QXQ_EQCI_Lab_6_[SOLUTIONS].ipynb

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        "# **Lab 6: Grover's Search**\n",
        "---\n",
        "\n",
        "### **Description**\n",
        "In today's lab, we will implement Grover's Algorithm using Qiskit's `Grover` function. Here, instead of creating the circuit gate-by-gate, we are going to use a built-in function to make the circuit for us. This approach will allow us to focus on Grover's search at a high-level.\n",
        "\n",
        "<br>\n",
        "\n",
        "### **Lab Structure**\n",
        "**Part 1**: [Defining the size of the problem](#p1)\n",
        "\n",
        "**Part 2**: [Setting up the Grover problem](#p2)\n",
        "\n",
        "**Part 3**: [Visualizing the results of Grover's algorithm](#p3)\n",
        "\n",
        "<br>\n",
        "\n",
        "### **Goals** \n",
        "By the end of this lab, you will:\n",
        "* Understand the Grover's search algorithm.\n",
        "* Implement Grover's search with the built-in Qiskit library. \n",
        "* Implement Grover's search from scratch for two qubits.\n",
        "\n",
        "\n",
        "<br>\n",
        "\n",
        "**Before starting, run the code below to import all necessary functions and libraries.**\n",
        "You will notice some new libraries here - `AmplificationProblem`, `Grover`, and `Statevector`. These will all be used to implement Grover's Algorithm. We will describe what each library is used for when we use them."
      ],
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      "source": [
        "!pip install qiskit\n",
        "\n",
        "import numpy as np\n",
        "import math\n",
        "import scipy\n",
        "\n",
        "# Importing standard Qiskit libraries\n",
        "from qiskit import QuantumCircuit, transpile, Aer, IBMQ\n",
        "from qiskit.tools.jupyter import *\n",
        "from qiskit.visualization import *\n",
        "\n",
        "# from ibm_quantum_widgets import *\n",
        "from qiskit.providers.aer import QasmSimulator\n",
        "from qiskit.algorithms import AmplificationProblem\n",
        "from qiskit.algorithms import Grover\n",
        "import math\n",
        "from qiskit.quantum_info import Statevector\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Loading your IBM Quantum account(s)\n",
        "# provider = IBMQ.load_account()\n",
        "\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "print(\"Libraries Imported Successfully!\")"
      ],
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    },
    {
      "cell_type": "markdown",
      "source": [
        "<a name=\"p1\"></a>\n",
        "\n",
        "---\n",
        "## **Part 1: Defining the size of the problem**\n",
        "---\n",
        "\n",
        "In this part, we will set up the search problem by specifying the number of choices we are searching through, and the choice we are searching for. Remember that in a search problem, we know what we are looking for - we just don't know where it is located."
      ],
      "metadata": {
        "id": "idga37M2FsMR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #1.1**\n",
        "**Together,** let's create a variable named `number_choices` to store the total number of choices you want to search through. Make sure that the number of choices you use is a power of 2, otherwise later code will produce errors. We recommend starting with 8 choices.\n",
        "\n",
        "Create a second variable named `correct_choice`, and give it the number of the choice you are searching for."
      ],
      "metadata": {
        "id": "E90o2LJcwsMI"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "ef77ha0_x9a_"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### **Solution**\n"
      ],
      "metadata": {
        "id": "qYYvoDbRx9bA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "number_choices= 8 # Total number of choices - please ensure that this number is a power of 2.\n",
        "correct_choice = 3 # Choice number you are searching for"
      ],
      "metadata": {
        "id": "see1xuAMx9bA"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #1.2**\n",
        "**Together**, let's determine how many qubits would be needed in Grover's algorithm for the number of choices you entered?"
      ],
      "metadata": {
        "id": "qu9c5nvQCBPX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# ENTER THE NUMBER HERE"
      ],
      "metadata": {
        "id": "GK5ZFdtCvLmu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### **Solution**\n",
        "3"
      ],
      "metadata": {
        "id": "e8y9NIP3CIba"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Run the code below to create a binary representation of each of the `number_choices` that you entered.**\n",
        "\n",
        "**This is important** because these binary representations will then get encoded into the corresponding quantum state. \n",
        "\n",
        "For example, suppose you entered `number_choices = 8`. Choice number 0 will be converted to $000$, and encoded in the quantum state $|000\\rangle$. Choice 5 will be converted to $101$, and be encoded in the quantum state $|101\\rangle$."
      ],
      "metadata": {
        "id": "H7ORnYAOEVNk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def generate_binary_strings(number_choices):\n",
        "    n = int(math.log(number_choices,2)) \n",
        "    binary_strings = []\n",
        "    for i in range(2**n):\n",
        "        binary_string = bin(i)[2:].zfill(n)\n",
        "        binary_strings.append(binary_string)\n",
        "    return binary_strings"
      ],
      "metadata": {
        "id": "Rv91EPyiEYO2"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #1.3**\n",
        "**Independently,** utilizing the provided function, generate a list named `ls`, that contains the binary representation of each of the`number_choices`."
      ],
      "metadata": {
        "id": "AV_AWeU7Lt6H"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE"
      ],
      "metadata": {
        "id": "FIczCG-TLpB1"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### **Solution**"
      ],
      "metadata": {
        "id": "9f43aVBOMqzu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "ls = generate_binary_strings(number_choices)\n",
        "ls"
      ],
      "metadata": {
        "id": "gVF22MEGMrnJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "508edf97-8ac4-41de-ba5b-2e078bb6afe2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['000', '001', '010', '011', '100', '101', '110', '111']"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XvDIuw6vlsKN"
      },
      "source": [
        "<a name=\"p2\"></a>\n",
        "\n",
        "---\n",
        "## **Part 2: Setting up the Grover problem**\n",
        "---\n",
        "\n",
        "In this part, we will use Qiskit's `AmplificationProblem` and `Grover` functions to set up Grover's search. `AmplificationProblem` sets up the oracle and defines the search problem. `Grover` solves the search problem by applying Grover's algorithm to it.\n",
        "\n",
        "First, we will define the search problem using `AmplificationProblem`. To do this, we have to create the Oracle. Remember from lecture that the Oracle flips the sign of the correct state. So, to create the oracle, we need to specify the correct state. After we have created the oracle, we use it as a paramter in the `AmplificationProblem` function to create the search problem.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #2.1**\n",
        "\n",
        "**Together**, let's create the oracle, and then use it to create the search problem."
      ],
      "metadata": {
        "id": "ApCmfZIh-ecP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "oracle = Statevector.from_label(ls[# COMPLETE THIS LINE\n",
        "problem = AmplificationProblem(oracle, is_good_state=[# COMPLETE THIS LINE"
      ],
      "metadata": {
        "id": "_TvLwwZv-ecQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### **Solution**\n"
      ],
      "metadata": {
        "id": "LW4voVux-ecQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Defining the grover problem using the AmplificationProblem function\n",
        "# In this step we take the binary representations we created in the last step and define the problem we want to solve.\n",
        "# We use the correct choice to create the oracle matrix\n",
        "# The AmplificationProblem function defines the grover problem\n",
        "\n",
        "oracle = Statevector.from_label(ls[correct_choice])\n",
        "problem = AmplificationProblem(oracle, is_good_state=[ls[correct_choice]])"
      ],
      "metadata": {
        "id": "7NkOXg5g-ecQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #2.2**\n",
        "\n",
        "**Together**, we will solve the search problem using Qiskit's `Grover` function. `Grover` needs two inputs - the number of iterations of the algorithm that you want to apply, and the backend you want to use.\n",
        "\n",
        "**Run the cell below as is and then rerun the cell after changing the number of iterations to 2.**"
      ],
      "metadata": {
        "id": "fgnsFh57-hkt"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')# Enter the QASM simulator here\n",
        "grover = Grover(iterations=0, quantum_instance=backend) # Enter the number of iterations here\n",
        "result = grover.amplify(problem) # This line of code applies Grover's algorithm to the problem and gets the result"
      ],
      "metadata": {
        "id": "gsEIMGZv-hkt"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###### **Solution**\n"
      ],
      "metadata": {
        "id": "SMK5MVBK-hku"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')# Enter the QASM simulator here\n",
        "grover = Grover(iterations=2, quantum_instance=backend) # Enter the number of iterations here\n",
        "result = grover.amplify(problem) # This line of code applies Grover's algorithm to the problem and gets the result"
      ],
      "metadata": {
        "id": "ieiAt5Jt-hku"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #2.3**\n",
        "\n",
        "**Together, let's run the code below to look at the state preparation part of the circuit.**"
      ],
      "metadata": {
        "id": "M6H_u-SG8LPU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "problem.grover_operator.state_preparation.draw()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "id": "Eh0t0-d-wbW9",
        "outputId": "1cd6687d-f0cc-4863-9b82-7d45997bffff"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     ┌───┐\n",
              "q_0: ┤ H ├\n",
              "     ├───┤\n",
              "q_1: ┤ H ├\n",
              "     ├───┤\n",
              "q_2: ┤ H ├\n",
              "     └───┘"
            ],
            "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",
              "     ├───┤\n",
              "q_1: ┤ H ├\n",
              "     ├───┤\n",
              "q_2: ┤ H ├\n",
              "     └───┘</pre>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #2.4**\n",
        "\n",
        "**Together, let's run the two cells below to look at the oracle and its decomposition.**"
      ],
      "metadata": {
        "id": "zrK2d1nX80QY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "problem.grover_operator.oracle.draw()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "id": "McpkHXr186C2",
        "outputId": "26a81c7c-08a4-4a52-87ef-e69fbcf8e9f0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "     ┌───────────┐\n",
              "q_0: ┤0          ├\n",
              "     │           │\n",
              "q_1: ┤1 Diagonal ├\n",
              "     │           │\n",
              "q_2: ┤2          ├\n",
              "     └───────────┘"
            ],
            "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: ┤0          ├\n",
              "     │           │\n",
              "q_1: ┤1 Diagonal ├\n",
              "     │           │\n",
              "q_2: ┤2          ├\n",
              "     └───────────┘</pre>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "problem.grover_operator.oracle.decompose().draw()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 140
        },
        "id": "mTDvANJB6duK",
        "outputId": "160c58a6-1d56-4102-abf0-67d910109786"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "global phase: π/8\n",
              "     ┌────────────────┐                              \n",
              "q_0: ┤0               ├──────────────────────────────\n",
              "     │                │┌──────────────┐              \n",
              "q_1: ┤1 Ucrz(0,π,0,0) ├┤0             ├──────────────\n",
              "     │                ││  Ucrz(π/2,0) │┌────────────┐\n",
              "q_2: ┤2               ├┤1             ├┤ Ucrz(-π/4) ├\n",
              "     └────────────────┘└──────────────┘└────────────┘"
            ],
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">global phase: π/8\n",
              "     ┌────────────────┐                              \n",
              "q_0: ┤0               ├──────────────────────────────\n",
              "     │                │┌──────────────┐              \n",
              "q_1: ┤1 Ucrz(0,π,0,0) ├┤0             ├──────────────\n",
              "     │                ││  Ucrz(π/2,0) │┌────────────┐\n",
              "q_2: ┤2               ├┤1             ├┤ Ucrz(-π/4) ├\n",
              "     └────────────────┘└──────────────┘└────────────┘</pre>"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #2.5**\n",
        "\n",
        "**Together, let's run the two cells below to look at the grover operator and the decomposed circuit.**"
      ],
      "metadata": {
        "id": "itxYGI3w9D-F"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "problem.grover_operator.draw()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        },
        "id": "k44Vys3G7nGz",
        "outputId": "e8a54191-e67a-430a-8b12-1ae73c721602"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "         ┌────┐\n",
              "state_0: ┤0   ├\n",
              "         │    │\n",
              "state_1: ┤1 Q ├\n",
              "         │    │\n",
              "state_2: ┤2   ├\n",
              "         └────┘"
            ],
            "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",
              "state_0: ┤0   ├\n",
              "         │    │\n",
              "state_1: ┤1 Q ├\n",
              "         │    │\n",
              "state_2: ┤2   ├\n",
              "         └────┘</pre>"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "problem.grover_operator.decompose().draw()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 140
        },
        "id": "77jQD_ej9M0J",
        "outputId": "b9add58e-68e0-46f2-f747-6d380d895916"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "global phase: π\n",
              "         ┌───────────┐┌───┐┌───┐          ┌───┐┌───┐     \n",
              "state_0: ┤0          ├┤ H ├┤ X ├───────■──┤ X ├┤ H ├─────\n",
              "         │           │├───┤├───┤       │  ├───┤├───┤     \n",
              "state_1: ┤1 Diagonal ├┤ H ├┤ X ├───────■──┤ X ├┤ H ├─────\n",
              "         │           │├───┤├───┤┌───┐┌─┴─┐├───┤├───┤┌───┐\n",
              "state_2: ┤2          ├┤ H ├┤ X ├┤ H ├┤ X ├┤ H ├┤ X ├┤ H ├\n",
              "         └───────────┘└───┘└───┘└───┘└───┘└───┘└───┘└───┘"
            ],
            "text/html": [
              "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">global phase: π\n",
              "         ┌───────────┐┌───┐┌───┐          ┌───┐┌───┐     \n",
              "state_0: ┤0          ├┤ H ├┤ X ├───────■──┤ X ├┤ H ├─────\n",
              "         │           │├───┤├───┤       │  ├───┤├───┤     \n",
              "state_1: ┤1 Diagonal ├┤ H ├┤ X ├───────■──┤ X ├┤ H ├─────\n",
              "         │           │├───┤├───┤┌───┐┌─┴─┐├───┤├───┤┌───┐\n",
              "state_2: ┤2          ├┤ H ├┤ X ├┤ H ├┤ X ├┤ H ├┤ X ├┤ H ├\n",
              "         └───────────┘└───┘└───┘└───┘└───┘└───┘└───┘└───┘</pre>"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "<a name=\"p3\"></a>\n",
        "\n",
        "---\n",
        "## **Part 3: Visualizing the results of Grover's algorithm**\n",
        "---\n",
        "In the final part of implementing Grover's, we will extract the results from running the algorithm and plot the results. The results will be shown in the form of the measurement probabilities of all the different choices. \n",
        "\n",
        "**Run the cell below to see the first measurement results.**"
      ],
      "metadata": {
        "id": "rK_mBaHsJjC-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "AKJEkRrwJsbv",
        "outputId": "608e65e0-14b6-4547-fd7d-007a810e1691"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #3.1**\n",
        "**Independently**, visualize the measurement outcomes you get with zero grover iterations. Do the results make sense?"
      ],
      "metadata": {
        "id": "hWUj2KtsNA5I"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE"
      ],
      "metadata": {
        "id": "RmG8d_-ZmBxz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **Solution**"
      ],
      "metadata": {
        "id": "LhqC-WDymCCs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=0, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "id": "jiDIZ8J2mEgY",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "outputId": "38480161-be65-4636-a18c-e8bc840295d3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "With zero iterations it is not clear which is the correct item - Grover's search has not been done for an optimal number of iterations."
      ],
      "metadata": {
        "id": "4Y4hvskTNFi-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #3.2**\n",
        "\n",
        "**Independently**, visualize the results for Grover's algorithm on this problem for 0 to 10 iterations. For each number of iterations, notice the histogram. What changes do you observe? Do you see amplitude amplification? Does the right choice's amplitude get amplified?\n",
        "\n",
        "**Using these results, answer what is the optimal number of iterations that maximizes the amplification of the right choice's amplitude?**"
      ],
      "metadata": {
        "id": "Whhj0tVANYFl"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE FOR 0 ITERATIONS"
      ],
      "metadata": {
        "id": "b4rXtyjy0t-G"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE FOR 1 ITERATIONS"
      ],
      "metadata": {
        "id": "Ju-NUVwY0t56"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE FOR 2 ITERATIONS"
      ],
      "metadata": {
        "id": "zd_AJgZj0t1x"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE FOR 3 ITERATIONS"
      ],
      "metadata": {
        "id": "686u4KXp0tzL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE FOR 4 ITERATIONS"
      ],
      "metadata": {
        "id": "apjEhCr-0twr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE FOR 5 ITERATIONS"
      ],
      "metadata": {
        "id": "vhgw_8PY0tt7"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE FOR 6 ITERATIONS"
      ],
      "metadata": {
        "id": "mVMsAezp0x0h"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE FOR 7 ITERATIONS"
      ],
      "metadata": {
        "id": "h-FOCC6s0yd3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE FOR 8 ITERATIONS"
      ],
      "metadata": {
        "id": "PNbh9-d30zHr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE FOR 9 ITERATIONS"
      ],
      "metadata": {
        "id": "lEQURS-s00Lr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# COMPLETE THIS CODE FOR 10 ITERATIONS"
      ],
      "metadata": {
        "id": "oBsEBG9t005J"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **Solution**"
      ],
      "metadata": {
        "id": "IFLFrffs5oLV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "2 is the optimal number. \n",
        "\n",
        "\n",
        "You will notice that the probability of the correct choice increases as you increase the number of iterations! This is amplitude amplification in action.\n",
        "\n",
        "\n",
        "You will also notice that if you exceed the optimal number of iterations, the probability of measuring the correct choice goes down. There is an **optimal** number of iterations - at this number of iterations, the probability of successfully finding the right state is maximized."
      ],
      "metadata": {
        "id": "Jyaip5s95o_w"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=0, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "nOeF5hrW0MzJ",
        "outputId": "ff2b5ac0-7b81-4863-c398-fd3d7fabfac1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=1, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "y8yRa9Sn0OKB",
        "outputId": "0d87f936-0738-4f3f-d1c2-1d25f89f0579"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=3, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "024qmofi0Pl8",
        "outputId": "ca29d175-c932-4e35-9069-7644b024a8ad"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=4, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "3nGx71d_0RPy",
        "outputId": "a9f0a263-946c-440c-da8b-5cd8ae46eaeb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=5, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "dAq4wW9W0Ss6",
        "outputId": "8396b912-64a8-4b28-bea5-f6925d55009a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=6, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "WnqY96YU0Uaq",
        "outputId": "3d555572-4c23-40be-c001-d0c7d7b56f96"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=7, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "FOAAFLRl0V8t",
        "outputId": "92eeaf67-aa99-45b6-bd43-d2ce3c26907d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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gJScn65tvvimU5wIAAACAnBTZILZhwwZNmDBBY8aM0fXXX3/F+StXrtTrr7+uN954Q/Pnz1dqamqO81asWCFJioyMzLYsKipKkhQTE1PwwgEAAADgCorkqYnnz59Xnz591Lx5c/3zn//M0/eMGTPG6XFAQIDeffdd9enTx2k8Pj5eklSvXr1s68gay5qTW23nz593PE5JSZF08TTKtLQ0SZKbm5vc3d2VkZGhzMxMx9ys8fT0dBljHOPu7u5yc3PLdTxrvVk8PC6+bOnp6Xka9/T0VGZmpjIyMhxjlmXJw8Mj1/HcaqcneqIneiqifzryrLS8TvRET/RET/Rkf09/X345RfKv6csvv6z4+Hj99ttvVzwlsVmzZvrkk0/UoUMHBQcHKykpST/88INefvll9evXTwEBAeratatj/smTJyVJ/v7+2dbl5+fnNCcnkyZN0rhx47KNR0dHq3z58pKkGjVqqEWLFtq8ebP27t3rmNOgQQOFhYUpNjZWR44ccYw3b95coaGhWrlypU6dOuUYv+WWW1S5cmVFR0c7/WBGRETIy8tLCxYscKqhc+fOOnv2rJYvX+4Y8/DwUJcuXZScnKy1a9c6xn19fXXbbbcpMTFRGzdudIxXqlRJrVu3Vnx8vOLi4hzj9ERP9ERPWT1JrVWclZbXiZ7oiZ7oiZ7s7+nMmTPKK8tcGvWKgLVr16pt27YaO3asRo8e7Rjv16+fPv30U61du1Y333zzFdezdOlSderUSY0bN9bmzZsd4/Xr11d8fLzS0tIcCTZLWlqaypQpo6ZNm2rTpk05rjenI2IhISFKTk52BDn2JtATPdFTSe7pqSlFch9ennw8lCNi9ERP9ERP9HTtekpJSVFgYKBOnjzpyAa5KVJBLD09Xddff728vb0VGxsrT09Px7L8BjHp4qmGCQkJThsiPDxc69evV3JysipWrOg0/+jRowoMDNStt96qlStX5uk5UlJS5O/vn6eNDQAlQf93XF1BwX081NUVAABKsvxkgyJ1s47U1FTFx8dr48aNKlOmjNMHM3/66aeSLh4WtCxL8+fPv+L6AgMDJTkfIrzcdWCXu34MAAAAAApLkTq/pGzZsnr88cdzXLZy5UrFx8era9euqlSpUo4f3nyp06dPa+vWrfL29nYEMklq3769vvjiC0VHR2c7srZ48WLHHAAAAAC4VorUqYmXk9OpiadOndLBgwdVv359p7lnz57V448/ri+++EKPPvqoPvnkE8ey48ePq1atWvL09NTvv//u+Cyxffv2qUWLFpKknTt35vkDnTk1EUBpw6mJAADkLD/ZoEgdEcuvo0ePKiwsTOHh4WrYsKGCgoJ06NAhLVmyRPv27VOTJk30xhtvOH1PhQoVNGXKFPXu3VstW7bUAw88IEmaM2eOjh49qjlz5uQ5hAEAAABAQRTrIHbdddfp6aefVmxsrBYsWKDjx4/Ly8tLDRs21JAhQzRo0CB5eXll+75HHnlEgYGBmjhxombOnCnLsnTDDTfopZdeUseOHV3QCQAAAIDSpNicmlhUcWoigNKGUxMBAMhZsb1rIgAAAACUBgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBQ5iK1eu1N69ey87JzExUStXrizoUwAAAABAiVTgIBYREaFZs2Zdds7s2bMVERFR0KcAAAAAgBKpwEHMGHPFOZmZmbIsq6BPAQAAAAAl0jW9Riw+Pl7+/v7X8ikAAAAAoNjxyM/kxx57zOnx/PnztXv37mzzMjIyHNeH3XnnnVdVIAAAAACUNPkKYpdeE2ZZljZu3KiNGzfmONeyLIWHh+vtt9++mvoAAAAAoMTJVxDbtWuXpIvXh9WuXVtDhw7VM888k22eu7u7KlSoIG9v78KpEgAAAABKkHwFsdDQUMe/Z86cqRYtWjiNAQAAAACuLF9B7FJ9+/YtzDoAAAAAoNQocBDLEhsbq19//VUnTpxQRkZGtuWWZWn06NFX+zQAAAAAUGIUOIgdO3ZM99xzj1avXn3ZzxQjiAEAAACAswIHseHDh2vVqlXq0KGD+vbtq+rVq8vD46oPsAEAAABAiVfg5PTDDz/opptu0tKlS2VZVmHWBAAAAAAlmltBv/Hs2bNq164dIQwAAAAA8qnAQax58+bavXt3IZYCAAAAAKVDgYPYmDFj9N1332ndunWFWQ8AAAAAlHgFvkYsKSlJXbp0Ufv27dWrVy+1bNlSfn5+Oc7t06dPgQsEAAAAgJLGMpe79/xluLm5ybIsp1vX//16MWOMLMvK8fPFSoqUlBT5+/vr5MmTuQZRAChJ+r/j6goK7uOhrq4AAFCS5ScbFPiI2MyZMwv6rQAAAABQqhU4iPXt27cw6wAAAACAUqPAN+sAAAAAABRMgY+I7d27N89za9SoUdCnAQAAAIASp8BBrGbNmnn6MGfLspSenl7QpwEAAACAEqfAQaxPnz45BrGTJ09q06ZN2rVrl9q3b6+aNWteTX0AAAAAUOIUOIjNmjUr12XGGL311luaPHmyZsyYUdCnAAAAAIAS6ZrcrMOyLD333HNq1KiRRowYcS2eAgAAAACKrWt618Qbb7xRy5Ytu5ZPAQAAAADFzjUNYjt27OBGHQAAAADwNwW+Riw3mZmZ2r9/v2bNmqVvv/1Wt99+e2E/BQAAAAAUawUOYm5ubpe9fb0xRhUqVNBbb71V0KcAAAAAgBKpwEGsXbt2OQYxNzc3VahQQeHh4Xr00UdVuXLlqyoQAAAAAEqaAgexFStWFGIZ/3Pu3DmNGjVK69evV0JCgo4dO6aAgADVqVNHTzzxhB555BF5eno6fU9KSorGjh2refPmKSkpScHBwerRo4fGjBkjHx+fbM+RmZmpDz74QNOmTVNCQoJ8fHzUsWNHTZgwQbVr174mfQEAAABAFssYY1xdxKWSk5MVEhKim266SfXr11elSpV0/PhxLVy4UHv27FFkZKQWLlwoN7eL9xk5ffq02rZtq40bNyoyMlItWrTQ77//rujoaIWHh2vlypUqV66c03P0799f06dPV6NGjdSlSxcdOHBAc+fOlY+Pj9atW6d69erlud6UlBT5+/vr5MmT8vPzK9RtAQBFUf93XF1BwX081NUVAABKsvxkg0K5Wcfq1au1ceNGpaSkyM/PT82bN1ebNm0KtK7rrrtOJ0+eVJkyZZzG09PT1alTJ0VHR2vhwoXq0qWLJGny5MnauHGjnn/+eb322muO+SNHjtTrr7+ut99+Wy+88IJjfPny5Zo+fbratWunn376yfE8Dz/8sDp37qxBgwZp8eLFBaodAAAAAPLiqm5fv2bNGjVo0EDt2rXTkCFD9OKLL2rIkCFq166dwsLCtHbt2vwX5OaWLYRJkoeHh7p37y5JSkhIkHTxhiDTp0+Xj4+PRo8e7TR/9OjR8vHx0fTp053GP/74Y0nS+PHjnZ7nzjvvVIcOHRQdHa29e/fmu24AAAAAyKsCB7GtW7cqMjJS8fHxjuurZs6cqYkTJ6pTp07666+/FBUVpT///LNQCs3MzNSiRYskSY0bN5YkxcfH68CBA2rTpo28vb2d5nt7e6tNmzbauXOnEhMTHeMrVqxwLPu7qKgoSVJMTEyh1AwAAAAAOSnwqYmvvPKKLly4oAULFuiOO+5wWvb8889r0aJF6tq1q1555RV9+eWX+V7/hQsXNHHiRBljdPToUS1dulTbt2/Xo48+6vhssvj4eEnK9ZquevXqafHixYqPj1dISIhOnz6tgwcPqnHjxnJ3d89x/qXrzcn58+d1/vx5x+OUlBRJUlpamtLS0iRdPKrn7u6ujIwMZWZmOuZmjaenp+vSS/Pc3d3l5uaW63jWerN4eFx82f7+Ydm5jXt6eiozM1MZGRmOMcuy5OHhket4brXTEz3REz1dg4+gtFVpeZ3oiZ7oiZ7oyf6e/r78cq7qron3339/thCW5Y477tD999+vpUuXFmj9Fy5c0Lhx4xyPLcvSc889p0mTJjnGTp48KUny9/fPcR1ZF8hlzcvv/JxMmjTJqa4s0dHRKl++vCSpRo0aatGihTZv3ux0mmODBg0UFham2NhYHTlyxDHevHlzhYaGauXKlTp16pRj/JZbblHlypUVHR3t9IMZEREhLy8vLViwwKmGzp076+zZs1q+fLljzMPDQ126dFFycrLTqaK+vr667bbblJiYqI0bNzrGK1WqpNatWys+Pl5xcXGOcXqiJ3qip6yepNYqzkrL60RP9ERP9ERP9vd05swZ5VWB75pYrlw5Pfvss5owYUKuc1588UW99dZbOnfuXEGeQtLFPZcHDhzQ999/r1GjRqlRo0ZasGCB/Pz89Pnnn6tXr1568cUX9eqrr+b4/BMnTtTXX3+t7t2768CBA6pWrZratGmjVatWZZv/008/KTIyUkOGDNG7776bYz05HRELCQlRcnKyI8ixN4Ge6ImeSnJPT00pvkfEPh7KETF6oid6oid6unY9paSkKDAw8NreNbFq1apat27dZef88ssvqlq1akGfQtLFjVS9enU99dRTCgwMVM+ePTVhwgS9/vrrjiNbuR3ByjptMGtefufnpGzZsipbtmy2cU9Pz2yfb+bu7p7jKZBZL1hex/++3oKMu7m5OW75n5fx3GqnJ3rK7zg9lcyeirPS9DrREz3lVmN+x+mJniR6yq3GS8dzW56TAv917dq1q1asWKHRo0dnO+J17tw5jRkzRsuXL1e3bt0K+hTZREZGSvrfh0lf6Zquv19D5u3treDgYO3atcspQec2HwAAAACuhQIHsdGjR6tWrVqaOHGiatSoobvuukuPP/647rrrLoWGhmr8+PGqVatWttvKX40DBw5I+l/SrFevnqpWrarVq1fr9OnTTnNPnz6t1atXq1atWgoJCXGMt2/f3rHs77I+P6xdu3aFVjMAAAAA/F2Bg1jFihW1bt069e3bV6mpqVqwYIFmzpypBQsW6NSpU3r00Ue1bt06XXfddfla759//pnjRW5nzpzR8OHDJV28oE+6eC7oE088odTUVI0fP95p/vjx45Wamqr+/fs7jQ8YMEDSxSB54cIFx/jChQu1YsUKRUZGKjQ0NF81AwAAAEB+FPhmHZdKS0vT9u3blZKSIj8/P4WFheXr/MhLjR07Vv/617/Utm1b1axZU35+ftq/f78WLlyoo0eP6tZbb9XixYvl5eUl6eKRrzZt2mjTpk2KjIxUy5YttWHDBkVHRys8PFwxMTGOuVn69++v6dOnq1GjRurSpYsOHjyoOXPmyMfHR2vXrlX9+vXzXG9KSor8/f3zdEEeAJQE/d9xdQUF9/FQV1cAACjJ8pMN8h3EJkyYoNOnT2vcuHG5hq2sW8/7+vpq5MiR+Vm91q9fr2nTpmnNmjXav3+/UlNT5e/vr6ZNm+rBBx/UY489lu3iuZMnT2rs2LGaN2+ekpKSFBwcrB49emjMmDHy9fXN9hyZmZmaMmWKpk2bpoSEBPn4+Dg+lLpOnTr5qpcgBqC0IYgBAJCzaxbElixZoqioKE2ePFnPPvvsZef+61//0ogRI7RkyRJFRETk9SmKHYIYgNKGIAYAQM7ykw3ydY3Y7NmzVaFCBQ0aNOiKcwcOHKjrrrtOM2fOzM9TAAAAAECJl68gtmbNGnXs2DHHz9H6u7Jly6pjx4453p0QAAAAAEqzfAWxAwcOqHbt2nmeX6tWLR08eDDfRQEAAABASZavIObm5qa0tLQ8z09LS8vxE68BAAAAoDTLV0qqWrWqtmzZkuf5W7ZsUbVq1fJdFAAAAACUZPkKYrfeequWLVum3bt3X3Hu7t27tWzZMrVr166gtQEAAABAiZSvIDZw4EClpaXp/vvvV3Jycq7zjh49qh49eig9PV1PPfXUVRcJAAAAACWJx5Wn/E/Lli01dOhQvfPOO7r++uv15JNPKiIiQtWrV5ck7d+/X0uXLtW0adN05MgRDR8+XC1btrwmhQMAAABAcZWvICZJb731lsqVK6c33nhDEyZM0IQJE5yWG2Pk7u6uF154Qa+++mqhFQoAAAAAJUW+g5hlWZo4caIef/xxzZw5U2vWrFFSUpIkKSgoSG3atFG/fv1Up06dQi8WAAAAAEqCfAexLHXq1OGIFwAAAAAUAB/yBQAAAAA2I4gBAAAAgM0IYgAAAABgM4IYAAAAANiMIAYAAAAANiOIAQAAAIDNCGIAAAAAYDOCGAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2IwgBgAAAAA2I4gBAAAAgM0IYgAAAABgM4IYAAAAANiMIAYAAAAANiOIAQAAAIDNCGIAAAAAYDOCGAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2IwgBgAAAAA2I4gBAAAAgM0IYgAAAABgM4IYAAAAANiMIAYAAAAANiOIAQAAAIDNCGIAAAAAYDOCGAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2IwgBgAAAAA2I4gBAAAAgM0IYgAAAABgM4IYAAAAANiMIAYAAAAANiOIAQAAAIDNCGIAAAAAYDOCGAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2IwgBgAAAAA2I4gBAAAAgM0IYgAAAABgM4IYAAAAANiMIAYAAAAANiOIAQAAAIDNCGIAAAAAYDOCGAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2IwgBgAAAAA2I4gBAAAAgM0IYgAAAABgM4IYAAAAANiMIAYAAAAANiuSQeyzzz7TP/7xD914440qW7asLMvSrFmzcpw7duxYWZaV69fu3btz/L7Fixerffv28vX1lZ+fnyIiIrR06dJr1xQAAAAA/H8eri4gJy+99JL27NmjwMBABQcHa8+ePVf8nr59+6pmzZrZxgMCArKNffbZZ+rdu7cqVaqkfv36SZLmzJmjTp06ae7cubr//vuvsgMAAAAAyF2RDGLTp09XvXr1FBoaqtdee00vvPDCFb+nX79+6tChwxXnHT9+XIMHD1ZgYKA2bNig6tWrS5Kef/55tWjRQk899ZSioqLk6+t7tW0AAAAAQI6K5KmJHTt2VGho6DVZ91dffaUTJ05o8ODBjhAmSdWrV9egQYOUnJysb7755po8NwAAAABIRTSIFcTKlSv1+uuv64033tD8+fOVmpqa47wVK1ZIkiIjI7Mti4qKkiTFxMRcszoBAAAAoEiemlgQY8aMcXocEBCgd999V3369HEaj4+PlyTVq1cv2zqyxrLm5OT8+fM6f/6843FKSookKS0tTWlpaZIkNzc3ubu7KyMjQ5mZmY65WePp6ekyxjjG3d3d5ebmlut41nqzeHhcfNnS09PzNO7p6anMzExlZGQ4xizLkoeHR67judVOT/RET/RU3P90lJbXiZ7oiZ7oiZ7s7+nvyy+neP81ldSsWTN98skn6tChg4KDg5WUlKQffvhBL7/8svr166eAgAB17drVMf/kyZOSJH9//2zr8vPzc5qTk0mTJmncuHHZxqOjo1W+fHlJUo0aNdSiRQtt3rxZe/fudcxp0KCBwsLCFBsbqyNHjjjGmzdvrtDQUK1cuVKnTp1yjN9yyy2qXLmyoqOjnX4wIyIi5OXlpQULFjjV0LlzZ509e1bLly93jHl4eKhLly5KTk7W2rVrHeO+vr667bbblJiYqI0bNzrGK1WqpNatWys+Pl5xcXGOcXqiJ3qip6yepNYqzkrL60RP9ERP9ERP9vd05swZ5ZVlLo16RVDWzTpmzpzpuMNhXixdulSdOnVS48aNtXnzZsd4/fr1FR8fr7S0NEeCzZKWlqYyZcqoadOm2rRpU47rzemIWEhIiJKTkx1Bjr0J9ERP9FSSe3pqSvHdh/fxUI6I0RM90RM90dO16yklJUWBgYE6efKkIxvkpvj+Nb2C22+/XXXq1NEff/yhlJQUx4bIOhJ28uRJVaxY0el7sk4zzOloWZayZcuqbNmy2cY9PT3l6enpNObu7i53d/dsc/8eAK80/vf1FmTczc1Nbm7ZLwnMbTy32umJnvI7Tk8ls6firDS9TvRET7nVmN9xeqIniZ5yq/HS8dyW56Rk/XX9m8DAQEnOhwgvdx3Y5a4fAwAAAIDCUmKD2OnTp7V161Z5e3s7ApkktW/fXtLFa7r+bvHixU5zAAAAAOBaKNZB7NSpU/rrr7+yjZ89e1b9+/fXqVOn1LNnT6dDiz179pS/v7/ef/997du3zzG+b98+TZkyRYGBgerevbst9QMAAAAonYrkNWLTp0/XqlWrJEl//PGHY2zF//8MsLZt2+qJJ57Q0aNHFRYWpvDwcDVs2FBBQUE6dOiQlixZon379qlJkyZ64403nNZdoUIFTZkyRb1791bLli31wAMPSJLmzJmjo0ePas6cOfL19bWvWQAAAAClTpEMYqtWrdKnn37qNLZ69WqtXr3a8fiJJ57Qddddp6efflqxsbFasGCBjh8/Li8vLzVs2FBDhgzRoEGD5OXllW39jzzyiAIDAzVx4kTNnDlTlmXphhtu0EsvvaSOHTte8/4AAAAAlG5F/vb1RV1KSor8/f3zdItKACgJ+r/j6goK7uOhrq4AAFCS5ScbFOtrxAAAAACgOCKIAQAAAIDNCGIAAAAAYDOCGAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2IwgBgAAAAA2I4gBAAAAgM0IYgAAAABgM4IYAAAAANiMIAYAAAAANiOIAQAAAIDNCGIAAAAAYDOCGAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2IwgBgAAAAA2I4gBAAAAuGo1a9aUZVnZvgYOHChJ6tChQ7ZlTz75pIurdh0PVxcAAAAAoPj79ddflZGR4Xi8ZcsWderUST169HCM9e/fX6+88orjcfny5W2tsSghiAEAAAC4apUqVXJ6/Nprr6lOnTpq3769Y6x8+fIKCgqyu7QiiVMTAQAAABSqCxcu6LPPPtNjjz0my7Ic4//5z38UGBioxo0b64UXXtCZM2dcWKVrcUQMAAAAQKGaP3++Tpw4oX79+jnGHn74YYWGhqpq1aravHmznn/+ecXFxenrr792XaEuxBExoIjYv3+/HnnkEVWsWFFeXl5q0qSJ1q9f71ie08WvlmXpjTfecGHVAAAA2c2YMUN33nmnqlat6hgbMGCAoqKi1KRJE/Xq1UuzZ8/WN998ox07driwUtchiCGbKwUCSdq2bZu6du0qf39/eXt7Kzw8XHv37nVRxcXf8ePH1aZNG3l6emrhwoX6888/9dZbb6lChQqOOQcPHnT6+uSTT2RZlu677z4XVg4AAOBsz549WrJkiZ544onLzmvVqpUkKSEhwY6yihyCGJzkJRDs2LFDbdu2VVhYmFasWKHNmzdr9OjRKleunAsrL95ef/11hYSEaObMmbrppptUq1YtRUZGqk6dOo45QUFBTl/ffvutIiIiVLt2bRdWDgBA0ZSXHctZnnzySVmWpXfeecfeIkuomTNnqnLlyurSpctl523cuFGSFBwcbENVRQ/XiMHJpYEgS61atZzmvPjii+rcubMmT57sGLs0MCD/vvvuO0VFRalHjx6KiYlRtWrV9PTTT6t///45zj906JB+/PFHffrppzZXCgBA0Ze1YzkiIkILFy5UpUqVFB8f77RjOcs333yjdevWOZ1Ch4LLzMzUzJkz1bdvX3l4/C9q7NixQ59//rk6d+6sihUravPmzRo2bJjatWunpk2burBi1+GIGJx89913uvHGG9WjRw9VrlxZLVq00Mcff+xYnpmZqR9//FH169dXVFSUKleurFatWmn+/PmuK7oE2Llzp6ZOnap69epp8eLFeuqppzRkyJBcg9ann34qX19f3XvvvTZXCgBA0ZeXM02ki0fNBg8erP/85z/y9PR0UbUly5IlS7R371499thjTuNlypTRkiVLFBkZqbCwMD377LO677779P3337uoUtcjiMHJlQLB4cOHlZqaqtdee0133HGHoqOj1b17d917772KiYlxcfXFV2Zmplq2bKmJEyeqRYsWGjBggPr3768PP/wwx/mffPKJevXqxemgAPLlSqdqGWP08ssvKzg4WF5eXurYsaPi4+NdWDFQMFfasSxd/Nvbu3dvjRgxQo0aNXJRpSVPZGSkjDGqX7++03hISIhiYmJ09OhRnTt3TvHx8Zo8ebL8/PxcVKnrEcTg5EqBIDMzU5LUrVs3DRs2TM2bN9fIkSN111135RoacGXBwcG6/vrrncYaNmyY4w1Qfv75Z8XFxV3xAlhc2dixY7PdhTIsLMyxPCkpSb1791ZQUJC8vb3VsmVLzZs3z4UVAwWXl2uAJ0+erPfee08ffvihfvnlF3l7eysqKkrnzp1zYeVA/uXlTJPXX39dHh4eGjJkiAsrRWlGEIOTKwWCwMBAeXh45Dk0IG/atGmjuLg4p7G//vpLoaGh2ebOmDFDN9xwg5o1a2ZXeSVao0aNnO5GuWrVKseyPn36KC4uTt99953++OMP3XvvverZs6d+//13F1YMFMyVTtUyxuidd97RSy+9pG7duqlp06aaPXu2Dhw4wOnnV+FKO3wkae3atbrtttvk7e0tPz8/tWvXTmfPnnVRxSXDlXYs//bbb3r33Xc1a9Yspw8bBuxEEIOTKwWCMmXKKDw8PM+hAXkzbNgwrVu3ThMnTlRCQoI+//xzTZs2TQMHDnSal5KSoq+++oqjYYXIw8PD6W6UgYGBjmVr1qzR4MGDddNNN6l27dp66aWXFBAQoN9++82FFQMFc6VTtXbt2qWkpCR17NjRMebv769WrVpp7dq1rii5xLjcDp+1a9fqjjvuUGRkpGJjY/Xrr79q0KBBcnPjLdrVuNKO5Z9//lmHDx9WjRo15OHhIQ8PD+3Zs0fPPvusatas6YKKURpx10Q4GTZsmFq3bq2JEyeqZ8+eio2N1bRp0zRt2jTHnBEjRuiBBx5Qu3btFBERoUWLFun777/XihUrXFd4MRceHq5vvvlGL7zwgl555RXVqlVL77zzjnr16uU078svv5QxRg899JCLKi154uPjVbVqVZUrV0633HKLJk2apBo1akiSWrdurTlz5qhLly4KCAjQ3Llzde7cOXXo0MG1RQMFkHWq1vDhwzVq1Cj9+uuvGjJkiMqUKaO+ffsqKSlJklSlShWn76tSpYpjGQoma4dPToYNG6YhQ4Zo5MiRjrEGDRrYVVqJdaUdy71793ba6SBJUVFR6t27tx599FHb6kTpRhCDk7wEgu7du+vDDz/UpEmTNGTIEDVo0EDz5s1T27ZtXVh58XfXXXfprrvuuuycAQMGaMCAATZVVPK1atVKs2bNUoMGDXTw4EGNGzdOt956q7Zs2SJfX1/NnTtXDzzwgCpWrCgPDw+VL19e33zzjerWrevq0oF8y8zM1I033qiJEydKklq0aKEtW7boww8/VN++fV1cXcmW2w6fw4cP65dfflGvXr3UunVr7dixQ2FhYZowYQJ/U6/SlXYsV6xYURUrVnT6Hk9PTwUFBZXqINz/HVdXUHAfD3V1BflHEEM2eQkEjz32WLbbkgLFzZ133un4d9OmTdWqVSuFhoZq7ty5evzxxzV69GidOHFCS5YsUWBgoObPn6+ePXvq559/VpMmTVxYOZB/uZ2qlXUDmqwjNocOHXL6cNVDhw6pefPmttVZ0lxuh8/OnTslXbyO7M0331Tz5s01e/Zs3X777dqyZYvq1avn4uqLr7yeaQK4EkEMAP6/gIAA1a9fXwkJCdqxY4emTJmiLVu2OG5r3KxZM/3888/64IMPuEsoip0rnapVq1YtBQUFaenSpY7glZKSol9++UVPPfWU3eWWGJfb4dOwYUNJ0j/+8Q/H6XAtWrTQ0qVL9cknn2jSpEkuqbmkyMuO5Uvt3r372hUD5IArQQHg/0tNTdWOHTsUHBysM2fOSFK2C+bd3d0dH+MAFCdXuimQZVkaOnSoXn31VcedQvv06aOqVavqnnvucW3xJcilO3yyjjxyJ2KgdCKIASi1nnvuOcXExGj37t1as2aNunfvLnd3dz300EMKCwtT3bp19Y9//EOxsbHasWOH3nrrLf3000+8KUWxlHWq1hdffKHGjRtr/Pjx2U7V+uc//6nBgwdrwIABCg8PV2pqqhYtWsSHxxeiS3f41KxZU1WrVuVOxEApxamJQCHhAtfiZ9++fXrooYd09OhRVapUSW3bttW6detUqVIlSdKCBQs0cuRI3X333UpNTVXdunX16aefqnPnzi6uHCiYK52qZVmWXnnlFb3yyis2VlWyPffcc7r77rsVGhqqAwcOaMyYMY4dPpZlacSIERozZoyaNWum5s2b69NPP9X27dv13//+19WlA7jGCGIlEIEAyJsvv/zyssvr1avnuJEBABTElXb4DB06VOfOndOwYcN07NgxNWvWTD/99JPjg7YBlFwEMQAAgGvkSjt8JGnkyJFOnyMGdiqjdOAaMQAAAACwGUfEAAAoBjhCAAAlC0EMQLFWXN+c8sYUAIDSjVMTAQAAAMBmHBEDAADIRXE96i5x5B0o6jgiBgAAAAA2I4gBAAAAgM0IYgAAAABgM4IYAAAAANiMIAYAAAAANiOIAQAAAIDNCGIAAAAAYDOCGAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2IwgBgAAAAA2I4gBAAAAgM0IYgAAAABgM4IYAAAAANiMIAYAAAAANiOIAQAAAIDNCGIAAAAAYDOCGAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2IwgBgAAAAA2I4gBAAAAgM1KdRD79ddf1blzZwUEBMjb21s333yz5s6d6+qyAAAAAJRwHq4uwFWWL1+uqKgolStXTg8++KB8fX01b948PfDAA0pMTNSzzz7r6hIBAAAAlFCl8ohYenq6+vfvLzc3N61cuVLTpk3TW2+9pU2bNql+/foaNWqU9uzZ4+oyAQAAAJRQpTKILVu2TDt27NDDDz+s5s2bO8b9/f01atQoXbhwQZ9++qnrCgQAAABQopXKILZixQpJUmRkZLZlUVFRkqSYmBg7SwIAAABQipTKa8Ti4+MlSfXq1cu2LCgoSD4+Po45f3f+/HmdP3/e8fjkyZOSpGPHjiktLU2S5ObmJnd3d2VkZCgzM9MxN2s8PT1dxhjHuLu7u9zc3HIdz1pvFg+Piy9benp6juMXzllX2AJF19GjeevV09NTmZmZysjIcIxZliUPD49cx3N7PQrrdbpw7iqbd6FjxwrnZ88Vr1Nx3e4pKXLZ74irfZ0unCu+fzpSUuSy3xFX+zpdOOdZ0LZd7uTJi9ujOPwu//vrVJy3+4kTmcXmd/nfX4/ivN2PH88oFr/Lc3qdivN2P3YsvUj8Lj916pQkOX1vbiyTl1klTGRkpH766SfFx8erbt262ZZXq1ZNqampjpB1qbFjx2rcuHF2lAkAAACgGEpMTFT16tUvO6f47tZ0kRdeeEHDhw93PM7MzNSxY8dUsWJFWVbxPRKVFykpKQoJCVFiYqL8/PxcXU6pwXZ3Dba7a7DdXYPt7hpsd9dgu7tGadnuxhidOnVKVatWveLcUhnE/P39JSnHI17SxR+UChUq5LisbNmyKlu2rNNYQEBAodZX1Pn5+ZXo/0BFFdvdNdjursF2dw22u2uw3V2D7e4apWG7Z2WNKymVN+vIujYsp+vAkpKSlJqamuP1YwAAAABQGEplEGvfvr0kKTo6OtuyxYsXO80BAAAAgMJWKoPY7bffrtq1a+vzzz/Xxo0bHeMnT57UxIkTVaZMGfXp08d1BRZRZcuW1ZgxY7Kdmolri+3uGmx312C7uwbb3TXY7q7BdncNtnt2pfKuiZK0fPlyRUVFqVy5cnrwwQfl6+urefPmac+ePXrzzTf17LPPurpEAAAAACVUqQ1ikhQbG6sxY8ZozZo1SktLU5MmTTR8+HA98MADri4NAAAAQAlWqoMYAAAAALhCqbxGDAAAAABciSAGAAAAADYjiAEAAACAzQhiAAAAAGAzghiyybp/C/dxQWmSmZnp6hJKFba3a2RkZLi6BAAl3Jo1a3T69GlJvJe8EoIYsrEsS8YYWZalpKQk3jChVHBz+9+vQ/5wXHtubm66cOGCEhMTdfDgQUls92vtzJkzevHFF7V8+XIdPXo01+3N73yUBOnp6fr666/1008/KT093THO75lr69SpU+rWrZsmTpwo6eJ7SuSOIAYn6enpiomJUb9+/XTLLbfovvvuU2RkpJ577jmtWbPG1eUBhW7z5s0aNWqU7rnnHr322muKj4/nD8c1dv78ec2ePVsNGzZUp06dNGzYMK1fv57tfo19+OGHmjx5su68805FRkZq0qRJ2rBhg1JTU53mvf/++/r9998JZIXk/PnzWrJkCUcjbTZ//nz169dPs2bNkoeHh2PcsiydOHHCdYWVcJ999pmOHj2qyZMnq1+/ftq5c6ckjsbnygCXeOONN4yfn5+xLMvUrVvXhIWFGcuyHF8NGzY0b7/9tjl48KCrSy3RMjMzXV1CqTBnzhxTpUoVp5/xgIAA89lnn7m6tBJt0qRJJiAgwAQEBJjw8HDj7u5urr/+erN//35jjDH79+83CxcuNHv37nVxpSXLSy+9ZCzLMp06dTINGjQwlmWZ8uXLmzvvvNNMnTrVJCUlmdWrVxvLssy4ceNcXW6J8d5775nQ0FCzbt06V5dSqtx8882mTZs2ZuPGjY6xP/74w0ycONHcfvvtpmHDhubJJ580K1ascGGVJU+TJk1M3bp1TbVq1YxlWebBBx80ycnJri6ryCKIwWHnzp3G29vb3HrrrWbnzp1m3759Ji0tzSQmJpoPPvjAREREON6s3n777ea3335zdcklxpkzZ8z27dvNmTNnXF1KqbFnzx5TrVo1U61aNTNv3jzzww8/mJEjRzp2Qmzfvt0YY0xGRobjezIyMpweI/92795tKlWqZFq3bm2OHDlidu3aZV555RVjWZb5/vvvzaBBg0zFihWNZVmmSpUqZtSoUeb48eOuLrtE2Lx5swkLCzMdOnQwMTExZvLkyaZTp04mICDAWJZlgoKCTFhYmPH29jazZ882xhh+3gtBw4YNTUREhNm3b5/T+KZNm8zcuXPNG2+8YebOncsOzkK0c+dO4+7ubsaPH+8YS0xMNM2bNzeWZRlvb2+nHXDdunUzu3fvdmHFJUN8fLyxLMu8++675sCBA+bBBx80lmWZ5s2bmyVLlhhjLu5oZmfz/xDE4DB69GhTuXJlx38WY7Ifmdm8ebPp06ePKVeunGnQoIFZv3693WWWSJMmTTI33nijmThxolm2bJnZv3+/SU9Pv+z3HDlyxKSlpdlUYcnzwgsvmICAADNnzhyn8S+//NJYlmUeeughx1jW/4PffvvNfPTRR+bQoUO21lqSjBo1ygQFBZnvv//eMXbo0CHj5eVlWrVqZapVq2ZGjhxp+vbta/z9/U358uXN//3f/xljCAWF4YcffjC+vr5m6tSpxhhjDh48aH744QczYsQI06pVK+Pm5mYsyzJ16tQxI0eONAsWLDDnz593cdXFV9Yb08mTJzuNDx8+3HH2SdZXq1atzDfffOOaQkuYWbNmGT8/P8fv9+TkZPPkk08aDw8PM2bMGHPw4EETFxdn3n//fdOwYUNjWZZ54YUXjDGckXI1RowYYSpWrOg4yvjHH3+Yrl27GsuyzM0332x+//131xZYBBHE4HDvvfea2rVrmz179hhjjONNfmZmZrZQ8M477xjLsky/fv1sr7MkyjqE7+HhYSpWrGjuvvtu8/7775vY2NgcD+mnpqaa5557zjz66KO8OS2gZs2amXvuuccRqi5cuGDS09NNenq66dq1q/Hz8zOrVq1yzD937pwZOHCgcXNzM+fOnXNV2cVe48aNzV133WUOHz7sGFu+fLnx8vIyt912m9m8ebNjfM2aNcbPz8/UqVOHn/NCkLUNR48ebSpVqmTWrl3rtHzGjBnGsixz0003meuvv95YlmXc3NwIYlch643p8uXLjTEXz36YOnWqsSzLNGnSxIwYMcJMmTLF3H///aZ8+fKmevXqjrkEgoKbP3++8fDwMMuWLTPGGLNu3ToTHBxsBg0alG1uSkqKad26tSlbtqw5cuSI3aWWKEFBQaZHjx7Z3reMHz/ecSTyo48+MhcuXDDG8DNuDEEMl8j6j7J169Zc51z6n+a+++4zNWrUMDt27LCjvBIrLi7O+Pj4mNatW5spU6aYbt26mcqVKxvLskxoaKjp27ev+fe//222bNniOEVr3bp1xt/f33Tr1s2ltRdXO3bsMDVr1jT/+Mc/cly+dOlSU65cOfPYY485xrZt22aaNm1q7rjjDrvKLHHi4uJMrVq1zHPPPec0PmXKFOPm5uZ4A2qMMWfPnjXGGNO7d29TvXp1p4CGq5OUlGTatWtn6tWrZ5KSkhzj99xzjwkKCjKrVq0yO3fuNJMnTzZvvvmmCyst/oKCgkzv3r3NsWPHjDHG/Pzzz6Z27drm9ttvN3FxcY55aWlp5u233zaWZZn77rvPVeWWGNu2bTPe3t5m2LBhxhhjEhISjIeHh1m5cqUx5uJ7mYyMDMfvmUmTJpny5cubb7/91mU1F3c///yzsSzLTJs2zTGWtRP/yJEjZtSoUcbd3d0EBwc7Tn2GMdw1EQ4RERGSpF69emnZsmW6cOFCjvOy7nzToEEDJScnZ7vjFvLnr7/+0rlz5xQZGamBAwfq3Xff1b///W+NGTNGoaGhmjdvnh599FE9/PDDGjdunBYvXqx58+YpJSVF/fv3d3X5xdKpU6d08uRJeXt7S8p+N6fbbrtNHTt21Ndff61t27ZJkmJjY/XHH3/o6aeftr3ekmLPnj3avXu3rrvuOsfYyZMntXDhQnl4eKhDhw6O8XLlykmSypYtqzNnzjh9vACuTpUqVfT+++/r0KFDGj58uC5cuKAzZ87ou+++06233qobb7xRtWrV0ogRIzRs2DBXl1ts/fLLLzp06JD8/f1VoUIFSdKuXbu0a9cuTZ48WfXr15d08XbqHh4eeuaZZ3TzzTdr69atOnz4sCtLL9aMMapVq5a6d++ud999V9OmTdOBAwdUrlw5rV+/XtL/bqlepkwZSRd/z5w/f97pdxPyZ+rUqapYsaJuuOEGSRdfB3d3d0lSYGCgJkyYoM8//1wZGRnq27evRowYwftHibsm4n/S09PNs88+67g74pQpU5z2ll7q2LFjpk+fPqZSpUo2V1nyfPXVV8ayrGzXKl24cMHEx8eb//73v+aZZ54xzZo1M2XKlDHe3t6mfPnypkKFCi6quPhLSkoyERER5u233862LGsP3qJFi4xlWY49qr179za+vr52llninD592rz11lvmr7/+Msb871S5xMREExMTY4wxTtc9Hj9+3PTo0cOEhITYX2wJlnVmw2effWa8vLzM999/b+bMmWMsyzIfffSRMebi68BpQ1cn6+Y/lmWZ+vXrm8GDB5u77rrL1KpVyxjjfIZJ1v+F++67zwQFBZn4+HiX1FySbNy40XHa/5NPPmlatmxpbrzxRrNr1y6necnJyaZr166mYsWKrim0hJg+fbqZPn16jjcdy8jIMJmZmebChQtm7ty5pmbNmqZcuXLmmWeeMUePHnVBtUUHQQzZfPjhh6ZOnTrGsixTrVo1M2jQIPPjjz+azZs3m61bt5r9+/ebkSNHmnLlypnhw4e7utxiLzMz0/z5559m586djsd/l5qaajZs2GC++OILExkZaSzLMoMHD7a71BIlKSkp19PdssJARESEqVGjhpk9e7apW7eu06mKuHay3pQuW7bMVK1a1QwYMMDFFZU8mZmZ5uzZs+bxxx83VatWNVWqVDFNmzY1W7ZsMcZwY5TCcP78efPf//7XPPTQQ447gVqWleN1SsZc3PHQtWtXU7t2bZsrLbni4uJM586djYeHh2P716hRw/zzn/803333nVm2bJnp3r27KVOmjBk9erSryy328noDsd9++83ccMMNxrIsM2nSpGtcVdFGEEM2mZmZ5q+//jIjRowwISEhjl9eVapUMdWrVzfu7u7Gsizz8MMPm8TERFeXW6LlFMoGDx5sLMsyGzZscEFFpcsXX3xhPDw8TNOmTY1lWSY2NtbVJZUqgwYNMr6+vk6fA4TClZiYaOrXr28syzK9evUigF0jhw4dMh9++KGJiIgww4cPd7rhz6U7HoKDg9nxUMiOHDliPvjgAxMVFWVq165typQp43S3SsuyzIgRI7gbrk2y3tds377dtG3bttTfSdEyxhhXnx6Jouv06dOKjY3Vd999pwMHDujw4cPy8/NTz549dd999zmu48C1lZmZKTc3N+3evVvdunXT8ePHtXfvXleXVeKdPn1aUVFRWrNmjWrXrq2EhARXl1Rq/PDDD+rWrZsefPBB/ec//3F1OSVaenq6Fi1aJF9fX7Vv397x+wbXxrFjx3K8FumZZ57RjBkztHr1ajVr1swFlZVsZ8+e1ZYtW7Rq1SolJydr586dqlGjhu644w7HNfKw14kTJxQQEODqMlzKw9UFoGjz9vZWRESEIiIilJaWJk9PT1eXVCplvSnav3+/0tLSuGGEDYwx8vb21jPPPKO4uDgNHDjQ1SWVGqdOnVJ8fLyeeOIJtrsNPDw8dNdddzkeE8KurZxC2I8//qj3339f99xzDyHsGvHy8lJ4eLjCw8NdXQr+v9IewiSJI2JAMWKM0b59+3Tdddc57viHa8sYo8TERAUGBqp8+fKuLqfUMMbowoULKlu2rKtLAa6p1NRUzZgxQ+vXr9egQYPUqlUrV5cEwCYEMQAAABcyxujs2bPy8vJy3FodQMlHEAMAAAAAm3EiOAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2IwgBgAo8izL0vz5869qHR06dNDQoUMLpZ6iZtasWXw4KgAUMwQxAIBLJSUlafDgwapdu7bKli2rkJAQ3X333Vq6dGmhPs/XX3+t8ePHF+o6AQAoKA9XFwAAKL12796tNm3aKCAgQG+88YaaNGmitLQ0LV68WAMHDtT27dsL7bmuu+66QltXaZGWliZPT09XlwEAJRJHxAAALvP000/LsizFxsbqvvvuU/369dWoUSMNHz5c69atc5qbnJys7t27q3z58qpXr56+++47p+UxMTG66aabVLZsWQUHB2vkyJFKT093LP/7qYnnz5/X888/r5CQEJUtW1Z169bVjBkzHMu3bNmiO++8Uz4+PqpSpYp69+6t5OTkXHvJOj1w8eLFatiwoXx8fHTHHXfo4MGDudYgSffcc4/69evneFyzZk29+uqr6tOnj3x8fBQaGqrvvvtOR44cUbdu3eTj46OmTZtq/fr12WqYP3++6tWrp3LlyikqKkqJiYlOy7/99lu1bNlS5cqVU+3atTVu3DinbWRZlqZOnaquXbvK29tbEyZMyLVfAMDVIYgBAFzi2LFjWrRokQYOHChvb+9sy/9+zdO4cePUs2dPbd68WZ07d1avXr107NgxSdL+/fvVuXNnhYeHa9OmTZo6dapmzJihV199Ndfn79Onj7744gu999572rZtmz766CP5+PhIkk6cOKHbbrtNLVq00Pr167Vo0SIdOnRIPXv2vGxPZ86c0Ztvvql///vfWrlypfbu3avnnnsun1tGevvtt9WmTRv9/vvv6tKli3r37q0+ffrokUce0YYNG1SnTh316dNHxhin554wYYJmz56t1atX68SJE3rwwQcdy3/++Wf16dNHzzzzjP7880999NFHmjVrVrawNXbsWHXv3l1//PGHHnvssXzXDgDIIwMAgAv88ssvRpL5+uuvrzhXknnppZccj1NTU40ks3DhQmOMMaNGjTINGjQwmZmZjjkffPCB8fHxMRkZGcYYY9q3b2+eeeYZY4wxcXFxRpL56aefcny+8ePHm8jISKexxMREI8nExcXl+D0zZ840kkxCQoJTDVWqVHE8vrSGLN26dTN9+/Z1PA4NDTWPPPKI4/HBgweNJDN69GjH2Nq1a40kc/DgQafnXrdunWPOtm3bjCTzyy+/GGOMuf32283EiROdnvvf//63CQ4OdjyWZIYOHZpjfwCAwsU1YgAAlzCXHM3Ji6ZNmzr+7e3tLT8/Px0+fFiStG3bNt1yyy2yLMsxp02bNkpNTdW+fftUo0YNp3Vt3LhR7u7uat++fY7PtWnTJi1fvtxxhOxSO3bsUP369XP8vvLly6tOnTqOx8HBwY4a8+PSXqtUqSJJatKkSbaxw4cPKygoSJLk4eGh8PBwx5ywsDAFBARo27Ztuummm7Rp0yatXr3a6QhYRkaGzp07pzNnzqh8+fKSpBtvvDHf9QIA8o8gBgBwiXr16smyrDzfkOPvN42wLEuZmZkFem4vL6/LLk9NTdXdd9+t119/Pduy4ODgfNV4aeB0c3PLFkDT0tIuu56scJnTWH76T01N1bhx43TvvfdmW1auXDnHv3M6TRQAUPi4RgwA4BLXXXedoqKi9MEHH+j06dPZlp84cSLP62rYsKHWrl3rFHJWr14tX19fVa9ePdv8Jk2aKDMzUzExMTmur2XLltq6datq1qypunXrOn1dTVCpVKmS0807MjIytGXLlgKv71Lp6elON/CIi4vTiRMn1LBhQ0kXe4qLi8vWT926deXmxtsBALAbv3kBAC7zwQcfKCMjQzfddJPmzZun+Ph4bdu2Te+9955uueWWPK/n6aefVmJiogYPHqzt27fr22+/1ZgxYzR8+PAcQ0bNmjXVt29fPfbYY5o/f7527dqlFStWaO7cuZKkgQMH6tixY3rooYf066+/aseOHVq8eLEeffRRZWRkFLjf2267TT/++KN+/PFHbd++XU899VS+AufleHp6avDgwfrll1/022+/qV+/frr55pt10003SZJefvllzZ49W+PGjdPWrVu1bds2ffnll3rppZcK5fkBAPlDEAMAuEzt2rW1YcMGRURE6Nlnn1Xjxo3VqVMnLV26VFOnTs3zeqpVq6YFCxYoNjZWzZo105NPPqnHH3/8siFj6tSpuv/++/X0008rLCxM/fv3dxyZq1q1qlavXq2MjAxFRkaqSZMmGjp0qAICAq7q6NFjjz2mvn37qk+fPmrfvr1q166tiIiIAq/vUuXLl9fzzz+vhx9+WG3atJGPj4/mzJnjWB4VFaUffvhB0dHRCg8P180336y3335boaGhhfL8AID8sUx+r5YGAAAAAFwVjogBAAAAgM0IYgAAAABgM4IYAAAAANiMIAYAAAAANiOIAQAAAIDNCGIAAAAAYDOCGAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2Oz/AX2WrgqO/PxaAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=8, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "uYmhjbDN0X-9",
        "outputId": "fb723c08-b16a-4391-ef4a-e595e0b177c2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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yOBxyOBw6dOiQxo4dq/r167v0PXbsmCIjI9WhQwctWLDAPQUDAACPRhADSpncmZnY2NgrmplB8RgwYIB27typ+Ph457/atWtr3LhxWrlypbPf0aNH1blzZ/3xj39UTEyMvLw4jaJ0utyiQFOmTFFERIT8/f1VuXJlde3aVd98841Lnx07dqhbt24KCQlRaGio/vKXvygtLc3GUQBXhvc7PBG/QQClTGFmZlA4aWlpzpAlSQcOHFB8fLwOHz6s0NBQ/eEPf3D55+Pjo5o1a6pZs2aS/hfCwsLC9OKLL+rkyZNKSkpSUlKSG0cF5O9yiwI1bdpUr732mr7//ntt2LBB9evXV/fu3XXy5ElJF2Z+u3btqsaNG+ubb77RF198oR9++EGDBw+2cRTAleH9Dk/EPWJAKTNgwAB17drVpa1Hjx4aMGCAhgwZ4qaqyoZt27YpMjLS+XjMmDGSpEGDBl3RoierV6/Wvn37tG/fPtWtW9dlmzGmWGsFrtblFgW6//77XR6//PLLWrRokXbu3Klbb71Vy5cvl4+Pj+bMmeOc+Z03b56uu+467du3T40bNy7R+oHC4P0OT0QQA9wgLS1N+/btcz7OnZmpUqWKwsLCFBoa6tL/4pkZSTp8+LBOnTqlw4cPKzs72znL07hxYwUEBNgyDk/TuXPnQgWmgwcPujwePHgw346iTMrIyNCCBQsUHBysli1bSpLS09NVoUIFl8tv/fz8JEkbNmzgF1N4LN7vKC24NBFwg23btql169Zq3bq1pAszM61bt9bTTz99xc/x9NNPq3Xr1po8ebLS0tKcz7dt27aSKhtAGbN8+XIFBASoYsWKio6O1urVq1W1alVJUpcuXZSUlKQXXnhBGRkZOn36tMaPHy9JOn78uDvLBoqE9ztKG4IY4Aa5MzMX/yvo8riDBw9q1KhRLm2xsbH5Pkfnzp1LvH4AZUNkZKTi4+O1adMm9ezZU/fcc49OnDghSbr22mv15ptv6qWXXlKlSpVUs2ZNNWjQQDVq1GCRGngk3u8obXhnAQBQTvn7+6tx48Zq166dFi1aJIfDoUWLFjm333///UpKStLRo0f1yy+/aMqUKTp58qQaNmzoxqqBouH9jtKGe8QAAICkC39MPj09PU97jRo1JElvvPGGKlasqG7dutldGlDseL/D3QhiAACUQZdaFCg0NFTTp09XVFSUatWqpeTkZM2ZM0dHjx7V3Xff7fyZ1157TR06dFBAQIBWr16tcePGadasWQoJCXHDiICC8X6HJyKIAQBQBl3qzzXMmzdPe/bs0Ztvvqnk5GSFhoaqbdu2+vrrr3Xttdc6f2br1q3OBYEiIiI0f/58DRgwwPaxAJfD+x2eyDL88ZurkpqaquDgYKWkpCgoKMjd5UiShs52dwVF8/ood1cAAIArT/1/qsT/VwF3KEw2YLEOAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABs5nB3AQBQVENnu7uCont9lLsrAAAA7sSMGAAAAIBCW79+ve644w7Vrl1blmVpyZIlzm2ZmZl64okn1KJFC/n7+6t27doaOHCgjh075vIcO3bsULdu3RQSEqLQ0FD95S9/UVpams0jcQ9mxIBiwMwMAAAob86ePauWLVvqwQcf1F133eWy7dy5c9qxY4cmTZqkli1b6vTp0xo5cqSioqK0bds2SdKxY8fUtWtX/elPf9Jrr72m1NRUjRo1SoMHD9ZHH33kjiHZiiAGAAAAoNB69eqlXr165bstODhYq1evdml77bXXdMMNN+jw4cMKCwvT8uXL5ePjozlz5sjL68KFevPmzdN1112nffv2qXHjxiU+Bnfi0kQAAAAAJS4lJUWWZSkkJESSlJ6ergoVKjhDmCT5+flJkjZs2OCOEm1FEAMAAABQos6fP68nnnhC9913n4KCgiRJXbp0UVJSkl544QVlZGTo9OnTGj9+vCTp+PHj7izXFlyaCACAB+BeVJQnvN/LlszMTN1zzz0yxmju3LnO9muvvVZvvvmmxowZoyeffFLe3t7629/+pho1arjMkpVVZX+EAAAAANwiN4QdOnRIq1evds6G5br//vuVlJSko0eP6pdfftGUKVN08uRJNWzY0E0V24cZMQAAAADFLjeEJSQkKC4uTqGhoQX2rVGjhiTpjTfeUMWKFdWtWze7ynQbghgAAACAQktLS9O+ffucjw8cOKD4+HhVqVJFtWrVUv/+/bVjxw4tX75c2dnZSkpKkiRVqVJFFSpUkHRhJcUOHTooICBAq1ev1rhx4zRr1izngh5lGUEMAAAAQKFt27ZNkZGRzsdjxoyRJA0aNEhTpkzRsmXLJEmtWrVy+bm4uDh17txZkrR161ZNnjxZaWlpioiI0Pz58zVgwABb6nc3ghgAAACAQuvcubOMMQVuv9S2XG+99VZxluRRWKwDAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmDncXAAAAAMD9hs52dwVF9/ood1dQeMyIAQAAAIDNCGIAAAAAYDOCGAAAAADYjCAGAAAAADYjiAEAAACAzQhiAAAAAGAzghgAAAAA2IwgBgAAAAA2I4gBAAAAgM0IYgAAAABgM4IYAAAAANiMIAYAAAAANiOIAQAAAIDNSmUQe+edd/TII4/o+uuvl6+vryzLUmxsbJ5+mZmZWrx4sQYNGqTmzZsrICBAgYGBuvHGGzV37lxlZ2cX+Br//Oc/dcMNN8jf31+VK1fW7bffrh07dpTgqAAAAADgAoe7C8jPU089pUOHDqlq1aqqVauWDh06lG+/n376Sf3791dAQIBuvfVWRUVFKSUlRZ9++qkeffRRrVixQsuWLZNlWS4/N336dD311FMKDw/XsGHDdObMGb3//vvq0KGDvvrqK3Xs2NGOYQIAAAAop0rljNjChQt18OBBnTx5UsOGDSuwX2BgoObMmaOkpCQtWbJEzz33nObNm6cff/xR119/vZYvX66PPvrI5WcSEhI0ZcoUNW3aVN99951eeuklLViwQOvXr5ckDR06VDk5OSU6PgAAAADlW6kMYl27dlV4ePhl+9WpU0ePPvqo/P39Xdr9/f01ZswYSdK6detctsXExCgrK0sTJ05UcHCws71Vq1a67777tHv3bm3YsKEYRgEAAAAA+SuVQaw4+Pj4SJIcDterL9euXStJ6t69e56f6dGjh6S84Q0AAAAAilOpvEesOLzxxhuS8gauhIQEBQQEqGbNmnl+pkmTJs4+BUlPT1d6errzcWpqqqQLC4dkZmZKkry8vOTt7a3s7GyXyxxz27OysmSMcbZ7e3vLy8urwPbc582VGy6zsrLybZdc74nzFMaYAsd0cbuPj49ycnJcFmSxLEsOh6PA9oKOR3EcJ0//TqO43nt2HyfJu4gjLh3cdY4o7Z8nxpR/u+QjT5W7PzzxOHnyfs/JyfHYz5Mn7/fs7GyPPe958n7PysoqFefyvOeQgpXJILZgwQJ9/vnn6tKli3r37u2yLSUlRdWrV8/354KCgpx9CjJz5kxNnTo1T/uqVatUqVIlSVJYWJhat26tnTt36vDhw84+zZo1U0REhLZu3aqTJ08621u1aqXw8HCtX79eZ86ccba3b99e1atX16pVq1w+bJGRkfLz89OKFStcaujdu7d+++03SUEF1l+aZWVlFTimuLg4Z5vD4dBtt92m5ORkbd682dkeGBioLl26KDExUfHx8c72atWqqUOHDkpISNDevXud7cV5nKT831Oeorjee3YfJymiOIbvNu46R5T2zxNjyn9M0m3yVFlZWR57nKQ+xbQX7JecnOyxnydP3u8JCQkee97z5P2+devWUnEuP3fu3BXXbBnXrx9KnVmzZunJJ59UTEyMBg8efNn+y5cv11133aXatWtr8+bNqlWrlsv2ChUqqHr16jpy5Eien01ISFDTpk0VFRWlpUuX5vv8+c2I1atXT8nJyc4g5+5vUf/yimfOiC0Y6bkzYo/8w3NnxF4f5bkzYsNe9dwZsddHMSPGmAo3pkfneO431QtGeu6MmCfv9/l/89wZMU/e7/NGeO6MmCfv97mPlY4ZsdTUVFWtWlUpKSnObFCQMjUjtmLFCvXv3181atTQmjVr8oQwSQoODi5wxiv3MsPfL+JxMV9fX/n6+uZp9/Hxcd6Xlsvb2/u/l625uvi+tcu1X/y8l2v3VJZlFWqsXl5e/7087craCzoexXWcPFlxvffccZw8mbvOEZ7weWJMZescn/tnZDz5OHmi3P3nyZ8nT5Q7Pk8+73mi3P3q7nN5Yc4hnvs1/kU+++wz3XXXXapatari4uLUsGHDfPs1adJEaWlpSkpKyrMt996w3HvFAAAAAKAklIkg9tlnn6lfv36qUqWK4uLi1Lhx4wL7durUSdKFe7outnLlSpc+AAAAAFASPD6Iff755+rXr58qV66suLi4y85mDRkyRA6HQ9OnT3e5RDE+Pl7vvfeemjdvrptuuqmkywYAAABQjpXKC3IXLlzo/KPK33//vbMt92+A3XTTTXr44Ye1Z88e3XnnnUpPT1fnzp313nvv5Xmu+vXruyzy0bRpU02ZMkVPPfWUWrZsqX79+unMmTN6//33JUmvv/56vtfQAgAAAEBxKZVBbMOGDXrzzTdd2jZu3KiNGzc6Hz/88MNKSkpyrmCYG6Qu1qlTpzyrLU6cOFH169fX7NmzNXfuXFWoUEE333yzpk2bpjZt2hTvYAAAAADgIqUyiMXGxio2Nvay/Tp37qyirr7/wAMP6IEHHijSzwIAAADA1eAaPAAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsVuQgtn79eh0+fPiSfRITE7V+/fqivgQAAAAAlElFDmKRkZGKjY29ZJ+33npLkZGRRX0JAAAAACiTihzEjDGX7ZOTkyPLsor6EgAAAABQJpXoPWIJCQkKDg4uyZcAAAAAAI/jKEznBx980OXxkiVLdPDgwTz9srOznfeH9erV66oKBAAAAICyplBB7Pf3hFmWpfj4eMXHx+fb17IstW3bVtHR0VdTHwAAAACUOYUKYgcOHJB04f6whg0batSoURo5cmSeft7e3qpcubL8/f2Lp0oAAAAAKEMKFcTCw8Od/x0TE6PWrVu7tAEAAAAALq9QQez3Bg0aVJx1AAAAAEC5UeQglmvr1q3697//rV9//VXZ2dl5tluWpUmTJl3tywAAAABAmVHkIHbq1Cn17dtXGzduvOTfFCOIAQAAAICrIgexMWPGaMOGDercubMGDRqkunXryuG46gk2AAAAACjzipycli9frhtuuEFfffWVLMsqzpoAAAAAoEzzKuoP/vbbb7rlllsIYQAAAABQSEUOYq1atdLBgweLsRQAAAAAKB+KHMQmT56sZcuWacuWLcVZDwAAAACUeUW+RywpKUm33XabOnXqpAceeEBt2rRRUFBQvn0HDhxY5AIBAAAAoKwpchAbPHiwLMuSMUaxsbGKjY3Nc7+YMUaWZRHEAAAAAOB3ihzEYmJiirMOAAAAACg3ihzEBg0aVJx1AAAAAEC5UeTFOgAAAAAARVPkGbHDhw9fcd+wsLCivgwAAAAAlDlFDmL169e/oj/mbFmWsrKyivoyAAAAAFDmFDmIDRw4MN8glpKSou+++04HDhxQp06dVL9+/aupDwAAAADKnCIHsdjY2AK3GWP00ksv6fnnn9eiRYuK+hIAAAAAUCaVyGIdlmXp8ccf17XXXqtx48aVxEsAAAAAgMcq0VUTr7/+eq1Zs6YkXwIAAAAAPE6JBrGffvqJhToAAAAA4CJFvkesIDk5OTp69KhiY2O1dOlS3XrrrcX9EgAAAADg0YocxLy8vC65fL0xRpUrV9ZLL71U1JcAAAAAgDKpyEHslltuyTeIeXl5qXLlymrbtq2GDBmi6tWrX1WBAAAAAFDWFDmIrV27thjLAAAAAIDyo0QX6wAAAAAA5FUsi3Vs3LhR8fHxSk1NVVBQkFq1aqWOHTsWx1MDAAAAQJlzVUFs06ZNGjJkiPbt2yfpwgIdufeNNWnSRDExMWrfvv3VVwkAAAAAZUiRg9gPP/yg7t2769y5c+rWrZsiIyNVq1YtJSUlKS4uTqtWrVKPHj20ZcsWXXPNNcVZMwAAAAB4tCIHsWeeeUYZGRlasWKFevbs6bLtiSee0BdffKGoqCg988wzev/996+6UAAAAAAoK4q8WMfatWvVv3//PCEsV8+ePdW/f3/FxcUVuTgAAAAAKIuKHMRSUlLUoEGDS/Zp0KCBUlJSivoSAAAAAFAmFTmI1a5dW1u2bLlkn2+++Ua1a9cu6ksAAAAAQJlU5CAWFRWltWvXatKkSTp//rzLtvPnz2vy5MmKi4tTnz59rrpIAAAAAChLihzEJk2apAYNGmjGjBkKCwvT7bffroceeki33367wsPDNW3aNDVo0ECTJk0qznrzZYzRxx9/7Fy5sVKlSmrWrJkeeeQR7d+/P0//1NRUjRkzRuHh4fL19VX9+vU1btw4paWllXitAAAAAFDkIBYaGqotW7Zo0KBBSktL04oVKxQTE6MVK1bozJkzGjJkiLZs2aIqVaoUZ735evzxx9WvXz/t3btXffv21YgRI9SgQQO9/vrratWqlXbt2uXse/bsWXXq1EnR0dGKiIjQ6NGj1axZM7344ovq0qVLntk9AAAAAChuV/UHnatWrao33nhD8+fP1549e5SamqqgoCBFRETIx8enuGq8pKSkJM2ePVvh4eH67rvvFBwc7NwWHR2tMWPG6OWXX9Ybb7whSXr++ecVHx+vJ554QrNmzXL2HT9+vJ577jlFR0frySeftKV2AAAAAOVToWfEpk+frgkTJigzM9PZ5uPjoxYtWqhjx45q0aKFjDGaOHGiS9ApKQcPHlROTo46duzoEsIk6fbbb5cknTx5UtKFSxgXLlyogICAPJdMTpo0SQEBAVq4cGGJ1wwAAACgfCtUEPvyyy/19NNPKzQ09JIzXhUqVFBoaKgmTpxY4n9HrEmTJqpQoYI2btyo1NRUl23Lly+XJN16662SpISEBB07dkwdO3aUv7+/S19/f3917NhR+/fvV2JiYonWDAAAAKB8K9SliW+99ZYqV66sxx577LJ9hw8frpkzZyomJkaRkZFFLvByQkNDNWvWLI0dO1YRERHq06ePgoKC9N1332nNmjV69NFHnfUmJCRIuhDe8tOkSROtXLlSCQkJqlevXr590tPTlZ6e7nycG/4yMzOds4ReXl7y9vZWdna2cnJynH1z27OysmSMcbZ7e3vLy8urwPbfzz5KksNx4bBlZWXl2y5Z+e+sUs4YU+CYLm738fFRTk6OsrOznW2WZcnhcBTYXtDxKI7jdBW3W5YKxfXes/s4Sd5FHHHp4K5zRGn/PDGm/Nsley75Lwm5+8MTj5Mn7/ecnByP/Tx58n7Pzs722POeJ+/3rKysUnEuz3sOKVihgtimTZvUtWtX+fr6Xravr6+vunbtqo0bNxbmJYpk9OjRqlOnjh5++GHNmzfP2X7TTTfp/vvvd+6g3D8uffEljLmCgoJc+uVn5syZmjp1ap72VatWqVKlSpKksLAwtW7dWjt37tThw4edfZo1a6aIiAht3brVebmkJLVq1Urh4eFav369zpw542xv3769qlevrlWrVrl82CIjI+Xn56cVK1a41NC7d2/99ttvkoIKrL80y8rKKnBMv59ZdTgcuu2225ScnKzNmzc72wMDA9WlSxclJiYqPj7e2V6tWjV16NBBCQkJ2rt3r7O9OI+TVL04doHbFNd7z+7jJEUUx/Ddxl3niNL+eWJM+Y9Juk2eKisry2OPk+S5f4YnOTnZYz9PnrzfExISPPa858n7fevWraXiXH7u3Lkrrtkyrl8/XFKlSpU0atQozZgx44r6T5gwQbNnzy5UQUXxzDPP6Nlnn9UzzzyjP//5zwoJCVF8fLxGjx6t+Ph4LV68WFFRUXr33Xf1wAMPaOLEiXr22WfzPM/EiRM1Y8YMffzxx7rzzjvzfa38ZsTq1aun5ORkZ5Bz97eof3nFM2fEFoz03BmxR/7huTNir4/y3BmxYa967ozY66OYEWNMhRvTo3M895vqBSM9d0bMk/f7/L957oyYJ+/3eSM8d0bMk/f73MdKx4xYamqqqlatqpSUFGc2KEihZsTyn7IvWGZm5n8vHyo5X375pSZPnqzRo0dr/PjxzvabbrpJn376qRo2bKixY8cqKirKORNW0IxX7mWGBc2YSRdm+vKbEfTx8clz35y3t/d/L1tz9b9LCK+svaD78examdIulmUVaqxeXl75vr8Kai/oeBTXcfJkxfXec8dx8mTuOkd4wueJMZWtc7xlXfiC0JOPkyfK3X+e/HnyRLnj8+TznifK3a/uPpcX5hxSqJRUu3Ztl7/JdTm7du1SnTp1CvMShfb5559LUr73odWsWVMRERHat2+f0tLSnPeG5d4rdrHL3UMGAAAAAMWhUEHs5ptv1po1a3Tw4MHL9j148KDWrFmjW265pai1XZGMjAxJuui64v85efKkvLy85OPjoyZNmqh27drauHGjzp4969Lv7Nmz2rhxoxo0aFDgQh0AAAAAUBwKFcSGDx+uzMxM9e/fX8nJyQX2++WXX3T33XcrKytLf/3rX6+6yEvp2LGjJOnll1/Oc8nhvHnzdOTIEbVv316+vr6yLEsPP/yw0tLSNG3aNJe+06ZNU1pamoYOHVqi9QIAAABAoS7IbdOmjUaNGqXZs2frmmuu0bBhwxQZGam6detKko4ePaqvvvpKCxYs0MmTJzVmzBi1adOmRArPdffdd2vu3Llav369mjZtqqioKIWEhGjHjh1as2aN/Pz89PLLLzv7//3vf9fSpUv13HPP6dtvv1WbNm20Y8cOrVq1Sm3bttWoUaNKtF4AAAAAKPSdkS+99JIqVqyoF154QdOnT9f06dNdthtj5O3trSeffDLflQmLm7e3t1atWqXo6Gh9+OGHevfdd5WRkaEaNWroz3/+syZMmKDmzZs7+/v7+2vdunWaMmWKFi9erLi4ONWqVUtjx47V5MmT5efnV+I1AwAAACjfCh3ELMvSjBkz9NBDDykmJkabNm1SUlKSpAuLY3Ts2FGDBw9Wo0aNir3Ygvj6+mr8+PEuqyZeSnBwsKKjoxUdHV3ClQEAAABAXkVeK7RRo0a2zHgBAAAAQFnjuX+FFgAAAAA8FEEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbFZmg9hzzz0ny7JkWZa2bNmSZ3tqaqrGjBmj8PBw+fr6qn79+ho3bpzS0tLcUC0AAACA8qRMBrFdu3Zp8uTJ8vf3z3f72bNn1alTJ0VHRysiIkKjR49Ws2bN9OKLL6pLly46f/68zRUDAAAAKE/KXBDLzMzUoEGD1KpVK91555359nn++ecVHx+vJ554QitXrtSsWbO0cuVKPfHEE/r3v/+t6Ohom6sGAAAAUJ6UuSA2ffp0/fDDD3rjjTfk7e2dZ7sxRgsXLlRAQIAmTZrksm3SpEkKCAjQwoUL7SoXAAAAQDlUpoLYjh07NH36dE2ePFnXXHNNvn0SEhJ07NgxdezYMc+li/7+/urYsaP279+vxMREO0oGAAAAUA453F1AcUlPT9fAgQPVqlUr/f3vfy+wX0JCgiSpSZMm+W5v0qSJVq5cqYSEBNWrVy/f10lPT3c+Tk1NlXThksjMzExJkpeXl7y9vZWdna2cnBxn39z2rKwsGWOc7d7e3vLy8iqwPfd5czkcFw5bVlZWvu2SVeD4SzNjTIFjurjdx8dHOTk5ys7OdrZZliWHw1Fge0HHoziOk6d/p1Fc7z27j5OUd9bbk7jrHFHaP0+MKf92yUeeKnd/eOJx8uT9npOT47GfJ0/e79nZ2R573vPk/Z6VlVUqzuV5zyEFKzNB7Omnn1ZCQoK2b9+e7yWJuVJSUiRJwcHB+W4PCgpy6XexmTNnaurUqXnaV61apUqVKkmSwsLC1Lp1a+3cuVOHDx929mnWrJkiIiK0detWnTx50tneqlUrhYeHa/369Tpz5oyzvX379qpevbpWrVrl8mGLjIyUn5+fVqxY4VJD79699dtvv0kKKnD8pVlWVlaBY4qLi3O2ORwO3XbbbUpOTtbmzZud7YGBgerSpYsSExMVHx/vbK9WrZo6dOighIQE7d2719lenMdJql4cu8Btiuu9Z/dxkiKKY/hu465zRGn/PDGm/Mck3SZPlZWV5bHHSepTTHvBfsnJyR77efLk/Z6QkOCx5z1P3u9bt24tFefyc+fOXXHNlnH9+sEjbd68WTfddJOmTJnict/X4MGD9eabb2rz5s1q166dJOndd9/VAw88oIkTJ+rZZ5/N81wTJ07UjBkz9PHHH+e72Ed+M2L16tVTcnKyM8S5+1vUv7zimTNiC0Z67ozYI//w3Bmx10d57ozYsFc9d0bs9VHMiDGmwo3p0Tme+031gpGeOyPmyft9/t88d0bMk/f7vBGeOyPmyft97mOlY0YsNTVVVatWVUpKijMbFMTjZ8SysrI0aNAgXXfddRo/fvxl++fOhBU045V7qWFBM2a+vr7y9fXN0+7j4yMfH9c3r7e3d76zc/+7hPDK2i9+3su1eyrLsgo1Vi8vr/9ennZl7QUdj+I6Tp6suN577jhOnsxd5whP+DwxprJ1jresC18QevJx8kS5+8+TP0+eKHd8nnze80S5+9Xd5/LCnEM8/l2flpbmvO+rQoUK+fa5cOmY9MknnzgX8cj9mYtd7h4yAAAAALhaHh/EfH199dBDD+W7bf369UpISFBUVJSqVaum+vXrq0mTJqpdu7Y2btyos2fPuqycePbsWW3cuFENGjTId6EOAAAAACgOHh/E/Pz8Cvy7X4MHD1ZCQoKefPJJ5z1ikvTwww/rmWee0bRp0zRr1ixn+7Rp05SWlqYJEyaUeN0AAAAAyi+PD2JF8fe//11Lly7Vc889p2+//VZt2rTRjh07tGrVKrVt21ajRo1yd4kAAAAAyjDPXertKvj7+2vdunUaNWqUdu/erZdeekl79uzR2LFj9dVXX8nPz8/dJQIAAAAow8r0jFhsbKxiY2Pz3RYcHKzo6GhFR0fbWxQAAACAcq9czogBAAAAgDsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAgK1mzpyptm3bKjAwUNWrV1ffvn21d+/efPsaY9SrVy9ZlqUlS5bYWygAACWIIAYAsNW6des0fPhwbdmyRatXr1ZmZqa6d++us2fP5uk7e/ZsWZblhioBAChZDncXAAAoX7744guXx7Gxsapevbq2b9+uW265xdkeHx+vl156Sdu2bVOtWrXsLhMAgBLFjBgAwK1SUlIkSVWqVHG2nTt3Tvfff7/mzJmjmjVruqs0AABKDEEMAOA2OTk5GjVqlDp27Kg//OEPzvbRo0erQ4cO6tOnjxurAwCg5HBpIgDAbYYPH65du3Zpw4YNzrZly5ZpzZo1+vbbb91YGQAAJYsZMQCAWzz22GNavny54uLiVLduXWf7mjVr9NNPPykkJEQOh0MOx4XvDPv166fOnTu7qVoAAIoXM2IAAFsZYzRixAh98sknWrt2rRo0aOCyffz48Xr44Ydd2lq0aKHo6GjdcccddpYKAECJIYgBAGw1fPhwvfvuu1q6dKkCAwOVlJQkSQoODpafn59q1qyZ7wIdYWFheUIbAACeiksTAQC2mjt3rlJSUtS5c2fVqlXL+e+DDz5wd2kAANiGGTEAgK2MMbb8DAAApRkzYgAAAABgM4IYAAAAANiMIAYAAAAANiOIAQAAAIDNWKwDAFAoQ2e7u4Kie32UuysAAOACZsQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJuV6yD273//W71791ZISIj8/f3Vrl07ffjhh+4uCwAAAEAZ53B3Ae4SFxenHj16qGLFirr33nsVGBioxYsX609/+pMSExM1duxYd5cIAAAAoIwqlzNiWVlZGjp0qLy8vLR+/XotWLBAL730kr777js1bdpUEyZM0KFDh9xdJgAAAIAyqlwGsTVr1uinn37S/fffr1atWjnbg4ODNWHCBGVkZOjNN990X4EAAAAAyrRyGcTWrl0rSerevXuebT169JAkrVu3zs6SAAAAAJQj5fIesYSEBElSkyZN8myrWbOmAgICnH0ulp6ervT0dOfjlJQUSdKpU6eUmZkpSfLy8pK3t7eys7OVk5Pj7JvbnpWVJWOMs93b21teXl4Ftuc+by6H48Jhy8rKyrc947x1mT1QOqWkmALHdHG7j4+PcnJylJ2d7WyzLEsOh6PA9oKOR3Ecp4zznvudRmqqiu29Z/dxyjjvXdRhu11qqtx2jrja45Rx3nP/15GaKrecI4rjOGWc9ynqsN0uJeXC/ijt5/L8jpMn7/dff83xiHN5fsfJk/f76dPZHnEuz+84efJ+P3Uqq1Scy8+cOSNJLj9bEMtcSa8ypnv37lq9erUSEhLUuHHjPNvr1KmjtLQ0Z8j6vSlTpmjq1Kl2lAkAAADAAyUmJqpu3bqX7OO5X2u6yZNPPqkxY8Y4H+fk5OjUqVMKDQ2VZXnmTNSVSk1NVb169ZSYmKigoCB3l1NusN/dg/3uHux392C/uwf73T3Y7+5RXva7MUZnzpxR7dq1L9u3XAax4OBgScp3xku68EapXLlyvtt8fX3l6+vr0hYSElKs9ZV2QUFBZfoDVFqx392D/e4e7Hf3YL+7B/vdPdjv7lEe9ntu1rgcz72x5Srk3huW331gSUlJSktLy/f+MQAAAAAoDuUyiHXq1EmStGrVqjzbVq5c6dIHAAAAAIpbuQxit956qxo2bKh3331X8fHxzvaUlBTNmDFDFSpU0MCBA91XYCnl6+uryZMn57k0EyWL/e4e7Hf3YL+7B/vdPdjv7sF+dw/2e17lctVESYqLi1OPHj1UsWJF3XvvvQoMDNTixYt16NAhvfjiixo7dqy7SwQAAABQRpXbICZJW7du1eTJk7Vp0yZlZmaqRYsWGjNmjP70pz+5uzQAAAAAZVi5DmIAAAAA4A7l8h4xAAAAAHAnghgAAAAA2IwgBgAAAAA2I4gBAAAAgM0IYsgjd/0W1nFBeZKTk+PuEsoV9rd7ZGdnu7sEAGXcpk2bdPbsWUn8Lnk5BDHkYVmWjDGyLEtJSUn8woRywcvrf6dD/sdR8ry8vJSRkaHExEQdP35cEvu9pJ07d04TJ05UXFycfvnllwL3N+d8lAVZWVn6+OOPtXr1amVlZTnbOc+UrDNnzqhPnz6aMWOGpAu/U6JgBDG4yMrK0rp16zR48GC1b99e/fr1U/fu3fX4449r06ZN7i4PKHY7d+7UhAkT1LdvX82aNUsJCQn8j6OEpaen66233lLz5s3VrVs3jR49Wtu2bWO/l7B58+bp+eefV69evdS9e3fNnDlTO3bsUFpamku/V199Vd9++y2BrJikp6fryy+/ZDbSZkuWLNHgwYMVGxsrh8PhbLcsS7/++qv7Civj3nnnHf3yyy96/vnnNXjwYO3fv18Ss/EFMsDvvPDCCyYoKMhYlmUaN25sIiIijGVZzn/Nmzc30dHR5vjx4+4utUzLyclxdwnlwgcffGBq1Kjh8h4PCQkx77zzjrtLK9NmzpxpQkJCTEhIiGnbtq3x9vY211xzjTl69KgxxpijR4+azz//3Bw+fNjNlZYtTz31lLEsy3Tr1s00a9bMWJZlKlWqZHr16mXmzp1rkpKSzMaNG41lWWbq1KnuLrfM+Mc//mHCw8PNli1b3F1KudKuXTvTsWNHEx8f72z7/vvvzYwZM8ytt95qmjdvboYNG2bWrl3rxirLnhYtWpjGjRubOnXqGMuyzL333muSk5PdXVapRRCD0/79+42/v7+5+eabzf79+82RI0dMZmamSUxMNHPmzDGRkZHOX1ZvvfVWs337dneXXGacO3fO7Nmzx5w7d87dpZQbhw4dMnXq1DF16tQxixcvNsuXLzfjx493fgmxZ88eY4wx2dnZzp/Jzs52eYzCO3jwoKlWrZrp0KGDOXnypDlw4IB55plnjGVZ5tNPPzWPPfaYCQ0NNZZlmRo1apgJEyaY06dPu7vsMmHnzp0mIiLCdO7c2axbt848//zzplu3biYkJMRYlmVq1qxpIiIijL+/v3nrrbeMMYb3ezFo3ry5iYyMNEeOHHFp/+6778yHH35oXnjhBfPhhx/yBWcx2r9/v/H29jbTpk1ztiUmJppWrVoZy7KMv7+/yxdwffr0MQcPHnRjxWVDQkKCsSzLvPLKK+bYsWPm3nvvNZZlmVatWpkvv/zSGHPhi2a+bP4fghicJk2aZKpXr+78sBiTd2Zm586dZuDAgaZixYqmWbNmZtu2bXaXWSbNnDnTXH/99WbGjBlmzZo15ujRoyYrK+uSP3Py5EmTmZlpU4Vlz5NPPmlCQkLMBx984NL+/vvvG8uyzH333edsy/0cbN++3cyfP9/8/PPPttZalkyYMMHUrFnTfPrpp862n3/+2fj5+Zkbb7zR1KlTx4wfP94MGjTIBAcHm0qVKpn/+7//M8YQCorD8uXLTWBgoJk7d64xxpjjx4+b5cuXm3Hjxpkbb7zReHl5GcuyTKNGjcz48ePNihUrTHp6upur9ly5v5g+//zzLu1jxoxxXn2S++/GG280n3zyiXsKLWNiY2NNUFCQ8/yenJxshg0bZhwOh5k8ebI5fvy42bt3r3n11VdN8+bNjWVZ5sknnzTGcEXK1Rg3bpwJDQ11zjJ+//33JioqyliWZdq1a2e+/fZb9xZYChHE4HTXXXeZhg0bmkOHDhljjPOX/JycnDyhYPbs2cayLDN48GDb6yyLcqfwHQ6HCQ0NNXfccYd59dVXzdatW/Od0k9LSzOPP/64GTJkCL+cFlHLli1N3759naEqIyPDZGVlmaysLBMVFWWCgoLMhg0bnP3Pnz9vhg8fbry8vMz58+fdVbbH+8Mf/mBuv/12c+LECWdbXFyc8fPzM126dDE7d+50tm/atMkEBQWZRo0a8T4vBrn7cNKkSaZatWpm8+bNLtsXLVpkLMsyN9xwg7nmmmuMZVnGy8uLIHYVcn8xjYuLM8ZcuPph7ty5xrIs06JFCzNu3Djz2muvmf79+5tKlSqZunXrOvsSCIpuyZIlxuFwmDVr1hhjjNmyZYupVauWeeyxx/L0TU1NNR06dDC+vr7m5MmTdpdaptSsWdPcfffdeX5vmTZtmnMmcv78+SYjI8MYw3vcGIIYfif3g/LDDz8U2Of3H5p+/fqZsLAw89NPP9lRXpm1d+9eExAQYDp06GBee+0106dPH1O9enVjWZYJDw83gwYNMm+//bbZtWuX8xKtLVu2mODgYNOnTx+31u6pfvrpJ1O/fn3zyCOP5Lv9q6++MhUrVjQPPvigs2337t3muuuuMz179rSrzDJn7969pkGDBubxxx93aX/ttdeMl5eX8xdQY4z57bffjDHGDBgwwNStW9cloOHqJCUlmVtuucU0adLEJCUlOdv79u1ratasaTZs2GD2799vnn/+efPiiy+6sVLPV7NmTTNgwABz6tQpY4wxX3/9tWnYsKG59dZbzd69e539MjMzTXR0tLEsy/Tr189d5ZYZu3fvNv7+/mb06NHGGGP27dtnHA6HWb9+vTHmwu8y2dnZzvPMzJkzTaVKlczSpUvdVrOn+/rrr41lWWbBggXOttwv8U+ePGkmTJhgvL29Ta1atZyXPsMYVk2EU2RkpCTpgQce0Jo1a5SRkZFvv9yVb5o1a6bk5OQ8K26hcH788UedP39e3bt31/Dhw/XKK6/o7bff1uTJkxUeHq7FixdryJAhuv/++zV16lStXLlSixcvVmpqqoYOHeru8j3SmTNnlJKSIn9/f0l5V3Pq0qWLunbtqo8//li7d++WJG3dulXff/+9Hn30UdvrLSsOHTqkgwcPqkqVKs62lJQUff7553I4HOrcubOzvWLFipIkX19fnTt3zuXPC+Dq1KhRQ6+++qp+/vlnjRkzRhkZGTp37pyWLVumm2++Wddff70aNGigcePGafTo0e4u12N98803+vnnnxUcHKzKlStLkg4cOKADBw7o+eefV9OmTSVdWE7d4XBo5MiRateunX744QedOHHCnaV7NGOMGjRooDvvvFOvvPKKFixYoGPHjqlixYratm2bpP8tqV6hQgVJF84z6enpLucmFM7cuXMVGhqqP/7xj5IuHAdvb29JUtWqVTV9+nS9++67ys7O1qBBgzRu3Dh+f5RYNRH/k5WVZcaOHetcHfG1115z+bb0906dOmUGDhxoqlWrZnOVZc+//vUvY1lWnnuVMjIyTEJCgvnoo4/MyJEjTcuWLU2FChWMv7+/qVSpkqlcubKbKvZ8SUlJJjIy0kRHR+fZlvsN3hdffGEsy3J+ozpgwAATGBhoZ5llztmzZ81LL71kfvzxR2PM/y6VS0xMNOvWrTPGGJf7Hk+fPm3uvvtuU69ePfuLLcNyr2x45513jJ+fn/n000/NBx98YCzLMvPnzzfGXDgOXDZ0dXIX/7EsyzRt2tSMGDHC3H777aZBgwbGGNcrTHI/C/369TM1a9Y0CQkJbqm5LImPj3de9j9s2DDTpk0bc/3115sDBw649EtOTjZRUVEmNDTUPYWWEQsXLjQLFy7Md9Gx7Oxsk5OTYzIyMsyHH35o6tevbypWrGhGjhxpfvnlFzdUW3oQxJDHvHnzTKNGjYxlWaZOnTrmscceM5999pnZuXOn+eGHH8zRo0fN+PHjTcWKFc2YMWPcXa7Hy8nJMf/5z3/M/v37nY8vlpaWZnbs2GHee+890717d2NZlhkxYoTdpZYpSUlJBV7ulhsGIiMjTVhYmHnrrbdM48aNXS5VRMnJ/aV0zZo1pnbt2uYvf/mLmysqe3Jycsxvv/1mHnroIVO7dm1To0YNc91115ldu3YZY1gYpTikp6ebjz76yNx3333OlUAty8r3PiVjLnzxEBUVZRo2bGhzpWXX3r17Te/evY3D4XDu/7CwMPP3v//dLFu2zKxZs8bceeedpkKFCmbSpEnuLtfjXekCYtu3bzd//OMfjWVZZubMmSVcVelGEEMeOTk55scffzTjxo0z9erVc568atSoYerWrWu8vb2NZVnm/vvvN4mJie4ut0zLL5SNGDHCWJZlduzY4YaKypf33nvPOBwOc9111xnLsszWrVvdXVK58thjj5nAwECXvwOE4pWYmGiaNm1qLMsyDzzwAAGshPz8889m3rx5JjIy0owZM8ZlwZ/ff/FQq1YtvngoZidPnjRz5swxPXr0MA0bNjQVKlRwWa3Ssiwzbtw4VsO1Se7vNXv27DE33XRTuV9J0TLGGHdfHonS6+zZs9q6dauWLVumY8eO6cSJEwoKCtI999yjfv36Oe/jQMnKycmRl5eXDh48qD59+uj06dM6fPiwu8sq886ePasePXpo06ZNatiwofbt2+fuksqN5cuXq0+fPrr33nv1z3/+093llGlZWVn64osvFBgYqE6dOjnPNygZp06dyvdepJEjR2rRokXauHGjWrZs6YbKyrbffvtNu3bt0oYNG5ScnKz9+/crLCxMPXv2dN4jD3v9+uuvCgkJcXcZbuVwdwEo3fz9/RUZGanIyEhlZmbKx8fH3SWVS7m/FB09elSZmZksGGEDY4z8/f01cuRI7d27V8OHD3d3SeXGmTNnlJCQoIcffpj9bgOHw6Hbb7/d+ZgQVrLyC2GfffaZXn31VfXt25cQVkL8/PzUtm1btW3b1t2l4L/KewiTJGbEAA9ijNGRI0dUpUoV54p/KFnGGCUmJqpq1aqqVKmSu8spN4wxysjIkK+vr7tLAUpUWlqaFi1apG3btumxxx7TjTfe6O6SANiEIAYAAOBGxhj99ttv8vPzcy6tDqDsI4gBAAAAgM24EBwAAAAAbEYQAwAAAACbEcQAAAAAwGYEMQAAAACwGUEMAAAAAGxGEAMAlHqWZWnJkiVX9RydO3fWqFGjiqWe0iY2NpY/jgoAHoYgBgBwq6SkJI0YMUINGzaUr6+v6tWrpzvuuENfffVVsb7Oxx9/rGnTphXrcwIAUFQOdxcAACi/Dh48qI4dOyokJEQvvPCCWrRooczMTK1cuVLDhw/Xnj17iu21qlSpUmzPVV5kZmbKx8fH3WUAQJnEjBgAwG0effRRWZalrVu3ql+/fmratKmuvfZajRkzRlu2bHHpm5ycrDvvvFOVKlVSkyZNtGzZMpft69at0w033CBfX1/VqlVL48ePV1ZWlnP7xZcmpqen64knnlC9evXk6+urxo0ba9GiRc7tu3btUq9evRQQEKAaNWpowIABSk5OLnAsuZcHrly5Us2bN1dAQIB69uyp48ePF1iDJPXt21eDBw92Pq5fv76effZZDRw4UAEBAQoPD9eyZct08uRJ9enTRwEBAbruuuu0bdu2PDUsWbJETZo0UcWKFdWjRw8lJia6bF+6dKnatGmjihUrqmHDhpo6darLPrIsS3PnzlVUVJT8/f01ffr0AscLALg6BDEAgFucOnVKX3zxhYYPHy5/f/882y++52nq1Km65557tHPnTvXu3VsPPPCATp06JUk6evSoevfurbZt2+q7777T3LlztWjRIj377LMFvv7AgQP13nvv6R//+Id2796t+fPnKyAgQJL066+/qkuXLmrdurW2bdumL774Qj///LPuueeeS47p3LlzevHFF/X2229r/fr1Onz4sB5//PFC7hkpOjpaHTt21LfffqvbbrtNAwYM0MCBA/XnP/9ZO3bsUKNGjTRw4EAZY1xee/r06Xrrrbe0ceNG/frrr7r33nud27/++msNHDhQI0eO1H/+8x/Nnz9fsbGxecLWlClTdOedd+r777/Xgw8+WOjaAQBXyAAA4AbffPONkWQ+/vjjy/aVZJ566inn47S0NCPJfP7558YYYyZMmGCaNWtmcnJynH3mzJljAgICTHZ2tjHGmE6dOpmRI0caY4zZu3evkWRWr16d7+tNmzbNdO/e3aUtMTHRSDJ79+7N92diYmKMJLNv3z6XGmrUqOF8/PsacvXp08cMGjTI+Tg8PNz8+c9/dj4+fvy4kWQmTZrkbNu8ebORZI4fP+7y2lu2bHH22b17t5FkvvnmG2OMMbfeequZMWOGy2u//fbbplatWs7HksyoUaPyHR8AoHhxjxgAwC3M72ZzrsR1113n/G9/f38FBQXpxIkTkqTdu3erffv2sizL2adjx45KS0vTkSNHFBYW5vJc8fHx8vb2VqdOnfJ9re+++05xcXHOGbLf++mnn9S0adN8f65SpUpq1KiR83GtWrWcNRbG78dao0YNSVKLFi3ytJ04cUI1a9aUJDkcDrVt29bZJyIiQiEhIdq9e7duuOEGfffdd9q4caPLDFh2drbOnz+vc+fOqVKlSpKk66+/vtD1AgAKjyAGAHCLJk2ayLKsK16Q4+JFIyzLUk5OTpFe28/P75Lb09LSdMcdd+i5557Ls61WrVqFqvH3gdPLyytPAM3MzLzk8+SGy/zaCjP+tLQ0TZ06VXfddVeebRUrVnT+d36XiQIAih/3iAEA3KJKlSrq0aOH5syZo7Nnz+bZ/uuvv17xczVv3lybN292CTkbN25UYGCg6tatm6d/ixYtlJOTo3Xr1uX7fG3atNEPP/yg+vXrq3Hjxi7/riaoVKtWzWXxjuzsbO3atavIz/d7WVlZLgt47N27V7/++quaN28u6cKY9u7dm2c8jRs3lpcXvw4AgN048wIA3GbOnDnKzs7WDTfcoMWLFyshIUG7d+/WP/7xD7Vv3/6Kn+fRRx9VYmKiRowYoT179mjp0qWaPHmyxowZk2/IqF+/vgYNGqQHH3xQS5Ys0YEDB7R27Vp9+OGHkqThw4fr1KlTuu+++/Tvf/9bP/30k1auXKkhQ4YoOzu7yOPt0qWLPvvsM3322Wfas2eP/vrXvxYqcF6Kj4+PRowYoW+++Ubbt2/X4MGD1a5dO91www2SpKefflpvvfWWpk6dqh9++EG7d+/W+++/r6eeeqpYXh8AUDgEMQCA2zRs2FA7duxQZGSkxo4dqz/84Q/q1q2bvvrqK82dO/eKn6dOnTpasWKFtm7dqpYtW2rYsGF66KGHLhky5s6dq/79++vRRx9VRESEhg4d6pyZq127tjZu3Kjs7Gx1795dLVq00KhRoxQSEnJVs0cPPvigBg0apIEDB6pTp05q2LChIiMji/x8v1epUiU98cQTuv/++9WxY0cFBATogw8+cG7v0aOHli9frlWrVqlt27Zq166doqOjFR4eXiyvDwAoHMsU9m5pAAAAAMBVYUYMAAAAAGxGEAMAAAAAmxHEAAAAAMBmBDEAAAAAsBlBDAAAAABsRhADAAAAAJsRxAAAAADAZgQxAAAAALAZQQwAAAAAbEYQAwAAAACbEcQAAAAAwGb/D0hqh8ROAil3AAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=9, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "329qtkX90ZTW",
        "outputId": "3d062c87-bcfd-475c-c1d3-b55513fcb14e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=10, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        },
        "id": "iM2LEgTq0awU",
        "outputId": "d23e8497-3c72-4df8-89f9-abd34a06af34"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #3.3**\n",
        "Now, let's play around with the size of the problem by changing the list to contain 32 elements. Change the value of `number_choices`. **Keep in mind that this number has to be a power of 2, otherwise the code will produce an error.** \n",
        " \n",
        "\n",
        "**Independently**, find the element 28, in a list of 32 elements using the code given above. Answer the following:\n",
        "1. How many qubits are required?\n",
        "2. How many Grover iterations did you need? "
      ],
      "metadata": {
        "id": "ugNgwjyHOyFs"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "1dXSx4xO1BGq"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "##### **Solution**"
      ],
      "metadata": {
        "id": "kJ6ZYutO9jZa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "number_choices= 32\n",
        "correct_choice = 28\n",
        "ls = generate_binary_strings(number_choices)\n",
        "\n",
        "oracle = Statevector.from_label(ls[correct_choice])\n",
        "problem = AmplificationProblem(oracle, is_good_state=[ls[correct_choice]])"
      ],
      "metadata": {
        "id": "FgjeDGzg1BQr"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=0, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 481
        },
        "id": "8x6NNmqH1Rxq",
        "outputId": "e0187703-124c-4f59-812b-bcaeafbc35b7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=1, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 481
        },
        "id": "RliyyuAJ1Ve_",
        "outputId": "1a3f85b0-0f42-4acb-a241-71c052ca956b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=3, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 485
        },
        "id": "2n0-nABE1Wzj",
        "outputId": "a542eccb-2eb0-4581-d3b3-925d9c9cfc96"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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AACAij73v/LSfDnZVLVBQ+ckN3H6oZE4WLlwoZ8+elc6dO5tJW0F88803Eh8fL88884yZtImIhIeHy6BBg+TMmTPy/fffF0WVAQAAACBbbj9UMiczZswQEZFHH30028/Xrl0rmzdvFg8PD4mKipJ27dpJQEBAlulWr14tIiIdOnTI8lnHjh1lzJgxsmbNGunbt2+2v3PlyhW5cuWK+e/ExEQREUlNTZXU1FQREfHw8BBPT09JT08Xm81mTmsvT0tLk4wdo56enuLh4ZFjuT2unZfX1cWclpbmVLm3t7fYbDZJT083ywzDEC8vrxzLc6o7baJNtIk20SbaRJtoE21yZZu8xVkZ54O123TVjbWcsq975s9zc0Mmbv/884+sWLFCwsPD5c4778x2msz3xYWEhMjkyZOzJGAxMTEiIhIVFZUlhr3MPk12JkyYIGPHjs1SvmzZMvHz8xMRkUqVKkn9+vVl586dcvToUXOaGjVqSM2aNWXLli1y+vRps7xevXoSEREha9eulQsXLpjlTZs2lTJlysiyZcscVuTo6Gjx9fWVxYsXO9Th7rvvlkuXLsmqVavMMi8vL+nUqZOcOXNGNm7caJYHBgZKmzZtJDY2VrZv326Wly5dWpo1ayYxMTGyb98+s5w20SbaRJtoE22iTbSJNl2LNnUTZ9nba/02XXVjLafs23Tx4kVx1g15j5v9PrZXXnlFXn/9dYfPvv/+e4mPj5fWrVtL+fLl5eTJk7Jo0SJ59dVXJT4+XhYuXChdu3Y1p69evbrExMRIamqqmSHbpaamSrFixaROnTqyY8eObOuSXY9bxYoV5cyZM+Y4Vq5W0CbaRJtoE22iTbSJNtGmgrTp6Q+c73H7cCA9blZrU2JiooSGhjp1j9sNl7jZbDapUqWKxMbGysGDB6VKlSpOfW/FihXSvn17ue2222Tnzp1meWETt8x4OAkAAACKCg8ncW839cNJfv31Vzl69Ki0adPG6aRNRKRt27ZStWpV+euvv8z70EREgoODRUQkISEhy3fs09mnAQAAAABXuOESt7weSpKb0NBQEXEca5rbfWy53f8GAAAAAEXlhkrczp49Kz/88IOULFlS7rnnnnx9Nzk5WXbv3i3+/v5mAici0qpVKxG5+jCRzJYuXeowDQAAAAC4wg2VuM2ZM0dSUlLk4YcfFh8fnyyfX7hwQfbv35+l/NKlS/LYY4/JhQsXpGfPng73svXs2VOCg4Nl6tSpEhcXZ5bHxcXJtGnTJDQ0NN9JIgAAAADkxw31OoD//e9/IpLzMMmzZ89KzZo1pVGjRlKrVi0pV66c/Pvvv/Lrr79KXFyc1K5dWyZOnOjwnRIlSsi0adOkT58+0qBBA+nVq5eIiMyfP1/Onj0r8+fPl8DAQNc2DAAAAMBN7YZJ3LZs2SK7du2Sxo0bS+3atbOdpmTJkvL000/Lli1bZPHixXL+/Hnx9fWVWrVqybPPPiuDBg0SX1/fLN97+OGHJTQ0VMaPHy8zZ84UwzDkP//5j7zyyivSrl07VzcNAAAAwE3uhnsdgNXxOgAAAAAUFV4H4N5u6tcBAAAAAMCNhsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyuwInb2rVr5ejRo7lOExsbK2vXri3oTwAAAAAApBCJW3R0tMyaNSvXaWbPni3R0dEF/QkAAAAAgBQicVPVPKex2WxiGEZBfwIAAAAAIC6+xy0mJkaCg4Nd+RMAAAAAcMPzys/EjzzyiMO/Fy5cKEeOHMkyXXp6unl/21133VWoCgIAAADAzS5fiVvGe9oMw5Dt27fL9u3bs53WMAxp1KiRvPfee4WpHwAAAADc9PKVuB0+fFhErt7fFhkZKYMHD5bnnnsuy3Senp5SokQJ8ff3L5paAgAAAMBNLF+JW0REhPn/M2fOlPr16zuUAQAAAACKXr4St4z69etXlPUAAAAAAOSgwImb3ZYtW+T333+X+Ph4SU9Pz/K5YRgyatSowv4MAAAAANy0Cpy4nTt3Trp37y7r16/P9Z1uJG4AAAAAUDgFTtyGDh0q69atk9atW0u/fv0kPDxcvLwK3YEHAAAAAMikwJnWokWLpHHjxrJixQoxDKMo6wQAAAAAyMCjoF+8dOmStGzZkqQNAAAAAFyswIlbvXr15MiRI0VYFQAAAABAdgqcuI0ePVp+/PFH2bRpU1HWBwAAAACQSYHvcTt58qR06tRJWrVqJQ899JA0aNBAgoKCsp22b9++Ba4gAAAAANzsDM3tWf658PDwEMMwHF4FkPl+N1UVwzCyfb/bzSoxMVGCg4MlISEhx0QXAAAAcMZj7zs/7aeDXVULFFR+coMC97jNnDmzoF8FAAAAAORDgRO3fv36FWU9AAAAAAA5KPDDSQAAAAAA10aBE7ejR486/edqlStXFsMwsv1r3bp1lumvXLkir732mkRFRUnx4sUlLCxMHn/8cTl16lSOv/HFF19I48aNxd/fX0qUKCGdO3eWbdu2ubBVAAAAAHBVgYdK2pOlvBiGIWlpaQX9GacFBwfL4MGDs5RXrlzZ4d82m026desmS5culdtvv13uu+8+iYmJkRkzZsiKFStk06ZNUrp0aYfvjBs3Tl555RWJiIiQJ598Ui5cuCBfffWVNGvWTFasWCHNmzd3YcsAAAAA3OwKnLj17ds328QtISFBduzYIYcPH5ZWrVplSZxcJSQkRMaMGZPndJ9//rksXbpUevfuLV988YXZho8//lieeuopeeWVV2T69Onm9DExMTJmzBipXr26bNmyRYKDg0VE5Omnn5bbb79dHnvsMdm1a5d4eDDqFAAAAIBrFPh1ALlRVXn33Xfl7bfflk2bNklkZGRR/4QDe3J45MiRPKdt1qyZbNy4UY4cOSIRERFmuapKtWrV5N9//5XTp0+Lr6+viIiMHDlSJkyYIJ9//nmW99ENGDBAZs2aJWvWrJGWLVs6VVdeBwAAAICiwusA3Ft+cgOXdBMZhiHPP/+83HrrrfLCCy+44ieyuHLlisyaNUvGjx8v06ZNk82bN2eZ5vLly7J582apUaOGQ9Jmr3P79u0lOTlZtm7dapavXr1aREQ6dOiQJV7Hjh1FRGTNmjVF2BIAAAAAcFTgoZLOaNiwocyYMcOVP2E6efKkDBgwwKGsUaNGMm/ePKlataqIiBw8eFBsNptERUVlG8NeHhMTIy1atDD/PyAgQMqVK5fr9Dm5cuWKXLlyxfx3YmKiiIikpqZKamqqiFx9mbmnp6ekp6eLzWYzp7WXp6WlObzo3NPTUzw8PHIst8e18/K6upgz32uYU7m3t7fYbDaHF6cbhiFeXl45ludUd9pEm2gTbaJNtIk20Sba5Mo2eYuzMs4Ha7fpqhtrOWVf98yf58alidvBgwevyYNJBgwYIC1atJDbbrtNAgICZP/+/TJp0iSZM2eOtG3bVv766y8JDAyUhIQEERHzPrXM7N2T9uns/1+mTBmnp89swoQJMnbs2Czly5YtEz8/PxERqVSpktSvX1927tzp8BTOGjVqSM2aNWXLli1y+vRps7xevXoSEREha9eulQsXLpjlTZs2lTJlysiyZcsc5nt0dLT4+vrK4sWLHepw9913y6VLl2TVqlVmmZeXl3Tq1EnOnDkjGzduNMsDAwOlTZs2EhsbK9u3bzfLS5cuLc2aNZOYmBjZt2+fWU6baBNtok20iTbRJtpEm65Fm7qJs+zttX6brrqxllP2bbp48aI4q8jvcbPZbHLs2DGZNWuWjBkzRtq2bSvLli0ryp9wWt++fWXOnDny7rvvytChQ2XDhg3SvHlzeeihh2Tu3LlZpv/000/l8ccfl0mTJsmQIUNERKRYsWJSpkwZiYuLyzJ9TEyMVK9eXbp27So//PBDtnXIrsetYsWKcubMGTPx42oFbaJNtIk20SbaRJtoE20qSJue/sD5HrcPB9LjZrU2JSYmSmhoqFP3uBW4x83DwyPX1wGoqpQoUULefffdgv5EoT3xxBMyZ84cWb9+vQwdOtTsacuph8w+jDFjj5z9ZkFnp8/Mx8dHfHx8spR7e3uLt7fjhubp6Smenp5ZprUvYGfLM8ctSLmHh0e2T8rMqTynutMm2pTfctpEm0RoU051zG85baJNIrQppzrmt9xd2pSbzN9xlzbdiMvJXp6f5VjgxK1ly5bZJm4eHh5SokQJadSokQwYMCDHYYbXQmhoqIiIJCcni4hIZGSkeHh45HhPmr084z1wUVFRsnHjRjl58mSW+9yymx4AAAAAilqBE7fV//9pi1Zmf7Kk/XUBvr6+0rhxY9m0aZP8888/WV4HsHz5cvH395eGDRua5a1atZKNGzfKsmXLsrwOYOnSpeY0AAAAAOAqbv/W6L1792Z7U9/evXvlpZdeEhGRBx980Cx//PHHRURkxIgRDuNQp0+fLocOHZKHHnrIfIebyNUHn3h5ecm4ceMchkxu375d5s2bJ7Vq1ZI77rijyNsFAAAAAHZF8lTJ9evXy/bt2yUxMVGCgoKkXr160rx586IInaevvvpKJk2aJC1btpSIiAjx9/eX/fv3y+LFiyU1NVVGjBjh8HLsfv36yfz582XevHly+PBhadWqlRw4cEAWLFggVapUkTfeeMMhfvXq1WXMmDHyyiuvSN26deW+++6TCxcuyFdffSUiVx9okt14WQAAAAAoKoV6quSGDRtkwIABcuDAARG5OtzQft9bVFSUzJw5U5o2bVo0Nc3BmjVr5MMPP5Q///xT/v33X7l48aKEhoZKkyZN5Omnn872xdlXrlyRN998U+bMmSOxsbFSsmRJ6dy5s7zxxhtStmzZbH/niy++kPfff192794txYoVk+bNm8vrr78uDRo0yFd98/N2dAAAACA3j73v/LSfDnZVLVBQ+ckNCpy47d69W5o0aSIXL16U9u3bS3R0tJQvX15Onjwpq1atkmXLlklAQIBs2rRJbrnllgI15EZE4gYAAICiQuLm3vKTGxR4qORrr70mKSkpsnjxYrnzzjsdPnvppZfkl19+ka5du8prr71mDisEAAAAAORfgW/OWr16tfTo0SNL0mZ35513So8ePRzeaA4AAAAAyL8CJ24JCQlSpUqVXKepUqVKji+vBgAAAAA4p8CJW1hYmGzatCnXaTZv3ixhYWEF/QkAAAAAgBQicevatausXr1aRo0aJZcvX3b47PLlyzJ69GhZtWqVdOvWrdCVBAAAAICbWYGfKnn27Flp0qSJHD58WEqVKiWNGzeWsmXLyr///iu///67nD59WiIjI2XLli1SsmTJoq632+KpkgAAACgqPFXSvV2Tp0qWKlVKNm3aJC+++KJ89dVXsnjxYvOz4sWLy4ABA+Stt94iaQMAAACAQipw4iYiEhoaKp999plMnz5d9u7dK4mJiRIUFCQ1a9YUb2/voqojAAAAANzU8p24jRs3TpKTk2Xs2LFmcubt7S21a9c2p0lJSZGXX35ZAgMDZfjw4UVXWwAAAAC4CeXr4SS//vqrvPrqq1KqVKlce9SKFSsmpUqVkpdffpn3uAEAAABAIeUrcZs9e7aUKFFCBg0alOe0AwcOlJIlS8rMmTMLXDkAAAAAQD4Ttw0bNki7du3Ex8cnz2l9fHykXbt2sn79+gJXDgAAAACQz8Tt+PHjEhkZ6fT0VapUkRMnTuS7UgAAAACA/5OvxM3Dw0NSU1Odnj41NVU8PAr8jm8AAAAAgOQzcQsLC5Ndu3Y5Pf2uXbukQoUK+a4UAAAAAOD/5Ctxa9GihaxcuVKOHDmS57RHjhyRlStXSsuWLQtaNwAAAACA5DNxGzhwoKSmpkqPHj3kzJkzOU539uxZuf/++yUtLU2eeuqpQlcSAAAAAG5m+XoBd4MGDWTw4MHy/vvvyy233CJPPvmkREdHS3h4uIiIHDt2TFasWCGffPKJnD59WoYOHSoNGjRwScUBAAAA4GaRr8RNROTdd9+V4sWLy8SJE2XcuHEybtw4h89VVTw9PWXEiBHyxhtvFFlFAQAAAOBmle/EzTAMGT9+vPz3v/+VmTNnyoYNG+TkyZMiIlKuXDlp3ry59O/fX6pWrVrklQUAAACAm1G+Eze7qlWr0qMGAAAAANcAL1kDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLI3EDAAAAAIsjcQMAAAAAiyNxAwAAAACLc/vE7dixY/L+++9Lhw4dpFKlSlKsWDEpV66c3HfffbJ58+Ys048ZM0YMw8jx78iRI9n+ztKlS6VVq1YSGBgoQUFBEh0dLStWrHBx6wAAAABAxOt6V6Cwpk6dKm+99ZZUrVpVOnToIKVLl5aYmBhZuHChLFy4UL788kvp1atXlu/169dPKleunKU8JCQkS9ncuXOlT58+Urp0aenfv7+IiMyfP1/at28vX3/9tfTo0aOIWwUAAAAA/8dQVb3elSiMBQsWSKlSpaRVq1YO5b/99pu0bdtWAgIC5MSJE+Lj4yMiV3vcxo4dK6tWrZLWrVvnGf/8+fMSGRkpXl5e8ueff0p4eLiIiMTFxUn9+vVFROTQoUMSGBjoVH0TExMlODhYEhISJCgoKB8tBQAAABw99r7z03462FW1QEHlJzdw+6GS9957b5akTUSkRYsWEh0dLefPn5e//vqrwPG/+eYbiY+Pl2eeecZM2kREwsPDZdCgQXLmzBn5/vvvCxwfAAAAAPLi9kMlc+Pt7S0iIl5eWZu5du1a2bx5s3h4eEhUVJS0a9dOAgICsky3evVqERHp0KFDls86duwoY8aMkTVr1kjfvn2zrcOVK1fkypUr5r8TExNFRCQ1NVVSU1NFRMTDw0M8PT0lPT1dbDabOa29PC0tTTJ2jHp6eoqHh0eO5fa4dvb2p6WlOVXu7e0tNptN0tPTzTLDMMTLyyvH8pzqTptoE22iTbSJNtEm2kSbXNkmb3FWxvlg7TZddWMtp+zrnvnz3NywidvRo0fl119/lfLly0vt2rWzfD569GiHf4eEhMjkyZOzJGAxMTEiIhIVFZUlhr3MPk12JkyYIGPHjs1SvmzZMvHz8xMRkUqVKkn9+vVl586dcvToUXOaGjVqSM2aNWXLli1y+vRps7xevXoSEREha9eulQsXLpjlTZs2lTJlysiyZcscVuTo6Gjx9fWVxYsXO9Th7rvvlkuXLsmqVavMMi8vL+nUqZOcOXNGNm7caJYHBgZKmzZtJDY2VrZv326Wly5dWpo1ayYxMTGyb98+s5w20SbaRJtoE22iTbSJNl2LNnUTZ9nba/02XXVjLafs23Tx4kVxltvf45ad1NRUadeunaxdu1Zmz54tffr0MT/7/vvvJT4+Xlq3bi3ly5eXkydPyqJFi+TVV1+V+Ph4WbhwoXTt2tWcvnr16hITEyOpqalZeu5SU1OlWLFiUqdOHdmxY0e2dcmux61ixYpy5swZcxwrVytoE22iTbSJNtEm2kSbaFNB2vT0B873uH04kB43q7UpMTFRQkNDnbrH7YZL3Gw2m/Tp00e+/PJLeeyxx+STTz5x6nsrVqyQ9u3by2233SY7d+40ywubuGXGw0kAAABQVHg4iXu7qR5OkpHNZpNHHnlEvvzyS3n44Yfl448/dvq7bdu2lapVq8pff/1l3ocmIhIcHCwiIgkJCVm+Y5/OPg0AAAAAuMINk7jZbDYZMGCAfP7559K7d2+ZNWuWeHjkr3mhoaEi4jjWNLf72HK7/w0AAAAAisoNkbjZk7bZs2dLr169ZM6cOeLp6ZmvGMnJybJ7927x9/c3EzgRMV81sGzZsizfWbp0qcM0AAAAAOAKbp+42YdHzp49W+6//36ZO3dujknbhQsXZP/+/VnKL126JI899phcuHBBevbs6XAvW8+ePSU4OFimTp0qcXFxZnlcXJxMmzZNQkND5Z577in6hgEAAADA/+f2rwN47bXX5PPPP5eAgACpXr26vPHGG1mm6d69u9SrV0/Onj0rNWvWlEaNGkmtWrWkXLly8u+//8qvv/4qcXFxUrt2bZk4caLDd0uUKCHTpk2TPn36SIMGDaRXr14iIjJ//nw5e/aszJ8/XwIDA69JWwEAAADcnNw+cTty5IiIiCQlJcm4ceOynaZy5cpSr149KVmypDz99NOyZcsWWbx4sZw/f158fX2lVq1a8uyzz8qgQYPE19c3y/cffvhhCQ0NlfHjx8vMmTPFMAz5z3/+I6+88oq0a9fOlc0DAAAAgBvvdQBWx+sAAAAAUFR4HYB7u2lfBwAAAAAANyISNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3AAAAALA4EjcAAAAAsDgSNwAAAACwOBI3ALCAY8eOycMPPyylSpUSX19fqV27tmzduvV6VwtOcsfl5451Bm4UbH8oCBI3mMaMGSOGYTj81axZs9BxP/roI6lTp44EBQVJUFCQNG3aVJYsWVIENXZ/b775phiGIYMHD7ZsXJaf650/f16aN28u3t7esmTJEvn777/l3XfflRIlShT5bxXVuuGq/UVmrtpGitK1XH5FxZV1vlbrhqu4w/7T3eexK7HPcC9sI/lD4gYHt956q5w4ccL8W7duXaFjhoeHy5tvvil//PGHbN26Vdq0aSPdunWT3bt3Fzr2hAkTpFGjRhIYGChlypSR7t27y759+ywbN6Pff/9dpk+fLnXq1LF0XFctP1fOY1fGXrt2rXTp0kXCwsLEMAxZuHBhoWO+9dZbUrFiRZk5c6Y0btxYqlSpIh06dJCqVasWvsIZFPW64Yr9RUZFXV9XrReuXH7uWGcR16wb7rhfduXxz93msbstP1fW91rt84uKK+eFu20j1xuJGxx4eXlJuXLlzL/Q0NBCx+zSpYvcfffdEhUVJdWrV5dx48ZJQECAbNq0qdCx16xZIwMHDpRNmzbJ8uXLJTU1VTp06CDJycmWjGuXlJQkDz30kHz66adFeoXNFXFdtfxcOY9dGTs5OVnq1q0rH3zwQaFj2f3444/SsGFDuf/++6VMmTJSv359+fTTT4ssvohr1g1X7C/sXFFfV60Xrlx+7lhnEdesG+64X3bl8c/d5rG7LT9X1vda7POLkivnhbttI9ed4ppKSEhQEdGEhITrXZUsRo8erX5+flq+fHmtUqWKPvjgg/rPP/8U6W+kpaXpvHnztFixYrp79+4ija2qeurUKRURXbNmjaXj9u3bVwcPHqyqqq1atdLnnnvO0nHtXLn8XLXsXBlbRPT7778vdBwfHx/18fHRESNG6LZt23T69OlavHhxnTVrVuEr+f8V9brh6v2Fq9dl1aJbL67F8rNzhzpfi2OJqvvsl+2Kcv/prvPYlbFdvfyKsr5Fvf09+p7zf0XBVeuFO24jRSE/uYHX9UgWYU1NmjSRWbNmSY0aNeTEiRMyduxYadGihezatUsCAwMLFfuvv/6Spk2byuXLlyUgIEC+//57ueWWW4qo5v8nISFBRERKlixp2bhfffWVbNu2TX7//fdCx7oWcUWuzfJz1bJzdeyiYLPZpGHDhjJ+/HgREalfv77s2rVLPv74Y+nXr1+h47ti3XDl/sKV63JGRbVeuHr5ZeQOdXblupGRO+yXRVyz/3THeezK2Ndin1GU9b2W+wxXKOr1wp23kWvuGiSSyMDKPW6ZnT9/XoOCgnTGjBmFjnXlyhWNiYnRrVu36vDhwzU0NLTIe2zS09O1U6dO2rx5c8vGPXr0qJYpU0Z37NhhlhXFlUFXxbVz9fJz1bJzdWwpoh63SpUq6X//+1+Hsg8//FDDwsIKHdvV64ZdUe0vrlV9i3K9cOXyy8gd66xatMcSO3fYL9tdi+Of1eexK2Nfi31GUc+Lot7+rmWPmyvWC3fdRooKPW4oEiEhIVK9enU5cOBAoWMVK1ZMqlWrJiIi//nPf+T333+XyZMny/Tp0wsd227gwIGya9euIr/5tCjj/vHHH3Lq1Clp0KCBWZaeni5r166VadOmyZUrV8TT09Myce1cvfxctexcHbuoNG/ePMuN3vv375eIiIhCx3b1umFXVPuLa1XfolwvXLn8MnLHOosU7bHEzh32y3bX4vhn9XnsytjXYp9R1PPiWm5/Rc0V64W7biPXA4kbcpSUlCQHDx6UPn36FHlsm80mV65cKbJ4gwYNkkWLFsnatWslPDzcsnHbtm0rf/31l0PZgAEDpGbNmvLSSy8V+ODiqrg5Kcrl56pl5+rYRWnIkCHSrFkzGT9+vPTs2VO2bNkin3zyiXzyySeFjn2t1o2i2l9ci/oW9XrhyuVn5451tivqY4m77JdzUtTHPxHrz2NXxnb18nPFvLiW219RulbHVHfYRq6ba9ADeMPYsmWL3nXXXRocHKx+fn7apEkTnT9/fr5iWHmo5LBhw3T16tV6+PBhXb9+vbZr105DQ0P11KlThYo7fPhwXbNmjR4+fFh37typw4cPV8MwdNmyZYWus81m04EDB2pYWJju37+/0PFcHTc7rnrwQlHFddXyc+U8vlbLT4poqKSq6k8//aS33Xab+vj4aM2aNfWTTz4pkrjZKYp1w1X7i+wU1brsyvXCVcvPHevsqnXDHffLrtp/uuM8drfl5+r6FuX25+qhkq6cF+62jbgCQyVdYNWqVdKxY0cpXry4PPDAAxIYGCjfffed9OrVS2JjY2XYsGHXu4qFFhcXJ71795azZ89K6dKl5Y477pBNmzZJ6dKlCxX31KlT0rdvXzlx4oQEBwdLnTp1ZOnSpdK+fftC13ngwIHy5Zdfyg8//CCBgYFy8uRJEREJDg4WX19fy8V1R65afq6cx66MnZSU5DDU4vDhw7J9+3YpWbKkVKpUqcBxO3fuLJ07dy5U3a4lV+0vXMmV64Wrlp871tlV64Y77pddtf90x3nsbsvP1fV1p32+K+eFu20j15uhqnq9K2F1aWlpUrNmTYmLi5NNmzZJvXr1ROTqU3UaN24sR44ccXpscmJiogQHB0tCQoIEBQW5uOY3PsMwsi2fOXOm9O/f33Jx8X9cOY9dGXv16tUSHR2dpbxfv34ya9asQsWGa7njdu2OdXYV5oXruet+2RXcqb6Pve/8tJ8Ozn98d5oX7ig/uQE9bk5YuXKlHDx4UAYMGGAmbSJXrzSMHDlS+vfvL59//rm8+uqr16+SNylXXXfgeobruXIeuzJ269atWT/clDsuN3ess6swL1zPXffLruBu9XUl5oV1kLg5YfXq1SIi0qFDhyyfdezYUUSuvlXeXbn6Sg1cN4/zEze/seF6rtz2rLDO3ejrsjvuO62w/G70eeFK7lhnV3HHeeGOdXY3N/o8JnFzQkxMjIiIREVFZfmsXLlyEhAQYE6T2ZUrVxyejGN/aeG5c+ckNTVVREQ8PDzE09NT0tPTxWazmdPay9PS0hyudnh6eoqHh0eO5fa4dl5eVxdzWlpatuUpl7PvAs9OfLxN0tPTzX8bhiFeXl7Z1n3wdOef5DT5SZvTbRr6qbfTcUVEJj2WKt7e3mKzZV/3jOX5iT3pMcfll9tySrns/KZ29qxzy8/b21tSLjsdVkREzp/Pfh0rquXnzLqX33mc3XISyX7dK8jyc2Z7Kkhcu9zWvfwsv8REydc+IuWyh9Oxr94XnfM+ImN5ymXn58XZs6m57iMyrnv5iWuPLeLcfq+gyy+vdS+/y8/ZfXl+93FTnsp++WW37uV3+Tl7fMpvXLu8jk9FsfxyqntRLb/M615+l9/Up8Wp45NIwZdfXuteQedxbscnm80mz33s/H4oc+y81r38Lj9nz43yMy/eezzN6eOTSP6Xn7PnewXd/vI6N8rP8nv/ifydwz7zodOhZcpT6tTxSSR/8+LcuTSnjk/Otqmg5+UXLlwQEed6NrnHzQkdOnSQ5cuXS0xMjPmeiYwqVKggSUlJZlKW0ZgxY2Ts2LHXopoAAAAA3FBsbGyer1mgx83FRowYIUOHDjX/bbPZ5Ny5c1KqVKkcb/a83hITE6VixYoSGxtb5A9QcVVsd4vrytjuFteVsamz6+O6Mra7xXVlbHeL68rY1Nn1cV0Z293iujK2u8V1ZWx3rHNRUVW5cOGChIWF5TktiZsTgoODRUSy7VETubpClChRItvPfHx8xMfHx6EsJCSkSOvnKkFBQS5bwV0V293iujK2u8V1ZWzq7Pq4roztbnFdGdvd4royNnV2fVxXxna3uK6M7W5xXRnbHetcFOy5Rl7yN/j4JmW/ty27+9hOnjwpSUlJ2d7/BgAAAABFgcTNCa1atRIRkWXLlmX5bOnSpQ7TAAAAAEBRI3FzQtu2bSUyMlK+/PJL2b59u1mekJAg48ePl2LFiknfvn2vXwWLmI+Pj4wePTrLEE8rx3a3uK6M7W5xXRmbOrs+ritju1tcV8Z2t7iujE2dXR/XlbHdLa4rY7tbXFfGdsc6Xw88VdJJq1atko4dO0rx4sXlgQcekMDAQPnuu+/kn3/+kXfeeUeGDRt2vasIAAAA4AZF4pYPW7ZskdGjR8uGDRskNTVVateuLUOHDpVevXpd76oBAAAAuIGRuAEAAACAxXGPGwAAAABYHIkbAAAAAFgciRsAAAAAWByJGwAAAABYHInbTc7+bBp3e0aNzWZzi5giIunp6S6J6442bNggycnJIuJ+65y71RcAUHDs82FFJG43OcMwRFXFMAw5efKky5KXoubh8X+rblHtXD08PCQlJUViY2PlxIkTRRL74sWL8vLLL8uqVavk7NmzOcYryHy/cuWK/Prrr0WeGKalpcmCBQtk+fLlkpaWZpYXdl5cuHBBunXrJuPHjxeRq+teUUpLS5Pt27fLrFmzZPPmzUV60LVvIydOnHCbbQQ3BleePLIuX2WfxzabzW1O1l190bUo54Wqus18zaioj1Eirt3mMs7jol6XXbmNuOP2dz2RuN3E0tLSZM2aNdK/f39p2rSp3HfffdKhQwd5/vnnZcOGDde7etnauXOnjBw5Urp37y5vvvmmxMTEFMnO9cqVKzJ79mypVauWtG/fXoYMGSJbt24tdOyPP/5Y3n77bbnrrrukQ4cOMmHCBNm2bZskJSU5TDd16lT5888/87VT/+STT+TRRx+VrVu3FqqOmS1cuFD69+8vs2bNEi8vL7PcMAyJj48vcNy5c+fK2bNn5e2335b+/fvLoUOHRKRoeiSPHj0qQ4YMkQYNGsgjjzwiPXr0kC+++KLQcW02m2zYsEEef/xxcxtp3bq1PPvss7J27dpCx8/IfsBypx5aV588pqenF1lsdz0pcMXJo30+ZLwA5gpFfcLuqm3EPo89PDxcMr9dwV5PV9W3KOeFYRhmrKJOCF3BZrPJH3/8ITt37sz2s4L+/oULF6RVq1ayYsWKAsfIjWEYEhcXJykpKUW+LrtyG3HH7e+6Uty0Jk6cqEFBQWoYhlarVk1r1qyphmGYf7Vq1dL33ntPT5w4UajfsdlsRVLf+fPna9myZR3qGBISonPnzi107AkTJmhISIiGhIRoo0aN1NPTU2+55RY9duyYqqoeO3ZMlyxZokePHs1X3FdeeUUNw9D27dtrjRo11DAM9fPz07vuuks/+ugjPXnypK5fv14Nw9CxY8fmK3atWrU0Ojpa4+LiHMp37NihX3/9tU6cOFG//vrrfC+/22+/XZs3b67bt283y/766y8dP368tm3bVmvVqqVPPvmkrl69Ol9xa9eurdWqVdMKFSqoYRj6wAMP6JkzZ/IVIyePPfaYFi9eXO+8804dMWKEVqhQQevWrauxsbF65MgR/eyzz3Ts2LG6ZcuWfMWdMmWKhoSEqGEYWrFiRa1cubLD+letWjWdMmWKnj59WlWLbl2/2V2+fNml8dPT07MtL8jyS0pKyvXzgq4TJ0+e1CVLlmhsbGyWz9LS0goVf/r06dq+fXvdt2+fquY8PwoiKSlJ9+/fn2tMK20nhw8f1vnz5+vzzz+vw4YN0y+//FI3b96sx44d05SUlALHTUtLc1k7T548qcuXL9dZs2bp999/r//++6+qFn45bty4UYcPH66dO3fWt956yzz+2RWkPevXr9fPPvtMjxw5kuWzwtZ3ypQp2r179yz1zCy/9f7ll1+0cePG+sILLxTo+zmZPn26GoahERER+sMPPxRJTLvExESdMWOGVq9eXX18fPSBBx4wt+/C1v+ff/7Rb7/9VocNG6ZDhw7VOXPm6Jo1a/TAgQN66dKlQv2GO25/1xuJ203q0KFD6u/vry1atNBDhw5pXFycpqamamxsrH7wwQcaHR1tnpy2bdtW//jjD6djX7x4Uffu3asXL14ssvr+888/WqFCBa1QoYJ+9913umjRIh0+fLh58rx3715VdTwQpKenO3VgOHLkiJYuXVqbNWump0+f1sOHD+trr72mhmHoTz/9pIMGDdJSpUqpYRhatmxZHTlypJ4/f96peu/cuVNr1qyprVu31jVr1ujbb7+t7du3N5OBcuXKac2aNdXf319nz56dpQ05iYmJUcMw9O2333YoHzp0qJmM2/+aNGmi33//vVP1PXTokHp6eurrr79ulsXGxmq9evXUMAz19/d3iN2tW7dsD8g51Xfy5Ml6/PhxfeCBB9QwDK1Xr57++uuvqnp1x1+QHe3BgwfV19dX+/fvb57wr1u3TkuUKKEjR47U+vXrO9S5efPmTq3Phw8f1qCgIG3QoIHu3btXDxw4oH/++ae+9dZbGhQUpMWKFTNjDhgwQOPj4/Ndd7slS5boxIkT9eGHH9YhQ4bovHnz9Pfff9d///3XPEkvyLzJeIJf1NatW6dffPGFTp06VZcsWaIXLlxQ1cKfjE2dOlV79eqld999t86YMSPLfqQg82HKlCn63XffmSe4GWMVdh41adJE33jjDfMEJjsFWbeHDRumt956q65atUpVsy7LwtT7P//5jxqGoe3atdMDBw4UOE5m+/fv1wEDBmixYsU0KChIhw0bpgkJCUWSGC5fvlwnTZqkDz74oA4dOlS/+OILXbt2rR49elRTU1NVNf/r3vz587NcsDQMQwMDAzU6OlonTZqkBw8eLFS9bTZbkSbG69at0zZt2ph1DQ4O1kcffbTQF8Hmzp2rpUuXdpgPQ4cONT/PfDHF2TY1a9ZMS5UqpW3bttVRo0bpsmXLstT16NGjumDBgnyfM9SqVUsbNGig//zzj0P5pUuXdPv27Xro0CGHcme3wXbt2mn16tV1/fr1ZtnFixd16dKlOmbMGJ08ebJ++eWX+vfff+crQahTp46WLVtWS5YsqUFBQTpp0iRNTExU1cLvq19++WU1DENDQ0O1UqVKahiG9u7dW1WvJnX79+/X7du36/79+82EyJl6L1y4UOvWrZtlGyldurR27NhRJ06cmGX+O8sdtz8rIHG7SY0aNUrLlCljnjSrZt2Id+7cqX379tXixYtrjRo1dOvWrU7FnjBhgjZs2FDHjx+vK1eu1GPHjuW5Uzp9+rR58M3OiBEjNCQkROfPn+9Q/tVXXznsoDK2448//tDp06dnOVnLbOTIkVquXDn96aefzLJ///1XfX19tUmTJlqhQgUdPny49uvXT4ODg9XPz08//PBDVXXu4LVo0SINDAzUjz76SFVVT5w4oYsWLdIXXnhBmzRpoh4eHmoYhlatWlWHDx+uixcv1itXruQa84UXXtBSpUqZJ3UXL17Ujz76SA3D0Nq1a+sLL7yg06ZN0x49eqifn5+Gh4eb0+a2s541a5YGBQWZ8/nMmTP65JNPqpeXl44ePVpPnDih+/bt06lTp2qtWrXUMAwdMWJEnnHt9bX30v3111/atWtXNQxDb7/9dv3zzz/znI85ef311zUsLMxhXT579qxGRERoeHi4duzYURcvXqzvv/++NmrUSA3D0J49e+Z5kjBy5EgtVaqUw3qherVHYciQIdqgQQNdsmSJdurUSQ3D0Pvuuy/Xk/fsnD9/Xl988UU1DEO9vLwcDl6lSpXSrl276syZM52+UGCXeb109uDlzIE8OTlZP/74Y4cLBGFhYTpx4sR81TGz8+fP67PPPmuejBqGocWLF9cFCxaY02Tu3XKmTQcPHlTDMDQqKkrvuusuffPNN3XdunVmomm3YMECXbVqVb4O8gcOHFDDMHT06NFZPjt27JiuXLky2x6zvBw+fFhLlCihvXr1cig/fvy4TpgwQV966SV9++239ZtvvjEvnDhbb3ud69atq56enlqtWjX94YcfzBPQgp7knDx5Ulu1amXugypWrKiGYZgjIvbv369bt27VjRs36uHDh1XVufUtISFBR48erZ6enua+0v4XHh6u3bt31//973/57qW1XwysWrWqTps2Tbdv365ff/21vvHGG3r//febJ78RERE6efJkp3sW4uLi9N5779UvvvhCT5065fCZsxcTc3L8+HGtV6+eFitWTHv06KGvvfaa3n333WoYhnbq1EmTk5MLFDc2NlarVaumNWrU0MWLF+uOHTu0e/fuahiGHjlyRL/88ktt0aKF1qxZU4cMGeJ0sn/ixAk1DEM9PT3NpLBMmTLapUsXfffdd83EaPDgwRoVFWWeYzgzj+zrceb9zrfffqvR0dHmRcZatWrp22+/bSZIeS0/+/4i4wiYpKQk7dixo8M+2s/PT1u1aqVLlixxal7Y6ztmzBh99913zflS2P2m6tWLz6Ghodq2bVtNSkrS06dP69ixY7V06dL6/fffa48ePdTT01ODg4O1RYsWOmfOHKfiHj16VCMiIjQsLEzffPNN3bx5s77zzjsaFRWVZeTJ7Nmz85V8uuP2ZxUkbjepe++9VyMjI80rJfakKbsr0O+//74ahqH9+/d3KrZ9KJyXl5eWKlVKu3TpolOnTtUtW7Zke1UwKSlJn3/+eR0wYECOG1XdunW1e/fuZhKWkpKiaWlpmpaWpl27dtWgoCBdt26dOf3ly5d14MCB6uHhkecB/bbbbtPOnTs7bOSrVq1SX19fbdOmje7cudMs37BhgwYFBWnVqlWd2gHYpxk1apSWLl1aN27c6PD5//73PzUMQxs3bqy33HKLGoahHh4eeSZu5cqV0z59+ui5c+dUVfW3337TyMhIbdu2rTk8QvXqcn3vvffMxCIvCxcuVC8vL125cqWqqm7atEnLly+vgwYNyjJtYmKiNmvWTH18fMyhgrnV9/7778+y/F9//XWzJ2/69On5uhJo17VrV61Vq5bDkNH169draGio3n///Q4n6CkpKdqlSxc1DMPspc1J69attXbt2uZQ07S0NHN5/vjjjxocHKybNm3S2NhYve+++9QwjHwPf3n77bfVz89P77nnHl21apXu27dPv/rqKx07dqx27tzZPNlp0KCB072mqqoffvih9uzZUxctWpQlQSnswevTTz9VPz8/rVWrlr7wwgs6ceJE84rsa6+9VuC4kydP1uDgYO3Tp48eOnRIV69erZGRkdqgQQONj4/X5557TsuUKaP169fXcePGOX2S+uGHH6phGFq5cmUzIaxUqZL26tVLP/roI/3rr79UVTUsLEz79evn9AmequqLL76ooaGhunbtWrPs9OnT+sorr2h4eLh5YnP77bfr3LlznZ7vL7/8spYuXVqXLl1q1mX16tUaGhrqcMIUHBys999/f756zV588UUtVaqUfvnll/r000+bJ17OnoDmZPz48RoSEqLjx49X1asnZl26dNHGjRvrggULtHz58maPQJcuXXTDhg1OxZ00aZL6+Phox44dddGiRbpjxw595ZVXzGXp7e1t9qTbLww5s+xefvllLVmyZJYLM6pXL1itWrVKR44caS7Hxx9/3Km4o0ePNk/sb731Vn3uued02bJlWS4Upaenm8fdRYsW6ddff51n7FdffVX9/Px02rRpqnr1OHfgwAFzn/b5559n+c7evXuzHHcyGzVqlJYsWdKhDr/++qt6eHhonz591MvLS6tUqWIm44GBgXkOO7fPqxdffFEjIiL0m2++0U8++URbt26tvr6+ahiGRkZGar9+/bR48eLaqFEjPXnyZJ7zwM6+HtsvSKampurChQvNhKhjx45av359M4GLjo526gLYlClTtFSpUrpo0SJVvXpBacSIEWoYht5zzz06ZcoUnTRpkg4YMMAcifPdd985XV/7sli+fLnedtttahiG9unTx+xZKsi+2X5+8csvv5hlcXFx6u3trXXr1tXKlSvrAw88oL179zaX4bhx4/Jcn0eOHKmBgYFZLphfuHBBW7durVWrVjVHz3h4eOTrGOWO259VkLjdpOwnzLt3785xmowbyX333aeVKlXKs9t63759GhAQoM2aNdNp06Zpt27dtEyZMuaVk379+umcOXN0165d5k5006ZNGhwcrN26dcs25sGDB7Vy5cr6xBNPZPv5ihUrtHjx4vrII4+YZXv27NE6deronXfemWd9q1Spos8//7xD+bRp09TDw8M8KKiqecWnT58+Gh4e7pDQ5eXkyZPasmVLjYqKcjg4de/eXcuVK6fr1q3TQ4cO6dtvv63vvPNOrrE2bdqkhmE4JFOzZ89WwzAchgDal5/NZtOmTZtqzZo18+x93LNnj/r7++uQIUNU9epVQi8vL/PE1H5F3j4vJkyYoH5+frkmLL/99psahqGffPKJWWa/OHD69GkdOXKkenp6avny5c3hos5KSUnRp556SoOCghx2zKNGjVLDMPS3334zf8/++XvvvadeXl76xRdf5Bj3woULeu+992pYWFi2VxFnzpyp/v7+unz5clW92kMSFham999/v6o6n3hGRERop06dsr2gcezYMV20aJE+/vjj5pXeTz/91Km49nvxihcvrk2aNNFRo0bpxo0bs9TLfuBKTk7W9957z0zYcxMVFaX169c3e00uX76sK1eu1MjISA0NDc2SEKempuqqVavy3F6qVq2q7dq10+PHj5tlgwYN0qCgIO3YsaP6+/tr3bp1zQSgefPmWZLS7Fy8eFGbNm2q7du315UrV+r48eO1YcOG6uXlpR4eHlqnTh2z1yLzfiAv5cuX1/vuu8/crhISEvThhx9WwzC0Ro0a2rNnT4ehusOHD3cq7h133KFt2rQx793Zvn27NmzYUENDQ3XMmDE6a9YsnTJlit5zzz3mvtXZ5K18+fLao0cPM/GdMmWKBgcHq7e3t44fP14TEhJUNf8nkJGRkdq9e3eH5TdlyhTzwlTjxo31ueee0549e6q3t7cGBgY6nGjmJCIiQqOjo7Psu9atW6dlypTRO++8Uzt06KCGYegtt9ySZXhcTlq1aqWNGzc2t73U1NRs27x161Zt3769enp66ptvvpln3MaNG6ufn5/eeeedZoLi7e2tzZs319dff11///13h+mTk5O1ffv2ahhGnqMAoqKissxj1as9I5GRkVqzZk1NTU0191lXrlzRl156SStWrJjrBczq1atr165dHe6HXr58uXp7e+vtt99untTu3r1bBw8erIZx9R7lvNhsNj1+/LjWr19f27Vrp8nJyXrx4kVdv369vvLKK9q4cWP18PBQT09PDQsL0yFDhujXX3/t1NC78uXLO1wM3Lp1q9auXVvr1atnJl2qqlu2bNE777xTDcPQV199Nc+4EydOVH9/f/PcaN26dRoWFqb9+/c3L6imp6frqVOnzHvWWrVqledoC/t2Z79AbLPZdOHChVqlShUzMXFmf5adNm3aaKtWrRwuPttvF+jYsaN5MffUqVP61VdfafHixbVmzZrmhd+c2Jebfb1ITU012/nmm2/qbbfdpmfOnNFffvlFK1eurGXKlNH9+/c7VWd33P6sgsTtJrVu3TrzHqMVK1Zk28OTsfdt5MiR6ufnpzt27Mg17k8//aReXl46ZswYVb3ahW8fF96yZUsNCAhQLy8vrVOnjg4ePFh/+eUXfeGFF9QwDIedbUbbt2/XEiVKmOPtszuR7ty5s4aEhOjff/+tqqqff/65GoahP/74Y671XbZsmRqGYV4lVlWNj4/XTp06abFixbL9zqOPPqolS5bUXbt25Ro7sx07dmhQUJA++OCDeuXKFU1OTlYPDw+9//77HQ6qeZ0w2e/tMwxDq1evrs8884x27txZq1SpoqqOSYM91n333aflypXTmJiYHOPabDa9fPmyPvzww+rh4aHTp0/XtWvXakBAgE6aNMkhpj3upEmT1NPT00yQsvPggw9qaGiomVRml9TMnz/fTPCff/55pw5g9jj2IaJ33nmnfvbZZ/rmm2+qYVx9cE12D2aZOHGienh4OPSSZBd37Nix5sl2xt6dixcv6p133qmBgYEObWnVqpV5n6Qz9uzZowEBATpy5EizLLvesCtXrujPP/+skZGRWrJkyTx7Knbt2qWGYWjDhg3NA5JhGBoQEKAdO3bUyZMn6549exy+Y0+umzdvnmvsLVu2qJeXl06ZMiXLZ99//70ahqEvvfSSqv5fUrhnzx5t2LBhrj329rjvvfeeQ7l9GOnAgQPNIYebN2/Wu+66Sw3DcHrIz/Lly7VUqVLm8KdTp07psmXL9NlnnzV7uj09PbV27dr62muv6YIFC8wEJif2hwpNnz7dLJsxY4Z6e3vrs88+aya2V65c0SVLlmjVqlU1ICDA4WJQdi5cuKDt2rXTpk2bmmX2XvOMiU5qaqoePnzYHF6a+X7X7Nj3+x9//LFZlpiYqBMnTlRPT0/19/fXqVOn5hkns7///ltDQ0OzDBl966231DCu3ttqXx9iY2P11VdfVcMw9Nlnn1XVnC907NixQ4sVK+awf05PTzd75ps2barDhg3TlJQUs2e1R48eeZ6AXbx4Ue+77z6tWLGiub1mfuBLxjqdOHFCIyMj9Y477tD09PQc6xsXF6dRUVHaoEED83sff/yxtmzZ0twOQ0JCtEuXLjpt2jQ9efKk/v777xoeHp7jhUu7vXv3atmyZc2h6Xb2ek+dOlUNw3DoHdmzZ4/ecsst2qFDhxzj7tq1K9tlZx9p8/PPPzuUp6ena9OmTfWWW27R5ORkpy5SLV26VIsXL67PPfecWWbfpzZp0kT9/Pw0LCzMHAr7yiuv5BrPvu1lvMhpr++yZcuyTL97924NCgoy50NudV6xYoUahqGLFy82624YhnnCn/mWjieffFJDQkKy7FOzq2/G7c7u2LFj5gWYRo0aOYwcckZCQoJGR0drnTp1HNo1ceJENQxD16xZk+U7Q4cO1eLFi+d4DFS92utVr149vf32282yjMenKVOmOPS8zpkzJ8syyYk7bn9WQuJ2k0pLS9Nhw4aZY8DtK3F2zp07p3379tXSpUvnGfebb77JcvBQvdozEhMTo99++60+99xzWrduXS1WrJj6+/urn5+flihRIseYJ0+e1Ojo6CwndfZ2qF59CpRhGGZPUZ8+fTQwMDDP+iYnJ+u7775rXiWy75RiY2PNHV7GHfX58+f1/vvv14oVK+YZOyP7jmbu3Lnq6+urP/30k86fP9/hxC81NdWpg+CVK1f022+/1d69e5tDNTL3wGV0/vx57dq1q0ZGRjpV1+3bt5vDXZ988klt0KCBNmzY0DwRtTtz5ox27dpVS5UqlWu8GTNmZPuQCVU1d8IpKSn69ddfa+XKlc0D/NmzZ52q78GDBx0SFMMw9IknntB27drpvHnzHKY9ffq0Pvjgg7mub3Y7d+7UOnXqqKenp9577706c+ZMffvtt7Vt27YOCYrq1WS/Y8eOWq9ePafqrHr1ZDc8PNy8jynzFcfMBy/7MKC33nor17jz5s1TwzDMZHvfvn361ltvmQ+YMQxDy5cvr71799bZs2fruXPnzHsucrp4Yvf2229r+fLlzSF8GQ+iFy9e1HvuuUeLFSvmcOV37ty5ahiGLly4MMe4r732moaHh+uKFSvMspMnT2qnTp20QoUKWU4Qd+zYoV5eXllOYnNjTxbsw5rsdd+7d696eHhoRESEefHAMIw87+nt06ePli5d2kzEjh07pnfddZdWq1bNvBcv48nItGnT1DAM8/7Y7Njb+Nhjj2lISIgeP35cbTabPvHEE1qhQgVVvdrDmXk/UaFCBe3evXueCUvfvn21SpUqum3bNoffU1Vdu3at+aCAfv36mb0ezuyTNm3apCEhIfriiy+aZSdPntSOHTtqeHi4qma9IFW5cmVt2bJlrg/VWL58uXp5eZlX2u3D41WvDrHv0qWL1q1b15z+kUceUcMw8rzAqPp/SaX9ImNGGdts3//37dtXK1asmGuPwrZt27R06dLZ9rzv2bNHx44da14osA/ZbdiwoRqGke2QsYxWrlypgYGB+v7776tq1vl54sQJrVy5statW9e8EGvf9nIbEfH9999raGiow4iIs2fPaq9evTQsLMxhWvu86Natm1apUiXXC4GZffzxxxoQEOBwMTUlJcXcv+7cuVO//vprbd++vcP9ytl56aWX1DAMrVOnjk6aNEnXrFmjvXv31urVq6uq47yx17lx48Zar169PO85/ffff7V69epap04dvXTpku7bt09DQ0N18+bN2c6Ll19+WX18fHLdX9xzzz0aGRlp3stt37fb67ljxw7zXukWLVo4tf7a46iq/ve//1XDMPTbb79V1avLNDw8XMuVK+ewj7b/3siRI9Xb2zvP4a69evVSb29v3bRpk0N5fHy89u3bVwMDAx3mdaVKlbRfv35O3evmbtuflZC43eQ+/vhjrVq1qhqGoRUqVNBBgwbpzz//rDt37tTdu3frsWPHdPjw4Vq8eHGHJ0zlxGaz6d9//20OV8nuoJ+UlKTbtm3TefPmmUNcnnnmmVzjnjx5MsehVvYNOzo6WitVqqSzZ8/WatWqOQydLCz7zmnlypUaFhamjz/+eL5j2Gw2vXTpkv73v//VsLAwLVu2rNapU8fsuSvI2PZ///1XP/74Y42OjtahQ4dm23O3cuVKLV++fL7qvG/fPr377rsdbsauVKmSvvjii/rjjz/qypUrzZP0UaNG5RkvtwfPZPTHH3+YT7ybMGGC0/VNS0vTBQsW6NixY3XevHmakpKi7du312bNmunWrVvNk8N3331Xvby8HK785mbTpk3mAxcy/g0bNszhEdRr167VihUr6pNPPul0nVWvXm0ODAw0r+5mlPlge/bsWa1SpYr26NEj15j24TvZxdyyZYsOGTLEvM/B3mtbrlw5DQ4OzrO+o0aNUl9fX7PtGYfjqqouXrxYDeP/HliTkJCgjzzyiAYFBeUa99lnn9WKFSs6zNONGzdqmTJlzOGFGU/ajx8/rqVLl9aHHnoozzpndM8992itWrUchhXa7zOdPHmyHj58WKdOnZrnPFZVc4hTdHS0Tp8+XX/88UctU6aM2Ttkr6v9v4cOHTJ74/KycuVKhx6p119/XZs0aeLQ82tfL86cOaNNmjTRhg0b5hnXfjEm40Ne7Cd2aWlp+vPPP5snNv/973+d7j1OTk7WkiVL6q233qpbt27Vc+fO6aBBg8zfU3W8MHX69Glt3LixeWU8JydOnNDAwEBt2bJllhPu1atXa0REhMM6sG3bNjUMI8/7VWw2m8bHx5tD6Lp3767Lli3L0stq79lLSEjQ3r17Z0lkMjt+/LgOHTrUPIG2/1bm3167dq0+88wzWq5cOTUMw6kLSX/88YcahqHvvvtutnFVVd955x2zlyw5OVn79++f5wXMDRs2aPPmzc0hzjabTc+dO6evvvqqOTQ74/77zJkz2q5dO61Zs2aedbaz99TY7623D9379NNPHYbRp6Wl5fl6DdWrF4gHDhyodevWVQ8PDw0MDHQ4j8h8LD19+rQ2a9bMIcnPzWeffaaenp4aFRWlr776qpYvX14feughc5igfZuOj4/XBx54IM+Lly1atNC+ffua989mx2azmSMMAgMDs1x0zM3GjRvNdcl+8emWW27Rxo0bm6OQ7OtyfHy8PvTQQxoaGppnXPvFwkqVKuk777yjq1at0piYGLOeGY939m26TZs2ecZ1x+3PSkjcbnI2m03379+vL7zwgsPJXNmyZTU8PFw9PT3VMAx98MEHC/R0tMy/ldkzzzyjhmGYV4ALY968eeYwTMMw8v3OLmcMGjRIAwMDHd5xll+xsbFavXp1NQxDH3rooSJ7ylFOPVTPPvus+vv757vOp0+f1g8++EA7duyokZGRDo+/t/+98MILed435yz7+rF371694447CvWkSdWrTxezH3S6deumNWrUUA8PD61Xr16+HjGcmpqq27Zt03feeUenTZuW7dXrp556Sv38/Jyus72tmzdvNns3Bw8erJs3b85yr4Q9Gd+wYYOGhYXleuJvs9l048aNWZ78lnnbu3Tpki5atMh8UmpuPbYZY9iH3+T0YJeUlBRt1aqVBgcHa3x8vP7xxx8aHh6uAwYMyDGufZhbz549Heq6d+9efeKJJ8yRABl7IH/99VcNCQnRl19+Odc629m3sUOHDmm1atXMK7KqV6/ER0VFOZzg5NVzlZCQoNOmTdPHH39cIyMj1TD+71UZmYey2uv8yy+/qL+/v1Pva7x8+bI++uij5v0zTzzxhHp7e+uMGTPMaewnj/aLSTndA2y3d+9ejYqKyvYBFhkdOnTIvOevUaNGTt/La7+fzTAMcyRA+/btHR6KZO8Jst83lNeFjvT0dH3uueccEuSVK1fqhg0btH79+urt7e3w4I2ff/5Zg4ODdfLkyU7V+bffftPGjRurYVx9QuWjjz6qc+bM0e3btzskyZ988omGhIToU089lWfM5OTkHIfZZt4OFyxYoIZh6NNPP51n3PT0dF26dGmuw9vi4uK0VKlS2q1bN92wYUOe255dTvc6ZX69jurVYX8VKlTIc33Lzs6dO7VChQrmkGz7tpef+8XtkpOTdfv27Tpjxgzt27ev1q1bVydNmuTQ25Oxzs5sIxnZH69vGFcftBYaGqrDhw/XQ4cO6eXLl80hv56enjp48GCn6puTjPd8jxo1SgMDAzUwMNCpe47t3583b57edddd2qRJE3322Wf1zJkzGhUVpSNHjnRIvOfMmaMhISFOXWS8fPmyvvrqq1qyZEn18PAwjxWGYWjnzp0djqMbN27U8PBwHThwoFN1Vr16wdP+pOei3P5yejVPYbY/KyFxgykpKUlXrlypgwcP1p49e2rr1q21a9euOnfu3Hw/5jw39p3p4cOHtU6dOvkedpiTpKQkbd68uRrG1UfrF7WffvpJPTw89MEHHyx0rNTUVP3pp5/Mp6C56hG1ixYtUsO4+jSsgrp48aJu2bJFJ02apCNHjtQHHnhAX3zxRacPKgWR38ff5+Szzz7T+vXra2hoqPr4+GibNm2KLKG3HwSWLFmifn5+Tp0gZZaWlqazZs0yH7hx66236pAhQ/Sbb77R3bt3m+tFXFyc9u7dW728vJx6B92FCxdyfDJp5oPXwIED1TAMp5LOhIQEXbx4ca4PD7Df6/bBBx/oBx984HB/SG7sB1tnhubZh3bm5/2S9rizZs1Sw7j6GPHjx4+bQ2sL8h6l+Ph43bRpk/mgkLZt2+Z4Ym3vDXG2znFxcdq5c2c1DEN9fHzMYe1Tp07VEydO6L///qu///67Nm3aVH18fJy+MGNfL7Kbz/Z5sG/fPu3Vq5d6eXnpbbfd5tT2GB8fr++99562adNGe/bsqV988YVu375dvb29dcmSJWbs9PR0c0ijM/PC/t5HX19fh4tHnp6eOm7cOIdpJ02a5PS6nNGHH36ojRs3Vi8vL/X19dUaNWpoixYttGvXrhodHa2enp7asGHDfA0NdIb9/m5n1wln3jtoHxJsf0hObvu7jOtATv+f2ZAhQ7RYsWJOXWzN7ri2ZMkS9ff3Ny/aPvnkk/k6/mVXtzNnzujatWuzDGe0GzZsmNP7zozzd/Xq1dqlS5cs7y+tW7eu+YTXLl265Lo/zNjT7OxDq2bOnKmGYeTYntxkTMLt61fXrl111KhROnr0aA0MDNSwsLBc78nL7Ndff9UXX3xR77zzTr399tv1vffey9Ib/+KLL2qxYsXynMfZLeui2P4Kcg6V3+3PKkjckK3CvLHeWevWrdNatWrla0hcTuw7xK+//lpDQ0MdHqZRFBITE3XSpEn6+OOPOz3+/Hq7cOGCvv/++/rwww9nGaN+M4mPj9c///xTDxw4YJ6AFuQlzjlJSUnRZcuWZbkHMD9OnTqlr776qtasWVM9PDw0ICBAa9Soof/5z3+0ffv2WrFiRS1evLhTVxydYW//gQMH9D//+Y9Wq1atSOKqXp3fjRs31pCQEG3btm2BL8xkPhDb/33gwAFt0qSJ1q5du8B1HDJkiFaqVEk7deqknp6e5j25zh78s1t/jh07pqtXr3YYRmqPd/DgQb399tv11ltvzXdd586dqy1atDBHPxiGocWKFdNq1aqpYRhasmRJff311/OM4+xwZbuUlBTzPr78svcSJyYmmu8de/DBB3X48OHmgxjuvfdep+MlJibqd999p0OGDNGOHTtqv3799Ndff3Vo0969e7VFixb5msf25XP58mXds2ePfvnll/rkk09qvXr1zAdlVKtWTXv06FGg7Tu3BykcO3ZM69SpoyEhIfmOm11s+///9ddf5mtE7Pd8FVWdf/nlF61UqZJ26dIl33HT0tLM8wr7A7bCw8PNBwwV5T45o6VLl2rFihXzfMJ0ThITE3XDhg06ceJE7dixo5YoUUKrVaumLVq00OHDhxfoImNO89i+Pqanp5sXdfMTM/P/Hzp0SNu1a+eQdEZERDi8G9NZ2T0wzN6G9evXa0hIiHbu3NmpWCkpKXrkyBE9evSoql69mLRv3z798ssv9YknntA6deoUaPtLSUnRf/75x3woWXbDJO0Ku/1dTyRuuG5sNpsePXrUqTHt+Yn5zz//FPhFpHnFzu9LXq83m83m9JO/cO1lvIJ+8eJF3bFjh86YMUMHDBigt9xyi3p4eGjZsmW1YcOG+vHHHxfptqJ6tRfZMAyHh0oUhn09s9+7YhiGU0lFfjz++ONapkwZp1+NkF39Ll26pNHR0erh4aGtW7c2h/wUZDtx5jtPPfWUlihRQj/66COn42Y8ETt9+rSuWLFCX3/9db3jjjs0PDxcmzVrpvfdd5/+9NNPRd5jb4934cIF8z13ecmpN2jJkiXm+6rsfw8//HCe71HMTm69hc8//7wGBgbmuV7s2LFDR4wYod26ddPx48dnedhBUlKSXrhwQc+ePaubN292ODHPbVlnjDthwoQ8H4uenJys3333nVMPRchvbHtvVnYPfiho3MuXL2vv3r21SpUqeY62yCvusWPHdOzYsTps2LB8PQSnIHW238+V14OXnI178eLFLEPti3K9cDaus7FTUlJ0+fLl+s477+ikSZOc+v2McceNG5fnd3799VedMGFCnj3dly9f1s8//1wjIyPN16VkHI2R8aEtp0+f1vXr1zu1/eUVNzObzaZJSUlOb39WQ+IGABaSnp6uycnJmpqaqmfOnMn3aydUnT8JOnnypM6aNcvpJ3g6G/v06dNaq1YtNQzD4cXohY178OBBjYiI0P79++d6o39uce3//v333/Wll17KVzKVW+yc6n/o0CGNiIjQLl26OH11Pq95ER8f7/Dkzvxwdt3IbxKb2/SnTp3SJUuW6OTJk/XHH3/M1/uSMj9dNbsk9dKlSzpz5kydPXt2rhftMr52xP4XEhKis2fPLlTym1PcuXPn5vo9Z36zILETEhL0s88+y/U9XfmNa7PZ9MqVK3r06NFch2vmJ25+L4QWtM4HDhzIdRRRTnHnzJmT57pXlPXNWO/Cxs683RS2znm9eiWnofkZTZgwQUNCQjQkJEQbNWqknp6eWqtWLY2Li9P09HQ9fvy4Ll261GHoqTPzPKe49tEPx44d08WLF5s9fHbuekGbxA0ArpGLFy/q3r17c301gl3mg0puB7Dc4uYlr3tmChr70KFDDk/3Kqq4ly5dyvUR8vmNm/HkMa8DeUHrfPHixSwvTXY2buZ1IqchpEVd57xiFyZubpydF9nJ7eT8n3/+0QoVKmiFChX0u+++00WLFplD9qpVq2b2AGbcHnJ6KXBB4mYeyubMPZUFiZ2Wlnbd6uxs3JSUFDO2M/W1Qp2v1Tx21by4cuWKy+aFM8Owjxw5oqVLl9ZmzZrpmTNn9PDhw+a7Un/66ScdOHCglixZ0nw43ogRI/J8Qbizce0PSypbtqy+/PLLRXYP/fVC4gYA18iECRO0YcOGOn78eF25cqUeO3Ysy8E085XSU6dO5XlgdCZuZs7ELUzsvKZxVZ2dnccZHxrg6nlRVHXOb9yC1vn06dNFts5lXJ9PnDjhknX55MmTecYdMWKEhoSEZHnH6FdffaWGYWjv3r0d6qx69RH806dPz/XJua6KW9DYW7du1enTp+faI1uYuO44L65Hna02L653nUeOHKnlypVzGJr477//qq+vrzZp0kQrVKigw4cPN5907OfnZ77zMrdk1lVxrYzEDQCuEfuj/728vLRUqVLapUsXnTp1qm7ZsiXbXqSkpCR9/vnndcCAAbkeZAoTN6+T4oLEHjZsmEvqbI+bW51dNY9vpjq7ep27Huty3bp1tXv37uYJZkpKivluwK5du2pQUJCuW7fOnP7y5cs6cOBA9fDwyHVIn6viumOdmRfMi5zcdttt2rlzZ4cLCqtWrVJfX19t06aNwyshNmzYoEFBQVq1atU892+uimtlJG4AcA3s27dPAwICtFmzZjpt2jTt1q2beS9BRESE9uvXT+fMmaO7du0yh3Js2rRJg4ODtVu3btc8rjvWmXnh3nV2VdyDBw9q5cqVc3yP14oVK7R48eL6yCOPmGV79uzROnXq5Po0QlfFdcc6My9cH9dd67xv3z6tUqWKPv/88w7l06ZNUw8PD121apVZZn/1VJ8+fTQ8PDzXd/y5Kq7VkbgBwDXw008/qZeXl/mktyNHjujSpUt1zJgx2rJlSw0ICDBfID948GD95ZdfzPfM5PZENFfFdcc6My/cu86uirt9+3YtUaKEDh06VFWzv6+zc+fOGhISYr6I/fPPP1fDMPTHH3+85nHdsc7MC9fHddc6L1u2TA3D0PHjx5tl8fHx2qlTJy1WrFi233n00Ue1ZMmSuT6cy1VxrY7EDQCugW+++UYNw8hy/0BKSorGxMTot99+q88995zWrVtXixUrpv7+/urn56clSpS4LnHdsc7MC/eus6vinjx5UqOjo/W9997L8pn9BPWXX35RwzB0yJAhqnr1ynxgYOB1ieuOdWZeuD6uu9Y5OTlZ3333XfO1AvZhirGxsbpmzRpVdXzP5Pnz5/X+++/P8x2groprdSRuAHAN2Gw2/fvvv/XQoUPmvzNLSkrSbdu26bx587RDhw5qGIY+88wz1yWuO9aZeeHedXblvDh58mSOw6PsJ3fR0dFaqVIlnT17tlarVs1hWNi1juuOdWZeuD6uu9bZGfbEa+XKlRoWFqaPP/64peNeLyRuAHCdZXeCan+J7rZt2ywX15Wx3S2uK2NTZ9fHzWjevHnmUEzDMHTLli2WjuvK2O4W15Wx3S2uK2O7ss52gwYN0sDAQN2+fbtbxL3WSNwAwCLsVwYPHz6sderUKbIhHa6K68rY7hbXlbGps+vjql7tzWvevLkahqFVq1a1fFxXxna3uK6M7W5xXRnblXVWvXqfq4eHhz744INuEfd68BAAgCV4eFzdJR87dkxSU1Pl6aeftnRcV8Z2t7iujE2dXR9XVcXf31+ee+45KVWqlAwcONDScV0Z293iujK2u8V1ZWxX1llE5MKFCxITEyOPPvqovPTSS5aPe70YqqrXuxIAgP+jqhIXFyclS5YUf39/y8d1ZWx3i+vK2NT52sSNjY2V0NBQ8fPzs3xcV8Z2t7iujO1ucV0Z29V1TklJER8fH7eIez2QuAEAAACAxTFUEgAAAAAsjsQNAAAAACyOxA0AAAAALI7EDQAAAAAsjsQNAAAAACyOxA0AcMMxDEMWLlxYqBitW7eWwYMHF0l9rGbWrFkSEhJyvasBAMgHEjcAgFs5efKkPPPMMxIZGSk+Pj5SsWJF6dKli6xYsaJIf2fBggXy+uuvF2lMAAAKyut6VwAAAGcdOXJEmjdvLiEhITJx4kSpXbu2pKamytKlS2XgwIGyd+/eIvutkiVLFlmsm0Vqaqp4e3tf72oAwA2JHjcAgNt4+umnxTAM2bJli9x3331SvXp1ufXWW2Xo0KGyadMmh2nPnDkj99xzj/j5+UlUVJT8+OOPDp+vWbNGGjduLD4+PlK+fHkZPny4pKWlmZ9nHip55coVeemll6RixYri4+Mj1apVk//973/m57t27ZK77rpLAgICpGzZstKnTx85c+ZMjm2xD1dcunSp1KpVSwICAuTOO++UEydO5FgHEZHu3btL//79zX9XrlxZ3njjDenbt68EBARIRESE/Pjjj3L69Gnp1q2bBAQESJ06dWTr1q1Z6rBw4UKJioqS4sWLS8eOHSU2Ntbh8x9++EEaNGggxYsXl8jISBk7dqzDPDIMQz766CPp2rWr+Pv7y7hx43JsLwCgcEjcAABu4dy5c/LLL7/IwIEDxd/fP8vnme/ZGjt2rPTs2VN27twpd999tzz00ENy7tw5ERE5duyY3H333dKoUSPZsWOHfPTRR/K///1P3njjjRx/v2/fvjJv3jyZMmWK7NmzR6ZPny4BAQEiIhIfHy9t2rSR+vXry9atW+WXX36Rf//9V3r27Jlrmy5evCjvvPOOzJkzR9auXStHjx6V559/Pp9zRuS9996T5s2by59//imdOnWSPn36SN++feXhhx+Wbdu2SdWqVaVv376iqg6/PW7cOJk9e7asX79e4uPj5YEHHjA//+2336Rv377y3HPPyd9//y3Tp0+XWbNmZUnOxowZI/fcc4/89ddf8sgjj+S77gAAJykAAG5g8+bNKiK6YMGCPKcVEX3llVfMfyclJamI6JIlS1RVdeTIkVqjRg212WzmNB988IEGBARoenq6qqq2atVKn3vuOVVV3bdvn4qILl++PNvfe/3117VDhw4OZbGxsSoium/fvmy/M3PmTBURPXDggEMdypYta/47Yx3sunXrpv369TP/HRERoQ8//LD57xMnTqiI6KhRo8yyjRs3qojoiRMnHH5706ZN5jR79uxREdHNmzerqmrbtm11/PjxDr89Z84cLV++vPlvEdHBgwdn2z4AQNHiHjcAgFvQDL1FzqhTp475//7+/hIUFCSnTp0SEZE9e/ZI06ZNxTAMc5rmzZtLUlKSxMXFSaVKlRxibd++XTw9PaVVq1bZ/taOHTtk1apVZg9cRgcPHpTq1atn+z0/Pz+pWrWq+e/y5cubdcyPjG0tW7asiIjUrl07S9mpU6ekXLlyIiLi5eUljRo1MqepWbOmhISEyJ49e6Rx48ayY8cOWb9+vUMPW3p6uly+fFkuXrwofn5+IiLSsGHDfNcXAJB/JG4AALcQFRUlhmE4/QCSzA/JMAxDbDZbgX7b19c318+TkpKkS5cu8tZbb2X5rHz58vmqY8YE1cPDI0vCmpqammscezKaXVl+2p+UlCRjx46Ve++9N8tnxYsXN/8/u2GrAICixz1uAAC3ULJkSenYsaN88MEHkpycnOXz+Ph4p2PVqlVLNm7c6JAUrV+/XgIDAyU8PDzL9LVr1xabzSZr1qzJNl6DBg1k9+7dUrlyZalWrZrDX2ESm9KlSzs8rCQ9PV127dpV4HgZpaWlOTywZN++fRIfHy+1atUSkatt2rdvX5b2VKtWTTw8OH0AgGuNPS8AwG188MEHkp6eLo0bN5bvvvtOYmJiZM+ePTJlyhRp2rSp03GefvppiY2NlWeeeUb27t0rP/zwg4wePVqGDh2abVJSuXJl6devnzzyyCOycOFCOXz4sKxevVq+/vprEREZOHCgnDt3Tnr37i2///67HDx4UJYuXSoDBgyQ9PT0Are3TZs28vPPP8vPP/8se/fulaeeeipfCWpuvL295ZlnnpHNmzfLH3/8If3795fbb79dGjduLCIir776qsyePVvGjh0ru3fvlj179shXX30lr7zySpH8PgAgf0jcAABuIzIyUrZt2ybR0dEybNgwue2226R9+/ayYsUK+eijj5yOU6FCBVm8eLFs2bJF6tatK08++aT897//zTUp+eijj6RHjx7y9NNPS82aNeWxxx4ze/7CwsJk/fr1kp6eLh06dJDatWvL4MGDJSQkpFC9U4888oj069dP+vbtK61atZLIyEiJjo4ucLyM/Pz85KWXXpIHH3xQmjdvLgEBATJ//nzz844dO8qiRYtk2bJl0qhRI7n99tvlvffek4iIiCL5fQBA/hia37u9AQAAAADXFD1uAAAAAGBxJG4AAAAAYHEkbgAAAABgcSRuAAAAAGBxJG4AAAAAYHEkbgAAAABgcSRuAAAAAGBxJG4AAAAAYHEkbgAAAABgcSRuAAAAAGBxJG4AAAAAYHH/DxCVbg+yjlQ0AAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=4, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 481
        },
        "id": "IfDGhJ6X1YoF",
        "outputId": "16cebdfe-dcd5-437e-ec3b-ce0fe61d785a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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q1ZWXl6fAwEDZbDYFBATU7OJq2biX3V0BAAAAUH+WTHZ3BedVJxs0+KWSlUlJSdHx48d15513OkNbTXzwwQc6deqUJk2a5AxtktSmTRtNnDhRx44d00cffVQbJQMAAABAha7a4LZ06VJJ0mOPPVZhf0ZGhubNm6f58+crJSVFBQUFFY5bt26dJCk+Pr5cX9kSzPXr19dCxQAAAABQsQb/jFtFvv/+e6Wnp6tNmzYaOHBghWMufi4uKChIr7zyikaOHOnSnpWVJUmKiIgod4yytrIxAAAAAFAXrsrglpSUJLvdrtGjR8vDw8Ol7+abb9Zbb72lvn37qlWrVjp8+LA++eQTzZgxQ6NHj1ZQUJDuvvtu53ibzSZJCgwMLHeesnWoZWMqUlRUpKKiIufnvLw8SVJxcbGKi4slSVarVR4eHiotLZXdbneOLWsvKSnRhY8ienh4yGq1Vtpedtwynp7n/8wlJSUVtkuWSusHAAAArjYlJSXy9PSs9P67vu7LL+6/lKsuuNntdiUlJclisWjs2LHl+u+77z6Xz2FhYZo4caI6d+6sAQMGaNq0aS7B7UrNnTtXiYmJ5drT0tLUuHFjSVK7du3UrVs3ffvttzpw4IBzTMeOHdWpUydlZmbq6NGjzvbIyEiFhoYqIyND+fn5zvaePXuqRYsWSktLcwlpcXFx8vHx0erVq11qGDRokM6cOSPJjE1SAAAAgPqQmZmpXr16KSsrS3v27HG21/d9+enTp6tc81W3q2RaWpoSEhLUr18/rVmzplrfjYiIUHZ2tsuuLlFRUdqyZYuOHTumZs2auYw/fvy4goOD1bt3b2VkZFR4zIpm3Nq2batjx445z+HuGbfxrzDjBgAAgGvH6xPNmHHLy8tTcHBwlXaVvOpm3C63KcmlBAcHKzs7W6dPn3b+4iIiIrRlyxZlZWWVC26Xev6tjLe3t7y9vcu1e3l5ycvLy6XNw8Oj3NJO6cIljVVrv/i4l2sHAAAAriVl99GV3X/X1315de7Pr6pdJY8fP66PP/5YTZs2Lbck8nIKCwu1c+dO+fr6Kjg42NkeGxsr6fxM3sVSU1NdxgAAAABAXbiqgtvy5ct17tw5PfLIIxXOcuXn5+u7774r137mzBmNGzdO+fn5Gjp0qEtiHjp0qAIDA7Vw4ULl5uY623Nzc7Vo0SIFBwdXOyQCAAAAQHVcVUsl33zzTUmVL5M8fvy4OnXqpKioKHXu3FktW7bUkSNHtGbNGuXm5qpr166aP3++y3eaNGmiRYsWacSIEerevbuGDRsmSVq5cqWOHz+ulStXyt/fv24vDAAAAMA17aoJbpmZmdqxY4eio6PVtWvXCsc0bdpUEyZMUGZmplavXq2TJ0/Kx8dHnTt31lNPPaWJEyfKx8en3PceeeQRBQcHa86cOc4dK2+55RZNmzZN/fv3r+tLAwAAAHCNu+p2lTRdXl6eAgMDq7RzTH0Z97K7KwAAAADqz5LJ7q7gvOpkg6vqGTcAAAAAuBoR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADD1Ti4ZWRk6MCBA5ccc/DgQWVkZNT0FAAAAAAAXUFwi4uLU3Jy8iXHLFu2THFxcTU9BQAAAABAVxDcHA7HZcfY7XZZLJaangIAAAAAoDp+xi0rK0uBgYF1eQoAAAAAuOp5Vmfw2LFjXT6npKQoJyen3LjS0lLn822//OUvr6hAAAAAALjWVSu4XfhMm8Vi0bZt27Rt27YKx1osFkVFRWnBggVXUh8AAAAAXPOqFdz2798v6fzzbeHh4Zo8ebKefvrpcuM8PDzUpEkT+fr61k6VAAAAAHANq1ZwCw0Ndf6clJSkbt26ubQBAAAAAGpftYLbhUaNGlWbdQAAAAAAKlHj4FYmMzNTX331lU6dOqXS0tJy/RaLRdOnT7/S0wAAAADANavGwe3EiRO69957tWHDhku+043gBgAAAABXpsbBbcqUKfriiy/Ut29fjRo1Sm3atJGn5xVP4AEAAAAALlLjpPXJJ58oOjpa6enpslgstVkTAAAAAOAC1pp+8cyZM+rTpw+hDQAAAADqWI2DW2RkpHJycmqxFAAAAABARWoc3GbOnKl//OMf2rRpU23WAwAAAAC4SI2fcTt8+LDuuOMOxcbG6uGHH1b37t0VEBBQ4diRI0fWuEAAAAAAuNZZHJfay/8SrFarLBaLy6sALn7ezeFwyGKxVPh+t2tVXl6eAgMDZbPZKg269W3cy+6uAAAAAKg/Sya7u4LzqpMNajzjlpSUVNOvAgAAAACqocbBbdSoUbVZBwAAAACgEjXenAQAAAAAUD9qPON24MCBKo9t165dTU8DAAAAANe8Gge3sLCwKr1822KxqKSkpKanAQAAAIBrXo2D28iRIysMbjabTd98843279+v2NhYhYWFXUl9AAAAAHDNq3FwS05OrrTP4XDoL3/5i/785z/rzTffrOkpAAAAAACqo81JLBaLfvvb3+rnP/+5fve739XFKQAAAADgmlGnu0reeuut+vzzz+vyFAAAAABw1avT4LZ37142JgEAAACAK1TjZ9wqY7fbdejQISUnJ+vjjz9Wv379avsUAAAAAHBNqXFws1qtl3wdgMPhUJMmTfSXv/ylpqcAAAAAAOgKglufPn0qDG5Wq1VNmjRRVFSUxowZoxYtWlxRgQAAAABwratxcFu3bl0tlgEAAAAAqEydbk4CAAAAALhytbI5yYYNG7Rt2zbl5eUpICBAkZGRiomJqY1DAwAAAMA174qC25dffqkxY8YoOztb0vkNScqee4uIiFBSUpJ69ux55VUCAAAAwDWsxsFt586dio+P1+nTpzVgwADFxcWpVatWOnz4sNauXau0tDQlJCRo06ZN6tKlS23WDAAAAADXlBoHt+eff17nzp3T6tWrNXDgQJe+qVOn6rPPPtPdd9+t559/Xu+9994VFwoAAAAA16oab06ybt06DR48uFxoKzNw4EANHjxYa9eurXFxAAAAAIArCG42m03t27e/5Jj27dvLZrPV9BQAAAAAAF1BcGvdurU2bdp0yTGbN29W69ata3oKAAAAAICuILjdfffdWrdunaZPn66zZ8+69J09e1YzZ87U2rVrdc8991xxkQAAAABwLbM4HA5HTb54/Phx/eIXv9D+/fvVrFkzRUdHKyQkREeOHNFXX32lo0ePKjw8XJmZmWratGlt191g5eXlKTAwUDabTQEBAe4uR5I07mV3VwAAAADUnyWT3V3BedXJBjWecWvWrJk2bdqkUaNGqaCgQKtXr1ZSUpJWr16t/Px8jRkzRps2baqX0BYWFiaLxVLhv759+5YbX1RUpOeff14RERFq1KiRWrdurfHjx+unn36q9BzvvPOOoqOj5evrqyZNmujOO+/U1q1b6/CqAAAAAOC8K3oBd3BwsN566y0tXrxYu3fvVl5engICAtSpUyd5eXnVVo1VEhgYqMmTJ5drDwsLc/lst9t1zz33KDU1VT169NADDzygrKwsLV26VOnp6dq0aZOaN2/u8p3Zs2dr2rRpCg0N1a9+9Svl5+frvffeU69evZSenq6YmJg6vDIAAAAA17pqL5WcPXu2CgsLlZiYWGk4O3funBITE+Xv768//OEPtVLopZSFs5ycnMuOTUpK0tixYzV8+HC98847slgskqQ33nhDTzzxhMaPH6/Fixc7x2dlZalLly7OZZ+BgYGSpG3btqlHjx4KDw/Xjh07ZLVWbfKSpZIAAACAe131SyXXrFmjGTNmqFmzZpecUbvuuuvUrFkz/fGPfzTuPW5LliyRJM2dO9cZ2iTp8ccfV3h4uN555x2dOXPG2Z6UlKSSkhL98Y9/dIY2SYqMjNTw4cO1a9cuffHFF/V3AQAAAACuOdUKbsuWLVOTJk00ceLEy4598skn1bRpUyUlJdW4uOooKipScnKy5syZo0WLFmnz5s3lxpw9e1abN29Wx44dFRoa6tJnsVg0YMAAFRYWasuWLc72devWSZLi4+PLHS8hIUGStH79+lq8EgAAAABwVa1n3L788kv1799f3t7elx3r7e2t/v37a8OGDTUurjoOHz6sMWPGuLRFRUXp3XffVYcOHSRJe/fuld1uV0RERIXHKGvPyspS7969nT/7+fmpZcuWlxxfmaKiIhUVFTk/5+XlSZKKi4tVXFwsSbJarfLw8FBpaansdrtzbFl7SUmJLlzR6uHhIavVWml72XHLeHqe/zOXlJRU2C5ZBAAAAFwrSkpK5OnpWen9d33dl1/cfynVCm4//PCDwsPDqzy+ffv2+vjjj6tzihoZM2aMevfurRtvvFF+fn767rvv9NJLL2n58uXq16+ftm/fLn9/f9lsNklyWfJ4obJ1pWXjyn5u0aJFlcdfbO7cuUpMTCzXnpaWpsaNG0uS2rVrp27duunbb7/VgQMHnGM6duyoTp06KTMzU0ePHnW2R0ZGKjQ0VBkZGcrPz3e29+zZUy1atFBaWppLSIuLi5OPj49Wr17tUsOgQYP+/7JQM561AwAAAOpDZmamevXqpaysLO3Zs8fZXt/35adPn65yzdUKbhWlxkspLi6u8qYdV2LmzJkunyMjI7Vs2TJJ0vLly7VkyRJNmTKlzuuoyDPPPONy7ry8PLVt21bx8fHO4Ff2O7rpppt04403OseWtUdHR5dL8JLUp0+fCtsvXtZZluwHDRpUrt3f3//KLhAAAABoYKKjoyWdX0FXtjpPqv/78rLVeFVRreDWunVr7dixo8rjd+zYoZ/97GfVOUWtevzxx7V8+XJt2LBBU6ZMcc60VTZDVvaLu3BGrmyXl6qOv5i3t3eFS0u9vLzKbfDi4eHh/CNf6P+WNFatvbKNY+r7FQ0AAACAicruoyu7/66v+/Lq3J9Xazqsd+/e+vzzz6u07X5OTo4+//xz9enTpzqnqFXBwcGSpMLCQklSeHi4rFZrpc+klbVf+AxcRESECgoKdPjw4SqNBwAAAIDaVq3g9uSTT6q4uFiDBw/WsWPHKh13/PhxDRkyRCUlJXriiSeuuMiaKttZsuw9bz4+PoqOjtaePXv0/fffu4x1OBz617/+JV9fX916663O9tjYWEnnn0m7WGpqqssYAAAAAKgL1Qpu3bt31+TJk7V161Z16dJFM2bM0Nq1a5WVlaWsrCytW7dO06dPV5cuXfSf//xHv/71r9W9e/e6ql2StHv37gof6tu9e7emTp0qSXrooYec7ePHj5d0/tmzC9ehLl68WPv27dPDDz8sHx8fZ/uYMWPk6emp2bNnuyyZ3LZtm95991117txZt912W61fFwAAAACUsTguTC9V4HA49Mc//lHz58932SLzwn4PDw/9/ve/16xZs1xecl0XnnvuOb300kvq06ePQkND5evrq++++06rV69WcXGxnnnmGc2ZM8c53m63a9CgQUpNTVWPHj0UGxur7OxsrVq1SmFhYdq8ebOaN2/uco7Zs2dr2rRpCg0N1QMPPKD8/Hy99957OnfunNLT0xUTE1PleqvzdvT6Mu5ld1cAAAAA1J8lk91dwXnVyQbVDm5l9u7dq6SkJH355ZfO579atmypmJgYjR492mV3lrq0fv16/c///I++/vprHTlyRKdPn1ZwcLB+8YtfaMKECRW+OLuoqEh/+tOftHz5ch08eFBNmzbVnXfeqVmzZikkJKTC87zzzjt6+eWXtXPnTl133XWKiYnRCy+8UO0ZRYIbAAAA4F7XVHBDzRDcAAAAAPdqiMGt7l+yBgAAAAC4IgQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMFyDD26HDh3Syy+/rPj4eLVr107XXXedWrZsqQceeECbN28uN/65556TxWKp9F9OTk6F50lNTVVsbKz8/f0VEBCguLg4paen1/HVAQAAAIDk6e4CrtTChQs1b948dejQQfHx8WrevLmysrKUkpKilJQU/e1vf9OwYcPKfW/UqFEKCwsr1x4UFFSubcWKFRoxYoSaN2+u0aNHS5JWrlypAQMG6P3339fgwYNr+aoAAAAA4P9YHA6Hw91FXIlVq1apWbNmio2NdWn/97//rX79+snPz08//vijvL29JZ2fcUtMTNTatWvVt2/fyx7/5MmTCg8Pl6enp77++mu1adNGkpSbm6tu3bpJkvbt2yd/f/8q1ZuXl6fAwEDZbDYFBARU40rrzriX3V0BAAAAUH+WTHZ3BedVJxs0+KWS999/f7nQJkm9e/dWXFycTp48qe3bt9f4+B988IFOnTqlSZMmOUObJLVp00YTJ07UsWPH9NFHH9X4+AAAAABwOQ0+uF2Kl5eXJMnTs/yK0IyMDM2bN0/z589XSkqKCgoKKjzGunXrJEnx8fHl+hISEiRJ69evr6WKAQAAAKC8Bv+MW2UOHDigNWvWqFWrVuratWu5/pkzZ7p8DgoK0iuvvKKRI0e6tGdlZUmSIiIiyh2jrK1sDAAAAADUhasyuBUXF2vEiBEqKirSvHnz5OHh4ey7+eab9dZbb6lv375q1aqVDh8+rE8++UQzZszQ6NGjFRQUpLvvvts53mazSZICAwPLnadsHWrZmIoUFRWpqKjI+TkvL89ZY3FxsSTJarXKw8NDpaWlstvtzrFl7SUlJbrwUUQPDw9ZrdZK28uOW6ZsxrGkpKTCdslSaf0AAADA1aakpESenp6V3n/X1335xf2XctUFN7vdrtGjRysjI0Pjxo3TiBEjXPrvu+8+l89hYWGaOHGiOnfurAEDBmjatGkuwe1KzZ07V4mJieXa09LS1LhxY0lSu3bt1K1bN3377bc6cOCAc0zHjh3VqVMnZWZm6ujRo872yMhIhYaGKiMjQ/n5+c72nj17qkWLFkpLS3MJaXFxcfLx8dHq1atdahg0aJDOnDkjyYxNUgAAAID6kJmZqV69eikrK0t79uxxttf3ffnp06erXHOD31XyQna7XWPHjtXbb7+tRx55RG+//bas1qo/xhcREaHs7GyXXV2ioqK0ZcsWHTt2TM2aNXMZf/z4cQUHB6t3797KyMio8JgVzbi1bdtWx44dc57D3TNu419hxg0AAADXjtcnmjHjlpeXp+Dg4CrtKnnVzLjZ7XaNGTNGy5Yt0/Dhw5WcnFyt0CZJwcHBys7O1unTp52/uIiICG3ZskVZWVnlgtulnn8r4+3t7XwVwYW8vLycm6eU8fDwcFnWWaaizVUu1X7xcS/XDgAAAFxLyu6jK7v/rq/78urcn18Vu0peGNqGDRum5cuXV/iLvpTCwkLt3LlTvr6+Cg4OdraXvWogLS2t3HdSU1NdxgAAAABAXWjwwa1seeSyZcs0ZMgQrVixotLQlp+fr++++65c+5kzZzRu3Djl5+dr6NChLol56NChCgwM1MKFC5Wbm+tsz83N1aJFixQcHFzuuTkAAAAAqE0Nfqnk888/r7ffflt+fn664YYbNGvWrHJj7r33XkVGRur48ePq1KmToqKi1LlzZ7Vs2VJHjhzRmjVrlJubq65du2r+/Pku323SpIkWLVqkESNGqHv37ho2bJgkaeXKlTp+/LhWrlwpf3//erlWAAAAANemBh/ccnJyJEkFBQWaPXt2hWPCwsIUGRmppk2basKECcrMzNTq1at18uRJ+fj4qHPnznrqqac0ceJE+fj4lPv+I488ouDgYM2ZM0dJSUmyWCy65ZZbNG3aNPXv378uLw8AAAAArq5dJRuCvLw8BQYGVmnnmPoy7mV3VwAAAADUnyWT3V3BedXJBg3+GTcAAAAAuNoR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBLdq+OqrrzRo0CAFBQXJ19dXPXr00Pvvv+/usgAAAABc5TzdXUBDsXbtWiUkJKhRo0Z68MEH5e/vrw8//FDDhg3TwYMH9Zvf/MbdJQIAAAC4SlkcDofD3UWYrqSkRJ06dVJubq42bdqkyMhISZLNZlN0dLRycnL03XffKTQ09LLHysvLU2BgoGw2mwICAuq48qoZ97K7KwAAAADqz5LJ7q7gvOpkA5ZKVsHnn3+uvXv36qGHHnKGNkkKDAzUs88+q3Pnzuntt992X4EAAAAArmoEtypYt26dJCk+Pr5cX0JCgiRp/fr19VkSAAAAgGsIwa0KsrKyJEkRERHl+lq2bCk/Pz/nGAAAAACobWxOUgU2m03S+aWRFQkICHCOuVhRUZGKiorKHevEiRMqLi6WJFmtVnl4eKi0tFR2u905tqy9pKREFz6K6OHhIavVWml72XHLeHqe/zOXlJRU2H7urOUSVw8AAABcXU6cKJGnp2el99/1dV+en58vSarKtiMEtzo2d+5cJSYmlmtv3769G6oBAAAAsOwZd1fgKj8/v9JJojIEtyoo+yVWNquWl5enJk2aVNj3zDPPaMqUKc7PdrtdJ06cULNmzWSxMNMFANeqvLw8tW3bVgcPHjRml2EAQP1yOBzKz89X69atLzuW4FYFZc+2ZWVl6ZZbbnHpO3z4sAoKChQdHV3hd729veXt7e3SFhQUVCd1AgAanoCAAIIbAFzDLjfTVobNSaogNjZWkpSWllauLzU11WUMAAAAANQ2XsBdBSUlJerYsaMOHTpU6Qu49+zZo7CwMLfWCQBoOKrz0lUAAFgqWQWenp5aunSpEhIS1KdPHz344IPy9/fXhx9+qO+//14vvvgioQ0AUC3e3t6aOXNmueX0AABUhBm3asjMzNTMmTP15Zdfqri4WF27dtWUKVM0bNgwd5cGAAAA4CpGcAMAAAAAw7E5CQAAAAAYjuAGAAAAAIYjuAEAAACA4QhuAAAAAGA4ghsAAAAAGI7gBgBAPbhwE2e73S42dQYAVAfBDQCAemCxWJSbm6tz587JarXKYrG4uyQAQANCcAMAoI7l5+frzTffVL9+/RQQEKDhw4fru+++kyRm3gAAVeLp7gIAALjazZs3T3PmzFGzZs0UEhKilStXymKx6G9/+5sKCgp0+PBhnT59Wo0bN1ZYWJi8vLzkcDiYlQMAODHjBgBAHfr++++1ePFi3X777crJydF//vMfPffcc1qzZo1SUlI0duxYde7cWbGxsXr00Ue1cuVKSSK0AQBcWBys0QAAoM7MmDFDb7zxhpYvX66EhARJ0qFDh9S+fXt16dJFNptNPXr0kMVi0RdffKHc3FzNmjVLzzzzDOENAODEjBsAAHVow4YN6tKli7p37+5sy8nJkZ+fn1q2bKnU1FS9++67euWVVzR//nx5e3tr+fLlOnXqlPuKBgAYh+AGAEAdycvLk8Ph0MmTJxUcHOxs37hxo06dOqVnn31WN9xwgySpefPmGjZsmCZMmKCcnBzt2LHDXWUDAAxEcAMAoA44HA4FBAQoPDxc27dv16pVqyRJKSkpeuWVVxQSEqLbbrvNuauk3W6XJDVq1EilpaVq1KiR22oHAJiH4AYAQB0oez7tscceU0hIiIYMGaKQkBDdf//9CggIULt27bRnzx5ZLBYVFxfLarXKZrPp+++/V2BgoKKiotx8BQAAkxDcAACoQ1FRUVqwYIEGDhyo9u3ba9KkScrIyNDJkye1YsUKlZSUyMvLS5L0v//7v/r00081ePBgN1cNADANu0oCAFBPTp48qSZNmkiSfv/73+vFF1/UXXfdpZtvvllWq1UvvfSS/P39lZ6erk6dOrm5WgCASQhuAADUMbvdLqvV6vLz/v37NX78eKWnpzvHtWvXTgsWLNB9993nrlIBAIYiuAEAUAe+/fZbvffee/rvf/+rHj166IEHHlBERITLmOLiYq1fv17ffPONrFar7rzzznJjAACQCG4AANS6999/X5MmTdLRo0edbYGBgVq0aJEefvhh506SvGAbAFBVBDcAAGrRgQMH1KtXL0nSq6++Km9vb33xxReaN2+eOnTooE8++UQdO3Z0WT557tw5eXh4yMPDw52lAwAMxq6SAADUojfeeEOFhYV66aWXdP/99+uOO+7Q3Llz9e6772rv3r1KTEyUJFmtVufM244dO/Tmm2/qp59+cmfpAACDEdwAAKhFq1evVt++fdW3b19J559jKy0t1eDBg3XXXXfp008/1YYNGySdXypZVFSkt956S0888YQCAwPdWDkAwGQENwAAasm+fftks9kUEhKiFi1aSJK8vLycyyCffvppnTt3Tm+99ZbzO/v379e///1vxcfHy9vb212lAwAMR3ADAKCW5Ofny2azydfXV5JUWlrq0n/77berf//+WrVqlXbt2iVJyszM1Pbt2zVhwoR6rxcA0HAQ3AAAqCUtW7ZUZGSk2rZtK0kum42UhbiJEyfKZrNpyZIlkqQ1a9bIz89Pd911V/0XDABoMDzdXQAAAFeLkJAQvfvuuxVuMuLh4aGSkhIlJCSob9+++vDDD9WtWzdt3LhRQ4YMcUO1AICGhNcBAABQz9577z2NGDFCXbp00fbt27V582ZFRUW5uywAgMEIbgAA1LPCwkIlJCToyy+/VHh4uLKzs91dEgDAcDzjBgBAPXI4HPL19dXTTz+tZs2a6cknn3R3SQCABoAZNwAA3MDhcOjgwYMKDg5W48aN3V0OAMBwBDcAAAAAMBxLJQEAAADAcAQ3AAAAADAcwQ0AAAAADEdwAwAAAADDEdwAAAAAwHAENwDAVcdisSglJeWKjtG3b19Nnjy5VuoxTXJysoKCgtxdBgCgGghuAIAG5fDhw5o0aZLCw8Pl7e2ttm3b6q677lJ6enqtnmfVqlV64YUXavWYAADUlKe7CwAAoKpycnIUExOjoKAgzZ8/X127dlVxcbFSU1P15JNPavfu3bV2rqZNm9basa4VxcXF8vLycncZAHBVYsYNANBgTJgwQRaLRZmZmXrggQd0ww036Oc//7mmTJmiTZs2uYw9duyY7rvvPjVu3FgRERH6xz/+4dK/fv16RUdHy9vbW61atdIf/vAHlZSUOPsvXipZVFSkqVOnqm3btvL29tb111+vN99809m/Y8cO/fKXv5Sfn59CQkI0YsQIHTt2rNJrKVuumJqaqs6dO8vPz08DBw7Ujz/+WGkNknTvvfdq9OjRzs9hYWGaNWuWRo4cKT8/P4WGhuof//iHjh49qnvuuUd+fn666aabtGXLlnI1pKSkKCIiQo0aNVJCQoIOHjzo0v/xxx+re/fuatSokcLDw5WYmOjyO7JYLHr99dd19913y9fXV7Nnz670egEAV4bgBgBoEE6cOKHPPvtMTz75pHx9fcv1X/zMVmJiooYOHapvv/1WgwYN0sMPP6wTJ05Ikg4dOqRBgwYpKipK33zzjV5//XW9+eabmjVrVqXnHzlypN599129+uqr2rVrlxYvXiw/Pz9J0qlTp3T77berW7du2rJliz777DMdOXJEQ4cOveQ1nT59Wi+++KKWL1+ujIwMHThwQL/97W+r+ZuRFixYoJiYGH399de64447NGLECI0cOVKPPPKItm7dqg4dOmjkyJFyOBwu5549e7aWLVumDRs26NSpU3rwwQed/f/+9781cuRIPf300/rvf/+rxYsXKzk5uVw4e+6553Tfffdp+/btGjt2bLVrBwBUkQMAgAZg8+bNDkmOVatWXXasJMe0adOcnwsKChySHP/85z8dDofD8eyzzzo6duzosNvtzjGvvfaaw8/Pz1FaWupwOByO2NhYx9NPP+1wOByOPXv2OCQ5/vWvf1V4vhdeeMERHx/v0nbw4EGHJMeePXsq/E5SUpJDkiM7O9ulhpCQEOfnC2soc8899zhGjRrl/BwaGup45JFHnJ9//PFHhyTH9OnTnW0bN250SHL8+OOPLufetGmTc8yuXbsckhybN292OBwOR79+/Rxz5sxxOffy5csdrVq1cn6W5Jg8eXKF1wcAqF084wYAaBAcF8wWVcVNN93k/NnX11cBAQH66aefJEm7du1Sz549ZbFYnGNiYmJUUFCg3NxctWvXzuVY27Ztk4eHh2JjYys81zfffKO1a9c6Z+AutHfvXt1www0Vfq9x48bq0KGD83OrVq2cNVbHhdcaEhIiSeratWu5tp9++kktW7aUJHl6eioqKso5plOnTgoKCtKuXbsUHR2tb775Rhs2bHCZYSstLdXZs2d1+vRpNW7cWJJ06623VrteAED1EdwAAA1CRESELBZLlTcguXiTDIvFIrvdXqNz+/j4XLK/oKBAd911l+bNm1eur1WrVtWq8cKAarVaywXW4uLiSx6nLIxW1Fad6y8oKFBiYqLuv//+cn2NGjVy/lzRslUAQO3jGTcAQIPQtGlTJSQk6LXXXlNhYWG5/lOnTlX5WJ07d9bGjRtdQtGGDRvk7++vNm3alBvftWtX2e12rV+/vsLjde/eXTt37lRYWJiuv/56l39XEmyaN2/usllJaWmpduzYUePjXaikpMRlw5I9e/bo1KlT6ty5s6Tz17Rnz55y13P99dfLauX2AQDqG//lBQA0GK+99ppKS0sVHR2tDz/8UFlZWdq1a5deffVV9ezZs8rHmTBhgg4ePKhJkyZp9+7d+vjjjzVz5kxNmTKlwlASFhamUaNGaezYsUpJSdH+/fu1bt06vf/++5KkJ598UidOnNDw4cP11Vdfae/evUpNTdWYMWNUWlpa4+u9/fbb9emnn+rTTz/V7t279cQTT1QroF6Kl5eXJk2apM2bN+s///mPRo8erR49eig6OlqSNGPGDC1btkyJiYnauXOndu3apffee0/Tpk2rlfMDAKqH4AYAaDDCw8O1detWxcXF6Te/+Y1uvPFGDRgwQOnp6Xr99derfJyf/exnWr16tTIzM3XzzTfrV7/6lR599NFLhpLXX39dgwcP1oQJE9SpUyeNGzfOOfPXunVrbdiwQaWlpYqPj1fXrl01efJkBQUFXdHs1NixYzVq1CiNHDlSsbGxCg8PV1xcXI2Pd6HGjRtr6tSpeuihhxQTEyM/Pz+tXLnS2Z+QkKBPPvlEaWlpioqKUo8ePbRgwQKFhobWyvkBANVjcVT3aW8AAAAAQL1ixg0AAAAADEdwAwAAAADDEdwAAAAAwHAENwAAAAAwHMENAAAAAAxHcAMAAAAAwxHcAAAAAMBwBDcAAAAAMBzBDQAAAAAMR3ADAAAAAMMR3AAAAADAcAQ3AAAAADDc/wNJnb+M+mIDtgAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=5, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 481
        },
        "id": "znJxUunE1aMp",
        "outputId": "c66c5bbc-7780-472f-8d0a-de02c973c7e1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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AAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4Wb4uxL755htp3769lCxZUooWLSpVq1aVPn36yLlz52ymi46OllGjRklAQIC4u7tLlSpVZMyYMRITE5Nu3KSkJFm4cKHUr19fPDw8pHTp0tKnTx85deqUM7oFAAAA4B7nercTSI+qyvPPPy/vv/++VK9eXZ544gnx9vaWixcvyrZt2+TPP/+USpUqiYhIbGystG7dWsLDw6VDhw7Sp08f+eWXX2TWrFmybds22b59uxQtWtQm/nPPPSdLliyRunXryvDhw+XixYuycuVKCQsLkz179khgYODd6DYAAACAe0S+LMQWLFgg77//vrz44ouyYMECcXFxsfk8ISHB/P8zZ86U8PBwGTt2rEyfPt1sHzdunMyYMUPmzp0r48ePN9u3bNkiS5YskVatWsnGjRulSJEiIiLSt29f6dKliwwdOlQ2bNjg4B4CAAAAuJcZqqp3O4mUbt26JRUqVJDixYvL8ePHxdU141pRVaVixYoSHR0tkZGR4unpaX4WGxsr5cqVkzJlysjJkyfN9r59+8rnn38u27Ztk1atWtnECwkJka1bt8qff/4plStXtivf6Oho8fX1laioKPHx8clmbwEAAID/M2ie/dN+MMJRWSCnslMb5Lt7xMLCwuSff/6RXr16SWJioqxevVqmT58u7733npw4ccJm2oiICLl48aIEBwfbFGEiIp6enhIcHCynTp2yuads69at5mepdezYUUREtm3b5oCeAQAAAECyfDc08eeffxYRERcXF2nQoIH88ccf5mcWi0VGjhwps2bNEpHkQkxEMrynKzAwUDZs2CARERFSqVIliY2NlUuXLkm9evXSDHdMGccaFwAAAAAcId8VYpcvXxYRkTlz5kiTJk1k3759Urt2bfnll19k8ODBMnv2bKlevbq88MILEhUVJSIivr6+6cayXg60Tpfd6dNz584duXPnjvnv6OhoERGJj4+X+Ph4EUkuGF1cXCQxMVGSkpLMaa3tCQkJknJEqIuLi1gslgzbrXGtrMM1U94rl1m7m5ubJCUlSWJiotlmGIa4urpm2J5R7vSJPtEn+kSf6BN9ok/0yZF9chN7pZwP+btPyQrXcko/99SfZybfFWLWGVSkSBFZs2aN+Pv7i4jIgw8+KF999ZU0bNhQZs+eLS+88MJdyW/atGkyadKkNO1hYWFSrFgxERGpXLmyNG7cWA4fPixnz541p6lVq5YEBQXJvn375MqVK2Z7o0aNJCAgQLZv3y43btww21u0aCFlypSRsLAwmxUzJCREPDw8ZN26dTY5dOnSRW7duiVbtmwx21xdXaVr165y9epV2b17t9nu7e0tbdq0kXPnzkl4eLjZXrp0aWnZsqVERETI8ePHzXb6RJ/oE32iT/SJPtEn+uSMPvUUe1n7m//7lKxwLaf0+3Tz5k2xV757WMeYMWNk1qxZ8uCDD8r27dvTfB4YGCgnTpyQf/75R3bu3CndunWToUOHysKFC9NMO2zYMFm0aJFs2rRJ2rRpI7GxseLl5SX16tWTX3/9Nc30q1atkt69e0toaKhMnjw53fzSuyJWqVIluXr1qnlFjbMJ9Ik+0Sf6RJ/oE32iT/QpJ3168R37r4j9dwhXxPJbn6Kjo6VUqVJ2Pawj310Rq1WrloiI+Pn5pfu5tf3WrVtZ3tOV+h4yT09PKV++vJw+fVoSExPT3CeW1T1nIiLu7u7i7u6ept3NzU3c3Gw3HBcXl3TvRcvoSZAZtaeOm5N2i8UiFkvaZ7Nk1J5R7vSJPmW3nT7RJxH6lFGO2W2nT/RJhD5llGN22wtKnzKT+m8KSp8K43KytmdnOea7pyaGhISIiMjRo0fTfBYfHy8nTpwQT09PKV26tAQGBoq/v7/s3LlTYmNjbaaNjY2VnTt3StWqVc2XP4uItG7d2vwsNev7w1I/1h4AAAAA8lK+K8SqV68uHTp0kBMnTsiSJUtsPps+fbpcv35dHn74YXF1dRXDMOTZZ5+VmJgYmTJlis20U6ZMkZiYGBk0aJBN++DBg0VEJDQ0VOLi4sz29evXy9atW6VDhw4SEBDgoN4BAAAAQD68R0xE5OTJk9KyZUu5fPmydO3aVYKCguSXX36RzZs3S0BAgOzZs0fKlSsnIslXvoKDg+XQoUPSoUMHadKkiRw8eFDCwsKkWbNmsm3bNvHw8LCJP2jQIFmyZInUrVtXunbtKpcuXZIvv/xSvLy8ZPfu3VKzZk27c+WFzgAAAMgrvNC5YCvQL3QWSb4qduDAARkwYID8/PPPsmDBAomIiJAhQ4bIvn37zCJMJPm+r23btsmIESPk6NGjMnv2bDl27JiMHj1aNm3alKYIExFZvHixzJ8/X0RE5s+fL+vWrZOHH35Y9u3bl60iDAAAAAByIl9eEStIuCIGAACAvMIVsYKtwF8RAwAAAIDCjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcLMeF2Pbt2+Xs2bOZTnPu3DnZvn17Tr8CAAAAAAqlHBdiISEhsmzZskynWb58uYSEhOT0KwAAAACgUMpxIaaqWU6TlJQkhmHk9CsAAAAAoFBy6D1iERER4uvr68ivAAAAAIACxzU7Ez/zzDM2/16zZo2cOXMmzXSJiYnm/WGdO3fOVYIAAAAAUNhkqxBLeU+YYRgSHh4u4eHh6U5rGIY0a9ZM5s6dm5v8AAAAAKDQyVYhdvr0aRFJvj+sWrVqMmLECHnppZfSTOfi4iLFixcXT0/PvMkSAAAAAAqRbBViAQEB5v9funSpNG7c2KYNAAAAAJC1bBViKfXv3z8v8wAAAACAe0aOCzGrffv2yf79++X69euSmJiY5nPDMCQ0NDS3XwMAAAAAhUaOC7Fr165Jr169ZOfOnZm+U4xCDAAAAABs5bgQGzVqlOzYsUMeeugh6d+/v1SsWFFcXXN9gQ0AAAAACr0cV05r166V5s2by6ZNm8QwjLzMCQAAAAAKNUtO//DWrVvSqlUrijAAAAAAyKYcF2KNGjWSM2fO5GEqAAAAAHBvyHEhNnHiRPnuu+9kz549eZkPAAAAABR6Ob5HLDIyUrp27SqtW7eWJ598Upo0aSI+Pj7pTtuvX78cJwgAAAAAhY2hmT17PhMWi0UMw7B5dH3q+8VUVQzDSPf9YoVFdHS0+Pr6SlRUVIaFKAAAAGCPQfPsn/aDEY7KAjmVndogx1fEli5dmtM/BQAAAIB7Wo4Lsf79++dlHgAAAABwz8jxwzoAAAAAADmT4ytiZ8+etXvaypUr5/RrAAAAAKDQyXEhVqVKFbte5mwYhiQkJOT0awAAAACg0MlxIdavX790C7GoqCg5dOiQnD59Wlq3bi1VqlTJTX4AAAAAUOjkuBBbtmxZhp+pqsyePVtmzpwpH374YU6/AgAAAAAKJYc8rMMwDHn55Zelbt26MmbMGEd8BQAAAAAUWA59amLTpk1l8+bNjvwKAAAAAChwHFqInTx5kgd1AAAAAEAqOb5HLCNJSUly4cIFWbZsmXz77bfStm3bvP4KAAAAACjQclyIWSyWTB9fr6pSvHhxmT17dk6/AgAAAAAKpRwXYq1atUq3ELNYLFK8eHFp1qyZDBw4UMqUKZOrBAEAAACgsMlxIbZ169Y8TAMAAAAA7h0OfVgHAAAAACCtPHlYx86dOyU8PFyio6PFx8dHGjVqJMHBwXkRGgAAAAAKnVwVYrt27ZKBAwfKiRMnRCT5AR3W+8YCAwNl6dKl0qJFi9xnCQAAAACFSI4Lsd9++006dOggN2/elPbt20tISIiUL19eIiMjZcuWLRIWFiYdO3aUPXv2SJ06dfIyZwAAAAAo0HJciE2ePFni4uJk3bp10qlTJ5vPxo4dKz/++KP06NFDJk+eLF988UWuEwUAAACAwiLHD+vYunWr9O7dO00RZtWpUyfp3bu3bNmyJcfJAQAAAEBhlONCLCoqSqpWrZrpNFWrVpWoqKicfgUAAAAAFEo5LsT8/f1lz549mU6zd+9e8ff3z+lXAAAAAEChlONCrEePHrJ161YJDQ2V27dv23x2+/ZtmThxomzZskV69uyZ6yQBAAAAoDAxVFVz8od///233HfffXL69GkpWbKkNG/eXMqWLSt//fWX7N+/X65cuSLVqlWTffv2SYkSJfI673wjOjpafH19JSoqSnx8fO52OgAAACjABs2zf9oPRjgqC+RUdmqDHD81sWTJkrJnzx555ZVX5IsvvpB169aZnxUtWlQGDhwoM2bMKNRFGAAAAADkRK5e6FyqVCn56KOPZPHixXLs2DGJjo4WHx8fCQoKEjc3t7zKEQAAAAAKlWwXYlOnTpXY2FiZNGmSWWy5ublJ/fr1zWni4uLk1VdfFW9vbxk3blzeZQsAAAAAhUC2Htbx008/yeuvvy4lS5bM9IpXkSJFpGTJkvLqq6/yHjEAAAAASCVbhdjy5culePHiMnTo0CynHTJkiJQoUUKWLl2a4+QAAAAAoDDKViG2a9cuadeunbi7u2c5rbu7u7Rr10527tyZ4+QAAAAAoDDKViF28eJFqVatmt3TV61aVS5dupTtpAAAAACgMMtWIWaxWCQ+Pt7u6ePj48ViyfE7owEAAACgUMpWleTv7y9Hjhyxe/ojR45IhQoVsp0UAAAAABRm2SrEHnzwQdm8ebOcOXMmy2nPnDkjmzdvllatWuU0NwAAAAAolLJViA0ZMkTi4+Old+/ecvXq1Qyn+/vvv+XRRx+VhIQEeeGFF3KdJAAAAAAUJtl6oXOTJk1kxIgRMm/ePKlTp448//zzEhISIhUrVhQRkQsXLsimTZvk/ffflytXrsioUaOkSZMmDkkcAAAAAAqqbD9JY/bs2TJu3Dj5559/ZOrUqdKuXTsJCgqSoKAgadu2rUydOlWuXbsm48ePl7fffjtPkpwxY4YYhiGGYciePXvSfB4dHS2jRo2SgIAAcXd3lypVqsiYMWMkJiYm3XhJSUmycOFCqV+/vnh4eEjp0qWlT58+curUqTzJFwAAAAAyY6iq5uQPT548KUuXLpVdu3ZJZGSkiIiUK1dOgoODZcCAAVK9evU8SfDIkSPStGlTcXV1ldjYWNm9e7fcf//95uexsbHywAMPSHh4uHTo0EEaN24sv/zyi4SFhUmzZs1k+/btUrRoUZuYgwYNkiVLlkjdunWla9eucvHiRVm5cqV4eXnJnj17JDAw0O78oqOjxdfXV6KiosTHxydP+gwAAIB706B59k/7wQhHZYGcyk5tkK2hiSlVr15d3nzzzZz+uV3i4+Olf//+0qhRIwkMDJQVK1akmWbmzJkSHh4uY8eOlenTp5vt48aNkxkzZsjcuXNl/PjxZvuWLVtkyZIl0qpVK9m4caMUKVJERET69u0rXbp0kaFDh8qGDRsc2i8AAAAA97Z8/ZKvqVOnym+//SYfffSRuLi4pPlcVWXJkiXi5eUloaGhNp+FhoaKl5eXLFmyxKb9gw8+EBGRKVOmmEWYiEjnzp3loYcekrCwMDl79qwDegMAAAAAyfJtIXbw4EGZOnWqTJw4UerUqZPuNBEREXLx4kUJDg4WT09Pm888PT0lODhYTp06JefOnTPbt27dan6WWseOHUVEZNu2bXnYEwAAAACwlS8LsTt37ki/fv2kUaNG8sorr2Q4XUREhIhIhvd0Wdut08XGxsqlS5ekatWq6V5hSz09AAAAADhCju8Rc6TXX39dIiIi5Oeff063YLKKiooSERFfX990P7feIGedLrvTp+fOnTty584d89/R0dEiknw/W3x8vIiIWCwWcXFxkcTERElKSjKntbYnJCRIymekuLi4iMViybDdGtfK1TV5sSUkJNjV7ubmJklJSZKYmGi2GYYhrq6uGbZnlDt9ok/0iT7RJ/pEn+gTfXJkn9zEXinnQ/7uU7LCtZzSzz3155nJd4XY7t27ZdasWfLGG29IvXr17nY6aUybNk0mTZqUpj0sLEyKFSsmIiKVK1eWxo0by+HDh23uN6tVq5YEBQXJvn375MqVK2Z7o0aNJCAgQLZv3y43btww21u0aCFlypSRsLAwmxUzJCREPDw8ZN26dTY5dOnSRW7duiVbtmwx21xdXaVr165y9epV2b17t9nu7e0tbdq0kXPnzkl4eLjZXrp0aWnZsqVERETI8ePHzXb6RJ/oE32iT/SJPtEn+uSMPvUUe1n7m//7lKxwLaf0+3Tz5k2xV44fX+8ICQkJUqdOHfH09JR9+/aJm9v/nREYMGCAfPzxxzaPr//hhx+kW7duMnToUFm4cGGaeMOGDZNFixbJpk2bpE2bNhIbGyteXl5Sr149+fXXX9NMv2rVKundu7eEhobK5MmT080xvStilSpVkqtXr5pX1DibQJ/oE32iT/SJPtEn+kSfctKnF9+x/4rYf4dwRSy/9Sk6OlpKlSrl2MfXO0JMTIx5f1bKJxqm1KJFCxER+eabb8yHeGR0T1fqe8g8PT2lfPnycvr0aUlMTEwz7DGre85ERNzd3cXd3T1Nu5ubm03hKJK8wNIbWmldYPa2p46bk3aLxSIWS9pbAjNqzyh3+kSfsttOn+iTCH3KKMfsttMn+iRCnzLKMbvtBaVPmUn9NwWlT4VxOVnbs7Mc81Uh5u7uLv/5z3/S/Wz79u0SEREhPXr0kNKlS0uVKlUkMDBQ/P39ZefOnRIbG2vz5MTY2FjZuXOnVK1aVSpVqmS2t27dWr744gvZuXOntGrVyuY7rO8PS90OAAAAAHkpXxViHh4ead77ZTVgwACJiIiQ8ePHm0MTRUSeffZZmTx5skyZMsXmhc5TpkyRmJgYmTBhgk2cwYMHyxdffCGhoaE2L3Rev369bN26VTp06CABAQEO6B0AAAAAJMtXhVhOvPLKK/Ltt9/KjBkz5JdffpEmTZrIwYMHJSwsTJo1ayYjRoywmT4kJESeffZZWbJkiTRp0kS6du0qly5dki+//FJKlCiR7r1mAAAAAJCX8uV7xLLD09NTtm3bJiNGjJCjR4/K7Nmz5dixYzJ69GjZtGmTeHh4pPmbxYsXy/z580VEZP78+bJu3Tp5+OGHZd++fVKzZk1ndwEAAADAPSZfPTWxIIqOjhZfX1+7nowCAAAAZGbQPPun/WCEo7JATmWnNijwV8QAAAAAoKChEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACejEAMAAAAAJ6MQAwAAAAAnoxADAAAAACfLd4XYhQsXZN68edKhQwepXLmyFClSRMqVKyePPPKI7N27N92/iY6OllGjRklAQIC4u7tLlSpVZMyYMRITE5Pu9ElJSbJw4UKpX7++eHh4SOnSpaVPnz5y6tQpR3YNAAAAAEQkHxZiCxculJEjR8qpU6ekQ4cOMnr0aHnggQfk22+/lZYtW8qXX35pM31sbKy0bt1a5s6dK0FBQTJy5EipVauWzJo1S9q0aSO3b99O8x3PPfecDB8+XFRVhg8fLp06dZLVq1dLs2bNJCIiwlldBQAAAHCPcr3bCaTWvHlz2bp1q7Ru3dqm/X//+5+0bdtWXnjhBenVq5e4u7uLiMjMmTMlPDxcxo4dK9OnTzenHzdunMyYMUPmzp0r48ePN9u3bNkiS5YskVatWsnGjRulSJEiIiLSt29f6dKliwwdOlQ2bNjghJ4CAAAAuFcZqqp3Owl7dezYUcLCwmT//v3StGlTUVWpWLGiREdHS2RkpHh6eprTxsbGSrly5aRMmTJy8uRJs71v377y+eefy7Zt26RVq1Y28UNCQmTr1q3y559/SuXKle3KKTo6Wnx9fSUqKkp8fHzypqMAAAC4Jw2aZ/+0H4xwVBbIqezUBvluaGJm3NzcRETE1TX5Ql5ERIRcvHhRgoODbYowERFPT08JDg6WU6dOyblz58z2rVu3mp+l1rFjRxER2bZtm6O6AAAAAAAFpxA7e/as/PTTT1K+fHmpX7++iIh5P1dgYGC6f2Ntt04XGxsrly5dkqpVq4qLi0uW0wMAAACAI+S7e8TSEx8fL08//bTcuXNHZsyYYRZRUVFRIiLi6+ub7t9ZLwdap8vu9Om5c+eO3Llzx/x3dHS0mWN8fLyIiFgsFnFxcZHExERJSkoyp7W2JyQkSMoRoS4uLmKxWDJst8a1sl4RTEhIsKvdzc1NkpKSJDEx0WwzDENcXV0zbM8od/pEn+gTfaJP9Ik+0Sf65Mg+uYm9Us6H/N2nZIVrOaWfe+rPM5PvC7GkpCQZMGCAbN++XQYNGiRPP/30Xc1n2rRpMmnSpDTtYWFhUqxYMRERqVy5sjRu3FgOHz4sZ8+eNaepVauWBAUFyb59++TKlStme6NGjSQgIEC2b98uN27cMNtbtGghZcqUkbCwMJsVMyQkRDw8PGTdunU2OXTp0kVu3bolW7ZsMdtcXV2la9eucvXqVdm9e7fZ7u3tLW3atJFz585JeHi42V66dGlp2bKlREREyPHjx812+kSf6BN9ok/0iT7RJ/rkjD71FHtZ+5v/+5SscC2n9Pt08+ZNsVe+flhHUlKSPPPMM/Lxxx/LU089JR9//LFYLP83mvKHH36Qbt26ydChQ2XhwoVp/n7YsGGyaNEi2bRpk7Rp00ZiY2PFy8tL6tWrJ7/++mua6VetWiW9e/eW0NBQmTx5cro5pXdFrFKlSnL16lXzihpnE+gTfaJP9Ik+0Sf6RJ/oU0769OI79l8R++8Qrojltz5FR0dLqVKl7HpYR769IpaUlCQDBw6U5cuXS58+fWTZsmU2RZhI1vd0pb6HzNPTU8qXLy+nT5+WxMTENPeJZXXPmYiIu7u7+ej8lNzc3MyHiVi5uLikey+adYHZ2546bk7aLRZLmvmXWXtGudMn+pTddvpEn0ToU0Y5ZredPtEnEfqUUY7ZbS8ofcpM6r8pKH0qjMvJ2p6d5ZgvH9aRsgh7/PHH5ZNPPkl3xgUGBoq/v7/s3LlTYmNjbT6LjY2VnTt3StWqVaVSpUpme+vWrc3PUrO+Pyz1Y+0BAAAAIC/lu0LMOhxx+fLl8uijj8qKFSvSLcJEki9BPvvssxITEyNTpkyx+WzKlCkSExMjgwYNsmkfPHiwiIiEhoZKXFyc2b5+/XrZunWrdOjQQQICAvK4VwAAAADwf/LdPWJvvPGGTJo0Sby8vOSll15K97Jgr169pFGjRiKSfOUrODhYDh06JB06dJAmTZrIwYMHJSwsTJo1aybbtm0TDw8Pm78fNGiQLFmyROrWrStdu3aVS5cuyZdffileXl6ye/duqVmzpt358kJnAAAA5BVe6FywZac2yHf3iJ05c0ZERGJiYmTq1KnpTlOlShWzEPP09JRt27bJG2+8IatWrZItW7ZI+fLlZfTo0TJx4sQ0RZiIyOLFi6V+/fry/vvvy/z588XLy0sefvhhmTp1qlSvXt1RXQMAAAAAEcmHV8QKGq6IAQAAIK9wRaxgy05tkO/uEQMAAACAwo5CDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDAAAAACcjEIMAAAAAJyMQgwAAAAAnIxCDMinqlSpIoZhpPlvyJAhdzs1p2NeoDBITEyU0NBQqVq1qnh4eEj16tVlypQpoqp3O7UMse39H+YF0lMQt2vkHxRihdgbb7yR5gcjKCjobqeVIUfne+HCBXnqqaekZMmS4uHhIfXr15cDBw7k27j79++XS5cumf9t3LhRREQeffTRXMd2FOZFMmdte9OnTxfDMGTEiBEFKrYjFIR5MWPGDHn33Xdl0aJFcvToUZkxY4bMnDlTFi5cmOscHbXOOWvbKwjrmyPnRUH7vU6tICy/1ArCdo3Cj0KskKtbt67ND8eOHTvudkqZclS+//zzjwQHB4ubm5usX79efv/9d5k9e7YUL148X8YVESldurSUK1fO/G/t2rVSvXp1ad26da5jO0JBnBfvvvuuNGjQQHx8fMTHx0datGgh69evz3W+Io7f9vbv3y+LFy+WBg0a5GncvI7tyHlsVVDmxa5du6Rnz57StWtXqVKlivTu3Vs6dOgg+/bty4NMHbPOOWM/lNfLz1HrnKPnhSOWX0Hc/gpazo7erh1h2rRp0qxZM/H29pYyZcpIr1695Pjx4/k6tiNzvpsoxAo5V1dXmx+OUqVK5Trm9u3bpXv37uLv7y+GYciaNWtyn+j/54h8RZLPWFWqVEmWLl0qzZs3l6pVq0qHDh2kevXq+TJuanFxcbJixQp55plnxDCMXMVy1PIriPOiYsWKMn36dPn555/lwIED0qZNG+nZs6f89ttvuc7TUeuyiEhMTIw8+eST8sEHH+RJoevI2I6cxyIFa160bNlSNm3aJH/88YeIiBw6dEh27NghnTt3znVsEceucyJ5u+1ZOWL5OXqdE3HMvHDE8iuI219By9nR27UjbNu2TYYMGSJ79uyRjRs3Snx8vHTo0EFiY2PzbWxH5nw3UYgVchEREeLv7y/VqlWTJ598Us6ePZvrmLGxsdKwYUN555138iBDW47IV0Tku+++k6ZNm8qjjz4qZcqUkcaNG8sHH3yQb+OmtmbNGrl+/boMGDAg17EctfwK4rzo3r27dOnSRQIDA6VmzZoydepU8fLykj179uQ6tqPWZRGRIUOGSNeuXaVdu3Z5FtNRsR05j0UK1rwYN26cPPHEExIUFCRubm7SuHFjGTFihDz55JN5Et+R65xI3m57Vo5Yfo5e50QcMy8csfwK4vZX0HJ29HbtCD/++KMMGDBA6tatKw0bNpRly5bJ2bNn5eeff863sR2Z893kercTgOPcd999smzZMqlVq5ZcunRJJk2aJA8++KAcOXJEvL29cxy3c+fODjnT46h8RUROnTol7777rowaNUomTJgg+/fvl+HDh0uRIkWkf//++S5uah9++KF07txZ/P39cx3LUcuvIM6LlBITE+Wrr76S2NhYadGiRa5iOXJd/uKLL+TgwYOyf//+XMVxdmyRvJ3HIgVvXqxcuVI+/fRT+eyzz6Ru3boSHh4uI0aMEH9//1xvI45c56zyettz9PomkvfrnFVezwtnLL+CtP1ZFYScHbldO0tUVJSIiJQoUaLAxHZkzk6lyJWoqCgVEY2KirrbqWTpn3/+UR8fH12yZEmexRQR/eabb/IsXkp5ma+bm5u2aNHCpm3YsGF6//3358u4KZ05c0YtFouuWbMmz2Ja5eXyK6jz4vDhw+rp6akuLi7q6+urP/zwQ57Ftsqrdfns2bNapkwZPXTokNnWunVrfemll3KZoWNjO2IeF8R5UbFiRV20aJFN25QpU7RWrVq5ipuevN7f5/W258jlp+rY7dqR+2SrvFx+BW37Uy1YOTtiu352rv3/5VZiYqJ27dpVg4ODcx/MSbEdmXNeyE5twNDEe4ifn5/UrFlTTpw4cbdTsUte5lu+fHmpU6eOTVvt2rVzPfTDUXFTWrp0qZQpU0a6du2aZzEdoaDOi1q1akl4eLjs3btXXnjhBenfv7/8/vvveRZfJO/W5Z9//lkuX74sTZo0EVdXV3F1dZVt27bJggULxNXVVRITE/NlbEfM44I4L27evCkWi+3ProuLiyQlJeU414zk9f4+r7c9Ry4/Ecdu187YJ+fl8ito219By9mZ27UjDBkyRI4cOSJffPFFgYntyJydjaGJ95CYmBg5efKkPP3003c7FbvkZb7BwcFpnq7zxx9/SEBAQL6Ma5WUlCRLly6V/v37i6tr/t5cC+q8KFKkiNSoUUNERP71r3/J/v37Zf78+bJ48eI8+468Wpfbtm0rv/76q03bwIEDJSgoSMaOHSsuLi75MrYj5nFBnBfdu3eXqVOnSuXKlaVu3bryyy+/yJw5c+SZZ57Jca4Zycv9pyO2PUcuPxHHbdfO2ifn5fIraNtfQcvZmdt1Xhs6dKisXbtWtm/fLhUrViwQsR2Z892Qv4/skCsvv/yydO/eXQICAuTixYsyceJEcXFxkT59+tzt1NLlyHxHjhwpLVu2lLfeeksee+wx2bdvn7z//vvy/vvv58u4Vj/99JOcPXu2QOzQC8u8SEpKkjt37uQqhqPWZW9vb6lXr55Nm6enp5QsWTJNe36KnVpezOOCOC8WLlwooaGh8uKLL8rly5fF399fnnvuOXn99ddzla+IY/efjtj2nLm+ieTNOifiuP2QM3+v8/v2l578nLMjt2tHUVUZNmyYfPPNN7J161apWrVqvo/tyJzvpnu2ENu/f79MnDhRdu3aJfHx8VK/fn0ZNWqUPPbYY3c7tTxz/vx56dOnj/z9999SunRpeeCBB2TPnj1SunTpu51auhyZb7NmzeSbb76R8ePHy+TJk6Vq1aoyb968XD/VyFFxrTp06CCqmiexHK0gzovx48dL586dpXLlynLjxg357LPPZOvWrbJhw4ZcxS1o254jOWoeF0Te3t4yb948mTdvXp7HduQ6V5D2QyKOXeccNS8ctfwK4vZX0HJ25HbtKEOGDJHPPvtMvv32W/H29pbIyEgREfH19RUPD498GduROd9NhhakvWse2bJli3Ts2FGKFi0qTzzxhHh7e8uqVavkzz//lFmzZsno0aPtjhUdHS2+vr4SFRUlPj4+Dsw6/4iJiTHHrTdu3FjmzJkjISEhUqJECalcufJdzg5ZYfn9n//85z+yadMmuXTpkvj6+kqDBg1k7Nix0r59+7udWqHBPIazsc79n4I4Lwpiznlt0Dz7p/1gRPbjZ/Tuu6VLl+b6lQyOiu3InPNadmqDe64QS0hIkKCgIDl//rzs2bNHGjVqJCLJj8Fs3ry5nDlzJlv3tdyLhdjWrVslJCQkTXv//v1l2bJlzk8I2cLyAwAg/3J0IQbHyk5tcM8NTdy8ebOcPHlSBg4caBZhIsmXNidMmCADBgyQjz/+OF+P7b3bHnrooQIxTCU7OzKR7O3MHLWTdMbON6+XX0GeF4AzFMR1uSDm7CjMC6SH9QJ54Z4rxLZu3SoiyeO8U+vYsaOIiGzbts2ZKeUpRxYfjsLODIVFfihKHRk7v2x/+WE+F/Z54SgF8TfKUQrivCho65tIwcwZ9457rhCLiIgQEZHAwMA0n5UrV068vLzMadJz584dmyf3WN/sfe3aNYmPjxcREYvFIi4uLpKYmGjzHglre0JCgs0VCRcXF7FYLBm2W+NaWR+Zm5CQkKY97nb6Y2gzcv16ks27MwzDMN+nkTr3EYvtf7Tr/OeT7O5T3G03u+P+/Xfy37m5uUlSUvq5W9uzEzdlbHuWU9xt+zcda1yrjJafm5ubxN22P9/oaMlwHcur5WfPupfd5Zd6OVmlXvdysl6I2Lc9jfrA/thzBtnOg8zWvbxafqlzz+66nPwuyfT3Eanbc7r8slr3cjqP7dnv5XTdyGrdy+7ys3dfnt18M9tHpM49u7Ht/X3K6TzO7PcpOd/s/Ualt/wyyn3Yf+2Pu/DFjJdf6nUvu/PCnt+n7Ma1xrb3OCKn219W617cbftfP/vPP/b/PuVk+dl7bJSd+XztWoJdv0/ZjWtdj+093svp9pfVuvfSe/Yvv3nP2X8Mm524IiILXlC7fp9EJFvr8tzBCXb9PtnTp9wcl9+4cUNExK7RR/fcPWIdOnSQjRs3SkREhPmOipQqVKggMTExZoGV2htvvCGTJk1ydJoAAAAACqhz585l+a6ze+6KWG6NHz9eRo0aZf47KSlJrl27JiVLlszwiS53W3R0tFSqVEnOnTuXpw8UcVRcR8YuaHEdGZucHR/XkbELWlxHxi5ocR0Zm5wdH9eRsQtaXEfGJmfHx3Vk7IIWNy+pqty4cUP8/f2znPaeK8R8fX1FRDK84hUdHS3FixfP8O/d3d3F3d3dps3Pzy/P8nMkHx8fh6y0jorryNgFLa4jY5Oz4+M6MnZBi+vI2AUtriNjk7Pj4zoydkGL68jY5Oz4uI6MXdDi5hVrvZGV7A3qLASs94aldx9YZGSkxMTEpHv/GAAAAADklXuuEGvdurWIiISFhaX5zPrWdus0AAAAAOAI91wh1rZtW6lWrZp89tlnEh4ebrZHRUXJW2+9JUWKFJF+/frdvQQdwN3dXSZOnJhmSGV+jevI2AUtriNjk7Pj4zoydkGL68jYBS2uI2OTs+PjOjJ2QYvryNjk7Pi4joxd0OLeLffcUxNFRLZs2SIdO3aUokWLyhNPPCHe3t6yatUq+fPPP2XWrFkyevTou50iAAAAgELsnizERET27dsnEydOlF27dkl8fLzUr19fRo0aJY8//vjdTg0AAABAIXfPFmIAAAAAcLfcc/eIAQAAAMDdRiEGAAAAAE5GIQYAAAAATkYhVohYb/criLf9JSUlFYiYiYmJeR6zINu1a5fExsaKSMFb7wpavgCAnGOfj/yIQqwQMQxDVFUMw5DIyEiHFCKOYrH836qYVztLi8UicXFxcu7cObl06VKuY9+8eVNeffVV2bJli/z9998Zxspv8z0hIUFWr14tGzdulISEBLM9t/P5xo0b0rNnT3nrrbdEJHn9yysJCQkSHh4uy5Ytk7179+b5D6h1O7l06VK+W14o3Bx1MMh6/H+s8zgpKalAHHw74yRqXs4LVS0Q8zW1vPyNsnLkdpdyHuf1uuyobaSgbXv5AYVYIZGQkCDbtm2TAQMGSIsWLeSRRx6RDh06yMsvvyy7du262+ll6PDhwzJhwgTp1auXTJ8+XSIiIvJkZ3nnzh1Zvny51K5dW9q3by8jR46UAwcO5Cr2e++9JzNnzpTOnTtLhw4dZNq0aXLw4EGJiYmxmW7hwoXyyy+/ZGsHfefOHfnpp58ccsVtzZo1MmDAAFm2bJm4urqa7YZhyPXr13Mcd8WKFfL333/LzJkzZcCAAXLq1CkRyf1Vw7Nnz8rIkSOlSZMm8swzz0jv3r3l008/zVVMq6SkJNm1a5cMHjzY3E4eeughGT58uGzfvj1PvsPK+iNUUK6iOuNgMDExMc/iF9Qf+rw+GLTOg5Qnsxwlrw/AHbWNWOexxWJxyMF3XrPm6Mhc83JeGIZhxsqr7dDRRejPP/8shw8fTveznOZw48YNad26tWzatCnHMTJjGIacP39e4uLi8nxddtQ2UtC2vXxBUSi8/fbb6uPjo4ZhaI0aNTQoKEgNwzD/q127ts6dO1cvXbqU6+9KSkrKg4xVv/zySy1btqxNnn5+frpixYpcx542bZr6+fmpn5+fNmvWTF1cXLROnTp64cIFVVW9cOGCrl+/Xs+ePWt3zNdee00Nw9D27dtrrVq11DAMLVasmHbu3FnfffddjYyM1J07d6phGDpp0qRs5btgwQINCAjQPXv2ZOvv7HH//fdrcHCwhoeHm22//vqrvvXWW9q2bVutXbu2Pv/887p169Zsxa1fv77WqFFDK1SooIZh6BNPPKFXr17Ndb6DBg3SokWLaqdOnXT8+PFaoUIFbdiwoZ47d07PnDmjH330kU6aNEn37duX7dgLFixQPz8/NQxDK1WqpFWqVLFZ/2rUqKELFizQK1euqGrerev3utu3bzs0fmJiYrrtOVl+MTExmX6e03UiMjJS169fr+fOnUvzWUJCQo7jL168WNu3b6/Hjx9X1YznRU7FxMToH3/8kWnc/LSdnD59Wr/88kt9+eWXdfTo0frZZ5/p3r179cKFCxoXF5fjuAkJCQ7pZ2RkpG7cuFGXLVum33zzjf7111+qmjfLcffu3Tpu3Djt1q2bzpgxw/z9s8pJf3bu3KkfffSRnjlzJs1nucl5wYIF2qtXrzQ5ppaTnH/88Udt3ry5jhkzJscx0rN48WI1DEMDAgL022+/zZOYVtHR0bpkyRKtWbOmuru76xNPPGFu47nN/88//9Svv/5aR48eraNGjdJPPvlEt23bpidOnNBbt27l+Dscte2pOm77yw8oxAqBU6dOqaenpz744IN66tQpPX/+vMbHx+u5c+f0nXfe0ZCQEPNAs23btvrzzz9nK/7Nmzf12LFjevPmzTzL+c8//9QKFSpohQoVdNWqVbp27VodN26ceTB87NgxVbXdsScmJtq1oz9z5oyWLl1aW7ZsqVeuXNHTp0/r5MmT1TAM/f7773Xo0KFasmRJNQxDy5YtqxMmTNB//vkny7iHDx/WoKAgfeihh3Tbtm06c+ZMbd++vXlgX65cOQ0KClJPT09dvnx5mvwzU7t2bQ0JCdHz58/btB86dEhXrlypb7/9tq5cuTLbhfSpU6fUxcVFp0yZYradO3dOGzVqpIZhqKenp00h0rNnz3R/YFOLiIhQwzB0/vz5evHiRX3iiSfUMAxt1KiR/vTTT6qavCPP7o7z5MmT6uHhoQMGDDAP3nfs2KHFixfXCRMmaOPGjW3yDQ4Otnt9Pn36tPr4+GiTJk302LFjeuLECf3ll190xowZ6uPjo0WKFDHjDhw4UK9fv56t3FNav369vv322/rUU0/pyJEj9fPPP9f9+/frX3/9ZR505+RHJeUBe17asWOHfvrpp7pw4UJdv3693rhxQ1Xz5mBw4cKF+vjjj2uXLl10yZIlafYjOZkPCxYs0FWrVpkHrSlj5XYe3Xffffrmm2+aByTpycm6PXr0aK1bt65u2bJFVdMuy5zm/a9//UsNw9B27drpiRMnchQjI3/88YcOHDhQixQpoj4+Pjp69GiNiorKk/Vi48aNOmfOHO3bt6+OGjVKP/30U92+fbuePXtW4+PjVTX769+XX36Z5iSkYRjq7e2tISEhOmfOHD158mSu8k5KSsqzYnfHjh3apk0bM09fX1999tln8+SE1ooVK7R06dI282HUqFHm56lPjtjbp5YtW2rJkiW1bdu2GhoaqmFhYWnyPXv2rK5evTpbxwy1a9fWJk2a6J9//mnTfuvWLQ0PD9dTp07ZtGdn+2vXrp3WrFlTd+7cabbdvHlTN2zYoG+88YbOnz9fP/vsM/3999+zdcDfoEEDLVu2rJYoUUJ9fHx0zpw5Gh0draq531e/+uqrahiGlipVSitXrqyGYWifPn1UNblI++OPPzQ8PFz/+OMPs8ixJ+81a9Zow4YN02wjpUuX1o4dO+rbb7+dZhnYwxnbnmrebn/5BYVYIRAaGqplypQxD4BV026Qhw8f1n79+mnRokW1Vq1aeuDAAbvjT5s2TZs2bapvvfWWbt68WS9cuJDlTubKlSvmj2l6xo8fr35+fvrll1/atH/xxRc2O5yUffn555918eLFaQ6+UpswYYKWK1dOv//+e7Ptr7/+Ug8PD73vvvu0QoUKOm7cOO3fv7/6+vpqsWLF9L///a+qZv1jtHbtWvX29tZ3331XVVUvXbqka9eu1TFjxuh9992nFotFDcPQ6tWr67hx43TdunV6586dTGNai5qZM2fatI8aNcq8ymn977777tNvvvkm03gpLVu2TH18fMz5fPXqVX3++efV1dVVJ06cqJcuXdLjx4/rwoULtXbt2moYho4fP15VM9+pjxkzRkuWLGleRfv111+1R48eahiG3n///frLL7/YnWNKU6ZMUX9/f5t1+e+//9aAgACtWLGiduzYUdetW6fz5s3TZs2aqWEY+thjj9n1gz9hwgQtWbKkzXqhmnzGf+TIkdqkSRNdv369du3aVQ3D0EceeSTTg/H0/PPPP/rKK6+oYRjq6upqs+xKliypPXr00KVLl9pV+KeUer2098coqx/m2NhYfe+992zWM39/f3377bezlV96/vnnHx0+fLh5gGkYhhYtWlRXr15tTpP66pM9fTp58qQahqGBgYHauXNnnT59uu7YscMsHq1Wr16tW7ZsydaP9okTJ9QwDJ04cWKazy5cuKCbN29O94pWVk6fPq3FixfXxx9/3Kb94sWLOm3aNB07dqzOnDlTv/rqK/NEiD15W/Nt2LChuri4aI0aNfTbb781DyZzc8ASGRmprVu3VsMwtH79+lqpUiU1DMMcsfDHH3/ogQMHdPfu3Xr69GlVte9AMCoqSidOnKguLi7m/tL6X8WKFbVXr1764YcfZvsqqvXkXvXq1XXRokUaHh6uK1eu1DfffFMfffRR82A2ICBA58+fb/eZ//Pnz+u///1v/fTTT/Xy5cs2n9l7cjA9Fy9e1EaNGmmRIkW0d+/eOnnyZO3SpYsahqFdu3bV2NjYHMVVTT7ZVqNGDa1Vq5auW7dODx06pL169VLDMPTMmTP62Wef6YMPPqhBQUE6cuRIuwv4S5cuqWEY6uLiYhZ5ZcqU0e7du+vs2bPNQmfEiBEaGBhoHmdkNY+s63Hq/c7XX3+tISEh5gnD2rVr68yZM81ix571zbq/SDlKJSYmRjt27Gizjy5WrJi2bt1a169fb9e8sOb8xhtv6OzZs835khf7zjNnzmipUqW0bdu2GhMTo1euXNFJkyZp6dKl9ZtvvtHevXuri4uL+vr66oMPPqiffPKJXXHPnj2rAQEB6u/vr9OnT9e9e/fqrFmzNDAwMM3IkOXLl9tdTDpq21N13PaXn1CIFQL//ve/tVq1auZZDGsBlN7Z4Xnz5qlhGDpgwAC741uHnrm6umrJkiW1e/fuunDhQt23b1+6Z+5iYmL05Zdf1oEDB2a4kTRs2FB79eplFlVxcXGakJCgCQkJ2qNHD/Xx8dEdO3aY09++fVuHDBmiFoslyx/oevXqabdu3Ww22i1btqiHh4e2adNGDx8+bLbv2rVLfXx8tHr16llu0NbPQ0NDtXTp0rp7926bzz/88EM1DEObN2+uderUUcMw1GKxZFmIWYsa65nymzdv6rvvvmseAI0ZM0YXLVqkvXv31mLFimnFihXNabPaka1Zs0ZdXV118+bNqqq6Z88eLV++vA4dOjTNtNHR0dqyZUt1d3c3h+ZlpFy5cvroo4+mWf5Tpkwxr7QtXrw4W2fqVFV79OihtWvXtrkyuHPnTi1VqpQ++uijNgfbcXFx2r17dzUMw7yCmpmHHnpI69evb15VTEhIMJfpd999p76+vrpnzx49d+6cPvLII2oYRraHm8ycOVOLFSumDz/8sG7ZskWPHz+uX3zxhU6aNEm7detmHrw0adIkWwX1f//7X33sscd07dq1aQqO3PwYffDBB1qsWDGtXbu2jhkzRt9++23zbOnkyZNzFNNq/vz56uvrq08//bSeOnVKt27dqtWqVdMmTZro9evX9aWXXtIyZcpo48aNderUqXYfeP73v/9VwzC0SpUqZoFXuXJlffzxx/Xdd9/VX3/9VVVV/f39tX///tk6aHvllVe0VKlSun37drPtypUr+tprr2nFihXNA5X7779fV6xYYfd8f/XVV7V06dK6YcMGM5etW7dqqVKlbA6AfH199dFHH7X7wPiVV17RkiVL6meffaYvvviieRBl78FkZt566y318/PTt956S1WTD7a6d++uzZs319WrV2v58uXNM/bdu3fXXbt22RV3zpw56u7urh07dtS1a9fqoUOH9LXXXjOXpZubm3m123qix55l9+qrr2qJEiXSnGhRTT4BtWXLFp0wYYK5HAcPHmxX3IkTJ5oH6nXr1tWXXnpJw8LC0pz8SUxMNH97165dqytXrsw07uuvv67FihXTRYsWqWryb9yJEyfMfdrHH3+c5m+OHTuW5ncnPaGhoVqiRAmbHH766Se1WCz69NNPq6urq1atWtUsrr29vbMc6m2dV6+88ooGBAToV199pe+//74+9NBD6uHhoYZhaLVq1bR///5atGhRbdasmUZGRmaZqzVmyt/A+Ph4XbNmjVncdOzYURs3bmwWZCEhIXafzFqwYIGWLFlS165dq6rJJ4jGjx+vhmHoww8/rAsWLNA5c+bowIEDzZEyq1atsjtn6/LYuHGj1qtXTw3D0Kefftq8+pOTfbP1GOPHH380286fP69ubm7asGFDrVKlij7xxBPap08fcxlOnTo1y/V5woQJ6u3tneYE+I0bN/Shhx7S6tWrm6NbLBaL3b9Rjtr2VB23/eUnFGKFgPXg97fffstwmpQr/SOPPKKVK1e26zLx8ePH1cvLS1u2bKmLFi3Snj17apkyZcyzG/3799dPPvlEjxw5Yu4Y9+zZo76+vtqzZ890Y548eVKrVKmizz33XLqfb9q0SYsWLarPPPOM2Xb06FFt0KCBdurUKct8q1atqi+//LJN+6JFi9RisZg7elU1z8o8/fTTWrFiRZsCLTORkZHaqlUrDQwMtPmh6dWrl5YrV0537Nihp06d0pkzZ+qsWbOyjFeuXDl9+umn9dq1a6qq+r///U+rVaumbdu2NceEqyb/OM2dO9e8WmOPo0ePqqenp44cOVJVk8/iubq6mgea1rPm1nkxbdo0LVasWKYFyP/+9z81DEPff/99s81a8F+5ckUnTJigLi4uWr58eXOIpj3i4uL0hRdeUB8fH5udbGhoqBqGof/73//M77J+PnfuXHV1ddVPP/0009g3btzQf//73+rv75/uWb6lS5eqp6enbty4UVWTr2D4+/vro48+qqr2F5IBAQHatWvXdE9QXLhwQdeuXauDBw82z8R+8MEHdsW13stWtGhRve+++zQ0NFR3796dJi/rD1FsbKzOnTvXLMAzEhgYqI0bNzavaNy+fVs3b96s1apV01KlSqUpcOPj43XLli12bSvVq1fXdu3a6cWLF822oUOHqo+Pj3bs2FE9PT21YcOG5gF9cHBwmiIzPTdv3tQWLVpo+/btdfPmzfrWW29p06ZN1dXVVS0WizZo0MC8spB6P5CV8uXL6yOPPGKeIIqKitKnnnpKDcPQWrVq6WOPPWYzPHbcuHF2xX3ggQe0TZs25v0v4eHh2rRpUy1VqpS+8cYbumzZMl2wYIE+/PDD5r7VnmKsfPny2rt3b7OIXbBggfr6+qqbm5u+9dZbGhUVpao5OxisVq2a9urVy2b5LViwwDzZ1Lx5c33ppZf0scceUzc3N/X29rY5cMxIQECAhoSEpBnZsGPHDi1Tpox26tRJO3TooIZhaJ06ddIMSctI69attXnz5ua2Fx8fn26/Dxw4oO3bt1cXFxedPn16lnGbN2+uxYoV006dOpkFh5ubmwYHB+uUKVN0//79NtPHxsZq+/bt1TCMTK/UBwYGppm/qslXLapVq6ZBQUEaHx9v7q/u3LmjY8eO1UqVKmV5MrJmzZrao0cPm6HsGzduVDc3N73//vvNg9TffvtNR4wYoYaRfI9vVpKSkvTixYvauHFjbdeuncbGxurNmzd1586d+tprr2nz5s3VYrGoi4uL+vv768iRI3XlypVZDnUrX768zYm9AwcOaP369bVRo0ZmAaWqum/fPu3UqZMahqGvv/56lvmqJt8/7+npaR4f7dixQ/39/XXAgAHmSdLExES9fPmyec9X69atsxwNYd32rCd8k5KSdM2aNVq1alWz2LBnf5aeNm3aaOvWrW1OJluH6Hfs2NE8Lrh8+bJ+8cUXWrRoUQ0KCjKPITJiXW7W9SI+Pt7s5/Tp07VevXp69epV/fHHH7VKlSpapkwZ/eOPP7LM11Hbnqrjtr/8hEKsENixY4d5f86mTZvSvQKT8urYhAkTtFixYnro0KEsY3///ffq6uqqb7zxhqomXzK3jqtu1aqVenl5qaurqzZo0EBHjBihP/74o44ZM0YNw7DZgaYUHh6uxYsXN8erp3dg3K1bN/Xz89Pff/9dVVU//vhjNQxDv/vuu0zzDQsLU8MwzLO4qqrXr1/Xrl27apEiRdL9m2effVZLlCihR44cyXJ+WB06dEh9fHy0b9++eufOHY2NjVWLxaKPPvqozY9kVgdAe/bsUcMwbK5QLV++XA3DsLn3yXrAnZSUpC1atNCgoKAsh2gmJSXp7du39amnnlKLxaKLFy/W7du3q5eXl86ZM8cmR2uec+bMURcXF7PoSU/fvn21VKlSZn7pFSlffvmlWbC//PLLWf4gWWNYrwR26tRJP/roI50+fboaRvJDXNK7P+7tt99Wi8VicwUjo9iTJk0yD55TXn25efOmdurUSb29vW360rp1a/M+Q3scPXpUvby8dMKECWZbeler7ty5oz/88INWq1ZNS5QokeWVhCNHjqhhGNq0aVPzB8YwDPXy8tKOHTvq/Pnz9ejRozZ/Yy2Wg4ODM4y7b98+dXV11QULFqT57JtvvlHDMHTs2LGq+n8F3tGjR7Vp06ZZXlG3xp47d65Nu3XY5pAhQ8whfnv37tXOnTurYRh2D7HZuHGjlixZ0hxudPnyZQ0LC9Phw4ebV6NdXFy0fv36OnnyZF29erVZlGTE+qCdxYsXm21LlixRNzc3HT58uFms3rlzR9evX6/Vq1dXLy8vm5M76blx44a2a9dOW7RoYbZZT6ikLFzi4+P19OnT5nDO1EOVU7Pu99977z2zLTo6Wt9++211cXFRT09PXbhwYaYxMvL7779rqVKl0gzRnDFjhhpG8r2h1nXi3Llz+vrrr6thGDp8+HBVzfjExaFDh7RIkSI2++fExETzynmLFi109OjRGhcXZ1757N27d5YHVDdv3tRHHnlEK1WqZG6vqR+AkjKnS5cuabVq1fSBBx7QxMTEDPM9f/68BgYGapMmTcy/e++997RVq1bmdujn56fdu3fXRYsWaWRkpO7fv18rVqyY4YlI1eQrW2XLljWHgVtZc164cKEahmFz5eLo0aNap04d7dChQ6bz4siRI+kuO+tomB9++MGmPTExUVu0aKF16tTR2NhYu046bdiwQYsWLaovvfSS2Wbdp953331arFgx9ff3N4eevvbaaxnGsm53KU9aWnMNCwtLM/1vv/2mPj4+5nzIKt9NmzapYRi6bt06M3fDMMwD+NS3UDz//PPq5+eXZp+aXs4ptz2rCxcumCdUmjVrZjOyxx5RUVEaEhKiDRo0sOnb22+/rYZh6LZt29L8zahRo7Ro0aKZ/g5evXpVGzVqpPfff7/ZlvL3acGCBTZXRj/55JM0yyU9jtr2VB23/eU3FGKFQEJCgo4ePdocQ21dIdNz7do17devn5YuXdqu2F999VWaHwTV5KsXERER+vXXX+tLL72kDRs21CJFiqinp6cWK1ZMixcvnmHMyMhIDQkJSXOQZu2LavJTjgzDMK/kPP300+rt7Z1lvrGxsTp79mzzLI51J3Pu3DlzB5Zyx/vPP//oo48+qpUqVcoytpV1x7FixQr18PDQ77//Xr/88kubg7j4+Hi7ftCsDygxDENr1qypw4YN027dumnVqlVtvitlXx555BEtV66cRkRE2JVveHi4Obz0+eef1yZNmmjTpk3NA0urq1evao8ePbRkyZKZxluyZEm6D12w5piUlKRxcXG6cuVKrVKlivmD/ffff2eZ68mTJ22KDcMw9LnnntN27drp559/bjPtlStXtG/fvpmuaykdPnxYGzRooC4uLvrvf/9bly5dqjNnztS2bdvaFB2qycV7x44dtVGjRnbFVk0+eK1YsaJ5H1Dqs4Kpf5CsQ29mzJiRadzPP/9cDcMwi+fjx4/rjBkzzAeuGIah5cuX1z59+ujy5cv12rVr5j0LGZ0MUU0eRlm+fHlzuFzKH8WbN2/qww8/rEWKFLE5K7tixQo1DEPXrFmTac6TJ0/WihUr6qZNm8y2yMhI7dq1q1aoUCHNAd+hQ4fU1dU1zYFpZqwH/9ZhRNb8jx07phaLRQMCAsyTAYZhZHlf7NNPP62lS5c2C6sLFy5o586dtUaNGua9bCkPMBYtWqSGYZj3l6bH2sdBgwapn5+fXrx4UZOSkvS5557TChUqqGryVcjU+4oKFSpor169Mi1A+vXrp1WrVtWDBw/afJeq6vbt280b5/v3729ekbD3yu6ePXvUz89PX3nlFbMtMjJSO3bsqBUrVlTVtCeZqlSpoq1atcr0QRMbN25UV1dX82y4dTi6avKQ9u7du2vDhg3N6Z955hk1DMOuk4bWItF60jCllP227v/79eunlSpVyvSM/8GDB7V06dLpXhk/evSoTpo0ySz8rUNkmzZtqoZhpDtMy2rz5s3q7e2t8+bNU9W08/LSpUtapUoVbdiwoXli1brtZTVc+ptvvtFSpUrZjFj4+++/9fHHH1d/f3+baa3zomfPnlq1alW7f1NUVd977z318vKyOTkaFxdn7l8PHz6sK1eu1Pbt29vc85va2LFj1TAMbdCggc6ZM0e3bdumffr00Zo1a6qq7byx5tu8eXNt1KiRXfdr/vXXX1qzZk1t0KCB3rp1S48fP66lSpXSvXv3pjsvXn31VXV3d890f/Hwww9rtWrVzHuhrft2a66HDh0y7zV+8MEH7Vp/rXFUVf/zn/+oYRj69ddfq2ryMq1YsaKWK1fOZj9t/b4JEyaom5tblsNLH3/8cXVzc0vzdObr169rv3791Nvb22Z+V65cWfv375/lvWKO2PZUHbf95TcUYoXIe++9p9WrV1fDMLRChQo6dOhQ/eGHH/Tw4cP622+/6YULF3TcuHFatGhRm6cnZSYpKUl///13c3hIej/kMTExevDgQf3888/NISXDhg3LNG5kZGSGw5usG2tISIhWrlxZly9frjVq1LAZqphb1p3N5s2b1d/fXwcPHpytv09KStJbt27pf/7zH/X399eyZctqgwYNzKtq9g4FunPnjn799dfap08fc3x66itkKf3zzz/ao0cPrVatWrbyPX78uHbp0sXm5uTKlSvrK6+8ot99951u3rzZPPAODQ3NMl5mD2JJ6eeffzaf6jZt2jS7/iYhIUFXr16tkyZN0s8//1zj4uK0ffv22rJlSz1w4IB5oDd79mx1dXW1OSublT179pgPIEj53+jRo20em7x9+3atVKmSPv/883bHVk0+G+zt7W2efU0p9Y/n33//rVWrVtXevXtnGtM6XCa9mPv27dORI0ea9wlYC/py5cqpr69vpnFDQ0PVw8PD7HfKq66qquvWrVPD+L+Ht0RFRekzzzyjPj4+mcZVVR0+fLhWqlTJZp7u3r1by5QpYw7nS3kQfvHiRS1durQ++eSTWcZO6eGHH9batWvbDOOz3qs5f/58PX36tC5cuDDLeayq5pCikJAQXbx4sX733XdapkwZ8+qNNVfr/546dcq8WpaVzZs321wxmjJlit533302V2at68XVq1f1vvvu06ZNm2Ya03piJeUDT6wHaQkJCfrDDz+YByn/+c9/7L6yq5p8QqtEiRJat25dPXDggF67dk2HDh1qfqeq7cmmK1euaPPmzc0z1xm5dOmSent7a6tWrdIcRG/dulUDAgJs1oGDBw+qYRhZ3u+RlJSk169fN4et9erVS8PCwtJcBbVeeYuKitI+ffqkKUxSu3jxoo4aNco8ILZ+V+rv3r59uw4bNkzLlSunhmFkeXLo559/VsMwdPbs2enGVFWdNWuWeQUrNjZWBwwYYNfJyF27dmlwcLA5rDgpKUmvXbumr7/+ujkUOuX+++rVq9quXTsNCgrKMraV9UqK9f5061C5Dz74wGbYekJCQpavg/jqq690yJAh2rBhQ7VYLOrt7W1zDJH6t/TKlSvasmVLm4I9Kx999JG6uLhoYGCgvv7661q+fHl98sknzWF51m36+vXr+sQTT2R5MvLBBx/Ufv36mfefpicpKckcAeDt7Z3mRGJmdu/eba5L1pNJderU0ebNm5ujhKzr8vXr1/XJJ5/UUqVKZRnXevKvcuXKOmvWLN2yZYtGRESYeab8vbNu023atMk0pqO2PVXHbX/5DYVYIZKUlKR//PGHjhkzxubArGzZslqxYkV1cXFRwzC0b9++OXryV3rfl9qwYcPUMAzzLG1ufP755+awR8MwcvTeqKwMHTpUvb29bd6xlR3nzp3TmjVrqmEY+uSTT+bqCT5//fWXvvfeexoSEqKjRo1Kd4jj5s2btXz58tkuHFWTd6zvvPOOduzYUatVq2bzuHbrf2PGjMlyyKO9rOvHsWPH9IEHHsjxkxRVk5+eZf0B6dmzp9aqVUstFos2atQo24/EjY+P14MHD+qsWbN00aJF6Z5hfuGFF7RYsWJ252zt6969e82rjyNGjNC9e/emudfAulx37dql/v7+mR7IJyUl6e7du9M82Sz1tnfr1i1du3at+STQzIp5699bh7pk9KCTuLg4bd26tfr6+ur169f1559/1ooVK+rAgQMznRfWYWWPPfaYTa7Hjh3T5557zrxan/IK4U8//aR+fn766quvZhrbyro9nDp1SmvUqGGeMVVNPlseGBhoc8CS1dC2qKgoXbRokQ4ePFirVaumhvF/r3ZIPXTUmvOPP/6onp6edr0z8Pbt2/rss8+qYSTff/Lcc8+pm5ubLlmyxJzGejBoPTmU0T20qsnzMjAwMN0HOqR06tQp8365Zs2a2X0frOr/3Q9mGIZ5kqh9+/Y296dar9ZY77vJ6sRFYmKivvTSSzYF7+bNm3XXrl3auHFjdXNzs3kYxQ8//KC+vr46f/58u3L+3//+p82bN1fDSH4C47PPPquffPKJhoeH2xS977//vvr5+ekLL7yQZczY2NgMh7Wm3g5Xr16thmHoiy++mGnMxMRE3bBhQ6ZDyc6fP68lS5bUnj176q5du+za9qwyulco9etgVJOH2VWoUCHT9S0jhw8f1goVKphDoK3bXnbWM9XkeRweHq5LlizRfv36acOGDXXOnDk2V2JS5pvV9pEe6+PgDSP5wWOlSpXScePG6alTp/T27dvmEFsXFxcdMWKEXTlnJOU906Ghoert7a3e3t5Z3rOb8u8///xz7dy5s9533306fPhwvXr1qgYGBuqECRNsCulPPvlE/fz87DppePv2bX399de1RIkSarFYzN8KwzC0W7duNr+lu3fv1ooVK+qQIUPsynn79u3mk4zzattTTZ7PGb1KJqfbX35DIVZIxcTE6ObNm3XEiBH62GOP6UMPPaQ9evTQFStWZPuR3Fmx7iBPnz6tDRo0yNYwv8zExMRocHCwGkby4+Dz2vfff68Wi0X79u2bqzjx8fH6/fffm0/4yovHqWY0jG/48OHq6emZ48JRNXnY2b59+3TOnDk6YcIEfeKJJ/SVV16x+0ciJ7L7uPb0fPTRR9q4cWMtVaqUuru7a5s2bfK0OLfu1NevX6/FihWz+6AnpYSEBF22bJn5AIq6devqyJEj9auvvtLffvvNXDfOnz+vffr0UVdXV7veg3bjxo0Mn76Z+sdoyJAhahhGlkVkVFSUrlu3LtMb6a33ir3zzjv6zjvv2NxbkRXrj6c9w+GsQymz845Da9xly5apYSQ/+vrixYvmcNacvMfn+vXrumfPHvPBGW3bts3wYNl6xcLenM+fP6/dunVTwzDU3d3dHEq+cOFCvXTpkv7111+6f/9+bdGihbq7u9u1jVvXifTmsbX/x48f18cff1xdXV21Xr16dm+L169f17lz52qbNm30scce008//VTDw8PVzc1N169fb8ZPTEw0hxDaMy+s7x308PCwORnk4uKiU6dOtZl2zpw5dq3Lqf33v//V5s2bq6urq3p4eGitWrX0wQcf1B49emhISIi6uLho06ZNszUUzx7W+6PtmQ/2vPPOOvzW+sAYe59smNn/T23kyJFapEgRu06epvfbtn79evX09DRPwj7//PN2/waml9fVq1d1+/btaYYOWo0ePdru/aaq7XDirVu3avfu3dO8P7Nhw4bmE0y7d++e6T4x5ZVge4f6Ll26VA3DyLBPmUlZVFvXrx49emhoaKhOnDhRvb291d/fP9N72lL76aef9JVXXtFOnTrp/fffr3Pnzk1zxfyVV17RIkWKZDqf01vOebXt5eQ4KjvbX35CIXYPyO0bze21Y8cOrV27tt1D0DJj3cGtXLlSS5UqZfNwibwQHR2tc+bM0cGDB9s9fvtuW7t2rRpG8iN371XXr1/XX375RU+cOGEeUObkhcCZiYuL07CwsDT30GXH5cuX9fXXX9egoCC1WCzq5eWltWrV0n/961/avn17rVSpkhYtWtTus4JZsc6DEydO6L/+9S+tUaNGnsS9fv26Nm/eXP38/LRt27a5OsmS+ofV+u8TJ07offfdp/Xr189x7JEjR2rlypW1a9eu6uLiYt7TmpsDwgsXLujWrVtthm5a4508eVLvv/9+rVu3brZzXbFihT744IPmCAXDMLRIkSJao0YNNQxDS5QoYfMC9vTYOzTYKi4uzrwHLiesV3Gjo6PNd1/17dtXx40bZz6Y4N///rfd8aKjo3XVqlU6cuRI7dixo/bv319/+uknm34dO3ZMH3zwwWzNY+vyuX37th49elQ/++wzff7557VRo0bmgyNq1KihvXv3ztH2ndnDBS5cuKANGjRQPz+/XMe1/v9ff/3VfOWF9Z6pvMz5xx9/1MqVK2v37t2zHTchIcE8trDe61yxYkXzgTt5vV9WTX7QRqVKlbJ8enJmoqOjddeuXfr2229rx44dtXjx4lqjRg198MEHddy4cTk6aZjRPLauj4mJieaJ2uzETP3/T506pe3atbMpIgMCAmzezWiv9B6gZe3Dzp071c/PT7t165ZlnLi4OD1z5oyePXtWVZNPDh0/flw/++wzfe6557RBgwY53vbi4uL0zz//NB/Uld6wRKvcbH93G4UY8kxSUpKePXs2yzHh2Y35559/5urllpnFzu5LQ++WGzdu6Lx58/Spp55Kc6Mt8o+UZ7lv3ryphw4d0iVLlujAgQO1Tp06arFYtGzZstq0aVN977338nRbUU2+ymsYhs1DFnLK+iNnve/DMIwsC4ScGDx4sJYpU8buR/mnZM3x1q1bGhISohaLRR966CFziE1ODgbt+ZsXXnhBixcvbr7Y3R4pD6yuXLmimzZt0ilTpugDDzygFStW1JYtW+ojjzyi33//fZ6+pNQa68aNG+Y71uyR0RWb9evXm+9Lsv731FNP2fUuv9Qyu6L38ssvq7e3d5brxaFDh3T8+PHas2dPfeutt9I8ACAmJkZv3Lihf//9t+7du9fmQDuzZZ0y7rRp07J8sEBsbKyuWrUqy4cEZDeu9UpTeg9CyE3s27dva58+fbRq1apZjobIKu6FCxd00qRJOnr06Gw9GCa7+VrvhcrsIUTZjX3z5s00w9vzcr2wN669sePi4nTjxo06a9YsnTNnjl3fnzLu1KlTs/ybn376SadNm5bplejbt2/rxx9/rNWqVTNf7ZFytETKB5hcuXJFd+7cafe2l1Xs1JKSkjQmJsau7S8/ohADCoikpCS7Hy+M/CMxMVFjY2M1Pj5er169mq3XJFjZu8wjIyN12bJldj2h0t64V65c0dq1a6thGDYv2s6L2CdPntSAgAAdMGBApje+ZxbX+u/9+/fr2LFjs1UcZRY7o/xPnTqlAQEB2r17d7vPnmc1L65fv27zdEp72bte5HVBevnyZV2/fr3Onz9fv/vuu2y9ryf100PTKzpv3bqlS5cu1eXLl2d6Ei7lazKs//n5+eny5ctzVcxmFHfFihWZ/l1W35mTuFFRUfrRRx9l+Y6o7MZOSkrSO3fu6NmzZzMdIpmduNk5sZnTfE+cOJHlKJ+MYn/yySdZrnt5mXPK3HMbO/V2k9ucs3pVSEZD4a2mTZumfn5+6ufnp82aNVMXFxetXbu2nj9/XhMTE/XixYu6YcMGm2Ge9s7vjGJbRydcuHBB161bZ16Fsyqox0YUYgCQQzdv3tRjx45l+ih/q9Q/Epn9KGUWNyuZHVTlNO6pU6dsnlyVl7Fv3bqV6SPPsxs35cFgVj/MOc355s2baV7Ea2/c1OtERkM28zLfrOLmNnZO42a1fDI74P7zzz+1QoUKWqFCBV21apWuXbvWHCJXo0YN8wpdyu0hoxfN5iRu6qFjWd3vlZO4CQkJdh283u2c4+LizNj25OyofHMa25E5O2r53blzx2HrXFZDn8+cOaOlS5fWli1b6tWrV/X06dPmezq///57HTJkiJYoUcJ8WNz48eOzPJGQndjWhweVLVtWX3311Ty5B/1uohADgByaNm2aNm3aVN966y3dvHmzXrhwIc2PY+ozmZcvX87yh86euKk5Mq49B0B3M+ekpCSbm+jtiZsfcnZE3NSuXLmSp/Mi5fp86dIlh+QcGRmZZdzx48ern59fmndcfvHFF2oYhvbp08cmZ9Xkx8YvXrw40yfD5qe4Bw4c0MWLF2d5tTQ3sQvavMjqqb75KWd74hbEnCdMmKDlypWzGQb4119/qYeHh953331aoUIFHTdunPkU32LFipnvW8yqMHVk7PyKQgwAcsj6qHpXV1ctWbKkdu/eXRcuXKj79u1L9ypPTEyMvvzyyzpw4MBMfzRyEzezg9ycxB09enSW+eY2dl7nbM88Log557d5cTfX5YYNG2qvXr3MA8a4uDjz3XQ9evRQHx8f3bFjhzn97du3dciQIWqxWDIdQlfQ4hbEnJkXBTvnevXqabdu3WxOEGzZskU9PDy0TZs2Nq8v2LVrl/r4+Gj16tXtKpQcGTu/ohADgBw4fvy4enl5acuWLXXRokXas2dPcyx+QECA9u/fXz/55BM9cuSIOXRiz5496uvrqz179iw0ccm5YMctiDmfPHlSq1SpkuG7pDZt2qRFixbVZ555xmw7evSoNmjQINMn7hW0uAUxZ+ZFwc75+PHjWrVqVX355Zdt2hctWqQWi0W3bNlitllflfT0009rxYoVs3y/nCNj52cUYgCQA99//726urqaTzM7c+aMbtiwQd944w1t1aqVenl5mS8kHzFihP7444/me04ye+pXQYtLzgU7bkHMOTw8XIsXL66jRo1S1fTvi+zWrZv6+fmZL/b++OOP1TAM/e677wpN3IKYM/OiYOccFhamhmHoW2+9ZbZdv35du3btqkWKFEn3b5599lktUaJElg+qcmTs/IxCDABy4KuvvlLDMNKMv4+Li9OIiAj9+uuv9aWXXtKGDRtqkSJF1NPTU4sVK6bFixcvVHHJuWDHLYg5R0ZGakhIiM6dOzfNZ9YDzh9//FENw9CRI0eqavKZc29v70IVtyDmzLwo2DnHxsbq7NmzzUfgW4cEnjt3Trdt26aqtu85/Oeff/TRRx+16x2Ujoydn1GIAUAOJCUl6e+//66nTp0y/51aTEyMHjx4UD///HPt0KGDGoahw4YNK1Rxyblgxy2oOUdGRmY4HMl6sBYSEqKVK1fW5cuXa40aNWyGYRWWuAUxZ+ZFwc85K9YiavPmzerv76+DBw/Ok7iOjn03UIgBQB5L74DT+mLWgwcP3jNxHRmbnB0f15GxHZmz1eeff24OfTQMQ/ft23dPxnVk7IIW15GxyTmtoUOHqre3t4aHh+dpXEfHdiYKMQBwEOuZu9OnT2uDBg3ybAhFQYvryNjk7Pi4joztyJxjYmI0ODhYDcPQ6tWr37NxHRm7oMV1ZGxytvX999+rxWLRvn375mlcR8d2NosAABzCYknexV64cEHi4+PlxRdfvCfjOjI2OTs+riNjOyquqoqnp6e89NJLUrJkSRkyZMg9GdeRsQtaXEfGJmdbN27ckIiICHn22Wdl7NixeRbX0bHvBkNV9W4nAQCFmarK+fPnpUSJEuLp6XnPxnVkbHJ2fFxHxnZk3HPnzkmpUqWkWLFi92xcR8YuaHEdGZucbePGxcWJu7t7nsV0RmxnoxADAAAAACdjaCIAAAAAOBmFGAAAAAA4GYUYAAAAADgZhRgAAAAAOBmFGAAAAAA4GYUYACDfMwxD1qxZk6sYDz30kIwYMSJP8slvli1bJn5+fnc7DQBANlCIAQDuqsjISBk2bJhUq1ZN3N3dpVKlStK9e3fZtGlTnn7P6tWrZcqUKXkaEwCAnHK92wkAAO5dZ86ckeDgYPHz85O3335b6tevL/Hx8bJhwwYZMmSIHDt2LM++q0SJEnkW614RHx8vbm5udzsNACiUuCIGALhrXnzxRTEMQ/bt2yePPPKI1KxZU+rWrSujRo2SPXv22Ex79epVefjhh6VYsWISGBgo3333nc3n27Ztk+bNm4u7u7uUL19exo0bJwkJCebnqYcm3rlzR8aOHSuVKlUSd3d3qVGjhnz44Yfm50eOHJHOnTuLl5eXlC1bVp5++mm5evVqhn2xDg/csGGD1K5dW7y8vKRTp05y6dKlDHMQEenVq5cMGDDA/HeVKlXkzTfflH79+omXl5cEBATId999J1euXJGePXuKl5eXNGjQQA4cOJAmhzVr1khgYKAULVpUOnbsKOfOnbP5/Ntvv5UmTZpI0aJFpVq1ajJp0iSbeWQYhrz77rvSo0cP8fT0lKlTp2bYXwBA7lCIAQDuimvXrsmPP/4oQ4YMEU9PzzSfp77nadKkSfLYY4/J4cOHpUuXLvLkk0/KtWvXRETkwoUL0qVLF2nWrJkcOnRI3n33Xfnwww/lzTffzPD7+/XrJ59//rksWLBAjh49KosXLxYvLy8REbl+/bq0adNGGjduLAcOHJAff/xR/vrrL3nssccy7dPNmzdl1qxZ8sknn8j27dvl7Nmz8vLLL2dzzojMnTtXgoOD5ZdffpGuXbvK008/Lf369ZOnnnpKDh48KNWrV5d+/fqJqtp899SpU2X58uWyc+dOuX79ujzxxBPm5//73/+kX79+8tJLL8nvv/8uixcvlmXLlqUptt544w15+OGH5ddff5Vnnnkm27kDAOykAADcBXv37lUR0dWrV2c5rYjoa6+9Zv47JiZGRUTXr1+vqqoTJkzQWrVqaVJSkjnNO++8o15eXpqYmKiqqq1bt9aXXnpJVVWPHz+uIqIbN25M9/umTJmiHTp0sGk7d+6ciogeP3483b9ZunSpioieOHHCJoeyZcua/06Zg1XPnj21f//+5r8DAgL0qaeeMv996dIlFRENDQ0123bv3q0iopcuXbL57j179pjTHD16VEVE9+7dq6qqbdu21bfeesvmuz/55BMtX768+W8R0REjRqTbPwBA3uIeMQDAXaEprubYo0GDBub/9/T0FB8fH7l8+bKIiBw9elRatGghhmGY0wQHB0tMTIycP39eKleubBMrPDxcXFxcpHXr1ul+16FDh2TLli3mFbKUTp48KTVr1kz374oVKybVq1c3/12+fHkzx+xI2deyZcuKiEj9+vXTtF2+fFnKlSsnIiKurq7SrFkzc5qgoCDx8/OTo0ePSvPmzeXQoUOyc+dOmytgiYmJcvv2bbl586YUK1ZMRESaNm2a7XwBANlHIQYAuCsCAwPFMAy7H8iR+qERhmFIUlJSjr7bw8Mj089jYmKke/fuMmPGjDSflS9fPls5piw4LRZLmgI0Pj4+0zjW4jK9tuz0PyYmRiZNmiT//ve/03xWtGhR8/+nN0wUAJD3uEcMAHBXlChRQjp27CjvvPOOxMbGpvn8+vXrdseqXbu27N6926bI2blzp3h7e0vFihXTTF+/fn1JSkqSbdu2pRuvSZMm8ttvv0mVKlWkRo0aNv/lplApXbq0zcM7EhMT5ciRIzmOl1JCQoLNAzyOHz8u169fl9q1a4tIcp+OHz+epj81atQQi4XDAQBwNva8AIC75p133pHExERp3ry5rFq1SiIiIuTo0aOyYMECadGihd1xXnzxRTl37pwMGzZMjh07Jt9++61MnDhRRo0alW6RUaVKFenfv78888wzsmbNGjl9+rRs3bpVVq5cKSIiQ4YMkWvXrkmfPn1k//79cvLkSdmwYYMMHDhQEhMTc9zfNm3ayA8//CA//PCDHDt2TF544YVsFZyZcXNzk2HDhsnevXvl559/lgEDBsj9998vzZs3FxGR119/XZYvXy6TJk2S3377TY4ePSpffPGFvPbaa3ny/QCA7KEQAwDcNdWqVZODBw9KSEiIjB49WurVqyft27eXTZs2ybvvvmt3nAoVKsi6detk37590rBhQ3n++eflP//5T6ZFxrvvviu9e/eWF198UYKCgmTQoEHmlTl/f3/ZuXOnJCYmSocOHaR+/foyYsQI8fPzy9XVo2eeeUb69+8v/fr1k9atW0u1atUkJCQkx/FSKlasmIwdO1b69u0rwcHB4uXlJV9++aX5eceOHWXt2rUSFhYmzZo1k/vvv1/mzp0rAQEBefL9AIDsMTS7d0sDAAAAAHKFK2IAAAAA4GQUYgAAAADgZBRiAAAAAOBkFGIAAAAA4GQUYgAAAADgZBRiAAAAAOBkFGIAAAAA4GQUYgAAAADgZBRiAAAAAOBkFGIAAAAA4GQUYgAAAADgZBRiAAAAAOBk/w/ogguges9nbQAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "backend = Aer.get_backend('qasm_simulator')\n",
        "grover = Grover(iterations=6, quantum_instance=backend)\n",
        "result = grover.amplify(problem)\n",
        "\n",
        "# Extracting probabilities from the result of solving Grover\n",
        "counts = result.circuit_results[0]\n",
        "counts = counts.int_outcomes()\n",
        "\n",
        "# Plotting probabilities \n",
        "# Don't worry about all the details of how the plot is made\n",
        "# All the code after the first line just makes the plot look nice\n",
        "plot = plot_histogram(counts,figsize=(10, 5))\n",
        "ax = plot.gca()\n",
        "xticks = []\n",
        "ax.set_xlabel(\"Choice number\")\n",
        "display(plot)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 481
        },
        "id": "B8pZgwR81cvk",
        "outputId": "206fa3e9-c390-4cc0-9245-c050ac250418"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "1. 5\n",
        "2. 4"
      ],
      "metadata": {
        "id": "NLu3bg-b9jZc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### **Problem #3.4**\n",
        "**Independently,** play around with the size of the problem (`number_choices`) and the number of iterations and see how the circuit scales. You will find that the circuit becomes really big even for `number_choices=16`!"
      ],
      "metadata": {
        "id": "IyFgJd2M53IR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#End of notebook\n",
        "---\n",
        "© 2023 The Coding School, All rights reserved"
      ],
      "metadata": {
        "id": "7dzC09dLlEhm"
      }
    }
  ]
}