{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "591b2061",
   "metadata": {},
   "source": [
    "# Core functionality tutorial\n",
    "This notebook will go over each primitive in the package and show their intended use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e1a2dbcc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sympy as sp\n",
    "import matplotlib.pyplot as plt\n",
    "from hierarqcal import (\n",
    "    Qhierarchy,\n",
    "    Qcycle,\n",
    "    Qpermute,\n",
    "    Qpivot,\n",
    "    Qmask,\n",
    "    Qunmask,\n",
    "    Qinit,\n",
    "    Qmotif,\n",
    "    Qmotifs,\n",
    "    Qsplit,\n",
    "    plot_motif,\n",
    "    Qunitary,\n",
    "    plot_circuit,\n",
    ")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "cb58f0e9",
   "metadata": {},
   "source": [
    "## Specify backend\n",
    "It is possible to use the package without a specific backend, but we choose one here for visualisation purposes. We're mainly going to use the backends plotting functionality to display the circuits, so pick the one you have installed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cc862069",
   "metadata": {},
   "outputs": [],
   "source": [
    "backend = \"qiskit\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "346f7a15",
   "metadata": {},
   "outputs": [],
   "source": [
    "if backend == \"qiskit\":\n",
    "    import qiskit\n",
    "    from hierarqcal.qiskit.qiskit_circuits import V2, U2, V4\n",
    "\n",
    "    def get_circuit(hierq):\n",
    "        return hierq(backend=\"qiskit\")\n",
    "\n",
    "    def draw_circuit(circuit, **kwargs):\n",
    "        return circuit.draw(output=\"mpl\", **kwargs)\n",
    "\n",
    "elif backend == \"cirq\":\n",
    "    import cirq\n",
    "    from cirq.contrib.svg import SVGCircuit\n",
    "    from hierarqcal.cirq.cirq_circuits import V2, U2, V4\n",
    "    import logging\n",
    "    logging.getLogger('matplotlib.font_manager').disabled = True\n",
    "    def get_circuit(hierq):\n",
    "        return hierq(backend=\"cirq\")\n",
    "\n",
    "    def draw_circuit(circuit, **kwargs):\n",
    "        return SVGCircuit(circuit, **kwargs)\n",
    "\n",
    "elif backend == \"pennylane\":\n",
    "    import pennylane as qml\n",
    "    from hierarqcal.pennylane.pennylane_circuits import V2, U2, V4\n",
    "\n",
    "    def get_circuit(hierq):\n",
    "        dev = qml.device(\"default.qubit\", wires=hierq.tail.Q)\n",
    "\n",
    "        @qml.qnode(dev)\n",
    "        def circuit():\n",
    "            if isinstance(next(hierq.get_symbols(), False), sp.Symbol):\n",
    "                # Pennylane doesn't support symbolic parameters, so if no symbols were set (i.e. they are still symbolic), we initialize them randomly\n",
    "                hierq.set_symbols(np.random.uniform(0, 2 * np.pi, hierq.n_symbols))\n",
    "            hierq(\n",
    "                backend=\"pennylane\"\n",
    "            )  # This executes the compute graph in order\n",
    "            return [qml.expval(qml.PauliZ(wire)) for wire in hierq.tail.Q]\n",
    "\n",
    "        return circuit\n",
    "\n",
    "    def draw_circuit(circuit, **kwargs):\n",
    "        fig, ax = qml.draw_mpl(circuit)(**kwargs)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "64b2d3fc",
   "metadata": {},
   "source": [
    "## Building blocks\n",
    "Circuit architectures are created by stacking motifs hierarchacially, the lowest level motifs (primitives) are building blocks for higher level ones. On a high level you can regard a primitive as a layer capturing some design motif (cycle, mask, etc) and we're creating a sequence of layers for the circuit. This view only captures hierarchical architectures of two levels (*level 1 -> primitives, level 2 -> sequence of primitves*). The framework is more general in that there is no limit to the number of levels used to represent an architecture. See the comparison below:\n",
    "\n",
    "**Layer view**\n",
    " - architecture = (Cycle, Mask, Cycle, Mask, Cycle, Cycle, Cycle, Mask, Cycle, Mask)\n",
    "\n",
    "**Hierarchical view**\n",
    " - m2_1 = (Cycle, Mask)\n",
    " - m2_2 = (Cycle, Cycle)\n",
    " - m3_1 = (m2_1, m2_1)\n",
    " - architecture = (m3_1, m2_2, m3_1)\n",
    "\n",
    " <img src=\"https://github.com/matt-lourens/hierarqcal/blob/master/img/hierarchical_motifs.drawio.png?raw=true\" >\n",
    " Consider the figure above, to create the architecture on the right we want to **repeat the alternation between a cycle of stride 1 and masking from bottom to top three times**. The semantic description is simple and intuitive, the package is designed to allow building circuits this way. Notice a cycle of stride 1 and masking from bottom to top are both primitves. Alternating between them, is a level two motif (p1+p2), then repeating that 3 times is a level 3 motif. This gives a concise description of the circuit on the right. The circuit being a binary tree architecture (which is hierarchical)."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "c7ec3740",
   "metadata": {},
   "source": [
    "There are two main classes to generate circuit architectures: `Qhierarchy` and `Qmotif`. We call our building blocks primitives, all are instances of `Qmotif`. A primitive is a directed graph with nodes representing qubits and edges unitaries applied between them. The edges are determined by its rules and the number of available qubits. Primitives are stacked with addition or mutliplication operations which act as append and extend, ex: `Qcycle()+Qpermute() = (Qcycle,Qpermute)` which is a `Qmotifs` object, a sequence of `Qmotif`. Simlarly `Qcycle()*3 = (Qcycle(), Qcycle(), Qcycle)` is again an instance of `Qmotifs`. Note it's possible to add motifs together without specifying qubits, when you have a motif ready, it's initialized with `Qinit` in the following way: `Qinit(8)+motif`. This creates a `Qhierarchy` object, which runs through all the motifs generates their edges.\n",
    "\n",
    " The types of primitves are:\n",
    " - `Qcycle`: Create a cycle of unitaries, sometimes called `ladders` or `convolutions`. It's hyperparamaters are used to generate cycles in directed graphs\n",
    " - `Qpermute`: unitaries permuted across qubits.\n",
    " - `Qmask`: Mask certain qubits based on a pattern, a mapping can be provided to *save* it's information. Also reffered to as `entanglers` or `pooling` layers.\n",
    " - `Qunmask`: Unmask previously masked unitaries\n",
    " - `Qinit`: specify the qubit names, order and amount."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "aeb07490",
   "metadata": {},
   "source": [
    "### Qunitary\n",
    "The edges of primitves encode the connectivity of the unitary, 1-qubit unitaries correspond to edges with arity 1 (1-ary tuples primitive.E=[(1,),(2),,...]). 2 qubit unitaries correspond to 2-ary tuples primitive.E=[(1,2),(3,4),...] and `N`-qubit unitaries to N-ary tuples ex: primitive.E=[(1,2,...,7),(3,4,...,8),...]. `Qunitary` tells a primitive the arity of it's operation, each primitive has a mapping hyperparamater that expects a `Qunitary` object. The arguments for `Qunitary` are:\n",
    "\n",
    " - function: the function that get's executed at every edge\n",
    " - n_symbols: the number of symbols the function expects\n",
    " - arity: the arity of the function (number of qubits it acts upon)\n",
    "\n",
    "Notice that any function is permitted, there is no restriction to unitarity or even quantumness. In this sense the package is a dynamic datatrstructe to construct of hierarchichal compute graphs, but we work mainly in the context of quantum computing. This is also why the packages is framework agnostic, since no matter the framework, you will be able to create a function that does it's circuit execution. HierarQcal manages the order in which these circuits get executed (well it generates the order, and number of executions.). For creating architectures, we only need to know the arity and number of symbols our function expects. This way, you can generate a circuit architecture without specifying the specific function corresponding to a unitary and framework. Once the architecture is ready, you can specify the functions and execute it on a backend by calling `hierq(backend=\"qiskit\")` where `hierq` is the `Qhierarchy` object containing the architecture (or more generally, the compute graph).\n",
    "\n",
    "For the examples below, we specify an arbitrary `Qunitary` object with no specific function connected to it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "518153a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "u0_1 = Qunitary(function=None, n_symbols=0, arity=1)\n",
    "u0_2 = Qunitary(function=None, n_symbols=0, arity=2)\n",
    "u1_2 = Qunitary(function=None, n_symbols=1, arity=2)\n",
    "u2_3 = Qunitary(function=None, n_symbols=2, arity=3)\n",
    "u2_4 = Qunitary(function=None, n_symbols=2, arity=4)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "a0c08305",
   "metadata": {},
   "source": [
    "### Qinit primitive\n",
    "`Qinit` is a special primitive with no operational effect. It initializes a set of qubit labels as reference for operations. `Qinit` is always provided at the start of a statement ex: `Qinit(3)+motifs` which causes a `Qhierarchy` object to be created. `Qhierarchy` manages the edge creation of motifs. Use `Qinit` is usually used in the final statement combining all motifs into an architecture or in statements that create sub hierarchies. Providing an integer $n$ labels the qubits $1, 2, \\dots, n$, but providing a list with specific qubit order is also possible:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "da63fd41",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "init_primitive = Qinit(10)\n",
    "fig, ax = plot_motif(init_primitive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d9880564",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "init_primitive = Qinit([2,6,4,10])\n",
    "fig, ax = plot_motif(init_primitive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a32e3cd2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "init_primitive = Qinit([\"q1\", \"q2\"])\n",
    "fig, ax = plot_motif(init_primitive)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "65f14b48",
   "metadata": {},
   "source": [
    "### Cycle primitive\n",
    "`Qcycle` is a primitve that creates a cycle or ladder or convolution of unitaries. It has four main hyperparameters:\n",
    " - `stride`: The number of nodes to skip, before connecting the edge\n",
    " - `step`: The number of nodes to step over after the edge was connected\n",
    " - `offset`: The node to start the procedure with\n",
    " - `boundary`: The boundary condition of the cycle, can be `open` or `periodic`\n",
    "The action is best seen through examples, but the general procedure for edge creation is staring at `offset` step in units of `step` at each `step` connect to `stride` units away."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "907610db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type of object\t <class 'hierarqcal.core.Qhierarchy'>\n",
      "First motif\t <class 'hierarqcal.core.Qinit'>\n",
      "Second motif\t <class 'hierarqcal.core.Qcycle'>\n"
     ]
    }
   ],
   "source": [
    "# Convolution of stride 3, try out other stride values\n",
    "cycle = Qcycle(stride=5, mapping=u1_2)\n",
    "cycle_on_8_qubits = Qinit(8) + cycle\n",
    "\n",
    "# Note the type of 'conv_on_8_qubits', it's a qcnn with two motifs: (Qfree, Qconv)\n",
    "print(f\"Type of object\\t {type(cycle_on_8_qubits)}\")\n",
    "print(f\"First motif\\t {type(cycle_on_8_qubits.tail)}\")\n",
    "print(f\"Second motif\\t {type(cycle_on_8_qubits.tail.next)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6696c730",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<Figure size 400x400 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_motif(cycle_on_8_qubits[0])\n",
    "plot_motif(cycle_on_8_qubits[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e204e33c-b567-4b12-92e6-f4bb40d27394",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# There is a minimal circuit plotter which converts the sequence of digraph into a two dimensional view.\n",
    "# Notice no specific unitary needs to be specified, it's seen as a black box where we're only building the connectivity.\n",
    "plot_circuit(cycle_on_8_qubits)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "e0cfb2a0",
   "metadata": {},
   "source": [
    "#### Stride examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a29c806d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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d1OJW3dTi1mL3G1m2nKrEVFdSUpJph/gVeqRea6Xl+yWbxSbFNpWqNtZD/wnTewekJV2kMB+i3bv7pD7rJIukwp+OVUw6Lr28S9r4e6lxeVOGDQAAAJgu4Hc0duzYIUmqWafBNe87tnZ9bd++3bR6ryRLK/YX/ew2LEU/2Iqy3Ir90qvJ3tc6lC09/KnkMX4JGVLR37MKpJ4fS8F3pjsAAABQJOB3NFJTU2W1WlWxauw177tKTE0lfb5GTqfzqmsZhvRqsl1F1/6WC5+XoVeSpeGNXbJc+PQF5nxjlduwybhILbch7T0lbTjo0u3VSBslzfnfN6fTKbvdHsDRAAAA+M7hxZKHgAeN/Px82R0OWa3X/uaKo1QpnTl7VpMmTbrqWgUWhzIqjbvMKyzKyJGenzJNpYwrB5v3yv5BnlKNL5ZZiqoZHk1b8qm+yNtWvAEjYM4PGlOnTvXqf1QAAIBgMn78+Cu+JuBTp8LCwuQp7krpq+R2u00LODajUBbj8u/DYnhkMwq9qucwnLLo0vUMWeTwIrAAAAAAgRDwOxrly5eXy+VUXm62wstEXtO+s8+cUpUqVTRu3OXuRHjvm0+lDw4av6zPOI/NYqhHbelvj4/xqlbcQYt6rrNd8nm7TZo99LeqUPq3xR0uAiQnJ0cTJ06UVHRQZURERIBHBAAAYL6AB43mzZtLkjL2p6p+k+ZetyvIz9Pxo4d+/vuJY0eVkZaqMpE3KLpiFa9qHEpLVav4eNOmrvz9FunjDMnwFC3aPsdqkRxWi8a3tnjdV486Uruq0tYfi9Zk/K8xLSyqVpYpNyWRy+X6+WeHw8HUKQAAcF0K+NSpRo0aKTy8jNJ/+N6ndgf3fad/jhmsf44ZLElasXi2/jlmsD5autCr9h6PRxlpqYqPj/d1yJfUrKK0oYfUKOrXjzeOktb3KHreWzartKab1Lte0d2QcyLDDL1wi/SP1qYMGQAAAPALi2EEfpPUzp07K+PHLA1/bto16zNl9y7NeH6kNm3apPbt25ta2zCkrzKljGypeqTUoqK82mnqUn7IzFXdjn+Q3C4d27JClcox1aYky8nJUWRk0TTB7Oxspk4BAIDrUsCnTknSwIED1adPHx3NOKCq1Wtdkz43r12lBg0bql27dqbXtliklpWK/pihSrghffORJKlMUHxiAAAAwOUFfOqUJPXs2VOVKlXS55+8f036O5V1XLu2faHhw4bJcjW3GgAAAABcVFAEDYfDoaeeekpfrl+tgz6u1fCVYRh6b8EMRUeXV79+/fzaFwAAABCqgiJoSEXbfDZt2lRvJ7wol8t/50Mkbd6g5MTNSkhIULly5fzWDwAAABDKgiZo2O12LV60SMcOp+u9BdPljzXqhw7s03sLpqtXr17q2bOn6fUBAAAAFAmaoCFJcXFxmj9/vrZsWKN3F0yXx2PeieGHDuzT7Ilj1LBBfc2ZM8e0ugAAAAAuFHR7GPXt21f5+fkaPHiwTmdlqtfAp1Q2KrrY9QzDUNLmDXpvwXQ1bFBfn3zyCVOmAAAAAD8Lqjsa5wwcOFArV67U0QMpmjx6gBI3rSvW3Y1TWcc1f9p4LZ4xUd3v6abPPvtMlSqZtOcsAAAAgEsKigP7LiUzM1PDhw/XkiVLVLlarNp0vke3duiqyLKXviPh8Xi0b+/X2rx2lXZt+0LR0eWVkJBQotdkcMDb9YXPEwAAhIKgDhrnbNmyRbNnz9aSJUvkdDpVJaa6YmvXV5WYmnKUKiW3263sM6d0KC1VGWmpysvNUYOGDTV82DD169evxE+V4sL0+sLnCQAAQkGJCBrnHD9+XB9//LGSkpKUuH27UlNTVZCfL1tYmKLKRSk+vqXi4+PVrl07tWvX7ro5jI8L0+sLnycAAAgFJSpohCouTK8vfJ4AACAUBOVicAAAAAAlG0EDAAAAgOkIGgAAAABMR9AAAAAAYDqCBgAAAADThQV6AL4wDEPp6elKSkpSUlKSUlNTlZ+fr7CwMJUvX17NmzdXfHy8mjVrpvDw8EAPFwAAAAhZJSJo5Obm6q233tJrM2dq186dkqSo6IqqHFNDYXaHDI9HOWeTtXDhQhUWFqpMmQj17ftHDR06VM2aNQvs4AEAAIAQFNTnaBiGoTlz5mjs2LE6c+aMmrS8Tbd26Kra9RurXHTFC17vcjl1JD1N3yZt1dbPVuvkiUx16dJFc+fOVa1atQLwDszBuQvXFz5PAAAQCoI2aBw4cECPPfaYNmzYoDadfqcu9z2sCpWret3eXVio5MTNWvnmHBXk5mjatKkaNGhQiTwtnAvT6wufJwAACAVBGTS2b9+url27ymKzq/egUWoYF1/sWnm5OVr5xhx9uX61HnvsMc2dO1c2m83E0fofF6bXFz5PAAAQCoJujcZXX32lTp06q2LV6ho09gVFRJa9qnrhZSLUe9BI1Wl4sxbOmSqPx6P58+fLamXDLQAAAMBfgipoZGZm6u6771aFKjEa8pfJCi9j3r/03tKhi6w2mxa9Nkn16tXTs88+a1ptAAAAAL8WVP+sP2zYMOXm5evxpyeYGjLOadW+s+76fR89//zzSk5ONr0+AAAAgCJBEzSWL1+upUuX6v5HR6hsVLTf+ul6f19Vjqmhfo88osLCQr/1AwAAAISyoAgahmHor3/7m25qcYtatu3o177sdod6DRypXTt3auXKlX7tCwAAAAhVQRE0Nm3apD27d6tjtz9ck+1na9dvrLqNmmrmzJl+7wsAAAAIRUGxGHzWrNmqGltTDW5u4dXr1654S8nbvtCPhw/K7iilGxvcpB4PD1KVmBpe99m+Sw8tmv6CvvvuOzVs2LC4Q78mDENSqQjJbc5UL6dbKnBLkXapBB4rAgAAgBIg4Hc0DMPQuk/XqfltHby+m5G6J1m3d+2hkf/3moY9+0+53W7NeuEZFeTned1vXOv2CgsL0/r164s7dL8zDGn+Hil+Zbj0crY0PV/3rC2ljYeLV29XpnT/x1L4PKnsfKnWG9LUnVKhx9RhAwAAAIEPGunp6co6cUI16jbwus0Tf5msW++4W9Vq1FZs7bp6+IlndDLzmNJ/SPG6ht3hUEzNG5WUlFScYV8To7dIj/9HSjnzSwDb9KNNnVZJy3/wrdaWo9Jty6WVaZLnpyMa07OlZ7ZIvdZKbsIGAAAATBTwoHHuQr/mjd4Hjf+Vn5sjSSoTeYNP7WJr11di4vZi9+tPO45LL+0q+tnQL0HDbVhkGEUBpMDtXa1zr3d6JPf/nANvSFq+X/rggBmjBgAAAIoEfI3GkSNHZLOFqVx0xWK193g8Wr5opuo0vFkxNW/0qW10papKSU6U0+ksVt/+9Ppum8IsVhUaF04nMySdLJBW7nPp97WNCxv/jx2ZFu0+ab/k8zaLobnfGvpdLNv9Xgvnf9+cTqfs9kt/NgAAAMHI4XBc8TUBDxpXe6H17oLpOpKepj89/6rPbcPCwpSdfVaTJk0qdv/+8lnZB1VYqpF0iWUrFsOjf73/qfbkbbtirb2OBlJUn0s+7zYsStp/TJMmJRR3uPDB+UFj6tSpXv2PCgAAEEzGjx9/xdcEfOqUw+GQy+UqVtt3F0zXtzu2asRz01S+QiWf2xcWFsoWFvCsdVFlPWdl1aUXThgWq8p6znhd63Ishkfl3Kd9Gh8AAABwORbDMK4898aPVqxYoZ49e2rC7CVeT58yDEPv/WuGkrd9oRHjX1LlatWL1ffbc6bp7LF0JSUF3zqNrzItum3lxe/0WGQoyiEdeMilUrYr1zIMqcXyMH132iLPRaZiSdLSzi7d68U0LFy9nJwcRUdHS5KysrIUERER4BEBAAD4pkRMnYqPj5ckHdz/vZp6GTTenT9dSZvX6/GnJ6h0eBmdOZUlSSpdJkIORymv+z6UlqI777g9KKeu3BojjWxWtCDcoqJ1GZJksxQtDn+9o3RDuPfjnt9R6rRKcnkMuX8OG4Yssui+G6We9eyyBfz+Vmg4/w6ew+EIyu8fAADA1Qp40KhRo4aiK1RQ+r7v1TS+rVdtvli3SpI04/mRv3r84aFP69Y77vaqhsvp1OGD+xUf/2efxnstTW0jNSkvTd0l7TlZ9FjHWOlv8dJvYnyr1aaqtLWnNP6/bq3cL8kWpuplDP25mUV/ihMhAwAAAKYK+NQpSerdu482fvGlxk1b4PWhfVcrafMGLZr+gvbu3VsiTgbPLZTCrPJqqtTl5OTkKLJceSmslM5mHlVkJNN2rrWcnBxFRkZKkrKzs5k6BQAArktB8e/YTzwxVEcPHdT333x1zfr8Yu0qdezYMehDhiRZLFKE/epDxs/cLqkgW9co0wEAACAEBUXQuP3229X4ppv02ep3dS1usKSl7NG+vV9r2LBhfu8LAAAACEVBETQsFov+b8IE7f5qm3Z8+Zlf+3K5nHpn7jQ1b9FC9957r1/7AgAAAEJVUAQNSerZs6cefPBBLfvXjJ93kfKHT5b9W8ePZGjxokUKC9IzNAAAAICSLmiChiTNnDlTEWXCNe/FvyovN8f0+tu/WK9177+t8ePHq2nTpqbXBwAAAFAkqIJGxYoVtWbNGp08dkQJE8cqJ9u7k6+9sW3jWr0xa4oeeeQRjRs3zrS6AAAAAC4UVEFDklq0aKH169fr9Imjmjp2iPYmX92p3Xm5OXpn7kt6Y9YUPdq/v15//XVZrUH3tgEAAIDrSlBecbdq1Uo7duxQs6ZNNOuFMXorYapOHDviUw13YaF2bPmPpjwzULu2blRCQoLmzZsnm82sPWIBAAAAXEpQHNh3KYZhaO7cuRozZozOnDmjJi1u1S13dNWN9W9SueiKF7ze5XLqyMH9+nbHf7X1s9U6eSJTXbp00dy5c1WrVq0AvIPgw2FxgcdnAAAAQkFQB41zcnNz9fbbb2vGa69p186dkqSo6AqqXK2Gwhyl5PG4lXPmtI6k71dhYaHKlIlQv359NXToUMXFxQV28EGGi9zA4zMAAAChoEQEjXMMw1BGRoaSkpKUlJSk1NRU5efnKywsTFFRUWrRooXi4+MVFxen8PDwQA83KHGRG3h8BgAAIBSUqKCBq8dFbuDxGQAAgFAQlIvBAQAAAJRsBA0AAAAApiNoAAAAADAdQQMAAACA6QgaAAAAAEwXFugB+OL48eNas2aNkpKSlLh9u1JTU1WQny9bWJjKR5VXy5ZF29u2b99e7dq1k8ViCfSQAQAAgJBUIoLGli1bNGvWLC1dulROp1NVYmqo+o311arDb+VwlJLH49HZMye1a0+KVn+0Rnm5OWrQsKGGPfGEHnnkEZUrVy7QbwEAAAAIKUF9jkZmZqaGDRumpUuXqnK1WLXtfI9u6dBVkWUvHRw8Ho/27f1am9d9oF3/3aTo6PJKSEhQz549r+HIgxdnOAQenwEAAAgFQRs0PvjgAw0YMEB5+QW675Fhim/XSVarb0tKTmUd13sLZig5cbN69eqlOXPmhPzdDS5yA4/PAAAAhIKgDBrz5s3T4MGDdXN8G/Ua+JTKRkUXu5ZhGNrx5Wd6d/6rql+/ntatXatKlSqZONqShYvcwOMzAAAAoSDodp1avHixBg0apPZdemjAqOevKmRIksViUXy7Thox/iXtTzugu7p00enTp00aLQAAAICLCaqgkZycrMcff1xtOv1WDzw6wuepUpcTW6uuhv5lilJSUjV48GDT6gIAAAC4UNAEDZfLpX6PPKLKMTX0wGNP+mVr2thadfXAY09qyZIlWr58uen1AQAAABQJmqAxdepUff311+oz5GnZ7Q6/9RPfrpPiWrfTkCFDmEIFAAAA+ElQBA2n06mXX35ZbTt3U806Dfzal8Vi0QOPjVBW1kktXrzYr30BAAAAoSoogsby5ct1/Phx/abr769Jf1HRldTslvZ6beZMBeGmWwAAAECJFxQng8+dN08NmjRX1eq1vHr9prWrtHndKp04/qMkqVr1Wrr7/r66qcWtXvfZrksPzXh+pDZv3qz27dsXa9wlkcsjqcEdUqlIpZ21qMlV7qy6O0tKPS1VKC21qSpZzV9aAwAAgBIo4EHD7XZr65at6np/X6/bRFWoqO4PDVSlqrGSYWjb52s178Xn9MyUOapWo7ZXNeo2aqrwMhEhFTRe3y2N3VpG+vNnkqSmKwzdXUNa0EmqWsa3Wt+dlPpvkLYe++WxWpHSjNul7rXNGzMAAABKpoBPndq7d6/y8nJVw4e1GU3j26pJi1tVuVp1VY6poXt6D1Cp0uFKS9ntdQ2r1arqtespKSmpOMMucV7fLQ3cKJ0o+OWWgyGL1mVIt78vnXV6XysjW2r3vpR4/NePH8yW7l0jfXLQlCEDAACgBAv4HY2dO3dKkqrfWK9Y7T0et77aslEFBfmq3eAmn9rG1q6n7UlJcjp9uMougVweadxWu6QL5zUVGtK+04YW7HZr6E0er+pN+8qmUwVWuY1f1zMkWWRozBZDHasWmjDy69P53zen0ym73R7A0QAAAPjO4bjyLrEBDxonT56U3e5QeJlIn9odPviDXvrrCBW6nCpVOlyPj35e1arX9qlGZNko/fjjj5o0aZJP7Uqa/fbayiz/yCWfNwxp2sbDOrXyX17Ve73CU3Lbyl68lizalWXRM1Nmq7znVHGGe907P2hMnTrVq/9RAQAAgsn48eOv+JqAB43CwkJZbb7P4KocU0Nj/jlXebk52rn1c70xc4qe/PtLPoUNm80mj8e7f8UvyZyWK1zIWiwqsJbyup7rSvW86RMAAADXNYsR4P1dExISNGzYML305ieyWou/ZOS1CU+rYpVq6j1opNdt1ry7WEmfr1F6enqx+y0J9p+VGi+1y7jI1ClJCrMYeqieR/N+4/aqXqcPw7T1mOWCqVPnhNsMZTzsUiQzgi4qJydH0dHRkqSsrCxFRFzl1l8AAADXWImYOlWvXj15PB5lHj2kyjE1il3HMDwqLHT51ObHwwdVv379637qSsMK0t01pHUZRWsy/lehYdHwOJscDptX9f7cTPrD2os/Z7NIAxpbFB1xff9Or4bL9cv31OFwXPffPwAAEJoCvutUy5YtJUkHf/je6zar3npdqbuTdeLYUR0++MNPf9+lVu07+9T3obQUtWrVyqc2JdWCTlLtskXLwc/dhwj76YdX2kmtK3tf6/460p+aFv1ss/yUXDxFd0NuqSxNus2UIQMAAKAEC/gdjejoaNWqXVtpKXu8DgrZZ07qjVmTdfpklsLLRCimZh0N/ctkNYrzPjRknzmtHw9nKD4+vrhDL1GqlpF2PCAt/l56O0U645TiK0lP3OxbyJAki0V6uV3ReRkzk91a8eUe6eyPmjfgdvVtUkqlvLsxAgAAgOtYwNdoSNKoUaM07/X5+vvMd2S/RtNI1n+wVGveXahDGRmqWLHiNenzepSTk6PIyKIdw7Kzs1lv4AV+ZwAAIBQEfOqUJA0ZMkRnz5zWV1s3XpP+PB6Pvvz0A/V68EFCBgAAAOAHQRE06tevr7vuuksbVr0jl8v/h+clbV6v40cPa+jQoX7vCwAAAAhFQRE0pKKDy44fPaRPlr3h137OnMrSikWz1KtXL7Vp08avfQEAAAChKmiCRlxcnP72t7/p01XvKC1lj1/68Hg8WjLvZYWXLqXXXnvNL30AAAAACKKgIUljx47VLa1ba96Lf9WRjDRTaxuGoff+NUPfJG3R/PnzWZsBAAAA+FFQBQ273a7Vq1erZo3qeu0fo0y7s+FyOfXO3Gn6Yu0qzZkzR927dzelLgAAAICLC6qgIRWdq/H5xo1q0riRXhn/J334zoKrWiB+cN93eunZYdq+6VMtXrxYAwcONHG0AAAAAC4m4Af2XUx0dLQ+//xzTZ48WRMmTNA32zerU/deatHmDq/P2TiSkaZNH6/UlxtWKy4uTh+tWqG4uDg/jxwAAACAFCQH9l1OcnKyRo8erXXr1umGsuXUok1H1W5wk2rUaaBKVWNltRbdlMnLzVb6DylK35+iPV/9V99/u1OVKlfWyKee0qhRo2S32wP8Tq5PHD7nO35nAAAgFAR90DgnJSVFc+bM0bJly5WWtl+SZLVaZXc45Ha7VehySZLCw8uoTZvbNGjQIN13331yXKOTxkMVF82+43cGAABCQYkJGufLysrSjh07tG/fPuXn5yssLExRUVFq0aKFGjZsKJvNFughhgwumn3H7wwAAISCEhk0EDy4aPYdvzMAABAKgm7XKQAAAAAlH0EDAAAAgOkIGgAAAABMR9AAAAAAYLqgPLDPG3l5eTpw4MDPu06VL19eMTExslgsgR4aAAAAEPJKTNBwu9366KOPtGLFCiUmbteePbvldrt/9ZroChXUulUrtW/fXv3791f16tUDNFoAAAAgtAX99rY5OTl69dVXNTshQRnp6apeq45q1musGnUaqEpMTdkdDnk8HmWfOaX0/SnK2P+9Uncny+UsUPfu3fX000+rbdu2gX4b1y22avUdvzMAABAKgjpobNy4Uf0ffVSHDx1Wy3Yd1f6uHqpZt+EV2+Xn5Wr7F+u1ed0qHTrwg0aMGKFJkyZxQecHXDT7jt8ZAAAIBUEZNDwej8aOHasXX3xR9RrHqc+Q0apUNbZYdT7/eIU+fGeBYmKqadXKlWratKkfRhy6uGj2Hb8zAAAQCoIuaLjdbvXv/6jefPMN3fvwIN3R7QFZrVe3Odbxo4e08JUJOpN1TOvWrVPr1q1NGi24aPYdvzMAABAKgm572xEjRuitt95UvxF/UafuD151yJCkSlVjNfy5qapQtbq6du2qPXv2mDBSAAAAAJcSVEFj2bJlmj17th58/M+Kb9fJ1NrhZSI1aMxElY4oq4ceflgul8vU+gAAAAB+ETRBIzMzU0OHDlWzW9qrTaff+aWPMhGRenjYWCUnJ2vKlCl+6QMAAABAEAWNsWPHKi+/QH8Y8Ce/HrpXs04D3dmjt/7xj39o//79fusHAAAACGVBETROnDihN958Ux3veVBlo6L93l+X+x6So1RpzZkzx+99AQAAAKEoKILGwoUL5Xa7dVun3xar/br339aTvTpr2cKZXr3eUaq0Wnfootdff135+fnF6hMAAADApQVF0Fj8738rrnV73VA2yue2B1L3avOnHyqmZh2f2rW7s7tOnDihtWvX+twnipwqkObuDZPunybd/RelnS3+lDePIa1Nl57ZUvRnbXrRYwAAACiZAh408vLy9O0336h+k+Y+ty3Iz9Pi1yaqz6CRKhN5g09tK1errqjoCkpMTPS5X0jv7ZOqLZJGbXNIHYZL3Z5X0xXhemaL5OvJLIdzpOZLpa4fSi/vKvrT9cOixw7n+Gf8AAAA8K+AB41du3bJ7XarRp0GPrd9d/6ratLiNjWMi/e5rcViUWzt+gSNYkg8JvVeJxW4JUMWKcwh2cJkyKIXd0rTv/a+lseQ7v5Q2nOy6O+FRtEfqeixuz/kzgYAAEBJFBboAXz77beSpGo1avvULmnzBqXvT9XoibOK3XdsrTr6ettGOZ3OYtcIRVO/sskia1HIuIChyTukgQ1cCvMixq7LsOjrLPtFnys0pK+zpI/TXLoz9vpJG+d/35xOp+z2i79/AACAYOVwOK74moAHjZycHDlKlZbdfuXBnnMy85iWL5qpJ579p+xevMlLKRVeRiezsjRp0qRi1whFqyo+o0Jr+CWetehonvT01Hmq7M68Yq21EXfKWuY2eSy2iz5vNdx6Ydk2JeZ8ehUjDi7nB42pU6d69T8qAABAMBk/fvwVXxPwoFEc6fu/19nTp/Ti2CE/P+bxeLRvT7I2ffK+XnrzY1mtF79wBQAAAOB/FsPwdemuuebPn6/HH39c095Y4/Vdjfy8XGUd//FXj701+0VVjq2hO3v0VkzNG72q8+E78/XNto3a/8MPPo87lPX9zKbl+60qNC4+dapquLSvt/dTp+755PJTh1bffX1NncrJyVF0dNF5MVlZWYqIiAjwiAAAAHxTIqZONWnSRJJ0JD1NNb1cEF46vMwFYcJRurQiIst6HTIk6dCBH9T05puZuuKj0S2kZfsli6QLL/8tGttSKlPau9/pb2+UmkYXLfwu/J9iYRapcXnp7tp2Wf13WPw153K5fv7Z4XDw/QMAANelgO861axZM9lsNqX/8P017dcwDB1KS1Hr1q2vab/Xg9aVpXfukkrbisKG3SrZLEU/P9NcerKp97WsFunje4oChSSp0Fn0R0WPfXyPrquQAQAAECoCfkcjPDxcTW6+WSnf7lS7O+8pdp0nx7/k0+uPHcnQqawTBI1ieqCudFd16a0UKeW0VLG01Ke+dGNZ32vFREg7H5RWp+apx5gZkqRVU0aoW71wQgYAAEAJFfA1GpI0bdo0jR03Ts/PeqdYp4MXx/LFs/T11v8oIyNDpUuXviZ94vJycnIUGRkpScrOzr5u1y6EyvsEAAChLeBTpySpf//+stls2rphzTXpz1mQr8SNa/X4448TMgAAAAA/CIqgUaFCBf3x4Yf12YdLdeZUlt/7W7viLTkL8jV48GC/9wUAAACEoqAIGpI0efJkhZcupaWvvyJ/zuY6uO87fbrqHT333HO68Ubvd6gCAAAA4L2gCRoVK1ZUQkKCkhM3a8uGj/zSR272Wb05a4ri4uI0ZswYv/QBAAAAIIiChiT17NlTQ4cO1dLXX1HS5g2m1s7Lzdbcfz6r/Jwzevutt2S3X/6QOAAAAADFF/Dtbf/XjBkzdPZsthbPmKjTWZm6o9sDslqvLg8dP3pIC1+ZoDNZx7Ru3To1atTIpNECAAAAuJigCxo2m02LFi1UtWpV9eKLL+qbpC3qM2S0KlWN9bmWx+PR5x+v0IfvLFBMTDVt2rRJTZv6cJocAAAAgGIJinM0LmXjxo3q/+ijOnTokFq27aTbu/RQzboNr9guPy9XiZs+1eZ1q3T44H49+eSTmjhxIucVBLlQOV8iVN4nAAAIbUEdNKSii7Lp06dr1uzZykhPV2ytOqpZt5Fq1mmgyrE15XCUksfj1tnTp5SxP0Xp+1O0b0+yXM4C9ejRQ6NHj1bbtm0D/TbghVC5AA+V9wkAAEJb0AeNc9xut9asWaMVK1YoMXG7du/+Vm63+1evqVCxolrFx6t9+/bq37+/qlevHqDRojhC5QI8VN4nAAAIbSUmaPyvvLw8HTx4UPn5+QoLC1NUVJRiYmJksVgCPTQUU6hcgIfK+wQAAKEt6BaDeys8PFwNG155vQYAAACAay+oztEAAAAAcH0gaAAAAAAwHUEDAAAAgOkIGgAAAABMVyIXg2dlZWnHjh1KTU39edep8uXLq3nz5mrUqJFsNlughwgAAACEtBITNFJSUpSQkKBly5frQFqaJMlqtcrucMjj9sjlckqSwsPLqE2b2zRw4ED17NlTDocjgKMGAAAAQlPQB43k5GSNGjVKn376qW4oW04t2nZSh+4PqWadBqpYNVZWa9Hsr7zcbGXsT1X6D99r91f/VZ8+fVSpUiWNHDlSo0aNkt1uD/A7AQAAAEJH0B7Y53K5NHnyZE2YMEGVqsaqU4/eanFbB9m9vENxJCNNmz5ZqS/Xr1ZcXJwWLVyouLg4P48aVyNUDrILlfcJAABCW1AGjaysLHXr1k3bEhN117191KXnw7LbizcF6uC+7/T2nKk6djhd8+fPV9++fU0eLcwSKhfgofI+AQBAaAu6qVNZWVn6TYcOOpieoT8//6pq1298VfVq1m2okS/M1HsLpqtfv37Kz8/XwIEDTRotAAAAgIsJqqDhcrnUrVs3HUzP0PDnpqla9dqm1LXbHeo9aJRsYXYNHjxYVatWVffu3U2pDQAAAOBCQXWOxuTJk7UtMVEDn/4/00LGORaLRQ88OkI3x7fRgAEDlJmZaWp9AAAAAL8ImqCRnJysCRMm6M4eva96utSlWK1W9Rr4lPLyCzR8+HC/9AEAAAAgiILG6NGjValqrLre/0e/9lM2Klr3PfKElixZoi1btvi1LwAAACBUBUXQSElJ0bp169SpR+9i7y7li/h2nVWpaoxmz57t974AAACAUBQUi8ETEhIUWbacWtzWwavXf/TuIn383uJfPVY5pob++vJCr9pbrVa1vbO7liz5l1566SVVrFjR1yEDAAAAuIygCBrLli9Xy7advD6MT5KqVa+tYX978ee/W602n/q8tUNXrXxjjtasWcPZGkHg4Flpxk67NDZJkvT3HXaNaC7VvMH3WgVuaUmqtHCvdDxfahQlDW4idY6VLBZThw0AAIBLCPjUqaysLB1IS/N5AbjVZlPZqOif/0SWLedT+8iy5VQlprqSkpJ8agfzbTosNX5Hevlbu1SzpVSzpV7+1q7G7xQ954tsl9RxpfTIBmnjEembLOn9/dJdH0gjv5SC73hKAACA61PA72js2LFDklSzTgOf2h0/ekh/HfKg7HaHate/Sd0fGqDoilV8qhFbu762b9/uUxuYK69QuvdjKd8teYxfbje4DYvy3UXPHeonhXv5TR27Vdp2rOhnz0+hovCn/76SLLWvKt1f18Q3AAAAgIsKeNBITU2V1WpVxaqxXrepXa+RHh76jCrHVNeZk1las2yxXh3/Z42bOl+lw8t4XadKTE0lfb5GTqezOEOHCd5KsepkwcW/hh5DOlkgvf1dof5Y33PFWtkuacEeu9zGxedH2SyGXtllqHuNwqsa89U6//vmdDplt9sDOBoAAADfObxY8hDwoJGfny+7wyGr1ftZXDe1uPXnn2Nr1VWt+o3192EP6ast/1GbTr/zuo6jVCmdOXtWkyZN8mnMMM8nkV1kDb9FHsvF19hYDbde/zhR6e+tvWKtH22VlVdh6CWfdxsWJR4p0KRJU4o9XjOcHzSmTp3q1f+oAAAAwWT8+PFXfE3A12iEhYXJ477yv1ZfTpmISFWuVl3Hj/o2od/tdvsUcGA+h+HU5ZZNGD+9xttaV2L3shYAAACuTsDvaJQvX14ul1N5udkKLxNZrBoF+XnK/PGwWv/mTp/aZZ85pSpVqmjcuHHF6hdXr0eWRS1XXHrHMMNi0yt92+qm8m28qvfZCo++zrLI0IXTp2wWQwObR2jcLYH9vHNycjRx4kRJRQdVRkREBHQ8AAAA/hDwoNG8eXNJUsb+VNVv0tyrNu//O0FN4tsoumIVnT55QmveXSiL1aqW7Tr51PehtFS1io9n6koAtagqPVRfejtFF9zZsEjqU19qXsX7NQz/bCP9drVkkfGrsGGzSFGlLBrZ3CaHw7etkM3mcrl+/tnhcPD9AwAA16WAB41GjRopPLyM0n/43uugcerEcS2a/oJyzp5RZNlyqtvwZo38v9d0Q9kor/v1eDzKSEvVgH59ijdwmGZhR6lSaSnhW6ngp1l0pazSkCbSi97dyPhZ15rSyt9Kwz43lJ7zS9C4pbL0r45S9eLdNAMAAICPLIYR+JMFOnfurIwfszT8uWnXrM+U3bs04/mR2rRpk9q3b3/N+sWlnSqQvjxa9HPbqlJUqeLXOpudo7LN7pIiKipxzTtqFev9bmT+lpOTo8jIosSTnZ3N1CkAAHBdCvgdDUkaOHCg+vTpo6MZB1S1eq1r0ufmtavUoGFDtWvX7pr0hyuLKiX9zqSP32qR9MMWSVLjqIBnaQAAgJATFFsu9ezZU5UqVdLnn7x/Tfo7lXVcu7Z9oeHDhsliufiZCwAAAACKLyiChsPh0FNPPaUv16/WwR++92tfhmHovQUzFB1dXv369fNrXwAAAECoCoqgIRVt89m0aVO9nfCiXC7/nXWQtHmDkhM3KyEhQeXKlfNbPwAAAEAoC5qgYbfbtXjRIh07nK73FkyXP9aoHzqwT+8tmK5evXqpZ8+eptcHAAAAUCRogoYkxcXFaf78+dqyYY3eXTBdHs/VnRh+vkMH9mn2xDFq2KC+5syZY1pdAAAAABcKil2nzte3b1/l5+dr8ODBOp2VqV4Dn1LZqOhi1zMMQ0mbN+i9BdPVsEF9ffLJJ0yZAgAAAPwsqO5onDNw4ECtXLlSRw+kaPLoAUrctK5YdzdOZR3X/GnjtXjGRHW/p5s+++wzVapUyQ8jBgAAAHC+oDiw71IyMzM1fPhwLVmyRJWrxapN53t0a4euiix76TsSHo9H+/Z+rc1rV2nXti8UHV1eCQkJrMkIMcF8KF4wjw0AAMAsQR00ztmyZYtmz56tJUuWyOl0qkpMdcXWrq8qMTXlKFVKbrdb2WdO6VBaqjLSUpWXm6MGDRtq+LBh6tevH1OlQlAwX8wH89gAAADMUiKCxjnHjx/Xxx9/rKSkJCVu367U1FQV5OfLFhamqHJRio9vqfj4eLVr107t2rXjML4QFswX88E8NgAAALOUqKABeCuYL+aDeWwAAABmCcrF4AAAAABKNoIGAAAAANMRNAAAAACYjqABAAAAwHQEDQAAAACmCwv0AHxhGIbS09OVlJSkpKQkpaamKj8/X2FhYSpfvryaN2+u+Ph4NWvWTOHh4YEeLgAAABCySkTQyM3N1VtvvaXXZs7Urp07JUlR0RVVOaaGwuwOGR6Pcs4ma+HChSosLFSZMhHq2/ePGjp0qJo1axbYwQMAAAAhKKjP0TAMQ3PmzNHYsWN15swZNWl5m27t0FW16zdWueiKF7ze5XLqSHqavk3aqq2frdbJE5nq0qWL5s6dq1q1agXgHSBQgvmsimAeGwAAgFmCNmgcOHBAjz32mDZs2KA2nX6nLvc9rAqVq3rd3l1YqOTEzVr55hwV5OZo2rSpGjRoEKeFh4hgvpgP5rEBAACYJSiDxvbt29W1a1dZbHb1HjRKDePii10rLzdHK9+Yoy/Xr9Zjjz2muXPnymazmThaBKNgvpgP5rEBAACYJejWaHz11Vfq1KmzKlatrkFjX1BEZNmrqhdeJkK9B41UnYY3a+GcqfJ4PJo/f76sVjbcAgAAAPwlqIJGZmam7r77blWoEqMhf5ms8DLm/UvvLR26yGqzadFrk1SvXj09++yzptUGAAAA8GtB9c/6w4YNU25evh5/eoKpIeOcVu07667f99Hzzz+v5ORk0+sDAAAAKBI0QWP58uVaunSp7n90hMpGRfutn67391XlmBrq98gjKiws9Fs/AAAAQCgLiqBhGIb++re/6aYWt6hl245+7ctud6jXwJHatXOnVq5c6de+AAAAgFAVFEFj06ZN2rN7tzp2+8M12X62dv3GqtuoqWbOnOn3vgAAAIBQFBSLwWfNmq2qsTXV4OYWXrc5lXVcq96cp907t8lVUKCKVWP18NCnVbNuQ6/at+/SQ4umv6DvvvtODRt61wYljNUmOcrIY8IGzoYhZbukUjbJwe7IAAAAVxTwoGEYhtZ9uk633PE7r+9m5Gaf1SvP/Un1b2quoeMmK7JsOR07ckjhETd43W9c6/YKCwvT+vXrCRrXmf1npOe2OqRXcqSwUqq91NATN0tjW0gRdt9qFXqkV5Kl6V9L6dmS1SL9vrb0XCup2YWH0wMAAOAnAQ8a6enpyjpxQjXqNvC6zaer3lFUhUp6+Ilnfn6sQuVqPvVrdzgUU/NGJSUl+dQOwS3llHTbcumMM0wKKwquWQUWTdohfZohre8ulfEybLg9Uq+10or90rmbIh5DWpkmfXRQ2tBDauP9YfUAAAAhJeBrNM5d6Ne80fug8fX2L1WzTkMteOl5/WXg/ZoyZrC+XL/a575ja9dXYuJ2n9sheI38UjrtlAqNX98dcxvSth+lubu9r7UqTVp+Xsg4v5bTIz3+n6IpVQAAALhQwO9oHDlyRDZbmMpFez8P5cSxI/pi3Sp17PaA7rrvIR3c952W/es12cLCdGuHrl7Xia5UVSnJiXI6ncUZOoLMsTxp9QG7DF18Cp4hQwnfGnqisXfbGs/9Nkw2i0Vu48J6HkPafVLadsSlFhV9Sxvnf9+cTqfsdh/ncwEAAASYw+G44msCHjSKc6FleAzVqNtA3fs8LkmqcWN9HUlP0+Z1H/gUNMLCwpSdfVaTJk3yqX8Ep6O2yjIqDL3k84Ys2n/SqUmTJntVb0f0ELnDqlz2Na8sek+NnN/7NM7zg8bUqVO9+h8VAAAgmIwfP/6Krwn41CmHwyGXy+VTm7Llo1U1ttavHqsSW1MnM4/5VKewsFC2sIBnLZgk0pN9+blMhqGynjNe1yvnPi2L4bnsa3ypBwAAEEoCfpVdrVo1ud2FOp2V6fX0qToNb9axI+m/euz4kQyVr3T5f33+X1nHj+rG2jdq3LhxPrVD8Nq91tAnGbrodCeLRRrTrryevNm7z/umNIseXH/xLG61GGpUztD0xx6Vr0e/5OTkaOLEiZKk0aNHKyIiwrcCAAAAJUDAg0Z8fLwk6eD+79XUy6Bxx+/u18vPPam1K95UizZ36EDqXn25frV6DXzKp74PpaXozjtuZ+rKdeSV9ud2nZIKz7u5YbVIt1S2aFhcmBxefut71pN6/nBu1ylD+mnth81iyGG16PWOFpUq5ft35/w7eA6Hg+8fAAC4LgV86lSNGjUUXaGC0vd5P8+9Vr1GenzU80ra/JkmjR6gT5a9oZ6PPKHWt9/pdQ2X06nDB/f/HHRwfagfJW1/QOrbUHL89O2uUFr6S8uirW3DfYjWNqu0pIv0YhupepmfUou7UPfUcGtLT7a2BQAAuByLYQR+g87evfto4xdfaty0BV4f2ne1kjZv0KLpL2jv3r0c2HedKvRIuYVSpL3ojsbVyM7O0Q0Vq0qFBco+ffKqpjvl5OQoMjLyp7rZTJ0CAADXpYDf0ZCkJ54YqqOHDur7b766Zn1+sXaVOnbsSMi4joVZpbKOqw8ZUtH6DhVkS27fNi4AAAAIVUERNG6//XY1vukmfbb6XV2LGyxpKXu0b+/XGjZsmN/7AgAAAEJRUAQNi8Wi/5swQbu/2qYdX37m175cLqfemTtNzVu00L333uvXvgAAAIBQFRRBQ5J69uypBx98UMv+NUNnTmX5rZ9Plv1bx49kaPGiRQrjDA0AAADAL4ImaEjSzJkzFVEmXPNe/KvycnNMr7/9i/Va9/7bGj9+vJo2bWp6fQAAAABFgipoVKxYUWvWrNHJY0eUMHGscrLNO3V528a1emPWFD3yyCMc0AcAAAD4WVAFDUlq0aKF1q9fr9Mnjmrq2CHam7z9qurl5ebonbkv6Y1ZU/Ro//56/fXXZbUG3dsGAAAAritBecXdqlUr7dixQ82aNtGsF8borYSpOnHsiE813IWF2rHlP5ryzEDt2rpRCQkJmjdvnmw2m59GDQAAAOCcoDiw71IMw9DcuXM1ZswYnTlzRk1a3Kpb7uiqG+vfpHLRFS94vcvl1JGD+/Xtjv9q62erdfJEprp06aK5c+eqVq1aAXgHuF6YecgeB/YBAIBQENRB45zc3Fy9/fbbmvHaa9q1c6ckKSq6gipXq6EwRyl5PG7lnDmtI+n7VVhYqDJlItSvX18NHTpUcXFxgR08rgsEDQAAAN+UiKBxjmEYysjIUFJSkpKSkpSamqr8/HyFhYUpKipKLVq0UHx8vOLi4hQeHh7o4eI6QtAAAADwTYkKGkCgEDQAAAB8E5SLwQEAAACUbAQNAAAAAKYjaAAAAAAwHUEDAAAAgOkIGgAAAABMFxboAfji+PHjWrNmjZKSkpS4fbtSU1NVkJ8vW1iYykeVV8uWRdvbtm/fXu3atZPFYgn0kAEAAICQVCKCxpYtWzRr1iwtXbpUTqdTVWJqqPqN9dWqw2/lcJSSx+PR2TMntWtPilZ/tEZ5uTlq0LChhj3xhB555BGVK1cu0G8BAAAACClBfY5GZmamhg0bpqVLl6pytVi17XyPbunQVZFlLx0cPB6P9u39WpvXfaBd/92k6OjySkhIUM+ePa/hyHG94RwNAAAA3wRt0Pjggw80YMAA5eUX6L5Hhim+XSdZrb4tKTmVdVzvLZih5MTN6tWrl+bMmcPdDRQLQQMAAMA3QRk05s2bp8GDB+vm+DbqNfAplY2KLnYtwzC048vP9O78V1W/fj2tW7tWlSpVMnG0CAUEDQAAAN8E3a5Tixcv1qBBg9S+Sw8NGPX8VYUMSbJYLIpv10kjxr+k/WkHdFeXLjp9+rRJowUAAABwMUEVNJKTk/X444+rTaff6oFHR/g8VepyYmvV1dC/TFFKSqoGDx5sWl0AAAAAFwqaoOFyudTvkUdUOaaGHnjsSb9sTRtbq64eeOxJLVmyRMuXLze9PgAAAIAiQRM0pk6dqq+//lp9hjwtu93ht37i23VSXOt2GjJkCFOoAAAAAD8JiqDhdDr18ssvq23nbqpZp4Ff+7JYLHrgsRHKyjqpxYsX+7UvAAAAIFQFRdBYvny5jh8/rt90/f016S8qupKa3dJer82cqSDcdAsAAAAo8YLiZPC58+apQZPmqlq9ltdt/j78IWUd//GCx9t36aEHB/zpiu3bdemhGc+P1ObNm9W+fXufxovQk3bWIjW9RyrIlstzdbVyCyU1vkuyOfRjnkV12N0WAABchwIeNNxut7Zu2aqu9/f1qd2oibNkeH654jtycL9mvvCMWtzWwav2dRs1VXiZCIIGLutorvTYBunj9HBp6AeSpHrvGprSRhrQ2LdahiFN3CFN3lFGGrFWktTgPUO96kkJv5Fu8N/SJAAAgGsu4EFj7969ysvLVQ0f12bcUDbqV39f9/7bqlglRvVuauZVe6vVquq16ykpKcmnfhE6zjql29+X0s5Ihn7ZBe1EgUWP/6foZ1/CxnOJ0v8lSTqvltuwaEmqdOCstPFeyRYUkxkBAACuXsCDxs6dOyVJ1W+sV+wahYUubf/iU3Xs9oBP2+LG1q6n7UlJcjqdxe4b16/5u63ad9r2q5BxvrFbDfW+0SW7F+EgM1+avMMuXaSW25A2H5U++MGl39VkzRAAAAh+DseVp2IEPGicPHlSdrtD4WUii10jOXGz8nKydWuHrj61iywbpR9//FGTJk0qdt+4fs2PelSGvcbFsoEkKTPfomEvva0bXWlXrPVV6eYqvKHHJWtZDLf+vupb7Tq7svgDBgAAuEbGjx9/xdcEfKJGYWGhrFc5X2TrhjVq3PwWlYuu6FM7m80mj+cqV/biulVgLSVd4Q6Z0+LdwgqnxSGLLn23wpDV61oAAAAlQcDvaJQuXVoup1Mej0dWq++BI+v4j/ru6x0aMOrvPrd1FhSo7A03aNy4cT63xfVv3+c2vZ1qqNC4eNiwyND4QffrxhuuXOvzIxat+ejS32+rVfpD2wYa14LvIgAAuD4EPGjUq1dPHo9HmUcPqXJMDZ/bb/3Px7qhXJSatLzN57Y/Hj6o+vXrezXHDKFnRJz075SLPxdmkbrUsKhhBe++O51rSo2ipJTTRWsyzmeRZLNYNKhJmPgqAgCA60XAp061bNlSknTwh+99buvxePTf/3ysWzp0kc1m87n9obQUtWrVyud2CA2tK0svty36OeynmxqWn/7ULivN7+h9LYtFWn63FF1Ksp53gyTMItks0lt3SrHFX6YEAAAQdAJ+RyM6Olq1atdWWsoetWrf2ae23329Qyczj+m2O+72ud/sM6f14+EMxcfH+9wWoePPzaR21aRZ30hJx6WyDqlPfalfA9/PvWhcXtrdW3p9j7R8v+R0S7dXk4bdLDUq75/xAwAABIrFMIyA76c5atQozXt9vv4+8x3Zr9HckfUfLNWadxfqUEaGKlb0bRE5AAAAgMsL+NQpSRoyZIjOnjmtr7ZuvCb9eTweffnpB+r14IOEDAAAAMAPgiJo1K9fX3fddZc2rHpHLpf/D89L2rxex48e1tChQ/3eFwAAABCKgiJoSNLUqVN1/OghfbLsDb/2c+ZUllYsmqVevXqpTZs2fu0LAAAACFVBEzTi4uL0t7/9TZ+uekdpKXv80ofH49GSeS8rvHQpvfbaa37pAwAAAECQLAY/x+Vy6Te/+Y2+3bNXw5+bpmrVa5tW2zAMvbtgujav+0ArV65U9+7dTasNAAAA4NeC5o6GJNntdq1evVo1a1TXa/8YZdqdDZfLqXfmTtMXa1dpzpw5hAwAAADAz4LqjsY5WVlZ6tatm7YlJurOHr3V9f4/ym4v3ra3B/d9p7fnTNWxw+maP3+++vbta/JoAQAAAPyvoAwaUtE0qsmTJ2vChAmqVDVWnbr3Uos2d3h9zsaRjDRt+nilvtywWnFxcVq0cKHi4uL8PGoAAAAAUhAHjXOSk5M1evRorVu3TjeULacWbTqqdoObVKNOA1WqGiurtWj2V15uttJ/SFH6/hTt+eq/+v7bnapUubJGPvWURo0aJbvdHuB3AgAAAISOoA8a56SkpGjOnDlatmy50tL2S5KsVqvsDofcbrcKXS5JUnh4GbVpc5sGDRqk++67T45rdNI4AAAAgF+UmKBxvqysLO3YsUP79u1Tfn6+wsLCFBUVpRYtWqhhw4ay2WyBHiIAAAAQ0kpk0AAAAAAQ3IJqe1sAAAAA1weCBgAAAADTETQAAAAAmI6gAQAAAMB0BA0AAAAApiNoAAAAADAdQQMAAACA6QgaAAAAAExH0AAAAABgOoIGAAAAANMRNAAAAACYjqABAAAAwHQEDQAAAACmI2gAAAAAMB1BAwAAAIDpCBoAAAAATEfQAAAAAGA6ggYAAAAA0xE0AAAAAJiOoAEAAADAdAQNAAAAAKYjaAAAAAAwHUEDAAAAgOkIGgAAAABMR9AAAAAAYDqCBgAAAADTETQAAAAAmI6gAQAAAMB0BA0AAAAApiNoAAAAADAdQQMAAACA6f4fO8ni02ybNWkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=1, step=1,offset=0, mapping=u1_2)\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_motif(cycle[1])\n",
    "plot_circuit(cycle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3d40b4c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=2, step=1,offset=0, mapping=u1_2)\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_motif(cycle[1])\n",
    "plot_circuit(cycle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7a333b16",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=3, step=1,offset=0, mapping=u1_2)\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_motif(cycle[1])\n",
    "plot_circuit(cycle)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "d143e5d8",
   "metadata": {},
   "source": [
    "#### Step examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "07974664",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=1, step=2,offset=0, mapping=u1_2)\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_motif(cycle[1])\n",
    "plot_circuit(cycle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0dfb5217",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=1, step=3,offset=0, mapping=u1_2)\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_motif(cycle[1])\n",
    "plot_circuit(cycle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9243eb89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=1, step=4,offset=0, mapping=u1_2)\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_motif(cycle[1])\n",
    "plot_circuit(cycle)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6eca4b49",
   "metadata": {},
   "source": [
    "#### Offset examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fb3cb1e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=1, step=1,offset=3, mapping=u1_2)\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_motif(cycle[1])\n",
    "plot_circuit(cycle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "357d0bc3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=1, step=1,offset=7, mapping=u1_2)\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_motif(cycle[1])\n",
    "plot_circuit(cycle)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "010f3ebd",
   "metadata": {},
   "source": [
    "#### Boundary examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "039ad4ee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=1, step=1,offset=0, mapping=u1_2, boundary=\"open\")\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_motif(cycle[1])\n",
    "plot_circuit(cycle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0ad93add",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=5, step=1,offset=0, mapping=u1_2, boundary=\"open\")\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_motif(cycle[1])\n",
    "plot_circuit(cycle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "ca38fabe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=5, step=1,offset=0, mapping=u1_2, boundary=\"periodic\")\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_motif(cycle[1])\n",
    "plot_circuit(cycle)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "885e6307",
   "metadata": {},
   "source": [
    "#### N qubit unitaries\n",
    "For N-qubit unitaries other than N=2, the cycle primitive becomes a hypergraph. `stride`, `step` and `offset` still has the same meaning but now the edges are N-ary tuples. For example a stride of 3 causes edges of the form (1,4,7) for a 3-qubit unitary. This means the function gets sent bits 1,4,7 in that order. Consider the same 3 qubit unitary defined with pennylane, qiskit or cirq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "e741e077",
   "metadata": {},
   "outputs": [],
   "source": [
    "if backend == \"qiskit\":\n",
    "    from qiskit.circuit import QuantumRegister\n",
    "    def U3(bits, symbols=None, circuit=None, **kwargs):\n",
    "        q0, q1, q2 = QuantumRegister(1, bits[0]), QuantumRegister(1, bits[1]), QuantumRegister(1, bits[2])\n",
    "        circuit.crz(symbols[0], q0, q1)\n",
    "        circuit.crx(symbols[1], q2, q1)\n",
    "        return circuit\n",
    "\n",
    "elif backend == \"cirq\":\n",
    "    import cirq\n",
    "    def U3(bits, symbols=None, circuit=None):\n",
    "        q0, q1, q2 = cirq.LineQubit(bits[0]), cirq.LineQubit(bits[1]), cirq.LineQubit(bits[2])\n",
    "        circuit += cirq.rz(symbols[0]).on(q1).controlled_by(q0)\n",
    "        circuit += cirq.rx(symbols[1]).on(q1).controlled_by(q2)\n",
    "        return circuit\n",
    "\n",
    "elif backend == \"pennylane\":\n",
    "    def U3(bits, symbols=None):\n",
    "        qml.CRZ(symbols[0], wires=[bits[0], bits[1]])\n",
    "        qml.CRX(symbols[1], wires=[bits[2], bits[1]])\n",
    "u3 = Qunitary(U3, 2, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "f68c13f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1123.61x702.333 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=1, step=1,offset=0, mapping=u3, boundary=\"open\")\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_circuit(cycle)\n",
    "circuit = get_circuit(cycle)\n",
    "draw_circuit(circuit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "017d0918",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 789.163x702.333 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=2, step=1,offset=0, mapping=u3, boundary=\"open\")\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_circuit(cycle)\n",
    "circuit = get_circuit(cycle)\n",
    "draw_circuit(circuit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5cd6d0a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 621.941x702.333 with 1 Axes>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cycle = Qcycle(stride=1, step=2,offset=1, mapping=u3, boundary=\"open\")\n",
    "cycle = Qinit(8) + cycle\n",
    "plot_circuit(cycle)\n",
    "circuit = get_circuit(cycle)\n",
    "draw_circuit(circuit)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "89200f86",
   "metadata": {},
   "source": [
    "### Qpermute primitive\n",
    "`Qpermute` is a simple primitive that generates all combinations or permutations of edges based on the `combinations` hyperparameter and `arity` of corresponding function:\n",
    "```python\n",
    "if self.combinations:\n",
    "    E = list(it.combinations(Q, r=self.arity))\n",
    "else:\n",
    "    E = list(it.permutations(Q, r=self.arity))\n",
    "```\n",
    "Where E is the generated edges and Q the available qubits of the primitive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "fec6720f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permute = Qpermute()\n",
    "permute_5_qubits = Qinit(5) + permute\n",
    "plot_motif(permute_5_qubits[1])\n",
    "plot_circuit(permute_5_qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "8dcb4a99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "permute = Qpermute(combinations=False)\n",
    "permute_5_qubits = Qinit(5) + permute\n",
    "plot_motif(permute_5_qubits[1])\n",
    "plot_circuit(permute_5_qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "100e4e70",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 3, 2), (1, 3, 4), (1, 3, 5), (1, 4, 2), (1, 4, 3), (1, 4, 5), (1, 5, 2), (1, 5, 3), (1, 5, 4), (2, 1, 3), (2, 1, 4), (2, 1, 5), (2, 3, 1), (2, 3, 4), (2, 3, 5), (2, 4, 1), (2, 4, 3), (2, 4, 5), (2, 5, 1), (2, 5, 3), (2, 5, 4), (3, 1, 2), (3, 1, 4), (3, 1, 5), (3, 2, 1), (3, 2, 4), (3, 2, 5), (3, 4, 1), (3, 4, 2), (3, 4, 5), (3, 5, 1), (3, 5, 2), (3, 5, 4), (4, 1, 2), (4, 1, 3), (4, 1, 5), (4, 2, 1), (4, 2, 3), (4, 2, 5), (4, 3, 1), (4, 3, 2), (4, 3, 5), (4, 5, 1), (4, 5, 2), (4, 5, 3), (5, 1, 2), (5, 1, 3), (5, 1, 4), (5, 2, 1), (5, 2, 3), (5, 2, 4), (5, 3, 1), (5, 3, 2), (5, 3, 4), (5, 4, 1), (5, 4, 2), (5, 4, 3)]\n"
     ]
    }
   ],
   "source": [
    "permute = Qpermute(combinations=False, mapping=u2_3)\n",
    "permute_5_qubits = Qinit(5) + permute\n",
    "print(permute_5_qubits[1].E)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "2edf029b",
   "metadata": {},
   "source": [
    "### Qmask and Qunmask primitive\n",
    "\n",
    "The `Qmask` primitive allows you to \"mask\" qubits according to a chosen pattern. Masking qubits in this context implies rendering certain qubits temporarily unavailable for subsequent operations, which facilitates specialized architectures and computations. You have the option to associate a unitary operation with the mask. The utility of this is that it \"preserves\" the information of the masked qubits, usually through a controlled unitary operation. This feature enables patterns of pooling in quantum neural networks, coarse graining,  entanglers and \"deferred measurement\" where masked qubits are the controls of unmasked ones.\n",
    "\n",
    "For 2-qubit unitaries there are predefined masking patterns such as \"right\", \"left\", \"inside\", \"outside\", \"even\", \"odd\" which halves the circuit size. Alternatively, you can provide your own string such as \"1\\*1\" where '1' signifies mask and \"*\" means to fill with 0's based on the number of available qubits. '0' signifies keeping the qubit active.\n",
    "\n",
    "When specifying a unitary, there are three `connection_type` options (how to generate the edges):\n",
    "  - \"cycle\", simlar to the cycle primitive, generate edges with a stride, step and offset parameter\n",
    "  - \"nearest_circle\" connect each masked qubit to the nearest available qubit in a circular topology\n",
    "  - \"nearest_tower\"  connect each masked qubit to the nearest available qubit in a tower topology\n",
    "\n",
    "The Qunmask primitive allows you to \"unmask\" previously masked qubits, making them available for subsequent operations.\n",
    "\n",
    "Examples will make this clearer:"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "ab3c4b67",
   "metadata": {},
   "source": [
    "#### Masking without a mapping\n",
    "The small nodes are the masked ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "87c9dbe6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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boGGxWLR82TKdPZWj95fMkcvlMrxH7vGjen/JHCUkJGjgwIGG1wcAAABwld8EDUmKjY3V4sWLtXPrJr23ZI6cTuNODM89flQLX35BMS2ilZSUZFhdAAAAAD/k8+1tv2/w4MEqLS3V6NGjdbEgXwkjn1NoWHi567lcLqWnbNX7S+YopkW0Pv74Yx6ZAgAAALzM5PLGM0oG2LBhg0aMGKGS0it6ZOg4xcX3ltns2Q2YCwV5en/JXGWkpighIUFJSUmEDAAAAKAC+G3QkKT8/HxNmDBBK1euVO16UerS+yHd072vqoXePCw4nU4dPfylUjav1/7dOxQeXkOJiYm8kwEAAABUIL8OGtfs3LlTCxcu1MqVK2Wz2VQnsr6iGkerTmRDWStVksPh0OXCC8rNztLJ7CyVFBepRUyMJowfryFDhnAXAwAAAKhgt0XQuCYvL08fffSR0tPTlZqWpqysLF0pLVVQcLDCqocpLq6D4uLiFB8fr/j4eA7jAwAAAHzktgoaAAAAAG4PfrW9LQAAAICfB4IGAAAAAMMRNAAAAAAYjqABAAAAwHAEDQAAAACGC/b1AJ5wuVzKyclRenq60tPTlZWVpdLSUgUHB6tGjRpq166d4uLi1LZtW4WEhPh6XAAAACBg3Rbb2xYXF+udd97RvPnztX/fPklSWHgt1Y5soGCLVS6nU0WXLujUiWMqKytTlSpVNXjwbzR27Fi1bdvWt8MDAAAAAcivg4bL5VJSUpKmTJmiwsJCte7QWfd076vG0a1UPbzWD6632206nZOtA+m7tOvTjTp/Ll99+vTRokWL1KhRIx98AwAAACAw+W3QOH78uIYPH66tW7eqS69fqs8jT6pm7bpur3eUlSkjNUXr3k7SleIizZ49S6NGjeK0cAAAAKAC+GXQSEtLU9++fWUKsmjQqEmKiY0rd62S4iKteytJn2/ZqOHDh2vRokUKCgoycFoAAAAA3+d3QWPv3r3q3r2HatWtr1FT/qKq1UINqbt722a9kzRLQwYP1uLFi2U2s+EWAAAA4C1+tetUfn6+HnzwQdWsE6kxv52pkCpVDat9d/c+MgcFadm8GWrevLlefPFFw2oDAAAAuJ5f3dFISEjQh5s+0pRZixUaFu6VHh+sWKxPP3hPaWlpio2N9UoPAAAAIND5zfNDa9as0apVq/ToU894LWRIUt9HB6t2ZAMNGTpUZWVlXusDAAAABDK/CBoul0u/+/3vdWf7u9Wha0+v9rJYrEoYOVH79+3TunXrvNoLAAAACFR+ETS2b9+uQwcPqme/X1XI9rONo1upWcs2mj9/vtd7AQAAAIHIL14GX7BgoepGNVSLu9q7df3mte8oY/cOfXPqhCzWSmrS4k4NeHKU6kQ2cLtntz4DtGzOX/TVV18pJiamvKMDAAAAuAGf39FwuVxK/iRZ7Tp3d/tuRtahDN3bd4Am/nmexr/4v3I4HFrwl//RldISt/vGduqm4OBgbdmypbyjAwAAALgJnweNnJwcFZw7pwbNWri9ZtxvZ+qeHg+qXoPGimrcTE+O+x+dzz+rnK8z3a5hsVoV2bCJ0tPTyzM2AAAAgB/h86Bx7S/6DZu4HzS+r7S4SJJUpdodHq2Lahyt1NS0cvcFAAAAcGM+f0fj9OnTCgoKVvXwWuVa73Q6tWbZfDWNuUuRDZt4tDY8oq4yM1Jls9nK1RsAAAAIRFar9ZbX+Dxo2Gw2WSyWcq9/b8kcnc7J1n//8XWP1wYHB+vy5UuaMWNGufsDAAAAgWbatGm3vMbnj05ZrVbZ7fZyrX1vyRwd2LNLz7w0WzVqRni8vqysTEHBPs9aAAAAwM+Oz/+WXa9ePTkcZbpYkO/241Mul0vv/99cZezeoWem/VU1a9crV++CvDNq0riJpk6dWq71AAAAAG7M50EjLi5OknTi2BG1cTNovLd4jtJTtujp56erckgVFV4okCRVrlJVVmslt3vnZmfq/h73uvWMGQAAAAD3+TxoNGjQQOE1ayrn6BG1ievq1podyeslSXP/OPG6z58c+7zu6fGgWzXsNptOnTimuLj/59G8AAAAAG7N50HDZDLpgfsf0LYd2/SLXw1169C+OSt/+iF7Gak7VFZWpt69e//kWgAAAACu5/OXwSVp3LixOpN7Qkf+tbfCeu7YvF49e/ZUTExMhfUEAAAAAoVfBI17771Xre68U59ufE8ul8vr/bIzD+no4S81fvx4r/cCAAAAApFfBA2TyaQ/T5+ug3t3a8/nn3q1l91u04pFs9WufXs9/PDDXu0FAAAABCq/CBqSNHDgQD3++ONa/X9zv91Fyhs+Xv135Z0+qeXLlimYMzQAAAAAr/CboCFJ8+fPV9UqIXrj1d+ppLjI8PppO7Yo+R/vatq0aWrTpo3h9QEAAABcZXJVxEsRHti7d6969OihmnXqa9SUv6hqtVBD6u7etlnvJM3SkMGDtXjxYpnNfpWxAAAAgJ8VvwsakpSWlqa+ffvKFGRRwqiJahnbsdy1SoqLtO6tJH2+ZaNGjBihpKQkBQUFGTgtAAAAgO/zy6AhScePH9fw4cO1detWde75C/Ud+KRq1q7n9npHWZn2p+7Q+rcX6UpxkWbPnqVRo0a5dU4HAAAAgJ/Gb4OGJLlcLi1atEgvvPCCCgsL1br9Pbq7R181ib5T1cNr/eB6u92m0yeO6cCeL7Tr0406fy5fffr00aJFi9SoUSMffAMAAAAgMPl10LimuLhY7777rubOm6f9+/ZJksLCa6p2vQYKtlaS0+lQUeFFnc45prKyMlWpUlVDhgzW2LFjFRsb69vhAQAAgAB0WwSNa1wul06ePKn09HSlp6crKytLpaWlCg4OVlhYmNq3b6+4uDjFxsYqJCTE1+MCAAAAAeu2ChoAAAAAbg/s8QoAAADAcAQNAAAAAIYjaAAAAAAwHEEDAAAAgOEIGgAAAAAMF+zrATyRl5enTZs2KT09XalpacrKytKV0lIFBQerRlgNdehwdXvbbt26KT4+nlPAAQAAAB+5Lba33blzpxYsWKBVq1bJZrOpTmQD1W8SrdqRDWS1VpLT6dSlwvPKzc7SyWNZKikuUouYGI0fN05Dhw5V9erVff0VAAAAgIDi10EjPz9f48eP16pVq1S7XpS69n5Id3fvq2qhNw8OTqdTRw9/qZTkDdr/xXaFh9dQYmKiBg4cWIGTAwAAAIHNb4PGhg0bNGLECJWUXtEjQ8crLr6XzGbPXim5UJCn95fMVUZqihISEpSUlMTdDQAAAKAC+GXQeOONNzR69GjdFddFCSOfU2hYeLlruVwu7fn8U723+HVFRzdX8ubNioiIMHBaAAAAAN/nd0Fj+fLlGjp0qO7t+7AeHTbB47sYN5N7/KgWvvyCmjRupG3//Cd3NgAAAAAv8qugkZGRoY4dO6rjvfdr0KhJhu8alXv8qOb+caL6P9RPK1asMLQ2AAAAgP/wm3M07Ha7hgwdqtqRDfTY8Ge9sjVtVKNmemz4s1q5cqXWrFljeH0AAAAAV/lN0Jg1a5a+/PJLPTHmeVksVq/1iYvvpdhO8RozZowuXrzotT4AAABAIPOLoGGz2fTaa6+pa+9+ati0hVd7mUwmPTb8GRUUnNfy5cu92gsAAAAIVH4RNNasWaO8vDzd1/e/KqRfWHiE2t7dTfPmz5cfvaICAAAA/GwE+3oASVr0xhtq0bqd6tZv5Nb12zevV0ryep3L+0aSVK9+Iz346GDd2f4et3vG9xmguX+cqJSUFHXr1q1ccwMAAAC4MZ/f0XA4HNq1c5dHISGsZi31//VIPT9joZ5/eYFa3NVeb7z6kk7nZLtdo1nLNgqpUlUpKSnlmBoAAADAj/H5HY3Dhw+rpKRYDTx4N6NNXNfr/vzQoBHasXmDsjMPql6Dxm7VMJvNqt+4udLT0z0ZFwAAAIAbfB409u3bJ0mq36R5udY7nQ7t3blNV66UqnGLOz1aG9W4udLS02Wz2crVGwAAAAhEVuutd4n1edA4f/68LBarQqpU82jdqRNf66+/e0ZldpsqVQ7R05P/qHr1G3tUo1pomL755hvNmDHDo3UAAABAIJs2bdotr/F50CgrK5M5yPNXRWpHNtAL/7tIJcVF2rfrM701/xU9+4e/ehQ2goKC5HQ6Pe4NAAAA4Mf5PGhUrlxZdptNTqdTZrP7gSM42KKIulGSpIZNW+jE0a+07cM1GjRqots1bFeuKPSOOzR16lSP5wYAAABwcz4PGs2bN5fT6VT+mVzVjmxQ7joul1NlZXaP1nxz6oSio6PdesYMAAAAgPt8vr1thw4dJEknvj7i9pr177yprIMZOnf2jE6d+Prff96vjt16e9Q7NztTHTt29GgNAAAAgFvz+R2N8PBwNWrcWNmZh9wOCpcLz+utBTN18XyBQqpUVWTDphr725lqGet+aLhceFHfnDqpuLi48o4OAAAA4CZ8HjQk6dGBA/XGm4v18JOjZHHjMaZfj3n+J/f8YtvHslaqpF/84hc/uRYAAACA6/n80SlJGjNmjC4VXtTeXdsqpJ/T6dTnn2xQwuOPq1atWhXSEwAAAAgkfhE0oqOj9cADD2jr+hWy271/eF56yhblnTmlsWPHer0XAAAAEIj8ImhI0qxZs5R3Jlcfr37Lq30KLxRo7bIFSkhIUJcuXbzaCwAAAAhUfhM0YmNj9fvf/16frF+h7MxDXunhdDq18o3XFFK5kubNm+eVHgAAAAAkk8vlcvl6iGvsdrvuu+8+HTh0WBNemu3RKd+34nK59N6SOUpJ3qB169apf//+htUGAAAAcD2/uaMhSRaLRRs3blTDBvU170+TDLuzYbfbtGLRbO3YvF5JSUmEDAAAAMDL/OqOxjUFBQXq16+fdqem6v4Bg9T30d/IYinf6d0njn6ld5Nm6eypHC1evFiDBw82eFoAAAAA3+eXQUO6+hjVzJkzNX36dEXUjVKv/glq36WHW+dsSNLpk9na/tE6fb51o2JjY7Vs6VLFxsZ6eWoAAAAAkh8HjWsyMjI0efJkJScn647Q6mrfpacat7hTDZq2UETdKJnNV5/+Kim+rJyvM5VzLFOH9n6hIwf2KaJ2bU187jlNmjRJFovFx98EAAAACBx+HzSuyczMVFJSklavXqPs7GOSJLPZLIvVKofDoTK7XZIUElJFXbp01qhRo/TII4/I6uYdEAAAAADGuW2CxncVFBRoz549Onr0qEpLSxUcHKywsDC1b99eMTExCgoK8vWIAAAAQEC7LYMGAAAAAP/mV9vbAgAAAPh5IGgAAAAAMBxBAwAAAIDhCBoAAAAADBfs6wHKq6SkRMePH/9216kaNWooMjJSJpPJ16MBAAAAAe+2CRoOh0Mffvih1q5dq9TUNB06dFAOh+O6a8Jr1lSnjh3VrVs3DRs2TPXr1/fRtAAAAEBg8/vtbYuKivT6669rYWKiTubkqH6jpmrYvJUaNG2hOpENZbFa5XQ6dbnwgnKOZerksSPKOpghu+2K+vfvr+eff15du3b19dcAAAAAAopfB41t27Zp2FNP6VTuKXWI76luDwxQw2Yxt1xXWlKstB1blJK8XrnHv9YzzzyjGTNmqGrVqhUwNQAAAAC/DBpOp1NTpkzRq6++quatYvXEmMmKqBtVrjqffbRWH6xYosjIelq/bp3atGnjhYkBAAAAfJffBQ2Hw6Fhw57S22+/pYefHKUe/R6T2fzTNsfKO5OrpX+brsKCs0pOTlanTp0MmhYAAADAjfhd0Bg3bpySkpI0eMJUxcX3MqxuSfFlJc38rc6fPaWUlBS1atXKsNoAAAAArudXQWP16tV67LHHNGjURHXt3c/w+sVFl/X6S8+qTkS4dn/xhSwWi+E9AAAAAPjRgX35+fkaO3as2t7dTV16/dIrPapUraYnx09RRkaGXnnlFa/0AAAAAOBHQWPKlCkqKb2iX434b68eutewaQvdP2CQ/vSnP+nYsWNe6wMAAAAEMr8IGufOndNbb7+tng89rtCwcK/36/PIr2WtVFlJSUle7wUAAAAEIr8IGkuXLpXD4VDnXr8o1/rkf7yrZxN6a/XS+W5db61UWZ2699Gbb76p0tLScvUEAAAAcHN+ETSW//3viu3UTXeEhnm89njWYaV88oEiGzb1aF38/f117tw5bd682eOet3TpkpSyXfpo49Wfly8Z3wMAAADwYz4PGiUlJTrwr38punU7j9deKS3R8nkv64lRE1Wl2h0era1dr77CwmsqNTXV474/atfn0l9fkZI/kr7YefXn7Feufg4AAAAECJ8Hjf3798vhcKhB0xYer31v8etq3b6zYmLjPF5rMpkU1Tja2KBx6KC06QPJ6ZRcrut/bvrg6u8BAACAABDs6wEOHDggSarXoLFH69JTtirnWJYmv7yg3L2jGjXVl7u3yWazlbvGdwVv2yqTySTTDY4mcZlMcn32qcqaNTekFwAAAOArVqv1ltf4PGgUFRXJWqmyLJZbD3vN+fyzWrNsvsa9+L+yuPElb6ZSSBWdLyjQjBkzyl3jmmCXSy+6bh5YTC6XTKdy9erLL6vMi9v3AgAAAN42bdq0W17j86BRHjnHjujSxQt6dcqYbz9zOp06eihD2z/+h/769kcym4N8OCEAAAAQ2HweNKpWrSrblVLZ7Ta372q0uKuDprz65nWfvbPwVdWOaqD7BwxyO2RcKSlWjfBwTZ061eO5b8S5ZJFMZ07f/NGpepF6/qmRhvQCAAAA/JnPg0br1q0lSadzstXQzRfCK4dUUWTDJtd9Zq1cWVWrhf7g8x+Te/xrtbnrLreeMXNL917Sirdu+CuTyyXTfT2N6wUAAAD4MZ/vOtW2bVsFBQUp5+sjFdrX5XIpNztTnTp1Mq5oqzulXzwkmc2SySSZg/7903z181Z3GtcLAAAA8GM+v6MREhKi1nfdpcwD+xR//0PlrvPstL96dP3Z0yd1oeCcsUFDkjp3le5qI2XslwovSqHVpdi2kofnfAAAAAC3M58HDUkaMniwpkydqkuFF8p1Onh5pHyyQTVr1lSfPn2ML17tDqlrN+PrAgAAALcJnz86JUnDhg1TUFCQdm3dVCH9bFdKlbpts55++mlVrly5QnoCAAAAgcQvgkbNmjX1myef1KcfrFLhhQKv99u89h3ZrpRq9OjRXu8FAAAABCK/CBqSNHPmTIVUrqRVb/5NrhtsD2uUE0e/0ifrV+ill15Skybu71AFAAAAwH1+EzRq1aqlxMREZaSmaOfWD73So/jyJb294BXFxsbqhRde8EoPAAAAAH4UNCRp4MCBGjt2rFa9+Telp2w1tHZJ8WUt+t8XVVpUqHffeUcWi8XQ+gAAAAD+wy92nfquuXPn6tKly1o+92VdLMhXj36PyWz+aXko70yulv5tugoLzio5OVktW7Y0aFoAAAAAN+J3QSMoKEjLli1VvXp19eqrr+pf6Tv1xJjJiqgb5XEtp9Opzz5aqw9WLFFkZD1t375dbdq08cLUAAAAAL7L5PLmm9c/0bZt2zTsqaeUm5urDl176d4+A9SwWcwt15WWFCt1+ydKSV6vUyeO6dlnn9XLL7+sqlWrVsDUAAAAAPw6aEhSUVGR5syZowULF+pkTo6iGjVVw2Yt1bBpC9WOaiirtZKcTocuXbygk8cylXMsU0cPZchuu6IBAwZo8uTJ6tq1q6+/BgAAABBQ/D5oXONwOLRp0yatXbtWqalpOnjwgBwOx3XX1KxVSx3j4tStWzcNGzZM9evX99G0AAAAQGC7bYLG95WUlOjEiRMqLS1VcHCwwsLCFBkZKZPJ5OvRAAAAgIB32wYNAAAAAP7Lr87RAAAAAPDzQNAAAAAAYDiCBgAAAADDETQAAAAAGM7vTgZ3R0FBgfbs2aOsrKxvd52qUaOG2rVrp5YtWyooKMjXIwIAAAAB7bYJGpmZmUpMTNTqNWt0PDtbkmQ2m2WxWuV0OGW32yRJISFV1KVLZ40cOVIDBw6U1Wr14dQAAABAYPL77W0zMjI0adIkffLJJ7ojtLrad+2lxtGt1LBpC9WqGyWz+erTXyXFl3XyWJZyvj6ig3u/0JED+xQREaGJEydq0qRJslgsPv4mAAAAQODw26Bht9s1c+ZMTZ8+XRF1o9RrwCC179xdFjfvUJw+ma3tH6/T51s2KjY2VsuWLlVsbKyXpwYAAAAg+WnQKCgoUL9+/bQ7NVUPPPyE+gx8UhZL+R6BOnH0K72bNEtnT+Vo8eLFGjx4sMHTAgAAAPg+vwsaBQUFuq97d53IOamRz/9ZjaNb/eSadrtN7y+Zo51bN2nRokUaOXKkAZMCAAAAuBm/ehncbrerX79+OpFzUhNemq169RsbUtdisWrQqEkKCrZo9OjRqlu3rvr3729IbQAAAAA/5FfnaMycOVO7U1M18vk/GxYyrjGZTHrsqWd0V1wXjRgxQvn5+YbWBwAAAPAffhM0MjIyNH36dN0/YJAhj0vdiNlsVsLI51RSekUTJkzwSg8AAAAAfhQ0Jk+erIi6Uer76G+82ic0LFyPDB2nlStXaufOnV7tBQAAAAQqvwgamZmZSk5OVq8Bg8q9u5Qn4uJ7K6JupBYuXOj1XgAAAEAg8ouXwRMTE1UttLrad+7u1vUfvrdMH72//LrPakc20O9eW+rWerPZrK7399fKlf+nv/71r6pVq5anIwMAAAD4EX4RNFavWaMOXXu5fRifJNWr31jjf//qt382m4M86nlP975a91aSNm3aZOzZGk6n9NUhKT1VunhRql5diuskxbSSzH5xAwkAAADwOp8HjYKCAh3Pzlb3/r/2aJ05KEihYeHl7lsttLrqRNZXenq6cUHD4ZDeWyEdOiCZTJLLJeWdlTKPSK1aS78aJAV5FogAAACA25HPg8aePXskSQ2btvBoXd6ZXP1uzOOyWKxqHH2n+v96hMJr1fGoRlTjaKWlpXm05kft+vxqyJCuhozv/jx04Orv4+81rh8AAADgp3weNLKysmQ2m1WrbpTbaxo3b6knx/6PakfWV+H5Am1avVyvT/t/mjprsSqHVHG7Tp3Ihkr/bJNsNlt5Rr+eyyXLrhRJkulGv5akXSmyd7z76t0OAAAA4DZldeOVB58HjdLSUlmsVpk9eH/hzvb3fPvvUY2aqVF0K/1h/K+1d+c/1aXXL92uY61USYWXLmnGjBkezXzDWi6XprpuHlhMklRYqNkzZshG0AAAAMBtbNq0abe8xudvJwcHB8vpcP6kGlWqVlPtevWVd+aUR+scDodHAefHlEm61bdw/vs6AAAA4OfO53c0atSoIbvdppLiywqpUq1cNa6Ulij/m1PqdN/9Hq27XHhBderU0dSpU8vV9wfeXyHXka9kuvZexne4TCYppqVeeDTBmF4AAACAH/N50GjXrp0k6eSxLEW3bufWmn/8PVGt47oovFYdXTx/TpveWyqT2awO8b086p2bnaWOcXFuPWPmll4PSEezru4+9d2wYTLJFBQkU8/7jesFAAAA+DGfB42WLVsqJKSKcr4+4nbQuHAuT8vm/EVFlwpVLbS6msXcpYl/nqc7QsPc7ut0OnUyO0sjhjxRvsFvpG49adjT0ro1V7e1vaZWhPTwwKu/BwAAAAKAyeW6wXM+Fax37946+U2BJrw0u8J6Zh7cr7l/nKjt27erW7duxhZ3uaTTp6TCQik0VKoXyU5TAAAACCg+fxlckkaOHKkjB/bpzMnjFdYzZfN6tYiJUXx8vPHFTSYpMkpq2erqT0IGAAAAAoxfBI2BAwcqIiJCn338jwrpd6EgT/t379CE8eNlIgQAAAAAhvOLoGG1WvXcc8/p8y0bdeLrI17t5XK59P6SuQoPr6EhQ4Z4tRcAAAAQqPwiaEjS5MmT1aZNG72b+KrsdgNO6r6J9JStykhNUWJioqpXr+61PgAAAEAg85ugYbFYtHzZMp09laP3l8yRN95Rzz1+VO8vmaOEhAQNHDjQ8PoAAAAArvKboCFJsbGxWrx4sXZu3aT3lsyR0/nTTgz/rtzjR7Xw5RcU0yJaSUlJhtUFAAAA8EM+P0fj+wYPHqzS0lKNHj1aFwvylTDyOYWGhZe7nsvlUnrKVr2/ZI5iWkTr448/5pEpAAAAwMv84hyNG9mwYYNGjBihktIremToOMXF95bZ7NkNmAsFeXp/yVxlpKYoISFBSUlJhAwAAACgAvht0JCk/Px8TZgwQStXrlTtelHq0vsh3dO9r6qF3jwsOJ1OHT38pVI2r9f+3TsUHl5DiYmJvJMBAAAAVCC/DhrX7Ny5UwsXLtTKlStls9lUJ7K+ohpHq05kQ1krVZLD4dDlwgvKzc7SyewslRQXqUVMjCaMH68hQ4ZwFwMAAACoYLdF0LgmLy9PH330kdLT05WalqasrCxdKS1VUHCwwqqHKS6ug+Li4hQfH6/4+HgO4wMAAAB85LYKGgAAAABuD361vS0AAACAnweCBgAAAADDETQAAAAAGI6gAQAAAMBwBA0AAAAAhgv29QCecLlcysnJUXp6utLT05WVlaXS0lIFBwerRo0aateuneLi4tS2bVuFhIT4elwAAAAgYN0W29sWFxfrnXfe0bz587V/3z5JUlh4LdWObKBgi1Uup1NFly7o1IljKisrU5UqVTV48G80duxYtW3b1rfDAwAAAAHIr4OGy+VSUlKSpkyZosLCQrXu0Fn3dO+rxtGtVD281g+ut9ttOp2TrQPpu7Tr0406fy5fffr00aJFi9SoUSMffAMAAAAgMPlt0Dh+/LiGDx+urVu3qkuvX6rPI0+qZu26bq93lJUpIzVF695O0pXiIs2ePUujRo3itHAAAACgAvhl0EhLS1Pfvn1lCrJo0KhJiomNK3etkuIirXsrSZ9v2ajhw4dr0aJFCgoKMnBaAAAAAN/nd0Fj79696t69h2rVra9RU/6iqtVCDam7e9tmvZM0S0MGD9bixYtlNrPhFgAAAOAtfrXrVH5+vh588EHVrBOpMb+dqZAqVQ2rfXf3PjIHBWnZvBlq3ry5XnzxRcNqAwAAALieX93RSEhI0IebPtKUWYsVGhbulR4frFisTz94T2lpaYqNjfVKDwAAACDQ+c3zQ2vWrNGqVav06FPPeC1kSFLfRwerdmQDDRk6VGVlZV7rAwAAAAQyvwgaLpdLv/v973Vn+7vVoWtPr/ayWKxKGDlR+/ft07p167zaCwAAAAhUfhE0tm/frkMHD6pnv19VyPazjaNbqVnLNpo/f77XewEAAACByC9eBl+wYKHqRjVUi7vau73mQkGe1r/9hg7u2y37lSuqVTdKT459Xg2bxbi1vlufAVo25y/66quvFBPj3hqPOJ2SzSZZrRI7XAEAACDA+DxouFwuJX+SrLt7/NLtuxnFly/pby/9t6LvbKexU2eqWmh1nT2dq5Cqd7jdN7ZTNwUHB2vLli3GBo2iy9K2T6W96f8JGu3jpO49parVjOsDAAAA+DGfB42cnBwVnDunBs1auL3mk/UrFFYzQk+O+59vP6tZu55HfS1WqyIbNlF6erpH635U0WXpjUTpwnnp2mZeNpu0e5d05Ctp5BjCBgAAAAKCz4PGtb/oN2ziftD4Mu1ztWrbSUv++kdlHcpQ9fBaurfPAHXt3c+j3lGNo5WamubRmh+17dPrQ8Y1LtfVzz/7p/SLh4zrBwAAAPgpnweN06dPKygoWNXDa7m95tzZ09qRvF49+z2mBx75tU4c/Uqr/2+egoKDdU/3vm7XCY+oq8yMVNlstvKMfj2nU5Y96TLd7FgSl0uu9DTZe97POxsAAAC4rVmt1lte4/OgYbPZZLFYPFrjcrrUoFkL9X/iaUlSgybROp2TrZTkDR4FjeDgYF2+fEkzZszwqP+NWF0uTXX9eGAx2W2aPXOmbBWwsxYAAADgLdOmTbvlNT7/X+tWq1V2u92jNaE1wlU3qtF1n9WJaqjz+Wc9qlNWVqagYGOyll3SlVtcc+Xf1wEAAAA/dz6/o1GvXj05HGW6WJDv9uNTTWPu0tnTOdd9lnf6pGpE1PGod0HeGTVp3ERTp071aN3NBG3eJFfa7hs+PuUymRTc8W5N6fMLQ3oBAAAA/sznQSMuLk6SdOLYEbVxM2j0+OWjeu2lZ7V57dtq36WHjmcd1udbNiph5HMe9c7NztT9Pe516xkzt/TsLWVl/vCFcJNJprAaCurZW0FG9QIAAAD8mM8fnWrQoIHCa9ZUztEjbq9p1Lylnp70R6WnfKoZk0fo49VvaeDQcep07/1u17DbbDp14ti3QccQVatd3cL2ni5Xz8+Qrv68pwtb2wIAACCgmFyum22TVHEGDXpC23Z8rqmzl7h9aN9PlZ6yVcvm/EWHDx/mZHAAAADAYH7xN+Bx48bqTO4JHfnX3grruWPzevXs2dM7IUO6Gi4qVyZkAAAAICD5xd+C7733XrW68059uvE9VcQNluzMQzp6+EuNHz/e670AAACAQOQXQcNkMunP06fr4N7d2vP5p17tZbfbtGLRbLVr314PP/ywV3sBAAAAgcovgoYkDRw4UI8//rhW/99cFV4o8Fqfj1f/XXmnT2r5smUKNugMDQAAAADX85ugIUnz589X1SoheuPV36mkuMjw+mk7tij5H+9q2rRpatOmjeH1AQAAAFzlF7tOfdfevXvVo0cP1axTX6Om/EVVq4UaUnf3ts16J2mWhgwerMWLF8vMS9oAAACA1/hd0JCktLQ09e3bV6YgixJGTVTL2I7lrlVSXKR1byXp8y0bNWLECCUlJSkoKMjAaQEAAAB8n18GDUk6fvy4hg8frq1bt6pzz1+o78AnVbN2PbfXO8rKtD91h9a/vUhXios0e/YsjRo1qsLO6QAAAAACmd8GDUlyuVxatGiRXnjhBRUWFqp1+3t0d4++ahJ9p6qH1/rB9Xa7TadPHNOBPV9o16cbdf5cvvr06aNFixapUaNGPvgGAAAAQGDy66BxTXFxsd59913NnTdP+/ftkySFhddU7XoNFGytJKfToaLCizqdc0xlZWWqUqWqhgwZrLFjxyo2Nta3wwMAAAAB6LYIGte4XC6dPHlS6enpSk9PV1ZWlkpLSxUcHKywsDC1b99ecXFxio2NVUhIiK/HBQAAAALWbRU0AAAAANwe2OMVAAAAgOEIGgAAAAAMR9AAAAAAYDiCBgAAAADDETQAAAAAGC7Y1wN4Ii8vT5s2bVJ6erpS09KUlZWlK6WlCgoOVo2wGurQ4er2tt26dVN8fDyngAMAAAA+cltsb7tz504tWLBAq1atks1mU53IBqrfJFq1IxvIaq0kp9OpS4XnlZudpZPHslRSXKQWMTEaP26chg4dqurVq/v6KwAAAAABxa+DRn5+vsaPH69Vq1apdr0ode39kO7u3lfVQm8eHJxOp44e/lIpyRu0/4vtCg+vocTERA0cOLACJwcAAAACm98GjQ0bNmjEiBEqKb2iR4aOV1x8L5nNnr1ScqEgT+8vmauM1BQlJCQoKSmJuxsAAABABfDLoPHGG29o9OjRuiuuixJGPqfQsPBy13K5XNrz+ad6b/Hrio5uruTNmxUREWHgtAAAAAC+z++CxvLlyzV06FDd2/dhPTpsgsd3MW4m9/hRLXz5BTVp3Ejb/vlP7mwAAAAAXuRXQSMjI0MdO3ZUx3vv16BRkwzfNSr3+FHN/eNE9X+on1asWGFobQAAAAD/4TfnaNjtdg0ZOlS1IxvoseHPemVr2qhGzfTY8Ge1cuVKrVmzxvD6AAAAAK7ym6Axa9Ysffnll3pizPOyWKxe6xMX30uxneI1ZswYXbx40Wt9AAAAgEDmF0HDZrPptddeU9fe/dSwaQuv9jKZTHps+DMqKDiv5cuXe7UXAAAAEKj8ImisWbNGeXl5uq/vf1VIv7DwCLW9u5vmzZ8vP3pFBQAAAPjZCPb1AJK06I031KJ1O9Wt38jtNX+Y8GsV5H3zg8+79Rmgx0f89y3Xx/cZoLl/nKiUlBR169bNo3lvyeWSTp+SCgul0FCpXqTkhXdOAAAAAH/l86DhcDi0a+cu9X10sEfrJr28QC6n89s/nz5xTPP/8j9q37m7W+ubtWyjkCpVjQ8aOSekdWukvLP/+SyitvTwQKlBQ+P6AAAAAH7M549OHT58WCUlxWrg4bsZd4SGKTQs/Nt//rVnl2rViVTzO9u6td5sNqt+4+ZKT08vz9g3dua0tPRNKT/v+s/z865+fua0cb0AAAAAP+bzOxr79u2TJNVv0rzcNcrK7Erb8Yl69nvMo21xoxo3V1p6umw2W7l7f1fw1mSZHA6Zvv/eh8sll8Mh16efqOzRBEN6AQAAAL5itd56l1ifB43z58/LYrEqpEq1ctfISE1RSdFl3dO9r0frqoWG6ZtvvtGMGTPK3fsas8ulF1023SzmmFwuuQ4f0isvvywn72sAAADgNjZt2rRbXuPzR6fKyspkDvppY+zaukmt2t2t6uG1PFoXFBQk53fe8/gpgnXr/5hm+UGyAwAAACqAz//eW7lyZdltNjmdTpnNngeOgrxv9NWXezRi0h88Xmu7ckWhd9yhqVOnerz2B1wuuea9JhUW3vCuhkuSQkM1acJz7EAFAACAnz2fB43mzZvL6XQq/0yuakc28Hj9rn9+pDuqh6l1h84er/3m1AlFR0e79YyZWzrHS5s33fBXpn//3lqpkjG9AAAAAD/m80enOnToIEk68fURj9c6nU598c+PdHf3PgoKCvJ4fW52pjp27Ojxupvq3FVq1frqv1+7a3HtZ6vWV38PAAAABACf39EIDw9Xo8aNlZ15SB279fZo7Vdf7tH5/LPq3ONBj/teLryob06dVFxcnMdrbyooSHr8Cemrw1J6qnTxglQ9TIrrJMW0lMrxaBgAAABwOzK5XN/fi7XiTZo0SW+8uVh/mL9CFqMeY7qFLRtWadN7S5V78qRq1fLsJXIAAAAAP84v/hf7mDFjdKnwovbu2lYh/ZxOpz7/ZIMSHn+ckAEAAAB4gV8EjejoaD3wwAPaun6F7HZjDs/7MekpW5R35pTGjh3r9V4AAABAIPKLoCFJs2bNUt6ZXH28+i2v9im8UKC1yxYoISFBXbp08WovAAAAIFD5TdCIjY3V73//e32yfoWyMw95pYfT6dTKN15TSOVKmjdvnld6AAAAAPCTl8Gvsdvtuu+++3Tg0GFNeGm26tVvbFhtl8ul95bMUUryBq1bt079+/c3rDYAAACA6/nNHQ1Jslgs2rhxoxo2qK95f5pk2J0Nu92mFYtma8fm9UpKSiJkAAAAAF7mV3c0rikoKFC/fv20OzVV9w8YpL6P/kYWS/m2vT1x9Cu9mzRLZ0/laPHixRo8eLDB0wIAAAD4Pr8MGtLVx6hmzpyp6dOnK6JulHr1T1D7Lj3cPmfj9Mlsbf9onT7fulGxsbFatnSpYmNjvTw1AAAAAMmPg8Y1GRkZmjx5spKTk3VHaHW179JTjVvcqQZNWyiibpTM/z5tu6T4snK+zlTOsUwd2vuFjhzYp4jatTXxuec0adIkWSwWH38TAAAAIHD4fdC4JjMzU0lJSVq9eo2ys49JksxmsyxWqxwOh8rsdklSSEgVdenSWaNGjdIjjzwiawWdNA4AAADgP26boPFdBQUF2rNnj44eParS0lIFBwcrLCxM7du3V0xMjIKCgnw9IgAAABDQbsugAQAAAMC/+dX2tgAAAAB+HggaAAAAAAxH0AAAAABgOIIGAAAAAMMRNAAAAAAYjqABAAAAwHAEDQAAAACGI2gAAAAAMBxBAwAAAIDhCBoAAAAADEfQAAAAAGA4ggYAAAAAwxE0AAAAABiOoAEAAADAcAQNAAAAAIYjaAAAAAAwHEEDAAAAgOEIGgAAAAAMR9AAAAAAYDiCBgAAAADDETQAAAAAGI6gAQAAAMBwBA0AAAAAhiNoAAAAADAcQQMAAACA4QgaAAAAAAxH0AAAAABgOIIGAAAAAMMRNAAAAAAYjqABAAAAwHAEDQAAAACG+/8wvp0ioWI4NwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = Qinit(8) + Qmask(\"right\")\n",
    "plot_motif(mask[1])\n",
    "plot_circuit(mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "1b59cba4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = Qinit(8) + Qmask(\"01\")\n",
    "plot_motif(mask[1])\n",
    "plot_circuit(mask)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "6bf655a7",
   "metadata": {},
   "source": [
    "This might be easier to see with a circuit and a mask between two cycles. We'll use the following 2 qubit unitaries for the cycles:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "a8892ecc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = Qinit(8) + Qcycle(mapping=u0_2) + Qmask(\"01\") + Qcycle(mapping=u0_2)\n",
    "plot_circuit(mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "7aea986d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = Qinit(8) + Qcycle(mapping=u0_2) + Qmask(\"right\") + Qcycle(mapping=u0_2)\n",
    "plot_circuit(mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "5d9db704",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = Qinit(8) + Qcycle(mapping=u0_2) + (Qmask(\"1*1\") + Qcycle(mapping=u0_2))*3\n",
    "plot_circuit(mask)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "ad2ada58",
   "metadata": {},
   "source": [
    "#### Masking with a mapping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "0e340760",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ass3qLQaAHScyueyduXh5eXHw4EE6drT9JnpjUlBQUH1Xtvz8fO2jbqC0tDSio6MxDIPtDz1Ar4jwWp//3+07+PHIMR69oi+xYf87nnM8L58Ri5awNeME4y/tzvu33lzrfM6UlBDz5kyyC4v49NNPufnm2p8vF6ZjDA0wY8YMACb2jqtTFIrKynho+Uq6h4Xy+JVX1Hm5vSLCGdopioqKCmbNmlXn6UXsadasWRiGwbWdoi4aBYB7L+vFOyOHWUQBoE2zpvx72PUAfLJnH6Vmc63zad6kCQ/EXQb8b92U+lEY6unAgQN8/fXXmEzwUHxcnab9+7ofOHg6h7eH34ivd/3+EyQm9AFg9uzZlJeX12seIrZWXl7OnDlzAEjs26fB87usdQQAJWYzJ8+e1Fabh+J7YzLBV199VX3VAak7haGe1q1bB1Re5sLaM5qhcjfQKxs2cV9cLwZ0bF/v5d90SRea+fmRlZXFnj176j0fEVvavXs3WVlZNPPzY1TXhl/G5eDpHAB8vbxoGeB/0ed3CglmQPvK9eq7775r8PIbK4WhnpKTkwG4vK313wqqMAwmfrGCYP8m/PPaaxq0fB8vL3qf/TRVNRYRZ6v6XezTpjU+Nrh8y+sbNwNwY+domlh5MLnv2UtsaL2oP4WhnpKSkgBIiLT+NPw3NyWxOf04L107hFaBgQ0eQ8LZFaBqLCLOVr1etGn45SlW/PwLc7dux9fLi+cGD7R6Oq0XDacw1NPBgwcBiLXyrNjDubn8+dvvGNSxA7+J62WTMXQ/e7Cuaiwizla9XoQ17GzxvdknuXvpFxjAS9cNqT7WYA2tFw2nMNRTcXExAEG+vlY9/7crvqLUbObtETfabAxVyy4quvhBORFHqFovmvpZt17U5NiZPG587wNOFxcztd/lPHJF3zpNr/Wi4XQGSD1VnQlrYN1pIMt+/oVgf38mL//S4ufFZ79RdCwvn8H/fQ+AxbfdTOuz36uvTdWydSlucRXV60U9z446VVTE9e8t5lBuLvfF9eLl64bUeR4VhtaLhlIY6ikoKIi8vDxyi62/0mlOcTHrDh2u8bHi8vLqx4qt/PppztllB9rgeIWILVSdHJhzdsuhLvJLSxn23gfszsrm1m6XMHvksHpdiiS3ROtFQykM9RQbG0tGRgbbT2RadaMR4681X9wrLSeHTm/MrNOZz1Wq7vTWvXv3Ok0nYi+xsbEsW7bM4i6E1igpL+fmxR+xKf04N8R0YtFtN+Ndz0/8Wi8aTtta9RQfHw9A8nHnXQM++fhxi7GIOFt91gtzRQXjP/mMNWmHGNChPZ/cfht+3t71HoPWi4bTFkM9Vf3SrT9y1CnLzyspYceJLIuxiDhb1e/i9hOZ5JWU0MyKS8W8tTmZpXv3A5W3wk1csarG57183RBCrdg99OORYxZjkbpTGOpp6NCh+Pn5sf1EJsnpx62+b62tvLczhVKzma5duxIdHe3QZYtcSExMDF27dmX//v28v2s3D8X3vug0p4v+dzyiKhA1+dugqy8ahqT042w/kYmfnx9DhtT9wLVUUhjqKSwsjDFjxvD+++8zI2kLc28aUa/5RAUHX/D4w4UYhsGMpC0ATJkyRfcKEJdhMpmYPHkyU6dOZUbSFib1ibvo7+ffBg/gb4MH2GT5VevF2LFjCQsLs8k8GyMdY2iAxMREAN7ftZu0nByHLXflLwfYmZlFQEAA9957r8OWK2KN3/zmNwQEBLDjRCYrf3HchezScnJYtGs38L91U+pHYWiA/v37M2DAAIrLy5n4xUoccWuL3OJiHjp7LsTkyZMJscNtREUaIiQkhMmTJwPw0PIvya3HV1fryjAMHvh8BcXl5QwYMIArr7zS7sv0ZApDA5hMJubOnUtAQACrU9OYtWWb3Zc59avVHD2TR0xMDM8995zdlydSH8899xwxMTEcPZPHY1+vsfvy3kneypq0QwQEBDBv3jztXm0ghaGBunTpwosvvgjAI6u+5tvUQ3Zb1usbNzNv2w5MJhPvvvuu7jQmLisoKIh58+YBMHfrdt44e5VUe1iTmsYjq74BYPr06XTu3Nluy2osFAYbePjhhxk9ejQl5WZGLv6Qrw+k2nwZr2/czKNnf/mfffZZBgywzcE6EXsZOHAgzz77LACPrPrGLnH4+kAqoxZ/RKnZzOjRo3n44YdtvozGSPd8tpGSkhJuueUWvvzyS3y9vfj7oAH8sX+/Bl+TPre4mKlfrWbeth0A/PGPf+T//u//tKlsQ7rns/0YhsGf/vQnXnrpJQDuj+vFq9cPpYX/xW+6U5vyigpe+nEDz6z7njJzBTfeeCOffvopTepwi125MIXBhkpKSrj33nv54IMPgMp7NcwdNcKq+96eyzAMVv5ygIeWf8nRM3lA5X7bp59+WlGwMYXBvgzD4IUXXuAvf/kLAO2aN+OdETcyrHNMvX6Xd5zI5IEvlpOUXnl29R133MH8+fPx8/Oz6bgbM4XBxgzDYP78+TzyyCPk5uYCMLRTFIkJfbjpki4X3YLIKynhvZ0pzEjaws7MyjObY2JimDdvHgMH/u9mJV988QV///vfmThxIhMmTNCbWQMoDLZTUFDAggULmDNnDs888wyjRo2qfuy7777jvvvuq75PQs/wMBIT+nBXzx4XPUO6vKKCz/btZ8bmLaxJqzyOFxwczOuvv86ECRP0YcnGFAY7OXbsGI8++igff/xx9ddYm/n50bt1BAmRbegeFkqQry8GBjnFJZVnUB8/zo4TWZSazQAEBAQwefJknnvuufPerBISEqpvXejv78/IkSO5/fbbGT58uN7Y6khhaJiCggJWrFjBkiVLWLZsWfU9GeLj48+7i1pBQQF/+ctfePvtt6vvl+Dn7U2viDDi27Thsohwgv2bYMJEQVkZu7OySUo/ztaME+SVlgKVl9O+9dZbef3114mMtP7WulIHhthVWlqaMW3aNCMsLMwArPrTtWtX47XXXjNOnTp1wfnOnDmzxmkDAgKMMWPGGEuWLDHy8/Md+ErdV35+fvW/n/7NrJOfn28sWbLEGDNmjBEQEFDj7+LMmTMvOP2pU6eM1157zejatavV60V4eLgxbdo0Iy0tzYGvtHHSFoODlJeXs2fPHpKTk0lKSuLgwYMUFRXh5eVFYGAg3bt3Jz4+nvj4eKKjoy+6aVxQUEBoaGj1p7OaBAQEMGLECG6//XZGjBih69NfgLYYrFNYWMjy5ctZsmQJy5cvr/UOaQEBAWRlZV3039IwDA4ePEhycjLJycns3r2bwsJCKioqCAgIIDo6moSEBOLj44mNjcXHR1fxcQSFwY2NHTuWjz76yKrnduvWjd27d2tfbA0UhoszDIPY2Fj27dtn1fPHjh3LkiVL7DwqsRedx+DGbr/9dqufGxgY6JBLdohnMgyjTsEcO3asHUcj9qYtBjdWUFBAWFjYRW96Hhsby7fffktERISDRuZetMVgnRMnTnDNNdewZ8+eWp8XGBhIZmam/h3dmLYY3FhQUBAjRtR+uW9FQWwlIiKCb7/9ltjY2FqfN2LECEXBzSkMbq623Um+vr4sXLhQURCbiYiIYOHChfj6+l7wOdqN5P60K8nNXWh3kq+vL2VlZURHR7N27Vrat2/vpBG6Pu1Kst6RI0cYPHgwBw8erP4d+zXtRvIM2mJwczXtToqNjWXDhg1ER0dz8OBBBg8ezJEjR5w0QvEUv45CdHQ0GzZsOG+3knYjeQaFwQP8endS1TGFPn36sHbtWsVBbOLcKKxdu5Y+ffqcd8xBu5E8g3YleYDCwkLi4+MJDAxkxYoVFscUalqhtVvJknYl1e5iv0MnTpxg+PDhFBYWkpycrBMpPYDC4CEMw8AwDLxquEif4lA7heHCrP3dqaiowGQy6QRKD6FdSR7CZDLVGAWA9u3ba7eS1FldPlB4eXkpCh5EYWgkFAepC21lNm4KQyOiOIg1FAVRGBoZxUFqoygIKAyNkuIgNVEUpIrC0EgpDvJrioL8msLQiCkOAoqCnE9haOQUh8ZNUZCaKAyiODRSioJciMIggOLQ2CgKUhuFQaopDo2DoiAXozCIBcXBsykKYg2FQc6jOHgmRUGspTBIjRQHz6IoSF0oDHJBioNnUBSkrhQGqZXi4N4UBakPhUEuSnFwT4qC1JfCIFZRHNyLoiANoTCI1RQH96AoSEMpDFInioNrUxTEFhQGqTPFwTUpCmIrCoPUi+LgWhQFsSWFQepNcXANioLYmsIgDaI4OJeiIPagMEiDKQ7OoSiIvSgMYhOKg2MpCmJPCoPYjOLgGIqC2JvCIDalONiXoiCOoDCIzSkO9qEoiKMoDGIXioNtKQriSAqD2I3iYBuKgjiawiB2pTg0jKIgzqAwiN0pDvWjKIizKAziEIpD3SgK4kwKgziM4mAdRUGcTWEQh1IcaqcoiCtQGMThFIeaKQriKhQGcQrFwZKiIK5EYRCnURwqKQriahQGcarGHgdFQVyRwiBO11jjoCiIq1IYxCU0tjgoCuLKFAZxGY0lDoqCuDqFQVyKp8dBURB3oDCIy/HUOCgK4i4UBnFJnhYHRUHcicIgLstT4qAoiLtRGMSluXscFAVxRwqDuDx3jYOiIO5KYRC34G5xUBTEnSkM4jbcJQ6Kgrg7hUHciqvHQVEQT6AwiNtx1TgoCuIpTIZhGM4ehEh92OqNuKCggKZNmwKQn59PUFCQ08Yirqe0tJTNmzeTnJxMUlISu3fvpqCggIqKCvz9/YmKiiI+Pp74+Hj69etHq1atnD3kBlMYxK3Z4g25oWFQFDzToUOHmDVrFnPmzCEzM9OqaXx9fRk7diyJiYn0798fk8lk51Hah8Igbq+hb8wNCYOi4HlOnTrFH/7wBxYuXEhFRQUAYYGBXNE2koTI1lwWEUGIvz9eJhOFZWXsyc4m+XgGm9OPs+/kqer5JCQkMGvWLHr37u2sl1JvCoN4hIa8Qdc3DIqC5/n888956KGHyMjIAGBopygSE/owqmtnfL29Lzp9cvpxZiZv5f2dKRSVl+Pj48O0adN4+umn8fPzs/fwbUZhEI9R3zfq+oRBUfAshmHwxBNP8PLLLwPQLbQV7940gn7t2tZrfifyC/jtylV8vGcfAFdccQUrVqygZcuWNhuzPXlcGEpLS9mzZw85OTl4e3sTGRlJp06d3HZfn9RNfd6w6xoGRcGzGIZBYmIib7/9NgCPX3kFz10zEH8fnwbPd8nuPUxZvorTxcX07NmTb7/91i0OTntEGHJzc5k/fz4LFy5k27ZtlJaWWjweEhLC1VdfzYMPPsjw4cPxtmKTUNxXXd+46xIGRcHzTJs2jenTp+NlMjFn1HDui+tl0/mnZGZx3cLFHM/Pp2/fvqxdu5bAwECbLsPW3DoMZrOZV199lb/97W8UFhZW/zzY35+IoEDMhsHh3DOUms3Vj8XExDBr1iyGDBnijCGLg9TlDdzaMCgKnmfNmjUMHToUgDmjhvNA78vsspzdWdkM/M9CThYVMXXqVF555RW7LMdW3DYM6enp3HbbbWzYsAGAHmGhlJjN/HLq9AWnaernS35pGQC///3vefXVV7X14MGsfSO3JgyKgufJy8ujZ8+eHDp0iMnxvZk54sZan5+cfpyvD6axKT2dTceOcywvDwDjr09Ztbzl+39h5OIPMZlMfP/991x11VUNfg324pZhOHbsGAMHDuTgwYM0b9KEV68fyv1xvbhm/vusO3SY22IvoWkN3wCYHB/H/B27mJm0FYBx48axcOFCxcGDWfOGfrEwKAqe6dFHH+X111+nY4sW7Jz8AM2aNKn1+bd88BGf7fv5vJ9bGwaA33y2jP9u30nXrl1JSUnBp4HHMezFNUdVi9LSUkaOHFm5koYE8/Xd44gOCbF4zsvXDSEqOLjG6fu1a8fQTlGM/+QzFi9eTFRUFNOnT3fAyMUZqi6fUfXGPnjw4Dq9sSsKniknJ4dZs2YB8PaIGy4aBYAr27WlV3g4fSPb0LdtG6Jen0HJr3ZTW+NfN1zL8p9/Yf/+/XzxxReMHj26XuO3N7e7VtILL7zAtm3bCA0MYM2EO8+LgjVui+3G/JtHAfDPf/6TjRs32nqY4kLqe20lRcF1GYZBQ3Z2zJ8/n6KiIi4ND+OGmGirpvnTVVfy7DUDGXVJF1qf3cKsq2B/fx7sHQfAjBkz6jUPR3CrMBw+fJgXX3wRgH8Pu4GOwS3qPa9xl3bnrp49qKio4OGHH7bVEMVF1TUOioJre/TRRwkJCeGpp54iOzu7TtMahsHMmTMBSEzo4/Cvsj8U3xuTCb755hv279/v0GVby63CMGvWLMrLyxnUsQO394i94PPmbt1O4oov+d3KVbyxcTOHc3NrfN6r1w/Fz9ubzZs3s3nzZnsNW1yEtXFQFFzf2rVryc3N5R//+AdRUVF1CsSxY8fYu3cv3iYTd/XsYeeRnq9jcAuGREUBsHr1aocv3xpuEwbDMHj33XcB+F3f+Fqf+/z3PzIzaSv/3ryFR1Z9Q+c33+a5734473nhQUHc3r0bAPPmzbP9oMXl1BSHo0ePVj9+9OhRRcHNFBQU1CkQycnJAPQID6O5FccW7OGKtpEWY3E1bhOGo0ePkp6ejo+XFyO6xNT4nIEd2rPgllEceHgyhU89zr7fTuKFawbh4+XFX9d+z+sbz98qGN3tEoDqr72K5zs3DsOGDat+7MYbb1QU3JS1gah6M45v09qRw7NQtWxXDYPbfCtpy5YtQOX5CgG+vjU+59lrBlr8vWurVkwb0J+EyNbc8N4H/G3dD0zqE2cxfdV/oF27dnHq1CmaOOkThDhWy5YtWbFiBcOGDSM1NbX652lpaXTq1Kn6ujYFBQVOHKVcSNVVT2tSFYg333yTyZMn8/jjj9O69f8iULVfv2d4mN3HeSFVy963b5/TxlAbtwlDVlYWAO2bN6/ztNfHRJMQ2Zqk9Aw2HktncFTH6sc6tKicX3l5uVtcw0TsLzU1lW7dujl7GNJABQUFvPLKK7z66qts376dnj17AlBUVARAMyde7bRZE7/qsRiG4XLXcnObXUkN1eXsVQ2P5+c7eSQiIpVcLQhV3GaLISysctPryJkz9Zr+dFExAEG+lp8SDudWzs/Hx4cTJ05oV1IjcvTo0fN2JQF06tSJlStX0q5dOyeNTC6mX79+7Nq1q9bnBAUF1bgrKSAgAIC8cy626Uh5JZXL9vf3d8k4uE0Y+vTpA0BKVjZFZWUXPM5Qk6yCQr4/XPm1xD5tIiweSz5eeUOOSy+91G2ulS4Nd+TIEYYPH05qaipRUVGkpaUBlVFITU1l+PDhOvjswry8LryzIygoiIcffpjHHnuM0NDQ8x7v2rUrADszs+w2voupWvYll1zitDHUxm12JbVr147IyEjKKypY/vOB8x7/8chRPt27H/M5B6XScnIYveRjCsrKuKlrF9qdc4xi6d7Kgz/9+vWz3+DFpZx7nsKXX35Z/djKlSvrfIa0uIagoCCefPJJ0tLSmD59eo1RAIiPr/y6e9WHQmeoWnbVWFyN22wxmEwm7rvvPl544QXe2pzMmO6WBwf3nzzFfZ8vp3XTIPq0bk2wfxMO5Z4h+XgGxeXl9AgLZfaoYRbTZBYUsGT3XgDuv/9+h70WcZ6aTl779ZZiu3btGnRtJXG8i20hnKvqzTglM4szJSVWn8uwfP8vPPf9+uq/V13Ov9/c/1b/7C8DrmJE184XndfGY+kWY3E1brPFADBp0iR8fHxYd+gwS1L2WDx2RdtIpiT0JrJZMzanH2fJ7r3syswiLiKcV64byuaJvyH8nKtmTv1qNaVmM3379qVv376OfCniBNae0VzfayuJ4wwePJgWLVpYtYVwrrZt29KtWzfMhsF7O1OsXmZWYSEbj6VX/6m6UtOvf5b1q/vCXEhaTg5rzu66rLoXhKtxu8tuP/PMMzz77LOEBgaweeJvLngV1YtZvGs34z/5DC8vL3766Scuv/xy2w5UXEptUbjQZbd1aQzXVfW2Vd8Dt2+88QaPPPIIl4aHseOhBxx6AHja6rVMX/8T1157LV9//bXDllsXbrXFAPD0008TFxdHdmERQxcs4uDpC9+Y50I+3rOXez77AoAnnnhCUfBw9X2D15aD6zKZTA16M7/nnnsIDAxkV2YWqw4ctOHIapdTXMzsrdsASExMdNhy68rtwuDn58eyZcsqV9bTOfSe9S5zt2636hK8eSUlTFn+JWM+XEqZuYLx48fz/PPPO2DU4iwN/dSvOHim4OBgHnzwQQAmL19FXkmJQ5b76KpvyC4somvXrowaNcohy6wPt9uVVOXcW3t2DwtlSnxvhnWOITokuPrTRKnZzI4TmXyQsod527Zz6uz5DI888givvPKK7t7mwXRrT6lNfn4+PXv2JC0tzapbezaUbu3pIGazmddee41nnnmGwl8d9An29yc8KBBzRQWHc89Q9quvsMbExDBr1iyGDBnijCGLg9TljdyaMNR1nuIe1qxZU30AeM6o4TzQ+zK7LGd3VjYD/7OQk0VFTJ06lVdeecUuy7EVtw5DldzcXBYsWMCCBQvYtm0bpeec0RgSEsLVV1/NpEmTGDZsmLYSPFxd38CtDUN95i2ub9q0aUyfPh0vk4nZI4dxv43jkJKZxXULF3M8P5++ffuydu1aAgMDbboMW/OIMPxaaWkpe/fuJScnB29vbyIjI4mKinLJ087F9urzxl2XMNR3GeK6DMMgMTGRt99+G4DHr7yCZwcPqNPVFS403yW79zBl+SpOFxfTs2dPvv32W7e4WKfHhUEar/q+Ydc1DA1ZlrgmwzB44oknePnllwHoFtqKd28aQb92bes1vxP5BSSuWMUnv7qywvLly93msjsKg3iEhrxR1ycMDV2muKbPP/+chx56iIyMyktWDInqSGLfPtzUtQu+VuyCTk4/zoykLSzatZui8nJ8fHx4+umnmTZtGn5OvMx3XSkM4vYa+gZd3zDYYtniek6dOsXUqVNZsGBB9Q2BQgMDuKJtJAlt2hDXOoJg/yZ4m7woKCtlT/ZJko9nsDn9OPtPnqqeT0JCArNnzyYuLs5Jr6T+FAZxa7Z4Y25IGGw1BnE9hw8fZtasWcyePZvMzEyrpvHz82Ps2LEkJiZy5ZVXuu2xTYVB3Jat3pAbGgZbjkVcT2lpKUlJSSQnJ5OUlERKSgqFhYWYzWb8/f3p1KkT8fHxxMfHc8UVV7jFweWLURjELdnyjdgWYbD1mEScye0uiSHiqm/AunyGeAqFQdyKq0ahiuIgnkBhELfh6lGoojiIu1MYxC24SxSqKA7izhQGcXnuFoUqioO4K4VBXJq7RqGK4iDuSGEQl+XuUaiiOIi7URjEJXlKFKooDuJOFAZxOZ4WhSqKg7gLhUFciqdGoYriIO5AYRCX4elRqKI4iKtTGMQlNJYoVFEcxJUpDOJ0jS0KVRQHcVUKgzhVY41CFcVBXJHCIE7T2KNQRXEQV6MwiFMoCpYUB3ElCoM4nKJQM8VBXIXCIA6lKNROcRBXoDCIwygK1lEcxNkUBnEIRaFuFAdxJoVB7E5RqB/FQZxFYRC7UhQaRnEQZ1AYxG4UBdtQHMTRFAaxC0XBthQHcSSFQWxOUbAPxUEcRWEQm1IU7EtxEEdQGMRmFAXHUBzE3hQGsQlFwbEUB7EnhUEaTFFwDsVB7EVhkAZRFJxLcRB7UBik3hQF16A4iK0pDFIvioJrURzElhQGqTNFwTUpDmIrCoPUiaLg2hQHsQWFQaymKLgHxUEaSmEQqygK7kVxkIZQGOSiFAX3pDhIfSkMUitFwb0pDlIfCoNckKLgGRQHqSuFQWqkKHgWxUHqQmGQ8ygKnklxEGspDGJBUfBsioNYQ2GQaopC46A4yMUoDAIoCo2N4iC1URhEUWikFAe5EIWhkVMUGjfFQWqiMDRiioKA4iDnUxgaKUVBfk1xkF9TGBohRUFqojhIFYWhkVEUpDaKg4DC0KgoCmINxUEUhkZCUZC6UBwaN4WhEVAUpD4Uh8ZLYfBwioI0hOLQOCkMHkxREFtQHBofhcFDKQpiS4pD46IweCBFQexBcWg8FAYPoyiIPSkOjYPC4EEUBXEExcHzKQweQlEQR1IcPJvC4AEUBXEGxcFzKQxuTlEQZ1IcPJPC4MYUBXEFioPnURjclKIgrkRx8CwKgxtSFMQVKQ6eQ2FwM4qCuDLFwTMoDG5EURB3oDi4P5NhGIazB9EYnTx5ktOnT2MymQgPD6dZs2a1Pl9RsJ+CggKaNm0KQH5+PkFBQU4ekWeoz+9sXl4emZmZGIZBSEgIrVq1ctBo5de0xeAgZrOZzz//nDFjxtChQwdCQ0Pp0qULnTt3pkWLFsTGxjJx4kQ2bNjAua1WFMQdWbPlYBgGGzZsYOLEiXTr1o0WLVrQuXNnunTpQmhoKB06dGDMmDF8/vnnmM1mJ72SRsgQu/v444+Njh07GoDFn6Z+fkaQr+95P+/bt6+RlJRkGIZhHD582IiOjjYAIzo62jh8+LCTX43nyc/Pr/63z8/Pd/ZwPM6Ffoc3b95s9O3b97zf/yBfX6Opn995P+/YsaPxySefOPnVNA7alWRHBQUFTJw4kcWLFwPQKiCA++N6MaJLZ9q3aMaMzVv44udfOJyTi4+3F37e3uQWl2A2DLy9vXn44Yf57LPPSE1N1ZaCHWlXkv39equ3U6dO3HTTTbz11luYzWb8fXwY1yOWyyLC+TbtEJvTM8gqLCTI15cOLZoT2awZm44d43RxCQDjxo1jzpw5+u9kRwqDneTl5XHjjTfy448/4u1l4k/9r+TPA/oT4OtLcvpxbnjvA04WFdEjLJRLw8M4U1LC7qyTHD1zhjHdu/FByp7qeXXq1Il169YpCnaiMDjGkSNHGDRoEKmpqdU/u6NHLG/ceB3fHz7CHR99itkw6NOmNZ1DQsgqLOT7w0cor6jgju6xxLQM4f9+/AlzhcFVV13Fl19+Wf3fTWzLx9kD8ESGYTB+/Hh+/PFHQvz9+WLcWK7q0A6ArIJCbnz/A4rKy/nsjjHcdEkXi2k3HUvn8raR3BATzcQvVlBhGNx8882Kgri99u3bc9NNN/H666/jbTIxe9Rw7ovrRXlFBYkrVmE2DN4bfRN39uxRPc2erGyu/s8CPti9hzUT7mR45xhGLf6Q9evXM27cOL744gtMJpMTX5Vn0sFnO5g7dy7Lly+niY83q+66ozoKAM+s+47swiJeuvaa86IAcHnbSADui+vF7JHDAHjzzTdJTk52zOBF7CQpKYm33noLoDoKAHuzT5JZUMglrVpaRAEgNiyUu3teCsDm9ONc1aEdX951B018vFm+fDnz5s1z7ItoJBQGG8vNzeWxxx4D4PnBg+h79o0eoKisjIU7Ugjy9a1eKWpzf+/LuL17LGazmSlTppz3bSURd2EYBlOmTMFsNnNHj1iL3/8m3t5WzaNVYABQ+eHpucEDAZg6dSq5ubm2H3AjpzDY2IIFCzhz5gyxoa34Q7++Fo8lpWeQV1pK79YRBPj6svLnA0xd9Q2JK77kXxs2kZ6Xd9783hx2HU28vdm8eTObNm1y1MsQsamNGzeSlJSEv48Pb9x4ncVj0SHBxIQEs+/kKd7fmWLx2J6sbBbu3EWIvz+ju3Wt/vnUfpfTLbQVZ86cYeHChQ55DY2JwmBjc+bMAeC3fePx9rL8592dnQ1AeFAQt3zwEcMXLeG1jZuZmbSVP3y1ms5vvs2iXZYrRnhQEOMu7Q7A7NmzHfAKRGyvar0Y1yOW8HMO7nt7efHfm0cR7O/PXUs/J372u4z7+FOGzH+fXu/MpV3z5qyeMJ6WAQEW0/w2oQ+g9cIeFAYbOnPmDNu3bwdgbPdu5z1+uqgYgM/3/8yXvxzk38OuJ/OxR0j7fSKPX3kFReXl3PvpMrZlnLCYbmxs5bzWr19v51cgYh8//PADUPN6AXBVh3asu/cuokOC2XI8gw9S9vBt2iG8TCau6xRFdEjwedOM7R4LwI4dO8irYWtb6k9hsKFt27YB0L558/M+FQFUnD1GUF5RwbODB5LYN56woEA6BrfgpeuGMLZ7N8oqKnjpxw0W0yVEtgFg37595Ofn2/dFiNhYXl4e+/fvB/73u3yuRbtSuHzOf2jfvDkbH7iX/CcfY/9vH+I3l/XklQ2bGLJgESXl5RbTRDQNol3zZhiGwdatW+3+OhoThcGGjh8/DlDjpxuApn6+1f+/poPP911W+bN1hywvGxDRNIhAX18MwyAzM9NGoxVxjKprHwX5+tb4gennk6e499NlhAYGsmz8WC5vG0mQnx9dWrXknZHDGNmlM1uOZzBv247zpo0JCQEgIyPD7q+jMVEYbKjqW0NeF/hedcfgFgAE+voSFhR43uNRZx/PLCg477GqeVZUVNhkrCKOUrVeXOh8g8UpuymrqODGztE09fM77/Hbe1Tufvru0OHzHquao9YL21IYbCjk7KeXmr5dBNC7dQRQ+bXVczeLAU6dPQZx7spxpqSE/NJSAFq2bGmz8Yo4QtV6kV9aypmSkvMeP3qmcn1p0aRJjdO3aOIPwOni4vMeSz+7a1XrhW0pDDbUu3dvAPafPEVeDStAhxYtuCwiHANYV8Onn6qfVQWkypbjlZvJHTp00AogbqdVq1bVZ+5vPX7ivMdbN63cvZSUfrzG6TenpwMQFRxs8fMzJSXsP3kK+N+6J7ahMNhQeHg4HTt2xABW/HKgxuc80b8fAI9/vYbjef87kLwt4wSvbNgIwOQEy1/y5T9Xzuvyyy+3w6hF7K/qd3fZz7+c99jNl1Sen/Dd4SPMTNpi8diGo8d4bcNmAMbEXmLx2Mqz61hUVBRhYWE2H3NjpjDY2D333APAjM1banz8zp49uPeynuzMzKL7zNmMeH8JQ+a/T7+5/+VUUTEP9omr/hoeVO52mrdtu8W8RdxN1e/uvG3bKSors3isT5vWPH7lFQAkrljFpTNnc/tHS7n63QVc9e4CCsrKmNQnjmujO1lMV7WOab2wPV1d1caOHj1KVFQUZrOZT26/ldHdLjnvOYZhMGfrdt5J3sqe7JOYgF4R4TwUH8e9l1l+W2na6rVMX/8THTt25MCBA3hbefkAsZ6urmp/ZrOZmJgYDh06xLSr+/PCkEHnPWfp3n28nbSV5OMZ5JaU0MzPj7jWETzY5zLGX2p5DaVP9uzjtg8/wdvbm7S0NNq1a3fe/KT+FAY7mDZtGtOnTyc8KJCtk+4n8iK37byQ9YePMvC/C6kwDD755BNGjx5t45EKKAyO8sknn3Dbbbfh7WVi3T13W1xcsi7S8/LoPWsemQWFTJs2jRdeeMHGIxWFwQ5KSkqIj48nJSWF2NBWfDNhfJ3jsOlYOje89wE5xcWMHz+e999/306jFYXBccaPH8/ixYsJ8ffny7vuqL6asLXS8/K4dsEi9mSfpEePHiQnJ9PkAt9mkvpTGOwkNTWVAQMGcOzYMcKDAnl7xI017lY6l7miglc3bOIva7+jpNzMVVddxapVq/RmZUcKg+MUFBRw/fXX8+OPP9LEx5vnBw/iD/36nnddsZos3buPycu/JLOgkHbt2vH9998TFRVl/0E3QgqDHaWmpjJq1ChSUiovjDewQ3sS+/ZhWOcYmp/zKedEfgEf7t7Dv5O2sDf7JAAjRoxg8eLFukuVnSkMjpWfn8+4ceNYvnw5AN1CW/HbhD6M7R5LRFPLf/szJSWs/OUAMzZv4bvDlVcE6NGjB8uWLVMU7EhhsLOSkhL+/ve/889//hOz2Vz9866tWhLZtCkGcOD06eqTfACaN2/Oq6++yv3336+7UzmAwuB4hmEwb948pk6dypkzZ6p/3q55M2JCQjBRefJa1XkKAN7e3vzpT3/ir3/9q3Yf2ZnC4CBHjx5l9uzZzJ8/n7S0tPMeN5lM9OrViwcffJAJEybQvHlzxw+ykVIYnCc3N5eFCxcye/ZsduzYUePNqKKiorjnnnt48MEH9e0jB1EYnCAzM5Nt27Zx6tQpvLy8aN26Nb1796ZZPb+9JA2jMLiGvLw8tm7dSkZGBhUVFbRs2ZLevXvr5DUnUBik0VMYRCzpzGcREbGgMIiIiAWFQURELCgMIiJiQWEQERELCoOIiFhQGERExILCICIiFhQGERGxoDCIiIgFhUFERCwoDCIiYkFhEBERCwqDiIhYUBik0SspKanx/4s0VgqDNDqGYbBp0yamTJlCXFwcERER1Y9FREQQFxfHlClT2LRpU413FBPxdLpRjzQqGzdu5He/+x1JSUlWPT8hIYG33nqLK664ws4jE3Ed2mKQRsFsNvPUU0/Rv39/kpKS8PWy7lc/KSmJ/v3789RTT2E2m+08ShHXoC0G8Xjl5eVMmDCBxYsXA3B3zx5Mju/N7K3ba3y+uaKChTtTALi2UxTfpKYBMG7cOBYuXIi3t7dDxi3iLD7OHoCIvT322GMsXrwYX28v5t88inGXdgfgqg7ta3z+yp8PsHBnCu2bN+eru8fxQcoe7vnsCxYvXkxERAT/+te/HDh6EcfTriTxaGvWrOGNN94AYNGtN1dHoTYLd+4C4K6ePTCZTIy7tDuLbr0ZgNdff501a9bYb8AiLkBhEI9lNpuZNGkSAFMSenNbbLeLTlNQWspn+34GYEKvS6t/fltsNybH9wZg0qRJOt4gHk1hEI+1YsUKDhw4QMsAf/5v6DVWTfPJ3n0UlJXRu3UE3cNCLR7757XX0DLAnwMHDrBy5Up7DFnEJSgM4rFmz54NwANxl9GsSROrplm4o/Kg86+3Fqo0a9KE++MuA2DWrFk2GqWI61EYxCMZhsEPP/wAwB09Yq2a5nhePqtT0/A2mRh/gWMRVfP64YcfdPKbeCyFQTxSamoqp0+fxs/bm54R4VZNs2jXbsyGwXXRnWjdtGmNz+kZHoavlxenT58mLS3NhiMWcR0Kg3ik9PR0ADq0aI6flecdVH0bqabdSFWa+PjQoUVzi2WIeBqFQTxS1beGvE0mq56/JyubrRknaOrnxy3dutb6XO+zZ03rm0niqRQG8UjBwcEAnCgotOpYwIIdlVsLt3brSqCv7wWfZxgGmQWFFssQ8TQKg3ik2NhY/Pz8yCkuJjUnp9bnGobB+7t2A7XvRgI4eDqHnOJi/Pz86Nbt4udFiLgjhUE8kp+fH3FxcQCs/OVgrc/9/vARDuXm0rZZM4Z0iqr1uSt/OQBAXFwcfn5+thiqiMtRGMRj3X333QDMSNpS6+6kqgvm3Xlpd7xqOSZhGAYzk7cCMGHCBBuOVMS1KAzise655x4CAwPZnZXNvG07anxOSXk5H+3eC8DdF9mNNHfrdnZnZRMUFKQwiEfTZbfFo7300ks88cQTNG/ShK2T7iM6JKRe8zlw6jS9Z80jr7SUl156iccff9zGIxVxHQqDeDSz2czVV1/Nhg0biA4JZvWE8UTV8dtEaTk5DF2wiIOnc+jXrx8//PCD7skgHk1hEI+Xnp7OgAEDOHjwIKGBAfx72A3cbsVlMgzDYMnuPfx2xVecLCoiOjqa77//nsjISAeMWsR5FAZpFI4dO8bIkSPZtm0bAIM6duC3ffswsktnAs45b6GorIxlP//CvzdvYd2hw0Dlt5CWLVtG27ZtHT10EYdTGKTRKC0t5cUXX+SFF16gvLwcqDwzukd4GB2aV17m4vCZM6RkZmE+u1r4+Pjw9NNPM23aNH09VRoNhUEanSNHjjBr1izmzZt3wesdRUZGcv/99zNp0iTat6/5FqAinkphkEbLMAyOHTvGli1byMzMBCA8PJw+ffrQtm1bTFZeZ0nE0ygMIiJiQSe4iYiIBYVBREQsKAwiImJBYRAREQsKg4iIWFAYRETEgsIgIiIWFAYREbGgMIiIiAWFQURELCgMIiJiQWEQERELCoOIiFhQGERExILCICIiFhQGERGxoDCIiIgFhUFERCwoDCIiYkFhEBERCwqDiIhYUBhERMSCwiAiIhYUBhERsaAwiIiIBYVBREQsKAwiImJBYRAREQsKg4iIWFAYRETEgsIgIiIWFAYREbGgMIiIiAWFQURELCgMIiJiQWEQERELCoOIiFhQGERExILCICIiFhQGERGxoDCIiIiF/wcN8EyICz0+BQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = Qinit(8) + Qmask(\"right\", mapping=u0_2)\n",
    "plot_motif(mask[1])\n",
    "plot_circuit(mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "0f80d612",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = Qinit(8) + Qmask(\"01\", mapping=u0_2)\n",
    "plot_motif(mask[1])\n",
    "plot_circuit(mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "991338de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = Qinit(8) + Qcycle(mapping=u0_2) + Qmask(\"*!\", mapping=u0_2) + Qcycle(mapping=u0_2)\n",
    "plot_circuit(mask)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "01cf02b9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = Qinit(8) + Qcycle(mapping=u0_2) + (Qmask(\"1*\", mapping=u0_2) + Qcycle(mapping=u0_2))*6\n",
    "plot_circuit(mask, depth=30)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "4fe8976b",
   "metadata": {},
   "source": [
    "#### N-qubit unitaries\n",
    "For N qubit unitaries, the pattern provided applies within the unitary. For example a pattern of \"101\" means for each edge of the form (a,b,c), a and c are going to be masked. Therefore the pattern string needs to be the same length as the arity for N>2 unitaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "fa0134cd",
   "metadata": {},
   "outputs": [],
   "source": [
    "if backend == \"qiskit\":\n",
    "    from qiskit.circuit import QuantumRegister\n",
    "    def V3(bits, symbols=None, circuit=None, **kwargs):\n",
    "        q0, q1, q2 = QuantumRegister(1, bits[0]), QuantumRegister(1, bits[1]), QuantumRegister(1, bits[2])\n",
    "        circuit.cnot(q0, q1)\n",
    "        circuit.cnot(q2, q1)\n",
    "        return circuit\n",
    "\n",
    "elif backend == \"cirq\":\n",
    "    import cirq\n",
    "    def V3(bits, symbols=None, circuit=None):\n",
    "        q0, q1, q2 = cirq.LineQubit(bits[0]), cirq.LineQubit(bits[1]), cirq.LineQubit(bits[2])\n",
    "        circuit += cirq.CNOT(q1, q0)\n",
    "        circuit += cirq.CNOT(q1, q2)\n",
    "        return circuit\n",
    "\n",
    "elif backend == \"pennylane\":\n",
    "    def V3(bits, symbols=None):\n",
    "        qml.CNOT(wires=[bits[0], bits[1]])\n",
    "        qml.CNOT(wires=[bits[2], bits[1]])\n",
    "v3 = Qunitary(V3, 0, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "c07e1223",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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csjQLPjd75PV8TcKvuM5z8OIH7glA9uX6r6yKHvprBH7HZtOnPj//gWu/quxC46P0a/zpvp3S4TAJvwDg4wZ4pRIazzjf9tJYuDUTsu1/N2pMONsFL1XA/nrnf21XWIh+ip+fObZ+YamEXwyw2eDoKf2Ze4eaoGOY591FhMH0y/R72OmX+efAnitau/SHfJbXDT8fIujfU5bnpem/qXcshb6fhF/YZbPB6Q79CTRnu/Qn4YQE69f0yXH6KHagBH4o3b36E4hOnIWX90O3BSJC4b8Ww+RL/GPK8miM8fKFp2gaxEXrf1RlCNUn6Uy7DN74SA9/WAik+ucXN50m9/mFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfhH4aWXXuK+++5j3rx5JCYmEh4eTkxMDNnZ2Tz88MOYzWZflyjEkDSbzWbzdRFj1Q033MDbb79NWFgYkydPJj4+npMnT3L8+HFsNhsTJ07kjTfeIDs729elilHa9Dyc7YJxEfC9L/q6GveQI/8o3HPPPbz55pu0tbVx9OhRysrKqK+v58CBA8yePZtTp05x5513+rpMIeySI7+H/Otf/2L+/PkAfPzxx8ycOdPHFQlXdPTAh8fhxQ+gxwIRofqRPyzE15WNnhz5L2A2mykoKGDatGkYDAaSk5NZt24dHR0drFq1Ck3T2LZtm0PbujDsnZ2dnipZeEhzO/z5Pdj0AhS9rwcfoKsXHnlB/zDoPOfbGkcrAD6/3KOyspL8/HxMJhNRUVFkZGTQ2NjI1q1bqa2tpaWlBcDh6/fS0lIAoqKiuOKKKzxVtvAAYws8+U9o77a/vPMcvHUIDjXBfYthXKR363MXOfKjH/GXLVuGyWRi/fr1NDU1UVFRgclkorCwkOLiYsrKytA0jczMzCG3Y7VaaWpq4plnnmHlypUA/PjHPyY6OtpLeyJG60wn7Bgm+BcynYUdb8E5i8fL8ggJP7B27VqMRiNr1qxhy5YtxMTEDCwrKCggKysLi8VCamoqsbGxF7V/8skn0TSN4OBgJk+ezN13301SUhIvv/wya9eu9eauiFF6qxpaHQh+v4bTUFHvuXo8SfnwV1dXU1RURHx8PJs3b7a7Tk5ODgBZWVl2l0+aNIlFixYxf/58Jk+ejKZpfPjhh/z5z3/m7NmzHqtduNc5C/zrU+fb7a2BsThsrnz4d+7cidVqZcWKFUOenkdERABDh3/58uXs3buXffv20dDQwIEDB1iwYAE7d+5k6dKlHqtduFeNybVBPGOLPkA41ig/4Ldnzx4A8vLyhlzHaDQCQ4f/s+bMmUNxcTFpaWmUlpaye/dulixZ4nRtubm5mEwmp9sJ16Tm3kHul3/mUtvFNy2j5fh+N1c0soSEBMrLy11qq3z46+v1C7aUlBS7yy0Wy8DIvaPhB4iJieH666/nb3/7GwcOHHAp/CaTiYaGBqfbCddEp55wua2pycipMfZvpXz4Ozo6AOjq6rK7vKioCLPZTExMDFOmTHFq2xaLPgzc19fnUm0JCQkutROuCe3Vb+fabDY0TXO4XZ+lh6jQc4QlJnqqtCGN5j2ifPgTEhI4ffo0FRUVLFy4cNCypqYmNmzYAEBmZqZTb4iWlhbefvttwPG5AZ/l6umccI3NBj97FYynHf93Bpg/LZxfHq7yUFWeo/yAX//peGFhITU1NQOvl5WVkZeXN/DNvM8GuLy8nO9+97scOXLkom3u37+f/Px8zpw5w5w5c7jxxhs9twPCbTQNrpnufLtFLrTxB8rP7TcajWRnZ9Pc3ExISAgzZsygu7ubI0eOkJ+fj9Vq5fXXX2fHjh2sXr16oN1bb701MEh46aWXkpycTHBwMEajkcbGRgCmT5/Oq6++Slpamk/2TTjPaoXf79Xn8zvic7NgabZHS/IY5Y/8SUlJlJSUsHTpUgwGA3V1dcTFxbF9+3aKi4sHzgY+O9iXlZXF448/zhe+8AViY2Opqalh//799PX1sWTJEn71q19x4MABCf4YExQEX18EOakjr3vzHLjV8TFgv6P8kX847e3txMbGomkabW1tREaO0Uncwmk2G9SZobQG9h+DPqv+uiEU5qXB1emQMM63NY6W8gN+w6mqqsJmszF9+nQJvmI0DaZM1P98dQF0nIMgDSLDIDhAzpcl/MM4ePAg4Nz9fRF4QoL1J/gEmgD5DPMMCb8IZBL+YUj4RSCTAT8hFCVHfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfjd66qmn0DQNTdO44YYbfF2OEMOS8LuJyWSioKDA12UI4TAJv5t8+9vfprW1ldtuu83XpbiVzQadPdDSDh09+t9FYAjxdQGB4KWXXuK5557j29/+NnFxcbzyyiu+LmnUeixQUQd7a6Dh9PnXL4uFRdNh7hSICPNZecIN5Mj/b2azmYKCAqZNm4bBYCA5OZl169bR0dHBqlWr0DSNbdu2XdSura2Nb33rW0yePJkf/vCHPqjc/RpPw+aXoej9wcEHONEKz5fDD1+COrNv6hPuIUd+oLKykvz8fEwmE1FRUWRkZNDY2MjWrVupra2lpaUFgOzs7IvaPvTQQxiNRp599lliY2O9XLn7nWiFbbuh89zw63X0wK/fhG9/DpLjvFObcC/lj/xms5lly5ZhMplYv349TU1NVFRUYDKZKCwspLi4mLKyMjRNIzMzc1Db9957jyeeeIL8/Hy+/OUv+2gP3Osv740c/H7nLPC/pTIOMFYpH/61a9diNBpZs2YNW7ZsISYmZmBZQUEBWVlZWCwWUlNTBx3Ze3t7Wb16NeHh4XYvB8YiYwscdfJU/mQrHD7hmXqEZykd/urqaoqKioiPj2fz5s1218nJyQEgKytr0Os/+clPqKqqYuPGjaSlpXm8Vm9474hr7d497N46hHcofc2/c+dOrFYrK1asIDo62u46ERERwODwf/LJJ/zoRz9i5syZbNiwwWP15ebmYjKZPLb9z7pu9V+4dNo1Trd7a18VG//zZg9UJEaSkJBAeXm5S22VDv+ePXsAyMvLG3Ido9EIDA7/fffdR09PD08++SShoaEeq89kMtHQ0OCx7X9Wb59rF+99Ns2rdQr3UDr89fX1AKSkpNhdbrFYKC0tBQaHv6KigqCgIL7yla9c1Ka9vR2Ad999l4SEBABqampcuhPQ395rettdambtaSUxMdHNxQhHjOY9onT4Ozo6AOjq6rK7vKioCLPZTExMDFOmTBm0zGq1cuLE0CNdvb29A8utVqtL9bl6Oueqijp4ptT5dvfdsYA//T+j2+sRnqX0gF//p2ZFRcVFy5qamgau5zMzM9E0bWDZmTNnsNlsdv9s2rQJgOuvv37gtUsuucTzO+MGmckQY3CuTXgI5E4ZeT3hf5QO/5IlSwAoLCykpqZm4PWysjLy8vIwm/X7XvYm9wSikGBYmjXyehe6eQ4YPDfsITxI6fAXFBQwYcIEjh8/zqxZs5gzZw7p6enMmzePtLQ0Fi9eDFx8my+QLZjm+AfA4pmQN9Oz9QjPUTr8SUlJlJSUsHTpUgwGA3V1dcTFxbF9+3aKi4sHzgZUCj/A52bDN66HtIn2lyfHwdcXweevgguuhsQYo9lsMjnTnvb2dmJjY9E0jba2NiIjI31dkk80noaaE/DqAf2bflHh8KP/8HVVwh2UPvIPp6qqCpvNRnp6urLBB5g8Hm6Ycf66PkTeMQFD/imHcPDgQUC9U36hDgn/ECT8ItBJ+Icg4ReBTukZfsPpn/cvRKCSI78QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QigrxdQHCP9ls0NwOx1vgbBf09Oqvn7PAiVaYGANBmm9r9LTOc2BsgRNnobdPfy08FCZfAonjIWyMp0ez2Ww2Xxch/IPNBp+ehL2H4ZMm/c0/lPAQmJ4Ai6br/w2UD4KznfDeEfigDk61Db2epukfAvPSYG4aRIZ5q0L3kfALAKoa4JX90HTW+bYTYyA/E65M0UMxFp3phF0VcOAYWJ1MRFgwLJgGt2aBIdQz9XmChF9xnT3wwgdQdnT028pMhi/PhZiI0W/LW2w2fd+fL4fu3tFta3wkfHUBXDHJPbV5moRfYSdb4Yk34XSn+7YZbYB78yApzn3b9JQ+K/xln3s++C50ayZ8brb/nwVJ+BV1shW2/gPau92/bUMofGsJJPvxB4DVCs+UQuUxz2z/ptn6ZYA/k1t9o7By5Uo0TRv2z6FDh3xd5kU6evQjvieCD/rp8/Y9+nW0v3qxwnPBB3jjIyg97Lntu8MYv1nhH9LT07n00kvtLouMjPRyNSN7odz5U/3/uQViI6C1C37+2sjrt/dA0fvwzRv87/S3xgTvfOJcG2f3H2DXB3BFAsTHOF+jN0j43eDhhx9m5cqVvi7DIR8ZobzO+XaxEXCJk59j1Y3wr09h/lTn+/OU7l7Yuc/5dq7s/7k+va9vLfHPW6Fy2q8Qmw1e2u/dPosr9YE1f7G3Bk53eK+/2pNQ3eC9/pwh4b+A2WymoKCAadOmYTAYSE5OZt26dXR0dLBq1So0TWPbtm2+LtNlh0/oA33e1NoNB497t8+hWK3wrg+uw/f66bW/nPb/W2VlJfn5+ZhMJqKiosjIyKCxsZGtW7dSW1tLS0sLANnZ2Re1fe6553jxxRdpbW0lPj6eBQsWcNdddzFx4kQv78XwSmt80+/ew5Cd4pu+L1TdBC1ePOr3O9QI5jb/u/aXIz/6EX/ZsmWYTCbWr19PU1MTFRUVmEwmCgsLKS4upqysDE3TyMzMvKh9cXExu3bt4p///Cd//etfWb9+PVOmTOGPf/yjD/bGPqsNDjX5pu/ak9Bj8U3fF6pu9E2/Nnz3sx+OhB9Yu3YtRqORNWvWsGXLFmJizn9EFxQUkJWVhcViITU1ldjY2IFl06dP5xe/+AWVlZWcOXOGjo4O3nnnHW666SY6Ojr4+te/TnFxsS926SKnWn0XQJsNGlp80/eFjvuwBqMf7P9nKR/+6upqioqKiI+PZ/PmzXbXycnJASAra/CsjYcffpgHHniArKwsxo0bR2RkJNdeey2vvfYay5cvx2az8cADD+AP86h8+cb3h/77rNB42nf9H5Pw+5+dO3ditVpZsWIF0dHRdteJiNAnq382/EPRNI3CwkIAjhw5wsGDB91T7Cj4esLNWR/333nu/NdyfcHX+2+P8gN+e/bsASAvL2/IdYxGI+B4+AGuuOIK4uLiaGlp4fDhw3bHCkaSm5uLyWRyup09M5f8N7M+t97usv4JLMOJNZz/7yO3D73eUJNgtj/1NPe/vMnBat0vYtwklj5cNuTykX4Go93/M2fbSEqa6WC1jktISKC8vNyltsqHv76+HoCUFPvD0RaLhdLSUsC58AOEhoYObMMVJpOJhgb33CSe1GIecpkzE1iCgpyf7ALQerbFbfviisi24b+y5+jPwNX9t/T2+HT/7VE+/B0d+r2frq4uu8uLioowm83ExMQwZcoUh7d76tQpTp48CUBSUpJLtSUkJLjUzp6woJ4hl7Xa3/VBYg36G99q1e/dO7utULpJTEwcuSMP0YJDsVrOERRi/6kbI/0MRrv/vZ0tHtn/0bxHlP9WX0ZGBtXV1Wzbto1vfetbg5Y1NTWRk5NDU1MTixYtYu/evQ5v9zvf+Q6FhYWMGzeOkydPEhbm20e9NJyGn/7d9faP3K4f8c50wiMvON/+/hv1J/740pa/g9HFQb/R7n9uKnxtkWt9e4ryA35LliwBoLCwkJqa87NgysrKyMvLw2zWT5c/O7nnH//4B9/5zneora0d9HpnZyff//73efTRRwF46KGHfB58gIRxEOLDf21/+H6/L2tImuC7voeifPgLCgqYMGECx48fZ9asWcyZM4f09HTmzZtHWloaixcvBi6+3u/o6KCwsJBp06YxefJk5s6dS05ODvHx8WzatAmbzcY3v/lNCgoKfLFbFwkOgqmX+abv5Dj/eMadL888pvvoZz8c5cOflJRESUkJS5cuxWAwUFdXR1xcHNu3b6e4uHjgbOCz4c/JyWHjxo3ceOONhIWF8fHHH1NVVcXEiRO544472L17N9u3b0fzo++zLkpXq9/PykzWnzTkbVMmwuTx3u93JMoP+AHMnDmTV1555aLX29vbqaurIygoiNmzZw9alpyczA9+8ANvlegWsxLPX7d6S0QYXJXqvf6GExIMC6fCP6q82+81073bn6OUP/IPp6qqCpvNRnp6ul8+lMNZwUFw8xzv9rkkw7+eb3/dDIgK915/ky6BrGTv9ecMCf8w+mfmOXt/358tmOq9p8tePgFucP+8llGJMcCXcr3TV5AGdy7Uzzj8kYR/GIEYfk2Dr87XT8ed0dqlXy44MicAIDRYf+MH++E77MoUyLrcuTbO7j/oT/D154eY+tEJmf8JxPADjI/Sn633xJv6o6Yc4ehz60AP/D3X6bcX/ZGmwYqF0NYFn55yrI0z+w8wd4r3L7GcpfwkH5V9ehJ2vDX6X1ZxodBgPfgzJ7tvm57S3QtPv60/4cid5k+FO+bpMwL9mYRfceY2/SGTtSdHv63kOP1Uf9Ilo9+Wt1j69NH/f3zk/K/p+qzwEPhCjj6u4kd3eIck4RdYbfqDLV/7cPhfzjkUQyjcmAGLM/zzGt8RxhZ49l9wrNm19rMS4T/m6pdUY4WEXww4Z9F/kcXeGsdCMHm8PoEnN1X/1dVjnc2m7/few1BZP/L3/yPD9N/Qe3U6XBY7/Lr+SMIv7Ors0b8Ec7wZznbpp8chwfqtsqQ4/RTfF7PlvKXPCk1n9DOCE636w0/P9emn9l+eB8kT9N9O7I/P43eUjPYLuyLD9bnwvv4mnq8EB+kfcv1fBqqog3Nd+iVOruPf7PZrY/QKTQgxWhJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4XeTF198kWXLljFp0iTCw8OZNGkSeXl5/PSnP/V1aULYpdlsNpuvixjLzp07x4oVK3juuecASEtLY8KECZw4cYKGhgYuueQSzGazj6sUo7XpeTjbBeMi4Htf9HU17hHi6wLGum984xs899xz3HLLLWzbto2pU6cOLDtz5gzvvPOOD6sTYmhy5B+FN954g5tvvpn58+ezd+9eQkLkszTQWK1Qewp++zZ09UJUOPzwS6Bpvq5s9OSa/wJms5mCggKmTZuGwWAgOTmZdevW0dHRwapVq9A0jW3btg2s/4tf/AKAjRs3SvADTNc5+MdH8INd8KvdevABOnrg0b9DaQ1Y+nxb42jJkf/fKisryc/Px2QyERUVxfTp02lsbOTEiRMsXbqUlpYW3nvvPUpKSrjmmmvo6uoiNjYWq9VKa2srH330Eb/73e84cuQI0dHRLFiwgG984xvEx8f7eteEk053wPZ/guns8OtNT4B7rgNDqHfqcjcJP/oR/8orr8RoNLJ+/Xo2bdpETEwMAI8++igPPvggISEh9PX1cebMGWJjY9m3bx8LFy5k4sSJrF+/noceeojP/igvueQSnn/+efLy8nyxW8IFnefg8dfhRKtj68+YBKtvgOAxeA49Bkt2v7Vr12I0GlmzZg1btmwZCD5AQUEBWVlZWCwWUlNTiY2NBaCpqQmA06dP853vfIdbb72Vqqoqenp6+PDDD1m8eDFnzpzhi1/8Ikaj0Sf7JZz3zieOBx/gUBN8NEb/eZUPf3V1NUVFRcTHx7N582a76+Tk5ACQlZU18FpHRwcAFouFqVOn8sILL5CRkUFYWBhz5szh5ZdfJiEhgTNnzvDYY495fD/E6PVZ4b3DzrfbW+P+WrxB+fDv3LkTq9XKihUriI6OtrtOREQEMDj8BoNh4P/XrFlDaOjgC7/IyEjuu+8+AF577TV3ly084PAJ/V6+K+3OdLq/Hk9Tfoh6z549AMNel/eftl8Y/vHjxw/8/8yZM+2263/96NGjLtWWm5uLyWRyqa1wXkrOl5n7lV+41Pbaxbdx2ljp3oIckJCQQHl5uUttlQ9/fX09ACkpKXaXWywWSktLgcHhnzFjxsD/h4WF2W3bf3bQ1+faPSGTyURDQ4NLbYXzYtNaXG578qSJk2Ps30r58Pdfu3d12T/fKyoqwmw2ExMTw5QpUwZeT0xM5PLLL+fYsWN8+umnds8camtrAUhKSnKptoSEBJfaCdeE2fT3gs1mQ3NiFo/NaiU6zEJoYqKnShvSaN4jyoc/ISGB06dPU1FRwcKFCwcta2pqYsOGDQBkZmZe9Ib4yle+wpYtW/jDH/7AqlWrBi2z2Wz8/ve/B2Dx4sUu1ebq6ZxwjdUGP34ZzG3OTd+bnRzE44cqPVOUByk/4LdkyRIACgsLqak5P2xbVlZGXl7ewJdysrOzL2q7YcMGYmNjKSkp4Qc/+MHA6b3FYuHBBx/kwIEDhIeH89///d+e3xExakEaLEp3vt01091fizcoP8nHaDSSnZ1Nc3MzISEhzJgxg+7ubo4cOUJ+fj5Wq5XXX3+dHTt2sHr16ovav/rqq9x+++309PQwceJEpkyZQm1t7cD2fve73/G1r33NB3smXHHOAr9+E+oc/CJmTip87eqxOddf+SN/UlISJSUlLF26FIPBQF1dHXFxcWzfvp3i4uKBs4ELB/sulJ+fz/79+/na175GSEgI+/fvJyQkhK985Su8//77EvwxJixEn7GXNnHkdXNS4T8XjM3ggxz5h9Xe3k5sbCyaptHW1kZkZKSvSxJeYumD/fWw9zDUX3AWoAEzJuuXB7MSx27wQQb8hlVVVYXNZmP69OkSfMWEBMPcNP3PqTZo7YSgIBgfBZcEyFtBwj+MgwcPAkOf8gs1TIzR/wQa5a/5hyPhF4FMwj8MCb8IZDLgJ4Si5MgvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsIvhKIk/EIoSsLvorq6OjRNc+jP9773PV+XK8RFQnxdwFhlMBhYtGjRkMvb2tr48MMPAbj66qu9VZYQDtNsNpvN10UEokcffZQHH3yQpKQk6uvrCQqSkyzhX+TI7yHPPPMMAHfdddeYDL7NBkdOwN7DcNgEPRYIC4G0ibAoHWZMhiDN11WK0Rh770oPMpvNFBQUMG3aNAwGA8nJyaxbt46Ojg5WrVqFpmls27ZtxO188MEHVFVVAXD33Xd7umy3O9sFv3gdfvUmHDgGneegzwpd56CqAXa8BT8thuZ2X1cqRkOO/P9WWVlJfn4+JpOJqKgoMjIyaGxsZOvWrdTW1tLS0gJAdnb2iNv6wx/+AMD8+fO54oorPFm227V1wy/fAPMIwW46C4+/AQ/cBHHR3qlNuJcc+dGP+MuWLcNkMrF+/XqampqoqKjAZDJRWFhIcXExZWVlaJpGZmbmsNvq7e1l586dAKxcudIL1bvXX/aNHPx+rV3wTKln6xGeI+EH1q5di9FoZM2aNWzZsoWYmJiBZQUFBWRlZWGxWEhNTSU2NnbYbRUXF2M2mwkPD+eOO+7wdOluZW7TT+udUWeGY82eqUd4lvLhr66upqioiPj4eDZv3mx3nZycHACysrJG3F7/QN/nP/95xo8f775CveDdw66121vj3jqEdyh/zb9z506sVisrVqwgOtr+xWtERAQwcvibm5spLi4G3HPKn5ubi8lkGvV2HHXtN/7MZenXOd3u9ZKDFHw53wMViZEkJCRQXl7uUlvlw79nzx4A8vLyhlzHaDQCI4d/586dnDt3joSEBG6++eZR12YymWhocPI8fBT6rK6dCNoI8Wqdwj2UD399fT0AKSkpdpdbLBZKS/VRrZHC3z/Kv2LFCoKDg0ddW0JCwqi34ZS+Lpea2SydJCYmurkY4YjRvEeUD39HRwcAXV323/hFRUWYzWZiYmKYMmXKkNv5+OOPB06/3DXK7+rpnKvePQzP/sv5dl//fA7/+7DR/QUJj1J+wK//k7OiouKiZU1NTWzYsAGAzMxMNG3oKW39A31XXXUVs2fP9kClnpeTCoZQ59oEB8GCaR4pR3iY8uFfsmQJAIWFhdTUnB+2LisrIy8vD7PZDAw/ucdqtfLHP/4RGJsz+vqFh8Limc61uWY6xBg8U4/wLOXDX1BQwIQJEzh+/DizZs1izpw5pKenM2/ePNLS0li8eDEw/PX+7t27aWhoIDQ0lDvvvNNbpXvE52bDgqmOrZuVDJ+/0rP1CM9RPvxJSUmUlJSwdOlSDAYDdXV1xMXFsX37doqLiwfOBoYLf/9A39KlS4mPj/dK3Z6iaXDHfPhCDoyLsL9OdDjcmgl3X6Of9ouxSb7SO4z29nZiY2PRNI22tjYiIyN9XZJX9Vn1GX81Jni/Fnr7ICIUfvAlCBn9zQzhY/K5PYyqqipsNhvp6enKBR/0o3pmMvzHXIgM018LC5HgBwoJ/zAOHjwIODatV4ixRsI/DAm/CGQS/mFI+EUgU36G33D65/0LEYjkyC+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EokJ8XYDwX5Y+MJ2Fs53Q2/fv16z6/4cG+7Y2b7DZ4Eyn/jPo339DKEy6BGIMPi3NLTSbzWbzdRHCf5zugHcPw6EmaDwDfdaL1wnS9ABMT4Cr02FijLer9BxLH1Qegw/q4FgzdPTYX++SSEiJh/lpMGMSBI3Bc2gJvwCg8TT8/UOoatCPeM6YMQluyYTUeM/U5g09FnizCkoPDx34oUyIhutnwDXpY+tDQMKvuD4r7K6CNz6yf5R3lKZB3kzIzxx7lwS1J2Hne2BuH912UuLhzgVw2Tj31OVpEn6FtXfDjrf001t3SRgH/5UH46Pct01Psdn0D73XPgR3hSAkCP5zAeRMcdMGPUjCr6i2btj2DzjR6v5tj4+Eb38O4qLdv213sdng5f2wp9r929aAOxbAgqnu37Y7jaErFP9kNpt58MEHmTNnDlFRUYSHh5OSksJdd91FRUWFr8uz65wFtv/TM8EHON0JT+yBznOe2b47/LPaM8EH/Syi6H34yOiZ7buLHPlH4ZNPPuGGG27AZDIRFBTElClTiI6Opra2lvb2doKDg/nDH/7AihUrfF3qILsq9De/M/7nFoiNgNYu+PlrjrWZP1U/BfY3DafhZ6+C1Yl3viv7Hx0O37kNov30tqAc+Ufhvvvuw2QyccUVV1BVVcWRI0eorKzEZDLxzW9+k76+Pu69915aWlp8XeqAo6fgLReOeLER+u2t2AjH27xfCx83ON+XJ/VZ4c/vORd8cG3/23vguTLn+vEmCb+L2traeOuttwD46U9/yowZMwaWRUVF8atf/Yr4+Hja29t55513fFTlxV74wH2DW47252zQPGlfrX7k95bKY/DpSe/15wwJ/wXMZjMFBQVMmzYNg8FAcnIy69ato6Ojg1WrVqFpGtu2bQOgp6eH/iumtLS0i7YVEhJCSkoKAL29vd7biWEca3bvyL4jTrVBjcm7fQ7FZoO9Nd7vt8QHfTpCpvf+W2VlJfn5+ZhMJqKiosjIyKCxsZGtW7dSW1s7cOqenZ0NQHx8PImJiTQ0NPDuu+8ya9asQdtraWnh0KFDBAUFcdVVV3l7d+wqPeybfvfW6BOBfO3oKWg64/1+PzyujxU4c8ngDXLkRz/iL1u2DJPJxPr162lqaqKiogKTyURhYSHFxcWUlZWhaRqZmZkD7X784x+jaRobNmzgd7/7HSdOnKCjo4PS0lJuu+02Ojo6+J//+R+mTvX9PR+bDQ4e903f1Y36tFlf+9BH+99nhY8bfdP3cCT8wNq1azEajaxZs4YtW7YQE3N+snpBQQFZWVlYLBZSU1OJjY0dWPb1r3+dF154gfT0dO655x4SEhKIjo7mmmuuobGxkWeeeYaf/vSnvtili7R0+O7WW59V/56Arx334bir0cuXW45QPvzV1dUUFRURHx/P5s2b7a6Tk5MDQFZW1qDXbTYbtbW1nDp1iqCgIFJTU8nMzCQyMpL6+nq2b99OdbWHbiY7yZdvfH/o32oDow9r8PX+26N8+Hfu3InVamXFihVER9ufkhYRoV+sfTb89913H+vXr+fSSy+lurqao0ePcuDAAcxmMxs2bKC0tJSFCxdy/LiPzjcv0Nzm2/5bRjlvfrQ6e/Qv7/hKs4/33x7lB/z27NkDQF5e3pDrGI36VK0Lw3/gwAF27NhBaGgof/3rXwdG9kH/sHj00UepqKjgzTff5Mc//jFPPPGE07Xl5uZiMrlnqHzmjQ8w66b/a3dZ/wSW4cQazv/3kduHXm+oSTBP7nia+17e5GC17hcxbhJLHx76pvtIP4PR7v/ps20kJc10sFrHJSQkUF5e7lJb5cNfX18PMCi8F7JYLJSWlgKDw19aWorNZiM9PX3ItjfddBNvvvkmZWWuzfQwmUw0NLhnlszkM0Ofd/ZPYHFEUJDj616o9expt+2LKyLbhz/sO/ozcHX/Lb3nfLr/9igf/o6ODgC6urrsLi8qKsJsNhMTE8OUKee/qtXW5vh5dHd3t0u1JSQkuNTOnvCQoYfbW+3v+iCxBv2Nb7VC6zC7M9S2woMtJCYmjtyRhwSFGLBZ+9CC7H/feKSfwWj3v6+nzSP7P5r3iPLhT0hI4PTp01RUVLBw4cJBy5qamtiwYQMAmZmZaJo2sGz69OkAHD58mPr6ertH/zfeeAOAK664wqXaXD2ds6feDL943f4yR+aqP3K7fsRr7YZHXnC+/60/+Q4Zid9xvqEb/eQV/ZFc9oz0Mxjt/l9zVSq/MfrXN32UH/BbsmQJAIWFhdTUnJ+KVVZWRl5eHmazGTg/uaffTTfdxKWXXkpvby9f/vKXB7Xt6uqioKCAN998E9BvCfra5PH647d8JXmC7/rulxSnZt9DUT78BQUFTJgwgePHjzNr1izmzJlDeno68+bNIy0tjcWLFwMXj/RHRUXxpz/9iaioKMrKypg5cyZpaWlkZWURHx8/cH//W9/6FsuXL/f6fn1WaDCk+CiAE2P844GXUy9Vs++hKB/+pKQkSkpKWLp0KQaDgbq6OuLi4ti+fTvFxcUDR/TPhh/0s4YPP/yQNWvWMH36dEwmE9XV1YwbN47ly5fzyiuvDHwXwB8sTPdNv1f7qN/PujIFwn1woTtpnH8+31D5a36AmTNn8sorr1z0ent7O3V1dQQFBTF79my7bdPS0vjlL3/p6RLdIvtyePED7870Cw2GeRd/78knDKEwN837X+5ZNF1/xqG/Uf7IP5yqqqqB23mRkS7c3/EzYSH6Qza9aVE6RIV7t8/h3DDDuw8YvSQS5vrp8/wk/MM4ePAgYP+Uf6xanOG9waf4GLjVz3508TGw1Is13TEfwkO9158zJPzDCMTwBwfpj5cOdvJfvrVL/+01jswJAP0hlv+5QD/b8DfXXQFpE51r4+z+g/4Az5mTnevHm/zwn8Z/BGL4Qb/td9fV8IdSx39Bh6PPrev3lfn+OcIN+mSd/3MtbP2H/rARRzi7/+mXwZfmOl+bN8kDPBVWUQd/fNe9j9nSgP+Yp1/r+7sznfDknqEn/rhqegKsus5/T/f7SfgV9+lJ/YGWo/1tNaAPbt0x379PdT+roweeL9d/N99o9f/WolszIWQM/NYiCb+gxwLFlfqz5lx5N2jAvKnwhasgIszd1XnHh8f1J+06c01/oYRx8NUF/nk/fygSfjHgdAe8d0T/0+bAd5Eiw/Rn8y9K10fRxzpLHxw4ps8DOGoeeX0NyEjU93/GZN9On3aFhF9cpM+qP976eLP+BJrWLrBY9TsEMQZIjtPn6ieOH3u/lNNRze36vh9v1n+z0aFG/WcQEgRLZuk/g8snQIyfPZTTGRJ+IRyw6Xk42wXjIuB7X/R1Ne4h9/mFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEf5ROnTpFQUEBM2fOJCIigvHjx3Pdddfx5z//2delCTGsEF8XMJZVV1ezZMkSGhsbCQ0NZfbs2XR3d7N3715KSkp48803efrpp31dphB2yZHfRX19fXzpS1+isbGRa665hmPHjlFRUcHHH3/MgQMHuPzyy/ntb3/LU0895etSxSid6QSLVf9/q823tbiTZrPZAmh3vOfll1/m85//POHh4Rw6dIjU1NRBy1955RWWLVvG5MmTOXbsGMHBwb4pVLikzwoHj8Pew3DkxOBlmcmwKB2mJ4Cm+aY+d5Aj/wXMZjMFBQVMmzYNg8FAcnIy69ato6Ojg1WrVqFpGtu2bQNg7969AOTm5l4UfIDbbruNqKgoGhsbKSkp8eZuiFHqOgfb/wm/33tx8AE+PA5P7IG/vK9/SIxVcs3/b5WVleTn52MymYiKiiIjI4PGxka2bt1KbW0tLS0tAGRnZwMM/D0xMXHIbSYmJlJTU8O7777LDTfc4OldEG5g6YPfvA21J0de9/1a0IA75o/NMwA58qMf8ZctW4bJZGL9+vU0NTVRUVGByWSisLCQ4uJiysrK0DSNzMxMAC655BIAGhoahtxu/7JPPvnE4/sg3KP0sGPB77evFmpMnqvHkyT8wNq1azEajaxZs4YtW7YQExMzsKygoICsrCwsFgupqanExsYCMHfuXADKy8upr6+/aJt///vf6ejoAOD06dNe2AsxWjYb7K1xvl3pYffX4g3Kh7+6upqioiLi4+PZvHmz3XVycnIAyMrKGnht+fLlJCUl0dPTw1e/+lWOHz8+sKysrIx777134O+dnZ0eql6409FTcKrN+XYHjdDW7f56PE35a/6dO3ditVpZsWIF0dHRdteJiIgABoc/PDycZ599lvz8fPbt28eUKVNIT0+nu7uburo6JkyYwBe/+EWef/75QWcSzsjNzcVkGqPnlGPQ5Vd9iXl3PO50O5sNFl6fz5mGgx6oangJCQmUl5e71Fb58O/ZsweAvLy8IdcxGo3A4PADLFy4kP379/OTn/yE119/nU8//ZTx48ezcuVKvv/97/PjH/8Y0P+BXGEymYYdUxDuNW5qq8ttzeZmToyxfyvlw99/vZ6SkmJ3ucViobS0FLg4/ABTpkxh+/btdttWVVUB+hHcFa5+aAjXGIJ7nW5js9nQNI2YCAgZ5s6Pp4zmPaJ8+PsH5bq6uuwuLyoqwmw2ExMTw5QpUxzertls5r333iMkJIRbb73VpdpcPZ0TrrH0wfdfhFYnrt81TWPqpXD4o395rC5PUX7Ar/+Ts6Ki4qJlTU1NbNiwAYDMzEw0J27mbty4EYvFwh133MGkSZPcU6zwqJBgWDDN+XaL0t1fizcoH/4lS5YAUFhYSE3N+fs8ZWVl5OXlYTabgfOTey7097//feCSoN+ZM2d44IEH2L59OxMnTuRnP/uZ54oXbnf9DJjoxPhs+mWQdbnn6vEk5cNfUFDAhAkTOH78OLNmzWLOnDmkp6czb9480tLSWLx4MWD/ev+NN97gmmuuYdy4cWRlZZGVlcVll13G448/TmJiIm+++SaXXXaZt3dJjEJUONy72LEPgLSJ8H+ug+AxmqIxWrb7JCUlUVJSwtKlSzEYDNTV1REXF8f27dspLi4eOBuwF/4vfOELfPWrXyU+Pp7Dhw9z9OhRMjIy+P73v091dTVz5szx9u4IN5gQDQ/cDDfNhhjDxcsnxsAXroL7boTIMO/X5y7yrb5htLe3Exsbi6ZptLW1ERkZ6euShJdZ+vTpu63dEKTBhCiYcqn+/2Od8qP9w6mqqsJmszF9+nQJvqJCgiHD+3fwvEL50/7hHDyoz9iyd8ovxFgn4R+GhF8EMgn/MCT8IpDJgJ8QipIjvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKkvALoSgJvxCKUj78dXV1PP3009x7773k5OQQFhaGpmmsXLnSofZvvPEGt9xyCxMmTCAyMpI5c+awefNmzp0759nChRgtm+LWrVtnAy76c/fdd4/YdsuWLQPrp6Sk2LKzs20hISE2wHb11VfbOjs7Pb8DQrhI+SN/fHw8t956K5s2beLll1/m/vvvd6jdv/71LzZs2ICmafz+97+nrq6O/fv3c+jQIaZNm8a7777LQw895OHqhXBdiK8L8LWNGzcO+vu+ffscaveDH/wAm83GPffcw9133z3w+tSpU3n66ae5/vrreeKJJ3j44Ye59NJL3Vqzt7S0w7tHoMYEPb0QFgJpl8KidLg01tfVidEKuCO/2WymoKCAadOmYTAYSE5OZt26dXR0dLBq1So0TWPbtm2j6qOtrY033ngDgNWrV1+0/LrrrmP69OmcO3eOl156aVR9+UKPBf63FH6wC3ZXwbFmONEKx1vg7UPw45fhN29DZ4+vKxWjEVDhr6ysZM6cOfz0pz/FZDKRkZFBb28vW7du5Y477qC6uhqA7OzsUfWzf/9+zp07R3h4OLm5uXbXueaaawDHzyT8RY8FnngTPqjTBzOG8pERfvkP+QAYywIm/GazmWXLlmEymVi/fj1NTU1UVFRgMpkoLCykuLiYsrIyNE0jMzNzVH3V1NQAkJKSQkiI/SunqVOnDlp3rPhbGdSZHVu36Sz8eWx9tokLBEz4165di9FoZM2aNWzZsoWYmJiBZQUFBWRlZWGxWEhNTSU2dnQXrKdPnwZg/PjxQ67Tv6x/3bGgtQvKjzrX5iMjnGz1TD3CswIi/NXV1RQVFREfH8/mzZvtrpOTkwNAVlbWqPvr7u4GICwsbMh1wsPDAejq6hp1f96y7whYhzvXH0LpYffXIjwvIEb7d+7cidVqZcWKFURHR9tdJyIiAnBP+A0GA8CwE3l6enoG9euK3NxcTCaTy+2ddc2qP5Iw/Qan272w+wDfXr7U/QWJESUkJFBeXu5S24AI/549ewDIy8sbch2j0Qi4J/yOnNI7cmkwEpPJRENDg8vtnWUl1LWGQeFerVO4R0CEv76+HtAH4OyxWCyUlpYC7gn/9OnTB/q1WCx2B/1qa2sHreuKhIQEl9u6Isjm4pTkvm4SExPdW4xwyGjeIwER/o6ODmDo6+uioiLMZjMxMTFMmTJl1P1deeWVhIWF0dPTQ3l5OQsWLLhonb179wIwf/58l/tx9XTOVXs+hpf2O9/uyzdn88x3jO4vSHhUQAz49X/6VVRUXLSsqamJDRs2AJCZmYmmaaPuLyYmhs997nMAPPXUUxctf+edd6ipqSEsLIzly5ePuj9vmZcGIU6+IzTg6nSPlCM8LCDCv2TJEgAKCwsH3VcvKysjLy8Ps1m/cT3ayT0X2rhxI5qm8bvf/Y4//OEPA6/X1tayatUqAP7rv/5rTE3tjTbAgmnOtclOgQn2x1iFn9NsNpsLN3f8i9FoJDs7m+bmZkJCQpgxYwbd3d0cOXKE/Px8rFYrr7/+Ojt27LhoOm5paemgo3NnZyddXV2Eh4cPunOwa9cuFi1aNKjto48+yoMPPgjo4w3jx4/no48+wmKxMH/+fPbs2UNkZKQH99z9LH3w1FvwiQM3GVImwP03QriL44TCtwLiyJ+UlERJSQlLly7FYDBQV1dHXFwc27dvp7i4eOBswN5gX29vL83NzQN/+scNenp6Br3e29t7UduCggJee+01Pve5z3H27FkOHTrE9OnT+dGPfsTbb7895oIPEBIMq2+Aa6YPfQkQpMHcNLh/iQR/LAuII/9w2tvbiY2NRdM02traxmQgfaW9G/71qf6tvsMnoM8K4SHw8OdhnOvTF4SfCIgj/3Cqqqqw2Wykp6dL8J0UbYDFGXDvYojWJyxiCJXgB4qAD//BgwcB99zfFyKQSPiFUJSEXwhFBcQMv+H0z/sXQgwW8Ed+IYR9En4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JREn4hFCXhF0JRIb4uQPi37l442wl9Vv3vNptv6/G2Piuc7oBzFtA0MITCJZH6/491ms2m2j+nGM45C1Qeg0ONcLwFTrVdvM6EaEiOg+kJkJMK4aFeL9NjbDaob4aKOjjWDA2nobdv8DqGUH3/U+JhbhpcFuuTUkdNwi8AaOuCPdXwfi10nnO8XXgIzEuDxRkwPspz9Xma1QblR+GdT8DY4lzb6QlwwwzISPRMbZ4i4VeczQYV9fC3MudC/1nhIfCFHFgwdeydEpvbYOc+qD05uu1clQJfmgtR4e6py9Mk/Arr7YM/vauf5rvLzMlw9zX6qfFYUH4Unn0fzvWNvK4jog3wf66FqZe6Z3ueJOFX1DkLPPUWHD7h/m0nx8F9N0JkmPu37U6lNfDXMvdvNzQYvnE9XDHJ/dt2J7nVB9TV1fH0009z7733kpOTQ1hYGJqmsXLlSo+08zWrFX5f4pnggz5Q+NRbYHHT0dQTKuo8E3zQz6h+8zbUmT2zfXeRW33AY489xuOPP+61dr729ifwcaNzbf7nFoiNgNYu+PlrI69/9BS8fhCWZrtUoke1tEPR+861cXb/e/vgj6WwYak+HuKP5MgPxMfHc+utt7Jp0yZefvll7r//fo+286UTrfD3A863i43Q72/HRjje5s2P9dtl/sRmg7+8Dz0W59q5sv/mdiiudK4fb/LTzyTv2rhx46C/79u3z6PtfOmF8ovvW3uK1QbPlcF/3+w/dwAqj0GNyXv9vfOJfgdk8njv9emogDzym81mCgoKmDZtGgaDgeTkZNatW0dHRwerVq1C0zS2bdvm6zK97mQrHGrybp/HmvVJM/6i5BPv97m3xvt9OiLgjvyVlZXk5+djMpmIiooiIyODxsZGtm7dSm1tLS0t+gyO7Oxs3xbqA6WHfdRvDaTG+6bvCzWehk9Peb/f8jpYdiVE+Nndj4A68pvNZpYtW4bJZGL9+vU0NTVRUVGByWSisLCQ4uJiysrK0DSNzMxMX5frdfvrfdPvgWPnvxvgS77a/3MW+LjBN30PJ6DCv3btWoxGI2vWrGHLli3ExMQMLCsoKCArKwuLxUJqaiqxsWN0QraLznbqI9W+cK5Pv+TwteNOTtt1p2M+7HsoARP+6upqioqKiI+PZ/PmzXbXycnJASArK8ubpfkFX77x/aF/m823NTj7fQFvCJjw79y5E6vVyooVK4iOjra7TkSEfp9GxfD7+sjr6/47z0FHj+/69/X+2xMwA3579uwBIC8vb8h1jEYjMHbCn5ubi8nknvtSM29cx6ybNthd1j+BZTixhvP/feT2odcbahLME9t/w70vP+JYsR5giE3gtv+vfMjlI/0MRrv/LWdaSUrKcLBaxyUkJFBePvR+DSdgwl9fr4/mpKSk2F1usVgoLS0Fxk74TSYTDQ3uGSmafObMkMv6J7A4IijI8XUv1NZ61m374orIjuEnNzj6M3B1//ssFp/uvz0BE/6Ojg4Aurrsj2oVFRVhNpuJiYlhypQp3izNZQkJCW7bVkTY0LNsHBkIjDXob3yrFVq7h15vqG2Fh0Jiou++8B4cOvypzUg/g9Huf19vp0f2fzTvkYAJf0JCAqdPn6aiooKFCxcOWtbU1MSGDfopb2ZmJpq/TDcbgaunc/bUnoBf7ra/zJG56o/crh/xWrvhkRec7/9nP1hP5u/XO9/QjX64S59ya89IP4PR7v+82Uk89e/LTn8RMAN+S5YsAaCwsJCamvNTqsrKysjLy8Ns1r9ipeLkHoDEOPDlR15ynA87/7ckH9aQPMF3fQ8lYMJfUFDAhAkTOH78OLNmzWLOnDmkp6czb9480tLSWLx4MWD/er+0tJT4+PiBPz//+c8B+Mtf/jLo9f4xg9G28wVDKEy6xDd9j3NiTMGTUif6ru8pfjDD8bMCJvxJSUmUlJSwdOlSDAYDdXV1xMXFsX37doqLiwfOBuyFv7e3l+bm5oE//eMGPT09g17v7e11SztfmT/VN/0umOYfX+zJTYVgH7zjx0dB+mXe73ckAXPNDzBz5kxeeeWVi15vb2+nrq6OoKAgZs+efdHyG264AVceaORqO1+Zm6Z/xdRdj6xyRJAGC6d5r7/hRBvgysv1ufbetChdHyz0N35YkvtVVVVhs9lIT08nMtIPzj99JDIMFqZ7t8+rUv3jlL/fDTO9exYSEaZ/pdcfKRH+gwcPAmPn/r4n3ZqpP3ffG6IN8IWrvNOXo5LiIG+m9/q7PUf/OfgjCb9iwkPhq/Odb9faBWec/HLQl+f65xs/P9P5X7Thyv7PSoS5fjylJKCu+Yci4R8sPQGWXwW7Khxv48hcgAstmQVZlzvXxltCg+Ge6+CX/4B2B+f7O7v/CePgzoX+MdA5FHl0t8J2V8Erle7fbt5M+PyV/v3GB/3hHr/eA+3DzNhzxaRxcO+N+i1OfybhV1z5Uf05e91uuBsZFgyfv0of3fb34Pczt8H/vgv1bnrMdmYy3DF/bPzWHgm/4Eyn/ltrnH2c94WmXgr/uQDiY0Ze199YrfDWIf2pxhYXnzgUFQ5fyoUrU8bOB5+EXwD6wy4+PaU/bPLD4449dkvTYHYiXDNdH0cIGiNv+qGc7YT3juh/zjo4sHdprH6mMzfN/39D0WdJ+MVF2rr03+ZzvEX/c7ZT/+07IcEQY9Bvl10+AaZd5l/38N2lzwpHLtj/E2f133dgs+kfcFelQNIE/aGkKRPGzpH+syT8Qjhg0/P62cC4CPjeF31djXsocZ9fCHExCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCb8QipLwC6EoCT9QV1fH008/zb333ktOTg5hYWFomsbKlSuHbGOz2SgtLeXBBx/k6quvJi4ujtDQUC677DJuu+02XnrpJe/tgBAuCPF1Af7gscce4/HHH3eqzZ49e1iyZAkAmqYxdepU0tLSOHLkCMXFxRQXF3PPPffwm9/8Bk3TPFG2EKMiR34gPj6eW2+9lU2bNvHyyy9z//33j9jGZrORlpbGL3/5S06ePMnhw4cpLy+nubmZX/ziF2iaxm9/+1ueeOIJL+yB8CSrDWw2/f/7/xsI5MgPbNy4cdDf9+3bN2KbefPmcejQIUJDQwe9HhwczAMPPMChQ4fYvn07O3bscOjDRPgfYwvsrYGKOjjXp7/W1g0vVcDV6RAf49PyRi0gj/xms5mCggKmTZuGwWAgOTmZdevW0dHRwapVq9A0jW3bto2qj9jY2IuCf6Gbb74ZgE8++WRU/Qjv67PCX/bBlldhX+354APYgD3V8KOXYHfV2D4TCLgjf2VlJfn5+ZhMJqKiosjIyKCxsZGtW7dSW1tLS0sLANnZ2R6to7u7G4DIyEiP9iPcy2qDP70LFfXDr2cDXqnUPyhunuONytwvoI78ZrOZZcuWYTKZWL9+PU1NTVRUVGAymSgsLKS4uJiysjI0TSMzM9OjtRQVFQFw7bXXerQf4V7lR0cO/oVe/RCONXuuHk8KqPCvXbsWo9HImjVr2LJlCzEx5y/KCgoKyMrKwmKxkJqaSmxsrMfq+Pvf/86uXbsG+hVjx94a77TxBwET/urqaoqKioiPj2fz5s1218nJyQEgKyvLY3XU1tZy1113AfqH0dVXX+2xvoR7HW9x7SheUQ+d59xfj6cFzDX/zp07sVqtrFixgujoaLvrREREAJ4Lv8lk4pZbbqGlpYWbbrqJLVu2jGp7ubm5mEwmN1UnRnL5lV9k3le3Ot3O0gfzrrmZM41VHqhqeAkJCZSXl7vUNmDCv2fPHgDy8vKGXMdoNAKeCX9/4I8cOcKiRYt44YUXhr0b4AiTyURDQ4ObKhQjuWRah8ttm1vOYhpj/1YBE/76en2UJiUlxe5yi8VCaWkp4P7wt7a2csstt3Dw4EGuuuoqiouL3TLKn5CQ4IbqhKMiwpy/b2ez2dA0jdioEIITEz1Q1fBG8x4JmPB3dOif2l1dXXaXFxUVYTabiYmJYcqUKW7rt7Ozk9tuu42ysjJmzpzJ66+/zrhx49yybVdP54Rreiyw6Xno7nW8jaZpTB4Phyr3MtZmcQfMgF//J2BFRcVFy5qamtiwYQMAmZmZbptrf+7cOW6//XZKSkqYOnUqu3fvJj4+3i3bFt4XHgLz0pxvd006Yy74EEDh7/+STWFhITU15++9lJWVkZeXh9lsBtw3uaevr48777yTN954g6SkJHbv3s3kyZPdsm3hO3kzITrc8fUTxkGO+04kvUqz2cbyBMXzjEYj2dnZNDc3ExISwowZM+ju7ubIkSPk5+djtVp5/fXX2bFjB6tXrx7UtrS0lOXLlw/8vbOzk66uLsLDwwfdOdi1axeLFi0C9LsLd955JwBpaWlMmjRpyNqee+45uX4fQ441w5N7Rr59NzEG7r8Rxkd5py53C5hr/qSkJEpKStiwYQNvv/02dXV1ZGRksH37dlavXs3UqVMB+4N9vb29NDdffIO3p6eHnp6eQetduKzfp59+yqeffjpkbf1TfcXYcPkE+O+b9dl7B47rU3gvFB4Cc6fALZkQbfBNje4QMEf+4bS3txMbG4umabS1tcl8e+Gwti7YfwxauyBIg7hoyL4cDKO7i+sXAubIP5yqqipsNhvTp0+X4AunxETAdVf4ugrPCJgBv+EcPHgQ8Oy0XiHGGgm/EIqS8AuhKCUG/IQQF1PiyC+EuJiEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEXwhFSfiFUJSEH6irq+Ppp5/m3nvvJScnh7CwMDRNY+XKlcO2e+mll7jvvvuYN28eiYmJhIeHExMTQ3Z2Ng8//DBms9k7OyCEK2zCtm7dOhtw0Z+777572HbXX3+9DbCFhYXZUlNTbbm5ubbLL7/cpmmaDbBNnDjRtn//fq/sgxDOkiM/EB8fz6233sqmTZt4+eWXuf/++x1qd8899/Dmm2/S1tbG0aNHKSsro76+ngMHDjB79mxOnTrFnXfe6eHqhXBNiK8L8AcbN24c9Pd9+/Y51O7rX/+63dfnzJnD008/zfz586murqa6upqZM2eOuk5vO2eBino4bILuXggLgbSJMDcNDKG+rk6MVkAe+c1mMwUFBUybNg2DwUBycjLr1q2jo6ODVatWoWka27Zt82gNF4a9s7PTo325m9UKr34Im16Av+yDD+qgqgH218PfymHT8/DiB2Dp83WlYjQC7shfWVlJfn4+JpOJqKgoMjIyaGxsZOvWrdTW1tLS0gJAdna2R+soLS0FICoqiiuuuMKjfbmT1QrPlELlsaHX6bHAW4eg6Sysvh5Cgr1Xn3CfgDrym81mli1bhslkYv369TQ1NVFRUYHJZKKwsJDi4mLKysrQNI3MzEy392+1WmlqauKZZ54ZuFPw4x//mOjoaLf35SnFB4YP/oU+adLPBMTYFFDhX7t2LUajkTVr1rBlyxZiYmIGlhUUFJCVlYXFYiE1NZXY2Fi39fvkk0+iaRrBwcFMnjyZu+++m6SkJF5++WXWrl3rtn48resclHziXJv3a+HM2LqqEf8WMOGvrq6mqKiI+Ph4Nm/ebHednJwcALKystza96RJk1i0aBHz589n8uTJaJrGhx9+yJ///GfOnj3r1r48qewonHPyOt5qg/eOeKYe4VkBE/6dO3ditVpZsWLFkKfZERERgPvDv3z5cvbu3cu+fftoaGjgwIEDLFiwgJ07d7J06VK39uVJhxpda1ftYjvhWwEz4Ldnzx4A8vLyhlzHaDQC7g//Z82ZM4fi4mLS0tIoLS1l9+7dLFmyxOnt5ObmYjKZPFChfTfc+zzxU+Y53e6j6iMkfeMG9xckRpSQkEB5uWsDLwET/vr6egBSUlLsLrdYLAMj8J4OP0BMTAzXX389f/vb3zhw4IBL4TeZTDQ0NHigOvs62s8Q70K7ro6zXq1TuEfAhL+jowOArq4uu8uLioowm83ExMQwZcoUr9RksVgA6Otz7YZ4QkKCO8sZUefJauAmp9u1m6pITEx0f0FiRKN5jwRM+BMSEjh9+jQVFRUsXLhw0LKmpiY2bNgAQGZmJpqmebyelpYW3n77bcD1OQWuns656nQHfH8X2GzOtdv+g68zeZv92Y7CfwXMgF//aXVhYSE1NTUDr5eVlZGXlzfwDTt3Te4pLy/nu9/9LkeOXDzUvX//fvLz8zlz5gxz5szhxhtvdEufnjY+CjKTnWuTfhlMHu+ZeoRnaTabs5/z/sloNJKdnU1zczMhISHMmDGD7u5ujhw5Qn5+Plarlddff50dO3awevXqQW1LS0tZvnz5wN87Ozvp6uoiPDx80J2DXbt2sWjRIgDeeuutgcHFSy+9lOTkZIKDgzEajTQ26sPf06dP59VXXyUtLc3Tu+82nT2w9R9gcuAOZVwUPHAzxEZ4vi7hfgFz5E9KSqKkpISlS5diMBioq6sjLi6O7du3U1xcPHA2YG+wr7e3l+bm5oE//eMGPT09g17v7e0daJOVlcXjjz/OF77wBWJjY6mpqWH//v309fWxZMkSfvWrX3HgwIExFXyAyHD49ufgiknDrzclHtZJ8Me0gDnyD6e9vZ3Y2Fg0TaOtrY3IyEhflzQmGFug9DDUmKClXX/IQWgwfGsJpEwALwydCA8KmCP/cKqqqrDZbKSnp0vwnZAUB3fMh/+3/PwRPjIMUuMl+IFAifAfPHgQ8M79fSHGCgm/EIqS8AuhqICZ5DOc/nn/QojzlDjyCyEuJuEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUJeEXQlESfiEUFeLrAoT/67OCzebrKnzHagNLH2gahATp/w0Ems2m8j+r+CybDY6egkNNcLxF/9PefX65BkxPgOQJ+n/TLwucMPRr7YLKY3CsGYwtcKL1/IdfcBBMugSS4yAlHrIvB0OoT8t1mYRfANDbB//6FEproPGM4+0ujYVF6bBgKoSP0RD0+/QkvPMJfHhcP9o7IiwEclPhuhmQMM6j5bmdhF9QZ4Y/vwcnW13fRlwUfHWBfjYw1nSegxc/0D/8XBWkwZJZcNNsCAl2X22eJOFXmNUGrx6A3R+775r+2unwhRz99HgsqD0Jz+yFs13u2d7kS2DltfoZkb+T8CvKaoWd70PZKI52Q5mdBCuv8f8j4McN8Nt3wGJ173ajDXD/Ypg83r3bdbcx8vnsOXV1dTz99NPce++95OTkEBYWhqZprFy50ultPfXUU2iahqZp3HDDDW6v1V1sNniuzDPBB/jICH981/HrZl84fMIzwQd9gPTXe+DUKC6jvEH5W32PPfYYjz/++Ki3YzKZKCgocENFnvdBHbx7xLN9VB6DtBq47grP9uOKjh79VN8Twe/X3g3PlMIDN/vvJZCfluU98fHx3HrrrWzatImXX36Z+++/36XtfPvb36a1tZXbbrvNzRW619kueL7c+Xb/cws8crv+X0e9sh/Mbc735WnPl0Nb98jrXciV/T/eAns+dq4fb1L+yL9x48ZBf9+3b5/T23jppZd47rnn+Pa3v01cXByvvPKKu8pzu10f6KPbzoqNgEsinWtzrk+/vLh3sfP9econTfqZj7Nc2X+A1w7CVakwIdr5tp4WcEd+s9lMQUEB06ZNw2AwkJyczLp16+jo6GDVqlVomsa2bdvc1l9bWxvf+ta3mDx5Mj/84Q/dtl1PONupn45706EmMJ31bp/DeecT7/bXZ4V3D3u3T0cF1JG/srKS/Px8TCYTUVFRZGRk0NjYyNatW6mtraWlpQWA7Oxst/X50EMPYTQaefbZZ4mN9e/7O+8d8c0gXOlh+FKu9/v9rOZ2fYTf2/bVwi2ZEOpndz8C5shvNptZtmwZJpOJ9evX09TUREVFBSaTicLCQoqLiykrK0PTNDIzM93S53vvvccTTzxBfn4+X/7yl92yTU8qP+qbfj846h8j/x/UgS/K6OiB6kYfdDyCgAn/2rVrMRqNrFmzhi1bthATEzOwrKCggKysLCwWC6mpqW45Qvf29rJ69WrCw8PdehnhKR09YG73Td+d56DZDwb+jjWr2fdQAiL81dXVFBUVER8fz+bNm+2uk5OTA0BWVpZb+vzJT35CVVUVGzduJC0tzS3b9KTjLWr3D3DchwH0Zd9DCYjw79y5E6vVyooVK4iOtj+sGhERAbgn/J988gk/+tGPmDlzJhs2bBj19rzBdMbH/ft40K/rnPum8LrC1/tvT0AM+O3ZsweAvLy8IdcxGo2Ae8J/33330dPTw5NPPkloqOe+ypabm4vJZHLLtmbeuI5ZN9n/oPqfW/RbWcOJNZz/7yO3D71eaxf8/LWLX//VE0/xzVe+52C17meITeC2/2/oCQ4j/QxGu//m060kJWU4WK3jEhISKC93YeIGARL++vp6AFJSUuwut1gslJaWAu4Jf0VFBUFBQXzlK1+5aFl7u35h/e6775KQoH/FraamxqVxBpPJREODe4anJ58d+tDjzD3soCDX7ne3tbe5bV9cEdUx/HQ+R38Gru5/X1+fT/ffnoAIf0dHBwBdXfbP64qKijCbzcTExDBlyhS39Gm1Wjlx4sSQy3t7eweWW62uzSPt//Bwh0jD0PeZWh04HY416G98qxVah5kdN9S2IsKCSExMHLkjDwkJH36WzUg/g9Huv83S45H9H817JCDCn5CQwOnTp6moqGDhwoWDljU1NQ1cl2dmZqK54bEzZ86cGXLZI488wve+9z2uv/563nrrrVH14+rpnD2fNMETe+wvs3ea+lmP3K4f8Vq74ZEXnO9/83cf4KrfPuB8Qzd65AU402l/2Ug/g9Huf/aMBLb/+9LTXwTEgN+SJUsAKCwspKamZuD1srIy8vLyMJvNgHsn94w1SXG+7T95gm/7B9/+DJJ9/PO3JyDCX1BQwIQJEzh+/DizZs1izpw5pKenM2/ePNLS0li8WJ9cbu96v7S0lPj4+IE/P//5zwH4y1/+Muj1/jGDsSoqHOJjRl7PEyLDIN4P5ran+PAD6HI/+PD7rIAIf1JSEiUlJSxduhSDwUBdXR1xcXFs376d4uLigbMBe+Hv7e2lubl54E//uEFPT8+g13t7e726T54w1z3DHU7LneIfD/nMSdUfQOptUeGQMdkHHY8g4J/k097eTmxsLJqm0dbWRmSkC0O1AeJsF3zvBdem2vZf857pdP6a96FlcJmffO3hqbegyoVB99Hs/40ZsOxK5/v0tIA48g+nqqoKm81Genq60sEHGBcBV9m/G+oxMyf7T/ABbpjh3f5CgvSnG/ujgA//wYMHAfdN6x3rll+ln4Z6Q1gI/Mdc7/TlqPQE717+5GdCnB+Md9gj4VdMTIRrX69t7dJPeR2ZE9Dv81f650Msbs/Rz4Kc4cr+p0yAvJnO9eNNAXGffzgS/otdmQKfnoK9NSOv28+RuQAXuioFrvbT093IcLj7Gn3eQ2+fY22c3f9YA9y1SJ8Y5K8CfsBP2Ge1wbPv6w+acLesZPj6Nf774Mp+1Y36E3wd/QBwVKwB7rtR/7Ve/kzCrzCbTX/G3D8+ct/DNq6foZ/u+3vw+x09pT/J9/QQM/+clTQe7r4WJvpoToUzJPyCY836r+sazddO46PhPxfA1MvcV5e3dPfCrgr9MWeuCg7Sf1XXkllj54NPwi8A/VdQl9fp4wBGJx68kTAOrpkO89L00f2xrM4Mez+B/cf0B286whAKc9P0X1M2Fn5F14Uk/GIQm00/E+j/Fd3GFv2pv/1vkliDPke+/1d0p030j9l77tTerT/luP9XlJ84O/jDIGXC+V/RnZk8dn87sYRfjMhm08cEgrTAC7qjvvs3/Rt94yLge1/0dTXuMcZP1IQ3aBoEKxr6foH4oTdGhiaEEO4m4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+IRQl4RdCURJ+oK6ujqeffpp7772XnJwcwsLC0DSNlStXDttu5cqVaJo27J9Dhw55ZyeEcFKIrwvwB4899hiPP/64y+3T09O59NJL7S6LjIx0ebtCeJKEH4iPj+fWW29l7ty55Obm8uqrr/LrX//a4fYPP/zwiGcJQvgbCT+wcePGQX/ft2+fjyoR/qS9G/bVwgdHobXr/GvvHoacKRA+xtMTkNf8ZrOZgoICpk2bhsFgIDk5mXXr1tHR0cGqVavQNI1t27b5ukzhp2w22F0Fm16AVyqh6SzY/r2szwbP/gs2PQ/7631Z5eiN8c+ui1VWVpKfn4/JZCIqKoqMjAwaGxvZunUrtbW1tLS0AJCdne22Pp977jlefPFFWltbiY+PZ8GCBdx1111MnDjRbX0I7yk+oId/ON298Ie9YOmDuWneqcvdAir8ZrOZZcuWYTKZWL9+PZs2bSImJgaARx99lAcffJCQkBA0TSMzM9Nt/RYXFw/6+1//+le++93v8uSTT/K1r33Nbf0Iz6tqGDn4F9q5Dy6Ph8tiPVeTpwTUaf/atWsxGo2sWbOGLVu2DAQfoKCggKysLCwWC6mpqcTGjv5fa/r06fziF7+gsrKSM2fO0NHRwTvvvMNNN91ER0cHX//61y/6YBD+7W0n78xabVBa45laPC1gwl9dXU1RURHx8fFs3rzZ7jo5OTkAZGVluaXPhx9+mAceeICsrCzGjRtHZGQk1157La+99hrLly/HZrPxwAMPYLPZRt6Y8LmTrVBjcr7dvz6FHov76/G0gDnt37lzJ1arlRUrVhAdHW13nYiICMB94R+KpmkUFhaya9cujhw5wsGDB126zMjNzcVkcuHdKFySnLWc+Xf+yul23b1w1YLPcdZU7YGqhpeQkEB5eblLbQMm/Hv27AEgLy9vyHWMRiPg+fADXHHFFcTFxdHS0sLhw4ddCr/JZKKhocED1Ql7LpnW7XLblrPtmMbYv1XAhL++Xr/vkpKSYne5xWKhtLQU8E74AUJDQwf6dkVCQoI7yxEjiIpwPQ6XxIQTnJjoxmocM5r3SMCEv6OjA4Curi67y4uKijCbzcTExDBlyhSP13Pq1ClOnjwJQFJSkkvbcPV0Trimo0e/f2+xOtduQjRUffAWQZpn6vKUgBnw6/8ErKiouGhZU1MTGzZsACAzMxNN8/y/0s9+9jNsNhvjxo1j7ty5Hu9PjF5UOFyZ6ny7RemMueBDAIV/yZIlABQWFlJTc/7eS1lZGXl5eZjNZsB9k3v+8Y9/8J3vfIfa2tpBr3d2dvL973+fRx99FICHHnqIsLAwt/QpPC9vBoQGO75+bATMn+q5ejxJswXIfSij0Uh2djbNzc2EhIQwY8YMuru7OXLkCPn5+VitVl5//XV27NjB6tWrB7UtLS1l+fLlA3/v7Oykq6uL8PDwQXcOdu3axaJFiwB48cUXuf322wGYNGkSiYmJWK1WqqurBy49vvnNb/Lkk0965UxDuM9HRvhdCfSNcPofFQ73LYakOO/U5W4Bc+RPSkqipKSEpUuXYjAYqKurIy4uju3bt1NcXDxwNmBvsK+3t5fm5uaBP/3h7enpGfR6b2/vQJucnBw2btzIjTfeSFhYGB9//DFVVVVMnDiRO+64g927d7N9+3YJ/hg0OwnuvxGShwn1FQmw7qaxG3wIoCP/cNrb24mNjUXTNNra2uQ79sJhx5qh/N/f6tM0fXBvfhpMHIPTeT8rYEb7h1NVVYXNZmP69OkSfOGUyyfofwJRwJz2D+fgwYOA9+7vCzEWSPiFUJSEXwhFKTHgJ4S4mBJHfiHExST8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8QihKwi+EoiT8Qijq/wdc4rWjwCe4FAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 305.727x1287.61 with 1 Axes>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mask = Qinit(15) + Qmask(global_pattern=\"101\",merge_within=\"101\", strides=[1,0,0], steps=[2,1,1], offsets=[0,0,0], mapping=v3)\n",
    "plot_circuit(mask)\n",
    "circuit = get_circuit(mask)\n",
    "draw_circuit(circuit)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "e2c90eb1",
   "metadata": {},
   "source": [
    "#### Qunmask example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "c5745a64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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R+kJb60917i5LxR6Czp+j/VakJub5czgq9uIc/0CHZZtam8jbmoeJSauzFeD6v3lb88hIzCDE2nGi4svrdsdX27njajsnKBgTk7xdZpftvN11X+Xt6w6090hfqPP+KtDamgQ+V+6zvZpoXL58GYfDQURkVK+9RkTkQFpbW3nppZd6lM2viZyFGTyYm+4GME1Y8YdzfLllbYdlq4KHUD/w8dv8xaC+Geb8Zh2JLZ93OyZxzVc/ZBcvXtyjRNOb+kJb60917q5ZzmYGd/C3c+9vY235Bx2WraKKeupv+7f6pnrm/HoOiXS8Yakvr9sd7rZzf7juQHuP9IU6768Cra1J4MvPz+/yGJ9t2CciIiIiIn2XV+do2O12QkNDyZz1NBMfmuFyue7M0dhdtoV3fvc6Fy9e7FE2v+ywhQUV7R/7AhiYvDK+6+EsCeuCqW9uK3GDSaQNvsjW0KnedOXKFaKi2p6W1dXV+f341L7Q1vpTnbvLsu8jgt7fdvMXvW1DVNK/1+XQqYQVCdQ31d/yt8g7Ivni6S86HTrly+t2h7vt3B+uO9DeI32hzvurQGtrEvj8buhUSEgIo0cnc/azT7s81t70Zy5U/9/rP//Xf1Zz9vNT3BkW3ukmf2eqTjJ6dPL1CVHd9eRYWF91u4lsBnkpVmydDHm02aBw0rUJumbb2Pmrk+gKJxmED9BjzN7U0tJy/b9tNpvfPzbuC22tP9W521IfgKNHbpkMbsTFYU2d0PY/tQM2m43CjMLbTgYvzCgk/M7wTl/ap9fthvbt/KuLHhgUTqLLdn7jum+dBO+t6w6090hfqPP+KtDamvQPXl91Kicnh/e2bWfB4jUYxs3f7d3w6dFPWPHSc7f8PnXyNB578ue3LWOaJr987mdkfP8hVq9e3eMYG1tgVSVsvLo038wkyO3G0nxtywK28vYHn0DNcXbkZ/LgkAE9jkdcE4grbgR6W+uPde4WDy1ve6L2BCOjR3Z7eVufXbebri3jfOIijOzmMs6NLfDGJ3YWrP8jAL/66bd46t4Qr113IL5HILDrvL8K1LYmfZvXE42ysjKmTZvGvEXLSBqV4tFznz52iNcKnqWsrMytfTQ8QW947+uvde7L6+6vdS6BRe8R7+uv1+1LqnPxR16fDD516lSShg3jg60bPX7uHVs3Mmz4cNLS0jx+bhERERERcZ3XEw2LxcKiggIOVuzm0P7dHjtv2/k+pCA/H4tFi2mJiIiIiPiST+7Is7OzmT59Om+vXkZdbY3b56urrWHDmmXMmDGD7OxsD0QoIiIiIiLu8EmiYRgGq1atIvKuCApffsGtZKOutoaVv3iBgZF3UVRU1OkEcxERERER8Q6fjTGKjY1lR3k5IcFBLF34FAcruj+M6mDFbpYufIoBIVZ2lJcTGxvbC5GKiIiIiEh3+XQyQ2JiIvv27mXSxO+wZkk+qxe/yOljh+hsISzTNDl97BCrF7/ImiX5TP7uRPbu2cPQoUO9GLmIiIiIiHTGqxv23U5sbCybN2+muLiY/IICXit4lrj4BIaM+CaDE0cQETkQgIb6i5ypOsnnJ49y/uyfSBo2jLfeeovs7GwNlxIRERER8TM+TzSgbc7Go48+yiOPPEJ5eTklJSVUVOxn085/x+FwAGC1Whk9OpkffC+drKws0tLStLqUiIiIiIif8otE4xqLxUJ6evr1zfaam5tpaGgAICIiApvN5svwRERERETERX6VaNzMZrMRHR3t6zBERERERKSbNPZIREREREQ8TomGiIiIiIh4nF8PnbLb7Vy+fBmA8PBwQkJCfByRiIiIiIi4wq+eaDidTsrKysjJySElZSyhoaHExMQQExNDaGgoKSljycnJoaysDKfT6etwRURERESkA37xRMM0zev7aJw+dYq4+ASGjhxD5oSpRERGAdBQX8fZzz7lvW3befPNN0kaNoxFBQXaR0NERERExA/5PNGorq4mNzeX0tJS7kmdyLxFc0gcOabD5ME0TapOHGFH6QYee+wx1q9fT1FREbGxsV6OXEREREREOuLTRKOqqoopaWnUX2rgiecXMfb+iV2WMQyDpFEpJI1K4WDFbjasWcb4CRPYUV5OYmKiF6IWEREREZGu+GyORnV1NVPS0rC3OJj/8hsuJRk3uyd1IvNffgN7i4MpaWlUV1f3QqQiIiIiItJdPkk0TNMkNzeX+ksN5C18lajoQT0+V1T0IPIWvkr9pQZmz56NaZoejFRERERERHrCJ4lGcXExpaWlPPzEM24lGddERQ/iJznPsGXLFoqLiz0QoYiIiIiIuMPrczScTif5BQXckzqx0+FS2/6lmEMVu6k59wXBthCGjkjmh4/OZtDXB9/2+LbzfYf8ggIeeeQRLBa/WrlXRERERKRf8frd+Pbt2zl96hQPZszs9LhTxw7x3e/9kPm/eJ2nFr6Kw+Fg5csvYG/6c4dlpmTM5PSpU5SXl3s6bBERERER6QavP9EoKSkhLj6BxJFjOj3uyf/1q3Y/P/rkCyzMzeRM1acMSx572zKJo1KIi0+gpKSE9PR0j8XcXftqYOmBEPj5fqg5zv4LFh4Mda1sYwsUVcKm020/ZybB7GQIC+69eCVw9du2dvYM7P0Iai9AdAxM+DbE3/5pp1+x2+Hj/VB5pO3n5DFw3/0QEuJS8X1n97G8YjnHa48zKnoUc1PnMj5+fC8G7BmNzY0UfVzEpspNAGQmZzL7vtmE2cJ6/7Vb4PVKKzy3G4AVlVbm3Ot6O99XA8sPw/GLMGogzE2B8e6P+O3TVOcico1henn2dErKWCIG3U3W7PndKneh+v/yd/P+Jwt+vZqv3z20w+PW/XYJjRfOcujQQXdD7ZGSTyH7fbAYJg7TAEcLRpCV4nSDrOGdl21sgcm/hwO1cO1/igGMi4adPw6QG0AfunLlCmFhbTcujY2NhIa6eMcdoPyhrfmkzg8fhI1vg8UApxMsFnCaMPNhSLmn91+/p+x2WLsKzp+nXa3HxcGs3C6TjZIjJWRvyibIEkSrsxWrxYrD6aA4s5isMVm9Hn5PNTY3MnntZA5UH8C8et0GBuNix7Fz1s5eTTZutHPz+kIhhmEwLtpwqZ1fe48FGdBqgtUAhwnF6XT5Hrumv30u+UOd91f9ra1JYPDqEw273c6xY5VkTpjarXJOp5N3/vENEkeO6TTJABicOIJ3dm2jsbERm83mTrjd1tQKebuCMaHtxg8gKBgTk7xdJhnxLYQEdVx+5WELB2qDMLmxWaFJ2wd24WEH88Y4ezX+QNfc3Nzuv4OD+25m5i9tzet13tpCcOm7gInhvHqz7nS23b6WvktL0nCw+nwf0tuyVOwh6Pw52m9FamKeP4ejYi/O8Q90WLaptYm8rXmYmLQ6WwGu/5u3NY+MxAxCrK49FfG2lRUr2yUZACYmB6oPUFhRyLzUeb332l9t51c3gXW1nX/1PdZ69T3WaradIW8XXb7HrulPn0vgH3XeX/W3tia+58p9tld75MuXL+NwOIiIjOpWuQ1vLuf8mc+Zt+i1Lo+NiBxIa2srL730ktez+argIdQPfPw2fzGob4Y5v1lHYsvnHZZfEzkLM3gwN92JYJqw4g/n+HLLWo/G29d89UN28eLFXk80vclf2pq363yI6eRxs+WW3xsATU2se/UVPjf8cyGIWc5mOhrcde79bawt/6DDslVUUU/9bf9W31TPnF/PIRH/3LB0DWvaJRnXmJis2L6CL7d/2Xuv7UY7d/c9dk1/+lwC/6jz/qq/tTXxvfz8/C6P8c8e+Ss2vLmco/+xl6dfXMLAv4jxdTgiIiIiIuICr87RsNvthIaGkjnraSY+NKPTY03TZOPaFRyq2M3T+Uv5Wly8S6+xu2wL7/zudS5evOiToVMJ64Kpb4b2X+eYRNrgi+zOH/suO2xhQUX74SxtZzJ5ZbyGTnXlypUrREW1PS2rq6vr0+NT/aWteb3OW1sIfm0JNDXddNXAHXfQMu95/x06te8jgt7fdvMXvW3D39K/1+XQqYQVCdQ31d/yt8g7Ivni6S/8dujUsoplLNi+4JanGgYGr0x9pVeHTrnTzt19j13Tnz6XwD/qvL/qb21NfM/vhk6FhIQwenQyZz/7tMtjN6xZzscfbueJv/k77hhwJw31dQDccWcoNlvHHeqZqpOMHp18fUKUN9lsUDjpdhPZDAonQfiAzv+HPDkW1lfdfhJdXooVm4Zbdqql5caQGpvN1qcfG/tLW/N6ndtsMP1Ht0wGN5wmTP8Rtjvv7N3Xd0fqA3D0yC2TwY24OKypE9qurQM2m43CjMLbTgYvzCgk/M5wr1xCTzyZ+iTrj66/dTJ43DjyUvN6tc3caOc3L3rQdTtv/x4z2+YMXF1woXCS0eV77Jr+9LkE/lHn/VV/a2sSGLy+6lROTg7vbdvOgsVrMIybv9u7Ye5Pbz9h/NG8v2H8g9+/7d9M0+SXz/2MjO8/xOrVqz0Sb09cW5rvxEUY2c2l+Rpb4I1P7CxY/0cAfvXTb/HUvSFaccoF/XHFDV+3NZ/VeT9f3vZE7QlGRo8MqOVtV328io2VGwGYmTyT3Ptyvba87apK2Hh1GeeZSZDbjWWc25aQbuXtDz6BmuPsyM/kwSEDXH79/vi55Os676/6Y1sT/+f1RKOsrIxp06Yxb9EykkalePTcp48d4rWCZykrK/PpPhru0odFz6jeus/dOlOdS3/gTjvXe6RnVG/dpzoTf+T1yeBTp04ladgwPti60ePn3rF1I8OGDyctLc3j5xYREREREdd5PdGwWCwsKijgYMVuDu3f7bHztp3vQwry87FY/H4xLRERERGRPs0nd+TZ2dlMnz6dt1cvo662xu3z1dXWsGHNMmbMmEF2drYHIhQREREREXf4JNEwDINVq1YReVcEhS+/4FayUVdbw8pfvMDAyLsoKirqdIK5iIiIiIh4h8/GGMXGxrKjvJyQ4CCWLnyKgxXdH0Z1sGI3Sxc+xYAQKzvKy4mNje2FSEVEREREpLt8OpkhMTGRfXv3Mmnid1izJJ/Vi1/k9LFDdLYQlmmanD52iNWLX2TNknwmf3cie/fsYejQoV6MXEREREREOuPzLXRjY2PZvHkzxcXF5BcU8FrBs8TFJzBkxDcZnDiCiMiBADTUX+RM1Uk+P3mU82f/RNKwYbz11ltkZ2druJSIiIiIiJ/xeaIBbXM2Hn30UR555BHKy8spKSmhomI/m3b+Ow6HAwCr1cro0cn84HvpZGVlkZaWptWlRERERET8lF8kGtdYLBbS09Ovb7bX3NxMQ0MDABEREdhsNl+GJyIiIiIiLvKrRONmNpuN6OhoX4chIiIiIiLdpLFHIiIiIiLicUo0RERERETE4/x66JTdbufy5csAhIeHExIS4uOIRERERETEFX71RMPpdFJWVkZOTg4pKWMJDQ0lJiaGmJgYQkNDSUkZS05ODmVlZTidTl+HKyIiIiIiHfCLJxqmaV7fR+P0qVPExScwdOQYMidMJSIyCoCG+jrOfvYp723bzptvvknSsGEsKijQPhoiIiIiIn7I54lGdXU1ubm5lJaWck/qROYtmkPiyDEdJg+maVJ14gg7Sjfw2GOPsX79eoqKioiNjfVy5CIiIiIi0hGfJhpVVVVMSUuj/lIDTzy/iLH3T+yyjGEYJI1KIWlUCgcrdrNhzTLGT5jAjvJyEhMTvRC1iIiIiIh0xWdzNKqrq5mSloa9xcH8l99wKcm42T2pE5n/8hvYWxxMSUujurq6FyIVEREREZHu8kmiYZomubm51F9qIG/hq0RFD+rxuaKiB5G38FXqLzUwe/ZsTNP0YKQiIiIiItITPkk0iouLKS0t5eEnnnErybgmKnoQP8l5hi1btlBcXOyBCEVERERExB1en6PhdDrJLyjgntSJnQ6X+sO2zXxYtpn/ulADQFx8At/P/B8kjxt/2+Pbzvcd8gsKeOSRR7BY/GrlXhERERGRfsXrd+Pbt2/n9KlTPJgxs9PjIv8imhnZufzNLwv5m79fyYgx41j16xc5f+bzDstMyZjJ6VOnKC8v93DUIiIiIiLSHV5/olFSUkJcfAKJI8d0elzKfd9u9/P0rBx2b9vC559WEjd4yG3LJI5KIS4+gZKSEtLT0z0Vslc1tsDrlVZ4bjcAKyqtzLkXwoJdK7+vBpYfhuMXYdRAmJsC490fnSZ9kCfa2tIDIfDz/VBznP0XLDwY2nvxtnP2DOz9CGovQHQMTPg2xA/20ou7wW6Hj/dD5ZG2n5PHwH33Q0iIS8X3nd3H8orlHK89zqjoUcxNncv4+Ns/5fUnjc2NFH1cxKbKTQBkJmcy+77ZhNnCfBxZ19xp5+6+x/ord+u8qBI2nW77OTMJZierzkV8xTC9PHs6JWUsEYPuJmv2fJfLOJ0ODuzZyVsrX+WFV/6BuPghHR677rdLaLxwlkOHDnogWu9qbIHJv4cDteb1Se2GYTAu2mDnj7v+oCz5FLLfhyADWk2wGuAwoTgdsob3evg+d+XKFcLC2m5cGhsbCQ311l1v4PFUW7MYJg7TAEcLRpCV4nSj99va4YOw8W2wGOB0gsUCThNmPgwp9/Tyi7vBboe1q+D8eeDax64BcXEwK7fLZKPkSAnZm7IJsgTR6mzFarHicDooziwma0xWr4ffU43NjUxeO5kD1Qcwr163gcG42HHsnLXTr5MNd9q5u++x/sozdd7uHca4aPpFnasPFH/k1ScadrudY8cqyZww1aXjz31RxdL//TStLc2E3DGAJ55f1GmSATA4cQTv7NpGY2MjNpvNA1F7z8rDFg7UBmFiwNUNC03aOqrCww7mjXF2WLapFfJ2BWMCrWZb2Vaz7Qx5uyAjvoWQoF6/BJ9qbm5u99/BwX28V3GDp9qa42pbIygYE5O8XWbvtrXWFoJL3wVMDOfVWwmns+2movRdWpKGg9Xn+5DelqViD0Hnz9F+K1IT8/w5HBV7cY5/oMOyTa1N5G3Nw8Sk1dkKcP3fvK15ZCRmEGJ17amIt62sWNkuyQAwMTlQfYDCikLmpc7zYXQdc7edu/Me6688WudX9ac6Vx8o3ubKfbZXe+TLly/jcDiIiIxy6fivfX0wP3+1iD9/eYVP9u7irTdeYW7B0k6TjYjIgbS2tvLSSy8FXDa/JnIWZvBgbroTwTRhxR/O8eWWtR2WrQoeQv3Ax2/zF4P6Zpjzm3Uktnzu0Xj9zVc/ZBcvXhxwiaY3BWpbG2I6edxsuc0rA01NrHv1FT43/HMhiFnOZjoa3HXu/W2sLf+gw7JVVFFP/W3/Vt9Uz5xfzyER/9ywdA1r2iUZ15iYrNi+gi+3f+mDqLrmbjt35z3WX6nO3aM+ULwtPz+/y2P8s0e+ymoNJib2G9ydOIIfZj/BNxKS2Pmv7/g6LBERERER6YJX52jY7XZCQ0PJnPU0Ex+a0e3yK156joHRX+OxJ3/e4TG7y7bwzu9e5+LFiwGXzS87bGFBRfvHvgAGJq+M73o4S8K6YOqb20rcYBJpgy+y+/7QqStXrhAV1fa0rK6uLuCeaHlTwLa11haCX1sCTU03vTJwxx20zHvef4dO7fuIoPe33fxla9swkfTvdTl0KmFFAvVN9bf8LfKOSL54+gu/HTq1rGIZC7YvuOWphoHBK1Nf8euhU+60c3feY/2V6tw96gPF2/xu6FRISAijRydz9rNPuzx2c/Fqku9NZWD017A3fckfd5dzqvIgef/rV52WO1N1ktGjk69PiAokT46F9VW3m8hmkJdixdbJcEubDQonXZsMbrbN07g6ia5wkkH4gMBKunqipeXGkBqbzRZwiaY3ea6tfXXhAYPCSfRuW7PZYPqPbpkMbjhNmP4jbHfe2Xuv7a7UB+DokVsmgxtxcVhTJ7RdWwdsNhuFGYW3nQxemFFI+J3hXrmEnngy9UnWH11/62TwuHHkpeb57fvU3Xbuznusv/Jcnd86Ab8/1Ln6QPFHXl91Kicnh/e2bWfB4jUYxs3f7d1Q/A+/5uSRA1y6WMeAO0P5+t2JpP/op4wa+60Oy5imyS+f+xkZ33+I1atX90b4va6xBVZVwsarS/PNTILcbizN17YsYCtvf/AJ1BxnR34mDw4Z0Gvx+hOtuNE9nmhryw/DiYsw0ttLKffz5W1P1J5gZPTIgFredtXHq9hYuRGAmckzyb0v169XnLrGnXbu7nusv3K3zt/4xM6C9X8E4Fc//RZP3RvSL+pcfaD4I68nGmVlZUybNo15i5aRNCrFo+c+fewQrxU8S1lZWcDuo+EJ/fXDpr9et4iI3NBf+4L+et3i37w+GXzq1KkkDRvGB1s3evzcO7ZuZNjw4aSlpXn83CIiIiIi4jqvJxoWi4VFBQUcrNjNof27PXbetvN9SEF+PhaLXy+mJSIiIiLS5/nkjjw7O5vp06fz9upl1NXWuH2+utoaNqxZxowZM8jOzvZAhCIiIiIi4g6fJBqGYbBq1Soi74qg8OUX3Eo26mprWPmLFxgYeRdFRUWdTjAXERERERHv8NkYo9jYWHaUlxMSHMTShU9xsKL7w6gOVuxm6cKnGBBiZUd5ObGxsb0QqYiIiIiIdJdPJzMkJiayb+9eJk38DmuW5LN68YucPnaIzhbCMk2T08cOsXrxi6xZks/k705k7549DB061IuRi4iIiIhIZ3y+hW5sbCybN2+muLiY/IICXit4lrj4BIaM+CaDE0cQETkQgIb6i5ypOsnnJ49y/uyfSBo2jLfeeovs7GwNlxIRERER8TNe30ejM06nk/LyckpKSqio2E9l5VEcDgcAVquV0aOTSU29n6ysLNLS0rS6VAf661ra/fW6RUTkhv7aF/TX6xb/5vMnGl9lsVhIT0+/vtlec3MzDQ0NAERERGCz2XwZnoiIiIiIuMivEo2b2Ww2oqOjfR2GiIiIiIh0k8YeiYiIiIiIxynREBERERERj/ProVN2u53Lly8DEB4eTkhIiI8jEhERERERV/jVEw2n00lZWRk5OTmkpIwlNDSUmJgYYmJiCA0NJSVlLDk5OZSVleF0On0droiIiIiIdMAvnmiYpnl9H43Tp04RF5/A0JFjyJwwlYjIKAAa6us4+9mnvLdtO2+++SZJw4axqKBA+2iIiIiIiPghnyca1dXV5ObmUlpayj2pE5m3aA6JI8d0mDyYpknViSPsKN3AY489xvr16ykqKiI2NtbLkYuIiIiISEd8mmhUVVUxJS2N+ksNPPH8IsbeP7HLMoZhkDQqhaRRKRys2M2GNcsYP2ECO8rLSUxM9ELUIiIiIiLSFZ/N0aiurmZKWhr2FgfzX37DpSTjZvekTmT+y29gb3EwJS2N6urqXohURERERES6yyeJhmma5ObmUn+pgbyFrxIVPajH54qKHkTewlepv9TA7NmzMU3Tg5GKiIiIiEhP+CTRKC4uprS0lIefeMatJOOaqOhB/CTnGbZs2UJxcbEHIhQREREREXd4PdFwOp3kFxRwT+pEl4dLlf1+HXN/OpVNv3ujw2Pazvcd8gsKtPStiIiIiIiPeT3R2L59O6dPneLBjJkuHf+nU8f58P1Svn531xO9p2TM5PSpU5SXl7sbpoiIiIiIuMHrq06VlJQQF59A4sgxXR5rb/oz//T63/PI7Pn8+7/8c5fHJ45KIS4+gZKSEtLT0z0RbsDZVwNLD4TAz/dDzXH2X7DwYKhrZRtboKgSNp1u+zkzCWYnQ1hw78XbJ5w9A3s/gtoLEB0DE74N8YN9HVXfFqh1brfDx/uh8kjbz8lj4L77ISTEpeL7zu5jecVyjtceZ1T0KOamzmV8/PheDNgzGpsbKfq4iE2VmwDITM5k9n2zCbOF+Tiyvqu/1nljC7xeaYXndgOwotLKnHtd78f21cDyw3D8IowaCHNTYLz7I7xF+i3D9PLs6ZSUsUQMupus2fO7PPatN37FnWER/NXjT7J80Xy+kZBE5v/zVKdl1v12CY0XznLo0EFPhRwwSj6F7PfBYpg4TAMcLRhBVorTDbKGd162sQUm/x4O1MK1BmEA46Jh548DI9m4cuUKYWFtnWhjYyOhoS5mWO44fBA2vg0WA5xOsFjAacLMhyHlnt5//f4oUOvcboe1q+D8edq9y+LiYFZul8lGyZESsjdlE2QJotXZitVixeF0UJxZTNaYrF4Pv6camxuZvHYyB6oPYF69bgODcbHj2DlrZ5+/8fWF/lrnN/ox8/rCMIZhMC7acKkfu9aHBhnQaoLVAIcJxel02Yf6A5/0gSJd8OoTDbvdzrFjlWROmNrlsR9/WM6Zz07x/N+v7NZrDE4cwTu7ttHY2IjNZutpqAGnqRXydgVjQluSARAUjIlJ3i6TjPgWQoI6Lr/ysIUDtUGY3Ngo0aTtA7vwsIN5Y/x/3ktzc3O7/w4O7uXsqLWF4NJ3ARPDefXG0els69ZL36UlaThYfb4nZt8SwHVuqdhD0PlztN+K1MQ8fw5HxV6c4x/osGxTaxN5W/MwMWl1tgJc/zdvax4ZiRmEWF17KuJtKytWtrvhBTAxOVB9gMKKQualzvNhdH1Tf63zdv3Y1U1/Xe3HvtqHtl7tQ1vNtjPk7aLLPtQfeL0PlH7Plftsr/bIly9fxuFwEBEZ1elxF2v/k3f+8Q2eXPgqwd1MFiIiB9La2spLL73Ur7L5quAh1A98/DZ/Mahvhjm/WUdiy+cdll8TOQszeDA33QVhmrDiD+f4cstaj8bbG776Ibt48eJeTzSHmE4eN1tu+b0B0NTEuldf4XPDZ1vV9EmBXOeznM10NLjr3PvbWFv+QYdlq6iinvrb/q2+qZ45v55DIv65Yeka1rS74b3GxGTF9hV8uf1LH0TVt/XXOnenH3O3D/UH3u4DRfLz87s8xi+/+jvz2UkuX6rn1wv++vrvnE4np48d4g///nuW/vO/YbH4+VcLIiIiIiL9mFfnaNjtdkJDQ8mc9TQTH5rR4XFNf/6Sugs17X5XXPhrvvaNwaT/MIuv3z20w7K7y7bwzu9e5+LFi/0qm29qhYR1wdQ3Q/uvc0wibfBFduePfZcdtrCgov3QqbYzmbwyPjCGTl25coWoqLanZXV1db3/RKu1heDXlkBT0001DtxxBy3znvfbYTwBK4Dr3LLvI4Le33bzl61twx3Tv9fl0KmEFQnUN9Xf8rfIOyL54ukv/Hbo1LKKZSzYvuCWb9gNDF6Z+kqfHcbjS/21zt3px9ztQ/2B1/tA6ff8buhUSEgIo0cnc/azTzs97o4Bd96STNjuuIPQsIhOkwyAM1UnGT06+fqEqP7CZoPCSbebyGZQOAnCB3TeGJ4cC+urbj+JLi/Fii0Ahnq2tNwYUmOz2Xo/0bTZYPqPbpmYbDhNmP4jbHfe2buv3x8Fcp2nPgBHj9wyGdyIi8OaOqHt2jpgs9kozCi87WTwwoxCwu8M98ol9MSTqU+y/uj6Wycmx40jLzWvX30h5C39tc5v9GM3L2rSdT/Wvg812+ZpXF1QpXCS0WUf6g+83geKuMDrX/2lpt7Pe9u2Y5omhnHzd3vuMU2Tz04cIeP7D3n0vIEiazgMjWhbmu/ERRjZjaX5woLbVpd645NmFqz/IwC//Om3eOrekIBYccpnUu6BgVGBudRqoArUOg8JaVtdqofL22aNyWJo5FCWVyznRO0JRkaPDIjlbcNsYeyctZNVH69iY+VGAGYmzyT3vtw+u/qRr/XXOr/Wj62qhI1Xl2mfmQS5Li7Tfq0PXXrAwdsffAI1xynPz+TBIQN6M2yRPs3ry9uWlZUxbdo05i1aRtKoFI+e+/SxQ7xW8CxlZWX9dh8NdwXy8niBHLuIiPiHQO1LAjVu6du8vjzL1KlTSRo2jA+2bvT4uXds3ciw4cNJS0vz+LlFRERERMR1Xk80LBYLiwoKOFixm0P7d3vsvG3n+5CC/HwsFv9c3lJEREREpL/wyR15dnY206dP5+3Vy6irrem6QBfqamvYsGYZM2bMIDs72wMRioiIiIiIO3ySaBiGwapVq4i8K4LCl19wK9moq61h5S9eYGDkXRQVFXl8grmIiIiIiHSfz8YYxcbGsqO8nJDgIJYufIqDFd0fRnWwYjdLFz7FgBArO8rLiY2N7YVIRURERESku3w6mSExMZF9e/cyaeJ3WLMkn9WLX+T0sUN0thCWaZqcPnaI1YtfZM2SfCZ/dyJ79+xh6NDO99cQERERERHv8fkWurGxsWzevJni4mLyCwp4reBZ4uITGDLimwxOHEFE5EAAGuovcqbqJJ+fPMr5s38iadgw3nrrLbKzszVcSkRERETEz3h9H43OOJ1OysvLKSkpoaJiP5WVR3E4HABYrVZGj04mNfV+srKySEtL0+pSvSCQ1+EO5NhFRMQ/BGpfEqhxS9/m8ycaX2WxWEhPT7++2V5zczMNDQ0AREREYLPZfBmeiIiIiIi4yK8SjZvZbDaio6N9HYaIiIiIiHSTxh6JiIiIiIjHKdEQERERERGP8+uhU3a7ncuXLwMQHh5OSEiIjyMSERERERFX+NUTDafTSVlZGTk5OaSkjCU0NJSYmBhiYmIIDQ0lJWUsOTk5lJWV4XQ6fR2uiIiIiIh0wC+eaJimeX0fjdOnThEXn8DQkWPInDCViMgoABrq6zj72ae8t207b775JknDhrGooED7aIiIiIiI+CGfJxrV1dXk5uZSWlrKPakTmbdoDokjx3SYPJimSdWJI+wo3cBjjz3G+vXrKSoqIjY21suRi4iIiIhIR3yaaFRVVTElLY36Sw088fwixt4/scsyhmGQNCqFpFEpHKzYzYY1yxg/YQI7ystJTEz0QtQiIiIiItIVn83RqK6uZkpaGvYWB/NffsOlJONm96ROZP7Lb2BvcTAlLY3q6upeiFRERERERLrLJ4mGaZrk5uZSf6mBvIWvEhU9qMfniooeRN7CV6m/1MDs2bMxTdODkYqIiIiISE/4JNEoLi6mtLSUh594xq0k45qo6EH8JOcZtmzZQnFxsQciFBERERERdximlx8BOJ1ORowcSVhULDnPLerwuH/d8I/828Z/ave7r319MP/7N7/rsMzqxS9y5WINJ0+cwGLxq5V7A8aVK1cICwsDoLGxkdDQUB9H5LpAjl1ERPxDoPYlgRq39G1enwy+fft2Tp86xbxFc7o8Ni5+CE/9n19f/9liCer0+CkZM3mt4FnKy8tJT093O1YREREREekZrycaJSUlxMUnkDhyTJfHWoKCru+j4YrEUSnExSdQUlKiRKMHGlvg9UorPLcbgBWVVubcC2HBrpXfVwPLD8PxizBqIMxNgfHuj4zzf2fPwN6PoPYCRMfAhG9D/GBfR9W3BWqd2+3w8X6oPNL2c/IYuO9+CAlxqfi+s/tYXrGc47XHGRU9irmpcxkfP74XA/aMxuZGij4uYlPlJgAykzOZfd9swmxhPo6s71Kd98y+Glh6IAR+vh9qjrP/goUHXXww0NgCRZWw6XTbz5lJMDvZ9T5UpC/y+tCplJSxRAy6m6zZ8zs97l83/CPlW97mjjtDCQ62MWR4MjOyc7qc07Hut0tovHCWQ4cOejLsPq+xBSb/Hg7Umtcn1BuGwbhog50/7vqDsuRTyH4fggxoNcFqgMOE4nTIGt7r4QM+emx8+CBsfBssBjidYLGA04SZD0PKPb3/+v1RoNa53Q5rV8H588C1j10D4uJgVm6XyUbJkRKyN2UTZAmi1dmK1WLF4XRQnFlM1pisXg+/pxqbG5m8djIHqg9gXr1uA4NxsePYOWunbnx7geq8Z671YxbDxGEa4GjBCLJSnG502Y/d6EPbvbsZF41LfagnaOiU+COvPtGw2+0cO1ZJ5oSpXR47ZNgoHs17ga99PZ6Gi3W8t+mfeC3/Gf528RruGHBnh+UGJ47gnV3baGxsxGazeTL8Pm3lYQsHaoMwMeDqZokmbYlH4WEH88Y4Oyzb1Ap5u4IxgVazrWyr2XaGvF2QEd9CSOej3jyiubm53X8HB/fyJ3trC8Gl7wImhvNq1+J0tnUype/SkjQcrD7fE7NvCeA6t1TsIej8OdpvRWpinj+Ho2IvzvEPdFi2qbWJvK15mJi0OlsBrv+btzWPjMQMQqyuPRXxtpUVK9vd8AKYmByoPkBhRSHzUuf5MLq+SXXefV/txxxX+zGCgjExydtldtmPtetDr3K1D/UUr/eB0u+5cp/t1R758uXLOBwOl4ZDJY+7MRzgGwlJJAwfTcFT2RzY8wEPpP2gw3IRkQNpbW3lpZdeUjbfDWsiZ2EGD+amuyBME1b84RxfblnbYdmq4CHUD3z8Nn8xqG+GOb9ZR2LL5x6N93a++iG7ePHiXk80h5hOHjdbbvm9AdDUxLpXX+FzQ4sSeFIg1/ksZzMdDe469/421pZ/0GHZKqqop/62f6tvqmfOr+eQiH9uWLqGNe1ueK8xMVmxfQVfbv/SB1H1barz7nO3H3OnD/UUb/eBIvn5+V0e45898m3cGRrG1+LiuVB9ztehiIiIiIhIF7w6R8NutxMaGkrmrKeZ+NCM7pVt+jP5Tz7CX/7kfzL5L/+qw+N2l23hnd+9zsWLF5XNd8OywxYWVLR/7AtgYPLK+K6HTiWsC6a+ua3EDSaRNvgi2ztDp65cuUJUVNvTsrq6ut5/otXaQvBrS6Cp6aarBu64g5Z5z/vtMJ6AFcB1btn3EUHvb7v5C8+2oRrp3+ty6FTCigTqm+pv+VvkHZF88fQXfjt0alnFMhZsX3DLN+wGBq9MfUXDeHqB6rz73O3H3OlDPcXrfaD0e343dCokJITRo5M5+9mnXR77+//vH/jmfQ8QFT2ISxf/i/c2/A7DYuG/fSet03Jnqk4yenTy9QlR4ponx8L6qttNZDPIS7Fi62Sop80GhZOuTQY32+ZpXJ1EVzjJIHyAdxK+lpYbQ2psNlvvJ5o2G0z/0S0Tkw2nCdN/hO3OjucSSQ8Fcp2nPgBHj9wyGdyIi8OaOqHt2jpgs9kozCi87WTwwoxCwu8M98ol9MSTqU+y/uj6Wycmx40jLzVPXwj1AtV597Xvx766qIlB4SS67Mdu9KG3LqjSVR/qKV7vA0Vc4PVVp3Jycnhv23YWLF6DYdz83d4Nv1v2d5w6fpgrlxsIi7iLpJFjyMjKISb26x2WMU2TXz73MzK+/xCrV6/ujfD7tMYWWFUJG68uzTczCXK7sTRf27KArbz9wSdQc5wd+Zk8OGRAr8V7M5+tuBGoS60GskCtcw8tb3ui9gQjo0cG1PK2qz5excbKjQDMTJ5J7n25Wv2oF6nOe+baMu0nLsLIbi7T3tgCb3xiZ8H6PwLwq59+i6fuDfHa8rZadUr8kdcTjbKyMqZNm8a8RctIGpXi0XOfPnaI1wqepaysTPto+IgvP+j0ISsiIr6kPlCkPa9PBp86dSpJw4bxwdaNHj/3jq0bGTZ8OGlpnQ+vEhERERGR3uX1RMNisbCooICDFbs5tH+3x87bdr4PKcjPx2IJmMW0RERERET6JJ/ckWdnZzN9+nTeXr2Mutoat89XV1vDhjXLmDFjBtnZ2R6IUERERERE3OGTRMMwDFatWkXkXREUvvyCW8lGXW0NK3/xAgMj76KoqKjTCeYiIiIiIuIdPhtjFBsby47yckKCg1i68CkOVnR/GNXBit0sXfgUA0Ks7CgvJzY2thciFRERERGR7vLpZIbExET27d3LpInfYc2SfFYvfpHTxw7R2UJYpmly+tghVi9+kTVL8pn83Yns3bOHoUOHejFyERERERHpjM+30I2NjWXz5s0UFxeTX1DAawXPEhefwJAR32Rw4ggiIgcC0FB/kTNVJ/n85FHOn/0TScOG8dZbb5Gdna3hUiIiIiIifsbr+2h0xul0Ul5eTklJCRUV+6msPIrD4QDAarUyenQyqan3k5WVRVpamlaX8kNaQ1xERPor9YEi7fn8icZXWSwW0tPTr2+219zcTENDAwARERHYbDZfhiciIiIiIi7yq0TjZjabjejoaF+HISIiIiIi3aSxRyIiIiIi4nFKNERERERExOP8euiU3W7n8uXLAISHhxMSEuLjiERERERExBV+9UTD6XRSVlZGTk4OKSljCQ0NJSYmhpiYGEJDQ0lJGUtOTg5lZWU4nU5fhysiIiIiIh3wiycapmle30fj9KlTxMUnMHTkGDInTCUiMgqAhvo6zn72Ke9t286bb75J0rBhLCoo0D4aIiIiIiJ+yOeJRnV1Nbm5uZSWlnJP6kTmLZpD4sgxHSYPpmlSdeIIO0o38Nhjj7F+/XqKioqIjY31cuQiIiIiItIRnyYaVVVVTElLo/5SA088v4ix90/ssoxhGCSNSiFpVAoHK3azYc0yxk+YwI7ychITE70QtYiIiIiIdMVnczSqq6uZkpaGvcXB/JffcCnJuNk9qROZ//Ib2FscTElLo7q6uhciFRERERGR7vJJomGaJrm5udRfaiBv4atERQ/q8bmiogeRt/BV6i81MHv2bEzT9GCkIiIiIiLSEz5JNIqLiyktLeXhJ55xK8m4Jip6ED/JeYYtW7ZQXFzsgQhFRERERMQdhunlRwBOp5MRI0cSFhVLznOLOj22vu4Cm/95FZWfVNBitxMd+w0ezfsb7k4aedvjVy9+kSsXazh54gQWi1+t3NtvXLlyhbCwMAAaGxsJDQ3tF68tIiKiPlCkPa/fjW/fvp3Tp07xYMbMTo/7svEyy16cR1CQlby//RX/a+mb/Ph//DUDQsM7LDMlYyanT52ivLzc02GLiIiIiEg3eH3VqZKSEuLiE0gcOabT497fXELkX8Tw6JMvXP/dX3wtrtMyiaNSiItPoKSkhPT0dI/EK67bVwNLD4TAz/dDzXH2X7DwoItfqDS2QFElbDrd9nNmEsxOhrDg3ovXY86egb0fQe0FiI6BCd+G+MG+jqpvC9Q6t9vh4/1QeaTt5+QxcN/9EBLiUvF9Z/exvGI5x2uPMyp6FHNT5zI+fnwvBuwZjc2NFH1cxKbKTQBkJmcy+77ZhNnCfBxZ36U6977GFni90grP7QZgRaWVOfe63o/tq4Hlh+H4RRg1EOamwHj3R5eL+JTXh06lpIwlYtDdZM2e3+lxL8+fxeh77qf+vy5w6tgh7oqK5rvTfsi3p2Z0Wm7db5fQeOEshw4d9GTY0oWSTyH7fbAYJg7TAEcLRpCV4nSDrOGdl21sgcm/hwO1cK0xGsC4aNj5Y9c/pH3y2PjwQdj4NlgMcDrBYgGnCTMfhpR7ev/1+6NArXO7HdaugvPnadfS4+JgVm6XyUbJkRKyN2UTZAmi1dmK1WLF4XRQnFlM1pisXg+/pxqbG5m8djIHqg9gXr1uA4NxsePYOWunbnx7gerc+270Y+b1RWkMw2BctOFSP3atDw0yoNUEqwEOE4rT6bIPvUZDp8QfefWJht1u59ixSjInTO3y2P/6z/PsLtvMlIyZPPTfs/ni9Ak2rX2dIKuV8ZO/12G5wYkjeGfXNhobG7HZbJ4MXzrQ1Ap5u4IxoS3JAAgKxsQkb5dJRnwLIUEdl1952MKB2iBMbmzSaNL2gV142MG8MU6X4mhubm7338HBvfw4pLWF4NJ3ARPDefXG0els69ZL36UlaThYfb4nZt8SwHVuqdhD0PlztN+K1MQ8fw5HxV6c4x/osGxTaxN5W/MwMWl1tgJc/zdvax4ZiRmEWF17KuJtKytWtrvhBTAxOVB9gMKKQualzvNhdH2T6tz72vVjVzccdrUf+2of2nq1D201286Qt4su+9BrvN4HSr/nyn22V3vky5cv43A4iIiM6vJY02kyOGkEMx55AoDBQ4dz/sznfFi2pdNEIyJyIK2trbz00kvK5r2kKngI9QMfv81fDOqbYc5v1pHY8nmH5ddEzsIMHsxNd2CYJqz4wzm+3LLWpTi++iG7ePHiXk80h5hOHjdbbvm9AdDUxLpXX+FzQ4sSeFIg1/ksZzMdDe469/421pZ/0GHZKqqop/62f6tvqmfOr+eQiH9uWLqGNe1ueK8xMVmxfQVfbv/SB1H1bapz73OnH3O3D73G232gSH5+fpfH+GePDEQMjCL2GwntfjfoG3dzsfY/fRSRiIiIiIi4yqtzNOx2O6GhoWTOepqJD83o9Nh/XP4yF//rP3lm0WvXf/fOP67k81PHmP93Kzost7tsC+/87nUuXryobN5LmlohYV0w9c3Q/usck0gbfJHd+WPfZYctLKhoP3Sq7Uwmr4x3fejUlStXiIpqe1pWV1fX+0+0WlsIfm0JNDXddNXAHXfQMu95vx3GE7ACuM4t+z4i6P1tN3/h2TbkMP17XQ6dSliRQH1T/S1/i7wjki+e/sJvh04tq1jGgu0LbvmG3cDglamvaBhPL1Cde587/Zi7feg1Xu8Dpd/zu6FTISEhjB6dzNnPPu3y2Ad/kMlvXpzLtn/5Z8Y98CB/OnWcj7Zv5ae5z3Za7kzVSUaPTr4+IUp6n80GhZNuN5HNoHAShA/ovCE+ORbWV91+El1eihWbi8NMW1puDKmx2Wy9n2jabDD9R7dMTDacJkz/EbY77+zd1++PArnOUx+Ao0dumQxuxMVhTZ3Qdm0dsNlsFGYU3nYyeGFGIeF3drzst689mfok64+uv3Victw48lLz9IVQL1Cde9+NfuzmRU267sfa96Fm2zyNqwuqFE4yuuxDr/F6HyjiAq+vOpWTk8N727azYPEaDOPm7/baO/LxHrasW8OF6rP8RUwcU6bP7HTVKdM0+eVzPyPj+w+xevVqT4cuXbi2NN+JizCym0vzNbbAG5/YWbD+jwD86qff4ql7Q7q1vK3PVtwI1KVWA1mg1rmHlrc9UXuCkdEjA2p521Ufr2Jj5UYAZibPJPe+XK1+1ItU597X2AKrKmHj1WXaZyZBbjeWaW9bIr6Vtz/4BGqOsyM/kweHDHD59bXqlPgjrycaZWVlTJs2jXmLlpE0KsWj5z597BCvFTxLWVmZ9tEIQO5+SOpDVkREApk7/Zj6QPFHXp8MPnXqVJKGDeODrRs9fu4dWzcybPhw0tLSPH5uERERERFxndcTDYvFwqKCAg5W7ObQ/t0eO2/b+T6kID8fi8VvF9MSEREREekXfHJHnp2dzfTp03l79TLqamvcPl9dbQ0b1ixjxowZZGdneyBCERERERFxh08SDcMwWLVqFZF3RVD48gtuJRt1tTWs/MULDIy8i6Kioi4nmIuIiIiISO/z2Rij2NhYdpSXExIcxNKFT3GwovvDqA5W7GbpwqcYEGJlR3k5sbGxvRCpiIiIiIh0l08nMyQmJrJv714mTfwOa5bks3rxi5w+dojOFsIyTZPTxw6xevGLrFmSz+TvTmTvnj0MHTrUi5GLiIiIiEhnfL6FbmxsLJs3b6a4uJj8ggJeK3iWuPgEhoz4JoMTRxARORCAhvqLnKk6yecnj3L+7J9IGjaMt956i+zsbA2XEhERERHxM17fR6MzTqeT8vJySkpKqKjYT2XlURwOBwBWq5XRo5NJTb2frKws0tLStLpUH6N9NEREpD/TPhrS1/j8icZXWSwW0tPTr2+219zcTENDAwARERHYbDZfhiciIiIiIi7yq0TjZjabjejoaF+HISIiIiIi3aSxRyIiIiIi4nFKNERERERExOP8euiU3W7n8uXLAISHhxMSEuLjiERERERExBV+9UTD6XRSVlZGTk4OKSljCQ0NJSYmhpiYGEJDQ0lJGUtOTg5lZWU4nU5fhysiIiIiIh3wiycapmle30fj9KlTxMUnMHTkGDInTCUiMgqAhvo6zn72Ke9t286bb75J0rBhLCoo0D4aIiIiIiJ+yOeJRnV1Nbm5uZSWlnJP6kTmLZpD4sgxHSYPpmlSdeIIO0o38Nhjj7F+/XqKioqIjY31cuQiIiIiItIRnyYaVVVVTElLo/5SA088v4ix90/ssoxhGCSNSiFpVAoHK3azYc0yxk+YwI7ychITE70QtYiIiIiIdMVnczSqq6uZkpaGvcXB/JffcCnJuNk9qROZ//Ib2FscTElLo7q6uhciFRERERGR7vJJomGaJrm5udRfaiBv4atERQ/q8bmiogeRt/BV6i81MHv2bEzT9GCkIiIiIiLSEz5JNIqLiyktLeXhJ55xK8m4Jip6ED/JeYYtW7ZQXFzsgQhFRERERMQdhunlRwBOp5MRI0cSFhVLznOLOjyuYE42dRdqbvn9xGk/5OGcebcts3rxi1y5WMPJEyewWPxq5V5xwZUrVwgLCwOgsbGR0NBQr5YXERHxJXf6MfWB4o+8Phl8+/btnD51inmL5nR63HN/vxLzK3tlnP/iM954+QXGTZjcYZkpGTN5reBZysvLSU9P91jMIiIiIiLSPV5PNEpKSoiLTyBx5JhOjwuPiGz3c9nv1xE96OsMS76nwzKJo1KIi0+gpKREiUaAaWyB1yut8NxuAFZUWplzL4QFu1Z+Xw0sPRACP98PNcfZf8HCg976MufsGdj7EdRegOgYmPBtiB/spRfvpwK1zu12+Hg/VB5p+zl5DNx3P4SEuFR839l9LK9YzvHa44yKHsXc1LmMjx/fiwF7RmNzI0UfF7GpchMAmcmZzL5vNmG2MB9H1nepzgOPO/2Yu32oSG/x+tCplJSxRAy6m6zZ810u09rawv/564eZkjGTaf/90U6PXffbJTReOMuhQwfdDVW8pLEFJv8eDtSa1yfzG4bBuGiDnT/u+oOy5FPIfh8shonDNMDRghFkpTjdIGt4Lwd/+CBsfBssBjidYLGA04SZD0NKx0mxuCFQ69xuh7Wr4Px54NrHrgFxcTArt8tko+RICdmbsgmyBNHqbMVqseJwOijOLCZrTFavh99Tjc2NTF47mQPVBzCvXreBwbjYceyctVM3vr1AdR543OnH3O1DRXqTV59o2O12jh2rJHPC1G6VO7T/Q/58pZHxk7/X5bGDE0fwzq5tNDY2YrPZehqqeNHKwxYO1AZhYsDVjRpN2j40Cw87mDfG2WHZplbI2xWMCW0fzgBBwZiY5O0yyYhvISSolwJvbSG49F3AxHBevXF0Otu69dJ3aUkaDlaf74nZtwRwnVsq9hB0/hzttyI1Mc+fw1GxF+f4Bzos29TaRN7WPExMWp2tANf/zduaR0ZiBiFW156KeNvKipXtbngBTEwOVB+gsKKQeam3n3MnPac6Dyzu9mPu9KEi7nDlPturPfLly5dxOBxEREZ1q9ze8vcYfW8qd0VFd3lsRORAWltbeemllzQRKkCsiZyFGTyYm+7AME1Y8YdzfLllbYdlq4KHUD/w8dv8xaC+Geb8Zh2JLZ97NN5rhphOHjdbbvPKQFMT6159hc8NLUrgSYFc57OczXQ0uOvc+9tYW/5Bh2WrqKKe+tv+rb6pnjm/nkMi/rlh6RrWtLvhvcbEZMX2FXy5/UsfRNW3qc4Di7v9mDt9qIg78vPzuzzGP3vkr6i7UMOJw//BA2k/8HUoIiIiIiLiIq8+0QgPDycoKIiG+jqXy+z94N8IvyuSb/63CS4d31B/EavVyosvvqihUwFiwGELCyq45fs3w4Cnv/t15o352w7LNrXC5nUm9c3Q/usck0gbvP7sI706dMp8bQk0Nd30ysAdd/DIvOf9dhhPwArgOrfs+wje33bbv309fRp/28XQqc0rNlPfVH/L3yLviOT1p1/326FTAyoGsGD7glu+YTcweHrq0xrG0wtU54HF3X7MnT5UpLd5tUcOCQlh9Ohkzn72qUvHO51O9n3wb6ROnkZQkGt3i2eqTjJ6dPL1taTF/z05FtZXwYHadlNkGRdtkJdixdbJRDabDQontU2iCzKg1QSr0TbOtXAShA/oxWTTZoPpP7plYrLhNGH6j7DdeWfvvXZ/Fch1nvoAHD1yy2RwIy4Oa+qEtmvrgM1mozCj8LaTwQszCgm/M9wrl9ATT6Y+yfqj62+dmBw3jrzUPH0h1AtU54HF3X7MnT5UpLd5/au/1NT7eW/bdkzTxDCMTo89cfg/uFj7n0x48Psunds0TT47cYSM7z/kiVDFS8KCYeePYVUlbDzd9ruZSZCb7NpqGVnDYWgELD8MJy7CyIEwNwXGu7/pfNdS7oGBUYG51GqgCtQ6DwlpW12qh8vbZo3JYmjkUJZXLOdE7QlGRo8MiOVtw2xh7Jy1k1Ufr2Jj5UYAZibPJPe+XK1+1EtU54HHnX7M3T5UpDd5fXnbsrIypk2bxrxFy0galeLRc58+dojXCp6lrKxM+2iIiIiIiPiQ1xMNp9PJiJEjCYuKJee5RR499+rFL/Jl/X9y4vhxLBa/n+cuIiIiItJnef1u3GKxsKiggIMVuzm0f7fHztt2vg8pyM9XkiEiIiIi4mNef6IBbXMpfvjDH7Jr94fMf/kNoqLdG0xfV1vD0oVPMfm7E3n33Xe7nPshIiIiIiK9yyeJBkB1dTXjJ0zA3uIgb+GrPU426mprWPmLFxgQYmXvnj3ExsZ6OFIREREREekun40xio2NZUd5OSHBQSxd+BQHK7o/jOpgxW6WLnyKASFWdpSXK8kQEREREfETPnuicU11dTW5ubmUlpYy9v7vMCVjJomjUjoc/mSaJlXHD7Nj60YO7f+QGTNmUFRUpCRDRERERMSP+DzRgLbkobi4mPyCAk6fOkVcfAJDRnyTwYkjiIgcCLTt+H2m6iSfnzzK+bN/ImnYMBYVFJCdna05GSIiIiIifsYvEo1rnE4n5eXllJSUUFGxn8rKozgcDgCsViujRyeTmno/WVlZpKWlaXUpERERERE/5VeJxs2am5tpaGgAICIiApvN5uOIRERERETEFX6daIiIiIiISGDS2CMREREREfE4JRoiIiIiIuJxSjRERERERMTjlGiIiIiIiIjHKdEQERERERGPU6IhIiIiIiIep0RDREREREQ8TomGiIiIiIh4nBINERERERHxOCUaIiIiIiLicUo0RERERETE45RoiIiIiIiIxynREBERERERj1OiISIiIiIiHqdEQ0REREREPE6JhoiIiIiIeJwSDRERERER8TglGiIiIiIi4nFKNERERERExOOUaIiIiIiIiMcp0RAREREREY9ToiEiIiIiIh6nRENERERERDxOiYaIiIiIiHicEg0REREREfE4JRoiIiIiIuJx/z8KOKPYIwNO3gAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hierq = Qinit(8) + (Qcycle(1, 1, 0, mapping=u0_2) + Qmask(\"*!\"))*3 + (Qunmask(\"previous\") + Qcycle(1, 1, 0, mapping=u0_2))*3\n",
    "plot_circuit(hierq, depth=25)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "422104be-3109-469c-bf12-741ffdbb65d4",
   "metadata": {},
   "source": [
    "## Qpivot primitive\n",
    "\n",
    "Qpivot is new, and this part of the tutorial will still get fleshed out. The pivot primitve connects the set of available qubits sequentially to a fixed set of qubits. The global pattern determines the pivot points while the merge pattern determines how the qubits are passed to the mapping. For detailed usage please see the grover and qft tutorials. Here are some quick examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "12f765bc-e127-4817-9ef5-da03248088f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hierq = Qinit(8) + Qpivot(\n",
    "    global_pattern=\"1*\",\n",
    "    merge_within=\"*1\",\n",
    "    merge_between=None,\n",
    "    strides=[1, 1, 0],\n",
    "    steps=[1, 1, 1],\n",
    "    offsets=[0, 0, 0],\n",
    "    boundaries=[\"open\", \"open\", \"periodic\"],\n",
    "    mapping=u1_2)\n",
    "plot_motif(hierq[1])\n",
    "plot_circuit(hierq)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c9d51d7-958c-470a-bbe6-4348a06a578a",
   "metadata": {},
   "source": [
    "## Classical and Quantum computation (Advanced usage + experimental features)\n",
    "\n",
    "At the end of the day we are just building a compute graph in a hierarchichal manner with these primitves. For this reason we aren't limited to quantum computation and can create classical algorithms also. This section will show how this can be achieved. We'll also show how a naive quantum state vector simulation can be performed. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "776ad58f-ff30-4154-b8fd-c9221102ebde",
   "metadata": {},
   "source": [
    "### Classical computation (addition example)\n",
    "\n",
    "Here is a completely classical computation for arbitrary integer addition. Notice we define two functions (half_adder and or_top) which changes a `state` variable directly (no matrix multiplication, just logic and overwriting, similar to classical circuits). The state is initialised with Qinit, then hierarqcal just executes these functions in the correct order. So you can create any function that changes the `state` as you desire."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "a3715af1-b160-4bd2-8092-94e068c9496e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def half_adder(bits, symbols=None, state=None):\n",
    "    b1, b2 = state[bits[0]], state[bits[1]]\n",
    "    xor = b1 ^ b2\n",
    "    carry = b1 and b2\n",
    "    state[bits[0]] = carry\n",
    "    state[bits[1]] = xor\n",
    "    return state\n",
    "\n",
    "\n",
    "def or_top(bits, symbols=None, state=None):\n",
    "    b1, b2 = state[bits[0]], state[bits[1]]\n",
    "    state[bits[0]] = b1 or b2\n",
    "    return state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "e72fceef-31c6-4b18-8b82-d4b3dd771856",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [int(b) for b in bin(np.random.randint(0,512))[2:]]\n",
    "y = [int(b) for b in bin(np.random.randint(0,512))[2:]]\n",
    "bits = max(len(x),len(y))\n",
    "n = 2 * bits\n",
    "x = [0]*(bits - len(x)) + x\n",
    "y = [0]*(bits - len(y)) + y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "8da4d2be-4fc8-40b2-a3c8-d3b168769297",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 1000x600 with 1 Axes>, <AxesSubplot:>)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# program\n",
    "full_adder = (\n",
    "    Qinit(3)\n",
    "    + Qcycle(mapping=Qunitary(half_adder, 0, 2), boundary=\"open\")\n",
    "    + Qpivot(global_pattern=\"1*\", merge_within=\"11\", mapping=Qunitary(or_top, 0, 2))\n",
    ")\n",
    "addition = (\n",
    "    Qinit([i for i in range(n)], state=[elem for pair in zip(x, y) for elem in pair])\n",
    "    + Qpivot(\"*1\", \"11\", mapping=Qunitary(half_adder, 0, 2))\n",
    "    + Qcycle(step=2, edge_order=[-1], mapping=full_adder, boundary=\"open\")\n",
    ")\n",
    "plot_circuit(addition)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "5e159127-3d0a-4dd4-85b0-c0a76e508376",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the answer, we generate a bitstring and then turn it into a function that return only the array items with corresponding index 1\n",
    "# Qsplit is a lower level primitve that Qmask and Qpivot inherhtis from, the bitstrings we generate for them also gets turned into functions via get_pattern_fn\n",
    "# Don't run this twice! then you won't get the correct answer\n",
    "b = addition()\n",
    "pattern_fn = Qsplit.get_pattern_fn(\n",
    "    None, pattern=\"1\" + \"01\" * (int(n / 2) - 1) + \"1\", length=n\n",
    ")\n",
    "z = pattern_fn(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "2e4f74cb-5038-4310-b7d3-3f70388e6d1a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "        350\n",
      "        +\n",
      "        82\n",
      "        =\n",
      "        432\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    f\"\"\"\n",
    "        {sum([x[i]*2**((len(x)-1)-i) for i in range(len(x))])}\n",
    "        +\n",
    "        {sum([y[i]*2**((len(y)-1)-i) for i in range(len(y))])}\n",
    "        =\n",
    "        {sum([z[i]*2**((len(z)-1)-i) for i in range(len(z))])}\n",
    "    \"\"\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7918db2-8154-4638-84b3-9941f4cbe8a3",
   "metadata": {},
   "source": [
    "### Lower level control (create your own edge patterns) + custom Quantum simulation\n",
    "\n",
    "Below we are show two things at the same time, first how you can specify individual edges to the `Qmotif` primitive. Depending on the `arity`, `E` is a list of `arity`-tuples which you can generate. For example `E=[(0,2,4),(1,3,5)]` means your `Qunitary` function takes 3 inputs (`arity`=3) and will apply the function to `bits` 0,2,4 and 1,3,5 seperatly, in the order that's provided. This will works for 3rd party quantum packages (so you can do this with Qiskit, Cirq, or Pennylane). We're combining this with a custom circuit simulation where we perform tensor contraction to calculate the final state vector. This way it's possible to simulate qutrits, qudits or even more general tensor networks.\n",
    "\n",
    "This is a quick demonstration, for details check out `Qhierarchy.__call__` method in `core.py` and `get_tensor_as_f` in `utils.py`\n",
    "\n",
    "The code below creates a Toffoli gate, we apply two bitflips on the first two qubits to see if the third will be flipped."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "afe04beb-417b-4680-92bd-e98ca90a7e6c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.+0.000000e+00j 0.+0.000000e+00j 0.+0.000000e+00j 0.+0.000000e+00j\n",
      " 0.+0.000000e+00j 0.+0.000000e+00j 0.+6.123234e-17j 1.-6.123234e-17j]\n"
     ]
    }
   ],
   "source": [
    "from hierarqcal import get_tensor_as_f\n",
    "H_m = (1 / np.sqrt(2)) * np.array([[1, 1], [1, -1]])\n",
    "X_m = np.array([[0, 1], [1, 0]])\n",
    "CN_m = sp.Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])\n",
    "x0 = sp.symbols(\"x\")\n",
    "CP_m = sp.Matrix(\n",
    "    [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, sp.exp(sp.I * x0)]]\n",
    ")\n",
    "H = Qunitary(get_tensor_as_f(H_m), 0, 1)\n",
    "X = Qunitary(get_tensor_as_f(X_m), 0, 1)\n",
    "CP = Qunitary(get_tensor_as_f(CP_m), 1, 2)\n",
    "CN = Qunitary(get_tensor_as_f(CN_m), 0, 2)\n",
    "\n",
    "tensors = [np.array([1, 0], dtype=np.complex256)] * 3\n",
    "hierq = (\n",
    "    Qinit([i for i in range(3)], tensors=tensors)\n",
    "    + Qmotif(E=[(0,)], mapping=X)\n",
    "    + Qmotif(E=[(1,)], mapping=X)\n",
    "    + Qmotif(E=[(2,)], mapping=H)\n",
    "    + Qmotif(E=[(0,2)], mapping=Qunitary(get_tensor_as_f(CP_m), symbols=[np.pi/2], arity=2))\n",
    "    + Qmotif(E=[(1,2)], mapping=Qunitary(get_tensor_as_f(CP_m), symbols=[np.pi/2], arity=2))\n",
    "    + Qmotif(E=[(0,1)], mapping=Qunitary(get_tensor_as_f(CN_m), arity=2))\n",
    "    + Qmotif(E=[(1,2)], mapping=Qunitary(get_tensor_as_f(CP_m), symbols=[-np.pi/2], arity=2))\n",
    "    + Qmotif(E=[(0,1)], mapping=Qunitary(get_tensor_as_f(CN_m), arity=2))\n",
    "    + Qmotif(E=[(2,)], mapping=H)\n",
    ")\n",
    "\n",
    "plot_circuit(hierq)\n",
    "print(hierq().flatten())"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "unitary_hack",
   "language": "python",
   "name": "unitary_hack"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}