Reproduce-RMP-75-1-2003-vanderWiel.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Reproduce: Electron Transport through Double Quantum Dots"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "W. G. van der Wiel, S. De Franceschi, J. M. Elzerman, T. Fujisawa, S. Tarucha, and L. P. Kouwenhove, <i>Electron transport through double quantum dots</i>,<br> <a href=\"http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.75.1\">Rev. Mod. Phys. <b>75</b>, 1 (2003).</a>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Reproduced by <b>Eunjong Kim</b> (<a href=\"mailto:ekim7206@gmail.com\">ekim7206@gmail.com</a>)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Status: Work in progress"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We derive the formulae and results of the excellent review paper on double quantum dots, in the language of SymPy. Most of the text in the paper is used without paraphrasing."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy import *\n",
      "init_printing()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Linear Transport Regime"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "A. Classical Theory"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "CL, CR, Cm, Cg1, Cg2 = symbols(\"C_L, C_R, C_m, C_g1, C_g2\")\n",
      "VL, VR, Vg1, Vg2, V1, V2 = symbols(\"V_L, V_R, V_g1, V_g2, V_1, V_2\", real=True)\n",
      "Q1, Q2 = symbols(\"Q_1, Q_2\")\n",
      "N0, N1, N2 = symbols(\"N_0, N_1, N_2\", int=True)\n",
      "e = symbols(\"|e|\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Eq(Q1, CL * (V1-VL) + Cg1 * (V1-Vg1) + Cm * (V1-V2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$Q_{1} = C_{L} \\left(V_{1} - V_{L}\\right) + C_{g1} \\left(V_{1} - V_{g1}\\right) + C_{m} \\left(V_{1} - V_{2}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
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       "prompt_number": 3,
       "text": [
        "Q\u2081 = C_L\u22c5(V\u2081 - V_L) + C_g1\u22c5(V\u2081 - V_g1) + C_m\u22c5(V\u2081 - V\u2082)"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Eq(Q2, CR * (V2-VR) + Cg2 * (V2-Vg2) + Cm * (V2-V1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$Q_{2} = C_{R} \\left(V_{2} - V_{R}\\right) + C_{g2} \\left(V_{2} - V_{g2}\\right) + C_{m} \\left(- V_{1} + V_{2}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
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       "prompt_number": 4,
       "text": [
        "Q\u2082 = C_R\u22c5(V\u2082 - V_R) + C_g2\u22c5(V\u2082 - V_g2) + C_m\u22c5(-V\u2081 + V\u2082)"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "C1, C2 = symbols(\"C_1, C_2\")\n",
      "\n",
      "Qvec = Matrix([[Q1 + CL*VL + Cg1*Vg1], [Q2 + CR*VR + Cg2*Vg2]])\n",
      "Cmat = Matrix([[C1, -Cm], [-Cm, C2]])\n",
      "Vvec = Matrix([[V1], [V2]])\n",
      "\n",
      "L1 = Qvec\n",
      "R1 = Cmat * Vvec\n",
      "\n",
      "Eq(L1, R1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}C_{L} V_{L} + C_{g1} V_{g1} + Q_{1}\\\\C_{R} V_{R} + C_{g2} V_{g2} + Q_{2}\\end{matrix}\\right] = \\left[\\begin{matrix}C_{1} V_{1} - C_{m} V_{2}\\\\C_{2} V_{2} - C_{m} V_{1}\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAAyBAMAAACg8g0WAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n7ENQ3ftCAAAAAElFTkSuQmCC\n",
       "prompt_number": 5,
       "text": [
        "\u23a1C_L\u22c5V_L + C_g1\u22c5V_g1 + Q\u2081\u23a4 = \u23a1C\u2081\u22c5V\u2081 - C_m\u22c5V\u2082\u23a4\n",
        "\u23a2                        \u23a5   \u23a2              \u23a5\n",
        "\u23a3C_R\u22c5V_R + C_g2\u22c5V_g2 + Q\u2082\u23a6   \u23a3C\u2082\u22c5V\u2082 - C_m\u22c5V\u2081\u23a6"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here, $C_{1(2)}$ is the sum of all capacitances attached to dot $1(2)$ including $C_m$.\n",
      "\\begin{align}\n",
      "C_{1(2)} = C_{L(R)} + C_{g1(2)} + C_m.\n",
      "\\end{align}"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "L2 = Vvec\n",
      "R2 = Cmat.inv() * Qvec\n",
      "\n",
      "Eq(L2, R2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\left[\\begin{matrix}V_{1}\\\\V_{2}\\end{matrix}\\right] = \\left[\\begin{matrix}\\left(\\frac{1}{C_{1}} + \\frac{C_{m}^{2}}{C_{1}^{2} \\left(C_{2} - \\frac{C_{m}^{2}}{C_{1}}\\right)}\\right) \\left(C_{L} V_{L} + C_{g1} V_{g1} + Q_{1}\\right) + \\frac{C_{m} \\left(C_{R} V_{R} + C_{g2} V_{g2} + Q_{2}\\right)}{C_{1} \\left(C_{2} - \\frac{C_{m}^{2}}{C_{1}}\\right)}\\\\\\frac{1}{C_{2} - \\frac{C_{m}^{2}}{C_{1}}} \\left(C_{R} V_{R} + C_{g2} V_{g2} + Q_{2}\\right) + \\frac{C_{m} \\left(C_{L} V_{L} + C_{g1} V_{g1} + Q_{1}\\right)}{C_{1} \\left(C_{2} - \\frac{C_{m}^{2}}{C_{1}}\\right)}\\end{matrix}\\right]$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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SwFKPNecAF5p0P2Ii/x5FzqquM1JKAuN6Rx/PpMs+4CCVlXXhv8i0WCeAk0tL\nYIP6eYo8xPqN5aV8KnJ5GR8iBXmiU36WfZOu09vS5/PvFfNU5L0keXCcYAeYleXxD1ZbCbOY7VTk\nxSL7pQzLthpKCeHHdjE8FTlVJX8u3O7DuKncHZ4CtwllDfO+iqwXbfyE79Oaop88ngSebi9bj5D/\ndweI/MQwppqBhAv/br93vb68bSO3454IH5JAxkHB8znZDDAPn6A+jN4lqGfwKYGDSeD/yvEUQigg\n6MwAAAAASUVORK5CYII=\n",
       "prompt_number": 6,
       "text": [
        "       \u23a1\u239b              2     \u239e                                                \n",
        "       \u23a2\u239c1          C_m      \u239f                              C_m\u22c5(C_R\u22c5V_R + C_g\n",
        "\u23a1V\u2081\u23a4 = \u23a2\u239c\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5(C_L\u22c5V_L + C_g1\u22c5V_g1 + Q\u2081) + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u23a2  \u23a5   \u23a2\u239cC\u2081       \u239b        2\u239e\u239f                                         \u239b      \n",
        "\u23a3V\u2082\u23a6   \u23a2\u239c       2 \u239c     C_m \u239f\u239f                                         \u239c     C\n",
        "       \u23a2\u239c     C\u2081 \u22c5\u239cC\u2082 - \u2500\u2500\u2500\u2500\u239f\u239f                                      C\u2081\u22c5\u239cC\u2082 - \u2500\n",
        "       \u23a2\u239d         \u239d      C\u2081 \u23a0\u23a0                                         \u239d      \n",
        "       \u23a2                                                                      \n",
        "       \u23a2            C_R\u22c5V_R + C_g2\u22c5V_g2 + Q\u2082   C_m\u22c5(C_L\u22c5V_L + C_g1\u22c5V_g1 + Q\u2081) \n",
        "       \u23a2            \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 \n",
        "       \u23a2                           2                      \u239b        2\u239e         \n",
        "       \u23a2                        C_m                       \u239c     C_m \u239f         \n",
        "       \u23a2                   C\u2082 - \u2500\u2500\u2500\u2500                   C\u2081\u22c5\u239cC\u2082 - \u2500\u2500\u2500\u2500\u239f         \n",
        "       \u23a3                         C\u2081                       \u239d      C\u2081 \u23a0         \n",
        "\n",
        "            \u23a4\n",
        "2\u22c5V_g2 + Q\u2082)\u23a5\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u23a5\n",
        "  2\u239e        \u23a5\n",
        "_m \u239f        \u23a5\n",
        "\u2500\u2500\u2500\u239f        \u23a5\n",
        "C\u2081 \u23a0        \u23a5\n",
        "            \u23a5\n",
        "            \u23a5\n",
        "            \u23a5\n",
        "            \u23a5\n",
        "            \u23a5\n",
        "            \u23a5\n",
        "            \u23a6"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Eq(Vvec[0], R2[0])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$V_{1} = \\left(\\frac{1}{C_{1}} + \\frac{C_{m}^{2}}{C_{1}^{2} \\left(C_{2} - \\frac{C_{m}^{2}}{C_{1}}\\right)}\\right) \\left(C_{L} V_{L} + C_{g1} V_{g1} + Q_{1}\\right) + \\frac{C_{m} \\left(C_{R} V_{R} + C_{g2} V_{g2} + Q_{2}\\right)}{C_{1} \\left(C_{2} - \\frac{C_{m}^{2}}{C_{1}}\\right)}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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E1b5w+bkQBf5brAOt+5+z92ZZsXhB8dl5wDJRw8PYFXJDrqLDuRbSqy3tgB0p8P/S8LSb\n1ViwpYHnBf9kkV+DzrAL1tgWGfhwroX0ar4ZsCMF/tcannazGgt4wgPgfslL1zgx15Dtsazk9iWc\nayE9mjwcsCMFXmTlRSe5m7VoEGusZ66VzBw/scYRC2bMGrR9CeVaWF8M37ur1Exvtsx3vIc6A8X4\nPPt0icpzeGQMEwZ2N0K5ZlcTkMOuyQGKerNFTGH3HrehaJsZ+JkWgybq7DjuJZRroZ1Sz+YCasjW\nvIHRDvy4agZ+D0fvb3h3Gg9pKNdCm07/hCKoAsNvRf7kLR9GXXSpuZ7p5VuToAOsHy6Ma2uwdlef\nfY8LhJeBF3cGevAaqOc6gkK4tgZro5X+OifwQuJbLn6nwjF44cGy3OKNsT+EcG0NPsWv6a9zttwH\n/lmOPbOPHusJDeHaWsz9U5+dXwqOT13LsKlK8B7ri+zbtZGae0eQa42w6I7KSC1b82Dj7VpK3jgD\nuPnfAJhxgoy5a78IGiujHRQ5LrhBuvY/Gj8amtqmgWIAAAAASUVORK5CYII=\n",
       "prompt_number": 7,
       "text": [
        "     \u239b              2     \u239e                                                   \n",
        "     \u239c1          C_m      \u239f                              C_m\u22c5(C_R\u22c5V_R + C_g2\u22c5V\n",
        "V\u2081 = \u239c\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5(C_L\u22c5V_L + C_g1\u22c5V_g1 + Q\u2081) + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "     \u239cC\u2081       \u239b        2\u239e\u239f                                         \u239b        2\n",
        "     \u239c       2 \u239c     C_m \u239f\u239f                                         \u239c     C_m \n",
        "     \u239c     C\u2081 \u22c5\u239cC\u2082 - \u2500\u2500\u2500\u2500\u239f\u239f                                      C\u2081\u22c5\u239cC\u2082 - \u2500\u2500\u2500\u2500\n",
        "     \u239d         \u239d      C\u2081 \u23a0\u23a0                                         \u239d      C\u2081 \n",
        "\n",
        "         \n",
        "_g2 + Q\u2082)\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "\u239e        \n",
        "\u239f        \n",
        "\u239f        \n",
        "\u23a0        "
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Eq(Vvec[1], R2[1])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$V_{2} = \\frac{1}{C_{2} - \\frac{C_{m}^{2}}{C_{1}}} \\left(C_{R} V_{R} + C_{g2} V_{g2} + Q_{2}\\right) + \\frac{C_{m} \\left(C_{L} V_{L} + C_{g1} V_{g1} + Q_{1}\\right)}{C_{1} \\left(C_{2} - \\frac{C_{m}^{2}}{C_{1}}\\right)}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
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       "prompt_number": 8,
       "text": [
        "     C_R\u22c5V_R + C_g2\u22c5V_g2 + Q\u2082   C_m\u22c5(C_L\u22c5V_L + C_g1\u22c5V_g1 + Q\u2081)\n",
        "V\u2082 = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                    2                      \u239b        2\u239e        \n",
        "                 C_m                       \u239c     C_m \u239f        \n",
        "            C\u2082 - \u2500\u2500\u2500\u2500                   C\u2081\u22c5\u239cC\u2082 - \u2500\u2500\u2500\u2500\u239f        \n",
        "                  C\u2081                       \u239d      C\u2081 \u23a0        "
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Substituting $Q_{1(2)} = -N_{1(2)} |e|$, the potential energy becomes (for easier calculation, we substitute $D\\equiv C_1C_2-C_m^2$)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Usym, D = symbols(\"U, D\")\n",
      "U0 = simplify(( Qvec.T * Cmat.inv() * Qvec/2)[0].subs({Q1: -N1*e, Q2: -N2*e}).expand()).subs(C1*C2-Cm**2, D).expand()\n",
      "\n",
      "Eq(Usym, U0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$U = \\frac{C_{1} C_{R}^{2} V_{R}^{2}}{2 D} + \\frac{C_{1} C_{R}}{D} C_{g2} V_{R} V_{g2} - \\frac{C_{1} C_{R}}{D} N_{2} V_{R} |e| + \\frac{C_{1} C_{g2}^{2} V_{g2}^{2}}{2 D} - \\frac{C_{1} C_{g2}}{D} N_{2} V_{g2} |e| + \\frac{C_{1} N_{2}^{2} |e|^{2}}{2 D} + \\frac{C_{2} C_{L}^{2} V_{L}^{2}}{2 D} + \\frac{C_{2} C_{L}}{D} C_{g1} V_{L} V_{g1} - \\frac{C_{2} C_{L}}{D} N_{1} V_{L} |e| + \\frac{C_{2} C_{g1}^{2} V_{g1}^{2}}{2 D} - \\frac{C_{2} C_{g1}}{D} N_{1} V_{g1} |e| + \\frac{C_{2} N_{1}^{2} |e|^{2}}{2 D} + \\frac{C_{L} C_{R}}{D} C_{m} V_{L} V_{R} + \\frac{C_{L} C_{g2}}{D} C_{m} V_{L} V_{g2} - \\frac{C_{L} C_{m}}{D} N_{2} V_{L} |e| + \\frac{C_{R} C_{g1}}{D} C_{m} V_{R} V_{g1} - \\frac{C_{R} C_{m}}{D} N_{1} V_{R} |e| + \\frac{C_{g1} C_{g2}}{D} C_{m} V_{g1} V_{g2} - \\frac{C_{g1} C_{m}}{D} N_{2} V_{g1} |e| - \\frac{C_{g2} C_{m}}{D} N_{1} V_{g2} |e| + \\frac{C_{m} N_{1}}{D} N_{2} |e|^{2}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
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LzJ18yQbIiBSWUJPqRWDXnPy8b/ljiDBxmMSqiVICsGzYg4wQk0nbIg3Y03xnILxLZWxG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\n3P8DqJQMeRdrMyAAAAAASUVORK5CYII=\n",
       "prompt_number": 9,
       "text": [
        "          2    2                                                     2     2  \n",
        "    C\u2081\u22c5C_R \u22c5V_R    C\u2081\u22c5C_R\u22c5C_g2\u22c5V_R\u22c5V_g2   C\u2081\u22c5C_R\u22c5N\u2082\u22c5V_R\u22c5|e|   C\u2081\u22c5C_g2 \u22c5V_g2   \n",
        "U = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 -\n",
        "        2\u22c5D                 D                     D                2\u22c5D        \n",
        "\n",
        "                            2    2         2    2                             \n",
        " C\u2081\u22c5C_g2\u22c5N\u2082\u22c5V_g2\u22c5|e|   C\u2081\u22c5N\u2082 \u22c5|e|    C\u2082\u22c5C_L \u22c5V_L    C\u2082\u22c5C_L\u22c5C_g1\u22c5V_L\u22c5V_g1   C\u2082\u22c5\n",
        " \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\n",
        "          D                2\u22c5D           2\u22c5D                 D                \n",
        "\n",
        "                        2     2                              2    2           \n",
        "C_L\u22c5N\u2081\u22c5V_L\u22c5|e|   C\u2082\u22c5C_g1 \u22c5V_g1    C\u2082\u22c5C_g1\u22c5N\u2081\u22c5V_g1\u22c5|e|   C\u2082\u22c5N\u2081 \u22c5|e|    C_L\u22c5C_R\u22c5\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "     D                2\u22c5D                  D                2\u22c5D               \n",
        "\n",
        "                                                                              \n",
        "C_m\u22c5V_L\u22c5V_R   C_L\u22c5C_g2\u22c5C_m\u22c5V_L\u22c5V_g2   C_L\u22c5C_m\u22c5N\u2082\u22c5V_L\u22c5|e|   C_R\u22c5C_g1\u22c5C_m\u22c5V_R\u22c5V_\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        " D                      D                     D                      D        \n",
        "\n",
        "                                                                              \n",
        "g1   C_R\u22c5C_m\u22c5N\u2081\u22c5V_R\u22c5|e|   C_g1\u22c5C_g2\u22c5C_m\u22c5V_g1\u22c5V_g2   C_g1\u22c5C_m\u22c5N\u2082\u22c5V_g1\u22c5|e|   C_g\n",
        "\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\n",
        "             D                       D                       D                \n",
        "\n",
        "                                 2\n",
        "2\u22c5C_m\u22c5N\u2081\u22c5V_g2\u22c5|e|   C_m\u22c5N\u2081\u22c5N\u2082\u22c5|e| \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "      D                   D       "
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We consider the linear transport regime where $V_L-V_R \\approx 0$. We let $V_L = V_R=0$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def simplify_by_term(e):\n",
      "    new_args = []\n",
      "    for term in e.args: \n",
      "        temp = simplify(term.factor())\n",
      "        new_args.append(temp)\n",
      "    e = Add(*new_args)\n",
      "    return e"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "EC1, EC2, ECm = symbols(\"E_C1, E_C2, E_Cm\")\n",
      "\n",
      "U1 = U0.subs({C2: D*EC1/e**2, C1: D*EC2/e**2, Cm: D*ECm/e**2})\n",
      "\n",
      "U2 = U1.subs({VL: 0, VR: 0})\n",
      "\n",
      "U3 = collect(U2, [1/e, 1/e**2])\n",
      "\n",
      "U3 = simplify_by_term(U3)\n",
      "\n",
      "Eq(Usym, U3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$U = \\frac{E_{C1} N_{1}^{2}}{2} + \\frac{E_{C2} N_{2}^{2}}{2} + E_{Cm} N_{1} N_{2} - \\frac{1}{|e|} \\left(C_{g1} E_{C1} N_{1} V_{g1} + C_{g1} E_{Cm} N_{2} V_{g1} + C_{g2} E_{C2} N_{2} V_{g2} + C_{g2} E_{Cm} N_{1} V_{g2}\\right) + \\frac{1}{2 |e|^{2}} \\left(C_{g1}^{2} E_{C1} V_{g1}^{2} + 2 C_{g1} C_{g2} E_{Cm} V_{g1} V_{g2} + C_{g2}^{2} E_{C2} V_{g2}^{2}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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       "prompt_number": 11,
       "text": [
        "           2          2                                                       \n",
        "    E_C1\u22c5N\u2081    E_C2\u22c5N\u2082                 C_g1\u22c5E_C1\u22c5N\u2081\u22c5V_g1 + C_g1\u22c5E_Cm\u22c5N\u2082\u22c5V_g1 +\n",
        "U = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + E_Cm\u22c5N\u2081\u22c5N\u2082 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "       2          2                                                         |e\n",
        "                                                                              \n",
        "\n",
        "                                             2          2                     \n",
        " C_g2\u22c5E_C2\u22c5N\u2082\u22c5V_g2 + C_g2\u22c5E_Cm\u22c5N\u2081\u22c5V_g2   C_g1 \u22c5E_C1\u22c5V_g1  + 2\u22c5C_g1\u22c5C_g2\u22c5E_Cm\u22c5V\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "|                                                                          2  \n",
        "                                                                      2\u22c5|e|   \n",
        "\n",
        "               2          2\n",
        "_g1\u22c5V_g2 + C_g2 \u22c5E_C2\u22c5V_g2 \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                           \n",
        "                           "
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U4 = rcollect(U3, Cg1 * Vg1, Cg2 * Vg2)  # recursively collecting terms\n",
      "\n",
      "Eq(Usym, U4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$U = \\frac{E_{C1} N_{1}^{2}}{2} + \\frac{E_{C2} N_{2}^{2}}{2} + E_{Cm} N_{1} N_{2} - \\frac{1}{|e|} \\left(C_{g1} V_{g1} \\left(E_{C1} N_{1} + E_{Cm} N_{2}\\right) + C_{g2} V_{g2} \\left(E_{C2} N_{2} + E_{Cm} N_{1}\\right)\\right) + \\frac{1}{2 |e|^{2}} \\left(C_{g1}^{2} E_{C1} V_{g1}^{2} + 2 C_{g1} C_{g2} E_{Cm} V_{g1} V_{g2} + C_{g2}^{2} E_{C2} V_{g2}^{2}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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       "prompt_number": 12,
       "text": [
        "           2          2                                                       \n",
        "    E_C1\u22c5N\u2081    E_C2\u22c5N\u2082                 C_g1\u22c5V_g1\u22c5(E_C1\u22c5N\u2081 + E_Cm\u22c5N\u2082) + C_g2\u22c5V_\n",
        "U = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + E_Cm\u22c5N\u2081\u22c5N\u2082 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "       2          2                                                 |e|       \n",
        "                                                                              \n",
        "\n",
        "                             2          2                                    2\n",
        "g2\u22c5(E_C2\u22c5N\u2082 + E_Cm\u22c5N\u2081)   C_g1 \u22c5E_C1\u22c5V_g1  + 2\u22c5C_g1\u22c5C_g2\u22c5E_Cm\u22c5V_g1\u22c5V_g2 + C_g2 \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                           2                  \n",
        "                                                      2\u22c5|e|                   \n",
        "\n",
        "          2\n",
        "\u22c5E_C2\u22c5V_g2 \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "           \n",
        "           "
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where $E_{C1(2)}$ is the charing energy of the individual dot $1(2)$, $E_{Cm}$ is the electrostatic coupling energy, and $-|e|$ is the electron charge. The coupling energy $E_{Cm}$ is the change in energy of one dot when an electron is added to the other dot."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{align}\n",
      "E_{C1} = \\frac{e^2}{C_1} \\left( \\frac{1}{1-\\frac{C_m^2}{C_1C_2}}\\right),\\quad\n",
      "E_{C1} = \\frac{e^2}{C_2} \\left( \\frac{1}{1-\\frac{C_m^2}{C_1C_2}}\\right),\\quad\n",
      "E_{C1} = \\frac{e^2}{C_m} \\left( \\frac{1}{\\frac{C_1C_2}{C_m^2}-1}\\right).\n",
      "\\end{align}"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def U(N1, N2, Vg1, Vg2):\n",
      "    \"\"\"\n",
      "    The double dot electrostatic energy function\n",
      "    \"\"\"\n",
      "    return N1**2*EC1/2 + N2**2*EC2/2 + N1*N2*ECm + f(N1, N2, Vg1, Vg2)\n",
      "\n",
      "def f(N1, N2, Vg1, Vg2):\n",
      "    term1 = -((Cg1*Vg1*(N1*EC1+N2*ECm) + Cg2*Vg2*(N1*ECm+N2*EC2))/e)\n",
      "    term2 = (Cg1**2*Vg1**2*EC1/2 + Cg2**2*Vg2**2*EC2/2 + Cg1*Vg1*Cg2*Vg2*ECm)/e**2\n",
      "    return term1 + term2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U(N1, N2, Vg1, Vg2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{E_{C1} N_{1}^{2}}{2} + \\frac{E_{C2} N_{2}^{2}}{2} + E_{Cm} N_{1} N_{2} - \\frac{1}{|e|} \\left(C_{g1} V_{g1} \\left(E_{C1} N_{1} + E_{Cm} N_{2}\\right) + C_{g2} V_{g2} \\left(E_{C2} N_{2} + E_{Cm} N_{1}\\right)\\right) + \\frac{1}{|e|^{2}} \\left(\\frac{C_{g1}^{2} E_{C1}}{2} V_{g1}^{2} + C_{g1} C_{g2} E_{Cm} V_{g1} V_{g2} + \\frac{C_{g2}^{2} E_{C2}}{2} V_{g2}^{2}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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       "prompt_number": 14,
       "text": [
        "                                                                              \n",
        "                                                                              \n",
        "       2          2                                                           \n",
        "E_C1\u22c5N\u2081    E_C2\u22c5N\u2082                 C_g1\u22c5V_g1\u22c5(E_C1\u22c5N\u2081 + E_Cm\u22c5N\u2082) + C_g2\u22c5V_g2\u22c5(\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + E_Cm\u22c5N\u2081\u22c5N\u2082 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "   2          2                                                 |e|           \n",
        "                                                                              \n",
        "\n",
        "                         2          2                                  2      \n",
        "                     C_g1 \u22c5E_C1\u22c5V_g1                               C_g2 \u22c5E_C2\u22c5\n",
        "                     \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + C_g1\u22c5C_g2\u22c5E_Cm\u22c5V_g1\u22c5V_g2 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "E_C2\u22c5N\u2082 + E_Cm\u22c5N\u2081)          2                                             2   \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                                     2                        \n",
        "                                                  |e|                         \n",
        "\n",
        "    2\n",
        "V_g2 \n",
        "\u2500\u2500\u2500\u2500\u2500\n",
        "     \n",
        "\u2500\u2500\u2500\u2500\u2500\n",
        "     \n",
        "     "
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Different Coupling Regime"
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "a. $C_m = 0$ Case"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$E_{Cm} = 0$, the electrostatic energy becomes"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U_zero_Cm1 = U(N1, N2, Vg1, Vg2).subs({ECm: 0, EC1: e**2/C1, EC2: e**2/C2})\n",
      "U_zero_Cm2 = collect(U_zero_Cm1.expand(), [1/C1, 1/C2])\n",
      "\n",
      "U_zero_Cm2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{1}{C_{2}} \\left(\\frac{C_{g2}^{2} V_{g2}^{2}}{2} - C_{g2} N_{2} V_{g2} |e| + \\frac{N_{2}^{2} |e|^{2}}{2}\\right) + \\frac{1}{C_{1}} \\left(\\frac{C_{g1}^{2} V_{g1}^{2}}{2} - C_{g1} N_{1} V_{g1} |e| + \\frac{N_{1}^{2} |e|^{2}}{2}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
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       "prompt_number": 15,
       "text": [
        "    2     2                        2    2       2     2                       \n",
        "C_g2 \u22c5V_g2                       N\u2082 \u22c5|e|    C_g1 \u22c5V_g1                       N\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - C_g2\u22c5N\u2082\u22c5V_g2\u22c5|e| + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500   \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - C_g1\u22c5N\u2081\u22c5V_g1\u22c5|e| + \u2500\n",
        "     2                              2            2                            \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                    C\u2082                                          C\u2081            \n",
        "\n",
        " 2    2\n",
        "\u2081 \u22c5|e| \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "  2    \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "       "
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U_zero_Cm = simplify_by_term(U_zero_Cm2)\n",
      "Eq(Usym, U_zero_Cm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$U = \\frac{1}{2 C_{2}} \\left(C_{g2} V_{g2} - N_{2} |e|\\right)^{2} + \\frac{1}{2 C_{1}} \\left(C_{g1} V_{g1} - N_{1} |e|\\right)^{2}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
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       "prompt_number": 16,
       "text": [
        "                        2                       2\n",
        "    (C_g2\u22c5V_g2 - N\u2082\u22c5|e|)    (C_g1\u22c5V_g1 - N\u2081\u22c5|e|) \n",
        "U = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "             2\u22c5C\u2082                    2\u22c5C\u2081        "
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "which is the sum of energies of two independent dots."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "b. Dominant $C_m$ Case"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$C_m / C_{1(2)}\\rightarrow 1$, so that the energies approaches the values\n",
      "\\begin{align}\n",
      "E_{C1} \\rightarrow \\frac{e^2}{\\tilde{C}},\\quad E_{C2} = \\frac{e^2}{\\tilde{C}}, \\quad E_{Cm} = \\frac{e^2}{\\tilde{C}}.\n",
      "\\end{align}\n",
      "the electrostatic energy is given by"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Ctilde = symbols(\"Ctilde\")\n",
      "\n",
      "U_dominant_Cm1 = U(N1, N2, Vg1, Vg2).subs({EC1: e**2/Ctilde, EC2: e**2/Ctilde, ECm: e**2/Ctilde})\n",
      "U_dominant_Cm2 = U_dominant_Cm1.expand()\n",
      "U_dominant_Cm3 = simplify_by_term(U_dominant_Cm2).factor()\n",
      "U_dominant_Cm = rcollect(U_dominant_Cm3, e)\n",
      "\n",
      "U_dominant_Cm"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{1}{2 \\tilde{C}} \\left(C_{g1} V_{g1} + C_{g2} V_{g2} + |e| \\left(- N_{1} - N_{2}\\right)\\right)^{2}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAAAtBAMAAACT9ff0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n2to5POV39ckhbfEM9a4BKt2jMCG98CsAAAAASUVORK5CYII=\n",
       "prompt_number": 17,
       "text": [
        "                                        2\n",
        "(C_g1\u22c5V_g1 + C_g2\u22c5V_g2 + |e|\u22c5(-N\u2081 - N\u2082)) \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                   2\u22c5C\u0303                  "
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A large interdot capacitance $C_m$ effectively leads to one big dot."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Electrochemical Potential"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The electrochemical potential $\\mu_{1(2)}(N_1, N_2)$ of dot $1(2)$ is defined as the energy needed to add the $N_{1(2)}$th electron to dot $1(2)$, while having $N_{2(1)}$ electrons on dot $2(1)$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mu1(N1, N2, Vg1, Vg2):\n",
      "    \"\"\"\n",
      "    The electrochemical potential of dot 1\n",
      "    \"\"\"\n",
      "    ee = U(N1, N2, Vg1, Vg2) - U(N1-1, N2, Vg1, Vg2)\n",
      "    ee = simplify_by_term(collect(ee.expand(), [1/e]))\n",
      "    return collect(ee, [EC1, ECm])\n",
      "\n",
      "def mu2(N1, N2, Vg1, Vg2):\n",
      "    \"\"\"\n",
      "    The electrochemical potential of dot 2\n",
      "    \"\"\"\n",
      "    ee = U(N1, N2, Vg1, Vg2) - U(N1, N2-1, Vg1, Vg2)\n",
      "    ee = simplify_by_term(collect(ee.expand(), [1/e]))\n",
      "    return collect(ee, [EC2, ECm])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mu_1 (N_1, N_2) = U(N_1, N_2) - U(N_1-1, N_2)$ :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu1(N1, N2, Vg1, Vg2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$E_{C1} \\left(N_{1} - \\frac{1}{2}\\right) + E_{Cm} N_{2} - \\frac{1}{|e|} \\left(C_{g1} E_{C1} V_{g1} + C_{g2} E_{Cm} V_{g2}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAhcAAAAyBAMAAAAdCeTXAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nMb44t8XH32DR/wPgwnRNFaSvpQAAAABJRU5ErkJggg==\n",
       "prompt_number": 19,
       "text": [
        "                            C_g1\u22c5E_C1\u22c5V_g1 + C_g2\u22c5E_Cm\u22c5V_g2\n",
        "E_C1\u22c5(N\u2081 - 1/2) + E_Cm\u22c5N\u2082 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                          |e|              "
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\mu_2 (N_1, N_2) = U(N_1, N_2) - U(N_1, N_2-1)$ :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mu2(N1, N2, Vg1, Vg2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$E_{C2} \\left(N_{2} - \\frac{1}{2}\\right) + E_{Cm} N_{1} - \\frac{1}{|e|} \\left(C_{g1} E_{Cm} V_{g1} + C_{g2} E_{C2} V_{g2}\\right)$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAhcAAAAyBAMAAAAdCeTXAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n",
       "prompt_number": 20,
       "text": [
        "                            C_g1\u22c5E_Cm\u22c5V_g1 + C_g2\u22c5E_C2\u22c5V_g2\n",
        "E_C2\u22c5(N\u2082 - 1/2) + E_Cm\u22c5N\u2081 - \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                          |e|              "
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "a. Addition Energy of Dot 1"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The change in $\\mu_1(N_1, N_2)$ at fixed gate voltages, if $N_1$ is changed by $1$, $\\mu_1(N_1+1, N_2) - \\mu_1(N_1, N_2)$ :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "simplify(mu1(N1+1, N2, Vg1, Vg2) - mu1(N1, N2, Vg1, Vg2).expand())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$E_{C1}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACMAAAARBAMAAAClRQjMAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdrur3c1mRBCZiTIi\n71SC2pmSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwUlEQVQYGWNgYBD6r2xs8pUBBYC4SSgi7B+B\n3E4UIa7fQG4jihDrBwYuBh4UIX4FBjEUAQaG+mCTPyChJMsVMgzcCiDm+g0MAUDqaAJD0wXuyQ4g\noXgGhgkMG7i/MzCwKTDwgYU+MTA0cAjwLmBg4BaACIGdxdUg38DAwNEAEQI7azODE9AIIABrZPnA\nwMB+m+EnQqg5/rOxkX8AgxdQ6BhUFUSWYRKQnoEqxJLA0LUBKHQBqgRELZ4lwcDAM+WzAAAQACoD\ncTysuAAAAABJRU5ErkJggg==\n",
       "prompt_number": 21,
       "text": [
        "E_C1"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "is called the <i>addition energy</i> of dot 1 and equals the charging energy of dot 1 in this classical regime."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "b. Addition Energy of Dot 2"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Similarly, the change in $\\mu_2(N_1, N_2)$ at fixed gate voltages, if $N_2$ is changed by $1$, $\\mu_2(N_1, N_2+1) - \\mu_2(N_1, N_2)$ :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "simplify(mu2(N1, N2+1, Vg1, Vg2) - mu2(N1, N2, Vg1, Vg2).expand())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$E_{C2}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACQAAAARBAMAAABHmRO1AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdrur3c1mRBCZiTIi\n71SC2pmSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVQYGWNgYBD6r2xs8pUBBYC4SSgi7B+B\n3E4UIa7fQG4jihDrBwYuBh4UIX4FBjEUAQaG+mCTPyChJMsVMgwrNRuAzPUbGAKA1NEEhqYLXAeY\nQex4BoYJDBu4vzMwsCmwHOAG6fjEwNDAIcC7gIGBW4C3gAcoBXYWV4N8AwMDBxDz/WBgADtrM4MT\nUD0IsAgA8QegytsMPyEiDCsZGJrjPxsb+QcweAGFjgFtmACVAlKTgHgGA0MVQzVcjCWBoWsDA3fc\nOw24EMPiWRIMDLz//38AADADMdmJwSuSAAAAAElFTkSuQmCC\n",
       "prompt_number": 22,
       "text": [
        "E_C2"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "is called the <i>addition energy</i> of dot 2 and equals the charging energy of dot 2 in this classical regime."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "c. Coupling Energy"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The change in $\\mu_1(N_1, N_2)$ at fixed gate voltages, if $N_2$ is changed by $1$, $\\mu_1(N_1, N_2+1) - \\mu_1(N_1, N_2)$ :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "simplify(mu1(N1, N2+1, Vg1, Vg2) - mu1(N1, N2, Vg1, Vg2).expand())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$E_{Cm}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACoAAAARBAMAAABZUCMGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdrur3c1mRBCZiTIi\n71SC2pmSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVQYGWNgYBD6r2xs8pUBHYBEktAF2T8C\nRTrRRbl+A0Ua0UVZPzBwMfCgi/IrMIihizEw1Aeb/AGJJlmukEHIrt/AEADkHU1gaLqAEI1nYJjA\nsIH7OwMDmwJC9BMDQwOHAO8CBgZuAbgo2LlcDfINDAwcDWzTNkoyCm1gYAA7dzODE1gZW30CrwWj\nAQMDywcGBvbbDD/BoidEGPgLOBcwNMd/NjbyD2DwAooeY2AwZNjLwPIArAJETALiGQwMtxmEGM5z\nw0VZEhi6NjDwfACqTuKCizIsniUBtMCAIYbh8AoApLUxD2DxomMAAAAASUVORK5CYII=\n",
       "prompt_number": 23,
       "text": [
        "E_Cm"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "and the change in $\\mu_2(N_1, N_2)$ at fixed gate voltages, if $N_1$ is changed by $1$, $\\mu_2(N_1+1, N_2) - \\mu_1(N_1, N_2)$ :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "simplify(mu2(N1+1, N2, Vg1, Vg2) - mu2(N1, N2, Vg1, Vg2).expand())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$E_{Cm}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAACoAAAARBAMAAABZUCMGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdrur3c1mRBCZiTIi\n71SC2pmSAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVQYGWNgYBD6r2xs8pUBHYBEktAF2T8C\nRTrRRbl+A0Ua0UVZPzBwMfCgi/IrMIihizEw1Aeb/AGJJlmukEHIrt/AEADkHU1gaLqAEI1nYJjA\nsIH7OwMDmwJC9BMDQwOHAO8CBgZuAbgo2LlcDfINDAwcDWzTNkoyCm1gYAA7dzODE1gZW30CrwWj\nAQMDywcGBvbbDD/BoidEGPgLOBcwNMd/NjbyD2DwAooeY2AwZNjLwPIArAJETALiGQwMtxmEGM5z\nw0VZEhi6NjDwfACqTuKCizIsniUBtMCAIYbh8AoApLUxD2DxomMAAAAASUVORK5CYII=\n",
       "prompt_number": 24,
       "text": [
        "E_Cm"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "is the same and has the value $E_{Cm}$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Charge Stability Diagram"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Update the matplotlib configuration parameters:\n",
      "import matplotlib\n",
      "matplotlib.rcParams.update({'font.size': 18, 'font.family': 'STIXGeneral', 'mathtext.fontset': 'stix'})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# method1 (generating honeycombs for given values of (n1, n2))\n",
      "fig, ax = plt.subplots(nrows=2, ncols=2, figsize=(10, 10))\n",
      "fig_color = ['red', 'blue', 'green', 'black']\n",
      "    \n",
      "for idx_ECm, ECm_EC in enumerate([0.001, 0.3, 0.6, 0.999]):\n",
      "    subs_dic={Cg1: 1, Cg2: 1, EC1: 1, EC2: 1, ECm: ECm_EC, e: 1}\n",
      "    mumu1 = mu1(N1, N2, Vg1, Vg2).subs(subs_dic)\n",
      "    mumu2 = mu2(N1, N2, Vg1, Vg2).subs(subs_dic)        \n",
      "    \n",
      "    fig_row = idx_ECm // 2\n",
      "    fig_col = idx_ECm % 2\n",
      "    for n1 in range(5):\n",
      "        for n2 in range(5):\n",
      "            sol=[]\n",
      "            # Getting six lines forming each honeycomb structure\n",
      "            \"\"\"\n",
      "            electrochemical potential conditions:\n",
      "            1. The addition energy of dot 1 to (n1, n2) should be negative.\n",
      "            2. The addition energy of dot 2 to (n1, n2) should be negative.\n",
      "            3. The addition energy of dot 1 to (n1+1, n2) should be positive.\n",
      "            since n1 should be the largest possible number whose addition energy is negative.\n",
      "            4. The addition energy of dot 2 to (n1, n2+1) should be positive.\n",
      "            since n2 should be the largest possible number whose addition energy is negative.\n",
      "            \"\"\"\n",
      "            sol.append(solve(mumu1.subs({N1:n1, N2:n2}), Vg2)[0])\n",
      "            sol.append(solve(mumu2.subs({N1:n1, N2:n2}), Vg2)[0])\n",
      "            sol.append(solve(mumu1.subs({N1:n1+1, N2:n2}), Vg2)[0])\n",
      "            sol.append(solve(mumu2.subs({N1:n1, N2:n2+1}), Vg2)[0])            \n",
      "            \"\"\"\n",
      "            degeneracy conditions:\n",
      "            1. The energy gain is the same in (n1, n2-1)\n",
      "            when increasing either N1 or N2 by 1 at the boundary.\n",
      "            2. The energy gain is the same in (n1-1, n2)\n",
      "            when increasing either N1 or N2 by 1 at the boundary.\n",
      "            \"\"\"\n",
      "            sol.append(solve(mumu2.subs({N1:n1, N2:n2})\n",
      "                         -mumu1.subs({N1:n1+1, N2:n2-1}), Vg2)[0])\n",
      "            sol.append(solve(mumu1.subs({N1:n1, N2:n2})\n",
      "                         -mumu2.subs({N1:n1-1, N2:n2+1}), Vg2)[0])\n",
      "\n",
      "            # getting honeycomb x range\n",
      "            \"\"\"\n",
      "            intersection of sol[0] and sol[5] corresponds to the leftmost point of the comb:\n",
      "            \"\"\"\n",
      "            x_start = solve(sol[0]-sol[5], Vg1)[0]\n",
      "            y_start = sol[0].subs(Vg1, x_start)\n",
      "            \"\"\"\n",
      "            intersection of sol[2] and sol[4] corresponds to the rightmost point of the comb: \n",
      "            \"\"\"\n",
      "            x_end = solve(sol[2]-sol[4], Vg1)[0]\n",
      "            y_end = sol[2].subs(Vg1, x_end)\n",
      "\n",
      "            x_vec = np.arange(x_start, x_end, 0.01)\n",
      "            y_vec = np.zeros((6, len(x_vec)))\n",
      "                \n",
      "            for idx in range(6):\n",
      "                g = lambdify([Vg1], sol[idx], 'numpy')\n",
      "                y_vec[idx, :] = g(x_vec)\n",
      "\n",
      "            upper = np.minimum(np.minimum(y_vec[3, :], y_vec[5, :]), y_vec[2, :])  # upper part of each honeycomb\n",
      "            lower = np.maximum(np.maximum(y_vec[0, :], y_vec[1, :]), y_vec[4, :])  # lower part of each honeycomb\n",
      "        \n",
      "            ax[fig_row, fig_col].plot(x_vec, upper, color=fig_color[idx_ECm], lw=2)\n",
      "            ax[fig_row, fig_col].plot(x_vec, lower, color=fig_color[idx_ECm], lw=2)\n",
      "            # annotating (n1, n2) values to each honeycomb\n",
      "            ax[fig_row, fig_col].text((x_start+x_end-0.4)/2, (y_start+y_end)/2,\n",
      "                r\"$(%d, %d)$\"% (n1, n2), fontsize=15, color=\"black\")\n",
      "            # marking electron-like and hole-like triple points\n",
      "            ax[fig_row, fig_col].scatter(x_start, y_start, zorder=10, s=50, c='black', lw=2)\n",
      "            ax[fig_row, fig_col].scatter(x_end, y_end, zorder=10, s=150, c='white', lw=2)\n",
      "\n",
      "    # figure settings\n",
      "    ax[fig_row, fig_col].set_xlabel(r'$V_{g1}$', labelpad=10)\n",
      "    ax[fig_row, fig_col].set_ylabel(r'$V_{g2}$', labelpad=10)\n",
      "    ax[fig_row, fig_col].set_xlim([-0.25, 4.3])\n",
      "    ax[fig_row, fig_col].set_ylim([-0.25, 4.3])\n",
      "    ax[fig_row, fig_col].set_title(r\"$C_m/C_{1(2)} = %.2f$\" % ECm_EC)\n",
      "    ax[fig_row, fig_col].set_xticks([])\n",
      "    ax[fig_row, fig_col].set_yticks([])\n",
      "fig.tight_layout();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7DxddRPT00+HngRvoxnl45RV+KKU7D7GxRK1bEw0fTrRzZwhP1AdFRY4GmTEe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fUcgL8DWALgfiIqtr1HRPlKqZEAkgDsDuA+6wG4HsAjZognWCilogGsB5AP4CYiIqVUYwA7lVLN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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ef60c18>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# method 2 (connecting triple points)\n",
      "fig, ax = plt.subplots(nrows=2, ncols=2, figsize=(10, 10))\n",
      "fig_color = ['red', 'blue', 'green', 'black']\n",
      "\n",
      "n=9 # largest N = n1+n2  to generate the stability diagram\n",
      "\n",
      "def vecs_two_points(x1,y1,x2,y2):\n",
      "    xstart = min(x1,x2)\n",
      "    xend = max(x1,x2)\n",
      "    x_vec = np.linspace(xstart, xend, 2)\n",
      "    y_vec = (y2-y1)/(x2-x1) * (x_vec - x1) + y1\n",
      "    return x_vec, y_vec\n",
      "\n",
      "for idx_ECm, ECm_EC in enumerate([0.001, 0.3, 0.6, 0.999]):\n",
      "    subs_dic={Cg1: 1, Cg2: 1, EC1: 1, EC2: 1, ECm: ECm_EC, e: 1}\n",
      "    mumu1 = mu1(N1, N2, Vg1, Vg2).subs(subs_dic)\n",
      "    mumu2 = mu2(N1, N2, Vg1, Vg2).subs(subs_dic)        \n",
      "    \n",
      "    row = idx_ECm // 2\n",
      "    col = idx_ECm % 2\n",
      "    \n",
      "    #creating n by n numpy array\n",
      "    elecX = np.zeros((n+1,n+1), dtype=float); elecY = np.zeros((n+1,n+1), dtype=float)\n",
      "    holeX = np.zeros((n+1,n+1), dtype=float); holeY = np.zeros((n+1,n+1), dtype=float)\n",
      "    \n",
      "    for N in range(n):  # N = n1 + n2\n",
      "        for n1 in range(N+1):\n",
      "            n2 = N - n1\n",
      "            \n",
      "            sol=[]\n",
      "            # Getting six lines forming each honeycomb structure\n",
      "            \"\"\"\n",
      "            electrochemical potential conditions:\n",
      "            \"\"\"\n",
      "            sol.append(solve(mumu2.subs({N1:n1, N2:n2+1}), Vg2)[0])\n",
      "            sol.append(solve(mumu1.subs({N1:n1+1, N2:n2}), Vg2)[0])\n",
      "            sol.append(solve(mumu1.subs({N1:n1+1, N2:n2+1}), Vg2)[0])\n",
      "            sol.append(solve(mumu2.subs({N1:n1+1, N2:n2+1}), Vg2)[0])\n",
      "            \"\"\"\n",
      "            intersection of sol[0] and sol[1] corresponds to the electron-like triple point:\n",
      "            \"\"\"\n",
      "            elecX[n1,n2] = solve(sol[0]-sol[1], Vg1)[0]\n",
      "            elecY[n1,n2] = sol[0].subs(Vg1, elecX[n1,n2])\n",
      "            \"\"\"\n",
      "            intersection of sol[2] and sol[3] corresponds to the hole-like triple point: \n",
      "            \"\"\"\n",
      "            holeX[n1,n2] = solve(sol[2]-sol[3], Vg1)[0]\n",
      "            holeY[n1,n2] = sol[2].subs(Vg1, holeX[n1,n2])\n",
      "            holeX[-1, n2] = elecX[0,n2] - 2\n",
      "            holeY[-1, n2] = sol[0].subs(Vg1, holeX[-1,n2])\n",
      "            holeX[n1, -1] = elecX[n1,0] + 2\n",
      "            holeY[n1, -1] = sol[1].subs(Vg1, holeX[n1,-1])\n",
      "            \n",
      "            coord0 = (elecX[n1,n2], elecY[n1,n2])\n",
      "            x_vec, y_vec = [0,0,0],[0,0,0]\n",
      "            x_vec[0], y_vec[0] = vecs_two_points(elecX[n1,n2], elecY[n1,n2], holeX[n1,n2-1],holeY[n1,n2-1])\n",
      "            x_vec[1], y_vec[1] = vecs_two_points(elecX[n1,n2], elecY[n1,n2], holeX[n1-1,n2],holeY[n1-1,n2])\n",
      "            x_vec[2], y_vec[2] = vecs_two_points(elecX[n1,n2], elecY[n1,n2], holeX[n1,n2],holeY[n1,n2])\n",
      "            \n",
      "            for j in range(3):\n",
      "                ax[row, col].plot(x_vec[j], y_vec[j], color=fig_color[idx_ECm], lw=2)\n",
      "            # marking electron-like and hole-like triple points\n",
      "            ax[row, col].scatter(elecX[n1,n2], elecY[n1,n2], zorder=10, s=50, c='black', lw=2)\n",
      "            ax[row, col].scatter(holeX[n1,n2], holeY[n1,n2], zorder=9, s=150, c='white', lw=2)    \n",
      "\n",
      "            # annotating (n1, n2) values to each honeycomb\n",
      "            if n1<5 and n2<5:\n",
      "                ax[row, col].text(elecX[n1,n2]-0.6, elecY[n1,n2]-0.3,\n",
      "                    r\"$(%d, %d)$\"% (n1, n2), fontsize=15, color=\"black\")\n",
      " \n",
      "    # figure settings\n",
      "    ax[row, col].set_xlabel(r'$V_{g1}$', labelpad=10); ax[row, col].set_ylabel(r'$V_{g2}$', labelpad=10)\n",
      "    ax[row, col].set_xlim([-0.7, 4.6]); ax[row, col].set_ylim([-0.7, 4.6])\n",
      "    ax[row, col].set_title(r\"$C_m/C_{1(2)} = %.2f$\" % ECm_EC)\n",
      "    ax[row, col].set_xticks([]); ax[row, col].set_yticks([])\n",
      "fig.tight_layout();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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FCrKz52DPHm38ACAhQZTL2LHiOkePCreNG0WE8OBBkV56CWjZEhg2zBH97NPH842aQKio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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f0222e8>"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Interpretation:\n",
      "<ol>\n",
      "<li>For a completely decoupled dots ($C_m = 0$) the diagram looks as in the 1st figure above (<b><font color=\"red\">red</font></b>). In this regime, the gate voltage $V_{1(2)}$ changes the charge on dot $1(2)$, without affecting the charge on the other.</li>\n",
      "<li>If the coupling is increased, the domains become <i>hexagonal</i> as in the 2nd and 3rd figure above (<b><font color=\"blue\">blue</font></b> and <b><font color=\"green\">green</font></b>). The vertices of the square domains have separated into \"<b>triple points</b>.\"</li>\n",
      "<li>When $C_m$ becomes the dominant capacitance ($C_m/C_{1(2)} \\rightarrow 1$), the triple-point separation reaches its maximum, as in the last figure (<font color=\"black\"><b>black</b></font>). The double dot behaves like one dot with charge $N_1 + N_2$.</li>\n",
      "</ol>"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Dimensions of the honeycomb cell"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The dimensions of the honeycomb cell can be related to the capacitances"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "a. From $\\mu_1(N_1, N_2; V_{g1}, V_{g2}) = \\mu_1 (N_1+1, N_2; V_{g1}+\\Delta V_{g1}, V_{g2})$, we obtain"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "delta = symbols(\"delta\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dVg1 = solve(mu1(N1+1, N2, Vg1+delta, Vg2) - mu1(N1, N2, Vg1, Vg2), delta)[0]\n",
      "Eq(Symbol(\"{\\Delta}V_{g1}\"), dVg1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$${\\Delta}V_{{g1}} = \\frac{|e|}{C_{g1}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAG8AAAAzBAMAAABrp0vfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRK5CYII=\n",
       "prompt_number": 31,
       "text": [
        "                 |e| \n",
        "{\\Delta}V_{g1} = \u2500\u2500\u2500\u2500\n",
        "                 C_g1"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Similarly, from $\\mu_2(N_1, N_2; V_{g1}, V_{g2}) = \\mu_2 (N_1, N_2+1; V_{g1}, V_{g2}+\\Delta V_{g2})$,"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dVg2 = solve(mu1(N1, N2+1, Vg1, Vg2+delta) - mu1(N1, N2, Vg1, Vg2), delta)[0]\n",
      "Eq(Symbol(\"{\\Delta}V_{g2}\"), dVg2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$${\\Delta}V_{{g2}} = \\frac{|e|}{C_{g2}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAG8AAAAzBAMAAABrp0vfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 32,
       "text": [
        "                 |e| \n",
        "{\\Delta}V_{g2} = \u2500\u2500\u2500\u2500\n",
        "                 C_g2"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "b. From $\\mu_1 (N_1, N_2; V_{g1}, V_{g2}) = \\mu_1 (N_1, N_2+1; V_{g1} + \\Delta V_{g1}^m, V_{g2})$,"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dVg1m = solve(mu1(N1, N2+1, Vg1+delta, Vg2) - mu1(N1, N2, Vg1, Vg2), delta)[0]\n",
      "dVg1m = dVg1m.subs({EC1: e**2*C2/D, EC2: e**2*C1/D, ECm: e**2*Cm/D})\n",
      "Eq(Symbol(\"{\\Delta}V_{g1}^m\"), dVg1m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$${\\Delta}V^{m}_{{g1}} = \\frac{C_{m} |e|}{C_{2} C_{g1}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAIkAAAAzBAMAAABRWzbpAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nLii46KKwrBTdf5gk9rYvsaNcAAAAAElFTkSuQmCC\n",
       "prompt_number": 33,
       "text": [
        "                    C_m\u22c5|e|\n",
        "{\\Delta}V_{g1}__m = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                    C\u2082\u22c5C_g1"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Similarly, from $\\mu_2 (N_1, N_2; V_{g1}, V_{g2}) = \\mu_2 (N_1+1, N_2; V_{g1} , V_{g2}+ \\Delta V_{g2}^m)$,"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dVg2m = solve(mu2(N1+1, N2, Vg1, Vg2+delta) - mu2(N1, N2, Vg1, Vg2), delta)[0]\n",
      "dVg2m = dVg2m.subs({EC1: e**2*C2/D, EC2: e**2*C1/D, ECm: e**2*Cm/D})\n",
      "Eq(Symbol(\"{\\Delta}V_{g2}^m\"), dVg2m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$${\\Delta}V^{m}_{{g2}} = \\frac{C_{m} |e|}{C_{1} C_{g2}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAIkAAAAzBAMAAABRWzbpAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 34,
       "text": [
        "                    C_m\u22c5|e|\n",
        "{\\Delta}V_{g2}__m = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                    C\u2081\u22c5C_g2"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For a full characterization of all capacitances in the system, an analysis in the <i>nonlinear transport regime</i> is required."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the above discussion, we have assumed that $V_{g1}$ and $V_{g2}$ only couple directly to the respective dots. However, there is a finite cross capacitance from one gate to the other in practice. The respective cross capacitances result in a change of the slope of the charge domain boundaries in teh honeycomb diagram."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "B. Quantized States"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "m, n = symbols(\"m, n\", int=True)\n",
      "\n",
      "def E_level(m):\n",
      "    \"\"\"\n",
      "    Symbolic Expression for discrete Energy Levels\n",
      "    \"\"\"\n",
      "    e = Symbol(\"E_{%s}\" % m)\n",
      "    return e"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The strong conefinement of electrons in the dots can lead to the formation of a discrete energy spectrum."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The electrochemical potential for adding an electron into energy level $n$ of dot $i$ is denoted by $\\mu_{i, n}$. Within the constant interaction model, $\\mu_{i,n}$ is the sum of the classical electrochemical potential $\\mu_{i}^{class}$ and the single-particle energy $E_n$:\\begin{align}\n",
      "\\mu_{i, n} = \\mu_{i}^{class} + E_n\n",
      "\\end{align}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the language of SymPy, we express these into the following:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mu1_quant(m, N1, N2, Vg1, Vg2):\n",
      "    return mu1(N1, N2, Vg1, Vg2).expand() + E_level(m)\n",
      "\n",
      "def mu2_quant(m, N1, N2, Vg1, Vg2):\n",
      "    return mu2(N1, N2, Vg1, Vg2).expand() + E_level(m)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the quantum regime, the addition energy for the $(N_1+1)$th electron occupying discrete level $m$, with the $N_1$ electron occupying discrete level $n$, becomes $\\mu_{1, m}(N_1+1, N_2) - \\mu_{1, n}(N_1, N_2)$ :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# addition energy of the dot 1\n",
      "add_energy1 = mu1_quant(m, N1+1, N2, Vg1, Vg2) - mu1_quant(n, N1, N2, Vg1, Vg2)\n",
      "add_energy1.subs(E_level(m)-E_level(n), Symbol(\"{\\Delta} E\"))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$E_{C1} + {\\Delta} E$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGAAAAASBAMAAABWXMbBAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAABJRU5ErkJggg==\n",
       "prompt_number": 37,
       "text": [
        "E_C1 + {\\Delta} E"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Similarly, we find the addition energy $\\mu_{2,m}(N_1 , N_2+1) - \\mu_{2, n}(N_1, N_2)$ of dot 2 :"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# addition energy of the dot 2\n",
      "add_energy2 = mu2_quant(m, N1, N2+1, Vg1, Vg2) - mu2_quant(n, N1, N2, Vg1, Vg2)\n",
      "add_energy2.subs(E_level(m)-E_level(n), Symbol(\"{\\Delta} E\"))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$E_{C2} + {\\Delta} E$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAGAAAAASBAMAAABWXMbBAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nd2WrZBJmfnQ4RqW255mNv/kv0YV10jhzFMIAAAAASUVORK5CYII=\n",
       "prompt_number": 38,
       "text": [
        "E_C2 + {\\Delta} E"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The dimensions of the honeycomb cell are obtained as follows:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dVg1_quant = solve(mu2_quant(m, N1+1, N2, Vg1+delta, Vg2) - mu1_quant(n, N1, N2, Vg1, Vg2), delta)[0]\n",
      "dVg1_quant = dVg1.subs(E_level(m)-E_level(n), Symbol(\"{\\Delta} E\"))\n",
      "Eq(Symbol(\"{\\Delta}V_{g2}\"), dVg1_quant)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$${\\Delta}V_{{g2}} = \\frac{|e|}{C_{g1}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAG8AAAAzBAMAAABrp0vfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nUgjC3Zuef1tkoaFkx5ivAAAAAElFTkSuQmCC\n",
       "prompt_number": 39,
       "text": [
        "                 |e| \n",
        "{\\Delta}V_{g2} = \u2500\u2500\u2500\u2500\n",
        "                 C_g1"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dVg2_quant = solve(mu2_quant(m, N1, N2+1, Vg1, Vg2+delta) - mu2_quant(n, N1, N2, Vg1, Vg2), delta)[0]\n",
      "dVg2_quant = dVg2.subs(E_level(m)-E_level(n), Symbol(\"{\\Delta} E\"))\n",
      "Eq(Symbol(\"{\\Delta}V_{g2}\"), dVg2_quant)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$${\\Delta}V_{{g2}} = \\frac{|e|}{C_{g2}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAG8AAAAzBAMAAABrp0vfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 40,
       "text": [
        "                 |e| \n",
        "{\\Delta}V_{g2} = \u2500\u2500\u2500\u2500\n",
        "                 C_g2"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dVg1m_quant = solve(mu1_quant(m, N1, N2+1, Vg1+delta, Vg2) - mu1_quant(n, N1, N2, Vg1, Vg2), delta)[0]\n",
      "dVg1m_quant = dVg1m_quant.subs({EC1: e**2*C2/D, EC2: e**2*C1/D}).subs(D, e**2*Cm/ECm)\n",
      "dVg1m_quant = dVg1m_quant.subs(E_level(m)-E_level(n), Symbol(\"{\\Delta} E\"))\n",
      "Eq(Symbol(\"{\\Delta}V_{g1}^m\"), dVg1m_quant)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$${\\Delta}V^{m}_{{g1}} = \\frac{C_{m} |e| \\left(E_{Cm} + {\\Delta} E\\right)}{C_{2} C_{g1} E_{Cm}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAAzBAMAAACqDMM2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nQmCC\n",
       "prompt_number": 41,
       "text": [
        "                    C_m\u22c5|e|\u22c5(E_Cm + {\\Delta} E)\n",
        "{\\Delta}V_{g1}__m = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                            C\u2082\u22c5C_g1\u22c5E_Cm       "
       ]
      }
     ],
     "prompt_number": 41
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dVg2m_quant = solve(mu2_quant(m, N1+1, N2, Vg1, Vg2+delta) - mu2_quant(n, N1, N2, Vg1, Vg2), delta)[0]\n",
      "dVg2m_quant = dVg2m_quant.subs({EC1: e**2*C2/D, EC2: e**2*C1/D}).subs(D, e**2*Cm/ECm)\n",
      "dVg2m_quant = dVg2m_quant.subs(E_level(m)-E_level(n), Symbol(\"{\\Delta} E\"))\n",
      "Eq(Symbol(\"{\\Delta}V_{g2}^m\"), dVg2m_quant)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$${\\Delta}V^{m}_{{g2}} = \\frac{C_{m} |e| \\left(E_{Cm} + {\\Delta} E\\right)}{C_{1} C_{g2} E_{Cm}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAP8AAAAzBAMAAACqDMM2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nPSGX9vN7aDbyH6kP68usYaDDAAAAAElFTkSuQmCC\n",
       "prompt_number": 42,
       "text": [
        "                    C_m\u22c5|e|\u22c5(E_Cm + {\\Delta} E)\n",
        "{\\Delta}V_{g2}__m = \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                            C\u2081\u22c5C_g2\u22c5E_Cm       "
       ]
      }
     ],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The electronic configuration that gives the lowest possible total energy in dot $1(2)$ is referred to as the dot <i>ground state</i>; any configuration with a higher total energy is referred to as an <i>excited state</i>."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The electrochemical potential for adding the $N_{1(2)}$th electron to the lowest unfilled energy level of the $(N_{1(2)}-1)$th electron ground state is labeled $\\mu_{1, 0}(N_1, N_2)\\ \\{\\mu_{2, 0}(N_1, N_2)\\}$; "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The electrochemical potential for adding the $N_{1(2)}$th "
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "Charge Stability Diagram (in a detailed picture)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(6, 6))\n",
      "\n",
      "ECm_EC = 0.3\n",
      "\n",
      "subs_dic={Cg1: 1, Cg2: 1, EC1: 1, EC2: 1, ECm: ECm_EC, e: 1}\n",
      "mumu1 = mu1(N1, N2, Vg1, Vg2).subs(subs_dic)\n",
      "mumu2 = mu2(N1, N2, Vg1, Vg2).subs(subs_dic)        \n",
      "    \n",
      "sol=[]\n",
      "\n",
      "# Getting lines forming a honeycomb\n",
      "\"\"\"\n",
      "electrochemical potential conditions:\n",
      "1. The addition energy of dot 1 to (1, 0) should be negative.\n",
      "2. The addition energy of dot 2 to (0, 1) should be negative.\n",
      "\"\"\"\n",
      "sol.append(solve(mumu1.subs({N1:1, N2:0}), Vg2)[0])   #(0,0) --> (1,0)\n",
      "sol.append(solve(mumu2.subs({N1:0, N2:1}), Vg2)[0])   #(0,0) --> (0,1)\n",
      "\"\"\"\n",
      "3. The addition energy of dot 1 to (1, 1) should be positive.\n",
      "4. The addition energy of dot 2 to (1, 1) should be positive.\n",
      "\"\"\"\n",
      "sol.append(solve(mumu1.subs({N1:1, N2:1}), Vg2)[0])   #(0,1) --> (1,1)\n",
      "sol.append(solve(mumu2.subs({N1:1, N2:1}), Vg2)[0])   #(1,0) --> (1,1)\n",
      "\"\"\"\n",
      "degeneracy condition:\n",
      "The transitions (0,0)->(1,0) and (0,0)->(0,1) are equally probable\n",
      "\"\"\"\n",
      "sol.append(solve(mumu2.subs({N1:0, N2:1})\n",
      "            -mumu1.subs({N1:1, N2:0}), Vg2)[0])\n",
      "\n",
      "# Getting the coordinates of triple points\n",
      "\"\"\"\n",
      "intersection of sol[0] and sol[4] corresponds to the left triple point\n",
      "\"\"\"\n",
      "x1 = solve(sol[0]-sol[4], Vg1)[0]; y1 = sol[0].subs(Vg1, x1)\n",
      "\"\"\"\n",
      "intersection of sol[2] and sol[4] corresponds to the right triple point \n",
      "\"\"\"\n",
      "x2 = solve(sol[2]-sol[4], Vg1)[0]; y2 = sol[2].subs(Vg1, x2)\n",
      "\n",
      "x_vec = np.arange(x1-1, x2+1, 0.01); \n",
      "y_vec = np.zeros((5, len(x_vec)))\n",
      "\n",
      "labels = [r'$\\mu_1 (1,0)=0$', r'$\\mu_2 (0,1)=0$', r'$\\mu_1 (1,1)=0$',\n",
      "          r'$\\mu_2 (1,1)=0$', r'$\\mu_1(1,0)=\\mu_2(0,1)$']\n",
      "\n",
      "for idx in range(5):\n",
      "    func = lambdify([Vg1], sol[idx], 'numpy')\n",
      "    y_vec[idx, :] = func(x_vec)\n",
      "    \n",
      "    ax.plot(x_vec, y_vec[idx], ls='--', lw=2, label=labels[idx])\n",
      "\n",
      "boundary1 = np.minimum(y_vec[0], y_vec[1])\n",
      "boundary2 = np.maximum(y_vec[2], y_vec[3])\n",
      "\n",
      "x_vec2 = np.arange(x1, x2, 0.01)\n",
      "degeneracy = lambdify([Vg1], sol[4], 'numpy')(x_vec2)\n",
      "\n",
      "ax.plot(x_vec, boundary1, ls='-', lw=3, color='black')\n",
      "ax.plot(x_vec, boundary2, ls='-', lw=3, color='black')\n",
      "ax.plot(x_vec2, degeneracy, ls='-', lw=3, color='black')\n",
      "\n",
      "ax.scatter(x1, y1, zorder=10, s=300, c='black', lw=3)\n",
      "ax.scatter(x2, y2, zorder=10, s=300, c='white', lw=3)\n",
      "\n",
      "# marking the charge states\n",
      "ax.text(x1-0.2, y1-0.2, r\"$(0, 0)$\", fontsize=30, color=\"black\")\n",
      "ax.text(x1+0.3, y1-0.2, r\"$(1, 0)$\", fontsize=30, color=\"black\")\n",
      "ax.text(x1-0.2, y1+0.4, r\"$(0, 1)$\", fontsize=30, color=\"black\")\n",
      "ax.text(x1+0.3, y1+0.4, r\"$(1, 1)$\", fontsize=30, color=\"black\")\n",
      "\n",
      "ax.text(x1+0.05, y1, r\"$e$\", fontsize=30, color=\"black\")\n",
      "ax.text(x2-0.08, y2-0.03, r\"$h$\", fontsize=30, color=\"black\")\n",
      "\n",
      "ax.set_xlabel(r'$V_{g1}$', labelpad=10); ax.set_ylabel(r'$V_{g2}$', labelpad=10)\n",
      "ax.set_xlim([0.1, 0.9]); ax.set_ylim([0.1, 0.9])\n",
      "ax.set_xticks([]); ax.set_yticks([])\n",
      "fig.tight_layout()\n",
      "ax.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0., fontsize=16);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ggLKyMgBAeXk5vL29O6zf29tbPRuDrbGrZApQlgP/HhyMvAceQOVDDyEzIgL9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\ny3wAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x111e2eac8>"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Nonlinear transport regime"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "A. Classical Theory"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Assume that the bias voltage is applied to the left lead ($\\mu_L = -|e|V$ where $V<0$) and that the right lead is grounded ($\\mu_R = 0$)."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The conductance regions at finite change from triple points to <i>triangularly shaped</i> regions. The conditions\n",
      "\\begin{align}\n",
      "-|e|V = \\mu_L \\geq \\mu_1,\\quad \\mu_1 \\geq  \\mu_2,\\quad \\mu_2 \\geq \\mu_R=0\n",
      "\\end{align}\n",
      "determine the boundaries of the triangular regions."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "The double dot stability diagram at finite bias voltage"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "V = Symbol(\"V\", real=True)\n",
      "muL = lambda V: -e * V"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(nrows=2, ncols=2, figsize=(12, 12))\n",
      "\n",
      "n1, n2 = 0, 0\n",
      "ECm_EC = 0.3\n",
      "for fig_idx, Vbias in enumerate([-0.1, -0.2, -0.3, -0.5]):\n",
      "    row = fig_idx//2\n",
      "    col = fig_idx%2\n",
      "    \n",
      "    subs_dic = {Cg1: 1, Cg2: 1, EC1: 1, EC2: 1, ECm: ECm_EC, e: 1, V: Vbias}\n",
      "    mumu1 = mu1(N1, N2, Vg1, Vg2).subs(subs_dic); mumu2 = mu2(N1, N2, Vg1, Vg2).subs(subs_dic)        \n",
      "    mumuL = muL(V).subs(subs_dic)\n",
      "\n",
      "    sol=[]\n",
      "    # Getting lines forming a honeycomb\n",
      "    \"\"\"\n",
      "    electrochemical potential conditions:\n",
      "    1. The addition energy of dot 1 to (1, 0) should be negative.\n",
      "    2. The addition energy of dot 2 to (0, 1) should be negative.\n",
      "    \"\"\"\n",
      "    sol.append(solve(mumu1.subs({N1:n1+1, N2:n2}), Vg2)[0])   #(0,0) --> (1,0)\n",
      "    sol.append(solve(mumu2.subs({N1:n1, N2:n2+1}), Vg2)[0])   #(0,0) --> (0,1)\n",
      "    \"\"\"\n",
      "    3. The addition energy of dot 1 to (1, 1) should be positive.\n",
      "    4. The addition energy of dot 2 to (1, 1) should be positive.\n",
      "    \"\"\"\n",
      "    sol.append(solve(mumu1.subs({N1:n1+1, N2:n2+1}), Vg2)[0])   #(0,1) --> (1,1)\n",
      "    sol.append(solve(mumu2.subs({N1:n1+1, N2:n2+1}), Vg2)[0])   #(1,0) --> (1,1)\n",
      "    \"\"\"\n",
      "    degeneracy condition:\n",
      "    The transitions (0,0)->(1,0) and (0,0)->(0,1) are equally probable\n",
      "    \"\"\"\n",
      "    sol.append(solve(mumu2.subs({N1:n1, N2:n2+1})\n",
      "                -mumu1.subs({N1:n1+1, N2:n2}), Vg2)[0])\n",
      "\n",
      "    sol.append(solve(mumu1.subs({N1:n1+1, N2:n2}) - mumuL, Vg2)[0])\n",
      "    sol.append(solve(mumu1.subs({N1:n1+1, N2:n2+1}) - mumuL, Vg2)[0])\n",
      "\n",
      "    funcs = [lambdify([Vg1], sol[idx], 'numpy') for idx in range(7)]\n",
      "\n",
      "    # Getting the coordinates of triple points\n",
      "    elec_x, elec_y, hole_x, hole_y = [], [], [], []\n",
      "    \"\"\"\n",
      "    intersection of sol[0] and sol[4] corresponds to the electron-like triple point (linear transport regime)\n",
      "    \"\"\"\n",
      "    elec_x.append(solve(sol[0]-sol[4], Vg1)[0]); elec_y.append(sol[0].subs(Vg1, elec_x[0]))\n",
      "    \"\"\"\n",
      "    intersection of sol[2] and sol[4] corresponds to the hole-like triple point (linear transport regime)\n",
      "    \"\"\"\n",
      "    hole_x.append(solve(sol[2]-sol[4], Vg1)[0]); hole_y.append(sol[2].subs(Vg1, hole_x[0]))\n",
      "    \"\"\"\n",
      "    Other electron-like and hole-like triple points generated in the non-linear transport regime\n",
      "    \"\"\"\n",
      "    elec_x.append(solve(sol[5]-sol[4], Vg1)[0]); elec_y.append(sol[5].subs(Vg1, elec_x[1]))\n",
      "    elec_x.append(solve(sol[5]-sol[1], Vg1)[0]); elec_y.append(sol[5].subs(Vg1, elec_x[2]))\n",
      "    hole_x.append(solve(sol[6]-sol[4], Vg1)[0]); hole_y.append(sol[6].subs(Vg1, hole_x[1]))\n",
      "    hole_x.append(solve(sol[6]-sol[3], Vg1)[0]); hole_y.append(sol[6].subs(Vg1, hole_x[2]))\n",
      "\n",
      "    s_list = [300, 100, 100]\n",
      "\n",
      "    for idx in range(3):\n",
      "        ax[row,col].scatter(elec_x[idx], elec_y[idx], zorder=10, s=s_list[idx], c='black', lw=3)\n",
      "        ax[row,col].scatter(hole_x[idx], hole_y[idx], zorder=10, s=s_list[idx], c='white', lw=3)\n",
      "\n",
      "    x_vecs = []\n",
      "\n",
      "    x_vecs.append(np.arange(elec_x[0], elec_x[0]+1, 0.001))\n",
      "    x_vecs.append(np.arange(elec_x[2]-1, elec_x[0], 0.001))\n",
      "    x_vecs.append(np.arange(hole_x[0]-1, hole_x[0], 0.001))\n",
      "    x_vecs.append(np.arange(hole_x[0], hole_x[0]+1, 0.001))\n",
      "    x_vecs.append(np.arange(elec_x[2]-1, hole_x[0]+1, 0.001))\n",
      "    x_vecs.append(np.arange(elec_x[2], elec_x[2]+1, 0.001))\n",
      "    x_vecs.append(np.arange(hole_x[1]-1, hole_x[1], 0.001))\n",
      "\n",
      "    label_list = [r'$\\mu_1 (1,0)=0$', r'$\\mu_2 (0,1)=0$', r'$\\mu_1 (1,1)=0$', r'$\\mu_2 (1,1)=0$', \n",
      "                  r'$\\mu_1(1,0)=\\mu_2(0,1)$', r'$\\mu_1(1,0)=-|e|V$', r'$\\mu_1(1,1)=-|e|V$']\n",
      "    ls_list = ['-.', '-', '-.', '-', '--', '-', '-']; lw_list = [2, 3, 2, 3, 2, 3, 3]\n",
      "    color_list = ['red', 'green', 'magenta', 'blue', 'orange', 'red', 'magenta']\n",
      "\n",
      "    for idx in range(7):\n",
      "        ax[row,col].plot(x_vecs[idx], (funcs[idx])(x_vecs[idx]), ls = ls_list[idx],\n",
      "                label=label_list[idx], lw=lw_list[idx], color = color_list[idx])\n",
      "\n",
      "    xvec_t1 = np.arange(elec_x[2], elec_x[0], 0.001, dtype=float)\n",
      "    xvec_t2 = np.arange(hole_x[2], hole_x[0], 0.001, dtype=float)\n",
      "\n",
      "    lower_t1 = np.maximum(funcs[4](xvec_t1), funcs[5](xvec_t1))\n",
      "    upper_t1 = funcs[1](xvec_t1)\n",
      "    lower_t2 = np.maximum(funcs[4](xvec_t2), funcs[6](xvec_t2))\n",
      "    upper_t2 = funcs[3](xvec_t2)\n",
      "\n",
      "    ax[row,col].plot(xvec_t1, lower_t1, ls='-', color='black', lw=3)\n",
      "    ax[row,col].plot(xvec_t1, upper_t1, ls='-', color='black', lw=3)\n",
      "    ax[row,col].fill_between(xvec_t1, lower_t1, upper_t1, color='gray', alpha=0.5)\n",
      "\n",
      "    ax[row,col].plot(xvec_t2, lower_t2, ls='-', color='black', lw=3)\n",
      "    ax[row,col].plot(xvec_t2, upper_t2, ls='-', color='black', lw=3)\n",
      "    ax[row,col].fill_between(xvec_t2, lower_t2, upper_t2, color='gray', alpha=0.5)\n",
      "\n",
      "    xvec_d = np.arange(elec_x[0], hole_x[0], 0.001)\n",
      "    ax[row,col].plot(xvec_d, funcs[4](xvec_d), ls='-', color='black', lw=3)\n",
      "\n",
      "    #marking the charge states\n",
      "    ax[row,col].text(elec_x[1]-0.3, elec_y[1], r\"$(%d, %d)$\" % (n1, n2), fontsize=30, color=\"black\")\n",
      "    ax[row,col].text(elec_x[0]+0.25, elec_y[0]-0.2, r\"$(%d, %d)$\" % (n1+1, n2), fontsize=30, color=\"black\")\n",
      "    ax[row,col].text(hole_x[2]-0.3, hole_y[2]+0.1, r\"$(%d, %d)$\"% (n1, n2+1), fontsize=30, color=\"black\")\n",
      "    ax[row,col].text(hole_x[0]+0.05, hole_y[0]+0.2, r\"$(%d, %d)$\"% (n1+1, n2+1), fontsize=30, color=\"black\")\n",
      "\n",
      "    ax[row,col].set_xlabel(r'$V_{g1}$', labelpad=10)\n",
      "    ax[row,col].set_ylabel(r'$V_{g2}$', labelpad=10)\n",
      "    ax[row,col].set_xlim([float(elec_x[2])-0.3, float(hole_x[0])+0.3])\n",
      "    ax[row,col].set_ylim([float(elec_y[1])-0.2, float(hole_y[2])+0.3])\n",
      "    ax[row,col].set_xticks([]); ax[row,col].set_yticks([])\n",
      "\n",
      "ax[0,1].legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0., fontsize=16)\n",
      "fig.tight_layout();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2IA0DEg0hPz/f7vra/j7fvL3UnKg7SQYIoSd6nyowHfgf4G6tA6mb5ORk+vTp\nw5QpU2zmYtbFCy+8wJUrV1izZo1L9mdNVVXmzp3Lbbfdxo4dO/D+bj0c/3/mIoH3b4Z2rk8+CNHQ\npk+fzrlz53jvvfdsvpGvTISVlpbyxBNP0Lp1a5v3BQQEEBcXR3FxMXPnzr15t04bN24c9957Ly1a\ntKB//9p9U/mnP/0JgMcee+yWj+9yUjfAsTuBZ4G/YB45oXMe1R732B/54WgqAIriRUTkbzQOSNS3\npKQkvvzyS5t1WVlZjB8/npiYGKf24Wj7oqIiEhMTa9WRqSYGg4Fnn32WtWvXsmTJEuLj4ykqKnLZ\n/vVGkgFC6MnNRQRVrQJx4DfA69wYfuqmmjRpQkpKCg888ACxsbEuuYgsWLDAqS4CtaWqKnFxcXTv\n3p1NmzbhW/AFfFnxgSfir9B5nMuPKURDe++999ixYwfz58+3fOiptHXrVrKzs1EUhUmT7E+JqVyf\nlZXFvn11H7pU0/SAm/n4+PDKK6+wdetWtm3bVufju8T9QLOK5TO47fSueqEAKzAnuJtoHIsTPKo9\nbvthHP+xGaDYb48rPEpiYiJlZWU2xZENBgPBwcEYjUZUteYb3eq279KlC9OmTSM+Pt5lMU+dOpWA\ngACeeuopEhISaNeuHXFxcS7bv95IMkAIPbkHqKwTdB74VsNYGoEXXniBlStXuqRVk3WBJ1dSFIV5\n8+aRkJBgXtH2XujxGIS/AndKNwHh/kpKSliwYAF+fn52b7g2bdoEgK+vLwMGDLC7jwEDBuDj4wNA\nSkpK/QVbjYkTJxIYGMjzzz/vdJvQetUUeMDquR5HmwmneUx73DtG8GnxeKCa9rieTrF6OHrdle/T\nSGZmJqmpqcyaNctmffPmzWnfvj0BAQFOJQNq2r5z584EBweTmJhY55j379/Pnj17mDx5smXdjBkz\n2LRpE6dPe2bnC0kGCKEnTTAXEqzkxnPz3UVISAheXvr+UxgSEnLjiZcP3PM3+NVC7QISwoXeffdd\nfvrpJyIjI2nevHmV17OysgAIDg522FatadOmBAcHA1g+oDQ0RVEYM2YMOTk5miUkqpC6AR7Do9rj\n7tkn7XHdRHBwMKmpqZbnERERVWq6OLJkyRLGjx9fX6HZiI6OZtGiRXUe6Zmeno6vry+hoaGWdcHB\nwfj6+rJnz566hqlL+r4DFqIxunmqgBA3UxTzQwgPsHHjRgDuueeeKq9dvHjRMhS5puHEHTt2BCA3\nN5dffvkapZ28AAAgAElEQVTFxVE6JyIiAoB33nlHk+NXYX09+TduMT9eOOZx7XF9fZ0/eU+iWj0c\nve7K992i3NxccnJyiIyMBODKlSscOXKEUaNuFLjKz8/nu+++q/LeoqIidu/eTb9+/VwblAPh4eEY\nDAZ2795tsz4jIwMvL69qH97e3uTm5gKQl5dHmzZtquy/TZs2nDt3rkHOpaFJMkAIvbEuIpgGlGsV\niAMq8DwQAbiuXosQohEqKCjg4MGDAPTq1avK61euXLEs31w48GbWr+fl5bkowtqp7EKQmZmpjyrX\nvYHKrnRXgUMaxqJHmZivufO1DsQ5btce1/AdfH+j5adNe9zfSOFAvUtPT6d3794EBAQA5ilYgYGB\nlr/Vp06dYuTIkaSnV+1dmpOTg6qqdj9Y1wcvLy9atmzJsWPHbNZHRkZiMpmqfRiNRrp06QKYR5lV\nTjmzZjKZnJrS4I4kGSCctnfvXpe3YquN0tJS3n33XYevq6rKli1bGjCienIXUPkF2M/Al9VsqwUF\ncyXm1UAjTeo3GON1OPTfUKKDDxVC1IOjR4+iqiqKoli+2bd29epVy3JNtT2sX9fqWlXZ8tBkMvHZ\nZ59pEoMNBekqUJ32wDPAi1oH4jy3aY9bchHSxkBmLHy/o2p7XKF76enpDB8+HDC3fn3jjTcYMWKE\n5fXQ0FD69etnt+BqQUEBgN0P1vXFz8+P8vK6fYMWFBTEtWvXqqzPz8+na9euddq3XkkyQNTo+vXr\nzJkzhw8++IAWLVrYvHby5Elmz55Njx496N69O926dWPWrFmcOnXKZccvLy9n/fr19OzZk9mzZzvc\nTlEULly4QExMjN1/yG7j5ps3PU4VeAIYBNifvitcQTXBpzPh1ArYP0XraISoF9bXirZt21Z53fom\ns6YK/9a1P7T6BqeyE4Kqqnz11VeaxFCF1A1wLBQYx43CvW5C9+1xy36BjCgwnIFWfVHbP2DbHtdB\n7Q+hLxkZGZYpAklJSRiNRkaOHFllO3t/b4OCggDzh+jq1LZzS3XbX7t2jW7dutmsq+00gaioKAwG\nA+fPn7fs4+TJk5SWlhIVFVWrWN2FJANEtfLz8xk1ahQ+Pj6sWrXK5rXU1FT69+9PdnY2Bw8eJCcn\nh48//phvvvmGgQMHsmPHDgd7dY7JZGLDhg306tWLuLg4cnNza/yj8cwzzxAbG8vQoUP54Ycf6nR8\nTVlPFZCbt8bpyPNwbhP4+MNAx/NDhXBn1olbe9/8WyegS0pKqt2X9ev11d2jJn5+fpZlXUwTANvr\nyUFAm3IKwoV03R7XWAqZkyD/EDTvgfrAh8Q99T832uM21joBbiY7O5vc3FwKCwt5++23ad26NadP\nn6ZPnz7s2rWrxvcHBQUREhJCdna2w20ctRZcvnw5W7dudXp7MI8iKyoq4r777rNZX9tpAmFhYYwe\nPZrk5GTLPrZs2UJUVJRtMWcPIskA4VBhYSFjxozB39+/SuXQAwcOMGPGDJo1a8b27dstQyO7du3K\nzp078fb25uGHH65VP9yb7dq1i7vuuotDhw5Z5mE6Y/bs2YwbN44HH3wQg8Fwy8fXlPXNWxbgpqch\nbtGJ5XByOXg1gWHboHXDFOARoqFZf6tp79vCyhs0qHnov3XRQOv3NSTrhIZWRQyrCAT6ViyXAx9r\nGItwKV22x/3iSfhxH/i1h+H/QrntDtv2uMItpKen07FjRxISEvD39+fuu++mVatW7Ny5k+joaJtt\nHX1RFx8fz759VdtilZSUkJqaSlpaGmfOnCElJYVLly4BUFxczPLly3nooYcsUw2q275SWloaI0eO\nJCwsrM7nvnnzZs6ePcvSpUtZsmQJeXl5lkK3nqjhJnIItzN9+nTOnTvHrl27bP6hV877Ki0t5bnn\nnqtS1CkgIIC4uDgSExOZO3cuBw4cuKXjjxs3zrLcv39/jh8/7vR7//SnP7Fr1y4ee+wxm5YobiMQ\n6AN8xY2bt+hq36ENFSgBmmkdiAe5mAlH/mBeHvQe3DGq2s2FcGfWH0CuX79u9/XOnTvz/fff1zja\nq7JoYFBQkN0WhQ3BOrmhVQx2/RqozM3vBWI0jEWvrgCtcbuvyXT3beWdv4ef0mDoVvC/E9BhjKJG\n6enpvPjiizz55JOWdfaG/Kuq6vDb+rlz57Jr1y5Onz5Nz549Lev9/PyYMmUKU6ZUnQLZrFkzvv/+\ne+bPn2/5G1rd9mD+XJKUlMSbb75Zq3N0pGXLli7blztwsz95oqG899577Nixg/nz51vmQFbaunUr\n2dnZKIrCpEmT7L6/cn1WVpbdrGBt1XZOkY+PD6+88gpbt25l27ZtdT6+JvQ+VeBfQHcgXutAPEzA\n/RD6HPR/Hbo9onU0QtSrDh06WJYLCwvtblNZwOrMmTMObzrLy8s5c+YMgN05rQ3FeqqCvRoImpG6\nAdWLBQIwJ+BF3bQbBONOQ5sBWkcibpHJZCItLc2mWKA93377LceOHSMrK8vutChvb2+Sk5N57bXX\nalXLa9u2bYwdO9bp2hLLli1j3rx5BAcHO30McYMkA0QVJSUlLFiwAD8/P+Li4qq8vmnTJgB8fX0Z\nMMD+H/sBAwZYKoimpKTUX7DVmDhxIoGBgTz//PMYjW7YXNm6iGDd8ymu1x44h/nG0jO7rWhD8YKB\ny+GuP2gdiRD1rm9f8/h1VVW5cOGC3W0qW5AVFxc7LMp39OhRy8gCR0nqhmB9Q9y7d2/N4qhiCFA5\nkvwkcL6abRujNpivY9JtwTW8mmgdgaiDvXv30qpVK0JDQ6vdLiQkhEOHDrF+/XratWtnd5u2bduy\nfv169u/f7/TxJ06caClcWJPDhw8zc+ZMBg8e7PT+hS1JBogq3n33XX766SciIyPtDnPMysoCIDg4\n2GHWrmnTppYMXVpaWv0FWw1FURgzZgw5OTmaJSTqZCg3Wvd9DeitHmJfoC3m3tU/ahyLJ6rlaBgh\n3FFISIhl9NnZs2ftbhMTE0O3bt1QVZXt27fb3aay2FRISEiV+awNqXIqg6IoREREaBZHFc2AYVbP\nZXSArV9jviPO0zoQIbQ3duxYTpw44bL9+fj4EBPj/Nwk684wNRkwYECVEcyidiQZIKqoLJJxzz33\nVHnt4sWL/Pij+ZNfp06dqt1PZc/o3NxczQopVd6MvfPOO5ocv05uB6wTnf/WKhAHvIADQD7QoYZt\nhRDCDkVRmDBhAoDDgrNeXl6sW7cOgHXr1lUpJJifn8+bb75ps12lgoIChg4dir+/P9OnT3e66nrl\ndQ6oVaX2yto2AwcOrPEa2eCsR5vJN+C2xmOuGfAXrQNxM5c/hZy/ax2FEKIOJBkgbBQUFHDw4EEA\nevXqVeX1K1euWJZvLhx4M+vXKws7NbTKLgSZmZn6afNUG9Y3b3r8JicUkNGAt668GD77PRTpbdiH\nEA3n8ccfB8x/px0ZO3Ysa9eu5erVq0ycONEypeD7779nwoQJFBYWsm7duir1Aj766CMOHDhAYWEh\nKSkpTrVOS0tLs4xoU1WV1atXOz3V7NNPPwVg5syZTm3foKzrBuwDTFoFokO3Aa20DsLNFJyAjGjI\nmgE/7NE6GiHELZJkgLBx9OhRVFVFURTLN/vWrl69almuqZWN9es1tYSqL5UtD00mE5999pkmMdSJ\ndRHBfcjcfE9iKoeDD0P2evN/HRRGE8LTRUREMGLECE6dOsXXX3/tcLsnn3ySL774gk6dOjFs2DCC\ng4OJjIykR48efP7553Zr3AwePJiwsDC8vLxQFIUvvvjC4f7ffPNN2rVrx6hRozAajSiKgqIozJ8/\nn5YtWzJ69GiH7wUoKyvjww8/pEOHDpYEh66EY671AuZvwY9oGItwb0XfQ/oYKM2HTuOk640QbkyS\nAcLGqVOnLMv2KiFbV/WvqcK/9ZwfRxWg61vlPCJVVR0WntK1gZhbHQFcAL7RMBbhOqoKX8bD9/8H\nvq0h4k2pESAatRUrVuDj48OKFSuq3a5fv34kJSXx7bffkp2dzZkzZ9iwYYOlEOHNOnbsyPHjxykv\nL+f111+nc+fODvc9Z84cLl++jMlkwmg0Wh4mkwmDwcDevdWPrX///ffJz89n1apV+Pr6VrutJrzQ\n/2gzoX+lVyF9LBSdh3aD4f5N4CWdyoVwV5IMEDasW3/Y++a/RYsWlmXrFkr2WL9u3Uu6Ifn5+VmW\n3XKagDdg3dlFrzdvOci3TLVxfBGc+St4+8EDO6Fl1Sk5QjQm4eHhvPTSS2zYsIHDhw/XyzH27dvH\no48+Wi/7zs/PZ+HChTz22GOW7ge6JHUDqncN2I555ISw7+AMKPgaWoaZr18+t2kdkRCiDiQZIGyU\nlpZalu11CujSpYtluaah/9ZFA63f15CsExpaFTGsM+vRd3pMBuwGBgEfah2Im7iYCccWmlsIDk6B\ngPu1jkgIXVi4cCGxsbHMmDHD5VPLFi9eTI8ePRg0aJBL9wvmaWgzZ84kPDyct956y+X7dynrZMAB\noFCrQHRqNvAmcFHrQHSs72vQ9l6I3ANN22gdjRCijiQZIGxYf4Nf2bP55tcrh1lWtlBypLJoYFBQ\nkN0WhQ3BOrmhVQx1Zn3z9jFQ6mhDjYzG3FrwRa0DcRMBQyD8Fbh7DQRN1DoaIXQlOTmZPn36MGXK\nFJu/33XxwgsvcOXKFdasWeOS/VlTVZW5c+dy2223sWPHDoftdnWjI9C7YrkU+ETDWPToH8C/ABms\n5VjrPjA6C24P0joSIYQLSDJA2OjQ4UaPuMJC+18ZDB8+HIAzZ844rAVQXl7OmTNnAKpUd25I1lMV\n7NVAcAvBQPeK5ULgUw1jsccbkOnuzlMUCH8ZQp7UOhIhdKdJkyakpKTwwAMPEBsbW6u2fo4sWLDA\nqS4CtaWqKnFxcXTv3p1Nmzbps06APdZ1EPU42kxLci1zjtS4EcJjSDJA2KgswqSqqqV1080q50MW\nFxc7LMp39OhRy8iCSZMm1UOkzrGuE9C7d+9qttQ5vU8VEEIIF3rhhRdYuXJljV1rnFFfNWsURWHe\nvHkkJCTUy/7rjdQNEEIIUUGSAcJGSEiIpQL/2bNn7W4TExNDt27dUFWV7du3291m69atlv1FR0fX\nS6zOqJzKoCgKERERmsVRZ9Y3b/s0i0IIIRpMSEiITVcaPQoJCdE6hNobBlQOYvgaqH7Gn2jMclPh\n9FqtoxBC1CN9X2VFg1MUhQkTJgDmb/ft8fLyYt26dQCsW7euSqGn/Px83nzzTZvtKhUUFDB06FD8\n/f2ZPn2600NAf/zxR8tybYaNHj9+HICBAwfSqVMnp9+nOyO4MXzxc8wVj/XmGLAMc/0AYVb2C+yf\nBoYcrSMRQgiz2wHruqWSYLb1C7ABWKp1IBr7KR0O/tbcBveiFJcQwlNJMkBU8fjjjwOQmZnpcJux\nY8eydu1arl69ysSJEy1TCr7//nsmTJhAYWEh69atq1Iv4KOPPuLAgQMUFhaSkpLi1DzOtLQ00tLS\nAPP0hdWrV2M0Gp06l08/NU+wnzlzplPb61ZbYEDFsgnI0C4Uh+YDzyPTGCoZSyFzMuRugaxHwUF9\nDSGEaHDWdQNkqoCtImAm8ApQfQdlz5V/BD6eAKZS6PlfEDBU64iEm8vPz7e73tGUZEdu3t4t24br\njCQDRBURERGMGDGCU6dO8fXXXzvc7sknn+SLL76gU6dODBs2jODgYCIjI+nRoweff/45cXFxVd4z\nePBgwsLC8PLyQlEUvvjiC4f7f/PNN2nXrh2jRo3CaDSiKAqKojB//nxatmzJ6NGjHb4XoKysjA8/\n/JAOHTpYEhxuzXqqgB4/cFfGp8fYGpqqwmePw497wa89DHpPCi4JIfTj5qlnJq0C0aFAoC9QDBzU\nOBYtGL6DjAeh/BfoMg0GrpDrl6iTpKQkvvzyS5t1WVlZjB8/npiYGKf24Wj7oqIiEhMTXVJstpLB\nYODZZ59l7dq1LFmyhPj4eIqKily2f72RZICwa8WKFfj4+LBixYpqt+vXrx9JSUl8++23ZGdnc+bM\nGTZs2GApRHizjh07cvz4ccrLy3n99dctbQrtmTNnDpcvX8ZkMmE0Gi0Pk8mEwWBg797qv854//33\nyc/PZ9WqVe5T5bk6ei8iOBaYBjj3d92zHV0AZ5PA53Z4YBf4B2sdkRBC3NAf84gzgJ8wT/MSNzwF\nLAbu1DqQBqaq5qkBJT9B4Ei4bwMo8lFB3LrExETKyspsvsAzGAwEBwdjNBoddiWzVt32Xbp0Ydq0\nacTHx7ss5qlTpxIQEMBTTz1FQkIC7dq1s/sFp6eQf+HCrvDwcF566SU2bNjA4cOH6+UY+/bt49FH\nH62Xfefn57Nw4UIee+wxS/cDt3c/4Fex/C1wTsNY7LkL2ARM1ToQjV3cD98sAcUHhvwD2t6tdURC\nCGHLC/0nmLX0e8xT37poHUgDUxQYtAGCJsGwbeBd924ewpaiNMxDDzIzM0lNTWXWrFk265s3b077\n9u0JCAhwKhlQ0/adO3cmODiYxMTEOse8f/9+9uzZw+TJky3rZsyYwaZNmzh9+nSd969HkgwQDi1c\nuJDY2FhmzJhRpUhgXS1evJgePXowaNAgl+4XwGQyMXPmTMLDw3nrrbdcvn/N+GGuAl1Jij7pU/sh\n0D8R7l0PHcdqHY0QQtgndQOEPS1CYOhWaNJC60iEDgQHB5Oammp5HhERwerVq51675IlSxg/fnx9\nhWYjOjqaRYsW1Xm6QHp6Or6+voSGhlrWBQcH4+vry549e+oapi5JMkBUKzk5mT59+jBlyhRKS0td\nss8XXniBK1eusGbNGpfsz5qqqsydO5fbbruNHTt24O3t7fJjaEq+yXEPvf4bevxO6yiEEMIx67oB\nmZjnyAshRIXc3FxycnKIjIwE4MqVKxw5coRRo0ZV/0bMc/l3795Nv3796jlKs/DwcAwGA7t377ZZ\nn5GRgZeXV7UPb29vcnNzAcjLy6NNmzZV9t+mTRvOndPbkFzXkGSAqFaTJk1ISUnhgQceIDY21iUF\nOhYsWOBUF4HaUlWVuLg4unfvzqZNmzyjTsDNrG/e/o0UfRJCCHFrgjBP7wJz1fz9GsYiRCOhqg3z\ncIX09HR69+5NQEAAACkpKQQGBtKrVy+Ki4uZM2cOAwYMoG/fvlXakefk5KCqqt0P1vXBy8uLli1b\ncuyYbQGUyMhITCZTtQ+j0UiXLuY5QU2bNsXHx6fK/k0mk1NTGtyRJAOEU1544QVWrlxJ06Z1nz/m\n7+/vgoiqUhSFefPmkZCQUC/714U+QEDF8mXgaDXbamUjEE3jrMIshBDuRO9darT0M+YWg/cCnvkZ\nAL5ZCl8vlta3wq709HSGDx8OQGFhIW+88QYjRowAYOfOnSxbtozDhw8TGxvLyy+/bPPegoICALsf\nrOuLn58f5eXlddpHUFAQ165dq7I+Pz+frl271mnfeiXJAOG0kJAQvLz0/SsTEhKidQj1ywsYafVc\njzdvPphvoHprHEdDKL0K6VFQcELrSIQQovakboBjzYHBQLLWgdST796D/yTA0Rfh6n+0jkboUEZG\nhmWKQFJSEkajkZEjzTehsbGxNG/eHDDXEQgMDLR5b1BQEGD+EF0dpZbVDqvb/tq1a3Tr1s1mXW2n\nCURFRWEwGDh//rxlHydPnqS0tJSoqKhaxeou9P3JTghR1c39ofVmKjAFaKl1IPXMWAIfT4ALu+Hz\nJ+SbFSGE+3kAcwIXzCPNftIwFr3xAuIwtxfUSXV2l8nbBZ89bl4e+Bdo01/beITuZGdnk5ubS2Fh\nIW+//TatW7fm9OnT9OnTh127dtGkSRPLtpmZmbz44os27w8KCiIkJITs7GyHx3DUWnD58uVs3brV\n6e0Brl69SlFREffdd5/N+tpOEwgLC2P06NEkJ9/IAm7ZsoWoqCiP/cJRkgFCuBvrui2ZmOd6ioZl\nMpp7MV/KhGadYHCyfnr5CCGEs/wxf/tdSY8JZuFal7Jg/xRQjdD7BQh9WuuIhA6lp6fTsWNHEhIS\n8Pf35+6776ZVq1bs3LmT6Ohoy3ZpaWlMnjzZ8mHaWnx8PPv2Vf2jUlJSQmpqKmlpaZw5c4aUlBQu\nXboEQHFxMcuXL+ehhx6yTDWobnvrOEaOHElYWFidz33z5s2cPXuWpUuXsmTJEvLy8ti4cWOd96tX\nip6LISiKouo5PiE0EwpUtjvdh+3UAVG/VBUO/RecXgNNWsKv90OrX2kdle4pioKqqm6fMZHrkvA4\ni4D/rVj+HfCedqGIeqaaYPcAuHYUeswyt8BtxIlsV16XPO3aMH36dIYMGcKTTz7pcJtPPvmE1q1b\nEx4eTklJCfn5+XTs2NHyutFoJDo6mlWrVtGzZ89aHX/+/Pm8+uqrTnUFM5lMTJo0icTERIKDg2t1\nnMbE0e+7JAOEcEfxwNqK5QTgzxrGUp1ybgxB9RSXDsBHQ8DLF4bvhcAHtI7ILUgyQAid+hxzkTyA\nDkAenjcsvq7KMY/Ca651IC5QmAsnl0P/ZeDlaRfo2pFkgH0mk4lOnTqRkZFBaGio3W22b99OfHy8\nTbeAw4cP20wfAHM7wj/84Q+sXLmSVq1aOXX8bdu20aZNG0u9gposXbqUIUOGMHjw4Jo3bsQkGSCE\nJ/knEFuxPAA4pGEs9vwATAPyga81jqU+ZL8NTVpAlylaR+I2JBkghE4ZMXepuVrx/DiNowCss94F\nnsOchF+kcSzCpSQZYN+ePXt47rnnOHHCNcWRy8vL2bNnDzExMU5tbzKZnC5YfvjwYTp37kz79u3r\nEmKjIMkAITxJAdAW802cAlwE2mkaka1yzPEUAGcBz+zGImpBkgFC6NgU4B8Vy8sxf/gVZruBKCAC\n8ygK4TEkGSAaE0e/71JAUAh31BK4p2JZBdI0jMUeH2B4xfIXWgYihBCiRtZdavTYslZLwwBfzJ0W\n3K1gr3w4FULUQJIBQrgr664Cerx5W4r55mmy1oHUkdxMCSE8nXUyIAO4rlEcenQ75oK9ZwE/bUOp\nFVWFz+PgPwvkOiaEcEiSAUK4q5u/ydHbtT4EcPcpXCUXYd8wyD+sdSRCCFF/ugN3ViwXAwc1jEWP\nuuJ+RRW/WgjZ6+HUX+CXb7WORgihU5IMEMJdDeJGZeNzQLaGsXiiMgNkxMCl/XD4OflmRQjh2awT\nzHs1i0K4wum18PUiULxhyBZoUbu2bkKIxkOSAUK4qyaAdVc7PU4VcFemMtg/FfK/gNu7w/2bG3Uv\nZiFEIzDaalmuJ+4rNxW+fNq8fM/foJNzFdyFEI2TJAOEcGfW3+Ts0yyK6hXiXhWYVRU+nwMXdkPT\ntjB8DzS7Q+uohBCifg0HvCuWDwOXNYxFj4zAl+ivla81UzkcewVQoe9rEPyY1hEJIXROkgFCuDPr\nZEAa5psVPSkAOgAL0V9NA0cuZ8F374B3M3hglwyvFEI0Di2BeyuWVeDfGsaiR0nA74CjWgdSDS8f\nGJEG/RMhbL7W0Qgh3ICi556Y0rNTiBqoQGfgh4rnn3Gj5aBeFAG3aR1ELZ3bDD63y/BKF3JlP2ct\nyXVJeLRXgD9WLM8C3tYuFN1Rcb8igqJarrwuybVB6J2j33cfLYIRQriIgrnF4PsVzz9Cf8kAd0sE\nAHSdpnUEQgjR8EbD9T9eZxe7OLX1FARD6F2hxMTE4Ovrq3V02pJEgBDCA0kyQAh3d3My4EUNYxFC\nCOGWjEYjS9OXslJZyUX1onmaV8X1pH379jz77LPMmzcPb2/vavcjGpDxOnj5SoFbIcQtk2kCQri7\nC0DHiuUmwFXgdu3CcTuqCRQpn1LfZJqAEPplNBqZPn06mzdvrna7adOmkZycLAkBPTCWwsfR4B8K\nA/8CXvL/pLZkmoBoTBz9vssdsBDurgPwq4rlMuATDWNx5AqwGfhC60BuUpQHewbCxf1aRyKEEJpZ\nunSpTSKgU6dOPP300zz99NN06tTJsn7z5s28/vrrWoSoHx8DC4BrGsagmuDTmfDjPjifCiU/ahiM\nEDXLz8+3u/7ChQt12u/ly/pue+LovGvr5p+TK89bkgFCeIJRVst67A/9N+Ah4C2tA7FSWgAZUXD1\nP3DsZXNLQSGEaGSuX7/OypUrLc/nzJlDTk4Oq1atYtWqVeTk5PDEE09YXl+xYgWlpaVahKoP/wv8\nGXMHHy2oKhz+bziXAj7+ELkHbutU8/uE0EhSUhJffvmlzbqsrCzGjx9PTEzNhZoNBgPPPvssa9eu\nZcmSJcTHx1NUVARAUVERiYmJFBcX10vsdWF93tWdQ3Uc/Zxced6SDBDCE1i3GNynWRSOVcb3Efpo\nMWi8Dp9MhGtfQYtQGLJF5lwKIRqlXbt2cfHiRcA8ImDVqlU0adLE8nqTJk1YvXo1HTua56NdvHiR\nXbt2aRKrLoyu+K9WifcTS+HUX8y1Aob9E9r01ygQIWqWmJhIWVkZo0ePtqwzGAwEBwdjNBpxZmrF\n1KlTCQgI4KmnniIhIYF27doRFxcHQJcuXZg2bRrx8fH1dg634ubzru4cHKnu5+TK85ZkgBCeYBjm\negEAxwC9jRjsB4wFZgLl2oaCaoKsR+FiBvjdYf5WpWlbjYMSQghtnDp1yrI8adIkm0RApSZNmjBp\n0iS772l0xgFzgckaHNtYAjl/BxS4LwnuGKFBEKLONir2H67aXicyMzNJTU1l1qxZNuubN29O+/bt\nCQgIqDEZsH//fvbs2cPkyTf+wc2YMYNNmzZx+vRpADp37kxwcDCJiYmuP4lbcPN5O3MO9tT0c3LV\neUsyQAhP0By4z+q53kYHeAO7Mfewrnqf2bCufA7nt5qHVw7fDc27aRyQEEK4l2+++YaSkhKtw9BG\nX2AtMFKDY3v7wa8/MY9m6zpVgwBEYxMcHExqaqrleUREBKtXr3bqvUuWLGH8+PF1On56ejq+vr6E\nhobaxOTr68uePXss66Kjo1m0aJHLpgu48rydPYdb4YrzlmSAEJ5C71MF9KLdIBj2fzBsG7Tup3U0\nQpWti3sAACAASURBVAihKesb1G3btlFWVlZlm7KyMrZt22Z5npSURPv27Zk+fTr//Oc/G29iQAu+\nraGLFsMShMs8otp/uGp7F8nNzSUnJ4fIyEgArly5wpEjRxg16kahqvz8fL777rsq7y0qKmL37t30\n61e3+6y8vDzatGlTZX2bNm04d+6c5Xl4eDgGg4Hdu3fbbJeRkYGXl1e1D29vb3Jzc2t13o7YO29n\nz+FWODrv2pBkgBCewjoZoJe5+XrVKRruqPmPuhBCeLro6Gjat28PmG9an376aZuEQFlZGU8//TQ/\n/PCDzft++eUXNm7cSGxsLAEBATzyyCNs375dl4W8hBC1l56eTu/evQkICAAgJSWFwMBAevXqBZin\nC40cOZL09PQq783JyUFVVbsfgmujadOm+Pj4VFlvMplshs57eXnRsmVLjh07ZrNdZGQkJpOp2ofR\naKRLly5OnXdxcTFz5sxhwIAB9O3bl6NHj9Z43s6ew61wdN612kedIhBC6MdAoGXF8g/ASQ1jEUII\n4RaaNm3Ks88+a3n+17/+le7du1taC3br1o2//vWvltf79u1rKSZYyWAwkJKSwqRJk2jfvj0PP/ww\nW7dudapatqjG9XxznRshNJCens7w4cMBKCws5I033mDEiBt1KkJDQ+nXrx+KnQLMBQUFAHY/BNdG\nUFAQ165V7eOZn59P165dbdb5+flRXl73wlTVnffOnTtZtmwZhw8fJjY2lpdfftnmvfbOuzbncCvq\net6SDBDCU/gA1rWE9Nhi8DAwh4ZtMWjSumKhEELo27x585g2bZrleV5eHmvWrGHNmjU2IwKGDx9O\nYmIif//733nrrbd45JFH6NTJtq2dwWBg06ZNTJ48mfbt2zNt2jT+8Y9/eF5iYA0wCPi8nvZfehX2\nDYOsmWCqOnVDiPqWkZFhGSqflJSE0Whk5MiqxTLsfbsdFBQEmD/wVsdeIsFaVFQUBoOB8+fPW9ad\nPHmS0tJSoqKibLa9du0a3bp1q3IOtZ0mUN15x8bG0rx5c8BcRyAwMLDG867NOThS3c/J3nnXhiQD\nhPAkN08V0JtioCcwvIGOZzgLu8Lgwt4GOqAQQrgfb29vkpOTWbx4sWXKwM0eiXqEF198EW9vbxRF\nISQkhN///vckJSXxt7/9jd/+9reWG+FKhYWFbNmyhSlTphAQEMDUqVNJTU2lsLCwIU6rfgUBizEX\nFHS18mL4eBwUfA1XD0G5oR4OIoRj2dnZ5ObmUlhYyNtvv03r1q05ffo0ffr0caq1aFBQECEhIWRn\nZzvcxlFrweXLl7N161YAwsLCGD16NMnJyZbXt2zZQlRUFCEhIZZ1V69epaioiPvuu89mX7WdJlDT\neVt3W8nMzOTFF1+s8bydOQfrc3b251TdedeGJAOE8CTW0+AzAL19mXA/8N9ASE0busD1K5AxFn75\nFk4kQh3nZQkhhCfz9vZm/vz5nD9/nm3btrF48WLuan6X5fU7i+7E29u7yvsUReHOO+9k9uzZbNiw\ngfXr1zNjxowqiYGioiJSU1Mt/banTJnCli1bMBjc9IPuBMyJ7aYu3q+pHA48BJcOwG1BMPxf5qKB\nQjSg9PR0OnbsSEJCAv7+/tx99920atWKnTt3Eh0dbbOto2+t4+Pj2bevakXrkpISUlNTSUtL48yZ\nM6SkpHDp0iUAiouLWb58OQ899JBlyP3mzZs5e/YsS5cuZcmSJeTl5bFx40abfaalpTFy5EjCwsIa\n5LzT0tKYPHmyTa2B6s67unOwd841/Zxced5KXQsX1CdFUVQ9xyeE7qhAd6CyOGkmMES7cDRTXgRp\no+ByFrTqA6M+Ad+WNb9P1BtFUVBVVf+NkWsg1yXRmKyZsoan//E0AGPbjCVha4LT71VVlbNnz5KR\nkcHHH3/ssGp2s2bNePDBB5kyZQoxMTGWIbiNkqrC53GQvd6cAPj1AWjZS+uoPJYrr0uedm2YPn06\nQ4YM4cknn6x2u5kzZzJ06FBmz55d5TWj0Uh0dDSrVq2iZ8+etTr+/PnzefXVV+0mIG9mMpmYNGkS\niYmJBAcH1+o4N3PmvD/55BNat25NeHg4JSUl5Ofn29RRudXzrs05Q+3P29HvuyQDhPA0jwNvVywv\nBP6oYSxaMJVD5m8gb8f/Z+/O46Kq9z+Ov4ZdYxFyF5fCFcXdTKPUEJfADQVNumWWW2lpZpr2s7qV\nqblnaXvmRROUXDJxSTG3LNcUFDcUBXdFRQRh5vz+ODkwOiDLMAMzn+fjweN6hu+c86Erfs+8z3eB\n8rWgyy4oX/3h7xMlSsIAIcqehHUJNHxOHR3gjjvRMdHYOxfsRvV+iYmJbN26ldjY2DyDARcXF4Ng\nwM3Nrci1l0lZt+D3Z9XpAc/+DpWKPvRXPJyEAcbpdDpq1KhBbGyswdaj9zt+/DgDBgygRYsWTJ06\nlYoVKz7Q5urVq4wdO5Y5c+ZQoUKFAl0/OjoaLy8v/bz9h5k+fTr+/v60b9++QO3zUpCf+5dffmHk\nyJEGuwXs27fPYPoAFP7nLuzPDIX/uSUMEMJWLIPMAZmsZS0JtRJguLria3BwME5OTpauLocClMRH\nw6t/w0Z/cHhEnqqUIhIGCFH2KDqFOk51SNKqi2t9N+Y7Hu/5eLHPe/r0aX0wcPr0aaNtnJ2dDYIB\nd3f3Yl+3xKQBphrQkJUGqQeh0lMmOqHIi4QBxsXExDBmzBiOHDlikvNlZ2cTExNDcHBwgdrrdDrs\n7Ao2k33fvn14e3vnudZJYVjy5y7MzwxF+7klDBDCBmi1Wqa/P505n8zhEpcMvle5cmVGjx7NO++8\nU+AhSCVmCLAaOAhULYHzX4wFO0e5mSpFJAwQomwa0mAI3x77FoBRzUYRMifEpOc/c+YMW7duZevW\nrZw6dcpoG2dnZ7p27UpoaCg9evTAw6OUTPs6DXRHDbdlO98yR8IAYUskDBDCymm1WsLDw1m2bFm+\n7fr3709ERIRlA4HuQAywGHjBcmUI85EwQIiyKXJ0JP3nqtsOPlHuCab9Nq3ErpWUlKQfMZBXMODk\n5GQQDBR06HGJyAIeBW6hBgPF3zJcmJGEAcKWSBgghJX79NNPmThxov64Ro0ahISoT3Cio6NJTk42\naDthwgSz16g3CxgLDAcWWK4MYT4SBghRNl09dpVKDSqhoGCHHWuWrqF81fIlft2zZ8/qg4G8tidz\ndHSkS5cuhIaG0qtXL8sEA71Rw+0VQNBD2t4vLVFd28bOwqP1bJSEAcKWSBgghBXLzMykVq1aXLqk\nTg0YPnw48+bN0y9okpWVxahRo/jqq68AdcrA2bNnLbeGwAXgPOr+zMXd4FSbAfYuxa9JlCgJA4Qo\nu9o80oY96XsAmPP8HJoNbWbW6587d04/leD48eNG2zg6OhIYGKgPBjw9zbQd3znU0QHlCvm+tFOw\noT1UbAdPLZV+zAIkDBC2RMIAIaxYdHQ0ffv2BdQRAYmJiQ+sbJqVlUWdOnVISUnRv6dPnz5mr9Wk\nbh5TV15uNRdq9bV0NSIfEgYIUXZNaj+JKbumAPCfOv9h8A+DLVZLcnKyfsRAfsFA586d9cFA7pW/\nS4U7F2HjU5B2Eqp2hg6/gr2zpauyORIGCFuS19/34j6TE0KUAgkJCfo/h4SEPBAEgHpzdG/awP3v\nKZPuXIAtXeFOMiQuUvdnFkIIYXKBoYH6P+84u8OClaiB98CBA/n666+JiIhg6NChD2wDlpWVxbp1\n6xg8eDBVqlShW7dufPfdd1y9erVEa0tNTeXUqVOcOnWK1NRU442ybkHsc2oQ4NkSno6WIEAIYTES\nBghho+bMmcPHH3/MsWPHLF1K4d27mbp9GrzaqEMsNWX+obMQQpRK7V5pxyM8AsAp7SmuHLhi4YpU\n1atX5/nnn2fhwoUsWbKEYcOG0bBhQ4M22dnZrF+/nldffZWqVavStWtXvv32W65cMc3PkJqayty5\nc2nUqBGenp74+Pjg4+ODp6cnjRo1Yt68eTnBgPYubAuB6/vA1Qc6/gaObiapQwghikKmCQhhBYoy\nTSC3Zs2aERoaSlhYGPXq1TNLzYC6HVMc0AB4cDCDcdq7sDUYLmwE17rQZSe4VCq5GoVJyDQBIcq2\n4MrBrL28FoAPAj6gw3sdLFxR3i5cuKCfSnD0qPE9/+zt7Xn22WcJDQ2ld+/eVKpUuH4kIyODCRMm\n8M0335Cenp5v2/LlyzNkyBCmfjQRl92hcDMBAneAm0+hrilMS6YJCFsiawYIYcXuX0Bw2LBhfP75\n53kuIJifFi1a6IMBH58SvlHpCCQBG4GCXuraPtj4NDi6Qpdd4Pp4iZUnTEfCACHKtrl95jJ65WgA\ngioG8XbU2xauqGAuXLjAH3/8wdatW4mPjzfaxt7eno4dOxIaGkpISMhDg4Hr16/To0cPduwwnDLh\n7OxM1apV9dfNzMw0+L6/vz+rf4nE0+kWuNcvxk8lTEHCAGFLJAwQwsoZ21rw3gKB0dHRBiMCXnrp\nJWrWrElsbCy7d+8mKyvL6DlbtmxJWFgYYWFhPPbYY6YvOhWooA6zvHbtGgBeXl4P3x7qyl/qVkxe\nrUxfkygREgYIUbYdWX0E316+AHjgwYr1K7B3Kltb4l28eFEfDMTFxRltY2dnZxAMVK5c2eD7GRkZ\ndO7c2SAI8PPz4/XXXyc8PBxXV1cA0tLSiIiI4IsvvuDQoUP6tv7+/mzcuBEXF9k9wNIkDBC2RMIA\nIaycVqslPDycZcuW5duuU6dOTJo0CXt79Sbu9u3b7Ny5k61bt/LXX3/lGQy0bt2asLAwQkNDqVOn\nTrHrTU1NZdGiRSxcuPCBYZwNGzZkxIgRvPjii5bZN1qYnIQBQpRtik6hpmNNknXJAPww7gfqPFfH\nskUVw6VLl/jjjz+IjY3NNxjo0KEDoaGh9OnTh6pVqzJ69Gjmzp2rbzNjxgzeeustNHmsW6MoCrNm\nzeLtt3NGUowePZrZs2eb9gcShSZhgLAlEgYIYQO0Wi2fffYZs2fP1k8ZyO2VF1/h+Ref1wcB97sX\nDGzZsoU9e/bkGQw88cQT+mCgVq1ahaqxSPMsp06VpyhlnIQBQpR9g+sN5ocTPwAwusVoes3qZeGK\nTOPy5cv6EQOHDx/G2O+4RqOhffv2/P3339y9exdQg4CxY8cW6BozZsxg3LhxgNq3paSk4OHhYbof\nQhSahAHClkgYIIQNuXv3LmvXriUhIYEZk2ZwVadup/T1iK+pF1awBQLT0tLYsWMHsbGx7Nmzh+zs\nbKPt2rZtS//+/enXrx81a9bM95zFmme5ejWenp4Fql2UPhIGCFH2LX19KQO/HAhA2/Jtmbp2qoUr\nMr0rV67og4FDhw4ZDQYAmjZtyoEDB/IcEXA/RVFo1qyZfsrAvHnzGDVqlMnqFoUnYYD5XLt2DS8v\nrwdeP3/+PNWqVSvyea9cuULFihWLU5rNyOvvu2wtKIQVcnJyok+fPkyYMIGwRmH61w9sPVDgc7i6\nutK1a1c+/fRToqOjGT9+PG3btn1gVMHu3bt56623qFWrFu3bt2fOnDkkJyc/cL6MjIwHggA/Pz8W\nLlzIlStXOH36NKdPn+bKlSssXLgQPz8/fbvt27fTs2dPMjIyCvOfQQghhAl1fq2z/s970veQccX6\n/k2uWLEiISEhzJ07l6ioKN544w2aNWv2wIf+1157rcBBAKg34q+99pr+eMGCBSarWYjSbPHixezZ\ns8fgtV27dtGzZ0+Cg4Mf+v60tDRGjx7NF198wbRp0xg5cqR+ZGl6ejozZ87kzp07JVL7w9SpU4ek\npKRCtVu7di1ubm64ubkRERGBVqvVt/vxxx+xs7MzWAOspEkYIISVCwwK1P/5z1N/Fukcbm5udOvW\njalTpxIdHc24ceNo06bNA8HArl27GDNmDN7e3vj7+zNv3jz9woUTJkwwCAJmzJjBwYMHGTZsmH7B\nJVBDiGHDhnHw4EFmzJihf3379u28++67RapfCCFE8VVqXImW5VoCoEXLsVXHLFxRyXr00Ufp06cP\nc+bMYdGiRfrXnZ2dCQ8PL/T5wsPDcXZ2BuDIkSOkpqaarFYhSqOZM2eSlZVFly5d9K+lpaXh4+OD\nVqvNc+RNbmFhYVSqVInXX3+d8ePHU7FiRYYOHQpArVq16N+/PyNHjiyxnyE/BQ0Ec7cLCgqia9eu\neHh4EB4ebnAv3bBhQ3r37s2UKVNMXmteJAwQwsp1eq0Tdv/+qu/P2E96cv7z9B/G3d2d5557junT\np7NixQrefvttWrdujZ2d4T8nO3bs4M0338Tb25v27dsbPAW5N88yv39ENRoNY8eO5bPPPtO/9vXX\nX3Pjxo1i1S+EEKLoAv1yAuZ9O/dZsBLzyn3DXrVqVYMQu6Dc3NyoUqWK/vj69esmqU2UIRqNeb5K\ngW3bthEVFcXgwYMNXnd1daVy5cpUqlTpoWHA9u3biYmJoV+/fvrX/vOf//Dzzz9z7JgaRnp7e+Pj\n48PMmTNN/0OUkFatWpGSkkJaWpr+NUVRmDJlitlHDUkYIISVq1C7Am0eaQOAgkLCqgSTndvDw4Og\noCA+++wzoqOjeeutt2jZsqVBMKAoCrt27dIvuNS0aVPeeuutAl9j7Nix+ikD6enp/PTTTyarXwgh\nROF06ZvzhG9H0o58WgohyjofHx+ioqL0x23atOHzzz8v0HunTZtGz549i3X9LVu24OTkRIMGDQxq\ncnJyIiYmRv9aUFAQH3/8scWmC9yTmprKxIkT+eKLLwgODmbp0qVG2927r829m9b3339PSEiIQWBo\nDhIGCGEDOjfPmee5b3fJPMnx8PCgR48ezJw5k+XLlzNmzBhatGjxwIgBmWcphBBl11NDn6Ic5QA4\nkX2Ca4evWbgi83B3d9f/+cKFCwZP9Arq1q1bXLx4MdexLIorSq+kpCQSExPp2LEjAFevXmX//v10\n7pxzT3nt2jVOnTr1wHvT09NZt24dzZs3L1YNycnJRhce9PLy4syZM/pjPz8/0tLSWLdunUG72NhY\n7Ozs8v2yt7cv0Lz/hzl//jzt27fnmWee4fXXX6dixYokJiYabXt/GHDp0iU2bdrEoEGDil1HYUkY\nIIQNCAzNGda5I7nkn+R4enrSs2dPZs2aJfMshRDCijhXcKbDox30x4fXHLZgNebj6uqq30o3MzOT\niIiIQp8jIiIi1245jWjWrAJt28KMGXD6tOlqFaWYopjnywS2bNlC48aNqVSpEgBLly6lSpUqNGrU\nCICEhAQCAgLYsmXLA+9NTExEURSjH+QLw9nZGQcHhwde1+l0BlMM7Ozs8PDw0O/WcU/Hjh3R6XT5\nfmm1WoNtsh8WHlSvXt1orQMGDKBVq1Z069aNH374gZSUFEaPHm20be3atXF3d9eHAZMnT2b69OmF\n/u9jChIGCGED2r3SjvKUByBRm8jVA1fNdu3cIwNknqUQQpR9ge1yAuY9+/fk09K65B7y/OWXXxZo\n8bN7FEXhyy+/zPXKCAD++gvGjYPHHoM2bWD6dMjjYaIQZrVlyxY6deoEwO3bt1mwYAHPPvus/vsN\nGjSgefPmRkd73lvfydgH+cKoWbOm0QdA165do3bt2gavubi45LkNdmGkpqbm+3VvrYLctm7dyrZt\n26hbty6zZs3C29ubDRs2UL58+Tyv06RJE44cOcLGjRtp2rTpQ7fnLikSBghhA5xcnehQKedJTtyv\ncRasRgghRFnWZVDOugHbL29Hm6XNp7X16Nq1Ky4uLgD8888/zJo1q8DvnTlzpv6ppZNTeQICXuT+\nz0l79sD48fD449C6NUybBkZGYAthFrGxsfopAosXL0ar1RIQEPBAO2Oh2L0Ptteu5T+N6GHTRp97\n7jnS0tI4e/as/rWjR49y9+5dnnvuOYO2qamp1KlT54GfobDTBNzd3fP9uv+hlqIo7N69G09PT95/\n/33eeustAgMDeRg/Pz8OHjzIkiVLDKbDmpuEAULYiMD2uZ7kHDTfk5ySmGep0cg8SyGEsJTGvRtT\nza4aANe5zrnfz1m4IvNwdXUlKChIf/z2228zY8aMfEcIKIrCjBkzGDdunP61114byqZNHly8CN9/\nD927g6Oj4fv27oUJE8DHB1q1gqlT4cQJk/9IQhh18uRJkpKSuH37Nt999x2enp4cO3aMpk2bsnbt\n2oe+v2bNmtSrV4+TJ0/m2SavrQVnzZrFihUrAPD19aVLly4G03IiIyN57rnnqFevnv6169evk56e\nTrt27QzOVZRpAoWl0WioUqUKaWlpXLhwAVDXAMhr8cB7mjRpQkpKCpMmTSrytU1BwgAhbETnF3MW\nfNl+ZTvau+Z5klMS8yzr169AUBAsWgSyfIAQQpiXxl5DYO2cgPmf3/+xYDXmFRQURO5nmePGjaNZ\ns2YsXLiQW7du6V+/desWCxcupFmzZgZBgL+/P59++ikAXl7w8svw229w8SL8+CMEBT0YDOzbB+++\nC/XqQYsWMGUKHD9egj+ksHlbtmyhevXqjB8/Hjc3N1q3bk2FChVYs2aNQSAGeT/dHzlyJJs2bXrg\n9YyMDKKioti8eTMnTpxg6dKlXL58GYA7d+4wa9YsBgwYoJ9qsGzZMk6fPs306dOZNm0aycnJLFmy\nxOCcmzdvJiAgAF9fX1P8+IU2cOBA+vTpw5NPPkl4eDiLFy8mNDQ03/c0bdqUDz/8kLp165qpSuM0\nhZnvZG4ajUYpzfUJUZYoOoXqjtW5oFNTy58m/ETNruaZn7RixQrmz58PqP/4HThwoMA7CiiKQrNm\nzXItCjMPGKX/vqMjdO0KYWHQsyd4eJi4eGESGo0GRVFKx+bHxSD9khCqiOERvPDVCwC0d23PJ2s+\nsXBFJS81NZXwgQNIv5Np9PvOzs769W0uXryYK8RW+fv7s3r1ajw98x/dlpoKq1dDVBRs2AD/7sz7\ngGbNIDRU/apfv/A/j60zZb9kbX1DeHg4/v7+jBgxIt92gwYN4umnn+aVV1554HtarZagoCDmzZtH\n/UL+BZ0wYQKffPIJ9vb2D22r0+kICQlh5syZ+Pj4FOo6tiSvv+8yMkAIG6Gx09C5ds7ogH82me9J\njqnmWTo6lqdlyxcNvp+VBb/+Ci++CJUrq4HA//4HN2+arn4hhBCGOo/I6U/+TvubjKsZFqym5N29\ne5fBL79kEAQ0b97MYIGwzMxMkpKSSEpKMggCypcvz+jRo9m4ceNDgwCAChXUPm3NGrh0CX76CXr0\nACcnw3YHD8J770GDBtC0KXz0EeTatlyIItHpdGzevNlgsUBjjh8/zqFDh9i1axdXrlx54Pv29vZE\nREQwZcqUQu0CFR0dTbdu3QoUBADMmDGDd955R4KAIpKRAULYkJ+G/sRL37wEwDOuz/Dhmg/Ndu35\n8+fr54ABfPbZZ4wdOzbPEQKKojBz5kyD4ZWjR49m9uzZJCbC8uUQGakuuGSMszN066aOGOjRA9zc\nTPrjiEKSkQFCWJ/m5ZpzMOMgAPNemoffID8LV1QydDodL730EufO5ayNENKnNyuif+HGjRssWrSI\nBQsW6LcJu6dRo0aMGDGCF198EQ8TDFu7cUMNv6OiICYGMo0PUKBJk5wRA//uAieMkJEBxsXExDBm\nzBiOHDlikvNlZ2cTExNDcHBwgdrrdDqDnajys2/fPry9valcuXJxSrQJef19lzBACBuSvCcZ7zbe\nADjhxJpf1uBUwekh7zKNu3fv0r9/f4N02M/Pj9dee43w8HDc/v20fuvWLSIiIvjyyy8N9ov19/dn\n48aN+hEG95w6pd4YRUaq8yqNcXaG555Tg4HgYCjC7oaimCQMEML6jGs9jhl7ZwAwqO4gfdhsbUaO\nHElcXM4uPO2ebMvOXX8+0C41NVW/9a2npycVKlQosZpu3swJBtatyzsYaNw4Jxiw0HTqUkvCAGFL\nJAwQQgDQ2KUx8ZnxAHw5+Esa/cc8jw2+/fbbPBcPNNU8yxMncoKBAweMt3FxURdoCgtT//eRRwr/\ns4jCkzBACOuz8ZONdHlP3WawvmN9vtrwlYUrMr3Jkyezbds2/XG9evU4evRogZ9cmsOtW7B2rdr/\n/fYbZOQxY6NRo5xgoHFjKODSPVZLwgBhSyQMEEIA8GaLN5l3YB4AwxoMY8DCASV+zTVr1hisE+Dg\n4ICjoyN37tzJ933ly5dn6NChfPrppw+MCHiY48dzgoGDB423KVdOHSkQFqaOHMg19VOYmIQBQlif\nO1fu4FXJiwzUT5/RC6LxbGg9W79+/vnnREdH648rV67MmTNnCt0fmVNammEwkFc327BhTjDQpIlt\nBgMSBghbIgsICiEACOyRsx3UzsSdJX69P//8k9mzZ+uPHRwc2L9/P+fPn2fu3Lk0bNjwgfc0atSI\nefPmkZKSwuzZs4t041WvHkycqI4QOHpUXVjJ777prHfuqDdMoaFQqRIMGADR0XnfPAkhhMhRrmI5\nnvZ8Wn8ctzoun9Zly9IlSwyCAFdXV+Li4kp1EADqNLj+/dV1dS5dgmXLoF8/NfzO7V6/2LSpOmLg\nvffU4Fw+zwphW2RkgBA25lbKLbxqeJFNNgBrvl+D62MlM4n+2LFjjBgxAp1OB6ip5MaNGwkICDBo\nZ855lkeO5IwYiMvjvvWRR9RFB8PC1EUI77+JEoUnIwOEsE4znpvBuHXqQq+9qvRi9M+jLVxR8W3a\ntIlPPsnZKtHJyYn4+PgyvVr57dvqSIHly9W1BtLTjberVy9nxECzZtY9YkBGBghbItMEhBB6T3s8\nzfab2wGY3ns6bd5sY/JrXLp0iRf/8wKZd7P0r/3444+89FLpWWAqLk4NBpYty3s7JldXdbvCsDDo\n2lVdc0AUnoQBQling0sP0nxgcwAe1TxK5IZI7BzK7sDTffv28fbbY/VPyO3t7Nixcydt27a1bGEm\nlJ6uLjoYFaUGA7dvG29Xt25OMNC8ufUFAxIGCFsiYYAQQu/DTh/yQewHAPSv0Z/h/xtu0vOniDr/\nrAAAIABJREFUpaUx8Pn+3ErLefTw4QcfMPn99016HVNRFDUYiIxUvxISjLdzc4NevdRgoEsXdZcC\nUTASBghhnXTZOqo7VeeichGARe8tolZALQtXVTSnTp1i6NAhaLX3RrPBL7+spFevXhaurOTcuaMG\nA8uXw5o16poDxvj4qNMNQkOhZUvrCAYkDBC2RMIAIYTezq938tSwpwCoYVeDxRsXo7EzTc+enZ3N\nf8Kf58KlK/rXBr/8Mt99/71Jzl/SFAUOHcoJBo4fN97O3R1691aDgcBAcDLPDo1lloQBQlivF+q8\nQMQZdbeYsU+MJXhawfYTL00uX77Mf/4TTmZmzmi2hQsXMmzYMAtWZV537sD69eqIgdWr8w4GHn88\nJxho1arsBgMSBghbImGAEEIvOyObR8s9yk1uAhA5NZJKbSuZ5NzDhw0h4dgJ/XHngGfZuOl3k5zb\n3BRFXVDp3lSCkyeNt/PwyAkGOneWYMAYCQOEsF4/vfoTL32nTgHzd/Pno9UfWbiiwklLS+P5558n\nLden3/cmTeKjjz+2YFWWlZFhGAzcumW8XZ06OcFAmzZlKxiQMEDYEgkDhBAGelfrzaoLqwD4vw7/\nx7MfPFvsc7733nvs2LFDf9zYtyH/HIorVfsxF5WiqDsT3BsxcOqU8XYVKkCfPmowEBAAjo7mrbO0\nkjBACOt1fs95qrepDoAjjqxZuQZnj7Ixjyo7O5uBAwdy+fJl/WuDXnyRHxYtsmBVpUtGBmzYoE4l\nWLUKbt403q527Zxg4IknSn8wIGGAsCUSBgghDMwPm8+oqFEAdPfqzjsr3inW+ebNm8cvv/yiP65W\ntTKnz5zFyQofkysK7NuXEwycPm28nZdXTjDQqZNtBwMSBghh3fxc/DiceRiA+a/Mp/ELjS1c0cPp\ndDqGDBnCqVzpbmBgIBs2bLBgVaVbZiZs3KiOGFi1Cm7cMN6uVq2cYKBt29IZDEgYIGyJhAFCCAMJ\n6xJo+FxDANxxJ3p9NPZO9kU6V2RkJAsWLNAfu7m5cfr0aby8vExSa2mmKLBnT04wkJRkvN2jj0JI\niBoMdOwIDg5mLdPiJAwQwrqNbTGWWQdmAfBK/Vd44asXLFzRw40bN449e/boj5s2bcr+/futYjSb\nOWRmwqZN6oiBlSshNdV4u5o1oW9fNRh48kkoLf95JQwQtiSvv++l5NdRCGFu9bvWp5a9uuLzTW6S\nFJPHp9iHiI2NNQgCnJyc2L9/v00EAaA+7WjTBj77TB0h8Oef8NZb6s1PblevwjffqIsNVqsGw4fD\n5s2QnW2RsoUQwqQCewfq/7wjcUc+LUuHqVM/NQgCatasyd69eyUIKARnZwgKgh9+gIsX4bff4OWX\nwdPTsN3ZszBnDjz1lDqVYPRo2LEDdDrL1C3M79q1a0ZfP3/+fKHOc3/7K1eu5NFSFJT8iyeEjdLY\naej8eGf98cEtBwt9jkOHDvHRf/+rP7azsyM2NhYfHx+T1FjWaDTqcMiZM9VgYOdOGDMGatQwbHfl\nCnz1lbqmQI0aMGIEbNkCWq1FyhZCiGJ7ZvgzOKFOCzuadZTU43k8Ji4FvvvuO9avz5kK4OnpyeHD\nh3GwtSFbJuTkBN27w/ffw4UL6naFgwer0+VyO3cO5s4Ff391KsGbb8K2bRIMWLPFixcbBG8Au3bt\nomfPngQHF2znkbzap6enM3PmTO7cuWOyegujTp06JOU1JDSPdmvXrsXNzQ03NzciIiLQ5rr5+/HH\nH7Gzs2PixIklVvP9JAwQwoZ17poTBuw+trtQ7z137hxj3xqDLtewuMjISNq1a2ey+soyOzto1w5m\nzVKnDuzYod70VK9u2O7SJVi4EJ59Vg0GXn8dtm6VYEAIUbaUr1Kepys8rT+OWx1nwWrytnr1av73\nv//pj8u5OPPPP//g7u5uwaqsi5MTdOsG332nBgMxMfDqq+p0udySk2HePHjmGfD2hlGj4I8/pP+z\nJjNnziQrK4suXbroX0tLS8PHxwetVktBplbk175WrVr079+fkSNHmrz2gtAUcDGM3O2CgoLo2rUr\nHh4ehIeHY2+fM0W3YcOG9O7dmylTppi81rxIGCCEDQsYHqD/8570PWReySzQ+27evMmwoUPIys7p\nsWfNmkXfvn1NXqM1sLOD9u3VYZJnz6pPQUaNgqpVDdtdvAhffqmuKXDvxkiemAghyorANjlTBfbu\n2WvBSozbvn07c2bP1h87ONjz19978Pb2tmBV1s3REbp2VafJnT+v7kowZAhUrGjY7vx5mD8fOnRQ\n+7+RI600GNeY6asU2LZtG1FRUQwePNjgdVdXVypXrkylSpUKFAY8rL23tzc+Pj7MnDnTZLWXtFat\nWpGSkmKwnamiKEyZMsVg6q05SBgghA2r3LgyzVyaAZBNNsdXH3/oe+7evcvgl18i/U6G/rXRb77B\nmDFjSqxOa2Jnpw6PnDdPHS65das6GqBKFcN2Fy6oN0bPPKOuP/DmmzLHUghRunX5T87Tv+0Xt6PT\nlp5/sOLj43n//cnc+yih0WiIiVlPkyZNLFqXLXF0VNfN+fpr9cP/xo0wbBhUqmTY7sIF+OILNRiv\nUQNee02m0lmKj48PUVFR+uM2bdrw+eefF+i906ZNo2fPniVVmoGgoCA+/vhji00XuCc1NZWJEyfy\nxRdfEBwczNKlS4228/PzA+Do0aP6177//ntCQkKocv8NYQmTMEAIGxfYJOdJzv6d+/Ntq9PpGDbk\nFa5ey5kL2rtXT2bPmVti9Vkze3v1w/78+epwyS1b1PUDKlc2bJeSooYH9+ZYjhkDu3ZJMCCEKF2a\nDWhGJY36ye6ycpmU7SkWrkiVnJzM6NGj0elyniouXryYgICAfN4lSpKDA3TurE6TS0mB339XF9a9\nv/+7eBEWLFCn0lWvrvaRsviueSQlJZGYmEjHjh0BuHr1Kvv376dz55wppteuXTPYmvOe9PR01q1b\nR/Pmzc1Sq5+fH2lpaaxbt87g9djYWOzs7PL9sre3L9C8/4c5f/487du355lnnuH111+nYsWKJCYm\n5lkv5IQBly5dYtOmTQwaNKjYdRSWhAFC2LjAkFwrQCflvwL0uHHjOJ10Tn/cplVLflm5qsRqsyX2\n9upTkC+/VIOB339Xn5jcP5QyOVmdbtC+PdSpA2PHqjsYyI5G5tN0QVM+2voRR68cfXhjIWyInaMd\nnb1zPij8s/4fC1ajSk1NZciQIWRlZelfmzZ1KuHh4RasSuTm4KB+2F+wQA0GNm9WP/Tf/4D03ho7\nAQFqMDB8uNpXlqlgQDHTlwls2bKFxo0bU+nfoRtLly6lSpUqNGrUCICEhAQCAgLYsmXLA+9NTExE\nURSz7SxlZ2eHh4cHhw4dMni9Y8eO6HS6fL+0Wi21atUyOFd+X9XvX/zpXwMGDKBVq1Z069aNH374\ngZSUFEaPHm20be3atXF3d9eHAZMnT2b69Okm+q9ROBIGCGHj/If461eATshK4EbCDaPtpk2bxr59\n+/THdWrXZOefhVt0UBTMvRujhQtzhlIOGfLg4ktnz6oLFLZrpwYDb78Nf/0lwUBJO3TpEJNjJ9Po\ni0b4LfDjv1v/y5HLRyxdlhClQmCnnIB5d5xl+4i7d+8yePBgg6HDb7zxBu+MH2/BqkR+7O2hU6ec\nYHzLFnWawP3BwOXL6q48nTur2/UOHar2lWUqGCjltmzZQqdOnQC4ffs2CxYs4Nlnn9V/v0GDBjRv\n3tzoIno3bqj3kubcocPFxYVsE/wFSE1Nzffr2LFjD7xn69atbNu2jbp16zJr1iy8vb3ZsGED5cuX\nz/M6TZo04ciRI2zcuJGmTZtS8/49qc1EwgAhbFz5iuXx9/TXH8evjn+gzY8//khMTIz+2MvLi0OH\n42UbJjO4N5Ty3hzLDRvUVZnvD9uTktQtDdu2hcceg3fegT17JBgoaYcvHeb92Pfx/dKXJl824cPY\nD4m//ODvkBC2InBYrjDg5m4ybxZsYVpT0+l0DB48mOvXr+tf69u3L3PnyrS2suLeiLkvvlCDga1b\n1YUFq1UzbHflirpAYZcu6sK8Q4aofWWuwSCiCGJjY/VTBBYvXoxWqzU6tcbYon73Ptheu3Yt32sU\ndDX+grRPTU2lTp06Bq8VZZqAu7t7vl+urq4G11AUhd27d+Pp6cn777/PW2+9RWBgIA/j5+fHwYMH\nWbJkCa+99lqh/juYkoQBQggCn8j5R2vJH0uIiIjgjz/+ICsri3Xr1rFo0SL998uVK8fBgwcf+MdQ\nlLx7iy99803Odk2DB4Onp2G7M2fgs8+gTRvw8YEJE2DfPgkGTGVp36WENArBxcHF4PW4y3F8sPUD\nGn/ZGN8vfHl/y/scvnS4QKslC2EtvNt74+vkC0AmmZxce9Iidbwx6nWSk5P1x+3atWP58uUWqUUU\n3701dj7/XF18948/1B137h+xffUqfPutuoNB1apqeB4TI8FAYZ08eZKkpCRu377Nd999h6enJ8eO\nHaNp06asXbv2oe+vWbMm9erV4+TJvH//89pacNasWaxYsaLA7QGuX79Oenr6A9tbF2WaQGFpNBqq\nVKlCWloaFy5cANQ1APJaPPCeJk2akJKSwqRJk4p8bVOQMEAIG6fVajnrdlZ/fDjtMN9++y3vv/8+\nISEhBnOYHBwc2LVrl2zDVArc267p3j7Ov/0GgwaBh4dhu8REmDYNWrWCevVg4kTYv1+CgeIY0GQA\nK8JWcHncZX7u+zN9G/WlnEM5gzZHrhzhv3/8F78Ffvh+6cvkLZM5dPGQBAPCJgQ2zAmYD/xxwOzX\nf3/ye8TF56zpUa9ePbZv3272OkTJsLODp59WF9Y9exa2b1d33KlRw7DdtWtqH9m9uzrNYPBgWLcO\n7t61TN1lyZYtW6hevTrjx4/Hzc2N1q1bU6FCBdasWUNQUJBB27ye1o8cOZJNmzY98HpGRgZRUVFs\n3ryZEydOsHTpUi5fvgzAnTt3mDVrFgMGDNBPNciv/T2bN28mICAAX19fU/z4hTZw4ED69OnDk08+\nSXh4OIsXLyY0NDTf9zRt2pQPP/yQunXrmqlK4zRFvTHRaDQtgPrAHkVRTuZ6vQ/QRlGUicUuTqNR\n5MZJiJKj1WoJDw9n2bJlBWr/22+/0b179xKuShTH3bvqvMnISFi5Em7eNN6ubl0IC1O/mjaFQo7U\nKzSNRoOiKCV6FUv2S2l30/jt+G9ExUex9tha7mQb396owaMNCPUNpZ9vP5pWaVroIZJClAW//d9v\nBH2sfmBo7NSY+evnm+3a8+bN5ZdfVuqPK1d6lDNJ53BxccnnXcIa6HTqgrpRUbB8uTqCwJgKFaB3\nb/jxR9P1S9b2mSU8PBx/f39GjBiRb7tBgwbx9NNP88orrzzwPa1WS1BQEPPmzaN+/fqFuv6ECRP4\n5JNPsLe3f2hbnU5HSEgIM2fOxMfHp1DXsSV53YcVKQzQaDRjgWnAQcAJ+AsYpShKukajsQcyFUUp\n9mRia/vFEqK0+fTTT5k4MefzUY0aNQgJCQEgOjraYIhlSEiI0WFbovTKzFTnTUZGwqpVcOuW8Xb1\n6+cEA02alEwwUNJhQGnql27fvc26E+uIio/i12O/kp6VbrRdPa96hPqGEto4lGZVmkkwIKzG7ZTb\neNbwJAt1bPbK71fi8ZjHQ95VfEuXLOHrb77RH7s+Up7E02eoeP+2LMLq6XSwe3dOMHD2rLFWEgYY\no9PpqFGjBrGxsTRo0CDPdsePH2fAgAG0aNGCqVOnGv09u3r1KmPHjmXOnDlUqFChQNePjo7Gy8tL\nv17Bw0yfPh1/f3/at29foPa2ytRhwEVgqKIoq/49rgcMA2YpipKi0WiyFEVxNEHRVvOLJURpk5mZ\nSa1atbh06RIAw4cPZ968eTg6qr+6WVlZjBo1iq+++gqAypUrc/bsWZycnCxWsyi6jAzDYCAtzXi7\nhg1zgoHGjU13fTOEAaWyX0rPSmfd8Zxg4HbWbaPt6nrVVYMB31CaVzW+OrMQZUknj07E3owFYEqv\nKbQb3S7/NxTTpk2b+OSTT/THTk4OxMcflSeFAkVRd9q5FwycOXPvOxIGGBMTE8OYMWM4csQ0u+Rk\nZ2cTExNDcHBwgdrrdDrs7Ao2k33fvn14e3tTuXLl4pRoE0wdBpwDaub+W6/RaOyAN4EY4B8JA4Qo\n3aKjo+nbty+gjghITEzUBwH3ZGVlUadOHVJSUvTv6dOnj9lrFaZ15w6sX68GA6tXw23jn0/x9c0J\nBv7dVrjIzBAGlPp+6U7WHdadWMfy+OWsObaGtLvGExkfTx/6+fYj1DeUltVaSjAgyqQpAVOYtFld\nGKtv9b6MjBhZYtfau3cv48aN06/JYW9nx46dO2nbtm2JXVOUTYoCf/+tBgMzZkgYIGxHXvdhRV1A\n8FNgYO4XFEXRKYoyG3iiiOcUQphRQkKC/s8hISEPBAEAjo6O+mkD979HlF3lyqnzJZcsUfdqXrEC\n+veH+7fDjY+HDz5QQwE/P/joIzh61OgpS4NS3y+VcyxHSKMQlvRdwqW3L/FL/18Y6DcQVyfDnTlO\nXj/JtB3TaP1Na+p+XpfxG8ezJ2WPLD4oypQuA7vo/7z9wnYUXcn8/T158iTjx4/X/35oNBpWREdL\nECCM0mjgiSfUHXeEEEUMAxRF+QI4rtFoHhjzpSjKIiCsuIUJIYQoeeXKQUgI/PyzGgxERUFoqPp6\nbocPw+TJ6giBpk3h44/h2DHL1GxMWeuXyjmWo3fD3kSERHB53GVW9l9JuF84bk5uBu1OXT/F9J3T\nafNNG3zm+fDOxnf4O/lvCQZEqdfihRY8qnkUgIu6i6TsTDH5NS5fvszrr7+OVqvVv7ZgwQJ69epl\n8msJIYQ1KvJuAuYgQ26EKDkyTUDk5/ZtWLtWnUqwdq265oAxzZrlTCXIb3ccc+wmYA4l3S9lZGew\n4eQGlscvZ1XCKm5mGt8OorZHbf1UgidqPCFTCUSp1N+7P5HJkQCMf2o83T7uZrJzp6Wl8fzzz5OW\nawGU9957j48++shk1xDWzZT9knxmEaWdSdcMuO/EXwL/AInABlP+JsgvlhAl5/4FBIcNG8bnn38u\nCwiKB6Slwa+/qsHAb7+puxQY06KFGgqEhsL9a3aZMwywln4pMzuTjac2EhUfxaqjq7iRecNou1oe\ntejXqB+hjUNpW6OtBAOi1Pjuhe94NeJVADp6dOT9le+b5LzZ2dmEDxzApctX9a8NGjSIH374wSTn\nF7ZBwgBhS0oyDPgVOAPUAioAPRVFuf7vzdjjwDhFUQ4V8dzyiyVECRo9ejRz587VH9eoUUP/5D86\nOlo/IgDUbQgnTJhg9hpF6XLrVk4wsG5d3sFAq1Y5wcBjj5k9DLC6fikzO5NNpzapwUDCKlIzUo22\nq+leUz9ioK13W+w0RV0aSIjiS/ojidodagPgggurfl2F0yPFC5R1Oh1DXh3MqUT9kvAEBgayYcOG\nYp1X2B4JA4QtKckwYICiKD//++cawHPACeBDoCPwoqIoPxbx3PKLJUQJOXv2LO2eaE7yhWsPbdu/\nf38iIiKwt7c3Q2WirLh5E9asUYOBmBi4e9d4uzZt4O+/zRoGWHW/dFd7l02nNrE8fjkrj67kesZ1\no+283b3p26gvob6htKvZToIBYX4KNHRuSEKWuvjsghELaBjWsFinHPf2W+zZu19/3NSvMfsP/FPg\nrciEuEfCAGFLihwGaDSauoqinMjn+1OBu0AsoKDedNUGliuKEqnRaLopihJTxKLlF0uIEnD9+nWe\nbteSuITTADg52uPq5sG1a4bBQOXKlRkzZgzjxo2TIEDk68YNdZvCyEh128KsrPtbmPSmS/qlf93V\n3mVz4mai4qJYmbCSa3eMh3s13GqowUDjUNrXbC/BgDCbUU1GMT9uPgBDfYfy/BfPF/lcU6d+yvr1\nOSMAanpX41RiEg4ODsWuU9geU4cBpjiPECWpqGHAX0AfRVGS8/i+AzAGCABOA3OAyUCEoihrNRrN\nCEVRFhSl4NJ20yWENcjIyKBrgD9/7NwLgKODHb/9FsMzHTqwdu1a/faBDRo0ICgoSNYIEIWWmgqr\nVqnBwIYNkJ0NJg4DpF8yIkubxebEzSyPX84vR3/h6p2rRttVc62mDwaeqvkU9nYS9ImSs+bdNfSc\n2hMAP2c/5sXMK9J5vv32WyIiIvTHnhXcOX3mLO7u7iapU9gea1nYVojiKEgYcAtIB6YDsxVF0RXo\nxBrNM8AoYIeiKHOKVFwpvukSoizSarX079uDFavW6V+LWLyYgS+8YMGqhDW7dk0NBgYPNmkYIP3S\nQ2Rps4g9HUtUfBTRR6LzDAaqulbVTyXwr+UvwYAwuVtJt/Cq7UU22QCsWrQK91qF+wC/atUq5szJ\n+ZUt5+LMseMn8Pb2NmmtwrZIGCBEwcKAwcAy4E0gCHhHUZQdZqitzNx0CVEWKIrCG2+8wfz58/Wv\nfTZtCm+/864FqxK2wsTDMaVfKoRsXbYaDMRFEX00mivpV4y2q+palZCGIYQ2DuXpWk9LMCBM5hn3\nZ9h2axsA00Km8cSoJwr83u3bt/N///d/+mMHBwf27duHn5+fyesUtkXCACEKuYCgRqOpCkwBdMB4\nRVGMP2owkbJ40yVEaTVt2jSD3QDeHDmc2fO+lG3IhFmU1E2X9EuFk63LZuvprSyPX0700Wgu3b5k\ntF2VR6oQ0iiEfr79eKb2MzjYyZxsUXQfd/yY/9uqfqAP9Q7ltcWvFeh98fHxjBo1Cp1OHfyj0WjY\nuHEjAQEBJVarsB0SBghRxN0ENBpNW+ADIFpRlG9MXVSu65Tpmy4hSovFixfz4osv6o/DwsJYunSp\nrL4szKakb7qkXyo8rU7LH2f+ICo+ihVHVuQZDFQqX4mQRiGE+obSoU4HCQZEoe3+ajdPDn8SgKp2\nVVmycQkau/z/OUhOTublQYPIUhcdAeB///sf4eHhJVqrsB0SBghRjK0FNerjxEFAL+B9RVEOmrCu\ne9ewmpsuISxl/fr1BAcHk/3vDVXHjh2JiYnB2dnZwpUJW2KOmy7pl4pOq9OyLWkbUXFqMHDx9kWj\n7SqVr0Sfhn0IbRxKxzodJRgQBaLN0FKxXEVSSQVgydQlVGtbLc/2qamphA8cQPqdTP1r06ZN4513\n3inxWoXtkDBACHjoY0GNRvN0Ht96FDgGbAE2azSaORqNxtWUxQEcuXzE1KcUwmbs3buXviG99UGA\nn58fK1eulCBAlGmW7peskb2dPR3rdOSLoC9IfiuZ2Jdieb3N61R1rWrQ7nL6Zb7e9zWBiwOpOqMq\nQ1YPYcPJDWRpH9hLUgg9exd7AqrlDO0/tPZQnm0zMjIY/PJLBkHAG2+8IUGAEEKUgIIsILgeWAQ8\nDtTP9VXhvqZXgY2Kogw0WXEajcIH0KRyE8J8wwhrHEaDig1MdXohrNqpU6do90QLLl29CUDNmjXZ\ntWsXNWrUsHBlwhaZeAFBi/ZL1jgyIC9anZadZ3cSFR/F8vjlnE87b7SdVzkvdcSAbyjPPvYsjvaO\nZq5UlHZfD/iaYcuGARDgGcB70e890Ean0/HSiy9wLjnn71nfPr1ZHv2L2eoUtkNGBghRsDDg/i2b\nLgPxub7igDhFUS6bvLh/w4DcmlZpqg8G6j1az9SXFMIqXL58mfZPNOfE6RQAPD3Ks33n3/j6+lq4\nMmGrTBwGWLRfsqUwIDedolODgX+nEiTfSjbazqucF70b9Kafbz8CHg/Ayd7JzJWK0ijx90Qe7/w4\nAOUox6rfVuFYzjA0Gvn6COLij+qP2z35BDt37TZrncJ2SBggRMHCgJPAl8Be4FBJr9R837UVl49d\nyMjOMPr95lWbE+YbRmjjUOp61TVXWUKUardv36bT00/w9/54AFycHdi4aQv+/v4WrkzYMhOHARbt\nl2w1DMhNp+j489yfRMVFsfzIcs7dPGe0naeLJ70a9iLUN5TOj3eWYMCWKVDPqR4nsk8A0OvJXlRq\nUomaNWvSrl07/vvf/7J9+3Z983o+j3H02AlZ6FaUGAkDhChYGOCvKMr2fBuVEI1Go9zKvMWvx34l\nMi6S347/RqY202jbltVa6oOBxz0fN3OlQpQOWVlZ9A7uwm8bYgGws9OwPGo5fUJCLFuYsHkmDgMs\n2i9JGGBIp+jYfW63firB2Ztnjbar4FKBXg3UYCDQJ1CCARuj1Wp5qtpT7L784JN+Z2dnMjNz7u8q\nV3qUM0nncHFxMWeJwsZIGCBEMXYTMIf7b7r0wUB8JOuOr8szGGhdvbU+GKhToY6ZqhXCshRF4dVX\nX+X777/Xv/bl/M8Z8fpIC1YlhMpabrokDMifTtHxV/Jf+hEDSTeSjLbzcPagV8Ne9GvUjy4+XXB2\nkEVNrZlWqyU8PJxly5Y9tO0jjzzC6dOnqVixohkqE7bMWvolIYqjTIUBud3MvMmahDVExkcScyKG\nu9q7Rtu1qd6GsMZhhPqGUrtC7ZIsVwiLmjx5Mh999JH+eOL4t/lk6mcWrEiIHNZy0yVhQMEpisLf\nKX8TFRdFVHwUZ26cMdrO3dmdng16EuobShefLrg4yNNga/Ppp58yceJE/XGNGjUI+XfEWnR0NMnJ\nOetPvP3223z2mfRdouRZS78kRHGU2TAgtxsZN1idsJrI+EjWn1hPls74Fkdta7TVBwM1PWqaulwh\nLOarr75i+PDh+uNBgwbx/fffo267LoTlWctNl4QBRaMoCntS9hAVrwYDp1NPG23n5uSmDwa61u0q\nwYAVyMzMpFatWly6dAmA4cOHM2/ePBwd1cUDs7KyGDVqFF999RUAlStX5uzZszg5yTQSUbKspV8S\nojisIgzILTUjlVVHVxEZH8mGkxvI1mUbbdfOux1hjcPo59sPb3dvU5QrhEWsXLmSvn37otOpC6x3\n796dVatW6W+0hCgNrOWmS8KA4lMUhb3n9+pHDCSmJhpt5+bkRo8GPejXqB/d6najnGMvgpw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8o9txDOxF2uS0JUhiQDqhCj0cgPF38wH1d4JuOM1X51qtVh9AOjefLBJ+nbsi+eOjkmSA25ubkM\nGzaM+Ph4AHQ6hW++/oZhw4drHJkQ9ucuN11yXXI9G159leFvvQVAB29vFm7erHFEpTt15RRRm6PY\n//3+EhMDNYJq0G9oP2aHz6Z7++6ljpuWlsbw4cNJTEyscGxLly5l4sSJFf68EM7CXa5LQlSGJAOq\nKKPRyIGLB8zHFZ67ec5qv3p+9cyJgT4t+khioIIMBgN/+9vfWLlypflnn378Mc+Eh2sYlRCO4y43\nXXJdcj23LlygTtOm5Be8jl26FP+WLTWNqTxOXz3Nqi2r2Ld7H7dO3LKZGKjesjp9h/YlYnIEj3Z8\ntNj72dnZDBgwoFKJgDfeeIM5c+ZU+PNCOBN3uS4JURmSDBAYjAb2X9jP2qNrWXdsHedvnrfar75f\nfR5v+zhPPvgkve/rjYfOw8GRuq6IiAj+85//mF+//vrrvPbaaxpGJIRjuctNl1yXXFOfmjXZdfMm\nAP8ZOZJu06drHFHFnLl6hqj4KPbt3sfN326WmBgI/WMoEeER9OzYE4Dp06fz3nvvVWr+adOmsWDB\ngkqNIYSzcJfrkhCVIckAUYTBaGDv+b3mxMDFWxet9mtQvYE5MdCrea8yJQZycnKIi4sjOTkZgPvv\nv59hw4bh7e3eJxq8//77vPjii+bXkydP5uOPP0ZR5Pojqg53uemS65Jreqt/f17dtg2AJ5s0YUpU\nlMYRVd656+dYuWUle3fv5Way7cSA331+9Ojfg+9XfU92dnal5vTz8+PixYvUrFmzUuMI4Qzc5bok\nRGVIMkDYZDAaSDqXxNqja/nq2Fdcun3Jar+G1Rvyp3Z/4skHn+TRZo8WSwzo9XreeecdFixYwNWr\nV4u816BBA6ZPn87MmTPx8HC/lQbr1n7JmD8/ReGf4xEjRhAdHY2np2y3EFWLu9x0yXXJNe3/7DMe\nfuYZABrrdETFx6PodBpHpZ5zN86xassq9uzeQ0ZyBhjsN9fChQt54YUX7DeBEA7iLtclISpDkgGi\nTPQGPYnnEs2JgSuZV6z2a1yjsTkx0KNZD4wGI2PHjuXLL78scfwxY8YQFRXlVgmBnTt3Mmhgf3Lz\n9AB0796drVu34ufnp3FkQjieu9x0yXXJNelzcqhfrRppBf/tVv3rXzTu2VPjqOzjwo0LRMVHkbQ7\niYzj6icG2rZty7Fjx9QdVAgNuMt1SYjKkGSAKDe9Qc/us7tZe3Qt0b9GczXzqtV+Tfyb0OJwC5KW\nJ5Vp3Llz5xIREaFmqJo5fPgwvR7tRsYt05LMNkFNSdz3E/Xq1dM4MiG04S43XXJdcl1PNG3KVxcu\nADD70UcZVHDCgDu7lHqJZRuWEb8sXtVx09LSqFWrlqpjCuFo7nJdEqIyJBkgKkVv0LPrzC5zYuDa\nnWt338wH5gOZZRurQYMGnDt3zuVrCJw7d45HunXiwuVUABrVr8me/T/TokULbQMTQkPuctMl1yXX\n9elf/0p4Qa2A/jVr8srXX2sckWNcvHiRsWPHqjrmqVOnaOlCJzIIYY27XJeEqAz32TAnNOGh86Bv\ny758NOwjLv7jIgnjEgjvEk7danXhN8qcCAC4evUqcXFxdovVEdLS0hgyqK85EeBf3YfvtuyQRIAQ\nQmhsoMVRrkkZGeRlluMCJYQQQrghSQYI1XjqPOkf1J+Ph3/MpX9cYmKzieUeo/CkAVeUnZ3NyJEj\nOXY8BQAvTx3rv95Ap06dNI5MCCFEi969ae3lBUAWcGrjRm0DcpCAgADVx6xdu7bqYwohhHA8SQYI\nu/Dy8KJ13dbl/tyHqz5k5aaVGAx2LIVsB3q9nrFjx7J7927zz5Yv/5z+AwZoGJUQQghLA9u0MbcP\n7dihXSAOVKNGDZo3b67aeG3btpV6AUII4SYkGSDs5v777y/3Z84fPs+4x8bh09CHR556hNVbVjt9\nYsBoNDJt2jRiYmLMP/vvf//LX1TeoymEEKJyBg0bZm4npaRoGIljjRgxQrWxpkyZotpYQgghtCUF\nBIXd5OTk0Lx5c65etX7aQFl51fciZGAI056exp/6/gmdk50N/X//93/Mnj3b/Hr69OnMmzcPRZGa\nNEIUcpdCTXJdcm0ZZ85Qt0UL9AWvY1eswF/Fp+bO6vbt2zzxxBNkZ2dXahw/Pz8uXrxIzZo1VYpM\nCO24y3VJiMpwrm9Vwq34+Pgwffr0Mvfv3Kczjbs1Bp+iP8+7lkfSqiTGDBiDb2Nfeo3rRfSOaLuv\nGEhPT+fUqVOcOnWK9PR0q30+X768SCJgzJgx/O9//5NEgBBCOKGa991Hd39/8+vjsbEaRuM4NWrU\nYOjQoZUeJzw8XBIBQgjhRmRlgLCrwr30X375ZYn9+vbtyz//+U88PDy4nX2bNdvXsHX7Vi4fugy5\n1j/j3dCbhwc/zN8n/Z2RvUaq8gU8PT2dFStWsHjxYo4fP17kvQceeIApU6Ywfvx4atWqxabvvmP4\n8GHk601JidDQUDZt2oSPj4+1oYWo0tzlCYxcl1zfm6GhvLZzJwBjmjbluS++0Dgix8jNzeWZZ57h\n3LlzFfp8z549iY+Px9fXV+XIhNCGu1yXhKgMSQYIu9Pr9fz3v/9l/vz5xbYM+Oh0jJ80iTFjxuDh\n4VHsszfv3GTN9jVs27GNK79csZ0YaOTNI4Mf4e/P/J0RPcu/NzI7O5uIiAg+/fRT7ty5U2JfPz8/\nRowYQezX0dzJzgOgQ9sgdu/5UZ6YCGGDu9x0yXXJ9e1ZvJgeBfveA3U6voiPR3Gy7Wf2cPDgQSJm\nvUy+vvS+9+rZsyexsbFyioBwK+5yXRKiMiQZIBwmNzeXuLg4tnzxBYvXrwegsaIQlZBQphuxm3du\nsmrbKrbv2M7VX65CnvV+Po196DGkBy9Pfpk/PvLHUsdNS0tj+PDhJCYmluvXU6h5YD2S9v1MYGBg\nhT4vRFXgLjddcl1yfflZWdTz8yOj4PXquXNp1L27pjHZW3JyMi+99BJZWVkA1KnlT3auvkzJ7/Dw\ncObOnSsrAoTbcZfrkhCVIckA4XD52dnUq1bNfCP25dy5NCjnjVh6Zjqrtq1ix/YdXDtyzWZiwLeJ\nL48+9igvT36ZIQ8PKfZ+dnY2AwYMqHAiwNNDx4EfDtKpU6cKfV6IqsJdbrrkuuQeRjduzPrLlwGI\n7N2bgW+8oXFE9nPhwgWef/55c+2bpk0DSUraQ0BAACtWrOCjjz4qti2ubZs2THn+ecaPHy8r3oTb\ncpfrkhCVIckAoYmwJk34+tIlAF7t3Zt+lbgRS7udxqqtq9ixYwfXj163nRho6kuvx3ox45kZDOw2\nEDBV/n/vvfcqPHfhGPPnz6/UGEK4O3e56ZLrkntY/Oc/M6Wgls3A2rWJtDga1p2kpqby/PPPc6ng\nelu7dm2+//572rVrV6Rfeno6aWlp5j61atVyeKxCOJq7XJeEqAxJBghNfPjkkzy/bh0AQ2rXZpZK\nN2Kpt1NZGb+SXTt3cePoDci33q9as2p079edPV/ukaOWhHAAd7npkuuSe0hJSKDVQFNSuDrw9caN\neFarpm1QKsvMzGT69OmcPHkSgGrVqpGQkECPHj00jkwI5+Au1yUhKkOSAUITv23ezP1DTMv2/YH1\n332Hh8r7Ea/fvE7U1ih27dhF6rFUm4kBNSxcuJAXXnjBfhMI4eLc5aZLrktuwmgk2NubU/mmC8On\nL7xAq9GjNQ5KPbm5ufxz1nR++PlXADw8PFi/fj3Dhw/XODIhnIe7XJeEqAz3L58rnFLrgQNpXnB6\nwC3gzJYtqs9RL6Ae08KmEf1eNGu/WsuI50dQu0NtKH5oQaV99NFH6g8qhBDCPhSFQa1amV/+tGOH\ndrGoTK/X859/v2ZOBAB8+umn5U8E3L4NCQkqRyeEEMKZSDJAaELR6RgQFGR+/cv27Xadr37N+rz0\n+EvELIxhTfQaBk8arOr4v/76q7k4kxBCCOc3cOhQc3vviRMaRqIeo9HIovfnsW3XXvPP3n7rDSZO\nnFi+gQwGCAqCgQPh99/VDVIIIYTTkGSA0MzAIXer++//7TeHzduwZkPG9xuv+riFxZeEEEI4v35T\np5pvgn7Kzibz4kVN41HDqpXLiflmo/n1i/8vnIjIV8s/kE4HPXua2vHxKkUnhBDC2UgyQGim/3PP\nmdsH7twh59o1DaMRQghRldQKCqJb9eoAGIFfv/5a24AqKS4ujiVLPze/HvOn4cxf+BGKUsEt0YMH\nQ8eOoHI9HyGEEM5DkgFCM/XbtaNTQfXmfOC32FiHzR0QEKD6mLVr11Z9TCGEEPYzqHNnc/vHffs0\njKRyEhMTmTdvnvl1/z7dWbFyHTpdJW7zwsPh0CEYN06FCIUQQjgjSQYITQ1s397c/ikpyWHz1qhR\ng+bNm6s2Xtu2beVcZiGEcDGDxowxt7+/cAFXPCni8OHDvPnmmxgMBgC6dOlCTOxmfHx8KjdwRVcU\nCCGEcBmSDBCaGhAWZm4nnj3r0LlHjBih2lhTpkxRbSwhhBCO0W3iRPwL2uf0eq4dPKhpPOV1+vRp\nIiMjyc3NBSA4OJiNGzfaZfWbEEII9yPJAKGpXs8+S+Gzi9/y88k4ftxhcw8ePBhfFfZC+vn5MX68\n+gUJhRBC2JdX9er0a9jQ/PrIxo0l9HYuV65cYebMmdy+fRuABg0asHnzZhpa/HqEEEKIkkgyQGiq\nWp06PGqx1/7Yt986bO4aNWow1OJoqYoKDw+nZs2aKkQkhBDC0QYWVs0HDhw6pGEkZZeRkcHsGS9y\n/fp1APz9/dm0aRPBwcHqTxYfD//4BxQkHYQQQrgPSQYIzQ3s1s3cPvjjjw6dOzw8nLp161b48z17\n9mTu3LkqRiSEEMKRBk2aZG5/n5qKPidHw2hKl5WVxauzX+L0uasAeHl58vXXX9PZohiiqmJioFYt\nyMuzz/hCCCE0I8kAobmBf/2ruf39lSsYC4ogOcI367/ixo0bFfpsz549iY2NVWWrgRBCCG20GjyY\n+zw8ALgN/L55s7YBlSA/P5+33ojk8K+nAVONv5VffEG/fv3sN+lHH8Grr4KcmCOEEG5HkgFCc53H\njKFOQdXiK0Yjl7//3iHzbk1IYNHiT82vg4OD8fPzK/Vzfn5+TJ8+nfj4eDlOUAghXJyi0zHIYnn9\noW3bNIzGNqPRyPx33yZp38/mn703fx5PjvmzhlEJIYRwZZIMEJrTeXnRPzDQ/PqwA57KHDx4kP/8\n523z657dO3P48GEuXrzIe++9xwMPPFDsM23btmXhwoVcvHiR+fPny4oAIYRwE4Mee8zc3vPbbxpG\nYtuSJUvYuHm7+XXkrJd5YdpLGkYkhBDC1SnOfKauoihGZ45PqOeTceN4duVKAPrXrMkrX39tt7lO\nnjzJ9Benkpll2v/Yrs19fL/3p2JP+dPT00lLSwOgdu3a1KpVy24xCeHuFEXBaDS6/MHlcl1yT6m/\n/Ua9++/HiOkpybdr1uDnRFX5v/rqKz788EPz66f/9hRLlkWhKC7/v5QQmnGX65IQlSErA4RTGDh5\nsrmdlJFBnp2qFl++fJnZs142JwICG9Xhu/hdVpf716pVi5YtW9KyZUtJBAghhBur06YNIQXbxAzA\n8W++0TYgC9u2bSuSCBg+fDgfL/ncsYmAEycgPNx0qoAQQgi3IckA4RRa9u5NsKcnAFnAmU2bVJ8j\nIyODmTNncj01A4Ca/r58t2UHzZs3V30uIYQQrmXgQw+Z2z/t2aNhJHf98MMPRU6s6dGjB2vWrMGz\n4HrpMAYDfPopfP65qS2EEMItSDJAOI2BbdqY2z/v2KHq2NnZ2fzzn//k3LlzAHh7e/PNt5vo0KFD\n2QcxGk1PRxxU4FAIIYTjDHriCXN797lzaL0dJDk5mTlz5pCfnw9Au3bt+Pbbb8tU6FZ1bdpAs2Zw\n/Tr8/HPp/YUQQriEKpkM2LJlCzdv3tQ6DJuMRiNr167VOgyHG/DHP5rbe1NSVBtXr9fzr3/9i6NH\njwKmPWIrV66kT58+5Rto717TDZHFlgYhhBDuofukSVQvaJ/R67l+6JBmsZw/f7hbrf4AACAASURB\nVJ7IWX8nKysLgKZNm7Jp0ybq1KmjTUCKAgsXwq5dUJ4kuhBCCKdWpZIBOTk5PPfcc2zYsIGAgIAi\n7x0/fpxJkyYRFBREy5YtadGiBU8//TTJycmqzF2e8RVF4dKlSwwbNoz09HRV5ncF/aZONf+B/Ck7\nm6xLlyo9ptFoZMGCBSQlJZl/tmDBAp6weAJUZn/4A9SoAcePw/nzlY5NCCGE8/AOCKBv/frm10fj\n4jSJIzU1lYgZL5KacQeA2rX82bx5M82aNdMkHrNRo6BXL/Dy0jYOIYQQqqkyyYDU1FQGDBiAp6cn\nCxcuLPLeunXr6Ny5MykpKSQlJXH69Gl27tzJsWPH6Nq1K7GxsZWauyLjT5s2jbCwMHr16sXFixcr\nNb+rqN2yJX+obnouo1YBpy9WLGXDhg3m1zNnzuTFF1+s2GBeXjBiBAwfDrduVTo2IYQQzmXQo4+a\n2/t/+snh82dmZhI5cxoXLptOsqnm68mGuE20a9fO4bEIIYRwf1XiaMHMzExCQ0OpX78+cXFxRSrw\nJiYm0r9/f/z8/EhJSSlSVf7atWu0atWK/Px8kpKSeMiiuFBZVXb8yMhI4uLiSExMpEaNGuWe39X8\n89FHebvgKf5f77uPScuXV3isjXEb+O+7/zO/Hjv2L3z++RfodFUmByaE03CXI5zkaEH3djw2lrYj\nRwIQAMRs3oyHt7dD5s7NzSVy5jQOHjoOgIeHwvqYrxk+YoRD5heiqnGX65IQlVElvhWNHTuWM2fO\nsHz58iKJAIPBwIQJE8jNzeXZZ58tdrxc/fr1CQ8PJysri6lTp5Z7XjXGf/PNNwGYOHFiued3RQMt\nlu/vqcRS/D1JScybN+/uuH17sHTpMkkECCGEsOn+YcNoVnCduAmciY93yLx6vZ63337bnAgA+PTj\nT5w3EeDEdZeEEEKUndt/M1q+fDmxsbFERETQoEGDIu9FR0eTkpKCoiiMHj3a6ucLf75nzx4SEhLK\nNbca43t6evL6668THR1NTExMueZ3RY88/TSFdZJT9HrSfvml3GMcO3aMN9+Yg95genrXuUMbor/Z\nhLeDnu4IIYRwTYpOx8CWLc2vD23davc5jUYjH3zwATt37jT/7O233mDipGfsPne5nTwJrVtDweoJ\nIYQQrs2tkwHZ2dnMnj0bX19fwsPDi72/Zs0awHTMXJcuXayO0aVLF/N5vqtXry7X/GqNP2rUKBo2\nbMiMGTPQ6/XlisHV+AQE0KdePfPrwxb7/cvi/PnzRM6eRXau6fepZbOGbNyyE39/f1XjFEII4Z4G\nDR5sbu9VqYhwSaKiovj666/Nr1988UUiIl+1+7wV0rw5REfDtm1aRyKEEEIFbp0MWLZsGVeuXCE0\nNNTqfvs9e/YAEBwcjIeHh9UxfHx8CA4OBmBbOS9+ao2vKAqDBw/m9OnT5U5IuKIBPXqY2wfLcZ5x\namoqM2fOJOPmbQDq1qrOpoRdNGrUSN0AMzLgk0/g7bfVHVcIIYTm+k+ZQuGGwoN37pB1/brd5oqL\ni+Ozzz4zvx4zZgzz588vsqXRqXh7Q8eOpqMGhRBCuDy3TgasWrUKgG7duhV77+rVq1y+fBmAwMDA\nEsdp0qQJAGfPnuVWGavIqz1+SEgIAEuXLi3T/K5s4Pjx5vb3169jyM8v9TN37twhIiKCSwXHEVar\nVo24TVtp06aN+gFmZZnOWg4KUn9sIYQQmqrXvj1dqlUDQA8kq3CyjTWJiYlFatv079+fFStWSG0b\nIYQQDuO2V5yMjAzz2fJt27Yt9v6NGzfM7XsL+93L8v0LFy6UaX61x2/fvj0Au3fv5rodn1I4g/Zh\nYTQsuBlKNRq5UMqKjLy8PF577TVOnDgBgE6nY+3atTz88MP2CbBRI1i5Ev78Z/uML4QQQlODOnQw\nt38suJdQ0+HDh/nXm69hMBgA05bBmJgYfHx8VJ9LCCGEsMVtkwGHDh3CaDSiKIr5ybultLQ0c7u0\ni6/l+zfLWEFX7fELl7obDAb27dtXphhclaLTMaB5c/PrwyUUbjQYDPz3nXf44YcfzD/7+OOPGTZs\nmF1jFEII4b4GPv64uZ109qyqY58+fZpXZs8gp6C2TXDLZmzcuJGAgABV57EroxF++QUKVkAKIYRw\nTW6bDEi2KPpTt27dYu9b7scrbW+e5ZK9sp4vrfb4hSchGI1GfqlAhX1XM7B/f3N73/HjNvst+WQR\n8RbJgjfeeINnnnHCCsxCCKGCLVu2lDkprQWj0cjatWu1DqPSekyefPdkm/x8rh85osq4V65cYfaM\nadzMzAGgQd0ANsdvp2HDhqqM7zAvvAAPPQRRUVpHIoQQohLcNhmQnp5ublt7Mm+Zgc/Ozi5xLMv3\ny1qVXu3xfX19zW133yYAMOC558ztfbdukZuRUaxPTPRaVn8ZbX4dPnkyr77qpBWYhRCiEnJycnju\nuefYsGFDsSfIx48fZ9KkSQQFBdGyZUtatGjB008/XSQpXhnlGV9RFC5dusSwYcOKXIddjU/t2vSx\neJBw9NtvKz1mRkYGs2e8yJUbptpA/tV92BS/w1xE2KUUFvrdskXbOIQQQlSK2yYDcnNzzW1rlfyb\nWyxDL+0pi2VRP8vPlUTt8S0TGmUtYujKAv/wB9p6ewOQAyz697+Jiopi165d5OXlsWP7dj748CNz\n/xF/HMCHixY5tgLzunUweDCocJMohBC2pKamMmDAADw9PVm4cGGR99atW0fnzp1JSUkhKSmJ06dP\ns3PnTo4dO0bXrl2JjY2t1NwVGX/atGmEhYXRq1cvLl68WKn5tTTokUfM7QM//VSpsbKysoiMnM3p\nc1cB8PLU8fU3cXTu3LlS42pmwACoVw+sbMMUQgjhOjy1DsBeLJ+w5+TkWH2/adOmnD9/vtSblcKi\nfs2aNbN6RKGt+dUc3zK5UdYYXJler6dWnTrm/YjfHDgABw4Apl9/1p1MCndUPBLSkdXrvsHT08F/\nnH/7zfRUpGVLGD7csXMLIaqEzMxMBg8eTP369Xn//feLvJeYmMi4cePw8/Nj/fr15mK09913H99+\n+y2tWrXiqaeeIikpiYceeqjcc1dm/EmTJpGSksJjjz1GYmKiS163Bv7tb7BhAwCJ167xUl4eHl5e\n5R4nPz+fN998k2PHfgVMp/KtXBlFP4vtcC6nQQO4cgXk5AMhhHBpbvu3eOPGjc3tzMxMq3369u0L\nwMmTJ23u1c/Pz+fkyZOA6dif8lBzfMutBNZqILgTvV7P2LFj2WOjMNHt27fRG0y/n22CAvn2u234\n+flZ7WtXAwea/h0f7/i5hRBVwtixYzlz5gzLly8vsvLJYDAwYcIEcnNzefbZZ4udWlO/fn3Cw8PJ\nyspi6tSp5Z5XjfHffPNNACZOnFju+Z1Bu7AwmhR82U0HzpVyso01RqORd999l71795p/9t57C3ly\njBucRiOJACGEcHlu+zd54VMKo9FoPnv+Xo8XVAvOysqyWZTv0KFD5pUFo0ePLlcMao5vWSfgwQcf\nLFccruadd97hyy+/LFPfUX8aq11ypGtXWLoUKnCDKIQQpVm+fDmxsbFERESYi8gWio6OJiUlBUVR\nbF47Cn++Z88eEko4lcUaNcb39PTk9ddfJzo6mpiYmHLN7wwUDw8G3Xef+fWhcv4eAixZsoTNmzeb\nX0dGRvLCCy+oEp8QQghRWW6bDGjdurX55un333+32mfYsGG0aNECo9HI+vXrrfaJjo42jzd06NBy\nxaDm+IVbDRRFISQkpFxxuJKcnBwWLFhQ5v7Lly8vsoXCoTw8YOJEsLhZFEIINWRnZzN79mx8fX0J\nDw8v9v6aNWsA8Pb2pkuXLlbH6NKli3n71OrVq8s1v1rjjxo1ioYNGzJjxgz0en25YnAGAwtXgFHy\nyTbWfLVuLatWrTK/fvrpp3nrrbdUi00IIYSoLLdNBiiKwsiRIwHT03drdDodixYtAmDRokXFCv2l\npqayePHiIv0KZWRk0KtXL/z9/Rk7dixZWVmqjn+vIwXHGnXt2pXAwMAS+7qyuLg4rl69Wub+V69e\nJS4uzo4RCSGE4y1btowrV64QGhpqdb/9nj17AAgODrZaJBdMhWcLK9VvK+cKJrXGVxSFwYMHc/r0\n6XInJJzBAIstEAdu3ybrxo0yfW5rQgIfLrpb5Hb48OF8/PHHji1y6winTsF778GOHVpHIoQQogLc\nNhkAmM+b3717t80+Q4YM4cMPPyQtLY1Ro0aZtxScP3+ekSNHkpmZyaJFi4rt54+PjycxMZHMzExW\nr17Nu+++q+r49yrcbzhhwoQy/dpdVUWOwlLr+CwhhHAWhU+Uu3XrVuy9q1evcrmgpkppyeEmBdXe\nz549W+aTaNQev3A129KlS8s0vzNp8NBDdCo42jcf+K0Mp8f8cOAA//nP2+bXPR7uypo1axxf5NYR\ndu6Eo0dBi7o9QgghKs2tkwEhISH069eP5ORkjh49arPflClTOHDgAIGBgfTu3Zvg4GBCQ0MJCgpi\n//79Vpdo9ujRg3bt2qHT6VAUhQMFle7VGt9SXl4eGzdupHHjxuYEh3Ayublw+7bWUQgh3EBGRgZJ\nSUkAtG3bttj7NyyeTt9b2O9elu8XnlxTGrXHb9++PWBKzFvWv3EVgyzq9PycmFhi3+TkZF6f80/y\n8k1Fbtu1uY9vN27RpsitI0ycCJ98AlaSVkIIIZyfG6api5o/fz5du3Zl/vz5LFmyxGa/Tp068cUX\nX5R53CZNmpiX7s+bN898IoBa41v6/PPPSU1NZd26dXh7e1doDFdx//33O+Qzqlq4EF55BebPh0mT\ntI1FCOHyDh06hNFoRFEU85N3S2lpaea2j49PiWNZvn/vVjVb1B6/UaNGgOmEgn379pW7/o7WBoaF\n8c7BgwB8f+YMf7PR7/z580TO+juZ2XkANG1cl00Ju6lTp46DIhVCCCHKx61XBgB06NCBV155hRUr\nVvDjjz/aZY6EhATGjx9vl7FTU1OZM2cOEydONJ9O4M6GDh1arGp2SRo0aKD9jeXo0XD6tCQChBCq\nsNz6ZO20FMt956XtQddZHP9m64hbe49f+He60Wi0ebKOM+v53HP4FrRP5uWRaqWQYGpqKjNnziA1\n4w4AtWv6sTlhF82aNXNgpEIIIUT5uH0yAGDOnDmEhYUxbty4Mj8ZKau5c+cSFBRE9+7dVR0X7p7z\n3KFDBz755BPVx3dGPj4+TJ82rcz9X3rpJe1XSzRtClodbyiEcDvp6enmtrUn8wEBAeZ2dnZ2iWNZ\nvu/v71+m+dUe39fX19x2xW0CvnXr0sdiO8TR2Ngi79++fZuZM2dy6ZKpzkI1Xy82bIynXbt2Do1T\nCCGEKK8qkQwAiIqKomPHjjzxxBOqHUUXGRnJjRs3+OCDD1QZz5LRaGTq1Kn4+fkRGxtrs5qzO5r5\n3AjGPFL6H80xY8YwY8YMB0QkhBCOY3mNsvZ3f/Pmzc3t0hLclkX9LD9XErXHt0xolLWIobMZaJHw\nX7V7N1FRUezatYvMzExeffVVUlJSANN/ry/XRtOjRw+tQnU8gwH+9S8YMABycrSORgghRDm4fc2A\nQl5eXqxevZq3336bsLAwvvrqK6pVq1apMWfPnl3mJy3lYTQaCQ8Pp1WrVsyaNUv18Z2dR532RH0V\nT6f3lzN/6eZiRw02qF6dl155hRkzZlSpJIkQomqwvK7kWPly5e/vT9OmTTl//jwXL14scazCon7N\nmjWzekShrfnVHN8yuVHWGJyJXq/nrMVqieO3b3O8oAaRl5cXeXl55vc+/fRThg8f7vAYNaXTwdq1\ncOQI7NkDoaFaRySEEKKMqszKgEKRkZEsWLCg1KJIZWGPRACY9mjOnDmzSiYCCnk06UfE3M85d+4c\nMTExzB0zhrlADHCuUyciIiKcLxFw6xZs3651FEIIF9e4cWNzOzMz02qfvn37AnDy5Embe/Xz8/PN\nxW1LO77WnuNbbiWwVgPBmen1esaOHcvCL7+0+r5lIuCtt95i4sSJjgrNuQwaZPr3li3axiGEEKJc\nqlwyAKB169ZFih45o9atW2sdglPw9vYmLCyMiPfeIwIIA7z37XO+Y/zy8iAwEPr1g3tWMgghRHk8\n9NBDgGmV2KVLl6z2KSwom5WVZbMo36FDh8wrC0aPHl2uGNQc37JOwIMWx/S5gnfeeYcvbSQC7uXs\n9xV29be/QVQUTJ+udSRCCCHKoQpfuYTTMOSX3qdhQ+jY0dTOz4edO+0bU3l5eUHhntKtW7WNRQjh\n0lq3bm2uwP/7779b7TNs2DBatGiB0Whk/fr1VvtER0ebxyvvqStqjl+41UBRFEJCQsoVh5ZycnJY\nsGBBmfsvWLBAtZpELqdjR/jLX6AcpwEJIYTQniQDhLayrsB3neBsdOl9Bw68246Pt19MFTV4MHTq\nBJ5VphSHEMIOFEVh5MiRgOnpuzU6nY5FixYBsGjRomKF/lJTU1m8eHGRfoUyMjLo1asX/v7+jB07\nlqysLFXHv9eRI0cA6Nq1K4GBgSX2dSZxcXHFataU5OrVq8TFxdkxIlFVbNmypcTinbm5uSxbtsyB\nERVlNBpZu3atZvMLIdQjyQChnbzbsHMoZByFX98Bg77k/gMG3G0nJNg3tor4+9/hp5/giSe0jkQI\n4eKeeeYZAHbv3m2zz5AhQ/jwww9JS0tj1KhR5i0F58+fZ+TIkWRmZrJo0aJi+/nj4+NJTEwkMzOT\n1atX8+6776o6/r327t0LwIQJE8r0a3cWycnJDvmMEIVycnJ47rnn2LBhQ5EjPgvl5+ezZMkS2rRp\nw6RJk1Sd+/jx40yaNImgoCBatmxJixYtePrpp63+mVYUhUuXLjFs2LAiR6EKIVyPJAOENgx58P2f\nIPUg1AiG3rGgK6UgYO/e4O1tah89CqVUuXY4RdE6AiGEmwgJCaFfv34kJydz9OhRm/2mTJnCgQMH\nCAwMpHfv3gQHBxMaGkpQUBD79+8nPDy82Gd69OhBu3bt0Ol0KIrCgQMHVB3fUl5eHhs3bqRx48bm\nBIdwc3fugI2ik8K21NRUBgwYgKenJwsXLizynsFgYMWKFbRt25bw8HDOnj2LouI9x7p16+jcuTMp\nKSkkJSVx+vRpdu7cybFjx+jatSuxsbHFPjNt2jTCwsLo1atXqaeOCCGcl2KrSrAzUBTF6MzxiQoy\nGmHvBDj9OfjUh0FJ4N+qbJ/t1+9uxf7PP4dx4+wWphBCPYqiYDQaXT5j5sjr0uHDh+natSvjx49n\nScFRdmqbN28eJ0+eLHWpf0V99tlnTJ48mXXr1pmLErqKmJiYcsccExNDWFiYnSJyAU8+Cd99Z0rY\nN2+udTQuIzMzk9DQUOrXr09cXFyxL/rffvstDRo0oG3btvTs2ZMjR46gKAp6fSkrKssgMTGR/v37\n4+fnR0pKCrVr1za/d+3aNVq1akV+fj5JSUnm4qaWIiMjiYuLIzEx0eWODnWX65IQlSErA4Tj3UyG\ns1+Bhx+ExpU9EQBFtwo4Y90AIYRQSYcOHXjllVdYsWIFP/74o13mSEhIYPz48XYZOzU1lTlz5jBx\n4kSXSwQADB061FzIsSwaNGhQ7kKNbiciwrRqTxIB5TJ27FjOnDnD8uXLrT7xHz58OA8//DABAQF0\n7txZtXkNBgMTJkwgNzeXZ599tkgiAKB+/fqEh4eTlZXF1KlTrY7x5ptvAlTdYzWFcHGSDBCOV/MB\nGLADesVA3XJWlrYsIpiQ4HxLEY1G01ORmTNNpx4IIUQlzJkzh7CwMMaNG1diQbGKmDt3LkFBQXQv\nPAlFRYVfMjp06MAnn3yi+viO4OPjw/RyHJX30ksv4V24la2q6tIF/P21jsKlLF++nNjYWCIiIsqU\nfFJze0B0dDQpKSkoimLzeNDCn+/Zs4cEK/WaPD09ef3114mOjiYmJka12IQQjiHJAKGNuiHQZHD5\nP9elCxRmri9dgmPH1I2rshQFVq6EgADIztY6GiGEG4iKiqJjx4488cQTqh1dFxkZyY0bN/jggw9U\nGc+S0Whk6tSp+Pn5ERsbi4dHKfVgnFX2VWbOeJkxY8aU2nXMmDHMmDHDAUEJd5Kdnc3s2bPx9fUt\ntf6GPaxZswYAb29vunTpYrVPly5d8Cw4JWn16tVW+4waNYqGDRsyY8YMVbYuCCEcR5IBwrV4eJjq\nBhRyxq0CUVHwyivgYnvnhBDOycvLi9WrV9OnTx/CwsKsHgVYXrNnz7Z5ikBlGI1GwsPDadmyJWvW\nrHHdJ+VZV2DLI3jsm0DU58uYO3eu1ae2DXQ65r79NlFRUa6b9BCaWbZsGVeuXCE0NFST/fZ79uwB\nIDg42OafXx8fH4KDgwHYtm2b1T6KojB48GBOnz5tM2EghHBOkgwQ9qdX+Qm55VYBZ0wGCCGEHURG\nRrJgwQJ8fHwqPZa/nZZyK4rCzJkzmTVrll3Gd4i8m7DjMbh9Cm4l46HoiYiI4Ny5c8TExDD33/9m\nrq8vMcA5g4GIkSMlEXCv69fhyBGto3B6q1atAqBbt24On/vq1atcvnwZgMDAwBL7NmnSBICzZ89y\n69Ytq31CQkzbPpcuXapilEIIe5NkgLCvzHOwoR2cWq7emJZFBHfuBJWWzQohhLNr3bo1Op1zX7pb\nt26tdQgVp8+BXWGQ9hPUaAWhG8HL9MTW29ubsLAwIiIjifjjHwkDvAG2bNEyYuezaxc0aABylGSJ\nMjIySEpKAqBt27YOn//GjRvm9r2FA+9l+f6FCxes9mnfvj0Au3fv5vr16ypEKIRwBOe+oxCuLTfd\n9HQl8zSkfAYGlfaRBQdDy5amdmYm7N2rzrhCCCGqLqMB9oyHK9vAtxH02wK+Ngq6DRp0ty0r1Irq\n0gU8PeHAAUhL0zoap3Xo0CGMRiOKopifvDtSmsV/m9JWG1m+b6uQaaNGjQBT8dB9+/apEKEQwhEk\nGSDsQ58Nu0ZCxlEIaAu9vwGdissonX2rwC+/mJ6KvP221pEIIYQoi/zbkHkGPP2h73dQo6XtvpbX\noB07ICfH7uG5jBo1oHdv6N4dCpahi+KSk5PN7bp16zp8fstTCUo7ocByNZLRxilOhTU1jEYjv/zy\niwoRCiEcQZIBQn0GPSSNg6u7oFoT6LsJfOqoO4flVgErR91oLj0dPvvMVExQCCGE8/MKgP5bYcB2\nqN2p5L5BQaZVagB37kBBITZRYPNmSEwEDZa/u4r09HRzW406IOUVEBBgbmeXcvqR5fu26o34+vqa\n27JNQAjXIckAob7bKXA5wXRj1XcTVG+u/hz9+pmO8QPYv9/05duZdO8O1aubjj68eFHraIQQQpSF\nZ3Wo07VsfZ19hZqWpKBiqSyPCdWiAGXz5nfvzWwt/S9kWTTQ8nOWLBMatooMCiGcjyQDhPoC2sDA\n3dDnW6jVwT5z1K0LXQtu2AwG0zJNZ+LtDR9/DN9/byqkJIQQwr1Y1g2QIoKinCyfsOdosM3E39+f\npk2bAnCxlIcWhUUDmzVrZvMIRMvkhhbHJAohKkaSAcI+arWHBr3tO4flVgFnfCozdiw8+qipkJIQ\nQgjnknEcDPkV/3zfvlC4l/rgQbCozi5EaRo3bmxuZ2ZmahJD3759ATh58qTNWgD5+fmcPHkSgP79\n+9scy3IrgRY1EIQQFSPJAOG6ZImmEEKIikg/Clsegd2PQ35WxcaoVQseftjUNhph61b14nMHmZkQ\nEwOLF2sdiVN66KGHAFPBvUuXLmkSw+OPPw5AVlaWzaJ/hw4dMq9cGD16tM2xLOsEPPjggypGKYSw\nJ0kGiMrL02hvWI8eUK2aqX3iBJw5o00cQgghXEfmOdgxBPLSTbVndF4VH0uS0rZdvw6ffHK3vo8o\nonXr1uYK/L///rsmMQwbNowWLVpgNBpZv3691T7R0dGAKd6hQ4faHKtwq4GiKISEhKgfrBDCLiQZ\nICrn9inYcD8kv+/4uX19oVevu6+d8VSBQhotARRCCGEh5wZsHwx3zkP9ntBjNegqsZXr3roBNpZa\nV0n33QebNsGzz2odiVNSFIWRI0cCpqfvZXXZ4rjGrCzbq1oyMjLo1asX/v7+jB071mpfnU7HokWL\nAFi0aFGxQoKpqaksXry4SD9bjhw5AkDXrl0JDAws869HCKEtSQaIisu+BtuHQNYluBBrOlLQ0Zz9\nqczevabjp555RutIhBCiasvPhB3D4OavUPNB6BMLntUqN2a3blBYCO7sWdMqNSHK6JmCe4Pdu3eX\nqf+2bdvYtm0bYNpe8P7776PXW7/3io+PJzExkczMTFavXs27775rtd+QIUP48MMPSUtLY9SoUeYt\nC+fPn2fkyJFkZmayaNGiEusFAOzduxeACRMmlOnXIoRwDpIMEBWTnwk7h8GtE6bzmHtFg06Do4Qs\niwhu3Wo6WcCZPPAAfPMNrFqldSRCCFG1GfWmL/9+zaHvZvCuXfkxvbxMR90WklMFRDmEhITQr18/\nkpOTOXr0qM1+ixcvpl69egwYMAC9Xo+iKCiKQkREBDVr1mSQ5QqVAj169KBdu3bodDoUReHAgQM2\nx58yZQoHDhwgMDCQ3r17ExwcTGhoKEFBQezfv5/w8PASfx15eXls3LiRxo0bmxMcQgjXoNiqHuoM\nFEUxOnN8VZYhH3aNgotxUL0FDEqCao1L/Zh9YjFAo0Zw7Zrp9Y8/QufO2sQihLBJURSMRqPLbx6W\n65KL0+eYVrPVaKHemB9+CM8/b2qPGGFKAAtRRocPH6Zr166MHz+eJUuW2GWOefPmcfLkyVKX+lfU\nZ599xuTJk1m3bp25KKErcJfrkhCVISsDRPll/g439oNPXei7SbtEAJiOdbJcHeDMdQOEEEJoy8NH\n3UQAFK0bsH075OWpO76r++47+MtfZNWEDR06dOCVV15hxYoV/Pjjj3aZIyEhgfHjx9tl7NTUVObM\nmcPEiRNdKhEghDCRZIAoP/9WptUAfTZCwP1aR1M0GeCMdQOEEEK4r1at4z2N4AAAIABJREFUTMXy\nAG7dgn37tI3H2Rw4AKtXy4qJEsyZM4ewsDDGjRtXrIhfZc2dO5egoCC6d++u6rgABoOBCRMm0KFD\nBz755BPVxxdC2J8kA0TF+LeCet20jsLEsojg7t2Qna1dLLYYDPDzz3D7ttaRCCFE1XD1e9O2AHtT\nlOKnCoi7Cq/RkqwvUVRUFB07duSJJ54gNzdXlTEjIyO5ceMGH3zwgSrjWTIajUydOhU/Pz9iY2Px\n8NCgbpQQotIkGSBcX7NmcH/BCoXsbEhM1DYea0aNMtUykJshIYSwv8sJsK0f7PijYxICzn6yjZZC\nQuC//4Uvv5SjF0vg5eXF6tWr6dOnD2FhYSUeG1hWs2fPtnmKQGUYjUbCw8Np2bIla9aswdvbW/U5\nhBCOIckAUbrs61pHUDpn3yoQEmL6t9Q0sLstW7aUuMwyNzeXZcuWOTCiooxGI2vXrtVsfiHcXupB\n2BUGhjyo1RF0Dvii0r+/aYUAwP79kJZm/zldhacnvPyyKSGuSK220kRGRrJgwQJ8fHwqPZZ/4bGX\nKlMUhZkzZzJr1iy7jC+EcBxJBoiSZRyHuAfgyFvOndF39qcyAwdC/fpQvbrWkbitnJwcnnvuOTZs\n2EBAQECx9/Pz81myZAlt2rRh0qRJqs59/PhxJk2aRFBQEC1btqRFixY8/fTTJCcnF+urKAqXLl1i\n2LBhpKenqxqHEFXerZOw/THIvw33PQVd/ueYL6B16sAf/mBqGwymQoJCVFDr1q3R6Zz7Fr1169Za\nhyCEUIFz/00jtHXnImwfDDk34Po+MBq0jsi20FAo3K/2009w3clWM3TrBpcvwzvvaB2JW0pNTWXA\ngAF4enqycOHCIu8ZDAZWrFhB27ZtCQ8P5+zZsygqfjlYt24dnTt3JiUlhaSkJE6fPs3OnTs5duwY\nXbt2JTY2tthnpk2bRlhYGL169eLixYuqxSJElZZ1peCadQ0aDYTuy0Fx4G2OZVJa6gYIIYRwAZIM\nENblZsCOx+DOWajbHXp+CTonLg5Ts6bpCzeYVjBs26ZtPPfS6Uz/CNVlZmYyePBg/P39ef/994u9\nHxcXxwMPPMDBgwdp3769qnMnJiYybtw4qlWrxvr162nUqBEA9913H99++y0eHh489dRTHDp0qNhn\nJ02axPDhw3nssce4LYUlhag8L38IaAd1ukKvaPBw8D5myyKCzrhCzRkYjZDjgBoOQgghykS+nYji\n9DmwezSk/wL+baDPt+Dpp3VUpXP2rQLCLsaOHcuZM2dYvny51Sf+w4cP5+GHHyYgIIDOnTurNm/h\nkUq5ubk8++yz1K5du8j79evXJzw8nKysLKZOnWp1jDfffBOAiRMnqhaXEFWWpx/0Xg99t5gSA472\nyCN3t4KdOgUpKY6PwZmtWAGBgfDRR1pHIoQQooAkA0RxWRfh1m/g2wj6bgLfelpHVDb3FhF05hoH\nQhXLly8nNjaWiIgIGjRoUGp/NbcHREdHk5KSgqIojB492mqfwp/v2bOHBCvFIz09PXn99deJjo4m\nJiZGtdiEqLJ0nuBTR5u5vb1NW9YKSVK6qJ49Tcf/Tp+udSRCCCEKSDJAFFejJQzaA303m9quont3\nqFHD1D5zxjmfyhw/DvPnw2+/aR2Jy8vOzmb27Nn4+voSHh7u8PnXrFkDgLe3N126dLHap0uXLnh6\negKwevVqq31GjRpFw4YNmTFjBnq93j7BCiEcQ+oG2BYcbPpHCCGE05BkgLDOrynU7qh1FOXj5VX0\nqYwzHuMXFWVKCBicuBiji1i2bBlXrlwhNDSUGoVJIAfas2cPAMHBwXh4WK+n4ePjQ3DBze82G3Us\nFEVh8ODBnD592mbCQAhhxZm1kJ+pdRRFWdYN2LYN8vO1i0UIIYQohSQDhHu5d6uAs/nXv+Djj+GB\nB7SOxOWtWrUKgG6FhSMd6OrVq1y+fBmAwMDAEvs2adIEgLNnz3Lr1i2rfUJCQgBYunSpilEK4cZS\nPoPEMabTAwxOtKLmgQdM++IBMjLgwAFt4xFCCCFKIMkAAXfOax2BeiyXaG7bBrLs2i1lZGSQlJQE\nQNu2bR0+/40bN8ztewsH3svy/QsXLljtU3jKwe7du7nubMdiCuFszsfC/oKtQff9xblOulEUOVWg\nNPn58MMPWkchhBACSQaItEOwoR38NAuMbrB0vW1bKHgSS3o6HDyobTzCLg4dOoTRaERRFPOTd0dK\nS0szt318fErsa/n+zZs3rfYpPJLQYDCwb98+FSIUwk1dSzStCDAaoP2r0Mb6SR2akroBthmNEBQE\nISFw7pzW0QghRJUnyYCq7PbvsOMxyL8Fmb9rHY06FMX5twqISktOTja369at6/D5LU8lKO2EAp3u\n7l+zRhsnXBSehGA0Gvnll19UiFAIN3TzBOwYBvpsCJ4MHd7QOiLrLK9Be/eCjSRglaQoUHjEq1yf\nhRBCc5IMqKpybsCOIZB1CRqEwiOfg+Imfxwsn8o4481Gejq88QZMmqR1JC4rPT3d3C7tybw9BAQE\nmNvZ2dkl9rV839/f+tnnvr6+5rZsExDChur3QZMh0HQkhCwyfbF0RvXr3/3Cq9fD9u3axuNsBg6E\nZs2kuKIQQjgBN/n2J8ol/w7sHA43k6FWB+j9NXg4/guV3fTvf7edlASZTlZt2scH5s6FpUtBvvhV\nSG5urrltq5K/PTVv3tzctrX0v5Bl0UDLz1myTGjYKjIoRJXn4Q09ouDRL0HnqXU0JZO6AbY995zp\n+F8NjoQVQghRlCQDqqKcG5B9DfyaQeh34F1T64jU1bgxFBRkIy8Pdu3SNp57VasGPXua2jaOmxMl\ns3zCnpOTo8n8TZs2BeDixYsl9i0sGtisWTObRyBaJje0OCZRCJeh6FwjeS11A2zz9HTeVR1CCFHF\nSDKgKqreDAYlQr948Cv5WDSXZXkjlpCgXRy2/OMfsHp10b2loswaN25sbmdqtPKjb9++AJw8edJm\nLYD8/HxOnjwJQH/LFSv3sNxKoEUNBCGEyh591JT4BThxAn7/XdNwhBBCCGskGVBV+TaAgPu1jsJ+\nnL2I4GOPwZ//DHXqaB2JS3rooYcAU8G9S5cuaRLD448/DkBWVpbNon+HDh0yr1wYPXq0zbEs6wQ8\n+OCDKkYphIsyGuHX/0FuhtaRVIyvL/Tuffe1M16HhBBCVHmSDBDuqU8f8PIytQ8fhsuXtY1HqKp1\n69bmCvy/a/TEbdiwYbRo0QKj0cj69eut9omOjgZM8Q4dOtTmWIVbDRRFISQkRP1ghXA1h/4JP70M\nO/5oSgy4IqkbULIffoB//xvu3NE6EiGEqLIkGVAV3DzhujdTFVW9OvTocff11q3axSJUpygKI0eO\nBExP38vqskVSKCsry2a/jIwMevXqhb+/P2PHjrXaV6fTsWjRIgAWLVpUrJBgamoqixcvLtLPliNH\njgDQtWtXAgPddOuOEGV1/D04NhcUD2j/iuvuL793u5per10szmjePLhxQ5IBQgihIUkGuLvr++G7\nTnBgChiq2I2Is28VKJSXp3UELumZZ54BYPfu3WXqv23bNrYVFGw0Go28//776G3cnMfHx5OYmEhm\nZiarV6/m3XfftdpvyJAhfPjhh6SlpTFq1CjzloXz588zcuRIMjMzWbRoUYn1AgD27t0LwIQJE8r0\naxHCbf2+Bn6cbmo/vBSaPKZtPJXRvj00amRqp6XBjz9qG4+zWbXKlBCoV0/rSIQQosqSZIA7u/kb\n7BwK+jugzzZVYa5KLJ/KxMc73+qIzEzTdoagIDAYtI7G5YSEhNCvXz+Sk5M5evSozX6LFy+mXr16\nDBgwAL1ej6IoKIpCREQENWvWZJDlUt4CPXr0oF27duh0OhRF4cCBAzbHnzJlCgcOHCAwMJDevXsT\nHBxMaGgoQUFB7N+/n/BSjs/Ky8tj48aNNG7c2JzgEKJKSv0R9o43tTv9B4LGaxtPZSmKnCoghBDC\nqSm2qmA7A0VRjM4cn1PLugJbHoHM09B4CPSJBZ2X1lE5ll4PdetCRkEBqmPHoG1bbWO619at8PDD\nIMfJVcjhw4fp2rUr48ePZ8mSJXaZY968eZw8ebLUpf4V9dlnnzF58mTWrVtnLkrojhRFwWg0uuh6\n77vkumRHhnw4MBU8a0CX/7nu9gBLK1fCuHGmdp8+sGOHpuEIIe5yl+uSEJVRxR4VVxF5t0xFlzJP\nQ50/QM91VS8RAODhAf363X3tjFsF+veXREAldOjQgVdeeYUVK1bwo52W4CYkJDB+vH2eUKampjJn\nzhwmTpzo1okAIcpE5wndPoYu77pHIgCKbldLSoLbt7WLRQghhLiHJAPcUf5tMORCjWAIjQOvKvxl\n896tAsLtzJkzh7CwMMaNG1esiF9lzZ07l6CgILp3767quAAGg4EJEybQoUMHPvnkE9XHF8IlKYp7\nbWlr1Ag6djS18/Jg505t43E2Z87ArFnw2mtaRyKEEFWSG11xhVm1xjBwN/SLB98GWkejLcunMjt2\nSLE+NxUVFUXHjh154oknyM3NVWXMyMhIbty4wQcffKDKeJaMRiNTp07Fz8+P2NhYPDw8VJ9DCOEk\npG6AbZmZ8M478PHHUjtHCCE0IDUDhHszGqFlS9PTB4Ddu6FnT21jsubaNVOiokkTrSNxaW+//TaJ\niYl89dVXVKtWrVJj3bp1C39/f5Uiu8toNBIeHk6rVq2YNWuW6uM7K3fZmynXJZXoc+DnWfDgP8G3\nvtbR2NeWLTB4sKndtq2pfo0wMRqhWTO4cAF+/hkeekjriEQV4i7XJSEqQ5IBwv1NngyFxeVeew1e\nf13TcIpZuBCmTYPp02H+fK2jcXknTpwgODgYnc55Fz6dOHGC1q1bax2GQ7nLTZdcl1Rg0EPSU3B2\nHTToA/23u0+NAGuysqB2bcjJMb0+dw6aNtU2JmeyciUEBJhq6FSvrnU0ogpxl+uSEJXhvHfLouzS\nDoFRltfZZLlVwBnrBhTuJ01I0DYON9G6dWunTgQAVS4RIISZ0Qg/TjclArwCoOsC904EAFSrBr16\n3X3tjNchLf31rzBihCQChBBCA859xyxKd3UXbH4Y9ow3Hcskiuvf/+7N5r59d48adBaPPAI1a0Kt\nWpCdrXU0QghhP8fmwm8fgM4ben8DtTtpHZFjSN0AIYQQTkiSAa4s/QjsHAGGHPCqBYoUIbOqXj3o\n3NnU1uudr5qzjw9cvmyqZ+Drq3U0QghhH1e2w6F/Agr0iIKGoVpH5DiDBt1tJyRIsTwhhBBOQZIB\nrirzHGwfAnkZ0Gw0dH3P/ZdaVoazbxWQJIAQwt016AMP/AP+8AE0/5PW0ThWx45Qv6BQ4vXrpmJ5\nojg58UcIIRxKkgGuKDcNdgyBrAtQvyc8shJ0siqgRJZLNJ0xGSCEEO5O0UGXd6HNVK0jcTydTq5D\nJTl9Grp1g759tY5ECCGqFEkGuCKDHjxrQM120CcWPCt3hFqV0LPn3afvycmmas5CCCGEo0jdANsa\nN4Z33oGtW7WORAghqhQ5WtBV5WdCbgb4ybn0ZTZw4N2K/UuXwsSJ2sZzr7Q0041QnTrQr5/W0Qih\nKnc5wkmuS6LCLly4e6Sgt7fp73w/P21jEqIKc5frkhCVISsDXJVndUkElJflUxlnPMZvyxZYtgxu\n39Y6EiGEqJycG7D7CbhzQetInEdgILRrZ2rn5sKuXdrGI4QQosqTZICoOiyLCDpjNecxYyAuznTe\nshBCuKr8TNgxDM59Bfuf1Toa52J5qoDUDRBCCKExSQa4gmt7wJCvdRSur1Mn0zGDAFevwuHD2sYj\nhBDuxpAH34+BG3vBrzl0+1jriJyL1A0o3blzcOOG1lEIIUSVIMkAZ3dpCyT0ht2PS0KgsnQ66N//\n7mtn3CoghBCuymiE/eFwMQ6860DfzeAXqHVUzqVPH/DyMrWPHIFLl7SNx9nMmAHNm8Pnn2sdiRBC\nVAmSDHBmqT+akgDGfAi4H3SeWkfk+iy3CsgSTSGEUM+FWDi1HDyqQWgc1HxA64icT/Xq8Oijd1/L\ndaiojh1N/5bfFyGEcAhJBjir26dgx2OQfxtajIVO/6d1RO7Bconmrl2Qna1dLLZ8/jk89RRkZGgd\niRBClF3gCOj4L+i5Dup11zoa5yV1A2wbMACqVQMfH9NKEyGEEHYlRws6o+xrsKUH3D4JjQZCnw3g\n4a11VO6jTRs4ccLU3rYN+vbVNp579ewJiYmwfj2MGqV1NEKowl2OcKqy1yWhnh9+gJAQU7thQ9NW\nAcXl/9dQT06OKRkghJ25y3VJiMqQlQHOSOcNfk2hdmfoFS2JALU5+1aBwtULUtNACCHcT+fOULeu\nqX3lihSzvZckAoQQwmEkGeCMvGtC302m4kte/lpH434stwo4YzLg8cfhnXdg6lStIxFCCNtkhUTF\neHgULWYrpwoIIYTQiCQDnJWHD/jW1zoK99S3r+lkAYCDByE1Vdt47tW+vamicrt2WkcihBDW3TwB\n8T1N9W1E+UndACGEEE5AkgGi6qlV6+5+TaPRVDdACCFE2WRdhu2D4XoS/DJH62hckysUs9XSlSum\nYrp792odiRBCuDVJBjiDywmgz9E6iqrF8kZM9uYLIUTZ5N00nXSTeRrq/AFCPtI6ItfUvDncf7+p\nnZ0N33+vbTzOJjoaYmNNxQSFEELYjSQDtHbua9MTlh1DwZCvdTRVh7MXESxkNMq+XCGEc9DnwK4w\nSPsZ/FtDaJzUtakMy6S01A0oaupU+Oor6NNH60iEEMKtSTJAS9cSIekpMBqgQW/QeWodUdXxyCNQ\nvbqpfeqU6R9n8/LL0LgxHD2qdSRCCAHnYuDKNvBtZCpw69tA64hcm9QNEEIIoTFJBmgl41fYORz0\n2RA8Gdq/qnVEVYu3d9EnDs64VWD4cEhKMhUUFEIIrbV4CrouhL7fQY2WWkfj+kJDwbPgIcDPP5v2\nyQshhBAOJMkALWRdgu1DIDcNAodDyCJQFK2jqnqcfatAnz4QFKR1FEIIcdf9L0DtTlpH4R78/U2r\n1P4/e3ceH1V1/3/8dZOw7/sSZJUlCCK7IjthK2sysf4s1a+KItL2q/1aFdGvX2sXbLVCUSlaq6JV\nXEq0IC6AaCZsQlEQQVZBZBMkYQsh29zfH5MMA0ySSWa5M3fez8fDB3e4Z+79gLmcM58553NKfPKJ\ndbGIiEhMUjLAClXqQv3u0OhauP5NLQ+wivd6zU8+gaIi62IREZHYo7oBpTNNePZZuOEGKCiwOhoR\nEVsyzAguTmYYhhnJ8QXEVQiFZ6FqfasjiV2mCS1bwtGj7tcbN0KfPtbGJGJThmFgmmbUT4Gydb90\nKVehktWh9vnncO217uOWLeHgQc0U9Na1K3zzjXv7xUGDrI5GbMYu/ZJIIDQzwCpxCUoEWM0wIn+p\nALi/Efn+e6ujEJFYcnwNLOsKp7ZbHYm99ekD9YvHAocPw3b9fV+kZOaEZk2IiISEkgES27ynaEZi\nMuCLL6BRI0hJsToSEYkVJ7fBZ+PhzG7Y86LV0dhbfDyMGHHhdST2Q1b6+c/dSwVuv93qSEREbCni\nlwlYHYOIiASHHaZjql8SEbEPO/RLIoGI6GSAiIiIiIiIiASflgmIiIiIiIiIxBglA0RERERERERi\njJIBIiIiIiIiIjFGyQARERERERGRGKNkgIiIiIiIiEiMUTJAREREREREJMYoGSAiIiIiIiISY5QM\nEBEREREREYkxSgaIiIiIiIiIxBglA0RERERERERijJIBIiFiGMZAwzD2GobhMgzjY8MwBl1y/nbD\nMM4YhrHBMIwrrYpTRERig/olERHxpmSASIiYprkamF/8cqFpmpmXNHkLOAekmKa5J6zBiYhIzFG/\nJCIi3pQMEAmtTcW/tvdx7h7gz6ZpHgpjPCIiEtvUL4mICAAJVgcgYnNbi3/t5P2bhmE0B8YBgy57\nh4iISOioXxIREUAzA0RCyjTNE8BxLhl0AX8EHjBN0xX+qEREJFapXxIRkRJKBoiE3na8Bl2GYfQH\nXKZprvHnzYZhVDcM4+ehCk5ERGKO+iUREVEyQCQMtgP1DcNobBiGATwGPOjPGw3DaAX8FZgduvBE\nRCTGqF8SERElA0TCYHvxr52BW4H04mma5TJN8yDwRojiEhGR2KR+SUREVEBQJAy2Ff/aBxhmmuZk\n75OGYSQAvwc2Az8HDpimOcO7SViiFBGRWKF+SURElAwQCYOSQdejwHAf538N5Jum+aZhGIO4UOlZ\nREQkFNQviYiIlgmIhJppmseBE8Brpmlu8dFkBPBZ8XFrYF+YQhMRkRikfklEREDJAJFwWQE8Usq5\n/YBpGEYiUB9YHq6gREQkZqlfEhGJcVomIBIGpmn+rIzTc4GpwJXARNM0zfBEJSIisUr9koiIaGaA\niPUeBdoAe0zTzPY+YRhGcyAFaGgYxhjDMOKtCFBERGKK+iURkRhgKNkrYh3DMAYDdYBawC+Bry+p\n2CwiIhI26pdERGKHkgEiFjIM4x3TNG8oPo4DPjBNc4zFYYmISIxSvyQiEjuUDBCxkGEY9wJ5uCs1\nNwc2maapLZxERMQS6pdERGKHkgEiIiIiIiIiMUYFBEVERERERERijJIBIiIiIiIiIjFGyQARERER\nERGRGKNkgIiIiIiIiEiMUTJAREREREREJMYoGSAiIiIiIiISY5QMEBEREREREYkxSgaIiIiIiIiI\nxBglA0RERERERERijJIBIiIiIiIiIjFGyQARERERERGRGKNkgIiIiIiIiEiMUTJAREREREREJMYo\nGSAiIiIiIiISY5QMEBEREREREYkxSgaIiIiIiIiIxBglA0RERERERERijJIBIiIiIiIiIjFGyQAR\nERERERGRGKNkgIiIiIiIiEiMSbA6gLIYhmFaHYOIiASHaZqG1TEESv2SiIh92KFfEglERCcDAExT\n4y7xQyHQCDhd/PoboIt14cS0Y0ATQN2reDEM+/xAqF+ymS3ANcXHDXH/GxZvXTgSYbYD/wZGAb0t\njkWCyk79kkhlaZmA2EMCMMLr9XKrAolxyUAzYK/VgYiI+OlqoHnxcRawycJYJPK8DMwC3rY6EBGR\n4FMyQOxjlNexkgHWaFz8q/7+RSRaGFzcf3xsVSASkUYX/6qfCxGxISUDxD68B3OfAnlWBRLDRuGe\npXHI6kBERCpgjNexPvSJt4HAzcB9gFYIiYjNGJG89tEwDDOS45MIdCUXpqivAoZZGEssygFcQB2r\nA5FIYxiGLQo1qV+yqR+Bprg/7MUXv65vaUQiEmJ26ZdEAqGZAWIvo72ONVU9/GqhRICIRJ/GXCgO\nVwR8YmEsIiIiYaJkgNiL6gaIiEhleCeTtVRARERigJIBYi/DuLAl1BfAcQtjERGR6HFp3QCtBhER\nEZtTMkDspS5wndfrlVYFEuNOAG8B2VYHIiLip/64+xCAA8AOC2ORyPMJ7tkjT1kdiIhI8CgZIPaj\nLaKsNxX4J+6kgIhINKgCjPB6rf5DvDUEpgN3Wh2IiEjwaDcBsZ/PgWuLj1vg3uZOtWLDy0R/53IR\nu1RtVr9kc8/j/sAH7mUDH1oYi4iElF36JZFAKBkg9lMENOHCFPWtQDfrwhER+wy61C/Z3H6gXfFx\nDdyzm2pYFo2IhJBd+iWRQGiZgNhPPJDs9Vq7CoiIiD/aAp2Lj3OBTOtCERERCTUlA8SetMWgiIhU\nhrYYlPKcRLtNiIgtKBkg9jTS6zgDOG9VIDHsFPAi8ITVgYiIVICSAVKWSUAjYJfVgYiIBE7JALGn\nNlyY6nkeTfW0wjncVZd/B+RZHIuIiL+GAFWLj7cBBy2MRSJPbcAFfGR1ICIigVMyQOzL+9sdLRUI\nvxZAd9xJgbUWxyIi4q9awGCv1+o/xNto3Lvl7Lc4DhGRIFAyQOxLdQOsdw/wF6CT1YGIiFSAdzJZ\n3wCLt1TgODDH6kBERAKnrQXFvs4CDYGC4teHcX9bLSJhZ5ctnNQvxYitwNXFxw1wf/iLty4cEQk+\nu/RLIoHQzACxr9rA9V6vV1oViIiIRJVuQMvi42xgo4WxiIiIhIiSAWJv3ksFVBVaRET8YaBdBURE\nxPaUDBB7804GrMBdAVhERKQ8qhsgZTkDLMG9hEREJEopGSD21hNoXHx8DPjKwlhi1RlgCnANoKXW\nIhItknHPEADYgHu5gEiJO4B5wA9WByIiUnlKBoi9xQEjvV5rV4Hwq437/8F7XBhYi4hEukZA3+Jj\nF6o7Ixd7E/fPRDerAxERqTwlA8T+tMWgtQzgVqCttWGIiFTYGK9j1Q0Qb0pui4gNKBkg9uc9MyAT\nOGdVICIiElUurRugpU4iImIjSgaI/SUCVxUf5wMZFsYiIiLRox9Qr/j4ELDdwlhERESCTMkAiQ3e\n3+5oqYB18oGTVgchIuKnBNyFBEtoqYB4ywVeBx63OhARkcpRMkBig+oGWO8VoCHwe4vjEBGpCNUN\nkNIU4q6J81u024SIRCUlAyQ2DAKqFR9vBw5aGEusagPkoGSMiEQX75llGajujFxQB7ge924Tn1gc\ni4hIJSgZILGhJu6EQIkVVgUSwwbg/v9wFndSQEQkGlwBJBUf5wFOC2ORyDMN+B3Q0+pAREQqTskA\niR3eSwU01TP8qgF7gL1ALYtjERGpCO/ZAeo/xNvPgEeADlYHIiJScUoGSOzwTgasAIqsCiSGtUB7\nM4tI9FEyQEREbEjJAIkdVwPNio+zgC8tjEUkVhTlWR2BSOCGANWLj78BDlgYi4iISJAoGSCxw0C7\nCoiE06kdsLQTHPrA6khEAlMDGOz1WrMDRETEBpQMkNiiZID1CoG1wGqrA5GQOncQPh0N5w7A3hes\njkYkcFoqIKVx4S4k2AnItTgWEZEKUDJAYkuy1/Ea4IxVgcSw94AZuKfaij3lZV1IBDQeAAPesDoi\nkcB5JwNW4k5sioB7ND0IWMKF5SQiIlFAyQCJLc2BHsXHhcBn1oVEDkCTAAAgAElEQVQSsxzAZuBO\nqwORkCjMgYzxcGo71LsKhiyFhJpWRyVhsHz5ck6fPm3Z/fPz83n55ZdLPW+aJm+//Xblb9AVaFV8\nfArYUPlLiQ3dDHRBRXJFJKooGSCxx/vbHS0VCD8NlOwtezNkfwk1W8Owj6BaQ6sjkhDLy8tj+vTp\nvP/++9StW/eiczt27GDq1Km0b9+edu3a0bZtW26//XZ27twZtPsXFhby4osv0qlTJ6ZOnVpqO8Mw\nOHLkCOPHj+fkyZMVv5HBxf3HRxW/hIiISCRRMkBij+oGiIROk+th2HIY9jHUbFV+e4lqWVlZJCcn\nk5CQwLx58y46984779CzZ0/27t3L2rVr2bdvHxkZGWzfvp3evXuzZMmSgO7tcrlYuHAhSUlJTJs2\njQMHDmAYZWcb77nnHlJSUhg0aBCHDx+u+E1VN0BERGzEME3T6hhKZRiGGcnxSZQ6DzTkQpGffUBb\ny6IRiQmGYWCaZtTPC1G/dEFOTg5Dhw6lSZMmLFu27KIP4mvWrGHEiBHUrFmTvXv30qBBA8+548eP\nc+WVV1JYWMjatWvp0aOHr8uXa+nSpTRt2pSkpCQGDhzI119/jWEYFBUVlfveWbNmsWzZMtasWUPt\n2rX9v2k20Bh3wTgDOA40qlT4YldFwEn0cxEF7NIviQRCMwMk9lTHvWd0iRVWBRLjPgXuAw5ZHYiI\nVMaUKVP47rvveOWVVy5KBLhcLm699Vby8/O56667LkoEADRp0oRp06aRm5vLjBkzKn3/CRMm0L9/\nf+rWrUvPnj0r9N7HH38cgNtuu61iN20A9C8+NnEXEhQpsRxoCky3OhAREf8oGSCxyXupgKZ6WmMu\n8DT6+492uT9YHYFY4JVXXmHJkiXMnDmTpk2bXnRu8eLF7N27F8MwSE1N9fn+kt9ft24dK1cG/om6\nvOUBl0pISOCxxx5j8eLFpKenV+xmqhsgpbkSyEK7TYhI1FAyQGKTdzLgE9RpW6Hk/4HqNkSv79+D\nJe3guwAqtEvUOX/+PA899BDVq1dn2rRpl51/8803AahatSq9evXyeY1evXqRkJAAwKJFi0IXbBkm\nT55Ms2bNuP/++/1aWuBxaRFarRqREu1xJwSqA99ZHIuIiB+UDJDY1BVILD4+CfzHwlhi1VjgHuDy\nzxISDX7IgDX/D4py3dsISsx4+eWX+eGHHxg6dKjP9fbr1q0DoEOHDsTHx/u8RrVq1ejQoQMAq1at\nCl2wZTAMg9GjR7Nv376KJST64l4uAHAY+DoEwUn0ysT9c9HB6kBERMqnZIDEJgPtKmC19riXCgy3\nOhCpsOzN4JwIrjzoeDd0/z+rI5IweuONNwDo16/fZeeOHTvG0aNHAUhMTLzsvLeWLVsCcODAAc6c\nORPkKP3Tt29fAF566SX/3xQPjPR6raVO4q052kI3GqgQrAigZIDEMiUDRCruzF74dAwUnIbWN0Dv\nZ6CC67Ulep06dYq1a9cCkJSUdNn5EydOeI4vLRx4Ke/zhw5ZU0m0W7duAGRmZvLjjz/6/0bVDRCJ\nXq5C98w2EVEyQGJYMhey9+uBUxbGIhItzh2EwhxoNgKuew3ifE8DF3vasmULpmliGIbnm31v2dnZ\nnuNq1aqVeS3v86dPnw5ekBXQvHlzwL0Dwueff+7/G72TyZlATlDDEpFQMU3YcBccUK0bEVAyQGJZ\nY6CktlURYM2yVZHo0mwIjFwNg9+F+LI/7In97Ny503PcqNHlG6l7V/Uvr8J/XNyFIYhp0ZTdkp0Q\nTNPkq6++8v+NrYCrio/zgYxgRyZRzQV8CXxgdSByEdOEL++Hb1+C+BpWRyMSEZQMiBHLly+37JsX\ngPz8fF5++eVSz5umydtvW5ClvbQqtITfC7iTMu9bHUjgynvOynsOAhW256xBD6hSJ/DrSNQ5efKk\n59jXN/9169b1HJ8/f77Ma3mfr1PHmp+n6tWre44rtEwALu4/VDdAvG0FbkTFiSPNwX/Djr9AXBUY\nVMEtRUVsSskAm8vLy2P69Om8//77Fw3SAHbs2MHUqVNp37497dq1o23bttx+++0XffMTqMLCQl58\n8UU6derE1KlTS21nGAZHjhxh/PjxFw02Q051A6zXEZjHxQPrKFPWcwb+PweVFfHPmdhGfn6+59jX\nTgGtW7f2HJeXgPYuGuj9vnDyTmhUuIjhGK9jJQPE29XALuBRqwORiyROgI4z3EvcWo4pv71IDFAy\nwMaysrJITk4mISGBefPmXXTunXfeoWfPnuzdu5e1a9eyb98+MjIy2L59O71792bJkiUB3dvlcrFw\n4UKSkpKYNm0aBw4cKHfK6D333ENKSgqDBg3i8OHDAd3fb9cBtYqPvwX2hue24mUYMBCoYnUglVPW\nc1aZ56AiQv6cmSZkfRm0eCX6eX+Dn5eX5/N8q1atAMr9+SopGnjFFVf43KIwHLyTGxWOYRBQMtN4\nJ7A/SEFJ9FNN1cgUFw99n4M2N1odiUjEUDLApnJychg9ejR16tThmWeeuejcmjVruPnmm6lRowbv\nvvuup4BSmzZtWLp0KfHx8dx0001s2bKl0vdftmwZXbp0YdOmTZ5qzf6YOnUqEyZMYOzYsZw9e7bS\n9/dbVdwfRktodoBUQFnPGVT+OfBXyJ+zrx6Bj/vAt68EHqzYQosWLTzHOTm+q+YNG+b+R3XPnj2l\n1gIoLCxkz549AIwYMSLIUfrPe6mCrxoIZaoODPF6rdkBIiISZZQMsKkpU6bw3Xff8corr1z0TaHL\n5eLWW28lPz+fu+6667Ktn5o0acK0adPIzc1lxowZlb7/hAkT6N+/P3Xr1qVnz54Veu/jjz8OwG23\n3Vbp+1eI91IBDeakAkp7zkoE8hz4I6TP2Y65sO2PgAHVmgQYqdhFjx49AHf9iSNHjvhs43A4AMjN\nzS21KN+WLVs8MwtSU1NDEKl/vOsEXHXVVWW0LIXqBoiISBRTMsCGXnnlFZYsWcLMmTM9lZJLLF68\nmL1792IYRqkDsJLfX7duHStXrgw4nopOi05ISOCxxx5j8eLFpKeHocCLdzJgFVAQ+ltKKSpYv8tK\nZT1nvgRzeUAwrl/mc7bvdfji1+7j/i9B4rggRSnRrmPHjp6f9/379/tsM378eNq2bYtpmrz77rs+\n2yxevNhzvXHjrPv5KlnKYBgGffv2rfgFvJcdf4L6D7nYl8AjwFqrA4lB2V/BJ8Mh9werIxGJaEoG\n2Mz58+d56KGHqF69OtOmTbvs/JtvvglA1apV6dWr12XnAXr16kVCQgIAixYtCl2wZZg8eTLNmjXj\n/vvvp6ioKLQ36wS0KT4+A1Rgq2kJklPAlcX/FVocix/Ke86ihc/n7PBHsP5W93HPp6D9LZbFJ5HH\nMAwmTZoEUOpSsri4OObPnw/A/PnzLyskmJWVxYIFCy5qV+LUqVMMGjSIOnXqMGXKFHJzc/2K6+jR\no55jf98D8PXXXwPQu3dvEhMT/X6fR2egpPbhaWB9xS8hNrYY+AOgLe3D68xe+HQU/PBp8Qw3ESmN\nkgE28/LLL/PDDz8wdOhQn8WQ1q1bB0CHDh18VoIGd3XlDh06ALBq1arQBVsGwzAYPXo0+/btC31C\nwkC7ClitHu5/jU4BGy2OxQ/lPWfRwudzVqWee9vApAcg6T5rA5SIdMcddwCQmZlZapsxY8bw3HPP\nkZ2dzeTJkz1LCg4ePMikSZPIyclh/vz5l9ULWLFiBWvWrCEnJ4dFixbx1FNPlRvPqlWrPH2VaZo8\n88wzfieR1693f3q/9dZb/Wp/GQMtFZDSlfxsRNnPRVRvk3vuMKwaCed/gGbDoeefQhSliD0oGWAz\nb7zxBgD9+vW77NyxY8c8356U9w1Iy5YtAThw4EDFt1sKkpIpmy+99FLob6ZkgPVGATWJih0dynrO\nos1lz1mT62DsFrjmCQujkkjWt29fhg8fzs6dO9m2bVup7e6++242btxIYmIigwcPpkOHDgwdOpT2\n7duzYcMGn7NqBgwYQNeuXYmLi8MwDDZuLD07uGDBAho3bkxycjJFRUUYhoFhGMycOZN69eoxatSo\nUt8LUFBQwAcffECLFi08CY5KUTJASnMtMAP37ADftTQjStRvk5uX5Z4RkLMPGvaFwe9BfPWgxyli\nJwlWByDBc+rUKdaudS9MS0pKuuz8iRMnPMeXFg68lPf5Q4cO0aVLlyBF6b+S6uiZmZn8+OOPNG7c\nOHQ3G447NebC/c10FtAwdLcTH34L/AWoVl5Da5X3nEUbn89ZrSssjkoi3Zw5c+jduzdz5szhxRdf\nLLXdNddcw2uvveb3dVu2bOmZuv/00097dhzwZfr06UyfPt3/oC/x6quvkpWVxTvvvEPVqlUrfR1G\nAPFAEbAJOA6o5qaAe8vc56wOwj9ZWVlMmjSJHj16+Nwm97XXXuP3v/89e/e6M/bB3ia3ote/5557\nqF27NoMGDeLjjz92f4m19x9wahvUTYJhH7pnuYlImTQzwEa2bNmCaZoYhuH5Zt9bdna257hatbI/\ncXmfL2uqWCiVbHnocrn4/PMQL+RvCJTUjnLhLgQl4dWIiE8EQPnPWbQJ63MmttG9e3ceeeQRFi5c\nyBdffBGSe6xcuZJbbglNzYqsrCweffRRbrvtNs/uB5VWH/c3wOD+9ndFgMGJhJlttslN+g30mA3D\nl0O1Cm4VKhKjlAywkZ07d3qOfe2X7J1lLS/jGhd34UejtH2iQ62kYrVpmqVuTxVU3lM9tVRASlHe\ncxZVCs7StPBLIIzPmdjGo48+SkpKCjfffHPQk8azZ8+mffv2XHvtteU3rqCSLXa7d+/OCy+8EJyL\naqmARDHbbJNrGHDVTKjZKugxitiVkgE24r1uytc3/97rv86fP1/mtbzP16ljzTSr6tUvrPPy3gs6\nZC6tGxAF6/sk/Mp7zqJGUT5kplJ9402e3wrLcya28vrrr3P11Vdzww03kJ+fH5Rrzpo1ixMnTvDs\ns88G5XreTNNkxowZ1KxZkyVLlpRaSLfCLk0mq/8QXyLw58LW2+SKSLmUDLAR74GYrwFO69atPcfl\nfYvjXTTQ+33h5P1BKyxFDPsBJfmSA8Cu0N9SfPgeeIOIHDRB+c9ZVDBdsP6/4OgKqtW6UIvDqmKh\nEr2qVKnCokWLGDJkCCkpKRXa1q80Dz30kF+7CFSUaZpMmzaNdu3a8eabbwZWJ+BSvXEvdQI4CmiS\njXj7GLge+J3VgVws6rfJLcwBwrwdtYjNKBlgI97f4Ofl5fk836qVe+rU4cOHy7zWoUOHALjiiiss\n2zrN+0NXWGKogruQYAktFQg/FzASWAoE/pkiJMp7ziKeacKme+C7NyGhDvnXL/GciuZtEsVas2bN\nYu7cuUGZLROq2WiGYfDAAw/w4IMPBv/i8bj/7SrxUfBvIVGsFfAY8IDFcVwiqrfJ3f5n+Kg35Hwf\n3u2oRWxGyQAbadGihec4JyfHZ5thw4YBsGfPnlJrARQWFnoqOF+6B3Q4eS9VCNvabO+lAlr3GX5x\nwDfAItzbDEYgf56ziPbNk7DrWYirCoPf43zNCzsiRH0NBLFUx44dL6o3E4k6duwYuourboCU5irc\nyaII2+UuarfJ3fMibH4QTu+EE+uBMG9HLWIjkd1rS4X06NEDcE+FPHLkiM82JVWTc3NzSy0WtmXL\nFs83nqmpqSGI1D/e65evuuqq8NzUOxnwKRCFX/xGvdAuRwyYP89ZRGsxCmq0hAFvQPPh1jxnInbk\n3X+sBs5aFYhI+aJ2m9wDi2HjXe7j3s9A6xuAy7fJFRH/KBlgIx07dvQUf9m/f7/PNuPHj6dt27aY\npsm7777rs83ixYs91xs3blxIYvVHyVIGwzA8Gd+Q61D8H8A5YF14bivRw5/nLKI1uAYm7ILW7sSg\nJc+ZiB21BLoXHxcAn1kXikh5onKb3KMrYe3P3HVvuv8WOv/Sc0rb5IpUjpIBNmIYBpMmTQLc/8j7\nEhcXx/z58wGYP3/+ZYUEs7KyWLBgwUXtSpw6dYpBgwZRp04dpkyZ4nehqKNHj3qOK1Jc6uuvvwag\nd+/eJCYm+v2+gF26q4CIF3+eM1/8fQ7C8pwl1PIcWvacidjRGK9jLRUQX44QEQVyo3Kb3KOrwJUP\nne+Bbv970amwb0ctYhNKBtjMHXfcAbinSZVmzJgxPPfcc2RnZzN58mTPVOeDBw8yadIkcnJymD9/\n/mX1AlasWMGaNWvIyclh0aJFflV7XrVqFatWrQLc/0A/88wzfld6Xb/evQ7s1ltv9at90CgZYL2D\nwFzgn1YH4ps/z5m3ijwHMfOcidiRd90AFRGUS43BPYNkq9WBROk2uT3+AIPfg15PwyVbEIZ9O2oR\nm1AywGb69u3L8OHD2blzJ9u2bSu13d13383GjRtJTExk8ODBdOjQgaFDh9K+fXs2bNjgc4uZAQMG\n0LVrV+Li4jAMg40bN5Z6/QULFtC4cWOSk5MpKirCMAwMw2DmzJnUq1ePUaNGlfpegIKCAj744ANa\ntGjh+eAVNsNwV4YG+AI4Ht7bC+5tuX4NPGN1IL75+5xV5jkI6nM2fCDsLb2YkqXPmYgdDeRC8dM9\nwLcWxiKRp6T+bATMGonKbXINA1pNAuPyjy9h345axCaUDLChOXPmkJCQwJw5c8psd8011/Daa6+x\ne/du9u7dy549e1i4cKGnQNqlWrZsyddff01hYSFPPvmkZ5tCX6ZPn86PP/6Iy+WiqKjI85/L5eLs\n2bMsX172V+6vvvoqWVlZzJs3L7h7QfujHnBt8bEJrAzv7QUYAlQFNgJZFsdSCn+es8o8B0F7zo7t\nYvk9B+HzqbD/DZ/vt/Q5E7GjasBQr9cR8KFPIsho3NsYR8CXDFG/Te4lwr4dtYhNKBlgQ927d+eR\nRx5h4cKFfPHFFyG5x8qVK7nllltCcu2srCweffRRbrvtNs/uB2HnPdVTSwXCrxYwE/gbkGBxLKWI\n6OcsPxs+HQ0530GjfpA48bImEfGcidiR6gZIaSbhTnD/2epAomSb3HOH/W5qyXbUIjagZIBNPfro\no6SkpHDzzTdfViQwULNnz6Z9+/Zce+215TeuIJfLxa233kr37t154YUXgn59v11aNyACiv3EnN8C\ndwF1rQ6kdBH5nBWeg4wJcOprqNsFhiyDKhd/SxIxz5mIHXknkz8B8ktrKDGnBhAhX1pH/ja5Llhx\nPZzZ41drbZMrUjlKBtjY66+/ztVXX80NN9xw0fSpQMyaNYsTJ07w7LPPBuV63kzTZMaMGdSsWZMl\nS5ZYu4atD1C/+PgwsN26UCSyRdxztnEGHF8DNVvBsOVQvfFFpyPqOROxo45A2+Ljs2iLWolIEbtN\nrukCTPeXMGYhxPm3hE3b5IpUjpIBNlalShUWLVrEkCFDSElJqdC2fqV56KGH/KpuXlGmaTJt2jTa\ntWvHm2++af365Xgg2eu1pnpKKSLuOes6Exr0cicCal1x0amIe85E7Mjg4tkB6j8kAkXkNrmuIo7u\nWFEcIOReuxRqtfYrLm2TK1I5SgbEgFmzZjF37tygbB3jXXAmmAzD4IEHHuDBBx8MyfUrRVsMSgVE\nzHNWrwuM+Q/US7rsVEQ+ZyJ2pLoBUpbjwBu4Zx5aKKK2yTVNVi1IYdWmo8UvDZ55dbm2yRUJMcM0\nI3cxtGEYZiTHJzb3HRemelYHsot/lfDZCTyIe6su3wXxJUoYhoFpmkb5LSOb+iXxy2mgEVBY/Poo\n0My6cCTC3I67kOAfAIuXtycnJ7Nq1Sq2bt1a6lr7BQsW8Mgjj5CVlYVhXPhn3DRNatasyYABAy7b\nHefw4cOMGjWKHTt2YJom48aNY8mSJeVc/wQGeLYOLOv63goKCmjRogXVqlVj3759fs96s0u/JBII\nJQNEytIF9wdSgBVcvHRAQu847q0dk4EmFsciAbHLoEv9kvhtMFDyhetrwM8tjEWkFFu3bqV3797c\ncsstvPjiiyG5x9NPP82ePXuYP39++Y3P7oPa7Sp0/X/84x/ceeedvPPOOxXaHccu/ZJIILRMQKQs\nWipgrSbATSgRUJpD78P2J62OQkR8Ud0AiQIRt01uBRMB2iZXJDCaGSBSlveBCcXHPYDNFsYi4u3Y\navh0JBSdh6EfQssx5b/HQnb5Bkb9kvhtE+T1yWMZy9hZayfMgs5dOjN+/HgV75SI89Of/pRt27ax\nbt066tYN3p6+s2fP5tChQyHZhcrlcjF58mTy8/NZtmxZhXfHsUu/JBIIJQNEynIWaAgUFL8+AjS3\nLhwRAE5uhRWDoeAkdLgT+j0PRmSPZ+wy6FK/JP4oKiriz3/6M3Mfmcsx89hF55o2bcq9997LAw88\noK09JWIUFBRwyy23kJWVxdKlS4OSsJo1axb5+fm+iwcec7q3wK3dvlLXNk2Tu+++m5MnT/Lqq69W\nKl679EsigVAyQKQ8Q4GM4uNXgZutCyWm5eBe2FTD6kAsdnY/rBgAuUfgilS4/m2Ii/wPFHYZdKlf\nkvIUFRUxZcoU3nrrrTLb3Xjjjbz++utKCMSqHOB1YBcQ/B2bK+2Pf/wja9as4V//+hc1agTW4Z45\nc8b37jgnNsInw6FKHRi9wZ0UqICSbXKvvPLKgHbHsUu/JBIIJQNEyjMbmFV8/HPchaAkvB4A5gIL\ncdcQiGUrh8Gxz6DpUBj2IcRHxxYXdhl0qV+S8syePZtZs2Z5XicmJpKamgpAeno6hw4duqjtzJkz\nwx6jRIBzuGce5gE/AE2tDcfb7t276dChA3FxISgtdmo7rBwMeSeg7RS47lXP7gEVjbFjx44BhWKX\nfkkkEEoGiJRnE9Cn+LgZ7n2BVXozvJ4C7gduBV62NhTLnd0Pmx+E/n+HKsFb1xlqdhl0qV+SsuTl\n5dG6dWuOHXMvDZg+fTrz5s2jSpUqgHsq9q9+9Suef/55wL1k4Pvvv1cNgVg1Gndx4n8CUyyOJRxy\nvoPl10PuIWg5Dga/C3FVLAvHLv2SSCCUDBApjwt3xv5E8evNuIsJSvh8hfvvfBSqyh2l7DLoUr8k\nZUlPT/dUNE9MTGTfvn2eRECJgoIC2rZty+HDhz3vSUlJCXusEgHeA/YDqUBra0MJuYKz8FEvOLMb\nmgyCYR9DgrXr/uzSL4kEQt9vipQnDhjp9VofRsOvO3AI/d2LSETbuXOn5zg1NfWyRABAlSpVPMsG\nLn2PxJjJwL3YPxEAUKU2XHkXNOgJQ5ZanggQETclA0T8McrreLllUcQuA2hpdRAW0DfQIra3efNm\nTp8+bXUYIqGXdB+MWgdV61kdiYgUUzJAxB/eMwMycRf+EQm1rb+FLf+rpIBIlOjcubPnOD09nYKC\ngsvaFBQUkJ6e7nn91ltv0aRJE8aNG8dLL73EiRMnLnuPiG3EV7M6AhHxopoBIv7qBmwrPv4QGGNh\nLGJ/u56D//zSXWV59H+gYU+rIwqIXdZmql+SslxaQPCuu+7imWeeKbWAoC/x8fEMHToUh8PB5MmT\nadGiRVhiF4uZuGfBSdjYpV8SCYSSASL++h9gTvHxr4GnLYwlVuUCq3Gvr+xcTtto9t1bsOYmwIT+\n/4AOt1sdUcDsMuhSvyTl8bW1YEmBwPT0dE/hQIA+ffpw6tQpdu/e7fNahmEwYMAAHA4HqamptGnT\nJrTBS/i5gFuAVcBuoJa14QSFabpntrX5KdTranU0pbJLvyQSCCUDRPz1ETC2+Pgq4GsLY4lV/wt8\nCvwfFy/dsJMjKyBjHLgK4JonoOuDVkcUFHYZdKlfkvIUFRUxZcoU3nrrrTLbDRs2jIcffpj4+HiO\nHDlCZmYmTqeTbdu2lfqePn36eBIDnTp1CnboYpV/A72AK6wOJEi++j/4+nGokQgTdkdssUC79Esi\ngVAyQMRf54AGQH7x6++BVtaFE5PsPo3SdMGHPeHkV9Dlf6DnU2DY4w9sl0GX+iXxR1FREU8++SRz\n5szxLBnwltI/hV/84RfEx8dfdu748eOsXr2azMxMtmzZgsvl8nmPbt264XA4cDgcdOvWDcMm/1ZI\nlNvxV/jiXvcSt4GL4YrJVkdUKrv0SyKBUDJApCKSgU+Kj18CbrMwFrGn3COw+3no/qh7MGUTdhl0\nqV+SisjPz2fZsmXs3LmTf8/9N+t/WA/A9KTp3Dj/xnLff/LkSdasWYPT6eSLL76gsLDQZ7srr7zS\nkxjo06ePEgNijW9fhfX/5T7u/xJ0iOxBkl36JZFAKBkgUhFPAg8UH/8/YJGFsYhEEbsMutQvSWUt\nfWQpE/8wEYBuVbvxzMfPVOj9Z8+eZd26dTidTjZs2EB+fr7Pdq1btyY1NZXU1FQGDBjgc/aBSNCd\n2QvvdwGz0D2rLek+qyMql136JZFAKBkgUhFbgGuKjxsBx9AGnSJ+sMugS/2SVNbZI2dp2LIhBbi3\nG/z3i/+mboe6lbpWbm4un3/+OZmZmaxbt47c3Fyf7Zo1a0ZKSgoOh4MhQ4Z4djWQCJUHnABaWh1I\nJe15AXIOQI/fWx2JX+zSL4kEQskAkYpw4e6kfyh+/R+gt3XhxKQi4D0gE/eODtGcjCnKh7gqtqkL\nUBa7DLrUL0kghtUfxmenPgPgj+P+yHW/uS7ga+bn5/Of//wHp9PJ2rVrOXPmjM92DRs2ZOLEiTgc\nDkaOHEm1atrvPaIsB1KAEcASi2OJEXbpl0QCoWSASEXdDPyz+PgPwKwy2krwmbi3FjwIfMmFmRrR\nxlUAGROhTifoPcdW9QF8scugS/2SBOJPY//EzI9mAjC52WTuefOeoF6/sLCQzZs343Q6Wb16NdnZ\n2T7b1alTh/Hjx+NwOBgzZgy1atlhP7sodxD3bgK1cc8OqGptOLHALv2SSCCUDBCpqNcg75Y8lrGM\nne12wp3QuXNnxo8fT9Wq6r3DYiruAo5/4kINh2hiumDdLbD/dajWGMZ+CTXtvTWFXQZd6pckEJvf\n3EzPm3oC0MhoxFsfv0V8ldCs6S8qKuLrr7/G6XSSmZnJ8USInI8AACAASURBVOPHfbarUaMGY8aM\nweFwMH78eOrVqxeSeMQP3XAvFfgQuNLiWMpjmlE/q80u/ZJIIJQMEKmAoqIi/vy/f2bu7Lkc4+Lt\nopo2bcq9997LAw88oIJNobYSyADSgB4Wx1JRpglf/Bp2/hUSasOIT6FRH6ujCjm7DLrUL0kgXIUu\nWlZryQ8u91qzhTMX0np065Df1zRNduzYgdPpxOl0cvjwYZ/tqlSpQnJyMg6Hg0mTJtG4ceOQxyZe\nTgHRkIs5fxxWp0GvOdCwl9XRVJpd+iWRQCgZIOKnoqIipkyZwltvvVVmuxtvvJHXX39dCQHxbdts\n2DLLXStg6AfQPNnqiMLCLoMu9UsSqP/q8F+8+u2rANzb614m/WVSWO9vmiZ79+4lMzMTp9PJ/v37\nfbaLj49nyJAhOBwOUlJSaNGiRVjjlAhVcBo+GQ5Zm6DJIEjOiNoZAnbpl0QCoWSAiJ9mz57NrFkX\nCgQkJiaSmpoKQHp6OocOHbqo7cyZM8Meo0S4wlz4uA+c+gaufxPa/NTqiMLGLoMu9UsSqDdmvMGU\nv00BoH/N/jyx7AlL4zlw4IBnxsDu3bt9tjEMg+uuuw6Hw0Fqaipt27YNb5ASGYrOw6dj4dhnULsD\njMyEGtGbJLJLvyQSCCUDRPyQl5dH69atOXbMvTRg+vTpzJs3z7NNU0FBAb/61a94/vnnAfeSge+/\n/141BORyeSfgh1XQ+garIwkruwy61C9JoI5vP06zq5phYhJPPEsWLaFm85pWhwXAkSNHPDMGtm3b\nVmq73r17exIDnTt3DmOEYhlXIWQ64NASdwJg5Bqo3c7qqAJil35JJBBKBoj4IT09HYfDAbhnBOzb\nt++y/ZoLCgpo27atZy1meno6KSkpYY9VJBLZZdClfkmCoW+tvvzn3H8AePrGp+k5vafFEV3uxx9/\nJDMzk8zMTLZs2YLL5fLZ7qqrrsLhcOBwOOjevTtGlE4ZjxgFwHrgKBBJOeOjK2HVSKjaAJKdUL+b\n1REFzC79kkgg7L2XlUiQ7Ny503Ocmpp6WSIA3IWXSpYNXPoeCZGHgM7A91YHIiLiv9HXjPYcb1q3\nycJISte4cWNSUlJ4+umnSU9P5ze/+Q39+/cnISHhonbbtm3j8ccfp0ePHnTq1IkHH3yQDRs2oKRZ\nJe0F7gG+tTqQSzRPhgFvuGvd2CARICJuSgaIhMjhw4c1GAq13sBbQKLVgZTi/HH37gEiIl5G/78L\nyQDnQSemK7L/nahXrx7jxo3jiSee4N1332XWrFkMGjTosqVwe/bs4c9//jP9+/enTZs23HvvvTid\nToqKiiyKPAp1Ab4AHrQ6EB/a3gSNr7U6ChEJIi0TEPFDZZYJAHTo0IG0tDTS0tLo3bu3pk/Gktyj\nsOJ6aDoE+r0AcQnlv8fG7DIdU/2SBENBTgGNazfmNKcBWDR7Ec2vbW5xVBWXm5vLhg0bcDqdrFu3\njtzcXJ/tmjVrxuTJk3E4HAwdOtTn7DqRcLNLvyQSCCUDRPxwaQHBu+66i2eeeabUAoK+tGnTxpMY\n6NevH3FxmphjW/mnYOUQOLkFGvaGEZ9BldpWR2Upuwy61C9JsKS2TOXdI+8CMGvgLEb+bqTFEQUm\nPz+fTZs24XQ6WbNmDWfOnPHZrkGDBkycOBGHw8HIkSOpXr16mCMVvxSctX2/ZZd+SSQQSgaI+MnX\n1oIlBQLT09MvmhFw5ZVXcvjwYc6dO+fzWq1atcLhcJCWlsaAAQOUGLCTovPw6Wg45oQ6nWDkaqje\nxOqoLGeXQZf6JQmW53/2PNMXTQdgRL0RPPLeIxZHFDyFhYVs3rzZU4AwOzvbZ7vatWszfvx4HA4H\nY8eOpVatWmGOVHw69AGsvxUGvwtNrrc6mpCxS78kEgglA0T8VFRUxJQpU3jrrbfKbDds2DAefvhh\nioqK2LRpExkZGaxZs4azZ8/6bN+iRQtSU1NJS0tj0KBBxMfHhyJ8ezOBbKChxXG4CmH1DXDwPajR\nsnjrpbYWBxUZ7DLoUr8kwbLfuZ92Q9xbs9WgBu8teY+qdey3HW1RURHbtm3D6XSSmZnpmWF3qerV\nqzNmzBgcDgfjx4+nfv36YY40wqwH3gQmAsPDeN9jmfDpKHdi+6pHoMfvwnjz8LJLvyQSCCUDRCqg\nqKiIJ598kjlz5vgc0Nx60638fOrPL/tAX1BQwJdffklGRgarV6/m9OnTPq/ftGlTT2JgyJAhl1Vt\nFh/+A0zAvavAZ9aGQn42fJIMZ7+FkZmquOzFLoMu9UsSTF2qdmFngXvnmfl3zifpZ0kWRxRapmmy\nY8cOMjMzcTqdHDp0yGe7KlWqkJycTGpqKpMmTaJJkxicXfU74FFgOvC3MN0ze7N7iVvBaehwJ/R7\nHmxc68gu/ZJIIJQMEKmE/Px8li1bxs6dO3n20Wc5VOAe0My9aS49pvUo872FhYVs2bKFjIwMMjMz\nOXnypM92jRo1IiUlhbS0NIYPH66CS6XJBhoD8cAJoI614VBwGs7shYaRt2+4lewy6FK/JMF0T497\nmPfVPADu6HQHU56fYnFE4WOaJt9++y1OpxOn08n+/ft9touLi2PIkCE4HA5SUlJo2bJleAO1ygag\nP9AW9zaDof7X8/RuWDkQzh+DK9Lg+jchzt4zFe3SL4kEQskAkQA9fP3D/HHtHwG4uc3N3P7K7X6/\nt6ioiK1bt5KRkYHT6SQrK8tnuwYNGjBp0iTS0tJITk6mWrVqQYndNq4DdgHLcW83KBHHLoMu9UsS\nTB8+9iE/+e1PAEiqksT85fMtjsg6Bw4c8MwY2LVrV6ntrrvuOhwOBw6Hg7Zt24YvwHArAh4GhgGj\nCH0y4MA7sOYmaDYchiyFePuPM+zSL4kEQskAkQBlzM1g6K+HAtAuvh0vrXypUtcpKipi+/btZGRk\nkJGRwY8//uizXd26dZk4cSJpaWmMGjWKGjVqVDZ0+zgCNMU9O0Aikl0GXeqXJJjOHTtHw2YNySMP\ngPS/pdOgSwOLo7Le0aNHPTUGtm3bRmnPXK9evXA4HKSmptKlS5cwR2lDR1dBo36230WghF36JZFA\nKBkgEqD8M/k0qtuIs7gLBL791Ns06R3Y+kaXy8WOHTs8iYEffvjBZ7uSSsxpaWmMHTuWmjVrBnRf\nqaDsr6DeVbafShkMdhl0qV+SYBvZcCQrs1cC8Lsxv2PggwMtjiiynDhxwjNjYMuWLbhcLp/tunbt\n6pkxcPXVV2PYeK27BIdd+iWRQCgZIBIEE5tNZOmxpQA8OuxRhj06LGjXNk2TXbt2eRID3lsYeqtZ\nsyY/+clPSEtLY9y4cdSuHRuZfcscXwerRkDLcTDgdYi3XxXwYLLLoEv9kgTbX8b/hd8s+w0AE5tM\n5Ndv/9riiCLXqVOnWLNmDU6nk02bNlFYWOizXYcOHUhNTcXhcNCvXz8lBsQnu/RLIoFQMkAkCJ69\n4Vl+9a9fATCm4RgeXPxgSO5jmiZ79uzxJAYOHjzos13JFk1paWmMHz+eevXqhSSemHVyG6wc5N49\noP3t0P9FW1dcDga7DLrUL0mwfb34a7qndQegPvX518f/Ir6qZhuV5+zZs6xbt47MzEw2bNhAXl6e\nz3atWrUiNTWV1NRUBg4cGL3b97qAuGBdqxDO7IZ69t69ojx26ZdEAqFkgEgQ7PpoF53HdgagDnV4\n98N3ia8e2gGHaZrs27fPkxj47rvvfLarWrUqo0aNIi0tjYkTJ9KggU3Xo5rATmAvMC6E98k5AMsH\nQO4hSJwIgxZDnLaALI9dBl3qlyTYTJfJFVWu4JDLvSvNS795iXbj2lkcVXTJzc1lw4YNOJ1O1q9f\nz7lz53y2a9q0KZMnT8bhcDBs2LDo2KXnA+Ah3Fvo/j4I1zNN+PwOOPAWDH4PmicH4aLRyS79kkgg\nlAwQCQLTZdKuaju+K3J/IH/xnhfpMLlDWGPYv38/TqeTjIwMvv32W59tEhISSE5OJi0tjUmTJtG4\nceOwxhhS+4HBwE+Bp0J0j/M/urdeOr0TmgyEYcshQQUc/WGXQZf6JQmFqR2n8tIed/HZ/77mv0mZ\nk2JxRNErPz+fTZs24XQ6Wbt2LadPn/bZrn79+kycOBGHw8GoUaOoXr16mCP10x7gONAXCDTvbJrw\n5f2w4y8QXwOGr4QmAwKPMUrZpV8SCYSSASJBclfSXbyw4wUAftn9lzjmOSyL5fvvv/ckBnbv3u2z\nTXx8PMOGDSMtLY2UlBSaNm0a5ihDwCS02y/ln4SMCVBwCpKdULV+CG9mL3YZdKlfklB4+563uXHe\njQD0qdGHJz940uKI7KGwsJAtW7Z4dibIzs722a527dqMGzcOh8PB2LFj7VtzZ9ts2DIL4qrA4KXQ\ncrTVEVnKLv2SSCCUDBAJksX3LSbt6TQAelfvzVMfhurr6Yo5fPiwJzGwY8cOn23i4uIYPHgwN9xw\nAykpKbRo0SLMUUaRwlwoOA01mlkdSVSxy6BL/ZKEQtbuLJp0aoILF3HEsfSNpdRsod1hgqlk+96S\nxEBpu/RUr16d0aNH43A4mDBhAvXr2yTpu/t52DgdMOD6RdDmRqsjspxd+iWRQCgZIBIk2d9m07hD\nY1y4MDB4/5/vUzMxsgZzR48eJTMzk4yMDLZt2+azjWEYDBw4kLS0NFJTU2nVqlWYoxQ7ssugS/2S\nhMp1ta9jfc56AJ5Me5I+v+hjcUT2ZZomO3fuxOl04nQ6OXTokM92VapUYcSIEaSmpjJ58mSaNAls\n22BLfZ8Oa26C3vOg411WRxMR7NIviQRCyQCRILquznWsP+sezD2V9hS9f9Hb4ohKd/z4cU9iYOvW\nrZT2rF133XWkpaXhcDho06ZNmKMUu7DLoEv9koTKY4Mf47eZvwXgxlY3Mv216RZHFBtKivGWJAb2\n7dvns13JDDqHw0FKSgqJiYlhDhR3/YD2QGXrE+d8B7XUj5ewS78kEgglA0SC6LEhj/Fbp3swd9MV\nNzHt1WkWR+SfEydOkJmZidPpZMuWLbhcLp/t+vbt60kMdOgQ3gKJftsOpOMuJjg4wGsd/De0/Il7\nfaUExC6DLvVLEirrFqxjwN3uYm4t4lrw+orXMeKi/pGJOt9//72nP9y5c2ep7a699locDgcOh4N2\n7cKw+8Mw4DNgA+5ighIwu/RLIoFQMkAkiNb+bS3Xz7gegFZxrXh1xatRN5jLzs5m9erVOJ1Ovvji\ni1ITAz179iQtLY20tDQ6deoU5ijL8Hvgf4HpwN8CuE7J+sqW42HIEjCi6/9jpLHLoEv9koRKYW4h\nTWs2JRt3kbs3fv8GLa5X/RYrlSytczqdbNu2rdQZdD179sThcJCamkpSUlJogpkOPA8nZ50ka2oW\nAA0bNrRPTQML2KVfEgmEkgEiQVSYW0jjmo05xSkAFs1eRPNrm1scVeWdOnWKNWvW4HQ62bRpE4WF\nhT7bde/e3ZMY6Nq1a5ijvMQGoD/uqZR7K3mNA/+C1T8FTOj3Alx5Z9DCi1V2GXSpX5JQ+mmrn/LO\noXcAeHDAg4z5wxiLI5ISJ06c8CTKN2/eXGqiPCkpyTNjoEePHhhBSCSfPHmShfctZMHLC9hhXlwI\nuEuXLtx9993ccsstFxIDZ/bAuUPQbEjA97Yzu/RLIoFQMkAkyBwtHaQfSQfg4UEPk/x4ssURBceZ\nM2dYu3YtTqeTjRs3UlBQ4LNdUlKSJzHQvXv3oAyEKqQImIF7icBNQFwF3390FXw2Flz5cPXvodvD\nQQ8xFtll0GUYhpmTn0PNKpFVHFTs4R+3/IM7XrsDgCF1h/DYvx+zNiDxyd9Eefv27UlNTcXhcNCv\nXz/i4irWIZ0/f56ZM2fy97//nXPnzpXZtmbNmtx555088eh/Uz1zBOQegeHLoWmg6+Xsyy79kkgg\nlAwQCbLnf/Y80xe5Cz8l10/m4Xft92EyJyeHdevW4XQ6+fzzz8nPz/fZrmPHjp7EQM+ePcOfGKio\n7K9gxfVQeBY6/Tf0nqvlAUFil0GXYRhmzT/UZOyVY3EkORjXaRx1q9W1OiyxiYPrDnLFgCsAqEpV\nlry3hGr1qlkclZTl7NmzrF+/HqfTyYYNG8jLy/PZLjEx0ZMYGDhwIPHxZVcBzM7OZsKECaxZs+ai\n369WrRrNm7tnHB49evSy+w3sWpMl956jwRV9YcQnUKVOAH86e7NLvyQSCCUDRIJs32f7aD+sPQA1\nqcl7779HlVr2LUCXm5vL+vXrycjI4PPPP+f8+fM+27Vv396TGOjTp09kJgYKzkJmKlRrDAP+CUZF\npxVIaewy6DIMw+SxC6+rxldlVIdRpHZJZWLniTSq2ciy2MQeulXrxrZ899avz9z2DN1u6WZxROKv\n3NxcNm7ciNPpZN26daV+m9+kSRMmT56Mw+Fg2LBhVK1a9aLz58+fJzk5+aJEQPfu3fnFL37BlClT\nqF27NuBORLz++us899xzbN261dN2YNcarFizi+r1tTVwWezSL4kEQskAkRDoWKUjewr3ALBgxgI6\n39DZ4ojC4/z582zYsIGMjAzWrVtHbm6uz3atW7f2JAb69+9f4amTFXHy5EmysipQbKmoeJZDfNWy\n20mF2GXQdWkywFu8Ec+wdsNwJDmY3GUyzWtHb70Qsc59ve7j6S+fBuC2K2/jlr/fYnFEUhn5+fls\n2rQJp9PJ2rVrOX36tM929evXZ8KECTgcDkaNGkWNGjW49957+etf/+pp89RTT/E///M/pSbRTdPk\n6aef5je/+Y3n9+69917mzJkT3D+UzdilXxIJhJIBIiHwy26/5LltzwEwvet0bnzuRosjCr+8vDzP\nNyRr164lJyfHZ7vExEQcDgdpaWkMGDCg3KmT/jh58iQLFy5kwYIF7NjhR7ElCTm7DLoMwzC3H9vO\n4m8Ws/ibxWw+utl3OwwGth5IalIqqUmptK7XOsyRSrRa/vvljP7f0QB0TOjICytesDgiCVRRURGb\nN2/G6XSyevVqT4L6UrVq1WLkyJF8+OGHnun/Tz31FPfdd59f93nqqae4//77AXcNgcOHD1OvXr3g\n/CFsyC79kkgglAwQCYElDy1h0hOTAOhRrQdzP5prcUTW8v6GZPXq1Zw9e9Znu+bNm5OamkpaWhqD\nBg0iISGhQvepVLGlJ56gevXqFbqPVJxdBl2X9kvfZn9L+jfpLP5mMesPri/1fX1b9sWR5CA1KZWO\njTqGI1SJUudPnKdh44bk4p5ZtfjZxTS8qqHFUUmwFBUVsX37dpxOJ5mZmfzwww+ltr366qvZvHmz\n38vqTNOkR48eniUD8+bN41e/+lVQ4rYju/RLIoFQMkAkBE5/f5pGrRtRiLvC8NKXl1K7bW2Lo4oM\nBQUFfPnll56BUGlTJ5s0aUJKSgppaWkMHTqUKlXKrrtQ6WJL1w9gydL3adCgQQB/KimPXQZdZfVL\nB08f5N1v3mXxN4vJPJCJy/S99Vj3pt1xJDlwdHVwVZOrIrN+hlhqbOOxfHTiIwAeG/kYQ2Zpizg7\nMk2TXbt24XQ6cTqdHDx48KLzCxYs4K677qrQNRcsWMDdd98NuHf32b59e9DitRu79EsigVAyQCRE\nBtcbTObpTAD+NPlP9Lunn8URRR7vqZOZmZlkZ2f7bNewYUMmT55MWloaI0aMCH6xpYEDWbFihWYI\nhJBdBl3+9kvHco7x7x3/ZvE3i/lk3ycUunxvPdapUSdSu6Ti6Oqgd4veSgwIAHMnzeXXS34NwE8a\n/4T737nf4ogk1EzTZPv27fzyl78E3InsH3/80dN/+evMmTM0adLEk/jOzs7WkrhS2KVfEgmEkgEi\nIfKHEX/gkVWPAHBDyxuY8foMiyOKbEVFRWzdutXzDcmJEyd8tqtXrx6TJk0iLS2NkSNHUr16dRVb\nigJ2GXRVpl/Kzs1m6a6lpH+Tzkd7PiKvyPfWY23qtSE1KRVHkoPrrriOOO1mEbN2LNlB0qQkAOpQ\nh/SP0kmoVrFlUxJ9Dh8+zJQpUwBo06YN+/fvr9R12rRpw4EDBwD49ttvadeuXbBCtBW79EsigVAy\nQCRENr60kX5T3bMBmhvNeWPlGxhx6nP84XK52LZtG06nk4yMDI4fP+6zXZ06dRg9ejRLly5VsaUI\nZ5dBV6D90tn8s3yw+wMWf7OYZbuWkVPgu7Bm89rNSemSgiPJwZC2Q0iI0wfBWGK6TNpWbcuBIvcH\nuhd//SIdJnawOCoJNSUDwssu/ZJIIJQMEAmRorwimtZoSpbprhr8z9/+k8TBiRZHFX1cLhc7duzw\nJAaOHj1aalsVW4pcdhl0BbNfyi3IZcW3K1j8zWKW7FzCyfMnfbZrVKMRkzpPIjUpleT2yVRLqBaU\n+0tkm9Z5Gn/f9XcAfnH1L0j7a5rFEUmonT17lgkTJgDBWyaQkZHNoEH10Qqky9mlXxIJhOYgioRI\nfLV4RiaO9Lze+tHWMlrL/2fvvqOiuroGDv+G3hSxYMcuQuwtRlFjRY0dfC0o1tjymmg0ajS9mc8S\nSzQafRMTjSYaQEWxQCyxxN4VLIgtYu+oMMDM98eYAeOgwJTLDPtZy7XuvZy5d2M7h33P2ScrdnZ2\n+Pv7M3z4cJYvX86CBQvo06cPpUqVeq7tyJEjc7TmWqVSMXJkxvKN+fPnmyRmIbLD1dGVzr6d+bnr\nz1wfd52NIRt5s+6bFHMr9ky7209u8+ORH+n4a0e8p3sTEhFCRFwEj1NfvGOGsG7tOrbTH+86s+sF\nLYWt8PDwwMdHtw1pSkoKy5Yty/E9li1blqlQrh/NmxeicmV47z3Yswc0huuaCiHyKZkZIIQZ/dj/\nRwYvGQzA6wVf5+M1Hyscke3QarUcP36cd955B5BiS3mdrbyBsUS/lK5JZ+elnYTHhRMRF8GVh1cM\ntnN1cKV9lfYE+QXRsWpHCjoXNGtcwrLun79PkYpFSCcdFSrWLF1DgTIFlA5LmFl4eDhz584FjJ/t\nBnOAZ2e7lS4N3bpBUBA0bQr29iYM3srYSr8khDFkZoAQZtRmWMbMgN0PdpP6MFXBaGyLSqWiaNGi\n+vMSJUrkOBEAuroDxYsX159ntaOBEJZib2dP8/LNmdN+DpfGXGL34N281/g9KnpVfKbdk7QnRMRF\nEBIRQrFpxei4vCOLDy/m9mPDxTeFdfGs4Ekjj0YAaNEStypO4YiEJQQGBup3tjl27BjffPNNtj87\nY8YMfSLA2dmNHj1CKfivHOGVKzB3LrRoASVLwtChsHEjqNUm+xaEEFZEkgFCmFHZxmXxc9JVhE4h\nhfi18QpHJISwJnYqOxqVacTUNlOJHxXP4WGH+aDpB/gV9XumnTpdTdTZKAZFDqL49OK0XtKa+fvn\ncy0p6xobIu9rVz9jqcD+vfsVjERYioeHB2+88Yb+fNy4cUyfPp0XzUjSarXPFMQFGDFiKCtXenLj\nBkRFwaBBUKTIs5+7eRMWLYL27aF4cQgNhTVr4MkTk39bQog8SpYJCGFmY2qPYdbRWQAMqTqEkO9D\nFI7Idpij2NLp03epWlWWCZiarUzHzEv9UtzNOCLiIgiPC+fwtcMG26hQ0cSnCd2rdae7X3fKFSpn\n4SiFMfb/sJ+GQ3S70hRXFWd5zHLs7OU9jq1LTk6mW7duJCcn66/VqFGDkSNHEhISQoECuuUiDx8+\nZNmyZXz33XeZlgZAQEAAMTEx+hkG/0hLg+3bITwcVq2Cq1cNP9/dHTp00C0l6NABCtjo6hRb6ZeE\nMIYkA4Qwsw2fbKDDpx0A8HfyZ96meQpHZFv69++v30JpwYIFDBs2LEefX7BgASNGjHh65odKFUuz\nZhAcDN27g4E6hSIXbGXQlVf7pYS7CUTERRARF8Huv3dn2a5+qfoE+QUR5BdElSJVLBihyI30lHSK\nuxbntla39GPpJ0sp07yMwlEJc3v33Xc5fNhwgs/Z2Vm/tO369euZigXqBAQEEBkZiZeX1wufodHA\n7t26xEBEBFy8aLidszMEBuoSA506wUtua1VspV8SwhiSDBDCzB5de0ThkoVRo1uQt3rRajwry172\npmLOYksqFTRpkpEYKFvWxMHnI7Yy6LKGfunKgyusOrWK8Lhwtl/cjkZruHx4de/q+sRAde/qOdqJ\nQ1hOH58+/Hr5VwDGvTqON75+4yWfENbs008+Ztuf2/XnHh4eaDQaHj9+8e4hbm5uDB06lClTpjw3\nI+BltFo4dEiXGAgPhzNnDLdzcICWLXWJga5dwds7R4/Jc2ylXxLCGJIMEMICWnm1Ysu9LQB82fFL\nGo9trHBEtiMpKYkePXrop1NOnz6dsWPHZuuzmddYOjm5Ub9+Irt3e5LVfzuNGukSA0FBUL68KaLP\nP2xl0GVt/dKNRzeIPB1JeFw4mxM2k6oxXMS0SuEqBPkF0d2vO/VL1ZfEQB7y86CfGbB4AAABBQL4\nPPJzZQMSZjNr1kzWrInUnxcu7MX58xfQarX8/PPPzJ8/n1OnTj3zGT8/P0aMGEFoaCiensa/aNBq\n4eRJ3WyB8HA4dsxwOzs7CAjQ9Yfdu0MZK5ywYiv9khDGkGSAEBYwtd1UJmyaAEC3Et14+9e3FY7I\ntsydO5fw8HD9+bRp0xg7dmyWP9BotVpmzJjxTLGl0aNHM3PmTK5d062lDAuDbduy3pO5fv2MxEDl\nyqb8bmyTrQy6rLlfupd8j7Wn1xIeF86mc5tITks22M7H04fu1boT5B9E47KNsVPJGnUlXT1wlVIN\ndOuVHHEkMjwSl8I5e/Mr8r7FixezZMkS/bmHuytn4xMoUaLEM+3u3bun3/XGy8vL7FvhxsdnzBjY\n/4Ialq++qusPg4KgYsWs2+UlttIvCWEMSQYIYQFHlh2hTt86ABRVFWVF9ArsHGSAbSoRERF8++23\nz1wzRbGlmzdh9WpdYmDzZkhPN/z82rV1iYHgYPD1Ne33ZitsZdBlK/1SkjqJDWc3EB4XTtTZKJLU\nSQbblfAoQVffrgT5B9G8XHMc7R0tHKkAqO1Sm6MpIi7N5wAAIABJREFURwGY3X82NQfUVDgiYUqr\nVq1izpw5+nNnJ0dOxsZRqVIlBaN63qVLumR5eDjs3EmWs+hq1cpIDPj7WzbGnLCVfkkIY0gyQAgL\n0KRqKOlckhvaGwD8/MHP+LTyUTgq27Bjxw4++uijLL9uqmJLt29DZKQuMRATA6mGZ1tTvXpGYsDf\nX1d3QNjOoMsW+6XktGSiz0UTERfBmtNruJd8z2C7wq6F6eLbhSC/IFpXbI2zg3O2n5GSkkJUVBSn\nT58GwNfXl44dO+Lk5GSS78HWTag/gakHpwIQWimUgf8bqHBEwlQ2b97MF198oT93sLdj77791K1b\nV8GoXu7aNd02hOHhsGVL1snyatV0ywiCgqBOnbzVJ9pKvySEMSQZIISF9Cvfj18u/gLA2IZj6fh/\nHRWOyPodP36cd95555n9l7t168amTZvMWmzp3j1Yu1aXGNi4EdRqw+2qVctIDNSsmbcGQZZmK4Mu\nW++XUtNT2XphK+Gx4aw+vZobj24YbFfAqQAdq3YkyC+IdpXb4e7kbrBdeno6U6dOZdasWdy48ey9\nvL29GT16NOPHj8fe3t7k34st2fL1Flq93wqAig4V+SHmB4UjEqZw4MABxo8fr+/D7FQqomNiaNWq\nlcKR5cydO7pkeXg4REdn3SdWqJCRGHj1VV3dASXZSr8khDEkGSCEhSx9cymh/wsFIMAjgM/XShEo\nY1y8eJEhQ4aQlpamv/bLL78QEhLC/fv3LVZs6cEDWLdOlxjYsAGSDS/DpnLljMRA3br5LzFgK4Ou\n/NQvpWvS2XV5F+Gx4USciuDvB38bbOfq4Er7Ku3pXq07Hat2xNNF9+8qPT2dkJAQVqxY8cLn9OzZ\nk2XLlklC4AVS7qVQxKsIj3gEwMpZKylWq5jCUQljnDp1irfeegvN08I0KpWKlStXEhwcrHBkxnnw\nANav1yUG1q+HrPLypUpBt266xEDTprqdCizNVvolIYwhyQAhLOTqwauUqp+pCFREJC5eUgQqN27d\nukW/viEkp2S8fpgxYwbvvvvuc20tWWwpKUk3+AkLg6iorAdB5ctnJAYaNswfiQFbGXTl135Jo9Ww\n/8p+wuPCCY8LJ+FugsF2TvZOtK7YmiC/IM5HnueLT74w2O7fpkyZwsSJE00Zss3pVKwT626tA+DD\nlh/S8sOWCkckcuvy5csMHjyY1EzrzebPn8/w4cMVjMr0Hj+GTZt0OxOsXQv37xtuV7SobqvC7t2h\nVSuw1OohW+mXhDCGJAOEsKBaLrU4lqLbp2fOgDnU6F9D4YisT1JSEiG9e/Eg6ZH+2rhx45g2bZqC\nUT3v8WPdEoKwMN0gKMlwfTbKltW9GQkOhtdeU37apLnYyqBL+iXdbhzHrh/TJwZib8Y+3ygNmAk8\nev5Lhnh7e3P58mWpIfACc7vPZdSqUQAEFg5kYrgkT6zRrVu36NevL8nJGfVrPv/8cz744AMFozI/\ntVpXiDc8XFeY9/Ztw+08PaFTJ12/GBgIrq7mi8lW+iUhjCHJACEsaHz98Uw7qPuhdUDlAfRf1F/h\niKyLWq2mX0hvbty6o7/Wp3cvli3/VcGoXi45WbeOMixMV3DpwQPD7UqV0r0ZCQ7W7d9sS7OmbWXQ\nJf3S807dOkVEXAThceEcunpIdzEWWJmz+0RERNCtWzeTx2cr4jfEU6VDFQDccWf1htU4uCgwt1rk\nWlJSEn169+RhUsa0sbfffpvZs2crGJXlpaXBjh26xEBEBFy9aridmxt06KBLDLzxBjzdGMhkbKVf\nEsIYeT4ZsOLECjpU6YCHk4fS4QhhtD+++oM2k9sAUMWhCgtjFiockfXQaDQMGTyQ8xcu6a+1avk6\nf2zeqlxQuZCSons7EhamezvydAXDc4oXz0gMNGumzHpKU7KVQZckA17s/N3zRMRFMGfGHC5FXHr5\nBzKRpQIvoYVKjpVISNct0VgwagG+3WUvU2uhVqsJ6d2TW3cyduvo07s3y5YvVzAq5Wk0sGePLikQ\nHg4XLhhu5+wMbdvqEgOdOkHhwsY/21b6JSGMkeeTAXwCLg4utK/cnmD/YDpW7UhB54JKhyZEriTf\nTqZw0cI84QkA4fPCKexvgh4tHxgzZgxHjhzRn9es8QqHjxzDzorn1aemwtatusTAqlVw65bhdkWL\n6gotBQdDixbgaIVbvdvKoEuSAdkzZcoUJk2alKPPhLwZwpIFS6z637S5jfQbyfxT8wEY/spwes7t\nqXBEIjs0Gg39Q/vy95WMV+BtW7diU8wfCkaV92i1cPiwLikQHg5PdyJ9joODri8MCtLVGni6e3CO\n2Uq/JIQxrCIZkJmTvROBlQIJ9g+ms29nCrmYrxiYEObQvmh7Nt7eCMCngZ/SbGIzhSPK+z777DO2\nbs2YAVCubGniEy7gYO2vyzNJS4Pt23WJgYgIuH7dcDsvL93gJzgYWre2XKElY9nKoEuSAdkTERFB\nUFBQjj/nWMyRui3rMqLfCPq17yeJgX+JnBBJl6ldAKjhXIM5G+coHJF4GY1Gw8gRwzh9Jl5/rV7d\n2uzbf1D+fr+AVguxsRkzBo4eNdxOpdLtRtC9u+5X2bLZf4at9EtCGCPPJwOqf1edEzdOGPy6o50j\nrSu2Jtg/mC6+XSjiVsTCEQqRczM7zeTddbqq9x2LdWTsyrEKR5S3zZs3j7CwMP15kSJFuHDhAh4e\ntrt0KD0ddu7UJQbCw7NeT+npCZ076xIDbduCSx7enMJWBl2SDMielJQUfHx8uHHjRq7vYe9lT43m\nNRjcZzBDuw7FydFKMl9m9PDSQwqXK0waui1VVy9ejWd547dIFebz3nvvceDAAf15lUoVOHUmXhIB\nORQfr0sMRETA3r1Zt2vYUDdjICgIKlV68T1tpV8Swhh5Phmg1Wo5desU4bHhhMWFceTaEYNt7VX2\ntKzQkmD/YLpW64q3u7eFoxUie06Gn6R6cHUAClGIsOgw7B1tqFKcCf36668sXJhRV8Hd3Z34+HhK\nlCihYFSWpdHA7t26xEBYGPxteKt3PDx06yiDg6FdO13hpbzEVgZdkgzIvpwsFXAv7c6jm49Abfjr\ndh52VGtajdBeoYz6zyjcXPLYX3ALet3zdf588CcAX3b+ksZjGisckcjK559/zpYtW/TnJUt4k3D+\nIi55OXNrBS5f1i2tCw/XFSLM6r/kmjUzEgP+/s9v42sr/ZIQxrCKZEBm8Xfi9YmBA4kHDH7OTmVH\n83LNCfYPprtfd0p45J8fHETep03XUtapLFc0VwD4cfyPVGhfQeGo8p7o6GimTJmiP3dycuLYsWP4\n+ubfglkaDezfn5EYyKrQkpubrvJycLCuEnNemERhK4MuSQZkX3p6OiEhIaxYseKF7Vq0aMHkyZN5\nkvqEFdtWsGX7FhKPJPK0tMpzVG4qKjWqRO//9GZc33EUdM9fdYS+bv01729+H4BuJbvx9vK3FY5I\nGPLtt98SERGhP/fy8iIhIYFChWR5qyldv67bpSc8HLZs0S25M8TXV7eMICgI6tbVJQZspV8SwhhW\nlwzI7MK9C/rEwJ6/9xi+ByqalmtKsJ8uMVC6YGlzhStEtg2qNIjFCYsBGF13NF1mdFE4orxl3759\nTJw4QZ/tt7e3Z8eOHbz22mvKBpaHaLVw6JAuKfD773DunOF2Li7Qvr0uMdCxIxRU6OcmWxl0STIg\nZ9LT05k2bRozZ840uGRgUGgofUJDsf/XPprJ6mQidkUQvS2aSwcvoX2Uxe+5M/g08KFHUA/G9x+P\nt5ftzwo8/PNh6g6oC0BRVVFWxKzAzl6mnOclS5cu5ccff9Sfu7u7c+bMGUqVKqVgVLbvzh1Yu1aX\nGIiO1u3eY0j58rrEwDff2Ea/JIQxrDoZkNnl+5eJiIsgLC6MXZd2ocXw5xqXbUywXzBB/kH4ePqY\nMlwhsu23t36j93e9AXjV/VW+Xve1whHlHadPn+atkSNI1+j+DatUsHr1Gjp37qxwZHmXVgvHjmUk\nBrKqwOzsDIGBusRAp05gyRdUkgzI39RqNVFRUZw+fZoZH3zArfR0AOYPGUK1kJAXfzZNzbp969iw\nZQMJBxLQ3NcYbugIJWuXpEu3Lrw/6H18ittmH69J1VDSuSQ3tLrkyk8f/kS5luUUjkr8Y82aNcya\nNUt/7uTkxPHjx6lataqCUeU/Dx/C+vW6xMD69fDokaFWttEvCWEMm0kGZJb4MJFVcasIiwtj+8Xt\naLSGBw4NSzfUJwYqelU0Nlwhsu3WiVt41/BGixZ77Fn7+1pci7oqHZbirly5wsCBA0hNzZjnt2jR\nIoYMGaJgVNblnwrM/ywlOGG4/iqOjtCmjS4x0KWLafZsfhFJBoh/jK5Th9lPtwl9s2pV+nz/fbY/\nq9Fo2HRoE5GbIzm7/yzpt9MNN7SHYtWL0aFzB94f8j6+Pra1vCi0fChLLy4F4N0G79JpaieFIxIA\n27Zt49NPP9Wf29vbs3v3bho0aKBgVOLJE9i0SVd8MDIS7t//5yu20S8JYQybTAZkdj3pOqtOrSIs\nNoxtF7aRrjU8cKhbsi7BfsEE+wdTpUgVo54pRHbUd6vPwScHAZgZMpPaQ2orHJGy7t27R0if3jx+\nkqy/9vlnn/HBhx8qGJX1O3VK92YkLAyOGK6/ioMDtGypSwx07QrFipk+DkkGiH9s+OwzOnz8MQB+\njo58Fx2dq/toNBq2n9zOqj9WEbc3jtTrqYYb2kEh30K07diWiW9OpE6VOrkNPc9YNnQZfRf1BaCR\neyOmrJvykk8Iczt06BDjxo3jn/8fVCoVGzdupG3btgpHJjJTq3W1BcLD4X//s41+SQhj2HwyILOb\nj26y5vQawmLD2Hx+M2kaw1VGahavqU8M+BXzM9nzhchscqPJfLX3KwD6VujL4B8HKxyRcpKTk+nd\nuzf37t3TXxs5fDjz5s9XMCrbEx+fkRg4YLj+KnZ28PrrusRAt25gqo0bJBkg/vH45k0Ke3vzz3Le\n1fPn41mtmtH33XtmL2ExYRzfc5yUv7NYLAwUqFyAFu1b8N6Q9wioGWD0c5Vw48gNitcpDoA99kT+\nHolb0fy7w4LSzpw5w8iRI0hPz5iJ+uuvv9KrVy8FoxIvYyv9khDGyFfJgMzuPLlD5OlIwmLDiD4X\nTarG8BsF/2L++sRAde/qqP69L4kQufTnjD95fdzrAFSwr8CPf/z44g/YqLS0NEJDQ7l69ar+Wreu\nXYhYtVrBqGzf+fMZiYGs9mxWqaBpU11ioHt3KG1E/VVbGXRJMsA02hYpQsydOwB8HhhIwMSJJr3/\n8YvH+W3TbxzefZgnF7LYlgBw83EjoF0AoweOpn2j9iaNwdzqu9bnYLJudtk3fb+hzmDrn/FgjQwt\nb/v222/573//q2BUIjtspV8Swhj5NhmQ2f3k+6w9s5aw2DA2xm8kJd3wG4WqRarqEwO1S9SWxIAw\nivq+miKFipBEEgArZ62kWC0zzM/OwzQaDSNGjODMmTP6a40bN2bXrl0KRpX/XLqkW0sZFgYv+q1v\n3FiXGAgKAp8c1mazlUGXJANMY0anToxbtw6AzsWKMWblSrM960ziGX6N/pUDfx0gKT6JLOoL41zS\nmYZtGjKq/yiCXg/Czi5vV+if/Opkvtqnm10WUj6EIYultoql3blzh759+/LkSUbC6eOPPuKTTHUD\nRN5lK/2SEMaQZMC/PEx5SNTZKMJiw1h/dj1P0gy/UajoVVGfGKhfqr4kBkSudPbuzNqbawH4qNVH\ntPighcIRWdaECRPYt2+f/tzX15fY2Ng8Pwi3ZVeuwKpVusTA9u2Q1X/BDRtmJAYqZqP+qq0MuiQZ\nYBonIiKoERQEgBfw+6ZN2Ds5mf25l29dZln0Mvbu2su90/cgi/qDjkUdqdOyDsP7Dad/h/558v+k\n7TO203xccwB87H34KeYnGYtYUFJSEiEhITx48EB/TZa3WRdb6ZeEMIYkA17gkfoRG+I3EBYbxroz\n63iUanBfEsp5liPIL4ger/SgYemG2Kny3qBB5E1zu89l1KpRALQr0o4JYRMUjshy/u//prBxY0bh\nsJIlS5KQkICLi4uCUYnMrl2D1at1iYGtW0GTxY5udevqEgPBwVAli/qrtjLoUrpfshVajYayjo5c\nefqXavHYsZTv2NGiMVy/f53lfyxn145d3I69DVnUH7QvZE+N5jUY1GcQw7oNw8nR/EmL7Eh9mEqR\ngkV4yEMAfpvxG8XrFlc4qvxBrVYTEhLCrVu39Nd69OjBSjPOcBGmZyv9khDGkGRANj1JfcKmc5sI\niw0j8nQkD9UPDbYrU7AMQX5BBPsH07hsY0kMiBc6s+4Mvp10W14VoAARGyNwcHZQOCrz+9+iRSxb\nvlx/7unpyYULFyhkyY3vRY7cvAlr1ugSA5s3Q5rh+qvUrJmRGPDLVH/VVgZdealfsnaDq1blx7Nn\nAXinVi26Ztqb3dLuJt3lt62/8ef2P7l+/DpkUX/QzsMO3wBf+vXqxzs938HNRdmifd2Kd2P1DV19\nlUnNJ9HmkzaKxpMfaDQaBgwYwOXLl/XXWrRowZYtWxSMSuSGrfRLQhhDkgG5kJyWzB8JfxAWG8aa\n02u4l3zPYLuSHiXp7tedYP9gmvo0xd7O3sKRirxOq9FSwakCF9MvArBozCIqd66scFTmFRERwbff\nfqs/d3Vx5tTpM/jkdBG6UMydO7q9msPCIDoaUrN4o+rvn5EYqFnTNgZdebVfskYrR4+m5+zZADRw\ndWXq+vUKR6STlJzE73/+zuY/N3PlyBXIov6gylVFxUYV6d2jN2P7jaWQh+WTmQt6LGBE2AgAWnm1\n4oOIDyweQ37z1sjhxMad1p/Xrl2bgwcP5smlJOLFJBkghCQDjKZOV7Pl/BbCYsNYdWoVd57cMdjO\n292bbtW6EewfzOvlX8fBzvbf/orsGeY7jIVnFgLw31r/JWhWkMIRmc/WrVv57LPP9OcODvYcPnyE\n6tWrKxiVMMa9e7BunS4xsHEjpGS5o5ttDLqsoV+yFnfi4ylWpQoawA5Yu2wZbqVKKR3WM5LVyUTs\niiB6WzSXDl1Cm5TFn70T+DTwITgomPEDxlPcyzLT9c//cZ6KbXRFO1xxZXXUapzc8sYyBls0ccJ4\n9u7brz+vWLEip0+fxsFBxnTWSJIBQkgywKRS01PZdmGbPjFw8/FNg+2KuBaha7WuBPsH07JCS5zs\npePOz8LHhBM8KxiAeq71mL5+usIRmceRI0d49913+efftJ2dis2bt/D6668rG5gwmYcPISpKlxhY\nvx6ePPNG1TYGXdbWL+V1r3l4sOeRrh7P9OBg6r31lsIRZU2dpiZqXxTrt64nYX8CmvtZFNFwgJJ1\nStKlaxcmDppIuRLlzBeUFnydfDmTptuR5bsR3+H3H7+XfEjkxpSvviQ65g/9eQnvoiRcuISrq6uC\nUQljSDJACEkGmE2aJo0dF3cQFhtGxKkIriVdM9iukEshuvh2Idg/mDYV2+Ds4GzhSIXS7p69S9Gq\nRdGgQYWKtb+uxb2Eu9JhmVRCQgJDhw4lPT2jdPeKFSv4z3/+o2BUwpwePdIlBMLCdAmCR49sY9Bl\nzf1SXvRJ8+Z8un07AL3KlGHY0qUKR5Q9Go2G6MPRRG6O5My+M6TfzmJbAnsoWr0oHTp1YOLgifiV\nN/0P6m9Xf5tvT+qWXr3p9yZ9vutj8mfkd999N4/ffw/Tn3sWLMCFi5ekzo2Vk2SAEJIMsIh0TTp/\nXf6LsNgwwuPCufLwisF2BZ0L0qlqJ4L9gwmsFIiro2Sb84vXPF5jz6M9AEz7zzTqj6ivcESmc/Pm\nTfr160dKpvnjc+bMYdSoUQpGJSzp8WNwd7eNQZet9Et5xe6FC2k8bBgApezs+CUmBpWVrb3WaDTs\niN1BxB8RxO2NI/VaFkU0VFCoWiHavNGGCUMmUM+3nkmev37yet746g0A/J38mbdpnknuK3SWL1/O\nokWL9Odurs6cPhNPmTJlFIxKmIIkA4SQZIDFabQa9v69l7DYMMLiwrh0/5LBdu6O7nSs2pFg/2Da\nV26Pu5NtvSkWz/ok4BM+3fUpAL18ejHs52EKR2QaSUlJ9O7dm6SkJP21999/n6+++krBqIQSbGXQ\nZYv9kpLSkpPxdnPj7tPf0+WffUbJpk0Vjso4+87u4/fo3zm+5zgpf2dZRAOPSh683v51xg8ZT9Na\nuf+eH115ROEyhVGjBiBiUQRelb1yfT+RISoqiunTM5buOTk6cOToMfz8ZCmGLbCVfkkIY0gyQEFa\nrZYDiQf0iYGEuwkG27k6uNKhSgd6+PegQ5UOFHAuYOFIhbn99e1fNHm7CQBl7MuwJGYJKpV1909q\ntZo+ffpw+/Zt/bUBAwawePFiBaMSSrGVQZet90tK+E+ZMvx+RTdjbuJrrxFoQ8nC4xePsyJ6BYd3\nH+bx+cdZtnP1caVJ2yaMGTSGDq91yPFzWhdqzeb7mwH4/I3PCRgXkOuYhc6OHTv46KOP9Of29vbs\n3LmTRo0aKRiVMCVb6ZeEMEaukwEqlaoOUBU4oNVqz2W63g1ooNVqJxkdXD4adGm1Wo5cO0JYbBi/\nx/7O2TtnDbZzcXChXeV2BPsF07FqRzxdPC0cqTCHtEdpFPUoyn3uA/Dr1F8p0aCEwlHlnkajYdDA\n/ly89Lf+Wrt27diwYYOCUQklWWLQJf2Sdfqhf3+GLFkCQPMCBfgkMlLhiMwjPjGeZdHLOLD7AEln\nkyCLv0bOJZxp2KYhb/V/ix4temRry7rpgdN5L/o9ADoX78yY38aYMvR85+jRo4wZM0Zf8FalUhEV\nFUX79u0VjkyYkiQDhMhlMkClUo0F/g84CjgB+4BRWq32sUqlsgdStFqt0fus5NdBl1ar5cSNE/rE\nQNytOIPtnOydaFupLcF+wXT27YyXq0wLtGZBJYOIuBYBwKTmk2jzSRuFI8q9t0e9xfETsfrzunXr\nsn//ftmHOR8z96BL+iXr9ffevZR9+rbVGYhctQonGy/MdvnWZZbHLGfPzj3cO30Psqg/6FDUgTot\n6jCs3zAGvDEAezt7g+2OLz9OzZCaAHipvPg9+nfsHQy3FS927tw5hg0b9kzB219++YWQkBAFoxLm\nIMkAIXKfDLgODNVqtWuenlcBhgHfaLXaRJVKlarVah2NDk4GXQDE3ozVLSWIDeP4jeMG2zjYOdC6\nYmuC/YLpUq0LRd2KWjhKYazve37P8JXDAWjt1ZrJEZMVjih3Pv7oA7bv2KU/r1DehzNnz8k+zPmc\nBZIB0i9ZseouLpx8WmR03sCB+IeGKhyR5Vy/f51f//iVnTt2cjv2NmRRf9C+kD3Vm1VnYO+BjAga\ngZNjxrbE2jQtZZzKkKhNBOCHiT9QMbCiJcK3KVevXmXAgFDU6jT9tZkzZzJ69GgFoxLmIskAIXKf\nDPgbKJt5RKRSqeyAd4CNwDEZdJnH6VunCY8LJyw2jMPXDhtsY6+yp0WFFgT7BdPNrxve7t7Zvn9K\nSgpRUVGcPn0aAF9fXzp27IiTk9NLPimMdf6P81Rsoxu8ueHG6qjVOLoZ/c/IombNmsmaNRlTfIsV\nLcyFi5dxc3NTMCqRF1ggGSD9khUbW68e3xw6BMDAypUJzVS9PT+5m3SX37b+xp/b/+T68euQRf1B\nlYcK3ya+hPYK5Z1e7+Dm4sagioNYfF5Xk+Xtem/TbXo3C0Zu/e7evUvfkD48fpKsvzZp0iS+/PJL\nBaMS5iTJACFynwx4C7in1WqXGfhaf+B/Mugyv3N3zukTA/sT9xtsY6eyo1m5ZgT7BdPdrzslC5Q0\n2C49PZ2pU6cya9Ysbty48czXvL29GT16NOPHj8feXqYdmo0WqjhVIT4tHoD5/51PtaBqCgeVfUuX\nLOHHTMUBC3i4cS7hAsWKFVMwKpFXWCAZIP2SFYv56ivaTtbNhqri4MDCmBiFI1JeUnISv2//nc1/\nbibxcCLaJ4b/3qlcVFRoVIGA9ACW7NDVXqjvVp9pUdMsGa5Ve/z4MX369OL+/Yf6a0PffJPvFy5U\nMCphbpIMEMK4AoINAXutVrvbwNe6abXaVUYHJ4OubLt476I+MbD77+f+SABQoaKJTxN9YqCsZ1lA\nlwgICQlhxYoVL3xGz549WbZsmSQEzOi//v9lXpxuj+jhrwyn59yeCkeUPf/efsnZyZGTsXFUqlRJ\nwahEXmKhAoLSL1mp5Dt3KFykCE+enofPmUPhGjUUjSkvSVYns+qvVURvi+biwYtok178d1CFiqU/\nLqV0hdIWitB6qdVq+vXtw42bGTvfdOvahYhVqxWMSliCJAOEkK0FbdLfD/4mIi6CsNgwdl7aiTaL\nksWNyjQi2C+Y6xuvM+3z7L1BmDJlChMnTjRluCKTyAmRdJnaBYCaLjWZvWG2whG93O7du5k8ebK+\n6rK9vT27d++mQYMGCkcm8hJbGXRJv2Q+7YsWZePTrUg/ad2a5pOts26KuanT1Kzfv56oLVEkHEhA\nc09jsJ3KToXXK140btqYkDYhlChkvTvUmItGo2HQoEFcvHhRf61ZQBP+3LFTwaiEpdhKvySEMYxO\nBqhUqu+AY8B5INqUoyQZdBnv6sOrrDq1irDYMP68+Cca7b8GDWnATOBR9u7n7e3N5cuXpYaAmTy4\n8IAiFYqQhq54UeSSSAqULaBwVFmLjY1l1KhRaDS6v1ey/ZLIiiUHXdIvWafZXbsyes0aADoUKcJ7\nYWEKR5T3aTQaYg7HELklkjP7zpB2K81wQ3vwrOpJwyYNCWkTQjnvcpYNNI8aNWoUJ06c0J/XqO7P\nkaPHZeebfEKSAUKYJhmwDrgI+ACFgM5arfbu08FYReA9rVZruAT+y+8tgy4TuvHoBqtPrSYsNowt\n57eQrk2HWGBlzu4TERFBt25SmMhcmhVsxo6HOwD4uvvXvDrqVYUjMuzy5csMGjSItLSMwedPP/1E\n//79FYxK5FUWTgZIv2SFTq1di1/nzgAUBCIJWcCZAAAgAElEQVQ2bsTe2VnZoKyIRqNh/XfrmRE+\n48UNVeBRyYN6jevRu21vfEv7WibAPGby5Mn89ddf+vPy5ctz9uxZ2fkmH5FkgBBgitTnL1qt9i2t\nVtsJ6AUEq1SqFkB1oANQzwTPECbg7e7N0HpDie4XzfVx1/mh8w9UpWqO7/PPTgPCPALrBeqPD+w9\noGAkWbtz5w7Dhr75TCJgypQpkggQeYX0S1bI94038Hlak+YBcGHDBmUDsjJ2dna0H9yeQhTSX6vZ\nsCZOpf81k08LSfFJ/LnkT4b3HU6HAR14//v3OXr+qIUjVs7UqVOfSQR4e3tz8uRJSQQIIfKdlyYD\nVCpV5Zc0qa1SqT5TqVQtgapPf40A5mq1Wg1wzfgwhakVcSvCoDqDGFB7QI4/eyLhhH5auDC9tr3b\n6o93Xt2JVpO33kI+fvyYQQP78yQ5Y8+r0aNHSy0JYTHSL9kmlZ0d7Spn/NEe3rxZwWisk72rPc0K\nN9OfN0tvxvdffM+krydRp1sdXMq7PPeZJxefsOe3PYweNJp2fdsx9tux7D5luBCxLfj+++/ZkCnR\nVLBgQWJjY2ULXCFEvpSdmQHLVSrVi8rRfgA8BMYDPYEf0K1E/2cVegWjIhRm5eub8+mByxYtw6Wk\nC01CmrA8erkkBkysbmhdClMYgGuaayTuSVQ4ogxpaWkMHjSA+w+S9Nd69ghm5syZCkYl8iHpl2xU\nYMeO+uO/4uMVjMR6NazdUH989IzubX+V4lV4u/PbzP94Pp9M+4SGPRriXtkd/jVBOuVKCociDjFp\nxCTa9mzL2zPeZsuxLTbTz//222/89ttv+nNXV1eOHTtGkSJFFIxKCCGU89KaASqV6iHwGJgKzHz6\nVuXlN1apmgGjgF1arXZWroKTtZlml5KSgo+PDzdu3Mj1PRyKOFC3VV1GhI4gtH2oFN4xgV5lerHi\nim6rxwkBE2j3eTuFI9KtRx02dAjx587rrzVr2oQ/t0vVZfFyplybKf2S7bp/8SJFypcnHd3PqWt+\n/pkCPj5Kh2VVHhx5QJcxul1pnHHm27nf4ujuaLDt9fvXWbd/HUcPHuXh2YeQbvie9oXtqdygMp1a\ndSKwbiAO9tY3nX7jxo383//9n/7c0dGBQ4cOU716dQWjEkqSmgFCZG9mwDvoCi45AztUKlWT7NxY\nq9Vu12q1PXI74BKW4ezszOjRo7Pd3r20O/xr+WHa7TT2rdzHwI4DcSrqRL2geixcvZC09CyqGouX\navt6xlKBvcf3KhhJhgnj33smEeDv58vWbdsVjEjkY9Iv2SjPcuV4rYBuBxUtELdqlbIBWaGCtQri\n5+AHQAopXPsz61UxxT2LM7j1YOZMmMP02dNp2b8lXjW84F+5g/Q76ZzedJrp46cT2D2QwZ8PJmxn\nGOo0tTm/FZPZtWsXU6dmJALs7FRs2bJVEgFCiHwvR7sJqFSqEsBXgAaYoNVqb5srsKfPkzcwFpCe\nnk5ISAgrVqx4YbsWLVowefJkHqU8YsWfK9i6bStXj16FFMPt7TztqNG8BoP7DmZY12E4Ocp2hNl1\necdlfJrp3oY540zk2kicPJT7/fvqq6+IiYnRn5cpVYJz5y/KFpMi28z1Bkb6JdvzRcuWfLh1KwA9\nSpVi5LJlCkdkfZYPXs6ihEUAhJQPofXHrXP0+YdPHrL+8Hr279/P7bjbWfbzKncVZeqUoc3rbQgK\nCMLNOe+tuz9+/DijR7+D5mn9HZUKVq9eQ+enO1eI/EtmBgiRy60FVSrVq8AnQIRWq11k6qAyPUcG\nXRaSnp7OtGnTmDlzpsElAwP79iVkwADsn1Z6/kdSchK/b/+dzds2c+XwFUg2fH+7Anb4NfNjUJ9B\njAweiYvT80WMRCZa8Hf2Jy41DoC5w+bySq9XFAllwYIFzySKvLwKceHCRQoWLKhIPMI6mXvQJf2S\n7dj/4480HDwYgOIqFctjYrD7V98jXuzMT2cY9vMwAKo4VGHSokm5vtdj9WOij0Sz58Aerp+8rlug\nY4gLlKxVkhbNW9CzeU8Kupm3j0hKSuLBgweArgigh4fHc20SEhIYNnQoaekZ6x8WL17MgAEDzBqb\nsA6SDBAil8kAAJVKpQIGAF2Aj7Varcn3pJFBl+Wp1WqioqI4ffo0sz78kOtPt46b278/r7yk83yc\n8pjwneHEbI3h78N/o31s+M9O5a7CN8CX/r3783bPt3FzyXtvEvKCMTXHMOu4bjbzkGpDCJkfYvEY\nVq5cyfz58/Xnbm5unD17llKlSlk8FmHdLDHokn7JNmhSUynu7Mytp7/Pv3z8MaVff13ZoKxM2p00\nOgV1Ivlphn7OR3MoUKGA0fdVp6nZfHwzO/fv5Orxq2iTsvi34ATFqhejWbNm9GnVh8IehY1+NugS\nABs3bmTt2rVcunTpma/5+PjQuXNnAgMD8fDw4Pr164SGhqJWZyxlmDZ1KuPee88ksQjrJ8kAIbJX\nQLCpVqvdYeB6UcAXqA98BCwFPtBqtUn/bpvr4GTQpaj3GjRg+gHdPveDKlWi3//+l+3PqtPUROyK\nYOOWjVw6eAntoywSA24qKr9Wmb69+vJuyLt4uD6f2c+vNny4gQ5fdADA38mfeZvmWfT5mzdv5osv\nvtCfOzo6cuTIEfz9/S0ah7ANJi4gKP2Sjevj48Ovly8D8N6rr9Lh668Vjsj6fNHpCzYn6bZnHBsw\nluqDTbs+Pi09je2ntrN933YuH72M5n4WdTwdwMvPi8YBjQlpHULJwiVz/Cy1Ws3ChQuJiooiOTmL\nKYhPubi40Lp1a7Zs2cLjxxnTGCZMmMDX8vdIZCLJACGylwzYBPyMrlhT1Uy/Cv2r6W0gRqvV9jFZ\ncDLoUlTMlCm0naSbWljVwYHvM60Zzwl1mprIPZGs37KeCwcuoH2YxZ+pC1RsVJGQniGM7TcWT3fP\n3IZuEx5deUThMoVRo3ursfrH1XhWsMzvycGDB3nvvXH888/Pzs6OP//8k4CAAIs8X9geEycDpF+y\ncT8PGsSAxYsBCPDw4PO1axWOyPpsnriZL/bqErqBhQPpNaOX2Z6l0WjYHb+brfu2cuHoBdJvZbEt\ngR0UrFqQhk0a0qdtHyp4v3yXz4cPHzJp0iROnDiR6/gGDhzIjz/+mOvPC9skyQAhspcM+Heq9yYQ\nm+nXSeCkVqu9afLgZNClqCd37lC4SBF9GYCIefPwMvKtcFp6GlH7o1i3eR0J+xOyfpPgDOVfLU/P\n4J6M7z+ewgVNM8XQ2rQq1Iot97cA8EXnL2gyJltF040SHx/P8OHDSE/X/dmoVBAWFk737t3N/mxh\nu0ycDJB+ycZdPXiQUvXrA7rC9pHh4bgUzp/9QG7d3HaT/3z6HwAKUpAZ38/Awcn8WwJqNBoOXzxM\nzN4YEo4kkHo91XBDFbhXdKdek3r0btObamWqPddErVYzduxYoxIBHTp0ICoqKtefF7ZLkgFCZC8Z\ncA74DjgIHDd3peZ/PVsGXQprV7Qom27r/sg/Cwyk6cSJJrt3Wnoamw5tIvKPSOL3xaO5l0ViwAnK\n1i9Lj+AeTBgwAW8vb5PFkNdNbTOVCX9MAKBrya68s/wdsz7v2rVr9O/fD7U6Y1vI7777jhEjRpj1\nucL2mTgZIP1SPlDb1ZWjT6eEzw4NpebAgQpHZF206Vr6t+nPZa1uucWUgVMo0ayExeM48fcJNu3d\nxJkjZ1D/nfVWhC4+LtR6rRa92vaidsXaAMydO5fw8HCjnj969Ghmzpxp1D2EbZJkgBDZSwYEaLXa\nnRaK59/PlkGXwr7p3JmxT6dndi5WjDErV5rlORqNhj+O/MHqP1ZzZt8Z0m9nMcXQEUrVLUX37t15\nf9D7lCpq24Xsjvx8hDoD6gBQVFWUFTErsLO3M8uzHjx4QJ/ePXn0OGM95kcffsinn31mlueJ/MXE\nyQDpl/KBCQ0aMPVp3ZrQihUZ+MMPCkdkfX4I+YFfEn8BYHC1wQRMUHapV/z1eNbvXc+pw6d4cuFJ\nlu2cSjlRrW414qLjSFVnMbMgm9zc3EhMTMTTM38vPRTPk2SAEEbsJmAJMuhS3omICGoEBQHgBfy+\naRP2Zt5bXqPRsO3ENlbFrOLUnlOk3Uoz3NABStQuQdduXXl/8Pv4FPcxa1xK0Kg1lHQpyQ2tbrvH\nnz/+GZ/XTf99qtVqevfqyZ279/TX3hwyhIWLzLZDm8hnbGXQJf2S5WydOpWWE3Qzoyo6OPBDLuvW\n5GdHZx9l9OrRANR2qc078807uywnLt+5TNTeKE4cOsGjc4/AjP+s5syZw6hRo8z3AGGVbKVfEsIY\nkgwQL6TVaCjj6EiiRjeF/6cJEyjXrp3Fnq/RaNgVt4vwmHBi98RmvfbQHrxreNOpWyfeH/w+lUpX\nsliM5tavXD9+uaR7szO20Vg6Tulo0vtrNBpCQ0O5cuWK/lrHNzqwdp2ssRSmYyuDLumXLEf94AGF\nPT159PR85cyZFKtdW9GYrE3K5RTeCH2DdNJRoWLe1Hm4FnNVOqznXL9/nXX713Hs0DEenHkAWUwO\nzC0/Pz9iY2NNe1Nh9WylXxLCGOaZbyxshsrOjrYVMqr9HrHwmxk7OzuavtKUWaNnEf1bNF/N/4q6\n3eviVPJfsxPS4caRG/zw8Q9U9qlM0ZpF6f9hf05fOm3ReM2hbau2+uM9J/eY/P6jRo16JhHQsGFD\nSQQIIRTnVLAgLYoV058fj4xUMBrr5FzWmQYuDQDQouXvzX8rHJFhxT2LM7j1YGaPn82M2TNo1ruZ\nSe8fFxfHvXv3Xt5QCCHyGUkGiJdqm2kmwJ5TpxSMBF6r9hozRs1g0/JNTFs4jQY9GuBcxvnZRhq4\nffw2S75YQrUK1Sj8SmH6vN+HEwm5r0aspNbDWuuP9z3cR/L9F++xnBOTJk165m1J5cqV2b17t8nu\nL4QQxmjXLOOHwn1HjyoYifVqXKWx/jj2aN5/O17YvTBv1H7D5Pe9e/euye8phBDWTpIB4qVajxyp\nP97/+DHJN02+W1eu1K9Sn6kjp7Jx6UZm/TiLRr0a4eLj8mwjDdyNvcuvX/9Kjco1KFStED3e68Gh\nM4eUCToXSr5akppONQFIJZUzkWdMct8ZM2Y884N/8eLFOX78OHZ28t+CECJvCBwyRH+8884d0p5k\nXXROGFanZR398e4bu5FlLkIIIf4ho37xUsX8/anrqltjmA6cWbNG2YAMqFWhFlOGTWHDzxuY+/Nc\nmoQ0wa2C27ONtHD/9H3CpodRz7cenlU96TamG3tP7lUm6BwIfCVQf3x4x2Gj77d48WLWrVunPy9Y\nsCAnT57ExcXlBZ8SQgjLqhwYSEUHBwAeAQnr1ysbkBUq1a4URSgCwHXNde4cuaNwRC/n4eFh8nt6\neXmZ/J5CCGHtJBkgsiWwVi398cG//lIwkpd7xecVvhjyBVE/RrHglwU0C22GeyX359o9OPuA1bNW\n06h6IwpUKkCnUZ3YcXSHAhG/XNtuGXUDdl3YZdS9IiMjWbJkif7cxdmZo0ePUqRIEaPuK4QQJqdS\n0a5qVf3p4a1bFQzGOtm52NGsaMZyi/M7zisYTfa4ublRsmRJk93Pz8+PQoUKmex+QghhKyQZILKl\nbY8e+uOdly4pGEnO+Jb25dOBn7Luf+v436//o8XAFnhU8YB/1Y5NSkhi3dx1NKvdDPfy7rQf0Z7N\nBzYrE7QBAcMDcEH31v5s6llun7qdq/vs2LGDmTNn6s8d7O34a/duypcvb4owhRDC5AI7ddIf74qP\nVzAS69WwdkP98eGzxs8us4QWLVqY7F4jRoww2b2EEMKWSDJAZEvjN9/kn3frCenp3DpyRNF4cqNS\niUp8FPoRaxeu5afffqLNkDYUrFbwucTA44uP2bhgI60btMa1rCut32zNhj0blAn6KZdiLjT3aq4/\nPxl5Msf3OH78OJ98/LH+XKVSsX7DRurUqfOCTwkhhLJavPUWDk+Pj6ek8OB83n+zndfU6FJDf7w/\naT/qJLWC0WRPkyZNcHJyennDl3BzcyM0NNQEEQkhhO2RZIDIFqcCBWjh7a0/P5Fpvbk1Kuddjkkh\nk1gzfw1Lfl9C+2HtKeRfCOyfbZf8dzKb/7eZDq91wKW0Cy0GtmDN9jVoNBqLxxzYKKNuwP6D+3P0\n2YsXL/Luu2PQZCoctXTpUtq0aWOy+IQQwhwKlC1Lk4IF9ecnV61SMBrr5F7dnRoOuoRAKqlc3XpV\n4Yhezs3NjebNm7+84UsMHToUT09PE0QkhBC2R5IBItvaBgToj/dZ4cyArJQtUpbxvcazat4qfg37\nlY4jO+JVwwv9q6inUhJT2PbTNro274prKVea9mvKys0rLZYYaBuaUTdg582dpKelZ+tzt27dYvjw\n4aRlaj99+nRCQkJMHqMQQphDu4YZ09z3789ZMlToNCnfRH986qCy2wRnV+fOnbG3z/1QNSAggClT\nppgwIiGEsC2SDBDZ1nbwYP3xrtu3SU9JUTAa8yhRqARje4wlYk4EK8NW0vXtrhSpVeS5xID6upqd\nv+ykZ+ueuJRw4bXer/HLxl/MmhjwD/antKo0APe097i09eW1G5KSkhg0aBDJycn6a+PGjWPs2LFm\ni1MIIUwtMNM07x3Xr6NJz14yVGSo17Se/njflX0KRpI9aWlpfPbZZ6Sn565fDQgIIDIyUnbJEUKI\nF5BkgMi2qu3a4WOvm0f/ALi4aZOyAZlZMc9ivNPtHcJmhRG+Kpzg0cEUq1sMHJ9tl3ozlT2/7aFf\n+344F3OmQY8G/LD2B5MnBlQOKtqWz5gdsG/9PhITE0lMTCQpKem59mq1mkGDBvHw4UP9tZCQEKZN\nm2bSuIQQwtxq9eqFt0pX4OWWVstl2VUgxyp0qYAbui13E9ISuH/uvsIRZU2j0fDZZ59x8+ZN/bUS\nxb1xc3N7wad03NzcGD16NDExMbKdoBBCvIQkA0S2qezsCKxUSX9+ZMsWBaOxrMIehXmry1usnLGS\nVatW0XNsT4rXLw7/qm2UdieNA2EHGNJ5CE5FnKjbrS7zw+eTlp5mkjiaNMuY5rngyAJCQkIICQmh\nU6dO9O/fn/DwcJKSktBoNAwbNuyZgVSrVq345ZdfTBKHEEJYkp2jI4E+PvrzYzaejDYHe097Agpk\nLPe7uOWigtG82LRp07h8+bL+3NfXlyuJV0lMTGT27NlUq1btuc/4+fkxZ84cEhMTmTlzpswIEEKI\nbFBpMxUUy2tUKpU2L8eXH4WNGUOPWbMAqO/qyrT16xWOSFlJyUn8tvU3tvy5hatHr0Ky4XZ2Be14\npdkrDA4ZzIigETg55qxCcnJyMhMnTmTR94t4nPz4hW1dXFzw8HDn1q2M7Qdr1arFoUOHsLOT/J9Q\nhkqlQqvVql7eMm+Tfkk5y4YNo+/ChQA0cndnipUXslXCtsnb+PSvTwFo5dWKvt/0VTii582bN48D\nBw7oz8uUKcO5c+ee21ng3r173L17FwAvLy8KFSpk0TiF9bOVfkkIY0gyQOTInfh4ilWpggbdtJK1\ny5fjVrKk0mHlCUnJSYTtCOOPbX9w5fAVeGK4nZ2HHX7N/BjYZyBv9XgLF6cXv724e/cunTp1Yteu\nXbmKq5yPD/HnzuHg4PDyxkKYia0MuqRfUs6NY8coXqsWoNv4Ze3vv+NatKiyQVmZOzvvEPRhEAAe\neDDz+5k4OOWdvmHp0iVs2ZKxBKRw4cKcP3+egpl2kxDCVGylXxLCGPKaUORI4cqVaeDuDoAGOLV6\ntbIB5SEeLh4MaDOAX778hQ2rNzDkwyGUDSiLyu3ZfkaTpOHk+pOM6zsOt8Ju+AX6MeWnKQbf+Ccn\nJxuVCHBwsOfAwYOSCBBCWD3vmjWp5+oKQDpwWvqfHPN6zYvyduUBSCKJG7tuKBtQJqtXr3omEeDh\n4cHJkyclESCEEGYkyQCRY4F16uiPD+7Zo2AkeZeLkwshLUNY8vkSNq7ZyPBPh1O+eXlUHs8mBrSP\ntJyKPsWkgZPwKOxB1dZV+XTRpzx8rCv6N3HixFwnAgDS0tL58ssvjfpehBAirwisWVN/fMCI/xvz\nK5W9iualmuvPz+45q2A0GTZv3syaNZH6c2dnR44cOUKJEiWyfxOtFo4dgzlzdMdCCCFeSpYJiBzb\nNW8eAf/9LwBl7ez4OSYGlaxFzxZ1mpp1e9cRtSWK8wfOo32Qxd9vFyhXrxyJ+xNJVaca9Uw3NzcS\nExPx9PQ06j5CGMNWpmNKv6Ss7TNn0vzddwHwsbfnp5gYVCqr/2tlUSfmnWBU2CgAqjtXZ+wCZbea\n3bNnD99//73+3MHenr379lG3bt2c3UirhdKl4epVXVKgRg0TRypsja30S0IYQ36CEznWcMAA/pm0\nd1mj4ebBg4rGY02cHJzo3qQ7P3z4A9ER0Yz5egxVWlfBzvNf/xST4eKuiy9MBJQuXZpRo0YxatQo\nSpcunWW7x48fs2TJElN9C0IIoZjX3nyTAk+PL6Wnc0P6nxyr2rUqDuiWjp1IOcHjay8uSmtOJ06c\nYOHCjESAnUrFxk2bcp4IAFCpIDBQd7xxo4kiFEII2ybJAJFjju7utMo0de9YVJSC0VgvB3sHOr/a\nmYWTFxITEcP4aeOpFlgNey/7l352+PDhnD9/njlz5jBnzhzOnz/PsGHDsmw/f/58U4YuhBCKcPTw\noFXx4vrzY7KjQI45lXaikWsj/fnlzZdf0Np8EhISmDlzpn5GvwpYsXIlrVq1yv1Nu3WD//wHMi0n\nEUIIkTVJBohcads8Y83hvmPHFIzENtjZ2dG+fnvmT5xPdFg0Y74ck2Xb0qVLM2fOHBwdHfXXHB0d\n+fbbbylVqpTBz8TFxXHv3j2Txy2EEJYW2KyZ/njv0aMKRmK9Xqv6mv745LGTFn/+1atXmTJlChqN\nRn/tu/nzCQ4ONu7GnTvDihUZMwSEEEK8kCQDRK60ffNN/fGuu3dJfazcNENbY2dnR/3y9bP8evfu\n3Z9JBPzD0dGR7t27Z/m5f/ZjFkIIaxaYaRbUX/fuoX70SMForFPtVrX1x3/d/AtNuuYFrU3r7t27\nfPLJJ6Slpemvff755wwfPtxiMQghhNCRZIDIlYotW1Lp6XZ1j4ELGzYoG5AQQoh8oULLllR92v88\nAc7JUoEcK9m2JN54A3Bbe5vbR25b5LmPHz/mgw8+QK1W66+9/fbbfPDBBxZ5vhBCiGdJMkDkjkpF\nYNWq+tPDW7e+oLHIqRftqxwREUFq6vOFBVNTU4mIiMjyc15eXiaJTQghFKVSEVitmv708LZtysVi\npVTOKpoXy1jul7AjwezPVKvVTJ40kceZZhL26dOH2bNnm/3ZQgghDJNkgMi1th076o//io9XMBLb\n4+HhgY+Pj8GvXblyhVGjRj2TEEhNTWXUqFEkJiYa/Iyfnx+FChUyS6xCCGFp7bp00R/vSjD/D7K2\nqEHdBvrjQ/GHzPosjUbDxx9O5t79h/prbdu2ZdmyZeZ54A8/wBtvwIUL5rm/EELYCEkGiFxr8dZb\n/FP3/mhKCg8vXVI0HlvTuXPnLL/2/fffU6FCBf3WguXLl39mn+Z/GzFihDlCFEIIRTQfORKnp8ex\najV3z55VNB5r9EqXV/THhx4dIuVBilmeo9Fo+OLzT7h245b+Wr26tdlgzuWFKSkwYAAUK2a+Zwgh\nhA2QZIDItYI+PrxWoID+/NSaNQpGY3sCAwNxcXHJ8utXrlxh7ty5zJ07N8sZAQBubm6EhoaaI0Qh\nhFCEe6lSNM002+mk9D855ubnRm1HXSHBNNJI3Jp1P2KMmd9M5/yFjO0Lq1SqwL79B7GzM+MQdORI\n6NED3N3N9wwhhLABkgwQRgmsn1H1/sDevQpGYns8PDx44403jL7P0KFD8fT0NEFEQgiRd7Rr1Eh/\nvP/AAQUjsV5NKjTRH8cdjDP5/RcsWMCJkxn3LVnCm2MnYs2bCBBCCJFt8r+xMErbPn30x9uvXkWr\nsdz2RPlBo0aNUKlUuf58QEAAU6ZMMWFEQgiRNwT2768/3nHjBukGCquKF6vXrJ7+eG/iXrRarcnu\nvWzZMvZmekngVaggsXGnXzjjTQghhGVJMkAYpV6/fng9/WH1mkbDtT17FI7IdsTHx/PJJ5/kenAW\nEBBAZGSkDLyEEDapeo8elHr6hvmuVsulzZsVjsj6lOtUjgLolvtdSr/EvTP3THLfyMhI/vjjD/25\nu7s7J07GKVPINj3d8s8UQggrIckAYRR7Z2dalyqlPz+6fr2C0diOxMREJkwYz6NHjwAoXrw4AwYM\nwM3N7aWfdXNzY/To0cTExMh2gkIIm6WytyewfHn9+dGYGOWCsVJ2Be1o6tlUf35x20Wj77llyxZW\nrVqlP3dycuLQoUOUyjRWsIjz56FZMwgIsOxzhRDCikgyQBgtsGVL/fG+EycUjMQ23Llzh4njRnHn\nzl0APD09iY6OZvHixSQmJjJ79myqZdpj+x9+fn7MmTOHxMREZs6cKTMChBA2L7BdO/3xX6dOKRiJ\n9Xq1xqv646NxR4261/79+1m6dKn+3N7enp07d1K1alWj7psrxYvDvn2wdy/cvGn55/8/e/cdHkW5\n9nH8O2k0g6gUaQJBRFC6IKJBQCCoIEU96uGgKBoB+9HQBQ6ieNRXlBJRkeahKMYoVRJEEUIVFQUE\n6UgvoYb0nfePTYYNJCQhm53d5Pe5Li+fyc4+c+Mlmd17nue+RUR8gJIBUmAdwsOt8erTp0k5e/Yy\nZ8vlnDt3jiEDXuLvQ/EAlCwRwPz582nYsCHgTAy8+OKL/Pnnn5w8eZJdu3axa9cuTp48yZYtW3jh\nhRdULFBEio32zz1HZlWVDefPc/7IEVvj8UUN72tojdedXkdactoVzbN582Y++ijSOjYMg0WLFtG8\nefMCx3hFSpd2rgwwTWdCQERELqFkgBTYDXfdxc2BgQAkAbsWLrQ3IB+VkpLCiGERbNu5HwB/f4Mv\nvviK0NDQbM8vV64ctWrVolatWvbsw4RWjXsAACAASURBVBQRsdl19evTImP7lAP402V5uuRNuZbl\nuNHvRgDOc54jK/OfUNmzZw/vv/9/uJa4mTVrFh07dnRXmFfmww/hyBHo3NneOEREvJSSAeIWYfXq\nWeNfli+3MRLflJ6ezlujhvHLxgvLXD/9+BMe6NrVxqhERLxfWOPG1nj96tU2RuKjDGhdtbV1uG3N\ntny9/ciRI7z15mgcjguZgPHjx/Poo4+6LcQrVq8eVKxodxQiIl5LyQBxi44PPGCNV+3aZWMkvsc0\nTcaOHcvyuPXWz95+6w2e7PN0/ibavh1efx0+/dTNEYqIeK8wly+dK/bvd2t7vOLitla3WeOf9/2c\n5/edOnWKkSNeJzXtQsX+EcOH8/zzz7s1PhERKRxKBohb3N2/P4EZ480pKZzeudPWeHzJlClTWOiy\nteLfLz3HgEFD8z/Rjh0werSSASJSrLTo04fMjVIHHQ4Or1tnazy+qE73OgQRBMCfKX+ScDAh1/ec\nP3+eYcOGkZScav2sf79+jPzPfwotThERcS8lA8QtylSuzF0uheu2fPutjdH4jq+++or//e9/1nGv\nXr149/1xGIZxmXfloHVrCAqCn3+GEyfcGKWIiPcKKF2a9pUrW8cbFyywMRrfFFApgJalW1rHe7+/\nfIvBtLQ0hg0bZrW/BXj4oQeZGBl5mXfZKCEBtIVEROQSSgaI24S1aGGN1/+c92WGxVVsbCwTJ060\nju+77z4+++wz/Pyu8K9lmTIwZgzMneusoiwiUkyEtWljjdf+8Yd9gfiwO+veaY03/7E5x/McDgev\nv/46J0+etH7Wrl07vpz7VaHGd8USEqBqVRgxAhwOu6MREfEqSgaI23Ts1csarzx8GEd6+mXOLt7W\nrV3Lf//7X+u4VatWzJ07l8DAwMu8Kw/+/W948EEoVaqAEYqI+I6wfv2s8erTp0lWi9t8a9SxkTVe\nfXw1jvTsvzi/+eabHD582Dpu3LgxsbGxhR7fFStTBg4dgpgYuNJku4hIEaXfiuI2jR59lAoZy9uP\nmSYHV6ywOSLvtGXLFkaOGEZ6RrLklltuYf78+ZTW03wRkStSPTSU+hnJ1GRg+/z59gbkgyrdU4nK\nhnO7xUnzJMd+PnbJOWPf/z92uRQJDgkJYf369Ve+os1TlCAXEcmWl//2Fl/iFxhIh+rVreON331n\nYzTeae/evQwZ9CqJyWkA3FC1PEuWLOHaa6+1OTIREd/m2uL2V7W4zb9AuLvi3dZhVHQUCxYs4Oef\nfyYtLY1PP/2Y3//YZL1+/fXXs2nTJgICAuyIVgogJiaGM2fO5Ph6SkoKU6dO9WBEWZmmyZdffmnb\n9UWKEyUDxK3C2re3xmu2bLExEu9z9OhRBr72IqfPJgFQ/pqriPl+JVWrVi2cC2pvpIgUI2Hdu1vj\nlbt32xiJb0pPT+fM1Re+IK4/sp6oqCgmTpzIc889x6pVa6zXri4bzJ9//kkpPXH3KcnJyfTt25cF\nCxZQtmzZS15PS0tj8uTJ3HTTTfTp08et1966dSt9+vQhJCSEWrVqUbNmTZ566im2bdt2ybmGYXDo\n0CE6d+7MqVOn3BqHiGSlZIC4VYe+fa3x2rNnST592sZovMfp06cZ9NoLHDnu/KB1VekgFsf8QN26\ndd1/sd9/h7vugocecv/cIiJeqnX//pTMGP+Vmkr81q22xuNL0tPTefPNN1n016JsX09JSbHGpUoG\nsWnzFsqVK5ftuV4rPh7mzIFly+yOxBbx8fG0b9+egIAAxo0bl+U1h8PB9OnTqVevHuHh4ezbt+/K\nuhrlYO7cuTRp0oSdO3eyatUqdu/ezfLly9myZQvNmjVj3rx5l7znpZdeonv37oSGhnLw4EG3xSIi\nWSkZIG5VuXlzGpQoAUAqsD2bX/DFTWJiIoMHD2b330cBCAzwI/qbBdx2222Fc8GqVWH4cJg5s3Dm\nFxHxQqUqVuTua66xjv9Qi9s8mzNnDj/88IN1XLVqVV544QVeeOGFS1av9e33HNWqVfN0iAUXHQ2P\nPQYffmh3JB6XkJBAWFgYwcHBjB8//pLXFy5cyM0338yGDRu49dZb3XrtuLg4evXqRalSpYiOjub6\n668HoEaNGsyfPx9/f38ee+wxNm7ceMl7+/TpQ5cuXbj33ns5d+6cW+MSESclA8Ttwm65xRr/UsyL\nCKampjJixAj+/PNPwLn07X//m0n7Dh0K76LXXQcdO6pgkogUO2F33GGN12/YYGMkviMlJYWoqCjr\nuG/fvuzevZtx48Yxbtw4du/ezbPPPmu9PnPmzCwrBXxGWJjz38uWgS/GXwA9e/Zk7969TJs2Ldsn\n/l26dOH222+nbNmyNGnSxG3XdTgc9O7dm5SUFJ599lmucUnWAVSoUIHw8HASExPp379/tnOMGjUK\ngCeffNJtcYnIBUoGiNt1dNm3Gbdnj32B2MzhcPD222+zfv1662cTJ07kH488amNUIiJFV6ennrLG\nK44dI62Yfem7EmvWrOHkyZOAc0XAuHHjsrS5DQwMZPz48VSpUgVw1r9ZuHChLbEWSLVq0LMnvPYa\nJCXZHY3HTJs2jXnz5jFo0CAqVqyY6/nu3B4QFRXFzp07MQyDHj16ZHtO5s9Xr17N0qVLL3k9ICCA\nkSNHEhUVxddff+222ETESckAcbu7+vYt9vs2TdNkwoQJLHPZmzhy5Ej6ufTCFhER97q5WzeqZ7S5\nOwPsjY21NyAf8Pfff1vjHj16ZEkEZAoMDMzyZS67om8+4X//gxEjIJvieUVRUlISgwcPpmTJkoSH\nh3v8+nPmzAEgKCiIpk2bZntO06ZNrY4Us2fPzvacbt26UalSJSIiIqy2zCLiHkoGiNuVKl+e1i5L\nwbYUw7oBs/43jejoaOu4f//+DB8+3POBHDoE2mcnIsWE4e9PWEiIdfxrNk8aRYqLqVOncuTIEdq0\nacNVV13l8euvXr0agNq1a+Pv75/tOSVKlKB27doAWR6guDIMg7CwMHbv3p1jwkBEroySAVIoXPdt\nritm+zYXzP+WyVNmWMf/+Mc/GDdunFuX3uVJ375QpQoUw2SMiBRfne67zxqv8tUn2B5UvXp1a/z1\n11+Tmpp6yTmpqalZlmgXSicccbtZs2YB0KJFC49f++jRoxw+fBgg1xbKmVtQ9u3bx9mzZ7M9p3nz\n5gBMmTLFjVGKiJIBUig6PvGENV557Bjp2Xy4KIqWL/+RsR98YB3fc3dLZsyYkWNGvFDVqeP895Il\nnr+2iIhN7nn+eTJ/4/6WmMjZAwdsjcfbtWzZ0moTeODAAV544YUsCYHU1FReeOEFq71bxYoVuf/+\n+22JVfLu9OnTrFq1CoB69ep5/PonTpywxhcXDryY6+sHcvj7mtnlYMWKFRw/ftwNEYoIKBkgheSW\nBx+kcsa+zZOmyf4ff7Q3IA/49ddfeWv0GzgczuNmjW4men4MJTJaLXpcx44QGAjJyfZcX0TEBuXq\n1OH2MmUAMIE/v/nG3oC8nL+/P9ddc2EP/ccff0ytWrWs1oI1a9bk448/tl5/5ZVXCAoKsiNU99ix\nA/r1gwED7I6kUG3cuBHTNDEMw3ry7kmZRSmBXD8Hub5+5syZbM/JbEnocDhYu3atGyIUEVAyQAqJ\n4e9Pxxo1rOPfYmJsjKbw/fXXX7w+dCApac5MwE0hVVkc+xPBwcH2BXXrrRAfDxkFfEREiotOLsXK\n1q9ZY2Mk3s00TSZ88B47d+/L8vMDBw4wYcIEJkyYYK0IAHjkkUeIiIjwdJju5e8PN94IRbxVnWuR\nx+uuu87j13fdGpnbNkk/vwtfR0zTzPaczE4Ipmny+++/uyFCEQElA6QQhWX29AXW/PmnjZEUrv37\n9zNw4EASEp3LKqtUuoYl36+kQoUK9gZmGGBDwSAREbuF/fOf1njFwYOYmUu2JIupkz/mmwXfWcd3\n3N482/ZzFStWZMyYMcycOdOebW/uVKsWvPoq2LB03pNOnTplje1YoVjWpWNDUi6tHF1fz+khSsmS\nJa2xtgmIuE+A3QFI0dW+f3+YNAmA9QkJJJ44QSkbstOF6cSJE0RERFg33XLlrmbJ0p+oWbOmvYGJ\niBRjzZ54gmv79SMeOOJwcGDVKqrddZfdYXmVL7/8ks9nfWEd93ykBzNmzSUtLY2FCxdaT5br1q3L\n/fff79tbA4qhlJQUa2xHAueGG26wxjkt/c/kWjTQ9X2uXBMaORUZFJH8UzJACk2FBg1oWrIkvyQl\nkQ789e23NHrqKbvDcptz584xYMAAq1puqVKlWLBgoVXkRkRE7OFfqhQdq1ZlTkYxso2LFikZ4GLx\n4sV89NFH1vH9ndoz9fM5+Pn5ERQURPfu3W2MTtzB9Ql7sg21g4KDg6lWrRr79+/PstUkO5lFA6tX\nr55jC0TX5IYdbRJFiiptE5BCFdawoTXeEBdnYyTulZyczNChQ9m1axfgzLrPnTuXO++80+bIsnH8\nuLNuwB9/2B2JiIjHhLVrZ43XbN5sYyTeZcWKFbz33nvWcWhoKHO/nkdgYKCNUdnE4YC0NLujKBSV\nK1e2xgkJCbbE0LZtWwB27NiRYy2AtLQ0duzYAcA999yT41yuWwnsqIEgUlQpGSCFquODD1rjuH37\nLnOm70hPT+fN/wzNUsBmypQp3ttqadIkmD0bclmmJyJSlHTs188arz1zhsTTp22Mxjts2LCBN954\nA0dGDYXGjRszf/58SpUqZXNkNhg9Gq6/HhYutDuSQtGoUSPAWXDv0KFDtsTwYMZnwMTExByL/m3c\nuNFaudCjR48c53KtE3DLLbe4MUqR4k3JAClUd4SHUyZjvCstjWM+XgHWNE3ef/ctVqzeYP3s//7v\n/3j88cdtjCoXw4bBt9+CN65aEBEpJFXuuIOGGfvcU3FuVSvOtm7dyvDXh5Ca6ix2W6dOHZYsWcLV\nV19tc2Q2cTjg2DH47rvcz/VBderUsYpB7tmzx5YYOnfuTM2aNTFNk+jo6GzPiYqKApzxXu6hSuZW\nA8MwaN68ufuDFSmmlAyQQlWiXDnalC9vHW9esMDGaApu8ieRLFqyzDoe+NrL/Pvf/7YxIhERyUmY\nyxPEX1assDESe+3Zs4fBA17hfKJz33XVqlWJjY3NtnNAsZHZ8eiXX+yNo5AYhkHXrl0B59P3vMqs\ngwTOJ/o5OX36NKGhoQQHB9OzZ89sz/Xz8yMyMhKAyMjISwoJxsfHM2nSpCzn5WTTpk0ANGvWjKpV\nq+b5zyMil6dkgBS6MJcn0ut+/dXGSApm7hezmDXnK+v4qccfY8w779sYkYiIXE6Y61Y1m56O2u3w\n4cMMeu1FTp117rm+rlwZYmJiqFGjhs2R2ey222DDBli92u5ICs3TTz8NOOtE5MWyZctYtsz5wMM0\nTcaPH096enq258bGxhIXF0dCQgKzZ8/OUofCVadOnZg4cSInT56kW7du1paF/fv307VrVxISEoiM\njLxsvQCANWvWANC7d+88/VlEJG+UDJBC19Glg0Dc8eOk2VDVtqCWLFlC5KRPreMH7mvPx5/NwDAM\nG6MSEZHLuatvX0pnjHempXE04+licREfH8/AV1/gyAlnK7arSgexOOYH6tevb3NkXsDfH5o2Bb+i\n+1G4efPmtGvXjm3btrH5MkU0J02aRPny5Wnfvj3p6ekYhoFhGAwaNIirr76ajh07XvKeVq1aUb9+\nffz8/DAMg/Xr1+c4f79+/Vi/fj1Vq1aldevW1K5dmzZt2hASEsK6desIDw+/7J8jNTWVRYsWUbly\nZSvBISLuYeRU3dMbGIZhenN8kjemw0HNwED2ZRQsmvzaa9T21mJ72Vi9ejXDhg2zCi6F3tGUJd+v\n9K2CS2lpMGUKxMXB1KlF+sOPeCfDMDBN0+ezZ7ov+Z7O5cuz8MQJAF7v0IF2Q4bYHJFnnDt3jldf\nfo6/djqL9wYF+rN48RLa5fIEVoqWP/74g2bNmvH4448zefLkQrnG+++/z44dO3Jd6n+lPvvsM555\n5hnmzp1rFSV0h6JyXxIpCH0jkEJn+PnRMSTEOv5t6VIbo8mfP/74g//85z9WIqBhw4bMW/S9byUC\nwPkEZPRomDED8rF3UETE14W1amWNfXmrWn4kJSUxdOhQKxHg52fwxRdzlQgohho0aMCwYcOYPn06\nvxRSfYSlS5cWWiHl+Ph4hg8fzpNPPunWRICIOCkZIB4Rdt991njNX3/ZGEne7d69myFDhlgtb2rV\nqsV3331HuXLlbI7sChgGZC7zi4mxNxYREQ/q1KePNY47fpxUl37lRVFaWhr/+c9/srRym/zJp3Tr\n3t3GqLyYacIff0ARrikxfPhwunfvTq9evS4p4ldQY8aMISQkhJYtW7p1XgCHw0Hv3r1p0KABn3zy\nidvnFxElA8RD2vXrZ/3P9sv58yQcOWJrPLk5fPgwERERnDt3DoCKFSsSExND5cqVbY6sAJ54AsaO\nhYcesjsSERGPubFLF2r5+wNwDti1ZIm9ARUih8PB22+/bRVbA2f72yddEiJykZEjoWtXKOKrRmbO\nnEnDhg15+OGHSUlJccucQ4YM4cSJE0yYMMEt87kyTZP+/ftTunRp5s2bh3/G32ERcS/VDBCPaVmm\nDGvPnwfgvcceo1kuBWPscvLkSV5+IZx9B44DEBwczI8//kjTpk1tjkzEdxWVvZm6L/mmfnXrMilj\nVVrfBg14ZNw4myNyv8zq76793IcOHcro0aNtjMoHpKRAYKBzBV0x8NZbbxEXF8dXX31V4C2PZ8+e\nJTg42E2RXWCaJuHh4dx4440MHDjQ7fNnKir3JZGC0MoA8Ziwxo2t8YZVq2yMJGfnz59n6MCXrURA\nUFAA3377rRIBIiI+rJNL0dpV27fbGEnhmTF1cpZEQN++fXnjjTdsjMhHBAUVm0QAOJ/mf/DBB5Qo\nUaLAcxVGIgCcX9IHDBhQqIkAEXFSMkA8puM//mGNV+7fj7c9XUtJSWHksAj+3H6h4NLsWbNp27at\nzZGJiEhBtH3+eQIyxr8nJXHm779tjcfdor76gmmfz7KOH330USZMmKD2t5KtOnXq4OflXYXq1Klj\ndwgixYJ3/yaQIqVFnz6UzRj/nZ7OUS/an5eens5/3xzB+l+3WD/7aOJEejxYRPfXZ3RHEBEpDsqG\nhNDqqqus480uT9B93ZIli5kwcZJ13Kl9KNOnT9ceaxERyZWSAeIxgVddRbtKlazjPxYssDGaCzL3\nWS776ULBpdGjRhDet5+NURWiZ5+FSpXg4EG7IxER8ZhOt91mjX9eu9bGSNwnbuVK3n3nXeu4VYtG\nRH37HUFBQTZG5YNME1atgjffVLJcRIoVJQPEo8JCQ63xOi/pdz9jxgy+/fZb6/jF58IZMmyEjREV\nsocegl9+gSpV7I5ERMRjwnr2tMY/HTqEIz3dxmgK7rfffmPUqJGkO5xb7hrWr82C736gdOnSNkfm\no/75Txg2zHl/FBEpJpQMEI/q+PTT1jguPp7UxEQbo4FvvvmGadOmWcePPfYYY8d9VLT3WXboANWr\n2x2FT4mJiblsb+aUlBSmTp3qwYiyMk2TL7/80rbri/iCxr16USHjd/tx0+TvlSttjujKbdu2jaFD\nh5KS6kxo1K5RmSXfr+Saa66xOTIfZRgQFuYcF+HWkyIiF1MyQDwqpGNHamfsYzwP7LbxpvvDDz8w\nzqW9VFhYGNOmTfP6ojriOcnJyfTt25cFCxZQtmzZS15PS0tj8uTJ3HTTTfRxcx/vrVu30qdPH0JC\nQqhVqxY1a9bkqaeeYtu2bZecaxgGhw4donPnzpw6dcqtcYgUFX4lShBWrZp1/PvixTZGc+X27dvH\nwIEDOZ/Rqrdy5crE/hDH9ddfb3NkPu7BB+Gpp6BVK7sjERHxGH3rEc8yDDq6VIj9ddkyW8LYsGED\nb731ltXR4PbbbycqKkr7LMUSHx9P+/btCQgIyJI0AnA4HEyfPp169eoRHh7Ovn373LqaZO7cuTRp\n0oSdO3eyatUqdu/ezfLly9myZQvNmjVj3rx5l7znpZdeonv37oSGhnJQ9SBEshXWvr01XrVly2XO\n9E5HjhwhIiKC06dPA3DNNdcQExNDrVq1bI6sCOjYET77DNRBSESKESUDxOPCOne2xqtt6Pe8detW\nhg8bRFpaGgD16tVj4cKFlClTxuOx2Co5GYpYey13SUhIICwsjODgYMaPH3/J6wsXLuTmm29mw4YN\n3HrrrW69dlxcHL169aJUqVJER0dbT/tq1KjB/Pnz8ff357HHHmNjNjU3+vTpQ5cuXbj33ns5d+6c\nW+MSKQo69u9vjX8+e5bE+Hgbo8mfU6dOERERwdGjRwEoU6YMixYtcvvvIBERKT6UDBCPa9u/P5kN\njzYmJXH2wAGPXXvfvn0MGfhvzic5EwHVqlRiyZIlXHfddR6LwSvExcF118G//mV3JF6pZ8+e7N27\nl2nTpmX7xL9Lly7cfvvtlC1bliZNmrjtug6Hg969e5OSksKzzz57yf7fChUqEB4eTmJiIv1dvtS4\nGjVqFABPPvmk2+ISKSoq3nYbTUqUACAN2OpSPNabJSQkMDjiRf7OSOAGBgYSHR1Ny5YtbY5MRER8\nmZIB4nFla9XiDpd+z39+841Hrnvs2DEGvfYiJ884ixZee3VpYpb+QPXiWEzvllsgMdHZSunsWbuj\n8SrTpk1j3rx5DBo0iIoVK+Z6vju3B0RFRbFz504Mw6BHjx7ZnpP589WrV7N06dJLXg8ICGDkyJFE\nRUXx9ddfuy02kaKik8uT9A0+UEQwOTmZ4UNeZesOZyLAz89g1qxZdOjQwebIRETE1ykZILbo2LSp\nNfZEv+czZ84wOOJFDh1z7rMsXTKQRUuWUa9evUK/tlcqVw5uvx1q1IA9e+yOxmskJSUxePBgSpYs\nSXh4uMevP2fOHACCgoJo6vJ3xFXTpk0JCAgAYPbs2dme061bNypVqkRERATpPt4+TcTdwh5+2Bqv\n3LfPqh3jjdLT03nzP0P55fcLhUM//ugjHnroIRujKuImToTWreGvv+yORESk0CkZILYIe+wxa7zi\nwIFC/TCWlJTEkMGD2bn3MAAB/n58HT2P22+/vdCu6ROWLIEdO6BBA7sj8RpTp07lyJEjtGnThqtc\nVq94yurVqwGoXbs2/v7+2Z5TokQJateuDcCyHApwGoZBWFgYu3fvzjFhIFJc3REeTubf7r1paRz9\n/Xdb48mJw+Hgvf+OZsXqDdbP3nn7TZ4Of9bGqIqB4GAYPFgteEWkWFAyQGzR7IknyNwNfdjh4FAh\nrQ5IS0tj5MiRbHapGj192nTCOnUqlOv5lOBguyPwOrNmzQKgRYsWHr/20aNHOXzYmbCqWrXqZc+t\nUqUK4KyBcTaHbR7NmzcHYMqUKW6MUsT3BV1zDfeUL28d/55Ndw67maZJZGQk38X+aP1s4GsvEzFw\niH1BFRePPw733gulStkdiYhIoVMyQGzhX6oU7StXto7/WLTI7ddwOBy88847rHVJNHz44Yf8U0Xz\nJBunT59m1apVALZsHzlx4oQ1vrhw4MVcXz+QQwHOzArjK1as4Pjx426IUKToCAsNtcbrfvvNxkiy\n9/nnnxMVFWUdP/NUL8a8876NEYmISFGkZIDYJsyll++aP/5w69ymaTJp0iRiY2Otnw0dOpQXX3zR\nrdeRomPjxo2YpolhGNaTd086efKkNS6RUe08J66vnzlzJttzMlsSOhyOLAkxEYGwZ56xxqvi40lJ\nTLQxmqyio6OZOnWqdfzwww/z0SdT3VqsVEREBJQMKLCYmJgcP4x7A9M0+fLLL+0OI1sdXD6MrTl1\nipSEBLfN/cWc2cydO9c6fuaZZ3jjjTfcNn+RkZbmbDOYUbiuONu27UKBLjtaTbp+0M/tQ7+f34Vf\n3TnV28jshGCaJr976Z5oEbuEdOpEnYy6HOeBnYsX2xtQhqVLlzJu3DjruEOHDnz++ec51hCRQpaU\nZHcEIiKFSsmAK5ScnEzfvn1ZsGABZcuWzfLa1q1b6dOnDyEhIdSqVYuaNWvy1FNPZfmyURD5md8w\nDA4dOkTnzp05deqUW67vLjfcfTc3Z1RFTwJ2ummrwOJFC/j4k0+t4x49evDRRx/pqUp29u+H55+H\nnTvtjsR2rn8/cnsyXxhcf48k5fIB1PX14BxqP5QsWdIaa5uAyEUMg7A6dazDX3MoxulJq1ev5u23\n37aOW7Zsyddff23L76Nib/duaNoUWra0OxIRkUKlZMAViI+Pp3379gQEBGTJ4APMnTuXJk2asHPn\nTlatWsXu3btZvnw5W7ZsoVmzZswrYKGiK5n/pZdeonv37oSGhnLw4MECXd+tDIOON99sHf7y448F\nnjJu5Ure+7//s47bhLZk5syZeqqSk5o14ddfYehQuyOxXUpKijW24/+XG264wRrnttrItWig6/tc\nuX6ByKnIoEhxFtalizWO27HDxkjg999/5z8jX7dagd56660sXLjQlq4mAlSp4mwtuHEjeNPnJhER\nN1MyIJ8SEhIICwsjODiY8ePHZ3ktLi6OXr16UapUKaKjo609uzVq1GD+/Pn4+/vz2GOPsXHjxiu6\ndkHm79OnD126dOHee+/l3LlzV3T9whD2wAPWeHUBn05v3LiRN94YicPhPG7S4Ca+XbAkyxNSkZy4\nPmFPTk625frVqlUDyDVpl1k0sHr16jl+WXBNbugLhcil2jz3HEEZ4y3JyZzcs8eWOLZv387QwREk\npzgTAbVuqMSSJUu49tprbYlHgBIloG1bCAiAX36xOxoRkUKjZEA+9ezZk7179zJt2rQsy84dDge9\ne/cmJSWFZ5999pJq4BUqVCA8PJzExET69++f7+u6Y/5Ro0YB8OSTT+b7+oXl7n79CMwYb05O5tQV\nfhjbsWMHrw8dYH2Yql2jMotjf7pkC4dITiq7dLdIcGP9ivxom1FUc8eOHTnWAkhLS2NHxlPMe+65\nJ8e5XLcS2FEDQcTbXVWjBne5LwIXBgAAIABJREFU3CM2R0d7PIb9+/czeMDLnDvvTN5dX+FqYpfF\n2VLEVC4ybhycOAGdO9sdiYhIoVEyIB+mTZvGvHnzGDRokFWcK1NUVBQ7d+7EMAx69OiR7fszf756\n9WqWLl2ar2u7Y/6AgABGjhxJVFQUX3/9db6uX1jKVKuW5cPYlm+/zfccBw8eZODAAZxNuPBhKmbZ\nSipVquS2OKXoa9SoEeAsuHfo0CFbYnjwwQcBSExMzLHo38aNG62VCzn9LoCsdQJuueUWN0YpUnSE\nNW9ujdevX+/Rax87doyBr77AiVPnAShXthRLlv5E7dq1PRqH5KBWLdADBREp4pQMyKOkpCQGDx5M\nyZIlCQ8Pv+T1ORnV2IOCgmjatGm2czRt2pSAjIJ5s2fPztf13TV/t27dqFSpEhEREdbeRLt1vO02\na/zzunX5em98fDwRERHExzvbsl0dXJolS38iJCTErTEWeWvWwCuvwPff2x2JberUqWMl+fbYtFy4\nc+fO1KxZE9M0ic7hKWVm7/E6depw//335zhX5lYDwzBo7vKFR0Qu6NSrlzVecfgw6WlpHrnu6dOn\niYiI4OBRZ+HSUiUDWLh4KQ0bNvTI9UVEREDJgDybOnUqR44coU2bNtnuv129ejUAtWvXzrH4WIkS\nJayM/7J8Vi521/yGYRAWFsbu3bvznZAoLGH/+pc1XnnoEI48JinOnTvHwIEDrS89JUuWZP7C7/Rh\n6kp8/z188AG4tGMsbgzDoGvXrgD5qutx+PBha5x4mV7lp0+fJjQ0lODgYHr27JntuX5+fkRGRgIQ\nGRl5SSHB+Ph4Jk2alOW8nGzatAmAZs2aUbVq1Tz/eUSKkwb//CeVM7b8nTRN9rqhkG1uzp8/z6BB\ng9i7dy8AgYEBREfPp1WrVoV+bREREVdKBuTRrFmzAGjRosUlrx09etT6QpDbh+7MfYD79u3Lc4Vv\nd8+f+ZRwypQpebp+YWvUsycVMj6MHTNNDqxalet7UlJSeP3116290/7+/nzxxReEhoYWaqxFVseO\nzn8vWQI57FUvDp5++mkAVqxYkafzly1bZiXeTNNk/PjxOa64iY2NJS4ujoSEBGbPns17772X7Xmd\nOnVi4sSJnDx5km7dullbFvbv30/Xrl1JSEggMjLysvUCANasWQNA79698/RnESmOjMBAOrp05NgY\nE1Oo10tJSWHYsGFs3brVeX3D4PPP/0dYp06Fel0pgPh4yOfWThERX6FkQB6cPn2aVRlfUOvVq3fJ\n6ydOnLDGFxf2u5jr65kVwXPj7vlvvfVWwPmFxxv6j/sFBdHBJcnx++LFlz0/PT2dN98YwW+//Wb9\n7NNPP+UBl84Ekk9Nm8LAgfDRR3ZHYqvmzZvTrl07tm3bxubNm3M8b9KkSZQvX5727duTnp6OYRgY\nhsGgQYO4+uqr6ZiZXHHRqlUr6tevj5+fH4ZhXHZ/cr9+/Vi/fj1Vq1aldevW1K5dmzZt2hASEsK6\ndeuy3arkKjU1lUWLFlG5cmUrwSEi2evUoYM1Xr1lS6FdJz09ndGjR/Prr79aP/voo4945JFHCu2a\nUkCJiVCnDowfj9WqSESkCFEyIA82btyIaZoYhpFthd+TJ09aY9fe3tlxfT23XuKFNX9mS0KHw8Ha\ntWvzFENhC3N5yrnmMl/CTNPkw/f/y08r11g/++9//+tVHRJ8kr8/vP02dOoELl0yiqOxY8cSEBDA\n2LFjczynb9++HD9+HIfDQXp6uvWPw+Hg3LlzxGTzdLFKlSps2rSJtLQ03n33XauNYE4aN27M559/\nzvbt29m5cyc7duxg+vTpVqHDy5kxYwbx8fGMGzeOoKCgXM8XKc46PP88mb/1NiQkkHDsmNuvYZom\n77/7VpZVR2+99RbPPvus268lblSqFBw5At9+C376yCwiRY9+s+XBtm3brHF2LbpcWwwauXyR8nO5\nmeTUOqyw588skmaaZo4Vyz2tQ9++1njtmTMk5ZDImPrZx8xfFGsdv/rK80RERBR6fFJ8NGjQgGHD\nhjF9+nR+KaT+0kuXLuXxxx8vlLnj4+MZPnw4Tz75pNWdQERydl2jRtxWsiQADmDrFXS1uRzTNPn4\no3EsWnKhls+rr77KoEGD3HodKSQZhZlFRIoiJQPy4NSpU9Y4uyfzrr3sXXt7Z8f19eDg4Dxd393z\nl8z40AN4xTYBgMotW9Ig4wlmKrB9wYJLzon66gs+n/mFddzrnw/xznsf5pogEcmv4cOH0717d3r1\n6pXnFTx5NWbMGEJCQmjZsqVb5wXnap/evXvToEEDPvnkE7fPL0VXTEyM2/9fdyfTNPnyyy8Lbf5O\nLitufo6Lc+vcs2fO4Iu531jHTz3xGO+++67uXSIiYjslA/IgJSXFGmdXyf8Gl+JDuX2Yci3q5/q+\ny3H3/K4JjbwWMfSEji71GKZFRzNz5kx++uknUlNTiY2NYcLESdbr93Vsw2fTZmVZCSFupL2RzJw5\nk4YNG/Lwww9n+R1QEEOGDOHEiRNMmDDBLfO5Mk2T/v37U7p0aebNm5dj1xERV8nJyfTt25cFCxZk\nSTwDbN26lT59+hASEkKtWrWoWbMmTz31VJbVcgWRn/kNw+DQoUN07tw5S4LeXcIeftgar/j77zyv\n3MvNvG+j+fSzadZx9y5hfDx5hhIBIiLiFfRNKg9cn7AnJydn+3rm/t/MNnc5ySzqV7169WxbFOZ0\nfXfO7/rFJq8xFLb09HTiy5e3jn85fpzJkyczYsQIevTowZgxb1uvtWrRiLnRCwkMDLQj1KJt3jxo\n3BjeeMPuSGwXGBjI7Nmzufvuu+nevftl2wbm1eDBg3PsIlAQpmkSHh5OrVq1mDNnjuoESJ7Ex8fT\nvn17AgICGDduXJbX5s6dS5MmTdi5cyerVq1i9+7dLF++nC1bttCsWTPmzZtXoGtfyfwvvfQS3bt3\nJzQ0NNd7YX7d/swzXJ0xPpCeziE3bBFatmwZH3x44b/rPXe3ZNaX3xCgZee+58gR+OwzWLjQ7khE\nRNxKyYA8qFy5sjVOSEjI9py2bdsCsGPHjhyfKKSlpVmt8HJrC1aY87tuJciuBoKnpaen07NnT6Z+\n/322r587d876M9evW4v5i5dRunRpT4ZYfNSt6+woMHSo3ZF4jSFDhvDBBx/kWrwzL/K6NSi/DMNg\nwIABDBw4sFDml6InISGBsLAwgoODGT9+fJbX4uLi6NWrF6VKlSI6OtoqOlujRg3mz5+Pv78/jz32\nGBs3bryiaxdk/j59+tClSxfuvfdezp07d0XXz05A2bK0z6inA/D7/PkFmm/dunW89dZbVqfW5k3q\nEz0/Jss2PfEhsbHw9NPOrgIiIkWIkgF5kFm92zRNq+f3xTILdSUmJuZYlG/jxo3WyoIePXrkKwZ3\nzu9aJ+CWW27JVxyF4Z133uGLL77I/UTgge6PcO211xZyRMVY3bpwxx0qmHSROnXqeP2WlDp16tgd\ngviQnj17snfvXqZNm5ZlyXpm3YmUlBSeffbZS9rZVqhQgfDwcBITE+nfv3++r+uO+UeNGgXg9i4y\nYXffbY3XFqC47qZNmxg+fDjp6ekA1K93E4tjfyq0ZKB4QGa72OXLne0GRUSKCO/+dOsl6tSpY1Xg\n37NnT7bndO7cmZo1a2KaJtHR0dmeExUVZc13//335ysGd86fubzSMAyaN2+erzjcLTk5mQ8++CDP\n50+ZMsVt+7dFRIqjadOmMW/ePAYNGmTd2zJFRUWxc+dODMPIMamc+fPVq1ezdOnSfF3bHfMHBAQw\ncuRIoqKi+Prrr/N1/csJCw+3xmtOniTl/Pl8z7Fz504GDx5sJeZr1KhBTOwyr1iFJwVQsSL06wej\nR0Namt3RiIi4jZIBeWAYBl27dgXIcVmkn58fkZGRAERGRl5S6C8+Pp5JkyZlOS/T6dOnCQ0NJTg4\nmJ49e2a7N7kg819s06ZNADRr1oyqVate9tzCtnDhQo4ePZrn848ePcpC7dkTEbkiSUlJDB48mJIl\nSxLu8uU305w5cwAICgqiadOm2c7RtGlTa9/77Nmz83V9d83frVs3KlWqREREhPUEvqBuuOce6mVc\nNwn4K59bBQ4cOEBERIS1faFixYrExsbafp8VN4mMhFdfBa3wEJEiRMmAPHr66acBWLFiRY7ndOrU\niYkTJ3Ly5Em6detmbSnYv38/Xbt2JSEhgcjIyEv288fGxhIXF0dCQgKzZ8/OscDYlc5/sTVr1gDQ\nu3fvPP3ZC9OVVKV2VyVrycWuXeCmitoi4h2mTp3KkSNHaNOmTbYFZFevXg1A7dq1c+xIUaJECWrX\nrg04i+Tlh7vmNwyDsLAwdu/ene+ERI4Mg7C6da3DX3/8Mc9vPX78OANfe4GTJ08CzpbAS5Ys0fYd\nERHxakoG5FHz5s1p164d27ZtY/PmzTme169fP9avX0/VqlVp3bo1tWvXpk2bNoSEhLBu3bpsn8S0\natWK+vXr4+fnh2EYrF+/3q3zu0pNTWXRokVUrlzZSnCIXKJVK6hdG5R4ESlSZs2aBUCLFi0uee3o\n0aMcPnwYINen2VWqVAFg3759eW5R6+75M7e5TZkyJU/Xz4uwBx6wxnG7duXpPWfOnGHQay9w4LAz\nEVCyZAkWLFhA48aN3RaXiIhIYVCVsHwYO3YszZo1Y+zYsUyePDnH8xo3bsznn3+e53mrVKliLd1/\n//33rY4A7prf1YwZM4iPj2fu3Lle0X6srstTmMJ8j+RTSAisXg0xMXDzzXZHIyJucPr0aVatWgVA\nvXr1Lnn9xIkT1vjiwn4Xc339wIED3JyH3xPunv/WW28FnCv2jh8/TnmX9rRX6u7nnqPkmDEkAdtS\nUjixYwfX3XhjjucnJiYybNDL7NzrTHIE+Bt8NfcrQkNDCxyLiIhIYdPKgHxo0KABw4YNY/r06fzi\nhh7E2Vm6dCmPP/54ocwdHx/P8OHDefLJJ63uBHa7//77LylgdTkVK1bMd/FFuQIdO0KZMnDqlN2R\niIibbNy4EdM0MQzDevLuKnOJO5BrK03X1y+uYZMTd8+f2ZLQ4XCwdu3aPMWQm1JVq9L66qut403f\nfJPjuSkpKYwcFsEff+4GwDBg+rQZ3N+5s1tiES/011/QqxdcQScNERFvpGRAPg0fPpzu3bvTq1ev\nPH8AyqsxY8YQEhJCy5Yt3TovXGjn1KBBAz755BO3z3+lSpQowcsvv5zn81955RWvWNFQ5P3jHxAf\nD8OH2x2JiLiJa72V7Krbu7YYdB1nx7XVppnH2iLunj8zkWyaZo4td69E2O23W+P1P/+c7Tnp6emM\neXMU6365sG1w/Icf8M9//cttcYgXKl0aQkNh4EC7IxERcQslA67AzJkzadiwIQ8//LDb2twNGTKE\nEydOMGHCBLfM58o0Tfr370/p0qWZN29ejkWb7DJgwAAeeeSRXM975JFHiIiI8EBEQsmSoKSLSJFy\nymWlT3ZP5suWLWuNk5KSLjuX6+vBeayu7u75S5YsaY2PHz+epxjyotMTT1jjlUePkn5RKznTNBk7\ndiw//hRn/WzUyNd57oWX3BaDeKlq1SA8HGrUsDsSERG3UDLgCgQGBjJ79mzuvvtuunfvnm0rwPwa\nPHhwjl0ECsI0TcLDw6lVqxZz5szxyqfq/v7+zJw5kzFjxmS7ZaBiQABjxoxh5syZXpfIEBHxFa7J\n6+x+l95www3WOLeVb65F/Vzfdznunt81oZHXIoZ5Ue/hh8ksb3jaNJk4ejQ//fQTqampAHz66adZ\nWty+/NKLDBv+H7ddX0RExFNUQLAAhgwZwvbt23Pd+5gXeX2ykl+GYTBgwACvb2/k7+/PoEGD+Pe/\n/83ChQvZ9vvvMGoUdR0O7k9LI+iJJ0CJABGRK+Z6n0lOTs729WrVqrF//34OHjx42bkOHDgAQPXq\n1bNtUZjT9d05v2tyI68x5CY9PZ133nuPE35+4HAAEL18OdHLl3PNNddw4403Zun488QTT/B/74/N\ndduDiIiIN9LKgAKqU6dOlr2N3sgrEwEHF4Mj7ZIfBwUF0b17dwaNGMGg1q3pDgQBLF3q6QgFYN8+\nmDwZ3LgEV0TsUblyZWuckJCQ7Tlt27YFYMeOHTnu1U9LS7O63txzzz35isGd87tuJciuBkJ+paen\n07NnT4YMGUJSRiLA1cmTJ7MkAh544AEmT57s9Z8BpJCkpDj/ERHxYbqDieftnAo/3gcrH4LLFZ7q\n2PHCOCam8OOSSw0eDD/8AG5cgisi9mjUqBHg3D526NChbM/J7DSTmJiYY1G+jRs3WisLevToka8Y\n3Dm/a52AW265JV9xZOedd97hiy++yNO5tWrV4osvviAgQAssi6URI+C66+Ay3SZERHyBkgHiWfvn\nwbpnnONK7Zy9mHJycTIgmyc1UshmznT+U6uW3ZGISAHVqVPHqsuyZ8+ebM/p3LkzNWvWxDRNoqOj\nsz0nKirKmi+/rV7dOX/mVgPDMGjevHm+4rhYcnIyH3zwQZ7PP3funFYEFGelS8O5c7Bkid2RiIgU\niO5k4jlHV0DcI2Cmwy3DoO6Llz+/SRMoXz7jvUfBja2jRESKG8Mw6Nq1K+B8+p4dPz8/IiMjAYiM\njLyk0F98fDyTJk3Kcl6m06dPExoaSnBwMD179sy2uG5B5r/Ypk2bAGjWrBlVq1a97Lm5WbhwIUeP\nHs3z+ceOHctSRFCKmbAw579d2nWKiPgiJQPEM05vgeVdID0JbgyHhqNyf4+fH3TocOFYWwVERArk\n6aefBmDFihU5ntOpUycmTpzIyZMn6datm7WlYP/+/XTt2pWEhAQiIyMv2c8fGxtLXFwcCQkJzJ49\nO8cOOVc6/8XWrFkDQO/evfP0Z7+cbVfwpe5K3iNFRKNGzkTAZf4eiYj4AiUDxDNKV4Nrm0H1HnBb\n5OW3B7hS3QAREbdp3rw57dq1Y9u2bWzevDnH8/r168f69eupWrUqrVu3pnbt2rRp04aQkBDWrVtH\neHj4Je9p1aoV9evXx8/PD8MwshTbc8f8rlJTU1m0aBGVK1e2EhwiHmMYcNNNef8sIyLipVT5Rjwj\nsCy0WQSY4JePFoGuKwNWrIDz55179cRz4uNh2jTnv0ePtjsaESmgsWPH0qxZM8aOHcvkyZNzPK9x\n48Z8/vnneZ63SpUq1tL9999/3+oI4K75Xc2YMYP4+Hjmzp1LUFDQFc3hqm7duh55j4iIiDcxcmrt\n4w0MwzC9OT7xkFtvhcwnWIsXQ6dO9sZT3Bw9CpUqQcmSzoRAqVJ2RyQ+yDAMTNP0+cdoReW+NGrU\nKN544w3Wrl1L06ZN3T7/fffdx/Dhw2nZsqXb546Pj6dBgwZ06tSJzz77zC1zJicnc8MNN+S5bkDF\nihX5+++/3ZKIEBF7FJX7kkhBaJuAeL/MQj2gyr12qFjRWcwxKQlWrrQ7GhFxg+HDh9O9e3d69ep1\nSRG/ghozZgwhISGFkghwOBz07t2bBg0a8Mknn7ht3hIlSvDyyy/n+fxXXnlFiQCB9HRYswb++svu\nSEREroiSAeJ+jnTYOhbSk90zn+oG2O+11+CTT5xFk0SkSJg5cyYNGzbk4YcfJiUlxS1zDhkyhBMn\nTjBhwgS3zOfKNE369+9P6dKlmTdvHv7++dhylgcDIiJ45JFHcj3vkUceISIiwq3XFh81ejSEh8PW\nrXZHIiJyRbRNQNzLNGF9X9jxibNYYGhUwec8fx6uvRaSM5ILf/8N1aoVfF4R8ZiishyzKN6X3nrr\nLeLi4vjqq68oVcBtQGfPniU4ONhNkV1gmibh4eHceOONDBw40O3zc34/LH+A9KbjeXfqCsaOHXvJ\nloGKwCtt2xIRG+v2RIT4KIfD2flIfFJRuS+JFISSAeJeG1+HzaPBvyS0jYWKd7ln3g4dYOlS53jK\nFHjySffMKyIeUVQ+dBXV+9L27dupXbs2fl78xWb79u3UqVPH/RMnHYelreHMn3B9e2gbQ0pqKgsX\nLnS2D9y0ibozZ3I/EHTbbXCZLgki4juKyn1JpCCUDBD32TYONrwEhj+ERkO1Lu6b+913YcAA5/jR\nR2H2bPfNLSKFrqh86NJ9qYhJPQvf3wPx6+HqW6H9cihxbdZzTp2C8uWd+8MNA44cgQoV7IlXRNym\nqNyXRArCex8BiG85+J0zEQBw+2fuTQRA1roBsbHOD2ViD30REpGiID0JfurmTASUqQVtl1yaCAAo\nVw5uv905Nk3nPUhERKQIUDJA3KPi3VC1CzR+B0KecP/8DRs629sBnDgBv/7q/mvI5Z05A126wE03\nKSEgIr7v2Eo4+iOUvB7axULpKjmfq642khPTdBY3HjgQUlPtjkZEJF+0TUDcx5EOfoVYVOnxx+Hz\nz53jN9+EIUMK71pyKdOE6Gho3dq5ZFYkH4rKckzdl4qYv7+Bq0LgmoaXP2/dugurA66/Hg4edG4Z\nEAGoW9fZXnDFCrjLTbWSpNAVlfuSSEFoZYC4T2EmAkAtBu1mGNCjhxIBIlJ0VO+WeyIAoFkzZ1cb\ngMOH4fffCzcu8S2ZK0e0akREfIySAeI72re/MF61Cs6etS8WEREpPvz9nV1tMn33nX2xiPd56CF4\n8UXo1MnuSERE8kXJAMm/5BOw/nlIS/Dsda+/Hho1co5TU2H5cs9eX0REfFdyfMHer7oBkpPWreHD\nD+HOO+2OREQkX5QMkPxJS4Af74ftE+HnFzx/fX0Y8w5nz8LRo3ZHISKSN3vmwLxacOSHK5/D9f6z\nciWcO1fwuERERGykZIDkXXoKrHgQTqyFMjWg4WjPx6C6Afb79FO47joYM8buSEREcnfwO1jdC1LP\nwIn1Vz5PlSrQoIFznJoKP/7olvBERETsomSA5I3pgDVPwqElUKICtI25fBumwnLnnVCqlHP811+w\nZ4/nYyjubr7Z+UFYKzNExNsdi4MVPcBMg3qvQb2Igs3nujpAdQNERMTHKRkgebPjU9g7CwKugraL\noexN9sRRsiTcffeF49hYe+Iozlq2hLJlISgIEjxcN0JEJK9ObnRua0tPhJCnoPE7BW8HqK1qcjnv\nvQdNm6rbhIj4DCUDJG9CnoRaT0Drb+DaZvbGoq0C9goMhL//ht9+gzJl7I5GRCR753ZC+nmo3gNa\nfFzwRAA4e8hnrk7bsQN27Sr4nFJ01KrlLCRYr57dkYiI5IlhmqbdMeTIMAzTm+MTm2zeDLfe6hyX\nKwfHjkFAgL0xichlGYaBaZpu+DZmL92XfMyx1XBtU/Av4b45778fFi1yjiMjoV8/980tIh5TVO5L\nIgWhlQHie+rXh6pVneNTp+Dnn+2NR0REvFOFO9ybCADVDRARkSJDyQDxPYahrQIiImIP12TAsmWQ\nkmJfLCIiIgWgZIBcKv5X+LEzpJyyO5KcKRlgv8REZwGtpUvtjkREirv0ZOe9yxNuuglq1HCOz52D\n1as9c13xLadP2x2BiEiulAyQrM7ugB87wcGFsOUdu6PJWfv2F4pBrVmjm64dYmJg9Gg4fNjuSESk\nOHOkw6p/QWwrOLi48K9nGNCp04VjdRUQV3v2OBNGLVrYHYmISK6UDJALEg/Bso6QdBSu7wANRtod\nUc7Kl3e27wFIT4cffrA3nuKoa1dYsQL+9S+7IxGR4so0YX1f+Psr8AuCUpU9c13VDZCcVKsGR4/C\nX385EwMiIl5MyQBxSjkFP3SChN1wbXMIjQL/ILujujz1exYRKd5+GwQ7J4N/Sbh7AVzT2DPXbdcO\n/P2d419/hSNHPHNd8X4BAXDPPVC6tLP7kYiIF1MyQJy2jYNTv0PwTdBmIQQG2x1R7lQ3QESk+Nry\nLvz5DhgBcNdXUDHUc9e++mq4444Lx7Gxnru2eL8JE+DECWcbShERL6ZkgDjdMhTqD4J2MVCygt3R\n5M0dd0CZMs7xrl2wc6e98YiIiOdcXQ/8S8Md06GqDV+6VDdAclK5MpQsaXcUIiK5UjJAnPz8ofE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       "text": [
        "<matplotlib.figure.Figure at 0x1113955f8>"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As the absolute value of the bias voltage $|V|$ increases ($V$ becomes more negative), the triangular regions grow and even overlap."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The dimensions of the triangles $\\delta V_{g1}$ and $\\delta V_{g2}$ are defined by the following equations:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{align}\n",
      "\\mu_1 (N_1, N_2; V_{g1}+\\delta V_{g1}, V_{g2}) = \\mu_1 (N_1, N_2; V_{g1}, V_{g2}) + |e|V\n",
      "\\end{align}"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dVg1 = solve(mu1(N1, N2, Vg1+delta, Vg2) - mu1(N1, N2, Vg1, Vg2) - e*V, delta)[0].subs(EC1, e**2/C1)\n",
      "deltaVg1 = Symbol(\"{\\delta} V_g1\")\n",
      "Eq(deltaVg1, dVg1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$${\\delta} V_{g1} = - \\frac{C_{1} V}{C_{g1}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAAwBAMAAADKnbiZAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAElFTkSuQmCC\n",
       "prompt_number": 46,
       "text": [
        "                -C\u2081\u22c5V \n",
        "{\\delta} V_g1 = \u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                 C_g1 "
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{align}\n",
      "\\mu_2(N_1, N_2; V_{g1}, V_{g2}+\\delta V_{g2}) = \\mu_2 (N_1, N_2; V_{g1}, V_{g2}) + |e|V\n",
      "\\end{align}"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dVg2 = solve(mu2(N1, N2, Vg1, Vg2+delta) - mu2(N1, N2, Vg1, Vg2) - e*V, delta)[0].subs(EC2, e**2/C2)\n",
      "deltaVg2 = Symbol(\"{\\delta} V_g2\")\n",
      "Eq(deltaVg2, dVg2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$${\\delta} V_{g2} = - \\frac{C_{2} V}{C_{g2}}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAH8AAAAwBAMAAADKnbiZAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
       "prompt_number": 47,
       "text": [
        "                -C\u2082\u22c5V \n",
        "{\\delta} V_g2 = \u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                 C_g2 "
       ]
      }
     ],
     "prompt_number": 47
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Introducing the conversion factors between the gate voltage and energy \n",
      "\\begin{align}\n",
      "\\alpha_1 = \\frac{C_{g1}}{C_2} |e|,\\quad \\alpha_2 = \\frac{C_{g2}}{C_2} |e|,\n",
      "\\end{align}\n",
      "the equalities can be expressed as:\n",
      "\\begin{align}\n",
      "\\alpha_1 \\delta V_{g1} = \\alpha_2 \\delta V_{g2} = |eV|.\n",
      "\\end{align}"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "B. Quantized States"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(6, 6))\n",
      "\n",
      "n1, n2 = 1, 0\n",
      "ECm_EC = 0.3\n",
      "Vbias = -0.4\n",
      "\n",
      "subs_dic = {Cg1: 1, Cg2: 1, EC1: 1, EC2: 1, ECm: ECm_EC, e: 1, V: Vbias}\n",
      "mumu1 = mu1(N1, N2, Vg1, Vg2).subs(subs_dic); mumu2 = mu2(N1, N2, Vg1, Vg2).subs(subs_dic)        \n",
      "mumuL = muL(V).subs(subs_dic)\n",
      "\n",
      "sol=[]\n",
      "# Getting lines forming a honeycomb\n",
      "\"\"\"\n",
      "electrochemical potential conditions:\n",
      "\"\"\"\n",
      "sol.append(solve(mumu1.subs({N1:n1+1, N2:n2}), Vg2)[0])   #(0,0) --> (1,0)\n",
      "sol.append(solve(mumu2.subs({N1:n1, N2:n2+1}), Vg2)[0])   #(0,0) --> (0,1)\n",
      "sol.append(solve(mumu1.subs({N1:n1+1, N2:n2+1}), Vg2)[0])   #(0,1) --> (1,1)\n",
      "sol.append(solve(mumu2.subs({N1:n1+1, N2:n2+1}), Vg2)[0])   #(1,0) --> (1,1)\n",
      "\n",
      "sol.append(solve(mumu1.subs({N1:n1+1, N2:n2}) - mumuL, Vg2)[0])\n",
      "sol.append(solve(mumu1.subs({N1:n1+1, N2:n2+1}) - mumuL, Vg2)[0])\n",
      "\n",
      "dE1, dE2 = 0.2, 0.14\n",
      "\n",
      "sol.append(solve(mumu2.subs({N1:n1, N2:n2+1})\n",
      "            -mumu1.subs({N1:n1+1, N2:n2}), Vg2)[0]) # G1-G2\n",
      "sol.append(solve(mumu2.subs({N1:n1, N2:n2+1})+dE2\n",
      "            -mumu1.subs({N1:n1+1, N2:n2}), Vg2)[0])  # G1-X2\n",
      "sol.append(solve(mumu2.subs({N1:n1, N2:n2+1})\n",
      "            -mumu1.subs({N1:n1+1, N2:n2})+dE1, Vg2)[0]) # X1-G2\n",
      "sol.append(solve(mumu2.subs({N1:n1, N2:n2+1})+dE2\n",
      "            -mumu1.subs({N1:n1+1, N2:n2})+dE1, Vg2)[0]) # X1-X2\n",
      "\n",
      "funcs = [lambdify([Vg1], sol[idx], 'numpy') for idx in range(10)]\n",
      "\n",
      "\n",
      "# Getting the coordinates of triple points\n",
      "elec_x, elec_y, hole_x, hole_y = [], [], [], []\n",
      "\"\"\"\n",
      "intersection of sol[0] and sol[6] corresponds to the electron-like triple point (linear transport regime)\n",
      "\"\"\"\n",
      "elec_x.append(solve(sol[0]-sol[6], Vg1)[0]); elec_y.append(sol[0].subs(Vg1, elec_x[0]))\n",
      "\"\"\"\n",
      "intersection of sol[2] and sol[6] corresponds to the hole-like triple point (linear transport regime)\n",
      "\"\"\"\n",
      "hole_x.append(solve(sol[2]-sol[6], Vg1)[0]); hole_y.append(sol[2].subs(Vg1, hole_x[0]))\n",
      "\"\"\"\n",
      "Other electron-like and hole-like triple points generated in the non-linear transport regime\n",
      "\"\"\"\n",
      "elec_x.append(solve(sol[4]-sol[6], Vg1)[0]); elec_y.append(sol[4].subs(Vg1, elec_x[1]))\n",
      "elec_x.append(solve(sol[4]-sol[1], Vg1)[0]); elec_y.append(sol[4].subs(Vg1, elec_x[2]))\n",
      "hole_x.append(solve(sol[5]-sol[6], Vg1)[0]); hole_y.append(sol[5].subs(Vg1, hole_x[1]))\n",
      "hole_x.append(solve(sol[5]-sol[3], Vg1)[0]); hole_y.append(sol[5].subs(Vg1, hole_x[2]))\n",
      "\n",
      "s_list = [300, 100, 100]\n",
      "\n",
      "for idx in range(3):\n",
      "    ax.scatter(elec_x[idx], elec_y[idx], zorder=10, s=s_list[idx], c='black', lw=3)\n",
      "    ax.scatter(hole_x[idx], hole_y[idx], zorder=10, s=s_list[idx], c='white', lw=3)\n",
      "\n",
      "x_vecs = []\n",
      "\n",
      "x_vecs.append(np.arange(elec_x[0], elec_x[0]+1, 0.001))\n",
      "x_vecs.append(np.arange(elec_x[2]-1, elec_x[0], 0.001))\n",
      "x_vecs.append(np.arange(hole_x[0]-1, hole_x[0], 0.001))\n",
      "x_vecs.append(np.arange(hole_x[0], hole_x[0]+1, 0.001))\n",
      "x_vecs.append(np.arange(elec_x[2]-1, hole_x[0]+1, 0.001))\n",
      "x_vecs.append(np.arange(elec_x[2], elec_x[2]+1, 0.001))\n",
      "x_vecs.append(np.arange(hole_x[1]-1, hole_x[1], 0.001))\n",
      "\n",
      "label_list = [r'$\\mu_1 (1,0)=0$', r'$\\mu_2 (0,1)=0$', r'$\\mu_1 (1,1)=0$', r'$\\mu_2 (1,1)=0$', \n",
      "                r'$\\mu_1(1,0)=-|e|V$', r'$\\mu_1(1,1)=-|e|V$', r'$\\mu_1(1,0)=\\mu_2(0,1)$']\n",
      "ls_list = ['-.', '-', '-.', '-', '--', '-', '-']; lw_list = [2, 3, 2, 3, 3, 3, 2]\n",
      "color_list = ['red', 'green', 'magenta', 'blue', 'red', 'magenta', 'orange']\n",
      "\n",
      "for idx in range(7):\n",
      "    ax.plot(x_vecs[idx], (funcs[idx])(x_vecs[idx]), ls = ls_list[idx],\n",
      "            label=label_list[idx], lw=lw_list[idx], color = color_list[idx])\n",
      "\n",
      "xvecs_quant = [[],[]]\n",
      "\n",
      "#xvecs_quant[0].append(np.arange(elec_x[1], hole_x[0], 0.001)) # G1-G2\n",
      "for idx in range(6, 10): # G1-X2, X1-G2, X1-X2\n",
      "    xvecs_quant[0].append(np.arange(solve(sol[4]-sol[idx], Vg1)[0], solve(sol[1]-sol[idx], Vg1)[0], 0.001))\n",
      "    \n",
      "#xvecs_quant[1].append(np.arange(elec_x[1], hole_x[0], 0.001)) # G1-G2\n",
      "for idx in range(6, 10): # G1-X2, X1-G2, X1-X2\n",
      "    xvecs_quant[1].append(np.arange(solve(sol[5]-sol[idx], Vg1)[0], solve(sol[3]-sol[idx], Vg1)[0], 0.001))\n",
      "    \n",
      "color_list_quant = ['#092b4c', '#0c3966', '#0f487f', '#125699']\n",
      "label_list_quant = [r'$G_1 - G_2$', r'$G_1 - X_2$', r'$X_1 - G_2$', r'$X_1 - X_2$']\n",
      "\n",
      "for i in range(2):\n",
      "    for idx in range(6, 10):\n",
      "        idx_ = idx-6\n",
      "        ax.plot(xvecs_quant[i][idx_], funcs[idx](xvecs_quant[i][idx_]), lw=6, zorder=9,\n",
      "                color=color_list_quant[idx_], label=(label_list_quant[idx_] if i==0 else None))\n",
      "    \n",
      "xvec_t1 = np.arange(elec_x[2], elec_x[0], 0.001, dtype=float)\n",
      "xvec_t2 = np.arange(hole_x[2], hole_x[0], 0.001, dtype=float)\n",
      "\n",
      "lower_t1 = np.maximum(funcs[6](xvec_t1), funcs[4](xvec_t1)); upper_t1 = funcs[1](xvec_t1)\n",
      "lower_t2 = np.maximum(funcs[6](xvec_t2), funcs[5](xvec_t2)); upper_t2 = funcs[3](xvec_t2)\n",
      "\n",
      "ax.plot(xvec_t1, lower_t1, ls='-', color='black', lw=3)\n",
      "ax.plot(xvec_t1, upper_t1, ls='-', color='black', lw=3)\n",
      "ax.fill_between(xvec_t1, lower_t1, upper_t1, color='gray', alpha=0.5)\n",
      "\n",
      "ax.plot(xvec_t2, lower_t2, ls='-', color='black', lw=3)\n",
      "ax.plot(xvec_t2, upper_t2, ls='-', color='black', lw=3)\n",
      "ax.fill_between(xvec_t2, lower_t2, upper_t2, color='gray', alpha=0.5)\n",
      "\n",
      "xvec_d = np.arange(elec_x[0], hole_x[0], 0.001)\n",
      "ax.plot(xvec_d, funcs[6](xvec_d), ls='-', color='black', lw=3)\n",
      "\n",
      "#marking the charge states\n",
      "ax.text(elec_x[1]-0.3, elec_y[1], r\"$(%d, %d)$\" % (n1, n2), fontsize=30, color=\"black\")\n",
      "ax.text(elec_x[0]+0.25, elec_y[0]-0.2, r\"$(%d, %d)$\" % (n1+1, n2), fontsize=30, color=\"black\")\n",
      "ax.text(hole_x[2]-0.3, hole_y[2]+0.1, r\"$(%d, %d)$\"% (n1, n2+1), fontsize=30, color=\"black\")\n",
      "ax.text(hole_x[0]+0.05, hole_y[0]+0.2, r\"$(%d, %d)$\"% (n1+1, n2+1), fontsize=30, color=\"black\")\n",
      "\n",
      "ax.set_xlabel(r'$V_{g1}$', labelpad=10)\n",
      "ax.set_ylabel(r'$V_{g2}$', labelpad=10)\n",
      "ax.set_xlim([float(elec_x[2])-0.3, float(hole_x[0])+0.3])\n",
      "ax.set_ylim([float(elec_y[1])-0.2, float(hole_y[2])+0.3])\n",
      "ax.set_xticks([]); ax.set_yticks([])\n",
      "\n",
      "ax.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0., fontsize=16)\n",
      "fig.tight_layout();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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j999/5+677zbaeQ3t/9lnn+XRRx/lkUceQS43cMaxqDdlWeSAZc5NFdqo9PR03N3diY6O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KS6z2KqVwth0YzJdG7voz1GVwEdnOMsYJ1vprnM009DWBisX2/ThOVDRkYGEydOpFq1asTExBS6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\n5p09G/r1c5zSVJsgE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       "text": [
        "<matplotlib.figure.Figure at 0x10fb1aa20>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Version Information"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%reload_ext version_information\n",
      "\n",
      "%version_information numpy, matplotlib, sympy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.4.1 (default, Sep 20 2014, 19:44:17) [GCC 4.2.1 Compatible Apple LLVM 5.1 (clang-503.0.40)]</td></tr><tr><td>IPython</td><td>2.3.0</td></tr><tr><td>OS</td><td>posix [darwin]</td></tr><tr><td>numpy</td><td>1.9.0</td></tr><tr><td>matplotlib</td><td>1.4.0</td></tr><tr><td>sympy</td><td>0.7.5-git</td></tr><tr><td colspan='2'>Tue Oct 07 16:20:06 2014 JST</td></tr></table>"
       ],
       "json": [
        "{\"Software versions\": [{\"version\": \"3.4.1 (default, Sep 20 2014, 19:44:17) [GCC 4.2.1 Compatible Apple LLVM 5.1 (clang-503.0.40)]\", \"module\": \"Python\"}, {\"version\": \"2.3.0\", \"module\": \"IPython\"}, {\"version\": \"posix [darwin]\", \"module\": \"OS\"}, {\"version\": \"1.9.0\", \"module\": \"numpy\"}, {\"version\": \"1.4.0\", \"module\": \"matplotlib\"}, {\"version\": \"0.7.5-git\", \"module\": \"sympy\"}]}"
       ],
       "latex": [
        "\\begin{tabular}{|l|l|}\\hline\n",
        "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
        "Python & 3.4.1 (default, Sep 20 2014, 19:44:17) [GCC 4.2.1 Compatible Apple LLVM 5.1 (clang-503.0.40)] \\\\ \\hline\n",
        "IPython & 2.3.0 \\\\ \\hline\n",
        "OS & posix [darwin] \\\\ \\hline\n",
        "numpy & 1.9.0 \\\\ \\hline\n",
        "matplotlib & 1.4.0 \\\\ \\hline\n",
        "sympy & 0.7.5-git \\\\ \\hline\n",
        "\\hline \\multicolumn{2}{|l|}{Tue Oct 07 16:20:06 2014 JST} \\\\ \\hline\n",
        "\\end{tabular}\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "Software versions\n",
        "Python 3.4.1 (default, Sep 20 2014, 19:44:17) [GCC 4.2.1 Compatible Apple LLVM 5.1 (clang-503.0.40)]\n",
        "IPython 2.3.0\n",
        "OS posix [darwin]\n",
        "numpy 1.9.0\n",
        "matplotlib 1.4.0\n",
        "sympy 0.7.5-git\n",
        "<tr><td colspan='2'>Tue Oct 07 16:20:06 2014 JST</td></tr>"
       ]
      }
     ],
     "prompt_number": 1
    }
   ],
   "metadata": {}
  }
 ]
}