OSQF_Screening_Task_1.ipynb

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      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Quantum State Vector Simulator\n",
        "\n",
        "This notebook presents a quantum circuit simulation using two approaches.\n",
        "The simulation involves initializing quantum states, applying quantum gates (Hadamard, Pauli-X, and CNOT),\n",
        "and measuring the performance in terms of runtime as the number of qubits increases. This approach leverages tensor multiplications to simulate the action of quantum gates on a quantum state.\n",
        "\n",
        "---\n",
        "\n",
        "## Overview\n",
        "There are two approaches we are using to simualte the statevector.\n",
        "1. **Naive Matrix Multiplication**\n",
        "2. **Advanced Tensor Multiplication**\n",
        "\n",
        "The code for each approach is structured into several main sections:\n",
        "1. **Quantum State Initialization** - We create an initial quantum state (tensor) representing the |0⟩ state for all qubits.\n",
        "2. **Defining Quantum Gates** - We define the Hadamard, Pauli-X, and CNOT gates as matrices.\n",
        "3. **Applying Single and Two-Qubit Gates** - We implement tensor-based functions to apply gates on specific qubits.\n",
        "4. **Circuit Simulation** - We simulate a quantum circuit by initializing a state, applying gates, and returning the final state.\n",
        "5. **Performance Measurement** - We measure the simulation runtime as a function of the number of qubits.\n",
        "\n"
      ],
      "metadata": {
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    {
      "cell_type": "markdown",
      "source": [
        "# Naive Simulation Using Matrix Multiplication\n",
        "\n",
        "In this approach, we represent quantum states as vectors and gates as matrices. By sequentially applying matrix multiplications, we can evolve the quantum state based on the gates in the circuit.\n",
        "\n",
        "### Key Concepts\n",
        "- **Qubit State**: In quantum computing, a qubit can exist in a state represented by a two-dimensional vector. The |0⟩ and |1⟩ states are represented as [1, 0] and [0, 1] respectively.\n",
        "- **Quantum Gates**: Gates like X (NOT gate), H (Hadamard), and CNOT are represented by specific matrices. Applying a gate to a qubit is equivalent to matrix-vector multiplication.\n",
        "\n",
        "### Objective\n",
        "1. Define basic quantum gates using matrix representations.\n",
        "2. Build a function to apply these gates to an initial state using matrix multiplication.\n",
        "3. Measure the runtime for different numbers of qubits to analyze performance.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "L_UvEtVzJrZE"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "Y2VMnGSay5gX"
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      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import time\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def initialize_state(n_qubits):\n",
        "    # Start with single |0> state\n",
        "    state = np.array([1, 0], dtype=complex)\n",
        "    for _ in range(n_qubits - 1):\n",
        "        state = np.kron(state, [1, 0])\n",
        "    return state\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Defining Quantum Gates\n",
        "\n",
        "Below, we define the fundamental gates we’ll use in the circuit:\n",
        "- **X Gate (NOT)**: Flips the state of the qubit.\n",
        "- **H Gate (Hadamard)**: Creates superposition by transforming |0⟩ to (|0⟩ + |1⟩)/√2.\n",
        "- **CNOT Gate**: Acts as a control gate, flipping the target qubit if the control qubit is |1⟩.\n",
        "\n",
        "Each gate is represented by a 2x2 or 4x4 matrix, depending on whether it acts on one or two qubits.\n"
      ],
      "metadata": {
        "id": "2-UdMmmeYM9l"
      }
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    {
      "cell_type": "code",
      "source": [
        "# Single-qubit gates\n",
        "I = np.array([[1, 0],\n",
        "              [0, 1]], dtype=complex)\n",
        "\n",
        "X = np.array([[0, 1],\n",
        "              [1, 0]], dtype=complex)\n",
        "\n",
        "H = (1 / np.sqrt(2)) * np.array([[1, 1],\n",
        "                                 [1, -1]], dtype=complex)\n",
        "\n",
        "# Two-qubit gate\n",
        "def cnot_gate(control, target, n_qubits):\n",
        "    # Create a full 2^n x 2^n matrix for the CNOT gate\n",
        "    size = 2 ** n_qubits\n",
        "    cnot = np.zeros((size, size), dtype=complex)\n",
        "    for i in range(size):\n",
        "        binary = format(i, '0' + str(n_qubits) + 'b')\n",
        "        if binary[control] == '1':\n",
        "            flipped = list(binary)\n",
        "            flipped[target] = '1' if binary[target] == '0' else '0'\n",
        "            j = int(''.join(flipped), 2)\n",
        "            cnot[i, j] = 1\n",
        "        else:\n",
        "            cnot[i, i] = 1\n",
        "    return cnot\n",
        "\n",
        "def get_two_qubit_cnot_tensor():\n",
        "    \"\"\"\n",
        "    Create a tensor representation of the CNOT gate.\n",
        "\n",
        "    Returns:\n",
        "        np.ndarray: CNOT gate tensor of shape (2, 2, 2, 2).\n",
        "    \"\"\"\n",
        "    CNOT = np.zeros((2, 2, 2, 2), dtype=complex)\n",
        "    CNOT[0, 0, 0, 0] = 1\n",
        "    CNOT[0, 1, 0, 1] = 1\n",
        "    CNOT[1, 0, 1, 1] = 1\n",
        "    CNOT[1, 1, 1, 0] = 1\n",
        "    return CNOT\n"
      ],
      "metadata": {
        "id": "EJZrmM5GiS5v"
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def apply_gate(state, gate_matrix):\n",
        "    return gate_matrix @ state\n"
      ],
      "metadata": {
        "id": "j-r7MZFPzayo"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Applying Gates to the Statevector\n",
        "\n",
        "We apply the gates sequentially to the initial quantum state |0⟩. By using matrix multiplication, each gate operation transforms the statevector. This process simulates how a quantum state evolves through a circuit.\n"
      ],
      "metadata": {
        "id": "lBjTVCb_YXle"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def simulate_circuit(n_qubits):\n",
        "    state = initialize_state(n_qubits)\n",
        "\n",
        "    # Example circuit: Apply H to qubit 0, X to qubit 1, then CNOT with control qubit 0 and target qubit 1\n",
        "    # Build the full gate matrices\n",
        "    H_full = 1\n",
        "    for qubit in range(n_qubits):\n",
        "        H_full = np.kron(H_full, H if qubit == 0 else I)\n",
        "    X_full = 1\n",
        "    for qubit in range(n_qubits):\n",
        "        X_full = np.kron(X_full, X if qubit == 1 else I)\n",
        "    CNOT_full = cnot_gate(control=0, target=1, n_qubits=n_qubits)\n",
        "\n",
        "    # Apply gates sequentially\n",
        "    state = apply_gate(state, H_full)\n",
        "    state = apply_gate(state, X_full)\n",
        "    state = apply_gate(state, CNOT_full)\n",
        "\n",
        "    return state\n"
      ],
      "metadata": {
        "id": "CCNPFIyQzdCF"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Runtime Analysis for Naive Simulation\n",
        "\n",
        "To understand the efficiency of matrix multiplication in quantum state evolution, we measure the runtime as a function of the number of qubits.\n",
        "\n",
        "**Objective**: Plot the runtime and analyze how scaling the number of qubits affects performance. This analysis helps determine the computational limits of the naive simulation approach.\n"
      ],
      "metadata": {
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      }
    },
    {
      "cell_type": "code",
      "source": [
        "qubit_counts = range(2, 12)  # Adjust the range as needed\n",
        "runtimes = []\n",
        "\n",
        "for n in qubit_counts:\n",
        "    start_time = time.time()\n",
        "    simulate_circuit(n)\n",
        "    end_time = time.time()\n",
        "    runtimes.append(end_time - start_time)\n",
        "\n",
        "# Plot the runtime\n",
        "plt.figure(figsize=(8, 5))\n",
        "plt.plot(qubit_counts, runtimes, marker='o')\n",
        "plt.xlabel('Number of Qubits')\n",
        "plt.ylabel('Runtime (s)')\n",
        "plt.title('Runtime vs Number of Qubits (Naive Matrix Multiplication)')\n",
        "plt.grid(True)\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "cEOIHRGYzfzC",
        "outputId": "47dec82a-613f-49db-cda8-5afce8c3c685"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Advanced Simulation Using Tensor Multiplication\n",
        "\n",
        "Instead of representing the quantum state as a single vector, we represent it as an n-dimensional tensor. This approach makes it easier to manipulate individual qubits directly, especially for larger systems.\n",
        "\n",
        "### Key Concepts\n",
        "- **Tensor Representation**: An n-qubit quantum state can be represented by a tensor of shape (2, 2, ..., 2) with n dimensions.\n",
        "- **Tensor Multiplication**: Using tensor operations allows us to apply gates directly along specific qubit axes, providing a more scalable way to handle multi-qubit systems.\n",
        "\n",
        "### Objective\n",
        "1. Define the quantum state as an n-dimensional tensor.\n",
        "2. Apply gates using tensor-based operations to efficiently evolve the quantum state.\n",
        "3. Compare the runtime of this method with the naive matrix multiplication approach.\n"
      ],
      "metadata": {
        "id": "Jb8B_biH3PeL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Initialize the Quantum State Tensor\n",
        "\n",
        "def initialize_state_tensor(n_qubits):\n",
        "    # Start with single |0> state tensor\n",
        "    state = np.array([1, 0], dtype=complex)\n",
        "    state = state.reshape([2] + [1]*(n_qubits - 1))\n",
        "    for _ in range(n_qubits - 1):\n",
        "        state = np.tensordot(state, [1, 0], axes=0)\n",
        "    state = state.reshape([2]*n_qubits)\n",
        "    return state\n"
      ],
      "metadata": {
        "id": "fzZy2dKj3TSD"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Applying Gates with Tensor Operations\n",
        "\n",
        "Using functions like `np.tensordot` and `np.einsum`, we apply single- and two-qubit gates directly on the n-dimensional tensor. This method helps reduce the complexity of handling large statevectors.\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "-TaVYq1FZXzp"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Apply Gates Using Tensor Multiplication\n",
        "\n",
        "# Single-Qubit Gate Application\n",
        "def apply_single_qubit_gate_tensor(state, gate, target_qubit):\n",
        "    axes = ([target_qubit], [0])\n",
        "    state = np.tensordot(state, gate, axes=axes)\n",
        "    # Move the new axis to the target qubit position\n",
        "    order = list(range(state.ndim))\n",
        "    order.insert(target_qubit, order.pop())\n",
        "    state = state.transpose(order)\n",
        "    return state\n"
      ],
      "metadata": {
        "id": "7xNKZZzc3d3H"
      },
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Two-Qubit Gate Application\n",
        "# For a two-qubit gate like CNOT, we need to reshape and apply it to the correct axes.\n",
        "\n",
        "def apply_two_qubit_gate_tensor(state, gate, qubit1, qubit2):\n",
        "    # Ensure qubit1 < qubit2\n",
        "    if qubit1 > qubit2:\n",
        "        qubit1, qubit2 = qubit2, qubit1\n",
        "    axes = ([qubit1, qubit2], [0, 1])\n",
        "    state = np.tensordot(state, gate, axes=axes)\n",
        "    # Move the new axes to the qubit positions\n",
        "    order = list(range(state.ndim))\n",
        "    new_axes = [state.ndim - 2, state.ndim - 1]\n",
        "    for idx, qubit in zip(new_axes, [qubit1, qubit2]):\n",
        "        order.insert(qubit, order.pop(idx))\n",
        "    state = state.transpose(order)\n",
        "    return state\n",
        "\n"
      ],
      "metadata": {
        "id": "ao_bJ6ti3u_g"
      },
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Simulate the Circuit\n",
        "\n",
        "def simulate_circuit_tensor(n_qubits):\n",
        "    state = initialize_state_tensor(n_qubits)\n",
        "\n",
        "    # Define gates\n",
        "    # Reshape gates for tensor operations\n",
        "    H_gate = H.reshape(2, 2)\n",
        "    X_gate = X.reshape(2, 2)\n",
        "    CNOT_gate = get_two_qubit_cnot_tensor()\n",
        "\n",
        "    # Apply gates\n",
        "    state = apply_single_qubit_gate_tensor(state, H_gate, target_qubit=0)\n",
        "    state = apply_single_qubit_gate_tensor(state, X_gate, target_qubit=1)\n",
        "    state = apply_two_qubit_gate_tensor(state, CNOT_gate, qubit1=0, qubit2=1)\n",
        "\n",
        "    return state\n",
        "\n"
      ],
      "metadata": {
        "id": "ORk3OReR34xK"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Runtime Analysis for Tensor Simulation\n",
        "\n",
        "To understand the efficiency of tensor multiplication in quantum state evolution, we measure the runtime as a function of the number of qubits.\n",
        "\n",
        "Objective: Plot the runtime and analyze how scaling the number of qubits affects performance. This analysis helps determine the computational limits of the tensor simulation approach."
      ],
      "metadata": {
        "id": "qNC30FKaaEJK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# Measure Runtime\n",
        "import time\n",
        "qubit_counts = range(2, 14)  # Adjust the range as needed\n",
        "runtimes = []\n",
        "\n",
        "for n in qubit_counts:\n",
        "    start_time = time.time()\n",
        "    simulate_circuit_tensor(n)\n",
        "    end_time = time.time()\n",
        "    runtimes.append(end_time - start_time)\n",
        "\n",
        "# Plot the runtime\n",
        "plt.figure(figsize=(8, 5))\n",
        "plt.plot(qubit_counts, runtimes, marker='o', color='green')\n",
        "plt.xlabel('Number of Qubits')\n",
        "plt.ylabel('Runtime (s)')\n",
        "plt.title('Runtime vs Number of Qubits (Tensor Multiplication)')\n",
        "plt.grid(True)\n",
        "plt.show()\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Oun6q9mi4AKZ",
        "outputId": "490fe21a-788b-44d3-d83e-2e45e2030fcf"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Performance Analysis\n",
        "\n",
        "## Comparison of Naive and Tensor-Based Simulations\n",
        "\n",
        "After implementing both approaches, we compare the results and the runtime performance.\n",
        "\n",
        "### Observations\n",
        "1. **Accuracy**: Both methods yield the same quantum state for the same circuit, validating the tensor-based method.\n",
        "2. **Runtime**: Tensor operations improve scalability and enable us to simulate circuits with more qubits than the naive approach.\n",
        "\n",
        "The runtime plot below shows the comparative efficiency of each method as the number of qubits increases.\n"
      ],
      "metadata": {
        "id": "SvmoJIPAotiq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import time\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Define the range of qubits to test\n",
        "qubit_counts = range(2, 14)  # Adjust the range as needed\n",
        "\n",
        "# Measure runtime of the original simulation function\n",
        "runtimes_tensor = []\n",
        "for n in qubit_counts:\n",
        "    start_time = time.time()\n",
        "    simulate_circuit_tensor(n)\n",
        "    end_time = time.time()\n",
        "    runtimes_tensor.append(end_time - start_time)\n",
        "\n",
        "# Measure runtime of the matrix simulation function\n",
        "runtimes_matrix = []\n",
        "for n in qubit_counts:\n",
        "    start_time = time.time()\n",
        "    simulate_circuit(n)  # Replace with the alternative function's name\n",
        "    end_time = time.time()\n",
        "    runtimes_matrix.append(end_time - start_time)\n",
        "\n",
        "# Plotting the performance comparison\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(qubit_counts, runtimes_tensor, marker='o', linestyle='-', label=\"Tensor Multiplication Approach\")\n",
        "plt.plot(qubit_counts, runtimes_matrix, marker='x', linestyle='--', label=\"Matrix Approach\")\n",
        "plt.xlabel('Number of Qubits')\n",
        "plt.ylabel('Runtime (s)')\n",
        "plt.title('Performance Comparison of Quantum Circuit Simulation Approaches')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 564
        },
        "id": "gr3-gfzsoxlD",
        "outputId": "7c873960-a1dc-4a95-e856-0cf7013883b3"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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+0fvll1+EXC4Xf//9t8nyH374QQAQ//zzj9m6Bn/88YcAIObOnZtumbTmzZsnAIhff/3VOC8lJUXUq1dPuLm5GVutDL9menl5mbTQjB8/XgAQoaGhJi0dvXr1Eo6Ojia/AhrOUdoWpri4OOHn5yeqV69unJeUlCS0Wq1JnFFRUUKlUompU6ca5xnqt3Tp0mb19PKv1sePHxcAzH6RTis777nM6tuSjRs3CgDiiy++MJnftWtXIZPJxJUrV4zzDL/EZsZQjxs2bEi3zOPHjwUA0blzZ+M8WNnilNU6qVSpkkhOTjbOnz9/vgBg8st3u3btLLasZLXFCYBYuXKlcd6FCxcEACGXy8W///5rnL9jxw6TFu30VK9eXRQqVCjDMmml1+Lk4eEh7t+/b1K2UaNGwt3dXdy4ccNkftpf87Pb4iSEEGvXrs20lSmtxYsXCwDC0dFRNG3aVEycOFH8/fffZnUtRPotTkOGDDHO02g0okSJEkImk4kvv/zSOP/JkyfC2dnZJNactji9/DefkpIiqlSpIpo1a2Yy39XV1WS/6e3//v37wtHRUbRs2dLk+BcsWCAAiCVLlhjnGd53y5cvN85LTk4Wvr6+okuXLmb7suTNN98UDRo0ME7/9NNPwsHBwew9ExYWJgCIkSNHGufpdDrRrl074ejoaOypYHjfGf4/Gxw6dEgAEB988IHZNj/++GOTfWXls8ma/42xsbHC3d1d1K1bVzx//tykbNr3vLXn09r/jXPnzhUATHpx0Kul4F65TK+85s2bw8vLCwEBAejZsyfc3NywYcMGFC9eHOvXr4dOp0P37t3x8OFD48PX1xflypUzubAY0PfH79+/v1X73bZtGwBg9OjRJvPHjBkDAGbXaQQFBaFVq1YWt9W3b1+TXwrr1q0LIQQGDBhgUq5u3bq4desWNBqNcV7a66Ti4uLw8OFDNG7cGNeuXUNcXJzJ+pUrV0bDhg2N015eXqhQoQKuXbtmnPf7778jNDQUb731llmchguU165di0qVKqFixYom57VZs2YAYHZe04qPjwcAq1qbAP159vX1NbleTalU4r333kNCQgL27t1rUr5bt27G1hlAf84AoE+fPiYtHXXr1kVKSgru3Lljsr6/v7/JsXt4eKBv3744fvw4YmJiAOjfJ4YBHbRaLR49egQ3NzdUqFAB//33n9kxhIWFZXo9myHmHTt2pDu6XFbfc9bUd3r7USgUeO+998z2I4TI1uhaT58+BZBxvRuWGcpmRVbrpH///iYtf4bzlNm5yQ43Nzf07NnTOF2hQgUULlwYlSpVMr4/gdT3amYxxMfHW/33k5EuXbrAy8vLOP3gwQPs27cPAwYMQMmSJU3KSjU4wYABA7B9+3Y0adIE+/fvx+eff46GDRuiXLlyOHDggFXbGDRokPG1QqFArVq1IITAwIEDjfMLFy5s1d9GVqT9m3/y5Ani4uLQsGFDi+9Ha+zatQspKSkYNWqUyYAygwcPhoeHh9nfv5ubG/r06WOcdnR0RJ06daw6xkePHmHHjh0mn7tdunSBTCbDmjVrLK4zYsQI42uZTIYRI0YgJSUFu3btMinXqVMnFC9e3Dhdp04d1K1b1/j5ltawYcNMprPy2WTN/8aIiAg8ffoUH3/8sdk1ci+/5605n9b+bzT0dPnjjz+g0+nMjpsKPiZOZLO+++47REREYM+ePTh37hyuXbtmTFAuX74MIQTKlSsHLy8vk8f58+fNLi4uXry41RdH37hxA3K5HGXLljWZ7+vri8KFC+PGjRsm84OCgtLd1stfUgxfogMCAszm63Q6k4Ton3/+QfPmzeHq6orChQvDy8sLn3zyCQCYJU4v7wcAihQpgidPnhinr169mun9Ki5fvoyzZ8+andPy5csDML9oOy0PDw8A1n85vnHjBsqVK2c28pyhe8/L5zkr5xKAybEDQNmyZc3+YRqOyzBilk6nw9y5c1GuXDmoVCp4enrCy8sLp06dMjvnQMZ1n7bM6NGjsWjRInh6eqJVq1b47rvvTLaX1fecNfVtyY0bN+Dv72/25Ty9c24Na5Iiw7LsjKqX1Tp5+dwUKVIEgPn7ITeUKFHC7D1VqFAhq9+TL/Pw8MhWcvmyl9+Xhi+Atna/mlatWmHHjh2IjY3Fvn37MHz4cNy4cQNvvvlmhp81BpY+E5ycnODp6Wk2Pzfrf8uWLXjttdfg5OSEokWLwsvLCwsXLrT4frSG4e8ubTdvQP8FvnTp0mZ/l5bed9b8/QPA6tWroVarUb16dVy5cgVXrlzB48ePUbduXaxYscKsvFwuR+nSpU3mvfy5aVCuXDmz9cuXL29WzsHBwax7ZlY+m6z532jo2m/Ne96a82nt/8YePXqgQYMGGDRoEHx8fNCzZ0+sWbOGSdQrhNc4kc2qU6eOcVS9l+l0OuP9JyyNTvTyNQvZGeXO2l9iM9p2eiMnpTdfvLg7wNWrV/HGG2+gYsWKmDNnDgICAuDo6Iht27Zh7ty5Zh/CmW3PWjqdDiEhIZgzZ47F5S9/IUyrYsWKAIDTp09naZ/Wyu65zIrp06dj4sSJGDBgAD7//HMULVoUcrkco0aNsviPz9r31ezZs9GvXz/88ccf2LlzJ9577z3MmDED//77r8kXCGvfc7l5zDlVuXJlAMCpU6fSvUnuqVOnAMDsC5glWq3WZDqrdZKTc5Pe+X85psz2ld0YKlasiOPHj+PWrVsZ/q1lJrujemb1+HOLi4sLGjZsiIYNG8LT0xNTpkzBn3/+ibCwsAzXs3SerTn3OTnOv//+Gx06dECjRo3w/fffw8/PD0qlEkuXLs23+0/l5D1uSI4aNGhgcfm1a9es+jvNibStyFmV1f+N1rDmfFr7v9HZ2Rn79u3Dnj17sHXrVmzfvh2rV69Gs2bNsHPnTslHU6ScY+JEBVKZMmUghEBQUJDxF5/cEhgYCJ1Oh8uXL5tc3Hzv3j3ExsYiMDAwV/dnyebNm5GcnIxNmzaZ/KqaUVe5zJQpUybTe1WUKVMGJ0+exBtvvJHlLjzly5dHhQoV8Mcff2D+/PmZXnAfGBiIU6dOQafTmfwTvXDhgnF5brpy5QqEECbHZbgfTqlSpQDoh1Nv2rQpFi9ebLJubGys2a/YWRUSEoKQkBB8+umnOHDgABo0aIAffvgBX3zxRb695wIDA7Fr1y48ffrU5JfdnJzzBg0aoHDhwli5ciUmTJhg8YvB8uXLAei7WxoUKVIEsbGxJuVSUlIQHR1tMi8v6iS997ahderluLLTEpcd7du3x2+//YZff/0V48ePz7XtGr4IZ/b3b6lOAOuOP7e6/Bl+LHv5fZCbclLPv//+O5ycnLBjxw6TIdmXLl1qVtbac2L4u7t48aJJ0pKSkoKoqCg0b97cqu1kJioqCgcOHMCIESPQuHFjk2U6nQ7vvPMOVq5ciU8//dRk/rVr10z+z778uWlw+fJls31eunTJrJwl1n42Wfu/0TAQx5kzZ8xa8rMjK/8b5XI53njjDbzxxhuYM2cOpk+fjgkTJmDPnj25VpckHXbVowKpc+fOUCgUmDJlitmvbEIIPHr0KNvbbtu2LQBg3rx5JvMNvzQZRk3KS4Yvn2mPLS4uzuI/Z2t16dIFJ0+eNBuhLe1+unfvjjt37uDnn382K/P8+XM8e/Ysw31MmTIFjx49wqBBg0yu1zLYuXMntmzZAkB/nmNiYrB69Wrjco1Gg2+//RZubm5m/9hz6u7duybHHh8fj+XLl6NatWrw9fUFoD/vL7+f1q5da3a9VFbEx8ebnYuQkBDI5XIkJycDyL/3XNu2baHVarFgwQKT+XPnzoVMJrNqRK6Xubi4YOzYsbh48SImTJhgtnzr1q0IDw9H+/btERISYpxfpkwZ7Nu3z6TsTz/9ZParf17Uiaurq8VuVYYvW2nj0mq1+Omnn7K9r6zo2rUrQkJCMG3aNBw8eNBs+dOnTy2e48x4eXmhUaNGWLJkCW7evGmyLO25LVOmDOLi4owthIA+gbH0mfEyw314LCVeluzevdvifMP1MC93W8tNOalnhUIBmUxm8j69fv26xRFHXV1drTofzZs3h6OjI7755huT+li8eDHi4uJy7e/f0No0duxYdO3a1eTRvXt3NG7c2GJ3vbSfF0IILFiwAEqlEm+88YZJuY0bN5r8XR4+fBiHDh2y6nPF2s8ma/83tmzZEu7u7pgxYwaSkpJMlmWnZd7a/42PHz82W16tWjUAMH7eU8HGFicqkMqUKYMvvvgC48ePx/Xr19GpUye4u7sjKioKGzZswJAhQ/Dhhx9ma9uhoaEICwvDTz/9hNjYWDRu3BiHDx/GsmXL0KlTJzRt2jSXj8Zcy5Yt4ejoiPbt2+N///sfEhIS8PPPP8Pb2zvbv8R+9NFHWLduHbp164YBAwagZs2aePz4MTZt2oQffvgBoaGheOedd7BmzRoMHToUe/bsQYMGDaDVanHhwgWsWbMGO3bsSLf7JKDv33369GlMmzYNx48fR69evRAYGIhHjx5h+/bt2L17t7E7y5AhQ/Djjz+iX79+OHbsGEqVKoV169bhn3/+wbx583LlIvm0ypcvj4EDB+LIkSPw8fHBkiVLcO/ePZN/uG+++SamTp2K/v37o379+jh9+jRWrFiRo64rf/31F0aMGIFu3bqhfPny0Gg0+OWXX6BQKNClSxcA+feea9++PZo2bYoJEybg+vXrCA0Nxc6dO/HHH39g1KhRGQ6XnJGxY8fixIkT+Oqrr3Dw4EF06dIFzs7O2L9/P3799VcEBwcjPDzcZJ1BgwZh6NCh6NKlC1q0aIGTJ09ix44dZq1IeVEnNWvWxOrVqzF69GjUrl0bbm5uaN++PYKDg/Haa69h/PjxePz4MYoWLYpVq1ZZ/BEgLyiVSqxfvx7NmzdHo0aN0L17dzRo0ABKpRJnz57FypUrUaRIkWwNH/7NN9/g9ddfR40aNTBkyBAEBQXh+vXr2Lp1K06cOAEA6NmzJ8aNG4e33noL7733HhITE7Fw4UKUL18+04EPqlWrBoVCga+++gpxcXFQqVRo1qxZute1dezYEUFBQWjfvj3KlCmDZ8+eYdeuXdi8eTNq166N9u3bZ/kYrZWTem7Xrh3mzJmD1q1bo3fv3rh//z6+++47lC1b1iThBPTvs127dmHOnDnw9/dHUFCQyaAhBl5eXhg/fjymTJmC1q1bo0OHDrh48SK+//571K5d22TggpxYsWIFqlWrlm430A4dOmDkyJH477//UKNGDQD6mw9v374dYWFhqFu3Lv78809s3boVn3zyickAJID+OtLXX38dw4YNQ3JyMubNm4dixYph7NixmcZm7WeTtf8bPTw8MHfuXAwaNAi1a9dG7969UaRIEZw8eRKJiYlYtmxZls6dtf8bp06din379qFdu3YIDAzE/fv38f3336NEiRJmN7SmAiqfRu8jslp6N8C15Pfffxevv/66cHV1Fa6urqJixYpi+PDh4uLFi8YyGQ2rbGk4ciH0NyOdMmWKCAoKEkqlUgQEBGR4M9KXGYa1fXkI6vSOzTC8btohTDdt2iSqVq0qnJycRKlSpcRXX30llixZYjaMbnoxNG7cWDRu3Nhk3qNHj8SIESNE8eLFjTfwCwsLEw8fPjSWSUlJEV999ZUIDg4WKpVKFClSRNSsWVNMmTJFxMXFmZ9EC3bv3i06duwovL29hYODg/Dy8hLt27cXf/zxh0m5e/fuif79+wtPT0/h6OgoQkJCzIZsTntzxbSyco7T3gC3atWqQqVSiYoVK5qtm5SUJMaMGSP8/PyEs7OzaNCggTh48KDZuUxv32mXGYY0vnbtmhgwYIAoU6aMcHJyEkWLFhVNmzYVu3btMlkvp+85S/VtydOnT8UHH3wg/P39hVKpFOXKlbN4k0lrhyM30Ol0Ijw8XDRo0EC4u7sbb/rZvHlzk+HBDbRarRg3bpzw9PQULi4uolWrVuLKlSsWhyPPSZ0Y3j9p31cJCQmid+/eonDhwgJpboArhBBXr14VzZs3FyqVSvj4+IhPPvlEREREWByO3NL5Sa9+AIjhw4dnfiKFfgjtzz77TISEhAgXFxfh5OQkqlSpIsaPHy+io6ON5TK6Aa4lZ86cEW+99ZYoXLiwcHJyEhUqVBATJ040KbNz505RpUoV4ejoKCpUqCB+/fVXq4YjF0KIn3/+WZQuXVooFIpMhyb/7bffRM+ePUWZMmWEs7OzcHJyEpUrVxYTJkwwu4E20hmO/OUhn9P7PLdUV9bWs6XhyBcvXizKlStn/BxZunSpxXN04cIF482RYcUNcBcsWCAqVqwolEql8PHxEcOGDUv3BrgvS28oeYNjx44JAGb1ndb169dNhg+3dANcHx8fMWnSJJNh09O+72bPni0CAgKESqUSDRs2FCdPnjSL01IdCWH9Z5O1/xsNZevXry+cnZ2Fh4eHqFOnjvjtt9+My7NyPq3532j43+fv7y8cHR2Fv7+/6NWrl7h06VK6550KFpkQElxNTESUj0qVKoUqVaoYuwlS3lOr1Wjfvj12796NzZs3o3Xr1lKHRERZ0K9fP6xbtw4JCQkZlrt+/TqCgoIwa9asbPf0ICooeI0TERHlOqVSid9//x3VqlVDt27dsn2PGyIiIlvBa5yIiChPuLq64siRI1KHQURElCvY4kRERERERJQJXuNERERERESUCbY4ERERERERZYKJExERERERUSbsbnAInU6Hu3fvwt3dHTKZTOpwiIiIiIhIIkIIPH36FP7+/pDLM25TsrvE6e7du+neNZuIiIiIiOzPrVu3UKJEiQzL2F3i5O7uDkB/cjw8PCSORn+TyJ07d6Jly5ZQKpVSh0P5jPVv31j/9o31b99Y//aN9W874uPjERAQYMwRMmJ3iZOhe56Hh4fNJE4uLi7w8PDgH44dYv3bN9a/fWP92zfWv31j/dseay7h4eAQREREREREmWDiRERERERElAkmTkRERERERJmwu2ucrCGEgEajgVarzfN9qdVqODg4ICkpKV/2R7aF9V8wKJVKKBQKqcMgIiIiCTFxeklKSgqio6ORmJiYL/sTQsDX1xe3bt3ifaXsEOu/YJDJZChRogTc3NykDoWIiIgkwsQpDZ1Oh6ioKCgUCvj7+8PR0THPv8zqdDokJCTAzc0t05tu0auH9W/7hBB48OABbt++jXLlyrHliYiIyE4xcUojJSUFOp0OAQEBcHFxyZd96nQ6pKSkwMnJiV+c7RDrv2Dw8vLC9evXoVarmTgRERHZKX5Ts4BfYIkoLXajJCIiImYIREREREREmWDiRERERERElAkmTnlEqxM4ePUR/jhxBwevPoJWJ6QOyS6VKlUK8+bNy7DM5MmTUa1atSxtt0mTJhg1alSW9pNTkZGRkMlkiI2NzdP92AOeSyIiIsoqJk55YPuZaLz+1V/o9fO/eH/VCfT6+V+8/tVf2H4mOk/2J5PJMnxMnjw5T/ab2yZPngyZTIbWrVubLZs1axZkMhmaNGmSo33IZDJs3LjRZN6HH36I3bt352i7R44cwZAhQ3K0jbReTswAoH79+oiOjkahQoVybT8ZOXjwIBQKBdq1a5cv+yMiIiKyZUycctn2M9EY9ut/iI5LMpkfE5eEYb/+lyfJU3R0tPExb948eHh4mMz78MMPc32fOZGSkpLuMj8/P+zZswe3b982mb9kyRKULFkyT+Jxc3NDsWLFcrQNLy+vPB+J0dHREb6+vvk2UMHixYsxcuRI7Nu3D3fv3s2XfWb03iAiIiKSEhOnTAghkJiiserxNEmNSZvOwlKnPMO8yZvO4WmS2mS95ylai9sTwrrufb6+vsZHoUKFIJPJTOatWrUKlSpVgpOTEypWrIjvv//euO7169chk8mwfv16NG3aFC4uLggNDcXBgweNZW7cuIH27dujSJEicHV1RXBwMLZt22ZcvnfvXtSpUwcqlQp+fn74+OOPodFojMubNGmCESNGYNSoUfD09ESrVq3SPRZvb2+0bNkSy5YtM847cOAAHj58aNbyYalVplOnTujXr5/FbZcqVQoA8NZbb0EmkxmnX+6q169fP3Tq1AlTpkyBl5cXPDw8MHTo0Ay/1L/cVS82Nhb/+9//4OPjAycnJ1SpUgVbtmwBADx69Ai9evVC8eLF4ebmhvr16+O3334z2f/evXsxf/58Y6vh9evXLXYv+/333xEcHAyVSoVSpUph9uzZZnFNnz4dAwYMgLu7O0qWLImffvop3eMwSEhIwOrVqzFs2DC0a9cO4eHhJssNsWzduhVVq1aFk5MTXnvtNZw5c8ZYJjw8HIULF8bGjRtRrlw5ODk5oVWrVrh165axjOHcL1q0CEFBQXBycgIA3Lx5Ex07doSbmxs8PDzQvXt33Lt3z7je1atX0bFjR/j4+MDNzQ21a9fGrl27TGJMTk7GuHHjEBAQAJVKhbJly2Lx4sUmZY4dO4ZatWrBxcUF9evXx8WLFzM9N0RERGSfeB+nTDxXa1H5sx25si0BICY+CSGTd1pV/tzUVnBxzFkVrVixAp999hkWLFiA6tWr4/jx4xg8eDBcXV0RFhZmLDdhwgR8/fXXKFeuHCZMmIBevXrhypUrcHBwwPDhw5GSkoJ9+/bB1dUV586dg5ubGwDgzp07aNu2Lfr164fly5fjwoULGDx4MJycnEy6CC5btgzDhg3DP//8k2nMAwYMwNixYzFhwgQA+tamt99+O0fnAdB3p/P29sbSpUvRunXrDO/Hs3v3bjg5OSEyMhLXr19H//79UaxYMUybNi3T/eh0OrRp0wZPnz7Fr7/+ijJlyuDcuXPG/SUlJaFmzZoYN24c3NzcsH79eoSFhaFcuXKoU6cO5s+fj0uXLqFKlSqYOnUqgNT7CKV17NgxdO/eHZMnT0aPHj1w4MABvPvuuyhWrJhJ8jh79mx8/vnn+OSTT7Bu3ToMGzYMjRs3RoUKFdI9hjVr1qBixYqoUKEC+vTpg1GjRmH8+PFmrV0fffQR5s+fD19fX3zyySdo3749Ll26BKVSCQBITEzEtGnTsHz5cjg6OuLdd99Fz549Td4HV65cwe+//47169dDoVBAp9MZk6a9e/dCo9Fg+PDh6NGjByIjIwHoE7u2bdti2rRpUKlUWL58Odq3b4+LFy8aWyb79u2LgwcP4ptvvkFoaCiioqLw8OFDk/gnTJiA2bNnw8vLC0OHDsWAAQOseo8SERFRFu2ZAcgVQOOx5sv2zgR0WqDp+PyPKwuYOL3iJk2ahNmzZ6Nz584AgKCgIJw7dw4//vijSeL04YcfGlt0pkyZguDgYFy5cgUVK1bEzZs30aVLF4SEhAAASpcubVzv+++/R0BAABYsWACZTIaKFSvi7t27GDduHD777DPjPbHKlSuHmTNnWhXzm2++iaFDh2Lfvn2oWbMm1qxZg/3792PJkiU5OhdeXl4AgMKFC8PX1zfDso6OjliyZAlcXFwQHByMqVOn4qOPPsLnn3+e6X2+du3ahcOHD+P8+fMoX748ANNzVrx4cWP3SZ1OhyFDhmDv3r1Ys2YN6tSpg0KFCsHR0REuLi4Zxjlnzhy88cYbmDhxIgCgfPnyOHfuHGbNmmWSOLVt2xbvvvsuAGDcuHGYO3cu9uzZk2HitHjxYvTp0wcA0Lp1a8TFxWHv3r1m15hNmjQJLVq0AKBPjkuUKIENGzage/fuAAC1Wo0FCxagbt26xjKVKlXC4cOHUadOHQD67nnLly831k9ERAROnz6NqKgoBAQEAACWL1+O4OBgHDlyBLVr10ZoaChCQ0ONcXz++efYsGEDNm3ahBEjRuDSpUtYs2YNIiIi0Lx5c7M6MJg2bRoaN24MAPj444/Rrl07JCUlGVu+iIiIKJfIFcCeFz9Ap02e9s7Uz286QZq4soCJUyaclQqcm5p+17K0Dkc9Rr+lRzItF96/NuoEFQWg/+L8NP4p3D3czb6QOyvTbxGxxrNnz3D16lUMHDgQgwcPNs7XaDRmAwxUrVrV+NrPzw8AcP/+fVSsWBHvvfcehg0bhp07d6J58+bo0qWLsfz58+dRr149k5aIBg0aICEhAbdv3zb++l+zZk2r41YqlejTpw+WLl2Ka9euoXz58ibx5YfQ0FCTa5bq1auHhIQE3Lp1C4GBgRmue+LECZQoUcKYNL1Mq9Vi+vTpWLNmDe7cuYOUlBQkJyfD1dU1SzGeP38eHTt2NJnXoEEDzJs3D1qt1tjClfbcGbpx3r9/P93tXrx4EYcPH8aGDRsAAA4ODujRowcWL15sljjVq1fP+Lpo0aKoUKECzp8/b5zn4OCA2rVrG6crVqyIwoUL4/z588bEKTAw0Jg0GY4rICDAmDQBQOXKlY3r1a5dGwkJCZg8eTK2bt2K6OhoaDQaPH/+HDdv3gSgrwOFQmFMitKT3vs+r66nIyIisluGZClt8pQ2abLUEmVjmDhlQiaTWd1drmE5L/gVckJMXJLF65xkAHwLOaFhOS8o5PpEQ6fTQeOogIujQ6YtGVmVkJAAAPj555+Nv/gbvNxNzdC1CoAxCdLpdACAQYMGoVWrVti6dSt27tyJGTNmYPbs2Rg5cqTVsWQ1KRgwYADq1q2LM2fOYMCAARbLyOVys+vA1Gp1lvaTF5ydnTNcPmvWLMyfPx/z5s1DcHAwhBCYOHFing2MkLZuAX39GurWksWLF0Oj0cDf3984TwgBlUqFBQsW5Pqofll9bwD6FtKIiAh8/fXXKFu2LJydndG1a1fjOcysDgwyet8TERFRLms8FhA6fbK0dyagUxeYpAng4BC5SiGXYVL7ygD0SVJahulJ7Ssbk6a85uPjA39/f1y7dg1ly5Y1eQQFBWVpWwEBARg6dCjWr1+PMWPG4OeffwYAVKpUCQcPHjRJYP755x+4u7ujRIkS2Y49ODgYwcHBOHPmDHr37m2xjJeXF6KjU0cp1Gq1JoMTWKJUKqHVajPd/8mTJ/H8+XPj9L///gs3NzeTVpD0VK1aFbdv38alS5csLv/nn3/QsWNH9OnTB6GhoShVqhQuX75sUsbR0THTOCtVqmR2Pc4///yD8uXLZ3j9VkY0Gg2WL1+O2bNn48SJE8bHyZMn4e/vbzKIBaA/LwZPnjzBpUuXUKlSJZPtHT161Dh98eJFxMbGmpSxdFy3bt0yGUTi3LlziI2NReXKlY3H2a9fP7z11lsICQmBr6+vyTVgISEh0Ol02Lt3b7bOAxEREeWRhmMAuYM+aVI4FpikCWDilOtaV/HDwj414FvI9BoJ30JOWNinBlpX8cvXeKZMmYIZM2bgm2++waVLl3D69GksXboUc+bMsXobo0aNwo4dOxAVFYX//vsPe/bsMX7xfffdd3Hr1i2MHDkSFy5cwB9//IFJkyZh9OjROW5B++uvvxAdHY3ChQtbXN6sWTNs3boVW7duxYULFzBs2LBMb2haqlQp7N69GzExMXjy5Em65VJSUjBw4ECcO3cO27Ztw6RJkzBixAirjqlx48Zo1KgRunTpgoiICERFReHPP//E9u3bAeiv94qIiMCBAwdw/vx5fPDBByYjxhniPHToEK5fv46HDx9abAUZM2YMdu/ejc8//xyXLl3CsmXLsGDBghwNP79lyxY8efIEAwcORJUqVUweXbp0MRuVburUqdi9ezfOnDmDfv36wdPTE506dTIuVyqVGDlyJA4dOoRjx46hX79+eO2114zd9Cxp3rw5QkJC8Pbbb+O///7D4cOH0bdvXzRu3Bi1atUynsP169cbk7revXubnKNSpUohLCwMAwYMwMaNGxEVFYXIyEisWbMm2+eGiIiIcsH+uYBOo0+atCn6lqcCgolTHmhdxQ/7xzXDb4Nfw/ye1fDb4Newf1yzfE+aAH03u0WLFmHp0qUICQlB48aNER4enqUWJ61Wi+HDh6NSpUpo3bo1ypcvbxzSvHjx4ti2bRsOHz6M0NBQDB06FAMHDsSnn36a49hdXV3TTZoAfXe+sLAw45fq0qVLo2nTphluc/bs2YiIiEBAQACqV6+ebrk33ngD5cqVQ6NGjdCjRw906NAhSzcS/v3331G7dm306tULlStXxtixY40tSJ9++ilq1KiBVq1aoVmzZvD29ja7VunDDz+EQqFA5cqV4eXlZbx2J60aNWpgzZo1WLVqFapUqYLPPvsMU6dOTXc4dmssXrwYzZs3t9gdr0uXLjh69ChOnTplnPfll1/i/fffR82aNRETE4PNmzfD0dHRuNzFxQXjxo1D79690aBBA7i5uWH16tUZxiCTyfDHH3+gSJEiaNSoEZo3b47SpUubrDdnzhwUKVIE9evXR/v27dGqVSvUqFHDZDsLFy5E165d8e6776JixYoYPHgwnj17lt1TQ0RERDmV9pqmiQ/0z4ZuewWATFh7s6BXRHx8PAoVKoS4uDh4eHiYLEtKSkJUVJTJ/WTymk6nQ3x8PDw8PHL9GifKnn79+iE2NhYbN27M830V1PqPjIxE06ZN8eTJk3ST2/DwcIwaNSrTVsCCIK8+G9RqNbZt24a2bduaXYtGrz7Wv31j/ds3u6x/Q9JU8U2gWm+gVEPAyUPyASIyyg1eVnC+qRERERERUcGk0wJNPgGi/gZW9QZib+jnNx6rT5p0mV+DLjWOqkdERERERHmr6XjgcRQQOV1/fZNXxdRlBWSACCZORC8JDw+XOgSb16RJE7Oh4F/Wr1+/HF1vRURERK+Y6JP6Z+/KgKLgdVFkVz0iIiIiIsp7MS8GmPILlTaObGLiREREREREec/Q4uRXVdo4somJExERERER5S0h0iRO1SQNJbuYOBERERERUd56GgM8ewDIFIBPsNTRZAsHhyAiIiIiorzl5g0MPwI8ugIonaWOJluYOBERERERUd6SKwCv8vpHAcWuepQrSpUqhXnz5kkdhs3jeSIiIiIqmJg45bY9M4C9My0v2ztTvzwP9OvXDzKZDEOHDjVbNnz4cMhksizdU+f69euQyWQ4ceKEVeWPHDmCIUOGWL39jFSsWBEqlQoxMTG5sj0iIiIikti2scCBb4HnsVJHkm1MnHKbXAHsmWaePO2dqZ8vV+TZrgMCArBq1So8f/7cOC8pKQkrV65EyZIl82SfKSkpAAAvLy+4uLjkeHv79+/H8+fP0bVrVyxbtizH27OWWq3Ot30RERER2ZXEx8DhH4GdnwIymdTRZJukidPChQtRtWpVeHh4wMPDA/Xq1cOff/6Z4Tpr165FxYoV4eTkhJCQEGzbti1/gk15lv5DnZRarvFYoNFH+iTpry/0y//6Qj/d6COg/kjz7aoTzbeZDTVq1EBAQADWr19vnLd+/XqULFkS1atXNym7fft2vP766yhcuDCKFSuGN998E1evXjUuDwoKAgBUr14dMpkMTZo0AaBv2erUqROmTZsGf39/VKhQAYBpF7TIyEg4Ojri77//Nm5v5syZ8Pb2xr179zI8hsWLF6N379545513sGTJErPlpUqVwueff45evXrB1dUVxYsXx3fffWdSRiaTYeHChWjTpg2cnZ1RunRprFu3zrjc0Jq2evVqNG7cGE5OTlixYgV0Oh2mTp2KEiVKQKVSoVq1ati+fbvJtseNG4fy5cvDxcUFpUuXxsSJE82Srs2bN6N27dpwcnKCp6cn3nrrLZPliYmJGDBgANzd3VGqVCmEh4dneE6IiIiICjTDjW+LBAFOhaSNJQckTZxKlCiBL7/8EseOHcPRo0fRrFkzdOzYEWfPnrVY/sCBA+jVqxcGDhyI48ePo1OnTujUqRPOnDmT98FO90//seYd07IHX3yR3zdLv3zfrNTpX7uaFJV9E4rC31WC/MsSptvMpgEDBmDp0qXG6SVLlqB///5m5Z49e4bRo0fj6NGj2L17N+RyOd566y3odDoAwOHDhwEAu3btQnR0tEkytnv3bly8eBERERHYsmWL2babNGmCUaNG4Z133kFcXByOHz+OiRMnYtGiRfDx8Uk39qdPn2Lt2rXo06cPWrRogbi4OJPky2DWrFkIDQ3F8ePH8fHHH+P9999HRESESZmJEyeiS5cuOHnyJN5++2307NkT58+fNyljWPf8+fNo1aoV5s+fj9mzZ+Prr7/GqVOn0KpVK3To0AGXL182ruPu7o7w8HCcO3cO8+fPx88//4y5c+cal2/duhVvvfUW2rZti+PHj2P37t2oU6eOyX5nz56NWrVq4fjx4xg2bBjGjBmDixcvpnteiIiIiAq0An7jWyNhY4oUKSIWLVpkcVn37t1Fu3btTObVrVtX/O9//7N6+3FxcQKAiIuLM1v2/Plzce7cOfH8+XPzFSd5pP/4tatp2S980y+7pK1JUd1XQZbLZVFYWJjo2LGjuH//vlCpVOL69evi+vXrwsnJSTx48EB07NhRhIWFpbv+gwcPBABx+vRpIYQQUVFRAoA4fvy42X58fHxEcnKyyfzAwEAxd+5c43RycrKoVq2a6N69u6hcubIYPHhwpsfw008/iWrVqhmn33//fbOYAwMDRevWrU3m9ejRQ7Rp08Y4DUAMHTrUpEzdunXFsGHDTI5t3rx5JmX8/f3FtGnTTObVrl1bvPvuu+nGPGvWLFGzZk3jdL169cTbb7+dbvnAwEDRp08f47RGoxFeXl7iu+++S3cdkl6Gnw05kJKSIjZu3ChSUlJydbtUMLD+7Rvr377ZXf2v7a//frvva6kjMZNRbvAymxmOXKvVYu3atXj27Bnq1atnsczBgwcxevRok3mtWrXCxo0b091ucnIykpOTjdPx8fEA9Ne0vNzFSq1WQwgBnU5nbHkx+vh2+sHLFUDa8mMuAf/Mg/zvryEUjpBpU6Br+CHQYBQgk5uUFSNP4GlCAtzd3CBL2+fz5f1nQggBIQSKFSuGtm3bYunSpRBCoG3btihatKhxueG4Ll++jEmTJuHw4cN4+PChcf7169dRuXJl4/TL50IIgSpVqsDBwcHsHKXdvoODA3755RdUq1YNgYGBmD17tvk5fcmSJUvw9ttvG8v17t0bTZs2xfz58+Hu7m4s99prr5ls67XXXsP8+fNN5tWtW9eszMmTJ02Op0aNGsbX8fHxuHv3LurVq2eyXv369XHq1CnjvNWrV2PBggW4evUqEhISoNFo4OHhYVx+4sQJDBw4MMNjDQkJMVnu7e2N+/fvZ3p+SDo6nQ5CCKjVaigUuXedouEziNfY2SfWv31j/ds3e6t/h+iTkAHQeAVD2NgxZ6UOJE+cTp8+jXr16iEpKQlubm7YsGEDKleubLFsTEyMWVcvHx+fDEdfmzFjBqZMmWI2f+fOnWaDGTg4OMDX1xcJCQnGQQ+sowWQWl51aD6cD87B83qjkVz3ff3031/juUaH5LrvA89fqiClC54mv/SlOSk+C/vXV7pGo0F8fDx69OiBsWPHAtB3a4uPj4dGo4FarTYmju3bt0dAQADmzp0LX19f6HQ61K9fH3FxcYiPj0dCQgIAfZc+wzqG/ahUKpN5gP6LZVJSksn8v/76CwDw6NEj3LhxAyVKlEg3/gsXLuDff//F4cOH8fHHHxvna7VahIeHIywszLif5ORkk/0kJSVBp9OZzUs7nZKSYjw/hmMDUhNpw3NiYmK66x0+fBjvvPMOPv74Y3zxxRfw8PDA+vXrsWDBAuM6Tk5OZvt++TxptVqT5TKZLMN1SHopKSl4/vw59u3bB41Gk+vbf7mrKdkX1r99Y/3bN3uofwftc7R9pL+OfteZ+0i+mE/jE1gpMTHR6rKSJ04VKlTAiRMnEBcXh3Xr1iEsLAx79+5NN3nKqvHjx5u0UsXHxyMgIAAtW7aEh4eHSdmkpCTcunULbm5ucHJyyt4O982C/OAc6Jp8AlWjj6ACgBYToVM5wTlyOlQqJ/0gES8IIfD06VO4u7ubtjhlkVKphIODAzw8PNC5c2eMHj0aMpkMb731FhQKBRwcHKBUKuHh4YFHjx7h8uXL+Pnnn9GwYUMA+tHsAMDZ2RkeHh4oWrQoAH0ikPY8pd1PWnK53KTs1atXMWHCBPz4449Ys2YN3nvvPezcuRNyueXL6tasWYNGjRrh22+/NZkfHh6O3377DSNHjjTu5/jx4yb7P3HiBCpXrmwy7+TJkybDox8/fhzVqlWDh4cH3NzcAACurq7GdTw8PODv748TJ06gTZs2xvWOHj2K2rVrw8PDA6dOnUJgYCCmTp1qXP79999DJpMZtxMaGooDBw5g2LBhFo/z5fMkhAAAODo6mp1Tsh1JSUlwdnZGo0aNsv/ZYIFarUZERARatGgBpVKZa9ulgoH1b99Y//bNruo/+gRwWgbh5os3OvaSOhozWfnhWvLEydHREWXLlgUA1KxZE0eOHMH8+fPx448/mpX19fU1G5Xt3r178PX1TXf7KpUKKpXKbL5SqTR7o2q1WshkMsjl8nS/4GdK6ICmEyBvPNZ0fpNxgEwGuU4LpNm2oXuWYb/ZJZPJTGI3DIRgOMa0y4sVK4ZixYph0aJFKF68OG7evGls5TGs7+vrC2dnZ+zcuRMlS5aEk5MTChUqZLIdSzHI5XJotVr07dsXrVq1wsCBA9G2bVuEhIRg7ty5+Oijj8zWU6vV+PXXXzF16lRUrWp60eDgwYMxd+5cnD9/HsHBwQD0g4R8/fXX6NSpEyIiIrBu3Tps3brVJKZ169ahdu3aeP3117FixQocPnwYixcvNqnbl+v5o48+wqRJk1C2bFlUq1YNS5cuxYkTJ7BixQrI5XKUL18eN2/exJo1a1C7dm1s3brV2E3UsJ1JkybhjTfeQNmyZdGzZ09oNBps27YN48aNMztPQO7VP+UtuVwOmUxm8XMjN+TVdqlgYP3bN9a/fbOL+i9ZG/jkLhB3xyaPNSsx2dw3NUNXLEvq1auH3bt3m8yLiIhI95ooSTQdrx+S3JLGY/XL84FhiHdL5HI5Vq1ahWPHjqFKlSr44IMPMGvWLJMyDg4O+Oabb/Djjz/C398fHTt2tHrf06ZNw40bN4zJr5+fH3766Sd8+umnOHnypFn5TZs24dGjR2bDdgNApUqVUKlSJSxevNg4b8yYMTh69CiqV6+OL774AnPmzEGrVq1M1psyZQpWrVqFqlWrYvny5fjtt98ybcV87733MHr0aIwZMwYhISHYvn07Nm3ahHLlygEAOnTogA8++AAjRoxAtWrVcODAAUycONFkG02aNMHatWuxadMmVKtWDc2aNTOOUEhERERkl5TOgGdZqaPIMZkw9BWSwPjx49GmTRuULFkST58+xcqVK/HVV19hx44daNGiBfr27YvixYtjxowZAPQtDY0bN8aXX36Jdu3aYdWqVZg+fTr+++8/VKlSxap9xsfHo1ChQoiLi7PYVS8qKgpBQUG52h0nI4Zrczw8PNjiYIVSpUph1KhRGDVqVLplZDIZNmzYgE6dOuVbXNnF+i8Y8uqzQa1WY9u2bWjbtq1N/gpHeYv1b99Y//aN9W87MsoNXiZpV7379++jb9++iI6ORqFChVC1alVj0gQAN2/eNPkyWb9+faxcuRKffvopPvnkE5QrVw4bN260OmkiIiIiIqJ8okkGlrUHfIKBVtP1LU8FmKSJU9ruV5ZERkaazevWrRu6deuWRxEREREREVGuuH8OuHUIeHgJaDdH6mhyTPLBIYiy4vr165mWkbD3KREREREZRL+4tt0vFMjB6NG2ghdVEBERERFR7os+pX/2C5U2jlzCxMkCtlgQUVr8TCAiIsoGQ4uTb9WMyxUQTJzSMIxqkpU7CBPRqy8lJQUAoFAoJI6EiIiogNBqgHtn9K/9qkkaSm7hNU5pKBQKFC5cGPfv3wcAuLi4QJbH/TF1Oh1SUlKQlJTE4ajtEOvf9ul0Ojx48AAuLi5wcOBHJhERkVUeXQY0SYCjG1C0tNTR5Ap+C3iJr68vABiTp7wmhMDz58/h7Oyc50ka2R7Wf8Egl8tRsmRJ1hEREZG1nj0ECpUEChUHXpEfh5k4vUQmk8HPzw/e3t5Qq9V5vj+1Wo19+/ahUaNGvAGaHWL9FwyOjo5sESQiIsqKoIbAB6cBdZLUkeQaJk7pUCgU+XI9g0KhgEajgZOTE7842yHWPxEREb3SlE5SR5Br+BMqERERERHlHiH0j1cMEyciIiIiIso9j68BM0sDK3u8UgkUEyciIiIiIso9MaeA54+BhHvAKzSwEhMnIiIiIiLKPYYb3/qFShtHLmPiREREREREuSf6lP7Zt6q0ceQyJk5ERERERJQ7hEjT4lRN0lByGxMnIiIiIiLKHU+jgcSHgEwB+FSWOppcxcSJiIiIiIhyh6G1yasCoHSWNpZcxhvgEhERERFR7nBQAUGNAa+KUkeS65g4ERERERFR7ijTTP94BbGrHhERERERUSaYOBERERERUc5pkoHnT6SOIs8wcSIiIiIiopy78Q/wVSlgWXupI8kTTJyIiIiIiCjnDDe+dSkmbRx5hIkTERERERHlnPHGt6HSxpFHmDgREREREVHOGRIn36rSxpFHmDgREREREVHOJMUDj6/qX7PFiYiIiIiIyIJ7Z/TPHsUBV09pY8kjTJyIiIiIiChnXvHrmwDAQeoAiIiIiIiogPMJBmr2B4rXkDqSPMPEiYiIiIiIciaokf7xCmNXPSIiIiIiokwwcSIiIiIiouxLuA/c+Q9QJ0kdSZ5i4kRERERERNl3YQvwc1NgVW+pI8lTTJyIiIiIiCj7ok/pn31DpI0jjzFxIiIiIiKi7LODocgBJk5ERERERJRdWjVw76z+NRMnIiIiIiIiCx5eArTJgKM7UCRI6mjyFBMnIiIiIiLKHsP1TX5VAfmrnVq82kdHRERERER5x06ubwIAB6kDICIiIiKiAiq0B+DhD5SoJXUkeY6JExERERERZY9/df3DDrCrHhERERERUSaYOBERERERUdbFnAZOrwOe3JA6knzBxImIiIiIiLLu9Drg94HA/rlSR5IvmDgREREREVHWxRiGIn/1R9QDmDgREREREVFWCZFmKPKq0saST5g4ERERERFR1sTfARIfATIF4B0sdTT5gokTERERERFlTfSLbnrelQClk7Sx5BMmTkRERERElDWGbnq+9tFND2DiREREREREWWW8vsk+BoYAAAepAyAiIiIiogKm7Syg+tuAb4jUkeQbJk5ERERERJQ1hQP0DzvCrnpERERERESZYIsTERERERFZ7/xm4P4FoFwLwL+a1NHkGyZORERERERkvTO/A2c3AAoHu0qc2FWPiIiIiIisZ4cj6gFMnIiIiIiIyFpJ8cDja/rXvkyc8s2MGTNQu3ZtuLu7w9vbG506dcLFixczXCc8PBwymczk4eRkH3crJiIiIiKSVMxp/bNHCcC1mLSx5DNJE6e9e/di+PDh+PfffxEREQG1Wo2WLVvi2bNnGa7n4eGB6Oho4+PGjRv5FDERERERkR2z0256gMSDQ2zfvt1kOjw8HN7e3jh27BgaNWqU7noymQy+vr55HR4REREREaUVc0r/zMRJWnFxcQCAokWLZlguISEBgYGB0Ol0qFGjBqZPn47g4GCLZZOTk5GcnGycjo+PBwCo1Wqo1epcijz7DDHYQiyU/1j/9o31b99Y//aN9W/fCnL9O9w7CxkAjXcwRAGM/2VZqQOZEELkYSxW0+l06NChA2JjY7F///50yx08eBCXL19G1apVERcXh6+//hr79u3D2bNnUaJECbPykydPxpQpU8zmr1y5Ei4uLrl6DERERERErzKZ0MAtKRrPHT2hUThLHU6OJSYmonfv3oiLi4OHh0eGZW0mcRo2bBj+/PNP7N+/32IClB61Wo1KlSqhV69e+Pzzz82WW2pxCggIwMOHDzM9OflBrVYjIiICLVq0gFKplDocymesf/vG+rdvrH/7xvq3b6x/2xEfHw9PT0+rEieb6Ko3YsQIbNmyBfv27ctS0gQASqUS1atXx5UrVywuV6lUUKlUFtezpTeqrcVD+Yv1b99Y//aN9W/fWP/2jfUvvaycf0lH1RNCYMSIEdiwYQP++usvBAUFZXkbWq0Wp0+fhp+fXx5ESEREREREAIB9s4ANw4Cbh6SORBKStjgNHz4cK1euxB9//AF3d3fExMQAAAoVKgRnZ32fyb59+6J48eKYMWMGAGDq1Kl47bXXULZsWcTGxmLWrFm4ceMGBg0aJNlxEBERERG98i5sBe4eB8q3lDoSSUiaOC1cuBAA0KRJE5P5S5cuRb9+/QAAN2/ehFye2jD25MkTDB48GDExMShSpAhq1qyJAwcOoHLlyvkVNhERERGRfdGqgXtn9a/tcChyQOLEyZpxKSIjI02m586di7lz5+ZRREREREREZObBRUCbAqg8gMKlpI5GEpJe40RERERERAVA9En9s29VQG6fKYR9HjUREREREVkv5pT+2a+qtHFIiIkTERERERFlzNDiZKfXNwFMnIiIiIiIKDOaJAAyu06cbOIGuEREREREZMOGRALJCYDSWepIJMPEiYiIiIiIMqdykzoCSbGrHhERERERUSaYOBERERERUfpWvQ0sbgXcPCR1JJJiVz0iIiIiIrJMCODGAeD5Y8DBUepoJMUWJyIiIiIisizutj5pkjsA3pWljkZSTJyIiIiIiMgyw41vvSoBDippY5EYEyciIiIiIrKMN741YuJERERERESWRb9ocfKrKm0cNoCJExERERERWcYWJyOOqkdEREREROY0yfqWJpkM8KkidTSSY+JERERERETmHFRA79VSR2Ez2FWPiIiIiIgoE0yciIiIiIjIXFK81BHYFCZORERERERk7sdGwKxyqQNE2Dle40RERERERKaexwJPovSvCwVIGoqtYIsTERERERGZijmtfy5UEnApKm0sNoKJExERERERmYrhjW9fxsSJiIiIiIhM8ca3Zpg4ERERERGRqegXLU6+bHEyYOJERERERESpUhKBhxf1r9niZMRR9YiIiIiIKJUmCag7FHhyHXD3lToam8HEiYiIiIiIUrkUBVrPkDoKm8OuekRERERERJlg4kRERERERKnungCS4qWOwuYwcSIiIiIiIj2tGljcAvgyAIi9JXU0NoWJExERERER6T24AGhTAFUhoFAJqaOxKUyciIiIiIhIz3jj26qATCZtLDaGiRMREREREekZEyfev+llTJyIiIiIiEgv+pT+mYmTGSZOREREREQE6LRAzGn9a9+q0sZig5g4ERERERER8OgqoH4GODgDnuWkjsbmOEgdABERERER2QCXokDbr4GkWECukDoam8PEiYiIiIiIAFdPoM5gqaOwWeyqR0RERERElAkmTkRERERE9k4I4MRv+lH1dFqpo7FJ7KpHRERERGTv4m4BG4cCcgfgk7u8xskCtjgREREREdk7w41vvSsBDippY7FRTJyIiIiIiOwdb3ybKSZORERERET2ztDi5FdN0jBsGRMnIiIiIiJ7Z0icfKtKG4cNY+JERERERGTPnt4DEmIAyADfKlJHY7OYOBERERER2bOYF9c3eZYHHF2ljcWGcThyIiIiIiJ7FlAH6PM7oEmWOhKbxsSJiIiIiMieORUCyjaXOgqbx656REREREREmWDiRERERERkr57HArunAuf+AISQOhqbxq56RERERET2KuYU8PdsoHBJoHJHqaOxaWxxIiIiIiKyV8Yb34ZKG0cBwMSJiIiIiMheRb8YityXiVNmmDgREREREdkrtjhZjYkTEREREZE9SnkGPLykf+1XVdpYCgBJE6cZM2agdu3acHd3h7e3Nzp16oSLFy9mut7atWtRsWJFODk5ISQkBNu2bcuHaImIiIiIXiH3zgIQgJsP4O4rdTQ2T9LEae/evRg+fDj+/fdfREREQK1Wo2XLlnj27Fm66xw4cAC9evXCwIEDcfz4cXTq1AmdOnXCmTNn8jFyIiIiIqICLsZwfRNbm6wh6XDk27dvN5kODw+Ht7c3jh07hkaNGllcZ/78+WjdujU++ugjAMDnn3+OiIgILFiwAD/88INZ+eTkZCQnJxun4+PjAQBqtRpqtTq3DiXbDDHYQiyU/1j/9o31b99Y//aN9W/fbKb+Q98BSjYENMmA1LFIJCt1YFP3cYqLiwMAFC1aNN0yBw8exOjRo03mtWrVChs3brRYfsaMGZgyZYrZ/J07d8LFxSX7weayiIgIqUMgCbH+7Rvr376x/u0b69++2Vb9R0kdgCQSExOtLmsziZNOp8OoUaPQoEEDVKlSJd1yMTEx8PHxMZnn4+ODmJgYi+XHjx9vkmjFx8cjICAALVu2hIeHR+4EnwNqtRoRERFo0aIFlEql1OFQPmP92zfWv31j/ds31r99Y/3bDkNvNGvYTOI0fPhwnDlzBvv378/V7apUKqhUKrP5SqXSpt6othYP5S/Wv31j/ds31r99Y/3bN0nr//4FIHIGENgAqDtEmhhsQFbOv00MRz5ixAhs2bIFe/bsQYkSJTIs6+vri3v37pnMu3fvHnx9ORIIEREREZFVbh8Bzm0Ezm+SOpICQ9LESQiBESNGYMOGDfjrr78QFBSU6Tr16tXD7t27TeZFRESgXr16eRUmEREREdGrhTe+zTJJu+oNHz4cK1euxB9//AF3d3fjdUqFChWCs7MzAKBv374oXrw4ZsyYAQB4//330bhxY8yePRvt2rXDqlWrcPToUfz000+SHQcRERERUYFiGIrcr5qkYRQkkrY4LVy4EHFxcWjSpAn8/PyMj9WrVxvL3Lx5E9HR0cbp+vXrY+XKlfjpp58QGhqKdevWYePGjRkOKEFERERERC/otEDMaf1rP97DyVqStjgJITItExkZaTavW7du6NatWx5ERERERET0int0FVAnAkoXoFhZqaMpMGxicAgiIiIiIsonhuubfEMAuULaWAoQJk5ERERERPYk4R4gVwK+7KaXFTZzHyciIiIiIsoH9UcAdYYA6mdSR1KgMHEiIiIiIrI3Do76B1mNXfWIiIiIiIgywcSJiIiIiMheXNgG/NAQ2DdL6kgKHCZORERERET24s4x/c1vn9yQOpICh4kTEREREZG9MAxF7hcqbRwFEBMnIiIiIiJ7EXNK/8zEKcuYOBERERER2YOnMfp7OMnkgE+w1NEUODlOnJKTk3MjDiIiIiIiykvRL1qbipUDHF2ljaUAynLi9OeffyIsLAylS5eGUqmEi4sLPDw80LhxY0ybNg13797NiziJiIiIiCgneH1TjlidOG3YsAHly5fHgAED4ODggHHjxmH9+vXYsWMHFi1ahMaNG2PXrl0oXbo0hg4digcPHuRl3ERERERElBVKJ6BoaSZO2eRgbcGZM2di7ty5aNOmDeRy83yre/fuAIA7d+7g22+/xa+//ooPPvgg9yIlIiIiIqLsqz9S/xBC6kgKJKsTp4MHD1pVrnjx4vjyyy+zHRAREREREeUhmUzqCAqkXBlVT6vV4sSJE3jy5ElubI6IiIiIiHKTJpktTTmUrcRp1KhRWLx4MQB90tS4cWPUqFEDAQEBiIyMzM34iIiIiIgopw79CHxZEtgzXepICqxsJU7r1q1DaKj+orLNmzcjKioKFy5cwAcffIAJEybkaoBERERERJRDMaeA5HhA4Sh1JAVWthKnhw8fwtfXFwCwbds2dOvWzTji3unTp3M1QCIiIiIiyiHjUOTVJA2jIMtW4uTj44Nz585Bq9Vi+/btaNGiBQAgMTERCoUiVwMkIiIiIqIcSE4AHl7Wv/arKm0sBZjVo+ql1b9/f3Tv3h1+fn6QyWRo3rw5AODQoUOoWLFirgZIREREREQ5cO8sAAG4+wFu3lJHU2BlK3GaPHkyqlSpglu3bqFbt25QqVQAAIVCgY8//jhXAyQiIiIiohwwdNPzZWtTTmQrcQKArl27ms0LCwvLUTBERERERJTLjNc3hUobRwFn9TVOq1atsnqjt27dwj///JOtgIiIiIiIKBf5VwPKNgdK1pU6kgLN6sRp4cKFqFSpEmbOnInz58+bLY+Li8O2bdvQu3dv1KhRA48ePcrVQImIiIiIKBvqDAb6/K5PnijbrO6qt3fvXmzatAnffvstxo8fD1dXV/j4+MDJyQlPnjxBTEwMPD090a9fP5w5cwY+Pj55GTcREREREVG+ydI1Th06dECHDh3w8OFD7N+/Hzdu3MDz58/h6emJ6tWro3r16pDLszXCORERERER5bb4u/qb3rp6Sh1JgZetwSE8PT3RqVOnXA6FiIiIiIhy1d+zgSOLgCbjgSYc/Ton2DxERERERPSqMoyoV6ystHG8Apg4ERERERG9inRaIOaM/jWHIs8xJk5ERERERK+ih5cBzXNA6QoULSN1NAUeEyciIiIioleRoZuebwjAAdxyLEdnMCUlBRcvXoRGo8mteIiIiIiIKDfEnNI/s5tershW4pSYmIiBAwfCxcUFwcHBuHnzJgBg5MiR+PLLL3M1QCIiIiIiygZDixMTp1yRrcRp/PjxOHnyJCIjI+Hk5GSc37x5c6xevTrXgiMiIiIiomyq2Q+oMwQIqCt1JK+EbN3HaePGjVi9ejVee+01yGQy4/zg4GBcvXo114IjIiIiIqJsCumqf1CuyFaL04MHD+Dt7W02/9mzZyaJFBERERER0asgW4lTrVq1sHXrVuO0IVlatGgR6tWrlzuRERERERFR9tw+Ctw6DKQkSh3JKyNbXfWmT5+ONm3a4Ny5c9BoNJg/fz7OnTuHAwcOYO/evbkdIxERERERZUXkl8CVCKDdbKD2IKmjeSVkq8Xp9ddfx4kTJ6DRaBASEoKdO3fC29sbBw8eRM2aNXM7RiIiIiIispYQQPQJ/Wu/alJG8krJVosTAJQpUwY///xzbsZCREREREQ59TQGePYAkMkB78pSR/PKyHbiBAD379/H/fv3odPpTOZXrVo1R0EREREREVE2Ge7f5FkBcHSRNpZXSLYSp2PHjiEsLAznz5+HEMJkmUwmg1arzZXgiIiIiIgoi2JO6Z/92JiRm7KVOA0YMADly5fH4sWL4ePjwyHIiYiIiIhshaHFyS9U2jheMdlKnK5du4bff/8dZcuWze14iIiIiIgoJ5g45YlsJU5vvPEGTp48ycSJiIiIiMjWdP5Jnzz5sqtebspW4rRo0SKEhYXhzJkzqFKlCpRKpcnyDh065EpwRERERESURYH19Q/KVdlKnA4ePIh//vkHf/75p9kyDg5BRERERESvmmzdAHfkyJHo06cPoqOjodPpTB5MmoiIiIiIJHJylf6RcF/qSF452UqcHj16hA8++AA+Pj65HQ8REREREWXXvq+BDf8Dok9JHckrJ1uJU+fOnbFnz57cjoWIiIiIiLIrOQF4dEX/mvdwynXZusapfPnyGD9+PPbv34+QkBCzwSHee++9XAmOiIiIiIisdO8MAAG4+wNu3lJH88rJ9qh6bm5u2Lt3L/bu3WuyTCaTMXEiIiIiIspvxvs3sbUpL2QrcYqKisrtOIiIiIiIKCcM1zXxxrd5IlvXOBERERERkY0xtjgxccoLVrc4jR49Gp9//jlcXV0xevToDMvOmTPHqm3u27cPs2bNwrFjxxAdHY0NGzagU6dO6ZaPjIxE06ZNzeZHR0fD19fXqn0SEREREb1yNMnAg/P6177sqpcXrE6cjh8/DrVabXydG549e4bQ0FAMGDAAnTt3tnq9ixcvwsPDwzjt7c2L34iIiIjIjikcgVFngJjTQKESUkfzSrI6cUo7/HhuDUXepk0btGnTJsvreXt7o3DhwrkSAxERERFRgSeTAR5++gfliWwNDjFgwADMnz8f7u7uJvOfPXuGkSNHYsmSJbkSXHqqVauG5ORkVKlSBZMnT0aDBg3SLZucnIzk5GTjdHx8PABArVYbW9CkZIjBFmKh/Mf6t2+sf/vG+rdvrH/7xvq3HVmpA5kQQmR1BwqFAtHR0WZd5B4+fAhfX19oNJqsbhIymSzTa5wuXryIyMhI1KpVC8nJyVi0aBF++eUXHDp0CDVq1LC4zuTJkzFlyhSz+StXroSLi0uW4yQiIiIisjXBt1dCo3DCjWJNkORYVOpwCozExET07t0bcXFxJpcCWZKlxCk+Ph5CCBQpUgSXL1+Gl5eXcZlWq8XmzZvx8ccf4+7du1kO2prEyZLGjRujZMmS+OWXXywut9TiFBAQgIcPH2Z6cvKDWq1GREQEWrRoYXYjYXr1sf7tG+vfvrH+7Rvr377lev3rNHCYVQoyTRLUQ/8FipXN+TbtRHx8PDw9Pa1KnLLUVa9w4cKQyWSQyWQoX7682XKZTGaxdScv1alTB/v37093uUqlgkqlMpuvVCpt6oPK1uKh/MX6t2+sf/vG+rdvrH/7lmv1f+8yoEkCHN2g9K4AyHnHIWtl5fxnKXHas2cPhBBo1qwZfv/9dxQtmtoM6OjoiMDAQPj7+2dlkzl24sQJ+PnxIjgiIiIislMxL2586xvCpCkPZSlxaty4MQAgKioKAQEBkOewYhISEnDlyhXjdFRUFE6cOIGiRYuiZMmSGD9+PO7cuYPly5cDAObNm4egoCAEBwcjKSkJixYtwl9//YWdO3fmKA4iIiIiogKLN77NF9kaVS8wMBCxsbE4fPgw7t+/D51OZ7K8b9++Vm3n6NGjJje0NdxYNywsDOHh4YiOjsbNmzeNy1NSUjBmzBjcuXMHLi4uqFq1Knbt2mXxprhERERERHYh2tDixBvf5qVsJU6bN2/G22+/jYSEBHh4eEAmkxmXyWQyqxOnJk2aIKOxKcLDw02mx44di7Fjx2YnZCIiIiKiV49Ol9pVjy1OeSpbfe3GjBmDAQMGICEhAbGxsXjy5Inx8fjx49yOkYiIiIiILEmIAXRaQKECvCpIHc0rLVstTnfu3MF7773H+yAREREREUnJwx8YfwuIuw0oOEJjXspWi1OrVq1w9OjR3I6FiIiIiIiySq4AigRKHcUrL1stTu3atcNHH32Ec+fOISQkxGz88w4dOuRKcERERERERLYgW4nT4MGDAQBTp041WyaTyaDVanMWFRERERERZUwIYElroHAA0Go64OYtdUSvtGx11dPpdOk+mDQREREREeWDp9HArX+BM+sBlbvU0bzyeGthIiIiIqKCyHDjW6+KgNJZ2ljsQLa66lnqopfWZ599lq1giIiIiIjISobEyY83vs0P2UqcNmzYYDKtVqsRFRUFBwcHlClThokTEREREVFei+aNb/NTthKn48ePm82Lj49Hv3798NZbb+U4KCIiIiIiyoShxcmXLU75IdeucfLw8MCUKVMwceLE3NokERERERFZ8uwREH9b/9o3RNpY7ES2WpzSExcXh7i4uNzcJBERERERvezZfcA7GNCpAScPqaOxC9lKnL755huTaSEEoqOj8csvv6BNmza5EhgREREREaXDuxLw7gFAx1sB5ZdsJU5z5841mZbL5fDy8kJYWBjGjx+fK4EREREREVEm5AqpI7Ab2UqcoqKi0l32/PnzbAdDRERERERW0GmZNOWzXBscIjk5GXPmzEFQUFBubZKIiIiIiF6WFA9MLw783AxQs9Eiv2QpcUpOTsb48eNRq1Yt1K9fHxs3bgQALFmyBEFBQZg7dy4++OCDvIiTiIiIiIgA4N4ZQPMceBoDKJ2ljsZuZKmr3meffYYff/wRzZs3x4EDB9CtWzf0798f//77L+bMmYNu3bpBoWCTIRERERFRnjHcv4k3vs1XWUqc1q5di+XLl6NDhw44c+YMqlatCo1Gg5MnT0Imk+VVjEREREREZBB9Sv/MG9/mqyx11bt9+zZq1qwJAKhSpQpUKhU++OADJk1ERERERPmFLU6SyFLipNVq4ejoaJx2cHCAm5tbrgdFREREREQWqJOABxf0r/3Y4pSfstRVTwiBfv36QaVSAQCSkpIwdOhQuLq6mpRbv3597kVIRERERER6988CQgu4FAM8iksdjV3JUuIUFhZmMt2nT59cDYaIiIiIiDIgUwAV3wRUHgAvl8lXWUqcli5dmldxEBERERFRZvyrAT1XSB2FXcq1G+ASERERERG9qpg4EREREREVBDotEHsLEELqSOwSEyciIiIiooLgwUVgXhVgfiiTJwkwcSIiIiIiKggM928qVIIDQ0iAiRMRERERUUFgSJx8ef8mKTBxIiIiIiIqCGJO6Z/9QqWNw04xcSIiIiIisnU6HRDNxElKTJyIiIiIiGzdkygg5Sng4AR4lpc6GrvExImIiIiIyNZFn9A/+wQDCgdJQ7FXPOtERERERLauWDmg/nuAR3GpI7FbTJyIiIiIiGydX1X9gyTDrnpERERERESZYOJERERERGTLnj8BrkUCiY+ljsSuMXEiIiIiIrJlNw4CyzsC4W9KHYldY+JERERERGTLok/qn3n/JkkxcSIiIiIismUxvPGtLWDiRERERERky4wtThxVT0pMnIiIiIiIbNWzh0D8Hf1r3xBpY7FzTJyIiIiIiGyVobWpWFlA5S5tLHaOiRMRERERka3iwBA2w0HqAIiIiIiIKB2VOwLORYDCJaWOxO4xcSIiIiIislXFyugfJDl21SMiIiIiIsoEEyciIiIiIlv08DJwdAkQc1rqSAhMnIiIiIiIbNPlCGDLB8CeGVJHQmDiRERERERkmziink1h4kREREREZItiTumf/apKGwcBYOJERERERGR71M+BBxf1r9niZBOYOBERERER2Zp75wChBVw8AXc/qaMhMHEiIiIiIrI90Sf0z36hgEwmaSikx8SJiIiIiMjWcGAIm+MgdQBERERERPSSFlOAKl0AD3+pI6EXJG1x2rdvH9q3bw9/f3/IZDJs3Lgx03UiIyNRo0YNqFQqlC1bFuHh4XkeJxERERFRvnIuApRuDHiWkzoSekHSxOnZs2cIDQ3Fd999Z1X5qKgotGvXDk2bNsWJEycwatQoDBo0CDt27MjjSImIiIiIyJ5J2lWvTZs2aNOmjdXlf/jhBwQFBWH27NkAgEqVKmH//v2YO3cuWrVqlVdhEhERERHlnyu7gWt7gLIt9K1OZBMK1DVOBw8eRPPmzU3mtWrVCqNGjUp3neTkZCQnJxun4+PjAQBqtRpqtTpP4swKQwy2EAvlP9a/fWP92zfWv31j/du3zOpffnE7FEd+glajhi6gfn6GZney8jdYoBKnmJgY+Pj4mMzz8fFBfHw8nj9/DmdnZ7N1ZsyYgSlTppjN37lzJ1xcXPIs1qyKiIiQOgSSEOvfvrH+7Rvr376x/u1bevX/+qVIFANw4p7A7W3b8jcoO5OYmGh12QKVOGXH+PHjMXr0aON0fHw8AgIC0LJlS3h4eEgYmZ5arUZERARatGgBpVIpdTiUz1j/9o31b99Y//aN9W/fMqx/oYPD2WEAgKqt3kFVr4oSRGg/DL3RrFGgEidfX1/cu3fPZN69e/fg4eFhsbUJAFQqFVQqldl8pVJpUx9UthYP5S/Wv31j/ds31r99Y/3bN4v1//AKkPIMcHCG0qcSoChQX9cLnKz8/RWoG+DWq1cPu3fvNpkXERGBevXqSRQREREREVEuinlx41ufYCZNNkbSxCkhIQEnTpzAiRMnAOiHGz9x4gRu3rwJQN/Nrm/fvsbyQ4cOxbVr1zB27FhcuHAB33//PdasWYMPPvhAivCJiIiIiHJX9IvEyS9U2jjIjKSJ09GjR1G9enVUr14dADB69GhUr14dn332GQAgOjramEQBQFBQELZu3YqIiAiEhoZi9uzZWLRoEYciJyIiIqJXw6Or+me/qtLGQWYkbf9r0qQJhBDpLg8PD7e4zvHjx/MwKiIiIiIiifT4FYi7DajcpI6EXsKOk0REREREtkImAwoHSB0FWVCgBocgIiIiIiKSAhMnIiIiIiJb8O8PwKq3gYt/Sh0JWcDEiYiIiIjIFlzbA1zYAsTezLws5TsmTkREREREtoBDkds0Jk5ERERERFJLuA88jQYgA3yqSB0NWcDEiYiIiIhIatGn9M/FynIochvFxImIiIiISGoxhm56vPGtrWLiREREREQkNV7fZPOYOBERERER2QIHJ8CXLU62ykHqAIiIiIiI7F735YBWI3UUlAEmTkREREREtkDBr+a2jF31iIiIiIikJITUEZAVmDgREREREUnpjxHA9/WAC1uljoQywPZAIiIiIiIp3TkGPDgPyPnV3JaxxYmIiIiISCopicDDi/rXHIrcpjFxIiIiIiKSyr2zgNABrt6Au6/U0VAGmDgREREREUklhje+LSiYOBERERERSSXakDjxxre2jokTEREREZFUotniVFBw6A4iIiIiIqn4hADqJMCXLU62jokTEREREZFUOn0ndQRkJXbVIyIiIiIiygQTJyIiIiIiKTx7COi0UkdBVmLiREREREQkAcW6MGBGCeByhNShkBWYOBERERER5Tehg+zeGUCdCBQKkDoasgITJyIiIiKifOaWHAOZ+hng4Ax4lpM6HLICEyciIiIionxWKPGG/oVvFUCukDYYsgoTJyIiIiKifFbo+XX9C974tsBg4kRERERElM8KG1qcmDgVGEyciIiIiIjykxAo9JyJU0HjIHUARERERER2RZuCa14tUN49CXKvSlJHQ1ZiixMRERERUV7bMwPYO1P/2kGFi36doe3+K+DgqJ+/Z4a08VGmmDgREREREeU1uQLYMy01eTLYO1M/nyPr2Tx21SMiIiIiymuNx+qf90yDPPYWnFJqQP7318C+L4GmE1KXk81i4kRERERElB8ajwWEDorIGWiF5fp5TJoKDHbVIyIiIiLKD1oN8OiKcVIoHJk0FSBMnIiIiIiI8pomBVjXHzi9FgCggxwybYr5NU9ks9hVj4iIiIgoL6mTgLVhwKXtAABtcBdsceyIN93PQbFnmr4MW55sHhMnIiIiIqK8okkGVvUCrv6ln67aE7r2C4Bt26Br+CEUihej7QFMnmwcEyciIiIioryicAQKBwJyJVC1O9Dpe0CtTl1uSJZ0WmniI6sxcSIiIiIiyisyGdBuDlBvOOBZznIZtjQVCBwcgoiIiIgoNyU+BiImAdoXLUtyefpJExUYbHEiIiIiIsotCfeB5Z2A+2eB5KfAm3OkjohyCRMnIiIiIqLcEH8XWN4ReHgJcPMF6gyROiLKRUyciIiIiIhyKvYmsKwD8CQK8CgBhG0CipWROirKRUyciIiIiIhy4vE1fdIUd0s/gl7YZqBIoNRRUS5j4kRERERElF1aDbCimz5pKlYW6LsJKFRc6qgoD3BUPSIiIiKi7FI46Icb968O9NvGpOkVxhYnIiIiIqKs0mr0SRMAlG4MDPpLP+w4vbJYu0REREREWXHrCPBdHeD+hdR5TJpeeaxhIiIiIiJrXf8H+KUT8PgqEDld6mgoH7GrHhERERGRNa7uAX7rBWieA0GNgE4LpY6I8hFbnIiIiIiIMnNpB7Cyhz5pKtsC6L0GcHSVOirKR0yciIiIiIgycn4zsOptQJsMVHwT6LkCUDpLHRXlM5tInL777juUKlUKTk5OqFu3Lg4fPpxu2fDwcMhkMpOHk5NTPkZLRERERHZDCODfHwCdGqjSBegWDjiopI6KJCB54rR69WqMHj0akyZNwn///YfQ0FC0atUK9+/fT3cdDw8PREdHGx83btzIx4iJiIiIyG7IZECvlUCzT4HOPwMKpdQRkUQkT5zmzJmDwYMHo3///qhcuTJ++OEHuLi4YMmSJemuI5PJ4Ovra3z4+PjkY8RERERE9Mq7ezz1tVMhoNFHgFwhXTwkOUlH1UtJScGxY8cwfvx44zy5XI7mzZvj4MGD6a6XkJCAwMBA6HQ61KhRA9OnT0dwcLDFssnJyUhOTjZOx8fHAwDUajXUanUuHUn2GWKwhVgo/7H+7Rvr376x/u0b69+2yQ8thGLXRGibTYKu3shc3z7r33ZkpQ5kQgiRh7Fk6O7duyhevDgOHDiAevXqGeePHTsWe/fuxaFDh8zWOXjwIC5fvoyqVasiLi4OX3/9Nfbt24ezZ8+iRIkSZuUnT56MKVOmmM1fuXIlXFxccveAiIiIiKhAKxezCZWj1wEALvm8ifP+3SWOiPJSYmIievfujbi4OHh4eGRYtsDdx6levXomSVb9+vVRqVIl/Pjjj/j888/Nyo8fPx6jR482TsfHxyMgIAAtW7bM9OTkB7VajYiICLRo0QJKJfvM2hvWv31j/ds31r99Y/3bICEg3/clFC+SJm2jcQh6/UMEyWS5vivWv+0w9EazhqSJk6enJxQKBe7du2cy/969e/D19bVqG0qlEtWrV8eVK1csLlepVFCpzEc+USqVNvVGtbV4KH+x/u0b69++sf7tG+vfRggBREwEDnyrn24+BYrXRyGvr2hi/UsvK+df0sEhHB0dUbNmTezevds4T6fTYffu3SatShnRarU4ffo0/Pz88ipMIiIiInqV/TkuNWlqMxN4fZSk4ZBtkryr3ujRoxEWFoZatWqhTp06mDdvHp49e4b+/fsDAPr27YvixYtjxowZAICpU6fitddeQ9myZREbG4tZs2bhxo0bGDRokJSHQUREREQFVZFSAGRA+3lAzX7SxkI2S/LEqUePHnjw4AE+++wzxMTEoFq1ati+fbtxiPGbN29CLk9tGHvy5AkGDx6MmJgYFClSBDVr1sSBAwdQuXJlqQ6BiIiIiAqyeu8CpZsAPvw+SemTPHECgBEjRmDEiBEWl0VGRppMz507F3Pnzs2HqIiIiIjolaRVA5EzgPojAeci+nlMmigTkt8Al4iIiIgo32iSgTV9gb9nA7/11g8MQWQFm2hxIiIiIiLKcymJwOo+wNXdgIMT0HA0kAfDjdOriYkTEREREb36khOA33oC1/8GlC5Ar1VA6cZSR0UFCBMnIiIiInq1JcUBK7oBtw4Bju7A22uBQOtufUNkwMSJiIiIiF5tG9/VJ01OhYA+G4ASNaWOiAogJk5ERERE9GprPhl4fA1460fAr6rU0VABxcSJiIiIiF49Oi0gV+hfe5YDhv4DyDmgNGUf3z1ERERE9GqJvQX88Dpw9a/UeUyaKIf4DiIiIiKiV8fjKGBpW+D+OWD7eH3LE1EuYFc9IiIiIno1PLwMLOsAPL0LFC0D9Pk9tbseUQ4xcSIiIiKigu/eOWB5R+DZfcCrItD3D8DdV+qo6BXCxImIiIiICrbok8DyTsDzx4BPCNB3I+DqKXVU9Iph4kREREREBduxZfqkyb+GvnueS1GpI6JXEBMnIiIiIirY2swE3LyB194FnDykjoZeURxVj4iIiIgKnpgzqSPmKRyAJh8zaaI8xcSJiIiIiAqWSzuBn5sBm98HdDqpoyE7wcSJiIiIiAqO85uBVb0BbTKQ+BjQaaSOiOwEEyciIiIiKhhOrwPWhAE6NRD8FtB9GeDgKHVUZCeYOBERERGR7TuxElg/GBBaoGpPoPMiQKGUOiqyI0yciIiIiMi2HV0KbBwGCB1QIwzotFA/IARRPuI7joiIiIhsm7sfIHcAag8CWn8JyGRSR0R2iIkTEREREdm2Cq2BIXsBn2AmTSQZdtUjIiIiItsiBHDgW+DxtdR5vlWYNJGkmDgRERERke0QAtg1Cdj5KbCsI5D8VOqIiACwqx4RERER2QohgO0fA4d+0E+/NgxQuUsbE9ELTJyIiIiISHo6HbD1A+BYuH663Ryg9kBJQyJKi4kTEREREUlLqwE2jQBO/gbI5ECHBUD1t6WOisgEEyciIiIiktbeL18kTQqg809ASFepIyIyw8EhiIiIiCjv7ZkB7J1peZlOA7j5AN2XMWkim8XEiYiIiIjynlwB7JmWmjzptPrnvTOB/XOBWgOASu2li48oE+yqR0RERER5r/FY/fOeaYAmGbh9GFC6AJe2A00npC4nslFMnIiIiIgof4R0BW4dAv7+OnVegw+YNFGBwMSJiIiIiPLO/QvAqVXAxT+BBxdMl8mVQIvJkoRFlFW8xomIiIiIck/KMyD5aer07cP6a5geXADkDkDhUvr5CiWgU6c/YASRjWHiREREREQ5Ex8NHF0KrOgOfBUE/PdL6rLyrYEqXYAui4H67wGx1/XXNE18qH9OO2AEkQ1jVz0iIiIiyhohgHtn9d3vLm4D7v5nuvzOsdTXbt5A1yUvRs+bYzoQRNoBI9JOE9kgJk5ERERElDkhAJlM/zrlGfBzU0Cbkrq8eC2gQhugQlvAu5L5+jqt5dHzDNOG4cmJbBQTJyIiIiKy7PkT4PIufatSwn2g/1b9fJWbvgueTqNPlsq1Atx9Mt5W0/HpL2NLExUATJyIiIiIKNXja8DF7fpk6cYBQKRpCYq9BRQO0L/uvjy1BYrIDjBxIiIiIiK9nZ8CB741nedVKbULnkfx1PlMmsjOMHEiIiIisjcpicC1SH2rUr3hqdck+VcHZAogsL4+UarQGihaWtJQiWwFEyciIiIie/D0HnBpu34kvGt7AE2Sfn7hwNTEqUJbYOxVwLmIdHES2SgmTkRERESvstibwNr+wJ2jpvMLl9QnSmWapc5TOusfRGSGiRMRERHRq0KrBm78AyQnAJXe1M9z8wUeXNS/Ll4zzZDhlXmdElEWMHEiIiIiKsiePwGu7NZfr3R5F5AcBxQJAiq20ydGDo5Aj1/03fHcfaWOlqjAYuJEREREVBCdWAmc/E0/ZLhOkzrfxRMo1UB/DZOh212ZptLESPQKYeJEREREZOt0OuDuf/pR7+QK/bxbh4GoffrXXpX0I+BVaKvvjmcoQ0S5hokTERERkS1KSQSi9uq74F3cDjy7DwzYCZSsq19e7W3AszyHDCfKJ0yciIiIiPLDnhn6lqDGY82X7Z0J6LRA3f8BF7bohwy/ugfQPE8to/IAYm+kJk4BtfUPIsoXTJyIiIiI8oNcAeyZpn9d/wP9sxDAX18A+2YBTScAj64Am0amrlOo5ItR8NoAgQ30Az0QkSSYOBERERHlhwajgKQ4YM80yO+dR5UHCXCYM1I/r+kEfUuUTqu/r1LJ+vpkySeYQ4YT2QgmTkRERETZJYR+OPCnMUDCPSDhvv7Z0RWoPTC13Le1gEeXjZOKc+tRxjDhVBho9JH+tVwBvLMhv6Inoixg4kRERET0spTEF4nQvdSEyMEJqPFOapkfGgL3zwM6tfn6XpVMEyfFiy52cgfAzQci/i5kEBByB8hGn2OrElEBwMSJiIiI7INWAyQ+TE2EnsboE5rQHqllFrXQJ0MpT83X96pomjgJXWrS5FwUcPMB3Lz1zy+PctfrN0Dlrm9d+vtryPZMg1bmAIVOAxz8zvKAEURkU5g4ERERUf6wZlS5puOztk0h9NcIGbrIJdzT7yP4rdQyyzoA988Bzx4CEKbre5Y3TZzUialJk4Mz4O6TmhC9nAx1W6a/wayrV+aDNhQJTD3OPdOgbfQxtjytjDfdz0FhGDCCyRORTWPiJCGtTuBQ1GMceyhDsajHqFfWGwq5/TTVa3UCh6Me4/7TJHi7O6FOUFG7O37WP+vf7ur/xRdnbcOPzOv/71nZ++JckKQ5frP6t4fjfzGqnE4IHAoYZKz/urcWQR45XT9AgoEm+UUy9CIhAoCKbVOXr+wJ3D+rX65JMt1PsXKmiVPiY+DZA/1rmRxw9U6/ZajzT4BCpU+YHN0y7kLnWTZrx/8iadI1+QQH/fvh2N+HUKzSANRvIofcjpInfv7b6ef/CwW5/m0icfruu+8wa9YsxMTEIDQ0FN9++y3q1KmTbvm1a9di4sSJuH79OsqVK4evvvoKbdu2Tbe8zdkzA5cfJKLv1SaIjksCoMDyy0fhV8gJy8tEopyXy6v9j9Ps+PXs9/hZ/wDr326O/8UX58X7rmL6sw7G2Z+4bsIQ7SrTL86vIrPj19d/gTt+9XNAp3nx0Jq+liuAQiVSy947q79eSKcBStbD7cBOKBE5HTGavdigex2hsquop1yHy5XfQ7n754AFdfSJUlKs6T6LlTNNnOJvA7E3U6dVhVKToWIvJUMdvgEUSv0yl2L6GNPjE5zt05IpnRaXK7+HvgdrITruKFL//mtheeX3UE6nzbt924jtZ6IxZfM5s8//Se0ro3UVPwkjyx+mx5/6+W+fx69XkI5f8sRp9erVGD16NH744QfUrVsX8+bNQ6tWrXDx4kV4e3ublT9w4AB69eqFGTNm4M0338TKlSvRqVMn/Pfff6hSpYoER5B1lx8koty5b9BVfRfforNxfreElSh37sU/Dwnjy2s8fh4/j99+j397sXdwTn0Ro7EKTxUafKvtjJGK9RiiXYc56q6oXOwdtJYqOCFeXLOiBYT2RRLgACid9Mu1GuDZ/RfLdS/K6FLLOhcGPPz1ZTUpwN3jqctePB9NCcQtTQMMSXP8oxTrMES7Htu1tVAi3glVjiw2TUaKlU1NGHQ6YPeU1O0aE5YXSYtPMFBveOoxrXpb33JjKcnxrwa8OTe17A8N9aPDvbxNnQbwqwYM+DO17Dc1gKd3LZ9H72Dg3QOp02v66u9N9IIhpXrL4R90Ev9AJgPmqLvi2/9ewwnfXSgUezF1XbkytZtcsTIw0fZrfeuRIVlSOqdft8VrpL8sH2336odhO/6DgGkLWUxcElr+9xoW9qkh3fs/H2w/E41hv/73cmdJxMQlYdiv/+mPvwB8ec4uHn/BP36ZEOLl+PNV3bp1Ubt2bSxYsAAAoNPpEBAQgJEjR+Ljjz82K9+jRw88e/YMW7ZsMc577bXXUK1aNfzwww+Z7i8+Ph6FChVCXFwcPDw8cu9ArKTVCbz+1V/omrASY5TrsEzTAsd05dFKfgTtHA5jq6YO9itfQ5caJSCXyfDAuwFSVEUAAG7xV+ERdyHdXgMPveoixckTAOCacB2Fnpw1Lnt5lUeetZHs7AMAcH52C0UenzTf4IuVnhStjiTX4gAAp8S7KPLov3SPL65IKJ67BQAAVM/voejDIybLhQ5YfewWGqr/RTuHQ5it7opvtZ0xTvEbhik3G4+/R60Ak+OML1wJzzz0XSKUyU/gGfN3ujEkFCqPp4UrAgAcUuLhHf1X+mXdyyC+aAgAQKF5Bp/bO9McvumfxjP3IMQWqw4AkGuT4XdrC9KT6FoST7z0d3OX6TTwv7FRf/xCYP3xO6inOYJWimPYoa2JZdpWqCm7hDHKdZit7opnjp7oVM3fYveQJGdfPPBpaJwucf13yITGYgxJTl6479f0xX6BEjc3QqFNNiljOMIUxyKILt7SOL/4rc1wUCdY3K5a6YE7JVJ/9fW//Scc1XGw9EmidXDBrYAOEC/25Hd7B3YfO4e62mNorjiO3drqiNSFoon8JN5QHMdsdVf84tgDE9+shOIxu+GcdM9ke4YzopM54HpQT+N83+i/4JJ4J00502CulXnHeD59YvbCNeF6+mVL94aQ669V8L73N9zjU4cPlr1UJ9eDekHroP+y5nn/AArHnkuz1HS7N0r1QIqDOyZtOotP1N+iu8M+/K2tgoO6YNSTn0FDxVns1wbjhEMIyrQaAY1zMQBA0YdHUOzhEeP2ZMJ0+zdLdUPSi7/log+Pwev+/vTLBnZBoltJAECRR8fhG707NU5hej5uBnZGwou/uUJPTqP4ra1pzpXpsd0q2QnxhSsDADxiz6Hkjd9heEOkXUcIYPL1EOxNKo2RivUYo1wHrZBBIRM4qyuJy6IEnBRAiL87ZNDhRqluxve7R9wFBJ+eCQgdZEILmeEZ+udrZd7B7ZKdAADusRdQ+/D7qWWEDjLojOteKTcQV8rpRztzj7+MJnu6vNiW+Zv4ctkBOFflQwCAy7PbaBHR0qyMQVRQL5wKnQgAUCU9ROvtjdIte0YbiCqKG0gWDlDJLP8NG9z2b4Ujtefoz6JOh86bQ9ItG+3dCAfqLjROd9xaEw66JItl7xethb31w43THXY2hCrlicWyjwsFY1fD1caqb/dXS7g+T02cdJBDyBUQMgfEuZXBrtd/My5r/O8guD2/Ax0UeJCoQYpODi0UqCy7DrkMSBYOqJC8HADQ3OkietUpgWSVF5JUnkhRehj/drMy6JzM7L9eugWzsM0slLUQrE4ITNt6HnHPLYzA90JhZyU+aVcJ8nQONjtf2bL1JS8bK4lMVtIJgS//vJjh8RdyVmJc6wqQyyz9Nb60v0wKZBZP5uvnLICXl+qEwJydlxCflP7fu4eTA0Y1L2dW/5b2ZGn3lstZV5mWt2c+0/r9mk7rhMAPkVfxNNny8csA+BZywv5xzfK9215WcgNJE6eUlBS4uLhg3bp16NSpk3F+WFgYYmNj8ccff5itU7JkSYwePRqjRo0yzps0aRI2btyIkyfNv/wnJycjOTn1y2J8fDwCAgLw8OFDSRKnQ1GP0WfJUQAwfnHISKfkqTgh9F9eBiu2YIJyZbple6VMwEGdvotBH0UEvlAuTbfsgJQP8ZdO/wtcF/k+zHZMP+kckTISW3T1AABt5Iew0HF+umU/Ug/BWm0TAEAT+QmEO85Mt+xubTW8oThh1ReHGepe+FHbHgAQIruGzapP0y07X9MZczVdAQBlZbexS5V+f/GfNO0wXfM2AKA4HuAfp/fTLfuLpjkmagYAAIogHsedhqZb9ndtQ4xRDwMAOCEZF5z6p1vW8MXRkERed+qdbtlIbSj6qccZp8+q+sNVlmyx7CFdRfRI+cw4fUQ1FF6yeItlT+mC0CFlmnH6b8f3ESB/YLHsFZ0/mqd8bZze4TgWFeS3LZa9LTzxevI3xumNjhNRTX7VYtlE4YjKyeHG6d+UX6Ce4pzFss+FIyqlKbtYOQtvKI5bLAsApZJWwPC1Z4FyPt5UHEq3bOWkJUiEvoVhlsMP6OawL92yNZMW4hEKAQCmOCxFmENEumVfT56H20Lfiv6xw0oMdUg/8W6RPBOXhf53+fcVv+MD5e/plu2YPBUnX3xGDFFsxifK39Itm5XPiP4pH2GPTv9DQWafEcNT3sNW3WsAgLbyf/G94zfplk37GXFZ9Q6UsvS7Jn2mDsNybSsAQF3ZeaxWfZ5u2S/VPfGDVt/1L/PPiLcwV9MNQNY+I/zxEPtUo6CFHDrITZ61kGOdthG+1Oj/fj2QgE2OE6GFHAIys7J/aavjXYc/oJJpkCIc8K+uErSQQwMFtFBAA7nx+aSujPE8AMCnDr+82I4CaiigFanlbwgfbNeldnXvLN8HGZBmewrjfp4Id+P/FwCoIrsGGZAmDrnxdbJwxAMUNpZ1QZJxuf4Y5emeQ0sM//8Mn/+Gzz8ism+/DqiFukFF83Wf8fHx8PT0tCpxkrSr3sOHD6HVauHj42My38fHBxcuXLC4TkxMjMXyMTExFsvPmDEDU6ZMMZu/c+dOuLi4ZDPy7Dv2UAZA37f6W21nvO+wHg4yHXRChgO6ysZyjgrAQQYUdVOhrEwHANBpi+I/Xfp9rz1cXFBW/uJXXl0R/KfVl7WUGbs4u6HMi7IKXSEcy2C7js4exrIqnXuGZeVOhVH6RVkXnZtZWa0AUl58T1qtbYrX5WegkmmgFgr8q6tkcvyKND84qJ2KGbdbRDjhiDb9X1wTVd4o7awv6ylUOKytarI87fl4qvI1li0ilDikDU13u48dixvLugoFDmqrpVv2nrIkSjvpyyqFDAe0+iRVI4DkNN8T35Afh0ImkCwcjF8aIrQ14agQcLDwg8t1ZSmUcRLGX16PaKpBmU6L03WH4ijrpDNOH9eEwkUkWiwb7eCDcmnKntSE4Lp4avEn1keKIijvnFr2rKYK7gvLTevxcEeFQvqyMgCnkivjjraYcXlr+REoZAJaIcMWbT3jfH9nHa7IKyJFuJtsT7wISAMH43YBIEpTAXuEU5pypsp76Iw/V9/QVsBunen1DSLNgQZ5AOoXf3O3teUQodO9VDZVCXcFir4oG6Mtgx3C8i/7AODr5giNRoeY53Kc0pXGak0TdFXsNR7/Wm1jYxxOKieUc9Rv95GuFLbompnEmRqDDO5u7ij3IoZYXSA26ExbRFLXkUHlWsRYNkEXgHW6Nha3KyCD3NXTWPa5rjh+07VPd7spLn4oJ9eXTdH54xfdW6bbe3Huk7UynNWVAqD/4qyUaaERcjjIdNirDcE+XVXoIIerUgalQo5ohwrG7eqEL2bohkEHOXSy1CREQAYd5Lip9DfGC+GLUeKzF2X0y4Uh0ZHJEadMPWcO8EYvfKPfLuTQvShveGgcFShv2C6Koi2Wp1vHAFAehrIuGILZJsviU4CY53Lj8atkGmPicERXwfgZ4OusQ6GXBmirgNS/o3V4O8MYKiL1PXte9nqGZSulKatDKeNrB5h/QfBC2r8Fx5dagFKXpfdbcWwKcPuZ3Jg0GZKltD8ifqvtjBKuOhTOZIC6jFj7a3Be/Wyc3mbjUoC7iZknmP4u5vWfVn79Fp+d20pltIqh/jOTtv5zeqw5vTVWZqtnuvk0BZ4kAzcSMj/+QDcdiqqysS9DuRw0tlpc1cJMq2NJ8/phEnD1aebHv/PvQ3h0Pn/bdBITLX83skTSFqe7d++iePHiOHDgAOrVS/3SNHbsWOzduxeHDpn/Kuzo6Ihly5ahV69exnnff/89pkyZgnv37pmVLwgtTpZ+cZMi484PPH4eP4+fx5/eF2fDNI//1T3+Q8s+MTlWg7TnoG7Y9Ff2+A1//xl5leufx8/jzwxbnDLg6ekJhUJhlvDcu3cPvr6+Ftfx9fXNUnmVSgWVyjx1VyqVUCqV2Yw8++qV9YZfISd0S1iJ0Rb+ccoArHXr/coOTcnj5/Hz+O37+PWjx5l+cTY8j1Gug7uTA+qVbcvjf0WP/4KTHHOSzLvlfavtDBmAQk7yV/r971fICTFxSRZbpQzXePD4efw8/vw9/qzkA1nrlJzLHB0dUbNmTezevds4T6f7f3v3H1RVnf9x/HUFLxA/g/ACg6AmIiIruOwasJljKuuuNDa5ppml/rPuwgD5Y9RaxWENgUnHCIW1adVmzW37TrrmbBQhajJmIFLrriKamZv4o9VAZWuJe79/uN28gVwovYe8z8fMnfGeczj39TnvYS5vzzmfY1VVVZXDGagbpaSkOGwvSZWVlTfdvq/x6GfSy/fu0YL+12eQuvGLc237NC3o/396+d49d+QvjcT4GT/jd/fxjx8WorXt01T6rT+cS/93DMYPC2H8d/D4Ix/OtzdJNzLpf5fpPZx/R48/L+P6JfldjV+S8jJGMH7G79JcrnKnjN/QxkmSFixYoBdffFFbtmzR0aNH9Zvf/EbXrl3T3LnXb6Z/4okntGzZN880ycnJUUVFhdasWaNjx45p5cqVqqurU1ZWllFD6LWY0LvUNCJbr/k5TgLwmt9j16ciDnX9vVeuxPgZP+N33/EPfbRAI2auUligt8PysEBvjZi5SkMfLTAomWu4+/h/PjJcZY+P7nL8P4SpiL8vxs/4Gf8Pe/yGT0cuSaWlpfYH4CYmJqqkpERjxoyRJI0bN06DBg3S5s2b7du/9tpr+t3vfmd/AG5xcXGPH4Br9HTkN+qw2nTgxAW9/e5BTbp/zB17evZmfshPjr4VqD/1p/7Un/pTf+pP/am/sfX/wUxHboS+1DhJUnt7u/72t7/pF7/4hSH3XMFY1N+9UX/3Rv3dG/V3b9S/7+hNb2D4pXoAAAAA0NfROAEAAACAEzROAAAAAOAEjRMAAAAAOEHjBAAAAABO0DgBAAAAgBM0TgAAAADgBI0TAAAAADhB4wQAAAAATtA4AQAAAIATNE4AAAAA4ASNEwAAAAA4QeMEAAAAAE54Gh3A1Ww2mySptbXV4CTXtbe3q62tTa2trerfv7/RceBi1N+9UX/3Rv3dG/V3b9S/7/i6J/i6R+iO2zVOV65ckSQNHDjQ4CQAAAAA+oIrV64oMDCw221Mtp60V3cQq9Wqs2fPyt/fXyaTyeg4am1t1cCBA3XmzBkFBAQYHQcuRv3dG/V3b9TfvVF/90b9+w6bzaYrV64oIiJC/fp1fxeT251x6tevnyIjI42O0UlAQAC/OG6M+rs36u/eqL97o/7ujfr3Dc7ONH2NySEAAAAAwAkaJwAAAABwgsbJYF5eXsrLy5OXl5fRUWAA6u/eqL97o/7ujfq7N+r/w+R2k0MAAAAAQG9xxgkAAAAAnKBxAgAAAAAnaJwAAAAAwAkaJwAAAABwgsbJAKtXr9ZPfvIT+fv7a8CAAZo6daoaGxuNjgWDFBYWymQyKTc31+gocJFPP/1Ujz/+uEJCQuTj46OEhATV1dUZHQsu0NHRoeXLl2vw4MHy8fHRvffeq9///vdinqY71759+5SRkaGIiAiZTCbt2LHDYb3NZtOKFSsUHh4uHx8fTZgwQU1NTcaExS3XXf3b29u1ZMkSJSQkyNfXVxEREXriiSd09uxZ4wKjWzROBti7d68yMzP13nvvqbKyUu3t7Zo0aZKuXbtmdDS4WG1trf7whz/oRz/6kdFR4CKXL19WWlqa+vfvrzfffFP//Oc/tWbNGt19991GR4MLFBUVqaysTKWlpTp69KiKiopUXFysF154wehouE2uXbumUaNGaf369V2uLy4uVklJicrLy3Xw4EH5+voqPT1dX3zxhYuT4nborv5tbW2qr6/X8uXLVV9fr9dff12NjY166KGHDEiKnmA68j7g4sWLGjBggPbu3auxY8caHQcucvXqVY0ePVobNmzQqlWrlJiYqHXr1hkdC7fZ0qVLVVNTo3fffdfoKDDAlClTZLFY9NJLL9mXPfLII/Lx8dGf/vQnA5PBFUwmk7Zv366pU6dKun62KSIiQgsXLtSiRYskSS0tLbJYLNq8ebNmzJhhYFrcat+uf1dqa2v105/+VKdPn1ZUVJTrwqFHOOPUB7S0tEiSgoODDU4CV8rMzNQvf/lLTZgwwegocKGdO3cqOTlZv/rVrzRgwAAlJSXpxRdfNDoWXCQ1NVVVVVU6fvy4JOmDDz7Q/v37NXnyZIOTwQinTp3SuXPnHL4HAgMDNWbMGB04cMDAZDBKS0uLTCaTgoKCjI6CLngaHcDdWa1W5ebmKi0tTSNHjjQ6Dlzkz3/+s+rr61VbW2t0FLjYRx99pLKyMi1YsEBPP/20amtrlZ2dLbPZrCeffNLoeLjNli5dqtbWVg0fPlweHh7q6OjQs88+q1mzZhkdDQY4d+6cJMlisTgst1gs9nVwH1988YWWLFmimTNnKiAgwOg46AKNk8EyMzN15MgR7d+/3+gocJEzZ84oJydHlZWV8vb2NjoOXMxqtSo5OVkFBQWSpKSkJB05ckTl5eU0Tm7gL3/5i7Zu3apXXnlF8fHxamhoUG5uriIiIqg/4Mba29s1ffp02Ww2lZWVGR0HN8GlegbKysrSrl27VF1drcjISKPjwEUOHTqkCxcuaPTo0fL09JSnp6f27t2rkpISeXp6qqOjw+iIuI3Cw8M1YsQIh2VxcXH65JNPDEoEV1q8eLGWLl2qGTNmKCEhQbNnz9ZTTz2l1atXGx0NBggLC5MknT9/3mH5+fPn7etw5/u6aTp9+rQqKys529SH0TgZwGazKSsrS9u3b9fu3bs1ePBgoyPBhR588EH9/e9/V0NDg/2VnJysWbNmqaGhQR4eHkZHxG2UlpbW6fEDx48fV3R0tEGJ4EptbW3q18/xq9fDw0NWq9WgRDDS4MGDFRYWpqqqKvuy1tZWHTx4UCkpKQYmg6t83TQ1NTXpnXfeUUhIiNGR0A0u1TNAZmamXnnlFf31r3+Vv7+//TrmwMBA+fj4GJwOt5u/v3+n+9l8fX0VEhLCfW5u4KmnnlJqaqoKCgo0ffp0vf/++9q4caM2btxodDS4QEZGhp599llFRUUpPj5ehw8f1tq1azVv3jyjo+E2uXr1qk6cOGF/f+rUKTU0NCg4OFhRUVHKzc3VqlWrFBMTo8GDB2v58uWKiIjoduY1/HB0V//w8HBNmzZN9fX12rVrlzo6Oux/EwYHB8tsNhsVGzdjg8tJ6vK1adMmo6PBIA888IAtJyfH6BhwkTfeeMM2cuRIm5eXl2348OG2jRs3Gh0JLtLa2mrLycmxRUVF2by9vW1DhgyxPfPMM7Yvv/zS6Gi4Taqrq7v8zn/yySdtNpvNZrVabcuXL7dZLBabl5eX7cEHH7Q1NjYaGxq3THf1P3Xq1E3/JqyurjY6OrrAc5wAAAAAwAnucQIAAAAAJ2icAAAAAMAJGicAAAAAcILGCQAAAACcoHECAAAAACdonAAAAADACRonAAAAAHCCxgkAAAAAnKBxAgD0CR9//LFMJpMaGhqMjmJ37Ngx3XffffL29lZiYuJt/7yeHIM9e/bIZDLp888/v+15AADfoHECAEiS5syZI5PJpMLCQoflO3bskMlkMiiVsfLy8uTr66vGxkZVVVXddLszZ85o3rx5ioiIkNlsVnR0tHJycvTvf//7lmdKTU1Vc3OzAgMDJUmbN29WUFDQLf8cAIAjGicAgJ23t7eKiop0+fJlo6PcMv/973+/88+ePHlSP/vZzxQdHa2QkJAut/noo4+UnJyspqYmbdu2TSdOnFB5ebmqqqqUkpKiS5cufefP74rZbFZYWJjbNrMAYBQaJwCA3YQJExQWFqbVq1ffdJuVK1d2umxt3bp1GjRokP39nDlzNHXqVBUUFMhisSgoKEj5+fn66quvtHjxYgUHBysyMlKbNm3qtP9jx44pNTVV3t7eGjlypPbu3euw/siRI5o8ebL8/PxksVg0e/ZsffbZZ/b148aNU1ZWlnJzc3XPPfcoPT29y3FYrVbl5+crMjJSXl5eSkxMVEVFhX29yWTSoUOHlJ+fL5PJpJUrV3a5n8zMTJnNZr399tt64IEHFBUVpcmTJ+udd97Rp59+qmeeecZhnzt27HD4+aCgIG3evLnHx+DGS/X27NmjuXPnqqWlRSaTySHnhg0bFBMTI29vb1ksFk2bNq3L/ACAnqFxAgDYeXh4qKCgQC+88IL+9a9/fa997d69W2fPntW+ffu0du1a5eXlacqUKbr77rt18OBBzZ8/X7/+9a87fc7ixYu1cOFCHT58WCkpKcrIyLBf8vb5559r/PjxSkpKUl1dnSoqKnT+/HlNnz7dYR9btmyR2WxWTU2NysvLu8z3/PPPa82aNXruuef04YcfKj09XQ899JCampokSc3NzYqPj9fChQvV3NysRYsWddrHpUuX9NZbb+m3v/2tfHx8HNaFhYVp1qxZevXVV2Wz2Xp17Lo7BjdKTU3VunXrFBAQoObmZnvOuro6ZWdnKz8/X42NjaqoqNDYsWN7lQEA4IjGCQDg4OGHH1ZiYqLy8vK+136Cg4NVUlKi2NhYzZs3T7GxsWpra9PTTz+tmJgYLVu2TGazWfv373f4uaysLD3yyCOKi4tTWVmZAgMD9dJLL0mSSktLlZSUpIKCAg0fPlxJSUn64x//qOrqah0/fty+j5iYGBUXFys2NlaxsbFd5nvuuee0ZMkSzZgxQ7GxsSoqKlJiYqLWrVsn6Xrj4+npKT8/P4WFhcnPz6/TPpqammSz2RQXF9flZ8TFxeny5cu6ePFir45dd8fgRmazWYGBgTKZTAoLC7Pn/OSTT+Tr66spU6YoOjpaSUlJys7O7lUGAIAjGicAQCdFRUXasmWLjh49+p33ER8fr379vvmasVgsSkhIsL/38PBQSEiILly44PBzKSkp9n97enoqOTnZnuODDz5QdXW1/Pz87K/hw4dLun4/0td+/OMfd5uttbVVZ8+eVVpamsPytLS07zRmZ2eUzGZzr/bX3THoiYkTJyo6OlpDhgzR7NmztXXrVrW1tfUqAwDAEY0TAKCTsWPHKj09XcuWLeu0rl+/fp0ahfb29k7b9e/f3+G9yWTqcpnVau1xrqtXryojI0MNDQ0Or6amJodL0Xx9fXu8z+9j6NChMplMN21qjh49qtDQUPusdyaTqUfH7vvy9/dXfX29tm3bpvDwcK1YsUKjRo1iCnMA+B5onAAAXSosLNQbb7yhAwcOOCwPDQ3VuXPnHBqAW/nspffee8/+76+++kqHDh2yXwo3evRo/eMf/9CgQYM0dOhQh1dvmqWAgABFRESopqbGYXlNTY1GjBjR4/2EhIRo4sSJ2rBhg/7zn/84rDt37py2bt2qOXPm2JeFhoaqubnZ/r6pqanLM0HdHYNvM5vN6ujo6LTc09NTEyZMUHFxsT788EN9/PHH2r17d4/HBgBwROMEAOhSQkKCZs2apZKSEofl48aN08WLF1VcXKyTJ09q/fr1evPNN2/Z565fv17bt2/XsWPHlJmZqcuXL2vevHmSrs9gd+nSJc2cOVO1tbU6efKk3nrrLc2dO7fL5qE7ixcvVlFRkV599VU1NjZq6dKlamhoUE5OTq/2U1paqi+//FLp6enat2+fzpw5o4qKCk2cOFHDhg3TihUr7NuOHz9epaWlOnz4sOrq6jR//vxOZ+GcHYNvGzRokK5evaqqqip99tlnamtr065du1RSUqKGhgadPn1aL7/8sqxW603v9wIAOEfjBAC4qfz8/E6X0sXFxWnDhg1av369Ro0apffff7/LGee+q8LCQhUWFmrUqFHav3+/du7cqXvuuUeS7GeJOjo6NGnSJCUkJCg3N1dBQUEO91P1RHZ2thYsWKCFCxcqISFBFRUV2rlzp2JiYnq1n5iYGNXW1mrIkCGaPn26oqOjNXnyZA0bNkw1NTUOk0qsWbNGAwcO1P3336/HHntMixYt0l133dWrY/Btqampmj9/vh599FGFhoaquLhYQUFBev311zV+/HjFxcWpvLxc27ZtU3x8fK/GBgD4hsnW2zlSAQBAt/Ly8rR27VpVVlbqvvvuMzoOAOAWoHECAOA22LRpk1paWpSdnd3rs2EAgL6HxgkAAAAAnOC/wAAAAADACRonAAAAAHCCxgkAAAAAnKBxAgAAAAAnaJwAAAAAwAkaJwAAAABwgsYJAAAAAJygcQIAAAAAJ2icAAAAAMCJ/wdQN3MIJ5q/lwAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import time\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Define the range of qubits to test\n",
        "qubit_counts = range(2, 14)  # Adjust the range as needed\n",
        "\n",
        "# Measure runtime of the original simulation function\n",
        "runtimes_tensor = []\n",
        "for n in qubit_counts:\n",
        "    start_time = time.time()\n",
        "    simulate_circuit_tensor(n)\n",
        "    end_time = time.time()\n",
        "    runtimes_tensor.append(end_time - start_time)\n",
        "\n",
        "# Measure runtime of the matrix simulation function\n",
        "runtimes_matrix = []\n",
        "for n in qubit_counts:\n",
        "    start_time = time.time()\n",
        "    simulate_circuit(n)  # Replace with the alternative function's name\n",
        "    end_time = time.time()\n",
        "    runtimes_matrix.append(end_time - start_time)\n",
        "\n",
        "\n",
        "\n",
        "# Plotting the performance comparison\n",
        "plt.figure(figsize=(12, 8))\n",
        "plt.plot(qubit_counts, runtimes_tensor, marker='o', linestyle='-', label=\"Tensor Multiplication Approach\")\n",
        "plt.plot(qubit_counts, runtimes_matrix, marker='x', linestyle='--', label=\"Matrix Approach\")\n",
        "plt.xlabel('Number of Qubits')\n",
        "plt.ylabel('Runtime (s)')\n",
        "plt.yscale('log')  # Set y-axis to a logarithmic scale for finer detail\n",
        "plt.ylim(1e-4, max(runtimes_matrix) * 1.2)  # Adjust y-axis limit to a minimum value for clarity\n",
        "plt.title('Performance Comparison of Quantum Circuit Simulation Approaches')\n",
        "plt.legend()\n",
        "plt.grid(True, which=\"both\", linestyle='--', linewidth=0.5)  # Add minor grid lines for better readability\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 718
        },
        "id": "Y7DDCPFV7uW1",
        "outputId": "a9c4a35a-a790-4265-911d-9e38a772c2f0"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1200x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Bonus Section: Sampling and Expectation Values\n",
        "\n",
        "In this section, we explore additional features:\n",
        "1. **Sampling Final State**: We can simulate measurements by probabilistically sampling from the statevector's squared amplitudes.\n",
        "2. **Expectation Values**: For an operator \\( O \\), the expectation value in state \\( |Ψ⟩ \\) can be computed as ⟨Ψ| O |Ψ⟩.\n",
        "\n",
        "These functionalities extend the simulator to provide insights similar to what would be obtained on a real quantum device.\n"
      ],
      "metadata": {
        "id": "_oqbO691FIQb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Sampling of Final States**"
      ],
      "metadata": {
        "id": "QcOnd-XTFWK9"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def sample_measurements(state, num_samples=1000):\n",
        "    # Flatten the state to a vector\n",
        "    state_vector = state.flatten()\n",
        "    # Compute probabilities\n",
        "    probabilities = np.abs(state_vector) ** 2\n",
        "    # Generate possible outcomes\n",
        "    outcomes = np.arange(len(state_vector))\n",
        "    # Sample outcomes based on probabilities\n",
        "    samples = np.random.choice(outcomes, size=num_samples, p=probabilities)\n",
        "    return samples\n",
        "\n",
        "# Example usage\n",
        "state = simulate_circuit_tensor(n_qubits=5)\n",
        "samples = sample_measurements(state, num_samples=1000)\n",
        "#Convert outcomes to bitstrings\n",
        "bitstrings = [format(sample, '03b') for sample in samples]\n",
        "print(f\"Sampled bitstrings: {bitstrings[:10]}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ynu0CZtMFHXJ",
        "outputId": "4c2b574a-ebab-400a-f723-1fa383ccbec8"
      },
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Sampled bitstrings: ['1000', '10000', '10000', '10000', '10000', '10000', '10000', '10000', '10000', '10000']\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def compute_expectation_value(state, operator, target_qubit):\n",
        "    \"\"\"\n",
        "    Compute the expectation value <Psi|Op|Psi> for a single-qubit operator.\n",
        "\n",
        "    \"\"\"\n",
        "    # Apply operator to the target qubit\n",
        "    state_op = apply_single_qubit_gate_tensor(state, operator.reshape(2, 2), target_qubit)\n",
        "    # Compute the inner product <Psi|Op|Psi>\n",
        "    state_conj = np.conj(state)\n",
        "    expectation = np.tensordot(state_conj, state_op, axes=state.ndim)\n",
        "    return expectation\n",
        "\n",
        "\n",
        "\n",
        "#Example Usage\n",
        "\n",
        "n_qubits = 10\n",
        "state = simulate_circuit_tensor(n_qubits)\n",
        "Z = np.array([[1, 0],\n",
        "              [0, -1]], dtype=complex)\n",
        "expectation = compute_expectation_value(state, Z, target_qubit=0)\n",
        "print(f\"Expectation value of Z on qubit 0: {expectation}\")\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ScCfiRR-HxRS",
        "outputId": "f8a2c031-b03e-4357-f412-a08584a29b02"
      },
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Expectation value of Z on qubit 0: (-2.2371143170757382e-17+0j)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Summary and Final Analysis\n",
        "\n",
        "### Comparison of Naive Matrix Multiplication and Tensor-Based Operations\n",
        "\n",
        "- **Naive Matrix Multiplication**: This approach scales poorly with the number of qubits due to its exponential complexity \\( O(2^{2n}) \\). It quickly becomes infeasible for larger systems (beyond 12-14 qubits) as computation time and memory requirements grow exponentially.\n",
        "- **Tensor-Based Operations**: Tensor operations allow for a more efficient way to apply gates to individual qubits or pairs of qubits within the system. The improved scalability of this approach means it can handle larger systems (up to 20 qubits or more, depending on hardware) with a relatively lower increase in computation time. (On my system I was able to 17 qubits before it crashes.)\n",
        "\n",
        "### Runtime Plot Analysis\n",
        "\n",
        "The runtime plot illustrates a steep, exponential increase in computation time for naive matrix multiplication, while the tensor-based approach grows more slowly, highlighting its better scalability. for larger systems.\n",
        "\n",
        "### Practical Takeaways\n",
        "\n",
        "- For small systems (up to ~5 qubits), both methods perform similarly and can be used effectively.\n",
        "- For larger systems, **tensor-based operations** are essential due to the exponential complexity of matrix multiplication.\n",
        "- Despite improvements from tensor-based methods, both approaches face exponential growth, reflecting the inherent difficulty of simulating large quantum systems on classical hardware.\n",
        "\n",
        "### Conclusion\n",
        "\n",
        "In summary, while **naive matrix multiplication** is useful for small-scale quantum simulations, **tensor-based operations** offer the efficiency needed for larger systems. This study emphasizes the limitations of classical simulation for large quantum circuits, underscoring the need for specialized quantum hardware to efficiently simulate complex quantum systems.\n"
      ],
      "metadata": {
        "id": "TSe9RbGubF4r"
      }
    }
  ]
}