Analysis of an explicit energy-conserving discretization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sympy import symbols, simplify, lambdify, dsolve, Eq, Function, expand\n",
    "import sympy\n",
    "one = sympy.Rational(1)\n",
    "from BSeries import bs\n",
    "from scipy.integrate import solve_ivp\n",
    "from nodepy import rk, ivp\n",
    "\n",
    "h = sympy.Symbol('h')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As described in [this notebook](https://nbviewer.jupyter.org/gist/ketch/de14e33acabce66fd0bda2b979b5d16f) and [this paper](https://epubs.siam.org/doi/abs/10.1137/19M1290346), when the explicit 2-stage midpoint Runge-Kutta method is applied to the nonlinear oscillator problem\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix} p \\\\ q \\end{bmatrix} = \\frac{1}{p^2 + q^2}\\begin{bmatrix} -q \\\\ p \\end{bmatrix}\n",
    "$$\n",
    "\n",
    "the numerical solution energy $E=u^2+v^2$ is constant regardless of the step size.  Here we use the method of modified equations to get some insight into this behavior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we set up the right hand side of the ODE system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{q}{p^{2} + q^{2}} & \\frac{p}{p^{2} + q^{2}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[-q/(p**2 + q**2), p/(p**2 + q**2)]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p, q = symbols('p,q')\n",
    "u = [p,q]\n",
    "f = np.array([-u[1]/(u[0]**2+u[1]**2), u[0]/(u[0]**2+u[1]**2)])\n",
    "IC = [1.,0.]\n",
    "simplify(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the midpoint Runge-Kutta method coefficients:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Runge's Method\n",
    "A = np.array([[0,0],[one/2,0]])\n",
    "b = np.array([0,one])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modified equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we generate the modified equation.  This is a differential equation that is satisfied exactly by the numerical solution.  In principle it is in an infinite series (in the step size $h$), so we must truncate it at some order."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "series = bs.modified_equation(u, f, A, b, order=5)\n",
    "series = simplify(series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{q \\left(- 3 h^{4} + 20 h^{2} p^{4} + 40 h^{2} p^{2} q^{2} + 20 h^{2} q^{4} - 240 p^{8} - 960 p^{6} q^{2} - 1440 p^{4} q^{4} - 960 p^{2} q^{6} - 240 q^{8}\\right)}{240 \\left(p^{10} + 5 p^{8} q^{2} + 10 p^{6} q^{4} + 10 p^{4} q^{6} + 5 p^{2} q^{8} + q^{10}\\right)} & \\frac{p \\left(3 h^{4} - 20 h^{2} p^{4} - 40 h^{2} p^{2} q^{2} - 20 h^{2} q^{4} + 240 p^{8} + 960 p^{6} q^{2} + 1440 p^{4} q^{4} + 960 p^{2} q^{6} + 240 q^{8}\\right)}{240 \\left(p^{10} + 5 p^{8} q^{2} + 10 p^{6} q^{4} + 10 p^{4} q^{6} + 5 p^{2} q^{8} + q^{10}\\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[q*(-3*h**4 + 20*h**2*p**4 + 40*h**2*p**2*q**2 + 20*h**2*q**4 - 240*p**8 - 960*p**6*q**2 - 1440*p**4*q**4 - 960*p**2*q**6 - 240*q**8)/(240*(p**10 + 5*p**8*q**2 + 10*p**6*q**4 + 10*p**4*q**6 + 5*p**2*q**8 + q**10)), p*(3*h**4 - 20*h**2*p**4 - 40*h**2*p**2*q**2 - 20*h**2*q**4 + 240*p**8 + 960*p**6*q**2 + 1440*p**4*q**4 + 960*p**2*q**6 + 240*q**8)/(240*(p**10 + 5*p**8*q**2 + 10*p**6*q**4 + 10*p**4*q**6 + 5*p**2*q**8 + q**10))]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "series"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected for a 2nd-order method, the modified equations contain no terms of order $h$.  Notice that in this case, there are also no terms of order $h^3$.  In fact, because of the symmetry of this method, only even powers of $h$ will appear in the modified equations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solutions of the modified equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we will solve the modified equations directly and compare with the exact solution.  We consider the modified equations truncated to different orders in $h$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8f9105f3d0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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fT/7K3zb8jVfOf4WpfaeqHrsgdAk//Qs0unObTbWYlW0E7n6dFVWPIUnSblmWR/7xdVX2wMqyfIMsy2GyLOtlWe4jy/L7siy/JcvyW43tsizLd8uy3F+W5SFNg9fGtg9kWR7Q+KfNwWtXFjzxZtxn+RBaYGbLwrk0mBucHZIgCO2V8asygB16A4z6c/vP02hg1ktw+0+gU24uLVXV1B05QuCCBXhcdgl///XvVJmqeGP6G60OXgEkvZ498/5Ohl84N235FJ1JT/mxW6nKvJVfkis7/v0JgtCy0X+Baz5q/+AVlN/9y1+DoFhYfgdU5KkaUkNBAaf++lf0vXvT5+WXzhq8Avx767+58Ycbqay3/b7gNXkybn36IFssVO/Za9U+Nmws8b3ieXDTgxwrO6Zq7ILQJRz5GX5/Vdnvfi40WmXwWlcJax6EqqJOCa8n6zJJnLoFnYH4RZ9QkljPoL3FfPvaImdHJAhCe9RXK4kbevWHS1849zT5enfQG6G6GHa+j9bLk8hPlhF4z93Um+sJ8Qzh8fGPN5e1aMszvxznyVG38NjYP2HS6pHN3tRURPDs2jTSitNQY2WNIAhAfZXy+68zKPvbzpWbhzLwrSuH1X9XLSxZlsn51yNYKivp8/praP38zmpfnbGa7zO+55rYa/Bya7k8EkDxRx9zYu5cqv+wss2oM/LS1JfQa/T8c+M/MVlMqsUvCC6vtgxWLoCgeJjx3471UXIcdr4HP9ynamiCGMA6XuBAJi64j7zeFqI+WE9enniqKQgu7+Q2KM+GWS8rN6QdJO/5lPwlj9Gw8ys0BgOSRoOn3pPnpzzPxVEXt7uf7NIacj17keGnlHoJaXy6m2dK4upVV/PTiZ86HKMgCGf4dQm8PkaZSemo4HiY/ij0Ga1aZlJzURF1x44R/Pe/Yxgw4Ky23Kpc/rP9PwwNGspfhrQ9Y+x/3bXow8LIeeRRLHV1Z7WFeYXx2LjHSClO4b0D76kSuyB0Cb8+pSRimv2G8hC6I0ITYPIDkLwSjv6iang9nRjAOoE09k6GXBqOYeElhISIfbCC4PL6nw/3HjxdIqeDitM8KEr2pnrp4zTUVfL4749zpOQI0jnO6J5Ztmv2kY28teE5wqoKCdYPYVCvQfzf9v+jtLbUrlgFoccrSFfKYfSbAobWZzHbNO5umPC3c1+90QJdYCD9Vq7Af+5NVm1P73gak9nE/038P3SatotNaDw9Cf33v6k/dozCN9+0ap8eOZ1rYq4h0L2Hl1ASeo7qYtj9ESTeCuEj7Otr/N/AP1opu9dQr0Z0AmIA6xwaLb3u+5mE218AoLRSrI0XBJeVd0j52zvErm4aiooofPMtPBMH4R1wik/X38c3h7/hRPmJc+7rgRmxuOuV0j0bw4dikTTMT/6Bf8wYxBPjn6CsrozXkl6zK15B6PHWPQJ6T5j+mDr9yTLs+x/s+8KubirWr8dSU4PGwwNJc/ZtnMlsQiNpmH/efCJ8Itrdp9fECfhecTlF739AfWamVfuj4x7lmphr7IpbELoMjwC4Y5OycsJeeiPMfBaKDsOej+3vTwDEANZ5JAksZn564Aq2XzaFsprWC84LguAEWbvhzfGw91O7uyp46SUstbWEPPksJf0m82b+70wOG8/5EeeemXT28HCWXDWEcD93Stx9WTvkIsZmHeBCUxaxAbFcE3MNX6d/zdHSo3bHLQg90qldkL5GmTX1ClKnT0mCvZ8o2YzrqzrURc3BQ5z6698oeu99m+16rZ7npz7Pn4ecQ6K5RkH3/R3DwAGYi4tttltkCysOr2DTqU3n3LcgdBmmGuXvwAHKQFYNAy6Aaf+CfqJeu1rEANaZ8lPoW7qLiFwzP779UNvHC4LgWL8sAY9eED/Lrm7qMjIo/WY5/jfegKFfP97tG0ONRuLvg28/5+XDTWYPD2fL4vM59tSlLP7wCXRhYeQ/9TSyxcKCYQsI9ggWmUMFoaMOLld+98fcoW6/0x+FqgLY/laHTi94+WW0Pj4E3DrPqu337N85UnIEoEPvK/qQYKK/+Qb3YcNstltkC0uTl7JkxxKR0Enovj67FlbcpW6fkgRTHlAGxS5g1c/7mLhkPdGLf2DCUxtYuTfL2SGdMzGAdabQBOKmTaIoWKb357+RU2K9bEcQBCfJPQBH1sHYBWD0sasrjbs7fnOuIvDOO8mqzOKLrF+YPfAq+oWPUSVUjdFI0MK/YcrKwnTyJP5Gf3646gcuiLxAlf4FoceZ8V/4yy9g8Fa3376jYeBFsPX10zM97VS9ezdVmzbRa/5f0HqfHVdtQy2PbHmEJ7Y9YVd4kiRhrqyk7LvvrNp0Gh33jriXkxUnWXV0lV3XEQSXlLkNjm2E0CGd039eMqy8G0y1ndN/O6zcfRLNw3/ntrVvIQNZpTU8uPxAlxvEigGsk0lT/0nfhFKCymR+eedxZ4cjCEKTzS+Bm/e51XxtgT4sjLAnn0QXEICfwY+/DPkLdw29S/kwUykzoe9ll9H/559xi4xUrqnRY5Et7MzdqUr/gtBjmGqUGRP/yM7pf8JCqC6CfZ+f02kFL7+CNjAQ/xtvtGr7Iu0L8qvz+evwv9odXtny5WT/4582a8NO7jOZhF4JvL3vbUxmMQsrdDO/vwru/kryps5QVQBJn8B++/bB22PDu1/QrzSLzeFDm1+rMZl5dm2a02LqCDGAdbbew4kYOYKiEAhdtYOac3wiKwhCJ6irgIxfYOStSjFyOxQvXUbN/v3NX3vqPblr2F2EeobC9/cq9WXNDXZdA0DS6dB6eSKbzZjy8gFYfng5t6+9naT8JLv7F4QeoeQEPBcDqT903jUiJ8DQG8E7rN2nWKqUPbOBf/kzGvezS3rUm+v5+NDHjAkdw6jQUXaH53f11Wj9/W1mJJYkibuH3012VTYrj660+1qC4DKKjiq/9yP/ZFe5vFZFT1Zmd7e+rlpJrXMhyzIXJK3llGcgv/UZdlZbdmnXGn+IAawLkMYtoP8UNxJefQH3jtaaEgRBPQZvWHRIqd9mB1NWFnlPP035j2sA+DTlU9adWHf6gPF/hdITkLbaruuc6eSCBWQtWgTAzOiZBBgDeGf/O6r1Lwjd2va3wVQNYcM67xqSBFe+CbGXtPsUjacnkUs/xv/mm63aVh1dRUFNAX8a8idVwtN4eBBw221UbdpEzaFDVu0Tek/gygFXEuoRqsr1BMEl7HgXtHoY3Xbt5A6TJBj3VyhMgyPrO+86Lajeto2Bpaf4ZuBULNLZQ8Azy/N1BWIA6wpiZxL2+F6Ch18EKIkSBEFwEosZLBalcLnR166uipcuBUki4JabKasr4+U9L/PryV9PHxA7E3z6wK4P7LrOmbwmTKBmzx5q9u/HQ+/BDXE3sClrExmlGapdQxC6pfoq2LsMBs0G3/DOv15NCSRb7zX9I1NefvOqij+WzQGoNFUyMmQkY8PGqhaa/w3Xo/HwoGTpUqs2SZJ4YsITTOozSbXrCYLTTV0M130K3p38YCbhKvAKVQbMDla2ciUNfgH83m/0Wa+767U8MCPW4fHYQwxgXYFGAxoNZUcPsWr2aL5b8YyzIxKEnuvAV/DaSCjPtqsbc3k5pV99jc/MS9CHhbHi8ApqGmqYN/iM7KEarbLXJuMXZfmSCnyvmoPGy4vij5R6c9fGXotBa2BZyjJV+heEbuvQCqgrV2Xfe7tsewu+vAVKjrd6WOFbb5Jx6aVYqqttts8bPI8PZnzQ4Yzmtmi9vfGdM4eGkhJki+2H6mV1Zaw4vEK1awqCU7n7QcxFnX8drR7G3wOhCQ5fRhz23/8S8+lSnrhmBOF+7khAuJ87S64awuzhDnhopyIxgHUVplq8v7iC8OOVVH/+NWaL2dkRCULPtPN9kDTntD/NlrLvVmGpribglnmYLWa+SPuCxJBEYvxjzj5wxM3KTG/eQbuu10Tr5Ynf1VdTvnYtppwcAowBzOo/i715e8X7iiC0ZvfHEBgDEerNZLZqxM3KksLdH7d4iLmyivJvv8P7ggvQeFjvy0srTkOWZVUHr01CFv+TiHfesTnrC/B9xvc8+vujHCq0XmYsCF3Kt/d07r73Pxr/V6WkVif83rZElmUknQ5D//5nleHbsvj8Ljd4BTGAdR16I5r+4zDFmhlyqIrN+9peViQIgsoKj8CpHTDiFvs/WGQZz8mTcE8YzJbsLZyqPMX1cddbH+cdCvcfhkFX2He9M/jPvQnMZsq+/x6A+xLv45vLv0Gr0ap2DUHodi57EWY+57ibSt8+SkmdvZ9ACxl9y3/4AUt1NX7XXWvVllmeydWrruaz1M86JTxJq7xfNBQUIJus47u8/+W469z5Kv2rTrm+IDhEzj5l60DZKcde12JW9sGqkMSxzUvV1HDs8sspX/tTp1/LUcQA1pWMmMd5fQvQWeDYp+85OxpB6Hn2f6HMvg65xu6uAm6eS8Q7p5MnjQkbw/SI6bYP1hmUpUT1VXZfF8CtTx8iP/uUXrfdBoC3mzdajRaT2YTshMyHQs/wxhtvEB0djdFoJDExkU2bNjk7pHMTmgD9pjj2msNvhqp8m+W0ZFmm5Iv/YYiNxX3YMKv2r9K/QitpuTDywk4Lr2b/fg5PnUblxo1Wbd5u3lwcdTGrj62msr6y02IQhE6V9BloDXCe9UOiTpW+Bj6ZA8d+6/RLla9eTd3hI+h6BXT6tRxFDGBdSf9puPcOpSjKjajNGeRW5Dg7IkHoOWRZGcBGTwEf+5YP16alI5tPL9ed3Gcy7130HnqNvuWTll4OK++y67pn8hgxAkmna/46uSiZC76+gF15u1S7hiA0+eKLL1i4cCEPPfQQe/fuZfz48VxyySVkZmY6O7S2Wcyw+h+QneT4aw+8CNwDIGu3VZPpxAnqUtPwv/46qyXCtQ21rDiygvMjzifYI7jTwjMOGoQuIIDSr7622X5t7LXUNNTwQ4YDl18KglrMDXBwOcTMUOq/OtKAC5TtQw6oCVvyvy8wDByAe2Jip1/LUcQA1pVotDD4Svr0K0KeOQVvTddKaS0IXZpsgQufgEn32dWNuayM49deS8FLLwFwqOgQVaZ2zKwGD4a0NUpmUpUUvf8Buf/5LwDRvtGYzCa+Trd9Iyr0PPPmzSM4OJiqKuv/P1988UUkSeKzz9q3PPWFF17g1ltv5S9/+Qvx8fG8+uqrhIWF8eYfaonu3r0bSZJ47z0XWmV0fDPseBuKnZCpW+cGf9sL0x60anKLimLA+nX4Xn65VdtPJ36irK6Ma2M7d9ZI0unwnT2byo0bWfXzPiY8tYHoxT8w4akNrNybxeBegxnUaxBHy9RJQicIDnV8k7ICYsjVjr+2zgCDr4SUVVDXeSsYag4eovbAAfyuu75T9so7ixjAuprRfyHq4W+Z9sibeHr6OTsaQeg5NFoYPFspNG6HslXfI9fV4XPJJZgtZv768195ZMsjbZ849Dow18GhlXZd/0wN+fmUfPEFDcXFuOvcubTfpaw/sZ6yujLVriE4X0ZGBg8//DDDhw8nICAAg8FAVFQUt956K/v27bN5zs6dO1m2bBmLFy/G09PTqn33bmVGcMSIEW1ev76+nt27d3PRRWdn8Lzooov4/fffz3otMTGR2bNn88gjj1BZ6SLLTg9+DW5eEHOxc67v7qf8bSPbr753bzQ2fj5rjq0h0ieSMaFjOjk48JtzFVgsbHtzGVmlNchAVmkNDy4/wLdJ2Sy9ZCkPjXmo0+MQBNVJEvSbqqyEcIbzrlPqTqtYC/6PypYvRzIY8L3C+kFYVyYGsK7GPwrCE6muLmfNe//iwIkdzo5IELq/hjrY9ILdpXNAqbNmGBSPcdAgtudsp6CmgEuiL2n7xLBh0GuAUspDJX5XzwGTibIVKwG4OuZq6i31rDq6SrVrCM4jyzJPPvkkgwYNYsmSJfj5+XHTTTexaNEi4uLiWLp0KaNGjeKDD6zrDD/88MP4+Phw1122l63v2bMHLy8vYmJibLafqbCwELPZTEhIyFmvh4SEkJuba3X8gw8+SG5uLq+88ko7v9NO1FCv1GKNnQlu1ll+HebHf8L/bmj+suyHH8j8y3zMpaU2D39p2ku8Pv11h8youEVFkRYykKnHtp9V9qPGZObZtWkYtAZAWdYsCF1Kv6lwy7dK3Xdn6DsWfCMg7cdOu4T3RRcSfP/9aL29O+0aziAGsK6o6Cj1799N5HPfsO2zF50djSB0f0fWw8//hrxku7qpO3aM2oMH8b1sFgDfZXyHt5s3U/q0IzGMJCmZiI9vhqoiu+JoYhg4EOPQ8yhbpQxYYwNiGdxrMN8e/VaV/gXnkWWZ22+/nUcffZQhQ4aQmprKL7/8wquvvspTTz3FmjVrWLduHbIsM3/+fPbu3dt8bnp6OuvXr+faa6/F3d36xq2qqoq0tDSGDh2KpoUSKvYYPXo0cXFxvP3221haqDHqMEd/htpS5ywhPJPOqLwPNW4hKFv5LfUZGWh8fW0e7qZ1I9In0mHhvTJoFg9NuMMqQ3N2aQ0AHx78kBnfzKDeXO+wmATBLiUnVN2y0yEaDdz2A8zpvC0VnmPHEnDz3E7r31nEANYVNdTiW7SK8iADgRv2U22yXbxcEASVpKwCo5/dGUgrfloHkoTPzEuoMlWxIXMDl0RdgpvWrX0dDLsJrnxb1afBvpdeSl1qKnVHlT1q9ybeywMjHxDZiLu4p556io8++qg526+tmdLp06dz1113YTabealxTzbABx98gCzLXHfddTb7TkpKwmKxMGLECJKTk5k7dy6hoaF4eXkxfvx4tm/fftbxgYGBaLVa8vLyzno9Ly+P0NBQm9e4/vrryczMZN26def4nausthyCB0G/ac6NY9DlYGmAtB9pKCqi6vff8bnsMqsZVlmWWbB+gcNXUdRF9qfAwzrJTW8/5b1qgN8AimuL2Zy12aFxCUKHrXsE3px41qoCp/CLULYwdYKyH35o/uzvbsQA1hUFD0IKjsMY50bcSQub9orZEkHoNGaTsnwn5mLQtpIluB16/el2ov73OfrQULZlb6OmoYZZ/WedQwf94bxrVF3K6H3xxfjMnNn89diwsYwOG92tkjn0NMeOHeOxxx7DaDTy1VdfYTQaWzx2xowZAGzdurX5tfXr16PVahk7dqzNc/bs2QPAiRMnGDlyJGVlZdxyyy1MmTKFrVu3cvnll1NRUdF8vJubG4mJiVaD0XXr1jF+/Hib15gwYULzMU419Dq463clmZIz9R4BPn0g+TvKV/8IZjO+l11qdVhyUTKbsjY5fKbzgRmxDC87wT92fYrGomRYd9dreWBGLABje48lwBggshELXUN9NaT/BLGXOK7uc2s2Pgs/3K9ql+bKKnIe/hfFn3yiar+uQgxgXZEkweCriPU+AkDmd/9zckCC0I2d2KIsIYy/zO6uJJ0O96FDAZgeOZ0Vl69gaNDQc+ukMh+2vAI1pXbHA6APDib8hecx9O/f/NrR0qO8te8tMQvbRT333HOYTCbuuOMOoqOjWz22b9++AJSVKYm7qqqqSEpKIj4+3mbyJjidwGnbtm1s3ryZVatW8cwzz/DDDz9w1VVXkZ+fT1JS0lnn3HfffXz00Ue89957pKSksHDhQrKzs7nzzjttXmPUqFEAbLRRX9RhasuVxEmucAMrSRA/C45uoOy7bzHExWEYONDqsO8zvkev0XNhVOfVfrVl9vBw7h4WwLRTexlWeJRwP3eWXDWE2cPDAdBr9FwUeRG/nfpN1IQVXF/GL9BQA3HWD4mcojIf9n6iWi14gIr165Bra/GddQ4P0bsQXduHCE4RNxPjr/9HeZgHvTKKscgWNJJ43iAIqitIB4Mv9J9uVzdF772HuaqK4IULm18b4D/g3DsqOaEsbfIKhqHX2xXTmeoyMtC4u6MPCyMpP4nXk15nUp9JDO41WLVrON2HNm5GBs+G0X9Rnrh/eo11+7AbYfhNyr7jL2+xbh91OyTMgbJTsPwO6/bx9yhP8QsPw6p7rdsn3w/9p0HOfgg771y/IyuyLLNihZLoa+7ctvc1FRUp+6kDAwMByMrKwmw2ExbWcq3jphnYjz76yCoLcXx8PAC1tWcn7LnuuusoKiriP//5Dzk5OSQkJLB69WoiI23v0/T19cVoNDq3TuxP/1IeYN2zyzUGsUOvQzb44d3LA13vCKvmBksDq4+tZmrfqfi4+Tg8vPPnzebw28/yWu8iei8+36r90n6X8r+0//Fz5s9cMeAKh8cnCO2Wulr53I+a6OxIFPGzYMc7cORnZTuBCspXfY8+PBz34cNV6c/ViBGRqwpJgPCRjPjXLVz56UYxeBWEzjJmPtyfbteyXdlioXjZJ9SlpQOw8shK/rHxHx3LyhmeCD7hSmZUlZjLy8m4/ApKPv0UgAsiL0Cn0bE6o/NS9wudIycnh5ycHHQ6HcOGDWvz+G3btgGny+E0DWj9/a33M4IyME1JSaFfv35ccol19uyMDKVWav8zZvSbLFiwgOPHj1NXV8fu3buZPLn1klQBAQEUFha2+T10CosF0tcon7WuMHgF6D0c6fzFBC74G36zZ1s178rbRXFtMZdGO2fWSGM04nXBdCp+Wodcb72EeWjQUBaPXsyYsM4v7SMIHWYxK7/7Ay+0e9uQaiLGg3sApKjzuW8uLaVq2zZ8Zs7sttuFxAysq5Ik+MvPNP1q1TTU4K5zUppvQeiuZFn5XdO3vIewPWqS9tGQl4fP/coellVHV1FQU4BR14F+NRrlaeyuD5VZQxX2w2p9fPCcMJ6y1asJuu8+fA2+TOw9kTXH1nBf4n1oOymBhMPd1sr+OzeP1ts9e7Xe7tun9fbAga23qzD7CjQP+Ly9vdHpWv8Il2WZTxsfWlx11VUAzVmH/ziD2mTfvn00NDRY1XRtsmfPHnx9fdtcutweNTU1NrMgO0T2HqjMU8rnuJDK3zbg4V2CZshMq2RuXnovLom6hAnhE5wUHfjMnEn5d6uo/P13vKdOPatNkiRuir/JOYEJQntptHD7WpDNzo7kNK1OWc6c/K1S1k9nsKu72tRUJJ0O74scu9XAkcS0nquTZTY9sYCVs0dRXFvs7GgEoXvZ8B/46DLliawdKn5eD3o9XlOnUFxbzK68XVwYaccHR8wMMNfB8U12xXUmn4svoSE7h9pDhwC4JPoS8mvy2VewT7VrCJ3Pz88PgNLSUqqrW89Q/9lnn3Ho0CHi4+O54gplSWdwcDBweib2j5qWDycmJlq1VVRUkJ6ezvDhw+1+qm+xWCgtLW2Ox+HSVoOkVWZhXIQpO5uTd9xN8dN/g+NbrNoTAhN4ZsozHXswphKv8eNxHzECzLbfM80WMz9k/MD2nO022wXBJQQOgKBYZ0dxtiHXQNxlyt58O3mOHUvM1t8xJiSoEJhrEgNYVybL8PoYggqPMOyImU27Vzg7IkHoXlJ/UGZg7ZiBlGWZivXr8Rw9Gq23NxsyN2CRLfYNYCMnKPtzCtM73scfeE2dAlotFT//DMDkPpMJMAaQXZWt2jWEzhcREUF4eDiyLLeawTc9PZ0FCxag0+l4//33m+u5hoWFERQURFpams3zmhI42RrA7t27F1mWbbadq7S0NGRZbtcy6E6R9iNEjgePAOdc34aK9crvpnekDEfO/tnmVOZwsuKkM8I6i+TmRtRnn+I93XbOAI2k4ZU9r7A0eamDIxOEdlrzIBxT7+GwavpNgSvfBK8gu7ppSs6o8fDotsuHQQxgXZskQVAs0b5KkovcNertiROEHq/sFBSkwEDbSyXbS66txT1hCD6zlCzG60+sp693X2L97Xi6qzMo+3LH/9Wu2M7q0t8fj8REKhuzvnq5ebHhmg1c1s/+7MuCYy1atAhQMv9mZ1s/gPj++++ZMGECVVVVvPfee4wbN665TZIkJk+eTGFhIUeOHLE6d8+ePRgMBhJsPLlvGtz+MbFTRzTtzZ02zQn1V2UZLnxCSbDlQirWr8cwcACGoRPg8E9ntS1LWcYVK69wmbrwlro6zKWlVq9LksT5EeezNXsrVSb1MqoKgioKD8O2N6Ag1dmR2CbLUGj9vnwuKn5ax7Gr5mDKyVEpKNckBrCuLvYSDNocKoM98dt9xGU+vAShyzuizHYw4AK7utG4uxP+/HP4zZ6NLMvE94rnutjr7H/yaee+XFtC//04kR9/3Px1097XBkuD6tcSOs+iRYuYO3cuGRkZxMXFcfPNN/Pwww8zf/58Bg8ezKxZs9DpdKxYsYJ58+ZZnT9nzhwA1q5de9br9fX1HDx4kCFDhqDXWyc3aW129lz99NNPaLXa5qXNDiVJytLhflMdf+0WrPotmcqdO/lIiuL5Y5FQnAFFRwFlRuXnEz8zrvc4PPTq1YjuKNlk4siUqRS++ZbN9ukR0zFZTGzKcsFZLqFnS298z4u52LlxtGT3R/BaIpQc73AXFevWYcrORhdk30yuqxMDWFc38CJAwm1wEPEnLGw9ssHZEQlC93BkvZLtNyjOrm7qT2U1/7ckSSwcsZB5g60HDefMVKOUhdn2pv19NTJER6P19m7+us5cx+yVs/ng4AeqXUPofBqNhmXLlvH1118zceJE1qxZwzPPPMO3335Lr169eOGFF0hLS2NWC/X/5syZQ3BwMEuXnr3M88CBA5hMphZnWHfv3o2XlxcxMTF2xV9WVsbKlSu57LLLmuvUOtT+LyHHdfZ+r9ybxXcfrEQjy2zpncDKqkEAJP22EoDk4mSyq7K5IMK+h21qkfR6jEPPo2LDBpu1pIcHDyfAGMCGE+J+RXAxRzdAYCz4OeF9pz2iJil/H255e0hrLPX1VP76K17Tz0dqI8lfVycGsK7OMxB6D6N/eDWFFycS4xnl7IgEoXsYcAGM/5tdJTRMOTkcveACSj7/HICjpUcxWUzqxKd3h5piJdmMisq+/Zbc//4fAAatAU83TzZkihvNrmjOnDmsXr2agoICTCYTeXl5bNy4kUWLFuHj03KdUDc3N+6991527NjB3r17m19PTExElmXefvttm+elpKRQUVFh9+qCpUuXUltby/33O2EJb0MdrFoIez9x/LVb8OzaNNaFnsed5/+do77hnJRDuLDuGe5OGwbAzyd+Ritpmdp3qlPjPJP3tPMxnTxJvY1l6FqNEuupylM2B7iC4BSmWqXuc3/rGsYuo1d/8I9SHrB3QPX2HVgqK/G+wDUednUmMYDtCib/A69rFnP+85/QN6L7ZhQTBIdKnAdj77Sri4qflYGfx5ixmMwmblp9E8/seEaN6BQDL4QTW1XJStik7tgxSj79lIaSEgDO73s+h4oOkVuVq9o1BNe3aNEiIiIiePTRRx163ZqaGpYsWcKcOXOYOHGiQ68NwMntYKp2qZvY7NIakCRO+IQ1P1A7LPchu0wpdbQ5azPDg4fjb7Rdu9cZvBr3Lje9B/7RQ2Me4rNLP+vWSWSELqbsFPj2hQG2E5C5BEmCARfCsY3KgPscVW7ciGQw4HlG3oOWbMvZRl5VXkeidAliANsVxM2E2Euoq6vmtx/e4kiReplJBaFHyj0IVYV2d1O58TfcIiMx9Itmd/5uqkxVjO89XoUAGw28CCwmOPabal16T58OFguVvyp9nh+h3MiLWdiexWg0smzZMkaOHElVleOS7Rw/fpz58+fz3HPPOeyaZzm6ATQ6iHLC4LkFU2tPsWjP//CrrWh+LYByXvH8AI5t5O0L3+ZfY//lxAit6UOCMQ4ZQsUvtt83DFqljqWYgRVcRuAA+Osuu/NedLqBFyoP2TJ/P+dTPRJH0OuO+WiMrefQaLA0cN8v9/F60usdjdLpxAC2q8jZR9myFwn++8v8ssb28i5BENrp27vhi5vt6sJSW0v19h14Tp4MwG8nf8NN48aYsDFqRKjoOwb0npDxq2pdGgcPRhcUROVGZQAb7RtNlE8UG7M2qnYNoWuYPHkyjz32GJ6eng67Znx8PI8//jhRUVEOu+ZZjm6APqPB4N32sQ7yF04w5dQ+qs9I3Nag9+ISNkPK9/gb/env19+JEdoWfP/9hP6r5YH1Rwc/4rrvrxODWME1WCzK366+KiBqEly7FPqMOudTfS6+mKAFC9o8bl/BPipMFUzqM6kjEboEMYDtKjb8h16l32DWSNRvPPenMoIgNKosgJwku5cRVe/ciVxXh9ckZSZnU9YmRoeNVjdLqFYP4xZA7+GqdSlpNHhOnEjV71uRzWYA5p83n9n9Z6t2DUFwSXUVSokKF1o+DBCcshvTecMJ6uWDBIT7ufPEVSPQRY3nzVPr+e6oa5bQ8xwzGvchQ1ps99B7kFKcwrHyYw6MShBsqMiFZ/tByvfOjqRtbh4w6IpzfshWd/gwprz2LQnedGoTOknH2LCxHYnQJXTvFFXdSb9paA//RHXsKPqlZHGy4iR9vV00i5oguLKm5bj97Ks/6T50KL2ffw6PUaM4XnacE+UnuCn+JhUC/IPz1V866DVtKqbcHMwlJegCA5nV33a2WkHoVgze8I8MMNc7O5Jm9SdOYDqRSf+bb2HL3LMH1vWVE/jwSDqXZ2/n8v6XOynC1lVt24YpJxe/K2dbtU0MVx7ubT61mX6+/RwcmSCc4egGqCkBvwhnR9I+ZVlw4EsYMQ88Atp1St7Tz2DKzqb/6h/aPNbH4MMl0Zfg7eY6K1HOlZiB7Sr6Kzfb/oPDicqHHQfXtnGCIAg2Hd8EBh8IG2pXN1ofH3wvvVSpA+sdzgczPuDCyAtVCvIPqouVBBQq8bnoIiI//BBdYGDza5nlmezM3anaNQTBJemNYGw5Q7OjVW5UaqV6TbZeyrfLN4gajYbJkpejw2q30uXLyX/mGeSm5Zln6O3Vm/6+/UU9WMH5jm4AzyAI6SKJUMuzYf3jSjKndrBUV1O9YwdejVua2nJ7wu3836T/syNA5xMD2K4iKA68w+gTpCTbKN0s9qsJQocc2wSR40Hb8QUoppwcij78iIaiIgD0Gj2jQkcR6B7YxpkdIMvw2ij4Rf0PG3Pl6eQ9S3Ys4fHfH1f9GoLgEmQZPrkaDnzt7EjOIul1eI4fj1uE9czQpppsDDKM9ujthMjax2viRMwlJdQeSrbZPqnPJHbl7aLaVO3gyAShkSwrA8HoKaDpIsOe3sPBzbvdA9iq7duR6+ttPgj7o9LaUiyy9QOnrqaL/CQFJAn6TcVYfwD/d1/h1r+96+yIBKFruukrmG5f6ZCKDRvIf/ppzOXlVJuqeWHXCxwr66R9XpIEURMg4zflg1glJV9+Sfq4cc3ldCaGTySzIpPM8kzVriEILqM4A46sg9pSZ0dyFv/rryfig/dttm3M2szoPpMwjpjn4Kjaz3PCBACqtmy22X5R5EXcHH8zdeY6R4YlCKcVHYHKPIjuQgmLtDrlQXs7KxBUbtyI5OGB+8iRbR772O+PccMPN9gbodOJAWxXcuETSAv3EjrpQrQGg7OjEYSuqVd/CBlsVxdVmzaj79sXt6goduXt4sNDH3ZuHdXoyVB+SrkJV4kxJgZMJqq3bgVgUrjy4b45y/aNqCB0aSe2KH9Huc5NrKWqyubSW4AqUxWB7oFM7TtVeXBlNjk2uHbS9eqFcdAgKjfbft8YEjSE+0be51I1bIUeRmeACQuh31RnR3Juoicrg++yrDYPrfr9dzzHjEHj5tbqcfXmerblbCOhVxdZSt0KMYDtSryCwc2D+rw8li+6ks9+fMbZEQlC17L7I7uXEMr19VTt2IHXpElIksTW7K0YtAZGhIxQJ0Zboqcqf6tYD9Y4ZAgaX18qNyk3nhE+EUR4R4gBrNA9Hd+i7IELjHF2JM0KXn2NI1OnITc0WLV56j35+JKPuTZsEjw3EPb9zwkRto/nxImYTp5CrredHMtkNrE3f68opyM4h18EXPgE+Ec5O5JzEz0ZtG6Qn9LmoZEff0zw/X9v87h9BfuobqhmQvgENSJ0KjGA7Wq2vo70+2vE/5hK3rq2M40JgnCGTc/DoRV2dVGzfz9ydTWe48cBsC1nGyOCR2DQduKqiF79wbu3soxYJZJWi9eE8VRu3tR8YzkxfCK78nZhsrjmbI8gdIgsw/HNEDnBpWpAVm3bhlt0NJLOej9+8++gd6jydzv3wjlD4F13MuCXDUgtzP4sP7ycW368hZMVJx0cmdDjyTKc2AoNXXAJe0gC/PMEDLygzUP1oaEY+rddK3pr9la0kpZRoedeY9bViAFsV5OdhP7I51T1DaR3cgH51fnOjkgQuoaSE1CaqTzVtENdRgaSXo/H6NHkV+dzpPQI43uPVynIFkgSXPmW6iV1PMePx1xQSP3RowD8ecifWXf1OvQavarXEQSnMtVA72EQM8PZkTRrKCqiLjUVz3HWdRjNFjMXfnUh7x14T/ndj56sDGBddAZT4+6O1EpynLG9le9xW842R4UkCIqio/DhxZD0mbMjOXcajVITtg3FH39M2apV7epye+52BgcO7tLlc5qIAWxXEzUBqgrwGJlA/EmZHcdEenpBaJfjjb8rdu6B87/2WmJ2bEfr48OJ8hP4uPkwrvc4FQJsQ78pEDhQ1S49J00i5KGH0Por+9OCPILwNfiqeg1BcDo3D7j+Uxh2o7MjaVa9fTsAnmOtB7ApxSkU1RbR27Mx+3DkBKjMVXUPvNqKP/mUzD/92WZbhHcEoZ6hYgArOJ5Kn/tOc3IHvD9DeQBvg2yxUPj2O1Ruat9Y4O6hd3PX0LvUjNBpxAC2q4lUCoP3HdALvRlObBH1YAWhXY5vBo9ACI63uyuNuzsAo0JHsfG6jcT4O2BfnblBeYp84nfVutSHhBBwy83oevVqfm11xmqe3vG0atcQBKerq3R2BFaqtm5D4+WFMcE6mUrTQG9M2BjlhcjGFR6ZrjsAlOvrqdqyBVOe9aowSZIYGzaWHbk7MFvMTohO6LGObwavUGUbTlek94CT2yBzq83musOHMRcX4zm2fQ/Rx4ePZ2L4RDUjdBoxgO1qevUHrxA83bOo8zYSVmt0dkSC0DVUFSg3gnbsgav6/XdO3HwL9adOZwXUarRIjthXp9HCT4/AnmWqdttQXEzZ9z80Z0M9UnqEz1M/p7Le9W76BaFD3hwHqx9wdhRn8b18FiEPLra5/3Vr9lZi/WPp5d74YCkwFibcCyGDHBvkOfAcqwy2q3dst9k+NmwsZXVlpJakOjIsoSdr2vseNdGl9r6fk+B4MPi2OICtaqwiYGsrwh9tPLWRfQX7VA3PmcQAtquRJIi5GI2nB0N37OGqv73i7IgEoWuY+w1c/aFdXVRu3kJNUhK6XgGkFacxa8Us9hfsVynANkgSRIyFTPVmYAGqNm8m+/77qUtVbizHho3FLJvZnbdb1esIglM07X3vpe7ye3t5jBqF35w5Vq/XNNSwN38vY8POuCHVaODCf0Pv4Q6M8NwY4uLQ+PpStc32LPHE8Il8fPHHxPi5ThZooZsrzlCW3kd14Yy7Gi30Hd3i6ouqrVtxi45GHxbWZlfP73qeN/e9qXaETiMGsF3R5a/AFa8jSRJmi5myujJnRyQIXYPWerbjXFRt24r7sGFo3N3ZkbuD4+XHCfYIVim4dogcDyXHoTxHtS49xigzJ1XblJmTocFDMWgNYr+acE6WLFnCqFGj8PHxISgoiFmzZnHw4EFnh3V65iKykxOtnYPa5GSqd++2WQPWbDHz1+F/5eLoi//QYIKTO6HWNT/vJY0Gz9GjqN6+w2a7r8GXESEj0GtFgjjBQXz7wu1rIe4yZ0din8hxUJAK1cVnvSzLMnJ1DZ7j235vy6vKI6Msg3FhDsjX4SBiANuF1R05wuapI/jovYXODkUQXNsv/wdf3WpXFw0lJdSlpOLRuFRnZ+5O+nr3JdQzVIUA2ymi8cNHxVlYfUgIbtHRVG1XBqwGrYFhwcPYnmt7KaAg2PLrr7+yYMECfv/9dzZs2IBOp+OCCy6guLi47ZM708ntYPCBYNdZflv0/gecuvdem8savdy8uC3hNhIC/7A3NnsvvH+BqqW01OZ90UV4jB2DpYV6sEdLj/L8ruepM3fBkiZC16NzU1YteTnwIXNniJ4CMRdDTclZL0uSROSypYQ8/FCbXTR9np+1sqOLEwPYruqDS9Dve4leRSbkPQdEgXBBaE36WqgqtKuL6p07QZbxHDsOi2xhd95ux9dSCz0P9J7tKmx+LjzGjqFm5y5kk1J7clL4JHzcfKg3274RFbqHefPmERwcTFVVlVXbiy++iCRJfPZZ+8pPrF27lttuu42EhASGDBnCsmXLKCgoYMuWLWcdt3v3biRJ4r333lPle2hT5nboM0pZhusCZFmmescOPEeNtrl3fnvOdkprS61PDBsGOmOLe+Fcge+sWfT+z3/QtFAP9lTFKT469BFJ+UmODUzomTa/pKxa6Or6jIQbv2gxEVVrJayabM/Zjr/Bn4H+rrWVwh6u8Y4unDuDF5rcXdTFRNA/o5ojpUecHZEguKa6Ssg9oDyJtYPG0xOvKVNwTxhMekk65fXljAwZqVKQ7aTVwaKD6teDHTMWS3U1tY37YOcNnsdHF3+Em9b2jajgWjIyMnj44YcZPnw4AQEBGAwGoqKiuPXWW9m3z3bSjp07d7Js2TIWL16Mp6enVfvu3coe6BEjRnQopoqKCiwWC/6NJZqaJCYmMnv2bB555BEqKx2QKGz8PTD6L51/nXYyZWbSUFCAx2jrh1/VpmruWHcHS5OXWp+oc4PwkS49gAVlgG4rEzFAYkgiGknDrrxdDo5K6HGqi2H9Y3DMdVcsnLPa8rO+PPW3heQ89ni7Tj1YeJCRoSPRSN1n2Nd9vpOeps9oKEjBf/Ro+uXCrgxRD1YQbMraBbLZ7gGs14QJ9H37LSQ3N3SSjsv7X+74GVgAjwDVu/SaNJH+69fjPmTIWa+LkheuTZZlnnzySQYNGsSSJUvw8/PjpptuYtGiRcTFxbF06VJGjRrFBx98YHXuww8/jI+PD3fdZbsm4J49e/Dy8iImpmNJdxYuXMiwYcMYN856z9WDDz5Ibm4ur7zigCSEw26E2Es6/zrtVL1LGbx5jLR++LU3fy9m2czI0BYejEWOg5z9LlkWqEnOI49w/JprbK4K83LzIi4gjl25YgArdLJTjTOvdn7uu4wtL8Oz/aG+GgC5oYGqzZtB077syl/P+pqHxrS91LgrEQPYrqrvaABCBoagkSFny89ODkgQXFTmNkBSlhF2kKWuDnP56aefA/wH8N+J/3Xs/tcm5dnwxVw4tlG1LjWenrj1CT/rtWd3Pst131+n2jUEdcmyzO23386jjz7KkCFDSE1N5ZdffuHVV1/lqaeeYs2aNaxbtw5Zlpk/fz579+5tPjc9PZ3169dz7bXX4t5Y0/hMVVVVpKWlMXToUDQdWHp73333sXnzZr755hu0Wq1V++jRo4mLi+Ptt9/GYiORkWqyk6AgvfP674Dq3XvQ+vvj1t96OeCuvF3oJB3DgobZPjlirPIw7pTtREmuwH3wYBry8zGdPGmzfWTISPYX7BfbE4TOlbkNNDro3bEVJC4nMBbM9ZC9B4DalBQs1dV4jmrffY1eqyfQPbAzI3Q4MYDtqsITQdLg7l1E1QWjmDJklrMjEgTX5NMbht4ARt8Od1G1dSvpY8ZSs28fFtnC8bLjztt3bvCB1B/gmLqrLqp27CB78YPIZmXWNcAYQFpJGsW1Tk7CI9j01FNP8dFHH5GYmMimTZtszpROnz6du+66C7PZzEsvvdT8+gcffIAsy1x3ne0HFElJSVgsFkaMGEFycjJz584lNDQULy8vxo8fz/btLSf4WrRoEZ9//jkbNmygX79+LR53/fXXk5mZybp169r/TZ+r9Y/BN7d3Xv8dEPr4Y0R++onN/a87c3cyOHAwHnoP2ydHjINbf4C+rjur5J6YCED1LttluBJDEnHXu3OywvYAVxBUcXKHkjPCrYXfpa6mcdKqaQtB9U5lFYO7jZUcf/Tu/ne7VfmcJmIA21UZvGDiIjRRoxj52lISp13v7IgEwTWNuAWutO/Nu2bXLtDpMMTEkF6SzqyVs1hzfI1KAZ4jgxcEDz69REolDXl5lK1cSV26MmOVGKLciO7J26PqdQT7HTt2jMceewyj0chXX32F0Whs8dgZM2YAsHXr6b2T69evR6vVMnas7YHQnj3Kz/zEiROMHDmSsrIybrnlFqZMmcLWrVu5/PLLqaiosDpv4cKFzYPXuLi4Vr+HCROU2oydNoA1N8CpXdB3TOf030EaNzcMNgb21aZqDhUean1fvZsnRE106Ztyw4ABaHx9qd5jewA7uc9kNl63kf5+thPSCILdLBYoOeZyv/t28QiAwBjlPQ0lqaRbZCT64LYzLK88spLkouTOjtDh7CuKKDjX9EcBZZ/a3j0/4h7eh8Fhw5wbkyC4kvpqpRC4zmBXN9W7duOekIDG3Z2dx5SB4/Dg4WpE2DF9RsLBb5QPapWyq3qcMXNijI9ncK/BGLVGduft5oLIC1S5hqCO5557DpPJxIIFC4iOjm712L59+wJQVqbUD62qqiIpKYn4+HibyZvgdAKnbdu2sXnz5rMSOc2ZM4fly5eTlJTEpEmTml+/++67WbZsGStXrsTf35/c3FwAvLy88PLysrrGqMalbxs3qrcU/iz5yVBf6VKzlZWbNlO1dSuBCxag9Tr7395d587yK5Zj1Lb8MAJQ9sCmrYYp/7RZhsfZJI0GjxEjqGlhBlanEbedQifTaODeg9BQ4+xI1NVnFKSvAVnGY/RoPEaPbvOU/Op8MisyuTb2WgcE6FjinaQrk2UoPUH1rkN4/vUB1tw/gcF/dlBpAkHoCg58CT/cDwuTwLdPh7qw1NRQc/AgvW67DVCW+fXx6uOc/a9N+o6G3R9CYToEtz7T1V763r3R9Q6jevduAm6ei16rZ2jQUHbn2b4RdUW3rbnN6rUZUTO4Pu56ahpqWLB+gVX7FQOuYPaA2ZTUlnDfr/dZtV8Xex0XR19MblUuD2560Kp93uB5TO07lWNlx3hi6xNW7fPPm8+43uNILU4lLsD+n5Usy6xYsQKAuXPntnl8UVERAIGByv6nrKwszGYzYWFhLZ7TNAP70UcfWWUhjo+PB6C2tvas19944w1AWbZ8pscee4zHH3/c6hq+vr4YjUYyMzPb/B465GTjMue+bd/kOUrFunWUr15N8N+t/z+TJIlo39YfRgBKPdhfl0DC1RA4oBOitF/ArbdiqapElmWbS6V/PPYjHxz8gM8u/Qy9Ru+ECIVuT6NRVix0J0NvUAaxFjO9bru1Xac0JUxrMTFcFyYGsF1ZaSa8PBSPqf8FoGHvAScHJAguJmu3suTWJ7ztY1tQs28fNDTgMWoksiyTlJ/E5D6TVQyyA/qMVpJT1JW3few58EgcSdW2rc03nnNi5pBfnd/ijajgeDk5OeTk5KDT6Rg2bFibx2/btg04XQ6naUD7x/I2TWpra0lJSaFfv35ccol19t6MjAwA+v8hCVFH9oQHBASQl5d3zue1y8kd4B0GfhGd038HVO/ahXviCCQbia3e2f8OcQFxbb+3NCWjO7XTZQewnmNaf2iglbSkFqeSXJTM0KChDopK6DF++hdo9HDBY86ORF3RkyB6EqacHDTePlarOGzZlbcLT70nsf6xDgjQscQAtivziwCvELTF+6mJCKJPRiHZldn09urt7MgEwTWc2t2Y8Kzjgy+36H6EPPIv3EeM4Hj5cUrqSpy7fBiUG9f5v6jerceokdSlp2MpK0Pr58cl0a5TfqQ9Prz4wxbb3HXurbb7G/1bbQ/1DG21Pdo3utV2NWZfAQoLCwHw9vZGp2v9I1yWZT799FMArrrqKoDmrMN/nEFtsm/fPhoaGrjoootstu/ZswdfX982ly63R01Njc0syKqY8V8oO+Uyy2wbioqoz8jA76orrdrqzHW8te8t5sbPbXsAGxQLbt7KAHbYDZ0Urf1q9u/HUlWFp40ySiNClIcpu/N2iwGsoL7kb7tP9uE/KjpK3uNPUJuRw4B1P7V5uFFnZFrfad1y6b5I4tSVSY2lQU7txD0xkZgsmd3Z6iZ2EYQuq64SClKUAawd9CHBBNx0E1ovL4I9gnlh6gtM6jOp7RMdQeU6rX7XXEO/b1ei9fNrfq24tpgjJUdUvY7QcX6NP5vS0lKqq6tbPfazzz7j0KFDxMfHc8UVVwAQ3Jj0o2km9o+alg8nJlr/3lRUVJCens7w4cPtnpG3WCyUlpY2x6M6r2AId52b2JrGMkbuI6z/XZOLkjFZTAwLHtZ2Rxqt8n2pnMRNbfnPv0D+s8/ZbAt0DyTaN1rUgxXUV1WorE6083PfZX33N2p277Kq2d6Sf4z6B0smLenkoJxDDGC7uvBEKM4gbMQoPOohY++vzo5IEFxDThLIFgjv+N4PuaGBslXf09A46+Wp9+TCyAsJ9uikm+5zsfcTeCoC6qyzwXZU06DkzOWgCzcs5LGt3WwpVhcWERFBeHg4siy3msE3PT2dBQsWoNPpeP/995vruYaFhREUFERaWprN85oSONkawO7duxdZlm22nau0tDRkWW7XMuhzlrMPNr8ENaXq991B5rJydCEhGAcPsmpLyk8CaP9sZN/RUHYSGly3lqpH4ghqU1MxV1babB8RPIJ9BUpZMkFQTVZj1vxuOoA1eQ6iodKC+3kJbR5rVvkBt6sRA9iurvGX1CvaA/3/PcQdMx5xckCC4CL8IuDCJ5SMvR1Ul55O9gMPULVV2Uf4Tfo3ZJRmqBWhfbxDlSyrWeqWuSl44w2OX31N89cjQkaQXJRMnblO1esIHbdo0SIA7rvvPrKzs63av//+eyZMmEBVVRXvvfce485YxilJEpMnT6awsJAjR6xn1vfs2YPBYCAhwfoGqWlw+8fETh3RtDd32rRpdvdlJX0trH/cZZYPA/jNuYoBv/6CxmCdEX1v/l4ifSLp5d6rfZ1NXAQPHAWdm8pRqsc9MREsFmqS9tlsnxQ+ial9p1Jtan0VgSCck6zdIGkgrHsuTa8p9wPAvW/bpbRe2fsKs1fO7rYDWTGA7erCE+Gaj9ANmsyAq27G6Bfg7IgEwTX4RcCEhUr9tA6qTkoCwH34MEpqS3h86+NsOLlBpQDt1DSzrPJSQo2bG7WHDtFQXAwos0INloZuWUeuq1q0aBFz584lIyODuLg4br75Zh5++GHmz5/P4MGDmTVrFjqdjhUrVjBv3jyr8+fMmQPA2rVrz3q9vr6egwcPMmTIEPR66+ywrc3OnquffvoJrVbbvLRZVVl7IHAgGH3V79sOLS27LqktYVjQsPZ35OapLCV2YR7DhoFGQ00L9WCnR07nvxP/i5ebdYklQegwgxfEXKz83Q1Vn6pB0lowurWd/C4pPwlPvSdaF3+v6CgxgO3qDF4w+ErwCKAw7QBfLLmNPbldp+yFIHSaw+uhyvY+v/aqSUpCGxSIPjy8eZmf0xM4NXH3g8DY5sLmqnU7VHlyXbNPmTlpWtbY9P0LzqfRaFi2bBlff/01EydOZM2aNTzzzDN8++239OrVixdeeIG0tDRmzZpl8/w5c+YQHBzM0qVLz3r9wIEDmEymFmdYd+/ejZeXFzExMXbFX1ZWxsqVK7nsssua69SqRpaVWRgXWkJYc+AARy+ZSc2Bgzbbl81cxuPjHz+3Tn9ZomRbdVEaT08MMTHU7G+5OoIsy5TUljgwKqHbG/9XuOFzZ0fRafxvmkfvaTqk3L2tHmcymzhUdIihwd1zJhpUykIsSdLFwMuAFnhPluWn/tD+ItC0TsgDCJZl2a+xzQw0vcNlyrJ8uRox9ShFR+HYb1gOSZz38TZ+G9GPEaGu8+EtCA5XngOfzoGLn4Kxd3Woi5V7s/D/ZSuHvUK57elfOO+8zeg0Ogb3GqxysHYIHwFH1c1GbExIAJ2OmqR9eE+bRi/3XkR4R7CvwPZSQMF55syZ0zybei7c3Ny49957eeihh9i7dy/DhysPZRITE1sth5OSktLhWM+0dOlSamtruf/++1Xp7yzlWVCV71JZSGv27KH+2DF0wUEtHnPOWUKLM+D4ZrjoP3ZG13n6vPoKuqCWv+d/bvonqcWpfDf7OwdGJXRbFrOyfNiFtg6ozTBwIIbFH7dZGjC1OJU6c925rezoYuyegZUkSQu8DlwCDAJukCTprCwFsiwvkmV5mCzLw4BXgeVnNNc0tYnBawcd3QDfL8I7Rql3V7rXtbMTCkKny2pchdDBWZiVe7NY8vlWgisKSQmIJKu0hk2ZOwkzDsCoM6oYqJ0GzYaRt4G5QbUuNe7uGGNjqWlcPg3w7/H/ZlHiItWuITjfokWLiIiI4NFHH3XodWtqaliyZAlz5sxh4sSJ6l+g8LBSA9KFZmCrk5LQ9Q5DHxJi1fbi7hd5ePPD595p72FQkQ2V+fYH2Enc+vZFY2z5/TLGP4ZjZccorS11XFBC95W8Ep4doDzc6YbqT5ygfPVqLAGDwCes1WOTCpIA2pfZvItSYwnxaOCILMsZsizXA/8DWtvUcgPQfef3naGxVIDRoxSzXotb6nEaLOrd0ApCl5O1GzQ6CD2vQ6c/uzaNPI07N1/0L9ZHjALM4JZNXn7rHxoOF3sxTF0MWnVrvPleeSWe48Y2fz0ydCSRPpGqXkNwLqPRyLJlyxg5ciRVVVUOu+7x48eZP38+zz1nu8SK3fpPg4eylAGei6hJ2qfsCbXht5O/dWwZbe/GrQzZSR2Oq7NZamvJf/55Kn/7zWZ70/aE/YX7HRmW0F1l7VGy8vuqvC3BRVSsW0fWfX/HUpoPv78GuS0vz4/1j2XeoHmuUTGhk6gxgA0HTp7x9anG16xIkhQJRANnZkExSpK0S5KkbZIkzW7pIpIkzW88bldBQYEKYXcjIQmgdUPK34dpYATRJ02kl6Q7OypBcJ6sXcrvhb5js6XZpTUAFHr4UWbwArRUHv4XxdmdMGNkr5oSKDmuapcBc28i8M47m7+uN9ez/PBysYy4m5k8eTKPPfYYnp6eDrtmfHw8jz/+OFFRUZ13EZ3BZZIcmXJzacjJwX2Y9d75sroyjpYd7dgsSeh5gATZre+FcybJYKDky6+oWL/eZntCYAJaSSv21wvqyNqjZB/WWieg6w6q9ybhFhWFLsAffnoY0te0eOzosNHcP6oTtmi4EEcncboe+FqW5TNzOkfKsjwSuBF4SZKk/rZOlGX5HVmWR8qyPDKolT0VPZLOoNysZ+3BZ3giUQUShZVtZygThG7JYoGsvXaVz+nt586NqT8xMeuMAZvsRm/vQBUCVNmHl8LqB1Tv1lJdTUPjw0KNpOHpHU/z/dHvVb+OIKjGYoFlV0Gy6+yplBsa8L3ySjzGjLFqa3og1KHEcAYvGHBBhx/SOYIkSbgPPa/FUjruOnfiAuLEgzHBfuYGpfZ7uOvsfVeTLMvU7N2L+7BhSnb1gP4trr6oqK8goyyj1XwG3YEaA9gs4Mz5+j6Nr9lyPX9YPizLclbj3xnAr4CLpPjsYsITIWc/kQvu5bytO5kc2Qm19QShK5Ak+PN6GLugw108ML0/1x7+hcFFxwFwC/oJj8CtPDAjVqUgVdR7mDILo+KHlSzLHJ1xMfkvvAgoCWaGBA0RN5qCays6Akd/VpYRugi3Pn3oveT/MMZaZ25Oyk9CK2k7nhhu7tdKqTAX5j50KHVHjmCurLTZ/pfz/sItg25xcFRCt1OQCqZql9r7riZTZibm4mLcGxPuKZ/7STaP3Zy1mStWXkFqcarD4nMGNQawO4GBkiRFS5LkhjJItXr8KUlSHOAPbD3jNX9JkgyN/x0ITABEscGOmPJPuO8Qul690DpwOZgguBxJguA46GVzMUe7zHCvxGA2kdd3IBIyRv/tjIypYvbw1jP/OUXv4VBVoGRfVYkkSRgTEs5K5DQ0aCjpJelUm6pVu44gqKo5eZvrzMKYsrNbnAkJ9QxlVv9ZeOg97LuIC8+0uA8dBrJM7X7b+1ynR0xnSt8pjg1K6H7cPGHcPRAxtu1ju6CmclTuw4cpL/QeDuWnoNJ6S2VSfhLuOncG+g90YISOZ/cAVpblBuAeYC2QAnwpy/IhSZKekCTpzKzC1wP/k89+J48HdkmStA/4BXhKlmUxgO0IryAweAOw88VHeG7hBAprCp0clCA4waEVsO8Lu7poGrg9+9hNbHxoKLK2istix6kQXCdoTuai7l4492HDqD92DHNpKQDDgoZhls0cLLRdy1IQnC57D7h5QaB9dWrVYqmr48iMiyl89VWb7dfGXsuTE57s+AUK0uC5WEhf2/E+Opn70PPQ+vnRUFRss12WZfYV7COlSJ0STUIPFRANM/4LfhHOjqRT+Fx2Kf3Xr8PQv/HBfNgwkLRQaJ3vJqkgifMCzzv30lxdjCp7YGVZXi3Lcowsy/1lWf5v42uPyrL83RnHPC7L8uI/nPe7LMtDZFke2vj3+2rE02NtfBZ2f4x78glG7Chmf4HI7Cf0QNvfgV32vZXUJCWhCw5GFxbGgULlyed5QR3LaNzpQgYrH2RqD2CHKhlCaxpnTs4LOg8JiSOlR1S9jiCoJmu3cmPnIgmcag8dApMJ42DrJcK1DbWYzCb7LuDbR6l568KJnLTe3gzc+ju+sy5r8Zj7fr2PDw996MCohG4n7xA01Dk7ik4jSRJuffogaRvf2yLGKtnWoyacdVy1qZq04jSGBg91QpSO5egkTkJnSlsD+78kaNR4wkogOWO7syMSBMeyWCB3v5KJ0J5uqqpwTxyBJEkcKDyAUWtkgN8AlYJUmd4d5rwLQ29QtVv3IQmg0TTPRvsafNl0/SZujL9R1esIgipkGbzDlDI6LqIpeVHTw6AzfXf0O8Z+NpaCajuqKrh5QmCsSw9gQbn5bq1tWNAwkYlY6LiGOnh7Mvy6xNmRdApLTQ3Z//znWVt60OqVz/4/OFR0CLNsbi5R1Z2JAWx3EjYUcvfjPUzZ/1O8e5uTAxIEByvOgPpKuwewfd98g/DnnweUG6yxYWNdezlOwhwIVHe/i8bTk7D/+y8+l1zS/JqvwVfVawiCaiQJrv8UJrtO6YiaA/vR9+6NLtA6e/mBwgN4uXkR6G5nZvPew5Xsqy68D7Z6506OXnYZ9ceP22wfGjSUnKoc+wbzQs+VnwyWBrs/911VbUoKZd9+R0PxH5bhH/gavrr1rJdiA2J5ZdorHcts3sWIAWx3EjYU6soxhnth0UjoU45hsti5REkQupKcJOVvFT7IJI3y9viPUf/g1em297C5jOpi2P+VzYQO9vCbPRvDwNMD47TiNP624W9klmeqeh1BsJsLDuBqDxzEOGSIzbaDhQdJCExodXayXXoPg8o8qMixr59OpPH1pf7IUarPnEE6w5Ag5d9I7K8XOiSncbtcqItu87FT0zYeY0LC2Q0VuUrOjzM+933cfJgWMQ1vN29HhugUYgDbnTTetGtK0zAPiSHGp7/IGCr0LMXHQOsGQXEd7qLo/Q/IvP1PyGZz2we7ipLjsPzPkPm7qt2aKyspX/sTprx8QJmN/uXkL6KcjuB61jwIb01ymYGsLMsE//Mf+N9kveS+ylTF0dKjJAQm2DjzHEVNhDF3ucz3bYuhf380np5nL4E8Q1xAHFpJy8EiMYAVOiB3P7h5g3+0syPpFLUHDqILDUUfHHx2Q+9hyt9ND+6Bz1M/50hJz8hTIQaw3UlwPHj0gpoSzvtiJXNeWCGW/Ak9y5QH4IGjyv6QDqrasZ2GgnwkrZYv077kym+vpLy+XMUgO0HIYNDoVd8L15CbS9bChVRtVQbG/Xz74a5z51DRIVWvIwh2y0lS9oTZO6OpEkmS8LnwQjxHj7ZqSy5KRkZmSKDt2dlzEjIYLnkKfF2wxFcjSavFOGQItQdtv2+469z59NJP+VPCnxwcmdAt5OyHsPNA0z2HNDUHDyg5Kf4o9DxAav7cL6gu4P+2/x+/Z6v7INtVdc+fdk+lMyg37yNvB8AiWyiutZ26XhC6LaNPh0+VZVlZ9peg3FjuK9hHSW0J3noXX46jM0DIINUHsG7R0UgeHs03njqNjviA+ObMzILgEiwWyD3gUksIa/bvp3qv7d/HMM8wFo5YqM4AFqChXll94sLcEwZTm5aGpb7eZvvgXoPtr4cr9EwX/humLm77uC7IUl+Pxs1gMxEcRh/oNQCyk4DTS/CbluR3d2IA2900Pn1uKCjg9wvG8uqSq50ckCA4SOlJ+N9Ndg3iGrKzMRcXY2x82nmg8ABDAofYv0/NEXoPV753FZcSSlotxkHx1B44PWBNCEwgrThN7K8XXEdz8jbXGcAWvvkWOQ//y2ZbH+8+/HnIn9VbIfXDInj/QpdeRuwxbhy+M2diqaqy2Z5VmcUre14hp9J19/IKLipyPERPdnYUnULj5ka/Vd8R8KcWVif0mwoG5QH7gcIDaCUtcQEd30LVlYgBbHeT8Ru8NRGtthrfwlp8juSJfbBCz5C9F1K/B9nS4S5qGmca3RMSqKiv4FjZsa7zNDN0CNSWQdlJVbt1TxhCbWoqskkZsA4PHk5sQCwltSWqXkcQOiy3cU+2i8zAyrLc8rI/4Pfs3ymrK1PvgqFDoaoAyrPV61NlXhMm0Pvpp9D5+9tsr6yv5N0D77Inf4+DIxO6tLxDkPYj2FtT2cW1+BD90ufgqrcBpYTOAL8BuOusy+t0R2IA293o3SH3AFL+QSwxkUTnWkgpTnF2VILQ+XL2gaSF4MEd7kLj4YHnhAkY4uKal+OokmjFEQZfBYsOgW9fVbs1JiQg19VRd0RJDHFB5AV8OvNTgj2C2zhT6KmWLFmCJEncc889jrmgb18YfrOSB8IFNOTlYS4obN6KcKb86nzuWHcHq46uUu+CoY3XyXPtJEiyLGMusz1w7+/XH6PWKDIRC+dm3+fw5TxnR9Fpshc/SM4jj7Z5nCzLpBandp37FRW4cGFDoUNCBoOkgZz9+J43gugvjpCUt5/EkERnRyYInStnn5J9WG/scBdekybiNWkiAN5u3lzW77Ku84HgEQAEqN6t15TJ9P9pLfq+Zw+MZVnuGkurBYfatm0b77zzDued58DZ0L6jlT8uoqZxyb2tGdhOeTAW0vjQLnc/xMxQr1+VZd27iPoTJ+i3coVVm06jI75XvBjACucmZ5+S/8GOxI2urGrLFjzGjW35gIY6eHsy0rCbWDtnLTUNNY4LzsnEDGx34+YJgTGQsw//YaNwa4DsA9udHZUgdC5ZVrKQ2lH/VbZYsFSfXm6fEJjAkklL8HHreFIoh0v6DLa+oWqXWm9v3CIizhqsPrPzGeaunqvqdQTHmzdvHsHBwVTZ2Jf44osvIkkSn332Wbv7Kysr46abbuKDDz7Av4Wlort370aSJN57770Ox30WWVYSGFk6vnVAbbUHDoJOhyHeekb4YOFBdJJO3X1qRh+lhEiuaw/+3KKjqDt8GEttrc32hMAEUopTxP56oX1kWclA7CJbB9RmysujoaAAdxsrOZrpDFBfDTlJGHVG/I2233e7IzGA7Y5Cz4OcfbgPG0rFtOGcH3WBsyMShM5VXwX+UdB3VMe7OHGCtJGjKF+zFlmWya7MRnbhpCg2Hf4Jtr+lercVG36h4JVXm79uKqXTk572urKMjAwefvhhhg8fTkBAAAaDgaioKG699Vb27bNds3fnzp0sW7aMxYsX4+npadW+e/duAEaMGNHuOObPn8/VV1/NtGnTWjwmMTGR2bNn88gjj1BZWdnuvltUkQuvDINd79vfl0oC77yDqC/+h8ZgsGo7UHiAgf4DMeo6vlLEpouehDF3qtunytwTEsBspi411WZ7Qq8E9Bq9SOQktE/ZSagttevBtStrSp5obGEvfbPQIXxelMTrSa87ICrXIQaw3VH/8yFyHG5hIYx+8zPGTBCZiIVuzuAFf17fXEKqI2oPHgSLBbfoKHKrcpnxzQy+Sv9KxSAdIHQIlJ5QkjmpqGbvXgrffRdLXR2g3GiaZTOpxbZvRAXHkGWZJ598kkGDBrFkyRL8/Py46aabWLRoEXFxcSxdupRRo0bxwQcfWJ378MMP4+Pjw1133WWz7z179uDl5UVMTEy7Ynn33Xc5cuQI//nPf9o89sEHHyQ3N5dXXnmlXX23KqdxgB7iOkv9NR4euA+23otvkS0cKjykXvmcM8XPgshx6verImOC8jOqOWB7pvjCqAvZcsMWInwiHBmW0FU1/e530wFszf4DoNNhtLGS4yyhCfxAJTuytzomMBchBrDd0bAb4OoPQOdGvbme3akbyKrMcnZUguDSag4cQDIaMfTvz8Ei5QYrPsA1ksK0W0hTMpdDqnZrTEgAk4m6tDTg9P49sV/NeWRZ5vbbb+fRRx9lyJAhpKam8ssvv/Dqq6/y1FNPsWbNGtatW4csy8yfP5+9Z9QkTU9PZ/369Vx77bW4u1tnrKyqqiItLY2hQ4ei0bR9m5CWlsZDDz3EZ599hl7f9l600aNHExcXx9tvv43F3qW/ufsBCUJdYwBrys4m//kXqD9l/ZkrIfHRJR9x86Cb1b9wfTUcXgdlp9TvWyW6kBC0gYHKw0Ib9Bo9GknclgrtFDsT7t5xOolZN+MWGYHfVVehMba+WsMUFE+qm54E91AHReYaxDtFd9ZQR/7LL6Gbczer079zdjSC0HmW32F3JsLaAwcxDhqEpNORXJSMTtIRE9C+2SeX0fRBnnug9ePOkXuCMptU03jjGeQRRLBHsBjAOtFTTz3FRx99RGJiIps2bbI5Uzp9+nTuuusuzGYzL730UvPrH3zwAbIsc91119nsOykpCYvFwogRI0hOTmbu3LmEhobi5eXF+PHj2b797LwKW7dupbCwkMGDB6PT6dDpdPz222+88cYb6HQ66hpn7s90/fXXk5mZybp16+z7h8jZBwH9mmshOlv17j0UvfsulsoKqzZJkojxjyHKN6oTLlwEn14N6WvV71slkiQRvOhefC67rMVjPk35lL//+ncHRiV0WRotBMUq+0C7Ib85cwh74t9tHnfEy586jYYh/rEOiMp1iAFsd/XONFh5F96xg3EzQ/aBHc6OSBA6z6kddtV/lRsaqE1Jac4amlyUTH+//hi0XeyD0TsUvEKhMl/VbnW9e6MNCKD24OmZ3RvibmBk6EhVryO0z7Fjx3jssccwGo189dVXGFt5Qj9jhpKVduvW08vL1q9fj1arZexY29kt9+xRanGeOHGCkSNHUlZWxi233MKUKVPYunUrl19+ORUVpwdos2fP5sCBAyQlJTX/GTlyJNdffz1JSUm4ublZXWPChAkA9g9gc/e71BLC2oONKzkGDLBqW3diHaszVnfOhX37gNFP9YdXavObM6c507stJbUlrM9cL+rXC2376RE4ttHZUXQKS11di8nO/uhAnfJ5n9D/ks4MyeWIMjrdlXco5B3C/VKlfpQpWdSCFbqpukolC+nQGzrchdzQQPB9izAmDEGWZZKLkpnWt+VENC5LkpRasFp139olScJ9yBDMpaXNr/15yJ9VvYYaTtx8i9Vr3pdcTMCNN2KpqeHk/Dus2n2vvBK/q66koaSErL8ttGr3v+F6fGbOxJSTQ/Y//mnVHnDbbXifP426jGPkPvaYVXvgXXfiOX48tSkpbe9laqfnnnsOk8nEggULiI6ObvXYvo3lj8oa629WVVWRlJREfHy8zeRNcDqB07Zt29i8efNZiZzmzJnD8uXLSUpKYtKkSQD4+fnh5+d3Vh+enp4EBASQkGB7ae+oUUrCtY0b7bgBlWW46L/g0avjfais5tAhjHFxSDrr38FPkj/BIluY2W+m+heWJGUFhosPYGWTidrkZHShoehDQqzaEwITsMhK/XpR/k9oUVUh/P4KeIVA9GRnR6O6yl9+Ievv99Nv5QoMAwe2emxtQy3RvtGEY/2gsDsTM7DdVchgKDyMPiyYBg8DQZnl5FerOysjCC4hPwWQT9dC7ACN0UjALbfgMWI4FtnCg6Mf5KqBV6kXoyOpPHht0ueN1+n7xtlZDktrSymtLe2U6wm2ybLMihVKHc25c9suZVRUVARAYGAgAFlZWZjNZsLCwlo8p2kG9qOPPrLKQhzfOAivbefsQEt8fX0xGo1kZmZ2vBNJgkGXQ9QEu2JRi2yxUJecgtFGAiezxUxKcQqDeg3qvABCh0B+MljMnXcNO5lLSzl+3fWU//ijzfbBvZR/O5EgTmhV04MaF9n7rrbaQ8kgSegjI9s89pbBt/Cd+xCkV0e4VDmxziZmYLurkMEgm5GKDyPFDaBf9iEOFR4iOCLY2ZEJgrryGvdh2jGArU1LQ+vlhT48HK1G2zkzJI6SnQTrHoWZzyr7g1QiabVnfV1ZX8mkLyaxcMRCl5mNjVy2tMU2jbt7q+06f/9W2/VhYa22G/pFt9qu1uxrTk4OOTk56HQ6hg0b1ubx27ZtA06Xw2ka0LZUp7W2tpaUlBT69evHJZdYL0nLyMgAoH///q1e99dff20ztoCAAPLy8to8rkW5B6GuHCLGKYNZJ2soKACtFuMg65/1iYoT1DTUEN+rExPDhQ4BUzUUZ0Bg67M2zqILCkIXGnrWdoQzBXkEEegeSHJRsoMjE7qUpkSFLpR9XE21yckYBg5EY2P7hU2BMVBfAaXHlZwAPYCYge2umn6pcw/S+093ELngXsb1du0U+4LQIT7hkDAH/Np+UtmS3H8/QdYD/wDgQMEBDhWqm8XXoXQGOPabMpBVkaWmhsz58yldsRIALzcv+nj1IaVIbE9wpMLCQgC8vb3R2VimeiZZlvn0008BuOoqZUVBU9bhlmZQ9+3bR0NDAxdddJHN9j179uDr69vm0uX2qKmpsZkFud22vwVfdEJG3w7Sh4QQs2M7vpdfbtXWNCDr1BnYmIvhzi1KTWwXZkwY3Fzj0pbz+55PkHuQAyMSupz8ZGX5sGegsyNRnSzLypYTGw/C/iilKIUrVl7B/qb30dyek1hRzMB2VwH9YNw9EBRHwPBEApwdjyB0lpiLlD8dJFss1Kam4td4g//GvjfIr87nm8u/UStCx+o1ELQGJbnNUNtZZjtCMhqpPXgIXWAQflfOBiC+VzwpxWIA60hNe01LS0uprq7Gw8OjxWM/++wzDh06RHx8PFdccQUAwcHKKpymmdg/alo+nJhovf+woqKC9PR0pkyZgmTnjKfFYqG0tNS+gXDeIQgZ5BKzr00kSQIbpYROlJ/AoDXQz7cTZ0c8ApQ/Ls598GAq1/+MubISrZeXVfsj4x5xQlRCl1JVaNeqK1fWkJeHubgY46C2H3YlFyWTUZaBf+hwkDTK0upB1g/QuiMxA9tdabQw47/QJxFZljmwaSVLf/ivs6MSBHXJMtSU2NVF/fETyNXVGOPjmxM4dbn6r2fS6iA4/vTSapVIkoQxPp7alNMD1kG9BnGy4iTl9eWqXktoWUREBOHh4ciy3GoG3/T0dBYsWIBOp+P9999vrucaFhZGUFAQaY01ff+oKYGTrQHs3r17kWXZZtu5SktLQ5bldi2DtslihoJUl1pCmPvEExS88YbNtruH3c2Gazeg03TyvEHqD7Dzvc69hp0Mjcvp61r4f7CJ2YX38gpOdtOXcOOXzo6iU0gGA8GL/4nnuPFtHptSnIK33ps+/gOUh9cqf+67MjGA7c4a6pSnMbIM9/6b0mWfUlBd4OyoBEE9pZnwdBQkfd7hLmpTlKV9xkHx5FXnUVxb3LnL/ByhKRupLKvarXFQPHVHjiDX1wMQFxAHQFpx6zeigroWLVoEwH333Ud2drZV+/fff8+ECROoqqrivffeY9y409tHJEli8uTJFBYWcuTIEatz9+zZg8FgsJk9uGlw+8fETh3RtDd32rQOZvsuOa7s93SRWRhZlin/cQ0mGz+PJj5uPp0fSMoq+O3Zzr+OHTwSE4lY+nGL+8JLakuY9uU0vk7/2sGRCV2K1nqlQ3eg8/en1623YujX9uqU5KJk4nrFKSs/pvwDEm/t/ABdhBjAdme7P4K3JiJV5SMNjCYqTxbL/YTupSmRQy/rmovtVZeSgqTXY+jf3zH71BwhcrxSG1PlWorG+HgwmahrHPgMCRzC4+MeJ8onStXrCK1btGgRc+fOJSMjg7i4OG6++WYefvhh5s+fz+DBg5k1axY6nY4VK1Ywb948q/PnzJkDwNq1a896vb6+noMHDzJkyBD0NpbBtjY7e65++ukntFpt89Lmc6ZC8jY1NeTmYi4psTkoO1Vxivt+vc8xD3pCEqAyFypd92G11tsbz9Gj0bSw/N3P4EeDpUHcrwi2HV4Hn9+oer1zV1Gzbx+mdiS3M1lMpBWnnV4xNuRqiJnRydG5DjGA7c6aPtjzDuI7ZDiRBZBaIDL7Cd1I001scMeX/PrfeCN93ngDyc2N5KJkNJKG2AD1svc6xbAb4eYV4Ga7zmdHGRMS8Bg1CtlkAsDX4MucmDkEeYiEK46k0WhYtmwZX3/9NRMnTmTNmjU888wzfPvtt/Tq1YsXXniBtLQ0Zs2aZfP8OXPmEBwczNKlZ2dNPnDgACaTqcUZ1t27d+Pl5UVMTIxd8ZeVlbFy5Uouu+yy5jq152zABfCndRDsGg+bmpbW29q3drDwIOtOrMMiO6DERegQ5e88164HW71nL8WNCcb+SJIk4gPiRSZiwbbMbZC+Boy+zo6kU5xaeC/5zz7X5nHVpmoujr6YMWFjlBca6uHkTihveRVIdyKSOHVnTR/seYfwHjyEygbISdkNw50bliCoJu8g+EeDwToRSHvpe/dG37s3APMGz2NSn0m46+zIjOpKZFnVBDduERFWpWKyKrNILU5lesR01a4jtM+cOXOaZ1PPhZubG/feey8PPfQQe/fuZfhw5UMhMVHJmdCSlBR1ZsSWLl1KbW0t999/f8c7cfOEvqNViUcNTXUbjbHWD7+Si5LRa/QM8Ov4SpF2a35wnQz9z+/863VQ5S8bKProY/yvuQbJRqmQ+F7xLE1eSr25HjdtO0uJCD1D3iGlbIzO4OxIVNdQXExDbm67Ejj5Gnz578QzctvUlMD7F8DFT8HYuzoxStcgZmC7M48ApcRI7kGM8covg3T4mJODEgQV5R2yq5B5Q1ERxZ99hilfWYrk7ebN0KChakXnXB9dBt/e0yldy+bTyVW+PfIti35ZRLXKy5WFzrVo0SIiIiJ49NFHHXrdmpoalixZwpw5c5g4cWLHO9ryMmRuVy8wO2k8PfGaPNnmstjk4mQG+g9E74g9e56B4Bms5AdwYc3bEY4etdke3yueBksDR0qt92kLPVzeIZfZOqC22uSWV3L8UUV9xdkPHL2CwaOXUmKoBxAD2O4uZDDkHcLQL5qQ99/ioftWODsiQVDPhIUw/JYOn16TlETeE09iysqiqKaI15Ne52TFSRUDdCKtG+TuU73bwnfeJX38hOZBbHxAPDIy6SXpql9L6DxGo5Fly5YxcuRIqqqqHHbd48ePM3/+fJ57ru0lci2qq4R1jyr1jl1Er9tvo+/bb1m9LssyKUUpjt1X/7e9MPMZx12vA5oyETfdsP/RsKBh3DzoZjz16m6DELq42jIoy+zGA9jTSSXbcs/P93DXz2fMtEqSsvIyv2fsHRdLiLu7iYvAbELS6wmYMMXZ0QiCukZ0fPAKjTdPjcv+dhTu4K19bzG+93j6endwX54rCRkE2zeDuUEpraMSXa9eWMrKqD+RiaFfNPG9lA/alOIUhgUPU+06QuebPHkykydPdug14+Pjefzxx+3rpCBV+dtFbmKbZkFs1cYtry+nr3dfzgs8z3EB2bGlwlHcIiORPDzOKst1plDPUP4x6h8OjkpwedVF0HcM9O6ee+Fqk5PR9+mD1qf1jOVmi5mU4hSuGnjV2Q3BgyDpU7BYQNO95yi793cnKNlI+ykD18pDB/j8oatZdeQ7JwclCCoozlCeNNpRKqY2JQW3fv3QeHiQUpSChESsfxdP4NQkeDCY65R/JxU1PRluKj8U4hGCv8GflKKe8dRXcAEuloG4asvvHJ44idrUVKs2X4Mv/7vsf1w58ErHBZSzH76cByUnHHfNcyRpNBhjY6nPsL2EGKDeXE9GmbrvX0IXF9AP/vQT9O9g+S0XF3zfIno/taTN405UnKCmoca6Zn1wPNRXQlk3WUnWCjGA7e7MJkj/CfKSqd+7n2HLD7Hn0HpnRyUI9tv2Frx3gX0D2OTk5rIXqcWpRPpE4qG3Xdqhy2nKzKzyfhhD//6g11PXOHMiSRLxveJFyQvBcfIOgZsX+EY4OxJAeR8xFxWhDwtzdigKswmSVyq1oF1Ynzdep+9777XY/vKel7l21bU0WBocGJUgOI9bRAQeI0e2eVzTA+OmFVDNYi6GW38Ar5DOCM+liAFstyfBFzfBvs+aZ06qkw85OSZBUEHeIWWQ1sFlMuayMiXbX+MANq0kreuXzzlTUCwMvRG81b2pltzcMAwccNbetcWjF/P69NdVvY4gtKg4Q1kq5yJL5GpTGpf9+VqX9bj/t/t5ZMsjjg0oOE7528WTuej8/ZFa+RnG94qnzlzHsTKRfFJotPQKWLXQ2VF0irqMY5T87wvM5eVtHptclIxBa6Cfb7+zG3zCIGoi6I2dFKXrEHtguzutDoLilERO4x9ElsD9WC7VpuruM9Mk9DyyrNycxduuc9keWl9fYnbtBIuFmoYaSmpLiAuIUzFIJ9O7w5VvdkrX/tddD5bTmYijfaM75TqCYNNNXyvJXFzEmSs5/mhP3h7G9R7n2IDcPME/SnnI58IaSkooeOEFfGbOxHOc9b/RoAAl8VVKcQoD/Qc6OjzB1VgscGq3UkKnG6ravIm8/1uC9/S2y19N7TuV3l690WlsDOOOrIf6Khh0RSdE6Tpc4/Gl0LmC4yE/Fa2XJ+bewUTliYyhQhdXmQ81xadrHXeQ1ssLrY8P7jp3fr/hd+bGz1UpQBchy51S1Nz/umvxv+GG5q/rzfV8ePBDtud0flmT1uqUCt2T1c9cksDdzymx/JG5sgrTiUwM8dYPv4pqiiioKXDOvvrgwS6fjVTj6UnpipVUbd1msz3SJxJ3nbvYXy8oyjKhvsLuz31XVZuWhrZXL3RBQW0eOyp0FDfF32S7cfs78OvTKkfnesQAticIjoeKbKgpxT0+nqgSvajZKHRtTUvjgjs+Y1r0wYcUf/xx89dajRajrpstu9n4HLwwCOrV/3035efTUFQEgF6j59397/LT8Z9Uv86ZtFotJpOpU68huB6TyYRWq1W+yNwOKxdAeY5zg2okm+oJuPVWPMdazyCmlaQBOGdrQvhwMPoos1YuSuPmhqF//xYzEWs1Wgb4DWj+dxR6uKYVBSEdr/3uyupS0zDGtj27XFFfwb6CfdSZ62wfEBwPhenKXvhuTAxge4KgxqVNBalE//dppvyyh/Hh450bkyDYo/cwuPFLu1Lpl61YTtU2ZcbwvQPv8eLuF1UKzoUExQDy6bIjKrFUVXFkylRK/vc/QEnkFBMQ0+k3mt7e3pS3Y3+Q0L2Ul5fj7e2tfJH5u1ImwkX2eOn8/QlZ/E88Rli/F6UXKyudnDIDO/kB+PN6l9kn3BJjfHyLA1iAe4bdw4KhCxwYkeCyVHhw7arkhgbqjhzBENv297Ynbw9zV89teWVCyGCwmKDoiMpRuhbXfmcT1BE1ARZsg/BEVmVUMvHZ34he/AMTntrAyr1Zzo5OEM6duz/EzACjddKU9rDU1VGXcQxD49POdSfWdc9lasGNZUZUXkqo8fTELSKCurTTWxFi/GNIL0nHInfejE9AQAAlJSUUFhZSX18vlhN3Y7IsU19fT2FhISUlJQQEBCgN+Sng3Vt5D3ABprw8LHW2Z0LCvcO5vP/l+Bn9HBtUF2IcFI+5sBBTfr7N9vHh4xkZ2nZWVqEHCIyBxNvA4O3sSFRnOnUKua6u+Z6kNU0PilvcF95JFQhcjUji1BMYvCE4npV7s3jk673cduBNkmMLWF/6Lx5crqTZnz083MlBCsI52P8V9OoH4YkdOr3+6FEwmzHGxmKymDhScoQb429UOUgXEBANOmOnfJAZYmOpSzs94xrrH0tNQw2nKk4R4dM55U0MBgMREREUFxdz/PhxzGZz2ycJXZZWq8Xb25uIiAgMBoPyYn6KS83AZC26DzQSUZ98YtV2YeSFXBh5oROiQtn//vEsiJ4CUx5wTgztYBw0CH1EBObCQvTBwVbtdeY6tudsJ9InkkifSCdEKLiMQVd028REblFRxOzYjtS0VaIVqcWp9PXui6fe0/YBvQaCpIV8dVdeuRoxgO0pUn8g44dfqDBPY2xmNkZDHRviC6mpD+HZtWliACt0HbIMP9wH513b4QFsbePMoSE2luNlx6m31HevEjpNNFqlnE6nDGBjqFi3Dkt1NRoPD2IDYtFJOk5WnOy0ASwog9iwsDDCXKXmpuA4FrOytytqkrMjAZRZ4rq0NHyvuNyqrcHSQE1DDd5uTpotkiSoKYFTO51z/XbyGDmSAT+tbbHdZDZx989389fhf2X+efMdGJngUixmJfO4R4CzI+k0Wh+fdh2XXpLe+rYEvREWJoFPH3UCc1FiCXFPkbqam01fApDhF0pUvozGqCTByC6tcWZkgnBuyrOgrvz0MpkOsFRUoA0MxC0y8nSiFWfsU3OEiffBaPVv/IyxsSDL1B1R9tnEB8Sz/abtTAifoPq1BAGA6mLwi4BQ10jiYsrKwlJVZXPfWnpJOuM/H88vmb84IbJGwfFdfhmhl5sX4V7hpBWLRE49WnEGPBMNB752diSdovDNN5tzSrSm2lRNZnkmMQFtLDX2i3D5/e/26t7fnXBacBxBUhn+lJPhFUGfQtDplf2vvf3cnRycIJyDpmUxQR0fwAbccjMDN21E0moxW8xE+0YT5RulTnyuZvBsiL1E9W7dhw+n99NPoe+jPOXVarS4ad1Uv44gNPMKgnt2wjDXWO7ftITeVubQpgGXU2skBw+CspNQ69qJzwpee53Mv7T8kC0uIE6U/uvpmvI4BPRzbhydpOSLL6nevafN4/RaPR9e/CGXRV/W+oGndsOqhUo92G5KDGB7isbZqiH6HI77hKM3Q9/aTNz1Wh6Y0U1nnoTuqTkTYccHsKBkzgW4YsAVfDf7O/Qavb2RuaaGeji5Q/WyI7pevfC94gp0AaeXdH139Dv+sfEfql5HEFxVbWoqSBKGGOsBbHpJOu46d/p693VCZI2a6mW6eD1Yua6Wqm3bkOvrbbbH+sdyovyEKP/XkzX9PxzU/e5XzaWlNOTmYoxr+3vTa/QkhiTS16eN95WKbNj9keoVCFyJGMD2FI2zVX8fbqGqTzS5Xh4E1YSx5KohYv+r0LUUpIJXSIf3wjQUFHDsqjlUbtmicmAuqroI3r8QUlap3nXd0aNU/Ppr89d5VXn8eOxHKuorVL+WIPDjYlh+h7OjaOZ9/vmEPv44Gg8Pq7bU4lQG+g9Eq2k7KUunCU2A2EtB69rpTgwxsWAyUXfsuM32mIAYZGSOlh51bGCC6yhIAb9IcGshcVEX1pyTI6btAexvJ39j46mNbXfa9PAqr2tvIWiNa7+rCerx6Q0GX4Z6l/PFM/cDNzPN2TEJQkdc+oLydLGDatPSqU1ORtLpKagu4IYfbuDhMQ8zLaKb/kZ4h4LBt1OexBYvXUb5mjXEbNuKJEnNibAOlxxmRMgI1a8n9HAnNisPr1yEMT4eY7z1ShBZlkkrSePiqIudENUZfPvADZ85N4Z2aCodUpeebnM59pjQMSy/fLlzl2MLzpWfaveqK1dVl6Z8NrdnBvbdA++ilbRM7jO59QP9o0Dn7vKrL+whZmB7CkmCv6fAhU80v1RnrhNLcoSuR2+0ax9M0741Q8xAUotTyavOc16mUEeQJGXZVYH6SVAMsTFYyspoyMsDlFqwcLpOnSCoxmKGwsMQ5BoldCy1tVT8+ivm0lKrtga5gXtH3MvM6JmOD8wWU62zI2iVIToa9Hrq0m2/b3i5eTHQfyA6jZhz6bEm/E2pAdsNWaqr0fftizYwsPXjZIuSgbg9FRM6sQKBqxAD2J7kjKUXWe+8weoZw/nm8DdODEgQzlF5Nqx9GAqPdLiL2rRUdCEh6Pz9mwdabWb06+qCYjtlBtYYq3yQNj0UCPEIwdfgKxKuCOorOQ4NtS4zC1OXlsapO++ietcuqza9Rs+1sdcyMnSkEyL7gzUPwivDnB1FqyS9Ht9Zs9D37t3iMb+d/I2PD33swKgElzLsRoh18oqGThJ45530/2ltc16OlpyqOEVNQ037KyYExyvvmd2UGMD2JCd3whdzobIAg6wj7pRMxqmDzo5KENovZx9sfQ1qijvcRV1aOobGpTppxWmEe4Xj49a++mtdVlAcVBdCVZGq3TYlr2nawyNJEmPDxmLUGlW9jiCcTuLiGgPY2qaVHHHWM8JHS49yrOyYo0OyzTsUKnKUmrAurPf//Rf/G25osX1z1mbe3PcmFtniwKgEl1B2CvIOKaswuqm2Bq9wemVTu2vWX/EG3L7GnrBcmhjA9iSmKiWRS/6h5j0n5aliACt0Ic03sR1bRijLMoaYGLzGjweURCvdtv7rmQZdAbf9CAYvVbvVenuj7927eQYW4Lkpz/HP0f9U9TqCgN4doqdAkGuslqhLTUPj6Wlz1vC1va9xz8/3OCEqGwIb398KXH9VhNzQgNzQYLMtNiCWKlMVWZVZDo5KcLq9n8CbE8BsO0t1V1aXcYxj11xL9d69bR57pOQIGknDAL8B7etc1IEVuo2mJ9f5qRgbZ060GSdpsNj+wBAEl5OfAj59wNixGVNJkgh/9hkC5s1DlmUmhE/ovsmbzuTXFyLHg86getd93nidkIcfUr1fQTjLgOkw7zswuMZ+9dr0NAyxsUg2bhLTStLaP0vS2ZrKjhS69r706j17SRs+osVamE0PGtOLXX8gLqgsP0VJSqR3d3YkqqtLTaH2wAE07m1/b3cMvYMfr/oRo66dK5yqi+HTazqlAoErEAPYnsQrGNwDID8ZXVgYZk8jvfMaOFF+wtmRCUL7FKTYtQfuzKf7kiSxePRiZg+YrUJgXUDqaji8XvVujXFxZ9WCzarMYtaKWaw7sU71awk9mNl1HrTKsqxsRbCRMbfKVMXJipOus7LDLwJ0xk5J4qYmfZ9wZJPprNUcZ+rv1x8JSSSI64kKum8G4trUNNDpcOvXdmJKjaSht1fL+8StGHwg41c4tbPjAbowMYDtSSRJeRMoSEWSJIwzZxB33tTuv/9P6B5kGWrKILjjWUjzX3yRI9MvQLZYqKivwGQxqRigi9v4DGx9VfVuTXn5FL75JvUnTwIQ6B7IyYqTpBR13/T9goOZG+DpSNj8krMjaRb12af0uvVWq9cPlxwGzmGfWmfTaGHyAxA1ydmRtEoXFITW35/aFjIRe+g9iPSJJLcq18GRCU7VUA9FR1wm+7jaatNSMfTrh8bNrdXjyuvLefz3xzlUdKj9nWt10Gugyz+86iiRk7ynCU+E3P0ADHjyKdq5kl4QnE+SYNEBu2Zi6tLS0fj4IGk0vLznZdadWMev1/7argQKXV5QHGT8pnq3lqpKCl5+BV1YGG59+2LQGoj2jW6+kRcEu5Ucg/pKZRWRC5AkCcPAgTbbUouVbN9xAS50wz35fmdH0CZJkjDExlKX3vL7xpezvsRd1/2WkQqtKDoCloZuOwNbl5aOx6hRbR6XXpzON4e/YXrE9HO7QFAMZLe9v7YrEjOwPc1FT8It3zZ/mVeezYGc7vk/t9BNaTv+3K02LbW59MvhksNE+kT2jMErKHvhKrKhtkzVbt0iIpAMBurSTu9NG+g/UCz1E9TTnLzNNWY1KzdtpuSrr5Bl2artgsgLePX8VwnxCHFCZC0wNyg1dBvqnB1Jq4yxMdQdPoxstp1tVgxeeyC/vnDT10oCt25GNplwP+88PMeOafPYc85A3CQoDkpOgKmmIyG6NDGA7cFqU1PJn3Ah773nItkSBaE1SZ/BV7d2eAa2oagIc0EhhthYZFnmcOnh9mfz6w6almCpnI1U0ukwDBhw1t61WP9YcqpyKKtTd7As9FBNNYwDXWMAW/rNNxS9867Nh1+B7oFM7TvVtR6Mpa2G10YqpUhcmNf50wm8805kk+2tHZnlmSz6ZdG5LaMUujaDNwy8ELxd6IGQSiS9nj6vvIzfnDltHptWnIa/wZ8g96Bzu0jYMCWBo4uX0eoIMYDtaWrL4d3psGcZ+j590Jks+J4qpaS2+/3PLXQzxzbBia0dnoGtS1cGbsbYGPKq86ior2Cgv+1lgN1S0+xV02BARYbYWGrTTw+ME0MSuaL/FdSZXXvGR+gi8lOUZEQql4HqqLrUVIxx1oNpWZb5NOVTMsoynBBVK5ofXrn2qgjPMaMJvGM+GqPtLKtuWjfWZ65nf8F+B0cmOE3aj3B8i7Oj6BQtrTSwJb0knZiAmHN/MBZ7Mdy2GnzOIflTFyEGsD2NwVv5EMtJQuvlhTk0kIh8mfQSkZpecHGFaXbVgNT26oX/LTdjiI9v3p850K8HDWD9ImHhPhh2k+pdG2NjsJSXYy5TZlyHBQ/jPxP/Q7CHa+xZFLq4gRfCmDudHQUAltpa6k+cwBBjPYDNrsrmqR1PsTtvtxMia0VANGj0Ll9KB5SVMvWnTtlsC/EIwcfNR9yv9CTr/w1bX3N2FJ0i999PkHHF7DaPk2WZeks9cf4utK/eBYgkTj2NJCmDgMYnse4xsUQkbyG9JJ0xYW2vwxcEp5BlZenr0Os73IUxJobQh5R6pZHaSBaOWEhMQMcHxF2ORqvU0usEftddh/9NNyHpTn+kyLJMeX05vgbfTrmm0IMMu9HZETSrO3oUZNlmEieXfTCm1UOvAS4/AwtwYu7NGAb0p8+r1hnTJUlioP9AjpQccUJkgsOZG5QkTjEznB1Jp6g7fBitT9tVQCRJYvnly23uuW+X/92k1NCd817HzndRYga2JwqMVRI6AN6DEuhdDIfzkp0clCC0oiIH6ivsSuJSf+IElvp6ACJ8IvjzkD/3vBJSh9fBukdV71ZjNJ41eAX464a/cuc615g1E7qw+iooy1IeYrkA0wmlbrohxnqQeqRUGVi55N76oNhO2T6gNkNsLLVpLc+wDvAbwJHSIx2/mRe6jpLjYDFBYPd70CzLMnWHD2MY2P73Crv21efs6/i5LkoMYHuioBiozIXaMrwmT8F061X8KW6es6MShJbVlkHoeRAyuEOnyxYLGbOvJP+55wBIyk+iuLZYzQi7huwk2PKyMihQWf7LL1P4zrvNX/f17svRsqNYZIvq1xJ6kOOb4cVBcHK7syMBwGfmTGK2b8MtMtKqLb0knTDPMLzcXGOv7lnG3AEzljg7ijYZYgZiyszEUmX7PSohMIFo32gqTBUOjkxwuMLGBxkukn1cTQ25uVgqK1ssx3Wmz1M/5+6f78Zsaf+e2bMExUJxhlJTtxsRA9ieKHwkxF0GdZV4jBjO8H/8l8gwsbZecGHB8XDnJiWbXgeYsrKQa2owDBxIg6WBP639Ex8c+EDlILuApj3EhervIavdt4+Kn35q/nqA3wBqGmrIqsxS/VpCD9L0/6oLzcJofX2RtFqr14+WHnXdxHCR45WELi6uqczZmUnhzjR7wGw+u/Sznrd6pidq2rMd6KK/U3aoO6ysgmzPAHZ33m4ySjPQaqzfc9olKE6ppVvsYsnl7CQGsD1R9CS4/lPwDQcgP+sw3/72DgXVBU4OTBA6R9OHhXHgQDIrMqm31LvujWZn6sRspIaBA6k7ehTZosy4DvBXlkaJ/WqCXQrSwDMIPAKcHQkAOY8+Rvnan2y2fTLzEx4b95iDI2onswkyfoVC1/59bLqhrzvi2nEKDjDmLliwDYzdL4+CLjgY/5tvbtcA9nDJYfvuV5oe/nWBLQTnQgxge7LGepqFdy2k+qmX2FfQ/dbIC93EF3Nh1b0dPr3usHIz5DZgQPOAqkcOYAP6gUbXKQNYtwEDkGtqMGUpM679ffsDp/cFCkKHFB52mdlXc2UlpV9+Sf3x4zbb3XXurpt522KGZVfCgS+dHUmr9H36EPbUErzGt7zaZuGGhTy59UkHRiU4hd6orL7qhoxxcYQ+/BBa39YH5/Xmek6Un7BvX31gDCTMAS8XfW/qIDGA7ak+ngVf3gyAV9wgIgpkcaMpuK6TO5QZhA6qO3wYXe8wtF5eHC49jEbS0M+3n4oBdhFavfJhVqP+/l/DAOUDtmm228vNi0WJixgVOkr1awk9hCwrywhdZABb3zgraGvWZGfuTp7f9TwV9S66N1NvBP9ol5+FkTQa/GbPRh8e3uIxdZY69heKWrDdmizDuscgc5uzI+kU9ZmZyPVt70k9VnYMs2y274G7mwdc/UGHt2C5KjGA7anc/Zs/yDxj4giohMysFCcHJQg21JRCZZ5dNWD9b7yBkH/8E1CW40R4R2DUGVUKsIu5YxPMeln1bg0DB6IPD0euq2t+7faE2xkWPEz1awk9hCzDJc/A0BucHQkAtc371qxnQ7Zmb2VZ8jIMWoOjw2q/oNguUUqn/uRJylevbrF9oN9AMkozaLA0ODAqwaEq82DLS5DT/R5UyBYLGZdfQf7zL7R5rMliIjEkkVh/OxNZyTLUlNjXh4sRdWB7qsBYSFkFplrcGmdOqtJTYKaT4xKEP1IhiYvHiBHN/33PsHv+n737jm+jPh84/jlN7xnb8ZZsZzIDhL3KCjusQilQaCm0jNIFFAodtKwCbYGW/tpSWvbetEAYIewRNiSQOLbkEdvxkC15at7vj7OUOJaXfKeT5O/79cqr+O6ke36/ONI93/E89HpT64N8RozafOwbs7Koe/WVMceG/ENs7N3IDvN2wGwwa3JfIYUZDLDzqXpHEeHbtAkpPT3q7GB9Xz22HBsWo0WHyKapaBHUv6SsZjEm7r/H/pdeovPmW8jcb7+oSywX5C/AF/LR3N88N1fSzAXhgZZZDFwnKn9rK/LISNRWXNvbcd6O3H3k3bO/6epr4Z2/wFXtSk/4FKDKDKwkSUdKkrRBkqRNkiRdEeX8OZIkdUmS9Onon+9vc+5sSZLqR/+IXi7xUrQI5BC4GrDWKf+ITM52/LNYpikImgh/kcWYwAZ6exl44w2CAwOAUlxoTi9rbf8c7j8FutSvRLy91S2rOeuFs2j2NGt+LyEFddcr2wdCidGKSfYHSN9pJyTD+Een+t76SOGyhBWpRurQO5JJRbYjTFDIKbwfUBSIS2EJWH1cLZEKxHVTf16o1u843wZBL/Q1qfN+CWDWCawkSUbgDuAoYClwuiRJS6Nc+ogsy7uO/vnX6GsLgN8AewF7Ar+RJCl/tjEJ0xCpSrYBc1kpOddcxS9/9CjmBB6VFeaorBKl7VO+LaaXD32wlpbzf4DP2UTbQBvPbHoGt9etbozJRDLAppdhyxeqv3XfE0/ScMyxyEGlX92CPGVwrL6vXvV7CXPAh/+Ge1fqHUXE/F//iup77xl3fMg/xOaBzZHf94RVdzicvwbyx/ewTSRb99NHT1Brcms4pPIQcq2pV51WGNW9ESzZkF2qdySqCyewltqpE9jjnz6eP3009VLjKYV76SbBFoLpUmMGdk9gkyzLjbIs+4CHgel+46wAXpZl2SXLci/wMpD4jcpSwbwFsOcPIN+GZDBQftqZFNamZrU3IcktPEJp+xTjshfvpnqQJKy1Nbzf/j5Xv301vSNzeAlxYZ2SxHZqUMxFkvA1NOBrVmZcbbk2jJJRzJQIseneqPy+RpnxTCQdgx3kWfMSfwY2sxDKloEpgffpAqayMgwZGRPOwKaZ0rjtkNvYq3SvOEcmxE1/h7J8WJL0jkR13o31mMvLMWZlTnrdgG8Ap8dJtjl79jdNwVY6anwrlAMt2/zcOnpseydLkvS5JEmPS5JUOcPXIknS+ZIkfShJ0oddXaJf6ayZ0+Hom6Bc2Rvoa93Mk3//Oc83Tlw4QRB04R+e1cu99ZswV1ZiSE+nvq+eNGMaldmVU78wVZnTIK8aetSfFd2+h6PVaKUqp4r6XjEDK8Sga+PWmQOdDX3yCY7TTmNk4/il9zV5Nbxx2ht8o/IbOkQ2Q189B188rncUk5IkCUtdXWSmaiJD/qE4RSTE3Wn3wTmp+Tya/+3TKb7ssimvC3cGmVULnbD0PMiaH5etQ/ESr2HN5wCbLMs7o8yyjl+DMwVZlv8py/IesizvUVRUpHqAc1LQH9kL079qFUtufZ7V657VOShB2IZ/GK4vV4oPxMhbXx9JrDb1bqImrwZjihQxiNm8BdCt/qyotVYpqLLtg2ddXp1o0SXMnG8I3M0Jswdu5KuvGPnsc4w5OVHPS5KEQUrsmWJAWZb9zu16RzGlshuup/yPt0x4/j9f/od9HtqHkcBIHKMS4sqcmp0CMvbYg5wjV0x5Xfh7U7We9QdfAUsTZ0vGbKnxabsZ2HY6o2L0WIQsyz2yLId7K/wL2H26rxU09Mpv4W97QygYaQswtDF11scLKaBnE8hByCmL6eUhnw9fU1NkT1V9X706o5nJrmK5Jk3NDRkZmCsqIv0yAc7d8Vyu3f9a1e8lpLjwCoEESWC99fUYsrMxlZSMO/e7d3/HHZ/eoUNUMZi3UBm8Uqs4jEastbWY5s2b8HxZVhkhOUSjuzGOUQlxsWU9PHp2Ss0WhgVcLgbefIvgwOCU127q20S6KZ2yrNief8bZ47uwKHV2aaqRwK4FFkiSZJckyQJ8CxgzjSdJ0ra7sI8Hwg1HVwFHSJKUP1q86YjRY0I8zFsIgRHoa4484Kc1d4plOULiiFQgjm0ZoWQ0Yn/icfJP/SZ9I310D3ezMD8xHoh1ddDlcNaTmrx1zlFHRlpzAewwbweWFS/T5F5CCiusg3P+B7YD9I4EAF/9Jqx1dUhR9uStbl7NlsEtOkQVg8I68A+Cp03vSCYVcLno/sc/J9wHG56VEqs7UlD7Z7D+6ZTc/zr0/vu0nHce/papK/PvPG9nzlp6lnorO/wjyv9vfVMnz8lg1g0BZVkOSJJ0MUriaQT+LcvyOkmSfgd8KMvys8AlkiQdDwQAF3DO6GtdkiT9HiUJBvidLMuu2cYkTFN4b1H3RkwLjiCUkUZFt5dGdyM7zttR39gEAUZL6UvKQ1cMJKORtEXK73muLPPaqa+JfqQaK/75z8f87A/6Wd2ymqrsKpYUikJxwjRZMsG2v95RAEorC299Pdkrxi/7c4246BnpSZ6VHeEZ7Z56yI1aciQhyH4/XX/+M4bsrKjtRqqyq7AYLKJAXCrq3gAGc8ydBxKZt34TGAxYaqbuX3x0zdHq3rzpbbj/pNGBwcT4bJ0NVdJ6WZafl2V5oSzLtbIsXzd67NejySuyLF8py/IOsizvIsvyN2RZ/nqb1/5bluW60T//USMeYZq2aaUjSRKmGhvVPQY6hzr1jUsQwro2KC0fYtwLM/D66/Q9+RSg7FGblz5PtF4A8PbD3/aFtXdp8vZyKITsV3pKGyQDv3zzl/yv8X+a3EtIUeuehk2v6h0FALLXS8aey8lYvse4c+EESrV9alqbNxpnT4O+cUzBVFyMITt7wkJOJoOJmrwa0aIrFXVthIIaSMG2jt76eixVVRisk1cC9wa9dA93q9cHFrY+83enxr+ZWc/ACkksowAyi5TRLqD6hpuw52RjKZmvc2CCMGrJcbMaKex99DF8Tid5J53Ik/VPMhwY5owlZ6gYYJKyZIG7FbasU/2tvY0OHCedRNmNN5Bz5JEYDUZq82rFUj9hZtbcqMzA1B2qdyQY0tKo+Ev0QnLhBCppEtjsUri0XvnuT2CSJGGtq8M3QS9YgLOWnoVJEo+xKad7IxQv1jsKTWxbVHIyn3R+wnkvncddR9zFnqV7qnPznHIwpYsEVkgRK26A3AoA0qbxj0oQ4mqnU2b1cu+metIWK8tWn970NBKSSGBB2Vs0b4EmrXTM5WXIPh/ejfVwpFIwoi6vjvc73lf9XkKKCgbA1QALDtc7EgDkYBDJGL1yebopnd1LdqcwrTDOUcVIkjQp4KYF64IF9L/0ErIsR917fHzt8TpEJWgqFIK0XCjdRe9IVBcaGcHX3EzO0VMvDQ6v7KjJm3qp8bQZDMp2LA2+9/WQBDXfBU3t/E2o3gdQiia8fsNP+NX95+gbkyAAeAeUapnBQEwvDw0P429uwbpgAbIss6lvU/LsU4uHeQs0GYk1WK1YKivHFF+py6+jc6gTt9et+v2EFNTXBEFfwvSA7fjtb2k86aSo505acBJ3H3l31AQrYX39P3jhF3pHMSVrXR2hwUGCfX1RzwdCARr6GnCNiNIpKcNggPNehQOn7pOabCSzGfsTj5N3cvTPkm1t6ttEvjVf/YExjb739SAS2LluuA8aXgNvP7LPR/E9qxj+YK140BT01/Q2/HV32PxhTC/3NjaCLGNdsIDu4W76ff3qjmYmu8I66G9X9sOqzLpwwdgEdnTgQCwjFqale7R9RqK00NlYjzF7fP9XWZbV3aMWL1vWwft/V3rtJrC8U7/Joo8/wpSfH/V851AnJzxzAq80vRLnyARh5iSjkbQlSzCXT108rb63ngX5C9QfGNvnIjjuVnXfUycigZ3rWj+E+06Aji8wlZQolYi7ZPGgKeivZ/R3sDC2pe0+pxMA64K6yO+zmIHdRuWesNM3NXmItdTV4WtqIuTzAbBHyR48f9Lzop2OMD2RBFb/bS2yLOPdtCnqvrXOoU4OfOTA5EugwlXdXYldyMmQloZknriQT2lmKVnmLDb2pl6/0Dnrvb/DXUdA0K93JKobeP113M88M+V14RVjtXm16gdRsQfUHKz+++pA7IGd6wpH/4F01yNV74u5rpaKnnVs6t3E7iW76xubMLd110N6PmTGtoQm95hjyNx3X4w5OXQ712E2mLX5QkhW9gOVPxrIOuBAJJMJ2ecHi4UMcwYZ5gxN7iWkoH0uhqUrlX//Ogu0txMaHMRaN/6zo8HdQJ+3L/kqm29bjXT+TvrGMoXOP9+KMS+Pwu+eM+6cJEnU5NXgcDviH5igjbaPwb05JSsQ9z7yKP6WZnJXrpz0uqAc5Jd7/ZLqnGr1g/CPQONrysTAvOQe0BczsHNdXhUYrZFN3VkLl1DVLYnS9IL+ejbF3P81zJSfj2Q0clztcXxwxgfJU2glXmRZ+UJTWcZuyyi66CKMWZmRY6ucq/j3l/9W/V5CCjIYE6YHpLehEQBr7fgEtrFPOVeTm2RbEwprASkp9sINf/QR/S+/POH52lxR4TyldNcnfWI1EW/DJiw1Uw+imwwmVtatZNfiXdUPIhSAh74FX009E5zoRAI71xmMSr+tbuULIG1BHZkjUOCz6ByYMOf1bIp5+TBAx+9+j+fFVZGfTQZTchVaiYc7vwFP/UCTtw709uJr3Rz5+d22d7ln3T2a3EtIMS9eCY1r9I4CAFPRPPLPOANL3fiH6gZ3A3nWPArSCnSIbBbM6crgoG9A70imZFlQh7e+fsK9xrV5tbhGXPSO9MY5MkF1sjzr7/1EFfJ68be0Yq2derCrsa+RdT3rtNlfb82C7LKkGLyailhCLCijXZ1fA5B36qnkf/vb7DDJvhNB0Jwsw9E3Q2Zs7R5CIyP0PvQQxsICZPkILl59MUfbj+aYmmNUDjTJZRZr9kXWdNZZWKptVN7xV0CZpXqi/glcI67ke+AX4mewB977m9LeLQH2aqUtXsz8X10d9VxDXwM1uTXJOTB28VqlpU6Cs9bVEervJ9DZibmkZNz5QyoPwZZjI92UrkN0gqoGu8DrmfXKq0TkczZBKIQlykqO7d27/l5ea3mN1097XZtgUqQSsUhgBTjoCpBDABjSxZeAkAAkCZYcF/PLfQ6HUoG4tpaekR7eaH2DfUr3UTHAFDFvATheV3rvGdRdkGOtqcW7YUPk5/D+48a+RgrmiwRWmECkeFtiPMT6N2/GVFwctZjQvmX7Jt/+17AkSF4BrHXKbJx3Y33UBLYyp5LKnMp4hyVowT8Mi45OyR6wkaKS00hgwwNjmpm3AL54TJkoSJLPgWjEEmIB5u8IpTtHflx/w9Vc97N9WNuxVseghDmtpwEaX4+5EqF3k1Jd01JTQ0Of8t+igFMU8xZAYATcLaq/taW2Bl9LS6QScSSBdTeqfi8hhSRQAivLMo6TTqbj2uuinv/hLj/k9MWnxzkqlTjfgruPBU+73pFMylpXi6mslNDwxNXS13asFc8rqSC/Gk5/CKpTb7A5Z8URLHj3HaxRtiJsS5ZlGtwN2j6vFC6AEbcy453ERAIrKH0gP7kfupTZEvOnG1jyeV/kwV8Q4u6Lx+DelRAKxvRyb2MDGI1YbDaRwE4mvNdIg+VE1ppaCIUiI88lGSVkm7PpHu5W/V5CCunZBAYT5GlQgXOGgi4XQbc76r61If8Qw4FhHaJSSSgIzjehe8PU1+rIVFjIgtWryTniiAmv+eOHf+TOz++MY1SCJmL8vk8Wpvx8JNPkC18jPeu1nIHd8SS46ANIT+6VUCKBFZRZrmcugvqXAMhatITKHomGXlHZT9BJdz3kVYI5LaaXy14f1kULMVgsNLobybZkU5RepHKQKaB4Cez3Y8idurH6TIUf+n0NygCCJEm8ftrrXLjrharfS0ghw71QUAtG/Xc4bV3JMX7w66lNT7HXA3sl74DMPO0Gr+KtNq+WBrcYcE96j5wF98S+dSiRbbnpZjzPPz/ldeHfY00H3LOKoWhRQnzGzoZIYAXIKICMwsjSLWttLVnDMh2bRXNwQSezrERYcvll2J94AoBMcyZ7l+6dnIVWtJZRAIf/TklkVWapqaH0umtJ32XrfiZzCvb2E1R23K1wwTt6RwGAr1F5mIzWA7axr5EsS1bytubKLgVLVlIksK4HHsBx6mkTnq/JraFzqJN+X38coxJU11MP1hy9o1CdHAjguu8+Rtavn/LaHQt35J+H/5MdCnfQNqiP74Wv/qvtPTQmElhBUVgXaaUTHm32NogRTUEH4VL682ZXSj+csP5095/yp4P/pEZkqck7oOw5VpkhLY28k0/GXFYWOba2Yy0XvHIBbq9b9fsJKSRBZga8mxowZGZiilI8qMHdQF1eXfIOjEmS8r3fk/gJrOzzM/L55wRcrqjnxf76FBAMgMsx6+/9RORrbgG/H0vt1Pv6syxZ7FO2D1mWLG2Dev8fShKbxEQCKygKF0S+yKy1NQTm5bFXzs4EQgGdAxPmnIEtSn/CGIu4+JxOnKd/m6FPPlE5sBT1/GVwtzbthf734lp+ePHt2K/4H/vduJrVG1p4a/NbONwOTe4nJDn3ZnjgVGhJjII8OcceQ8lVV41LUmVZ1r5SaDzY9ldmYhNceAbcN8Ggem3u1grnQpJyN0PInxDF29QWWckxjR6wzzU8x8dbPtY6JGWgIAkGryYjElhBMa9OSRxG3JjLytjprXc594L/w2RIjJFwYQ5JL4DzVsfcRmdk40aGP/kEyWzhw44POfrJo/mq5yuVg0wh8xZAf7tSzE1FT3+ymS/+9m8uWH0nkhxic98wd69Rit6ImRIhqq6voX4VBL16RwJAxrJl5J104rjjrhEXfd6+5C8Mt+I6OOFvekcxJWuN8uDvbYj+uVGWVcZjxz3GUfaj4hmWoKbucPXx1JuBnWwv/bZkWeYPa//Ac43PaR9U4QLodUIgMT5rYyESWEGx29lw6aYx+w8CoQCD/kEdgxLmJJMFyneH7PkxvdzXqDzkWGvsbOrbREt/C/lp+WpGmFo0KuZy86oNNGYWYwkFKBlSlv4ND+eAbBYVzoXowkvZE+AhNjQ8zOA77xD0eMadMxlM/GL5L0Rv6TgxlZYipacr1eWjMBqMLC5YTJoptqJ/QgLIng97np+SS4hDw8NYbDaMWZmTXucaceH2uiMrCjQ1bwHIIWXZdpISCaygyCiArKJIU+Oeu+/hv0ct445P79A5MGHO2fgSfPlEzC/3bmrAVFaKISODhr4GssxZlGSM38MmjAonCz3qVh1v6xumObsYgMr+ztGjBoLeIlExVIiuZxNYspUqmTrzbthA8/fOZejDj8ady7XmcubSM6nLT/Lljr1NcNuusO5pvSOZlGQwkHPUUWP2029vbcda/v7Z3+MYlaCq0p3h6JuVZ9EUU/zTn1DzwtQViMMrk2ry4rA1ITxQ0OvU/l4aEQmssNWbf4T1zwAgjwyzqClAS4eoRCzE2dp/wZuxF13yNjYoPUhRCq3U5NUkb6GVeCiwg2SEbnX/rZflpdOSpQwcVPVviRxPC9aSY069SpOCCnrqle0sCfDvNVzEMNq+tfreelr7W+MdkvqyipUH2K7E7gULUHb9dRSec86E5z/p/IQ7Pr1DrBpLVp42paVjiprOM8imPmUQOS4zsCU7wRUtsOhI7e+lEZHAClt9fC+sewoAS63yD2ioIbk3eQtJqKd+VoUcrDY7GXvuCUBDX0N8vgySmckKK/8KS1eq+raXrVhEKDMLlzWbytEENt1s5Nf7XMVNB92k6r2EFJGWBxXL9Y4CUPZbShYL5oqKcedu+OAGfvHmL3SISmXmdMitVH3wSityKIQcCkU9F/6cFwXiktS/DoNnf6R3FKrzt7fjPONMhtZOXZiusa+RLHMWxRlxWIFiNEFacg8kiwo9wlaFC8b0ggVIa+1m0D9IpnnytfuCoIqAT1nWtsNJMb9F+Z/+CIA/5Ocbld9g79K91Youde36bdXf8oRl5QD8bfgCvvZbKc9L57IViyLHBWGcb/5H7wgivA2bsNjtSEbjuHMNfQ0cXHlw/IPSQmEtuBJ/Sf/gu+/ScuFFVN97L+k77TjufHjZZUNfAzvOG39eSGC+QfBsVn4XU4y3vp7hjz4Cw9TzhZfveTnf3fG78VsxtmUdhILK8u0kJBJYYat5C6DpbQiFsFRWIhsNlPfIONwO8YUgxEevE+RgzIUcZFmOfPibDWZ+u+9v1YstlfV3QNsnsPBIVZdvnrCsnBOWfXfMse7hbs5/+XzO3fFcjqnRpn2PIMyWr6GR9J3HP9j1jvTiGnElfwudsMI6+PwRpf92AizdnoippAR5eBhfY0PUBLYyuxKTwST21yejBCrepratFYin/rwwG8yUZU28z1t1JTvE714aEEuIha0K68A/BP1tSGYzlsMOZucl36AwrVDvyIS5omd2pfRdd99D/SGHEBoaYsg/REiOvtxM2M5Xz8FD31JaaanM19pKz113EejtBSDPmofT7WRDb+LvuxPiaMOL8H/7JUxRkYrbb6PwBz8YdzxcQTvpW+iE2Q+EHU6AoE/vSCZlqawEk2nCVjomgwlbjo2OgY44RybMWuR7P8mLokXhbWzAWFiIKX/yTghur5vr3ruOr11fxymy5CdmYIWt5i0Ao1XZTJ9bQd1td5B6HydCQlt0FPx8I6TH1vbGu6ke2evDkJHBbe/fwCrnKl479TVRxGkq4aVbPZtibl80EX9rK50330La0qWY9tlHedDMtdHYJ3rBCtvoXAdbvoSMxBgwTVu6NOrxcKXQlNlbv/R45U+Ck8xmLNXVkeJa0Txw9ANkmDPiGJWginACW5Aiqxq24dvUEOljPJlNfZt4eMPDHFhxIIsLFschsuQnElhhq+r94KqOMWv1u4a66BnuYXGh+AclxIEkQXbsLW98DY2R/dsNfQ2UZZWJ5HU6wiPfPZvAtr+qbx1eOuVtaCRzH6VvZk1uDeu616l6HyHJ9TRAdilYs/WOhJH16xn5egM5xxyNwWodc+7gyoPJT8tnfqa6Az26CoUg6FWKOiUwa00N3vqJC0uK5DVJ1R0GablgSb2/P3NlJZbq6imvS7mVHXEglhALWxmMY5LXgddfp22fb/CHRy/WMShhTnnjZvjskZheKssy3sZGLKNtLxrcDamzT01rORXK6guVe8ECmIqKMGRn423Y+t61ubVsHtjMSGBE9fsJSapnU8IsIfS89BLtv/pV1MGv4oxiDq8+PHUGxkIh+EM1vJ74lcFzjjqSnOOPm/B8o7uRy9+4XKzuSDblu8Fe45frp4Lym2+i6OKLpryu0d1IhimD0szSOESVGkQCK4z15h/hpV8BYCych8UbxNjcIR40hfh4/x/gfDOmlwa6ugh5PFhranF73XQPd4vRzOkyGJTlWz3qP/hJkoS1pgbfNnvXdi3elaNrjhY9G4WtuusTpgqpr6ERS1UVksUy7txT9U9FlhGnBINB6QerweCV2nKOPpqiCy+c8Lwsy7zgeIH1rvVxjEqYFVkGxxsw5NI7EtXJsjztaxv6lAH3lBkYiwORwApjbVkP658BwFpjB6C8R6bJ06RnVMJcMNwHg10xVyBGlsk7/VukL1smluPEYuUdcMTvNXlrS10tvqatnyH7lO3DjQfcSGF6Yux3FHQW8EHtIco2lgSw7UqObbm9bn79zq95veV1HaLSUGEduJIjKQ/29RHs64t6riq7CpNkEjOwyWSwG+45TqmEnWJ6H3qITYceRtDtnvLaAd9ApBWUMD1iD6wwVmEdfPkE+EcwZGTA/CLKu7tp6GtgUcEivaMTUtksS+mbS0oo/c1vACjqb+HCXS5kaWH0QixCFBW7a/bWJZdfjuE3Y/fXybKMN+glzZSm2X2FJGGywCl36R0FALLfj6+piexDDx13LlLAKdUGxgpqofF1ZTnxNPpV6iU0PMzGvfdh3iU/ijoTazaaqcqpigxgCkmgZ3RPcwq20PFt2kTQ48GQkzPltQ8d+xDBUDAOUaWOxP2kEvRRWAfI0OsAIL12ARU9iN5qgvYiX2Sx7YML9PYiBwKA0hPwgl0vYF76PLWiS33uzfDBncqIuMqMubnjlmOe+fyZXPHmFarfS0hCwYDeEUT4WlogEMBaNz5JDSdGKbe3vrAWAsPQ3653JJMypKdjLisbsx1he7V5tam1xDvVRVropNigEEoPWGvN9JcFGw1GjSNKLSKBFcYqHP1iHp0Nyzv2OAqPOpbjaxO/zL6Q5IZcYM6AfFtML9/8k5/SdPY5AGzq3UTfSJ9qoc0JvU54/lJo/0z1tw4NDdFx/fUMvLl1f3NxRrGYKREUa66HmxdAAsxAWOx2Frz9FlmHjJ+BbehrIM2YRllWmQ6RaahqHzj4SjCa9Y5kSpbaWryNEyeoiwsWk25KF7NZyaK7HowWyKvSOxLVKVsRpk7MX2l6hR+v/jEenycOUaUOkcAKYxXUKgnEaFPzvBNPYK8rbqI6Z+oy4IIwK/tcCFe2KssJY+BtaIiUq7/o1Yu44YMb1Iwu9UV6waqfVEpWK32PPsbg2+9EjtXk1dDS34Jv9LNGmMN6NkFajlIJX2eSJGEqLMSYlTnunMPtwJ5rxyCl2KNTyVI4+AqlmFOCs9bU4HM4kEOhqOfP3/l8Hj3uUTGblSx6GpQCgin29xXs6yPY3R1p6zeZTzo/4Z22d8g0jf/MESYm9sAKY6XnwY/HzsC0dWzi486PWLHDSZiTYIRWSGIxfokF3e7RL4sahvxDtA22cWLuiSoHl+KySsCSBS4NElijEYvdjrdh63vX5tYSlIM0eZpYkJ96+5+EGehOnBY6rgceQDIYyD/99HHnbj7oZvq8ffEPKh4Ge8A/mPAzYZbaGuSREfxtbVgqKvQOR5itQ66C4V69o1Cd7PeTd9pppO+2bMprG/oasOfaxaDLDKXYMKKgtkBvL+6Dj+Otf/yO5v5mvcMRUlUoBPedBOuejunl3tE9UZba2kjF7JTbp6Y1SRptpaNNOw2llc42CexoIRyxv36OC4WUQZMESWD7Hnuc/tdei3ou25JNZXZlnCOKk3uOg+cv1zuKKWXuvTfzf3cNxqysqOdDcojvrfoed395d3wDE2JTsgPY9tc7CtWZiooovea3ZCybOoENr+wQZkYksMJ47/wF7joCAFN+PuTlUN4ji/1qgnYGOqDhVRiKrYCQr1H53bTW1uJwKwXIxBdCDArrNEtgLbU1+NvaCA0NAVCdU813d/wuthybJvcTkoRnMwRGEqKIixwK4XM4sNrHD3619Ldw+8e30z6Q2IWOYlao3eCVmixVVeSfeirGvLyo5w2SgS2DW/iy58v4BibM3GA3fPoQDHTqHYnqgm43cnDqfdjhFWNiwH3mRAIrjOcfgZb3wTcIKElBebeYKRE0FO5BWBDbh3jaTjtT9NOfYi4ro9HdiEEyiH3bsTjyBvjBm1NfFwNrbR2m4mICncrDSpopjZ/t/jMWFyzW5H5CkjCYYN9LoGJPvSPB39aO7PVG7QH7RdcX3PnFnQz4B3SILA4K65RCbglUEXoi3oYGhr/4YsLz9lx7ZCBTSGBtn8DTP0yaHsQz0faLK3B+89Qpr/P4POxctLNoUxkDsQdWGC9cidjVCPN3Ir12AVXrP+PdXpHAChpxjT5s5Mc2a5q2aCFpixYCcHTN0dTl1WExxlYMak7Lnq/dWx9xODkrjhhzbMg/RPtge+r11RSmL6cUjvi93lEA4HMoD9LWmvEJrMPjSO2BsYJaCPnB3RzzQGK8dFzzO2SfD9vDD0U9b8+18177ewRDQbGvMJF1z651XiLzOhpJWzJ1H/r5mfN54OgH4hBR6hEzsMJ44Q+TnvCyzBoyh0N0tG3UMSghpbkalZmY3Nj2lw19/AmBXqUQRE1uDUfaj1QzurljsAde+S1s/lj1t47WC+9vn/6N0/57mmh5MZd52iOrffQWdLmQLBYs9vEDaQ63g4qsitQdGIt87yf+bJiltgZvYyOyLEc9b8+14w16aR9M0eXeqcLVAGm5kFGodySqCvl8+FtasdhteoeS0kQCK4wXHn0drUaauf/+WK+4hD8edruOQQkpzZwB1fuCceaLQkI+H01nnknvffcRDAV5wfECHYMdGgQ5B0gSvPVnaHpn6mtj0HHd9Wy54cbIz+JBU+DZH8G/E2PAKXflShZ98jHGgoJx5xrdjam9r75kKRz/VyheonckU7LW1BLyeAh2R6+ZsLhgMQdVHIQvJFp0JTRXo/K8GWVwM5n5m5shFIq6kmN7v3771/z0tZ/GIarUIxJYYTxrNiw+FrKU5YTW2lpqzrmA4mKbvnEJqeugy+Ds52J6qb+pCUIhLPYa2gbauPyNy3m37V2VA5wjMgogvUCzYi7+1lYG33k78nNNnvIFL/arzWHhh9gEIRmN41YLyLJMz3BPaiewabmw21mQW653JFOy1Ch/D97G6J8bSwuX8tdD/yoK4yS6BPu3rxZv42hXhCjF4La3rmcd/pBf65BSkkhghei+9QAsOyPyY9f6T3nw2ev42vW1jkEJwnjhhxiL3Y7DIyoQz1phrSa9YEF58PQ5myLVGe05yt+TSGDnqGAA+poS5iG29UeX0PfU0+OOS5LEmlPXcPGyi+MfVDx1bQTnW3pHMaXwzFZ4z/JExNaEBPe9VXDYb/WOQnVv+bJ5atlx7Hb3Bva7cTVPf7I56nXBkNIHXTyvxEYksMLEQqHIf/ZdfQ2Gvz3AB+0f6BiQkJIGe+Avu8NX/43p5T6HkvxY7TYa+5QHGvGFMAuFdZH972qz2u3Ifj/+zcoXel5aHvnW/MjAgzDHeFohFEiIBDY4MED/yy8T6O6Kel6SJKxGa5yjirPX/wBPX6h3FFMylZRQeec/yT788Amv+dman3HuS+fGMSphxrLnQ16V3lGo6ulPNvPz9938s/oghk1WNvcNc+WTX0RNYtsG2/AGveJ5JUYigRWi++huuL4URjwAZNQuoKJXEg+agvpcjcqSVaM5ppf7HA5M8+djyMzE4XFQkFZArjVX5SDnkMJa8A1AwKv6W4eL44QHHQCu3vtqTllwiur3EpJApH2W/g9wWwfCxsfyfOPzXPXWVam/1K+wFtwtmvzbV5NkMJB1wAGYCicu/pNjyYkMaAoJaMs6eONmZQA7hdy8agNlXU3keLcWphv2B7l51YZx14qe9bMjElghuvR8pbm8K7yW30ahO0RLV+I3OheSTPghNsYWOoXfP5fSa68FoLEvxQutxMN+P4FfNIFJ/dkmS00NaTvtNKZoxxG2I9hh3g6q30tIAoV1cNRNUDx1uwmthRNYS5TCKx90fMBbm9/CbIhtkC1pFNaBHFL6wSa4kfXr6X3k0QnP23Pt9Hp76R3pjWNUwrQ1vQOrr1VWYKSQtt4hbnzr75z59aqxx/uGx12bbcnm8OrDI1tphJkRfWCF6ApG+zK6GqBs18iekyGH6AUrqMzVCEiQH1t/ReuCBVgXLADg5oNuZtCfGC05klaMM+HTYcrPx/7Y2IfO3pFePu38lL1K9yLDnKHZvYUElFcFe/1A7yiA0cIrRiOWiopx5xxuB7YcW/yDirfw937PJihapG8sU+h/dTXdf/sbuSesxGAdP9gWHsh0epzkp+XHOzxhKq5GMGdCVrHekahqsdVPVmCE1qyiMcfL8tLHXbuseBnLipfFK7SUI2ZghejCe5J6wjOwypdBTscAA74BvaISUlGvA3IrYprxC3o89D39NP7OTkBpCl6bV6t2hHNLKAhPng+fPhiX233R/QWXvHYJG3tFn+k5Z/PH4EqMbSmGtHQy9lyOZBnf57XR3RipmJ3SCsPf+4m/0spit4Ms43M2RT0fTmBFgbgE5WpUtg6kWAudnyxSnmNas7cm5ulmI5etGD8gNBwYPysrTJ9IYIXoLBmQUx6pRmqx2ym543Zuu/RVsixZOgcnpJR5C2HJcTG9dOTrr2m/4kq8G+txuB3c/eXduEZcKgc4xxiM4HgDHG9q8vZdf/sbDUcdHflZVCKew56+EFb9Uu8oAJj3wx9Q/Z//jDveO9JLn7dvbizzS8+H7zwLu3xb70imZK0Zv59+W2WZZZy26DSqslOrSFDKcDkSYu+72vY09gPgL6tCAsrz0rnhpJ04Ydn49lQrHl/BTWtvinOEqUMsIRYmtsf3lCpxgMFioeDQiSv+CULMDrw05pf6RlvoWGvsfLjlbf740R85wnaEWpHNXQXatdIxWCz4HA6C/f0Ys7MpyyrDbDCLBHauCY3utaw7VO9IJtU70ktNbg11eXV6hxIfNQfpHcG0WGw2AHzO6J8bRoORq/e+Oo4RCdMmy+Bpg4Ur9I5EdT6HAyk9nWd/dxKSYeI5wt6RXnq9vZRklMQxutQiZmCFiR14KSw7M/Lj8BdfcP+t5/P4xsd1DEpIKaGQ8mUWI5+jESktDdP8+TjcDtJN6czPnK9igHNUYa1mywi3r0RsNBipzqkWCexcM9ABgeGEmIXxtbSw6YgVDLw5vgdqTV4Nz5zwDPuW76tDZDpo/ww+uFPvKKZkyMjANH++snd5AsFQkPaB9jhGJUyLJMEVTXDwlXpHorq8U79J+S03T5q8grI3G0QF4tkQCawwMVmGwW4I+ABwP/scO/77bV5vWaNrWEIK6fgcri+DhtUxvdzrcGCx25EMBhrdjdhybBgk8bE2a4W1MNQDw+pX8LTYlX122z541uTWiBZdc01472uM1cfV5GtsxN/cjCFjfKGVOaf+ZXj+UvAmfq2L6vvvp/T3v5/w/D8+/wdHPnkkvqAvjlEJ02IwKlvVUoy1tpbsQ6deVSJa6MyeeNITJrbxRbi5Fjq+AJRWOlZfCFeLqEQsqMTVCP4hyIytEqGv0YHVbgPA6XZiy7WpF9tcVrRE+TOk/n5iS2UFmEz4HM7IsYt2vYi/HPIX1e8lJLBID1j9iyN5J2mhc/VbV/P7dydOklJO4ehSaVfi91C1VJRHrUAcZsuxEZJDNHmiF3oSdLLxJXjuJ0kxSDITIZ8P97PP4u/omPJah9uBxWChLLMsDpGlJpHAChMLj4yP7oWLNHhv3ow/mOIN3YX46B2dhYlxGWH1gw9Q/POf4w162TK0RYxmqmXhEXDRe8pMrMoks5n8U0/FWrd1T2FNXo34u5trFhwOpz0AuZV6R4Kv0YExNxdT/vh2Kx9u+ZB+X78OUemkcJtWOgnOW1/PlhtuJOCKPtAmKhEnqKa34JP7wZxaKx58Didtl/+CoY8+mvLavUr34oJdL8BoMMYhstQkijgJE8u3ARL0bK1EDDC/O0hLf8vcaCsgaMvVCFklYMmM6eXm4q0zt+9/+338ITGwkgzm//pXY34e8g/xTMMzLCtexuKCxTpFJcRV9nxYcqzeUQDKEuJos68jgRHaBtpYWbtSh6h0Emmhl/grrfydnbjuuYesQw7BtNee485X5yi9xUUCm2BcDuX5MsWSN59DWbVgjfJZsr39y/dn//L9tQ4ppYkZWGFi5jRldHx0BtZUUoKcnsaC/gzcPrfOwQkpweWIeQnh8Bdf0P2PfxLsV2ZHLEYLmebYEmEhisfPhReu0OztgwMDyKFQ5Ofr37+eN1u1ad0jJKB1TykFgxJA+q67kHXIN8Ydb/I0ISPPrdUBlkzILtOsCrmawonCRK10MswZlGWWif31iSZFW+iEfw8t1dWTXucP+anvrRd7s2dJJLDC5AprIiOxkiRR++STnP9/b7KseJnOgQkpYfExsPOpMb108O236frzn5GMRp5reI6b1t6EPIuKxsJ2Brugda0mb+1+9lk27rEcf2sroDxozs+cT6M78ffdCSqQZXj2x/DxfXpHAkDxpZcy77zzxh2fs4VWzn0JjrtN7yimZCopQUpPj8x8RfOj3X7ECXUnxC8oYXKyrGwdSoC972rzNjowlZViyJi8OJXT7eSkZ0/ilaZX4hRZahJLiIXJ7Xk++IcjP0b2wQqCGva5KOaXehsbMZUqXxavt77O+p71XL78chWDm+MKamD9M5q8tbmiAlBGrC1VVQDYc+xiqd9cMeQCrzshHmJlnw9MpqhtLzLNmexdujdVOVU6RKajPP33JU+HZDBgsdkiRbiiObYmMZapC6O8Hsgo2FosLIX4Ghux2qf+TAt/z4lteLMjZmCFyS0+BnY6JfLj8Lp1vPjz07n8pZ/oF5OQGnxDyoNsjLOmPoczMqDicDvm3iyJ1gpqYNilUSsd5e9q2wdPe66SwIpZ9DkgUoFY/3+z7v89z4Zlu+Fr3Tzu3AEVB3DnEXeSbkqtYjNTavtE2T7gTfziVVa7nWDfxFuahvxDrO1Yy4AvtSreJq20XPjJF7Dn+BUPya7ib3dQcvVVU14XTmDDe7SF2IgEVphcwAttn8JgDwA+p5Pq/32KY9074kFTmJ2G1XCTXXlYmiFZlpXCK3Y7wVAQp9uJPUf/h+GUEp4dc6k/K2rKz8eYl4evcet723JtDAWG6BruUv1+QoKJVB/XfwbC19iIHAxiLhnfyisYCuoQUQLobYL3/0+Tf/tqK/vDjdgffWTC8+t61vG9Vd/j8+7P4xiVMBeZS0qmtUrR4XFQllk29wbGVCYSWGFyfc3wz4Og/iVg6xLivC2DdA936xmZkOxm0UIn2NtLyOfDUmOnbbANX8gnluOorWgx1B0GkqTJ21vs9jHFV46vPZ73vv0exRmx9QQWkoirEZAgT/8ZCJ9TWcYumc1jjofkEPs/vD93fn6nTpHpKDJ4lfh70rf/e9ueaKWTYD64Ex46PeaVV4nKu2kT3f+8c8KWTtsSK8bUIfbACpPLqwbJEKlIaLHZAChzKf8IizKKdAxOSGquRkjLg/TxvRenYiooYPEnHyMHg7R4vqYovUh8IahtXh2c+YRmb59/xhkQDER+FhWk55C9L1S2p5jT9I4Eb6MjsqR9Wx2DHQz4B8hPm/nnU9ILDyomQQIb6Oqi47rryT/1m2Tuu++484VphWSbs0UCmyha3octX2o2MKqXobVr6frTn8hdefyU1/54tx9jkkT6NVvi/4PC5EwWyKuKVCI2ZGQglRRT1tOFw+1gz9LxvdcEYVpcjbNaQiiZTEgmE7sU7cLqU1eLJe1akWVNHjZyjz1m3LF/fv5PCtMKOXnhyarfT0ggaTkwfye9o0AOBPA1N5MdpYVOuCL2nBwYs2Yr/bmTIIE1ZGTQ/+KLpC1eFDWBlSQpsr9eSACz/N5PVN5GB4aMDEzFU68g2rds/O+pMHNiCbEwtYLaMT3h0mtqqQ7kkG3J1jEoIenNohec68EH2fKHm8Yck1JsRDchPP49uHt8oqkGORDAu2kTwb6+yLHXml/jReeLmtxPSCBv3AzN7+kdBbLPx7wf/oDMAw4Yd27OttAJK6hRiuwlOENmJqb58yfsBQvK/nqRwCYIVyPkp96/qXBNjqmeQzYPbOatzW8xEhiJU2SpSySwwtQKa6GnMbJnofIff+fIZ97j6JqjdQ5MSGoHXga7nhHTSwdWv8bg+8oD8FVvXcVfP/mrmpEJYeYM6N6oyVv7mltoPPY4+tesiRwTMyVzgLcfVl8Lze/qHQmGjAyKLrqIzD3HryRyuB3kWfMoSCvQIbIEcPZzcPqDekcxLdYaO97GiT83ztnhHP78jT/HMSIhquFe5U8qzsA6GrHUTP1/15qWNVzwygUM+EVV7NkSS4iFqe1+Diw6KrKU0GCxAEolWDHrJcRst7NifqnP4SB9110BeKP1DQ6rPkyloIQxCmpgsAtGPMqyTxVZKivAZBpTidiea+e5xucY9A+KPbGpypU4FYj9WzqRzCZMBeOT1OXzlzM/c74OUSUI4+TFkRKJxWbH/eyzEz6TLMhfoENUwjjefqjaF0qW6h2JqkJeL8Gubix225TXOtwOsi3ZFKYVah9YilNlBlaSpCMlSdogSdImSZKuiHL+Z5IkrZck6XNJkl6VJKl6m3NBSZI+Hf3zrBrxCCor2QFqD4HRRu++lhbePe+bnHbLHgz5h3QOTkhK/Vug/XMI+mf80tDICP62Nix2O70jvfR5+0QLHa0U1ir/26v+rKhkNmOprByz9C+8XNPpcap+PyFBhPdVJsAywq6/3E7jscdFPXeU/SjO3/n8OEeUQDq+gEfOjNS/SGTWJYuxVFcTGoz+POIL+vhv43/5querOEcmjJFXBd97Qalun0IMViuLPv6IwnPOmfLacAViMfkze7NOYCVJMgJ3AEcBS4HTJUnafnjlE2APWZZ3Bh4Htt28NizL8q6jf6Yu3yXEX8AHXz8PnV8DIBmN5L35JeWbR2jyNOkcnJCU1j8D/zggpj1WvqYmkGWsNXaxT01rGrfTsNjt+JxjE9hsczau4cTfeyfEKPy7FOP+dzX5HE4sNePj8AV9dAx2zO3CcEE/fPUcdCZ+0pf/zW9if+JxjFnRV21IksSv3voVLzW9FOfIhLlCMpsxZGRMeZ3D7RAD7ipRYwZ2T2CTLMuNsiz7gIeBldteIMvya7Ish4fG3gMqVLivEDcyPHIGrHsSANP8+WC1UN4ji/1qQmxcjWDOhKyZ9/wMut2Yykqx1NREBlBsuTaVAxQAZZZst7MhR5uPbIvdhs/ZhBwMAlCTW8Pbp7/NARXji+oIKcLdCpnFSqVbnfkaGyO9zbe1vmc9hz9+OG9uflOHqBJEErXSmYrZYKYyp1I8r+jtf5fCvSfoHYXq3M8+S8d110854NXv66druEv0rFeJGglsOdCyzc+to8cmci7wwjY/p0mS9KEkSe9JknSCCvEIajNZIbcisndJMhiw2O1KL1iP+EIQYtDrUGb3YlhGk7nnnixYvZq0xYtJN6WzS9EulGWWaRCkgDULjr8dKpdr8va5x6+k/LbbIBQClJkSsbQqxR3zR7h4rd5REOjtJdjbi8U+/mEynOjYcmxxjiqBpOdDesGYDgSJrOm736Xr9r9MeN6eIwrE6W7LOgh49Y5CdQNrXmfgtdem/O5KN6Xz+HGPc4xdm8r+c01cqxBLknQmsAdw8zaHq2VZ3gP4NnCrJEm1E7z2/NFE98Ourq44RCuMkW8fMxKbVlNDZa8Rp9upX0xC8nI1QoFt1m9zpP1I7j/6fowG4+xjEqILhWBAm8/ctEULyT7kG0jmrQVj7lt/H5e/frkm9xMSgCRBep7eUeBzOAGiFl5xepyYDCbKsub4wFhBTdLMwAZ7+xj+8osJz9tz7TR7mvGHZl53QVBJeOA6xXgdDixRVnJsz2QwsahgESWZJXGIKvWpkcBuBiq3+bli9NgYkiQdBlwFHC/LcmQIRpblzaP/2wisAZZFu4ksy/+UZXkPWZb3KCoqUiFsYUa2+yKzLllCWn4hy4t21zEoISmFgtDrjPmLrPWSH0860i6o7LkfKfuVNSDLMgNvv83I+vWRY13DXbzS/ArBUFCTewo68g/DUz8E59t6R4KlsoLS664lfeedx51r8jRRmV2JyTDHGzWU7qJs9UgC1hp7ZFAiGnuunYAcoKW/ZcJrBA35BqG/XZWB60Qih0L4nE6sUfbSb+/N1jd5etPT2gc1R6iRwK4FFkiSZJckyQJ8CxhTTViSpGXAP1CS185tjudLkmQd/e95wH7AeoTEU1ADwy4Y7gNg3nnnsfx/azh16bf0jUtIPrIMpz8Eu5wew0tlBt96i2B/P4FQgIMeOYgHvnpAgyCFiHyb8uDhG1T9rSVJou3nl9L78CORY/YcO/6Qn7aBNtXvJ+istwk+ewg8+v/dmoqKyDv5ZEyF49tZNHma5vby4bBj/wTffljvKKbFYrPjb20l5I2+RPWQqkN4+ZSXRQEdvfQ6lf9NsRnYQGcn8vAwFpttymufrH+Su764S/ug5ohZDy/KshyQJOliYBVgBP4ty/I6SZJ+B3woy/KzKEuGs4DHRteIN49WHF4C/EOSpBBKMn2jLMsigU1EO58GC1eMK7zRN9JHmimNNFOaToEJScdoirmMfqCzk9DQENYaO+0D7bhGXGSYpq78J8xC+IGj16m01FKZpaYGX+PW1R3hitKN7kYqcyonepmQjBKoAvHQhx9izM/HWjt+19IPdvkBOWZ1+x4L2rLY7SDL+JqaSFu4cNz5bEs22Rb9C4fNWQYT7HgKFKv/HaKnoMuFaf78qHvpt+f0OEXBSRWpsj5GluXngee3O/brbf476tOqLMvvADupEYOgsewS5c8oORBg/eknc/f8TRz/i7+LqqHC9G1ZB30tShJrnNlHULhnqMVmixQQE18IGtu2lY4WCazdxsDrb0R+3rYX7EEcpPr9BB2F+wknwCxM+29+i8Vuo/Kvfx137kjbkTpElIBcjfD4uXDI1VB3qN7RTCpt8SL699iX79z1Pmulesry0rlsxSJOWLa1pugjXz+C1WTlhLoT9At0ripaBKek3uxj2tKlLFjz2pTXBUNBmj3N7F++fxyimhviWsRJSGKyDB/cCQ2rAZBMJkxbeqltF610hBn67GF49Dsgzfzjx+d0Aspoe6SFjljqpy2Ne8Fa7XaC3d0EPR4Acq257Fa8G+mmdE3uJ+jI1QhpuUqFWx3JwSD+5masUZb9dQx28Gnnp/iDotgPaXnQ9jF0fa13JFN6YSCDs+3f5AOpABnY3DfMlU9+wdOfbC3J8rzjeZ6qf0q/IOcy/4jeEeiqY6gDX8gnnldUJBJYYXokCd78I3zxROSQUonYEEkkBGFaeh2QXw2GmX/8GLKzydhrL0zFxTjdTnIsOeRZ89SPUdgqLRcOuwaqtRk5ttQoCfK2y4jvOeoeTl10qib3E3QU9EHRkpjaZ6nJ396O7PdH3bf2StMrnPXCWXh8nvgHlmjS85V//0lQifjmVRsY9gcxblP8bdgf5OZVGyI/23JtOD1OHaITePBUuOd4vaNQXfs117DlhhunvK7Z0wxAdU611iHNGXO8xJ4wI9u10rHW1FD26Yc8KWZghZlwxV5KP/eYY8g9RumhtsO8HciyZIm+ofGw/080e+uM5cuxP/kElih7EYUUc/xflNU8Oou00ImSwDo9TrIt2RSkFcQ3qEQkSUnTSqetb5hfrL2f+UMufnrQJWOOh9lybLhGXHh8HnIsYo9zXPU6oHIvvaNQ3dA772JdumTK6/Yp24c3T3uTDLOo2aEWMQMrTN92X2QWm520kSA97Yn/5SYkCFmeVQIrb/Pwe9KCk/jp7j9VKzJhMsO90PqRJm9tzM4mbelSDFZr5Nh/G//LIY8eQr+vX5N7CjpKgAGnyFaECRJYW45NDIyFJUkCW5aXjseSQUV/55hBkrK8rVsRwss3m9xi1VhcBbzgbk2Ive9qkv1+fK2tWKqnN6ual5aHxWjROKq5QySwwvQV2GGgI9JOI23HHfDvswvfqz1jTGIhCBMa6AT/oDKbP0Oy38/GPffCdd/9BEIBBnwDGgQoRPX+P+Bfhyh9PDXgeekl3M89F/k53ZhO13CX2J6QSnqb4O5jofk9vSMh55ijqfr3XRhFC52pVe0DpbsmxMz5ZC5bsYjO3BKyAiPkjn43pJuNXLZiUeSa6txqTJKJzqHOid5G0EJfM8ihmL73E5mvtRWCwWm10Lnz8zt5YuMTU14nTJ9IYIXpC7c+6FPW8mfsths7/+dhjj/wPDFaLUxPRiFc+B7scMKMX+prbSXU348hO4v63nr2eWgfXmueuvqfoIJIKx1tEsq+J56g565/R34OV5YW+9VSSE89ON9UHmR1ZiooIHPffcd9bw35h+gY7BCVzbe153lw6j0JMXM+mROWlbNixXIAKga6Kc9L54aTdhpThdiWY+ODMz/g0OrErqicclyJU31cTeGVHNGKwW3vsY2PsXbLWm0DmmPEHlhh+hYdDVduBmtW5FAwFKTetZHctDxKs0p1DE5ICkYTFE+9XySabb8swolNeXb5xC8Q1FMwuj/V1QjFi1V/e6vNxtAHa5FDISSDgcrsSgySAafbqfq9BJ2EH2ITYBam9+GHSdtxJ9J3HNsWymw0858V/6Eks2SCV85hspzwSezBh+1Bwx/ggSNLyTv5kHHnDZIBQwzV74VZyq2A/X4M8xboHYmqJJOJ9F13nXIGdjgwTPtgu1jZoTLxL1mYPnP6mOQVoOX75/HBd0/m6U1P6xOTkFzqX4GP7o7ppT6nMvtnsdlwup1ISFRlV6kYnDCh8OoLjfbCWWw25OFhAp3K0j6L0UJZZpmYgU0lLgeY0iF7vq5hhEZG6LjmdwysWTPunNlgZo/5e1CZXRn/wBLVcB/csgg++KfekUzJXFZG/plnYrFPPEjy6IZHuebda+IYlUDJUjj8d5CRWoXRsg44ANvDD2HMy5v0unAFYpHAqksksMLMvHELfPifyI+mrGyqeo04PKISsTANnz0Ib/05ppf6HA6MeXkY8/JwepyUZpaSZkpTOUAhqowCpSekhgksbJ1lBzim5hh2mreTJvcTdOBqVAZCdJ7F8zU3gyxHnTX5eMvHvNz0cvyDSmRpuUrdiyQo5CQZjcy/+ioydtttwmuaPE38t+G/hBJgKfuc0esE79ytWRHpWS+2JqhKJLDCzGx4AdZtbQRusdmY5wrS0uvULyYhebgaY94Hk77rruSd/i1gtFKo+DKIrxP+D5afq8lbRxLY5ubIsYuXXczZO5ytyf0EHWSXKAWBdOZrGl3JYbeNO/fYxse4ae1NcY4owUmSMvCQBAkshCvDbp7wvC3XxkhwhI7BjjhGNcfdfwo8fYHeUaiu4aij6br9L1Ne5/a5STelixVjKhN7YIWZKagZU0XSYrNhDMkMNDuQZVkUcxIm53LATrvH9NK8k06M/Pe3Fn2LLEvWJFcLqlt8tGZvbZo/nwXvvjNuKZYv6EOSJMwGs2b3FuLkuNv0jgDYpoVOtW3cOafbKZb5RVNQA1u+1DuKaem89VZ677ufRZ98jGQ0jjsf/vt1up2UZZXFObo5KBRUZmAXH6N3JKoKDQ7icziQtmn/NpFvLvwmpyw4RTwfq0zMwAozU2AHd4vS14utMyf5nUN0DXfpGJiQ8IZcMNIXWwudQIBgX1/k5xMXnMjh1YerF5swNfdm+OJxCPpVf2tJkjDl54/5gv+081OWP7CcDzs+VP1+wtzlczoxFRVhzMocc1yWZdFCZyIFNUoF8mBA70imZLHZkH0+/O3RZ1jDf79i21OceDZDyJ96FYibttbkmA6RvKpPJLDCzBTUAHKklY61xo7llOO54NCryLZk6xubkNjCy8xj+CLz1tezce998Lz8Mr0jvTT2NRIIJf7DVEpxvAFPnKtZKx3Pi6vYcsMNkZ9LM0sJySHRCzYVNL0Dty+D9s/0joT5v/kNtkceHne8Z6SHfn+/2JoQjf0AZftAYETvSKZkjbKfflvz0udRk5tayVRCCy89L9C/+riaIis5pkhgZVnmhy//kOcanpv0OmHmRAIrzExBjVLUYVCZbTXm5VF77R/Y5+Bvk25K1zk4IaGV7wZXNEPtN2b80siXRVUVrzS/wspnVrJlaIvKAQqTCg88aLQXbuSrr3Dd/wCyX5nhLc4oJsOUISoRp4KeTcrvTVqe3pFgsFgwl41fOhoptCJmYMerPQSO+sO4LgSJKFpBuG1JksQzJzzDGUvOiF9Qc1kkgU2tQQNvZCvC5Ptae729vN32Nm6vOw5RzS0igRVmpmK5koRU7xs5JAcCvPvZ/1jbIZo0C1NIy1XaMc3Qtglsk7sJq9FKaaboOxxXGiewFrsNgkF8ra2A8qBZnVMtesGmAlcjGMxKP0gdBfv76bj+ekbWrx93bteiXXn+pOdZVrxMh8iSQMAHIx69o5iScd48DJmZ+BxiiXBCqN4fjroZslNrv7G1ppa8b52GIW3yTgjh76/qnOo4RDW3iARWmJko6/jbr7oafnAF//nyP1FeIAijPrgT3o6tkIvP6cRUWoohPR2nx0lVTpVoSB9vmfPAkq1ZAhtt6Z8txyZmYFOBqxHyq8EwvqhOPPkcDnrvvQ9/x/j9kUaDkcrsSjLMGTpEluBkGW6yw5ob9Y5kSpIkUfLLX5JzzMRF5150vMjKp1cyHBiOY2RzVNFC2Ot8MKTW93XOkSso/e1vp7xOtNDRTmr9RgnxsfpaePGXkR8ttmry+gK0d4sRT2ESXzwGG1+K6aVepxOLTRnBdHpEpVBdRNppNGjy9luX/m3d83p0zdGcvvh0ZFnW5J5CnLgcCbGEcLJ9aw9//bDYpzYRSYK8qqRppZN38kmT9oIFaHQ30uxpnvQaQQWON6GvRe8oVCXLMsH+/mld6/A4MBvMlGWm1gx0IhAJrDBz3RuhflXkx/DDQLBlM34NKpQKKcLlgAJbTC8tOPNM8k8/HX/IT2t/q0hg9XLi3+G42zV5a2NeHqbSUkKDg5FjB1cezNk7nC0qOCa76n2h7jC9o1ASWIMBS8X4pcwPfPUAq5tXxz+oZFFQkzQJbNDtZvDdd5F9vqjnw7NhYnWHxmQZHjwV3vub3pGoKtjby8ble9L70ENTXptlzmKfsn0w6rz6JBWJPrDCzBXUwNfPKyX1jaZIAlvSE6Slv4WaPP1H2oUE4+2Hwc6YZ2FyjzsOAH/Qz58P/jMV2frupZuzSnbQ9O3rVr86JlkNySE6BjuwGq0Uphdqem9BQ0f9Qe8IAGV231xRgWSxjDkeCAVo7W/l0KpDdYosCRTUQP1LSl/PBH8YH3jzLdouvZSa557FumDBuPNV2UrhHbG/XmMDW8A/lBCrL9QU3l9tLi+f8trzdz5f63DmLDEDK8xcQY3S18ujFFuxVClfBqUuMaIpTGAWLXQCvb2MbNiA7PdjNpr5RtU3WJA//qFEiIO+Znj7dhjo1OTtt59pHQ4Ms+KJFTxZ/6Qm9xPiIOiHUEjvKABlZi68FWFbmwc2E5ADYp/aZApqIOgDT5vekUwpPKjunaAScYY5g5KMEvG8orXwjH0Mvd8T2XRb6AjaEgmsMHPhD6PRDydDZiaFV1zGmWffzP7l++sYmJCwBruVAkAxfJENvLYGx8oT8Le18VXPV7yz+R2xJ1IvfS3w8q+g4wtN3n7g9ddxnnkmwQFlGXGmOZPi9GLxoJnMvnwCri9VthDorOquf1H5t/HLGUULnWmo3hcO/11MVeTjLTxIMVErHYDDqg8TlWG1Fv43n4o9YM3mqO24ttXS38KKx1fw1ua34hPYHCOWEAszV1gLxTsoS4lGFZ/zPYp1DElIcLXfgCtjK+TgczrBZMJcXs4jH1zLay2v8fppr6sbnzA94Rn0Xm2SkdCIl+EPP8Lf3IRx6VJA2a8mEtgk5mqEgBdyEqOIiWQa/9jTOdSJhCQS2MkULVL+JAFjVhbGonmTJrBX7HlF/AKaq3odIBmVAmApxOd0YqmsjPpZsi2H20HbYBuZ5sw4RTa3iBlYYeZyyuDCd2DB4ZFDgd5e3vrvP3ngqwd0DExIaJIUtQ3TVLb9snB6nGLUXE/Z88GUrtlsmiVKK51wL1gx656kXA7IrQSTVdcwhr/4gtYfXYKvqWncuVMWnsLaM9eSl5YX/8CSSV9L0hRyslbb8Dmck14jyzIhOTGWt6ek3c6GMx4Fo1nvSFSVc8yxFH7vu1NeJ3rAaksksIIq3E8/Q+Glf+aB9/6udyhCInr+cnj9pphe6nM6I4lNk6dJzJLoKdJKR5uHWEu1MlLv3a4XrMfnoc/bp8k9BY25GmOuPq6mkfVf0f/yy0jm6A/TVqO+CXZSuO9EePk3ekcxLcWXXcr8X1094flPOz9l7wf35uMtH8cxqjkmrzIhqo+rLefIFeSdcsqU1zV5msix5JBvzY9DVHOPSGCF2LxyDdxzXOTH8J6TtLZe3F63XlEJiWrD89CzacYvk0MhfE1NWOx2BnwDdA93i9FMvRXUbC3KpTJDWhqmstIxM7AHVR7EzQfeLBKMZNWbOD1gJasV0/z5485d+eaVvOB4QYeokkxBTULsZZ6O9F12IW3JkgnPz0ufx1BgSGxP0NJH90DXBr2jUFVocJCRjRsJTdCiaVtOjxNbrk20gdOISGCF2AR90PJBpLpkeIaszCVHCmIIAqDsf3O3xvYQK8tU/PUv5J6wMvKgISqF6uz4v8D52u1Bztxrb0z5BZGfq3OqOdJ+JBnmDM3uKWgkFII9z4dFR+sdibKSo7oayTD2sWfQP8h/G//L5oHNOkWWRApqlAGJJFjOH+zro++pp/G3Ra+aXJpZisVgEa10tDLkgucugfqX9Y5EVUOffIrj+JUMf/rplNfuUrSLaM2lIVHESYhNgR0CIzDQATllSmN4o4HSXhmnx8nORTvrHaGQKHqbADmmBFYyGsk64AAAFgS9PHrso5RnT917TdBQRsHU18xC2Q3Xjzv2WddnGCUjO87bUdN7CyozGODgxCiW43M6o/YEFRWIZ6DADr4BGOyCrMQu2xjo6aH9yispu+kP5B5//LjzRoORqpwqMQOrlUgFYv1XX6hpJi10LtntEm2DmePEDKwQm/CH0uheOMlsxlxRSZlLon2gXcfAhIQzi15wI19/Tf+aNcjBIFajlSWFS8ix5KgcoDAj7lZ44RfQ8WXcbvnrt3/NnZ/fGbf7CSoZcsFgj+4zdk9/3MqXgwb+0mJkvxtX8/QnW2dbRaGVGdjuez+RmSsrwWCYtBKxPdcuVoxppTd1W+gYMjIwFRVNep0/6CcQCsQpqrlJJLBCbKJ8kZVe81tOuPYBfrDLD3QKSkhIcgiKlsQ0Etv3xJNs/tnPwWDgf43/45WmVzQIUJiRoB/e/zu0aVP8ZPiLL9l02OEMfbz1/W05opVOUvrw33BzDfiHdAvh6U82c+VTX/LjfS/gkUWHsrlvmCuf/CKSxDZ5mpCQqMpJrVYfmijbDU75NxTW6R3JlAwWC+by8kkT2MOrD+dou/7L21NSZODapmsYavM5nVjs9in3tb7S/ArLH1iOw50ce8aTkVhCLMQmpwIWrIDMraNQmXvvjeh2JYyz+GjlTwyUCsTVSJLE3evuZl76PA6rTr2qhkkltxIMJs1mYYx5ufhbW/E5HGTsthsA1bnVvLH5DQKhACaD+NpKGr0OyCoBi37fDDev2sCwPzjm2LA/yM2rNnDCMmU7wg6FO4giYdORWQg7nqx3FNNmsdnGVDTf3lH2o+IXzFzjaoTsMjCn6x2JqnxOJ+m77DLldU63k2AoSGlmaRyimpvEDKwQG6NJ6e+1aOsXQKCriw/uvpmrn/+J6K0mqMLX1ITVZiMkh0QLnURhNEFetWbVSM1lZWA2j5k5sefYCYQCtA1EL8giJCiX/hWI2/qGOcr5HreuuQ1rwDvmOMAFu17AQ8c+pFd4yWfzx+B8S+8opsVis+FzNk3aQ9rj8+DxeeIY1Rxx1E1w9nN6R6G6+b/+FflnnjHldU6Pk9LMUtJMaXGIam4SCawwO8Gta/y9DQ1k3/hvGta+TMdgh45BCQnlP0fDmhtn/DLZ58Pf2orFZqNzqJPhwLBIYBOFhr1gJaMRS1XVmAQ2XHlaLCNOMq7GmPa+q6ksL50a92bKBrvxGi1jjgsxePUaeOlXekcxLYXnfZ+6VS9OeN7j87DfQ/vxxMYn4hjVHJGWA/MSf6n5TGUdeCAZy5ZNeV24hY6gHZHACrF77Xplf9Po6Ga4KlupC1GaXlAEA9DyvtJ2aYZ8ra0QCmGx2bZWChVfCImhoAb8w5q9vTJz4oz8vCh/EfcedS+7l+yu2T0FlfmGoL9d9xnYy1YsonKwm81ZRTC6by3dbOSyFYvoGuri5GdP5q3NyTGjmBDCrXSSgLm4GFNR0YT7FXMsORSkFYhCTmrzDcIr10DHF3pHoipfczMDb7xByOud9DpZVtpJisJw2hIJrBC79HwYccNQDwCm4mJIS6PMJePwJMcXnKAxdwuEAjHNwlgqK6l57lmyDjyQlv4WQLS6SBhH/gF+9KFmb5914IFk7LV35OcMcwbLipeRaRa77JPK8X+BRUfqGsIJy8pZGuzDVTAfCSjPS+eGk3bihGXlONwONvZuxCCJR6Fpy7fDcK9SYTrBhbxeuv/v/xh87/0Jr7Hl2EShHbW5GuGtP0HPJr0jUVX/Sy/Rcv4PkH2TD8gH5ADn7ngu36j8Rpwim5tENQwhdttWIs6ch2QwYLXbqOjdRKMY0RRg6zLTWHrAms2Rvo0n557MIVWHkG/NVzM6IVYGbR/48087ddyx99rfY8vgFlbWrdT03oJKLBmw23f0joLQ8DDmni5Wnnk6515wzJhz4SXp9pzUavWhqfBnea9D857QsyWZzXT//R/kf/vbZO69V9RrqnOqeb319ThHluJStAes1+nEOG8exuzsSa8zG8yct/N5cYpq7hLDjkLsIgns1tFLi81GVZ9JFHESFL2xf5F5XnwR97PPAiBJEgVpBVOWrhfiZLAHHjkTNr6k2S3kYJDQNiPdzzU8x+0f367Z/QSVdW+C9s907wEbGhwk+/DDSdtp53HnnB4nacY0SjJLdIgsSYX7empUxE1NksGApbp60lY6tlwbrhGXKOSkpln0fk9k4a4IU+ke7qZrqGvS4mHC7IkEVohdXhUggashcqj455ey/IlVXL331frFJSSOzGJYeCRkz5/xS3sfeJDehx8B4A8f/IGXm15WOzohVtYs+Oq/sPkjTd4+0NvLhmW70ffoY5Fj9lw7ncOdDPoHNbmnoLL3/gb3HB/Zd6oX07x5VPzldrL232/cOafbSVVOlVhCPBOFdfC9VbDgcL0jmRaL3T5pAntA+QH8au9fYZSM8Qsq1bkaIWOeUsgphficTZFaL5O5+8u7OerJo5ARCayWxKe2EDuTFfb7MZRvLaxiqSjHXFKsY1BCQll6PHz7kZgeYpXRThu+oI8Hv36Qjb0bNQhQiInJCrkVmhVzMeblIW3XSie8/1kUXEkSrsaEWEIoB4MTnqvJreGA8gPiGE0KMFmham9Iy9U7kmmx2Gz4WlqQA4Go5xfkL+DURaeK/fVq6m/fOlOfIoL9/QS7u7FOI4F1esTAWDyIPbDC7Bx+zZgfg243X911K//O+pSLT/0jNXn6P8AIOgoFwTDzke3gwCCBri4sNhst/S2E5JCo6JdotGylI0nKg6dja4Ic/vt3up0sLVyqyX0FFfU6oHwPvaOg/aqr8W7ciP3J8a1SLl1+qQ4RpYDGNeBuhWVn6h3JlCw2G5IkEdiyBXN5edRrGvqUVWS1ebXxDC11fftRpRJxCjGkp2N/5mmMeXlTXtvkaWJB/gLtg5rjxPCAMDuhIPS1bP1ZljH+82Gsn25kU19qVaATZigUghur4Y1bZvxSX5MTAIutOtKSSRRaSTD52iWwMH7pX1VOFRKSmIFNBgEf9DUnxCyMz+nEEKXoitifNgufPwav/l7vKKYl95ijWfTpJxMmrwCXrL6EOz69I45RpThJUraZpBDJZCJt0SLMJZPvl/eH/LT2t4qOCXEgElhhdt79K9y6I4woBRCMeXkY8vModcmRCo/CHNXfDr5+pd3SDPlbWgFl9DzckknMwCaY+TtBXjUEJu+JFyuLzYa/rS3Sc89qtPLSKS/xg11+oMn9BBW5W0AOJcQS4vBWhO2taVnD/g/vz6ZeMdA6YwV2GOhIilk2yWJBMk6+CsiWaxMDY2rpdcKTP4At6/SORFUDb71N3+OPT3lda38rATkgnlfiQCSwwuzk25T/3WYvnNVmp9ptjsycCXPULFro5By5goUfvI+1pobhwDDlWeVkWVJrRDfp7XkenP+asidOA5n77UvRJT9C9m/duzY/c77YV5QMsufDmU9Cjb59EAO9vQT7+qImsE6PE7fXTVFGUfwDS3aRVjpOXcOYrs5bbsF1zz0Tnrfl2Gj2NIvuCWro/Bo+fxh8Q3pHoir3U0/R/fd/THldQVoB1+1/HcvnL49DVHObeBIQZmfbXrCjLDYbpS5RbGXOm0ULHQBjTg6SycSPlv2IF056QcXAhGSQsWwZ8y64AGPW1uIq77e/z+/f/b1Y/pnoLJlQdyjklOoahr9J+Q6K1vrC6XFSkFZArjU5ihEllEgrHe22EKhpaO2H9L+2ZsLztlwbI8EROgY74hdUqprFwHUim2glx/ZyrbkcX3s8ZVll2gc1x4kEVpid8Azsdr1gMwcC1KZV6BOTkBhcjWAwK9VqZ6jzj3+i76mnIz+L/q8JKOiHf34D3p96VDpWge5u/B1bHyodbgePbnyUzqFOze4pqMDxJtTr3/bKkJNL/llnkbZo0bhzTrdT7FOLVX5yJbAWm23yXrCjvwdi25MKeh1gzYGMAr0jUY0sy9NOYD/v+pyver7SPihBJLDCLFmzIbNozBdZwXfOYulnn/G7Q/+gY2CC7sr3gH1/NOMqxLIs0/vww4x88QVur5tzXjyHdza/o1GQQsyMZqUSaccXmt2i8cQT6br9L5Gfbbk2QDxoJrx3/gKv/FbvKLDW2Jl/1S8xl42fDXF6nJHfJ2GG0vPgp+tgn4v1jmRaLHYbgY4OQkPRl7UuKVjCHYfewQ6FO8Q5shTkalRm6FNo0DnY3U1ocHBaCeyfPvoT179/vfZBCSKBFVRw2G9h51MjPxrS05FMSocmsdRvDltyLBz2mxm/LOhyEervx2Kz4fQ4+WjLR/hCPg0CFGatoGbM6gu1WattohdsMup1JEQFYv+WTkK+8Z8dwVCQlbUrObD8QB2iShG5FTG1SNNDOPHwNTdHPZ9lyeLAigPFcnJVSFC0RO8gVBX+vZlOAtvkaRIDY3EiElhh9padCfatDwKyLOP49S/5xdX78PSmp/WLS9CPLCuzc6GZF8UIJywWuy1SCEws9UtQBTVjCripzWIfm8AWZxSTbkrH4dbunsIshYJKcZ98/RPYlvPPZ/OPLhl33Ggw8rM9fsah1YfqEFWK2PAivPxrvaOYFovdjrm8nKDHM+E1n3Z+yqtNr8YxqhR15uNwknbbSvSQsfvuLHzvXTKWT97XesA3QPdwt3heiRORwAqzN+KGpneV3n8o+xUDb75H3df9kRYowhwz2A1/3gE+mPkXWSSBtSmtDUySifLsiXv4CToqsINnM/iHNXl7i81G0OUi6HYDYJAM1OTWMOAf0OR+ggo8bRD06V7ERQ6F8DU1RZ018fg8DPlTq0pq3LV9rCwVDyT+6pi0RYuoe/UVMvfcc8JrHvr6IW5ae1McoxKSiTEvD4N18or74ZVBIoGND5HACrO3cRX858ixrXTsNtFKZy6bRSXC0OAgxrw8zGVlOD1OKrIrMBvMKgcoqKJsN1hyHHi1SSgjS/+ati4ZfvCYB/n9fr/X5H6CCiLVx/WdgQ10diKPjGCx28adu2fdPez30H74g/74B5YqCmqUXr990ZflJhtbjo32wXZGAiN6h5K8mt6Fu4+F7tTqrdxz179xPfjglNeFJ2zEEuL4EAmsMHsTtNIp7g7QJBLYuSn8EBvDMsKC73yHBe++g2Q0UphWKPqpJbIFh8Fp90OWNr0003femdLrr8dcvnUGXvSBTXCVe8NFH0CFvv9ut13Jsb0mTxOlWaWYjWJgLGZJVom489Zbaf3pTyc8b8u1ISPT3J8aCbkuOteB802wZOgdiar6nnySoXffnfK6A8oP4K4j7qIquyoOUQniSUCYvcgX2dhWOtbhAL1bmgmEAjoFJujG1QhIkD++/+J0hNvmXLX3Vfx6n+TYZzWnxbDXeTpMRUXknXQipsLCyLF13ev44cs/FIWcEpXJAkWLlF6wOtq6l378IJpooaOCKAPXiSzodjP0zsRJSKSVjhh0j53LAaZ0yJqvdySqkYNBfM3N0+4Bu2fpnmJgLE5EAivMXkaB0vdr2xlYu51gcQHfLDocb9CrY3CCLlwOyK0E0+R7RrYnB4M4zzwTz/PPaxSYoLq/7gkvXKbZ249s3MjQxx9HfpaRebvtbTb1pdYytZTxyf3wxeN6R0H6brtRfPnlmIqLxxwPySGaPE1U58Q2uCaMypwHaXkw3Kt3JNNitdkIut0EeqPHG/59EC26ZsHlgHwbGFIntfC3tYHfP60E9sn6J/m081PNYxIUJr0DEFKAJCn7nbbZA5t1wAHs+Mbb7KhjWIKOdvkW1B4y45f52zsY/vAjgitX8m7bu1zz7jXcfsjtLMxfqEGQgiosGZrOwnTecguB7m5qnnwS2PqgKWZgE9R7f4ecUtjpFF3DSFu4kLSF4z83Ooc6GQmOYM/Vv0pyUpMkuLwx+VrpOJ2Y8vPHnc8wZ/DU8U+JgoGz4WrUvXib2nwO5bl2qgRWlmVu/OBGTl5wMrsW76p9YIJIYAWVrLgeLFnjDvtDfkYCI2RbsnUIStBNXWztKcLL/qw2G43ujWwe2ExBWoGKgQmqK6iBzR9p9vYWm42hDz9ClmUkSSLbkk1hWqFY6peIZFl5iLXtp3ckDH34IRabDdO8eWOOpxnTuGLPK8TeejUkSfIK2yawTWQsWxb1mrr8ujhGlIIKa6Fi8lYzySbY14eUnj5lArtlaAvDgWGxNSGOUmeeX9CXbX8o23XMoY7f/Z5/fncv/vzRn/WJSdCHfwSa3wdv/4xfun0LnSxzFoVphZO/SNBXvh36WkCjiq4Wmw15aIhAZ2fkmC3XJmZgE9FgF/gHdZ+FkX0+ms4+B9f99487l5eWxxlLzhAzsGr4+nl44FSl92+CM5eXk7F8OYbMiQsMfbzlY27/+HZkWY5jZCnkWw/A/hMXykpGuccfz6KPP8JYMPlAeqSFjqhAHDcigRXUMdCl7HsackUO+Ts62LFJFntK5pqur+HfR0Djmhm/1OdwYMjMxDhvHk63k+qc6khBJyFBFdSAHNSsnYZ1tAiPz+GMHNulaBcK08XARsIJLyWPofq4mnytmyEYjDpr0tDXQLNHVJpVxWAX1K8Cd6vekUxJMpmovu9eco44YsJr1vWs484v7qTXmxz7eoX4kCRpyueQ8Iogsbc+fkQCK6ijewM8cS60fxo5ZLHZKOz20dzr1C0sQQezeIg15uWRuf/+SJJEk6dJjGYmg/LdYK8LwGjR5O23Lv3busf+p7v/lD8d/CdN7ifMQjiR0XkGNrIVIUoF4ps/vJlLX780zhGlqCSrRAxMOrsaXv4pVnfE4NOH4LZdoX+L3pGoqvVHl9D76KNTXuf0OEk3pVOcUTzltYI6RAIrqCNqK51qjIEQwc5OBv2DOgUmxF34YaZg5gls0Y8upuK2W5Flmf3L92ffsn1VDk5QXfESOOpGyKvU5O1NJSVU/fsusles0OT9BRXtdApc2RrTv301+ZqUBMRSPX42JLyyQ1BB+O95mwKOiaznrn9Tv8++yBO0/RKtdGaheyO4WyAjdVbGhEZG6H/lFQLd3VNe+7M9fsbTK58WfcrjSPx/WlBHdikYrWNb6YzOnJT1yGJEcy7pdSh94GbRB1KSJH61z684vvZ4FQMTNBPwwuDUX/KxkAwGMvfdd0zl0K6hLk585kSebxTtlhKONVv34j4+pxNjfj7GvLyxx4M+2gbaxMoOtWSXjfveT2SGrCyCfX0EOjqini/LKsNkMIltT7HodUBeFRhTpzasr6kZZBnrNFromA1myrLKtA9KiBAJrKAOg2G0lY4zcshqt2PcZUdOXHiyqCQ7l7gcMc3AeDdtov7gbzD4zjuMBEYIJkFhEGHUnYfAMxdr9vbDn39O7yNbl3HlWfNwuB2iF2yiefk38PG9ekdBwTlnU3bLzeOON3uakZFFpVC1GAxQtZeSxCaBbVvpRGM0GKnKrqJzqDPqeWESqdhCZ5uikpNeF/Rx7XvX8lnXZ9oHJUSkzlCJoL98+5iRWFNREQsfeQzRwXOOOfz3EPTO+GVeh4NARweG7BzuXX8vd35+J29+603STGkaBCmoKt8G3fWavX3/q6vpuesu8k46Eclsxmw0U5FdIWZKEs3H98AOJ8Ju39E1DKvdHnX/a/j3RSSwKjr7Ob0jmLZwIuJ1OMjcN/r2lIePfZh0U3oco0oBsgwuJ1TsqXckqgonsOaqybcctPa38siGR9i1eFd2KdolDpEJIGZgBTWtuA7OeGzc4c6hTjb1ipmSOaNid6ie+d7VraOd1TjdTnKtuSJ5TRbh1RcT7C2bLYvNBoEA/s2bI8dsOTaRwCaS4V7lj84ViEPDw/Q98QT+trZx53Yt3pVbD76VmrzUmikSpsdUXISUkYHPOfGWJpG8xiDohx1Wgv0AvSNRlSE9jfTdd8eYNfl2KIdH2QMuBsbiSySwgnoKayG3Ysyhzj/+ka+PPZqr3r5Kp6CEuBrohC+fHNNOabp8TifGefMwZmcrFYjFl0HyKKhRZt37xycNarDYlBFw7zZL/6pzqmn2NBOStUmahRkKF/DTuwKxw0H7VVcz/MWX487NS5/HodWHiiRFTRtfgr/tA/3R95UmEkmSKDjzTNJ33mnCa77q+YrLXr+M9oH2OEaW5EwWOP4vsHSl3pGoquA738H2wPhe0tsTLXT0IRJYQT0DnfDWrdC9dbZVMluY1z5Ea49DNAefC1o+gMe/O2Yv9HT5nE1YbNXIsozD4xCFVpJJlCrkaoq2d233kt05vPpwhgPDmtxTmKFZVB9X02T71l5peoV1PeviG1CqMxigc33SFHIq/tlPyT3uuAnPjwRHeNH5IvV92m2JSDn+Ec1W3ySDJk8ThWmFZFuy9Q5lThEJrKAebz+88htoeT9yyGK3Icky2d1DdA9rU6VUSCDhdgoxPMRmLN+D7MMOo9fbS7+vX4xmJpOSHeGIa5UqlBow5edjzM3F53BGjh1SdQg3HHADmebYq10LKvINQlqush9aR+FZekv1+N/F3737Ox7bMH6bizALGg9eaSHQ24scjF4kMPy9IzonzMDbt8IN5RDw6R2JaoJ9fWw65FA8L7445bUenwd7rr4Dd3ORKkWcJEk6ErgNMAL/kmX5xu3OW4F7gd2BHuA0WZado+euBM4FgsAlsiyvUiMmQQe5lSAZo7fScck4PU6KMop0Ck6IC1cjpOcrf2ao+Cc/AaBvpI+Ldr2I5fOXqxycoJmsItj3R5rewv7Uk5jmzRtzTJZl/CE/FqNF03sL07D72cofnfmcTkxlpRjSxu6fd3vd9Hp7xYOm2vKqxn3vJzL3f/9H26WXUvO//2KtrR13Pt+aT44lR/SCnQlXI6QXKEuJU4SvqQl/WxuSZeoK27d+41bRNUEHs56BlSTJCNwBHAUsBU6XJGnpdpedC/TKslwH/Bn4w+hrlwLfAnYAjgT+Nvp+QjIyWZQ9sNs0NQ83ki91gcOdPCO0QoxiLKUf8vmQ/X4A8tLy+OEuP2RxwWK1oxO05G6FjvH7DtViLitDsox9QDriiSP444d/1OyeQvLxNTVF7dsY/v4Re+tVZjQrSWySJLCWqkpg4lY6kiSJAnEzFWPrvEQ23RY6YUade1/PRWosId4T2CTLcqMsyz7gYWD7ndwrgXtG//tx4FBJkqTR4w/LsuyVZdkBbBp9PyFZFdSM+SIz5uSQe8rJHLb/d9i/fH8dAxPiwuWIKYHtX7WKr5fths/pZPPAZnqGezQITtDUf38KT/9Qs7cf/uJLOq69jtDQUORYQVqBeNBMFA+cCh/+R+8oqPy//2P+NdeMOx5eEiq2Jmhg0VEwb4HeUUxLeFB9ogQWYEnhEswGc5wiSgGuxpRLYL1OJxiNWCrKJ71ug2sDP1r9Ixr6GuITmBChxhLicqBlm59bgb0mukaW5YAkSW6gcPT4e9u9dvLfFiGxFdhh/TNjDpVdey1lOoUjxNnZz0EMVWF9DicEg5jKyvjDW5fS5GnimROemfJ1QgIpqIGmd5SegJKk+tv7N7fSe//95J1yMmmLldn56pxqPusUzeN15xuE+lVQqf+yf1NBARQUjDvu9DgxSSbKs8UjhuqOvEHvCKbNmJuLsaBg0gT26r2vjl9AyW7EA0PdulcfV5vP6cRcUT5u1c/2NvRuYE3LGn62+8/iE5gQkTRFnCRJOl+SpA8lSfqwq6tL73CEiRz2W/jZ1+MON7Z+wctNL8c/HiG+8qtjGon1OZ2Yy8sxWCyihU6yyreDbwAGtSnWFq0SsT3HTvtgOyOBEU3uKUxTuOq4zg+x3kYHXXfcgb+zc9y57+/0fR4+9mExs6YVWVb+JAGLzTamIJwwC3IIDr4SbAfqHYmq0pYsJefIo6a8zul2YpSMVGRXTHmtoC41EtjNQOU2P1eMHot6jSRJJiAXpZjTdF4LgCzL/5RleQ9ZlvcoKhKFgBJWWu64jfw9d9+N97BT+fWqS/GH/DoFJmhuy3p45y8w3Dvjl/qcTiw2G4FQgOb+ZtFCJxmFBy402gtnqVKqym6bwNpybcjINPc3a3JPYZoSpAfs8Cef0P2XvyKPjB/QyDRnsqhgkQ5RzQGON+HGatj8sd6RTEvBd84i7/RvTXh+y+AWznr+LFY3r45jVEkqPQ8OvgIqdtc7ElXNO/88in/6kymvc3qcVGRXiIExHaiRwK4FFkiSZJckyYJSlOnZ7a55FgiXJzwFWC0rTUGfBb4lSZJVkiQ7sAD4QIWYBL0MueD5y8H5VuSQuVxZslXsCtLa36pXZILWnG/CS1dDMDCjl8myrCSwdjttA20EQgExA5uMwsmLRgmsISMD0/z5Y2ZOdizckXN3PJcsc5Ym9xSmKfx3np8APWDNZsxlYzethOQQt398O+u6RQ9YTWTOA687aQo55Rx5JLnHHDPh+VxrLp91fcaG3g1xjCpJedphILVWRcqBAHJges8xYsWYfmadwMqyHAAuBlYBXwGPyrK8TpKk30mSdPzoZXcBhZIkbQJ+Blwx+tp1wKPAeuBF4CJZlkUt6mRmssIH/4CmdyOHwhUhS12yKE2fylyNYMlSHmZmwu+n8IIfkn3oIZGCPGIGNgnlVcMp/wG7dkvJLHYbQbc78nNlTiU/2f0nlGWJXfa6smRC1T7KbIyOfE4nlspKJNPY8h7tg+3c+cWdfOX6SqfIUly4929vcnQaCPl8jHz1FcG+vqjn00xplGaWiueV6VhzPfzfvnpHoaqhDz/k62W7MfTxJ1Nem5+Wzw6FO8QhKmF7qvSBlWX5eeD57Y79epv/HgG+OcFrrwOuUyMOIQFYMiFr/pgvMnNVFUgSZS5ZNAdPZeFKhDMs4CNZLMw77zwAFg1u4ff7/Z66vDotIhS0ZLLAjidpeouqO+8cl5wM+gdxe90iidXT8nOVPzoLb0XYXpNbVCDWlDkdcsqTZgbW53TiOPEkym65hdxjo8/EVudUi+eV6UjVFjp+P+bS+VNe+68j/qV9QEJUSVPESUgiBTVb90QBBqsVc1kZ1W6LaHmRymJsoePv7MTf0YEsy5RklnBC3QlkW7I1CFDQXMeXsOEFzd5+++QV4Merf8xlb1ym2T2F5CDLMv7OzqgJrMOjfB/Zc1PrQTuh5NvHfO8nMsvooPpklYhtuUovWDlJClPpJsbe74nM52xCSkvDVFKidyjCJEQCK6ivwD5uJLbw/PPZ89s/4ZLdLtEpKEFToRC4W2LaA+e6+x4ajlgBoRDvtb9Hozs5RvGFKNb+C565SLO39zY20nLxxYx8tXUpqJgp0VnAB3/aAT66Z+prNSRJEgvffYeiH1087pzT7STTnElhWqEOkc0RO54EC1foHcW0GNLSMJeWTprA7lK0C8tLljMcGI5fYMnGPwyezSmYwCorOSTD5CnSExuf4NTnTmXANxCnyIRtqbKEWBDGKKgBwxrlwWa0InH+aaeSr29UgpYMBriiGQLeGb/U53Riqa5CMhq56q2r2Lt0b67bX+wqSEoFdhjqgeE+TfZDSgYDA6+8Svahh5G2ZAmgJLBur5vekV7y08SnTNz1NYOnFYyT90uMB8lgQEpPH3e8Y7ADW44NSYP+xMKoBFhCPhMWm23SBPaYmmM4pmbiQk8C0Ds6cKhz8Ta1+ZxOrKO9xiezoXcDzf3NZJoz4xCVsD0xAyuo74Cfw8/Wj2mnE/J62fThq9z5wV8Z9A/qGJygGZMV0nJm/DJfUxMWm50h/xCdQ51in1oyC4/Ea1TMxVxeDibTuFY6gNieoJfwahud98H1v/IK7b/6FaEoLXRuP+R2sVctHkY8yqxcErDY7ficUy8RFkuIJ5FZBMf/Far21jsSVeWdcjI5R03dA7bJ00R1TrUYGNOJSGAF9UX5xzz0wVr8Z17My6v+jsOdHPtkhBmofwVe+AX4ZjY4IQeD+JqbsdhskWWgoiR9Eou00tHm37hkNmOpqBibwI7+voiKoTrpTYwesIPvf4Dnf88jWa3jzkmSRJZFtFrSVMcXcGMl1L+kdyTTkvfNUyj/859hggRVlmWOf/p4/vzRn+McWRLJLITdzoK8Sr0jUVXh979PzoojprzO6XaK5xUdiQRWUF/ABw+fAZ8+FDlksduA0VY6YqYk9TjWwIf/AdP45XuT8be1gd+PxWYTLXRSQbidhobVSLdf+leWVcYv9/olu5Xsptk9hUlE2mcV6RpGZN/adgOoTZ4mfvnmL2noa9Apsjkib3TlTJJUIk5bvJisA/afcJ+jJEmYDCZRk2EybZ8qhftSSKC3F/+Wziln3kcCI7QPtosEVkcigRXUZ7KA8y1o/SByyFxaimSxUNYrZkpSksuhJC9TFD3YnjE3l7KbbyJjr71wup1ISFRlV2kTo6A9SyZ8f7Wm++HSdtgBY15e5GeTwcTpi08XS8/1UrQYdvnWjNtnqU1JYMf/DmxwbeC5xufwh/w6RDWHpOVAxrykqUQsBwL0r36NkQ0bJ7zGlmMTBeIm8+o1mhbt04P76WfYdNBBE/YIDhsKDHGE7Qh2Lto5PoEJ44giToI2tmulIxmNWKqrqHG38b6YgU09MfaCM+bkkHvccQCcWngqy+cvJ82UpnZ0QjxV7K7p20erMts+0I7T42Sfsn00vbcQxR7f1TsCQj4f/s2bI58l2wqv7BADY3EQpQNBwpIkNv/4xxSc/R3SFl0a9RJbjo3Xml/DH/JjNpjjHGAScDVCWWqtfPE5nRjz8jDlT14QsCCtgFsOuiVOUQnRiBlYQRtRvsgsNhtlvdDa36pTUIImZFnZBxfDHrjhzz5j+Mt1ABSmF7LH/D3Ujk6It5YP4O3b43rLhzY8xEWvXkQwFIzrfec8WVa2jOgs2NODuaICS+34z6AmTxMlGSVkmDN0iGyOKaiBXqfeUUyLZDRirq7CO0Uv2IAcEM8s0QT90Neie/E2tYW3IkwlEApoH4wwKZHACtooqAF3q/IhFz50zjnU/fYGHjj6AR0DE1Q33AvW7JgS2K7bbqPjd79DlmXuWXcPG1wbNAhQiKvG1+HlX4FvSJO3D3o8OE4+hb4nn4ocs+XY8If8tA22aXJPYQLuFriuBD5/TNcwzKWl1L20itxjxrc9EYVW4mjnU2H/n+gdxbRN1Upnh8IdOG3RaWL2NZq+ZpCDuhdvU9t0E9jfvPMbTnn2FO0DEiYkElhBGyU7QPluSj/IURm7707JwUdgNBj1i0tQX0YBXLoRln9/xi/1ju5b6xnp4ZYPb+GjLR9pEKAQV+EReY1mYgzZ2XgbG/Fu+DpyLJygiP1qceZqBDkE2SV6RzIho8HIgvwFeocxN9QdFtP3gF6sNhv+pmbkYPSVG7V5tVy999VUZFfEObIkkCDVx9UUGhwksGXLtBJYp8dJrjVX+6CECYkEVtDGDifC91+BrK2VKUPDw7S8+BS3PHs563vW6xicoIkZFnEJjYwQaGvHYrNFWiuJCsQpINJKR5u9cJIkYbHZxiz9CxdwEgXi4iz8d5yv7zLCzltvZfNll0c9d+9R9/KLPX8R54jmqGAAOr+GgU69I5kWi82G7Pfjb2+f8JpAKEDvSG8co0oS5bvDWU/B/J30jkQ9BgNlf7iRrEO+MellsiyLlR0JQCSwQtyEhoYY+Mkv6Xzpf3zR9YXe4Qhq+eBOeOycCfvpTcTX1Awoo+CRFjriCyH5RWZgtatGarFVj1n6V5BWQLYlW7ToijeXA4xWyCnXNYyhDz9UWnIJ+hpxw9/2gi+f0DuSack69FBq/vsc5vnzJ7zmvJfO46drVqDqRgAA075JREFUfhrHqJJEej7UHqJsH0oRhvR0cleuJG3hwkmv6/X24vF5ROV7nYkEVtDOf46G1ddGfjQWFGDIzqayzygeNFNJ87tKP7gZzsCGExCLzUaTuwmr0cr8zIkfJIQkkZ6v/NGwmIvFZsPfuhnZpxQQkiSJ275xG9/b8Xua3VOIwtUI+dUzbp+lNp+zKWoLnVXOVZy76lz6RvriH9RclFEA1pykqURsys/HWleHZJq4IUdldqVY2RHNV/8Fx5t6R6GqkQ0bGf5i6smV8FYVsWJMX6KNjqCd4b4xTa7DS/9sbgfPiwQ2dbgaZ1yJ8OlPNvPX9/2k738BnidbKFr6NVU5VRgkMaaWEi76QOkJqZH0XXYh+7DDCA4OYrJYAFg+f7lm9xMmsPgY8B6kawjB/n6C3d1R962t71nPJ52fkG1JnVmihCZJydVKB+h78ikMmZnkrDgi6vnqHKVGQ7+vX/webWv176GwDuwH6B2Jalz/vovBD9ay4LXVk16XZ83jO0u/w6L8RXGKTIhGJLCCdgrs0F0/5pDFZqPknU1iRDOVuBphp29O+/KnP9nMlU9+wbAfmFcLAwE6PzmBK48TfRpTRlaxpm+fffDBZB988JhjLZ4W3tz8JicuOJF0U7qm9xdG7fptvSPA51RmQ6IlsE63k6rsKlE4MJ4KaqD9c72jmLbeBx/EmJs7YQIbnmVr8jSx47wd4xhZAguFlO0DCw7XOxJVhYtKTsWea+ey5ZfFISJhMmK6Q9BOgV1ZRhgKRQ5ZbNVkuYYxB2TRszEVDLmUfU8zqER486oNDPuDHNa0lp26GwAY9kv8Y3W3VlEK8db0Djz7I817hG5bPXS9az03fHCDqEQcL/4RpZWG3p/jcoiMPffEWlc37lSTp0nsU4u3fDv0NSkFnZLAVK107DnK6qJwoUEB6G+DoDelKhDLsozPMb0WOu0D7YwERrQPSpiUSGAF7eTblQ+5/q0V/vJOPpmap5/hmVP+J0bFU8GIG8p2g6LF035JW98wAN9f9xwHtX6CZOrDWvIM7UMi8UgZvU74+F6lT6hGGo87jo7fXhP5OVwATKzuiJO2T+DWnaDhNV3DSN95Z6rvvQerfew2hmAoSHN/M9W5IoGNq52+CafeB8ysqJ9eLDYb/rY2Ql5v1PMV2RVcsuwSlhQsiXNkCcyVei10gn19hDwerNNIYC945QJ+8YaobK43sYRY0E7pLrB0JYT8kUPm+fMnrfgnJJkCO5w/swfYsrx0PJ3d5PqG2JxVhCGtDUvBu+SF9tYoSCHutm2lU1iryS0MWdn4mrYOelTlKEvQRYG4OAnvc5zh/ne1ybKMFKWA3IB/gD3n78mOhWLZZ1yVLFX+JAmLzQayjL+5GeuC8f2CLUYL5+18XvwDS2QJ0j5LTT6HE4i+FWFb4YGxgyr13fsviBlYQUsVe8Cp90K+LXJIlmV6Hn6I6+/4Fk9sTI5S+4K6LluxiJoRF4CSwFqUpcM/OXBfPcMS1BR+sNGwmMv2S//STenMz5wvEth46XWAZIQ8ffeuN337DNp//Ztxx3Otufz98L9zhC363kZBI6EgbHoFtiRHr/dwwuJraZ3wGteIiy+7v5zw/Jyzy7fgorWQW6F3JKqxLlxI1d13k77rrpNe1zbQhj/kFy3/EoBIYAXtbbMXRpIkXHf8HyVvbeTTrk/1i0lQx/OXw0Onz+glJywr58eLrAC0ZRWRnd1LpjGX05dPfxmykOCyisGcuXWpmQYsNhuBzk5Cg4ORY7Ycm1hCHC+uRsirBKNZtxBkWca7YQPSaCXq7c8JepDg4TPg0wf0DmRa0hYvYuHaD8g+5BsTXnPn53fyvVXfIySHJrxmTjFZoWghpNA2MGNWJpl774UxN3fS6xwe5TtNtNDRn0hgBW3963B4YmxvRovNRlWfSRRbSQXtn4K3f8Yv21F2g9HIm38+g51sXhZptMxU0Ikkwbw68M38d2O6IjMn2ywj/v1+v+ffK/6t2T2Fbbgcuu+BC3R1ERoairrs74YPbuDb/9O/SvKcYzAoKzA0HLxSk2QyYcyevD2OLcfGcGCYzqHOOEWV4N6+DTa8qHcUqvKseomBt9+e8rrwAKkoDqc/kcAK2krLGfdFZrHZmNftEzMlqcDliGkPXNHFF1P38ktIZjPDgWHsuamzl0YYdd4aWHmHZm+ftnQJBWd/B0NmZuTY/Mz5ZJgzNLunsI0Dfg57X6hrCOEl5Ba7bdy5hr6GqHtjhThItl6wjz9O5623Tng+PNsmticAsgyv3wQNk/dKTTbdf/0rvQ88OOV1e5ftzZV7Xkm+NT8OUQmTEQmsoK2CGqUi6TbLuSw2G2n9Xnx9Ltxet36xCbPj7YfBzpgKOUgmE+ayMgAePe5RfrX3r9SOTtCbQduvF0tlJSVXXomleutI+JbBLfzpoz9R31s/ySsFVSw5Vvc+kOEENlrlUKfbKfap6SX8vR9KjiW3w599Rt9jj094PjzbJgbdgcFu8A3ovvpCTXIohK+paVotdBbmL+TbS74tBscSgEhgBW3l28HrUfqFjgqPlh8kLaJfwyWGgsZiLKUvh0J0/O73DH7wQeSYaKmUgprfg/tOAvdmzW4R8vnwb9m6rM8f8vOfL//DZ12faXZPAeUhtuld8A3pGoalooLclSsxlZaOOT7oH6RzuFMksHopsENgGAY69I5kWiw2G8GeHoIeT9TzJRklpJvSxbYnSJjq42ryt7Uj+3xYbFMvC3637V26h0XP+kQgElhBW9u20xiVue++LHz/Pf7wgyeoyE6dKnZzjsEIS46D4pm1TAhs2ULvgw/ia2zkjdY3+MlrP6FvpE+bGAX9BLzQ8Cr0bNLsFq0/vIDWiy+O/FyaWYrFYBEPmlprXAP/ORL69P3/c+a++1L2hxuRtpvtDy/1FIVWdLLkePjBm5BZpHck0xLZT79NVfNtSZLETQfexDcXfTN+QSWq3tTrARvZijDFDOyQf4jzXz6fp+qf0j4oYUoigRW0VbID7H0RpG/dL2BIS5uy0puQBEp2gNPuV6oRzsC2XxafdX3GmpY1ZJozJ32NkIQK4tFKpxqf0xmpOGs0GKnKqRJ71bQW6QNp0zWMYF9f1GrD6cZ0TlpwEovzRWVzXWQVQ+nOulaonompEliAgysPpiY3dZK2mPW3g2TQvX2WmqabwIYHRsXAWGIQCaygrbxKOPJ6pSLpNlz33se/rj6Bq966SqfAhFnbpj3STGwtvGLH6XZSnlWOOUkedIQZyCkHo2XriL0GLDYbof5+gr29kWOilU4cuByQXQbmdN1CkAMBNh5wIF233z7uXE1eDdfsew2VOZU6RCYA8OmDSj/YJGCurMSQmzumJdf2OgY7eK7hOXxBXxwjS0D7/xSubFVa6aSI/G+dRu2LL2AqmnzFQHhgVFQgTgwigRW05x+B/rF7YQbeepOF77fxlesrnYISZu2+E+DBb834ZV6HAyk9HVNxMU6PU4xmpiqDEfKqNZ6BtQFjZ05suTY8Po/o2aglV6PuSwj9bW3g92OpGJ+kur1u8fevtzduhk/u1zuKaTFYLCx8713yT5+4p/lHWz7il2/9kmZPcxwjS1CW1FoxJZlMWGy2KQszOT1OJCSqslNn9jmZiQRW0N4Dp8Cj3xlzyGKzkd85TLO7STxoJCuXA9LzZvyykKcfq92OjEyzp1kUWklllXuN2T6gtkgC63BGjl2464WsOXUNBkl8vWmm1wEFNl1DmKyFznkvncePV/84vgEJYxXUJFUrnamSl/D31JzfX//UBfDVc3pHoarOW29l4M03p7zO6XZSllVGmiktDlEJUzHpHYAwBxTYxzW9tthsmLwBMtwyHYMdlGWV6RScEBP/MHhaY2qhU3bjDcjBIB5fPwvzF7K4QOxTS1knaNcHFsBcVkbx5ZeTvsvOW48ZxHJ0zZ16L1izdQ1hon1rsizj9DjZrWS3+AclbJVvh5YPlBZ6SdByxP3ss/Q99jhV994TNZkNLxt1eLTbEpHwhvvgswehOHW+s0M+Hz3/+CfSBReQdcABk1574a4X0jXUFafIhKmIBFbQXr5d6Rfq7Y889IT79pW55MiolpBEekdHoWNcRigZjeQac3ngmAdUDEqYaySTicLvfXfMMX/Qz9VvX82BFQdyTM0xOkWW4qr21jsCfE4nhtxcjPljZ/g7hzoZDgyLlR16K6jZ2kIvs1DvaKYU7O9naO1aAp1dmEuKx53PsmRRlF40t2dgU7ACsb+5GWQ56kqO7VXnVIv9rwlErLEStBf+sOt1Rg5ZbDakjHQOzFpGliVLn7iE2MX4ReZrbqblBz9k+IsvNQhKSDhtn8Ade0Hrh5rdwt/ZydBHH0V+NhvNvNP2Dh9u0e6ec1rXBvjicd17wGYdcihFl/xo3GyZaKGTIOJQhVxN06lEXJ1TPbcLxEWqj6dOD9jpViB2e908tvExOgaTo7fxXCASWEF7Ub7ITKWlLProIy782f3sXLTzBC8UElZOGez1QyicWQLr3bSJgddfh1CQ2z6+je+v+r5GAQoJwZoDXV9Dd71mt3DdfQ/N3/0ecmjrXnpbjm1uz5RoacML8MS5EPLrGkbW/vtRcMYZ445HWl2IGVh91RwMlzVCxR56RzIt1mkksL/Z5zf86eA/xSegROQKD1ynYAJbPfnM6sbejfzu3d/R6E6OAZm5QCSwgvYKamHF9VCyY+SQJEmRkfMhv74j+UIMSneBo/4w4wI94WI7lupq1vesp9/fr0FwQsLIrVR6BmrcC1b2+Qi0t0eOzfmZEi31OiCjENL06+Ut+3wMr1tHaHh43Lkd5+3IhbteSHHG+GWgQhyZ05Wlw0mw/xWUQXXJYpk0gbXl2ijKmLzVSkoLBWDeopSqQhzocWEsmocxJ2fS6yIrO8TAWMIQCaygPWsW7HMRFNaOOex64AFWnXUEJz5zok6BCTHztEHAO+OX+ZxOjPn5GPPycLqd4ssg1ZksShIbh1Y63u1a6XQNdzHon7ivoxCjBGih43U4cJ58CgNr1ow7t7RwKRfscoGoQp0I3vs7rL1L7yimRTIYyDzwAIy5Ew/MdA93868v/jV3V3ccfAVc/IHeUaiq5BeXs+DVV6e8zul2YjVamZ85Pw5RCdMhPuGF+HBvhs0fjzkU2NJJxceb6fS0MRIY0SkwISb/ORqe+sGMX+ZzOrHYbIwERmgfbBf71OaCgpqte6Y1EG3v2oK8BSzIX0DvSK9m952zXA7d98BFVnJE2be2rmcdHp8nvgEJ0X39X/jsYb2jmLbKv/6VeT+c+HttwDfAbR/fxqedn8YvKEFzksUy5TVOj5OqnCoxMJZAxN+EEB+vXgOPnj3mkMVmwxAMMc8t09wvmoMnjaAf+ppjmoUx5uWRvssuNPc3IyOLGdi5oO5QKNOupYmpqAhDRgY+59ZZkYMqD+LJ45+kIrtCs/vOSQEvuFt1n4GN7Furqhp7POjj2//7Nvetv0+HqIRxNB68irfy7HJMkimynHRO8Q3BnYekVA/Y4MAALRdexOB77095bZOnSTyvJBjRRkeIj3w7fP6o8gBksgJbR89LR1vpLMxfqGOAwrT1NYMcjOkhtuIvtwPQ37uJw6sPZ1H+IrWjExLNvj/S9O0lSaL8ttuwVFVqeh8BMJjhJ5+D0aprGD6nE1NJCYbMsXvxWvpbCMkh0eoiURTYYbALRjyQNvkew0Qw8MYbtF/9K6rvuzdqUR+zwUxFdsXc3F/f64TNH8W0dShR+RxOBlavJu+kqbexPXD0AwwHxu+5F/QjZmCF+CioAWQl+RkV7rtV5mLu7ilJRuER9VksI6zLr+NPB/+JmrzU6ScnTEKWIRTU7O2zDth/3APnL974Bde9d51m95yTDAbIq4LsEl3DCG9F2F44sbDnpE6V1KQWaaGXHLOwhqwsAp2dkxdyyrHNzRnYFOwBO90WOgC51lyx/zXBiARWiI8orXSMeXmk7bIz+1YfyK7Fu+oTlzBzrti+yDwvvUTjCSfib2/HH9S3BYcQRz0NcGMVrHtKs1v4WjfT+9hjhHy+yDG3181nXZ9pds85qfF1ePs2CAZ0DaP45z9j3oUXjjvu8CifTWIGNkEU1IApHQa69I5kWqbTC9aWa6N9sJ2QHJrwmpQUfnZLtRY6BgPm7bYibO/L7i/5yyd/oW+kLy5xCdMjElghPsLJjmvrSKwkSdgfeYTjL/8/ls9frlNgwoxV7wtHXAfZMxuN9G6sx7thA8b8fM558Rx+tuZnGgUoJJTs+eD1jPm3r7bhTz6h41e/xt/SEjlmy1VmSmRZ1uy+c87X/4M3bgGDUdcwMpYvJ3OvPccdd7qdzEufR5YlS4eohHGKd4BftsGCw/SOZFqM+fkYcnLGVDTf3gW7XMBb33pr7hXzcTUqbfNm2DovkfmcTszl5RimKOK0tmMt//z8nxgMc+zvPMGJvw0hPjIK4dR7YfEx404NB4bZ4NogHjSTRckOsO/FM+7v53M6MZeVIVmtODwOCtIKNApQSCiWTMgu1bgSsTLjtu3MSXVONcOBYTqHOjW775zjaoR8m669Pf1bttD/6qsEBwbGnTtr6Vn8dp/fxj8oITqDQfmTJCRJwmKzTToDm2HOwGSYg+VjsuZDXXIMREyXlGYlfeedp7zO6XFSkFZAjiXx93HPJcnzySIkN0mCpSshb2yhFfezz7Lh4IM544mT6fWKlhdJofl96O+Y8cvC+9ZcIy76ff2iot9ckm/Xthds9fgENvz7JfbXq8jVqPsSwsF336X1oosJdI1flrqoYBEHVR6kQ1TChN78E7xwhd5RTFvOihVk7L7HhOd9QR/Xvnctq5tXxzGqBHDwL+Dkf+kdharKrruO8j/eMuV1omd9YhIJrBA/nV/Bl0+OOSSZzVi7PczvFQ+aSSEUgnuOg3f/OqOXybIcSWDDf89in9ocUlCj6RJiY04OxsLCMQlsbV4t+5fvj8U4dY8/YRqCAehrgoJaXcPwOZ1gNGKpGNsiadA/yIvOF+ke7tYnMCG67o3w1bN6RzFthed+j6KLL5rwvNlg5n+N/+PdtnfjGJWgJ6fHKXrWJyCRwArx89nD8OT5Y6qRbt9KR0hw/W0Q9M64gJPs9ZJ10EFk7LF7pIKj+EKYQxYdCcvOUKoRa8Ris+FzOCM/F2cU83+H/Z8oEKeW/naQQ7pXIfU5nFgqKpDM5jHH63vruez1y1jXvU6nyISo8u3g2Qz+5GlBIvt8YwrCbUuSJGw5trk14N5dD7csgvpX9I5ENUMff0LjSScxsmHD5Nf5hxgODIsZ2AQ0BxfyC7opsEPIr3yZ5SlV38JL/8p7DXOzNH2yiVQinNlDrCEtLbJUp6bzU85aehZlmWVqRyckqiXHKX80VHbjDRiyxhfvCYaCGHUuOpQS8irhqi1KEqsjn9OJxT5+GbMYGEtQkVY6TVC8WN9YpsG7aRONK0+g/I9/JOfIFVGvqc6t5uMtH8c5Mh25GmGgIyl6+U6Xd1M93vVfYYzynbGtDHMG73/7fQIhfSuvC+OJGVghfiKViLfuhTNkZGCaP5+6/vS5NaKZrGJMYOXA1g//XYt35fLll4ukYq4Z8cCIW7O3t1RWYsofWyHz2veu5YRnTtDsnnOOyQLmNN1uL4dC+JqaJuwBazKYKM8qj39gwsSifO8nMnNpKQSDU/aCbR9sZziQPLPKsxLj934i8zmbkCwWTKWlU14rSRJmo3nK64T4EgmsED/54V6wY/fC5RxzNAv3OIKzdzhbh6CEGXE1gtECOTN7SOy69VbqDzwIWZZp9jTjC0ZfniWkqBEP3FgJH92t2S38HR10/eWv+JqbI8dyrbm09LeIvsNq+OgeePk3+sYgSdiffJKCs84cd8rpcVKZXTk3K8QmsgK7sm86SWawDJmZmEpKJk1g7bl2SjNL585+a1cjWHOUbhIpwud0YqmuRpqiSvYTG5/gt+/8VnTJSEDik16In5xyMFrHjcSWXHYZJTqFJMzQbmdD1b4z7gPpdTox5uYQlIOsfGYl31n6HX66+081ClJIOGk5kF6gaSGn0MAA3XfcgcVuxzLamN6WYyMoB2kZaKEmN3VmD3Sx4QVwt8Dh1+gWgiRJWGuiV0F2up2iMFwiyiiAS5Jrue1UrXRW2FawwhZ9eXFKClcf17F9ltp8TifW2qkL0r3d9jYbXBuQUuj/9lQhElghfgwG+P4r41rpAPQN9vBp12csK92dXGuuDsEJ01JYq/yZIZ/DibXGzuaBzQRCAVEQYS4qqNF0GaG5qgokKWorHafbKRLY2XI1QtFCXUMY+ugjRr76mvzTTh1XxOmOw+4QM+2CKiw2G/2rVukdRuKo2gek1FqwmbbjDqTvvMuU1zV5msS++gSVWr+RQuIr3RnSx+5TG3zvPdr2PIjbH7iEz7s+1ykwYUqyDJ88MOMkRA4G8TU3Y7HZIpWm7bn69pIUdFBg13QG1mCxYC4vx+fYeo/qXGVGThSIm6VQEHoduu+B86xaRecf/wim8WPv5Vnl4kEzUb1xC9x9rN5RTFv2EYdT+P1zkYPBCa/57Tu/5daPbo1fUHo68FI44Gd6R6Gq8ptuouDMMya9JiSHaPY0iwH3BCUSWCG+Nn8Mr980pp2Gef58pGCQMpcsHjQT2cAWeOZC2PTqjF7mb2sDv19JYMOVQsUXwtxTUAOeVgh4NbuFpbp6zAxsjiWHs5aexaL8RZrdc07wtEHQp3sCG+4lvf1yvo29G7ln3T24vdoVCRNmwT8MTe9AksyQZ+23H4Xf/z6SceKtMq0DrXzQ8UEco9JJ0A+B1KpZIYemV0m9Y7CDkeCI2JqQoEQCK8RX61p47ToY7IocMpeXg8lEtdsiKhEnshgrEUpmMwXnfo/0nXfG6XGSZ80jLy1P/fiExLbwSDj65jF9oNVmsdnwb9kypuDG5csvZ7/y/TS755ww1A3ZpQmQwDZhsY1/mHy//X1u+fAWgrJ2v1vCLBTYQQ4qe6iTgCzL+NvbCXR1TXiNLUcZkE354j6O1+G6Emj9UO9IVNN7//1s3Hc/gh7PpNd5fB5sOTZq82a+bUrQnkhghfiKUlJfMpuxVFRQ40kTM7CJLMYE1jx/PiWXXYZ1wQJW1q7kF3v+QoPghIRXvhss/z5YMjS7RfGlP2fBG6+PmaELhoK0DbRpds85oWwZ/PxrsB+oWwiyz4e/tTVqC50mTxPZlmzyrfnjXyjoL8la6RAIsOmww3E98MCEl9hybPT7+nGNuOIYmA5cDqX3c26F3pGoxud0IgcCGLKzJ71uccFinjvxOXYv2T1OkQkzIRJYIb4maKVjsdkodcmRPZJCAuppAIMJcscX4ZqMf0snoaEhQOkBe2xN8uyFElQky9D5lbb7YNPTx7VFuG/9fax4YgUe3+Sj7UJi87e1QSiEdYIesPYcu6gUmqgm+N5PVOFBdZ9z4hVh4f3WKb9qzNUI5gzISp1eERNtRRCSi0hghfjKq1Kq2W03Ept7/HEUn3Ia/zj8HzoFJkzJ1Qh51WCcWfHy9iuvpOk7ZzMSGOHtzW+LfWpz2b8Og/f/rtnbBwcGabv6avrXrIkcC+9fanKn+IOmll68El7Qd+WExWZj0Ucfkn3EEePOOTwOUcApkWXPh7rDkqqP6FStdGpya9i1aFdkUnwJsatRmUFPoWTP63RG3Yqwvaveuorr3rsuDhEJsRAJrBBfJouyFKWveczhnKOPpu6HPxV7DRLZMX+Cbz0445f5nE4sdjsN7gZ++MoP+bAjdfbSCDMgSaOViLVbRmhIT8PzzLMMrV0bOSYqEaugcQ306j8AYMjMxJCePubYcGCYnuEeURgukUkSnPkE7HiS3pFMm8Vmw9fUNGHBn7KsMu47+r7UX14a7gGbIkIjIwTa2qNuRdjeR1s+Eit3EpjoAyvE3/mvw3ZFfGRZpn9zEy91rGEH+14sKVyiT2zCxDILlT8zEBoZwd/eTq6tOrI8XFT0m8MKamDLes3eXjIaMVdXjVn6V5lViVEy4nAnx/LFhBMKKUs/a76haxi9Dz9M0O1h3g/OH3M83ZTO+2e8T1DD4mCCSmQ5aWbyLHYb8vAwgc5OzPPn6x2Ofvb4HuSU6x2FamSvl4LvfpfMPfec9LqRwAhtA22srF0Zp8iEmRIzsEL8ZRTAdvvUAp2dbD7sKN6572Zeb31dp8CECQ33wpo/QHf9jF7ma24GWcZqt/P/7N13fFvV2cDx39X23k48Em87exEyIAkkjLD3LLRAC120lNJSoPRt6Vt4aQu0pbuFFiibll3CCAkjkEH2Trwz7DjeW9a87x/XcqJYku1YV1eSz/fz8SfJvUc+DySW7lnPU9tZi07SMTFxokpBCmEvpQDaalXPRHz81j+j3khOfE70n1VTS3cDOK2QpnEN2HdW0P2J788Gs95MrFG95GBCEHz2O/hlnjIhEgHiTj+d7EcfRRcf77fNIxsf4br/XhfCqDSw4Fsw5RKtowgafVIS4+75EbFz5wZsd7DrIDKyOJoQxsQAVgi9w5vgzduh79hZSENmJlJMDCVdsWKrXzhqKoeP/2/ESTg8AwlTfj61HbVkx2Vj0ptUCFCICKmF4HZAx2HVujDn52M/eBDZdWyQfPus27my9ErV+oxqJ5l9PNg8iVdOtKJ6BY9sfCT6y5lEOksi2Dqg64jWkQyLacIEki66EH2AAaxBZ2B/236cbmcIIwuh3lbl6ECETDoMh7OtDXdf35DtPDvGxNGE8CUGsELodR2Brc95l9KRJEz5+UxsN4pkK+GotUr5dYQPsZZJkxh3//2Y8vM50Hlg4DyiMEYVnwXXv6xqMhdTUTGm7GxcbW0D1y4ovIDTsk9Trc+oJsuQcwqkFWsWgqu7G2dTE6aC/EH3Pjn8CasOrhIZRcPdQCbiCCmlA1h37MC6c6ff+/mJ+Tjdzugt07XnDXh8BnRFz3/f0YcfpuqCC4ZsF2uMZX7WfHHkKYyJM7BC6B2fUj979sBlU34emVsODxQHFw8kYaS1WskenTyy7b+miRNJ/fKNADy46EFxTm2sS8pVvZ5g8uWXkXz5ZV7Xeh297G3dS1lKGfEm/ysqgg8Fi+G21ZqGYK9Rdn6YCwYnk6ntrBWrJJHg+FqwBYu1jWWYjvzsAYyZmUz4m+/M6Z7tpbWdtdF5NKa1GvRmSMjWOpKgsdfU+izFdaJFOYtYlLNI/YCEkyZWYIXQS8lXfj1hJtaUn09cUzfWvi5a+lpCH5fgX2u1Mng1jGz7b++mTUr9RqA0pVQk5xKg6iM4uD6kXe5u2c3N793Mzmb/qylC+HK1taFLTMRU6L0DRJaV2uFilSQCJOWCzghtkZNMzZSXh63Wf7yeiZOorV/fWqNkINZFx1BBlmXsNTWY8ofOquyWo2fbdLSKjn+VQmQxxytFsU/4IEtcvpy0h37Op1d/THpMukbBCT61Hxrx9mFZljn07dtpfuIJajtqea3iNbrsXSoFKESMd++BtX9QtYvDd36fpj/+aeDPngGOOF9/Ep66UPMasPFLllC6YT2mE1Zgm6xN9Dp7RaKVSKDTw8Jve+26Cnem/Dwch+uQ7Xaf91MsKVxadGl0rr7CsRqwUcLZ1IS7u3vQ+8iJZFnmzJfP5C/b/hKiyISTMaotxJIkpQIvA/lALXCNLMttJ7SZBfwFSARcwEOyLL/cf+9p4AzAk83nZlmWt40mJiFCpJeCw/sgvWXSJCyTJmkUkBDQV9+HEQ4+Xa2tuDs7MRcU8FH9Wh7+4mEW5ywmwZSgUpBCREgtHHEysJFy1Nfj6mgf+HNGTAaxhliRiXikZBmObIPx07SOxOeRkhZrC2mWNLGFOFKc879aRzAipvx8cLmwHz6MudD3QO7BRQ+GNqhQ8ZTPKlqmdSRBY6+pBcBUGHgA22xtps3WRpI5KQRRCSdrtCuw9wKrZFkuAVb1//lEvcBXZFmeCpwH/E6SpOTj7t8ty/Ks/q9to4xHiBQ3vQ1X/WPQZev27fzr7V/wVtVbGgQl+KXTgWVkb+b2amWLuKmgkJqOGuKN8WJlXVC2pLXVKIMjlZgLCgYeVkAZ/OQl5kXvVj+19DSBvVvzVZi6u35Ay1NPD7o+OW0yH1/7MQuyFoQ+KGHkZBm6G1X92Q8mz5nr48ty+dJp7wxBNCEmu+GyP8H0q7SOJGhME3IZd9+9WCYHPsrkqRlekDT0VmNBO6MdwF4KPNP/+2eAy05sIMtyuSzLFf2/rwcagYxR9itEOj8Jmg5/57voX3qHD2o/CHFAgl+N++CtO0acPdLWn3jF1F8DtiCpQCTmEpTBkKMXuo+q1oWpoABnQwOu7p6Ba/mJ+WIL8UiFQQkd2eWi68MPcTY1+W0j3lcixBdPwKMl0NOsdSTDYi4tJe+5Z4mdN89vm2d2P8PpL55Or6M3hJGFgN4A066MqC3fQzFmZ5N6000YUlMDthMD2Mgw2gHsOFmWPUW9GoBxgRpLkjQPMAFVx11+SJKkHZIk/VaSJPMo4xEiRd0WePZyaKnyumwqLCSnVRp4AxHCQMMO2PIMuBwjepm9phbJbMaYnUVNR434MBAUqcdlIVeJZ4vY8SsnX53+VX65+Jeq9RmVWk6ufFYwOerrke12nyV0frHuF/xu8+9CHpNwklL6k21FSCkdXUwMsXPnBqwFmx2vZOiNusmxlio4sA6iqHKAdefOgaSSgdR01hBjiGFcbMAhjaCxIQewkiR9KEnSLh9flx7fTlaqiPvdFyJJUhbwLHCLLA+k97oPmAScCqQCfjNFSJL0dUmSNkmStKkpwEysECFkGapWQ9N+r8umwgJSG60c7jqE3eU7cYIQYq3VgATJI8v0mXLDDeT++U9YXX0c7T0qBrCCYsJ8+MYaVWf2zSUlxM6fr2yD6zcpdRKzMmep1mdUShgPUy6FpAmahRCohM6aujU09DaEOiThZHkmQiIoE3HPhi9of/VVv/ejNhPx1mfhmYu1jiKo6u76AY2PPjpku1mZs7hp6k1iZ0eYGzKJkyzLZ/u7J0nSUUmSsmRZPtI/QG300y4ReAe4X5blgfoJx63e2iRJegr4YYA4/g78HWDu3LmRcYBC8G9gFcZ7JtZcUICxx0Z8j56DnQcpTinWIDjBS2u1UgLBaBnRy0y5OZhycwD49NpP0Uki6bkAmBMga4a6XRQUkPfM017X+px9rD64mtKUUvG+MlzFZylfGvIMYE8sodPr6OVIzxEKEsXEWMRInghIqidxC6bOFSvoev99kq+80uf9CQkTkJCiL0Fca7VS8lCn1zqSoHDbbDgOHybpkkuGbHte/nkhiEgYrdE+Ub4F3NT/+5uAN09sIEmSCXgd+Jcsy/854V5W/68SyvnZXaOMR4gUMSlKUqATZmJNBcpDSlGHhea+yDgnE/Vaqo5NOAyT226n7cUXsR88CCjlBkRGP2HA7tdhx79V70Y+LlmMW3Zzz5p7WH1oter9Rg2HVesIkCwxxMyZgz4lxeu6Z8AgdnZEEINZWc2PkC3EAKaCfFzt7Tjb2nzetxgsZMdnU9MZOYPyYWmJrhI69gMHQJaHLKHjcDto7G30+uwQwtNoB7C/BM6RJKkCOLv/z0iSNFeSpCf721wDLAFuliRpW//XrP57z0uStBPYCaQDUZqPXBhEkiClYNAHWcysmUx85hme+q7ILBk2ZLdS9mgEHAcO0PDz/8W6fTvv1b7H33f8XaXghIi0+RlY/6eh243CkZ//nNprrxv4c6wxlqy4LHG+frhkGR4rgw/+R9MwUq69hvwXnh+0nc/z91iYFD0P2WPCGT+C6VdrHcWwecrneHYC+PK16V9jef7yUIWkPlmOuhqwAyV0fJylP15VexVn/fssPjz4ofpBCaMyqjqwsiy3AIP2F8myvAm4tf/3zwHP+Xl99BSYEkZuwnzo6/C6pE9IIG6+/4x/gga+/tGIyx4cy0BcyAe1/6CirYKvz/i6GtEJkSi1EHb9Z+h2o6AzW7CVlyO73Ug6Za62IKmA6o7IWf3RlLVNeX9OGK91JD4Z9UampU1jYuJErUMRRmLOl7WOYEQ8W9ft1dXEzpnjs83VpZEzIB+W7kZw9ETZAFZ53zfn5wds55kYE7Wlw584lCZo54JfwxV/G3S5Z+1a3vrrj7j/s/s1CErwaYTJDAZmO/PzqemoIT8pP/gxCZErtVAZHPW2qtaFqbAAua8P55EjA9cKkgqo6agR28OGIwwyELu6uylfvJiOt98edO+cvHN48aIXMelNGkQmnDR7j1KFwNGndSTDYszKQjKZBiZlfbG77Oxv3R89pXRikuGr78OkC7WOJGiSLrmE3D//GV1cXMB21R3V6CSdmBiLAGIAK4SdXX97hsSnPuTNivc47ZereGNrndYhjV0VK+G5K6FrZDU77dXVGMaNQ441c6DzgDinJnjznKlWMRupJ2utrfpYH4VJhVidVo72qleDNmqEQQ1Ye00NrqZmdDExmsUgBFnVanhiKTTt1TqSYZH0eoo+eJ/Mu+7y22Zb4zauevsqtjdtD2FkKjKYYeICSMrROpKgMWZnk7Bs6ZDtajpqyInPwawXVT3DnRjACtpp3At/nAfVnwxcemNrHe91WkjvtGJ02zjSfZT7XtspBrFaqd8GlR8qmWNHwFZbg6mwgPruehxuh8gUKngbKKdRq1oXA1v/ao5tGV6ev5yVV60kMzZTtX6jhqd8Vkq+ZiH4y0DscrtY9soynt/7vBZhCaORon4d6GAzjh+PpPefjbcwWfn3GTXHE2rWwK7XtI4iaGRZpu3f/w64iu4hatZHDjGAFbRjSYbm/dBcPnDpkff3Uxubjl6G8W2gMzdidbh45P39/r+PoJ7WakjIBlPsiF428cknyX7oIY72HsWit4gPBMFbWgn8qAam+S5NEQz61FSSr77aK+tkkjmJ8XHjRUmn4Zg4H864R1mN0Yituhr0eky5uV7Xj/QcocnaRIxBrMxGHD8l9MJZ75atHPnpz5DtvmvTp1nSSDAmRE+CuM1Pwaqfax1F0Liam2n4n5/S89nnQ7a9bfptXFd23ZDtBO2NKomTIIxKwngwxHitwtS3W4lJUFZHsltlKpMacfWUUN+ufTmHMekkMxHqExLQJyRwKtlsuGGDCoEJEU1vgNhUVbuQJImsX/zvoOsv7nuReGM8FxddrGr/Ea9omfKlIXtNLabcXCST9zlXz0qXmBiLQKY4iB8XUSuwjrrDtL/yCqk3fQVzUdGg+5IkUZBcED0D2NZqSB383xmpjiWVHPr94rwCUQM2UohpaEE7Uv/2tONmYrOTY6iLSwcgqyEJZMPAdUEDrdUjrgFrq6ig8be/w9HYCIBO0okVL2Gwrc/Dx79UtQtZlnE2e9eT/m/Vf3mj8g1V+40KTeXgtGkaQsyMGSRePHiiwTNQEEcTIlRqoarn34PNlO85T+9/1bggMUoGsLIcfTVg+/MgmIcooXO05yg7mnbgcDlCEJUwWuKpUtBWWpHXAPbu5WUQG8fN59zHCxn34WifT4xRr1wXQsvlUOq/Zs8a0ct6t2yl5W9/A4eDB9c/yNO7nlYlPCHCHVwHG/+hahet//wnFYsW4+ruHrjmyUQsBGBtgz+dChsGZ4kPpbSvfZWM79w+6HpNRw0p5hSSLcmhD0oYvaU/hmXa1hceCc/KnSe7vi/XT7qen5/288jPcG5tA1tHdA1ga2qQLBYMWVkB231w4ANuWHED3Y7ugO2E8CC2EAvaKloK/SuuAJfNVrLePfL+fuR2KznJMdy9vGzguhBCeiPc8s6IX2avrh74sHh/zfucnXe2CsEJES+1AHoawdYN5nhVujBOVEoh2GtqiJk+HVAGsG9WvUmXvYsE08iSk40Znu2dGj7EynY7MqAzDS6TMy19GimWlNAHJQRHwRKtIxgRfXwchsxM7AFWYKemTw1hRCoKg+zjwWarrcGUnz9QD9yfmo4aks3J4r0lQogVWEFbp94KFz/udemy2Tl8cGYcL7rfxFLwIGdPTdIoOOFk2GprMOXl0W7voN3WLrb5Cb4NZCJWsZTOQCZi71I6gFiFDSQMHmJ71q9n/6zZWHfsGHTvqtKr+N6c72kQlRAU1jbY+zZ0N2kdybCZi4tx9/T4ve9wO/j08KdUtlWGMCoVZM+BO3dB/iKtIwmanEceIffx3w3ZTmQgjixiACtoT5aV7arHsVVUkPTWGmwtjdR21moT11i37k/w54Xg9J150R97TS2mwmPbNMUHguBTivrZSE0TJoBe73V2rSCpAL2kp6GnQbV+I57n70TrEjpuN8YTMhA73A56Hb0aRSUERWs1vHwjHP5C60iGbcKTT5D7h9/7vS8hcedHd/J29dshjEoFOh0kT1BtV4wW9ImJmPLyhmxX01FDfmK++gEJQSEGsIK2elrg4VzY/LTXZc+Zk+yWKKqtFmka90BPMxgGb+HzR3Y6cbW3Yy4QA1hhCKkFYIyFvg7VupBMJky5uV5n1yYmTmTjDRs5N/9c1fqNeC1VkJgz4vJZwWSrrkGXlIQ+xXs73+7m3cx/YT5r69dqFJkwap6V/QgqpTPU9lODzkBeYl7kP69sfho2P6N1FEHjqKuj8fHHsR+uC9iuw9ZBS1+LeF6JIOIMrKCt2NT+rHdVXpc92eImtEpiq59WWqohrXhEL5EMBko3rAeHA+nAfylOLiY7PlulAIWIZkmCH9cr2chVlPatb6JPPHYMQSfp0OnF3G1Ap9wMpcs1DcFeU4O5oADphH8fns+DCQkTtAhLCIaYFOUrgkrp2GpqOPrww2R85zvEzJjhs01BUgEVbRUhjizINj2lPJedcpPWkQSFdfduWv7yVxLOPhty/edSiTHE8M/l/xTPKxFEfIoL2pIkSCuEFu9zI4asLCSLhbKueDGA1UpLpZIleoQkSUIymbii5Apev/R1UUJH8E/lwStA8mWXkbBsqde11yte56ef/1T1viNW3kKYdoWmIdhqqn3WbazpqMGkM5EdJx40I1pKQUStwOpMJno+XUPf3n1+2xQkFXCo61DklmGRZeXvZIQT1+FsoIROfn7Adia9iVPHn0pOvEgYGinEk6WgvdQiaPVegZV0OkyFBZTos5iWPk2jwMawvk4lQ+wIB7Dtb7xB/b33IbtcKgUmRJXNT8MrX1G1C3dfH9adO3F1dQ1cO9R1iLer3sbhjtAHTTXZe6BylZJoRyOyLJN2y1dJvOD8QfeqO6rJS8pDr9NrEJkQNKmFETWA9UyqH58Q7kQFSQW4ZBcHuw6GMLIg6mkCW6fyTBYl7DU1GMaNQxcXF7DdF0e+4KODH4UoKiEYxABW0F5aMbQdGJTIqeCVV1j6t9e4dfqtGgU2hjmsMONayJk7opf1rltPz7p12HFy/qvn83ZVhCe0ENTVeQT2vAVOm2pd9O3eTe3V12DdsmXgWkFSAU7ZyaGuQ6r1G7GO7oHnroCD6zULQZIk0r56C/GLFw+6V9NRIzKbR4OlP4YbX9M6imGTdDpM+fnYavwPuhfnLObVS15lYuLEEEYWRJ6jXFG0AmurqfG5k+NEz+19jse3PD5kOyF8iDOwgvaK+rf3OW1K7dF+kkH55+nZjmM87p6gsoRxcMXfR/wyW00NpsICDnYe5HD3YQw68RYjBJBaCMjKBFZGqSpdmPpL6dhqaog/4wzguFI67TUDvxf6tWr/EOtobES2OzDmZA86A3vT1JsYHzdeo8iEoDmJ4ylaMxcWYN25y+/9JHMSSeYILvvXVQ+STjnWFSWcjY3ELz1zyHY1HTUUJ0fPwH0sECuwgvbyF8FZ/zMobXvf3r3s/eqXufj3p/BZ3WcaBTdGOfqU8zAjIMvyQOIVkYFYGJYQ1II1pKSgT0ryykScn5QPQE2nOF8/SEul8hCbPHTZCbW0vfACVcuXg2PwFu9ryq5hSe4SDaISgsraBuv/Co3+z5SGG8uMGRhzcpDdbr9t3q15N3J3Hk27Eu4/Csn5WkcSNMUfrWbcPfcEbONwOzjcdVg8r0QYMYAVwoO1fVBRc9nthrWbyG10RX5q+kjz1nfhL6eN6CWu5mbcXV2Y8o8NYPMStXsIFiJAqvq1YEFZhbUfVws2zhjH1LSpqvYZsVoqlcHrCMpnBZu9phZTbi6SyTuGxt5GajpqcMv+BxBChHDa4b17oOZTrSMZtrSbbybv6acCltR5veJ1ntv7XAijCjKDSakFGyUkSUJnsQRsc6jrEE7ZKQawESZ6/pUKke3xGfDxw16XPFnjSjpjRSbiUGutgvjMEb3E1d6OqbgIc0kxNZ01ZMdlE2OIUSlAISrEpkHWTK+jA2owFRRgq/V+D3npopfE+XpfWqo0395pr64e2Pp9vDcq3+CSNy6hz9mnQVRCUMVngjEuohI5DUdhcmHkTrL89/tKYr0o0bV6NfX3/Rh3T0/AdmLHWGQSB9SE8JBWPCgTsS4uDkNWFkWdTl4XW/1CR5aVVZhpV43oZeaSEor++18ASnbuITN2ZANgYQySJPiG+iswqTfeQNIlFyPL8qAzlcIJLv8ruJ2adS+7XNgPHCDOTwKnrLgsYo2xGkQmBJUkKTswVDw+EGyyw0HNVVeTdMklpH3tqz7bFCQWYHVaaextjKyz2m43bHsBouhnq/eLjXS++y5ZDz0YsN2ZuWfyzuXvRNbflyAGsEKYSC2Cg+sGXTYX5JN1pJya9hrx8Bkqva3Q1zGqJC5fm/61IAYkCKNjmTJl0LXP6j7jkY2P8MS5T4jJluON03ZrtePIEWS7HXOh7xqwYpUkiqQWQNN+raMYNsloxNXZSd9+/+d2C5OVnQPV7dWRNSDqqgdnn+a7L4LJXlODKT8/4JZvAL1OH7mZo8cwsYVYCA9pRdBxWEkedBzLjBkkZOZw24zbcMrarQqMKS2Vyq8j/CCrv+/HHPnpz3C6nTg1XMERIszmZ+D3s8Gl3r8Z2W6nc+VK+vaXD1wz6oxUd1SL8/XHa62GLf/StAasPjmZnN88RtzChV7XZVkWA9hok1qoZCAPkBQp3JgLCrwSwp3I8+/zcPfhEEUUJJ7P/SiqAauU0Mkfst0/dv6DVQdWqR+QEFRiACuEh7RilHIa3tuJMu+8kxnPvMwt027BqBNldEIiLh0WfR/GTRvRy3o3bcLd3cXGho3Me34eO5p2qBSgEFUkSRk4dar4wCdJ1H3/LjpXrBi45HnQFOfrj1OzRkng1tehWQj6+HgSL7gAY06O1/WjvUfpdfaKGrDRZNFdcE9NRCUNMhUUYK+uRvaTpT/NksZn133GNWXXhDiyUYqyGrBuux3H4cOYh6gBK8sy/9j5D9YdGbwDUAhvkfOuIUS3CfPhot9CXMagW7Is09DTQENPgwaBjUFpRXD2A5CUM2RTD7fNhqOubiADscPtIDs+W70YhejhKaXTUhW43ShIRiOmCRO8MhFnxGQQb4wXA9jjtVaB3gRJEzQLoXfLFqzbtw+6nmhK5PGlj7Mod5EGUQmqiEkGU5zWUYyIqbAAd08PzsYmn/clSYrMWrCyG1IKICFL60iCwtXSgikvD3NJScB2LX0tdDm6xM6OCCQGsEJ4SJ4Ac7+qrP4dx9XRQc3ll/PIA+fzzO5nNApujGk7ALauEb3EfkDZBmYqKKC6o5p4YzxpljSVAhSiimfGPxSldI7LRCxJEgVJBWIL8fFaqpSHWJ1esxCafvNbjv7yV4OuxxpjWTZxGTnxw59YE8Kcwwof/A9URs72zZjp00m86CJkHzWKPVYdXMXP1v4shFEFwbzb4HvbImo1PBBjVhZF764g8fzzA7arblfe/8XOjsgTHf9ShejQVA5HvGfedQkJ2A8cZGp7nFgpCZWXboD/+M6w6I+9Wvm7MRUWUNtRS0FSgUi4JQxP/DgwxR87g6USc0E+9toDyM5jZ22X5C6hLKVM1X4jSkuV5lsIbdXVmIoGl9DZ1LCJzUc3axCRoBq9Gb74O1St1jqSYYuZMYOcRx/BlOt/IuVA5wFeq3iNTntnCCMTToZnAtOTfEuIHGIAK4SPt74D7/3Y65Kk02EqyGdiq04MYENBlpVthCN8iNXFxRF32mmY+1dgxXYcYdgkCWZco3ryEFNBIbLDgaOubuDaN2d+k7tPvVvVfiOG262sgqdp9yDnbGvD1dqKuXDwv4W/7vgrj216TIOoBNXodMrPvcqTV8EmyzLuPv+1iAuTlJ+hiHlmcTnhL4tg+8taRxI0DQ8+RP299w3ZrtnaTIIxgXGx40IQlRBMooyOED7Sin3OxJoLi0hbf5j6njasTisxhhgNghsjuo6Ao3fEGYjjFy8ifvEi3LKb6yddT2lKqUoBClHpot+q3kXCWcuIPeVdjLm5XtdlWcYluzDoxvjHoSTBXXuVs3Aa8ZxRNhcPfv+paa9hQfaCUIckqC29GBp2aR3FiBy86WYkk4mJTz7h8/7xCeJmZswMZWgnp/0AHN0Jbv/boiNN78aNGMYPPSj9zuzv8PUZXxc7xiKQWIEVwkdqoTKAsnV7XTYXFWJp7sJsl6ntqNUmtrFioITOyFZgPdsydZKO22bcxhkTzgh2ZEK0c7tULaehT05WagLqj53vrOuuY+GLC3m35l3V+o0YkgRxaRA/OJFeqNiqlERephNWYLvsXTRaGwdWtoQoklYMbbXgipzBkyEjA1u1/6RzOfE5A2W6IoIn/0CUZCCWXS7sNTU+d3L4YtKbVI5IUIMYwArhw7Pqd0Iyl5jZszEtP4uHZv9EZLZV20nUgpNdLsrnzaf5b3+nqbeJZmuz3xIDguDT/nfhofHQvF/Vbtpff4OON98c+HNmbCY2py1yHjTVVPURfPxLcNo0CyHxggvIe+F5jNnemVA9fz9FydFTo1Lol1YMlkToipwqA+biIpz1R3D39Pi8b9AZmJw6GUekDMqjrAaso64O2W7H7OMs/fE6bB3cvup2NjZsDFFkQjCJAawQPgaykXrPbMYtWEDR439k+dzrIjM9fSTJXwwXPAqJw8/06aivx93biyEtlad2P8X5r56PW8NtiEIEShgPLrvqZ+E63niD1hdeGPizUWdkQuKEyDmrpqby9+Hz3ytldDSij48nds4cpBMyoXoyhRYlRccDtnCcGdfBPbVKJYII4dkhYKup9dvm+Quf555594QoolFqqQJz0qAqEJHK306OE9V01PDp4U+xOq2hCEsIMjGAFcJHWgl86RVlEOXDviM7WVcvik2rKr1ESac/glT6tkpl0GEqLBpI4KTXsAyHEIE8M//NFap2Yy4qxF5V7bVDoCCxQAxgoT95W6GylVgjLf/4J71btw66fl7Bebx00UtiB040isCyLZ4z2vaqyEo+5VdSLky+SNOf/WDSWSzELlww5ApsVbsy0BVHEyJT5L1zCNHLaIHS5T5nAWuv/xLVd36H/9vwfxoENoZUfQTth0b0koHEK0WFVLdXi3T0wshZEpVyOi3+z5UFg6moCHd3N87GxoFrhcmFHOw8iCOKEpiclJZKTbcQunt6aHzkEXrXrx90L8YQw9S0qWJiLFq98wNYEzkZpk0TJ5J269cwFfk/M7q9aTs3rrgxMo4nLLoTLvuz1lEETdzCheQ99RT6pMA79qo6qrDoLWJiLEKJAawQXg5vhl2vDbpsSE8ns9HOoa5D2F12DQIbA1xOeP5q2PjkiF5mq6pGn5FOX6yBIz1HxDY/4eSklahfC7bIs3JybKB8WvZp3DLtlrH9vuJyQNsBTZO4eLZj+tr298SOJ0QN2GjWsBMqI6cWrGQ0kvnDHxIzbarfNkadke1N2wdW+cKWLCtfUUR2uYbVrrpd2TGmk8RQKBKJvzUhvGx5Blb8cNBlU1EhsUc7kRxODnQe0CCwMaDjkJJGf4QPsXELF5J2000D2zDFdhzhpMy6HqZdoWoXngGso75+4Nqp40/ljjl3EGeMU7XvsNZZD3rjiMtnBZO9P6vridv+eh29/H7r78UANpqlFUdcLVh3by995eV+7+cn5gPHzm+Hrab98Ms8qFipdSRBIcsyFYsW0/THPw3ZNs4Yx4yMGSGISlDDGC98J4SdtGLobQFrG8SkDFw2FxUhud1ktemp6qiiJKVEwyCjlGf75ggfYpMuvggAqa+VB09/kJmZEVD3Tgg/s29UvQt9ejplmzehi/MerHbbu+l19pIZm6l6DGEpJQ9+fATk4a1cqMFWVQ0GA6aJE72ueybGxM6OKJZWBNueB1sXmBO0jmZYmp94gpa/P0HZ1i3oTIMTn8UaY8mKywr/LcQtlWDrgNhUrSMJCmdjE662NvTJyUO2fezMyNm2LgwmVmCF8OIZPLV4v+l7Vk5yW6Twn9GMVCdRA9bd14fjyBFkWSbVksqlxZeSHhMdmQyFEJNlpZRGX6dqXUiSNGjwCnD121fzyMZHVOs3Iuh0yiqsRuwHD2CaOBHphMFAVUd/ohVxtj56pfVPSKt8Bj6YzIVF4HJhr63126YouSj8txB7qj5ESQkdfzs5hOgjBrBCePG8iZ5QSsdUUEDqV7/Kdy56kBsm36BBYGNAaxWYEiAuY9gvsW7dSuXSZfRu2MAXR76gsi2ytoEJYaSlEh4rg/0rVO2m8/0PqLv7R17XipKLqGwfw/921/0Z3r9f0xByHnuMvOefG3S9qr0Kg87AhITIKbMijFBGGYybDo7IKWcykIm42v+E+rzx8yhIKghVSCenpRJi0yEmWetIgsJWpfx9DFVCZ0X1Cq5++2qarc2hCEtQgdhCLISX1AJAGjQTq4uJYdyP7macNlGNDad9FyZfMqJU+rZKT721Qh747GampE3h0TMeVStCIZol54GkV/0snKOujs6332bcj+/DkKIcUyhMLuTz+s9xup0YdGPwY7H8PbD3aBqCpNMN/H0c70j3EfIT88fm38tYkVEG3/pM6yhGxFRQAJI0UHPUl1um3RLCiE5SS7WmyduCzV5dhS4+HkNm4In4fW37qGqvItmcHJrAhKATnwhCeDGY4fYNkDR4tt1ttVKxby2rdeXcOv1WjDrttrtFpeSJytcI2Kqr0CUk4ExJ4HDXYS4qvEil4ISoZzApZzHVrgV73MqJ4ZRTAChOLsbpdnKo61D4r5iooaUK8hdp1r390CGa//pX0r761YHjIh6/WvIrehzaDq4F4UQ6iwVjTo5XRnN/ZFlGCtcaqyXngCl6EtjFzp2LPi1tyP/fNe015CXmiYmxCCa2EAvhJ6MMTLGDLjf9/g84v3Inf9nyJw51jaxWqTAEpw2+eGLEZ5DsVdWYi4o40HUAGVmcUxNGJ61E/Vqw/VvLjl858SQICvvzamqw90LnYU0zEPft2UvHq6/htvYNuidJEvGmeA2iEkLq/fvhWXWzkAfbuB/fR+pNN/m9b3fZOfc/5/KPXf8IYVQjtOhOmHeb1lEETeIFF5Bx++1DtqvqqKIoOTrO/Y5VYgArhJ9DX8DKnw6qTWYuLkLncJLZEQGp6SNNW61SvqhuZKUqbNXVmIoKB/4+RKZQYVQ85TTcbtW6MGZnIcXEeK2cFCYX8pP5P2Fy2mTV+g1bbUqW37AooVPovfpd01HDvWvuFe/3Y4HLrnz2R1BN0oRly4iZ6T/rvkmvJCQL2/P1DquS+TlKuO12HA0NyEP8G+pz9lHXXSeeVyKcGMAK4adhB3z+uFKb8DimQmV1L7dZHpsrJWrynDscQSZCWZYZd++9JF95JVUdVeglPXmJeSoFKIwJ066Ei36rajkXSacjZtZM4NgWsxhDDNdOupac+BzV+g1bti5ILTyWCVaLEKqqMWZno4v13nmzp2UP71S/g0vD8j5CiKSVgL0Luo9qHcmwuTo76Vq1Cmdbm982hcmF4TsBs38FPJwLR/doHUlQ9O3eTeWZS+n++OOA7XqdvSzPWy5K/kU4sflbCD8DKfUrIOnYA6XnbNSUrsSB0gpCkAyU0Bn+FmBJkki66EIAbujLZ1HOooEZZ0E4KbmnKF8qy3vqqUHX6rvrqe2s5bTs01TvP6xMXAB3bNU0BFtVFaaiwZNnVe1iYmzMGCihVwkJ47WNZZjs1dUcvv075P75TyQsW+azTVFSEZsaNuFyu9Dr9CGOcAjNFYDUnzwz8nkyQpsLAz/HpFpS+fUZvw5FSIKKxAqsEH7S+wewJyRz0ScmYsjIoKjdwqFOcQY2qJorlPI5MYOzgPpjq6mhd8tWZJeLVEsqszNnqxigMCa43co29ubQb7l7cd+LfHfVd3G5xWpfKMmyDLKMuXTwCnB1RzUTEiaIibGxwPO5r3IW8mDyTLoEykRcnFyMzWWjvrvebxvNNFdA8gQwxmgdSVDYqqqRTCaMubkB29ld9hBFJKhJDGCF8JOQBaZ4nx9k437yE8747kM8f+HzGgQWxZorRryFsP3lVzh4yy04XA6e3Pmk2NYtjJ4kwdMXwcYnVe3GunMX1VdcQd+eY1vnCpMKsbvtHO4+rGrfYeflG+HDBzTrXpIkCt94ncwf/nDQvap2kWhlzEjMhbILIC5T60iGTZ+QgCEzE3ul/8++6enTubbsWnS6MHzcbhn55344s1dVYcrPR9IHXum+d8293LDihhBFJahFbCEWwo8kKduJOgfPWCYuP1eDgMaAG1+FvvYRvcRWXYWpoIBDvXU8vuVxxseNFw+bwuh4fvZVXoXRxcVi27OXvvJyLFOmAAz8261qrxo7W1ZlGao/DYtBw4llL9yymxhDDGWpZRpFJISUTgfXv6h1FCNmKirEVu3/jGtxSjE/WfCTEEY0TLKs7HSZEz1HJmzV1VimTR2yXVV7FfmJ+eoHJKhKDGCF8HTLez5L6bg6Oji6/hOe0q/nvOlXcso49c/LjQnmeOVrBOxV1cTMmsXu/pVXkdFPCIq0EqhX90ymacIEMBqxVx178PQMYKs7qlmG7/NsUaenCWwdkF6qWQjtr75K57vvkfunP6Izmweu6yQdr1z8imZxCRpx2pWa0BHCXFRM+2uvBaz16nQ7abe1kx6THuLoAnA74Zyfw7hpWkcSNBnf+x6G9LSAbRwuBwc7D3LWxLNCFJWgljDc0yAI+By8AvTt3UfH9+5h92dvsrVR28QjUaNpP6z8GXTUDfsl7t5eHPX1mIoKqeqoQkIiPylfvRiFsSOtGNoPKLWJVSIZjZjyJnqdXYszxjE+bvzY2grfXK78ml6sWQi9W7fSt2eP1+BVGKPW/AYezgGXQ+tIhi315pso+M+/A7a5Y/UdfPvDb4coomHSG5X6r3kLtY4kaJIuupC4BQsCtjnYdRCn7KQgKToSV41lYgArhKfGvfDvWwYlczEXKdnlJncljK0HTTUd+gI+/x04+4b9EltNjZJ4pbCI6vZqsuOziTFERyIIQWNpxSC7ldrEKjIXFXvVggV4ZMkj3DH7DlX7DSueRHkanoOzV1UPZJg/3r92/4uvvf81kVRrLIkfp9SDbT+odSTDZsrNxVxY6Hf1FSA/KZ/qjurw+rfcVqtMXkdQ3d1A7IcPY92+HdnpDNjO89wojjtFPjGAFcKTywG7X4OjO70u69PT0SUlUdoRKwawwdJSAXoTJA//3J+5sJC8554ldv48DnQeEB8GQvAUnglfeQuSAmeSHK24BfOxTJvmVfR+VuYssuKzVO03rMSkQOFSSJqgSfeyLGOrrsZUNLjsxY7mHRzpORJ+pUcE9URgJmLZ5aL1+efpWb/Bb5uwzES87s/wRPQcleh47TVqr/8SstsdsN3ExIncPPVmcQY2CogzsEJ48tSEO2EFVpIkzIWF5DTVU9NRg1t2o5PEPMyoNFdCaiHoh/92oIuJIXbuXACev/B5uu3dakUnjDUJ45QvlaVcfz0p11/vde1oz1E+PPghy/OXh9d5NbVMvUz50oiruRl3RwfmQt81YMW5+jEmrX8re3MFlC7XNpZhkvR6mv/wRxLOOYe4BfN9tvFM8Fa2VzIhUZvJokGay5X/3wFWjiOJraoa44RcdKbA56cnpU5iUuqkEEUlqEk8+QvhyRSnpNVvqRh8q6iQpIZuMmIzaOtr0yC4KNNcfmzme5g6V6yge81nABh1RlIsw68fKwhDqvgQKlaGpCvZdWxbX0NvA7/84pfsbt4dkr41N8Rqherd9/QQO28elimTva473U5qO2spTB68MitEsdhUZVdABK3AApiKiwJmIi5MUv4dV3WE0a6xlkpNk7cFm726yudE2ImqO6rpG8FxKSF8iQGsEL7Si48lGTn+8q23Uvr8S7xz+TukxQTOOCcMwe1WyueM8IOs6Y9/ou3ll9jauJWH1j9Ea1+rOvEJY9Oax5SELiqSHQ7KFy+m+c9/GbjmedCsbI+sB+iT4rQpCXM2/E2zEEz5+eT965mB3Rweh7oO4XQ7xdGEsej070HRUq2jGBFzYRH2ykqv4wjHSzAlcO+8e1mYHSYJk+w90HFoxBPX4Up2OLDVHsBcHPj9wuV2cfVbV/OnbX8KUWSCmsQAVghf42eAcXA2YlN+Pubi4oBJE4Rh0unghxVw5n3DfonscGA/eBBzYRGbj27mpf0vYdaLDKJCEIWgFqxkNKKLicVWfWxVJMGUQGZsJtUd/ldTokZrNTh6ISZVsxD8PfA73U4W5SyiLEXUgB1zFn0fplyqdRQjYi4uwtXRgavV/0TuDZNvYGra0DVKQ6Kl/z0vTbvs48FkP3gQHA7MJYEH5Ie7D2N32wcmKoXIJs7ACuHr3F/4vCzb7bS/9hpP930M08v4/infD21c0UaSlJT6w2Q/cACcTsxFhVS1r2d83HjijHEqBiiMOWnF0PMs9HWAJUm1bsyFhdgrvbf1FSUVjY0VWE8GYg1L6By69Tb0qankPPJrr+slKSX85ey/+HmVENXcLiULcWJOxNSDNfVvXbUfOIAhzfeusA5bB3ta9jA/a772eTtS8uC6FyHnFG3jCBJjTg4T//WMz2zmx6tsU97Xi5OjY+A+1okVWCHyGAwc/dWvyVhXzsaGjVpHE9m2vwyv3jaiunu2CuXB11xSQmV7pfgwEILPs7WtWd2BpLm4CHttrVfphaLkImo7av2uDkYNz/EMDUvo9O3Zg84yePdGWJUbEUJr79vw+1nQuEfrSIYtdt6plG7aSOycOX7brDq4iq+v/Dp13cOvt64aSxJMuiAkyfJCQWexEDdvnt/JA4+KduXZRRxNiA5iACuEL2s7/GO5Msg6jqTTYS4qYkKzkqky6h801VT7KVR/PKIVWFtVNeh06PInUt1eTUlydJyjEcJIev/W0eb9qnZjKizq3xJ/aODaN2d+k4+v/Tj6jyi0VEJCNpjjNene2dKCq60Nc/HgCbDr37men37+Uw2iEjTnyccQQYmcdCYT+vjAP0eebavV7WFwPKHyQziwTusogqbzvffo/vzzIdtVtleSE59DrI+jaULkEQNYIXyZE+HIduXrxFvFxaTUd9Hr7KWhp0GD4KJEc8WIEzmkf/tbFH+4kja5h9SYVIpTxAqsEGSpBfDdLTD9GlW7iZk1k9YLruKqf26i4N53OP2Xq/loTzcxhhhV+w0L+Yth3q2adW+rUAYoJ55bc7qdVLZXkmxO1iAqQXNpRSDpoEndyatga3vpJZp+/we/9z0ZtcPieMKq/4VPfz10uwjR9Ps/0PbCi0O2u3Hyjdx96t0hiEgIBTGAFcKXTqechfORidhcUoKxrZv4XnlgW4hwEk5iACvpdBizsxkXN46VV63k4sKLVQpOGLN0euVBdgS1iU/Gux1mbo07nZ3OWGSgrt3Kfa9t51srfs6qA6tU7Vtzs2+AxT/QrHvPUQTTCSuwB7sO4nA7xMTYWGUwQ0q+z8/9cGbdvoO2f7/i936iKTE8EsTJsnI0I0pK6LjtduwHDvjcyXGiWZmzOGviWSGISggFMYAVwlt6sc9asOYS5c1qqVyKQSdykZ2Unhawto7og8xtt3Pkf/6H3q1bB65F/VZLQRsVK+Gjh1Xt4pH39+Ps6yOj91g9aatD5vOGD/jo0Eeq9q0ppw26G5WHWY2Y8vNJvvoqDBkZXtdFohWB9LKIG8CaS0pwNTXjbPNfmz4sEsR11oOjJ3oyENfUgss15AC22drMJ4c+odveHZrABNWJJ38hvKWVwJ43lQcuw7FkH7Hz51O68Qv+LyFBw+AinLUVMqdCxqRhv8ReU0P7v/9D3MKF/MrxAS7ZxY/n/1jFIIUx6+B6+Oy3yiqhStlI69ut/M/G58jqaeZbZx3bWuboy6SqvSrAKyPc4Y3w9IXw5dehaJkmIcQvXkT84kWDrle2V6KTdKLUxVi24JtKrdII4tkKb6uowDBvns82d8y5Q/sJd8+CQJSswNoqPUklAw9gNzZs5Eef/oj/XPwfylJFea5oIFZghfCWOxdKzoW+Tq/LOrMZff/g1S27tYgs8qWXwLfXQvHwt9TYyo9t+/u8/nMaexvVik4Y69JLQXZBW41qXWQnx3AgcRy53U0Y3McyEceSQ1VHVfS+t3hK6GiUgViWZRxHG30m4JuWPo1bpt6CxWDRIDIhLBSeCZMu1DqKETGXHhvA+jMtfRqTUoc/YayKgfJZ0ZF80V5VDXo9poKCgO0q2irQS3oKkgK3EyKHGMAK4a10OXzpZYjPGHSr7d//5sP7v8aiFxfhPO7hU1CPrbISDAaYkM3BzoNim5+gnoz+FQIVk7ncvbyMIynZGGQ32d3NAMQY9ZxfOgur00pdVxiUvFBDcwUYYpRamxpwNjZRecYZtL/00qB7S3KXcOcpd4Y+KCF8OO1Q+xm0HdA6kmEzZGZizM5Gtlr9tul19PJm5Zva7u6YdQN841NIyNIuhiBKv/3bFH/wPjrz4HJcx6tsryQvMQ+TPjJqCwtDEwNYITL4mKnv27GD8Su30WXv5FDXIR8vEgJ643blawRsFRWY8vM4YK3DJbtEohVBPZ7VQRXPwl02O4fLL18MQEFnAznJMTx8xXSumTmPZHMyjdYo3WHQUqGcgdNp8wgwkMCpwHubsMPt4HDX4ehd+RaGx9GrbHHf84bWkQybJEkUrfqQtFv9Z/Z2yk5+8vlP+PjQxyGLaxBTLGTNhCjJXSHp9Rhzhp6IEzXro48YwArh78lz4M3vDLpsLilB39lLUm+YpKaPNIfWg61z6HbHcVt7sZSWDWR+FjVgBdWY4yFpgpJsSEXLz58Pej2PnBrP5/cu47LZOUxPn86n137KKeNOUbVvzZxE9vFg8ndurbKtkvNfO5+VB1ZqEZYQLmKSIX4cNEVWIqehEhp6MhFr+rzy6SPK6nYUcNtsHPnpz7Bu2xawXa+jl8Ndh8WEe5QZ1QBWkqRUSZJWSpJU0f9rip92LkmStvV/vXXc9QJJkjZIklQpSdLLkiSJtX1hMGMMNO0ddNmTNGFik3K+QRgBpx1aa0b8EJv31FNkP/oIFr2F2ZmzmZg4UaUABQH47ma4QN16hTqzmayfP0DiOecMXJMkKbqza595L8z5imbd2yor0aemYkhL87ruebAXE2MC6aXQHFm1YHvWrqXmyqtwNPqfdCtJKdHuecXeC6sfhANrtek/yOzV1bS/8gqOI0cCtjPrzbx+6etcXnx5iCITQmG0K7D3AqtkWS4BVvX/2RerLMuz+r8uOe76r4DfyrJcDLQBXxtlPEI0yihTZmJP2EbsSZs+vStZrMCOVFutkiDnJDIRSjodZ+edzb/O/xdGnTH4sQmChyHwuaZgSb7qKixTpnhd+9fuf/H9j74fkv5DbuZ1ULRUs+5tFRU+y15UtFdg1BnFxJjQP4Ad/Lkf1vQG+nbvDpjIqTS5lOqOahxuRwgD69faf/Y2Skro2CqV576hSujodXqKkosYHzc+FGEJITLaAeylwDP9v38GuGy4L5SU6e1lwH9O5vXCGJJRBvYupX7ZcfTp6RhzcpibOI3Tsk/TKLgI5TlXOIIspJ0rV3Lw61/H2dbmM3uoIATdoY3w4vXQGXiGfbScbW10ffwxbptt4Fq7rZ2PDn2E3WVXte+Qaz8EdVvApV3iu7RbbiH1psErwJVtlRQmFWpfakTQXnop9HWofoQgmDxb4gMNYEtSSnC4HRzq1CBvR5RlILZVKEklTXl5AdutOrCK1yteD1FUQqiMdgA7TpZlz5NFAzDOTzuLJEmbJElaL0nSZf3X0oB2WZY9n6KHAb8nsSVJ+nr/99jU1NQ0yrCFiJLeX7OraZ/XZUmSKPpwJef89K9cVXqVBoFFMHM8FJ8D6cOfibVu20bvuvX0WXQseGEBr1W8pmKAggA4rbB/xaCf/WDr3bCBw9/8FvaqY9lBS1JKcMkuajrUK+OjiR0vwRNLwdmnWQiJ551HwlmDy3dVtFeIc2qCYsol8LUPIcbnybSwZEhNRZ+WFnAAu3TCUj665iNtyrk07QdJFz0rsP1JJSVT4NOH/y7/Ny/uezFEUQmhMuQ0pyRJHwK+1t3vP/4PsizLkiT5W5bJk2W5TpKkQmC1JEk7gY6RBCrL8t+BvwPMnTtXLP+MJZlTYO5XIW5wKR3PObVmazMWvYV4U3yoo4tMhWcqXyNgq6zEVFhIdfcBep29pJgj58FCiFCeyavmclW3vHq2oNkqKga2EnvOYVa0V0RX4fumciU5llmb90pHQwPOpiYskyYhGY8dQZBlmR/O/SHpMemaxCWEmcRs5SvCmEtKlJVBP+JN8cSj0XNK+0FIzlPyikQBd28vltKhj0FVtFcwb/y8EEQkhNKQA1hZls/2d0+SpKOSJGXJsnxEkqQswOdeD1mW6/p/rZYk6WNgNvAqkCxJkqF/FTYXiNKie8KoxKXBRb/1eatn/QYOPfJ/fOPMKn54wcNcXHRxiIOLUC4H6Ed2ftVWUUHsnFPY1n/eWKyUCKqLzwRLkqq1YAFlC5rR6LVykpeUh0FnoLItys7XN+1TjmVopPOdFTQ+8ggl69ZiSDk2CSZJEsvzl2sWlxCG9rwJBotSDz5CxJ1+GvbqwLs2Xqt4jS57FzdNvSlEUfW77M9g6wptnyrKe+ZpZHfgklud9k4aextFCZ0oNNotxG8Bnp/Am4A3T2wgSVKKJEnm/t+nA6cDe2TlEN1HwFWBXi8IgHJe64QzsACSXoe8u5yCFr3IRDxcsgy/LoKPHh72S1zdPTjrj2AuLqairYIYQww58UPXXhOEUZGkY8lc1OzGaMRcUOC1cmLUGVk6YSnJ5mRV+w4pt0v5f5kxSbMQbBUV6DPSvQavAFXtVWw5ukXUgBWO+ey3sP4vWkcxIum33Ub2w/8XsM3a+rXabGmVJLAkhr5fFUlD1LKualeOhZSkRMe5X+GY0Q5gfwmcI0lSBXB2/5+RJGmuJElP9reZDGySJGk7yoD1l7Is7+m/dw9wlyRJlShnYv8xyniEaLXih/DXRYMum/q3/s3oShmoTSoMobMObB3K6tYwuTvaiT31VCzTplHZXklRUhE6SZSRFkIg91Qwq//QZS4uHnR27Tdn/oabp92set8h035QOfuq4QqsrbLSZ9bQl/e/zLc+/JYGEQlhK71M9ckrtQRaGSxJLqGuu45eR2/oAmqrhf98DRp2ha5PFXV9+CGHvvFNnG1tAdsd7DwIIFZgo9CoUv3JstwCDMrEIMvyJuDW/t+vBab7eX01IDamC0NLL4HeFuhphrhjZ6QMKSnoM9IpaTOxQqzADo8nIc4IVmGMOTnkPfsvABbvrsKkFyWbhRA5b/g7BUYj/dvf8lmyw5NxOyrqwsaPg6+8dVLls4JBdruxVVWRfPXgpHuV7ZUUpxSLiTHhmPQSJemYrQvMCVpHMyzuvj6qzjmXlC9/mfSv3+azjWc1sLK9khkZM0ITWMNO2PUfWPjt0PSnst6tW+lZuxZ9QuB/F5cWX8rSiUtJMEbGvx9h+MQnhRAZPCsGPs7CWUpKGHfUwdHeo3TaO0McWATy/D8cwQD2+LI5X5n6Fa6bdF2woxIETZmLizGXeG8z29a4jSUvL2F703aNogoyUywUngGJWZp076ivR7ZaB63AyrJMRVvFQOIsQQCOfe43R87ktM5iAb0eW2XgUjpAaI89eT73NZq8CjZbZSWmggIkw9DrcImmxOiYgBS8iAGsEBn8lNIBiF24kKTSyfzi9F9gkET9wCE17YPYdCU51jAd/ta3qbvrB3TZu+iwjSiBuCCMTncT/G0J7PzP0G1HwW230/byK1i3bRu4lhGbQbutnfK2yNzGOEj5+1C1WrPuDenpTHz6KeLPONPrektfC+22drHNT/DmGWxF0AAWhs5EnBOfQ5I5iTZb4O2vQdW0vz/7eHSsRNorfB9FOJ4sy/x4zY9ZfVC79zxBPeJpX4gMSblgivd5Hib9tttIB6Ko0IW6CpdCatGIXtK3Zw9xCxfydtXbPPzFw6y+ejUZsYPLGglC0MWkQONeaNgB09Wr9yzp9Rx9+GFSrr2WmFmzAMiOyybWEBs9CeI++ZXyPlq0TJPudRYLcQsWDLru+f8rMpsLXlKL4Pt7Iq6cjrmkhN4NG5BdLiS9ftB9naTj02s/De12eY2zjweTq7sbR309yddcHbBdS18Lb1e/zZS0KSGKTAglMYAVIoMkKWfh0vxvMdvXvBe77AjdmZJINe2KETV3dXTgbGzEXFpCZXsliaZEUatRCB29QXmQVXkVRtLrMRcVeSVykiSJ4pRiKtujoJSOLCurMLO+pFkInStXoo+LI+6007yuz8yYybPnPysyhQre9AZIirxs9+aSEmS7HfvBg5gLCny2CengVZbBYIbx0fFs5GrvIGbuKVim+UyvM0BMjEU3sYVYiBxzvgJ5CwdddttsVJxxJqse/i6/3ey7XqzQz2FVshEOUTvteJ4Hek8JneLkYnGeRAitjFLVa8FCfybiSu/BaklyCRXtFV7nwCNSZx3YuzVdhWn+/R9o/dezg67HGmOZlTmLOGOcBlEJYW3v2/DhA1pHMSIxM2eSetNXkIz+kx1ubNjIze/dTLO1Wf2AJAlu/RDO/pn6fYWAKTeH/OeeI37R6QHbeY5+lKZEx7lfwZsYwAqRo68TataA3Tv1vM5sBr2OomZ9dDxoqunQF/D4TKj5ZNgv6duvDByMZaWUt5VTlhod25CECJJeqky8OG2qdmMuLcHZ2Iir49g57zNyz+CK4itwup2q9q26k0jeFkyy3Y6tpgZz6eCHyVf2v8LGho0aRCWEvbrNsPaP4HJoHcmwmQsLGHfffZhy/a8ey7LM5qObo+d8fQgN9xmvvK2cjJgMUi2pKkckaEEMYIXIUbsGnrkIGvcMumUpLSPziJUOW0doZjQjlechNnPysF9imjiRpCuv4Gisg15nr5jNFEJvwnyYcgnYulXtxpOF2FZdPXBt6cSl3DX3Lox6o6p9q07jAaytpgacTsxl3u8fbtnNo5seZdXBVZrEJYS59DJwO5QJrAgi2+04jhzxe9+zrTUk5+s3/ROeukD1CcBQOfS1r1F///3Dajsrc5a6wQiaEWdghciRflwpndy5XrfMZWVY1qzB4OyfdRMJhnxr2gfmJKUe5DDFL15M/OLFdNg6+NnCn7Ega3ASFkFQVck5ypfKYufPp3TDevRJSV7X+5x99Dp7I3smf95tyv/DOG3Or9v6d3JYyrx3cBzqOoTVaaUsRezsEHzwZCJu2q/UhY0Qh++6C3t1DUUr3vF5P9WSSpolLTQD2MOboaVSOQcb4WRZpnPrdj5tMfDIve+QnRzD3cvLuGz24NXuhxY9pEGEQqiIFVghcqTkg97ks5SOpawUyeUipwX2t6l/Vi5iNe1XzsAN8wyr7HbjbGpClmWSzElcVXoVuQm5KgcpCH447ap+e53ZPGjwCnDh6xfym02/UbVv1emNmg4AbBUVSEYjprw8r+v7W5X369JUsbND8GGgBvxebeMYIUtpKfbaWtx9fX7blKQo5+tVF0UZiN9ZuRW9tZddlgxkoK7dyn2v7eSNrXVahyaEmBjACpFDb4C0Yp+ldCwzZpBy4438bOn/cUXxyLLsjinN+0f0QeY4fJiKxUvoeONNNh/dzIHOAyoGJwgBPHkOvPo11bvpePNNGh991OtaYVJhaB401SLL8P79Sg4BjWTceSeF765AMnpvxd7fth+9pBc1YAXfzPGQWgjWdq0jGRFz2SRwu7FVVvltM2/8PHLiVc6y7Mk+nh4lA9g3lfewmuNKK1kdLh5533vh4oPaD/jSO1+iqbcppPEJoSO2EAuRJb0UjmwfdNmUm8v4n9zPeA1CihiyDBc8AonD/8D0JHAyFxfxk89+xJS0KTx25mNqRSgI/sVn+tx9EWzW3btp//d/yPj+9wdqOJamlPLy/pdxup0YdBH4sdnTBOv+CEkToGCxJiFIej2m3MG7N2o7aslPzMesj/ztjYJKvrMJdIPrqYYzS/9Zb9v+fcRMm+qzzW0zblM/kK4jYO+KmhXYxHplEv1AovfTXn271evPu5p3sa91H8mW5FCFJoSYWIEVIsviH8BV//B5S7bbqdq7jid3PonNFR3JCoJKkmDq5TBh3rBfYttfDpKEY2IWh7sPiwROgnYyJkFLleqJSCxlk5CtVhyHDg1cK0stw+aycbDzoKp9q8Yz8NfoIdbZ1saRBx6gb9/gCYhHz3iUp857SoOohIgRYYNXAOOECUgxMQOTwIGoWjnBYYWScyF7tnp9hFD3+Am8VXAavUaL1/Xs5BivP5e3lVOcXIxRF+HJ9wS/xABWiCxZMyDnFJ+3jvz851i/+j0e3/I4Ve3+t+2MWU374cC6kdWA3b8PU14e1bbDAKKEjqCdzMkgu6BZ3a285v4kQ337jx1V8CQY2teq/gqwKrTOQLx/P+0vvYyrtXXQPUmSSLGkaBCVEDEOb4Z/XQqt1UO3DROSXs/4n/2UpIsu8tvG6XZy8esX89cdf1UvkLQiuOHfgxJfRqpzvn4NT8+92utajFHP3cu9n032t+2nJCVykn4JIycGsEJkcfTB9pehYeegW5bSUvRtXST1yAOJQYTjbPonPHfliF7St78cc1nZwP9PkSlU0Ixn8KXyNmJzcRHodANZc0E5A3v33LuZmu57K2DYa9oH5kRI0OaQhef/pfmEDMR7WvbwP5//D0e6/ZcbEQQkoPpjaNildSQjknzZZcTMmOH3vuc4wr4WFd/T3C71vneIyQ4HF0208PAV08lJjkECcpJjePiK6V5ZiFusLTRbm8XzSpSLwMM8wpgmSfDGN2HxD2H8dK9bnoej4majKA7uS9M+yCgF3fDnrTK+czv6tDT2t60iwZTA+DhxyljQSHoJLLhdSeiiIp3FgmXKFNy2Y9lDjXojX5n6FVX7VVVP84iyjwdb3/5y9OnpGNLSvK5vbdzKG5VvcMfsOzSJS4gQAyX09gGXaBrKSLi6urBu3UrMzJk+s5sDTEqdxM7mwRPyQfPMJUrprGueUa+PEOkrL6f2yqs4649/4LJ7z/bbzuq0cvbEs5mR4X/yQIh8YgArRBaDWSmn0zx4hdVcqpzPnNOdxjZRSmewpv1QeOaIXpJ0ifKw8K3eUi4pugRJowdgQcBghvP+LyRd5f/7lUH/1putzexp2cOS3CUhiSGornkGXA7Nurft34+ldPD5+fK2clItqaTHaFObVogQ5nhIngiNkVVKx7Z/P4e+/g0m/O2vxJ9xhs82ZallvFf7Hp32ThJNicEPomkvpPnfxhxJbP3HOkyFRQHb5Sbk8tulvw1FSIKGxBZiIfJkTIbGwVtuDKmpGDIyKGk2UtNRo25ihEhjbVeyEY4giYutpgbr7t3IbjcZsRnMypylWniCMCyOvmPnOVXka6JmRfUKbl91O83WZtX7V4Vem2Qmsizj7uvDPGnw+dv9rco5NTExJgwpY3JIspAHk6/z9CfybHMtb1Vh11hPM/S2aHb2Pdhs+/cjmc2Y8iYGbieSeI4JYgArRJ7MydBS6TMb6bj77mXuN37MB1d9IB6KjuepnTuCD7K2557n4FduorG3kad3PU1DT4NKwQnCMH32G/jzAmUgq6K+/eXUXHst1u3HSnZNSlV+dlR50FRT/VZ48UvQXKlJ95IkUfTOf8n84Q+8rjvdTirbK8U5NWF48hYqZaAiaGJan5CAMTsbm4/s2x6T0yZzZcmVJJgSgh/AQPbx6KgeYKsox1xSMlDezJ8b3rmBe9fcG6KoBK2IAawQeQaykQ5+kEy84AIy5i8WqdNPNG4afPUDmLhw2C+x7d+PubSUnS27eGzzY5G78iREj8zJILt9/uwHkz4xgb7tO+jbs2fgmicD9762yFoFon4b7H9HsxVYD+mEs/dtfW1kxWUxOW2yRhEJEWXR9+GGVzQ7x32yzGVl9JX73zWSHpPOA6c9oE6Gf8+W6yhZgVWSSgYejDvcDqo6qsiMzQxRVIJWxABWiDyly+Gufcqg7ATunh661nzKYyt/yttVb2sQXJgyxcLE+RCTPKzmsizTt38/5rJS9rftRyfpKE4uVjdGQRhKRv9gR+WzcIbx49ElJtK379iDZ5I5ifFx4yMvw3nTPjDGKqtXGmj91784/N07Bh3pyIjN4O3L3+aiwug4nycIvpgnlWGvqcVt87+t1S271dnhlFEGp94GiTlDtw1zsttN5g9+QPJllwVsV9NRg9PtFDs7xgAxgBUijzkBErN8zsTa6+o4fNs3aFnzER8d+kiD4MLUthegavWwmzuPHMHd1YWlv4ROXmIeFoNl6BcKgprSikBnVBKTqEiSJCylpV6ldEA5rxZxA9jGPcrK9QiyjwdTz/oN2GqqxZEOYXRcTvjTfPj0Ua0jGZGUq66i4LXXkAz+c6b+YesfuOC1C3C4g5xorWAJXPhoxK1a+yLpdCRfcTmxp54asJ2nAkVpSnRsmxb8EwNYITJtfR7W/mHQZXNBARiNTGtPEKV0jrfqf5X6ucPUd1zdxvK2cvFhIIQHvRHSin0mcQs286RJ2MrLkd3ugWvfm/O9yMtuebR/AKsRJQPx4NWQ+z+7nwfXP6hBREJE0hvA2eezBnw4M+bkYCkrDXhusyS5BIfbQU1HTfA6lmVorYbj3r8ima2ykr49e4ZMzlneWo5RZyQ/KT80gQmaEQNYITJVrYIv/j7osmQ0Yi4qYmKjm4OdB+l19GoQXJjpbVUyEI+bMuyXxJ56KhOf+ifu4jyO9hwV23GE8HH2A3C6+nVDY+fOJe7003D39AxcK0kpoSCpQPW+g8beq9TNzZmrSfeuri4cdXUD2ViPt75+PT2OHh+vEgQ/IjATMUDH22/T+cEHfu97EsQFdXdHZz38fjZs+kfwvqeGWp78B4e+8c0hd3LMy5rHt2Z+S+RBGQNEHVghMmVOhl2vgq1L2VJ8HEtZKcmff4qMTEV7BTMzZmoUZJjwnBfMnDrsl+jj44lbqCR8Wn/DepxupxqRCcLIlZ0Xkm4Sz1tO4nnLva45XA5er3ydkpQSZmfODkkco2KKhVtXata9raICYFDilba+NhqtjWJiTBiZzElQuRKcdjCYtI5m2FqffQ5dTAyJ557r8/7ExImY9Wb2te7j4qKLg9PpwOd+dCRJs5WX+5wIO9GinEUsylkUgogErYkVWCEyZfavJvqoCWkuLUPf3E4B6XTYOkIcWBhq7M+kOoIPsrYXX8S6U9mqZdabiTPGqRGZIIycrRvKP4DOIyHpTnYcO5em1+l5dNOjvFfzXkj6jnguFzFz5mA54cFz4JxaqjiaIIxAxmRwO6G1SutIRsRSppyn97f91aAzUJJcEtwV2Mbdyq+Zw995Fa5kpxNbZSXm0sDvF72OXiraKoJ/llgIS2IAK0Qmz2Cscc+gW4kXXUTBG6/z5g0rWZK7JMSBhaHmCrAkQWL2sJq7bTYafvEg3R99xHN7nuMv2/6icoCCMAJdR+CFq6Fa/SRtB75yE3V3HatfqpN0lKaUsq81QrYxrvgRPHelZt3Hnnoq+S88jzEry+u650FdrMAKI5IzB2bdALrI2jxoLpuEq70dZ2Oj3za3zbiNr0z9SvA6bdwL8eMhNjV431MjtupqZLsdy+TA5YC2N23nireuYFPDphBFJmhJDGCFyJScrwzKegbXJjWOy8QyaVLArH9jyvm/gu9sGnYmQltlJbjdmEtLebfmXb5o+ELlAAVhBFIKQG9SvZQOgD4lZSChmcek1EmUt5UPmUwkLNRtBqf/8h1qk/0kkEmPSefsiWeTFpMW4oiEiJZeApf9Wfk1glj6t9CfmNX8eMsmLgvuhHvjnhHlvQhntr3Ke71lUuABrGdicXJqdGybFgITA1ghMul08KMaWHyXz9ud773Hyid/xpVvXYlbjo4sfCdNkiB++EW9PR8WhtISytvKmZwmPgyEMKI3QHppSAaw5rJSHAcPeiVyKk0ppdvRTV13ner9j4rbrfw/Gjf8s+/BJLtcVCw8jZZ/PjXo3gWFF0ReNmchPMiykpgwgnjObtpra/22cbgdbGrYxKGuQ8Hp9Ix7YeHtwfleGos/80wmPPkkpoLACfT2tu4lKy6LZEtyaAITNCUGsELk0vlPS9/+yr9Je20N5W3l1HWF+YOmmroa4I3boWHXsF/St2cvurg46pJc9Ln6xGymEH4yJoUkG6lnxr+v/FhJLk/G0KCWvFBD+wFw9GiWxMVeW4urowN9SorXdZfbhd1l1yQmIQq89nV4YpnWUYyIPjGR0vXrSP2K/y3Cdpedr77/VVZUrwhOp5MugOKzg/O9NKZPSiJ+0elD7qrb27JXPK+MIWIAK0Sumk/h6Yugp2XQLcuUyVgONqJ3yexri5Dzamo4sgO2Padkax4mW2Ul5kmT2NeubHcSHwhC2MmcDB2HoK9T1W4GBrB7j632Tk6bzNrr17I4d7GqfY/aSWQfD6a+Pf3b/qZ4v3+Ut5Uz//n5fFb3mRZhCZEurRjaapVkbhFEn5wc8H6cMY6JiRPZ3xaERE6t1VD7ObgiP5mRLMu0/OMf9O0vD9iu19HLgc4DTEoLvM1YiB5iACtELpcDatdA0+CthJYpU5CcLvJadOxtUX+rYdgayEQ4/EHoxH/+g9zHf4fVaSU7LlsUBBfCz6wvwbfWgknd7NiGrCxSb7oJy3HZL406IwmmhACvChMxyTD5EqX0iAb69u5FMpkwFxZ6Xd/buhen7GRiwkRN4hIi3LipgBxx9WB7N27k8B3fw221+m1TllIWnARxO16Bpy+MigGso66exkcexbp1S8B2Bp2BP571R87PPz9EkQlaEwNYIXJ50sP7OAtnnqwM2OZ1ZrCndXCm4jGjcS8k5igPs8MkGQwY0tO5puwa3r/qfQwRlvFRGAMSs5UH2QDHCIJBkiTG3XcvsXPnel1/v/Z9frb2Z6r2PWp5p8G1zw6qkx0qfXv3YC4pQTIava7vadlDvDGe3IRcTeISIpznTPfR3drGMUKujg66PvgAW7n/lcSy1DIOdR2i2z7K1eWjuyG1QKkDHeH69irPb5bJgSfhTXoTS3KXiAn3MUQMYIXIlTAeLMk+P8hMeXnoYmOZa89mUsoY3lJydM+I6sD1rFtHw//+L65OdbdmCsKo7XgFdr+uejey04mtosKrHuyhrkO8VvFaeNeZ7tM2toSly0i++qpB1/e27mVS6iR0knj8EE5Cch4Y4yJuAOsZgPXt8T+h7jlfX9FeMbrOGvdGRf1XANvefaDTDVkDds3hNWw5GniVVogu4hNEiFySpLxJ+1iBlXQ6ij/+iOW/epY7T7kz9LGFA0+Zj/HTh/2Sns8/p/3f/6HO2cKlb1zKF0dECR0hTG18Ejb8XfVuOt9/n+qLL1HKS/Wbkqo8HO5tDdPjCU47/LoQPnlEsxBSv/JlUq67zuua0+2kvLV84EFdEEZMp4Nzfg6TLtQ6khExZGejT0oaOBvuy5zMOTx7/rOjyzvh6IPWqqgZwPbt3YupoABdTEzAdo9veZy/71T/80AIH2JvoBDZ8k+Hlkqft/SJiUB/1ku3nRhD4DfAqCNJ8K3Pjg1kh6Fvj7Ltb29nOdUd1cSb4lUMUBBGYdxU2Pmq8u97mDWOT4ZlsvIg2Ldn78AqypS0/gFsy14WZC1Qre+T1lIBbqeyjVADztZWkCQMJ2Qgdrgd3D7rdqZnDH9STRAGmXeb1hGMmCRJmKdMpmHTdq765Wrq261kJ8dw9/IyLpudA0C8KZ5ZmbNG11HzfpDdmmUfDzZbdRUx02cEbGN32alqrwr/xHpCUIkVWCGyLfsJXP20z1t9+8s59L3vccWfT+PpXb7bjAnDfLiXZZm+PXsxT5nM3pa9GHQGipOLVQ5OEE7SuGlg64COw6p2Y8pXjiMcv/Uv2ZJMdlw2e1rC9Hz90f64NHqIbXv+BSpOOx13b6/X9RhDDDdPu5lTxp2iSVxClHBY4dAXqmchD7aDWcVUdTmpa+tFBurardz32k7e2Hqs1N/mo5t5ds+zJ99Jehl87UMoPHPU8YaDov/+l/E/uT9gm4r2CpyyU+zsGGPEAFaIDr5WGd0uut//gJktceH7oKmmtX+E568Gt3tYzZ0NDbja27FMnsze1r0UJxdj0ptUDlIQTtK4acqvR4df4/hkSDod5kmTvErpAMwdPzd8z3E27gGdAdJKNOm+b+9eTPn56GK9k8hUtVfR2NuoSUxCFKnbAv84Bw5t0DqSEbk3cSE/XPRtr0llq8PFI+8fK53zWd1n/GbTb7C5bCfXidECE06F2NTRhhsWJKNxyBJE+1qUzM2eox3C2BCmn76CMEwuB/xxHqx5bNAtc1ERktHI9Nb4sZmJ+OA6pV6ebng/5s6mJgzZWZgnTxYFwYXwN67/YaW1WvWuLFOm0LdvH/Jxk0EPLXqIXy35lep9n5TGPcrg1aDNBFTfvr0+s4b+Yv0vuOvjuzSISIgqnp/9CEvkVN/uu4TO8denpE3BKStnxU/KlmehctXJvTbMdLzzDg2/eBDZ6QzYbm/rXuKN8eQk5IQoMiEciAGsENn0RnA74Mj2QbckkwlzSQkTjjho7G2k2dqsQYAaOrp7RIkcYmbMoGT1avQzprA4dzGn5ZymYnCCMErmBLjnACy8XfWukq+8gpzfPDbs3Qyam3k9nH6HJl0729pw1h/BMsV7AOuW3exr3ScmxoTRi0mBxNyIG8BmJ8fwi7VPcMvudwZd9/Ccrz/pXWOrfwE7/3PSMYaT7tUf0bV6NZIhcLqeH536I1688MXw3REjqEL8bQuRb9w0v9sIzVMmk1jbDLIcnALhkcLWBW01MH7aiF9qMVh4aNFDnJd/ngqBCUIQjaC+8WhYJk8m4cwzvR6k+px9XP/f63lh7wshiWFEpl4Gs76kSde2fcr7rPmEFdhDXYfocfQwOU0MYIUgGDc14gawdy8vI85lZ2pLzcC1GKOeu5eXDfw5Oy6bZHPyye0a626E7qMjqjwQzvr27Ruy/isoNWBF/dexRwxghcg3fjq01oBtcPHvmJkzMeXkcnvpV8mJH0PbSzwf7OMDZ+87Xu2NN9Ly9NP0OHqQR5C5WBA0U/sZvPxlsPcO3XaUejZ8Qc8Xx8pKWQwWmqxNbGvapnrfI9LVoPz8u12adG8qKiLrwV8QM937IXpvi3KGWKzACkExboqScddp1zqSYbtsdg7j586kqLMenewmJzmGh6+YPpCFGJRsxVPSpnCg88DIO2jYqfx6EhPX4cZttWKvqcEyKXBipkNdh/jVF7/iUNehEEUmhAtRRkeIfOOmAbJy7mvCPK9bKVdfTcrVVzMmc+kWLBn2TKyzrQ3rps0knHkm9665l1ZrK89f+LzKAQrCKPW2wt63YNGdkKNuZtvGX/0KfXIycfOOvcdMSZsyMDALG7tehfd/DD+sgPjMkHdvzMwk+aqrBl3f07pHZDYXgmfWjVByLkTYttEpS07lyPtvsPcb0zAX+i5z9dgZjxFnjBv5N/cMYMdF/gDWtn8/uN2DjiKcaFvjNp7b+xxXlFwRosiEcBFZP/mC4Ev2LJh9I5j8v+F327vZ1rgtZCFpbuICuOltSMweVvPjt/3tbdlLbkKumtEJQnB4VhpCsJXQPGUyfXv2eO1O8KyU9Dh6VO9/2Bp2Qfw4TQavAJ0rV2I/PLi00dWlV/PbM3+LUW/UICoh6qQXQ95poI+sdRjLVE9daf9bhONN8UgnU9u6pUI5GxwFGYid7e0Yxo3DMiVwHo89LXsw680UJGlT81rQjhjACpEvMRsu/ZNyJsaH+nvuZcvtX+HL736ZDltHiIPTiCtw1r4T9e1RVpGsBeM52ntUbPMTIkNyPhjjlEGbyixTpuBqb8fZ0DBwbUraFGTk8FqFbdip2Rk4d08PdXd8j4433xx0b0LCBM6ccGbogxKi174VULVa6yhGxFxURPzZZ6FPSfbbxuq0cv9n9/N+7fsj++aX/BG+8enoAgwTCWeeScknH2PMDjwJv7tlN5NSJ2HQRdZEhjB6YgArRAdZVs5++brldJK2T7k3JurBupzwqzz47HfDfol1104M2VnsdSsF1aem+54MEISwotMpZ+FCsAIbM2XwysmUtCmck3cOZr1Z9f6HxWmHpn2abSHs27sXZJmYad79t1hbeLX8VVqsLZrEJUSpj/9PqXceQSSjkQl//CPxp5/ut41Fb+GTw5+wtn7tCL+5BHFpo4wwcjjdTva27GVaeuRvmRZGTgxghejwwU/g93N8lrmwTJuGrqmNpB55bAxgWyrA3g0JWcN+ibm4mKQLL2JX8y50ko6paWIAK0SI3HkhqXdqLisDnY6+3cfeQ9Jj0vnNmb9hekaYZP1s3q+UFdNoBda6U1kJt0z1fv/Y0riFB9Y9QH13vRZhCdFq3HS/FQjCnauz02+yREmSmJo2dWTPK4374PVvQktVkCLUjru3l6rl59H57rsB2zX2NhJnjBPPK2OUWHMXokPGJHD0KKVj0oq8bsVMU97c5rWlsrslstLun5STyESYcbtSS3Nh41ZiDbHEGmPViEwQgu+8/wtJN7qYGAreeB1Tfv6gex22DpLMSSGJI6CUfLjhP5A1S5Pu+3btwpCVhSE93ev6zuadGHQGylLL/LxSEE5C1gzY/gJ0HYWEcVpHM2wdb75J/T33UvThSky5vvNNTEmbwtO7nsbmsg1vh8fhL2D7i7Dk7iBHG3p9+/ZhP3AAyWwJ2C47PpuPrvkItxwh9bmFoBIrsEJ08AzWPIO341imTAGdjlPaktndPBYGsDtAb4L00mE1d1utyC6l5MbszNncPO1mFYMThMhlKS1FZ/Je7X1q11MseXkJvQ71S/kMyZwAJedAfIYm3fft2jVo+zDA7ubdTEqZhEmv/kq5MIZ4ysQ17NA2jhEyFSqT7H27/K8eT0mbglN2UtFWMbxv2rATTPGQEvnJjDz/X07cyeGLJEnodXq1QxLCkBjACtEhYzJIep/biXRxcSRfczVz5l7Eo2c8Gv01Tht2QeZkGGa2z9Zn/kX5qfNoa2tgW+M27K7IqasnCLgc8OQ5sO5Pqndlr63l6MMP4zgukVNBUgFu2c2+1n2q9z+kHf+Gw5s06z7vuWfJvPuHXtdcbhe7W3aLc/VC8Hm2yvuYuA5nlrJSJKMR607/cU9Nm0phUiHdjsH17X1q2KUkstRF/mO9ddcuDJmZGMcFzqR+18d38eTOJ0MUlRBuIv9fuiAAGC2QXuI3G2nWAw8w+bqvMz1j+smlp48kUy6BuV8ddvO+3bswZGSwsWMHX373y5S3lasYnCAEmd4IPU1waIPqXbm6umh95l9Yt20buOZJILKzWeOHaFmGFT+Arc9qFoIhIwPTxIle1w51HaLH0cP09DA5JyxED0sifG8HnH6n1pGMiGQyYZ40ib4d/t8zsuOzefOyN1mQtWDob+h2a5p9PNj6du3G4mMnx/HsLjsfHfqILntXiKISwo04AytEjzPuUbbQ+eHq6mJ1/SfExqdweo7/DIARbwSDV1ASr8TOncuull0YdAZKU4a39VgQwkbWTDiyTfVuzGVl0L9yknjeeYCSyCk7LptdzRonk+k4DH0dmj3Edq1ahb22ltSvftVrkjA/KZ81164R9V8FdaTkaR3BSYmZPp2ON95AdrmQ9P63wMqyPPSku7UNknKU98EIJ7vdxM471edRhOOVt5XjdDtFAqcxTKzACtFj2hXK+S8f+vbto/zUeXz6n9/x7F7tVihU190EnfXKaswwOJuacDY0YJk2ld3NuylLKRPn1ITIkzUT2mqVBzkV6UwmLGVl9O30HqxOS5+m/QqsZxvlOG0GsB1vvkXby6/4fNhOtiQTZ4zTICoh6tVvhTe/o0zeRJDEiy4i80c/Gsg/4ctbVW+x7N/LsDqtgb9ZXBrcvgHmfCXIUYaepNOR9cADJF91VcB2nglDUUJn7BIDWCF6OO1wcL2yEnECU2EhGI3Mak5gd/Pu6D0Hu+UZ+M1ksHUOq7m1P1mCeZqSsl98GAgRybPyEIKzcJbp0+jbvRv5uJJdV5VexTdnflPb95WjuwBJqYurASWB0+DVkMc2PcY71e9oEJEwJvQ0K9vmI+wcbOyc2aRcd+2gpHDHSzAm0GxtZm/L3hBGpi1XZ6fXe6s/u5p3kWpJJStu+OUChegiBrBC9LB1wj+Xw67XBt3SmUxYSkuZWG+n3dbO4e7Bg9yo0LATkvPAMrySHqa8fNK/8x2O5sTS7egW23GEyJQ1C8ouBEPgsgvBEDNtOpLFgrOpaeDawuyFXFZ8mbbn6xt2QmphwGMUanG2tuKor8cy1XsCzOFy8Pze59nfuj/kMQljhGfy6khkZSIGsB84MFA72RdPfekhd3e8eTu8dUcwQ9NMwwMPUH3JJUO2y0nI4bz886I/p4nglzgDK0SPuHRIzPV7Fs4ybRrx77yNJMvsbt7NhIQJoY0vFI7uGtEZOHNhARnfuZ1El42nz3ua/MR89WITBLXEpcH1L4Skq6TLLiXpissHPThVtlVid9uZkqbNCihXPgndRzXpevWbnzABuGVtFy1Nq7l7eRmXzc6hvK0ch9shdnYI6onPhPjxcGS71pGM2JGf/A9um42CV172ed9zvn5H0xCD8+pPIXeuChGGnnXXbixlQ9eL/tbMb4UgGiGciRVYIbpkz4L6bT5vxUyfBt29TOg0RWemXVs3tFQdq403BFmW6dnwBa7ubsx6M6eMO4W0mDSVgxQEFfUNb+v8aEh6vc9Z/3vW3MPvt/xe9f79MpgheeLQ7YLsja11/PfDrdh1BiqTc6lrt3Lfazt5Y2vdwMqRGMAKqsqaEXG1YAEs06dj27sX2e6/dN30jOmBV2B7WqDjoPLsE+FcHR04Dh7EMj3wJLzdZcctD73NWIhuYgArRJesWdBa5fNBNm7hQsb99H946qpX+O7s74Y+NrU17ARk5cN8GJxHjnDwppvoeOstXtr3EpuPblY3PkFQ07o/wa/ylIkclTX/5S/U3fUDr2vT05UHTU3OwdZvg3fvha6GIZsG2yPv7+etCfO58qIH6TUqW7itDhePvL9fnFMTQiNrFrhdylcEiZk+DdnhoK+8wm+bc/LOYXn+cpxup+8GR7Yqv2bPViHC0OrbswfA51n6472470UWvbhIlNAZ48QAVogunllIH7OxxpwcUr/0JTKzi6Pz3ER6KVz+d5gwf1jNPQmcjJMn8cjGR/jo4EdqRicI6kotAtndn8xIXa6OTrpWrUJ2OAauTUufRqe9k4NdB1Xvf5CaT2DDX0AX+lI19e1KhlSnzjDoulN2csq4U6Lz/VYIH0t/DN/5AnT+y9GEI89KY98u/yusy/OX84O5P8Cg83Piz7PjLApK6HjOA1umBD6Gsbt5N/GmeBJMoT/vL4QPMYAVosuE+XDLe5Bzis/bjvp6qj54jfvW3Ed1e3WIg1NZXBrMvBZiU4fVvG/nLjAaOTRej91tF9v8hMg2kMxF/bNwlmnTkG02bBXHVk6mpw8z4Yoa6rcp24fjQn8EYLLJxq/X/Jmpzd7vp9nJMfxy8S957IzHQh6TMMZE6ASJMScHfXIy1p2B3zNsLhsNPX52VyTlwoxrh524MZzFLVxI5t13o09ODthuR/MO8bwiiAGsEGUsiZC3EIwxPm+3PP009h/9Lysq32Zr49YQB6eynf9RzsAOk3XXTiwlJezs2AeIc2pChEsYD3GZIRnAxkxXflaOzyBalFxEjCFmoD5hSNVvVbZRauCuHDvTW6pxHbf6FWPUc/dyJRGLWH0VQuLVW2HVL7SOYkQkSSL3z38m43vfC9julvdu4Sef/8T3zZnXwRV/VyG60IuZPo20r301YJtmazN13XXMzIj8FWdhdMQAVog+h76Az30nU4mZPh36bEzqiNNmpUQtti7lA3zXq8NqLrtc9O3YScysmWxr2kZ6TDo58TkqBykIKpIkZRU2BANY48SJ6JKSvLb+GXQG/n7O3/nGjG+o3r8Xaxu01Wh2Bm565yHcBiPWvCIkICc5hoevmE63+SNuXHEjNpdNk7iEMaarAaoj7xhM7JzZGDMzA7aZkjaFXc27cJ14xtdpB4dVxehCx9nWRs+GL3D39QVst71ReX8XA1hBDGCF6FP1Eaz8qTKoO0HMTOVNb3FbJjuaIy9roV9HdgDy8B9iJYmJzzxDyo03UtVexcyMmWKlRIh8c2+B+d9UvRtJkki84HyM2dle12dlziLFkqJ6/146DkP8OM0GsNZt24mbOoVP7l9OzS8v5PN7l3HZ7By+aPiCtr42zHqzJnEJY8z4GXB0N7j8JDsKU862Nlr++RS2ykq/baanT6fH0UNNR433jZpP4f9y4HDkJ2DsWbuWgzfdhK0q8C6yvMQ8bp1+q3blyoSwIerACtEnexYgK4O6/NO9bhknTECfmsrUI0b+3lZJt72beFO8JmEGVX3/duhhbiOUdLqBTH8vFbxEt0P9zK2CoLpJF4asq6yf/WzQtRZrC69Xvs7ZE88mPyk/NIGMnw4/LAcNsh/LDgd9u3aRct213tdlme1N21mUsyjkMQljVPYscPZB0z4YH0HHYdxuGn/9a5DdmIuLfTaZnnHsfH1xynFtjmwF2QXpJaGIVFXW7duRLJYha8AWpxTzvZTAW66FsUGswArRxzOIO7Jt0C1JkoiZNYuM6laKkoto7G0MaWiqqd8KSRMgPmNYzTve/i9dq1cDoJN0JJoS1YxOEEJDlqFp/4jOgo+qO7fba8ubzWXj8S2Ps+7IupD070WDHRSujg5iF8wndv4Cr+uHuw7T2tcqtvkJoeNJ3FgXWauRhrQ0jBMnYt22zW+b/MR8EowJg3eN1W+DtGIl90eEs27fTsy0aUgG/+tqDreDTQ2bsDqjY9u0MDpiACtEn4RxkJB1LL38CTJ/+APKnn2R1y99ncLkwtDGppb6rSNKo9/8l7/Q/sq/eX7v8zy4/kFtalcKghr+cS58/rjq3bj7+qhYeBot//znwLWsuCwyYjLY1rhN9f4HPH0RrP9L6Po7jiE9nYl/+xsJy5Z6Xd/WtA1QtlQLQkikFkLRWRE5mIuZNZPebdv8fg7rJB0/XfhTriq9yvuGhsnbgsltt2Pbs5eYWYGfYfa37ueW92/hk8OfhCgyIZyNaguxJEmpwMtAPlALXCPLctsJbZYCvz3u0iTgOlmW35Ak6WngDKCj/97NsixvG01MggAob+otvs+UmAuPDVplWY6Os5+3fujzzK8vrvZ27NXVJF1yCSsPrMTuskfH/wNB8CRyqlc/w7jOYkGfke61ciJJErMyZ4VuANvbCrVroPjs0PR3Arfdjs5kGnQ9zZLGuXnnUpRUpEFUwpgkSfDl17SO4qTEzp5N51tv46irw5Sb67PNeQXneV/oboTOOs3OvgdT3+7dyA4HlpmBB7Dbm5QETrMyZoUgKiHcjXYF9l5glSzLJcCq/j97kWX5I1mWZ8myPAtYBvQCHxzX5G7PfTF4FYLmir/Brav83m594QXeefJ+znv1PNyyO4SBqSQ2FVLyhtXUukPZhmScOY3dzbvFNj8huuScAo17QpKdM3b2bKzbdyC7j72HzM6cTX1PPUd7jqre/8BAPXuW+n35UH3xxTQ8+NCg66flnMZjZz6G/rjSOoIQEk5bxCVyipk1C/T6gImcbC4bHx38iAOdB5QLOgOc+5Bmk1fBFDN1KvmvvEzcggUB221v3E5mbCbj48aHKDIhnI12AHsp8Ez/758BLhui/VXAu7Is946yX0EIzJIEOv//vDv+8yrjV+6gvqeeqvbQnJdTzd634ZNfg3t4A3Hrtu2g03E4x0yfq08MYIXokjsX3M7+zNzqipk1C3dHB/ba2oFrszJmYdKZqO6oVr3/Y8nbQv8z7GxpwXHgIMasLK/rdpedtr42P68SBBXVrIGHcyPuHKy5rIyyTRtJOPNMv236nH3c8dEdvFfznnIhNhVO+w5kTgpNkCqSTCZiZsxAn5AQsN32pu3ieUUYMNoB7DhZlo/0/74BGDdE++uAF0+49pAkSTskSfqtJEl+8+1LkvR1SZI2SZK0qampaRQhC2OC0w5v3g47/+PzdsysWcRW1CG55YHzWhFr539g63MBB+zHs9VUYy4tZVvPfkDUUxOizEAyl02qdxUzaxYA1q3HtixPSZvCui+tY2H2QtX758g25exfTIhL96AkXQEGnVvb0riFJS8vYWPDxpDHJIxx6SXgskfcAFbS6dDFxARsk2ROoji5mK1N/e81hzdB55GAr4kUTX/8E71bAx/7aOptor6nXjyvCAOGfOKVJOlDSZJ2+fi69Ph2snL63G8mGEmSsoDpwPvHXb4P5UzsqUAqcI+/18uy/HdZlufKsjw3I2N4mVaFMcxgUurB7n/X5+2YWTOh18q0zsTQJlxRw5FtIzoHk/Ob35D37L8wSAZmZ84W23GE6JIwHm74D8y4dui2o2QqKCD929/CMuVYTUK9To9JP/hcqCrSS2HKZaHp6wTWbdvBYMAydarX9W2N25CQmJQa+StDQoRJGA8J2VC/RetIRqxn7VoO3HQz7l7/GxRnZ85me+N2XG4XvPxlpd59hHMcbaT5j3+kb0fgHTPJlmSePf9ZlucvD1FkQrgbcgAry/LZsixP8/H1JnC0f2DqGaAGqklyDfC6LMuO4773EVlhA54C5o3uP0cQjpNzit9VGM/KyRlt4wcSA0Sk3lZoqx3RAFaSJPQJCVw76Vr+df6/RAInIfqUnANx6ap3I+l0ZNxxB5bJk72uf1b3GV959yv0OlQ+LXPWT+HswfVoQ8G6bRuWSZPQWSxe17c1baMouYgEU+DtgIKgipw5EbcCCyA7nfRu2IB15y6/bWZnzqbb0U1l3Qboqtfs7HswWXf07+QYIoGTUWdkVuYsMeEuDBjtFuK3gJv6f38T8GaAttdzwvbh4wa/Esr5Wf8/uYIwUrlzlcFdT/OgW8YJEzBkZDCTXM7JOydyEzl5at0OcwDb+d771P3ghzi7u0TpHCF6dRyGz3+vTPCozG2z0btpE+6enmPXZDdbG7eyq1nFjzR777DPvash6bLLSP3Kl72uuWU3Oxp3iPI5gnZy5kBrdUh+9oPJM4CzBthKOztT+ZzfXt2/syxnrupxqc26bRuS0Yj5uF0svryw9wVxLEHwMtoB7C+BcyRJqgDO7v8zkiTNlSTpSU8jSZLygQnAicWbnpckaSewE0gHHhxlPIJwjOfN3cdsrCRJFK/6kAUP/J7vzfkeOilCSyJ3HgFj3LCTuHSv+ZSezz7j4+b1LH1lKbUdterGJwhaaD8IK/8HDqv/wGPdsoUDN36Z3i3HHjw957RUPV//+e/gkUIl66oGkq+4nKRLLvG6Vt1eTZejS5S5ELRTci6c/YDWUYyYPikJU2GhV1muE+XE5/DmpW9ylV2nZCHOmhG6AFVi3bYd8+TJPstxeThcDn6z+Td8fOjjkMUlhL9R1YGVZbkFOMvH9U3Arcf9uRbI8dFu2Wj6F4SAsmcpZ8ScfT5vS/1vmFanlda+VnLiB/0TDX+zb1DO+umH96Ns3bYdy6yZbG3aRpe9i+z4bJUDFAQNZM0ESa8kOilV98yUZfoM0OmwbttG/OJFwHEJVxpVrEd7eCMk5oLBb+5D1diqa5AMeowTJngdQUiPSeeBhQ+wICtwOQxBUM346cpXBIqZPYvuD1f5rU8vSRKFyYXKpPz46WAMnPgp3MluN84jR0g499yA7Xa37MbmsjEnc06IIhMiwagGsIIQ1kxx8B3/KzCO+nrq77+ff8xs5UBZMs+c/4zftmFtmINXV3s79qoqki66kC1HP2V6xvTQJZsRhFAyxUHmlJBkItbHx2EuKRm0cjIzYyYfHPgAt+wO/g4PtxsOb4ZpVwT3+w5T85/+RO8XX1D8qfemqmRLMleWXqlJTIIwoKcZ2g8cy0geIeIWnobzaCPuri70iYk+21S3V/OviaV8a+IFQ5b9CHeSTkfRqg+RbYF3kWw6qryPzx43/FwfQvSL0H2TgjACsqx8nUCfkkLvxk2cetjCruZd2F12DYIbhZYqeGIZHNwwrOa9W5TMjLpZ09nbupdTxkXWh7sgjIgnmUsIzonGzJqFdft2ZJdr4NrpOadzyrhT6LJ3Bb/DlgqwdUDuqcH/3kOQZZnezZuJmXvKoFWid2vepaGnIeQxCYKX9++HF6/3+bkfzpIuupCJTz7hd/AK0Ofq49VDK9mid/htE0kkSRqUCO5EW45uoSCpgFRLaoiiEiKBGMAK0a1qNTxSDM0Vg27pYmKImTqVidXd2N12dROuqOHQF8oDujl+WM1lpxPz5Mnsy3Lhkl2ckikGsEIUy50L9h7oPKx6V7GnzMHd3Y2tvHzg2jl55/CHZX8gyZwU/A49Z3s1GMA66upxNjQQe4p3ApmjPUf50ac/4oPaD0IekyB4yZkD3Uehs17rSE6K2+5/Mr20s4lYnZEtDervLlHbkQceoPHxxwO2kWWZA50HxIS7MIgYwArRLSELepv9biWMPXUupvKDmBxEXoa7wxvBlAAZw6u3mHjuuRS+/hqZSTncOPlGZmaKguBCFJt2FdxXB8kTVe8qfskS8l54AXNR0aB7qpTSyZoJZ9wLacXB/95DsG5W3ktj53o/UG5pVHZ4nDJePGgKGvNsHQ7BEYJga/jFg9Rc7v9ogGH7K8ywWtkayeX/UM6/dq54F1dzS8B2kiTx38v/y91z7w5RZEKkEANYIbqllyqDvMN+6sHOnQtOJ0u7cgbOWUSMwxuVmWadfsimsss1sL2xOKWYe+bdQ5wxTu0IBUE7plgwBt6aFiz65GRi58weSAzn8fCGh7n8zcuD3+H46bD0PtCF/iO8d9NmdImJmEtKvK5vathEnDGOspSykMckCF7GzwC9WdmlFGGM2VnYq6pwNjX5bnB4I3NixlPeVq7O8YQQsVVU4O7sHDQR5oskScQaY0MQlRBJxABWiG46PeTM9r8CO2cOsQsWcM2k67hzzp2hjW007D1wdDdMmDes5r1ffEH5goV0btvCjqYdONzRcX5GEALa/DS8fWdIurLu2k3j737nVV85LzGP+p566rrrgteRvRdqPweHNXjfcwQy7vguE/70RyS998TZ5qObmZ05G4NO5IYUNGYwKZO7h4aXHyKcxM5Vtub3bh5c/g9rOzTvZ3bGbHLiczjScyS0wQWR578v5pTAA9hfb/w1j28JvM1YGJvEAFaIfrnzoGEX2LoH3dInJpL39FPMO/9mpqZP1SC4k9TXAZMugPzFw2reu3ET7u5uKhJ6uGHFDaw5vEblAAUhDLTWwNbnQjLY69u7h5a//g17Te3AtbnjlYfRoB5POLwRnr4ADnwevO85AoaMDGJP9T5722HroKqjSpxTE8LH8ofg0j9rHcWIWaZMQYqNpXejj0n3/pr284sv4t0r36U0pTTE0QWPddNmDOPGYczxX75QlmVWVK8QieEEn8QAVoh+pcthwbf81oMFcHX3sLpmJWvr14YwsFFIzIZrn4PCM4bVvHfzZsyTJ7GlZx+AqKcmjA0T5oPbAfUq1mPtN7BysunYYLU4uZhkczKbgplwxZPASYMSIdbt22l95hncvd7nepPMSXx0zUdcWSJK6AhhIucUyIi8AZ5kNBI7axa9m3y8Z7RUgqRDylV+9uUIy7J8PGNuLokXXeiz3q3Hgc4DtPS1MGeceF4RBhMDWCH6TZinzMbGpfu83f3555TPm8fr/32MZ3ZHSC1Y2/DPvsh2O9bt24k9ZS6bj25WHqotyerFJgjhYsJ85deD61TvypSfjz493evBUyfpmDtubnDP1x/eCGklEJMSvO85TJ0r3qXxN78Fw+Btwukx6aRYQh+TIPgky8rui4oPtY5kxJKvv46U668bPECd/w34UTVYklhRvYKz/302PY4ebYIcpcy7vs+4uwMnZhpIDCcqJgg+iAGsMDY47dC03+ctS1kZuN0saU5ja+PW8D8fKsvw+9nw3n3Dat63Zw9yXx/mU2axtXGr2OYnjB1xaZBeBgfXq96VJEnEnjp30MrJ1WVX840Z38AtB6Eerdut/LdMXDD673USejdvJmbGDHQnJKv61Re/YuWBlZrEJAg+SRJ89lvY9A+tIxmxxHPOIeW663yvTvZPXKVYUmi0NrLl6JYQRzd6ru5u5GHU5/6i4QtSLakUJBWEICoh0ogBrDA2fHA/PLEMXM5Btwzp6Zjy8ymqtWF1WtnTskeDAEegpRJ6miBjeNk+9WlppH396xwoiKPX2cup40NfO1IQNFN6LlhUqMXqQ+zcuci9VpxtbQPXTss+jctLLkcnBeHjtmkv9LVD3mmj/14j5OrspG/PHmLneSeO67R38vze56lsrwx5TIIQ0IT5SiKnCNxq66ivx7pr97ELR3fDC9cOTMTPypyFQWdg49EIK/8HHP3FL6i+5JIh242PHc9FhRcF3GYsjF1iACuMDbnzwN4Njbt93o499VRidx9A55bDvx7sgf5zuhOH9xBrmjCBzLu+z+TiBTx57pMszF6oYnCCEGbOfRCufDIkXaVcfTUlaz/HkOK9lfZQ56HgnINNK4GvrYSS5aP/XiPUu2kTuN3ELZjvdX1TwyZkZE4dJybGhDAzYR70tkBLldaRjFj9j+6h4YEHjl2oWQPl74FJKX8XY4hhRvoMNh4J8+eVE8iyTM/6DYPKcPly5yl3cvepov6r4JsYwApjg2fL3UHfafVjF8xH7u5mcU8u+1r3hTCwk3BwHcSmQ/rQHwCy3U7P+vW4+/ow683Mz5pPoikxBEEKQphxu1TvQjKZkHzUZn1s82P85POfjL4Dg0l5KI9LG/33GiF77QF0cXFYZs70ur7+yHpiDDHMzJjp55WCoJEJ/Z/7h9Q/QhBsMafOpW/PHlxd/fkuDq6DpAmQlDvQ5tTxp7KndU9E1YN1HDiA8+hR4ubPD9iuy94V0UmqBPWJAawwNiRPgMQcv8lc4k47jXH33cvPLv09jyx5JMTBjdCBtcqAfBjbaqw7dnDw5lto++Qjfr/l99R01IQgQEEIM89cDG98OyRdtb38CrU33uj18HXq+FOp666jvrv+5L+xLMNH/weHfdSHDIG0r95CydrPB51/3XBkA3PGzcGoN2oSlyD4lV4KlmRoLtc6khGLm78A3G6lnI4s95999949deaEM/nSpC9hc9k0inLkejZ8AUDsvMAD2J9+/lOuf+f6UIQkRChRcVwYOyYugAPrlA+DEwZ/hpQUUm+6SaPARsDthjPugcSsYTXvWb8BdDoqCkw8se4JZmXOEgkRhLEnJgUOhqhEltuFddNmHAcOYMrPB2DeeOXc6Poj67mi5IqT+77tB+GTXym7L3K1ScSmM5u9/tzn7CPeFM/p2adrEo8gBKTTwZ07wRJ5u45iZs9CsljoWb+OhFl50N0wKHnbtPRpTEufplGEJ6d3wwYMmZmYCvL9tnHLbr5o+IJlE5eFLjAh4ogVWGHsWPgduOLvfm+72ttp/+/b/PyTn/DyvpdDGNgI6HQw+wYoGt4be+/69VimTGFD9y4MkkFkIBbGpokLlQFgR53qXcUuUB4ye9Yf27ZYnFxMRkwG6+tHsZXRk0k5L/Rn2Ls+/JADN92Mo7HR67rFYOH5C57ny1O+HPKYBGFYInDwCspkUeycOfSuWw99HUpCqrzBE0VOtzP8E08eJ/nqq8i8+4cBEzPtb91Pp71zYOJPEHwRA1hh7MiZAwWL/W697d2yhSM//BE9W7fwbu27IQ5umA6sg+aKYTV1W630bt9O3IL5fHHkC6alTyPOGKdygIIQhgbOwIemHqxh/Hh61h0brEqSxIKsBWxo2HDy57oOrgVzImROCVKkw9f92Wf07dqFITXV67orBOeKBWFUelrgpRtgf5h+pgcw7r57mfDkE5A9G772AWROGtTm6d1Pc+1/r6W1r1WDCEcubuFCki6+OGCbDUeUXCXzswJvMxbGNjGAFcaWmjWw+w2ft2LnzgWdjsVHU9jeuD08C4S/8wN490fDatq7ZQs4HEinzGBXyy7xYSCMXeOmgykBDnyueleSJBG3cCG9GzZ41Tq8ffbtvHbJaydfEuLAOmUVRqcPUqTD17t+A7Fz5yIZjp06kmWZi9+4mL9s+0vI4xGEYbMkQfUnUBF5dYrNJSUYx41T6tj7sSBLmZwb1e6OELHu3Envli1DTuJtaNhAQVIBmbGZIYpMiERiACuMLRv+Cit/6vOWPjERy7Rp5Jd34pSdwSl7EUy9rdC4Z9jlc+LmzSP/pRdpKE4l1hArBrDC2KU3wBl3Q+HSkHSXcM7ZxC9bhrvn2CRYTnwOaTEnmT3Y3gvW1kFn4ELBcfQo9tpaYk/IGlrbWcuhrkMn/98kCKGgNyjb7ms/0zqSk9L+4jO03lwE230fa5qcOpkkcxJr60N0xn8UWv7+d+p/ePeQk3hfnvxlvj0rNEn3hMglkjgJY0v+Ytj3X+U8XPLEQbfj5s+n76mnSHaaWVu/ljMmnKFBkH4cXAfIwzoD98bWOh55fz/17Vayk2P44bkvMyczR/0YBSFcnf69kHWVsGwZCcsGn1N/p/odqtqruGPOHSP7hqZY+GEFOEOfbbRnrbLtOm6h9+DZs83PswIkCGErfxFUfADdjRAfWat63e+9hXWPhZS0YnwN+/Q6PQuyFrCufh2yLJ/8Dg+VyQ4HPevWk3j++UO2PS1neJP0wtgmVmCFsSV/kfJrzRqft+MWLgCnky+555JqSfXZRjM1n4IhBnJPDdjsja11PPTiei769EWyu5uoa7fyk9f38Pb2hhAFKghhSJahtQZaq0PUnYyj3rtszq7mXTyz+xn6nH0j/4aSBEZLkKIbPn1yEgnnnIO5rMzr+tr6tWTHZTMhYULIYxKEEcnr/9wPwRGCYIvLduPsNeCwp/htc1r2aTRaG6lqrwphZCNj3bEDd3c3cYsWBWy3tn4tu5p3hSgqIZKJAawwtmROgZhUqPU9gI2ZO5eiD97nW7f9lW/M/EaIgxtCzRplC6HBHLDZI+/vZ0r9Xi6r/ox4+Qixhb/Bbqjikff3hyhQQQhDshv+fgas+U1Iumv6zW+ouuBC3LZjq6YLsxdid9vZ0rhlZN/s2cthg/8M6mpKWLqU3D/8Hkl37HHB4XKw4cgGFuUsCtsVH0EYkDVTyeArhf78+GjFWpRBac+GDX7bLJ2wlH+c+w/yEvNCFdaIda9ZA3r9oJ0cJ3p006P8dvNvQxSVEMnEAFYYW3Q6ZRW2Yafv2yYTponK1mK37KbT3hnK6AK7+b9wwaNDNqtvtzL36D46TLHU5naiNzfidiZQ324NQZCCEKZ0emUlxs/kVbDFzp2L3NdH78ZjZ+nnjpuLQWdgXf0IsiF31EHVanD5T+SiFmdbG67Owe+Bdred22bcxkVFF4U8JkEYMb0BblkBUy7ROpKRaTuAyX0AY3oC3Wv8n+FNsaQwL2seRr0xhMGNTO+mTcTMmIE+0X9Zo6M9R6loq+D0HFFXWhiaGMAKY8/Fj8M3PvV721ZVRd1dd/GNpy/jf9f9bwgDG0JsKqQXD9ksJ8nMnMZytmSWoUuswG1LR3akkZ0cE4IgBSGMFSyBtlrlDLzKYufNQzKZ6Flz7L0m1hjLKeNOYc3hEQyia/pfX7AkyBEOre3FFyk/fRGuri6v63HGOG6dfiuzM2eHPCZBOGmOPuUrUhhjkc55gPglS3D39ATM3lvdUc1vN/8Wmyv05+SHY+I//0nOo48EbONJRHV6thjACkMTA1hh7IlNDViKQjIa6VzxLksOxbG2bi0OtyOEwfmx/i+w8clhNb2/zECqrYvN44rRx1bj7Cklxqjn7uVlQ79YEKJZwWLlVz9n4INJFxND7Lx5dH/q3dfSCUtJMCXQ6+gd3jeq+VQ59jBumgpRBtaz5jMskyahT0jwuv5Z3Wd027tDHo8gnLTmSvhVvpLEMVLEZ8Ci7zPuwV+T98zTAbfrH+46zD93/ZPNDZtDGODw6UwmjDmBE0l+Xv85GTEZlKaUhigqIZKJAawwNq1+CD58wOct08SJGPMmMq3SQZeji22N20Iamk/r/wxVHw2r6aJkN87EZA5NTkDSOUhiOg9fMZ3LZossxMIYlzEZYtOPrWqqLH7JYuw1NdgPHx64dsPkG3j2gmeJNcYO/Q1kGWo+UQbeutB+XLs6OrBu3078Yu+kK0e6j/CtD7/FqxWvhjQeQRiV1AIlCVrVaq0jGR5Zhn0rwNo+cP78+LrSJ5o3fh4WvYVPDn8SqgiHrelPf6L5b4HP8MuyzNbGrZyec7o4Vy8MixjACmNTazVsfR78fCDEL15CzI5KYt0GPjmk8QdCa42y5bFgeCV9EpYtY9qGtTz2jfO4oOACPvnu18TgVRBAGQRe9zyc+4uQdJewfDm5f/wDhrTBtVLtwznT6uyDomUwOfRn93rWrQe3e1DW0DV1yory4pzFIY9JEE6aTg+FZyoD2ABbccNGcwW8dD3seQOAxt/9jtqrrvbb3GKwMD9rPp8c/iTgVuNQk2WZ9pdepm/f3oDtJElixRUruHPOnaEJTIh4YgArjE3FZ0NPIxz1ncwpfsli5D4bl3QVaz+j6VktKhx6ACu73QO14KZnTOdXS35FjEGcfRWEARMXhKwWpHHcOBLOPhtdjPfP4Ev7XuKMl88YehuxMQYu/SNMv0rFKH3r/mwNuoQEYmbM8Lq+pm4N2XHZFCQVhDwmQRiVomXQdQSa9mkdydBq+p878pWJIkNKCn179njt5jjRGRPOoK67LqzK6dj27sXZ1ET8oqEnvMx6M2kxgyf7BMEXMYAVxqaiZcqvlR/6vB176qlYpkzh/JyzuWfePdrOaFZ/DPHjIX3ocyFdH6yk6uxzOFq+g0Odh9SPTRAijSzD+r/CnrdC0p39cB3Nf/2bVzmdvMQ8uh3dfNHwReAXtx/UbLUo/bbbyP7VL5EMhoFrNpdNlM8RIpfncz8SthFXrISUfEgtBCBuiZLErftT/8cfluQsIcGUwIGuA6GIcFi6Vn8EkkT80jMDtrvr47t4qyo078lCdBADWGFsShgH42dA5Sqft3UxMRS89ipzrvyG9g9rLjuULodhxNC1ehXu7m7esX7BBa9fQFNvUwgCFIQIIkmw5V/DToo2WvaqSpp+9zt6v9g4cG3uuLnEGmL59HCAs7hOO/z5NPjgJyGIcjBTXh4Jy5Z5Xdt8dDNWp5UzJ5ypSUyCMCpJuXDer44NZMOVo0/ZeVV8zsDnvik/H+PEifR86j8B3bi4cXx67aecNfGsUEU6pO7Vq4mZPRtDaqrfNgc6D7DywEq67F1+2wjCicQAVhi7pl+tzG4GWOGQ7Xb2Hd7GaxWvhTCwE1z3vFL6Zwiyw0H3J58Sf+aZrK77mClpU8iIzQhBgIIQYYrPgoPrwKZ+Jt3Y+fORYmLoWn1sssyoN7IweyGfHv7U/+6OQ+vB3gV5p6ke44k6V6yg8733Bl1fmLWQVy95lflZ80MekyAExYJvQuZkraMI7NAGcFqh5NyBS5IkEb9kCT3r1+O2+q/pbtApOybcsv+ET6EiOxwYJ0wg8YILArb7+NDHAGJiTBgRMYAVxq7T71DOl/lZ2XR191C+aDH7//YYv1j3C21mB11O5ddhrL72bt6Mu6MDefGp7GjawdIJS1UOThAiVPHZys6G2hCU07FYiF+0iO5Vq72yiJ454UyO9h5lT8se3y+s+AB0xmEnbwumpj/9mbaXXh50XZIkSlNKMelNIY9JEILCaYfy96Fpv9aR+FewBL694VjZr35Jl1xM2tdvQ3b4L+3X1NvExa9fzH+rtS8XJBmN5D7+O1JvvCFgu9UHV1OaUkpOvEg2KQyfGMAKY5ssQ7fvbbb6+DjMhYUU72zFKTsDb/dTy5NnwXv3Datp16rVSGYz6yfakJFZNjHMt0kJglYmLgBjnN8z8MGWcM7ZOBsb6dt5LGnc0glL+d6c75EZ6yehVMWHkH86mONDEqOHvbYWe1XVoO3DO5p2cP9n93O052hI4xGEoHI74KUblGME4UqSIHOSksTtODEzZpDx7W+jT0z0+9K0mDR6HD0Dq5pacra0DNmmra+NbU3bxIS7MGJiACuMbW99F55Y6ncbccLZZ6HbV02pPY2VB1aGNrbOejiyDRLGD6t5/JlnkPH9O1nd9Dk58TmUJJeoG58gRCqDGYqWgrUtJN3Fn3EGuthYbJXHsoMmmZO4dfqtvrf5tx+Epr3KGbgQ61qt1JuOP2EA+37t+7xb8y5xxriQxyQIQWOKg/xFyipsOGqrhde/Cc2VPm+7rVa6Vq3yuwqrk3Qsm7iMNYfXDJ3lXEWu7h4qz1xK8xNPBGzXZe/ijNwzwurcrhAZxABWGNty5kDHIb/bieLPUt5Ur27M47O6z0L7gVDxgfLrcedgAok//XTSbr6Zh05/iMfOeExkCRWEQK55Fq76Z0i60iclUbJ+HclXXuF1vc/Zx/u173Oo64SM4XEZcP1LMPWykMR3vK7VqzCXlWHKPbadT5ZlVh1cxfys+cSbQrsiLAhBV3YBtFQotVbDTfkHsP1Fv8eGetau5fDt36HnC/8ZzJfnL6fP1TdQs1kLPZ99huxwEDtrVsB2ExMn8vtlv2dyWpifSxbCjhjACmNbyXLl1/3v+LxtLijAVFTEtD096CQd5W3loYutYiUkTYCMSUM27d20CVuF8mGcbElmavpUtaMThMim6//4c4cm2YnOpJwbPT5pU7ejm7s/uZu3q972bmyMgbLzlaypISQ7HLja20k4y3v1tbytnLruOrFKIkSHsvOVX/ev0DYOXypXKskl04p83o47/XQlKdyH/o8/zMmcQ6ollQ9qP1AryiF1ffAB+pQUYmbP9tum19FLfXd9CKMSookYwApjW1IOZM+Bvf4THoy750fk33Uvn177KbMyZ4UmLqdNqf9acs6wEjg1/O8vOPKzB/jD1j8MfhgWBMG3FXfDvy4JSVduu53aa6+j5e/HttSlx6QzO3O29/EEhxU+eUTZShhiktFI4dtvk/7Nb3pdX3lgJRKSyBIqRIfkCTB+Ohxcr3Uk3mzdSvmcALuudBYL8YsX0/3hKq+kcMfT6/TcMfsOzi84X61IA3JbrXR9/DEJ557rVUf6RKsOrmL5q8vZ3xrGCbWEsCUGsIIw+SKo3wIddT5vxy9ZQvwpc7EYLAD+y14Ek9sJZ94HM64bsqmtogJbeTnmc5fy1K6n/Gc1FQTBW2w61H4G3Y2qd6UzmZCR6XzfuzzNufnnUtleSW1HrXKhchV89CC0Vqse04lkpxNJkpBM3lmG443xXFh4Iekx6SGPSRBUccOrcO3zWkfhrXIlOPtg8sUBmyWcczbOpias27f7bXNl6ZWcnXd2sCMclu5PPkHu7SXx/MAD6Hdr3iU7LpvSlNIQRSZEEzGAFYTp18A1/4JY/4W2rTt3UfP3P3DFW1fw4cEQZC41xcFp34GJQ9db7FixAnQ6Nk0143A7NJt1FYSIM/kiQIZ9vo8QBFvSBRdg27MXW/WxwalnW+77tf1JZfa+BTEpkL/Y17dQjePoUcpPX+Rza+LN027m4cUPhzQeQVBVwrhjxwjChdOu7AibuDBgs/gzz0Qymej57POA7Q53HWb1wdXBjHBY4hYuJOvhh4k9da7fNu197ayrX8fy/OUiX4dwUsLsp1cQNJA8AaZcOihl/fG6P/qIvt/+BUdjI+/WvKtuPC4H7Pg39HUM2VSWZTrfWUHcgvn8t/0zcuJzmJ4+Xd34BCFaZE6BlALYG5pt9wnnnw+SROd/jw2Yx8eN55Rxp7CjeYfyALv/PSi7EPTGkMTk0fXee7g7OjAVFnpdP9R5CJfbFdJYBCEkPnoY/vt9raM4Zua18PWPQKcP2EyfkEDh22+R/p3bA7Z7atdT3LvmXqxOazCjHJI+KYnkyy9D0vv/71h1cBVO2cl5Bef9f3v3HR5Vlf9x/H0yKUAICZ0QQpUigogiWFBZFBEsdMQGKi7rWtZ1V1Hsu1hwXfXn4q66iGuviIAIIiiogEiNdATpgRAglSSkzfn9cQcIYSZ9Jgn5vJ7Hh+TeM/ecyfHOvd+553xPAFsmpxMFsCIAafvhhxcgM8nr7nrXXA3WMnpfWxbtWURqdvHBZZntXAzT74AdxWcQzN2zh7yEBIKuuIyf9//MgDYD9G2mSEkZ4wzX2/FDib4wKq+QJk2oc0EvUmfPPmkqwiu/e4VX+74KO76H7FToHJh5uQWlzZlL2JlnElYggM135zP669E8ufTJgLdHxO8yD0PcR5BTecvNHJeVDKX4oii0Vatir/VXtbmKrLwsvt39bXlbV2IZS5eS9N77uHNyiiz39c6vaRnRkjMbKPuwlI0CWBFw1lz97ukTS9cUEta2LWGdz+SsuBRy3bknhvv5w8aZEBIOZxSf8TO0ZUvaL1lM5u/Oo1vjbho+LFJaZ18PfR/1uRZ0RWt42200HDsW8k/crEaGRWKMwX14u7OETts+AWnLMTl795L1yy+nzFlbcWAFh7IOcWmLSwPaHpGA6Hwd5GXBr18XX9bf5j0K/+5Zqs+hAy+8QMLTz/jcf17T84ipG8OsbbMqooUlkvTe+xx+880ikzcBTLpkEpMumaQv3KXMFMCKADTvDhHNneDRh8irr8Zs3ErP/JbM/M13uXJx5zvDGTv0L3JIc0GuiAg6RHfhnQHvKBmCSGk16wK974faUQGpru6ll1L/+pGn3OBN+3Ua1+6bRe6f10JwWEDackzaHGdaRL2BJwewc7bPITwkXAGsnJ5aXQx1m8H6zyu3Hfm5zjz8mB4lWnXgGHdaGinTp+PO9P4EOcgEcW27a1m2fxkJGQkV1Vqf8pKTObJ4MfUGDMAUM7+4Ye2GdG2s6U5SdgpgRcBJ5tBlqLP2qq9hxAMH4qpfnzHhVzCq4yj/ZCPetRQyDzlzcouRsexndoy8ngOb15ByNKXi2yJSU+RkwrppkJUSkOrykpNJ/uwzbF7e8W2NazVkd/puliQsD0gbCqp72WU0efABQlucWHc2MzeT+bvmc3nLy49nYBc5rQS5oMswZ+RVgM59r3b8AEdTSj11oN4112IzM0n/bqHPMte1vQ5XkIu4g3Hla2MJpM2aBbm5RA4Z4rOMtZYJP07gx73FT5ESKYoCWJFjuo0Cd67Pb2NDoqNp/+MPXHr9/Vzb7lr/DH3Z/RME13bWfy1GyqefkrNrF+8dnkv/z/uTmVsF5vGIVEcHN8PnY2HjjIBUl7liBQmPP0HGkhNZRC9aM40GBFXKOs61OnZwhjUX8O3ubzmSe4Rh7YcFvD0iAdPteufaX5nXz3WfQVgktCt+2lBBdc7vQXCzZqR+6XuIcGy9WBaNXMRVrf2bLMlaS8rn06nVtSu1OvoeCRZ3MI7Z22dzKOuQX9sjpz8FsCLHNO0C0d2c+bA+mOBgrNtNYuIOPtz0YcVn57xsPNy7yllGpwh5ycmkz59PxLVXM3PPXC6OuZg6IXUqti0iNUXz7tCoA/zySUCqi+jTB1fDhiR/+pmzITeLkI2zGBjajIV7FnI463BA2gGQMm0aWXFxp2wf2GYgU66cQvcm3QPWFpGAi+4G102Ges0rp/6cDGfa0FmDIKR0Ix1MUBCRgwaR8eNicvf5vm+JDIsE8Gs2cXd6OkH1IogaVvQXXtO3TqdOcB36t+7vt7ZIzaAAVuQYY+CO7+AK3xk3rbWsGTSCr2+9i+eWP8eFr/yHGWviK6b+Y0OSI2OKLZo6cyY2N5dNvVuQkp2ipyQi5WGMk8xp91JI3uX/6kJDiRo6lCOLFpF74ABsmQvZaYzoehu57ly+2PaF39sAkJ+eTsLTz5DyxYxT9rmCXFwQfYGSrMjpz1qIX+1z+pBfBdeGUR/CBUUvieNL1IgRRI0YUeTcWWstdy24i4nLJpa1lcVy1atH6/ffJ+r6kT7LZORmMG/nPAa0GaAv3KXcFMCKFOTyJFbJyfC6e2bcPr4xTei+Yzf1UsJJD13EhOnrKiaInf57JxNhMay1pHw2jdrduvFxzlKiw6O5IPqC8tcvUpOd7bnxWvtpQKqLGjkC8vNJmTYNfvkYIprTtvMI/nreXwOWNCntq6+wR48SNXz4Sdv/E/cfXot7LSBtEKl0h3+DKb9zzsNACwqCtpdBk05lenloixii//YUIdHRPssYY2ga3pTZ22f7JV+GOzubvKSk43X58vWOr8nKy2JIe99zZEVKSgGsSGFfT4DXL/Gazv6FeVv4MrYnwdbNpSubElz3V45ygBfmbSlfnRmHYUMJn7q43TS87VZCxt7I8oTlDGk/BFcxC5+LSDGiWkKr3rBvdUCqC42NJbx3b3J+3QTbFsDZIyDIxa1dbg1YNvGUz6YR1rEjtbqcdXxbVl4W7298n13p/n8SLVIlNDoDmp8La94L2HJaAKTGw9yHi5y2VBLWWjJXryFr7VqfZW7odAPZ+dl8vrXiMy6nzZnL1sv6kL11a5HlGtRqQL9W/Ti70dkV3gapeRTAihTWtAsk/eZkBC5kX0oW8RFNWNuwLf02HgR3EKH1f2JfSlb56oz7ANx50P3mYosal4uo4cOJufI6Zg2excgOvofsiEgpjPrAGc4XIC3+/SoxLzwPV/8Tzh1zfPuGwxt4e/3bfq07Ky6Ooxs2EDVixElPTeZsn0N6brqmJUjNct4YSNwIe1cErs4178HPr0F+TvmO43YT/9e/cvD/XvFZpEP9DvRs1pNPtnxCnjvPZ7nSstaS9N67hLZsSegZZxRZ9nctf8dLfV7StASpEApgRQo7awjUioSVU0/Z1TzKWZv1qzYXEZ2RTNf1LTHBR45vLxO3G1a+BS0vgiZnFlk090AiSe+8Q/4RZ4hzq3qtaFi7YdnrFpETakc5c8nyynlDWUJBYWEQGk5euyHQsN3x7d/v+Z6XVr3EnrQ9fqs7Jz6ekNhYooYMPr7Nbd28u/FdOjXoRI+mPfxWt0iV02UYhNaFVe8Epr78PFj9LrTrC/Vbl+tQxuWi/sgRZCxdSs7OnT7L3djpRvZn7GfRnkXlqq+grFWryN64iQa33FJkYPrD3h/IyPU+NUukLBTAihQWWgfOuQk2zoIjiSfterB/R2qHuFjcvCsTe45hmWss5uDNPNi/Y9nr274QkndAj9uLLZr84YccmPQ801f8jz999yey87PLXq+InGr9dHixIxw56P+6dv1E+hsPs/WSSzm65cQ0hOEdhhMcFMw7G/13Mx159dW0m/c1QeEnMp4vjl/M9tTtjO48Wk9JpGYJi3CC2O0LneDS37YtgLR4OO+2Cjlc1PDhmJAQDr/9ts8yfWL78GivRzm/2fkVUidA0rvvERQZSeQg32vYxh+J597v7mXqulMfCoiUlQJYEW963O6sCbvmvZM2D+4ew3NDuxLdoC4/Ne9KdIN6PDe0K+e1c5Przi1bXQ3PgN73F7uIuTszk5SPPyb88r789/BMUrNTCXOFla1OEfGuSWfISjrl3PeLxS9T5+A0TEgISW+9daIJdZpwXbvrmLFthl/WS8zeuhXrdmOCTr4FaFqnKcPaD+OqNv5dM1KkSur7GNyz4kQyR39a/gbUbQYdB1TI4YIbNyZy8GBSp39B3iHvnxmuIBejOo06vqxOeeUlJ3Nk4ULqjxxBUG3fo9D+t/5/BJkgRnbUdCepOApgRbxp1B6GTYUeY0/ZNbh7DEse7suOSVfzZfO9dPjsn1wz4xrm7phbtrrqt4IrnoLgooPR5E8/JT81lXX92pKQkcC4s8eVrT4R8a1JJ2h9CayYCvll/FKqJBI3w9Z5uHrfQdSI4aR+NYfc/fuP7771rFvJyc/hg00fVGi1ecnJ7Lh+FAdfeumUfR0bdOSpi54iJCikQusUqRbqNnHWYHe7wY9rppKfB/Vi4KJ7wFVx51qD228jKDy82GRKC3Yt4Pnlz5e7vuD69Wn71Wwa3Ob7KXJiZiLTt05n8BmDaRberNx1ihyjAFbEl67DnTlxRchLTsZM/5qLs1owZe2U0i8UvnwK7FxSbDF3VhaH35xK7Qt6MTnvG7o26spFzS8qXV0iUjIX/QnS9sK6af6r46fJzhqQ5/+ehrfeCsZw6I03ju9uHdmaQWcMIjwk3PcxyiDp7XewWVlEDh580va31r/FrjRlHpYaLnUv/Pv8kq8KUBauYBj0Klx0b4UeNqxNG9p/v4jwCy8ssty2lG28v+l9Nh3eVOa6bL5zrxPasiXBDRr4LPf2hrdxWze3dyl+ipRIaSiAFSnKtgXwyc0+v41teOutBNWty9jlddmZtpPZ22eX/NhHEp11X9cVv+5kflISYa1bs3nw2cQfiefObndqjpqIv7TvB03OgiWv+GdZjfQEZ73Z7jdBeENCmjcnavgwUmfOIj819XixiRdP5I6ud1RYtfkpKSS//z4RV/UnrEDG0NUHVvPyqpcrNLmLSLUU0dz512/n/gGIX1Xxx/UwoaFYt/ukOfWF3XjmjUSERPCfuP+UuZ6EiRPZ+6f7sEX8jay17E7bzdVtryY2IrbMdYl4owBWpChHU2HTl7BpltfdrshIGowZQ50la+mX1ZZX414teWKlpf9y0udfWPy3sCExMbR6/z0uHDCW8eeP55KYS0rzLkSkNIyBa16C4VOdnytaVjJEnwMX3HV8U+O776btrJm4Ik+en2atZdGeRSRkJJS72kOvv4E7M5NGf/zjScd/edXLNKzVUHPURIKC4JIHIGEtbP6q4o///fMw9UpI21982TJKfPFFdo66gbyD3hPR1Qutx+1db2fR3kWsSCj9skHZ27eT8tk0ghs1KvKLdGMMk/tO5okLnyh1HSLFUQArUpTOg6FxJ/juaZ+ZCRvcOgZXgwbcvtBwOPMQvyT+UvxxU+Od4cPdRjmLqBchbd435CY62ZAjwyK5pXPR6epFpAK0vACanuWfYzc5E+6Yf9LSOcGNGhEa6zylcGecWG4iMTORvyz6C5PXTC5XlTY3lyOLfyRy2FBqdehwfPu8nfOIOxjHn879E7WDy7EcmMjpousIJ7niwmed+bAVJXmns3TOuaOhXnTFHbeQ+iNGYHNyOPjqv32WufnMm2lapykvrnwRty3de0x86SWCatWi0T13+yyzJ30PCRkJGGOUbFL8QgGsSFGCXHD5E3B4G8S977WIKyKC6Il/p+1DT/LNiPn0jO5Z/HG/f94ZltxnQpHFcvbuZd8DD7DrpecZPXc0Gw9vLMu7EJGyyD4Cn90Ga7yf+2Wy4QvIOOxz975HHmX3uD8cH5rXNLwpozuPZtZvs1h9YHWZqzUhIbSdPp2mDz10fNvRvKO8vOplOjXoxKB2g8p8bJHTiisYLnsYEjfA1m8q7riLngcTBJc+WHHH9CK0dWvq33QjKZ9+Stb6DV7L1AquxYReE7il8y2lOnbGsp85suBbGv7+9z7nvrqtm8eXPM5NX91U9tUZRIqhAFakOB0HQmwvWPgcZKd7LRJx+eXUObc7jWo3wrrdrD24tuhjNunsZCCs38pnEWstCX/7OwQH83qPZDYnbSYqLKocb0RESiU0HFJ2w3fPOMFsee2Lg2m3w5KXfRap3f0cslatIu3LL49vG3f2OKLDo3n656fLdEN4dPNm3BkZmNBQXBERx7e7rZveMb0Zf/54XEGuUh9X5LTVZSiMfBfaX1kxx9u7En75CHqNg3rNK+aYRWh87724GjQgYeLfsT6eIl/e8nKubns1QabkocDByZMJiY2lwZjRPsvM2DaDVQdWcdc5dymjufiNAliR4hgDVz3nPIkNreuzmLWWhGeeZeVf7uCmOTfxzc4ivrm94E5n6ZwipH4xg4wffyRxzJXMy1jBfefeR/O6/r/wiYiHMdD/WUjfBwufKd+x3Pkw+36o08iZY+dD1NCh1O7WjYRnniX3gDN1oE5IHR7q+RBbk7cyZe2UUlWbn57OnnF/IP6vp9ZZJ6QOj1/4OOc3O79070XkdBfkgs6DnDmxuUfLf7zknc7yfJc9VGzRiuCKiKDJgw/gTkn1ORf2mA82fcATS54oMiHTMbH/fpUWr072ue5rYmYiL658kXObnMuQ9kPK1HaRklAAK1ISMec5GUON8ZmR2BhDUK1a1P36J4YktuSppU8RfyT+5EK/fAxrPys2u2HO3ngOTJpEULezeLjxIro17saojqMq6t2ISEm17OWsB/3z67C3HNlDV7wJ+1Y7AXERy3MZl4voSc9hs7PZ/9hjx28qL295OTd2upF2Ue18vrawY6M48g4dotHdJxJGpeekc99397HhkPfhhSLi8dtCePksiC/78H3AWZbvrmUQFlF82QoSOWgQbWbOIKRp0yLLZeRm8MW2L5ixbYbPMtk7dmBzc3FFRVGrY0evZfLd+Uz4cQK57lyeuuipUj3ZFSkt/d8lUhobvoDXe0NWitfdje69h7COHbnh00QaJ+Ux/vvxJ7ISH9gAX/4Z4j4othpXZD0ifteH2Te0xgS5+Mel/9AQP5HKcsWTULcZLHiybK/fvxa+eRzO6OfcyBYjrE0bmjzwAEc3buSrBWu4eNJ3tHn4K2Yv7EVWcheAEq05nfzRR6TNnk3je++hdteugDNs+LHFj/H93u/Jyssq2/sRqSmanwPBYfD5HWWbRrBvjTOH3lrnqW4AHftS3Z2dTeJLL5Oflua13NguY+nVrBfP/vwsvyb/esr+vMOH2T16DPsefbTI+vJtPrERsTzS6xHaRLapkPcg4ospyZCBqqZHjx525cqVld0MqYl2/wxvD3TmxVz/gTO8qJCcPXvYOXwER6Pq8PuhiVzaaQAv9HocpvSF7DT4w48Q4f0bUZufjzvrKK664QDkunPZmbqT9vXb+/VtiUgx4ldDvRif526RjhyEbx6D/s9AeKMSvcRay+wfNjJ+wR6yck8Eq7VDXAy7bC87chYypd8U6oTU8fr6jOXL2T32DsIvupDY117DBAVhreWV1a8wdf1Uxp8/vtQJXERqpJ2L4e1rnHmxQ9/0et33KjMJ3rzcGYJ8z/KAPn0tKGvtWnbeeBPhPXsS+8brmJBT56UeyjrEyC9HEmSCeG/Ae0TXdbIkuzMy2HX77WRv3kLrTz/x+fQ1Nz+XEJfmu0rFM8asstb2KLxdT2BFSqNlL7jyadgyB+Y84HUocGhsLDH/9zJhSUeY0OgmrmxxKXx4PSRth2FTfQevbjf7H3+CXaNv4Y0Vk0k6mkRIUIiCV5GqIOZc59zNz4O4j4qdBgA4T2xyMqFuYxj6RomDV3Cenkz66QBZOXnctuErLty3HoCs3Hy+WZfJ+kPrufvbuzmS4/2pUFjbttTr35+Yf/zjePD6+trXmbp+KsM7DOfmM28ucVtEarTWvZ0cGOs/h/mPl+w12enwwXBnybwR/6u04BWg9tlnE/3Uk2QsXUr8X/6KOyfnlDKNajfitSteIzMvk+UJywFwZ2ay9957ObpuPTEv/tNn8Dp3x1yGzBrC3vS9fn0fIgWVK4A1xowwxmwwxriNMadExwXKXWWM2WKM2WaMebjA9jbGmJ892z8xxoSWpz0iAdHrTrj4Plg5FWb/2euNbPiFF3LGtwsYPGwC/TKyyP11OUv7PUxKdFevh8xPTWXvXXeTOn06i2KP8OrG/7Jg1wI/vxERKbUN02HGnfDVXyDv1BvB49ITnBvYj64v81qS+1KyCMvP5exDv/Hoine57rfFYC0HD7Rj0iWTiEuM47Z5t7ErbdeJar/9FndODsGNGhHzzxdwRUYCztDhVQmruK7ddTx+weNaS1qkNHrfDz3HQV528WXT9sN7Q5ys4yPedtaUrmRRw4fTdMLDpM+fz55xf/Ca2Kljg47cc8ZU/jEtgjYPf8XHg0dz5KefiX76aSKuuOKU8vnufP679r+M/2E8DWs1pEEt78vqiPhDeZ/ArgeGAj/4KmCMcQH/BgYAnYEbjDGdPbufB1621p4BJANjy9keEf8zBq74m5NJNKye87u1Jwey+Xm40rYCkLavHtvmtmDh2x9w/UfXMO3Xacfnnlm3m5TPp/PboEGkLf6BjwaE8+p5B3m297OM7DiyMt6diBSl6wi4+M+w8i14sy/sWnrKuc8vn8Drl8D+X+C820o+5LCQ5lG1yQ4O5ZGLxrGqSQf+uG4GT/80hYtzExjQZgD/6vsv4o/EM+LLESSsW86eu+5m7933kPzBhwDkufOYt3Meu9J24Qpy8UrfV5h48UQlVxEpLWPgquedFQnAOe93/eS97O6lcGCjE7x2GhiwJhanwZgxRD/3HNlbtuA+empm5Rlr4nnh8y0kHUzG1NrNh3238eyAzsyMOXU+66oDq7h5zs1MXjOZgW0GMuVK39MZRPyhQubAGmMWAQ9Ya0+ZmGqMuRB4ylrb3/P7BM+uScBBoJm1Nq9wuaJoDqxUGdY6F7Zf5zlz3KLPAXeuM1c28xD8eT25WYYDEyeSPn8BecGGX6MtiY1DWTXmfB7o8QBh4x7jQFYiz/dOIvLcHjzS6xE61O9Q2e9MRIqyeQ7Mutc5z/tMgD4Pw+HfnLly6fugaVcYNgWanFnmKmasiWfC9HXOHFhruXbHEm7Z9A11wlx0XvwDQbVqsWPik6T8sJBaew4SFB7Oyv6tWNevLenuTOIS40jLSePmM2/moZ6BWb5DpEZ4dzBsXwhNu0DTs5wnsw3aOgnfANIPlG2+fAC4MzMJquMEm7t/Pw6bl0tww0YsW7WVMw78xtetevJa9wGENf6GkPrLMEDXxl1oUbcFz/R+hhBXCI8ufpQl8UsYf/54BrQZoBEd4je+5sAGB6DuGGBPgd/3Ar2AhkCKtTavwPYYXwcxxowDxgG0bNnSPy0VKa1jH9pBLmdx8t3LwBXszJc75yYIb0xIRBAtJk/m6ObNpM6ciVn2I02Tk1mcl0Wt4Fq0mPJfQkIyeSRjPz2a9tCFQKQ66DQQ2l7mzIuLjHW2hUVAi/PgnJegff8yP3k9ZnB355L4wrwt7EvJYvW5/bji/rFcWfsIQbVqARCafISGLTtQ95Y7qHv1QCateJD9SesIDwmnT2wf+sb2pU9sn3K1Q0QKGfUhrH4Htsx1nsS6QiC88Yn9VTR4BY4Hr+6jRwlp1oyjmzaRtTceVxbMaX0h37foBu7aZB8YRE5Sb0Ii11ArOpV1h9Zx+OhhmoU34/7z7uexCx6jdrD39WBF/K3YJ7DGmAVAMy+7HrXWzvSUWYTvJ7DDgaustXd4fr8FJ4B9CljmGT6MMSYWmGut7VJco/UEVkRERESkYlw86TviU05dWismqjZLHu5bCS0SKccTWGvtqTO3SyceiC3wewvPtsNAlDEm2PMU9th2EREREREJkAf7dzwxZcGjdoiLB/t7zz4sUpkCkclhBdDek3E4FBgFzLLOo9+FwLFV3ccAMwPQHhERERER8RjcPYbnhnYlJqo2BufJ63NDux6fyiBSlZQriZMxZggwGWgMpABx1tr+xpjmwJvW2oGecgOB/wNcwFvW2mc829sCHwMNgDXAzdbaYnOUawixiIiIiIjI6cvXEOIKyUIcaApgRURERERETl++AlgtBiciIiIiIiLVggJYERERERERqRYUwIqIiIiIiEi1oABWREREREREqgUFsCIiIiIiIlItKIAVERERERGRakEBrIiIiIiIiFQLCmBFRERERESkWlAAKyIiIiIiItWCAlgRERERERGpFhTAioiIiIiISLWgAFZERERERESqBQWwIiIiIiIiUi0ogBUREREREZFqQQGsiIiIiIiIVAsKYEVERERERKRaUAArIiIiIiIi1YICWBEREREREakWFMCKiIiIiIhItaAAVkRERERERKoFBbAiIiIiIiJSLSiAFRERERERkWpBAayIiIiIiIhUCwpgRUREREREpFow1trKbkOpGWMOArsqux1FaAQcquxGyCnUL1WP+qRqUr9UPeqTqkn9UvWoT6om9UvVUx36pJW1tnHhjdUygK3qjDErrbU9KrsdcjL1S9WjPqma1C9Vj/qkalK/VD3qk6pJ/VL1VOc+0RBiERERERERqRYUwIqIiIiIiEi1oADWP/5b2Q0Qr9QvVY/6pGpSv1Q96pOqSf1S9ahPqib1S9VTbftEc2BFRERERESkWtATWBEREREREakWFMCKiIiIiIhItaAAthyMMVcZY7YYY7YZYx72sj/MGPOJZ//PxpjWldDMGsUYE2uMWWiM2WiM2WCMuc9LmT7GmFRjTJznvycqo601iTFmpzFmnefvvdLLfmOM+ZfnXFlrjDm3MtpZkxhjOhY4B+KMMWnGmD8XKqNzxc+MMW8ZYxKNMesLbGtgjJlvjNnq+be+j9eO8ZTZaowZE7hWn/589MsLxpjNns+oL4wxUT5eW+TnnZSNjz55yhgTX+AzaqCP1xZ5vyZl56NfPinQJzuNMXE+XqtzxQ983QufTtcWzYEtI2OMC/gV6AfsBVYAN1hrNxYocxdwtrX2TmPMKGCItfb6SmlwDWGMiQairbWrjTERwCpgcKF+6QM8YK29pnJaWfMYY3YCPay1XhfM9tx03AsMBHoBr1hrewWuhTWb5/MsHuhlrd1VYHsfdK74lTHmUuAI8K61totn2z+AJGvtJM/Ndn1r7UOFXtcAWAn0ACzOZ9151trkgL6B05SPfrkS+M5am2eMeR6gcL94yu2kiM87KRsfffIUcMRa+88iXlfs/ZqUnbd+KbT/RSDVWvt3L/t2onOlwvm6FwZu5TS5tugJbNn1BLZZa7dba3OAj4FBhcoMAt7x/DwNuNwYYwLYxhrHWrvfWrva83M6sAmIqdxWSQkMwrn4WWvtMiDK8wEsgXE58FvB4FUCw1r7A5BUaHPBa8c7ODcehfUH5ltrkzw3FvOBq/zVzprGW79Ya7+x1uZ5fl0GtAh4w2owH+dKSZTkfk3KqKh+8dzzjgQ+Cmijargi7oVPm2uLAtiyiwH2FPh9L6cGSsfLeC56qUDDgLROMM6Q7e7Az152X2iM+cUYM9cYc1ZgW1YjWeAbY8wqY8w4L/tLcj6J/4zC9w2GzpXAa2qt3e/5OQFo6qWMzpnKdTsw18e+4j7vpGLd4xnW/ZaPIZE6VyrPJcABa+1WH/t1rvhZoXvh0+baogBWTkvGmLrA58CfrbVphXavBlpZa7sBk4EZAW5eTdTbWnsuMAC42zPkSKoAY0wocB3wmZfdOlcqmXXm+WiuTxVijHkUyAM+8FFEn3eB8xrQDjgH2A+8WKmtkcJuoOinrzpX/Kioe+Hqfm1RAFt28UBsgd9beLZ5LWOMCQYigcMBaV0NZowJwTlhP7DWTi+831qbZq094vl5DhBijGkU4GbWKNbaeM+/icAXOEO6CirJ+ST+MQBYba09UHiHzpVKc+DYEHrPv4leyuicqQTGmFuBa4CbrI8kIiX4vJMKYq09YK3Nt9a6gSl4/1vrXKkEnvveocAnvsroXPEfH/fCp821RQFs2a0A2htj2nieYIwCZhUqMws4lr1rOE7yh2r7bUd14JlvMRXYZK19yUeZZsfmIhtjeuKcB/piwU+MMeGeJAIYY8KBK4H1hYrNAkYbxwU4CR/2I4Hg8xtynSuVpuC1Ywww00uZecCVxpj6nmGTV3q2iZ8YY64CxgPXWWszfZQpyeedVJBCuRKG4P1vXZL7Nal4VwCbrbV7ve3UueI/RdwLnzbXluDKbkB15clCeA9Op7qAt6y1G4wxfwdWWmtn4fzP854xZhvOBPdRldfiGuNi4BZgnTmRtv0RoCWAtfZ1nC8T/miMyQOygFH6YsGvmgJfeOKgYOBDa+3Xxpg74XifzMHJQLwNyARuq6S21iiem4Z+wB8KbCvYLzpX/MwY8xHQB2hkjNkLPAlMAj41xowFduEkQcEY0wO401p7h7U2yRgzEefmHODv1tqyJLgRL3z0ywQgDJjv+Txb5llloDnwprV2ID4+7yrhLZx2fPRJH2PMOThDIXfi+Swr2Ce+7tcC/w5OT976xVo7FS+5FXSuBIyve+HT5tqiZXRERERERESkWtAQYhEREREREakWFMCKiIiIiIhItaAAVkRERERERKoFBbAiIiIiIiJSLSiAFRERERERkWpBAayIiIiIiIhUCwpgRUREREREpFr4f2zpzDDYdlSWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "dt = 1.\n",
    "T = 20\n",
    "N=1000\n",
    "f = simplify(np.array([term.series(h,0,1).removeO() for term in series]))\n",
    "\n",
    "def solve_truncated_modified_equations(order,dt):\n",
    "    f = simplify(np.array([term.series(h,0,order+1).removeO() for term in series]))\n",
    "    f_ = lambdify([p,q,h],f)\n",
    "    \n",
    "    def f_p_vec(t,u,h=dt):\n",
    "        return f_(*u,h)\n",
    "\n",
    "    soln = solve_ivp(f_p_vec,[0,T],IC,t_eval=np.linspace(0,T,N),rtol=1.e-12,atol=1.e-12,method='RK45')\n",
    "\n",
    "    return soln.t, soln.y\n",
    "\n",
    "tt = []\n",
    "yy = []\n",
    "for order in range(5):\n",
    "    t, y = solve_truncated_modified_equations(order,dt=dt)\n",
    "    tt.append(t)\n",
    "    yy.append(y)\n",
    "    \n",
    "rk2 = rk.ExplicitRungeKuttaMethod(A,b)\n",
    "\n",
    "f_ex = lambdify([p,q],f)\n",
    "f_ex(0.,1.)\n",
    "\n",
    "def f_vec(t,u):\n",
    "    return f_ex(*u)\n",
    "\n",
    "\n",
    "myivp = ivp.IVP(f=f_vec,u0=np.array(IC),T=T)\n",
    "\n",
    "t_rk2, y = rk2(myivp,dt=dt)\n",
    "y = np.array(y)\n",
    "y_rk2 = y[:,0]\n",
    "\n",
    "plt.figure(figsize=(16,12))\n",
    "\n",
    "plt.plot(t_rk2,y_rk2,'o')\n",
    "for i in [0,2,4]:\n",
    "    plt.plot(tt[i],yy[i][0,:],'--')\n",
    "\n",
    "plt.legend(['RK2']+['$O(h^'+str(p)+')$' for p in [0,2,4]],fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, we see that including more terms in the modified equations yields a solution that is accurate to longer times.  But what is remarkable is that all solutions of the modified equations (like the numerical solution from the RK method itself) seem to be indeed periodic.  This suggests that the truncated modified equations are energy-conserving at every order.  Let's check this by looking more closely at the modified equations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Structure of the modified equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we generate the modified equations to a higher order than before; this may take a few minutes if you are running the notebook yourself.  Then we extract the numerator and denominator of each of the series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{q \\left(15 h^{6} - 84 h^{4} p^{4} - 168 h^{4} p^{2} q^{2} - 84 h^{4} q^{4} + 560 h^{2} p^{8} + 2240 h^{2} p^{6} q^{2} + 3360 h^{2} p^{4} q^{4} + 2240 h^{2} p^{2} q^{6} + 560 h^{2} q^{8} - 6720 p^{12} - 40320 p^{10} q^{2} - 100800 p^{8} q^{4} - 134400 p^{6} q^{6} - 100800 p^{4} q^{8} - 40320 p^{2} q^{10} - 6720 q^{12}\\right)}{6720 \\left(p^{14} + 7 p^{12} q^{2} + 21 p^{10} q^{4} + 35 p^{8} q^{6} + 35 p^{6} q^{8} + 21 p^{4} q^{10} + 7 p^{2} q^{12} + q^{14}\\right)} & \\frac{p \\left(- 15 h^{6} + 84 h^{4} p^{4} + 168 h^{4} p^{2} q^{2} + 84 h^{4} q^{4} - 560 h^{2} p^{8} - 2240 h^{2} p^{6} q^{2} - 3360 h^{2} p^{4} q^{4} - 2240 h^{2} p^{2} q^{6} - 560 h^{2} q^{8} + 6720 p^{12} + 40320 p^{10} q^{2} + 100800 p^{8} q^{4} + 134400 p^{6} q^{6} + 100800 p^{4} q^{8} + 40320 p^{2} q^{10} + 6720 q^{12}\\right)}{6720 \\left(p^{14} + 7 p^{12} q^{2} + 21 p^{10} q^{4} + 35 p^{8} q^{6} + 35 p^{6} q^{8} + 21 p^{4} q^{10} + 7 p^{2} q^{12} + q^{14}\\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[q*(15*h**6 - 84*h**4*p**4 - 168*h**4*p**2*q**2 - 84*h**4*q**4 + 560*h**2*p**8 + 2240*h**2*p**6*q**2 + 3360*h**2*p**4*q**4 + 2240*h**2*p**2*q**6 + 560*h**2*q**8 - 6720*p**12 - 40320*p**10*q**2 - 100800*p**8*q**4 - 134400*p**6*q**6 - 100800*p**4*q**8 - 40320*p**2*q**10 - 6720*q**12)/(6720*(p**14 + 7*p**12*q**2 + 21*p**10*q**4 + 35*p**8*q**6 + 35*p**6*q**8 + 21*p**4*q**10 + 7*p**2*q**12 + q**14)), p*(-15*h**6 + 84*h**4*p**4 + 168*h**4*p**2*q**2 + 84*h**4*q**4 - 560*h**2*p**8 - 2240*h**2*p**6*q**2 - 3360*h**2*p**4*q**4 - 2240*h**2*p**2*q**6 - 560*h**2*q**8 + 6720*p**12 + 40320*p**10*q**2 + 100800*p**8*q**4 + 134400*p**6*q**6 + 100800*p**4*q**8 + 40320*p**2*q**10 + 6720*q**12)/(6720*(p**14 + 7*p**12*q**2 + 21*p**10*q**4 + 35*p**8*q**6 + 35*p**6*q**8 + 21*p**4*q**10 + 7*p**2*q**12 + q**14))]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "series = bs.modified_equation(u, f, A, b, order=7)\n",
    "series = simplify(series)\n",
    "series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "rhs_p=simplify(series[0])\n",
    "numerator_p = rhs_p.as_numer_denom()[0]\n",
    "denominator_p = sympy.factor(rhs_p.as_numer_denom()[1])\n",
    "rhs_q=simplify(series[1])\n",
    "numerator_q = rhs_q.as_numer_denom()[0]\n",
    "denominator_q = sympy.factor(rhs_q.as_numer_denom()[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we loop over the terms (by powers of $h$) and simplify (symbolically) the ratios:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{h^{6} q}{448 \\left(p^{2} + q^{2}\\right)^{7}} - \\frac{h^{4} q}{80 \\left(p^{2} + q^{2}\\right)^{5}} + \\frac{h^{2} q}{12 \\left(p^{2} + q^{2}\\right)^{3}} - \\frac{q}{p^{2} + q^{2}}$"
      ],
      "text/plain": [
       "h**6*q/(448*(p**2 + q**2)**7) - h**4*q/(80*(p**2 + q**2)**5) + h**2*q/(12*(p**2 + q**2)**3) - q/(p**2 + q**2)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Numer_p = sympy.Poly(numerator_p,h)\n",
    "coeffs = Numer_p.all_coeffs()[::-1]\n",
    "series_p = 0\n",
    "for j, coeff in enumerate(coeffs):\n",
    "    series_p += h**j*sympy.factor(coeff)/denominator_p\n",
    "series_p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are the terms in the right-hand side for $p'(t)$; we see that all the odd orders of $h$ vanish identically.  Meanwhile, the even order terms have a simple structure that is obvious except for the values of the coefficients appearing in each denominator.\n",
    "\n",
    "This is just to double-check that the manipulations above actually gave us back the correct right-hand side:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(series_p - rhs_p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can simplify the right-hand side series for $q$ in the same way, and find a complementary structure:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{h^{6} p}{448 \\left(p^{2} + q^{2}\\right)^{7}} + \\frac{h^{4} p}{80 \\left(p^{2} + q^{2}\\right)^{5}} - \\frac{h^{2} p}{12 \\left(p^{2} + q^{2}\\right)^{3}} + \\frac{p}{p^{2} + q^{2}}$"
      ],
      "text/plain": [
       "-h**6*p/(448*(p**2 + q**2)**7) + h**4*p/(80*(p**2 + q**2)**5) - h**2*p/(12*(p**2 + q**2)**3) + p/(p**2 + q**2)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Numer_q = sympy.Poly(numerator_q,h)\n",
    "coeffs = Numer_q.all_coeffs()[::-1]\n",
    "series_q = 0\n",
    "for j, coeff in enumerate(coeffs):\n",
    "    series_q += h**j*sympy.factor(coeff)/denominator_q\n",
    "series_q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We conjecture that the modified equation for this numerical solution has the form\n",
    "\n",
    "$$\n",
    "\\begin{bmatrix} p'(t) \\\\ q'(t) \\end{bmatrix} = \\sum_{j=0}^\\infty \\alpha_j \\frac{(ih)^j}{(p^2+q^2)^{j+1}} \\begin{bmatrix} -q \\\\ p \\end{bmatrix},\n",
    "$$\n",
    "\n",
    "where $\\alpha_j=0$ for every odd value of $j$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since each term of the series on the RHS is energy-conservative, the full modified equation is energy-conservative."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note also that this means the modified equation has the form\n",
    "$$\n",
    "    \\tilde{u}'(t) = f(\\tilde{u}) P(h/\\|u\\|^2_2)\n",
    "$$\n",
    "where $P$ is a polynomial and $u'(t)=f(u)$ is the original ODE system."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Open problem 1**: Use the theory of B-series to prove the above conjecture, possibly also giving a formula for the coefficients $\\alpha_j$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Open problem 2**: Find another combination of ODE system and explicit Runge-Kutta method (or other B-series integrator) that yields a modified equation with this kind of structure?  I.e., find another example of unconditionally stable explicit integration?\n",
    "\n",
    "Note that for unconditional stability, is not necessary that each term in the modified equation be orthogonal to the vector $[p,q]$; it only needs to have non-positive inner product with that vector."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modifying integrator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Complementary to the above approach, we can instead derive a modified system of ODEs such that when the explicit midpoint method is applied to the modified system it gives the exact solution of the original oscillator equation.  It may be revealing to examine the structure of this *modifying integrator*.\n",
    "\n",
    "For some other examples of modifying integrators, see [this notebook](cac0b451425f6e76afb533d61adbca8c)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- \\frac{q \\left(3 h^{4} + 5 h^{2} p^{4} + 10 h^{2} p^{2} q^{2} + 5 h^{2} q^{4} + 60 p^{8} + 240 p^{6} q^{2} + 360 p^{4} q^{4} + 240 p^{2} q^{6} + 60 q^{8}\\right)}{60 p^{10} + 300 p^{8} q^{2} + 600 p^{6} q^{4} + 600 p^{4} q^{6} + 300 p^{2} q^{8} + 60 q^{10}} & \\frac{p \\left(3 h^{4} + 5 h^{2} p^{4} + 10 h^{2} p^{2} q^{2} + 5 h^{2} q^{4} + 60 p^{8} + 240 p^{6} q^{2} + 360 p^{4} q^{4} + 240 p^{2} q^{6} + 60 q^{8}\\right)}{60 \\left(p^{10} + 5 p^{8} q^{2} + 10 p^{6} q^{4} + 10 p^{4} q^{6} + 5 p^{2} q^{8} + q^{10}\\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[-q*(3*h**4 + 5*h**2*p**4 + 10*h**2*p**2*q**2 + 5*h**2*q**4 + 60*p**8 + 240*p**6*q**2 + 360*p**4*q**4 + 240*p**2*q**6 + 60*q**8)/(60*p**10 + 300*p**8*q**2 + 600*p**6*q**4 + 600*p**4*q**6 + 300*p**2*q**8 + 60*q**10), p*(3*h**4 + 5*h**2*p**4 + 10*h**2*p**2*q**2 + 5*h**2*q**4 + 60*p**8 + 240*p**6*q**2 + 360*p**4*q**4 + 240*p**2*q**6 + 60*q**8)/(60*(p**10 + 5*p**8*q**2 + 10*p**6*q**4 + 10*p**4*q**6 + 5*p**2*q**8 + q**10))]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "series = bs.modifying_integrator(u, f, A, b, order=5)\n",
    "simplify(series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "rhs_p=simplify(series[0])\n",
    "numerator_p = rhs_p.as_numer_denom()[0]\n",
    "denominator_p = sympy.factor(rhs_p.as_numer_denom()[1])\n",
    "rhs_q=simplify(series[1])\n",
    "numerator_q = rhs_q.as_numer_denom()[0]\n",
    "denominator_q = sympy.factor(rhs_q.as_numer_denom()[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{h^{4} q}{20 \\left(p^{2} + q^{2}\\right)^{5}} - \\frac{h^{2} q}{12 \\left(p^{2} + q^{2}\\right)^{3}} - \\frac{q}{p^{2} + q^{2}}$"
      ],
      "text/plain": [
       "-h**4*q/(20*(p**2 + q**2)**5) - h**2*q/(12*(p**2 + q**2)**3) - q/(p**2 + q**2)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Numer_p = sympy.Poly(numerator_p,h)\n",
    "coeffs = Numer_p.all_coeffs()[::-1]\n",
    "series_p = 0\n",
    "for j, coeff in enumerate(coeffs):\n",
    "    series_p += h**j*sympy.factor(coeff)/denominator_p\n",
    "series_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{h^{4} p}{20 \\left(p^{2} + q^{2}\\right)^{5}} + \\frac{h^{2} p}{12 \\left(p^{2} + q^{2}\\right)^{3}} + \\frac{p}{p^{2} + q^{2}}$"
      ],
      "text/plain": [
       "h**4*p/(20*(p**2 + q**2)**5) + h**2*p/(12*(p**2 + q**2)**3) + p/(p**2 + q**2)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Numer_q = sympy.Poly(numerator_q,h)\n",
    "coeffs = Numer_q.all_coeffs()[::-1]\n",
    "series_q = 0\n",
    "for j, coeff in enumerate(coeffs):\n",
    "    series_q += h**j*sympy.factor(coeff)/denominator_q\n",
    "series_q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see a similar structure again.  Namely, the modifying integrator system seems to take the form\n",
    "\n",
    "$$\n",
    "    u'(t) = f(u) \\hat{P}(h/\\|u\\|^2_2)\n",
    "$$\n",
    "\n",
    "\n",
    "though the polynomial $\\hat{P}$ has different coefficients compared to $P$ that appeared above in the modified equation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We might easily conjecture that all terms take the form given above.  However, if we go ahead and compute more terms, we find a surprise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{\\frac{h^{5} p}{48} - \\frac{h^{4} p^{2} q}{20} - \\frac{h^{4} q^{3}}{20} - \\frac{h^{2} p^{6} q}{12} - \\frac{h^{2} p^{4} q^{3}}{4} - \\frac{h^{2} p^{2} q^{5}}{4} - \\frac{h^{2} q^{7}}{12} - p^{10} q - 5 p^{8} q^{3} - 10 p^{6} q^{5} - 10 p^{4} q^{7} - 5 p^{2} q^{9} - q^{11}}{p^{12} + 6 p^{10} q^{2} + 15 p^{8} q^{4} + 20 p^{6} q^{6} + 15 p^{4} q^{8} + 6 p^{2} q^{10} + q^{12}} & \\frac{\\frac{h^{5} q}{48} + \\frac{h^{4} p^{3}}{20} + \\frac{h^{4} p q^{2}}{20} + \\frac{h^{2} p^{7}}{12} + \\frac{h^{2} p^{5} q^{2}}{4} + \\frac{h^{2} p^{3} q^{4}}{4} + \\frac{h^{2} p q^{6}}{12} + p^{11} + 5 p^{9} q^{2} + 10 p^{7} q^{4} + 10 p^{5} q^{6} + 5 p^{3} q^{8} + p q^{10}}{p^{12} + 6 p^{10} q^{2} + 15 p^{8} q^{4} + 20 p^{6} q^{6} + 15 p^{4} q^{8} + 6 p^{2} q^{10} + q^{12}}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[(h**5*p/48 - h**4*p**2*q/20 - h**4*q**3/20 - h**2*p**6*q/12 - h**2*p**4*q**3/4 - h**2*p**2*q**5/4 - h**2*q**7/12 - p**10*q - 5*p**8*q**3 - 10*p**6*q**5 - 10*p**4*q**7 - 5*p**2*q**9 - q**11)/(p**12 + 6*p**10*q**2 + 15*p**8*q**4 + 20*p**6*q**6 + 15*p**4*q**8 + 6*p**2*q**10 + q**12), (h**5*q/48 + h**4*p**3/20 + h**4*p*q**2/20 + h**2*p**7/12 + h**2*p**5*q**2/4 + h**2*p**3*q**4/4 + h**2*p*q**6/12 + p**11 + 5*p**9*q**2 + 10*p**7*q**4 + 10*p**5*q**6 + 5*p**3*q**8 + p*q**10)/(p**12 + 6*p**10*q**2 + 15*p**8*q**4 + 20*p**6*q**6 + 15*p**4*q**8 + 6*p**2*q**10 + q**12)]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "series = bs.modifying_integrator(u, f, A, b, order=6)\n",
    "simplify(series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "rhs_p=simplify(series[0])\n",
    "numerator_p = rhs_p.as_numer_denom()[0]\n",
    "denominator_p = sympy.factor(rhs_p.as_numer_denom()[1])\n",
    "rhs_q=simplify(series[1])\n",
    "numerator_q = rhs_q.as_numer_denom()[0]\n",
    "denominator_q = sympy.factor(rhs_q.as_numer_denom()[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{h^{5} p}{48 \\left(p^{2} + q^{2}\\right)^{6}} - \\frac{h^{4} q}{20 \\left(p^{2} + q^{2}\\right)^{5}} - \\frac{h^{2} q}{12 \\left(p^{2} + q^{2}\\right)^{3}} - \\frac{q}{p^{2} + q^{2}}$"
      ],
      "text/plain": [
       "h**5*p/(48*(p**2 + q**2)**6) - h**4*q/(20*(p**2 + q**2)**5) - h**2*q/(12*(p**2 + q**2)**3) - q/(p**2 + q**2)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Numer_p = sympy.Poly(numerator_p,h)\n",
    "coeffs = Numer_p.all_coeffs()[::-1]\n",
    "series_p = 0\n",
    "for j, coeff in enumerate(coeffs):\n",
    "    series_p += h**j*sympy.factor(coeff)/denominator_p\n",
    "series_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{h^{5} q}{48 \\left(p^{2} + q^{2}\\right)^{6}} + \\frac{h^{4} p}{20 \\left(p^{2} + q^{2}\\right)^{5}} + \\frac{h^{2} p}{12 \\left(p^{2} + q^{2}\\right)^{3}} + \\frac{p}{p^{2} + q^{2}}$"
      ],
      "text/plain": [
       "h**5*q/(48*(p**2 + q**2)**6) + h**4*p/(20*(p**2 + q**2)**5) + h**2*p/(12*(p**2 + q**2)**3) + p/(p**2 + q**2)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Numer_q = sympy.Poly(numerator_q,h)\n",
    "coeffs = Numer_q.all_coeffs()[::-1]\n",
    "series_q = 0\n",
    "for j, coeff in enumerate(coeffs):\n",
    "    series_q += h**j*sympy.factor(coeff)/denominator_q\n",
    "series_q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Surprisingly, we get a term of order $h^5$, and it is proportional to $u$!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we go further, we have a similar $h^7$ term:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{1953 h^{7} p - 2540 h^{6} p^{2} q - 2540 h^{6} q^{3} + 840 h^{5} p^{5} + 1680 h^{5} p^{3} q^{2} + 840 h^{5} p q^{4} - 2016 h^{4} p^{6} q - 6048 h^{4} p^{4} q^{3} - 6048 h^{4} p^{2} q^{5} - 2016 h^{4} q^{7} - 3360 h^{2} p^{10} q - 16800 h^{2} p^{8} q^{3} - 33600 h^{2} p^{6} q^{5} - 33600 h^{2} p^{4} q^{7} - 16800 h^{2} p^{2} q^{9} - 3360 h^{2} q^{11} - 40320 p^{14} q - 282240 p^{12} q^{3} - 846720 p^{10} q^{5} - 1411200 p^{8} q^{7} - 1411200 p^{6} q^{9} - 846720 p^{4} q^{11} - 282240 p^{2} q^{13} - 40320 q^{15}}{40320 \\left(p^{16} + 8 p^{14} q^{2} + 28 p^{12} q^{4} + 56 p^{10} q^{6} + 70 p^{8} q^{8} + 56 p^{6} q^{10} + 28 p^{4} q^{12} + 8 p^{2} q^{14} + q^{16}\\right)} & \\frac{1953 h^{7} q + 2540 h^{6} p^{3} + 2540 h^{6} p q^{2} + 840 h^{5} p^{4} q + 1680 h^{5} p^{2} q^{3} + 840 h^{5} q^{5} + 2016 h^{4} p^{7} + 6048 h^{4} p^{5} q^{2} + 6048 h^{4} p^{3} q^{4} + 2016 h^{4} p q^{6} + 3360 h^{2} p^{11} + 16800 h^{2} p^{9} q^{2} + 33600 h^{2} p^{7} q^{4} + 33600 h^{2} p^{5} q^{6} + 16800 h^{2} p^{3} q^{8} + 3360 h^{2} p q^{10} + 40320 p^{15} + 282240 p^{13} q^{2} + 846720 p^{11} q^{4} + 1411200 p^{9} q^{6} + 1411200 p^{7} q^{8} + 846720 p^{5} q^{10} + 282240 p^{3} q^{12} + 40320 p q^{14}}{40320 \\left(p^{16} + 8 p^{14} q^{2} + 28 p^{12} q^{4} + 56 p^{10} q^{6} + 70 p^{8} q^{8} + 56 p^{6} q^{10} + 28 p^{4} q^{12} + 8 p^{2} q^{14} + q^{16}\\right)}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[(1953*h**7*p - 2540*h**6*p**2*q - 2540*h**6*q**3 + 840*h**5*p**5 + 1680*h**5*p**3*q**2 + 840*h**5*p*q**4 - 2016*h**4*p**6*q - 6048*h**4*p**4*q**3 - 6048*h**4*p**2*q**5 - 2016*h**4*q**7 - 3360*h**2*p**10*q - 16800*h**2*p**8*q**3 - 33600*h**2*p**6*q**5 - 33600*h**2*p**4*q**7 - 16800*h**2*p**2*q**9 - 3360*h**2*q**11 - 40320*p**14*q - 282240*p**12*q**3 - 846720*p**10*q**5 - 1411200*p**8*q**7 - 1411200*p**6*q**9 - 846720*p**4*q**11 - 282240*p**2*q**13 - 40320*q**15)/(40320*(p**16 + 8*p**14*q**2 + 28*p**12*q**4 + 56*p**10*q**6 + 70*p**8*q**8 + 56*p**6*q**10 + 28*p**4*q**12 + 8*p**2*q**14 + q**16)), (1953*h**7*q + 2540*h**6*p**3 + 2540*h**6*p*q**2 + 840*h**5*p**4*q + 1680*h**5*p**2*q**3 + 840*h**5*q**5 + 2016*h**4*p**7 + 6048*h**4*p**5*q**2 + 6048*h**4*p**3*q**4 + 2016*h**4*p*q**6 + 3360*h**2*p**11 + 16800*h**2*p**9*q**2 + 33600*h**2*p**7*q**4 + 33600*h**2*p**5*q**6 + 16800*h**2*p**3*q**8 + 3360*h**2*p*q**10 + 40320*p**15 + 282240*p**13*q**2 + 846720*p**11*q**4 + 1411200*p**9*q**6 + 1411200*p**7*q**8 + 846720*p**5*q**10 + 282240*p**3*q**12 + 40320*p*q**14)/(40320*(p**16 + 8*p**14*q**2 + 28*p**12*q**4 + 56*p**10*q**6 + 70*p**8*q**8 + 56*p**6*q**10 + 28*p**4*q**12 + 8*p**2*q**14 + q**16))]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "series = bs.modifying_integrator(u, f, A, b, order=8)\n",
    "simplify(series)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "rhs_p=simplify(series[0])\n",
    "numerator_p = rhs_p.as_numer_denom()[0]\n",
    "denominator_p = sympy.factor(rhs_p.as_numer_denom()[1])\n",
    "rhs_q=simplify(series[1])\n",
    "numerator_q = rhs_q.as_numer_denom()[0]\n",
    "denominator_q = sympy.factor(rhs_q.as_numer_denom()[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{31 h^{7} p}{640 \\left(p^{2} + q^{2}\\right)^{8}} - \\frac{127 h^{6} q}{2016 \\left(p^{2} + q^{2}\\right)^{7}} + \\frac{h^{5} p}{48 \\left(p^{2} + q^{2}\\right)^{6}} - \\frac{h^{4} q}{20 \\left(p^{2} + q^{2}\\right)^{5}} - \\frac{h^{2} q}{12 \\left(p^{2} + q^{2}\\right)^{3}} - \\frac{q}{p^{2} + q^{2}}$"
      ],
      "text/plain": [
       "31*h**7*p/(640*(p**2 + q**2)**8) - 127*h**6*q/(2016*(p**2 + q**2)**7) + h**5*p/(48*(p**2 + q**2)**6) - h**4*q/(20*(p**2 + q**2)**5) - h**2*q/(12*(p**2 + q**2)**3) - q/(p**2 + q**2)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Numer_p = sympy.Poly(numerator_p,h)\n",
    "coeffs = Numer_p.all_coeffs()[::-1]\n",
    "series_p = 0\n",
    "for j, coeff in enumerate(coeffs):\n",
    "    series_p += h**j*sympy.factor(coeff)/denominator_p\n",
    "series_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{31 h^{7} q}{640 \\left(p^{2} + q^{2}\\right)^{8}} + \\frac{127 h^{6} p}{2016 \\left(p^{2} + q^{2}\\right)^{7}} + \\frac{h^{5} q}{48 \\left(p^{2} + q^{2}\\right)^{6}} + \\frac{h^{4} p}{20 \\left(p^{2} + q^{2}\\right)^{5}} + \\frac{h^{2} p}{12 \\left(p^{2} + q^{2}\\right)^{3}} + \\frac{p}{p^{2} + q^{2}}$"
      ],
      "text/plain": [
       "31*h**7*q/(640*(p**2 + q**2)**8) + 127*h**6*p/(2016*(p**2 + q**2)**7) + h**5*q/(48*(p**2 + q**2)**6) + h**4*p/(20*(p**2 + q**2)**5) + h**2*p/(12*(p**2 + q**2)**3) + p/(p**2 + q**2)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Numer_q = sympy.Poly(numerator_q,h)\n",
    "coeffs = Numer_q.all_coeffs()[::-1]\n",
    "series_q = 0\n",
    "for j, coeff in enumerate(coeffs):\n",
    "    series_q += h**j*sympy.factor(coeff)/denominator_q\n",
    "series_q"
   ]
  }
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