IBMQuantumChallenge.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Playing with the IBM Quantum Challenge\n",
    "\n",
    "For 4 days last June, IBM put out a set of 4 Quantum Computing problems as part of its (annual?) Quantum Challenge. These ranged from basic problems to one problem which was challenging, even to the experts --according to the IBM team.\n",
    "\n",
    "I took Problem 4 as an opportunity to develop more intuition about quantum circuits. In that problem, a 16-by-16 unitary matrix, $U$, was provided, and participants were asked to find the quantum circuit which reproduces it with some fidelity. Furthermore, the contestants were asked to minimize the number of gates in the solution circuit, by minimizing a cost function\n",
    "\n",
    "$cost = n_{u3} + 10 n_{cx}$\n",
    "\n",
    "where $n_{u3}$ is the number of U3 gates (simple 1-qubit rotations) and $n_{cx}$ the number of CNOT gates. These were the only two gates allowed, reflecting the hardware restrictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from unitary2circuit import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First order of business was to look at the matrix $U$, in search of patterns and symmetries. I vizualized the real and imaginary parts of the matrix representation of $U$, as seen below.\n",
    "\n",
    "Looking at the numerical values of each element, it became clear that there are many symmetries:\n",
    "- The matrix is symmetric about the diagonal\n",
    "- The matrix is symmetric about the \"other diagonal\"\n",
    "- There is a repetition of 2x2, 4x4 and 8x8 sub-matrices if we look along the two diagonal directions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f40036f2ac8>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.figure(figsize=(15,10))\n",
    "pl.subplot(121)\n",
    "pl.imshow(uu.real)\n",
    "pl.subplot(122)\n",
    "pl.imshow(uu.imag)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The repitition is expected due to how tensor operations work. If operator $\\mathbf{A}$ is acting on qubit 1, and $\\mathbf{B}$ on qubit 2, then the overall matrix on this 2-qubit system is : \n",
    "\n",
    "$A \\otimes B = \n",
    "\\begin{pmatrix}\n",
    "A_{11}\\mathbf{B} & A_{12}\\mathbf{B} \\\\\n",
    "A_{21}\\mathbf{B} & A_{22}\\mathbf{B} \n",
    "\\end{pmatrix} = \n",
    "\\begin{pmatrix}\n",
    "A_{11}\\begin{pmatrix}B_{11} & B_{12} \\\\ B_{21} & B_{22}\\end{pmatrix} & \n",
    "A_{12}\\begin{pmatrix}B_{11} & B_{12} \\\\ B_{21} & B_{22}\\end{pmatrix} \\\\\n",
    "A_{21}\\begin{pmatrix}B_{11} & B_{12} \\\\ B_{21} & B_{22}\\end{pmatrix} & \n",
    "A_{22}\\begin{pmatrix}B_{11} & B_{12} \\\\ B_{21} & B_{22}\\end{pmatrix} \n",
    "\\end{pmatrix}\n",
    "$,\n",
    "\n",
    "which is a 4-by-4 matrix. So one can see how $\\mathbf{B}$ is repeated, and how the elements of $\\mathbf{A}$ are factors of larger 2-by-2 blocks in the product matrix.\n",
    "\n",
    "Now, in addition there are those two symmetries about each of the two diagonals of the matrix. This suggested that if we tensor multiply together matrices of the form $\\begin{pmatrix}a & b \\\\ b & a\\end{pmatrix}$, then we might obtain a matrix with the above symmetries. I checked and indeed it does. My initial hypothesis was to see if only four gates of this form --one on each qubit-- can reproduce this matrix. Such circuit will surely correspond to a matrix satisfying the above three bullet points. But will it be able to replicate the matrix $U$?\n",
    "\n",
    "\n",
    "\n",
    "So what does a unitary matrix of the above form look like? In general, and up to an overall phase, any unitary matrix can be paramatrized as \n",
    "\n",
    "$\n",
    "U_{gen} = \n",
    "\\begin{pmatrix}\n",
    "\\cos{\\frac{\\theta}{2}}            & -e^{i \\phi} \\sin{\\frac{\\theta}{2}} \\\\ \n",
    "e^{i \\lambda} \\sin{\\frac{\\theta}{2}} & e^{i(\\phi+\\lambda)} \\cos{\\frac{\\theta}{2}} \\end{pmatrix}$\n",
    "\n",
    "Imposing the above diagonal symmetries, this simplifies to a form depending on only one parameter, $\\theta$:\n",
    "\n",
    "$\n",
    "U_{sym} = \n",
    "\\begin{pmatrix}\n",
    "\\cos{\\frac{\\theta}{2}}   & i \\sin{\\frac{\\theta}{2}} \\\\ \n",
    "i \\sin{\\frac{\\theta}{2}} & \\cos{\\frac{\\theta}{2}} \\end{pmatrix}$\n",
    "\n",
    "This is simply an X rotation, sometimes denoted $R_X(\\theta)$. Therefore, our four gates would only depend on four independent angles, one for each gate, and so optimizing over a four-dimensional parameter space wouldn't be that hard.\n",
    "\n",
    "In fact, what's more intersting, if we divide the matrix $U$ in 2x2 adjacent matrices, then any of these are either proportional to $U_{22}$ or to $XU_{22}$, where $U_{22}$ is the matrix formed by the first 2 rows and first 2 columns of $U$, and $X$ is the Pauli X matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U22 = \n",
      "[[-0.21338835+0.33838835j -0.14016504-0.08838835j]\n",
      " [-0.14016504-0.08838835j -0.21338835+0.33838835j]]\n",
      "\n",
      "The adjacent 2x2 matrix is proportional to U22\n",
      "[[-0.47140453-0.33333333j -0.47140453-0.33333335j]\n",
      " [-0.47140453-0.33333335j -0.47140453-0.33333333j]]\n"
     ]
    }
   ],
   "source": [
    "print('U22 = ')\n",
    "print(uu[0:2,0:2])\n",
    "print()\n",
    "print('The adjacent 2x2 matrix is proportional to U22')\n",
    "print(uu[0:2,2:4] / uu[0:2,0:2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XU22 causes the elements to rotate around the matrix\n",
      "[[-0.14016504-0.08838835j -0.21338835+0.33838835j]\n",
      " [-0.21338835+0.33838835j -0.14016504-0.08838835j]]\n",
      "\n",
      "The 2x2 matrix starting at the 5th element is proportional to XU22:\n",
      "[[-0.33333335+0.47140453j -0.33333333+0.47140453j]\n",
      " [-0.33333333+0.47140453j -0.33333335+0.47140453j]]\n"
     ]
    }
   ],
   "source": [
    "print('XU22 causes the elements to rotate around the matrix')\n",
    "print(X @ uu[0:2,0:2]) \n",
    "print()\n",
    "print('The 2x2 matrix starting at the 5th element is proportional to XU22:')\n",
    "print(uu[4:6,0:2] / (X @ uu[0:2,0:2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If I make a mozaic of $U_{22}$ and $XU_{22}$ matrices and divide $U$ by that mosaic, I get the matrix below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plu() plots the input matrix's element norms, and adds the phase (in degrees) as text\n",
    "pl.figure(figsize=(15,10))\n",
    "pl.subplot(121)\n",
    "plu(uu)\n",
    "pl.subplot(122)\n",
    "plu(uu / compru(uu[0:2, 0:2])) # compru makes the mosaic of U22 and XU22 matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This means that there are much fewer independent numbers that describe this matrix than the 256 elements in it! This further reinforces the idea that perhaps it is represented by a very small circuit. \n",
    "\n",
    "So I set out to solve this optimization problem of four gates with one independent angles each. I used the *differential_evolution()* function in the *optimize* package in SciPy. This function does a better job than others in sampling the parameters space, and is less likely to get stuck in the nearest local minimum of the cost function.\n",
    "\n",
    "Below, I run the *opt4gates()* function I wrote to implement this optimization. After it finishes, it plots a histogram and image representation of $Re(U_{circ})/Re(U)$ where $U_{circ}$ is the calculated circuit's unitary. And it does the same for the imaginary parts of the two matrices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/tyk/mysoft/anaconda3/envs/env_qiskit/lib/python3.6/site-packages/scipy/optimize/_differentialevolution.py:461: UserWarning: differential_evolution: the 'workers' keyword has overridden updating='immediate' to updating='deferred'\n",
      "  \" updating='deferred'\", UserWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x1080 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.figure(figsize=(15,15))\n",
    "res, uc = opt4gates()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way to look at this, and to also take into account any overall phase shift between the two matrices is to plot the ratio of the two matrices, and plot the magnitudes (as colors) and the difference in their phase (as labels on each element.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$|U_{circ}|/|U|$ as colors, and phase difference as labels')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.figure(figsize=(10,10))\n",
    "\n",
    "plu(uc/uu)\n",
    "pl.title(r'$|U_{circ}|/|U|$ as colors, and phase difference as labels')\n",
    "\n",
    "#pl.subplot(222)\n",
    "#pl.imshow(uc.real/uu.real)\n",
    "#pl.title(r'Re($U_{circ}$)/Re($U$)')\n",
    "\n",
    "#pl.subplot(223)\n",
    "#pl.imshow(np.abs(uc)/np.abs(uu), vmin=0)\n",
    "#pl.title(r'|$U_{circ}$|/|$U$|')\n",
    "\n",
    "#pl.subplot(224)\n",
    "#pl.imshow((np.angle(uc)-np.angle(uu))/pi, vmin=-1, vmax=1)\n",
    "#pl.title(r'(Phase($U_{circ}$)-Phase($U$))/2$\\pi$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In an interactive environment, it would be possible to hover over the figure and read the pixel values, corresponding to entries in the matrix. In this Jupyter notebook, I will instead print the ranges of the ratio images:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum ratio of magnitudes =  3.36566314483488\n",
      "Minimum ratio of magnitudes =  0.09895486554899799\n",
      "Maximum phase difference in degrees  =  292.5000003157188\n",
      "Minimum phase difference in degrees  =  -122.23561042248497\n"
     ]
    }
   ],
   "source": [
    "print('Maximum ratio of magnitudes = ', np.max(np.abs(uc)/np.abs(uu)) )\n",
    "print('Minimum ratio of magnitudes = ', np.min(np.abs(uc)/np.abs(uu)) )\n",
    "print('Maximum phase difference in degrees  = ', np.max( np.angle(uc) - np.angle(uu) ) * 180/pi )\n",
    "print('Minimum phase difference in degrees  = ', np.min( np.angle(uc) - np.angle(uu) ) * 180/pi )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The optimization's result is too different from $U$. It looks like the circuit is a bit more complex than four one-qubit rotations, after all.**\n",
    "\n",
    "So it turns out that despite the similar symmetry in the matrices, my hypothesis circuit could not reproduce the give matrix $U$.\n",
    "\n",
    "## Actually figuring it out\n",
    "\n",
    "At some point during my investigation I became aware that one hint in the problem was \"Hadamard.\" Applying a Hadamard operator to the matrix perhaps would simplify it? Indeed, that is the case. However, it's the application of 2 Hadamard gates (one before, and one after) that transforms U into a diagonal matrix, making it much simpler to handle:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# a Hadamard gate on 1 qubit\n",
    "hh=np.array([[1,1],[1,-1]]) / 2**.5\n",
    "\n",
    "# 4 Hadamard gates tensored together, equivalent to the matrix\n",
    "# due one Hadamard on each of the 4 qubits\n",
    "hh4=np.kron(hh, np.kron(hh, np.kron(hh,hh)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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bNWb2sAVE9rye6KFd+GjFdroP68rAib2Jf3yVJTX/E09vD269tzNLJq0kqle7ivNu7m7UbxxO4g/JltStLXtpbXyOq9E7QadPpBAXm8AbszdyLiWTwNAAAMIbhZGW5LhkaHh0wPDoiOE1EMPnfuC3SWJmg+HpsD5u6HYdbbu1psf9NzNgQq+KjSv3fC4eXu4O68NW4g/JTB88FxcXg9AGIRV9Zaaex8ff27K6Z5PKNnEAw8WwrM7lVJ6n2Rk5vPq3N4h/7DVyMnNIOZnqsD66D+tK7LwRBNcNqnL+bFI6dSJCMAzHj1FWes5F6zbm0X783z3zmNJjOreP6mZJ3fKx2L72C5ZOfpW0pHSSjiU7fCzK+2jRoSmDH7+DJZNWOqTupfqoLeNhO0eh7O7Q071nMmhyHwBM06S0tJTiwmLL+kg5mUpJcQnZGTl4+3kBsG31TiZ2fJr+E3rZve7lNI28hqA6gUxa+gBNI6+hRYemAHQeGMWu9/9lWd3aspfWxuc4w5GvEAKMEPNGI7riuGnkNfQa3Q0ffx/WzHiLqN7tCG8Uhrunu6WfCdqSvL/6H3jfCWYhhufNYOZDaSZmzlzL+ujZ4IZqz982/BaKCoqI6tWOgvxCstKzLXmf+FJ8A30YM3sobaPbsG31jiq39xdOWM69Tw2kTsMwAkP9WTxphWWvfMvfxy4qKObQ50f5dN0XltS5HNt5OnBSH1zdXDix76Rld8H+k+ihXbhzUh9On0hhzYwN5GbmMnrWUEpKSti2eicHPjvMwId70y+2J4c+P8LKqW+QmXrebvUrz4/NCVspKS6tsm5vuLU1vcdEcyE3n9PHz7B+zvt2q21rxIx7CAj1JzP1PKueW09o/eCLxsIR3kiKZ/eWAxQVFvH6C2/X2N3B2jIetnO0ZcemNGnbGN9AHzYnbCMz9Tx3TxmAiclPB07x7oLNlvTRdXBHbri1Nd5+XsQ/9hqtOjenbfR1ePl48u2He9m54WtL6lZmu17K18PTax+p+IzQ39Y/xpwRi8jPK7Ckh9qyl5ariee4beaGPaZpRtqer9EQVFMuGYIc7FIhSEREROznUiFI/4m8iIiIOCWFIBEREXFKCkEiIiLilBSCRERExCkpBImIiIhTUggSERERp6QQJCIiIk5JIUhERESckkKQiIiIOKUa/QWqNaW2fFOzvrlaRESk5uhOkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQpKQSJiIiIU1IIEhEREaekECQiIiJOSSFIREREnJJCkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQp/eEQZBhGQ8MwPjUM46hhGIcNw5hkz8ZERERErHQlv0W+GHjMNM29hmH4A3sMw9hqmuYRO/UmIiIiYpk/fCfINM0zpmnu/e3/ZwNHgavs1ZiIiIiIlezymSDDMP4MtAW+scfjiYiIiFjtSt4OA8AwDD/gbeAR0zSzqvn5WGAsgBc+V1pORERExC6u6E6QYRjulAWg103TfKe6P2Oa5jLTNCNN04x0x/NKyomIiIjYzR++E2QYhgEsB46apvmPK2li0OS+RA/twqyhcST+kIyXrxfDn78Ld0939nx8gF0f7GbS0gcAaBvdhql9Z5F0LPlKSlbRpmtL+sX2JDcrj62rdtA08mqualIfF1cXFjyUYLc6v5vPSAzv/piZj0LJT+DZDcPzFnCpj5m7CIoOYIRtg8KvMIsOw4U37Vrey8eT8QtHUVJcyv7th/jsza/s+vi/l+11ierVlq4xHRh7/eMUFRQ5vJ9JL48F4EL2BZY9sZqQekE88OIwSktL2bLyUw7utPa/CWjRoSm3Db8ZVzdXGrWI4NieH/H09sAv0Jc5o5aQn5tvaf1ytWm91PQ1KfdI/Djc3FwBmDtmKaZpOqSuLdu99MY+7ejQtz2+gb5gmiycuJxRM4fg7evF6RNnWP38W3bvoV7jcIY8MwgvH09mDpnPQ3Ejq8xTH38vh12j2jI/bK9Ls780IebRfqT8nMryp16nXuNwhk4dhIenB8f3/cSGuR/YvQfb6zJwUu8q67bH/TfT+qbmBIcHsWLqOn7+7he791Cb9o5yV3InqDMwDOhmGMb+3/7X+4880NvzNrHrg90Vx70fiMbVzRVXNxfSktIBiItNYNHEFZw6nGjXAATQJaYDLz/6KgtiE4iZ3Jcm1zdm0cTlnDqcSKvOze1a63fJWwkFn/z7uGA7ZtazmDnzwL112TkzDwxPKDlt9/I33XkjO9/axfxx8XTqH2X3x/+9Kl+XgRN7sXLqOo58daxGevEP8cMwDOIeXEZ68jladWpGrzHRrJv1Di+NWkKfsT0s7+Ho18eIi01g1we72bZ6B8HhQcwbG8/xfT8R3jDU8vrlast6qQ3XpNz8cfG8NHoJedkXCK4b6LC6tmz30m/+uZe42ASOfn2Mj1ftIDsjh7gHlzF72ALqNAyzpIeUk6n8Y8zSimPbeeqoa1Sb5oftdfnhXyd45a9rKo5TTqYyd/RSZt0XR4uoay3pofJ1cXN3u2jdbl21g3lj43ntuTfp0LedJT3Ulr2jsj98J8g0zS8Aw469VGjYrAFfbvwX+7d/x5OrJvJ/984DoOMdkXy9afdl/vZ/b+OCzdz3bAzZGTn4Bfty5uSvAPx6Ko3whqEctnvFP8BnJIZ3P8zMKQCY6f0BAyPoZczCL+xaKiwihBP7TpbVKa2ZV7RQ9bp4+3vXWB8A2Rk5JH5/mth5I/AL8uXs6QzCIkJJTUx3+Kv+W++5ifnj4qnTMIxpbz+BYcD6Oe87rH5tWS+16ZpA2b7l7ulGRkqmw2tfTrvubdi48EMAWnZsyv3T7mL31gMOqZ38Y0qVeeqoa1Tb5sfvccvdndi3/ZDldQJC/TifXvYR3srr1sXVhYETe/PaNPu+u1CutuwdldXoN0Z3H9aV2HkjCK4bVOV8WlI62Rk5FBcVY1SKWbfe3dmSt2ZOn0ghLjaBN2Zv5FxKJoGhAQCENwqruBPlEF4DMPyfAZdqXqHlrcTMGIPhO+K3EyZQCtj/baGzSWWbBYDhYknO/V0qX5fsjJwa66N8nm5f+wVLJ79KWlI6SceSOZuUTp2IEAzDcWMUWj+Y/LwC3DzcCAjz5/lBc9i5YRcd+rZ3WA+1Yb3UlmtS3keLDk0Z/PgdLJm00iF1L9WH7V4K0DyqCcf3/lTxxH9k1zH+evsLtOpk/SvvgFD/i+apI65RbZsf1V0XW11jOlD3T3XYFL/V8r6y0nMuWreubq5MXDSad+L+adk6rg17hy3DkYk4wAgxbzSiLzofPbQLd07qw+kTKayZsYHsjBzGzB5KUWExe7ceYOeGrwm7KoT7nh3M/HHxdu+raeQ19BrdDR9/H9bMeIuo3u0IbxSGu6e7pe9TbkneX/0PvO4oCzvFpzBzFoPHDRhuLcElADPvTShNx/AdC5iYxd9D3mtX1EfPBjdULf/bZ4KKCoo59PlRPl1n3ztNv5ftdYnseQP9Ynty6PMjrJz6Bpmp5x3az4gZ9xAQ6k9m6nlWPbee0PrBjJ41lJKSErat3smBz6x/HXPvUwM59PlRvvvieyYvG0dxUQkhdYNY9PAK0pMzLK8PNbdeqlMbrgnAG0nx7N5ygKLCIl5/4W3OnnbMtbBlu5f+cjSJSUsfYN2sd0n95Sx/ahnBHQ/1xHBx4XxaliWv+H0DfRgzeyhto9vw4SvbaNCkXpV5imk67BrVlvlhe12KCooY/vzd/KllBO8t/ojvvz3BrA+f4etNu8nPKyT+sSvb06tT+bpsTthKSXFplXU75sX7aHHjtfxyNIl9nxxi54av7d5DTe4d28wNe0zTjLQ9XytCkLO6ZAhyMNsQJCIi8r/kUiFIv0BVREREnJJCkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQpKQSJiIiIU1IIEhEREaekECQiIiJOSSFIREREnNIf/gWqcuVqyzc165urRUTEGelOkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQpKQSJiIiIU1IIEhEREaekECQiIiJOSSFIREREnJJCkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQpKQSJiIiIU1IIEhEREaekECQiIiJOSSFIREREnJJCkIiIiDglhSARERFxSm413QDAqJlDCK4biKe3J7OHLeAvt99Ah77t8Q30BdNk5tA4S+vXaxzOkGcG4eXjycwh83kobiSe3h74BfoyZ9QSfPy9eODFYZSWlrJl5acc3HnE0n4Abh/VjW733sSUHtO5bfgtdI3pSFrSWd5bvIWfv/vF2uLuURg+Q8DMxrywEdyvw3BtBIYrZtY0a2tXYntdRr5wL11jOjD2+scpKigiqldb+o+/nV0f7GZT/FaH9QFw95MDuOb6PzNzyHxC6gVxz1MDcXV1Yfu6Lzn85feW9QIwaHJfood2YdbQOBJ/SCakXtBF89N2Dufn5tutvu14dOwXSfvbrqe0pJSEJ9dQVFBESL0g5n/xAs/0mUniD8l2q23rkfhxuLm5AjB3zFI8fTwZ/vxduHu6s+fjA+z6YLdltct5+Xgyd8d0Vk5dR+cBfwGgbXQbpvadRdIx6/7tlbXp2pJ+sT3Jzcpj66odNI28mqua1MfF1YUFDyU4pIdyLTo05bbhN+Pq5kqjFhE8ctPUKuvFUbx8PBm/cBQlxaXs336Iz978ymG1bY184V4CQv1oHnUty596Hd8gXzr0bU9RQRFvvfS+pWsEatdYVF4v9z93Fz/uP8mvp9J4Y/bGGumnVtwJWvH0WuaOXsrZ0+l4+3nxzT/3EhebwNGvj/Hxqh2W1085mco/xiytOA4OD2Le2HiO7/uJ8Iah9BoTzbpZ7/DSqCX0GdvD8n7qNQ7HP8SPzLQsAEpLSym4UAiGQcaZc5bXN7x6YmbPxMyahuE7CsO9BWb2dMzi4+De3vL65Wyvy8qp6zjy1bGK428/3Mebc95zeB8tOjQlPTmj4njQo/0oyCvEcHEh/XRGdQ9hV2/P21Tlyb26+Wk7h+2p8ni4uLjQ98HbKCkuISczl6KCIgDumtKfnRt22bVudeaPi+el0UvIy75AcN1Aej8QjaubK65uLqQlpVteH8oC8Y71XwIQF5vAookrOHU40WEBCKBLTAdefvRVFsQmEDO5L02ub8yiics5dTiRVp2bO6wPgKNfHyMuNoFdH+xm2+odF60XR7npzhvZ+dYu5o+Lp1P/KIfXr2zl1HXExSaQlpTO3m2H6DwgijkjF5MwZQ0xj/WzvH5tGovK6yU/twA3DzfSEh2zVqtTK0JQUJ0AnnxtInUiwsjPLag43657G/Z8fMDh/ST/mMK0t5+gedS1JB0/Q1hEKKmJ6ZimaXltwzCIebQf78Ztrjj3yZrPmXHXXN5f/BF3TelveQ9m3ioMvwkYfo+AEQClv21gJcngWt/y+rWZp7cHt97bmW2rd1aca9y6ER+/+ikrn1nHkKmDHN5TdfPTdg5bJbBOAH5Bviyd/Crn07Jo2601PUfeys63dpUFdwdo2KwB7p5uZKRk0rBZA779cB+LH17J3VMGWF67fY82nPzuFzJTsyrOdbwjkq83WX8HqrKNCzZz37MxjJhxN37BvpxPL+vn11Npdg/Bv9et99zE9rVfXLReHCUsIqTiydUstX7vvpxr213NTwdPUVpaytvzNjFx0WgGPNwL/2A/y2vXlrGwXS9P9pjO3NFLubFPe3wCfGqkpxoNQd2HdSV23ggMFxdeHL6QY3t+pHlUEwCaRzXh+N6fHBI8KgsI9ScgzJ/nB81h54ZddOjbnrNJ6dSJCMEwDEtrdx/WlRnv/5VGLSIYv2AkTSOv4cY+7SrGIDM1Cx9/b0t7AKDkFGbWs5i5y6D0LLiElJ13rQ8lKdbXr8WaRl5DUJ1AJi19gKaR19CiQ1POnk4nOyOHvOwLeHi6W1a7fL0E1w2qct52flY3h62SnZHD2d/ufmVl5ODl50XLjk3pcf/NdOjTngETe1lSt3wsWnRoyuDH72DJpJUApCWVXYviomIsXq4A3NDtOtp2a02P+29mwISyf+utd3d2+NsNp0+kEBebwBuzN3IuJZPA0AAAwhuFOeyOWGWh9YPJzyvgmhv+fNF6cTgzm/MAACAASURBVJSzSRmERZQFQMPFAZOhGpXX7O2jbuWjFdsB+OFfJ4iLTeCTNZ875PrUhrGAi9dL+XNb7vlcPLys2zv/E8ORISPACDFvNKKrnHNxdWH8glGYpSbevl4sGJ9AwYVCJi19gHWz3iX1l7OW9+Ub6MOY2UNpG92GD1/ZRoMm9SguKiGkbhCLHl4BpsnoWUMpKSlh2+qdHPjssOU9ATy99hFmDplPn7HdadK2MQEh/qx6fj2njiTZtc6W5P1VT7hdh+EzGAw/zJxF4HkzhmsDMDws/UxQzwY3VDmufF02J2ylqKCYfrE9OfT5EVZOfYO6f6rD0GcG4Rvkw9vzNvHVe/+ypC/bPtbPeR/49/Vp1CKCu58ou0P34YpP+O4Laz8TFD20C3dO6sPpEymsmbGB3Mzci+bn5GXjqsxhe74dYTsehflFNLimHr4BPsyPXVbxltiwaYP57I0vLf28wxtJ8ezecoCiwiJef+FtSopLGTN7KEWFxezdeoCdG762rHZltw2/hYyUTH7+7hfue3Yw88fFO6RuuaaR19BrdDd8/H1YM+Mtonq3I7xRGO6e7g7/TBDAvU8N5NDnR6ushfL14ijln4MpKijm0OdH+XTdFw6rbcvDy4On1jzM8zEvARDVqy0d+kXi7evFsimrOfdrpqX1a9NYQNl6KftcZzsK8gvJSs9mxdNrLa25zdywxzTNSNvzNR6CpOZdFIJqiG0IEhERsYdLhaBa8ZkgEREREUdTCBIRERGnpBAkIiIiTkkhSERERJySQpCIiIg4JYUgERERcUoKQSIiIuKUFIJERETEKSkEiYiIiFNyq+kGpObVlm9q1jdXi4iII+lOkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQpKQSJiIiIU1IIEhEREaekECQiIiJOSSFIREREnJJCkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQpXXEIMgzD1TCMfYZhbLJHQyIiIiKOYI87QZOAo3Z4HBERERGHuaIQZBhGBNAHeMU+7YiIiIg4xpXeCZoPTAFK7dCLiIiIiMP84RBkGEZfINU0zT2X+XNjDcPYbRjG7iIK/mg5EREREbu6kjtBnYE7DMP4GXgD6GYYxhrbP2Sa5jLTNCNN04x0x/MKyomIiIjYj9sf/YumaT4FPAVgGMYtwOOmad733zyGYRiMmHEPvoE+HN/zI1c1bUBw3UA8vT2ZPWwBpSWOeZfNy8eT8QtHUVJcyv7th/jsza8cUtdWvcbhDHlmEF4+nswcMp9H4sfh4enOhdx8Fo5/hWHTBtOw2VXkns9lzfQNpJ85Z0kfbW5uyfDn7+aXo0l888+9dLmzA4aLwbnU8yRMWW1JzWq5R2H4DAEzG/PCRnC/DsO1ERiumFnTHNaG7XV5KG4knt4e+AX6MmfUEnz8vXjgxWGUlpayZeWnHNx55H+6j3KDJvclemgXZg2NI/GHZABC6gUx/4sXeKbPTIoKixk6dRAenh4c3/cTG+Z+YNf6bbq2pF9sT3Kz8ti6agdNI6/mqib1cXF1YcFDCXatdTmTXh4LwIXsCyx7YjUh9YIcei3KXe6aZJ/LZeLC0ZxPz+bEvpNsTthm9x5qyzz18vFk7o7prJy6jvufu4sf95/k11NpvDF7oyX1LqXyeMwb+zITFoyusp/2HHELzTs0pc5VoSyauJyUn1Mt62XkC/cSEOpH86hrWf7U65w/m82QZwaRn5PP3k8OsnXVDstqV1Zb1gvU8PcEder/F8IahGAYcPZ0BiueXsvc0Us5ezodbz8vh/Vx0503svOtXcwfF0+n/lEOq2sr5WQq/xiztOJ4/rh4/j5iEe4eZVm1pLiE4sJiigqKyT6Xa10jJuTnFuDu4c7PhxOZM2oxfx+xiPCGYdbVrIbh1RMzeyZm1jQM31EY7i0ws6djFh8H9/YO68P2ugSHBzFvbDzH9/1EeMNQeo2JZt2sd3hp1BL6jO3xP99HubfnbWLXB7urnLtrSn92bthV0e/c0UuZdV8cLaKutXv9LjEdePnRV1kQm0DM5L40ub4xiyYu59ThRFp1bm73epfiH+KHYRjEPbiM9ORztOrUzOHXotzlrknrm5rzxcZvWfBQAjfc2hpXN1e791Bb5undTw5gx/ovgbL9zM3DjbTEdMvqXUrl8biQk3/Rfrrl1c+Ie3AZHy7/hEYtIyztZeXUdcTFJpCWlM7ebYe4tv3VvLfoQ+aMWkybm1taWrtcbVovcAV3giozTfMz4LP/9u9FNGvA0W+OsSl+K9M2PM6P+39m3EvDcfNwIz/XcZ8fCosI4cS+kwCYpabD6l5Ow2YNGPnCvRV3fNbNfBfTNOnYL5KeI2/hg6UfW1L30OdHObjzCEHhgTzw4n3MGbmY1jc1J+lYsiX1LsXMW4XhNwFKM8EIgJJfyn5Qkgyu9aHIoe1USP4xhWlvP4FhwPo57xMWEUpqYjqm6di5U1v6KNdz5K3sfGsX7W+7vsr5W+7uxL7th+xeb+OCzdz3bAzZGTn4Bfty5uSvAPx6Ko3whqEctnvF6mVn5JD4/Wli543AL8iXs6czavxalLO9Jt9u3seomffStP3VBNUJwD/Ej8zU85b2UBPztH2PNpz87he8fMo+gvFkj+mYpsnTax9h1wd7yMvKs6z272G7n46eNZTrurRgxuC5lte+tt3V/HTwFKWlpezddpAnVo6npKiE9XPes7w21L71UqN3gs4mpZOVkQOU3eXITMvixeELObbnR5pHNXFgH2UXAcBwMRxW93ISf0hm+uC5uLgYhDYIqZggmann8fH3tqxueZ2cc7m4e7rT+qbmdB4QxWvT3rSsZrVKTmFmPYuZuwxKz4JLSNl51/pQkuLYXn4TEOpPQJg/zw+aw84Nu+jQtz1nk9KpExGCYThu7tRkH92HdSV23giC6wZVOd+yY1N63H8zHfq0Z8DEXgB0jelA3T/VYVP8Vrv3cfpECnGxCbwxeyPnUjIJDA0AILxRGGlJjnnFXz4W29d+wdLJr5KWlE7SsWSHz4nfe00K8wt5+dHXiH98FRdy8jmflmVpXzU1T2/odh1tu7Wmx/03M2BCr4o9Lfd8Lh5e7pbV/T2q20+XP/U6Sx5ZSc+Rt1pSs/L8uH3UrXy0YjsAMY/24//umceUHtO5fVQ3S2pX10dNr5fKDEcmrwAjxLzRiK449vT2YPzC0RTkFZB0LJlGLSIwS028fb1YMD6BgguFDumr/DNBRQXFHPr8KJ+u+8IhdW35BvowZvZQ2ka3YdvqHQTXDaz42cIJy7n3qYHUaRhGYKg/iyetICMl05I+bhoYReTtbfEN8GHnhl1MXDyGLzd+C6bJ0smvUZhvzXXZkry/6gm36zB8BoPhh5mzCDxvxnBtAIaHpZ8J6tnghirHla/Lh69so0GTehQXlRBSN4hFD68A02T0rKGUlJSwbfVODnxmzT2I2tJHueihXbhzUh9On0hhzYwN/HI0CYBh0wbz2Rtf4uruxqwPn+HrTbvJzysk/rHX7Fq/aeQ19BrdDR9/H9bMeIuo3u0IbxSGu6e7wz8TNGLGPQSE+pOZep5Vz60ntH6wQ69Fuctdk7TEdMYvHIWLiwu73v8XX7z7rd17qE3z9Lbht1BUUERUr3YU5BeSlZ7NiqfXWlavOpXHY3PCVmIeu6PKfjpg4u2EN6qDf7Afr7+wgV++P21ZLx5eHjy15mGej3kJgBtubU3vMdFcyM3n9PEzrJ/zvmW1K6uJ9bLN3LDHNM1I2/M1GoJEKrsoBNUQ2xAkIiL/f7tUCNIvUBURERGnpBAkIiIiTkkhSERERJySQpCIiIg4JYUgERERcUoKQSIiIuKUFIJERETEKSkEiYiIiFNSCBIRERGnZJdfoCpiD7Xlm5r1zdUiIs5Bd4JERETEKSkEiYiIiFNSCBIRERGnpBAkIiIiTkkhSERERJySQpCIiIg4JYUgERERcUoKQSIiIuKUFIJERETEKSkEiYiIiFNSCBIRERGnpBAkIiIiTkkhSERERJySQpCIiIg4JYUgERERcUoKQSIiIuKUFIJERETEKSkEiYiIiFNyq+kGACa9PBaAC9kXWPbEakLqBfHAi8MoLS1ly8pPObjziKX1W3VqRvdhXQmpF8xHK7YD0P626yktKSXhyTUUFRRZWr9cvcbhDHlmEF4+nswcMp+O/SKr9PHnVg0Z8swg8nPy2fvJQbau2mFJH7bjcWPf9nh4unMhN5+F41+xpGZ1vHw8Gb9wFCXFpezffojP3vzKYbUvyTsGw6sf5rnh4H0nhmcvKD2DmbcGio85rI3bR3Wj2703MaXHdG4bfgtdYzqSlnSW9xZv4efvfrG0tmEYjJhxD76BPhzf8yNbXv2sSj+ONGhyX6KHdmHW0DgSf0i+aCzSkzMYNXMI3r5enD5xhtXPv2X3HmzXS1TvtgC0jW7D1L6zSDqWbPeal1LTe2m5R+LH4ebmCsDcMUvx9PFk+PN34e7pzp6PD7Drg92W92C7nz4UNxJPbw/8An2ZM2oJPv5eDhsb2+vi6DULtWc8bPsY+cK9dI3pwNjrH6eooIiQekHc89RAXF1d2L7uSw5/+b0lfZSr8TtB/iF+GIZB3IPLSE8+R6tOzeg1Jpp1s97hpVFL6DO2h+U9HP7qB+JiE5gzcjGtu7Sg74O3UVJcQk5mrsMCEEDKyVT+MWYpAC4uLhf1cW37q3lv0YfMGbWYNje3tKwP2/GYPy6ev49YhLuHYzPzTXfeyM63djF/XDyd+kc5tHa1XBuCEQSlGWXHZimQDxhQkuawNuo1Dsc/xI/MtCwASktLKbhQCIZBxplzltfv1P8vhDUIwTDg7OmMi/pxpLfnbaryhGo7FtkZOcQ9uIzZwxZQp2GYJT3Yrpe42AQWTVzBqcOJDg1AtWEvLTd/XDwvjV5CXvYFgusG0vuBaFzdXHF1cyEtKd0hPVTeTwGCw4OYNzae4/t+IrxhqMPGprrr4ug1C7VnPGz7WDl1HUe++vcLyEGP9qMgrxDDxYX00xmW9VGuxkNQdkYOid+fJnbeCK5u8yfCIkIJiwglNTEd0zQd1kf3YV158eO/8c2mPfgF+bJ08qucT8uibbfWDuuhssA6ARf1sXfbQYZNG8zsj6ayw+K7IpXHo2GzBjz71mNli9aBwiJCSEss2zDNUsfNheoZGD4jIe+1f5/Kfw8zcyJm3hoM3wcc04VhEPNoP96N21xx7pM1nzPjrrm8v/gj7prS3/IeIpo14Og3x1g4YTl9x912UT81qbqxaNmxKbM/msovR5Msq1t5vQB0vCOSrzdZf7ejstqyl5Zr2KwB7p5uZKRk0rBZA779cB+LH17J3VMGOLwXgOQfU5j29hM0j7qWpONnHDY21V0XR6/Z6tTUeFxO49aN+PjVT1n5zDqGTB1keb0aDUHdh3Uldt4Itq/9gqWTXyUtKZ2kY8mcTUqnTkQIhmE4rJdtq3cysePTDHy4N2d/S59ZGTl4+Xk5rIfKsjNyLuoj5tF+/N8985jSYzq3j+pmaf3y8eg/oReJPyQzffBcXFwMQhuEWFq3srNJGYRFhAJguDhuLlzEawBG0DJwa4IR8Ddwvw48bwV+2yxK08HF1/I2ug/ryoz3/0qjFhGMXzCSppHXcGOfdhWbVmZqFj7+3pb3cTYpnayMnLIDwyC0fnCVfhyhfO8IrhtU5Xx1Y3Fk1zH+evsLtOrU3LJ+Kq8XgFvv7uzQt29ry15a3keLDk0Z/PgdLJm0EoC0pHSyM3IoLirGgdt6hYBQfwLC/Hl+0Bx2bthFh77tHTI2l7oujl6ztmpqPH6Ps6fL5kpe9gU8PN0tr2c4MvUFGCHmjUb0RedHzLiHgFB/MlPPs+q59YTWD2b0rKGUlJSwbfVODnx22NK+Og+Iom30dXj5ePLth3sJqR9Mg2vq4Rvgw/zYZQ57S8w30Icxs4fSNroNmxO2UphfVKWPVp2a0XtMNBdy8zl9/Azr57xvSR+Vx2P/p9/RosO1FT9bOGG5JTWrU/6ZoKKCYg59fpRP133hkLpbkvf/x58bgfMwz08G73sw3FuCSxBmzgIoPmHXPno2uOE//vzptY8wc8h8+oztTpO2jQkI8WfV8+s5dcS6Ox4Ant4ejF84moK8ApKOJfPeoo+q9ONI0UO7cOekPpw+kcKaGRu4rkvzKmMBcMdDPTFcXDiflsVr0960ew+2+8eRXce479nBzB8Xb/dal1PTe2m5N5Li2b3lAEWFRbz+wtuUFJcyZvZQigqL2bv1ADs3fG15D5X30w9f2UaDJvUoLiohpG4Qix5eAabpsLGxvS6OXrNQe8bD9nmuqKCYfrE9OfT5EVZOfYOAUH/ufqLs7tiHKz7huy/s85mgbeaGPaZpRtqerxUhSKQ2uVwIcpTLhSAREfl9LhWCavwzQSIiIiI1QSFIREREnJJCkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQpKQSJiIiIU1IIEhEREaekECQiIiJOybG/Flzk/wO15Zua9c3VIiLW0p0gERERcUoKQSIiIuKUFIJERETEKSkEiYiIiFNSCBIRERGnpBAkIiIiTkkhSERERJySQpCIiIg4JYUgERERcUoKQSIiIuKUFIJERETEKSkEiYiIiFO6ohBkGEaQYRgbDMP43jCMo4ZhdLRXYyIiIiJWutLfIh8HfGSaZoxhGB6Ajx16EhEREbHcHw5BhmEEAF2BEQCmaRYChfZpS0RERMRaV/J22NVAGrDSMIx9hmG8YhiGr536EhEREbHUlYQgN6AdsNQ0zbZALvBX2z9kGMZYwzB2G4axu4iCKygnIiIiYj9XEoKSgCTTNL/57XgDZaGoCtM0l5mmGWmaZqQ7nldQTkRERMR+/vBngkzTTDEMI9EwjGamaf4ARANH/pvHqNc4nCHPDMLLx5OZQ+b/0VaumG0fD8WNxNPbA79AX+aMWoKPvxcPvDiM0tJStqz8lIM7/6t/5h9y+6hudLv3Jqb0mM5tw2+ha0xH0pLO8t7iLfz83S+W1vby8WT8wlGUFJeyf/shPnvzK0vrXYrtdRk4qTdXNamPi6sLCx5KoMf9N9P6puYEhwexYuo6y8altowHrg0xfGPB8MY8PxkjYAYYnmDmYWY9h+E3EVyvBjMbM2cRlKZa2s6kl8cCcCH7AsueWE1IvSCHrhPb+bFg10x+3H+SX0+l8cbsjfQccQvNOzSlzlWhLJq4nJSfrRmPy/XR4/6badmxKXUiwvjp0ClWPL3W8j7mjX2ZCQtGY7gYnEs9T8KU1ZbUrE5tWS+1aV+3XSuO2rvKtenakn6xPcnNymPb6h30GhVdI3Ojch9bV+2gaeTVVfb0mnCl3xM0EXjdMIyDwA3AzP/mL6ecTOUfY5ZeYQtXzraP4PAg5o2N5/i+nwhvGEqvMdGsm/UOL41aQp+xPSzvp17jcPxD/MhMywKgtLSUgguFYBhknDlnef2b7ryRnW/tYv64eDr1j7K83qVUvi5u7m40ub4xiyYu59ThRFp1bs7WVTuYNzae1557kw59L7oJaTe1ZTwoScTMerri0Mz6G+b5KYB72bFZAhSBWQil5y1txT/ED8MwiHtwGenJ52jVqZnD14ntus3PLcDNw420xHQAtrz6GXEPLuPD5Z/QqGVEjfWxddUO4mITSDyWzNbXPnNIHxdy8pkzajF/H7GI8IZhltWsTm1ZL7VlX69urThq7yrXJaYDLz/6KgtiExgwoVeNzY3KfcRM7nvRnl4TrigEmaa5/7e3utqYpjnANE3rn6EdIPnHFKa9/QTNo64l6fgZwiJCSU1MxzRNy2sbhkHMo/14N25zxblP1nzOjLvm8v7ij7hrSn/LewiLCKnYwM1S6//Nv0dAqB/n08tC4a+n0ghvGAqAi6sLAyf25pM1n1tWuzaOBwCuV2MELQIzv+w4dynm+SmYhV+B9yBLS2dn5JD4/Wli543g6jZ/Iiwi1KHrpDpP9pjO3NFLubFPe3wCyr6tY/SsoQx+/A5+3HeyRvtwc3ejfuNwEn9IdlgfAK1vak7SMcfWrK3rpab29erWCjhm7yq3ccFm7ns2hhEz7sbb3xuomblRuQ+/YN9q93RH0zdG2wgI9ScgzJ/nB81h54ZddOjbnrNJ6dSJCMEwDEtrdx/WlRnv/5VGLSIYv2AkTSOv4cY+7SoWaWZqFj6/TWArnU3KqFiohou1/+bfKys9h8DQAADCG4WRlpSOq5srExeN5p24f5KWlG5Z7do4HgCU/ISZOQFwAZe6wG+beWkGuPhZVrb7sK7EzhvB9rVfsHTyq6QlpZN0LNlh6+RSytdJ7vlcPLzK7o4tf+p1ljyykp4jb63RPjoPjGLX+/9yWA9Q9iTXeUAUr01706F1a+N6qal9/VJrxVF7V7nTJ1KIi03gjdkbyc7IqbG5UbmPcymZF+3pNcFw5Ku2ACPEvNGIrjj2DfRhzOyhtI1uw+aErayf877Deqmsch8fvrKNBk3qUVxUQkjdIBY9vAJMk9GzhlJSUsK21Ts58Nlhh/T19NpHmDlkPn3GdqdJ28YEhPiz6vn1nDqSZGnd8vf0iwqKOfT5UT5d94Wl9S7Fdn6UFJcS3igMd093FjyUwJgX76PFjdfyy9Ek9n1yiJ0bvrakj5oajy3J+6ueMPwx/J8Aj06YFzZiuPz7lZOZ/Tz4PojhWh9cgjGzZkBpml366NnghmrPj5hxDwGh/mSmnmfVc+sJrR/s0HViu27/3KoRBfmFZKVns+Lptdz1xB2EN6qDf7Afr7+wgV++P10jfQD8bf1jzBmxiPw86/4LWdv1EvPYHXy58VswTZZOfo3CfMd8jVtt3D9qel+3XSuO2rvKNY28hl6ju+Hj78P7S7cw7e3Ha2RuVO5jzYy3iOrdrsqebqVt5oY9pmlG2p6v0RAkIpd2UQiqIZcKQSIi/7+4VAjS22EiIiLilBSCRERExCkpBImIiIhTUggSERERp6QQJCIiIk5JIUhERESckkKQiIiIOCWFIBEREXFKCkEiIiLilNxqugERqV5t+aZmfXO1iPyv0p0gERERcUoKQSIiIuKUFIJERETEKSkEiYiIiFNSCBIRERGnpBAkIiIiTkkhSERERJySQpCIiIg4JYUgERERcUoKQSIiIuKUFIJERETEKSkEiYiIiFNSCBIRERGnpBAkIiIiTkkhSERERJySQpCIiIg4JYUgERERcUoKQSIiIuKU3Gq6AYBBk/sSPbQLs4bGkfhDMrcNv4WuMR1JSzrLe4u3cOpwIlNem0BhfiFubm68NHoJpmnavY9WnZtz6z2dMU2TdTPfof7Vdek+rCsh9YL5aMV2dn2w2+41q2M7Hte2u5ohzwwiPyefvZ8cZOuqHTXSR0i9IB54cRilpaVsWfkpB3ceYdLSBwBoG92GqX1nkXQs2W7129zckuHP380vR5P45p976XJnBwwXg3Op50mYstpudX6vSS+PBeBC9gWWPbGam+/qRIe+7SkqKOKtl94n8Qf7/dsvxcvHk7k7prNy6jruf+4uftx/kl9PpfHG7I2W176Iz0gM7/6YmY9CyU/g1grD7yEw8zALvoL8d8FnBIZrIzBcMbOm2bV8m64t6Rfbk9ysPLau2kHTyKu5qkl9XFxdWPBQgl1r1eYealMf5Wz3jo79Ionq3ZY6EWGsmfEW3397glePLWTfJwc5vvckmxO22b0HwzAYMeMefAN9OL7nR65q2oDguoF4ensye9gCSktK7V6zOvUahzPkmUF4+Xgyc8h8FuyaWWXdDps2mIbNriL3fC5rpm8g/cw5h/TxUNxIPL098Av0Zc6oJfj4e120v/8v91GuVtwJenvepioBo7S0lIILhWAYZJw5h6ePJ0WFxcwbG09+Xj5evp6W9DFgQi+KCospKigi+1wuh7/6gbjYBOaMXEzrLi0sqVkd2/G4tv3VvLfoQ+aMWkybm1vWWB+9xkSzbtY7vDRqCX3G9gAgLjaBRRNXcOpwol0DEAAm5OcW4O7hzs+HE5kzajF/H7GI8IZh9q3zO/iH+GEYBnEPLiM9+RytOjWj84Ao5oxcTMKUNcQ81s8hfdz95AB2rP8SKBsbNw830hLTHVL7InkroeCTfx+7t8bMW415/q8YHlGAO4Z7C8zs6ZjFx8G9vV3Ld4npwMuPvsqC2ARiJvelyfWNWTRxOacOJ9Kqc3O71qrNPdSmPsrZ7h27PthNXGwCK/+2jqaR1wCQn5uPh5cHqafSLOmhU/+/ENYgBMOAs6czWPH0WuaOXsrZ0+l4+3lZUrM6KSdT+ceYpRXHtuu2pLiE4sJiigqKyT6X67A+gsODmDc2nuP7fiK8YWi1+/v/ch/lasWdIFufrPmcbat30vi6Rtw1pT/L//o6hgHPvvUY2edyuJCTb0nda9s1ZvawBUT2vJ7ooV34aMV2ug/rysCJvYl/fJUlNX+PvdsO8sTK8ZQUlbB+zns11kdYRCipiekX3YXreEckX2+y/12yQ58f5eDOIwSFB/LAi/eVhdGbmts/bP0O2Rk5JH5/mth5I/AL8uXs6QzenreJiYtGk5GSiX+wn+U9tO/RhpPf/YKXT9mLgCd7TMc0TZ5e+wi7PthDXlae5T38R4VfYQS+CGYRZm4CuARBaUbZz0qSwbU+FNmv3MYFm7nv2RiyM3LwC/blzMlfAfj1VBrhDUM5bL9StbqH2tTHfzJocl+63XsTLw5fBEBsuykYhsHzG6ew++MDdq8X0awBR785xqb4rUzb8Dg/7v+ZcS8Nx83DjfzcArvX+71s1+26me9imiYd+0XSc+QtfLD0Y4f0kfxjCtPefgLDgPVz3r/k/v6/3keN3gnqPqwrsfNGEFw3qMr58n98ZmoWPv7eXNuuMaePn2H64Ln8+nMa11z/Z0v6SDmZSklxCdkZORWvFLat3snEjk/Tf0Ivu9b8T33YjkfMo/34v3vmnHNQXAAAIABJREFU8f/Yu/O4qur8j+Ovw76DgLiElvuSaS7jUi4pmbmlpmZq5ppGZqZTlunkuIw6maO4pqTmUlja3lgmmmJl05SlppbaoiIRCILsspzfHyjhFbPsngvzu+/n49FDz7nI58P3fM/3vu+5h9uUrrO4e1SXcuvjbHwKlcODMQzjsv2dB93O7lc/tXsfl+ZB5rks3D3dadK+Ibf3bc36Ga/avdZvuTQeu175mJWTXiI5PoX4Ywl8998TREVGs3PTXpLjrb8ac2uXW2jepQldH+xE30e7l4xPVnoWHl7ultcv4dUXw38auFx+Rc7wGYmZNhHz3HAM74FQlAYuwcUPulaDwkS7tnHmRCJRkdFsnv8W5xLTCAwJACCsZqhDjkdF6aEi9XG1tQOKrw4902Mu/Sf1BIrP76KiIgouFFjSy9n4FM6nZgLFV1vSks/zz+FLOfbl9zRsXdeSmr+H7Xn76/NdOj7+3g7pISDEn4BQf2b2X0Dc1n207dXyquv7//c+DEemvgAj2GxjRFyxP2JoB+6d2JMzJxLZNHsrt3RoSN3mtQgI9mfDzNdI/DGJydGRZKZnERjiz/OjVpCbbf8k33FgO27t3ARvPy9W/XU9N9/ekOYRt+Dl48nn7+8nbutndq9ZFtvxCK4aRI8xEeRk5XLm+M+8tuCdcukjKy2L0fOGUlhYSOzGOA7sPkzoDcE88OxAFo9bZff67fu1ptXdzfEN8CFu6z4mLB/DJ299DqbJyknruZB7we41f8uI2fcTEOJPWlI6G/7+Gq27N6dt71Z4+3qxespGzv2S5pA+7hp+B/l5+bTu3oK83AucT8lg7TOvWFZve8LXZT/gdQ+G7wgoOImZuRxcQzG8B4GZhVl4ErKii+8bcq0OhsefvieoW/VbL9uu36oO3Ud3wcffh02zt9C6RwvCaobi7unusPtgKkIPFamPS2zXjsbt6lO3eS18A33YFh1LWlI6g6b0xcTkhwMneXPJNrv34Ontwfilo8nLziP+WAI1G4VjFpl4+3qxZHx08S0XDuAb6MOY+UNpHtGU91+M5aaba1523g6e2o/KNUIJDPFn+cS1pCZas47Y9lG9blUK8gsJrhLEssfWgmlesb7/f+oj1tz6pWmarWz3V4gQJCIV11VDkIPZhiARkd/raiGoQtwYLSIiIuJoCkEiIiLilBSCRERExCkpBImIiIhTUggSERERp6QQJCIiIk5JIUhERESckkKQiIiIOCWFIBEREXFKFfJ/oCoiFUdF+aRmfXK1iNibrgSJiIiIU1IIEhEREaekECQiIiJOSSFIREREnJJCkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQpKQSJiIiIU1IIEhEREaekECQiIiJOSSFIREREnNKfCkGGYUwyDOOwYRjfGIYRYxiGl70aExEREbHSdYcgwzBuAB4DWpmm2QRwBe63V2MiIiIiVvqzb4e5Ad6GYbgBPkDCn29JRERExHrXHYJM0zwDPA+cAn4G0k3T/NBejYmIiIhY6c+8HVYJ6APUAqoDvoZhPFDG1401DOMLwzC+yCfv+jsVERERsaM/83bYncCPpmkmm6aZD7wB3Gb7RaZprjZNs5Vpmq3c8fwT5URERETsx+1P/NtTQFvDMHyAHCAC+OKPfAPDMBgx+358A304/uX33FC/OpWqBOLp7cn8YUsoKiz6E+39cf0n9SJiaAfmDY3i9HcJtOvditY9mlM5PJRNs7fw7ecneOnYUr7aeZDj+39kW3SsXetXrRXGkGn98fLxZO6QxTy+ahwenu7kZOWydPyLDJsxkBoNbiArPYtNs7aS8vM5u9a3ZTseDf5SlwGTe5P4UxJrpr4MYOl42M6PvJwL3NrlFtzcXFn66Ivk5Vywa72r8fLxZPzSURQWFPH1rkPsfvVTh9StqH1cYjs/7hp+Bx0HtCM5/ixvL9/OT9+cAmDiyofITMsumTN241oDwzcSDG/M9EkYAbPB8AQzG/P83zH8JoBrbTAzMDOXQVGSfeuXYjsWAMFVg1j88Rym9Zxbss+yseDK9aNd71a0vKsZRYVFRD+1iZtursGQaf3Jzcxl/86D7Niwx+49QMWZp9caj9pNb7xiPbPKkGn3Uq12FfyC/Fg2YQ0pCal4+XiycM8s1k2P4YvtX1ta/+bbGnDnsI4EV63EB+t20b5vGwwXg3NJ6URP2Whp7dKadmxM78huZJ3PZseGPdRvVZsb6lbDxdWFJY9EO6yP0v7MPUH/AbYC+4FDF7/X6j/yPW7r8xdCqwdjGHD2TCprn3mFhaNXcvZMCt5+jv9t+9cXvce+d3/Ncfve/YKoyGjW/S2G+q3qAJCblYuHlwdJJ5PtXj/xxyT+NWZlyfbicat4bsQy3D2Ks2phQSEFFwrIzysg41yW3evbsh2P7/57ghef3nTZ11g5Hrbzo13vv7B43Cr2vvEZ7e9tY/d6V9P+3jbEbdnH4nGruK1Pa4fVrah9XGI7P4qKioqDqWGQejGgdxzQlu/++701DRSexjz/TMmmef5vmOlTAPfibbMQyAfzAhSlW9PDRbZjAXDflD7Ebd1Xsm3pWHD5+uHi4kKvh++isKCQzLQs8vPyqdeyNm8ve58Fo5bTtFNjy/qoKPP0WuNR1npmlVpNbmTh6JXEbfmU2k1rAjDoqb7see0Th9Q//Ol3REVGs2Dkcpq0b8SCUct5bsQywmqEOqT+JR0GtOWFyS+xJDKaAZN6UbdZLZZNWMPJw6e5+faGDu3lkj/122Gmac4wTbOhaZpNTNMcZprmH7rpJ7xBdY7+5xhLH11Dr3F3EVQ5gKfWT6ByeCi5WRXj/qH+k3oxefXDfP3RYQAiW0xh4eiV9Hm0u+W1azSozrNb/lpyxSNm7ps8N2IZX+08RLeRd1he//ewcjxs58clv5w8S+UaIXavdzWh4cEkn04BwCwyHVa3ovZxNTs37WX2fQt5Z/kH3DelD5WqBFG72U18tfOQYxpwrY0RtAzM3OLtrJWY6VMwL3wK3v0d08NF3UZ2Jm7LvpJz19FjEVg5AL8gX1ZOeon05PM079KE/bEHGTZjIPM/mM4eC6/OVMR5WtZ4ONKB3d8w592pdB8dweFPvqNl16b8+M0p0pLOO6yHO4d15J8f/o3/vPclAE3aNyT+mGN/ofutJdt44NkBjJg9CL9KvqSnFP/8v5xMJsyBa3pp5fqJ0WfjUzifmgkUX+VISz7PP4cv5diX39OwdV2H9XHnsI5ELhpBpSpBVzz2+qL3eKbHXPpP6gmAaZoUFRVRcKHA8r5Of5fArIELcXExCKkejGkWLyhpSen4+HtbVve3xsOWleNhOz8uCasZytn4VLvXu3ofqYSGF5+ghovhsLoVtY+rzY9f5+d5fPy9aXZHYyqHhzByzmBa3dWMG+pVs7axwh8w0x4FXMClCnDxCbgoFVz8LCl5tbFo3K4+XR/sRNueLek7obvDxyIjNZOzZ4rPkfOpmXj5eTFgcm/+cf8ipnSdxd2julhWu6LM09LKGg9HuDQ/Og68jem957F+xqt0G9WZW7vcQvMuTej6YCf6OuAFNUDsxjgmtHuGPo92p0n7htzetzXrZ7zqkNqXnDmRSFRkNJvnv8W5xDQCQwKA4jU9OT7Fob1cYlxauBwhwAg22xgRJdue3h6MXzqavOw84o8lULNROGaRibevF0vGRzvsno9LIoZ24N6JPTlzIpFNs7fSuF196javhW+gD9uiY0lLSmfQlL6YmPxw4CRvLtlm1/q+gT6MmT+U5hFNid24h0pVAkseW/roGgZP7UflGqEEhvizfOJaUhPT7Frflu145OflM3zmIG5sHM7byz/g8CffWjoetvPjfEomTdo3xNPLg2UT1pCb7ZirhZfuccjPK+DQ3qN8FPOxQ+pW1D4usZ0ft3RoSN3mtQgI9mfDzNc4eSQegCo3VqbXw3f96fsutifY3Ddh+GP4Pwket2HmvIXh8usrSTNjJvg+jOFaDVwqYZ6fDUX2ecu2W/Vbr9hnOxanjhb/7MNmDGT35k9K7gmy11iUpfT6sS16Bxdy86lepyq+AT4sjlzNzbc1oMeYCHKycjlz/GdeW/CO3XuAijNPrzUeoTcEX7aefbB2l2W9jJo7BL8gX4IqB7Bp9lZ+OHgSgLuG30FqYprl9wTd3rc1zSNuwcvHk8/f38+jy8bwyVufg2myctJ6LuQ65rm2fqs6dB/dBR9/HzbN3kLrHi0IqxmKu6e75fcExZpbvzRNs5Xt/nINQSIiv9cVIaiclBWCRKRiu1oI0v9AVURERJySQpCIiIg4JYUgERERcUoKQSIiIuKUFIJERETEKSkEiYiIiFNSCBIRERGnpBAkIiIiTkkhSERERJySW3k3ICLye1SUT2rWJ1eL/P+hK0EiIiLilBSCRERExCkpBImIiIhTUggSERERp6QQJCIiIk5JIUhERESckkKQiIiIOCWFIBEREXFKCkEiIiLilBSCRERExCkpBImIiIhTUggSERERp6QQJCIiIk5JIUhERESckkKQiIiIOCWFIBEREXFKCkEiIiLilBSCRERExCm5lXcDABNfGAtATkYOq5/cSHDVIB765zCKiorYvu4jDsYdcUgf/Sf1ImJoB+YNjeL0dwl0fbATTdo3pFJYEGunx3Dy8GmmrH+UC7kXcHNz4/nRKzBN0/I+2vVuResezakcHsqm2Vv49vMTvHRsKV/tPMjx/T+yLTrWrvWr1gpjyLT+ePl4MnfIYpbsm8v3X//ILyeT2Tz/LYbNGEiNBjeQlZ7FpllbSfn5nF3rX62PR6JG4untgV+gLwtGrcDH38uh8+Qf700l6fRZcjJzy3WejpwzmIAQPxq2rseaqS+TcS6LAZN7k/hTEmumvmx5/WvND4CbmtTkudhnGXpjJPl5+Zb1UlHWDnxGYnj3wUybDIU/gNvNGH6PgJmNmfcp5L4JPiMwXGuC4Yp5foZdyzft2Jjekd3IOp/Njg17qN+qNjfUrYaLqwtLHom2a63fw3YN8/L1YvjM+3D3dOfLDw+w790vGDlnMB0HtGVssycsmSPXmqd/uftW7h7ZBdM0eX/NTr7ccdDuPVxiO0/LGg+rVZT11MvHk4V7ZrFuegwP/v2+K9YORyv3K0H+wX4YhkHUw6tJSTjHzbc1oPuYCGLmvcHzo1bQc2xXh/Xy+qL3LpuMOzbsYdHYVaz/+6u07dUCTx9P8i8UsGjsKnKzc/Hy9XRIH/ve/YKoyGjW/S2G+q3qAJCblYuHlwdJJ5PtXj/xxyT+NWZlyXZuVh5uHm4kn04BoLCgkIILBeTnFZBxLsvu9a/WR6WwIBaNXcXxr34grEaIw+dJbvYFDBcXUi+GvvKap+umxxAVGU1yfAr7Yw/x3X9P8OLTmxxW/1rzw83djR5jIvjv+19Z2kdFWjvIXgd5O3/ddm+Cmb0RM/1pDI/WgDuGeyPMjFmYBcfBvaVdy3cY0JYXJr/EkshoBkzqRd1mtVg2YQ0nD5/m5tsb2rXW72G7hvV4KAJXN1dc3VxIji+eJ+umx3Dk02OW9XCteXpLh0ZEP72JFY+vo3nELZb1UdY8LWs8rFZR1tNBT/Vlz2ufAFcek/JQ7iEoIzWT09+eIXLRCGo3vZHQ8BBCw0NIOp1iyVWWP8rF1YV+E3qwc9Ne8rLzMAx4dstfcfNwIycz12F99J/Ui8mrH+brjw4DENliCgtHr6TPo90tr/1U11ksHL2SNj1b4hPgQ8zcN3luxDK+2nmIbiPvsLz+JQnfJzLj9Sdp2Loe8cd/dvg8mTPoXywet4qQG0Ko2Si8XOdpvRa1+eHgSYqKihxe25bt/Bj4RG/eXLINLB6WCr12XPgUw+8xjEprMXP/DS5BUJRa/FhhArhWs2u5t5Zs44FnBzBi9iD8KvmSnnIegF9OJhNWI8Suta5HjQbV+fz9r1j+2DoGTelbLj3YztOP3/ycJ9eOZ/qrk9n1yseW1S1rnlaE8SiP9bRl16b8+M0p0pKK56ftMSkP5RqC7hzWkchFI9j1ysesnPQSyfEpxB9L4Gx8CpXDgzEMw6F9VKoSdNl+VzdXJiwbzRtR/yY5PoV6LWpx5vjPzBq4kF9+SqZOs5sc0gcUv7J6psdc+k/qCYBpmhQVFVFwocCuPZTl0kmRlZ6Fh5d7yXZaUjo+/t6W1wcICPEnINSfmf0XELd1H217tXTYPLl0XILCAoFLP7dXuc7Tu0d15oO1uxxS91ps50f9lnW478l7aNSuPn0nWBPSK8ragVdfDP9p4BJ62W7DZyRm2kTMc8MxvAdCURq4BBc/6FoNChPt2saZE4lERUazef5bnEtMIzAkAICwmqEOu9IAV1/DkuNTyEjNpCC/AEcdGlu283TgX+/hyTtn8mTETMuCyNXmaXmPR3mtp7d2uYXmXZrQ9cFO9H20+xXHpDwYjnzFFGAEm22MiCv2j5h9PwEh/qQlpbPh768RUq0So+cNpbCwkNiNcRzYfdgh/UUM7cC9E3ty5kQim2Zv5a4Rd9CoTT1OHY3nq52H+M+/9zM5OpLM9CwCQ/x5ftQKcrPzLO+jcbv61G1eC99AH7ZFx5KWlM6gKX0xMfnhwMniV9125Bvow5j5Q2ke0ZT3X4zlpptrkpd7gfMpGax95hUGT+1H5RqhBIb4s3ziWlIT0+xa/2p9VK9blYL8QoKrBLHssbVgmg6dJ0+uG09ezgVc3VxYPG41wVWDymWeenh5MHXTY8wc8DwA1WpXYfjMQdzYOJy3l39geTi61vy45Mm141kcudrSe4LKY+3YnvD1lTu97sHwHQEFJzEzl4NrKIb3IDCzMAtPQlZ08X1DrtXB8LDLPUHdqt9a8vf6rerQfXQXfPx92DR7C617tCCsZijunu7lck+Q7RqWkZrJmPlDyb9QwP4dB4jb+hn9HutB78huHNp7hHXTN5OWlG7XHq41TzsPbk+rrs0wXAz27zxI7MY4u9YvzXaeVqoSdMV4WK0irad3Db+D/Lx8WndvUebaYYVYc+uXpmm2st1fIUKQiMj/ijJDUDkoHYJE5LddLQSV+z1BIiIiIuVBIUhERESckkKQiIiIOCWFIBEREXFKCkEiIiLilBSCRERExCkpBImIiIhTUggSERERp6QQJCIiIk7JrbwbEBH5X1JRPqlZn1wt8ufpSpCIiIg4JYUgERERcUoKQSIiIuKUFIJERETEKSkEiYiIiFNSCBIRERGnpBAkIiIiTkkhSERERJySQpCIiIg4JYUgERERcUoKQSIiIuKUFIJERETEKV0zBBmGsdYwjCTDML4ptS/YMIwdhmEcv/hnJWvbFBEREbGv33Ml6CXgbpt9TwM7TdOsB+y8uC0iIiLyP+OaIcg0zTgg1WZ3H2D9xb+vB/rauS8RERERS13vPUFVTNP8GeDin2H2a0lERETEem5WFzAMYywwFsALH6vLiYiIiPwu13sl6BfDMKoBXPwz6WpfaJrmatM0W5mm2codz+ssJyIiImJf13sl6B1gODD/4p9vX883qVorjCHT+uPl48ncIYuvsxX7untUF7oMbs+UrrO4a/gddBzQjuT4s7y9fDs/fXPK0tqN2tbnruGdcHVzpWajcA7sPkzHAW0Z2+wJ8vPyLa1dmu1xeSRqJJ7eHvgF+rJg1Ap8/L146J/DKCoqYvu6jzgYd8TSfkbOGUxAiB8NW9djzdSXcXV3pW2vlvgG+oJpMndolKX1vXw8Gb90FIUFRXy96xC7X/3U0nrX0n9SLyKGdmDe0ChOf5dAvRa1GTKtP7mZuezfeZAdG/Y4pI+JL4wFICcjh9VPbiS4apBD5wVcORYAwVWDWPzxHKb1nFuyz0qlz5dFY1/g0SWjMVwMziWlEz1lIwA3NanJc7HPMvTGSOvOZdcaGL6RYHhjpk/C8P8bGJ7gEoCZ/jQYvhj+U4AizOzXIf9zS9qoSOuH7fywXdNTElIZNXcI3r5enDnxMxtnbrF7DxVlPEo/v9RtXotTR8+QnZFD8umzxMx705KaV1MR1o5Lfs+vyMcA+4AGhmHEG4YxmuLw09UwjONA14vbf1jij0n8a8zK6/mnlqhaKwz/YD/Sks8DUFRURF7OBTAMUn8+Z3n9o58dIyoymn3vfkHsxj2smx7DkU+PWV7Xlu1xqRQWxKKxqzj+1Q+E1Qih+5gIYua9wfOjVtBzbFfL+1k3PYaoyGiS41PYH3uI//x7P1GR0Rz97BgfOuAJv/29bYjbso/F41ZxW5/Wlte7ltcXvce+d78o2a7XsjZvL3ufBaOW07RTY4f04B/sh2EYRD28mpSEc9x8WwOHzwu4ciwA7pvSh7it+xxSHy4/X3Iyc1kwajnPjVhGWI1QANzc3egxJoL/vv+VtY0UnsY8/8yv2y4hmOenY+YfBpdq4H0fZuYLmOlPY/jcb1kbFWn9sJ0ftmt6RmomUQ+vZv6wJVS+eLzsraKMR+nnl4/f+A8nj5xmySPRVKoSROgNwZbVtVVR1o5Lfs9vhw02TbOaaZrupmmGm6a5xjTNFNM0I0zTrHfxT9vfHvufYxgGAyb35s2obSX7dm7ay+z7FvLO8g+4b0ofh/XS+f727HrlY4fVu5aE7xOZ8fqTNGxdj/jjPxMaHkLS6RRM03RYD/Va1OaHgycpKioq2dfizqZ8+eEBy2uHhgeTfDoFALPIcT/z77U/9iDDZgxk/gfT2eOgq1QZqZmc/vYMkYtGULvpjYSGh5TLvLDVbWRn4rbsK36iK0dN2jck/ljxVaiBT/TmzSXbwNHDUngSI2g5hnszKPwJw7UqFP2MoxupCOvHJWWt6Y3b1Wf+B9M5dTTeIT2U93h0vr89by19H08fT8YtHE7lGqEODUEVbe3QJ0YDdw7ryOx3nqZmo3DGLxlJ/VZ1aNOzRckBSUs6j4+/t0N6CalWidzsPLIzchxS71oCQvwJCPVnZv8FxG3dR9teLTkbn0Ll8GAMw7C09p3DOhK5aASVqgRx96jOfLB2V8ljDVvX5fj+Hxxy0pyNTyU0PAQAw8Xan/m3lB6P0gZM7s0/7l/ElK6zuHtUF4f1seuVj1k56SWS41OIP5bgsHlRugfbsWjcrj5dH+xE254t6Tuhu+V9lKVJ+4bc3rc162e8CkD9lnW478l7aNSuvuN6MiqBSzBm2njM3A/AszNmYSK4VAUcN4fLa/242vwoa00/su8YT989h5tva2hZP5eU53oKlz+/vPS3zaz663oy0zJJ/PGqt/XaVUVYO2wZjkxeAUaw2caIKNn2DfRhzPyhNI9oyrboHby24B2H9fJbnnnlceYOWUzPsXdSt3ktAoL92TDzNU4esf6VwuCp/Ti09yjffPwt/R7rQe/Ibhzae4R10zeTlpRueX24/Li8/2Is1etWpSC/kOAqQSx7bC2YJqPnDaWwsJDYjXEc2H3Y0n48vDyYuukxZg54vmTfxJUPETPvTZJOnbW0Nvx6T1B+XgGH9h7lo5jyvUoXMbQD907syZkTiWyavZXgqkH0GBNBTlYuZ47/7LDzaMTs+wkI8SctKZ0Nf3+NkGqVHDov4MqxuPRqftiMgeze/IlD7gmyXccG/PUePnnrczBNVk5az4Xc4qtST64dz+LI1Xa7J2h7wteX7zD8MfyfBI/bMHNew3CtCRSAS2XM87MAE8P/CTALMXPfggv/sUsf3arfetl2RVo/bOfHLR0aXramA9zzSDcMFxfSk8+XBFd7qkjjUfr55bEVD+Hq5sKJr37k3ZUfWlazLOWxdsSaW780TbOV7f5yDUEiInJ9rghB5cQ2BIlURFcLQXo7TERERJySQpCIiIg4JYUgERERcUoKQSIiIuKUFIJERETEKSkEiYiIiFNSCBIRERGnpBAkIiIiTkkhSERERJySW3k3ICIif1xF+aRmfXK1/C/TlSARERFxSgpBIiIi4pQUgkRERMQpKQSJiIiIU1IIEhEREaekECQiIiJOSSFIREREnJJCkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQpKQSJiIiIU1IIEhEREaekECQiIiJOSSFIREREnJJCkIiIiDglhSARERFxSgpBIiIi4pTcyrN41VphDJnWHy8fT+YOWQzAoKf6UqfZTcwdsph+j/WgdrMbKSosYt30zaQlpVvSh5ePJ+OXjqKwoIivdx1i96ufWlLnWmzH4/FV4/DwdCcnK5el419k2IyB1GhwA1npWWyatZWUn89Z2k//Sb2IGNqBeUOjOP1dAsFVg3jon8MoKipi+7qPOBh35IoerXDz7Q3pfP/tmKZJzNw3CG9QneEzB3HqaDwfbf6Eg3uOWFLX1qi5Q6hUJRBPb0/mD1tCmx4taN2jOZXDQ9k0ewvffn7CIX2MnDOYgBA/Graux5qpL5N+NoMh0/qTm5nL/p0H2bFhj6X1rzVPB0zuRY2GN1ApLIioyNWWzlPbOdr1wU40ad+QSmFBrJ0eQ0pCKqPmDsHb14szJ35m48wtDunjruF30HFAO5Ljz/L28u389M0pACaufIjMtGzWTH3Zkj4mvjAWgJyMHFY/ubHMc9ZyhjdG8CuYGf/C8JsIBUcwC89A1irra5dSUdZ1uPKc/eHgSYcfF9vz9pGokXh6e+AX6MuCUSvw8fdySE+2fYycM5iOA9oyttkT5OflE1w1iPun9sPV1YVdMZ9w+JNvLenjknK9EpT4YxL/GrOyZLtR2/qkJKSWbDdp34iFo1fy7soP6TEmwrI+2t/bhrgt+1g8bhW39WltWZ1rsR2PxeNW8dyIZbh7FGfVwoJCCi4UkJ9XQMa5LMv7eX3Re+x794uS7e5jIoiZ9wbPj1pBz7Fdy+zRCn0f7U7+hQLy8/KLf24TcrPycPdwJ+nUWcvq2lr7zCssHL2Ss2dS8PbzYt+7XxAVGc26v8VQv1Udh/WxbnoMUZHRJMensD/2EPVa1ubtZe+zYNRymnZqbHn9a82hIoRgAAAgAElEQVTTrf96j0VjV7H9pY8s78d2ju7YsIdFY1ex/u+v0rZXCzJSM4l6eDXzhy2hco1Qh/VRVFREXs4FMAxSL4bAjgPa8t1/v7esB/9gPwzDIOrh1aQknOPm2xqUec5azfAdi5m7rXjDzAbcofBnh9QuraKs63DlOVsex8X2vK0UFsSisas4/tUPhNUIcVhPtn2smx7DkU+PlWz3n9ybvOwLGC4upJxJLetb2FWFeTvM09uDzoNvJ3ZjXMm+D9buZMLyMbS/tw2h4SGW1Q4NDyb5dAoAZpFpWZ0/qkaD6jy75a/FiykQM/dNnhuxjK92HqLbyDsc3k9oeAhJp1MwzV/HyLZHK9RrUYsXn9rEgd2HiRjagUN7jzKt51xenPoyw54daFldW0GVA3hq/QQqh4eSm5UHFF8BmLz6Yb7+6LDD+gCo16I2Pxw8SVFREftjDzJsxkDmfzCdPeXwaresOeDl40mnge347L0vHd6Pi6sL/Sb0YOemvQA0blef+R9M59TReIf1sHPTXmbft5B3ln/AfVP6UKlKELWb3cRXOw9ZVjMjNZPT354hctEIaje9kdDwkDLPWUt5tMcsOAZFF9fTc8Mxz0/F8OwMhp9jeriooq3rpc9Zhx+XMiR8n8iM15+kYet6xB//uUL0BFCrSU0+fOkj1k2LYcj0/pbXqzAhqH6rOgRVDmTiyoeo36oOjdrW578ffM3S8S9yYPdhTn93xrLaZ+NTS0KW4WJYVuePOv1dArMGLsTFxSCkenDJ5ExLSsfH39uyuncO60jkohFUqhJ02f6z8SlUDg/GMH4dI9seregj8cckCgsKyUjNxNvPq2QcMs9l4e7pbteav9WH4eLCP4cv5diX39OwdV2g+ArAMz3m0n9ST4f1UalKEHeP6swHa3cBMGByb/5x/yKmdJ3F3aO6WN6HLds54O3nxYTlY4h++mVyMnMtqXm1Oerq5sqEZaN5I+rfJMcXPwEe2XeMp++ew823NXRYH7+eq+fx8fem2R2NqRwewsg5g2l1VzNuqFfNkj52vfIxKye9RHJ8CvHHEso8Z61keLTF8GiH4dUPw+dB4OITqpkBhqdDerikIqzrVztnHX1cbAWE+BMQ6s/M/guI27qPtr1alntPl5w9k0JGaibZGTl4OGB9NxyZ+gKMYLON8evbWr6BPoyZP5TmEU3ZFr2D1xa8A8AzrzzO3CGLufOBjjRqVx93T3dWPLaW3Ow8S/q69N5xfl4Bh/Ye5aOYjy2pcy2lxyN24x4qVQkseWzpo2sYPLUflWuEEhjiz/KJa0lNTLO0n4ihHbh3Yk/OnEhk0+ytZKVlMXreUAoLC4ndGMepo2d44G+/JvWlj66xpI+OA9txa+cmePt5seqv62nSviGt7m6Ob4AP776w3SH3BLm4ujB+ySjMIhNvXy+WjI+m8+D21G1eC99AH7ZFx3Jo71HL+wDw8PJg6qbHmDngeQBu7dyEHmMiyMnK5czxn0vOI6tca55O3zwJL18vkuPPsue1fXz90TeW9WI7R+8acQeN2tTj1NF4vtp5iJNH4rnnkW4YLi6kJ59n/YxXHdLHLR0aUrd5LQKC/dkw8zVOHim+ClXlxsr0evguy+4JGjH7fgJC/ElLSmfD318jpFqly87ZA7vtf8Vye8LXV+70vhfMCxiencDMhaI0zMyFdq9dWrfqt162XVHWdbjynHXEcbFV+rx9/8VYqtetSkF+IcFVglj22FowTYf0ZPu8n59XQO/Ibhzae4R10zcTEOLPoCf7APD+2p1887F97gmKNbd+aZpmK9v95RqCRETkf1uZIagc2IYgkdKuFoIqzNthIiIiIo6kECQiIiJOSSFIREREnJJCkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQpKQSJiIiIU1IIEhEREadk3f/6W0RE/t+rKJ/UrE+uluuhK0EiIiLilBSCRERExCkpBImIiIhTUggSERERp6QQJCIiIk5JIUhERESckkKQiIiIOCWFIBEREXFKCkEiIiLilBSCRERExCkpBImIiIhTUggSERERp3TNEGQYxlrDMJIMw/im1L4FhmF8axjGQcMw3jQMI8jaNkVERETs6/dcCXoJuNtm3w6giWmaTYFjwFQ79yUiIiJiqWuGINM044BUm30fmqZZcHHzMyDcgt5ERERELGOPe4JGAe/b4fuIiIiIOIzbn/nHhmFMAwqAl3/ja8YCYwG88Pkz5URERETs5rpDkGEYw4FeQIRpmubVvs40zdXAaoAAI/iqXyciIiLiSNcVggzDuBt4Cuhkmmb29RavWiuMIdP64+XjyaKxL/DoktEYLgbnktKJnrKRmo3CGfx0PzAgZt6bnDoaf72lfpOXjyfjl46isKCIr3cdYvern1pS51pKj8fcIYt5fNU4PDzdycnKZen4Fxk2YyA1GtxAVnoWm2ZtJeXnc5b2c/PtDel8/+2YpknM3DdITUzDy8eThXtmsW56DF9s/9rS+pf0n9SLiKEdmDc0itPfJdD1wU40ad+QSmFBrJ0eQ0pCKqPmDsHb14szJ35m48wtlvVy96gudBncnildZ3HX8DvoOKAdyfFneXv5dn765pRldUuzHY8Gf6nLgMm9SfwpiTVTiy/KdhvZmbrNa5GTkcPaaTGW9PH4qnG4ubkCsHDMSro+2Mmh49G0Y2N6R3Yj63w2OzbsoX6r2txQtxouri4seSTa0tqX9dGpMcNnDuLU0Xg+2vwJB/cccVjt0q61ng6Y3IsaDW+gUlgQUZGrLVs/bNexR6JG4untgV+gLwtGrcDH34uH/jmMoqIitq/7iINxFo6Xz0gM7z6YaZOh8Afw7ILheQe4VMPMWgb5BzBCY+HCp5j5hyHnVUva+Md7U0k6fZaczFxWP7kRgOCqQSz+eA7Tes7l9HcJltS1Zbt2BFcNuuJYjJwzmI4D2jK22RPk5+XbtX5FOWdL+z2/Ih8D7AMaGIYRbxjGaGAZ4A/sMAzja8MwXrie4ok/JvGvMSsByMnMZcGo5Tw3YhlhNUIB6DexB0vGR7P00TX0m9jjekr8Lu3vbUPcln0sHreK2/q0tqzOtZQeD4DF41bx3IhluHsUZ9XCgkIKLhSQn1dAxrksy/vp+2h38i8UkJ+XX1Jv0FN92fPaJ5bXLu31Re+x790vSrZ3bNjDorGrWP/3V2nbqwUZqZlEPbya+cOWUPni3LFC1Vph+Af7kZZ8HoCioiLyci6AYZBqcSAtzXY8vvvvCV58elPJdlDlADoOaEdhQSHnfkm3rI/F41bx/OgVZGfkUKlKoMPHo8OAtrww+SWWREYzYFIv6jarxbIJazh5+DQ3397Q8volTMjNysPdw52kU2cdV9fGtdbTrf96j0VjV7H9pY9o2qmxQ/oAqBQWxKKxqzj+1Q+E1Qih+5gIYua9wfOjVtBzbFfL+gAgex3k7fx1O28X5vlnMTMXgXuT4n1mNhieUHjGsjZysy9guLhcdl7cN6UPcVv3WVazLLZrR1nHYt30GI58esyS+hXmnC3l9/x22GDTNKuZpulumma4aZprTNOsa5pmDdM0b73438P2aqhJ+4bEHytOxT5+3uRk5pJ9PhsfP297lbhCaHgwyadTADCLKs47djUaVOfZLX8tfmIBYua+yXMjlvHVzkN0G3mH5fXrtajFi09t4sDuw0QM7UDLrk358ZtTpCWdt7z2tbi4utBvQg92btoLQON29Zn/wXTLrhYahsGAyb15M2pbyb6dm/Yy+76FvLP8A+6b0seSutejWu0qZKVn88Lk9VSuEUK12lUsq1WjQXXcPd1ITUxz+Hi8tWQbDzw7gBGzB+FXyZf0lOJ5+cvJZMJqhFhe/5JDe48yredcXpz6MsOeHeiwur9H6fUUiq96dxrYjs/e+9JhPSR8n8iM15+kYet6xB//mdDwEJJOp/Abd1FYy2ckRuAcyPsPAGZKH8z0qRg+D1pWcs6gf7F43CpCbgihZqNwuo3sTNyWfSVre3lx9LGoKOdsaRXqE6ObtG/I7X1bs35G8SXJ7MwcvP288PH3Jjszx7K6Z+NTCQ0vPgCGi2FZnT/q9HcJzBq4EBcXg5DqwSUTNS0pHR9/60LhncM6ErloBIk/JlFYUEhGaibefl7c2uUWmndpQtcHO9H30e6W1bfto1KVyz+L09XNlQnLRvNG1L9Jji8Or0f2HePpu+dw8232fzVx57COzH7naWo2Cmf8kpHUb1WHNj1blDoe5y09HqX7KGs8bJ09k0pGagZAybGzoo9Gbesz8Il7WDFxHYDDx+PMiUSiIqPZPP8tziWmERgSAEBYzdCSeeEIl37uzHNZuHu6O6zutdiup95+XkxYPobop18mJzPXIT0EhPgTEOrPzP4LiNu6j7a9WnI2PoXK4cEYhoVrrVdfDP9p4FLGleHsdZipYzB8R1zcYQJFgH3f+oFfz5WgsEDg0trtReN29en6YCfa9mxJ3wnlt5Y65FiUUlHO2dIMR6bxACPYbGNElGz7BvowZv5Qmkc0ZVv0Dgb89R4+eetzME1WTlpP9TpVGPjEPRiGwWsL3uanw6ct6evSPUH5eQUc2nuUj2I+tqTOtZQej9iNe6hUJbDksaWPrmHw1H5UrhFKYIg/yyeuJTUxzdJ+Og5sx62dm+Dt58Wqv64veRvoruF3kJqY5rB7giKGduDeiT05cyKRTbO3cteIO2jUph6njsbz1c5DnDwSzz2PdMNwcSE9+XzJom+VZ155nLlDFtNz7J3UbV6LgGB/Nsx8jZNHrLkKZct2PPLz8hk+cxA3Ng7n7eUf8MHaXQyfNQgvXy88vNxZOv5FS/rYHL+KL7YfIP9CPi/PeZ02PVs4dDzqt6pD99Fd8PH3YdPsLbTu0YKwmqG4e7o79P6C9v1a0+ru5vgG+PDuC9vL7Z6ga62nU14aj5evF8nxZ9nz2j6+/uiba3/TP9nH+y/GUr1uVQryCwmuEsSyx9aCaTJ63lAKCwuJ3RjHgd2H7VJ3e0IZ65HXPcVhp+AkZuZy8LgVw60xuARgZr8KRSkYvmMBE7PgW8he/6f76Fb91iv2PbluPHk5F3B1c2HxuNUlwXnYjIHs3vyJw+4Jsl07stKyrjgW/R7rQe/Ibhzae4R10zeTlmS/t9TL85yNNbd+aZpmK9v95RqCRERE7KHMEFQOygpBUv6uFoIq1NthIiIiIo6iECQiIiJOSSFIREREnJJCkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQpKQSJiIiIU1IIEhEREafkVt4NiIiI/FkV5ZOa9cnV/1t0JUhERESckkKQiIiIOCWFIBEREXFKCkEiIiLilBSCRERExCkpBImIiIhTUggSERERp6QQJCIiIk5JIUhERESckkKQiIiIOCWFIBEREXFKCkEiIiLilBSCRERExCkpBImIiIhTUggSERERp6QQJCIiIk5JIUhERESckkKQiIiIOCW38izetGNjekd2I+t8Njs27KF+q9rcULcaLq4uLHkk2uH9THxhLAA5GTmsfnIjwVWDeOifwygqKmL7uo84GHfEIX30n9SLiKEdmDc0itPfJeDl68Xwmffh7unOlx8eYN+7XzByzmA6DmjL2GZPkJ+Xb9f6TTs1ZvjMQZw6Gs9Hmz/h4J4jDHqqL3Wa3cTcIYvtWuu3VK0VxpBp/fHy8WTukMU8EjUST28P/AJ9WTBqBT7+Xg45PrZ9AJeNR3DVIO6f2g9XVxd2xXzC4U++dUgfj68ah4enOzlZuSwd/yLDZgykRoMbyErPYtOsraT8fM6SPmznx5j5D/D91z/yy8lkNs9/y5KaZTEMgxGz78c30IfjX35PyA3BVKtdBb8gP5ZNWENKQqpD+rA9Lkv2zb1sPLo+2InG7epTOTyUHw6dZO0zr9i9h4q2lj6+ahxubq4ALByzEk8fzyvWMKtViPXDvTWGzxAwMzBz3gL3WzBca4Lhinl+hv3rXYWXjyfjl46isKCIr3cdYvernzqsti3b49JvYo8r5mpw1SAWfzyHaT3ncvq7BEv7KdcrQR0GtOWFyS+xJDKaAZN6UbdZLZZNWMPJw6e5+faGDu3FP9gPwzCIeng1KQnnuPm2BnQfE0HMvDd4ftQKeo7t6rBeXl/03mWLRI+HInB1c8XVzYXk+BQA1k2P4cinx6xpwITcrDzcPdxJOnWWRm3rO+wJpbTEH5P415iVJduVwoJYNHYVx7/6gbAaIQ47PrZ92I5H/8m9ycu+gOHiQsoZ68bJto/F41bx3IhluHsUv5YpLCik4EIB+XkFZJzLsqwP2/mRm5WHm4cbyadTrKtZhtv6/IXQ6sEYBpw9k0qtJjeycPRK4rZ8Su2mNR3Wh+1xsR2PHRv2EBUZzeljCexYv9uSHirSWgrFc/P50SvIzsihUpXAMtcwq1WE9cPw6oaZMRfz/AwM31EY7o0wM2ZhFhwH95aW1CxL+3vbELdlH4vHreK2Pq0dVrcspY+Lm7tbmXP1vil9iNu6zyH9lOuVoLeWbOOBZweQkZqJXyVffv7xFwB+OZlMWI0QDjuwl4zUTE5/e4bIRSPwC/Ll7JlUQsNDSDqdgmmaDuzkSjUaVOeTt/7L17u+4akNE/jH4EWW1ju09ygH444QFBbIhKWjSUk8x4qJ62jdvYWlda8l4ftEZrz+JIYBry14p1yOj6e3B50H337ZeNRqUpOVk9aRlnSehxYMu2zhtVKNBtUZOWdwyRWfmLlvYpom7Xq3otvIO3h35YeW1C09Px765wM81XUWpmnyzCuPs+/dL8k+n21JXVvhDapz9D/HeG/VDmZsfYIvdxxgzrtT8fBy5+/3LnBID2Upazzc3N2oVivMsle1FWktvaRGg+q4e7qRmpjm8DWsLOWxfpjZGzD8HoWiNDACoPBU8QOFCeBaDex7Ef+qQsODOfHVj8U9FZXv81lpASF+pKecB36dq+EjOxO3ZR8t72rmkB7K9UrQmROJREVGs3n+W5xLTCMwJACAsJqhDnu1AHDnsI5ELhrBrlc+ZuWkl0iOTyH+WAJn41OoHB6MYRgO7aNSlaDL9ifHp5CRmklBfgGOaOXSopB5Lgv/EH+CKgcyceVD1G9Vh0Zt61vfQBkCQvwJCPVnZv8FxG3dR9teLR1+fADqt6pzxXicPVN8fLIzcvDwdHdYL6e/S2DWwIW4uBiEVA8uOW5pSen4+HtbVrf0/HD3dC/ZzkrPwsPLcT//2fgUzqdmAsVXwVp2bcb03vNYP+NVuo3q7LA+bJU1Hrf3a82+d/5rWc2KtpY2alufgU/cw4qJ6wDHr2G2ym39KDyJef5ZzKzVUHQWXIKL97tWg8JE6+raOBtf/KIewHAphwNwFedTMq+Yq43b1afrg51o27MlfSd0t7wHw5GvogOMYLONEVGyXb9VHbqP7oKPvw+bZm+hdY8WhNUMxd3TvVzexx4x+34CQvxJS0pnw99fI6RaJUbPG0phYSGxG+M4sNsxr6cihnbg3ok9OXMikU2zt5KRmsmY+UPJv1DA/h0HiNv6Gf0e60HvyG4c2nuEddM3k5aUbrf67fu1ptXdzfEN8OHdF7ZzcE/xe+XPvPK4Q+8J8g30Ycz8oTSPaMr7L8ZSvW5VCvILCa4SxLLH1oJpOuT4lO5jW/QOXlvwDvDreNRsFM6gJ/sA8P7anXzzsTX3BJXuI3bjHipVCSx5bOmjaxg8tR+Va4QSGOLP8olrSU1Ms6SP0vNj96uf0L5fG/JyL3A+JcOS+12uxtPbg/FLR5OXnUf8sQRCqgfjF+RLUOUANs3eyg8HTzqkD9t5etPNNa8Yj7+99lcWjFhGbnaeJT1UtLV0c/wqvth+gPwL+bw853UKC4quWMOsVl7rx/aEr3/dcLsFw2cgGH6YmcvAsxOGa3UwPCy/J6hb9VtL/n7pnqD8vAIO7T3KRzEfW1r7t9iup4UFRWXO1WEzBrJ78yd2u3oaa2790jTNVrb7yzUEiYiI/H9yWQgqR6VDkFw9BOlX5EVERMQpKQSJiIiIU1IIEhEREaekECQiIiJOSSFIREREnJJCkIiIiDglhSARERFxSgpBIiIi4pQUgkRERMQplev/QFVEROT/k4rySc365OrfR1eCRERExCkpBImIiIhTUggSERERp6QQJCIiIk5JIUhERESckkKQiIiIOCWFIBEREXFKCkEiIiLilBSCRERExCkpBImIiIhTUggSERERp6QQJCIiIk7pmiHIMIy1hmEkGYbxTRmPPWEYhmkYRqg17YmIiIhY4/dcCXoJuNt2p2EYNYCuwCk79yQiIiJiuWuGINM044DUMh5aBEwBTHs3JSIiImK167onyDCMe4AzpmkesHM/IiIiIg7h9kf/gWEYPsA04K7f+fVjgbEAXvj80XIiIiIilrieK0F1gFrAAcMwfgLCgf2GYVQt64tN01xtmmYr0zRbueN5/Z2KiIiI2NEfvhJkmuYhIOzS9sUg1Mo0zbPX20T/Sb2IGNqBeUOjOP1dAl6+XgyfeR/unu58+eEB9r37BRNXPgRA84imTO81j/hjCddb7gpePp6MXzqKwoIivt51iN2vfmq37309bMcjuGoQD/1zGEVFRWxf9xEH447wSNRIPL098Av0ZcGoFeRm5dqtftVaYQyZ1h8vH0/mDll8RS0ff68r+rHSkGn3Uq12FfyC/Fg2YQ1hNUO5a3gnXN1cqdkonMfbT7e0/iW2x6Vd71a07tGcyuGhbJq9hW8/P8FLx5by1c6DHN//I9uiYy3pY+ScwQSE+NGwdT3WTH2ZjHNZDJjcm8Sfklgz9WVLapbWtGNjekd2I+t8Njs27KF+q9rcULcaLq4uLHkk2vL6l5Sep4vGvsCjS0ZjuBicS0onespGuo24g4Zt61P5hhCWTVhD4k9Jdu+hoozFJY+vGoebmysAC8espHWP5rTt1RLfQF8wTeYOjbK8h4q0ftiesw3+UveKc6XbyM7UbV6LnIwc1k6LsWv9m29rwJ3DOhJctRIfrN3Fvne/YNBTfanT7CbmDlls11q/yb01hs8QMDMwc94C91swXGuC4Yp5fobD2qho5wv8vl+RjwH2AQ0Mw4g3DGO0vZt4fdF77Hv3i5LtHg9F4OrmiqubC8nxKQBERUazbMJaTh4+bdcABND+3jbEbdnH4nGruK1Pa7t+7+thOx7dx0QQM+8Nnh+1gp5juwJQKSyIRWNXcfyrHwirEWLX+ok/JvGvMStLtm1rldWPlWo1uZGFo1cSt+VTajetydHPjhEVGc2+d78gduMey+tfYntc9r37BVGR0az7Wwz1W9UBIDcrFw8vD5JOJlvWx7rpMURFRpMcn8L+2EN8998TvPj0Jsvq2eowoC0vTH6JJZHRDJjUi7rNarFswhpOHj7Nzbc3dFgfpedpTmYuC0Yt57kRywirUfyJHdtf2k3Uw6t5f81OajYOt6SHijIWlywet4rnR68gOyOHSlUC+c+/9xMVGc3Rz47x4QbHnCsVaf2wPWdtz5WgygF0HNCOwoJCzv2Sbvf6hz/9jqjIaBaMXE6TDo1o1LY+KQll/Z6RtQyvbpgZczHPz8DwHYXh3ggzYxZmwXFwb+mwPira+QK/77fDBpumWc00TXfTNMNN01xj8/hNf+YqUFlqNKjO5+9/xfLH1jFoSt+S/e3uacVn733xG//y+oSGB5N8ujhsmUUV75fdQsNDSDqdgmn+2lvC94nMeP1JGrauR/zxny2tb1urrH6sdGD3N8x5dyrdR0dw+JPvSvZ3vr89u1752CE9XE3/Sb2YvPphvv7oMACRLaawcPRK+jza3dK69VrU5oeDJykqKrK0TlneWrKNB54dwIjZg/Cr5Et6ynkAfjmZbPdA/kc1ad/wshdJo+cNZeAT9/D9Vz9aUq8ijkWNBtVx93QjNTGtZF+LO5vy5Yfl83ss5b1+/JZqtauQlZ7NC5PXU7lGCNVqV7F7jTuHdeSfH/6N/7z3JZ0H307sxji717gWM3sDht+jGH6PgxEARReDWGECuFZzWB8V8Xwp10+MvnNYRyIXjaBSlaDL9ifHp5CRmklBfgGG8ev+zoNut+StqrPxqYSGFx8Aw8W4xldb52rjcTY+hcrhwRgXByMgxJ+AUH9m9l9A3NZ9tO1lXZIvq5ZtP1a5NB4dB97G9N7zWD/jVbqN6gxASLVK5GbnkZ2RY2kPpfuwPS5Q/ErzmR5z6T+pJwCmaVJUVETBhQJL+7h7VGc+WLvL7jV+jzMnEomKjGbz/Lc4l5hGYEgAAGE1Q0uu3JaHJu0bcnvf1qyf8WrJvjVTX2bF4+voNrKzJTUrylhcmhuN2tZn4BP3sGLiupLHGrauy/H9P5RL6Civ9eO3ztnSzp5JJSM1A4CM1Ey8/bzs3kvsxjgmtHuGB54dSFDlQCaufIj6rerQqG19u9e6qsKTmOefxcxaDUVnwSW4eL9rNShMdFgbFeV8Kc1w5IkRYASbbYyIK/ZHDO3AvRN7cuZEIptmbyUjNZMx84eSf6GA/TsOELf1M0JvCOaBZweyeNwqu/d16Z6g/LwCDu09ykcx5Xt1wXY8stKyGD1vKIWFhcRujOPA7sNMWj2OgvxCgqsEseyxtXa9xOob6MOY+UNpHtGU91+MpXrdqpfVwjSv6MdKo+YOwS/Il6DKAWyavZUfDp5k8NR+HNp7lG8+/tbS2qXZHpfG7epTt3ktfAN92BYdS1pSOoOm9MXE5IcDJ3lzyTZL+vDw8mDqpseYOeB5oPjV7PCZg7ixcThvL//A8nBUv1Uduo/ugo+/D5tmb6F1jxaE1QzF3dPdoe/rl56n26J3MOCv9/DJW5+DabJy0nr6TribsJqV8a/kx8tztnLq2zN276GijMUlm+NX8cX2A+RfyOflOa9z9kwqE1c+RMy8N0k6ZdcL9ldVkdYP23M2Py//inNl+KxBePl64eHlztLxL9q1/u19W9M84ha8fMtfcvgAAA5YSURBVDz5/P39xG39DIBnXnnc8nuCtid8/euG2y0YPgPB8MPMXAaenTBcq4PhYfk9Qd2q31ry9/I8X2L/r717j7O53vc4/vrMDObiMpghGuVSCEc4cs8+0kUoTnSEbKKbjV20U6H27ijs3Tk7t45CIUrFblfbVm0pqZ22ckvlWsKYmGFixjAuM9/zx1pkDTo9zl7z+834vZ+Ph4dZP4/HfN+Pz/zmO+/1Wz9r3OI1zrmWRY+XiBIkIiIi0RNRgnx0Zgny0/lKkH6BqoiIiASSSpCIiIgEkkqQiIiIBJJKkIiIiASSSpCIiIgEkkqQiIiIBJJKkIiIiASSSpCIiIgEkkqQiIiIBFKc3wFEREQkukrKOzWXlHeuPt/vidWVIBEREQkklSAREREJJJUgERERCSSVIBEREQkklSAREREJJJUgERERCSSVIBEREQkklSAREREJJJUgERERCSSVIBEREQkklSAREREJJJUgERERCSSVIBEREQkklSAREREJJJUgERERCSSVIBEREQkklSAREREJJJUgERERCaQ4Pxdv1bUF7XteRaWUirw5/W3Wvf8lfR7qSb0razOh32TPcpgZg8bfRlKlRLat+YaL69ekcvVKlEsox6QBUyksKPQkx0V1qtFvbC/iE8sxod9k7niiLx17t+HuK3/DiWMnPMlwpl4ju9O5/9VM7D+F3VsyAKhyUTKTP36Csd0msHtLBjfc0YnLmtfhaO5RXhi70JMc1/3yFzTp0JDK1ZJ5YdxCvvtyF3c80ZeE8vHk5+VHPUdqrRSGTx1MTnYu6Vsy2Lczi2bX/AtxcbFMGz6bY0ePR3W9/0vRebS9qSWtujYnNS2FBeMXsXn1duZunca65V+wbe0Ols56z5McDa66jN6jbmLvd5k8/8hLVKhSnsET+pGQFM+e7d8z//FFUV2/acdG3DT0BvJyjrDsxQ+p37IuF19Wg5jYGKb+alZU1/opRfexjre2BaB556aM6z6R9K0ZnmW579m7ATiae5SZD86nykXJ3PX7ARQWFvLunA/4YuXXnuQoKefo4An9Ivby1l1bnJXDC43bN6TTbe1xzrFwwuvElomL2FNe/cObxbp+fGI5hk0bTMHJQta/v5EVr35SrOv9pNhaWNJQsATcoZFYxfFg5cAdweX8Dis/AmLrgsvFHZ4OhZnFGsfXErR66VpWL11L+eQkhkzqT/6R4xzIyKbelbU9zdGux1Wk1KxC/pF89u/J5t25KwC4+6kBJJSPJ+/QEU9y7N2RyR/vnMGYl+8HYM64haTUrOLJ2ufyp6eXkFgxIeLYf4zuwcrFqwBITq1Ix95t2b1lDz/sO+RZjmUvfsiyFz+kXrPatOnegryDecTGxfA/98/hrj8MIDWtKlnpB6K2/iUNa/LJW5/x7pwPGD13OHWb1mbi7VNo3a0FHW5pzfKXPoraWj9H0Xms+svnrPrL59RrVpvG7RqwefV28vPyKRtflsydWZ7l2PLZdmY/vIDu914PQG72YabcOxOAUbOHRn39q3u34dlRc/lh3yEefW0UR3KO8tTgZ+gxrAuN2zfkq79vjvqa51J0H5ty70xi42J5bNEDnhagClXKY2ZMvuc5eo3sTuN2DWh2TRMWTnyd3VsyeHj+rz0rQSXlHH1hzMvAj3v5uXJ4oefwG9mfkY0rLCT3hzyadrwiYk8pbh1uac3KRav47J31jHn5fn9LUMFuXM4YrNLTALicRwGwik+GHrsCjBPgjkNh8f1cOaVEvBzWf1wvls1bQae+7Xlv/krP109rUJNN/9jKtOHP0/2e60lOrchD80aQmpZCft4xz/OUVDfc0YmVi1advvJRo2518g4d4dlR80itVZUadat7liUmNoZ/H9GV5Qs+IiWtKlm7Q6Unc1cWKWlVo7rW1jXfck3fDjy55BE2fPjV6eP7du4ntVZ01/r/6jWyO6Nm3sv6D0L5hrYYzX8PmUGP4Tf6mqtR2/pMemccuzalR/1zvzF1Kbc/1ptB4/tQvnIShw7kALBvZxbVfPi69B/Xi78+twyAtje35NMln3u6fm72YXZv3sPQpwdRt+mlpKRVJSWtKpm7D+Cc8zTLufhxjp5rLy+awwuXt6jD7IcWsGHFV3Tuf/V595TikpJW5fQe6Qr9PxcixNbFkqeDyw89zpuBOzQad/wTSOhV7Mv7XoIGT+jH6rfXERsXS3JqJe6bcRf1W9bjijb1PcuwP/0AOdmHASg4WcDBrBx+P3AaW9d8Q8NWl3mWo6S4dkBHhj49iMrVkyOON2pbn+t++QvadPtXeo64kf17ssnNzgVCG3BC+XhPcsTGxTJi+hBen/JXstIPsH9P9unik1orhf1RvAoEofI397FXGdt9Iq26ND99vNolKexPz47qWj/lfPOA0DPvMV0n0GtkNwCccxQWFnLy+ElPcxT19aqtPNzlCRq3axj1HHu272XK0Fm8MukNfth7kEpVKwKhr0s0rwT+HKf2se3rdgDQqU97T59tn/qavP/yx8wYOZes9AOkb81gf/oBUtOqYGae5igp56jFxJy1lxfNUZxO5di7I5OCkwWn98nz7SnFZX/6j3ukxXhzLvxsBd/iDg4HYiCmOhAuaYXZEFO+2Jc3L58hVLQqrrV1Pv34pqHX0/XOa9m8ehvfrP+OJeFnUWNevt/Te4LKJZRl2LQhHDtyjPStGVxyRRqu0JGQFM/UYbM8u+cjqVIid07qT/POTVk6axknjp3kpqE3sPGjr5kz7hUOZhb/pcEzde5/Nbfc14092/eyYPzi08/mB/z2Vla88nd2b8lg4H/2IT4pnrLxZZg2bLYnOa4f9G9c0fpydm1KZ93yjaxc/CmDn+xLmfiynDh24vQl8Gip3bgWtz/am9wfDnP0cD7b1u6gSYeGlIsvy/QRz5N/xNurhUXn0ahtfS5rXoekSoksnfUeBzMP0Wd0TxyObzfs5M9Tl3qS48SxEwx8vA+XNkrjzWfeYdOnW7n5VzdgMTEcysph3m9fjer69VvW48Yh15BYIZEF4xfRqmsLql2SQplyZTy9J6joPvbpkjXc/titTL7nOc8ynDJo/G1UrFqBg5mHePF3r1G1RmWGTOxPQUEB781fyYYV3lz9KAnnaExsDMOmDo7Yyzv17RCRY+NHm6K+7rl0vLUtzTo1IaF8PM89MI/kapUi9pSZD84v1vVP3RN04thJNn60iQ8Wflys653p3Yz1kQesAlbhQSjbDnf0DSzmx6u2LvdxSLoXi60BMZVxOeOhMDovl8bW2L7GOdey6HFfS5CIiIhcuM4qQT45Xwny/eUwERERET+oBImIiEggqQSJiIhIIKkEiYiISCCpBImIiEggqQSJiIhIIKkEiYiISCCpBImIiEggqQSJiIhIIHn6jtFmlgXs/Cc/TQqwPwpxLhSaRyTNI5LmEUnziKR5RNI8Il1I87jUOZda9KCnJSgazOzzc731dVBpHpE0j0iaRyTNI5LmEUnziBSEeejlMBEREQkklSAREREJpNJYgmb6HaCE0TwiaR6RNI9ImkckzSOS5hHpgp9HqbsnSERERCQaSuOVIBEREZF/WqkpQWbWxcy2mNl2M3vY7zx+MrNaZvaBmW0ys6/M7D6/M5UEZhZrZuvMbInfWfxmZslmttjMNofPk7Z+Z/KTmY0Mf698aWYLzSze70xeMrMXzCzTzL4841gVM1tmZtvCf1f2M6OXzjOPp8LfL1+Y2Z/NLNnPjF461zzO+LffmJkzsxQ/shW3UlGCzCwWeAa4EWgE9DWzRv6m8tVJ4AHn3BVAG2BYwOdxyn3AJr9DlBBTgHeccw2BKwnwXMzsYuDXQEvnXBMgFrjN31Semwt0KXLsYWC5c+5yYHn4cVDM5ex5LAOaOOeaAluBR7wO5aO5nD0PzKwWcB2wy+tAXikVJQhoBWx3zn3rnDsOvAL08DmTb5xz3zvn1oY/ziX0A+5if1P5y8zSgG7AbL+z+M3MKgIdgecBnHPHnXMH/U3luzggwczigEQgw+c8nnLOrQSyixzuAcwLfzwP6OlpKB+dax7Oub85506GH34KpHkezCfnOT8AngZGAxfszcOlpQRdDOw+43E6Af+hf4qZ1QaaA//wN4nvJhP6Zi30O0gJUBfIAuaEXx6cbWZJfofyi3NuD/BfhJ7Nfg8ccs79zd9UJUJ159z3EHpiBVTzOU9JMhh42+8QfjKzm4E9zrkNfmcpTqWlBNk5jl2wzfTnMrPywJ+A+51zOX7n8YuZdQcynXNr/M5SQsQBLYAZzrnmQB7BeqkjQvhelx5AHaAmkGRmt/ubSkoqMxtL6JaDl/zO4hczSwTGAo/5naW4lZYSlA7UOuNxGgG7nF2UmZUhVIBecs697ncen7UHbjaz7wi9VHqNmS3wN5Kv0oF059ypq4OLCZWioLoW2OGcy3LOnQBeB9r5nKkk2GdmNQDCf2f6nMd3ZjYQ6A70d8F+/5h6hJ40bAjvq2nAWjO7yNdUxaC0lKDPgMvNrI6ZlSV0U+NbPmfyjZkZofs9Njnn/uh3Hr855x5xzqU552oTOjfed84F9pm+c24vsNvMGoQPdQa+9jGS33YBbcwsMfy905kA3yh+hreAgeGPBwJv+pjFd2bWBXgIuNk5d8TvPH5yzm10zlVzztUO76vpQIvw3nJBKRUlKHyz2nDgXUKb12vOua/8TeWr9sAAQlc81of/dPU7lJQoI4CXzOwLoBkwwec8vglfEVsMrAU2Etr3Lvh3wj2TmS0EVgENzCzdzIYAk4DrzGwbof8BNMnPjF46zzymAxWAZeE99VlfQ3roPPMIBL1jtIiIiARSqbgSJCIiIhJtKkEiIiISSCpBIiIiEkgqQSIiIhJIKkEiIiISSCpBIiIiEkgqQSIiIhJIKkEiIiISSP8L84pWidFgYqIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pl.figure(figsize=(10,10))\n",
    "plu(hh4 @ uu @ hh4) # diagonal elements all have norm 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Such a transformation of the form $A^\\dagger U A$ is how one finds the equivalent matrix of an opperator in a *different* basis. In this case $H^\\dagger$ happens to be equal to $H$. So the transformation becomes $HUH$.\n",
    "\n",
    "So at this point, to solve the problem the clear path was to find the gates making up the diagonal matrices. This can be done either manually or using Qiskit functionality:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "huh = hh4 @ uu @ hh4\n",
    "\n",
    "qc = QuantumCircuit(4)\n",
    "qc.h([0,1,2,3])\n",
    "qc.diagonal( list( np.diagonal(huh)/np.abs( np.diagonal(huh) )) , [0,1,2,3] )\n",
    "qc.h([0,1,2,3])\n",
    "\n",
    "from qiskit.transpiler.passes import Unroller\n",
    "from qiskit import transpile\n",
    "from qiskit.transpiler import PassManager\n",
    "\n",
    "qct = transpile( qc, basis_gates=['u3', 'cx'] )\n",
    "\n",
    "pass_ = Unroller(['u3', 'cx'])\n",
    "pm = PassManager( pass_ )\n",
    "qct2 = pm.run(qct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which does indeed resolve the diagonal matrix, albeit into a very large circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1683.19x565.88 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qct2.draw(output='mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The manual solution, which is covered [here](https://www.youtube.com/watch?v=3oNXkCZ9odQ) can give a much shorter NISQ-friendly circuit.\n",
    "\n",
    "## By products!\n",
    "\n",
    "As a by-product of my working on this project here is a little interactive function that shows the matrix for a cicuit as you add gates to it. It plots the resulting $U_{circ}$ matrix on the right, and $U_{circ}/U$ on the right, since I used it to compare to the matrix of the problem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Next gate: qc.h(0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Next gate: qc.cx(0,2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Next gate: qc.h(2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Next gate: q\n"
     ]
    }
   ],
   "source": [
    "pl.rcParams['figure.figsize'] = [15,10]\n",
    "circ2matrix()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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