MiscFewBosonCalcs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some Misc Bosons calculations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let's start by just considering two bosons in a single well and calculating the impact if the interaction between them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let the single-particle solutions be $$\\psi\\{x_i\\} = \\Big(\\frac{4}{\\pi w_0^2}\\Big)^{1/4} \\exp\\Big\\{-\\frac{2x_i^2}{w_0^2}\\Big\\}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "for the appropriate waist w_0. Then let's do first order perturbation theory here. Our normal hamiltonian for two particles is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "H_0\\{x_1,x_2\\} = \\frac{p_1^2+p_2^2}{2m}+\\frac{1}{2} m \\omega_0^2 (x_1^2+x_2^2)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ground-state of the non-interacting hamiltonian is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\Psi\\{x_1,x_2\\} = \\frac{2}{\\pi w_0^2} \\exp\\Big\\{-\\frac{2(x_1^2+x_2^2)}{w_0^2}\\Big\\}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let the perturbation be\n",
    "$$\n",
    "H_1 = a \\delta\\{x_1-x_2\\}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Identical states"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Energy change"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then the energy change of the ground-state is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "E^1 = a \\frac{4}{\\pi w_0^2} \\iint[dx_1,dx_2]\\exp\\Big\\{-\\frac{4(x_1^2+x_2^2)}{w_0^2}\\Big\\}\\delta\\{x_1-x_2\\}\\\\\n",
    "= a \\frac{4}{\\pi w_0^2} \\int[dx]\\exp\\Big\\{-\\frac{8x^2}{w_0^2}\\Big\\}\\\\\n",
    "= a \\frac{4}{\\pi w_0^2} \\frac{\\sqrt{2\\pi}w_0}{4}\\\\\n",
    "= \\frac{a\\sqrt{2}}{\\pi w_0}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import display\n",
    "import sympy as sp\n",
    "import numpy as np\n",
    "sp.init_printing(use_latex=True)\n",
    "from sympy.functions.special.delta_functions import DiracDelta\n",
    "import MarksConstants as mc\n",
    "from sympy import diff as D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.style\n",
    "matplotlib.style.use('dark_background')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import interp1d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Miscellaneous as misc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wavefunction change"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "... todo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Triplet and singlet states"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "now I need to consider two locations for the gaussian spaed by $\\Delta x$. The symetric wavefunction is the important one since for these considerations the bosons have the same spin so the siglet state is forbidden. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\Psi_{\\text{Sym}}\\{x_1, x_2\\} = \\psi\\{x_1-\\Delta/2\\}\\psi\\{x_2+\\Delta/2\\}+\\psi\\{x_1+\\Delta/2\\}\\psi\\{x_2-\\Delta/2\\}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### wavefunctions for ref"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ea56c3fd68>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xp = np.linspace(-2,2,1000)\n",
    "ypts1   = np.exp(-2*(xp-0.5)**2) + np.exp(-2*(xp+0.5)**2)\n",
    "ypts1_2 = np.exp(-2*(xp-0.52)**2) + np.exp(-2*(xp+0.52)**2)\n",
    "ypts2   = np.exp(-2*(xp-0.75)**2) + np.exp(-2*(xp+0.75)**2)\n",
    "ypts3   = np.exp(-2*(xp-1)**2) + np.exp(-2*(xp+1)**2)\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(xp, ypts1, label='r=1')\n",
    "ax.plot(xp, ypts1_2, label='r=1.1')\n",
    "ax.plot(xp, ypts2, label='r=1.5')\n",
    "ax.plot(xp, ypts3, label='r=2')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1ea56cc99e8>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xp = np.linspace(-2,2,1000)\n",
    "ypts1 = np.exp(-2*(xp-0.5)**2) + np.exp(-2*(xp+0.5)**2)\n",
    "ypts2 = np.exp(-2*(xp-0.75)**2) + np.exp(-2*(xp+0.75)**2)\n",
    "ypts3 = np.exp(-2*(xp-1)**2) + np.exp(-2*(xp+1)**2)\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(xp, ypts1, label='r=1')\n",
    "ax.plot(xp, ypts2, label='r=1.5')\n",
    "ax.plot(xp, ypts3, label='r=2')\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### wavefunction modifications"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "first thought seems more non-trivial... todo...?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# With 3D Variational Calculations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def psi(x, w0):\n",
    "    return sp.exp(-2*x**2/w0**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1, x2, y1, y2, z1, z2, w0x, w0y, w0z, Delta = sp.symbols('x1 x2 y1 y2 z1 z2 w_x w_y w_z Delta', real=True, positive=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Double-Filled\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{8 e^{- \\frac{2 \\left(- \\frac{\\Delta}{2} + x_{1}\\right)^{2}}{w_{x}^{2}}} e^{- \\frac{2 \\left(- \\frac{\\Delta}{2} + x_{2}\\right)^{2}}{w_{x}^{2}}} e^{- \\frac{2 y_{1}^{2}}{w_{y}^{2}}} e^{- \\frac{2 y_{2}^{2}}{w_{y}^{2}}} e^{- \\frac{2 z_{1}^{2}}{w_{z}^{2}}} e^{- \\frac{2 z_{2}^{2}}{w_{z}^{2}}}}{\\pi^{\\frac{3}{2}} w_{x} w_{y} w_{z}}$"
      ],
      "text/plain": [
       "                2                2                                     \n",
       "      ⎛  Δ     ⎞       ⎛  Δ     ⎞                                      \n",
       "   -2⋅⎜- ─ + x₁⎟    -2⋅⎜- ─ + x₂⎟         2        2        2        2 \n",
       "      ⎝  2     ⎠       ⎝  2     ⎠    -2⋅y₁    -2⋅y₂    -2⋅z₁    -2⋅z₂  \n",
       "   ───────────────  ───────────────  ───────  ───────  ───────  ───────\n",
       "           2                2             2        2        2        2 \n",
       "         wₓ               wₓ           w_y      w_y      w_z      w_z  \n",
       "8⋅ℯ               ⋅ℯ               ⋅ℯ       ⋅ℯ       ⋅ℯ       ⋅ℯ       \n",
       "───────────────────────────────────────────────────────────────────────\n",
       "                             3/2                                       \n",
       "                            π   ⋅wₓ⋅w_y⋅w_z                            "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mott-Insulator\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\left(e^{- \\frac{2 \\left(- \\frac{\\Delta}{2} + x_{2}\\right)^{2}}{w_{x}^{2}}} e^{- \\frac{2 \\left(\\frac{\\Delta}{2} + x_{1}\\right)^{2}}{w_{x}^{2}}} + e^{- \\frac{2 \\left(- \\frac{\\Delta}{2} + x_{1}\\right)^{2}}{w_{x}^{2}}} e^{- \\frac{2 \\left(\\frac{\\Delta}{2} + x_{2}\\right)^{2}}{w_{x}^{2}}}\\right) e^{- \\frac{2 y_{1}^{2}}{w_{y}^{2}}} e^{- \\frac{2 y_{2}^{2}}{w_{y}^{2}}} e^{- \\frac{2 z_{1}^{2}}{w_{z}^{2}}} e^{- \\frac{2 z_{2}^{2}}{w_{z}^{2}}}}{\\sqrt{\\frac{\\pi^{3} w_{x}^{2} w_{y}^{2} w_{z}^{2}}{32} + \\frac{\\pi^{3} w_{x}^{2} w_{y}^{2} w_{z}^{2} e^{- \\frac{2 \\Delta^{2}}{w_{x}^{2}}}}{32}}}$"
      ],
      "text/plain": [
       "⎛              2              2                  2              2 ⎞           \n",
       "⎜    ⎛  Δ     ⎞       ⎛Δ     ⎞         ⎛  Δ     ⎞       ⎛Δ     ⎞  ⎟           \n",
       "⎜ -2⋅⎜- ─ + x₂⎟    -2⋅⎜─ + x₁⎟      -2⋅⎜- ─ + x₁⎟    -2⋅⎜─ + x₂⎟  ⎟       2   \n",
       "⎜    ⎝  2     ⎠       ⎝2     ⎠         ⎝  2     ⎠       ⎝2     ⎠  ⎟  -2⋅y₁    \n",
       "⎜ ───────────────  ─────────────    ───────────────  ─────────────⎟  ───────  \n",
       "⎜         2               2                 2               2     ⎟       2   \n",
       "⎜       wₓ              wₓ                wₓ              wₓ      ⎟    w_y    \n",
       "⎝ℯ               ⋅ℯ              + ℯ               ⋅ℯ             ⎠⋅ℯ       ⋅ℯ\n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                  ____________________________________________\n",
       "                                 ╱                                          2 \n",
       "                                ╱                                       -2⋅Δ  \n",
       "                               ╱                                        ──────\n",
       "                              ╱                                            2  \n",
       "                             ╱      3   2    2    2    3   2    2    2   wₓ   \n",
       "                            ╱      π ⋅wₓ ⋅w_y ⋅w_z    π ⋅wₓ ⋅w_y ⋅w_z ⋅ℯ      \n",
       "                           ╱       ──────────────── + ────────────────────────\n",
       "                         ╲╱               32                     32           \n",
       "\n",
       "                         \n",
       "                         \n",
       "     2        2        2 \n",
       "-2⋅y₂    -2⋅z₁    -2⋅z₂  \n",
       "───────  ───────  ───────\n",
       "     2        2        2 \n",
       "  w_y      w_z      w_z  \n",
       "       ⋅ℯ       ⋅ℯ       \n",
       "─────────────────────────\n",
       "_                        \n",
       "                         \n",
       "                         \n",
       "                         \n",
       "                         \n",
       "                         \n",
       "                         \n",
       "                         \n",
       "                         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Superfluid\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\left(e^{- \\frac{2 \\left(\\frac{\\Delta}{2} + x_{1}\\right)^{2}}{w_{x}^{2}}} + e^{- \\frac{2 \\left(- \\frac{\\Delta}{2} + x_{1}\\right)^{2}}{w_{x}^{2}}}\\right) \\left(e^{- \\frac{2 \\left(\\frac{\\Delta}{2} + x_{2}\\right)^{2}}{w_{x}^{2}}} + e^{- \\frac{2 \\left(- \\frac{\\Delta}{2} + x_{2}\\right)^{2}}{w_{x}^{2}}}\\right) e^{- \\frac{2 y_{1}^{2}}{w_{y}^{2}}} e^{- \\frac{2 y_{2}^{2}}{w_{y}^{2}}} e^{- \\frac{2 z_{1}^{2}}{w_{z}^{2}}} e^{- \\frac{2 z_{2}^{2}}{w_{z}^{2}}}}{\\sqrt{\\frac{\\pi^{3} w_{x}^{2} w_{y}^{2} w_{z}^{2}}{16} + \\frac{\\pi^{3} w_{x}^{2} w_{y}^{2} w_{z}^{2} e^{- \\frac{\\Delta^{2}}{w_{x}^{2}}}}{8} + \\frac{\\pi^{3} w_{x}^{2} w_{y}^{2} w_{z}^{2} e^{- \\frac{2 \\Delta^{2}}{w_{x}^{2}}}}{16}}}$"
      ],
      "text/plain": [
       "⎛            2                  2 ⎞ ⎛            2                  2 ⎞       \n",
       "⎜    ⎛Δ     ⎞         ⎛  Δ     ⎞  ⎟ ⎜    ⎛Δ     ⎞         ⎛  Δ     ⎞  ⎟       \n",
       "⎜ -2⋅⎜─ + x₁⎟      -2⋅⎜- ─ + x₁⎟  ⎟ ⎜ -2⋅⎜─ + x₂⎟      -2⋅⎜- ─ + x₂⎟  ⎟       \n",
       "⎜    ⎝2     ⎠         ⎝  2     ⎠  ⎟ ⎜    ⎝2     ⎠         ⎝  2     ⎠  ⎟  -2⋅y₁\n",
       "⎜ ─────────────    ───────────────⎟ ⎜ ─────────────    ───────────────⎟  ─────\n",
       "⎜        2                 2      ⎟ ⎜        2                 2      ⎟       \n",
       "⎜      wₓ                wₓ       ⎟ ⎜      wₓ                wₓ       ⎟    w_y\n",
       "⎝ℯ              + ℯ               ⎠⋅⎝ℯ              + ℯ               ⎠⋅ℯ     \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                       _______________________________________________________\n",
       "                      ╱                                        2              \n",
       "                     ╱                                       -Δ               \n",
       "                    ╱                                        ────             \n",
       "                   ╱                                           2              \n",
       "                  ╱      3   2    2    2    3   2    2    2  wₓ      3   2    \n",
       "                 ╱      π ⋅wₓ ⋅w_y ⋅w_z    π ⋅wₓ ⋅w_y ⋅w_z ⋅ℯ       π ⋅wₓ ⋅w_y\n",
       "                ╱       ──────────────── + ────────────────────── + ──────────\n",
       "              ╲╱               16                    8                        \n",
       "\n",
       "                             \n",
       "                             \n",
       "2        2        2        2 \n",
       "    -2⋅y₂    -2⋅z₁    -2⋅z₂  \n",
       "──  ───────  ───────  ───────\n",
       "2        2        2        2 \n",
       "      w_y      w_z      w_z  \n",
       "  ⋅ℯ       ⋅ℯ       ⋅ℯ       \n",
       "─────────────────────────────\n",
       "_______________              \n",
       "            2                \n",
       "        -2⋅Δ                 \n",
       "        ──────               \n",
       "           2                 \n",
       "2    2   wₓ                  \n",
       " ⋅w_z ⋅ℯ                     \n",
       "──────────────               \n",
       " 16                          "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Anti-Superfluid\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left(- e^{- \\frac{2 \\left(\\frac{\\Delta}{2} + x_{1}\\right)^{2}}{w_{x}^{2}}} + e^{- \\frac{2 \\left(- \\frac{\\Delta}{2} + x_{1}\\right)^{2}}{w_{x}^{2}}}\\right) \\left(- e^{- \\frac{2 \\left(\\frac{\\Delta}{2} + x_{2}\\right)^{2}}{w_{x}^{2}}} + e^{- \\frac{2 \\left(- \\frac{\\Delta}{2} + x_{2}\\right)^{2}}{w_{x}^{2}}}\\right) \\sqrt{\\frac{1}{\\frac{\\pi^{3} w_{x}^{2} w_{y}^{2} w_{z}^{2}}{16} - \\frac{\\pi^{3} w_{x}^{2} w_{y}^{2} w_{z}^{2} e^{- \\frac{\\Delta^{2}}{w_{x}^{2}}}}{8} + \\frac{\\pi^{3} w_{x}^{2} w_{y}^{2} w_{z}^{2} e^{- \\frac{2 \\Delta^{2}}{w_{x}^{2}}}}{16}}} e^{- \\frac{2 y_{1}^{2}}{w_{y}^{2}}} e^{- \\frac{2 y_{2}^{2}}{w_{y}^{2}}} e^{- \\frac{2 z_{1}^{2}}{w_{z}^{2}}} e^{- \\frac{2 z_{2}^{2}}{w_{z}^{2}}}$"
      ],
      "text/plain": [
       "⎛              2                  2 ⎞ ⎛              2                  2 ⎞   \n",
       "⎜      ⎛Δ     ⎞         ⎛  Δ     ⎞  ⎟ ⎜      ⎛Δ     ⎞         ⎛  Δ     ⎞  ⎟   \n",
       "⎜   -2⋅⎜─ + x₁⎟      -2⋅⎜- ─ + x₁⎟  ⎟ ⎜   -2⋅⎜─ + x₂⎟      -2⋅⎜- ─ + x₂⎟  ⎟   \n",
       "⎜      ⎝2     ⎠         ⎝  2     ⎠  ⎟ ⎜      ⎝2     ⎠         ⎝  2     ⎠  ⎟   \n",
       "⎜   ─────────────    ───────────────⎟ ⎜   ─────────────    ───────────────⎟   \n",
       "⎜          2                 2      ⎟ ⎜          2                 2      ⎟   \n",
       "⎜        wₓ                wₓ       ⎟ ⎜        wₓ                wₓ       ⎟   \n",
       "⎝- ℯ              + ℯ               ⎠⋅⎝- ℯ              + ℯ               ⎠⋅  \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                            ╲╱\n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "         _____________________________________________________________________\n",
       "        ╱                                  1                                  \n",
       "       ╱  ────────────────────────────────────────────────────────────────────\n",
       "      ╱                                          2                          2 \n",
       "     ╱                                         -Δ                       -2⋅Δ  \n",
       "    ╱                                          ────                     ──────\n",
       "   ╱                                             2                         2  \n",
       "  ╱        3   2    2    2    3   2    2    2  wₓ      3   2    2    2   wₓ   \n",
       " ╱        π ⋅wₓ ⋅w_y ⋅w_z    π ⋅wₓ ⋅w_y ⋅w_z ⋅ℯ       π ⋅wₓ ⋅w_y ⋅w_z ⋅ℯ      \n",
       "╱         ──────────────── - ────────────────────── + ────────────────────────\n",
       "                 16                    8                         16           \n",
       "\n",
       "                                     \n",
       "                                     \n",
       "        2        2        2        2 \n",
       "   -2⋅y₁    -2⋅y₂    -2⋅z₁    -2⋅z₂  \n",
       "   ───────  ───────  ───────  ───────\n",
       "_       2        2        2        2 \n",
       "     w_y      w_y      w_z      w_z  \n",
       " ⋅ℯ       ⋅ℯ       ⋅ℯ       ⋅ℯ       \n",
       "                                     \n",
       "                                     \n",
       "                                     \n",
       "                                     \n",
       "                                     \n",
       "                                     \n",
       "                                     \n",
       "                                     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Anti-Mott-Insulator\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\left(- e^{- \\frac{2 \\left(- \\frac{\\Delta}{2} + x_{2}\\right)^{2}}{w_{x}^{2}}} e^{- \\frac{2 \\left(\\frac{\\Delta}{2} + x_{1}\\right)^{2}}{w_{x}^{2}}} + e^{- \\frac{2 \\left(- \\frac{\\Delta}{2} + x_{1}\\right)^{2}}{w_{x}^{2}}} e^{- \\frac{2 \\left(\\frac{\\Delta}{2} + x_{2}\\right)^{2}}{w_{x}^{2}}}\\right) \\sqrt{\\frac{1}{\\frac{\\pi^{3} w_{x}^{2} w_{y}^{2} w_{z}^{2}}{32} - \\frac{\\pi^{3} w_{x}^{2} w_{y}^{2} w_{z}^{2} e^{- \\frac{2 \\Delta^{2}}{w_{x}^{2}}}}{32}}} e^{- \\frac{2 y_{1}^{2}}{w_{y}^{2}}} e^{- \\frac{2 y_{2}^{2}}{w_{y}^{2}}} e^{- \\frac{2 z_{1}^{2}}{w_{z}^{2}}} e^{- \\frac{2 z_{2}^{2}}{w_{z}^{2}}}$"
      ],
      "text/plain": [
       "⎛                2              2                  2              2 ⎞         \n",
       "⎜      ⎛  Δ     ⎞       ⎛Δ     ⎞         ⎛  Δ     ⎞       ⎛Δ     ⎞  ⎟         \n",
       "⎜   -2⋅⎜- ─ + x₂⎟    -2⋅⎜─ + x₁⎟      -2⋅⎜- ─ + x₁⎟    -2⋅⎜─ + x₂⎟  ⎟         \n",
       "⎜      ⎝  2     ⎠       ⎝2     ⎠         ⎝  2     ⎠       ⎝2     ⎠  ⎟         \n",
       "⎜   ───────────────  ─────────────    ───────────────  ─────────────⎟         \n",
       "⎜           2               2                 2               2     ⎟         \n",
       "⎜         wₓ              wₓ                wₓ              wₓ      ⎟         \n",
       "⎝- ℯ               ⋅ℯ              + ℯ               ⋅ℯ             ⎠⋅        \n",
       "                                                                              \n",
       "                                                                             ╱\n",
       "                                                                            ╱ \n",
       "                                                                           ╱  \n",
       "                                                                          ╱   \n",
       "                                                                         ╱    \n",
       "                                                                        ╱     \n",
       "                                                                      ╲╱      \n",
       "\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                       2        2        2    \n",
       "                                                  -2⋅y₁    -2⋅y₂    -2⋅z₁    -\n",
       "                                                  ───────  ───────  ───────  ─\n",
       "   _____________________________________________       2        2        2    \n",
       "  ╱                      1                          w_y      w_y      w_z     \n",
       " ╱  ─────────────────────────────────────────── ⋅ℯ       ⋅ℯ       ⋅ℯ       ⋅ℯ \n",
       "╱                                            2                                \n",
       "                                         -2⋅Δ                                 \n",
       "                                         ──────                               \n",
       "                                            2                                 \n",
       "     3   2    2    2    3   2    2    2   wₓ                                  \n",
       "    π ⋅wₓ ⋅w_y ⋅w_z    π ⋅wₓ ⋅w_y ⋅w_z ⋅ℯ                                     \n",
       "    ──────────────── - ────────────────────────                               \n",
       "           32                     32                                          \n",
       "\n",
       "      \n",
       "      \n",
       "    2 \n",
       "2⋅z₂  \n",
       "──────\n",
       "    2 \n",
       " w_z  \n",
       "      \n",
       "      \n",
       "      \n",
       "      \n",
       "      \n",
       "      \n",
       "      \n",
       "      \n",
       "      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "psiyz = psi(y1, w0y) * psi(y2, w0y) * psi(z1, w0z) * psi(z2, w0z)\n",
    "xspace = ((x1,-sp.oo,sp.oo), (x2,-sp.oo,sp.oo),)\n",
    "allspace = ((x1,-sp.oo,sp.oo), (x2,-sp.oo,sp.oo),(y1,-sp.oo,sp.oo), (y2,-sp.oo,sp.oo),(z1,-sp.oo,sp.oo), (z2,-sp.oo,sp.oo),)\n",
    "\n",
    "wavefunctionsx = []\n",
    "wavefunctions = []\n",
    "names = ['Double-Filled', 'Mott-Insulator', 'Superfluid', 'Anti-Superfluid', 'Anti-Mott-Insulator']\n",
    "norms = []\n",
    "normsx = []\n",
    "\n",
    "wavefunctionsx.append((psi(x1-Delta/2, w0x) * psi(x2-Delta/2, w0x)))\n",
    "wavefunctionsx.append((psi(x1-Delta/2, w0x)*psi(x2+Delta/2, w0x)+psi(x1+Delta/2, w0x)*psi(x2-Delta/2, w0x)))\n",
    "wavefunctionsx.append(((psi(x1-Delta/2, w0x)+psi(x1+Delta/2, w0x))*(psi(x2-Delta/2, w0x)+psi(x2+Delta/2, w0x))))\n",
    "wavefunctionsx.append(((psi(x1-Delta/2, w0x)-psi(x1+Delta/2, w0x))*(psi(x2-Delta/2, w0x)-psi(x2+Delta/2, w0x))))\n",
    "wavefunctionsx.append((psi(x1-Delta/2, w0x)*psi(x2+Delta/2, w0x)-psi(x1+Delta/2, w0x)*psi(x2-Delta/2, w0x)))\n",
    "\n",
    "for wavefunctionx, name in zip(wavefunctionsx, names):\n",
    "    print(name)\n",
    "    normsx.append(sp.sqrt(1/(sp.integrate(wavefunctionx**2, *xspace))))\n",
    "    wavefunctions.append(wavefunctionx*psiyz)\n",
    "    norms.append(sp.sqrt(1/(sp.integrate(wavefunctions[-1]**2, *allspace))))\n",
    "    assert(norms[-1]**2*sp.integrate(wavefunctions[-1]**2,*allspace))\n",
    "    assert(normsx[-1]**2*sp.integrate(wavefunctionx**2,*xspace))\n",
    "    display(norms[-1]*wavefunctions[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### interaction energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def interactionInt(base):\n",
    "    xint = sp.integrate( base * DiracDelta(x2-x1), (x1, -sp.oo, sp.oo), (x2, -sp.oo, sp.oo))\n",
    "    xyint = sp.integrate( xint * DiracDelta(y2-y1), (y2,-sp.oo,sp.oo), (y1,-sp.oo,sp.oo) )\n",
    "    xyzint = sp.integrate( xyint * DiracDelta(z2-z1), (z2,-sp.oo,sp.oo), (z1,-sp.oo,sp.oo) )\n",
    "    return xyzint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From adam's thesis:\n",
    "$$\n",
    "a=\\frac{4\\pi\\hbar^2 a_s}{m}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And from sources the scattering consetant is 95.44*a0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "from the spin exchange paper there was U/h ~ 200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "scatteringConstant = 4*np.pi*mc.hbar**2*95.44*mc.a0/mc.Rb87_M\n",
    "V=10e-6*mc.k_B\n",
    "spotSize = 650e-9\n",
    "a_sc = sp.symbols('a_s_c',real=True,positive=True)\n",
    "sympifyArgs = [a_sc, w0x, w0y, w0z, Delta]\n",
    "DDelta3D = DiracDelta(x1-x2)*DiracDelta(y1-y2)*DiracDelta(z1-z2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Double-Filled\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{2 \\sqrt{2} a_{s c}}{\\pi^{\\frac{3}{2}} w_{x} w_{y} w_{z}}$"
      ],
      "text/plain": [
       "   2⋅√2⋅a_s_c  \n",
       "───────────────\n",
       " 3/2           \n",
       "π   ⋅wₓ⋅w_y⋅w_z"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mott-Insulator\n"
     ]
    },
    {
     "data": {
      "image/png": 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7e6qJiC5I/bXKYhW8oGKdfVF49cTKbXE+xdM7qdbbBsILTFWuE+u4dcice3Txykl13AppZk1kYqJMb5mvijbL3zPaRkCY80oHGV28clJdgbTWv+zde6rK9lXA49Qgr0PY1H05Zs5JNYbOwu+pcukxqeCLhRd19cUT1gyzb+uw94yDz+SkGoRmNTeoZD4QdG912CozLzW4QGHmnVSGxErD6K3YYeHe6kB1GL0UnupJjQknVQ1Ky9ehsplbMTxxaY8AK63hf7DVZO2kqkFp4ToiE56KjcVUvktDBIQtmLKZe/Blb9+ck6qPyEqvVel8M8VLSf+at1EdCkveSfHZ0aTXFk6qRhWwhGxi5fONlr1PWUKxVlkGYciHpMxT+UxnkjipJsG1fGU1BrbRMP73nRZ7VpewYyWVLxbu6Xz0nVTJxH/J2vg8esBofwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\frac{4 \\sqrt{2} a_{s c}}{\\pi^{\\frac{3}{2}} w_{x} w_{y} w_{z} \\left(e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} + 1\\right)}$"
      ],
      "text/plain": [
       "         4⋅√2⋅a_s_c        \n",
       "───────────────────────────\n",
       "                ⎛    2    ⎞\n",
       "                ⎜ 2⋅Δ     ⎟\n",
       "                ⎜ ────    ⎟\n",
       "                ⎜   2     ⎟\n",
       " 3/2            ⎜ wₓ      ⎟\n",
       "π   ⋅wₓ⋅w_y⋅w_z⋅⎝ℯ     + 1⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Superfluid\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{2} a_{s c} \\left(4 e^{\\frac{\\Delta^{2}}{2 w_{x}^{2}}} + e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} + 3\\right)}{\\pi^{\\frac{3}{2}} w_{x} w_{y} w_{z} \\left(e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} + 2 e^{\\frac{\\Delta^{2}}{w_{x}^{2}}} + 1\\right)}$"
      ],
      "text/plain": [
       "           ⎛      2        2    ⎞   \n",
       "           ⎜     Δ      2⋅Δ     ⎟   \n",
       "           ⎜   ─────    ────    ⎟   \n",
       "           ⎜       2      2     ⎟   \n",
       "           ⎜   2⋅wₓ     wₓ      ⎟   \n",
       "  √2⋅a_s_c⋅⎝4⋅ℯ      + ℯ     + 3⎠   \n",
       "────────────────────────────────────\n",
       "                ⎛    2        2    ⎞\n",
       "                ⎜ 2⋅Δ        Δ     ⎟\n",
       "                ⎜ ────      ───    ⎟\n",
       "                ⎜   2         2    ⎟\n",
       " 3/2            ⎜ wₓ        wₓ     ⎟\n",
       "π   ⋅wₓ⋅w_y⋅w_z⋅⎝ℯ     + 2⋅ℯ    + 1⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Anti-Superfluid\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{2} a_{s c} \\left(- 4 e^{\\frac{\\Delta^{2}}{2 w_{x}^{2}}} + e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} + 3\\right)}{\\pi^{\\frac{3}{2}} w_{x} w_{y} w_{z} \\left(e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} - 2 e^{\\frac{\\Delta^{2}}{w_{x}^{2}}} + 1\\right)}$"
      ],
      "text/plain": [
       "          ⎛        2        2    ⎞  \n",
       "          ⎜       Δ      2⋅Δ     ⎟  \n",
       "          ⎜     ─────    ────    ⎟  \n",
       "          ⎜         2      2     ⎟  \n",
       "          ⎜     2⋅wₓ     wₓ      ⎟  \n",
       " √2⋅a_s_c⋅⎝- 4⋅ℯ      + ℯ     + 3⎠  \n",
       "────────────────────────────────────\n",
       "                ⎛    2        2    ⎞\n",
       "                ⎜ 2⋅Δ        Δ     ⎟\n",
       "                ⎜ ────      ───    ⎟\n",
       "                ⎜   2         2    ⎟\n",
       " 3/2            ⎜ wₓ        wₓ     ⎟\n",
       "π   ⋅wₓ⋅w_y⋅w_z⋅⎝ℯ     - 2⋅ℯ    + 1⎠"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Anti-Mott-Insulator\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOCAYAAAAWo42rAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVQoFXWR0Q2CQBBEhVgAwQ60BLUCsQO0A+3BP/4MJWgLWgIdGCmBDiB2gG+OW0PIuckyO3Ozu5cj6vt+ZlEURenrFlyRJVojLTIjwht+BZ86ABNA2p66ib14BhMzee0Dqukm7ozggawlTOIFzzTdjBlCNzGJaqoii/1dBvr/m2pi6s+te2y3Lb/V48NQvdBE6woZbFurO9rKJOA0bXhHDBW5DBhtYmXP88C0CRjXaLW2OiPFHaEDczNTa+2RPEmb6+ND3RcMdoUtfAd3f+wLrOY/XeyA6s8AAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle 0$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interactionEnergies = []\n",
    "for wave, norm, name in zip(wavefunctions, norms, names):    \n",
    "    print(name)\n",
    "    ie = sp.simplify(a_sc*norm**2*interactionInt(wave**2))\n",
    "    interactionEnergies.append(sp.lambdify(sympifyArgs, ie, 'numpy'))    \n",
    "    display(ie)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Potential Energy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From adam's thesis:\n",
    "$$\n",
    "a=\\frac{4\\pi\\hbar^2 a_s}{m}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And from sources the scattering consetant is 95.44*a0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "from the spin exchange paper there was U/h ~ 200"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Delta_tw, V_tw, w_twx, w_twy, w_twz = sp.symbols('Delta_t V w_t_x w_t_y w_t_z', real=True, positive=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def potential3D(Xp, Yp, Zp, x0, V, w_x, w_y, w_z):\n",
    "    return potentialDipW0(Xp, V, x0, w_x)*potentialDipW0(Yp, 1, 0, w_y) * potentialDipW0(Zp, 1, 0, w_z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def potentialDipW0(x, V, x0, w0):\n",
    "    return V * sp.exp(-2*(x-x0)**2/w0**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def int3D(base, t1, t2, t3, t4):\n",
    "    print('xint...')\n",
    "    xint = (sp.integrate( base*t1, (x1, -sp.oo, sp.oo), (x2, -sp.oo, sp.oo)) + sp.integrate( base*t2, (x1, -sp.oo, sp.oo), (x2, -sp.oo, sp.oo))\n",
    "         + sp.integrate( base*t3, (x1, -sp.oo, sp.oo), (x2, -sp.oo, sp.oo)) + sp.integrate( base*t4, (x1, -sp.oo, sp.oo), (x2, -sp.oo, sp.oo)))\n",
    "    print('yint...')\n",
    "    xyint = (sp.integrate( xint*t1, (y2,-sp.oo,sp.oo), (y1,-sp.oo,sp.oo) )+sp.integrate( xint*t2, (y2,-sp.oo,sp.oo), (y1,-sp.oo,sp.oo) )\n",
    "             +sp.integrate( xint*t3, (y2,-sp.oo,sp.oo), (y1,-sp.oo,sp.oo) )+sp.integrate( xint*t1, (y4,-sp.oo,sp.oo), (y1,-sp.oo,sp.oo) ))\n",
    "    print('zint...')\n",
    "    xyzint = sp.integrate( xyzint*t1, (z2,-sp.oo,sp.oo), (z1,-sp.oo,sp.oo) )\n",
    "    return xyzint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{2} \\pi^{\\frac{3}{2}} V w_{t x} w_{t y}^{2} w_{x} w_{y} w_{z} e^{- \\frac{2 \\Delta^{2}}{w_{x}^{2}} + \\frac{4 \\Delta x_{2}}{w_{x}^{2}} - \\frac{\\Delta_{t}^{2}}{2 w_{t x}^{2}} + \\frac{\\left(2 \\Delta w_{t x}^{2} - \\Delta_{t} w_{x}^{2}\\right)^{2}}{4 w_{t x}^{4} w_{x}^{2} + 2 w_{t x}^{2} w_{x}^{4}} - \\frac{4 z_{2}^{2}}{w_{z}^{2}} - \\frac{4 y_{2}^{2}}{w_{y}^{2}} - \\frac{4 x_{2}^{2}}{w_{x}^{2}}}}{4 \\sqrt{2 w_{t x}^{2} + w_{x}^{2}} \\sqrt{2 w_{t y}^{2} + w_{y}^{2}} \\sqrt{2 w_{t y}^{2} + w_{z}^{2}}}$"
      ],
      "text/plain": [
       "                                                                              \n",
       "                                       2                2       ⎛        2    \n",
       "                                    2⋅Δ    4⋅Δ⋅x₂     Δₜ        ⎝2⋅Δ⋅wₜ ₓ  - Δ\n",
       "                                  - ──── + ────── - ─────── + ────────────────\n",
       "                                      2       2           2         4   2     \n",
       "    3/2             2               wₓ      wₓ      2⋅wₜ ₓ    4⋅wₜ ₓ ⋅wₓ  + 2⋅\n",
       "√2⋅π   ⋅V⋅wₜ ₓ⋅w_t_y ⋅wₓ⋅w_y⋅w_z⋅ℯ                                            \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                              _______________    _________________    ________\n",
       "                             ╱       2     2    ╱        2      2    ╱        \n",
       "                         4⋅╲╱  2⋅wₜ ₓ  + wₓ  ⋅╲╱  2⋅w_t_y  + w_y  ⋅╲╱  2⋅w_t_y\n",
       "\n",
       "      2                          \n",
       "    2⎞          2       2       2\n",
       "ₜ⋅wₓ ⎠      4⋅z₂    4⋅y₂    4⋅x₂ \n",
       "───────── - ───── - ───── - ─────\n",
       "    2   4       2       2      2 \n",
       "wₜ ₓ ⋅wₓ     w_z     w_y     wₓ  \n",
       "                                 \n",
       "─────────────────────────────────\n",
       "_________                        \n",
       "2      2                         \n",
       "  + w_z                          "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.simplify(sp.integrate(wavefunctions[0]**2 * potentialDipW0(x1, V_tw, -Delta_tw/2, w_twx) * potentialDipW0(y1, 1, 0, w_twy) * potentialDipW0(z1, 1, 0, w_twy), \n",
    "             (y1, -sp.oo,sp.oo), (z1, -sp.oo, sp.oo), (x1,-sp.oo,sp.oo)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def potentialInt(base, potentialTerms):\n",
    "    total = sp.S(0)\n",
    "    for potentialTerm in potentialTerms:\n",
    "        print('.',end='')\n",
    "        int1   = sp.simplify(sp.integrate(base * potentialTerm, (y1, -sp.oo,sp.oo), (z1, -sp.oo, sp.oo), (x1,-sp.oo,sp.oo)))\n",
    "        total += sp.simplify(sp.integrate(int1, (y2, -sp.oo,sp.oo), (z2, -sp.oo, sp.oo), (x2,-sp.oo,sp.oo)))\n",
    "    return total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle V e^{- \\frac{2 \\left(\\frac{\\Delta_{t}}{2} + x_{2}\\right)^{2}}{w_{t x}^{2}}} e^{- \\frac{2 y_{2}^{2}}{w_{t y}^{2}}} e^{- \\frac{2 z_{2}^{2}}{w_{t z}^{2}}} + V e^{- \\frac{2 \\left(\\frac{\\Delta_{t}}{2} + x_{1}\\right)^{2}}{w_{t x}^{2}}} e^{- \\frac{2 y_{1}^{2}}{w_{t y}^{2}}} e^{- \\frac{2 z_{1}^{2}}{w_{t z}^{2}}} + V e^{- \\frac{2 \\left(- \\frac{\\Delta_{t}}{2} + x_{2}\\right)^{2}}{w_{t x}^{2}}} e^{- \\frac{2 y_{2}^{2}}{w_{t y}^{2}}} e^{- \\frac{2 z_{2}^{2}}{w_{t z}^{2}}} + V e^{- \\frac{2 \\left(- \\frac{\\Delta_{t}}{2} + x_{1}\\right)^{2}}{w_{t x}^{2}}} e^{- \\frac{2 y_{1}^{2}}{w_{t y}^{2}}} e^{- \\frac{2 z_{1}^{2}}{w_{t z}^{2}}}$"
      ],
      "text/plain": [
       "               2                                     2                        \n",
       "      ⎛Δₜ     ⎞                             ⎛Δₜ     ⎞                         \n",
       "   -2⋅⎜── + x₂⎟         2        2       -2⋅⎜── + x₁⎟         2        2      \n",
       "      ⎝2      ⎠    -2⋅y₂    -2⋅z₂           ⎝2      ⎠    -2⋅y₁    -2⋅z₁       \n",
       "   ──────────────  ───────  ───────      ──────────────  ───────  ───────     \n",
       "           2             2        2              2             2        2     \n",
       "       wₜ ₓ         w_t_y    w_t_z           wₜ ₓ         w_t_y    w_t_z      \n",
       "V⋅ℯ              ⋅ℯ       ⋅ℯ        + V⋅ℯ              ⋅ℯ       ⋅ℯ        + V⋅\n",
       "\n",
       "               2                                       2                   \n",
       "    ⎛  Δₜ     ⎞                             ⎛  Δₜ     ⎞                    \n",
       " -2⋅⎜- ── + x₂⎟         2        2       -2⋅⎜- ── + x₁⎟         2        2 \n",
       "    ⎝  2      ⎠    -2⋅y₂    -2⋅z₂           ⎝  2      ⎠    -2⋅y₁    -2⋅z₁  \n",
       " ────────────────  ───────  ───────      ────────────────  ───────  ───────\n",
       "          2              2        2               2              2        2\n",
       "      wₜ ₓ          w_t_y    w_t_z            wₜ ₓ          w_t_y    w_t_z \n",
       "ℯ                ⋅ℯ       ⋅ℯ        + V⋅ℯ                ⋅ℯ       ⋅ℯ       "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "potential = ( potential3D(x1, y1, z1, -Delta_tw/2, V_tw, w_twx, w_twy, w_twz) + potential3D(x1, y1, z1, Delta_tw/2, V_tw, w_twx, w_twy, w_twz)\n",
    "            + potential3D(x2, y2, z2, -Delta_tw/2, V_tw, w_twx, w_twy, w_twz) + potential3D(x2, y2, z2, Delta_tw/2, V_tw, w_twx, w_twy, w_twz))\n",
    "potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "peSympifyArgs = [V_tw, w0x, w0y, w0z, w_twx, w_twy, w_twz, Delta, Delta_tw]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ V, \\  w_{x}, \\  w_{y}, \\  w_{z}, \\  w_{t x}, \\  w_{t y}, \\  w_{t z}, \\  \\Delta, \\  \\Delta_{t}\\right]$"
      ],
      "text/plain": [
       "[V, wₓ, w_y, w_z, wₜ ₓ, w_t_y, w_t_z, Δ, Δₜ]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "peSympifyArgs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Double-Filled',\n",
       " 'Mott-Insulator',\n",
       " 'Superfluid',\n",
       " 'Anti-Superfluid',\n",
       " 'Anti-Mott-Insulator']"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "nMI = norms[1]\n",
    "wfMI = wavefunctions[1]\n",
    "nSF = norms[2]\n",
    "wfSF = wavefunctions[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Double-Filled\n",
      "...."
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{4 \\sqrt{2} V w_{t x} w_{t y} w_{t z} \\left(e^{\\frac{4 \\Delta \\Delta_{t}}{2 w_{t x}^{2} + w_{x}^{2}}} + 1\\right) e^{- \\frac{\\Delta^{2} + 2 \\Delta \\Delta_{t} + \\Delta_{t}^{2}}{2 w_{t x}^{2} + w_{x}^{2}}}}{\\sqrt{2 w_{t x}^{2} + w_{x}^{2}} \\sqrt{2 w_{t y}^{2} + w_{y}^{2}} \\sqrt{2 w_{t z}^{2} + w_{z}^{2}}}$"
      ],
      "text/plain": [
       "                                               ⎛ 2              2⎞ \n",
       "                        ⎛     4⋅Δ⋅Δₜ       ⎞  -⎝Δ  + 2⋅Δ⋅Δₜ + Δₜ ⎠ \n",
       "                        ⎜ ─────────────    ⎟  ─────────────────────\n",
       "                        ⎜       2     2    ⎟            2     2    \n",
       "                        ⎜ 2⋅wₜ ₓ  + wₓ     ⎟      2⋅wₜ ₓ  + wₓ     \n",
       "4⋅√2⋅V⋅wₜ ₓ⋅w_t_y⋅w_t_z⋅⎝ℯ              + 1⎠⋅ℯ                     \n",
       "───────────────────────────────────────────────────────────────────\n",
       "       _______________    _________________    _________________   \n",
       "      ╱       2     2    ╱        2      2    ╱        2      2    \n",
       "    ╲╱  2⋅wₜ ₓ  + wₓ  ⋅╲╱  2⋅w_t_y  + w_y  ⋅╲╱  2⋅w_t_z  + w_z     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mott-Insulator\n",
      "...."
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{2 \\sqrt{2} V w_{t x} w_{t y} w_{t z} \\left(\\left(2 e^{\\frac{2 \\Delta \\Delta_{t}}{2 w_{t x}^{2} + w_{x}^{2}}} + e^{\\frac{\\Delta \\left(2 \\Delta w_{t x}^{2} + \\Delta \\left(2 w_{t x}^{2} + w_{x}^{2}\\right) + 4 \\Delta_{t} w_{x}^{2}\\right)}{w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}} + e^{\\frac{\\Delta^{2} \\left(4 w_{t x}^{2} + w_{x}^{2}\\right)}{w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}}\\right) e^{\\frac{4 \\Delta^{2} w_{t x}^{4} - 4 \\Delta \\Delta_{t} w_{t x}^{2} w_{x}^{2} + \\Delta_{t}^{2} w_{x}^{4} + 2 w_{t x}^{2} w_{x}^{2} \\left(2 \\Delta^{2} + 2 \\Delta \\Delta_{t} + \\Delta_{t}^{2}\\right)}{2 w_{t x}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}} + e^{\\frac{6 \\Delta^{2} w_{t x}^{2} + \\Delta_{t}^{2} w_{x}^{2}}{2 w_{t x}^{2} w_{x}^{2}}} + 2 e^{\\frac{4 \\Delta^{2} w_{t x}^{4} + \\Delta_{t}^{2} w_{x}^{4} + 2 w_{t x}^{2} w_{x}^{2} \\left(2 \\Delta^{2} + 2 \\Delta \\Delta_{t} + \\Delta_{t}^{2}\\right)}{2 w_{t x}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}} + e^{\\frac{6 \\Delta^{2} w_{t x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right) + 8 \\Delta \\Delta_{t} w_{t x}^{2} w_{x}^{2} + \\Delta_{t}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}{2 w_{t x}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}}\\right) e^{- \\frac{4 \\Delta^{2} w_{t x}^{4} + \\Delta_{t}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right) + 2 w_{t x}^{2} w_{x}^{2} \\left(2 \\Delta^{2} + 2 \\Delta \\Delta_{t} + \\Delta_{t}^{2}\\right)}{2 w_{t x}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}}}{\\sqrt{2 w_{t x}^{2} + w_{x}^{2}} \\sqrt{2 w_{t y}^{2} + w_{y}^{2}} \\sqrt{2 w_{t z}^{2} + w_{z}^{2}} \\left(e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} + 1\\right)}$"
      ],
      "text/plain": [
       "                        ⎛⎛                      ⎛        2     ⎛      2     2⎞\n",
       "                        ⎜⎜       2⋅Δ⋅Δₜ       Δ⋅⎝2⋅Δ⋅wₜ ₓ  + Δ⋅⎝2⋅wₜ ₓ  + wₓ ⎠\n",
       "                        ⎜⎜   ─────────────    ────────────────────────────────\n",
       "                        ⎜⎜         2     2                  2 ⎛      2     2⎞ \n",
       "                        ⎜⎜   2⋅wₜ ₓ  + wₓ                 wₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠ \n",
       "2⋅√2⋅V⋅wₜ ₓ⋅w_t_y⋅w_t_z⋅⎝⎝2⋅ℯ              + ℯ                                \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "          2⎞      2 ⎛      2     2⎞⎞     2     4              2   2     2   4 \n",
       " + 4⋅Δₜ⋅wₓ ⎠     Δ ⋅⎝4⋅wₜ ₓ  + wₓ ⎠⎟  4⋅Δ ⋅wₜ ₓ  - 4⋅Δ⋅Δₜ⋅wₜ ₓ ⋅wₓ  + Δₜ ⋅wₓ  \n",
       "────────────    ───────────────────⎟  ────────────────────────────────────────\n",
       "                  2 ⎛      2     2⎞⎟                                2   2 ⎛   \n",
       "                wₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠⎟                          2⋅wₜ ₓ ⋅wₓ ⋅⎝2⋅w\n",
       "             + ℯ                   ⎠⋅ℯ                                        \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "        2   2 ⎛   2              2⎞       2     2     2   2         2     4   \n",
       "+ 2⋅wₜ ₓ ⋅wₓ ⋅⎝2⋅Δ  + 2⋅Δ⋅Δₜ + Δₜ ⎠    6⋅Δ ⋅wₜ ₓ  + Δₜ ⋅wₓ       4⋅Δ ⋅wₜ ₓ  + \n",
       "───────────────────────────────────    ────────────────────      ─────────────\n",
       "   2     2⎞                                      2   2                        \n",
       "ₜ ₓ  + wₓ ⎠                                2⋅wₜ ₓ ⋅wₓ                         \n",
       "                                    + ℯ                     + 2⋅ℯ             \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                           _______________    _________________    ___________\n",
       "                          ╱       2     2    ╱        2      2    ╱        2  \n",
       "                        ╲╱  2⋅wₜ ₓ  + wₓ  ⋅╲╱  2⋅w_t_y  + w_y  ⋅╲╱  2⋅w_t_z  +\n",
       "\n",
       "  2   4         2   2 ⎛   2              2⎞       2     2 ⎛      2     2⎞     \n",
       "Δₜ ⋅wₓ  + 2⋅wₜ ₓ ⋅wₓ ⋅⎝2⋅Δ  + 2⋅Δ⋅Δₜ + Δₜ ⎠    6⋅Δ ⋅wₜ ₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠ + 8⋅\n",
       "───────────────────────────────────────────    ───────────────────────────────\n",
       "       2   2 ⎛      2     2⎞                                               2  \n",
       " 2⋅wₜ ₓ ⋅wₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠                                         2⋅wₜ ₓ ⋅w\n",
       "                                            + ℯ                               \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "       ⎛    2    ⎞                                                            \n",
       "       ⎜ 2⋅Δ     ⎟                                                            \n",
       "       ⎜ ────    ⎟                                                            \n",
       "______ ⎜   2     ⎟                                                            \n",
       "    2  ⎜ wₓ      ⎟                                                            \n",
       " w_z  ⋅⎝ℯ     + 1⎠                                                            \n",
       "\n",
       "         2   2     2   2 ⎛      2     2⎞⎞   ⎛   2     4     2   2 ⎛      2    \n",
       "Δ⋅Δₜ⋅wₜ ₓ ⋅wₓ  + Δₜ ⋅wₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠⎟  -⎝4⋅Δ ⋅wₜ ₓ  + Δₜ ⋅wₓ ⋅⎝2⋅wₜ ₓ  + w\n",
       "────────────────────────────────────────⎟  ───────────────────────────────────\n",
       " 2 ⎛      2     2⎞                      ⎟                                2   2\n",
       "ₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠                      ⎟                          2⋅wₜ ₓ ⋅wₓ \n",
       "                                        ⎠⋅ℯ                                   \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       " 2⎞         2   2 ⎛   2              2⎞⎞ \n",
       "ₓ ⎠ + 2⋅wₜ ₓ ⋅wₓ ⋅⎝2⋅Δ  + 2⋅Δ⋅Δₜ + Δₜ ⎠⎠ \n",
       "─────────────────────────────────────────\n",
       " ⎛      2     2⎞                         \n",
       "⋅⎝2⋅wₜ ₓ  + wₓ ⎠                         \n",
       "                                         \n",
       "─────────────────────────────────────────\n",
       "                                         \n",
       "                                         \n",
       "                                         \n",
       "                                         \n",
       "                                         \n",
       "                                         "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Superfluid\n",
      "...."
     ]
    },
    {
     "data": {
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\n",
      "text/latex": [
       "$\\displaystyle \\frac{4 \\sqrt{2} V w_{t x} w_{t y} w_{t z} \\left(2 e^{\\frac{2 \\Delta \\Delta_{t}}{2 w_{t x}^{2} + w_{x}^{2}}} + e^{\\frac{2 \\Delta \\left(\\frac{\\Delta w_{t x}^{2}}{w_{x}^{2}} + 2 \\Delta_{t}\\right)}{2 w_{t x}^{2} + w_{x}^{2}}} + 2 e^{\\frac{\\Delta \\left(\\frac{2 \\Delta w_{t x}^{2}}{w_{x}^{2}} + \\Delta + 2 \\Delta_{t}\\right)}{2 w_{t x}^{2} + w_{x}^{2}}} + e^{\\frac{\\Delta \\left(\\frac{4 \\Delta w_{t x}^{2}}{w_{x}^{2}} + \\Delta + 4 \\Delta_{t}\\right)}{2 w_{t x}^{2} + w_{x}^{2}}} + e^{\\frac{\\Delta^{2} \\left(\\frac{4 w_{t x}^{2}}{w_{x}^{2}} + 1\\right)}{2 w_{t x}^{2} + w_{x}^{2}}} + e^{\\frac{2 \\Delta^{2} w_{t x}^{2}}{w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}}\\right) e^{- \\frac{4 \\Delta^{2} w_{t x}^{2}}{w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)} - \\frac{2 \\Delta^{2}}{2 w_{t x}^{2} + w_{x}^{2}} + \\frac{2 \\Delta^{2}}{w_{x}^{2}} - \\frac{2 \\Delta \\Delta_{t}}{2 w_{t x}^{2} + w_{x}^{2}} - \\frac{\\Delta_{t}^{2}}{2 w_{t x}^{2} + w_{x}^{2}}}}{\\sqrt{2 w_{t x}^{2} + w_{x}^{2}} \\sqrt{2 w_{t y}^{2} + w_{y}^{2}} \\sqrt{2 w_{t z}^{2} + w_{z}^{2}} \\left(e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} + 2 e^{\\frac{\\Delta^{2}}{w_{x}^{2}}} + 1\\right)}$"
      ],
      "text/plain": [
       "                        ⎛                        ⎛      2       ⎞        ⎛    \n",
       "                        ⎜                        ⎜Δ⋅wₜ ₓ        ⎟        ⎜2⋅Δ⋅\n",
       "                        ⎜                    2⋅Δ⋅⎜─────── + 2⋅Δₜ⎟      Δ⋅⎜────\n",
       "                        ⎜                        ⎜    2         ⎟        ⎜    \n",
       "                        ⎜       2⋅Δ⋅Δₜ           ⎝  wₓ          ⎠        ⎝   w\n",
       "                        ⎜   ─────────────    ────────────────────      ───────\n",
       "                        ⎜         2     2             2     2                 \n",
       "                        ⎜   2⋅wₜ ₓ  + wₓ        2⋅wₜ ₓ  + wₓ                2⋅\n",
       "4⋅√2⋅V⋅wₜ ₓ⋅w_t_y⋅w_t_z⋅⎝2⋅ℯ              + ℯ                     + 2⋅ℯ       \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "    2           ⎞      ⎛        2           ⎞       ⎛      2    ⎞             \n",
       "wₜ ₓ            ⎟      ⎜4⋅Δ⋅wₜ ₓ            ⎟     2 ⎜4⋅wₜ ₓ     ⎟             \n",
       "───── + Δ + 2⋅Δₜ⎟    Δ⋅⎜───────── + Δ + 4⋅Δₜ⎟    Δ ⋅⎜─────── + 1⎟             \n",
       " 2              ⎟      ⎜     2              ⎟       ⎜    2      ⎟            2\n",
       "ₓ               ⎠      ⎝   wₓ               ⎠       ⎝  wₓ       ⎠         2⋅Δ \n",
       "─────────────────    ────────────────────────    ────────────────    ─────────\n",
       "    2     2                     2     2                 2     2        2 ⎛    \n",
       "wₜ ₓ  + wₓ                2⋅wₜ ₓ  + wₓ            2⋅wₜ ₓ  + wₓ       wₓ ⋅⎝2⋅wₜ\n",
       "                  + ℯ                         + ℯ                 + ℯ         \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                 ⎛    2       \n",
       "                                                                 ⎜ 2⋅Δ        \n",
       "                                                                 ⎜ ────      ─\n",
       "       _______________    _________________    _________________ ⎜   2        \n",
       "      ╱       2     2    ╱        2      2    ╱        2      2  ⎜ wₓ        w\n",
       "    ╲╱  2⋅wₜ ₓ  + wₓ  ⋅╲╱  2⋅w_t_y  + w_y  ⋅╲╱  2⋅w_t_z  + w_z  ⋅⎝ℯ     + 2⋅ℯ \n",
       "\n",
       "          ⎞                                                                   \n",
       "          ⎟                                                                   \n",
       "          ⎟                                                                   \n",
       "     2    ⎟            2     2               2          2                     \n",
       "⋅wₜ ₓ     ⎟         4⋅Δ ⋅wₜ ₓ             2⋅Δ        2⋅Δ        2⋅Δ⋅Δₜ        \n",
       "──────────⎟  - ─────────────────── - ───────────── + ──── - ───────────── - ──\n",
       "  2     2⎞⎟      2 ⎛      2     2⎞         2     2     2          2     2     \n",
       " ₓ  + wₓ ⎠⎟    wₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠   2⋅wₜ ₓ  + wₓ    wₓ     2⋅wₜ ₓ  + wₓ    2⋅\n",
       "          ⎠⋅ℯ                                                                 \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       " 2    ⎞                                                                       \n",
       "Δ     ⎟                                                                       \n",
       "──    ⎟                                                                       \n",
       " 2    ⎟                                                                       \n",
       "ₓ     ⎟                                                                       \n",
       "   + 1⎠                                                                       \n",
       "\n",
       "           \n",
       "           \n",
       "           \n",
       "     2     \n",
       "   Δₜ      \n",
       "───────────\n",
       "    2     2\n",
       "wₜ ₓ  + wₓ \n",
       "           \n",
       "───────────\n",
       "           \n",
       "           \n",
       "           \n",
       "           \n",
       "           \n",
       "           "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Anti-Superfluid\n",
      "...."
     ]
    },
    {
     "data": {
      "image/png": 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ym8a05TXsU0m0oE+n0uGhBE1V1zQrFF5atjW73pTS7inr6hV2oUzJHXqb+00I0gAB/GgATMHZsukTTX672m/++HtVVXykYJWiRJeeh9Q7Cs6BC8kvVvmvvAYxwfNrqLFPEgI6MNzz1gdHO6CYpG4qgcAIAfuc/W+TJN8PHzFM+tBI9YahbJbUq7q5UVsOnI/J/4nKcHyfW2NT/2uLs5QvdtpYxC/x9zblTZYP5ccmvJTPLVVvxys4d3eATFhd3dflE0mvExL6GP/rLccR16jgj8r5fue/Lt/a/WxR25PZPWVdZ4IulxHOU4cIHvZhlN3eauoNHtX5+FEfuLLzPBSFh1bz9fIXmo7yRv5R9S7bWxeUfotz3BR1CJ5PoUXZ1ARCz4LdB9fqE0EUvylloyqkUB8B95z2DeDsJHuFGyd/jO1G6x9o8kfdvOweBCc3SvW2rzX/rV520WKSZK4+wKr5914eEdyvuY+VGalil5uT+V+bjlgfyhfbui+1bP/V5DH+8fdzyPjxOZNsc/DlWaaZ5etiv6dzM//rp64UG/x5od2eanL5ocCorx2TXB+qjWR1naq7+JqPNadwj3i3dpBf2c0dUy517sGP9ukLmw5FsSHS3eg9dF7vYzulbN/+O89b9Rw3lSXB86nEKJ+SQBjvPLyml7LuxevSiS/cDF18xao+QY72ErDAU8ouruC+G/AT/fYf9lxtHSAOY1+7t8yfdYUnPQdkX3+000H2v7V8q/lJYL3eZxcz6eeL/yKP7RUMkNr/2iLji20aKy0f1N/x45X8a81mDurLY4hT+Hrx52Z8o9dN2teSvu551y0lbr4u/EFzv63n6XVPmYvXh9o33HOMdtRQ2Yt1ddvObN2yO/3rbnacX9tY2g6+0ant+NFO3UG2bXc08oMvP2jbfcpdbx+TmkaH01GZqDeLbNApZXfvAB0FxWb2Oa5TZfLVB8lrpEIIxBMIPX9/jt8lq5LuPfKeJapPhH9r8V6PhOEJmscw+0nT2YV1a58pZVu7sTiRgIO6Ve/wifudFZc932j6Tht8c+3kh0JeD6kJIKtc+yYrbN/r3H+AgzcBe1U6Uq9k/tduD19s01h9+Yj+jh+v7marNHhEXx4DO8vXd3Ruxjc6niLbxgS9PlK58DFWD8ngDjWPNTXXSFqOuT50W6HjkW3xZy2Orz+b3uyRddW7ZjcLPc+t32GSbOae9u8099tuQ3rjR0NkCsiXXUc/Oq0yvn+s3j4pQKUoEQvXm1hPlJWTFUp1jksmULciep53ibC+JgH30HBqX3je5ZTx277Qvbq3SVBVfy6+ULzYM8VlVc7DgvwY9mM+nYD42ed8kdrcbEyv5WQPPwgKN0G+AA4X/7ZVqf59ouAVK+410X6IcEUV+9xlAf9rg8IX2zTWWz6cv+PH6znXyi0dzpfH+Cby9T2cm/GNAWeRj4SgV7gWrEoq370WQ+D8RsvuQOMA+qTreO33Rvs4cN7uqNF0zlB+s6yyJd8nhGvmVNfnQpN3kr2s6yean/hOW2ptw4/aQDJZll2S9UxWXcUMtXQgvYn1rHSsTTnHqexm/3EPVuJBMxDoIxAujMKFUl+ZbPN04LblHnrFavQJWkvB2LIOspfaW7+l7uaLvtF5oSnFxwxd13P5hG+Kqnq1/LuWmwthn+i1btt5eBf3FnLZz5Tvm9FdJenkY/uR5u1jZFc6JlAmpf+1xcEX2zRWWD64v+PHK/jYWk0c3JfHMM/19aLPzfjGsHuITQh6uVOGh3Ksris1d2eKJqgdalC+31j0tzS+8zzkR8z9ACZcs3Y7ajTXmypT7H2CeJhhhULzo3RAeSSF3Su5GpJHy75feKF1+4d7ouNHlUdk+ZOkZ7Js7OGKbGc/JLGivn8Kx7rXc0uH0NvHXws8sZ4WjJSLV5zjNvuPe5BSceqCQCwBHSSh1/mNlh1ELDZJft8Qnb1ipfyzXgLKC71NquFegtKxZV1O+/hC28O/+Gm3e6KQriAgdv4AoAPcsy9OXFeECH444jZ9wre/OHAexkmP2L2oIv7gkY8L0gCB2heS+F+7CdfbXh9YPpIvDiBImn1Yf8ePk/pRDpUd1pfH4M/19R2cm/GNHieRXS8Fvdy73B0Jeva8G2ZF2xwgPQuw9+2gvJgHML33CWqjpA4cDlhZXk/t4JVW95dkG+v4SnN3PPFx1k34UZdIPutTeib/Jhv7IZe/eXDScUr57Xry0W5Ykra8Pk7PYjnSyfe7fqO+eL2lA7GeYV9IsSX6HCdb9P7HpRAiqo7b29sbJhis7QP//ve/n2i61fT72m2nbE/yf6vpoev0cqhbyx9pehzW23Plv9X0XcibUtb7qHzRzILeOczF0vZ7sqYsau8rT2u2uXZb0u/t2m2W2J44re5/bU5H8MW2vkstH93f8eP9XEMe3ZfHzhFr+braye46Ad8o5ziXrc7uE5RXXetq/jjYUvPmvmXM99fcLrl+1XSr6fma7dLWqY+Lf9F+tLY9xcv392f3/spr7vm0/FDT333l1pa3rz3J1cQn+rb35Wmf4vXu0yvkST9iPZnFi2WTs3NTsNfS8/tREXYKQSA9AT+ldDp7UnmXnf+vnny5t4mffv2t5VvNn7Sk9hM0fyDU204m5ftJ7HPl+/Usp+iy2se9EoplVmmb0Y94utf5lFdmr5ZebdlXnDxmZfV6rfLaPlNtLP1HOlWvL5euxxryr+l/bX2O4ottnZdaxt+r73Csdh5t2xE/btOYv4wvjzMUo0V9PVefxjfGfSOXErJV732C8sObqr73qMZNV97sNy8X0jv0Nt/r25kLYUtX7U78KB2QkZrEK/RMbg+fdKP8s7fQVVV4C32k1k02h/hMVOM70rtXX+lHrKeXzHaZsknvf9xaEj1YqyHagUCHwPv1+l+d/GJWdfC2X1k6kVvboi/4ppRVIw68Vx+j1H4OwMcM0XAiGytnBDyESjNG5dnWdBkepsUPPnzT8kzLHruysmW6JratSTpVD4Q0j30FeVuB82h9Lf9ra7t7X2wru9Qy/n5CFj8+wVHWCr48yV5L+np252Z8Y5Jv5FC49z5BdgxBPHfgqILmyst1+MdwbzgpkJcD/B3JsAc/WsUcOo7W+ubBKvrENnIEvaUjsZ5Yh1ivXO+5aa3m77lrOwkCaxPQyci9rd3r1h/NORn3a21ZSmpPrHwh6YtePwn1uOehd0ZJamQnqzjaFz0uJQ8jrrSO2PlJsD9wlGtPpis1W343/G95xqlbwN/PieLH50xKyMGXp1vpKL6Ob0z3ja33kM167xOU744bvvfytZo7MPmbK78oP7vODpLJwUi/ren7HAf7SSsTEPfi/WgNZOIUvnkQmvMHXqsOdJr7GHsUNnTmPg6dPla5bI5ByfJW0+gxpzK70vvOFHn8im3vsZeHdNtLsTUfgufb+8AhJZDj+yLOT478AcVVhs04JGiUjiYgP/SX7t0znHQFAfhdAa21C/xaMApYxF79RoJLP5ecc7HZddY5Arcj6Hid9dlrSQLyuxA894cGB3t+LikDdUPgiAR0vEUFz4/IBp0hYAIEz/GDTQjo5ByeWG4ePJcsh379Qvrf28QJIhs9un0iMRVTLHd/mwIS35xC67hlc/d5/Pi4vjlFc/x4Cq3jlM3dL2wJznHb+uNUH1F59zp3AL3pxZtSA9XvIQZd/1j6UmWbN3y1fOj7xTFYS28X/+Z+9VobWsaj2zFw1NzjtLuXczv1DSnqb7g1b2avyS/IagG1fNVxW+976GM3cIRh29WnLQeGqwXPa2M9k5jho3mjEgchRwtSoDgCsm0Inr/S8m6GeZAuHv7Df0R+JdLz75R38vEQ5ZF2TgA/2LmBD6AePnwAIx9ERXz5IIbORE38LRNDFC7Gkf1Iuj+X+RzYWyR4XrhrTBL/yH40CdQVhffIVjot3vO8dG6ly3+FqyffpWSGD5LTGK7QT3j9kZ3dBEqHVWVLBIEw1ldE0aKKvJaPv2eJNbeOf2tqnpQ7f80kGQjmrwn8n7bwg39YsFQmgax82Ag5n5XpSBlInZUv48cZeMSyImTlb1YVn5tm8Km86vIeYqTppTytxd7SWflRDBOVCR8l7VXoisyh8aKvqGr9XWKYtaWqy+NH6f2ojTnlclbHqBWb6nMpYUyoKztuE2R30azkL8TmXcTFMlwleC6j+jULH9DZfBCha0HWNyPw52YtL9Nwe2w+9zzfegztrE5OyyDPslb8IEuzINQEArn5sEXnfDbBgBRtCOTmy/hxY5pdLuTmb4aMz01ztWheurd1L2n3kE4ZOLe0ufnRKBMx8NvEfuN27res/qrNVXpHq1FmtZ43YoYf1TDEIpUfBbxLzXM7Rq1ntM8tBSWi3hy5RYjdFMlN/hJs3sCrF4pleL+ryULrL1RvzNhiCzVPtRkSCL0Jtg4uJ0WjP/z2xbN9/mnSBqZXltvJaboGBe6BHxRoNEQ+IZChD1s+zmcnVmIlhkCGvowfxxiu0DIZ+ptJ4nPT/CmKl2zt4O5nmicfnjFDP4piIh4eH5l7/jt/i2KGH/UenNn7UYbHqEFG+Vwv8ZUyM+UWrX2G8mdv8y7ckhkO9jyXUu4t7g9lzHp6rP3d+/YDzU8uLOr8MISLP07gp8we1uWkd7rWPUa6x0qveq9r7nr8VPuN5k3S+mOthA8fOID5k/Jmyd5UzsISBK7qTSCb2p9G/WaqwKo36fAmqs++eObPsXJp/281BT1jdzsrpzpyC+afyZhThnhl5QdmI5lm+wJ+UHFc5NyRk/8GWVL6seqadS5L5cN1PZzPgpEPME/px7X/ZOHLnI/zdd6UPse5M187j0k24Rh1kNjnlSal9CFXmosfxTJROd9/+7r1oaZrO0hdu19jhxwWpH/sNQt+1DGY2KXwo06t/6yq/mT3e6ori2sLaydZYn3uHxinS+39T7ckXkvBbYpIai+Zzd1uCvlVR1H3+DC8ubnU8/xH+UXoHTzFN7tlHQA8CQIKvIMYdpYqOK+5n5g4aP6rlh0Eb5LWX2nl0zrD44D5Cf9J4NzblOegutt5o+UPNRE4N5j80//EiiibRvtNbJ2tcn7lJXy89Avlv21tm7SoenwRVAXO6+VJ+9eFr3q4MNSQ5Ah/7CcPsYbKHzg/Nz+wKZL5wlH9QHovee7I8XBJ4sf1+WvuuSypD7uyo/pxjo62sExJ/Lj2mRT/y66K8/HCRt+4+iQ+x7lzYysmaj7iv+axynSvq5P4kFXI0Y8imFh0Mzm5n3fmhPT/Qlm1l+ycG+pcex7BDD/qN8pcP+qv9S43yXGa4zFq9SJ8rpeN9rsqfqb9nmjyNw/c6fVGc3ec9XWXlx3zc+C6SfW2FPcXTZ0RC0ls7nYSyp/s/CaZ1oj1HJ5hb/Bc8CvHj3DCi0VUjx3iE827FxY+mBygbJLKOPD9TpOD9idJ25zvyQGQS+mZym49TMYl+dh2TuD/nmcN5kzym8Fa+jcMvvIin4r+Q1DZX1W9j5+/tXyr+cmfRX/T03KnyOOaVT5V0GCaoGWWLsYPattO8c0j+8GS544cPX22H+u8sfi5bKoP1+UP48eywWNNHgf1qGm2Hxtcjr4smfDjPL16ts/l6G/1cXAYn+tzLdkl+nophpfq8z2p7027abYPucIc/UgyxfrQz1Lhsy6YPayLAX7UY8gpXDLxo9nHqfTgOvnUF9xr/cM6yw/PwnftTjokrsXtVLRqbbbNXcta8qud6HONysaem3uwTMo6PMMHXVyC7+FRQrC6u3nqug35smcnH1AOLr6nqX3h4SC7HcVPq7qvjXg9DN1yVqXKO2DZ19ZZWTKyIjAleH6N30Qp2/E3+233IYz9L1wIdv8QHoZGVE/7pBKyl5jHyuM/dh83fhpsObzfyZsgziTdESjQDyz4qC9Ir6P7wWLnjhyPnRR+rDrWOpdF+bALHdCP/d/S/L+YwZFSCj82L9WTlS/jx/l6cQqfy83f6mPg6NcAwelGr5cm8HLwPHzYMtR/k8KHahlKPm/53n6swyABzVUAACAASURBVFvDrGfh//Tk5ZSFH/VbY5SLjo8p56K5ftQvpXJTHKeqI6tj1MpKpil8B/lM3aB2PfKDez6HQLljJl4PqRmWWeXW5Bbav1G79s+QSoj1WNbUx1TQ/6o5DG9uHvSQc+9tv0Zx1WsboT7t7xu+xwP1OEj+kbb5pNiXvG832Xm8z1lg3Xna9r7mzYHZ3Zn1XRC4xm8mKS4fCq+8NL6kvOg/hEmNtQqrDZ/E237vY6f9p+MPp1RvcEyRR2U3+YNqqVbkYs2+ep0sKDCFe9jnmrnaSe4L+EH1CvHU/5xrzJfVPlv58RI+bLD4cVbutZowW/lx7XOcj1ezdD4NbeVzaje5v9V+fPhrQbGNvpZX2RhevmYfuo+9UR2b3E/U9k7uR5FMwkF89lAhbCh9Lg740T9GnHxvmpsfbXWcqt3kx6jNMpHvP5ZMs/SJqgkd9Nxx75e62rNvH6Zp7rpatrK5pVXbye2+hc2PzPAkeC4Q7r3dDthd55V3e73QzA5yltROt1dvKFP1LNf2JnAZNmgenhY5UB6Ww2aPpdRbp/J9cePXnv0aicdU/z7spGW313wUVeseYsMyf6zlwQuisH/MXPVs1v6WbcewmVpG+vTaWPX0+k2tv/3wz7ot+4ADor22Vb5tX233sqbwB+Ddo/4QtI/9c9AfXVFf6rR1o3V/FPfSA6woefrayilPOvr4iLbRGrJLps38wPqp/bbfef0QvrCkbcVw0XPHkrJfW7d03syP1TY+fK3hEu8nW2R3jp2i4pZ+bDnx5SnWWq7smn68pc/hb9N9aKJvpLx29r2oz69naUsfsjAZ+FHfvfoZp6UyJvrENWLgR/3UUnJxC4v60ZbHaQbHaL8F5+U6hvhcujnO4uUXWv5d86rzn+Y3WrdN/TawYzKOz7isv2c4dJ+mzemS2tns3shaqP3i74+OzrAJnguEnfmd5t3A9JnHqsyTumxzMJwVuht+JYx71LP5NEt1OgBqGU6cqlXKB5+TyzRJ+zkw7gN0KDmQ6QC5ZX6tqQmea9lBu/aFjw9g1++T/yXdtDk6bdn+lm1HA5pTcMhvlO8Ts/3iqZarhzF1Wdv8zMe0bew1J9d18Q9B253crsf6WzqNyiOd7Mub/UGNAZB8k2w0Vl+K7QX6gdUu3hdS2G5qHbJ1739Ojn55hW6cz6ZC22H50n2Z8/EOnfIKldb04wJ97tD//1f4RjJeavs3TSf3pHZv5ZX2/2uxk3FxZUrmEu7bq4y1fsR/jXuLZLwkL340HDxdzI8KPE6T+dxSx6KYtmNsQ834LeDvNfk4dYdFB86j44VDlcbkqx3OzTGgLpSB4emwLQ4wnwUVu/xUxr3TX2hykL33tba6jA/yKckfCvXB9GpgpxDUbw4wlfVJ9UPNew/WersPFCePvRTqqDL04wO3GSdd5X/S5EDrSTnluQ4HYU/ylXcxqbzl26T9Ldu+CCX9xjO/qXX3mFv26fZbDLZ3GIvrRBKV6/XlUEjbe30sbPdcZXxsuLe4/chj97+p8+0HbjvZU1bVPSqP2tvsD8p6X0qS30wm2ehSfam2Sa6i/MB6l+4LqWx3RT1Jzh1XtLv4LqX5MT6c3iXENMtz7BRNS/Nj64YvT7HweNm1/bg0nzuyv13jGwvw+sNyaGruD7XMdeTdPfelt2fHD/4rStgW2m3xewu1k/oeDD/qt7djN4v4UWnH6QI+10984VzpUcVG1Iw7MFUxGeWNxh9TiFWaza2zZE59rpmFEoZ18FwgxnpvV6BVzn9KNuL7mvwBQgfn2sHJqpx+HLRsgtwhc2iusg60O+B46QQZxk2qhuio6xobHuMv1Rmc7nPt8zLIoHzX417n3R7mv2hb+yLIZaxnkxfqiJhv2f6WbUegmV9ENhnym/Dg5qHKOKBtf3V6q/Wuve+2JPhV3a802fe7fnxNENtvQcxKkiPJH5Tq8THwv5o8j01Nj/+BHTax0YAsSbPFK6UfWLZsfCEpqIHKFvK3k9bURlbnjhPhMllJ7MeH8uGpJqz90Q9Yu+mRM7S9+5/ibPdWu/Sa627PsVY+NokR5+NYWDPLibV97vB+nNjndnHuFBNfPxZxHSlZp1w7ewgAn5+TBn8S+5DEW+86srb1jebX3Ddb1jkpm/896Y8f9VgylovK+Zxxo/kWftQj+XmWZEt5fbGLc/05pdMcMXP80B1l/WCkOm9qvelweFo6v7XENreCh7B725KlM3wgBRwQd5Bx9OQUymjuIHTogX5y86ZtUYH4ALEuf6N5381hKObtHlLG65bX66PteJ+6rC/mfRIOgXRnO891doP/XSd2uW4Z7z+atmx/y7ZHwSQoIP1s/xvN+/zGNvMHXYbeYkggwXkVas8+1vUfyzjlAqqqWPvMvhBXHUn+oFSPdbrYk+acxmjOJjYalSpBAfFK5gcWR/Vl4wsJ8IxWsZC/Ne2q/uzOHY1wGS2IUzI/PpoPTzWj+PT9j90o38PNuVfjNf9luz3HTuErdsn82O2qvkOdjyeyxo/vfCSZz+3F36THO6Ep4jpSskZfO6usO365s8hJ7/Mpx01fWdWXzIdcv+pb87z1Qk2exAb6dFwoL5v/PTHHj3qMPIHLln7UI/l5lnRJdpyufIyeK7Nejodp8f+Be50/07KHSv5lvebntZTS5pZE9a15bp6nfKK9S2d4XxwcjP6XFPEXk5tJee6Z/bjO85P1JinPTu9AtJ8UVcHsZuPdU6R2kLq16XRR+/rG0MOuNBfcrq+nzrCjA/ze7pOV94vtRew/cffSstwh+YnXycGq7dY5vELidqx3pbuX6+3V/lr2n6Inf8yvKhuWqwKnP0nbVzu2i9v2sANN0nole5Nxt5C0bVepdtyT+ndN/gCrdbc8ZrdKUlsxfjP6MGgBYX3RVvmUZKwCdG5Dy37Q5GSfq3y21qHKXPDHf1CWI/xBeXkLLkMq5iTLkIzX5OfmB9Yhd1+4hvPkferjbuw/Z69+OZVXbn6MD0+1YF7n++nSp9kjNz+2VvjyNNuWdk7Ozef27G9L+MYkXrqu8D2s3zr1vWmqlJsPWa9RLuGeQ/P2/XYqJrH1LOETsW23y43yahfGj/6hkYkf/SPQ8FJux+kknxtWa7ktsq1lrIZp1txjnnv5qk6qy0l5sebcbG5hs7d7h2jRDB/IYR3MOwtCK/9v52s+9PTYQWUH4/zEpAp+q6yDmu7xO/qnqTIOtjpo333i4jqGgu/+Q3Sw3kF+ByJjk/fp/pk6L/QIDvX4CVglj+Yu74PaBn6peVNWyw6GWk+PUeYAtgPodtzwIYK+tvrymjpVh1NU+yrntizbrSa/NeAe9Ob5iSvppKS613U/0zz4RbB9144dMdKs1nqO+U2XddO49l/y1SCf/MMJrH1MOc/HRAhi205VkL0RbIEFtTnlGFlAgotVbmWji0Il2piVH1inzH0hEfbL1YhBzH/Onv3yMqDzrVn5MT58bqCRHHz5DlBWfmyR8OURzz3dXKIfZ+VzO/a3RXzjGl7ax/dkKYPnWfnQhPPWf8RhNAZweognXVvEJ66RED/qpxbJZWs/6hf+PDer4zSS7bkW5EwhkJXNLXiBdi+a4YML3uKLgMELARnKgWMHCJ9r7osG/1n6FZtPNV1MKlsFwFXIwfkwPpn3eaTJvZqHXlEOf4onPeG940iykRwEr5Lq97LbshxVqvP6em474NIOhLq8g9VBFjMK+32hfLfVTcnaV/2W2cF862AbmLuT1/sCssnarlrRj9oMDxgqfmE9bF9qrnZi/cb+0bzNYHm0r+3k/Km+492jktqwT5y06x2Vn3MQO0q3BQptYqMF9DirEj84Q7J5hmyS9bljc0A9AuDHPVDKytrtOXaKGfDjKbSyLFucH+Nzq/lRVr4hu4f7sdkASvWhlAyuhJiVT1yjQ0qG+NE1Fojfp1S+8RpSsksAm3eJTF8vneG929vbE62lkIPZ7hnroLGTA8f+0OJZQFt5Dtg6cOxgqgOH7mF7FjxU/klSmdBD+yS/XvHwKr3j4infPd0/jmmjW7H2CUF6X9z8qcm9219r+lmTPyjpYUhOerxr3fq5l/t7mvcmbTNAy9QXNG/20fak7as+93h38DwEsr3+s9b77JS0bSulduwfj/va8/axpP2C43mswG4P/N7dVS7ab1Q2fCjUtq6S8s7YhG3M1yeAjdZnftQWOXcc1fJl6y2/9Zt4Hhrtqv8uzrFl238v0uPHe7FkfnpwjsvPJikkkl19j+l7Pqf3tB79YAKfuIPGLwQgAAEIpCdwFjyf2oT+pPzn5l59Dp47EBp6ZE+tKrvy9R+whwixXu65/Kitn5arP3fN71l4zX2Tm0x/1eUAcG/72va7tnmMvapXvOYeZudTzS8G8VUmKqmeS22fBM5V1vb/S/MpFzfex0POJJE3SikKQQACEIAABAohoP/HWcHzQtREzJ0TwI93bmDUg8ACBHTe8L3mjebcJy7AlyohAAEIQGA6gfvTdznb46VyHFh2L+hkgeOzVrbJ+FDNume60wvrp8kBcgeqnZ5pav+pj/a6r/aK/zlrv7PrX16XPO4hnzoQ3du29Vdb7rFvFh5ix237Y6rRgXOVd3Lw3x8c9f4kCEAAAhCAAAROCfh/dep/62kNrEFgewL48fY2QAIIFEPA95cS1p3zfJ/4sBjBERQCEIAABHZN4MFc7fSnVn04U/VUw4fMrS+z/T0Uinude7iYH2rZHLD2WO3Oq8Y613IYIsQPElKmvvZD/ebtnue+uPDHO9tB/FBmznyobT8g8Lj2n2uqguiah4+HanFy4qJoMjJ2gAAEIACBvRPQ/3v3eyt7Vxn9dkgAP96hUVEJAisR0PmDB8grsaYZCEAAAhC4TGD2sC2Xq2frEgR0IeGAczOEjNYdxPfY7Cdjti/Rdqo6Jat771sPP5yIGvM8VdvUAwEIQAACEIAABCAAAQhAAAJ5EdB9od9KDh3UqqFR85IQaSAAAQhA4IgEUgzbckRuW+vsHt8eC/WmvsBwIL2YwHkNrxpyRsuP6nVmEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAASyITB72JZsNDmWIB5CxgHzargYzT8+lvpoCwEIQAACEIAABCAAAQhAAAIQgAAEIAABCEBgWQIEz5flu0jtCpbvYZgTxrBbxDuoFAIQgAAEIAABCEAAAhCAQJEEPKynE/eKdxz4hQAEIACBDAgwbEsGRjioCGHYlnCBdFAMqA0BCEAAAhCAAAQgAAEIQAACIsCQnrgBBCAAAQhkR4DgeXYmOZxA7x9OYxSGAAQgAAEIQAACEIAABCAAgS6B0LEqdLTqbmcdAhCAAAQgsDoBguerI6fBmkB4FS9cIAEGAhCAAAQgAAEIQAACEIAABI5LIHSsCveKxyWB5hCAAAQgkA0BgufZmOJwgoTeBLyadzjTozAEIAABCEAAAhCAAAQgAIEzAqFjVbhXPCtABgQgAAEIQGBtAgTP1yZOe4HA7/VCuEAK+cwhAAEIQAACEIAABCAAAQhA4HgEQseqP46nOhpDAAIQgECuBAie52qZ/csVLojCBdL+NUZDCEAAAhCAAAQgAAEIQAACEBgiEDpWhY5WQ+XIhwAEIAABCKxGgOD5aqhpqEMgBM8/6OSzCgEIQAACEIAABCAAAQhAAALHIxA6VoV7xeMRQGMIQAACEMiOAMHz7ExyGIHCBVHoXXAYxVEUAhCAAAQgAAEIQAACEIAABM4IhI5V4V7xrAAZEIAABCAAgbUJEDxfmzjtVQS++eabdwGFlsNFUshiDgEIQAACEIAABCAAAQhAAAIHIaB7QneqCh2rCJ4fxO6oCQEIQKAEAgTPS7DSfmUMF0UEz/drYzSDAAQgAAEIQAACEIAABCAwRiDcE75rd7Qa24ntEIAABCAAgaUJEDxfmjD1XyLwW70xXChdKss2CEAAAhCAAAQgAAEIQAACENgngU9qtUIHq31qiVYQgAAEIFAcAYLnxZlsVwL/XGvz8a60QhkIQAACEIAABCAAAQhAAAIQmELgw7rwT1N2oiwEIAABCEBgaQIEz5cmTP2XCIQLo9DL4FJZtkEAAhCAAAQgAAEIQAACEIDAPgl8VKsVOljtU0u0ggAEIACB4ggQPC/OZPsRWGPZhWFbwoXSfpRDEwhAAAIQgAAEIAABCEAAAhCIJRCG8gwdrGL3oxwEIAABCEBgUQIEzxfFS+URBKox7RRIDxdLEbtQBAIQgAAEIAABCEAAAhCAAAT2QED3gg+lh+8H+VjoHgyKDhCAAAR2RoDg+c4MWqA6b2qZHxcoOyJDAAIQgAAEIAABCEAAAhCAwDwC4V6QXufzOLI3BCAAAQgsQIDg+QJQqXISgbd16c8m7UVhCEAAAhCAAAQgAAEIQAACENgDgWe1Ej/sQRl0gAAEIACBfREgeL4vexanjV7Rc++Cd5pCb4PidEBgCEAAAhCAAAQgAAEIQAACELiaQHUvqHvD8Fby1RWxIwQgAAEIQCA1AYLnqYlS3zUE/qOdHupiiQ+HXkOPfSAAAQhAAAIQgAAEIAABCBRIoL4H9JjnBM4LtB8iQwACEDgCAYLnR7By/jr+WIsYXtfLX2IkhAAEIAABCEAAAhCAAAQgAIG5BMIbyAzZMpck+0MAAhCAwCIECJ4vgpVKpxBoDd3yfMp+lIUABCAAAQhAAAIQgAAEIACBogm4A9U7hmwp2oYIDwEIQGDXBAie79q8RSn3UtJ66JbQ86Ao4REWAhCAAAQgAAEIQAACEIAABOIJ1EO2eOjO7+P3oiQEIAABCEBgXQIEz9flTWsDBHTh9Kre9OVAEbIhAAEIQAACEIAABCAAAQhAYD8EXtSquCMVCQIQgAAEIJAlAYLnWZrlsEI5gP5EgXR/MIYEAQhAAAIQgAAEIAABCEAAAjskUN/zPZFqb7T8bocqohIEIAABCOyEAMHznRhyJ2qEHgehB8JO1EINCEAAAhCAAAQgAAEIQAACEGgRCN+7+rqVxyIEIAABCEAgOwIEz7MzyXEFqnsc+OLpK3qfH9cP0BwCEIAABCAAAQhAAAIQ2D0Bd5j6Xvd9f+xeUxSEAAQgAIGiCRA8L9p8+xNeF08eusWv7dH7fH/mRSMIQAACEIAABCAAAQhA4OAEdM/3lRB4qE56nR/cF1AfAhCAQAkECJ6XYKXjyfiFVHbv8w+OpzoaQwACEIAABCAAAQhAAAIQ2CcB3eM5aP6tpi+1zFjn+zQzWkEAAhDYFQGC57sy5z6U0UXUG2ni6bt9aIQWEIAABCAAAQhAAAIQgAAEICACrzX9pHu+76EBAQhAAAIQKIEAwfMSrHRAGXUx9VRqf6B5+JDMASmgMgQgAAEIQAACEIAABCAAgX0Q0L3dY2niyfd6JAhAAAIQgEARBAieF2Gmwwrpi6pvdZHlV/tIEIAABCAAAQhAAAIQgAAEIFAuAb9Z/FT3dwzXUq4NkRwCEIDA4QgQPD+cyctRWBdVv0laB9AflSM1kkIAAhCAAAQgAAEIQAACEIBAm0DdIcrjnP/UzmcZAhCAAAQgkDuBe7e3t7nLiHwQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAgVUJ0PN8Vdw0BgEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAiUQuPfvf/+bruclWAoZIQABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAYDUCDNuyGmoaggAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAgVIIMGxLKZZCTghAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEFiNwIPVWqIhCEAAAhCAAAQgAAEIQAACmRL45ptvfpRo32n+U6YiIlahBORTDyW6/euplt8VqgZiQwACEIAABA5JgGFbDml2lIYABCAAAQhAAAIQgAAEAoE6cP5W8+9D3hZztf9E7X6g6f16TjC/NkTpbCT/R1LltaZPtUwAvbYrMwhAAAIQgEDuBOh5nruFkA8CEIAABCAAAQhAAAIQWIyAApnuEfyH5psGzmsFX0uO97ysuXsr/63pntdJN0WzkT1/0/RSdvxV04fYEwIQgAAEIACBMggw5nkZdkJKCEAAAhCAAAQgAAEIQCAxAQUzn6vKjzT/OnHVg9WpLQfFh9LHrQ3ugX6oHsp7ZyP93simP2nuBzYkCEAAAhCAAAQKIEDwvAAjISIEIAABCEAAAhCAAAQgkJaAApgOTn+n6encmlXXE01fafpW04+aHvfVqXwHzv+ruYdnOUvK/6OV+a2WZ8vWqi/rxaOwkZ5fyhB+YOMHNyQIQAACEIAABDInQPA8cwMhHgQgAAEIQAACEIAABCCwCIG3qvWVgpi/JajdQ4q4Lvdg/0KT6+5LL5TpgLjLD/ZA1zYH9b/W/EgfLz0SG/uJH7QM+oC2kyAAAQhAAAIQyIAAY55nYAREgAAEIAABCEAAAl0CCqr4tf7e3qndsqynISDmjC2dBmX2tcjW7vX7SPNUw7WMDreittwb/QfNPfa1g+L+eORZz3Jtc49zB87feVlTKhlVbZ5JOh6KjfR9o8kPC2xr90QnQQACEIAABCCQKQGC55kaBrEgAAEIQAACEDguAQVV3BvRr/UTzD2uG6D5sgQctEz2gVAdqzHDrfiYflWr5d7pHr7lsaamd7mW/THJjzR5CBjNblzv7oPn0vGIbGzXt7KzH5C0/UfZJAhAAAIQgAAEciFA8DwXSyAHBCAAAQhAAAIQ+IeAe2H6w3IkCEAgMQEFKr9SlX5A9TJx1TeqOwy3cjIUjNvUFALnLude5Q6g+w2T94Icymv3YA/Zu55L50Oykd7+cKj9xEF0ep/v2stRDgIQgAAESibAmOclWw/ZIQABCEAAAhDYK4FnUuyHvSqHXhDYmIADlR42411KOVRfGG7Fw7J4uUpadk/yk2C6NyjfD8h+0dwB90Mm2FQPcJ6LA2OfH/IIQGkIQAACECiBAD3PS7ASMkIAAhCAAAQgcDQCHsLgLNh2NAjoC4HUBOpg7Qeq92ys8Tltqd5Lw624d/kjlelrogqaatt3mo54zB+dTRiyx2PwN28m9DkKeRCAAAQgAAEIbEPg3u3t7TYt0yoEIAABCEAAAosRUBCGP/jF6PZXLOZJxidXPR6y5anmvMbfj7qIXNnvrQS1LUkrEYg5BlXGwVqPM94MlbKSeDQDgV4C9bniA80/7C1AJgQgAAEIQAACmxKg5/mm+GkcAhCAAAQgkJ6AbsA9RICHJEjaszK9pNQ4QMBB88MO4zDApKjs+hj0mNZJHqgUpXz+wvqBRujtm0Ra2Xm1h5V78qnU3Apm4wc6fvPAAXQ+HJrkqKQSCEAAAhCAQDoCBM/TsaQmCEAAAhCAQC4EqnF31xJGN/seduBF3Z6HQ3D6QvlJxxO+q/YQvx6yJWlwb4waNhwjNHn7qsegpcOG4zYSIz9Y9PnKbwUkS6qXhyRX0IRbA+0/WvIDUz/Y+b7JZQECEIAABCAAgSwIEDzPwgwIAQEIQAACEEhDoA4O3Wi+5ti536q9ZogRLTsI4PF/d/MKunRa5QGB2nHwZE3bBcfDhoHEzLls6ADtjeZr23HXNhTPFMegP8TrtOrDqbsm+3+l1xNt8UPH9+u5eyBnI1+/1Nvk7pWV9PJbKn7Y/JkmgufbuBetQgACEIAABAYJ3B/cwgYIQAACEIAABEok4B7gX68s+HPd+DvoG5J73fr18yqIGDILnzsw+XU9eTicvzT5AUHq5Lp/SF1pRH3YMAJSZJEtjkGLtncbpjgGfU5yoDKnoTFeS55XPrdIti80Je0Vr/r2lPbM6hcZak//mXvyO3SBAAQgAIGDE6Dn+cEdAPUhAAEIQGA/BBR8ce/Fh5o3PV7rvBBM/0TbHfR1ELgpk4CAe537xn/PyYHJHzWFHqF+QOA8D7GSkqU/ZNj04g9AlWfbLmlHbBhgz5jXdjo5Bl3dCvZzM3u3YYpj0OfA3M5VH9t4dfJx7h7IWaaV/PiS7tmzEiMHwD2G+cdanmJL/4+0H0Jf4sA2CEAAAhCAAARWJEDwfEXYNAUBCEAAAhBYmIADup6qVAc63Fuz+XColr39V80/0xQCwfUe181UT/c1cwfx/lB+yqDydcKl22vxwKR4Oehyxkz5DqgtakdsmMxRTo5B17qG/ep29n4czjoGZQcP++Ipp17n9o+2PPaf5nxtu+aS1vLjS/rmykpy2a9ea/pLkx/Q+Jw9Nf3uHVSXH6Am+W+eKgDlIQABCEAAAhDoJ3C/P5tcCEAAAhCAAARKIqCbbd+se6iU9k23AzEeBqBJ2u7ey+4N555xyZPqdwDYY/i2ewgma0f1O7DwPFmFkRWpze81mVtISzwgeKbKfwgNtOar2lF6YsMW/NhFces7Br37qvZzg0vaUHWXegzaPk5VkPJuMZ9fcfW3IvxWUPscno+AG/jxkPJLsJrj19rXQwE91eT/hb5z+JAq7fzwRoTPvyQIQAACEIAABDIicD8jWRAFAhCAAAQgAIHrCTgo/rKzu18B/1s39O4V104OznhoiRBMam+7ermuz4HCqa+rT2nTunT1mbL/7LLSc6ngsh869AXOVrMjNpzlHn3HoCtczX5ubAUblnoMhvNdu6e3kS2SZIcnmr7y5AY098NNnx+97DdJfLxXqc6vhtOql8OmnOaL+LE5aIriZBg1nyVYbe3XwS9386HtnJwXWSAAAQhAAAJzCDyYszP7QgACEIAABCCwPQEFE3zT/4nm7vXWTg7Eekzud+3M1rL3S5LUhgNTDgh95go1d4DZvfFCQMDZxSfpU+kpRZI+IKjr9VA3fbZaxY5BN82x4URPFbOhY9A1rWI/N3QEGwYdpe7UY/CRGSmteU5yW9XxpLmDz39qcvJHQavzr/Txh4d9vnQAWbNKPj+IyS0t6cejnAyjIFaTbSfd/H/p/YKfTq6DHSAAAQhAAAIQWIYAwfNl9RAsSwAAD2tJREFUuFIrBCAAAQhAYE0CL9RYt9e5Aw1DY+c6UOPt1fjamjuI46FQ3OPN46E3Yydr2WW/1LwKzGvu3pInvcuV54ByGHKgqtv7aMoqACQ5U+i51AMCc+0dSkdyL25HbDj7IU/vMSib3qxhv7qd7I9DsdjyGKyC1WL1zrxiUy2z7RsC3z5PuufzxXq0/Y0mnxcdKHdyEN3rIYXz7yJDXIVGUs2lS9R5KLSn8uY9yi2Wk+tV2SJYBQZXzoOfXrk7u0EAAhCAAAQgkJrA/dQVUh8EIAABCEAAAusRqAMUfu39TUyrKufgtoNs7cC2A8KvlOcgTzWsgOYhOfjh8iE5YOT1T0KG5u456V6Vnofpueq8GFxS2bXT1XpKF+vswNdLM/SkZT8g8AfiUqRnquQ/sRXV7ae0IzaMhd8pJ1s42BV9DHr3Beznakuw4ZbH4PuGpBR9zMpO4bz2g5ZfedL+Pg/4vBiTfJ50j20nnzPCuNYewmXNHvCVAKl/pEPf/8mN8qdy2zWnCdz9n/loQnmKQgACEIAABCCwAgF6nq8AmSYgAAEIQAACUwko+OCAnIMQYwFo9xjvBrwvNefezf74pYNArt8BWAfdnNwzshvQcRCk6dWu8j9pco/JppzW39N61imBnmZkmwRWlb6qt+qRP0d51RFr63YzSe2IDdto75Yn2GXqMegGktrPFeZuQ8k391wz9xisjjOzikm1vH6g6Ddvql7i9X4+J4be5GNVOdAeHiRWQXfV5Q+WhoD6Td2O63SP9j81+Zz/mfKHenprczbpxI8tVa3PVG575xRrMD/YmeSnsRVTDgIQgAAEIACB6wkQPL+eHXtCAAIQgAAEFiGg4IN78/2vJvdEHgvOOrAT9YExlXOAwsHvdp1/aT0M0/K5trcD5ZbDN/JNoEfLTr9onyZ4fpeV9reW1QGlbqp65XV0CGV+U/5QwGmWnqp3yQcE5v5DUGJsXrPJ3o61nEXaULIvcgzattiv8vDJ5xpxm3sMhnOHg9MxyedLJ39c2R/9DD3X32q9e06sCnZ/VC6cW7ub2ut+k8UPNH2seDgYB86jzuntStrL2t/nbf+HTAnEPtV+7YcE7SrPllW27//E5SZzU12rcarlTnleOmMzM6Py05l1sDsEIAABCEAAAgkJPEhYF1VBAAIQgAAEIDCTgG7sPfa1k1/vd4/WdqDb+U1SWQd0QqCiye9bUFnXdaP5SX1arwJJmjuY4EBLO4jhPH/ErBtQqfbRtiapjHuFOviSJKiuek7kDA0p33w85EHVcz7kj81VPomeY+20t6tNvxHws+ZjQ+o44N+rb7s+L6uuYuwoWXt1Un7WNqzlM+6kxyD2W/8YNPMZyec/j1s+6VwztT3VH84PfmBT9WhXXntYralV3mh/n+8WGx9c9feeh2pBF+GmNpNwUj1Jz0uTjcMOEIAABCAAAQgUR+B+cRIjMAQgAAEIQGDHBBwgqIME1VAsWq6CFAMqu9f5aGBHZRys/FDzJmigZQegPYxCSA7guud2OzDuYVwcQGyStjcBnpCpvIdadu/JJIHzUO9C86v1nCKPWJi5H254LPOxFDX+cV0ndtRDGgG9ylfHDOHt4pz8GKzr5Ti8M8Ci9rtrovfXQ2LYvj5fxabFz2mSx+cJJ59vqx7tyrOvZJlq2cbOQ8m5lcZphvEqP52xP7tCAAIQgAAEIJCYAMHzxECpDgIQgAAEIJCCgAIFDqI4ANHbA1HbHVQPPfEGm1Q5B7v/pXm3Hgdn2jfpDqR3Ax7O6/Y6f1bLpk1Nck/DbrlmY2YLc/SMUqVm7rJmYjaDSWVtB+w4SKh3w+I2dKu1n88+Buu6OA7/MeUq9vunuWYpPBh81ORcXuieD5vS9XHbrM9c8DAtPp+717nPr14ebHtmW7N2l2wxfjwo+0xuxXCaAdm+Gfx0RjXsCgEIQAACEIBASgIPUlZGXRCAAAQgAAEIJCXg3uffKeDwWFN3jF0Hwy++lq99HKTyB908PnZ7eBffoLuneLvX+kmgV9sc9HU511GlOq/5UJ7Wvc292R0A9vAulvcHzatAuuahR6XH7/U2l3Wvz2+1bTDAou1Lpsl6BmEm6GMW7r1sPtbVrCsmoa7W3D3TX7bWzxbrejaxo9q2H4SAmXsMV0n5HvfZPWW3SFfZ8EpdZh2DhqN2tz4ObT/7j4NytqHl8TcAhnxSmxdNV9nPEknmObr4Y5xOPgfFpHDOasqq/er8pQxvS5JU51bH0ST5JWesHy/CrRROk6D2F97qv7FfGnIhAAEIQAACELi5d3t7CwYIQAACEIAABDIloICB/6gd/G4CLFp2sLqvN/mJFirnccgdbOpLHvbiJPiu9RBgd5DNgSaPf/5a08+a/LG831WmPSa6sqqAltt5qW1ND2otO3DuAPIfmhy480f33HPwrKy2RSftb90nj3nebkB1TNZT+0zWR/uYvfV9peVuz/9KJOWb6cWPA2q769jKjg7++yOG9sP3NPeDAcvyv5pf9QFH7beVDa/SRfJefQzayNp/M/vV7TuY+YOXlfywxjL1+qO3jSXtu4n9LJfavloX7ese3T72P9Zy1IMDlfNx73Pfn5qqpLz2Q8eQvfu59I724xK5SeZZfq39q/85OcInmvyQxUFw+5m/exHlMyrnc40/HtsMsaZ1EgQgAAEIQAACGxOg5/nGBqB5CEAAAhCAwAgBB6uf62a6PS72C+V9OrLfjfY5CY5HlO+7YW96G1/Y38HUbs94B1lDDzoHEkKP9S+UHxW4utDerE1q/xo9J+tjPTX5QYR7b58lbXN+l1tfuU3sKPnc09QPRSynH4JYFyevn4yFX+Wu+CNZJtlwpi5XH4NGorY3sV8wh9qvAuU1A8tzdeA81Dl3Lhkm2S+0F2TX3L55E9bD9pH5X/X2RyPlms2qPyro2eyw4wWxiPbjI3KTzjH/lYMeov39P+kUzrN3a/xCAAIQgAAEILA5gfubS4AAEIAABCAAAQhcIuCelk4hAFYFLnWjncUNtuSwPA4sn8ij9XYPdZepgsTKnxs4dzsnbWl98TRDH+vtYVse9gjpYIt7K26eJN+ZHZUXAuYOdDZvFWj5X5rCw5BrZF/dhjN1yfoYtAH67Nc2jLb7AdcTzVMEzle3XyJdwsO8KvDerpNlCIjApn6t9oNfNm85YBUIQAACEIAABPIgQPA8DzsgBQQgAAEIQKCXgIJdDvg4AOshB5wcyAvBvCpj45+m17lkfagpBAAqsbTu7TeaV0Hz7vapsmt/D2HTDsxPrWJWebU9VZ8f6gYdnO6mx9anm7nR+iU7els7WN48DLlG1o1tOFkXyZv7MWgzDNqv9ln7WtWLWnO/xdL3MCfKnNp3s2NQbVvPq3TRvuHBXXQP6iggFNoFgS39ugYY/jvDQ55dcEUJCEAAAhCAwB4IEDzfgxXRAQIQgAAE9k6gCpbr5t69lN0bOKeba4/X/XNtgBeWTZODc3/Xec80D0ErZ/UN11AXzXM2U58QHDeHJqlOBwHbXJptGy2c2bEjx19el9wOnPshSU6yd0QdXb1Gl5yPQSvcaz/ZyQE5f7fAx6XfgLD9PPa7e9kWlRLp4nOnx6QmQSA3AiF4XvK5NTemyAMBCEAAAhBIQuBBklqoBAIQgAAEIACBxQgoaOSeng76+INmDpLllBzQfyr53DM+9LJ2cNIyO6/qsazl8OG9l8orLV2tj/T2kDYOhjho2U4Opgde7fytlvvsGGTxUB9fSg9/MNBDzZQc3LlKF+me8zFoOw3Zzw+rPtX0uaYqiK75rLGZtf9WKYUufcfiVvrQLgTaBDwc1o3ONTk9HG/LxzIEIAABCEDgsATu3d76o94kCEAAAhCAAARyJqAbageiP9O81MBXzngXlU0284MD91z+WMtV4Fnz3zXl9iDkjINk9PAejzSvAjqa+2HIj5pvNnTOmZCRGXN10f4cg5Gscy1W2/A7yfeelovrfZ8rV+SaT0D+6Le1ftH8s/m1UQMEIAABCEAAAikJ0PM8JU3qggAEIAABCCxEQDfUDlYWF7BcCEdp1baHbvlNtvTr+aX0LnRvZQ/L80pyu/e8A+ml+uEsXTgGZf3y0y+1Cvbl9kdwy9cMDYolUP8n+EGlH06SIAABCEAAAhDIjABjnmdmEMSBAAQgAAEIQGBfBBQYcW9z93INQ7d4+An3fi0heWgZDz3j3vN+86Hkjy3uSZcSfCc7GVvH4sk3CLITFIGORiD8N/BA52iWR18IQAACECiCwIMipERICEAAAhCAAAQgUDYB9z5/ouCdexc6UFLE2O+SdzfBnD3pUvahsLn0/5EEHgOeBIFcCHioltw+Bp4LG+SAAAQgAAEIbE6AnuebmwABIAABCEAAAhA4AIHwcdAX0vUvBXIZb/kARkfFLAn446oPdQyG3r5ZColQhyLgj4GX8jbSoQyDshCAAAQgAAETIHiOH0AAAhCAAAQgAIHlCYRxzz38iYN3JAhAYAMCCpr7WPQ3B/j48gb8afKUgPzRHyJ2KvVbEnfS8wsBCEAAAhDYMQGC5zs2LqpBAAIQgAAEIJAHgbqnucc+d/KwESQIQGA7At+q6ec6Lj2MEgkCWxL4Wo2/qf8jtpSDtiEAAQhAAAIQGCBA8HwADNkQgAAEIAABCEAgMQEP3fIbQZLEVKkOAhMJ6Bh0L18PneRhlEgQ2ISA/NBDB32gyQF0EgQgAAEIQAACmRIgeJ6pYRALAhCAAAQgAIHdEXDA7ovdaYVCECiTgAOWXymASe/zMu23B6lDr3MPI0SCAAQgAAEIQCBTAvdub28zFQ2xIAABCEAAAhCAAAQgAAEILENAgfNfVfNPmtPzdxnE1DpAoO51/lab39MyH5Ae4EQ2BCAAAQhAIAcC9DzPwQrIAAEIQAACEIAABCAAAQisTcBvgnjscw+dQYLAmgT84einBM7XRE5bEIAABCAAgesIEDy/jht7QQACEIAABCAAAQhAAAIFE1Dg0h/xfanJgUwSBFYhIL+zv/mNhzerNEgjEIAABCAAAQjMIkDwfBY+doYABCAAAQhAAAIQgAAESiWgAOYryf6H5t+WqgNyl0NAfvZE0n6g+dNypEZSCEAAAhCAwLEJEDw/tv3RHgIQgAAEIAABCEAAAocmUAcyP9L8+aFBoPyiBORfH6mBF5o+XbQhKocABCAAAQhAICkBgudJcVIZBCAAAQhAAAIQgAAEIFAaAQU2P5PMHoP6cWmyI2/+BORXDyXla02fapkPhOZvMiSEAAQgAAEINAT+P2l68t7tLOhGAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\frac{4 \\sqrt{2} V w_{t x} w_{t y} w_{t z} \\left(2 e^{\\frac{2 \\Delta \\Delta_{t}}{2 w_{t x}^{2} + w_{x}^{2}}} - e^{\\frac{2 \\Delta \\left(\\frac{\\Delta w_{t x}^{2}}{w_{x}^{2}} + 2 \\Delta_{t}\\right)}{2 w_{t x}^{2} + w_{x}^{2}}} - 2 e^{\\frac{\\Delta \\left(\\frac{2 \\Delta w_{t x}^{2}}{w_{x}^{2}} + \\Delta + 2 \\Delta_{t}\\right)}{2 w_{t x}^{2} + w_{x}^{2}}} + e^{\\frac{\\Delta \\left(\\frac{4 \\Delta w_{t x}^{2}}{w_{x}^{2}} + \\Delta + 4 \\Delta_{t}\\right)}{2 w_{t x}^{2} + w_{x}^{2}}} + e^{\\frac{\\Delta^{2} \\left(\\frac{4 w_{t x}^{2}}{w_{x}^{2}} + 1\\right)}{2 w_{t x}^{2} + w_{x}^{2}}} - e^{\\frac{2 \\Delta^{2} w_{t x}^{2}}{w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}}\\right) e^{- \\frac{4 \\Delta^{2} w_{t x}^{2}}{w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)} - \\frac{2 \\Delta^{2}}{2 w_{t x}^{2} + w_{x}^{2}} + \\frac{2 \\Delta^{2}}{w_{x}^{2}} - \\frac{2 \\Delta \\Delta_{t}}{2 w_{t x}^{2} + w_{x}^{2}} - \\frac{\\Delta_{t}^{2}}{2 w_{t x}^{2} + w_{x}^{2}}}}{\\sqrt{2 w_{t x}^{2} + w_{x}^{2}} \\sqrt{2 w_{t y}^{2} + w_{y}^{2}} \\sqrt{2 w_{t z}^{2} + w_{z}^{2}} \\left(e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} - 2 e^{\\frac{\\Delta^{2}}{w_{x}^{2}}} + 1\\right)}$"
      ],
      "text/plain": [
       "                        ⎛                        ⎛      2       ⎞        ⎛    \n",
       "                        ⎜                        ⎜Δ⋅wₜ ₓ        ⎟        ⎜2⋅Δ⋅\n",
       "                        ⎜                    2⋅Δ⋅⎜─────── + 2⋅Δₜ⎟      Δ⋅⎜────\n",
       "                        ⎜                        ⎜    2         ⎟        ⎜    \n",
       "                        ⎜       2⋅Δ⋅Δₜ           ⎝  wₓ          ⎠        ⎝   w\n",
       "                        ⎜   ─────────────    ────────────────────      ───────\n",
       "                        ⎜         2     2             2     2                 \n",
       "                        ⎜   2⋅wₜ ₓ  + wₓ        2⋅wₜ ₓ  + wₓ                2⋅\n",
       "4⋅√2⋅V⋅wₜ ₓ⋅w_t_y⋅w_t_z⋅⎝2⋅ℯ              - ℯ                     - 2⋅ℯ       \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "    2           ⎞      ⎛        2           ⎞       ⎛      2    ⎞             \n",
       "wₜ ₓ            ⎟      ⎜4⋅Δ⋅wₜ ₓ            ⎟     2 ⎜4⋅wₜ ₓ     ⎟             \n",
       "───── + Δ + 2⋅Δₜ⎟    Δ⋅⎜───────── + Δ + 4⋅Δₜ⎟    Δ ⋅⎜─────── + 1⎟             \n",
       " 2              ⎟      ⎜     2              ⎟       ⎜    2      ⎟            2\n",
       "ₓ               ⎠      ⎝   wₓ               ⎠       ⎝  wₓ       ⎠         2⋅Δ \n",
       "─────────────────    ────────────────────────    ────────────────    ─────────\n",
       "    2     2                     2     2                 2     2        2 ⎛    \n",
       "wₜ ₓ  + wₓ                2⋅wₜ ₓ  + wₓ            2⋅wₜ ₓ  + wₓ       wₓ ⋅⎝2⋅wₜ\n",
       "                  + ℯ                         + ℯ                 - ℯ         \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                 ⎛    2       \n",
       "                                                                 ⎜ 2⋅Δ        \n",
       "                                                                 ⎜ ────      ─\n",
       "       _______________    _________________    _________________ ⎜   2        \n",
       "      ╱       2     2    ╱        2      2    ╱        2      2  ⎜ wₓ        w\n",
       "    ╲╱  2⋅wₜ ₓ  + wₓ  ⋅╲╱  2⋅w_t_y  + w_y  ⋅╲╱  2⋅w_t_z  + w_z  ⋅⎝ℯ     - 2⋅ℯ \n",
       "\n",
       "          ⎞                                                                   \n",
       "          ⎟                                                                   \n",
       "          ⎟                                                                   \n",
       "     2    ⎟            2     2               2          2                     \n",
       "⋅wₜ ₓ     ⎟         4⋅Δ ⋅wₜ ₓ             2⋅Δ        2⋅Δ        2⋅Δ⋅Δₜ        \n",
       "──────────⎟  - ─────────────────── - ───────────── + ──── - ───────────── - ──\n",
       "  2     2⎞⎟      2 ⎛      2     2⎞         2     2     2          2     2     \n",
       " ₓ  + wₓ ⎠⎟    wₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠   2⋅wₜ ₓ  + wₓ    wₓ     2⋅wₜ ₓ  + wₓ    2⋅\n",
       "          ⎠⋅ℯ                                                                 \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       " 2    ⎞                                                                       \n",
       "Δ     ⎟                                                                       \n",
       "──    ⎟                                                                       \n",
       " 2    ⎟                                                                       \n",
       "ₓ     ⎟                                                                       \n",
       "   + 1⎠                                                                       \n",
       "\n",
       "           \n",
       "           \n",
       "           \n",
       "     2     \n",
       "   Δₜ      \n",
       "───────────\n",
       "    2     2\n",
       "wₜ ₓ  + wₓ \n",
       "           \n",
       "───────────\n",
       "           \n",
       "           \n",
       "           \n",
       "           \n",
       "           \n",
       "           "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Anti-Mott-Insulator\n",
      "...."
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{2 \\sqrt{2} V w_{t x} w_{t y} w_{t z} \\left(\\left(- 2 e^{\\frac{2 \\Delta \\Delta_{t}}{2 w_{t x}^{2} + w_{x}^{2}}} + e^{\\frac{\\Delta \\left(2 \\Delta w_{t x}^{2} + \\Delta \\left(2 w_{t x}^{2} + w_{x}^{2}\\right) + 4 \\Delta_{t} w_{x}^{2}\\right)}{w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}} + e^{\\frac{\\Delta^{2} \\left(4 w_{t x}^{2} + w_{x}^{2}\\right)}{w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}}\\right) e^{\\frac{4 \\Delta^{2} w_{t x}^{4} - 4 \\Delta \\Delta_{t} w_{t x}^{2} w_{x}^{2} + \\Delta_{t}^{2} w_{x}^{4} + 2 w_{t x}^{2} w_{x}^{2} \\left(2 \\Delta^{2} + 2 \\Delta \\Delta_{t} + \\Delta_{t}^{2}\\right)}{2 w_{t x}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}} + e^{\\frac{6 \\Delta^{2} w_{t x}^{2} + \\Delta_{t}^{2} w_{x}^{2}}{2 w_{t x}^{2} w_{x}^{2}}} - 2 e^{\\frac{4 \\Delta^{2} w_{t x}^{4} + \\Delta_{t}^{2} w_{x}^{4} + 2 w_{t x}^{2} w_{x}^{2} \\left(2 \\Delta^{2} + 2 \\Delta \\Delta_{t} + \\Delta_{t}^{2}\\right)}{2 w_{t x}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}} + e^{\\frac{6 \\Delta^{2} w_{t x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right) + 8 \\Delta \\Delta_{t} w_{t x}^{2} w_{x}^{2} + \\Delta_{t}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}{2 w_{t x}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}}\\right) e^{- \\frac{4 \\Delta^{2} w_{t x}^{4} + \\Delta_{t}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right) + 2 w_{t x}^{2} w_{x}^{2} \\left(2 \\Delta^{2} + 2 \\Delta \\Delta_{t} + \\Delta_{t}^{2}\\right)}{2 w_{t x}^{2} w_{x}^{2} \\left(2 w_{t x}^{2} + w_{x}^{2}\\right)}}}{\\sqrt{2 w_{t x}^{2} + w_{x}^{2}} \\sqrt{2 w_{t y}^{2} + w_{y}^{2}} \\sqrt{2 w_{t z}^{2} + w_{z}^{2}} \\left(e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} - 1\\right)}$"
      ],
      "text/plain": [
       "                        ⎛⎛                        ⎛        2     ⎛      2     \n",
       "                        ⎜⎜         2⋅Δ⋅Δₜ       Δ⋅⎝2⋅Δ⋅wₜ ₓ  + Δ⋅⎝2⋅wₜ ₓ  + wₓ\n",
       "                        ⎜⎜     ─────────────    ──────────────────────────────\n",
       "                        ⎜⎜           2     2                  2 ⎛      2     2\n",
       "                        ⎜⎜     2⋅wₜ ₓ  + wₓ                 wₓ ⋅⎝2⋅wₜ ₓ  + wₓ \n",
       "2⋅√2⋅V⋅wₜ ₓ⋅w_t_y⋅w_t_z⋅⎝⎝- 2⋅ℯ              + ℯ                              \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "2⎞          2⎞      2 ⎛      2     2⎞⎞     2     4              2   2     2   \n",
       " ⎠ + 4⋅Δₜ⋅wₓ ⎠     Δ ⋅⎝4⋅wₜ ₓ  + wₓ ⎠⎟  4⋅Δ ⋅wₜ ₓ  - 4⋅Δ⋅Δₜ⋅wₜ ₓ ⋅wₓ  + Δₜ ⋅wₓ\n",
       "──────────────    ───────────────────⎟  ──────────────────────────────────────\n",
       "⎞                   2 ⎛      2     2⎞⎟                                2   2 ⎛ \n",
       "⎠                 wₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠⎟                          2⋅wₜ ₓ ⋅wₓ ⋅⎝2\n",
       "               + ℯ                   ⎠⋅ℯ                                      \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "4         2   2 ⎛   2              2⎞       2     2     2   2         2     4 \n",
       "  + 2⋅wₜ ₓ ⋅wₓ ⋅⎝2⋅Δ  + 2⋅Δ⋅Δₜ + Δₜ ⎠    6⋅Δ ⋅wₜ ₓ  + Δₜ ⋅wₓ       4⋅Δ ⋅wₜ ₓ  \n",
       "─────────────────────────────────────    ────────────────────      ───────────\n",
       "     2     2⎞                                      2   2                      \n",
       "⋅wₜ ₓ  + wₓ ⎠                                2⋅wₜ ₓ ⋅wₓ                       \n",
       "                                      + ℯ                     - 2⋅ℯ           \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                            _______________    _________________    __________\n",
       "                           ╱       2     2    ╱        2      2    ╱        2 \n",
       "                         ╲╱  2⋅wₜ ₓ  + wₓ  ⋅╲╱  2⋅w_t_y  + w_y  ⋅╲╱  2⋅w_t_z  \n",
       "\n",
       "    2   4         2   2 ⎛   2              2⎞       2     2 ⎛      2     2⎞   \n",
       "+ Δₜ ⋅wₓ  + 2⋅wₜ ₓ ⋅wₓ ⋅⎝2⋅Δ  + 2⋅Δ⋅Δₜ + Δₜ ⎠    6⋅Δ ⋅wₜ ₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠ + \n",
       "─────────────────────────────────────────────    ─────────────────────────────\n",
       "         2   2 ⎛      2     2⎞                                               2\n",
       "   2⋅wₜ ₓ ⋅wₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠                                         2⋅wₜ ₓ \n",
       "                                              + ℯ                             \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "        ⎛    2    ⎞                                                           \n",
       "        ⎜ 2⋅Δ     ⎟                                                           \n",
       "        ⎜ ────    ⎟                                                           \n",
       "_______ ⎜   2     ⎟                                                           \n",
       "     2  ⎜ wₓ      ⎟                                                           \n",
       "+ w_z  ⋅⎝ℯ     - 1⎠                                                           \n",
       "\n",
       "           2   2     2   2 ⎛      2     2⎞⎞   ⎛   2     4     2   2 ⎛      2  \n",
       "8⋅Δ⋅Δₜ⋅wₜ ₓ ⋅wₓ  + Δₜ ⋅wₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠⎟  -⎝4⋅Δ ⋅wₜ ₓ  + Δₜ ⋅wₓ ⋅⎝2⋅wₜ ₓ  +\n",
       "──────────────────────────────────────────⎟  ─────────────────────────────────\n",
       "   2 ⎛      2     2⎞                      ⎟                                2  \n",
       "⋅wₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠                      ⎟                          2⋅wₜ ₓ ⋅w\n",
       "                                          ⎠⋅ℯ                                 \n",
       "──────────────────────────────────────────────────────────────────────────────\n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "                                                                              \n",
       "\n",
       "   2⎞         2   2 ⎛   2              2⎞⎞ \n",
       " wₓ ⎠ + 2⋅wₜ ₓ ⋅wₓ ⋅⎝2⋅Δ  + 2⋅Δ⋅Δₜ + Δₜ ⎠⎠ \n",
       "───────────────────────────────────────────\n",
       " 2 ⎛      2     2⎞                         \n",
       "ₓ ⋅⎝2⋅wₜ ₓ  + wₓ ⎠                         \n",
       "                                           \n",
       "───────────────────────────────────────────\n",
       "                                           \n",
       "                                           \n",
       "                                           \n",
       "                                           \n",
       "                                           \n",
       "                                           "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "potentialEnergies = []\n",
    "for wave, norm, name in zip(wavefunctions, norms, names):    \n",
    "    print(name)\n",
    "    potentialTerms = ( potential3D(x1, y1, z1, -Delta_tw/2, V_tw, w_twx, w_twy, w_twz), potential3D(x1, y1, z1, Delta_tw/2, V_tw, w_twx, w_twy, w_twz),\n",
    "                       potential3D(x2, y2, z2, -Delta_tw/2, V_tw, w_twx, w_twy, w_twz), potential3D(x2, y2, z2, Delta_tw/2, V_tw, w_twx, w_twy, w_twz))\n",
    "    pe = sp.simplify(norm**2*potentialInt(wave**2, potentialTerms))\n",
    "    potentialEnergies.append(sp.lambdify(peSympifyArgs, pe, 'numpy'))    \n",
    "    display(pe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "...."
     ]
    }
   ],
   "source": [
    "offDiagTerm = sp.simplify(nMI*nSF*potentialInt(wfMI*wfSF, potentialTerms))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "offDiagFunc = sp.lambdify(peSympifyArgs, offDiagTerm, 'numpy')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Kinetic Energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def KE(func,v1, v2):\n",
    "    return -hbar**2/(2*m)*(D(D(func,v1),v1) + D(D(func,v2),v2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "hbar, m = sp.symbols('hbar m')\n",
    "keSympifyArgs = [w0x, w0y, w0z, Delta]\n",
    "N_d = norms[0]\n",
    "Psi_d = wavefunctions[0]\n",
    "yKE = N_d**2*sp.integrate(Psi_d*KE(wavefunctions[0],y1,y2),*allspace)\n",
    "zKE = N_d**2*sp.integrate(Psi_d*KE(wavefunctions[0],z1,z2),*allspace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Double-Filled\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAL8AAAA2CAYAAACWVUgWAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAIfUlEQVR4Ae2d73XUOBTFnTkpgA0VbOgASAWEDgJUkNABe/iUfMuBDmAr4EAH0MECHUAHG9JB9v40klYje2LNMBnL46dzFP21/XTflfQke5S9m5ubZtvu4uLinp752j/30Ienyr/etiy1Ps8wKtPM7+C0X/aIjdd6I6Ffhrsq/k7xb/IPQp6FjWFURoK1cZqV3X/jtc5E+OPkrm8UP1TewyRv6lHDqIwBa+O00ZFf5MWc+Sj/WP5K6WUjOaP+V/nJOcOoTOXbwGmvxOaXINjlf3mxHbFJK/97V1OUjwnzU+GzrvI8T/UY+U8ULuss+SXVpSW7YVSglZpw6iW/Fxa7KhJZccj6Sv6p4l9CmxU/UfzIl5Gfdo4fKn8f6oZQeZg6zBaPFB/lgldyQ3zDKCh1SVgbTiXkh5itnRg15BdtVPhH2lalIbNbvCr+My3L4yqHNCx2nyk+SuLTJsluGAFEj6sNp1mPvBSzMP0lwbHnU8fIfk/5EDh11L9WfgnxGS2ZPaj/UD6/V3rfmuOGUZl2qsJpv0BmSA4xl43Mead4qvpuMatraCyE/qp4NIE8yRnxWTeEHR4WwWFdoeionGFUpq6qcOo1e5a1SaT9oTK2J/fSOkrz1gzbns7yQZ4ZADOIUd7Z/AoxmfJO0yh/4V6qM2qn9hhGBRocCqeSkb8lvoRltGZEXxipfT716RTMAM4pTo9nwRzIv7BOmNfarb+GUZk+h8RpViZiqxYLvPcS/G1WgpmDiztD86Tb919mNvkqOxcYRmUqHQynlckvwmOrf1EYP09I2shoT1lOdGaKz0m9nY4aRmXqHRqnlcgvYc9olsIu4lPEC7AFkqtumA0wfXbeGUZlKq4Bp2LyS1heYD1QGImvOLb9Ic31IYvYnOSYQLztdVufClsLXa7fBae2GUYFiqwFpyLyS1jMliOFCwtc5aHsK99eN8KrTtzS9PnPFWIqNSpzM4fP36lAbTOMCjRaE069uz0SlpGdRQm2vCOxb+OBQvb/w6LX2fu+LA3S2YCXYvl6IK07yrhhVKa22nDqJb+aBfHpAF2jdjrKUyftHEo6R+d4oYbj85nDVxl9YBiVqbAqnNZ+yVXWVqtlCNSLQJHNX6/4JpkhsD4CkyG/TK5j+S7TbX30duzKqWE0GfKLpyy8d3abdUP9cFIYTYn8G+KH3WZXEDDy74omrR0rI2DkXxkyu2BXEDDy74omrR0rI7B3fn6+/SPbVhZzfoF2I3p/7KI6vGgLH9OlT+KNNC58jjFPzf9+13X5Z9hpeaPy0eCE4JJ3KVYqM4yE0WRecknhfIfEh3jhcww4Yi5BYGoYmdmTKN+i00LAyD8tfVtrEwRKPmxLqt9tVNMuL1le+6cc+rB1ZtDdSlH33Q2jMv2U4FQV+dUsTnhIfyzDwsxOb17Ut2G0iMeyVC9OtZk9ZyJ/ulNjpze3VWsYtTHpyunFqTbyM+rf1enN17o3fuzOMCrTYC9OVW91ahYY/enNZXpav5ZhVIZdF061jfyxJRKW38SyN/8oZlpkAQHDaAGOpYllOFVJfgl7qJYw6o/22PKlmthQgWFUBuRtOLndHlVgkckP0CFd+J0tNtO/8kfy/6jOW3lG4xc+n/qsqONRJYqzVckPRvgnE9+Ujufx+2tfKuS+jUJG9RbBle+Ir5D7U49n9p76TN27dpKlCpwkh2HUNL/NpZknDMeEQ3rIy/Yi/yWFE5T5FOBUHpJD6oMkn3r8IDl11OMaDq6C2Klj/x6lBcfik/TjkKFrSXPfS8U5GQLi01m6vsdR9tbd4DgZRk7nG+HSzBMsnLLmiKi89PuXA08xDqyKo7zyyKezOOeVwp48jlE7P5+fUTM8p/H34vSHtB7XU48weLas6CiDOslARwzyD4mTYTTnSNDF2lzal0I5TY2vGiEyPh+xUTruch7EvxA87Qz8A7pg5nBQVayvfO7BvdP6Srpz+yP5Va/m05urwMkw2hyXGPnDqMqI2yidExSS0zlCParh8pHclase+RA9dIRQF7s9PeeH/Pye5FXpkvYbTks0NDaMgs1Pc1jI5uQkH2UvdIiE4J+ooDRkD47v4vPOQgdaeHmla1IzIlw7htBw6tfSKDBKyd9FckjNIjTaV77dLEIhOKYA5W409GWkoymT5OUdixPcFjqVr1t7YDj1a2gUGO3TDk9giP4haxe2O+U5SSF4yGPLiZ2i4CB57AwqI34gzzXO+by8QzXKZzZgBwlziBmEa1hL5B1H2dt3kgN5BsVJMoAnOHFwcPz1meKf5ZlhB3WSYXCMAEBy8K9ycWy7s45lwEZ37Ei6wXmmBA6B3YLOpf7/Q+XUdg8lLGY5dJYHsDUZnfLoCPwDunfyPBRF/UkFpV/5PH5RFToPRcExXaLQU3mEZWuxCuJLFlwNOIEJu3FsR6OfRiEYxy1j8gZ0g2MkPODlJ4XgdCAPF+ElGIGVc1V+2yNBATCfUbzI0w08LldCACWiUPcf6xWibDrF4CN/DdoRDmfybtBWiIXBrOhe0iqMg+msBmFTGSQcPdO9ZEvzLe5GeGbna2HBrOg2GzwuRwpbZqQvm1wgjFJrBTPRWRkp8QGlKvJ74h8rdC/ZFGIeual9chq8vcEMECnZo4Jvv2xapZ5PjUI32ivEoohuP8YGjnjB/pYY7tMGhdhqmD5xUTewiLU9HvOnET4Qn/VXnM5rE3Sb8ggHCM53ZbwwZQ2Z4sKMie3vXDXklzQI9kT+uTydgBW5EV8gdDgUyMDApw5glCq4o/qkshgU+C9CfIvmZkfFWRPdl7+Uj67KBW+UziItBKRIzEA+MHTbdQpR8EeFqZ3bus4y2ghUZfO3xbOcDgSYFU/IF+ExeegIRnwAWdHZyL8iYENXF9EhPushZoD7SkcbdmjZxvb8/wBtari2AkIg+QAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle \\frac{2 \\hbar^{2}}{m w_{z}^{2}} + \\frac{2 \\hbar^{2}}{m w_{y}^{2}} + \\frac{2 \\hbar^{2}}{m w_{x}^{2}}$"
      ],
      "text/plain": [
       "    2        2        2\n",
       "2⋅h̅     2⋅h̅     2⋅h̅ \n",
       "────── + ────── + ─────\n",
       "     2        2       2\n",
       "m⋅w_z    m⋅w_y    m⋅wₓ "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mott-Insulator\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{2 \\hbar^{2}}{m w_{z}^{2}} + \\frac{2 \\hbar^{2}}{m w_{y}^{2}} + \\frac{2 \\hbar^{2} \\left(- 2 \\Delta^{2} + w_{x}^{2} e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} + w_{x}^{2}\\right)}{m w_{x}^{4} \\left(e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} + 1\\right)}$"
      ],
      "text/plain": [
       "                       ⎛                 2      ⎞\n",
       "                       ⎜              2⋅Δ       ⎟\n",
       "                       ⎜              ────      ⎟\n",
       "                       ⎜                2       ⎟\n",
       "    2        2       2 ⎜     2     2  wₓ       2⎟\n",
       "2⋅h̅     2⋅h̅     2⋅h̅ ⋅⎝- 2⋅Δ  + wₓ ⋅ℯ     + wₓ ⎠\n",
       "────── + ────── + ───────────────────────────────\n",
       "     2        2                ⎛    2    ⎞       \n",
       "m⋅w_z    m⋅w_y                 ⎜ 2⋅Δ     ⎟       \n",
       "                               ⎜ ────    ⎟       \n",
       "                               ⎜   2     ⎟       \n",
       "                             4 ⎜ wₓ      ⎟       \n",
       "                         m⋅wₓ ⋅⎝ℯ     + 1⎠       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Superfluid\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{2 \\hbar^{2}}{m w_{z}^{2}} + \\frac{2 \\hbar^{2}}{m w_{y}^{2}} + \\frac{2 \\hbar^{2} \\left(- 2 \\Delta^{2} + w_{x}^{2} e^{\\frac{\\Delta^{2}}{w_{x}^{2}}} + w_{x}^{2}\\right)}{m w_{x}^{4} \\left(e^{\\frac{\\Delta^{2}}{w_{x}^{2}}} + 1\\right)}$"
      ],
      "text/plain": [
       "                       ⎛                2      ⎞\n",
       "                       ⎜               Δ       ⎟\n",
       "                       ⎜              ───      ⎟\n",
       "                       ⎜                2      ⎟\n",
       "    2        2       2 ⎜     2     2  wₓ      2⎟\n",
       "2⋅h̅     2⋅h̅     2⋅h̅ ⋅⎝- 2⋅Δ  + wₓ ⋅ℯ    + wₓ ⎠\n",
       "────── + ────── + ──────────────────────────────\n",
       "     2        2                ⎛   2    ⎞       \n",
       "m⋅w_z    m⋅w_y                 ⎜  Δ     ⎟       \n",
       "                               ⎜ ───    ⎟       \n",
       "                               ⎜   2    ⎟       \n",
       "                             4 ⎜ wₓ     ⎟       \n",
       "                         m⋅wₓ ⋅⎝ℯ    + 1⎠       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Anti-Superfluid\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{2 \\hbar^{2}}{m w_{z}^{2}} + \\frac{2 \\hbar^{2}}{m w_{y}^{2}} + \\frac{2 \\hbar^{2} \\left(2 \\Delta^{2} + w_{x}^{2} e^{\\frac{\\Delta^{2}}{w_{x}^{2}}} - w_{x}^{2}\\right)}{m w_{x}^{4} \\left(e^{\\frac{\\Delta^{2}}{w_{x}^{2}}} - 1\\right)}$"
      ],
      "text/plain": [
       "                       ⎛              2      ⎞\n",
       "                       ⎜             Δ       ⎟\n",
       "                       ⎜            ───      ⎟\n",
       "                       ⎜              2      ⎟\n",
       "    2        2       2 ⎜   2     2  wₓ      2⎟\n",
       "2⋅h̅     2⋅h̅     2⋅h̅ ⋅⎝2⋅Δ  + wₓ ⋅ℯ    - wₓ ⎠\n",
       "────── + ────── + ────────────────────────────\n",
       "     2        2               ⎛   2    ⎞      \n",
       "m⋅w_z    m⋅w_y                ⎜  Δ     ⎟      \n",
       "                              ⎜ ───    ⎟      \n",
       "                              ⎜   2    ⎟      \n",
       "                            4 ⎜ wₓ     ⎟      \n",
       "                        m⋅wₓ ⋅⎝ℯ    - 1⎠      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Anti-Mott-Insulator\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/latex": [
       "$\\displaystyle \\frac{2 \\hbar^{2}}{m w_{z}^{2}} + \\frac{2 \\hbar^{2}}{m w_{y}^{2}} + \\frac{2 \\hbar^{2} \\left(2 \\Delta^{2} + w_{x}^{2} e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} - w_{x}^{2}\\right)}{m w_{x}^{4} \\left(e^{\\frac{2 \\Delta^{2}}{w_{x}^{2}}} - 1\\right)}$"
      ],
      "text/plain": [
       "                       ⎛               2      ⎞\n",
       "                       ⎜            2⋅Δ       ⎟\n",
       "                       ⎜            ────      ⎟\n",
       "                       ⎜              2       ⎟\n",
       "    2        2       2 ⎜   2     2  wₓ       2⎟\n",
       "2⋅h̅     2⋅h̅     2⋅h̅ ⋅⎝2⋅Δ  + wₓ ⋅ℯ     - wₓ ⎠\n",
       "────── + ────── + ─────────────────────────────\n",
       "     2        2               ⎛    2    ⎞      \n",
       "m⋅w_z    m⋅w_y                ⎜ 2⋅Δ     ⎟      \n",
       "                              ⎜ ────    ⎟      \n",
       "                              ⎜   2     ⎟      \n",
       "                            4 ⎜ wₓ      ⎟      \n",
       "                        m⋅wₓ ⋅⎝ℯ     - 1⎠      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kineticEnergies = []\n",
    "for wavex, normx, name in zip(wavefunctionsx, normsx, names):    \n",
    "    print(name)\n",
    "    ke = sp.simplify(normx**2*sp.integrate(wavex*KE(wavex,x1,x2),*xspace)) + yKE + zKE\n",
    "    kineticEnergies.append(sp.lambdify(keSympifyArgs, ke.subs(hbar,mc.hbar).subs(m,mc.Rb87_M), 'numpy'))    \n",
    "    display(ke)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Total summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variational Calibration Loading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "DeltaLoad3d = np.load('Deltas.npy')\n",
    "VDeltaLoad3d = np.load('VDeltas.npy')\n",
    "xFreqLoad = np.load('xFreqs.npy')\n",
    "yFreqLoad = np.load('yFreqs.npy')\n",
    "zFreqLoad = np.load('zFreqs.npy')\n",
    "\n",
    "DeltaLoad3dZoom = np.load('Deltas_z.npy')\n",
    "VDeltaLoad3dZoom = np.load('VDeltas_z.npy')\n",
    "xFreqLoadZoom = np.load('xFreqs_z.npy')\n",
    "yFreqLoadZoom = np.load('yFreqs_z.npy')\n",
    "zFreqLoadZoom = np.load('zFreqs_z.npy')\n",
    "\n",
    "allTweezerDelta = np.append(DeltaLoad3d,DeltaLoad3dZoom)\n",
    "allPsiDelta = np.append(VDeltaLoad3d,VDeltaLoad3dZoom)\n",
    "allXFreq = np.append(xFreqLoad, xFreqLoadZoom)\n",
    "allYFreq = np.append(yFreqLoad, yFreqLoadZoom)\n",
    "allZFreq = np.append(zFreqLoad, zFreqLoadZoom)\n",
    "\n",
    "interpSpacing = interp1d(allTweezerDelta, allPsiDelta)\n",
    "xFreqInterp = interp1d(allTweezerDelta, allXFreq)\n",
    "yFreqInterp = interp1d(allTweezerDelta, allYFreq)\n",
    "zFreqInterp = interp1d(allTweezerDelta, allZFreq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "potentialEnergies[0](0, wfWx[0], wfWy[0], wfWz[0], wfDeltas[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.mean(potentialEnergyVals, axis=0).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Double-Filled',\n",
       " 'Mott-Insulator',\n",
       " 'Superfluid',\n",
       " 'Anti-Superfluid',\n",
       " 'Anti-Mott-Insulator']"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x576 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trapDeltas = np.linspace(0.55e-6,2e-6,1000)\n",
    "#trapDeltas = np.linspace(0.72e-6,0.78e-6,1000)\n",
    "#trapDeltas = np.linspace(0.65e-6,0.85e-6,1000)\n",
    "wfDeltas = interpSpacing(trapDeltas)\n",
    "wfXFreqs = xFreqInterp(trapDeltas)\n",
    "wfYFreqs = yFreqInterp(trapDeltas)\n",
    "wfZFreqs = zFreqInterp(trapDeltas)\n",
    "\n",
    "wfWx = 2*np.sqrt(mc.hbar/(mc.Rb87_M*(2*np.pi*wfXFreqs)))\n",
    "wfWy = 2*np.sqrt(mc.hbar/(mc.Rb87_M*(2*np.pi*wfYFreqs)))\n",
    "wfWz = 2*np.sqrt(mc.hbar/(mc.Rb87_M*(2*np.pi*wfZFreqs)))\n",
    "dbl_vals, mi_vals, sup_vals, asup_vals, aMi_vals = [[] for _ in range(5)]\n",
    "dblIv, dblKev, miIv, miKev, supIv, supKev, asupIv, asupKev, aMiIv, aMiKev = [[] for _ in range(10)]\n",
    "interactionEnergyVals = [[] for _ in interactionEnergies]\n",
    "kineticEnergyVals = [[] for _ in kineticEnergies]\n",
    "potentialEnergyVals = [[] for _ in potentialEnergies]\n",
    "totalE = [[] for _ in potentialEnergies]\n",
    "offDiagVals = []\n",
    "for trDelta, delta, w0x, w0y, w0z in zip(trapDeltas, wfDeltas, wfWx, wfWy, wfWz):\n",
    "    for num, (potEnergyF, potEnergyVals) in enumerate(zip(potentialEnergies, potentialEnergyVals)):\n",
    "        potentialEnergyVals[num] = np.append(potEnergyVals, potEnergyF(-V, w0x, w0y, w0z, 650e-9, 650e-9, 1.5e-6, delta, trDelta ))\n",
    "    for num, (intEnergyF, intEnergyVals) in enumerate(zip(interactionEnergies, interactionEnergyVals)):\n",
    "        interactionEnergyVals[num] = np.append(intEnergyVals, intEnergyF(scatteringConstant, w0x, w0y, w0z, delta))\n",
    "    for num, (kinEnergyF, kinEnergyVals) in enumerate(zip(kineticEnergies, kineticEnergyVals)):\n",
    "        kineticEnergyVals[num] = np.append(kinEnergyVals, kinEnergyF(w0x, w0y, w0z, delta))\n",
    "    offDiagVals = np.append(offDiagVals, offDiagFunc(-V, w0x, w0y, w0z, 650e-9, 650e-9, 1.5e-6, delta, trDelta ))\n",
    "    for num in range(len(names)):\n",
    "        totalE[num] = np.append(totalE[num], potentialEnergyVals[num] + interactionEnergyVals[num] + kineticEnergyVals[num])\n",
    "    \n",
    "diagV1 = []\n",
    "diagV2 = []\n",
    "for valNum in range(len(offDiagVals)):\n",
    "    mat = np.array([[totalE[1][valNum], offDiagVals[valNum]], [offDiagVals[valNum], totalE[2][valNum]]])\n",
    "    res = np.linalg.eigvals(mat)\n",
    "    diagV1 = np.append(diagV1, min(res))\n",
    "    diagV2 = np.append(diagV2, max(res))\n",
    "\n",
    "fig, axs = plt.subplots(3,2,figsize=(20,8))\n",
    "colors, _ = misc.getColors(5)\n",
    "titles = ['Total-mean(U)', 'Interaction Energy', 'Kinetic Energy', 'PotentialEnergy']\n",
    "linestyles = ['--','--','-','-']\n",
    "for ax, vals, title, in zip( [axs[0,0],axs[1,0],axs[1,1], axs[2,0]], \n",
    "                            [np.array(interactionEnergyVals) + np.array(kineticEnergyVals)+np.array(potentialEnergyVals)-np.mean(potentialEnergyVals, axis=0), \n",
    "                             interactionEnergyVals, kineticEnergyVals, potentialEnergyVals], \n",
    "                            titles ):\n",
    "    for wfVals, name, color, ls in zip(vals[:-1], names, colors, linestyles):\n",
    "        ax.plot(trapDeltas*1e9,wfVals/mc.h*1e-3, label=name, linestyle=ls, color=color)\n",
    "    ax.set_xlabel('Tweezer Spacing (nm)')\n",
    "    ax.set_ylabel('Energy (kHz)')\n",
    "    ax.set_title(title)\n",
    "    ax.grid(alpha=0.2)\n",
    "#axs[0,0].plot(trapDeltas*1e9, diagV1/mc.h*1e-3,label='lower')\n",
    "#axs[0,0].plot(trapDeltas*1e9, diagV2/mc.h*1e-3,label='upper')\n",
    "axs[0,0].set_ylim(13,17)\n",
    "axs[0,0].legend();\n",
    "ax2 = axs[0,1]\n",
    "ax2.set_title('Trap Parameters')\n",
    "ax2.grid(alpha=0.2)\n",
    "ax2.plot(trapDeltas*1e9, wfDeltas*1e9,':', color='c')\n",
    "ax2.set_ylabel(r'Effective $\\Delta$', color='c')\n",
    "ax2.spines['left'].set_color('c')\n",
    "ax2.tick_params(axis='y', colors='c')\n",
    "\n",
    "ax3 = ax2.twinx()\n",
    "ax3.plot(trapDeltas*1e9, wfXFreqs*1e-3, color='r', label=r'$\\nu_x$')\n",
    "ax3.plot(trapDeltas*1e9, wfYFreqs*1e-3, color='orange', label=r'$\\nu_y$')\n",
    "ax3.plot(trapDeltas*1e9, wfZFreqs*1e-3, color='purple', label=r'$\\nu_z$')\n",
    "ax3.legend()\n",
    "ax3.set_ylabel(r'Effective $\\nu_x$ (kHz)', color='r')\n",
    "ax3.spines['right'].set_color('red')\n",
    "ax3.tick_params(axis='y', colors='red')\n",
    "\n",
    "fig.subplots_adjust(hspace=0.45)\n",
    "ax = axs[1,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "matplotlib.style.use('default')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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9niNHjojbI0eOhI2NTaX7el7cuXMHly5dQkxMDDIyMlBQUCAWO4F/n2NycjIeP36Mxo0b10peZ8+eRVFREQDAzs4O/fv3Vxuvq6uLoKAgzJo1C0DZNcGUGTJkiNrjVlZWcHZ2RkxMDGQyGeLi4sRCViknJyc8ePAAKSkp2LFjB4YOHVrueYmIiIiI5LHIREREREQvlNjYWLz11lvIz88HALRv3x4//vhjjZ6zV69eSkdSFBQUICEhAWfOnMHy5ctx9epVREREoFu3bggLC1MompT6888/xW0PDw+Nzu/h4SEWmf744w+FYwMGDICpqSlycnJw6dIltG7dGkFBQejfvz86deqk0UgXqVSKK1euVCgvAwMDdOnSRbwvf/zxh9oiU/v27cvts0GDBuK2fGGmMszNzcXt8kZZVVZubi4WLlyItWvX4unTpxq1SUlJqfT5IiMjxe0ePXpUup/nwf79+/Hll19WqOiWkpJSa0Um+c9pt27doKurW24b+c/Ns59TZTT9TMTExABQ/pkYNmwYli1bBgAYPnw4tm7dimHDhqFnz55o1KhRuf0TEREREbHIREREREQvjMePH6N3795ITEwEALRo0QJHjx5VO41VamoqvvjiC7X9duvWDaNGjapwPoaGhnB2doazszOGDx+Ofv364dSpU8jMzERAQACuXr1apsjz5MkTcbtZs2Yanad58+bi9rNFCltbW6xfvx5jxoxBUVER4uPjsWDBAixYsAAmJiZ49dVX4enpCV9fX6VFLwBIS0uDVCqt1ryepe4ZldLX1xe3S0eRVJb8KJ/09PQq9aXM06dP0bNnT4XinCbkR1hVVFJSkrjdokWLSvejbXPmzMGiRYsq3K4q966iqvo5zcvLQ25urspRhTo6OhqNsCvvM/HFF1/gzJkzOH/+PARBwP79+7F//34AJT8j3bt3R+/evTFw4ECFwisRERERUSkWmYiIiIjohfD06VP07t1b/Kv+xo0b48SJE+WObMjMzMTq1avVxmRnZ1eqyCTPwMAAq1atQtu2bQEAt27dwoEDBzBo0CCFuNzcXHHb1NRUo77l45R90T58+HC4urriq6++wm+//SZ+GZ2bm4uwsDCEhYVh/vz56NKlC1auXInXX39dof2zI32qKy955U2/V92aN2+O06dPAyhZz6a6TZo0SSwwGRkZISgoCD4+PmjTpg0aNWoEY2NjcfRLdHS0uLaQTCar9Dnln1NNTwFYUw4dOqRQYOrevTsCAwPRuXNnODk5wdTUVGFttddffx3nzp0DULV7V1Hy97oynweg5DOhqshUXZ8HU1NThIWFYdWqVVi9ejXu3bsnHrt37x7u3buHkJAQmJiY4IMPPsD8+fPLnaKTiIiIiF4sOtpOgIiIiIiopmVmZqJv3764fv06gJIppI4fPw5nZ2ctZ6bI1dUVTk5O4v7JkyfLxMh/6ZyTk6NRv/JxqkYjdOjQAbt27cKTJ0/w22+/YcaMGejWrZvCSIioqCh4eXlhz549Cm2fLVhUZ17aIl9IS0hIQHx8fLX1/eDBA+zcuRMAoKenhxMnTuCHH37AgAED8NJLL8HMzExherXqGoEj/5xqagpAVaqrwLN8+XJxe9KkSQgPD8f48ePRoUMH2NjYKBSYgNodvSRP/l5X5vMA1N5nwsDAAFOnTkVMTAyuXLmCVatWYdiwYXBwcBBjcnNzsWzZMvTs2VOcapSIiIiICGCRiYiIiIjquZycHPj4+ODSpUsAAAsLCxw9ehRubm4atW/evDkEQVD72rRpU7XlKz+y6sGDB2WON2zYUNx++PChRn3K92Nra6s21tLSEgMGDMCyZctw/vx5PHnyBBs2bBCn/JJKpZg4cSIKCgrENtbW1gpFkZrIq7b17NlTYX/btm3V1vepU6fE7bfeeqvcNayU/RxUhr29vbgdGxtbpb7ki4/FxcXlxld1jSwAKCwsxNmzZwEAurq6WLhwodp4QRAQFxdX5fNWRlU/p8bGxipHMdWk9u3b4/3338f27dvx6NEjXL58GUFBQeLx8+fP43//+1+t50VEREREzy8WmYiIiIio3srPz8fAgQPF6bJMTExw6NAhdOrUScuZqSY/HZ6OTtn/XJdfFykiIkKjPuXjXnnllQrlY2lpiaCgIJw8eRIGBgYAgOTkZFy4cEGM0dXVxX/+858K5VVUVISoqKhK51XTWrRogTfffFPcX7NmTbWN4EhISBC3NSl2hoeHV8t5u3XrJm7LF7oqQ36UzdOnT8uNv3r1apXOB5Ssc1Q6lWPjxo0V1s1Sdc60tLRy+62JqRjlP6eRkZEajeQq/T0FPD+fh1deeQUbNmzAuHHjxPdK12wiIiIiIgJYZCIiIiKieqqoqAj+/v7il+mGhobYt29fuaNGtCknJwe3b98W9x0dHcvEyI+w+eWXX1BYWKi2z4sXL4rTBAJAjx49KpWbi4sL2rRpI+4nJSWpzEuTkV179uxBeno6gJJRG/IFkOfFp59+Km7fv38fn332WYX7EAQBx48fV3hPvngoX1RUJjs7G5s3b67weZXp16+fuL1t2zakpqZWui/5qSb/+usvtbG5ubk4cOBApc9VqiL3DSgpDGpCfo2h0iJWVb3++utiUTYpKQlHjhxRGy+TyRASEiLuPzuSTtsGDBggbj/72SciIiKiFxuLTERERERU70ilUgQEBODQoUMASta92bFjB7y9vbWcmXqrV69W+JK7V69eZWJGjRoFU1NTAEB8fDwWLFigsr+CggJ8+OGH4n7v3r3h4uKiEJOSkqJRbkVFRUhMTBT35acDA4B3331XHBESFRWFn376SWVf6enpmDVrlrg/atSoMus6PQ969OiBd999V9wPDg7G/PnzNW6fnJyMt99+G0uXLlV4v0WLFuL2gQMHIJVKVfbxySefaPyMyjNkyBBxza/MzEyMGzdOo6nulHn11VfF7f3796stWM2ZM0ejEUXlsbOzE39OUlNTxanzlAkPD8e6des06rdBgwbi9qNHj6qW5D9sbGwwePBgcX/69Olq18H673//KxaDdXV1MWHChGrJQ538/HyN14uSn/Lv2c8+EREREb3YWGQiIiIionpFEARMmDABoaGhAEpGP2zevBkDBw7UcmaqFRUVYdWqVZg9e7b4XsuWLRVGD5SysrLC559/Lu4vXLgQ8+bNKzMCIzExEYMGDRKntdPX18fixYvL9PfJJ5/A09MTP//8sziy6FnJyckYO3YskpOTAZSswfTaa68pxLRq1Urhi/FJkybhf//7HwRBUIiLjo5G7969cf/+fQAl0/HNmTNH6XmfB9999x26du0q7s+bNw9vvPEGfv/9d5VToMXExOCLL76Ai4sL9u7dW+Z4r169xNEzd+7cQVBQUJk1izIyMjB+/HisX79eLCpWlb6+Pr7//ntxf9++ffDx8VEYPScvNjYWc+bMwdatW8scc3d3R/PmzQGUFKwCAgLK/Pzk5ORg6tSp+Pbbb2FoaFjl/HV1ddG3b19xPzAwUFxrTd727dsxYMAASKVSje5d+/btxe29e/dW22imefPmiee/efMm+vbtK/7cl5LJZAgODsa0adPE9z788EM0bdq0WnJQJz4+Hk5OTpg+fbrS+wiU/D49dOiQQnHVx8enxnMjIiIiorpDT9sJEBERERFVpzVr1ihM1+bi4oKzZ8+qHfVQqkGDBhUaqaKp27dv44MPPijzfmFhIR4/fozz588rrGtjZmaGn3/+WZxu61mzZs3CuXPnxJFa8+fPx+rVq+Hl5QVra2s8fPgQYWFhKCgoENusXLkSnTt3LtOXIAgIDw9HeHg4dHV10aZNG7i6usLa2hq5ubl49OgRzp07p/DF+4oVK5QWDb799lv88ccfuHz5MoqKijBp0iQsWrQI3bt3h6mpKaKjo3HmzBlx5I6+vj42btxYK1+oV5aRkRFOnTqF0aNHY/fu3QCAM2fOoGfPnrCxscGrr76Khg0bwtDQEElJSbh9+zbu3Lmj0If8+kUAYGtri6lTp4pFv82bN+PQoUPo2rUrHBwckJCQgLCwMOTm5kJPTw+rV6/G2LFjq+V6fH19sXDhQrGwd/z4cbi6uuLll19G27ZtYWpqitTUVFy9elUsPskXpkpJJBIsXrwYAQEBAICjR4/C2dkZvXr1QoMGDfD48WOEh4cjIyMDTZo0wXvvvYe5c+dWOf8vvvgCv/32GwoKCnDv3j107doVr732Glq2bImCggKcP39eLORMmjQJV65cUVjrSBkfHx8YGRkhPz8fly9fhqurK7y8vGBpaSmOzuvXr5/SkYXqtGzZEj/++CMCAwMhlUpx7tw5tGzZEm+88QZatGiB7OxshIeHK6zR5eHhga+//rpiN6UK0tLSsGLFCqxYsQI2Njbo2LEjHB0dYWhoiOTkZPz9998KhTFXV1elv8uIiIiI6AUm1DOXL18WFi1aJPTt21do0qSJYGBgIJiamgotW7YUAgMDhfDw8Ar1d/jwYcHPz09wdHQUDAwMBEdHR8HPz084fPhwDV0BEREREVXFl19+KQCo1KtZs2bVlsfs2bMrlUP79u2FS5culdt/YWGhMGnSJEFHR0dtf1ZWVsLPP/+ssp+JEydqnJuFhYWwfv16tXllZmYK/v7+5fbl4OAgHDlyRON7uGDBgnLvyfHjx8X4Xr16lRtfETKZTAgJCRFcXFw0vl8ODg7CihUrhIKCgjL9FRcXCyNHjlTb3traWti/f79w9+5d8T0XFxel+RUVFYkxurq65V7P1q1bBTs7O42uY8OGDSr7mTt3rtq2rq6uwo0bN4R169aJ740fP15pX5o+v127dgnGxsZqzztp0iShoKBA8PDwEN87c+aMyj7XrFkjSCQSlf09+/Mn/+w2b96s9l7v3btXo3s9cuRIITc3V2U/FX3GgiCovf4HDx4IhoaGGv889+zZU0hMTNTovERERET04qhXI5k8PT0RHh5e5v3CwkLcvXsXd+/eRUhICEaPHo3169er/MtQABAEARMnTsTatWsV3n/06BH27NmDPXv24N1338X//vc/8a/biIiIiIgqQk9PDxYWFnByckLnzp3x9ttvo2/fvtDRKX9Wa319ffzwww+YNGkSNm7ciJMnTyIuLg7Z2dmwsbFB69at4ePjg3feeQc2NjYq+1mzZg2mTJmCEydOIDIyEtevX8fDhw+RlZUFAwMDNGjQAG5ubnjzzTcxevToctdjMTc3R2hoKM6dO4ctW7YgLCwMjx8/Rl5eHmxtbdG+fXsMGDAA48aNg4mJSYXvmbZIJBKMGTMGAQEBOH78OI4dO4Zz584hMTERKSkpEAQB1tbWcHZ2RpcuXdC3b1/07t0burq6SvvT1dXFli1bMHToUKxbtw4XL15EWloarK2t0axZM/j6+mLcuHFo3LgxoqOjq/16AgICMHDgQPz88884fPgwrly5gidPnkAqlcLa2hqtW7dG9+7dMWTIEHTo0EFlP1999RX69OmDVatW4cyZM3jy5AksLCzQsmVLjBgxAuPGjYOpqWm5o4kq4u2338a1a9ewcuVKHDt2DHFxcdDX14eDgwM8PDwwduxYdO/evUJ9Tpw4Ee3bt8ePP/6IyMhIJCQkIDc3t8x0j5Xh6+uLnj17YsOGDThw4ACuX7+Op0+fwtjYGI6OjujRowfGjBmjsM5VbWjatClSUlJw6tQpnDlzBpcvX0Z0dDRSUlJQWFgIc3NzNG/eHF26dMHw4cPRs2fPWs2PiIiIiOoGiVAd/9X8nHjppZcQExMDBwcHDBkyBN27d0fTpk0hlUpx/vx5rFixQlzIdcSIEdi2bZvKvmbPni1OX9GxY0fMnDkTLi4uiImJwbJly/Dnn3+KcQsXLqz5iyMiIiIiIiIiIiIiInqO1Ksi04ABAzBmzBj4+/sr/YvBlJQUeHh4iHOkh4eHK/0Lt+joaLi6uqK4uBidO3dGeHg4jI2NxeO5ubnw9PTEpUuXoKenh1u3bsHFxaXmLoyIiIiIiIiIiIiIiOg5U/48HHXIgQMHMHToUJVTUtja2mLFihXifmhoqNK4b7/9FsXFxQBKFrmVLzABgImJibj4bXFxMYKDg6sjfSIiIiIiIiIiIiIiojqjXhWZNOHl5SVux9dW/aAAACAASURBVMTElDkuCAL27dsHAGjTpg26deumtJ9u3bqhdevWAIC9e/dWy1zdREREREREREREREREdcULV2QqLCwUt5UtqBwbGyuu2+Tp6am2r9Lj8fHxuH//fvUlSURERERERERERERE9Jx74YpMp0+fFrfbtGlT5vjNmzfVHpcnf1y+HRERERERERERERERUX33QhWZZDIZlixZIu4PHTq0TExcXJy43aRJE7X9OTk5KW1HRERERERERERERERU3+lpO4Ha9O233+LixYsAAD8/P3Tu3LlMTFZWlrhtZmamtj9TU1NxOzs7W2VcQUEBCgoKxH2ZTIbU1FQ0aNAAEolE4/yJiIiIiIiIiIiIiKj+EQQBWVlZcHBwULrUz/PqhSkynT59Gp9++ikAwM7ODmvWrFEal5+fL24bGBio7dPQ0FDczsvLUxn39ddfY/78+RVJl4iIiIiIiIiIiIiIXjBxcXHlzrL2PHkhikzXr1+Hn58fiouLYWhoiB07dsDe3l5prJGRkbhdWFiotl/50UnGxsYq4z777DNMnTpV3M/IyEDTpk0RFxcHCwsLTS+DiOj5UpAObGtWsj08GjBuqN18iIiIiIiIiIiI6qjMzEw4OTnB3Nxc26lUSL0vMsXGxuLNN99EWloadHV18csvv8DT01NlvPwDVDcFHgDk5OSI2+qm1jM0NFQY9VTKwsKCRSYiqsMsAAc3IO06kHcdsB+o7YSIiIiIiIiIiIjqtLq2xE7dmdivEhISEuDt7Y2EhARIJBJs2LABfn5+atvID0OLj49XGxsXFyduOzk5VS1ZIqK6yP61kn+TIrSbBxEREREREREREdW6eltkSklJQe/evXHv3j0AwPfff48xY8aU265t27bi9q1bt9TGyh93dXWtZKZERHWYvXvJv8nntZsHERERERERERER1bp6WWTKyMhAnz59cOPGDQDAkiVL8P7772vU1tnZGQ4ODgCA06dPq40NDw8HADg6OqJ58+aVT5iIqK4qHcmUHAXIirSbCxEREREREREREdWqeldkys3NRf/+/fHHH38AAGbPno1Zs2Zp3F4ikcDX1xdAyUilyMhIpXGRkZHiSCZfX986N08iEVG1sGwFGFoD0jzg6d/azoaIiIiIiIiIiIhqUb0qMhUWFsLPzw/nzp0DAHz00UdYuHBhhfv5+OOPoaenBwCYMmUK8vLyFI7n5eVhypQpAAA9PT18/PHHVcyciKiOkugAdlyXiYiIiIiIiIiI6EWkp+0EqtOIESNw7NgxAEDPnj0xfvx4XLt2TWW8gYEBWrVqVeb9Vq1aYfr06ViyZAkuXboEDw8PzJo1Cy4uLoiJicHSpUvx559/AgBmzJiBli1b1swFERHVBfavAXGHgKTzQLsPtZ0NERERERERERER1RKJIAiCtpOoLhWdsq5Zs2a4f/++0mMymQzvvPMONmzYoLL9+PHjsXbtWujoVGxAWGZmJiwtLZGRkQELC4sKtSUieu48OgUc7AWYNQMC7ms7GyIiIiIiIiIiojqnrtYN6tV0edVJR0cHP/30Ew4ePAhfX184ODjAwMAADg4O8PX1xaFDh7B+/foKF5iIiOodu1dLps3LfgDkJGg7GyIiIiIiIiIiIqol9Wq6vJoYlOXj4wMfH59q77cqBEFAUVERZDKZtlMhojpCR0cH+vr6FR7xqRF9M8CmPfD075Ip81r4V/85iIiIiIiIiIiI6LlTr4pM9Z1UKkVKSgqysrJQVFSk7XSIqI7R19eHubk5bG1toaurW72d27v/U2SKYJGJiIiIiIiIiIjoBcEiUx0hlUoRFxeHgoICWFpawszMDLq6ujUzKoGI6hVBECCVSpGdnY309HTk5eXBycmpegtNdq8BN9YAyeerr08iIiIiIiIiIiJ6rrHIVEekpKSgoKAATZs2hbGxsbbTIaI6yMzMDJaWlnj48CFSUlJgb29ffZ03ci/598llQFoA6BpWX99ERERERERERET0XNLRdgJUPkEQkJWVBUtLSxaYiKhKjI2NYWFhgaysrOpdx868BWBsB8gKSwpNREREREREREREVO+xyFQHFBUVoaioCGZmZtpOhYjqAXNzc/H3SrWRSEqmzANK1mUiIiIiIiIiIiKieo9FpjpAJpMBQPWun0JEL6zS3yWlv1uqTSOPkn+TzlVvv0RERERERERERPRcYpGpDpFIJNpOgYjqgRr7XWL/T5Ep8RxQnVPxERERERERERER0XOJRSYiIqoeDTsBuoZA/hMgM1rb2RAREREREREREVENY5GJiIiqh64hYNu5ZDuRU+YRERERERERERHVdywyERFR9eG6TERERERERERERC8MFpmIiKj6yK/LRERERERERERERPUai0xEdVBYWBgkEgkkEolW2mtLdHS0mHd8fHy1HKsNo0aNgkQiwYQJE2r93LWukXvJv+k3gfxU7eZCRERERERERERENYpFJnrhzJs3Tyw4lL50dHRgYWGBJk2awN3dHe+//z5CQ0NRWFio7XTrJWXPQNWL6hgjW8CyVcl28nnt5kJEREREREREREQ1Sk/bCRBpk729vbidl5eHhIQEPHr0COfPn8cPP/yABg0aYMGCBZg4cSILHjVE/hmUx8DAAK1btwYA6Ovr11RKVFX2HkDGnZIp85r213Y2REREREREREREVENYZKIXWmJiosK+VCrFjRs3cPz4caxatQqxsbGYPHkyzp49iy1btrDQVAOefQbqNG3aFLdu3arBbKhaNPIA7mwEkrguExERERERERERUX3G6fKI5Ojq6qJ9+/aYOnUqrl27huHDhwMAtm3bhiVLlmg5O6I6opFHyb/JFwEpp5wkIiIiIiIiIiKqr1hkIlLBxMQEISEh6NixIwBgyZIlSE1NLROXmJiIGTNmwM3NDWZmZjA1NYWbmxtmzpyJpKQkpX2HhYVptOZQaUxYWJjauEuXLmHw4MFo3LgxjIyM8NJLL2HGjBlIT0/X7GKVkEql2LRpE/r06QN7e3sYGBigYcOG6NOnD7Zv3w5BECrdd2VFR0eL9yQ+Pr5a+xYEAbt374avry8cHBxgYGAAGxsbeHl5Ye3atSgqKlLbfvPmzXB3d4e5uTksLS3RrVs3rF+/vlpzrDMsWwOGDQBpPvD0T21nQ0RERERERERERDWERSYiNQwMDPD5558DADIzM7F3716F46dPn4arqyuWL1+OGzduQBAESCQS3LhxA9988w1cXV1x9uzZGs1x37598PDwwK5du5CbmwtBEBATE4Ply5fj5Zdfxv379yvcZ1JSEjw8PBAUFIRjx44hOTkZJiYmSElJwbFjxzBixAgMGjQIhYX1Y5RKVlYW+vfvD39/f+zfvx+PHz+GsbEx0tPTcfr0abz33nvo2bMnMjIyyrSVyWQYM2YMxowZg/PnzyMnJwe6urqIiorCO++8g9GjR2vhirRMIgHs3Uu2EzllHhERERERERERUX3FIlM9k5MjU/nKz5dpHJuXV/nY3FzVsbm5msU+T/r27QtdXV0AJUWlUnFxcRg0aBDS09PRtm1bnD17Fjk5OcjOzkZ4eDhat26NtLQ0+Pr64tGjRzWWX2BgINzd3XHjxg1kZGQgJycHv/76K6ytrfHgwQMMHToUUqlU4/4KCwvx1ltv4cKFC3jllVdw8OBB5OTkID09HdnZ2QgJCYGdnR3279+PWbNm1dh11RZBEBAQEIDDhw+jZcuW2L59OzIzM5GRkYHc3Fzs2bMHzs7OOHv2LCZMmFCmfXBwMDZv3gwA+Oijj/DkyROkpqbi6dOnmDt3LrZs2YKDBw/W9mVpX+mUeSwyERERERERERER1Vt62k6AqpeZ2X2Vx3x8jHHwYGNx387uAXJzlU955ulphLAwB3G/efOHSElRXvzp3NkQUVGO4n7btvF48KBYaWzbtvq4ft1J3O/S5RFu3Cg7DZkgtFB5HbXNzMwMLVq0wN27dxETEyO+v3jxYqSnp8Pa2honT55Eo0aNxGPdu3fHiRMn4ObmhtTUVHz99ddYtWpVjeRnb2+PQ4cOwdjYGACgp6eHoUOHwsbGBr1790ZUVBR2796NIUOGaNTfunXrEBUVBTc3N4SFhcHc3Fw8ZmpqijFjxsDNzQ1dunTBDz/8gM8++wx2dnaVzl/+vj3r5MmTcHNzq3Tfmti/fz8OHDgABwcHnD59Go0b//sZMTIywqBBg9CxY0e4uroiNDQU165dQ7t27QAAubm5WLBgAQAgKCgIwcHBYlsrKyt89dVXyMvLw/Lly2v0Gp5LpUWmpHOAIJSMbiIiIiIiIiIiIqJ6hSOZiDRgY2MDAOKaTIIgYMeOHQCAiRMnKi2UNGnSBBMnTgQAbN++vcZymzFjhlhgkuft7Q13d/cKn790HaHJkycrFJjkderUCW5ubigsLMTvv/9eiaz/lZSUpPJV3jpI1aH0egMDAxUKTPKaNWsGT09PAMDRo0fF948cOSKuezV37lylbT///HMYGBhUZ8p1g21nQEcfyEsCsmK1nQ0RERERERERERHVAI5kqmeys5urPPbPjG+i5ORmKmN1nik/3r/fVOPYGzeaQFA+QKrMYIaoKEeVsc8T4ZkkY2NjxYKTt7e3yna9e/fGsmXL8PTpU8TGxsLZ2bnac+vZs6faYxEREbh06ZJGfWVlZeHKlSsASoomX331lcrY0ut/8OBBBbIt69l7W9tK18z64YcfsGHDBpVxpesxyV9v6X11dnZW+Wytra3RsWNHXLhwobpSrhv0jADbTkByZMmUeRbPz+hEIiIiIiIiIiIiqh4sMtUzpqaaD06rqVgTk5qJ1aa0tDQAQIMGDQAAycnJ4jFHR0elbYCS0UylkpOTa6TIpO78pcfk81UnMTERMlnJtIilRaTy5ObmittdunRBXFxcmRh3d3fs3r1bo/5qU35+vjgSKSMjQywkqSN/vaX3Vd0zAEp+Dl64IhNQMmVecmTJlHmtRms7GyIiIiIiIiIiIqpmLDIRlSM7Oxv37t0DALi4uJQ5LtFwrRlN47RJKpWK25GRkejatWuF2j958gRJSUll3te0YFXbiov/XTssNDQU/v7+leqnLjxbrbD3ALCiZCQTERERERERERER1Tt1YxgJkRYdOXJELL54eXkBAOzs7MTjykbulIqPjxe3GzZsKG7r6f1b383Pz1faVpNRNQDw6NGjco/J56uOvb29uH316lWN2si7f/8+BEEo8woLC6twX7XBzMwMpqamACp3vaX3Vf45K6PuGdVr9iVrgiHtOlCQrt1ciIiIiIiIiIiIqNqxyESkRmFhIRYvXgwAsLS0xKBBgwCUrMFjY2MDADh58qTK9idOnABQMs2e/FR51tbW4raqIpWm06v9/vvv5R7r3LmzRn1ZW1ujbdu2AIDt27dr1Kau8/DwAADs2LGjwutDld7X2NhY3L9/X2lMeno6/vzzzyrlWGeZ2AMWLwEQgKTz2s6GiIiIiIiIiIiIqhmLTEQq5OXlYezYsWKB4LPPPoOVlRWAkunRhg0bBgD48ccfkZiYWKZ9QkICfvzxRwDAiBEjFI61atUKxsbGAIBdu3aVaSuTyfD1119rlOfy5cuVjob6/fffce5cyTRlpblq4t133wVQUjwrr9D0vE6DVxGl13vz5k2sXLlSbWx2djaKiorE/b59+8LS0hIAsHDhQqVtlixZgoKCgmrKtg5qVFLEQxKnzCMiIiIiIiIiIqpvWGQikiOTyXDt2jWsXLkSbm5u+OWXXwAAo0ePxsyZMxViP//8c1hZWSE1NRXe3t6IiIgQj507dw7e3t5IT0+HjY0NPv30U4W2+vr64vo/ixcvxo4dO1BYWAgAuH37Nvz8/PD3339rlPPjx4/Rv39/3L59G0DJOkOhoaEYPHgwAOCVV17B22+/rfE9mDhxorgW0+jRozFnzhyF0Va5ubkICwvDBx98oHSNqrrm7bffxsCBAwEA06dPxwcffIC7d++KxwsKChAZGYmZM2eiWbNmePr0qXjMxMQEs2fPBgD89NNPmDZtmlh4y8jIwPz587Fs2TKxOPlCsv+nyMR1mYiIiIiIiIiIiOodvfJDiOqvRo0aidsFBQXIzMyETCYT37O1tcXChQvx3nvvlWnbpEkT7N27F76+vrh+/To8PDzE9X1ycnIAAFZWVti7dy8cHR3LtP/6669x6tQpJCQkYNiwYdDX14exsTEyMzNhbm6O3377TVwDSp2QkBAMGTIEbdq0gaWlJfLz88WRM02bNkVoaKjCGlDlMTQ0xIEDBzBs2DCcOnUKixYtwqJFi2BhYQEdHR1kZGSI08pVpN/nlUQiwbZt2xAUFISdO3di9erVWL16NUxNTWFgYICMjAyFnwmJRKLQftq0afjrr7+wbds2rFy5EsHBwbC0tERmZiakUilGjhwJANi6dWutXtdzo3Qk05OLgKwI0NHXbj5ERERERERERERUbTiSiV5oSUlJSEpKQnJyMoqLi9GoUSN069YNkyZNQmhoKB49eqS0wFTK09MTt27dwrRp0+Dq6gqZTAZBEODq6orp06fj5s2b6N69u9K2TZo0wYULFzBhwgSxCGVmZoYxY8bgjz/+gKenp0bX4Ovri4iICPj7+8PIyAiCIMDZ2VksfsivBaUpW1tbnDhxAvv27cPgwYPh5OSEgoIC5OXlwdHREf369cOqVatUrkNU15iammLHjh04efIkRo0aBWdnZ8hkMmRnZ8Pe3h69evXCN998g+joaNjb2yu01dHRwZYtW7Bp0yZ07doVxsbGKC4uRqdOnbB27Vps3rxZS1f1nLBqAxhYAcW5wFPNRucRERERERERERFR3SARKrrSPVVZZmYmLC0tkZGRAQsLi3Lj8/PzERsbC2dnZxgZGdVChkRUn9X675TD/YG4Q8BrwUD7j2r+fERERERERERERHVMResGzwuOZCIioppVOmVeEtdlIiIiIiIiIiIiqk9YZCIioppl/0+RKfEcwMGzRERERERERERE9QaLTEREVLPsugASPSA3Ach+oO1siIiIiIiIiIiIqJqwyERERDVLzwSwfaVkO5FT5hEREREREREREdUXLDIREVHN47pMRERERERERERE9Q6LTEREVPPk12UiIiIiIiIiIiKieoFFJiIiqnmN3Ev+Tb0KFGZqNxciIiIiIiIiIiKqFiwyERFRzTNpDJg7AxCA5EhtZ0NERERERERERETVgEUmIiKqHZwyj4iIiIiIiIiIqF5hkYmIiGpHo3+KTEksMhEREREREREREdUHLDIREVHtEItMkYCsWLu5EBERERERERERUZWxyERERLXD2g0wsASKc4DUK9rOhoiIiIiIiIiIiKqIRSYiIqodEh3A/rWSba7LREREREREREREVOexyERERLXH/p8p81hkIiIiIiIiIiIiqvNYZCIiotojrssUod08iIiIiIiIiIiIqMpYZCIiotrT8FVAogvkxAHZcdrOhoiIiIiIiIiIiKqARSYiqvO8vLwgkUgwb948badC5dE3BRq8XLLNKfOIiIiIiIiIiIjqNBaZ6IUzb948SCQS8bV9+/Zy2/Tv31+hzf3796stn+DgYMybNw9//fWXypj09HTMmzcP8+bNQ3p6epXPWXodLMqot3fvXsybNw979+7Vdir1izhlHotMREREREREREREdRmLTPTC27hxo9rjCQkJOHr0aI2dPzg4GPPnzy+3yDR//nzMnz+/WopMpJm9e/di/vz5LDJVN/t/ikwcyURERERERERERFSnschELyxbW1uYmprixIkTiItTvTbMzz//DKlUiubNm9deckT1WelIptS/gcIs7eZCRERERERERERElcYiE72wTE1NMXjwYMhkMoSEhKiMKx3pNHbs2FrKjKieM3UEzJoBggxIvqDtbIiIiIiIiIiIiKiSWGSiF1pQUBAAYNOmTRAEoczxs2fP4s6dO2jRogXeeOMNtX3l5+cjODgY7u7usLa2hpGREZo1a4YxY8YonQqvdG2oBw8eiLnIr/skkUgAAF5eXnB2dhbbOTs7K8R4eXlV9vKV8vLyEtdrEgQB69atQ9euXWFhYQFzc3O89tpr2LJli8r2xcXFWLt2Lby8vGBrawt9fX00aNAArVu3xrBhw7Bhw4YybZo3bw6JRIJNmzap7Hfs2LGQSCQVLvYlJydjw4YNePvtt+Hq6gpLS0sYGxvjpZdewoQJE3D9+vUybcLCwiCRSMTiY0hISJlnExYWVqbd7t27MWDAANjb28PAwAD29vYYMGAA9uzZo9F1CYKA9evX4/XXX0eDBg3KvSd1GtdlIiIiIiIiIiIiqvP0tJ0AkTa98cYbcHFxQUxMDM6cOVOmkCQ/iqm06KPMo0eP0LdvX1y7dg0AoK+vDxMTEzx8+BCbN2/G1q1bERwcjClTpohtzMzMYG9vjydPnkAmk8HCwgLGxsZl+raxsYGtrS1SUlIAlEzzp6urq3C8JkilUvj5+WHfvn3Q09ODiYkJsrKyEBkZicjISNy9exfz588v08bHxwfHjx8X37O0tEROTg5SU1Nx584d7NixA+PGjauRnJWZOXOmwkg1CwsLFBcXIyYmBjExMdiyZQu2bt0Kf39/Maa0QJSRkYH8/HwYGRnB0tJSoV8DAwNxu7CwEGPGjMGvv/4KANDR0YGlpSVSUlJw8OBBHDx4ECNGjEBISAj09fWV5ikIAoYOHYrQ0FCxvY5OPf47AHsPIHobkBSh7UyIiIiIiIiIiIiokurxN5hE5ZMfGfPsCJucnBzs2LEDOjo6akfPSKVS+Pv749q1a7C0tMSWLVuQnZ2N9PR0xMTEYMCAAZDJZPjwww9x+PBhsd306dORmJgIJycnAMB3332HxMREhRdQMjomKipKbBcVFaUQs3v37mq6G4pWr16NsLAwbNq0CZmZmcjIyEBcXBzeeustAMDChQtx9+5dhTa//PILjh8/DiMjI6xfvx5ZWVlIT09HXl4ekpKSsHv3boViTm1wdnbGnDlz8OeffyI7OxsZGRkoKCjAtWvXMHLkSBQUFCAwMBAJCQliG3d3dyQmJmLYsGEAgGHDhpV5Nu7u7mL8559/jl9//RUSiQRz587F06dPkZqaipSUFHz++efivZk7d67KPHfv3o29e/di+fLlSEtLQ2pqKjIyMtCnT58aujNaJo5kOg/IpNrNhYiIiIiIiIiIiCqFRaZ6Jqe4UOUrX1qscWyetKjSsbnFRSpjc4s1i61NgYGB0NHRQWhoKLKzs8X3d+zYgezsbPTq1UssBCkTGhqKCxdK1pX59ddfMXLkSHGUS4sWLbBnzx507doVQMmomroiLS0Ne/bsQWBgoDjCqkmTJti5cyccHBwgk8mwY8cOhTYRESWjUsaMGYPx48fDzMwMQEkxz87ODn5+fggNDa3V6/jyyy+xYMECvPzyyzA1NQVQMtLIzc0NW7ZsQf/+/ZGTk6N0Gj9NPHr0CN999x0A4NNPP8VXX30FKysrAIC1tTUWLVqEqVOnAgBWrlyJx48fK+0nOzsbK1euxLRp02BhYQGgZLRb48aNK5XXc8+6HaBvDhRlAWnXtJ0NERERERERERERVQKny6tnzPasVHnMp5ELDnYfIu7b7f8euc8UiEp5NnRCmNdIcb/5wTVIKcxTGtvZuhGivMeK+22PrsOD3EylsW0tbHG9zwRxv8vJENzITCkTJwz5VOV1VDcnJyd4e3vj2LFjClO5lU6VV97UbqVTpL322mtKR53o6enhyy+/hI+PD65du4arV6+iffv21XwV1c/DwwM9evQo876hoSH69OmDjRs34sqVKwrHSosrpaOw6oL+/fvj4MGDOHv2bKXa79q1C8XFxTAyMsKnnyr/uZ0zZw5Wr16NgoIChIaGKkybWMra2hrvvfdepXKok3R0AbtuwKPjQOI5oEEHbWdEREREREREREREFcSRTEQAgoKCAPw7ZV50dDTOnDkDKysrDBo0SG3bS5cuAQC8vb1VxvTo0UNcR6k0/nlXOvpKGQcHBwBAamqqwvs+Pj6QSCTYv38/+vXrh19++UVhGjpt+fvvvzF58mT85z//gYWFBXR0dCCRSCCRSDB58mQAQHx8fKX6Ln2eXbp0EUcgPcva2hqdO3dWiH9Wly5dFNZ5eiGIU+ad024eREREREREREREVCkcyVTPZPtNVXlMV6JYU0weWHY0RSkdiURh/37/SRrH3ujzDgQISmMlUIyN6hWoMrY2+fn5wdraGufOncOdO3cQEhICAAgICICRkZHatsnJyQAAR0dHlTFGRkawtbVFUlKSGF/dfv31V3z00UdKj+3evVthDSFNmJubqzymp1fyq6OoSHEk3Ouvv46lS5dizpw5OHLkCI4cOQKgZJo9b29vjBkzRunoqJq0atUqfPTRR5DJZABKpu6ztLSEoaEhACAvLw+ZmZnIycmpVP+aPH+g5B7Ixz/Lzs6uUuev0+z/KTIlsshERERERERERERUF3EkUz1jqmeg8mWkq6dxrLGufqVjTfT0Vcaa6GkWW9sMDQ0xYsQIAMBPP/2En3/+GcC/I5w0IXmm2FbVuIrKy8tDUlKS0ldhYe2tczVjxgzExsbi22+/xaBBg2BnZ4f4+Hhs2rQJPXv2xJAhQ8oUp2rKzZs38fHHH0Mmk2HIkCG4ePEi8vPzkZaWhsTERCQmJmLlypIpJgWhasXOqj7/0pFuLxS7roBEB8h+AOQ80nY2REREREREREREVEEsMhH9o7SgFBwcjPj4eLRr106c4kyd0hEocXFxKmPy8/Px9OlTAEDDhg2rIduyxo4dC0EQlL68vLxq5JyqODg44OOPP8aePXuQlJSEK1euYMKEkrW4QkNDsWbNGoX40pFR+fn5KvvMyMiocB6hoaGQSqVwdXXF9u3blU5JV9X1ozR5/sC/0/HV1POvkwzMAZt/1mLiaCYiIiIiIiIiIqI6h0Um0FyHVQAAIABJREFUon907twZ7du3F0f9jBs3TuN2AHDy5EmVMWFhYSguLgZQsvaOPB2dko+hupE0pTHlxT2v2rdvj3Xr1sHDo2R6tOPHjysct7a2BqC6UCOTySq1llVpfx06dFC4h/JOnDihsr0mz0Z+rSVVhbD09HSFtZtIDtdlIiIiIiIiIiIiqrNYZCKSs3TpUkybNg3Tpk3DqFGjNGozfPhwAMD58+dx7NixMseLi4vx1VdfAQDatWuHdu3aKRy3sLAAUFKIUKU0prw4bSsoKFB73NjYGEDZqeE6dCgZzbJnzx6lBZ2QkBBxJFBFWFpaAgCuXr2qtN/Dhw8jLCxMZXtNno2/vz/09PSQn5+PpUuXKo1ZvHgxCgoKoK+vD39//wpcwQugdF2mpAjt5kFEREREREREREQVxiITkZx+/fph+fLlWL58ucbTmvn7+6Nr164AgKFDh2Lbtm3imkOxsbHw9/fH+fPnAQDLli0r07606BQaGoq0tDSl57CysoKjoyMAYOPGjeKoqOfNoEGD/s/enYdHVd7vH3+fWZJJMslkJSFhCbhAXBAXcAEVUHAHqQtaF0BFUcRWS7/aVimodS+K/lBQqhEVd6u4Uq1AAUGCrFZRsOyQhJB9nfX3x5CThEwgYGBCcr96zXVO5jznzOccbC6dm8/zcNNNN/H55583CGYKCwt5+OGHzW6viy++uMF5teth/fjjj9x6663m1IKlpaU8/fTTjB07lsTExAOu58ILLwTgv//9L+PGjaOwsBCAiooKZsyYwZVXXklSUlKT59f+2SxcuJB169aFHJORkcHvfvc7AB577DH++te/mvdeXFzMAw88wJNPPgnAPffcQ8eOHQ/4Ptq02k6mgpXgqQhvLSIiIiIiIiIiInJAFDKJ/EpWq5X333+f448/npKSEq677jqcTicJCQl0796dOXPmYLFYmDp1KhdddFGj82+99VYMw+Cbb74hJSWF9PR0MjMzyczMbDBu7NixADz33HM4nU66dOlCZmam2UnVGlRVVfHKK69w8cUXk5CQgMvlwuVykZSUxAMPPEAgEODKK68012eqdd5553HjjTcCMHPmTJKTk0lISCAhIYF77rmHW2+9lcsuu+yA6znvvPPM5/PCCy+QlJRk1jV27FiysrKYNGlSk+dfccUVpKSkUFRURFZWFikpKeafzdKlS81xjzzyCFdffTWBQIAHH3yQpKQkEhMTSUpK4uGHHwaCQdpDDz10wPfQ5jk7Q0wnCPhg17JwVyMiIiIiIiIiIiIHQCGTSAvIyMhg+fLlTJkyhTPOOIOoqCgqKyvp3LkzN9xwA9999x133XVXyHPPOeccPv30U84//3xcLhd5eXls3ryZzZs3Nxj35z//malTp3Laaadht9vZtm0bmzdvJjc393DcYrM899xzPP7441x88cUcc8wxBAIBqqqqSE9PZ+jQobz//vu8++67IddHevnll5k6dSq9e/cmKioKv99Pv379ePvtt3nuuecOuqY33niDZ555hl69ehEZGYnP5+PEE0/k0UcfZfHixTidzibPTUhI4D//+Q/XXHMNGRkZlJSUmH821dXV5riIiAjefvtt3n//fS666CKSkpIoKysjKSmJiy66iA8++IDZs2djt9sP+j7atNop83K1LpOIiIiIiIiIiMiRxAjsa0X7I1B+fj7Lli1j2bJl5OTkkJOTY069NXLkSLKzs5t9rY0bN/Lss8/y5ZdfsnnzZvx+PxkZGQwePJg77riD448//qBqLC0txeVyUVJS0mCtnaZUV1ezceNGunXrhsPhOKjPFBGp1ep+p3z/HHxzF3S+EC76PNzViIiIiIiIiIiIHHYHmhu0FrZwF9DSUlNTW+Q6L774IuPHj8ftdjd4f/369axfv56ZM2fyzDPPcPvtt7fI54mItFu16zLlLYGAHww12YqIiIiIiIiIiBwJ2vQ3eZ07d2bIkCEHfN5bb73FbbfdhtvtxuVy8eCDD7Jo0SJycnJ48cUXOfroo3G73YwbN4733nvvEFQuItKOJPYCWwy4S6Dov+GuRkRERERERERERJqpzXUyTZw4kT59+tCnTx9SU1PZtGkT3bp1a/b5lZWV/O53vwPA6XSyaNEiTjjhBPP4aaedxogRI+jfvz9r165l/PjxXHTRRcTExLT4vYiItAsWG6SeAdv/HVyXKfHEcFckIiIiIiIiIiIizdDmOpkmT57MpZdeetDT5n3++efk5+cD8Lvf/a5BwFQrLi6OKVOmAJCbm3tA6zyJiEgIqbVT5n0T3jpERERERERERESk2dpcyPRr5eTkmPsXXXRRk+MGDBiAw+EA0JR5IiK/Vu26TLmLw1uHiIiIiIiIiIiINJtCpr0UFhaa+/vqhrLZbCQmJgLwzTff4PV6D3ltIiJtVofTAQPK/geVueGuRkRERERERERERJpBIdNe6q+tVFJS0uS4QCBAaWkpAG63mw0bNhzy2kRE2qwIV91aTOpmEhEREREREREROSIoZNpLVlaWub9gwYImx61cuZLy8nLz5y1bthzSukRE2rzaKfPyFDKJiIiIiIiIiIgcCRQy7eXiiy/GbrcDMGXKFAoKChqN8fv9/OUvf2nwXllZWZPXrKmpobS0tMFLRET2kqp1mURERERERERERI4kCpn20qlTJ26//XYAtm/fTr9+/fjoo48oLS2lurqapUuXcvHFF/PFF18QERFhnldVVdXkNR999FFcLpf56ty58yG/DxGRI05tJ1PBCvBWhrcWERERERERERER2S+FTCE8+eSTXHbZZQD8/PPPXH755bhcLqKiojjzzDOZO3cu3bt356677jLPiY2NbfJ6f/rTnygpKTFfW7duPeT3ICJyxHF2heh0CHghPyfc1YiIiIiIiIiIiMh+KGQKISIigo8++ohXXnmFU089FYul7jHFx8czfvx4VqxYQSAQMN9PSEho8nqRkZHExcU1eImIyF4MQ+syiYiIiIiIiIiIHEFs4S6gtTIMg1GjRjFq1CjKy8vJy8sjIiKC9PR0rFYrAGvWrDHHH3fcceEqVUSk7UjrD/97F3IXhbsSERERERERERER2Q+FTM3gdDpxOp0N3nO73SxbtgyA7t27k5ycHI7SRETalrT+wW3eN+D3gcUa3npERERERERERESkSZou7yB99tlnlJSUAHD11VeHuRoRkTYisRfYY8FdAkXfh7saERERERERERER2QeFTAfB6/Xy17/+FQC73c6YMWPCXJGISBthsUHqmcF9TZknIiIiIiIiIiLSqilkCqGgoIDKysqQx9xuNzfddJO5HtO9995L9+7dD2d5IiJtW+2UeTsXhrcOERERERERERER2ac2tybTokWL2LBhg/lzQUGBub9hwways7MbjB81alSja8yfP58xY8Zw3XXXcf7559OlSxcqKytZuXIl06dP54cffgBgyJAhPPDAA4fkPkTCbe3atTz00EMsXLiQXbt24fP5OOmkk1i1ahXz589n4MCBAAQCgRb93OzsbEaPHk3Xrl3ZtGnTYT9fWoG0s4Pb3IUQCIBhhLceERERERERERERCanNhUwzZ87k1VdfDXls8eLFLF68uMF7oUImgOLiYqZNm8a0adNCHh81ahQvvPACERERv6peCY9AIMB7773H7NmzWbFiBfn5+VitVlJTU+nYsSN9+/bl7LPP5rzzziMuLi7c5R52GzdupF+/fpSVlQGQmJiI3W4nOTk5zJVJu9ChL1jsULkDyjZBXLdwVyQiIiIiIiIiIiIhtLmQqSWcffbZPPnkk3z99desW7eOvLw8LBYL6enpDBw4kFGjRnHGGWeEu0w5SMXFxVx++eUsWLDAfM9msxEdHc2WLVv43//+x+LFi3n66ad55ZVXmgwi27IZM2ZQVlbG0Ucfzbx58+jUqdNh+2yXy0WPHj3IyMg4bJ8prYwtGpJPhfylwXWZFDKJiIiIiIiIiIi0Sm0uZMrOzm40Jd6BSk1NZcKECUyYMKFlipJW5cYbb2TBggVYrVZ+//vfc9ttt3HUUUdhsVjwer388MMPfPHFF8yePTvcpYbN2rVrARg2bNhhDZgAhg8fzvDhww/rZ0orlNZ/T8i0EI69IdzViIiIiIiIiIiISAhtLmQS2Zf169fz8ccfA/Dwww9z3333NThus9no1asXvXr14v/+7/+oqqoKR5lhV1lZCYDT6QxzJdJupZ0Na54KdjKJiIiIiIiIiIhIq2QJdwEih9OqVavM/WHDhu13fFRUVIOfDcPAMAzmz5/f5DkDBgzAMAwmTZrU6Fj983Nzc7nzzjvp1q0bDoeDtLQ0rrvuOtatW7ffuubPn8+1115Lly5dcDgcuFwu+vbtyxNPPEFFRUXIc0aNGoVhGIwaNYpAIMDMmTPp378/SUlJGIZBdnY2mZmZDe5v8uTJZs37u+9akyZNwjAMBgwYsM/6a6+5t+zsbAzDIDMzs8nzly5dyuWXX05ycjJRUVH06NGDv/zlL5SXl++3PjlCpPULbot/hOqC8NYiIiIiIiIiIiIiISlkknZr27ZtYfvsjRs3cvLJJzNt2jTy8vKw2+3k5eUxe/ZsTj75ZL744ouQ53m9XsaMGcPAgQN566232Lp1K3a7nYqKCnJycrj33ns59dRT2bx5c5OfHQgEuPrqqxkzZgxLliwhEAhgsQR/FaSkpJCamordbgcgJiaG1NRU8xUREdHyD+MAvfzyy/Tr14+PPvqI3bt3ExkZyaZNm3jkkUfo06cPRUVF4S5RWoIjCRKOC+7nLg5vLSIiIiIiIiIiIhKSQqY2IkCAijb2vwCBFn9Offr0Mbtn/vCHP/Dzzz+3+Gc0x913301ERAT/+te/qKiooKysjG+//ZYTTzyR6upqRowYETIEmzBhAjNnziQ1NZXnn3+e3bt3U1ZWRlVVFfPmzePkk0/mp59+4je/+Q1+vz/kZ3/wwQd8+OGHPPXUUxQVFVFYWEhJSQkXXHABOTk55ObmctZZZ5mfl5uba75q3w+XFStWcNttt+H3+xkwYAA//vgjxcXFlJeX8+abb5Kbm8uDDz4Y1hqlBaX2D241ZZ6IiIiIiIiIiEirpDWZ2ohKKnHSttbPKaecGGJa9JqZmZnccsstvPTSS6xdu5aePXvSu3dvzjzzTE499VT69u3L8ccfH3Iat5ZUVVXFkiVLyMrKMt/r27cvX331FVlZWRQWFvLoo48ybdo08/j333/Ps88+S3R0NF9++SUnnniiecxutzNgwAAWLFjAcccdx4oVK5gzZw6XX355o88uLy/n2WefZfz48eZ7TqfziFh/6f7778fr9XLsscfy2WefmdMZ2u12rrnmGhISErjwwgvDXKW0mLT+sO5FyF0Y7kpEREREREREREQkBHUySbvz/PPP88ADDxATE0MgEGDlypU8//zz3HzzzZx44omkpaVxzz33kJeXd8hquOqqqxoETLU6dOjA2LFjAXj77bcbHPvHP/5BIBDgkksuaRAw1RcbG2sGS3Pnzg05JiEhgdtuu+3XlB8WxcXF5j398Y9/bLReFsAFF1zAmWeeebhLk0Ol49nB7a7vwFsZ3lpERERERERERESkEXUytRHRRFNOebjLaFHRRB+S69psNh588EH+8Ic/8PHHH7NgwQJycnL48ccfcbvd5Ofn8/TTT/Paa6/x6aef0rdv3xavYdCgQfs89sgjj7B79242btxIt27dAFi0KDhl2Oeff05aWlqT55eXB/85aGpdpj59+rSKtZUO1IoVK8wpAPf3/JYsWXK4ypJDydkVYjKgYjvkfwvpA8NdkYiIiIiIiIiIiNSjkKmNMDBafGq5ts7lcnH99ddz/fXXA1BdXc2iRYt49tln+fjjjykoKOCKK65g/fr1OByOFv3sjIyMZh3Lz883Q6YdO3YAwRCpNkjal8rK0J0fHTp0OJBSW438/Hxzf1/Pr1OnToejHDkcDAPSzoZf3gquy6SQSUREREREREREpFXRdHkiezgcDs4//3zmzJnDyJEjAdi2bRtffPFFi3/Wwaz55PP5AHjssccIBAL7fc2fPz/kdaxW668pXeTwSusf3O7UukwiIiIiIiIiIiKtjUImkRBuvfVWc/+nn34y92sDmurq6ibPLSkp2e/1t23b1uSx7du3m/v1u45qp8hbu3btfq8fTjZbsEHy1z6jvdV/FvWf0d72dUyOQGl71mXKXwJ+b3hrERERERERERERkQYUMomE4HQ6zf3IyEhzPyEhAYCtW7eGPK+srIwff/xxv9efN2/efo8lJiaaU+UB9OvXD4BPP/20WdPlhcv+nhHAt99+e8DXPeWUU7BYgr+y9vX8vv766wO+trRiCcdDhAs85bB7dbirERERERERERERkXoUMkm7snHjRn7++ef9jnv11VfN/VNOOcXcP+mkkwB4//33Q5731FNPUVNTs9/rv/vuuw06pGoVFBQwY8YMAEaMGNHg2JgxYzAMg+LiYv74xz/u8/oejydsQVTtM9qxYwdLly5tdDw/P5+XXnrpgK8bHx/PkCFDgOBzDtUp9dVXX/HNN98c8LWlFbNYITUYsJK7KLy1iIiIiIiIiIiISAMKmaRd+e9//0tWVhaXXHIJs2bNYtOmTeYxj8fDypUrGT16NFOmTAGgb9++9O/f3xxz7bXXAjB37lz++te/UlpaCgTDoT//+c88/PDDxMfH77cOh8PBhRdeyFdffUUgEAAgJyeH888/n4KCAmJjY7nvvvsanNO7d29+//vfAzB9+nSuuuoqVq1aZZ7v8/lYvXo1Dz30EEcddRSrVq06yKf065x11ll07doVgFGjRrF8+XICgQB+v5/58+czYMAA/H7/QV37oYcewmq1sm7dOi655BIzqPN6vbzzzjtcffXVzXr+coSpXZcpV+syiYiIiIiIiIiItCYKmaRdsdvt+P1+PvvsM0aOHEm3bt2IjIwkKSmJyMhITjnlFLKzs4FgB9M///lPc4o2CIYmAwcOBODBBx8kPj6exMREOnTowGOPPcbjjz9udvLsy5QpU6iurmbw4ME4nU5iY2Pp27cvq1evJjIykjfffJMuXbo0Ou/JJ580g6b33nuPk08+mejoaJKTk3E4HPTu3ZuJEyeydetWDMNogSd24CwWCzNmzMBut/PTTz/Rp08fnE4nMTExDBw4EK/Xy7Rp0w7q2qeddhrPP/88hmHw9ddf07NnT+Lj43E6nYwYMYLU1FQmTpzYwnckYWeGTItgT6gqIiIiIiIiIiIi4aeQSdqVCy64gPXr1zN16lSuuuoqsrKyiIyMpLi4mOjoaI455hiuvvpq3nrrLXJyckhPT29wvtVq5dNPP2Xy5Mn07NmTiIgIDMNgyJAhfPnll0yYMKFZdXTv3p2VK1cybtw4UlJScLvddOjQgWuvvZaVK1dyySWXhDzParXy9NNPs2LFCm699VZ69OiB1WqlpKSEhIQE+vXrx6RJk1i1apW5hlM4XHDBBSxcuJBLL72UhIQEfD4fnTt35r777uO7774jLS3toK996623snjxYi677DISExOpqamha9eu/OlPf2LZsmXmmlDShqT0AUsEVOVB6YZwVyMiIiIiIiIiIiJ7GIGA/lr44VZaWorL5aKkpIS4uLj9jq+urmbjxo1069YNh8NxGCqUQ6W2u2jevHkMGDAgvMVIu3VE/k75qD/kLYZzX4Yeo8NdjYiIiIiIiIiISIs60NygtVAnk4iItH4dzw5ud2pdJhERERERERERkdZCIZOIiLR+tesy5S0Kbx0iIiIiIiIiIiJiUsgkIiKtX+pZgAEl66EyN9zViIiIiIiIiIiICAqZRETkSBCZAIknBPdz1c0kIiIiIiIiIiLSGtjCXYBIexIIBMJdgsiRK+1sKFwLuQuh+5XhrkZERERERERERKTdUyeTiIgcGTqeG9zuXBDeOkRERERERERERARQyCQiIkeKjucEt7vXQE1ReGsRERERERERERERhUwiInKEiE4DVw8gADsXhrsaERERERERERGRdk8hk4iIHDk0ZZ6IiIiIiIiIiEiroZBJRESOHLVT5ilkEhERERERERERCTuFTCIicuSo7WTavRLcJeGtRUREREREREREpJ1TyCQiIkcOZyeI7Q4BP+QuDnc1IiIiIiIiIiIi7ZpCJhERObJoXSYREREREREREZFWQSGTiIgcWdIVMomIiIiIiIiIiLQGCplEROTIUtvJtGs5eMrDW4uIiIiIiIiIiEg7ppBJRESOLLGZ4OwCAR/kLQl3NSIiIiIiIiIiIu2WQiaRVigzMxPDMMjOzg53KW3ewoULueSSS0hJScFqtWIYBpdffjkA2dnZGIZBZmZmi3/upEmTMAyDAQMGhOX8I57WZRIREREREREREQk7W7gLEAmnoqIiOnbsSE1NDQA///wzxxxzzCH7vOzsbDZt2sSAAQMOeTjg8Xh47bXXeO+991i9ejUFBQU4HA5SU1PJyMjgjDPO4JxzzmHgwIE4HI5DWktrtXTpUgYNGoTX68UwDJKSkrBarSQkJIS7NNmfjufC+tcUMomIiIiIiIiIiISRQiZp19544w0zYAJ4+eWXefTRRw/Z52VnZ7NgQfBL8X2FTEcddRQOhwOXy3VQn7N161Yuvvhivv/+e/O9iIgIrFYrv/zyC+vXr2f+/Pk89thjzJs3r912wzzzzDN4vV769evHnDlzSExMPGyfnZycTI8ePejSpcth+8w2pbaTKX8ZeKvAFhXeekRERERERERERNohTZcn7do//vEPAMaPHw/Aq6++is/nC2dJAPz73/9m3bp1DB8+/IDP9fl8DBs2jO+//57o6GgeeughtmzZQnV1NYWFhVRWVrJs2TImTZrEUUcddQiqP3KsXbsWgGuuueawBkwAd955J+vWrWPWrFmH9XPbjLijIDod/G7IXxruakRERERERERERNolhUzSbq1YsYJVq1YRHx/PE088Qffu3dm5cyeff/55uEv7Vb7++mtWrlwJBEO0+++/n86dO2MYBgCRkZH06dOHv/71r6xfv54zzzwznOWGVWVlJQBOpzPMlcgBM4y6bqYdmjJPREREREREREQkHBQySbtV28U0YsQIHA4HN9xwQ4P3Qxk1ahSGYTBq1CgA3nvvPQYMGEBiYiLR0dH07t2bqVOn4vf7G5yXnZ2NYRjmVHmTJ0/GMIwGr02bNpnjMzMzMQyD7OzsA76vVatWmfvDhg3b51jDMIiMjGzw3qZNm0LWtLematz7/PXr1zNq1Cg6depEZGQkXbp0YezYsWzfvn2/9/Lhhx9y+eWXk56eTkREBAkJCZxzzjlMnz4dj8cT8pwBAwZgGAaTJk3C4/Hw97//ndNOO434+HgMw2D+/PmN7m/06NFN/lk0Ze9/FkKp/XPPzMxsdGzSpEkYhrHPqQo///xzBg8eTHx8PE6nk5NOOoknnniiyXtvd2pDJq3LJCIiIiIiIiIiEhYKmaRdqq6uZvbs2QDceOON5tYwDD755BPy8vL2e40777yTq666ioULFxIIBKiqqmL16tX8/ve/Z/To0Q3GRkVFkZqait1uByAmJobU1NQGL6vV2sJ3Cdu2bWvxax6Ib7/9llNPPZVXX32VkpISrFYrW7duZcaMGfTq1YsVK1aEPK+8vJzLLruM4cOH89FHH7Fz506ioqIoKSlh4cKF3H777Zx77rkUFRU1+dnV1dUMGDCACRMmsHr1aiyWul93tc+89r24uLhD/mdxoCZNmsTFF1/MV199RUlJCXa7nR9++IF7772X888/H7fbHe4Swy+9dl2mpeCr2fdYERERERERERERaXEKmaRdev/99ykuLuboo4/mrLPOAqB79+70798fr9fLa6+9ts/z58yZw0svvcSUKVMoKiqiqKiIgoICbrnlFgBmzZrF119/bY4fMWIEubm55mdNmDCB3NzcBq/OnTu3yL317dvX3G9ux9Chctttt9GtWze+/fZbysrKqKioYO7cuXTp0oXCwkKGDx9OWVlZo/NuuOEGPvnkE44++mhmz55NaWkpJSUlVFZW8tFHH9G9e3eWLFnCTTfd1ORnT5s2jTVr1vDKK69QWlpKYWEhBQUF9OrVq9Eznzp16iH5szhYc+bMYfLkyQBcddVVbNmyhaKiIkpLS5k2bRpLly7lhRdeCGuNrYKrB0Slgq8a8peFuxoREREREREREZF2RyFTWxEIgKeibb0CgUP2uGqnxKvtYqpV+/O+pswDKCoqYsaMGdx9993ExcUBkJSUxEsvvcSpp54KwJtvvtnSZTfLueeey+DBg4Hg+kxdu3blrLPO4u677+b1119n/fr1h60Wm83Gl19+aQZfhmEwZMgQvvjiCyIiItiyZQvTp09vcM6nn37Khx9+SFpaGvPnz+faa68lNjYWAIfDwdChQ1mwYAExMTF8+OGHDaYHrK+8vJzZs2czatQooqKigOCfUWJi4iG845bxpz/9CQj+Wb711ltm6BUVFcUdd9zBs88+S3FxcThLbB0MAzqeE9zXlHkiIiIiIiIiIiKHnS3cBUgL8VbCK85wV9GyRpeDPabFL/u///3PXJendh2mWldffTV33XUX69at45tvvjE7j/bWuXPnRgFVraFDh/Ldd9+xZs2aFq+9uf75z3/yf//3f7z00kt4PB6WLFnCkiVLzONdu3Zl9OjRDUKyQ2Hs2LF06NCh0ftZWVlceeWVzJ49m7feeos//vGP5rGZM2cCwW6mjIyMkNft1KkTAwcO5JNPPmHu3Ln07t270Zjjjz+eyy67rIXu5PBZs2YNP/zwAwD3339/g2n+ao0ZM4aHHnoorF1qrUbaOfC/d/eETPeHuxoREREREREREZF2RZ1M0u68/PLLBAIBzj77bDIzMxsci4uL4/LLLzfHNaVPnz4hv/wHSE9PB6CwsLBlCj4IMTExTJs2jW3btvHiiy9yww03kJWUWeMRAAAgAElEQVSVZa41tHnzZiZNmkTv3r355ZdfDlkdgwYN2u+xNWvW4PF4zPcXLVoEwIsvvkhaWlqTr6+++sq8l1D69evXUrdxWC1fvhwIdoGdffbZIcdYLBYGDBhwGKtqxWrXZcr7BvyefY8VERERERERERGRFqVOprbCFh3s/GlLbNEtfkm/38+rr74KNJ4qr9bIkSN58803efvtt3nmmWdwOht3iNVO3xaKzRb8v1X94KSlpKWlhXx/xIgRTJ06tdH7HTp0YMyYMYwZMwYITiH39ddf8+STT7Jo0SI2btzINddcQ05OTovXCjTZiVT/mNfrpbCwkNTUVDweDwUFBQCUlJRQUlKy38+orKwM+X6oDqojQX5+PgDJyclERkY2Oa5Tp06Hq6TWLeF4iEyEmkLY9R2knhHuikRERERERERERNoNhUxthWEckqnl2pq5c+eybds2AG655RZuueWWJseWl5fzzjvvcNNNNx2u8vYrLy8v5PvNCWMAnE4nQ4cO5dJLL+X8889n3rx5LF++nFWrVoWccu7XMgzjgMb7fD5z/6233mLEiBEH/dm1XVtHqgN9du2WYQmuy7Tpw+CUeQqZREREREREREREDhtNlyftyj/+8Y8DGr+vKfPCIRAIhHxlZ2cf0HUsFkuDgO2nn34y92s7sQCqq6ubvEZzgq3aQC+U2vWEbDYbiYmJADgcDlwuFwBr167d7/XDqfY5/dpntLfaDqxdu3ZRU1PT5Ditx1RPxz1T5u1cEN46RERERERERERE2hmFTNJu7Nq1izlz5gDw3nvvUVZW1uRr2bJlACxevJh169a1WA216zgFAoEWu+bBqj8NYP1p2RISEsz9rVu3hjz3559/pri4eL+fMW/evP0e69WrF3a73Xy/di2ld999F7/fv9/PCJfa59TUMwL49ttvD/i6p512GhCcRrB2faq9+f1+5s+ff8DXbrNqQ6bcReD3hrcWERERERERERGRdkQhk7Qbr732Gh6PB5fLxWWXXYbT6Wzy1adPH3r27Am0bDdTXFwcQLMCmoP1/fffN6vLZdasWeb+ySefbO7HxMRw1FFHAfD++++HPPdvf/tbs2qZPn26ucZSfT/99BPvvfceQKMp8W699VYgGGQ9+eST+7x+RUUFbre7WbW0tJNOOgmAnJyckEHTjz/+yAcffHDA1+3VqxdZWVlA8DmHCtpefvnlfXaJtTuJvSDCBZ4y2L0q3NWIiIiIiIiIiIi0GwqZpN2oDYuGDRtGRETEfsdfddVVQDCM8XpbpjvihBNOAOCzzz47ZNOdzZ8/n+7duzNixAjeffdddu7caR6rrq5m0aJFDB061AyQrrzySrp27drgGtdeey0QfGbPP/88VVVVQLBr55ZbbuHtt98mOjp6v7V4PB4GDx5MTk4OEOzg+uqrr7jggguoqamhc+fOjB07tsE5w4YNY/jw4QDcd9993H777fz888/mcbfbzbfffsu9995L165dyc/PP9BH1CJqg0qPx8PVV19tTjno8Xj46KOPOP/884mJObh10mpDvHnz5vHb3/7WDJSqq6uZPn06d955J/Hx8S1zI22BxQpp5wT3d8wPZyUiIiIiIiIiIiLtikImaReWLl3Kf//7X6AuPNqf2nF5eXl8+umnLVLHyJEjcTgcbNiwgS5dupCWlkZmZiaZmZkt1plit9txu9288847XH311aSnpxMVFUViYiJRUVGcffbZfPzxxwAMGTIk5DpV9957L8cddxwej4dx48bhdDpJSEigS5cuzJo1i+zsbFJSUvZby4wZM/jll1/o27cvsbGxOJ1OBg8ezObNm4mPj+eDDz4wu7vqe/3117nmmmuAYDdUjx49cDqd5j2cccYZPPHEE+zevRvDMH7lEzs4LpeLZ555Bgj+89WzZ0/i4uJwOp1cfvnldOnShQcffPCgrj18+HD+8pe/APD222/TuXNnEhMTiY2N5fbbb6dv377cfvvtLXYvbUL6wOB2x9fhrUNERERERERERKQdUcgk7UJtkOJyuRgyZEizzjnxxBPNactCBTEH45hjjmHevHkMHTqUlJQUdu/ezebNm9m8eXOLdUvddtttrF69mscff5xhw4Zx9NFHY7VaKSkpITY2luOOO44bb7yRzz77jLlz54YMeZxOJ4sWLeKee+6hW7du2Gw27HY7V1xxBUuWLDEDoP05/fTTWb58OTfeeCMulwuv10tGRgZjxoxh7dq15vpDe4uOjubNN99k3rx53HDDDXTv3h2/3095eTkdOnRg0KBBPPHEE6xfv56MjIxf9bx+jZtvvpnPPvuMQYMGERcXh9fr5dhjj+Wxxx5jwYIFB93JBPDwww/zySefmNeuqakhKyuLxx57jH//+9/N6sZrVzIGBbe5C8HvCW8tIiIiIiIiIiIi7YQRCAQC4S6ivSktLcXlclFSUhLyC/69VVdXs3HjRrp164bD4TgMFYocvE2bNtGtWzcANm7cSGZmZngLkkba5O+UgB9mdYCa3TDsG0g9M9wViYiIiIiIiIiINNuB5gathTqZRETkyGdYIH1AcH+7pswTERERERERERE5HBQyiYhI25C+Z8q8nfPCW4eIiIiIiIiIiEg7oZBJRETahvSBwW3uYvBWh7cWERERERERERGRZvD7A1RV+Skt9Ye7lINiC3cBIiIiLSK+J0SlQVUu5C+tmz5PRERERERERETarEAgAIBhGAAUF/vYvduP2x3A7Q7g8YDHE9jzgtNPj8TpDPbfrF3rZtWqGvNYcHzdOaNHx5KREYxR/v3vKt57r7zB9dzuuv1HH03kpJMiAXj33XL+9rfiENcNnvPWWx248MJoAGbNKmf06F1A2WF+ci1DIZOItKjMzEzzF7vIYWUYkDEINsyGHfMUMomIiIiIiIiIHEKBQDBAsdvrAp6dO70UFvqprg5QXR2gpqbh9sorY7Dbg2M//bSS776rMY/XH1tTE+DFF5OJj7cC8OSTxbzxRnmj69Xur1/fme7d7QA8+mgxTzxR0mTdq1dn0KtXMAz68MMKJk4sanLsoEFRZsi0Zk0N06c3HQTdfbfP3C8q8rN6tbvJsVVVdd+f2u1NDjsiKGQSEZG2I33gnpDpa2ByuKsREREREREREWlxgUAwWHG7IS6ubkWcDRs8FBX56gU1UF3tp6YmOCXb9dfHmmNnzSrjxx895vH6W58PPvwwzRx7110FfPFFVaMgqLo6GJTU1HQjIiI4dsKEQmbPLm+y9gsv7EpCQjA4mjOnghdfbDq0+fvfk4iPD+7v3OnbZ2hTU1MX2sTEWIiJMYiMNLDbDSIiwG439rwwQy6Ao4+2M2RIlHksIqLhuJQUqzn2zDMdTJqUYB7b+9rHHRdhjr3oomjmzk1r9LnB62MGVwBXXeVk6NAYqqpKSU1t8hZbLYVMIiLSdqQPCm7zloKnAuwx4a1HRERERERERNoMn6+uy8bvh6SkugBi5coaysr8Ibt3YmIsXHut0xz71FPFbN3qbdS5U10dIDHRyuuvdzDHDh+ey/LlNQ3GuvdkLSkpFvLzM82xN920i4ULQ69THRVlNAiZ3n67nM8+q2ryXv3+ABZLMIzJzfWxfr2nybE1NQEiIoJjExIspKRYiIw0cDiMRtv6EyCdc44DIOS4yEgDl6suQBszJpYLL4xqcmz9MGjixAQmTkxost76rr3W2eDPZl/OOMPBGWc4mjW2c2cbnTs3L36JiAiGT4GAZf+DWyGFTCIi0nbEdgNnVyjfDLmLoPMF4a5IRERERERERA6xyko/FRUBKiqC27qfA7hcFvr3rwsGHn64iOJivzm2osJPZWUwwOnZ084LL6SYY08+eRvbtnnNcMdTL2c55ZQIvvuuk/nzlVfm8b//eUPWd8wx9gZBxqxZ5axdG7orJz3d2uDn/Hwf27b5Qo6t370D0LGjlc6drTgcFiIjabCNjjYajB02LIZjj7WHHBsZSYMwaOLEBMaPj2syOHI66679//5fMv/v/yWHrHdv110Xy3XXxe5/IJCVFUFWVsT+B8php5BJRETaDsMITpn3c3ZwXSaFTCIiIiIiIiKtgt8fYMcOX4Nwp/62UycbgwZFAcGOod/9bneDsKg2DKqo8NOvn4MZM+rCIJdrE97Q+Q6DBjn497/TzZ+nTCmhqMgfcmxlZcPQZvduHwUFocfuHfAcdZQduz10l02nTg2Do9Gjneza5TfH1B9ff/o7gBkzUqipCYS8bmRkw+Do7bebP9farbfGNXvsCSco3JGmKWQ6ggQCgf0PEhHZjzb/uyR90J6Q6etwVyIiIiIiIiJyRAgEAhhGMLDweAL88IPbDHT2DnmysuwMGRINQGmpn9tvL2jUFVT78/DhMUybFuxqqaoK0LnzliZr+M1vos2QyWKBF14oxR863yE9veHX2jExFkpK/DgcBjExhrkmT0yMhR49GgYkt98eh8cTnMIuOjo4PjraQlSUQYcODcOgzz/vCNAoCIqMNLDt9c36v/7VcR9PuKG7745v9lgFPNLaKWQ6AlgswfTa5wvdFikiciBqf5fU/m5pc9IHBrcF34G7BCJc4a1HRERERERE5FcKBAJUVQUwDIiKCv73fEWFn5ycmiamifNz5pkOLrwwGAbt2OHl5pt3hewgqqjwM3ZsHFOnBsOgXbt89O69vclaRo92miGTYcDs2eVNjs3Pr/s+MyoqGM5ERdUFQbUhT0yMhd69I82xhmEwaVICdrvRYEztNjW1YRi0fXsXHA4Dq7VhZ08of/tb4n7H1Dr+eAU8IvujkOkIYLfbsdvtlJeX43Q2bxEyEZGmlJWVmb9X2iRnJ3AdAyXrYed/oOtl4a5IRERERERE2rhAILheT21wExtrweUKhkG7d/tYsKC6yWniLr002gyDfvzRzciRu0KsMRSclWTixHgmTw6GJJs3exk4cGeTNd19t8u8rs8HX3xR1eTYioq6WU+czmCIE+zwaRjuxMQY9O1bt75RdLTBlCmJREdbGgVBMTEGKSl1YZDFYlBd3a3Zz/SBBxKaPTYmpo3+RVqRI4BCpiOAYRjExsZSXFyMy+UiKioq3CWJyBGqqqqK0tJS4uPjzTb4Nil9UDBk2v61QiYREREREREJye8P4PeDzRb87+P8fB9Ll1ZTUuKnpMRPcbHf3K+oCDBqlJPBg4OhzTffVDNyZH6DIKj+JERTpiSaU6L9/LOHK67Ia7KOlBRrgzAoJ6emybH11wxyuSxkZdkbdQTVbvv1q+sMSk62kJ2d0mBM/WAoPr4upImLs5Cb27VZz9BqNQ5o6jcRaXsUMh0hkpOTqaqqYsuWLcTFxREbG4vVam3bXxKLSIsIBAL4fD7KysooLS0lMjKS5OTkcJd1aKUPgh9naF0mERERERGRNqy6ui4Iqr/t2zeSzMzg7B3Ll9cwdWpJozElJX5KS/288koKI0fGmmOHDWs6DOrbN5LBg4P7fj9s2OANOc5uB2+9Q8nJVvr1i2wQANXvEDrnnLrOoMxMG3PmpDYaU3teVFTdd4EZGTZ++KFzs55VVJTFvE8RkZbU5kKm/Px8li1bxrJly8jJySEnJ4fdu3cDMHLkSLKzs5t9rc2bN/PCCy/w5Zdf8ssvv1BRUUFsbCw9e/bkoosuYuzYsaSkpByiO2nIarXSuXNnCgoKKCsro7i4+LB8roi0HXa7nfj4eJKTk7Farfs/4UiWPiC4LVwD1QXgaOOhmoiIiIiIyBHG7w8QCGCuobN9u5fly2sadRDV7t99t4uzzgqGMe+/X8511+2ipiYQ8trZ2SlmyJSf7+P115teM6i42G/ud+xopW/fSOLjg1Pd1W7j4iw4nQ3DoF69Ili0KD3klHJ2e8O/FH7MMXYWLcpo1nNxOi1cdllMs8aKiLQGbS5kSk1NbZHrzJ49mzFjxlBZWdng/aKiIpYsWcKSJUuYOnUq77zzDoMGDWqRz9wfq9VKamoqHTp0wOPx4Pf793+SiAhgsViw2+3tp/sxqgMknABF38OO+dD9ynBXJCIiIiIi0mYEAgGqqwMhu4P693eQnh78yvE//6nixRfL9hrn29NFFODDD1MZNiwYqCxYUM111+U3+ZmXXhpthkwOh8UMmAwjOL1b/WAoIaFu6rfjj7fz5JOJjYKj2m1CQt1fwjz55Ei+/bZ5YVBcnIV+/Rz7Hygi0sa1uZCpvs6dO5OVlcW//vWvAzpvyZIl3Hjjjfh8PiwWCyNHjmTYsGGkp6ezZcsWXn31VT7++GN2797N0KFD+f7778nMzDw0NxGCYRhEREQcts8TETkiZQzaEzJ9rZBJRERERESkHp8vGNDUdhFt3uxh1Sp3k11EDzwQT69ewfV9Xn65lNtvL8DtDn3tYHAU/Mpx61Yvb7zRvC6ijIzQXUS1+3371q0vNGCAg82bu+ByWYiNNbBYmv4LlV272pkwQWsGiYgcKm0uZJo4cSJ9+vShT58+pKamsmnTJrp163ZA13jkkUfw7Vmp77nnnuOOO+4wj/Xp04crrriCP/zhD0yZMoWKigqmTJnCs88+26L3ISIiv1L6QPj+WdgxL9yViIiIiIiItJhAIEBVVeguovPOiyI5OdiZM3duJa+9Vt6og6i42E9ZWYAFCzpyzjlRAHzySSV33rm7yc+84QanGTJFRhpmwGQYNOoOio2t6yI67bRInnoqsdGY+Hjrni6iurHnnhvV7C6i4NR0lv0PFBGRQ67NhUyTJ0/+1ddYvHgxAElJSQ0CpvomTpzIlClTAPjmm29+9WeKiEgL63guYEDxOqjYATHp4a5IREREREQEny+AYWB23/zyi4e1a5vuInr88USOOiq4vtCUKcXcd18hHk/oa9cPjjZs8DS7i6hrVxunn950F9EJJ9TNqDN0aAxbtkThcgXXKdpXF1GPHhH06KHZeERE2rI2FzK1BPeev46xrw4ol8tFcnIyBQUF1NTUHK7SRESkuSITIPkUKPgu2M10zHXhrkhERERERNqQqio/u3b5yc/3sWuXj3POcZjdNR98UMH771c06iAqKQl2Ea1enWF2Br31Vjn331/U5OfcdVecGTJFRBhmwGSxNF6LyOGoC3z693fw1FOh1iIKdhElJtZ1Al16aQyXXhrTrPuOjW3YrSQiIu2bQqYQjj32WFauXMnGjRubHFNaWkpBQYE5XkREWqH0gQqZRERERESkWTyeAAUFPvLz617DhsXgdAYDlZkzS/nHP8rMY+XlgQbnr1nTiRNPDHbt/PCDm9mzm9dF1K2bvVEXUf397t3t5tjrr3cybFhMs7qITjopkpNOimzyuIiISEtQyBTCbbfdxtixY9m9ezfTp09n7NixjcY89NBDDcaLiEgrlD4I1jwFO74OdyUiIiIiInKY+XwBCgv97NrVMDi64YZYXK5gcPTccyVMm1ZKfr6PoiJ/o2usWRNpBkf5+T6WLm04m01EBHToYCUlxYrPVxc6DR4cRXS00ah7qPbn+l1Ev/2tk9/+1tmse4qPtxIff8CPQkRE5JBRyBTCLbfcwsKFC3njjTcYN24c3333HUOHDqVjx45s2bKF119/nX/+858A3HvvvQwZMiTMFYuISEhp/cGwQdlGKN0IcU1PgyoiIiIiIq1bIBCgtDRgTk9XPzgaNy6OhAQrAI8/XsyUKSUUFPjwN86NOPtsh9nhU1bm56ef6hY4slggJcW6JziyYNRrFPrNb2I47rgIM1Tq0MFKXJyBYTTuJjr9dAenn+5o2QcgIiIHLBDw4/FX4vFX4vVXmVuvvwqfvxqPvwKfv9p8+f01dVtfFX6/m4C/xtwG/O49Lw/4a8DvafAy/F7wezH8Hix+L4bfi8Xvw/D7sOx5WX0+rH4fFr8fq9+Pze/H6g9QWe4L9+M6KAqZQrBarbz++usMHTqUxx57jJkzZzJz5swGYwYOHMh9993XrICppqamwbpNpaWlLV6ziIiEEBELHfpC3jfBbqa4m8NdkYiIiIiI1FNZ6TeDotr1jWpff/5zPElJweBo8uQiHnmkiD3LaDdy2WXRZsgUCAS7jmolJFjo0KEuOIqMrAuFrr3WSb9+DjM4Sky0NDkFXc+eEfTsGdFCdy4i0nb5A17cvnJqfCW4fWXU+Erw+Mrx+Mvxesvx+ivw+irw+Srw+Srx+Srw+6oI+KoJ7NniqwFfNfjcGL4aLD43hs+D1efG4vNi9Xux+YIvu8+HzefH7vMT4fMT4QsQ4QsQ6QN7ACIIvlq70qpwV3BwFDI1Yd26dcyePZu1a9eGPL5kyRJmzZrFiSeeSMeOHfd5rUcffZTJkycfijJFRGR/Ms4PhkzbvoSeCplERERERA4ltzvQoMto746jxx9PIiUlGAbde+9unniipMlr3XCD0wyZIiMNM2CKjTXMTqLaV0xM3fRzN97o5KKLoujQwUpyshW7vel1i7p1s9Otm73J4yIiR4rajp1qXzFuXxkeXzluX2kw3PGV4fVVBMMdbzl+fxU+XyV+X+WecGfvYKcGw+fG8Lmx+NxYfB6svmBnjs3rxeb3YvP5sPv82H0+Inx+7HuCHYcPIvzgIPhqjbwGeCzBl9di4LEYePe8fBYLPouB12IJ7lut+C0WfBYr/j2vgLlvJ2CxEbDYwNza97wizK1hsWNYIva8IrFYI7FYGr6sFgeVFX74/e/D/XgOmEKmEBYuXMjQoUMpLi6ma9euPPzwwwwePJjExETy8vKYM2cO999/P2+88QYLFizgX//6F1lZWU1e709/+hP33HOP+XNpaSmdO3c+HLciIiKdBsOKB2HHvyHgB8Oy/3NERERERMRUXOxj27aGYVH98Gj69GRSU4NfMf35z4X8/e9NB0fjx7vMkCkxsS5ASk0NdhnVD47i4+v+3X3MmFh++1snKSkWoqL2/e/06ek20tP1lZeIHB5ef7UZ7ARfwWDH66uoC3d85cFQx1+Fz1tJwF9lhjuNg50aDJ9nT7DjxurzYt3TsWPz+7B7fdj8wa6dyD1dO5E+guEOrbNjp8oKbiu4rQY1VgseqwWvxYLHZsVrseK12fBZbPisNnzWCPxWOwGrnYA1koA1AqwOsEaCNRLDGoXFGoVhicJqi8ZiicJmc2K1RGOzxmC3xu7ZOrFbndgsUdgt0dgtMdgt0dgsDmyGDRsQFe4Hs5fgDGgKmY54NTU1XHvttRQXF5OWlsbSpUtJS0szj3fq1Ik77riDc889l9NOO41t27Zx4403kpOT0+Q1IyMjiYyMPBzli4jI3jqcDvZYqC6A3asg+ZRwVyQiIiIiEnY7d3r55Rdvk8HR7Nkd6Ngx+LXR3/5WzFNPNR0cPfCAzwyZOnSwYrXSqNOoQweLOSVdrXHj4rjjjjicztDrGtWXlGQlKakFblxE2jR/wEuVt5Aq726qvbup9uzG7S3G7S3C4y3G6y3F5ynF5y0l4K0ATwV4KzC81Vh8NVjMcMdjBjtWnw97bdeO30+E10+Ev65rxxYAZ7hvPAS3Bar3BDseq4HbasFjtQYDHqsVr8WG12bDb7Hhs9rxW+34rREE9ryCoY5jT7DjMMMdizUaq7Uu3LFZYrDZnNgtwVAnwhq3ZxuLwxqP3RJNlGFpdYGOtByFTHv54osv2L59OwDjx49vEDDVd/zxx3P99dczc+ZMli9fzurVqznppJMOZ6kiItIcFjt0HABbPg5OmaeQSURERETaqF9+8fDDD+69gqO6dY4++SSNTp2CXwU9/XQJTz7ZdHC0Y4fPDJlSU60kJdVf16hhgJSeXhcc3X23iwkTXE2ua1Sf06lZBkTam9oQqNK7ixpvEdWe3dR4C/F4S/B4i/F4SvB7y4IhkKccvJVmCGT1VmH1VGPzurF73UR4PUR4fTg8XhxeP1HeADFeiCH4CgevURfsuM1gx4J3T8DjtdrwWoNdO/49XTsBM9yJhHpdO7XBjmF1YLFGYbXGYLVGY7XGYLPGNAp3Iq0uIqyxe7ZOIgxbq+xqkrZHIdNefvzxR3P/lFP2/UXkqaeeysyZM4HgGk4KmUREWqlOg4Mh0/Yvofe94a5GRERERKTZ1q51s3JlTYiOo2B4tHBhOl26BL/eefHF0n2ucZSb6zNDpq5dbRx9tK3J4Cgzs+4rowkT4pkwIb5Z9e5r/SMRaf0ONgSyeKuweKsbhUCRHi+RXh8Or59oT4Bo3+ELgSqtUGUzqLJbqLFZqbHZcNvteGwReG0R+GyR+O1R+G0OsEWDNQqsDgxrJBZrdIOuHas1GpvVidUaHQx1bLHYLU4ibHFEWGL3hDtx2CyOVtnVJHIoKWTai81W90i8Xu8+x3o8npDniYhIK9NpcHCbuwi8VWBTk7aIiIiIhM9339WwdGk1O3aEnqpuzZpOZGbaAXjjjTIef7zp4Cgvz2uGTMcea6dPn8hG09PVBkfHHGM3zxs3zsW4ca5De6Mi0uLabwgUA7YYDFsMFnssVpsLmy0Wuz2eCFsCEbZ4HLYkHPYkomxJRNuSiTZsRB+G+xBp75SM7KVbt27m/sKFC7n00kubHLtgwYKQ54mISCvj6gExnaBiG+QuhE5Dwl2RiIiIiLQxPl+AHTt8bNniZfNm756tx/x57tyOZGQEv4Z5553yfXYc5ef7zJDphBMiGDw4qkGXUUpK3dR1xx1XNxnSzTfHcfPNcYf2RkVknxQCKQQSaW8UMu3lvPPOIzo6msrKSl544QWuv/56TjzxxEbjPv/8c/75z38CkJGRQe/evQ93qSIi0lyGARnnw8/ZwXWZFDKJiIiIyAEqL/ezZYvXfG3e7OXuu10kJwfXI/rznwv3GRxt3uw1Q6Y+fSIZPjya9HQbqal7T1dnoWvXuo6j66+P5frrYw/tzYm0Yz6/mzLPdspqtlLp3kmVO5cadx4edwE+dyEBdzG4SxQCiYg0oc2FTIsWLWLDhg3mzwUFBeb+hg0byM7ObjB+1KhRDX6Oj4/nvvvuY+LEiZSVlXHWWWcxfvjzmfMAACAASURBVPx4Bg8eTEJCAnl5eXz00Ue89NJL+P1+AB577DEsFi1WKSLSqnUaHAyZtn8Z7kpEREREpJXx+wPk5we7kI4/PoKYmOB/47/6ahnPPFPCli1eCgv9jc675JJoM2Tq0sWGzQadOtno2tVGly4Nt8cdVxccXXmlkyuv1KodIr9WIOCnzLODcvd2Ktw7zIDI7d6Fz12Iv6YwGBC5y7C6K4hwVxLpribK7cbp9uB0+4n1QDzBV0tTCCQi7YERCAQC4S6iJY0aNYpXX3212eND3X4gEOCee+5h6tSpIY/XstvtPPLII0yYMOGAaiwtLcXlclFSUkJcnNrYRUQOi6p8eC01uH9DHkR1CG89IiIiIhIWy5fX8MknFQ2mtdu61UdNTfC//xcvTuessxwATJtWwp137jbPdbksDYKjcePiyMoKTldXUxPAZgOr1Tj8NyVyBAoE/FT5Cilzb6PCvYPK/8/encfXVdf7/n/teZ4y7szpkLbpXDpR6Ai0gAUVQZRBwKPCcUA4Xq/nyvGqcD14PV5Exav+zgX0HE9xAFREQZAKLaV0oC0tdEjnpEmzm2knO3se1vr9sdOV7CahKaRJ03yej0ceayf7u9b6rk1bstd7fz7fxEniyVMkk22kk+0oyXZIdqFLhjAkwpiSUSypOLZkAkfidECkYhimO5sxA4TMeiJmI1GziYTZQtJiJ2V2oJicYDr3EEivu+g+3y+EOI/Gam4g/9INQKfT8eijj3L77bfz+OOPs2nTJurr64lGozidTiZPnsyKFSu45557mDJlymhPVwghxFDYiiB/DrTvhqb1MPmW0Z6REEIIIYQYJt3dCocOpXKCo76Pf//7Yi042ro1zoMPdvY7hl4PpaUGIpHeiqW1a+1UV5uorMwGSx7P4F1MLBYJl8T4ksyECSVPEEmeJJJs6gmIWkklWskkg5DsRJcMoU92Y0pGMCfj2JJx7MkUjmQGd1LFrjAslTgpHXRZdETMBqJmEzGzlaTZmg2IzC5UsxvMXgxmHyZLIWZzIVZzMQ5zGQ5zKW5zBTaDE9swzEUIIcabi66SaSwYq4mkEEKMeVv+O+z5PzDl07DyydGejRBCCCGEGIJUSqWxsX9wdN99HmbMyFYRnVlxdKZf/7qIT34y255u69Y4Tz7ZrQVHpyuTysqMmEwSFInxYeB1iFpI9bSZy65D1Ik+GcaUjGBKxrAmTgdEadxJBVtmmOaig26TjrBZT8RiIma2kDBZSZntZCzOnoDIg96cj9Gcj9lcgNVcjN1SisNcistcjs2Qh04nS1kIIca2sZobSCWTEEKI8aN8dTZkavobqCro5CaCEEIIIcRo6+pStADpkkvMlJRkb1U880yY++9v5+TJDAN9PPaKK2xayFRdbcLvN/QLjk4/rqnpXQ9p8WIrixdbR+TahDgfzroOUTIIic4B1yFyJNO4kplhXYeo2wTdZgMRs5GY2UzCbCVptpPpqSLC4kVv9mEw52E2F2IxF2Mz+3sCogqcJj9enf68rIkkhBDi/JOQSQghxPjhXwYGC0QaoasOvNNGe0ZCCCGEEBe1TEZFUdAqhHbuTPDEE905Le26unrb0/WtOLJYdDQ1ZUslzGZ6AiMTlZXZMGn69N7gaO1aO83NVSN4ZUK8P8O1DpFbheH4jHvUAN191iGKW6ykzLaeNnNOMHvRmb0YzHmYzIVYzEXYzH7s5hJclgpcpjJcejOuYZiLEEKIsUlCJiGEEOOH0Qb+pdk1mRr/JiGTEEIIIcQwaG/PsGNHQguO+m4bG9P86le9wVFTU5qf/jTU7xj5+XoqK42Yzb2V5kuXWtm6tZTKSiNFRQb0eqlCFxcORU0TTByhM3aI7tgRYvEGkrEm1PgpdImuEVmHKKmHkDm7DlHEbCZutgy8DpElD5O5YMB1iOwG57DMRQghxPglIZMQQojxpWx1b8g0897Rno0QQgghxAVLVVVaWjL9gqOGhjSf/7ybNWuyt6Y3b47z4Q+fGvQ49fVp7fHs2Wb+5V+8OS3tKiqMOJ3911Lx+QwsWmQY/gsTYgCKmqYrUU8wXkd37CjRWD2peBNKLIAu3oYp1okt3o0zFsMbT5IXV8lXIf99nm/QdYgsDjJmx8DrEFmyFUR91yEq0OkpGNZXQgghhDg3EjIJIYQYX8pXw7b/Ac2vgZICvemsuwghhBBCXIwSCZXGxt7gaMECCzNnZtc4Wr8+xtq1ARKJARZDAi691KqFTBMnmpg1y6ytgXTmmkilpb1BUVWVie98J+/8X5wY91RVoStZT0fsAOH4MaKxepKxRpT4KXSxVkzxTqyxbpzxGN5Ykry4gk8F3zmep9OsI2gz0m21ErU5SVo9KBbPGesQFWlt5mQdIiGEEBcbCZmEEEKML/lzwZIPiXZo2ZptnyeEEEIIcZFRVZVgUEGvB683G/Ls25fk298OaqFSIJDJ2ed738vTQqaCAj2JhIpOByUlBi00Or1dtsyq7Tdjhpk9e8pH7uLEuKSqCqHkCYLxg4Rih4nFG0jETqDETqGLt2GMBbHGu3HGonjiSfJjCl6Vcw5xuswQtJoI2azErA4SNi+KNQ+drRijrQSbtQqHrRqvbQp51il49XYJioQQYoxTVZW0qmDU6dHpsu15u1JxulIJUopCSlFIKhlSqkJKyZBSFOb7/NiN2Q8u7+1qZW+oLTtWzWj7pNQMSUXhjqqZFFsdAKw/dZy/NB/pNy6lKES7w6P2GnwQEjIJIYQYX3R6KLsSjv4u2zJPQiYhhBBCjGHt7RlefDGa08ru9Fc4rPK97+Xxta9lb4GnUipPPx3J2d9m02nBUXl57y2C2lozR45UUF6eu06SEMNFVRVCqUY6Y4cIxY8QjR0nGW8iE2tGF2vDGO/AGuvGEY/hiSXIjyt4FPCc43m6TNBpMxKyWYlanSStbjK2fLAWYbKVYrVV4LROxG2bRJ51Ch6D+5zPIYQQYmgyqkIikyGhZIhn0iSUNAklQ1LJMMtTpI17q6OZhmiIuJI+Y3yGhJLmgWmXYdRnW+0+fnQ3G9saSGQy/cYnlQzrV9yC15z9cMzX33mNXx5/p1+4k1YVABrWfoEKuxuAB/e+waOHtg96Lfuv/hzT3Nmmqb85sZ/v7N886NhVhZVayPRWMDD4caPxIb6SFxYJmYQQQow/5auzIVPTK7DgwdGejRBCCCHEgMJhhf37k+zdm6KuLkV9fYqGhjSf+pSLe+7J3gBpbEzzqU+1DnqMtrbeaqWJE008+mh+TlVSfn7vJ3b7Mpt1TJwobYXF0KmqQjgVoCN+gO7YUSKxY9nQKB6AWGtPpVEIRyyKN54gL/b+QqNuE3RYjXTbLESsTpK23tDIaC3BaqvIVhpZp+Cz1uAxeiU0EkKMe9F0ilifUKdvIKPTwaK8Um3si81HaI6HiWcy/cab9QYenLFMG/vNdzeyq/NUbgjUE/LodTr2Xv1Zbez1m57mz81HBp2jctM/a7+TfK9uC8801g069itTFuHUZ6uv32hv5Ff1ewcdm1B6fxfqTiUJxCODjk0pivbYajBi0Rsw6Q2YdHpMej0mvQGzXo9JZ0Df5/enSU4vKworMOkMPeP0OY995t4K8EvzS/nnqZcOOC4djvFVxt59KgmZhBBCjD9lq7Pblq2Q7AKzvO0UQgghxOiJRBTicZX8/Gxbu7q6JNdcE+D48fSA4+fOtWiPq6qMrFpl7dfOrqrKRHm5AZtNr411ufTcf7/83iOGRlUVIukWgrGDdMUPEY3Vk4id6A2N4kEs8RDOWAR3LEl+PIMrA65zPE/YCEGbkS6rhajNQcLqIWPzge10aFSJw1rdU2k0FZcx75zPIYQQo+lkrJu4FuqcrsbJhjJOo5nLC3pbzj55bDfBZPyMyp1scOO3OvjWjN5uLHdse55jka6eUCedEwpV2t1svfJObezi9f/Ju6GBP5RSZnPReN0Xte8f2vcGWzpODjjWY7LkhEyb25tY31I/4FjDGR9iMer0Od/r6A1yLHojKVXBrMv+LlTryufy/HKshuxzFoMBi96gje975JvLpzHDXZDzvEU7rgGPqff3pq9NW8xnJ87BpNNj1hu04CgbIuWOfXjWCh6etWLAazvTXdWzuat69pDGriisZEVh5YDPhUIhvjqko1xYJGQSQggx/riqwFMDXYfg5GtQ/ZHRnpEQQgghxoFIROHAgRR79yZ7vlLs25fk+PE0X/yim8ceKwCgpMSoBUzFxQamTzdRW2tmwoRsgDR7tlk7ptdr4O9/Lx3wfEKcKZJq6VnT6AiR+DESsUbSsZMQb8UY68AS78YRj+COJciLZXBmwAlUnMM5ogbosBnoslmJWu0kbG7S1jywFWK0lWKxluOwTcBtnUSebSpOY8E5n0MIIYZCVVWimRTRTJpIOtmzTRHNpIikUxRa7CzMKwFAUVUe3r+5T6iTJt6zTSgZ5niL+B/TlmjHvuzvv6I7lRywMmhZYTkvL/+kNnbGS4/TmUoMOMfFeaVsufIO7ftv7d1EY6x7wLEz3AU5IdP2jgAHutsHHGvV5972txiy4Y0eXZ8gxoBVb8Tf08bttMsLysm32HJDm56gx2U054y9v2Yhn6yY3i8EOh30qKqqVSc9uXAtj6uqNrbv+kdnemjmch4a8Jn+ri2ZxLUlk4Y0ttLuodIuH7gZbhIyCSGEGJ/KVmdDpsa/ScgkhBBCiGEVjWbDJIBLLsl+IjYYzJCfX4+qDrxPY2Nv1ZLbrWfz5lJqakwUFBjO+3zF2BVLd9Ae208ofoRI7BiJeCPpWDPEWjDEg1hjXdjjUTyxOL54BkcaHGc/bO45DNBuMxCyWojYHCSsLtK2PLAWYrD5sdoqsVur8Nhq8Fmn4DAVYQfKz3pkIYTISisK9dGunADo9DaSSVHj9LG8p/KjO5Xga3teI5JJEk2niWRSRHvGRdMpriudzL/NXgVAJJPC9YcfDHrem8qn8vSSG4BsVc3/3Pv6oGM7U4mckGlPZwuRTGrAsdF0biWy02gmpShaqGPpqc6xGgxMcflyxn60rIZgMpETAp0OZUqszpyxj8y5glgmNWClj+OMMGjTqtsx6vTaOkbv5f/MueKsY067rnTykMf2bRknLi4SMgkhhBifylfDvp9C099GeyZCCCGEGKNUVeXtt3urkk5XKB07lkZV4dprbbzwQvYT0j6fgcJCA6qqMmOGmenTzcyYYdIeFxbmhklLlsiNmPEonu6kI15HV+wQkfhx4rEG0vGe0CgWxBLvwh6L4I4nyIulcabPPcyJG6DDaqDLZiZitRO3eUhbfWArxGD1Y7FVYLdV9VQaTcNhLKJcd/abkkKIi4uqqtpaNlZD9hZyJJ1kV+epM8Kg3iqhxXmlXFVcDWRbxH1h58v9QqPT4z83ca4WBgXiYSa/+P8NOpfPTJithUwKKj8/umvQsbOjRdpjm6H31rdVb8RhNGE3mHq2RiY4vNrzOp2Of5w4D6Nelw1tclqvGZjYZyzA7y/7GHqdrredW07Ak7um4Yk+rejO5rF5a4Y89kNDrN6B3v+GQpwP8qdLCCHE+FS6CnQG6DoI3fXZFnpCCCGEEAOIxXrb3KkqfOpTvSvCrFrVTFeX0m+fggI9Hk/ujflDhypwu+Vm/XiUUqKciuykPbyLcHgfqfAR9OFGLJEOHPEwrlgCXzyNOwWlZL+GKqGHDpueTquFiM1OwuoiZcsDawEGWwlmaxkO2wRctonkWafhNPkp1enP6RxCiAuPoqrE+gQ4HpNVqxRpS0R5taVhgIAnu72+dDJX+ycCsC/Uxj9sf6Ff9VA0nUJB5dvTl2ot2o5Hulj26rpB5/TfpizSQqaUovDcyUODju3q0z7OYTTjNJpxGEzYjUYcBnPP1oTdaGK2pzc4chjMfHv6UuxG04DjS229/4826PR03/AV7AYT+kHasvX1s/lXn3XMaWv8E4Y8VoiLnYRMQgghxiezB4oWw6nN0PgS1N492jMSQgghxAXi2WfD7NyZ1CqTjh5No/TkSDU1Ji1k0ul0LFtmpatL0aqSTn8VFfVvcycB08VJVRWCiSO0hN+iK/wO8fBB1HA95vApXOEgBeEoxVGFcoZWdZTSQZtNT8hmJmy1E7e5SFvzUG0F6K1+LLZy7NYq3LbJeG01uE3llOj0lJzvCxVCnJO0ogzY0m2iw0txzxo4xyKd/Pnk4Zzn+4Y990ycp4UZr7ee4PZtz2vPxzK5Ldl+OPdK7qtZCEBddwc3b/njoHMrtjq0kCmlZNjacXLQsdE+LeHcJgs1Tl+faqDc7aK83n+JCi12fn7J1QOOsxtMFFhs2lif2Ur3DV8Z0utq1Otz1iU6G+cZbeOEEMNPQiYhhBDjV8W12ZDpxIsSMgkhhBDjSDyucPBgSmtx192t8KMfFWjPP/xwJzt3JnP28fn0zJhhZvZsc84i1s8/7x/RuYuRl8iECETeoiP8NpHwftLho+jDTdjDbfjC3fjDSfLSkHe24+ih2Wmiw+kk4swn4yxFby/HYq/EZq3EZZ1Inm0abnOFhEZCjLC0ohBKJ+hK9X7NcBdQYLEDsCsY4OnGOq0t3JnVQQ/NWMaVPRU8zzYe4JYtfyKl9q9yBfjFwg9xV/VsIFtF9OW3Xxl0XisLK7WQSUWlIRoacJzNYETps+hfgcXGsoJyHEYzdsOZbeJMLCvojbwnOrw8d/mNWtVQ7jZbJXRahd3NwWvvGcIrCnajiXsmzRvSWCHE2CYhkxBCiPGr4lp4639C0yuQSYJBPuEkhBBCXKx++tMuXnklxt69KQ4fTmmVSQAmEzzySD5GYzY4uvFGBwsWWPpUJpkoLjZowZK4eKiqQnu8jtbwDrrC75AIH0INN2AJB3CFOykMxyiOKVQBZ2uu3GLT0+q00e3wkHAWozorsThr8DhnUuicT75tGtU6I9UjcF1CjFeBeJi67g4tKOpMxnOCo/tqFjDDUwjAUw17+e+7X6UrlSDSp1rntD9e9jE+UjYFgP3d7Xz3wJuDnrcp1q09NukNOQGTHl1OaGPR996OrbS7ubl82qDVPssKe8Oged5itl15Z7/QyDZAK7iprnw2rrp9SK+Zy2Thw6U1QxorhBADGbaQqaWlhW3btvH2229z7NgxAoEAkUgEAIfDQUlJCdXV1cydO5dFixZRVFR0liMKIYQQ51nBPLAVQawFTr2RXadJCCGEEGNOMqn2VCbltrjbsaMMvT57423Dhjh/+ENU28fr1TNjhonp07NBUiqlaiHTAw/4RuU6xPCLpTsIhLcTjOwhEt5PJnwMQ7gJe7idvHA3/nCKggwUnOU4UQMEnGaCTidRZwEZZxlG50QczlrynHMpdsynyOhF7nQIcW4GqiDqSiVYWlBOnjnbTu3vLcf5TcP+fmNOf/1l2cdZUVgJwLONdXxp198GPd/akklayKSqcDIeznnebjDhMVnwmCyY9L1tT2td+dxXs6BPAGTMqRKa7+utar2qqJqGtV/QgiCLfvAPKczyFPHbJR8d0mvlMllYmCc1jkKIC88HCpnq6ur4r//6L/785z+zZ8+ec9p39uzZXHfdddx2221Mmzbtg0xDCCGEeH90eii/Gg79ChpelJBJCCGEuMAlkyomE9rNuu9/v5Mnn+zm0KEUmUz/8fX1aSZMMAHwqU85uewyK9OnZ9dOKimRyqSxTlHTtMX20RreQSj8LonwYXThBizhU7jDXRSGYxTGVSYAZ1uePWDX0+a00e30kXAWo3NWYXVOwe2cSZFzAXmWGibqZE0tIfpKKwp6nU6rojkSDrI31DZgBVFXKsF3Z61kotMLwI8Obedf3tk4YAURwGsrb9WCo/2hdv7fsd2DzqMrldAel9qcTHPla0HRmV9TXL2NLa/xT2THVXflPN83WOprns/PPN/Q2qPajdl2c0IIMV6cc8ikKArPPPMMP/rRj9iyZYv2c7VP38+h2LNnD3v27OHhhx9m8eLF3H///dx0003o9fJLmxBCiBFUcW02ZGr8K/Bvoz0bIYQQQpANkw4d6luZlH186FCKhoZKSkuzb2U7OxUOHMjeoHS7dX3a25mZPj3b4u60665zjMq1iPcvkmrhVOQtguHdRMMHyISPYQyfxBFuJy8cxh9OU6Rw1uqhsBECLgudDidRZyFKTxWS0zm9pwrpEvwGN7K6lhhPBqsg6kol+HDpZDwmK5BdX+h3Jw4MOC6SSbF79T8w25v9W/ibE/v5xrsbBz3nFydfooVMBp0+J2CyGYw5YY+5T9hzaX4ZD81YNmhwVGpzamNvKJvKDWVTh/Qa5Fts5FtsQ3/RhBBCDOicQqZ169bx4IMPcuTIESA3WHK73cycOZPa2lrKysooKCjAZrOhqirxeJzW1laampo4cOAA7777LqFQ70J1W7du5ZZbbuFf/uVf+Pa3v81tt902TJcnhBBCnEX5mmxFU8c7EG4EZ/nZ9xFCCCHEsEilsmHShAlGbLbsBw6/971OvvGNDtLpgffZty+phUy33+5k+XIrM2aYKSuTyqSxRFHTtET30BbeSSi8l2T4ELrwCazhFtzhLorCcfITKhPPcpyMDk7ZDbQ57YSdPpJOPzpnFTbnVDzOWRQ7F+IxVzFZqpDERSSjKoRSSdwmM4aeP9u7O0+xp6t10CqiXyxcS0lPGPPAOxvec32hbHCUDZn2h9r5XeOBQcd2puLa4wkOD4vySgYNgyY4vNrYWyunc61/4lkriADm+/w57eiEEEJcWIYUMr355pvce++97Nq1C8iGS3q9nqVLl3LDDTewatUq5syZc04n3r17N6+++ip/+MMfeOONN1AUhSNHjnDHHXfw6KOP8pOf/IRLL7303K9ICCGEOBfWfChcBC1bstVM0z472jMSQgghLjqplMrhw6mcqqR9+5IcPJgilYING0pYvjz7afLCQj3pNLhcOm29pBkzTFqFUllZnzUyas3U1ppH67LEe+hOnuRUeDvB8G5i4TqUSD3GcDPOcDt54Qj+SBq/wlmrh0ImOOW00Ol0E3MWojjLMTkn4XROJ985j2LHPEr1dkpH5KqE+OBOB0Rdqf5BUGcqwWcmzMZmyLZa+/ejb/OHpoP9xoXTSQDq136eSrsHgF/V7+WRg9sGPW9rIqqFTHZD7+1Aq96I12w5o2Vcbyi7xj8Bl8l8RmBk1R7nma3a2FsrZ3Br5YwhvQ55Zpu25pIQQoixTacOoc+dXq9Hp9OhqioVFRXcfffdfPrTn6a0dHh+jWtubuaJJ57g8ccfp6GhQTtnerCPro1xoVAIj8dDV1cXbrd7tKcjhBBix0Ow41tQ/TFY8+xoz0YIIYQYs1IplSNHsiHSokVWKiqyNzJ/9rMQX/hC24D7OJ06fvGLQm66KXvzs7MzQyikUlEhlUkXqrQSpyW6m7bwTsLhfSTDh9GFG7GFW/CEQxSHE3iTZ2+pn9ZBwGGg3ekg7PSRcpagd1afUYVUOQJXJMQH81ZHM3tDbbQmorQmonSeEQq9tOxmXCYLAJ996wWeODb4uuYNa79AhT17r+iru//+nsHRO2s+w0xPIQBPHtvNb07sH7SK6PqSGq01XFcqTlJR+rWlE0IIMbrGam4w5HZ5NTU1PPDAA9x6660Yjee8lNN7Kikp4Rvf+AZf//rXWbduHQ8//DCHDh0a1nMIIYQQg6q4JhsyNb0CSgr0skirEEIIcTZtbRk2boz3WTcpSV1dtjIJ4MknC/n0p10AzJhhwunMViZNn27KWTvpzDDJ6zXg9Q50RjFSupINnApvpyv8TrYKKXwcU7gZZzhIfjiCP5KhVOWs1UNBi44Wp4VOh4e4swjVWY7ZORmns5YC5yUU2edQrrcizYrFaFNVlUgmhdPYWxm5/tRxdgQDWnDUmoj1eRzl1IfvxdEz/qdHdvKL4+8MevzOVEILmTw9W6s+uwbRmVVE+j7/Ht5cMY2ZnoIBK4jODIj+YcIc/mHC0LoMnV5vSQghhBgOQ0qLfvazn/HZz34Wg+H8frrBYDBwxx13cNttt/HEE0+c13MJIYQQmsIFYC2AeBsENkPpitGekRBCCHFBSKezlUn79mWrk1atsnH55dmbk7t2JbjxxlP99nE4smGSzdZ7o3TpUitdXdXo9VKZNNpSSpRTkV20h3cRDu8jFT6CPtyILdyKNxyiKJzAkwLP2Y6jg2ankQ6ng7Azn3RPFZLdOQ2vczbFjgX4zKX4RuSqhMilqiqhdIK2RIyJDq8WZP++sY432hu10KglHtHCo7iSJnzDV7Tg6KmGfTx5fPCKo9ZEVBs7z1tMU3GYQoudQosNnzk3DOrbUu47M5fz3Vkrh1RBtCivlEV50gxSCCHEhW1IIdM999xzvueRw2AwcPfdd4/oOYUQQoxjOj2UXw2H18GJFyVkEkIIMW4FAmmeeKJbWzupri5FItHb9uyBB1QtZJo508yCBRZtvaTs+kkmKiuN/cIkCZdGhqoqdCaO0RJ+i87wHuLhg6jheszhAM5IJwXhKMXRDOUqZ60earfoaHFaCTlPVyFVYHbW4HbOoMB5CYW2mVTqzUgzOzESVFWlM5WgNRGlLRFlSX6ZFhw9eWw361vq+1UcJZUMAN03fEWrUHohcOQ9W9X1DY6WFpSTUjM9wVHvV1HPttzW28bo3poF3FuzYEjXcnq9JSGEEOJiMbx974QQQoixquLabMjU+FdY/L9HezZCCCHEeZHJqBw9ms5pcbdqlY3PfS57szQaVfnGN4I5+9hsOq3F3YIFFu3nJSVGtm8vG9H5j3fJTJhA5C06wm8TDu8jHT6KPtyEPdyKL9xNcTiJL81Zq4cSemh2muhwOok680g7SzE4J2B3TsPnnEOxYwH5piLyR+SqxHikqCrBZDyn/dwNZVO04OgHB7fxQvMRLTRqS0RJqYq2f+ij/6S1n3uz/SRPNewb8DwOg4lgMq6FTNf4J+IzWSmyOii02PoFSI4+AdCnJ8zm0xNmSXJJ1QAAIABJREFUn6+XQAghhLhoSMgkhBBCAFRcDeigfTdEToJD2lIIIYS4OASDGe69t529e5McOJAiHldzns9k0EKm6mojd93lZOpUs1ahVF3dvzJJnD+qqtAW309T8G90BbdAcC/uYCMlXSGKogqVcNbqoVabjlanjZDDS8JZjOqsxOKsweOcSaFzPvm2aVTrjFSPwPWI8SGjKrTnrFkUoy0Z5R8nztOCo2++u5E/NB2iJRGhPRkjo+b+W9T10X/C3RMc7Q+1s76lvt95XEYzhRY7oXRSC5luLJ/KNFdebrWRNbs9s2ropvJp3FQ+7Xy8BEIIIcS49YFDpo0bNwKg0+m47LLLznndpiNHjtDU1ATA8uXLP+h0hBBCiPfHWgCFC6F1G5z4K0z7h9GekRBCCDFkra0ZXn89zsaNMTZtirNggYWf/7wQAKdTz+9+FyaVyo61WnXU1mYDpBkzzCxZ0ludpNfr+MUvikbjEsYdVVVoie2hKfg3uoNb0QX34Qk2UR7spjChUjjIfjEDBJwmOpwuos58Ms4yDM4JOJy15DnnUuyYT6Exb9D9hRiKtKLQloz2a0HXlojyrelLteDoy7v+xq8b9tGejKEOcJxbK6fjMWVbbAbiEd4NteY87zFZtGAomklpIdNd1bNYUViR06KuwGLHauh/G+sa/0Su8U8c3hdACCGEEEP2gUOmlStXar9crFixgmeffRafb+hLe/7whz/kpz/9KTqdjnQ6/UGnI4QQQrx/Fdf0hEwvSsgkhBDigqaqKr/5TYSNG2Ns2BBn//7UoGNNJh0/+UkBfr+B6dPNTJhgxGCQyqSRoqoKgcgOTna+Qji4DV3wAN5gE5XBMMVJleIB9lGAE24jAW8+MV81Rt9s8ryXU+RaRL51KhN0eiaM9IWIMS2lZPoFRq2JKC09wdHPLrlau7dz57Y/85/17w56rPtrFuI1Z4OjhJKhLRnTnsszW3MqipJKb4u7L02ez80VtVqbugKLHbN+4A8qX15QzuUFZ1s5TAghhBAXgmFrl6eqKhs2bGDx4sU8//zzTJ069Zz2FUIIIUZdxbWw8yFo+hsoadBLV1khhBCjT1Wz6ygdPpzi6qvtQLaTxDe/2cHhw70f1Js508Ty5TaWLbOycKEl5xh33+1GnF+KmuZkeCvNwfVEOrdjCNbhC56kMhihJAUlA+yT0UGD28QpXwFx7wRMvjkU+FZQ6V1NlTGPqhG/CjGWnIpHaIp156xrdDpAak/GeGbJDeh7gqNbtvyJZ5vqBj3Wd2etxNcTHNl6qoV0QL65/7pFSp+apX+eeilfmnwJhRY7+WYbpkFCI4DZXqmSFEIIIS5Gw3r3TFVVDh8+zKWXXsrvfvc7Vq9ePZyHF0IIIc6vwoVgyYdEO5x6E0qWjfaMhBBCjEOKorJ/f4qNG7Pt7zZujHPyZAaXS0dHRzVGY/am8ac/7aK9XWH5citLl1rJzz+31uXi/VHUNI3dmwgE/040+BbGzoP4ggGqghHK0zBQ7UVKBw0eMy2+QhK+iZi9cynwLafScxUTjF6pShKauu52joY7B6w6ak/GeH3V7Vpw9KVdL/NM4+DBUWcqTp7ZBkChxY4eHQWW/qFRocVG32XX/tfM5fyvmcvJM1sx6PTvOd+JTu8Hv2ghhBBCjGnDFjKtXbuWo0ePsn//frq6uli7di2PPvooX/ziF4frFEIIIcT5pTdA+Ro48uvsukwSMgkhhBhhDz4Y5LHHumhvV3J+bjLB7NlmWlszlJRk38Y98MDQ25SLc5dRkpzo3sCp4KvEgjswBg+R3xmgKhijMgOVA+yT1EO9x0Krr4ikbxIW3zwKvSuo9FzJJIOTSSN+FeJC0JGMcTzSRUM0xIloKLuNddMQDdESj3Dw2nu04Oh/vvs6TzceGPRYwWScfEs2OCq1OvFbHdqaRX2Do6IzWtE9OvdK/u8la7TzvJdCi/0DXrEQQgghxpNhC5kmTJjAU089xc0338xLL71EOp3my1/+Mvv27eOxxx5Dr3/vT78IIYQQF4SKa3tCphdh0b+O9myEEEJchJJJlbfeSmiVSr/4RSHFxdm3Zno9tLcr2Gw6liyxsHy5jeXLrSxebMFul/dU50NaidMQepWW4KvEgzsxBQ9T0HmKqs441RmoHmCfhB6Oe620+YpJ+SZj9V1CkW8lFe6V1Ojt1Iz0RYhRE0knORHt7gmOsgFSU6yb/zf/Wm2No8+99SK/bzo46DH6BkdTXXnM9Rb1qzY6HSLZjb23cX40bzU/mje0DjJWg7SBFkIIIcT5May/ZbhcLv7yl7/wla98hR//+McA/PznP+fQoUM8/fTTeDye4TydEEIIMfwqrs5u23dBNAB2/+jORwghxJgXjSps3ZoNlTZsiLFlS4JYrHdNk02b4tx4oxOAO+5wctVVNubPt2A2n73iQAxdMhOmIfR3WoOvkQjuwhw8QmGwhaquBBMVmDjAPjEDHPfaaPf5SftqsPnmU+xbRblrGVP1Voa+ErEYi9KKwsl4T4AU7eaTFbVacPTV3X/nF8f30JGMD7jvwzNXUGR1AFBl9+C3Oqiwuam0u6mwu3q2bkqtTlwms7bf6VZ1QgghhBBjxbB/lEWv1/PDH/6QGTNm8KUvfYl0Os369eu59NJLef7555k8efJwn1IIIYQYPrYiKJgPbTuyLfOm3jXaMxJCCDHGhEIKiqLi9WZbVT3zTIQ772zNGVNQoGf5civLl9tYsMCi/byqykRVlWlE53uxSWRC1Hf9jbbgRpLBXViCRykKtlLZlWSyCgO9Iw0bocFnp8PrJ+2bit23AL/vCsqcl1GrNw+whxjrVFWlLRmjwGzTgqNf1b/LX5qPaG3tTsbCKPQGwlcWVWnBUUZVtIDJZTRTaXdrwVGl3Y2xTzeXR+ZcwQ/mXjmCVyeEEEIIMXLOW7305z73OWpqarjpppsIBoPU1dWxePFinnnmGVatWnW+TiuEEEJ8cBXX9oRML0rIJIQQ4qza2jK8/nq29d3GjXHefjvJ97+fx1e+4gVgxQorZWUGli+3smJFtv3dtGkm7ca2eH9i6Q4aOv9GW+dGUsHdWINHKQ62URlKMUWFKQPsEzJBg89B0FtKxjcFh28RJb4rKXUuZrpO2oldjHZ3nuKtYCBnPaTTlUlxJU3g+nsp7gmOdgYD/PbE/pz9TTo95T2VR5FMSvv5fTUL+MyEOVTYXXhM1vecg/xdF0IIIcTF7Lz+Fr1y5Uq2bt3KddddR11dHcFgkGuuuYbHHnuMu++++3yeWgghhHj/Kq6FXd+BxpdBSYNebjoJIYTI1daW4ZvfDLJxY4y9e1P9nj9woPdnVVUmTpyolBvN71Mk1UJD58u0BzeR7tyNreMY/s52KkJppsKALeu6zFDvc9HpK0XxTsOVt5hS71X4HfOZqZO1rca6vm3sTgdGfUOkl5d/Qqs4+uXxd/jhobcGPdbJWLcWMn20bEpONVKFzU2x1YF+gL+71Q7v+bk4IYQQQogx5rzfNZs0aRJbt27l5ptv5uWXXyaVSvH5z3+effv28eijj57v0wshhBDnrmgxWPIg0QGn3oSSZaM9IyGEEKNEVVWOHUuzcWMcs1nHrbdm105yOnU88USIZDI7bsYME8uXZ6uUli2zUlaW+1ZLAqaz606epKHzJYLBN0gH92DvrKck2EFFd5raQfbpsOg44XPR5StD9dXi8i6mLG8NRbbZzJYwaUw63cbuhBYgZbdfr11CntkGwNf2vMqjh7YPeoyGaEgLmeb7/Fzrn9gnOHL1tLbzUGZzYjH0/l1dUVjJisLK83uBQgghhBAXmRH5aLbb7eaFF17g/vvv5yc/+QmqqvLYY49RV1dHUVHRSExBCCGEGDq9IVvNdHgd1D8vIZMQQowjqqpy4ECKDRt62981NWUAmDPHrIVMVque738/n8pKI0uXWikoMIzmtMeUrmQDDcG/0hncTCb4Lo7OekqCQcrDGWYMsk+rVUejz0PIVw6+Wty+Syn3rqHANp08CZPGlEg6qVUeXVZQhtOYXfPqZ0d28ujB7VobuzN9oqKWvLxsyFRhd2HS6amwu6noaWVXYetdE2my06ftd3vVTG6vmjkyFyeEEEIIMQ6NWP8fvV7Pj3/8Y2bOnMm9995LOp3m5ZdfHqnTCyGEEOem6vpsyNTwPFz6b6M9GyGEEOeJqqo5VUYLFzaxY0cyZ4zJBAsXWli50pYz/stf9ozoXMeaYPwIJzpfojO4GTW4F2ewgdLOTkoiCrMG2eeUTU+Tz0O3rwKdbwYe3xLKvFdRaKulcERnL96PtKKg04GhJ/j7e8txnm082FuVFAvRkYxr47ddeScL80oAiGfSHAoHtef8Vkef4MiF19y77tEXJ8/nvpqFA7axE0IIIYQQI2vEF5m4++67qamp4eMf/zjBYPDsOwghhBCjoeIa0Bmh8wB0HQJPzWjPSAghxDBIJlV27EiwcWO2UmnfvhRHjlSg12dvVk+fbmbfvhRLlli09neLF1uw26VaZjDt8TpOdPyVUOcW1OBeXMFGyoJdFMcUfIPs0+zQc9LrJeyrQuebide3hArvGoqtkyge0dmLc3UiGmJHMNAnOOpdD+lkLMyWK+/QgqPdnS389MjOfsdwGc1U2t0klYz2s4+VTWWet3jANnZnMuulclAIIYQQ4kIxLCGTqqrnNH7VqlVs2bKF6667joMHDw7HFIQQQojhZfZA6QpoWp9tmTf7K6M9IyGEEO/Tzp0Jnn8+ysaNMd58M0Eslvv+5d13k8yebQHgkUfyefzxQsxmqZDoS1UV2mL7aOx8mVDHm+g69+MONlIWDFEYV8kfZL9Gp4Fmn4+ItwqDbxY+3+VU+NZQYq6kZESvQJxN3zZ2J2K56yE9OvdKZnmyre6fbazjn3avH/Q4DdEuLWRaWlDBA9OWaG3sTlcleUzWfvtVOTxUOaQ6UAghhBBirPnAIZOiKO9rv8mTJ7N161aee+65cw6phBBCiBFReb2ETEIIMcaEQgqbN8dZssSKx5OtPvrDHyJ85zud2piCAj3Ll1u1SqUZM8zac4WF47tCQlUVTkXf5mTwFbqDW9AF9+PpPElFsJvChDpoy7oGl5GAL4+otwpj3hzyvEup8K6m3FxK+YhegRhISslwMhbuEx5184mKaVQ7vAD89PBOvrhr8Hb2h7qDWsg01ZXHQl+JFhjlBEg2N8VWh7bfwrwSLXASQgghhBAXpxFvl9eXx+PhjjvuGM0pCCGEEIOruh7evB8Cr0MiCJbBmv4IIYQYLW1tGTZtimvt73btSqIo8NxzxXz4w9mb3ddcY+fIkZQWKtXWmnLWYRqPVFWhObKdk8FXCAe3Ywjux9t5kspgGH8S/APsowANbhOnfPnEfNUYvXPIz1tGpWc1laYiKkf6IgSQ7SzSloxxIhqi2uEhz2wD4C/Nh/nX/W/SEA3RHAujkPvhzhqnTwuZiq12oLeNXW5w5MoJiq4tmcS1JZNG6OqEEEIIIcSFblRDJiGEEOKC5p4IvukQ3Acn/gqTbxntGQkhhOixeXOcu+9uZe/eVL/nJk405rTEu/xyK5df3r8913igqGlOhrfQHFxPJLgdQ7AOX7CZys4IpSkoHWCftA4a3GZafPnEfRMx+eZQ4F1OpXc11cY8qkf6IoTm3a5Wnm48kNPK7kS0m7iSBuCZJR/lxvJpAMQzad5sb9L2Nen0lJ+uPDqj4uhDJZPo/Oj9A7axE0IIIYQQ4r1IyCSEEEK8l8rrsyFT/Z8kZBJCiBGmqirHj6fZuDHOhg0xrrzSxm23uYBsW7vTAdP06Sat/d2yZVbKy8fn25xkJkxd6zraT/0JY8cB8oIBqjqjlKcZsGVdSgf1Xgut3gISvkmYfXMp8C2nyrOaiQY3E0f8Csa3tKJwNNLJvlAb+0Pt2W13Ow/PXMEa/wQA6rrbeWjfGwPuX2J1klAy2veX5Zfz9JKP5oRK+kEq+GwGEzaDafgvSgghhBBCXPTG57svIYQQYqiqPgy7vwcnXgQlBXq5ASOEEOeLqqrU1aXYsKG3/V1jY+9N8+5uVQuZJk828txzxSxZYh236yh1J09ysOU/6G5+AW/gHaa2dDEr039cUg/1HgutviKSvslYfPMo9K2g0n0Fkw1OJo/81Me1RCZNWlVwGLNrgW1qO8Hnd7zMwXAHSaX/f8DdXS1ayDTTU8g9E+dqrexOB0hlNicWQ+7b+xKbk5t6qpqEEEIIIYQ4X4YcMhkM5/eNm06nI51On9dzCCGEEOesaDFYCyDeBoFNULpqtGckhBAXjUxGpbU1g9+ffVsSjarMmtVI37cFRiMsXGhh+XIra9bYtZ/rdDptzaXxoi22n8OBXxIPvEJR4ABT2qLMV88YY9Vx2O8nXjADq+8SinwrqXSvokZvpWZ0pj1uhdNJDoTa2d/dnlOddCTcyQ/mXsF9NQsBcBrNvBtqBcBmMFLryme6u4Bad3bbdz2kqa58fj7/mlG5HiGEEEIIIQYy5JBJVVV0Oh2qqp59sBBCCHGx0Bugci0c/A+of15CJiGE+ABSKZUdOxI9VUpxNm2KM2WKiW3bygBwOPQsXWpFp0Nrf3fppRbsdv0oz3x0NHa/QX3zr8gENlAWOMqkziQFZ4w54TJQ769C8V9OecknmeC5hgLd+Hy9RkswGWd/qA2f2UqtO/tfaGcwwPxXfjnoPofDQe3xNFc+f1n6caa786m0ewZtaSeEEEIIIcSF6Jza5Q01YNL1/FIsgZQQQoiLQuX1PSHTn+DSR0Bu/gghxDl57LEunnsuyptvxolGc98jHD6cIpFQsViy/7b+/e8l2vuJ8URVMxwN/oWmwG8wBDZT3dxIeSTTby2lQz4Lzf5JGEpWMsF/BxXOxVSMyozHn0Qmzeb2ppz1kvaF2gjEIwB8afIlPDZvDQCTnF4ACi12prvzqXUVZLfu7LbE6tSOazUY+VDJpJG/ICGEEEIIIYbBkEOmV199dUjjfvSjH/HHP/4RnU435H2EEEKIC1r5GtCbIXQEOg+Ar3a0ZySEEBek7m6FN96Is3Vrgm9+06uFRW+8EWf9+hgA+fl6rUpp+XIrs2ebMRp7Q6XxEjCllCgH235LW/PvsQbeoiZwikkJlb5RQ0oHdQUO2kpqsfnXUOO/ixprjbS9O49UVeVELKQFSeU2Nx+vyK5rFE6nuGLDrwfcr9zmwmEwa997TFbaP3IfeWbbiMxbCCGEEEKI0TLkkGnFihVDGvfMM8+c8z5CCCHEBc3syrbJa3wp2zJPQiYhhACgvT3Dpk1xrf3dzp0JFCX73Cc+4WDatOxN9898xsWKFdlQqbbWhF4/PoKkvqLpNupO/QddgT/jDuxm6qkgM85YkjZihLoiHyH/bNwla5ladCczTUWjM+FxIqVkeOTgNi1UOtDdQTid1J6/1j9RC5nyLTYW5ZVQZLHnrJk0zZWP22Tpd2wJmIQQQgghxHhwTu3yhBBCiHGr6vpsyNTwPMz92mjPRgghRsXpdVoBHnmkk69+taPfmIkTjSxfbs3pLLp6tZ3Vq0dqlheGzvhRDgaeJBZ4mfzAfqa2hpl3RjfxoEXHQX8RMf8CCkpuYErBJ7lE7xidCV+kkkqGw+Eg+0Jt2RZ3oXZKrE5+MPdKAIw6Pf/7wBa6UgltH6NOT43Tx3R3AUsLchsWbr3yzhGdvxBCCCGEEBc6CZmEEEKIoai8Dt74EpzaDPE2sJ659LoQQlx8TpxIs2FDjNdei7NhQ4zHHivgmmvsANTWZquUpk83ae3vli2zUl4+Pt9iNIe3cyzwn6QDr1LSfJiaYIJFZ4w56TBwzF9GpuQySvw3M8l3PYt14/P1Gm5pRcGo12vf37HtebZ3BDgU7iBzxlrBU5x5Wsik0+n48uT5mPUGrTJpstOHSW8Y0fkLIYQQQggxVsk7GiGEEGIoXFWQNxs69kDDCzDljtGekRBCDLtgMMPzz0fZsCHOa6/FOHo0t5/bxo1xLWS64gorLS1VFBaOv5vxqqpwvOtlGpufQh94g8pAAxXdaUrOGHfUY6axZAJ6/wqqSm6n3Hk5pTr9gMcUQ9OVirM/1K61t9sXamd/dxsuo5ndaz6jjdsXaudAdzsALqNZC5BqXfnM9BTmHPOhmctH9BqEEEIIIYS4mEjIJIQQQgxV1fXZkKn+eQmZhBAXhaamNJGIwpQp5p7vM9x5Z6v2vMEAl1xiYeVKKytW2Fi61Ko9Z7XqsVr7HfKilFESHGx/hpbAM1iatzHpVDMTYioT+o7RQV2+nRb/FCwlVzHJfycTbTOZOGqzHttaE1HqI10syOuN7q7a8GvWt9QPON6k0+dUM/3rzOXodTpqXfmU2Vxam0chhBBCCCHE8JKQSQghhBiqqg/Drn/Nrs2USYCh/yLfQghxoQsGMzz7bIR168Js2BDnllucrFtXBGRb361ZY2PePDMrVti4/HIrbvf4q7yJpzupa/0VweY/4QrsouZUO7UpqO07xgAHitx0+mfhLPkQU4ruZLq5jOmjNuuxqTkW5t1Qa5/KpOy6SW3JGDaDkfAN/w19T0CUb7YBUGp1ZquSTlcn9Wz7tsu72i/xnhBCCCGEECNBQiYhhBBiqAoXgM0PsQA0b4DyNaM9IyGEGJJ4XOHPf46ybl2YF16Ikkz2PheJKNpjvV7HSy+d2fTt4teVbOBQ4JeEA38lr3kvU1tDzFFyx3Sa4WBxIZGSS8jzf5hphbcz1+AenQmPMYqqcjzSxb5QGwfDHfxTzUKtsugLO1/ijycPDbhfscVBWyJKkdUBwA/mXsm/L7gGj2mclNAJIYQQQggxBkjIJIQQQgyVTg+Va6HuiWzLPAmZhBBjxMqVzWzdmtC+nznTxG23ubjlFgdVVaZRnNnoaI2+w+HAL0k2r6c4cJAp7TEWnDHmlE3PkZJSkv7F+Es+To3vBhbpzaMy37Fmc1sjr7Y2aJVJB0IdxJXe9b0+WVFLqc0FwGxvEfu727X1kk5XJk115eEw5r7eZT37CCGEEEIIIS4cEjIJIYQQ56Lq+t6Q6bIfg6zxIIS4gKiqyo4dSX772zAPPeTDZsu2D7vuOjsnT6a59VYnt93mYtas8ROWqKrCidBrnAg8hdq8kfLAcapDKQrPGHfcbeSEvxpKllHhv5Uq9xUU68Zfq8ChiGVSHOzuYF9Pi7v9oXZ+Pv9qCix2AH7fdJBHDm7L2ceiNzDVlUetu4CEktF+/uCMZTw4Y9mIzl8IIYQQQggxfCRkEkIIIc5F2VVgsEK4Htp3Q8Hc0Z6REEJw+HCKdevCPPVUmIMHUwAsXGjh5pudAHz1qx4eeMCLXn/xB+OKkuJw8I8Emp/GFNjChEATlVGFyr5jgIP5Vk75azCWXMkk/x1U2+dRPUpzHgv+dPIQjx/dzb5QG0cjnahnPP/lmvksL8y+yisKK2hNRHPWS5rg8GCQ0E4IIYQQQoiLjoRMQgghxLkwOaDiGjj+Rzj+ewmZhBCjJhjM8KtfhVm3Lsy2bb2t8KxWHR/5iJ2qKmOfn128N/eTmW4Otj5Fe+CP2Jt3MuVUK1OSKlP6jEno4UChi46S6Tj81zCl+C6mWaqZNmqzvrC0J2Ls725jX6id/aHT23aeXvJRFueXAnAyFub55sPaPj6TlenuAqa786l151Pt8GjPXV9aw/WlNSN+HUIIIYQQQoiRN+SQ6YorrhjSuEOHehdtHeo+ADqdjvXr1w95vBBCCDFqqj+WDZmO/R4WPDTasxFCjCOqqqLradPZ3q5w333tAOj1sHq1jVtvdXLDDQ5cros3VAonmznY8h90N7+AJ7CHqS1dzMzkjuk2QV1xPt3+OXhLPszUwtuZY8wfnQlfIFRVJRCP4DSacJksADzTeIAv7nyZlkR0wH32hdq0kOmKoir+77w1WmVSkcWu/VkUQgghhBBCjF9DDplee+21Ib+JOD1uw4YNQxrf982yEEIIccGrug50Rgjuhc468E4d7RkJIS5iyaTKX/8aZd26MAYDPPVUMQCTJ5v43OdczJxp5hOfcFBcfHE2KWiPHeBw4BfEm1+hKHCAmvYol5zRq63VquOw30+8ZBFF/o8xNf9mFuitozPhUaaqKidiId7tauutSurOrp3UlUrwX4uu57aqGQB4TBYtYKqyu6k9XZnkym5neXpXrpriymOKK29UrkkIIYQQQghx4Tqnd6KqembnbSGEEGIcsvig7EpofClbzTTv66M9IyHERUZRVDZtirNuXZinn44QDCoAmM3Q2ZnB6zUA8O//Xvhehxl7VJWm8Gbqm/+LTOA1SgNHmdSZ5MwapBMuA8f9lSglSyn3f5KJnmsoHKfr/WRUhUQmg91oAuC5k4e4YfPvBxyrR0dzPKx9f2leKW9ddRdTXXk4jeYRma8QQgghhBDi4jLkkOlb3/rW+ZyHEEIIMbZM+Fg2ZDouIZMQYnj9/OchHn44yIkTvT3gSkoMfPKTTm67zYnHc/GEKaqa4WjwL5wM/BZD8xtUBxopi2QoO2PcQZ+F5pJJGPwrmeC/gwrnYipGZcajL5ZJsb2jmU1tjWxqa2RzexNfm7qYB2ovA2BRXglGnZ6prrw+ayZltzXOPKyG3reALpOF+T7/aF2KEEIIIYQQ4iJw0YVMLS0tbNu2jW3btrF9+3a2b99Oe3u2V/2dd97JL3/5y/fc//jx40yYMOGczllVVcXx48ff54yFEEKMSVUfgdf/EVrfgnADOCtHe0ZCiDGqvj5FXp5BW0cpkVA5cSKD263jxhsd3Habi5UrrRgMY7+9dFqJcbDtN7Q2/x5b4C0mB04xKaEyqc+YlA4OFDpo80/D5l9Djf8uplinMGXUZj36QqkE/7p/M6+3NfJWRzMpVcl5fltHs/a41Oai66P/pFU2CSGEEEIIIcT5dNE1bi8uLh7xc06dKmtxCCHEuGMvBv9SCLwOx/4As+4b7RkJIcaQ9vYMTz8dYd26MJvowVL4AAAgAElEQVQ2xXn88QI+8xk3ALfc4qS83MCHPmTHZhvbVUuxdDt1p/6DrsCfcTfvZkpLB9PTuWMiRjhQ7CXkn4Pbv5apRXcwyzTyv9NfCFRVpT7axettjQB8qmomADaDkZ8c3kk0kwKgxOpkaUE5ywrKWVpQzixPUc5xJGASQgghhBBCjJQLJmRSVRWdbng/nVlRUUFtbS0vv/zykPcpKyvjnXfeOeu47373uzz11FNAtkJKCCHEODThxp6Q6VkJmYQQ/z979x0eVZmwcfg3M+m9k4QUIKFXQaQjiICFtVAUQUVhZWWti2vBuura2+ruWlZE1AVBFAErooAKIqB06aGkQ3pvM3O+PwYG+FYlkEkmA899XVzJnHPmnAf3kJ3MM+/7nlRlpZ0lSyqZM6ecL7+sxHqkbDGZYMeOOudxMTEWxowJclPKhimp3s/u3LepzP2SyNwdtM8rp8f/W9a10NfE7tgYqmJ7ERU3mvZR4+llDnRPYDezGXa2leTx/ZGp71blZ5JVVQZAh+BIZ8nkbbbwWOeBRPsGMDAqkdaBoS7/3UlEREREROR0NLhkWr58ORdccEGDzmG327n22mudpU1DPPzww/Tu3ZvevXvTokWLU57+ztvbmy5duvzuMTabjZUrVwIQHBzMFVdc0ZDIIiLiqVpfCWvuhNxVUHnIMbpJRORXlJfbSUhIp6Tk2DRn55zjw4QJQYwfH0RCQrP57NcpyS3/if2571KXu4L4nD2kFtXQ+/8dkxVoYX9cS6yx/YiLvYq24ZfR1+SZf9+GqrPb8DZbnI/7ffMe64tyTjjGy2Tm3PBYBkYlYDcMzEfKpLva92nSrCIiIiIiIvXR4N/urrzySpYvX06vXr1O6/mGYTBx4kQ++OADl5RMjz76aIPPcTJff/012dnZAIwdO5aAgIBGv6aIiDRDQUkQfa5jXaaDi6HjVHcnEpFmwDAM1q6tYd26Gm6/PRSAoCAzvXv7kpZWx4QJQUycGETHjj5uTnpqDMPOwZKvyMx5H1PuapJyD5JYZiX2/x2XFuZDZmxrzLGDSY67jsTggbTk7Bx1U1BTxeqCY6OUdpYWcOiy25xFU/ewGHaWFdA/siUDj0x9d15EvKa7ExERERERj9HgkqmsrIxLLrmEVatW0bZt21N6rs1m49prr2X+/PkeNd3Du+++6/xeU+WJiJzlWo12lEz7F6pkEjnL7dxZy5w55cydW86+fVZMJhgzJpCWLR0vuefPjyE83Owxr3vthpV9hYvJyZmHd86PpOZk06raTqvjjrGZYGdUAIdj2+EbeyEpsZNI8e9CirtCNwPLDx9gfsZOvs/LYEdZwf/s31KSR69wRzX3XLehvNZzJF5mz157S0REREREzl4umaciPz+fESNGsHr1auLj4+v1HJvNxsSJE1mwYAEA/v7+rojS6MrKyli0aBEAycnJDB482M2JRETErVqPgfX3Q9Y3UFMMvmHuTiQiTSg318rcueXMmVPOhg21zu2BgSauuCKQ6upjCxJFRFh+7RTNhs1ew578DzicswC/nPW0yz1Eaq1B6nHHVFlgZ0wIRbFdCI67hHYxk+jsk0Bnt6V2H5thZ2tJHt/nZTA+qRPRvo7ZDdYUZPOffZucx3UMjnSOUhoUnUirgFDnvjAfvybPLSIiIiIi4koNLpluuukm3nzzTdLT0xkxYgTfffcdERERv/uc4wsmwzAICAhwFjfN3YcffkhlZSUA119/vcd8ElVERBpJWDsI7wxFv0D6p9D2WncnEpEm9Pnnldx1VyEAXl4wcmQAEycGcdllAQQGNu/RKYZhZ3f++xzKfI/AnJ9pdyifDnXQ4bhjyrxhZ2wkZbHnEBF3BR2ir+UcS+hvnvNMVmWrY11hDt/nZbAqP5MfCrIoszqKxTj/IMYmOP7LXRzbhuLaagZFJ9I/siVRvppaW0REREREzlwNLplef/11CgoKWLhwITt27ODSSy/lm2+++c11imw2GxMmTODDDz88oWC68MILGxqlSRw/Vd7111/vxiQiItJstB7tKJn2f6SSSeQMVV1t54svqpgzp5xhw/yZNi0EgDFjgnjvvXLGjQvkqquCiIpq3qOVAA4WfcHBvU+TnLaG9qV1tD9uX7EP7IqNoTK+N1Gxo+kQdQ29zZ4x44CrGYbh/EDZFzlpXL76I+oM+wnHhHj50j+qJSFevs5tPcNj6Rn+/1eqEhEREREROTM1uGQymUzMnTuXiy++mBUrVrBu3TpGjx7Np59+ipfXiaf/tYJp8eLFDBs2rKExmkR6ejrffvstAP379yc1NfUkz3CoqamhpqbG+bi0tLRR8omIiJu0Gg0bHoeML6GuArwD3Z1IRFzAZjP47rtq5swp58MPKygpcRQMBw9anSVTaKiZFSvqN120O+WW/cietMdpsXcF7QqrSD6yvdICmxNjqY7vS2zc1bQLH00fs49bs7qDYRjsryhhVb5jlNKq/ExubN2Nu9v3AaBTSBR1hp14vyAGRSc6p7/rGhqNxdS8R6yJiIiIiIg0JpesyeTj48PixYsZMmQIGzZsYNmyZVx77bXMmzfPeYzNZuOaa67ho48+8siCCeC///0vhuGYV/9URjE99dRTPProo40VS0RE3C2yOwS3gbJ9jqKpzRh3JxKRBnrwwUJmzy4jK8vm3JaQYOGaa4KYODHIjcnqr7ByBzv2PUZo2ud0OVTK0bE1dSbYkBhNbeoYuic/RD/v5l+SNYYKay2z9m9xlkrZ1eUn7P8uL91ZMiUFhLD/kptJDgjVdNkiIiIiIiLHcUnJBBAUFMSXX37JgAED2LNnDwsWLCAyMpJ///vfWK1WrrnmGhYuXOgsmJYsWcIFF1zgqss3iffeew8AX19frr766no/b8aMGUyfPt35uLS0lMTERJfnExERNzGZHFPmbXkeDixUySTigTIzrSQkHHtpvH17LVlZNsLCzIwbF8jEiUEMGuSH2dy8C4bymky2HXgc370L6ZadzwDH56OwA5viQilNvYQurR+hj1/73z3PmabSWse6wmyqbFYujksBwMtk5u4tK6ixO4pEb5OZcyPinKOUBkQmOJ9vMploFRjmluwiIiIiIiLNmctKJoCoqCi++uorBgwYQHZ2Nq+//jphYWHs3r2bjz76CMBjC6Z169axc+dOAC677DLCwur/S6avry++vr4nP1BERDzX0ZLp4KdgqwGLfu6LNHd5eTbmzy9n7txy1qypYffuRNq29QbgnnvCmDQpmIsuCsDXt3kXS7XWYrYcfBIjbS7d0rPoe9yyQduiAziccgHtUx6iZ+B57gvZxPJrKlmdn8n3R0Yp/VyUi9Ww0zU02lky+Vq8uL3tuYR6+zIwKoHzIuLwt3i7ObmIiIiIiIhncWnJBJCcnMzSpUsZPHgwxcXFPP300859nlowAbz77rvO709lqjwRETlLxPSBgHiozIasbyDpEncnEpFfUV5uZ/HiCubMKeerr6qwHZkNz2yGH36odpZMffv6uTHlydns1WzLfJGqvbPofDCNc+uO7dsT7kN6Sn+SU+6lS+hF7gvpJhd//wFf5u77n+0t/YPpGhqNzbA711F6ttvQpo4nIiIiIiJyRnF5yQTQuXNnPvnkE0aMGEFVVRWGYeDv788nn3zC0KGe94tcXV0d8+fPByAmJoaLLjr7flkXEZGTMJmh1ZWw/d+wf6FKJpFmaO3aai64IIfKSsO5rXdvXyZODOKqqwKJi2uUl8YuY9it7Mx9k6K9r9Jh/y90rzn290gPtrAnpSctUu6kc8R42h4pUc5EVrudLSWHnWspbS3JY9vIKc7iKMY3AIBOIVEMOjL13cCoBK2nJCIiIiIi0gga7Tfp/v37s2DBAi6//HJ8fHz49NNPGTJkSGNdrlF99tln5OfnAzBhwgS8vJr3GxAiIuImrUc7SqYDi2DQ62DW/1+IuIvdbrBmTQ2lpXYuvthROnTr5oOXF6SmejFxYhATJgTRrp2Pm5OehGGwP+8Dcva+SJt9P9Ox0ubcdcjfxLY2nQhPnUb3mD+RZDpzf+ZsLMrl05w0VuVnsqYgizJr7Qn7fynJp1tYDACPdxnEi92HEenr746oIiIiIiIiZ5V6/SZqsVgadJGqqiqGDRv2u8eYTCasVmuDrtNYjp8qb9KkSW5MIiIizVrcYPCLhuo8yF4OCSPcnUjkrPPLL7XMmeNYZ+ngQSvt23tz0UX+mEwm/P3NbNmSQFKSV7Mf0ZJb+DX7056iZdoqWpfW0vrI9iIf2NS6DX4pN9Ar/i6GmQPcGbNR5B1ZT+n86CTCfRzTFi7K3sNj21c7jwnx8mVAVEvnKKX2wRHOfUkBoU2eWURERERE5GxVr5LJMAxMJhOGYZz84P/n6C/wp/Pc5qCwsJDPPvsMgK5du9KjRw83JxIRkWbL7AVtxsL212DvPJVMIk0kL8/G+++X8847ZWzYcGyES1CQiT59fKmsNAgMdLwmTU72dlfMkyos/Yk9aY8Tvfdr2hRVEntke4UX/JwcDynX0CvxfoZaIn73PJ7EMAz2VRQ7p777Pj+DXWWFAHzcfzRXtGwHwPAWrdhdVsjAqAQGRSXSOTTKOT2eiIiIiIiIuE+959Q43ZKoqculVatWsXfvXufjo9PcAezdu5fZs2efcPwNN9zwu+ebN28etbWONys0iklERE4qZbyjZDqwEGyvgcXX3YlEznh//WsB775bDoCXF1xySQATJwYxalQAAQHNu4ioqNzLjrRHCUr7lA6Hi+lzZHutGdYlRlKTciU9kh9isHeSW3M2hpWHDzJh7SfkVJf/z77OIVFYDbvz8cCoRAZGJTZlPBEREREREakHk+GpQ4x+ww033MA777xT7+NP9tfv27cva9euxWKxkJmZSWxs7O8eXx+lpaWEhoZSUlJCSEhIg88nIiLNiGGHOYlQmQ0jFkOry9ydSOSMkplp5YUXipk8OYSuXR3rKX39dSUzZhRx/fVBjB8fRHR0w6Z6bmy11bls3/93vNIW0Cn7MEdrMJsJfooPpjjlIrq0fpiWvl3cmtMVKqy1rC3Mdo5UGtOyPX9KOQeAtPIiUr94A2+Tmd4Rcc5RSv2jWhLho/WURERERETk7OKpvcGZuzqwC+zZs4e1a9cCMHz4cJcUTCIicoYzmSHlatj6EqTNU8kk4iJpaXU8/XQx77xTRl2dY0rmF1+MBGDYMH/Wr2/eaxPZ6krYdeBZrGnv0TEjgx7Hfc5pQws/clOG0K7NA/QJGOi+kC5QY7PyeW6as1TaUHTohBFJIV6+zpKpTWAY3w+dSK/wWPwtzXcaQxEREREREfltZ9xIJk/gqY2kiIjU0+F1sKgPeAXAdYfBO9DdiUQ81vbttTz1VDFz55ZjP9JVDBnix0MPhXPBBc17tIthrWJfxr8pS3uT9gf34G879rL7l0gvDqT0JTHlbroG/wETJjcmPT2GYZBWUUxhbRXnRcQDUGmtI2zRS9QdVywl+AczKCqRgVEJDIlJolNIlLsii4iIiIiINFue2htoJJOIiIirRfeG4NZQth/SP4OUq9ydSMQjTZmSx9tvl3H0I1EXX+zPAw+EM2CAn3uD/R67lYzsd8jf+y9S928hpe5Y2ZIWYmZ7andiUm7j3PDr6Uzzntbv/7Pa7WwuOcyq/Ay+z3OMVDpUU0Gv8Fh+uvAGAAK8vBmf1JFAi49j+rvoBJICQt0bXERERERERBqNSiYRERFXM5kgZTxsesoxZZ5KJpHT0qKFBcOAK68M4IEHwunVy9fdkX6dYSfv0GKy9j5P0r51JFZbSTyyKysQNqa0JzhlKn2j/kyKqRkXZL/j+nWf8HHWHsqttSds9zFbCPLyxmbYsZgcq0u9e94f3BFRRERERERE3KBeJdOhQ4do0aJFY2dx+zVFRERc5mjJlPE51JaCj+cMcxZpaoZhsHJlNX//exH33x/OsGGOafCmTw9lwoQgunTxcXPCX2EYlBR8y4G9TxGb9i0tKmqIPrIrzw/WtUnCJ+V6+sXezSiTZ/z7L6mr5of8LL7Pz2RT8SE+HTgOs8kxjZ/VblBurSXU25cBkY4RSgOjEjg3PA4/iz63JiIiIiIicraq12+EqampTJ8+nenTpxMa2rjTXRQXF/P888/zyiuvUFpa2qjXEhERaTQRXSGsAxTvhAOLod117k4k0uwYhsEXX1TxxBNF/PBDDQAWS7GzZIqKshAV1bymlKss3si+vU8QlvYlCSUVdD+yvdQbfmgVgy31Kvq0vJ9LzXFuzVkftXYbyw7tZ9mhA3yXl8Hm4sPYObZu1I7SfDqHOqqz+zv2474OfekSGu0snkRERERERERMhmEYJzvIbDZjMpkICgpi6tSpTJs2jTZt2rg0SFpaGq+++ipvvvkmFRUVANhsNpdeo7nw1AW8RETkFP38KPz8N0i8BC7+zN1pRJoNu93g448reOKJYjZudEy/5utr4qabgrn77jCSkprXyJi68jT2pj2B395FtC4ocm6vssCqpFAqUi+jV+KDJHq1c2PKUzd90ze8tGf9CdtSAsMYFJ3I4KhELm/ZlggffzelExERERERObt4am9Qr5Lp1ltv5Y033sBms2EymTCZTJx//vlcffXVXH755ac9rd2hQ4dYtGgR8+fP59tvvwUcn2i1WCxMmzaNV1555bTO29x56s0iIiKnqHgnfNARTF5wXS74Rbo7kUizcOWVuSxaVAlAYKCJadNCmD49lLi45lMu2atySdv3DKa980g9lOvcXmeC1QkB5KdcSJdWD9DB5zw3pqwfu2GwOj+TeRk7uC65M30jWwKwKj+Dq9Ys5vL4tpwfncig6ERa+ge7Oa2IiIiIiMjZyVN7g3qVTABbtmzh7rvvZtmyZY4nHjdNRseOHRk4cCDdunWjQ4cOJCQkEBkZib+/PyaTicrKSvLz88nMzGTXrl1s3ryZVatWsXPnTuc5jsYYOXIkzz77LF27dnXl37NZ8dSbRURETsNH50DBJhj0H+h4k7vTiLhFba3jdZ6Pj+P147vvlnH77QXcfnsId9wRSmRk85gSz6gpIv3Ay1SnvUNK1gG8jrxKtgM/xnmTmTKI1Db3co7fcEw07ynjDMNgfVEO89J38EHmTrKqygCYlnIOr/YcCTjKJwMDi8nszqgiIiIiIiKC5/YG9S6Zjlq1ahVPP/00X3zxhbMYMp3mvOzHP//SSy/lvvvuo3///qd1Lk/iqTeLiIichk3PwLr7IP4CGPWNu9OINKmqKjszZ5bx7LPFzJgRxp//7Fjbs67OoLLSIDS0GZQb1kpyD86kOO112qTvxMd+7KXxz9EW9qb0omXKdPoFjsVC8yjDfk+VrY7Htq9mfsYO9leUOLeHePkyOqEdk5K7MCQm2Y0JRURERERE5Nd4am9wyiXTUXv27GHWrFm8//77pKenn9bFk5KSmDhxIjfeeCOpqamndQ5P5Kk3i4iInIayA/B+a8AE12ZBQJy7E4k0urIyO6+9VsoLL5Rw+LBjjc1+/Xz54YeWbk52hK2Wwsx5HE57maQDmwiw2p27toeb2JLSiciUWxgcOhlffN0YtH7yaiqJ9g0AHB/iav35axysLCXA4s3l8W0Zn9SRkS1a42tpPtMRioiIiIiIyIk8tTc47ZLpeFu3bmXZsmWsXbuWLVu2cPDgQaqrq084xs/Pj+TkZLp37855553H8OHDz+gp8X6Pp94sIiJymhb1g8M/Qv9XoMtt7k4j0mgKC23885+lvPxyCUVFjuKmVSsv7r03jBtuCMLPz40jl+w2ynI/I2vvC8Tv/4GQGqtz1/5gWJvShoCUGxkScRshplD35ayn/RXFzM/Ywbz0HWRWlZHzh1vxNjtGWv334DZ8zBYujUsh0MvHzUlFRERERESkPjy1N3BJyfRrSkpKqKioACAwMJDQ0Ob/y3pT8dSbRURETtPWl2HNndCiP1y+2t1pRBrNVVcdYsECx+u/du28uf/+MCZMCMLb203rFxkG1Xnfkb73WaL2LSei8tiHoHL8YVVKHKaUCQyOuZsYUwv3ZDwFWVVlfJCxg3kZO1hXmOPc7mUy88MF19E7QiMlRUREREREPJWn9gaNNmdGaGioiiURERGANuNgzV/g0A9Qng5BSe5OJOISmZlWfHxMxMQ4RtBMnx7Kzp11PPBAGGPHBmKxuKdcqivcQPreZwlK+4wWZeW0O7K90BdWtA6nNmU0/eJmMM6c4pZ8p+P1tI38ecNSjn46zIyJoTFJXJ3YkdEt2xPp6+/WfCIiIiIiInJ20sTsIiIijS0wHuIGQ863kPYBdP+ruxOJNEhmppUnnihi1qwybr45hJdfjgKgb18/Nm9uicnU9OWSUZ5O5t5nsex5n/iiQo7WRxVe8HVyIKWpl9AzYQZjLOc0ebZTVVRbzcdZu+gUEkXfSMc6Vv0i4zGAAZEJjE/qyNiE9sT6Bbk3qIiIiIiIiJz1VDKJiIg0hZTxjpJp71yVTOKxCgpsPPVUMf/6Vyk1NY4xNbt21WEYhrNYatKCqaaYgv1vUL7nDZJz9pN4dLMZlif6kJs6lM5J93KZ9xBMuGnKvnoqq6thSfZe5mfs4MvcfdQZdq5N6uwsmbqFxpA56hZa+ge7OamIiIiIiIjIMSqZREREmkKbsbD6NijYCEXbIbyTuxOJ1JvVavDyyyU89lgRpaWOcmnQID/+/vdwBg9u4mnaDDuVGR9xeNezxKdvINJmJ/LIru/izOxu25vWrf/KcN8r8GrmL3UNw2Bh1i7mZezg0+w0qu1W576uodH0Co91PjaZTCqYREREREREpNlp3r95i4iInCn8oiDxYkj/BPa8B+c95e5EIvX22GNFPP54MQA9evjw5JMRXHSRf9OOWrLXUbb3P1Ru/hstivJpdWTztnD4oW0bwlP/zEVBUxlM8y5i7IaB+bhRX4/8sopfSvMBaBcUwfikjlyd2JFOIVHujCkiIiIiIiJSLybDMIyTHyauVFpaSmhoKCUlJYSEhLg7joiINJV9C+DrqyAwESYcAJPZ3YlE6iUvz0b//lnce28YkycHYzY3YblUV0HJrhexbXmOiPIyAEq8YWGHMKztJjIi4q8km1o1XZ7TYLXbWZmXzryM7SzN3c/Oi24i0MsHgDfSNrK/ooSrEzvQI6yFW9azEhEREREREffz1N5AI5lERESaStIfwCcUKjIc6zPFD3V3IpFf9eOP1Xz0UQXPPeeYiC462sKOHYl4eTVhAVJdQNEvT+C97TVCa6oByPWHBV1b0qrT00zymYCZ5lvU2g2D1fmZzMvYwYLMneTVVDr3fZG7j7EJHQD4U8o57oooIiIiIiIi0mAqmURERJqKlx+0GQc7Z8Lu91QySbNTXm7nwQcLeeWVUgwD+vXzY/ToQICmK5jKDlK09SECdr5PuNWxRtHeEPi4Wwrd273IrV5/wETzHu3zzaEDTFr/GVlVZc5tkT7+jEvowPikjgyMSnBjOhERERERERHXUckkIiLSlNpe5yiZ9n8IA/8FXgHuTiQCwLJllUydms+BA45iZ9KkIM4/36/pAhRsoXjzAwSnfUb4kdmcN0TC5z26Mrj1y9xtbp6lrGEYbCk5jN0wOCc8FoDWgWFkVZUR6u3LlS3bMT6xIxfEJONttrg5rYiIiIiIiIhrqWQ6g1itBlVVBrW1BjYb2GwGdjvO76OiLAQHO6aVKSuzs39/3Qn77Xbw9TXh728iNtZCWJjeCBERcbnYgRCUDOUH4cASSB3v7kRylisqsnHXXQW8/XY5AElJXvznP1GMHNkEBahhQM63lGx+gNCMHwg7snlZS/i+e19GtfwHD5r6NH6O07CztIB5GduZl7GDXWWFXBafyuIBYwFoExTG8vOvoX9kS3wterktIiIiIiIiZy791utGW7fWkJVVTkaGlbw8G3l5dgoKbNx/fxjnnef45PBnn1Xy0EOF1NYa1NVBba1xwp9Zs6IZMyYIgI8/ruCqqw7/5vXeeiuKyZMdC4atWlXNJZfk/uaxL7wQwfTpjrd6tm2rZcKEw0RHm4mJsRAdffwfM+ec40ubNt6u+s8iInJmM5mh7bWw8QnY855KJnErwzC49NJc1qypwWSCW28N4YknIpwfSmk0dhscWETZ5ocJzttOKGAzwYetYUP3YVwT/TyP0aNxM5yG/RXFzM/Ywbz0HWwuOfaay9dsIcDijWEYmEyOqfyGxiS7K6aIiIiIiIhIk1HJ5EYDB2YDwf+zfdKkY9tKSuxs3Fj7m+eoqjKc3/v4nLg+gdkMFguYzSbn16P8/U20aGE5st2xz2x2lFiVlcYJby5lZVnZuvW3Mzz7bAR33+0opDZurOGSS3KJjbUQF2chLs7ryFcLsbEWevb0pXVrFVIicpZre52jZMpcCpWHIKCFuxPJWcpkMvG3v4Vzxx0FzJwZzYABjTw9nrUaY887VG35OwElmQQDVRaY3R72drucKSFPcjWdGjdDA1y79hN+KMgCwMtkZkSL1oxP6sjl8W0J8fZ1czoRERERERGRpqeSyY3Cw8106OAoXaKjzURHW4iMtHDOOT7OY4YM8eOLL2Lx8THh42PC25sTvo+LO/Y/4aWXBlBZ2Qpvb9NJF+ceMsSf3Nz6fcL23HN9Wbo01jnayvHVxuHDjq+pqcdKo0OHbOTmOv5s2vS/53rmmQjuucdRSG3ZUsPVVx92llEJCRaSkrycf9q08W78T1KLiLhDWHuIPg/y1sHu2dDjXncnkrOEYRi8/XYZZrOJG25wfKhlxIgAtm71P+lrhwapKcbY/iq1257Ht6qIAKDQF17rZCKvy3hu9X+MaaQ23vVP0eHqCj7M3MWHmTtZ0O9KIn39AZiY1Bl/ixfjEztxZct2zu0iIiIiIiIiZyuTYRjGyQ/7bXv37iU1tfm8KeAJSktLCQ0NpaSkhJCQEHfHcamKCju7dtWRk2MjN9dKTo7tyB8rubk27rknjCuuCPrxqi0AACAASURBVATg888rufTS356y7+mnI7j3XkchlZlp5ZVXSujY0YcOHbzp2NFba0aJiGfbOQu+m+JYn2l8Gpj1M00a1759dfzpT/l8/XUVwcEmduxIpGXLRv68UUUWxtaXsO54Fe+6KgDSA+GVbhZsHW7kTu8HSaZ5TCtXVFvNx1m7mJexg28OHcSO4yXym70u5o9turs5nYiIiIiIiJzpPLU3aPA7C+3bt2fw4MFMmTKFsWPH4ufXyNOsSLMWGGimZ8/6TRfTr58v33wTR06OlexsG5mZVjIyrKSnO/4kJR27PTdurOG550pOeH6LFhY6dvSmQwdvJk0Kpm9f3Xsi4kFSr4G190D5QUj/BFpd4e5Ecoay2Qz++c9SHnigkMpKAz8/Ew89FE6LFo1YbBbtwNj8LMbe9zDbbXgD28LhH929CUudxnTzvcQT33jXPwW7ywr56+blfJm7jzrD7tzeOzyO8UkduSSujRvTiYiIiIiIiDRvDR7JZDabnQsch4SEMGHCBKZMmULPnj1dEvBM5KmNZFM7fvHsjRtrmDWrjJ0769ixo5asLNsJx77/fgzjxwcB8M03VdxzTwEdO/rQubM3Xbv60KWLD8nJXs7ziYg0C2vvg83PQMthcOnX7k4jZ6BffqllypQ81q6tAeD88/2YOTP6hKluXSp3NfbNz2A++Ilz07dx8M/ufqQm3s50013EENM4166nKlsdudUVtA50jJY+XF1B3Cf/wo5Bt9Boxid24qrEDqQEhbs1p4iIiIiIiJxdPLU3aHDJFBAQQHV19bETHnkTv1u3btx0001MmDCBsLCwhqU8w3jqzdKclJXZ2bmz9kjpVMeUKcGkpDjeMHvppWKmTy/8n+cEB5vo0sWH556LbPyFzUVE6qPsIMxrA4Ydxv0C4Z3cnUjOIIcP22jVKp2qKoOQEBPPPRfJH/8YjNns4g9cGHZI/wz7pqcxH/oBADuwqBW82j2QAS3u4g7uIIII1173FNTabXyVu595GTtYnL2Hc8NjWTFkgnP/7ANbOC8ink4hUW7LKCIiIiIiImc3T+0NGlwylZaWMnfuXGbNmsVPP/107MRHyiZfX1/GjBnD5MmTGTp0aMPSniE89WbxFNnZVtavr2H79lq2batj69Zadu6spa7OsX/dunh693aUTDNnlvLiiyX07OlLr14+9OrlS48evoSEmN34NxCRs8pXV8KBRdBpGgx81d1p5Axzzz0F7NxZx2uvRbl+/SVbLeydi33Ls5iLdgBQY4b32sLM7mFcFnY3t3ALoYS69rr1ZLXbWZF3kHnpO1iYtYviuhrnvjaBYWwbOQV/SyON6BIRERERERE5RZ7aGzS4ZDretm3bmDlzJnPmzKGgoODYRY4UTq1bt2bKlClMmjSJ+PjmMQ+/O3jqzeLJ6uoMdu92FE6XXx6Av7+jRJo6NY833yw74ViTCdq29aZXLx+eeSaSxMRGXhRdRM5uWcvhs2HgFQjXZoGPe96QF89XWWnnkUeKuOGGYDp39gHAajWwWHDtdLG2Gtj5FvZNT2KuyAKgxBte7wRzu0RxfeB93MzNBBLoumuehqvXLOKDzJ3Ox3F+QVyV2IHxiR3pExGvKXRFRERERESkWfHU3sClJdNRdXV1LFq0iFmzZrFs2TLsdsciykd/mbdYLIwcOZI//vGPjBo1CoulEReeboY89WY5Ex0+bOOnn2r4+ecaNmxwfM3IOLbeU2FhMuHhjvvztddK2bq1ln79fOnXz4+UFK3xJCIuYBjwYVco+gX6/QO63uHuROKBli+v4qab8ti3z0rfvr6sXh3v+mnxjpRLxqYnMR0pl7ID4B9d4NNO8fzZZwZTmII//q69bj38UpLHnPTt3JLak5b+wQC8c2Arf928nLEJHRif1JGBUQlYTBqpLCIiIiIiIs2Tp/YGjVIyHS8rK4tZs2Yxe/Zs9u/ff+zCR96cj4mJYdKkSUyePJl27do1ZpRmw1NvlrNFXp6NDRtq2L27jttuOzaiYOjQbFauPLb+WFSUmb59/Zyl0/nn+7n+DT0ROTtsfx1WTYOQFLhqF5jPrg9fyOkrLrZx992FzJzpGJWbmGjh9dejueSSANdeKHMZxupbMJXscTwMhCd7wPL2ydzl9QCTmIQPPq695klkVZXxfvp25qT/wqbiwwA8320od7XvAzjWYTIB3vr3JCIiIiIiIh7AU3uDRi+Zjrd8+XLeeustFi1aRFVV1bEQRwqnAQMGcNNNN3HVVVfh6+vbVLGanKfeLGe7JUsqWLmymh9/rObnn2uorT22LyLCTH5+svNe3rChhuRkLyIj9caWiNRDXQXMTYSaIhixCFpd7u5E4gEWL65g2rR8cnIcI3BvuSWEp56KIDjYhaN1KrJgzXTY9wEAOf7weE/4tEMM91seZQpT8Kbp1jUyDIPlhw/y3K61fHVoP0dfxHqbzFwc14bbUs/lwhatmiyPiIiIiIiIiKt4am/QpCXTUdnZ2YwbN441a9Y435Q3DMP5fXh4ONOmTeOuu+4iLCysqeM1Ok+9WeSYmhqDjRtrWLOmmh9/rCE42MzMmdHO/a1apXPwoJXOnb0ZPNifQYP8GDzYz/WLrovImWPdDNj0NMSdD39Y6e400swtXlzBFVccAqBdO29mzoxi0CAXTlNnr4Nt/8T4+RFMdeXYTPDPzvDcuYH82WcGd3KnW9ZcOlxdQeJnr1JrdxRrA6MSuDapM2MTOhDp2/TT9ImIiIiIiIi4iqf2Bk1aMq1bt4633nqL+fPnU1ZW5tz+axFMJhNRUVHMmjWLSy+9tKkiNglPvVmkfkpL7fTrl8X27XX/s69NGy+uvz6YRx4Jd0MyEWnWKrJgbiswrDD6Z4jq6e5E0oxZrQaDB2czZIg/Dz8chp+fC0cv5a6CVX+Gwq0A/NAC/jwAoqKGMZOZtKKV6651EtU2K18fOsCo+FTntjs3fY3dMLizbW/aBJ15H0YSERERERGRs5On9gaNvvpxQUEB//jHP+jatSv9+vVj5syZlJaWYhgGhmHQsWNHXnrpJdLT05k1axYDBgwAHMVTXl4eV155JT/++GNjxxRxmZAQM7/8ksjhw8ksXNiCv/wllF69fDCbYd8+KwUFNuexNTUG06blMX9+OYcP237nrCJyxgtsCSlXO77f8pJ7s0izU1Bg4557CqipcXwwx8vLxHffxfPkkxGuK5iq8mDljbBkEBRuJd8XpgyGiy4LZFrU6yxjWZMVTCV11Tyz80daf/4af1j9IRuLcp37/tHjQl45Z7gKJhEREREREZFmoFFGMhmGwdKlS3nrrbf45JNPqKurc24H8Pf3Z+zYsUydOtVZKh3v559/5vbbb2fNmjUAjBo1iiVLlrg6ptt4aiMpDVNaamfNmmri473o2tWxOPq331YxZEiO85iuXX244AI/hg3zZ/Bgf0JDG70HFpHmJO9n+PhcMHnBhAOO4knOekuXVnLjjXnk5Ni4555Qnnkm0rUXsNtg50xYP8OxLhjwnw4w4zzo6XchM5lJMsmuveZvyKkq5+U9P/Fa2kZKrTUAJPqH8EavkVwcl9IkGURERERERETcwVN7A5eWTPv37+ftt99m9uzZZGVlASdOhde1a1duuukmrrvuOkJDQ3/3XDU1NbRv35709HQiIiLIz893VUy389SbRVxv585a/vOfMpYvr2Lz5toT9pnNMHNmNDfeGOymdCLiFp+cDznfQY/74Lyn3J1G3Oyf/yzh9tsLAOjQwZv//jeGXr18XXeBvJ9h1TTIWw/ApkgTNw80+KVFEM/zPFOZigmT6673Gwprq5ix9VtmH9jqXG+pU0gU97bvwzVJnfA2Wxo9g4iIiIiIiIg7eWpv4NXQE9TU1LBw4ULeeustVq5c6SyVjn4NCAjg6quvZurUqfTp06fe5/X19WX48OG89dZbFBcXNzSmSLPUoYMPL77o+ER6Xp6NlSurWL68im++qWbPnjq6d/dxHrtoUQXvvVfGyJEBjBzpT3Kyt7tii0hj6jrdUTLteAPOeRC8A92dSNzk2WeLuffeQgBuvjmYF1+MxN/fRSNca4ph/YOw/VXAoNzbwv29bbzayWCo+UK2NeHoJYBAizefZO+l1m6jf2RL7uvQl0vjUjGbGr/gEhEREREREZHT1+CSKS4ujpKSEuDEUUs9evTgpptu4tprryU4+PRGYoSFhf3PeUXOVNHRFsaNC2LcuCAAMjKstGx57JPbixZVsHBhJQsXVgLQvr03I0f6M3JkAOef70dgoKbWEzkjJI2CkFQo3Qu7ZkGX29ydSJqYYRg8/ngxjzzimLru4YfD+NvfwjG5onAx7LDnPVh7D1QdBmBeqpm/9LVRHhDEq7zATdzUqKOXDMPgm8MH+e/BbbzV+xIsJjO+Fi/+3XM40b4BDIxKbLRri4iIiIiIiIhrNXi6PLPZjMlkwjAMgoKCGD9+PFOnTuXcc89tcLjXX3+d+fPnA7BixYoGn6+58NRhb+JeGzfW8OmnlSxdWsmPP9Zgsx3b5+trIjMziagoTSckckbY/hqs+jMEJcP4PWDWyMWzSWamlc6dMygtNXjyyXBmzAh3zYnzfobVt8LhHwE4EObP5AFVrGgJF9L4ay/ZDDsLM3fzzK4f+bkoF4AP+l7BuMQOjXZNEREREREREU/hqb2BS0qmXr16MXXqVCZMmEBgoKb1ORlPvVmk+SgutrF8eTVLl1aydGkVoaFmNm9OcO6/4458AgPNjBoVQJ8+vlgsmm5IxKNYq+D9Vo6RJkP/C20nujuRNLHVq6vZsKGG2277/TUs66U6H9Y9ADvfBAxqvXx4tKed57pa8bUE8UIjj16qtll59+A2ntu1lr3ljtFZ/hYvbmrdnbvan0dSgAv+jiIiIiIiIiIezlN7gwaXTJs2baJHjx6uynNW8NSbRZonwzAoLrYTHu4YxVRRYScy8iA1NY5/2lFRZi69NIBRowIYMSKAkBBNqyfiETY8AT89CBHdYMwm0No0ZzS73eDAAStt2rhw1Jrd5ljb66cHocZR7nyVGsWNffLJDoThDOdN3mzU0Us5VeWcs+xtDtVUABDh48dtqb24NbUXUb4BjXZdEREREREREU/jqb1Bg0smOXWeerOIZ6iutrNwYSWffFLBF19UUVJid+7z9oY77wzl2Wcj3ZhQROqlpgjmJkFdOVz0OSRd7O5E0khsNoM//jGPxYsrWb48jh49fBt+0txVsPo2KNgEQF5EHNcMKOCbuFqCCeYFXuCP/LFRRi9V2erwtzjKMsMwGLDiv2RWlnFX+978sXV3Ar18XH5NEREREREREU/nqb2BhjSInGH8/MxMmBDE+++3IC8vmRUr4rjrrlDatfOmrg7i472cxxYU2Hj55RIyMqxuTCwiv8o3HDpMdXy/+Rn3ZpFGU1dnMHHiYWbPLqe01M6ePXUNO2FlDiy/DpYMgoJN2HxCeGlAKnGjc/gmrpbhDGcb2xplerw9ZYVM/ekLEj99laLaagBMJhPz+15O2iV/4o62vVUwiYiIiIiIiJxhNJLJDTy1kRTPt2tXLZGRFqKiHFPrzZpVypQp+QCcd54vo0cHMmZMIKmpLpyuSUROX3kmzGsD9jq44keI6ePuROJCNTUG48cfYtGiSry9Yd68FowefZprW9pqYdvLsOExqCvHwMSuDoO4uPfPHPCvIJBAXuAFpjLV5eXST4U5PLPrRz7K3MXRF5Uzz72YKa27u/Q6IiIiIiIiImcyT+0NGlwyTZ48uUEBzGYzwcHBhIWF0bFjR3r37k3r1q0bdM7mzlNvFjnzLFlSwfPPl7BqVTXH/yTo2tWHMWMC+fOfQ4iOtrgvoIjAyhth92xodQWM+NjdacRFqqrsjBlziC++qMLX18RHH7Xg0ktPc42izK9g9e1QsguA2pie3DPAn5ejVwMwkIG8wzu0oY2r4mMYBt8cPshTO9ew/PBB5/ZRcSnc26EvA6MSXXYtERERERERkbOBp/YGDS6ZzGYzJhcvRt67d2/uueceRo8e7dLzNheeerPImSs318rixZV89FEFK1ZUYbWC2QxZWUnExjqm16upMfD1df3aHSJyEkU7YEFnwICxWyCiq7sTSQNVVNi57LJcli+vxt/fxJIlLbjwwtMomMoOwJrpcOBI+egfw/rzxnJJu3nkmwrxwYcneIK/8BcsuPYDAxmVpbT+/DVshoHFZGJCUifuad+XLqHRLr2OiIiIiIiIyNnCU3sDl5RM/3NSk4nfO2199gNce+21zJ492+Ullrt56s0iZ4fCQhuffFLJnj11/P3vEc7tF1yQTVWVwfjxQYwbF3jC2k4i0si+vgr2LYA2V8OF89ydRhqoqsrOpZfmsn59DZ99Fsvgwf6ndgJrNWx+FjY9BbZqMFmo7nwTt51bwEyfBQD0oAfv8R5d6OKy3DlV5cT5Bzkf375xGQB3tTuP5MBQl11HRERERERE5Gzkqb1Bg0umd955B4D09HSefPJJampqMJvNDB48mN69e9OyZUsCAwOpqKggKyuL9evX8/3332Oz2fDz8+P+++8nNjaWwsJCtmzZwueff05xcbEjnMnEHXfcwYsvvtjwv2kz4qk3i5y9iopsxMQcxGp1PDaZ4Pzz/Rg/PogxYwKdazyJSCMp2AIfdQdMcNUOCGvv7kTSQBUVdvbsqaNHD99Te+LBT+GHO6Bsn+Nx3BB+GHANV0U8RhZZmDEzgxk8zMP44OOSrKV1NTy47Tv+s28T6y+cRNfQGJecV0RERERERESO8dTeoMElE8CaNWsYNWoUxcXFjB07lhdeeIGEhITfPD4zM5O77rqLBQsWEB4ezmeffUbfvn0BqKys5IEHHuDll18GwMvLi19++YW2bds2NGaz4ak3i5zdcnKsfPhhBfPmlfPDDzXO7RYLzJgRxuOPR/zOs0WkwZZeAQcXQ9vrYeg77k4jpyg/38a8eeXcckvI6Y3QLk1zlEvpnzkeB8RT3fcJ7kpZx6um1wBoS1ve5V360tclmQ3D4OOs3dy2cRnZ1eUAPNnlfGZ07OeS84uIiIiIiIjIMZ7aG/zvXHenqKCggLFjx1JcXMzNN9/M/Pnzf7dgAkhISGD+/Pn86U9/oqioiHHjxlFYWAhAQEAAL730EjfffDMANpuNWbNmNTSmiDRQXJwXt90WyurVLTlwIJFnnongnHN8sNmgTRtv53GHD9v4+OMKamoa3F+LyPF6Puj4uncOlO5zbxY5Jbm5VoYMyea22wp44YWSU3uyvQ5+esSxLlf6Z2D2hu73sPbqd+ma+oSzYLqVW9nIRpcVTAcrSrhs9YeMWfMx2dXlpAaFs2zweBVMIiIiIiIiInKCBpdMb775Jjk5OYSFhfHCCy+c0nNffPFFwsLCyM7O5s033zxh3+OPP46vr2MKmZUrVzY0poi4UHKyN/fcE8aGDQns3JnA2LGBzn1z5pQxevQh4uIOMm1aHmvWVP/uGmwiUk/R50LiRWDYHGvxiEfIzLRy/vk5/PJLHfHxFkaNCqj/k2uK4POLYMNjYKuBlsOpHfsT9/ex0N97BHvZS0ta8hVf8U/+SSCBJz9nPby6dwOdls7k05w0vE1mHuzYny0jJnNhi1YuOb+IiIiIiIiInDkaXDJ99NFHmEwmhg4dip+f3yk919/fnwsuuADDMPjwww9P2BcZGUmfPn0wDIMDBw40NKaINJL27X0IDj72o8Tb20RcnIWiIjuvv15G//7ZtGuXwaOPFpGWVufGpCJngHMecnzd/Q6UHXRvFjmpAwfqGDw4m92760hK8uK77+Lp0KGe6ySV7IVFfSF7OXgFwrB5pF3yKv3CbuQpnsKOneu4jm1sYzjDXZq71m6j0lbHoKgENo+YzONdBuNv8T75E0VERERERETkrNPgkuloARQVFXVaz4+MjDzhPMdr3bo1AEVFRad1bhFperfeGkpGRhJffRXLddcFERBgYu9eK3/7WxGdO2dSVmZ3d0QRzxXbH1oOc0yhtvHv7k4jv2PPHkfBtH+/lZQUL77/Pp6UlHoWNdnfwqI+ULIbAhPh8tUsSDHT09SLDWwgkkg+5EPe5V3CCGtw1tK6Gn4pyXM+vjW1Fx/0vYKVQybSMeT0Xt+JiIiIiIiIyNmhwSVTZWUlAJmZmaf1/KysrBPOc7yj0+UFBJzC1DIi4nYWi4nhwwN4990YDh1K5t13oxk+3J/LLw84YdTT3/5WyPLlVdjtmk5PpN56Peb4uuttKE1zbxb5VeXldoYMySYjw0aHDt589108SUle9Xvyrrfh8+FQUwjR51F35WpujXyTq7iKUkoZwAA2sYkxjGlwTsMwWJi5i45fvskVPyyk2mYFwMtsZlxiB8wmU4OvISIiIiIiIiJntgaXTC1btsQwDFasWEFBQcEpPTc/P58VK1ZgMpmIj4//n/1Hz3e6o6RExP2Cgsxcd10wX30Vx9y5Mc7tO3bU8uijxQwblkO7dhk8/XQxublWNyYV8RCx/Y+tzfTzY+5OI78iKMjMI4+E062bD99+G098fD0KJsMOa++Dbyc7Rqq1uQrbH77h+oB7+Df/BmAGM1jJShJIaHDGgxUlXLb6Q8as+Zjs6nIA0itLG3xeERERERERETm7NLhkuvDCCwGorq5m8uTJWK31e5PYarVy4403UlVVdcJ5jrd161ZMJhMtWrRoaEwRaQYslmOfivfzM/GnPwUTHGwiLc3KjBmFJCamM3p0Ll9+WYnNptFNIr/p6Gimvf+F4p3uzSJOhnHs59bUqSGsX9+SmBjLyZ9YVwHLxsLmZxyPez6EfdgcpnrdwTzm4Y03H/MxT/IkXtRzRNRvsNrtvLBrLZ2WzuTTnDS8TWYe6tifrSOm0C44okHnFhEREREREZGzT4NLpltuuQVvb8caA59++ikDBw7ku++++93nfPvttwwYMIDPP/8cAC8vL2699dYTjklLS2P37t0A9OzZs6ExRaSZad3am9dfjyY7O5m33oqib19frFb4+ONKLr44l0WLKtwdUaT5iukNyZc5Rr/8/Ki70wiwenU1gwZlk59vc27z8anHdHMVWfDJYDjwMZh9YOh/Mc59lDtMf2EWszBjZi5zuYIrGpyxqLaa3t/M5q9bVlBpq2NQVAKbR0zmsS6D8bM0rLwSERERERERkbNTg99R6Ny5M48//jj33XcfJpOJ9evXM3ToUOLi4ujduzcJCQkEBARQWVlJZmYmP/30E9nZ2cCxT/w+9thjdO7c+YTzvvHGG87vL7rooobGFJFmKijIzOTJIUyeHMK2bbW8+WYpX3xRxahRgc5jFi+uwM/PxPDh/pjNWiNEBIBzH4ODSyBtPpzzAER0cXeis9bKlVWMGpVLRYXBww8X8eqr9ZzmN+9nWHoZVGaDXzSM+Bgjtj/3cR//4l+YMPEO7zCWsS7JGebtS5xfEAe9S3m++1BuaNVN6y6JiIiIiIiISIOYjOPndmmAF198kfvvv5/a2tpjJ/+VNy6Ov5y3tzdPPPEEf/3rX//nuI8++ojycscaARMnTsTL68z5hG1paSmhoaGUlJQQEhLi7jgizY5hGM6fH3a7Qdu2GezbZ6VtW2+mTQvmhhuCCQ+vxxRUIme6ZeNg/4eQfDmMXOTuNGelpUsrueKKQ1RXGwwf7s+iRS0ICKjHQPH9C2HFdWCthPBOMPJTCGnNYzzGIzwCwBu8wVSmnnY2wzD4OGs350cnEenrD0BWVRneJjMxfoEnebaIiIiIiIiINCVP7Q1cVjIBbN++nUceeYQlS5ZQV1f3m8d5e3tz2WWX8cgjj9Cly9n3yWtPvVlE3KG83M4DDxQye3YZpaWOH1cBASYmTgzilltC6N7d180JRdyoaDt82NUxbd5lqyG2v7sTnVWWLKlg3LhD1NbCH/4QwAcfxODnd5KCybDDz3+DDY87HieMhAvng08oz/M8d3M3AC/xEndy52lnO1hRwq0bv+LTnDSmtO7GzHMvOe1ziYiIiIiIiEjj89TewKUl01FFRUX88MMPbNq0ifz8fMrLywkMDCQqKooePXrQv39/IiLO3sWlPfVmEXGn8nI7c+aU869/lbBt27ES++GHw3j00bP354kI3/4Rdr0FsQPhD9+Bpj9rEgsWlDNhwmGsVhgzJpC5c2NOvgZTbalj9NLBJY7HXe6Evs+B2YtXeZVbuAWAv/N3HuCB08pltdt5ec96Hv5lFZW2OrxNZmZ07MffOg381RHmIiIiIiIiItI8eGpv0Cglk/w+T71ZRJoDwzD4/vtq/v3vUhYurGD58jgGDXJMA5WdbcVuh4SEM2d6TZGTKs+E+W3BVg0jl0DyH9yd6IxXU2PQuXMGaWlWJk4MYvbsaLy8TlLglOyBpZdD8Q6w+MKg/0C76wH+j737jm+q+v84/kq6N7RAoew9ZMgoo8gUUKAgogiCKOJCwI0oqICCIoKi8gMVV0GmE1BA9pC9VECG7BaKtIzumeT+/sjXKkKhtClp4P18PPL4Jjcn534u32uax33fcw6zmEV/+gMwkpG8yZv5qmvb+Vie2PkzvyXEAdCqRDk+aXwntQPzuEaUiIiIiIiIiDiNq+YGBQ6ZPvzwQ3tHJhODBg3Cw8PDIYXdyFz1ZBEpas6csVCqlFvO3flPPXWWjz5K4q67fBk6NIi2bb11577cHLa+DL9PsK/tc89uMGvNssJ29Gg206cn8eabwbi5XeV7JuZnWHU/ZCWAX1no+D2UagrAj/zI3dyNFStP8zTv8z4mrv17a170PvpuXYQBFPfwZlKDdgyoVB+zvgNFREREREREXIKr5gYFDpnMZjMmk4lGjRqxfft2R9V1Q3PVk0WkKDMMgx49zrBoUVrOtjp1PBg8OJAHHwwgIOAq66SIuLLMCzCvqv1/23wBNR92dkU3pOhoCxUqXMNIScOA3yfC9hH2tZhCI6Djd+BbGoB1rONO7iSDDPrTnyiiMJO/76rzWenUoYWJxgAAIABJREFU/vlT7ihdmUn121PK2y9f/YiIiIiIiIiIc7hqblDgq65+fvaLGHXr1i1wMY4QFxfHTz/9xKhRo+jcuTMlSpTAZDJhMpkYMGBAvvrctm0bgwcPpnbt2gQGBuLv70/VqlXp2rUr7733HvHx8Y49CBG5ZiaTiYULS7NnTzkGDQrAz8/Evn3ZDB16jrCwE7z22nlnlyhSeLyKw60j7c93jAJL2pXbyzX76KMkqlePZtGi1Lx9ICsZVvWBbS/ZA6Zaj0Lk6pyAaRe76EY3MsigO935nM+vKWA6kZrIG/s28Pe9QsGePvxxx6PMbNpNAZOIiIiIiIiIXDcFXrikTJkyHDlypMhMSRUaGuqwvjIzMxk6dCiff/45/x3wdfToUY4ePcqSJUuoUqUKPXr0cNh+RST/6tb15KOPSvL22yHMnJnM1KlJHDyYTXb2P/8N22wGNhtXX0NFxJXcMhT2fgipMbD7PWj0qrMrumFMmZLI00+fA2DTpgy6d79KiHNhP6zoCQkHwOQOER9AnSfhf7+VDnKQO7mTZJJpQxvmMx8P8jbdsMVm44ND2xn1xwbSrNnUDAihd/naAJTw8s3/QYqIiIiIiIiI5EOBRzI1adIEwzDYv3+/I+pxqPLly9OpU6d8fTYrK4u7776bzz77DMMwaNWqFZ9++ikbNmxgy5YtzJ8/n5EjR1K9enUHVy0ijhAUZOapp4LYv78cK1eWYejQoJz3VqxIp1q1GN5/P5HkZJsTqxRxIHdvaDbB/vy3tyE11rn13CAmT07ICZiGDw9i/PjgK3/gyHz4IdweMPmVhW7r4JbBOQFTDDF0pCPxxNOIRixiEd5456mWPYlxNFs1g2G715BmzaZ1ifLUDypZoOMTERERERERESmIAq/JtHTpUrp27YrZbGb37t3UqVPHUbXly+jRowkPDyc8PJzQ0FCOHz9O5cqVAXjooYeIiorKUz+jRo1i7NixAEyaNIkXXngh17bZ2dl4eOTtDmRw3bkVRW4U/frFMWdOCmAPo554IoCnnw6ibNkCD+4UcS7DgIURELcFagyAtl86uyKXNnFiAsOH26fafOWVYowdWzz3kdvWLNg6HPZ+YH8d1h5unws+pXKaxBNPa1pzgAPUpCa/8AsluXpIZLHZmHBwC6//sYFsw0ZxD2/ebdCeAZXqFZmR5CIiIiIiIiJSMK6aGxQ4ZALo2bMnCxYsoEGDBqxevZrixYs7ojaHyE/IdPToUWrVqkV2djYDBgzgyy8de5HOVU8WkRtFerqNr75K4d13E/nzz2wA3N2hb19/XnghiPr1vZxcoUgBnNkCC1sAJrh7O5Rs7OyKXNK/A6bRo4sxevQVAqbUU7DyPjizyf761hHQZCyY3XKaJJFEe9qzk52Upzwb2EAFKly1DsMw6Lh+HqviTgBwV1h1Pm58B6W9/Qt2gCIiIiIiIiJSpLhqblDg6fIAoqKiiIyM5Pfff6du3bpMnz6dhIQER3TtFNOnTyc7OxuTycSoUaOcXY6IOJiPj5nHHw9k//5yLFoUSuvW3lgsMHNmCvfdF4fNVuDsXcR5QptDtX6AAZufs49ukmtisxls25YJwBtvFGfMmODcA6aTK+H7RvaAyTMIOi2Epm9dFDBlkEEPerCTnZSgBCtYkaeACbD/FqnTkjBvf75qGskPET0VMImIiIiIiIhIkVHgkUzt27cH7Hfabty4EYvFgslkwmQyUalSJUqWLImPj8/VCzGZWLVqVUFKuaz8jGSqWrUqR48eJTw8nG3btgFgs9mIjY0lOzub0qVL5+mYcuOqiaTIjWz79gzefTeRrl196d8/AICMDBvr1mXQqZOPpqQS15ISA/NrgjUdOnwNVXo5uyKXYxgGa9Zk0L59Ln/vbdmwYxT8NgEwIKQBdPwOAqte1MyChXu5l4UsJIAA1rCGxlx9dFm2zYrHv4Kq/74WERERERERkRuLq+YGBV6AZO3atRddfP37uc1m49ixYxw7duyqfRiGUWQu4MbHx3P06FEAWrRoQVJSEqNGjWLmzJlcuHABAHd3dyIiIhg+fDhdu3Z1Zrki4iDh4d7Mm+d90bYvv0xh8OCzNGzoyciRxejZ0w+zuWh8V4lckX95aPAi7HoDNr8A5buAh5+zqyryLBYDNzdybpbJNWBKOgar+9rXvgKo/QS0eA/cfS9qZsPGozzKQhbihRc/8mOeAqYNZ2Pov/UnFra8h/rF7Gs6KWASERERERERkaLIIdPlGYZxySO37bm1LSr27duX89zHx4dGjRrxwQcf5ARMABaLhfXr1xMZGcnzzz/vjDJF5DpISbHh52fi11+z6NUrjltuOcmsWclYLEXre0vksm59CfwrQmoM/Pqms6txCc8+e47eveNISrLl3ujI1/DdrfaAybMYdPgGWn18ScAEMJzhzGAGbrjxNV/ThjZXrWHJ6SN0Wj+f42mJjNu/qSCHIyIiIiIiIiJS6Ao8kmnNmjWOqKPIOH/+fM7z999/n8zMTCIiIhg/fjzh4eFkZGSwdOlShg0bxunTp5k8eTI1atRg0KBBufaZmZlJZmZmzuukpKRCPQYRcYwXXyzGwIEBfPhhIh9+mMSBA9n07x/P2LEJvPpqMR54wL/IjMIUuYS7L0R8AMt7wO5JUOMhKFbT2VUVWXPmpDB1qv3v82OPBdCx439CI0sabHoGDnxmfx0aAe3nQEDFy/Y3mcm8y7sAfMEXdKf7VWuYG72PB7f9hMWwEVmmKjOaarS0iIiIiIiIiBRtBV6Tqai71jWZZs2aRf/+/XNeN27cmA0bNuDtffE0WocOHaJhw4akpqZSsmRJTpw4kes6TWPGjOH111+/ZLurza0ocjNLSrIxdWoi776byLlzNrp08WHx4jLOLkvkygwDfo6EmCVQrhN0/hkUjF5i374smjY9RWqqwSuvFGPcuOCLG5zfAyt7Q8J+wAQNR0LjMWC+/L0685jH/dwPwAQmMJzhV63hoyO7GLJrOQbQr8ItfBneRVPkiYiIiIiIiNxEXHVNJodMl3cj+W+Y9Oabb16yDaB69eo8+eSTgH0dp5UrV+ba54gRI0hMTMx5xMTEOLZoESl0gYFmRowozrFjFRg/PpjXX//nInRsrIUZMzSNnhRBJhO0/BDcvODkcjj2vbMrKnJSUmzce+8ZUlMN2rf35vXXi//zpmHAH9Pgh3B7wORbBrquhPBxuQZMa1jDQzwEwFM8xYu8eMX9G4bBW/s3Mfh/AdOQqo2Y2TRSAZOIiIiIiIiIuASFTP8REBCQ89zT05N27drl2vaOO+7Ieb59+/Zc23l5eREYGHjRQ0RcU0CAmZdfLkaTJl452yZMSGDAgHhq1YohKkphkxQxgVWhwUv255ufhaxk59ZThBiGweOPx7N/fzZlyrgxZ04p3Nz+N9Ir4zysuAc2DgFrJpTvAvf8DmXb59rfbnbTgx5kkcW93MtkJmPiyiPHLIaNlWeOA/Ba7QimNOyIWaPNRERERERERMRFKGT6j/Lly+c8Dw0NxdPTM09t4+LiCrUuESm6qlTxoEQJM0eOWHj4YXvY9OWXyWRnK2ySIuLWlyGgMqSehB2vOruaIuPjj5OZOzcVNzeYP78UoaH/G52UeNg+eun4D2D2gBaT4c6fwKdkrn1FE01nOpNEEq1pzVd8hRtXH43kYXZjYct7+KppJG/Uba113kRERERERETEpTg8ZNq+fTvPPvssTZo0yQlp3N0vnVImISGBJUuWsGTJEnbv3u3oMvKtevXqeHh4AGC1Wq/Y9t/vX+4YReTm8MwzQRw7VoF33gmmZEl72DRwoD1smj1bo0akCHD3gVaf2J/vnQJxW51bTxFRt64HZcq48fbbwbRq9b91Fc/ugkUtIfmoPZjrsQXqPXvFtazOc547uZNYYrmFW1jAAry5dKrdv2VaLcw6sZe/l8UM8PDigYp1HXpsIiIiIiIiIiLXg8NCpvj4eCIjI2nevDlTpkzh119/JT4+HovFknMR5d/8/Px4/PHH6datGz179nRUGQXm4eFBixYtADhz5gypqam5tj1y5EjO87JlyxZ6bSJSdPn7m3nxxWIcO1aBiRODKVXKjaNHLezaleXs0kTsynWE6v0BA9Y/BrZsZ1fkdK1a+bB3bzleeCHIvuHUKvixDaTHQUhDuGszlGh0xT7SSac73dnPfspSlqUspTjFc22fYskicsO39N/2E+8cVNgnIiIiIiIiIq7NISFTbGws4eHhLF26FMMwch5X4uHhwZNPPolhGBw7dowtW7Y4ohSHuOeeewD7SKWFCxfm2u777/9ZQL1Vq1aFXpeIFH1+fmaGDSvG0aPlmTQpmBdfDMp5b/v2DD77LImsLE2jJ07S4j3wLgHn98DvE51djVPYbAbHjv0TsAUHu9mnqDvyNSztAtkpENYeuq0F39Ar94WNB3mQjWwkiCB+5mfKUz7X9uez0umwbh4r447j5+ZBk+KlHXVYIiIiIiIiIiJO4ZCQ6d577yU6OhrDMKhduzZz587lzJkzDB48+Iqf69OnT87zZcuWOaIUhxg4cCClSpUCYOTIkZw5c+aSNmvXruWrr74CoG7durRs2fK61igiRZufn5kXXihG6dL/TKX56qsXeOyxs9SoEcOnnypsEifwLgEt3rc/3/UGJPzp3HqcYMKEBOrVO8n8+Sn/bNz7f7CqD9iyoPK90HkJeAZeta+RjORbvsUDDxawgLrkPuVdbHoyrdfMZuv5WII9vVnd9n5uD63kgCMSEREREREREXGeAi8ktGDBArZs2YLJZOK2225j6dKl+Pr6Alx18eqqVatSrlw5Tp065bCRTBs2bODw4cM5r8+ePZvz/PDhw0RFRV3UfsCAAZf04e/vz4cffsj999/PiRMnCA8P5+WXX6Zp06ZkZGSwdOlSJk+ejNVqxd3dnY8//lgLdYvIFRmGwZ13+vD771mcOGHh8cfP8uabCYwcWYwBAwLw9NR3iFwn1frCoa/g5DJY9zB0Ww9mN2dXdV2sWZPOq69ewGaD1FQbGAbsGAW/jrM3qDMEIj7I07/Hp3zKBCYA8AVf0Ja2ubY9knKBjuvncSw1kTBvf5a37s0tQSUdcUgiIiIiIiIiIk5lMq42r91V9O3bl3nz5uHh4cHBgwepVKlSzntPPfUUU6dOxWQyYbVaL/v5bt26sXjxYipXrnzRGkf5NWDAAGbMmJHn9lc6/KlTp/L888+TlXX5NVX8/f2ZNWsWd9111zXVmJSURFBQEImJiQQGXv1OaRG5caSl2Zg+PZkJExL46y/792KFCu68804wvXv7O7k6uWmkRMM3dSE7GZpNhAbDnF1RoYuNtdCw4Sni4qw8/LA/X3xaDDYMhoOf2xs0GQsNX4E83DSyjGV0pStWrIxhDKMZnWvbFEsWNZdOJzYjhap+xVjRpg+V/Yo56rBERERERERE5AbhqrlBgafL+3sUU4sWLS4KmPKqZEn7nbzx8fEFLcXhhgwZwq5du3jyySepVq0aPj4++Pv7U79+fYYPH86ff/55zQGTiNzcfH3NPPtsEEePluf990MoXdqN6GgLiYk2Z5cmNxP/CtBisv35jlfhwj7n1lPIsrMNeveOIy7OSv36nvzfu2ZYcoc9YDKZodUn0OjVPAVMe9hDL3phxUp/+jOKUVds7+/uyat1IqgfVJJf2j2ggElEREREREREbigFni4vLi4OgBo1auTr856engBkZmYWtBQAoqKiLpkSryBuueUWpk2b5rD+REQAfHzMPPNMEI8/HsCMGSkMGBCQ897SpWlkZRl07+6rqTil8NQcCMe+h5glsPYhuGszmAv8s6BIeuWV82zYkEFgoImFMxPwXXY3JB0GjwC4fR5U6JKnfmKJpStdSSaZNrThUz7FxOX/G7UaNtxM9nt5nqzaiIGV6uPldmP++4qIiIiIiIjIzavAI5nMZnsXuU2HdzV/r5lUrJju7BWRm4+Pj5lBgwJz1mTKzDQYMuQsPXqcoXXr02zenOHkCuWGZTJB60/BsxjE74Bf33J2RYVi7dp0Jk5MBGDJJ79T6ddW9oDJvyLctSnPAVMqqXSjGzHEUJOafM/3eOF12bbfnjxA+MoZnMtMz9mmgElEREREREREbkQFDpn+nu7u+PHj+fr89u3bMZlMhIWFFbQUERGXZ7Ua9Onjj4+PiQ0bMoiIiKVnz784ePDya8OJFIhfGLScYn++czTsfs+59RSC227z5uWXAljy5ue0TOoJWQkQGgF3b4Pgunnqw4qV+7mfXeyiBCVYzGKCCb5s28+O/k7vzQv5NeEMHx7e4chDEREREREREREpcgocMjVp0gTDMNiyZQsJCQnX9NlVq1YRExMDQMuWLQtaioiIy/P1NfPWW8EcOlSeRx4JwGyGH35I45ZbTjJkyFnOns3fqFGRXFXrB/VfsD/f8gJsfRkMw7k1OZC7LZnx7R6jc4m3AANqPwGRq8GnVJ77eJmX+ZEf8cKLhSykKlUv227iwa08tnMpNgweq9yAUXX020ZEREREREREbmwFDpm6desGQEZGBuPGjcvz55KTkxk6dGjO6x49ehS0FBGRG0bZsu589llJ9uwpR/fuvlitMG1aEr/95pj160RymEzQbCI0nWB//fsEWP8o2CzOrauA5s1LIfv0Tvi+MZxYCGZPaP0ZtPoY3C4/zd3lzGY2k5gEQBRRRBBxSRvDMBixZy3Dd68BYHjNZnzS+M6cNZlERERERERERG5UBb760adPH6pUqQLA5MmTefvttzGucgf0H3/8QevWrTl48CAmk4nGjRvToUOHgpYiInLDqVPHk4ULS7NmTRlefDGIDh18c947diz7qt+3InliMsGtw6H152Ayw8EvYGkXyLzg7MryJerLJDZOn4ixIMK+/pJfeej+C9R65Jr62clOHuVRAEYwgj70uaSN1bDx5K5lvH1gCwBv12vLhPrtMJlMBT8QEREREREREZEizmQ44Arl2rVrueOOO7BY7Hc916hRg169erFp0yZWr16NyWRiwYIFHDp0iGXLlrFq1SoMw8AwDPz8/Ni0aRP16tUr8MG4iqSkJIKCgkhMTCQwMNDZ5YiIC/rrLwvVq8cQEeHN5Mkh1Knj6eyS5EZxfBGs7guWVAiqDnf8CMVqOruqPNu74xRHowbSvf5y+4aK3aHNl+B9+TWUcnOGMzShCSc5SRe6sIhFuOF2Sbv4zDTCV0YRnZbEJ43v5LEqtzriMERERERERETkJuOquYFDQiaAb775hocffpi0tLSr3r379y79/f2ZO3cuXbt2dUQJLsNVTxYRKTq++y6Fvn3jyMoCNzcYPDiQN94oTrFil14EF7lm536HZd0hJRo8g6D9XKjQ2dlVXVXq/kWk/fwoJf3iybZ64tbyHcz1nraP1LoGBga3cztrWEMNarCNbQQRlGv7wykX2J0QR89yrhPGiYiIiIiIiEjR4qq5gcMWC+jVqxdbt26lXbt2OaOU/n4Al7xu27YtmzdvvukCJhERR7jnHn/27StPjx729ZqmTEmiRo0YvvgiCZtNU+hJAYU0gLu3Q+nbICsRfu4C20aALdvZlV1eVhLGukfw++UuSvrF82d8dVI7bsBc/5lrDpgAZjKTNazBF18WsvCSgCkhK4Nlfx3NeV3Nv7gCJhERERERERG5KTlsJNO/7d69myVLlrB582ZiY2NJTEzEz8+P0NBQmjVrRmRkJOHh4Y7erctw1URSRIqmlSvTeOqpcxw4YA8AWrb0Yu3aMNzdtSaMFJA1EzY/B/s+sr8OjYDb54J/BefW9W/HF8DGoZB6CpvNxPtrBtLquUmENy+Wr+4ucIGa1CSeeCYwgeEMv+j9uIxU7vhlPnsTz7Ko5T10LlPVEUchIiIiIiIiIjc5V80N3Auj0/r161O/fv3C6FpERP6jQwdfdu/2YcqURMaMuUDTpt4KmMQx3LzgtmkQ1h7WPQJnNsF3t0LEh1CtX75GCTlMyknY9JQ9ZAKOnavAQ19OoM+znQlvnvvUdlfzCq8QTzy1qc2zPHvRezFpSXRcP4+DyecJ9fIjzMe/QIcgIiIiIiIiIuLqCmUkk1yZqyaSIlL0/fWXBV9fM4GB9tlQd+/O5Oef0xk6NBBfX4fNkCo3o6SjsKoPxG+3v67QFW77GPzLXd86LBmwZzL89hZkp4DJHRq8yJGgl5k5x8KYMcWvujZkbraznWY0w8BgDWtoS9uc946kXOD2dXM5kZZEeZ9AVrbpQ42AYAcdlIiIiIiIiIjc7Fw1N1DI5ASuerKIiGsxDIM2bU7zyy8ZlCnjxqhRxXnkkQA8PDTKSfLJlg2/TYBdb9ifewRCs7eh1uNgdivcfRsGHPsWtg6H5OP2baWaQ+vpEFyvwN1bsdKc5uxgB/3oxyxm5bz3R2I8HdfP53RGCtX8i7OqTR8q+OZ/tJSIiIiIiIiIyH+5am6g29pFRG5QhgGPPhpAxYrunD5t5cknz1K7dgxz5qRgs+n+AskHswc0ehV6/golwyE7CTYMhu8bwqnVhbNPw4CYZbCgOay8zx4w+ZWFdrOYeGgxK3Y6Zk2k6UxnBzsIJJBJTMrZfiI1kdZrZ3M6I4V6QSX5pV0/BUwiIiIiIiIiIv/j8JFMNpuNAwcOcPz4cRITE8nOzs7zZx988EFHllJkuWoiKSKuKTPTYPr0JMaNSyAuzgpA/fqevPtuMB06+Dq5OnFZNivsmwY7R0PmBfu2indBkzcgxAHrMhoGnFoJO8fY14ICcPeFBsOh/jAWLzcRGfkXJhPs2VOOW27xzPeu4oijJjVJIIEP+ZCneOpfZRg8tnMpexLjWdrqPoI9fQp4YCIiIiIiIiIil3LV3MBhIdOJEycYO3Ys33zzDSkpKddeiMmExWJxRClFnqueLCLi2lJSbHzwQSITJyaSmGhj+vQSPPaYvoOkgDLOwc7X7YGTYQ8xqdQDGr0GJRpde3+WdDg8G/Z8ABf22re5eUOdwXDrS+BTihMnsmnY8BQXLtgYMiSQ//u/EgU6hAEMYAYzaEhDtrENd9wvet9q2Ei3WvB3z3+QJSIiIiIiIiJyJa6aGzgkZFqyZAm9e/cmLS2N/HZnMpmwWq0FLcUluOrJIiI3hvPnrXz8cRIvvlgsZ32mrVszKF/enbAw96t8WiQXF/bbw6ajXwP/+y1QMhwqdLU/SjQCk9k+QsmwQsZZSI+zP5KPwYV9kLAf4rf9MzLK3Q9qPWoPl3zLAPaRebfdFsuOHZmEh3vxyy9heHnlf52xX/iF1rTGhInNbKYZzdiTGMcXx3YzoX47PAt7rSkREREREREREVw3NyhwyBQdHU3t2rVJT0/P2Va6dGkaNGhASEgIHh4eee7ryy+/LEgpLsNVTxYRuTFlZNioU+ckZ85YeemlYgwbFoSvr5bsk3y6sB9+fROOzAXD9s92kxtgXLwtN/4Voe7TUHMgeBW76K0hQ84ybVoSwcFmdu0qS8WKef+d8V/ZZNOIRuxlL4/xGNOZzoWsDMJXRnEkNYFhNZoysUH7fPcvIiIiIiIiIpJXrpobFPiW9UmTJpGeno7JZCIsLIxPPvmELl26OKI2ERG5DuLjbZQu7caxYxZGj77A9OlJjB8fTL9+/pjN+R8hIjep4rWh/SxoPhGil0L0Yji1HLL/M5WuyQzeJcC7FPiXg2K1oXgdKFYHSjUF86U/UebMSWHatCQAZs0qVaCACWAKU9jLXkIIYTzjsRkGD2z9kSOpCVT0DeTlWi0K1L+IiIiIiIiIyI2uwCHTihUr7B25u7N8+XJq165d4KJEROT6KV/enY0bw/j661Reeuk8J05YePDBeD76KImpU0vQsKGXs0sUV+RbBmoNtD+sWfZp8cxu9hFNJnfwDLK/vgYbN2YA8Oqrxejc2bdA5f3FX4xhDAATmEAIIYz6Yz1L/jqCt9mdHyJ6EuLlU6B9iIiIiIiIiIjc6Ao8XZ6/vz/p6el06NCBZcuWOaquG5qrDnsTkRtferqN999P5M03E0hNNTCbYc+ectSp4+ns0kQwDIMff0yja1df3NwKNsruER7hC74gnHC2sIUfTx2mx6bvAZjZNJL+Fes6omQRERERERERkTxx1dygwItu/L3mUuXKlQtcjIiIOJePj5kRI4pz4EB5evf2o1s3XwVM4lSGYWCz2e+HMZlMdO/uV+CAaSc7+RL7OpAf8AGHki/Qf9tPADxVrbECJhERERERERGRPCpwyFSxYkXAnrKJiMiNoVw5d+bNC+Xrr0Nztp05Y+HOO0+zc2emEyuTm820aUl0736G8+etDunPwOAZnsHAoB/9aEELYtKSMWGiVYlyvNugvUP2IyIiIiIiIiJyMyhwyNStWzcMw2Dz5s2OqEdERIoQT89/RoyMGnWBZcvSadr0FM88c5bkZJsTK5ObwdatGTz33DkWL07jm29SHdLn13zNRjbiiy9v8zYAHUIrsb3DQ3zdogce17hOlIiIiIiIiIjIzazAIdOgQYMIDAwkOjqauXPnOqImEREpgkaPLk7fvv7YbPDhh0nUqRPDwoWOufAv8l/nzlnp1esM2dlwzz1+PP54QIH7TCONF3kRgJd5meKWUjnv1QgIprS3f4H3ISIiIiIiIiJyMylwyFS2bFmioqIwm8088cQTrFixwhF1iYhIERMW5s7s2aVYvrw0Vaq4c/KklR49ztCz51+cOmVxdnlyA7HZDB54II6YGCvVq3vwxRclMZkKtg4TwEQmEkMMFahAg7/uocqSj1l15njBCxYRERERERERuUmZDMMwCtJBdHQ0ACtXrmTIkCFkZ2cTGRlJr169qFevHkFBQXm+MFShQoWClOIykpKSCAoKIjExkcDAQGeXIyJyzdLSbIwdm8CkSQlYLPDss4FMnlzC2WXJDWLs2AuMGnUBHx8TW7eWpV49zwL3GUMMNalJOulMyfiCUT8nciE7g8cqN2B6k84OqFpERET98WDCAAAgAElEQVREREREJP9cNTcocMhkNpsvCpEMw8jX3cYmkwmL5ea4E95VTxYRkf/asyeLUaPOExVViqAg++DY/P4dEAFYuTKNTp3+wjAgKqokDz1U8GnyAPrSl7nMpaVxG8krBrA7MZ7w4mVY364f3m7uDtmHiIiIiIiIiEh+uWpu4LCrKn9fVPz7wmIBsysREXEB9ep58sMPpXNeG4ZB165/0ayZNyNGFMPTU2GTXJvixd2oUMGdjh19HBYwbWQjc5mLyTARuPceNibGU8rLl+8i7lbAJCIiIiIiIiJSAAW+slKhQgXdsS4iIgAsW5bO0qX2x3ffpfL55yUID/d2dlniQho39mLXrrL4+jrmt4UNG8/wDADNkrqz9EAGbiYTX7foQXlf17krSERERERERESkKCpwyHT8+HEHlCEiIjeCO+7wYe7cUjz11Fn27MmiefNYnn8+iNdfL46vr9nZ5UkRlZVlsHt3Fk2aeAEQHOzmsL5nMpOd7MTPFsC29XUBeLdBe9qUvDnWgRQRERERERERKUy64iciIg5jMpno08ef/fvL07evPzYbTJqUSIMGJ1m7Nt3Z5UkRZBgGjz0WT0TEKebNS3Fo36mk8gqvAPAKr/BAaHP6VbiFp6s1ceh+RERERERERERuVlqIQEREHK5ECTdmzy7F/ff7MWjQWQ4ftvDss+fYtassZrOmWJV/jBp1gZkzU3Bzg6Agx9778j7vE0sslanM8+Zn8Qz3xGLYNM2viIiIiIiIiIiDKGQSEZFCExnpxx9/+DBixHnuu88vJ2DKyLBhtYKfnwbU3symT09i3LgEAD75pASdO/s6rO844pjABADGGuPwMnmBCTxMjpuKT0RERERERETkZqereyIiUqiCgsxMm1aCtm19crZNmpRIjRoxfPVVMjab4cTqxFkWL05j8OCzAIwaVYxHHgl0aP9jGUsyyXC+LPM3uWMzdJ6JiIiIiIiIiDhankOmgQMHMnDgQObMmXPFdgkJCURHRxMdHZ2nfl966SWCg4MJCQnJaykiIuLCrFaD+fNTiI218uCD8URExLJlS4azy5LraMeOTO677wxWKwwY4M+YMcUd2v8hDvGR8bH9xe7OtAguj1lT5ImIiIiIiIiIOFyeQ6aoqChmzJjBli1brtjutddeo3LlylSpUiVP/aalpZGQkEBCQkJeSxERERfm5mZi+/ayjB8fjL+/ia1bM2nRIpYHHojj5EmLs8uT62DWrGTS0gw6dfJh+vSSDl8j6XnrcKwmC5yuSU/Pzrxcq7lD+xcREREREREREbtCmS7PMAwMTUsjIiK58PY28/LLxTh0qDwDBwZgMsHs2SnUrBnDt9+mOLs8KWSTJ4fwwQchfPNNKB4ejg2YNtg28pPbAjBMVD7Sh6jwrg4PsURERERERERExE5rMomIiNOULu3O55+XZPv2stx2mzcWi0HDhl7OLksKQUaGDavVfgOKyWTi6aeDCAx07M8QA4PeaYMA8DgRztIGTxHgofNJRERERERERKSwKGQSERGna9zYi/Xry7BjRzmqVvXI2f7OOwls26b1mlyd1WrQt28cvXvHkZ5uK7T9fJYxl1j/vWDx4GPvSdQM0HqPIiIiIiIiIiKFSSGTiIgUCSaTiXr1PHNeb9+ewUsvnadZs1juu+8Mf/6Z5cTqJL9sNoOhQ8/yww9p/PhjKnv3Fs7/jxYsvOc9FoAOSf0YWLpVoexHRERERERERET+oZBJRESKpLJl3XnwQX9MJvjmm1Tq1DnJoEHxnD5tcXZpkkcZGTZ6947j44+TAfjqq1KEh3sXyr6+4AsOcIAQQvg2+P1C2YeIiIiIiIiIiFxMIZOIiBRJYWHuzJhRit9+K0vXrr5YrfDJJ8lUrRrDyJHnSUkpvGnXpODOn7fSseNffPttKh4eMHt2Ke67z9/h+7HYbDyw81tG2l4DYBSjCCLI4fsREREREREREZFLKWQSEZEirX59L376qTTr15ehRQsv0tMNPv882dllyRUcOpRNREQsGzZkEBRkZtmyMvTt6/iACeCVveuY7fUJ58xxVDYqM4hBhbIfERERERERERG5lLuzCxAREcmLVq182LgxjEWL0sjMNPD3t98nYRgGq1alc/vtPphMJidXKWBfh+nkSQvly7uxZEkZ6tb1vPqH8uGbmAO8c3QtdNkAwFumt/CkcPYlIiIiIiIiIiKX0kgmERFxGSaTibvu8rto2rX581Pp2PEv2rU7za5dmU6s7uZmsxk5z2vW9OT770PZurVsoQVMfyTG8/D2xVBjA3hmUJe63Md9hbIvERERERERERG5PIVMTjR45zJ2XfjL2WWIiLi0uDgr3t4m1q3LoEmTUzz8cByxsRZnl3VT2bcvi4YNT7FuXXrOtk6dfClTpnAGTCdkZXD3pu9JNSfiVmMzAGMYg1k/a0REREREREREriuTYRjG1ZuB2WzGZDIRHh5Oly5dcm23ePFitm/fjslkYvTo0Vft99/trVZr3it3YUlJSQQFBUHUaPD1pkVIWYZWa8S95WrhaXZzdnkiIi4nOtrCyJHnmT07BQBfXxMvvVSMYcOC8PVV8FCYoqKSGTLkLGlpBo0be7J9e9lCnbbQZhjctfFbfjp9hMBb15FU/WfqU59f+VUhk4iIiIiIiIi4rL9zg8TERAIDA51dTp5dc8hUGAzDuClDpl6r5rLgfDTZhg2AUC8/nqh6Ky/VbI6vu4eTqxQRcT1bt2bw/PPn2LTJPm1ely4+LF5cxslV3ZhSUmwMGXKWmTPtwV7Hjj589VVJQkMLd7nHVEsWvbcsZMWFP3CPnESaKZXv+Z67ubtQ9ysiIiIiIiIiUphcNWS65lt+DcNw+ONm9VmTLkRHDuaNW1oR5u3PmcxU5kbvw8tNo5lERPKjWTNvNmwIY/78UlSq5M4LLxTLee9m/nvjaL/9lknjxqeYOTMFsxnGjSvOzz+XLvSACcDP3ZNFLe+lX4fzpJlSuZVb6UGPQt+viIiIiIiIiIhcKs8jmdq2bVuo098ArFmzplD7Lyoul0hm26z8cOpPvN3c6R5WHYAMq4XHdizl8Sq3cluJcoX+7y8iciPJzjbw8Pjne3PcuAv8+msmEyaEUK2aRovm1/79Wdx660mysqBsWTfmzClF69Y+hb7fhKwMgjy8MJlMnOUslalMCiksYAF3cVeh719EREREREREpDC56kimPIdM4jh/nyznE89TPLB4ru0+Pfobj+/8GYBmwWEMq9mUu8vWwM2kNSdERK5FSoqNcuWiSUy04eEBvXr507u3H506+eDtre/Ua2EYBvffH0damsGXX5YkJKTwR9+mWLJotmom4cVL81HjO3jd7TUmMIFGNGIHOzChmzBERERERERExLW5asikK2tO1IIW/MAPGFw+52tbsgKPVW6Al9mNredj6bV5ATWXTmfa4V2kWbKvc7UiIq7L39/Mhg1h3HmnD9nZMGdOCnfddYZSpU7Qv38ca9emO7vEIm3jxgwuXLCvm2gymYiKKsnChaHXJWAyDIOHty9mX9JZlp85zpHsk0xhCgBjGKOASURERERERETEiRQyOdFBDtKTnjSlKctZfknYVD0gmOlNOnOi62BerR1BcQ9vjqQmMOTX5VRa8hHns3RRVEQkr+rW9WTp0jJs2RLGc88FUa6cG8nJBrNmpbB69T/fp9nZBpmZGuQLYLUajB17gdatY3n00ficda28vc3XbQrXiQe38u3Jg3iYzHwXcTczvKeRRhpNaEIkkdelBhERERERERERuTyFTE70Ii/ihx872MEd3EE72rGRjZe0C/X2Y2zd1sREDubDWztQyTeIxsVLE+z5zxoYJ1ITr2fpIiIuq1kzb957L4QTJyqwcWMYzz4bSJ8+/jnvL16cRmjoCR56KI4lS9LIzr45A6dTpyx06HCaUaMuYLOBn5+ZrKzrW8OKM8cYsWcdAB827EiVEHemMhWA13ldo5hERERERERERJxMazI5wb/nVswIzGA845nGNLKwX73rTncmMIFa1Lrs5y02G+ez0inl7QfAqfRkKi3+iBYhYTxTvQl3hdXA3az8UEQkP558Mp6PP07OeR0SYua++/zp18+fiAiv6zaCx5kWL07joYfiOHfOhp+fiWnTSvDggwHXtYbjqQk0XhnF+awMBlaqz2dNOjPMNIz3eI9mNGMzmxUyiYiIiIiIiMgNw1XXZFLI5ASXO1liiGEsY/mCL7BixQ03nuAJRjOaUpS6Yn/zY/bzwNYfsRg2ACr6BjK0WmMeqdyA4p7ehX48IiI3EpvNYNOmTObPT+Hrr1OJi7PmvFepkjs7d5YlOLjw1yJyhsxMgxEjzjN5sn107K23ejJ/filq1PC8rnXYDIPmq2ay/cJpmhQvzS/tHiDB7SxVqEI66SxlKXdy53WtSURERERERESkMLlqyKThLkVEecoznensZS/d6Y4VK9OYRjWqMZ7xpJP7+ku9y9fmeNcneaV2BCGePpxIS+LF3Wso99NUhuxazpmM1Ot4JCIirs1sNnHbbd5MmVKCU6cqsGxZaR580B9/fxNBQeaLAqZFi1KJibE4sVrHSk218e23KQA8/XQgW7aUve4BE4DZZOKtem2oHRDCdxF34+3mzgQmkE46zWnOHdxx3WsSEREREREREZFLaSSTE+QlkVzLWl7gBXaxC7CHUG/xFn3pi/kK2WC6NZs50fv44NAO9iTG4+vmwcnIIRrRJCJSQGlpNmJiLNSsaQ9dkpNthIaeICPDoHVrb/r18+fee/0oXtx1RjklJdn4889sihc3U7WqBwCbNmVw9qyV7t39nFwdWA0bbiYzscRShSpkkskyltGJTs4uTURERERERETEoVx1JJNCJifI68liw8Yc5jCSkcQQA0AjGvEu79KWtlfch2EYrIk/weGUBB6vcmvO9l6bfyC8eBkeqdyAEC8fhxyPiMjN6NChbB59NJ716zNytnl6QpcuvvTt609kpC8+PkVjwHBKio3Fi9M4fDj7fw8Lhw9n89df9qkAhw0LYuLEECdXCZvOnqSkly/VA4Iv2v40TzOFKUQQwQY2aC0mEREREREREbnhKGSSPLvWkyWddD7gA97iLZKxL0bfjW68wzvUolae97vtfCzNVs0EwMvsxv0V6jCkaiOaBJfJ34GIiAjR0Rbmzk1hzpwUdu/Oytn+zjvBvPhisULfv2EYnDtn48iRiwOkFi28GDw4CIDTpy2EhUVf9vOhoW48/HAA48cHX/b96+WPxHhuWzMLA1jRug/h//vbdIpTVKUqmWSyghV0oINT6xQRERERERERKQwKmSTP8nuyxBHHG7zBx3yMFStuuPEETzCa0ZSi1FU/n2bJZl7MPqYe3sWuhDM525sFhzGkWiPuK1cLLzf3fB2TiIjA3r1ZzJ6dwrx5KaxfH0b58vbv1IULU1m/PoN+/fxp2NATk+naRuIkJto4fjwbd3cTt9zimbOtbdtYjh2zkJhou+QzPXv68t13pQF7ENWhw2nKl3enWjUPqlXzoGpVd2rU8CQoyPmjrU6mJdFi9VecTE8mIqQsK9v0wcfNPn3fUIYylam0ohXrWKdRTCIiIiIiIiJyQ1LIJHlW0JPlAAd4iZdYxCIAAghgBCN4lmfx4epT4BmGwdbzsfzf4V18HbOfbMN+cXJBRE/uKlvjmusREZGLGYZxUZDUufNpfv45HYBatTzo18+ffv38qVzZ46LPZWUZfPRREsePZ3P8uCXnkZBg/56+5x4/vv02NGcfvr7Hyciw/xkvW9YtJ0CqVs2DJk086dDB93ocboEkZmfQas1s9iTGUysghA3tHsiZzjWGGKpRjSyyWM1q2tHOydWKiIiIiIiIiBQOhUySZ446WdaylmEMYyc7AQgjjDGM4WEexp28jUg6k5HKZ8d+Z+npo6xt2xd3s/2O9m9iDhDs6U37UhWv+Y57ERG52E8/pTJzZgqLFqWRmfnPn93q1T1o1cqbzz8vCYDNZg+O/t3mbyVLmunc2ZcZM/4ZubpmTTqlSrlRpYp7kVn/6VpkWi10/uVr1sRHU9rbj83t+1PJ758pBgczmI/4iDa0YS1rnVeoiIiIiIiIiEghU8gkeebIk8WGjbnM5RVe4QQnAKhJTd7iLe7m7nxNK5Rts1Jx8UeczkihUbFQhtdqzr3lauJmcr0LmCIiRUlioo3vv09l9uwUVq9OxzCgSRMvtm8vm9Pm6afP4u1tolIldypV8qBSJXcqVnTHz+/G+g62GQb9ti5iXsx+Atw9Wd+uH7cWC815P5poqlGNbLJZy1ra0MaJ1YqIiIiIiIiIFC6FTJJnhXGyZJLJR3zEOMZxjnMANKMZE5hwzRfmErIyeGXver48vpt0qwWAqn7FGFazGQ9VqpuzToaIiORfbKyFvXuzqFjRnZo1PZ1dznWXaskicsO3bDh7kqWt7qNDaKWL3n+CJ5jOdNrRjtWsdk6RIiIiIiIiIiLXiUImybPCPFmSSGISk3iXd0kjDYDOdGY842lAg2vq62xmGv93eCdTDu/kfFYGAKW8fPm0SWe6h1V3aN0iInLzybRa2Ho+ltYlK1y0/TjHqU51LFhYz3pa0cpJFYqIiIiIiIiIXB+uGjLdWHPvAHFxcfz000+MGjWKzp07U6JECUwmEyaTiQEDBuSpj6ioqJzPXO0RFRVVqMdzrQIJ5A3e4AhHGMxg3HFnKUtpSEP6059jHMtzXyW8fBlzSyuiuw7mg1s7UME3kLjMNCr4/nOCK6MUEZFrcSj5fM5zLzf3SwImgDd5EwsWbud2BUwiIiIiIiIiIkWYu7MLcLTQ0NCrN7oJlKY0U5nKczzHa7zGPOYxi1nMZz5P8iSv8iolKZmnvvzcPXm6ehOerNqQtfHRF62ZMfTXFaRbs3mhRlNuCcpbfyIicnNaFx9Np/XzeapaY96p3w6z6dJ1A49xjCiiAHid169zhSIiIiIiIiIici1uuJDp38qXL0/t2rVZvnx5vvtYtmwZYWFhub5frly5fPd9PVSjGnOZyzCGMYIRrGAFH/IhX/IlwxjG8zyPP/556svD7EbH0Mo5r89mpvHZsd/Jsln58vgeOoZW4tnq4dxZusplLxyKiMjN64/EeHps/I4sm5WjqQkYGMClfyvGMQ4LFjrRiZa0vP6FioiIiIiIiIhInt1wIdOoUaMIDw8nPDyc0NBQjh8/TuXKla/+wVzUqFGDSpUqOa5AJ2lMY5aznJWs5GVeZic7Gc1opjKVV3iFJ3gCL7yuqc8SXr6sa9uXiQe3suDUIVacOc6KM8ep4R/MM9Wb8GCluvi733yL2YuIyMVOpiVx5y9fk5CdScuQcsxu1g0306Uz9h7hCDOYAWgUk4iIiIiIiIiIK7jh1mR6/fXXiYyM1LR5uehAB7axjfnMpxrViCOOZ3iG6lTncz7HguWa+mseUpbvInpypMsTvFCjKYHuXvyZcp4hvy5nyqGdhXQUIiLiKmLSkui4fj4n05OpGRDMwpb34OPmcdm2YxmLFSt3cifNaX6dKxURERERERERkWt1w4VMcnVmzNzHfexjH9OZTlnKEkMMj/IoDWjAClZcc5+V/IoxqUF7TkYOZkrDjtQLKsmjVRrkvL/l3Ck2nT2JYRiOPBQRESnC/kiMp8XqrziQfI6yPgH83Oo+Qrx8Ltv2EIf4iq8AjWISEREREREREXEVCpluYh548BiPcZjDvMd7hBDCPvbRiU70oAdHOHLNfQZ4eDG0WmN+7ziQkl6+Odtf2r2Wlmtm0WzVTGYe30Om9dpGTImIiOs5mHye2PRkageEsLl9fyr5Fcu17VjGYsNGF7rQlKbXsUoREREREREREckvhUxXMWDAAEJDQ/H09KREiRI0b96cV199lVOnTjm7NIfxxpvneI5DHOIZnsENNxaykDrUYQQjSCb5mvs0mf5ZzD3LZqV6QHG8zG5sv3Cah7YvpvziabyyZx0n05IceSgiIlKE9CxXk29a9GBD+wco7xuYa7uDHGQ2swEYw5jrVJ2IiIiIiIiIiBSUQqarWLduHXFxcWRnZ3Pu3Dm2bt3Km2++SbVq1fjkk0+cXZ5DFac47/M+u9lNJzqRRRZv8zY1qclXfIUNW7769TS78VmTLsREDuGtum0o5xNAfGYabx3YTKUlHzH6j18cfCQiIuIM2TYrL+1ew9GUhJxt95SrRbDn5afI+9vfo5giiSSc8MIuU0REREREREREHEQhUy6qVKnCsGHD+O6779i2bRvbtm1j3rx59OrVC5PJREZGBoMGDWL69OlX7SszM5OkpKSLHkVZHerwMz+zkIVUpSqnOc2DPEgEEWxne777Lenly4jaLTjW5Um+bdGDtiUrYDUMagWE5LRJtWSRaslyxGGIiMh19FdGCu3XzeWdg1u5d/MPWI283ZhwgAPMZS6gUUwiIiIiIiIiIq7GZBiG4ewiCtPx48epXLkyAA899BBRUVFX/UxiYiKBgYEXTfn2bz/99BM9e/YkOzsbX19fjhw5QunSpXPtb8yYMbz++qWLmP+9n6Isk0ze533GMY4UUgAYyEDe4i1CCS1w/3sS46gZEIKn2Q2AiQe38tb+TQysXJ8hVRtTxT/39TtERKRo2HT2JPduXsDpjBQC3b2Y1SySbmHV8/TZvvRlLnO5i7tYwIJCrlREREREREREpGhKSkoiKCjIJXKDf9NIpssICgrKNWACiIyMZPTo0QCk/T97dx6nY734f/x1z8owM3bC2NdkS4tQUqJTnPaj9SDVqbSntCrtdYiitEpKqZxWLVIniYpC2XeD7MYyw2C2+/cH3/kd55w6ysxcc8+8nvdjHtzXdc11vYcPHo95+3w+mZm8/PLLv3m/O++8k507d+Z/rF27tkDzFqZ44hnIQJawhMu4DIDRjKYJTRjGMLLJPqz7t0yull8wAUzauJId2ft4cukPNPr0OXpOe4fPN64ir2R3oZIUkcLhMM8un83JU95gw95dHJlUhR+69j7kgmkJSxjPeADu477CjCpJkiRJkqRCYMn0B1155ZX5RdTXX3/9m9fGx8eTlJR00EekqUlNxjKWb/mWdrQjnXRu4RZa0YrP+bzAnvP5SRcysdP5dK9enzAwccMKun/zFs0/e5HnVswpsOdIkg7P3twcLv/xE/rP+ZzscB4X1G7GjFP/SpPESod8j0d5lDBhetKTtrQtxLSSJEmSJEkqDJZMf1C1atWoUqUKAOvWrQs4TdE5gROYyUxe4iWqUpXFLKY73TmLs1jBisO+f1QoxJlHNOKzk3qx5PSruKFROxJj4li6axtTt0TODDBJKunChJm/cwtRhPh7qy681f4sysfEHfLnp5LK67wOwN3cXVgxJUmSJEmSVIgsmQ5DCd/O6ldFEUU/+rGUpdzMzcQQw4d8yJEcyd3cnb930+FqkliJp9qexroe/XmmbTcGND0u/9zC9K10mzqeD9cvO+TN5SVJBadsdCzvdTiXyZ17MaDp8b+5zOx/8ziPk0suXenK8RxfSCklSZIkSZJUmCyZ/qDNmzeTlpYGQM2aNQNOE4wKVOBJnuRnfqYrXckii0d4hKY0ZQxjyKNgyp/E2HiubXQ0R1eskX/smeWzmbwplbOm/4NGnzzPE4u/J23fngJ5niTpvxubOo+HFk7Pf187IYlTqtX73fdZz3pGMxqAe7inoOJJkiRJkiSpiFky/UEvvPBC/kymzp07B5wmWEdyJJ/zOe/xHvWpz3rW05e+HMMxTGFKoTxzQNPjuL3p8VSKK0Nq5k4GzptC7YnP0PeHj/lx24ZCeaYklVY5eXnc+vOX9P7hY+5d8A3fHObypUMYQhZZdKQjJ3FSAaWUJEmSJElSUbNk+jepqanMmTPnN6+ZOHEiDz74IABlypShb9++RRGtWAsR4mzOZiELeYInSCKJOcyhC104h3NYxrICfV79chV4vFUXfunRn9HHnMHRFaqzNy+HManzOGPaO2Tl5Rbo8ySptNqetZczp73Dk0t/AODe5h3oWKX2H77fFrbwPM8D+2cxhfh9y+xJkiRJkiSp+IgJOkBBmzZtGsuXL89/v3Xr1vyfL1++nDFjxhx0fZ8+fQ56n5qaSpcuXTjhhBPo2bMnbdq0oVq1aoTDYVauXMmECROYMGFC/iymIUOGUKtWrUL7eiJNGcpwG7fRhz7cz/08z/O8z/tMZCLXcR33ci+VqFRgzysbHUvf+q3oU68lM7atZ+Ty2TQuX5G4qGgA8sJhnljyPRfXOZI6CckF9lxJKg2WZKTRc9oElu3aTkJ0LGOOPZMLUpod1j2HM5xMMmlHO7rTvYCSSpIkSZIkKQih8P+1JSVEnz59ePXVVw/5+n//8qdMmUKXLl3+5+clJCQwbNgwrrrqqt+dMT09neTkZHbu3ElSUtLv/vxIspCF3MZtfMInAFSkIvdxH9dwDXHEFfrzP92wgjOmvUMUIf5csxHXNWrHKdXq/u4N6iWptJmyeTXnfvse27P3UichiQ86nkebCtUP65472EFd6pJOOu/yLudwTgGllSRJkiRJimyR2hu4XN6/adeuHa+//jr9+/fn+OOPp06dOiQkJBAXF0f16tU55ZRTePjhh1m1atUfKphKmyM5ko/5mElM4iiOYjvbuYmbOIqj+IAPCFO4HWdybDynVqtLHmHeX7+MrlPH02LSSzy7fDa7crIK9dmSFMlSM3eyPXsv7SvVZOapvQ+7YAJ4hmdIJ50WtOAsziqAlJIkSZIkSQpSiZvJFAkitZE8XDnk8AqvcA/3sJnNAJzESQxhCMdybKE+e1H6Vp5ZPptXV8/PL5eSYuL5qVtf6perUKjPlqRI9dbaRfy5ZiPKRsce9r12sYt61CONNMYxjou5uAASSpIkSZIklQyR2hs4k0lFJoYYruRKlrGMO7mTMpRhKlM5juO4mItJJbXQnt08qQojj+7GLz2u5ak2XWlcviL1yiVR71/2aaaSVBAAACAASURBVFqcnkaenaukUmpPbjY3zpnM5r2784/1SmleIAUTwAu8QBppNKIRf+EvBXJPSZIkSZIkBcuZTAGI1EayoK1hDfdwD6/zOmHCxBHHDdzAXdxFRSoW6rPzwmE27d3NEWXLA7ArJ4taHz1DtTIJ9G94NH3rtyQ5tkyhZpCk4mLT3t38efoEZm7bQOeqKXzV+eIC3btuL3upT302spGXeIl+9Cuwe0uSJEmSJJUEkdobOJNJgalDHcYyllnM4hROIYsshjCERjRiOMPJovD2TIoKhfILJoC5OzYTFYLlu7Zz889fUuujZ7hm1iQW7NxSaBkkKUg5eXl8tXk1/Wd/zlGTXmLmtg1UiivDAy1OLNCCCeAVXmEjG0khhcu4rEDvLUmSJEmSpOA4kykAkdpIFqYwYT7lU27ndhawAIAGNOAxHuN8zidEwX7D87/ZnZPFuDULGbFsFvPT/3+5dEq1ugxvcyotk6sVegZJKgrPr5jDvQu+Ycu+zPxjTcpXYmKn82mcWKlAn7WPfTShCWtYwwhGcB3XFej9JUmSJEmSSoJI7Q2cyaRiIUSIMziDn/iJF3mRGtRgJSv5C3+hAx34ju8KPUO5mDiuatCGud0u56vOF3FurSZEEWLK5jUkxsTlX2cvKymShMNhpm1dy6Z/2WspMTaOLfsyqRRXhn71W/HpiX9hXvd+BV4wATzHc6xhDTWp6TJ5kiRJkiRJJYwzmQIQqY1kUdrFLoYylCd4gkz2/0/73vTmcR6nOtWLLMeazJ1M2byGv9ZrmX/swu8/oGx0DNc3asfRFWsUWRZJ+j3WZqYzdvV8xqTOY/mu7TzasjN3NDsBgIzsfcw4sP9SbFR0oWXIIIOGNGQLW3ie57mKqwrtWZIkSZIkSZEsUnsDS6YAROpgCcIGNnAP9zCa0QAkkcQDPEB/+hNDTJHnWZuZTt2Pn+X//tB0qFyL6xq147zaTYkrxG/UStKh2JObzfvrljEmdR6TN63K/7uqXHQsA5oex/0tTizSPA/wAPdxH41pzAIWEEtskT5fkiRJkiQpUkRqb2DJFIBIHSxBmsEM+tOfWcwC4CiOYgQjOJmTizRHOBzm+23rGbl8Fu+sXUx2OA+AGmXKcXWDtlzVoA1HlC1fpJkkCWBfbg4NPnmO9Xt35R/rXDWFvvVacV7tppT/l2U/i8JWttKABmSQwXjG04teRfp8SZIkSZKkSBKpvYElUwAidbAELZdcXuZl7uROtrENgAu5kCEMoRa1ijzPhj27eGHlTzy3cg4bD+x18uzR3bim4dFFnkVS6bQkI42miZXz3/eZOZF/bl5Dn3pH0bteSxqWrxhYtlu5lSd5kra05Ud+JMptICVJkiRJkn5VpPYGlkwBiNTBUlykkca93MtzPEeYMOUoxyAGcRM3EUfR/k99gKy8XN79ZQmvpM7jHx3OyZ8t8OH6ZWzL2sOFKUdSJrrol/aTVDLlhvP4YN0yhi/7gW+2/sJPp/WldYX9e9XtyNpL+Zg4YqKCLXTWspbGNGYf+/iMz+hO90DzSJIkSZIkFXeR2htYMgUgUgdLcTOb2VzHdXzHdwA0pSlP8zTd6BZwsv3L6rWePJp5O7dQJa4sVzZow9UN21AnITnoaJIiVHZeLm+sWcjDi75l2a7tAMSEonjm6G5c1aBNwOkO1pvejGUsnenMV3xFiFDQkSRJkiRJkoq1SO0NLJkCEKmDpTjKI4/XeI3buZ3NbAbgbM5mKENpQIPAcmXn5TJ06UyeXT6HtXvSAYgixNm1GnNdo3acXLUOoZDfdJX0v2Xn5TJ29XweWfQdK3fvAKBSXBmubtCW/o2OpmbZxIATHmw2szmGYwgTZiYzOZZjg44kSZIkSZJU7EVqb2DJFIBIHSzF2U52ch/3MZKR5JJLPPEMYAB3ciflKBdYrpy8PD7asIwRy2bx1ZY1+cf7NzyakUcHP+NKUvG3KyeLBp88x5Z9mVSNT+C2psdzTcO2+UtzFidhwpzKqXzFV1zMxYxjXNCRJEmSJEmSIkKk9gaWTAGI1MESCRawgBu5kS/5EoBa1GIIQ+hFr8CXa5q/cwvPLJ/N2NXzefuEszjziEYArN69k9k7NnLmEY2Ii4oONKOk4uG7tHUcX6kmUQdmPI5Jncu2rL1c3aAtCTGxAaf7dROZSE96Ek88S1hCXeoGHUmSJEmSJCkiRGpvYMkUgEgdLJEiTJj3eZ9buIVUUgE4kRN5mqdpQ/D7lqRn7yMhOpaYqCgA7p73NY8s/o6q8QlcVrcFveu2pFWFagGnlBSE5bu2M+Dnf/LB+mW83f5sLkhpFnSkQ5ZNNq1oxWIWM5CBPMZjQUeSJEmSJEmKGJHaG0QFHUAqaCFCnMM5LGQhD/AAZSnLN3xDO9pxDdewla2B5kuKjc8vmAAqxJWhRplybNmXyZNLf6D15NG0/vxl/r5kBuv2ZASYVFJR2ZWTxR1zp9Bi0kt8sH4Z0aEQK3ZvDzrW7/ISL7GYxVShCndyZ9BxJEmSJEmSVAScyRSASG0kI9Ua1nA7t/MWbwFQgQo8yINczdXEEBNwuv1y8vL4bONKXkmdy8QNK8jKywWgclxZNva8/qBSSlLJ8sG6pVw/5wvW7kkHoFv1+jzZ+hRaJFcNONmhyyCDRjRiM5sZyUj60z/oSJIkSZIkSRElUnsDS6YAROpgiXRf8zU3cANzmQvAURzFUzzFKZwScLKDbc/ayzu/LOa11fM5Kqkqo9p1ByAcDnPTT19weo0GnFa9vsWTVALc/NMXDF/2IwD1EpJ5um1XehzRiFAo2D3kfq/BDOZ+7qcRjVjIQmIpvvtGSZIkSZIkFUeR2htYMgUgUgdLSZBDDi/yIvdwD9vYBsD5nM8QhhTLDepzw3lEh/aXSd+lraPDP18DoHp8OS6peyRXNWhD08TKQUaU9CvC4TBrMtOZs2MTi9LTWJSxlUXpaQxoejy9UpoD8NXm1XSf+hYDmh7PPc07kBATeeXMJjbRiEbsYhdv8zYXcEHQkSRJkiRJkiJOpPYGlkwBiNTBUpJsYxuDGMQoRpFHHmUow13cxW3cRhnKBB3vv1q+aztPLfuB8WsWsTVrT/7xLlXrcHXDtpxdqwlxUdEBJpQEMH/nFu6cN4WZ2zaweV/mf5wf2LQ9j7U6Of/9+j0Z1CybWIQJC9b1XM9IRnIsxzKDGYSIrFlYkiRJkiRJxUGk9gaWTAGI1MFSEs1lLjdwA1/zNQANaMBTPEUPegSc7Ndl5+Xy2caVvLjyZz7esII89v8R/vykXpxWvX7A6aTSZcWu7Xy0fjl1EpI4t3ZTANZmplPn42cBiAlF0TK5Ki2SqtA8qTLNEivTrmIN6pZLDjJ2gVnBCprTnGyy+ZIvi93yo5IkSZIkSZEiUnsDS6YAROpgKanChHmLt7iVW1nPegB60IPhDKchDQNO99vWZqbz0qqf+WrzaqacfAlRB/ZxeWHlTyTGxHF2rcaUjY685bek4iocDvPzzs2MX7OID9YvY3FGGgBnHtGQiZ3+/zJxL638maOSq9CmQnXKRMcEFbfQXczFvMmbdKc7n/FZ0HEkSZIkSZIiVqT2BpZMAYjUwVLSZZDBgzzIMIaRQw7xxHM7t3MHd5BAQtDxDllWXi61PhrJ1qw9JMXEc2Gd5vSp15L2lWoSCrmMlfRH5IXDPLhwOm+uXciSjG35x2NCUZxUNYW/1G7G3xq2DTBh0ZvNbNrRDoA5zKENbQJOJEmSJEmSFLkitTewZApApA6W0mIxi7me6/mCLwCoS12GM5yzOCsi9hrJyN7HkKUzeTV1Hqsz0/OPNylfiT71WnJZ3RbUTnDcSf9LbjiP6FBU/vuTp4zj6y1riY+KpscRjTi/dlNOr9GACnHFcx+3wtaNbkxmMhdzMeMYF3QcSZIkSZKkiBapvYElUwAidbCUJmHCvMu73MzNrGUtAN3pztM8TROaBJzu0OSFw3y9ZQ1jUucx4ZclZOZmAzCwaXsea3VysOGkYmz9ngyeXTGHV1bNZc5pfalWphwAX25KZcPeXfy5ZmOSYuMDThmsL/iC0ziNWGJZzGIa0CDoSJIkSZIkSREtUnsDS6YAROpgKY12s5tHeZS/83eyyCKWWO7iLu7kTuKJnG8yZ2TvY8IvSxiTOo+n2nalTYXqAEzauJJhS3/gwjrNOadWE5JjS+eMDAng5x2b+PuSmby1dhE54TwAnm7TlesbHxNwsuIljzyO4zhmMYsbuIGneCroSJIkSZIkSREvUnsDS6YAROpgKc2WsYwbuZFP+RSA5jTnJV6iAx0CTnZ4LpvxEa+vWQBAXFQ03avX59zaTeh5RGMqx5cNOJ1UNL5LW8cji75l4oYV+cc6VanNjY2P4eyaTYiJivqNzy593uItLuRCEklkBSuoStWgI0mSJEmSJEW8SO0NLJkCEKmDpbQLE2YCE7iO69jMZkKEuJZreYRHSCIyfx+X79rO+DULeXPtIhamb80/Hh0KcVKVFD7sdD7lY+ICTCgVri37Mqn10Uiyw3mEgL+kNOe2psfTrmKNoKMVS1lkcSRHsoIVDGYwgxgUdCRJkiRJkqQSIVJ7A0umAETqYNF+29jGbdzGaEYDUJvajGIUPegRcLI/LhwOMz99C++tW8q7vyzl552bOTKpCgu6X5F/zTtrF9M8qTItkqoQCoUCTCsdnjWZO6mTkJz//rrZn7MnN4eBzdrTJLFSgMmKv2d5lv70pxrVWMEKylM+6EiSJEmSJEklQqT2BpZMAYjUwaKDfcmXXMVVrGQlAL3oxVM8RXWqB5zs8K3ctYMNe3fRsUptAPbkZlPlg6fJzM2mXkIyf67ZiJ41G3NS1RTioqIDTiv9unA4zKKMNL7ZspZvtv7CN1vXsiYzndld+9D2wGylcDhscXoIMsmkIQ3ZyEZGMpL+9A86kiRJkiRJUokRqb2BJVMAInWw6D9lkslgBjOUoeSSS0UqMpSh9KEPIUrON63XZqZzzexJfLEplX15ufnHk2LiOb1Gfa5s0Iau1esFF1D6Nz9u28DDi77lm62/kJa156Bz0aEQj7Y8mduaHh9Qusj0BE8wkIHUox5LWEIcLqUpSZIkSZJUUCK1N7BkCkCkDhb9utnM5gquYA5zADiVU3me52lIw4CTFazdOVlM3pTKR+uXM3HDcjbvywTg0ZaduaPZCQDszc0hN5xHOfdyUhHZnZPFZxtXUichmWMrHQHAjLT1tP/nWADKRMXQvnJNTqxSm5Oq1qF95ZruNfY77WQnDWjANrYxhjH0pnfQkSRJkiRJkkqUSO0NLJkCEKmDRb8thxyGMYxBDGIve4knnju4g4EMpCxlg45X4PLCYWZuW8/765ZxVYM2NChfAYBxqxdw5axPOaNGQy5IacafajQgKTY+4LQqaXZm72Xi+hX8Y90SPtu4kj25OVxRvzUvHvMnALLzchm+7Ec6ValNu4o1XNbxMA1mMPdzP81oxnzmE42/npIkSZIkSQUpUnsDS6YAROpg0aFZznKu4Rq+4AsAGtCAEYzgDM4IOFnR+Nusz3hh5U/572NDUXSuWoeeNRvR44hG+WWU9Htl5+Xyaup83l23hC82pZIdzss/V79cMn9r0JaBzdoHmLBkSiON+tQngwze4i3+wl+CjiRJkiRJklTiRGpvYMkUgEgdLDp0YcK8wzvczM2sZz0AZ3EWwxlOPeoFG66QhcNhftqxibd/Wcw/flnCsl3b88+FgM1/voEq8QnBBVRECYfDhEKh/J83+vR5Vu7eAcCRSVU4r1YTzq3dlNbJ1fKvU8EayECe4Ala05rZzCaKqKAjSZIkSZIklTiR2htYMgUgUgeLfr8MMniABxjOcHLIoSxluZu7GcAA4ikdS8gtzdjGxA3L+Wj9crLz8ph2yqX55/48bQKhEHStVo/TqtenaWIliwIBsDg9jTGp8/hk4wp+OLU38dExAIxe9TMb9+7m3FpNaZZUOeCUJd9GNtKABuxhDx/xET3oEXQkSZIkSZKkEilSewNLpgBE6mDRH7eABfSnP1/zNQCNacxIRtKNbgEnK1q54TyiQ/tnQezKyaLS+8MPWvKsdtlEulavx6nV6tK5ah1SEvzzUVrk5OUxa/tGvtycykfrl/P9tvX55yaccDbn1W4WYLrS6wZuYAQjOJ7j+Y7vCGEJLEmSJEmSVBgitTewZApApA4WHZ4wYd7kTW7lVjayEYDzOI9hDCOFlIDTFb28cJg5OzbxxaZUJm9axbStv7AvLzf//Lm1mvCPDucC+5dJW5SRRrPEykQ506nEmbh+OZfM+Ij0nH35x6JDIc6o0ZA+9VrSo2Yj4qKiA0xYOq1hDY1pTBZZfMEXnMqpQUeSJEmSJEkqsSK1N7BkCkCkDhYVjHTSuY/7GMEIcsklgQTu4A4GMICylA06XmD25GYzfes6Jm9axT83r6Z3vZZc16gdACt2bafRp89TKa4MHSvXpn3lmhxfqSbHVjqCpNjSsexgSbAjay//3Lyazzetomv1epx/YHbS4vQ0mk96kQqx8XSpVpdTq9XlvNpNqVGmfMCJS7cruIKXeZkudOGf/DPoOJIkSZIkSSVapPYGlkwBiNTBooI1l7n0pz/TmAZACik8wRP0opdLUv2bzzau5Lxv3yMzN/ug4yGgeVIVBrfolF9YqHjIysvlw/XLWJSexsL0rSxKT2N++hZyD/yTc0HtZrx9wtnA/plqc3ZsonWFavnLKSpYy1hGc5qTSy7TmU4HOgQdSZIkSZIkqUSL1N7AkikAkTpYVPDChHmLt7id21nLWgA60IHhDOdYjg04XfGSnZfLnB2bmL71F2Zs28CMtPWkZu4E4L0O53J2rSYA/HNzKoMXTM+f7dS+ck1qlk0MMnqJtSc3m4UHSqSF6Vs5okx5bmh8DLD/9yvh3aHk/MueWwDNEivTrXo9etZsTNfq9QJIrUNxCZfwBm9wBmfwMR8HHUeSJEmSJKnEi9TewJIpAJE6WFR49rCHoQzlUR4lk0wA/spfeZRHqUnNgNMVX5v27mbGtvV0qlKbSnH7lxocvGAa9y+cdtB1tcsmcnylmhxfuSaX1DnS0ukPCofDPL7ke37asZmfd2xmacY28vj//4QcW/EIZnbtnf/+ou8/oEx0DM0TK9M8qTJtKlQnJcG/84q7+cynFa0IE2Y2s2lL26AjSZIkSZIklXiR2htYMgUgUgeLCt861nEXdzGWsQAkkMBt3MYABlAe96c5FKt27+CrzauZsW0D36etY/7OrQcVIT+fdjmtKlQD4IN1S5m1fSMtkqvSIqkKTRIrERcVHVT0YiEzJ5sF6Vv5ecdm5u7cTAh4qu1p+ecbffIcK3bvyH9fOa4sRyVXoXliFY6uWJ0rG7QJILUK0rmcy3u8x/mczzu8E3QcSZIkSZKkUiFSewNLpgBE6mBR0ZnJTG7mZr7lWwBqUIPBDOZyLieGmIDTRZZdOVnM2r6RGWnrmb1jE+OO75m/70/vmRMZu3p+/rXRoRCNy1eicfmKNCxfgfuO7ESFuDLA/lk8oVDJ3Ctr5PJZTN2ylrk7N7MsY/tBpVyF2Hi2nXVT/tc+fOkPZOXl0rpCNVolV6NGmXIl9telNPqRHzmWYwkRYj7zOZIjg44kSZIkSZJUKkRqb2DJFIBIHSwqWmHC/IN/cAd3sIIVALSmNSMZSSc6BZyuZBi/ZiFfbl7NgvStLNi5lfScffnnQkDmuQMoE72/1Lvyx0/5fNMq6iQkUbts4v6PhERSyiZROyGRoyvUICYqKqCv5Lel7dvDvJ2bmbdzC/N2bmH93l1M7HRB/vnTp77FpE2r8t9XjU+gdXI1WlWoSuvkalxcp0Wx/dpUsE7ndCYxicu4LH9GpSRJkiRJkgpfpPYGlkwBiNTBomBkkcUoRjGYwWxnOwCXcilP8ARHcETA6UqOcDjMuj0ZLExPY8Xu7Wzem8l9Lf5/mdf5q3FM3br2Vz9/33m35S+1d/2cz5m29Rcqx5WlclxZKsaVoWx0DGWiYygbHcPdzTvkz6aasnk1azLTCYVChIAQIUKh/T+GCXNhypFEHZgp9OmGFSxI30p2Xh7Z4Vyy8/LIytv/4+7cbEa0PS0/w30LvmHCL0tI27eHTft2/0feLX++gSrxCQC8tXYRazPTaZlcldYVqlGjjEszlkbf8A0ncRIxxLCEJTSgQdCRJEmSJEmSSo1I7Q1cd0sq5uKI40Zu5BIu4W7u5kVe5HVe50M+ZBjD6Etf9tcTOhyhUIjaCUnUTkgC6v/H+bdPOJuVu3ewNjOdX/Zk8EtmBmv3pPNLZgb78nIP2stpUXoaP+3Y/N+fA9zbvGP++6eXz+K9dUt/Ndd5tZoSf2A21bg1Cxm3ZsGvXvvIUZ2pHF8WgM17M1mYvjX/XP1yybRMrkrL5Gq0TK6aP0MLoFdK81+9p0qHMGHu5m4A+tHPgkmSJEmSJEmHxJJJihBVqMLzPM+VXMm1XMsP/EA/+vE2b/MiL5JCStARS7TqZcpRvUw5Tqhc639eO7xNV9ZmppOWtYe0rD3syNrH3rwc9ubmkBPOO2gPo7YVqpOZk02Y/d/oD4cP/Hjg/L/uj9SpSm2iQhAbiiY2KorYqCjioqKJDUVTPiaWuH9Z0u76xu34S0ozkmLjaVK+Iomx8QX1S6ESaDKT+YZviCeee7gn6DiSJEmSJEmKEC6XF4BInfam4iOXXIYxjHu4h33sI5FEhjKUK7jCWU2Sfpc88mhPe37gB27iJoYxLOhIkiRJkiRJpU6k9gbu5C5FoGiiGcAAfuZnOtCBDDK4iqvoTndWszroeJIiyDCG8QM/UI5y3MmdQceRJEmSJElSBLFkkiJYU5oylak8yZOUoQyTmcxRHMUoRpFHXtDxJBVzP/JjfrE0lKFUo1rAiSRJkiRJkhRJLJmkCBdNNDdzM3OZSyc6sYtdXMu1nMiJLGBB0PEkFVPppHMhF5JNNudxHldxVdCRJEmSJEmSFGEsmaQSojGN+ZqveZqnKU95vuVb2tKWQQxiL3uDjiepGAkT5lquZQUrqEMdXuRF93OTJEmSJEnS72bJJJUgUURxPdezkIX0pCfZZPMgD9Ka1kxhStDxJBUTr/Ea4xhHNNG8yZtUpGLQkSRJkiRJkhSBLJmkEiiFFD7gAyYwgSM4gqUspQtd6Ec/trEt6HiSArSCFfSnPwCDGUwHOgScSJIkSZIkSZHKkkkqoUKEOI/zWMhCruZqAEYzmqY0ZTSjySMv4ISSiloOOVzKpexiFydxEndwR9CRJEmSJEmSFMEsmaQSrgIVGMUopjGNFrRgK1vpRz860pHZzA46nqQi9BAP8T3fk0wyYxlLNNFBR5IkSZIkSVIEs2SSSomOdGQOcxjKUMpTnu/5nmM4hv70Zzvbg44nqZB9y7c8yIMAjGIUdakbcCJJkiRJkiRFOksmqRSJJZZbuIUlLOFiLiZMmGd5liY0cQk9qQRLJ51LuZQ88riUS7mIi4KOJEmSJEmSpBLAkkkqhWpSk3GM4yu+4kiOzF9C7wRO4Fu+DTqepAJ2PdezilXUpS4jGRl0HEmSJEmSJJUQlkxSKXYyJ/MTPzGUoSSSyExm0pGOXMiFrGZ10PEkFYC3eIuxjCWKKF7ndZJJDjqSJEmSJEmSSghLJqmU+78l9JaylCu4ghAh3uItmtKUu7mbDDKCjijpD1rLWq7magDu4i460SngRJIkSZIkSSpJLJkkAVCDGrzIi8xmNl3owj728QiP5O/XlEtu0BEl/Q655HIZl7GDHRzHcQxiUNCRJEmSJEmSVMJYMkk6SBva8CVf8j7v04hGbGQj/ejH0RzNZ3xGmHDQESUdgiEM4Wu+phzlGMc4YokNOpIkSZIkSZJKGEsmSf8hRIizOIsFLGAoQ0kmmbnM5U/8ia50ZRazgo4o6TfMYhb3ci8AT/M0jWgUcCJJkiRJkiSVRJZMkn5VHHHcwi2sYAW3cAtxxPFP/skxHENf+rKBDUFHlPRvMsnkEi4hm2zO5Vz60jfoSJIkSZIkSSqhSlzJtHnzZiZOnMigQYP405/+RJUqVQiFQoRCIfr06XNY987MzKRBgwb596tXr16BZJaKu8pUZihDWcISLuESAMYwhiY04QmeYB/7Ak4o6f/cyq0sYQk1qckLvECIUNCRJEmSJEmSVELFBB2goFWvXr3Q7j1o0CBWrVpVaPeXirt61ON1Xuc6ruNGbmQmMxnIQMYylld4hWM5NuiIUqn2IR/yHM8BMJaxVKZywIkkSZIkSZJUkpW4mUz/KiUlhW7duhXIvebMmcPw4cMpU6YMiYmJBXJPKVK1pz3f8R2v8irVqMYCFtCe9tzBHexlb9DxpFJpIxvpRz9g/2ymUzk14ESSJEmSJEkq6UpcyTRo0CA++ugjNm7cyJo1a3j++ecP+565ublceeWV5Obmctddd1GpUqUCSCpFtiii+Ct/ZQELuJiLySOPx3mctrTle74POp5UquSRRx/6sJWttKY1D/Nw0JEkSZIkSZJUCpS4kmnw4MH06NGjQJfNe+qpp5g1axZNmzZl4MCBBXZfqSSoQhXGMY73eZ8a1GAxi+lIRwYwgD3sCTqeVCqMZCSTmEQZyvAGbxBPfNCRJEmSJEmSVAqUuJKpoK1evZpBgwYBMGrUKOLi4gJOJBVPZ3EWC1jAZVxGHnkMZShtaMNUpgYdTSrR5jOf27kdgCEM4UiODDiRJEmSJEmSSgtLpv/h2muvZffu3Vx22WV06dIl6DhSsVaJSoxlLB/xETWpyVKW0pnOXM7lpJEWdDypxNnLXi7mYvaxjzM4g2u5NuhIkiRJkiRJKkUsmX7D+PHj+eSTT6hYsSJDhgwJOo4UMXrQgwUs4CquAuAVXqEpTRnDGMKEA04nlRx3cRfzmEdVqjKa0YQIBR1JkiRJkiRJpYgl06/Yvn07N910EwCPPfYY1apVCziRFFkqUIHneZ7pTOcolb0ePQAAIABJREFUjiKNNPrSly50YTGLg44nRbzP+ZxhDANgNKOpTsHtRShJkiRJkiQdCkumX3HbbbexadMmTjjhBK688srDute+fftIT08/6EMqLTrQgdnM5nEepyxl+ZqvaUUr7uVe9rAn6HhSRNrKVvrQB4BruZYe9Ag2kCRJkiRJkkolS6b/YurUqYwePZqYmBiee+45QqHDW37o0UcfJTk5Of8jJSWlgJJKkSGWWG7ndhaykDM5k2yyeYiHaE5zJjDBJfSk3yFMmCu4gg1soBnN+Dt/DzqSJEmSJEmSSilLpn+zb98+rrrqKsLhMDfeeCOtWrU67Hveeeed7Ny5M/9j7dq1BZBUijz1qMdHfMQEJpBCCqtZzQVcwKmcylzmBh1Piggv8RIf8AGxxPIGb5BAQtCRJEmSJEmSVEpZMv2bhx9+mCVLlpCSksL9999fIPeMj48nKSnpoA+ptAoR4jzOYzGLGcQgylCGr/iKtrSlP/1JIy3oiFKxtZSl3MT+/QIf4RHa0jbgRJIkSZIkSSrNYoIOUNw8/vjjAHTt2pWJEyf+12t2796d/+P48eMBqFatGqecckrRhJRKgAQSGMxg+tKX27mdd3iHZ3mWN3mTB3iAv/E3YokNOqZUbGSRxcVcTCaZnMIp3MItQUeSJEmSJElSKRcKh8MlejOU1NRU6tevD0Dv3r0ZM2bMb17/R/df6ty5M1OmTDmka9PT00lOTmbnzp3OapIOmMIUbuTG/GXzmtCER3iEczmXEIe3L5pUEtzFXTzKo1SkInOZS21qBx1JkiRJkiRJBSRSewOXy5NULJzMycxiFs/yLFWowlKWcj7ncwInMJWpQceTAjWVqTzGYwC8yIsWTJIkSZIkSSoWLJn+TTgc/p8fdevWBaBu3br5xw51FpOkXxdDDNdwDStYwSAGUY5yzGAGnelMD3owj3lBR5SK3A52cCmXEiZMX/pyHucFHUmSJEmSJEkCLJkkFUNJJDGYwSxnOddwDdFE8zEf05rW9KEPq1gVdESpSIQJcw3XsJa1NKQhT/FU0JEkSZIkSZKkfDFBByho06ZNY/ny5fnvt27dmv/z5cuX/8eeTH369CmiZJJ+rxrU4Fme5SZu4m7uZgITeJVXGcc4+tGPu7mbFFKCjikVmnGMYzzjiSaacYwjkcSgI0mSJEmSJEn5QuFwOBx0iILUp08fXn311UO+/o98+fXq1WP16tXUrVuX1NTU3/35kbqBlxS0mczkHu5hMpMBiCOO/vTnPu4jmeSA00kFaxWraE1rMsjgAR7gXu4NOpIkSZIkSZIKSaT2Bi6XJyliHMdxfM7nTGUqXehCFlkMYxhNaMIYxpBHXtARpQKRQw6XcRkZZNCRjtzJnUFHkiRJkiRJkv5DiZvJFAkitZGUiptJTOJGbmQJSwBoT3te4AVa0jLgZNLheZAHGcQgEknkZ36mPvWDjiRJkiRJkqRCFKm9gTOZJEWs7nRnLnP5O3+nPOX5nu85mqMZxCD2sS/oeNIf8g3fcD/3A/AMz1gwSZIkSZIkqdiyZJIU0eKIYwADWMxizuZscsjhQR6kLW35lm+Djif9LmmkcTEXk0celx14SZIkSZIkScWVJZOkEqEWtXiXd3mHd6hGNRaxiE504gZuYBe7go4n/U9hwlzO5fzCLzSmMc/ybNCRJEmSJEmSpN9kySSpxAgR4nzOZxGL6EMfwoQZwQiO4ig+47Og40m/6Wme5kM+JI443uZtylM+6EiSJEmSJEnSb7JkklTiVKISr/AKk5hEPeqxmtX8iT9xPuezmtVBx5P+wyxmcRu3ATCUobShTcCJJEmSJEmSpP/NkklSidWNbsxjHjdxE1FE8Q/+QXOa8xAPsZe9QceTAEgnnV70IptszuEc+tM/6EiSJEmSJEnSIbFkklSilac8wxjGHOZwEiexhz3cy720oAUTmRh0PJVyYcJczdWsYAV1qMPLvEyIUNCxJEmSJEmSpENiySSpVGhFK6YwhTd4g5rUZCUr6UlPzuRMlrEs6HgqpV7hFd7kTaKJ5k3epCIVg44kSZIkSZIkHTJLJkmlRogQF3ERS1jCQAYSSyyf8AktaMGN3MgWtgQdUaXIQhZyHdcB8CAP0oEOASeSJEmSJEmSfh9LJkmlTnnK8xiPMY95nM7pZJPN0zxNQxryIA+yi11BR1QJN495dKMbe9jDaZzGQAYGHUmSJEmSJEn63SyZJJVaTWnKp3zKZCbTjnZkkMEgBtGIRjzHc2STHXRElUBTmMKJnMg61tGMZrzGa0T5z7EkSZIkSZIikN/VklTqdaUrM5nJeMbTgAZsYhPXcA0taMHbvE0eeUFHVAnxNm/Tne7sZCcd6ch0plOd6kHHkiRJkiRJkv4QSyZJAqKIohe9WMQiRjCCqlRlGcvoRS+O4ijGMY4ccoKOqQgVJsxjPEYvepFFFudyLpOZTCUqBR1NkiRJkiRJ+sMsmSTpX8QRx3VcxwpWcD/3k0wyi1jEpVxKc5rzCq+4jJ5+lyyy6Ec/7uROAK7net7mbcpSNuBkkiRJkiRJ0uGxZJKk/yKRRO7jPlazmod5mMpUZjnLuZzLaUxjnuM59rEv6Jgq5raxje505xVeIYooRjCCp3maaKKDjiZJkiRJkiQdNksmSfoNySRzF3eRSipDGEJ1qrOa1VzDNdSnPo/zODvYEXRMFUPLWMYJnMAUplCe8nzER1zHdUHHkiRJkiRJkgqMJZMkHYLylOdWbmUVq3iap6lNbTawgTu4gzrUYQAD+IVfgo6pYmIqU2lPe5aylBRSmM50zuCMoGNJkiRJkiRJBcqSSZJ+h7KU5XquZwUrGMMYWtCCDDIYylDqU5+/8lfmMS/omArQWMbSla5sYxvHcRwzmUkrWgUdS5IkSZIkSSpwlkyS9AfEEUdvejOPeXzMx5zMyeSQw2u8RitacTZns4xlQcdUEcohh1u5ld70JptsLuACpjCFGtQIOpokSZIkSZJUKCyZJOkwhAhxBmfwFV8xk5lcwAVEEcUHfEALWnArt7pnUymQRhqnczpP8iQAd3M34xlPWcoGnEySJEmSJEkqPJZMklRAjuVY3uZtFrCAMziDbLJ5kidpTGNGMYoccoKOqELwMz9zDMfwJV9SjnK8wzs8xENE+U+sJEmSJEmSSji/AyZJBawZzfiYj/mUT2lOc7aylWu5lja0YTKTg46nAvQ2b9OBDqSSSgMa8B3fcT7nBx1LkiRJkiRJKhKWTJJUSE7ndH7mZ0YwgkpUYgEL6EY3Tud0ZjAj6Hg6DLnkcgd30IteZJLJaZzGD/xAS1oGHU2SJEmSJEkqMpZMklSIYonlOq5jGcu4kRuJIYZJTKI97TmDM5jJzKAj6nfawhbO5Ewe53EAbuM2PuETKlEp4GSSJEmSJElS0bJkkqQiUIlKDGc4i1lMH/oQTTSf8inHczxnciY/8EPQEXUIvuIrWtOaSUyiLGV5kzd5gieIISboaJIkSZIkSVKRs2SSpCLUkIa8wisHlU2f8AnHcRw96MG3fEuYcNAx9W9yyGEQgziVU9nABprTnBnM4EIuDDqaJEmSJEmSFBhLJkkKQCMa5ZdNvelNFFF8zMd0pCPHcRyv8zpZZAUdU8Ba1nIKp/AgDxImTD/6uf+SJEmSJEmShCWTJAWqEY0YwxgWs5jLuZx44vmRH7mMy6hLXQYzmE1sCjpmqfUhH9KGNnzDNySSyBu8wUu8RDnKBR1NkiRJkiRJCpwlkyQVA41pzMu8zFrW8hAPUZOabGQj93M/dahDb3q7lF4RyiSTG7iBsziLbWyjHe2YzWwu4qKgo0mSJEmSJEnFhiWTJBUjVanK3dxNKqm8wRu0pz1ZZDGWsXSkI41pzGAGs5KVQUctsb7lW9rQhhGMAOBmbmY602lEo4CTSZIkSZIkScWLJZMkFUOxxHIRF/Ed3zGDGfSmN+UoxwpWcD/305CGnMiJvMiL7GBH0HFLhD3s4TZuoxOdWMYyalKTT/iEJ3mSeOKDjidJkiRJkiQVO6FwOOzaS0UsPT2d5ORkdu7cSVJSUtBxJEWI3ezmPd7jNV7jC74gjzwA4omnG904h3PoSU+qUCXgpJFnEpO4lmvzZ4j1pjfDGEZFKgacTJIkSZIkSaVBpPYGlkwBiNTBIqn4WMc63uANxjKW+czPPx5FFCdxEudwDmdzNnWoE2DK4m8jG7mZmxnPeABqUYtRjKInPQNOJkmSJEmSpNIkUnsDS6YAROpgkVT8hAkzn/m8d+D1Ez8ddL4d7bicy7mUS0nCv2/+z172MoxhPMIj7GIXUURxAzfwAA+QSGLQ8SRJkiRJklTKRGpvYMkUgEgdLJKKv1Ws4n3e5z3eYxrTCLP/r/jylOcSLuFv/I02tCFEKOCkwcghhwlM4A7uYDWrATiO4xjFKI7m6IDTSZIkSZIkqbSK1N7AkikAkTpYJEWWTWxiPOMZxSiWsCT/eEtachmXcQmXUJOaASYsOstZzmhG8yqvsp71ANSmNo/xGBdxEVFEBZxQkiRJkiRJpVmk9gaWTAGI1MEiKTKFCTOFKYxiFB/wAVlkARAiRCc6cS7ncg7nUJe6ASctWOtZzwQm8DZvM53p+ccrU5kbuIEBDCCBhAATSpIkSZIkSftFam9gyRSASB0skiLfdrbzDu8wlrEHFS8ArWlN9wOvjnQknviAUv4xYcIsZjETmciHfMh0pucvFxgiRHe6049+9KRnxH1tkiRJkiRJKtkitTewZApApA4WSSXLGtbwPu/zLu/yDd+QR17+ubKU5XiOp9OB13EcR0UqBpj2v9vEJqYceH3O56xk5UHnO9KRC7iA8zmfWtQKKKUkSZIkSZL02yK1N7BkCkCkDhZJJdcWtjCZyUxiEp/zORvZ+B/X1KUubWlLa1rT9MCrCU0oT/kiyZhBBgtYwA8HXjOZedBeUwDxxNOFLvSgB3/mz6SQUiTZJEmSJEmSpMMRqb2BJVMAInWwSCodwoRZxCKmM51pTGM601nBil+9vgpVSCGF2tTmCI4gmWQqUIHkf3lVoAKJJJJw4FWWsgDkHXjtZS8ZB1472MH6A691rGM5y1nMYtax7r8+vzWt6XLgdQqnFFnpJUmSJEmSJBWU/9fe3cfVeP9/AH+dOt2ne1IUkZKMKGKMmtnG3AxzM/uS2cyYm9mMfW0T28yXzYzv7A6TGSa3IzNiKyJLkpu5C7WEqCSU7j+/P/qe63dOndukOno9PXo8rtP1vt7X5xy9O6fzPp/PZax9AzaZ6oCx/rAQUcN1B3eQjGScwAmcwRlc+N+/bGTX6jhc4YpABKLL//51Qzc4w7lWx0BERERERERERFTTjLVvIK/rARARUf3nAAeE/O+fslzkIh3pyEAGruIqbuIm8jT8u4d7KPjfvxKUqOSxgAUa/e+fPezhBje4wx3N0Awt0RJ+8IMvfOvldaGIiIiIiIiIiIgaKjaZiIio2hz/968jOhp0XClKIYMMJjCBDLJHNDoiIiIiIiIiIiJ6lNhkIiKiWifn0w8REREREREREZHRM6nrARAREREREREREREREZHxYZOJiIiIiIiIiIiIiIiIDMYmExERERERERERERERERmMTSYiIiIiIiIiIiIiIiIyGJtMREREREREREREREREZDA2mYiIiIiIiIiIiIiIiMhgbDIRERERERERERERERGRwdhkIiIiIiIiIiIiIiIiIoOxyUREREREREREREREREQGY5OJiIiIiIiIiIiIiIiIDMYmExERERERERERERERERmMTSYiIiIiIiIiIiIiIiIyGJtMREREREREREREREREZDA2mYiIiIiIiIiIiIiIiMhgbDIRERERERERERERERGRwdhkIiIiIiIiIiIiIiIiIoOxyUREREREREREREREREQGY5OJiIiIiIiIiIiIiIiIDMYmExERERERERERERERERmMTSYiIiIiIiIiIiIiIiIyGJtMREREREREREREREREZDB5XQ+gpt26dQsJCQlISEjAsWPHcOzYMeTk5AAAwsLCEBERoTPHuXPncODAARw7dgynT5/GrVu3kJ2dDVNTU7i6uqJLly4YPXo0Bg0aBJlM9ojvERERERERERERERERUf3z2DWZXF1dHzrHggULsH79erX7UlNTkZqaisjISPTu3Rvbtm2Dk5PTQ5+TiIiIiIiIiIiIiIjImDx2TSZlHh4e8PPzw759+ww6Ti6XIzg4GD169MATTzyBpk2bonHjxsjNzcX58+fx/fff48yZM4iNjcXAgQNx6NAhmJhw5UEiIiIiIiIiIiIiImo4ZEIIUdeDqEnh4eHo0qULunTpAldXV6SlpcHLywuA/svllZaWQi7X3H8rKyvDiBEjsG3bNgDAzp07MXDgQL3HePfuXdjb2yMvLw92dnZ6H0dERERERERERERERI8fY+0bPHbTb+bPn48BAwY81LJ52hpMAGBqaopZs2ZJtw8ePFjtcxERERERERERERERERmjx67JVFtsbGyk7cLCwjocCRERERERERERERERUe1jk6maNm7cKG23bdu2DkdCRERERERERERERERU+7SvC0cqsrOzkZKSglWrVmHNmjUAAGdnZ7zyyit1PDIiIiIiIiIiIiIiIqLaxSaTDiEhIYiNjVW7z8nJCdu2bYODg0Mtj4qIiIiIiIiIiIiIiKhusclUTVOnTsWHH36IJk2a6IwtKipCUVGRdDsvLw8AcPfu3Uc2PiIiIiIiIiIiIiIiMg6KfoEQoo5HYhg2mXRYs2YN8vPzIYTAnTt3kJiYiG+//RYrVqxAamoqVq1aBVdXV605Fi5ciPnz51f5voeHx6MaNhERERERERERERERGZmcnBzY29vX9TD0JhPG1hYzUFpaGry8vAAAYWFhiIiIeOichYWFGD58OKKiouDh4YEjR46gefPmGuMrz2QqLy/H7du34ezsDJlM9tDjofrj7t278PDwwNWrV2FnZ1fXwyEiPbBuiYwTa5fI+LBuiYwTa5fI+LBuiYxTXl4ePD09kZuba1SX6OFMpmqwtLTEmjVr0KJFC1y9ehWzZs3Chg0bNMZbWFjAwsJC5XvG9ENChrOzs+OTOJGRYd0SGSfWLpHxYd0SGSfWLpHxYd0SGScTE5O6HoJBjGu09YiLiwt69OgBAPj1119RWlpaxyMiIiIiIiIiIiIiIiKqPWwyPYTGjRsDAAoKCpCVlVXHoyEiIiIiIiIiIiIiIqo9bDI9hGvXrknbtra2dTgSqi8sLCwQHh5eZXlEIqq/WLdExom1S2R8WLdExom1S2R8WLdExslYa1cmhBB1PYhHKS0tDV5eXgCAsLAwRERE1Ejea9euoVWrViguLkaLFi2QlpZWI3mJiIiIiIiIiIiIiIiMAWcyVXLx4kX88ccfWmPy8vLw8ssvo7i4GAAwZsyY2hgaERERERERERERERFRvSGv6wHUtLi4OFy6dEm6nZ2dLW1funSpykymcePGqdy+fv06+vTpg44dO+LFF19EYGAgmjZtCrlcjszMTBw+fBirV69GZmYmAKB9+/Z4//33H9n9ISIiIiIiIiIiIiIiqo8eu+Xyxo0bh7Vr1+odX/nux8TEIDQ0VK9jX3jhBaxZswaNGzc2aIxERERERERERERERETG7rGbyfSwevTogdjYWPzxxx+Ii4tDeno6bt68iYKCAtjZ2cHLywvBwcEYPXo0evToUdfDJSIiIiIiIiIiIiIiqhOP3TWZIiIiIITQ+6syMzMz9OrVC/PmzcP+/ftx8eJF5OXloaSkBDk5OUhMTMSKFSvYYHpMZGdnY/HixejRoweaNm0KCwsLuLu7Izg4GO+99x7i4+N15oiPj8eYMWPQsmVLWFpaws3NDc8//zx++eUXg8byyy+/4LnnnoObmxssLS3RsmVLjBkzBkePHq3u3SN6bISEhEAmkxn0FRMTozHf77//jqFDh6J58+awsLBA8+bNMXToUPz+++96j6m0tBTff/89evXqhcaNG8PKygre3t548803cfbs2Rq410SPj+LiYqxevRrPP/883NzcYGFhAVtbW/j6+mL8+PF6P9exdolqT2FhIb755hv06dMHjRs3hrm5OZo1a4YXXngBmzZt0jsPXysTPbxbt24hKioKc+fORb9+/eDi4iK95q18CQB91Kfn05ycHISHh6Njx46wt7eHnZ0dOnbsiPDwcOTk5Bh834jqk5qo3fLycpw9exYRERGYPHkyunTpAgsLC73+7lWnoKAAn3/+Obp27QonJyfY2trCz88PM2fORHp6ut550tPTMXPmTPj5+cHGxgZOTk7o2rUrvvjiCxQUFBg0JqL6pCbqtrCwEL/++iumTp2K4OBgODk5wczMDE5OTujevTvmzZuHGzdu6D0mo6hbQdRARUZGCmdnZwFA49fgwYO15pg/f74wMTHRePzAgQPFgwcPtOZ48OCBGDBggMYcJiYm4uOPP67Ju05kdHr37q21VtXVTUZGRpU85eXl4o033tB67BtvvCHKy8u1jic7O1sEBwdrzGFhYSFWr179qB4OIqOSnp4unnjiCZ11O2PGDI21x9olql3nz58Xvr6+Wmvu+eefF/fv39eah6+ViWqGtloMCwvTO099ez5NSEgQbm5uGvO4u7uLY8eO6X3/iOqbmqjdiIgIrXn+/PNPvcdz6dIlrc/v9vb2Yvfu3TrzREVFCXt7e415fH19xeXLl/UeF1F98rB1e/LkSdGoUSOdf/82atRIbNq0SWc+Y6lbNpmoQVq7dq30B2+TJk1EeHi4iI6OFsePHxe7d+8Wy5cvF3379hUvvfSSxhwrV66UCrF169Zi9erVIiEhQezYsUOEhoZK+1555RWtYxk9erQUGxoaKnbs2CESEhLE6tWrRevWraV9K1eurOmHgchoXLlyRZw+fVrr16ZNm6R66du3r9o8c+bMkWI6deokNm7cKBISEsTGjRtFp06dpH0ffPCBxrGUlpaKXr16SbFDhw4Ve/bsEX/99ZdYvny5aNKkiQAgTE1Nxe+///6oHhIio1BSUqLSYOrQoYOIiIgQ8fHxYt++fWLu3LnCxsZG2r948WK1eVi7RLXn1q1bwsPDQ6qV4cOHi6ioKJGUlCSioqLE8OHDVZpEmvC1MlHNUX4TyMPDQzz77LPVajLVp+fTjIwM4erqKgAIuVwuZs2aJQ4ePCgOHjwoZs2aJeRyuQAgXF1d1X54jMgY1ETtrlmzRjrGzMxMdOrUSeX1tb5Npnv37om2bdtKx02YMEEcOHBAHDlyRCxYsEDY2toKAMLa2lqcPHlSY57k5GRhbW0tAAhbW1uxYMECceTIEXHgwAExYcIEKX/btm3FvXv39BobUX3ysHV76NAhKb5Hjx5i4cKFIjo6WiQlJYm9e/eKiRMnClNTU+m58rffftOYy5jqlk0manDOnj0rLCwsBADx1FNPiTt37miMLSoqUvv93Nxc4eDgIAAIT09PkZWVpbK/tLRUDBw4UCrS2NhYtXliYmJU/kgvLS1V2Z+VlSU8PT0FAOHo6Chyc3MNvLdEDcesWbOkelq3bl2V/SkpKdIfq0FBQaKgoEBlf35+vggKCpL+0L106ZLa8yi/yJ88ebLa89jZ2QkAok2bNqKkpKRm7iCREdqyZYtUL927d6/yPCeEEImJicLMzEx6rqtcM6xdotr11ltvSbUSHh6uNmbu3LlSzNatW6vs52tlopo1d+5csWvXLpGZmSmEECI1NdXgN6rr2/NpWFiYlCcyMrLK/sjISGn/q6++qtd9JKpvaqJ2//rrL7Fs2TIRHx8vzf4NDw83uMmkfIy6D3YdOXJE+h0RGhqqMU9ISIj0e+LIkSNV9i9evFg6z/z58/UaG1F98rB1e/jwYTFixAjx999/a4zZsWOHkMlk0oexNM0gNqa6ZZOJGpw+ffoIAMLFxaXKH7z6Ui6+jRs3qo25evWq1JkeMGCA2pj+/ftLneurV6+qjdm4caN0ri+++KJa4yV63JWVlYlmzZpJn8rIz8+vEjN58mSpluLj49XmiY+Pl2KmTJmiNqZdu3bSm1nqziOEEAsXLpTybNmypfp3jMjIzZgxQ6qFnTt3aowbMmSIFHf69GmVfaxdotpTWloqNYdatGihtjGsiFM0d4KCgqrs52tlokerOm9U16fn08zMTKn+n3vuOY1jfu6556TfAYo3+4iMWXVqVx1Dm0zFxcXS87ufn58oKytTGzdx4kQpb2JiYpX9CQkJ0v6JEyeqzVFWVib8/Pyk3xPFxcUG3Tei+qam6rayYcOGSXmTkpKq7De2ujUBUQNy/vx5HDhwAAAwZcoUuLi4VCvPjh07AAB2dnYYOnSo2pjmzZvjmWeeAQBER0fj/v37Kvvv378vjaVv375o3ry52jxDhw6FnZ0dAGDbtm3VGi/R4+7AgQO4du0aAOCll16CtbW1yn4hBH799VcAQNu2bdGtWze1ebp16wZfX18AFXUuhFDZn5KSIl3IeOTIkVXOo6B8MUjWLTVkxcXF0narVq00xrVu3VraLioqkrZZu0S1KyUlBXfu3AFQ8frU1NRUbZypqSn69u0LAEhMTERaWprKfr5WJqpf6tvz6c6dO1FWVgYAePXVVzWOW5GnrKwMO3fu1BhHRNrFxMRIz+9hYWEwMVH/drCu2lU8vwOaa9fExARjx44FAOTm5iImJqaaoyZ6vIWGhkrbly9frrLf2OqWTSZqUDZv3ixtDx8+XNrOzc1FSkoKcnJydOYoLi5GQkICAKB79+4wNzfXGNu7d28AFW+YHTt2TGVfQkKC9EaaIk4dc3Nz6Y+AhIQElJSU6BwjUUPz008/SduKJ0ZlqampUhNKW70p78/IyKjyptmhQ4eqxKnTtGlT+Pj4AADi4uK0D57oMaaoAwC4cuWKxjjFi2qZTIY2bdpI32ftEtWu27dvS9uurq5aY5X3Hzx4UNo7GfSdAAAgAElEQVTma2Wi+qe+PZ/qm0d5H5+XiapP35oLCgqCjY0NAO21a2Njg8DAQI15WLtEuil/uFJdA8nY6pZNJmpQjh49CgCwt7eHn58f1q9fj44dO8LJyQk+Pj5wcXFBq1atMH/+/CqfplRISUlBaWkpgIpPgWmjvP/cuXMq+5Rv65untLQUKSkpWmOJGpr79+9j+/btAABPT0+EhIRUialOvVU+rrp5rl69ivz8fK2xRI+rl19+WZphsGjRIulTy8pOnDiB3bt3AwBGjRolxQOsXaLapvgDFQDy8vK0xirvV8xsAPhamag+qm/Pp4o89vb2aNq0qcYcbm5u0uuCymMhIv3pW7tyuVxaYUBdzSm+5+3tDblcrjGPtt8jRFQhNjZW2lZXl8ZWt2wyUYOi+AO4ZcuWmDp1Kv71r3/h1KlTKjGpqamYN28eunfvjuvXr1fJcfXqVWlb07IdCh4eHmqPq8k8RA3d1q1bpT9cx4wZA5lMViWmLutWCIGMjAytsUSPq8aNGyMiIgJWVlY4fPgwunTpgp9++glHjx7F/v37MX/+fPTu3RvFxcUICAjAl19+qXI8a5eodnl7e8PMzAyA6uwkdZT3p6enS9t8rUxU/9S351NFHl05lPOwtomqT1E/NjY2cHBw0BqrqLmsrCyVmRaFhYXIzs4GoLt2HR0dpQ+usHaJqjp58qT0QUt/f3+0a9euSoyx1S2bTNSgKJYAOX/+PFasWAEHBwd89913uHXrFgoLC3Hs2DH069cPAHDmzBkMHz4c5eXlKjnu3bsnbdva2mo9n/KnQSvPjKqpPEQNna6l8gDWLVFdGjJkCBITE/Haa68hOTkZYWFh6N69O/r27Yt58+bB2toaX375JeLi4qp8mpm1S1S7bGxs0KdPHwDAqVOnsHHjRrVxGzduxOnTp6XbyjXGuiWqf+pbXSry6MqhnIe1TVR91ak5QLXuDKl/5TysXSJVRUVFeP3116VVPj777DO1ccZWt2wyUYOimO1QVFQEU1NT7NmzBxMnTkTjxo1hYWGBoKAgREVFSY2mI0eOVLloWmFhobStbY15ALCwsJC2Hzx48EjyEDVkGRkZ0gUJu3XrpnL9F2WsW6K6U1JSgg0bNmDXrl1VLiAOADdv3sTGjRvVXlyUtUtU++bPny8tpREWFoZPP/0U6enpKCkpQXp6Oj799FOEhYWp1JJyrbBuieqf+laXijy6cijnYW0TVV91ag6o/vO7ch7WLpGqKVOmIDExEUDFa+1BgwapjTO2umWTiRoUS0tLaXv48OHSRYKVmZiY4PPPP5duV/4Ep3KO4uJiredTnqJoZWX1SPIQNWQ///yzNNswLCxMYxzrlqhu5Ofn45lnnsGCBQuQk5ODWbNm4dy5cygqKkJeXh727duHnj174tixYxg4cCCWLVumcjxrl6j2de3aFatXr4a5uTlKSkrw0UcfoUWLFjA3N0eLFi3w0Ucfoby8HEuWLJGOadSokbTNuiWqf+pbXSry6MqhnIe1TVR91ak5QLXuDKl/5TysXaL/t3DhQqxatQoAEBgYiBUrVmiMNba6ZZOJGhTlP4AVs5XU8ff3R7NmzQAAx44d05hD1/RB5QucVp6WWFN5iBqydevWAaj4tMXIkSM1xrFuiepGeHi4dN2W1atXY9GiRWjbti3Mzc1hZ2eHvn374s8//0RoaCiEEHjnnXdUrpXI2iWqG2PHjkVCQgKGDx+uUj8mJibo06cPDh8+jJCQEOn7jo6O0jbrlqj+qW91qcijz3I8ijysbaLqq07NAap1Z0j9K+dh7RJV+P777zFnzhwAgK+vL/bs2aOyzF1lxla3bDJRg6J8EVN9L1R669Ytle8rH6frguDKF0pTPndN5iFqqBITE3H27FkAwIABA1Te4KqsLutWJpPpdVFjoseNEAJr1qwBAPj4+GicbSiXy/HJJ58AAMrLy6VjANYuUV3q2LEjIiMjkZubi6tXryIlJQX37t3D/v37ERwcrNIQVr5YMV8rE9U/9e35VHFbVw7lPKxtoupT1Fx+fj7u3LmjNVZRc4rLSihYWlrCxcUFgO7azc3Nld6sZu0SVaySNXnyZABAixYtsH//fjRu3FjrMcZWt2wyUYPi7+8vbSsusKaJYr9iTXoFHx8fmJqaAgDOnz+vNYfyfj8/P5V9yn+M65tHLpfD29tbayxRQ/HTTz9J29qWygOqV29AzdSth4eH1k+nED2ubt68idu3bwMAOnXqpDU2MDBQ2lauLdYuUd0zNTVF8+bN4e3tDWtra+n7cXFx0nZwcLC0zdfKRPVPfXs+VeTJy8tDZmamxhw3btzA3bt31Y6FiPSnb+2Wlpbi8uXLANTXnOJ7ly5dQmlpqcY82n6PEDU0O3fuxNixY1FeXg43NzccOHBArw8zGlvdsslEDUqvXr2kbUUBanLlyhUAkJbNUzA3N0fXrl0BAPHx8VrXtIyNjQVQsZRXUFCQyr4uXbpIF11TxKlTXFyMo0ePVjmGqCErKSnBL7/8AqDikxralr8EAC8vL7i7uwPQXm8ApKW9mjVrhpYtW6rs69mzp7StLU9mZiYuXrwIAOjRo4fW8xE9rpQ/pKHtxSxQUdPqjmPtEtVPxcXF2LJlC4CKmnvyySelfXytTFT/1LfnU33zKO/j8zJR9elbc4mJidJMBm21m5+fj+PHj2vMw9olqnDgwAGMGDECpaWlcHZ2RnR0NFq3bq3XscZWt2wyUYMyaNAgmJmZAQC2bdumMS42NhY5OTkAgKeeeqrK/hdffBEAcPfuXY15MjIysH//fgBAnz59VNbBBCrWxezTpw8AYP/+/RqnLW7btk369NaQIUM0jpmoIdmzZw+ysrIAAKNHj64y47AymUyGwYMHA6j4dIbizajKjh49Kn16Y/DgwZDJZCr7fXx8pE90REZGoqCgQG2eiIgIaZt1Sw2Vk5MT7OzsAFS80ayt0aT8gtbLy0vaZu0S1U/Lli2TnofffPNNaeaSAl8rE9Uv9e35dNCgQTAxqXg7SnmZXE15TExMMGjQII1xRKRdSEgI7O3tAQBr166FEEJtnK7aVTy/A5prt7y8XFp1xMHBAaGhodUdNpFRO3LkCAYPHoyioiLY2dlh7969Kits6WJ0dSuIGphJkyYJAAKA2LhxY5X9d+/eFQEBAVJMQkJClZicnBxhb28vAIgWLVqI7Oxslf2lpaVi4MCBUo4//vhD7VgOHDggxQwaNEiUlpaq7M/KyhKenp4CgHBwcBC3b99+iHtO9PgYNmyYVDvHjx/X65gLFy4IuVwuAIigoCBRUFCgsr+goEAEBQUJAEIul4uLFy+qzbN69Wrp3G+99VaV/ZcuXRJ2dnYCgGjdurUoKSkx/A4SPSZefvllqV7mzZunNub27duiXbt2UtzevXtV9rN2iWrfP//8o3Hfzp07hZmZmQAg2rRpIx48eFAlhq+ViR6t1NRUqTbCwsL0Oqa+PZ+OGTNGyrN58+Yq+yMjIw2+j0T1XXVqV53w8HApz59//qnXMR999JF0zOLFi6vsP3LkiPQ7onfv3hrzPPXUU9LviSNHjlTZv3jxYuk84eHhet4jovqrOnV74sQJ4eDgIAAIGxsbERcXV61zG1Pdms6bN2+e4a0pIuPVtWtXbNq0CXl5efj111+RlZUFKysr3L59G/v27cO4ceNw5swZAMCkSZPwxhtvVMlhZWUFR0dHREVFIS8vD1u3bkWjRo1QVlaGxMREvPXWW9i7dy8A4OWXX8bMmTPVjsXLywsXLlzAmTNncOHCBRw6dAiOjo64d+8e9u7di7CwMKSlpQEAvvrqK5WpkkQNVW5uLiZOnIiysjK0b98en3zyiV7HOTs748GDB4iLi8P169fx22+/wcHBAYWFhTh06BDGjx+PpKQkAMDs2bMxYsQItXk6dOiAAwcO4OrVqzh27BjOnDkDe3t73L59G9u3b0dYWBhu374NExMT/Pzzz/D19a2x+05kbPz9/bFmzRqUlJQgJiYGSUlJMDc3R1FREdLS0rBlyxaMGzcOly5dAlAxm2H+/PkqOVi7RLXPw8MDMTExKCoqQlFREW7duoX4+Hh8/PHH+PDDD1FeXg5HR0fs2rVL7YWB+VqZqGbFxcXhjz/+QHJyMpKTk5GYmIjo6GgAgK2tLUxMTKR9ycnJCAgIqJKjvj2fBgUF4eeff0ZBQQG2b9+OgoICWFpaIj09Hd988w1mzpyJ8vJyNG7cGJs2bZJmRxMZk5qoXaBipoJyXExMDC5cuAAAaNq0KTIyMqR99+/fh6enZ5UcQUFB2Lp1K3JychAdHY0bN27A1tYWN2/exLp16/DGG2+gsLAQVlZW2Lx5M5o2bap2LAEBAfjpp59QXFyMTZs2QSaTwczMDCkpKfjPf/6D//znPwAqZj5GRETAwsKiJh5KolrzsHV7+fJlhIaGSitkLV68GO3atcOtW7c0fgFQez1go6rbarWmiIzc2bNnhbe3t9SlVfc1fvx4UVxcrDXP3LlzhUwm05ijf//+aj/dqaygoED0799fYw4TExN++oNIybfffqv1kxzalJWVifHjx2ut/ddee02UlZVpzZOVlSW6dOmiMYe5ubn44YcfHuZuEj02oqOjhYuLi9a6AyCefvppjbMQWLtEtcvGxkZrvbVr104kJSXpzMPXykQ1IywsTOfzqPKXJvXt+fTo0aOiadOmGvM0bdpUHD161ODHi6i+qKnaNSSHtpkWKSkpok2bNhqPtbOzE7t27dJ5v3bu3CnNWFT35ePjI1JSUqrzkBHVuYet2zVr1hh0PKB99pCx1C2bTNRg3b9/X3z++eciODhYODk5CXNzc9G8eXMxcuRIjUt2qHP48GExevRo4eHhIczNzUWTJk1E3759xYYNGwwaz/r160Xfvn1FkyZNhLm5ufDw8BCjR49WO42RqCF78sknBQBhamoqrl27Vq0cu3fvFoMHDxbu7u7C3NxcuLu7i8GDB4vffvtN7xwlJSXim2++ET179hTOzs7C0tJStGrVSkyYMEGcOXOmWuMielxlZ2eLRYsWiZCQENG4cWNhZmYmrKyshJeXlxgxYoTYsWOHKC8v15mHtUtUOzZu3CheffVV4e/vL71ObtasmejXr59YvXq1zg9iKeNrZaKHV1NvVCvUp+fTrKws8eGHH4r27dsLW1tbYWtrK5544gnx4YcfVllqk8jY1LcmkxAV74UtWrRIBAUFCQcHB2FtbS18fX3FjBkzRFpamt73LS0tTcyYMUP4+PgIa2tr4eDgIIKCgsSiRYtEfn6+3nmI6pv61mQSwjjqViaEhqtGEREREREREREREREREWlgUtcDICIiIiIiIiIiIiIiIuPDJhMREREREREREREREREZjE0mIiIiIiIiIiIiIiIiMhibTERERERERERERERERGQwNpmIiIiIiIiIiIiIiIjIYGwyERERERERERERERERkcHYZCIiIiIiIiIiIiIiIiKDsclEREREREREREREREREBmOTiYiIiIiIiIiIiIiIiAzGJhMREREREREREREREREZjE0mIiIiIiIiIiIiIiIiMhibTERERERERFRttra2kMlkkMlkuH//fl0Pp868//77kMlksLCwQGpqal0Pp9Z8+umnkMlkMDMzw99//13XwyEiIiKiWsYmExERERHVS2lpadIb1zX1FRERUdd3i+qpgoICrF27FqNGjYKPjw8cHBwgl8tha2sLT09P9OrVC5MmTcKPP/6ItLS0uh4u1TMXL17E0qVLAQCTJk2Cl5dXHY+o9rzzzjtwc3NDaWkppk2bVtfDISIiIqJaxiYTERERERE1aJGRkWjZsiXGjRuHTZs2ISUlBXl5eSgrK0N+fj6uXr2KQ4cO4bvvvsNrr70GLy8vzJw5s66HTfXIv//9bxQXF8PCwgKzZ8+u6+HUKmtra7z77rsAgD/++AN79uyp4xERERERUW2S1/UAiIiIiIjUsbOzw1tvvaU1JiEhAceOHQMAuLu7Y8iQIVrj/fz8amx89Hj46quvMGPGDJXvtW3bFk888QScnJxQWFiImzdv4sSJE7h586YUc+fOndoeKtVTJ06cwPbt2wEAY8eOhZubWx2PqPZNnDgRCxYsQG5uLj766CP069evrodERERERLWETSYiIiIiqpecnJzw9ddfa42ZN2+e1GRq06aNzngiZUlJSdIMDAAICQnBf//7X7Rv315t/Llz57Bt2zb8+OOPtTVEo9CQr8MEAIsWLYIQAgB0NsYfV7a2thg7diyWLVuG48ePY//+/XjmmWfqelhEREREVAu4XB4RERERETVIixcvRnl5OQAgODgY+/bt09hgAipmwn3wwQdISUnBBx98UFvDpHosIyMDW7duBQAEBQWhY8eOdTyiuvP6669L28uWLavDkRARERFRbWKTiYiIiIiIGqR9+/ZJ2++++y7MzMz0Os7ExAReXl6PalhkRNauXYvS0lIAwMiRI+t4NHWrffv20pKke/bsQWZmZh2PiIiIiIhqA5tMRERERNRgREVFQSaTQSaTab1+U2ZmphSnKzYrKwsmJiaQyWR6XYslKioK48ePR9u2beHg4ABLS0s0b94cAwcOxKpVq1BSUmLQfbpx4wYWLlyIkJAQNGvWDBYWFnB0dESHDh3w9ttv4++//9Z6fPv27VXuq75fupYmvHTpEubOnYvu3bujadOmMDc3h4uLC4KCgjBnzhykp6frvG8DBgyQzhcVFQUAuHXrFhYvXozu3bvDzc0NpqamkMsNXwW8oKAAubm50u2aahplZ2dLY3ZxcZG+HxcXh7Fjx6JNmzawtraGs7MzunfvjiVLlqCgoECv3Dk5Ofjpp58wfvx4BAYGwsnJCWZmZrC3t4ePjw/Gjh0rPU6G+uuvv/Duu+8iMDAQrq6uMDc3R6NGjeDv749//etfWLduHfLz89Uea2trK91nTUvnKf+cnTlzBkBFnc2fPx8BAQFwdHSEtbU1fHx8MGnSJFy+fNmg8e/fvx8jR46Ep6cnLC0t4e7ujpCQEKxcuRKFhYUAgClTpuj986uvDRs2SNsvvviiznh1j9Xly5fx3nvvwd/fH3Z2dmjUqBHat2+P9957T69GjbrH9sqVK5g1axbat28Pe3t7WFlZoVOnTvjiiy9QVFRUJUdycjLGjx8PPz8/2NjYwNnZGX369MHmzZv1fSgAQPpdWVZWho0bNxp0LBEREREZKUFEREREZKTCw8MFAAFA9O7dW2f8nTt3hKmpqQAgHB0dRVlZmdq4DRs2SHl1xUZGRkpxo0aN0nju8+fPi65du6rkVffVqlUrkZSUpPO+lJeXiwULFghra2ut+UxMTMSMGTNEaWmp2jz+/v46x6Tu67///a/afMXFxWL69OlCLpdrPd7CwkIsWrRI63184YUXpPhdu3aJ33//XTRu3LhKLlNTU52PV2UPHjxQyREZGWlwDnWysrKknM7OzqKsrEzMmDFD62Ph5eWl8/981apVOh9TxVePHj3EjRs39BpvZmamyuOs7cvf319tDhsbGynm3r17amOUf85Onz4t9uzZI5ydnTWey9zcXGzevFnn+EtKSkRYWJjWcXfu3FmkpaWJt956S+fPryEuX74s5fPw8NDrmMqP1dq1a7XWsL29vTh06JDWnJUf219++UXlPJW/evbsKe7fvy+EqPg9Mn36dK2P34QJE0R5eble9y86Olo67umnn9brGCIiIiIyboZ/5I+IiIiIyEjZ29sjICAAx48fR25uLk6ePIlOnTpViYuJiVG5rW9sSEiI2vMmJCSgX79+uH37NgDA1NQUgYGBaNu2LSwsLJCeno5Dhw6hoKAAV65cQa9evRAbG4vOnTurzSeEQFhYGNatWyd9z9XVFd26dYOrqyvy8/ORmJiICxcuoLy8HEuXLsXNmzexfv36KrlGjx6N69evqz2Psrt376qcTyaTVYkpKirCCy+8gAMHDkjf8/T0RJcuXeDs7Iy8vDzEx8cjPT0dRUVFmD17Nu7cuYPPPvtM5/lPnDiBzz77DIWFhXB0dESvXr3QpEkTZGdnIy4uTufxlSlmuyju+9KlSzFkyJBqzYrSZt68eVi6dCmAims6BQYGwtTUFCdPnkRycjIAIDU1Fc888wzi4uKk5cYqu3HjhrQsW8uWLeHn54cmTZrAysoKd+/exZkzZ3Dq1CkAwOHDhxEaGorExETY2NhoHNulS5fQp08flVllLi4uePLJJ+Hq6oqioiKkpqbi+PHjKCgokGYEPawjR45g6tSpKC4uRrNmzdCjRw/Y29vjn3/+QUxMDIqLi1FcXIxXXnkF/v7+Gh8TABg7dqzKjBknJyeEhobC0dERV69eRUxMDJKSkjBo0CB06dKlRsavEB0dLW337NnT4OO3bNmC8ePHQwgBb29vdOnSBTY2NkhJScGhQ4dQXl6OvLw8DB48GOfPn0fjxo115oyJicHbb7+NsrIytGnTBsHBwTA3N8eJEydw4sQJABWz6iZMmIANGzbgnXfewbJlyyCTydC1a1e0a9cOpaWliI2NlX4uVq5cicDAQEycOFHn+Z988kmYmJigvLwccXFxePDgAaysrAx+bIiIiIjIiNR1l4uIiIiIqLoMnckkhBDvvvuudMySJUvUxvj4+AgAKrNmNMX6+flJMefPn6+yPycnR3h4eEgxQ4YMEWlpaVXisrKyxOjRo6U4b29vUVhYqPacixYtkuKcnJzEunXr1M5U2rlzp8pskdWrV2t7aDQqKysT/fr1U5l5k5WVVSVu0qRJUoynp6eIiopSm+vHH38UVlZWAoCQyWRi//79as+rPMNGMYtnzpw5VR4XTY+TLsozWwCI4OBgsX37dlFQUFCtfEKozmSSy+XCxMRE2NnZiR07dlSJPXDggGjSpIkU37VrV40zzn7++Wfx5Zdfin/++Ufjuc+ePSt69Ogh5Zs9e7bG2Pz8fPHEE0+ozJiJiIhQO2OvoKBAREZGitGjR6vNZehMJgsLC2FhYSFWrlxZ5XwXL14UXl5eUuzw4cM13of169er/P/NmDGjys/C9evXRZ8+faTzKmJrYibTq6++KuVbuHChXscoP1YWFhbC0dFR7c/G0aNHhZOTkxT73nvvacyp/Niam5sLGxsbsWnTpipxq1atEjKZTKq7pUuXCgDC19dXnDhxQiW2uLhYvPbaa1JeV1dXjT+blSl+fwIQhw8f1usYIiIiIjJebDIRERERkdGqTpMpKipKOmbgwIFV9l+/fl3ljV1FE0BdbGZmphTr5uam9nzTpk2TYl5++WWty06Vl5eLAQMGSPGrVq2qEnPjxg3pzXJLS8sqbw5XFh8fL0xMTAQA0bJlS73fKFb29ttvS2Oys7MTZ86cqRKTlJQkxTRp0kRrM0QI1WUGe/bsqTam8jJu77//vsFj1+batWsqTR7Fl6WlpXjyySfFtGnTxLp168Tly5f1zqncZFJ8RUdHa4w/duyYyjJ46poDhrh//75o0aKF1IDU1IBbuHChdE5ra2uRnJxc7XMa2mQCILZs2aIxX0xMjEojJj8/v0pMeXm5aNWqlRT36quvasxXUFBQ5fw10WQKDAyU8m3fvl2vY5QfK7lcLo4ePaoxNiIiQopt3ry5xrjK923Xrl0aY4cNG6YS6+TkJDIyMtTGFhYWCnd3dylWUzO4ssGDB0vHrFixQq9jiIiIiMh4mYCIiIiIqAF56qmnYGpqCgA4ePAgysrKVPb/+eef0nZoaCh69+6tMVbXUnl3797F6tWrAQBWVlb4+uuv1S4zpyCTybBw4ULptrrl7VasWIGioiIAwPTp0xEQEKAxHwB069YNQ4YMAQCkpaXh8OHDWuMrW716Nb766isAgImJCTZu3Ah/f/8qcV9++aW0PX/+fHh6emrNO3z4cAQGBgKoWL5Leck2dZycnBAeHm7Q2HVxd3dHdHQ0vL29Vb5fWFiII0eOYPny5RgzZgxat26NFi1a4P3338fVq1cNOsfQoUPxzDPPaNwfFBSE1157Tbq9cuVKw+5EJTY2NhgxYgQA4Pbt20hKSqoSU1ZWJv2fAhX/Xx07dnyo8xoiNDQUw4YN07i/d+/eaNWqFYCKJRgVywAqi42NxZUrVwAAFhYWWLx4scZ8VlZWei3JaKjU1FRpu3nz5gYfP2bMGAQHB2vcP2rUKFhbWwMAMjIykJmZqTNn3759MWDAAI37R44cqXJ75syZaNasmdpYCwsLvPjii9LtY8eO6Tw/AJV8yo8RERERET2e2GQiIiIiogbFzs5OurZSXl6edJ0SBUXjSC6Xo2fPnlLzSFssoL7JFBsbi/z8fADAs88+CycnJ53ja9++vXTtlaNHj0rX4VH47bffpO1Ro0bpzAcATz/9tLRtyPWLYmNjMWnSJOn2kiVL0L9//ypxQgjs2bNHul35jeyaGNeLL74IS0tLvfIaokOHDjh9+jS++uortGvXTmNceno6Fi1aBB8fH60NjcrGjh2rMyYsLEzajouLQ0lJidb47OxsREVFYfHixfj3v/+NadOmYcqUKdKXciNRcd0nZcnJybh58yaAikbChAkT9L07NWL48OE6Y5Svf5aWllZlv3Lt9e3bFy4uLlrz9e/fHw4ODnqPUZfS0lLpGmsA4OzsbHAOXY+DhYWFyvWo1D0OlWlr3gEVv1+qG69vw0j5/0KfxhgRERERGbeavaotEREREZERCAkJQWJiIoCKmUtBQUHSPsWb10FBQWjUqBFCQ0OlfZVjlWc9qWsyxcfHS9v//PMPpkyZotf4FE2GBw8eICcnB66urtLtkydPSnHffvstzMzMdOZLSUmRtvWdiXP58mUMGzZMGsuECRPw9ttva8yfk5MDoOKN8Y8++kivcyjPstE1LsWsp0fB0tIS06dPx/Tp03HhwgUcPHgQR48exYkTJ3D69GmVRl9hYSFmz56NmzdvYsmSJTpzd2ee6cQAAA/dSURBVOvWTWdMYGAgzMzMUFJSgsLCQpw/fx5PPPFElbhLly5h9uzZ2LVrl85GlEJ2dnaV7x09elTa7ty5M+zt7fXKVVPU3bfKlJs2eXl5VfYrN8+6du2qM59cLkenTp1UavZhKJrHClZWVgbnqInHoTJ1swyVOTo6SttyuRw+Pj56x9+9e1fn+QHVx6Ly40REREREjx82mYiIiIiowQkJCcEXX3wBoKKp9N577wEArl+/LjVkFE0jPz8/uLq64ubNmyqxmZmZuHDhAoCKZdfUvVl7/fp1aTs5OVntrBJdcnNzpSbTzZs3VZbs++GHH6qVT5e7d+9i4MCBUuMoJCQEK1as0BivfD+Lioq0xlZ3XIrZXY+ar68vfH19pdk9+fn52L9/P7799lvs3btXivvyyy8xaNAgaTlFdczNzaX/O20UcRkZGQCArKysKjGxsbHo378/CgoKDLo/9+7dq/I9xSwmANKydLVJn6aWcvNUXUNNuXmm71J1mpaFqwnalsHUpCYeB0NzyuX//xaAnZ2dznzK8fo2NoUQesURERER0eOBy+URERERUYOjfF2mQ4cOSTNVlJfgUp7BpGgkKMfqmsUE6DfzQBflWTQ1nU+dsrIyjBw5EufOnQMAeHt7Y+vWrVpnTNXGuKozU6Qm2NjYYPDgwfj999/x/fffq+xbvny51mMV19PR9zwKlRtDeXl5GD58uNRg8vDwwIIFC3Do0CFcu3YNBQUFKC8vhxACQgh8/vnn0rHl5eVVzqWc39bWVu8x1pTqNGQqu3//vrSt7+Os/Bg/rMq5DG3+ATXzODxMzkdxfqBitp9CTT7mRERERFQ/sclERERERA2OnZ0dOnfuDKDiDffjx48D+P/GkZmZGXr06CHFKxpOyrG6rscEqL7B+umnn0pNAEO+lK+JopzP3NwcZWVlBufbsmWL1sfm3Xffxe+//w6gYlbErl27dF5LSnlc3t7e1bqfipll9dkbb7yBIUOGSLcPHTqkNd6QxoPysmKNGjVS2bd27VppdpOfnx9OnTqFOXPmoGfPnnB3d4eVlZVKw0Dd7CVlyvmVmzXGRPlnTt/HuSaXbpPL5SpL2alblrChUp6J5+bmVocjISIiIqLawCYTERERETVIyo0hRXNJ0Tjq2rWrypvY6mL1mcmkvFSa8nWRqqtJkybSdnFxMdLT0x86p7KVK1di2bJlAABTU1NERkaibdu2Oo9Tvp/p6ekoKiqq0XHVJ/369ZO2s7KytM7AKi4uVlmaTt84FxcXlf0HDhyQtt9//304ODhozffPP/9o3a/8/5WamqpzfPWR8mOkWGZQl2vXrtXoGFq2bGnwGBoC5cdZ+TEiIiIioscTm0xERERE1CApN4ZiYmJw/fp1XLp0qco+AGjbtq30iXxFrKJp5O7ujjZt2qg9R3BwsLQdHR2tdukyQ9jZ2cHPz0+6rXyNoIcVExODt956S7q9bNkyPPvss3od6+fnJ13fpbi4WGWW1+PG0tJS2pbL5dKyi5rEx8frzHn8+HHpejeWlpYq/8eA6jWv/P39debTNcOqW7duKue+e/euzpz1TUBAgLSdkJCgM760tBQnTpyo0TF07NhR2lZcn42A8+fPS9vK/09ERERE9Hhik4mIiIiIGiTl6zLFxcVh37590j7l6zEpKK7LVDlW0ywmAHjmmWdgYWEBoKJREBkZ+dDjHjBggLS9fPnyh25cAcDly5cxbNgwqdExefJklYaTLnK5HM8995x0e+nSpQ89pvoqOTlZ2vbw8NB5XZt169bpzBkRESFt9+zZs8r1r0xM/v/PNl1Lw+3duxdXrlzRGhMQEICmTZsCAIqKirBy5UqdY6xvlOsuOjpa53J1v/32G+7cuVOjY+jatau0ffLkyRrNbawKCgqkZr2ZmRk6depUxyMiIiIiokeNTSYiIiIiapAaNWqEwMBAABXXalmyZAmAimsdPfnkk1XiFY0n5Vjl76vj5OSECRMmSLenTZum9/JkQgjcunWryvenT58uNa7Onj2LWbNm6ZUPADIzM6t8Ly8vDwMGDMDt27cBVDTGFEvmGUJ5HHv37sXXX3/9UOOqDZMnT0ZaWpre8ampqVi1apV0+/nnn9d5zLZt27B//36N+48fP44ff/xRuv36669XiWnVqpW0/euvv2rMdefOHUydOlXnmExNTTF9+nTp9ty5c3Hq1Cmdx9UnISEh8PLyAlDRKJs9e7bG2AcPHmDOnDk1PgblmX6HDx+u8fzG6MiRI1Lj+6mnnoKVlVUdj4iIiIiIHjU2mYiIiIiowVKeDXHmzBkAFUvcqXtjVF1s5e+rEx4ejhYtWgCouIZPcHAwNmzYgLKyMrXxmZmZWLFiBdq3b6/SfFBo1qwZPv30U+n2kiVLMGrUKI3Nq/LycsTExOC1116Dr6+vyr6ysjKMHDlSWt7K19cXmzdvhlwu13qf1AkKClKZ/TR16lRMnTpVbaMMqFhWb/fu3RgxYgT69Olj8Plqwg8//AAfHx+89NJL2LlzJx48eKA2rqysDFu3bkXPnj2lpeUsLCzwzjvvaM0vl8thYmKCYcOGYefOnVX2//nnn+jfv790XaegoCC89NJLVeKUZ68tW7YMq1atghBCJebMmTMIDQ1FSkqKyvXENJk2bZq09F5BQQF69+6NtWvXqp0ZV1hYiM2bN+Nf//qXzry1RSaTYf78+dLtH3/8Ee+++26V64HduHEDAwcOxN9//y01Z2uKl5cX2rVrBwC4evVqjVx3zdgpX6tO+eeWiIiIiB5fhv/1SERERET0mAgJCcHixYtVvqdpZpKPjw/c3d1Vro/TrFkzeHt7az2Hi4sLdu7cieeeew6ZmZnIysrCK6+8gmnTpqFbt25wc3NDeXk5bt++jb///huXLl2q0kCobObMmUhNTcU333wDANi0aRM2b96MgIAA+Pn5wdbWFvfu3UNGRgaSk5NVGiPKkpOTVa7r1KpVK3z44Ydaz60wYsQI9OrVS+V7X331FTIyMqTZNl9//TW+//57BAUFwdvbG9bW1sjLy0NqaipOnTolNXUqN79qU0lJCbZu3YqtW7dCLpejQ4cOaNWqFZycnFBWVobr16/j2LFjKsuxmZiY4LvvvtP5f29vb4/Jkyfjk08+weDBg9GuXTsEBQXBxMQEJ0+eVLlGkKOjIyIiItRe42nkyJFYvHgxTp06hdLSUkyYMAGff/45AgICYGNjg3PnzuGvv/6CEAI+Pj4YNWoUPv74Y61js7a2xrZt2/D000/j2rVruHPnDsaNG4eZM2eiR48ecHV1RVFREVJTU3H8+HHk5+ejdevWBj66j9aYMWMQFRUlLUP55ZdfYu3atQgJCYGTkxPS09MRExODoqIidOjQAV26dMHq1asBqC5B+DBeeeUVfPDBBwCAHTt24L333quRvMZq+/btACpmy40aNaqOR0NEREREtYFNJiIiIiJqsJ566inI5XJpJgmgffm7kJAQbNiwQeW2Pjp06IDjx49jwoQJ+O233wAAOTk52L17t8ZjXFxc4Ofnp3H/ihUr0KlTJ/z73/9GdnY2ysvLkZSUhKSkJLXxMpkMPXv2VPle5WbWnj179Lo/ANC2bdsqTSa5XI7t27dj4cKFWLhwIe7fv4+SkhLEx8cjPj5ebR5TU1N0795d7/PWpJEjR2LXrl24d+8eAKC0tFTrYwgA3t7e+Prrr1WuQaVNeHg48vLysHz5cpw9exZnz56tEtOiRQts3bpVmllUmVwux6+//op+/fpJs84uXryIixcvqsQFBQVh8+bN2LJli15j8/HxQUJCAsaNG4fo6GgAQHZ2tsYl+WxtbfXKW5t+/vlnmJub4+effwZQUVdbt25ViencuTO2bduGzz77TPpeo0aNauT8Y8eORXh4OEpLS7Fp06YG3WT6+++/ce7cOQAVS0m6ubnV8YiIiIiIqDawyUREREREDZatrS0CAwPx119/AaiY6dOtWzeN8aGhodVqMgGAu7s7du/ejcTERGzatAmxsbFIT0/H7du3IZfL4ejoCB8fH3Tu3BnPPvssnn76aZiZmWnN+frrr+Pll1/G+vXrER0djaSkJGRlZeHBgwewtbVFs2bN4O/vj169euGFF15Ay5Yt9R5vdclkMsyZMwdvvvkmfvrpJ+zfvx9nzpxBdnY2ioqKYGdnB09PT7Rv3x6hoaF44YUX4Orq+sjHpc769etRVFSEw4cP49ChQ0hKSsLFixdx48YN3L9/H+bm5rC3t4eXlxcCAgIwaNAg9O3bV+1sI01MTU2xbNkyDB06FCtXrkR8fDyuX78OKysrtGnTBsOHD8ekSZN0LnHXsmVLJCYm4ttvv8WWLVtw7tw5FBUVwdXVFf7+/hg1ahRGjRoFc3Nzgx4Dd3d37Nu3DwcPHkRkZCRiY2Nx/fp15OXlwdraGp6enujcuTP69++PF1980aDctcHMzAzr1q3D2LFj8cMPP+Do0aO4desWnJyc4OPjg1deeQVjx46FpaWldN0xAHBwcKiR8zdv3hwvvfQSfvnlFxw/fhzJyckICAiokdzGZuXKldK28jW/iIiIiOjxJhO61uIgIiIiIiIivWRnZ6Nx48YAAGdnZ5Vl9qhu+fr6SrO/UlJSdC53qK/k5GR07twZQgi8/vrrKs2WhuL+/fvw9PREbm4uOnfujOPHj9f1kIiIiIioltTMQtRERERERERE9dTJkyelBpOjo2ONXl8qICAAQ4cOBQCsW7cON27cqLHcxuKHH35Abm4uAOCTTz6p49EQERERUW1ik4mIiIiIiIgeW2VlZXj77bel26NGjYJMJqvRcyxcuBDm5uYoKirCf/7znxrNXd8VFBTgiy++AAA8/fTT6N+/fx2PiIiIiIhqE5tMREREREREZJQ+++wzLFmyBLdu3VK7PyUlBf369UNMTAyAiuuuTZs2rcbH0aZNG8yYMQMA8N133yE1NbXGz1FfLV26FDdu3IBcLsfy5cvrejhEREREVMt4TSYiIiIiIqIawmsy1a4pU6ZgxYoVMDU1RYcOHdC2bVvY2dkhPz8fZ8+eRXJyMsrLy6X4pUuXqsxqIiIiIiKihyOv6wEQERERERERPYyysjKcOHECJ06cULvfxsYGX3zxBd58881aHhkRERER0eONM5mIiIiIiIhqCGcy1a67d+9i586dOHDgAM6cOYOsrCxkZWWhrKwMTk5O8PPzQ58+fTBhwgTp/4WIiIiIiGoOm0xERERERERERERERERkMJO6HgAREREREREREREREREZHzaZiIiIiIiIiIiIiIiIyGBsMhEREREREREREREREZHB2GQiIiIiIiIiIiIiIiIig7HJRERERERERERERERERAZjk4mIiIiIiIiIiIiIiIgMxiYTERERERERERERERERGYxNJiIiIiIiIiIiIiIiIjLY/wF9ivhFREyd/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 2000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(20,8))\n",
    "colors, _ = misc.getColors(5)\n",
    "titles = ['Total-mean(U)', 'Interaction Energy', 'Kinetic Energy', 'PotentialEnergy']\n",
    "linestyles = ['--','--','-','-']\n",
    "vals = np.array(interactionEnergyVals) + np.array(kineticEnergyVals)+np.array(potentialEnergyVals)-np.mean(potentialEnergyVals, axis=0)\n",
    "for wfVals, name, color, ls in zip(vals[:-1], names, colors, linestyles):\n",
    "    ax.plot(trapDeltas*1e9,wfVals/mc.h*1e-3, label=name, linestyle=ls, color=color)\n",
    "ax.set_xlabel('Tweezer Spacing (nm)', fontsize=24)\n",
    "ax.set_ylabel('Energy (kHz)', fontsize=24)\n",
    "\n",
    "ax.set_title('2-Boson Calculations', fontsize=24)\n",
    "#ax.grid(alpha=1)\n",
    "ax.set_ylim(13,20)\n",
    "ax.set_xlim(550,1200)\n",
    "ax.tick_params(axis='both', which='major', labelsize=20)\n",
    "leg = ax.legend(fontsize=18);\n",
    "for text in leg.get_texts():\n",
    "    text.set_color(\"k\")\n",
    "\n",
    "fig.subplots_adjust(hspace=0.45)\n",
    "ax = axs[1,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "matplotlib.style.available"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.style\n",
    "matplotlib.style.use('Solarize_Light2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "DeltaLoad3d = np.load('Deltas.npy')\n",
    "VDeltaLoad3d = np.load('VDeltas.npy')\n",
    "xFreqLoad = np.load('xFreqs.npy')\n",
    "yFreqLoad = np.load('yFreqs.npy')\n",
    "zFreqLoad = np.load('zFreqs.npy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "import Miscellaneous as misc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x252b0823cf8>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "xf = xFreqLoad\n",
    "yf = yFreqLoad\n",
    "zf = zFreqLoad\n",
    "vDeltas = VDeltaLoad3d\n",
    "def ref(freqs):\n",
    "    return freqs[-1]\n",
    "colors, _ = misc.getColors(4)\n",
    "pltDeltas = DeltaLoad3d\n",
    "#ax.plot(pltDeltas*1e9, [(freq - ref(xf))/ref(xf) for freq in xf],'o', color=colors[0], label=r'$\\nu_x$')\n",
    "#ax.plot(pltDeltas*1e9, [(freq - ref(yf))/ref(yf) for freq in yf],'o', color=colors[1], label=r'$\\nu_y$')\n",
    "#ax.plot(pltDeltas*1e9, [(freq - ref(zf))/ref(zf) for freq in zf],'.', color=colors[2], label=r'$\\nu_z$')\n",
    "ax.plot(pltDeltas*1e9, xf*1e-3, 'o', color=colors[0], label=r'$\\nu_x$')\n",
    "ax.plot(pltDeltas*1e9, yf*1e-3, 'o', color=colors[1], label=r'$\\nu_y$')\n",
    "ax.plot(pltDeltas*1e9, zf*1e-3, 'o', color=colors[2], label=r'$\\nu_z$')\n",
    "ax2 = ax.twinx()\n",
    "ax2.plot(pltDeltas*1e9, vDeltas*1e9,'o', color='r', label='vDelta')\n",
    "ax2.plot(pltDeltas*1e9, pltDeltas*1e9,'-', color='r', alpha=0.5, label='Trap Delta')\n",
    "ax.set_xlabel('Delta (nm)')\n",
    "ax.set_ylabel('Freq (kHz)')\n",
    "ax.grid(alpha=0.1)\n",
    "ax2.set_ylabel('Variational Delta',color='r')\n",
    "ax.set_title(misc.round_sig_str(ref(xf))+', ' + misc.round_sig_str(ref(yf)) + ', ' + misc.round_sig_str(ref(zf)))\n",
    "ax.legend(loc='center right')\n",
    "ax2.legend(loc='upper center')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'dblInteractionEnergy' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-51-ca6e8ae9f450>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     15\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mintEnergyF\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mintEnergyVals\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0minteractionEnergies\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minteractionEnergyVals\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     16\u001b[0m         \u001b[0mintEnergyVals\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mintEnergyVals\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mintEnergyF\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mscatteringConstant\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0x\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0y\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0z\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdelta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 17\u001b[1;33m     \u001b[0mdblIv\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdblIv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdblInteractionEnergy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mscatteringConstant\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0x\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0y\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0z\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdelta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     18\u001b[0m     \u001b[0mmiIv\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmiIv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmiInteractionEnergy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mscatteringConstant\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0x\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0y\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0z\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdelta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     19\u001b[0m     \u001b[0msupIv\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msupIv\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msupInteractionEnergy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mscatteringConstant\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0x\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0y\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw0z\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdelta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'dblInteractionEnergy' is not defined"
     ]
    }
   ],
   "source": [
    "deltas = np.linspace(0.65e-6,0.8e-6,1000)\n",
    "wfDeltas = interpSpacing(deltas)\n",
    "wfXFreqs = xFreqInterp(deltas)\n",
    "wfYFreqs = yFreqInterp(deltas)\n",
    "wfZFreqs = zFreqInterp(deltas)\n",
    "\n",
    "wfWx = 2*np.sqrt(mc.hbar/(mc.Rb87_M*(2*np.pi*wfXFreqs)))\n",
    "wfWy = 2*np.sqrt(mc.hbar/(mc.Rb87_M*(2*np.pi*wfYFreqs)))\n",
    "wfWz = 2*np.sqrt(mc.hbar/(mc.Rb87_M*(2*np.pi*wfZFreqs)))\n",
    "dbl_vals, mi_vals, sup_vals, asup_vals, aMi_vals = [[] for _ in range(5)]\n",
    "dblIv, dblKev, miIv, miKev, supIv, supKev, asupIv, asupKev, aMiIv, aMiKev = [[] for _ in range(10)]\n",
    "interactionEnergyVals = [[] for _ in interactionEnergies]\n",
    "kineticEnergyVals = [[] for _ in kineticEnergies]\n",
    "for delta, w0x, w0y, w0z in zip(wfDeltas, wfWx, wfWy, wfWz):\n",
    "    for intEnergyF, intEnergyVals in zip(interactionEnergies, interactionEnergyVals):\n",
    "        intEnergyVals = np.append(intEnergyVals, intEnergyF(scatteringConstant, w0x, w0y, w0z, delta))\n",
    "    dblIv = np.append(dblIv, dblInteractionEnergy(scatteringConstant, w0x, w0y, w0z, delta))\n",
    "    miIv = np.append(miIv, miInteractionEnergy(scatteringConstant, w0x, w0y, w0z, delta))\n",
    "    supIv = np.append(supIv, supInteractionEnergy(scatteringConstant, w0x, w0y, w0z, delta))\n",
    "    asupIv = np.append(asupIv, aSupInteractionEnergy(scatteringConstant, w0x, w0y, w0z, delta))\n",
    "    aMiIv = np.append(aMiIv, aMiInteractionEnergy(scatteringConstant, w0x, w0y, w0z, delta))\n",
    "    \n",
    "    dblKev = np.append(dblKev, dblKe(w0x, w0y, w0z, delta))\n",
    "    miKev = np.append(miKev, miKe(w0x, w0y, w0z, delta))\n",
    "    supKev = np.append(supKev, supKe(w0x, w0y, w0z, delta))\n",
    "    asupKev = np.append(asupKev, aSupKe(w0x, w0y, w0z, delta))\n",
    "    aMiKev = np.append(aMiKev, aMiKe(w0x, w0y, w0z, delta))    \n",
    "fig, axs = plt.subplots(2,2,figsize=(15,8))\n",
    "colors, _ = misc.getColors(4)\n",
    "interactionEnergies = np.array([dblIv, miIv, supIv, asupIv, aMiIv])\n",
    "kineticEnergies = np.array([dblKev, miKev, supKev, asupKev, aMiKev])\n",
    "titles = ['Total Energy', 'Interaction Energy', 'Kinetic Energy']\n",
    "for ax, vals, title in zip([axs[0,0],axs[1,0],axs[1,1]], [interactionEnergies + kineticEnergies, interactionEnergies, kineticEnergies], titles):\n",
    "    ax.plot(deltas*1e9,vals[1]/mc.h*1e-3, label='Mott-Insulator', linestyle='--', color=colors[0])\n",
    "    ax.plot(deltas*1e9,vals[0]/mc.h*1e-3, label='Double-Filled', linestyle='--', color=colors[1])\n",
    "    ax.plot(deltas*1e9,vals[2]/mc.h*1e-3, label='Superfluid',linestyle='-', color=colors[2])\n",
    "    ax.plot(deltas*1e9,vals[3]/mc.h*1e-3, label='Anti-Superfluid', color=colors[3])\n",
    "    #ax.plot(deltas*1e9,aMi_vals, label='Anti-MI (Fermionic)',color='r',linestyle='-.', zorder=-10)\n",
    "    ax.set_xlabel('Tweezer Spacing (nm)')\n",
    "    ax.set_ylabel('Energy (kHz)')\n",
    "    ax.set_title(title)\n",
    "    ax.grid(alpha=0.2)\n",
    "axs[0,0].set_ylim(13,18)\n",
    "axs[0,0].legend();\n",
    "ax2 = axs[0,1]\n",
    "ax2.set_title('Trap Parameters')\n",
    "ax2.grid(alpha=0.2)\n",
    "ax2.plot(deltas*1e9, wfDeltas*1e9,':', color='c')\n",
    "ax2.set_ylabel(r'Effective $\\Delta$', color='c')\n",
    "ax2.spines['left'].set_color('c')\n",
    "ax2.tick_params(axis='y', colors='c')\n",
    "\n",
    "ax3 = ax2.twinx()\n",
    "ax3.plot(deltas*1e9, wfXFreqs*1e-3, color='r', label=r'$\\nu_x$')\n",
    "ax3.plot(deltas*1e9, wfYFreqs*1e-3, color='orange', label=r'$\\nu_y$')\n",
    "ax3.plot(deltas*1e9, wfZFreqs*1e-3, color='purple', label=r'$\\nu_z$')\n",
    "ax3.legend()\n",
    "ax3.set_ylabel(r'Effective $\\nu_x$ (kHz)', color='r')\n",
    "ax3.spines['right'].set_color('red')\n",
    "ax3.tick_params(axis='y', colors='red')\n",
    "fig.subplots_adjust(hspace=0.3)\n",
    "ax = axs[1,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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