnb5NJcMnEfqzJrWJrYa1udhyMqWnhhPpZ+DJTjfZQguIoycyrprbZZqjaE0t2lVNe38pZOpSabrU5ePrnnQyLC2LW0GiX9/f4jzsoqW3myfNH6lYFVKFwFUIIHjtnOGF+Xszb0EKz1T2iwuxh4q+nDCanopH3VurrHZgzJh4vs4n3fjeml8LTw8Spw2L4eVsJ9TrX8NAbJSiOkt92lOJhEkxNM84QxQXrCwjx1afA1oJ1+eRXNXHniQNc7rHZmF/NuytzuWxSEiMTgl3al0KhFyF+Fh4/dwTFDZLnf3VfjYjpAyOYmhrO87/t1nXOimBfC6ePiOWL9QXUNhtzCOkZI2Nptjr4aYsxcz3chRIUR0nGjjLGJIYQ5GOMuTvqmq38tKWY04bHuj0ZU0rJa0uzGRIbyLEDIlzal90h+dvnmwn39+KOE9032ZhCoQdT08KZEmvmpUV72FHsnsqMQghuOz6NyoZWPlyV55Y+O+OySUk0ttr5fJ0xwwpj+oUQH+LT50d7KEFxFJTWNrOlsJZjB7r25nk4fL+5mBabg7NGuz/csWhnGbtL67l6muvrXry3MpdNBTX8/bR0Ag00EZtC4SouGGQhwNvMfQs2um3Ux9ikUCYkh/Lq4ixdh24Oiw9iREIw767M1X3kSUcIITh9RCzLdpcbelIzV6MExVGQ4czqnW4gQfH5ugKSw/0YpUMI4PWl2UQFenHqMNcOny2tbebxH3cwNTWc2W6abEyh0JsAi+Dvp6Wzbm8176/a67Z+bz4uleLaZhbo7B24dGI/dpfWsyKrQlc7OuPMUXHYHZIfNhfpbYpuKEFxFCzaUUZkgBfpMcYYLlpY3cTK7ArOHBnn9hEn24trWbKrnMsnJ7k81PLod9tosTl4+IwhhhlZo1C4g7NGxTE1NZz/fr+dktpmt/Q5NTWcEfFBzMvY49b5RQ7ktOExBPt66p4k2hkDogLoF+bLbzv67vBRJSiOEJvdweJdZUwfaJzhol9kFiAluozueH1JNj6eHlzk4roXm/Jr+DKzkGuOSSYlwvWTjSkURkIIwaNnDaXV7uDBr7a4rc8bZ6Syt7KRbzbq9/Tt7enBuWPi+WlLiWFnIZ0+IILle8rdNhrHaChBcYSs21tNncGGi36xvoBxSSEkhrl3hs3Suma+zCzk3LHxBPtaXNrXf3/cToivJ9cd29+l/SgURqVfmB9/mZnG95uLWekm9/8Jg6MYEOXPixm7dZ0I68xRcdgc0rCVM6cPjKTZ6mBVdt+c20MJiiMkwzlcdIpBZrTMKqtnZ0k9s0e4v/z3eytysTocXOHiKdKX7y5nya5ybpqRqhIxFX2aq6YmExPkzb++2+aWG7zJJLhpRio7S+pZuE2/6pnpMYGkRPjx9QZjjqaYmBKGxWwio4+GPZSgOEJWZlUwMiHYMMNFf92uzUp43CD3ekxsdgcfrs5j5qBIksP9XNaPlJLHftxBTJA3l0zs57J+FIqegLenB3eeOJCN+TV8u8k9YYhTh8XQL8yXlxftcUt/HSGEYPbwWFZmV7gth+Rw8LF4MDEljIyd7p0l1igoQXEEtNjsbC6oZUy/EL1N2cev20sZGBVAfIh7wx1LdmnDpM518YyiP24pZkNeNbcfPwBvTw+X9qVQ9ATOGhXHoOgA/vvjdrcM6TR7mLhsUhLr9lbrWgZ79ohYpIRvdcznOBjTB0SQVdbA3opGvU1xO0pQHAFbC2tptTt0GZrZEXXNVlZlVzLDzd4JgE/X5hPqZ2GGC3NJHFLyvx930D/Cj7N1qK+hUBgRD5PgvlMGk1fZxPsr3TOM9JzRcXiZTXywSr+RFqmR/qTHBPL1RmOGPdrKCPRFL4WugkIIMUsIsUMIsVsI8X8dLJ8uhKgRQmQ6X//Qw84DWbe3GoDRBvFQLNlVjs0hmTnYvYKiptHKwq0lnD7CtVU515bY2VPWwB0nDMTsoTSwQtHGMWnhTE0N57lfd1HT5Pqy1MG+Fk4dHsMX6wtp0HHeitkjYlm/t5q8SuN5AZLD/UgM9e2TeRS6XZ2FEB7AC8DJQDpwoRAivYNVl0gpRzpfD7vVyE5Yv7eK2CBvogK99TYFgF+2lRLs6+l2j8lXGwtptTuYMybeZX1IKfk+20q/MF+3TDamUPQkhBD838mDqGq08uriLLf0efGEftS32PhKx8TI05wF7YzopRBCMH1g3xw+qufj3nhgt5QyS0rZCnwEnKGjPV1m/d5qRhnEO+FwSDJ2lHLsgAi3P71/tjafQdEBDIl1XWGv1TlVZNU4uHpqssunQlcoeiJD44I4eWg0b6/Ioc4Nk2eNTgxmUHQA7+lYBjsh1JdRicF8vcGgeRQDI/rk8FE9BUUc0H7GmXznZwcySQixQQjxvRBiiHtM65yS2mYKqpsYnWgMQbEhv5qKhla3j+7YXVpPZl4154yOd2lhr1cWZ+HvCXPGuDbpU6HoyVx/bH/qmm188LvrcymEEFw8sR9bCmvZmF/j8v464/QRsWwrqmV3qXsmSzscJqWE98nho2Yd++7oLnSg3F0H9JNS1gshTgG+ANI6bEyIa4FrAaKiosjIyOgWI+vr6/dra02xFjeU5VlkZOhfAnbBrlYE4FG6k4yMXW7r95MdrZgERDTlkJHhmotYUb2Dn7c1cXKC5PflS1zSh6JrHHgeKNzPofZBepiJF3/dQbJtLxYP13rzwm0SLw94/IvfuWqYl0v76oyQZgcCeO7LFZyV5tqCem0cznkwIEjwXWYOxwT0neRMPQVFPtD+sTMe2C8gJqWsbff+OyHEi0KIcCll+YGNSSlfAV4BGDt2rJw+fXq3GJmRkUH7tpZ/tw2LRw6XnjYdL7P+wxcf37SEcUkBnHbiJLf1KaXkgdUZTEsL5syTxrusn/sWbMTLXMDJqd501/5UHBkHngcK93OofWCOK+eS13+nIqA/F7q4BD7A4tqNfL6+gBcmTtGt0Nw7WcvIaYXp06e4pb/DOQ/2mLN55JutpI4Y7/bh/HqhZ8hjNZAmhEgWQliAC4Cv2q8ghIgWTn+6EGI8mr26TjW3fm8VQ+MCDSEmaputbCmsZXJqmFv73V1aT25FIycOiXJZHzWNVhasK+Ds0XEEeqncCYXiUExJDWN4fBAvL9qD3Q3VM88bm0Cz1cFPW/SrnHnMgAg25ldTZcC5PSYkhwJ/jArsC+gmKKSUNuBm4EdgG/CxlHKLEOJ6IcT1ztXmAJuFEBuAZ4ELpF5ZQECrzcHG/BpGGSR/InNvNVLC2H6hbu23rfTuzEGuExRfbSykxebg4gmqKqZC0RWEENxwbH9yKhrdMtfFyIRg4oJ9+M5NlTo74pgBEUgJS3f/yWmtO4OiA/D2NLEut0pvU9yGroP6pZTfSSkHSCn7SykfdX72kpTyJef756WUQ6SUI6SUE6WUy/W0d3txLS02h2ESMtfkVmESMDIx2K39/ry1hOHxQUQHuW7Y7Cdr8hgcE+jSESQKRW/jxCHRJIf78dpS1w8hFUJw6vAYluwqo6bR9aNLOmJEfDCB3mYW7zRe8qPZw8Tw+GDW51XrbYrbUFWCDoNNBVpG8/D4IJ0t0VibW8ngmED8vdyXClNW18L6vGqXeie2FWnZ4+eNde0IEoWit+FhElw8IZH1e6vZXuz68tinDovBapf8tFWf2T89TIKpaeEs3lWm2xDWgzE6MYSthTV9ph6FEhSHwe7SenwtHsQF++htCja7g/V7q90+n8hv20uREo5Pd90w1U/W5GPxMHHmSFVmW6E4XM4eHY/Fw8RHq/IOvfJRMjw+iPgQH7dNUNYRx6RFUFLbwq7Set1s6IxRicFY7ZIthfoNr3UnSlAcBnvKGkiJ8MNkgAJL24vraGy1u11QLNxWQmyQN+kxrglFtNocfL4+nxPSowjxc89QMIWiNxHqZ+GkodEsWJfv8ifjtrDH0l3lVDfqkxh5zABt7gwjhj1GOcPR6/tIYqYSFIfBntJ6UiP89TYDgLXORJ+xSe5LyGy22lmyq4zj06NcFor4dXsJVY1Wzh3runLeCkVv58LxCdQ229ySMHnasFhsDqnbaI/YYB9SI/1ZZEBBERngTXyIjxIUiv1parVTUN1Ef4MIijW5VUQHehPrwsTIP/WZU0Wz1eHSmUW/21RMqJ+FaWkRLutDoejtTEoJIynM1y1hj6FxgSSG+uoe9liVXWnIXIVRiSGs29s3RnooQdFF9pRp8bn+kcYQFGtzKhmTFOLWpMVVOZWYBIxNck2YpdXm4LftpRw/OFLN26FQHAVCCM4fl8iqnEqXl6YWQnDKsBiW7S53y4ynHXHMgHBabA5+N+DcGaMTgymqaaaopklvU1yOEhRdZJ+gMICHoqimicKaZsa4efjq6mxtVEmAi6rircyqoK7FxonpalZRheJomTMmHg+TYMG6Apf3ddygSGwOyYo9+tQdnJAchsXDxDID1qNoq1uU2QfCHkpQdJE9ZQ2YBCSF619CdXuR9sQxzI3DV1ttDtbnVTHOhTkbP20txtfiwdS0cJf1oVD0FSICvJiYEsr3m4tdPqRyVGIwfhYP3W7oPhYPhsQFkmnAmg/pMYFYzKY+EfZQgqKL7CmrJzHU1xAlt3c5XZhpbgy/bC6sodnqYHyyawSFwyFZuLWEYwdE4O2p/2+sUPQGTh4aQ3Z5AztKXBv28PQwMSElTNeKlSPig9mUX4PN7tDNho6wmE0MiwvqE4mZSlB0kT2l9YYIdwDsLKknIsCLYF/3Datc7YxNuspDsbGghpLaFpfOD6JQ9DVOHBKFEPD9JtcXnpqaGk52eQP5VY0u76sjRiYE02S1G7MeRUIwmwpqsBpM7HQ3SlB0AbtDklXeYJiEzF2l9W71TgCszqkkOdyPiADXTFX867YSPEzCpSNIFIq+RmSAN+OSQvl+s+tHYExzhiqX7tLHSzEiIRiADQYMewyJC6TF5iC3Qh+x5S6UoOgCBVVNtNoc9I/w09sUpJTsLqljQFSA2/p0OCSrc6oY68IiWiuzKhkaG+hWr4tC0Rc4eWg0O0vq9yWWu4rUSH+iAr10C3skhfkS5OPJhvxqXfo/GG3ebVfvA71RgqIL7CnXDoIUA4Q8CmuaaWi1k+pGD0V2RQM1TVaXDRdtttrJzKtmQop7p2FXKPoCs4Zqo6ZcPQOpEIIpqeEs31OBww3Tp3fU/4iEYDLzjFfmOkUJCkUbpbXNAMS4sYhUZ+xyJle500Oxo1jrMz3GNaNK1u2totXuYIKLEj4Vir5MTJAPIxOC+WmLe/IoKhta2Vrk+onJOmJkfBA7S+pobLXp0n9n+HuZiQ70Zk9pg96muBQlKLpAaW0LgMvyBw6HXSWawnVnDsX24jpMAtKiXNPn71mVCOHeMuIKRV/imAERbCqocXnhqampWh7Fyix96lGMSAjG7pBsKdRH0ByM/pF+ykOhgLL6FoJ8PA0zZDTc38utE2ftLK4jKczPZcM5f8+uID0mkCAf1xTMUij6OpP7h+GQsMrFlSQjndMBbMzXJ+wwPD4YMGZiZv8If/aU1RtymvXuQgmKLlBW12II7wToM8JjhwuTQFtsdtbvrWZCssqfUChcxajEYLw93VNJclh8EJsK9BEUEQFexAX7sN6ggqKu2UZZfYveprgMJSi6QFldCxH+xhAU+VVNJIa6r1pns9VOTkUDA6NdIyi2FdXRYnMwzkUJnwqFArzMHoxLCnVLaezh8cFklzfoNq/HiIQgNuskaA7GvpEevTiPQgmKLlBa10JkoP6Cwmp3UF7fQpQbk0N3ldQjJS4TFNudyVvpsYEuaV+hUGhM7h/OjpI6yupc+4Q8LE5L3t6i0009NcKfvMpGWm3GKiLVP1IrO9Cb8yiUoDgEUkrDeCjK61uQEqLcKG7aSva6zkNRi5/Fg4QQ/edIUSh6M5P7a2HFFS5OmGwTFBt1EhTJEX44JOytNFYRqehAb3wtHkpQ9GWa7dBktRsih6LEOdokOtCdHoo6LGYTSWGuKeq1rbiOgdEBmNR05QqFSxkaF0Sgt9nlYY8QPwsJoT5s0ikxs+1alV1urNCCEMKZmGksu7oTJSgOQU2LlpFrDEGh1cOIcqOgyK9uIj7YBw8X3PCllGwrqmVwjAp3KBSuxsOkFX7aVFDt8r6GxwWz0Q39dERyeJugMJ4noH+EH3sMONdId6EExSEwoqBwZz5HUXUT0S7K2Sisaaau2cYgJSgUCrcwJDaIHcV1Ls8vGBYfRF5lE1UNrS7tpyOCfS2E+lkM56EALTGzoLqJpla73qa4BCUoDkGboIgM0L9KZkltMx4mQbif+wRFcU0zMUE+Lml7m7P4THqM+6p+KhR9maFxgVjtkp0uns58aKyWR6FXxczkcD9DCookp/ckt9J4tnUHXRIUQojHuvJZb6TaUB6KFiIDvNyWb2B3SErqWlxWcjynQjupjDItvELR2xnSdqN3cSXJFOdEim3nuLsxqqBoC1e7eqSNXnTVQ3FCB5+d3J2GGJUmmyYojFDFsaS2mUg35k+U1bVgd0iXhTwKqpvws3gY4rdVKPoC/UJ98fcys7nQtQmT0YHeWMwm3abrTg73o6S2hYYWY83p0fZg2icFhRDiBiHEJmCgEGJju1c2sNE9JupLqx08PYRLkhIPl5LaZqLc6CkpqmkCIDbYRYKiqom4EB+E0P+3VSj6AiaTID020OWFn0wmQWKoL7k6eShSwo050qNPCwrgA2A28JXzb9trjJTyEhfbZgisDmmIOTwAqhqthPm7bw6PohotCTQ60DU5FIU1TcQGu6ZthULRMUNjg9haVIvdxVOMJ4X56uehiDCmoPCzeODj6dFnBYUHUAvcBNS1eyGE6BNTQ7Y6wNvTGLmrza12fDzNbuuvTVC4KoeioKqJOCUoFAq3MjDan2arg8LqJpf20y/Mj5yKBl0mw2qrRaGXh6QzhBBEBHj12vk8DnV3WgtIQACJQJXzfTCwF0h2pXFGwGrHEB4KKSWNVjs+FveJm6qGVkwCgn27P8ehsdVGVaNVeSgUCjeTGKrdbPdWNpLgwnmBksJ8abY6KK1rcWvtHABvTw8CvM2U17t/2OqhiAjw6pseCillspQyBfgRmC2lDJdShgGnAQvcYaDeWB0SLwN4KKx2id0h8bW4z0NR32LDz8vskhyHwmrN+xEfogSFQuFOEkK1c87Vpan7Ob0EOTqFHcL9vSg3oCcgwr+PCop2jJNSftf2j5Tye+BY15hkLKwOY3go2gqheHu6z5aGFhv+Xq4RMFWN2pNDqJ/7ckIUCgXEBPlgNgk3CArN+5Gr05waYX4WKozqoTCg0OkOuiooyoUQ9wshkoQQ/YQQfwNcPw+uAbDajZFD0WjVhj/5WtwnKBpb7S7rr75Z254AbzVkVKFwJx4mQXyID3kuvtHHOUv2u7qfzgjzt1DRYLwbd0SAF9WNVlpsva9aZlfvlBcCEcDnzleE87NeT6tD4mXWX1C0eSh83OihqHehh6K22QrgsvYVCkXnJIT6uvxGb/YwEezjSYUO5bcBwvy9DOuhAAxp29FyqDoU9wkhRkkpK6WUt0opR0kpR0spb5NSVrrLSD2xOtwbZuiMxjZB4UYPRUOLzWU5G3VOD0WgtxIUCoW7SQz1dcv03iF+Fl3m8wAI97NQ2djq8uGxh0tkgBcR9ZUEzjoeiov1NqdbOdSjdzZwqxBivRDiLSHE+UKIEHcYZhSsdmN4KJqt7vdQNLTa8XORB6FOhTwUCt2ID/GlqtHq8kqSob4WKnX0UEj5R76WUYgI8OIvyz7Eb9UKePhhvc3pVg56t5BSfgR8BCCEGAXMAhYIITyAn4EfpJSrXG6ljhjNQ+HOHAotKdM1/dU1W/EwCUPkpygUfY22AnlVja0ue2gACPHzJKdcvxwK0EIL4f76z8UEgI8Pw5ubGd72/7x52svbG5pcWxfEHXT5ai6lXC+l/LeUcgbasNEtwNUus8wg2BxgNul/07PatemGPT3cZ0uz1e4yMdU2gkSV3VYo3E/b/DnVjVaX9hPqDDvoQZhfW66CgRIzs7KwX3AhLRanwPH1hYsvhuxsfe3qJro62+gaIcRNbeEOKWWtlPIzKeW1rjVPf8ymP27metI2l4jNjfFAkxC4qsidXUpDzI+iUPRFgp2CoqbJtYIixFfLodCjWmZEgNNDoVPIpUNiYvAIDsLLZtW8Es3NEBgI0dF6W9YtdPVx9wIgFlgthPhICHGS6COPlmYTtNr0FxRtngmbG8WNh0lgd9GFQCB0ucgoFAoI9tVutq72UIT4WrA5JHU6zPoZakQPBUBJCVx/Paxcqf3tRYmZXQqeSSl3A38TQvwdLdzxBuAQQrwBPHOkIz6EELOAZ9DmDHlNSvmfA5YL5/JTgEZgrpRy3ZH0daSYTYJWA3go9gkKd3ooTOBwUX9CaDXdFQqF+2krp1/d5Nqn9xBn4bqqhlYC3ZyA3ZbA3myAB8L9WNCuyPQLL+hnhwvockBeCDEceBL4H/AZMAdt4rBfj6RjZ2LnC8DJQDpwoRAi/YDVTgbSnK9rgXlH0tfR4GkQD4XZQ3MIuVPceAhXeihwWThFoehtFNUVcWvmrRTXd8/TbJDbQh5aP1Uu9oR0hKfzmmk1wPW7r9DVHIq1wFPA78BwKeVfpJS/SymfALKOsO/xwG4pZZaUshVtNMkZB6xzBvCO1FgJBAshYo6wvyPC04QhKpp5mtpCHu70UAiXjeEWQoU8FIqu8sjiR9hUs4mHF3XPMENvTw+8zCZqXHyjb0vq1uOhzOxhwiSMkQPXVzhoyEMIcYfz7XzABsQAN7WlT0gpn5RSnn2EfccBee3+zwcmdGGdOKDoCPs8bMwmYSgPhVtzKITA4cKbvpITCsXB8XnUh2Zb877/562Zx7w18/A2e9P0t6MbZujnZaah1bW5DX8kk+tzDfX0MNGiBIXbOFQORYDz70BgHPCV8//ZwOKj7LujpM4D7zFdWUdbUYhr0cIiREVFkZGRcVTG7WvXYaOypq7b2jtSCuu1k2LD5i34VOxwS59NjY2UlDa5ZNuLClqwWm1daru+vl7337+vo/aBPrw39j3mZc3j15KlSNGCl8mLaeHTuKH/DUe9P2zWVvILCsnIcN20TLuqNO/uuvUbaM1zfz0fEw6yc/aSkVHSLe2p8+DgHKqw1UMAQoifgNFSyjrn/w8Cnxxl3/lAQrv/44HCI1inzdZXgFcAxo4dK6dPn36U5mm8mPkDnh7edFd7R0pOeQMszWDAwEFMHx3vlj6DNi4hJMib6dPHdXvb6607+TF3F9OOOfaQw0czMjJ0//37Omof6MfP3/zMLyW/4oEFq7SSlpjG2SceqWP4D7yW/UxMTCTTpw8/9MpHSNDeKvh9OUOGDWP6wEiX9dMZPksWEhUTw/TpQ7ulPXUeHJyulkhLBNqnA7cCSUfZ92ogTQiRDBSgDU296IB1vgJuFkJ8hBYOqZFSui3cAc6QR4v+LrM/Qh7uCxT4e5mpbXaNSzTQmRRW12zdN4RNoVD8mZKGEgLsJ3NqzGmE9ttMUX33XAJNAlwdiWgrCmh343WrPZ4eQuVQuJGuCop3gVVCiM/RQg5nAW8fTcdSSpsQ4mbgR7Rho29IKbcIIa53Ln8J+A5tyOhutGGjVxxNn0eC2QQtBsihsDjnE3FngmiwryfZ5Q0uabt9lrkSFApF5yw4fwEpmd8S7unJc6fe0G3tmlycIwXGyKEwwrD/vkJX61A8KoT4Hpjm/OgKKeX6o+1cSvkdmmho/9lL7d5L4Kaj7edoMMqw0WAf7aZb2eC+4VchvhbWNVa7pG13DVtTKBQdowkK1/bRNnTTnfVz2mMxmwxx/e4rdHlWGGdBKbcWlTICRhk2ajGbCPA2U9ngvqpvwb4WahqtSCm7fc6NNkFR2+T+CnoKhcJZXM5NHgq9phC3eJhUyMON6D/rlcHx9RQ0Wx37pg/XkzA/i1vr0of4etJqd+yb6bQ7UR4KhaJr2B0Sh+z+i7UQuDzk0ZZDYdUth0J5KNyJEhSHIMiiKexyA9SDD/WzUOlWQfHHFMfd37YmKNzpcVEoeiL1zsRoX8/u9RI2tTrwsbh2KGfrvlmS9Zn6ye6QeBhgtui+gvqlD0GgV5ug0H/GulA/L7cKiiBf101xHO7vhcVsIr/q6IrzKBS9ndpm7fzz7XKAumvUt1jx9+rmRg+gyend9LO4tp/OaLba8fZUtzl3oX7pQxDUJijq9H+Sdn/Iw3UeCpNJEB/sowSFQnEI9gmKbvRQ2OwOmq0O/L1cO2FXWyVOXxd7QjqjyWrfN0mYwvUoQXEIDBXy8LdQ1dDqtjkwIgO06X+La5oPseaRERfiQ15Vo0vaVih6C22Jyz7m7hMUDS2a58Df2z0eCl8Xe0I6Q/NQKEHhLpSgOAQBBhIUYX4WbA7ptpERscE+mATsrXTNTT8h1Jc8F7WtUPQW6lwQ8qh3eg4CXHyjN4SHQqe++yJKUBwCi4cgwNtskBwKLQRR4aZERovZRGywj8sERXyID1WNVupb1NBRhaIzqpu6P+TRlujp52JB0ej0hOghKKSUNFsdeJvVbc5dqF+6C0T4e1FmBA+FvxaCcKe46RfmS26FizwUIb4A5Kuwh0LRKYXVTQgBId7dKCicIt7VIY/GfR4K94c82ioceysPhdtQgqILhPt7GSIpMzFUuwHnVrimHHbHffq5zEORHO4HwO7Sepe0r1D0BvKrmogM8MLzEJPoHQ7VzkTrtnowrqKhVT8PRVvtIG+zEhTuQgmKLhAeYDFEDkV8iA8eJkGOWwWFL5UNrfviuN1JWpQ/ZpNga2Ftt7etUPQWCqqaiHd687qLwmptdFVskHe3tnsgTa12TAK8dAg7NDkFhcqhcB9KUHSBcH8vQ+RQeHqYiA/xIafcfSGCfmHahcwVXgovswepkf5sUYJCoeiU/OpG4oJ9urXNwppmPD0E4c4wqquoamwlyMez20v3d4VmqzPkoepQuA31S3eBcH8vapqshijhmhTm53YPBcBeF+VRpMcGKkGhUHSC3SEpqm4mPqSbBUV1E9FB3pi6MYzSESW1zUQFutYL0hltQ1ZVHQr3oQRFF4h2ugXb3IR6khzuR055g9tqUSS5OM9hSGwQ5fUtlNa5ptaFQtGTKa5txuaQxHWzoCiqbiY2qHvb7LCfmmZiXBxW6Yy2gmCuLt6l+AMlKLpA/wjtpppVrn/yYFKYLw2tdreNOvH3MpMc7sfmwhqXtD8kNhBAeSkUig7YUaydFwOiArq13YLqJmK7OYzSESW1zfseyNxNqTORPjLQtWEdxR8oQdEFUsL9Acgqc1+ooTPaPAbuzKMYGhfE5gLX3PDT2wRFgWsEi0LRk2lLWB4U3X2Cwu6QlNQ2Exvs2ht9q81BeX2rbiGP0lrN6xkVoE//fRElKLpAiJ+FEF9P9hhAUCTvExTus2VYXCAF1U0umZgs0NuTtEh/VuVUdXvbCkVPZ1tRHf3CfAnw7j63fWmdFkaJcXHIo8R5Q9cr5FFa14LFbCLQR5+y330RJSi6SEqEP1ll+oc84oJ9MJsE2W5MzBwaFwTAJhd5ESb1D2NNTiVWu/5JrwqFkdhaVEt6TGC3trmrRLuOpThDua6iTVDo6aGIDPDSZYRJX0UJii6SEu5Hlhu9Ap1h9jCRGOrrVnHTJig2u0pQpITR2GpnY361S9pXKHoi9S02cioaGNzNgmJHcR0Ag6K7t90DKXJOKqhnDkXbBIcK96AERRdJifCnrK7FJQWeDpf02ECX5TR0RKC3J0lhvmzKd42gmJgSBsDy3RUuaV+h6IlsL6pFSrrdQ7GtuJbIAK99cwO5in0hj0DXJ3921r9e3pG+ihIUXaTNPZhtAC/FiPhgCqqbKHNjOfAhcUEuC3mE+FkYHBPIiiwlKBSKNtbkanlFIxKCu7XdHcV1DOpmkdIR+VVN+Fk8dMthUB4K96MERRfZN3TUAImZw+O1EIQ7QwQj4oMoqG5yWb2ISSlhrM2tosVmd0n7CkVPY8WeCtIi/Ynoxpuize5gV2l9t44a6YydJXWkRgXoVCXTTl2zjUjloXArSlB0kcRQPzxMwhCJmUPjgjAJ2OCiEERHtIUlVuxxjRdhSmoYLTYHq7IrXdK+QtGTsNodrMmp3HfedRc5FQ202hxuExQDIv1d3k9HlNY6a1AoD4VbUYKii1jMJhJCfNhjgJCHn5eZtMgAt3oohsQGEeTjybLd5S5pf0pqOD6eHvy4pdgl7SsUPYnNBTU0tNq7XVBsK9ISMge6WFBU1LdQXt/q8n46o8TpSVUeCveiBMVhoA0d1V9QgBb22Jhf47YS3B4mwaSUMJbtrnBJn96eHswYFMGPW0pwONyzTQqFUVmZpXnqJqSEdmu7mwtqsHiYSHWx52Cnc2hqWjdX+OwqbdMkRCtB4VaUoDgM0iL92VNWb4hJwoYnBFPZ0Ep+lfvmF5mSFk5BdRO5Lpoo7KQh0ZTVtbBurypypejbrMjS8ie6ezbQ37MrGZEQhJfZtRNm7Sp1ekJ0EhR7SusxCUgK795p3xUHRwmKw2B4fDCtNgfbi/Wfd2LEvsRM9+VRTOmvuV+XuijscdygSCweJn7YrMIeir5LfYuNlXsqmJYW0a3tNrTY2FxQw/jk7vV6dMSO4joCvM1E6TSPxq7SevqF+blcOCn2RwmKw2BkYjAAmXnVutoBWlEai4fJrXkUyeF+xAZ5s3yPawRFgLcnU9PC+X5zsdtCOQqF0cjYUUqr3cFJQ6K6td31e6uxOSTjk7s3L6MjdpXUM1CnER6gzY7cP0KfhNC+jBIUh0FskDcRAV5k7q3W2xQsZhODYwPdGh4QQjA5NZzleypclucwa2g0BdVNLqt5oVAYnR+3lBDmZ2FsUvd6ElZlV2ASMKZfSLe2eyBSSnaW1umWP2G1O8ipaCAtSgkKd6MExWEghGBkQjDrDeChAC0EsX5vNfUtNrf1OS0tnOpGK5ku8oyclB6NxWzi07X5LmlfoTAyLTY7v20v5YT0KDxM3ft0/3t2JUPjgvD3cm2hqaKaZqobrQzU6YaeW9GI1S5JVR4Kt6MExWEyKjGY7PIGqhu7f+bNw2VqWjg2h2Sli2pDdMT0gZF4egiX5TkE+XpyytBoPl9fQLNVFblS9C2W766gvsXGSUOiu7XdFpud9XnVjO9mr0dHtFX4HNPP9X11xO5SbYSJq0eyKP6MEhSHyUhnGVwj5FGM6ReCj6cHS3aVua3PIB9PpqaG8+3GIpflOZw/LpG6ZhvfbSpySfsKhVH5YXMx/l5mJqd2b55D5t5qWm0OxrkhIXNtTiW+Fg8Gx+g0wsNZfLC/EhRuRwmKw2R4fDBCGENQeJk9mJgSypJdrkmS7IxThsVQUN3kshEmE1NCSQrz5aPVeS5pX6EwIk2tdr7bVMSJQ6K6fXTCL9tL8fQQTO7v+oTM1TlVjE4Mweyhz+1lV0kdsUHeLg/tKP6MEhSHib+XmQGRAaw3QGImwLS0CLLKG8ivck1tiI44MT0as0m4zIMghOC8cQmsyq40RKlzhcIdfLepiLoWG+ePTejWdqWULNxawqT+4QR4e3Zr2wdS22xle3GtyxM/D8busnpSdUoI7esoQXEEjEwIZkN+tSGGNk5LCwdgqRu9FEG+nkxJDee7za4Le8wZHY+HSTBfeSkUfYT5a/JIDvfr9joRe8rqyS5v4IT07h2G2hHr91bjkDDODbkaHeFwSPb8f3v3HR5VtTVw+Ldn0nvvvdMhhN5Bqg0UFAsoigV7Qa9ey1Wveu29IhaUKkoVpAmh1xACgZBCEtJI7z2ZOd8fCX5eb0CEzJxJst/n4UkyDnMWnszMmn3WXquwRhZkqkQmFJehX4AT5bVNZBqoY+TfEeZhh5eDldEve1zdy5vs0joScw3T5MvDwYrx3TxZfjib+mb1EzdJMqSM4hoOZZQyI8av3Xs3bDlVAMD4boZPKI5klqLViN979hhbdlktdU06uWVUJTKhuAz/3+BK/RbRQghGhLuxJ60YnRFnYEzo4YmZRrDBgIWT94wMoaKuiZ05xtsWK0lq+PFINlqNYHq0X7s/9tZTBfT2c8TL0fBzLQ5nltLd20G1+oXzfXnOF89LxiUTissQ7mGPvaWZyYzaHh7uRkVdk1GbQTnZWDAszI21x3INlsj0D3RmYJALmzObaNKpPz9FkgyhsVnPT3E5jIl0b/fpmIWV9RzLLucqI6xONOn0HMsuJyZIvfqJo2fLW+rcZA2FKmRCcRm0GsHQMFd2pRSbSB2FOxoBW08ZdwbGzAH+nKuoJza50GDHuH90CKX1CuuO5RnsGJKkprXHcimqamDWkKB2f+xtSYUoCkapn0jILqe+Sa9a/QRA3Nky+vo7tXtTMOnSyITiMo2K8CC3vO73Pc9qcrG1YGioG78YsDdEW67q7om7vSXLDmUZ7BhjIj3wsxN8ueuMSSRvktSe9HqFBbvSifKyZ2RrgXV7WhOfS4ibLVFehv/Evv10IWYawbCw9v93XIrqhmZO51cSreIOk65OJhSXaWREy5MmNtl4TaUu5pre3pwtqTVYkWRbzLUaborxY/vpQvLKDTNGXQjB5GBzUgqq2WHAlRBJUkNsSiGphdXcNyqk3YsxM4trOJRZyo3927/Qsy2/JRUyIMgFR2vDbk29kOPZLTtMolUqCJVUSiiEEC5CiK1CiNTWr22mlEKITCHECSHEMSHEEWPHeTF+zjaEedixM8U0EopJPVt6Q/xywriXBmYOCEABg27vHORthq+TNe9vTTXYUDJJUsMXO9PxcbTimt4+7f7YPx/NQSPgRgMUev5ZdmktyQVVjOvmYfBjXUhca8vvfgFyhUItaq1QPAP8pihKOPBb688XMkZRlL6KosQYJ7RLNyrCnYMZpdQ1qj9zwsnGguHhhm2J3RZ/FxtGhLvz45Fsmg1UOGmmETwxPoITuRX8IttxS51EfFYZhzJKuXtECObt3FVSr1f4OS6H4eHuRtndsf10y+rhOCMUf15IXFYZEZ52qq2QSOolFNcDi1q/XwRMVSmOKzIqwp3GZj0HMow3nOtiruntQ05ZndHbgt86MKC1ONNwqzVT+/kS5WXPO5uTaWyWOz6kju/j7Wk4WJlx84D27YwJsO9MCXkV9czob/jVCYBtSQWEuNsS7GZrlOP9mV6vEJ9VTrRcnVCVWgmFp6Io5wBav15onUwBtggh4oQQ9xotuks0MNgFK3MNO02kjmJCD08stBp+OW7cT/Hjunngbm/J4oNnDXYMrUbwzOQoskprWWrA40iSMRxML2H76ULmjQ4zSM+GlXHZOFiZGWV3R3VDMwfTS42yNfVC0ourqahrkgWZKjNY9xEhxDagrRm8z/2NhxmmKEqeEMID2CqEOK0oyq4LHO9e4F4AT09PYmNj/27Ibaqurr7oY0U4CjYdO8toB9NIKnq4ClYdzmSYbQEaIxRinTfcU8/q5CIWr9+On3375qnnz4GiKHRz0fDuplN41mVibSa3hhnLXz0PpEunKAqvHqjHyVIQossiNvbS6o8u9RzUNilsPF7LCF8zDuzdfYXR/rUj+c006vS41OcRG1tg8OO1ZVdOEwC6/FRiY88Y7DjyeXBxBksoFEW56kL/TQhRIITwVhTlnBDCG2izfF9RlLzWr4VCiNXAQKDNhEJRlAXAAoCYmBhl9OjRV/gvaBEbG8vFHivTPIOX1p8ipNdAAlxt2uWYV6LCKZdHlx/DPriPUfeD9x3YyOY3tnOkxpnbr+3Xro/9x3PgGl7OdZ/s5aTOh/lXRbbrcaQL+6vngXTpNp/M50xFHG/c0IuJAwMu+e9d6jlYuDudJn0Sj18/mF5+jlcQ6aX5ZWUCjtYFzL1+jGoTRtf/mICTTQEzrx5j0B0t8nlwcWpd8lgH3NH6/R3A2j/fQQhhK4SwP/89MAFINFqEl2hUZMvVmp2pprFCMa6bJ5ZmGtYeyzXqcZ1sLLhtUADrEvLIMuCMk95+TlzXx4cFu9PJKK4x2HEkyRCadXre2nSaUHdbphugvqFZp+fbvZkMDHYxSjLR2Kznt6QCxkS6q5ZM6PUKO1OKGBHubpTtsdKFqZVQvAGMF0KkAuNbf0YI4SOE2Nh6H09gjxAiATgEbFAUZZMq0V5EkKsNAS427DSRHgl2lmZM6eXNmvg8ahqMOwNj7ogQzDQavtxluCVHgOeu7oalVsPza07IZldSh7IyLoczRTU8NTHKIG/AGxPzyS2v454RIe3+2G3ZkVxIWW0T1/fzNcrx2pKYV0FxdQNjIt1Vi0FqoUpCoShKiaIo4xRFCW/9Wtp6e56iKFNav09XFKVP658eiqK8pkasf0UIwdgoD3anFlNV36R2OADcPjiA6oZm1hq5XbWngxU39vdj5ZEcCivrDXqcpydHsTethDVGXomRpMtVWtPIW5tOMyDImYk92r+AUVEUvtqVToibLeOijNMPYtXRHNzsLBmhUndMgB2nixCiZdedpC7ZKbMdXNvHm4ZmPVtPqVOQ9GfRAc5Eedmz+MBZo3+Cv39UCM16PV/vyTDocW4bGEBffyf+/UsSZTWNBj2WJLWH/2xMoqq+mVen9jLI0vzBjFJO5FZw94hgNEaYZVFW08j204VM7euj2uUOgO3JhfTxc8LVzlK1GKQWMqFoB9EBzvg6WbMuwTQGWAkhuH1wIKfOVRJv5J4Uga62XNPbh8UHzlJea7g3eo1G8J8belFZ18Qbv5422HEkqT0cTC9hZVwOc0eEEGmguRoLd6fjYmthlM6YAOuP59GkU7jRSL0u2lJc3cDxnHLGGmlFRro4mVC0AyEE1/X1YXdqMSXVDWqHA7Q0grK10LL4gPF7NjwwJpSaRh1f7ko36HG6eTswd0QIK45ksy+t2KDHkqTL1dis57k1ifg5W/PouHCDHONMUTXbkgq5fXAgVuZagxzjz34+mks3bwe6eTsY5Xht2ZlchKK0DBGU1CcTinZyXR8fdHqFjYnGHSF+IXaWZkyL9uWX4+eMfkkgysuBaf18+XpPBrkGGhp23qPjwglxs+WJHxMMuiIiSZfrq93ppBVW88r1PbC2MMyb/YfbUrE21zJ7SKBBHv/P0gqrScgu58Zo9YoxoaUo1N3ekh4+6iU10v+TCUU7ifKyJ9zDjvVGLoS8mNsHB9LYrOenuByjH3v+xJYeEe9uTjbocawttHw4sx8lNQ08u0ru+pBMS9K5Sj7clsrknl6MjTJMJ8lTeZWsS8hjzrAg3IxUR7DqaA5aTcvKrFqadXp2pRQxOsLdKDUj0l+TCUU7EUJwfV8fDmWWGvxT+aWK8nIgJtCZxQfPGn1Kp6+TNXcPD2ZVfC6JuRUGPVYvP0eenBDJr4n5/HjEcFNPJenvqG/S8djyYzhYm/Pq1J4GO847W5JxsDLjvpGhBjvGH+n0CmvicxkZ7oaHveEHj13I0axyKuubGSPrJ0yGTCja0bV9WrL1X0ykOBNaVinOltSyW4Uag3mjQ3GxteC1DUkGXzm4d0QIQ0NdeWndKc4UVRv0WJJ0Kd749TTJBVW8M6O3wXYgHMksZfvpQu4fHYqjjXGmbG4/XUheRT3T+7f/ULO/G4eZRjA8XL0tq9J/kwlFOwp0taWPv5PJ7PYAmNzLCw97S74wYH/7C3GwMufRceHsTy9hh4Ebf2k0gvdu6ouluYZHl8fLiaSSqmKTC/luXyZ3Dg1itIEKBhVF4a3NybjbW3Ln0CCDHKMtX+9Jx9fJ2iC9NC6VoihsOZXPgCAXHKzkuHJTIROKdnZ9Hx9O5lWSVmgan5ItzbTcOzKE/eklHMksNfrxbx0UQLCbLf/ZeJpmnWHf5L0crXjjht4k5lbyr3WJsp5CUkVJdQPzVx4n0tOeZyZHGew4O1OKOJRRysNjw7CxMNhYpv9yMq+CA+ml3DE0UNXeEydyK0gvqlG1hkP6XzKhaGfX9PZGIzCpVYpbBwXgYmvBJzvSjH5sc62Gf0yKIrWwmu/3G34L66SeXswbHcqyQ9mqbJmVurZmnZ5Hlx+jsq6JD2b2NdgWTp1e4e3Nyfi7WDNzwKUPGLtS3+zJxMZCy81GPGZbVsfnYqHVMKWnt6pxSP9NJhTtzMPBisEhrqw9lmv0QsgLsbEw4+7hwcQmF3Eix7AFkm2Z2MOT0ZHuvLMl2SgFq/MnRDI2yoOX159i/5kSgx9Pks5749fT7Ekr5tWpPQ3an2HpwbOczKvkqYlRWJgZ52W8sKqe9Ql5zOjvh6O1epcZmnV61ifkMTbKw2h1I9KlkQmFAdw8wF+1QsgLmT0kEAcrMz7ZkWr0Ywshfq9yf2GN4S9FaDWCD2b2JdDVhgeXHiW71HDTTyXpvFVHc1i4J4M7hgRy0wDDFSwWVTXw1uZkhoW5cm1v431CX3wgiya9njuHBRvtmG3Ze6aE4upGpqo4kExqm0woDGByT2/c7Cz5fl+m2qH8zt7KnDuHBbP5ZAHJ+VVGP76fsw1PTohk++lCfjl+zuDHc7Ay56vZMTTp9Nzz/RGjT16VupbjOeU8s+oEg4JdeP6a7gY91n9+TaK+Sccr1/c02rju+iYdSw6cZVyUB8FutkY55oWsic/FwcqMMVFyGJipkQmFAViYabhloD/bkwtN6tPxnKFB2Fpo+VSFWgqAO4cG0cfPkZfXnzRKV8sQdzs+uTWalIIqHlx6VO78kAyiqKqB+36Iw93Oks9ui8bcgMWKB9JLWHU0l3tHhhDqbmew4/zZumN5lNQ0ctdwdVcnahqa2ZSYz9W9fbA0M06LcenSyYTCQG4dFIBGCJMqDHS2teD2IYH8cjyPdBV6NWg1gv/c0Juy2iZe35hklGOOinDntWm9iE0uYv7KBJOpa5E6h+qGZu767jBltY18Oau/QSdeNusVXliTiK+TNQ+NMcxMkLbo9Apf7U4nysueISGuRjtuW7aeKqCuScc0ebnDJMmEwkC8Ha2Z0N2TFUeyqW/SqR3O7+YOD8Fcq+HTHcbvSwHQ3ceBe0eG8OORHKMN9LplYABPT4pkXUIeL60/KbeTSu2ivknHvd8f4dS5Sj67LZqevo4GPd6Ws02kFlbz8nWGmwnSll+O55FaWM3DY8ONdonlQlbH5+LrZE1MoLOqcUhtkwmFAc0eEkR5bZNJbSF1t7dk9pBAVsXncCqvUpUYHh0XTpCrDU/9dJyKuiajHHPeqFDuHRnC9/vP8sE24xemSp2LTq/w+Ipj7DtTwtvTextsTsd5Z4qqWZPaxFXdPLiqu/EaSjXr9Ly/NYVu3g5M7ulltOO2paiqgd2pRVzf10fO7jBRMqEwoMEhLkR42vH9/kyT+lT80JhwHK3NeXXDKVXisjLX8sHMfhRU1vPsquNGiUEIwbOTo7gpxo8Pf0vl270ZBj+m1DkpisLzaxL5NTGf56/uxg3RfgY9XpNOz+MrjmGuhdem9TLosf5s1dFcMktqeXJ8hOpv4usS8tAryMsdJkwmFAYkhGDW4EAScyuJzy5XO5zfOdqY89i4cPadKWH7acO2xL6Qvv5OzJ8YycYT+Sw/bJyBXkIIXp/Wi4k9PHl5/SkW7k43ynGlzuN8u+tlh7J4YHQoc0eEGPyYH29P43hOBXf2sMTTwXjDuBqadXz4Wyp9/J0Y103dAVx6vcLSg2fp4+dIuKe9qrFIFyYTCgObFu2HnaUZPxihS+TfcdvgQELcbXltYxJNBm6JfSH3jghhRLgbL68/SWqBcbaymmk1fHxLNFN6efHqhiQ+/i3VpFaPJNOlKAqvbUji89gz3DYogKcmRhr8mEezyvh0Rxo3RPsywMs47bXPW3E4m9zyOuZPiFC9dmJPWjFnimq4c1iQqnFIFycTCgOzszTjxmhfNhw/R3F1g9rh/M5cq+G5Kd1IL6phiUo7UTQawbs39cHWwoyHl8UbrXjVwkzDRzP7cUO0L+9uTeHNTckyqZAuSq9XeGFtIgv3ZHDn0CBenWr4HhA1Dc08seIYXg5WvHRdD4Me68/qGnV8vD2NgcEuDA9Tf5rnt3szcLOzZEov2WrblMmEwghmDQmiUadn2cEstUP5L2OjPBgW5soHv6VSUWuc4sg/87C34p2b+nA6v4rXNhhnKym0rFS8M70Ptw0K4IudZ3hp3Um5pVRqk06v8PTPx1l8IIv7R4Xyr2u7G+UT+6sbkjhbWsu7N/Ux+kTNxQfOUlTVwJPj1V+dyCiuYUdyEbcNCpC9J0ycTCiMIMzDjlER7nyzN8OkOjYKIXhuSncq6pr4eLt6Ox/GRHowd3gwPxw4y8YThu+ieZ5G09IS/N6RISzaf5YnVybQ0Gw6W3wl9TXp9Dy24hg/xeXw+FUR/GNSpFHeYH89cY5lh7K4d0QIg43c+6GyvonPd55hRLgbg1TuOwGwaF8m5lrBbYPUHUgm/TWZUBjJI+PCKattMqlGV9DSF+Km/v4s2p9JRnGNanE8NSmSvv5OPPljAifzjDfA7Pzuj/kTIlgdn8vtCw9SYkKXpiT1VNQ2ccc3h1ifkMezk6N49Crj9GFILahi/soE+vo78cSECIMf788+2JpKWW0jT0803Oj1S1VV38RPcTlc3csbDyMWpEqXRyYURtI/0JkR4W4s2JVObaPprFIAPDkxAnOthldUbPpkaaZlwaz+OFqbc8+iIxRVGe9NXQjBQ2PD+eTWfhzPqWDqZ3tJMVKRqGSaMotrmPb5Xo5klvHeTX24b1SoUY5bWd/EvT/EYW2h5fPbo42+xH86v5JF+zOZOSCAXn6GbdR1KX6Oy6G6oZk5Kg8kky6NTCiM6NFx4ZTUNLLUxGopPOyteGJ8BDuSi1RtwuXhYMVXs2MorW3k/sVxRr/8cE1vH1bcN4T6Jj03fraP2GR1ttRK6jqYXsLUz/ZSVtPI4rmDDN5n4jy9XuGJFcfILq3l01uj8Xa0Nspxz1MUhRfXnsTeyoynjbCD5a/o9QqL9p+lX4ATffyd1A5HugQyoTCimCAXhoa68sXOdOoaTeta/ZxhwfTxd+Ll9adUXfLv5efIuzP6Ene2jOdWG37U+Z/19Xdi7YPD8HOx4a7vDrNwd7rcAdKF/BSXw+1fH8TV1oI1Dw5jYLCL0Y798fY0tiUV8vzV3VSpXViXkMehjFKemhiJs62F0Y//ZztTisgoruHOoUFqhyJdIplQGNmj48Iprm5g2SHTWqXQagRv3dibqvomXvnllKqxXN3bm8euCuenuBwW7jZ+R0sfJ2t+un8IV3Xz5NUNSdzzfZxRpqNK6qlv0vHP1SeYvzKBgcEurJo3jEBX443p/i2pgA9+S+GGaF/uUOENtKq+idc2JNHL15GZA0yj+PHbfZl42FsyuafcKtpRyITCyAaFuDI4xIUvdp4xqaFhAJFe9jw4Joy1x/L4LalA1VgeGRvO1b28ef3XJI4VGr/mxNbSjC9n9eeFa7qzM6WQKR/u5nBmqdHjkAzvTFE1Uz/dy9KDWdw3KoTv5gzE0cZ42zRP51fy2PJj9PBx4PVpvVTZpvnRb6kUVjXwyvU90JrAnIykc5XsSili1uBALMzk21RHIc+UCh4ZF05hVQPLTWyVAuCB0WFEetrz3OpEqurV6U0BLVs635nRh54+jnx6rIGD6SVGj0EIwd3Dg/l53lDMtBpmLjjAJ9tT0cl+FZ3G6vgcrv14D4VVDXw7ZwDPTu6GudZ4L4s5ZbXc8c0hbCy1fDkrBitz4/dZSC2o4tu9mdwc40+/ANOY4vnBthTsrcyYPSRI7VCkv0EmFCoYEuLKwCAXPjfBVQoLMw1vTu9NYVU9b/x6WtVYrC20fDdnAG7WgrsXHeFEjvG2k/5Rbz8nfnlkOJN7evHOlhRmf3OQ7NJaVWKR2kdVfRNPrUzg8RUJ9PRxZOMjIxgTadx5FWU1jcz+5hC1jToW3TUQXyfjFmHC/3cAtbHQ8vQk9QsxARJzK9h8soC7hwcbdaVIunIyoVCBEIJHrwqnoLKBlUeMMxjr7+jr78Rdw4JZcjCLAyqsDPyRq50lTw2wwtHanNnfHDTazI8/c7Ay5+Nb+vHGDb2Izypn4ge7+HZvhlyt6IB2JBcy8f1d/HQ0h4fGhLH0nkF4ORq3x0FtYzN3LTpMTlkdC2fHEOXlYNTjn/fDgbMcSC/l2SndcLWzVCWGP/tgWyoOVmbcNVxuFe1oZEKhkqGhrvQPdOazWNNbpQB4YkIE/i7WPPPzcdX7ZrhYaVgydxBmWg23f63e6oAQgpkDA9jy+EgGBLnw8vpTTP9in2pJjvT3lNU08sSKY8z59jC2lmb8PG8o8ydGYmbESxzQ0n3zoaXxJGSX89HMfqp1o0wvquY/vyYxOtKdmQP8VYnhz47nlLMtqYB7RoQYvd24dOVkQqESIQTzJ0RyrqKer3aZ3hhtGwsz3rqxD2dLa3lx7Um1wyHIzZYf7h5IfZOe2xYepKCyXrVY/Jxt+G7OAN6/uQ+ZxTVM+Wg3H2xLobFZnamt0sUpisKG4+cY//5O1iXk8cjYMH55ZDjRKtQLKIrCP1edYPvpQl65vieTenoZPQaAZp2eJ35MwNJMy5s39lZ9Xsd5H2xLxcnGXE4V7aBkQqGiIaGuTOrhxWexZ8ivUO8N8kKGhLry8JgwforLYdXRHLXDIcrLge/mDKC4uoFZXx80ajfNPxNCMK2fH1ufGMXknt58sC2VCe/vZFPiOdm3woSkFFRxx7eHeXDpUbwdrVn30HCemBCpypApvV7h+TWJrIzL4ZFx4dw+ONDoMZz35a50jmWX8++pPfE0kZbWx7LL2X66kHtGhGAvVyc6JJlQqOyfU7qh0yu8tUndAsgLeWRcOAODXXh+TSJniqrVDod+Ac4svCOGrNJabv5yP7nldarG42ZnyUe39GPRXQMx12q4f/FRbv7yAAnZ5arG1dUVVzfw3OoTTPpgF8eyynj+6m6sfmAo3X3UqVXQ6xWeXXWCJQdbJpY+flW4KnEAnMyr4INtKVzT25vr+vioFsefvb81BWcbc1X6cEjtQyYUKgtwteHuEcGsis8lPqtM7XD+h5lWw0cz+2FppuHBJUdNot5jaKgbP9w9iKKqBmZ8vo90E0h0RkW48+ujI3htWk/Si6u5/tO9PLo8npwyuRvEmOqbdHwee4bRb8ey/HA2s4cEsfOpMcwdEWL0WonzdHqF+T8lsOJINo+MDTPaxNK2NDTreGJFAk42Fvz7+p6qxNCWuLNl7Ewp4r5RodhZmqkdjnSZZEJhAh4cE4a7vSWv/HLKJJfLvRytePemPpzOr+LVDep20TxvQJALy+4dTEOznpu+3M+pvEq1Q8JMq+G2QYHsmD+aB8eEsikxn7Hv7uSFNYlym6mB1Tfp+OHAWca9u5M3N51mcIgLmx8byUvX9VC1jXSzTs/jK46x6mguT4yP4IkJ6iUTAO9tTSG5oIq3buxtEu21z/tgWwquthbMHqLeZSDpysmEwgTYWZrx1MRI4rPKWXtMveFcFzM2ypN7R4aw+EAWG0+cUzscAHr6OvLj/UMw12qYuWA/cWdNo5OlvZU5T02MYsf80dzQz5flh7MY804sT/6YQFqh+qspnUltYzMLd6cz8q0dvLAmEU8HS5bMHcTCOwYQ5mGnamxNOj2PLI9nXUIeT0+K5JFx6l3mANibVsyCXencMtCfMVHG7blxMfvOFLM7tZj7RoVgYyFXJzoymVCYiOnRfvTydeSNX0+rvk3zQuZPiKSPvxP/+Ok4WSWm8Yk71N2OlfcPwdXOktsXHmJParHaIf3Ox8maN27sza6nxzB7SBAbTuQx/v2dzFscp1qTrs6ioq6JT7anMuyN7by6IYkwDzuW3jOIn+cNZViYm9rhUdPQzH0/xLHxRD7PX92NB0aHqRpPXnkdDy+LJ9Tdjuev7q5qLH/UrNPz8rpT+Dlby66YnYAqCYUQYoYQ4qQQQi+EiLnI/SYJIZKFEGlCiGeMGaOxaTSCF6/tTn5lPV/sNL1tpNDSRfOTW/qBgIeWmUY9BbRs4/zxviEEutow57tDrDhsWi3NvR2tefHa7uz9x1geHB3GntRirv1kD1M/3cuPR7JNNoE0NYqikJBdztM/JTDo9W28syWFfgHO/DxvKEvvGczQUDeT2P5YUFnPTV/uJza5kFen9mTuiBBV42lo1jFvyVEam/V8cXt/bE2oRmHJwSySC6p4/uruqrQdl9qXWisUicANwK4L3UEIoQU+BSYD3YFbhBCmk1obwIAgF67p7c2XO8+ovnvhQvxdbHhnRh+O51Tw9E/HTabmw93ekhX3DWFwiCv/+PkEr6w/RbPOtPpCuNpZMn9iJHufHcsL13Snqr6Jp386zqDXf+PFtYmczle/DsQU1TQ0s+xQFtd+sofrP93LL8fPMa2fHxseGc43dw6gf6BpzJ+AlqFWUz/dS2ZxDV/fMUDVraHnvbL+FAnZ5bwzo7fql4H+qLSmkXe3JDMi3I2JPTzVDkdqB6qkqoqiJAF/9WliIJCmKEp6632XA9cDplEVaCDPTunG1lMFvPHraT6+pZ/a4bRpYg8vnp4UyVubkgl1t+NRFbfA/ZGjtTnf3jmA1zYm8c3eDNKKqvn4ln44WpvWnnYHK3PuHh7MXcOCOJRRyrJDWSw/nM33+8/SL8CJa3v7MLmXF96Oxp/tYCqadHr2phWz4fg5NiXmU9XQTJSXPf+e2pOpfX1Msk9BbHIhDy2Nx87SjB/vH0IPH0e1Q+KnuByWtE5RnWRiY8Df3pxMbaOOf13b3SRWlqQrZzprX//LF/jjoIscYJBKsRiNr5M1940K5aPfUpnR34+REe5qh9SmeaNCOVNYw/vbUgh2tzWZ/exmWg3/urYHkZ72vLA2kWmf7WXh7BhC3E3nk9l5QggGhbgyKMSVf9U08vPRHH6Ky+GVX07xyi+niA5wYkovbyb19MLP2UbtcA3uj0nEllMFVNQ1YW9pxoQeXtw6yJ/oAGeTfeNZcvAsL649SYSnPd/cGWMSyeDJvAqeW32CISGuPDXBNAZ/nZeYW8Hyw1ncNSyYMA97tcOR2okw1JK1EGIb0FZf2ecURVnbep9YYL6iKEfa+PszgImKosxt/XkWMFBRlIcvcLx7gXsBPD09+y9fvrxd/h3V1dXY2Rn3zahRp/DSvjoadPDqcGuszUzzRbRJr/D24XrSK/Q8O9CKUCfDXAO93HOQXKrjk/h6dAo80NeKnm4d4xptfo2ew/nNHM7XkVXVctkm2EFDTzct3V21hDppsNAa93fCUM+D4jo9J0t0JJXoOFGso6YJrM2gn4cZA7y09HTTYq4xzd9/aHkOLD/dyG9ZzfR21zKvj6XBnq9/5xzUNLW8hjTr4eWh1jhYms7/Q0VReO1gPYW1et4YYYONuenE9lfUeD+4VGPGjIlTFOWCNYnGYLAVCkVRrrrCh8gB/jixxg+44J5KRVEWAAsAYmJilNGjR1/h4VvExsbSXo/1d7iFlzH9833sqXLjtWm9jH78S9V/UCNTP93L54k61j40yCAjmC/3HIwGpoyuZe6iI7wXV8XjV0XwwJgwtCb8BnXezNavmcU1/JqYz+aT+WzIKGd9ehOWZhpigpwZGurG0FBXevg4YmFm2HKo9noeFFbVcySzjD1pxexLKyazpKVWyN3ekom9vJjS05sREW6qtMb+u7JLa3lo6VEScmq5a1gw/5wSZdDmWZd6Dpp1euZ+f4TyxjpW3DdElZklF7MmPpe08mO8dWNvppjIULJLpdb7QUdhypc8DgPhQohgIJeW19hb1Q3JeKIDnLl7eDBf7c7g6l7eDDWBrXBtcbG14Js7Y5j22T7u/u4wP80balKd7vxdbPj5gaE8t/oE725NYU9aMR/M7GsSS9KXIsjNlnmjQ5k3OpTK+iYOpZey70wJ+84U8/bmZAAstBoivOzo4e1ID18Hevg40s3bXtU9/YqikF9ZT2JuJSdyKziZW8GJ3AoKW+ev2FmaMTjEhdlDghge7ka4h53JXs5oy7ZTBTy5MgG9XuGL26NNpj5BURReWHuS2OQiXp/Wy+SSieqGZl7fmERvP0em9/dTOxypnanyiiOEmAZ8DLgDG4QQxxRFmSiE8AEWKooyRVGUZiHEQ8BmQAt8oyiK+mMvjeiJ8ZFsPVXAP1YdZ9OjI01qu9cfhXnY8+mt0cz57jCPLY/ny1kxJrUKYGdpxgc392VEuDsvrk1k8oe7efPG3kzsoc6kx8vlYGXOVd09uap7S0V8cXUDB9JLOJFTwcm8SracymfFkZayI41o2U7r72KNv7MNfs7W+Lu0fPV1ssHJxhxLM81lv4nr9AqVdU2U1TaSU1ZHdlktWaW15JTWkVXa8n1FXdPvsYS62zEszI0ePg70C3Cit58T5iq1wr4STTo972xO5std6fTwceCz26IJdLVVO6zffbI9jWWHsnhgdCi3DgpQO5z/8emONAqrGvhiVn80JvQaIbUPtXZ5rAZWt3F7HjDlDz9vBDYaMTSTYm2h5a3pfbh5wX7e3pzMS9f1UDukCxoZ4c5L1/XghTWJPL/mBK9P62VSnziFEEzv70d0gBOPLj/GfT/EMWtwIM9d3a3D7n93s7Pkmt4+XNO7pSBWURTyKuo5mVtBYl4l6UXV5JTVsS2pgOLqxv/5+xZaDfZWZjhYm+PQ+tVMI/hjVdX5EqvC4jreSthNRV0TlXVNVDX8b+8MC60GP2dr/Fxs6O3nSISnPT19Hejm7dApOiCeq6jjkWXxHM4s47ZBAbxwjWn1Tlh5JJt3t6ZwQz9fnppoWkWYAKfyKlm4O50bo/1MbuVEah8d/1neyQ0MduGOIUF8ty+TKb28GRjsonZIFzRrcCCFlfV8vD0NK3MtL15jetvBQtzt+HneUN7ZksyCXekcyijlw1v6EuWlzhTK9iSEwNfJGl8nayb8afWlrlFHTlktOWV15JbXUVnfRGVdM5X1TVTVN1NZ10RlfRM6fUsGIf77gWnWQ4CjFVFe9jhYm+PY+sfJxhxfp5bVD08HK5NamWoviqKwMi6Hf/9yCp1e4cOZfbm+r6/aYf2XnSlFPLvqBMPD3Hjjxt4m97xrbNbz5MoEHK0teP7qbmqHIxmITCg6gKcnRfLb6QKe/imBXx8dibWF6Xwq+rMnxkdQ26jj6z0Z2FqYMd8EPylZmGn455RuDAtz48kfE7jmoz3cPyqUh8aGmdQnzvZkbaEl3NOecM/L26LXUow2oJ2jMn155XU8u+oEO1OKGBjkwlvTexPkZjqXOKBlC+a8xXFEeNrz+e3RBi/QvRyf7Egj6VwlC2b1N6mhZFL7Mr3fPOl/2FiY8eaNvcksqeWdLclqh3NRQgiev7obtwwM4JMdaXy6I03tkC5oVIQ7Wx4fyfV9fflkRxqTP9zNvjOmMwtEUo+iKKw4nMXE93dxKKOUl6/rwfJ7B5tcMpFdWsud3x7G2caCb+cMMMmGX4m5FXy6I40b+vn+z8qZ1LnIhKKDGBrqxm2DAvhmb4bJTNW8ECEEr7Z2NHx7czLf7s1QO6QLcrG14N2b+rBk7iD0isKtXx3kqZUJlNX8b82B1DXkltcx+5tD/OPnE/TwdWDzYyO5Y2iQyRURFlU1cMc3h2hs1vHdnAF4OlipHdL/aGjW8cSPx3Czs+Bf15puDZjUPmRC0YE8O6UbPo7WPL4igcr6JrXDuSitRvDOjD5M7OHJy+tPmdzArj8bFubG5sdGMm90KKvic7nqvZ2sPZZrMrNKJMOrb9Lx6Y40Jry3k6Nny/j31J4snTuYAFfT61JaWFXPLV8d4FxFPQvvGHDZl7IM7cNtqaQUVPPGDb1xtDG91ROpfcmEogOxszTjw5l9yS2v4x8mNJjrQsy0Gj66pR+jItx5ZtUJ1h7LVTuki7Iy1/KPSVH88vBw/FxseHT5MW7+8gDxWWVqhyYZkKIo/HriHFe9t5O3NyczLMyNTY+NZNbgQJNblQAorKznlgUHyC2r49s5A0y2UDs+q4wvdp7hphg/xkR5qB2OZAQyoehgYoJceHpiJL8m5rNoX6ba4fwlSzMtX87qz6BgF574MYGf43LUDukvdfN2YNW8obw6tSfpxdVM+2wfDy45SmZxjdqhSe3sZF4FMxccYN6So9hZmrF07iAWzI7B38X0ViWgJZmY2boy8d2cAQwOcVU7pDbVN+mYvzIBLwcrnr+mUw+Jlv5A7vLogO4ZEcKhjFJe25hEvwBn+vg7qR3SRVmZa/n6jgHc+8MRnlyZQFltI3NHhKgd1kVpNYLbBwcytZ8vX+1KZ8GudLacyue2QYE8PDYMVztLtUOUrkBxdQPvbklh+eEsnKzN+ffUntwywN+grbOvVFm9npkLDpBfWc93cwaa7MoEwHtbUzhTVMMPdw/EwQQLRSXDMN1nj3RBmtb6BHc7Sx5cepSKWtOupwCwtTTjmzsHMLmnF69uSOKdzckmf8kGWi4zPT4+gp1PjWZGjD8/HDjL6Ldj+XRHGjVtNHeSTFthVT2vbTjFiDd3sPJINnOGBhM7fwyzBgeadDJRUFnPm4fqKaisZ9Fdpp1MHEgv4avd6dw6KIAR4aY5LVkyDNN9BkkX5WxrwSe3RZNfUc/8nxI6xJuzpZmWT26N5paB/nyyI43n1iT+3kjJ1Hk4WPH6tF5sfmwEg0NdW661v7md97amUCp3hJi8gsp6Xl5/khFv7uDrPRlM7unFlsdH8uK13U2+WDC/op6ZCw5Q3qCw6K6BDAgy3WSisLKeh5fFE+xqyz+nyAZWXY285NGBRQc488zkKF7dkMQ3ezO5e3iw2iH9Ja1G8Pq0XjjbWPBZ7Bkq6pp4/6a+JtmMpy1hHvZ8NTuGo1llfB57ho9+S2XBrjPMHBDA3BHB+Dmb5rX3rupcRR1fxJ5h2eFsdHqFaf18eXBMGMEm1k/iQtIKq5nz3SHKapp4MsaKGBNOJpp1eh5eFk9VfRM/3D3QpIYESsYhz3gHd/fwYA5mlPKfjUlEBzjRrwP0yBdC8PSkKJxtLHhtYxKVdU18cXt/kx1+1pboAGe+mh1DakEVX+5KZ/GBsyw+cJbr+vhw36hQIr1McxtfV5GYW8H3+zNZE5+HXlG4MdqPB8eEmeQW0As5nFnK3EVHMNcKlswdRNmZY2qHdFHvbEnhYEYp793Up1O0spf+vo7zCi61SQjBO9P7cPXHu3loaTwbHhmOk03HaG17z8gQHG3Meebn49y28CBf3xHT4Yodwz3teWdGH54YH8HC3RksO5TFqvhcRoS7cfMAf8Z398TSrHO28zY19U06Np44x/f7z3Isuxxrcy0zYvy4f1Soye7auJBfjufxxI8J+DlZ892cgQS42hB7Ru2oLmzrqQK+2HmGWwcFcEO0HEveVcmEohNwtDHn01ujmf7FPp74MYGvZpvW+PCLuSnGHydrcx5eFs91n+xlwez+9PBxVDusv83HyZoXr+3Ow2PDWHzgLMsPZ/PQ0nhcbC24oZ8vMwf6E+YhVy0MIbu0liUHs/jxSDalNY2EuNvyr2u7c0O0H47Wpl0f8WeKovDV7nRe33iamMCWVTBTn32RVVLLEz8eo6evAy/KLaJdmkwoOok+/k68cE13Xlx7kjd+TeK5qzvOE3tCDy9W3j+Ee7+PY/rn+3lnRh+u7u2tdliXxdnWgofHhfPAmDD2pBWz4nAW3+3LZOGeDGICnbl5gD9X9/buFOO81VRR18SWk/msP36O3alFCGB8d09mDwliaKiryU3bvBQ6vcIr60+yaP9Zru7lzbs39TH5YXX1TTrmLYlDAJ/f1t/k45UMS76qdSKzBgeSVljNV7szCHKz5bZBgWqHdMl6+zmx7uFhzFt8lAeXHiXpXBhPjI8wyU6Fl0KrEYyKcGdUhDvF1Q2sOprD8sPZPPXTcV5ce5LRke5M6unFmCgPuU//EtU2NrMtqZD1CXnsTC6iUafHz9mah8aEccvAAHycrNUO8bLVNep4ZHk8W08VcM+IYJ6d3K1D/O6/vP4kJ/Mq+foO020GJhmPTCg6ESEEL17TnazSWl5cexI/ZxtGRXScfeAe9lYsvWcQL645ySc70jidX8n7N/dVO6wr5mZnyb0jQ7lnRAiHM8tYn5DH5pP5/JqYj7lWMCzMjYk9vBjf3RO3DlZDYmiV9U3sSyvml+Pn+C2pkLomHZ4OlswaEsi1fXzo4+fYIVcj/ii7tJYHlhwlMa+Cl67tzp3DTH+3FsBPcTksO5TNA6NDGdfNU+1wJBMgE4pOxkyr4ZNbo5n+eUu76J/nDe1QOw4szbS8cWMvevg68PL6U0z7bB9zI/Vqh9UuhBAMDHZhYLALL1/Xg/js8tbE4hzPrjrBc6tPEBPowsgINwaHuNLbz6nDbKdtL806PcdzK9idUszu1CLis8vR6RVcbC24sb8v1/b2YUCQS4f49H4pdpwu5LEVx9ArCl/NiuGq7h3jjTkxt4Ln15xgSIgrT4yPUDscyUTIhKITsmvtSjn1073c9d1hVj84FA970xttfCFCCGYPCSLcw54HlsTx8v4mPMMKGRPZeQYMaTSC/oHO9A905tnJUSSdq2LTyXy2nMznnS0pAFiba4kJcmZwiGtrguGIuQl3c7wcOr1CelE1hzPL2J1axN60YirrmxECevs6Mm9UKMPD3YgJdDbpTpZ/l06v8OG2FD7ankY3bwe+uD2aQNeO0Rsjp6yWOd8dxtXWko9u6depzot0ZWRC0Un5OFnz9R0DuOnL/dyz6AjL7x2CtUXHKpgaEurKuoeGc+vnO5nz7WHmDg/mqUmRnW4bphCC7j4OdPdx4InxEZTWNHIoo4QD6aXsP1PC25uTAbCx0BId4Ex3Hwe6edvTzduBUHe7DpNkKIpCVmktCTkVnMgpJyGngpO5FdQ06gDwdrRick9vRkS4MSzUzeR3N1yukuoGHltxjN2pxczo78e/p/bsMMWMFXVNzPn2MPVNOpbOHYS7vbxEJ/0/mVB0Yr38HPlwZl/uWxzH4yuO8dlt0R1uqdjfxYbnB1uxu8qNhXsy2HemhI9u6dupt2C62Fowqac3k3q27HQpqW7gUEYpB9JLiMsq47t9mTQ2t1wGstBqCPOwo5t3S5IR6mGHr5M1Pk7WqnUqrGvUkVVay9mSGs6W1JJZUkNGcQ0n8yqpqGuZO2NhpqGHjwPT+/vR28+JvgFOhLjZdvh6iL9yNKuMB5ccpaSmkTdv7MXNAwLUDumSNTbruf+HODJLalh010DCPTvvc1C6PDKh6OQm9PDiuSndeHVDEm9uOs2zHbC/vqVW8OrUXoyO8ODpn49z9Ud7eP6a7tw+KKDTvwEBuNpZMrmXN5N7tSQYzTo96cU1JJ2r5NS5SpLOVbErtYifj/73aHhHa3N8nKzxdbLCpzXJcLI2x87KDDtLM+ytzLC1bP3e0vz3FSy9oqDTK+gVBb2+5efKBoW88jrKahspq2mirLaR8tpGymqbWm9r5FxFPWdLasmvrP+vOJxszAl0sWFKLy96+TrR28+RSC/7DrOy0h4URWHRvkxe25iEl6MVq+YNpadvx+m3oigK//j5OPvTS3j/5j4MDXVTOyTJBMmEogu4e3gwmSU1fLkrnQBXmw61nfSPruruySa/ETy5MoEX1iSyM7mIN2/s1eG6a14pM62GCE97Ijztub6v7++3F1U1kFVaQ255PXnldeSW1ZFXXkdOWR2HMkqprL/C6ag7trd5s72lGU625njaWzEszI0gVxsCXG0IcrUl0NWmw3RuNZT8inqeWXWc2OQirurmwbsz+pr8QLI/e29rCqvjc5k/IYJp/WQnTKltMqHoAoQQvHRtD3LK6nh+TSK2FmZM7ef713/RBHk4WLFozkC+3ZfJm7+eZtKHu3l3Rh9GdqDtsYbibm+Ju70l/S+QL1Y3NFNR10RNQzNV9c1UNzRTXd/c8nNDM7UNLcWQGo1AKwQaIVq/hzNn0ugRFYmTjQXONuY421rgbGOBk415l1pp+DsURWHV0VxeWn+SZp3Cy9f1YNbgwA532fHHw9l8vD2NmQP8eXBMmNrhSCZMJhRdhJlWw+e39eeu7w7zxI/HMNdqOmw3So1GcPfwYIaGuvLIsnhmf3OIO4cGMX9ipJxweBF2rZc3Lkds01lGD+w41/vVVlhVzz9XJbItqYCYQGfemdGHoA4y4fSPdqYU8ezqE4yMcOffU3t2iUuM0uWTHy26EGsLLQvviCE6wJlHl8ez5WS+2iFdkW7eDqx/eDh3Dg1i0f5Mxr+3k02J+SiKonZoUhelKArrEvKY8P4udqUW8dyUbqy4b0iHTCZO5VXywOI4wj3s+PTWfnIlSvpL8jeki7G1NOPbOQPo4evIg0uPsiO5UO2QroiVuZaXruvBz/OG4mhtzv2L47jn+yPklNWqHZrUxZRUN/Dg0qM8siyeQFdbNj4ygntGhnSYQX1/lFpQxexvDmJvZc63cwZgL9vDS5dAJhRdkL2VOd/PGUiEpz33/RDHntRitUO6YtEBzqx/eDj/nBLF3rQSxr+3iwW7ztCk6xxdNiXTpdMrLDuUxfj3d7H1VAFPTYzk5/uHEOZhp3ZolyWtsJpbvjqIEILFcwfh7dhxZ6RIxiUTii7K0cacxXcPIsTNlrnfH+ZAeonaIV0xc62Ge0eGsvWJkQwLc+X1jae59uM9HM0qUzs0qZM6klnK9Z/u4dlVJwh1t2X9w8N5cExYh+0emV5Uza1fHQBg2T2DOmxSJKmjY/7WS+3C2daCxXMH4etkzV3fHSbubKnaIbULP2cbvpodwxe396e8tokbP9/HP1efoKiqQe3QpE6ioLKex1ccY/oX+ymuauTDmX358b4hRHk5qB3aZcsoruGWrw60rLjcM6hTN4+TDEMmFF2cm50lS+8ZjIe9JXd+c5iE7HK1Q2oXQggm9fRi25OjmDM0mBWHsxn19g7e25pCdcMV9mOQuqyGZh2fx55hzDuxbDh+jofGhLF9/iiu7+vboXdAZBbXcMuCAzTpFJbeM1h2wZQui0woJDwdrFh6z2CcbM2Z9fXBTrNSAS1bJV+8tjtbHx/JmEgPPvotlVFv7eDbvRk0NOvUDk/qIBRF4bekAia+v4s3N51mWJgbW58YyfyJkdhYdOytylkltdzy1QEamnUsmTuoQ00nlkyLTCgkoGWY2NK5g3GxteC2hQfZfrpA7ZDaVYi7HZ/eFs3aB4cR4WnPy+tPcdV7O1kTn4teL7eZSm1TFIVdKUXc8Pk+7l50BI1GsOiugXw1O6bDTAe9mOzSlmSirknH4rmD6ObdcS/ZSOqTCYX0O38XG36aN5RwD3vu+T6On+Jy/vovdTB9/J1Yes8gFt01EHtLcx5bcYyrP97DjuRC2b9C+p2iKOxJLWb6F/uZ/c0hCisbeH1aLzY9OpJRnaQra05ZLTMXHKC6oZnFdw+ih0/HmS0imaaOvVYntTs3O0uW3TuY+344wvyVCRRXN3DfyJAOfX34z4QQjIpwZ0SYG+uP5/HulhTmfHuYfgFO3DcyhPHdvTpk7wDpyimKwr4zJXywLYXDmWV4O1rx6tSezIjxw9KsY4wYvxQpBVXc8c0hahqaWTJ3cIcaVCaZLplQSP/DztKMb+4cwJM/JvDGr6cprmrgn1O6dbgZBH9FoxFc39eXyT29WXEkm692pXP/4qMEu9kyd0QwN0b7YWXeed5EpIvbf6aE97elcCijFE8HS/59fQ9uGuDfqRIJgEMZpcxddBhLcy3L7h0sVyakdiMTCqlNlmZaPprZDzc7SxbuyaC4uoG3pvfBwqzzXSWzMNMwa3Agtw4MYFNiPl/uOsNzqxN5b0sKdwwNYtbgQJxtu/bEzM6qoVnHhuPnWLQvk4ScCjzsLXnp2u7MHBjQKZPJjSfO8diKY/g5W7NozkD8XWzUDknqRGRCIV2QRiP417Xdcbe35O3NyZTWNvH5bdHYdtIBXFqN4Ore3kzp5cWB9FIW7DrDe1tT+Dz2DDfF+DF3RIh8Ae4kCirrWXLgLEsPZVFc3UiIuy2vXN+Dm2L8O2UiAfDd3gxe/uUU0QHOLJwdI5Nkqd11zncGqd0IIXhwTBiuthb8c/UJbl14kG/vHIBLJ34xEkIwJNSVIaGupBRUsWBXOksPZfHDgbOMinDnphh/xnXz7JSrNZ2ZoijEnS3ju32ZbErMR6cojI304I6hQQwPc+t0l/TO0+sV3tqczBc7zzChuycf3dKv0yZNkrpkQiFdkpkDA3CxteDhZfHc+Pk+vprdv0t00ovwtOedGX2YPyGSxQfO8lNcDvOWHMXF1oKpfX25aYBfh+6O2BVU1Tfx64l8Fu3P5GReJfZWZtw5NIhZQwI7xdbPi2ls1vOPn4+zOj6X2wcH8PJ1PWXBsWQwMqGQLtmEHl4smTuI+xfHMfXTfbx7Ux8m9vBSOyyj8HK0Yv7ESB4fH8Hu1CJWHsnhhwOZfLM3g95+jsyI8ee6Pj44WsupjKagoVlHbHIR647lsS2pgIZmPRGedrw2rSfT+vl2+GZUl6Kqvol5i4+yJ62YpyZG8sDo0E61W0syPao8q4QQM4CXgG7AQEVRjlzgfplAFaADmhVFiTFWjFLbYoJcWPfQcOYtjuO+H+J4ZGwYj10V0WmXi/9MqxGMjvRgdKQHpTWNrD2Wy4rD2bywJpF//3KKiT28uLqXNyMj3LrEm5Yp0esVDmSUsO5YHhtPnKOyvhlXWwtmDvDnur4+RAc4d5k31LzyOuYuOkJKQRVvT+/NjBh/tUOSugC1XvESgRuALy/hvmMURen487U7ER8na1bcN4Tn1yTy0fY0TuZV8v7MvjhYda1P5y62FswZFsydQ4M4mVfJj0eyWXssj/UJeViaaRgR7sb47p6M6+aJm52l2uF2Snq9woncCn45nsf6hHPkV9Zja6FlYg8vruvrw/Awtw47+fNy7Usr5uFl8TQ061l4RwyjIz3UDknqIlRJKBRFSQK6zKeFzsjKXMvb03vTx8+Rl9efYuone/lyVv8uOVRICEFPX0d6+jrywjXdOZxRypZTBWw9VcC2pEKEOEH/AGcm9PBkfHcvgt0693V7QyutaWR3ahGxyUXsSimipKYRc61gVIQHz13djau6eWJt0fWKDhVFYcGudN7cdJpQdzu+mNWfUHc5flwyHlNfk1WALUIIBfhSUZQFagck/T8hBLOGBBHp5cADS+KY+ule3ru5b5epq2iLuVbD0DA3hoa58a9ru3PqXCVbTrYkF69vPM3rG08T7mHH8HA3BgW7MCDIBVe5enFROr3CsexydqYUsTO5kOO5FShKywrRyHA3RkW6MybSAyebzrvz6K9UNzTz1MoEfk3M5+pe3rw1vXen3d4tmS5hqPkFQohtQFvvLM8pirK29T6xwPyL1FD4KIqSJ4TwALYCDyuKsusC970XuBfA09Oz//Lly9vhXwHV1dXY2cks/6+U1uv5JL6B9Ao914WaMzXMHE07rUB1lnNQVKsnvlDHsaJmUsv0NOlbbvexFUS4aIl01hLposHFyvSW6I15Dhp0Cmcr9Zwp13OmXEdSqY6aJhBAqJOGXm5aerlrCXLQtNvvWEdwoXOQV63n4/h6CmoVZkRYMCnITK7+GogpvxaNGTMmTu06Q4MlFJd08L9IKP5035eAakVR3vmr+8bExChHjvzlQ16S2NhYRo8e3S6P1dnVN+l4cW0iPx7JYWyUB+/O6NMuzXM64zlobNZzIrecgxmlHMooJS6zjKqGZgD8XawZGORK3wAnorzsifC0V333iKHOgV6vcKaomvjschKyyzmWXc7p/Cp0rRNgfZ2sGRLq2jJ7JdytS69CtHUOfj1xjvkrE7C20PLxLdEMCXVVJ7guwpRfi4QQqicUJrsmJoSwBTSKolS1fj8BeEXlsKSLsDLX8uaNvenl58Qr608y8YNdvDOjDyM7yXTG9mRhpqF/oAv9A114YHTLsn7SuUoOtSYYO5IL+fno/0979XG0ItLLnkgvByK97Ij0dCDUw7bDzJnQ6RVyy+pIL64mo7iGjOIa0gqrOZFT8XsiZW9pRh9/J+4fFUJff2f6+jvhbi8vB7WlWafn7c3JfLkrnX4BTnx2WzTejtZqhyV1cWptG50GfAy4AxuEEMcURZkohPABFiqKMgXwBFa3Lt2ZAUsVRdmkRrzSpRNCMGtwINEBTjy+4hizvznEnUODeGZylOzOdxFazf8Xdt41PBhFUcirqCc5v5LT+VWk5FdxOr+KPWnFNOlaPr2baQSBrjb4OFnj7WiFl+P5r1Z4O1rh7WCNg7Vxlr/rm3SU1DRSWt1IcU0DBRX1ZBTXkN6aPGSV1NKo0/9+f3tLM0Lcbbmurw99/Z3oF+BEiJtdl9l+fCUKKut5bPkx9qeXcPvgAF64pnuHSSylzk2tXR6rgdVt3J4HTGn9Ph3oY+TQpHbSw8eRdQ8N581Np/l2byZ70or54Oa+ckzyJRJC4Otkja+TNWOjPH+/vUmnJ6O45vckI62wmnOV9aQUFFFY1cCfr2DaWGjxcrDC0cYcWwszbCy0LX8szbC10GJt0fLVxtIMSzMNzTqFZr3+969NOoVmnUJaRiMH6k7TrNNTUddEaU0jxTWNlNY0UFrdSE2j7n/+DRZmGoJcbQh1t+Wqbp6EuNkS7G5LsJstrrYW8jr/ZViXkMcLaxJpaNbJ/hKSyTHZSx5Sx2dlruVf1/ZgbJQH81cmMO2zvTw+PoL7RobK9r+XyVyrIcKzpa7iz+l2k05PUVUD5yrqOVdRR35FPecq6smvqKeyvomahmaKqxuobdRR29jc+vV/E4G2CMD8bAZmGoGjtTkutha42FoQ4mb7+/dudha42FriYmuBh70lPk7W8jy3k/LaRj47Vs+h/Hj6BTjx7ow+hMgtoZKJkQmFZHAjwt3Z/NhInludyFubkok9XcS7N/WRkzvbmblWg4+TNT5O1oDzJf0dvV6hrqklsWho1mGm0WCmFZi3fj3//a5dO022GK2z25FcyD9+Ok5JtY6nJkZy38iQLtesS+oYZEIhGYWTjQWf3NqPcfEe/GvtSSZ/uJuXruvBjdG+culbRRqNwNbSTPYsMEE1Dc28tjGJpQeziPS058FegjvGhKkdliRdkExzJaMRQnBDtB+/PjaC7j4OzF+ZwLzFR8mvqFc7NEkyKYczS5n84W6WHcrivpEhrH1oGIEOsvBSMm0yoZCMzs/ZhmX3DOaZyVHsSC5k3LuxLNydTvMfdgFIUlfU0KzjP78mcdOX+1FQWHHvEJ6d0k3ukJI6BLnOKalCqxHcPyqUKT29+de6RF7dkMRPcTm8OrUnMUEuaocnSUa3K6WIl9adJL24hlsGBvDc1d2wk5eipA5ErlBIqgpwteGbOwfwxe39qaxrYvoX+3n6pwRKaxrVDk2SjCK3vI77f4hj9jeH0CsKi+4ayH9u6CWTCanDkb+xkuqEEEzq6cWIcDc+2p7K17sz2HKqgGcmRXGT3GcvdVINzTq+2pXOJzvSAHhqYiRzRwTLJlVShyUTCslk2Fqa8ezkbtwY7cfzaxJ5ZtUJVhzJZqrfpfVKkKSOYkdyIS+vO0lmSS2Te3rx/DXd8XWSrbOljk0mFJLJifC0Z8W9g1kdn8trG5J4KauRDE7y8NgwOepb6tCyS2t55ZdTbD1VQIi7LT/cPZAR4XLWjdQ5yIRCMknnt5iOi/Lk8W+38/3+TFYeyebuESHcMyIYeyt1p29K0t9R16hjwa50PotNQ6sRPDM5iruGBWNhJsvYpM5DJhSSSXO0MWd2D0v+OWMo725J4aPfUvlhfyYPjA5j1pBAuZ1OMmkNzTqWH8rmkx1pFFU1cHVvb56/upucDCp1SjKhkDqEMA97Pr+9P8dzynl7czKvbUzi6z0ZPDIunBkxfpjLVsSSCWnS6fkpLoePf0slr6KegcEufHprNAOD5ZZoqfOSCYXUofT2c+KHuwex/0wJb20+zT9Xn2DBrjM8Pj6Ca3v7yPHXkqp0eoU18bl8+FsqWaW19PV34q3pfRgW5ipbzEudnkwopA5pSKgrq+YN5bekQt7Zksyjy4/xxc50npoYwZhID/niLRmVXq+w4cQ5PtiWwpmiGnr4OPDNnTHyd1HqUmRCIXVYQgiu6u7J2CgP1h/P472tKdz13RG6ezswd0Qw1/T2kUVvkkEpisLWUwW8tzWF0/lVRHja8cXt0Uzo7iVXy6QuRyYUUoen0Qiu7+vLlF7erDqaw1e7M3jixwTe3HSaO4cGc+vAABxt5K4Qqf3UN+lYeyyXb/dmcjq/imA3Wz6c2ZdrevuglYmE1EXJhELqNMy1Gm4eEMCM/v7sTC1i4e503tx0mo+3p3JTjD9zhgUR6GqrdphSB1ZQWc8P+8+y5OBZymqbiPKy550ZfZja1wczWRgsdXEyoZA6HY1GMCbSgzGRHpzKq2ThnnSWHDzLov2ZTOjuyT0jQugf6CyvbUuXLCG7nG/2ZrDh+Dl0isJV3Ty5a1gwg0Nc5O+RJLWSCYXUqXX3ceC9m/ryj0lRLNqXyZKDWWw+WUBffyfuHh7MhB6ecnaC1KZmnZ5NJ/P5dm8mcWfLsLM0Y/aQIO4YGihXuiSpDTKhkLoETwcrnp4UxUNjw/g5Loev92Tw8LJ4nGzMua6PD9P7+9HL11F+2pTIr6hnVXwOi/efJa+inkBXG/51bXem9/eTHVol6SJkQiF1KTYWZswaEsStgwLZnVrEz0dzWX44m+/3nyXcw47p/f2Y1s8XDwcrtUOVjKi6oZlNifmsjs9h35kSFAWGhLjy8vU9GRvlIQstJekSyIRC6pK0GsHoSA9GR3pQUdfEhuPn+Ckum//8epo3N51mZIQ7N0b7Mb67p2zv3Uk16/TsTitmTXwum0/mU9+kJ8DFhofHhjOtny/BbvKyhiT9HTKhkLo8R2tzbh0UwK2DAkgvqubnozmsOprLw8vicbAy45o+PtwY7Us/f2fZW6CDUxSFk3mVrDqay7qEPIqrG3C0NufG6JaVKVmsK0mXTyYUkvQHIe52PDUxiifGR7L/TElrcpHD0oNZuNlZMjbKnau6eTI83A0bC/n06QjOJxHbTxeyLiGPtMJqzLWCsVEeTOvnx5god1mYK0ntQL4iSlIbtBrB8HA3hoe78cr1PfgtqZBtSQX8mpjPj0dysDDTMCzUlXHdPBnXzUNOjzQxVfVN7E0rZvvpQmKTiyisagCgf6Azr07tyTW9vXGysVA5SknqXGRCIUl/wd7KnKn9fJnaz5cmnZ7DGaVsa00wdiQn8vwa6OnrwLgoT67q5klPXwe5bG5kiqJwpqiG2ORCtp8u5HBmKU06BXtLM0ZGuDMmyoNREe6421uqHaokdVoyoZCkv8Fcq2FomBtDw9x44ZpupBVWsy2pkN+SCvh4eyof/paKp4Mlg4JdiQlyJibQhUgve7lLwABKaxqJzypjd2rLSkRWaS0AEZ523DU8mDGRHvQPdJaj7SXJSGRCIUmXSQhBuKc94Z72zBsdSkl1AzuSi4hNLuRgRgnrEvIAsLc0IzrQmZhAZ2KCXOjr74S1hbxm/3fo9AopBVUczSrj6NlyjmaVkVFcA4CVuYZhoW7cMzKEMZHu+DnbqBytJHVNMqGQpHbiamfJ9P5+TO/vh6Io5JTVEXe2jMOZpRzJLOO9bSkoCphpBD18HRnQmmD08nPEx9FKXib5g4raJo5mlxF/toy4rDISsiuobmgGwNXWguhAZ26K8Sc6wIk+/k5ya68kmQCZUEiSAQgh8Hexwd/Fhqn9fIHWN8ms1gTjbBnfHzjLwj0ZANhaaAnztCfCw45wT7uWlQ8PO3ydrDt1olFR10R6UTVphdWcKarhTOv351cfNAK6eTswrZ8v0YFORAc4E+Bi06n/n0hSRyUTCkkyEkcbc8ZEeTAmygOAhmYdibmVnM6vJLWgmtTCKmJTilgZl/P73zmfaIR72BHhaUeImx1ejlZ4OljhamvRIfpiNOn0FFTWtyQMhdWcKTr/p4ai1t0XAOZaQZCrLZGe9kzv70e/ACf6+DlhaylfpiSpI5DPVElSiaWZlv6BzvQPdP6v28trG0ktrCaloOr3RGNXShE//SHRgJZLJ+72lnjYW+LhYIWngyWe9i3JhoeDJR72VjhYm2FlrsXaXIuVubZdikMVRaFJp1Be10hxVSNF1Q0UVzVQVN1AUVUDxX/6Wlbb9F9/38HKjDAPO0ZHuBPqYUeYux2hHnb4O1vLEeCS1IHJhEKSTIyTjQUDglwYEOTyX7eX1zaSUVxDYVUDhZX1FFQ2UFBZT0FVA9mltRzJLP2fN+8/s9BqsDTX/CHJ0GBtrsXSXIuFVkOjTk9jc+ufP3xfU1ePsmPz77dfiLW5Fnd7S9zsLAh2s2VAkEtr0mNFiLstoe52uNlZyEsWktQJyYRCkjoIJxsL+gVcvBlTfZOOoqoGCqtaEo7q+mbqm3XUN+moa9RT36yjrlFHQ7OO+iY9dY2632+rbWzGXKvB3soMSzMNFmYaLLQtX4sL8gkK8G+5zUyDpZkGByuz1uSh5Y+7vaW8PCFJXZh89ktSJ2Jlrv29GLQ9xcaWMXp093Z9TEmSOhd5wVKSJEmSpCsmEwpJkiRJkq6YTCgkSZIkSbpiMqGQJEmSJOmKqZJQCCHeFkKcFkIcF0KsFkI4XeB+k4QQyUKINCHEM0YOU5IkSZKkS6TWCsVWoKeiKL2BFODZP99BCKEFPgUmA92BW4QQssxckiRJkkyQKgmFoihbFEVpbv3xAODXxt0GAmmKoqQritIILAeuN1aMkiRJkiRdOlOoobgL+LWN232B7D/8nNN6myRJkiRJJsZgja2EENsArzb+03OKoqxtvc9zQDOwpK2HaOM25SLHuxe4F8DT05PY2Ni/G3Kbqqur2+2xpMsjz4H65DlQnzwH6pPn4OIMllAoinLVxf67EOIO4BpgnKIobSUKOYD/H372A/IucrwFwAKAmJgYZfTo0X835DbFxsbSXo8lXR55DtQnz4H65DlQnzwHF6fWLo9JwD+A6xRFqb3A3Q4D4UKIYCGEBTATWGesGCVJkiRJunRq1VB8AtgDW4UQx4QQXwAIIXyEEBsBWos2HwI2A0nAj4qinFQpXkmSJEmSLkKV4WCKooRd4PY8YMofft4IbDRWXJIkSZIkXR5T2OUhSZIkSVIHJxMKSZIkSZKumEwoJEmSJEm6YjKhkCRJkiTpismEQpIkSZKkKyba7inVsQkhioCz7fRwbkBxOz2WdHnkOVCfPAfqk+dAfaZ8DgIVRXFXM4BOmVC0JyHEEUVRYtSOoyuT50B98hyoT54D9clzcHHykockSZIkSVdMJhSSJEmSJF0xmVD8tQVqByDJc2AC5DlQnzwH6pPn4CJkDYUkSZIkSVdMrlBIkiRJknTFZEJxCYQQbwshTgshjgshVgshnNSOqasRQswQQpwUQuiFELLK2kiEEJOEEMlCiDQhxDNqx9MVCSG+EUIUCiES1Y6lKxJC+Ashdgghklpfgx5VOyZTJROKS7MV6KkoSm8gBXhW5Xi6okTgBmCX2oF0FUIILfApMBnoDtwihOiublRd0nfAJLWD6MKagScVRekGDAYelM+DtsmE4hIoirJFUZTm1h8PAH5qxtMVKYqSpChKstpxdDEDgTRFUdIVRWkElgPXqxxTl6Moyi6gVO04uipFUc4pinK09fsqIAnwVTcq0yQTir/vLuBXtYOQJCPwBbL/8HMO8oVU6sKEEEFAP+CgyqGYJDO1AzAVQohtgFcb/+k5RVHWtt7nOVqWv5YYM7au4lLOgWRUoo3b5LYwqUsSQtgBPwOPKYpSqXY8pkgmFK0URbnqYv9dCHEHcA0wTpF7bQ3ir86BZHQ5gP8ffvYD8lSKRZJUI4QwpyWZWKIoyiq14zFV8pLHJRBCTAL+AVynKEqt2vFIkpEcBsKFEMFCCAtgJrBO5ZgkyaiEEAL4GkhSFOU9teMxZTKhuDSfAPbAViHEMSHEF2oH1NUIIaYJIXKAIcAGIcRmtWPq7FoLkR8CNtNSiPajoign1Y2q6xFCLAP2A5FCiBwhxN1qx9TFDANmAWNbX/+PCSGmqB2UKZKdMiVJkiRJumJyhUKSJEmSpCsmEwpJkiRJkq6YTCgkSZIkSbpiMqGQJEmSJOmKyYRCkiRJkqQrJhMKSZIkSZKumEwoJEmSJEm6YjKhkCTpiggh/i2EePQPP78mhHhEzZgkSTI+2dhKkqQr0jqBcZWiKNFCCA2QCgxUFKVE3cgkSTImORxMkqQroihKphCiRAjRD/AE4mUyIUldj0woJElqDwuBO2kZP/+NuqFIkqQGeclDkqQr1jqN9ARgDoQriqJTOSRJkoxMrlBIknTFFEVpFELsAMplMiFJXZNMKCRJumKtxZiDgRlqxyJJkjrktlFJkq6IEKI7kAb8pihKqtrxSJKkDllDIUmSJEnSFZMrFJIkSZIkXTGZUEiSJEmSdMVkQiFJkiRJ0hWTCYUkSZIkSVdMJhSSJEmSJF0xmVBIkiRJknTF/g864V3SB1cgoAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[8,8])  # Make axes equal length; orbits should be circular or \"circular spirals\" \n",
    "if D == 0.:\n",
    "    plt.title(f\"The orbits of the undamped mass-spring system, {k=} — by Euler with {n} steps\")\n",
    "else:\n",
    "    plt.title(f\"The orbits of the damped mass-spring system, k={k}, D={D} — by Euler with {n} steps\")\n",
    "plt.plot(y, Dy)\n",
    "plt.xlabel('y')\n",
    "plt.ylabel('dy/dt')\n",
    "plt.plot(y[0], Dy[0], \"g*\", label=\"start\")\n",
    "plt.plot(y[-1], Dy[-1], \"r*\", label=\"end\")\n",
    "plt.legend()\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "loose-ratio",
   "metadata": {},
   "source": [
    "## The \"Classical\" Runge-Kutta Method, Extended to Systems of Equations\n",
    "\n",
    "As above, the previous function for this method needs just three lines of code modified."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "international-possibility",
   "metadata": {},
   "source": [
    "Before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "increasing-transportation",
   "metadata": {},
   "outputs": [],
   "source": [
    "def RungeKutta(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use the (classical) Runge-Kutta Method\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "    U = np.empty_like(t)\n",
    "    U[0] = u_0\n",
    "    for i in range(n):\n",
    "        K_1 = f(t[i], U[i])*h\n",
    "        K_2 = f(t[i]+h/2, U[i]+K_1/2)*h\n",
    "        K_3 = f(t[i]+h/2, U[i]+K_2/2)*h\n",
    "        K_4 = f(t[i]+h, U[i]+K_3)*h\n",
    "        U[i+1] = U[i] + (K_1 + 2*K_2 + 2*K_3 + K_4)/6\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "regional-meaning",
   "metadata": {},
   "source": [
    "After:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "italian-helping",
   "metadata": {},
   "outputs": [],
   "source": [
    "def RungeKutta_system(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use the (classical) Runge-Kutta Method\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "\n",
    "    # Only the following three lines change for the systems version — the same lines as for euler_system and so on.\n",
    "    n_unknowns = len(u_0)\n",
    "    U = np.zeros([n+1, n_unknowns])\n",
    "    U[0] = np.array(u_0)\n",
    "\n",
    "    for i in range(n):\n",
    "        K_1 = f(t[i], U[i])*h\n",
    "        K_2 = f(t[i]+h/2, U[i]+K_1/2)*h\n",
    "        K_3 = f(t[i]+h/2, U[i]+K_2/2)*h\n",
    "        K_4 = f(t[i]+h, U[i]+K_3)*h\n",
    "        U[i+1] = U[i] + (K_1 + 2*K_2 + 2*K_3 + K_4)/6\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "technical-faculty",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = 1.0\n",
    "k = 1.0\n",
    "D = 0.0\n",
    "u_0 = [1.0, 0.0]\n",
    "a = 0.0\n",
    "b = 8 * np.pi # Four periods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "changed-longer",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_RK = 100\n",
    "n = n_RK"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "varying-gibraltar",
   "metadata": {},
   "outputs": [],
   "source": [
    "(t, U) = RungeKutta_system(f, a, b, u_0, n)\n",
    "y = U[:,0]\n",
    "Dy = U[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "bizarre-trail",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[12,6])\n",
    "plt.title(f\"U_0, = y with {k=}, {D=} — by Runge-Kutta with {n} steps\")\n",
    "plt.plot(t, y)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('y')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.figure(figsize=[12,6])\n",
    "plt.title(f\"U_1, = dy/dt with {k=}, {D=} — by Runge-Kutta with {n} steps\")\n",
    "plt.plot(t, Dy)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('dy/dt')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bacterial-heather",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[8,8])  # Make axes equal length; orbits should be circular or \"circular spirals\" \n",
    "if D == 0.:\n",
    "    plt.title(f\"The orbits of the undamped mass-spring system, {k=} — by Runge-Kutta with {n} steps\")\n",
    "else:\n",
    "    plt.title(f\"The orbits of the damped mass-spring system, k={k}, D={D} — by Runge-Kutta with {n} steps\")\n",
    "plt.plot(y, Dy)\n",
    "plt.xlabel('y')\n",
    "plt.ylabel('dy/dt')\n",
    "plt.plot(y[0], Dy[0], \"g*\", label=\"start\")\n",
    "plt.plot(y[-1], Dy[-1], \"r*\", label=\"end\")\n",
    "plt.legend()\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fuzzy-plenty",
   "metadata": {},
   "source": [
    "## Appendix: the Explicit Trapezoid and Midpoint Methods for systems\n",
    "\n",
    "Yet again, the previous functions for these methods need just three lines of code modified.\n",
    "\n",
    "The demos are just for the non-dissipative case, where the solution is known to be $y = \\cos t$, $dt/dt = -\\sin t$.\n",
    "\n",
    "For a fairer comparison of \"accuracy vs computtional effort\" to the Runge-Kutta method,\n",
    "twice as many time steps are used so that the same number of function evaluations are used for these three methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "dimensional-assurance",
   "metadata": {},
   "outputs": [],
   "source": [
    "def explicitTrapezoid_system(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use the Explict Trapezoid Method (a.k.a Improved Euler)\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "\n",
    "    # Only the following three lines change for the systems version — the same lines as for euler_system and so on.\n",
    "    n_unknowns = len(u_0)\n",
    "    U = np.zeros([n+1, n_unknowns])\n",
    "    U[0] = np.array(u_0)\n",
    "\n",
    "    for i in range(n):\n",
    "        K_1 = f(t[i], U[i])*h\n",
    "        K_2 = f(t[i]+h, U[i]+K_1)*h\n",
    "        U[i+1] = U[i] + (K_1 + K_2)/2.\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "north-employment",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = 1.0\n",
    "k = 1.0\n",
    "D = 0.0\n",
    "u_0 = [1.0, 0.0]\n",
    "a = 0.0\n",
    "b = 8 * np.pi # Four periods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "inner-click",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = n_RK * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "mobile-norway",
   "metadata": {},
   "outputs": [],
   "source": [
    "(t, U) = explicitTrapezoid_system(f, a, b, u_0, n)\n",
    "y = U[:,0]\n",
    "Dy = U[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "generous-recorder",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[12,6])\n",
    "plt.title(f\"U_0, = y with {k=}, {D=} — by Explict Trapezoid with {n} steps\")\n",
    "plt.plot(t, y)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('y')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "charming-message",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[8,8])  # Make axes equal length; orbits should be circular or \"circular spirals\" \n",
    "if D == 0.:\n",
    "    plt.title(f\"The orbits of the undamped mass-spring system, {k=} — by Explict Trapezoid with {n} steps\")\n",
    "else:\n",
    "    plt.title(f\"The orbits of the damped mass-spring system, k={k}, D={D} — by Explict Trapezoid with {n} steps\")\n",
    "plt.plot(y, Dy)\n",
    "plt.xlabel('y')\n",
    "plt.ylabel('dy/dt')\n",
    "plt.plot(y[0], Dy[0], \"g*\", label=\"start\")\n",
    "plt.plot(y[-1], Dy[-1], \"r*\", label=\"end\")\n",
    "plt.legend()\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "final-analyst",
   "metadata": {},
   "outputs": [],
   "source": [
    "def explicitMidpoint_system(f, a, b, u_0, n=100):\n",
    "    \"\"\"Use the Explicit Midpoint Method (a.k.a Modified Euler)\n",
    "    to solve du/dt = f(t, u) for t in [a, b], with initial value u(a) = u_0\"\"\"\n",
    "    h = (b-a)/n\n",
    "    t = np.linspace(a, b, n+1)  # Note: \"n\" counts steps, so there are n+1 values for t.\n",
    "\n",
    "    # Only the following three lines change for the systems version — the same lines as for euler_system and so on.\n",
    "    n_unknowns = len(u_0)\n",
    "    U = np.zeros([n+1, n_unknowns])\n",
    "    U[0] = np.array(u_0)\n",
    "\n",
    "    for i in range(n):\n",
    "        K_1 = f(t[i], U[i])*h\n",
    "        K_2 = f(t[i]+h/2, U[i]+K_1/2)*h\n",
    "        U[i+1] = U[i] + K_2\n",
    "    return (t, U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "retained-photography",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = 1.0\n",
    "k = 1.0\n",
    "D = 0.0\n",
    "u_0 = [1.0, 0.0]\n",
    "a = 0.0\n",
    "b = 8 * np.pi # Four periods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "basic-quality",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = n_RK * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "smaller-singles",
   "metadata": {},
   "outputs": [],
   "source": [
    "(t, U) = explicitMidpoint_system(f, a, b, u_0, n)\n",
    "y = U[:,0]\n",
    "Dy = U[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "bacterial-broad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[12,6])\n",
    "plt.title(f\"U_0, = y with {k=}, {D=} — by Explict Midpoint with {n} steps\")\n",
    "plt.plot(t, y)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('y')\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "defined-universe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkIAAAHwCAYAAABKTQDjAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAABzC0lEQVR4nO3dd5wV1fnH8c+zBZZeZekC0kQQkWLBAlIEbFETe4sagsYae+xd8zPGEkvU2AsaexQUEBZFRQUUpErvvS9t2/n9MZfZu8s2dvfu3PJ9v1772nOm3efcO3fmuTNnZsw5h4iIiEgiSgo6ABEREZGgKBESERGRhKVESERERBKWEiERERFJWEqEREREJGEpERIREZGEVaFEyMzuMbM3KyuY/XztS8xsUgnjR5vZxVUQx+lmttzMMs2sRxmm72dmKyIdV3mY2RIzGxh0HKUxM2dm7YOOo6qZ2flmNiboOKJdkNulqmBmGWZ2edBxlCR8W2JmfzOzl6r49Yvd/ptZm9A2JKUSXmeWmfWr6HL28zVL3A5E8z4mWpWYCIV27nv/8sxsV1j9/KoKsjycc0Odc69B6UlTBT0GXOWcq+2c+7nwyETdaUvlc8695ZwbHHQcZRHr672ZdTWzL81sg5mVerM1MzvMzKaa2c7Q/8OqIMwKCUsIMgv9nV2Zr+Oce8g5V2riZmavmtkDpUzjzGxteBJjZilmti78cwrf/keSc+4Q51xGWaatrB+ahbcDFf2umdljZjbfzLab2Vwzu6jQ+BLXbTO73szWmNlWM3vZzKqXI4ZSP/tIKjERCu3cazvnagPLgFPChr1VNSHuqzIy+Up0IDAr6CAkvkXZOp8IsoH3gMtKm9DMqgGfAG8CDYDXgE9Cw2NB/fBtvXPu3aADKsUWYGhYfRiwOZhQ4sIO4BSgHnAx8KSZHQ2lr9tmdiJwKzAAaAO0A+6t4vgrzjlXpj9gCTCw0LB78DYWrwPb8RKCXmHjmwMfAOuBxcA1JSy/Xmg564GlwB1AUmjcJcC3wD+BTcADYcOeBrYCc4EBYcvLAC4HDgZ2A7lAJrAlNH4YMDsU90rgxmLiSgrFshRYF4qxHlA9tDyHtyItLGLer8PGZwJnA/2AFcANoeWtBv4YNk91vKNMy4C1wPNAjWJiuwd4M6zeJvR6KWHvwf2h92k7MAZoHDb9haF2bQRuD/+MgT7A93gbndXAv4BqYfM64EpgfmjZ9wMHhebZFlovqoWm3dvmvwEbQq9zflnbDNwUimEVcGnotdsX855khNaP70Lv+f+ARsBbobh+AtqETf8ksDw0bipwbNi4PsCU0Li1wOOh4Wl4G4aNoffnJyC9mHjaAxPx1tENwLuF3sNrgEWhcf9H6ev8pELzjwh9BpuBZwALjUsG/hFa7mLgqvB1o4g4b8H7HmwH5uFt2JoCO4FGYdP1xPuOphbXNopY70PDTwZ+Cb1n3wGHFtq+3ATMCM33HyAdGB2KaRzQoIzbqnsIfS9Ccb6Dtx2qVpb5i/j8XCnTDA69dxY2bBkwZH9fr4wxZQAPAz+G3vtPgIahcZ8DVxeafgbwuyKW06a4dQKoFvqsrg5bn74F7gp7j98H3g19PtOA7oU+z4Fh04Zvp44Jff5b8L57lwDD8ZLPrNA6879i2u7wtsf/DRv2Pt72yxV6jy4Pi/2x0Dq6CPgL+24ni3w/Q+NPxdu3bQlNe3AJ7Sxyfwi8AeQBu0Ltu7mItk0Ezgx7jxwwLFQfCPwStm2YVNx3jVL2MWVYvz4FbijLug28DTwUNm4AsKaY5Rre9mxd6H2eAXQt7rOnhPyB0te/fbZnJbZ5P94c/wMvFMxuvKQiObQyTQ6NS8LbsdyF96Vqh7cSnljM8l8PrYB18L6gvwGXhX3wOcDVQApQI2zY9Xgbu7NDb+7eDUIG+V8Ef8UJe73VhHZ6eJnu4cXEdSmwIBR/beBD4I1CX8wid8pFjQ+tpDnAfaG4h+HtbBqExj+BtyI2DL0X/wMeLmbZ91B6IrQQ6Bh6zzKAR0LjuuCtdMfhJSKPh+La+6XuCRwZer/bAHOA6wq161OgLnAIsAf4KvQ+1cNLMi8u1ObHQ691PN4Xt1NpbQaG4CUhXYFaeF+80hKhBXhJ2d44fsPbkKTgrWevhE1/AV6ilIK34VgDpIXGfQ9cGCrXBo4Mlf8cirEm3nrfE6hbTDzv4G2kk/ASqGMKvYcTQu1uHYozfJ0tap0vnAh9BtQPzb+e/A3UiFDbW+Kt3+MofqfXCW+H1DxsPTooVB4FXBE27T+Bp8vYtvD1/nC8DeARoffsYrxtSvWw7ctkvOSnRWjaaUAPvHVmPHB3GbdV9+AlqjXwEoNXgeTQuPPwdmjF/bUutKyyJELXA6MLDfuM0M6ksv/w1vGV5H8nPiA/8TsL+CFs2u54Cfs+SSAlJEKh8V3xEuyDQ5/z5LD38R68ndfv8bZjN+LtrFLDPs99EiG89XQ7cG5ovkbAYaFxrwIPlNJ2F4prLd56X5/87YMr9B7t/S6NwPuh3ArvuzaBfbeTxb2fHfG2VYNC8d6Mt32pVkw7i9wfFp62mLbdR/5362942+5Hw8Y9GbZtKLwdKPM+ppT3twbevnHvdqTEdRuYTuiHTqjeOBRPoyKWfSJeTlAfLyk6GGhW1GdPKfkDJax/lLA9K+6vMq4am+ScG+Wcy8XLeruHhvcGDnDO3eecy3LOLQJeBM4pvAAzS8ZLZG5zzm13zi3B+zV7Ydhkq5xzTzvncpxzu0LD1gFPOOeynXc4dx5wUhnjzga6mFld59xm59y0YqY7H+9IwCLnXCZwG3BOBU9VZAP3heIehZeQdDIzA/4EXO+c2+Sc2w48RBHv2X54xTn3W+g9ew84LDT898BnzrmvnXN7gDvxfrEA4Jyb6pybHHq/lwD/xktgwj3qnNvmnJsFzATGhN6nrXi/5At3Hr/TObfHOTcRbwd1VhnafFaoDTOdczvwvgBlafPCsDgWOufGOedygP+Gx+Wce9M5tzHUzn/g7XQ7hUZnA+3NrLFzLtM5NzlseCO8jU9u6L3aVkws2XinT5s753Y75wr3VXs01O5leAnhuWHjilrnC3vEObclNP8E8j/fs/A2nCucc5uBR4p/u8gNtbuLmaU655Y45xaGxr2Glyzu/Z6ei/c9L0vbwv0J+Ldz7ofQe/YaXvJ8ZNg0Tzvn1jrnVgLf4O3Qfw6tnx+x7/pUkrrAF3g7kz+Gtk845952ztUv4W/ZfrzGXrXxfoSF24qX1EfKG2HfiTvxvkvJeD8mO5hZh9B0F+IdqcsqYVkbzGxL2N/BAM65mXhHIj/C29FcuPd9DJnqnHvfOZeN9yMnjYKfZ1HOB8Y5594Jbf82Oud+2b+msxvvh8jZeNuJT0PDinMW3n5iuXNuE16CUlhx7+fZwOfOubGhdj6GlywcXcxrFbc/LIuJ5G9jjwvFubd+fGh8WRW5jynDfM/jJTdfhuqlrduFx+8tF7XuZ4eGd8Y7wjTHObe6mDjKkj8Ut/6VtD0rUmUkQmvCyjuBtFCScCDQPPwLhpflphexjMZ4Wd/SsGFL8X4Z7rW8iPlWulDKFzZP8zLGfSZeprzUzCaa2VHFTNe8iLhSKLodZbUxtFPeayfeCnUA3lGGqWHv2Reh4eVV+POpHSo3J+w9DW0ANu6tm1lHM/ss1AluG15y0rjQsteGlXcVUa8dVt8ceo299n5WpbW5QJwU/CyKU+a4zOwGM5sT6ui3Be8o0t52Xob3i3Cumf1kZieHhr+Bt6EYaWarzOzvZpZqZseGdTjd22/sZrxfPz+GrjC5tFCshdvWvJhxxSnT51vSspxzC4Dr8JLMdWY20sz2xvEJ3galHd6v4q3OuR9D40prW7gDgRsKbQ9aUbC9+7M+leZI4FC8RNGVNnEFZeIlXuHq4h35KCD0vSrcObm4vzcKzx+m8HqTinfaew/eD54LzCyJgolrcRoXSgbnhI17De8X9Sjn3PziYnDO5eGdjilt+9sKLzmtqNeBi0J/r5cybVm2IUW+nxTa/ofauZyC+6Zwxe0Py+J7oKOZpeP9oHkdaGVmjfFO039dxuVA8fuYYpnZ/+EdFTsr7DtT2rpdePze8j7rvnNuPF4Xi2eAtWb2gpkVXvZeZckfilz/StmeFSmS9xFaDiwu9AWr45wbVsS0G8j/dblXa7zDlXsVtTFrETqiED7PqiKm22de59xPzrnTgCbAx3gbj6KsKiKuHApupCvLBrwN/iFh71k953VWL8oOvCRir6b78Vqr8TZKAJhZTbyjHHs9h3c4uYNzri7eSmiUXwMzqxVW3/tZldbmAnGG5qsUZnYs3rnks/AOG9fH+0VjAM65+c65c/HWkUeB982sVuhX1r3OuS54vwxPBi5yzn3j8jucHhJaxhrn3J+cc83xTqk9W+gKj8JtC19/K7IDX413Wqyo19lH6EjJMXjrusNrL8653XjfjfPxji68ETZPaW0Ltxx4sND2oKZz7p1ytq80Y/B+UX8V2rEA/qXHJSUf5Vm/ZgGHFtoWHUoRF1E47+hs7TL+XVh4/jCF15tsvO8SeMnL+Xj9NXY6574vR5v2ehbvVMiJZnZMcTGEkq6WFL39Dbcc77R1UfZnff8GaIa3YyztiuCybEOKez8LbP9Dn3ErCu6byqrE9jnnduKdDroWmBk6ivcd8Fe8o9obSpq/IszsXrwO6INdwaPbpa3bsyh41Ks7sNY5t5EiOOeecs71xOtO0RGvXyDs+96UJX8odv0rbntWnEgmQj8C28zsFjOrYWbJ5l2S2rvwhKHDiO8BD5pZHTM7EO/DL+1eIE2Aa0K/xv+Ad85xVBHTrQVahvV0rxbaINYLHVbbhnc4rSjvANebWVszq413ZOTdQtl2Sdbind8sVSirfRH4p5k1CcXawrye+UX5BTjOzFqbWT2803Zl9T5wspkdE3pf7qPg+lAH733JNLPOwBX7sezi3Bt674/FSx7+W4Y2vwdcYmZdQsna3ZUQx1518JLa9UCKmd1F2K8bM7vAzA4IxbglNDjXzPqbWTfzDp1vw9toFrn+mNkfzGxvQrIZ70sZPu1NZtbAzFrhbQAr64qd94BrQ+9lfbyEr0hm1snMTjDvstfdeIlpeIyv4/VLOJWw72QpbSu83r8IjDCzI8xTy8xOMrNynT4y71LkS0qaxjn3d7w+ZV+FflXjvEuPS0o+loWWb2aWhnekGjNLs+IvC84ItfsaM6tuZleFho8vT9vK6IKw78R9wPsu//Tf93inuf9B6UeDimVmF+L1f7sEr1P/a6Ft4F49zeyM0BGP6/BOdU4uvJxC3gIGmtlZ5l323sjyL8fen22lw7vS6dQyHPF7D++zaWlmDfCuciqsuPfzPeAkMxtgZql4/Qj34CUo+6ss7ZuId2HD3tNgGYXq5V1usczsNry+c4OKSGAyKHndfh24LPTeNcDryP5qMa/TO/T9T8X7Eb/3Iqai2lCW/KHI9a8M27N9RCwRCq1Ep+Ad4luMl12/hHfqoShX4705i/Ay/LeBl0t5mR+ADqFlPwj8vphMdDxe5rrGzPZm1RcCS8w77TOCUD+IIryMtzH5OtSO3aFYy+oevA3IFjM7qwzT34LXGW9yKLZxFHNu1zk3Fm/HOQPvl8RnZQ3Kef16/oL3Pq/G25GF34TrRrwvx3a8nVhFd9BrQq+xCm9jOMI5Nzc0rtg2O+dG4/WdGR+apjJ3Ll/i9SH6De/w924KHiIfAswys0y8q8vOCR0haYqXSG7D60Q+keKT9t7AD6FlfApc65xbHDb+E7zP7he8flP/qZSWeZ/ZGLx142e8Hwg5FL1BqI7Xh2gD3ufUBO8IIADOuW/xdqzTnNdfbK+S2nYPYeu9c24KXj+hf+GtBwvwdrD7LZS4N6L0nS7OufvxjviOM7OG+/EyB+JtQPf+8t2F1wdxbwyjzexvodfIAn6Hd5pmC94FFr9zJffLqag38HY4a/D6RlxTaPzrQDdK/zEJsMUKHhX7q3lHxp7AO9KZ6Zx7G+8Kyn+GzfcJXh+azXjb0zNCPyyLFUo0h+ElFJvw1vu9RxT+g3cadouZfVxa0M65WaHtWGlexPuuT8frgP9hEdMU+X465+bh7Ruexvt+nIJ3G5nyfLYPA3eE2ndjMdNMxPuB9nUx9aLcw/7tYwp7CO8o2PywdaBM67Zz7gvg73j9E5eG/or7sVoX77PYTP7Vyo+FxhX47MuYPxS3/pW4PSvK3kttRSLGvDuvvumca1nKpAnFvBvAdXDeOe1Iv9ZQ4Hnn3IGlTlz0/OOBt51zVXqH4GJiOQb4S+i0pRTBvJviDQ+dHojE8u/Bu1iguB+QMcPMMvC2T4Gv21I2lb3+6VljInEodDh5WOj0Qwu8X2kflXNZvfEuf4+KG+055yYpCSpe6PTOlcALQcciEguUCInEJ8O7w+tmvFNjc/DuybF/CzF7De9U5XXOu7WBRLFQ37r1eH0u3g44HJGYoFNjIiIikrB0REhEREQSlhIhERERSVh6onVI48aNXZs2bSp1mTt27KBWrVqlTxgD4qUt8dIOiJ+2xEs7IH7aEi/tgPhpS6TaMXXq1A3OuYo8vSDmKREKadOmDVOmTKnUZWZkZNCvX79KXWZQ4qUt8dIOiJ+2xEs7IH7aEi/tgPhpS6TaYWZleWxRXNOpMREREUlYSoREREQkYSkREhERkYSlPkIiIpKQsrOzWbFiBbt37w46lFLVq1ePOXPmlHv+tLQ0WrZsSWpqaiVGFR+UCImISEJasWIFderUoU2bNphZ0OGUaPv27dSpU6dc8zrn2LhxIytWrKBt27aVHFns06kxERFJSLt376ZRo0ZRnwRVlJnRqFGjmDjyFQQlQiIikrDiPQnaK1HaWR5KhERERKLIE088wc6dO/d7vldffZVVq1ZFIKL4pkRIRESkjFZvX83xrx7Pmsw1EXuN8iRCubm5SoTKSYmQiIhIGd3/9f1MWjaJ+ybeVynL27FjByeddBLdu3ena9eu3HvvvaxatYr+/fvTv39/AK644gqOP/54DjnkEO6++25/3jZt2nDfffdxzDHH8M477zBlyhTOP/98DjvsMHbt2lUp8SUCXTUmIiJSihoP1mB3Tn5n4+emPMdzU54jLSWNXbeXP+n44osvaN68OZ9//jkAW7du5ZVXXmHChAk0btwYgAcffJDU1FRq1qzJgAEDmDFjBoceeijgXRY/adIkAF566SUee+wxevXqVe54EpGOCImIiJRi0TWLOK/redRMqQlAzZSanN/tfBZfu7hCy+3WrRvjxo3jlltu4ZtvvqFevXr7TPPee+9x7LHH0qNHD2bNmsXs2bP9cWeffXaFXl90REhERKRUzeo0o271uuzO3U1aShq7c3dTt3pdmtZuWqHlduzYkalTpzJq1Chuu+02Bg8eXGD84sWLeeyxxxg/fjytW7fmkksuKXAZfCSeSJ9odERIRESkDNbuWMuIniOYfNlkRvQcUSkdpletWkXNmjW54IILuPHGG5k2bRp16tRh+/btAGzbto1atWpRr1491q5dy+jRo4tdVvh8UnY6IiQiIlIGH579oV9+5qRnKmWZv/76KzfddBNJSUmkpqby3HPP8f333zN06FCaNWvGhAkT6NGjB3369KF9+/b07du32GVdcskljBgxgho1avD9999To0aNSokx3kVtImRmLwMnA+ucc12LGG/Ak8AwYCdwiXNuWmjckNC4ZOAl59wjVRa4iIhIGZ144omceOKJBYb16tWLq6++2q+/+uqrRT5iY8mSJQXqZ555JmeeeWbEYo1X0Xxq7FVgSAnjhwIdQn/DgecAzCwZeCY0vgtwrpl1iWikIlIuu7Nz2ZPjcM4FHYqIJKioPSLknPvazNqUMMlpwOvO24JONrP6ZtYMaAMscM4tAjCzkaFpZxe7JBEplz05uWzblcO23dls25XNlp3ZLNu0k8UbdjBz5VamLN1ctgWNG7XPoJQkI71uGul1q9O0XhpN6qTRtJ5XP6B2GnVrpFAnLZW6ad7/ainR/LtORKJV1CZCZdACWB5WXxEaVtTwI6owLpGYtm77bmav2sb8tZks37yTJRt3snTjDpZu3P9b/ldETp5j5ZZdrNxSsRvDtTugFr0PbEjPAxtwcLO6dEivTVpqciVFKSKxLpYToaKeIOdKGL7vAsyG451WIz09nYyMjEoLDiAzM7PSlxmUeGlLvLQDKt6WPOdYnemYvDqH0UuyycmrvNgKO6CGYQZZubAn15GVC7lVdDZs0fodLFq/g3enLC8wvFGacVTzFDo1SKJV3STqV6/4EaV4Wb/ipR1Qclvq1asXM1dZ5ebmVjjW3bt3x83nWpliORFaAbQKq7cEVgHVihm+D+fcC8ALAL169XL9+vWr1AAzMjKo7GUGJV7aEi/tgP1ry66sXGav3sZnM1bxyrdLKvzaLerX4LBW9Tm0ZT26tahHq4Y1Sa+bVq7TUxX9THbsyWHZpp0s3biTJRt3MHnRRjLmrS91vo27HZ8tyuazQsN7HtiA3x3WnCPaNaJd41qkJJe9TfGyfsVLO6DktsyZM2efDsjRqqjO0vsrLS2NHj16VFJE8SOWE6FPgatCfYCOALY651ab2Xqgg5m1BVYC5wDnBRinSJVav30Ps1ZtZezstbz1w7L9mrduWgrdQwlOx/Q6NKtXg2b10sqd5FSFWtVTOLhZXQ5uVheAEccf5I/Lyc1j9dbdLNu0k7lrtjPxt/V8/VvJSdLUpZuZWkTfphM6N+H8I1rTq01D6tVIrdxGiEhgojYRMrN3gH5AYzNbAdwNpAI4554HRuFdOr8A7/L5P4bG5ZjZVcCXeJfPv+ycm1XlDRCJsDznWLg+k9mrtjFh7jo+/Hllmef9S/+DOLbDAbSoXyOqk5yKSklOolXDmrRqWJO+7Rtz2TFt/XHOObbszGbppp1MXbqZ8XPX8u2CjcUua/zcdYyfu67AsBb1azD8uHYc3/EAWjesGbF2iBSndu3aZGZmBh1GTIvaRMg5d24p4x3wl2LGjcJLlETihnOOeWu38/YPy3j9+6XewC8nljrfke0ackW/9hzZriHVU9RJeC8zo0GtajSoVY3DWtUvkCSBd2n/ko07mDB3PY+NmUdu3r6dmlZu2cXdn+b/zqpf3bi15jIGdUmnUe3qEW+DBGD1ajjnHHj3XWhascdrSHSI2kRIRCAvzzFh3jquHfkLmXtyyjTPpX3b8vueLenctA5JSUVdOyBlkZaaTOemdenctC5X9PNOt23ZmcX3Czfy3pTlTCiiH9KWPY5bP/yVWz/8FYCbTuzEqd2b00pHi+LH/ffDpElw333w7LOVssg333yTp556iqysLI444gieffZZ6tWrx7XXXstnn31GjRo1eOutt6hTpw6LFy/mvPPOIycnhyFDSrrVnpSVEiGRKJOdm8fomWu45p2fS522TaOaXHZMW47v2IRWDWvg3XBdIqV+zWoM7daMod2aAbBqyy4m/raef41fUORl/v/35Tz+78t5AJzTuxWX9G1Dp/Q6+pxiUY0aEPawU557zvtLS4Nd5b/Fw5w5c3j33Xf59ttvSU1N5corr+Stt95ix44dHHnkkTz44IPcfPPNvPrqq9x///1ce+21XHHFFVx00UU880zlPOYj0SkREokCu7Nz+d/0Vdz0/owSpxvUJZ0zD29BrzYNmTnl+7i5sidWNa9fg3P7tObcPq1xzvH2ZxNYXa0F/5qwYJ9pR/60nJE/eZfwH9aqPn8bdjC9Dmygo3axYtEiuPFG+Phj2LkTataE00+Hxx6r0GK/+uorpk6dSu/evQHYtWsXTZo0oVq1apx88skA9OzZk1GjvN4e3377LR988AEAF154IbfcckuFXl+UCIkEZuuubD79ZSV3flJ8X/5L+7alX6cDOPzABtSurq9rNDMzWtRJ4vx+nbjxxE7k5OYxfcUW/j1xEWNmry0w7S/Lt3DWv7/36/86rweDuqSrD1c0a9YM6tb1jgqlpXn/69atcD8h5xwXX3wxDz/8cIHhjz32mH/kMDk5mZyc/FPjOqJYubRlFalC67fv4aOfV/DQqLnFTvPvC3vSr9MB2inGuJTkJHoe2JAXLmoIePdyGj93HXd8/Cubd2YXmPaqt/NPg14zoAPDj2unxDcarV0LI0bA8OHwwgtex+kKGjBgAKeddhrXX389TZo0YdOmTSXeOLFv376MHDmSCy64gLfeeqvCry9KhEQibvmmnXw4bSX/HPdbsdPccdLBXHRUm7i9jF2gRrVkTjq0GScd6vUv2rwji1e/W8KTX80vMN1TX83nqdCwM3q04NahnWlSN63K45UifPhhfrmS+ud06dKFBx54gMGDB5OXl0dqamqJfX+efPJJzjvvPJ588kk9ab6SKBESqWTOOeavy+TDaSt5fuLCYqf7Q8+W3DbsYBrWqlaF0Um0aFCrGtcP6sj1gzqSk5vHF7PWFDgyBPDhzyv9+0Ndc0J7zu7Tmhb1awQRrkTQ2Wefzdlnn11gWPi9gX7/+99z4oknAtC2bVu+/z7/tOqtt95aNUHGMSVCIpUkJzePD6at4JYPfi12mq4t6vL3M7vTpXndKoxMol1KchInH9qckw9tzqotu3h50mJemrS4wDRPjV/AU+MX0LVFXR4541C6tqgXULQi8UWJkEgF7czK4Zp3fmbcnHVFjk9OMp45rwcDD07fr+dWSWJqXr8Gd5zchVuHdmbCvPVc887P7MrO9cfPXLmNk5+eBMArf+xNv44HqPOsSAUoERIppw2Zezjxn1+zcUdWkeNvHtKJ8/q0pn5NnfqS/ZeSnMSgLunMuX8Iq7bs4slx83l3yvIC0/zxlZ8AeOj0bvyhV0tSlWiL7DclQiL7afGGHfR/LKPIcWcc3oIr+x1E+yax8URriQ3N69fg0d8fyoOnd2Xs7LVc8da0AuP/9tGv/O2jX/nTsW25ZkAH6qTpobBl5ZxLiCNq3lOppChKhETKaNqyzZzx7Hf7DO/SrC63DO3MMe0bk6yb40kEpSQnMbRbM5Y8chKrQs85Gxt2j6IXv1nMi98spk/bhjx9bg/SdbVZidLS0ti4cSONGjWK62TIOcfGjRtJS9P6UBQlQiIlcM4xZvZa/vzG1H3G3Tq0M+cd0Zq6+vUtAWhevwYvXtSLnNw8PvllFTf8d7o/7sfFmzjioa8AGH3tsRzcTJ3zi9KyZUtWrFjB+vX7Pjcu2uzevbtCiUxaWhotW7asxIjihxIhkSLk5Obx7pTl3P7RzH3GvT/iKHq1aRhAVCL7SklO4syeLTmzZ0tWbN7JJa/8xIJ1+ZdeD33yGwBeuLAng7qkx/WRj/2VmppK27Ztgw6jTDIyMujRo0fQYcQlJUIiYXZm5fDviYv2uckdwNuXH8HR7RsHEJVI2bRsUJNxfz2enNw8Xv1uCQ98PscfNzx0VPOKfgdxw6COuoJRJESJkAiwMXMPj42Zxzs/Lt9n3EsX9WJgl/QAohIpn5TkJC4/th2XH9uOBeu2M/Dxr/1xz2Us5LmMhQzqks6T5xxGzWraDUhi0zdAEtrSjTu459NZTJi3bx+Bp8/twcmHNtOpBIlp7ZvUYckjJzFz5Vb//kMAY2evpctdX9K3fSOeOqcHjWpXDzBKkeAoEZKENHvVNm7473TmrN62z7hHz+zGWb1aKQGSuNK1RT0WPzyMCfPWcemrU/zh3y7YSM8HxjG0a1MeOr0bDfTIF0kwSoQkoezKcZzzwvdMXrRpn3F3n9KFi45qo0vgJW6ZGSd0TmfBg0N5c/JS7vnfbH/c6JlrGD1zDY+c0Y103XNGEogSIUkIzjmeGDefJ7/aCewsMO6mEzsx/Lh2uiuvJIyU5CQu6duWP/RqxYOj5vD2D8v8cbd+6D0rb9wh23VjUEkISoQk7i1cn8mAf0zcZ/hV/dtz1QntSUtNDiAqkeDVqp7CQ6d347oBHbj0tZ+YuTL/VPHAx7/mjMNb8ODvulGjmr4jEr+UCEncys7N47R/fcvsQv2ALu3blr8O7kjt6lr9RQCa1E3js6uPZd6a7Zz4RP4VZh9OW8mH01bywoU9GXxI0wAjFIkcnQuQuDTxt/V0uH10gSTo3D6t+NcJNbnrlC5KgkSK0Kmpd4XZdYcXvIJs+BtTaXPr56zZujugyEQiR4mQxJWtO7Npc+vnXPzyj/6wo9o14sfbB/DwGYdSu5o6QouU5rAmKSx6aBi3DOlcYPiRD3/FPZ/OIic3L6DIRCqfEiGJC845/jNpMd3vG1Ng+Dc39+ed4UfSpI4eNiiyP5KSjCv6HcTc+4cwoHMTf/ir3y2h/e2j+WHRxgCjE6k8Oj8gMW/xhh30fyyjwLD7f9eVC488MJiAROJIWmoy/7mkNxsz99DzgXH+8LNfmAzA9LsHU6+GHjwssUtHhCRm7cnJ5Zb3Z+yTBE2/a7CSIJFK1qh2dZY8chKjrjm2wPDu947hkdFzcbr3kMQoJUISk75buIFOd3zBu1Pynw12y5DOLHnkJOrV1K9TkUjp0rwuSx45iX/8obs/7PmJC2l72yhmr9r3Tu0i0U6nxiSmbNqRxR9f+ZHpK7YWGP7D3waQXlf9gESqypk9WzL4kHQOv38s2bne0aBhT31Dm0Y1+eK643R/LokZOiIkMcE5x1s/LOXw+8cWSIJGHH8Qix8epiRIJAB10lL57YGhPHpmN3/Yko076XznF4z6dXWAkYmUnY4ISdRbsG47w56aRFZOwUt2J9zYj7aNawUUlYiA9/yys3u3plebhgXu4H7lW9No36Q27/zpSA6ooyfbS/TSESGJWs45ns1YwMDHvy6QBJ3dqxULHhyqJEgkihx0QG3mPTCEk7o184ctWJdJ7wfHMW3Z5gAjEymZEiGJSntycjny4a/4+xfzCgz/31XH8OjvDyVFD0gViTrVU5J55vzDefGiXgWGn/Hsd7wxeWlAUYmUTHsTiTrLN+2k0x1fsHbbHn/Y4C7pzL1/CN1a1gswMhEpi0Fd0vnxbwMKDLvz45lc/tpPZOuu1BJllAhJVBk7ey3H/n1CgWFvX34EL1zUS1ehiMSQJnXTWPTQMC46Kv+eXuPmrKPD7aPZkLmnhDlFqpYSIYkaf333F/70+hS/3rtNA2bcM5ij2zcOMCoRKa+kJOO+07ry/oijCgzv9cA4ZqzYEkxQIoUoEZLA5eTm0ebWz/nw55X+sOfOP5z/jjiaumm6OaJIrOvVpiEz7hlMUtgzj0/917e8/v2SwGIS2UuJkARq044s2t8+usCwn24fyNCwK09EJPbVTUtl4UPDuG5gB3/YXZ/M4g/Pf6en2UuglAhJYH5dsZXD7x/r1y/t25bFDw/TPUdE4pSZcd3Ajnx53XH+sJ+WbKb97aPZvCMrwMgkkSkRkkC89cNSTvnXJL/+/oijuOuULphZCXOJSDzo1LQO8x4YQo2wCyB63D9W/YYkEFGbCJnZEDObZ2YLzOzWIsbfZGa/hP5mmlmumTUMjVtiZr+Gxk3Zd+kSlLw8x+WvTeH2j2b6w765uT+92jQMMCoRqWrVU5KZc/8Q7j6liz/s1H99y7MZCwKMShJRVCZCZpYMPAMMBboA55pZl/BpnHP/55w7zDl3GHAbMNE5tylskv6h8QXv7CWB2b47m3Z/G8W4OWv9YdPvHkyrhjUDjEpEgvTHvm2ZdEt/v/73L+Zx+P1jyc1zAUYliSQqEyGgD7DAObfIOZcFjAROK2H6c4F3qiQyKZdF6zPpds+YAsPmPTCEejV0VZhIomvZoCaLHhrm1zftyOKgv41i687sAKOSRBGtiVALYHlYfUVo2D7MrCYwBPggbLADxpjZVDMbHrEopUzGzV7LCWEPYzywkbfRq56iGySKiCcpyVj88DAGdUn3h3W/bwxTl+o5ZRJZ5lz0HX40sz8AJzrnLg/VLwT6OOeuLmLas4ELnHOnhA1r7pxbZWZNgLHA1c65r4uYdzgwHCA9Pb3nyJEjK7UdmZmZ1K5du1KXGZTytMU5x/u/ZfP54vxfdX2bp/CnQ4O7KizRP5NoFC/tgPhpS9Dt+HRhFh/Oz99unNEhlVMPqlauZQXdlsoSqXb0799/aqJ3IUkJOoBirABahdVbAquKmfYcCp0Wc86tCv1fZ2Yf4Z1q2ycRcs69ALwA0KtXL9evX78KBx4uIyODyl5mUPa3Lbuycjnnhe+ZvmKnP+yOkw7m8mPbRSC6skvkzyRaxUs7IH7aEnQ7+vWD7t8t4e5PZwHw4fxstqc25N8X9CQpaf+uLA26LZUlXtoRjaL11NhPQAcza2tm1fCSnU8LT2Rm9YDjgU/ChtUyszp7y8BgYGbheSVyVm7ZxcF3fcH0FVv9Yf++sGfgSZCIxI6Lj27DP8/u7tf3Podwx56cAKOSeBSViZBzLge4CvgSmAO855ybZWYjzGxE2KSnA2OcczvChqUDk8xsOvAj8Llz7ouqij3RLViXSd9HxhcY9ulVfTnxkKYBRSQiser0Hi158aL8szYrt+zi6EfGsysrN8CoJN5EZSIE4Jwb5Zzr6Jw7yDn3YGjY886558OmedU5d06h+RY557qH/g7ZO69E3uINOxj4+MQCw76+qT+HtqwfTEAiEvMGdUnn7cuP8Otbd2Vz7N8nsCdHyZBUjqhNhCS2LFiXSf/HMgoMm3rHQFo30j2CRKRijm7fmI//0tevb8jcwwmPTSRbzyiTSqBESCps5ZZdBY4ENapVjdn3nUij2npmmIhUjsNa1S/wjLKVW3Zx4hNf64GtUmFKhKRCNmTuKdAn6OiDGvHD3wZQs1q0XpAoIrGqU9M6TLypn19ftH4HJz89iTzdhVoqQImQlNvWXdn0emCcX7/4qAN56/IjSEnWaiUikXFgo1pMvm2AX5+7ZjunP/cd0XhPPIkN2mNJuezYk0P3e/MfmXH3KV2497Suenq8iERc03ppTLtzkF+fvnwLZ/97spIhKRclQrLfdmfncsjdX/r1J84+jD/2bRtgRCKSaBrWqsav9wz26z8u2cRFL/+oZEj2mxIh2S97cnLpfGf+bZmev+BwftejyMfAiYhEVJ20VObeP8SvfzN/A396fWqAEUksUiIkZZaTm0enO/KToIfP6MaQrs0CjEhEEl1aajK/PTDUr4+bs5a/vD0twIgk1igRkjLJc44uYafDLjzyQM7t0zrAiEREPNVSklj40DC//vmM1Vw38ucAI5JYokRISuWc42+TdpGV492vo0uzutz/u64BRyUiki85yVj8cH4y9PEvq7jl/RkBRiSxQomQlMg5xwX/+YE1O/I7IH5+zTEBRiQiUjSzgsnQu1OW8/rsPQFGJLFAiZCU6Lp3f+HbBRv9+vwHh+oSeRGJWmZW4DTZ+GU5PDJ6boARSbRTIiTFuufTWXzyyyq/PuOewaTqZokiEuWSk6zApfXPT1zIvycuDDAiiWbaq0mR/jn2N179bolff+z4GtRNSw0uIBGR/VAnLbXA4zgeHj2X179fElg8Er2UCMk+/jNpMU9+Nd+vf3Tl0TSuoVVFRGLLgY1qcXPvNL9+1yezGD93bYARSTTS3k0KeO+n5dz/2Wy//tS5PejRukGAEYmIlF+XRsncPuxgv37pq1OYunRzgBFJtFEiJL6xs9dy8wf5l5teM6ADp3ZvHmBEIiIV96fj2tGv0wF+/cznvmP11l0BRiTRRImQALBi807+9PoUvz7w4HT+OqhjgBGJiFSeFy/qVaB+7KMTyMnNCygaiSZKhITs3DyOeXSCX29RvwYvXNgzwIhERCpXanISP4c9sT4nz3HnJzMDjEiihRIh4ciHvipQ/+qG40lK0r2CRCS+NKhVjTHXH+fX3/lxORPmrQswIokGSoQS3GvfLWHjjiy/PvWOgaSlJgcYkYhI5HRMr8Mz5x3u1//4yk+s3bY7wIgkaEqEEtjKLbu4+9NZfn38DcfTqHb1ACMSEYm8kw5txvlH5D80+oiHviI3z5Uwh8QzJUIJKjfP0feR8X79vT8fRbsDagcYkYhI1Xngd12pk5bi1296f3qA0UiQlAglqBOf+NovP35Wd/q0bRhgNCIiVcvM+On2gX79w2krmTBX/YUSkRKhBPTlrDUsWJcJwNCuTTnj8JYBRyQiUvXSUpP58W8D/PofX/2J9dv1tPpEo0QowWzM3MOf35jq1589//ASphYRiW9N6qbx3p+P8uu9Hxyn/kIJRolQAsnLc/R8YJxfn3nviZjpMnkRSWx92jbkhrAbyP75jSklTC3xRolQAvnbR7/65cfP6k7t6iklTC0ikjiuHtCBFvVrADBuzjrGzdbDWROFEqEE8dOSTYz8ablfV78gEZGCvrm5v1++/PUpbMhUf6FEoEQoAWzdmc0fnv/er8+698QAoxERiU5JSVZg+9jrgXHkqb9Q3FMiFOeccxz9SP4jNJ6/4HBq6ZSYiEiRalVP4fVL+/j1oU9+E2A0UhWUCMW5f41fwI6sXAAOqFOdIV2bBRyRiEh0O67jARzWqj4A89ZuZ/Svq4MNSCJKiVAcm7lyK/8Y+5tfz7ixX3DBiIjEkNcvyz8qdMVb03R/oTimRChOZe7J4eSnJ/n1ly/ppVNiIiJlVDctlefC7rPW+8FxOKf+QvFIiVAccs5xwUs/+PUuzepyQuf0ACMSEYk9Q7s1o3XDmn795vdnBBiNRIoSoTj0zo/L+WX5Fr/+3xFHFT+xiIgU690/H+mX/zt1BdOWbQ4wGokEJUJxZsG67QVunPj6pX10SkxEpJya1avBTSd28utnPPsdu7NzA4xIKpsSoTjinGPYk/n9go5s15DjOh4QYEQiIrFvxPEHFag/P3FhQJFIJCgRiiOfTl9FVm6eX//Pxb0DjEZEJD4kJxmjrjnWrz8xbj4bddfpuKFEKE7k5OZx7chf/Ppblx+hU2IiIpWkS/O6nHhI/kUnN6njdNyI2kTIzIaY2TwzW2BmtxYxvp+ZbTWzX0J/d5V13nh0/XvT/fIJnZvQt33jAKMREYk/T5zdwy+Pn7uO+Wu3BxiNVJaoTITMLBl4BhgKdAHONbMuRUz6jXPusNDfffs5b9zYvjub/01f5defPrdHCVOLiEh51KiWzIsX9fLrJz7xdYDRSGWJykQI6AMscM4tcs5lASOB06pg3ph06L1j/PLbOiUmIhIxg7qkUz3F23XmORg/d23AEUlFRWsi1AJYHlZfERpW2FFmNt3MRpvZIfs5b1xYvmkne292OrhLOkfrlJiISER9d+sJfvnSV6eQE3aRisQei8ZbhpvZH4ATnXOXh+oXAn2cc1eHTVMXyHPOZZrZMOBJ51yHsswbtozhwHCA9PT0niNHjqzUdmRmZlK7du1KXWZhl3yxwy8/P7AmaSkWkdepirZUhXhpB8RPW+KlHRA/bYmXdkDk2vLxgiw+XpANwBkdUjn1oGqV/hrhItWO/v37T3XO9Sp9yvgVredQVgCtwuotgVXhEzjntoWVR5nZs2bWuCzzhs33AvACQK9evVy/fv0qJfi9MjIyqOxlhvth0UZgMgD/vrAnJx7SNGKvFem2VJV4aQfET1vipR0QP22Jl3ZA5Npy/PGOj28bBcCH87O59/z+1ElLrfTX2SuePpNoE62nxn4COphZWzOrBpwDfBo+gZk1NTMLlfvgtWVjWeaNB845zn5hsl+PZBIkIiIFmRlfXnecX7/stSkBRiMVEZWJkHMuB7gK+BKYA7znnJtlZiPMbERost8DM81sOvAUcI7zFDlv1bcist6bkt8NKvzLKCIiVaNT0zp0a1EPgB8Xb2L5pp0BRyTlEa2nxnDOjQJGFRr2fFj5X8C/yjpvPMnKyeOWD/KfJ9apaZ0AoxERSVwfXHE0He8YDcCxf5/AkkdOCjgi2V9ReURISvb3L+b65THX62iQiEhQqqUk8cx5h/v1b+avDzAaKQ8lQjFmy84sXpq02K93TNfRIBGRIJ10aDO/fOF/fiQar8aW4ikRijFXv/OzXx6ro0EiIlEh48Z+fvnRL+YFF4jsNyVCMWTJhh18M3+DX++go0EiIlGhTeNaVEv2dqnPT1zI7uzcgCOSslIiFEN+//x3fllHg0REostHfznaL5/+7HclTCnRRIlQjPhx8SY2ZGb5dR0NEhGJLoc0r0edNO9i7Dmrt7Fqy66AI5KyUCIUA/LyHGf9+3u/rivFRESi078v7OmXj35kfICRSFkpEYoBH/280i9XT0nSlWIiIlHqqHaNCtTnrN5WzJQSLZQIRbnd2bnc8N/pfv3Tq44JMBoRESmJmRW4r9DQJ7/R5fRRTolQlHt+4kK/XDctRXeRFhGJckO6Fnz2409LNgcUiZSFEqEolpObxxPj5vv190YcFWA0IiJSFslJxp0nd/HrD46aE2A0UholQlHs0+mr/HLj2tXp3LRugNGIiEhZnX9Ea788ffkWNmbuCTAaKYkSoSj21/fy+wa9fmmfACMREZH9kZaazCVHt/Hrr32/NLhgpERKhKLUovWZfrlZvTS6NNfRIBGRWPLXwR398lNfzScvT52mo5ESoSj1h+fz7xv04kW9AoxERETKo25aKsd2aOzXv124oYSpJShKhKJQTm4eG3d4d5FuUb8GXVvUCzgiEREpj3/8obtfvuLNaQFGIsVRIhSFXv1uiV9+/oKexU8oIiJRrUndNP+xG5l7cli3bXfAEUlhSoSi0AOf519q2a2ljgaJiMSyj//S1y//c9xvAUYiRVEiFGWWb9rplz+4QvcNEhGJdQcdUNsvv/PjcnLVaTqqKBGKMn989Se/3PPAhgFGIiIileWdPx3pl7+ctSbASKQwJUJRJDs3jwXrvMvmLziydSlTi4hIrDjqoPyHsV75ljpNRxMlQlHkk1/y7yR969CDA4xEREQq299/f6hfXrllV4CRSDglQlHkxrCnzNeunhJgJCIiUtn+0LOlXx7++pQAI5FwSoSiRHgn6fCH9YmISHwwMy488kAAZq3aRnZuXsARCSgRihr3fzbbL4c/rE9EROLHXafk/9B9Q88fiwpKhKJAdm4eY2av9etpqckBRiMiIpGSmpy/270v7AewBEeJUBQYPTP/Usqnzu0RYCQiIhJpz19wuF9esG57gJEIKBGKCte887NfHnJI0wAjERGRSDu+YxO/POzJSQFGIqBEKHBLN+7wy41rV6Naij4SEZF4VqNaMi0b1AAgKzePPTm5AUeU2LTXDdi/xi/wy4+fdVhwgYiISJW5fmBHv/zEuPkBRiJKhAKUlZPHf6eu8Ot92zcOMBoREakqAw9O98vPZSwMMBJRIhSgMbPzO0kf3ro+yUkWYDQiIlJV6tVMLVDf+3glqXpKhAJ06we/+uXbT9IjNUREEsntw/K3+698uzjASBKbEqGAbN6RReaeHL9+eOsGAUYjIiJV7ZTuzf3yWz8sCzCSxKZEKCAZv63zyycd2gwznRYTEUkkTeulFahvzNwTUCSJTYlQQO76eJZfvuL4gwKMREREgnLJ0W388veLNgYXSAJTIhSQ7WGnxQ5pXjfASEREJCgXHXWgX9azx4KhRCgAq7fu8suXHN1Gp8VERBJUuwNq++UfFm8KMJLEpUQoAP/5Jv/qAD1pXkQksR3X8QC/vGLzzgAjSUxKhALw0qT8RKhDep0AIxERkaDdODj/LtMT5q4rYUqJBCVCAbqynzpJi4gkum4t6vnl//tyXoCRJKaoTYTMbIiZzTOzBWZ2axHjzzezGaG/78yse9i4JWb2q5n9YmZTqjbyki3bmH/Y85zeOi0mIpLozIyGtaoBsG13Ds65gCNKLFGZCJlZMvAMMBToApxrZl0KTbYYON45dyhwP/BCofH9nXOHOed6RTzg/fDWj/lXBbRuVDPASEREJFo89odD/fJ8PW6jSkVlIgT0ARY45xY557KAkcBp4RM4575zzm0OVScDLas4xnL598RFQYcgIiJR5rgO+R2m3w97GLdEnkXjITgz+z0wxDl3eah+IXCEc+6qYqa/EegcNv1iYDPggH875wofLdo733BgOEB6enrPkSNHVmo7MjMzqV07/9JI5xx//NI7NXZ2p2oMbZta3KxRp3BbYlW8tAPipy3x0g6In7bESzsgttpyyRc7/PKrQ2oVGBepdvTv339qtJ05qWopQQdQjKJurFNkxmZm/YHLgGPCBvd1zq0ysybAWDOb65z7ep8FegnSCwC9evVy/fr1q3Dg4TIyMghf5vy12+FLL4y/nnks6XXTipkz+hRuS6yKl3ZA/LQlXtoB8dOWeGkHxFZb7q22hLs/9Z46cMyxx5GSnH/SJpbaEWui9dTYCqBVWL0lsKrwRGZ2KPAScJpzzr83uXNuVej/OuAjvFNtgfvw55V+OZaSIBERibyze+fv9n5ZviW4QBJMtCZCPwEdzKytmVUDzgE+DZ/AzFoDHwIXOud+Cxtey8zq7C0Dg4GZVRZ5CZ7LWBh0CCIiEqXSUpP98kOj5gQYSWKJylNjzrkcM7sK+BJIBl52zs0ysxGh8c8DdwGNgGdDj6jICZ3nTAc+Cg1LAd52zn0RQDMKyM3LP7N3RNuGAUYiIiLR6oi2Dflh8SamLdsSdCgJIyoTIQDn3ChgVKFhz4eVLwcuL2K+RUD3wsODNnvVNr8c/rRhERGRvYYf185/5tju7NwCR4kkMqL11FjcGTVztV8+ol2jACMREZFodUjz/LtMj5m9NsBIEocSoSoS3j9o7x1ERUREwqXXre6Xb/rv9AAjSRxKhKpAVk5e0CGIiEgMCPVvBWCP9h1VQolQFZixYotfPu8IPV9MRESKN+SQpn55667sACNJDEqEqsDYOfnneU8+tFmAkYiISLTr1yn/cRtjZq0JMJLEoESoCoQ/X6xbi3olTCkiIonu4GZ1/fLbPy4LMJLEoEQownZl5Rao10mLneeLiYhI1euYXscv/6z7CUWcEqEIm716q19uUb9GgJGIiEgsqFGt4L2Dwm/IK5VPiVCELVyf/zRhdZQWEZGyqJ6Sv3teu213gJHEPyVCEfbFzPyObke206M1RESkdCcf2twvL9+0M8BI4p8SoQgbP3edX+7STB2lRUSkdIO6NPHLyzfvCjCS+KdEqAoVPu8rIiJSlPBHbcxcubWEKaWilAhVkaP0fDERESmj8Itrvpm/PsBI4p8SoQjKc/k9/U/SjRRFRKSMkpLyH7URftGNVD4lQhG0bU9+ItS9Zf3gAhERkZhTJy0l6BASghKhCFq7Mz8R6tS0TglTioiIFHRGjxZ+OUf3EooYJUIRtHBr/l2lq6XorRYRkbI7sWv+w1c37VYiFCnaO0fQ3I15QYcgIiIxqmvYsyk37FIiFClKhCJoxobc0icSEREpQt2wZ1Mu3KL9SaQoEaoCBzaqGXQIIiISw6avVyIUKUqEqkDvNnq0hoiIlN+CLepqESlKhCLEhd1DqGN67QAjERGRWPXn49oFHULcUyIUIRsys/xy+yZKhEREZP8d3/GAoEOIe0qEImTF5vynBTetW6OEKUVERIrWqHZ1v7w7W/2EIkGJUISEPy24fs3UEqYUEREpWs2wh3Wv0FPoI0KJUISEPy24Qc1qAUYiIiKxqlb1/MdsTFu2OcBI4pcSoQiZujR/ha0RltGLiIiUVa3q+fuPb+ZvCDCS+KVEKELCEyEREZHyqJacv5v+Zv76ACOJX0qEREREopSZ+eUtO7MDjCR+KRGKgPB7CImIiEj0UiIUARt35N9DKMlKmFBEREQCpUQoAsIvcezQpE6AkYiISDzRvYQqnxKhCNi2K/88bns9XkNERCpJnrpeVLoKJ0Jm9mhZhiWSsL5ttD9AiZCIiFQOQ/0tKltlHBEaVMSwoZWw3Ji1Ozv/KcEt6uvxGiIiUn61dC+6iEopfZKimdkVwJVAOzObETaqDvBtRQOLZVvDTo3p8RoiIlIRDWtXY8cmr++p6YBQpSt3IgS8DYwGHgZuDRu+3Tm3qUJRxbjU5Pw1tUEtPV5DRETKr2HNaizfpOeMRUpFEqFkYBvwl8IjzKxhIidD1VPyzzjWr6EjQiIiUn76QR1ZFUmEpgIOMKA1sDlUrg8sA9pWNLhYVT0l/3xufT1wVUREKqBhWCKkU2OVr9ydpZ1zbZ1z7YAvgVOcc42dc42Ak4EPKyvAWFQt/IiQ+giJiEgFNAz7Qa2rxipfZVw11ts5N2pvxTk3Gji+ogs1syFmNs/MFpjZrUWMNzN7KjR+hpkdXtZ5Iy08EUpN1q2aRESk/JJStrCm2q3kood5R0Jl7KU3mNkdZtbGzA40s9uBjRVZoJklA8/gXYbfBTjXzLoUmmwo0CH0Nxx4bj/mjagkHbsUEZFKMmHVc+xJmsWW1Ld1aiwCKtJHaK9zgbuBj/D6DH0dGlYRfYAFzrlFAGY2EjgNmB02zWnA6857wulkM6tvZs2ANmWYN6L0fDEREamoGg/WYHfObq9ikJkymmoPJJOWksau23UVWWWpyH2EbgO+cM79DFxbeSEB0AJYHlZfARxRhmlalHFeAMxsON7RJNLT08nIyKhQ0Hst2pL/LJjKWmbQMjMz46It8dIOiJ+2xEs7IH7aEi/tgNhuy5u93uS5Rc+RsW4SuezBXHVOSD+GKw+6MmbbFI0qckRoMXCtmXUHpuPdU2iMc64yTmIWdUyl8ANWipumLPN6A517AXgBoFevXq5fv377EWLxGq7YApO9e0oed9zxJMXBIaKMjAwq6/0JUry0A+KnLfHSDoiftsRLOyD22zLus3GMXzceXCqOLNq36sAZg88IOqy4Uu5EyDk3EhgJYGY9gCHAh6E+OuPwjhb9WM7FrwBahdVbAqvKOE21MswbUeG9+ndk5VAnTVeOiYjI/lu7Yy09Gp3F6pV92Z7yBWsz1wYdUtyplEuanHM/O+ceds71x7t8fhZweQUW+RPQwczamlk14Bzg00LTfApcFLp67Ehgq3NudRnnjajwzmyZe3Kq8qVFRCSOfHj2h5yQfhvVXDsaZV/Jh2d/EHRIcafCnaXNbArwCvC2c26zc24b8EHor1ycczlmdhXePYqSgZedc7PMbERo/PPAKGAYsADYCfyxpHnL3cByCE+Etu/OoVm9qnx1ERGJJ6u2qmN0JFXGVWPn4CUhP4UlRWNCV3OVW+jeRKMKDXs+rOwo4vEexc1blcIvn9++W0eERESk/JZs2OmXTdfPV7oKnxpzzi1wzt0OdMR7EOvLwDIzu9fMGlZ0+bEofD3dsjMruEBERCTmrdyiI0KRVCl9hMzsUOBx4P/wTon9Hu+BrOMrY/mxJvyI0LrtewKMREREREpSGX2EpgJbgJeAW5xze/f8P5hZ34ouPxaFH7hct02JkIiISLSqyA0V/xoqvgvkAM2Av+w9f+mce9w5l5A3Owg/h7s+c3eAkYiIiEhJKnJqrE7o7zDgCvLv6jwC7xlfCSu8j5COCImISHnl5XnXHR2QuYl3374V1qwJOKL4U+5EyDl3r3PuXqAxcLhz7gbn3A1AT7ybGCaspAJHhJQIiYhI+WwP3Yvumm/foffyWXDffQFHFH8q4/L51kD4pVFZeA8+TVjqIyQiIpWhboO6LNkT1sXiuee8v7Q02KWrySpDZVw19gbwo5ndY2Z3Az8Ar1XCcmNWgSNCumpMRETKad53v/DxwcezK6W6N6BmTTj/fFi8ONjA4kiFjwg55x40s9HAsaFBfww9kT5h1auZ/2yxrNy8ACMREZFYtqleIzKr16R6ThbZqdVJ3b0b6taFpk2DDi1uVMapMZxz04BplbGseFCvhh6yKiIiFbchM4vGO7fwZo+hHHb/zRw66j1YvTrosOJKpSRCIiIiUvmWbNjB46ffDsA3R/WGk44POKL4Uyl3lhYREZHKt2TDDr+cXjctwEjilxKhCGmqFVZERCpoUVgiVC1Fu+xI0LsaIQMObuKXs9VhWkREyuGX5VuCDiHuKRGKkP6d8hOhzN05AUYiIiIixVEiFCGHtKjrlzP3KBESEZHyO7CudteRonc2QtLr5PcR2rorO8BIREQk1h1UX7vrSNE7GyFJSfl3l56zeluAkYiISKxrV0+760jRO1sF3pi8NOgQREQkhrWord11pOidjaBaoRtMz1ixNdhAREQk5uzKyvXLDdO0u44UvbMRdHRz3bhbRETKZ86a/G4VdaoFGEicUyIUQV0aJfvlrBzdS0hERMpuetg9hJLMip9QKkSJUASl18x/e39buz3ASEREJNaMm7M26BASghKhCGpcIz+D/3LWmgAjERGRWPPtgo1Bh5AQlAhFULXk/ETo/akrAoxERERiyZ6c/I7SenZlZCkRqiKrt+4OOgQREYkR89bkd6fo3bZhgJHEPyVCEdYxvbZfds4FGImIiMSK8I7SA8Me4i2VT4lQhIU/fHXF5l0BRiIiIrHiw59X+uUuzeqWMKVUlBKhCOvaop5fnr5iS3CBiIhIzPh52Ra/3Kx+jeACSQBKhCLswEY1/fLoX3XlmIiIlCw7t+B952pX1815I0mJUIQd2LCWX/7819UBRiIiIrFg/tpMv9xHHaUjTolQhNWrmRp0CCIiEkN+WJx//6CzerUKMJLEoESoim3ekRV0CCIiEsXe+XGZXz6ynY4IRZoSoSpwQuf8K8fmrN5WwpQiIpLofgs7NdayQc0SppTKoESoCpzbp7Vf/jns3hAiIiLhcvPy7zfXoUntEqaUyqJEqAr0bd/IL/9v+qoAIxERkWi2aH3+0aDLjmkbYCSJQ4lQFahZLf/Sx7lr9BR6EREp2tiwJ873bd84wEgShxKhKnJw2J1Bd2fnljCliIgkqhe+XuSXWzVU/6CqoESoitx50sF+OfweESIiIntt2ZkNQN003USxqigRqiJHtMvvJ/Tz8s0BRiIiItEoL6yj9LUDOwYYSWKJykTIzBqa2Vgzmx/636CIaVqZ2QQzm2Nms8zs2rBx95jZSjP7JfQ3rGpbsK/kJPPL9/1vdoCRiIhINFq0YYdfHtwlPcBIEktUJkLArcBXzrkOwFehemE5wA3OuYOBI4G/mFmXsPH/dM4dFvobFfmQS3fRUQcCkBOW9YuIiAC8P3WFX1b/oKoTrYnQacBrofJrwO8KT+CcW+2cmxYqbwfmAC2qKsDy+NOx7fzyJt1hWkREwjw/cWHQISSkaE2E0p1zq8FLeIAmJU1sZm2AHsAPYYOvMrMZZvZyUafWghCe4T88ak6AkYiISLS6ZkCHoENIKOZcMKdpzGwc0LSIUbcDrznn6odNu9k5V2QyY2a1gYnAg865D0PD0oENgAPuB5o55y4tYt7hwHCA9PT0niNHjqxQmwrLzMykdu2CdwYdMXYHu0NXz786pFYRc0WnotoSi+KlHRA/bYmXdkD8tCVe2gGx05ZNu/P4a8YuAP7vuBocULPgcYpItaN///5TnXO9Kn3BMSSw6/OccwOLG2dma82smXNutZk1A9YVM10q8AHw1t4kKLTstWHTvAh8VkwMLwAvAPTq1cv169evPE0pVkZGBoWX+Wj9lVw78hcAehzRl3o1YuPp9EW1JRbFSzsgftoSL+2A+GlLvLQDYqctT381H/gNgN8P7Y+ZFRgfK+2IRdF6auxT4OJQ+WLgk8ITmLeW/AeY45x7vNC4ZmHV04GZEYpzv/UPewDrq98uCS4QERGJGv8Y+5tfLpwESWRFayL0CDDIzOYDg0J1zKy5me29AqwvcCFwQhGXyf/dzH41sxlAf+D6Ko6/WHXT8o8A/XPcbyVMKSIiiWDVll1++axeLQOMJDFF5a0rnXMbgQFFDF8FDAuVJwFFps3OuQsjGmAFndGjBR/+vBKAHXtyqFU9Kj8GERGpAh//stIvX9GvfYCRJKZoPSIU1847orVf/ujnlSVMKSIi8e7vX8zzy20a6f5BVU2JUAC6t6rvl+/4OGq6L4mISBVbGXZaDNQ/KAhKhAKQmpxEjdRkv66n0YuIJKb3flrul286sVOAkSQuJUIBuWFw/gP1xs5eW8KUIiISr578ar5fPuXQ5gFGkriUCAXkhLDL6O/6RKfHREQSzYrNOwvUWzWsEVAkiU2JUEDaNs6/q/TmndnsydHpMRGRRPL690v98l8HdVT/oIAoEQqImXF8xwP8+qT5GwKMRkREqtoLXy/yy+f0aRVgJIlNiVCAzuqVv+L/35fzSphSRETiyfJN+afFmtVLo0mdtACjSWxKhALUv3P+EaG5a7aTnZsXYDQiIlJVns1Y6JcfOr1bgJGIEqEA1ayWQpdmdf365EUbA4xGRESqyjs/LvPLx4V1k5Cqp0QoYP88+zC/HH6+WERE4lP4abGze7UiOUmdpIOkRChgnZrW8cvfzN9Abp4LMBoREYm0R0bP9ctXD9CzxYKmRCgKhN9N9KclmwKMREREIu3zX1f75ZYN9GyxoCkRigJ/Pq6dX37pm8UBRiIiIpG0ZMMOv/z4Wd0DjET2UiIUBVKSk2hcuzoA4+asJU+nx0RE4tIN/53ul0/WIzWighKhKPH5Ncf45UkLdHNFEZF4NHXpZgAOblaXainaBUcDfQpRIr1u/s20Lnr5xwAjERGRSJi/drtffvrcw4ILRApQIhRFXrmkt19evXVXgJGIiEhlO+eFyX65fZM6JUwpVUmJUBTp1yn/plpHPzI+wEhERKQy7cnJZeOOLACuOUGXzEcTJUJRxMwYHrqCzDnYujM74IhERKQyvDxpiV8e0e+g4AKRfSgRijJXh/1SuORV9RUSEYl12bl5PPpF/k0Ua1ZLCTAaKUyJUJSpk5ZK28a1APh52RZ2ZuUEHJGIiFTER9NW+uV3hx8ZYCRSFCVCUei5Cw73y/f9b3aAkYiISEXk5jlu/mCGXz+iXaMAo5GiKBGKQp2b5j+RfuRPy8nKyQswGhERKa/PZqzyy0O7Ng0wEimOEqEo9dgf8m+9/u+JCwOMREREyiMvz3HtyF/8+iNnHBpcMFIsJUJR6tTu+bde/8fY3/RUehGRGPPlrDV+2Qzq1UwNMBopjhKhKFUtJYlz+7Ty6x9MXRFgNCIisj+cc1zx1jS//vbl6iQdrZQIRbGrT+jgl2/+YAbO6aiQiEgsmDBvXYH6ke0aBhSJlEaJUBRrXr8GLerX8OtfzVlXwtQiIhINnHNc+uoUv/78BYdjZgFGJCVRIhTlHjmzm1++/PUpJUwpIiLRYNKCDQXqJx6iq8WimRKhKNf3oMYF6j8u3hRQJCIiUhYX/if/qQAfXHG0jgZFOSVCUS4pyXg07KjQhf/5IcBoRESkJD8s2uiXW9SvQc8DGwQYjZSFEqEY8Iee+VeP7cnJY+bKrQFGIyIixTn7hcl++c3LjwgwEikrJUIxICnJePmSXn79+nd/CS4YEREp0rRlm/1y3/aN/OdGSnRTIhQjTuic7pfnr8tk0frMAKMREZHCznj2O7/81Dk9AoxE9ocSoRgy4cZ+fvnOT2YGF4iIiBQQ3mXhvCNa06h29QCjkf2hRCiGtG1ci/qhW7R/u2Ajq7bsCjgiEREBOPnpSX75zpO6BBiJ7C8lQjHmu1tP8MunhH3xREQkGPPWbPfLtwzpTI1qyQFGI/tLiVCMqVkthSv7HQTAxh1ZOiokIhKwE5/42i8PP65dgJFIeSgRikE3ndjJLx/9yPgAIxERSWwL1uVfuPL0uT1ITtLNE2NNVCZCZtbQzMaa2fzQ/yLvSGVmS8zsVzP7xcym7O/8scrMGDk8/0nGL369KMBoREQS18DHJ/rlkw9tFmAkUl5RmQgBtwJfOec6AF+F6sXp75w7zDnXK2zY/swfk45s18gvPzhqDtt3ZwcYjYhI4vno5xV++f0RR+lRGjEqWhOh04DXQuXXgN9V8fwxYfJtA/xyt3vGBBiJiEhi2bIzi+vfne7Xe7VpGGA0UhHRmgilO+dWA4T+NylmOgeMMbOpZja8HPPHtKb10ji9Rwu/Pn7u2gCjERFJHFe8Oc0vZ4Td401ijznngnlhs3FA0yJG3Q685pyrHzbtZufcPv18zKy5c26VmTUBxgJXO+e+NrMtZZx/ODAcID09vefIkSMr2qwCMjMzqV27dqUus7CsXMfwsTv9+guDalItufIPz1ZFW6pCvLQD4qct8dIOiJ+2xEs7IDJtmbE+h8en7vHrrw6J/KM0IvWZ9O/ff2qhriUJJyWoF3bODSxunJmtNbNmzrnVZtYMWFfMMlaF/q8zs4+APsDXQFnnfwF4AaBXr16uX79+FWpTYRkZGVT2MovyWP0V3Phf7xDt64trRuRBf1XVlkiLl3ZA/LQlXtoB8dOWeGkHVH5btu/O5pKwrgg/3zmIBrWqVdryixNPn0m0idZTY58CF4fKFwOfFJ7AzGqZWZ29ZWAwMLOs88eTMw/PPz02acEGPZ1eRCRC/vL2z365b/tGVZIESWRFayL0CDDIzOYDg0J1zKy5mY0KTZMOTDKz6cCPwOfOuS9Kmj9emRmfXX2MXz/56Unk5gVzylNEJF59t3ADX/+23q+/fEnvAKORyhLYqbGSOOc2AgOKGL4KGBYqLwK678/88axri3r0OrABU5ZuBuDhUXO442Q970ZEpDLsysrlvBd/8OsPnt6V6il6lEY8iNYjQlIOz13Q0y+/NGkxyzftLGFqEREpq7+8Pa1A/dzerQOKRCqbEqE4ckCd6lxzQnu/fuzfJxDUVYEiIvFi6tJNjJ+bf83N+BuOJ0mP0ogbSoTizF/CEiGANycvDSgSEZHYtycnlzOf+96vP3R6N9odEB+3FhCPEqE4Uz0lmX9fmH+K7M5PZrF++54S5hARkeL85a38q8S6tqjLuX1aBRiNRIISoTg0uEs63VrU8+vnvTg5wGhERGLT9OVbGDcn/4797/zpSD1PLA4pEYpDZsa7f85/Ov38dZmMmbUmwIhERGJLdm4epz3zrV//6MqjqZOWGmBEEilKhOJUzWopfHTl0X59+BtT9YR6EZEyGvHGVL982TFt6dF6n6c0SZxQIhTHerRuwGXHtPXrN7w3vYSpRUQEYNaqrXwVdpXY7cMODjAaiTQlQnHuzrCbKo6ZvZbJizYGGI2ISHTLzXOc9NQkv/7j3wboUvk4p0QoAcy9f4hfPueFyezOzg0wGhGR6HXJKz/65WfOO5wmddMCjEaqghKhBJCWmszY64/z653v/KKEqUVEEtPcNdv4Zv4GADo3rcNJhzYLOCKpCkqEEkSH9DrcNrSzX7/rk5kBRiMiEl3y8hxDnvjGr39yVd8Ao5GqpEQogfz5+IOom+Y9Z/f175fyVdj9MUREElnvB8f55XF/PU4PVE0gSoQSzJQ7Bvnly16bwtKNOwKMRkQkeC9+vYiNO7IAGH5cO9o3qRNwRFKVlAglmGopSXxzc3+/fvz/ZbBjT06AEYmIBOe7BRt4cNQcvx7ehUASgxKhBNSqYU2eOreHXz/k7i/JzdNT6kUksSxYl8l5L/3g13+9Z7AeoZGAlAglqFO7N2dA5yZ+/Yxnvy1hahGR+LIxcw8DH5/o11++pJceoZGglAglsPCn1E9fsZWnvpofYDQiIlVjd3YuPR/I7xzdu00DTuicHmBEEiQlQgksJTmJybcN8OuPj/2Nib+tDzAiEZHIcs5x2r8KHgF/d/hRAUUj0UCJUIJrWi+NV//Y269f/PKPupJMROLWrR/8yry12/26HqEhSoSEfp2acNFRB/r14/8vg216Ur2IxJnXv1/Cu1OW+/X/XNxLj9AQJULiufuUQ6hTPcWvH3rPGHJy8wKMSESk8ny7YAN3fTLLr/91UEcGHKx+QaJESEKSk4wJN/UrMOyy16YEE4yISCVavGEH54ddJn/xUQdyzYAOAUYk0USJkPga167Oe3/O7zQ48bf1PJexMMCIREQqJjPL0f+xDL8+rFtT7jn1kOACkqijREgK6NO2IQ+f0c2vP/rFXF1JJiIxKSsnj6vG7/TrvQ5swL/OPVw3TZQClAjJPs7t05prww4bX/zyj6zKVH8hEYkdzjkOvusLv968Xhojhx+pK8RkH0qEpEjXD+rI7w5r7tf/NmkXm0MPJRQRiXYXvfxjgUcHTbipHynJ2uXJvrRWSLGeOKcHg7rkX1XR4/6xZOXoyJCIRLenv5rPN/M3+PU59w2hekpygBFJNFMiJCV68aJe9DqwgV/vds+XOKcHtIpIdBo3ey3/GPubX392QE1qVFMSJMVTIiSlev+Ko2lXz1tV9uTkccI/JpYyh4hI1Zu/djuXv55/249pdw6iZqr6BEnJlAhJmdx1VA0Oa1Uf8O7J0fP+sToyJCJRY/OOLAb982u/Pvm2ATSsVS3AiCRWKBGSMvv4L33pHkqGNu7Iou1to8jLUzIkIsFat203Pe4f69czbuxH03p6dIaUjRIh2S8fX3k0PcP6DLX72yiy9SgOEQnI4g076PPQV379s6uPoU3jWgFGJLFGiZDsFzPj/RFH0btNfjLU4fbR7M7ODTAqEUlEM1duLXDX6Lf/dARdW9QLLiCJSUqEZL+ZGe/9uWAy1PnOL9i6S0+sF5Gq8e2CDZz89CS//uQ5h3H0QY0DjEhilRIhKZe9yVD4pfXd7x3D+u17AoxKRBLBJ7+sLPAQ1XtPPYTTDmsRYEQSy5QISbmZGf8dcVSBPkO9HxzH8k07S5hLRKT8ns1YwLUjf/Hr15zQnouPbhNYPBL7lAhJhZgZ//3zURzeur4/7Ni/T2Dumm3BBSUiccc5xy3vz+DvX8zzh112TFv+OrhTgFFJPFAiJBWWlGS8P+Jo/z5DAEOe+IYpSzYFF5SIxI3cPMdZ//6ed6cs94dd2e8g7jy5S4BRSbxQIiSVIinJ+OCKo+neMv+Kjd8//z1fzVkbYFQiEut2Z+dy2L1j+GnJZn/Y9QM7cvOQzgFGJfEkKhMhM2toZmPNbH7of4MipulkZr+E/W0zs+tC4+4xs5Vh44ZVeSMSUHIoGeraoq4/7LLXpvDB1BUBRiUisWr77mw63/kF2/fk+MOev6An1w7sEGBUEm+iMhECbgW+cs51AL4K1Qtwzs1zzh3mnDsM6AnsBD4Km+Sfe8c750ZVRdACKclJfHRlX7o0y0+GbvjvdF76ZlGAUYlIrFm/fQ/d7hlTYNgX1x3LkK5NA4pI4lW0JkKnAa+Fyq8Bvytl+gHAQufc0kgGJWWTmpzEJ1f1ZUDnJv6wBz6fwyOj5+r5ZCJSqkXrM+n94LgCw6beMZDOTesWM4dI+UVrIpTunFsNEPrfpJTpzwHeKTTsKjObYWYvF3VqTSIrNTmJ/1zSm78O6ugPe37iQm787wwlQyJSrClLNnHCPyb69d5tGvDbA0NpVLt6gFFJPLOgdkpmNg4o6hjn7cBrzrn6YdNuds4VmcyYWTVgFXCIc25taFg6sAFwwP1AM+fcpUXMOxwYDpCent5z5MiRFWpTYZmZmdSuXbtSlxmUirRl+voc/jk1/0aLnRokcXPvNJKTrLLCKzN9JtEnXtoB8dOWoNrxw+ocnpuev6047aBUftc+FbPybyv0mZSsf//+U51zvSp9wTEksESoJGY2D+jnnFttZs2ADOdckTeLMLPTgL845wYXM74N8JlzrmtJr9mrVy83ZcqUCkZeUEZGBv369avUZQalom1Zt303fR78qsCwufcPIS01uYKR7R99JtEnXtoB8dOWINrx5Lj5/HPcb379lUt6079zaScDSqfPpGRmlvCJULSeGvsUuDhUvhj4pIRpz6XQabFQ8rTX6cDMSo1O9luTOmkseHBogWGd7/yCDZl6JIdIorv8tZ8KJEETbuxXKUmQSFlEayL0CDDIzOYDg0J1zKy5mflXgJlZzdD4DwvN/3cz+9XMZgD9geurJmwpSUpyEkseOYnrwi597fXAON77aXkJc4lIvMrLc3S4fRTj5qzzh824ZzBtG9cKMCpJNFGZCDnnNjrnBjjnOoT+bwoNX+WcGxY23U7nXCPn3NZC81/onOvmnDvUOXfq3o7XEh2uG9iRz64+xq/f/MEMut87hqycvACjEpGqtGrLLtr9bRTZuV73jFYNa7DwoWHUTUsNODJJNFGZCEn869qiHtPvzu/WtXVXNh3vGM28NdsDjEpEqsInv6zk6EfG+/U/H9eOb24+IZALKESUCElg6tVIZdFDwxjUJd0fduITX/PoF7rfkEg82rormzOe/bbA0+NfvqQXtw07OLigJOEpEZJAJSUZL17Ui6fO7eEPey5jIW1vG8XWndkBRiYilWnyoo10v3cM05Zt8Yd9fVN/TuicXvxMIlVAiZBEhVO7N2fCjf0KDOt+3xgmzFtX9AwiEhOycvK4buTPnPPC5ALD59w3hNaNagYUlUg+JUISNdo2rsWse0+kad00f9gfX/mJP70+hexcdaQWiTUL1m2n4x2j+fiXVf6w7i3rsfjhYdSoVrX3EBMpjhIhiSq1qqfw/W0ncEW/g/xhY2evpcPto1myYUeAkYlIWTnneHzMPAY+/nWB4Y+e2Y1PrjqmQneKFqlsSoQk6pgZtwzpzBuX9SkwvN9jGbzy7WJ1pBaJYuu276btbaN4avyCAsNHX3ssZ/duHVBUIsVTIiRR69gOBzDplv4Fht37v9mc8I+J6kgtEoXem7J8n0fpXHZMW+Y9MISDm+nJ8RKdlAhJVGvZoCZz7x/CcR0P8Ict3rCD7veNYfKijQFGJiJ77diTQ7d7vuTm92cUGD7ur8dx58ldqJ6i/kASvZQISdRLS03m9Uv78NJFBZ8LeM4Lk7nj41/VkVokQN/MX88hd3/J9t05/rA7TjqYRQ8No32TOgFGJlI2SoQkZgzsks7c+4dwSPP8Q+xvTl5Gh9tHs3SjOlKLVKWc3DyGPfkNF/7nR39Y/Zqp/Pi3AVx+bDuSdJdoiRFKhCSmpKUm8/k1xzL62mMLDD/+/zL4x5h56kgtUgXmrN5G+9tHM3v1Nn/YM+cdzi93DaZJ2O0vRGKBEiGJSQc3q8vih4dx/cCO/rCnxy+g7W2jmLlyawlzikh5Oef48xtTGPrkN/6wg5vVZea9J3LSoc0CjEyk/FKCDkCkvMyMawd24E/HteWYRyewaUcWACc/PQmAybcNoGk9/ToVqQxTlmzi989/X2DYf0ccRe82DQOKSKRyKBGSmFezWgrT7hzE3DXbGPJE/i/VIx/+ik7pdfjgyqOpXV2rukh5LFyfySlPT2JnVq4/rH+nA3jhol6kJuukgsQ+rcUSNzo39U6X3X1KF3/YvLXb6Xr3l9zx8a9k5ejqMpGyWr11Fxf+5wcG/GNigSToqxuO55U/9lESJHFDa7LEFTPjj33b8us9gzmsVX1/+JuTl9HxjtF8tSxbHapFSrB5RxbPT9/NUQ+P55v5G/zh5x/RmsUPD+OgA2oHGJ1I5VMiJHGpTloqH/+lL6OuKXh12Ruzs2h72ygy9FR7kQJ2ZuVwz6ez6HH/WCavzi0wbsodA3nw9G56RpjEJXWckLjWpXldFj00jDcmL+XuT2f5wy955ScARl1zLF2a69b/kriycvJ4LmMh/xz32z7jHjq9G+cdoeeDSXxTIiRxLynJuPjoNvzusBac98w4Zm3M7ys07KlvOOiAWrx2aR9aNqgZYJQiVSsvz/HmD0u565NZ+4zrlZ7Mm1cNIi1Vj8aQ+KdESBJGvZqp3NS7Bg3bH8ap//rWH75w/Q6OeXQCJ3VrxgO/60qDWtUCjFIkspxz/G/Gaq555+d9xvU8sAGPnNGNlXOmKgmShKFESBLOoS3rs/ChYbzx/RLu+d9sf/jnv67m819Xc/UJ7flL//baEUjc+Wb++gKPxNhrQOcm3HPqIbRq6B0VXTmnqiMTCY4SIUlIyUnGJX3bcnqPljz51Xxe/naxP+7p8Qt4evwCHj6jG2f1akWynpkkMW768i2c9sy3+ww/8/CW3Dq0MwfUqR5AVCLRQYmQJLR6NVO565Qu3Dq0Mw+NmsOr3y3xx9324a/c9uGv/PPs7vzusBa6YkZizsL1mQz4x8R9hl/aty3XDepA3bTUAKISiS5KhESAailJ3HPqIdx9Shc+mLaSG/873R93/bvTuf7d6VxwZGvuOKmLTplJ1FuzdTdHPvzVPsP/Oqgjw49rp3VYJIwSIZEwZsbve7bk9z1bMnPlVv+5ZeDdlPHNycsA+OjKo+nRukFQYYrsIzfPMfG3dVz66pR9xt176iGcf0RrUnQ3aJF9KBESKUbXFvVY8shJbMjcwx9f+Ylfw55qf/qz3wFw2TFtuW5gB+roFIMEZOnGHbzy7ZICp3X3evKcwzi1e3Od1hUpgRIhkVI0rl2d/119DLuzc3k2YyFPfTXfH/efSYv5z6TFJBm8/acjOaJtQ+10JOJ2ZeXyv+mruPmDGUWOf+WS3vTv3KSKoxKJTUqERMooLTWZvw7qyHUDOjBm9hpGvDnNH5fn4JwXJgNeR9S/9D+IRrV1JY5UHucc05Zt4e5PZzJz5bYip/ngiqPoeWDDKo5MJLYpERLZT0lJxpCuzVjyyEnMXLmVEW9OZcXmXf74l79dzMvfLqZWtWSeOf9wjutwAEm6BF/Kad323TwzfgGvfb+02GnGXH8cHdPrVGFUIvFDiZBIBXRtUY9Jt5zAmq27efSLuXz080p/3I6sXP+ZZhcfdSB/Pv4gmtevEVSoEkOyc/P43/RV/PW96cVOM7hLOg+e3k33ABKpICVCIpWgab00/nn2YTzwu6689cNSHho1t8D4175fymvfL6V29RT+7/eHMrBLOqm6gkcKmb1qG39+cwrLN+0qcnzrhjW5YXBHBhycTu3q2nyLVAZ9k0QqUa3qKQw/7iAuO6YdY2ev4Y6PZ7Ehc48/PnNPDle85fUtOrV7c64d2IGDDqgdVLgSBbbtzub+/83mv1NXFDm+Wb00bj/pYE7o3ISa1bTJFqls+laJREByqB/RkK7N2J2dy4fTVvK3j34tMM2n01fx6fRVAPRoXZ/7Tu1K1xZ1ddVZAsjLc7w/bQU3v1/0VV/1a6by8Ond6N+5iW5+KBJhSoREIiwtNZnzjmjNeUe0Ji/PMWnBBi56ueCDL39etoVT/pV/88bzjmjN5ce0pW3jWkqM4kBunmPO6m2Mm7OWJ8bNL3KaJINnzz+c/p2bUD1FyY9IVVEiJFKFkpKM4zoewJJHTgJgyYYdPDJ6Ll/MWlNgurd/WMbbPyzz6zcM6sjverTwnw4u0S0nN49Zq7Yx8bf1vPj1IrbvySl22ucv6MmAg5uoz5hIQJQIiQSoTeNaPH9hTwC27Mzig2kruf+z2ftM94+xv/GPsb8B3g0erx/UgRq786o0Viledm4eM1Zs5a05e7jki89Lnf75Cw5n4MHpeuSFSBRQIiQSJerXrMZlx7TlsmPasicnl+8WbOT/vpzH7NUFb563IXMPt380E4C/ZnxOtxb1uPzYthx1UCOa1EkLIvSEsycnl1+WbeGNyUv5bMbqMs3z3PmHM/iQpiTrnlIiUUWJkEgUqp6STP/OTejfuQnOOWau3MbbPy7jnR+X7TPtryu3cu3IX/z6wIPTOfPwFhzRrhENa1Wrwqjj1+7sXL5buIFnJixk6tLNZZqnR+v63DS4E0e2a6QbaopEMSVCIlHOzOjWsh4Pt+zGw2d0Y8XmnXwxcw2PjJpDjtt3+nFz1jJuztoCw24c3JETOqfT7oBaugqpDHZl5fLZjFXc/vFMsnLKdgryrF4taZy9nrMGHcWBjWqqk7tIjIjKRMjM/gDcAxwM9HHOTSlmuiHAk0Ay8JJz7pHQ8IbAu0AbYAlwlnOubD/jRKJcywY1ufzYdrTPXcaRfY9l/tpMxs9dxwtfL2RHVm6R8zw25jceG/PbPsPbNa7FCZ2bcHT7RrRrXJvm9WtQLSX++63szMph1ZZdrNi8i5VbdjF/bSajZ65m7bY9pc8MnNK9OSd1a0q3lvVpXi/NT3oyMjJo07hWJEMXkUoWlYkQMBM4A/h3cROYWTLwDDAIWAH8ZGafOudmA7cCXznnHjGzW0P1WyIftkjVSktNplvLenRrWY9rB3bwh2/M3MOPizfx1g/LmLRgQ7HzL9qwg0WTFvPSpMX7jKtXI5VjOzTmqIMa0bZxLVo1qEmzemlR38HXOceGzCxWbdnFko07+GX5FqYt28L05VvKtbx+nQ7gnN6tObx1fZrUVR8skXgTlYmQc24OUNqh5T7AAufcotC0I4HTgNmh//1C070GZKBESBJIo9rVGdqtGUO7NfOH5eU5lm3ayfQVWxj965p9LtkvbOuubD6bsbrYzsC9DmzgJ0ktG9SkZYMa1KqWAgZmsPfba2YYe4cZe7/We+s5eY6c3LyC05Xw3c/KyWPVll3MXLWVaUu38N3CDcxds30/3p3itW1cixsGd+Sodo1oVFvP8BJJBFGZCJVRC2B5WH0FcESonO6cWw3gnFttZk2qOjiRaJOUZLRpXIs2jWtx2mEt/OG7s3OZvzaT2au3Mnb2un36FxVnytLNTCljx+FSjRldOcspoySDfp2aMLRrUwZ3aUq9mqlV+voiEj3MuSJ6W1bFC5uNA5oWMep259wnoWkygBuL6iMU6kd0onPu8lD9Qrz+RFeb2RbnXP2waTc75xoUsYzhwHCA9PT0niNHjqx4w8JkZmZSu3Z8PEcqXtoSL+2AyLdlW5ZjxfY8VmbmsWJ7Hou35rFse/TeuygtGVrWSaJ57SSa1jIaVk+iVirUqmbUTjVqpRo1UiApgp2Y42X9ipd2QPy0JVLt6N+//1TnXK9KX3AMCeyIkHNuYAUXsQJoFVZvCawKldeaWbPQ0aBmwLpiYngBeAGgV69erl+/fhUMqaCMjAwqe5lBiZe2xEs7IDrbkp2bx449OWTuyWHHnlwy92STuSeXHXty2LIzmw2Ze9iYuYcNO7LYsH0PG3dksXpzJjuyCy4nLTWJAxvWon2T2hzUpDYHHVCLNo1q0bBWNerVTKVO9ZSovCorGj+T8oiXdkD8tCVe2hGNYvnU2E9ABzNrC6wEzgHOC437FLgYeCT0/5NAIhRJMKnJSdSvWY36Nct+/yJt4EUkSFF5+YeZnW5mK4CjgM/N7MvQ8OZmNgrAOZcDXAV8CcwB3nPOzQot4hFgkJnNx7uq7JGqboOIiIhEv6g8IuSc+wj4qIjhq4BhYfVRwKgiptsIDIhkjCIiIhL7ovKIkIiIiEhVUCIkIiIiCUuJkIiIiCQsJUIiIiKSsJQIiYiISMJSIiQiIiIJS4mQiIiIJCwlQiIiIpKwlAiJiIhIwlIiJCIiIglLiZCIiIgkLCVCIiIikrCUCImIiEjCUiIkIiIiCUuJkIiIiCQsJUIiIiKSsMw5F3QMUcHM1gNLK3mxjYENlbzMoMRLW+KlHRA/bYmXdkD8tCVe2gHx05ZIteNA59wBEVhuzFAiFEFmNsU51yvoOCpDvLQlXtoB8dOWeGkHxE9b4qUdED9tiZd2RCOdGhMREZGEpURIREREEpYSoch6IegAKlG8tCVe2gHx05Z4aQfET1vipR0QP22Jl3ZEHfUREhERkYSlI0IiIiKSsJQIVZCZ/cHMZplZnpkV26PfzIaY2TwzW2Bmt4YNb2hmY81sfuh/g6qJvMgYS43FzDqZ2S9hf9vM7LrQuHvMbGXYuGFV3gjK/p6a2RIz+zUU65T9nb8qlPEzaWVmE8xsTmhdvDZsXKCfSXHrfdh4M7OnQuNnmNnhZZ23KpWhHeeH4p9hZt+ZWfewcUWuZ0EpQ1v6mdnWsHXmrrLOW5XK0I6bwtow08xyzaxhaFzUfCZm9rKZrTOzmcWMj4nvSExzzumvAn/AwUAnIAPoVcw0ycBCoB1QDZgOdAmN+ztwa6h8K/BogG3Zr1hC7VqDdx8KgHuAG6PgMylTO4AlQOOKvg9BtwVoBhweKtcBfgtbvwL7TEpa78OmGQaMBgw4EvihrPNGWTuOBhqEykP3tqOk9SyK29IP+Kw880ZTOwpNfwowPko/k+OAw4GZxYyP+u9IrP/piFAFOefmOOfmlTJZH2CBc26Rcy4LGAmcFhp3GvBaqPwa8LuIBFo2+xvLAGChc66yb0RZURV9T2PqM3HOrXbOTQuVtwNzgBZVFWAJSlrv9zoNeN15JgP1zaxZGeetKqXG4pz7zjm3OVSdDLSs4hjLqiLva0x9JoWcC7xTJZHtJ+fc18CmEiaJhe9ITFMiVDVaAMvD6ivI31GlO+dWg7dDA5pUcWzh9jeWc9h343JV6PDtywGeUiprOxwwxsymmtnwcsxfFfYrFjNrA/QAfggbHNRnUtJ6X9o0ZZm3quxvLJfh/YLfq7j1LAhlbctRZjbdzEab2SH7OW9VKHMsZlYTGAJ8EDY4mj6T0sTCdySmpQQdQCwws3FA0yJG3e6c+6QsiyhiWCCX65XUlv1cTjXgVOC2sMHPAffjte1+4B/ApeWLtNTXr4x29HXOrTKzJsBYM5sb+nVWpSrxM6mNt7G/zjm3LTS4yj6TokIqYljh9b64aaLmO8N+xGJm/fESoWPCBkfFehZSlrZMwzvdnRnqU/Yx0KGM81aV/YnlFOBb51z4UZdo+kxKEwvfkZimRKgMnHMDK7iIFUCrsHpLYFWovNbMmjnnVocOd66r4GuVqKS2mNn+xDIUmOacWxu2bL9sZi8Cn1VGzEWpjHY451aF/q8zs4/wDjV/TQx+JmaWipcEveWc+zBs2VX2mRShpPW+tGmqlWHeqlKWdmBmhwIvAUOdcxv3Di9hPQtCqW0JS6Jxzo0ys2fNrHFZ5q1C+xPLPkeuo+wzKU0sfEdimk6NVY2fgA5m1jZ0JOUc4NPQuE+Bi0Pli4GyHGGKlP2JZZ9z7qEd9V6nA0VeBVEFSm2HmdUyszp7y8Bg8uONqc/EzAz4DzDHOfd4oXFBfiYlrfd7fQpcFLoy5khga+gUYFnmrSqlxmJmrYEPgQudc7+FDS9pPQtCWdrSNLROYWZ98PYTG8sybxUqUyxmVg84nrDvTRR+JqWJhe9IbAu6t3as/+HtXFYAe4C1wJeh4c2BUWHTDcO7mmch3im1vcMbAV8B80P/GwbYliJjKaItNfE2jPUKzf8G8CswA+8L2Sxa24F3pcX00N+sWP5M8E7DuND7/kvob1g0fCZFrffACGBEqGzAM6HxvxJ25WVx35mAPofS2vESsDns/Z9S2noWxW25KhTrdLyO30fH4mcSql8CjCw0X1R9Jng/KFcD2Xj7ksti8TsSy3+6s7SIiIgkLJ0aExERkYSlREhEREQSlhIhERERSVhKhERERCRhKRESERGRhKVESERERBKWEiERERFJWEqERCQQZna/mV0bVn/QzK4JMiYRSTy6oaKIBMLM2gAfOucON7MkvLtn93Fhz+kSEYk0PXRVRALhnFtiZhvNrAeQDvysJEhEqpoSIREJ0kt4z4NqCrwcbCgikoh0akxEAhN6avavQCrQwTmXG3BIIpJgdERIRALjnMsyswnAFiVBIhIEJUIiEphQJ+kjgT8EHYuIJCZdPi8igTCzLsAC4Cvn3Pyg4xGRxKQ+QiIiIpKwdERIREREEpYSIREREUlYSoREREQkYSkREhERkYSlREhEREQSlhIhERERSVj/D5n+CQuEAYKuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[8,8])  # Make axes equal length; orbits should be circular or \"circular spirals\" \n",
    "if D == 0.:\n",
    "    plt.title(f\"The orbits of the undamped mass-spring system, {k=} — by Explict Midpoint with {n} steps\")\n",
    "else:\n",
    "    plt.title(f\"The orbits of the damped mass-spring system, k={k}, D={D} — by Explict Midpoint with {n} steps\")\n",
    "plt.plot(y, Dy)\n",
    "plt.xlabel('y')\n",
    "plt.ylabel('dy/dt')\n",
    "plt.plot(y[0], Dy[0], \"g*\", label=\"start\")\n",
    "plt.plot(y[-1], Dy[-1], \"r*\", label=\"end\")\n",
    "plt.legend()\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fossil-basement",
   "metadata": {},
   "source": [
    "---\n",
    "This work is licensed under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
