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---
title: Examples - QAOA
keywords: fastai
sidebar: home_sidebar
summary: "Various QAOA examples using Quixotic"
description: "Various QAOA examples using Quixotic"
nb_path: "nbs/99b_examples_qaoa.ipynb"
---
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<h3 id="Maximum-Clique-with-QAOA">Maximum Clique with QAOA<a class="anchor-link" href="#Maximum-Clique-with-QAOA"> </a></h3>
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<div class=" highlight hl-ipython3"><pre><span></span>
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{% raw %}
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">networkx</span> <span class="k">as</span> <span class="nn">nx</span>
<span class="n">n_nodes</span> <span class="o">=</span> <span class="mi">6</span>
<span class="n">p</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="c1"># probability of an edge</span>
<span class="n">seed</span> <span class="o">=</span> <span class="mi">1967</span>
<span class="n">g</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">erdos_renyi_graph</span><span class="p">(</span><span class="n">n_nodes</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="n">p</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="n">seed</span><span class="p">)</span>
<span class="n">positions</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">spring_layout</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="n">seed</span><span class="p">)</span>
<span class="n">nx</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">with_labels</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">pos</span><span class="o">=</span><span class="n">positions</span><span class="p">,</span> <span class="n">node_size</span><span class="o">=</span><span class="mi">600</span><span class="p">)</span>
</pre></div>
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>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">quixotic.core</span> <span class="kn">import</span> <span class="n">QAOA</span>
<span class="n">qo</span> <span class="o">=</span> <span class="n">QAOA</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">task</span><span class="o">=</span><span class="s1">'maximum_clique'</span><span class="p">)</span>
<span class="n">qo</span><span class="o">.</span><span class="n">execute</span><span class="p">()</span>
<span class="n">nodes</span><span class="p">,</span> <span class="n">probs</span> <span class="o">=</span> <span class="n">qo</span><span class="o">.</span><span class="n">results</span><span class="p">(</span><span class="n">return_probs</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
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<pre>Optimize for 10 iterations...
[========================================] 100% cost: -1.8832 iteration:10</pre>
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{% raw %}
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">sub</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">subgraph</span><span class="p">(</span><span class="n">nodes</span><span class="p">)</span>
<span class="n">nx</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">pos</span><span class="o">=</span><span class="n">positions</span><span class="p">,</span> <span class="n">with_labels</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">nx</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">sub</span><span class="p">,</span> <span class="n">pos</span><span class="o">=</span><span class="n">positions</span><span class="p">,</span> <span class="n">node_color</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span> <span class="n">edge_color</span><span class="o">=</span><span class="s2">"r"</span><span class="p">)</span>
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
"
>
</div>
</div>
</div>
</div>
</div>
{% endraw %}
{% raw %}
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">qo</span><span class="o">.</span><span class="n">plot_samples</span><span class="p">(</span><span class="n">probs</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area">
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">QAOA</span><span class="o">.</span><span class="n">supported_tasks</span><span class="p">()</span>
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<pre>maximum_clique
minimum_vertex_cover
maximum_cut
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<h3 id="Minimum-Vertex-Cover-with-QAOA">Minimum Vertex Cover with QAOA<a class="anchor-link" href="#Minimum-Vertex-Cover-with-QAOA"> </a></h3>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="c1"># # input graph</span>
<span class="c1"># import networkx as nx</span>
<span class="c1"># edges = [(0, 1), (1, 2), (2, 0), (2, 3)]</span>
<span class="c1"># g = nx.Graph(edges)</span>
<span class="c1"># seed = 1967</span>
<span class="c1"># positions = nx.spring_layout(g, seed=seed)</span>
<span class="c1"># nx.draw(g, with_labels=True, pos=positions, node_size=600)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">networkx</span> <span class="k">as</span> <span class="nn">nx</span>
<span class="n">n_nodes</span> <span class="o">=</span> <span class="mi">6</span>
<span class="n">p</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="c1"># probability of an edge</span>
<span class="n">seed</span> <span class="o">=</span> <span class="mi">1967</span>
<span class="n">g</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">erdos_renyi_graph</span><span class="p">(</span><span class="n">n_nodes</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="n">p</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="n">seed</span><span class="p">)</span>
<span class="n">positions</span> <span class="o">=</span> <span class="n">nx</span><span class="o">.</span><span class="n">spring_layout</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">seed</span><span class="o">=</span><span class="n">seed</span><span class="p">)</span>
<span class="n">nx</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">with_labels</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">pos</span><span class="o">=</span><span class="n">positions</span><span class="p">,</span> <span class="n">node_size</span><span class="o">=</span><span class="mi">600</span><span class="p">)</span>
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KHg8/nYu3evQv03F4lE0NHRQWZmpkwWb9OkHZElKk6EMMRxHJ4+fVpljVJFRUWVotStWzeF+qZJmq6kpASffPIJ2rVrh4MHDyrkGjV7e3vs3r0bjo6OMvk8mrQjskLFiRAZ4jgOT548qbJGieM4cVESCAT46KOPqCipsLKyMnh4eEBNTQ0nT55U2HP/vLy8IBAIMHXqVJl9Jk3aEVmg4kSIFHEch4SEhCpFicfjVSlKH374IRUlAgCoqKiAl5cXXr16hQsXLkBLS4t1pEbbtGkTXr58iZ9++klmn0mTdkQWFPOvMoTIKY7j8Pjx4yqLudXV1dG3b1/069cPa9euhampKRUl8i8cx2HWrFnIyMjAX3/9pdClCfhnsm7v3r0y/UyatCOyQHecCGkCjuMQHx9fpShpaWlVWaPUtWtXKkqkVhzHYeHChQgPD0dAQAB0dHRYR2qyp0+fol+/fkhJSZH5Z9OkHZEmKk6ENADHcXj06FGVI0yaN29e5dFbly5dWMckCmb16tXw8/PDjRs30Lp1a9ZxJKKiogI6OjrIyspiUgRp0o5ICxUnQmrBcRxiY2PFJSkoKAgtW7ascoQJFSXSFJs3b8bBgwcRFBSEdu3asY4jUba2tvD19YWDgwOTz6dJOyINVJwIeYdIJBIXJaFQiODgYOjo6IhLkru7O0xMTFjHJEpiz5498PHxQXBwMDp06MA6jsRNmjQJAwYMgLe3N7MMNGlHJI2KE1FpIpEIMTExVdYo6enpVVmj1KlTJ9YxiRI6ePAgVq9ejaCgIHTt2pV1HKnYsGED8vLy8OOPPzLLQJN2RNJoqo6oFJFIhAcPHojXKAUHB6N169YQCAT49NNPsWPHDnTs2JF1TKLkTp06heXLl+PGjRtKW5qAfybrfvnlF6YZaNKOSBrdcSJKTSQS4e+//xbfTQoODkbbtm2rrFFSxkckRH5dunQJX375JQICAtCjRw/WcaQqISEBgwYNQlJSEuso4km706dPw83NjXUcosCoOBGlUlFRIS5KQqEQISEhaNeuXZWiZGxszDomUVGBgYGYMGECLl26xGzBtCyVl5dDR0cHL1++RMuWLVnHoUk7IhFUnIhCq6iowP3796sUJSMjoyqLudu3b886JiEICwvD6NGjcfbsWZW649GzZ0/8+uuvsLe3Zx0FALB7927s27ePJu1Io1FxIgqlvLwc0dHR4jVKISEhMDY2Fi/mdnNzg5GREeuYhFQRFRWFIUOG4PDhwxg8eDDrODLl6emJIUOGwMvLi3UUAP9sMTJnzhykpKTAz8+PJu1Ig1FxInKtvLwc9+7dE69RCg0NRYcOHaoUJUNDQ9YxCalRTEwM+vfvD19fX4wePZp1HJlbv349Xr9+jU2bNrGOIlY5adezZ09s3bqVdRyiYGiqjsiV8vJyREVFiR+9hYWFoXPnznB3d4e3tzd+++03pdskkCivJ0+eYPDgwfDx8VHJ0gQAfD4fBw8eZB2jincn7fh8Pk3akQahO06EqbKysipF6ebNmzAxMRGvUXJzc4OBgQHrmIQ0WGpqKtzc3LBy5UpMmzaNdRxm4uPjMWzYMDx9+pR1lH+hSTvSGFSciEyVlZUhMjJSvEbp5s2b6Nq1a5Wi1LZtW9YxCWmSzMxMuLm5Yc6cOfjmm29Yx2GqcrIuJycH2trarOP8C03akYai4kSkqrS0FJGRkeI1SuHh4TA1NRWvUXJ1dUWbNm1YxyREYnJycuDu7o4JEyZgxYoVrOPIBSsrK/z++++wsbFhHaVaNGlHGoKKE5Go0tJS3Llzp0pRMjMzE++j5OrqCn19fdYxCZGK/Px89O/fHwMHDsSGDRvA4/FYR5ILn3/+OUaMGIFJkyaxjlItmrQjDUHFiTRJSUmJuCgJhULcvn0b3bp1Ez96c3V1RevWrVnHJETq3rx5g8GDB8PGxgY7d+6k0vSOtWvXori4GBs2bGAdpUY0aUfqi6bqSIOUlJTg9u3b4jVKt2/fhrm5OQQCAebPnw9XV1fo6emxjkmITBUXF2P06NHo1q0bduzYQaXpPXw+H0eOHGEdo1Y0aUfqi+44kVoVFxfj9u3b4kdvERER+Pjjj8VrlFxcXKCrq8s6JiHMlJWVYezYsdDW1sbRo0fpMU81Hj16hFGjRiEhIYF1lDrRpB2pCxUnUkVxcTFu3bolLkp37twBn88XFyVnZ2cqSoT8T0VFBSZOnIi3b9/i7Nmz0NTUZB1JLpWVlUFHRwevXr1CixYtWMepE03akdpQcVJxRUVF4qIkFApx9+5dWFpaihdzOzs705QJIdUQiUSYNm0aUlNTcenSJTRv3px1JLlmYWGBY8eOoWfPnqyj1AtN2pGaUHFSMW/fvkV4eLh4jVJUVBSsrKzEi7mdnZ2ho6PDOiYhco3jOMyfPx9RUVG4cuUKWrZsyTqS3PPw8MDo0aPh6enJOkq90KQdqQkVJyX39u1b3Lx5U/zo7d69e+jRo0eVotSqVSvWMQlRKMuXL8eVK1dw/fp1enRdT2vWrEF5eTnWr1/POkq90aQdqQ5N1SmZN2/eVClK0dHR6NmzJwQCAVavXg0nJyf62zEhTbBhwwb4+flBKBRSaWoAPp+PEydOsI7RIDRpR6pDxUnBvX79WlyUhEIh/v77b9jY2MDd3R1r1qxBnz59qCgRIiE7duzAgQMHEBwcTEcDNRCfz0dMTAzrGA2mr6+PP/74A25ubjAzM6NJO0KP6hRNYWEhwsLCxGuUHjx4AFtbW/Fi7j59+sjleVCEKLr//ve/WL9+PYKDg9G5c2fWcRROaWkpPvjgA+Tn56NZs2as4zQYTdqRSlSc5FxhYSFCQ0PFRenhw4ews7MTr1FydHSkokSIlB0/fhyLFy+GUCiEmZkZ6zgK6+OPP8apU6dgZWXFOkqj0KQdAag4yZ2CggKEhoaK1yjFxMTA3t5evI9S7969FWIfFEKUxcWLFzFjxgxcu3YNlpaWrOMotLFjx8LDwwOfffYZ6yiNQpN2BKDixFx+fr64KAmFQjx69AgODg7iR2+9e/em/WEIYeTq1auYNGkSLl++DDs7O9ZxFN7q1asB/HN2naKiSTtCi8NlLC8vDyEhIeJHb3Fxcejduzfc3d2xdetWODg4UFEiRA6EhIRg0qRJOH/+PJUmCeHz+Thz5gzrGE1Ck3aEipOUvXr1qkpRio+Ph6OjIwQCAbZt2wYHBweFXChJiDK7c+cOxo4di+PHj8PZ2Zl1HKXB5/MRGxvLOkaT0aSdaqNHdRKWm5tbpSglJCSIi5K7uzt69epFRYkQOfb3339j0KBB2L9/P0aOHMk6jlIpKSmBrq4uCgoKoKWlxTpOk9GknWqi4tREubm5CA4OFi/mfvLkCfr06SNezG1vb68Uf0AQogoeP34svhusqAuY5V337t1x7tw5WFhYsI4iETRpp3pkXpw4jkNIQjaCE14iJecNnhcUo6yCg6Y6D0YfNIdJm5ZwM2sLVzMD8Hg8WUarl5ycHHFREgqFSEpKqlKU7OzsqCgRooCSk5Ph5uaG//znP5gyZQrrOEprzJgx8PT0xPjx41lHkQiatFM9MitOHMfheEQqzt9LR3RaHspENX+sphoP1p30MMamAyY4dGZaoLKzsxEcHCx+9JacnAxnZ2fx1JudnR00NTWZ5SOENF1GRgbc3NzwzTffYO7cuazjKLWVK1dCQ0MDa9asYR1FYmjSTrXIZHF4Rl4R1vwRg8BHWaioR00rE3G4k/IK99Je4UZ8Nv4zygLGerLZuyg7OxtBQUHiopSamgpnZ2cIBALs378ftra2VJQIUSLZ2dkYMGAAvvrqKypNMsDn83HhwgXWMSSKJu1Ui9TvOMVlFmD+yWjEZxU2+hrdDXWw4zNrmLeX/PPjFy9eiEtSUFAQnj17Ji5KAoEANjY20NCg4UNClFFeXh769u2LESNGYN26dazjqITo6GhMmjQJDx8+ZB1F4uLj4+Hm5obTp0/TpJ0Sk2pxysgrwpSDd5pUmip1N9TBwSm90F63aXeesrKyxEVJKBQiIyMDLi4u4qJkbW1NRYkQFfD69WsMHDgQjo6O8PHxkcs1lcqoqKgI+vr6KCgoUMq79zRpp/ykVpw4jsOMI3dxNTZLYtcczDeE7yS7Bv0B9/z58ypF6fnz53B1dRWvUbK2tqbFfISomKKiIgwfPhwffvghfvnlFypNMmZmZgY/Pz98/PHHrKNIBU3aKTepFadjt1Ow6uLDeq1pqi8NNWDtKEt49jap8TUZGRlV1ihlZWXBzc1NvI9Sz549qSgRosJKS0sxZswY6Onp4ffff6c/Dxj45JNP4OXlhbFjx7KOIhUcx2H27NlITU2lSTslpCaNi3Ich/P30utVmriKcuQG/hcpm0agvOBlra8tFwHno9PxbtdLT0/HsWPHMH36dHTv3h2WlpY4efIkzM3NceLECbx8+RIXL17EggULYGtrS7+ACVFh5eXlmDhxIrS0tHDw4EH684ARCwsLxMTEsI4hNTweDzt37kRxcTG+/fZb1nGIhEllMU9IQjai0/Lq9doXZ9ehWftu9b52dOor/OfnU0i/ew1CoRC5ubniO0pz5syBlZUV1NSk0gcJIQpMJBLhyy+/REFBAfz8/JRyfY2i4PP5uHTpEusYUqWpqYnTp0/TpJ0SkkpxCk54Wes+Te/Sc/4czTp8jPyw4/V6fZkI+CsqEZOsrDBv3jxYWlpSUSKE1IrjOMydOxdJSUnw9/enY48Y4/P5+PHHH1nHkDp9fX34+fnRmXZKRirFKSXnTb1f26xDwxcHWrsOwNdf9Grw+wghqofjOHz77beIjIzEtWvXoK2tzTqSyjM3N0dCQgLKy8uVforZ3NwcR48ehYeHB03aKQmp3Kp5XlAsjcuKZeaXSPX6hBDlsW7dOly5cgX+/v404SQntLW1YWxsjKdPn7KOIhMDBw7EypUrMXLkSBQUFLCOQ5pIKsWpTJKjdNUorxBJ9fqEEOWwdetWHD16FAEBAdDX12cdh7yDz+cjNjaWdQyZmTNnDtzc3DBhwgRUVFSwjkOaQCrFSVNdunuiPEmIx+TJk7FmzRocOnQIwcHBSEtLo1+MhBAxX19f7NmzB4GBgTA0NGQdh7xH1YoTTdopD6k8XDb6oDkepEvvdqSlaUe467kjKSkJAQEBSEpKQlJSEnJzc9GpUyeYmpqia9eu//rRpk0b2uiOEBVw+PBh/PDDDxAKhejYsSPrOKQaFhYW8Pf3Zx1DpmjSTjlIpTiZtGlZr9dVvHmF50e/E/9z1rHvADV1GE5YDw2dtjW+z667CaYOH/qvny8qKkJKSgoSExPFZSoiIkL8v8vLy9G1a9cai1XLlvXLTQiRX2fPnsW3336L69ev48MPP2Qdh9SAz+fDx8eHdQyZo0k7xSeVncODH7/Al4ci670lQUNoqvPwq5c93Lq1a/B7X716JS5R7/9ITk6Gjo6OuES9X646d+5M+74QIucuX74Mb29vXLlyBdbW1qzjkFq8fv0a7dq1Q2FhoUpuREpn2ikuqRQnjuPg8XM47qS8kvSl0atLa5ya3kfij9xEIhGysrKq3K1690dmZiaMjIxqLFZGRka0nxQhDAmFQnh4eMDPzw+Ojo6s45B66Nq1K65evQozMzPWUZigM+0Uk1Qe1fF4PIyx6YCo1FcSP6tujHUHqaxTUlNTQ/v27dG+fXs4Ozv/6/8vKytDWloakpKSxOXqzz//FBergoICmJiY1FisWrduLfHMhJB/3Lp1Cx4eHjh16hSVJgVSuUBcVYvTnDlzEBMTgwkTJtCZdgpEaof8chyHGUfu4mpslsSuOZhvCN9JdnK5wPvNmzdITk6u8Y6VmppajaWqS5cuaNGiBesvgRCFFB0djcGDB+PAgQMYNmwY6zikAZYsWQJ9fX189913db9YSZWVlWHIkCGwtrbG1q1bWcch9SC1LVt5PB7WjLRASs5bxGcVNvl63Q11sGaUhVyWJgBo2bIlLCwsYGFh8a//j+M45ObmVrlb9eDBA/j5+SEpKQmpqalo3bp1jcWqY8eOSr+7LiGN8ejRIwwbNgx79+6l0qSALCwscO3aNdYxmKJJO8UjtTtOleIyCzD/ZHSTylN3Qx3s+Mwa5u2V8xmwSCRCRkZGlWL17o8XL16gQx1rGSoAACAASURBVIcONRardu3ayW2hJERaEhMT4e7ujo0bN2LSpEms45BGiIiIwMyZMxEVFcU6CnNxcXFwc3PDmTNnaNJOzkm9OAFAZn4RvveLwfW4LJQ3ZNNvUTn4uiL8OmcI2uuq7qOskpISpKam1lisioqK0KVLlxqLFS06JMrm2bNncHNzw9KlSzFjxgzWcUgjFRYWwsjICAUFBbS+BzRppyhkUpyAfx5XHY9IxfnodESn5dV6LIumOg/WnfRgrVuK3QsmIDY2lhZX16KgoADJyck1FqvmzZtXKVLvFisTExM6KZ4olKysLLi7u2P69OlYuHAh6zikiUxMTHDjxg0qCv9Dk3byT2bFqRLHcQhJyEZwwkuk5r5BZn4JyitE0FBXQ3vdZuis3xJuZm3hamYAHo+H2bNnQyQSwdfXV5YxlQbHccjOzhaXqPeL1bNnz2BgYFBjsTI2Nqa/CRK5kZubC4FAgHHjxmH16tWs4xAJGDp0KGbPno2RI0eyjiIXOI7D7NmzkZqaSpN2ckrmxamh8vLywOfzcfbsWfTp04d1HKVTXl6O9PT0Gu9WVR5jU9NjQDrGhshKQUEBBgwYAIFAgM2bN9OvOyWxaNEitGvXDkuXLmUdRW7QpJ18k/viBADHjx/Hxo0bcffuXdq9W8Yqj7GpqVhVHmNT0x0rOsaGSMLbt28xZMgQWFpaYs+ePVSalMhvv/2GoKAgHDp0iHUUuZKbmwtHR0csXbqUJu3kjEIUJ47jMGjQIAwZMgSLFi1iHYe8Iy8vr8bHgO8fY/N+qaJjbEh9lJSUYNSoUTAyMsKBAwdoh34lc+vWLcydOxeRkZGso8gdmrSTTwpRnAAgISEBffr0QVRUFDp37sw6DqmHymNsaipW7x9j836xomNsSFlZGcaPHw9NTU0cP36c9jNTQvn5+TA2NkZhYSH9fq8GTdrJH4UpTgCwdu1aREVF4cKFC6yjEAl49xib6orV+8fYvF+saNJSuVVUVMDLywt5eXk4f/48tLS0WEciUtKxY0eEhoaiS5curKPIJZq0ky8KVZxKSkrQo0cP/Pjjj/jkk09YxyFSVnmMTU3F6t1jbN4vVnSMjWLjOA7Tp0/H06dP8eeff9J/SyU3ePBgfP311xg+fDjrKHKJJu3ki0IVJwC4fv06pkyZgpiYGLRq1Yp1HMLIu8fYVFes3j/G5v1iRcfYyC+O47BgwQJERETg6tWr9PtcBSxYsADGxsZYsmQJ6yhyiybt5IfCFScA+OKLL2BkZIQtW7awjkLk1LvH2FRXrN4/xub9YkXH2DTNu/u1peS8wfOCYpRVcNBU58Hog+YwaVN1v7Z3rVq1CpcuXcKNGzegp6fH6CsgsrR//37cvHkTBw4cYB1FrtGknXxQyOL04sULWFpaIiAgAD179mQdhyigd4+xqa5YvX+MzfvFitYZVE98QsC9/50QIKrlhAC1f04IGGPTARMcOoPH42HTpk34/fffERQUBAMDAxkmJyzdvHkT33zzDSIiIlhHkXs0aceeQhYnAPjll19w4MABhIWF0SQGkbjCwsJ/7Vn1brF6/xibd0uVqh5jk5FXhDV/xCDwURZqOVHpXzTUgL7dDdE19w5+270VwcHBMDY2ll5QIndevXqFzp07o6CggO701gNN2rGlsMVJJBLBxcUF3t7emD59Ous4RIW8f4zN+8WqumNs3i1XyniMTVxmAeafjEZ8VmGjr8G9eobfvnJDf7uPJZiMKApjY2PcunWLtpupJ5q0Y0dhixMA/P333xgwYAAePHgAQ0ND1nEIAVD1GJvq7la9f4zN+3esFO0Ym4y8Ikw5eKdJpalSd0MdHJzSC+11aYpO1QwcOBALFy7E0KFDWUdRCDRpx45CFycAWLJkCZ4/f47Dhw+zjkJIvbx7jE11xaq6Y2zeLVbydIwNx3GYceQursZmSeyag/mG8J1kp1DlkTTd/Pnz0blzZzodogFo0o4NhS9Ob968AZ/Px2+//Yb+/fuzjkNIk717jM37xaq6Y2zeLVayPsbm2O0UrLr4sEFrmuqioQasHWUJz94mkrsokXs///wzIiIi8Ouvv7KOolBo0k72FL44AYCfnx8WL16Mv//+G82bN2cdhxCpef8Ym/eLVXXH2LxbrCR5jA3HcfD4ORx3Ul7V+ro3caHIDzsOrqIc6i0+gP7gOdBq16XW9/Tq0hqnpvehu04qJDQ0FEuWLEF4eDjrKAqHJu1kSymKEwCMHj0atra2WL16NesohDDz/jE27xer6o6xebdYNeQYm+DHL/Dlochatxwoy3uO54cWor33dmjotkPBnYt4EyNEe+9ttV5bU52HX73s4datXb3zEMWWk5MDU1NT5OXlUWFuhKtXr8LLy4sm7WRAaYpTamoqbG1tER4eDjMzM9ZxCJFL7x9j836xqu4Ym8ofXbp0gba2tvha6/+MxX9Dk2r9vPLXuSjLTkGLrjYAgNKXqXh+eDE6LzhVZ9ZpLl2xcji/aV8wUShGRkaIjIxEx44dWUdRSDRpJxtKU5wAYOvWrfD398fVq1fpbyyENFB1x9i8W6zeP8YmpfNgPEOb+l9fVIFXN35DxZs8GIyq+2iNQfx2+OWLXk35koiC6d+/P5YuXYpBgwaxjqKQaNJONpSqOJWXl8Pe3h5Lly7FhAkTWMchRKm8f4zNjrhmyOHqd45cwZ2LyAs9Cs3WHWAwdiU0dOouXFYddPHHXJemxiYKZN68eTA1NcWCBQtYR1FYNGknfUq15baGhgZ8fX2xaNEi5OXlsY5DiFJRU1NDx44d4erqCi8vLxgYtq/3ez/o9Qk6fXMSOr1G4fmRbyEqK6nzPeUVoqbEJQqIz+cjNjaWdQyFpqmpidOnT8PPz48mFKVEqYoTADg6OmLUqFFYvnw56yiEKDVN9bofh5flpKEo+T4AgMfjoZVFX3ClRSjPTa/zvRrqSvfHE6kDFSfJ0NfXxx9//IHvvvsOwcHBrOMoHaX8k2njxo04f/48bt++zToKIUrL6IO6t/6oeFuAnEtbUf46FwBQnPYQXEUZNPSM6nyvnuod96fyLCwsEBMTAyVaQcKMubk5jhw5Ag8PDyQmJrKOo1SUao3Tu44ePYotW7YgMjISGhoarOMQonTqM1UHAIV3L6Eg6hLAATwNLbQWTEYLU7s631cS/Se0H1+Bi4sLnJ2d4eLiAnNzczrUW8m1a9cO0dHRdNCzhNCkneQpbXHiOA4DBw7E8OHDaaEhIVJQn32cGktTnYf9X9jBoPwlQkNDERYWhtDQUOTn58PZ2VlcpOzt7dGsGd2aUiYCgQArV67EgAEDWEdRCjRpJ3lKW5wA4PHjx3BycsK9e/fQqVMn1nEIUSr13Tm8MWraOTw9PR1hYWHiIhUXFwdbW1txkXJycoK+vr7E8xDZmTNnDrp164b58+ezjqI0aNJOspT6nne3bt0wd+5c+g1IiBTweDyMsemAeqwRbxANNWCMdYdq92Lr0KEDPDw8sGPHDty9exfPnz/H999/j+bNm2P79u0wMTGBhYUFZsyYgcOHDyMpKYnWyygYWiAueTRpJ1lKfccJAIqLi9GjRw9s3boVI0eOZB2HEKXCcRxmHLmLq7FZErvmYL4hfCfZNWoT2/Lycty/fx+hoaHiHzweDy4uLuK1Uj179qR1j3Lsxo0bWL16NUJCQlhHUTp0pp1kKH1xAoBr165h2rRpiImJQcuWLVnHIUSpZOQVYcrBO4jPKmzytbob6uDglF5or9tCAsn+KXZJSUlVitSzZ8/Qu3dvcZFydHREq1b128iTSN+LFy9gbm6OnJwcOgFCCuhMu6ZTieIEABMnTkTHjh2xefNm1lEIUTpxmQWYfzK6SeWpNa8Ix+cNgnl76U7+5OTk4ObNm+IiFR0djY8//rjK9F779vXf3JNIFsdxMDAwwMOHD2FkVPe2FaThaNKuaVSmOGVlZcHS0hLXr1+HlZUV6ziEKJ3M/CJ87xeD63FZKG/Apt8aaoBzV10E+czD6sXzMHXqVOmFrEZxcTEiIyPFRermzZto3bo1bYPAkJubG9asWYN+/fqxjqKUaNKuaVSmOAGAr68vDh8+jJCQEPpDkBAp4DgOxyNScT46HdFpeSirqPmPF011Hqw76WGMdQdMcOiMx48fw93dHQcOHMDQoUNlmLoqkUiER48e0TYIDM2aNQsWFhaYO3cu6yhKiybtGk+lipNIJIKzszOmTp2Kr776inUcQpQWx3EISchGcMJLpOa+QWZ+CcorRNBQV0N73WborN8SbmZt4WpmUGUdS3h4OD755BP89ddfsLe3Z/gVVEXbIMjWrl27EBsbi3379rGOotRyc3PRu3dvLFu2DF9++SXrOApDpYoTANy/fx8DBw7Ew4cP0a5dO9ZxCCHvuXjxImbNmoXQ0FC5XbxaWFiI27dvix/v3b59G507dxZP77m4uKBLly60uLmRAgMDsXbtWgQFBbGOovRo0q7hVK44AcCiRYvw8uVLHDp0iHUUQkg19u3bh23btiEsLAwGBgas49Sprm0QXFxc0KNHD9oGoZ6eP38OKysrZGdns46iEmjSrmFUsji9fv0afD4fhw4dQt++fVnHIYRUY8WKFQgMDMT169ehra3NOk6D1LUNgouLC3r37k3bINSA4zi0adMGcXFx9GRARmjSrv5UsjgBwIULF7Bs2TLcv3+fFnkSIoc4joO3tzdevXqFc+fOKfzdmtq2Qaic4KNtEP6fi4sL1q9fD4FAwDqKSqBJu/pT2eIEAJ988gl69eqFlStXso5CCKlGaWkpRowYAVNTU+zbt0+p1gzVtg1CZZFS5W0QZsyYgZ49e2L27Nmso6gMmrSrH5UuTikpKbCzs8OtW7fw0UcfsY5DCKlGYWEh3N3dMXbsWKxYsYJ1HKl5dxuEyq0QKrdBqCxSqrQNwo4dO/D48WPs2bOHdRSVQpN2dVPp4gQAW7ZswbVr1+Dv769Uf5slRJlkZmbCyckJ33//Pby9vVnHkRlV3gYhICAAGzZswI0bN1hHUTk0aVc7lS9OZWVlsLOzw/Lly/H555+zjkMIqUFcXBwEAgEOHTqEwYMHs47DRGFhIW7duiUuUrdv34aJiYm4SCnTNgjp6emwtbVFVpbkDpAm9UeTdjVT+eIEADdv3sS4ceMQGxsLPT091nEIITUICwvDmDFjcPnyZdjZ2bGOw1xZWRnu378vLlKhoaFQU1OrUqQUdRsEjuPQunVrPHnyBG3btmUdRyXRpF31qDj9z/Tp06GlpYXdu3ezjkIIqcX58+cxd+5chIaGomvXrqzjyBWO45CYmFilSCnyNghOTk7YtGkTPS5ihCbtqkfF6X9yc3NhYWGBixcvwsHBgXUcQkgt9uzZg507dyIsLIzuRtRBkbdBmDZtGuzt7TFz5kzWUVQWTdr9GxWndxw+fBjbtm1DRESEQt7aJkSVfPfddwgKCsK1a9cUboNMluraBsHFxQXdu3eXi20Qtm3bhsTEROzatYt1FJVGk3ZVUXF6B8dx6N+/P0aNGoVvvvmGdRxCSC04joOXlxcKCwtx9uxZeozQSPK8DcKVK1fw448/IjAwUOafTaqiSbv/R8XpPfHx8XB2dkZ0dDQ6duzIOg4hpBalpaUYPnw4zMzMsGfPHqWYJpMH8rINQlpaGhwcHJCZmSn1zyJ1o0m7f1Bxqsbq1asRGxuLM2fOsI5CCKlDQUEB3Nzc4OHhgeXLl7OOo5RYbYPAcRx0dXWRnJystPtVKRqatKPiVK3i4mJYWlpix44dGD58OOs4hJA6ZGRkwMnJCWvXroWXlxfrOEpPltsgODo64qeffoKLi4sEkpOmokk7Kk41CggIwPTp0xETE0MLTwlRAI8ePYJAIMDhw4cxaNAg1nFUijS3QZg6dSocHR0xffp0KSQnjaHqk3ZUnGrh6ekJExMTbNy4kXUUQkg9hIaGYsyYMbhy5QpsbW1Zx1FpktoGYevWrUhLS8P27dtlkJrUlypP2lFxqsXz589hZWWFGzduwNLSknUcQkg9nDt3DvPmzUNYWBi6dOnCOg75n8Zug3D58mX4+PggICCAUXJSE1WdtKPiVIe9e/fi+PHjCAoKkot9TQghddu9ezd2796NsLAwtGnThnUcUo36boPw/PlzODk5IT09nXVkUg1VnLSj4lSHiooKODk5Yfr06Sp3O5IQRbZ06VKEhIQgMDAQLVq0YB2H1EPlNgiVRSouLg42Nja4c+cODh06hEGDBtF0nRzatWsXfH19VWbSjopTPdy7dw+DBw9GTEwMDAwMWMchhNSDSCSCl5cX3rx5gzNnzqjk9I+iq9wGwdvbG+3bt0d8fDxMTEzEd6SktQ0CaRhVm7Sj4lRPCxYsQF5eHg4cOMA6CiGknkpLSzFs2DB0794du3fvpm+wCsrb2xsuLi6YPHky7t+/L74jVbkNwrtFSlLbIJCGqZy0s7GxwU8//cQ6jlRRcaqnwsJC8Pl8HDlyBO7u7qzjEELqKT8/H25ubpgwYQKWLVvGOg5phC1btiAzMxM+Pj5Vfr5yG4R3i9SzZ8/g6OgoLlKN3QaBNJyqTNpRcWqAc+fOYcWKFbh//z60tLRYxyGE1FPlBpnr1q3DF198wToOaaA///wTO3fuxJUrV+p87cuXL3Hz5k1xkYqOjgafz6+y6Lw+2yCQxlGFSTsqTg3AcRxGjRoFR0dHrFixgnUcQkgDxMbGom/fvjhy5AgGDhzIOg5pgKSkJLi5uSEtLa3B7y0qKkJkZGSVRedt2rSpssu5ubk5PcaVIGWftKPi1EDJycmws7NDREQEPvzwQ9ZxCCENEBISgrFjx+Lq1auwtrZmHYfUk0gkgo6ODjIzM5s8tfX+NgihoaEoLCyEk5OTuEjZ2dmhWbNmEkqvmpR50o6KUyNs3rwZQqEQf/31F/0thRAFc+bMGXzzzTcIDQ2lDTIViL29PXbv3g1HR0eJX7u6bRBsbW3FRcrJyQmtW7eW+OcqM2WetKPi1AhlZWWwsbHB6tWr4eHhwToOIaSBdu7ciX379iEsLIz2BVIQXl5eEAgEmDp1qtQ/q3IbhMoidfv2bfE2CJXrpGgbhLop66QdFadGCgsLg4eHB2JjY6Grq8s6DiGkgZYsWYLw8HAEBATQBpkKYNOmTXj58iWTb8BlZWU1boNQWaRoG4TqKeOkHRWnJvjqq6/QokUL7Ny5k3UUQkgDiUQiTJw4EaWlpTh16pRSPUpQRn/88Qf27duHv/76i3UU2gahgZRt0o6KUxPk5OTAwsICly5dgr29Pes4hJAGKikpwdChQ2FhYYGdO3fSoxc59vTpU/Tr1w8pKSmso1SLtkGonTJN2lFxaqJDhw5h586diIiIoL+xEqKA8vPz4erqikmTJuHbb79lHYfUoKKiAjo6OsjKyoKOjg7rOHWibRD+TVkm7ag4NRHHcejbty8+/fRTfP3116zjEEIa4dmzZ3B2dsaGDRswceJE1nFIDWxtbfHzzz+jV69erKM0mEgkQmxsrLhIqeI2CMoyaUfFSQLi4uLg4uKC+/fvo0OHDqzjEEIaISYmBv369cOxY8fQv39/1nFINSZNmoQBAwbA29ubdRSJeHcbhNDQUMTHxyv9NgjKMGlHxUlCVq1ahfj4eJw6dYp1FEJIIwUFBWH8+PEICAhAz549Wcch79mwYQPy8vLw448/so4iFe9ugxAaGoqIiAil3AZB0SftqDhJSFFRESwtLbF7924MHTqUdRxCSCOdOnUKCxcuRFhYGExMTFjHIe+4ePEi9u/fj0uXLrGOIhPvboNQ+UNdXV0ptkFQ5Ek7Kk4SdOXKFcyaNQsPHz6EtrY26ziEkEbavn07fvnlF4SGhtIGmXIkISEBgwYNQlJSEusoTLy7DULlgvPKbRAqi5QibYOgqJN2VJwk7PPPP4epqSk2bNjAOgohpAkWLVqEO3fu4OrVq2jevDnrOAT/P1mXnZ2Nli1bso4jFyq3QagsUpXbIFQWKXnfBkERJ+2oOElYRkYGevTogaCgIFhYWLCOQwhpJJFIBE9PT1RUVODEiRMKOwGkbKytrfHrr7/Czs6OdRS5VLkNQmWRqtwGobJIyds2CLVN2nEch5CEbAQnvERKzhs8LyhGWQUHTXUejD5oDpM2LeFm1hauZgYy/XqoOEnB7t27cerUKQQFBcnNL05CSMOVlJRgyJAh6NGjB7Zv306/n+WAp6cnhgwZAi8vL9ZRFIIibIPw/qQdx3E4HpGK8/fSEZ2WhzJRzTVFU40H6056GGPTARMcOsvk9ygVJymoqKiAo6MjZs+ejSlTprCOQwhpgry8PLi6umLy5MlYvHgx6zgqb/369Xj9+jU2bdrEOorCen8bhMePH8PGxobpNgiVk3azFi1HXEsrBD7KQkUD2omGGtC3uyH+M8oCxnrSPXuSipOUREVFYejQoYiJiUHbtm1ZxyGENMGzZ8/g5OSETZs2wdPTk3UclXbu3DkcPHgQfn5+rKMojbq2QXBxcYGJiYnU7+ZcDr+P6QfDoa7fqdHX6G6ogx2fWcO8vfTWS1FxkqJvvvkGBQUF+O2331hHIYQ00cOHD9GvXz+cOHEC/fr1Yx1HZcXHx2P48OF48uQJ6yhKq65tEFxcXGBlZSXRbRAy8oow5eAdxGcVNvla3Q11cHBKL7TXlc6dJypOUlRQUAA+n49jx44p3D4VhJB/EwqF8PDwwLVr19CjRw/WcVRSeXk5dHR0kJOTQ9u+yEhd2yC4uLigd+/ejZ505DgOM47cxdXYLIllHsw3hO8kO6ncJaPiJGVnzpzB999/j3v37kFLS4t1HEJIE508eRKLFy9GWFgYOnfuzDqOSrKyssLvv/8OGxsb1lFUVm3bIFRO8BkZGdXrWsdup2DVxYcNWtNUFw01YO0oS3j2lvwmtlScpIzjOIwYMQIuLi747rvvWMchhEiAj48Pfv31V4SGhirdWWKK4PPPP8fIkSPpQGY50thtEDiOg8fP4biT8qr26ydHI/eqL7jyEmjoGqLtyMXQ+KD29cO9urTGqel9JH7XiYqTDCQlJaFXr16IiIhQqN1RCSE1W7BgAaKionDlyhXaIFPG1q5di+LiYtpoWI7VtA1C5aacldsg3E7Jx5eHImvdckBUWoT0fV/CYOxKNO/IR/6tMyhOfQBDj//UmkFTnYdfvezh1q2dRL82NYlejVSra9euWLx4MebOnQvqqYQoh61bt8LIyAheXl4QiUSs46gUPp+P2NhY1jFILdTU1GBpaYkZM2bg8OHDSEpKwv379zFx4kQ8e/YMc+fORZs2bTBn3e5aSxMAFKf8DY3W7dG8Ix8AoGM7HMXJ9yEqeVvr+8oqOAQnvJTY11SJipOMLFy4ECkpKTh79izrKIQQCVBTU8OhQ4eQlZWFRYsWsY6jUiwsLKg4KaAOHTrAw8MDO3fuRFRUFDIyMmBq7Vjn+8pz06Gh9//rpdS0WkC9hQ7KX2XW+d7U3DdNylwdKk4yoqWlBV9fX/EWBYQQxde8eXNcuHABAQEB8PHxYR1HZXz00UdIS0tDcXEx6yikCT744AOImunU+TpReQl46ppVf1JDC6Kyojrfm5lf0th4NaLiJEOurq4YPHgwVq1axToKIURCWrdujcuXL2Pbtm04ceIE6zgqQVNTE6ampoiPj2cdhTRRWT1G6dQ0m4MrrfpYjit5CzXNuvdpKq+Q/GN0Kk4ytnnzZpw4cQJ3795lHYUQIiGdOnXCX3/9ha+//hpCoZB1HJVAj+uUg6Z63RNvGvodUZabIf7nirf5EJUVQaN1+7rfqy75mkPFScbatm2LTZs2YebMmaioqGAdhxAiIVZWVjh58iQ8PDzw4MED1nGUHp/PR0xMDOsYpImMPqh7IrW5SQ9UvM1DcepDAEBh1J9oYWoPtWZ1b4DaXlfyhxdTcWLA29sb2tra2LdvH+sohBAJ6tu3L3bs2IHhw4cjLS2NdRylRpN1ysGkTd27jatpNoPB6GXIvbIHz/Z4o+TZI7QZPKde1++s37jdzGsjuYNmSL3xeDzs27cP7u7u+PTTT2FsbMw6EiFEQiZMmID09HQMHToUoaGh0NPTYx1JKdGjOuXgZtYWB28mobyOpUjNO1nC+KuG3WzQVOfBzaz2TTIbg+44McLn8zF9+nQsWLCAdRRCiIQtWrQI/fv3x+jRo1FSIvmpHgKYmZkhOTmZ/v0qsPT0dJzbtxHF6dJZ5G/dSQ+uZgYSvy4VJ4ZWrFiBO3fuwN/fn3UUQogE8Xg8+Pj4wMDAgDbIlBItLS107doVjx8/Zh2FNFBSUhJmzpwJKysrqKupYbnnANRjjXiDaKgBY6w7SOWQXypODGlra2PPnj2YM2cOiorq3o+CEKI41NXVcfjwYWRmZmLJkiWs4yglelynWOLi4jB58mT06tULbdu2xePHj7F161bMGmiF/h8bSvSz+psbYoKDdA7hpuLE2NChQ2FnZ4cffviBdRRCiIQ1b94cFy9ehL+/P7Zt28Y6jtKhBeKKITo6Gh4eHnB3d0e3bt3w5MkTrF+/Hm3b/rP+iMfjYc1IC3Q3rHszzProbqiDNaMspHK3CaDiJBe2b98OX19fPHr0iHUUQoiEVW6Q6ePjg1OnTrGOo1RoSwL5Fh4ejhEjRmD48OFwdHREYmIiVqxYUe3AhLFeC3zragBRbtOmUbsb6mDHZ9Zor1v35piNRcVJDhgbG+P777/HrFmz6BBgQpRQ586dcenSJcydOxdBQUGs4ygNuuMkfziOw40bN9C/f39MmDABI0aMwNOnT7Fw4UK0bFnz1gCvX7/GgimfYXr3CgziG0Kjge1EQw0YzDfEwSm9YN7+gyZ+FbXjcfSdWi5UVFSgd+/emDdvHiZPnsw6DiFECgIDA+Hp6YnAwEBYWlqyjqPwSkpKoKenh/z8fGhpabGOo9I4jsPly5exfv165OTkYPny5fD09ISm5NtkywAAIABJREFUpmad7xWJRBg3bhz09fWxf/9+AMDxiFScj05HdFperceyaKrzYN1JD2OsO2CCQ2epPZ57FxUnORIZGYkRI0YgJiYGbdq0YR2HECIFx44dw7Jly3Dz5k107NiRdRyF1717d5w7dw4WFhaso6gkkUiE8+fP44cffkBFRQWWL1+OcePGQV1dvd7XWLNmDQICAnD9+nU0a/b/O31zHIeQhGwEJ7xEau4bZOaXoLxCBA11NbTXbYbO+i3hZtYWrmYGMilMlag4yZmvv/4ab9++xX//+1/WUQghUvLjjz/i8OHDCAkJoQ0ym2jMmDHw9PTE+PHjWUdRKeXl5Thx4gQ2bNgAHR0drFy5EiNGjGhwgTlz5gwWLVqEiIgIGBpKdrJOWmjncDmzbt06WFhYIDQ0FC4uLqzjEEKkYMmSJXj27BnGjBkDf3//Kn/LJg1DWxLIVklJCQ4dOoTNmzejU6dO2LlzJ/r379+oOz7R0dGYNWsWrly5ojClCaDF4XJHV1cX27Ztw8yZM1FWVsY6DiFECng8HrZt2wZ9fX14e3vTBplNQJN1svH27Vvs2LEDH330Ec6fP49Dhw5BKBRiwIABjSpNL168wOjRo7F7927Y2tpKIbH0UHGSQ+PGjUOnTp3g4+PDOgohRErU1dVx5MgRpKWlYenSpazjKCyarJOugoICbNq0CaampggODsaFCxdw+fLlJj0RKS0txbhx4zBp0iR89tlnEkwrG7TGSU4lJibCwcEBkZGR6NKlC+s4hBApyc3NhbOzM2bOnIn58+ezjqNwioqKoK+vj4KCgnpNcJH6ycnJwc6dO7F3714MHjwY3333nUQW4HMch5kzZyIrKwvnzp2Dmpri3b9RvMQqwtTUFAsXLsTcuXNpbydClJi+vj78/f2xZcsWnDlzhnUchdOiRQt07NgRT548YR1FKTx//hzffvstunXrhoyMDISHh+PIkSMSm1rct28fwsLCcPjwYYUsTQAVJ7m2ePFiJCYm4vz586yjEEKkyMTEBJcuXcLs2bMRHBzMOo7Cocd1TZeamop58+aBz+ejuLgY0dHR2L9/Pz766COJfcb169exdu1aXLx4ETo6kjlehQUqTnJMS0sL+/btw/z581FYWMg6DiFEiqytrXHs2DGMHz+eFjs3EE3WNV5CQgK+/PJL2NjYQFtbG48ePcLOnTvRqVMniX5OYmIiPD09cezYMXz44YcSvbasUXGSc+7u7hgwYABWr17NOgohRMoGDBiArVu3YtiwYUhPT2cdR2HQZF3DPXz4EJ6ennByckKnTp2QkJCAzZs3S2VbgMLCQnzyySdYuXIl+vXrJ/HryxoVJwWwZcsWHDt2DPfu3WMdhRAiZZMmTcKsWbMwdOhQ5Ofns46jEOhRXf1FRkZizJgxGDBgAKytrZGYmIg1a9ZAX19fKp8nEonwxRdfoE+fPpgzZ45UPkPWaKpOQfz222/w9fVFeHh4g7ayJ4QoHo7jMG/ePDx69AiXL1+mc9jq8PbtW7Rp0waFhYXQ0KB9nasTGhqK9evXIyYmBkuWLMG0adOgra0t9c9dtWoVhEIhAgMDlebXMd1xUhDe3t5o1qwZfv75Z9ZRCCFSxuPxsGPHDujq6mLKlCm0QWYdtLW1YWxsjMTERNZR5ArHcQgICIC7uzsmT56MsWPH4smTJ/j6669lUppOnTqFw4cP4+zZs0pTmgAqTgpDTU0Nvr6++P777/H8+XPWcQghUqauro6jR48iOTkZy5YtYx1H7tE6p/8nEong5+eH3r17Y/78+Zg+fTri4+Px1Vdfyex4n3v37mHOnDm4cOEC2rVrJ5PPlBUqTgrEwsIC06ZNw4IFC1hHIYTIQIsWLeDn5wc/Pz/s2rWLdRy5RpN1QEVFBU6cOAFra2usWbMGy5Ytw8OHDzFx4kSZPsLMysrC6NGjsXfvXlhbW8vsc2WFHgYrmFWrVsHCwgJXr17FoEGDWMchhEhZmzZt4O/vD2dnZxgbG2Ps2LGsI8klPp+PK1eusI7BRFlZGY4cOYJNmzahbdu22Lx5M4YMGdKoM+SaqrS0FGPHjsXkyZMxfvx4mX++LNAdJwWjra2NPXv2YPbs2SgqKmIdhxAiA126dMGlS5cwa9YshISEsI4jl1TxUV1xcTH27t0LMzMzHDt2DD///DNCQ0MxdOhQJqWJ4zjMnj0bBgYGWLNmjcw/X1aoOCmgYcOGwdraGhs3bmQdhRAiIzY2Njh69CjGjRuHR48esY4jd8zNzfH48WNUVFSwjiJ1r1+/xtatW2Fqagp/f3+cPHkSAQEBEAgETApTpd27dyMiIkKhj1OpD+X9ypTc9u3bsXfvXsTFxbGOQgiRkYEDB2LLli0YOnQoMjIyWMeRK61atYKhoSGSkpJYR5GavLw8rF+/HqampoiIiMDly5fFi8BZCwwMxA8//ICLFy+iVatWrONIFRUnBdWxY0esWrUKs2bNokOACVEhXl5emDFjBoYOHYqCggLWceSKsj6uy87OxooVK/DRRx/hyZMnCA4OxsmTJ9GzZ0/W0QAAT58+haenJ06cOIGuXbuyjiN1VJwU2Jw5c5Cfn48jR46wjkIIkaFly5bB2dkZn376KUpLS1nHkRvKtoN4eno6FixYgO7duyM3Nxd37tzBwYMHYW5uzjqaWEFBAUaNGoU1a9ZAIBCwjiMTVJwUmIaGBnx9fbFkyRLk5uayjkMIkREej4ddu3ahVatWmDp1Km2Q+T/KsiVBcnIyZs2aBSsrK/B4PDx8+BD79u2Tu7s5IpEIkyZNgqurK2bNmsU6jsxQcVJwDg4OGDduHG2QR4iKUVdXx7Fjx5CYmIjly5ezjiMXFP1RXXx8PLy9vWFvbw99fX3Ex8fDx8cHxsbGrKNV6//au8+wqK61DcDPUOwgKvYaqiD2ToSoSVRQKSpYgg0VQQWMDWEm9gFBxU4RFDVGIwqKlRhjgWDBRkSQIkTFDiqooJRhfz/OpyeeJDrAzKyZ2e/9x+uKzNqP5yTwuPde7/rhhx9QVFSETZs2sY6iUDTHSQ2IxWKYm5vjwoULsLS0ZB2HEKIg9erVw9GjRz+ccK8uh6hWl5mZGTIzMyGRSFTqTM8//vgDYrEY586dg5eXF+7cuQM9PT3WsT7p559/xt69e5GcnKxWx6lIg+44qYGGDRsiODgYM2fORHl5Oes4hBAFej8g09/fH4cOHWIdhykdHR3o6+vj3r17rKNI5dKlSxg5ciRsbGzQt29f5ObmQiQSKX1punbtGjw9PXH48GE0bdqUdRyFo+KkJpydndGqVSts2LCBdRRCiIJ98cUXOHr0KGbOnImkpCTWcZhS9sd1HMfh3Llz+OabbzBu3DjY2toiNzcX8+fPV4lt/E+ePIGjoyPCwsKUZlefolFxUhMCgQBbt25FYGCgyvxtixAiOz169MCPP/6I0aNH83pAprLurOM4DidOnMCAAQPg5uYGFxcXZGdnw8PDA3Xq1GEdTyqlpaUYNWoUpk2bxuujf6g4qREjIyPMnTsXnp6eNNuJEB4aOnQoVq9eDRsbGzx+/Jh1HCaUbWddZWUlYmJi0LNnTyxevBheXl64ffs2pkyZAm1tbdbxpMZxHDw8PNCqVSv88MMPrOMwRcVJzSxcuBBZWVmIi4tjHYUQwsCUKVMwY8YM2Nra8nJAprLccaqoqMCePXvQuXNnBAUFYdmyZUhJScHYsWNV6sX19zZt2oRr165h586dan2cijQEHN2aUDvnzp3DpEmTkJ6erhLPzAkhsvX+7kBOTg6OHz/Oq11PRUVFaN26NV69esXkB3xpaSl2796N1atXo23bthAKhfjmm2+YniFXU7/++ismTZqEixcvokOHDqzjMEfFSU1NnjwZ+vr6WLduHesohBAGKioqMGrUKOjp6WHXrl0q/YO7qtq2bYvExESF/pAvKSlBZGQk1qxZAwsLCwiFQgwYMEBh15eX7OxsDBgwAAcOHIC1tTXrOEqB3/fb1NiaNWvw448/IiUlhXUUQggDWlpa+Pnnn5GVlQWhUMg6jkIp8nHdq1evEBgYCAMDA5w7dw6HDx/GyZMn1aI0FRUVwd7eHitWrKDS9BdUnNRUs2bN4O/vD3d3d0gkEtZxCCEM1KtXD8eOHcPBgwcREhLCOo7CKGIkwYsXL7Bs2TIYGhri5s2bOH36NGJjY9GzZ0+5XldRJBIJvvvuOwwaNAgzZ85kHUepUHFSY66urtDU1ERERATrKIQQRvT19REfH49Vq1bh8OHDrOMohDzvOD19+hQ+Pj4wNjbGgwcPcPHiRfz000+wsLCQy/VYEYlEKC4uptmA/4CKkxrT0NBAWFgYfvjhBzx9+pR1HEIIIwYGBjhy5AhmzJiBCxcusI4jd/IYSZCXlwcvLy+YmZmhpKQEN27cQGRkJIyMjGR6HWWwd+9e7N+/HwcOHFCpkQmKQsVJzXXu3Bmurq6YN28e6yiEEIZ69eqF3bt3Y9SoUcjMzGQdR67MzMyQnp4uk3l2d+7cwfTp09GtWzfUqVMH6enp2Lx5M9q1ayeDpMrn6tWr8Pb2RlxcHPT19VnHUUpUnHhgyZIlSEpKwunTp1lHIYQwZGNjg4CAAAwbNgxPnjxhHUduGjVqBB0dHeTl5VV7jbS0NHz33Xfo378/WrdujaysLAQFBaFFixYyTKpcHj9+DEdHR2zbtg2dO3dmHUdpUXHigfr162PLli2YNWsW3r17xzoOIYShqVOnwtXVFba2tnj9+jXrOHJT3cd1165dw6hRo/D111+jS5cuyMnJwfLly9GkSRM5pFQe7969g6OjI9zc3ODo6Mg6jlKj4sQTI0aMgIWFBVavXs06CiGEMZFIhF69emHMmDEoLy9nHUcuqrqz7vfff4eNjQ0cHBwwcOBA5ObmwsfHB7q6unJMqRw4joO7uzvatWsHkUjEOo7So+LEIxs3bsSWLVuQlZXFOgohhCGBQICQkBDUqlUL06dPV8uzLaXZWcdxHH799VcMHDgQkydPxqhRo3Dnzh14eXmhXr16CkrK3oYNG/DHH38gKiqKV4NSq4uKE4+8H//v4eGhlt8oCSHSez8gMyMjQy0Pbf3UozqO43DkyBH069cP3t7emD59OjIzMzFjxgzUrl1bwUnZ+uWXXxAUFITDhw+jfv36rOOoBDpyhWcqKirQu3dvLFiwAN999x3rOIQQxvLz82FpaYn58+fD3d2ddRyZef78OQwMDFBYWPjhLopEIsHBgwchFouhpaUFoVAIR0dH3h5am5WVBSsrK8TExKjFpHNFoeLEQ5cvX4aDgwPS09PRqFEj1nEIIYzl5OTAysoKoaGhsLe3Zx1HZlq0aIGrV6+iefPm+OmnnxAQEAB9fX0IhULY2Njw+rFUUVER+vbti/nz52PGjBms46gUKk48NWvWLFRWViIsLIx1FEKIErhy5QpsbW1x5MgR9O/fn3UcmRg0aBAsLCxw9OhRGBkZQSQS4auvvuJ1YQL+c+dt5MiRMDQ0xObNm1nHUTlUnHiqsLAQ5ubmiImJUZtvkoSQmjlx4gRcXV2RkJAAExMT1nGqrbi4GOHh4ViyZAnat2+P7du3o1+/fqxjKY1Fixbh2rVriI+Pp8ng1cDPB7sEenp6WLduHdzd3dV2OzIhpGpsbW0hFotVdkBmYWEhxGIxDAwMcOnSJXh5ecHS0pJK01/s2bMHMTExiI6OptJUTVSceGzcuHFo1qwZNm3axDoKIURJTJs2DZMnT8bw4cNVZkBmQUEBRCIRjIyMkJWVhfPnzyM6OhrDhg2T22G/qig5ORnz5s1DXFyc2g/0lCd6VMdz2dnZ6N+/P65fv662Zy8RQqqG4zi4ubkhLy8PR48eVdo7E48ePcLatWuxc+dOODs7w8fHB1988cWH3y8oKICxsTFevHjB+/eaHj16hD59+iAkJAR2dnas46g0uuPEc8bGxvDy8oKXlxfrKIQQJSEQCBAaGgpNTU24ubkp3dy3u3fvwsPDAxYWFgCA1NRUhIWFfVSaAEBfXx/a2tp4/Pgxi5hK4/1xKh4eHlSaZICKE4GPjw9u376NuLg41lEIIUpCS0sL0dHRSEtLw9KlS1nHAQBkZmZiypQp6NWrFxo3bozMzEwEBwejdevW//qZ6p5Zpy7e3z384osv4OfnxzqOWqDiRFC7dm2EhobCy8sLb968YR2HEKIk6tevj2PHjmHv3r0IDw9nluOPP/7A2LFjYWVlBSMjI9y5cwdisRhNmzb97GelOXpFna1btw63bt3Cjh07eP+4UlaoOBEAwODBg2FtbY3ly5ezjkIIUSLNmjVDfHw8li1bhqNHjyr02pcvX4adnR1sbGzQp08f5ObmQiQSQU9PT+o1qnrYrzo5efIkgoODERcXx6uz9+SNihP5YO3atdi1axdu3rzJOgohRIkYGRkhLi4Orq6uuHz5slyvxXEczp07h2+//RZjx47FsGHDkJubi/nz56NBgwZVXo+vd5wyMjIwefJkHDhwAG3btmUdR63QrjrykW3btiEqKgpJSUm8Pb+JEPLPjh07hunTpyMxMRHGxsYyXZvjOMTHx2PVqlXIz8+Hr68vXFxcaryj79mzZ+jYsSOeP3/Om0dVhYWF6Nu3L3x8fODq6so6jtqh4kQ+UllZiQEDBmDKlClwc3NjHYcQomQiIiKwevVqXLhwAc2bN6/xepWVlTh8+DDEYjHKysogFArh5OQETU1NGaT9TyFr2rQpbt26hRYtWshkTWUmkUgwfPhwmJqaYuPGjazjqCUt1gGIctHQ0EBYWBi++eYb2Nvby+QbIyFEfcyYMQMPHjzA8OHDce7cuWo9PgOAiooK7N+/H/7+/qhfvz6WLFmCkSNHyvxOt0Ag+PC4jg/FycfHBxKJBOvWrWMdRW3RsxjyN126dMHkyZOxYMEC1lEIIUpo2bJl6Nq1K5ydnat8ZFNZWRkiIyPRsWNHbNu2DevXr8fly5dhb28vt9cD+DKSYPfu3YiLi8P+/fuhpUX3ReSFihP5R0uXLkVCQgLOnDnDOgohRMkIBAKEhYUBANzd3aUakPn27Vts3rwZRkZGOHjwIKKionD+/HkMGTJE7u8e8eEF8UuXLmHBggWIi4tD48aNWcdRa1ScyD9q0KABNm/eDA8PD5SWlrKOQwhRMtra2oiOjsYff/yBZcuW/evXvX79GkFBQTAwMMCZM2cQGxuL+Ph4WFlZKSyruo8kePjwIUaPHo3t27fD3NycdRy1R8WJ/Cs7OzuYmZkhMDCQdRRCiBJq0KABjh8/jj179iAiIuKj33vx4gWWLVsGAwMDpKSk4Ndff8WhQ4fQq1cvhedU50d1b9++hYODAzw9PTFy5EjWcXiBdtWRT7p//z569OiBixcvynz7MSFEPWRnZ8Pa2hoRERHo3bs3goODERkZCUdHR/j4+DD/3sFxHJo0aYLMzEyppo2rCo7jMHHiRFRWVuKnn37izbgF1uiOE/mkdu3awdfXF7NmzVK6gz4JIcrB2NgY4eHhcHJygrGxMUpKSnDjxg1ERkYyL03Af3fWqdvjujVr1iAjIwORkZFUmhSIihP5LC8vLzx79gw///wz6yiEECWTk5ODGTNmYOrUqbCxsUHdunXh7e2Ndu3asY72EXV7XHf8+HFs3LgRhw8fpuNUFIyKE/ksbW1thIeHY/78+SgsLGQdhxCiBNLS0uDi4oJ+/fqhVatWyMrKQmxsLFauXIlhw4bh2bNnrCN+RJ121t2+fRtTp07FwYMH0aZNG9ZxeIeKE5FKv379YGdnBz8/P9ZRCCEMXb9+HaNHj8bXX38NCwsL5OTkYPny5WjSpAkAwM3NDePHj8eIESNQXFzMOO1/qcujupcvX8LOzg6BgYHo378/6zi8RC+HE6m9fPkS5ubmOHz4MPr27cs6DiFEgZKSkiAWi3Hz5k0sXLgQM2bM+NdHRBzHwdXVFc+ePUNcXJxSDGN89OgRunfvjqdPn7KOUm0VFRWwtbWFhYUFgoODWcfhLbrjRKTWqFEjrF27Fu7u7qioqGAdhxAiZxzH4fTp0xg0aBAmTpwIBwcH5OTkwNvb+5Pv1QgEAmzbtg2VlZXw8PBQio0lLVu2RGlpKQoKClhHqbZFixYBAIKCghgn4TcqTqRKJkyYgCZNmmDz5s2soxBC5ITjOBw9ehT9+/eHp6cnXF1dkZWVBTc3N9SuXVuqNbS1tXHgwAFcv34dK1askHPiz/vrmXWqKCoqCseOHaPjVJQA/a9PqkQgECAkJASWlpYYM2YM2rZtyzoSIURGJBIJYmJiIBaLoaGhAaFQiFGjRlX7DLn3AzItLS3Rpk0bTJs2TcaJq+b9zjpra2umOarq4sWL8PHxwfnz59GoUSPWcXiPihOpMhMTE8yZMwfe3t6IjY1lHYcQUkPl5eXYu3cvAgIC0LhxY/j7+8PW1lYms4FatGiB+Ph4WFtbo2XLlrC1tZVB4upRxTtODx48wJgxY7Bz506YmZmxjkNAj+pINS1evBi3bt3C0aNHWUchhFTTu3fvEBYWBhMTE+zevRuhoaFISkrC8OHDZTpQ0cTEBIcOHcLkyZNx5coVma1bVaq2s66kpAQODg7w9vZmWjjJx2hXHam206dPY/r06UhLS0P9+vVZxyGESKm4uBjh4eFYt24dunfvDqFQqJCt7XFxcfDw8EBiYiIMDQ3lfr3/lZeXhz59+uDx48cKv3ZVcRyHCRMmQFNTEz/++CNNBlcidMeJVNs333yDL7/8Uile/CSEfF5RURHEYjEMDAxw6dIlHD9+HMeOHVPYPCB7e3ssWbIEw4YNQ35+vkKu+Vdt2rRBcXExXrx4ofBrV1VgYCDu3LmDiIgIKk1KhooTqZHg4GDs2LEDqamprKMQQv5FQUEBRCIRDA0NkZWVhXPnziE6OhrdunVTeBZ3d3c4OzszGZD5fmfd7du3FXrdqjp69Ci2bNmCw4cPo27duqzjkP9BxYnUSPPmzbFy5Uq4u7ujsrKSdRxCyF88evQI8+fPh4mJCQoKCpCcnIxdu3Yxf8l41apV6NixI8aNG6fwmXDK/p5Teno6pk2bhpiYGLRu3Zp1HPIPqDiRGnNzc4NEIsGOHTtYRyGEALh79y5mzZoFCwsLVFZWIjU1FWFhYTAwMGAdDcB/7vxERkairKwMs2bNUuiATGU+7PfFixews7PD2rVr6XQGJUbFidSYhoYGwsPD4efnp3QHexLCJ1lZWZg6dSp69uwJPT09ZGRkYP369Up550JbWxsHDx7E1atXsWrVKoVdV1lHElRUVMDZ2RkODg6YNGkS6zjkE6g4EZno2rUrJk6ciIULF7KOQgjv3Lx5E+PGjcOAAQNgYGCAO3fuwN/fH82aNWMd7ZN0dHRw4sQJREVFISoqSiHXVNZHdfPnz4e2tjYCAwNZRyGfQeMIiMy8efMG5ubm2LVrFwYNGsQ6DiFqLzk5GWKxGFeuXMG8efPg7u6OBg0asI5VZZmZmfjqq68QFRUFGxsbuV6L4zjo6uoiLy8Penp6cr2WtLZv346goCBcvnxZaTKRf0d3nIjMNGjQAJs2bYKHhwdKS0tZxyFELXEch/Pnz2PIkCFwcnLCkCFDkJOTgwULFqhkaQIAU1NTxMbGYtKkSbh69apcryUQCGBmZqY0O+uSkpLg6+uLI0eOUGlSEVSciEzZ29vDxMQEa9asYR2FELXCcRzi4+NhZWWF6dOnY9y4ccjOzsbs2bPVYsu6paUlIiIiYGdnh9zcXLleS1ke192/fx9OTk7YtWsXTE1NWcchUqKz6ohMCQQCbN68GT179sS4ceNgZGTEOhIhKq2yshJxcXEQi8UoLS2FUCiEk5MTNDU1WUeTOQcHBzx69AjDhg1DUlISmjZtKpfrKMPOuvfHqcybN0/ujyeJbNE7TkQu1qxZg9OnTyM+Pp6m3hJSDRUVFYiOjoa/vz/q1q0LkUiEkSNHQkND/R8U+Pn54cyZMzhz5gzq1asn8/WPHz+OzZs3Iz4+XuZrS4PjOIwbNw61a9fGrl276HukiqHiROSivLwcPXv2hFAoxNixY1nHIURllJWVYffu3Vi9ejVatWoFkUiEb7/9llc/XDmOw+TJk1FUVISYmBhoacn24ciff/4Ja2tr5OXlyXRdaYnFYhw5cgTnz59HnTp1mGQg1UfFicjNhQsX4OTkhLS0NHrpkZDPePv2LSIjI7FmzRqYm5tDKBTCysqKdSxmysrKMHz4cBgaGiI0NFSmxbGyshK6urp49OgRdHV1ZbauNOLi4jB79mwkJyejVatWCr02kQ31v+dLmLG0tMTw4cMhEolYRyFEab1+/RpBQUEwMDDAmTNnEBMT8+ElcD6rVasWYmJicPnyZfj7+8t0bQ0NDXTs2FHhO+tu3bqFGTNmIDY2lkqTCqPiRORq9erViImJQXJyMusohCiVFy9eYPny5TAwMEBKSgpOnTqFQ4cOoXfv3qyjKQ1dXV2cOHECkZGR2Llzp0zXVvTOuufPn8Pe3h7BwcHo06ePwq5LZI+KE5Grxo0bIygoCO7u7go/zJMQZfTs2TMsXrwYxsbGuH//Pi5cuIC9e/eic+fOrKMppZYtW+LEiRPw8fHBL7/8IrN1FXn0Snl5OZycnDB69Gi4uLgo5JpEfqg4EblzcXGBnp4etm7dyjoKIcw8ePAA3t7e6NixI968eYPr169j+/btMDY2Zh1N6ZmZmSE2NhYuLi64du2aTNZU5EiCefPmoU6dOggICFDI9Yh8UXEicicQCBAaGoqVK1fiwYMHrOMQolA5OTlwc3NDly5dUKtWLaSlpWHLli1o374962gq5csvv8S2bdswcuRI/PnnnzVeT1F3nCIiIvDrr79i3759ajl7i4+oOBGFMDU1xaxZszB37lzWUQhRiPT0dEycOBF9+/ZFixYtkJ2djTVr1qBly5aso6ksR0dH+Pn5YdiwYSguei50AAAWs0lEQVQoKKjRWh06dEB+fj7evHkjo3R/l5iYCJFIhCNHjqBhw4Zyuw5RLCpORGH8/PyQkpKC48ePs45CiNzcuHEDY8aMwaBBg2Bubo6cnBysWLECTZo0YR1NLcyZMweOjo6ws7NDSUlJtdfR1NSEqamp3HbW3bt3D87Ozti9ezdMTEzkcg3CBhUnojB16tRBSEgI5syZU6NveIQoowsXLsDW1hYjR47EgAEDkJubC19fX7rTIAf+/v4wMDDAhAkTIJFIqr2OvB7XFRcXw8HBAQsXLsTQoUNlvj5hi4oTUaghQ4agX79+WLlyJesohNQYx3H47bffMGjQILi4uMDBwQE5OTmYO3cu6tevzzqe2tLQ0MCOHTvw5s0beHp6orpznOUxkoDjOEyZMgVdu3bF999/L9O1iXKg4kQUbv369YiMjMStW7dYRyGkWjiOw7Fjx9C/f3/MmTMHrq6uyMrKgpubG2rXrs06Hi/UqlULsbGxuHDhAlavXl2tNeSxs27VqlV48OABwsLCeHVMDp/I9gAgQqTQokULLF++HB4eHjh//jwvDi0l6kEikSAmJubDJGuRSARHR0faLcXI+wGZlpaWaN26NSZNmlSlz8v6Ud2hQ4ewbds2JCcn0xl0aozOqiNMSCQS9O/fH+7u7nB1dWUdh5BPKi8vx969exEQEIBGjRpBJBLB1taW7igoidu3b2PgwIH48ccfMWTIEKk/J5FIoKOjg/z8/Bo/Wk1NTcXgwYNx4sQJmv6u5uiv+oQJTU1NhIeHw9fXF/n5+azjEPKP3r17h7CwMJiYmGD37t0ICQnBhQsXMHz4cCpNSsTMzAwxMTFwcXHBjRs3pP6cpqYmTExMkJGRUaPrFxQUwN7eHhs3bqTSxANUnAgz3bt3x4QJE7Bo0SLWUQj5SHFxMdavXw9DQ0McO3YMe/fuxW+//YbBgwdTYVJSAwYMQGhoKEaMGIG7d+9K/bmaPq57f5yKs7MzJkyYUO11iOqgd5wIUytWrIC5uTnOnz+Pr776inUcwnNFRUXYunUrNm7cCGtraxw7dgzdu3dnHYtIafTo0Xj06BGGDRuGpKQkqWZn1XRn3fsdlGKxuNprENVCd5wIUzo6Oti4cSPc3d1RVlbGOg7hqYKCAvzwww8wNDRERkYGzp07hwMHDlBpUkGenp6ws7ODnZ0d3r59+9mvr8nOuvDwcJw9exZ79+6lDQI8QsWJMOfo6AhDQ0OsXbuWdRTCM48fP8aCBQtgYmKCZ8+eITk5Gbt374aZmRnraKQGVq9ejfbt20s1ILO6j+oSEhKwZMkSxMXFQVdXt7pRiQqi4kSYEwgE2LJlC4KDg5GTk8M6DuGBe/fuYfbs2ejUqRMqKipw8+ZNhIeHw8DAgHU0IgMaGhqIiorCq1ev4OXl9ckBmYaGhnj48GGVTjO4e/cuxo4diz179sDY2FgWkYkKoeJElEKHDh2wcOFCzJkzp9pTgAn5nKysLLi6uqJHjx7Q1dVFRkYGNmzYgDZt2rCORmSsdu3aiI2Nxe+//47AwMB//TotLS0YGxsjMzNTqnXfvHkDe3t7LF68GN9++62s4hIVQnOciNIoLy9H9+7dsXTpUjg5ObGOQ9TIzZs34e/vjzNnzmDOnDnw9PREo0aNWMciCvDw4UNYWlpi1apVmDhx4ke/x3EcErPz4bN+Jxq2NYa2rj7KJRy0NQVooVsH7ZvUh7WxPqyMm0IgEKCyshLOzs7Q1dXF9u3baYclT1FxIkrl999/x7hx45CWlkaHo5IaS05OhlgsRnJyMubPn4+ZM2dCR0eHdSyiYGlpaRg8eDD27NmDb7/9FhzHYV/yfRy68RApeYUor/z3H4PaGgJ0a6sHx+6tkXVyJ06d+gVnz56lo3V4jIoTUTrTp09HvXr1sGnTJtZRiIpKSEjAqlWrkJGRAR8fH7i6uqJu3bqsYxGGEhISMGbMGPx0+AQO5AC/3X4KSRV++mmAg+T+HziydCK6mrSTX1Ci9Kg4EaXz/PlzdOrUCceOHUOvXr1YxyEqguM4/PLLLxCLxXjy5Al8fX3h4uKCWrVqsY5GlMSmXQex9uJzaDSq/jttps11sHFsN3RsSTvp+IqKE1FKu3btwqZNm5CcnEzzUcgnVVZWIi4uDmKxGKWlpfDz84OTkxO0tGi+L/mvR4VvMXXnFWQ+fV3jtUyb62Dn1N5o2ZDuYvIRFSeilDiOw6BBgzB69Gh4enqyjkOUUEVFBaKjo+Hv7486depAJBLBzs4OGhq0WZh8jOM4zNxzDafSn8pszaHmzRHm0pNeEOch+g5DlJJAIEBoaCiWL1+Ohw8fso5DlEhZWRm2b98OMzMzhIaGYt26dbhy5QocHByoNJF/tC/5Pn67LV1pKrlzBfdWj0BF4ae//reMp9iXfF8W8YiKoe8yRGmZmZnB3d0d33//PesoRAm8ffsWW7ZsgbGxMaKjo7F9+3YkJiZi6NCh9Ld+8q84jsOhGw+lehG8svwdCs/vgkadz++8rKgEDqU8pLlzPETFiSg1oVCIa9eu4eTJk6yjEEZev36NNWvWwMDAAKdPn8bBgwfxyy+/wNramnU0ogISs/ORklco1dcW/b4X9S0GQVBLuneXUvIKkZidX5N4RAVRcSJKrW7duti6dStmz55dpSMRiOp7+fIlVqxYAQMDA1y/fh2nTp3C4cOH0bt3b9bRiApJyC745Jym98qe3cW7u39At7eD1GuXSzgkZBfUJB5RQVSciNIbNmwYevfuDbFYzDoKUYBnz57B19cXRkZGuHv3LpKSkrBv3z507tyZdTSigu49L/7s13AchxenQtB4iDsEGlXbxXv/xefXJ+qFihNRCevXr8e2bduqdYo5UQ0PHjzA3Llz0bFjR7x69QrXr1/Hjh07YGJiwjoaUWFPXr377Ne8SYmHdtMOqN3arMrrPy4qrU4sosKoOBGV0KpVKyxduhTu7u70Mqaayc3NhZubG7p27QotLS2kpaVh69ataN++PetoRA2US/FWeEn2JZRkJiFvswvyNrtA8roAj3d9j3f3bn72sxWSSlnEJCqE5jgRlSGRSNCvXz/Mnj0bU6ZMYR2H1FB6ejoCAgJw8uRJzJo1C97e3mjSpAnrWETFlZaW4vbt20hNTcXNmzdxpNQMpfWbV2mNByGuaDEhAFp6n/9c59YNcXTOgOrGJSqIRusSlaGpqYmwsDDY2tpixIgR0NfXZx2JVMONGzcgFouRmJiIuXPnYsuWLXSgM6kyjuNw//79DwXp/a+5ubkwMDBAly5d0LlzZ5hoN0PqC/nlaNmQDvvlG7rjRFSOt7c33rx5g+3bt7OOQqrgwoULEIvFSElJwcKFCzFjxgzUr1+fdSyiAoqKinDr1q2PCtKtW7dQr169DwXp/a9mZmaoXfu/ZWbV8XRE/v6n3LJNH/AFRMPN5bY+UT5UnIjKefXqFczNzbFv3z5YWVmxjkM+geM4nD17FqtWrcKff/6JxYsXY8qUKR/9YCPkvYqKCmRlZX0oR++LUkFBATp16vRRQercubNUd50Tsp5h2q6rUo0kqCptTQG2T+oFa5NmMl+bKC8qTkQlHTx4EEuXLsWNGzdQq1Yt1nHI/+A4DsePH4dYLMbLly/h5+eH8ePHQ1tbm3U0ogQ4jsOTJ0/+9pgtMzMTbdq0+aggdenSBQYGBtU+TofjODiHX8SVey9l/KcAendohGi3/jS5nmeoOBGVxHEcRowYASsrKyxevJh1HPL/JBIJYmNj4e/vD47jIBQKMWrUKGhqVm02DlEfJSUlSEtL+6ggpaamguM4dOnS5aOCZG5uLpfHt3sv38MPcbekOnZFWloawAo7C0zoS7s/+YaKE1FZf/75J3r37o0rV67giy++YB2H18rLy7Fv3z4EBASgYcOGEIlEGD58OP1NnEcqKyuRm5v7t4KUl5eHjh07/u0uUosWLRT27wfHcZi55xpOpUt30K80hpo3R5hLT/p3nIeoOBGVFhAQgMTERBw/fpy+gTFQWlqKnTt3IjAwEB06dIBQKMTgwYPp/ws1V1BQgNTU1I8KUlpaGvT19f9WkIyNjZXiEe2jwreYuvMKMp++rvFaps11sHNqb7RsKN2ZdkS9UHEiKq2srAzdu3fH8uXLMWbMGNZxeKO4uBgRERFYu3YtunbtCqFQCEtLS9axiIz970yk978WFxf/rSBZWFgo/ViJjMev4L0/pUblybS5DjaO7YaOLXVlmIyoEipOROUlJCRgwoQJSE9Ph64ufTOTp6KiIoSEhGDDhg2wsrKCn58fevTowToWqSFpZyK9/7Vdu3Yqe1fxcdFbLD2ShjMZT1FRhaHfWhrA1x2bY5ldJ7rTxHNUnIhacHV1ha6uLjZs2MA6ilp6/vw5Nm7ciJCQENjY2MDX1xfm5jS7RhXVZCaSuuA4DvuS7+NQykOk5BV+8lgWbU0BurXVg2O31hjfR3ULI5EdKk5ELbyf83Ly5Em6AyJDjx8/xrp16xAVFYXRo0fDx8cHhoaGrGMRKchjJpK64TgOidn5SMguwP0XxXhcVIoKSSW0NDXQsmFttGtcH9bG+rAybkqFiXxAxYmojaioKISEhODSpUu0/b2G7t27h6CgIOzbtw+TJk3CggUL0KZNG9axyD9Q5EwkQggVJ6JGOI7DwIED4eTkhDlz5rCOo5KysrKwevVqxMXFwc3NDd9//z2aNaOpyMpCGWYiEcJ3VJyIWklPT4e1tTVu3ryJVq1asY6jMlJTU+Hv74/Tp0/D09MTnp6eaNSoEetYvKXMM5EI4TsqTkTt+Pn5ITc3Fz///DPrKErvypUrEIvFuHz5MubNmwd3d3fo6OiwjsUrqjgTiRA+o+JE1E5JSQksLCwQGhqKoUOHso6jlBISEiAWi3H79m0sWrQI06ZNQ926tMVantRtJhIhfEXFiailkydPYs6cObh16xYVgv/HcRxOnToFsViMR48ewdfXFxMnTqRDkmWM4zjk5eX97TFbTk6O2s1EIoSPqDgRteXs7AxTU1OsXLmSdRSmKisrceTIEYjFYrx9+xZ+fn5wdnaGlpYW62gq79WrV397zJaamsqrmUiE8A0VJ6K2Hj58iK5duyIxMRFmZmas4yicRCJBdHQ0/P39Ubt2bQiFQtjb29NW9Gr435lI73+lmUiE8A8VJ6LWNm3ahNjYWJw9e5Y3j0PKysqwZ88eBAQEoEWLFhAKhRg6dChv/vw18amZSK1bt/7bln+aiUQI/1BxImpNIpGgb9++8PT0xOTJk1nHkau3b99ix44dCAoKgqmpKUQiEaytrVnHUlqfm4n017tInTp1oplIhBAAVJwID1y9ehUjRoxAWloamjRpwjqOzL158wZhYWEIDg5G7969IRQK0adPH9axlAbNRCKEyBIVJ8ILnp6eePfuHSIiIlhHkZmXL19i8+bN2LJlCwYPHgw/Pz906dKFdSymnj9//reCRDORCCGyRMWJ8EJRURHMzc2xf/9+DBgwgHWcGsnPz8f69esRHh4Oe3t7LF68GCYmJqxjKVRpaSkyMjI+OryWZiIRQhSBihPhjejoaKxYsQI3btxQyTsNDx8+xNq1a7Fr1y6MHz8eixYtQvv27VnHkiuaiUQIUTZUnAhvcBwHW1tbDBw4ED4+PqzjSC03NxeBgYE4cOAApk6divnz56vlOXw0E4kQogqoOBFeycnJQZ8+fXDt2jV06NCBdZxPun37NgICAnDixAl4eHjA29tbLeYDfWomkrm5+d9Kkjr8mQkh6oOKE+EdsViMixcv4ujRo0r5WCclJQVisRgJCQnw9vbG7NmzVfIdHWlmIv21IBkYGEBTU5N1bEII+SQqToR3ysrK0K1bN6xatQqjRo1iHeeDixcvQiwW48aNG1iwYAHc3NxUZnYQzUQihPAFFSfCS+fPn4eLiwvS09Oho6PDLAfHcTh79izEYjFyc3Ph4+ODKVOmoE6dOswyfQrNRCKE8B0VJ8JbU6dORaNGjRAcHKzwa3MchxMnTkAsFuPFixfw9fXFhAkTlGq3H81EIoSQv6PiRHgrPz8fFhYWiI+PR/fu3cFxHBKz85GQXYB7z4vx5NU7lEs4aGsK0EK3Dto3qQ9rY31YGTet9l2UyspKxMbGQiwWo7KyEkKhEKNHj2b6bg/NRCKEEOlRcSK8tn37doSFh8N7UzTiUh4hJa8Q5ZX//p+EtoYA3drqwbF7a4zvI/3MoIqKCuzbtw/+/v5o2LAhRCIRhg8frtDHWDQTiRBCao6KE+G1By+K8Y1POEr1TcBB+pKgpQEMMm2O5Xad0Eqv7r9+XWlpKXbu3InAwEC0b98eIpEIgwcPlnshoZlIhBAiH1ScCG9lPH4F7/0pyHz6utprmDbXwcax3dCxpe5H/7ykpAQRERFYs2YNunTpAqFQiC+//LKmkf+GZiIRQohiUXEivPSo8C2m7rxSo9L0nmlzHeyc2hstG9bFq1evEBISgg0bNuDLL7+EUChEjx49anwNmolECCHKgYoT4R2O4zBzzzWcSn8qszUHGTVCm7vxCAsLxdChQ+Hr64tOnTpVay2aiUQIIcpLi3UAQhRtX/J9/Hb730tTReFTPNzmBi29lh/+We2WxtAfOf9fP3MmMx/mJbVw8eJFGBkZSZVD2plINjY2NBOJEEKUBBUnwiscx+HQjYeQfOY+q2aDJmjtFib1ugJNLTToPBiGhob/+PvSzERycnLCypUraSYSIYQoMSpOhFcSs/ORklcol7VT8gpxJv0x9CvyPzkTqWfPnpg6dSrNRCKEEBVExYnwSkJ2wSfnNL3HlZXg2cEVKH/xEFoNm6Hx127Q1m/7yc+USziM+34Zmj1M+vAO0pw5c2gmEiGEqBEqToRX7j0v/uzXCGrXRT0za+j2cYCWXku8Sj6EZwdXoJVbGAQan96pZj9hGiKnbJNVXEIIIUpGg3UAQhTpyat3n/0azbq6aDJ0FrQbtYJAIIBuH0dI3hah/PmDz3726ZtyWcQkhBCipKg4EV4p/9xb4QAkb1+jvPDJx/+Q4yDQ+vwL2xWSyupGI4QQogKoOBFe0db8/HtGZU+y8WyfEJKSIgDAm5R4aOo0gVbD5p/9rJYm/SdFCCHqjN5xIrzSQrcOUh+++uTX1P2iBxp0t8GTHxcCAgE0GzRBM0fhZ99vAoCWDenMN0IIUWdUnAivtG8i3ZTthv3GoGG/MVVev11jmuJNCCHqjJ4rEF6xNtaHtoZ8xgJoawpgbUyH6BJCiDqj4kR4xcq4Kbq11ZPL2t3a6sHKuKlc1iaEEKIcqDgRXhEIBHDs3hpSvCNeJVoagGO31jTkkhBC1BwVJ8I74/u0w9dmn98hVxVfd2yO8X3ayXRNQgghyoeKE+EdgUCAZSM7wbS5jkzWM22ug2V2nehuEyGE8AAVJ8JLrfTqYuPYbjUuT6bNdbBxbDe0bFhXRskIIYQoMwHHcZ8fpUyImnpc9BZLj6ThTMZTVFRh6LeWxn8ezy2z60SliRBCeISKE+E9juOwL/k+DqU8REpe4SePZdHWFKBbWz04dmuN8X3a0eM5QgjhGSpOhPw/juOQmJ2PhOwC3H9RjMdFpaiQVEJLUwMtG9ZGu8b1YW2sDyvjplSYCCGEp6g4EUIIIYRIiV4OJ4QQQgiREhUnQgghhBApUXEihBBCCJESFSdCCCGEEClRcSKEEEIIkRIVJ0IIIYQQKVFxIoQQQgiREhUnQgghhBApUXEihBBCCJESFSdCCCGEEClRcSKEEEIIkdL/AaGWWDsfROWYAAAAAElFTkSuQmCC
"
>
</div>
</div>
</div>
</div>
</div>
{% endraw %}
{% raw %}
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="inner_cell">
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">quixotic.core</span> <span class="kn">import</span> <span class="n">QAOA</span>
<span class="n">qo</span> <span class="o">=</span> <span class="n">QAOA</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">task</span><span class="o">=</span><span class="s1">'minimum_vertex_cover'</span><span class="p">,</span> <span class="n">n_layers</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">qo</span><span class="o">.</span><span class="n">execute</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span>
<span class="n">nodes</span><span class="p">,</span> <span class="n">probs</span> <span class="o">=</span> <span class="n">qo</span><span class="o">.</span><span class="n">results</span><span class="p">(</span><span class="n">return_probs</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
</pre></div>
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<pre>Optimize for 20 iterations...
[========================================] 100% cost: -1.1177 iteration:20</pre>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">qo</span><span class="o">.</span><span class="n">plot_samples</span><span class="p">(</span><span class="n">probs</span><span class="p">)</span>
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
"
>
</div>
</div>
</div>
</div>
</div>
{% endraw %}
{% raw %}
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">qo</span><span class="o">.</span><span class="n">execute</span><span class="p">(</span><span class="mi">50</span><span class="p">)</span>
<span class="n">nodes</span><span class="p">,</span> <span class="n">probs</span> <span class="o">=</span> <span class="n">qo</span><span class="o">.</span><span class="n">results</span><span class="p">(</span><span class="n">return_probs</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area">
<div class="output_subarea output_stream output_stdout output_text">
<pre>Optimize for 50 iterations...
[========================================] 100% cost: -1.2200 iteration:50</pre>
</div>
</div>
</div>
</div>
</div>
{% endraw %}
{% raw %}
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">qo</span><span class="o">.</span><span class="n">plot_samples</span><span class="p">(</span><span class="n">probs</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area">
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<img 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
"
>
</div>
</div>
</div>
</div>
</div>
{% endraw %}
{% raw %}
<div class="cell border-box-sizing code_cell rendered">
<div class="input">
<div class="inner_cell">
<div class="input_area">
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">sub</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">subgraph</span><span class="p">(</span><span class="n">nodes</span><span class="p">)</span>
<span class="n">nx</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">pos</span><span class="o">=</span><span class="n">positions</span><span class="p">,</span> <span class="n">with_labels</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">nx</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">sub</span><span class="p">,</span> <span class="n">pos</span><span class="o">=</span><span class="n">positions</span><span class="p">,</span> <span class="n">node_color</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span> <span class="n">edge_color</span><span class="o">=</span><span class="s2">"r"</span><span class="p">)</span>
</pre></div>
</div>
</div>
</div>
<div class="output_wrapper">
<div class="output">
<div class="output_area">
<div class="output_png output_subarea ">
<img 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<p>Interestingly, after the additional iterations, our approximation is slightly closer to the ground truth than the Local Ratio algorithm in networkx that simply returns all nodes. The Local Ratio algorithm returns "a set of vertices whose weight sum is no more than 2 * OPT" (see <a href="https://stackoverflow.com/questions/45451726/networkx-min-weighted-vertex-cover-in-python-returns-whole-set-instead-of-vertex">this post</a> for more information).</p>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">networkx.algorithms.approximation.vertex_cover</span> <span class="kn">import</span> <span class="o">*</span>
<span class="n">nx_nodes</span> <span class="o">=</span> <span class="n">min_weighted_vertex_cover</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
<span class="c1"># plot nodes comprising the solution</span>
<span class="n">sub</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">subgraph</span><span class="p">(</span><span class="n">nx_nodes</span><span class="p">)</span>
<span class="n">nx</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">pos</span><span class="o">=</span><span class="n">positions</span><span class="p">,</span> <span class="n">with_labels</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
<span class="n">nx</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">sub</span><span class="p">,</span> <span class="n">pos</span><span class="o">=</span><span class="n">positions</span><span class="p">,</span> <span class="n">node_color</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span> <span class="n">edge_color</span><span class="o">=</span><span class="s2">"r"</span><span class="p">)</span>
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
"
>
</div>
</div>
</div>
</div>
</div>
{% endraw %}
</div>