{ "cells": [ { "cell_type": "markdown", "id": "86c26a84", "metadata": {}, "source": [ "# Singular Vector Transformation" ] }, { "cell_type": "markdown", "id": "a444def8", "metadata": {}, "source": [ "## Overview" ] }, { "cell_type": "markdown", "id": "a4ab914e", "metadata": {}, "source": [ "The singular vector transformation implements a matraix that transforms the right singular vector to the corresponding left singular vector. Suppose that we have access to a unitary $U$, its inverse $U^\\dagger$ and the controlled reflection operators $(2\\Pi - I)$, $(2\\tilde{\\Pi}-I)$, just as in the singular value threshold projector example. Our matrix of interest is $A := \\tilde{\\Pi}U\\Pi$ with singular value decomposition $A = \\sum_k \\sigma_k |\\phi_k \\rangle \\langle \\psi_k$. The singular vector transformation algorithm performs the transformation\n", "$$ \\sum_k \\alpha_k |\\psi_k \\rangle \\mapsto \\sum_k \\alpha_k |\\phi_k \\rangle. $$\n", "This algorithm can be used for devising a new method for singular value estimation. It also has many applications, e.g. efficient ground state preparation of certain local Hamiltonians.\n", "\n", "As shown in the proof of Theorem 1 in [GSLW], this algorithm aims to apply the sign function $f$ to the singular values of $A$. In practice, we can find an odd polynomial approximation to $f$, denoted as $f_{\\text{poly}}$, on the interval $D_\\kappa = [-1,-\\delta]\\cup [\\delta, 1]$. By applying $f_{\\text{poly}}$ instead of $f$, this algorithm maps the right singular vector with singular value at least $\\delta$ to the corresponding left singular vector." ] }, { "cell_type": "markdown", "id": "6a5f11c2", "metadata": {}, "source": [ "## Polynomial approximation" ] }, { "cell_type": "markdown", "id": "653abb7b", "metadata": {}, "source": [ "For numerical demonstration, we scale the target function by a factor of 0.8 to improve numerical stability. We can again call our subroutine to find the best odd polynomial approximating $f(x)$ on the interval $D_\\kappa$, solving the problem by convex optimization." ] }, { "cell_type": "code", "execution_count": 1, "id": "e94bd673", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "norm error = 2.1228236946058132e-09\n", "max of solution = 0.8000006369361398\n" ] }, { "data": { "image/png": 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", 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VKqxatQpPP/00brnlFjz33HNo3ry51w8kmLk7hogVIiIiIt/wKBA9/PDDmDlzJkpLS9GnTx/cdddd6N27N5o0aWL5mv379+Onn37CZ599hgULFmDRokX45z//ibfffrvCja8q3O0yY4WIiIjINzwaVF2tWjX885//xPjx41GvXj2Pd3bs2DG8/PLL+PDDD5Gbm+vx6/3Fl4OqNU1DWJj5LeXq16+PmjVrYsuWLQCAP//8s9InsSQiIgpWPhtUvX//ftStW7fcDatfvz7eeustTJw4sdzbqGrsusF42T0REVHl8Ohu92oYOnDgQLl2WpFQVdXYhRx2mREREVUOjwKRqnv37vjjjz+81ZaQZBdy1KvMOKiaiIjINyoUiDIyMtC7d298++23LtcVkwuSkSeBiBUiIiIi36hQIPrhhx8QGRmJG264wfLGr9u2bcONN96IHj16VGRXVZarQMTL7omIiHyvQoHoiiuuwLp165CWloYRI0bg+eef15/bt28fhg4dig4dOmDp0qW2d5cPZXIgCg8PNzzHMURERESVo8K37mjZsiXWr1+P6667Ds8++ywOHjyIiIgIzJkzB8XFxahbty4mTJiABx54wBvtrXLkkBMREWF4zDFERERElcMr9zKrU6cOlixZgvbt22POnDkAgJSUFDzxxBN48MEHERMT443dVEkiADkcDqcKES+7JyIiqhwV6jIDgJycHEydOhVt2rRBeno6gPNdPd26dcOoUaMYhlwQISc8PNxpgkbe3JWIiKhyVCgQTZs2DY0bN8akSZOQn5+PMWPG4PDhw7jtttuwZMkSXHXVVThz5oy32lolyYHI4XAYnuNVZkRERJWjQoHoqaeeQlZWFkaMGIE9e/bgtddeQ/369bFgwQI8+uijWL9+PXr06IGDBw96qblVj12FiIGIiIioclQoEN15553YuXMnPvjgA9SvX9/w3BtvvIFXX30Ve/bsQffu3bFx48YKNbSqctVlxsvuiYiIfK9Cg6o//fRT2+fHjh2LtLQ0DBs2DH369EFWVlZFdlclscuMiIjI/yo8qNqVO+64A9999x0iIrxyQVuV40mXGStEREREvlEpKaVXr15Yu3ZtZewq6MiBSKV2mbFCRERE5BseVYh27dpV7h21bt3aK9upajzpMmOFiIiIyDc8CkRt2rTB0KFDsW3btnLtbPPmzRgyZAjatm1brtdXRXZdZvLz6tdERETkPR4FomeeeQZLly5F+/bt0alTJ7z22mvYsGEDiouLTdcvLCzEL7/8gmnTpqFt27bo3Lkzli9fjkmTJnml8VWBXYVIfl79moiIiLzHozFEkydPxoMPPoipU6di7ty5GDduHBwOByIjI9G4cWPUqFEDCQkJyMrKwtmzZ3Ho0CGUlJRA0zQkJSXh0UcfxcSJE5GSkuKr4wk6ciAyCzzqvc2IiIjI+zweVF27dm289dZbePHFF7FgwQIsW7YMa9euxV9//eW0bt26ddGzZ08MGjQId9xxB2/jYcJVl1lJSYnTukRERORdHgWiFi1a4KGHHsJjjz2G2NhYDB8+HMOHDwcAnD59GqdOnUJmZiaSkpJQu3ZtVoLc4EmXGStEREREvuFRINq3bx+2bNmiP54yZQoGDBiAbt26ISUlhQGoHDiomoiIyP88CkSxsbHIz8/XH0+ZMgWHDh1Ct27dvN6wUOEqEMlYISIiIvINj64ya968OdasWYPMzExftSfkiDFCVl1mMlaIiIiIfMOjQDR06FAcO3YMLVq0wH333QcAOHPmDANSBRQVFQEAoqOjXVaIGIiIiIh8w6Mus3HjxiEjIwNvv/02Zs+eDYfDgWXLliE5ORkNGjRAhw4d9H/t27dHkyZNfNXuKsOTQMQuMyIiIt/wKBA5HA688MILmDRpEtauXYv+/fvr8w/t2LEDS5YswZIlS/Sun8TERLRr1w4dOnRAx44dcc899/jiGIJaYWEhACAqKopdZkRERH5Srpu7xsTEoG/fvgCA3r17Y9asWSgtLcWOHTuwefNm/Pnnn/r/q1evxurVq+FwOBiITLBCRERE5H8Vutv9jz/+iIiI85sIDw9H27Zt0bZtW9x99936OkePHtXDETljhYiIiMj/KhSIevfu7XKdtLQ0pKWl4brrrqvIrqosUSGKiopihYiIiMhPPLrKjLxPVIh4lRkREZH/MBD5mVwhctVlxgoRERGRbzAQ+RnnISIiIvI/BiI/kwdVMxARERH5BwORn8kVInaZERER+YdXA9GGDRvw888/e3OTVR4rRERERP5XocvuVXfffTf27Nmj37CUXONl90RERP7n9S4zTdO8vckqTb7snhMzEhER+QfHEPkZK0RERET+x0DkZ7zsnoiIyP8YiPyM9zIjIiLyPwYiPyvP3e4PHTqE+fPnMyARERF5CQORn5WnQtS4cWMMGTIEc+fO9Xn7iIiIQgEDkZ9VZFA153wiIiLyDgYiP6vI3e6joqJ81i4iIqJQwkDkZxW52310dLTP2kVERBRKGIj8rCIVIgYiIiIi72Ag8rOKjCFiICIiIvIOr97L7JJLLkF8fLw3N1nleXK3e1aIiIiIfMOrgWjhwoXe3FxI8PRu93IoYiAiIiLyDnaZ+ZmnEzMWFBTojxmIiIiIvIOByM88nZgxPz9ff8zL7omIiLyDgciPSktL9YHS7g6qzsvLq4ymERERhRQGIj8S1SHA/cvu5QqRetUZERERlQ8DkR+J8UOA+xMzyoGIN3clIiLyDgYiP5IDUWRkJCtEREREfuKVy+6Li4uxe/dunD59GpmZmUhKSkJKSgpatmyJyMhIb+yiSlIHVHs6qJqBiIiIyDvKHYhOnz6NOXPm4JtvvsFvv/1mGA8jxMTEoGvXrhg0aBCGDx+OlJSUCjW2qpEvuQfg1qBqBiIiIiLv8zgQ7dmzB5MmTcLixYv1E3qtWrXQuXNnJCcnIzExEZmZmTh37hx27dqFVatWYdWqVXj66adxyy234LnnnkPz5s29fiDBSK4QAa4DkVoh4hgiIiIi7/AoED388MOYOXMmSktL0adPH9x1113o3bs3mjRpYvma/fv346effsJnn32GBQsWYNGiRfjnP/+Jt99+u8KND3byfcwAeDyomhUiIiIi7/BoUPVHH32EBx98EIcPH8aKFStw77332oYhAGjatCnuu+8+/O9//8OhQ4cwcuRIzJo1q0KNrirkO90DnleIGIiIiIi8w6MK0f79+1G3bt1y76x+/fp46623MHHixHJvoypRK0SejiFilxkREZF3eFQhqkgY8sV2gp1aIeJVZkRERP5RoXmIDhw44K12uO3nn3/G9ddfj3r16sHhcOCrr75y+ZpVq1ahc+fOiImJQdOmTfH+++/7vqFu8LRCVFpaarh1BwMRERGRd1QoEHXv3h1//PGHt9riltzcXLRv3x7vvPOOW+sfOHAA1157LXr27IlNmzbhySefxCOPPIJFixb5uKWuRUZGokGDBnrFjJfdExER+UeFJmbMyMhA7969sWDBAlxzzTW26/7666+47LLLKrI7AMDAgQMxcOBAt9d///330bBhQ7z55psAgNatW2PDhg149dVXceutt1a4PRXRv39/HD58WH/saZcZxxARERF5R4UqRD/88AMiIyNxww03YPbs2abrbNu2DTfeeCN69OhRkV2V2/r163H11Vcblg0YMAAbNmxAcXGxX9pkhRUiIiIi/6hQILriiiuwbt06pKWlYcSIEXj++ef15/bt24ehQ4eiQ4cOWLp0KVJTUyvc2PI4efIk6tSpY1hWp04dlJSUID093fQ1hYWFyMrKMvyrDBxUTURE5B8VvpdZy5YtsX79elx33XV49tlncfDgQURERGDOnDkoLi5G3bp1MWHCBDzwwAPeaG+5qEFD0zTT5cK0adMwZcoUn7dLxQoRERGRf3jlbvd16tTBkiVLULNmTcyZMwcffvghatSogddeew379+/HI488ol9aXtnq1q2LkydPGpadOnUKERERqFmzpulrJk6ciMzMTP3fkSNHKqOp5bp1R25uLn766SeUlJQYlpvdW46IiIjMVTgQ5eTkYOrUqWjTpo3eBaVpGrp164ZRo0YhJiamwo2siO7du2PFihWGZd9//z26dOmCyMhI09dER0cjMTHR8K8yWFWswsPDAZhXiIYMGYKrrroKU6dO1ZdfeeWVqF27NnJycnzbYCIioiqiQoFo2rRpaNy4MSZNmoT8/HyMGTMGhw8fxm233YYlS5bgqquuwpkzZ7zVVgDnA9jmzZuxefNmAOcvq9+8ebN+tdbEiRMxbNgwff2RI0fi0KFDGDt2LHbu3IlZs2bho48+wuOPP+7VdnmDVYUoIuJ8z6bZGKJly5YBAF577TV9+bp165CVlYWff/7Zh60lIiKqOioUiJ566ilkZWVhxIgR2LNnD1577TXUr18fCxYswKOPPor169ejR48eOHjwoJeaC2zYsAEdO3ZEx44dAQBjx45Fx44dMWnSJADAiRMnDJeyN2nSBMuXL8fKlSvRoUMHPP/885g+fbrfL7k3U55AJGRnZzu9jhUiIiIi91RoUPWdd96J5557Ds2aNXN67o033kCDBg0wbtw4dO/eHcuWLUPnzp0rsjsAQO/evfVB0WbmzJnjtKxXr16VPoFkeVh1mYlAVFZWZpip2tU8RGYhiYiIiJxVKBB9+umnts+PHTsWaWlpGDZsGPr06VNpl68HK6sKkRjr5M5l93JYZIWIiIjIPV65yszOHXfcge+++06vcpA1V4HIncvu5apRbm6ul1tIRERUNfk8EAHnu6zWrl1bGbsKaq66zMwuu4+NjTWsKwcidpkRERG5x6NAtGvXrnLvqHXr1l7ZTlXmalB1SUmJYX6hsrIyJCQkGNaVAxG7zIiIiNzjUSBq06YNhg4dim3btpVrZ5s3b8aQIUPQtm3bcr2+qnMViNTJFhmIiIiIvMOjQPTMM89g6dKlaN++PTp16oTXXnvN9iaphYWF+OWXXzBt2jS0bdsWnTt3xvLly/VL5MnIqsvMagLJsrIyw6SRJSUlDERERETl4NFI58mTJ+PBBx/E1KlTMXfuXIwbNw4OhwORkZFo3LgxatSogYSEBGRlZeHs2bM4dOgQSkpKoGkakpKS8Oijj2LixIlISUnx1fEENVcVIlVpaamhQpSZmcmrzIiIiMrB40u/ateujbfeegsvvvgiFixYgGXLlmHt2rX466+/nNatW7cuevbsiUGDBuGOO+7w+208Ap2rQdWqsrIyw2syMjIQHx+vP+Y0B0RERO4p97XwsbGxGD58OIYPHw4AOH36NE6dOoXMzEwkJSWhdu3arAR5yNVl96qysjLDpfcZGRmGq84yMzO920AiIqIqymuTA6WkpDAAVZAciMLDw/XxQHYVInnM0Llz51C7dm39MQMRERGRe3w2D5F6RRS5Jnd/ySHIbgyRHIgyMjIMjxmIiIiI3OOzQJSamoqxY8di9+7dvtpFlaNWiAS7CpHaZVZSUqI/zs7Odnm/MyIiIvJhIHruuefw448/4uKLL0avXr0wb948FBUV+Wp3VYIciOQQZDeGyK5CBHBgNRERkTt8FohGjx6NzZs3Y+3atWjatCnuv/9+1K9fH+PGjTO9Io0q3mV27tw5p0DEbjMiIiLXfH4vs27dumH27Nk4fvw4xo8fj7fffhutW7dG37598d///tfXuw8qVhUiNRDVqVMHgHmXmRqIMjIyfNBSIiKiqqVSbu66ZcsWPPXUU3jhhRdQvXp1jB8/Hmlpabj55psxfvz4ymhCUHB3DFGDBg0AuNdlxgoRERGRaz4LRPn5+Zg1axa6deuGjh07Ytu2bfjggw9w9OhRTJs2Df/5z3+wcOFCvP/++75qQtCx6jILCwszPNewYUMA5oFIHlQNMBARERG5w2vzEKnq1q2L8PBw3H333Zg9e7bhbvfCFVdcgZo1a/qqCUHHqsssLCwM4eHhetgRgcjVZfdiGREREdnzWSB6/fXXcddddxlmTlZVr14dBw4c8FUTgo5Vl5ldhUgeQ8RB1UREROXjs0B03333+WrTVZZdl1lxcbH+OC0tDYB7Y4hYISIiInLNq4HoqquucnvdH3/80Zu7rhKsuszUm76Km+RyUDUREZF3eDUQNWrUyJubCzl2FSIhMTFRf1xaWmroMsvPz3e6ZQoDERERkWteDUSzZ8/25uZCjt2gaiE1NVV/rFaIAOd7yLHLjIiIyLVKmYcoNzcXubm5lbGroOZOl5mngaigoMAXTSUiIqpSfBqI5syZg6ZNmyIxMRGJiYlo2rQpq0g25OCjXmUmpKam6s+pV5kBzoGIN3clIiJyzWdXmc2YMQNjx47Fgw8+iF69egEAVq5ciVGjRiEvLw8PPfSQr3YdtDztMlPnIQIYiIiIiMrDZ4Horbfewuuvv45Ro0bpy2666Sa0aNEC06dPZyAy4Y0xRGoXGQMRERGRaz7rMjt48CAGDBjgtPyaa67BoUOHfLXboGZ1lZnD4cDtt9+OGjVq4J577jEEIrXLTA1E6q08iIiIyJnPAlFqaip+//13p+W//fabfrd2MrKbqXr+/Pk4efIkatWqpT/HLjMiIiLv8FmX2fDhwzFq1CicPn3aMIbo2WefxejRo32126Bm12XmcDgQFRVlWM+dq8wYiIiIiFzzWSCaNGkSSkpKMH78eBQVFUHTNERHR2PMmDGYPHmyr3Yb1NyZmFF+zKvMiIiIvMNngSg8PBxTp07FM888g71790LTNLRo0UK/7QQ5c/fWHVYzVQMXxhCFh4ebdqkRERGRM58FImH9+vXYvn07HA4H0tPT0adPH1/vMmi5WyESY4jkAdNRUVEoKirSK0TR0dHIy8vjoGoiIiI3+CwQHT58GLfccgv++OMPJCUlATh/X62OHTviyy+/5H3PTLhz2b38uLi4WF8WHR1tGohYISIiInLNZ1eZPfDAAygrK8PWrVtx7tw5nDt3Dlu3boXD4cDIkSN9tdugZnWVmVWXmRqIgAtjiMQAbAYiIiIi13xWIVq5ciVWrlyJSy65RF92ySWX4J133sFVV13lq90GNU8HVcuBSAQgBiIiIiLP+axCVLt2bVSrVs1pebVq1VCzZk1f7TaoudtlJqpHZhUiMaiagYiIiMh9PgtETzzxBJ544glkZGToyzIyMvDkk09i/PjxvtptULObmNFsPbsuM/GYg6qJiIhc8ygQtWjRAm+++aZb637xxRdYu3Yt0tLS0LlzZ3Tp0gVpaWlYs2YNFi9ejKuuukr/R+fZ3bpDpgYkwLnLTASi0tJS5OfnY/jw4Vi4cKHLNhQWFmLWrFk4cuSI5wdAREQUpDwaQ7Rv3z5s2bJFfzxlyhQMGDAA3bp1c1q3cePGaNy4sWFZ27Zty9fKEOHpVWYyuzFEn376KebOnYu5c+dC0zTbNixevBj33Xcf7r77bsydO7d8B0JERBRkPApEsbGxyM/P1x9PmTIFhw4dMg1Es2fPrnjrQoy7XWbyc+L5yMhIAOaBSA5BBQUFtpNjHj9+HACQnp5enkMgIiIKSh51mTVv3hxr1qxBZmamr9oT0srbZRYWFqavLwZVy11mtWrV0tfds2ePbRtycnIAON8CpKLWrVuHJ598Um8fERFRIPEoEA0dOhTHjh1DixYtcN999wEAzpw5w4DkJeXtMgsPD9fXVytEJSUlhivNdu7caduG7Oxsw3bsrF69Gl27dsWvv/7qct0ePXpg2rRpePfdd12uS0REVNk86jIbN24cMjIy8Pbbb2P27NlwOBxYtmwZkpOT0aBBA3To0EH/1759ezRp0sRX7a6SvBmI5AqRXSASN4gVr/ekQnTllVcCAIYMGYIDBw64XB+A2+sRERFVJo8CkcPhwAsvvIBJkyZh7dq16N+/Pxo3bowaNWpgx44dWLJkCZYsWaJ38SQmJqJdu3bo0KEDOnbsiHvuuccXx1BleHovM/l5qwpRaWmp4dJ7ORAVFRWhQ4cOiI6Oxh9//AGHw6EHoqKiIrfbnZub6/a6iYmJLtf5/fffUVJSgu7du7u9XSIioooo10zVMTEx6Nu3LwCgd+/emDVrFkpLS7Fjxw5s3rwZf/75p/7/6tWrsXr1ajgcDgYiFzy9271g12VmF4h++ukn/XF+fj6qVavmUZeZkJaWZvu8HJjEfe2slJSUoG/fvigpKcGZM2cQGxvrdjuIiIjKq0K37vjxxx/1E3F4eDjatm2Ltm3b4u6779bXOXr0qB6OyJ6nt+4Q5EBkNqha7jLbvXs3SktLER4ejtWrV+vLxSSP7naZyc+7CkSnT5/WvxZBzUp2drYeys6ePYv69evbrk9EROQNFQpEvXv3drlOWloa0tLScN1111VkVyHB05mq5cciEInwI1eI5BmtCwsLcfDgQTRr1sw2ELnqMjt48KD+dfXq1W3XPXXqlGH/dsT+1a+JiIh8yWe37iDPudtlpo4hkitEgqgQAcZbfADnu83y8/MNV4eJbjV3u8z279+vf+0qPMmByNVl93L3mmgLERGRrzEQBRBvdJkJcteUGm7OnDmD9evXG5bbdZmdOHECX3/9NcrKyvRl+/bt07/2JBC5CloMRERE5A8edZn54lYOHTp0QLt27by+3WDkjS4zQa4QqYGltLQUK1euNCwTFSKzQPTwww9j0aJF+P7779G/f38ArBAREVHV4lEguueee5y6b8pL0zQ4HA5MnjyZgej/88Y8RIJdhaikpMTp5q2iQiRCSHFxsf4ZnThxAgBw+PBhff3yBiKOISIiokDkUSDyxf3JOnTo4PVtBis5bMoVovKMIZIDkVqVKSkpMVyKD5wPQEVFRYbxRkVFRYiOjtZDTFZWlv4cu8yIiKgq8SgQDR8+3FftIFyo/ISFhRlCkLe7zMwCUUlJiVNFprCw0BCIREDRNI1dZkREVKVwUHUAkQORHHrK02UWGRmpf23WZWZWIVIDiAg6aoUoPT0deXl5TutZKW+FiF1mRERUWRiIAoioCrkKRGZdaGogioiI0F/nTiCyqhDJ/4tAJIchs+2rWCEiIqJAx0AUQESACQ8PN4Qgs4Hs8jgis0AUHh6ur+NuhcjdQKTOayRXiPbu3Yu1a9fqj8vKygwzVXsyqJqBiIiIKgsDUQBxdwyRusxsDJHZ/c0EXwaiQYMG4corr9SvTMvIyDDsy5MKkTtdZgcPHnRqDxERkacYiAKIu11m6jKrLjNPKkQlJSVujyGyC0RHjx5FWVkZjh49CsDYXWbWFpUnXWYbN25EkyZNcM0119iuJ/vss8+wadMmt9cnIqLQwEAUQESA8XaXmTtXmXmjQqRpml4ByszMBOAciLw5hmjVqlUAzt9keNu2bbbrAsD27dsxdOhQXi1JREROGIgCSLNmzXDHHXdg7NixXuky88YYopKSEv2WHa4Ckdm6586dc9qmHU+6zOLj4/WvX331Vdt1AehVK9GdR0REJDAQBZCwsDDMnz8fzzzzTIW7zDwNRFZdZvJr1UAk5joSgUiu/ogKkXguJibGaR0zngyqltv22WefuQw6ok0crE1ERCoGogDljUCkDqoWr/GkQqQGIk3T9NfGxcXp68ndZWJdsV0ASEhIMLTFiiddZurNabdu3Wq7fkZGhv46V3MnERFRaGEgClByl5mrMURmXWZmg6pFRceTeYjk0FFaWor8/Hw95IhApGkaSktLTStEYl3RveXNMUTqtlyFLRGI3Nk2ERGFFgaiAOWLLjPRbSUHIhGSzGaqVgMRcL7yo4Yc4HzXmLcrRLm5ufqYJDPqtlxtW4Q0gIGIiIiMGIgClDcDkTqORw5EsbGxAMy7zNQxRIAxEIkKkVjXrkIkAlFBQQE0TbM8brkNmqY5zYotY4WIiIi8hYEoQLnqMivPVWZmgUhe5qrLDDgfJETIqVatmr7c3UAkLzMjV4jE/qx4WiFiICIiIisMRAHKVYXI1TxEERER+jIRVET3WGlpqWmFyNMus8jISERFRQFw3WUmd6+JKtFDDz2Ed999V1+uaZpTILK79J5dZkRE5C0MRAGqsrvM5ApR9erVAbgORBEREZaByGpQtdjuhg0bMGPGDIwePRqlpaX6cjFmSKxvF1zYZUZERN4SlIFoxowZaNKkCWJiYtC5c2esXr3act2VK1fC4XA4/du1a1cltthzngSiinSZmY0hqlmzJgDXY4jkClFhYaFthSgqKgqRkZEAzgcZuf2HDh0CYOwuq1OnDgDvdpmxQkRERFaCLhDNnz8fjz32GJ566ils2rQJPXv2xMCBA3H48GHb1+3evRsnTpzQ/7Vo0aKSWlw+nowhclUhEhUYs8vuzbrMRCCqSJeZOjFjZGSkHsgKCwsN44h27twJ4EL3WHR0tF6lsusyUytEruYWKk+FaP/+/YbXWSkrK8PJkyfd2iYREQWeoAtEr7/+Ou677z6MGDECrVu3xptvvokGDRrgvffes31d7dq1UbduXf2fPAYnEFV0DJEciAR3B1W7CkTitZ6MIYqMjNQDWUFBgWG7olonKkRxcXH6IGw5uCxfvhxvvPGG/lhsIzEx0fDYiieBqKCgAKNHj0azZs3Qr18/23UB4LHHHkNqairWr1/vcl0iIgo8QRWIioqKsHHjRlx99dWG5VdffTXWrVtn+9qOHTsiNTUVffv2xU8//WS7bmFhIbKysgz/KltFu8zkQdWCqy4zEWhEdcadLjP59h1yIMrOzkZpaalhXblCJFdzRIXIVSAaNGgQxo4di99//13fDgAkJSUZHptRr6JzFYgmTJigD/jeuHGj7boAsHnzZgDAhg0bXK5LRESBJ6gCUXp6OkpLS/XxJUKdOnUsuytSU1Mxc+ZMLFq0CF9++SVatmyJvn374ueff7bcz7Rp05CUlKT/a9CggVePwx3e7DITXHWZiUAhT6LoSZdZfn6+Yd2cnBzT8KRuVw1E8fHx+qBqEWLkbYvuOBHA3KkQqaHWVSDat2+f/rVotx2xvb///tvlukREFHgiXK8SeNSAoGmaaWgAgJYtW6Jly5b64+7du+PIkSN49dVXceWVV5q+ZuLEiRg7dqz+OCsrq9JDkTevMhPsuszkwFHeQKSO6cnMzDQMqpZv8KoGIk3T9PBjViE6fvy4vr4crAD3ApE6DsiT24KIq9/MPgd1ewxERETBKagqRLVq1UJ4eLhTNejUqVNOVSM73bp1w549eyyfj46ORmJiouFfZfNkDJGrq8wEEUiKi4udKkTyFV5ywPBWILKrEJ07dw6nT582dJmpl90fO3ZMX1/sx5NAJF9hJo7DjqeX9It2njp1ynY9IiIKTEEViKKiotC5c2esWLHCsHzFihW4/PLL3d7Opk2bkJqa6u3meZVc8SpPhUi+uasgj/cRRCCSx9eI6ow8hkgEH3cvuzdb16pCBJyvEpkFItEuORCJapZVl9nZs2fRvn17vPDCC/prKlIhkvdpxdMK0WuvvYZBgwa5DFpERFQ5gq7LbOzYsbj77rvRpUsXdO/eHTNnzsThw4cxcuRIAOe7u44dO4a5c+cCAN588000btwYl1xyCYqKivDJJ59g0aJFWLRokT8PwyU58JR3DJHVoGr5ZC+WiTASFham35JDruTUqlULx48f90mFCDh/pZkIavHx8fp2xevtKkTqoOpff/0VW7ZsQV5eHp588km9LTJPA5H6WFZSUqIHJncD0csvv4xTp05hw4YN6NGjh1uvISIi3wm6QDR48GCcOXMGzz33HE6cOIE2bdpg+fLlaNSoEQDgxIkThjmJioqK8Pjjj+PYsWOIjY3FJZdcgm+++QbXXnutvw7BLb4cQySf3NUus+joaEPVR4SMlJQUHD9+3HAvM7uZqgHPKkRnz57Vg19cXJxhu4BnFSJxQ9jTp0/rrxEVotjYWOTn57sMRGpFyK5CJFfX/v77b9sxbaKdomvNH1cwEhGRs6ALRAAwatQojBo1yvS5OXPmGB6PHz8e48ePr4RWeZerLrPyjCGS5wES1ApRdHS0oWtNhIzk5GQA1leOVbRCVFRUpK8bFxenz2rtToXIKhBlZmaisLAQ0dHReiBq0KAB/vrrL692mcmhJj8/Hzk5OYab2arkY+GM2UREgSGoxhCFEm90mXlSIRJVjqioKNPgIocOd7vMsrKyTGeqNqsQFRUV6UGmWrVqtoFIhBOrLjOxHeBClUh0maWlpQHwbpeZui1XA6uPHDli+VoiIvIPBqIAVdEuM7tB1SJQOBwOfZmrLjM5ELmaqVq0xZMKkTwPUkxMjMsKUVlZmR62rCpEwIVAJFeIgPMBUNM0WBHHIt5DuwqRGmpcjSM6evSo5WuJiMg/GIgClDdu7qouU7vM5NmszbrMylshql27NgDPxhAVFRXpAScqKsqwXU3TDPMQ5efnG66UswtEolojApGoEJWVlRnWmzlzpmEGc3EsNWrUMDw242kgYoWIiCjwBOUYolDgyRgiT7vMysrKAJwPRKISIwKR3GUmjyESoaOkpERfZnXZfZ06dXD8+HGPxxDJgUiuEKWnpxtuBltQUGAIKHZdZiIQiS6z+vXrw+FwQNM0ZGdnIy4uDj/99BMeeOABAOcn+SwuLtZviFujRg2kp6ezQkREVMWxQhSgfDmGSJArRCJwuKoQARfCk1WFSEyS6c5M1WKZXSCSu8uA8xUiOVCJOYvEMnmSSRGIRPBITEx0mvTxt99+M2xfDluiQuTNQORJhai0tBS///47Nm3aZKiKWZk1axaeffZZ2+5AIiJyxkAUoLxxc1d3ApEIHoKrMUTAhQHYVoFIDhGuKkTiaqzi4mLTLjOzQCQHqujoaMNNYwHzCpHYdnR0tNNtQdLT0522L4gb3XpzULUnFaJXX30VXbt2RadOndCrVy/bdQHgvvvuw5QpU/Drr7+6XJeIiC5gIApQFZ2p2u6ye8EqEJl1mYmqCmAMRGaX3YsQoY43kscwqYHIqkJUVFRkWiES+1IrWoD5oGp52yLciTAiz1dUXFysbzsqKkqfpNJfFaJdu3bpX2/cuNF2XblqtnfvXtt1gfPdg7t379a7B4mIQhkDUYDy5F5maiByOBxwOByWM1ULcpeZYHXZfUxMjL7cVYVIjOkpKCgwHVQtb1cELbsuM3XyQrXLzS4QqRWiqKgoPYSJ7coVndzcXP04YmJi9GkJ3KkQidvB2AWigoICQwBzFYjkYykuLjaMpbJqB+DePdW+/PJLtGrVCpMmTXK5LhFRVcdAFKA8GUOkdpmJsOTNLjO5EiMCkdVM1d6sEMldaeJ98KRCJIKBfE82tcvsxIkT+vp5eXl6NUgORGLZzJkzUb9+fWzdulV/jdhOs2bNABgrTiq12uVJIDJ7LJODozxbu5XNmzcDgOFYiIhCFQNRgKpIl5lVIDLrMjO7NN+sG8wsEHmjQmQViOQxROoEjOoYItGukpISp8vpzSpEcXFxAC6Ei0OHDunr5+Xl6ccRGxurt1kEogceeADHjx/H4MGD9deIUCMGk8vdaxkZGdiwYYP+WB4/JL/WijxAXG6zGTkQ7du3z3a7wIX35syZMy7XJSKq6hiIApSnEzOGhYXpIUqEnPJUiOQuM+BC+HEViAoLC/UgIFeI5Jmq7SpE6qBqswqRCETyVWZyl5nYp6sxRHKIy8rKwrlz5/T15UBk12W2c+dO/WsRalJSUpzWvffee3HppZfi999/B3ChGqWOY7JS3grR/v37bbcLXOjaUweVExGFIgaiAOWqy0y9lxngHITK22UmBwxxwpaXi3mMrOYhcqdCJAKKO4Oq1Rmp5XmI1PbKtwABzgeI3Nxcy0AkV4fE+nIgUitEZsR7VKtWLf34BDEoes+ePYbt1K1b1/BaKxUJROJzsuJJhai0tBQDBw7Ebbfd5nJdIqJgxEAUoDztMgOcA5HVTNWCVZeZCAzAhZOsGjwAYyCS7/juagyRO4Oq5S4zVxUiub1qhQg4f+IvbyBSK0Qi9Ih1AfsK0dmzZwFcmClbPCfWdXULEfVY1C40mRyICgoKcPLkSct1gQuB6OzZsy6vNNu8eTO+/fZbLFq0yDaUEREFKwaiAOVplxngnQpRVFSU4ZJ9q0oMYAw58snYrEJkNTGjJ4Oq5QqRPIbI4XAYKlUVDUR2g6rlu9jv2LEDgHmFSNM0aJrmMhBpmmYbcspbIQJcd5uJQKRpmt4+K7t377bcDxFRVcBAFKA8nZgRuBCIKjKGSAQcNfy4qhCZBSJvX2UmV4jkoCb/LweimjVrAnAORPKgcbsKkdmgarnrTFydpQYi0e6cnBz9RrgicIjjrlGjhv652XWbiWMRVTdPApHdwOr8/HzDfl11m23ZskX/WtwGhYioKmEgClCejCFyt0Ikdy2J9a261dR13Q1E8szRpaWlhvFGYpLDvLw8twdVm91PzezWH2aBSB6n460uMzmQqIFIVH3E+qI6BDhXiGJjY50u/zcj9ifClrcCkTpPkauB1XIgYoWIiKoiBqIA5Y0xRGpoCgsLM7zOqssMKH+FSB6IrK4rBwB3xxDJN5N1p0KUmZmpj8kRtxDJzc3Vl6nzLKlhxNWgajmQbNmyRb9JLHChIiW2bReIYmJinCaIBICpU6fikUce0W8yKypsIhC5O4YIsJ8PSQ1EripEf/75p/61qwrR8uXL8fzzz+O9996zHR+laRruuusuPPXUU7bbIyKqDLzbfYCqSJeZ2aBquTtNBA+7CpGngUgEBfUyeHldUeHJysrSq0WuuszkbctdcVaBSL6EXgQiOfSoFSIRtiIiIlBSUoK8vDy9m0utEBUXF+vPAefH1RQWFurLkpKSEBkZqd/+w91AJN9T7emnnwYAjBs3Tj9e4EL1yZ0KUXJyMs6ePWt7ZZwngSg9PR3Hjx/XH9sFoh07dmDQoEH6486dO6Nr166m6+7atQvz5s0DcP54RbegmcLCQvTt2xddunTBm2++abkeEVF5sUIUoLzdZWYVkioyhkieqVqIjY01vbGsXCEqKyvTr0pzdesO4EJVRA4I4qSsdpmJQCRPwChXTqwCkVxNsqoQmQ1wlsNWfHy8YWoBTwPRunXrDNsWxx0WFqa3z51AZDZBpMqTLjO5OiTvx4w68aTdbUzkYxHzNFnZunUr1q5di/fff9+26iS4mnKAiEjFQBSgKtJlZjaoWn1OfG3VZda4cWPDclcVIkENKPK+RECRiVAgV1rk0AJcuKRfVJiACwFDDXAihFSrVk1fJocW9XYjaiBSB1XLV5mpYUTucqtWrRrCw8MNA8c9DURr1641HLPYX7Vq1Zxm1z527BgWL15sCAciJJYnENlViNRbe9hViOTpF8weW23nl19+sVwPuBDYCgsLbbsCAWDbtm2oVasWXnnlFdv1iIhkDEQBytuX3ZsFosjISMsus3bt2hleGxYWZnvZvSACkTyOKCIiAg6HA2FhYXpFSBChQB4bY1UhiouL049JBAyrCpEciERFIyoqCg6Hw3CVmV0gUrvM1EBUUFCghxlxHPLgbk8D0Zo1awzHLAcieUA6AFx33XW45ZZbMHPmTP014jjFYHIRiMrKyvDQQw9h1qxZ+roiEIngbReI1OfsKkS+CkRyCHJ1n7YffvgB586dw7Jly2zXIyKSMRAFKG+MIapIl1nbtm2dlpW3QiTvQ57HB4BTQAIuBBfRZhGI5LmMrCpEciAS64rAIdoqD6oW3XRWgcisy0y8h6WlpfpJXVRw7LrMNE2zDEQFBQWGe55ZBSLxXogbs7700kv6a9QuM/H6P//8EzNmzMATTzyhryu6skQl0K7LTA2CnlSI7K6gk4PVL7/8YtsVJrfvyJEjluvJz6tVMDMnT57EsmXL2MVGRAxEgUruMivvGCKzQdVq1UitEImwIFeIyhOI5ApReQKR/Dpxko2KitIrNuKkbBeI1C4zNRBZVYjMJmaUK0TJycl6W0UwE+tZdZkVFxcbro5TA9GGDRv0cCaO2a5CJBw4cED/2moMkQgT6enp+j5EWLj44osB2FeIxD7F5+GLCtHZs2exd+9ey3XlQOSqQiSed9W1BgCdOnXC9ddfj6+++srlukRUtTEQBaiKdJlVZAyROKG3bt1aXyZO7OWtEMnryIFIvr+ZfFyi3eptQcwqROKxWNcbgchVhUgORGJ/IhBZVYhEm60C0caNGw3rqhUidQyRCEjAhRvGWgUi+co7URkSgUh8znLg+PXXXzFhwgR9X+q8Tr4YQwQ4D96WeRKIRIXo7NmzhqsCVWVlZfp797///c92m0RU9TEQBaiIiAikpqaievXqplUUT7vMrAKR3DUFXAgyZnMJeaNCJA+MVu+bBhjDk3iduM9WdHS0Hjzc6TKraCCSB1UXFxcbxguJtlmNZVIrRGJdq0CkVl1cjSGS39OVK1fqUwYA9oFIBABREbrooosMjwFg4sSJeOmll/DNN98Y9pmamgrAvkKkdpHZdZmpgchuu+WpEGmaZlv5kitS4tjs7Nu3j/dxI6rCGIgClMPhwIYNG/Dnn3+azutTnokZ5XXkr+Vl8r5ERcDsOaDiY4iio6Mtu+zU14nnyjOGSB5ULf/vyaBqwPwKNqsuM08rROoVYXKXWVxcnGEMkaZphsrLjz/+aAgeaiCS2yFu+Cqea9iwIYDzgUiM4REzXIsuJzUQuVMhEnMKeVIhslvX3UBUVFRkuKmtXbeZPGbLLrgBwNy5c9G8eXMMHz7cdr2cnByXN8oFzn8vyF2kROR/DEQBrF69evoJS+XpPERWFSLAGDzkQNKyZUvDPuWQI2a9VgOROrhY3b4aiBwOh+X+zQKRerNVd64yUytEcmhxt8sMuFBFkcOWWiGSb2Argoh4n+VAFB0drVf+cnJynAKRXYWoqKjIcNLdunWr4dYp8oze8nsCXKgQiXbUr18fwPkZwbOzs1FSUoJjx44Zjq08gUisaxdyzKpiVtwdVH3s2DHD4Gy7QCTPfSS/R6qDBw/qQWjhwoWW6+3fvx/Jycm4/fbbLdcBzh9LgwYN0LNnT9v1ysrK8PLLLxvmpyIi32EgClIVmanabpkceu655x4AF8KCWdUnOjpaP1k3atQIo0aNslwXcA5EgDEEWX0tHqtdeRXpMisoKNDHmFgNqg4PD9fbL1eIRDvE/szuqSbWF1dyqRUiOdyZVYhEQFADkRoy8vLy9HCRlJTkFBrlk/3JkyehaZr+XHJysj5oPzc3FydOnNDDlnidOobInUHV8n3krIhgJbpR7QKRHGxOnDihB1mVGpbsrjSTK0R2gejtt9/Wv5bvV6dau3YtiouLsXjxYvz444+W6/3yyy/IycnBb7/9podOMwsWLMATTzyBHj16WK4DnH9v3njjDZf3oyMiewxEQcrTQdV2IUkOLHKQGT58OObNm6f/JS0/J+/j66+/xueff469e/eiU6dOANyvEAHWIciuQiSoQUSc6OXQot7mQ+xDPllbVYjk/+0qROqgajn8NG3a1GlZTEyMHnLkQCQqbHaDqu0CUWJiot6WkpISlJSUGLrMTpw4geLiYv0yc3mcVEFBgeFmt+LYRFAxqxD9/vvvaNSoET755BMAzoHInS6zevXqGfajKisrcxoLJKpYKrU7zapCVFpaij/++EN/bBeI5Nm27cYQic8WAJ588knL9eRL/OU2qHbt2qV/bTclwRtvvIGxY8firbfeslxHbIPTCxBZYyAKUt6YmNFVl5nD4cCQIUPQrFkzANZVn379+mHw4MGWlSZvBiJXFSIhLi7OaZlaITILRPKtO0RQEP+702Um9inu/RUREYG0tDR9XVcVIvkmrlbzELkKRPIVaPn5+U4VIrkaFRsba7iSTg4UVhUieZxM165dcfjwYb1LyZMuM3cDUUZGhn4iF9U2q3FEaoXIKhCdOXPGEG7U8V4y+fskNzfX8so1OSj++uuvlgO65eVylUolf//K46JUf/31FwDjFAyqsrIydOvWDZdeeqlbY5yIQhEDUZCSw05FrjJTl5kN4DZ7Tg0rKnevMlOft7pcXzxWK0RWgUjuMlO3ZxaIxCBgswqR2KdZl5lVhUiM1UlOTtbDllUgkrvpRJeM3TxEasjIz883BCL5vc/Ly3MKRHIlQ75yTw1EVmOIxHsnhwi53YBzl9m2bdswbtw4Q1tEgBDbFYHo0KFDeOmll/TnRVdQYmKiPmDcqttOtF98T1t1manvoV2FSN2X1b7V7i+rsVby+2YXiOT17MKOqOrJN+BV7du3D7/99hv++OMP23BVUFCgD6onCjUMREHKm1eZWQUSlSeByBcVoujoaKcKkQgK5QlE4i9l+UawhYWF+onZky4zqwpRjRo19LB17tw5feyL2mUmQoqrCpF801cxeFquECUkJMDhcBiqPuqganmMlMPhsOwyUytENWrU0N+7rKwsLFiwQF+3SZMmAKy7zO6//368+uqrGDBggP4a0Wa1QnTDDTdgwoQJ+ng0EYhq1arlNGN3YWEh9uzZo29TdKWJCSetKkRqNcouEKnjoKyCjrrcavyUXCGyu6mt3FW3f/9+y/VECBQh3MyOHTtM96+67bbb0Lx5c/z666+W6xBVVQxEQcqdMUTlGVStVmVk3qgQeXMMUXh4OC655BKntgHG0KJuW11XHhgOXPjL3J0KkToxo9i2qEwkJSXpgUg+wVlViKwCkQhsxcXF+j5FVaaoqEgPF+LKNbnqo152L7arVrXMKkSaphnaIUJYZmYmPv/8c31dsX8RAtQuM1EJ+f3335GZmYnS0lL9OTUQbdmyBQDw2WefAbgQiFJSUpwmqPznP/+Jiy66SL8XmmhHixYtAFgHIrFv8X6JNplxNxCpFSKrSpL8eRw8eNByMLT8/WJVIcrPz9e/1+wCkXyDXqv95ebm6nNPzZs3z3Jbrhw5csQ26AHn586yq3qVlpZykDhVOgaiIOWtiRkB31eIrGaq9jQQqTNbt2vXTj9BlqdCJLfDbCJKuwqReuNYdV1xIk5MTLQMRGaDql11mcnblq94EicP8X6IsJOdnW04oRcVFeknTnWMVH5+vlOFqLi4WA8KaiCS183OzjbMjyQCUVFREYqKinDppZfq686aNcsQFlyNIRLHa1Yh2rRpk+F/sVyMNZK7zMrKyvRjEe1s0KCB/rzVFV9qsPFmhQiw7upyJxAdPXrUsH/1akVh27Zt+tdWIfG7777Tv65du7bpOjk5OXj66afRvXt37Ny503Sd2267DV27dsWSJUtMn9+xYwf69OmjX2xg5v/+7/+QkpJiOXv5n3/+iX/84x+2oYrIUwxEQcrTeYgqu8vMnQqRes8yeZn6dXh4OMLDww0Vou7du1u229NAFBYW5jQ+SQ0MckBRA5RaIRInVzkQibEbYu4lOYiIbZtViOLi4hAVFaUHX3GiFOsCF05yaiCSx4uI8VviJOIqEGVmZhrG2lSrVk3fRlZWliHAZGdno7CwUA8c8qSeOTk5hnDw+eef6+EhJiZGH2NlNQBb7jJTK0Ti+ETIE8tFIBLvS1lZGbp27YpLL70UZWVlhgkkRZXIqttMtL1mzZr6+2JGDVRWgUgdwG113O50mcmfF2BdJZIDkVXlRb6fm9V7MWLECEydOhW//PILli5darrOb7/9BgC4++67Ta+O2759u/61VRicO3cuAGDq1Kmmz1911VX49NNPMWTIENPn58+fj4suukgPyipecUdmGIiClDevMjNbZsafY4jEcjmIdOvWzXR/wPmuEKsuM7NABBjvDybvSw1KZoHI7JYlwPnjVQORGLsj70+cTOVAJM9DJK8vqh7yJfZimdplJsbUJCQk6Fe7iUCktvnkyZOGk3NZWZl+UhbzMckVIjUQqYPUxfuqBqKzZ8/qoSIpKckw1YA4LuHMmTP6yTk5OdlQISouLtZP7uK9VStE4n5mBw8exMaNG7Fp0yacOnVKXy8+Pl4PZGYhoLS0VF9XvH+uKkTqDOkqtUJkFojKysoMlRyrSoh6tZ1ZICoqKsLu3bv1x1YVop9//ln/2uqqO3kqALP3QQ4ZWVlZWLt2rdM6xcXF+tdmz8usgplonwhfqiFDhmDPnj0YOXKk6fM33ngjWrRoYVlRo9DEQBSkfNFlJmaOtuLPMURiuXzcVhWilJQUXHHFFR5ViADnQCSWy20W61kFInWfcoVI3KrBLGiJk6RVl5n8v1wNEtuw6jKTB3eLbhBxElUrROLqoho1auhtFK+Pi4uDw+HQw0pGRobhsvXS0lK9XbGxsQgPD9fDmXqvtpycHMNVcWogkidd3L17t6FSJleITp8+rVcg1AqRmIFb0zRkZ2cb7lt29uxZwxgiEYjUq7rkcU6A60AkQq3ohnNVITK72lE4c+aMYUzT0aNHDUFCcCcQ7dmzxzBVgFWFSK5wWQUR+djNuhjVECh36QlyIFyzZo3T8/Jx2g12d4dZKM3MzMTSpUuxf/9+03mgNm3ahC5duuCnn36q0L4p+DAQBSlPB1W702Vm112mPl/eCpHZZffuzFQtvpb/QhXzIwHG8PfOO+8YKhTqNtwJRBEREfr7I66gEuy6zOwqRIJYJyIiQn9vxElAdMvIV5OJdokwIFeDzEKS3B45EIn3Xg4u8v9m455EhUnsR2zD7HJ2cTIWQUgOROpcPlYVovz8fEMg+uuvvyznY5K7A8W+xXtWvXp1/fPLy8vT5+oBzp+QzQKROPm+9dZbaNq0Kd555x293RERES4v+RfHJAKRqwpRo0aNAJhXiERlTnwOZWVlpttTu8zMuqDUAGRWIRLBUbCqELkKRGqAMWuzvO3Vq1fbtrc8A6vlbjr1jxzgwqB9wDiZptCpUyds3LgR//jHP5yey8nJwbRp00wHjW/bts00wB08eBCPPvqoaZXv2WefxcyZM52Wz507Fy+99JLT8g0bNliO3aKKYyAKUt68l5n43+4KM8B8pmorvqoQ9e7dG8D5v9blatZll12G+Ph4DBs2TL+XlFUgMrucHzD+8pTb37x5c8P65a0QmW1b7Y4TXWbyndrVCpE4WcbHx1tWiMS6ItAkJyfrAUWEGatB43JIUAOR2IYcRsQ+1UAkPuszZ84YKhQ5OTn6yVQNROqJWA5EsbGxhgqR3IaTJ0+irKzMcnZvq0AUFxeH5ORkABdO5o899pj+vzydgdxdqJIDi12FqKCgQG+jCERm64nPuF69evrnYxacRAVGfI+ZVYjU15mFjLy8PEN3l9mJXdM0Q8Axex/cCURyhUjuyhPksH3kyBGn27SoIUYdpyR/X5j9kScP1Fa7L+V9qdstKytD69at8eSTT+Lxxx83PLd//360a9cODRs2dAqKo0ePxvTp03HllVcalu/ZswdTpkzBAw884LTf4cOHY8KECYarA0+fPo1LL70UF198saFta9asQevWrfH9998btr99+3bbCUfJGQNRkPJVl5kdb1SIoqKinC5/d+fmrmLdYcOGYeHChU4T2jVq1Ahnz57FnDlz9KBkNYbI4XCYhjBxAlW/litRgHuDqoWEhATExcUZPgu7QCQqRIDxMn/5f7MKkfglrFaIRKCpUaOGHlRcVYji4uIsK0Qi5IgTdmxsrB4URHVCrRCpVQtN0/TXy4FI0zSnE7rcZWZXIfr7778NXXhxcXGGuZvUQGQ2hujs2bOGW4J07txZDyuJiYmGQKRpGtatW6cPdhZX2QEXutbEsgkTJug3hRWfaVhYmN6tJwLL119/rZ8AxftTp04dw02AVSKUiHmXzAKRGrjMKkRqcDE7kebl5Rm68cwqRO5MPSCHEHWbavvKysoM3Z2A8/eTejzyAHSz47ALRKtWrdK/FlM3CJs3b9YDqDr2ac+ePfpVllOmTHF6HXA+vMpBRn5v5GOUg6b8/Sgfl/za/v37Y9euXYY5vrZs2YI2bdrot1ISVq5caTunlTvk9+zkyZN6G4uKinDw4EH9uWActM5AFKS8OTGj+N+bgciqQgRcOKmWp0IUGRmJW2+9Ve++kEVGRhqqRmbzDZntR51METgfvASzCpG6batB1YmJiXA4HIYqkbyOWtKXxwWp64j/xS95s3XtusxcBSK5yiRCgni9VYUoLi5O/zzFuuKxGojkYxW/ROUxRIDzrTf27t1ruD+dVYWopKTEMJ5GnczS3S4z+UqratWq6WFCrRAtXboUPXr0QLNmzTB48GA9CERHR+vjwLKysvDjjz/ipZdewu23346ioiL9s0tOTta7H3NycvDHH3/gpptuQrt27QAYA5E45pycHGRmZuKxxx7TBxOL4xAnb7NZqMU6IoCZVYjU0GQWJNSKkDcqRHL7BLU7Vp54E3AOROr3jHzCl6/UE+wCkdwdpR6fHPbUm/zK68pdcgDQtm1b07bJ75U8FMCqy1Deh/wemXX7zZ8/H4CxS3Xt2rXo06ePISQdP34cEyZM0ANZVlYWlixZonfh79u3D/3799erT++88w5q1aqFjz76CKWlpUhNTUVaWhry8vIwYMAANGnSBKtXr8YjjzyCunXr4sSJExgzZgw+/vhjZGdnW14ckJOTg++++04fZ+kvDERByiwQXX755YiJicHll19uWA4EToUIcD8QWX3tLrNbf5h9LdrRpk0b/Tn5ct969eoZjicuLs6jChEAy0Bkdqm/CBKCOoZIkCtEctvk7YoTW40aNfS2iPK81b3aPKkQyYHIqstMnMCqV6+ub0csS0pKQnh4uP6+qYNws7KyLGfsVk/+4pd6TEwMwsLCDAFS/svVLhDJc+dkZGRYdpnJJ84vv/xSP1lWr15dDzrZ2dmGqtXq1av191juwszOzjYEtpycHP1zq1mzpqFCtHDhQrz11luYPHkygAtjpkTYEe09cuQIvvzyS8MUA2IsXHp6ulN3kDqxZ15enlNXlV1AEDwdQySOX6YGInWbaiBSv2fkk25GRobTccjBWQ2HclvsjsUuHKrHIw8Sl2cAl98H+ftJbpMc9uTvd6tb0ghmQXD27NmGtmqahrS0NLz00kt45ZVXAAAvvfQSbrzxRgwaNAgAMHHiRPzwww969enhhx8GcH76BTnIHjlyBCtXrgQAfPDBB3j77bdx+vRpDBw4EG+++SaGDRuGli1bomnTppgxYwaeffZZ/abNzz//PBISEnDNNdfgn//8p+1x+RoDUZAyq/5cd911yMrKwl133QXAPPyYhSQRWDwZQ+RJhUjdbkUqRJ5wOByWVSGzQDR58mSMGTMGhw8fNuw7LCzMMLDak8vuxclRDkRym+RAExkZifDwcKfgIx6rV7vJY4jUddXlcoXIqs3i5C2HBLW6I9ogV4jEMVoNqhbLExISnKpGImSI5eIEILqd5PmY5DFEapcZcOEqOXUc1datWw0BQB1DJD6bjIwMwwkoMzPTsstMPjmWlJQYugDFe5SVlWUIDd98840h6Ij1cnJyDGOsdu/erQeduLg4/b3Jzc3VT+biL39xHKJiKh63a9cOt956KxYuXKgfg/geLi4udgoqYh15bJ4aCNwJRJ52mcn7FtSTvVpBkruRAOcKkTrQXN2evD+7ttjNK5Wfn28IOvJxqscjb0d+D+VAZFUhKm8gktcVFSR1TqZz587pPxdibqjFixcDAFasWIHi4mJD9UkN0eq0G2bryWFV/B546KGHMGXKFISHh6NWrVqYNGmSvs5//vMf2+PyNQaiIGU2hggwhghvd5mJyRHV/ZixC0/iBOrrQKS2wywEyV936tQJr7/+uml3nDhBA56NITILRFYVIvG1HIjq1Kmjn9jVmX3dqRAJqampToFIrRDJ27CqEMkVBLGuWgmyGkMkd4+J7YqQIZaLE4AYmGx3k1urQKR2MaqzHatjiORgop4QrbrM1BO9CCrVq1fXt5ednW0IFcuXL7esEMknwZ07d5oGopycHP29PHLkiGFmcPE9K14nTsLff/+9vo5865PTp0/j5MmT6Nu3LxYsWKAfT1JSkuk0BOK4gQszi6tBDoBhzij5NbKKBiK1QqR+H6ifjVwtKS0tNVTt7NqSlZVlGN9kN2O5/LW6nhyI5GORvzfkCqb8vSAHCvk4xHskV7/k3wXyWDLRHnlZcXGxIdCILkD5D7+8vDzD75yjR48azh/yscjvoxyI1O+PQMdAFKTMusxU3u4yk9fx5hgid2aq9nYgsgpHVuQ7vcfGxrp9lZmrLjP5l5gIJnJw6dixo/71RRddZNi2O2OIhHr16nkUiMRJUfxyUytE8rrudpmZVYhEYBTtFicAEYjy8/MN0w+YVYjEL23RZSbWEf+r4xbULjM5wMi/5LOysvSTVmJiot7WzMxMpxO9CERJSUmGLjP5pLd79279JqvyDNk5OTmGgcHuBKKcnBycOXNGH3MhByL5RJeQkGAIdeIqxvT0dIwaNQo//vgjBg8ebKiEWU1UKY65YcOGhvdIJl4jrqBTny8pKdG3I+bFsgpE8sSeMrWbS73li7q+HCTkMGS2Lbv71rkbiOwqRHLb5MApH4MnFSI5HMrnBPn7SbRNfl7+QwO48L7IATA/P98QaLKysgwXfchtlgORHNLM5s4KZAxEQcqbgcjdy+4B9wORXYXo1ltvRZMmTdCrVy+n/VZWhcjTQCT+KgbOv/fuzkNU0QqRXSDypEJkF4jUNssVIkGtEMnrikAhd7nJ/4ugJFeIRClerRCpgQi4cIKwqhCJ98iqy0ycEEWoVQOR1XxJgHGmb9HWrKwsp5OjOHHJFSK1ywy4UAlITEw0BDH5JLhr1y5DIJIHVcsnQLmbRe4yE+8DcP6EZBb+cnJyDBMPymOlRHXn7NmzyMjIwBVXXIFHH31UP7HK95Sz6kYTockqMMnrWF0FJ4KuGnDEeyMClRqI1MdyIFL35WqAt9xeu6CjTjwq/pDQNM2tQCSHE/l7QW6fWYVIDj45OTl6AJFn4BafkRxu1PFt4mv5dfIfI+Kx/LtSPha5qid/T/h7kLSnGIiClBx25HBktU4gVYhGjBiB/fv3o3Xr1gDcC0TutM1VO7xVIVK3Kz+uSIVILLcKROplwHZjiNSgVL9+fafqjtWtSeLj4w1/CcrbNasQyZNtitcDcFouV4gEqy6z1NRUfSyL+CUtjyFKT0/XT1BqIFK7zERwErfzUMcQiWNKT093ugRctEcORNnZ2U5Bx50KEWCsonlaIcrNzTUNRBEREXqIycvLM1yV9ffff+vvU3x8vKHCJh+DXEWS52UaO3Ys1q5di+nTpxu61cR7ceLECYwcORJz5syBpmmmFaItW7agZ8+eWL9+vX6Cl7vmsrOzMX78eAwePBilpaVO28jJycGBAwfw6quvIicnx3LclCAei+OwCiSA6+47+fNzt0KkaZr++eXm5hq+p6y6zKwqRHJokb9HRDhSbz0ijlV+nWibvEytEIn9qyFJbldBQYGh4iMfs9y1J7/f7DKjSuFOhcjbM1XL61SkQqQKhgrRnXfeiYiICPTt29f0NeKxHHbkK508qRDJ25Yvka1Vq5Z+IgLMK0Rm3WDR0dGmg6rtuszM5l4S+1TXVUOSOBHJ466A8wHJVSASJ4+aNWs6DS6XK0RCTEyMXkkQf5WroVBUo8wCkVw1kf/KFSdbEXTkQdWapjld2SSCkzyourCw0Gk8jNx9KFdr5JPg3r17DfNKyTeflbcnrkySg46maYbJ/P7++2/9WMWcWIDzhIjyrVREUNmzZ49+ZRJw4USdlJSkfz8vXrwYH3zwAe69914888wzpoHo0UcfxZo1a3D55ZfrAUQeVJ6ZmYlXXnkFCxYswKpVq/STsPgMsrOz0bdvX4wbNw5PPPGE0/O5ublYsmSJfsm32bgqMd5KPCd+xjIzMw0neXerQOK1Zl/L21GDs6ddZmahRW6L2gV49uxZaJpmWG62rlWFSF4m33QaOP9zJAccOUzKXwfzZJAMREHK311m5Z2p2oyvLrsHvBeIateujbNnz+Lbb78FYDy+6Oho/fOQt5WQkKBXOTwJRPK4AXmQo8PhMIQMefJB4HwAEO2Qt1uvXj04HA6PusyaN29umNPJnTFEQqtWrQBcOCkK8glZUMcQCTVq1DANROqyOnXq6ONi1Laq4Um8lyUlJfpf23KlRkwkV61aNb1CJleIYmJi9PdMBCXRHvFYnt5AXi6IapVcLcvOzjb89V9cXKwHFjkQqfPxiAqR+n0gJgIEzoc8OfyJ9v7www+GbclBTQSiZcuWGdYRV2/JFSK5e+6DDz7QA5HoDsvJyTFUSMQ4L/l9kt+jvXv3mlaAxDiwhQsXmj6/YMECHDx4EF9//bVpIHr44YdRs2ZN/bJ3uUv23LlzKC4udrp9iXhOsBtf5M1AJAev/Px8/ftSDSvqMrFNs+kSiouLnSpVnnaZuRuIrO7hFwwYiIKU1VVmMn92mXlSIXJnpuryBiKrLjOzq8xcSUhI0N8zebtWX8tdRp4MqpbnpFE/WzHfjHitHHzkwCMvF6/xpEIUGxtrCDTlCUSiIiO4UyESrCpaaltr167tFIisug1r167tFP7kCpG8THxe4kQn1hFX44iqggio4iSUkpKCiIgIvZ0iRIjvZTGmQh3Pow7uFSdFeQyR/H0BXAhE8fHxhmqkfFWd3GUmB9J169YZtiWPbRKfiRrm5EAk3h/5EvfMzEynCpF87ADw6aef6m0Rxy8Pet+xY4dTBUgOEQUFBaYVIhFcjx8/bvr8u+++i6KiIvzrX//Sj0G8X4cPH0aDBg1wyy236O+VGDPoboXIahoDNSjJAUMOW8XFxfr3lBpyRIVTDSvqMsA56Ig2qMvUCpG7XWZy2JIDnXqvwmDFQBSkzC6pd2cdORCJX1TuXnYvr1ORMUSqYOgyU1lVeeRtuROIzCpEYpbsa665xmm/6uBu+aQvhwq1QgQ4hxm7MUQA0LJlS32ZXHWRK0fqGKL4+Hh9fzVr1jS0z6xCZBWIkpOTDcvEjXDDwsIM7bULROo2ExISTMdGqcHL7Ia84hjVGYrVbkHRFjnsAMYrs8Tz8tggEYjU/crtUwORmPVYPC+OV76EOyMjQz9xqWOIZCKUyGOl1K4Ps9AkB6Li4mK9UlC3bl39Z0xeZ8WKFXpbzALRhg0b9GBQt25dAMZAJFct5MAkwtvx48edKkTycYjv3YSEBP1787XXXsPff/+Nr776Sj+xiwrSuXPn8Morr+Dmm2/Wj038geGqQlRaWmpaIdq4cSPOnj3rNJ5p27Zt2L17t+m4ILX7yqyLCzDeK09um7rMqkJk12WWl5dneGw1NkttfzBhIApS3uwyE7+s1V/aZqriGKLybNuqKhQREWH4pSt4UiGaOnUq5s2bp0+/L5MDkfwawHUg8qTLDDAPRGrXm1ohatWqlX78DofDUCVSK0Th4eGWs3DL8/TI+1e/rl27tlPIseoyS0xMNKzrcDgQGxtruL8eYKwQCWqFSJC7XoALgUgdUG4XiGRmc02p64kxWoJVABTkiTGt1hGhRZ5eQCVPpineH3VQsujekWfslgOafFxmgWj9+vX61yIQyeOm5KvmRODJysrSrwbcv3+/3gbxvHwrDflKSPFeyHeuF8FGBN0NGzZg/Pjx+Oqrr/TKm/jMV69ejdGjR2P27Nl6OBBXvg0ePBj16tXT9y1+Jn799Vd06dIFXbt2dQoOnTp1QqtWrZzmWWrVqhUaNWpkuGLr7NmzuOuuu/DRRx8Z1j137pxTcFaDDOBcISooKDDcHBlw7jKzm3TT7D57wYiBKEi502VmN15I/vq+++7DmjVrMG7cOJf7dTcQRURE6O1yFTiCYQyRyqrK43A49OfKWyGKi4vDkCFDTE9Md9xxB4ALV715UiGKiooyfG52XWaAeSAC4DIQyeSuEzUEJCUl6ScKeXnz5s2RmppqOB67QKQOtrbqMlMrRPHx8abh1axCJCoiaiCSuzAB5wqRoAYncYWg/LNbvXp1typYl156qdO25P8FMRZIXs8shMkSEhIsA5EgByIz4eHhiI+P17ejXrkn9iPeI7mCI8JMeHi4HvzUmanFiVkEnmPHjulVJXn8nQgn27Zt05eJbir5ggR5HJQgfr6++OILp+fEZ/nDDz/g3Xffxf/93//pYUUEqVOnTuHUqVN48sknAVwId8K+ffucxvoIZnMjqTewPXHiBObNm6ff004YPny4fuGHsGvXLrz44ouGZWZdaxkZGU7zEFlVhES75O1VBQxEQcrTCpGrmap79Ojh1S4z+bYZ3qgQeeOye3dmrS7PdtUKi9heeStEdtq3b4/Nmzfrf626UyGST9ryCdGqy8xVIJKPy1UgUitEchvlE6+8fMSIEU6VKKvgJ056creZXSASd4UHjO+FfAzx8fGGq/kiIiL045IDkTyBpSDaoQYGtWtNDLiX25CSkmLYr9iHGmLUO5irXWYAnMaAiX1aVYgEuwqRkJSU5BQMZTVq1IDD4bDdjtnYLZnZ2DSVCERmd1WPjY21fb1cIbLbthk13MrUCq4gvk/NuHq/K+rrr7/Ghx9+aFi2dOlSTJgwwbBMDWLyLWQA6PfPE+QbIatXXQYrBqIg5c4YIjk02VWIPOFuyAEunHD9Oai6sitE8nOeVojUYGWlffv2+gnJkwoRYDzxW1WIzMYQyd8raoVIPk67QGRWIRLkrpd77rnH9njUChFgDERWXWYJCQno16+foe1mx6RWiNq2bavvXw4C8pxDgqhqiBsFA+e/D9SApM7mLY7BLBCpJ265PfJxyOvVrFnT6aRuFgLUE7g8hshKcnKy7QleHGtFA5GrapZdaHEVeOzCodncWjI13MqvUwOyO21Vx8AJ5f0j0B2rV692WnbllVcaHr/88stBPUC6PBiIgpQcduRBrjKHw6Gv561AJH7g3fmrpqIVIl92mZXnKjOr7bpTIYqLi9ODq6suM09YVYjkMCCf9MyuRLMaQyRXluS/wu0qROoYGLlKoY4hkk+8N9xwAwDg5ptv1k8eVsdT3gpRYmIievfurT+Wr/JRK0RygJG7qORApFZTatSoof9Mde3a1bBcPfmLx3YVoqioKERERDgFg0aNGhm6YMy6zNTQEhMTg4iICKcQYHYloNmEmrKGDRvaBiLxO8IuWLkKRK669yIiIizDh3i9XSAym8NLkLvzzFhViOQ5qFRWgSgmJsbyOK2Ckq/IM2GHKgaiICWCjlV1SBDP23WZeeLJJ5/E888/j8GDB7tc190KkS8HVXtrpmqV/HqrWavlE4vD4dBPshXpMlNZBQX5mORZts0CkVWXmcPhwJtvvomhQ4eiT58++vNqIEpKSkKjRo2QmJho6JICnMcQyW2UT5iXXXYZDh06hAULFpi21W4MEQDD2Burgdpq5UeuStmNIZLDjV0gkk9g8mvMTv5mgejiiy827UZUT5gNGzY0BCKzClFycrIhnJp1qwHOgchsDJH8GYrB7mogkj9LEVTULjuZOxUi9YpG9fUxMTGW4yfdCURWz1sNeAfOf29ZhUGziqFgFYjM5tYSzAKRXQikimMgClJq0LGiVoYqGoiaN2+Op59+2mVZHbjwA61eFaPy91Vm5QlE8uBpNVCYVYgAmAYiX1WIUlJSMHHiRDz//PNO1Q9BtCMsLEx/P8SVV8Kjjz6KTz75xPB9pnaZhYWFYdu2bTh+/LjTeyl3L6gnGrMrseTvSasKkXrZPeD+GCLAeDsUs2OSBwQD7leI5FAm32bl6NGjhu07HA7TOYMeeughw8+VWSAKDw9HamqqaYVI7TLr0aOH7TqAceLP8PBww9VhgnyFnAg5aiiQ1xHf5/K998yu2rMKiaKdZlc0qs/bdXv5IhDVrl3bckC53diqGjVqmP5haBeI1AH2gPXvUne728keA1GQEn8ZWf2FJKiVoYoGIk98+OGHmD17Njp06GC7XjCOIQIu/BKy6jJTTyw9evRAtWrVDFUUX1WIAOCFF17A008/bVhmNXmjfB81q7/KBfXEJbZr9os9LS0No0ePxiOPPOI0qNpVqLZqq5ioDrgQhFwFopiYGP37aeHChejUqRM+++wz02NKSEgwBED587IbQyS3QX4PMzMznUKpeF7cIqV169ZIS0tzGYhq1qyJ8PBwt7rMunXrZmiDvE1BrhDdfvvtiI2Nta0Qia/VE78ciEQVQw6F6rQDZhWi5s2b61+bHbv8e8TsmOXxa+6MIbLqMjObFFSoU6eO5fdtYmKiZSXIakyUfH8+WXR0tOn6cXFxpuHH1R+d5B4GoiDlry4zT7Rv3x733HOPyxNsMF52D1hfpSUeqyeWOXPm4NSpU4YxCL6qEFkxG1Qtf+3ONqz+arfy9ttv46233nJ6ratAZFUhkgd6is/R1aBqdZzTxo0bceedd5o+Hx8fjz59+mDw4MF4/fXXDT8n7naZAcDAgQMBAN27d3cKXMLs2bMxYsQIrFy5EgBMA5H8OYmqgTtdZvJ+xHgp9fOSg8oTTzwB4PzPg/wzYVYhUudukkOTCERyhahWrVqGE3l8fDzq1q1rOJHL988T7ZT3cdNNN9keszyRqVkgUj9jq+/dtm3blisQJSUlWXanVatWzTQsWVWIYmNjTQNbtWrVTH8XmgUiu6kRyBwDUZDyNBD5o0LkrmC4273dttW/2EaNGoUBAwbg6quvNiw3K/H7skJkRvyij4qKMlQXPQlEZhUid3kjEJnNeeKqQuTqEm71KrOIiAh8/vnnGDNmjGG9xMRE/fvSVSD65JNP8Nxzz2HevHmW3Zbdu3fHv//9b/1EahaI5M9JBCL55GrVZQY4jzmR1wkLC8OVV16JXr164bHHHjNUYOTjMqsQAdbj1MSJWA5SeXl5TjOaR0VF4Z133tGXyQFKtFOe5VqeX8esQiQHIrMuMzlw2QWiDh062AYiq++lpKQk2wpR69atnZZbBaKSkhLTQBQVFeV0mxDA/e41swHh7lwxHCoYiIKUCDquusy8PYbIFyprDJFVwPJ2hWjw4MH49ttv3bpKpKIVoujoaL0C50kgshoI7osKkcxqHiJX+5HfG7NLgT2pEJmxCiwqh8OhV4kSExOdLpuXJScn45lnnkGjRo0sK0Qqq7mZBLMKkVkgEidDMdu5mHNGXkfcsHblypV44403LNthFYjkn0mzQdXy75f09HSnQAQAd955J9555x3MmDHD0H2nfgYRERGGY1YDfHR0NHr27Kk/n5ub6zRh6uTJk9G4cWMkJyejTZs2lt8frgKR1R+hrrrMzAJRbGys6e+J/Px8099LVjdONQtEZncekEOhwErSBQxEQaq8XWZmt/Pwt8roMouMjDR03XmjQiReV5EBjeo4F0/Jg6Bdzdsir2PVzefONsTJQ1wW7gn5eMtbITL7i1Y+IcjdLeL73VX4cjewABe6zZKSkhAREaG3zS4Au7t9swqRTAQdsy4zdQwRAPTv3x+nT5/GCy+84LRNu/dEfk4+scpfuwpEsuzsbMvQ+dBDD+HBBx80nJhFO8XVek8//bTh/RWzPIvtpKWlGb5HDh06ZPh5j4mJwU033YT9+/fj1KlTTjOhy39Ytm7d2nZQtZWkpCTTYCKOR57XS6hWrRoefPBBpyvySktLTW95Ik8VITP7nrr11ludlqnTYoh203kMREGqKnWZVcbd7tXXeyNsWVWIPFHRChFgfZm5GfGL0yoQebINT6tDwPnvR7EvTwZVyye7OXPmoGHDhoZB0WaTOMpXc3nSZebuhICi/SI82AUid7fvKhCJbiF3xhAJtWrVMq0iuhPM4uPjDSd5+apB+Q8Jud1ysHn33XcRFhaGf//73y73bXbsixYtwpw5c/D0008bfh+IblOxnloN0TTN8Fi01eFw6L8T5e+pQYMGATj/vkVFRVkGcLsJFkVANhMXF2c6oWN0dDQaNGiAXbt2Od1CRL25LmAdiOSrBYVevXo5LTMLRL6eKTuYMBAFKW8EIlevrSyV0WVmF4i8PYbIE5GRkfrnUN5AVJ4B0d7oMitPIJJfX94KUZcuXXDo0CHDoOjGjRujefPmaNu2reFk624g8qRCNGbMGNx88824/vrrAVwYl2F2shHCwsL04ylPhWjHjh34+OOPcfvttwMwnpjFfbzMxhCp5PfRnQpRYmIiYmNjMXv2bMycOdMQxOSfIXWCSmHUqFHIzs7G9ddfb6jCmIVCswpRWloahg8f7vS7SnSbiu2Iz+DLL79Es2bN8N577xnWN/sZld+v3r1745dffsGOHTsAGH83yu2y616y+36Oi4tDjx490LJlS1x22WX6cnHvsJiYGKfvn1deeQW1atXC3Llz9WXiakHRlq1bt2Lp0qWGqSTmz5+P48ePm45BMgtOars9/X2mXskazBiIgpQINuUNROHh4S6v/qos4oQeHh5uCEHeDERq6AmUQARcOEmVNxC1atUKYWFhhsuWrbjqMnMn5IjqQ3lL7VdccQWSk5OdJnFUWY0hMhMREYEdO3Zg48aNhhNveQKRqwrRNddcgy+//FIPJZ999hmWLl2Ktm3b2r7O7HYdqpiYGP17U/4sWrdujX/84x/6z6z8PSfGpsgnQKvLsMPCwvT30p2xTOL/e+65B/fff79hHTG7uHrlldplJtolfy5mP3NmgciKCESi+1J87998883Yu3evYcoBq/2p3YeXXXaZaQXIVdVO3oaVatWqITo6Gtu3b8e6dev05SUlJZav6dmzJ06dOoW7775b3688KLp69epo06YNrrvuOsP3Q7du3ZCammr6e8ksEKnrufpZAYDNmzfrX5t936u3AQkWDERBqk2bNhgwYAAefPBB2/XU4GRWKfK3lJQUPPHEE3jhhRcsx/kEYoVI/CJwdSJ0pX///mjUqJFbgcbMV199hf3799vODCyIrgX1Lu2ejCHq3r07xowZg2nTppWjtee7QY4dO+Zy7hSrCpGVyMhIp/FF4nWeDOB254Qga968Oa677jqX65nNTm1GtNVVKDhz5gwOHz6sv4/y7VXs3lt3KlVqIDLz3HPP4c0338T69estu8xk8s+22R9j8jZcBWDxHo4dOxYvvvgiRo0aZbu+WThwt1oWHh6OO++8E927dzfMQK4Sv0feeOMNVK9eHSNGjNCfE+95eHi4IRjaBSLgwvu0Zs0aXHPNNfj666/1rrCHH37Y9DVmE8A+88wz+Ouvv0w/G7V70ez7QkzJILRr107/uqioSL9CsWbNmvj111/x/PPP2x5XoAqcsyJ5JCoqCt9++63L9dTxJYEYiADgxRdfdFrmyzFEVvMTeeLll1/G448/bjuuwB0LFy5EWVlZubswq1Wr5lYYAs5XZ5YtW+Y0W7MnFaKIiAi8/vrrnjf0/5Nn+bbjaSAy44sKUXmJfbhqS1JSEtLT011+FsnJyYbgY3c7GVl8fLzTVV9mbQDsg0JsbCweffRRAOe7csLDwxEdHW1ZOXRVkZZfp56kha+//hoTJ07Exx9/DOD8ffrUk7UZdypEVhwOh2G8mt16APDYY4/hkUcewYcffqjfZd7qs1QDUVhYmCHYCh06dMB///tfAOffg99++w1XXXWV/rwYZA6Yd4tfcsklaNGiBQ4cOODyOMy+P1988UW89NJL+mP5sywuLsY333yDjz76CPfffz/q1q2Lw4cPu9xPIArKCtGMGTPQpEkTxMTEoHPnzqZ37pWtWrUKnTt31vtp33///Upqqf+9/PLLePrpp/W/bAI1EJnxxjxEF198MeLj453+shMnj6ioqHJ3HTocjgqHIbGdyhrP5XA4MGjQIKe7nIvg4KswUB7eCETuVEOACyfjqKgon91l3N0KkWiLp2O0rrjiCgwdOhRTp061Xc9bFSJZUlISFixYgEWLFln+bnH1cyafwK0qJzfccAO2b9+OTp06udUu0X4xSabMk0CkElftySFBrrqGhYUZXuduIPrggw8A2I/LSUpKQv/+/Q2/M+QJQ0UFSn4/zcYpTpw4Edu2bXM6voiICMyaNcty/6rU1FTUq1cPzzzzjD7GrGHDhli9ejW2b9/u9nYCQeCfFRXz58/HY489hhkzZqBHjx744IMPMHDgQOzYscN03oUDBw7g2muvxf33349PPvkEa9euxahRo5CSkmJ6WWJV079/f/Tv319/LEJGMEzGJcY5aZpW7ipO3bp18ffffzuV4MX2fHXyCzb/+Mc/sHv3bn3QbiCIiIhAdHQ0CgsLyz2+SoQPV3OtNGzYEA8//DDS0tJ8NrZOjK1x1Raxnqddd2FhYfjkk09crudOIOrRowdiY2MNN/V15ZZbbnHZPneJgeIV9ccff2Dp0qV44IEHnJ5zt8vM7PthwoQJuOuuu9CwYUO0bt0aR44cQfv27Q3ryMdr9QePGFQtjBgxAgMHDnT6g8WVbt264aWXXjJMbmk2xYockoYMGYJLLrkEffr00atPANCvXz/ce++9GD9+PNLT0y33uXz5cmzatAkDBgwwff6KK64AcP6WMF988YVbxzF9+nS31vMZLch07dpVGzlypGFZq1attAkTJpiuP378eK1Vq1aGZQ888IDWrVs3t/eZmZmpAdAyMzM9b3CAKSkp0W6++Wbtueee83dT3BIbG6sB0I4cOeLV7a5du1YDoNWqVcur2yXvqlmzpgZAW79+fble/8MPP2iDBw/WTp065eWWee7nn3/Whg8frp0+fdp2vW+++Ua77bbbtPT0dJ+0o0+fPhoA7cUXX7Rdr6ioyKv7vf322zUAmt1pZ8CAAVpERIR28uRJr+7bzLFjx/T2mH0m4nfPqFGjyrX9WbNmWR6vWH7vvfeWa9vuEvv53//+p2maphUUFOjLtmzZommaphUWFmozZszQvvvuO2369OlaXl6epmmalpKSYmh/mzZtNABanTp1PGpDbm6u9t1332k333yzvj2zf82aNfPikV/gyfk7qAJRYWGhFh4ern355ZeG5Y888oh25ZVXmr6mZ8+e2iOPPGJY9uWXX2oRERGWP/AFBQVaZmam/u/IkSNVJhAFm9dee00bM2aMVlZW5tXt/vnnnxoArXHjxl7dLnnXFVdcoUVGRlbKCTJU3HDDDRoA7b333qvU/R48eFBr06aNNnPmTMt1SktLtZycnEppjxwOzM4Fu3fv1v71r39pWVlZ5dr+iRMnNADaxRdf7PTc6tWrtXvvvddnoVd4+eWXteHDh2ulpaWapmlaWVmZfsyu9n3HHXdoALTq1atrmqZp+/fv1+6//35t586d5WrL8uXLDQGoX79+2ogRI/THvjq/ehKIgqrLLD09HaWlpU7jNurUqYOTJ0+avubkyZOm65eUlCA9Pd1wDx5h2rRpmDJlivcaTuU2duxYn2y3bdu2mDBhAjp37uyT7ZN3fPvttzh37pxXxmrReQ8//DDCw8Nx4403Vup+GzVqhK1bt9quI8/X5GvR0dE4fvw4wsLCTIcQXHTRRXjqqafKvf26devizJkzpmPGrrjiCr1LyZfGjRtneOxwOLB161bk5eVZzlUlvPfee2jVqhX+8Y9/ADh/yf7MmTPL3ZaBAwdi+/btaNKkCQ4cOIDmzZsjMjISx48fR2xsbEBMEBlUgUhQ+3Q1TbPt9zdb32y5MHHiRMOJOCsry/SmeBS8HA5HuS8bp8pjdpNOqph+/fqhX79+/m5GQDD7g9ibXE0t4Q9t2rRxa73k5GSvFwbE3GPyHGTffPONV/dREUEViGrVqoXw8HCnatCpU6cs/4KsW7eu6foRERGWCTk6OpqDbYmIiEJIUF12HxUVhc6dO2PFihWG5StWrMDll19u+pru3bs7rf/999+jS5cuQXGlFREREfleUAUi4PyYkg8//BCzZs3Czp07MWbMGBw+fBgjR44EcL67a9iwYfr6I0eOxKFDhzB27Fjs3LkTs2bNwkcffYTHH3/cX4dAREREASaouswAYPDgwThz5gyee+45nDhxAm3atMHy5cv1mXpPnDhhmCWzSZMmWL58OcaMGYN3330X9erVw/Tp00NiDiIiIiJyj0PTLOZIJ11WVhaSkpKQmZkZECPhiYiIyDVPzt9B12VGRERE5G0MRERERBTyGIiIiIgo5DEQERERUchjICIiIqKQx0BEREREIY+BiIiIiEIeAxERERGFPAYiIiIiCnlBd+sOfxCTeWdlZfm5JUREROQucd5256YcDERuyM7OBgA0aNDAzy0hIiIiT2VnZyMpKcl2Hd7LzA1lZWU4fvw4EhIS4HA4/N2cgJSVlYUGDRrgyJEjvN9bAODnEVj4eQQWfh6Bx1efiaZpyM7ORr169RAWZj9KiBUiN4SFhSEtLc3fzQgKiYmJ/AUTQPh5BBZ+HoGFn0fg8cVn4qoyJHBQNREREYU8BiIiIiIKeQxE5BXR0dGYPHkyoqOj/d0UAj+PQMPPI7Dw8wg8gfCZcFA1ERERhTxWiIiIiCjkMRARERFRyGMgIiIiopDHQERumzFjBpo0aYKYmBh07twZq1evtlz3yy+/RP/+/ZGSkoLExER0794d3333XSW2turz5POQrV27FhEREejQoYNvGxhiPP08CgsL8dRTT6FRo0aIjo5Gs2bNMGvWrEpqbdXn6efx6aefon379qhWrRpSU1Nx77334syZM5XU2qrt559/xvXXX4969erB4XDgq6++cvmaVatWoXPnzoiJiUHTpk3x/vvv+7ydDETklvnz5+Oxxx7DU089hU2bNqFnz54YOHAgDh8+bLr+zz//jP79+2P58uXYuHEj+vTpg+uvvx6bNm2q5JZXTZ5+HkJmZiaGDRuGvn37VlJLQ0N5Po877rgD//vf//DRRx9h9+7dmDdvHlq1alWJra66PP081qxZg2HDhuG+++7D9u3b8cUXX+D333/HiBEjKrnlVVNubi7at2+Pd955x631Dxw4gGuvvRY9e/bEpk2b8OSTT+KRRx7BokWLfNtQjcgNXbt21UaOHGlY1qpVK23ChAlub+Piiy/WpkyZ4u2mhaTyfh6DBw/Wnn76aW3y5Mla+/btfdjC0OLp5/Hf//5XS0pK0s6cOVMZzQs5nn4er7zyita0aVPDsunTp2tpaWk+a2OoAqAtXrzYdp3x48drrVq1Mix74IEHtG7duvmwZZrGChG5VFRUhI0bN+Lqq682LL/66quxbt06t7ZRVlaG7OxsJCcn+6KJIaW8n8fs2bOxb98+TJ482ddNDCnl+TyWLFmCLl264OWXX0b9+vVx0UUX4fHHH0d+fn5lNLlKK8/ncfnll+Po0aNYvnw5NE3D33//jYULF2LQoEGV0WRSrF+/3unzGzBgADZs2IDi4mKf7Zf3MiOX0tPTUVpaijp16hiW16lTBydPnnRrG6+99hpyc3Nxxx13+KKJIaU8n8eePXswYcIErF69GhER/LH3pvJ8Hvv378eaNWsQExODxYsXIz09HaNGjcLZs2c5jqiCyvN5XH755fj0008xePBgFBQUoKSkBDfccAPefvvtymgyKU6ePGn6+ZWUlCA9PR2pqak+2S8rROQ2h8NheKxpmtMyM/PmzcOzzz6L+fPno3bt2r5qXshx9/MoLS3FXXfdhSlTpuCiiy6qrOaFHE9+PsrKyuBwOPDpp5+ia9euuPbaa/H6669jzpw5rBJ5iSefx44dO/DII49g0qRJ2LhxI7799lscOHAAI0eOrIymkgmzz89suTfxT0VyqVatWggPD3f66+rUqVNOKV41f/583Hffffjiiy/Qr18/XzYzZHj6eWRnZ2PDhg3YtGkTRo8eDeD8CVnTNEREROD777/HVVddVSltr4rK8/ORmpqK+vXrG+7C3bp1a2iahqNHj6JFixY+bXNVVp7PY9q0aejRowfGjRsHAGjXrh3i4uLQs2dP/Otf//JZRYLM1a1b1/Tzi4iIQM2aNX22X1aIyKWoqCh07twZK1asMCxfsWIFLr/8csvXzZs3D/fccw8+++wz9sV7kaefR2JiIrZu3YrNmzfr/0aOHImWLVti8+bNuOyyyyqr6VVSeX4+evTogePHjyMnJ0df9tdffyEsLAxpaWk+bW9VV57PIy8vD2FhxtNheHg4gAuVCao83bt3d/r8vv/+e3Tp0gWRkZG+27FPh2xTlfH5559rkZGR2kcffaTt2LFDe+yxx7S4uDjt4MGDmqZp2oQJE7S7775bX/+zzz7TIiIitHfffVc7ceKE/i8jI8Nfh1ClePp5qHiVmXd5+nlkZ2draWlp2m233aZt375dW7VqldaiRQttxIgR/jqEKsXTz2P27NlaRESENmPGDG3fvn3amjVrtC5dumhdu3b11yFUKdnZ2dqmTZu0TZs2aQC0119/Xdu0aZN26NAhTdOcP4/9+/dr1apV08aMGaPt2LFD++ijj7TIyEht4cKFPm0nAxG57d1339UaNWqkRUVFaZ06ddJWrVqlPzd8+HCtV69e+uNevXppAJz+DR8+vPIbXkV58nmoGIi8z9PPY+fOnVq/fv202NhYLS0tTRs7dqyWl5dXya2uujz9PKZPn65dfPHFWmxsrJaamqoNHTpUO3r0aCW3umr66aefbM8HZp/HypUrtY4dO2pRUVFa48aNtffee8/n7eTd7omIiCjkcQwRERERhTwGIiIiIgp5DEREREQU8hiIiIiIKOQxEBEREVHIYyAiIiKikMdARERERCGPgYiIiIhCHgMRERERhTwGIiIiIgp5DEREREQU8hiIiIiIKOQxEBFRyLnrrrvgcDgwdepUp+fWrFmDmJgY1K5dG/v27fND64jIH3i3eyIKOXv37kXr1q2RkJCAgwcPIjExEQCwe/duXH755SgoKMDKlStx6aWX+rmlRFRZWCEiopDTvHlz3HvvvTh37hzeeustAMDff/+NgQMHIjMzEwsWLGAYIgoxrBARUUg6evQoWrRogZiYGGzfvh033ngjNmzYgH//+98YMWKEv5tHRJWMFSIiCklpaWl48MEHkZGRgfbt22PDhg2YPHkywxBRiGKFiIhC1tGjR9GwYUNomoZ77rkHs2fP9neTiMhPWCEiopCkaRrGjh0L8TdhRESEn1tERP7EQEREIWns2LH44osvcP3116N27dqYM2cO9uzZ4+9mEZGfMBARUch5/fXX8eabb+Kyyy7D/Pnz8cQTT6CkpASTJk3yd9OIyE84hoiIQsqCBQswZMgQNGvWDOvWrUNKSgry8/PRtGlT/P3339i8eTPatWvn72YSUSVjhYiIQsaqVaswbNgw1KpVC99++y1SUlIAALGxsZgwYQI0TcNTTz3l51YSkT+wQkREIWHHjh3o0aMHioqK8NNPP6Fr166G5wsKCtC8eXMcO3YM69atQ/fu3f3UUiLyBwYiIiIiCnnsMiMiIqKQx0BEREREIY+BiIiIiEIeAxERERGFPAYiIiIiCnkMRERERBTyGIiIiIgo5DEQERERUchjICIiIqKQx0BEREREIY+BiIiIiEIeAxERERGFPAYiIiIiCnn/DyHHpN1rJXziAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from qsppack.utils import cvx_poly_coef\n", "\n", "delta = 0.1\n", "targ = lambda x: 0.8 * np.sign(x)\n", "deg = 251\n", "parity = deg % 2\n", "\n", "opts = {\n", " 'intervals': [delta, 1],\n", " 'objnorm': np.inf,\n", " 'epsil': 0.1,\n", " 'npts': 500,\n", " 'isplot': True,\n", " 'fscale': 1,\n", " 'method': 'cvxpy'\n", "}\n", "\n", "coef_full = cvx_poly_coef(targ, deg, opts)\n", "coef = coef_full[parity::2]" ] }, { "cell_type": "markdown", "id": "722e4f20", "metadata": {}, "source": [ "## Solving the phase factors and verifying" ] }, { "cell_type": "markdown", "id": "7c58ba99", "metadata": {}, "source": [ "We can again use Newton's method to find the phase factors and verify the solution." ] }, { "cell_type": "code", "execution_count": 2, "id": "387bb391", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iter err \n", " 1 +4.2964e-01\n", " 2 +5.9888e-02\n", " 3 +1.8712e-03\n", " 4 +1.9232e-06\n", " 5 +1.9158e-12\n", "Stop criteria satisfied.\n", "The residual error is\n", "1.8762769116165146e-14\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "opts.update({\n", " 'maxiter': 100,\n", " 'criteria': 1e-12,\n", " 'useReal': False,\n", " 'targetPre': True,\n", " 'method': 'Newton'\n", "})\n", "\n", "from qsppack.solver import solve\n", "phi_proc, out = solve(coef, parity, opts)\n", "\n", "from qsppack.utils import chebyshev_to_func, get_entry\n", "import matplotlib.pyplot as plt\n", "\n", "xlist1 = np.linspace(-1,-delta,500)\n", "xlist2 = np.linspace(delta,1,500)\n", "xlist = np.concatenate([xlist1, xlist2])\n", "func = lambda x: chebyshev_to_func(x, coef, parity, True)\n", "targ_value = targ(xlist)\n", "func_value = func(xlist)\n", "QSP_value = get_entry(xlist, phi_proc, out)\n", "err = np.linalg.norm(QSP_value - func_value, np.inf)\n", "print('The residual error is')\n", "print(err)\n", "\n", "plt.plot(xlist, QSP_value - func_value)\n", "plt.xlabel('$x$', fontsize=12)\n", "plt.ylabel('$g(x,\\\\Phi^*)-f_\\\\mathrm{poly}(x)$', fontsize=12)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5e9d5b71", "metadata": {}, "source": [ "## Reference\n", "1. Gilyén, A., Su, Y., Low, G. H., & Wiebe, N. (2019, June). Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. In *Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing* (pp. 193-204).\n", "\n", "2. Dong, Y., Meng, X., Whaley, K. B., & Lin, L. (2021). Efficient phase-factor evaluation in quantum signal processing. *Physical Review A*, 103(4), 042419." ] } ], "metadata": { "kernelspec": { "display_name": "qspy", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.2" } }, "nbformat": 4, "nbformat_minor": 5 }