test_circuit_v2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "29a3fb1b-afd7-45b7-ae7a-9506012b7f52",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "88f68364-f1ed-4bcd-a213-5badb4168efd",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pennylane as qml\n",
    "import pennylane.numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "321593d6-cdb6-403c-9825-f76fd1ed3cac",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "12f61e32-a630-4874-b7d2-710acea76b9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ecd30b72-95f8-4d30-83ed-d5dc5cd7f4eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "interface = 'autograd'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "db78c73e-49bf-4420-9a9e-03854cdb7f45",
   "metadata": {},
   "outputs": [],
   "source": [
    "if interface == 'autograd':\n",
    "    import pennylane.numpy as np\n",
    "    dev = qml.device(\"default.qubit\", wires=range(3))\n",
    "    def reset_params():\n",
    "        return 0.0 * np.ones(18)\n",
    "\n",
    "elif interface == 'jax':\n",
    "    import jax\n",
    "    import jax.numpy as jnp\n",
    "    # next line raises TypeError with default.qubit.jax\n",
    "    # dev = qml.device(\"default.qubit.jax\", wires=range(3))\n",
    "    dev = qml.device(\"default.qubit\", wires=range(3))\n",
    "    def reset_params():\n",
    "        return jnp.array([0.0] * 18)\n",
    "    \n",
    "elif interface == 'torch':\n",
    "    import torch\n",
    "    dev = qml.device(\"default.qubit\", wires=range(3))\n",
    "    def reset_params():\n",
    "        return torch.tensor([0.0] * 18, requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2c078cf3-7549-47de-95ae-f955d9440b76",
   "metadata": {},
   "outputs": [],
   "source": [
    "@qml.qnode(dev, interface=interface)\n",
    "def three_spins_forward_state(params, delta_time, n=10):\n",
    "    circuit.three_spins_circuit(params)\n",
    "    qml.ApproxTimeEvolution(circuit.hamiltonian(), delta_time, n)\n",
    "    return qml.state()\n",
    "\n",
    "@qml.qnode(dev, interface=interface)\n",
    "def three_spins_current_state(params):\n",
    "    circuit.three_spins_circuit(params)\n",
    "    return qml.state()\n",
    "\n",
    "@qml.qnode(dev, interface=interface)\n",
    "def three_spins_obvservables(params):\n",
    "    circuit.three_spins_circuit(params)\n",
    "    retvals = [qml.expval(qml.PauliX(i)) for i in range(3)]\n",
    "    retvals += [qml.expval(qml.PauliZ(i)) for i in range(3)]\n",
    "    return retvals\n",
    "\n",
    "\n",
    "# qnode_three_spins_forward_state = qml.QNode(three_spins_forward_state, dev, interface=interface)\n",
    "# qnode_three_spins_current_state = qml.QNode(three_spins_current_state, dev, interface=interface)\n",
    "# qnode_three_spins_obvservables = qml.QNode(three_spins_obvservables, dev, interface=interface)\n",
    "\n",
    "qnode_three_spins_forward_state = three_spins_forward_state\n",
    "qnode_three_spins_current_state = three_spins_current_state\n",
    "qnode_three_spins_obvservables = three_spins_obvservables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "24bbc7fc-3cb5-4dd6-a6ed-74a7479bef2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.999392295714022"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test this works\n",
    "params = reset_params()\n",
    "dt = 0.0\n",
    "original_state = qnode_three_spins_current_state(params)\n",
    "forward_state = qnode_three_spins_forward_state(params + 0.01, dt)\n",
    "\n",
    "qml.math.fidelity(original_state, forward_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fb4c1c8e-fedc-4306-8491-93d62440b701",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9704090525562026"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# test this works\n",
    "params = reset_params()\n",
    "dt = 0.1\n",
    "original_state = qnode_three_spins_current_state(params)\n",
    "forward_state = qnode_three_spins_forward_state(params,dt)\n",
    "\n",
    "qml.math.fidelity(original_state, forward_state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "989cd8d9-9cff-47cd-a4c8-7de7f795f55d",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qml.drawer.use_style(\"black_white\")\n",
    "fig, ax = qml.draw_mpl(qnode_three_spins_current_state)(params)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "521379f4-fea4-4bd2-a8de-8a4b80d91e9a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qml.drawer.use_style(\"black_white\")\n",
    "fig, ax = qml.draw_mpl(qnode_three_spins_obvservables)(params)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "771e2b79-b2db-483f-8893-2b6ec286a0da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.savefig('circuit.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "01426cde-9b2e-4919-a10b-38d75da03614",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1700x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qml.drawer.use_style(\"black_white\")\n",
    "fig, ax = qml.draw_mpl(qnode_three_spins_forward_state)(params, 0.1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8bd1db11-e417-41e7-8348-54343759189f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.savefig('circuit_w_hamiltonian.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "ec9a90a2-42e5-45e4-b9fb-62113ec70849",
   "metadata": {},
   "outputs": [],
   "source": [
    "prev_params = params\n",
    "\n",
    "prev_state = qnode_three_spins_current_state(prev_params)\n",
    "\n",
    "shots = 800\n",
    "\n",
    "def cost_function(params):\n",
    "    \n",
    "    forward_state = qnode_three_spins_forward_state(params, dt, shots = None)\n",
    "\n",
    "    fidelity = qml.math.fidelity(prev_state, forward_state)\n",
    "    return 1 - fidelity\n",
    "\n",
    "\n",
    "recorded_costs = [cost_function(params)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "88db5fe1-3761-4a7b-9015-eb62747117ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.807619557484939"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prev_params = params\n",
    "cost_function(np.random.random(18))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "39f3c3ae-a6ad-4974-939c-c1d12e59cbf2",
   "metadata": {},
   "outputs": [],
   "source": [
    "total_time = 2.0\n",
    "#total_time = 0.5\n",
    "dt = 0.02\n",
    "max_iterations = 500\n",
    "cost_threshold = 0.0001\n",
    "n_qubits = 3\n",
    "\n",
    "prev_params = reset_params()\n",
    "params = reset_params()\n",
    "prev_state = qnode_three_spins_current_state(prev_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "0b5082ad-44e5-4cec-bef8-d9c78ed715fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "        0., 0.], requires_grad=True)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reset_params()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "b8b7d5dd-d91f-4057-b8ac-c9ec374257df",
   "metadata": {},
   "outputs": [],
   "source": [
    "opt = qml.GradientDescentOptimizer(stepsize=0.1)\n",
    "\n",
    "final_costs_v_time = []\n",
    "full_costs_v_time = []\n",
    "final_params_v_time = []\n",
    "full_params_v_time = []\n",
    "failed_to_converge_times = {}\n",
    "number_of_iterations_to_converge = []\n",
    "observables = []\n",
    "time = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a58da732-66bd-40a3-8ba9-e85eeef03f13",
   "metadata": {},
   "outputs": [],
   "source": [
    "for current_time in np.arange(0, total_time+dt, dt):\n",
    "    print(current_time)\n",
    "    \n",
    "    prev_params = params\n",
    "    recorded_params = [params]\n",
    "\n",
    "    recorded_costs = [cost_function(params)]\n",
    "\n",
    "    for n in range(max_iterations):\n",
    "        params, prev_cost = opt.step_and_cost(cost_function, params)\n",
    "\n",
    "        recorded_costs.append(cost_function(params))\n",
    "        recorded_params.append(params)\n",
    "\n",
    "        if recorded_costs[-1] <= cost_threshold:\n",
    "            break\n",
    "\n",
    "    print(f'{n} iterations to converge')\n",
    "    if recorded_costs[-1] > cost_threshold:\n",
    "        failed_to_converge_times[current_time] = recorded_costs[-1]\n",
    "        \n",
    "    \n",
    "    prev_state = qnode_three_spins_current_state(recorded_params[-1])\n",
    "    time.append(current_time)\n",
    "    observables.append(qnode_three_spins_obvservables(params, shots = 8000))\n",
    "    final_costs_v_time.append(recorded_costs[-1])\n",
    "    full_costs_v_time.append(recorded_costs)\n",
    "    final_params_v_time.append(recorded_params[-1])\n",
    "    full_params_v_time.append(recorded_params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "50e757e2-c862-470e-bc82-9d55b0053894",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{}"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "failed_to_converge_times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "5282a514-de2b-4eae-bb68-59f661e9f4dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[tensor([ 0.0185 , -0.00425, -0.00525,  0.99575,  0.996  ,  0.99675], requires_grad=True),\n",
       " tensor([ 0.00125,  0.00525, -0.00575,  0.9835 ,  0.98375,  0.98475], requires_grad=True),\n",
       " tensor([-0.01675, -0.01475, -0.017  ,  0.96275,  0.96325,  0.9645 ], requires_grad=True),\n",
       " tensor([-0.0275 , -0.027  , -0.00375,  0.93575,  0.93975,  0.939  ], requires_grad=True),\n",
       " tensor([-0.02975, -0.0485 , -0.02925,  0.9    ,  0.91075,  0.89775], requires_grad=True),\n",
       " tensor([-0.03875, -0.0685 , -0.023  ,  0.85775,  0.8655 ,  0.865  ], requires_grad=True),\n",
       " tensor([-0.03625, -0.10275, -0.0405 ,  0.81525,  0.809  ,  0.808  ], requires_grad=True),\n",
       " tensor([-0.071  , -0.1295 , -0.06175,  0.751  ,  0.7735 ,  0.76275], requires_grad=True),\n",
       " tensor([-0.081  , -0.13425, -0.0545 ,  0.69375,  0.71725,  0.698  ], requires_grad=True),\n",
       " tensor([-0.08925, -0.155  , -0.0735 ,  0.62175,  0.62825,  0.63175], requires_grad=True),\n",
       " tensor([-0.0895 , -0.2075 , -0.0985 ,  0.55925,  0.565  ,  0.552  ], requires_grad=True),\n",
       " tensor([-0.11275, -0.2055 , -0.12   ,  0.47075,  0.48525,  0.4885 ], requires_grad=True),\n",
       " tensor([-0.11275, -0.231  , -0.11475,  0.40375,  0.4175 ,  0.4045 ], requires_grad=True),\n",
       " tensor([-0.1505 , -0.26025, -0.128  ,  0.30625,  0.3205 ,  0.318  ], requires_grad=True),\n",
       " tensor([-0.13925, -0.25475, -0.136  ,  0.23825,  0.23925,  0.227  ], requires_grad=True),\n",
       " tensor([-0.1405 , -0.265  , -0.12075,  0.1325 ,  0.1705 ,  0.142  ], requires_grad=True),\n",
       " tensor([-0.1315 , -0.27025, -0.14325,  0.0465 ,  0.07175,  0.04325], requires_grad=True),\n",
       " tensor([-0.11675, -0.27   , -0.13325, -0.02275, -0.0265 , -0.045  ], requires_grad=True),\n",
       " tensor([-0.14625, -0.2625 , -0.14   , -0.13325, -0.08775, -0.127  ], requires_grad=True),\n",
       " tensor([-0.14725, -0.25525, -0.1495 , -0.24175, -0.186  , -0.22875], requires_grad=True),\n",
       " tensor([-0.12175, -0.2385 , -0.133  , -0.2965 , -0.2705 , -0.2895 ], requires_grad=True),\n",
       " tensor([-0.126  , -0.209  , -0.1315 , -0.39225, -0.339  , -0.37775], requires_grad=True),\n",
       " tensor([-0.10125, -0.207  , -0.1115 , -0.449  , -0.405  , -0.44625], requires_grad=True),\n",
       " tensor([-0.10925, -0.19825, -0.11475, -0.53225, -0.47   , -0.536  ], requires_grad=True),\n",
       " tensor([-0.09325, -0.1855 , -0.1075 , -0.58775, -0.53   , -0.59625], requires_grad=True),\n",
       " tensor([-0.094 , -0.136 , -0.087 , -0.674 , -0.5965, -0.668 ], requires_grad=True),\n",
       " tensor([-0.0805 , -0.13975, -0.0775 , -0.71125, -0.6465 , -0.7295 ], requires_grad=True),\n",
       " tensor([-0.0655 , -0.10875, -0.08325, -0.76175, -0.70975, -0.7765 ], requires_grad=True),\n",
       " tensor([-0.049  , -0.098  , -0.071  , -0.8135 , -0.73975, -0.81725], requires_grad=True),\n",
       " tensor([-0.065  , -0.07675, -0.07875, -0.8585 , -0.78525, -0.84375], requires_grad=True),\n",
       " tensor([-0.048  , -0.06575, -0.04125, -0.891  , -0.80875, -0.887  ], requires_grad=True),\n",
       " tensor([-0.052  , -0.07025, -0.0405 , -0.90175, -0.8235 , -0.902  ], requires_grad=True),\n",
       " tensor([-0.03625, -0.04625, -0.0565 , -0.91525, -0.8365 , -0.9085 ], requires_grad=True),\n",
       " tensor([-0.04625, -0.05475, -0.048  , -0.92525, -0.857  , -0.92725], requires_grad=True),\n",
       " tensor([-0.0475 , -0.0335 , -0.0455 , -0.92175, -0.8575 , -0.92   ], requires_grad=True),\n",
       " tensor([-0.05725, -0.0425 , -0.0545 , -0.91425, -0.85275, -0.9125 ], requires_grad=True),\n",
       " tensor([-0.066  , -0.0595 , -0.066  , -0.89725, -0.831  , -0.8855 ], requires_grad=True),\n",
       " tensor([-0.04775, -0.07875, -0.072  , -0.8705 , -0.8355 , -0.8615 ], requires_grad=True),\n",
       " tensor([-0.0715 , -0.08225, -0.0855 , -0.84075, -0.8015 , -0.8455 ], requires_grad=True),\n",
       " tensor([-0.07475, -0.09375, -0.0615 , -0.80175, -0.7575 , -0.795  ], requires_grad=True),\n",
       " tensor([-0.082  , -0.1005 , -0.068  , -0.737  , -0.74175, -0.75075], requires_grad=True)]"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "f45144ae-4dd4-470c-975f-2392fc80484d",
   "metadata": {},
   "outputs": [],
   "source": [
    "sig_x = np.tensor(observables)[:,:3]\n",
    "sig_z = np.tensor(observables)[:,3:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "4d03394b-03ba-4737-9dfb-ee70e3c61d9f",
   "metadata": {},
   "outputs": [],
   "source": [
    "sum_sig_x = np.sum(sig_x, axis=1)\n",
    "sum_sig_z = np.sum(sig_z, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "1b82ed23-1201-4be3-b575-114a83191493",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f984e935570>"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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76Nu3L40bN2bq1Km5QsrChQvp3r073t7euZ7r4eHB7bffTqtWrRg3bhzNmjXjo48+Kqq/ijzpDI4Uns0GYX+FgPrw3WNwZht82RmGTIdqLa2uTkTk5rmXMc+kWPXahVC1alXGjh3L2LFj2bRpE1OnTmXgwIGUK1eOhx9+mPDwcBo1apQTeFJSUnKutdm7dy/r1q3jrbfeytnf+vXrAfjHP/7BXXfdRbNmzcjKymL58uVMmzaNH374IecanylTplCjRo1ralqwYAFPPPFEvrUbhkFaWlqh+ltYOoMjN++2u2D4KvCvB4lRMLkX7JljdVUiIjfPZjO/JrJiuYXrGdu3b88XX3xBdHQ0//d//8fu3btp1qwZe/fupW3btnh7e/P3v/+dgwcP5tzCPXLkSNq3b59rP++//z5nz57lvffeA+C///0vDz74ID4+PqxcuZLDhw/zj3/8I89wExMTw/bt27nnnntybX/11VdZv349J0+eZO/evYwdO5Y1a9bw8MMP33R/C0JncOTWVLoNnlgJ80bA4aUwbzhE74Vub5hj6oiISInx8vJiyJAhDBkyhKioKHx8fPD19WXOnDm8+OKLNG3alODgYEaOHMlLL72U67mTJ09m48aNzJkzJ+fanPDwcP72t7/h5eWV72v/+OOPtG3bloCAgFzbz58/T3h4OOfOncPPz4+mTZvy008/0b1796LreB50F5Xuoioa2dmw+t+w3kz93N4dBn4N3uUtLUtE5M8KcrdOaTN//nw+//xzFi5ciKfnzd000q9fP+644w7+/ve/39Tzi/ouKn1FJUXDxQW6/hPunwRu3nB0BXzdDS4eyf+5IiJiqb/85S+cOHGCtm3b0rx585uaSuGOO+7gwQcfLIbqbk7pjatSPBoPhEq3w8yH4NIR+Kor3Pcl1Lvb6spEROQ6YmNjb3kfN3vmprjoDI4UvaBm5szkNcLMmclnDoYVr0NW4eYzERERuVkKOFI8fALg0YXQ9inz8cYPYWpfSLDo9ksRESlVFHCk+Lh5QK+34YGp4FEOTm+CzzvCsVX5P1dEROQWKOBI8Ws0AJ5cC1WawJWLMO0+WD0OsrOsrkxERJyULjKWklHpNnh8hTl/1c4psPZtiNwC930NPpWtrk5ESrkrV65QpkzhRhKWopWZWbTXaSrgSMlx94a+H0GN9rBoFBxfA5/fAQ9MhpD2+T1bRKRIuLhc++XF2bNnLahE8pPXe1Xg5xZhHSIF02wwDF9tTvGQFG1O1rnhA3OwQBGRYubi4nLTg9lJyXFzc7P/gPPZZ59Rq1YtvLy8CA0NzZnQKy/Dhg3DZrNdszRq1CinzZQpU/Jsk5qaWhLdkaIQUN+8lbzpYDCyYOUbMHMIXLlsdWUiUgoEBgbi7u5udRlyHTabjWrVqt3SPoo94MyePZtRo0YxduxYIiIi6NixI7169eL06dN5tv/oo484d+5czhIZGUnFihV54IEHcrXz9fXN1e7cuXMFmitD7IhHWbj3C/NrK1dPOLIMvu4KsaesrkxEnFzZsmWpXbs25cuXv6WzBFL03NzcqFGjxi1fE1Xsc1G1bduWli1bMmHChJxtDRo0YMCAAYwbNy7f5//www/cd999nDhxgpCQEMA8gzNq1Cji4uJuqibNRWWHzu2BWQ9D/GkoVxUe/QEq17O6KhEpJbKzs8nW1+SWc3FxuWHgLMznd7FeZJyens7OnTt55ZVXcm3v0aMHmzZtKtA+Jk6cSLdu3XLCzW+SkpIICQkhKyuL5s2b869//YsWLVrkuY+0tDTS0tJyHickJBSyJ1LsgprC48vgmwFw8RBMuhsemQvVWlpdmYiUAvl9sIrjKdZ38+LFi2RlZREYGJhre2BgINHR0fk+/9y5cyxdupQnnngi1/b69eszZcoUFi5cyMyZM/Hy8qJDhw7XzEL6m3HjxuHn55ezBAcH33ynpPj4VoXHlkLVlpByGab2gxPXv15LRETkekokrtpstlyPDcO4ZltepkyZQvny5RkwYECu7e3ateORRx6hWbNmdOzYkTlz5lC3bl0++eSTPPczZswY4uPjc5bIyMib7osUs7KVYOhCqNkR0hPh24FwqPCz2oqISOlWrAHH398fV1fXa87WxMTEXHNW588Mw2DSpEmEh4fj4eFxw7YuLi60bt36umdwPD098fX1zbWIHfMsBw9/D/V6Q1aaeW3O7tlWVyUiIg6kWAOOh4cHoaGhrFixItf2FStW0L79jQd2W7t2LUePHuXxxx/P93UMw2DXrl0EBQXdUr1iR9y9YNA0aDrEvI18/gjY+qXVVYmIiIMo9pGMR48eTXh4OK1atSIsLIwvv/yS06dPM3LkSMD8+ujs2bN88803uZ43ceJE2rZtS+PGja/Z55tvvkm7du2oU6cOCQkJfPzxx+zatYtPP/20uLsjJcnVDQZMAC8/2PYFLP0bpMbDnS9BAb7iFBGR0qvYA87gwYO5dOkSb731FufOnaNx48YsWbIk566oc+fOXTMmTnx8PHPnzuWjjz7Kc59xcXGMGDGC6Oho/Pz8aNGiBevWraNNmzbF3R0paS4u0Osd8K5gzl+1+t+QEgs9/6OQIyIi11Xs4+DYI42D46C2TDAn6wRo/sjVAQI1nZqISGlRmM9v3fQvjqPdU9D/M7C5wK5v4fvHIKtoZ58VERHnoIAjjqXFwzDoG3D1gAMLYdmrVlckIiJ2SAFHHE+DvjBworm+7QvY9pW19YiIiN1RwBHH1LAfdP2nub70ZTi2ytp6RETErijgiOO6YzQ0e9AcJ2fOMLhw2OqKRETETijgiOOy2cw7qYLbQVo8zBgEyZesrkpEROyAAo44NjdPGDIdyodA7AmYEw6Z6VZXJSIiFlPAEcdX1h8emg2evnBqIyx6AUrf8E4iIvIHCjjiHAIawP2Tfx8jZ9PHVlckIiIWUsAR51GnG9z9trm+4nU4sMjaekRExDIKOOJc2oyAVo8DBswbDud2W12RiIhYQAFHnIvNZk7OWbsLZFyBmQ9CYrTVVYmISAlTwBHn4+oOD0wB/7qQcNYMORkpVlclIiIlSAFHnJN3efPOKu+KEPULzB8J2dlWVyUiIiVEAUecV8XaMPhbcHGHX3+AFa/p9nERkVJCAUecW80O0O8Tc33zeFj/nrX1iIhIiVDAEefX/EHo+V9zfdW/YPvX1tYjIiLFTgFHSoewp+HOv5nri1+Cvd9bW4+IiBQrBRwpPbqMhdbDAQPmPwmHl1tdkYiIFBMFHCk9bDbo9T9o8gBkZ5oTc57aZHVVIiJSDBRwpHRxcYEBE6BOT8hMhRmDNdqxiIgTUsCR0sfVHQZNhZAOkJYA0+6Di0etrkpERIqQAo6UTu7e8OBMqNIUrlyEaQMg/qzVVYmISBFRwJHSy8sPHpkHlW6H+Egz5CRfsroqEREpAgo4Urr5VIbwH8C3Glw8DNMHQmqC1VWJiMgtUsARKR9shpwylSAqAmY9pMk5RUQcnAKOCEDluvDIXPAoByfXm+PkaHJOERGHpYAj8puqLeChWVcn51wA6/5ndUUiInKTFHBE/qjmHXDPB+b6mnGwf7619YiIyE1RwBH5s5bh0O5pc33+UxoIUETEASngiOSl+1twW1fITIGZD0FSjNUViYhIISjgiOTF1Q3unwSV6kDCGZj1MGSmWV2ViIgUkAKOyPV4l4cHZ5kDAp7ZBoteAMOwuioRESmAEgk4n332GbVq1cLLy4vQ0FDWr19/3bZr1qzBZrNdsxw8eDBXu7lz59KwYUM8PT1p2LAh8+frYlApBv63w/2TweYCu6bD5vFWVyQiIgVQ7AFn9uzZjBo1irFjxxIREUHHjh3p1asXp0+fvuHzDh06xLlz53KWOnXq5Pxs8+bNDB48mPDwcHbv3k14eDiDBg1i69atxd0dKY1u7wo9/2uur/gnHFlhbT0iIpIvm2EU7zn3tm3b0rJlSyZMmJCzrUGDBgwYMIBx48Zd037NmjV06dKF2NhYypcvn+c+Bw8eTEJCAkuXLs3Zdvfdd1OhQgVmzpyZb00JCQn4+fkRHx+Pr69v4TslpY9hwI/PwS/fgKcvPLESKtezuioRkVKlMJ/fxXoGJz09nZ07d9KjR49c23v06MGmTZtu+NwWLVoQFBRE165dWb16da6fbd68+Zp99uzZ87r7TEtLIyEhIdciUig2G/R+D2q0h7QEmDkErly2uioREbmOYg04Fy9eJCsri8DAwFzbAwMDiY6OzvM5QUFBfPnll8ydO5d58+ZRr149unbtyrp163LaREdHF2qf48aNw8/PL2cJDg6+xZ5JqeTmAYOngV8NuHwcvn8MsjKtrkpERPLgVhIvYrPZcj02DOOabb+pV68e9er9fuo/LCyMyMhI3n33Xe68886b2ueYMWMYPXp0zuOEhASFHLk5Zf3hwZkwsQccXwPLXoXemtJBRMTeFOsZHH9/f1xdXa85sxITE3PNGZgbadeuHUeOHMl5XKVKlULt09PTE19f31yLyE2r0hju+8Jc3/YF7JhkbT0iInKNYg04Hh4ehIaGsmJF7rtOVqxYQfv27Qu8n4iICIKCgnIeh4WFXbPP5cuXF2qfIrekQV/o8g9zffFLcPRna+sREZFciv0rqtGjRxMeHk6rVq0ICwvjyy+/5PTp04wcORIwvz46e/Ys33zzDQAffvghNWvWpFGjRqSnp/Ptt98yd+5c5s6dm7PP559/njvvvJN33nmH/v37s2DBAlauXMmGDRuKuzsiv7vzJbh0BPbMhjlD4S9LoUoTq6sSERFKIOAMHjyYS5cu8dZbb3Hu3DkaN27MkiVLCAkJAeDcuXO5xsRJT0/npZde4uzZs3h7e9OoUSMWL15M7969c9q0b9+eWbNm8Y9//IPXXnuN2267jdmzZ9O2bdvi7o7I72w26DceEqLg5HqYPsi8fdyvmtWViYiUesU+Do490jg4UqRSYmHS3XDhIAQ0Ms/kePlZXZWIiNOxm3FwREoF7wrw8HfgEwgx+2HOo5CVYXVVIiKlmgKOSFEoXwMemgPuZc3bx398XhNziohYSAFHpKhUbQ4PTAGbqzkx59p3rK5IRKTUUsARKUp1e0Cf98z1NeMgYrq19YiIlFIKOCJFrdVjcMfVkbN/fA6Orb5xexERKXIKOCLF4a7XoMkDkJ0Js8Mhep/VFYmIlCoKOCLFwcUF+n8KIXdAeiJMfwDiz1pdlYhIqaGAI1Jc3DxhyLfgXw8So2DGIEhNsLoqEZFSQQFHpDj9NkZO2QA4vw++GwpZmVZXJSLi9BRwRIpbhRB4eA64l4Fjq2Djh1ZXJCLi9BRwREpC1RbQ531zfc3bEL3X2npERJycAo5ISWk2BOrfA9kZMH8kZKZbXZGIiNNSwBEpKTYb3PMBlKlkXo+z9m2rKxIRcVoKOCIlySfg96+qNnwAZ3ZYW4+IiJNSwBEpaY0GmIMAGtkw/0lIv2J1RSIiTkcBR8QKvf4HPlXg0lFY9S+rqxERcToKOCJWKFMR+n1irm/5DE6st7YeEREno4AjYpW6PaDlUHN9wV8hLdHaekREnIgCjoiVev4HyteAuNOw/B9WVyMi4jQUcESs5FkO+n9mru+cAkdWWFqOiIizUMARsVqtjtD2KXN9wTNw5bK19YiIOAEFHBF70PWfUOl2SIqGpS9bXY2IiMNTwBGxBx5lYMDnYHOBvXPg1wVWVyQi4tAUcETsRXBr6DDKXF/0AiRdsLQcERFHpoAjYk86vwKBjeHKJVg0CgzD6opERBySAo6IPXHzhHs/Bxd3OLgIIqZZXZGIiENSwBGxN1WaQJcx5vril+DsTmvrERFxQAo4IvaowwtQtxdkpcHscF2PIyJSSAo4IvbIxQXu+8K8dTzhLHw3DLIyrK5KRMRhKOCI2CsvPxgyAzx84NQGWPFPqysSEXEYCjgi9qxyPfOiYzBnHd8929p6REQchAKOiL1r0Bc6vmSu//g8nNttbT0iIg5AAUfEEXR5FW7vDpkpMOsRSL5kdUUiInatRALOZ599Rq1atfDy8iI0NJT169dft+28efPo3r07lStXxtfXl7CwMJYtW5arzZQpU7DZbNcsqampxd0VEWu4uMLAr6BCLYg/Dd8/BlmZVlclImK3ij3gzJ49m1GjRjF27FgiIiLo2LEjvXr14vTp03m2X7duHd27d2fJkiXs3LmTLl260LdvXyIiInK18/X15dy5c7kWLy+v4u6OiHW8K8CQ6eBeBk6shZ/ftLoiERG7ZTOM4h0Lvm3btrRs2ZIJEybkbGvQoAEDBgxg3LhxBdpHo0aNGDx4MP/8p3kXyZQpUxg1ahRxcXE3VVNCQgJ+fn7Ex8fj6+t7U/sQscy+eeYZHID7J0Pj+6ytR0SkhBTm87tYz+Ckp6ezc+dOevTokWt7jx492LRpU4H2kZ2dTWJiIhUrVsy1PSkpiZCQEKpXr84999xzzRmeP0pLSyMhISHXIuKwGt8HHZ431xc8Def3W1uPiIgdKtaAc/HiRbKysggMDMy1PTAwkOjo6ALt47333iM5OZlBgwblbKtfvz5Tpkxh4cKFzJw5Ey8vLzp06MCRI0fy3Me4cePw8/PLWYKDg2++UyL24K5/Qu3OkHEFZj0EKbFWVyQiYldK5CJjm82W67FhGNdsy8vMmTN54403mD17NgEBATnb27VrxyOPPEKzZs3o2LEjc+bMoW7dunzyySd57mfMmDHEx8fnLJGRkbfWIRGrubqZX0+VrwGxJ2HucMjOsroqERG7UawBx9/fH1dX12vO1sTExFxzVufPZs+ezeOPP86cOXPo1q3bDdu6uLjQunXr657B8fT0xNfXN9ci4vDKVITB08HNG46ugDUFu6ZNRKQ0KNaA4+HhQWhoKCtWrMi1fcWKFbRv3/66z5s5cybDhg1jxowZ9OnTJ9/XMQyDXbt2ERQUdMs1iziUoKbQ72Nzfd27cGy1tfWIiNiJYv+KavTo0Xz99ddMmjSJAwcO8MILL3D69GlGjhwJmF8fPfroozntZ86cyaOPPsp7771Hu3btiI6OJjo6mvj4+Jw2b775JsuWLeP48ePs2rWLxx9/nF27duXsU6RUaToIQocBBswbAUkxVlckImK5Yg84gwcP5sMPP+Stt96iefPmrFu3jiVLlhASEgLAuXPnco2J88UXX5CZmcnTTz9NUFBQzvL888/ntImLi2PEiBE0aNCAHj16cPbsWdatW0ebNm2Kuzsi9qnnOKjcAJJjYP6TkJ1tdUUiIpYq9nFw7JHGwRGnFHMAvuxiTufQ7Q244wWrKxIRKVJ2Mw6OiJSggAbQ6x1z/ed/QeQ2a+sREbGQAo6IM2n5KDQeCEYWfP+4xscRkVJLAUfEmdhscM+HUKGmOSnnwmeh9H0LLSKigCPidLx8zUEAXdzhwI+wY6LVFYmIlDgFHBFnVK0ldL862/hPr0L0XmvrEREpYQo4Is6q3V+hTk/ISoPvHoP0ZKsrEhEpMQo4Is7KZoMBE6BcVbh0BJb8zeqKRERKjAKOiDMrWwkGfgU2F9g1HXbPtroiEZESoYAj4uxq3gGdXjbXF70AF49aW4+ISAlQwBEpDe78G4TcARnJ8P1jkJlmdUUiIsVKAUekNHBxNb+qKlMJovfA8tesrkhEpFgp4IiUFr5VYcDn5vq2L+DYKmvrEREpRgo4IqVJ3R7QZoS5vuBZSI23th4RkWKigCNS2nR7AyrUgoQzsOxVq6sRESkWCjgipY1HWRjwGWCDiG/h8DKrKxIRKXIKOCKlUUh7c6RjgIXPadZxEXE6CjgipVXX16BSHUiKhqUvW12NiEiRUsARKa3cvc2pHGwusGc2HFhkdUUiIkVGAUekNAtuDe2fM9cXjYLkS5aWIyJSVBRwREq7Lq9C5QaQfAGWvGh1NSIiRUIBR6S0c/OEeyeAzRX2z4d986yuSETklingiAhUbQEdr569WfwiJMVYW4+IyC1SwBER051/g8AmkHLZnHXcMKyuSETkpingiIjJzcP8qsrFHQ4ugr3fWV2RiMhNU8ARkd9VaQKdro6Js+QlSDhnbT0iIjdJAUdEcrtjFAQ1Nyfi/PF5fVUlIg5JAUdEcnN1h3s/B1cPOLIMdk23uiIRkUJTwBGRawU0MMfHAfhpDMSdtrYeEZFCUsARkby1fw6qt4G0BPj+L5CVYXVFIiIFpoAjInlzcYWBX4GnH5zZDj+/aXVFIiIFpoAjItdXoSYM+NRc3/QJHF5maTkiIgWlgCMiN9agL7Qdaa7PfxLiz1hbj4hIASjgiEj+ur9l3jqeEqvrcUTEISjgiEj+3DzhgSng6QuRW2HVv62uSETkhkok4Hz22WfUqlULLy8vQkNDWb9+/Q3br127ltDQULy8vKhduzaff/75NW3mzp1Lw4YN8fT0pGHDhsyfP7+4yi8wwzDIytagaOKkKtaCfp+Y6xs/hMPLLS1HRORGij3gzJ49m1GjRjF27FgiIiLo2LEjvXr14vTpvMfVOHHiBL1796Zjx45ERETw6quv8txzzzF37tycNps3b2bw4MGEh4eze/duwsPDGTRoEFu3bi3u7tzQ5eR06v1jKXf+bzUPf72FV+bu4dPVR1m4O4qI07FcTErD0Kiw4sgaDYDWw831+U9C/FlLyxERuR6bUcyfuG3btqVly5ZMmDAhZ1uDBg0YMGAA48aNu6b9yy+/zMKFCzlw4EDOtpEjR7J79242b94MwODBg0lISGDp0qU5be6++24qVKjAzJkz860pISEBPz8/4uPj8fX1vZXu5bIrMo4Bn268YZsyHq5Ur+BNcIUyBFcsQ7NgP/o3q4aLi63I6hApVhmpMKkHnNsNNcJg6CJwdbO6KhEpBQrz+V2s/yulp6ezc+dOXnnllVzbe/TowaZNm/J8zubNm+nRo0eubT179mTixIlkZGTg7u7O5s2beeGFF65p8+GHH+a5z7S0NNLS0nIeJyQk3ERv8tekmh+bXrmLyMtXiIxNufrnFc5cTiEy9grRCalcSc/i8PkkDp9Pynnegl1RfDi4OeXLeBRLXSJFyt0L7p8MX3SC05th9X+g2+tWVyUikkuxBpyLFy+SlZVFYGBgru2BgYFER0fn+Zzo6Og822dmZnLx4kWCgoKu2+Z6+xw3bhxvvln8g5S5utioWt6bquW9aZvHz9Mys4iKS+X05StEXr7CiYvJfLvlFGsOXaDPxxv4/JFQmlT3K/Y6RW5Zpdug38fw/WOw4X2o2QFu72Z1VSIiOUrkImObLffXL4ZhXLMtv/Z/3l6YfY4ZM4b4+PicJTIyslD1FxVPN1dq+ZelU93KPNIuhNfuaci8v7YnpFIZzsalMHDCJmZsPa3rdMQxNL4PWj1urs8bAQlR1tYjIvIHxRpw/P39cXV1vebMSkxMzDVnYH5TpUqVPNu7ublRqVKlG7a53j49PT3x9fXNtdiLRlX9WPjMHXRrEEh6Vjavzt/LS9/tISU9y+rSRPLX879QpQlcuQRzn4CsTKsrEhEBijngeHh4EBoayooVK3JtX7FiBe3bt8/zOWFhYde0X758Oa1atcLd3f2Gba63T3vn5+3Ol+GhvHx3fVxsMPeXM9z72UZOXky2ujSRG3P3ggemgocPnNoIa9+2uiIREaAEvqIaPXo0X3/9NZMmTeLAgQO88MILnD59mpEjzaHfx4wZw6OPPprTfuTIkZw6dYrRo0dz4MABJk2axMSJE3nppZdy2jz//PMsX76cd955h4MHD/LOO++wcuVKRo0aVdzdKTYuLjae6nwb3z7RFn8fDw5GJ9L3kw0s25/3dUUidqPSbdD3I3N93btw9Gdr6xERoQQCzuDBg/nwww956623aN68OevWrWPJkiWEhIQAcO7cuVxj4tSqVYslS5awZs0amjdvzr/+9S8+/vhjBg4cmNOmffv2zJo1i8mTJ9O0aVOmTJnC7Nmzads2r0t7HUv72/xZ9GxHQkMqkJiWyZPTdjJu6QEys7KtLk3k+prcD6HDAOPq9TjnrK5IREq5Yh8Hxx4V1zg4RSkjK5txSw4yaeMJANrVrsjHD7YgoJyXxZWJXEdGCnzdHc7vhZAO8OhCjY8jIkWqMJ/fCjh2GnB+s2hPFC9/v4fk9Cz8fTy5q35lalf24bbKPtSuXJYaFcvg7qopxcROXDwKX3aC9CTo+CJ0/afVFYmIE1HAyYcjBRyAozGJjPz2F47GJF3zMzcXGzUqlrkaespSu3LZnABUsawGDhQL7JtrzjgO8PBcqKPxcUSkaCjg5MPRAg5ASnoWPx88z5HzSRy/mMzxC0kcv5BMSsb1byfv2SiQ/w1shl8Z9xKsVARYNBp2TATvijByA/hVs7oiEXECCjj5cMSAkxfDMIhOSOVYTDLHL5qB59jV4HM2LgWAGhXLMOGRljSqqhGSpQRlpMLE7hC9B4LbwbBF4KqgLSK3RgEnH84ScG5k39l4Rn67kzOxKXi6ufCvAY0Z1CrY6rKkNLl83JyvKi0BOoyC7sU/XYqIOLfCfH7r6lQn1biaH4uevYO76geQlpnN37/fwytz95B6g6+0RIpUxdrQf7y5vvFDOLzM0nJEpHRRwHFi5ct48PWjrXipR11sNpi1PZL7P99E5OUrVpcmpUXD/tDmSXN9/pMQZ808cCJS+ijgODkXFxvP3FWHb/7ShoplPdh3NoE+H69n1cHzVpcmpUWPf0HVFpASa95dlZVhdUUiUgoo4JQSHetUZtGzd9CiRnkSUjP5y5QdvLvsEFnZpe4SLClpbp7wwBTw9IMz22DlG1ZXJCKlgAJOKVK1vDezR4QxrH1NAMavPsqjk7ZyKSnN2sLE+VWoCQM+Ndc3j4eDSywtR0ScnwJOKePh5sIb/Rrx0ZDmeLu7svHoJe75ZAObj12iFN5QJyWpQV9o91dz/YeREHvK2npExKnpNnEnvU28IA6fT2Tktzs5fiEZgNqVyzKgeTUGNK9GjUplLK5OnFJmOky+G87uhGqh8NhP4KYRt0WkYDQOTj4UcH6XlJbJvxf9yvyIs6Rl/j5jecsa5bm3RTX6NK2qKR+kaMWdhs87QmochD0DPf9jdUUi4iAUcPKhgHOtxNQMlu0/z4JdZ9l49CK/XXvs5mLjzrqVGdCiGt0bBOLt4WptoeIcDi2FmUMAGzzxM1QPtboiEXEACjj5UMC5sZiEVBbujmLBrij2no3P2V7Ww5Wejapwf2h12t/ub2GF4hTmjYA9s6FKUxi+GlzdrK5IpNBiElNZtPscC3dHkZCawcCW1XmoTQ0q6Mx3sVDAyYcCTsEdjUliwa6z/LDrLJGXU3K2D2pVnbf6N8bLXWd05CYlXYDxoZAaDz3HQdhfra5IpEASUjP4aV80C3dFsenY72e8f+Pp5sJ9LasxrH0t6lUpZ02RTkoBJx8KOIVnGAa/nI7l+51nmb39NNkGNAzy5fNHQnVBsty8HZNh0Sjw8IGnt2nWcSk28Vcy+HFPFGsOxeDn7cFtAWW5vbIPtwX4UKNiGdxdb3xTcWpGFmsOxbBgVxQ/H4wh/Q/XLIaGVKB/86qU8XBjyqYT7DubkPOzDrdX4i8datGlXgAuLrZi619poYCTDwWcW7PhyEWemxXB5eR0fL3ceH9Qc7o1DLS6LHFE2dnmXVWRW83byAd/a3VF4kQys7JZf/Qi3+88w4pfz+cKJX/k5mIjpFIZbrsaeG6r7MPtAT7UqlSWfVHxLNh1lqX7oklMzcx5Tp0AHwa0qEa/ZlUJrvj7L3mGYbDjVCyTN57gp33ROWd3alYqw9D2NXmgVTA+nvo69mYp4ORDAefWRcWl8PSMX4g4HQfA011uY3T3erjqNxQprPP7zbuqjCx4cDbUu9vqisTBHYpOZO4vZ5gfcZYLib8PZFq/Sjn6Na9KVpbBsQtJHLuQzLELSVxJL9gkxEF+XvRrXpX+zarRIKgcNtuN/787E3uFaZtPMXPbaRKuhqNynm480CqYYe1r6uz3TVDAyYcCTtFIz8zmv0sOMGXTSQDa31aJjx9sgb+Pp7WFieNZ/hps+hj8asDTW8CjrNUViUVSM7J4df5etp+8TJCfN9XLe1OtgjfV/vBn1fLe11z/F5uczsLdUXy/80yumyMqlvWgX7Oq3B9anUZVfa8JJYZhEJ2QytGYJI7F/B56jl1I4nxCGn7e7vRuEsSA5lVpXbPiTX3NlJyWybxfzjB508mcccdcbDCkTQ1e6lFPQ3EUggJOPhRwitaCXWd5Ze5eUjKyqOLrxacPtyA0pKLVZYkjSU+GT9tCfCR0eB66v2V1RWKB1IwsRkzbybrDF/Jt6+/jSbUK3lSv4E16ZjZrDsWQkWV+nLm52LirfgADQ6vTpV4AHm43N2h/clomnm4uuOVzfU5BZWcbrDtygUkbT+b00dfLjdHd6/JIu5Aiex1npoCTDwWconfk6qjIxy4k4+ZiY2yfBgxrXzPfU7giOX4bG8fFDZ5cB4GNrK5ISlB6ZjZPfbuTnw/G4O3uytsDm2Cz2Tgbm8KZ2CucjUvhbGwKZ+NSrvuVUqOqvtwfWp1+zapSyc7PJG87cZnXF+7nwDnzguS6gT683rcRHTQExw0p4ORDAad4JKVl8vLcPSzecw6Ae5oG8c7AppTVBXVSULMehoOLILitOY2Di36jLQ0ysrJ5ZsYvLNt/Hk83FyY/1pr2t+X9QW8YBnFXMjgbl8KZq4EnJT2Trg0CaRDkWP+fZ2UbzNp+mneXHSL2SgYAdzeqwtg+DXJduCy/U8DJhwJO8TEMg8kbT/LfJQfIzDa4rXJZJg1rTUglXVMhBRB/Fj5tA+lJ0PcjCB1mdUVSzDKzshk1exeL9pzDw9WFr4e24s66la0uq0TFXUnngxWHmbblFNmGOY7Ok51u46lOt2n0+D8pzOe3fj2SImWz2fjLHbWYNaIdgb6eHLuQzBNTd5Cclpn/k0X8qkGXV831Fa+bgwGK08rKNvj793tYtOcc7q42Pg9vWerCDUD5Mh682b8xS57vSFjtSqRlZvPxz0fo+t4aFu2JohSehygSOoOjMzjF5nxCKn0/2UBMYhr9m1flw8HNdU2O5C8rE77qDNF7oekQuO8LqyuSYpCdbTBm3l5m74jE1cXGpw+15O7GVawuy3KGYbB0XzT/WXyAs3Hm6PFta1VkYMvqVPHzomp5L6r4eZfasXT0FVU+FHBKzrYTl3nwqy1kZRv8q38jwsNqWl2SOIIzO+HrroABjy6E2p2srkiKkGEYvLZgH99uOY2LDT5+sAX3NK1qdVl2JSU9iy/WHWPCmmOk5TFAYTlPN6r4eVHFz4sgPzP0BF1db1zNz2mH61DAyYcCTsn6ev1x/r34AO6uNuY8GUaLGhWsLkkcweIXYfvXUOl2eGoTuDnnf9iljWEY/GvRASZtPIHNBu8Pasa9LapbXZbdOhN7hYkbTnD8QjLR8amci0/JGTTwerzdXXmxR12Gta/pdLeeK+DkQwGnZBmGwV+n/8LSfdFU9fNi0XMdNbCV5C81Hsa3hqTz0PlV6Pyy1RXJLTIMg3d+OsTna48B8L+BTRnUOtjiqhxPclom0QmpRMenEhWXYgafq49PXkzm+EVzMMEm1fx4e2ATGlX1s7jioqOAkw8FnJKXmJpBv/EbOXExmTvrVmbysNaa1kHyt/d7mPs4uHrCXzdDpdusrkhuwfsrDvPxz0cA+NeAxoS3C7G4IudjGAZzdkTyn8UHSEjNxNXFxvCOtRnVrc41oz87IgWcfCjgWONgdAIDPt1IakY2o7rVYVS3ulaXJPbOMODb++DYKqjVCcJ/0Ng4dsAwDH7aF830rafJNgy83V3x8nDF2/3q4uGK19X1Mle3Hz6fyNcbTgDwz3sa8pc7alncC+cWk5jKmwt/ZfFec1yympXK8N97m9DewQcSVMDJhwKOdebuPMOL3+3GZoMpj7WhUym8JVQK6dIxmNAeMlMh9DG45wPQ3XiWibx8hdcX7mfVwZibev6YXvV5spPOxJWU5fuj+eeC/UQnpAIwqFV1xvZuiF8Zd4sruzkKOPlQwLHWmHl7mbntNBXKuLPouY5UK+9tdUli7/Z+D3OfAAxo9zT0/I9CTgnLyMrm6/Un+Ojnw6RmZOPuauOJjrWpX6UcKelZpGSYS+of1lPSs0m9up6emU2fpkE82KaG1V0pdRJTM/jfT4eYtuUUYM7j9Ua/hvRpEnTdoTsMw+BycjonLyVz4uIVTl5MJiYxlRY1KtC9YaBld2nZTcCJjY3lueeeY+HChQD069ePTz75hPLly+fZPiMjg3/84x8sWbKE48eP4+fnR7du3Xj77bepWvX3Wwg7d+7M2rVrcz138ODBzJo1q0B1KeBYKzUji/s/38S+swk0Cy7PnCfb4enm+N8NSzH7ZRosfMZcv/PvcNdYa+spRXacvMzY+fs4dD4RMMdl+c+9jbk9oJzFlUlhbD95mVfm7uHY1RnNuzUI4JVeDUhOy+TExWROXEzm5KVkTl5dv97dWi42aF2zInc3rsLdjasQ5Fdyv6TaTcDp1asXZ86c4csvvwRgxIgR1KxZkx9//DHP9vHx8dx///0MHz6cZs2aERsby6hRo8jMzGTHjh057Tp37kzdunV5663fZxz29vbGz69gV4or4Fgv8vIV7vlkA/EpGTwaFsJb/RtbXZI4gq1fwNK/m+vd3oA7XrC0HGcXdyWdt5ceZNb2SAAqlHFnbJ+GDGxZTYN2Oqi0zCw+W32Mz9YczZl9/Uaq+nlR078sNf3LUt7bnfVHLrL3bHyuNs2Cy9OrcRXublSFmv7FOy2PXQScAwcO0LBhQ7Zs2ULbtm0B2LJlC2FhYRw8eJB69eoVaD/bt2+nTZs2nDp1iho1zFObnTt3pnnz5nz44Yc3VZsCjn1YdfA8f5liBtePhjSnf/NqFlckDmH9+/Dzm+Z6r/9B2yetrccJGYbB/Iiz/GfxAS4lpwPmtRtjejWggoZ4cAqHzycydv5etp+MJaCcJzX9y1KrkhlkavmXoZa/DyGVyuR559WZ2Cv8tC+aZfuj2XEqlj+miPpVyuWc2akXWK7Ig7BdBJxJkyYxevRo4uLicm0vX748H3zwAY899liB9rNy5Up69OhBXFxcTmc6d+7M/v37MQyDwMBAevXqxeuvv065cnmfLk1LSyMtLS3ncUJCAsHBwQo4duDdZYcYv/oo3u6uLHymA3UCdcpbCmDVv2Hd/5nr/cZDy3Br63Eixy4k8Y/5+9h8/BIAdQJ8+M+9TWhTq6LFlUlxSM/MxsPt5u9MjElIZfmv51m2P5pNxy6Rlf17pLg9wIclz3W8pf3/WWECTrFNZhEdHU1AQMA12wMCAoiOji7QPlJTU3nllVd46KGHcnXk4YcfplatWlSpUoV9+/YxZswYdu/ezYoVK/Lcz7hx43jzzTdvriNSrF7oXpeIyFg2Hr3EyG93suCZO0rtHCtSCF3GQvoV2PIpLHwW3L2hyf1WV+XQfvvqYsKaY6RnZePp5sJzXeswvGPtIv2AEvtyq+9tgK8Xj7QL4ZF2IcRdSWflgRh+2hfNuiMXCCjnaem/nUKfwXnjjTfyDQvbt29n+fLlTJ06lUOHDuX6WZ06dXj88cd55ZVXbriPjIwMHnjgAU6fPs2aNWtumNR27txJq1at2LlzJy1btrzm5zqDY98uJqVxz8cbiE5IpXI5T2r5l6VaeW+qlveianlvql1dqpb3pqzCj/zGMGDRC7BzMthcYfA0qN/H6qoc0tbjlxgzfy/Hr1582rleZd7q15galcpYXJk4qqS0TC4lpRFSqWivySnWMzjPPPMMQ4YMuWGbmjVrsmfPHs6fP3/Nzy5cuEBgYOANn5+RkcGgQYM4ceIEq1atyrcTLVu2xN3dnSNHjuQZcDw9PfH01Dw29srfx5NPH27B0EnbuZCYxoXEtOu29fN2vxp6vGhRo4J+uyzNbDbo8z5kXIE9s+G7YfDgTLi9m9WVOYz4KxmMW3og5yLigtw+LFIQPp5ulp+NL/Sr+/v74++f/0iIYWFhxMfHs23bNtq0aQPA1q1biY+Pp3379td93m/h5siRI6xevZpKlSrl+1r79+8nIyODoKCggndE7EpoSEU2vnwXRy8kcjYulbOxKUTFmcvZq38mpGYSn5JBfEoGB84lsPJADMv3RzP+oZYEV9RvmqWSiwv0/wwyUuDAQpj1CDwyF2p2sLoyu2YYBj/uOcdbP/7KxSTzF4oH29TglbvrO+wAcCJ/Vuy3iUdFRfHFF18A5m3iISEhuW4Tr1+/PuPGjePee+8lMzOTgQMH8ssvv7Bo0aJcZ3oqVqyIh4cHx44dY/r06fTu3Rt/f39+/fVXXnzxRby9vdm+fTuurvmPp6K7qBxTYmoG5+JTORuXwrGYJD5ZdZT4lAx8vdx494Fm9GhUxeoSxSqZ6TD7YTiyHDx84NGFUD3U6qrsUuTlK7y2YB9rDl0AzAtBx93XhNY1dRGx2D+7uIsK4PLly9cM9Dd+/PhcA/3ZbDYmT57MsGHDOHnyJLVq5T0/yerVq+ncuTORkZE88sgj7Nu3j6SkJIKDg+nTpw+vv/46FSsW7ABVwHEOZ2Kv8PSMCHZHxgHwxB21eLlXfdxd9ZVVqZSRAtMfgJPrwcsPHl8BlQs2HEVpkJmVzZRNJ3lv+WFSMrLwcHXhmbtu58lOtTXQpjgMuwk49koBx3mkZ2bzzk8HmXh1Er8WNcoz/qGWmv6htEpLgmn3wpltULk+DF8FHsU78Jgj2HsmnjHz97DvbAIAbWpVZNx9Tbitso/FlYkUjgJOPhRwnM+y/dG89N1uElMzKV/GnfcHNeOu+je+mF2cVFIMfN4RkqKh2YMwYEKpnLcqPTObbScus3hvFLO3R5JtmBfpv9q7Pg+EBuPiUvr+TsTxKeDkQwHHOUVevsLTM35hzxlzGPEnO9XmpR719JVVaXRyI0y9B4zsUjUQYGxyOmsOx7DyQAzrDl0gMe33uYT6NavKa/c0pHI53VEqjksBJx8KOM4rLTOLcUsOMmXTSQBahVTgk4dalOhkcGInfpvSwc0LnvgZqjjnfGfHLiTx84HzrDwQw46Tl/nDQLL4+3hwV/0ABrSoRvvb8r/7VcTeKeDkQwHH+S3Ze46Xv99DYlomFcq48/7g5nSpd+3I2uLEsrNh5mDzzqqKt8GINeDlHMf7L6djWbr3HCsPxHDiYnKun9WvUo5uDQLp2iCAZtXL66socSoKOPlQwCkdTl1K5ukZv+RcWPnh4OYMaKEJPUuVK5fN63ESzkCj++D+SQ5/Pc7X64/z78UHch67u9poV7sSXesH0LVBoMaEEqemgJMPBZzSIzUji9cX7Gf2jkg83Fz47skwmgWXt7osKUmR22ByL8jOhN7vQpvhVld0077feYaXvtsNQO8mVejTpCp31vWnnJcG55PSoTCf37r6Upyal7sr4+5rQrcGAaRnZjNi2g7OJ6RaXZaUpOA20P0tc33ZqxAVYW09N2nFr+d5ee4eAIZ3rMWnD7WkT9MghRuR61DAEafn4mLjg8HNqRPgw/mENEZM20lqRpbVZUlJavdXqH8PZKXDnKGQEmd1RYWy5fglnp7xC1nZBveHVufV3g00V5RIPhRwpFQo5+XO10Nb4eftzu7IOF6dt5dS+O1s6WWzQf9PoXwIxJ2CBU+bs5E7gH1n4xk+dQfpmdl0axDI2/c1UbgRKQAFHCk1QiqV5bOHW+LqYmNexFm+Xn/C6pKkJHmXh0FTwdUDDi6CLZ9ZXVG+TlxMZtjkbSSmZdKmVkXGP9QCN43rJFIgOlKkVOlwuz+v9WkAwLilB1h9KMbiiqREVW0BPf9rrq/4p3kBsp06n5BK+MStXExKp2GQL18PbYWXu+aMEikoBRwpdYa2r8mQ1sFkG/DcjAiOxiRZXZKUpNZPmLeMZ2fCd4+Zt5LbmfgrGTw6cRtnYlOoWakMU//SBl9dTCxSKAo4UurYbDbe6t+Y1jUrkJiWyYhvdhCfkmF1WVJSbDbo9zFUut0cH2f+k+aggHbiSnomf5m6nUPnEwko58m0x9tqegWRm6CAI6WSh5sLEx4JpaqfF8cvJvPszAiysh3jolMpAp7l4IGp5jQOR5bDmv9aXREAGVnZ/HX6L+w8FYuvlxvTHm+rgftEbpICjpRa/j6efDW0FV7uLqw7fIG3lx7I/0niPKo0hj7vmevr/g/WvGNpOdnZBi99t5s1hy7g5e7C5MdaU69KOUtrEnFkCjhSqjWq6sd7DzQH4Kv1J/h+5xlrC5KS1eIR6Pamub7mv5aFHMMwePPH/SzYFYWbi40Jj4QSGlLRklpEnIUCjpR6fZoG8dxdtwPw6ry9/HI61uKKpETdMcrSkBMVl8Lzs3YxdfMpbDZ4b1AzTQwrUgQUcESAUd3q0qNhIOlZ2Tw5bSdRcSlWlyQlyYKQk5yWyfvLD3HXe2tYuDsKgDf7NaJ/c00IK1IUFHBE+H06h/pVynEhMY2+n2xg6d5zVpclJamEQk52tsGcHZF0eXcNH686SmpGNm1qVmThMx14NKxmsbymSGmk2cQ1m7j8QeTlKzwxdQeHzicCcE/TIN7q35iKZT0srkxKzIYPYeXr5nrnV6Hzy0W2683HLvHvxb+yPyoBgBoVyzCmV33ublxF0y+IFEBhPr8VcBRw5E/SMrP45OejTFh7jKxsA38fD/5zbxN6NqpidWlSUoo45Jy4mMy4JQdY/ut5AMp5uvFs19sZ2r4mnm4anVikoBRw8qGAIwWx50wcL87ZzZGrIx0PaF6VN/o1onwZnc0pFfIIORlZ2VxJz8Lb3RV3V1u+Z13ir2Tw8aojfLP5JBlZBi42eKhtDV7oVpdKPhq8T6SwFHDyoYAjBZWakcVHPx/hi7XHyDagcjlPxt3bhG4NA60uTUrCH0LO0UbPMuhgJy4npwPg6mLD290VL3dXvD1c8HZ3/cNjV7zcXNly4hJxV8xRsjvXq8yrvRtQN1Bj24jcLAWcfCjgSGFFnI7lpe92c+xCMgD3tazG6/c0wq+M5gdydhnrPsB91RsAvJ9xPx9n3Veo59cJ8OEf9zSkU93KxVCdSOmigJMPBRy5GakZWXyw4jBfrj+OYUCgrydv39eULvU1ZomzOhqTyDMzIuh0YQZj3GcCkH7nq6SEjSY1I4uU9CxSMswl9Q/rKelZpGZkUaGsB3c3qoKbq25YFSkKCjj5UMCRW7Hz1GX+9t0ejl80z+Z0axBI32ZBdKkfoBmfnYRhGHy38wyvL9hPSkYWlcp68F2TbdTe9T+zwQNTodEAS2sUKY0UcPKhgCO3KjUji3eXHWLixhP8dgS5u9oIu82fuxtVoXvDQM0A7aASUzMYO39fzuB7HW6vxAeDmhPg6wXL/wGbPgH3svDECghsZHG1IqWLAk4+FHCkqByMTuDH3VEs23+eo1fvtgKw2SC0RgXublyFno2qaEZoB7HnTBzPzozg1KUruLrYGN29Lk91ug0Xl6t3S2VlwvSBcHwNVKgJw1dDGc0ZJVJSFHDyoYAjxeFoTBLL9kezfH80u8/E5/pZgyBfejYKpF+zqtSu7GNRhXI92dkGkzae4J2fDpKRZVCtvDcfP9g87wkvr1yGLztD3Cm47S54+Htw0Vg2IiVBAScfCjhS3KLiUli+P5pl+8+z7eRlsrLNw8zd1caUx9rQ4XZ/iyuU31xKSuPF73az5tAFAHo1rsLb9zW98R1y0ftgYnfIuAIdnofub5VQtSKlmwJOPhRwpCRdTk5n5YHzfLcjku0nY6lQxp0fn72D6hX0tZWV4lMymLvzDJ+vPUZMYhoebi78856GPNy2RsGmTdg3D75/zFwfOBGa3F+8BYuIAk5+FHDECqkZWdz/+Sb2nU2gcTVfvh/ZHi93fbVR0g5GJ/DN5lPM/+UsKRlZANwe4MP4h1pQv0oh/z9Y+QZs+ADcvOHx5RDUtOgLFpEcCjj5UMARq5yJvUK/8Ru5nJzOwJbVefeBpppksQRkZGWzbH8032w+xbYTl3O21w30ITysJve3rI63x02EzewsmDEIjq4EvxowYg2UrVR0hYtILoX5/C7W0adiY2MJDw/Hz88PPz8/wsPDiYuLu+Fzhg0bhs1my7W0a9cuV5u0tDSeffZZ/P39KVu2LP369ePMmTPF2BORolG9QhnGP9gCFxvM/eUM07acsrokpxaTkMqHKw/T4e1VPDMjgm0nLuPqYqN3kyrMHN6OZaPuJLxdyM2FGzAvLh74NVSoBfGn4fth5p1WImK5Yj2D06tXL86cOcOXX34JwIgRI6hZsyY//vjjdZ8zbNgwzp8/z+TJk3O2eXh4ULHi73czPPXUU/z4449MmTKFSpUq8eKLL3L58mV27tyJq2v+/1HpDI5Y7at1x/nPkgO4udiYMbwdbWrpVuOiYhgGO07FMnXTSX7aF03m1Qu8/X08eahNMA+2rUGQn3fRvmjMAfiqK2QkQ7un4e7/Fu3+RQSwk6+oDhw4QMOGDdmyZQtt27YFYMuWLYSFhXHw4EHq1auX5/OGDRtGXFwcP/zwQ54/j4+Pp3LlykybNo3BgwcDEBUVRXBwMEuWLKFnz5751qaAI1YzDIPnZu3ix91R+Pt4sujZO6ji52V1WQ4vLTOL0XN2s3jPuZxtrUIqEB4WQq/GQXi4FeNJ618Xwpxwc/3eL6DZkOJ7LZFSyi6+otq8eTN+fn454QagXbt2+Pn5sWnTphs+d82aNQQEBFC3bl2GDx9OTExMzs927txJRkYGPXr0yNlWtWpVGjdufN39pqWlkZCQkGsRsZLNZuOdgU2oX6UcF5PSeGr6TtIys6wuy6Elp2Xy+JQdLN5zDndXG0NaB7P4uTv4/qn29G9erXjDDUDDfnDn38z1H5+HqIjifT0RuaFiO+Kjo6MJCLh2EsKAgACio6Ov+7xevXoxffp0Vq1axXvvvcf27du56667SEtLy9mvh4cHFSpUyPW8wMDA6+533LhxOdcB+fn5ERwcfAs9EykaZTzc+CI8FF8vNyJOx/HGwl+tLslhXU5O56Gvt7Lh6EXKeLgyeVgb3h7YlEZV/Uq2kM6vQp2ekJkKsx6BpAsl+/oikqPQAeeNN9645iLgPy87duwAyPPuEMMwbnjXyODBg+nTpw+NGzemb9++LF26lMOHD7N48eIb1nWj/Y4ZM4b4+PicJTIyshA9Fik+IZXK8vGDLbDZYOa208zadtrqkhxOVFwKD3y+id2RcVQo486M4e24o45FAym6uMB9X0Kl2yHhDHw3FDJSralFpJRzK+wTnnnmGYYMufF3yzVr1mTPnj2cP3/+mp9duHCBwMDAAr9eUFAQISEhHDlyBIAqVaqQnp5ObGxsrrM4MTExtG/fPs99eHp64umpiQ/FPnWuF8CL3evy7vLD/HPBfupVKUeLGhXyf6KdiU/JYO+ZeJpU98PPu2RmVT92IYnwr7cSFZ9KkJ8X0x5vw+0B5Urkta/LuzwMmWFedHxqI0y/33zspev9REpSoQOOv78//v75/3YUFhZGfHw827Zto02bNgBs3bqV+Pj46waRvFy6dInIyEiCgoIACA0Nxd3dnRUrVjBo0CAAzp07x759+/jf//5X2O6I2IW/dr6dvWfjWbb/PE99+ws/PntHkc1GbhgGKRlZJKZmkpiaQWJqJv4+nkUyAahhGGw7cZnZ2yNZvPccaZnZlPVwZXDrGjzWoWaxTjK690w8Qydv43JyOrUrl2Xa422pVr6I7466WZXrwUOzYMYQOLkepvSBR+aBT2WrKxMpNYr9NvGoqCi++OILwLxNPCQkJNdt4vXr12fcuHHce++9JCUl8cYbbzBw4ECCgoI4efIkr776KqdPn+bAgQOUK2f+ZvbUU0+xaNEipkyZQsWKFXnppZe4dOmSbhMXh5aYmsGATzdy7EIybWpWZPrwtri75v0tclpmFmdiUzh96QqnLiUTGZtC7JX0XCEm4eqfSamZObdK/1HtymXpWj+ALvUDaF2z4nVfKy8Xk9KYu/MMs7dHcvxics52P2934lMyAHCxQe8mQQzvWJtmweUL95eRj03HLjJ86g6S07NoUs2PKY+1ppKPHZ6ljdoF3w6EKxehYm0I/wEqhFhdlYjDsovbxAEuX77Mc889x8KFCwHo168f48ePp3z58r8XYLMxefJkhg0bRkpKCgMGDCAiIoK4uDiCgoLo0qUL//rXv3JdGJyamsrf/vY3ZsyYQUpKCl27duWzzz4r8MXDCjhir45dSKL/+I0kpWXyaFgIg1oFc/ryFU5dusLpy8mcumSuR8WnUNgj18UG5bzc8fF043xCaq7QU87TjTvrVqZL/QA616uMfx5hISvbYP2RC8zeHsmKX8/nPL+Mhyv9mlVlcOtgmgeXZ92Ri3y9/jjrj1zMeW6bWhUZ3rE2XesH4OJyayM3/7QvmudmRpCelU1Y7Up8NbQVPp6FPhldci4ehWn3mgMBlgsyz+QENrS6KhGHZDcBx14p4Ig9W74/mhHTdubbroyHKzUqliGkUhlqVCxDJR9Pynm5Uc7LnXJebvjmWnenjIdrzoX4CakZrD98kVUHY1hzKIZLyek5+7XZoGn18nStH8Bd9QOoUNaD73ZE8t2OM5yNS8lp1yy4PA+2DuaeZlXzDBi/RiXw9Ybj/Lg7iows87+Z2v5lebxjLQa2rH5T83DN2R7JK/P2kG1Az0aBfDSkhWPM55UQBdPugwsHwKs8PDQHarTN92kikpsCTj4UcMTejV91hHeXH6ZSWQ9qVCpDSMUy1KhUlpDfAk2lMlT28SySeayysw12n4lj9cEYfj4Yw/6o648T5evlxn0tqzO4dTANggp27ETHpzJl00mmbz1FYqo5jUHFsh6EtwuhYx1/ynq64ePpRllPN8p6uuLplndg+WLtMcYtPQjA4FbB/OfexrgV4ms1y125DDMGw5lt5uScg6dBne5WVyXiUBRw8qGAI44gMyvbkg/w8wmpOWFn49GLXEnPol3tijzYpgY9G1W56TMmSWmZzNkeyaSNJzgTm3Lddu6uNjPsePwWfFxxsdnYcSoWgCc71eaVu+s75iSl6ckw51Fzck4XNxjwOTR9wOqqRByGAk4+FHBECiY1I4uU9CwqlPUosn1mZmXz0/5opm85TVR8CslpmSSlZZKakZ3vc8f0qs+TnW4rsloskZkOPzwF+743H/f6H7R90tqaRByEAk4+FHBE7E9mVjbJ6Vkkp2XmhJ7ktKyrf2ZSu3JZhxwfKE/Z2fDTy7DNnIiYTi9D5zHmBVAicl2F+fy241sPRKQ0cXN1wc/bpcQGCbSUi4t55qaMP6z5L6x9B5IvQu//AxcHuGhaxAE40BV6IiJOxGaDzi9Dn/cAG+yYCD+NsboqEaehgCMiYqXWT8B9X5nr276ArV9aW4+Ik1DAERGxWtMHoNub5vpPL8Ph5dbWI+IEFHBEROxBh+ehRTgY2fD9YxC9z+qKRByaAo6IiD2w2aDP+1DrTkhPMgcFTDxvdVUiDksBR0TEXrh5wKBvoFIdSDgDM4dA+hWrqxJxSAo4IiL2xLsCPDwHvCtC1C8w/0lz3BwRKRQFHBERe1OxNgyZAa4ecGAhrHrL6opEHI4CjoiIPQoJg/6fmusbPoBfpllbj4iDUcAREbFXTQdBp1fM9UWj4MQ6S8sRcSQKOCIi9qzzK9D4fsjOhNmPwMUjVlck4hAUcERE7JnNZn5VFdwWUuNh+gOQfMnqqkTsngKOiIi9c/cyLzouHwKxJ2D2w5CZZnVVInZNAUdExBGU9YeHvwNPPzi9GWaHQ0qc1VWJ2C0FHBERR1G5Hgz+xrx9/Mgy+KqLpnQQuQ4FHBERR1K7M/xlGfjVgMvH4etusHu21VWJ2B0FHBERR1OtJTy5Fm7rCpkpMH8ELH4RMtOtrkzEbijgiIg4ojIVzWtyOr1sPt7+NUzuBfFnra1LxE4o4IiIOCoXV+jyKjz0HXj5wdkd8MWdcHyt1ZWJWE4BR0TE0dXtASPWQpUmcOUiTBsA698Hw7C6MhHLKOCIiDiDirXg8RXQ/BEwsuHnN2HWw+bggCKlkAKOiIizcPeG/uOh70fmreSHFsOXneH8fqsrEylxCjgiIs7EZoPQYVdvJQ/+/VbyA4usrkykRCngiIg4o2ot4cl15rg5GVfMiTo3fKjrcqTUUMAREXFWZSrCw3Oh9ROAAStfhwVPa7wcKRUUcEREnJmrG/R5D3r9H9hcYNd0+Ka/ZiQXp6eAIyJSGrQdYY6X4+kLpzfB13fBhUNWVyVSbBRwRERKizrdzFvJy4dA7En4ujsc/dnqqkSKRbEGnNjYWMLDw/Hz88PPz4/w8HDi4uJu+BybzZbn8n//9385bTp37nzNz4cMGVKcXRERcQ4B9WH4KqgRBmnxMP0B2PaV1VWJFLliDTgPPfQQu3bt4qeffuKnn35i165dhIeH3/A5586dy7VMmjQJm83GwIEDc7UbPnx4rnZffPFFcXZFRMR5lPWHRxdAswfByIIlL8HilyAr0+rKxFlkpEBaoqUluBXXjg8cOMBPP/3Eli1baNu2LQBfffUVYWFhHDp0iHr16uX5vCpVquR6vGDBArp06ULt2rVzbS9Tpsw1bUVEpIDcPGHABPCva456vP0ruHwMHphizmslcrNObYaFz0BIe+j3iWVlFNsZnM2bN+Pn55cTbgDatWuHn58fmzZtKtA+zp8/z+LFi3n88cev+dn06dPx9/enUaNGvPTSSyQmXj8ppqWlkZCQkGsRESn1bDboOBoGfwvuZeDYKnNQwKhdVlcmjigtCZb8zZzV/tJROLICUmItK6fYAk50dDQBAQHXbA8ICCA6OrpA+5g6dSrlypXjvvvuy7X94YcfZubMmaxZs4bXXnuNuXPnXtPmj8aNG5dzHZCfnx/BwcGF64yIiDNr0BceWwrlguDiYfjqLlj+GqRfsboycRTHVsFnYbDtS8CAFo/AX7eAdwXLSip0wHnjjTeueyHwb8uOHTsA84LhPzMMI8/teZk0aRIPP/wwXl5eubYPHz6cbt260bhxY4YMGcL333/PypUr+eWXX/Lcz5gxY4iPj89ZIiMjC9lrEREnV7W5OfJxo/vM63I2fQwT2sPxtVZXJvYsJRZ+eBqm3Qvxp8GvBoTPh/6fgnd5S0sr9DU4zzzzTL53LNWsWZM9e/Zw/vz5a3524cIFAgMD832d9evXc+jQIWbPnp1v25YtW+Lu7s6RI0do2bLlNT/39PTE09Mz3/2IiJRqPgHwwGRoOggWvwixJ+CbfuZv493/ZY6MLPKbA4tg8WhIOg/YoM0I6PpP8PSxujLgJgKOv78//v7++bYLCwsjPj6ebdu20aZNGwC2bt1KfHw87du3z/f5EydOJDQ0lGbNmuXbdv/+/WRkZBAUFJR/B0RE5Mbq9YKQDvDzW7D9a4j4Fg4vh97/g4YDzGt3pPRKugBL/wb755uPK90O/cZDSJi1df2JzTCKb+a1Xr16ERUVlXML94gRIwgJCeHHH3/MaVO/fn3GjRvHvffem7MtISGBoKAg3nvvPUaOHJlrn8eOHWP69On07t0bf39/fv31V1588UW8vb3Zvn07rq6u+daVkJCAn58f8fHx+Pr6FlFvRUSc0OktsPA5uHh11ON6vaH3u+BXzdq6pOQZBuz9Dpa+DCmXweYK7Z+Fzq+Au3eJlFCYz+9iHQdn+vTpNGnShB49etCjRw+aNm3KtGnTcrU5dOgQ8fHxubbNmjULwzB48MEHr9mnh4cHP//8Mz179qRevXo899xz9OjRg5UrVxYo3IiISCHUaAcj10Onl8HFHQ4tgU/bmmd2srOtrk5KSsI5mDEY5g03w01gYxj+M3R/s8TCTWEV6xkce6UzOCIiN+H8r/Djc3Bmu/k4uB30/cgcHVmc1/758OMoSI0zQ26nv0OHUeDmUeKl2M0ZHBERcSKBDeEvy6DX/8C9LERugc87wMo3ID3Z6uqkqKXGw7wn4bthZrgJanb1bN7fLQk3haWAIyIiBefiCm2fhKe3mtfjZGfChg/g03ZwcInV1UlRObkRJnSAPbPA5gIdX4THV0JAA6srKzAFHBERKbzywfDgTBgyE/yCzTFQZj0IMx+EuNNWVyc3KzPNHORxSh+IjzRnnn9sqXn7twOctfkjBRwREbl59XubZ3PueAFc3MyLkMe3gfXvQ2a61dVJYZz/Fb7qag7y+NtoxE9tNC80d0C6yFgXGYuIFI2Yg+YAgac2mI8r14c+70HNO6ytS24sOxu2ToCVb0JWGpSpBH0/hgb3WF3ZNXSRsYiIlLyA+jBsEdz7BZTxhwsHza865o80B4cT+xN/Bqb1h2WvmuGmTk94arNdhpvCUsAREZGiY7NBsyHw7A5o9Thgg90zYXwobPncvMZDrJeWCFu/NOcbO7HOnE3+ng/godlQLv/plByBvqLSV1QiIsXnzE5Y/AKc220+9gs2bzNu9hC4Fnq2ILlVMQfMQRp3z4L0JHNbtVC490vwv93a2gqgMJ/fCjgKOCIixSs7C375Btb+DxKjzG0Vb4Mur5qzl7voy4RilZUBBxfB9olwcv3v2yvVMSfIbPUYuLpbV18hKODkQwFHRMQCGSmwY5J5h9WVi+a2gIbQZSzU76NJPItaYjTsnGIuiefMbTYXc/yiNsOhVieH+ztXwMmHAo6IiIXSksy7djZ+AmlX5yKs2hLu+gfcdpfDfejaFcOAUxth21fmWZvsTHN72crQcqh5tsavurU13gIFnHwo4IiI2IGUWNj0iXnxccbVqR5COsBdr0FImLW1OQrDgLhTcGqTGWxOboDYk7//PLidebamQT+HG6gvLwo4+VDAERGxI0kXYMP75jUiWVfvsgpuZ4acaq3Mi2B9g6yt0V4YBlw8bIaZU5vMJeFs7jbuZaDpIGj9BFRpYk2dxUQBJx8KOCIidij+LKz7H0R8+/tXK78pVxWqh5php1ooVG0BnuWsqbMkGQac32eemTm1EU5t/v36pd+4uJl/HyHtzTNgNcLAyzk/2xRw8qGAIyJix+JOw7HVcHYHnP0FYn4FI/tPjWzmSMnVQqFaCwhsbD72Lm9FxUUv5gDsm2sul4/n/pmbF1RvbYaZkPZQvRV4lLWmzhKmgJMPBRwREQeSngxRu+DszqvLL+bknnnxrWbOeB3QAAIamX9Wrgfu3iVa8k25dAz2z4N988xQ9xs3b6jZ4Wqg6WCerXGC62luhgJOPhRwREQcXOJ5iPrFDDxRu8wzHgln8m5rc4EKta6GnoZQo635NY49nPWIPwP755tnaqIift/u4g51ukPjgVD3bvD0sa5GO6KAkw8FHBERJ5QSZ85/FfOrGXhiDsD5/ZBy+dq2Lu7mVzu17jSX6q3BzbN460u/Yo5Hk3jOrGv/fDi9+fef21yhdicz1NTvA94VirceB6SAkw8FHBGRUsIwIPmCGShiDkD0HvOC3fjI3O3cvKBGu6uBpxMENS/YVBKZaea8TmkJcCX29wCTeA4SzuV+nBqf9z5qtIfG90HDAeBT+VZ77NQUcPKhgCMiUooZhjlWzIl1vy/JMbnbeJQzr3vxCTTnbEpLvLokmWHmt8fZGYV7bfcyUC4I/KqZM3c3utdclwJRwMmHAo6IiOQwDLhw6GrYWWue4UmNK9w+3Muad3CVq2IGmHJB5tg95YJyP/b01UjNt6Awn9+aylVEREo3mw0C6ptL2xHm5KDRe82gk3HFHG/Hw8f807OcGVI8//DYwwdcXK3uhfyJAo6IiMgfubhC1ebmIg5Lc9SLiIiI01HAEREREaejgCMiIiJORwFHREREnI4CjoiIiDgdBRwRERFxOgo4IiIi4nQUcERERMTpKOCIiIiI01HAEREREaejgCMiIiJORwFHREREnI4CjoiIiDidUjmbuGEYACQkJFhciYiIiBTUb5/bv32O30ipDDiJiYkABAcHW1yJiIiIFFZiYiJ+fn43bGMzChKDnEx2djZRUVGUK1cOm81WpPtOSEggODiYyMhIfH19i3Tf9sDZ+wfO30f1z/E5ex/VP8dXXH00DIPExESqVq2Ki8uNr7IplWdwXFxcqF69erG+hq+vr9P+wwXn7x84fx/VP8fn7H1U/xxfcfQxvzM3v9FFxiIiIuJ0FHBERETE6SjgFDFPT09ef/11PD09rS6lWDh7/8D5+6j+OT5n76P65/jsoY+l8iJjERERcW46gyMiIiJORwFHREREnI4CjoiIiDgdBRwRERFxOgo4+fjss8+oVasWXl5ehIaGsn79+hu2X7t2LaGhoXh5eVG7dm0+//zza9rMnTuXhg0b4unpScOGDZk/f35xlV8ghenjvHnz6N69O5UrV8bX15ewsDCWLVuWq82UKVOw2WzXLKmpqcXdlTwVpn9r1qzJs/aDBw/mamdP72Fh+jds2LA8+9eoUaOcNvb0/q1bt46+fftStWpVbDYbP/zwQ77PcbRjsLB9dLRjsLD9c8RjsLB9dKTjcNy4cbRu3Zpy5coREBDAgAEDOHToUL7Ps4fjUAHnBmbPns2oUaMYO3YsERERdOzYkV69enH69Ok82584cYLevXvTsWNHIiIiePXVV3nuueeYO3duTpvNmzczePBgwsPD2b17N+Hh4QwaNIitW7eWVLdyKWwf161bR/fu3VmyZAk7d+6kS5cu9O3bl4iIiFztfH19OXfuXK7Fy8urJLqUS2H795tDhw7lqr1OnTo5P7On97Cw/fvoo49y9SsyMpKKFSvywAMP5GpnL+9fcnIyzZo1Y/z48QVq74jHYGH76GjHYGH79xtHOQah8H10pONw7dq1PP3002zZsoUVK1aQmZlJjx49SE5Ovu5z7OY4NOS62rRpY4wcOTLXtvr16xuvvPJKnu3//ve/G/Xr18+17cknnzTatWuX83jQoEHG3XffnatNz549jSFDhhRR1YVT2D7mpWHDhsabb76Z83jy5MmGn59fUZV4Swrbv9WrVxuAERsbe9192tN7eKvv3/z58w2bzWacPHkyZ5s9vX9/BBjz58+/YRtHPAb/qCB9zIs9H4N/VJD+Odox+Gc38x460nEYExNjAMbatWuv28ZejkOdwbmO9PR0du7cSY8ePXJt79GjB5s2bcrzOZs3b76mfc+ePdmxYwcZGRk3bHO9fRanm+njn2VnZ5OYmEjFihVzbU9KSiIkJITq1atzzz33XPPbZUm4lf61aNGCoKAgunbtyurVq3P9zF7ew6J4/yZOnEi3bt0ICQnJtd0e3r+b4WjHYFGw52PwVjjCMVhUHOk4jI+PB7jm39sf2ctxqIBzHRcvXiQrK4vAwMBc2wMDA4mOjs7zOdHR0Xm2z8zM5OLFizdsc719Fqeb6eOfvffeeyQnJzNo0KCcbfXr12fKlCksXLiQmTNn4uXlRYcOHThy5EiR1p+fm+lfUFAQX375JXPnzmXevHnUq1ePrl27sm7dupw29vIe3ur7d+7cOZYuXcoTTzyRa7u9vH83w9GOwaJgz8fgzXCkY7AoONJxaBgGo0eP5o477qBx48bXbWcvx2GpnE28MGw2W67HhmFcsy2/9n/eXth9FrebrWfmzJm88cYbLFiwgICAgJzt7dq1o127djmPO3ToQMuWLfnkk0/4+OOPi67wAipM/+rVq0e9evVyHoeFhREZGcm7777LnXfeeVP7LG43W8uUKVMoX748AwYMyLXd3t6/wnLEY/BmOcoxWBiOeAzeCkc6Dp955hn27NnDhg0b8m1rD8ehzuBch7+/P66urtekyZiYmGtS52+qVKmSZ3s3NzcqVap0wzbX22dxupk+/mb27Nk8/vjjzJkzh27dut2wrYuLC61bty7x3zxupX9/1K5du1y128t7eCv9MwyDSZMmER4ejoeHxw3bWvX+3QxHOwZvhSMcg0XFXo/BW+VIx+Gzzz7LwoULWb16NdWrV79hW3s5DhVwrsPDw4PQ0FBWrFiRa/uKFSto3759ns8JCwu7pv3y5ctp1aoV7u7uN2xzvX0Wp5vpI5i/NQ4bNowZM2bQp0+ffF/HMAx27dpFUFDQLddcGDfbvz+LiIjIVbu9vIe30r+1a9dy9OhRHn/88Xxfx6r372Y42jF4sxzlGCwq9noM3ipHOA4Nw+CZZ55h3rx5rFq1ilq1auX7HLs5DovscmUnNGvWLMPd3d2YOHGi8euvvxqjRo0yypYtm3Ol+yuvvGKEh4fntD9+/LhRpkwZ44UXXjB+/fVXY+LEiYa7u7vx/fff57TZuHGj4erqarz99tvGgQMHjLfffttwc3MztmzZUuL9M4zC93HGjBmGm5ub8emnnxrnzp3LWeLi4nLavPHGG8ZPP/1kHDt2zIiIiDAee+wxw83Nzdi6davd9++DDz4w5s+fbxw+fNjYt2+f8corrxiAMXfu3Jw29vQeFrZ/v3nkkUeMtm3b5rlPe3r/EhMTjYiICCMiIsIAjPfff9+IiIgwTp06ZRiGcxyDhe2jox2Dhe2fox2DhlH4Pv7GEY7Dp556yvDz8zPWrFmT69/blStXctrY63GogJOPTz/91AgJCTE8PDyMli1b5ro1bujQoUanTp1ytV+zZo3RokULw8PDw6hZs6YxYcKEa/b53XffGfXq1TPc3d2N+vXr5zpwrVCYPnbq1MkArlmGDh2a02bUqFFGjRo1DA8PD6Ny5cpGjx49jE2bNpVgj3IrTP/eeecd47bbbjO8vLyMChUqGHfccYexePHia/ZpT+9hYf+NxsXFGd7e3saXX36Z5/7s6f377Zbh6/17c4ZjsLB9dLRjsLD9c8Rj8Gb+nTrKcZhXvwBj8uTJOW3s9Ti0Xe2AiIiIiNPQNTgiIiLidBRwRERExOko4IiIiIjTUcARERERp6OAIyIiIk5HAUdEREScjgKOiIiIOB0FHBEREXE6CjgiIiLidBRwRERExOko4IiIiIjTUcARERERp/P/F0zVkz1WBTIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# expectation value of pauliX on qubit 0, 1 and 2 versus time.\n",
    "\n",
    "plt.plot(time,sum_sig_x, label='<$\\sigma_x$>')\n",
    "plt.plot(time,sum_sig_z/3, label='<$\\sigma_z$>/3')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "b6e86bc9-9887-4577-9e59-38debf98f9c9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00386857258905271"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(final_costs_v_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5806a70d-3ff1-4b45-8251-5c36c4e2c354",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50a6e7d4-ceb8-4a34-9c5a-9b6078551973",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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