tutorial_day3_quantum_computing.ipynb

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    "colab": {
      "name": "Quantum Circuit .ipynb",
      "provenance": []
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "fmw96qCwTzBr"
      },
      "source": [
        "#Quantum Circuit written by Sakibul Islam Sazzad\n",
        "#B.Sc(Engr.) Electrical and Electronic Engineering\n",
        "#https://sites.google.com/view/sakibulislamsazzad/\n",
        "\n",
        "\n",
        "import numpy as np\n",
        "# Importing standard Qiskit libraries\n",
        "from qiskit import QuantumCircuit, transpile, Aer, IBMQ, assemble, execute\n",
        "from qiskit.tools.jupyter import *\n",
        "from qiskit.visualization import *\n",
        "from qiskit.providers.aer import QasmSimulator\n",
        "#from ibm_quantum_widgets import *"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0kjGBAnITzB3"
      },
      "source": [
        "Around 40 years ago Richard Feynman quoted \"Nature isn't classical, damn it....\" Since then researchers were exploring trying to harness the quantum power of nature using quantum simulations. Thats why we need a quantum computer, like existing computer laptop, mobile etc. Only difference is that we need quantum gates to create a quantum computers. These quantum gates will operate on ***qubits***, unit of quantum computing. \n",
        "\n",
        "Quantum gates are basically unitary operators, the conditions of being unitary operator is $UU^{\\dagger}= U^{\\dagger}U=I$, here $U$ is a unitary matrix and $U^{\\dagger}$ is its transpose conjugate, $I$ is the identity matrix. \n",
        "\n",
        "**Example:** Lets for an example at this moment we deal with $Pauli Y$ gate, it is famously known as $\\sigma_{y}$ gate. Its matrix representation is like this,\n",
        "$\n",
        "\\left[\n",
        "\\begin{matrix}\n",
        "0 & -i \\\\\n",
        "i & 0\n",
        "\\end{matrix}\n",
        "\\right]\n",
        "$\n",
        "As before mentioned, to check its unitary property we can **transpose** the matrix and convert the **conjugate** of complex number.. Transpose is done by swap rows into columns and vice versa. Hence $\\sigma_{y}^{T} = \\left[\\begin{matrix} \n",
        "0 & i\\\\\n",
        "-i & 0\n",
        "\\end{matrix}\n",
        "\\right]$ \n",
        "\n",
        "Now conjugate of the $\\sigma_{y}^{T}$ will convert it into $\\sigma_{y}^{\\dagger}= \\left[\\begin{matrix}\n",
        "0 & -i\\\\\n",
        "i & 0\n",
        "\\end{matrix}\n",
        "\\right]$. Now multiply $\\sigma_{y}\\sigma_{y}^{\\dagger}$, you will find the its equivalent to $I = \\left[\\begin{matrix}\n",
        "1 & 0\\\\\n",
        "0 & 1\n",
        "\\end{matrix}\n",
        "\\right]$\n",
        "\n",
        "Another special property of Qunatum gates are **Reversible**, that means $initialstates\\rightarrow quantumgates \\rightarrow outputstates \\rightarrow quantumgates \\rightarrow initialstates$. We will first prove this **reversible** property by **Hadamard** gate, basically it is known a H-gate also. Using H gates we can show the superposition property of a qubit."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NjVGD49MTzB7",
        "outputId": "e10ab821-3f05-4571-db7e-ad9554353a25"
      },
      "source": [
        "#At first we will make define a 1 qubit quantum circuit\n",
        "# we can follow this code to implement it\n",
        "qc = QuantumCircuit(1)\n",
        "#we already defined a qubit in 'qc' variable\n",
        "#now we can employ an H gate in here\n",
        "qc.h(0) \n",
        "#note that q.h(0) is written, here 0 means first qubit\n",
        "#if you deal with more than 1 qubit we will start with 0, 1 like this\n",
        "#now we will draw the circuit\n",
        "#we will find that in qubit 0 H-gate is employed\n",
        "qc.draw()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐\n",
              "q_0: ┤ H ├\n",
              "     └───┘</pre>"
            ],
            "text/plain": [
              "     ┌───┐\n",
              "q_0: ┤ H ├\n",
              "     └───┘"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hOGKCEDKTzCA"
      },
      "source": [
        "Now we will check the unitary matrix of H-gate by applying **unitary simulation**. This can be done by employing **unitary_simulator**. Remember whenever you will run a simulator, there are 3 steps to be followed.\n",
        "1. First get the simulator (Qasm, Unitary, Statevector, Pulse whatever it is)\n",
        "2. Then execute the simulator by **execute** command\n",
        "3. Get the result\n",
        "\n",
        "Now we will check the *reversible* property of a quantum gate using both unitary matrix and qasm simulator. At first we will check the unitary matrix of H gate. We will find its matrix\n",
        "$\n",
        "\\left[\n",
        "\\begin{matrix}\n",
        "\\frac{1}{\\sqrt{2}} & \\frac{1}{\\sqrt{2}}\\\\\n",
        "\\frac{1}{\\sqrt{2}} & -\\frac{1}{\\sqrt{2}}\n",
        "\\end{matrix}\n",
        "\\right]\n",
        "$\n",
        "\n",
        "after end of unitary simulation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CJeRS4HeTzCD",
        "outputId": "26401a95-c813-4d17-b3bb-666dc2a30b11"
      },
      "source": [
        "#wa want to see the matrices of H-gate \n",
        "#to do this we need unitary simulation\n",
        "#this is done by get unitary property\n",
        "\n",
        "backend = Aer.get_backend('unitary_simulator')\n",
        "job = execute(qc, backend)\n",
        "result = job.result()\n",
        "\n",
        "# Show the results\n",
        "print(result.get_unitary(qc, decimals=3))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 0.707+0.j  0.707-0.j]\n",
            " [ 0.707+0.j -0.707+0.j]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HL5iFqQwTzCH",
        "outputId": "7b42aadf-5743-4cd8-e2f9-5576150284f5"
      },
      "source": [
        "Aer.backends()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<QasmSimulator('qasm_simulator') from AerProvider()>,\n",
              " <StatevectorSimulator('statevector_simulator') from AerProvider()>,\n",
              " <UnitarySimulator('unitary_simulator') from AerProvider()>,\n",
              " <PulseSimulator('pulse_simulator') from AerProvider()>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TkMMBlHtTzCJ"
      },
      "source": [
        "As before said *reversible* circuit means, applying a quantum logic gate twice into a state will give us the initital state. We started with 0 state now, if I apply H-gate twice we will see that, after end of twice H-gate we are getting 0. We will check that using *qasm_simulator*. To implement *qasm_simulator* we need a measurement, so we will add a **measure** after applying 2 H-gate.\n",
        "In qiskit *shots* means how many times we will measure, here we did the measure 1024 times. And we will find the histogram plot for 0 state 1, that means we will always get 1 after applying 2 H-gates."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a14LXw1STzCL",
        "outputId": "a0a851bc-5f36-46bc-a7b4-3691859c38bd"
      },
      "source": [
        "qc.h(0)\n",
        "qc.draw()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐┌───┐\n",
              "q_0: ┤ H ├┤ H ├\n",
              "     └───┘└───┘</pre>"
            ],
            "text/plain": [
              "     ┌───┐┌───┐\n",
              "q_0: ┤ H ├┤ H ├\n",
              "     └───┘└───┘"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SoaYBkxQTzCN",
        "outputId": "028a48f9-258c-4b6e-8c2f-04dea3047e5b"
      },
      "source": [
        "meas  = QuantumCircuit(1,1)\n",
        "meas.measure(0,0)\n",
        "qc = qc+meas\n",
        "qc.draw()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐┌───┐┌─┐\n",
              "q_0: ┤ H ├┤ H ├┤M├\n",
              "     └───┘└───┘└╥┘\n",
              "c_0: ═══════════╩═\n",
              "                  </pre>"
            ],
            "text/plain": [
              "     ┌───┐┌───┐┌─┐\n",
              "q_0: ┤ H ├┤ H ├┤M├\n",
              "     └───┘└───┘└╥┘\n",
              "c_0: ═══════════╩═\n",
              "                  "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l6d91zDTTzCQ",
        "outputId": "043cf34f-02a9-4b08-9c76-8b197f55a4e5"
      },
      "source": [
        "backend_sim = Aer.get_backend('qasm_simulator')\n",
        "job_sim = execute(qc, backend_sim, shots=1024)\n",
        "result_sim = job_sim.result()\n",
        "\n",
        "counts = result_sim.get_counts(qc)\n",
        "print(counts)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{'0': 1024}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kUV-QwFDTzCS",
        "outputId": "69711306-be6c-4270-a045-df39240fc1d4"
      },
      "source": [
        "from qiskit.visualization import plot_histogram\n",
        "plot_histogram(counts)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "57Ooyhn6TzCV"
      },
      "source": [
        "Now lets be familiar with some other single qubits quantum gates, and we will check their state changeing properties by bloch-sphere. In this tutorial we will check the mostly used quantum gates like **Pauli X, Pauli Z gate, Pauli X gate**.\n",
        "\n",
        "**Pauli X gate:**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YmXGyG2iTzCW",
        "outputId": "4391adda-f3f7-4657-dd70-d06634d83a71"
      },
      "source": [
        "circ_x =  QuantumCircuit(1)\n",
        "circ_x.x(0)\n",
        "circ_x.draw()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐\n",
              "q_0: ┤ X ├\n",
              "     └───┘</pre>"
            ],
            "text/plain": [
              "     ┌───┐\n",
              "q_0: ┤ X ├\n",
              "     └───┘"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i21frZwpTzCX"
      },
      "source": [
        "It is important to note that, qubit states are initialised to 0 always. We can change the initial state, we will do that later. Now lets focus on role of Pauli X gate. Basically it is analogous to **classical not gate**, a NOT gate flips the bit state. Same thing is done by the **Pauli X/ $\\sigma_{x}$ gate**, it flips the qubit state $|0\\rangle$ to $|1\\rangle$. lets check that using qasm simulator. Remember whenever you want to run qasm simulator always add a measure to the circuit, otherwise it wont count. Can you guess why it cant count without measurement?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i59-Ws8LTzCY",
        "outputId": "bb330de0-6940-41a5-e4f0-aa4db7ca7042"
      },
      "source": [
        "meas  = QuantumCircuit(1,1)\n",
        "meas.measure(0,0)\n",
        "circ = circ_x+meas\n",
        "circ.draw()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐┌─┐\n",
              "q_0: ┤ X ├┤M├\n",
              "     └───┘└╥┘\n",
              "c_0: ══════╩═\n",
              "             </pre>"
            ],
            "text/plain": [
              "     ┌───┐┌─┐\n",
              "q_0: ┤ X ├┤M├\n",
              "     └───┘└╥┘\n",
              "c_0: ══════╩═\n",
              "             "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AmRKrPLUTzCa",
        "outputId": "e83064eb-52be-4510-8b91-5ee3a830166e"
      },
      "source": [
        "qa_sim = Aer.get_backend('qasm_simulator')\n",
        "job_qa = execute(circ, qa_sim, shots =1024)\n",
        "result_qa = job_qa.result()\n",
        "\n",
        "count_qa = result_qa.get_counts(circ)\n",
        "print(count_qa)\n",
        "\n",
        "from qiskit.visualization import plot_histogram\n",
        "plot_histogram(count_qa)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{'1': 1024}\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bokNGnmwTzCc"
      },
      "source": [
        "Now we will check the rotation of **Pauli X** gate from state $|0\\rangle$ to $|1\\rangle$ in bloch shpere. At first we will check how does $|0\\rangle$ state looks in bloch sphere"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "d9WJ5WJ_TzCe",
        "outputId": "21eb4021-4227-4856-cd75-8cf020a0d911"
      },
      "source": [
        "from qiskit.visualization import plot_bloch_vector\n",
        "%matplotlib inline\n",
        "\n",
        "plot_bloch_vector([0,0,1], title= \"0 State\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F_C9CMWDTzCf"
      },
      "source": [
        "So after applying X gate to this $|0\\rangle$ state, it will flip to $|1\\rangle$ state, basically Pauli X gate is $\\pi$ rotation around X axis. So lets check how does it will look in bloch shpere of $|1\\rangle$ state. Remember we are just doing bruce-force to show you $|0\\rangle$ state and $|1\\rangle$ state. We havent yet applied bloch sphere to our quantum circuit. We will do that just after it"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B5igNp2MTzCg",
        "outputId": "343b4372-fe6c-4bc1-841a-70df1407c50d"
      },
      "source": [
        "from qiskit.visualization import plot_bloch_vector\n",
        "%matplotlib inline\n",
        "\n",
        "plot_bloch_vector([0,0,-1], title = \"|1> state\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0FdzAbQiTzCi"
      },
      "source": [
        "Now we will apply Bloch Sphere in our quantum circuit, to do this we have to import *plot_state_qsphere*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vA0Q9ZeTTzCj"
      },
      "source": [
        "from qiskit.visualization import plot_state_qsphere\n",
        "\n",
        "back_x =  Aer.get_backend('statevector_simulator')\n",
        "result_x = execute(circ_x, back_x).result()\n",
        "state_x = result_x.get_statevector(circ_x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SIqDP-5fTzCj",
        "outputId": "93ba2fa2-f14a-4435-dab6-bbd365a4b4ff"
      },
      "source": [
        "plot_state_qsphere(state_x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x504 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kaYp2sJVTzCl"
      },
      "source": [
        "Have you noticed that we used used *statevector_simulator* to check the Bloch Sphere. And you are carefully check the color code of phase you will find that it is in phase 0. Reason behind is simple, **Pauli X** gate only change the bit state, that's why it stays in 0. But **Pauli Z** gate do the phase changes. Cool, now we have learnt all the necessary *Aer.backend()* simulalor. So lets check about **Pauli Z** gate and we will learn that it changes phase."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v6sirkRVTzCl"
      },
      "source": [
        "**Pauli Z gate**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OxgdBlU9TzCm",
        "outputId": "e195eb3a-e8ae-43dd-d7fa-4dc85cfdc215"
      },
      "source": [
        "circ_z = QuantumCircuit(1)\n",
        "circ_z.z(0)\n",
        "circ_z.draw()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌───┐\n",
              "q_0: ┤ Z ├\n",
              "     └───┘</pre>"
            ],
            "text/plain": [
              "     ┌───┐\n",
              "q_0: ┤ Z ├\n",
              "     └───┘"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t4weYKiXTzCn"
      },
      "source": [
        "Matrix of Pauli Z is $\\left[\n",
        "\\begin{matrix}\n",
        "1 & 0\\\\\n",
        "0 & -1\n",
        "\\end{matrix}\n",
        "\\right]$. Do you know how to read qubit states from matrix? Lets learn it, check about first column $\\left[\n",
        "\\begin{matrix}\n",
        "1\\\\\n",
        "0\n",
        "\\end{matrix}\n",
        "\\right]$, see this is $|0\\rangle$ state. This means **Pauli Z** gate has no effect on $|0|rangle$ state. Now if you look at second column, it is $\\left[\\begin{matrix}\n",
        "0\\\\\n",
        "-1\n",
        "\\end{matrix}\n",
        "\\right]$, see **Pauli Z** gate has changed the $|1\\rangle$ state to $-|1\\rangle$ state. That means **Pauli Z** gate changes phase of $|1\\rangle$ state only. Lets check that in bloch sphere. But before that we have to *initialize* qubit state to $|1\\rangle$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lSATdWtVTzCn",
        "outputId": "1e2561dd-dc17-4841-a1f5-b5461d07596a"
      },
      "source": [
        "circ_1 = QuantumCircuit(1)\n",
        "initial_state = [0,1]\n",
        "circ_1.initialize(initial_state, 0)\n",
        "circ_1.z(0)\n",
        "circ_1.draw()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">     ┌─────────────────┐┌───┐\n",
              "q_0: ┤ initialize(0,1) ├┤ Z ├\n",
              "     └─────────────────┘└───┘</pre>"
            ],
            "text/plain": [
              "     ┌─────────────────┐┌───┐\n",
              "q_0: ┤ initialize(0,1) ├┤ Z ├\n",
              "     └─────────────────┘└───┘"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-VAlTxaoTzCo",
        "outputId": "6fb16c15-a306-4981-b7b6-afb23f68496f"
      },
      "source": [
        "backend =  Aer.get_backend('statevector_simulator')\n",
        "result = execute(circ_1, backend).result()\n",
        "z_phase = result.get_statevector(circ_1)\n",
        "\n",
        "plot_state_qsphere(z_phase)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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IMzvXGkR2DrJay85QaTyGisBErwzKmU6l0L8zK9dC/6ZJtX4mjQ4ykb5DhkrjMVQEJtoOUe7cWwwM+6sliEQ6GBJtH2oGDBWBmT2mYsURr1nqPSV9pfeLRoTy1vId1bP8DJbGYqgIzOx16UWoeKpV78WzKr1fNHYrbza7l5/OY6gIrNQRlpUhYeeAoubClkpjMVRszEndUXZ04sQJvPbaazhx4kTBxzB8rcdQaSzF6gJQYdwZxHXixAn8y7/8CzRNg8vlwi233ILZs2fnPI7ha43MU9O5HzUWWyoC484grqNHj0LTNBiGAU3TcPToUauLRBmyZyumxmGoCKqZA8UOlUBfXx9kABIAl8uFuXPnWl0kIiEwVARWrHK1Q8VbLTt0GbXF41i6dy8uiMUKdn2RGOzwe3ISjqkISpblojsDdxRr6ckkWkdHMTsSYaAITpZ57NxI/LQFxp2hdoWmiTFhwzAA6A2YhJJqw/2osfhpC4w7w3nVVtx1myZGkiABkBswCaUZnBB81b4H7keNxU9bYHbZGRox9mOHiltklX5+lX5vZn3P9ZiZ2y77kVPw0xaYaDtDoR2eYz/OU+n3JklSej2afMsXlBs6Zi6pAIi3DzUDfuICE22HMCsgROiKEaEMVqjnTMKp9WhSAZN9X6kymVWGTKLtQ82An7jASu0Qdq0YqzkKbnQZyn1NM7+BRrTqUq8hUguyksCp9DfPUGk8fuICa9YdotaKpB5lKMTMqlnEg4R6lKmSbWYHjggHJFRcc9ZaNlEqVLjDiE/EoKiEFa3EShlFTuvmPtJ4DBWB1aul0ogzdWrhpIrA7u/FDqGYGsfJp1lb+1biJy6welVIZm3X7hUmlVbtdyxKGDFUGo+fuMBYaZNdifLbVRTORNVoDBWBcYcgqg33ocZjqAhMlmU234kqlNn1xlBpPNZYgnO73XlvF6XP2k5qnVwy+yyjSrZQy2nS/K4rk+p6UxSFB2UW4CcuOK/Xm/d2Ufqs7aTWySWzzzKqZAu1XG9h98Fyq3g8HquL0JQYKoITrfme74hbhIsVKVezH3gwVKzBUBFcOTtGIyvxfEfctV71TM5S6PfY6CWyGSrWYKgITpZluFyuoo9hJU4iKTSOUc74hpkHSKK18psFQ8UGKj3ickr3k1Peh4jq+dnWsm2zDpDYSrEOQ8UGCp0BVohTWi6Z76PRi0aV+/xGx16+clXzXp3yGymEoWIdhooNiL6DNKJF0ejZact9fqOr5nzlcnpAVINdX9ZhqNhAvXYQLvVLTpL5exb9QMzJGCo2IMtyxV1g5ci3Ql+1OP5BVksd3MiyzJaKhRgqNlGPUAE4Y3E9NSJoGea56rWvUHkYKjbB5rz9NHJ54GaXGa5+v9/CkhBDxSZ8Ph8rEBvImR9MwJaEiGWqRfYFuD6fz8LSEEPFJmRZLjgPWK3MqGTsVFEVOi3XjPeQMz9YHebtqrWcpcpkp+8SmH6lvs/n4ySSFuOnbyM+ny/vDt+o02dLbaNUZSRKZVXotFyRWoLFylLvcor0OZQjs7yBQMDCkhDAULGVQkdhIlfWldxPYiv0OxPl91fP1jyVj6FiI7IsmzoIma+SF6WCaIRmeq9mKHRQIMrBAscdxcBQsRkzByHzjSNwpyS74gC9GBgqNmP2QKRVISJCK8HMiz+dqJ4nC9Ty2vnIssxQEQRDxYZK7Tx2qCirXXlRhHKIoOwJL2tYQM1OJwtwgF4cDBUbKrUD2bWiLKXepz5n3lfOZ2jAvFmKK31vZU94WcECanY4GClURrZSxMFQsSGPxwNFUUwPD1ErFTPLVe7RdzmvKcG8WYpFOBAQoQyl5CujoiiccUIgDBWbKnTNSi1ErVRELReJgV1fYmGo2FRqRxK1dUGV4fdYHUmSONeXYBgqNpVq8jttyg0nMWtQnArz+/1wuVxWF4MyMFRsrLW11eoiNFS1p7jWez32QtuvJCiqPZurkuc6gWEY0z7XYDBoYWkoH4aKjXm93pIDlE46Aq72FNd6nvFk1pxh1Z7NVclzzXh9q8mynP7OAoEAF+MSEEPF5kKhUN7bRakkRD+KFuVzslK+1pao31tmuQr99slaDBWb83g8ec/Rr8eMwdU8x66VtqiVaj2Y1fppZDAFg0FOcS8ofisOUE2/cvY1GeVcJGdGRWMXdg1DKxX6DZn9G5BlmWMpAmOoOECh1kq58s2BZVZFwMqZzPgNZP4eA4EAWykC4zfjEMX6l1M7pF1bDfXWzJ+LWe+92u2U+7xUMLGVIj6GikMoilJyZchmajU06zUiVgVktZ9hpc/jWIr4+O04SCgU4nTuU0RYYtkKlZbbTu9TlmVOyWIDDBUHURQFgUBAuIrCjiFnxzI7HVsp9sBvyGFS/c0iVYqihRxNsvI3Uulru1wutLS01Kk0ZCaGisMoioJgMMiKPItZ07hkPrbYs+oxAG72d2rlb6TS1+7o6OBv2iYYKg4UCoXKmr5CpNZMLcpa+8SkVQwzH1vsWWZVgJWu8eIU2fN7cb0U+2CoOFRHR0fObdmVklMuZuQRbOUKfY+ifL+6rgOYvAaL07HYC0PFodxud87O2IiJB0WplKiwfDMopIiy3HCqHO3t7Q17TTIHQ8XBau02yFfBFKuQCj2HxFHq+yumlu+22BIBhZTbjUtiYag4XHt7e9WnYRa6kNKJrREnvqd87DI47/P5eOW8TTFUHE5RlLL6pOtZ2dihwha5hWXm51frtqp9fvbnW2w7siyz28vGGCpNIBAIlJxwstLKolmnQbGCmZ+fHWYaqKV1TdbjN9ckUjtqPU51tYoILaBaSyDC51guMz/vaadmZ3SplnMARGJjqDSJVJdCNQOmohJhfKfWSLC6/JWoVwCmTh4ot6uWxMZQaSI+n68uc4NZWTHa6Ui/GZU7k4EkSez2cgh+g02mra2trNOM7TRmkq+s1awhU1E4Gka666ueoWqXteMLKff0846ODl417xAMlSYjSRI6OzuhKErRCqqRQVHpa1UyLUu1U7CU8eB011c9P6tylnm2u/b2do6jOAhDpQnJsoyuri64XK70bY0+pXjaxIwVHn03Q0XbLEKhENdIcRiGSpNyuVyYMWNGug/brLmgiq08Weo2Ekc13W6V/laCwSAvcHQghkoTUxQFnZ2dRQdHK7loLd/jG8Fu4wx2VGpOMEmSKvruA4EAz/RyKIZKk/N4PGVdvZyquMs5jbfRlTxbPeardCyqku/c5/PxinkHY6gQfD4fOjs7ARQOhOyL1YppdCVfzZleTifqZ+HxeNK/NXImhgoBOH/0KPKiUKUCzyktllo+98wWpShSZUp1t5KzMVQoLbufW6SKCbCmPIVe08j6u1L1Op1btO8MQPpq+cwTQ8i5+A3TNGafkdPo1o7Zr1dwe7o+GShlnDWX798iVv5myf7MFEVBV1cXA6VJcAUcypFqrUQiEQDWLewk8utJsgypyOsVGoOqR/lq+X7qIbMsqTEUBkrzYKhQXqlV98LhcEMrrMwKUpQr/hupmoDI/LwqXa2znoHU0tKCtra2umybxMVQoYICgQAURcHQ0BB0XYckSem/zZRZsdX7qF509RhPKRY09fiMJUlCa2srL2xsUmyTUlEejwczZsxIzxVWr0qoGNHOQnOCYi2Xap+buq+jo4OB0sQYKlRS6sydcib9Kzd07DQLstNlT0FfyeMzuVwuzJw5k5NDNjmGCpVFlmV0dnZOOwLNd9FhuWHRqKBgK6e0WlotKR6PBzNnzoSisEe92TFUqCKhUCg9xUZqeo5CffaVMqsbrNIjbzvLHKQ3e/qccj+7QCDAa1AojYcVVLHsAfx8qqnMy5msUpTTZ9OtNEHKUc5nUo/Pra2tDS0tLaZvl+yLhxZUldQAvtvtBtC4bqZGVZ4lt2EYZV34WEq1n1sjXqOY1NIJDBTKxpYKVU1RFMycORORSASjo6M1b0+UVghQRqtJlqet/jjtPpNXm8z3udRtRcsyBINBTltPBTFUqGbBYBA+nw/hcBjxeByyLNc0ppLq5squTGsNHZFCqxK1zGaQ73OslsfjQVtbW7p1SpQPQ4VMkTrtOBqNYnR0tC4z7VZ6tXg2kcZkqlFJ2fOdrJB6fjnbyVwjRZZltLa2squLysJQIVMFAgH4fD6Mjo4iGo0WfJxZlbtIAVHvwKqkq6zYEs6lWn+ZgeTz+dDW1gaXy1VtsanJSCWOKK0+uYVsLJFIIBwOI5lM1tzKEEH02DEM7dqF0XfeQeTAAahjYwAAyeWCEgyipb8foWXL0LlmDQJ9fRaXtjLZU/DIsoy2tjb4/X6LS0aCKrjjMlSo7kZHRzE+Pl7zvGGVLltrBkPXMfTaazi+bRuiR4/C0DQYqlrw8ZKiQHK5EJg7F3M2bEDnZz4zOaifuc0Ku7FqmTCyGql1dXjdCRXBUCFrqaqKcDiMRCLR8NeuJowMw0Ds7Fns37wZ0Y8/hhGLlX4OMvY0SYLs8cA3bx4W33MP/D09OdsXrZWmKAra29vh8XisLgqJj6FCYojFYhgbG0Mymazr69RaaZ956SUc+p//E3oiAWPqAs+qtibLkD0e9N9+O7qvvrroQ7Nna25kq4ynCVOFGCoklkQigfHxcUxMTFT1/FJXktcSKiefew5H/tf/gh6Pl18eFA8d2evF/I0bMevGG6sqUzYzQkeSJPj9frS2tnIgnirFUCExqaqKSCQy7UyxUoFQz66jM//+75MtlOxAMQygxteUPB4s/PrX0X3VVTVtp6rXzjpFuKWlBS0tLRw3oWoxVEhsmqZhfHwc0Wg0PaBvVvdPuSEUO3MGA3ffDT3f+EmJUCnVUkndL/t8WPXjH8PX3V2yPJVIfWbF3qeiKGhpaYHf72eY1NGdd94Jn8+Hnp4ePPXUU/jggw/g9Xpx6aWX4qGHHsLy5cutLqIZCv7Q+MsiIbhcLoRCIfT09KCtrc3USq+s6zt0HR9s3gy9wIkERqmLBYsEYGbg6IkEPvzxj8sKzHxLC2Tfl/q3LMsF32dqnfju7m62TurMMAw888wz2LBhA7Zv345vfOMb2LlzJ1544QUoioLrrrsOQ0NDVhezrvjrIqFIkoSWlhb09PSgo6OjrClBSlW65dw3+OqriB45kj5d2JiaMNLA+ea6oevp/5f1JzXpZMaMxoauI3LkCIZee62sWZkz/84se75ll7ODxufzYcaMGWUvsEbFLVu2LN0azP7zwAMPAAB27dqFeDyOtWvX4ve//z3+8i//EsuXL8fFF1+MX/3qVzh79ixeeeUVa99InTFUSFh+vx8zZ87EzJkzi16EV+zq8Xz353v8iaefhpFIQJLlyZaFJKUnjEz/yf4/zrdA8t0HTLZw0uEw9ceIxXD8qacKdvEVC5tSS/m6XC4Eg0H09PSgs7OTpwebaOvWrQCA5557DidPnsSJEycQCATw6KOP4r777gMAbNu2DTfeeGPexcrGxsag6zo6OjoaWu5GY6iQ8NxuNzo6OjBr1ix0dHSkxwSKLUxVyWqU0aNHET16NP1/afJJuVPbS1LZg4ypYJoWAVMtH0jS5GseO5Y3WCqZkViSJHi9XoRCIXR3d6OnpwehUIgrMNbB6dOnIUkSrrzySvT29qbHANeuXZs+6Hn66aexYcOGvM/ftGkTVq1ahcsuu6yRxW44/vLINlKnwKZ24EQigVgshng8Pu26l3IG5jMfM/TGGzBUdTIIUgPyqS4llL4+Jf2c1LaznmNM3Z8ZMrquY2jXLgT6+kqeFp0KT5fLlR6Q9/l88Pl88Hq9HCNpkN27d6O/vz+9pPbAwAACgQAuuOACAMCBAwdw6NAh3HDDDTnPveeee7Bjxw7s2LHD8advM1TItjweT7p7R1VVxONxTExMlHXVfmZFPrp3L3RNm6zwp1ojqaCQAOiGATl1O6bOtMpTkRsAJF1Ph5JuGJAzX8swzg/4qypG3n0Xc//0T6fuym0DZY6pKIqSDhJ2aVljz549WLFiRfr/AwMDWL58eTrUt23bhnXr1uXM5nz33XfjiSeewIsvvoj+/v6GltkKDBVyBEVR0qfM6rqORCKR/pNMJouuKxL56CMAUwPyqUF1SYI0FQJSZrfX1JlW6dbIVPgYmOpLzmjlyFPbmXY68lQZdKoz6JMAAB2HSURBVMNA5ODBguWSZRkejycdIuzOst6ePXuwfv369P8HBgawcuXK9P+ffvppfPWrX532nE2bNmHLli148cUXsWTJkoaV1Ur8pZLjyLKcPqpPUVUViUQCmqZBVdX034ZhQB0bg5FxbYyUESgwjMnWCZD+W84cr8H0bipIEpCaOHPq+amWT7qlk9rm2BgURYHb7YbL5YLL5YLb7YaiKOzSEoyu69i3b196QB4ADh48mB4fOXv2LF599VU8+eST6fu/+c1v4le/+hW2bduGjo4OnDp1CsDklDipLjQnYqhQU0i1ZLLpuo42WYbmdkPVdehTtxmyDE3XoRvGZKBkdGdpmgZD189vT9ehZXRVSbI8+ZypbjOXLMNlGHBJEuSpP25ZhkuW0W3yRZBUHwcPHsT4+Pi07q+LL74YmzdvxurVq3Hy5EmsWbMGPRkThz7yyCMAgHXr1k3b1g9+8IP0KchOxFChpibLMjxeLwxNy3u/ngqarDEPPTV2gqmxj1RrBYBr6v9KiQFZyeEDtk5y4YUX5ox7/eY3v0n/++abb84566vRyzSIgqFCTU9pbUUyHM57nyzL+c+7NyEQFM4K7BhXXHEFbr31VquLIQR23FLTa120qKlel8z3ne98B3PnzrW6GEJgS4WaXtuqVRh+662iKzqaTVIUtGecOUT2kdDjGEp8jMHEUYwmz2JcCyOmjUHVE5jp7oKmDsEt+eBV2uB3dSDo7kHIMxchzxxIkvOP4xkq1PRmXH45jvzyl40NFVlG1+WXN+z1qHq6oeOjiffwfvRtHJzYhxF1CCFtNO9j3foiROP7c25vc89BqzqIoG8hOgIr0dlyCQKeOfUuuiUYKtT0WubPR8snPoGxDz5o3GsuWICW+fMb9npUuVPxo3h99HnsGXsF4/rYtPu6XR2IacNlb8vvaoWWPI6RiXcwMvEOPhp8HH73HPSErkZP62fhVpwzvsZQIQIw79Zb8d4Pf5h/LRWTyX4/5n35y3V/HarOvugePDv8NEbVMPTk8byP8SpdFYWKG0B2O3gieRzHw88iNvgUWlsvRUfHBng8vdUXXBAMFSIAM668Ei1btky2VqbWpK8LWUZwwQLMuPLK+r0GVeVw7CC2DP5vvD/xbvq2pe7ZCCdP5DzWkEovyTCNNpL35jb3bEB7D2Nj2zE29jJCoWvQ2XkLFKWtsu0LxPmjRkRlkGQZF33/+5DrPK+W7PHgov/8n+u2HDJVbkKbwC/P/Bx/d+z+aYECAIarNe9zokb5LVpZckNNns65XYILSuJkxi0aRkf/iI8/vgsjI3+07XUuDBWiKf7eXiy65x7IXm9dti97vVh0zz3w9dq/i8Mp3p3Yj/907EcYGN8NI8/CBofih+GRWnJuH0yeLfs1gko3Jif4mS7kXQDouddH6foExoZfxol9/wVq3H6rRDJUiDL0fu5z6L/9dtODRfZ60X/77ej93OdM3S5V7+nh3+PB4/8NJ5Kn4HF1I98iBwkjgTbvvJzbo3oEPld5i20FCrR2/Eb+sw1drjbETx3FRHgvjr79XUTD75T1OqJgqBBl6fvTP8Wie++F7PMBtU7sKMuQfT4suvde9E1Nc0/WShpJ/PfTj+HXg1uhT7UgjiSOY6FvRd7Hn1Dzt0q8SldZr6fkaQH5lG4YiY/yP36iC0YyCgDQkqM4se+/YOTkH8t6LREwVIjy6P3c57DmscfQungx5CJLGRcj+/0ILVmCNY89xhaKIBJ6Av/1xCPYMfZazn0H4ifR4ZqZc/s59Ry6PAtybi93sF7SIjm3tSqdeRd/8ymLER88lPVCGs4e+DmGPt5a1utZjWd/ERXg7+3F6p/+FOdefhkfP/44xg8fhqHrRS+SlBQFkiyjZcECzPvylzHjyis5KC+IhK7ip6e34kQif8sjbiTgcc0BtHNAVusiludK+KgRn/Z/GS7IkhuT3WjG1G0K1OSp6Y+TPHDFP87ZnsvVjvjJ3NtTxs++CSMCdF30hYKPEYFU4gwDe55+QFQH40eOYHDnToR378bY/v1QR0dhaBoklwtKKITWRYvQvnIlui6/nBc2CkY3DPzTySfwZnQ/OlytkDGEQe1c3scu883HwdjuabfJkNHvasO4NgyP5EWfbyEW+JZioa8f3d5+BFxtACQYMCBBggEN48mzGE0cQzT6NiLxQxiPHwFgoMO3GN5Y7oW23kR/bisldV/gAsQPHwJ0HTM+eRvaL/x/av1IalXwSImhQkSO96tzv8ez4VfT/y8WLB7JgxkuYEg9M+32a1s/i+X+pbg4eBlUIwm35IEil+4C0/QYDEOHAQ0nwr+DEd0LNf7htMf4lMWIHc0/o0NmoAAAJBmz1n4HLbNWlXztOmKoEFFz2jG2B//9dO54RLFgme+ZjdOJ9wAYWN2yBl/ovAU97h64JAUuqfplD3Q9AQCIRvdgaOgJJBLH4HK1Qz8Vh6FO5Dw+J1CmyJ4WzL3uH+AOWnZ6OkOFiJrP6eQw7vv4fyBmJPLeXyxY1gQuwnVtV2Kxfyl8si/Ps6tnGDoMI4nh4WcQPT2A+ODBnMcUCpT0/Z0XoO/av4NkzdLTBUOFZ38RkSMZhoHfDL6BYIHrRABgWBuDjk50uWZMu/2y4CX4eu/XsCxwsemBAgCSJEOWvejouBk9n/gGPIHpa7GUChQAgKYjvPtZ08tWK4YKETnSC6Pv45XIYYxqfizxLUWhg+vMYJEg4Wszv4I7uv8CAdkPRarvCbKy7IHbPwt9qx5Ey4zPACgdKLI7AF9gEeLvH8LQK79BInwq7+Oswu4vInKcCT2Bu45swYh2fpxinqcD4/opDKr5pz7pdIXw192fw0X+C+GT6zNVTzG6Fsfw0Wcx/MaThbu82vqRPDYIPXJ+gsqWhWsw6/P3NqqYKez+IqLm8Wx477RAAYCPE8MY01qmWi25bu1ah2X+RZYECgDILi86+m5EcPanc+9T/PD5FyP+/qFpgQIA4wd3IXbyw5znWIWhQkSOEtUSeDa8J+99CUPF+7Ew5nsuQpfSmb79ix1XY01wCbxyfWepLkVWvOj+9Nfh67owfZu3rR8IexE7VHgRuaHXnmxE8crCUCEiR3lx9H1M6MmijzmS0WqZ7+nBTR1XwGdxoKTIihe9l90FlycEX2CqdTKWO5txpuiR3UgMHmtQCYtjqBCRYxiGgZ2RMJb6FqGjyFlfwGSr5cPYKL496ytw13lAvlKypxWdF/5/iB0svcS1p3MuvKELMfLq8w0oWWkMFSJyjPdigzgYH8F7sTGEtSAWehdhgXdOwcd/sXM1gi4vZMHmZ5MVD1oXXQHfrEV575fcPvi6l0DBLCTePYr4/g8x9sZLMNTiLbRGYKgQkWO8Gjm/kqIB4GB8DIfjOrqUBVjquwBB6fw1JyGXDze2r4CvjKlWrCC7vZh5zX+Ydps71ANf5xLgDBDb8z7UU+ffrx4bR/TA3kYXM4dYbT4iohq8OZ7/mo1BNYZBFXBLXVjkC2JcG8Kaljl5V3sUibu9F57uBZAMBcZoAon9R5BE7tLEKePvvoGWJasbWMJcbKkQkSMcjY9hUC2+dnzS0LE/NooTSQWf71gFr6CtlBTJpaBj2U2I7/0QiSNHSj4+un93ycfUG0OFiBzhg9hg2Y/9ZKAbLsHGUfKRZBdaln4Ksre8heLUkUEkw/mn9G8UhgoROcLZpISlvvlY6O1BW4n5uj4bmge/4K2UFEPTECjWpSVJUDq64ZuzCL5ZSxE/8lHDypYPx1SIyBH2TYzjYDyOyRlE2hFyKZihKPBJBuJGDIPJUYT1yavsF/ray9rm9u3bcc011+Ds2bOYMWNG6SfUgezxwjfvQkR2vzIZIO3dUAJtgC5DD0eROHEa6okzUDG5/ku8bymCKz9lSVkBtlSIyCFOJaePp4xqKg7FY3g3FsfBuISw3oaQ3Iclvn60u863ZG677TZIkgRJkuB2u9Hf349vfetbGB8fb/RbyEuSZQQuXAWPfy4w5IH67mnE3tiP2FvvI3HoYyA2fVnj5JniE0w+8sgjWLBgAXw+Hy655BK8/PLLppaXoUJEthfTNYzrWsnHjeoqABmxrMded911OHnyJA4dOoQHH3wQjzzyCL71rW/VqbSVU9o7kTh8LCdA8lGHCo8tbdmyBZs2bcLf/u3f4u2338bll1+O9evX4+OPPzatrAwVIhLSsmXL0i2I7D8PPPDAtMeOaOVf9DffG4CSNUjv9XrR29uLuXPn4stf/jI2btyIbdu2pe/fvXs3PvOZzyAQCOBTn/oU3nrrrfR9g4ODuPXWW9HX1we/349ly5bhsccem7b9l156CZdeeimCwSDa2trw6U9/Gvv27Uvfv3PnTlx99dUIBAKYM2cOvv71r2N0dPT8BjQd7pndZb0/LfN5WTZv3ozbbrsNX/va17B06VL85Cc/waxZs/Czn/2srG2Xg6FCRELaunVyCeDnnnsOJ0+exIkTJxAIBPDoo4/ivvvum/bYaBmtlBS/7IJbKl71+f1+JJPng+p73/sefvjDH+Ktt95CV1cXNm7ciNSyIbFYDKtXr8Zvf/tbvPPOO9i0aRPuuOMOPP/85LQpqqri5ptvxtq1a7F792689tpruOuuu+ByTS5LvHfvXlx//fX4kz/5E+zevRtPPfUUBgYG8Fd/9Vfp1zd0DbK/vDPA9Gg07+2JRAJvvvkmrr/++mm3X3/99di5c2dZ2y4HB+qJSEinT5+GJEm48sorEQwGceDAAUSjUaxduxb+rArW0IGZcnmVbofsKToty+uvv47HH38c69atS9/293//97jmmmsAAN///vexdu1aHD9+HH19fZgzZw6+/e1vpx97++2344UXXsCvf/1rrFu3DqOjowiHw7jpppuwcOFCAMCSJUvSj//Hf/xHfOlLX8K9955fE+VnP/sZPvnJT+LMmTPo7u6eHKCfMQtapPh1OAAg+QN5bz937hw0TUNPT8+023t6evDHP/6x5HbLxVAhIiHt3r0b/f39CAaDAICBgQEEAgFccMEFOY81DBfORstb9ncsmFvt/du//RuCwSBUVUUymcTNN9+Mn/zkJ3j33XcBACtWrEg/dvbs2QCAM2fOoK+vD5qm4Yc//CG2bNmC48ePIx6PI5FI4LOf/SwAoLOzE7fddhtuuOEGrFu3DuvWrcMXv/hFzJs3DwDw5ptv4sCBA9iyZUvG+5lsBR08eHAyVHRAPR2Herz0mIrcam21zu4vIhLSnj17plXmAwMDWL58OWQ5t9pS5PIvZEzqBrSsFW+vuuoqDAwM4IMPPkAsFsNTTz01WZlPcbvPX9MiTbVy9KnVGR9++GH80z/9E7797W/j+eefx8DAADZs2IBEIpF+zmOPPYbXXnsNV111FZ555hksXrwYv//979Pb+eu//msMDAyk/+zevRsffvghVq1alXpVGMnyxo0kJX+ozJgxAy6XC6dPT5/m5fTp0+jt7S1r2+VgS4WIhLRnzx6sX78+/f+BgQGsXLky72ODU+MT5QirKhK6Dn/Gcwq1gMqxY8cO3HTTTfjzP/9zAJOtjP3796O9ffq1MCtXrsTKlStx3333Yf369fjlL3+JG264AatXr8Y777xT9PUltwItPFLw/kyu1mDe2z0eDy655BL84Q9/wC233JK+/Q9/+AP+7M/+rKxtl4MtFSISjq7r2Ldv37SWysGDBzF//vy8j29TXIUXTc9yaCJ1gaQ5Fi1ahOeffx47duzA+++/j7/5m7/B4cOH0/cfPnwY3/3ud7Fz504cOXIEL774Ivbs2YOLLroIAHDffffh9ddfx5133om3334bBw4cwG9/+1vccccd6W0YiQS0kbGyyuNqCxW875577sEvfvEL/PznP8d7772HTZs24cSJE7jzzjurfPe52FIhIuEcPHgQ4+Pj00Ll4osvxubNm7F69eppLRgAUCQJ7YoLw2r+s8AUAL2SG0HDBSkCuE2c9+v+++/H4cOHsX79evj9ftx2223YuHFjejwmEAhg//79uOWWW3Du3Dn09PRg48aN6TPYVqxYgZdeegn3338/rr76amiahv7+fnzhC19Iv0by9BB8S5cDWhzqSBjqmXOAkX+GZaWro2BZv/SlL2FwcBAPPvggTp48ieXLl+O5554rGNbVkIwCBZsi9rzQRERTHjx8HPvGJ+AG0CO5EdRdMJLAaEzDmWgSWkZt9vBl89AXFGP54FIMVcPQ1pcx/H/+/fyNXgWe7lbIQRegJaCNDCM5FTRdX/kzdHz+unoXq2Aqs6VCRI6wzOXHuREVZyaSOGYkARQe2N43FEVvwF3RAL9V9ISK2AdZV7zHVSSODmfc4AI8s+HpaYV3YX9Dy5eNYypE5AizvB6ciiahl9G/8sdjozlngInKSCYx8c5HpR+Y0JA4NgLf/MLLJzcCQ4WIHGFph6/s4ffxuIbBqFrX8phBT6iI7NoPyVNep5J3QS/kgLfOpSqOoUJEjtDmUdAfKlKhGsACrwcLNS9Gjmv4zdtDmEjqjStglYa27AWkHviWLILSU3gQHgACqy5sUKkKY6gQkWN8qrsl57aALGGp24cZEQWHjyRw8GwcugHsOhpBUhO3C8xIahh/4yPoY3EYMQ2x98egnvbBM/9CeC+cB7hyq+/gmiV5ttRYDBUicozLe1rTXWBzPG4shg/qaeC9ozGcG5/e3aXpwCOvnEZcFbO1oic1nPtF7kSPiSMRxD9MQg7OhW/phXC1TV7s6J7dBe+CWY0uZg6e/UVEjtETcOOaGa344FgMx08VPwMMAN45FcWHJ2JYNMsHj1ucY2w9piL8233QRgtPIKmPJBAbSQByK7wXzEHrVdZ3fQFsqRCRw6ye0YLj4dLzZM0NeNAeUbB56ynEVXG6wYykhol3BzH81HF4Fy6Aq63E7Ms6kDgaRevlyxtTwBIYKkTkKKv7WjA75C54v1sGlvp8OHYogbMjKqJxHf/t6VOICzBob2g6tEgSp382AACIH4xBT3bBt2h20eeFrlkCV9Das75SGCpE5CiyJOGWlZ1570u1Tt47HJs2y8k7H0/gkWdPI2Hh+IqhG9BjGo794BXoY+dnODaiGmL7DXgKtFokr4KODatybrcKQ4WIHOfS+UEs7Dp/5K7IwFL/+dZJPoNnVfyPX59BPNH4YDE0HdqYihM/2g8UOCMtUaDV0v75FVDa8y/MZQWGChE5jiRJ+MtPz4QkAX0BDzrHFbx3KFZoDkZc0OHF4Q/i2PlWBJsfO4WJmA61QeMsekxD8kwCx/72PcT3T8DQOqF05R9HSbVavAsXwBXyQ5nZio6b8i8HYBVOKElEjrX1jSH85sWhgmECnA8ULWOC47ZWF+7+i158os8Ln68+x96GbsBQDYSfPYWhJ09Oa6G42mVIriGogxMFny8FZcy6ezUCyyw5jbjg5AVsqRCRY924qh1zugrPRpwvUABgZEzDo/98Fv/8z2cwMaEjHje3S0yb0JE4ncSh+48hsjea0+WlhfWiLRYACF0xz6pAKYotFSJytOODCdz/q6OYSEyvzgoFCgAs7fXhvbcnrxFpaZFxzTUh3PwnHXC7Jfj81R2L66oBQzcQP5bAuaeHMfrGOKABkmwg2BNH8mTuNSmFWizehe3oe+BySO7yV7w0WcGWCkOFiBzvzQPjeHjryXQ3WLFAmRlSMHJYQyIrhD69xIeAR8Y1n2/HgsU+AJNdWG6vDDnPFPqaakBPGnApEtQJHWd2RfDxc2HM8MtIHIhPe6xvlgScCecdpM8OFleHD3P/YS2UzhLXr9QXQ4WImtu/vRXGL/54rmigAMBcjwdHjySm3dYSkNCpAsmMoLlwiQ9z2lyYfYEPM+Z6oHhkBIMy4qMakjEd5w7EMXEuieTuKJJj57vPuuZ74MnaPgCElgKJ98J5y5QKFj2axOzvXwbfgvYqPgFTMVSIiP7/N8L45RPnCgbK0h4f3hvI7Ya6ZIkPx9+ffvvSC70Ifzi9xbFskQ9D+6c/bm5AhhqdPiYzr1tB8sz0U5uLdYMBgLtXQfc35sG/KP81OA3GgXoious/1Y6NN81AviXqu0MKDrwTz7ldAhAdzL22xaeUt3qLtzt3ikWtM/c2Q5eQhB9w5W5XbnGh55sXiBIoRTFUiKip/L9Xt2PTX/TC65leeXsnZCSTuZ0ziz7hwfDZ3FDJbn0UlGdg/8yROCRvbnjEThrwLGqbdpu714u+v18K34XB8l7PYgwVImo6l64K4u/+Yx+6uyZbDEt7fTj6ce44BwC05mk5SABGz5SetBIAYnkuokxOGHB/Iv9cXWMfGHDPmjwRIPDJNvT9w1J4ZvvKei0RcEyFiJrWREzHlt8O4oVnRnPO9gKAznYXfKMa9KxGycwZCpRzua2XfGMqoS4FLXm6z0KzFLSczD9ljH++C13XtqD9hu4K3k1DcUyFiCib3yfjti/OxL33zkJvb+7MxgtnuXMCBQC6Osu/PmR0UIUSyK1qR0+q8MzNvTAzuDKAuff2iRwoRXGRLiJqeitXBvDww/Pwhz+MYNu2YYyMaHDJwPDx/F1cfpeEkQq2752pQM1zGnHcL6UP+X39XvR8qROtK3OXRLYThgoREQBFkbB+fTuuvTaE7dtH8eG+CRzYNZ73sdpEhdO25GmpAMCZQ3Es/FQAXde2oXW1vcMkhWMqREQFHHh3Am+8PIa9b0QwnnEB4ycCMuJ5zv7KN6YCAHMXeaHuP3+6cstsN7o/E8Tsq1sR6C08N5nAePEjEVG1dN3AkQMxfLhvAmePJxB+bwKRodwrKPOFiiQBvUt86O1S0L7Ij64VfrsGSSaGChGRmWIRDSPnVESGVUyMaVATBgKKBKgG3H4ZvpALgS4FLTMUKB7HnRPFUCEiItPwlGIiIqo/hgoREZmGoUJERKZhqBAR5fHTn/4UK1asQCgUQigUwmWXXYZnn322qm3deeeduOuuu/DQQw9hzZo1CIVCmDlzJm666Sbs27fP5JJbi6FCRJRHX18ffvSjH+Gtt97CG2+8gWuvvRYbNmzAnj17KtqOYRh45plnsGHDBmzfvh3f+MY3sHPnTrzwwgtQFAXXXXcdhoaG6vQuGo9nfxERlamzsxMPPfQQ7rjjDixbtgzvvvtu3sf94Ac/wAMPPAAAeP3117F+/XqcPn0aijJ9EpNIJIK2tjZs27YNN910U72Lbyae/UVEVC1N0/DEE08gEong8ssvBwBs3boVAPDcc8/h5MmTOHHiBAKBAB599FHcd9996edu27YNN954Y06gAMDY2Bh0XUdHR0dj3kgDMFSIiArYu3cvgsEgvF4v7rzzTmzduhUXX3wxAOD06dOQJAlXXnklent7MT4+jmg0irVr18Lv96e38fTTT2PDhg15t79p0yasWrUKl112WUPeTyNwQkkiogIWL16MgYEBjIyM4Mknn8RXv/pVbN++HcuXL8fu3bvR39+PYHByRcaBgQEEAgFccMEF6ecfOHAAhw4dwg033JCz7XvuuQc7duzAjh074HKVP5W+6BgqREQFeDyedEhccskl2LVrF3784x/j0UcfxZ49e7BixYr0YwcGBrB8+XLI8vkOoG3btmHdunVoaZk+A/Hdd9+NJ554Ai+++CL6+/sb82YahN1fRERl0nUd8fjkbMN79uzBypUr0/cNDAxM+z+Qv+tr06ZN+PWvf40XXngBS5YsqX+hG4yhQkSUx3e/+128/PLL+Oijj7B3715873vfw/bt27Fx40bouo59+/ZNa6kcPHgQ8+fPT///7NmzePXVV6ed1fXNb34Tjz32GB5//HF0dHTg1KlTOHXqFCKRSEPfWz0xVIiI8jh16hS+8pWvYPHixVi3bh127dqF3/3ud1i/fj0OHjyI8fHxaaFy8cUXY/Pmzfjd734HAPjXf/1XrFmzBj09PenHPPLIIxgbG8O6deswa9as9J+HH3644e+vXnidChFRHdx888244oor8J3vfMfqotQDr1MhImqkK664ArfeeqvVxWg4tlSIiKhSbKkQEVH9MVSIiMg0DBUiIjINQ4WIiEzDUCEiItOUmvur4Ag/ERFRNrZUiIjINAwVIiIyDUOFiIhMw1AhIiLTMFSIiMg0DBUiIjLN/wXBkM7g8FUi8AAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 504x504 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5HV19EkcTzCp"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}