{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cross Entropy Benchmarking (XEB)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "approximate-aurora", "metadata": {}, "source": [ "[![Open in Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/Infleqtion/client-superstaq/blob/main/docs/source/apps/supermarq/qcvv/qcvv_xeb_css.ipynb) [![Launch Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/Infleqtion/client-superstaq/HEAD?labpath=docs/source/apps/supermarq/qcvv/qcvv_xeb_css.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To demonstrate the cross entropy benchmarking routine, consider a noise model with two independent\n", "depolarising channels, one which only effects single qubit gates and a second that only effects\n", "two qubit gates." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "try:\n", " import supermarq\n", "except ImportError:\n", " print(\"Installing supermarq...\")\n", " %pip install --quiet supermarq\n", " print(\"Installed supermarq.\")\n", " print(\"You may need to restart the kernel to import newly installed packages.\")" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "from __future__ import annotations\n", "import cirq\n", "import numpy as np\n", "\n", "\n", "class IndependentDepolariseNoiseModel(cirq.NoiseModel):\n", " \"\"\"Applies single and two qubit depolarising channels independently\"\"\"\n", "\n", " def __init__(self, single_qubit_error: float, two_qubit_error: float) -> None:\n", " \"\"\"Args:\n", " single_qubit_error: Single qubit pauli error\n", " two_qubit_error: Two qubit pauli error\n", " \"\"\"\n", " super().__init__()\n", " self.single_qubit_error = single_qubit_error\n", " self.two_qubit_error = two_qubit_error\n", "\n", " self.single_qubit_depolarise = cirq.DepolarizingChannel(p=single_qubit_error, n_qubits=1)\n", " self.two_qubit_depolarise = cirq.DepolarizingChannel(p=two_qubit_error, n_qubits=2)\n", "\n", " def noisy_operation(self, operation: cirq.Operation) -> list[cirq.OP_TREE]:\n", " \"\"\"Produces a list of operations by applying each noise model\n", " to the provided operation depending on the number of qubits it acts on.\n", " \"\"\"\n", " if len(operation.qubits) == 1:\n", " return [operation, self.single_qubit_depolarise(*operation.qubits)]\n", "\n", " if len(operation.qubits) == 2:\n", " return [operation, self.two_qubit_depolarise(*operation.qubits)]\n", "\n", " return [operation]\n", "\n", "\n", "noise = IndependentDepolariseNoiseModel(single_qubit_error=0.005, two_qubit_error=0.02)\n", "simulator = cirq.DensityMatrixSimulator(\n", " noise=noise,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The XEB experiment allows us to estimate the fidelity of a \"cycle\" composed of pair of single \n", "qubit gates followed by a two qubit gate. If each single qubit gate is effected by a pauli error\n", "channel with rate $p_1$ and each two qubit gate is effected by a two qubit \n", "depolarising channel with pauli $p_2$ the overall cycle depolarising error is\n", "$$e_L = \\frac{16}{15}\\left( 1 - \\left(1- p_1\\right)^2 \\left(1-p_2\\right) \\right)$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "d9a5cc055a4543269844a578018d51f7", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Building circuits: 0%| | 0/100 [00:00" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "if experiment.collect_data():\n", " experiment.analyze_results(plot_results=True)\n", "cycle_depolarising_error = (\n", " 16 / 15 * (1 - (1 - noise.single_qubit_error) ** 2 * (1 - noise.two_qubit_error))\n", ")\n", "cycle_depolarising_error_estimate = 1 - experiment.results.cycle_fidelity_estimate\n", "print(f\"Cycle depolarising error: {cycle_depolarising_error:.5f}\")\n", "print(f\"Estimated cycle depolarising error: {cycle_depolarising_error_estimate:.5f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now lets repeat a similar experiment, still using two qubits but this time without entangling \n", "gates between them. In this case our noise model reduces to a pair of independent single \n", "qubit depolarising channels with pauli rates $p_1$, or equivalently depolarising rates of \n", "$e_{1q} = \\tfrac34 p_1$. \n", "\n", "Each cycle is made up of two single qubit gates (one on each qubit) so we obtain a cycle fidelity of\n", "$$f_L = (1- e_{1q})^2$$\n", "\n", "Thus we can estimate the single qubit pauli error as \n", "$$p_1 = \\frac{4}{3} \\left(1-\\sqrt{f_L}\\right)$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c08d7da06acb478cbee474414798a31e", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Building circuits: 0%| | 0/100 [00:00" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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PBzzD9RaLhaysLIqLi6sdtar4C7NFixZ1voaKEafIyMgmWSC1uLiY77//npiYGD788EOMRmOl7cnJyfVynri4OFJSUti7dy+nnXZale3V/btVfHaTJ09m5MiRtTpPQkIC27dvZ/fu3ZVu31Vn+/btbN++nd69e/PKK69U2X60a7/55pt58sknvX/1v/feewQHBzN27NhaxQn/fi3W9DVbH19/FY7nczmRcwDs3r27Vv0tFgsARUVF1W6vGAFriuLi4khKSmLv3r106dKlyvajfT2PGDGCu+++u8FjPJopU6awevVq3njjDS6//HK2bt3K4MGDG7Q2mjj5SR2rJs7lcnHddddRXFzMs88+y5IlS+jcuTNvvfUWn376aY37ffTRR9Ueq2KfiqVzzGazd97UBx98UGWfzZs3s3HjRgIDA09oaYuWLVvSuXNntm7desz6Nieq4heVy+Wq9T75+fnouk5cXFyVpMrpdLJs2bJ6ia1iPlR1/z7bt2+vchsQ4KKLLgI4rhgGDx4MwOuvv37Mvrm5uUD1t1tzc3OPWsOrdevWDB06lLVr1/LQQw+Rn5/Ptddei7+/f61jrfhMPv74Y9xud5XtS5YsqdTvRBzP51JXvXr1IjQ0lI0bN9ZqnlBFVffqvi9ycnJYv359rc9dl6/9E3G0r+ecnBzvfKrD1eXr+XjV9nMYPXo0ERERLF68mJdffhmo39FWcWqSxKqJe+SRR1i7di3Dhw/nlltuwc/PjyVLlmA2m7n55pu9cxyOtGrVqiojWrNnz2bfvn1069at0i+p6dOnA54Cg4ePThQWFjJt2jSUUtxyyy0nfNvj4YcfRtd1Ro4cWW0CkZ2d7Z34fCIqRkCSkpJqvU90dDQhISFs3ryZ3377zdvudru577776i0ZnDJlCgDz58+vNJeruLiY6dOnV3urceTIkXTp0oV3332XRx99tMqcMqUUv/32W6W4J0+eTGRkJN988w3z58+vctzff/+djIwMANq3b4/BYODHH3+sNDm/rKyMKVOmkJOTU6treu6554Dj/8U0aNAgzjjjDFJSUpg1a1alWJctW8bSpUsJDAzkhhtuOK7jVud4Ppe6slqt3HXXXQDceOONVUZt8vPz+fnnn73v27RpQ6tWrdi0aROff/65t724uJibb765UsHSY4mMjMRsNrN79+5qk9T6NmnSJKxWK++++673wQDw/DFy1113UVxcXGWffv36cdFFF/Hbb78xderUaq9v48aNLF++vM5x1fZngM1mY8KECWRkZPDee+8RFRXFiBEj6nxeIYDjLKokTgjlJRUOL1h35OvwmkyrV69WRqNRxcTEqIyMjErHevzxxxWgLrrookp1fyoezb711luVpmmqb9++6uqrr1Zdu3ZVgAoODq5UP6lCRYFQPz8/NWzYMDV69GhvvZ+zzjqrxgKhNZUZoIbHth944AFvXaozzzxTjR49Wo0aNUr17NlTGY1GFRIScsLnOXjwoLLZbMpoNKqhQ4eqG264Qd14441q+/btSqmaH8Wu+EyNRqO3QGhiYqLy8/NTU6dOVYCaPXv2ccVXnXvuuUeBp/DmkCFD1JgxY1RMTMxRC4Tu2LFDtWnTRgEqOjpaDR48WF1zzTXq4osvVtHR0QpQzz33XKV9fvrpJxUUFKQA1aZNGzVmzBg1fPjwagth3nTTTZX+/UeNGqViYmJUZGSkt9hnTeUrXC6Xt3hp7969a/05HO6ff/5RERERClCnnXaauvrqq9XZZ5+twFMg9MMPP6yyT13KLSh1fJ/Lscot1HRup9PpLeJrsVjUhRdeqK6++mp1zjnnVCkQqpRSixYt8n7tnX/++Wr48OEqJiZGdejQQV1xxRW1LreglPJ+DXXt2lVdf/316sYbb1RvvvlmrT6bmr5vj3a+l156yfs9PWjQIDVu3DiVmJioQkJCvKU6qisQWlGANjQ0VA0aNEhdc801atiwYd6vpSNrTB1PuQWllLcAaZ8+fdTEiRPVjTfeqD7//PMq/SpqsgHqnnvuqfGzEaK2JLFqRBWJ1dFeFQUXCwsLVdu2bRWgvvrqqyrHcrvd3uKdzz77rLf98F/0X375perfv7/y9/dXISEh6oorrlBbtmypMb533nlHDRgwQAUGBiqbzaa6du2qHn/8cVVSUlKlb10TK6WU+vnnn9Xo0aNVfHy8MpvNKiIiQnXr1k1NmzZN/fzzz/Vynm+//VadffbZKjAw0PvZVhzjaDVu3n77bdWzZ0/l7++vIiIi1BVXXKE2btyo3nrrrXpLrJTyVIfu1q2bslqtKjo6Wl133XXq4MGDRz1eXl6eeuyxx9SZZ57p/TdKTExUQ4YMUQsWLKhU/6tCcnKymjJlikpMTFQWi0WFh4erXr16qUceeUQVFBR4+7lcLvX//t//U126dFE2m03FxMSoa6+9VqWkpByzLphSylthu7paaLW1d+9eddNNN6mEhARlNptVZGSkGjFihPrjjz+q7V/XxEqp2n8udU2slPJ8jy5evFgNHDhQhYSEKKvVqhITE9WYMWOq/fd966231Omnn64sFouKiYlRkydPVllZWcdVx0opT9Jy/fXXq9jYWGU0Go+rZltdEiulPLXW+vXrp/z8/FRYWJi64oor1LZt2476tVNaWqpeeOEFNWDAABUSEqIsFotKSEhQ5513nnr66afV/v37a3X+mmLeuXOnGjFihIqIiFAGg6Ha798KFclcxR9fQpwITSkfPOYkGszEiRN5++23+emnnxg0aJCvwxGngJKSElq0aIHL5eLQoUPeMhhCNAdr1qxhwIABnHfeebVea1KIo5E5VkKIE7JgwQLy8vKYMGGCJFWi2Xn88ccBmDZtmo8jEScLKbcghDhu2dnZ3HfffaSnp/P1118TGBjI/fff7+uwhKiV1atXs2jRIjZv3szatWs588wza1zZQIjjJYmVEOK4FRYWsmjRIiwWCz179uSZZ56ptlyDEE3Rjh07ePPNNwkKCmLYsGEsWLCgUYoQi1ODzLESQgghhKgnkqILIYQQQtQTSayEEEIIIeqJJFbllFIUFBT4ZJFdIYQQQpwcJLEqV1hYSEhICIWFhb4ORQghhBDNlCRWQgghhBD1RBIrIYQQQoh6IomVEEIIIUQ9kcRKCCGEEKKeSGIlhBBCCFFPJLESQgghhKgnklgJIYQQQtQTSayEEEIIIeqJJFZCCCGEEPVEEishhBBCiHoiiZUQQgghRD2RxEoIIYQQop5IYiWEEEIIUU8ksRJCCCGEqCeSWAkhhBBC1BNJrIQQQggh6okkVkIIIYQQ9UQSqwailPJ1CEIIIYRoZJJY1TO9rIzstxaz56qrcJeU+DocIYQQQjQiSazqWeqs2WT83/9h37adpCeeQNd1X4ckhBBCiEYiiVU9Wrt6Na8n7/a+L/l0KXddfz1rV6/2YVRCCCGEaCySWNWTtatX8/hDD7F6/362+fkBEKAUiZs38/hDD0lyJYQQQpwCJLGqB7qus/i11ygpLiYqJoZfYqKpmLo+yOlCKyxk8WuvyW1BIYQQ4iQniVU92L5lCynJyQSHhqJpGplWK9sDAwGw6TqXopGSnMz2LVt8HKkQQgghGpIkVvUgLzcXp9OJxWLxtv0UFUnF+FTfoiL87HbycnN9E6AQQgghGoUkVvUgNCwMs9mMw+HwtuVYLGwNCgLAqhRD7Q5Cw8J8FaIQQgghGoEkVvWgc9euJLZtS0FeXqXCoCsjI3CX/38/p5O2IaE+iU8IIYQQjUMSq3pgMBiYeMst+AcEkJmeTllZGbquk6br/GU2A2DWdXJefdXHkQohhBCiITXZxGrBggUkJiZis9no168fa9eurbGv0+nkkUceoV27dthsNrp3787y5csbMVroO2AADz72GB06d6a0pISszExKS0rY2rULymgEoOB//8O+O7lR4xJCCCFE49FUE1zU7sMPP2T8+PG8+uqr9OvXj/nz5/Pxxx+TlJREdHR0lf733XcfS5YsYeHChXTu3Jlvv/2WGTNmsHr1anr27FmrcxYUFBASEkJ+fj7BwcF1jl3XdbZv2UJebi6hYWF07tqV9DlzyPvoYwCCLxtG/NNPo2lanc8hhBBCiKapSSZW/fr1o0+fPrz00kuAJ1lJSEhg+vTp3H///VX6x8fH8+CDDzJ16lRv28iRI/Hz82PJkiW1Omd9JVbVcWZksHvwRSiHA0wmEj/5GL/Onev1HEIIIYTwvSZ3K9DhcLBu3ToGDx7sbTMYDAwePJg1a9ZUu4/dbsdms1Vq8/PzY9WqVTWex263U1BQUOnVUMzR0YSOGe1543KR9fIrKCkWKoQQQpx0mlxilZWVhdvtJiYmplJ7TEwMaWlp1e4zZMgQnn32WXbu3Imu63z//fcsXbqU1NTUGs8zb948QkJCvK+EhIR6vY4jRU6dilae/BWtWEHZpk0Nej4hhBBCNL4ml1jVxfPPP0+HDh3o3LkzFouFadOmMWnSJAyGmi9v5syZ5Ofne1/79+9v0BhNYWGEXX21543bTebLr6BcrgY9pxBCCCEaV5NLrCIjIzEajaSnp1dqT09PJzY2ttp9oqKi+OyzzyguLmbv3r1s376dwMBA2rZtW+N5rFYrwcHBlV4NLWLKLRgCAgAo/uUXStatb/BzCiGEEKLxNLnEymKx0KtXL1asWOFt03WdFStW0L9//6Pua7PZaNGiBS6Xi08//ZQrrriiocM9LqaQEMKuv87zRikyX3rJM6FdCCGEECeFJpdYAcyYMYOFCxfy9ttvs23bNm699VaKi4uZNGkSAOPHj2fmzJne/n/88QdLly4lOTmZX3/9laFDh6LrOvfee6+vLqFGEZMnYwwNBaD0zz8p+OUX3wYkhBBCiHpj8nUA1Rk7diyZmZnMmjWLtLQ0evTowfLly70T2vft21dp/lRZWRkPPfQQycnJBAYGcumll/Lf//6X0PIEpikxBgYSMXkyGc88A0D2y68QdPbZGPz8fByZEEIIIU5Uk6xj5QsNWcfqSMrhYNdFF+Mqn0cW98TjhF51VYOeUwghhBANr0neCjzZaRYLkbfd6n2f9fpCXIWFPoxICCGEEPVBEisfCR01CnPr1gA4U1LI//RTZPBQCCGEaN4ksfIRzWgk6s47vO9zFr+NKyvLhxEJIYQQ4kRJYuVDwUOHYu1yGgCutDRy339flroRQgghmjFJrHxI0zSi7prhfZ/3/gc4Dx3yYURCCCGEOBGSWPlY0Lnn4NenDwDu3FxyFr8tS90IIYQQzZQkVk1A9N3/jlrlL1uGIyXFd8EIIYQQos4ksWoC/Hv0IPD8QQDoxcVkvfEGuix1I4QQQjQ7klg1EVF33QVGIwCF3yynbNt2H0ckhBBCiOMliVUTYevYkeBLLwVA2e1kv/46enGxj6MSQgghxPGQxKoJibrjdjSLBYCilSspXrfOxxEJIYQQ4nhIYtWEWFq2JGT0KM8bt5vs1xfizsvzaUxCCCGEqD1JrJqYyKlTMQQFAVD6118U/rRSioYKIYQQzYQkVk2MOTyc8IkTve+zFy3CmZnpu4CEEEIIUWuSWDVBERMnYIqNBcCxaxf5n3+Bcjp9HJUQQgghjkUSqybIEBBA5G23et/nvfcuztRUH0YkhBBCiNqQxKqJCrnySqwdOgDgSksn57330MvKfByVEEIIIY5GEqsmymA2E3Xnnd73+UuXYU9O9l1AQgghhDgmSayasMDzB+HXty8AekEBOYvfxl1Y6NughBBCCFEjSayaMM1gIPquO8Hg+Wcq/PZbyjZvRinl28CEEEIIUS1JrJo4vx49CLroIqB8qZu3FuPOyfFxVEIIIYSojiRWTZymaUTdfjua1QpA8apVFP+xFuVy+TgyIYQQQhxJEqtmwNquLSFXXeV5o+vkLF6MS4qGCiGEEE2OJFbNROStUzCEBANQ9s8/FPzwg5RfEEIIIZoYSayaCXN0NOHjx3vf5/53CY4DB30YkRBCCCGOJIlVMxJ+/fWY4uMBcO7bR/6yZbgLCnwclRBCCCEqSGLVjBiDg4mcNtX7Pv/TT7Hv2iXlF4QQQogmQhKrZiZk2DBs3c4AwJ2XR+777+POyvJxVEIIIYQASayaHYPVSvSdd/5bNPS77ynZsBHldPo2MCGEEEJIYtUc+ffpQ+CFFwKeoqG5776LIz3dx1EJIYQQQhKrZkgzm4maNg3Nzw+Akj/+oHjVKvSSEh9HJoQQQpzaJLFqpqzt2xE6cqTnjVLkvvse9gMHfBuUEEIIcYqTxKqZ0oxGwiffiDEqCgDHzp0UfrMcV26ujyMTQgghTl2SWDVj5pgYIiZN8r7P+/RT7HtSUG63D6MSQgghTl2SWDVjmqYRMvIqLB06AODOyCD/009xSfkFIYQQwicksWrmTCEhRE69DTQNgIJvvqF0yxZ0u93HkQkhhBCnHkmsTgJBAwfiP6A/AKqkhLwPP8J58JCPoxJCCCFOPZJYnQQM/v5ETp2KZrEAULxqFcV//inrCAohhBCNTBKrk4Tf6acTfNkwzxu3m7wPPsC+dx9K130bmBBCCHEKkcTqJGGwWIi46SaMYWEA2Ldto+iH73FlykR2IYQQorFIYnUSsSQkEDb+eu/7vKXLsO/aie5w+DAqIYQQ4tQhidVJRDOZCB016t/yC5mZ5H/2Oc4DB30cmRBCCHFqaLKJ1YIFC0hMTMRms9GvXz/Wrl171P7z58+nU6dO+Pn5kZCQwF133UVZWVkjRdt0mCIjiZpyi7f8QuH331O6ebNMZBdCCCEaQZNMrD788ENmzJjB7NmzWb9+Pd27d2fIkCFkZGRU2/+9997j/vvvZ/bs2Wzbto1Fixbx4Ycf8sADDzRy5L6naRoB55xDwMCBAKiyMvI/+QTHvv0ykV0IIYRoYE0ysXr22We56aabmDRpEl26dOHVV1/F39+fN998s9r+q1ev5uyzz+aaa64hMTGRiy++mKuvvvqYo1wnK2NICBG33Izm7w9Aydq1FK9ZLRPZhRBCiAbW5BIrh8PBunXrGDx4sLfNYDAwePBg1qxZU+0+AwYMYN26dd5EKjk5ma+//ppLL720xvPY7XYKCgoqvU4mfqedRsiVV3rf5326FHvKHpnILoQQQjSgJpdYZWVl4Xa7iYmJqdQeExNDWlpatftcc801PPLII5xzzjmYzWbatWvHoEGDjnorcN68eYSEhHhfCQkJ9Xodvmbw8yN8/HhMcXEAOFNSKPz2W5wHZSK7EEII0VCaXGJVFytXruSJJ57g5ZdfZv369SxdupSvvvqKRx99tMZ9Zs6cSX5+vve1f//+Roy4cVji4wifONH7vuCrrynbuVMmsgshhBANxOTrAI4UGRmJ0WgkPT29Unt6ejqxsbHV7vPwww9z/fXXM3nyZADOOOMMiouLufnmm3nwwQcxGKrmj1arFavVWv8X0IRoZjPBlwyl8JuvKd2wET0/n4LPv8AS3wJbl9PQqvlchBBCCFF3Te43q8VioVevXqxYscLbpus6K1asoH///tXuU1JSUiV5MhqNACilGi7YZsAUGUn4TTeDyZNDF61cSenGjbgyM30cmRBCCHHyaXKJFcCMGTNYuHAhb7/9Ntu2bePWW2+luLiYSZMmATB+/Hhmzpzp7T98+HBeeeUVPvjgA/bs2cP333/Pww8/zPDhw70J1qlKMxgI6HUmQRdf7Glwu8lbtgz7nj3op2CdLyGEEKIhNblbgQBjx44lMzOTWbNmkZaWRo8ePVi+fLl3Qvu+ffsqjVA99NBDaJrGQw89xMGDB4mKimL48OE8/vjjvrqEJsUYGkr4pImUrFmDOzcX++bNFK/6DVNkJLb27X0dnhBCCHHS0NSpfq+sXEFBASEhIeTn5xMcHOzrcOqdXlJC1htvkP3yKwAYIyKImT2bgD69MZUv3CyEEEKIE9MkbwWK+mfw9yd4xAisnToB4M7OpvDrr3Hs3YdyuXwcnRBCCHFykMTqFGKNjSX8xhuhfN5Z4Q8/ULZlM64jnsAUQgghRN1IYnUK0SwWAvr1I+jCCzwNLhf5yz6jLCUFvbjYt8EJIYQQJwFJrE4xpqhIwsZPwFg+r6ps82ZK1qzBsX//KV+aQgghhDhRklidYjSDAVuH9oSMGeNty1/2GfaUFNxZskizEEIIcSIksToFGUNCCLl8ONbOnYHyiezffod97z6ULNIshBBC1JkkVqcoS4sWhE+c8O9E9u+/p2z7NhypqT6OTAghhGi+JLE6RRlsNgL69iXwgn8nshd8/gX2vXtlkWYhhBCijiSxOoWZoqMJu/bafyeyb9pE6Z9/Yd+7F+V2+zg6IYQQovmRxOoUpplM2Dp2IHT0KG9b/rJlOPbuk9pWQgghRB1IYnWKM4aFEXTppf9OZM/KomjFCuxS20oIIYQ4bpJYneI0TcOakEDY9deBybMmd+F332HfuRPHvn1S20oIIYQ4DpJYCQwBAfj37UvQRYM9DW43+Z8uxXHwIK7MTN8GJ4QQQjQjklgJACwxMYSOHoMpOhoA+44dlPyxFkdKCrrd7uPohBBCiOZBEisBeNYRtHVoT+i4sd62/KVLcew/gGP/fh9GJoQQQjQfklgJL2NEBEHnnYd/n94A6MXFFH7zDc4DB3Dl5Pg4OiGEEKLpk8RKeGkGA+bWrQkddzWavz8AxatWUbY9CcfevSin08cRCiGEEE2bJFaiEmNgILbTuxIyfLi3Le+jj3AeSpXlboQQQohjkMRKVGGJiyNo2DAsbdsC4Dp0iKJVq3DIcjdCCCHEUUliJarQLBZsbRIJvXocGDxfIgX/+x/OAwdkuRshhBDiKCSxEtUyRkYS0Ls3geef72lwOslfugxnahqutDTfBieEEEI0UZJYiWppmoY5oRUhI6/CGBEBeBZpLtu8GXtKCu4iWe5GCCGEOJIkVqJGxsAArB06EHLVVd62vI8+wp2djXNvCkrXfRidEEII0fRIYiWOyhIbS9D5g7B17w6AnpdHwTfLcaam4kpP921wQgghRBMjiZU4Ks1sxtKqFWFjx6L5+QFQ9NNP2FP2Yk9JQS+WW4JCCCFEBUmsxDEZIyKwde1CyOX/1rbKXbIEd04Ojn375JagEEIIUU4SK3FMmqZhadmSwIsuwtKhAwCutDSKfv4F58GDuDIzfRyhEEII0TRIYiVqxRAQgDWxDaGjR4PJBHhqWznSM3DsSUEvLfVxhEIIIYTvSWIlas0cG4Nft24EDR3qadB18t57D1derueWoFK+DVAIIYTwMUmsRK1pJhOW1q0IHjoUc4sWADh276bkz7/klqAQQgiBJFbiOJnCwrC0SSRkzBjQNADyP/kEV14+jpQU9LIyH0cohBBC+I4kVuK4WVq2xL9nDwIGDQJA2e3kffghrrw8HHvllqAQQohTlyRW4rgZrFYsrRMJuWwYxvBwAMo2bsS+dRvOQ3JLUAghxKlLEitRJ6aoSKyJiYSMHuVty333XdwlpZ5bgvKUoBBCiFOQJFaiTjSDAXPrRAL69sWvb18A9MJC8pcuxZ2fL08JCiGEOCVJYiXqzBgYgLl1a0KuuBxDQAAAJb/9hj15j+cpwQy5JSiEEOLUIomVOCGW2Fis7dpXviX41lvoDieOPXvQS0p8GJ0QQgjRuCSxEiekoraVf7+zsHXvDoA7L4/8ZctwFxbg2LtX1hIUQghxypDESpwwU1gYllYJhF51FZqfHwDFP/+MY99+nIcOyVOCQgghThmSWIl6YWnZEkubRM9aguVyFi1Cd7mxJyfLLUEhhBCnBEmsRL2oqG3l368vttNPB8Cdk0PBF1+gFxXhSEmRW4JCCCFOek06sVqwYAGJiYnYbDb69evH2rVra+w7aNAgNE2r8ho2bFgjRnxqM0VHYYmPJ2T0KDSbDYCiFStwHkr13BJMT/dxhEIIIUTDarKJ1YcffsiMGTOYPXs269evp3v37gwZMoSMjIxq+y9dupTU1FTva/PmzRiNRkYfdmtKNCxN07C0bo2lVStCR470tme/8QYKDXtKCu6iYh9GKIQQQjSsJptYPfvss9x0001MmjSJLl268Oqrr+Lv78+bb75Zbf/w8HBiY2O9r++//x5/f39JrBqZwd8fa6LnlqC1SxcA3JmZ5H/55b+3BN1uH0cphBBCNIwmmVg5HA7WrVvH4MGDvW0Gg4HBgwezZs2aWh1j0aJFjBs3joDywpWi8ZhiYjDHtyBs9Cg0qxWAom+/xZWRiTM1FUdqqo8jFEIIIRpGk0yssrKycLvdxMTEVGqPiYkhLS3tmPuvXbuWzZs3M3ny5Br72O12CgoKKr1E/dAMBiyJrTEntCLkqqu87dkLF4LZjDMlBXd+vg8jFEIIIRpGk0ysTtSiRYs444wz6Fu+hl115s2bR0hIiPeVkJDQiBGe/IyBgZgTW+N/Vj+snToB4EpLo+Dzz9Htdux7UlBOp4+jFEIIIepXk0ysIiMjMRqNpB/xFFl6ejqxsbFH3be4uJgPPviAG2+88aj9Zs6cSX5+vve1f//+E45bVGaJjcUcG0vI2LFoFgsAhd98gzMtHVdmBo4DB3wcoRBCCFG/mmRiZbFY6NWrFytWrPC26brOihUr6N+//1H3/fjjj7Hb7Vx33XVH7We1WgkODq70EvVLM5mwJiZiadmSkMMeIsh+5RU0swXH3n24cnK87bquc2DjRpJ++okDGzeiS90rIYQQzYypLjvNnTuXG2+8kZYtW9Z3PF4zZsxgwoQJ9O7dm759+zJ//nyKi4uZNGkSAOPHj6dFixbMmzev0n6LFi1ixIgRRERENFhsovaMISGetQT79Kb077+xb92KOyuLvI8/JnTUKOzJezAEBJD855+sfPFFMnftwu10YjSbiWrfnkHTp9P+nHN8fRlCCCFErdRpxGru3Lm0adOG4cOH88UXXzTIyMLYsWN55plnmDVrFj169GDDhg0sX77cO6F93759pB7xdFlSUhKrVq065m1A0bgs8fGYo6MJu+aaSoVD7Xv34s7JYddnn7P0nntI3boVi78/gdHRWPz9Sd26laX/+Q+7Vq3y8RUIIYQQtaMppdTx7vTEE0+waNEi9uzZg6ZpxMbGcsMNN3DjjTeSmJjYAGE2vIKCAkJCQsjPz5fbgg3AlZND6T+bKFm7lpzyWmTG0FBinnicH556muQD+7HExaFpmncfpRQFaWnEdenCDe+/j8HQJO9cCyGEEF51+k31wAMPsHv3br777jtGjx5NdnY2jz/+OO3bt2fo0KF8+umnuFyu+o5VNGOm8HAsrRKwde+GrUcPANx5eaS/9hq5qalEBARgPCLH1zQN/9BQMnft4tCmTT6IWgghhDg+JzQEMHjwYD744AMOHjzIM888Q6dOnfjuu+8YM2YMLVu25P7772fnzp31Fato5swtW2KKiCRs7FgMgYEAuDf+Q7DTic1oxN/lgiOSK6PVitvppPiwSe5CCCFEU1Uv91YiIiKYMWMGW7ZsYdWqVVx99dVkZGTw9NNP07lzZy688EKWLVtWH6cSzZjBYsHatg3GsFDCrr/e295J13E6Xfi5XNiOWO7GbbdjNJsJCA9v7HCFEEKI41avk1Z2797Nl19+WalMQsuWLfnpp58YNWoUffv2lXpRpzjPLcFWWDt3wr9fPwAsQJuiQpyAv9OJqfxhCKUUJXl5RLVvT/wZZ/guaCGEEKKWTjixcjqdfPDBB1x44YV07NiR//u//8PlcjFjxgy2b9/O3r17+e2337jkkkv466+/mDZtWn3ELZqxiluCISNHYih/UCBKgX9ODqrMjs1ux1VSQkFaGtbAQAZNny4T14UQQjQLdXoqEGDbtm0sXLiQ//73v+Tk5KCUYsCAAUyZMoXRo0djLV9893BnnXUW27dvJy8v70TjrnfyVGDj8jwl+A9l27aT9fzzALgNBtaaTCi3m2KzCf+OHRl0++1Sx0oIIUSzUacCoeeccw5r1qxBKUVwcDC33norU6ZM4fTTTz/qfl27duXPP/+sU6Di5FJxS1A5HAScey7Fv/6KUdc5u0U8+uVXYLNaaDFsGJYjFuIWQgghmrI6JVarV6/mzDPPZMqUKVxzzTX4+/vXar/JkyczcODAupxSnITMLVviyskl5MorKdu2DXdWFvqeFMKyswk491ycKSmYgoIw1PLrSwghhPC1Ot0KXLduHb169WqIeHxGbgX6RsUtQce+/WTMm+cpt2AyEffEExhsNiwt4rGedhqazLESQgjRDNTpt9VXX33FF198ccx+X375JY888khdTiFOERW3BM2xMQRffrmn0eUi64UXMISE4DiUivNQ6tEPIoQQQjQRdUqs5syZw2effXbMfl988QVz586tyynEKcTcsiXG8AiCBg/GUr4kkvPAAfI+/BBDYCCOlD248/N9G6QQQghRCw16f8Xtdstj8uKYKgqHamYzEbfcgmaxAFD49dc4du9GtzuwJyejHA4fRyqEEEIcXYNmPVu2bCEsLKwhTyFOEhW3BA0B/oRec423PWvBAjSrFVdmJvZ9+6hjdRAhhBCiUdT6qcAbbrih0vtVq1ZVaavgcrlISkrir7/+YsSIEScUoDh1WFq2wJ2fh1/vXpT+/TdlGzfizs0l5403iLjtNpz792MMCsIsJRiEEEI0UbV+KvDwW3qaptVq5KBbt24sXbqUtm3b1j3CRiJPBTYN7rw8Sv7ZhF5cTNrDD6MXFQEQOW0atu7d0UxG/M44A2P5Is5CCCFEU1LrxOrnn38GPOu3XXDBBQwdOpT77ruv2r4Wi4X4+Hhat25df5E2MEmsmg77vn3Yk5Kw704ma/58ADQ/P+KfeQZN6RhjYvDr3BnNbPZtoEIIIcQRan0r8LzzzvP+/4QJEzj33HMrtQlRXyzx8bjz89EMBgIGDaJ45UpUaSlZzz9PzOzZuFLTcAQEYm3bxtehCiGEEJXUea3Ak42MWDUt7sJCSjf+g263kz53Lq6MDABCRo0i5PLL0YuL8Dv9dExRUT6OVAghhPiX1EIQTZIxKAhrm0TQdSKnTYPyOX75S5fiSEkBgxF7cjJ6cbFP4xRCCCEOV6sRq7Zt26JpGj/88ANt2rQ5rsnomqaxe/fuEwqyMciIVdOj3G7s27fjSE2l+LfV5L3/PgDGiAjinn4aVVyEOS4e22md0YxGH0crhBBC1HKOVUpKCgBOp7PSeyEakmY0YklMxFVQQMCgQZT98w9lW7bgzs4m59VXibzzTpyphzAEBWJtRg9KCCGEOHnV6lagruvouk7Hjh0rva/tS4i6MgQEYG3TBs3lJHzKFAzlZRZK1q6leOVKDMEhOFJScOXk+DhSIYQQQuZYiWbAFB2NuWVLNBQRt97qbc9ZvBh3Tg4osO/ejV5a6sMohRBCCEmsRDOgGQxYWrfGGBqKtV07goYMAUA5HGQ+9xyGoCDceXk4kpNRbrePoxVCCHEqk8RKNAsGmw1r27aAImT0aMytWgHg3LeP3CVLMEVG4Th0CMeBA74NVAghxCmtVomV0Wis88tkqnUNUiGOyhQRgaVVa1RJMZHTp6NZLAAUfvMNpRs3euZb7UnBlZXl40iFEEKcqmqV9SQkJKBpWkPHIsQxWRJa4i4swJWVRdj48eS88QYAWQsWEP/MM6Bp2HfvxuDnhyEgwMfRCiGEONVI5fVyUseq+XAXFFD6zyYUkP3aa5T++ScA1i5diJk1C3dWJubYOGydO6HJiKkQQohGJHOsRLNjDA72rBNYVkr45MkYIyMBsG/dSv7HH2OKiMR56BCOfft9HKkQQohTjSRWolkyxcZibtECHHYi77yz0pI3Zdu2YQwNxbE3BWf5GoNCCCFEYzihxOq7777jyiuvpEWLFlitVm688Ubvtm+//ZYZM2Zw6NChEw5SiCNpBgOWxESMISGYo6IIu/pqzwalyHz+eXS7HYwm7Lt34y6S9QSFEEI0jjonVnfccQeXXHIJn3/+OYWFhTidTg6frhUXF8f8+fP58MMP6yVQIY5k8PPD2qYN6G4CL74Yv549AdDz88l6/nkMwcGo4mLsybtR5csxCSGEEA2pTonVO++8w4svvkivXr1Yv349BQUFVfp069aNhIQEvvzyyxMOUoiamKKisLRujZ6fR8Rtt2EMDwegbPNmCpYuxRgZhSstDfu+fchzGkIIceJWrlyJpmnk5eU12DkSExOZP39+gx2/QkpKCpqmsWHDhno7Zp0Sq1deeYXQ0FC++uorevToUWO/bt26kZycXNfYhKgVS8uWmKJjUA47UYfNt8r7+GPKtm/HGBaOc+9eXOnpvg1UCCGEz0ycOJERI0Y0+HnqlFht3ryZAQMGEBUVddR+ISEhpMsvM9HANIsFa9s2GKw2zC1aEDp2rGeDUmTNn4+y29GsNuy7duPOz/dtsEIIIU5qdZ5jVZuCoYcOHcLPz6+upxCi1ozBwVjbtUWVlhB06aXYunUDwJ2XR+YLL2AICkJ32CnbuQu9rMzH0QohRMPTdZ2nnnqK9u3bY7VaadWqFY8//jgXXHAB06ZNq9Q3MzMTi8XCihUrALDb7dx3330kJCRgtVpp3749ixYtqvFcq1at4txzz8XPz4+EhARuv/12iotr9+BQRkYGw4cPx8/PjzZt2vDuu+9W6ZOXl8fkyZOJiooiODiYCy64gI0bN3q3z5kzhx49evDaa6+RkJCAv78/Y8aMIb/8j+k5c+bw9ttv8/nnn6NpGpqmsXLlSu/+ycnJnH/++fj7+9O9e3fWrFlTq9irU6fEqkOHDqxfvx7nUSYEFxYWsmHDBrp27Vrn4IQ4HqaYGMwJrdDzcomcNg1jaCgAZf/8Q/7SpZgio3Dn5uDYs0cWaxZCnPRmzpzJk08+ycMPP8zWrVt57733iImJYfLkybz33nvY7XZv3yVLltCiRQsuuOACAMaPH8/777/PCy+8wLZt23jttdcIDAys9jy7d+9m6NChjBw5kn/++YcPP/yQVatWVUneajJx4kT279/PTz/9xCeffMLLL79MxhGlckaPHk1GRgbffPMN69at48wzz+TCCy8kJyfH22fXrl189NFHfPnllyxfvpy///6b2267DYB77rmHMWPGMHToUFJTU0lNTWXAgAHefR988EHuueceNmzYQMeOHbn66qtxuVy1+6CPpOrgiSeeUJqmqRkzZnjbNE1TkyZN8r6fOnWqMhgM6qWXXqrLKRpdfn6+AlR+fr6vQxEnwF1Wpor+/Evlr/hRZb//gdp6Whe1tVNntfW0Lir73fdU8fq/Vf5336mylBRfhyqEEA2moKBAWa1WtXDhwirbSktLVVhYmPrwww+9bd26dVNz5sxRSimVlJSkAPX9999Xe+yffvpJASo3N1cppdSNN96obr755kp9fv31V2UwGFRpaelR46w419q1a71t27ZtU4B67rnnvMcKDg5WZWVllfZt166deu2115RSSs2ePVsZjUZ14MAB7/ZvvvlGGQwGlZqaqpRSasKECeqKK66odIw9e/YoQL3xxhveti1btihAbdu27aix16ROI1Z33nknZ5xxBvPnz6d///48+eSTgCdrfe655xg4cCAvv/wyPXv25KabbqpbxidEHRisVqzt2qKZTFhatyZ09GjPBl0nc/583AUF5Ys178GVmenbYIUQooFs27YNu93OhRdeWGWbzWbj+uuv58033wRg/fr1bN68mYkTJwKwYcMGjEYj5513Xq3OtXHjRhYvXkxgYKD3NWTIEHRdZ8+ePceM02Qy0atXL29b586dCS2/41Bx/KKiIiIiIiqdY8+ePezevdvbr1WrVrRo0cL7vn///ui6TlJS0jGvoVv59BHwlIsCqoya1VadFlLz8/Pjhx9+YOLEiXzzzTesXbsWgF9//ZVff/0VgIsuuoglS5ZgsVjqFJgQdWUKC8PSJhH79iSCL7+csqQkyjZsQC8oIPO554idMwd3WRllu3bh5+eHsYbhbSGEaK6ONb958uTJ9OjRgwMHDvDWW29xwQUX0Lp161rte6SioiJuueUWbr/99irbWrVqdVzHqun4cXFxleZEVTg8ATsRZrPZ+/8Vc8h1Xa/Tseq8Qm1UVBRfffUVGzdu5LvvviMlJQVd12nZsiUXXXQRffv2reuhhThhlvh4VEEBjkOHiJw+ndT77sOdlYV9+3ZylywhbMIE3Olp2Hfvxu+009DkDwAhxEmkQ4cO+Pn5sWLFCiZPnlxl+xlnnEHv3r1ZuHAh7733Hi+99FKlbbqu8/PPPzN48OBjnuvMM89k69attG/f/rjj7Ny5My6Xi3Xr1tGnTx8AkpKSKtXIOvPMM0lLS8NkMpGYmFjjsfbt28ehQ4eIj48H4Pfff8dgMNCpUycALBYL7kaYX1vnxKpC9+7d6d69e33EIkS90YxGLG3b4i4uRi8tI/ruu0l9+GFwuSj43/+wduqEf9++uNLTsPv5YW3fHs0gS2cKIU4ONpuN++67j3vvvReLxcLZZ59NZmYmW7Zs8S4/N3nyZKZNm0ZAQABXXnmld9/ExEQmTJjADTfcwAsvvED37t3Zu3cvGRkZjBkzpsq57rvvPs466yymTZvG5MmTCQgIYOvWrXz//feVErbqdOrUiaFDh3LLLbfwyiuvYDKZuPPOOyuNmg0ePJj+/fszYsQInnrqKTp27MihQ4f46quvuPLKK+ndu7f3midMmMAzzzxDQUEBt99+O2PGjCE2NtZ7Xd9++y1JSUlEREQQEhJywp9zdZrsb5IFCxaQmJiIzWajX79+3tuNNcnLy2Pq1KnExcVhtVrp2LEjX3/9dSNFK5oig58f1nbtQCnM8fGET5jg3Zb18su40tMxRkTi3LcPV2qqDyMVQoj69/DDD3P33Xcza9YsTjvtNMaOHVtp3tDVV1+NyWTi6quvxmazVdr3lVdeYdSoUdx222107tyZm266qcbyCd26dePnn39mx44dnHvuufTs2ZNZs2Z5R46O5a233iI+Pp7zzjuPq666iptvvpno6Gjvdk3T+Prrrxk4cCCTJk2iY8eOjBs3jr179xITE+Pt1759e6666iouvfRSLr74Yrp168bLL7/s3X7TTTfRqVMnevfuTVRUFL/99lut4jtemlLHXufjnXfeOaGTjB8//rj6f/jhh4wfP55XX32Vfv36MX/+fD7++GOSkpIqfdgVHA4HZ599NtHR0TzwwAO0aNGCvXv3EhoaWuvRtIKCAkJCQsjPzyc4OPi44hVNmz0lBfvOnRgjIsl++WWKV60CwNyqFXFPPIFyOlFOB36nn46pfEkcIYQ42aWkpNCuXTv+/PNPzjzzTF+Hc0LmzJnDZ599Vq9L09RVrRIrg8FQq4KgR1JKoWnacd/T7NevH3369PEOIeq6TkJCAtOnT+f++++v0v/VV1/l6aefZvv27ZUmoB0PSaxOXsrlomx7Es60VAzBIaQ98ADOAwcACBg4kMjp03FnZ2Pws2HrejrGwAAfRyyEEA3H6XSSnZ3NPffcw549exps5KYxNaXEqlZzrGbNmlUlsdq9ezdLlizB39+fiy++2DuhbO/evXz33XcUFxdz3XXX0a5du+MKyOFwsG7dOmbOnOltMxgMDB48uMZKqF988QX9+/dn6tSpfP7550RFRXHNNddw3333YTQaj+v84uSjmUxY27ZBLy5CLy0l6p57SL3/flRZGcW//IKtc2cCL7qofDL7LpnMLoQ4qf3222+cf/75dOzYkU8++aRBz/Xrr79yySWX1Li9qKioQc/vC7UasTrSzp076du3L8OHD2f+/PmEH3H7JDc3lzvvvJMvv/yS33//nY4dO9b62IcOHaJFixasXr2a/v37e9vvvfdefv75Z/74448q+3Tu3JmUlBSuvfZabrvtNnbt2sVtt93G7bffzuzZs6s9j91ur1R1tqCggISEBBmxOom5srIo3bwFzc+Psg0byHzuOc8Gk4m4xx7D0qYNrvQ0LK0TsXaQyexCCHGiSktLOXjwYI3b6/IkYVNXp8Rq1KhRrF+/np07d9Y4IuRyuejYsSM9e/bk008/rfWx65JYdezYkbKyMvbs2eON59lnn+Xpp58mtYZJyXPmzGHu3LlV2iWxOrnZ9+7FvmMHpsgoct55h8JvvgHAGBlJ/P/9H5rNhjsnB2vnTlgTEnwcrRBCiOamTn+Sr1y5krPOOuuot9lMJhNnnXUWP//883EdOzIyEqPRSHp6eqX29PR07yOTR4qLi6Njx46V4jnttNNIS0vD4XBUu8/MmTPJz8/3vvbv339ccYrmydKyJZb4eFyZmYRdfz3W8tFUd1YWmc8+i2YyYQgKwrE7GVdWlo+jFUII0dzUKbEqLS2tcSTocGlpaZSVlR3XsS0WC7169fKusA2eyesrVqyoNIJ1uLPPPptdu3ZVqpK6Y8cO4uLiaqz8brVaCQ4OrvQSJ7+K+lbGsFD0ggKi7rnn38Wat2whd8kSTyV2TaNs507cJ+H9fyGEEA2nTolVt27d+PXXX/nhhx9q7LNixQp++eWXSuvv1NaMGTNYuHAhb7/9Ntu2bePWW2+luLiYSZMmAZ7yDYdPbr/11lvJycnhjjvuYMeOHXz11Vc88cQTTJ069fgvTpz0vPWtNNAsFqLuuQfKRzsLvvySolWrMIaHo0pKsO/ciV7DqKcQQghxpDpVXp85cyYjRozgsssu45prrmHs2LHeNYb27t3LRx99xLvvvotSqtryCMcyduxYMjMzmTVrFmlpafTo0YPly5d7C4Ht27cPw2ETixMSEvj222+566676NatGy1atOCOO+7gvvvuq8vliVOAKTwcS5s22JN2YG3XjvBJk8h54w0Asl9+GUvLlpgTEnClp+NITsbaoQOaPGEqhBDiGOo0eR08taNmzJhBWVlZlVIMSimsViv/7//9P2677bZ6CbShSR2rU49yu7Fv347j0CGM0THkvPoqRT/9BIApJoa4J59Es1pxZ2dj7dAeS+vWdarnJoQQ4tRR58QKPCNHixYtYtWqVRw6dAjwTCQ/99xzmTRp0lEXS2xqJLE6NellZZRu3oJeWIghJIS0hx7CkZwMgK1HD2JmzkSVlaEXF2PrchrmGh6gEEIIIeAEE6uTiSRWpy5Xbi6lmzejGU0ou51D992HXlAAQMhVVxF2zTW48/IAha1rV0xhYT6NVwghTgW//PILTz/9NOvWrSM1NZVly5YxYsQI73alFLNnz2bhwoXk5eVx9tln88orr9ChQwffBU0TXoRZiMZiCgvD1q4dqqQYQ1AQUTNmQPkcvvylSyn+4w+MoaEopwv7rl3oNSxEKoQQJytd19m6aROrf/mFrZs2VXoKv6EUFxfTvXt3FixYUO32p556ihdeeIFXX32VP/74g4CAAIYMGXLc1Qjqm4xYlZMRq1ObUgr7rl049uzBFBNLwddfk/v22wBoNhtx8+ZhbtkSV1oqpuhoWfZGCHHKWLt6NYtfe42U5GScTidms5nEtm2ZeMst9B0woFFi0DSt0oiVUor4+Hjuvvtu7rnnHsBT4DsmJobFixczbty4RomrOrUasTIYDJhMJnbs2AGA0Wis9ctkqtODh0I0Kk3TsLZujSkmBndmBkHDhhFw9tkAqLIyMp58Er2oCFN0DK60dOx79qAa4S82IYTwpbWrV/P4Qw+xc/t2/Pz9iYyKws/fn53bt/P4Qw+xdvVqn8S1Z88e0tLSGDx4sLctJCSEfv361biucGOpVdbTqlUrNE3DbDYDnvIG8nSUONloFgvWdu0pLSlBz80l4tZbcR48iCMlBVd6OpnPPkvMQw9hjIzEsW8/ms2GtbzMiBBCnGx0XWfxa69RUlxMVEyM9/e+zWbDGhNDZno6i197jd5nnVWpBFJjSEtLA/CWYaoQExPj3eYrtUqsUlJSjvpeiJOFMTAAW/v2lG7ZgnK7ib7vPu9k9rJNm8h5+20ibrgBgoNx7E7GYLNhPuIbWwghTgbbt2whJTmZ4NDQKoMpmqYRHBpKSnIy27dsocsZZ/goyqanVinmI488whdffNHQsQjRJJiiorC0aYNekI8xNJTo//wHym9pF379NYUrVmAICECzWLDv3IUrN9fHEQshRP3Ly83F6XTWuDScxWLB6XSS54OfgRVrBx/PusKNpVaJ1Zw5c/jss8+8741GIzfeeGNDxSSEz1latsTSsiWurEysnToRcdNN3m3ZCxdStn07xtBQdIfDs+yNPCkohDjJhIaFYTabcdSwrJfD4cBsNhPqgxI0bdq0ITY2ttK6wgUFBfzxxx81rivcWGqVWBmNxkofrFIKeZhQnMz+Xaw5HFdWJkEXXkjQJZd4NrpcZDz9NK7MTExRUZ7bhDt3yZqCQoiTSueuXUls25aCvLwqv/OVUhTk5ZHYti2du3ZtkPMXFRWxYcMGNmzYAHgmrG/YsIF9+/ahaRp33nknjz32GF988QWbNm1i/PjxxMfHV6p15Qu1Sqzi4uL4888/KS0tbeh4hGgyDFYrtg7tMVisuPPyCJ84EVv5PAI9P5+Mp55CORwYo6JxZWbg2LkT5XL5OGohhKgfBoOBibfcgn9AAJnp6ZSVlaHrOmVlZWSmp+MfGMjEW25psInrf/31Fz179qRnz54AzJgxg549ezJr1iwA7r33XqZPn87NN99Mnz59KCoqYvny5dhstgaJp7ZqVcfq9ttv56WXXsLf35/o6GhSUlIIDAwkMjLy2CfQNHbv3l0vwTYkqWMlauJMT6dsyxYMgUEot5vUmTNxlT914j9gAFF33QUuF67MTCzt2mJt21aemhVCnDSaQh2r5qRWiVVJSQn3338/n3/+OQcOHAA4rluBjVGh9URJYiVqopTCsScF+65dmKKicKalkfrAA6jyEdzQq68mdORI9NJS9Pw8LJ06YU1I8HHUQghRf3RdZ/uWLeTl5hIaFkbnrl0bvcRCc1GnyusGg4GJEyfy5ptvNkRMPiGJlTga5XZj374dx6FDmGJiKV2/noz/+z8o//aJuuceAs46C3dhIcpehq1LF8zR0T6OWgghRGOrU7p53nnn0blz5/qORYgmSzMasbRvjyk8HFdmJv69exN6zTXe7VkvvIB91y6MQUFgNGHfubN84WYhhBCnElkrsJyMWInacBcUULp5M8qtYwwNJWvBAopXrgTAGBpK3JNPYoqMxJmRgTEoEL8uXTAEBPg2aCGEEI1GbpAKcRyMwcFY27cHlxNVUkLkLbdgPe00ANx5eZ41BUtLPWUY8vOlDIMQQpxiJLES4jiZo6OxtG2Lu6AApRTR//kPpvJlbRwpKWQ+/zzoupRhEEKIU5AkVkLUgacyewvc2VkYAgKIfuABNH9/AEr/+ovcd99FMxoxRUbhOHgQ+549qGbwdKwQQogTI4mVEHWgGY1Y2rXDFBmJOysTc3w80ffcA+WPHxd88QWFP/yAZjZjjIjEkbIXx759smKBEEKc5CSxEqKODBYL1g4dMAQE4s7Jwa9bN8IPW0Mze+FCSjdtwmC1YgwJwZGcjCs11YcRCyGEaGiSWAlxAoyBgVg7tAfN88Rg8JAhBA8b5tnodpP5zDM4Dx7E4O+PZvOjbOdOXJmZvg1aCCFEg6lTYnXDDTfUqjjo4sWLueGGG+pyCiGaDVNEBLb27VGlJeilpYSNH4/fmWcCoBcXk/7EE7jz8zEGB4NmoGzHDly5uT6OWgghmrY5c+agaVql1+E1NMvKypg6dSoREREEBgYycuRI0tPTfRixR50Sq8WLF7Nq1apj9vvtt994++2363IKIZoVU1wcljZtcOflgq4TddddmFu3BsCVnk76k0+i2+2YwsPR7Q5PAdGiIh9HLYQQtaPrOgc2biTpp584sHFjoy1V17VrV1JTU72vw3OPu+66iy+//JKPP/6Yn3/+mUOHDnHVVVc1SlxHY2rIgzscDoxGY0OeQogmQdM0LK1aoUpLPcveRMcQ88ADpM6ciTsnB8fOnWQ9/zxRd9+NKSoKd3oa9h07sHXpgsHHK7ELIcTR7Fq1ipUvvkjmrl24nU6MZjNR7dszaPp02p9zToOe22QyERsbW6U9Pz+fRYsW8d5773HBBRcA8NZbb3Haaafx+++/c9ZZZzVoXEfTYHOslFKsX7+eqKiohjqFEE2KZjJ5lr0pf1LQGB5OzAMPoPn5AVCydi2577yDpmmeGlfZ2ZTt3ImSAqJCiCZq16pVLP3Pf0jduhWLvz+B0dFY/P1J3bqVpf/5D7tqcffqROzcuZP4+Hjatm3Ltddey759+wBYt24dTqeTwYMHe/t27tyZVq1asWbNmgaN6VhqPWJVkRFWWL58eZW2Ci6Xi927d5OWlsb1119/YhEK0YwYrFasHTpQtnkL7pwcLImJRN99N+lPPAG6TsFXX2GKjiZ42DBMUdG4UtOwm0xYO3RAMzXoALIQQhwXXddZ+eKL2IuKCI6NRdM0AAx+fgTbbBSkpbHyxRdpO2AABkP9j9P069ePxYsX06lTJ1JTU5k7dy7nnnsumzdvJi0tDYvFQmhoaKV9YmJiSEtLq/dYjketf5KvLF8PDTy3PdLS0o4avNls5rLLLuOZZ545oQCFaG4qnhQs3bIFd0EBfj16EHHLLWS/8goAOYsXY4yKIqBvX0xRUTj2HwCTCWu7dmgN8MNJCCHq4tCmTWTu2oV/aKg3qaqgaRr+oaFk7trFoU2baNm9e72f/5JLLvH+f7du3ejXrx+tW7fmo48+wq/8TkBTVOvEas+ePYDnFl/btm0ZNWoUTz/9dLV9LRYLkZGRmM3m+olSiGam4knBsm3b0M1mgi68EFdGBvmffgpKkTV/Pqa5c7F26IAxIgJHyl40owlLm8QqP8CEEMIXinNyPHOqrNZqtxutVtz5+RTn5DRKPKGhoXTs2JFdu3Zx0UUX4XA4yMvLqzRqlZ6eXu2crMZU68SqdfkTTgCzZ8+mZ8+eldqEEJWZ4uKwlJVh37UbjEZCx43DlZ5O8apVKIeD9HnziJs3D3NMDISG4kjeDWYT1oQEX4cuhBAEhIdjNJtx2+0YqhkhctvtGM1mAsLDGyWeoqIidu/ezfXXX0+vXr0wm82sWLGCkSNHApCUlMS+ffvo379/o8RTE03JGhsAFBQUEBISQn5+PsHBwb4OR5wklNuNfccOHPsPeBZq1nXSHn0U+9atAJji44l77DGMwcG4i4pQpSXYOnfGHBfn48iFEKc6Xdd58+qrSd26tdIcK/DcvSpISyOuSxdueP/9Bpljdc899zB8+HBat27NoUOHmD17Nhs2bGDr1q1ERUVx66238vXXX7N48WKCg4OZPn06AKtXr673WI6HTOgQogF51xSMicaVkQ5GI9H33ou5RQsAXIcOkVFe48oYGIhmsUp1diFEk2AwGBg0fTrWwEAK0tJwlpai6zrO0lIK0tKwBgYyaPr0BkmqAA4cOMDVV19Np06dGDNmDBEREfz+++/eagPPPfccl112GSNHjmTgwIHExsaydOnSBonleNRqxMpgMGAwGNi6dSsdO3Y8rtpUmqbhcrlOKMjGICNWoiHpJSWUbt2GOz8fc0wMzowM0h54AHdeHgB+vXoRfe+9aEYjrpwcNKMBW5cumMLCfBu4EOKU58s6Vs1RrRKrxETPhNoff/yRNm3aeN/XVsXE96ZMEivR0Nz5+ZRu3YpyODFFRGDfs4e0WbNQpaUABF54IRFTpnj+GMnMxOBnw9ali2cpHCGE8CFd1zm0aRPFOTkEhIcTf8YZDTZS1dzJHKtykliJxuDKyqJ061Y0kxljcDClmzeT/thjUD6qGzJqFGHjxqGUwpWRgTE4CNtpXTAGBvg4ciGEELUh6aYQjcgUGelZsLmsFL2kBL/TTyfq9tuhfAQ4/5NPKPj2WzRNwxQdjZ6fjz1pO3pJiY8jF0IIURuSWAnRyExxcVgS2+DOz0O32wkYMIDwiRO923PeeIPi33/3LH0THYMrN5eyHTvRy8p8F7QQQohaqdMaGr/88stx9R84cGBdTiPESUnTNCytW6GcDhx796JFxxA8bBiu3FwKPvsMlCLz+ecxBgd7JrBHeZ4oLDMasHXqhMFi8fUlCCGEqEGd5lgZDIbjmrzudruP9xSNTuZYicamHA5Kk5JwpaVhio4Bg4Gsl16i+OefATAEBBD76KNYWrVCud24MtKxxMdj7dgRTVY1EEKIJqlOI1bjx4+vNrHSdZ39+/ezfv16CgoKuOKKK6oskCiE8NAsFmwdOlDmcuHOzMAYE0vkrbei5+dTumEDenEx6Y89Ruxjj2GOjsYUGYXj4EEwGGTRZiGEaKIa5KnA3NxcbrrpJjZv3syaNWsIawa1eGTESviKu6iYsq1bcBcXY46KRi8tJW3uXBy7dgFgio31VGcPDUV3OHBnZWFJbO1ZtPk4asoJIYRoeA0yeT0sLIx33nmH/Px8Zs6c2RCnEOKkYQwMwNaxIwarFVd2NgY/P2IeeODf6uxpaaQ99hju4mIMFotn0ea9e3Hs3YvSdR9HL4QQ4nAN9lSgv78/ffv25YsvvqjzMRYsWEBiYiI2m41+/fqxdu3aGvsuXrwYTdMqvWw2W53PLURjMoaGYuvYETQNd34+xuBgYh5+GGNkJADOlBQy5s1Dt9sxWK0YQ8Ow707GkbIXKUUnhBBNR4OWWygqKiI3N7dO+3744YfMmDGD2bNns379erp3786QIUPIyMiocZ/g4GBSU1O9r71799Y1dCEanSkyEluH9ii7HXdxMabISGJnzcJQfmvavn07mf/v/6FcLgx+fhhDQ3Ek78axb58kV0KIk84vv/zC8OHDiY+PR9M0Pvvss0rblVLMmjWLuLg4/Pz8GDx4MDt37qzUJycnh2uvvZbg4GBCQ0O58cYbKSoqatC4Gyyx+vLLL/nll1/o2LFjnfZ/9tlnuemmm5g0aRJdunTh1Vdfxd/fnzfffLPGfTRNIzY21vuKiYmpa/hC+IQ5Lg5L+3aowgL00lLM8fHEPPQQmp8fAKXr15P10ksoXcfg54chKBjHrl049u+X5EoI0WCUrlPw999k/fADBX//3SjTEIqLi+nevTsLFiyodvtTTz3FCy+8wKuvvsoff/xBQEAAQ4YMoeywmn/XXnstW7Zs4fvvv+d///sfv/zyCzfffHODxl2nx4puuOGGGrcVFRWxY8cONm3ahFKKu++++7iP73A4WLduXaX5WQaDgcGDB7NmzZqjnrt169bous6ZZ57JE088QdeuXavta7fbsdvt3vcFBQXHHacQDcHSsiXK6cSRnAxGI9a2bYm5/37SH38c5XBQvGoVhoAAwidPxhAQgAIcu3ejGYxYWrbwdfhCiJNMzsqV7Hn2WUp27EB3OjGYzfh37EibGTMIHzSowc57ySWXcMkll1S7TSnF/Pnzeeihh7jiiisAeOedd4iJieGzzz5j3LhxbNu2jeXLl/Pnn3/Su3dvAF588UUuvfRSnnnmGeLj4xsk7jolVosXLz5mn1atWjF79mzGjx9/3MfPysrC7XZXGXGKiYlh+/bt1e7TqVMn3nzzTbp160Z+fj7PPPMMAwYMYMuWLbRs2bJK/3nz5jF37tzjjk2IhqYZDFgTE8HpxLFvH1p0DLauXYmaMYOMp54CXafw228xBAURNm4cxoAA3LqOfccONA3vpHchhDhROStXsvWOO3AXFmIKD8dktaLb7RRt2cLWO+6gy/PPN2hyVZM9e/aQlpbG4MGDvW0hISH069ePNWvWMG7cONasWUNoaKg3qQIYPHgwBoOBP/74gyuvvLJBYqtTYvXTTz/VuM1isRAXF0diYmJdY6qT/v37079/f+/7AQMGcNppp/Haa6/x6KOPVuk/c+ZMZsyY4X1fUFBAQkJCo8QqxLFo5SNVyuXGmXoIU3QM/r17Ezl1Klkvvgh41hU0BAQQMnw4xqAg3EDZzp1gMGCOi/PtBQghmj2l6+x59lnchYVYyuc5ARj9/DDYbDhSU9nz7LOEDRyIZmjcFfLS0tIAqh2AqdiWlpZGdHR0pe0mk4nw8HBvn4ZQp8TqvPPOq+84KomMjMRoNJKenl6pPT09ndjY2Fodw2w207NnT3aV1wI6ktVqxWq1nnCsQjQUzWLB2qE9yu3ClZGOKSaWwPPOQy8qIuettwDIffttDFYrQRdf7EmudJ2ypB2e5ErmGAohTkDhxo2U7NiBKTy8SlFwTdMwhYVRsmMHhRs3Etyzp4+ibHqa5CLMFouFXr16sWLFCm+bruusWLGi0qjU0bjdbjZt2kSc/OUumjGD1YqtY0dM4eG4M9JRShE8bBihY8d6+2QvXEhR+TI4xpAQNLOZsqQknOk1P0ErhBDH4sjO9sypqmEQwmC1ojudOLKzGzkyvIMsRxuAiY2NrVJJwOVykZOTU+tBmrqoU2L1448/ctVVV/Hrr7/W2OeXX37hqquuOu4FmyvMmDGDhQsX8vbbb7Nt2zZuvfVWiouLmTRpEuBZVufwye2PPPII3333HcnJyaxfv57rrruOvXv3Mnny5DqdX4imwuDnh7VTZwzBwbgyPT8kQkaNIrh8wiZKkbVgAcXlD3YYQ0JAM3iSq6OUJxFCiKOxRERgMJvRD3vQ63C63Y7BbMYSEdHIkUGbNm2IjY2tNABTUFDAH3/84R2A6d+/P3l5eaxbt87b58cff0TXdfr169dgsdXpVuBrr73G999/z9tvv11jnx49evDdd99hs9kYOHDgcZ9j7NixZGZmMmvWLNLS0ujRowfLly/33k/dt28fhsPu6VYso5OWlkZYWBi9evVi9erVdOnS5fgvUIgmxhgYgK1TJ0q3bsWVlYUpMpKw665D2e0ULl8Ouk7m/PloFgv+vXphCgvDlZtLWVISAOYj5hkIIcSxBHXvjn/HjhRt2YLBZqt0O1AphSs3l8CuXQnq3r1Bzl9UVFRpOs+ePXvYsGED4eHhtGrVijvvvJPHHnuMDh060KZNGx5++GHi4+MZMWIEAKeddhpDhw7lpptu4tVXX8XpdDJt2jTGjRvXYE8EQh3XCmzTpg0JCQnHHI0aOHAgBw8eZPfu3XUOsLHIWoGiOXDl5FC2dRtKKUxhYShdJ/uVVyiqeKDEbCbmgQfwO+MMT//cXEDh17kzpqgo3wUuhGiWvE8FFhVhCgvz3P6z23Hl5mIMDGzQpwJXrlzJ+eefX6V9woQJLF68GKUUs2fP5vXXXycvL49zzjmHl19+uVL9zJycHKZNm8aXX36JwWBg5MiRvPDCCwQGBjZIzFDHxMrPz4+rrrqKd99996j9rr32WpYtW0ZJSUmdA2wskliJ5sKZkUHZtm1oJjPGkBCU203m889Tsno1AJrNRsxDD2Hr3BmQ5EoIcWJ8VcequarTrcCAgIAqE8aqk5GRIev1CVHPzNHR4HZTtn077qIijIGBRN1+OxkOB6V//YUqKyP9iSeInT0ba7t23tuCpdu34weSXAkhjkv4oEGEDRxI4caNOLKzsUREENS9e6OXWGgu6vSp9OzZk99++419+/bV2Gffvn38+uuvdG+ge69CnMrMcXFYOnRAlRSjFxejmUxEzZiBrVs3AFRJCemPPoojJQUAU1gYKChLSsKVmenDyIUQzZFmMBDcsyeRgwcT3LOnJFVHUadP5oYbbsBut3PZZZfx119/Vdn+119/MXz4cJxO51GXvxFC1J2lRQss7dqhl68raLBYiL73XqzltwD1oiLSHnkER/kfQKbwcJSuPMlVVpYvQxdCiJNWneZYAYwZM4ZPPvkETdPo3r077dq1A2D37t1s3LgRpRRXXnkln376ab0G3FBkjpVojpRSOPakYN+9G2NYGAabDb2khPTHHsO+YwcAhuBgYufOxVK+soArJwfNoGHr1EluCwohRD2rc2Kl6zpPPPEEzz77LHl5eZW2hYaGctddd/HAAw9gNBrrI84GJ4mVaK6UrmNPTsaxZw/G8AjPUzvFxaQ9+iiO8keVDaGhnuSqfB1BV04OaGDr1ElKMQghRD2qc2JVwel08tdff7F//34AEhIS6NWrFxaLpV4CbCySWInmTLnd2HftxrF3L8bISAwWC+7iYtLnzsWRnAyAMSyM2LlzMZfXb3Hl5oJSnuQqRpIrIYSoD3VKrMLDwznjjDP4uXwZjZOBJFaiuVMuF/Zdu3Ds24cpKhrNbMZdWEj6I4/g2LMHAGN4uCe5Kl/qyZNc6eXJlawtKIQQJ6pOk9ddLhctW7as71iEECdAM5mwtmuHpUULXJmZKJcLY1AQMbNmYU5MBMCdk0PanDk4y1d2N4WFoRmMlG3f7m0TQghRd3VKrLp27crBgwfrOxYhxAnSzGasHTpgjo/HlZmBcrsxBgURO2sW5latAHBnZ3uSq/JadMbQUDST2ZNcHTrky/CFEKLZq1NiNX36dFatWsWqVavqOx4hxAnSLBasHdpjionBlZHuSa6Cg4mdPRtz+UizOyuLtNmz/02uQkLQLFbPws3yR5MQQtRZnRKrc845h8mTJzNkyBDuuOMOfvjhB3bs2MG+ffuqfQkhGpfBavWUU4iO/je5Cgkhds6cysnVrFk4U1MBMAYHo9n8KEvagePAQU7wuRYhhKizefPm0adPH4KCgoiOjmbEiBEklS8qX6GsrIypU6cSERFBYGAgI0eOrLIqzL59+xg2bBj+/v5ER0fzn//8B5fL1aCx12nyusFgQNM0lFKVVruu9gSa1uAXUR9k8ro4GellZZRtT8KVmYEpOgbNaMSVm0v63Lk4DxwAyie0z56NubwUg7uwEFVWiqVdOywJCcf8HhdCnAJ0Hf7+G7KyIDISevaEBqy+PnToUMaNG0efPn1wuVw88MADbN68ma1btxIQEADArbfeyldffcXixYsJCQlh2rRpGAwGfvvtNwDcbjc9evQgNjaWp59+mtTUVMaPH89NN93EE0880WCx1ymxGjRo0HH9sP3pp5+O9xSNThIrcbLSS0sp274dV1aWN7ly5+eTNncuzvIRZWNoKDFz5mCpGM0qLkYVFXqSq1atZPkKIU5lP/4ITz4JSUngcIDFAp06wf33wwUXNEoImZmZREdH8/PPPzNw4EDy8/OJiorivffeY9SoUQBs376d0047jTVr1nDWWWfxzTffcNlll3Ho0CFiyp96fvXVV7nvvvvIzMxssLJQdVqEeeXKlfUchhCioRj8/LB16kQZeEeuKm4Lpj3yCM6UFNx5eaTNnk3s7NlYWrXCGBCArmmeAqO6jiUxUZIrIU5FP/4It9wChYUQEQFWK9jt8M8/nvbXXmuU5Co/Px/wlHsCWLduHU6nk8GDB3v7dO7cmVatWnkTqzVr1nDGGWd4kyqAIUOGcOutt7JlyxZ69uzZILHKT0ohTgEGf3/PnKuwMNwZ6Shd905ot7RtC4Cen0/anDnehZsN/v4YQkKx707Gvns3yu324RUIIRqdrntGqgoLoUUL8PPz3P7z8/O8Lyz0bNf1Bg5D58477+Tss8/m9NNPByAtLQ2LxUJoaGilvjExMaSVl45JS0urlFRVbK/Y1lAksRLiFGHw98fWuTOG0MOSq/I6V5b27QHQCwpImzMHe3m1doOfH8bwcBwpKdh37UI5nb68BCFEY/r7b8/tv4gIOHL6j6ZBeLhn+99/N2gYU6dOZfPmzXzwwQcNep76Uqtbge+88w4AV155JUFBQd73tTV+/Pjjj0wIUe8MAQHYOnembPt23BnpGKNjMAYGEvvww6Q//jj2HTvQi4pInzuXmIcfxtq+PQarFcIjcOzdC7qOtV07tGa2ZJUQog6ysjxzqqzW6rfbbJCb6+nXQKZNm8b//vc/fvnll0qFyWNjY3E4HOTl5VUatUpPTyc2NtbbZ+3atZWOV/HUYEWfhlCryesVTwFu27aNjh07et8fS8VTg+5mcAtBJq+LU4m7qJiy7dvR83IxRsegGQzoJSWkP/EE9u3bAdD8/IiZORNbly4AKKcTV2YG5vgWWDt2wCDJlRAnt3Xr4KqrIDDQc/vvSCUlUFwMS5dCr171emqlFNOnT2fZsmWsXLmSDh06VNpeMXn9/fffZ+TIkQAkJSXRuXPnKpPXU1NTiS5fbP7111/nP//5DxkZGVhrShhPUK1GrGbNmoWmaURGRlZ6L4RonoyBVUeuDP7+xDz4IOnz5mHfuhVVWkr6Y48Rfe+9+PXogWY2Y4qKxpl6CKV0bB06YLDZfH0pQoiG0rOn5+m/f/7xzKk6/Pe+UpCTA926efrVs6lTp/Lee+/x+eefExQU5J0TFRISgp+fHyEhIdx4443MmDGD8PBwgoODmT59Ov379+ess84C4OKLL6ZLly5cf/31PPXUU6SlpfHQQw8xderUBkuqoI7lFk5GMmIlTkXVjlzZ7WQ+/TSlGzZ4OplMRM+YgX/fvgAotxtXRjqmyEhsHTtiKK8pI4Q4CR3+VGB4uOf2X1mZJ6kKDoZXX22QpwJrGrx56623mDhxIuApEHr33Xfz/vvvY7fbGTJkCC+//HKl23x79+7l1ltvZeXKlQQEBDBhwgSefPJJTKY6FUWoXeySWHlIYiVOVXqxJ7ly5/6bXCmnk8z58yn54w9PJ4OByNtvJ/CccwBPcuXOzMAQGoatU0eMQUE+vAIhRINqAnWsmpNaJ1Y//vgjBw4coHfv3nQpn3NRk61bt/LXX3+RkJDA+eefXy+BNjRJrMSprCK5cuXkYIqJ9SRXbjdZCxZQ/Msvnk6aRsQttxBUXjdG6TquzAyMAYFYO3XEFBbmwysQQjSoRq683pzVKrHav38/HTt2JCEhgXXr1hF0jL9OCwsL6d27NwcOHGDnzp3Ex8fXW8ANRRIrcarTi4spS0ryJFdR0WhGI0rXyV64kKLvv/f2C580ieBhwwDPBFN3Vhaa1YKtY0dM5fMwhRDiVFWrdPONN97A4XDw1FNPHTOpAggKCuLpp5+mtLSURYsWnXCQQoiGV1GKwRQRgSszA+V2oxkMRNx8M8HDh3v75bz1Fnmffup96tcUFYVyuijdug3nEQugCiHEqaZWI1YDBgwgOTn5uCuVxsXF0aZNG1avXl3nABuLjFgJ4aGXlHhGrg5bW1ApRd5HH5H/8cfefsHDhxM2frx3kqk7Lw/lcmLr0AFTfLw8OSyEOCXVasRq+/bt9OnT57gP3rt3b5KSko57PyGE7xj8/bF27Ig9N5fc77+jaOsWNBRhY8cSdv313n4FX35J9ssve5e6MYaGolltlO3YgWPfPlQDL3MhhBBNUa2eNywuLiYkJOS4Dx4SEkJRUdFx7yeE8J2clSvZ8+yzlOzYgeZ0YTKbsCQk0OK66wi54goM/v5kL1wIuk7RTz/hLioi6q67MFgsGIOC0A0G7Dt2opxOrImJaA34WLMQQjQ1tRqxCgsL85aBPx7p6emEyZNCQjQbOStXsvWOOyjavBlDYCDGmGjw88OevIfkp5+mYN1fBF10EVF33QXlCVPpn3+S/thj6CUlgGeuljEsDEfyHuw7d6IcDl9ekhBCNKpaJVZdunTh999/p7S0tNYHLikpYc2aNccszSCEaBqUrrPn2WdxFxZiiY/H6OeHZjRCQACGyAgoLePgkiWgdAL69yfmgQfQyiuv27duJW3OHNz5+QAYbDaMkZE49h+gNCkJ/Th+dgghRHNWq8Tqsssuo7i4mMcee6zWB37ssccoLS1l+GFPEwkhmq7CjRsp2bEDU3h45YnnmoYym9GCg3Du30/Rli0A+HXrRuzs2RgCAwFwJCeT+vDDuDIzATBYLJiio3GlpVG2bRvuouJGvyYhhGhstUqspkyZQkxMDE8++SSPPfYY+lEmpeq6zqOPPsqTTz5JTEwMt9xyS70FK4RoOI7sbHSnE0N1a2hpGsrPD6fTif3gQXS7HQBrhw7EPvooxvBwAFyHDpH60EM49u/37GYyYYqOwZ2TQ9nWLbjz8hrrcoQQwidqXXl99erVDB48GLvdTsuWLRk9ejRnnnkmUVFRAGRmZrJ+/Xo+/vhjDhw4gNVqZcWKFfTv379BL6C+SLkFcaor+PtvNl59tWduVTUr2btLS9GLijjt6aex2GwYQ8MwlPdzZWaS9uijuA4dAsAQGEj0/fdj69wZ8BQSdWVlYrBapZCoEOKkdlxrBW7YsIHrr7+eLVu2VFujpuJQXbt2ZcmSJXTv3r3+Im1gkliJU53SddaPGEHRli1Y4uIqfY8rpXCkphLYtSs9P/0U5/79OJKTMQQFexdhdufnk/744ziSkwHQLBai7rzTu3gzgCs7GzQ8ta5iY6XWlRDipFOnRZiXL1/OV199xYYNG8jOzgYgIiKCHj16MGzYMIYOHVrvgTY0SayE+PepQHdREaawMAxWK7rdjis3F2NgIF2ef57wQYNQuo5j/34cu3ej+fl7F2HWS0rIeOYZyv75x3NAg4GIm24i6KKLvOdw5+ejHHYsbdpgadUKTdYbE0KcROqUWJ2MJLESwuPwOla604nBbMa/Y0fazJhB+KBB3n5KKRwHD+LYuRPNYsVYXutOOZ2exZtXrfL2DRk9mtAxY7wjVHpxMe6CAiytWmFt2wbNbG7UaxRCiIYiiVU5SayE+JfSdQo3bsSRnY0lIoKg7t1rHFlypqZStnMnaAZM5XXrlK6Tu2QJBV984e0XeOGFRNx8s6eEA6Db7bizszDHt8Davh2G8tINQgjRnEliVU4SKyHqzpmRgX3HDpRbxxQR4W3P/9//yF282Pver1cvombM8D55qJxOXFmZmCIjsXbogLG8dIMQQjRXMrlBCHHCzNHR2Lp0QbOYcWZkeB9kCbnsMiLvvPPfKu3r1pE+dy7uggIANLPZU44hO5uyLVtw5eb66hKEEKJeSGIlhKgXpvBw/E47DWOAP66MdO8izIHnnEPMgw+ilZdmsO/YQeoDD+BMTQVAMxoxxsSil5RStmULzjosnyWEEE2FJFZCiHpjDA3F1qULxpBQT3LldgPgd8YZxD36KMbyOViutDRSH3iAsu3bAdA0DVNUFKBRtnUr9n37vImZEEI0J5JYCSHqlTEoCL8up2GKjPIkV04nAJbEROKeeAJzq1YA6IWFpM2dS/Hq1f/uGxqK5h+APWkH9p27vPsKIURz0aQTqwULFpCYmIjNZqNfv36sXbu2Vvt98MEHaJrGiBEjGjZAIUS1DP7+2E7rjDkuHldGhncJHFNUFHGPPoqtWzdPR6eTzGefJf+zz7zzsowBARjDw3HsTaF0+3ZZwFkI0aw02cTqww8/ZMaMGcyePZv169fTvXt3hgwZQkZGxlH3S0lJ4Z577uHcc89tpEiFENUxWK3YOnXEktgad062N0EyBAQQ88ADBJ5/vrdv7pIl5Cxc6L11aLBaMUXH4EpLo3TLVtz5+T65BiGEOF5NttxCv3796NOnDy+99BLgWdw5ISGB6dOnc//991e7j9vtZuDAgdxwww38+uuv5OXl8dlnn9XqfFJuQYiGodxuHHv34khORgsKxli+BI5SivxPPyXvgw+8ff3OPJOou+7yrkGodB1XZiYGPxvW9u0xR0f75BqEEKK2muSIlcPhYN26dQwePNjbZjAYGDx4MGvWrKlxv0ceeYTo6GhuvPHGY57DbrdTUFBQ6SWEqH+a0ehZvqZjR1RxsXf0SdM0QkeNIvL22/8tx7B+PWkPP+xZUxDQDAbMMTEol5uyrduw799PE/1bUAghgCaaWGVlZeF2u4mJianUHhMTQ1paWrX7rFq1ikWLFrFw4cJanWPevHmEhIR4XwkJCScctxCiepqmYW3VCttpnVFulzdxAggcOJCYhx7yLubsSEkh9f77se/a5e1jCg9Hs1pxJCVh3yWT2oUQTVeTTKyOV2FhIddffz0LFy4kMjKyVvvMnDmT/Px872v//v0NHKUQwhwXh1+XLmhmE86MdO/ok9/ppxP7+OOYym/1uXNzSZs1q/ITg0FBGELDcOzZ45nUXlLik2sQQoijMfk6gOpERkZiNBpJP6JQYHp6OrGxsVX67969m5SUFIYPH+5t08tr4JhMJpKSkmjXrl2lfaxWK9byZTWEEI3HFBmJn9lM2Y4duNPTMEZFe24XtmxJ3Lx5ZDz9NPbt21EOB5nPPovz0CFCRo5E0zQMNhtaxaT2sjJsHTpgDA319SUJIYRXkxyxslgs9OrVixUrVnjbdF1nxYoV9O/fv0r/zp07s2nTJjZs2OB9XX755Zx//vls2LBBbvMJ0cQYQ0Lw69IF4xG1rowhIcTOnk3AoEHevnkffEDWCy+gOxwAaCYTpphY3IVFlG7ejDMtTeZdCSGajCY5YgUwY8YMJkyYQO/evenbty/z58+nuLiYSZMmATB+/HhatGjBvHnzsNlsnH766ZX2Dy3/K/bIdiFE02AICMDW5TQcO004Dh7CGB7uGZEym4mcOhVLixbkvvsuAMW//oorI4Poe+/FGBLimdQeHY07P5+yrVuxlJRiad0KzWj08VUJIU51TTaxGjt2LJmZmcyaNYu0tDR69OjB8uXLvRPa9+3bh8HQJAfchBC1ZLBYsHbqBBYLjpS9qGBPOQZN0wi58kpM8fFkvfACym7HnpRE6syZRN9/P5by6u3GkBD0ErNnQntpCZb27THILX4hhA812TpWjU3qWAnhO0rXcRw4gGPXbjSrFWNIiHebPTmZjCefxJ2TA4BmsxF5++0E9O377/5OJ66sTEwREVjbt8co38NCCB+RxKqcJFZC+J4zLY2ynTvBrWOMiEDTNABcOTlkPPkkjuRkb9/QsWMJGTXK20e53biyMjH4+WFt1x5zjBQTFUI0PkmsykliJUTT4MrJwb5zJ3phofeJQQDdbif7lVcoXrXK29f/rLOInDYNg8327/65ueB0YmmTiKWVzLsSQjQuSazKSWIlRNPhLirCvnMnrqwsTJFRaGYz4FkGp+Czz8h97z0o/9Flbt2a6Pvuq7TcjV5SgjsvD0uLeCzt2lVKvIQQoiFJYlVOEishmhbdbsexa5fnicGwMO/6gQAl69aR+fzzqPIioYbgYKLvvhtb167ePhXzroxh4djat5N6V0KIRiGJVTlJrIRoepTLhX3vXpx79qAFBGIMCvJucxw4QMb//R+u1FRPg9FI+A03EDxkyL/767pn3pXFirV9O0wxMd45WUII0RAksSoniZUQTZNSCufBQ9h37wLNgCk83LvNXVRE5vz5lG3Y4G0LvPBCwm+8EYPF8m+//HyUvQxLYiKWhATvrUUhhKhvkliVk8RKiKbNlZlJ2a5d6CWlmKKi0Mrr2Cm3m9wlSyj48ktvX0v79kTfcw+mw9YO1UtLcefmYIqLw9a2rXfRZyGEqE+SWJWTxEqIps9dUOCZ1J6TU2lSO0DRL7+Q/eqrqPKlbwzBwUTNmIHfYasvKJcLd1YmhsAgz63BWi7aLoQQtSWJVTlJrIRoHvSyMhy7d1c7qd2+Zw+ZTz+NKyPD02AwEHb99QRfdtm/9a6U8hQbVTqWNm2wtGwpJRmEEPVGEqtyklgJ0XwolwvHvn04UlLQrLZKldrdhYVkPv98pXlXAeecQ8SUKZXKLriLi9EL8rHEx2Np27ZSgiaEEHUliVU5SayEaF6UUrjS0ijbtQtcboyRkZWqsOd9+CH5S5d6+5tbtSL63nsxx8b+e4yKkgyhoVjbt8cUFtbo1yGEOLlIYlVOEishmidXbi72nTtx5+djio6pdFuv+I8/yHrpJVRpKQCGgAAip03Dv08fbx+l67izs8FoxNq2Leb4OO/EeCGEOF6SWJWTxEqI5ksvLqZs1y5c6ekYIyIxWK3ebY6DBz31rg4d8rYFjxhB2NVXV0rC3IWF6EVFWFq2wNKmjVRrF0LUiSRW5SSxEqJ5Uw4H9j0pOPfvq1JMVC8pIevllyn5/Xdvm7VLF6LuuqvS7T/d4cCdnYUxLBxru7Zya1AIcdwksSoniZUQzZ/SdZyHUrEn7wZdYYyIqPQ0YMFXX5H73/+C2w2AITSUqDvvrFySwXtr0OB5ajA+Xp4aFELUmiRW5SSxEuLk4crJwb5rF+6CAk+9K5PJu61s+3Yyn33WU3IBPCUZrr6a4CuuqDS3yntrMD5OnhoUQtSaJFblJLES4uSiFxdTlpyMKzUVY3hE5VIL+fmekgz//ONt8+vdm8hp0zAGBnrbKj012K5dpeV0hBCiOpJYlZPESoiTj3I6PYs4792LZvOrVO9Kud3kffIJ+Z98AuU/Bo1RUUTfdRfWjh3/7Vdxa9CgedYabNGi0giYEEIcThKrcpJYCXFyqqh3Zd+9G93hxBQZWemWX8nff5P1/PPoRUWeBqORsGuv9VRrP/zWYHExen4+5vh4LImJGANlrUEhRFWSWJWTxEqIk5srNxf77mTPQsxHrDPoyswkc/587ElJ3ja/M88kcvr0Sk8XKqcTd3YWWkAA1rbtMEVHeSfHCyEESGLlJYmVECc/7zqDhw5hCA7BGPDvqJNyuTzV2pct87YZIyKIuvNObKed9m8/pXDn5YHLibllS6ytW6NZLI15GUKIJkwSq3KSWAlxalBuN46DB3Ek7wFNwxgeXmnUqeTvv8l68UX0ggJPg8FA6LhxhIwYUenWoF5Whjs7G1N0FNY2bTCGhjbylQghmiJJrMpJYiXEqcWVne0pyVBYWKUkgysnh6znn6dsyxZvm617d6KmT6+UQCm3G1d2FprZjLVNW8xxsVLzSohTnCRW5SSxEuLUoxcXe6q1HzqEMTQUg7+/d1t1Tw0aQkI8aw327FnpOJVqXiUmYgiQie1CnKoksSoniZUQpyblcuHYtx9HSgqYzRhDQyvdGizdtIms55/3zKsqFzxsGGHXXVdpArxyOnFlZ2GQie1CnNIksSoniZUQpy6lFK7MTOy7d6OKizEecWvQnZ9P1oIFlK5f720zJyYSdeedWFq2rHQcd14eOB2YW7TEkti60oLQQoiTnyRW5SSxEkK4i4qx70nGlZpW9dagUhR+8w05//0vOJ0AaBYL4ZMmETh4cKXRKd1ux52T7VnMuW0bqdguxClEEqtyklgJIeCwW4N7U8BgrPLUoCMlhcz583EeOOBt8+/Xj4gpUyrXvKqo2K5pWFq3wtKyZaVbh0KIk5MkVuUksRJCHM5zazAZd1EhpojISkmRbreT+/bbFH73nbfNGB5O5LRp+HXrVuk4enEx7oJ8TFHRWNskVlpWRwhx8pHEqpwkVkKII3mfGkw9hDE4pMrTfsVr15L98sv/LoeDZ2J76LXXYjisaKhyu3FlZaFZzJ71BuPiZL1BIU5SkliVk8RKCFEd5XJ5CoruSQE8I1OHFwp1ZWeT9dJLlG3a5G0zJyQQdccdWBITKx3LXViIXliIKS4Wa2JipVuHQoiTgyRW5SSxEkIcjSs7G3tyMu68PIzhEZWe9lO6TsHXX5P77rveie2YTISNG0fw8OGVioYql8uz3qDVhrVNIqZYKSoqxMlEEqtyklgJIY5FLyvDkZKC88ABND//KvOlHPv2kfnCCzhTUrxt1i5diJo+HVNUVKW+7oIC9OJizHGeoqLGQCkqKsTJQBKrcpJYCSFqQ+k6rrQ07Ml70MtKMUVFVx6RcjrJ/fBDCj7/3FuxXfP395RlGDSo0hOGyun0jF75+2NNTMQUEyOjV0I0c5JYlZPESghxPNyFhdh3J+PKSMcYGlap5hVA2datZL74Iu7MTG+bX+/eRNxyC6awsMrHys9HLykpH71qjTEwsFGuQQhR/ySxKieJlRDieCmnE8f+AzXWvNKLi8l+6y2KV670thkCA4m46SYCzj67yrHc2Vlofn6e0SuZeyVEsySJVTlJrIQQdeXKyvJMbM/PrzKxHaBk7VqyXnsNPT/f2+Y/YAARkydjPOLnjYxeCdG8SWJVThIrIcSJ0MvKcOzdi3P/fjSbH8bQ0Erb3QUFZL/xBiWrV3vbDCEhRE6Zgn+fPpX6ekevbH5YEhMxx8nolRDNhSRW5SSxEkKcKKXruDIysO/Z41nM+YiK7QDFv/1G9sKFlYqKBpx3HuGTJlUZnfI8OViEKTYWa+vWVUa3hBBNjyRW5SSxEkLUF3dRsacsQ+ohDIFBVQqBunJzyX7tNUr/+svbZgwNJeLmm/Hv27dSX+V04srOQrNasbRqhSU+XtYcFKIJk8SqnCRWQoj6pNxuHKmpOPbsQTmcmCIjK5dlUIrin38m+803USUl3vaAs88m/IYbqtTIchcVoRcUYIqKxJKYWOXJQiFE0yCJVTlJrIQQDcGdn499TwqujHQMIaEYj1hv0JWdTfbrr1O6bp23zRAcTMSNN+I/YEDlulduN67sbDSDAUurBMwtW1Zak1AI4XuGY3fxnQULFpCYmIjNZqNfv36sXbu2xr5Lly6ld+/ehIaGEhAQQI8ePfjvf//biNEKIURVxpAQ/Lp2wdqxI8pehjMzA+V2e7ebIiKIvv9+Im+/HUP5HCu9oIDM554j8+mnceXmevtqRiPm6GgMAQHYd+2m9J9/cGVmIn8fC9F0NNkRqw8//JDx48fz6quv0q9fP+bPn8/HH39MUlIS0dHRVfqvXLmS3NxcOnfujMVi4X//+x933303X331FUOGDDnm+WTESgjR0Fy5uThSUnBlZmIMCcVwxOiVOy/P8+Tg77972wyBgYRPnEjAeedVHr3Sddy5ueB2YW7RAktCQpUipUKIxtdkE6t+/frRp08fXnrpJQB0XSchIYHp06dz//331+oYZ555JsOGDePRRx89Zl9JrIQQjUE5HDgOHMSxfx/oylNU9IhSCsVr1nieHCwo8LbZunUj4uabMcfGVuqr2+24s7MxBAVibd1alsURwsea5K1Ah8PBunXrGDx4sLfNYDAwePBg1qxZc8z9lVKsWLGCpKQkBg4cWG0fu91OQUFBpZcQQjQ0zWLB2rYNft26YQwJxpWehn7Y5HWAgP79aTF/PgHnnONtK/vnHw7NmEH+Z59VupVosFoxxcWBrijdspXSLVtw5+U11uUIIY7QJBOrrKws3G43MTExldpjYmJIS0urcb/8/HwCAwOxWCwMGzaMF198kYsuuqjavvPmzSMkJMT7SkhIqNdrEEKIozGFheF3+ulY27dHLynxzJU6LGEyBgcTdeedRD/wAMbISMAz2pW7ZAmp99+Pffdub19N0zCGhGCKisKVmUXJP/94Fol2OBr9uoQ41TXJxKqugoKC2LBhA3/++SePP/44M2bMYOVha3QdbubMmeTn53tf+/fvb9xghRCnPM/oVVv8up3x7+hVcXGlPv5nnkmL554jaNgwKJ9j5dizh9SZM8l5+230srJ/j2cyYY6JwWC1Yd+1k9J/NuHMyJDJ7UI0oiY5x8rhcODv788nn3zCiBEjvO0TJkwgLy+Pzz//vFbHmTx5Mvv37+fbb789Zl+ZYyWE8CXlcOA4eBDH/v0olwtTRGSVuVL2nTvJeuUVnPv2edtM0dGET56M/5lnVj7e4ZPb4+IwJyTIuoNCNIImOWJlsVjo1asXK1as8Lbpus6KFSvo379/rY+j6zp2u70hQhRCiHqlWSxY27TB74wzMIVH4EpPx33YsjcA1g7/v707j46qyvMA/q09WyVV2RMSEgQRBdkxMDSCEjYji7iwDoHGHRgcbUS6R2Cc0w0NjHpsHdoNwcaVVnBBWWVRCIss2tgtAgfIvidVlbW23/xRSUFRFRKwSCrw/ZyTc+De+17urUdevrx33303I3HFChimTgUaVl+3Fxej+E9/QvGqVbCXlV3Yn1IJdVQUlBEGWHNzUXv8B9RnZ0N4e5DomlK3dQea8vTTTyMzMxP9+/fHHXfcgZdffhnV1dWYNWsWAGDGjBno0KEDli1bBsA1Z6p///7o3Lkz6uvr8dVXX+Fvf/sbVq9e3ZbDICK6ImqjEaqwMFgjja6XOhcVuq5eqV2na4VaDcPEiQgdNAhlr7+OuhMnAAA1Bw6g9ocfYJw8GfrRo91Xu5Q6HZQJiXBYLKg/eRL24hLoUlOgioryWL6BiPwjYIPVpEmTUFJSgsWLF6OwsBC9e/fGli1b3BPas7OzoVReuOBWXV2NJ598Erm5uQgODka3bt2wfv16TJo0qa2GQER0VRQaDXQdO0JtMKD+3DnYi4qgDA3zeAmzJiEBcUuWoHrvXtdcK7MZUluL8nfeQdWePYh69FHounRxt1fp9VCGhMBRUYHaH39suD3YEaqwUF9dIKKrFJBzrNoC51gRUSASux32oiLUnz8PZ00NVJFRXq+xcVgsqHj/fVRt336hUKGAftQoGKdM8VqI1FlfD0d5GZQhIdB07AhtfDxf7EzkJwxWDRisiCiQOaqqYcvJhi0/H9BooTIYoFB6TpOt+/lnlL3xhsfkdpXBAOOMGQgdMsTr1p/DYoHTYoEqMhK6lI5QRUfz9iDRr8Rg1YDBiogCnTidsJeUwnr+HBwmE1QGI5TBwZ5t7HaYv/oKlR9/DLloKQbdrbciavZsaFNTPds7HK4FRR12aOLioOnYESq9vhVGQ3R9YrBqwGBFRO2Fs74e1pwc2HJzAYHP1+LYS0pQ/s47qLn45fVKJfRjxsD40EPetwetVjjLywCdDtoOSdB0SIRSp2uN4RBdVxisGjBYEVF7Yy8vh/X8edhLSqHU631eaao5dgzlb78N+0VvrVAaDIicPt3rxc4A4KiuhtNkgioiHNqUFKhjYvjuQaIrwGDVgMGKiNojsdlgLSyE7Xw2nLUNk9svudIkNhtMn38O0yefeKxjpevWDZGzZ0PXqZNne6cTDpMJUlcHdWwMtB07uuZ0cf4VUbMYrBowWBFRe+ae3F5QAKjUUBmNXpPb7SUlKF+3DjUHDlwoVCoRNnw4jFOmeCznALgCmb2yAgqFwrU8Q4ckLs9A1AwGqwYMVkTU3okI7CUlsGbnuJZTiDBAFeodhGqPH0fZmjWw5+e7y5ShoTA89BD0o0a5FyNt5Kyrg6OiHMrgEGiSk6BJSPBa8oGIXBisGjBYEdH1wmm1wpaXB2tOLsRa71q5/ZJ1qsRmg3nzZlT+/e8eTw9qkpIQOWsWgnv18tqvo6oKTrMJKoMB2o4dOf+KyAcGqwYMVkR0vXGYzbBm58BeWABodT7XvrJXVKDy/fdRtWuXR3nwgAGIzMyEJj7eo9xj/lVMDLTJSa6nEjn/iggAg5UbgxURXY/ca19ln4ejoqLJ24P1p0+jfM0a1P/yy4VCtRrhGRkwTJzotTyD2O1wVFQAItDExUKTlARVRMS1Hg5RwGOwasBgRUTXM6fVClt+Pqw5OUB9PZQ+Xo0jTieqv/0WFevXu0JTA2V4uGv+1YgRXrf+nPX1cFaUA1otNImJ0CYmQhkS0ipjIgpEDFYNGKyI6EbgsFhgy86GrajI9fSgweAdlmprYdq4EaYvvgBsNne5JikJxhkzENynj9etP2dNDRymStf7B5OToYmP5wR3uiExWDVgsCKiG4U4nbCXll54elAf7nNxUXtJCSreew/V333nUR7UsyciMzOhTUnx3K8InFVVcFrMrgnuycmuCe6XPGVIdD1jsGrAYEVENxqxWmEtKoItOxvOmhqf7x4EgLpffkHF2rWe86+USoTddRcMkydDbTR67vfiCe5RkdAkJUEdHe01cZ7oesRg1YDBiohuVM7qaljz8mDLL4A4HVAbI72XZxBBTVYWKtavh7242F2u0OkQPnYsIsaP934hdOMLnm1WqGJioE3iE4R0/WOwasBgRUQ3OntFBay5uXAUFTW5PIPTaoXlq69Q+emnkJoad7kyPByGBx90TXC/5Naf2GywV1RAAbieIOzQASqDoRVGRNT6GKwaMFgREbmuMrnmX2W7lmdoYv6Vw2RC5SefwLJtG2C3u8vVCQkwTp2KkIEDvSe419fDUVkBhUrtekVOYoLPfRO1ZwxWDRisiIgucFqtsBUWwpaTc9n5V7bCQlS8/z5q9u/3KNd17Qrj9OkIuu02733X1sJhqoRCq4MmMQGa+AS+g5CuGwxWDRisiIi8OaurYc3Phy0/H2KzQeVj/SugYYHRd99F/T//6VEe3KcPDFOnQtepk/e+G5doCA6GJrEDNPFxXAOL2j0GqwYMVkRETXOYTLDl5sJWXAxA4ZqEfsn6VyKC2qNHUbF+PWw5OR51oYMHwzB5MjQJCd77bliiQRkSAk1SEjRxcVAGBV3L4RBdMwxWDRisiIguT0TgKCuDNScH9tIyKIKCoIqI8JrgLg4HqvbuReVHH8FRWnqhQqlE2PDhMDzwANRRUV77dq2BZYFSH+YKWLGxUOp0rTE0Ir9hsGrAYEVE1DJit8NeUgJrTg4clZVQhumh1Ou9JquLzQbLtm2o/OQTOM1md7lCq4V+9GhE3Hef1+R1EYHTbIazugqq8HBokpKhjo3hKu7UbjBYNWCwIiK6Mk6rFbaiIthyc+GsqoIyPMLnC56dtbUwf/klTJ9/DqmtdZcrgoMRnpGB8LFjvbYTpxNOi6UhYEW4FhllwKJ2gMGqAYMVEdHVcdbWwlZQCFt+Hpy1tU0+Qegwm2HauBHmLVs83kGoDA1F+NixCM/I8F5k9OKAFREBTQcGLApsDFYNGKyIiH4dR1UVbHn5sBUWuJ4gNEb6nCNlLyuD6ZNPYNm5E3A43OVKvR4REyZAP3q013bugFVTDVV4uGsV9xgGLAo8DFYNGKyIiPzD/QRhUTEE4vMVOQBgKyqC6e9/R9WePYDT6S5XGgww3HcfwtLTfQcssxnO2hqo9OGuW4Qx0ZzkTgGDwaoBgxURkf+ICBwVFbDm5cFRUgIolK5X5PgKWPn5qPz4Y1Tv2wdc9CtJZTAgfMIE6EeMaPoKVnUVlHq96ynCmBgu00BtjsGqAYMVEZH/idMJR3k5rLl5cJSWAGoNVEaj1xpYAGDNyUHlRx+h5sABj3KlwYCI8eOhHznSO2Bd9BShUq+HpkMHV8DyMceLqDUwWDVgsCIiunbE4YC9rAy2vDzXGlg6nWsNLF8B69w5VG7YgJqDBz3KlRERFwLWJVemRMR1BauqCsqwUGgSE13rYHEld2plDFYNGKyIiK49sdthLyuDNScXjopyKIKCoQoPbzpg/f3v3lewIiIQMXYs9KNGeT9F2LjQaJUFyuAQaBIToI6NhSos7JqOi6gRg1UDBisiotYjNhvspaWuOVgVFZcPWNnZroCVleUxB0sZFobwe+6BfswYr4VGAcBRXQ2n2QSFLgiauDho4uOgioi4puMiYrBqwGBFRNT63AErNxeOysrLB6ycHNctwksCliIoCPpRoxAxdixUBoPXds6aGjjNJkCjgSY2Fur4eNdE+ktWiifyBwarBgxWRERtR2w212ty8vKaD1h5eTBt3IjqvXs9lmlQaLUIGz4cEePHQx0d7bWds64ODlMlFEolVNHR0CYkNDmRnuhqMVg1YLAiImp7YrVeuIJlMl02YNmKimD+7DNYvvkGsNsvVKjVCBsyBOHjx0OblOS1nbO+3rVvcUIVGQlNYiLUkb7X2iK6UgxWDRisiIgCh1itrknujbcIdUFNPkVoLy+H+YsvYNm2DVJf71EXcscdiJgwAbquXb2/h80Gh9kMsVqhMkRAm5gIVTQXG6Vfh8GqAYMVEVHgEZutIWA1THLXal3zo3wELIfZDPPmzbBs2QJndbVHXVD37gifMAHBvXt7za0Sh8MVsGprXGthJSZCEx0NpY8XShM1h8GqAYMVEVHg8lymoSFgRURAoVZ7tXXW1MCyfTvMmzfDUV7uUadJTUXEhAkIHTjQa1v3WljVVVAGB0MdF+dabDQighPdqcUYrBowWBERBT5XwCqHLT/PFZqUqiZflSM2G6r27oXps89gz8/3qFNFRyM8IwP69HSfq7Q7q6vhtJgBtRrq6BjXUg2c6E4twGDVgMGKiKj9EIfD9aqcggI4Sksh4nq3oK/5UeJwoObwYZg2bYL19GmPOkVICPQjRiD8nnugjory2tZjorvR6JroHhPDgEVNYrBqwGBFRNT+iNMJR2UlbAUFsJeUAA4HlOERPq9CiQjqfvoJ5s8/R+3Ro56VKhVCf/MbRIwdC21qqve2Niscx44BlZUI6dcPqiFDAKXyGo2K2jMGqwYMVkRE7ZeIwGkywVZYCFtxMcRqhVIfDlUTE9CtOTkwf/klqvbs8VyqAUBQz54Iz8hAcJ8+UCiVwPeHgbVrIefOwWF3IESlhOqWW4DnngPuvrs1hkftCINVAwYrIqLrg8Niga2oCPbCIjhra6AMDYMyLMwVki5hr6iAZcsWWLZuhbOqyqNOnZiI8B7dEfb111DW1EDCw+HQaBBit0NVXg7o9cDrrzNckYeAvo752muvITU1FUFBQUhLS8OhQ4eabPvmm29iyJAhMBqNMBqNSE9Pv2x7IiK6Pqn0egR16YKQvn1c61cpAHtRIewVFRCHw6Ot2miEccoUJP31r4j87W+hjotz19nz81G+bTtylSqUG4ywa7Wu23/BwUCHDoDFAixf7rH6O1HABquPPvoITz/9NJYsWYKjR4+iV69eGDVqFIqLi3223717N6ZMmYJdu3YhKysLycnJGDlyJPLy8lq550REFAiUISHQpaQgpG9fBHfvDmWQDvbiYthLSyE2m2fboCCE33MPOrzyCmKffRZB3bu765wKBcwOB/LqrSiz2lDrcAAKBRAZCZw8CRw71tpDowAWsLcC09LSMGDAALz66qsAAKfTieTkZMybNw/PPfdcs9s7HA4YjUa8+uqrmDFjRrPteSuQiOj6JjYb7OUVsBUUwFFe5nqSMCICyqAgn+3rP/8M5rfXoPqSpRyClEp0Cgl2XakqKADWrgVGjWqFEVB74L2yWgCwWq04cuQIFi1a5C5TKpVIT09HVlZWi/ZRU1MDm82GyMhIn/X19fWov+jVB2az+dd1moiIAppCo4EmLhbqmGg4KithLyyErbQUjopyKPXhUIaGeiwEquvaFTEOO4xaDSwqFSx2B5wAjJqGX511dYBWC/h44TPduALyVmBpaSkcDgfiLrrXDQBxcXEoLCxs0T4WLlyIxMREpKen+6xftmwZIiIi3F/Jycm/ut9ERBT4FEol1JGRCLrtNoT06QNd586Aww57QT4clZUX5mHdcguQmgq12QyjWoMknRZGjRphKhUgApSXu9r06dO2A6KAEpDB6tdavnw5PvzwQ2zcuBFBTVziXbRoEUwmk/srJyenlXtJRERtTaXXQ3fTTQjp2xdBt3WHQqtxz8Ny2uzAzJlASAhQUgxFvRWhCgUUtbVAXh4QHu5acoHrWdFFAvJWYHR0NFQqFYqKijzKi4qKEB8ff9ltV61aheXLl2PHjh3o2bNnk+10Oh10fIM5EREBUAYHQ5vUAZq4WNc8rMICOMrL4UxKgvKZ30H54QfAuXNAVRWgUgI9e3IdK/IpIIOVVqtFv379sHPnTkyYMAGAa/L6zp07MXfu3Ca3W7FiBf74xz9i69at6N+/fyv1loiIrhce87BMJtiLS2APCoJt0SIoCwqA0lJgwACAK69TEwIyWAHA008/jczMTPTv3x933HEHXn75ZVRXV2PWrFkAgBkzZqBDhw5YtmwZAODPf/4zFi9ejPfffx+pqanuuVhhYWEICwtrs3EQEVH7o1AqoTYaoTYa4UzqAFtZGewGA2CzAz26M1RRkwI2WE2aNAklJSVYvHgxCgsL0bt3b2zZssU9oT07OxvKi/5hr169GlarFQ888IDHfpYsWYKlS5e2ZteJiOg6ogwNhS40FNr4eDgsFij1+rbuEgWwgF3HqrVxHSsiIiL6tXgtk4iIiMhPGKyIiIiI/ITBioiIiMhPGKyIiIiI/ITBioiIiMhPGKyIiIiI/ITBioiIiMhPGKyIiIiI/ITBioiIiMhPGKyIiIiI/ITBioiIiMhPGKyIiIiI/ITBioiIiMhPGKyIiIiI/ITBioiIiMhPGKyIiIiI/ETd1h0IFCICADCbzW3cEyIiulHo9XooFIq27gb5EYNVA4vFAgBITk5u454QEdGNwmQyITw8vK27QX6kkMZLNTc4p9OJ/Pz8dv2/B7PZjOTkZOTk5LTbH1SOIXBcD+PgGALH9TCOazGG9vw7h3zjFasGSqUSSUlJbd0NvwgPD2+3J65GHEPguB7GwTEEjuthHNfDGOja4eR1IiIiIj9hsCIiIiLyEwar64hOp8OSJUug0+nauitXjWMIHNfDODiGwHE9jON6GANde5y8TkREROQnvGJFRERE5CcMVkRERER+wmBFRERE5CcMVkRERER+wmDVzixbtgwDBgyAXq9HbGwsJkyYgJMnT3q0GTZsGBQKhcfX448/3kY99rZ06VKv/nXr1s1dX1dXhzlz5iAqKgphYWG4//77UVRU1IY99i01NdVrHAqFAnPmzAEQmMdh7969GDt2LBITE6FQKLBp0yaPehHB4sWLkZCQgODgYKSnp+PUqVMebcrLyzFt2jSEh4fDYDBg9uzZqKqqCogx2Gw2LFy4ELfffjtCQ0ORmJiIGTNmID8/32Mfvo7d8uXLW20MzY0DAGbOnOnVx9GjR3u0CeRjAcDnz4dCocDKlSvdbdr6WLTknNqSc1J2djYyMjIQEhKC2NhYLFiwAHa7vdXGQYGDwaqd2bNnD+bMmYMDBw5g+/btsNlsGDlyJKqrqz3aPfLIIygoKHB/rVixoo167Fv37t09+vfdd9+56/7zP/8TX3zxBTZs2IA9e/YgPz8fEydObMPe+nb48GGPMWzfvh0A8OCDD7rbBNpxqK6uRq9evfDaa6/5rF+xYgVeeeUV/PWvf8XBgwcRGhqKUaNGoa6uzt1m2rRp+Omnn7B9+3Z8+eWX2Lt3Lx599NHWGsJlx1BTU4OjR4/i+eefx9GjR/Hpp5/i5MmTGDdunFfbF154wePYzJs3rzW679bcsQCA0aNHe/Txgw8+8KgP5GMBwKPvBQUFWLNmDRQKBe6//36Pdm15LFpyTm3unORwOJCRkQGr1Yr9+/dj3bp1WLt2LRYvXtxq46AAItSuFRcXCwDZs2ePu2zo0KEyf/78tutUM5YsWSK9evXyWVdZWSkajUY2bNjgLvvXv/4lACQrK6uVenh15s+fL507dxan0ykigX8cAMjGjRvdf3c6nRIfHy8rV650l1VWVopOp5MPPvhARET++c9/CgA5fPiwu83XX38tCoVC8vLyWq3vjS4dgy+HDh0SAHL+/Hl3WUpKirz00kvXtnNXwNc4MjMzZfz48U1u0x6Pxfjx4+Xuu+/2KAu0Y3HpObUl56SvvvpKlEqlFBYWutusXr1awsPDpb6+vnUHQG2OV6zaOZPJBACIjIz0KH/vvfcQHR2NHj16YNGiRaipqWmL7jXp1KlTSExMxE033YRp06YhOzsbAHDkyBHYbDakp6e723br1g0dO3ZEVlZWW3W3WVarFevXr8dvf/tbjxeqBvpxuNjZs2dRWFjo8dlHREQgLS3N/dlnZWXBYDCgf//+7jbp6elQKpU4ePBgq/e5JUwmExQKBQwGg0f58uXLERUVhT59+mDlypUBedtm9+7diI2NxS233IInnngCZWVl7rr2diyKioqwefNmzJ4926sukI7FpefUlpyTsrKycPvttyMuLs7dZtSoUTCbzfjpp59asfcUCPgS5nbM6XTiqaeewuDBg9GjRw93+dSpU5GSkoLExET8+OOPWLhwIU6ePIlPP/20DXt7QVpaGtauXYtbbrkFBQUF+O///m8MGTIEJ06cQGFhIbRardcvwbi4OBQWFrZNh1tg06ZNqKysxMyZM91lgX4cLtX4+V78y6Hx7411hYWFiI2N9ahXq9WIjIwMyONTV1eHhQsXYsqUKR4vzf2P//gP9O3bF5GRkdi/fz8WLVqEgoICvPjii23YW0+jR4/GxIkT0alTJ5w5cwa///3vMWbMGGRlZUGlUrW7Y7Fu3Tro9Xqv2/qBdCx8nVNbck4qLCz0+XPTWEc3FgardmzOnDk4ceKEx/wkAB5zLG6//XYkJCRg+PDhOHPmDDp37tza3fQyZswY95979uyJtLQ0pKSk4OOPP0ZwcHAb9uzqvf322xgzZgwSExPdZYF+HK53NpsNDz30EEQEq1ev9qh7+umn3X/u2bMntFotHnvsMSxbtixgXlcyefJk959vv/129OzZE507d8bu3bsxfPjwNuzZ1VmzZg2mTZuGoKAgj/JAOhZNnVOJrgRvBbZTc+fOxZdffoldu3YhKSnpsm3T0tIAAKdPn26Nrl0xg8GArl274vTp04iPj4fVakVlZaVHm6KiIsTHx7dNB5tx/vx57NixAw8//PBl2wX6cWj8fC992unizz4+Ph7FxcUe9Xa7HeXl5QF1fBpD1fnz57F9+3aPq1W+pKWlwW6349y5c63Twatw0003ITo62v3vp70cCwD49ttvcfLkyWZ/RoC2OxZNnVNbck6Kj4/3+XPTWEc3FgardkZEMHfuXGzcuBHffPMNOnXq1Ow2x48fBwAkJCRc495dnaqqKpw5cwYJCQno168fNBoNdu7c6a4/efIksrOzMWjQoDbsZdPeeecdxMbGIiMj47LtAv04dOrUCfHx8R6fvdlsxsGDB92f/aBBg1BZWYkjR46423zzzTdwOp3u4NjWGkPVqVOnsGPHDkRFRTW7zfHjx6FUKr1urQWS3NxclJWVuf/9tIdj0ejtt99Gv3790KtXr2bbtvaxaO6c2pJz0qBBg/CPf/zDI+g2BvrbbrutVcZBAaSNJ8/TFXriiSckIiJCdu/eLQUFBe6vmpoaERE5ffq0vPDCC/L999/L2bNn5bPPPpObbrpJ7rzzzjbu+QXPPPOM7N69W86ePSv79u2T9PR0iY6OluLiYhERefzxx6Vjx47yzTffyPfffy+DBg2SQYMGtXGvfXM4HNKxY0dZuHChR3mgHgeLxSLHjh2TY8eOCQB58cUX5dixY+4n5pYvXy4Gg0E+++wz+fHHH2X8+PHSqVMnqa2tde9j9OjR0qdPHzl48KB89913cvPNN8uUKVMCYgxWq1XGjRsnSUlJcvz4cY+fkcans/bv3y8vvfSSHD9+XM6cOSPr16+XmJgYmTFjRquNoblxWCwW+d3vfidZWVly9uxZ2bFjh/Tt21duvvlmqaurc+8jkI9FI5PJJCEhIbJ69Wqv7QPhWDR3ThVp/pxkt9ulR48eMnLkSDl+/Lhs2bJFYmJiZNGiRa02DgocDFbtDACfX++8846IiGRnZ8udd94pkZGRotPppEuXLrJgwQIxmUxt2/GLTJo0SRISEkSr1UqHDh1k0qRJcvr0aXd9bW2tPPnkk2I0GiUkJETuu+8+KSgoaMMeN23r1q0CQE6ePOlRHqjHYdeuXT7//WRmZoqIa8mF559/XuLi4kSn08nw4cO9xlZWViZTpkyRsLAwCQ8Pl1mzZonFYgmIMZw9e7bJn5Fdu3aJiMiRI0ckLS1NIiIiJCgoSG699Vb505/+5BFY2nocNTU1MnLkSImJiRGNRiMpKSnyyCOPeDzOLxLYx6LR66+/LsHBwVJZWem1fSAci+bOqSItOyedO3dOxowZI8HBwRIdHS3PPPOM2Gy2VhsHBQ6FiMg1uhhGREREdEPhHCsiIiIiP2GwIiIiIvITBisiIiIiP2GwIiIiIvITBisiIiIiP2GwIiIiIvITBisiIiIiP2GwIrpGqqur8eKLL+Kuu+5CXFwctFotjEYjBg0ahMWLFyM7O7tV+zNz5kwoFArs3r27Vb/vxYYNGwaFQhGw7+RLTU2FQqFo624QUTumbusOEF2P9u/fj/vvvx+FhYUICQnBwIEDERcXB5PJhMOHD+PAgQNYsWIFvvzyS6Snp7d1d28YCoUCKSkpARvsiKj9Y7Ai8rPjx49j+PDhqKurw8KFC/H8888jNDTUXe90OrFp0yY8++yzyM3NbcOeEhGRvzFYEfmRiODf//3fUVdXh6VLl2LJkiVebZRKJSZOnIjhw4cjJyenDXpJRETXCudYEfnRli1bcOLECSQlJeEPf/jDZdtGRESgR48eAIB7770XCoUC27Zt89m2pqYGBoMBer0eFovFo+5f//oXZs+ejdTUVOh0OsTGxmLw4MFYtWoV7HZ7i/pdU1ODZcuWoU+fPggLC0NYWBgGDhyIdevWtWj7izkcDqxatQrdunVDUFAQkpOTMX/+fJjN5stul5OTg7lz56Jz584ICgpCZGQk7r33Xuzfv9+r7e7du6FQKDBz5kwUFBRg5syZiIuLQ3BwMPr27Yt3333Xo/3atWvdc6fOnz8PhULh/ho2bJjP/rz11lvo2bMngoODER8fj8ceewyVlZVX/HkQ0Y2FwYrIjzZv3gwAePDBB6FWt/yC8GOPPQYAePPNN33Wb9iwASaTCZMnT4Zer/co79OnD9asWYOQkBDcd9996NevH3JycrBgwQJUVVU1+72Li4sxaNAg/P73v0dhYSGGDh2KO++8Ez///DNmzpyJefPmtXgcADB9+nQsWLAAOTk5GDlyJAYMGIB169bh7rvvRn19vc9tsrKy0KtXL7z22mvQaDTIyMhAjx49sHXrVtx555346KOPfG5XXl6OgQMHYsuWLRg2bBiGDBmCf/zjH8jMzMTSpUvd7bp06YLMzEwAQGhoKDIzM91fo0eP9trvs88+izlz5iAhIQFjxoyBiOCNN97AuHHjwPfWE9FlCRH5zeDBgwWA/O1vf7ui7ex2uyQnJ4tGo5GioqIm93vw4EF32S+//CJBQUGiVqvlvffe82jvdDpl69atUldX5y7LzMwUALJr1y6Ptvfcc48AkPnz53u0LywslP79+wsA+frrr1s0jg8//FAASMeOHeXs2bPu8qKiIunRo4cAEAAedSaTSRISEkSlUsn69es99nf48GExGo0SFhYmxcXF7vJdu3a59zVixAipqqpy1x06dEjCwsJEqVTKkSNHPPYHQFJSUprsf0pKigCQ+Ph4+fnnn93lJSUl0qVLFwEgO3fubNFnQUQ3Jl6xIvKjsrIyAEBMTMwVbadSqfDII4/AZrN53X77+eefsW/fPvTs2RN33HGHu/yll15CXV0dHn74YUydOtVjG4VCgZEjR0Kn0132+x4/fhxfffUVBgwYgBdffNGjfVxcHN544w0AwOrVq1s0jv/7v/8DACxduhSpqanu8tjYWKxcudLnNmvWrEFBQQGeeuopTJs2zaOuf//+eP7551FVVYX169d7batUKvGXv/zF4+GAAQMGYM6cOXA6ne7+XKn/+Z//wS233OL+e3R0NB5//HEAwN69e69qn0R0Y2CwIgoQDz/8MNRqNd566y2P8sbbg48++qhH+Y4dOwBcuI14NRrndE2YMAFKpffpoHHO1aFDh5rdl81mw4EDBwAAkyZN8qofPXo0jEZjk32YOHGiz/0OGTIEAHz2oXfv3h4BqNGUKVMAAN9++22z/fZl5MiRXmVdu3YFABQUFFzVPonoxsBgReRHUVFRAICSkpIr3jYhIQHjxo3DL7/8gj179gAArFYr3n33XQQHB3tdzWl8orBz585X3d/G9Zz+8Ic/eEzovvirqqoKpaWlze6rrKwMVqsVMTExCAkJ8dkmJSWlyT4MHjzY5/cfMGAAAPjsg6/9AXBfLcvPz2+2374kJSV5lTXObWtqnhgREcDlFoj8qnfv3ti3bx+OHj2K6dOnX/H2jz/+OD799FO8+eabGDp0KDZt2oTS0lLMmDEDBoPB7/11Op0AgN/85je/KqD5ow8PPPCAxy29S3Xr1q21uuTz6h0RUUswWBH5UUZGBl577TVs2LABK1asuKInAwEgPT0dXbp0wSeffIK//OUvTd4GBIDk5GScOnUKZ86cQe/eva+qv41XZiZMmIBnnnnmqvbRKCoqClqtFiUlJaitrUVwcLBXG1+v8UlKSsLJkyfx3HPPoV+/flf0Pc+fP3/Z8sTExCvaHxHRr8X/lhH50ejRo9G9e3fk5ubij3/842Xbms1m/PTTTx5lCoUCjz76KOrq6vDCCy9g586duPXWWzF48GCv7RtfhdM4wfxqjBgxAgCwcePGq95HI41Gg7S0NADAxx9/7FW/bds2lJeX+7UPx48fx6lTp7zKP/zwQwCuK3GX9rGla3sREV0NBisiP1IoFFi/fj2CgoKwdOlSLFq0CNXV1R5tRASff/45+vfvj8OHD3vtY9asWdDpdHj55ZchInjkkUd8fq+nnnoKQUFBePPNN73WeRIRbN++vdn5QGlpaRgxYgT27duHOXPm+FzE84cffsCWLVuaGzoA4IknngAALFmyxOPqVGlpKRYsWOBzm8ceewyxsbFYsWIF3njjDfetwUZ2ux1bt27FiRMnvLZ1Op2YN28eampq3GVHjhzBq6++CoVC4e5Po8TERBQVFXGhTyK6dtp4uQei69J3330ncXFxAkBCQkJk+PDhMnXqVMnIyHCXBwUFyY4dO3xuP3XqVAEgOp1OSktLm/w+H3zwgWg0GgEgt912m0yePFnGjBkjycnJAkAqKircbZtax6qoqEj69OkjAMRgMMiwYcPcfW3cz/z581s89gcffFAASGhoqIwbN04mTpwoBoNB+vbtKwMHDvRax0pEJCsrS6KjowWAJCcny5gxY2Tq1Kly9913i8FgEACyceNGd/vGdazuvfdeSU5Olvj4eHnooYdk1KhR7s/jv/7rv7z6Nm/ePAEgnTp1kmnTpsns2bNlxYoV7vrGdax8afyemZmZLf4siOjGw2BFdI1YLBZZtWqVDB06VGJiYkStVovBYJC0tDRZsmSJ5OTkNLntW2+9JQBkypQpzX6fH374QaZPny4dOnQQjUYjsbGxMnjwYPnf//1fsdls7nZNBSsRkdraWnnllVfk3/7t3yQiIkK0Wq0kJyfL0KFDZeXKlZft66VsNpv8+c9/lq5du4pWq5XExER58sknpbKyUoYOHeozWImIFBQUyLPPPivdu3eXkJAQCQkJkc6dO8v48eNl7dq1YrFY3G0vDjl5eXkyffp0iYmJEZ1OJ7169ZJ33nnHZ9+qqqpk7ty5kpycLGq1WgDI0KFD3fUMVkT0aylE+H4GokAzatQobNu2Dbt27WryXXY3st27d+Ouu+5CZmYm1q5d29bdISJy4xwrogBz6NAhbN++Hd27d2eoIiJqZ7jcAlGAeO6555CdnY3NmzdDRJp9qpCIiAIPgxVRgPjwww+Rk5ODlJQULFu2DOPHj2/rLhER0RXiHCsiIiIiP+EcKyIiIiI/YbAiIiIi8hMGKyIiIiI/YbAiIiIi8hMGKyIiIiI/YbAiIiIi8hMGKyIiIiI/YbAiIiIi8hMGKyIiIiI/+X9f7JFbVb7IsgAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "if single_qubit_experiment.collect_data():\n", " single_qubit_experiment.analyze_results(plot_results=True)\n", "single_qubit_pauli_error_estimate = (\n", " 4 / 3 * (1 - np.sqrt(single_qubit_experiment.results.cycle_fidelity_estimate))\n", ")\n", "\n", "print(f\"Single qubit pauli error: {noise.single_qubit_error:.5f}\")\n", "print(f\"Estimated single qubit pauli error: {single_qubit_pauli_error_estimate:.5f}\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now rearrange the equation above to estimate the two qubit depolarising error\n", "$$ e_{2q} = \\frac{16}{15} \\left(1 - \\frac{1-\\tfrac{15}{16}e_L}{\\left(1 - \\tfrac43 e_{1q}\\right)^2} \\right)$$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Two qubit depolarising error: 0.02133\n", "Estimated two qubit depolarising error: 0.02065\n" ] } ], "source": [ "two_qubit_depolarising_error = 16 / 15 * noise.two_qubit_error\n", "two_qubit_depolarising_error_estimate = (16 / 15) * (\n", " 1\n", " - (\n", " (1 - 15 / 16 * cycle_depolarising_error_estimate)\n", " / (1 - single_qubit_pauli_error_estimate) ** 2\n", " )\n", ")\n", "print(f\"Two qubit depolarising error: {two_qubit_depolarising_error:.5f}\")\n", "print(f\"Estimated two qubit depolarising error: {two_qubit_depolarising_error_estimate:.5f}\")" ] } ], "metadata": { "kernelspec": { "display_name": "client_superstaq", "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": "3.11.9" } }, "nbformat": 4, "nbformat_minor": 2 }