{
"cells": [
{
"cell_type": "markdown",
"id": "0a1c653f",
"metadata": {},
"source": [
"# Learning Outcomes \n",
"- Learn what phase kickback refers to.\n",
"- Some circuit identities. \n",
"- Constructing CZ,CY, CH, SWAP (controlled rotations by pi)\n",
"- Arbitrary controlled rotations. \n"
]
},
{
"cell_type": "markdown",
"id": "74e8e842",
"metadata": {
"tags": [
"remove_cell"
]
},
"source": [
"# Phase Kickback\n",
"( Taken directly from Qiskit Textbook, with some inserted exercises )"
]
},
{
"cell_type": "markdown",
"id": "8638038a",
"metadata": {
"tags": [
"contents"
]
},
"source": [
"## Contents\n",
"\n",
"1. [Exploring the CNOT-Gate](#exploring-cnot)\n",
"2. [Phase Kickback](#kickback) \n",
" 2.1 [Explaining the CNOT Circuit Identity](#explaining-identity) \n",
" 2.2 [Kickback with the T-gate](#kickback-t-gate) "
]
},
{
"cell_type": "markdown",
"id": "9b54dd21",
"metadata": {},
"source": [
"## 1. Exploring the CNOT-Gate \n",
"\n",
"In the previous section, we saw some very basic results with the CNOT gate. Here we will explore some more interesting results. \n",
"\n",
"We saw that we could entangle the two qubits by placing the control qubit in the state $|+\\rangle$:\n",
"\n",
"$$\n",
"\\text{CNOT}|0{+}\\rangle = \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle)\n",
"$$\n",
"\n",
"But what happens if we put the second qubit in superposition? "
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "5878088a",
"metadata": {
"tags": [
"thebelab-init"
]
},
"outputs": [],
"source": [
"from qiskit import QuantumCircuit, Aer, assemble\n",
"from math import pi\n",
"import numpy as np\n",
"from qiskit.visualization import plot_bloch_multivector, plot_histogram\n",
"# In Jupyter Notebooks we can display this nicely using Latex.\n",
"# If not using Jupyter Notebooks you may need to remove the \n",
"# array_to_latex function and use print() instead.\n",
"from qiskit_textbook.tools import array_to_latex"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "6aed4b54",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAKoAAAB7CAYAAADkFBsIAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Z1A+gAAAACXBIWXMAAAsTAAALEwEAmpwYAAAIWElEQVR4nO3df0zU9x3H8ecdA3G1qVqi1h+ooLjJwCkbNZp4mFRFt3ZuxR9kI9GSSMR1c/7VreI/KMmMf9htyTRrpmnSsk7GrF3VtNvg1GDrrJuo24pRUa+1CqibOESF2x8XESh4hx73/b7l9Ui+Cfe5u8/3TfLi873vl7t7e4LBYBARl/M6XYBIJBRUMUFBFRMUVDFBQRUTFFQxQUEVExRUMUFBFRMUVDFBQRUTFFQxQUEVExRUMUFBFRMUVDFBQRUTFFQxQUEVExRUMUFBFRMUVDFBQRUTFFQxQUEVExRUMeFLThfgdpVH4dNrzux7zDD43jec2bfbKKhhfHoNzlxxugrRoV9MUFDFBAVVTFBQxQQFVUxQUMUEBVVMUFDFBAVVumi9Czda4G6b05V05eqgtre3s2XLFiZPnkxiYiLTpk3D7/czZcoUVq1a5XR5ParYmMOR3RsjHneLM1fgN9XwyttQUgk/3QW/PwJNzU5XFuLqf6EWFhZSWVlJSUkJWVlZ1NTUkJ+fT0NDA+vWrXO6vMfG0XPwZk3o53u9nO60weHT8I/z8MPnYPQwx8oDXBzU8vJydu7cSXV1NT6fD4C5c+dy7NgxKisrmTFjhsMVPh6u3YS3Dt8PaGdBoOUO/PYg/Ox58HpiXd19rj30l5WVkZub2xHSeyZNmkR8fDyZmZkA1NfX4/P5SEtLIyMjg4MHDzpRrlk1p6H9AS3xgkFovAGnP49dTT1xZVADgQAnT55kyZIlX7jvwoULpKenM2jQIACKiopYtmwZdXV1bN++neXLl3P79u2w+/B4PBFtfn91n+s/8s4mfr1qaJfts7pDfZ7H76+OuM6H3d7YfZhwzRuDwSArf7ypX/YfKVce+gOBAACjRo3qMt7S0oLf72fhwoUANDY2cujQIfbs2QPArFmzGD16NFVVVSxYsCC2RXeS/Z1XyV68vstYxcYcZ4oJw+ONiyAwQbzeuJjU0xtXrqhJSUkA1NXVdRnfvHkzly5dIisrCwitriNHjuxYXQEmTpzI+fPnw+4jGAxGtPl8OdH7xfrI58uJuM6H3fJys8PW4fF4+dXPX+mX/UfKlStqSkoKmZmZlJWVMXz4cMaMGUNFRQV79+4F6AiqPLrZaXDodO/3e4AnBkHGuJiV1CNXrqher5ddu3aRnp7O6tWrWblyJUlJSaxZs4a4uLiOE6nk5GQuX75Ma2trx3PPnTvH+PHjnSrdnGeGQm5G6OfuLwA8gMcDP5gNcQ4nxWOpDXpBQQHHjx+ntra2Y2z+/PksXryY4uJiampqyMvLo76+noSEhKjs85cfOPdRlNQR8PK82OzrozPwwUlo7HSBP3UEfGsapIyITQ0P4spDf2+OHj3KzJkzu4xt27aNFStWsHXrVhISEigvL49aSAeSZ1MhOwV+8lbo9voXIOlJZ2vqzExQm5ubqauro7i4uMt4SkoKBw4ccKiqx0vnk383hRQMBXXIkCG0tbnsnRISM648mRLpTkEVExRUMUFBFRMUVDFBQRUTFFQxwcx1VKeMcfAjGE7u220U1DD0/aTuoEO/mKCgigkKqpigoIoJCqqYoKCKCQqqmKCgigkKqpigoIoJCqqYoKCKCQqqmKB3T4Wh7tLuoKCGoe7S7qBDv5igoIoJOvQL125C7UUIXL0/9ov3Q51Qkp+GzHGQGO9cfaCgDmiXrsN7x+FU4ItdUc42hDaAP/wNvjkRFk4LfamvExTUAag9CH85BftPQFt7+Me33g19K/Xxi7D8WUgf2/81dqfXqANMexDe/ii0kkYS0s5u3ILX/aEv/Y01BXWA2V/7aEELAr/7EP71WdRKioiCOoDUN4a+/vxBtn4/tD1IkNCq3BK+nVfUuDqoFpv2utkfP+65leTDuP4/+POpKE0WAVcHtbCwkNLSUoqKiti3bx9Lly4lPz+fs2fPuraFj1u7S19sgvON0Z3zwzOxa5fu2rN+Ne2NrmPhe8T12c1W+ORSbK4CuHZFjbRp74YNG0hLS8Pr9VJRUeFEqSZcaOqnea+Gf0w0uDKofWnam5uby/79+5kzZ06syzTl8//007zX+2fe7lx56I+0aS+EGvU+jEg7G7/4ahVjv5rTp7mPvLOJj/du6TJ251YzyV97rk/z+P3V/Gj+3D49pzfFrzcTn/hEx+1wZ/a93b/2za63d7/7Hi/5vv3QdUXaj8+VQe3ctHfRokUd492b9rqVG7tL371zq0tQo6Xt9q2oz9kTVwY1Fk17I/1LdrLFpM+XQ8XG6FxQeu19ONdw/3b3lfGeeytpb/d3V/zSi/zptf7vUurK16iRNu2VyI0bbmve7ly5ogKkpaVRVVXVZaygoICpU6cyePBgh6qya/p4OPBJdOccHA9TnonunL1xbVB70lPT3pKSEnbs2EFDQwMnTpxg7dq1+P1+UlNTHakxb311n8ZjZUISjB0GgSh+/is7FRJilCBXHvp7cq9pb/cL/aWlpQQCAVpbW2lqaiIQCDgWUjfzeGBxFM9BhyTCvPTozReOmRVVTXsf3aSR4PsK+P/d+2MiPYlamh0Ka6yYWVElOl6YDl9PfrQ5vpsV+nhKLJlZUSU64rxQMBueHgJ//Wff3k01OB7ysiFrQn9V1zsFdQCK88Lz0yFjHLz79/DXieO8MD059JynvhybGrtTUAewCUnw8rzQ+wBqL8DFq3Dlv3C3HQbFw+ihoU+hTh8PT8bw9WhPFFRh1FMwKsPpKh5MJ1NigoIqJujQH4aa9rqDJxjp24hEHKRDv5igoIoJCqqYoKCKCQqqmKCgigkKqpigoIoJCqqYoKCKCQqqmKCgigkKqpigoIoJCqqYoKCKCQqqmKCgign/Bwlu/X/t+/vGAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.h(0)\n",
"qc.h(1)\n",
"qc.cx(0,1)\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "6007a202",
"metadata": {},
"source": [
"In the circuit above, we have the CNOT acting on the state:\n",
"\n",
"$$ |{+}{+}\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle) $$\n",
"\n",
"Since the CNOT swaps the amplitudes of $|01\\rangle$ and $|11\\rangle$, we see no change:"
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "a2e96822",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle \n",
"\\text{Statevector} = \\begin{bmatrix}\n",
"\\tfrac{1}{2} \\\\\n",
"\\tfrac{1}{2} \\\\\n",
"\\tfrac{1}{2} \\\\\n",
"\\tfrac{1}{2}\n",
"\\end{bmatrix}\n",
"$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.h(0)\n",
"qc.h(1)\n",
"qc.cx(0,1)\n",
"display(qc.draw()) # `display` is a command for Jupyter notebooks\n",
" # similar to `print`, but for rich content\n",
"\n",
"# Let's see the result\n",
"svsim = Aer.get_backend('statevector_simulator')\n",
"qobj = assemble(qc)\n",
"final_state = svsim.run(qobj).result().get_statevector()\n",
"array_to_latex(final_state, pretext=\"\\\\text{Statevector} = \", precision=1)\n",
"plot_bloch_multivector(final_state)"
]
},
{
"cell_type": "markdown",
"id": "bce1dd21",
"metadata": {},
"source": [
"Let’s put the target qubit in the state $|-\\rangle$, so it has a negative phase:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "e9cc42cc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.h(0)\n",
"qc.x(1)\n",
"qc.h(1)\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "b2ec3831",
"metadata": {},
"source": [
"This creates the state:\n",
"\n",
"$$ |{-}{+}\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle - |10\\rangle - |11\\rangle) $$"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "ec94a3c0",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle \n",
"\\text{Statevector} = \\begin{bmatrix}\n",
"\\tfrac{1}{2} \\\\\n",
"\\tfrac{1}{2} \\\\\n",
"-\\tfrac{1}{2} \\\\\n",
"-\\tfrac{1}{2}\n",
"\\end{bmatrix}\n",
"$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.h(0)\n",
"qc.x(1)\n",
"qc.h(1)\n",
"display(qc.draw())\n",
"# See the result\n",
"qobj = assemble(qc)\n",
"final_state = svsim.run(qobj).result().get_statevector()\n",
"array_to_latex(final_state, pretext=\"\\\\text{Statevector} = \", precision=1)\n",
"plot_bloch_multivector(final_state)"
]
},
{
"cell_type": "markdown",
"id": "b78677df",
"metadata": {},
"source": [
"## Exercise 1\n",
"\n",
"What happens when we apply a H gate to both qubits in this state? "
]
},
{
"cell_type": "markdown",
"id": "3df30c2e",
"metadata": {},
"source": [
"## Answer\n",
"?"
]
},
{
"cell_type": "markdown",
"id": "2f63e13a",
"metadata": {},
"source": [
"If the CNOT acts on this state, we will swap the amplitudes of $|01\\rangle$ and $|11\\rangle$, resulting in the state:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\text{CNOT}|{-}{+}\\rangle & = \\tfrac{1}{2}(|00\\rangle - |01\\rangle - |10\\rangle + |11\\rangle) \\\\\n",
" & = |{-}{-}\\rangle\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"\n",
"This is interesting, because it affects the state of the _control_ qubit while leaving the state of the _target_ qubit unchanged. \n"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "f5d085e7",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle \n",
"\\text{Statevector} = \\begin{bmatrix}\n",
"\\tfrac{1}{2} \\\\\n",
"-\\tfrac{1}{2} \\\\\n",
"-\\tfrac{1}{2} \\\\\n",
"\\tfrac{1}{2}\n",
"\\end{bmatrix}\n",
"$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
]
},
{
"data": {
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alAqFJHVLsrpstNv4vs94rQaKwtWrV7l86RKTU1NMTU0xPz+fPjfkM4A4Tm0ZRUnJQ5A47EDYc73R4NadO3TabZ588kkmJyeZnJlhYnKSarU6Wn1ux8hhPkxEUYRt2zQ2N+k0GoSeRxhFtDsdFEWhVq2iqmpC5glDQt/HDwKCTEpW3uSqoiT/V9XkR1HQDYOCaaLpOp7v07EswjDENAyKxSKaqtK2LCzLolqtcv3aNa5evcqJEyeYnZ+n024TRhFjtVrirDUNTfyWK1EgXbEGUQTCCLN3Sqvd5q133qFULHLo8GHiOMbM5xkbH2d2fp7x8fGRsSUYOcxHGK7r0m61aG5u4llWat9eGFLK5ykUCumKLmvPURynTHVpO3Klmf13LpcjJ4Jd23GwHQcUhZIojURxzNr6OrlcjjAI+OCjj9AUhadOnkRRVdqdDqVCgUKhgK7raJqWZqskcUiWaeIo2nLWmXOMoojLly9z+do1nnrySXL5PIqqUqpUmJ6dZXp6mnK5PAqEE4wc5udFHMeJYbXbtOt1nE4HTxT6Lcui4zgoQKlQQNW0tD6hqepWFAhEkDLlwjAklO0icrUpyD1RHKOqKoauJytLkUI1DINKqUTbtmk0Gly+dAnDMHj8iSco5PNJnSSO8cKQKZlKlelceS4kBpQah4hcQ0FYUOMYhNEHQcB7Z84QBgHPv/ACfhDQbreJFIVSucz07CxTU1NUKpUv9wv5euFReMqM7DmDMAyxLItWo4HVauGIoNTzPBqtFmEYkhdMVAVSp6iramrfMhsUiXRokFlpSr4CkGrGaoZBzjBQNQ3f91FVlVKhgKZpNFot7t27x927dzl+7Bjz8/Oomoap69iOQ6lYpFQsbjsPeQxZyNWlCsQiGEe8b2lpiQ8++IBnn32Wyakp2p0OjuMkgfDkJDMzM0xMTKQZsW8pRg7zQRHHMZ1Oh1ajwcbaGp1WK01zGpqW1AuiiHyhQLVSQdc0DF1PV3SKoiR1BWE0cU80mIVM7Xi+j+u6+L6P63mpY/Z9H0uwaxcXF7E7HY4fP878vn2JcRsGqqombLtOh1KphClWgDLaVYUBKYpCnFlRZtM9PRcAgE/OnqW+scGbP/whqqriOA6tTgfbccgVCkxNT7P/wIFva5T6KJzwyJ4Bz/Not9tsrq/T3NjAdRyiMEwCRUXB8zxM06RaqZDP5VI71jIrOlkjhC17DkUqNgvpuDxhs67n4Xpe0kIWhjieh+e6bNbrrK6tUatWeez4ccrlMjnDSDJCmkar3SaOY6oiKFUyNqxrWhrcpqla8e9AtKP1or65ydtvv81zzz3Hvv37CcMwecZ1OqCqlKtV9u3fz+zs7LeVZTtymHuFbAdZW1tjZXGRTquFISI+M5dL6hmmiee66IZBpVLpuspyhRnFMUEQbHMi2dQJJCu5UAgS9P6EYZgaXqPV4urVq1iOw/79+6mUyylRoJDPp7XJZrNJLp+nINizvZMRksNLDE9TVRTh3OMoSmo02dQtQBzzzjvvUCyX+c53vpOeayRaW5rtNtWxMaYFpb1QKHybHOejcKLfanv2PI9Go8HK0hJrKysQhkkfo6alPABpb+VSKS01yPaPtDYoWLDy2Zn2X2bsKxTZIBlMR0KcQH7O930C38eyLBaXl7lz7x6RonDi2LHUlou5HKbosbRsG8/3GatW0xRs1OfZLcs6mvgdiyyVpuvbAuH1jQ3eeecdfvjDHyYrV+FsXc9js14nVhSm5uaYnZ2lJko73yKMHOawkCvK5eVl1tfWcNttTF1Pi/6FQiExpjim0Wrh+z7VWg19AItUOsHs9lEUfM8jCMMk2sxQ1BF1ETWzIowUhcDz6FgW58+fp1qtcvf+fd547TUs207TMrGiUBDO3AsC8rkc5VIpjT6DHifsBUFi0JljDKModZryx9B1UBQ81+WPfv5zvvv888xMT6fnJJ3rRr0OqsrY5CTj4+OMjY2Rz+e/iK/p64aRw/yaIggC1tfXWVlZYXNjAy0IKBWLVCoVCvk8+VwORVXxPY9Gs4mZy6WTQvp9qZ7vbwsEUzsWdc4wCNK+aYXEkWmCSauqKmEQ4Hoe9xYWuH/nDqdOnuTMRx/xyosvEkgnK8o5xWIRQ9MIwpCJsbE0vSqfK5LpHoQhfhCkKeIs815V1S1bNgw0Uaa5cOECK6urfO/119NzktwKu9OhadsUKxUmhD1XBTfjW4C+9vytChmGgeu63Lt3j5XlZcIgoKTrTM7OUq1Wk9QHW/UC27YJgoByqTTQWabvF+kRXyr6CPo3JBGqaRjoGfadrJdI8oF0luc+/ZTjx44xMzfH4v37TM/M0Gq3CYMAXdeTlK1lsVmv07YsTMNgbmaGcrmcGI2igKyvAiFAFCUrYeEovSDAEW0njuOk5yEN7tnnnuODDz7gz/3ar2Hmcl3R7kSthu26bKys0Gm1sG2bWq1GrVb7tqZ2RviKEMcxa2tr3L9/n1ajgamqTJfLVKrVbbXAKIpoWRaqplHuM1YrfV8co4r0q7RjPwgIgiB9j67rXeSctHWMpE3Fsm2iOOb27dtsbmzwvddfB0VBVxSmpqZwHCchEpH0VFuWlban+EHAxPg4OdNMW9MMmRoWx5emiMUzpmPbRGGI7/t4ngeQOtCjR4+ysrzM5StXePLJJ7dsOY7JFQpMmibNToelxcVEKGFigvHx8aTt5VuIkcMUCMOQW7dusbiwQOz7VAoFxmdmqJRKKfVbOhlFVQl8H9txErm5ftJUikIs2jNsx8H3/fQlTUR5hqahi5pjv3StLcQEUBQs2+bsJ5/wzLPPMj83R1vI5+maRrVSodVqEYUhlUqFyclJbNtmfXOTdrvNxuYmG/U61UqFWqWCJlMrMrsgI0tVBVUlJ1O0wolKJ+8LB1rI55mdneXdM2d46cUXMU0z+axoicnncmiaRrPV4s7161THxpiZm0vbUUYY4YvGxsYGt27dol2vY2gaM+PjjFUqXbaa2rOiJLW7KNpGXItFtoc4xheBpOu6XcGurmkYIuuUJfdl64kykJUtZFcuXcL3fX74gx9gu24qSlIsFlFVFcu2UVWVudlZwjim1Wqxtr5Op9PBchyKuRxjtRrFQoE4Q9zLipvImmtRvKYoCn4moyUd6ONPPsn7779PrVplanp6KxUdx6iaRq1SoWPbrC0tsbm+zvy+fYxNTHwb07QjhwnQaDS4dOECrmVRLZWYmZ+nXCptFfEFwzTr1Dq2DdAdqYr3+ZKwk4k68/k8hnCUUuGnF3LrniDsxHFMPp9nfW2NT8+d4+WXX2Z6ehpb7FtCFT1i7XabTqdDFEUU8nkmx8cp5vPkcjmarRbNVotGs0mlXGZc3OwqbNVCRKo4ypyrqqqYIihQSNJAQRDw1MmT/Nkvf8n9hQXGJyYwDYOcaSapW8AwDMZqtWS/9Tp2u83G+Dj7DhxgQqgXjTDCw0YURVy/fp3Fe/fQgfmpKSbGx9E1baA9+0L3NZ/Pp1kQ2eMYxjGebeO6bipIoGka+Xwe0zDS2mCvZKVsG4viGNuycH0/ESExTd5//32KhQKvvPxyYm+WhSnKFgpJwKmqKp1Oh2arRaVSYbxWI4oicqaJ73m0Oh2WVlYSO6tWqQiiXZYxm9ZY5TlDEqSrKko+n654i8UiTz75JBcvXeJZwdjNZQiEKErC5FUUmp0Od2/dYnNtjcnZWfbt3/+tEoP/VjvMKIq4d+8et2/cQAeOHjzImLgxZctF+ljPPOB93yfwPPKFQrqy8kVNIk15KAqFfB5DrL76OUhZ30ilsUhSMI7noasqpXKZtfV1Pj13ju9///tUq1UUwBfp10gYMCSr3nK1SqfdxrLtpFYiZLikfJYkPUhDLBWLjI2NbfVRZtKyKdEBupybpqqowoGeOnmSm7duMT83l567KoxNKqFUymWazSZBFNGq17nWbrP/4EHm9+8fpWhHeKhotVpcvnQJq9ViolLh4P793S1aoswBdNmzDH5zQk0rCkM8sfoKBcvUkAGhYWy1jPQGfdIJC3v2gyBZucYxBSF48Ktf/YqxWo1nnn0WSOqhkGSKoigiFk5PZm1a7TatdptKuZzYi6JQGxujNjZGSwTBq+vrbGxuUqtWKVcqXfKZkhvRRUaUr0PSsmYYPHbiBNevX8d1HErlMpZtYzlOVyCcz+eJFAWr3cZxHBbv3qXdanFUsHq/DfjWOkzLsrh65QrNjQ3KhQKHDhxI2i+Eo+y9ySRiwHIcUFUMw8AW0adcpeVME1MYVhaKqibyWEJcHehioXpBQLvTSdpT8nkK+Tz1ep0Pzpzhtddfp1qtJoZPQmLI53Lpw0AelwIUi8WkbtFuJ1GrKPorqopmGExNTVELAlrNJq12m3uLi+QMg7GxsZQlmNWuTZ169lyEwR08eJALFy/iOg5jY2N4QYDnuti2je04CZvYNCmWSnQ6HYIgQNc0bl27RqPR4LEnnuifzh5hhD0giiIWFxe5deMGahBwaG6OyYmJLhsexDCQ9cd8Pp/IzGUyQ5qmpUz4LNFFUxRCtlZwUSbwlTZj2TaO4yQ10XIZXdN498wZCvk8zzzzDIj3Bb5PFMdb/AgRWEdCwadULCZOs9VCYat3OopjKpUK5XIZy7JotFps1Ots1OuUKxVq5TKKZMnKFLHYfjYATtO3qsoTjz/O7Zs3efW11whEOSkNhKX4gq6DsGdVVWlubvLZ2bMcOX6c2bm5z/dFPgL41jnMKIpYXl5m4e5dvE6HuclJZqan0USEp0pmW29NMVNItywLgGarBSRRWlHI36UiAcmH0s8rioIq9qGQiBdIerjjONi2jSJWZIZh0Ol0eOedd3j+hReYmJiQGyESxtxbO8iKs5fLZZqCcENmtSgFog1dZ0LUIJrtNq1mk/uLi2iaxtTERJJ+FdG4TE31CyA0VeXxxx7jypUrvPzKK4nmrWEQRFFqaJ5ILRuGQQy4YmW+sbbG2Xabk08/TelbEp2O8PBhWRa3b92ivrZGQdPYf+QIRVEmUeMtTdesPUuWuiTV2I6TOj+ZGTJNM2WS9oOqqknLSMYZAYRS1EOUUwqFAgpw9tw5PM9LCT4SYRgm7Nme/cj/G4ZBqVikY1lp2hhIhRQASqUSpVIpUR5rNGg2m2xsbFCtVKhWKgmBSI7+Eyvg7LNJ4sjRo1y+dIlGo5GQ9ESbmuwFt20bW+w3Z5p4QYChaRBFXP7sM2zL4vDRo9/ocsu3gh8s4XkeV69cYfHuXZQgYH5mhrnZWTTD6IrEutKnsg6gqvi+z+rqKpZtp0y4sbExyoJMIMlBxHHfG1KVTcZiP2EQ0Gw2k8b/XI6a0HR0HYdf/epXnHzqKebn59PPK5lG5H7pzGwKtVIuownygGTwdRmM2MZ4rcb8/HxaI1lYXmZ9czNl2EWihyydv4lQKhLnd+TIETY3N2k3m2kNVNc0SoVCkiIS/Wyu66ZqQq5QLbFtm7MffsjSwsIDfJsjfNuxsrLC1UuX6NTrjJXLHDxwINE4JrEVoKsen9V2JY5ptdusb25CHGOaJpVyOcm0iDreIGcpg0cpMynt3XEcms0msQhai8UiiqJw5do1VldWeO3VV7fsVhxXEIbp6rJ3H9KJ50SbmB8EKX+hX2q5UCgwNzvLzNQU+VyORrPJ/aWlZJCDsOVUlUjYcvZHV1VOiAAYtoLsXC5HpVSiVq0maVmRso5FYKyoKrphcOfmzXSM4DcV3xqH6Xke169exW02KRsGkxMTjE9MJHU+IW4OdKU4ARB6sM1mk3qzie261KpVxsfG0rSoxKAUroxClcyPHwQ0Wy2iOKZcLlMqlRK6ehDw9jvvcOjwYY4eO7a1HeGMwiBIe7r67ktGyqpKTdQ822I/2WNAUON9oVhSrVbZPzdHVaRb7i0uJtMZ+m1fbEv2dx0/fjw1sixURUkfROVSKa33diwL27YpFQoEQcDtGze4cflyF5N4hBF2wuLiIou3b2PEMRPCHlMCXjZYzQoMkNy/tm2zWa9TbzTQVJXpqSlKxSK6yIIMggwYs5ArvVa7jW1ZmCLwlepad+/e5ca1a3zve9/rKtPEIlsVx3FfpmmWqAMJabCQy6Vj+HrfF0Fqz6ZpMjs7y/TkJCqwvLrK6vp6V+tLej7iJ4oiwjhO2kxWVrCytp8NhPN5arUaOZGFclyXZrNJXrS5rK+vc+Wzz9hcX9/hSj66+FY4TMdxuHr5MkGnw8T4eCJhVy5j9KhfSIOQqUjpKBvNJmEYYug65XKZcqWSpHREWmegoxT/VuJuM3NcF6vTwRRM0pxppj1U7733HrWxMU4++WTfc5F1wH7oNTJN0yiWSkRRlDpNSYAIRYNz9uGi6TpTU1PMzcxg6jobGxssLS+nRKZt+xMr6oMHDnB/cbFbfCFzTFnHKckL9UYjbctxXZdGvc6Ny5dxMw+DEUboh/v37rF27x5F06RSKiUroHJ5m9SktEFZy7Nsm81Gg47IEOXzeWpjY+iGkaZoByUTY+j7nigMk5auKKIs7m+ZqVpZXeXTTz/l9ddf7+pblCvUYEB5RULpYd+WRLbGsm08z0ttORLzdHtFaErlMvNzc9SqVWzbZmFpKS0jbduXODdd05ibm+PO3btdAu5Z8qOmaRSKRaqVCpVyGc/3WV1fT8VcbMfh3q1bLC8uDriajy6+8Q7TcRxuXrlCZNvMz86CULDJ5XKJg5T6rmw5Sj8IaLRa1IWjLJZKjI2NoZDU7fRM4/9O6DWuGGiLKemmaVKpVNL6haoonD93jlhR+O6zz3Y5npRcIFQ9tB16n3qPS56r5/u0xPlI0pGMjmWKSiKfzzM3O8v42BhBELC4vMzm5mZfpi9AsVSiUqmwtrbWpRoU90T6qqJg5nJJyiifp9VqJVqaoj7iui7XL12i2Wzuem1H+Hbi3t27bCwuUsrnmRgfB5LWLinpKGv5sJV6tYWjtGw7bXeSso2mYezqKOMBzlQG1FEUUSmX0xmTqqpiWxbvv/sur7z8MhUxDFpCyXxevr8vsqxeAZnVarRauJ6XOso0e9XzGU3XmRgfZ352lrxpUm80uL+42LVK7d3ngf37WV5eTm15m7602J+m61TKZSbGx4mjiFarRRAESRkoDFm+f587N24MfG48ivhGO0zHcbh5+TKB47Bvfj7VViwWCt29U+Imi4CG6FWMgoCScJSFfJ44igiiKO1H7IeuVWWf11qtFrbjbMnVZW7s5eVlFhcWeOnFF9NxQZJsI48zkCmcjOJQV20x3pqzKbVn4yhC0TQKQirP6VktSiPrNVpVVanVaszPzVEuFml1OtxfWkoJT73YNz/PYk9EmdZLMsLzCqCK2mlRSvYBm80mtpgWcfvqVZr1+oCrPMK3Fffu3KG+uEipWGRmdjaZUykn+YhsiVwJoqpp6rVjWRi6zlitlmY4XGEHg0bTZdOvvRkiSNpBpLPsnScZRRFn3n+fp06eZGp6OmXdy+1KOw1ESSPdX58fOUEoFDq0kWhR0RSFdrvdP0Wsqtv+nsvlmJubY2piAuKY5dVV1tbX03GDWczMzNBsNtNVbHrcvbYcJ6IOZVHfVBUFTddxbJuNjQ3iOKa+scHta9e2rX4fVXxjHaZlWVy7fJnI9zmwbx+FfB5X9AlKA8uqYkjjCoOAkiDzFAQjLYZUo9EcZGDidz9nGkYRzUYDz/cpFYspi0/Ctm0++OADXnzppe42CxnZimOUKRzp+CFjaFHUVa+JM9tAMPYMXce2rG0TDNJe0D4kB8MwmJ6eZmZqCl1VWV1fZ73PanP//v0sLS31jcTlMaWauoJkkc/l0FSVsVoNTVVptlqJLm4cc/fWrW0CDSN8e3Hn1i02lpcpl8vMzcwkJQUh0BHHicBAGviGIY1mM0m9ihWlzObIe9H3/S5VniwGpV8lHNel1WqhqSrVanUbn+DChQuYpsnx48fTv2VTmrKWGmYJPwMcpnxv9lkFSVYH6BvAyjJIPxdVLpfZNzdHVfRaLi4tpcGDhKppzMzMsLy8nOrKdl+geGvlKfgfsgZsGgblchnH82iKFWer2eT+3bt9jubRwzfSYXqex40rV1B8n/1zc2n6NQiCpL0hczOGUUSj1UrrGmNjYxR6HJpCpsG4Jx2a1knob1xBGKaN+9VyeZsqRhxFvP/++xw/fpzJycntG8hEZpGISIcRP06JDhnnWhLEm3ansz0yzTQ794sGi8Ui88LQOu02SysrXSSCSqWCruvUG40t56tsNY1nISPVvCAOeJ5HuVRC03Vc16XVbuN7HrevXRsRgUbg/v37bK6uMlYup4L/aa+k4CGo4h6zHScppcgMUbWa2Ky0B0F2CwU5ZhAGZZE6tk2708HQdSrVakIazGB5eZnbt2/zwvPP92XZZns34zjesbzSeyxKxu4NwyCfzyetW/1sJI77BgOQXLPJyUlmZ2bQgKXl5W21zf3797OwsJA6eHkuMaQrzK7/Czat7/vkczmK+TxhFNG2LFzPY2NlhZWlpV3P9euOb5zDjKKIW9evEwtnaQoHJRlpcuqGoiiJcTUaBGJ6Qa1SSSel0+NAPM/D6DGwnVaVIJiwzSYxUK1Utn0e4PKVK8RxzBOPP953G3Hmpg9Ez9ZuUCB1qjJCRfytVCpBFGH1rN6y5zAoOlVVlcnJSaYmJ4mCgIWlpWRyvMD8/HxiZD3H0TvzM31dVTFNk0Awf3XRqB1FEa12m067ze1r17ax+0b49qDRaLC+uEi1WGRqair9u+/7qEJ8HLHCbLRaafq1VqtREMo9QFcGxfM8YrrTsV0p2D7HEQPtdhvbtsnn8ynxLwvPdfngww954YUX0udO7zak45b3tLaHyR8pk1/YUz6fR9d1OpbV5cS6nl87bK+QzzM/N0cxl6Ner7O6vp5mjuZmZ1lbW0uVjnr33Q85Ua7yggBV0yjKrJZt07EsFu/efeTZs984h7m8uIjX6TA9MdF100o1DkXTkmK9MC5d1DZkaidGzJTLbDPok44dxlm2Wi1URaEmo1zoWjGur69z7do1XhR1y35ISUkihbMXAwO66ieQiUzFQNsBH0rOf0DdoVwuMzs7i6nrrKyustloAInDXF1d7XpvJKLPQc3MpmEkq0zR16UJ8QZN0+hYFuvr69y4cmXkNL+F8DyPhVu3MDWNaeEsszV9GTzarrsV+JZKVEXgK+/etFdSwPc8NEVJbSmbgu0HyT9wPI9isZiSjLrfFPPB++9z+NAhZmZmBmxoqydUOqKhAuBM8J4er/h/WbSj9WaNulLA/dKqApquMz0z08WklYuDsVqN9R4HF8VxOn2l33GappmwdkUWqVQqURA9pK12m1vXrrGxtrbrOX9d8Y1ymK1Gg+byMsV8nmoPMy2d8SbUMPyeVWWv0WQdWFYsoC/VugeBdJaixpGmUDNRrO/7nHnvPb773e8OHJWTVRySkd8wKZzMBrpWmBJ5MXqoNzLtgjC0QaX6XC7H7MxMQghqtVhaWaFaqdBsNLpYvVLZKK3F9hyLFHf3xMQGadilYpFcLofruqwsL3Pp3LmR0/yW4f7Nm0S+z9z0dGqPspaniravRqPRReopSPY7dN13WXsOwxAtMxwadmbJdtptPN+nXCqlvIbkxa17+dq1a7i+z1NPPTXUuUUDFH4GIatrnbVnVWRl4jDsyvb0OsidnleqqjI+Ps6MCEoWV1dpdzqMjY9TF+Q7SUBKtzMgCDZNk0hk5CRz2dT1dGRaq9Ph6uXLrPcE1o8KvjHSeJ7jsHLnDmEcMy+++CiKukZntTsddNGbWC6VuiNMum8oWTiPxMoOGKp2GIQhzVYrUdsRslT98NFHHzG/bx/z8/NdjLhYDn4Vxy/JAL7v49g2mqYR+H5aO+3IBuPMDSxv6BhwfR/fdVM9SFU8PMqlUpLC6nSo9ow02roIyUqzV1pMQtN1pqenyTWbbDYaLK+vY+ZytFstSpXKNmKQZPBF0PWwMXM5aLfxgyBx8GJfcuafZVmsb2xw4exZTj7zzLdupNC3ESt37+K0WozXal2ZIhXSjESr1aJULlMqFrsIev1Wi6pgwQdBQBTHmKqatIvswt7sdDrpynLQVI56vc6lS5f44Y9+hByJl1XUIcOMlWzetmWhKkoylQjSgQedTgepxpUG7+J3jFgdC+ESac+GaZITogaGGPaeba9J0SdgzaJYLDJvGKyurbG+uYmm62xubm7xEDKfza5gsw5cjhQLstkr8RwpFYvpyMKLn33Gk089xdTs7I7X/+uGb8STJwoCVu/cwXNdZmdm0MWKUTrLUKQDgiCgKFaVsKWeMyjyUsQXHXje1tifHY4jEL1IKEq6skxVNMKQUAg9Ly0vs762xsuvvEK9Xu+qn8jIuGsaQhwn2qxBQE60ikASpXpB0HUj99ZibNfFdV1UwepLIRSMHNtOCRBxHKdDabM6mjJwGBQNV6tVTNNkbWMDI5fj/tISx4vFwREtiVOUjliXdSjxoEkdv6qiAZVymbagqn929ixPPf30SLT9G4z2+jqNtTWMXI7a2FjXa4qi0LGstI+wJshmsPtqUQ5+Jk7UdXZ1lpaF47oUxTAEYMuWo2SAdBgEvH/mDMdPnMDzvOS4hKJV9pikprOEI9rLfN9PHZkMjGWts6sXm8S2HdclFLbSfXJqOvQg1Y8V7WKa0JKV12anszYMg7nZWTY3N3FEoOqJ0WT9IFfwWWKfoWmJklH2GEVAXywU8MRs0Ivnz/NEHDPzCIm2P/IOM/J9NhcXabVaVERDMmx9kb7v0xTDlsdrtTTS643iBkLcDIZocB4EPwio1+uJ0EGxSKfTSfVYYavgH4YhFy5c4OTJk1tTEEQ9RTYdq8LhpxGm6LkqCH1WMn+v9aSeJWTUZ1gWtmgwBtLRRHEco6sqnufRarcplkoJRVwauzQ24TylAcrIthf5fJ75mRnu37vHysoKU5OTjNVqgy8rSTopFg8gTdchilImsziJlIBUzOVo+T7r6+tc/PRTnvrOd0ZO8xuGOI7xmk1WFxcJ45h909PpvSjJd612G9d1KZdKSfYkCFLd12GSm3EYJg5zh9qhTMO2Ox0MwyCMY5qNRtKzmHGEcRxz7949FFVl3/796YpPzdpLZhB7VkEMEi6A5EXIILg6wGZk61gcRcnIrVwuGeAg/hbFMUUx2aTd6STqRZmgWx6LKlemmZ/eQFiS+0xd59y5cywsLDA/N7djZietrwpHr4mFSvo6W6t/0zCI8nlsy+LyZ59BHDOT0cz+OuORdpiR7+M2GmxubqIbBhOZaFRRFFzHodXppEQS1/Nodzr44qG8m4HJ5mJUNUlziJx8LG56+eP5Pu1mkzCOKRWLSY+XcDY54RTlyu3cuXNMTU5y5MiRXfedRSgIMcNC3sCqrqcNxVqfFWI+n6fZamHqOkalQhQEab9kFIbJZPaM04/Ecei6ji5+p9R6VWXf3BwXLl2iJZqqx3dymuJh6Au5P11VcT1v+2g0cfylUolWu83a+jqfnT3LqWeeGTnNbwiiKCK0LOrr61iuy+z0dFcQGUVR2tcn06NBvY7neYnCzhD7iBHSkqaZBGsizRhEUZr9CXwfy7axbRvdNNF1PbXnnGGgaloiuq6q2K7LzRs3eOONN9KAdBCyQWbKR9gLQ1aUUlRNQxGjBftB13U8z6NULm+lhcOQQP72vC5BFBkE67qOrutpQBzHMQVBoLJtm6XVVWYmJwfaWzZF64t+8wi6xOXT90h2fBjiuS6XL14kiiLm9u8f+np8VXhkHWYUhgTtNs1mEz8IEtm7OE5TD5ZlpVNFqoICbhoGmiD+DLrhJOQqNAjDxInEicSWL6LaGNIIznNdDNNkulbbNjsvi2a7zY2bN/m1H/1oT+cax4le5G7H3A/pkchVdQ90TSMv6h/SaHpvCukoI7ECDIIA3/PwMjUR6dTKlQqddptyqZSMOYoiJoWEWd9ziyI8103YsqqaTrbfNu4IQXAolehYFpubm1w6f57Tzz47VG15hK83IschsG1azSaFfJ6izBSJlUqz3SYMw0Q7Np8nDENypollWXi+T243e4bEOQrbdVyXwPfxfJ8oCIhVFSXeUsmqVatpb/EgnP/0U44cPryNYLgb9sKJ6MIQBKFCoYDv+1iOQ7lQSJyyrpOtvkr92TBjz7bjbBEERZlE0zRqY2MpyWp5bY3Zqakdg1TbtlGAQrFIR0xK2raaF0xbObDbdRyuXL6MmcsxkWkd+jrikXzSRFFEIAyo1W6Ty+XIFwppk36r3cay7XRkluwFVFSVYqmU1O52EPmOhGHJB3Or3caRdRNFoZjPUymVGKvV0FUVI5djcnKSfD6/oxF88tFHPPH44wNZsTudbww7ppF2QpcMYB/I4+44Tt/6hkISDRu6TiGfp1wuU63VKAvhaznn03GcZEWuJGoredOk3W539Xf1QvaDFguFJCBQlPSB0gtVRMOlQoE4ilhbXeXm1at7vRwjfM0Qui6R49BqtfDDkHHxkJYllboYHFCrVsnl8ynhTfYhWp3ONnGMru1HEY5t02g22azXkxWkGGieMwxK5TK1cplSoYCqJKPxxsfHd3SWa2trrKyu8uQQrNhB2aIHmRs5qEdaQlNVCoUCkch8DdqGruvkTJNSsUilUqFWrVIQ7HkpJmLZdjLIfnMzYblGEcurq9vkNSWCMMR13S4Vr2DAMUASDOUMg5yYuXnxs8++9upej+QKM3IcEFMCfN9nfm4OhcSxNNttfN+nUCik436kw1FImJeeaaZCzNIJRaLg7rkunui7VETKplgoJNFmz4y8druNH4bJzMddmJv37t3DcV1OnDix6/n1MzB4gIiUxDh2M0xVUSgWi4l+pOsOZANmIR2gYRjpylf2ihYKBWzHoVKp4AUBm5ub2I6TRqfZBnLf9ynk82kqSIrf931Yieuiy5Vsp8OtW7coVavMPSI1kBG6EYUhgWURCXZ5LpdLCTaO49Bqt9E0jWq5nLZUyXqfqigp29uyrLR1ARJOgRx8HAZBwuaMIsxcjkqlQjGf724dCwJagmVa3iW9GscxH3/8Mc8MwdhOVcUyNijZ+w+Cfq1ZvciZZjKUXkwD2sn6ZWpWllqywbxcaa+KXsxischmo8Hdu3eZnppK+6XleVqWhaqqaXbANAzsARmj9HxUlbyot9q2zfmPP+a7L7+8p/LTl4lHzmHKaFTWNKSBhVGUTheRaRtIvki1h/pcKhYJmk0ajQY500xSE1KoXPQFGqaJqes0ms2EINNjGI7j4HoepWIxnYIuCTW9N0cQBHz66ae88NJLDxRVyukivTJcQ0GQm3YzMlM4Plukl3tltWRULx9W/ST0FBG5FovFRGezUqFQKGBoWmJoCwtMjI2lAvau76fTVNLPixRcPyOLJZsQ0pVmx7a5dP48xVJpz6mxEb5aRFFE0OmgQCKHGATsm5pK2N22TavTSUsqvSLl8s7QRdbDtm3CIEATNUfZ2qFrGsViEcMwkr+1WokiTcZhxVFEu91GEex2eW9nlXmyuHbtGvlisWu4+0D0ISOFYThUUNp/czuvMOV7SqUS9UYDx3G6e0cFpC1L9nuWmCShaRqlchnf96lUKoRBQM40WV1dZXF5GcdxElvXtITdG8ddQyUMXU9S32I04g4HnKZnG80mF8+f5/QzzzzA1fni8UilZMMwJLQsUBSaYnU5OT5OFMe0Wi1iMTkg6yx7G/djktSBIrYhB6vmTZNatcrE2FiSahQKNNKJZhEEAZZols5GZDJlmOqoir9fuHiRmdnZZFLAA0BGpIO0IXfDsJ+S00NkWkQ6yUhEoL2yWIOcfz6Xw3Fd5PikmZkZ9s3Po2taIoptWaxtbmLbdsKmy6RgDcNItSl7HXLX/uNEh7NULBJGEZ+dPTsSNnjEEDsOcRB0rS7z+TyO42BZFjnDSEsq0L8dQipJOZ7H2sYGjWYTTdcplkqMj48nEnn5PLooG2R5DhLtTicd0ZVV1UkZr5n73LZtLl2+zLPPPDNc8NtzD0tHvlfFrix2a4cBUsKh67qpfUlbDqU9060i1C8gz+fzuKIuqYvV96FDh6iVy3QET6TeaNBotRKyYKb8owvCYSjKNFl0nYFw2KZhkM/lWFpc5P69ew9wZb54PDIOM4oiQtGkLw0sn8uRE3MVwzCkkpl0nm0dkaQVy7ap1+vJ+6OIifHxNCIyBSNu236hy1FFotdSUZSBqRtpbJoQOr91+zanTp8eqmjfD2FmDNADoY/z6QdZiHeFbJ5sixn02bQFpuf1XC6H01OLqJTLTAtx+UazSbFYTIfPttttmq0WjuuiiabrUOjLZvtTu/YjWcAindzpdLh04cJQl2OErx6h6xI4ThK4NpsEQcDk+Diu5yXKPaZJuVLpckrZBn7X92m2WmzW69iWRblYZHx8PGGli9rYtiyJZKf2OEDP9ykUi4MHOYv7XFUUzp0/z/FjxxJN5iHQazkPTPjJbnOI54hCougF0BaKXqktD7JntgfBOdNMZCszf9M0jdnZWUqFQqqVXavVknqyZaVBsZTyDIQgSdfzr/cYxDXOiefwlYsXv5ZzcR8dhynqlkAqQjA+Pp7+u1wuJ0w5mUoRqRDXdamLYr9t26hC5WZ8bIxqtcrY2BgxyRxMu4cIJKOlNCKNYzrtNlEcU85Eozvh4oULPPn44xRlWiRTU+x32/ZzTnttKemHfscqFTzkTxzHaRuMZVlDp497I9NCoYDjut37Eu8riBYAT6inyIxAJFjInU4H23WxxedTkkM/lq+ioGgahmD6Lt2//40ZI/RNRijqljKD0+p0ElUnXafdbqPrOpVMGlY+XKMwpGNZ1Ot12iJIzufz1KpVqtUq42Nj5PJ5HNdNVzxd+5W2Je4jX7SQSJLKbmi2WqytrvLEE0+kaczsPdnPdnstKG0p+Rz23E98IM0GITJC4n35XC5lwg617Z6Ur6ppGIaB22vPcTKXU9e0hOgjUuelUiltbWkJW3ZsO5XIlNerrySnaJ0p5HJEX9Os0SPhMCPfJxJfmALYloWhaYRhiC9lq7JU5zjGd102G42Ujp7P5xmr1RJVGjG1XCrbjNVqGLqOZds0BSMPtvdL2baN6/vpTbEbGo0GKysr6Vy8rJ6jXIWmGpE9TjQ7E+9BSQJprSfjEKVzDHuURyQURSEvasL+sEaWOX4QaZxM8BGKGpHrutRqNeZmZwnDkM1GI2HK5XKJsZXLGKaZ1qfbgskolYZ2Qj6XSyPTVC5whK8lIlG3JI6xHScZxVUu0xT6y5VKZcvRiJVRu9NJGK6CWFIul6nVakkNTZKB4physUipVEpmYjYaXbMe44wdReKe1FSVcs84v0G4cOECjz/+eJpqhK1VWdaeZbCedQny7g1FnXCv9rxtZdgn2O16j/idE2zVvbBPe7NGWXuOSfgb7U4HVVU5sH8/hXyetfV1PMFJkIFwXpD5HM9js15Pugx2sWPZnlYsFOh0Oly9dGno4/4y8Eg4zCAzJNUPAhzPQxGRTT4jWwVJ1FgXjjKOErX8MWFY/XL0CskqplqpUBSq+vV6HVsQi0AoBnkeluOQz+e7nfMOuHjhAk888cSWcx20YlO260ZKI+xlyMaZz6S6sz0Gk20jke/vdTr9Vo/yLznTRN+rkWUdpujrjMUDsZ35Lgr5PJVymUqphG1ZXXP4dE2jWChQq1QwdD1hLnY6tEUWYaCxiX0XCgWiOObKxYtDpaBH+PIRum6itkPCkHQcJ5WZk6QbeS9FUUTHcdKHrZnLMS6D3gzbGrpXd3nTTLajabQ7HVqtVtJPLVc5cUy71SKGvmO6+mGzXmd9fZ2jR49u21+KjBPtJfvIVWG2vNIlfSeJRgN+ut6/A+t0+yElAXC0xwA4+6yU9hwEAe12G0f0TZfLZUzTZHpqCk3TWBN8ELnfnOCFFAqFNDhqykzeLvZpCDWjhfv3UwH4rwO+9g4zdN1EIEDcJLbQd1RF3VG2jriuy0ajQUusLsqlEuO1WjqkuBdZpp1EIZ9PppeI1Wa9Xk/ZX1K4vTRkD+Vmvc76xkZqYMOgb4pWRKRylZsecxwnmpVDbENikBD8tvcpCrlCgTgM9zTAWaZPzXwex7ZptVq4rpsM2xVOUGJMyBg2ms1tU+M1TcM0zYTtbJqJQlO7jS3qIn0OOJEXFA53Y22N5W/AsNpvIkKxUlHYYqdKkle1XEZT1XTwcL3RwBWOckz0/fa958XDN2vPuqZRq1Qo5PN4QZDeZwrJEGg/CLoGMOyGi599NlzwmzmmbSxy8Xe115YRovJDHcnekTPNPa8ys/VMM5dLMz7EiZpZMTPizNB1JsfHiaNoW8+1nHNbyOfTlbxlWbRarWRCUS+xT66S45i8KA9dvXTpa5Oa/Vo7zCiKCMWXLL+clpDHKpVKlMtlgiCg3mwmerGC1jw+NpbUJAaQXWRPZj/ouk6tUqFcLqfTA1ZWV/F9PyH5DBnZXeg1MAZEpbsgfAg1D4ndjjx7dDnDQNP1bXXd3T4f+H7CzIsiVCFJmDWu9FgUhamJCXKmycbmZlcztIxu4zgmZxhUyuVECi0MsTqdpFE9Y5TZLRuGgZnLcfvmzW2OeISvFoHjJMGvgEzt5UyTSiZQ3azXcWwb0zAYGxtL+v2kk+kl8vRxlhJS7HusVkuIaK7LRr1OvV4nl8sNrZy1sbFBvdHYVc5y2/77/C0ccgj87hvfmcjXRZZ6wAA4FDXjOI7xhQRhuVLpe93y+TwTY2NEQcDG5mb3sahq2udZFP3xqsgutFstvKwQgqIkQZFIWxcLBZr1Ovfv3/9aZI2+3g5T6B7KFIfnujSaTUrFIuVyOVkFNpuEgvQjDaO3GJ9FHMddRjsIOcOgKog9ckJ7s9VKU407YUPQ2/diYIPUeLJp4c+LvWxBpnLiKNrVyCLRdNxstVJiVSSCl50eDoqiMD05ia5prK+tpVGkjMDDKEprPvlcjopIAQVi+ow0tG3zPk0Tq91mcWFhoGrQCF8uoihKVpcZe97Y2CAIAmZE72VdzLY0dZ2xsTHKojFe6qj2YidnmYWsU5aKRQKhlSx1pYdZuVwQo6j24uh2IvQ9aHtYL4bNGMHwAXAcJ7Ms2+12WgrRNQ1DEKN2OnI5vNtxHOpiqDyQZg1kSUgX8zGl45Rkv141MKluVigWWbx3L5kE9RXja+swoyhKiT4AxDHr6+tpO0i90cAWvVpjYkXZG1X1Mr5SAxvyhg1EjVBO3lBVNU3VdixroLF99tlnPPnkk3uOJPsdVfSwIlLo6g0dBqZhoGlaXyOTo4g6nQ7NZhPXdZOUdblMtVrd1rM5CJqmMTU5iQKsrq0lkah4EHiirrV1+InjLJdKaCQkLMlazr5PVVUKxSJrKyu0xaSaEb5aRJ6HIr8nRcF1XdrtNpVymTCKaDSbRGFItVKhUq1uu+cHKsXs4Rgk52F2ZiYdrdVstdL7t1/Aura+Tqvd5vChQ3s53b6QwdvntWd5lLtmjHo4CzsFwFLasiVUk6IoShnIexFZqNVqlDJTU2BrrFrv9dVFH7Vk8rbkajPzvpjkOeQ6Dmurq195APy1VfqJPI9Y9OIhape2EC3wfD9l05lCf7QfUqeZYYQOa2BxHGOJYa5SzUKublzXxRNzJmUPp2kYGLrO2vo6nU5neAOL42Q+nG3j2DaO2Lacu2fZNrFIZ8i/SeHkGHj7rbeS+ZVCWi4dLCv+BonQQrVapVQsJseay6XTV7quF92RsTSyTqeD53nogojji6kOsuUml8slmrIZBuJeek5N02RyYoLV9XVW19aYnpxMesYGbEPTNMoiknVdl1a7TV4M0UWcgy6Cm9WVlaFZzSN8MZDBr1xZRmFIo15PBEMKBRzHIWeaCTFvyFVTPw7CTpDzZCulEqZhYBoGxUIBx/NwXZeOZSX9n7qepPVF/eyzCxd46qmnth/XgCxTGIaJLJ1l4Yj5mIEQZ/B8Px3yHEM6GSgUTiwG3nnnna6ZtHK0ni7+JmUjx2o18rkcRi6HKWqUvei1b9MwcEQAbBhG0mUgBeiFI9INg3w+n0jqic9LLe5hMTE+ThAEbNbr6CJDIIc39F5HGQTrhoHV6SR9sZ5HQQrHi2stBQ0mJicZ65mR+mXia/kUiaKIyHFSZ+mLZua2ZZHL58mbJoVCIX19J0gj3auBSSHxYo+gupzoURRjvDzP63KeZz/9lOPHj6c3hy8mwzebzTSlm/1xHQddSPHl8/m0tiJHCCmKQr5QSATShRFJh3j33j2OHj2ajO6JkvE9UmwgFKO5giDAcV3azWY6uNVxHGIRQebz+eSa5nKY+TzlUomyqOFKgw2jiI3NzUQCUDhJqSGr93G86bXfpc6SRaFQYHxsjM16nY1GI93vTt+rFN+W19L3/a2HrjDE5cVFJqemGN9hYsoIXyxi1016qBUl6WW2LNrtNl4QpHUxU9eHCrKkcsxeShSRIO1pqoqZXS2Je0SucKTzsGwby7ZpNBp02m3m5+fT+7gjWLeSRJS1Y/nMME1zy6ZEcCqfIYZhJAGcDHI1LWlHUVUWFhY4dPhwlyOVwXEkRmE5nkfgeayvreE4Dh3LwvM8TF3fsudCIQ1iq9UqlXI5WV2SBJtWq0UgFh0AmlAsMwyjb8AiU8g7cT+yUBSFqclJllZWWFlbS0f87dQep6sqlXIZx3XTdHkhn08XRJqmYXc6rK6uUi6Xv7IA+GvpMGPPS0dnxUJZp91qoagqExMTicrGEAbTu1pK/rj7AzwIQzq2nbA6lf6DadOVpWkiJ6TcvXuXVqvF6uoqt+7cwep00vpqtVqlUCwm6WN5Y2dWZr06jpDcYI1Gg4JwmP2wm+i4rPeVSyUMw0h7MYMgwBUrNGnwrU6HO+IcLMtKon5hbLphMDkxwdTkJIVCYccHlhSIVtjSfx0Gsi7d6XQoFgq7pq4UEoaeViwm0+5dN/msYD+qmkbgOKwLI3uQ8WgjfD6ktUuRinVsm3azSeD75AsFJkU6fih7ljVAqQA1ZCajY1lEcZwEnQPeLwPhQqGA53lsbm5y+fJlCoUC7773Hp12G9txyOVylMtlKoKBK+1ZyvpJG+sHOYqs32B1Wd/bt4s9t0SJITsQPgpDXM9LnLbr4grh9c3NTe7evZsykUuijquJgH9ubo5atZr2sQ6CnAK1l5WmpmlMTkywvLJCo9lMW7523I8IYAxdxxKr9EgEHpB0MawuLzP1FQbAX1uHKWsd9Xqdjph8npfU5AcomqfqOkM8vDuisTpfLG6TeIPECW1ubrK2usr6xgabm5sJEyyOqVQqTExOcqBQIC/G5chitiSw6Jn0qZyk3s8BRZkHxIMi27eZ/EpSYjFJ+kUVUXdYLjM2MZEeq6qqeJ6Hbdu0223qm5tcXVvjEzGQe3JyksmJCSanphgbG+s6xmz9eBjRAXmucRwzXqvhuS7NVmtoMXVFVdMUmiXqmkUhdVbI56nX60y0Wkw8oJbvCJ8DQZDe277nsbG+nmQoTJPSkIOfJRSETYggNlbVXYMxT7C2C0Kjth9arRYbGxusra+zsbaWjAbM55PV5dwcZTFEIJ/LpfdyjBBCELYsJxntRNKLouihEX5SiABYU1VyIrAtFgpUoogpMVtS2qDjOCnnYHV1lTt37mA7DmPVKhOTk0xNTiZjCnta51RFwQvDoQPgGNL5vdVKhY16nciyhlJTQqy2i2LikSv64eVEI1us8L+qAPhr5zAjMTUERaHZaNBqNCiWSumE870sxdPaZZY4IlUsBnzptuPgB0EyMVy8z3Yc1tbWWN/YYGN9nVarRa1WY2JigmPHjzMxPk4cx/zLP/xDXn/99VTPViIMQ4IwJBDDp1MVHWl8ol6XalaKVGwYBEm6JXOjZcWSgXQgrpQETGXkhCHJFBNs1SLCDCNX9ngauo4i9ivroFlIQexypYLnuqyvr7O2tsadO3dodzqMjY0lTlT8yFWzTNkODFTieEuyjCQ9NDExwf3FRVrtNmNDOE1pyIZhUFRVrE6HjmWlk1I8kS7zPG/H4bcjPHxEgskcBAGrq6uEcczU2BhLKytb38WQTiTqeW9K6htwb8VxTLvdTvSGC4VUom19fT1xjuIe1nWdyclJJiYnOXbsGLVqlbNnz2Ls38/Jkye3bTMMQ3wxbzKSdp1hbMvavrRn+dt2HFQhuJJVBFIUJVUFCsSkHqBLP1lOFrFtO80SIWw5yy6VmZW8eE5qur4tUxNFEU0hUp8zTer1Omtra9y6c4ePPv4YwzBSO56anNwqaSkKKgwMgOV3IYMagGq1mgq0VyqVXe1PYes5VczncTwP3/OIooiSyLQ163VKpRKTQpv6y8TXzmHGgq3WbreTdGSxyOTkJKurq+nKbFgoA6KhLvZsJq0TCoF2VVHY3Nzkzp07LCwtoUCympqc5MAzzzA2NobecxwXLl7k4P7925wlJOkJTdOSUVbSAMSNLmuNkVT6j6JkvBWkpBbdMPAGPFRau7BApeCyHBqble+SxiUhjbIfTNPEFk6nUChw4MABDhw4ACRGvrGxwfr6OlevXuXMmTOEQcAnn3zCkSNHGO+zspMPg36p6Hw+T6lQoN5sYtl2Ol9vJ8gtaKpKqVTCtm1s2yYSYs5Wp0PTNNOoe4QvHlEUEQuC2Pr6OmEQMDUzk3zfUZSWPIaCDHJ7iWriXu4XBHdsm0jc+5cvX+bOnTs0Wi1qlQrjExMcOHiQZ559dkvnWcALAm7fucOPf/zjbYehCDvSBDkoe65RlIwJDIU9x+LvYRgi50Wapkm/7mDp8nayZxlEq5qGrqoouk5OONss5wF2tmWZVZKjv6RzlGi32+kC4erVq6lgQaVcZm5uLi1DZZE68T6YGBuj1WpR39zcxgnpe56IlaxI0aqqmgihiFm7spTkDjm792Hi6+cwgwDHtmk2Gpi5HBOTkyhKMnld34ERu31Dg1eRkEnRirSO63ncunWLhYUFGvU6Y+PjTE5O8tyzz7Jvfn7HVEoQRVy/fp3vf//7Ox9TxoFnV3KDpq93hFGO1WpdsljZm7Us6rlZZQ6ULY3aQDCNs0xRacg7HV8v5CQBx3G2tfDous7MzAwzMzOsr6/z7rvvEgO5fJ6PP/kE13WZm51lbn4+ldGKMtehH6qVCi2h9mIKctFOyK5iVVWlWCxii1pOXkxP8Uqlr8TIvq2IxQqs0WjgeR7jk5MU8nla7TYhDC0xmd6Tu9XN5T0QRaysrXHz5k3WNzYIw5D52VkOHT7MzMwM1V0GRN++eZO52dm+cyQHQWaGNE0j7hM0y/F4staZXRlnnU25XN5my7A1CF7uJzstZZCQ+U7PPzn6S7baZFEulymXyxw+fJiPPvoI3/cplcssLi3x6blz1CoVZmZn2bdvH+VSiYidS126kNHrWBatTodapTLwvVuHr6T1UlNMnunYdqrWFIYhLTES7svE18phRkGAa9uJsK+gTmsiheoJ0fOhkElp7AS70+H+wgKLi4usbWxQKZc5cOAAr7zySqIMIia+74b79+5RExqXwxxXLwY5Dclq24n8Mmwev59Cyrb97lKbMIWReZ7X90a9f/8+Z8+e5bnnnuP999/n1KlTnDp1CqvTYWFhgUuXL/Pue+8xMz3Nvvn5JFodcMMrmsZYtYojxCmGmiUqVi4yYCjk84RhiO046I0GE1NTCZlp5DC/FISi19Jx3YR5LaTRAt+HOE4C4IeEKAxZXV1lYWGB+wsLxEoiivHC888nxCJFYX1zc1cpvCiOuXbtGi+89NIDHccgxyF7hfU+KVL5OrDzoGWB3qdFv5LHrmIOmoah63i+35dQ6Ps+7777LqZpsv/AAfL5PI899lh6ne/dv88vfvELDNNkfn6effv2MT4+3vdZJm0xDkPa7TYF0Qqz2zlmmfK6EGRvdzp0bBvXttE0LRFW+BIZs18rh+m22wmjLQwpFYvpg83zPOI4Hvhw3QviKGJhYYEbN27QaDaZn5vj+PHjnDx5EkVVE6endLehyLRO3+0BV69e5ameWsfQx7ODk8o28T8o+m1dITM2aw+QqSi73iZeWsV55yb+Qh3F0Fn90Qy3W6u8/vrr5ERfVXIAMflikaPHj3P02DFs22Z5aYmFhQU+OXuWudlZjh47xtTUVJexSQasWalQb7XoWFaqGzwICqDqetpTpigKhUKBTrtNq9XCse20J+xzzRcdYVeEQUC7XscVwVWW2S6nWgz9HchUbJ+UbLvd5uaNG9y+c4dyucy+uTlee/VVwjiZXGLmclsDCNid9Le0vIyRyzH5gASxQa0X6SzOhyVCkkE/hzkMuTGXy+G7HtatVaILyzgf3QUvIDgxzrl5m7n5eZ4+fTqpawqnpKgq0zMzTM3M8J3vfIeNjQ0WFhf54IMPiOOYo0ePcuTw4e28C0WhUqvRaDbZqNeZmZoa7vvPrJR1XSdvmjiex/rqKsVyGdu2qQyxYn1Y+No4TM916TQaxFGEmcsl6RBhILKpd6jV1CBKd6fDzZs3uXXrFpVKhaPHjrFv3z5UVU2b38uZxukYtoSeo6iv6DPA+sYGnu8zNzu766HtpS8x2W30hUVPezmWyPIIbqzhXlvFvrlCu97EtGP0MLlON+YDWjfv8P2/8Oco1SrpTENZo0wfcopCLp/n4OHDHDx8mMD3uX3nDp+cPUscRRw9epTDhw51GVupXMZ2XeqNRjpcdsfz6jk3BdIB03dv3eL4E0/gOA7FIUc6jfBgaAnZO0307JqZACoIgqFWUttSsZn63MLCAjdu3qTRaHD40CHefPPNROs5jqk3GuhxTE6snBS2Miq73fNXr13jhBjHN9SxZf8kp6H0wcOSuOx79P3OSVXT+cG97w0WG3jX1/CurdBYWCOyPQqiGaBVhku5VQ6v1Tj949NAkhGQwilx1y5UxicmGJ+Y4NTJk2xsbHDz1i3+5c9+xtzcHEePHk1X94pg8o7XaqxvbNBotdL+zJ2gCIav/A5NMf6v0WhQ2dhIZ6d+WfhaOMw4jmmtrQGkzfmGaaY3gu/7RHHcl1DTs6Gu/0ZRxOLCAtdv3qRer3PowAHeeOONZKRP5jOWZaGLGp2EZI/uthK7LgxsGEPoKwTfLzWaee3zroQGHXs/enj2+CLbw/7lNdyLSwT3613vU0oKvhGjxHDpieSB9PR5UI6swOtlXM9L9WR7VwSqqhIGASgKumFw/Phxjh87xvrGBjdv3uTixYvMz89z4MCBRJxCUZgYG2N5ZYX1zU1mp6d3PWepWJStaRYKBSzHYWlxkUKhMHKYXyA6rRa+ZSXKUGHY1aYQQyowsRfEJEHvrZs3udkn6JVwPI8wDBPnmYGs//Wt3Qs0mk2ajQb7X3119wPqY7M7tVw8jBaxQfvuS27s+b93bQX77Rt411eJrS1pPMMAW4dIhc0aXDsOj12HSSeRtYtJVJI0oU7UexxpEKIoTAimse953L59m48+/hhFURLi39gYhhCcKRWLiTCBqOfueKpxjCacphzPlsvlCMOQhfv3KVUq+L7/pbWYfC0cZrvZJPJ9coaB43ndfUCZlcKwN1sYRenDt1gscvToUV599dW+n3eEDF2/KCUr4t6rS0scJw/g5WWeefbZoY5LPsi3NjHYWUZRMtLscxvYAMKEItpQuv8oDC+IqP/jXxIsNbdtTgFMH5p5uPQ4VJoxx24kRCR1X5UoTjRmd1oJps40s1/J1PNclzu3b/Pp2bOgKJw8dYr9+/ZRq9XYbDSwLGvHh61k2KmK0jX/TxcU+vXVVaZnZhgfHx+lZb8ARFGEJZSaIGFvpg8z4axi2JNweKPZ5ML58yyvrfUPeiXiGNuyUhnLXsipGSnhr+ez169f5+jRo0OVQbKr1uw2BiGKorTV5HNhBx5El3Zs5jXn47s0/5v3+35O90E1VO7tj1iegafOR5Q7EE+baXCxkz1nA2AJwzQ58dhjnDhxgvX1dW7evMmFzz5j3/79nDp1irFaDcd12Ww2mR+GWKVsCaHIcy0KvdqlxUXGx8e/PQ4ziiKsVgtTRKNdBgZJPZHhUhlxHHPr9m0uXbxIpVrltddeo7rDsj+OImzL2r5PuWu2DEP+P/2sonDr1i3279+faEPu4Pyy59J1w+9kYDIifUgG1m+8Vq9SinSi3q31vs5Sbs7WYq6eiJlejDh0N3nw6BMlzCMJNT0Igh0JHf32LWHmcpx4/HEOHDrE/fv3uXjhAleuXOGpJ59E13Wa7Xai2DLgoZb2rfW5tqZh4DgOK0ItZGgS2QhDo91sQhiiG0ZC9pErPbEKkYHgrg4zTtSzLl64wPLqKk889hjPPv/8joGYI5rcB6Xoeldi2bvPDwJu377NT3/60+FsOdng7u8RiB+WaMGAY9sWjGf+bb9zY4fNxdyfg81SxMlPY/IuxApU/sLp9D1BEOzokLYFwOlBKUxOTTE5OZn2bP/hz37G0SNHOHDgAC2h37sTNyGtCfd5fuVzOZqNBvV6nUql8vmDkSHwlTvMVquFFkVohoEjZ05CV4F/t7pDDNy9c4eLFy+Sz+d54aWXmJqYIGJA+4SA47oJOWDAg3M3daC7d+7wwgsvbGegiuPvJ27es4PBKZyM4s4Xhn7HDaj5LePI9rfFwOYYXHkMDt1TKW3G6adKf36L9LRrjUpRUEVNZCDimKmpKY4dOcL9hQXOnTuHbhjMzs1RFuPd+m9aSWn6iqoSZ+o4MjJtNptsbm6OHOZDRhiGWO02RV1PVyXpg1bc65L8stNd3bEsLl68yOLCAieOH+e5555L07uDEIseal1oHPeDCgPtbWFxkemZma4UYYwIIpX+8pgqWzaTChbskDH6qjIaSq7bnhObhkCHK08k6dgnbqjoUoB9qkzu1JZEn+95O9rzTgGw3Kdpmpw8dYonnnySS5cu8au332ZudpYojinsEABLlSKphpZ9FhuGgWVZbGxsMNPz3X1R+EodZhAEWK0WZcPA97yBK71BN2IMLC4s8Nn58+iGwbPPPcfMkI3pcZTMcDR3IJLIKLifw9zc3CSK476ahtmIKCUbsNWcnD2vQUhJAp+3htlndZweZ+YGjMXqMo5jtP019Cdn8D5b6hoFvzQDdw7ByUtQcGIsQyXUQsxCnvzT+9Pt+r6/uz5lstOBRiYL/SgK+/fvZ9++fdy9d48Ln33GwsIC33n66USFpM/5SiefNkD3GFlbKJvMzc2Nppg8RMjgV83lCD0vbSNJv+eM4+lnz67rcvHiRW7fvs3x48f5yU9/moiyk35o4L5tx0mkKXcSuZAqX31w584dDvZMGJL3X1/Wa5+Sxk4rHClf93kxcIiE6FvsTRHHQPFHj+FcWiSO4uQSKuAZcPEpKFlw/DrYBQXfUNCDmML3uklPfhDsbM+yPjzg2mZVxYqFAt997jk6jz/O+fPnOffJJ2weOsSpAfNGpXQosI3IpCgKxVKJ9dVVNmdnmd9Fh/dh4Cst4rTbbXSR2w+iqLt2mfni+zlM27Z55623+Oyzzzh1+jRvvvnm0M4StgysV+UjC1nD7Hcj3Ll7l0MHD+66n1TKju3p1SjzcM86LCCVB3xY2pNyLdi1P/kj1ICkKlAcx9T+Zy+glrbqQLcOwf198J1zUGmDFoAGBLpC/qUjoGWIF0IsYEeIVebA4+35zhVF4dDBg7z55puMjY/z7pkzfHL27LZVR0x3I/e2gENIbK0sL7OxsbHzMY4wNIIgwG42KYjZhV2rywzSezBr38CtW7f4wz/8QwB+8pOfcOrkyW5nSf+gD7ZmOe7GopYEvl5rdhyHtfX1XYXPu45FEF6SE9iSpexdcab/fkgrzDjZ+dZ+6D6frB3L54t+eJLiD59IL7lVgHNPw8QGnLieXFc9iIk1BXI6+e9uBQ6hUCratW9yl2Cht6xWKpV4+eWXOf3002xubPCzP/oj1tbXB59zcnLbgibTNLEti+WlpT11IDwovrLwOo5jHMuiZBjprEUjQz2n52GZfg64c+sW586f59ixY7z0yitoe3QqkVhd5kxz15VQP4X+KI65e+cOb7z55p72m0VMtwNN/yVWfWGGoi5TvPJ1EKmibJSbvWby3xnjUTLbkJ/Jqml0wQto/LcfENkekQJXT4BnwjPnQA+3jlePwNUV8i8f6fq4Y9tMDKHzmNaI+7wWi0CqF4VCgSMHDzIxMcHy4iI//6M/4vkXXthabfZG4JlrIU4a0zRprK/TbreZmZnZ9ThH2B2O46CJNHgYRVSy6e7MfS4b+OVfbNvm448+wnYcvve971HbSfxjQAnDlgLdu0goqqqaqsTomWDt3r177N+3b+89kvJ4REpS6XppK8OU7QvuZ69ZVve21zP3bTbIJe6/wpWtLdkg37u4iP1n1wCoV+Hy43DsFkyvbX1WD0AxFPRn93WVZBzbTlr8huBnDBy0IGyyX/A/NzeHpml0LIv3zpzhwL59nDp9Gl3TkuC3t+asbG8Nyudy1Dc3sW37C2e/f2UrzCAIiMUkgzAMu2WyemtromBu2zbvvP02V69d4/XvfY+nnnxyR2c56BUpYDyMRqmmadtWMSsrKxSKxYG1z6GOZ4doSJITpDakwlZEK51Ml3OU2+r9N6Si7oOOJ878GyBq2mz841/iXVrC1+H8qeRNpz7bcpYSegC5E9NE5e6VhCWEz3eFSOX0w6AJLpAIOhu6zokTJzj99NO8d+YMZ8+exRcanr3n2G87uqaxsb7+pUSl3wZ4rouuqgnhS1W3Vno911cGb4qqcvvWLX7+858zNj7OD37wg52d5QCEUYRj2+TFNIudIB1m70P99p07HBwiW9SLYcL0rJOU+0/tObON1Kb72LD8d9omtYcFgv32deq/8y6xH7A8DVceh6cudztLADUGLVZQnt3X9XfLssgP6YSygVAWaf9mn+POiVaTYqHAD954A8d1+fnPf87q2lpKENsRoj5qWRadTmeo4/w8+Mocpuu6aJKcoShJ3yX0vUBRHLOyusrPf/5zamNj/PCHP+w7U64veg1WpG/kQObdoPWJau/cuTNUOvbzIBqwwtozBtU8BLIU+2CxycY//BOChTp2Hj49DbUGPHGt/42ihlB47lA6qUGiY9sUPmekF9Hf0YEYwlsoYLsuk5OT/Lkf/QjHdfnDP/zDgWmdLmNVkskmjWYT13U/13GOkDhB17bRpVTZDsEvJGS7jz78kKvXrvG973+fp556aign0O8druMQC+LIbtDEHM0oEwC32m0sy2J6iP7enTAMH+Ghj/bqQVcmLoxo//NztP7ZWSDm9gG4tx9On4dqq//ni/PjaNNlwsz1GXb4gTiAgVwTGHz+1UoFRVWxXJcXX3yRU6dO8e4773D27NltOrkK3UTIOI7RNS0RvvlGO0zbxsxoAe7ELnv/zBmuX7+e6I/OzHSlF3dC10pM7td1E2HwIWX2FCEULvcWBAELCwvppI4HxY4rm3irSXeoY3zQ/WQ+611eYvMf/QlRw6ZZhnOn4cACHL6bvJ57evv56lNlyidmCcKwK2q3LWt44ep+q0wRZe/0gKlWq6gkDzzdNHnuu9/l1OnTvPvee1y+dKnrvPutMk3DwO50vhQj+6bD932UTI+luUPwu7iwwNlPP6VjWRw/cYL8Xsat9d4PcTLj0czlhgp+FVXdxkm4e+cO+w8c+FwtCbu1oaT722kfQ6ymZPlkp4wRQOQFNH7vXaxfXSUCLp+Axhh85zwUHdBmq2jj27NjlZcTARYvEwBbnc6e2Kf9RBR2O27DMCiXSrhiGtLc/Dw/+rVfw3Fd/vjnP6djbZ/vki0rSY3ejdXVLzxj9JXUMOM4xnNdiopC3FtQzlxU3/N49913KZVKHDh0CBX45OxZLMtianqa+bk5ZmdndyaYZL/AOJltaYhRW8NApnzDKEJXVRYXF5mYmPjcAt6pkWVqGWkLhzBqZQdWX7od+tcAMztKSQL9bldFUei8e5Pm//gBcRizNgXXjyaryrE6KLpG7X/xEuapeTo/q9D5o4vJBzWV6r/1XVTTRHFdfN9PJyAYhrFrbXgnpHJ6OzxgNE2jXKlQbzTSevS++XkmJiZ461e/wrJtnnn22dTpKohVq7gmuq4T+D6tVusrmav3TUKaLRLElkGp0Xt373Lu3DmOHj1KsVhkZWmJ8+fOUSwUmJ2bY25+nvGxsaFXYo7QmB5qMDHJva6parrCjIFbd+7w0oMKrdPNNM/+Pa0xSh4BgnQ0iEk6gJDU9Z4siUjYde+VCtsu9X/6Nu6tNQIDLj4BZgCnP0vSruYTc4z9uy8Rth3q/+Rtwo1kuIT55ByFZw8QWRau75MXzydLDJgeGn0Ys8M4sUq5TKfTYbPRYGpiAtM0efGFF7h67Rp/+qd/ymuvvsrY2Fj6fq1HtcnQdRrN5sDBEA8LX5nDVMTwUwX6NrnblsVbb73F9MwM+/fvp95ocPTIEU6dPo1lWSwKAe+zZ89SqVSYnZ1lbm4uUcwfsF/P9wmjiMIu432yUDUtqfUJPdnbd+5wqId+vuv5JiedOu8sgw75moSiPNQUjkx5p8eRPa4oov0HF2j90QWI4e7+mOVZhdOfQbkDSiXH2F99Df3AGAClnzxF7ul5guUW5vFp1EoSecqUSE7UEvaajlV6CAPDyoiVikUa9TpWp5PWwAv5PG+8+SZn3n2Xd999l5defDENjrIELlkfbjb7CzSMMDyiKEKJk8HKuexqJFNnv3r1KtcE96DZaFCu1XjqySeJooi1tTUWl5b46MMP01Fws7OzzMzO7jgCzHWcVKt2WKiZCRjrGxsoisJ45kE8DKQ9K9IZ9misSsgMl1QXelg6snKlnP0bQLDcZOP/9kvCTQs7DxeehIlNOHoHlBgKrx6l/K8/C6qClisz+R/+CPfKKkpOwzwxnRLiPN9PiFG6jm1ZzM/N7ek4e1eZ4RAMYU1VKRSLNNvtrgkkJ06coFgo8NZbb/HCiy8yK0h6MriQV9TQdSzbJgiCb57DBFDjGD8IKBQKyQ2QSVs0Gg3efustTpw4wWOPPUa90QC2mJPFQoFjR49y7MgRwjhmfX2dpcVFPvrwQxzXZU6sPGdmZ9ENI3VOrhgOvasmbfY4xYM1jCJC12VtbY0XX3xx4Pt7KfMp5N/EzbST8WT7lh4K+tUV/IDWf/cR9sd3iRW4dhRaJYXvnEuk79TZMmP/y9fRJkrpd6MoCsa+cYx9410O3zBNPMtKB3DvZY7g1iFuGZmsoQxaqaQPLCURIuhYVpeR6brOq6+9xkcffcSv/uzPePW118jlctsYuZqq0m4NKOiMMDyiCD8IMA1jq8E9EyB+8umnrK2u8oMf/IBCoUCz2Uzk1EiCwumpqaSG+PTTWJ0OS8vL3Lt3j48/+YRqtZrMUp2b61LtCnyfIAh2nWDTCzkSCuDu3bsDyT7yYbyrPcOOGrLyWjwMW0730Gdb/rUV6v/1e0Rth1YZzj8GB+/DvqXk9eKvP03pzRPdn80Z5J/e18XCN3Qdha2JMpZlDV/DzBxf1tYi4Xx3Oq9IkDDbYmJVrVpNj2vf/v3kcjnOnDnD6VOnOHzkSFrLTANgTcNvt/F9f+B+Hga+MocZBgFxGG6TwVtbXeXd997j2WeeSeuEkgLuB0Ey7Tvzfk1RmJmeTnown36ajmWxtLzM3bt3+fjjj6mIYafT09Ppl7KXmzedXhJFLC0uMjMzszWIuZ8xDbHt3RIUD1Plp199JW671P/rd/BvrhPqcOE4xFHM0+dBi8A4NkXtN19FLWRUWmD7qliw/kzDwFYUAt/HfhADy+wDtkgZ/VbYMXRF9KVSiY5lYTsOlUzmQFFVnn/+eS589hl/+qd/yuuvvUapXO5KoamqOqphPgxEEaHvo+bziUi3LCtEEWfOnMHzPN544400UNV1nSij85v97ovFYhIMHz1KEEWsr62xtLTEmfffxw8CpqammJubo1gsJvfeHlcTikgXxiQp4u+/8QbQkwUSGMTs7MVAMQGB6CHK4sH20orzwS2a/8PHEEZsTMGVIzEnrsLkJqCrVP/tF8g/04dz0dOaIp8TppgFHOfzD5QxgsR2w3irx3tQjTkmCZAVQcTL53JYtk2lXE7SruKYJqem+N73v887b7+N7Tg8+eSTW05ZpIHDMKTT6XSlbh82vpqUbBSl9HPDNFMDazWbvPvee7z80ktdrDVN09ILMjCSE1FeqVjk+NGjHBcGt7qywsLiIu+99x6u53Fg3z7m5ueZmZnZUyonCEMWFheZ37dvx0hvN+xlqslDkdKKu3U7w7U29X/6FuFqGycHF5+EUh2OXAdiyH33ILW/9Dzou+xbppfFceqahuv7yYDYB5Sck2nZQSmcmO1Sh6ZpJqlgYWS96e2Tp0+Ty+d56513+OEPfpCk/6UohKriOs6XPoT2m4YoCAjCsDtzE8d89PHHEEW8/vrrXSo3mhAqgT7BY2a1pqsqszMzaRquLQa+37p1i+WVFcZqNfbv38/s7CzVanUo25L31fr6elIHL5cf2J7lA3u3T0WCyfm50eMw4zjG+sNLdH52gZhEWGRhTuHUZwrFdoxSNBn7K69iHBmuRh9nVpmOomDZNijKgw36VpKRXoFwhr0qRzFbtdjs91YslbBdF9txtpSiBCqVCm+++SZ/9qtfkcvlOHr0aHr9VcF5aDWbsH8/XxS+GocZhoS+T6FSSdMenufx1ttv852nn95G8ZZ1xCAM9zT0WFdV5ubmmJqa4uDBg3i+T7vZ5NbNm3z44YeMj48zK+olWYPrKtpHEZqm4fk+y8vLPPvcc5/r3LdNPemDh5mSzUa//q116r/zNnHHo11KnOX8IszfUwhjKP74Kco/fvKBAgHDMPBtm2arxczs7LY01DDfm9Sk3JbCiWMiBpMHSqUSG5ubabtQL46fOEG73ebM++/z6iuvpOcnGYHhLimjEXZGIFpzsuzYa9eu0ajXefONN7Y9LDURXO0Y/GYh3lculTjx2GPMz8/T7nTwPY+VlRXefecdojhOeQy9WSCZVYgzzOvFxUXmPqeU2rCMzKHF3Ifcn6IoxEFI63/4COfDO0QK3DwKzQp857yC3olRpsuM/dXX0KaG52tI6CItW9/cpFapdNny0M9fRUlFLGLoWmH2C3wlCvk8uqrSsaykz73nGufyeV555RX+7Je/pFKpMDk52cWYtb7gjNFX8pSQ6RhpRjFw5swZ9u3b15dQI7/AIAi2pU26kCEZpH8imecWxzGTExPMzsxw/MQJgiBgdXWV5aUl3nn7bQBmZmaYnZtjenp66wEqKMvLKytUq9WHUlAeJoUDDyklS3IjOZ/co/Xfvk8cRGyMJ+o9x2/A1DpEmkr1Lz1H/vm9kZmy0HU9rT/XRK2p64GiKKhs19PtgogSZQonrYHs8mCS00s6ltVNOsngO9/5Dm+//XYipXjqVLLdKIIoSkhDXyBR4JuOOAy7WM1LKytcvnKFH/zgB30DEU3XifYS/PYw3V0RGE1PTbFv3z7iOKbdbrO0tMT169f54IMPGB8fZ2Z2lrnZ2STzII5NrvSWlpbS++BBoagqcTa13AfpKuohlVcAYtun8Xtn8K+vEmpw6TGI1WQmrR6CcmySyr/3Spe05V6gKAqGrlOv16kKhmyvLaer3J22A1216uyqcicUBfnH87y+q9tyuczzzz/Pe2fO8IM336RQLKZteK5tD32eD4KvxGGGvo8u+hsBzp49C6rK6dOn+75fE6ywQBrmbuhxnI7romXVR0ge8HPz88zNzfGdOKbVbLK0vMy1a9f44P33mZicTCNWwzBYW1t7KDJquzlLeIg1DxJnY71zg/APLgOwOAd3D8BTF6HaBiVvMP7vvYxyeOxz7UfXNALfT2j+/ZyWWCVmU8T9asCRSOHsNuw3C1VVKfVh2GWhqCovvvgif/qnf0qlUuHAgQOJILau0+l0GJ+Y2Ospj8DWvaqpKoHv4zgOH77/Pi+//PJAQo5sCRgkf7gTfDFhqJQJcBRFoVKpUKlUOH7iBL7nsba6ytLSEr+6ehVNVZkVRMDp6WnCMKT5sNqJVDWd89kPD5PxHgNhw2bzv3+PaLmNayYC6uU2HLuRtI3knz1I4S89S/w5d6cbBq12m4l+dpGtfcpsDf3T65FY1UdDOEqJUqlEq92mY9vUBqSDZ2ZnOXHiBO+++y5vfP/7SeqX5Fn/ReIrcZiBiBxi4MaNGywvL/PDH/5wx5tK13XCvTKgFAXf8wiCoEvGLtvPJFGpVqlUqzz22GP4vs/qygpLy8tcvXoVRaxeHn/8ccLdlPsfAnrJBr0TRboo20JeME35ZP4dBwHWH18i+uA+JnDrMGxMJA3MeQfUiWKStpmtblPr2TMUBcdxKO3WsqP06UXLOM5ItBvtFXKgrGTY9YOZy/HKK6/wy1/+kkKhgKbrqJo2Ysp+DsgVlqbr2I7DO2+/zVNPPcXUDoMQNE0jFgGwMazDFPeH47qoIusD/W3ZMAzm9+1jft8+iGMarRbLi4tcvXKF98+cwcznyeVySZ1sDy1mfbHLvZpNF259JN5my9KxZnVnxT/Sf/v36jT/3x9QWvFoF+HSUzC3BPvvJw6r+GtPUPrpSSK2VnYPCkPX6VjW7pKBmeufBsKZ16IwHKqfPAtN0yjk89iClzAo0/bYiRM0Gw0++vhjnnjyyYQp67pfKCfhK0vJGqaJ53mcO3++i0E3CJqmPZCMmef7qKqKKdpLhvniDMNg3/797Nu/H+KYxcVFfvXOOyzcv8+Vy5cTpt7sLLNzcw80UzGdJhBF3ZMFoogoTgbnSnbZbsfbarf7/j12A9p/cI7m8iZ6IUnBBjo8eTmRtOPwGNV/9yXUanHnNPceYHU6lEslwjAcXsha1mXENQiCYJv81TAwDIN8Po9tWTsaWaVa5emnn+bc+fM8+9xzaF9C3eObDFm/zOfzXL92jbHxcY4dO7bjZwzDQBX1470Q76Iowg/DNIORjn7a6d5VFGrVKrVqlcefeALf9/nlL39JpOv8yZ/8CaZpMjc3x9zsLJOTk3sOhiPhFLqmhGTs2vM8OpaVCr4PsmaZbWsOCN78a2ts/tF5gjiiNZsEv4fuwuQ6BKZC9S9+h8KLR5JTfoCAsxeaqmJ1OsNpQkNXICydp2zf2bOoPUna1XIcOsKeB+3zueee449+/nPW1tYYHx8nInkOVYeVTt0jvnSHGYlxMYZhcP3aNaanpoYSXc7lcnQsa89pHMdxMMRqVhHp0GwEtKujUBLR97nZWU6fPo1pGKyI1efFS5e2GVy2uB2GYXq+QRgShWFCMumTwlEgTUWqioJmmkkQoWRE1zPHKv9dKha7otUYiJoOjf/2Y+KVJnFV4eYRyLtw4oZCrEJ8cgrjz5/EUkIQBhqEYaLSIpRapGLLXsgK7XabcqVCEARDG0lvUBBE0c7Dp3dAuVzGcRwcx9lxasGhw4e5fPUqGxsbTE5O4nzBdY9vMuRKJo5j7ty9yw9/8INdP2OaJqqi4LjungJOz/MgihJ73kGcfyfomka73ea7zz/P1NQUrVaL5aUlLly4QKvVYnp6Ok3fZu+hOE6EGeRPJHpPfc/rL1ogV4aKgqZp6WSkrB33O/5isZjasbQL+92bOH94AcWExpTC2hQcvaVQ6oBf1qj8hdOEhyfT4DmME2EYNWPHqqYlqmVDXrOOZaU9mXsJqGXAIIUsYnigjJxpmuialgbAg6BqGk888QSXL1/m5ZdfBpIJK98YhxkLFqQfx9y/f58XXnxx9yV0HCekDGFkw0Q9cRzj+z5hHJM3jO7RO/I9Q94EC0tLzMzMJKndcpkDBw9y4OBB4jimXq+zvLTE+c8+o9VsMjExwcTUFBPj4109YqqSzH/M5XIpa05V1VQYIbsiiqIIXdeHGlVj9Cih+At1Wv/0bbSGjV2E24dgag2O3AaFZDhs6ddPp83CsYiGXd8nDAK8ngeAPEZZA5bOtB+azSbHZ2bwfH9nEo1MQ/VEwnEUEQVBog0qmpL3EisXcjkUVcVx3R2vne/7HD92jCtXrjAxPt43gBlhOAS+j6Kq3Lp1i9nZ2aE1XU3TxHWcofcTxzGO66KI+7BXn3SgwEAPNut1coUC+XyeMIoYHx9nfHycJ596Ctd1WVlZYXFxkfPnz5PL5ZicnGRiYoJKpdJ1bqo4DkkiUrK2nEmjuq6LHHS80wBpaQtZmdA4jGj/fz/F/9V1TBLx9I3xZCZtwYlRakXGfvNVtNlKly0HIjAPwpCop4ylq2riSDUNXfz0u27NZpNKpYIiUucDn8/xVs+thDx3ucKU12ivOq/FYpF6s7mjf4jjmInJSRRgdXWVqenpL9Sev3SHKZUYrl27xuHDhynk8zi2TblSGfiZWFHI5XJoJCvG3RymXLW4ngdxnKZ7e7+wbD9TysTruXnCMGR9bY1Tp07hCVKL/HsQBBiGkfR1zs3heR6bGxtsbGxw7epVCoUCszMzzM3PMzU1lfaShrsILUsd2b3Cu7RE4/feI3YDGlW49DjMLSci6ooC5X/1GYrfP5G+P/toMwwjvdEiEdSEUUQo/u15XnI92eq71HUdTdeTKRBxTLPVYnx8PHG6vZmA3jpsH8gxarpoI0q1X/vVPfsgInGalpiP2LeXM050jKemp7l16xZLy8tUHmCs1AgJwjDEc13u3rnD97///VQicZgAeFMoeO2ErL15vk8+l+vbmrWthUneLz32vLi4mEq9SUUpmQEKwpBqrUapXObY8eO0Wy02Nje5du0atm0nq8+ZGebn5xNmpkjH7kROS2Ue97gajt2Axn/zPt5nC0QqXDkOdhGeuBpTcEDfP8bYX3kNdSx5FmbvdCMrCBPH6RBome2S11JC2rKuackqWFEShmytlqZWe9u85HVO9a/7IBClGVVJlNJkW09WrnMQFJI5lwpsEyXJwvN94iji5MmTfHruHJOTk13TaB42vnSHGQYBtmWxcP8+P/npTyGOk54q3x9cz4jjVDPS3YGckqYlxRfouS66YWwVnQd8sdkCe5fzJIlaarUahq7T7nRoNBpd6RIZaRqGQU3IeEHidDY3NlhaXubcuXPYlsXMzAxT09NMT08PXIE9yMw7APudG7T+P59AFLM6BTeOwolrkPMBQ6P2b79E7vS+vp/tjc7lqlLvfhOhEJyQDxhpdKqi4LkupmGQM82UaCW/T8mO3Q1dNY+enlgpnbfjVsSD2LJt/CDoq0MqU+KFfJ6TJ0/y4YcfcuTIkV2PbYT+CIKA6zducPzYMarVKg0hhl/ZIQAG0u/G87zu4QsC22xZ3Gtdk1AG2IgMstLtZN6/tLTE6dOnCaIIT7QuRJnVqiSc6LrO5MREem84jsPy0hLLy8tcuHCBYqnEzMwMMzMzyeScQXNdRRloL+njqGnT+Kdv49+v4+tJv7TpwWPXEiUu88k5av/uSyj57c9LGZAqmWeZpmnbSiSx4AuEQnQiyy7VVZV6o8HMzAyaquKLQEU+H4cJXmUm0RQBjiLYxFkS1I71ZyVR/tFVtWt6Std1iqJ0Bb9v3z6uXL3KwsICTz/zzK7H96D48leYnsfC0hJHjx4lJ2TuNNvGsqxd1TrMXI52H5JLr3FBYshhHFMSD+2+tOc+yDrPwPe5e/culVqNTqeTTGXQNIqFArphJBHZgBSUqqpMTk0xOTXFqVOncGybpcVFFpaW+OSTTyiVSolowtxcMqFBGFzUk2raDXEU0fmDC1i/uJzIfe2H5blkOkHOA3fSYOJ/+iq5w4NZi8M4s36GF0ZRanAry8uUymXa7Ta2beOHIdVyeagUnUTg+4lIReY76FqZxslQ7X4GKx8QMhBxHGebw4yiCNfz0EQ0PT05SaFYZHlpaehjHGELgajhLS8v88Jzz6EoCoVCgXang+f7fYl88pszczk0wazudZgxpClXCc/3u9ixwzIvpRVFQLvVYrPRQNE0fMvCjyIKhQL5XC4tNwyyu3w+z+EjRzh85AhRGLKxucnC/ft88skntNvttOdzdna2Kxjea601WGpQ/6/eJtqwcPLw2VMwuQGHb4NVUsg/e5Dav/ZdlAF2pWR+duyRFA7JyGTfpC0HQUCj0WD//v04rosrFh6mYQx9LkEQEMPW95U5nqwzHwT53eaEPF+/jJEn+uuL+TwxiUDJpZ7Rfg8bX7rDDMKQzY0Nnn32WSC5kIVSiXarhet520b1ZE/dNE1CUZvMftH9Vh6uSJ+mxriHL9r1fXyxElnf2OCJJ56gUq0meX/DoFQqpXXIYZEvFDh89CgHDx8mDMNENGF5mY8/+gjHcdKeT9kbNuy2m/+v93HP3iNS4Pox6JTh6U+TlWW0r0L133wa8+BwPYZ7PSdNVdFME0MweyfHx8nn87ieh9XpJGxXTUtFuXdynpIhbGZSP9kJJtBjaAOMQtO0JBPRh1Htum7SJyruiQiYnJxkTUx3fyhShN8iBEHA+vo6E2Nj6dBo0zTRLAur08Go1bbfT7JWZxjbmO/yG+11lpFgm3bNztzhHuj9nO95+EKoZGxsjGI+T84wklp3oZB+78Pe+6qmMTU1xfjEBCdPnaLdbrO8vNw9PUkQAfU9OBmAzf/iT4kdn2YFLj2RMGHnlgEFCm+coPzK8YHOEjLPyyGuTxaKkkjg6YaBY9s4ts3U1BSu42DZNu1WC0PX0YWT3WmGMZCy3WXddtA7I6Gk1rvalE4vn8thWVby/Wf6u2Va2RCBDnHMWK2GbVl9F1UPC1+6w3Rtm45ldTXEygeqbVlpPj1F5kvPCXad67rb+rB64bluwvLKPAT7za6DZKXkuS6ucJIKSR+SYRhYlsWB/fvRNA3f89LUUPbhrWQc9jBTSFRVZVqkZk+LcWVLS0vcu3+fjz/+mGKxyPz8PPv376fW76FDQggAcM/eI9AS41KjRO1DC8E4MUP+334Wl93FHmTaSKpx7IYu+rjY9vrGBk+fPk0ul6NWrabEjjAME+YqyYMmZxgYprntnHojUtjhWvZZbWa/13w+T7OHLOB5XhJoZQ09jhkfG+PCZ5+NHOYDII6TSUFZKUtFUZIAWPTEZvufex/gppifCqQylP3uP9kjPKzQuuf7uI6DL+4pTVXJ5fM4jsO8YL8GQYDn+wRhSE7T0gxGl13vfgGQE3OOHj3K0aNHE87D+jrLy8t88MEHuK7L1NQUBw4cYGZmpm/6GcC9uJhs0vFZm0yC38euwkQdFEOj8j9/AefQ4Hapz4PeZ+L6xgbjExPpc1myXXVNw/f9lIdiGkaSKejjwP0wTOuhsMUa7t2XtOFBGYN8Po8iyJ7ZdiLbtomjiFwPn2VsfJz79+5xcoAIzufFl+4wF5eWGOszJLZUKtFqNmm321Sq1S1GWSZSMnM5VEXB3oUFGQjCyrapGT1RVxAEOK6bMkMNXSdfKGCKPrG1tTXGqtX0htB1Hc/304drV3Ox2GaX3mPP6ij9d8/xFotFjh07xrFjx7Adh4WFBVrNZjKhwfOScWVCI1OmuZwPbie/c8ncu1oLjt4Uah8vHqbybz6HE/jghLtGuKnj641K4zgdXRT3Oe60odr3aTYajI+PA8kqTwY+hUIhYUWLB5Qt2j6MXI6cYaSrzt6IVF6nQUGO/HtWJ1Qin8vRUpI+P13X0+9ZUdWuNG0YRZTL5YSstbm5TcN4hJ0RxzEb6+s89cQTXX83DINCoYBt29iqmpL0er/FfC5Hu9NJBywPuks930/m5vYEU9ntRYLM5bhuIt6vKOTzeUyxGgLY3Nzk8ccfB7bq5IGodfdr2eqyX3n8wtZ7bVv+X9O0tLb59NNPs7S8zMbmJnfu3OGjjz6iVqsxOzvL/Px8Vwmq+d9/BE8lJZXFOTh1QcykLZmM/ZXX0A9P4DQaQ69W+wbZIhCQWblB21pbW2NSLGgURUHTdcIgoFAsko8TQfVALB4830fTdXJidaooStKXGkVp1kEiHaDRB1nuRm9WyTAMPBlYxTGWGCVYyOeT50eGrDg5McG9e/eGukYPgi/fYS4scHBmpmvVo5DUJMqVCs1Wi3arlaRAez6rKgqGaWJbFoiHcz/I3HZvDUsRX4YrIlApp5TL5cjlctsmCshIS0IaXiDGjPVDP8MD0Z/UQzySD4kssUVVFCYE2UBTVdqdDstLS9y+dYuPPvyQsbGxRCx+LWm2P3ca9i3AvsVkW6WfnqT4555M9u252x5CXdJ8yhYdPFUf6S3EywCg79km2NjcTIIg4exkLUj226qaRk601ARBgOe66Y+u65i53LaINHsNd6pJyGPORqimaabtJZIEpMRbo93S4Eac+8TkJDdv3Bg5zD2i1WrheV6qHSyhkKwM4ijCdhwUVU1JI9n7X64YO53OwH7MKE7Y7v0IXIqi4Mug13XTDEVZBL3ZeymMYzYz9qwoSirnOAjb7kXxOxUpYMt+tzHwxWfz+TyHDx3i5JNPJqUYMa7s3XffJYqipPY5PUNoJS02q1Pw9DnIe6BNVxj7a6+hTZa32mj6HWg2oBX/jjLPG6XHnrOkqH5YX1/nqaeeSv9viIWCDFANXU8WF1GUOE3Pw7JtVBEII67JgwgWyNFrWeTz+bS9RGYF8pKJ3ZNhmpqe5vz583ve77D40h3m2uoqzz755La/xyQpu3K5TLvVotNuJ/MLe95TLBSwLQvX98kNYNV6noehaV3p2DiOcUQ+PooiNKE/Kpuo+x7r+no6kxOGc5iDIB/UsaIkqSf5RWfPL06YqLFIC8dxTKlU4qhYfYZhyMrqKitLS1wO7id9oR2FnAWhrjDxbz5P7oXDSRQp1UayDkdGmFs77IrUFUUZujc1i/W1NSYyupySbShZr1noup720bmivtRutZLWoj7tHcMcjapphEJ4IVv76Ng2hm1DHCeDykVaKGtkmkiP3759m5dE4/MIw+H+/fuMj49v7y8U1zhfKBCGIZZloapqlyBFjGhO13XaljXQYcpUfa+9BUGAZVm4npfMxTTNlLzTD816nWKp1EVEMgwDP5MxGhbZ9GJX0JuBbJ2IhIOK42SggJyOxHe+Q7vdZnFpiWs3b7D8QkQcxUyuRASKgn5kirG/8ipq0UyfC9JJZ3kbve000kmqCAGDPdqzJPxkFwqapiXb6+nHVFSVXC6HaZqJM/M8XJFBQlG2yQ7ulDHKnoN06vJdsr2k2WwmAXaGrJR+TnymVqngeh6tVmtXpvaD4Esv2gRCqWPQgei6TqlUwg8COp3O1sQKkpuhVCqhCtmmfohJUrJ6hhTkOg51QXc3NI1KucxYrUZepHj7bieOE0eQWckqgqX3oFO95c1AJt0ci7+nP5LUIl/LOFZV05ibm6NcqaDpSevHdL7K0hM53n9Z44x9h6tXr9JsNNIVbTZ9lHWGvSlkeTwPgvX19TSFI6FrWioP1g+KqpLP5ylXKsn9oCS6v20hoL4XRIKJmK2pmoK84DpOkrrp80CUD0rTNNMe0BGGh6wJ90LeRYqiUCqX0VWVdquVfq/ywa6oKsViEce2B06kkROK5IM6DALa7XZSow5DCvk8Y2NjlEulHXs/e7NFQEpcGZQmHAryuGUaV547pKnJrC2nP0CpXObA/v34nsfhQ4eT850tcvF5k/eOWXxy+TMWFhcJhFNPdtMd4JLZ39YhxdteHxb1ep1KpdKVbdvtOsm0aalUoixkKeM4mSDjiJ7ofsc5aFtAVzAglZ06nU6qmpQ5WYB0caAoCjnhwL8IfOkrzIEXLBP5G6ZJQYxdisKQYqmUrhY1XU+pxuN9Jmun6hK6jud52CLfrWkaxUqlSyVkJ3QsKzXoLAxdT8gEu0RvaeozcwOkY5D6EFXSz+1AQ4+jiPPnz7O0vMwbb7zB/+9f/Aue/nf+XHreUjD+2rVrqMD41BTT09MUi8U0PZIyEbPbTQ5mm8Pcqa4kEQkm8QsvvND1d/nwkiy4QZAPgFK5TM40cVyXtiB/5fP5RMRgp6i0J80nA4VAPKz69aBl37tXhuQIW0jJMf3qZWytKErlMs1Wi1a7TaFQ6FKnKhYKNFst7AGrTN/30VUV4piOZaUkoXw+TyFDAtkNveQk2FKg8TM9wzuda9ae5WoPudrrKbWk12DA9QFo1Ou8/c47nDh+nOMnTnD91k1e+nf+PMQxrVaLxaUlrl69yvtnzjA+McHY2BiHDh5MpT57yztAtzpWH9vY7T5fW1vbNqFEURKVsjAIYBfiVRRFGKZJOZ8nCgIcz8PzPHKinqz0HNM29ByvzAzKVXa2i0L2dkJmZa2qe1IH2yu+VIe5043dm9bIiYbXVrtN0GwmqypxgxcLBdZtu29aVjbjZnt3yqVSF8MuVZDZARt9Vk2Qmc0Zht0ppmwaQUSQ2ZtaEgbS8x3gBAbd1GEQ8P777+P7Pj94881tkni6rndNaGg2m9y6fZtbN29y7uxZJicnU/JQqc/klt4IedDx9P6/2WxSLBS2pcxShY9ddGUjobFritSOFKdwXZd2p4Op68m2Bxh6733j+z6WZaEI0se2a5z5fxRFqb7nCA8XKlvfi6ppVKtV2oKfkC8UEiKQ+I50Teublo1JnBlRlKgCCV5CoVBIyWI7CZJkIdvDuo5R6Kz2XY1k7LarfJLdV9Z2BgS/0F+EZHlpiQ8++IBnnn2WAwcObMv0yOlJjz/+OEEQsHj/PvcXF/nVr36FbhjMiTa0qamprWshPttbxsr+e7d7fX19nYMDZhIPM/zC9/1klWcYKKaJKVjytuMkKlBCvnJQkNXrMDudTsJkzuUgjgnjGL3fZzMr8C/Snr90hymjzr6vk/lCxTK/WqnQbrVoNpuUSyUM06RUKrG5uZkM/s2sMmMSIkLHtqkKLVbpeLOQOqU7YX1jo+8sOLlykukoeaNHO6wMxcnvuL/sOfRux3Ec3n3nHcrlMi+99NLuYgCKQrVW4/Dhwzx24gS6YSSrz6UlLl26hGGaSd/n7CwTk5Nbqyz6OGylp9WkZyW6trbWd5akqqrJxPVd0l2S+i8jfEVRyOdymNJxCjaeaZp968bZdI/jODiehypTfYLYlZ5KNiLd4WE2wnDYcWXX40QUSDJFmobjOIRhSElkjorFIs1mM52dKOE6Dq1mk1w+T6lYpChGsnXtBnaVWrMdB9fz+o7yMgwjbVFQxEp2t4HlsJ17MChDk1yK7r/fvHmTSxcv8sorrzC5wxg0CV3XmZmbo1KrUatUaLbbLAtbbjQaTE1Pp/acz3QG9GPqbzuzzLWTbULPPvfc9mPQNFyh3jPo+RPHSY98tvdU1zTKosTmOg6W46CS9KX3lkmyxxuJFGwYhuQLhSSQ9v2kVSyr9iQQZXzLN2aFKTHohLJRqUxzaJpGtVaj3W7TbrfT6NQUDa0yLRuGIe1Oh7ZlUcznGRc6iP0wzEVdW1vjGSGukD1uRUmE0n3PI+oZYrsXDExN9Bh/q9nk7bff5tChQwlzbQ/7iUW9tHdcWb3RYHl5mYsXL1JvNJiemkomNMzN7TpmjZ6Ux8rKCvv27esrP2joOo7nsZPyr+f7iQBCz3elqiqFfB5TsKJtxyEIAvJ96pGyL8vz/aSVRfRuaZpGMEBWSzrSB2HyjbA7siv/tGapKInTE1MoWq0W5XJ5Ky1r28n0HZLgp16vE0PCN+g3lBxA2ONOzntjY4OpiYm+mRI5csvf6wzFHkfU1y57sjfEMec/+4zFhQW+/8Ybe5rFmTpxVaVWq1Gr1ZJxZZ7H8spKOnHFlMHw3NxwQ9Ezz8J6vY5pGH1T3bINJ9zBYQaZ/sxeGLqOUS7jijJZW6bnM++V+/N9H1vUtUulUtIDT3JPhUEAsg0oc3zZnutvzAoTQDfNhLDTb9q5uAgxiQPMNr1WKhUsy8KxbQKhbVgXzclhENARUWI+l0v6mz5Hg28QBLRaLcbHxhIn2RN1moaBlY1Kh8CwUU92hbe6usr7Z85w6vRpDh8+vKdzGJgOUhTGxsYYGxvjiccfx3YcVlZWUo1M3TASwfi5OSYmJnZczYZBwOraGs9997ups8wGI1KBY9B1kunY3KCHIUlfZqlUQrFtHNclaLcpFItpOjwIAmzbTgkg2VWoruspK1pmFeTVkPeXpmm0O52k1WmEPaFSqbB861bf1RVkMkY9WYacaaKrKq12m0azmaRlVZVOp0M+n6fd6SR9uapKtVIZ7CwlVHXbPrLYEISfrEqUrI/JEosvgq1h0ZuJ6e0flO+BLQLQhx9+iGXbvPnmm0OLMGQ21rceapgmBw4cSNO6GxsbLC0t8dlnn9FoNrdKMTMzFHaZfrS4tMTc/HxXDVQ6JpkxCsKQQSG1L/pldwpCc6aZ2Fy7jWXbGEHQ5aAdkQ1QFYWyIHgCaemkX8ZKkgt1kV73PG+oSU8Pgi/VYaqqytTsLKurqxzqkyeX6ZVBxJdisZhMdhcDWT3PY2l5mWKxmMo1Iea47QZlh7Rss9VK6yn9RkwZhoEiVjy9tcSBGGBMvYjiGENRuHvnDp9++ikvvfQS0w/wMM8a60AoyRSYgwcPclCMK1tbX0/HG7XabWampxOD60n3QFLvqFYqXfKD6aoijtN5fEEUYfRxmJ7vp4IROx9molGq6zqWZWGJ7ziOIrwgSIglxeK2B56u66AoaRtQ9lrImZ2KolBvNPjhiROMsDccOHCAX/3xHydcgj52oCLsuU82RdN1qtUqdqeTsGSjiM16PflOVJVysUjHsoZyYgo78xLqjQaHDx/uW+/MMt+HHZY8DHkGtlaFvu/z3pkzFAsFvv+97+1JXznd55CatHJc2VNPPYUjRFCWl5c5f+4chUIhmd0rguHeIHZ5aamr/xK6OQ66UP0ZdHy+6Lve7Tg1TaNUKuFKdTWxOpSDEUwxDL43INE0LbX3LNKhDbrO8uoq8/v37zxe8HPgS19hHjp0iCtnz/L8gNezUWA/5MRg5bYQQ2+02zx+/DjVcpmOaDUZZmBpv94pWXRuNho7jhuTNGt/Dw6zd1+DUrJxHHP9xg0W7t/njTfeeODRU9JYd1oB9zumyclJxsfHOXnyJK7jsCQmNJw7d45isZg6z4mJCZaWlpgR01l6IVdvxMkIJMUwtgUJvu/vOF+za3tsGVq73WajXkcFqtXqNuOSkANwfTFjU15vOWpIF4znRrPZN4AbYWfkcjlK1SorKysczPQrS8RKovoyqIygqiqlSgXT92m127RaLQzT5ND+/SiqShTHQ6/61J56nVzdRnFMo9HYMf1pGgadIPhc8oj97Fmq0px57z327d/P6VOnHrh1K5L72Ak9+8/l8xw6fJhDhw8TR1G6+jx79iyWmJ4k7RlFoSlWpIPOT04ukcQiWTcE0S8bx7uyjWGLPS3LKxubm2m5pZohd/ZC13VcIUojtwNJeUUe3/rKCk+eOrXrMTwovnSHOT8/z1u/+EWiDdhHaF1RlF0JOXJe4/jYGJv1Oq1WC9hjWiVT6M6mggFa7faOU74hWWUOGjvTF32cY6/TjqKIixcvYlkWb/7gB7unonbcnbipdjCyfkFDFrnMhIaswX3yySfYtk0Yhjz++OO4gv3WC1VVQTz4JGtYGksgHlA7pWN7IZvgozhR7ZHz/Qax/2TgFIThVtowTqYyQEJIWF5d5eChQ3sWohgheYBNzsywvLzc32FmBDh2gu/7lEslKqUSjm3TbLXSPuph7TkrJIDYZ0xSNnBsu1vTtgcyYzRoJNyDYmNjg48+/JBTp09z9OjRz7WtYco/6bNMIEviU7LTk06fxrFtlpeXWVxc5Oynnyaj+XI5Go0GY2NjffelSs3dKALBdJX7cAU7di/fl23bOELFSdf1RDpvhzY0XdNwhIBDWu6J4y5Bhc1mk+PHjw91DA+CL91hGoZBZWyM1dXVbUbWT/2mF2EQ0BYryX0i3+4LTcN6o0GtWt2RyZWFVOLodWbNZjNpz9jlPFzPIxRDUndDv4d61mH5vs+7775LDLzy8sufy1kmO9zdYQ7TvybRa3Dra2u89dZbbG5ucuXq1WRCg4hYx8bH0/1qmpYOdM02JQ+bjoXE4XmuS8dxkuk2Yl6hJAd0Oh1KxeK21YEqSB2hYOLKVUAgVIFUVWV1dZUnvyCh5m86NE1j//79XD57lhee354zUhQlIYntEAB3xCzcQrHIvn37WF1bIxCchMD3+6ba+0G2f/QyZlvtdlID38EOZGreH5BaHga9lnTv3j0+/vhjTp08+bmdJSTntutTps85DhqokC8UusaVvfX22xDHfPjRR3iuy4xQJJqdnU2DSamfHUZR0huLIHSJMX/DZNviOE41pWWnQUEQvSzb3hJV7xOAG6ZJLJiz8liiMEzrl67nJcMy+gRvDwtfusPUNI3Zffu4c+dO36g0KzvVC9/36XQ6SW+lUJSoVipsbG6SE/PafM9js14nl8tRyOcHpmejKEpXlb23WavZ5Ik+8n1ZyKkXMq24G/qaq2hzsDod3n77bSanpzl86FAaXX8ePOik92HfXa/X2bd/P9/97neJo4i1tTWWlpf58MMP8TwvYd3OzFCpVrdNpI+jCN/zukd+9fm+gyBIW0PiOBnLZZomqqomDdKiXmLZNu1Op4skIKHrOr6QT4vFdy4j0jCOWV5Z4V8Vgtwj7A2qqjI1NcV7zSaNZpOaKB/Ih+hA9qiAVHUq5PNJY7tp0mw2U/JeRzDfbdsmn8/3bRGDLYJbbw8iMLREmmkYaYP8bqnPvoFmJvC+cuUK12/c4MUXXxy6Lrob4jjeeYU5KPjdoby19RaFRr3OD3/4QwrFIraYnnT/3j0++eQTatUqs7OzCZdCUbbZc9dwb5Eh7L2GkdSddd1Usq8kBFXkNS8WCslwBjmGr2fRoGdKLFIdLMt2v3fnDkePH/9Cme9ficN87LHHeOeP/5iNzU0mxse7DYz+Tf3SWWpCb1a+t1Kt0mj+/9t701g5zvQ89Km9qvc+p89Gno37IpISN0mURhKlWTwBcmHAceJrXwN2rp0x5jp2MkbuALH9I3eCwDdO4gSIA8TOj8CTZBzEDjKTyVyPPSNr5SJxEVdx3w/Js5/eqmuvuj++5VT36e7TlKjhonoAguQ5vVR111vv973v8z5PFZVaDQaVWvM8j7OtWAOZ+2fGRYwFAWIUrSiLsptvN7ChZ9fzVt0NdtvJlZeWcOToUWzatAnrJidRq9cfeESlHUIqydW1h/kAO8xWTM/MYHxsDADZfQ4MDmKAOjQ0Gg3MTE/jzp07mJufJ73PkRGMDA8jl89zIed4X5EtHqIoIjNbjsPF8fkMZrSsqckgyzLSlCDSLmlKoggr9viQsSMlCTdv3ECxWMSaVaoJCTpDURRsfeYZfHz+PA4cOMB/zmMZ7Uv/PFmmUnxXJ9GF8GK5jEw6jUIuB1XTYNPv1rIs6IYBnY4VRIKAKMamFwH4bXaYvSZMx3UJke8TLFhZter0qVNYKpfx+sGDCKhr0qcFY/R2vS90SIyrtV0AUjrWdZ2zaI1UCuvWr8e69esRBgHmFxYwPT2N48eOwfV99Pf1Ye2aNRgYHIRMnUQkSSKjYbHEzjxuXeoIFYKy3ulGppVAJAgCZ8w6tN0Vv7dKbIdLnxeFIXzfJwvoKMKFCxfwf37ta6uc7afDI0mYiqJg2zPP4Ny5c3jllVdWihm0fPFBGKLRaKxIlsBykM3OzxOzYirOmzIMrjDheB4Uql3a2qtidXMG0zSh01mx1fBJxkviuH/vHo4fP449e/ZgZM0azvZ6GAkziqJPJhTcw3sHvo/5+fm2ZTiAsJlZwNm2jampKZTLZXzwwQcIggB9fX0olUoYj1O/g4C4yDgOXzzpVP2HHREjPrQmeokOR9dNEw2qGMNvoi3fC1sNR4KACxcu4G/9nb/T2+eSoC0kScLmLVvw4VtvEU3h/v4VIh6t31nDsuD7/goxdADIUceiSrWKoaEhaKoKTVV5+b1Rr8OiNm2arjfP7worZzKr1SqGOxDT4mBJMm5O3wntEpDv+zh69CgQRXj1lVcgKwrqD2nx200xqNsxdft5HNPT04T40wZizK5s165dmJmZwezcHG7euoXjJ08in8uhSBNoOpVa5gkEARzHIeL2lAxkqCqXI+SzuS3vx3eaIEmTGdADMQIja93RBbQqy7h29SqK/f1Y/xn2L4FHlDABYN26dZi6eRMz09MYGh5ufpDQ7DnHhNZTHXoRuWwW83NzxPYrtks1DAOGrqNhWbBtG9V6HSIdpVBVlffP4qswNkzdC9jzvVXcS9pdtFevXcOVy5fx0ksvrRgwfhiDt6uWcDogThTohLm5OeRzuZ56FoqioL9Uwtq1a/Hc7t0oLy1h6u5d3L13D+fPnUOhUEB/qYRCsYgUVf/QDQNqh1J6p12xKIpIGQZMKnLAvVAZo4/exD3q33f1yhUMDA5+pv2OzwPYUPn2Z57B2bNn8drBgyuvnVjrg5XlmLboiteTZei6jkVqIMCgUIcK3/PQoK5Dlm1DofZwqqKQvhaa461arWJTjyNDiiQRKb4HRKPRwOEjR1AsFvHsrl0rTOs/Ldj5fBIlsV52mDMzM9jRYx8/m81C1TRs27YNge/j9p07mJ+bw7FjxxBGEQYHBlAsFpEvFCBRYwNV13mlIX5c3RTXdF1HGIawLQsyZdJLLcQuj1aqwijC5atX8ZWvfKWnc/g0eCQJkw2373jmGZw9dw6lgYGVMkkgX3SDzlym0+mVNkIUCi27Vur15ps9/XANw4Cu63CpELBFg02i9jRKzOKrXqsh16MtDGN2Mem2TohftFEU4ezZs5iZncWrr70GQ9eb1I3IEx5OSfaTijes9u5Td+/2XMZkN7EgDKGAfFdrR0awfnIStuNgfnERC/PzuHHzJgBghCoODZRKkOkoCjue1W4+sixDU1Uip0crDcDyZ8+o71EY4tr163j94MEVs6UJHgyyLCMEMDY+jitXruBuy7XB1KZESrZqmCYkqsbUCdlMBtLMDKkWxKoQURRBkmVkMxkEhkHm+BwHrmlCEASoigJVVfmQexiGqD/IAlhV4dL7TdcKUyw5VSoVHDlyBBs2bMDGjRubxAt6nddcDdyp5JO0V1bpYdZrNTQsq+M4SSsYf4AlrkKhgFJ/PxnHq9cxv7CAW7duoXr2LIrFIp/7zGQyK46lWzIXBAFGKoV6vQ6TVo1YSZY9h6mEXbt2DSMjIz8RP9tHIo2naRoc28bIyAguXb6MW7durWSSCQKvfWuxHmQnpGgfq0rJByso1nRnqWkaaUC7LlzHQaPRABoNshrSNFSq1bYash3PRVWbtSi7wPd9HD9+HL7vEwF1mhCiWIkBeHg7zG5F5W6rzm7SgYHv4/69e9j+xS/2dByM0u55HsIgQKVSIUQsKtk3PjaGDfS7r9VqmJ6ZwbWrV3H82DH09fdz5m0mk+mpvKRpGgK2MqXELCGKEIIEmEhLsaOjo8Qh5dOykT/nYGxGPwiwY8cOnDp9GoODgyuZrVEEk5Yo06uosLBdpmmaXNKu9buXJAmpVAqpVAqe55FFEtUeBki7hLFeex110FQVDcuC47rLFYo2YLvl6ZkZHD9+HLt378ZatkhoSZgPQ6t41ZLsp+Ai3Jma4tKWvUCiC2DHcbh9VyqVgiSKKBQKGBwYgLh9O3FPmpvD9MwMrrz/PiRRJHOfIyMo9ff39J2ItDxrUoW3FCv50t4lGyu7efMmvvilL/1EYvmRJUybztPt3rMH777zDnK5XNMqJwxDWPSm1201yiArCpHLo0PK3QaQRdrP1HWdKAZ5HhzLgtloYH5hAaX+fvLeirLq2ANj13Ury0ZRBMdxcPjwYWRzOSKgzo4vturqZXayVzC/wc4P6EJG6LIqnZ6eRj6fX3VnxhryPnMrsCxIsowIZAehMj3IGLLZLLLZLDZt3Ajf9zFL7couX7kCURQxPDyM/v5+DA4Odvx+WSm+Xq8ve6YKAgLPQxAEmJ6exsLSEg6+9hoAfGaKIJ8XKLQU6gUBEbQoFnH82DG88OKLTd+vbdsIwhDZVWITINdOOp1Gg85k5lYR72Dl2iiV4oQx27Yxv7AAVdNQN03IsgxFUTpWqQBy7SiSRIbzu13fUYQbN2/iwoULOHDgQLOrUWyh/tB2mOy+0OnYu8Rr13ePIty5cwd72oitNz+M9AoD+tnW6nUojgPXcWCkUshQvdc4ZFnGyMgIRkZGAACVahUz09O4cvkyPiyX0dfXh8GhIQwODHQ0D2evo2sasQmj0ntsLM0PApw4dgzbtm9HyjB+IrH8yBImQHYruUwGe/fuxZEjR/DG668jRT88x7b5tnw1hJQ5mcvnsVQuo1KttvXKbAdJkmBIEgxNg+N58Cjr1bJtwLYBkN6GTHue7eTXRFGE7TgdE2a1WsWhw4cxOTGBLVu2dAyiVqutT4q4rmvHx3R5frdSyZ2pKYxSdmzT64Uh/CAgSdL3l5lsIAsUha70NTogvRpkWcaaNWt4ea9cqWB6ehqXL1/Gh8eOccH44aGhFbqRoiCQioNp8rK853lYXFrC5cuX8eqrr5K+V4cxhQQPBk3T4JkmoGnYvXs33n//fXx8/jyeoX2xMAzhuC50TetpZxGGIQxdRxgEWOphAczAy7KKgrRhYGF+Hql0mu9AWd9MkWW+GG59XVXT4FIGb7tjDaMI58+fx/379/Haa6+tuNk37YZbqlyfFN18Rz8NKpUKgiBoK9IeBAH8IEDg+7xXCJB4Zv1iI5VCLpvt6bvJ53LIx+zKpqencX96Ghc+/hiKopBYHh5GKeaexKCqKjxq+ReBtHc8z8O5s2cxMDCAdevWIQJ+IjvMT65Q/ikgyzJkVeUN9pHhYWzZvBmHDh8mpTsaYKqqQumBrRqEIVmVplJI6Toq1SpXc+kZVKXCdRz0lUooFgrIZDLQNQ1hRNwwqrUaFpeWUKvV+K4ypEO2LGm3Ym5uDu+99x62b9uGrVu39pTEPm1YrFbCWe31OyVL3/OIO8nICEJ60dq2jToV0TZNE7brkotX05BKp5HP5QhrFQCi6JMp6ggCCvk8tm7ZgoMHD+KrX/0qxsbGsLS4iLfeegs/+tGPcPbsWczNzTWNjUiiyKW0ytUqzp87h+f37ydMa7TfXf7BH/wBBEHAv/pX/6rtoVy6dAmapuHVV1998PN4SsHK4MzJ4sUDB3Drzh3cvnULAFn8AoRL0Mu1zdjixWIRQhRhqVx+4GMSRBG+7yObyaBYKCCfzSJlGJAlCa7rom6aKFcqqFQqxJiajZTIMgRRbKviFQQBjn3wARYXF/Fqm2QJNFeHIjycalEUht0Zsp+wJDs1NYVR6mDERMsbjQYq1Spq9Tos0+QuLoZhIJvNIp/LQdM0+EHAE+eDQpZljI6OYt++ffgbf+NvYN++fVAVBRc+/hg/+MEPcPToUdy4cQMNywJAvkuVkoDCIIDvebh8+TJEQcDOnTs5C7s1YX4WsfxIdpgACTK30eCklw0bN6JSreLDDz/Es88+yx/Ty+AtI3OIkoS+vj5Y9+9jsVzGQA9ec3F4rkuSOU3SbLUKkFWv7/vwfB+e6xIRYPq8KAzJeEkU8Xq+JIq4MzWFc2fP4vnnn0epw7G0CwOuS7lasLXZRcZ7osxya8Vjur9q0w6TLQQC38edqSkU83lYto2IXszsc1fp7kGmNkCt8Cgx6hMNFce/fzpuEndoWCqXMUMdGmq1GgYHB0l5kJIRrEYD165dw+bNm1EaGCCfG9DWMeLll18GADIi0Aa/8Ru/gSAI8Id/+IcPfh5PKTRNQyQI8Ol3rKkqXn7pJbz7zjtENJ+ScfjIRw/xLMsy98GsUSLeg8xHCoIA23F4v1RuqQ6xSggv4ToOj0XbttGgc8yKJEGiqlJHjx6FYRh4+Qtf6FzabUNs4VglplewYWO7uk+aeFkyYX+HdDY0CALcun0bO3fuRKVabTpeWVEg0Vhup5jGNgoP7LhCDqj58xEEFPv6UCwWsXXrVriui5mZGUxTuzJd17nXp6rrpFUzN4dyuYzXXn2Vm1FHYbhiHv6ziOVHmjAtQWgqfTz33HM49P77OHP2LHbt3Mlvru2scxhCurtkjxOp6XS5UkEum32gujYjGLWDyCjSqgqkUrzhzEoXlm2jZprc3eQmHZnZs28f0pkMCUiBCAQLokhWjHTkgV9E8QABVm/mt5lJZJ8JO+a4GAQDY54yphtziGF/+3QV58d3zVGEO1NTGBkZ4X0rUZI6Jsg4fM8DouiTyY61uQExo+GAjor0FYvoow4NjuNwf8Dz589z49lSXx/XmBSpB2K73tiePXtgGAY++OCDFb/7sz/7M/zoRz/Cb/7mb2LXrl0Pfi5PKSTasvBoVQggo1779u/HkaNHsXfPHv5Zc3nENtdtBGr5FkssxWIRlmVhYXGxp3nKODzHgdaBwMcSqE6PJYglEgCo1uuoU03bhmnizJkzGB4ZwaZNm+BSk3KRzn0K9G9gubrDxx9aF/xdYpovwFses0IUnr4m/yxpHERhiJD+P4zFs+O6TbrLEYBquQwIxGheliRugrCapGgUhvApeU7+lItfNn8f1/NWVZW7J4VRhHK5jOnpaZw9dw6maUKm8fyFl1/mimhRFEHTtBW8is8ilh9pwoxo2YQlTEkU8dzu3Th65AjOnT2Lffv3c+PS+FwmQ0iTE/8pvYDy+TxM08T8wsIye60H2LbNd7yrreeYFilb9UqSBNM0kUqlcOrUKdTrdbz44ouQRJEwcdnxteyW2HwRBIEM+vo+XMfh5yy0JlYsX2gAuYBbRadd6kzu+z7XWmRqSlEYIqA3CJYk46/NGvwAuamwskvg+6iUyzhw4MCD+QZSSSy5Tb+op+e3Djez4wTVqW0pg+u6jvGxMYyPjaFhWXjnnXcAQcCGTZvYC/IVd18bKr2iKNi/fz/effdd3L9/n5MWTNPEb/3Wb2FwcBDf+ta3Hvg8nnZohgHbspraCkNDQ1i/fj2OnzyJAy++yGn/AtrbcTHN4XgykGQZ2VwOS0tLaFhWV/ZqKxzX7YkwyETD2VXNniOKxKPzo1OnsHnTJowMD3NhDXacfLEoCCSBxuLVsW1IsThuWry2xDKP31g8s/udS2UkPdpeYL+LoohUvlgs010xsLzoZvEuUR4BU+S5ce0axsfGuhJuOn2mgig+mNk2RTtLRV4Bo0z2plnN2GJ4+7ZtuHDhAq5cvYpiXx8f/WNVi3yxuOL9PotYfmQJUxAEqLoOr9GAEdspCYKA/fv34/Lly3j33Xdx4MABYt+E5iBrSpQtpQ5RFJHP5bCwuIh6vd7zHJbrODAMA2L8tXuEoijwfB9HjhwhdfHXXiNu7lEEnYp/R2HIraXYLFMYBGQnR3epfhDAZAm2GwQBAQj7jO9M6YXnuC48x4EoScsXICMO0AtMouUWttsVBIH4V9LXaVopUzbd0PDwAweK4zgQQRr37Xq8q52j0Loij/2fiRHwhVRs4VAul3Hk6FH09/cTRRkmIM2+E13vyPR9+eWX8e677+LIkSP4mZ/5GQDAt771LUxNTeE//sf/iHw+/2Dn8TmApmkwacUobu69ZmQE+UIBH3zwAXbs2IHJyUlAECABTVWjgN3s24xWFfJ51Ot1LCwsIPUAQhNMg/ZBwchDt+7cwZUrV7B//34MDQ6SXh9NTCyGQxrDvEpD2xe+78OiVSWmd9oNIUisVSoVAMv3nwhEuEVV1bYye6Ioks9TkkgplbmIxHa/zCw9nmjv3bv3wH34KAzhOA5Z/D5oiVggGrQrnhVbcEgArxoBy5ZtURTh9JkzmJ2ZweTkJLL5/IpRvEKbhAk8/Fh+ZAkTIKvSer0OPwggSxLCiFgvqZqG/c8/jwsXLuDtt97CSy+/jFwuR27m9ANq9dlr/SKy2SzxTVxaQqqNk0U72LYNhTInH7SRblsWPjp5EsVCAXv27Wv25xMEwq6ipY92CMOQO3DkstmmHSP9x/JOkv4tRssCxfHVq0CZgDk2LEx/zj6DVRNXFDWXwAUBt2/dwuatWyFE1BC4B4RUHktRVUQxpl0v6OU7aH0MWwzcv38fJ06cwDPPPANJUWA7Dj2t5bJ3vguLmvU+PvjgA/zMz/wMLl68iH/9r/81Dhw4gF/6pV/q+Rw+T1BVFQIl1KiKgpASSSAIGB4exquvvopDhw6hVqthZ4uqTNP12O47FwQUi0XMzc2hWq2uOmbC4DgOiY8eeBBNxxNFuHHjBq7fvIkXXngBpf7+pgV9PCEBAFp6qxG9j7ERJ1VRmuM5ap69ju8m2SKOvUcYhgjjmrux92cxv1o8x+NEAFH20Q2j59lmBttxgCiCoeucyNUzWitF7NjiD8HyjpEl2MD38cGHHyIMQ+zesweL5TIUqkOrUH1pAG2rRcDDj+VHwpJlSKVSgCgSujANsAjLBs3bt2/HtmeewTvvvIPp6Wn+4Qax0gOwTLtugiCgQIXd403tbrBsGwYlGvXUZKdlhPmFBbz19ttYNzmJjZs3N4kKrygprgLWR5DoH9ZrkRUFCu2hqlSAAQAXY2D9VTZrptDGvRTrT3xSVMplWLZNekg0+Yv0/LuB0cBZheBBEmanx7Z+LwIreYHcOK5cuYKPPvoIL774IorFIkRBILvbICAJlT6v0EXZ5KWXXoIgCJws8Pf//t9HEAT4d//u3z0U1uPTCEEQkMpk4Lku3yX4vk+uPUFANpvF66+/jsWFBRw5epSb/sbbCa2vF0c6nYau61iqVHqqVAR0tElRlJ7k4dj15gcBjh8/junpaTy/f/9KDkQP1zDbzTHOwop4prGsxGKZLXzj8awoCnkemyGl8RznJvQUUy2f5Y0bN7CeioUIsT/dEFKLPZUeUyf+RC/v3w3xxG5ZFt5+5x0YqRRxRQKgaxoEUSS7ZvrYTDbb0eHpYcfyI02YoihCT6eJkn0UM/aNlf3Gx8bw4osv4vjx47h0+XJn9f82X55hGGTMpFzmotvdYLMVKXvJtm9DewdRhCCKcHdqCocPH8bu3buxafNmroLB0euXEutpfFowUkw79HKRtz7z2o0bmJicXA5SLDP3ePJsPYYgICQqViaijgI9octn1vY7ASEWnTh5Erdu3cJrr73GbZVEUYRCST5xX85Clx1mkRKITpw4ge985zt488038Wu/9mvYvcqA9+cd6WwWkCS+AA4YP4F+n5qm4eWXX4YsSXjnnXdQrVZXWr91ef1ioQAhirC4uLjqsbBY5rvBbtcUjWebios4joNXX3sN2VyOJ95eju+zACfwdTj+B21zmI0GFhYW2lsronNCYFUaTdN4n7bnhNntcW0WwAARSHnrrbcwPjGBHTt2wPM8yIw3IsvclB7oXI4FHn4sP9KECQBpWo92qZ0TY57FUSqVcPDgQcxMT+Ov33wT5TYB02m10N/XB1mSMDs3t+rF5dg2X1G2BhlLEiENriiKcPXqVZw+fRovvfQSRkZGwBw2fN9HECul9gLe+H8IO5iuMn09vH685Op5Hu5OTWHd5GT7x2KZYBBn9tq0ZMM+TzHWF139AFZnEi4/NMK9+/fxVz/+MQRBwKuvvko0QT2P095lqirEeknZfH7VXuwXvvAFmKaJX/u1X0OpVMI/+2f/rLdj/xxDkiSoVOOVmXZL8T46CIln7759mJiYwFtvvYULFy+usHkC0PY61XQduVwOddNctc9vx2K5HVgsB7QPaTUaePfdd5FOp3HgxRcJg5ZeN06bmcyuoP1MchqfLp7563RRtloN8UfcvHEDo6OjHX2CWSyLsecFdJROo6NBQq+tHXKA3X/fEuu2beP4sWP46KOPsG/fPmzcuJFsQASBaARHxPkkfs0UVpEyfZix/MgTpqIoUHWdfCgRkXNrV75Lp9N46eWXsWnTJhw6fBinT58m4wptHhuHJMvo6+9H4Pso04Z6J7iuu2K2KIo3+BkRJgxx5vRp3Lx5E6+99hqKsRUOe74b32X2AJZsPm26ZDvgTiXYB91h3r59G4MDAz2TJwSBeBS6VMeTHYcYK4eu8gJdfx0//kajQRjV585h//792LtnD2RZhm3bpBSrKKQ33GJSXeyyImVgvY96vY7f+73f6+k5CQAjm+XEMwCcARmHIAhYv349vvjFL6JSqeDNH/8Y83NzAJZ3cJ0SQbFQgK5pmF9Y6CpO4sZGXOKvF49ldi2Vy2W8/c47mBgfx7PPPssTgkBHyVwqxtEzhO4+tA8CbgT/KV6PHXsYRbh56xbW9WCBxZ4jgtzLBIB/nqwNshraffcd3y+KcOvmTfzoxz+Gpuv40pe+hIGBATLe5vtEQCYMEYoi5JiFmyRJXatFwMON5UeeMAHAoGLpTWXTloBhiWB8fBxf/spX4LkufvSjH2F6epo8vMvrp9NpZFIpVKtVvvNphyAM+UAye79IaJ4B9X0fRz/4ALV6Ha+99toKWTZJkqDIMlGYAXomyPAL61OuSMMuK1tGGOoVESU/rFu/vvfnADAtizjBxJ1YennvHgKMESGuXr2KH7/5JvKFAr74xhvoL5UQ0ht1EATQY+/dSrTqRBCIg5kB7N+/H7/yK7+y6uMTEOipFGRV5W2J+AhFHGEUwTAMHHjxRezYsQMffvghTp48ufpCUxDQ398PAcDs/HzHh4Vh2PS9c3INmsuq09PTOHToEJ599lls3LRpRdwwk/N2yj/dwN/jIcRzp+Tba0mUHcG9u3eRyWaR7XFqAABcKu6g6zpP2pxxu8pze2nBCCCOKe+9/z6uXbuGL7z8Mnbs3El2wIIA27ZJ5YKy7EWgaVa0WzmW4WHG8iNlyTKoqRQkWYZNRZKB2HwORfz/mqpi//79mJmZwclTp5DNZLBp40Z0M+Xq6++H47qYnZvD2pGRtiWJiJKJ4qUGkV4cYRTBtm0cPnwYhXweu3fv7ngha5oGr14nslK9Dvc+JDJJ1GVF2gv5gb8OgIWFBYRh+EC2Oa7jIAwCIoPW4k/YNcB7XI2Wl5Zw7MQJSKKIgwcPNo8MRRFXa1JUFS4lHUnUkgiCgFwuh3QPN4x/8S/+BURRTIg+nwBGNgvHtrnEHSvzMUS0ZMk+17Vr12JwcBBnz53Dj998Exs2bMD6Los0VVVRLBSwuLSECnUnakVEh/2blK+A5fEGQcD169dx8eJFHDhwoKNDEdOPdhwHmqr2HD8P64p5WI4nAOEirO/QWun03lajQURbGBkSANh4yCrxvGIkrAVBEODCxYu4fOUKtmzejI0bNzbdUx3HQUCF+CGQ8RiZ8hEYhteuXfU8HmYsPxYJU5IkGLkc6vU6PM/jZBIGVkZpPdmhwUF8+Y03cPrMGbx/6BAmJiexdfPmtoLtoiii1N+P6ZkZLCwtYbBNEgh8v+1FIAgCqpUKDh8+jHWTk9jcRUAdWHZwcGwb8gMOBj+sHeanDTJBEHDtxg1MttqurfLetuOQXTYt3/BdHp0X64hVgmupXMbFixcxOzeHbdu2ERJS09MjNBoNhFRTGCASXgLtfXj0u10zPr7qeXznO9/B97//ffz6r/869u/fv+rjEzRDy2YhLS7CYlqgaF7wtpNrVBQFe557DmvXrsWJ48dx+/ZtbN++nQiPtLlucrkcbMvC0uIi9BhrnCGgoiat9w0B5F5w+vRpzMzM4OBrr3HDh05QNQ2NRqOneUqG+BjKp0HrTjn2Bg/EUq3UaqjXaj372AKE6BNFEbmfxgh/7DPs9O6rjYT5vo9r16/j2tWrSGezTaYb8cewRQrbRAW+z9mwAgg7drXy6sOO5cciYQKAnstBuH+f9AvYrFKsVt72whOIQsfmLVuwZs0azMzO4sdvvok1a9Zg8+bNyLYYQWu6jnwuh6VKpUnQgJVrglYJKoqZ2Vl8+MEH2LFzJ8Z7uOEKAvHetCxrxbzoqs/t+ZHtsRpJoFfYto2Z+/fxHNX17QWWZZE5rTaCAPHe1Ipg6rK7nJ+fx8WLF1GpVrFp0ybs3bu3rRKTQ0ljumHwG4xLHSoUWYYNMsbUSdP39u3b+M53voNr167h29/+Np555hn8/u//fs/nnmAZkiRBTaUQVqt8LjOeajreSmm59fn9+1Gr13H58mWcP3cOW7Zuxfj4+Ip7QH9/P1zPw9z8PNaMjCzL00URJ4W0Psf3fRw7dgy24xBP2h7kGjVFgSUQJS5N1x+orfFpEYZhew3dB+gPClGEG9euYWJiouf7gk8VxxS1jZ+oILRd9LDfcfWwFriui6vXruHatWsolUo4cOAAMvQeHT+TKAz5ztZIpcjIoechiCIYsdnLtR1ELD7LWH5sEqYkSdCzWVQXFmDbNhngjZaHeztCIJqGiqJgxzPPYPPmzbh+/TreefttDAwOYuvWrU1qDoVCAZZtY35xERoVDA9Zgm5zEdy8dQvnz53Diy++2FPvi0HTNFi2vWJU5bNGQC/Wdok/aKe00QE3rl/HmjVreha89qi6iaZp7fUoWS9LaJE5bBP4EYCZ6WlcvHQJjmVh05YtePHAAeL2TqsNre/t0BkxTdN4r9ahJK4gCMjusotKzA9/+EP843/8j1EoFPDTP/3T+Df/5t+s6E8n6B3Z/n4szMxwucimXWaXeBZFERBFDAwOYmxsDPPz87h08SIufPwxNm/ZgomJCb4gkmQZfcUiZhcWsFQuo7+vjyvutItl27Zx5MgRZDIZvPL88z3v/hj5x7FtKKrae/XmMakWedQ44Y033ujp8RHITLogitDbMI2bduyxqgH9x4p7jO04uHLlCm7cvImRoSG8+uqrfDPDZu/jr2M2GoiiCBnqchQBnESmaxqRPEylUBocbHv8n2UsPzYJEwDy/f1o0N0f8yrspbnMFS8iIt67detWbNq4Eddv3MB7779PlPA3byYG1YKAgVIJ9+/fx8zcHIYGBppWpkLs3x9//DHuTE3xLzgCuMzUahBFEZqqwrJtqGx2aTVEvavodHyJIIDQoW/a6yuzkskrr7zS23vGeh2dqPxNPQ86G9daVgrCEPfv38elS5cQhiE2b96M0bVrm1bFYkTEIhjCIIDdaECUpGWVFIDbxKmqSqyIVBWjXaoDX/va1/C1r32tp/NNsDpkRUE6n0eDEu0MqrizWhlRFATIosgrM6WBAZQGBrC4uIhLly7hwoUL2LxpEybXrYOiKEil08jaNiq1GjRV5dWNiBJEGGq1Gg4dOoTx8XFs27aNVzp6nQ3WNQ2O48Cx7bYVlHbgo1afEN2qRQ8iAnLt2jUMDQ31fNyMh5BKpbruSONjcLxyFDuuumni6tWruH37NkZHR0npNZa42pWtbcdBEARIGQY3SWDHJAhEAjDwfYxs2NDxPvxZxvJjlTA1w4BqGPBtGw3TRCabhRAR/cZuCUeSpBWlPkmWsWnTJmxYvx63bt3CyRMnEACYGBvD2Pg4CsUi5ufnsbi0hBLdOYb0ffwgwEcnT6Jer+Pga68ty8+hveB3JzAj6p6DTOg+YN0LwigiYu6fAjdu3ECpv39FSbsT2vU62iG+GIiTPhYWF3Hn9m3cmZpCNpvF1i1bMEznWuMQBAF+7DuOoojYqgHIGMaKwENEHFJcx8HI6OgnsxZL8ImRLhRg1+uwLAuKokCWpOX55C5oV6Ho6+vDgQMHUKlUcOXSJfzFhQsYHBzExMQESgMDaDQamJubw/DwMGFUYjnRzM3N4cMPP8QzO3ZgcmKCv+aDjD0wpqZlWdB0/aERcbqBibS0WomxRN/LEQRBgKvXruGlAwd6ek/GQxCpNm1HtHx27Fhs18Xdu3dx+9Yt1Op1jI+P44tf/OKK+x/fnMTupZ7nETUhqoIUOyjYtFrkBwFkRcHoA2gKP0w8VglTEARo2SxCaubKmr6rXZyMut5u1SVKEtatX49169ahXC7j9u3b+Ou//mukMxkMlErcSaOQz3P9yw8//BCqquKVV15pO+DeK9uUBRnrfax2HhE+fe8xDENIbS70XtejTF5u//PP9/T4rr2OOAQBQiw4LNvGrZs3cev2bSCKsHZ0FAcPHuzoniBgpdi6bdtkNZpK8ZssYxU6jkNkySg5odvuMsFnAz2Vgkrn5xqNBjHuFgTORu8ENjrUrt+dz+ex7/nniaDG3bu4fPkyPjh2DCMjI0in05ihBudMvOP27ds4c+YM9j//PBFQb4HIGNS9nA/lJTiO05MLCtB73LV9bocdptADA5Xh+vXr6OvrQ7ZH/V1m2tzNFaZ1IRuFIe7dv4/bU1OYmZlBqVTCpk2bMDQ83LY1xGI0/rmHQQDLskhrLvbZCgBc6rikKQrCIED/wMAja5c8VgkTAIx0Gm6tRmZwGo1laa0uFwgbpOVfRLvHCkRbNpfPY9v27ZidncWd27dx5epVpNJprJ+cROD7eP/QIaxdswY7duxou+Vn1PReSyK6rsN2HLi99jI/BaGgm2hBryo7N2/eRD6fR6FQWPUcea9DENr2Olrh+T5uXL+OW7dvo1arYXTtWuzfvx+FfJ4Lp3d8L9qTYqtuz/O40ES8z8pGSFzPg66qCIIAfaXSA9sYJfj0UBQFkmEAdGHDFo4R21l0SJoi0woFOsaaoiiYnJjgNm63b9/GrVu34DgO7t69i5RhYGlpCffv3cMrr7zS0ZWClU17iTpZlsmMteMQTdNu1RR2Lp9iJ/ppRQvY4veFF17o6fGu5yHoxkOIIYoi/vlOTU0hl89jfGwMu597jjirdGldcVWz2GuZlgUBJFG3Ps+xbQi0WuR4HtaOjj6yUa/HLmHquo6qqkKk8nKWZZHeVJek2WreylcvrSshWmOXRBEjw8PE387z8PHHH+Py1atwXRepdBqpdBp10yRN53ZJk5ZOe1mZypIElTpmaKsEWexAm469nUce+yzYGA4Abmj9SS+mKIpw+coV7N27t6fH25aF0PeRSqfb74zDEOVKBTMzM5iZmcH8wgIGBwexedMmDA4NNZWawihqu6PgYOdEGZBWo0FWo7FEzdxsHNdFFIZQNA0hJfv0Sl5K8PAgCAL0TAaW60ISyBC6LMvkWunCtBRFsbNmNEOM/JUyDGzdsgVbtmzB/fv3cfXqVVy6cweIIqxbvx6WZSGdTnesgLTzaewETdfh1WrLTiirofX8omUtavJfSjikv/Z8nydx9u+Vp97bovr27dvI5XIoFIvt5QdjCCkzVZKkjjwEx7YxNz+PmelpzExPIwQwPj6O1994g49ysXOUOmhHt8Z4RO/xYUulqPV9BUVBEEXoHxjo2a3ms8BjlzAlSUIql0NjaQmKJMGl/mu8nt6STACawFq+oNb/swBrvQA1RcHOnTsxUCrh6NGjGBsbw8LCAi5cuABREDAwNIThwUEMPIA8XCt0XYfrukSMvMPFGIYhPCr0zOZOmXdm/BzoCfMfNUyT/9vzfaJkFBGRBe51Sf9m5rGdyr537tyBoeso9fevOnPGd3i63vTdmKaJudlZzMzOYm52FpquY6BUwvjEBLZs24a+DjJWbCXe1nkmhoD6hQqiiHQq1SxuQf9majGiIGB4zRoUi8VEfOARIZvNwjJNCL4P+D4ajQYfRO/0jXCyH02o7VxN2t6MAawZGUEqlYJy4QKqtRo0TcOFCxdQLpfR19+PwYEBDA4NoVgoLCvXYOWNvBMURYGiKFx3uq2iFl3Ueb4Py7J4PHM5vpZrnbUbABrP9DjMRmP59Wl7gQmfy6IIkfpSdjqGS5cuYc+ePaueU0TfC4JASp1sAe77mJ+fx+zsLGZnZ2GaJkqlEgYGBjAwNIS+QqGrXm/rZ9rEjqf/ti0LnudBj1WK4mINYRTB9X1oug5ZlrF2dLRn8tJngccuYQJAJpNBo14njE9RRL3RQD6b7drfayfuHf/C2pqXUsiiiMHBQc7M3f3ccxBFEfV6HbNzc7h9+zZOnDyJdDqNwcFBDA4Ooq9Y5CMLq92MWSnHpg1tgNz4PaqTyJKkZZqQWBAA3BqJ2fmwPyzIBPpZ8Z4eJd+w+j4zuPUpJZvPQtLXZtZhEjVVvnTpEnbu2tX1XNjrNiyLOJAEAaampjA7M4PZ2VmEYYjBgQEMDw9j186dnLnaaDR68tBjCx1WWo4HGDPXFgSBJMvYDY8fGy3vSLKMTDaLwQdgByZ4+JAkCelsFvWlJei6jkZsvq5T1UikClFNQ/uxx7ayMVtRyOeRz+dRrdexdu1abNu6FX7s5n/8xAnYloXBgQEMDA5ioFQiBMNekmZEPGg9z+N6yWEYwqcScszdxPM8WI5DEhu15JJlmZi2s1gGmhYEAJHxZLtQn7q9aExHlRIgoyCAC9rXByAJZLROpsQqQRQxNTUFXddRopKR3WDTHZ6maVhaWsLs3BzmZmexuLiIQqGAUqmEZ599ltjl0ZZHtVpddWwmosQkrvTV8nvLtslnqGlkvpVCipVsG6aJMIqgyDLWjo0hn88/0sXvY5kwJUlCJpdDbWkJacNArVZDtVZDPpsFRLHtzKQky016j//vP//nOHf2LH7jN38T+/bt4z+PAPzRH/8x3nvvPfxvf/Nv4n//uZ8DAKiKgpRhwPM8zM7NYWhoCNlsFtlsFhvWr0cYRSiXy5idmcGlS5dQLpe58G8+n0cul0M+n0c2k2mb2DVNg1kuY9H3+QURgSRr5mHJxiDiSXA1xMtMvu+T82hpiLPZxSAI+N++7xMmKRVWXpifhyhJGOgw2B8EAarVKsqVCubn51GjyiGiKKJYLGJwcBAbNm4k59+mDBVGEfnuekDrTYS9f8M0ebKMl27iQgasvJPJZjEyOoosvREmeHTIZDJEhYneHBuWBbFL6Y8lST8IIEkSj+Xf/Af/AHv37uWL306xDBCB/ampKSwtLUGWZaQMA8PDwxgeHgZACGNzc3OYmZ3FlStXYDcayOZyyOXzyOdyyNO4VtsIG7CYK5fL0DUNURgSVi79HZvvlkQR+UKhp+uPXesKfW1mKK/r+orKVkB3q4HvIwhD+HQ361IpQlEQcOHiRTyzfXvH97MsC+VKBUt0hrVer8NqNJDJZtHf34+NGzag9MILbZmynCuxynkxWVGWOFvfn+3SW0k+POoFATXThCSKGBoZQS6ff+SL38cyYQJkpWWaJtwgQDabRbVWQ7VeRy6bbZrjY5BkGaHjkNEQUcQv/PzP43fPn8ef/9mfYfeePXwm6zvf+Q7ee+89vPH6600BBpDSKUuac/PzGCiV+EUhCgL6ikX0FYvYunUrr72XKxVUymXcnZrC+fPnYVsWsrkcCoUCctksdLoTkllCjyIUCwVCs2f9HArbcchF1mZB0AuCIFhBEODkA1rSiSMMQ/ieB8/3ceXKFazfsAFL5TIC30fDslCv1VCpVlFZWoJpWchks8ik00ilUlizeTP6+vq6lmSA5fJKr5qYLPnFe9BhGKJhmoiiqClZRmFI/h27Dur1OiAIGB0b46bDCR4tRFFEOp1GrVJBRtfh+z7Mep3sjFhCiseyJEESiAG1pqo8lv/7n/95k49ht1hm16WqKJibn8dQS0tF13WMjY1hbGwMAFlsVms1lMtlLC0tYWpqCpVqFYqicBJcOpOBLEl8PtBxHMiShHQqRRJkbPHq2DaRY0Tv5d44uGhBm3hm84it4vJsIXznzh2IoohUKoW5uTm49POuVquoViooVyoQRRG5bBaGYaBUKuGZ7duRyWZ7Ihh1M3hoRVOrhcKyLC4q0posl/8joGFZCIIAhUIBA0NDj7R3yfDYJkxRFJHNZlFZWoIEYgbdaDSWJe1aviy26vN9H6qqYnx8HC+//DLefucdHHrvPbzy6qv43ve+h//vL/4CLz7/PP7u3/27K95TpSvDfKGAcrm8ImnGIdB6fyqVwsjICL8gfN/HUrmMhfl5zC0soHLjBmxKRZeoiLFhGMhkszA0DUYqBd0wYOg6POpQ/0l3RGEbhqxAfx5FxHHBsixYlgWb/t2wLCxS3c9z585BEATSl5QkpNNp9Pf3Y9PGjcjl8/B9H5ZtQ5HlnlZ68WTZC6kiwvKqVKTzrmEYwqzXAaB5kJqda6yva9s2PM9Dsa8PfaXSYxFgCQgymQy53hwHqVQKddNErVZr9iaN9fdkReHi7SyW3333XbzPYvm73+0ay4qiwPN9DA0NYXpmBjNzcxgcGOg4DiJT1aC+YhHRunV80WqaJhYXF7GwsIDZ+XlUq1XSSnFdKPSGn0mnYRgGjFSK/K3ry/PaLb3XXtEuYbLdGkuOPJZtm/y70YBpWZiZnoYsy3j77bfJwlxRYBgGqZZt3Ii+vj6oqop6vY4wIoo6PTNx6fvH1Xk6IrZQYBsAy7KIV62qNtuvtT4vDFGvVoEowvi6dTAMY9XF+U8Cj23CBMgu0/M8NKpV6IIAgwoBiI0GEeuN7TLZzJ0fBGBfw8/+7M/i0OHD+B/f/S5sx8F/+2//Dbt27cLXv/71tklQVRS4nocCpaAvlcuYnZ3F4OBg190Ro797nke8GEURA0NDWDs6CpkKsYMmrIWFBZiNBkR6g19YWIDVaMC2bZiWBd/3Sd9SECDSsg5bTcqyTHohkkR21FGEI0eP8vIMY4dGtNcR0hWn7/tE3osGjm4YPFn39fXh/v372Lt3L4aGhyHLMmnG2zYcOg8bgawKPdddMSfVDWJ8Zb3KjpkFVBOxI54s0+mm4Iv3OZgUXr1eRwhgw+bNyOVybctpCR4NBEFAkYqF2K6LdDqNer2OWrWKXD6/QlRCkiTYVFdaEIQVsfxnf/7n2LVzZ+dYVlXuXDNMk+bs3BwGSqWuM4bAclnQcRz4vo90JoNsLgdN15cJhkEAs17HwuIiiTXfR8M0sTg/j4Ztk5h2XURBQO5NlHAnyjLfpcqUryDLMifEHD58GD7riXoehIiaXAcBvCAgxtyUharR5GwYBnRNQzqTget56Ovvx/59+6DT4w18Hw3bhuu6CCPi6OM4DsIoIoo6PSRLPhsL8Htut3jmu+oYH8NsNEiyVBTous6Z0Ozzjo8Rua4Lx3UxMDSEQqGwquflTwqPdcIEyKCy7/tolMtIGwbUMFzWOaQXRDxpxk1li319+OpXv4rvf//7+Pa3v40tW7bgG9/4Rke3cRZkACEOiIKAhaUlzMzMYGhoqGPSZCQYx3EQgpSDNE3jDfKQXjiqpmFwaAi1ahWKqiLdErjlahUy3b0FNNEFQYCA9R/p2Aj7c/PmTaxdu5bvSm3HQdowoOs6IQ9RRqxCA7Idzp0/j+Hh4SYhY0EQiBABdTa3bRvVSgVBGPZ24dLzbepBRlFXq7PWvm9Ab0AASZaiJHFqPNuFst0zW6yYjQZnxSZzl48fFEVBsVjEwtwcIttGJpNBvVYjO81sliRNSuhh12wQBGT319/fFMubN2/GN77xjY6jImyHGUURT5qzs7O8atQtabqui3qjgYD2UNPpNGdwMva4KEnI5vMQZRme4yCbyzWNSdmuC6vRIGpZdAHr+z6JYdp7jMeyHwS4cesWxqlWrud5iKIIuVyOs9slWebl2HbxbDsOLly4gIMHDzZVgES6yNU1jZxbvY6GbUNVFAg9xIkAqsxF/79ay4gvfGPlWJsmbLZoD2PJkj2HPRYAX/yupzviT2Og/TDx2CdMtjKd8zyYtRqymQxRs6cmxbKi8NEJWVEIjRvLfbC4vNvf+3t/b3nX0aanoNDnM+RyOQiCgPnFRUxPT2N4eLgpaUZRBMdxiDxbFPFE2VQubu21UrKD4zjwVXVFEhFAWGIi7YmsVpwdpX5wvu+jXq83BTcrbXRCw7Jw4+ZNvPH66yt/GVuERCCqLZJAZANr9Tp0XYfabraRldXi9HF6Xp1K2639HVY6FkCSJWPxAssBxkhT7LOuVqsAgM1btiSl2McYuq4jVyigMjsL13HITtM0Ydbr/LsWYsmBMUURRZ1jGVgRzyJljnq0/CfLMgaHhjA3M4O5uTmU+vtXLKrYyJLv+4AgIJvNrvBfbIVBGbOWbSMTI9vFE4EkSZABhF1mgSMAR48exZqREQBEhzVquX+xSkonXLhwAWNjY80esex55GAg0s+WzZg3TBMy3fF1jM+WewiT5es0o95aJbLoZ8qSJft500hYjLMQBAHK1SomJicxNDTUXUHsJ4zHI22vAkmS0F8qAbIM0zRhpFIQRRGmaRLbF1qGVGSZCKTTMuKRw4fxp3/6p1zl44c//OHyi7Z8sQDZYbY6q2ezWQz09yPwfdyfnua7nDAMUa3XYVoW77catLyxWm1fp0LU8eQMNDPEmDhCr2inCrJa7+T8+fNYNznZXmaKvl6DlonThoFcPo9MOs2H0NlCYfkpK5Ml/3k7xMo27HE2LWdJkoQM23UgxrRrk2A910WlUsHa8XEMDQ0lrNjHHNlsFkahwA2CDcPgM4usby2AiH74ngcAeP/Qoc6xDLQdcdBUFS59PujrDQwNQdd1zC8uoh6bYbYdB5VqFZ7vk6SezZJdrtAsQ9f6Lozt69MRsW7H8yBo9cFku7pOqNZquHv3LrZu3bryl/R5bEEgiiLyuRwhJWoaX2w3HT/aJ0t2LCt+Rp7QdM8JfB9104Tv+9ANg99nItD7FIt7+lyG+fl5yLKMbc8881j0LeN4IhImQHZ/fcPDCMIQ9XqdSCiJIuqmyT00RVGECLLbOvXRR/ijP/5jjI6O4vd+7/cwMjKCt99+G/fv3+ev2XpjTaVSXEsxjkwmg/5SCaHvY3pmBrZto0yb/6yZ3tSDidGo24UNKyezea3YAXVdQXYDL1fGSxddXov1Z7ds2dL291GMRKNrGnFcByFHZFsCrYk11+Y9QzpnGj82oSVZMr1RZqGUpkQEPkcbxZSOYt+b7/uYnp2FquvYtWvXY1O6SdAdfX19UOi4SRSGSKVSvFwYhSGCKIIoy8QI4dQp/Pt//++7xjKAFUkqRZn2cciSRERINA0LCwuo1mqomyafD81lsysECYQWclkrdFpVanfveFB2LHtOSLVwl0+ts9ADAJw7dw6bN2/uLIwSG8vKUGUuQRShGwaymQwkQSDxR0U/WBm27Wu17g6x8l7qui5ZkEQR0pnMiuPiBKaW8y6Xy6jVali3cSNxl3rM8ETdXVKpFIqDg4iiCHXThEHZnI1GAzYdpBcEARcvXcIf/MEfoK+vD9/85jeRzWbxt3/2ZxGGIf7rf/2vK1+Yftm5XA61arXtRZ5JpzEwMADHcXD95k14nkeCqw2xhA8ldzkXnfY4zdgurd3jew23kI5YCPFVW4dgjQCcPXMG27Zt61jucBwHjuNAoeWaJggCYQfSFWO9Xic7gQ7vF4YhX1Wy4GJSeABJ9nVaLWArUfY7SZI6rtY918Xi4iI8z8OuZ59NSrFPEARBwMDICFTqG+v7PlKpFIIgQK1WI8bJkoTr16/jD//tv0V/f3/Pscyuwlwuh1qttuIhsiRhaHAQuq7j7t27mF9chKppyHYZq+A/b3ONC6JIeAdUwxjosFDucdfJ2LVNO8wuj5+dm0O1VsP69es7vl6j0UAIQqRs5QtIkoRMJgNVUXiLqZvYQUh7u/SkVpxXU5Uok2m6xzDyUOs9NgpD1Gs1lJeWkC8We1IoehR4ohImAKTyeRSKRQggck6MnmzZNpFlm5/Hn/zJnyCdyeCb3/wmZ7zuf/55rF+3DidPnsSlS5eWX5B92SIxiRVEkcjLtYEkSYRVJggwY6uxtuiBcm1Qk2ynpQzMH4LuSTeOsM0MZifcuXMHruticnKy7e8Z21eiA9+dICsKWZ2KIinddpDTYyVzbsOG5ZuH53lkV9G6EqW7dLbaboXjOIS80GhgZGQEmzZv7uncEzw+kCQJ/cPDXDrS9zxkKBu6Xqvhzp07+M//6T8hXyjg//7mN3k5tmMsUwixBTDrbbeDYRikDeM4qNMk3Q3dWiSaqvI46JhsHiRhYtnWi1dW2iAIQ5w+dQo7d+xoa18XRcQCLwhDpFOpjhZ3Ap3b1A2DjI9RLsiKY6OsXT7+FjuuMAxhmuaKKlHrua3oiQYB6vU66o0GZFXFvn37Hqu+ZRxPXMIURRHpvj7kCgVCVTZNruRxf3oaf/xHfwRBEPAPv/ENDA4O8p4Iogh/hw43/+mf/unKF6Y7nkI+3zbIHNclxIRUCpOTk1BlGXPz86hUKh2PlUvZdbjYmSWWTS9odhxN59tjkAVhuMI3rx1sx8GZs2exZ+/etivewPeJtJwoEhZvt/enJIIMS5qUWdiKMAhWiCqzfmXDNCFKEjJUHDsCWW1GWO7Lxm9kURTxMRzbcZDJ5fD8gQNJKfYJhWIYyPX3I5VKkREyKpS+sLiIP/4P/wEQRfzqr/wKBgcG+DURrRbLACAIyOfzbXeYYRiiRnt2Y2NjGCiVYNk27k9PN7dI2r1sp+tMEMioWxTBii+44/Hc40xmu/ZKpyi8ePEiMtks1qxZ0/b3bCFrUC3WrhBF6HS2lCXNVoRBwOek473HwPc5p6S1ShS17ijjLRVaXWIyoZu3bMGaR+R12QsezzS+CkRZRqpYhEAHixuNBlRFwdjatfjt3/kdrpgDLF/gQRhi+/bt+E/f/nbXJJDP5VCt1zE4OMi/cJ/W/0VaYoAgYGRkBPMLCyhXKrBdFwP9/W1v2gJinntt3jeVTqNaq8E0zbY2Q70EWNsSTtTeYPbU6dOYGBtDsVhc8TtWGgXQ3W09Tu6hiwLOdrQsMggdKw3zZB4LroZtI/R9KKoKwzCWz72lR7lCHs+yELGeqCxj57PPrmAFJniyoGezCH2fszZN08TaNWvwO7/zO2QWmAr967rOe9jbtm/Ht7/97a4VmHiLJb44bFgWfM/jDib5fB6KomBhcRH3Z2ZQ6uvr7LcYk+VrBZPFc6jcZCsYU3y1vmZre6UTyuUybty4gS9+8Yttf29RYXNNUTgHoSNix6RrGhBFsB0Hjus2tZ1ayYVsUsCxbUAUkc5kCKsd4Frg8XhmGwP+PHqvdj0PQ8PDeGbnzu7H+YjxxC7LZVWFlsshlUpxlRzbtrnkXIMmUoa4+j1bpbZDPp9HrVollj8AV/sIwhDpmMKQIAgYKJVQLBTg9LA67XTxi6IIQ9e5h2PrDrOX/eWKFWkHgsDde/dQKZexbdu2la9BGW0A6XN09cNrk0hFSeI3GV7SpjcHljCZnCAjdhipFBHhBqWqtyMM0dWpbdtE9o6O7ziOg4l16zCeGEM/FdDzeUJAyeUg0iF3AaTUGfg+yuVyE9mEleuDLrGs0RaL47o8bh3XJRqmut5k+ZZKpTA8NARFkrpWjgQqDN8pLhlTnjHIW4+t13hejbwXRhFOnjyJHTt2tBUSaTQaZO5RVbkBQtvziS1849ApP8RxXc5BEETiU8oW54z059g2ZFVFlvYrmTh+pwW3T0uwjuNAU1Uww4hdzz332JZiGZ7YhAkAaioFJZ0mgUaZqq7rQqEOHEtLSzAbjabdHbtA2I289aLO5nKo0zKOIAhEE5KuRtslvXw+T8pFUYT7MzNNSZq9BlvhikJ7p3Qm1uy4blsfwNVWmrzn0SXJuZ6H06dPY++ePSuEG+LJMkP1MjuCBkM7yLLM2bM+DSy2+w3CEDXqI8j6G2y+DlgWI2h9L4cyJx3qJ5rNZNAwTfQPDmLLli1JKfYpgSiK0AoFwsLOZIjKFx3012iPs1wuNy1KBUHgHqhN9lnLD0AuFs9RFPFKUTvDc0VRMDIygnQ6TXxc5+ba9zVpVaVtu0QQ+MLRcd2VFaMeyrJhrL3S6bGXL1+GqqqYmJhY8fpmowGPJssU5UmsAE2SrazzOJjHZYPa6TFJPlBGrUm5B0Y6zY2fuWZ0B7a8ZdtEvSsiknySJMHzfWzYsqVt1etxwxN/t9GzWUiaxuf2UqkUMQ9WVVJWsG3U6vWm+crWVSoLuCiKkMlkSN+DJgabqlN0MyA2DGN5dUrV/+OBFr8cmyjqMbCaf7u+wWpgFHRGqGkX5GfOnMHIyAiZZ43B933UqRceu4DbodNKtBWM/WtbFiCQwfOG4xBnFHqe7eZV2yVLy7LIAoR+LynDQLlchpHJYPOWLZ3LZgmeSMiyDL1QAAQBmqY1qdww84J6vQ7TNJevcUFoms1lN3U2hpSPEX8cKg0X93xsRbvKUZzcF39WJ0MBWVGgqSrvy7W+fjdeAncCoXHY7pHVWg1Xr17F7hYmaRRFaDQa8D0PGpXMA9rHVi8jbIIgIG0YXE4PIGQ727bhuS4U6qzEHFaa7LxaztH3fZSrVbiOA1XTkMlkEIYhKrUaxp6gStETnzAFQYCey0FUFDC1nVwuh5RhIBIEeFQPtTXQOCEnhiiKCFNWEFCr1WA7DveJWw18dZpKoVatYnpmZnmmqeV92u2KREmCoevwgwAOXUVH0bIze4hldRv2c1Yq8X1/uQkfrdRknabqJjt27Gh6T5826gWgKVmuKCOtshKNP47d7AJKZS9Xq3BdF4auk+DqsvCgbw7HtlGpVtGwLP59KrKMpXIZqmFgy/btGBoa6v46CZ5IyKoKLZ9HhOVxh1Q6zUVFwjCE4zio1Wp8Ecx4AnwhzKpIYYhcLoe5hQVEYUiY35LUvYJCEa8czczOolyprFiINr1fC4xUCiLdifFkjuWEyGI5ZH9oJYapDIl0nKodp+HkiRPYunVr04KRtY583+fEnfjvmo65ByKhIAgAtR4U6UK+Ru+hoiQhRQXn46TGdr1dRgaqUSH1bCZDknBIPDVHJyawZcuWJ0b3+YlPmADtAxYKEGn9XJQk5PJ5FAsFYs5MdRsbjQaq9AYeR+sFPzIyQlaWto0Q6Lraa32dgVIJpVIJURhiemYGS0tLbXssArBihaeqKul/mCYxo6WJMWBEg1iwxY+7iSEbD2LaTD918iT27N7d1B/wPA9mvb7Mcm0388WIO91WojFCRfxxDctChVL187ncsu4vOnyONFFWazUiYM9uljQoK9UqZFXF5q1bOzICEzwdUHUdWjbLF2mapqHU3w9NUYhICchOp9a628TKWB4aGsLs9DRsx4HveVBUtck/tVvyMAwDI8PDSKVSqFYquD8zwxezcQht3lcSRWi6Dj8MYdo2AhrHLKY5c7SlxcFHsGKiHfwYBQFXrlyBIIrYsGEDf05TstT1JjPm1hL1aoQjgT2OOa1EEfwoIqpmjQZUTUM+l1vuVbYcHwNbjNfrdQSU3JejzjSe52GxUsGa8XFs27btibLge7w7rA8AURSR6uuDubiIiDLumHB7EAREWJ1SpV3XJaXBVKop0QggK72h4WFcvXoV/f39fOXDExXbwdGVVbvVJfNhXFpaQq1eR61eR19fX7P3W7yUFFuBqrQJbppmk41ZpwudlZI5SSe+E4wiHDt2DGvHxohknCgiCkM4TKuVCku3Zff2EFz0g+c7Xs/ziNwZdWiIQEZnWjU/o/hnFlG2HHVakWUZWoySDoCUyAUBGzdv5v6FCZ5uaKkUuTZqNTAzgL7+flRrNe7y4XoeatR5I00H7+OVI0Ym0Q0Di4uLUFWVyGdGy6pRIotltF/IybKMgVIJDcPA4tISZqenYaTTxJyhZeyDCXKw9xYE4kTi2DYkeg7LT2ifqBnhZ8V9RRAwPz+Pq1ev4vXXX29i8FumSUZH2lhgseOI32faIQqJjzAj3wVBAMd1ya4+CCBLEim90nMC2u+sfd8nOtmeB4EuGlS6SGE76KWlJawZG8PWJyxZAk/JDpOBzWiymzjTeGVq/Vla3okAlCsVLMzPEwZsECxL2YkihgYHsbiwAJ/6UzaBlUlYqZQRDtjuj/5ckiSUSiXupzk7N4eFhYWVvU36fEb2EWOqISv6mW0ueMaQlViQxS7iixcvIggCUoqlQWM7DhGup7OPTdqzUdS0k+2EKHauES2R1Wu1ZZkzXSfC9SAJXYuXYdnNLAybdpQSpaRns1lyLvThddOEH4bYuGXLE9PnSPBwoKXTUDMZvusyDAOyokAAGRnJZjJQqGjJ4sIClpaW4DjOihLkmqEhzMzMrEhEQjyWaZKIOsRzKp3mhCCzVsP9+/fbCpxE1JWEiXPomgZJFGFRM+TVwBxSWmPdtiwc+/BD7N27l/cmgyCA1WgQPd5Uqn3rqN3Cl8Y5YqVhNuMaUr3Zar0Ox3W5gbZOJxE6OR8xU3CzXkcQBOR+S/W12XsGvo/FpSUMrl2Lrdu2PZEchKdmh8kgiiIyfX2oLywgCENiCk2NVrO5HPKqSnw16c8WFxeJ8EEqxUuTiqKgr68PC4uLXF2kE+J1+6ZdKAAIREJuaHiYMHZNE5ZloY/OebEAbZ0TUxQFGk1EEm2SA+BMtThYEMoxRw8AmJ2dxY0bN/D6G2/wFSZbHGiaRox06YqYLxbo4+IECvoPvgNnwQW6o7Qdh8yNiSJSug6F9oBdx4EfBFDi0nZ0hclm6wDwHSUnDsT+VGs1+L6PjVu3YnJyMmHEfg6hZzKEAFarQRJFZDMZVCoVeFRKT9N1OFTlq0EN0TVVRZZqwgLA8Jo1OHbsGDZ0kI5jEFvaGnycgvwSoiiiVCpB1TSUl5YwOzeHdCqFQj4PQZIQttjPMaTprHWj0UCWVY06cAKCMOQ7OYYwDPHhsWNYt24d790zOztREJChrirxBMgWq0JLDPPYjmvV0oWv5Thc2k9VFELgY7yGMERErdbYuYVBANfz4NHeMtPIZtaGbOyHHe/S0hJKw8PYtm3bEzs7/dQlTIAIG2QGBtBYWoLnOMhQmrhj21wOS1HVZcFn00S1WkWtVuNi6sPDw5idn+dB1prU4uAlIJZUYokTIIFYLBZhGAYWFhYwMzsLVVWRz+WapODYRRZF0bLaBpWokyRpWVIqdhwBHXKO/8yyLBw/fhzP79/PRd7NRgNREEBPpaCr6nIZigUZXcW3lmKjKOKzZ+zYPNcliZL2WlKGAYWWw4DlG0YQhkgrCgJqhut6Hg9UTdOgKArx7YzdYIKQmGEvLC0hlU5jw5YtSbL8nEPPZiHKMqxKBbIsQ1VVONTPUWKSbtRmyzRNWLaNWRpjmUwGxWKRsDsdh6jxrAIeSdTMgRFyWG3IoJ6zS0tLqNfrqNZqZMfLDAPQvIgWaeuDiayk0ummBWgToohbm7E4PH/+PGRZJk4k0bK5uySKSMfIemzGnCVOgJIF40mTxnNI/x8EAZwOiZLdDwSQHWQYhpDp6J7rutx7WJZl6HSulZV1I9D7ITXLMG0bI2Nj2ETN3Z9UPJUJE6A7zf5+2PU67GoVmqrCdhyoqkp0EKOIixykUik4jsMv6Dr1iJufm1seIu6FWcb+jiWAuG6irusYGRnB4uIi6vU6ZmZmoBsG8rkc6fPRWTI/CCALZJ6rGjPYZSUl5h0XhCE832/aXYZBgCNHj2L9+vXoL5XIeVkWWYmywWJ6XKzfIwDwERsdAZZ3lbTv6fk+PNclprwAT5TME7N1RMShjumu63JKuqIoUA2D9EAovb51Ls2xLJRrNZQGB7Fh40YMDg4+6Fef4CmEahiQFAWNpSUYqRTKS0uwbJvPCoqiCJX60TKCX71ex8LiIiRKApyemUFfX1/T6zYRgFoQb9PEF8LsWu/r6yOuJ4uLKC8toVqtIpfLIUNVsgSQChCz6lLpPUi0baKeEysJs5IoIzoFQQBBEHD37l1M3bmDN954A0EYwmw0EPg+VE1rmn0EPS6J/p+1fuKxxe5Lge/DpfHMCIWaqi7vDEEWvSHbadNWThiGqNKRO9bmUhSliRTJPp8oiuD5PirlMkRZxsYtW7B+/fonhg3bCU9twmTQMxnITFSdqvrnYu7o7OJnVOxCoYC6aaJcLkMUBFy+fBlDQ0NI0YZ6fOi/l2Djc2K+T1Z2UYRCoYBcNotKtYqaacKenYVhGEgzsgv9I4AMD9frdTRMkxjexsqbEAREQQCRCQAIAk6fOQND17Fp0yZOcJJj/Uq+amxZAMiSxEvE7P19uiv0XRchPSdFUbghL//8aKD7vg/f9+FRZRbPdYlhtqqSHSj9zJsSJdudA1hcWoLv+5hYvx4bN258InscCT47SLKMdH8/pFoNnuOgbpoQBaGpTyYIxLA5m80ik8nwEZRMOo2pO3fQVyxC13VSFaHtA6D3WI4/JowiqJqGkZERWJaFcqVC7Klo4iSHtLwAjWu0stlShjgznfER6rUaPvroI7z80kuQZJnr4qbi/Uq6Y2zt2za5gggCwiAg8UxjFCAxn9J1yHRnyM5PACET+b4Pn7ZdGo0GN41X4vGP5g0Cg+O6WFpcRL6vD+s3bsTIyMhTUSV66hMmQGa7soODiEQR8zMzqFQqyOfzRHmnhRLNzFWzmQzm5+YwOzeHYqGARqMBic4l6bQkI8syl9DrxJhlOziRJiQBJNBESUKxWEQ+l0O5WiUNc9NEBLLakyWJmOjKMgzDIEP8to1UbDyDnx/dsV26dAkLCwt45ZVXuBC6SrVa48fTCYIgwKclH5cOeQOAKsuQKcMwviv1fJ+UW+nffNxFFBFEEQq5HHGMjyVpXq6KHYcfBJifm4ORzWLztm0YHR197CWyEjwaiKKIVD4PWdMQ3LkDk4pu6NTDsnVHpek6udGrKqampmDSka1arQaJKlPptFIix/ro7aKE/UwUBCLJF6seGYYBwzDI7HGlgiWqSpRKp0nfklZq0qkUqtSZI9OidgWAu4BYjQbeP3QIO3bsQCqdRr1eB9NsboqNdqQe+jmFUQTXceC5LlyaJEUqsK6ynSGNZdYKYUbYfF5dFOH7PlRVRX9fHx9ZERkjOPaZs50lG/dZMzaGDZs2rcoDeZLwubkriaKIwuAgREnC7L17fNUp0sTUOoQsiiI2btyIm7duIZvLQVUUNCwLDnVmr1WrZLelaaTMS1eMYmzltQKsdMJ2twAESUJfsUh2nJUK5ubnMTM7i3wuRzzqaKkkCkPYrgsbZCi6NciuXbuGGzdu4MCBA7BsGwKW7YtWk9bzPI+YWfs+L73IsgxdlpdXnyDlJTam4/s+D1RRFKFoGhRZhizLRAyBBnectt8a1gF1jTDrdQyOjGDDxo0YGBjo6ftM8PmGqusYnpjA3Zs3iXSbIKwYKwGW5wozmQzWrVuHhYUF7NmzB5Ztw7Is2JYFs9GALMtQaC9OkmXIksR7ia2L4dZoah1jSaVSaJgmZubmUC2XEYUhstkssQaUJGQzGXLdNxrEcitGNlJkGY7j4P1DhzA5OYn+Ugm2bfPW0WruRSHbGfo+bNpCEUHG1TRV5RWykJrXB0HA45mdmyzLZNFO2y1mo0FmY3W9qToUv2dGdKFdrlQgqyo2PCUl2FZ8bhImQ66/H5AkTN+5g0ajgXQ6TcQJmKhy7ILUDQPjo6O4dOkS9u3bB426JXiuS+ylbJtrKoqyDEkU+S5UpkQdkZJa4qvf+CXPAkCmzNyIsk/NRgOmaXJyUjqVQhgRbVVBEHhJRhRF3L17F5cuXcLevXsBAArdlXbyx/ODAL7rkkChzD4BpOTF+hgACSrbsuC3eNix+TL2J/4+jGCkSBJJ9C3vLwDwKRGgXqtBFEVs2rYNExMTSQk2wQNBVlWsXb8e927cgFmvQ6A9etbW4MklImLhY+PjeOftt+F5HrKZDLKZDAI6N2hRzehKuczLuqIkkWtcUSDT/0uULcuqL61jKgxGOo1hUUS5XEYURVhaWkK5XEbKMJBKpwkJiCbNbCbD2e5hGOLo0aMYGBjAyMgIwg7zlQxBLEHGF7GSKHJJT1EQEILoSftMWzsGFveKoiz7XFKYpgnPcZDLZpfvYW0SZaVSgeO66C+VsHnbNgwMDDwVJdhWfO4SJgDkCgVEUYTZqSk0LIvI6IUh6dPFAk1VFEyuW4e3330XNmXYCoJAdpWahkw2y0sYrufxFZtLL1wWeJIo8jIOe32BBh77IwjEW1JVFD6EXacBValUUKlWodMVnm3b3DZnYWEB58+fx+7du6HrOtKpFFEzYXNldKaM7SDD2CiLKIoQaJJnQeVQA1xefhJFyJIEWVXJDUOS2s5usiBiC4lMNrvc76Wr9JAmylq9jigIkM3nsef551EoFH5C33yCpw2yLGPt+vW4e/Mm6qbJ53gRRQgEIs4OuhjO5XIYHR3FpcuX8dxzz3FGakqWkUqneRwHvk9YoJRBalkWiRMaz2yEhOk383iWJIg0jtnfhmEgl8/DoSMvjUaD7GglCZquI6AlTIWS8T48dgzpdBqTk5NQFIVrTHPhc4CbGwS0dBrF7isSPQZBEODR42dg9yOWGCV6zK0VKCEWrzW6GdDZYpY9lla8KuUyXNeFKEnYun07Nm/d+lQmSgZhFTWXHqRenlwsLS5i4d49iIKAdCbTpOIQgSQLz3Vx4qOPoCgKnm3j1Rb/gEIqwde66gvpMLPn+02lVCGWLFmzv9Fo8EAByMXreR7qpkmMpukAsCRJOH7yJCRZxrYtW1AsFCBTPd2ICSHE5ikjgAS8LJPAZsw/gAe3AMCjg9PsT7tybgSqeCEITecTRkR30/N9DJRKkCRpeRiaymQxYfzxiQls27nzaQqu1WnUjx5PbTz7vo97t27BMU2kUinO3mZg1/Hs/Dzef+89/NRXv8oFNeKVn/gcY0CTkk8JM57vExGFIIDj+4jiQgTx5AnCWfCDAK7jcCcl8mYRSZymCZclvDBEJAj46KOPUCqVsHHjRtKTpX1PJtzA5yzZYpzeP/iumh/KshFDRHfXoii2rzihs3qN2Whgbn6eEKgoFyEMQ7iuyyVGBUFAoVDAjmefRV+LscMTjrbx/LncYTIU+/ogKwoW7t1DtVIhTXhFWU40tJc3OTGB9w8dwrp165BrGbhlnypLsJIoIqJqJAAtmYQhfM+DZdt8RRiEId/tMXaqFxGHDouSbuIBAhCGqu84cB0Hc7OzQBiiUCggDALU6nVuEyYJAikhxXawbEXJd7YsSdJ/AyThsXksfn5xVm7LOcd/FoFI2Dm2jWwuB58ek03NegHSRykUi5iYnMRIInGX4CFClmWsmZjA3PQ06pRtvcKYHEAhn8fAwADOnj2LvXv2rPC2FGJ/S7Qkq4LMK4eUCR5S2TjP8wj5JwhIUmPVnDAE6G7VsW0EdH4xokIIbLZZFAR4vo9qpYJ709OAIKCQz8OkjiOqpvFdoxCr7rDWjxD7WxSEFXwMx/f5e7aeZ+titxWe72ORjoToug7TNHn1CHR3nctkMDQygvWbNi3vQJ9yfK53mAye52F2ehqNchmaqnJ9Q1aaCMIQZ0+fxvTcHF579dWmFV0v2wr2Ifp098kuVqbBygItpPNjvu8jm802lTrZcdq2jfv37+P6jRvwPQ/btm/nZWIBRLtVoyMybAC56RjZ2EjLzwQAThAgbLEjWhW0XGRZFu7du0fUlVSV90lYPzVlGCj092N83TpuGv2UIdlhPgaIogiVSgWL09OIPI9UjmJSiwBRkPrrt97Cs7t2YXR0FMAym33V14+9j+v7RPgjFs/MYJlpK9eqVRipFCffxZ1LXMdBvV7H+XPnIIoiytUqtm/fzo2vmYC7pqrkbxrjLAG2+zL5LjkMiVA8I+j0eF6CQGZAp+/fR6VeJ/dCJnhAWccpw0A6ncbI2BiGn14jhLYfWZIwKcIwxNLSEirz8xB8v0mYPQIp+bz11lsoFgrY+eyznC0W36EB3S/MgAZRN9i2DduyUCgU+MiK77qwbBuB7+PajRtYnJ/Hrl27iKm1SHQqozCEIElEtcN1+fwVY67KksTJC5yQ1NKLZAHWCWx1HAQBESSgJWfLsjA/P48gDFGgziQGJTewne7w6CiGRkZ6+CaeWCQJ8zGCbduYn5mBVa3CoGMl8WrQ7du3ceKjj/DaK6+Q0SeK+NjUamAl2o6IIpTLZTKGxrwpqc2Y67owTRNnzpzB2rVrMTY6Cs0wYNEFs0RLuo7j8JEtMUYo5PHMGL0t5VaPlpO7IQKVt6MiBqxtVCmXUa3VkDIMGKkUDF3nakoCbV+NPb0LX4YkYfaCRqOB+dlZuKYJWSBasOxirFSreOutt7Bz1y6MrFkDOa4ARFeV7di28UDlu0z2u/huTyAarMyphCUmJs114eJFeK6L/S+8AMe2oRsGFFmGbdtEQk8kVl0CAMu2uRwY68MIUYSIEiIigFPnJVFEQBWGWhNmXLHI9TxEQdC0Yg0okScIQwwPDSGfzy/7agIoFItYMzr6eSjZJAnzMUMQBFhcXERtcRGR60KjZD22Czt+7Biq9Tr27d0LI5VaJrBRsP5+p5ESn/UXY5KVvCpE46haqUCkjHGXlnEFQUC1UsGZs2exa9culPr74XoeMpkMoihCvVaDH4Yw6CiH67pwaDy7noeQqgdFsfdhJVk2K+0GAde2jYOVp5kwQdSS8B16L0mlUhgaHoYeY+cqqorhtWtR+nyobyUJs1cElKRSWVyEY5oQARJsioJbt2/jzNmz2L9vH7LZ7ApD5I7lDzYgTBNOSKXp4gipQ8lf/vCHeOfdd/GNf/gPibdmFOHEyZPI5XLY/dxz8H2fjMSwsi3AiUHx4ebLly7h//nWt/DLv/RL+NKXvtRERGIsO8914XgeISxFEURgWe0nBlEQlneolK4eUaks23FQLBSaHN4LxSJG1q6F0YN251OCJGE+hmBjD9VqFWa5jJCaGaiqCkQR3nzzTQwND2N8fJwzUvlzsfJLjc8fMhIMk7Rrei7td37/f/5PHDl6FP/Xr/86+opFLqBw9coVvPDii+jv7ydJlYoosOcygQWNCo9cvnyZx/KXv/zlFcRC9seNzVS3m5kE/bckinyHqtJZ64ZloVqtEpGC/n7+HFVVMTAygtLg4NNE0lsNCemnV0iSRDQhMxmi3LGwAKteh2VZGBwcxMjQEE6dOoWdO3cik8msbo4MLPcSYqXcgIkAxHeSADfI1Q0D96encenSJWzevBnlchnf/s//GTP372NmZgZ3793DF77wBXz961+HrCjIZrOomyZqtRo0VcWGjRuRy2Zx/PhxfOUrX4FEh5G57ixTK6F92p78L+nzzHqdCzlkMxmSLAUB+UIBw2vX9iRynSDBZw1BELgKj1ssolqtorq4CKdWgyLL2LtvHw69/z4EQcCatWthUH1UoIvaT5zsFpvH9Gg8e57HiW4RyCJZp/PNx44dgx8EyGQy+F//63/h9u3bKJfLWFxcxJ49e/D1r3+dL3pZlcjzPEI4zGZx4sQJfPnLX+Zsd+Y1ydolrALUi5UYA9PRrjca0HSdKPMIAhRNw+Dw8OctUXZFkjC7QKQlznQ6Ddu2sbSwgEathvXU7fzEiRPYsmULMtksMun0sg1XSwmH9QrYeIlLmXaMUh6CkGN06vcX0dGRox98gGKhgFdffRXZbBa//du/jdt37mBwYACpVAp+EDQJNkuUucbYbK7nYc+ePXj//fdRN00yb4rlxj4jKgDoOVk6VFeSqQnl83nk8nkUikWUBgc/TzvKBE8YVFVFqVRCoVBArVpFZXERUhBg7969+OjUKdTrdYyNj3OtWS4q3rIYZgQ9tsvj4ybMzF0UiSMSjWXHcXD9+nUsLi5i69at2LB+PX73d38XN2/fRjGfx8DgIO7fvcu9ddn7GboOWZJgWhbq9Tr27tuH9957D2ajgVSsmgOAl1/jrPrVEIQhGqYJ23FgWxaZGc1mkSsU0FcqoVgqJYmyBUnC7AF8lTo6ipAaH/cNDeHi+fP4+Px5bNiwAZZlEQV/6oZCn7jMSo2PZbCxDyapR4XJI7rbXFhYgCjLGB8dxXO7d/MA+sVf/EXk83mkUincu3cP3/qn/3TFiAc7VkVV0Wg08MyOHTh+/DhOnTqFAwcOACBuBYipoTAvu/jrAM1sPC9GPHJcl5RtBgYwOj6OfLGYBFaCJwayLKPY14diXx8xPq7VkOvrw+H33sOVK1cwPjaGaqXCk16T3nRLMmIkIU1VycgHJeEAyy0WAKhWq3jjjTf4fPX/8Yu/iL6+PhipFG7euIHf//3fX8F9iCLiqJSnPIXt27fj5IkT+Oijj3DgwAEwgXW0PC+kFSz6IiuOPQxD2HQ8jREE84UCxiYnMTA8zKcEEqxEkjAfEKIoEuZYKoWBkRGMjI/jL37wA0ysWYORNWv4Ck+LkYUAIlUlSRJ3FghbAq9eq+H6tWu4decOXM+DLEkYHRtrCoTt27fzGa3V9GFlqln5zI4dUFUVp06dIpR1KoHFiUitxxJ/3SiCS2UAWamJNf5HJyYShZ4ETzxkWUa+WES+WMTadevw/f/xP3Dx8mVM0p0mM1znbjt0B8lk8kCTVpOAie/j7r17uHHjBqampgCAiKjTZBlFEZ555hn4vo9atdpxscnejy2Cn3vuOfyX//JfcPr0aWzdtg0a1bKO32ei1vtCPJHGEqVPmbeZfB4DQ0MYm5hoK2yQoBlJwvyU2Lh5M355ZASHDx/GoaNHMbpmDUbXruXuJCq1wxJiQSEIAgRadr13/z5uXL+Oaq2GiYkJvH7wIP7qL/8Sly5eXEEMCoMAnutCiQkat5Zf4v6SURQhk05jfGIC58+fR+D7aNDSjUZNtNsl3pCZytLRkSAIoGoahsbGMDA4iHw+/9SJKidIoGka/tbP/RwuXbqEI4cO4fK1a9gwOYmBwUGEVKFKVRQuSs4gUpZ5rVrFjRs3cPv2bRSLRWzYsAGzs7O4fft2EymI/e1Sn1gxnvCiqIlpy+I5iiKoqorJyUmcOXMGv/DzPw/H8+A4DteClUSRy3vGX89zXdILjbkK5YtFlIaGUOzrI8z6VRbgCQiShPkQkM1m8VM/9VM4ePAgjh07hmPHjkFXVaTp7JKuacik04hAxlZM00S1WkWtVkOpVML6DRswMjzcFDgAuIMAS4oOLZ9wK6MWJaA44sl27969+OjkSUzdvYutW7cSc2fP42oloiQ1DVv7ngdQVmwqnUZfqYSBoSGk0+kVrOAECZ4mCIKArVu3YuvWrbhz5w4Ov/8+zl+8iHw+T9oylLVqGAYc6slpUv9cQRAwPjGB119/nXjXgrDLmcNPFIYA3TUyiTkujh6r9MSViVqPjcXy7Tt3sH37dmLSTnkFjLjH2LGMNctmtDVdR3FgAAPDwyhQVnuSKB8MScJ8iNA0DV/4whdw4MABzM3NoVwuY35+Hgtzc7g+NQVZlpFNpdDf14fJdeuQo7Zh7S5alrhY4mPkASac3A0CqB8efe7u556DIAg4eeIEdu7cSST2fB+2bcOnpVZRlqFoGtLFIgqFArLZLLEto87qSbkmwecNY2Nj+Lmf/3nUajUsLCxgcXERc7OzWFhYgDU7i0w6jWwqhVJ/P57dtQt6KsX7l3EwuUnH86DRygxjxWu9kOTo7jSKIh7LJ44fx44dO2DoOnRVheu6aFDD+EAQICkKNMPAYD6PfKEAnbJ/FUXp6HySYHUkCfMzgCRJGB4exvDwMP8Zs+1i7gdmrQaXevH5QQCZEQaodZBFXUNY39CmmpTpLgHWOjcmUv3KdDaLTZs24czZs6jX61xgQUulUBwcRI4GFNOiTZAgwTKy2Syy2SwmJyf5z8IwhOM4ZCSjVoNlmnBtGw0qBsBmllkMC4IAx7ahyjJCOhvKVHs6IS5Xx5jwmWwWGzZuxKkzZ/C3qSoQqAB7oVRCtlBAOp2GpmlESi/ZQT5UJHfHnxAEQYCqqlBVFdlsFmGpxJU/bMtCdXGRUNTDEC4VN7YdBzOzs1AVBYHvQ9U0EqSuC9d1+Wq2YVl8zhNYFkdgpARRllGu1xGKIrKFAvoGBzmRoReD6QQJEjSDWXcZhoFCoQDP83g815aWyIKXxrIoSfCCAJVqFWajQV6A8gtM0ySxTBNnw7KaWiwRHWFhdn6iJKHWaBD1oFQK/YUCcrkcj+VkwfvZIvl0HxFEUST9TV1HNpvFwOAgn+tywhAnz5/H2vXrYRgGbMuCJEkwKN07CkNEioIl04Tl+0gXCsRaiOq2KjQxM4uuqakp/NVf/zX+0T/6R9i0bdsjPvMECZ4+sHInABSo3y6L5Y/On8fIxATy+TwqlQrCIECKGryHNJbnymVYvo9UPs9jmTHrlZi58507d/Cjt97Cb/3Wb2FbG7vBBJ8tkoT5GIElOIBYZeVyuaYyEEMURbg1NYXLV69i7/79WL9xY9dd4g9/+EO4rouf/umf/qwOPUGCBDEIgsATqGmaSKfTGB0d5e4oDFEU4dadO7hy7Rr2Pf88NmzaxJ/fDn/1V38F27aTWH5ESBLmEwg2LN1uaLkdvve972FkZAT79+//SRxeggQJekQSy08WkoT5BOG73/0uvvvd7wIApqenAQBHjhzBL//yLwMASqUS/uW//JdNz1lYWMD777+PX/3VX016lQkSPCZIYvnJRJIwnyCcOnUKf/Inf9L0s+vXr+P69esAgImJiRVB9oMf/ABBECQlnAQJHiMksfxkIhEAfYLwT/7JPyFiBR3+3Lx5c8Vzvve97yGTyeCNN974yR9wggQJ2iKJ5ScTScJ8imHbNv7yL/8SX/3qV5Nh5QQJnmAksfx4IEmYTzFOnz6NjRs34hd+4Rce9aEkSJDgUyCJ5ccDSQ/zKcYLL7yAU6dOPerDSJAgwadEEsuPB5KE+Rji4MGDAJDYZyVI8IQjieWnC8Iq7ty9WXcnSJDgSeD5J/GcIEFvaBvPSQ8zQYIECRIk6AFJwkyQIEGCBAl6QJIwEyRIkCBBgh6QJMwECRIkSJCgByQJM0GCBAkSJOgBScJMkCBBggQJekCSMBMkSJAgQYIekCTMBAkSJEiQoAckCTNBggQJEiToAUnCTJAgQYIECXpAkjATJEiQIEGCHrCa+PqToI+ZIEGC3pDEc4IEnwLJDjNBggQJEiToAUnCTJAgQYIECXpAkjATJEiQIEGCHpAkzAQJEiRIkKAHJAkzQYIECRIk6AFJwkyQIEGCBAl6wP8PZWtDXAfHGLAAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc.cx(0,1)\n",
"display(qc.draw())\n",
"\n",
"qobj = assemble(qc)\n",
"final_state = svsim.run(qobj).result().get_statevector()\n",
"array_to_latex(final_state, pretext=\"\\\\text{Statevector} = \", precision=1)\n",
"plot_bloch_multivector(final_state)"
]
},
{
"attachments": {
"image.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"id": "64367931",
"metadata": {},
"source": [
"If you remember the H-gate transforms $|{+}\\rangle \\rightarrow |0\\rangle$ and $|{-}\\rangle \\rightarrow |1\\rangle$, we can see that wrapping a CNOT in H-gates has the equivalent behaviour of a CNOT acting in the opposite direction: \n",
"\n",
"\n",
"\n",
"We can verify this using Qiskit's unitary simulator:"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "dc0b0c0f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle \n",
"\\text{Circuit = }\n",
"\\begin{bmatrix}\n",
"1 & 0 & 0 & 0 \\\\\n",
"0 & 1 & 0 & 0 \\\\\n",
"0 & 0 & 0 & 1 \\\\\n",
"0 & 0 & 1 & 0 \\\\\n",
"\\end{bmatrix}\n",
"$$\n",
"$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.h(0)\n",
"qc.h(1)\n",
"qc.cx(0,1)\n",
"qc.h(0)\n",
"qc.h(1)\n",
"display(qc.draw()) \n",
"\n",
"usim = Aer.get_backend('unitary_simulator')\n",
"qobj = assemble(qc)\n",
"unitary = usim.run(qobj).result().get_unitary()\n",
"array_to_latex(unitary, pretext=\"\\\\text{Circuit = }\\n\")"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "bacdc18c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle \n",
"\\text{Circuit = }\n",
"\\begin{bmatrix}\n",
"1 & 0 & 0 & 0 \\\\\n",
"0 & 1 & 0 & 0 \\\\\n",
"0 & 0 & 0 & 1 \\\\\n",
"0 & 0 & 1 & 0 \\\\\n",
"\\end{bmatrix}\n",
"$$\n",
"$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.cx(1,0)\n",
"display(qc.draw())\n",
"\n",
"qobj = assemble(qc)\n",
"unitary = usim.run(qobj).result().get_unitary()\n",
"array_to_latex(unitary, pretext=\"\\\\text{Circuit = }\\n\")"
]
},
{
"cell_type": "markdown",
"id": "e4acf424",
"metadata": {},
"source": [
"## Exercise 2\n",
"\n",
"Do you remember the operator whose eigenvectors was $|+\\rangle$ and $|-\\rangle$? What are the corresponding eigenvalues for each state ?"
]
},
{
"cell_type": "markdown",
"id": "2b5c22dc",
"metadata": {},
"source": [
"## Answer\n",
"?"
]
},
{
"attachments": {
"image.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"id": "1b5f99f3",
"metadata": {},
"source": [
"This identity is an example of _phase kickback,_ which leads us neatly on to the next section... \n",
"\n",
"## 2. Phase Kickback \n",
"\n",
"### 2.1 Explaining the CNOT Circuit Identity \n",
"In the previous section we saw this identity:\n",
"\n",
"\n",
"\n",
"This is an example of _kickback_ (or, _phase kickback_ ) which is very important and is used in almost every quantum algorithm. Kickback is where the eigenvalue added by a gate to a qubit is ‘kicked back’ into a different qubit via a controlled operation. For example, we saw that performing an X-gate on a $|{-}\\rangle$ qubit gives it the phase $-1$:\n",
"\n",
"$$\n",
"X|{-}\\rangle = -|{-}\\rangle\n",
"$$\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "d44ca77a",
"metadata": {},
"source": [
"## Exercise 2.5\n",
"\n",
"Prove that global phase of a state has no observable, or physical, effect. That is, the state $|\\psi\\rangle$ and $e^{i\\alpha} |\\psi\\rangle$ will always give the same expectation value for any observable $A$."
]
},
{
"cell_type": "markdown",
"id": "3cb4eb6d",
"metadata": {},
"source": [
"## Answer\n",
"\n",
"Expectation value of operator $A$ on state $|\\psi\\rangle$ is simply:\n",
"$$ \\langle \\psi | A | \\psi \\rangle $$\n",
"\n",
"Expectation value of operator $A$ on state $e^{i\\alpha}|\\psi\\rangle$ is simply:\n",
"$$\\langle \\psi |e^{-i\\alpha} A e^{i\\alpha} | \\psi \\rangle $$\n",
"$$ \\langle \\psi | A | \\psi \\rangle $$"
]
},
{
"cell_type": "markdown",
"id": "27b33372",
"metadata": {},
"source": [
"When our control qubit is in either $|0\\rangle$ or $|1\\rangle$, this phase affects the whole state, however it is a global phase and has no observable effects:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\text{CNOT}|{-}0\\rangle & = |{-}\\rangle \\otimes |0\\rangle \\\\\n",
" & = |{-}0\\rangle \\\\\n",
" \\quad & \\\\\n",
"\\text{CNOT}|{-}1\\rangle & = X|{-}\\rangle \\otimes |1\\rangle \\\\\n",
" & = -|{-}\\rangle \\otimes |1\\rangle \\\\\n",
" & = -|{-}1\\rangle \\\\\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"The interesting effect is when our control qubit is in superposition, the component of the control qubit that lies in the direction of $|1\\rangle$ applies this phase factor to the target qubit, which in turn kicks back a relative phase to our control qubit:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\text{CNOT}|{-}{+}\\rangle & = \\tfrac{1}{\\sqrt{2}}(\\text{CNOT}|{-}0\\rangle + \\text{CNOT}|{-}1\\rangle) \\\\\n",
" & = \\tfrac{1}{\\sqrt{2}}(|{-}0\\rangle + X|{-}1\\rangle) \\\\\n",
" & = \\tfrac{1}{\\sqrt{2}}(|{-}0\\rangle -|{-}1\\rangle) \\\\\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"This can then be written as the two separable qubit states:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\text{CNOT}|{-}{+}\\rangle & = |{-}\\rangle \\otimes \\tfrac{1}{\\sqrt{2}}(|{0}\\rangle - |1\\rangle )\\\\\n",
" & = |{-}{-}\\rangle \\\\\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"Wrapping the CNOT in H-gates transforms the qubits from the computational basis to the $(|+\\rangle, |-\\rangle)$ basis, where we see this effect. This identity is very useful in hardware, since some hardwares only allow for CNOTs in one direction between two specific qubits. We can use this identity to overcome this problem and allow CNOTs in both directions."
]
},
{
"cell_type": "markdown",
"id": "a7754dbc",
"metadata": {},
"source": [
"## Exercise 3\n",
"\n",
"Do the above calculations for when the target qubit is in $|+\\rangle$ state. That is, calculate teh following:\n",
"- $$CNOT(0,1) |+0\\rangle $$\n",
"- $$CNOT(0,1) |+1\\rangle $$\n",
"- Which one would experience phase kicback, if one of them experiences at all? $ CNOT(0,1) |++ \\rangle \\text{ or } CNOT(0,1) |+- \\rangle$ If they don't experience a phase kick back, please explain briefly why that is the case? "
]
},
{
"cell_type": "markdown",
"id": "efa83c86",
"metadata": {},
"source": [
"## Answer\n",
"\n",
"?"
]
},
{
"cell_type": "markdown",
"id": "4a5ba02c",
"metadata": {},
"source": [
"## Exercise 4\n",
"\n",
"How did we define an arbitrary rotation around z-axis operator, $R_z(\\theta)$? Write its action on $|0\\rangle,|1\\rangle$ and also the corresponding matrix."
]
},
{
"cell_type": "markdown",
"id": "336177c0",
"metadata": {},
"source": [
"## Answer\n",
"$$ Rz |0\\rangle = |0\\rangle $$\n",
"$$ Rz |1\\rangle = e^{i\\phi} |1\\rangle $$ "
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "1b61444a",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "7a0e4734feda4144b7244b12c4d313a8",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"VBox(children=(HBox(children=(Button(description='I', layout=Layout(height='3em', width='3em'), style=ButtonSt…"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "3c28e9f91c8442db849308fee239d96c",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Image(value=b'\\x89PNG\\r\\n\\x1a\\n\\x00\\x00\\x00\\rIHDR\\x00\\x00\\x01 \\x00\\x00\\x01 \\x08\\x06\\x00\\x00\\x00\\x14\\x83\\xae\\x8…"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
]
}
],
"source": [
"from qiskit_textbook.widgets import gate_demo\n",
"gate_demo()"
]
},
{
"cell_type": "markdown",
"id": "51c95b43",
"metadata": {},
"source": [
"### 2.2 Kickback with the T-gate \n",
"\n",
"Let’s look at another controlled operation, the controlled-T gate: \n"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "d8690c4d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.cp(pi/4, 0, 1)\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "3d790f01",
"metadata": {},
"source": [
"The T-gate has the matrix:\n",
"\n",
"$$\n",
"\\text{T} = \n",
"\\begin{bmatrix}\n",
"1 & 0 \\\\\n",
"0 & e^{i\\pi/4}\\\\\n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"And the controlled-T gate has the matrix:\n",
"\n",
"$$\n",
"\\text{Controlled-T} = \n",
"\\begin{bmatrix}\n",
"1 & 0 & 0 & 0 \\\\\n",
"0 & 1 & 0 & 0 \\\\\n",
"0 & 0 & 1 & 0 \\\\\n",
"0 & 0 & 0 & e^{i\\pi/4}\\\\\n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"We can verify this using Qiskit's unitary simulator:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "8e289027",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/latex": [
"$\\displaystyle \n",
"\\text{Controlled-T} = \n",
"\\begin{bmatrix}\n",
"1 & 0 & 0 & 0 \\\\\n",
"0 & 1 & 0 & 0 \\\\\n",
"0 & 0 & 1 & 0 \\\\\n",
"0 & 0 & 0 & \\tfrac{1}{\\sqrt{2}}(1 + i) \\\\\n",
"\\end{bmatrix}\n",
"$$\n",
"$"
],
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.cp(pi/4, 0, 1)\n",
"display(qc.draw())\n",
"# See Results:\n",
"qobj = assemble(qc)\n",
"unitary = usim.run(qobj).result().get_unitary()\n",
"array_to_latex(unitary, pretext=\"\\\\text{Controlled-T} = \\n\")"
]
},
{
"cell_type": "markdown",
"id": "85514460",
"metadata": {},
"source": [
"More generally, we can find the matrix of any controlled-U operation using the rule:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\text{U} & = \n",
"\\begin{bmatrix}\n",
"u_{00} & u_{01} \\\\\n",
"u_{10} & u_{11}\\\\\n",
"\\end{bmatrix} \\\\\n",
"\\quad & \\\\\n",
"\\text{Controlled-U} & = \n",
"\\begin{bmatrix}\n",
"I & 0 \\\\\n",
"0 & U\\\\\n",
"\\end{bmatrix}\n",
" = \n",
"\\begin{bmatrix}\n",
"1 & 0 & 0 & 0 \\\\\n",
"0 & 1 & 0 & 0 \\\\\n",
"0 & 0 & u_{00} & u_{01} \\\\\n",
"0 & 0 & u_{10} & u_{11}\\\\\n",
"\\end{bmatrix}\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"$$ 00 , 01 , 10, 11 $$"
]
},
{
"cell_type": "markdown",
"id": "f1bf5389",
"metadata": {},
"source": [
"## Exercise 5 \n",
"\n",
"Why is Controlled-U in block diagonal form? (I'll be giving the answer during the session)"
]
},
{
"cell_type": "markdown",
"id": "8811ad2c",
"metadata": {},
"source": [
"## Answer\n",
"?"
]
},
{
"cell_type": "markdown",
"id": "65bd2bcb",
"metadata": {},
"source": [
"Or, using Qiskit's qubit ordering:\n",
"\n",
"$$\n",
"\\text{Controlled-U} = \n",
"\\begin{bmatrix}\n",
"1 & 0 & 0 & 0 \\\\\n",
"0 & u_{00} & 0 & u_{01} \\\\\n",
"0 & 0 & 1 & 0 \\\\\n",
"0 & u_{10} & 0 & u_{11}\\\\\n",
"\\end{bmatrix}\n",
"$$\n",
"\n",
"\n",
"If we apply the T-gate to a qubit in the state $|1\\rangle$, we add a phase of $e^{i\\pi/4}$ to this qubit:\n",
"\n",
"$$\n",
"T|1\\rangle = e^{i\\pi/4}|1\\rangle\n",
"$$\n",
"\n",
"This is _global phase_ and is unobservable. But if we control this operation using another qubit in the $|{+}\\rangle$ state, the phase is no longer global but relative, which changes the _relative phase_ in our control qubit:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"|1{+}\\rangle & = |1\\rangle \\otimes \\tfrac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle) \\\\\n",
"& = \\tfrac{1}{\\sqrt{2}}(|10\\rangle + |11\\rangle) \\\\\n",
"& \\\\\n",
"\\text{Controlled-T}|1{+}\\rangle & = \\tfrac{1}{\\sqrt{2}}(|10\\rangle + e^{i\\pi/4}|11\\rangle) \\\\\n",
"& \\\\\n",
"& = |1\\rangle \\otimes \\tfrac{1}{\\sqrt{2}}(|0\\rangle + e^{i\\pi/4}|1\\rangle)\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"This has the effect of rotating our control qubit around the Z-axis of the Bloch sphere, while leaving the target qubit unchanged. Let's see this in Qiskit:"
]
},
{
"cell_type": "markdown",
"id": "5ea9092e",
"metadata": {},
"source": [
"## Exercise 6 \n",
"\n",
"Explain why do we represent Controlled-U differently in Qiskit?\n"
]
},
{
"cell_type": "markdown",
"id": "19900b10",
"metadata": {},
"source": [
"## Answer\n",
"?"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "1c368bf8",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.h(0)\n",
"qc.x(1)\n",
"display(qc.draw())\n",
"# See Results:\n",
"qobj = assemble(qc)\n",
"final_state = svsim.run(qobj).result().get_statevector()\n",
"plot_bloch_multivector(final_state)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "e28ccadb",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
]
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.h(0)\n",
"qc.x(1)\n",
"# Add Controlled-T\n",
"qc.cp(pi/4, 0, 1)\n",
"display(qc.draw())\n",
"# See Results:\n",
"qobj = assemble(qc)\n",
"final_state = svsim.run(qobj).result().get_statevector()\n",
"plot_bloch_multivector(final_state)"
]
},
{
"attachments": {
"image-4.png": {
"image/png": 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"
},
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"
},
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"
},
"image.png": {
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"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"
}
},
"cell_type": "markdown",
"id": "574881b7",
"metadata": {},
"source": [
"We can see the leftmost qubit has been rotated by $\\pi/4$ around the Z-axis of the Bloch sphere as expected. After exploring this behaviour, it may become clear why Qiskit draws the controlled-Z rotation gates in this symmetrical fashion (two controls instead of a control and a target). There is no clear control or target qubit for all cases.\n",
"\n",
"\n",
"\n",
"You can do the exercises below if you like, but they are not part of the homework exercises. \n",
"\n",
"### Quick Exercises:\n",
"\n",
"\n",
"1.What would be the resulting state of the control qubit (q0) if the target qubit (q1) was in the state $|0\\rangle$? (as shown in the circuit below)? Use Qiskit to check your answer.\n",
"\n",
"\n",
"\n",
"2.What would happen to the control qubit (q0) if the if the target qubit (q1) was in the state $|1\\rangle$, and the circuit used a controlled-Sdg gate instead of the controlled-T (as shown in the circuit below)?\n",
"\n",
"\n",
"\n",
"\n",
"3.What would happen to the control qubit (q0) if it was in the state $|1\\rangle$ instead of the state $|{+}\\rangle$ before application of the controlled-T (as shown in the circuit below)?\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "069e0be0",
"metadata": {},
"source": [
"## Exercise 7\n",
"\n",
"Prove that if we applying CZ(0,1) and CZ(1,0) to $|1+\\rangle$ produce the same states. You can either use LaTeX feature of Jupyter Markdown cells, or just write it on a piece of paper, take its picture and upload it below."
]
},
{
"cell_type": "markdown",
"id": "d7733e9b",
"metadata": {},
"source": [
"## Answer\n",
"?"
]
},
{
"cell_type": "markdown",
"id": "225ed519",
"metadata": {},
"source": [
"This below part is also taken directly from Qiskit textbook, with some simple exercises between the lines. However, this is not the whole notebook. If you are interested in learning more about them you should check Qiskit Textbook!!\n"
]
},
{
"cell_type": "markdown",
"id": "08df6462",
"metadata": {
"tags": [
"remove_cell"
]
},
"source": [
"# Basic Circuit Identities"
]
},
{
"cell_type": "markdown",
"id": "ae7bb6cb",
"metadata": {},
"source": [
"When we program quantum computers, our aim is always to build useful quantum circuits from the basic building blocks. But sometimes, we might not have all the basic building blocks we want. In this section, we'll look at how we can transform basic gates into each other, and how to use them to build some gates that are slightly more complex \\(but still pretty basic\\).\n",
"\n",
"Many of the techniques discussed in this chapter were first proposed in a paper by Barenco and coauthors in 1995 [1].\n",
"\n",
"## Contents\n",
"\n",
"1. [Making a Controlled-Z from a CNOT](#c-from-cnot)\n",
"2. [Swapping Qubits](#swapping) \n",
"3. [Controlled Rotations](#controlled-rotations)\n",
"4. [The Toffoli](#ccx)\n",
"5. [Arbitrary rotations from H and T](#arbitrary-rotations)\n",
"6. [References](#references)"
]
},
{
"cell_type": "markdown",
"id": "03553d4c",
"metadata": {},
"source": [
"## 1. Making a Controlled-Z from a CNOT \n",
"\n",
"The controlled-Z or `cz` gate is another well-used two-qubit gate. Just as the CNOT applies an $X$ to its target qubit whenever its control is in state $|1\\rangle$, the controlled-$Z$ applies a $Z$ in the same case. In Qiskit it can be invoked directly with"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "46c01b73",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from qiskit import QuantumCircuit\n",
"from qiskit.circuit import Gate\n",
"from math import pi\n",
"qc = QuantumCircuit(2)\n",
"c = 0\n",
"t = 1\n",
"# a controlled-Z\n",
"qc.cz(c,t)\n",
"qc.draw()"
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "6393b9b6",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "db079c5e93ec4e36aa353e7fff561d17",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"VBox(children=(HBox(children=(Button(description='I', layout=Layout(height='3em', width='3em'), style=ButtonSt…"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "b45d8e40a9dc4a7daa5cb414573ca073",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Image(value=b'\\x89PNG\\r\\n\\x1a\\n\\x00\\x00\\x00\\rIHDR\\x00\\x00\\x01 \\x00\\x00\\x01 \\x08\\x06\\x00\\x00\\x00\\x14\\x83\\xae\\x8…"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
]
}
],
"source": [
"gate_demo()"
]
},
{
"cell_type": "markdown",
"id": "ac8a33a3",
"metadata": {},
"source": [
"where c and t are the control and target qubits. In IBM Q devices, however, the only kind of two-qubit gate that can be directly applied is the CNOT. We therefore need a way to transform one to the other.\n",
"\n",
"The process for this is quite simple. We know that the Hadamard transforms the states $|0\\rangle$ and $|1\\rangle$ to the states $|+\\rangle$ and $|-\\rangle$ respectively. We also know that the effect of the $Z$ gate on the states $|+\\rangle$ and $|-\\rangle$ is the same as that for $X$ on the state $|0\\rangle$ and $|1\\rangle$. From this reasoning, or from simply multiplying matrices, we find that\n",
"\n",
"$$\n",
"H X H = Z,\\\\\\\\\n",
"H Z H = X.\n",
"$$\n",
"\n",
"The same trick can be used to transform a CNOT into a controlled-$Z$. All we need to do is precede and follow the CNOT with a Hadamard on the target qubit. This will transform any $X$ applied to that qubit into a $Z$."
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "ce860bf5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"# also a controlled-Z\n",
"qc.h(t)\n",
"qc.cx(c,t)\n",
"qc.h(t)\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "282c6142",
"metadata": {},
"source": [
"More generally, we can transform a single CNOT into a controlled version of any rotation around the Bloch sphere by an angle $\\pi$, by simply preceding and following it with the correct rotations. For example, a controlled-$Y$:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "a7cd3f0e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"# a controlled-Y\n",
"qc.sdg(t)\n",
"qc.cx(c,t)\n",
"qc.s(t)\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "4a6cd802",
"metadata": {},
"source": [
"and a controlled-$H$:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "03c2656b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"# a controlled-H\n",
"qc.ry(pi/4,t)\n",
"qc.cx(c,t)\n",
"qc.ry(-pi/4,t)\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "f2e7b5f3",
"metadata": {},
"source": [
"## Exercise 8\n",
"\n",
"- Write down the action of $S$ and $S^{\\dagger}$ on the computational basis states.\n",
"- Write the corresponding matrix.\n",
"- Write down the matrix for the Controlled-Y operation and compare it with the unitary transformation produced by the proposed circuit. Beware of the little-endian representation!"
]
},
{
"cell_type": "markdown",
"id": "a861c1f5",
"metadata": {},
"source": [
"## Answer"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "cd4e25f8",
"metadata": {},
"outputs": [],
"source": [
"qc = QuantumCircuit(2)\n",
"# a controlled-H\n",
"qc.ry(pi/4,t)\n",
"qc.cx(c,t)\n",
"qc.ry(-pi/4,t)\n",
"qc.draw()\n",
"# Get yoour necesary backend\n",
"# run your circucit on backend\n",
"# result -> get unitary -> print"
]
},
{
"cell_type": "markdown",
"id": "76ab04cf",
"metadata": {},
"source": [
"## 2. Swapping Qubits "
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "315c94dc",
"metadata": {},
"outputs": [],
"source": [
"a = 0\n",
"b = 1"
]
},
{
"cell_type": "markdown",
"id": "66209ce6",
"metadata": {},
"source": [
"Sometimes we need to move information around in a quantum computer. For some qubit implementations, this could be done by physically moving them. Another option is simply to move the state between two qubits. This is done by the SWAP gate."
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "7d4807cb",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"# swaps states of qubits a and b\n",
"qc.swap(a,b)\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "1c604dcb",
"metadata": {},
"source": [
"The command above directly invokes this gate, but let's see how we might make it using our standard gate set. For this, we'll need to consider a few examples.\n",
"\n",
"First, we'll look at the case that qubit a is in state $|1\\rangle$ and qubit b is in state $|0\\rangle$. For this we'll apply the following gates:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "663483f8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"# swap a 1 from a to b\n",
"qc.cx(a,b) # copies 1 from a to b\n",
"qc.cx(b,a) # uses the 1 on b to rotate the state of a to 0\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "75b465af",
"metadata": {},
"source": [
"This has the effect of putting qubit b in state $|1\\rangle$ and qubit a in state $|0\\rangle$. In this case at least, we have done a SWAP.\n",
"\n",
"Now let's take this state and SWAP back to the original one. As you may have guessed, we can do this with the reverse of the above process:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "d3d3aba4",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# swap a q from b to a\n",
"qc.cx(b,a) # copies 1 from b to a\n",
"qc.cx(a,b) # uses the 1 on a to rotate the state of b to 0\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "28131e8a",
"metadata": {},
"source": [
"Note that in these two processes, the first gate of one would have no effect on the initial state of the other. For example, when we swap the $|1\\rangle$ b to a, the first gate is `cx(b,a)`. If this were instead applied to a state where no $|1\\rangle$ was initially on b, it would have no effect.\n",
"\n",
"Note also that for these two processes, the final gate of one would have no effect on the final state of the other. For example, the final `cx(b,a)` that is required when we swap the $|1\\rangle$ from a to b has no effect on the state where the $|1\\rangle$ is not on b.\n",
"\n",
"With these observations, we can combine the two processes by adding an ineffective gate from one onto the other. For example,"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "73acb750",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAANgAAAB7CAYAAAAWqE6tAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Z1A+gAAAACXBIWXMAAAsTAAALEwEAmpwYAAANVUlEQVR4nO3df1DU953H8ed3FwSiiYqbiqCoCEsjcY2SKmIq4dK7YNpmem01pW3mznDFUc9pkskfaVPTzjjDzHnejL3JzXhzTfXu5ooWqpm0RZvmiqsWjUF7KslV/IGua1HxNyCi7G7/+BQEZX+4fD/7/YLvxwyj+92vn33PV17fz+f7+X73+zVCoVAIIYQWDqsLEGIkk4AJoZEETAiNJGBCaCQBE0IjCZgQGknAhNBIAiaERhIwITSSgAmhkQRMCI0kYEJoJAETQiMJmBAaScCE0EgCJoRGEjAhNJKACaGRBEwIjSRgQmgkARNCIwmYEBpJwITQSAImhEYSMCE0koAJoZEETAiNJGBCaCQBE0IjCZgQGiVZXcBIFAhCWzu03wIDGPsIuMaAYVhd2cjTE4CLN6CzGxwGjB+tfuyyrSVgJgkE4ehZaDgBLW1wJzDw/dRkcGfAwjzIy1C/DCI+t3vg/3yw/wScuay2fX+jU+Czk+AZN0xzWRs2Qx7AN3QnL0L1frjUHtv6UydA+QLIGKu3rpHoEz9sPQA3umJbPz8DvlGkejUrSMCGIBSC3zTBb47Ag27EJIf6j396upbSRpxgCLY3wp7mB/+3KUnwd8/AzCzz64pGAjYEdYfhg6ahtfHNBTAvx5x6RqpQCLZ+BPtPxt+G04B/eBaeyDStrJjILGKcPj0XPVwbvqV+Ivn5R3D+unl1jUQHTkUPV7RtHQjBf+2F6zEOLc0iAYvDrTtqj2qGniD8bJ8aAtlBdw+0d6nZOTu43gXbD5rTVtcdqDlgTluxsnXAgsEg69evJy8vj9TUVGbPno3X6yU/P5/KykrL6vr4lLl7Qt9lOH7evPbicfIi/McueHMrrNkG36uBnx+Ayx3W1rX3mNqhmaXJD63XzGsvGlsHrKKigrVr17J8+XJ27NjB0qVLKS8v59SpUxQWFlpW1++PD482Y9XYAu/8Vg17ezvSOwHYdxz+ZQf86ao1dQWCsG8Ix13hJHJb2/Y8WHV1NZs3b2bXrl2UlJQAUFpayqFDh9i2bRtz5861pK4bXXqOmY5fUAfziT5nc7VTDVEHG6GGUMOqn+6B73858efuWq9Bxy3z221O4GjBtj1YVVUVZWVlfeHqlZubS3JyMh6PB4DTp09TUlKC2+1m1qxZ7NmzR2tdZ6/oabfrNlyyYDjWcDzy8V8opM7vWTGE1bWt226YO+yMxJY9mN/vp6mpiddee+2+93w+HwUFBaSkpACwfPlyXnrpJVauXElDQwNLliyhpaWFUaNGRfwMI86u4sm/quS5V/59wLJoM4Xh3n/1fwa+njOvhHN/3B1XXfFa+sMGMnKLIm6PUCjEsu9Wsa/mBwmsDOZ/9YcUffVHA5aZsa1DwKRsN9fOxzdWfJAzW7bswfx+PwAZGRkDlnd1deH1evuGh5cuXWLv3r1UVFQAUFxcTGZmJvX19dpqM9A4TrLgmh7D4YxhZxPC4XAmpJ7+RsK2tmUP5nK5AGhubuaFF17oW75u3TpaW1v7Jjh8Ph8TJ07s680Apk+fzpkzZ6J+Rrzn1w/7YNM9o9B7e6JevXvTcO/f6+OGXUwaF1dZcas9AHuj7MgNw8E7//QmT215MzFF/cWeY/CLxoHLzNrW/pZjjE6Jvt5Q2TJgOTk5eDweqqqqSE9PJysri9raWurq6gAsnUGcnK6n3VFOmPiYnrYjWeiOHDADdfHsrCkJK6mPrm2dPpqEhAtsOkR0OBzU1NRQUFDAihUrWLZsGS6Xi1WrVuF0OvsmOLKzs7lw4QLd3d19/7alpYWpU6dqqy19NIx7xPx2pz0ODgv+NyaNg7JZ6u/3DpoM1Ejq2wvBaUFtWePVdYRmy/mM+W2GY8uAAbjdburr6+ns7MTn87F27VqOHj3KzJkzSUtLA9RQcuHChbz77rsANDQ0cO7cOUpLS7XVZRhQnGt+uzrajFWZB8qLYMKYgctzPgP/+AX11Q8rjEqCz2m4GDqR29q2ARtMY2PjfcPDjRs3smXLFtxuN5WVlVRXV0edQRyqBbnq+11mcY2xZgjW3/wZ8NaLd1//4EVY/deJ3dsP5vOfNbf3nOqC6Y+b1140tjwGG0xHRwfNzc2sXLlywPKcnBx2707s1PajafCVubDFpOsRy4usGYLdq//EmutR6+rob+Jj8PyTUHdk6G05HWpbJ3KydtgEbMyYMQQCNrkCFbXHP34BDp4Ov04sM1pls2DGRNPKGpGeK4ATFyNfgRHLtv7a04n/kqsN9pvDk2Go73IVTou/jb95Ep6fZVpJI5bTARUl8R8LGqhwFeeZWlZMhk0PZkdOB3y7GPImwnuHYr/8ZmwavDTfmm/YDlcpSVD5LHiPwa8Px/51mscfVTvCRB539ScBGyLDgKJcKMiCfSfUTW+u3Rx83Yyx6qY3n8sxd5LkYeFwQOkT8FS2uiJ+/8nwFwNPSVc3vZkzVc1GWkVuGWCyUAiudIL/yt0rPr5TApMnqJ7L7nqPZaJd82cHwRBcbgf/VfjPvWrZ8lIVrjGp1tbWS47BTGYY6nzS7Oy7ywomD49wDTcOAx5/TPVSvZ7ItE+4QAImhFYSMCE0koAJoZEETAiNJGBCaCQBE0IjCZgQGknAhNBIAiaERhIwITSSgAmhkQRMCI0kYEJoJAETQiMJmBAaScCE0EgCJoRGEjAhNJKACaGRBEwIjSRgQmgk90UUXO2EI2fVreZ6/esHkDkesieAZ4rcxzFeErCHWOs1dZfcT/zqucX9nWpTPwC/+Fg9Rmjx7MQ9uG6kkIA9hIIh+N9PYOdRCASjr9/do56CefgsfGO+us+jiI0cgz1kgiHY+pHquWIJV3/tt+AnXvjopJ7aRiIJ2ENm55GhBSQEbNkP//8n00oa0SRgD5HTl+C3TZHX2fCt6PelD6F6wa7bppU2Ytk6YMFgkPXr15OXl0dqaiqzZ8/G6/WSn59PZWWl1eWFdfM27D529/WBU3DHBs8O3H7w/smMeF27CR9+YlJjQ9B+Sx1P9jrse/Chr062nuSoqKhg27ZtrFmzhsLCQhoaGigvL6etrY3XX3/d6vIGdbBFPVq2f6B+tg/eOwgVi6x7muXZy3Dmkrlt7j8Jiz2Q5DS33Vh5/wjvH4JAv73Gpj0w7hH4zrOQNd6auvqzbQ9WXV3N5s2bef/993njjTcoLS3lrbfeYsGCBfT09DB37lyrS7zPp+fgvxsG7626bsPGejU1boVDZ8xvs7MbjrWa324sDpxSPXJgkC75ehf824fhn9OWSLYNWFVVFWVlZZSUlAxYnpubS3JyMh6PB4C3334bt9uNw+GgtrbWilL77DiiHlc6mBDqqYy/+zSRFd3lu6yp3SvR1zFbMAh1h8O/HwqpYfqeY+HXSRRbBszv99PU1MSSJUvue8/n81FQUEBKijrjWVZWxs6dO1m0aFGiyxzgwg04eyXyMU4I1ZNYcTx2/rqmdq/paTeSk22x9U52OJ1gy2Mwv98PQEZGxoDlXV1deL1eFi9e3LesuLg4rs8wjHB9TXwy8z/PkjW7o64XCMK4CRncvH7B1M+PZuVPOkhOHd33OtpMYbj3e5+A2eu9X/6aV0q+NMTqHkze/KW8sHpr1PXabwUxDPMPEB/kobC27MFcLhcAzc3NA5avW7eO1tZWCgsLrSgrolvtsc0gBAM9dN/U1J1E0HMnzMOMhyhwW0+7kdzqiG1bd3de1VxJdLbswXJycvB4PFRVVZGenk5WVha1tbXU1dUBmBIwsx9NHQrBP9epSYxwLRtAYU4SPbe7TP3sWPz4A2hpu/v63p6oV2/PFe79e6185Wv86seJfcx3IAg/2q6m6CN5/ukJbLT4EeS27MEcDgc1NTUUFBSwYsUKli1bhsvlYtWqVTidzr4JDjsxDCjzRA6XwwHPzUxkVXdNSR9e7UbidMDzs8K/bwApSbAoP2ElhWXLHgzA7XZTX18/YNnLL7/MzJkzSUuz5xPFPVNgyTx19XkwpEIHqndLToK/fwYmW/ALCepB4btNnlVLS4b8Sea2GauFeeo0wY4j6nX/bZ02CipL1cPorWbbgA2msbGRoqKiAcvWrFnDpk2baGtr4+jRo7z66qt4vV5mzJhhSY0L8+DJybD/hPp+lWFA7kT1dY+0UZaUBMA0F0weD34TD0vmzYBRFv0GGYbqxZ6eDvtOqFlSpwOeyIS5U62r615GyOyDEU06OjoYO3YsGzZsYPXq1VaXMyyduADvfBh5nViPwcakwptfVH+K8IZNwIQ5th9UlxgN1SuL1JBYRGbLSQ6hz4tz4KnsobXxt4USrlhJD/YQCvzlUqPfffpgV9enJcPX50HhNF2VjTwSsIfY6Uvwyz/AyYuR13M6YE42fHkOjH0kMbWNFBIwwfnrcMSnrqW8eAN6gpCSDJnj1F2l5kyFR2UyIy4SMCE0kkkOITSSgAmhkQRMCI0kYEJoJAETQiMJmBAaScCE0EgCJoRGEjAhNJKACaGRBEwIjSRgQmgkARNCIwmYEBpJwITQSAImhEYSMCE0koAJoZEETAiNJGBCaCQBE0IjCZgQGv0ZBILA98upSiMAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.cx(b,a)\n",
"qc.cx(a,b)\n",
"qc.cx(b,a)\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "fc94e9f1",
"metadata": {},
"source": [
"We can think of this as a process that swaps a $|1\\rangle$ from a to b, but with a useless `qc.cx(b,a)` at the beginning. We can also think of it as a process that swaps a $|1\\rangle$ from b to a, but with a useless `qc.cx(b,a)` at the end. Either way, the result is a process that can do the swap both ways around.\n",
"\n",
"It also has the correct effect on the $|00\\rangle$ state. This is symmetric, and so swapping the states should have no effect. Since the CNOT gates have no effect when their control qubits are $|0\\rangle$, the process correctly does nothing.\n",
"\n",
"The $|11\\rangle$ state is also symmetric, and so needs a trivial effect from the swap. In this case, the first CNOT gate in the process above will cause the second to have no effect, and the third undoes the first. Therefore, the whole effect is indeed trivial.\n",
"\n",
"We have thus found a way to decompose SWAP gates into our standard gate set of single-qubit rotations and CNOT gates."
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "8e873216",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"# swaps states of qubits a and b\n",
"qc.cx(b,a)\n",
"qc.cx(a,b)\n",
"qc.cx(b,a)\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "c00f7d7d",
"metadata": {},
"source": [
"It works for the states $|00\\rangle$, $|01\\rangle$, $|10\\rangle$ and $|11\\rangle$, and if it works for all the states in the computational basis, it must work for all states generally. This circuit therefore swaps all possible two-qubit states.\n",
"\n",
"The same effect would also result if we changed the order of the CNOT gates:"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "e66bc6db",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
""
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"# swaps states of qubits a and b\n",
"qc.cx(a,b)\n",
"qc.cx(b,a)\n",
"qc.cx(a,b)\n",
"qc.draw()"
]
},
{
"cell_type": "markdown",
"id": "a83f2127",
"metadata": {},
"source": [
"This is an equally valid way to get the SWAP gate.\n",
"\n",
"The derivation used here was very much based on the z basis states, but it could also be done by thinking about what is required to swap qubits in states $|+\\rangle$ and $|-\\rangle$. The resulting ways of implementing the SWAP gate will be completely equivalent to the ones here.\n",
"\n",
"#### Quick Exercise:\n",
"- Find different circuit that swaps qubits in the states $|+\\rangle$ and $|-\\rangle$, and show this is equivalent to the circuit shown above."
]
},
{
"cell_type": "markdown",
"id": "e3f2e015",
"metadata": {},
"source": [
"## Exercise 9\n",
"\n",
"Solve the above quick exercise:\n",
"\n",
"-Find different circuit that swaps qubits in the states |+⟩ and |−⟩, and show this is equivalent to the circuit shown above.\n"
]
},
{
"cell_type": "markdown",
"id": "65fe2453",
"metadata": {},
"source": [
"## Answer\n",
"?"
]
},
{
"cell_type": "markdown",
"id": "55cbdf64",
"metadata": {},
"source": [
"## 3. Controlled Rotations \n",
"\n",
"We have already seen how to build controlled $\\pi$ rotations from a single CNOT gate. Now we'll look at how to build any controlled rotation.\n",
"\n",
"First, let's consider arbitrary rotations around the y axis. Specifically, consider the following sequence of gates."
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "f0131966",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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hICIGhYKIGBQKImJQKIiIQaEgIgaFgogYFAoiYlAoiIhBoSAiBoWCiBgUCiJiUCiIiEGhICIGhYKIGBQKImJQKIiI4f8AVtqMOGoYWsIAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"theta = pi # theta can be anything (pi chosen arbitrarily)\n",
"qc.ry(theta/2,t)\n",
"qc.cx(c,t)\n",
"qc.ry(-theta/2,t)\n",
"qc.cx(c,t)\n",
"qc.draw()"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "31b511d3",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
]
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "34a339af51cf4ec38638b0ba3b2556e5",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"VBox(children=(HBox(children=(Button(description='I', layout=Layout(height='3em', width='3em'), style=ButtonSt…"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "1c6685be840f45b58fc71d5fa0cf7292",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"Image(value=b'\\x89PNG\\r\\n\\x1a\\n\\x00\\x00\\x00\\rIHDR\\x00\\x00\\x01 \\x00\\x00\\x01 \\x08\\x06\\x00\\x00\\x00\\x14\\x83\\xae\\x8…"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
"/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
"The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
" x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
]
}
],
"source": [
"gate_demo()"
]
},
{
"cell_type": "markdown",
"id": "658ce84f",
"metadata": {},
"source": [
"If the control qubit is in state $|0\\rangle$, all we have here is a $R_y(\\theta/2)$ immediately followed by its inverse, $R_y(-\\theta/2)$. The end effect is trivial. If the control qubit is in state $|1\\rangle$, however, the `ry(-theta/2)` is effectively preceded and followed by an X gate. This has the effect of flipping the direction of the y rotation and making a second $R_y(\\theta/2)$. The net effect in this case is therefore to make a controlled version of the rotation $R_y(\\theta)$. \n",
"\n",
"This method works because the x and y axis are orthogonal, which causes the x gates to flip the direction of the rotation. It therefore similarly works to make a controlled $R_z(\\theta)$. A controlled $R_x(\\theta)$ could similarly be made using CNOT gates.\n",
"\n",
"We can also make a controlled version of any single-qubit rotation, $V$. For this we simply need to find three rotations A, B and C, and a phase $\\alpha$ such that\n",
"\n",
"$$\n",
"ABC = I, ~~~e^{i\\alpha}AZBZC = V\n",
"$$\n",
"\n",
"We then use controlled-Z gates to cause the first of these relations to happen whenever the control is in state $|0\\rangle$, and the second to happen when the control is state $|1\\rangle$. An $R_z(2\\alpha)$ rotation is also used on the control to get the right phase, which will be important whenever there are superposition states."
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "c58b7e55",
"metadata": {},
"outputs": [],
"source": [
"A = Gate('A', 1, [])\n",
"B = Gate('B', 1, [])\n",
"C = Gate('C', 1, [])\n",
"alpha = 1 # arbitrarily define alpha to allow drawing of circuit"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "6cae1f0f",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
""
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qc = QuantumCircuit(2)\n",
"qc.append(C, [t])\n",
"qc.cz(c,t)\n",
"qc.append(B, [t])\n",
"qc.cz(c,t)\n",
"qc.append(A, [t])\n",
"qc.p(alpha,c)\n",
"qc.draw()"
]
},
{
"attachments": {
"image.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"id": "eb5471ee",
"metadata": {},
"source": [
"\n",
"\n",
"Here `A`, `B` and `C` are gates that implement $A$ , $B$ and $C$, respectively."
]
},
{
"cell_type": "markdown",
"id": "2819bfe9",
"metadata": {},
"source": [
"## 6. References \n",
"\n",
"[1] [Barenco, *et al.* 1995](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.52.3457?cm_mc_uid=43781767191014577577895&cm_mc_sid_50200000=1460741020)\n",
"\n",
"[2] [Shende and Markov, 2009](http://dl.acm.org/citation.cfm?id=2011799)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "248285e5",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.8.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}