diff --git a/challenges/PIQUE challenge/Solution_Jingle_Bell_States/Quantum_Random_Number_Generator.ipynb b/challenges/PIQUE challenge/Solution_Jingle_Bell_States/Quantum_Random_Number_Generator.ipynb
new file mode 100644
index 0000000..5249685
--- /dev/null
+++ b/challenges/PIQUE challenge/Solution_Jingle_Bell_States/Quantum_Random_Number_Generator.ipynb
@@ -0,0 +1,1138 @@
+{
+ "nbformat": 4,
+ "nbformat_minor": 0,
+ "metadata": {
+ "colab": {
+ "provenance": [],
+ "authorship_tag": "ABX9TyN1c/ObE7XnhBZcurGL+R+F",
+ "include_colab_link": true
+ },
+ "kernelspec": {
+ "name": "python3",
+ "display_name": "Python 3"
+ },
+ "language_info": {
+ "name": "python"
+ }
+ },
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "view-in-github",
+ "colab_type": "text"
+ },
+ "source": [
+ "![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\")
"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# **RANDOM NUMBERS GENERATION with Quantum Computing**\n",
+ "---\n",
+ "---\n",
+ "## **CONTEXT**\n",
+ "\n",
+ "*Random number generation* plays a crucial role in areas such as\n",
+ "\n",
+ "- Cryptography\n",
+ "- System Simulation\n",
+ "- Take decisions\n",
+ "- Games.\n",
+ "\n",
+ "Traditionally, random numbers have been generated in two ways:\n",
+ "\n",
+ "- Physical sources of randomness (such as flipping a coin or dice)\n",
+ "- Mathematical algorithms known as pseudorandom number generators (PRNG).\n",
+ "\n",
+ "**Quantum Computing**, instead of relying on deterministic algorithms, **use** the inherent properties of quantum mechanics, like **superposition and uncertainty, to produce randomness**.\n",
+ "\n",
+ "### **Classical 🆚 Quantum Computing**\n",
+ "\n",
+ "While PRNGs (from classical computing) may eventually repeat patterns or be susceptible to prediction if the seed value is known, quantum randomness does not suffer from such weaknesses, making it ideal for high-security applications and other areas where Genuine randomness is of utmost importance.\n",
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "rTcKiQIQHXCE"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title Importing libraries\n",
+ "\n",
+ "from google.colab import output # clear output when is not necessary\n",
+ "!pip install qiskit\n",
+ "!pip install pylatexenc\n",
+ "!pip install qiskit-aer\n",
+ "output.clear()\n",
+ "\n",
+ "import numpy as np"
+ ],
+ "metadata": {
+ "cellView": "form",
+ "id": "TIgIzgpb8sSV"
+ },
+ "execution_count": 1,
+ "outputs": []
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# **USED GATES INTRODUCTION**\n",
+ "\n",
+ "We are going to give a brief presentation of the gates that will be used for the circuit, their operation and how to implement them in Qiskit."
+ ],
+ "metadata": {
+ "id": "cVGh3At6xoL6"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **Pauli-X Gate**\n",
+ "\n",
+ "The Pauli-X gate is the quantum equivalent of the classical NOT gate. It flips the state of a qubit, turning\n",
+ "∣0⟩ into ∣1⟩ and vice versa.\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "bVihmFQm7wba"
+ }
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 127
+ },
+ "cellView": "form",
+ "id": "H7w0c9_PF1__",
+ "outputId": "c89c57f5-c043-414c-f21f-1e5bc0a3ba7c"
+ },
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": "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\n"
+ },
+ "metadata": {},
+ "execution_count": 2
+ }
+ ],
+ "source": [
+ "#@title Code\n",
+ "from qiskit import QuantumCircuit\n",
+ "\n",
+ "qc = QuantumCircuit(1)\n",
+ "qc.x(0) # Apply the X gate to qubit 0\n",
+ "\n",
+ "qc.draw(output='mpl', style=\"clifford\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Use:** To flip the state of a qubit."
+ ],
+ "metadata": {
+ "id": "eRfdBKDO9Zi3"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **CNOT Gate (Controlled-NOT)**\n",
+ "\n",
+ "The CNOT gate is a two-qubit quantum gate that performs a NOT operation on the second qubit (target) only when the first qubit (control) is in the state ∣1⟩.\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "18K6Yoob9q_z"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title Code\n",
+ "qc = QuantumCircuit(2)\n",
+ "qc.cx(0, 1) # Apply the CNOT gate with qubit 0 as control and qubit 1 as target\n",
+ "\n",
+ "qc.draw(output='mpl', style=\"clifford\")"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 191
+ },
+ "cellView": "form",
+ "id": "xPUgfWGWHWHV",
+ "outputId": "4b27eae1-ea23-4582-98d7-aacb201c2bc9"
+ },
+ "execution_count": 3,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAAALAAAACuCAYAAACWa4e1AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAMIUlEQVR4nO3dW0xUBxrA8f8gygDOrCC2ow4VULCAXKxIvex2xeJujdrqg4nR2GZjTPbBSLLGadKX2n1xacyaWPeimyZN9oGQrdawkt1ms9iVWNdiUWsFbyCGQcZ2BEVG0CKzDxN0KcNlhrnwHb5f0ljnnDnnq/6dOXPOnGryer1elBIqJtoDKDUeGrASTQNWomnASjQNWImmASvRNGAlmgasRNOAlWgasBJNA1aiacBKNA1YiaYBK9E0YCWaBqxE04CVaBqwEk0DVqJpwEo0DViJpgEr0TRgJZoGrETTgJVoGrASTQNWomnASjQNWImmASvRNGAlmgasRNOAlWgasBJNA1aiacBKNA1YiaYBK9E0YCWaBqxE04CVaBqwEk0DVqJpwEo0DViJpgEr0TRgJZoGrETTgJVoGrASTQNWomnASjTDB+x2u3E4HCxYsACz2UxqaiplZWV4PB527NiByWTi8OHD0R4z7B70QOMd+KYVbtyFH55Ge6LQiI32AOF08eJF1q5di8vlIjExkZycHO7cucOhQ4doamqio6MDgMLCwugOGkZNd+H0dbjcCv3e548nxsGrGfCzhZCUGL35xsvk9Xq9o68mj9vtZvHixTidTvbs2cP777+PxWIB4MMPP+Tdd98lNjaWp0+fcv/+faxWa5QnDr1/fQvVl0ZeJ34a7Pw5ZLwQmZlCzbABb926lYqKCnbt2sVHH300ZHlhYSGXLl0iPT2d5ubmKEwYXv+5Cp99PbZ142Kh7BcwJym8M4WDIY+BGxsbqaysJCUlhf379/tdZ8mSJQAUFBQMevzWrVu8+eabWCwWkpKSePvtt7l3717YZw6l7l6oujD29R/3wYn68M0TToYMuKKigv7+frZt28b06dP9rhMfHw8MDvjhw4eUlJTgdDqpqKjg6NGj1NbWsn79evr7+yMyeyica4KnAY573QV3u8IzTzgZ8kNcTU0NACUlJcOu43Q6gcEBHz16lLa2Nk6fPs1LL70EgN1uZ8WKFVRVVbFx48bwDR1CXwV5RHS+GdYVhnSUsDPkMXBqaipOp5MLFy74PcPQ19fH7NmzcbvdNDU1kZGRATwP/tSpU4PWnz9/PqtWreLjjz8Oap6ioiJcLldQzw3GW7+9ytQ4/+88I7ldf4y6yrIwTDQym83G+fPng3quIV+BPR4PAD09PX6XV1ZW4na7sVgspKenP3u8oaGBzZs3D1k/NzeXhoaGoOdxuVy0tbUF/fxABXu488jjieicoWDIgG02G52dndTX17N8+fJBy9rb29m7dy8A+fn5mEymZ8s6OzuZMWPGkO0lJydz7dq1cc0TSb1d7cTFB3Fa8If7zJ07N/QDjWI8vz6GDLi0tJTGxkbKy8tZs2YNWVlZANTV1bF9+3bcbjcQuQsYwb49BqumIbCzEAP+enA3L1h3h36gMDLkWQiHw8HMmTNpbW0lNzeXvLw8MjMzKS4uJiMjg9WrVwNDT6ElJSVx//79Idvr6OggOTk5EqOHxKvzITbA39mFNnhB4LUcQwZst9upra1l3bp1mM1mWlpaSE5O5siRI1RXV3P9+nVgaMDZ2dl+j3UbGhrIzs6OyOyhkBgHb70y9vXNU2HjkvDNE06GPAsxku7ubqxWKyaTiYcPH5KQkPBs2YEDB3jvvfdobm7GbrcDcO7cOZYtW8bx48fZtGlTtMYOylgOJRLjYOcqSEuJyEghN+kCHghy4cKFXL16ddCyrq4u8vLySElJ4YMPPqC3txeHw8GsWbM4e/YsMTHy3rBufQ+11+BS6+CLG9PNsHw+rMyCGQnDP3+iM+SHuJFcvnwZGHr4AGC1WqmpqaGsrIwtW7YQGxvL+vXrOXjwoMh4AdJn+f552Au/+zt4nkDiNNi3EWKnRHu68dOAf2T+/PmcPHkykiNFhMX8PNjYKcaIFwz6IW4kowWsZJl0r8AD35NQxjDpXoGVsWjASjQNWImmASvRNGAlmgasRNOAlWgasBJNA1aiacBKNA1YiaYBK9E0YCWaBqxE04CVaBqwEk0DVqJpwEo0DViJpgEr0TRgJZoGrETTgJVoGrASTQNWomnASjQNWImmASvRNGAlmgasRNOAlWgasBJNA1aiacBKNA1YiaYBK9E0YCXapPtbiiaT/n642wWtHdDWCY+e+B5/9AT+8Q2kJoM9GX4SDyZTdGcN1qT7q2Yng04PfHkDzjZBd+/o69uT4KdZ8EoaTBP2kqYBG8ijJ1BVD+eaIZjf1fhpsK4AVmRCjJBXZA3YIBraoPIcPOgZ/7YyX4Qty2Dm9PFvK9w0YAP44iqc+Dq020yMg1+XQOrM0G431PQshHDhiBfA8xj+8G9wdoR+26GkAQt2pS088Q7o/QGOnvLFPFEJ+8ypBjx67DvmDcRv3gBrPHT1wO//ObbndPXC8fOwfWXgM0bCpHgFdrvdOBwOFixYgNlsJjU1lbKyMjweDzt27MBkMnH48OFojxmQE/W+EANhjYcZCb4fA/F1C3zTGthzIsXwr8AXL15k7dq1uFwuEhMTycnJ4c6dOxw6dIimpiY6OnwHeYWFhdEdNAD3uqGuObL7/Pwy5Nkn3gUPQ78Cu91uNmzYgMvlYs+ePbS3t1NfX4/L5aK8vJzq6mrq6uowmUzk5+dHe9wx+/IGRPrUUVsn3L4X4Z2OgaED3r17N06nk127dnHgwAEsFsuzZQ6Hg4KCAvr6+khLS8NqtUZx0rF72g//bYrOvs/ciM5+R2LYgBsbG6msrCQlJYX9+/f7XWfJkiUAFBQUPHtsIPji4mLi4uIwTbD3zPb70TsrcPNudPY7EsMGXFFRQX9/P9u2bWP6dP+XlOLjfZ9m/j/gmzdvcuzYMWw2G0uXLo3IrIFojeJ52U7P2L5bEUmGDbimpgaAkpKSYddxOp3A4IBfe+012tvbqaqqorS0NLxDBqEtyhcWnJ3R3f+PGfYsxO3btwGYN2+e3+V9fX2cOXMGGBxwTEzo/0wXFRXhcrlCsq1Xt/2J1PwNfpcNnOcdjtX8/Md9m0bez3Dnin+1cxetF0+MbdgxstlsnD9/PqjnGjZgj8cDQE+P/5OllZWVuN1uLBYL6enpYZ3F5XLR1tYWkm09ftI37LKB87yjiYkZ23r+POjqDtl/SygYNmCbzUZnZyf19fUsX7580LL29nb27t0LQH5+ftg/qNlstpBtK27q8O8Qo13YsJp98fb3+66wjWS4bVktCcydO3eUKQMznl8fwwZcWlpKY2Mj5eXlrFmzhqysLADq6urYvn07brcbiMwFjGDfHv2pqoeaRv/LRrs8vG+T75W3qxf2fRbc/is++SPps/4Y3JPDwLAf4hwOBzNnzqS1tZXc3Fzy8vLIzMykuLiYjIwMVq9eDQw+/pXAnhy9fZtMMDcpevv3x7AB2+12amtrWbduHWazmZaWFpKTkzly5AjV1dVcv34dkBdwNL+fa7NOvFuOJtg4oZWdnc3JkyeHPN7d3U1LSwsxMTEsWrQoCpMFL2U6vGj13awZaTmhPfQNCUMHPJwrV67g9XrJysoiIWHox/FPP/0UgIaGhkE/T0tLo6ioKHKD+mEywcos31ccI7pffPfKTTSTMuDLly8Dwx8+bN682e/P33nnHT755JOwzjYWS9Ph5EUY4YxayGXPmZj3yGnAfkz02wTjp8EbeVB1ITL7mxIDGxZHZl+BMuyHuJGMFrAEq16GeSmR2dcbeTB7RmT2FahJ+Qo88D0JyWJiYOsyOPi57961sRi4OBHInRzps2B1TuDzRYreVi9c83fw5xp48jT0256TBLteh4S40G87VDRgA7j1Pfzli+f/77NQSE+BnasmdrygARvGgx7421fwrXN825kSA7/Mg9dzfP8+0WnABuL1Qn0LfP4tfBfghQ4T8PIc2FDoO3SQQgM2IK/Xd/vPmRtw87uR76KYZYFFdliZCSmW4debqDRgg/N6fYcXzg7fvXRP+yF2CiQn+r4YZJ4a7QnHRwNWogk4TFdqeBqwEk0DVqJpwEo0DViJpgEr0TRgJZoGrETTgJVoGrASTQNWomnASjQNWImmASvRNGAlmgasRNOAlWgasBJNA1aiacBKNA1YiaYBK9E0YCWaBqxE04CVaBqwEk0DVqJpwEo0DViJpgEr0TRgJdr/AJmlb2OpOZzYAAAAAElFTkSuQmCC\n"
+ },
+ "metadata": {},
+ "execution_count": 3
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Use:** To entangle pairs of qubits and is fundamental in quantum algorithms like quantum teleportation and quantum error correction."
+ ],
+ "metadata": {
+ "id": "xmHsT9dQ-RWM"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **Hadamard Gate**\n",
+ "\n",
+ "The Hadamard gate transforms the state\n",
+ "∣0⟩ into $\\frac{(∣0⟩+∣1⟩)}{\\sqrt{2}}$ and the state ∣1⟩ into $\\frac{(∣0⟩−∣1⟩)}{\\sqrt{2}}$, creating a superposition of states.\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "s5pOqc6nP7Ij"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title Code\n",
+ "qc = QuantumCircuit(1)\n",
+ "qc.h(0) # Apply the Hadamard gate to qubit 0\n",
+ "\n",
+ "qc.draw(output='mpl', style=\"clifford\")"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 127
+ },
+ "cellView": "form",
+ "id": "a8u7pcqzRs62",
+ "outputId": "3e3b4bb2-f71c-47d1-8636-ecdda0b84f6c"
+ },
+ "execution_count": 4,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": "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\n"
+ },
+ "metadata": {},
+ "execution_count": 4
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Use:** It is used to create superposition states and is essential in algorithms like Grover's algorithm and Shor's algorithm."
+ ],
+ "metadata": {
+ "id": "eagz0v6oR1ev"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **Phase S Gate**\n",
+ "\n",
+ "The S gate (or $π/2$ phase gate) applies a phase of $π/2$ to the ∣1⟩ state while leaving the ∣0⟩ state unchanged.\n"
+ ],
+ "metadata": {
+ "id": "9V6Z2FbsR_X1"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title Code\n",
+ "qc = QuantumCircuit(1)\n",
+ "qc.s(0) # Apply the S gate to qubit 0\n",
+ "\n",
+ "qc.draw(output='mpl', style=\"clifford\")"
+ ],
+ "metadata": {
+ "cellView": "form",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 127
+ },
+ "outputId": "28c7b106-b934-45a0-f37f-fe732e677a13",
+ "id": "6OVp4J1ZSd55"
+ },
+ "execution_count": 5,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": "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\n"
+ },
+ "metadata": {},
+ "execution_count": 5
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Use:** To introduce phase differences between quantum states and is important in constructing certain quantum functions and algorithms."
+ ],
+ "metadata": {
+ "id": "HBnNRFXUSk5g"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **T Gate**\n",
+ "\n",
+ "The T gate (or $π/4$ phase gate) applies a phase of $π/4$ to the ∣1⟩ state, while leaving the ∣0⟩ state unchanged.\n"
+ ],
+ "metadata": {
+ "id": "4tfdwS44S2U1"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title Code\n",
+ "qc = QuantumCircuit(1)\n",
+ "qc.t(0) # Apply the T gate to qubit 0\n",
+ "\n",
+ "qc.draw(output='mpl', style=\"clifford\")"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 127
+ },
+ "cellView": "form",
+ "id": "Ut8iTM6uTIk2",
+ "outputId": "8fbdcbfb-b78c-4b84-de54-94dd1d0871ca"
+ },
+ "execution_count": 6,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": "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\n"
+ },
+ "metadata": {},
+ "execution_count": 6
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Use:** The T gate is a more subtle phase gate than the S gate and is used for achieving finer control over phase manipulations in quantum algorithms."
+ ],
+ "metadata": {
+ "id": "OmG-3kU9TT6x"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **T' Gate (T-dagger or T-inverse)**\n",
+ "\n",
+ "The T' gate is the inverse of the T gate and undoes the $π/4$ phase applied by the T gate.\n"
+ ],
+ "metadata": {
+ "id": "gzb8MDR3Tl9c"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title Code\n",
+ "qc = QuantumCircuit(1)\n",
+ "qc.tdg(0) # Apply the T' (T-dagger) gate to qubit 0\n",
+ "\n",
+ "qc.draw(output='mpl', style=\"clifford\")"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 127
+ },
+ "cellView": "form",
+ "outputId": "449d5bfe-1eda-4cca-ba42-3ed9889c7f2a",
+ "id": "14d3cSW2T1DK"
+ },
+ "execution_count": 7,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": "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\n"
+ },
+ "metadata": {},
+ "execution_count": 7
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "**Use:** It is used to reverse the action of a T gate and is useful in algorithms that require the inversion of phase operations."
+ ],
+ "metadata": {
+ "id": "HuDTOOBKT6Nk"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# **THE SIMPLEST CIRCUIT TO GENERATE RANDOM NUMBERS**\n",
+ "\n",
+ "The simplest circuit to generate random numbers in quantum computing consists of just adding Hadamard gates to each qubit and due to the superposition property, when measuring each qubit they will collapse and can randomly give a state either 1 or 0.\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "b0gchvelwIbW"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "from qiskit import QuantumCircuit, Aer, execute\n",
+ "import matplotlib.pyplot as plt\n",
+ "\n",
+ "# Number of qubits and Hadamard gates\n",
+ "num_qubits = 4\n",
+ "\n",
+ "# Create a quantum circuit\n",
+ "qc = QuantumCircuit(num_qubits, num_qubits)\n",
+ "\n",
+ "# Apply Hadamard gates to all qubits\n",
+ "for qubit in range(num_qubits):\n",
+ " qc.h(qubit)\n",
+ "\n",
+ "# Measure all qubits\n",
+ "qc.measure(range(num_qubits), range(num_qubits))"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "id": "6oMoy9uywUrc",
+ "outputId": "1f680990-6837-462a-ad03-f896e1b62871"
+ },
+ "execution_count": 8,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "execution_count": 8
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "Since we added 4 qubits, the numbers that can come out as a result of the simulation are from 0 to 15. The domain is $[0, 2^n - 1]$"
+ ],
+ "metadata": {
+ "id": "mFoTm6zyy2IB"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Choose the backend for simulation (qasm_simulator)\n",
+ "backend = Aer.get_backend('qasm_simulator')\n",
+ "\n",
+ "# Execute the circuit and get measurement results\n",
+ "job = execute(qc, backend, shots=1)\n",
+ "result = job.result()\n",
+ "counts = result.get_counts()\n",
+ "\n",
+ "# Show the number generated\n",
+ "print(int([clave if valor == 1 else 0 for clave, valor in counts.items()][0], 2))"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "id": "tRmHHQ2YyDrh",
+ "outputId": "d1f91796-d205-4a2d-e199-684914d3632a"
+ },
+ "execution_count": 9,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "5\n"
+ ]
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "As we see, the number obtained is within the range. **But there is a problem**. As you might suspect, **the domain will always be subject to the number of qubits** as $[0, 2^n - 1]$\n",
+ "\n",
+ "To solve this, we need a more complex circuit, where we can define the domain we want and in addition, the implementation we will carry out can even use numbers that you can generate with n qubits.\n",
+ "\n",
+ "\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "Ph2w-Lhwzhbf"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# **Building Quantum Circuit to Generate Random Numbers**\n",
+ "\n",
+ "**(In a specific domain)**"
+ ],
+ "metadata": {
+ "id": "qlQ0leRsUTon"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## **STEP 1:**\n",
+ "\n",
+ "Define the temporary logical-AND gate. With this gate we can implement the comparator."
+ ],
+ "metadata": {
+ "id": "LRRWDoT_Vgdf"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title Temporary logical-AND gate\n",
+ "\n",
+ "# Creating a circuit where the AND gate will be designed\n",
+ "qc = QuantumCircuit(3)\n",
+ "\n",
+ "# Adding CNOTs\n",
+ "qc.cx(0,2)\n",
+ "qc.cx(1,2)\n",
+ "qc.cx(2,1)\n",
+ "qc.cx(2,0)\n",
+ "\n",
+ "# T and T-dagger gates\n",
+ "qc.tdg(0)\n",
+ "qc.tdg(1)\n",
+ "qc.t(2)\n",
+ "\n",
+ "# Inverse operation of the last 2 CNOTs\n",
+ "qc.cx(2,0)\n",
+ "qc.cx(2,1)\n",
+ "\n",
+ "# Hadamard and phase on the qubit with the result\n",
+ "qc.h(2)\n",
+ "qc.s(2)\n",
+ "\n",
+ "# Saving as a gate variable and naming it \"AND\"\n",
+ "temp_log_and = qc.to_gate()\n",
+ "temp_log_and.name = \"AND\"\n",
+ "\n",
+ "# Displaying the AND circuit\n",
+ "qc.draw(output='mpl', style=\"clifford\")"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 255
+ },
+ "cellView": "form",
+ "id": "Pm21OKIDVf2W",
+ "outputId": "e80a3b19-eff7-495a-95f2-aab977244961"
+ },
+ "execution_count": 10,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": 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\n"
+ },
+ "metadata": {},
+ "execution_count": 10
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## **STEP 2:**\n",
+ "\n",
+ "Here we going to create the comparator.\n",
+ "\n",
+ ""
+ ],
+ "metadata": {
+ "id": "vWViGSnhW-Gf"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "The previous image shows the design of the *Comparator*, the number of qubits, the purpose of each qubit, the gates that will be used and in which qubit the result will come out."
+ ],
+ "metadata": {
+ "id": "Q5Y7bZLifW3e"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **STEP 2.1**\n",
+ "\n",
+ "First of all, we are going to define the variables that we are going to use throughout the code."
+ ],
+ "metadata": {
+ "id": "sMYk7Qr9YLkv"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Binary numbers in the domain [a, b)\n",
+ "a_init = '000' # 0\n",
+ "b_init = '011' # 3\n",
+ "\n",
+ "# Number of qubits to represent a and b. They must have the same length.\n",
+ "nqubits = len(b_init)\n",
+ "\n",
+ "# Order to be read in the circuit\n",
+ "b = b_init[::-1]\n",
+ "a = a_init[::-1]\n",
+ "\n",
+ "# Creating the quantum circuit where the Comparator will be placed\n",
+ "qc = QuantumCircuit(2*nqubits + 1)\n",
+ "\n",
+ "# Defining the state (1/√2) (|0> + e^(iπ/4)|1>)\n",
+ "state = [1/np.sqrt(2), (1 + 1j)/2]\n",
+ "\n",
+ "# Positions of qubits 'a' and 'A'\n",
+ "qbits_ai_position = [2*i + 1 if i != 0 else i for i in range(nqubits)]\n",
+ "qbits_Ai_position = [2*i + 2 for i in range(nqubits)]"
+ ],
+ "metadata": {
+ "id": "8U3cMXP14IAy"
+ },
+ "execution_count": 11,
+ "outputs": []
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **STEP 2.2**\n",
+ "\n",
+ "Now we begin to add gates, for the implementation we divide into the initialization of the qbits and the comparison of the first digit of the binary number 'b' with that of the first of 'a'."
+ ],
+ "metadata": {
+ "id": "zMkamWQu39NS"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Initializing each qubit in 'a' to the value 1\n",
+ "for i in qbits_ai_position:\n",
+ " qc.x(i)\n",
+ "\n",
+ "# Implementing the Comparator\n",
+ "\n",
+ "# If the first digit of binary number 'b' is '1', apply a Pauli-X gate to qubit 1; otherwise, apply an identity gate\n",
+ "if b[0] == '1':\n",
+ " qc.x(1)\n",
+ "else:\n",
+ " qc.id(1) # Use 'i' for the identity gate\n",
+ "\n",
+ "# Compare qubits 0 (first qubit 'a') and 1 (auxiliary qubit |0>) with an AND gate and send the result to qubit 2 (first auxiliary qubit of 'A')\n",
+ "qc.append(temp_log_and, [0, 1, 2])\n",
+ "\n",
+ "# Perform the inverse operation on qubit 1\n",
+ "if b[0] == '1':\n",
+ " qc.x(1)\n",
+ "else:\n",
+ " qc.id(1) # Use 'i' for the identity gate\n",
+ "\n",
+ "# For aesthetic reasons, add an identity gate to qubit 2\n",
+ "qc.id(2)\n"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "id": "lJFh00pr6uDz",
+ "outputId": "25d64216-88ca-44f5-eb16-9bbc6f39c084"
+ },
+ "execution_count": 12,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {},
+ "execution_count": 12
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **STEP 2.3**\n",
+ "\n",
+ "After comparing the first digit, in the following digits the formula is repeated with the following instructions in a loop."
+ ],
+ "metadata": {
+ "id": "DEObxGFw5pDg"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Perform a loop from 1 to N-1 to compare each digit of binary 'a' with 'b'\n",
+ "for j in range(1, nqubits):\n",
+ "\n",
+ " # Compare the next digit of 'b'\n",
+ " if b[j] == '1':\n",
+ " qc.x(1)\n",
+ " else:\n",
+ " qc.id(1) # Use 'i' for the identity gate\n",
+ "\n",
+ " # Perform a CNOT gate that takes the result stored in the corresponding auxiliary qubit of 'A'\n",
+ " # and passes the result from the gate to the next qubit in 'a'\n",
+ " qc.cx(2*j, 2*j+1)\n",
+ "\n",
+ " # Take the result from 'A' to input into the AND gate at qubit 1\n",
+ " qc.cx(2*j, 1)\n",
+ "\n",
+ " # Apply an AND gate to compare the temporary value of qubit 1 with each qubit in 'a' and store the result in the auxiliaries 'A'\n",
+ " qc.append(temp_log_and, [1, 2*j+1, 2*j+2])\n",
+ "\n",
+ " # Perform the inverse CNOT operation to the previous one\n",
+ " qc.cx(2*j, 1)\n",
+ "\n",
+ " # Perform the inverse operation to the compared digit of 'b'\n",
+ " if b[j] == '1':\n",
+ " qc.x(1)\n",
+ " else:\n",
+ " qc.id(1) # Use 'i' for the identity gate\n",
+ "\n",
+ " # Pass the result to the next qubit in 'a'\n",
+ " qc.cx(2*j, 2*j+2)\n"
+ ],
+ "metadata": {
+ "id": "3mUqJUYk7HiM"
+ },
+ "execution_count": 13,
+ "outputs": []
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **STEP 2.4**\n",
+ "\n",
+ "Finally, we save the created circuit in a qiskit gate variable. With this we will have a more organized final circuit and the calculation of the uncomputation will be more direct."
+ ],
+ "metadata": {
+ "id": "-HYaiaqw7m25"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Convert the designed comparator to a gate named \"Comparator\"\n",
+ "COMPARATOR = qc.to_gate()\n",
+ "COMPARATOR.name = \"Comparator\"\n",
+ "\n",
+ "# Display the resulting circuit with the Comparator gate\n",
+ "qc.draw(output='mpl', style=\"clifford\")\n"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 437
+ },
+ "id": "W0gjM62L8HhC",
+ "outputId": "d1c6da49-d7d3-4d5e-a0c6-66535819311c"
+ },
+ "execution_count": 14,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": 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\n"
+ },
+ "metadata": {},
+ "execution_count": 14
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## **STEP 3:**\n",
+ "\n",
+ "In the next step, we will create the generator by initializing the qubits, adding the oracle (which consists of the comparator, a CNOT gate to obtain the result and the uncomputer), the amplifier and the measurements.\n",
+ "\n",
+ ""
+ ],
+ "metadata": {
+ "id": "NCV_nH8w8ufz"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **STEP 3.1**\n",
+ "We create the circuit where the generator will be, we initialize the qubits, the digits of 'a' with zeros, the auxiliary qubits for the AND gate 'A' will be initialized with\n",
+ "\n",
+ "$(\\frac{1}{\\sqrt{2}}) (|0> + e^{(iπ/4)}|1>)$\n",
+ "\n",
+ "Finally we calculate how many time we repeat the oracle with the following equation\n",
+ "\n",
+ "$ N = (\\pi/4) * \\sqrt{\\frac{2^{nqubits}}{l}}$\n",
+ "\n",
+ "where $l = b - a$\n"
+ ],
+ "metadata": {
+ "id": "J8kgUW-pF8N0"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Creating the quantum circuit with 2n + 2 qubits and n classical bits\n",
+ "qc = QuantumCircuit(2*nqubits + 2, nqubits)\n",
+ "\n",
+ "# Initializing the last qubit as 1\n",
+ "qc.x(2*nqubits + 1)\n",
+ "qc.barrier()\n",
+ "\n",
+ "# Initializing qubits 'a' and 'A'\n",
+ "for i, j in zip(qbits_ai_position, qbits_Ai_position):\n",
+ " qc.h(i) # Put qubits 'a' into superposition\n",
+ " qc.initialize(state, j) # Initialize qubits 'A' with the state (0.707, 0.5+0.5j)\n",
+ "qc.barrier()\n",
+ "\n",
+ "# Calculating the length of the range specified by the user\n",
+ "l = int(b_init, 2) - int(a_init, 2)\n",
+ "\n",
+ "# Number of times the oracle and amplifier will need to be used\n",
+ "N = int((np.pi/4) * np.sqrt(2**nqubits/l))\n"
+ ],
+ "metadata": {
+ "id": "cJkKpZkE5KqR"
+ },
+ "execution_count": 15,
+ "outputs": []
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **STEP 3.2**\n",
+ "\n",
+ "Now we proceed to put the oracle with the gate variable that we defined before. The amplifier must also be repeated N times, so it will be next to the oracle in the same loop.\n"
+ ],
+ "metadata": {
+ "id": "3LODS4qJJo1T"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Adding the Oracle and Amplifier circuits (repeated N times)\n",
+ "for t in range(N):\n",
+ "\n",
+ " # Adding the ORACLE to the circuit\n",
+ " qc.append(COMPARATOR, range(0, 2*nqubits+1))\n",
+ "\n",
+ " # Obtaining the result (0 if a < b, 1 otherwise)\n",
+ " qc.cx(2*nqubits, 2*nqubits+1)\n",
+ "\n",
+ " # Performing the inverse operations\n",
+ " qc.append(COMPARATOR.inverse(), range(0, 2*nqubits+1))\n",
+ "\n",
+ " # Barrier\n",
+ " qc.barrier()\n",
+ "\n",
+ " # Adding the AMPLIFIER to the circuit\n",
+ " for i in qbits_ai_position:\n",
+ " qc.h(i) # Hadamard gate\n",
+ " qc.x(i) # Pauli-X gate\n",
+ "\n",
+ " # Adding Hadamard gates on the last 'a' qubit on the sides of a Toffoli gate acting on 'a' qubits\n",
+ " qc.h(qbits_ai_position[-1])\n",
+ " qc.mcx(qbits_ai_position[:-1], qbits_ai_position[-1])\n",
+ " qc.h(qbits_ai_position[-1])\n",
+ "\n",
+ " # Barrier\n",
+ " qc.barrier()\n",
+ "\n",
+ " # Completing the amplifier with inverse operations\n",
+ " for i in qbits_ai_position:\n",
+ " qc.x(i) # Pauli-X gate\n",
+ " qc.h(i) # Hadamard gate\n",
+ "\n",
+ " # Hadamard gate on the last qubit for the inverse operation\n",
+ " qc.h(2*nqubits + 1)\n",
+ " qc.barrier()"
+ ],
+ "metadata": {
+ "id": "LnlolkmMJ2HR"
+ },
+ "execution_count": 16,
+ "outputs": []
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **STEP 3.3**\n",
+ "\n",
+ "Finally, we create the measurements in the qubits 'a'\n"
+ ],
+ "metadata": {
+ "id": "_ZFYXfvqKfOY"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Performing measurements on the resulting qubits (bits of the generated random number)\n",
+ "for j, k in enumerate([2*i + 1 if i != 0 else i for i in range(nqubits)]):\n",
+ " qc.measure(k, j)\n",
+ "\n",
+ "# Display the circuit\n",
+ "qc.draw(output='mpl', style=\"clifford\")\n"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 309
+ },
+ "id": "WS6viWZgKanp",
+ "outputId": "23e1caa5-d97c-4b97-830e-ffc975cecc5c"
+ },
+ "execution_count": 17,
+ "outputs": [
+ {
+ "output_type": "execute_result",
+ "data": {
+ "text/plain": [
+ ""
+ ],
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+ },
+ "metadata": {},
+ "execution_count": 17
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## **TEST RUN**\n",
+ "\n",
+ "In this point, we're going to test our circuit. We will simulate with Qiskit and we will display a histogram with the numbers obtained."
+ ],
+ "metadata": {
+ "id": "4J5rB3pKq7BB"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Choose the backend for simulation\n",
+ "backend = Aer.get_backend('qasm_simulator')\n",
+ "\n",
+ "# Create a job to execute the quantum circuit 'qc' on the chosen backend and specify the number of shots (repetitions)\n",
+ "job = execute(qc, backend, shots=500)\n",
+ "\n",
+ "# Retrieve the result of the job\n",
+ "result = job.result()\n",
+ "\n",
+ "# Extract the measurement counts\n",
+ "count = result.get_counts()\n",
+ "\n",
+ "print(count)"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/"
+ },
+ "id": "rBApuHaUq566",
+ "outputId": "5dfedafb-a2ab-4176-b44d-a812f529d087"
+ },
+ "execution_count": 20,
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "{'110': 39, '001': 101, '010': 93, '000': 119, '101': 41, '011': 32, '111': 42, '100': 33}\n"
+ ]
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "The counts are on the side of the respective binary value, so in the following graph we will show the numbers in decimal and their respective counts."
+ ],
+ "metadata": {
+ "id": "roPsaArX5MPl"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "# Sort the counts and decimal labels together based on decimal labels\n",
+ "sorted_counts = dict(sorted(count.items(), key=lambda x: int(x[0], 2)))\n",
+ "\n",
+ "# Convert binary keys to decimal for labeling\n",
+ "decimal_labels = [int(key, 2) for key in sorted_counts.keys()]\n",
+ "\n",
+ "# Create the histogram\n",
+ "plt.bar(decimal_labels, sorted_counts.values(), )\n",
+ "\n",
+ "# Add labels and title to the plot\n",
+ "plt.xlabel('Measurement Result (Decimal)')\n",
+ "plt.ylabel('Count')\n",
+ "plt.title('Histogram of Measurement Results')\n",
+ "\n",
+ "# Display the histogram\n",
+ "plt.show()"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 472
+ },
+ "id": "dCTgGEX-tQEb",
+ "outputId": "9c0312f6-05b4-4a0f-af67-5fe80f7117c7"
+ },
+ "execution_count": 19,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": 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\n"
+ },
+ "metadata": {}
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "### **CONCLUSION**\n",
+ "\n",
+ "As expected, **the most probable numbers are within the range** that we defined at the beginning of creating the circuit.\n",
+ "\n",
+ "It is important to remember that each range of numbers in principle has a different circuit construction. **Our implementation helps** in the sense **that you only define the 2 numbers** of the range **and when you execute you will have the circuit for that pair**.\n",
+ "\n",
+ "Another important clarification is that **in some ranges it can give very dispersed results**, so it must be taken into account to better change the domain to another but similar one."
+ ],
+ "metadata": {
+ "id": "JI4eGfb53eR9"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# **Glossary**\n",
+ "\n",
+ "**Quantum computing:** Quantum computing is a paradigm of computing that uses quantum bits or qubits, which can exist in superposition states of 0 and 1 simultaneously. It leverages quantum phenomena such as entanglement and interference to perform certain types of calculations exponentially faster than classical computers.\n",
+ "\n",
+ "**Superposition:** Superposition is a fundamental concept in quantum mechanics where a quantum system can exist in multiple states or values simultaneously. In the context of qubits, it means they can represent both 0 and 1 at the same time until measured.\n",
+ "\n",
+ "**Uncertainty:** Uncertainty, in the context of quantum mechanics, is a principle described by Heisenberg's Uncertainty Principle. It states that certain pairs of physical properties, like the position and momentum of a particle, cannot be precisely measured simultaneously. There is inherent uncertainty in knowing both properties accurately.\n",
+ "\n",
+ "**PRNG (Pseudo-Random Number Generator):**\n",
+ "A Pseudo-Random Number Generator (PRNG) is an algorithm or function that generates sequences of numbers that appear to be random but are actually generated by deterministic processes. PRNGs are commonly used in classical computing for various applications, such as simulations and cryptography.\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "VOpT4JThv3wI"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# **Authors**\n",
+ "\n",
+ "* Miguel Angel Hernandez Tapia [Github](https://github.com/MiguelAngel-ht)\n",
+ "* David Ángel Alba Bonilla [Github](https://github.com/DavidAlba2627) -- [Blog](https://datasciencelifelonglearn.blogspot.com/)\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "qUjJ-Fi9GunG"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# **Bibliography**\n",
+ "\n",
+ "1. Orts, F., Filatovas, E., Garzón, E. G., & Ortega, G. (2023). A quantum circuit to generate random numbers within a specific interval. EPJ Quantum Technology, 10(1). https://doi.org/10.1140/epjqt/s40507-023-00174-1"
+ ],
+ "metadata": {
+ "id": "rKOMpXT6laIn"
+ }
+ }
+ ]
+}
\ No newline at end of file
diff --git a/challenges/PIQUE challenge/Solution_Jingle_Bell_States/readme.md b/challenges/PIQUE challenge/Solution_Jingle_Bell_States/readme.md
new file mode 100644
index 0000000..ae1a55a
--- /dev/null
+++ b/challenges/PIQUE challenge/Solution_Jingle_Bell_States/readme.md
@@ -0,0 +1,8 @@
+# Challenges
+1. Quantum Universal Education
+2. IBM Hackathon
+# Equipo
+Jingle Bell States
+# Integrantes
+* David Angel Alba Bonilla
+* Miguel Angel Hernandez Tapia
diff --git a/hackathon/Solution_Jingle_Bell_States/IBM_Quantum_Image_Filter.ipynb b/hackathon/Solution_Jingle_Bell_States/IBM_Quantum_Image_Filter.ipynb
new file mode 100644
index 0000000..082eeea
--- /dev/null
+++ b/hackathon/Solution_Jingle_Bell_States/IBM_Quantum_Image_Filter.ipynb
@@ -0,0 +1,1662 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "view-in-github",
+ "colab_type": "text"
+ },
+ "source": [
+ ""
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "eo2pFJgPLMrC"
+ },
+ "source": [
+ "⚪\n",
+ "\n",
+ "---\n",
+ "---\n",
+ "# **⚛️— — — — — Quantum Image Filtering — — — — —⚛️**\n",
+ "---\n",
+ "---\n",
+ "\n",
+ "⚪\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "# Quantum Circuits for Random Number Generation and Image Modification\n",
+ "\n",
+ "In this notebook, we implement two types of quantum circuits to generate random numbers and use them to modify images in different ways.\n",
+ "\n",
+ "We have designed two processes/methodologies to build our quantum circuits depending on the problem at hand. The problems in question are:\n",
+ "\n",
+ "- **Black/White Images**\n",
+ "- **Grayscale Images**"
+ ],
+ "metadata": {
+ "id": "sQRj0Xgyy5fT"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## Black/White Images\n",
+ "\n",
+ "In black/white images, pixels can only have two values: 0 (black) or 255 (white). For such images, we decided that each pixel in the image would correspond to a qubit in a quantum circuit. Upon measurement, this qubit will collapse to 0 or 1 with a probability that the user can control. Depending on the outcome, the effect on the pixel is as follows:\n",
+ "\n",
+ "- Collapses to 0: The corresponding pixel remains unchanged.\n",
+ "- Collapses to 1: The corresponding pixel switches from white to black or vice versa.\n",
+ "\n",
+ "The user can control the following parameters:\n",
+ "\n",
+ "- **Input Image:** The user can upload and select the image on which to apply the filter. We recommend using 512x512 images for best results.\n",
+ "- **Threshold:** The image chosen by the user might not always be in Black/White style. In such cases, the user can control the threshold value for converting the image.\n",
+ "- **Probability/Noise:** This is a value between 0 - 1 that indicates the probability of each pixel to change (in other words, the qubits collapsing to 1). This is done by adding an RY gate, mapping the user-entered value to a phase in the range of -π/2 to π/2.\n",
+ "- **Modify:** This parameter indicates where in the image the pixel changes are made. The user can control whether the modification occurs on white pixels, black pixels, or all pixels.\n"
+ ],
+ "metadata": {
+ "id": "O5uuNC0VBb7V"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## Grayscale Images\n",
+ "\n",
+ "In grayscale images, pixels can have any value in the range from 0 (black) to 255 (white). For this case, we implemented a circuit that generates random numbers in a specific range [a, b), inspired by [[1]](https://doi.org/10.1140/epjqt/s40507-023-00174-1)\n",
+ "\n",
+ "Following a methodology similar to the \"filter\" technique in the field of digital image processing, we generate an ***nxn*** kernel that moves across the image and modifies it as follows:\n",
+ "\n",
+ "During each iteration, the kernel's center is positioned on an image pixel. The largest and smallest intensity values within the kernel's range are calculated. Based on this range of values, a circuit is automatically designed to generate random numbers within it. The result from measuring this circuit is assigned as the new value to the pixel at the kernel's center. This process is repeated until all the pixels in the image have been processed.\n",
+ "\n",
+ "This methodology has its limitations, as it generates and measures a quantum circuit for each image pixel. For a high-quality image (512x512 pixels), this means 262,144 circuits will be generated, implying substantial computational time. To address this, we have taken the following considerations:\n",
+ "\n",
+ "- **Image Resizing:** The user-uploaded image will be internally resized to a resolution of 128x128. The filter is applied to this resized image, and the output is then scaled back to the original image dimensions.\n",
+ "- **Intensity Range Mapping:** To reduce the number of qubits needed to build the circuit, the original intensity range of 0 to 255 is mapped to a grayscale range of 0 to 31. Since humans do not perceive many shades of gray, this modification rarely alters our perception of the result.\n",
+ "\n",
+ "The user can control the following parameters:\n",
+ "\n",
+ "- **Input Image:** The user can upload and select the image to apply the filter.\n",
+ "- **Kernel Size:** The user can choose from different kernel size configurations (e.g., 3x3, 5x5, etc.).\n",
+ "- **Internal Resize Value:** We strongly recommend keeping this parameter set to the default of 128x128. Increasing it to 256x256 will aproximately quadruple the execution time (as the number of pixels also increases).\n",
+ "\n"
+ ],
+ "metadata": {
+ "id": "x81nlTLzB_SU"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## **Note for Grayscale Images:**\n",
+ "\n",
+ " Depending on the complexity of the image and the chosen internal resize setting, the code execution may take approximately:\n",
+ "- **Resize 128x128:** About 3 to 6 minutes\n",
+ "- **Resize 256x256:** About 12 to 24 minutes"
+ ],
+ "metadata": {
+ "id": "DYwYNaJFDDdE"
+ }
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## ⬇️ Install Qiskit and Import Libraries"
+ ],
+ "metadata": {
+ "id": "K3Yt2r3KDKOL"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title ⬇️ *Install Qiskit*\n",
+ "from google.colab import output # clear output when is not necessary\n",
+ "!pip install qiskit\n",
+ "#!pip install qiskit-ibmq-provider # Date: 2023 - Installing apart of 'qiskit'\n",
+ "#!pip install qiskit[visualization] # Qiskit to parameter \"mpl\" works in colab\n",
+ "!pip install pylatexenc\n",
+ "!pip install qiskit-aer\n",
+ "output.clear()"
+ ],
+ "metadata": {
+ "id": "PpBrEICCGkkG",
+ "cellView": "form"
+ },
+ "execution_count": null,
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title ⬇️ *Import Libraries*\n",
+ "# Basic Libraries\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "import cv2\n",
+ "# Qiskit modules\n",
+ "from qiskit import QuantumCircuit, transpile, Aer, execute\n",
+ "from qiskit.primitives import Sampler\n",
+ "# Libraries for interactive notebook (Colab)\n",
+ "from google.colab import files, output\n",
+ "from IPython.display import Image, display\n",
+ "import ipywidgets as widgets\n",
+ "import os"
+ ],
+ "metadata": {
+ "id": "ZlVzoWn6Fvd4",
+ "cellView": "form"
+ },
+ "execution_count": null,
+ "outputs": []
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## ⬇️ Defining functions and Filter Classes"
+ ],
+ "metadata": {
+ "id": "2nrE1M5Pfn2t"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title ⬇️ *Auxiliary Functions for Gray Scale Filter*\n",
+ "\n",
+ "# Auxiliar Functions for Gray Scale Filter\n",
+ "def create_AND_gate():\n",
+ " # Creating a circuit where the AND gate will be designed\n",
+ " qc = QuantumCircuit(3)\n",
+ " # Adding CNOTs\n",
+ " qc.cx(0,2)\n",
+ " qc.cx(1,2)\n",
+ " qc.cx(2,1)\n",
+ " qc.cx(2,0)\n",
+ " # Adding T and T dagger gates\n",
+ " qc.tdg(0)\n",
+ " qc.tdg(1)\n",
+ " qc.t(2)\n",
+ " # Inverse operation of the last 2 CNOTs\n",
+ " qc.cx(2,0)\n",
+ " qc.cx(2,1)\n",
+ " # Hadamard and S gate on the qubit with the result\n",
+ " qc.h(2)\n",
+ " qc.s(2)\n",
+ " # Saving the circuit as a gate with the name \"AND\"\n",
+ " temp_log_and = qc.to_gate()\n",
+ " temp_log_and.name = \"AND\"\n",
+ " return temp_log_and\n",
+ "\n",
+ "def create_comparator(b, nqubits):\n",
+ " # Creating a circuit where the comparator will be designed\n",
+ " qc = QuantumCircuit(2*nqubits + 1)\n",
+ " # Create Temporary Logical AND Gate\n",
+ " temp_log_and = create_AND_gate()\n",
+ "\n",
+ " # Positions of 'a' qubits\n",
+ " qbits_ai_position = [2*i + 1 if i != 0 else i for i in range(nqubits)]\n",
+ "\n",
+ " # Add a CNOT to each 'a' qubit\n",
+ " for i in qbits_ai_position:\n",
+ " qc.x(i)\n",
+ "\n",
+ " # Implementing the Comparator\n",
+ "\n",
+ " # If the first digit of the binary number b is '1', place a Pauli X gate (on qubit 1), otherwise place an identity\n",
+ " if b[0] == '1':\n",
+ " qc.x(1)\n",
+ " else:\n",
+ " qc.id(1)\n",
+ "\n",
+ " # Compare with an AND gate the qubits 0 (first 'a' qubit) and 1 (auxiliary qubit |0>) and send the result to qubit 2 (first auxiliary 'A' qubit)\n",
+ " qc.append(temp_log_and, [0,1,2])\n",
+ "\n",
+ " # Perform the inverse operation on qubit 1\n",
+ " if b[0] == '1':\n",
+ " qc.x(1)\n",
+ " else:\n",
+ " qc.id(1)\n",
+ "\n",
+ " # For aesthetics, add an identity on qubit 2\n",
+ " qc.id(2)\n",
+ "\n",
+ " # Loop from 1 to N-1 to compare each digit of the binary number 'a' with 'b'\n",
+ " for j in range(1, nqubits):\n",
+ "\n",
+ " # Compare the next digit of b\n",
+ " if b[j] == '1':\n",
+ " qc.x(1)\n",
+ " else:\n",
+ " qc.id(1)\n",
+ "\n",
+ " # Perform a CNOT that takes the result stored in the corresponding auxiliary 'A' qubit\n",
+ " # and passes the outcome of the gate to the next 'a' qubit\n",
+ " qc.cx(2*j, 2*j+1)\n",
+ "\n",
+ " # Take the result of 'A' to input to the AND in qubit 1\n",
+ " qc.cx(2*j, 1)\n",
+ "\n",
+ " # AND gate that compares the temporary value of qubit 1 with each of the 'a' qubits and stores the result in the 'A' auxiliaries\n",
+ " qc.append(temp_log_and, [1, 2*j+1, 2*j+2])\n",
+ "\n",
+ " # Inverse CNOT operation to the previous one\n",
+ " qc.cx(2*j, 1)\n",
+ "\n",
+ " # Perform the inverse operation to the compared b digit\n",
+ " if b[j] == '1':\n",
+ " qc.x(1)\n",
+ " else:\n",
+ " qc.id(1)\n",
+ "\n",
+ " # Pass the result to the next 'a' qubit\n",
+ " qc.cx(2*j, 2*j+2)\n",
+ "\n",
+ " # Saving the circuit as a gate with the name \"COMPARATOR\"\n",
+ " COMPARATOR = qc.to_gate()\n",
+ " COMPARATOR.name = \"Comparator\"\n",
+ " return COMPARATOR\n",
+ "\n",
+ "def create_circuit(min_value,max_value):\n",
+ " # Computing the difference l between max_value - min_value (length of range)\n",
+ " l = max_value - min_value\n",
+ " # l can't be 0 because we need a range to generate the random numbers\n",
+ " if l==0:\n",
+ " l = 1\n",
+ " # Obtain the number of qubits needed to build the circuit\n",
+ " nqubits = len(bin(l)[2:])\n",
+ " # The minimun value of nqubits must be 3\n",
+ " if nqubits < 3:\n",
+ " nqubits = 3\n",
+ " # Convert the range to binary\n",
+ " b_init = format(l+1, '0{}b'.format(str(nqubits)))\n",
+ " a_init = format(0, '0{}b'.format(str(nqubits)))\n",
+ " a = a_init[::-1]\n",
+ " b = b_init[::-1]\n",
+ "\n",
+ " # Customed Comparator Gate\n",
+ " COMPARATOR = create_comparator(b, nqubits)\n",
+ "\n",
+ " # Defining intial states of A qubits (auxiliar qubits)\n",
+ " state = [1/np.sqrt(2), (1 + 1j)/2]\n",
+ "\n",
+ " # Creating the quantum circuit of 2n + 2 qubits and n classical qubits (for measuring the final digits)\n",
+ " qc = QuantumCircuit(2*nqubits + 2, nqubits)\n",
+ "\n",
+ " # Positions of qubits 'a' and 'A'\n",
+ " qbits_ai_position = [2*i + 1 if i != 0 else i for i in range(nqubits)]\n",
+ " qbits_Ai_position = [2*i + 2 for i in range(nqubits)]\n",
+ "\n",
+ " # Inicializar el último qbit como 1\n",
+ " qc.x(2*nqubits + 1)\n",
+ " qc.barrier()\n",
+ "\n",
+ " # Initialize the last qubit as 1\n",
+ " for i, j in zip(qbits_ai_position, qbits_Ai_position):\n",
+ " qc.h(i) # Put 'a' qubits into superposition\n",
+ " qc.initialize(state, j) # Initialize with the state (0.707, 0.5+0.5j) on 'A' qubits\n",
+ " qc.barrier()\n",
+ "\n",
+ " # Number of times the oracle and the amplifier should be used\n",
+ " N = int((np.pi/4) * np.sqrt(2**nqubits/l))\n",
+ "\n",
+ " # Placing the Oracle and the Amplifier (N times)\n",
+ " for t in range(N):\n",
+ "\n",
+ " # Adding the ORACLE to the circuit\n",
+ " qc.append(COMPARATOR, range(0, 2*nqubits+1))\n",
+ "\n",
+ " # Get the result (0 if a kernels[:, :, 1], kernels[:, :, 1], new_image)\n",
+ " # Scale up the pixel values from the 32 gray shades used to 255\n",
+ " new_image = new_image*8\n",
+ " # Resize the new image back to the original dimensions\n",
+ " self.modified_image = cv2.resize(new_image, self.original_size[::-1], cv2.INTER_LANCZOS4)\n",
+ " return self.original_image, self.modified_image\n",
+ "\n",
+ " def show_image(self, figsize = (8,4)):\n",
+ " # Show both the original and processed images\n",
+ " # Configure the plot to display both images\n",
+ " fig, axs = plt.subplots(1, 2, figsize = figsize)\n",
+ "\n",
+ " # Display the original image\n",
+ " axs[0].imshow(self.original_image, cmap='gray')\n",
+ " axs[0].set_title('Original Image')\n",
+ " axs[0].axis('off')\n",
+ "\n",
+ " # Display the modified image\n",
+ " axs[1].imshow(self.modified_image, cmap='gray')\n",
+ " axs[1].set_title('Modified Image')\n",
+ " axs[1].axis('off')\n",
+ "\n",
+ " # Adjust the layout of the images\n",
+ " plt.tight_layout()\n",
+ "\n",
+ " # Show the plot with the images\n",
+ " plt.show()"
+ ],
+ "metadata": {
+ "id": "GhsHQTJyFNFC",
+ "cellView": "form"
+ },
+ "execution_count": null,
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title ⬇️ *Auxiliary Functions for Black-White Filter*\n",
+ "\n",
+ "def expand_image_bw(img, m):\n",
+ " # Get the shape of the image\n",
+ " n = img.shape\n",
+ " # Compute the padding required to expand the image to a multiple of 'm' pixels\n",
+ " left_padding = m - (n[0] % m) # compute the remainder for the rows\n",
+ " top_padding = m - (n[1] % m) # compute the remainder for the columns\n",
+ "\n",
+ " # Expand the image by adding reflected padding to the top and left side\n",
+ " expanded_image = cv2.copyMakeBorder(img, top_padding, 0, left_padding, 0, cv2.BORDER_REFLECT)\n",
+ " return expanded_image, left_padding, top_padding\n",
+ "\n",
+ "def preprocess_image_bw(img, threshold = 128):\n",
+ " # Apply thresholding to convert the image to black and white\n",
+ " _ , thresholded_image = cv2.threshold(img, 128, 255, cv2.THRESH_BINARY)\n",
+ " # Expand the image to ensure its dimensions are a multiple of 3 pixels\n",
+ " expanded_image, left_padding, top_padding = expand_image_bw(thresholded_image, 3)\n",
+ " return expanded_image, left_padding, top_padding\n",
+ "\n",
+ "def create_circuit_bw(prob):\n",
+ " # Map a probability value from 0 - 1 to the range -pi/2 to pi/2 to set the phase\n",
+ " phase = -np.pi / 2 + prob * np.pi\n",
+ " # Build a quantum circuit for 9 qubits, with each qubit initialized to a Hadamard gate state\n",
+ " # followed by a rotation 'RY' gate based on the calculated phase\n",
+ " qc = QuantumCircuit(9, 9)\n",
+ " qc.h(range(9))\n",
+ " qc.ry(phase, range(9))\n",
+ " qc.measure(range(9),range(9))\n",
+ " return qc\n",
+ "\n",
+ "def simulate_circuit_bw(img, qc):\n",
+ " # Calculate the number of rows and columns in the expanded image\n",
+ " n_rows = int(img.shape[0]/3) # Number of 3-pixel high rows\n",
+ " n_col = int(img.shape[1]/3) # Number of 3-pixel wide columns\n",
+ " # Simulate the quantum circuit for each row block of the expanded image\n",
+ " backend = Aer.get_backend('qasm_simulator')\n",
+ " # Initialize an empty array for the new image\n",
+ " random_matrix = np.empty((0, img.shape[1]))\n",
+ " for i in range(n_rows):\n",
+ " row = np.empty((3, 0)) # Initialize an empty 3-pixel row\n",
+ " job = execute(qc, backend, shots=n_col, memory=True)\n",
+ " results = job.result().get_memory()\n",
+ " for result in results:\n",
+ " # Convert binary string results into a numpy array of integers\n",
+ " bin_array = np.array([int(bit) for bit in result])\n",
+ " # Reshape the 9 bits into a 3x3 block\n",
+ " bin_matrix = bin_array.reshape((3, 3))\n",
+ " # Concatenate to the row\n",
+ " row = np.concatenate((row, bin_matrix), axis=1)\n",
+ " # Add the 3-pixel row to the full image\n",
+ " random_matrix = np.concatenate((random_matrix, row), axis=0)\n",
+ " random_matrix = random_matrix.astype(np.uint8)\n",
+ " return random_matrix"
+ ],
+ "metadata": {
+ "id": "ziT7D4Rh4cUD",
+ "cellView": "form"
+ },
+ "execution_count": null,
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title ⬇️ *Black-White Filter class (Quantum_Filter_BW)*\n",
+ "\n",
+ "class Quantum_Filter_BW:\n",
+ " def __init__(self, image_path, threshold = 128):\n",
+ " # Load the image from the specified path as a grayscale image and store in self.original_image\n",
+ " self.original_image = cv2.imread(image_path, cv2.IMREAD_GRAYSCALE)\n",
+ " # Store the size of the original image\n",
+ " self.original_size = self.original_image.shape\n",
+ " # Store the threshold value for image preprocessing\n",
+ " self.threshold = 128\n",
+ "\n",
+ " def load_image(self, image_path, threshold = 128):\n",
+ " # Load the image from the specified path as a grayscale image and store in self.original_image\n",
+ " self.original_image = cv2.imread(image_path, cv2.IMREAD_GRAYSCALE)\n",
+ " # Store the size of the original image\n",
+ " self.original_size = self.original_image.shape\n",
+ " # Store the threshold value for image preprocessing\n",
+ " self.threshold = 128\n",
+ "\n",
+ " def apply_quantum_filter(self, prob = 0.5, modify = ''):\n",
+ " # Apply a quantum-inspired filter to the image\n",
+ " # Preprocess the image to black and white using the specified threshold\n",
+ " preprocessed_image, left_padding, top_padding = preprocess_image_bw(self.original_image, self.threshold)\n",
+ " # Define the quantum circuit based on the probability value\n",
+ " qc = create_circuit_bw(prob)\n",
+ " # Run the quantum circuit on the preprocessed image to get a random matrix\n",
+ " random_matrix = simulate_circuit_bw(preprocessed_image, qc)\n",
+ " # Use the random matrix to modify the preprocessed image based on quantum results\n",
+ " new_image = np.where(random_matrix == 1, 255 - preprocessed_image, preprocessed_image)\n",
+ " # If 'modify' is set to 'black', ensure that originally white pixels stay white\n",
+ " if modify == 'black':\n",
+ " new_image[np.where(preprocessed_image == 255)] = 255\n",
+ " # If 'modify' is set to 'white', ensure that originally black pixels stay black\n",
+ " if modify == 'white':\n",
+ " new_image[np.where(preprocessed_image == 0)] = 0\n",
+ "\n",
+ " # Trim the padded area from the modified image to restore original dimensions\n",
+ " self.modified_image = new_image[left_padding:, top_padding:]\n",
+ "\n",
+ " return self.original_image, self.modified_image\n",
+ "\n",
+ " def show_image(self, figsize = (8,4)):\n",
+ " # Display the original and processed images side by side\n",
+ " # Configure the figure to display two subplots\n",
+ " fig, axs = plt.subplots(1, 2, figsize = figsize)\n",
+ "\n",
+ " # Display the original image in the first subplot\n",
+ " axs[0].imshow(self.original_image, cmap='gray')\n",
+ " axs[0].set_title('Original Image')\n",
+ " axs[0].axis('off')\n",
+ "\n",
+ " # Display the original image in the first subplot\n",
+ " axs[1].imshow(self.modified_image, cmap='gray')\n",
+ " axs[1].set_title('Modified Image')\n",
+ " axs[1].axis('off')\n",
+ "\n",
+ " # Adjust the spacing between the images\n",
+ " plt.tight_layout()\n",
+ "\n",
+ " plt.show()"
+ ],
+ "metadata": {
+ "id": "IRI1LjfC4DtV",
+ "cellView": "form"
+ },
+ "execution_count": null,
+ "outputs": []
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "EkOR0vbYLC3L"
+ },
+ "source": [
+ "## **STEP 1:** Load Your Image 🏞️\n",
+ "\n",
+ "#### You should click on '***Choose File***' to upload an image file (of type .jpg, .jpeg, or .png) that is stored on your device."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 564
+ },
+ "id": "fPEUjgm2CjZj",
+ "outputId": "c5d1a11f-db31-4109-9be6-c80f272e5814",
+ "cellView": "form"
+ },
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "Uploaded image \"Image_512.jpg\" with a size of 31726 bytes \n",
+ "\n"
+ ]
+ },
+ {
+ "output_type": "display_data",
+ "data": {
+ "image/jpeg": 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+ "text/plain": [
+ ""
+ ]
+ },
+ "metadata": {}
+ }
+ ],
+ "source": [
+ "#@title ⬇️ *Run to load your image*\n",
+ "\n",
+ "# Upload files\n",
+ "uploaded = files.upload()\n",
+ "\n",
+ "# Process the uploaded files\n",
+ "for filename in uploaded.keys():\n",
+ " output.clear() # Clear the output to remove the upload button\n",
+ " print('Uploaded image \"{name}\" with a size of {length} bytes \\n'.format(\n",
+ " name=filename, length=len(uploaded[filename])))\n",
+ "\n",
+ " # If it's an image file, display it\n",
+ " if filename.lower().endswith(('.png', '.jpg', '.jpeg')):\n",
+ " display(Image(filename)) # Display the image\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "84PrlfywMz7a"
+ },
+ "source": [
+ "## **STEP 2:** Choose a Filter\n",
+ "\n",
+ "#### Select the filter you want to apply to your image. 🎨\n",
+ "\n",
+ "***Note that filter 2 may take longer to process** 🕒"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cellView": "form",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 145,
+ "referenced_widgets": [
+ "34b8aaef85844ad3a803d0e68712d6c5",
+ "6f519a2eb1e149c3b8edb196bc6f873d",
+ "bfd94c27154b46d68990be6b5e6302dd",
+ "17a0a8c6eb7c4a5cb27f5d5298cfdd42",
+ "09e555a01102405b8aade0411d755736",
+ "71bae5064178428abf3bda7690f2f2a0"
+ ]
+ },
+ "id": "PIhizXe_JEza",
+ "outputId": "95f7d12f-7cc4-499c-e817-e2e24c2dcf78"
+ },
+ "outputs": [
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "Choose one: \n",
+ "\n"
+ ]
+ },
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ "RadioButtons(options=('Filter 1 - Black/White', 'Filter 2 - Gray Scale'), value='Filter 1 - Black/White')"
+ ],
+ "application/vnd.jupyter.widget-view+json": {
+ "version_major": 2,
+ "version_minor": 0,
+ "model_id": "34b8aaef85844ad3a803d0e68712d6c5"
+ }
+ },
+ "metadata": {}
+ },
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ "Button(description='Confirm Selection', style=ButtonStyle())"
+ ],
+ "application/vnd.jupyter.widget-view+json": {
+ "version_major": 2,
+ "version_minor": 0,
+ "model_id": "17a0a8c6eb7c4a5cb27f5d5298cfdd42"
+ }
+ },
+ "metadata": {}
+ },
+ {
+ "output_type": "stream",
+ "name": "stdout",
+ "text": [
+ "You have selected: Filter 2 - Gray Scale 🎨\n"
+ ]
+ }
+ ],
+ "source": [
+ "#@title ⬇️ Run to select the filter\n",
+ "\n",
+ "# Create the radio button widget\n",
+ "filter_type = widgets.RadioButtons(\n",
+ " options=['Filter 1 - Black/White', 'Filter 2 - Gray Scale'],\n",
+ " description='',\n",
+ " disabled=False,\n",
+ " style={'options_width': 'initial'}\n",
+ ")\n",
+ "\n",
+ "# Function to handle the confirmation button click\n",
+ "def on_button_clicked(b):\n",
+ " global selection\n",
+ " selection = filter_type.value\n",
+ " print(\"You have selected:\", selection, \"🎨\")\n",
+ "\n",
+ "# Create and display the confirmation button\n",
+ "print('Choose one: \\n')\n",
+ "button = widgets.Button(description=\"Confirm Selection\")\n",
+ "button.on_click(on_button_clicked)\n",
+ "display(filter_type, button)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "id": "_EBikxniUcxE"
+ },
+ "source": [
+ "## **STEP 3:** Customize Values for Your Filter 🧐\n",
+ "\n",
+ "#### Enter the parameters depending the Filter Type (amount of noise, where to apply it, kernel size)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "cellView": "form",
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 164,
+ "referenced_widgets": [
+ "78aebba0de4c4e2388ae2c59bb504b9e",
+ "1e59859028444fddae618a726ec0d937",
+ "e67ad6e7707849109243cf95c7bf89cc",
+ "647ee895e304480f87dd89301010c552",
+ "6916ea66e78d43bbb81ac7fb2373783d",
+ "ad544e65d564466dbdf083448fe63310",
+ "8ef1a948cc76415fa101856d27b4300c",
+ "a739bcaa1a2a4f57b6b98d3a15e0874d"
+ ]
+ },
+ "id": "Lp7RFRgeVsmy",
+ "outputId": "9bf92288-f786-461f-8e9a-54cb73205cea"
+ },
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ "Accordion(children=(Dropdown(description='Kernel:', options=('3x3', '5x5', '7x7'), value='3x3'), Dropdown(desc…"
+ ],
+ "application/vnd.jupyter.widget-view+json": {
+ "version_major": 2,
+ "version_minor": 0,
+ "model_id": "78aebba0de4c4e2388ae2c59bb504b9e"
+ }
+ },
+ "metadata": {}
+ }
+ ],
+ "source": [
+ "#@title ⬇️ Run to Customize\n",
+ "\n",
+ "# If the selected filter is the first option which is Black/White filter\n",
+ "if filter_type.value[7] == '1':\n",
+ " # Accordion 1: Slider for noise amount\n",
+ " noise_slider = widgets.FloatSlider(\n",
+ " value=0.5,\n",
+ " min=0,\n",
+ " max=1,\n",
+ " step=0.1,\n",
+ " description='Noise:',\n",
+ " continuous_update=False,\n",
+ " disabled=False\n",
+ " )\n",
+ "\n",
+ " # Accordion 2: Dropdown menu with 2 options\n",
+ " options_menu = widgets.Dropdown(\n",
+ " options=['In Black', 'In White', 'Across the image'],\n",
+ " value='In Black',\n",
+ " description='Menu:',\n",
+ " disabled=False\n",
+ " )\n",
+ "\n",
+ " # Accordion 3: Threshold value\n",
+ " threshold_value = widgets.IntText(\n",
+ " value=128,\n",
+ " description='Threshold:',\n",
+ " disabled=False\n",
+ " )\n",
+ " # Create the accordions and assign the widgets to them\n",
+ " accordion = widgets.Accordion(children=[noise_slider, options_menu, threshold_value])\n",
+ " accordion.set_title(0, 'Noise Amount')\n",
+ " accordion.set_title(1, 'Where to apply the filter')\n",
+ " accordion.set_title(2, 'Threshold Value')\n",
+ "\n",
+ "else:\n",
+ " # Accordion 1: Selection list for kernel size\n",
+ " kernel_size_list = widgets.Dropdown(\n",
+ " options=['3x3', '5x5', '7x7'],\n",
+ " value='3x3',\n",
+ " description='Kernel:',\n",
+ " disabled=False\n",
+ " )\n",
+ " # Accordion 2: Resize options\n",
+ " resize_list = widgets.Dropdown(\n",
+ " options=['128x128 (Recommend)', '256x256'],\n",
+ " value='128x128 (Recommend)',\n",
+ " description='Resize:',\n",
+ " disabled=False\n",
+ " )\n",
+ " # Create the accordions and assign the widgets to them\n",
+ " accordion = widgets.Accordion(children=[kernel_size_list, resize_list])\n",
+ " accordion.set_title(0, 'Kernel Size')\n",
+ " accordion.set_title(1, 'Image Resize')\n",
+ "\n",
+ "# Display the accordion\n",
+ "display(accordion)\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title ⬇️ Select the image you want to apply the filter to\n",
+ "\n",
+ "# Get the list of files in the current directory (can be filtered by type if necessary)\n",
+ "file_list = os.listdir()\n",
+ "# Filter for image files if necessary, for example: .png, .jpg, .jpeg\n",
+ "image_files = [file for file in file_list if file.lower().endswith(('.png', '.jpg', '.jpeg'))]\n",
+ "\n",
+ "# Dropdown menu with options being the uploaded image files\n",
+ "images_menu = widgets.Dropdown(\n",
+ " options=image_files, # Use the list of image files as options\n",
+ " description='Files:',\n",
+ " disabled=False\n",
+ ")\n",
+ "\n",
+ "# Create the accordion and assign the widgets to it\n",
+ "accordion = widgets.Accordion(children=[images_menu])\n",
+ "accordion.set_title(0, 'Select Uploaded Image')\n",
+ "\n",
+ "# Display the accordion\n",
+ "display(accordion)"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 122,
+ "referenced_widgets": [
+ "06286ea639a14d33b97d4ca106181f69",
+ "32650be0e4004a4c96c5da4553cdcc9e",
+ "ecb27eca4fab4f21a7256a1d1bff6e39",
+ "8a515dd65a4948ca967ff35800fc29b6",
+ "f9db2084c00f49159ab9b1bfa21781e7"
+ ]
+ },
+ "cellView": "form",
+ "id": "fkQLf-X8KbXE",
+ "outputId": "a50105e5-79a2-464a-8707-9f2537a7eaed"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ "Accordion(children=(Dropdown(description='Files:', options=('Image_512.jpg', 'Apple.jpeg'), value='Image_512.j…"
+ ],
+ "application/vnd.jupyter.widget-view+json": {
+ "version_major": 2,
+ "version_minor": 0,
+ "model_id": "06286ea639a14d33b97d4ca106181f69"
+ }
+ },
+ "metadata": {}
+ }
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "source": [
+ "## **STEP 4:** Getting Results 📊"
+ ],
+ "metadata": {
+ "id": "tSzM_bMtOPLH"
+ }
+ },
+ {
+ "cell_type": "code",
+ "source": [
+ "#@title ⬇️ Run to observe the result\n",
+ "\n",
+ "filename = images_menu.value\n",
+ "\n",
+ "if selection[7] == '1':\n",
+ " options_dict = {'In Black': 'black', 'In White': 'white', 'Across the image': ''}\n",
+ " qf_bw = Quantum_Filter_BW(filename, threshold = threshold_value.value)\n",
+ " original_image, new_image = qf_bw.apply_quantum_filter(prob = noise_slider.value, modify = options_dict[options_menu.value])\n",
+ " qf_bw.show_image()\n",
+ "\n",
+ "if selection[7] == '2':\n",
+ " kernel_size = int(kernel_size_list.value[0])\n",
+ " resize = int(resize_list.value[:3])\n",
+ " qf_gray = Quantum_Filter(filename)\n",
+ " original_image, new_image = qf_gray.apply_quantum_filter(kernel_size = kernel_size, resize = resize)\n",
+ " qf_gray.show_image()\n",
+ "\n"
+ ],
+ "metadata": {
+ "colab": {
+ "base_uri": "https://localhost:8080/",
+ "height": 300
+ },
+ "cellView": "form",
+ "id": "NLlUBJRHOKBt",
+ "outputId": "d3655a50-d0e3-4556-ac13-71522710394f"
+ },
+ "execution_count": null,
+ "outputs": [
+ {
+ "output_type": "display_data",
+ "data": {
+ "text/plain": [
+ ""
+ ],
+ "image/png": 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N3/ANeNrTnoZXvepVePjhh/G4xz0O73//+7G+vg5gsM9+9Vd/FV/2ZV+Ge+65B9/5nd+JCxcuYGVlBR//+Mdx7dq1W3qOx5jGNKZ/mDTK1qsveMEL8OxnPxs/+qM/ikuXLuGJT3wi/uiP/gj//b//d7zyla90OuRJT3oSvumbvglvfvObsbm5iWc84xn4kz/5k1sexX71q1+N97///Xj+85+P++67D095ylPQbrfxmc98Bu95z3tw6dIlTE9P4wUveAGe+cxn4jWveQ0uXbqEu+++G+9973uxubl5S+tzHBrrijF9sdEYWIzpWPSN3/iNeNzjHoef+ZmfcWBiamoKz372s/EjP/IjePzjH39T5b/1rW/F/Pw83vnOd+J3f/d38ZznPAfvete7cOeddyKdTt+SNvzIj/wI2u023vGOd+Bd73oXnvzkJ+MDH/gAXvOa19yS8m8F3XfffVheXsav//qv4w//8A9x99134+1vfzve/e5348/+7M/cffF4HB/4wAfwgz/4g/jt3/5txGIxvOhFL8LrXvc6PPOZzxzos7vvvhv/9//+X/zET/wEfuu3fgu1Wg2zs7O499578WM/9mNfgFaOaUxj+odIsVgM73//+/FjP/ZjeNe73oW3vOUtOHfuHH7+538er3rVqwbu/a//9b9iZmYGv/M7v4P3ve99+Kqv+ip84AMfwOnTp29ZfbLZLD784Q/j9a9/Pd797nfjrW99K4rFIu644w78xE/8BEql0kC9X/nKV+Ltb387giDAC1/4QrzxjW/Evffee8vqcxwa64oxfbFRENqckDGN6YuMPvWpT+Hee+/F29/+drzsZS/7Qlfn/wl63/vehxe96EX46Ec/imc+85lf6OqMaUxjGtOYvghprCvGdKtpvMZiTF9U1O12D11705vehFgsFnlq6j90sn3GnN9isYgnP/nJX6BajWlMYxrTmL6YaKwrxvR3QeNUqDF9UdHP/dzP4ROf+ASe/exnI5FI4IMf/CA++MEP4ru+67tuaej77xN9//d/P7rdLp7+9Kdje3sb733ve/Gxj30Mr3/96//Otvkd05jGNKYxfXHTWFeM6e+CxqlQY/qioj/+4z/GT/zET+Czn/0sWq0Wzpw5g5e//OX40R/9USQSYxzso3e84x144xvfiIcffhhbW1u4ePEivvd7vxf/6l/9qy901cY0pjGNaUxfJDTWFWP6u6AxsBjTmMY0pjGNaUxjGtOYxnTTNF5jMaYxjWlMYxrTmMY0pjGN6aZpDCzGNKYxjWlMYxrTmMY0pjHdNI2ctP7Wt74Vsdg+Dtnd3UW320WtVsPKygrq9ToajQY6nQ729vbQ6/Wwt7eHvb099Pt9AMDe3h52dnawt7fnTogMwxCxWAzFYhHZbBZbW1vulMt+v+/uC4IAYRgiCAL3nR/+zsNd7N94PI4gCJBIJJBKpRCPx9Hv9xGPx5FIJAY+sVjMXedz8XgcyWTSlReLxRCLxdwzeh9PdI7H44jFYgP1Yl17vR6A/RMv2UZe0+tKNltND7IZdmic9pfvOsvWvmL77Lu1v/U31l3HxHdv1HvteOm9rAvvY1vYP3x/r9dz18ln/H93dxcAHD9q3W0/ax36/f7AmO/t7R2q/97e3kB/7e7uotPpYH19Ha1Wy5Wh4wsAyWTSrReJx+OYmJhAIpFAoVBAsVhEOp12/JXL5ZBOp5FMJjE9PY2LFy/i9OnTmJiYQKPRwKOPPoqHHnoI6+vrmJiYwOzsLLa2ttBsNt14cp7puPR6PUxMTGBrawthGGJ3d9f13+7urutX9uGwcR3Gn0q2v4eNxTBif4/C+/oOrSe/b29vA9jnj3g8jqc//el4/OMfj3w+j2Qy6T67u7uuD5PJJMIwdPIsFoshmUyi1+u5+zqdDpaXlxGLxTA3N4dsNotEIoFmswkASKfTTg6lUik3/qurq07+7e7uYnt7G1tbW4jH42g2m/jsZz+LxcVFbG9vo9/vI5/P4/Tp06hWq2i1WkgkEqjX69jd3XXl7uzsOD61faBzCQA+9KEPjTwOlj74wQ9id3cXKysruH79OlZWVtDpdLCzs+P6GdjnA/LXzs4Oms0mGo0Gut2uk6m8j3OW15PJJCYmJtyH8ppj2Ov1EIvFkEqlkEqlEASBu97pdNBoNNBqtZBOpzEzM4OZmRkn38MwxPb2NtrtNjqdDlKpFLLZLDKZDJLJpHs/9Rt5YWJiAqlUKpIPqRtUrpIo33gP5QXfQZ66VRnLQRC4tkSRjg91na/uJNWfShz33d1dN05s3420iXqc/aQynXWgTlA7wz4LwN3T7XbR6XTQ7XYH9AOJc4T3sywAbsxsX7J9o8g08ni/38f29jaazSaazSa2t7cH+Gp3dxc7OztIpVKYn5/H3NwcZmZmUKlUUKlUMDs7i7m5OSwsLCCbzQ7M7Vgshn6/j3q9jmvXruH69esA9s/uSKfT6PV6jue3trbcuNEeisfjThbZz422+4uZVPdls1kUi0WUSiXXx7Ozs8jn8043q41CPo/FYgPlsB/7/T5arRaazSba7faAzKL+z2azA3an1XN23lSrVTz22GO4fPkygiDA2bNncebMGXQ6HVy5cgVXr15Fu91297fbbTSbTbRaLcfTx5mLf/AHf3DkPSMDiyAI0G630W63nXDmJGi329je3h4AFWREGsqcQGpYs8NqtRo2NzedscaGqkFJsoNIgc3B1I+CBf3Ld1PQsEySXrPGLYWaXifp4OikVoOYf/W7Gj32/6OMp1HGzXef9oPtV9/9CuiGlaNk2+ADEQpsfODC1w5rJPvAE3AwBirofM+xDhwPji9/0/bp/QSS/MTjceRyOSSTSeTzebRaLXS73YEx5XsIeNTQp9JNp9PIZDLIZDLu3mQyiZ2dHXQ6HayurmJ6ehrZbBbz8/MolUpYXFxEo9HA1NSUAxKLi4toNpuHABHHmsrXZzT4lEOUce67z46fAtRR32WJ5encGoVs39syKHO2t7fx0EMP4YlPfKKTAVSeVBI0XmKxGCYmJhz/9/t9Z9Dyt52dHSwuLuLq1as4e/asA5CsgxrFHF8aX6xvOp3GiRMnkEgksLu7i+XlZSwuLjr+yWQyaDQazngjv7G/CHxoHGif3WoD4Nq1a+j1etjc3MT29vaAY4ZAbHd3F7u7u05HWHDGehFwE2T7jHPr1FDjj/qGOiCRSCCTyaDf7zsjlICR8538kEwmHZgfZoAP60PriLKyzSdvrW74uyBrfN8oKc+xXJWTQRA4OXojgAKAV1cft46qE3yOMp+c4nMcKwU3FlBF6XHfe3SsVWYmEgmnDzg3giBwQDeVSg2AYc4llkXHUqPRQDwedwBia2sL29vb2NnZcXOHhi+vKSDRv/wtip9Zd50vUe3/f5HCMES73Ua1WsX29jYymYxzOvB7Op3GxMQEwjB0cl1tRQADzuuJiYkB24fjQNlHWaQyQu1GUhAEmJiYQDabRa/Xw/b2NtbW1tBut7GxsYFOp4Pt7e0BIJxMJp2jnbqN7bwVYzYysLh+/TparRY6nY5Dt61WyzErlQSFO4GGTiLbIXZCxmIxpNPpgQms3hAqCD6rykaZXY1/n3ffGpb2uahn+U6910dapjVqfaDCR7aueu0oigII1hDT/4+61yoF7UMaV746RLXrqLao4tWxGNYv2p++fqUXwSoNggISjRQ+w7bRs0Ajks9bmpiYcOCCEYx2u+3awrKDIHDgm0Cm1+tha2vLGWCpVArb29tOMRDYr66uolKpoFgsAoA7NbXT6SAWi2F6ehqnT5/G4uIi2u22Uw62n9gu5U3tB+1PH7AY1VCwBv2w+4aVp3wzrCz1zlsgYmUQx3RiYgJra2u4//77ce+99zoFwWgGhb22RxUHyyEYrFQqmJiYwOLiIh566CGcO3fOGawEkQSnBBb6Gw1rAsqtra0Brz6BB6NOYRg6IKR8Ztvp63P9e6P0iU98YqCfCbQ4t3Z2drC1tYVWq+W8oqxjIpFAOp12XuggCJDNZlGpVJDNZp0soJe52+06gEKlrJ7qbreLeDyOdDqNfD6PbDaLbDaLfD7vjCmOE/uf/UrjjYbSKABWZb729zA9oXyj3k2rJz9fZOf8qG215Iu8s3ydL2wf/x+F1IFodcpROkRlE3lDAYJvbNQRavuC8y2dTjv+sECdz6m8tX1CMKAGPucIDU7WmQ4DOpsKhYKLptIpwqgLba52u41HH30Ujz76KOLxOE6ePImFhQUXEel0Oq5s2lPq/B3WZ5SHR0XfNJPg7wPt7e1hY2MDy8vL6PV6SKVSTrYwkjE3NzfgEFTHNQAn15k9Q/3PceTY7e7uIpfLDegcRjusg56UzWYxNTWFVquFRqOBtbU1By41Sk55nMlknLOJDh9fpO9GaWRgsbq66kKGRL0EF5rmZBnUMhiFDVEb0bcqbYIL9RhZwWK9ovrXZyRbhGe/a4RCy7DRC95ry1ey77ceChWuUYacj6zy8pGCCjWkNHLi8yT7ylGiAWTrq8Lb127fdd+1qHb5xjPqmn33MK+TbbeNSviUmN3uNgpg8HlO4mQy6SJ79BpzIgdBMOBJpkeVCoPekK2tLcRiMZRKJfT7fXS7XQdCgH2PN9Nn6PHl/KNy6nQ6CMMQuVzOeWo13UT51PahL1JxFMDygdNh5AMu2v/qBdXrPvK9y3eNoEG9cw899BBuu+02zMzMOAWRTqfRaDScV4jtU/nBsSNgUE/7Aw88gOXlZZw6dcqlH8Tjceeh0hQCyj4K/WaziWQy6QAi7ykWiwMASoEQAQnHiOPt63Pb1zdKDLcrUNW0HjqggAOQwfbTgQTA6YVcLuc+bLemo2jqCtOq+F71zBE0aCqMpur65jrvY3mUp9RfjMJoao0+H2W4KilY1/5SotzyGan6rihHjiXrTLL6j9/JD/a69oPqMt/7tc6ct9aB4wMavvcpQNGPOhH5LMdZnXfkSWsvMLoIwEUTlX/UOKShxxRDHXuC/k6n48qy/WJTwNQhRn2gdpQ6Tpn2RzBMub+9vY1Op4N+v+/spV6vh2az6UA30/t4T7FYdPLHjhvboJES5R3qC7WFVG+yn48rT3yO1uPytiXrKNMyNSPBOoksYNzZ2XH6h2OTzWaRy+VQqVRQKpWQy+WcLavObrW72DdMcWZ0Q53w7Atg0HnN9xJUEKT3ej3naKHzyQc8yGOq8/U+7V+r3+ycG4WOBSyoCMhYZHAaLMpUZBJWnhOe4aJMJuPQP7106onThrGzrfHm+xtl3EZRlKHN+lig4XvHUeWrF8rH7MOiOVERHh9ZoWnfYT3/VtBaQOIrR+ulZSh4Ow5o8JVt62PfG1WWRhOsord9od4lehL4Hv6fz+eRSCRciFLHSL2Lvr4k78diMecBzWazLs+bxuP29vaAF0uVzc7OjptvTOWgsgvD0KUiAkAqlRrwMN1+++342Mc+hmaziUwmg0Qi4ZRRpVJxwoVtVY+itk2/q2BRQ1xJ+8H3WxTZ3476X/vZ9/soc5RznHxAQ3VlZQUf+chH8MxnPhNTU1NIJBIuErS1teXeax0NTOWhQUsqFou47bbbcP36dVSrVQRBgFwuh0Qige3tbTd25C8aMbu7u2i1Wm49AY0NytHp6WmnkDhGTLeamppy4XALiIeBxZuhcrmMvb091Ot1rK2toV6vu4gcAOfNy2QyzjHFecWxyOVyLrJAvgUG0zFSqdShw7y47q/b7bp+YLifclyBDuefNST0Ho10WScX9RT7Xg0D8p4v/54UNX/sPbpe0UejREZsmVonNdqVfHXne6yjTq+rvqYRzEivRvx5j6av+d7vc05wbKxH2D6n5esc8JXBNDnSxMSEMxZps9D5ae2Bvb09rK2tYWtra8DRw7nINvPU6zA8iJDRS93tdl2kmnKZkTbVQUx72tracmCDjiumQOXzecRiMZw7d84BajqvisWii3L7+GVzcxO1Ws3NNc4jdVKxLI1Q0B6kAXscI5Rl65xj/WKxmEsPPQ5xTlqwonNFgQKvU66zXf1+341LJpNBPp9HoVDA6dOncfbsWSwsLDg5pbxoQZk68DQtk2t7tra2kEqlHM+w37lGjnyh9jXtA2YwLC0tod/vo1wuY3p6Gtvb247vaaMz0stnWVfOF40YA3B9oOlSo9DIwGJlZcWhIRplnEj83zITQ+HsKE5SLoazi7583mQVVCRr5FAxDfNeqsFjFYBFl4rktUwKCK2vT9D4jC/fJPMZalpnn1A9KufXhmYto1uAdJSHIKpPyYg+EKH9e5RAsBNQr9vx4KS3HsSo/iX5BBYVEMEtPan8v1wuY3Jy0glSLobmGgcNHyofap9YEFYoFJwxCewbWlb4Wc8aBRJzOLvdLlZXV13fJJNJl/ahY//Zz37W5d5vbW05MMG0qunpaaysrGBjY2MAHGlbLKDwpTrYOXWUQvHNbXudpIadr4yo91igd9S95KVUKuWir9euXcOjjz6KUqmEvb095HI5BEEwYMir91zfOTEx4Tz09IYWCgVMTk5idXUVQRA4g4FrMnTc+R4CUy70piJIJBIoFosDOb/0ajIlrlwuIx6P4/r1627x9qhjdKNUq9XQ7/exubmJzc1N5zW1cw/YN7zK5TLy+fxAGVTwfM6nzNSDrM8BB15n/q5eZVWWJFXUOob6rJWJOl/tb6P0qzqSfEa9BRS+lBLrzT+O4aVeyqOcVVq+dRjob+rd1DZavrNRjGF60RcNUX1m9bbVferMSyQSzsFDHWIdlfphVka9Xh/IrLDOL/2/XC47OUHeof5g1HhiYmLg2s7ODrrdrmsHHVC6SQHlA51AdObymUQigVar5da10oPOlCm2j5uLMJJp+YfOFXro0+m0A/osg+maGi33jYmCN+WPYcTxGpaS7iOOpZ2Lo4B6lTF2bLXf+v39jTJKpRLm5uYwPT2NYrGIiYkJdLtdBw650DuXyw3MGwU0dFT0+30UCgW3rlKd8dQj2WzW6RPdzIPglGPBjIhut4udnR1Uq1Xs7e25aBYBhjrEVL7xGt+jc2EUOWFpZGBRrVZdiIyDYT20/M6FcZwYGpnQkDSfYaXZqbrAkdetcrJKUsuynnn9y2d4TT8qFJUp7QQchdG1Xlp3nyGqz/kE+DCyIMlHKjisMaj9Y9voK1MN0CiFGgUUtJ1aL1uGbwz58SkbH8DR96pi4OQmoKV3lPdSkBJsrK2tuetMc5mcnHRha6YGAoOhbgsYGaKOx+MoFAoOlGt/2g8NTPUs0AtBhUFDUucTAHzyk59EoVAY2FmG/FWv15HNZl1aFReZW571AWM7L33fh12LisApT/hAtr1/WFkKlJRH1JDjdSpKAG58KKw/+9nPAgDuuusupwxsmpPPuGIUiiCSBhW9oLu7u2i3224HkE6n48LUCiwohwgQub6CCmdxcdEZJf1+3+XTTk9PIx6PY35+3i0gt3nRvr47jnHqo7W1NfR6BzvM6K4x9HxRcSWTSac0Vf52Oh2nZwj2Lfn4joZQKpUaMBjYTgUMbK9G+NgP6lnX/lJ5pOksnIs0FI7y6qlnlp5Yq5vUM23bqzLROuWOItUr6qX1RSb0u0Yp1ElnPbTsR41CsJ4KlobVjRRVRzXa9VmNmHCuKzhLJpPIZDIol8su1VodUxwT8mi1WkWj0cD6+jr6/b7zICvA4XsZaatUKs57zf5gnnur1XJ1oIeaMpfXKHtoK1kAysgDN9Gx12k/dTodFAoFtNvtAWDRarVQq9Wc0cm+1c0MmHqYz+eRTqedocy+IkBiG6z9RduN4IV2os8OiyI7/6Ke0bHj+23EyuoFymLNrhlm1+mcjsf3N2chD/V6PTQaDTQaDVSrVdTrdczPz7s26wYQPicFHUwst9VquZ2iCCxyudwA2KUuCMPQ7XyXTCadw2t9fR2NRgMbGxsDjk+1e/b29jAxMeF4XucT9ZDqe+toGYVGBha1Wm1g5wFWyC6wptJjp+o2fRb5+IxSHYBhHg3f/wpQfHQUc/s8H0c9awfG550ZZoBZEGIng++dUX1j76NwU4Fr22GVhA+UWfBiFZ2i2qPAEN/lA0RRgMSCGG0Xv2t5TLVjygh/y2az6Pf7LkWCYVsu7NRUh1QqhU6n41IuVCDRO0SeZgSO6yKazebAWgfbh8yv3NnZGTAsdTtm5WUamvrZ2tpCIpFwxqZSPp8fiMDEYjG0Wi2EYYhCoYDd3V3UajUUi0WcPHnSCcaNjY3IBaQKMiwQ9xk+Pj63NOo1+5udp9b7aL2ket2Wp7yoedkA0Gg08Fd/9VfY3d3F7bffjlOnTg0Y/VykR6FLHqHnj+CC/RIE+xGmWq3mdtIrl8su+qt9yPIIKrnoL5PJoFQqOaChaR4EPa1WC5ubm24dDuVQFEDT994MMXrNvG+mazBSTT1BB4EqSP7OuRmGodMhts46N3yRcpVnCpJtu308znHyeUq1zuowYJ1o5GlfalqB1oVGoJX3UQ40voNti6qjj3iPRm+idCTvt3pQU/W0vYzIsX0KBsnvfF7rMiqN4sgjKQih8dtut90c4LqeVCrltvbkPbqz5c7ODtLpNObm5lCpVJxzRg15tVOAA9mh0Wj1NLMONDoJYCif6bHW9vJZdabRScY+VSCsUYSdnR202+0BwNXpdFCv192mO+RFgiLqJc5R2neaBphIJFAul52zjZF7ruNoNBoDG0iw7rpmYxS+1Tnji7BZ55faBvq7neNRfKV1Upmi5W9vb2NjY8NlLjSbTbexRC6XQyaTQa/Xw5UrV3D9+nUUi0WUy2WUSiXnXNedoMgDjI7F43Hk83kHKNTpQl1Fe4b6gM7ObDaLQqEAYN/OKZfLzsHDxfrkFdsHnC9cr8G66d/j0sjAgkpKK0QvHtObqCA4WeznOOQzxqM8u1GeS5JlIut18AkvnQBRqVG+99k6qdKz3mjbRv5PAWPrQ7KTaVi9LBr39YMtx9dW2wb7fRj56uADFrYuGr7Tsvi/hjD7/b4LTc7OzroFn2EYOmOffMht4ujJJ/9ywhJ00MvM+hAgh2GIRx991KUR0etUKBQwNTWFfD7vFFq/3x9QbjQk6AED9pUQjTEai2qAkPr9gzxbAA7YqHFMYcX+yefzA1vfUlhxYTj3Pl9YWMC1a9ewtrbmAAbLYL1Zrm8M7FhHCaSj+EX5Ypjy0fZaGlUYWvBm60ZB+8lPfhLVahVf9VVfhUwmM7AvfzqdPuRN9S2cozyhd3Nvbw8rKysolUrI5/PY2dlBq9VyRrWmwFCZ0EifmJhAu9124XYaTfQMsy3ca14NyuP0z3GJc0ZTPQgUFFgAB+caUbZqeixTL9RjGaVDOE9UEapxyXfdijbbMqx85Piy/4dFMPisL3dZy7Lpdhrl8M2PKGeTgt8oY0uJ/W3BkJZr10Rq2TpmPt11XLLgS3nDZkiwXhpdZD04ryYmJlAqldzaBvIjdypjuig904xM0+ahQUfjv91uO4O9UCggFos5niZoYBoL662OKfafzh2fHcByFdCxnxlRZZv4HoILygkCEeoSpqvn83m34QidGgRjGu2n0y6fz7vICzduINBgv2vEPGrRt4/IazaiqKBLryuAIo9Qn1u+VZtOyYIZdV4GQYCtrS2srKxgc3MTpVLJAYepqSmXGnX58mVcuXIF9Xodk5OTOHHiBObn51EsFlEoFJwcDILARTw2NzcHHJx2fRn7jv1n15dRDzGrgm3Z3NzE8vKyA7YqIymbKGdu5VwFjgEsiLSpHBiZ4IeTTb021gDlgEbRqJ4JNdB9vw0TuBT61sAe1TOiz/pAhUYpbD3td1u3o4wua/z4AIEvfKiGvW+SAYNb9I5ClulYrk8B+Pratsveo1EJ1o08qMqLvJbL5TA7O4tKpYKTJ08iFouhXq9jeXnZpR3wQBsqH5bByc7Jm0qlUK/X0Ww23QSklygMQ3d+BAC3KxoNdx6oMzU15dpBgcRFYOQhGuCcO0y/4rayCiK4kJf9qvOQbVHBwdxKhrOB/UXbes5Bs9l0of4wDN2BYdVqFZcvX0a1Wh0w4G2qgR17BRQ6T0blb0u+uRzl3bV1IQ2b02qgWADHZ6lkH3roIXQ6HVQqFVy4cAFzc3MDh+epolL5p14zRjAqlYrLh+VOUUyRosKk169cLjsDnNsbVqtVxwPk3d3d3YFzNZgS0W63D3n9hvXDzVCj0XAGiRpOuoc6Pa46hwl2lcd8csOSevst7ykdR675nhumG/heprIAg5EvX11smpU13m2ahpKNGFhww3JUH+ictRGaUfLQLRgh4NB0Gn0fbQB9jnJUQZTVWT6yjkk7NynXy+UyyuUywvBgUwumAxaLxYGoLh1EjCwDcCDAeqkZceLufNo/BCPckYfpfxp94BzlM0yNpHOJ/eRbjzCM52yUWseE79HoGvuQjgk9eA/YX7TNKKymAnNxMBctp9Npl5LDNnNTHwCYnp7GzMyMA2ncXrrRaLgoidqCUc4C/a5jQn3oA7o+O4MpmJZGWYhsAQv5l8CPkeF6vY719XUnm2u1GjqdjhsnOi/VMUTnO1Op6AQsFovOJmAWBUErtwdWxyQBJgFdEATu/vX1dayvr7tNNGgzEAwzYsq+IpCkTBjmGDmKRgYWDEuT6ejljcrx5sBYssLSJ3itIWKZy3r3SZxAapCocTMKcLAC27bhKEQXBSj4N8ogH9X7r8Ld1kfraIGETrwo42tYmbZ9vrZaA8WGi7WMKJCkSlk9nOQbCgvNAwXg8mdLpZI7ebRUKrlJxd9pCBKkxGIxBw449rrzRbPZdJ6pTqfjFp1OTk4ikUi4PFyGnXd3d7G+vu7aRO9SpVJxAlbTBWKx2KF8V261SaVFTxNDmlSMFCZUiEGwv5PI+vr6gIBgjnGlUkGv1xsI5zJ8zr4tFos4f/48Ll68iOvXr+P+++93OxlRyFC4+1IAffw1LLrgIzuH9TppGKjwgRqOx3EoFosNePx5mvQjjzyCCxcu4KlPfarjeea7aj21f3hqLnNmycf1eh25XA4LCwsO1DHCRaObRgz7ZWtrC+vr647PyU/kpWw26xZqcqta8s3N9MdRROALDJ7G3O/3B7yeXLhOg5QKjOtdRs3lVePEggoro1Q36O9HlW+jED5jRg26YWWzvj6DSlMQWR6fUQ+n7izj03EasdS0MwWX2jYf0ZNp55jVD6wnZTNlCGU268K+offa9ocFQSTOE3VWEqQwXTWVSqFSqWB+ft6d1XD16lU0m00kEgksLCzgtttuc5FGOoHq9Trq9brTM4VCYSAduNlsOufSxMQECoWCm29MXeEuTDwpmzucKZ+wnjTc2EZdr8EoCQEl20x9oMSyfVFRjhfTJJliy7KpA7mbFOvV7/fdblCFQgGVSgWFQgHdbhfr6+tIJBKYnZ117dna2kK9Xneyis6q2dlZLCwsYGpqyh1F0Gg0UKvVBvjaAlwrh3xRvKjrw2xJnxxWgOvTIQomLMDTeURgUavVBsCaArhYLObW0dBoj8X2d+aanJx0m7HQCUgwxjUQjHxxkw6ea0Xgqsc0cH0Z12msra1hbW0NtVrNOQ91LZjuNMV5qe3VFO4biVyMDCzm5ubcNn96aIc1Xn10FPqOUgZK1vuh17UsH8MOe3cU+dDvUQY3MOjhOYp8Hi0KTZ8X2DK6BVD6u95nv9s22udI1ktkjUcLKnhvlMfF16faBn1O0XUYhi5vcHJy0i0m4zPsRy48o+Bg2JCKTz1SNMK2trZQrVbR7XaRz+fdwTQA3OFj3CJzaWnJTch0Ou0O78pkMi6cvrGx4dY/MNWJRj6BeBiGzlNBQaR8q+F29oFuRUgvGsdcDRF6vai4uGiQ0QrdtpT5xXad1M7ODubm5vDEJz4R99xzD65du4arV6/i8uXLWF9fd2kGFtTrGEaB/6PIekaVb45bzlGGc5RhpV5/KvZE4mDbv52dHTzyyCOYmJjAiRMnEI/HMTs7i+3tbWxubiIWi6FSqaBcLiMIDjz2zWYT1WoVAFyqRb1eR61Wc2Xk83mXd6trOMgTzWYTOzs7OH36NHq9Hur1upMROzs7LhyeSCTcoYxRAPBWE/ONCRrUKKLy09TCWwVsbDnUEVxASl5k3dSDqyklw+pEg8TqG11nOEzmKZjweQLt/wQSlFPA4fV72g7lZc4/vUc9r6Os0bDRI1u+z+DSvub93EmJUawoisfjLpWJRriuLwAOzjehHcKzBJg10e/vL7I+ffo05ubm3HhdunTJpYpkMpmBKCUzLzStUNcqKPE5Go267Sq3ItXIuDrW2JdMe+XheIxgsCyWzX619g4dBjwTKaovbRReo1NMt6Wxy6gKD1zlrka93sFGDARwsVgMhULBOdjW1tawsrKCdrvtZFQmk3FjzdRGgg160ZkNcFzHqiXqu6hNASxZe4XEcWSEgx+dX77r8Xh8ABjOzs7ixIkTmJ6edtsVx2IxLC0tYXFxEbu7u2778YWFBecs6Ha7aLVaaLVaA+uBlDd46G6hUHB2eCKRQLPZxPLyMq5cuYJut4tUKoULFy5gcnISV69edUCZMiEIAgdQdN6SHyg3gYPzsY4bvRgZWHCnESs8yQyKeNQjHeUZsR5rWx7JgogoI1fLjSILYNSL5zOCyEwqiHzed+ulGDZJ1BC2z0R5vHTwqRgUgBxXQVvwoIrCKhD73fcun6fY/m/BjS9EqTxDYZFKpTA5OYlyuYxKpYLp6WmXk64nVAP7QkzPVaFQo3efE1bPjtAUDS5C4x7T6ilTr756e2jU0fvACcy2qQGuxkWxWEQQBO4cCiWrTNXLmUwm0Wq1BjywuksN107wOY2G0HvN8DvLoOeDZcRiMWxubrp84bm5OZw8eRJPeMITcOnSJTz88MNYW1tzfekDGMPo82ncAoO8OqpnmqR9QIHKctQD1u128ZnPfAYPPPAAkskkzpw5g9XVVWxubiKbzWJychLT09OYnp7G1NSUSyMgP1KRT0xMYHl5GdVq1W1zvLe3h8XFRXQ6HRSLxYEtkXWbYwJIAG4zALtYmHxtvfU+Y/xmDf1sNuvmjO6io14w64Fl/x9l6NrxYZ19zxBoa0oRcBAJ07nty7Vm2SqHeM163IGDyIA1wElaR/XyW9708WGUXrFpoerRVyBly1eDKIoU0CsoibqH7/XNfS2Dddb26X1ctJpIJFwaDRepcs5wzRidQNxZTA2hSqWCdDqNTqeDxcVFLC0tIZFIYHJycgDocUcdOoeCIBhYG8RDJtlW7XO2iZ5qfueaIgIk1Rk0DGlIcl0C9Y7yJUEvv7OPt7a2UKvVnByIGj+CNAILygzKCDUiCay4TladVSpzCFB0S9xutzuQaqPgkGPKXRe5RS6NaJ33OkdobEcZstbei4pwHIc4Rpp2rY4EjRSR16j76Tyirs1ms24xPHcg43j3+33Mz8/j/PnzOH/+vCu70+ng+vXruH79Ora2tgbsUu7WRVDHtaQc6+3tbdRqNVy5cgX9fh/nz5/HiRMn3O6T3PZboyZ2lzMAA+tC1Q4bFhWKopGBhSqEKE+kz1utnmUOxqikXnCr8DmoWh99TuuggtZntOszCiJ8v6nAtqBiGCiyXmn7fp/CBAY9Wep14DPan/q7z6C39fApENtvwwzFo7wMvrFm+YVCAfl8HmG4vw0evfo0PqiIpqenceHCBaRSKSfkNjc3AWBgsvC3MAydh5gpQFROamh1u10nTDhp6Smm54hCkjtscGKzzRQaAFye/czMDIIgcMJBx1GNinQ67cLLbA/HMJlMutQRkp5QzzZorqTud03PnZ5rwLaF4cH2hnrgExVstVrF2toaSqUSSqUSVldXkc1mMTc3h3Q6jdtuuw2VSsXlJ6+vr2N1dRVra2tu5yk1wofxDgW4Rj7Zt5zfajAdVabO76ME4LCydH74PDX8nZEk4EAoAwc7cV24cAF33HEHTpw4MXCYlUZBeO+lS5ewsrKCQqHgeJ2evfPnz7tdx9bX17GxseHK4EYDBM5WJlAekL99XnXSzSpnGhBBcLAVqvWW+wxUjrM6oobpCR0TOgeUopxONAxUHgxzzNCQjAI+amwoyNOtZy2QsJ5+fnSxuZI6YWhwqYOJfahRDfYJIynD0o18FKUPrNNJU9lUF/uyClinKENQvd16WB0jXZp+TVnHPvN9WL98Po+pqSknP3jmD8tjXXloKfuHi7t57sTe3h42NzcH2heGoTPIKYuZB09+8PU1dZM6iyinuYlHIpHA9PQ0JicnBzYaaTab6HQ6A2mu5HEfAAzD0C2wtl59tpPRF3rMae/kcjm3c+Dk5KSTS61WCxsbG6jX665su+aWTj+d81q/IAgG0ukZier3+27dAtdkkHwRHF/E7kYoak6oka110Pfx2u7uLhYXF9Fut3Hp0iUHWHO5HCYnJ3HXXXdhamoKs7OzmJmZGZjvqVTK7fa3s7MzsJsUdy9T54w19hWckl/Z57QFyLs+eWzlpDrUrANlFBoZWBylqH1Kw/7Ov1GV83kzKJSsgWuNeX3WGin6TJRXSMsg4/i8eKy/RhHsu3zGuAVBUWDE3q91sMBIf9O2HdXXqlxU+atgHVY324dRADOKafme2dlZd3qwGvpUVt1u1wkfepNoyNEwYORCt2wDDkCHgkxOSM2xVMGs0SRGAZg+RWOBRCOR3+nlogeBHjdORnqGaERxwWE8HncL5DjhWZb2F/uUHr2trS1sbm4O5O0SVFBpK4hUw9cK+zAMB3Yj4nXyBdNq/vqv/xrXr19Hr9dzaWDxeBx33303YrEY1tbWsLi4iFqt5nKcLS8rX6r3lWQ92qqARyErDJV8QFw9+VHlsY9UsTHNgKk1PJOEHr8v+ZIvwVd+5VcOpD4Q2DEMTSOLu7F8+MMfRjabdYvor1+/7k5Kve2227C5uYnFxcUBjynHRoEF28koGxWN5s1q/x/H2TOMaBxZYKMGqvW4274ehXyy0xp81qtpy1Z5bOeC/g4MbvOqspJ/dbc0m/5COaMGiUZJtB5Wd1kHmuU/PmdTtGxfqrznXx+I0XeSt+xzWqaub+F4WoBj+9MaRPo/ZSq9sTSCCCZ4wB3TjLTt2q+U75yfPM+n399f1Kw7WXKbVC621XMkALgIMR0zuvWsns9FQEDHFCMP2m/a94wkULcw7ZYLotkm7Vtuo86+0K1KfQYvcOD952Ju/s4okEbkqbdYHndX5BaovV7PrU9ZXV1FtVp1YJAAiw5Bn0ylp5yHwjG6k8lk3IngQRC4s6NarZbry36/7/pG9Qj/qt0yStR8VLJ9qvOe71IHAhdL605NlUoFpVIJJ06cwJkzZ9Dr9VCtVrG8vOzWPbC8YrHonJ3kdwDOYcp02l6v56JlPIi1VCoBwEC6H+cxgQX5SnelJC/yPWw3x4xzKyq666ObAhZqkOkgWE/QzaJJa4BYo57XqEB8jGfLUoPNvkuNEy2D77fv9pVh38vr9hM1CWzbSBQgVln6vFH2/ao4AX8alG0zr/veqW23IM8CIqVer+cWhQVB4Bauav2ZS0olQS8TBZ+GgRnWptBnOzVXUBckUmHR08swsSpLprvQU8BUp16vN7D4lMCAnicAKJVKaLfbLt++VCpha2sLJ06cQBjunyXBxYJBELjFbwyNq5JWIdbr9dwCYCol9jO9Q5pXq2Oi2/3Z/qGnjeAmn8+7nT8mJiZw/fp1NJtNdLtdt1jt0qVLCMPQKbo77rgDd999N2677TYsLi6i2Ww6Q5jRHsvbrK81OvibhoMTicQAYLL8d1waFgFRQGbBvC/yyPFKJBK4++678dKXvhSnTp1CvV7Hww8/7Lah5IFV3KLQbhm5urqKT33qU3j605+OZDKJyclJXLt2zXnvHn30UbfPOOdlGB6swdBx5qLAKIDva/PNkrbHlkuZQCWs85DEMefY+JSYOglUsdNJoN5wdXBERRuYY04PeJSjhEQ5wS066YTgGoJhjhyfvKXjQseIbdH1VKyHj999qVVq7Khs06iZnUfW8UBHiY+sjrBeUDvevv7QcrSsXq/n0mX6/f7AOgpGNBRYUf7b9QnKC9ahQHnJ1KAoA5J9x3ex/vqhbqKMYh9bflA+JGDSdXP6vdvtYmNjA9euXUO/33cR5GQy6QzziYkJtFott+4qivc0GkZ9wvGnntGtdqknuOMTnSbUc1zjsbe350AF0zq3t7dRr9cHomsk7oiXTCYxNTXltvClIT0zMzMQwdja2nIAcHd3F0tLS1heXh4AHNbG1Ll/K4h8beWHpgxRN/M6eZ4OR/1/Z2cHly5dwv3334+lpSVUKhVUKhVMTU1hfn4e8/PzbpMZC+w7nQ4eeeQRPPjgg+h2u5iZmcHs7Kzjicc97nEDQJwgmmVRfjCVjem1eoZLlJP4uHRDwMJnMPO6rQgFpSJKXxmjvj/KOKeSVcHNSa5eSSvk1GC2QkQ92BSYvvrYfrFGuN6rysFGMdh/1rOr71SjXUGc3h+l4Ow9w36z4+QzqLRePqNF+9O+NxaLuYPC6vU6Ll68iJmZGSeQqei5lR13jKFQ1hxqGgYECRYUUmBrugXHW3fU4VirJ5p8y5C4bvkWhqHL77X8zdAkFRe3kqOC4MLbdrvt0l/q9TpWVlZcdITKwIIhpuDQK0KFQEHGhcaqbLgQkp4PghYKb6ZNMJ2q1Wq53YVWVlYwNTWFmZkZd+ooPWy5XA7r6+t45JFH8JnPfAax2H662L333ou77roLW1tbuHbtGh577DHU63XnWWf/U+BScVmDh9/VwGKffD5olHLJawRxHJeFhQW87GUvw4kTJ3DlyhUsLi5icXHRGRycu48++igeeeQRlEoll+KWTqdx77334m//9m9x7do1pFIpLC0tOaPp05/+NJaXl52HU/uFOenctYah72Qyic3NTe98P678vVHS/rTOEl9fc34PI/6uRoQqepKVPZZUf+gaQQW1tv4KCjiujEzQWNX0Pl/btX78qIGiH1t//W7TZK2O5P1ajo1Ma7usN1udGjo+ti9VZ2qfWV3Ce3xEgMZNMHhiNfuV8p5yVZ0t9IIrGIgCYXyXrjdQhyX70vKStlXBrTqiNHVV+0MBCZ/TiLTyL79zRydGpXkQqqb2cg0I5ZCNVvPDqAIBg20jQQV3MCIP0LnH9Xa6uYce6sotZamX9BA4yzN0rBQKBZd6RZ1RKpXcwuSpqSmEYei8/ru7u7h+/ToWFxedo0WdjOQR5e1hjlsfT9CuUucHQZnlcWsPaTSY5XDNkJ5fEYahW/fAbWm5cxMdhwQCNlJfrVYdKGk0Gjhx4gTW19dRLpfdOhnyFdd0MJpNPct1NPzL+tLOioo2HZduCFhQEPlIwYU1xm15tgE+Y93XSAsqgMOhVjKFndz61xrirLsSDQJrxKvXVdvua8cwhart01B3lCGgQErbae8dBVioErVKcBQ66j479qrAWO/t7W0sLi66e+bm5lxIlUYV04q4S4L2oX4nz3GC8iAZTX1ST41VvgQZQRA4Qcr1F3oCMg0JVaA09oIgcOHLfr/vIjMzMzMDvMpoCdtET83u7i7W1tZce9TrStDD53RhoSpShq0VWFCpWB5XQUiBposGGdrnjlcKtHhqOBdVrqysYH19HdVqFfl83i06u+eee/DEJz4R6+vrLlWK2z0yWkNlqbxDA42GO+lGQIX1HB6XLL+xDM6dcrmMl7zkJSgWi7hy5Ypb4B6Px53Bz7Yw4sW1PrqTx8zMDN797ndjZWXFrb9gNIuLAZkqNzc3h8nJSUxNTbl96BuNBnZ2dtwmAuqpUgfL54OiFpOSrPfvVoIbyjE7tjSefHVTWaLOB344L1RuafoPPbI03jinbVvVcFQi+FOHgb1Xy9E26V/Wi9c41toWuwmEGl6q49SgUeM9KvpjdbVGW7R/fdEL7dN+v+9kAeUtZRajtPl83tWJAIO79nFRK9enMZ1I66jAwZfWoYAjisc4JjZVLGpe2UiQT1fbqB77YGFhAeVy2Z2YzbMjWKZGGVQ3AAc7aDGaQmeIPqN6kQ4LEuWv3VKVzivqn0ajgeXlZZdyRtCgbdKoCdN3eD+NYe40lUqlUC6XXXoo+TEMQzzucY9zUfMrV67g6tWrbsMMbh1sI/wKrIeRdfpaxyqv6RonlWO8X6PXPFvr1KlTmJycdKlst99+O2ZmZrCxsYHl5WUsLS2h2+1icXERW1tbuH79ukstU5DGw2sZjV5ZWUGn03ERPfYl52ij0XApa4z8abSPUXQezKu8dLN0rAPyrMdevSi8xv99niOlKFAB+Lc39ZHPwFBjT40mFSqWWD/LKJxwik6HGSU6mRR4KLBQJrfgxIKtYQBulN999bV9qhGEYaRhPwvWjnq/nZxq5DD6sLKy4oDG1NSU2/Y1Fou5bSyBwbUTSoxUKGBUDxHboArFGjk295nhwiAI3B7S7DMdT+4kRVARi8VQLpedogbgFhDSeE+lUk4ZaqrQ2bNnsbe3h1qtdqgfKfi4wwkN7+XlZbdwiztg6S4V2tcUtAxV08MXBAf50RRoqtzDMHQLH5nmlE6n3aJHRjB6vZ7btUI9jlw7cPvtt7uTo9fW1rC6uoqrV6/iypUrAyeZAxgwlm6WopwA9h6fYapg2Od8SKVSuPfee5FMJnH//fe7A4qAgwXNTIfSA7mAfb4gyKjX67h69ao7OE/X2jD3fHJycuCEVhped999N3Z2dnD58mU8+OCD2NzcdIpCZZpvzt4qAz8qAqFzUY1k1Re+dIOjyDp7fHqDBoauHfIZlCrffc/7dJpGDlRfsC6c/5qXr/2isoegQo2bo2S/BRZqmGr6i+9ZjfZYR6D2kYIPrZNPB+h4EizYNkfpDGu0sV02CsCUJ3qp6TxhmxlBJsjT1BRrD/Bd6m1mn1hHhPKtBchqlKq8UPuI7/GNC3lDDX22leCTUQJ1uNGITCQSLj1Jt1imfqBxThCrwI31t/1M59He3h4ajYYz8gm4CcR17ZhGPFSO2qgOnVc0hjlmGxsb2NnZwZkzZzA1NeW2t7W0vr7uDGRGBXQHLzrC7M6RPnBPUuDM9vtsF/Kp7gSnv2v/pVIpt4PZ1tYWrl69inq9PnC6NrcoZ9SHi+P1TC6+hxvE5PN5Z48zPZtgGjhYM8H2chtkrk+iQ4vPMNKqHyWdN6PSyMCCne8jCzBshZQouI/ykKvgsgLKRgB89dEJbkOdFo2qkLWpU/YdLFPLUGHrYzbrYfe1Q8tXxG0nli1/VLKekSjDyvd9WH2HAQz1utl3ahtouC8tLWFzcxOlUglzc3OYmppy+ZZ8j13boLxE4cHvwMEib77fnmVBIU9vSRAELtQOwEU/KAhZtnrOaDhTyPf7fWeca4iWRibbzBC+LkiPx+PuZGZ6n+wcoiFPT54eumcNDlV+FIpUcvyfz9px4nfuzkHhF4vF3JaOPPCt2Wy6NjGtiwYADTsuHuTi5NOnTyMI9teYXLlyBQ888AA+97nPOU8MhbdGCHz8Y/nNpwx8oCJKUPoAu+Vd9fJdvHgRFy9edAqCC+Wp9JrNJtbW1txiaiq9U6dO4cyZM1haWsInP/lJBEHg+pdzn4aTGhFcNM+cZSrPVCqFxz/+8djd3cXHPvYxlxLHsaWBPKztt5oI7IcZq+pVVxk1CqlB7Tv7QA023q+OBvaJGj80nBSAk2KxmEtr4L0E1JxrR6VykSxg8cnWKGPI51Elf7AefJbGJmWTz+E2Clnnn/ar1oFeVt2pj7+NUr5Ghsi39XodYRi6XYroBGCUg+lC7IN8Pu886zR46eTQcdIIVFRUhffqQaS23jTWdM0O89s1vYV8Q2Kd9PwAfuhFZhrw7OysG0c6I3hA3+bmpkun4Zwn3zICrduKM+KjOtOOI9tN0GudBKPOUbaH6/gYBZ+dncXc3BzCMMTm5iY2NjZcuvP09DTK5bK3PG4pfPLkSWQyGTSbTZeKReIhfo1Gwx0ax+1efUQ+sJuHsC+OsnN8c4G0u7uLRx55xO3+ODMzg5MnT6JQKDi+pkOSET8Ah7IHwjDE/Pw8gP2dJDUyyHHpdDqoVquoVqsol8s4f/48Tp8+7Zx5jH4xxY38ymgft6ZV4pwYJfJDOhawiPJ2qxHvu1eFoHpHRvF623J8RpYKS+Dw1rZRjGEFCHCQNmO9u4rmNI9Rr9MrfJSHNcrTo+3RevO69rcvV9ZH1iizhgXfobvG6L1aV2t0aiTHNy7611635bGsdrvtlEGn03FnAFjjgwicyoNKiJ4YInYi8u3tbeTzeWcIUFhS0DMVh+0loKBxznt4GB7fBcB5JbWfmI40NTXlDPNerzeQMhUEgROeYRg6w51eic3NzQFeU8OZyhTYP2MmnU5jb2/PCVDyovKHfreRPTXAqdS4A1S73XaLweLx+MAJ5lyY3mw2ndHG6BE9KEEQoNFoIJvNukPb6GWip4xA8p577kGtVsPm5iauX7+OtbU1VKvVgQOrOE405jQio95J5UH1TlpDh/fb/0m+//nedDrtFs1xVxX1gG5ubmJtbQ31et0tbibo+NIv/VIEQYDl5WVcvnzZydFut4tSqeSUeqfTcQsli8UiwnB/AwB6+Pr9PprNJs6ePeuiGYVCwYG9qPlnrx/HyBxG6kSxXj7r5bX3+UBklGPG904rkzTlQ51M7AeVeao81Yvsc0RRhtAwVO+w1tEuiLReQZZvZSHv9ek8pWHgmH3gkwFWb1gHmV5nH1m9rfOMH9XFdgG6vk/lj68NWg7HhB50AO7ANt5HmaRlq9GujibqD7bF7orjmzO27j6drR55jU4ogPEZ5TQgARzaUIORaD0bgyCEBiltAe4UqJt+WFDf7+/vjKXvtfzls5WsDaHlca5why19n2982Vc6VnSWZDIZt80vZR/T2rgoWd/VarUGFp3rvKUDgNu1EvxxbQf7Wue49cyr7rB2pQX+8XjcraFkmlcstn8mFO0QAM5m4W5idIaQLyn3CYjJO1xXwrpSDnEsaVtQT+jZX1yw3Wq1BnbiIhi2u2paOsqmtTQysFDBbjuenaJCTMGGVfIafo16h3702qh11cH3eYSsIlU0DvgXHkfVV4WFIvthxskw8glan8CLIr3XKin9rmPH53z1UEXNjw+k2foNAz2++ylweFaFbnWnp/ZyMnNSKNCicUnFpl4znkLN8rjrExfCMX9Uw6m8tre3N3AqNz1D9EjpLiXq7WEYmwKAHhn2O3NKmUNfLpfRaDSccqGXxYIKnWfcKQWAy7W3i7k0f1xD2Owj8jsBDsfDhrunp6cdkMhkMnjkkUdQrVYHwN7U1JQzajlGYRg6BX/9+nVUKhWXR0sFubW15VKrMpkMZmdnce+996JWq+H69etYWVlBs9kc8BDbtDg1LK0DgNdpVOie8zo/hs1TnS97e3t48pOfjLNnz6JerzsDqt/vu0WW9Xod169fd8qC9fmar/kalMtlXLlyBeVyGQsLC9je3sb6+rqLgkxOTqLf7+Oxxx5znqV6ve7S35hqViwWsbW1hf/9v/+3q8/58+fxiU98ArHY/joZbgVryed0uBmiMag8y/foOSy2TwnM1YjVOlklHkXWYLHRC3pLmTaj83lYfjHns0YpFAyxfG0/77eyV5U3DRs1PNX4V6B8FA3rI/Y/02F0fcAw0nYPu4djSnlLg1ijUhpdYrs0aqx9oiCPfcLzhBjVLpVKbstuyjYATs5w/RIdHBxzlsf6UkYBOLRjlu175W1+2DYFznzfUVE46gDODe62pICTcjWXyznnGw/JY7ouU2u4O6Ke88E6qTHOqA6BCUnXa2j7NYqkPK7AjE4jAhe2j/VIJBIDJ6YztTiRSLgIBXdJyuVy2N7edid77+3tYW5uDnNzc+h2u1hfX8e1a9ewvLzs3q+H/nH7VZ4iTvuBOxVev37dgQsbKdLx9oFC6hjlYUbqTp48ifPnzx86aTydTrs01kKh4IAU9SJ3cNLzPJrNptspMgwPtptlFEZ3/iOIYSbD1NQUisUiJicnHU8T7ExNTTn7ZX19HUtLS1haWjoyongcOtbibSuwrIBkh6ui9iFAfQbwbx/JAWYZ1qtlPVj2fyvwLfGdFhyoB0aVgQKkqPawHDtAPk+QJWto+4wcfrf9bu/RdvD9+r/P26Jjp7/diBdTQQvLUS/ZMAbWvqZ3gQIplUo5ZaE7LgXBwU4O6kHUsPze3p7zbGioeFhqUBiGLhLAfHeCDfucekT7/b6b4BwjerQJXMjLvV7PeSYKhQKAfeW2sbHhDHzNXaURwvoDg6kDmUwG09PTbvcNpj8wWsLxpdeEeZZMp7GGerFYdB5ztlXrxbp1Oh0HEnjQ287ODjKZDFqtFgqFglM4FJI0ltWwWl1dRa1WQ6/XQ6lUQr1eR7FYxNzcnNulpF6vY3193a3R0HQVNQ4V7JG3+JfGv40EaVoE+1a/6/9zc3N42tOe5tYzMFUinU6jXq+7Reo0Zvm+22+/HbFYDEtLS1hfX8f29jaKxSIqlYrjD67tCcMQd911F2q1mlsQTg9msVgEcCAPkskkrl696vKPC4WC2+J2mGMiymt8M6SGIf8nWOc7rUGjil29njpfhgELn87Q9+hvlBkKRKIMeJWb1gCh4af6xN5nZao6razs9nmPhxHLt+NrDTqfgaR9osR1VToGvv618p19oU4KLZM8oM9EOZ9Uj5G4lWkstp8CRSNUQTMNfTor+Lxuw6zOH9UXYRgO5JtrmZQX+r/aJAQtwwAbAYOCNQWTwMGBl/yuuxwSBNG41JQZbuEaj8fdYlyCX/azHphKncoNIuwY01CnbtDIPd+ngEq3ydWF+1o/LqxvNpsOOFA35nI51+8so9vt4tq1a7hy5Qq2t7dx4sQJ1Ot1BEGAdrvtDpXTU9p1+1Q6DMk7BD2x2H4qL3fKomGvZ3joPFJ+UAcy+ZTXgf3TxTc2Nlz9Nzc3XcSfY8loDPuQkXuuueT/sVjMpbtpClmxWEQulxvYEUvT6XRDCPa33Qrc8jCv2XZbIDkqHTtiocJE80r5m1UCPi+/z1MNDBrTqpiiBNoo9SUpY/h+17qroNRngMPAQRmLDGfbfZTSjlIeFgD4yNbFByp8dfWResJ5/1F1oDFtf/MBpaOUJPufipppQfxfwR+9nExJUL6zoBAYPEW31WoNGBUMKRKAsDzd1lMNAc2/prCg0mHaUxAEbuJToDOfkkCFBnuj0UClUnFpRPF43IX6k8mkSwVShUhSowmAO5UWgKuT9ZjRS8YF5OplJMCgcgqC/bSldrvtFoqpR4heFaZ+MRWIuZo8vId1SyaTaLfbAztw0ZPG33Z2dpDL5QAAS0tL2NjYwKlTp9zOIQsLC7jzzjuxu7uLa9euodFoYGVlBSsrK04pceEmwRAjKlTu1rNNooFrDSMSf9vb28Mdd9yB7e1t1Go1Z8iwbRsbG1haWnIhb6634ZqUz3zmM4jH485QAIBmszmQ2kBFTsOF6VTkU6ansc+2t7dRKBRw//33DxhVbJcvTfNWA4phRNmoKWzAwcJdfuf81vz3Ucq2UQc1qlgOjR7er+ulokhBvc0zVkOLxivn8DCgovWyYJb36LuHkZW//O5buzJKm7jDleox9hHnh7ZNv9OAZYSBBrG+ywdwLPmcT3t7e24nOa5jsouOSRqRSqVSziHBBbI2OsT6UQbq/FMjy+pHdTr4DDTaSfY66616mnKZf9mvNPCZwkOdxw+3DJ+ensbCwgKazabzQtMYJR/QgGUfRY2BggWeJ8J20uuuC7rpxNF1G5rCRtDFeZdIJDA7O+tkAeUxDyoE9uXh4uIirl69iq2tLWxsbGBtbQ2FQgETExMoFovIZrNunUm/33dpU9o3XFvANC0uns7n8+6+TqfjTjX3RS59NqBGlciv6+vrLi1Yn2U0nmeQKH9zfSYzNHgwHlOlmALV6+0fplqpVBwA7fV62NzcRLVaxerq6sCJ5xwzRrBIKvvIT9ouAl/rSDsOHXvxtr6EisoiXjVgeL8vfx8YXFypE9MHKnQiq1AbRnYQ9d2+9lkD1YImKzSsUuJzdjD4rG8i30hk4CgvI+thU7qi7rORD32P3jtqPX1tPI4Rw7pTYPCwuXQ67SYi681woeYqWoNCt5vU6AaNRN1RgoKOwp/fVSnS+85rNFh1z2hGVCqVihNo9KioYg+CwOU90nCkUuQiwGq16s4k4Fgw7YtELxg9Ihbc+3iYz6kSZqSBgpbeEru9Ya1WcznkjOAAcFv1Eij1+wdb68ZiMayvr2NychJBsJ/yVKvVsLa2hiAI3FasDPMStDHFKx6PY3NzE5ubm8jn85iZmcHZs2dx8eLFATCzvLyMa9euuYiAevdsP2j/sO+1PbxX5RMVL5VuLBZDu93GxsYGLl++7KI5KtC5mPrhhx92Hjx6rrg2godg8X7Khmq1imw26zxa5XLZKXb1VvFAQg3v65oUpWFy4UaIvDBMTiig0HVJ/Kt8q+CCz6qBa/VCVNqQ9TYq6fO+OrO+UbLROsCsfhgWbbHean3ORguOIjXs+bwak8rjtt0+sKTOGu13CyJ4j44lDWOtl+0/vluNMpbDtutvrDsdOY1Gw4EXPWnYRmdYhi7qp7FO2U3PMY0tdXpYAGKjmRoV0r5QXWSjRgSd7HuN3LDtPnDHsUmn0yiVSgPncIRhiFwuh1Kp5HYbosNC+5/v0D5VUv3HXY0AOPmi62Wso0/7V6PIAA4BQI4BMxJY30QiMRBFZ1mJRMKlwWYyGbdrUr/fd+lG/D0Wi7m1GjMzM06XMK1Y19RQZhGkFgqFASeFEucTgTPHSqMebBPrzBQs9nu/33ebraytrQ0srN/e3h5YA8HNZIIgwOTkJGKxGPL5vDtcl2PCtsZiMZfWR3uG7VVSpyjnAXmLgNZGnRQgj0IjAwtbOTIHMJh37BNAPgM3SsirgrBCkA0bxcBVj7nPE0+Kip74lAkFod6j7Y2KDugztq+0HrZ+oygW24/6rIIGFd72d60/lfmo79X3279RxHf42qn10YnIcN7ExAS63a7bQk3zZjlZGDWgglPhp0qDxOfsQjfN8aXioReO9achyr6j4UoFQO8By+KCPNaXBwpRydGzzfx6Ap9sNouHH34Y7XbbCThtgyor9rHlO7ZJjTUdS95HwcyD2wiEqFT4LIWnRk3o0QyC4NCajlarhZWVFRSLRXcQ0szMjDskkfXngkJ64Gls1Ot1ZwRwVwt6SBlB4SLHixcvOoVSr9fx4IMPugPm6NVRmaBzT2Wdgn4d916vh8997nOYnp524OjSpUsu/5WRKo45sL/FLNvI0LyGwaenpxGPx13fq+ctl8u5ReITExOO/5vNpuMtnmnx0EMPuf5kvaPmnJ17N0OaW+0jNcKo/GhY0TCjgW/lAOcgMLgewhel0L9KUXJf+VbvoSywst0+ZxUu5wj5P2rdgy/6rgbLKHLY92wsdrCegmkR+k796yPWi2kVbJNtI8dTDRTdyUb7Rt/H61G6htd9jksS8++r1epASg7bTIcM/3Ks9LwRbp+tkTQrP6080PbbXXt4P1OWGL0leOFaOE1lZZ8BhyMI7LtEIuHOKtB+5G5za2trzgHDjU4ajQZKpZIz4HXR7zBiuyiH0uk0KpWKO+Gb+krTTAkitO84xmwLjVadT7HY/oJkgoK1tTX0ej2sr6+jVqshkUhgYWEBp0+fdrsf1mo1xGIHp3/v7u5idXUVKysr2N3ddY7HSqWCubk5nD592p3/sb6+jlarhUajMaDT+v391OVCoYBCoeD6zC7o5y6IXLPBNLJWq+XOZWIkjTxMHcq1MHSa0SlHoJBOpweiOVyLks/nUSqVMDs7655XZyjX2eVyORSLRbc+tV6vO95R3U6+8vGCOrR00wOO2XHk0bFToch81ghWb79OSvV4aBm8poa3Rb1atj5rDXmfN8QHGNQYPE57bVgrqgyN1mhdbJTCp0zUgNE2RXnLtD4+oa/l+AwL/V2NDZ8Qp8K3IMIHKmzZCurYbhra2q96L41uGupcG0A0PjEx4cKDNBBpYHEyq3LSHUFYB90SERjc354eI13DAMApJN5DoURjD4BT5KlUyglWrRfL7XQ6Lk2I9+rWjKdOnXLjwW1Ma7WaUxC+dBLWVQW3eiQ15KwGnDWo1ENMT3q/33eAjX1FbwiBGY1g5W967ugJ5C4f6+vrKJVK7pRpCtSNjQ2XnhUE+yHkfD6ParXqFqhRuKrBmUgk0Gq1BhbYU1DOz8/jzJkz7hlux5dKpVCr1dxCaCoTlUU+OcN+bTQa+OAHP+j4gREkBW5MU4jH4+68EwADKQ9chEpwRKUdBPtpe7//+7+PSqUCAO7ALJ4Dkslk8MlPfhKPPPKI4+sLFy7gGc94BpaWllx+sm/uK6/cCtL5QtmgDiHr5bSOJj5rPfnkJ/UyqhHoA9XWi6pEuaDvpWzw6ahhZNukERub3sV365y1kZkoGTzs/VoHtt+CGX2PrYf+7tMPPtK2co5THvAa+5B9S15QwKblAHDRFZVxvK59pHzF3zmnaNizD6hH6HTo9XounUq9yUoahdD+1CgFcACSaIzzdy1Xo0faNhp4TEulrrBGufKFRjaAfXDBa4x80tlleTxqLLVc64BVcE9DWkE+ZZiCCbV5WFfrxKFxTJ1uHV2VSsWlENMBp7qHOpQL+nkWFDdDKRaLA/UC9uc4nS/T09MO/IbhwXpOnhXCVC9Gn8Jwf+exmZkZdyaVploxXY1bjOuCfAW8BG4Eu8Vi0dWV85BjSZ5nKhd1BXe5oh5l6h7tGepY3aKcPM8tmXX7Y117o9ELAmHqRfbDKHRD51hYgW+NXwUYZNAoQ9Qn/FXQWMHjM77t8z7jX5XoUcrCerZUGNq6W9J77YT2vVeVjK2vj3zAxT4b1U4r1O39Omasg68cClv9X9uoIIEUBbqsUcF7rYALgmBgsRVP5GYEgBENVbQUvvo/JzrDxbFYzEUWqAwpjOgFsoCEwEfby3MXfH2cTqeRyWTc7iQkeua5rS5D+qwLy2FImjsHbWxsDLzbeuN0vJU416zhZ8dW26bX6XG3xDmiC/6Y+wkcLKLWxWY04DmmTL0A4AR0EOyvv+D/29vbDjgoMOQZI2EYDoShqewZAqegzmQybhvjO++80/XL1tYWlpaWXNoZ09aoBCnAycv0uFEBEXSSp6hEWA8KeioVRiZ4nQq41+s5pfHggw+6dm5tbeHBBx/E6uoqgH0DO51Oo9VqYWpqCvl8HvF4HFeuXEG328U/+kf/CE94whOwvLzsDtxTvuE8ViB5M0RD2hpePuOZ9bAOJgWOSgr21BPOMq2+USNXeVgNHd6r79fom9VZltTYY18quGEdfM8ooOfztn9YD997lazDQOWX7Q8AA0awLTMq3cFXDwtEKAfULlAQp2Wrga18owCdMsKmnviAPj3DBDVMp+GHmx3w9G46pgA4sKHt0BQpTc+j00gj2CovCSJojFtgoeNktxkFDiLa1CMKSBTsxGIxF42hV1qBE/tXQa2OpeUhC1x4n44P66j8QyMZOAD8jDBbB48S+YSOQVI8vr/VOlM9Y7GYS4tSucu+4zhSvnMbVS4G5+9BELjds86dO4fz58+7Q237/T5WVlZw6dIlt5U8d2js9XoDOyKePHkS8/PzaDQaWF9fd2sPCW6mp6cxPT2NYrE4AL503hMsxWIxFyXRzTo4HgDcToHcDXBubs71L8/v4O5Wuu6GuoF9u7e3h83NTTQaDSSTSddHHE/OHY4h5xQX3PNzy4GFChGf0ajEwWKnAgeee5IVYCoE9WNzaaPeOYzUwBzFO2cR+7BnfPWwwnYYyPBFL3z3+erne1/UM1q2j7T/tW46KWxfWKAYJciUXyyIIa9o2NsCOJ2UTIWil5xeBkYTKGBVuDOESMObZSlap/FIo5e5nAAOHcRHwzUWizlvMHMTya+NRsPVnSFaChVOegrWTCbjFtQBcACDAmRubg75fB6zs7PIZrP4i7/4i4EcSpuyof0fZShYXrA8y2sK9oYZWFSAFN4cD4I/FVhKmgrAxezcQo8eKAUEXAxNDx/HZ2dnxxkNbAuVPncQIV8QAHQ6HSwtLQE4WEczMTHhtjVkmtLExITzDO7t7TmwoXuRb2xsYHNzE4lEwuU5c1vBTCaDtbU1B5Loaet2uwD2twhWj2C9Xndri2is7O7uYnNzE1evXkUQBG49xuzsrEvpyOfzbtecQqGAhx9+GNPT07j99tuRyWRw6dKlgXQlG0G8WWChivQoWaPeejWsrez1he01KuAz5km+elhgovcpQNE5btMOfW2xkTr+ZknBBHCgm/i/BRXaJgt+9B6WqZFRTdFh36pBr57lKGLbFHz6ZIcuzNUIhs9ppe0aVXfxN8sjBEy6cx0Al3JEA7jf77u1VpRVjIASyLP/1HtMI9+CBx40R+cQZSD1mXrKLSBSUMD2c22YrmOjPFCQq4BEdwkinzIKQDnD3ZJ0vmi0m32jUW2bPqf9b/mU7QYOzhfS6BSv6zovzhVd9K3v4OL0o+adPsPdwejkoU1A3cMtWDm2zAJQp8/c3JxzUJF3aB9QrxWLRcTj++sb6vW6O6OINkm320W9Xh+IwlB3MR2KkQuCYTqWfG0lbzJbYX19HVeuXHGbtHBDFC5g51wkLywtLbn1jeSvbDbrgIimLLKNdp0Sx8w6aobRDaVC8X/r8eAEU4+1GnL8nYrMGtv8rpOA10bxpKjxp5OY/0cxqU+hWUPqKFCiQIBtVq/gKAABGOxXGo2+CISv79QAH5V83gwtT+vD8nVs7fVhgIjl+wAKcDg9Ttuj48p1CI1GwyFpPaSKnnD1PgIH2yha45veZk4cBUEayeAkZF3VSGVeogIUCiDdDi4MQ2fc0XDmgmkFM2psMeLBlKTLly9jcXHxUB+z/aOMqc9j5SP2lfLxMLCtBiJBlO7QoYc78bpGgRTEBUEw4P2iYaB7tFM4816OGQ0AlklPFK+pUu/1eq5Mfp+YmHC7eKRSKZfLzTozfSubzbrc3SDY30FLIzT5fN551HQnsG636xalc+E6dzshWGVUjcZLLBbDbbfd5pR/IpHA8vKyC/E3m03Mz88jHo+7EDkAXLp0CRcuXMDs7Kxb6Mi5yrxmzpubIWvwqiNKr/Hd+pd8qSmS1vOuZA0l1RuUGyrX+Yytmy2T/EDjkMaNDyj5wM+ojigaL+RTXrd6TtNibHtsvQEM8AbfZ+Wr1oPXgcMRJG2jOjB8fUG5w3QJ/vU5A306XmWub3xUr2jb+JvKEnrulR8ph7nFNRfIcvw0nUmNYK0f363ONhqJyuv8jWOpfGr7XttMUEYZyHpRj7CPNF2K6TGUL2tra86DTaOY8kfL1DFVoEd+t2CQ5LPfLAjxzS11PFo9q89x21flK9881vrSeUMHjIIKOhtjsZjb9IXb0VLOM/pNkKZbuCqgoM7ghia6Sxf7kmlbjPKwn7jrI6PUdJiF4cH5ThqdIu/plvCNRsNlK+RyOXdyOd9D4EDQyvM+eOYJqd/vO7uDQIvOqkKh4CLfUbJzFLohYKGGr/7vAxXWOLWVi6q8D1So0B5mPCmpIPShcN6jHgH17PjuiSrDRwqmfMa01j1KaA8zAo8DIqLqbZVh1Pjwf9sWBRlKWi5/p9DWsn3A0hr/wOBuJXwvFYHuP03+oVDhuPIZ9U7yXRS+NHIJDKikNdTI8CAjIXynAhl6w1qtFjY2NlAqlZyw4CJoeviDYD+Xnu3hxGe/csFcEATI5/M4ffo0arXawOJDyzs+Ja7jpx5qvTeKB4bxhPKB5Q1Ghfr9PnK5nANdBBgEGzaaqYqPCpz9T6FHjw2ViRrhYbifasTv9MIpEOQWoclkcmCBIw17RpHW19fR7XZRKBTQ7XZdf8XjcecRJC9whzKmTXW7Xbdgj6fEbmxsuNS4tbU1bG1toVAoOHBE/tBUDQAuJ3x2dtZtoTkxMYF6ve4Ua6vVcruhtFotAHCL/Obn5905J5VKBWEYup2zmD5yM6Q7r5FULpD3gQMeIv/S4LFyFxgu2xVA8l4FGj5ejTJUSFZGqMzxtS8KqAwj60AC/IsqNaoT9Q6tL5/R9Sj6u6bVsO2604+u74lqaxQAZT9wvlLe+fo3Stfp3FdjXdvBdyhQopzQ1Dg+r/cGQeDSjTY3N11kUddmUR6p08K2k+ckqNed7WU/qu6j40ufZ2SCC4LVU6xtp6FKhwk96NRNqVQKzWbTrR0j4Dh79qyTMWtrawNpeZSj+h7ymYJb7UPqUY6lDzxG8Q6va0RI10/qrkoqA+lUs5EN1fGMHhAE8LBABRzabjoS2Xd6PomNZNLTz4g1qdVqOQcTtxC39aVO2tvbQyaTGYhgMUrBMyp6vZ5LAeMaUuoM7nSVSCQc35B3Wq0WwjB0Bx8SINApRRBHniRPc1tzXf/BxfpREavj0LEOyAOiPfIWOOg9w4xfFQ5WAFmAMUx4+yIoqkB8kQutm0Xfo06WKFJjzFeWNa59v6t3Pcrw1zKGAQ5fNMD33lHaZd/j82pEjTuv2zJGeTcNRBre9NhSSNI73Wg0nNFNrw0nkp7toAqOhiq9CBT09EyrNzUIApdvyAgDAcfu7q4TVgwh1uv1AQHGBXbqGeHWqv1+3y3osmsS2JY77rgDjUYDDzzwwEAqkVUK7LOo+TjMQz2M33zj6QMV6g1jmRRi2WzWhcS3t7fdIj4ammqAUhGogaQeKCo7noXBNDMFgtwfnUAHODhzhO2j8udYcycUpnmsrKwgFou53aqYjsV2EmhwC0VuXbixseHWeVAZr66uOgVQKBRcO9hu9hn5r9vtolwuo9lsOuDT7/cxOTmJyclJTE9Pu9NYE4kE1tbW3Fok7nvOQ7Xy+byLxszPz+P22293yv1mKCqqbHmJPKPKy3pU2b5hMpR/1aGl5Vn+ptGpRq0tVyOFWu8bBRBHEfuC7bZ6TOt0lMxWYMF6arRD04L4nL5T17YMi9D43q1tUS8zUyB99Y7SDyovdGwVfPI3KxMsuKITQw0sepXpJMjlcgOOB67boodZAQ3lsV2TQVnDqLVu1EH5TWI6JXc1ov6iLqEuU+83jW7WJZfLOScYieuyAGB2dtbtktftdt3mFDqGvrnFORjlzNSoiW7WYEGyJeUrfieQsg5B6nGNEtln1UlHQzuVSg2AMAJI8pBGhKhruB0sx0VT5XhAIdObfM5x3qt2MSNmFlAqDxNA8xwjOjKp03idv7Ef2O9hGDp5z/eQj5i+C+w7paiHVPfqonLaR7rD2c3SsYEFcNiYVHChgpEMaoWZUpSnm7+pwgGiow5KUYaOVShWWNvJM8zwOop80Q7fb0paH+slHna/KkILMnxt9An1o96n46j/sz3sT+BwPr4FfKoUbJ2HKU/NDeX7er0eGo2GK8+GcjmJOenUuKbHR3e7AODAAZ+jQCY4Uc8GjU6ersk0G5ZDD8b6+rorc3Jy0i2c4hoEKjX2neZs8zvn0/z8PJ70pCehWq2iVqu5frKg3F4fBewP638d/6j7tWyNiihI5pzmb/SUsD+4AFwXRmo0h94senIYudjb2z9XgqCMxj6BHcPEMzMz2NzcdEY4AJde1263USqVsLW15ZTJ5OSkG1Ma56p06O3RqMTk5CQ2Nzcdz7Tbbef9zOfzrn08t0NTxJhCRsOE6VlcgNdsNpHNZt3pqxMTE1hdXUW/30ez2cS1a9dcZJD7nxPY0PCYn593O4RUq1W3A8itJk33ocGlhpMawcCBh93nYLK8QB7zgQgfWU+41jFqgTCJ77+VwMKmZqpsZX+x3lY3aZtUP+raCpLKXPYV55CvPaMYFmrIq55WY1/rpZEk7WO9Rz32tu7AwRiwfgqU+A6NctIwp0dY+4CGPD3mWk8rH1ke+Ve9+7yPBuv29rZLdSGfq0OB7QDg0rU4b/WEawAumqu57TQY2W9Mk+n1eiiXy0in0273n8cee2zgrAPKTI26AoNRIuUr7QPOV9af9dG+UT2jpOmE1G8692k053I5F2VWxxDTgehNB+DaaKOJTDPt9XpuhycFZuoc5LsAOGNcbQGODcGKTzfu7u6iXq+jWq2iXq9jZmbGGelc/8CINiMLBDjsO24LTPuAC8I1dZj8w2hVlJwisKCzi1kCOia8R4GO0lHBgFHoWKlQ1svDSaoTX0GHNdCP8roogrbRClKUVyyqTOBAuakhG9V56qnyecJ87fKRbbMV4ny/evCtsPK1RZ+3v/muWaChSibq/qj+sWBClZ22zRoGFOQ6EdivfJd+bJ1VqPJ3ll8sFp1Q5r0UCkTi9ErQeNAxoQdblZQCDKZ3MEJChRWLxQaMoDAMHTDggmzm0ycS+9uo8iRrKh0KElXI9IIzjUsNJwrKSqWC06dP49SpU9jY2IhM/bCK3ecQsONrx88HJpRYho6tvaZjbPlMjSkAbq9wbqlH4UqvvUZf1MvPlCYCPSoE9ea0Wi2k0+mBnas0HM481lqt5iJXExMT7rwMKqJYLOYWaodh6NIqgIOc4GaziWQyiXq97sApeYCRlUQigdXVVeRyOWeQJJNJrKysYHFx0S0On5ubw/T0tAM5a2trWF1dxdmzZ9Hv7+cZNxoNt+tHLpdzEY5cLjewGxnD9Azvc7FetVod2EDgVpI6EsiTChTIM1auqkxQo97qHM2FH0Y+3leetR5g24YbafNx6sR6qGGj+ieqbnYOKUCKaofte/6m+mcUEGUdQ3qNqRYkC554TWWD7TfbBmvcKgDjO7VcGzFQmaSpOCo/ddcj5V1fnyof0xFFp5U6/hSA2QhREATOcGR9KPtZd5WjumaMsjGZTDonQr1ex/Xr17GxsYF+v49CoYDJyUlsb2+7fHu1O4IgcP2jellJ555vHO1fknUsRZHqZRJBAg3jKPuQUQM9P4UGOQAXEWd6KuW9OihojOuuW8pz5DXeR73CDAmuuaBup8NHbQauBWWKKvlEdx9jaq09ZZ3AmPezf5TfWDflU+oxjeJQntKGId/GYjH3furmG3Wk3NR2sxpaBA5SH1Toq4fUCnafwcFyrRdi1PpZr7+d3CSfEaR/7T0WKIza4aMoFzXYgcF0ISsAtEwa7PqMr20kXx+oQD+qDB8AUS+E1sP2k22jjom2L6q/OBk0BzgIApfOwV13dPs7lq17oAMYWLRnc2EBOO92EATOy8wJq/ncFC7JZBL5fN55SWgA87wBRkt0j20N09I45OJselUobDSNJhbbX2CWzWZx5swZPPjggw5UcRzsvFLl7eMzH1lAEcVTtiyfR9XWaRTgQkXBPiGwYviXSpf3qtez0Wg4YEHlwoV9TFMC4CIP1WrVPUsFq7t+kU84XoweqIGsOcEcO90yd3V1dWCXKpZJbyK3HVxcXMSjjz7q+nx3dxcPPfQQ1tbWMDk56bYmbDabWFpacmlPVB71et0ZE7FYDLVaDeVy2Z0HwnnQ6XRw7do1tzDxVnipfKQpC9bJwndahWgBiBp8LJNe3OPoByU1FmlIHmX4qOE6Svk325/sA43UqDF01PutkcHrPmK5UfnmltTAtDpcDWE6dDhmOqYagSZZkKjjpO/jfRw7GnE2/TmVSiGbzbpceV23ZLdBVcNSt3Ed1gdsF3WxbtxAOc5o4Pb2tjPctH30lOt24fROa0otP3pQXTabdVubUk7u7u4il8shn88jmUzi9OnTbovUBx98ENVqdSCCr6R9a/mD40DDU++zgEP7iOXqX5bFeRUVedQUYiXqXAUunBc+EKP6Sc9tYJRZvfecB1x7R+OeJ5sXi0W02200m03nLEwk9ncD5GGvjFLk83l3FhS3wG00GqjX6+h0Oo43GIlgZKNer7stz3mgLOvMCIwehMcDFOlE1XlMxxbBFetVKBTQ6/Xc+lJGzICDQ4NttGNUOhawIEV5fiza1cG1HtVRPUzHbZRF2xYJ+zysltRI1nK0LaOSRib02SiE77umdfV5/u19Pi/CUW1lG9Vr6AN/ajzaqIUFGLweVZeoPoi6R4UI301jneFk/qZGC3Dg6SKC13Ehj2lYlWXT8FdFywPcuGCXXiT16nC7WQoTGm8UAMzFLxQKLlzLazMzM27xdzqdduHrRqOBcrns+npubg4zMzO4fPnyQF8PM7gsP/rmqPKDHVsf31mKKt/y2lEROhoOHEOuF6Ch3mw2nSBl+hAXsdk2qWLR7W87nc5ADmsYhm6HL20rr2n9tJ91YSWNE56SzlA+jQ4CHvbn3t7+yerXr1/H1atXXXSCIGdzc9MtBFxeXsbc3BzOnz+Pv/mbv0EQBG7bWr6fBkcsFnN8yK14uYiQERIALqWL5dxq0nkBHIw9x0QXkWp0Qg0XayBrNO5GiO+l55L1G+bguBVg4SjSOqiHm+/3kcos8qLW2RedsTLWzkPf/LbtV31v9aOVF/qeKAeDvTeqXnyWvxMEqAHKcpljzlQXRpV14bPNUjjKu8560DPO7V91YTLbxHoRdPBD73G/f7BDDx0k9CrTWNbIvqZWAQcRUgVdiUTC6YlMJoO5uTlMTU0hkUi48wt0vlk9YcG/tenogNE6sb0+gK7l2CiQ9rVd26H3AAfnZPC6rm1QWeADO6rPCVY0zYrGN9d2UIZzUwsuwG632243SjoNuYBbHYF8Trd6peOTW+Rznabd0KTX66FarWJ9fd3xg+qYINjPaOAaDHXE6C5YOt90q3Nu2d/pdBwA1c0L2J9cH3KcdFPSDQELJTILv5PZogBEFJpUsgbfqOQToMelKENI63jcellvoC8ycNTzw+rp+90CKAtOfOWrArN5rvzrU8JUENZAsN7qYTRK5EKFky7ujMVi7lCaarXqvMAU9CoAeRony6KHAjjY1YY7RtBbpIpaIxBcwEvjlB4pHoBDIagHF/V6PTSbTWQymYHrjUYD29vbqNfrzvtBoUrPE73vzWbTeeJuu+02XL161dtPSlF8dtS4sO903KPK8xksUUDEzjMLeIADY5Jjzj3KM5mMO9OD/cidUfb2Ds4IAQ62Emb56jVV2UUBrB4aNfCsp9iCFY61zm3ujU+lRxDQ7/ddrjTvvXr1KtbW1gbGnOkLnF9bW1vOi7WysuIW9rE8PkeeJB9fvXoVS0tLyOfzeNKTnoT5+Xlks1nHb2y/zzN4q0lTA2wKiY69yqSoqOnNEGUcjRPOc47zqJGJzwfZtRy2D5SskabebRrT+iyBFL37SuR/fve9S1NGNY1T5yrlK+eSeq2t80JJvdg2d59l6r1cXM1ohTp52A5uP8uzdayTSNOh1CC1gNcS20eDkbykwIL9zb7mWiym+DA1Rnfh0ciORhQ0sqaefqb58J4g2HemzczM4NSpUwPpOLHY/oYXk5OTzuHBiCz7lLzEtvsiSGyX5Rc1+JXIBwokdC0k300ZbHlOx8ZSv3+wM5Teo+NsQZ3qMnr06WwKw9AZ+ZRRLHt7e9tFvFlfjWyzPOp1to0Ags4cAj/lcQVlrA95hG3k+g/aPir3KcOYPkUQwvlBwMM1R+vr60gkEqhUKlhYWDi0+xkjOwQ01DOjOtVvGlhwgDQlZxRlcFQFR2mA7x0q/EZ9zzBD9laRjVhERUOU1NCy4CTqHQrKOCZqrA8bF18kQu9VsKJRAws2fGVbplUmjQIUKuiskapKkWHgdDrtFsNyAur6AwADE169o5yspJ2dHbfLEz28sVjMCTFORObl8/5cLjcgXOjZ4GItCuN8Pu8AyO7urjMSd3Z2sLq66g5ZSyaT7nAcbi0KAKVSCUEQuPz7tbU116ZhwNdn9EeNk/1fAYbvOQsqfA4HLVM9lvY564CwIJC7ovT7+wvnV1ZWnAKiwufzdtth9bIOC+GzDtZzrM/pXCE/KcDQhaT0SFJJ0Qjo9/cXVZOvuItUtVp1YW16qRjtarfbyOVyzpvGlIu5uTk8+clPxoc+9CEHRLa3t1GpVAAA/+f//B9MTU3h3Llzjq+5LuNmF2/rzjd2nK2xyN+1/+xctXOeEcVhxulRZOvCOTmKl/rvkpTXNEWMpPKchpr2iV0H5pPZdi7zPqujrMFpnQJ63coBBYhanoIGkgI95Qltu7bXHizG8tUW0TFmPShL2Dc09mx+PQ1LXb/FcmlwqTHKPmdZmuKnYFWBhnqhqbPZL7yu0Qj2uaYF0ujTyAjr3mq13A5U9HDzDA8+a3lL28h32UwJ1oN9a+WdlqMpphxDG3lS+a9tjeJF1om6W/mffabAl/drlEnXF7Av7M6AVvbTuUfQruAkaj4FQXDoMD5uJ+8jpuwS8O3s7LizN7TvNeWJAFN3J6PO0PQ8gjw63Agg2EfW6Ro1rkfRTQMLKxzIjCoY1Xi/WdDha5wP+VoFZg1jvd/WRT0rPqNjFCPf1x7tEyXfdTvZ7Ps4Ya1CPG7dWL7PYxxVF62rPuszBn3tBwZTunyGpL6XH7uGRxVhEOwjfaZFdbtdFw2gwFZhrh5SDR9SMdBLwInWbDadAOPWqPRUxWIxTE1NufzIIAjczg5hGDrvdL/fH1AIbEcmk3GLbAlw1OtGIcI8f0ZH2LenTp3C5uamEyJ2Tg4bV5L2axS4GOa984FC3/u0LDXuSb41QzqX2Z/JZBJXr151p41yoXM+n0etVhsQjDY6YRWX5W/1GFNmsQ+1XixHDQDWl981RK8L4/iXi/yDIEC5XEYQHCzk7PV6LmQdhqHbSYx9xLNPOA+4QPxjH/uY49FcLodKpeJAQ7vdxubmJv7mb/4Gc3NzzmtJj9bNkA9YWDmhgE0dHyQ1CKx3bhgQHIUUTPC7Kk6t9xcDKQCydbJeTl6z99HgscADGNQ7+uEYAIPAQYl9ZsfQ5wwisOa46oYZNOyAA4MbODCYwzAcMPxtREPXu6lXXNdHcA7zXuvU4/2UsalUyqWOUMZzrYiNeLAfNBefG1BErdHgmKmjgcaelTFad03FVLBJ45L90+/3nbOr0Wi43QOZ96/pmlqejr0COr0vinw2ij5DvafRJwtCOTbWmNfy2UYFFhw/3qd2gTqAGDWo1+suRVTHVUGayn+fUc3+D8Nw4AwkC6A5R8i/1sb06VwFlpwnrLvdnphynTYB5xLrqzuNqdzjO8MwHNgO3QKPfr+PbDaLUqk0sKblKBoZWFgDgGSNRypNX04sO9KW4zOOh72T74kin8eLdVWl7zPW+VGDwIeej5pk/HuUArSGig/B+yZt1PWosm3d9H+L9I+qL++1hr0l9rUFmfxuFZBtk/5ujQB9r52UTB2il7bRaByaxLFYzKU+aB0o3OkNI/JnmfRK0VNivV3k/2KxiCDYX6hl12HQk0TgE4vtbznH7ena7TZisZjzQnQ6HQdauFWp7hZx8eJFNBoNPProo5Fz57h84iPfPUc9O8r89aWdWEOF/8fj+7t9TU5OYnV1FfV63Sl1jp+mIGlExHegE/nJOj9U+em8VABulQONJGuM0YukY8O+4eI/gsu9vT23+5ka0WEYYnNz03km1cggf+3t7aFarbr37uzsuJ2euN1it9t13sqVlRUXXuf9N0PDDAu2l2Nkx/Wocvj8qOTzsJLUeNEFxDcCKCwfjCKTLTCysk/ro3/JBzT6KGvU+FO9q7yu5bIMTV+yPM3ntb98ZOW17Q+NUvFdmtJD0jpoeTTKaGBZoKVAlGXr+7S/KQ/YLtUjnLs0zPk/ZYamlFlnlRpbNPSP4icFcgq6GJ2Mx+MDKTqsj9pb1D0ERBxjyhrez3nPdiiAGxbB1foPm6vKt8Pu8Y3tsPnvM+Z9RjLvZ3sZdWC/EXwAcGsquKsWx5uLtbkWje05avzYLhrj3LCFgFR3+eJ4EQRQr3AMWQfqfgIF7XuOK/mCaVbkId+6M/a1AhzlfZ6jpafTKyDjhjS+wyKjaGRgoYxnO9gndDh59beogeIkte/zPWOZ3VdPHQRbhgUXvnpbz4a9V8uzIEWFqjVgfHSU8NHJaJUlGVq9vPyr5VrQZ9tgyTceWq4dA05cH0BRpWT7cRiwsJ443312HINgP+SYSqUwMzODyclJh+x1sZSGD7VfVMjSS8XyufCP7+WiP/I/9xNn/3HxrPWE0iDUCU2Br4cyxeNxt6C2VqvhxIkTzpPGyR8EgVvncf78eayurjovtm/sbJ/b8Rw2P4eRBQEkGj1HlenjV32OSpZ9ubm56bzrXIjGELfms+p71LOqHpthH/IXeVj7zbZdyyZPsM5UXioXNLIbBIFb2Nfr7e8aFY/HnVFDzy6NFioAtovvU08uz6hgvzAdIRaLuV3ECHjIezbicFxiZC6KqBRV0Vn5p0byjZLPa60OI114qso9ytAZpU3a/z7ZyXtp+PjArXqhfYa3Al410FkG+VN3PWN/UJ6RVzQFVMGGGt6ss82zt6QGn9aT77XzwnpNSQqYgmBwhzX1sEf1qzoRFDSp0aWeeDoUKL91TQg91wBcFIPnFGm7NBLOXXss8LHOjCji/OZcZa687gjFOlGPT0xMuAP+tD+Y7kSdQyOba9IoP1iuGpo6HgpCOda+OpOGzR8FmlH3++6x9/KdCvY4ZtzohNt6MwuAkRq7foWfTCbjFjHbXSSjyP6+t7eHlZUVLC0tOVlL3uCJ4DywkFvRc8co7hrFtUArKytYXl52zh5NrYvFYi5KQqep2hoEVpQFCsC07zTqwznAD4FQMpl00bvjOHaOBSx8pCkGt4J8wMHnFdX/VbHeKlLEFlVHn6GsdbWGNgWmDwzwPhoa9plhkzGqflF1UNL3q3C27Tiq/3mf717tSx0nbZs16PR3faf+puOuCi2VSmF6etptVTo/P++MUU4mCmkacpyMFAScgBwnGvQ8uVKFKd+vIAuAizLQyKVgU49SLBZz5ySUy2Vks1lnVPId9FBvbW1hZWXFrd9gGJS7O/CQNo6Fgv4oEK5tiOIrFT5R5ONPNXp8QFP5XJ0AXI/Ce3jSdTqdxvr6ulMiPBmb406vvC7Q3t3dHdiSktv/BcHBLiF2fgFw62O4GA442AKXXkFV9pqPGgTBgMJmO/gcUxK4iJMKgAf2KVhimbHY/sLLMDyIfJHnVFEGQeBOis1kMm4jAwIH9gn5u9/vuzM9jmtUWxr1eXXe+BxVt0qOsz428qO8yA/n5LBIR1RbVG7yfUeVY3WH8r/KQpJ1ZqnMVTCgBgTvIXBSg1jlLvvKNw+0fL1H+9KmDto0JL2udQQOtqbV99G41DUKtr0WjOkY63xkX2n7FaxoCkkikXAGKD38wEE+PYEzI9d23H2AUuVQFFkbgH3F9yng0AhVFBjmGjMa2OqE4NbW9NJrn1oHYBSvcCzo8NBxU0Nf/yppOXq/jtew69lsFlNTU5iamnL6s9FouDUGu7u7LrqrJ1eznrqOgs+wL7PZrNMLFiDqIYhcI6Hgnk4a6ktdwxKGoQMHevAdAUehUHDPck7wfoJEHrbLHZxYBre4pVOxWCyiVCq5w/vYF4yK8Hwv7oxFEKY6jTKRulg3ORiFjrXGgpPZGojKLKQor/dR5dvvwwxaJStQ1ctt79NyogS87zdei/I+DHtWDXufIe5rlzXSrfF9lNLSMVJvqf2N1ykE1CC17/F5vlWBRxmLLF89Iz7FRp6xClaFka+/VBjpAmsKZe4/zXUKDEW22+0BI5OLbLXfKDwpdFSxAgfnKHBuhGHocte5QwfPVuA2sr1ez0U4CEDCMESr1RowRhOJ/fMtNjY2cPnyZayvr2Nubg5nzpwBcAB4AGBubg7NZnMgpcUaCjpGek/UfCNxvNUoY3l6T5QxpLynoFpD7vyfBwfSCMjlciiXy7jzzjvxV3/1V7h69arzHtLQDoLALWymYqVBwPeXSiWcOnXKnXSqhhdJ+ZvtswYESQ0qaxzo1og0BjKZDGKx/cVyXHy/vr6ORx55xOVl6z7oVDCqaLjgjnxolR/5jnmxzJXd2Nhw/EmFSM8UtzS+lY6Zo4iKS8nO/xslK9t1MSbLtvzO+vR6vQGHwlFt0HdqxJMgxZYzzHOtetWnZ1iedfooKNTfoxbdcvwtKfAgqYGoxrxGAlgHNV5otFBO+lJX+FsUHxBc2P5Vbyxltaa9MFqoQIJGGZ1CnDs0FHd2dpxhyW1FWVe2h4tcubMgDU1dG6FtYNui5IfKQ9v3fA8dSJoao+MFHCzK5bM7OzvO6dJoNNyuhQQn2WwWu7u7botbXVdg9b6CNwsIWG8FTfyNYxBF1CcKDG00kzzC65yXxWIRCwsLOHXqFJLJJNbW1rC2tuacNGEYolarOYDBnZXUYCa/BkHgnC/U/XZusF+4KxQ3zigUCgML+m27aJgDcPqMtgKBXxiGbrtaXmd9mb1A3p2amsKJEydw8uRJl2odBAFWV1fx4IMP4tFHH0UsFsOdd96J22+/Hc1mEw8++CAefvhhd45RLpcbWGfDjIl2uz3Aw4x0B0HgIinFYnFkuXzDi7etN3JUJHMzNOwdCiysMTqsHCsMLFlDwz5zM3X2lX3Us9YQV2SvBlvUmPiUhjKLNbJ80ZVhYIDXfR5uy5Q+cKBjaAHiMFCohmK1WsXu7i7OnDmDqakpdwAOvUA01ui54O5LnEzAQahZFbaegUHhwXvo1dYF1J1OB81m0/1OrwcNQA2rM9WKwsXXZ1QQ3AdbDe+trS2cPHkSy8vL2NjY8PKoD5BGgYqj+FaVDO8fBZz4yrDPa7pEuVzGU5/6VCQSCTzwwAMAgHq97ozvfr+PTCbjdkqiJ856cfP5PGZmZlwObRQwV971gWMfX2v9WaamBdEQ4mFWBLmlUgkTExN4znOe44DC7u4uLl++jD//8z93p3Z3u12kUimcPXvWeYOVjxhVIaiIx+NukTbfzfbQU0UFS5DrOzDs80mUG74x0FSaYXLckk1foGFDY1RlCY1FPUhKvaLsI59RaPmDa1zUe2uNYPucrzxbV/aRGnK+lCCb6mAjogQSusDVvtsadlYuqEOI5fvmgbZZ54++x5eaYeU92+rrE6ZxcPzs3FNHlkbouGNgr9fD+vo6Go2GO+eCEVE9GC+ZTKJYLDpeVODCOnE81QvOutt+Zv3pDFGnEMeRRqQ6RAjgmALJcqgruMMcF/NyvHlIJuvR6/Vc1Lvf76NYLCKdTjtZ0Ww2B8C39cizPsPsK/LcsOi25XmO8TA7MplMolwuo1wuO3l/6dIlJ9vIUwRT7XYbExMTOHPmjAOOdMroVu5sE4GCnVs65uQhBc96DyPRs7OzLqWJfZnP55HJZJBIHGwlz7WY7C8a/QR7HG/KdQDY2NhAt9t125EzasOx3dvbw+LiopsDsVgM8/PzLhWckWw6uNLpNEqlktMZ3JJW5SF5UtfjHUXHBhY+hvIZGccxvn3vGOWaNTSj6ujzTJKsl2gY6e9HTRzfu6KAyzBwY421UcCT9WhRCPnqxYkZRaowtUyfYaZ1shESki8SosabD1TY61Egj/Xa3t5GrVYDAIfIqZB5ajU9tpxgnNzsDwoNepwILOjtYD/Ss8xdiagwmKbE3XY0/5/KUD2kusaCBqF6kuLxuAMOyWQSy8vLTrkC+0opn8+7qIXPWzTMQIvipVEAdRQgUT60f9XAsgqFY1ypVHDHHXdgbm4OGxsbbucNrpnh/6o4mDY2MTGByclJBMG+Z3N+fh6VSsXNBWvUqjJUHrbpAXqvj9dtW+jdtW2jMaKOARpss7Oz+PIv/3IX4l9bW0M2m8XjH/94tzMUjUACzY2NDayvr2NzcxObm5tYXl5GtVp1vM+0wHQ67dI/aNRxMwGfF/s4NAqv2H7QcVDPt/bfUaSyQY18Cy7VYOXc0R3bNEqm+sDKRzUqgcO7GekzNqIXJe+1rqpPNXWH/KZ9pu2i7GL9yIvq+FGArEay1onvHBZl8EVUNFpg22LnhraF79T2+vSHRkRs7riPT5QPCChojNfrdaysrDjjWlOdKN/p0acTivJY+0z7wy4WtnUij3J86LXW9S4+2UTjkgts+Xuvt38mEiPfjMRy/R/P1GB9aFy2Wi1nUGazWTf3de2WzieOh+VZX3+z//R/e7/OK6u/bX+RHzKZDCYnJzE3NwcAWF1ddVEJOmqoC5janM/nUalU3NkNm5ubiMf3z5/irl3a1lgs5hYu26gJecguzOd48kPgwY1jSMoPBBkABmQNMysYCaE9QdnOdC+CAwBue3s6TZnavbKy4sBAoVBAs9nE4uKi266eKVVcP2T1G/WmLx1xFBpZk2gKlI+swWcNW+Bw+o2lUbzs2jgrpPh9mKfbGrO8HuXhHWb8sE383baVZJUnGVfL9rXVvksN9yiPqyX1sPPdagxp/9h623K0fj4jynozfH1nQ/n6u/1Yr5kFU1ZAKWjZ3t7G4uIiVldXkcvlMDk5iUKhgJ2dHef54PkRVFicTMCBctFIhSoNVQ4U+LFYzAEMKgM1PlhXXTTOCUvgQeIWeDzAKB6Po1KpOK8Jd5UC9g/MI+g5efIkrly5cij3lWRBtgWq2q8+svf45qC9N2pO+xQPFeyFCxdw/vx51Ot1LC4uYnNzE/Pz89jd3UWlUnEKmR/dAaXf72Nqagpnz551CypVyUZ5yu2cVkPA9o8FHrYv7W+qWDh3dO97TZkgnzEXdmpqyt2/sbHhUr1oxDFawfUk+Xwe586dw/T0NNbX1x3Q0vopaO10Omi1WkPzwEchTQvQNDEfqdzkvLMGYtQ4aZ/65D1JQQXfYYEDw/2c51rmMIeLelitl1YNduo8yxfWc699oW3XZ9TJY73+VlYqsQwFPRr5UCeJOtrI91oO3xc1xiqLfc4hK2usc0T1p8pOXZ+hRrwtz8cj7FuuP6O8n56edimwrVYLrVbLpQ5SrrAMjRZpSouCAgIe9YZH9U2UM43zUdNZ6TzgbkNaPvWBrskgQGB+fzKZxNTUFHK5HBqNBoJgP82KKTEKViwPKQ+q/eCzP6JsKL1fI6hRz5C4HiCdTiOfzzsgRF1LHcs+SqfTmJ6exokTJ5yBzUXHfCf7jkCS9aLBzt2PGMUCcGieRjlFdTyHyQ61udRwZ+rW3t6eOy2eqdPcjp58kEjsH7JHEHnmzBnnNCJoYCpdLLa/DgXAwFqiINhfv7ixsYF6ve4iHqp7mCJGx92odOzF20d1mo+iAMMwskqe13zgRetGJtAJ7ns/J4sa3MDgvvM+g1UNIhu+Bga3sNO62f91p4WoyWyFjjKvBQVWCeg7ta7qibPPqoFviYrQ9xv70Rr+PoVp/7egQtvPOvqUhx0bFVQcC27/trGxgUajgdOnTwPYN9q5gJeTqVgsAoATyDbtSU84pkFIzy8VEj0mBDC7u7tOMOgJqfRYMEyfy+XcAXhUVsyJZ04wFQ5Pbp2ZmXF5nDztm9usKg/6jI0owEZS/lWyPOIDxFHgQsdef7PypFAo4JnPfCZSqRSuXLmCa9euOQHKFCeeSkrFSeOAi+KKxSLm5+dRLBYdkLU8p4rfehbpOWTd+FeBss4hG9K3HmJVNgSj9KxTofBZ8pXWl6CAu7u02220Wi0n7MmzumtMMpnE9PQ0JicnHf+Rj6x82t3dxUMPPeSUz42Seu1H0RP8nVEdBQA+8jlAVOaTtG0EDer5V2NToxRqQKghovxBwygWiw0Y1tb7ymsa7VUDX+9VPcD6qrxXY1u3n7Qy12fs6f9qBAMYAFoWuGhfWgNbQYdts/KXb67r3LDt1bpq1MOXFsX3a4qbzz5QHUknDY1w7poEwBnznU7H7dijAL9YLCKfzw9s18m1DZy/lj8VRPKa/saognrHCZp0y086nXQhdhgeRCKZysv+YjuYDlQul92BrNpXuqvSMADpA8pWn0TNdTvuQXCwZizqfoI0AgpuasJUIqZu5vN553Cp1WooFos4ceIE5ufnEYYhVldXnd7WPrXymg68VquFRqPhog7U3RYk2r6ijqHeGAaWlNgv3P1Mt5ennMnn845Xi8XiwK5N3OFrYmIC8/PzKJfLAPadaLoWlNkLlUrFpQsTWFCX1ut1N6d062L2t41EHkU3dI6FTgL+ZoWIz3uvwpr/83n9X8uxv1kjyCLJWGxwNx9brpZnQYMVqnxOozXWM6V/gQOlqvW096mSUUFrQYn2gYaKtc06SazxZNuibVDhb41LW18FYPoukvXo2vr4FJ72r+0b239aP9bZ96FRroaDKkZ6dTc2Nty1iYkJFz6Nx+MuLNzv9932rowwEEjQ+KMhv7m5iTAM3SLjYrGIer3uwACwbzCXy2Xs7Ow4gc4dHyhAa7Wa2+WBKVxsfzabRaVScSlAvd7+4WkEOwRQ9LRwO1Y1ZrjokNeV33ReRo2NlqfjMmxctQz2qxqeqnAqlQruvPNOtNttLC0todFoIJVKYWVlBXNzc9je3ka1WnWL4dvttjMUCDDIO8w99dVV5VPUXNWIog94qcfaygdgELQrP6qxoP1A3lUvrcow3UKURkaz2XTpddY7TlmhkTiVdyTy4eMe9zhsbGwcGrfjkF1Y6vPa+miUe23OOuA/+8D3jG/8dOwtAOSH/Mp+I6/Ra2zBjdaLu6soqbLWevjKID9EpSBoSpcu0lbDSXWKrceNEOUI+8RnZGidVH9oPzIypKCfO6gN4wM7V7XPRnF28v1qtNN7yx15rCOAbWI+OsdOnUr0mrN+msbKOUhe4ofySp/TOlK+M79eI+gKZtShSJ7jvdxhkHqIcoALf339re1n+fwoiLZyzpeKRtLno95LojMtm826cWG/KP9MTk4inU6jXq+7dYX1eh0bGxu4dOnSwFlAHHM9xI7jwTMaqB9nZmYGtt/27WTmIx/Itu1iGRbcKBEoUX/T4cg5Q55VsKzgAThIz+Yi/k6n49YlavptLLYfCZmdnXUpVdrPYRg6u4gLuEeV6ccCFj5kao1t3mv/t4bosIGyYTmrOHyI2Xo/tB4+cMLf6a3RiWs9nKyDD7mqgWL7Rieitknr51N8UYpO77eKzZZhvaq+/ve1w1d/nTRRSlzb4VPiRxmgWocowMnfrDdIU2LUo0VBu729jaWlJSwvL6NUKmFhYQFnz551ngkKD25Fqidcsh4sj2siaGQwd53hWS625XWCx3g87oCAXTTKtR4Ubqurq2g2m5iennZlcOE2Q8MUGAAGPNXc/UG97gDcgjDOEeAgaqbGsW9sLE8cJWCjxpRb19FLT0XHnbOmpqawtraGxcVFTE1NYW9vz4G2hx9+GE960pMQBPu7YHCsWq2WE64cK91JxoKDKN46qt0W2Pru1TKj5hKNM41KUBFQxqgxSM8dc6DJh9wikHxHHiXQtPXmu6O8b7lcDtls1tv2UUnljU++RwFO/eu7h2UpuOJ9yuMkjUBE6QlrkFvHBu9V0EjvnW2PTx9x3qsTikagNcL4TgUH6pVX+Wf1AQEGn9UIiQUrvr73AQSfE41tGmY8aX3UkNbnLOjRtvIdrDuf0/5VHa+RDN3pZxhx/tDzy3QTpkyq4aayk7/Rk6z9p6AewMAOToxC27MetA2+PmWaLuUb26rpOzbSwb5kGwhc+v2+MxCps9gGygtuQ8tovIJIBS8KyLUtRxHL0sigj9Q7z/ReLipm1IKGNrMM6G1vNBrOaZhOp1GpVFAulwfmgq7PoROv0Wi48gqFwkB7hsklXrfGuM8e1H5S/uEYkHgPZT23tlVwwXt0wwAFm0yj7nQ6WF9fd1vRMsrNyD8AZ09MTU05G4pRDGZiJBIJpx9GdUocO2Khk58MzN/1ugpk7UwlFV7sLB/TWQFuha0a2zrp+EwUsLAok22g8LDKghNMmcbWwypK/qaRDJbnI6s8bNv0ugUUlmFJPsFlFYZVrlHKhr9zfKOMB9+YjUK2f3yTXBG6VVx2kpPoYarX6y6l6NSpU4jFYi7NhhOS17a2tpyS6Xa7rs26m87Ozs5ALiKFdyaTccZzLHZwyrdua0vlxrz4VCrlDs1RQ4/vYwiUgEj3nQ6CwAmB6elpXLt2zRmdCuT1L/vYArqoMdHx9vHUMPCo85GpZpz3c3NzaLfbePTRR90WeAQfKysrTsh+/OMfd2c8BMH+4YC6rSvPgeChgWqc+No3iuGr81750PaDTx75ylVjTr1MWo4qQN2tSZWIGpCazqJrNRTYDjMIacyOYiAMo1wu59qlYJdkjWfruWO/+bzsPlLj2spqnwETix0sRtU0IGDQq+ozUC0g4ZbIHAsdS84vNUjV+BzWPp/hpjpA1xuonlK9FwWaLdkIhL1Oo9466KLGgfONKXq2Xsqr6lwDBp2JfE775CiKmrtqiNHw5g5yXFfEuZTJZFAul1EqlZzDg/xcq9WwtraGYrGIyclJt+ibxriecaByle8Kw9DJdaY/Uc+yXlpn5tsvLi66dYFcJ6GgWfWezdSgo4tAh79rNDQMQ5dqOjc3h1qthmq16tZyWcDN90bxQhR/WLtgGLGOvV4Pq6uruH79OlqtlnPIFQoFTE1NuQNw0+k0Tp8+jXK5jEajgWazOVDXbDaLhYUFVCoVxONxl1LlWzOg7VR5Qd7Wecx20RinHraOHp/TnRG9MAwdcKSRr+ek8MwiRvRUDhGEaUTG6tvjkM5J1kfbNKoNBxwTWJCRfS/wKVsqZJ+3YpT3KanQsUKX9+uHv9v7fAbGMIPfev71GR+4UA+V7x22vj4jxN5nQ7RHjYWWNcyg8JEFRGqYWSNA66vP8zkLBH1GqQUE2lfa32qQUenZa77FvPyo8b2ysuI8+gsLC5icnHTv0Xx2TmqGs1mPVquFIAic15ygkQcSMQ2KqRiMitAIoUfgc5/7HLrdLs6dO+f2suZWcgQmsVjMHapD7w0VlubI8m+73Xbef3rF9R4d06MAhaVhACNKcfCdum6FQq9QKODuu+/Gzs6O20o2m82iVqu5HTy4DzsjLhSwBHUAcObMGeRyOQfkNAp1FGCy9fbVHzi8u4+vLO1Py+8+hwPLt6kFVGhqKNBY45oK8pym+5BoqNh0LirHYf1wM6Qn1atCtcavKl3rYaeiHuaQUMNNZaO+Rw0LNYZ8ekJJx0rL0/dYLy6fY1son/huXtdIgE/OW1IjgsaWz7mk3m/tT+DwmTFKR3n3VU5o9MWnmxVYaP+oHrCAyjf39PtR6TWqg5XffP1r9QTBL1Nhtre3XaoHHUWUr81m0+22NjU15Q5JZS57EAQuPVF5M+qd7Etf3fr9g8M/q9UqqtUqer2e2yKUTiXqI+6INywLRDdl0H5lfcIwdEYt38+1YAq2b5Si5rEFQuq45rqS9fV1LC8vY3Nz07Wbi9i5tlDTDtVuYGSK8yObzTp9yvt0R0buAqYnXKvssNFKlWUcR8t3Widru1FOKA9ruVZW6/2aasjfrHOI79CtjckL6nTUNC3qDDq31El7HFvylu0KZTuSAkUFzFEoKkrwAP4Fp3rdZ8TqIPnKAw6f/8DffODI54HjPbbOdiJpHa13Rr25to6q0OxzPmPdGn1RRj/rxPYPM76UtAw1Tu29tt+HgUlrgPjeaf8qaNCQrf5PgW7BUr/fx7Vr19DpdNBoNPC4xz3OeTPI5xQijBZopCGTyTjPRzKZdDmarVYLq6urWF5expd8yZdgbm7OHYJDI5ATfXNzE9euXcPu7i4mJyfdSZk7OztOQaVSKfc/PWGNRsOt+YjH426LQUZktra2cPXqVZw/fx6nT5/GAw88gHq9PjDGynM23ULJjpmO01GAgu9jFEUF4eTkJBYWFtwJsNevX0ev18Py8rJLIeC2qrrrB88EyefzaDabyOVyuHDhAsrl8sCWwXbu+uSI5c9hhrXOc22v5X1VLLbv7K5POp/5vDWQWaZuN8lFmdwIADhY8KmKR+eBb5zsnNAxvVmiMayGse0TOza6YNt695V8TgeVqz7ZSk+n8gfnON/v02s05nW3qCAIBpQ020H+tvnvWj9bX1tnYDBaEASBM171UDcaRBrR4vsp84IgcNeBw9vgjkJqMOl4+KIXPp1r5TT7nb+pt572wajRKtbP1x6dR3Ye8HeurbDPd7tddw4QD60kaKhWq+j3+84ALRQKDmAor2h70un0gD6ijFedrs/V63VUq1Wsr68PnLUBHOygRYBp9buPl3QcORfIw0y1sjZAqVRCPp930Q6mXnLNx3F4KIrYN9zyVM+VoiHMc6CYdsz1g4zsr66uDqS18T72la5/UQDFk66ZFsb5lMvlXERIifPaRvZUFmkEwkaTKR9UJ/KjeqDX29/JimCHcos8AhxsLsP2cCdAZj1oRJDjRmCs6X/kQ65j4QJyko22RDliouiGUqGiGMsqDmBwEWSUYe4zlO19VmhZYMHvir6GGRUkBUw+hlBQwf/53XpwrBeLv/nqY7/7lI0KH22XHWCfgWONBAUEUcAj6ruNMFhgwes+kOGrr32/AjnLQz7wZo0nnfQ+cGF33eHkXlpacgu+7rnnHpw4cQJBELhDYoCDHWsIHCgM6ClRLws9TcytZd2bzabzpgdB4PbU5pZuDM/TMx+LxdziXvX48ZCgZDLpFqIVCgUsLS05YAHs55xOTEzgqU99Kp72tKfh8uXLuP/++3Ht2jUXvaHX4yhAcZTB6eN3Er1ze3t7TqHxtNStrS2sra25dvJkz1qthlQq5dKhuB0iozd7e3totVqYnp7GqVOnUKlUDnnnGXVSL6AFuVaeWLIOhVHBBXnGyhnrWWU56mmmgmL92YdWQXC9jZ3rWjaNEV0gqvLbBwRvFlhwDrKvVDbbPtF1MKq0rPJWWaHl2/61wEzBhtZP5bwaUz5dpOswfDJc66OGNA0l5Q+f3PcZgVoXGjx6aJuPfLxsHU1aZpRBru+37aTR5vOKD/NoW9CnC09tf2h9h9VNyRo+7HNGmwm0+C6OE41sGqkcS0aG4/GDRcSpVMptT84oaq/Xw9TUFGZmZgY84JrGo95+yl3rAAiCwBmzrHez2XTbf2oUQw1oPXNDx9iOj0bRNErDhefcgIRe+2w26w7upF7a3t7G5uYm6vW6ew8NX+5AxajJUcTxp/FsgaT12nMOEoRwy3WmPOkW7UxRJNBTntJ7OJcog1gn1kcdISozdD6o/QcczGUdd53nCiCsLOM9Oo9YD8p32h1BEAysoWN99KBEggXdMVD5hPfzf43QKKnz0MdbQ8d5pLswGH62gsAqbt4fBSR4nzX6fWQFsjWurVC1HWCFpM/Atx5OKnq9z9ad15RpVTnb+62AVUbTjwIKVSa+dmmdj2MUWG8zr/naqL8PC4ep4WLH1ldmFKixoMMCCt/HAgxNifJ5bVQQt9ttPPjgg84LMDk5iVqthlgshkqlgn6/77w1GxsbSCT2949uNpvOa87wNLf0m56edt4nAhWGdrluIp/P48KFC05x0RBRJaUnsyrIpKefAp8LD9m2ZDKJxcVFfOITn8CZM2dw6tQpnD9/HisrK3jooYewtrbm9su2RoaPB3z85btm5zD5Nx7f32eb5ymsrq46PqEHjG3mzlUcO90RhXw1PT2Ns2fPolgsDuzBrgaqhsbVG27nWxS/qgJQY3yYYcPnfN4dLmYlH1O+KOCgwWMNVS4yJM9xdzN9znqHWW++R8v0yVr19t0o6eFaNgWHxpr14Glao12HpoqcZakMjSKdK3yOoFvls68sXrPGmTWsqfhV5vF3OjPUs8iy9T6OneZ6E1jqPvsWVKiRqn2ihq3WXY00K3d9xqCWN4peUeNZSUER66UgTd/F78PIjquCGQXo3Haaxi75ykZ22DbyAI13OipoaDKH/+TJk6jValheXsba2hq2traQSqXc4WxWR/Z6+zs7NRoN5ymmMUt9wPGhM4GAh2voCGZ2dnbcGRQ8YZvyPsq5xzrwUDyCJvIN76Uhms1m3ba63CWIuk9lh54LVa1WsbKygvX19UORLDuelO/cjII6jMCJbeValFwu59J/t7a2XLvZXsobPZHbJ3uVT9WQVoBJPiBPMSqlMlozI1RucV77Urt8jhIFNtbJpHys+p/38xRsnePcEZKL2LlOiPxF3ucYKFixQIb1jrKjR6VjnWNhvV1qrI1yv1bMCnPfb9Yg94EFVfY+hWMNiSijV99rwYE1HoYZWT7gwjqqAaQIUcGSfvibjVawTE4MRcC+Pj3KC0RSb4EKLB8AsH3gAzjD3h9VzlGkbdXIhHqn1BDRNtg6hmHovIuPPvoo9vb2cPbsWWQyGZRKJSSTSayurqLRaKBer6NWq2Fqaspt3UfDnOHiZDKJ+fn5AcWgEQL1gNC7QiHDQ214D1NdqAwZImb4nW3gTg9huB/mDcPQ7SJBYfPwww9jbm4OU1NTeMITnuBCrszh5Y4RTOliHazC151e1HGgCoUKmh6tyclJVCoVZDIZXLp0aWC/7H6/77xw3W53oL9YDzU4eVgc06g4fj5lZo1kjruVGTrXrNdY28dnlJ980QqdoyxHQYq+h/nRVBr6bq0TjRCmumletX74LICBE6XV+PU5CNS4uxnSjTxsu1mHKE8ix1LntC9FyMpBJZ8s4T0WLKgRbstTPaAGKKNEugORdXTpuCngYxkaBdGIpNbLKnVbngIUX3tZtvKE1VHDMgksDetz7Xdf/xPQ0ICzRp99NsooZD2jbBDLaz7DT/UGP7rwmh5eXY/XbDaRz+ed00jnIe/neRZMVWQZ/N3aLxw7ymv1TMfjcZeGpNvUKvAh71rPtfKkflQfEWSkUikUCgW3TpDbu8ZiMbclO/ttYmIChUIBQRC49X/FYhHZbBZbW1uo1+sONGn6jk8WatoNvezUF6w7oxMTExMoFovuxHBun8uIDU+fLpVKbvtZ5athjlDyjqYoqe5QeUPSec7+tuXrOCuAs7yqGwOwvqof1ElBXuW9PiBOnuj3+w6IcbtZjSbFYjHHr5q5QDtD9SnH60bo2KlQqhjU62JJmcle85XtM14tgLBGgRrjnLw+YGGFvq+uWiZJBa5+t0JaDQz1hvOdFiyoV1Lf6QMj2gdWOPnaMQxEWKPaXosqN+p3NRAVCR+H7PtZf1uOzytrQYZ6zux9lhQ0sg1XrlxxJ3XPzc3htttuc4b38vKy4y0Kez10iF5R7oUdhqE7IZMLzmgI6K4VXLORz+fd9nrdbhc7OzvOO0NFCcClQXFvah6kx23yCHLo7WK92u02rl69ikwm4w5OO3v2LO666y6Xb7u2toaNjQ1sbm66tRy9Xm9gERf5Ub2F6vGhMLp48aIzJBqNBlZXV93WsQCcQt7Y2HCARtvK9zCHNJVKYXZ2FgsLC8jn8wMg2HrKhvGa1vMoR4N9znoEfeBbHQjKu7rGhAJdt9wNgoNzOPhRoEwvOA0Wjo3lfxpwPv63zgbbtpsl3a7W56Dg9TAM3firYqPxpDsKsS911yXrXLGk7aYBx75VUp5WR48aBGoUkEftrlc0ppR3WaY6PFh3KnA91MzWi2PNqIUaGTQW6Wn2GeyW+Cz7lTKM88e+n3XWtvh0+nHIN380skz5Oqx8poQAgzrZOpU0gqO6iWOk6x24nSnlJR0eq6urAA4OHGN/JxIJlEolt0aj2Wy6yATP1mE7eS8NOvI81wro7n67u7tIpVKYnJxELpdDs9l0aVcEB1ZeKZ/qZiO8X9eCNJtNl5paLBaxsLCAubk5t84gHo9jbW0N165dw9ra2oBjiCeV69jpIaUEDKVSCYVCYWCNgJLOW/aHRvV0fMJw/2yo+fl5531nWg+dTPF43EUqVCcoT/hsIgJ6Bb78n7KZqUXWecV2KABhvX0RObZL5Y2tk8prPq8yUfmbW8ayDvH4/lrLSqWCZrOJarWK69evu1PHVbcCcKCDDirOK/I3+YZ/j9KPPrqhXaF0cNTI8HW+JXtNGcEa51GGAO9VT4oKkWHv0N99xqsFAfZ33qNeE1uOr2763YeCrZHje862X8dDw3hRHiQbPRqVYah8oiYomZZ1td41rcuwd2q9fc9aYOHzQAHwGly+95DUy8jQb6PRQLVaRRjub8d3+vRpJ2iBg116ALjTsDmJCUIKhYLzzhCEaFoUPS/xeNwpNwDOg8PxZLoQIxXNZtN5JWhwVKtVd2pnEAROgVHJUCgnk0kXuubJnfl8HjMzM7jjjjscH21ubmJtbQ0rKyuo1Wouj5a8qIIqFtvfcePMmTPY2tpCuVxGOp12wo2LAHkAm+b6ttvtAQ8PlX0isX8QGY3C+fl5tz5Ded7OxSj+Vf7TOThMHvB+5St1Gvg8vXae2jKUb7luxM4vVYzsDzWa1LOlHn415Mk/6iWL8jhHtf1GycoyC2w4ZhxLK+s0bK+GMElBgG0jn6M+oGLU9vH9ts7ka+Dw2NKxw++aBqUOLdvfbIMuKtWUMJ+h6FsXoLxO8K5ptcNI2xIV4faR9TofF1CQN5muqOvMhgHDUcoFDkevVReozlDjTo1Aq0ssiKfRSxmqXn6uA1tcXHSpswomADiDmwYax6vf7zugwoW0dKCQ9vb2XBRbt/ykwceUUeor9i0AV1cLplk3nrrcbrextrbmNiFJJpMubYuyjhEOa4/pDmXsF24DWyqVvLZYr9dzMl/P5mB9gINNOrgboC505pqQIDiI8DOa32w2XVnq7FNSuU0ApnOIH13PoH/V0aByPhaLOVBq9aLKM/Kj8rDKfY34qoOcTgjKIAuE6KhIJBKOZ/WcK9tuyg/ypUbMOJ6awsh6H2euHmtXKN+E1SiGT6FGkQUTJBX6Vvj6jGEr9IYJwaPqp+3j81boWwNZF/VonexHmdCCI32X7ZeoPvQZLtp3Pi8hr/vK9F0fdp9OEFu+Ag0yqxo9PqPDMq7PaLPKQ8PdGrGwitPWT8tSLyW9p/QuLS8vO6Nc94vm1rAUZHt7e1heXh5YuA0AV69exblz5zA5Oek8jFoWF9Dl83m0Wi2sra0NCFsu5m61Wk54aQ7x9va22zFKw7JsbxAcHL5G7wsX63EHiVgshsuXL+Oxxx5DOp12hwRlMhmcPHnSLWjf2dnB0tISVldXUa/X3WF//X4fpVIJd9xxB65cuTJwuA7rqQuQAbj94/v9g22A6SVi/508eRLVahW5XA6nT592613YLsojFcg+UqOCfOeLWPhAOP/6ZIHlKwCH5rLeR4WlCzi5YxaVjxo1zM9mmhpBJA0L9htJFYMqN+V5C3p88uxmyEYaKI80tYkyXfPdyQfsa7tImGNmjWjOIfKStkW35AzDcCCFxAewRjGybUTcAjtLLFN3dAIGF2dbIwIY9MqzHTZTwOdFVfKBJ9ZJgYuP1IDR8o5LOq7MpaeMVV7g/8cxXLQdnEsqA9UBaHlMF2trW1mOXRvDdynY0HULYRhiamoKc3NzmJ6ePmTMk9dosPE6cLC2STf74HUeWmfHimVy1ySu92CUgKDCAgvdGYkpTDzfIpfLoVgsOn7ULdh1R6G9vT0UCgV3+NzExIQ7m6NcLmN6ehrlcnlgRynS7u4uarUaVlZW0Gq1UCqV3NkcWsdms4nV1VW3YxUjSNzyN5FIYH5+HsViEYnE/rlHvM6UKF2rqKAsDA92eNLrPnkDHBj51DcayfMBEhs1s1EbjYbYKKwuaCcv93r7h/3pYb50lqjuIn8yCkE+tfKS0R6uY1HARH7L5XKH6nyUzLB07IiFelLUaPSRNR59v1lFrIPq+91e0w/rYlMRbPk+8hneinrZdn1ejQ4V4goYokJjlumtR8BXdx+pEcmyfN4220Yl9bLZ37S+vnG0Hl8LLBT0DOMHkv6mIIYf9TRZQMHvel371XodWLcwPMhp5CTiGOzt7WF9fd2dXMqt6hiNaDabWFxcxGOPPebCzjMzMyiVSs6jlcvlEASB20JQPfedTge1Wg1hGLqdGuLxuAtb63xgrikFvM941PFi36lHn95DnsZJIRyPx11OJpUsFQzBxvnz53HHHXdga2sL169fx+rqKtrtNk6dOuUWNSYSCefxYn2pzCnsgIN8dfUSauh6fX0dJ0+exNTUlANiwMGC8DAMB1JAouYIx5R9GOWs8IEEBQQ0fFQ+KF9ap4GvDsBBFEIVEHmPCoW51IxiMVqkYX3ufKI8q4aSgnkaSuplVL6JcjYcl5jjrHXgOKs8IOn/VPrqiLHffUDKBxSBw1vW2gXEvIdjrjJX+1XvsZ5IfRfbox5KVcQqm3ndphr5ohiWP/VdmuZD3WT1J/vKAi+f3rJ1ZVuPQ6qHtD3sL+VB/u9b1D0q2aiDGou+slRHsH007JUXNCWP/be7u+u8wNwMgPezLB9QBPxrblhfRiCAA/lAI5UGLc/b0E0QGOmgB1p5W+UrDU0FXpQxei7Ozs6Oq4vuTBeLxZDJZFwkgCCEKVZc78a1EUGwf1gpU2r18ECCAzq6eK/KvXq97rbCVX2XSCQwNTXldq6iDOSuWolEwjn8LGDgvKDMoB5S8MlxstE8tSvtWJPnlbfsuKv9Q/nAOtg0Sb6Dc5rRh2az6ZyTXH/C8SbQ7Xa7aLfb6Pf7boG8gmaOAQC3KF7XmFl5ainKWeGjG1pjMapnQYWglsNrPmPb91dJoyPWeLcf4PBuR0o+Q1uFKn+LMj7UwNBnfKDC1sHnNbX19wGkW0lW0fuMDNt++6ytnxoQw4w+NXajJqMFGRqtUOHsi1LY9tl+5oTUsdN1DCTyPSfkzs4OVldXnWeIgICep06ng6tXrzoFxK1fK5UKarWaM+jVy6DRE/XA0WPIutp5pMajtln71II6TeHo9/sOMPE3Cmr2B/dV5/uSyaRbE/KEJzwBQRDg8uXL+Mu//Evs7u4im80OgAh6m3TM2D6+Q8Ej31Mul7GwsDAg5NRYsAZUlFFihaa9b9h31kkXrUfdo7zmcwwQSFiApeOoY9/pdNyCeruewhqg7FOSNTi59odnsSjfKOgaVWlEkQILbbsFwZYs2NFrKgN1nup6A0vaJyxD84VtbrQ+p/xivdt8N73uvrlHcOjjRxtx5TNqCPvao7LNAioanhb0WB2mXlrlDy3fvpN11r4/itQ40n6xhp7WVe8fVd9pne0Y0Eusc8pn9KnzSfnE6jVdk8G+pPynY4YOCB7IFlVfftSgZCSbQFy92UGwf+bE+vq6M8g1Gtfv9we84iqTuDia6Ue6BkDBFe/d3d1160Yo93i/nnfAD9uvII1taDabLo2WMky3Pw3D/YNmWSfdoIL3EZxwTeLCwgIWFhZcpIL8xGgJgAFw5ZMrHGsuFrfOAyXLwxo11X6mHPLpYzp2bPoSDX6CLr7Dkm4KEASBO++KAGpiYsL1t6Y/lUolJ6fIm8yAoP7RNX6JRGLAgaf1vxHAf6xdoYYZ/KyEvd9n9PgMPl+5vgb5DHG95is7Cmkpc1gDIQiCAYazBop6xKwX3Hq0rGJU5R7VFvu7r962fNvfdmyiQIIdH1tG1Hj7QKLvGds/vjKt8rReBFV0Vsna99qx8hHv8ylAflcvoBqXNB7oaQEO1rgQ5KyurjpA8LnPfQ6JRMIdlqf9zPLpiWK/qoBkfTR31/adbZuWfZTHlW2j0mw0GgDgwrI0SPr9Plqtltuqdm9vDxcuXBg4tI9pW+oNY07y8vKyU5Qsj4BMeX52dhanT58eUII0FKzxFTXXLEXxvjVorLHlk1P2d53flqd0TICDdSTcRlC921QwVLLcVlYVtyp+jd4RJKtX0qaKEKxqP2gO7ajGYxRZRw3/qjf+Rsq0dVN5Ocx4sA4elmdPIo56lvJd+5TEuWTllDo57L1qwKrzQnWUggb7vBoktk+tLFSDQMEEy4nia9sO3hsF4nwUpQ/suGjddf2ST3dY44+yg4BJQYbqCBrXOv8ZfeBvasxqmqIFVSpPGSlgfev1OnZ3d1Gv1w/1Jcvh2FG36NooBVgce9aNZxy1222nJ4alwun8pmNBZYUly6uURYxkx+NxB5hohHJHQzXwVcbVajWsr6+7Q03p2OCC4u3tbTQaDTQajQFnk9ZTZR9BHyMnGs338RV1mUYDLG9qXyvf8Lo6IFgG5646HVRfW6enjTDSMa/jbs/08Y2nb3wYgbB9yTUvKiMIenUnM8vvnIPKo2wf+2NUOhawiIpWWEWiz/ju9wEAS0cZ1laZH1WWBQAqiKwRYd+jwISCSd/v83pZgOBrjwr9YW31UVRdfQrDZ1QNU/LWILfje5SBoAKYykkVkzXi+H0YsPABDXvN9oMKbH2O3338bI1O/V/rb9um/AAMGhxqSFoDiX8pXHSs9B47qX33aNtsfXjN5xmOqtfu7q7byYmevFhsf6F2v993J8Q+8MADAyHZMAyd4Or3+5iZmcGpU6ewtLR0aD0IQQ29ZRMTE7jttttQLpcPnVFh55Rtj2/++MgnM3x96Jvbto+j+M7WQ3mQRj4waCBRRtn1PtawJFlgYQ0t1sEaYbYPfQD9RigqF9x6qUchVc7A4PxWhTkquGA7fd5931jRSGBZ1qi1W0myjuxrfY++j3Pdphuo91Q9oypzaNTogkvtG+03NZ6Aw/JD62VJ5asavMeNXti+0f/VyFfgrP2k9aTM0LrZaBJJ89MJ0IHBrbsZOVQvuhpbtq42CsN5yU0ymOaj7bAecXuGA9ulKU25XM6dCq2HwPk861G2AnmfBqLq3qjojY4T66R8yPawfT6QwXFjpHtjYwOdTselTaXTaayvr7uUWwI6Ta/XejAawx20stnsQHqPnR/adtbVRnJtf9kIDu0Cu807jW4FB6wn+5pOCOo98qj2mc4jtk/5VuU0+TgeP9j5imtx+DvBgp6/ks1mUS6XXXodeYB6R8EFN3zpdDqHdpfjO9SOGkW/AjeQChVVsCpavccat3rdGm2+54YBC2t0+Iwj+5114V9rINr3kOmAwQW/LJMhTC3HggjfNRX8Fk0PM1AsWYPIZzyqx8TXHz5F4QMX1qiiEoyiKJ7wKUQfiLCGhV7XtkWBVwU0qij1mu85+7/vmvKOj8d1/IaBF9//nGe2PJJvvCz4tfXS39TIizLK7Ds1h58LMev1ulN+vNeeFtvv93Hp0iWXP8syqJS4qDsW2w9p33XXXZiZmRk4UZXkAxk+Xo6aMz75EzXH7Fy3POszxu2c1+vkOcot5jXbxdx81i7YZZ+pE0I9TZqu4VvHYYGFGprD5PpxiPvKk2ikUMmSR4fJDJIvkhg1VnyP3q/eVjVYOe9985L3aDn6V6+rYc86cJxthMOmT3BeqIGkc1I916o7NIqp4FTrrvezLfp+bYsaMEo+wKFzYdTohcpsNU61nvrR+316XY0jBRpsO9umsicMw4Gd5NQLqwcQchw4PjoWfI+uiVG5yd9sP6rcVU+zNYbVsx6G+1GWWCw24JxhfRS8WtJx5jstD9s0OEsKQLTNWobWQQ+2U8DLLcabzSb6/b5bfMx1Ku12+5ChrA4QRmZKpdLAgXkEF1HgXOUcjXJtlyWNRuhc1PtV77BP2H+sg276QucQr9v3qU1IIKvAVqOenPe6c5et48TEhDsUj8CC/aR8yj5RvaFnuPB3Zh0oP3Hu3XJgYZGdCmafIUQ6qiI+LwXLGSbY+dfep8Ycr9MbQLLoXyedDqgakPqs1kMBlzKMDqgKdcuw2m5fW/Rdvvba37VP2ZfW42D7P8oA1jLsuFsgoH1uDW5bln2X770WVOj/vnttm9QwUdDHv5zgSr76DhsP7ZcoUKE8HfUOS6rMooxn4PCOReoVV6IRE4bhQDrVUca11od5ohzrra0tTE5OIgxDdDodlz4FHChKApDt7W3UajUX9WBuKfNGw3A/IjI7O4sv+ZIvQa1WQxAEA2sCWH8LhHzz56g+9s2fKHBtAYWd/77v6tnRucXTbVme7jNuvdp2nNQA4n2aOqAGPBWFGiY+ZwfrEcU3xyX1kLHN1is5CqhgGTY1REmNG1X0Og98uw2p8WN3EgIO5pR1RChF8YoazWqIqJHM93L3M/K2NaTtYnMr05VnFIRYMMU+UUNBeVoNnShSh86oXkv2h65js8/TsGQ/6FgqgGafavqQjXQQTKqxxPcSWNh5RvDO3Xg4p5jWqR5mTQ2zPOkz8i2Rj+hc0fHiu8JwP9Lb6XTcPTSi7djb91oe8NGoc0/fxXG0qUcKXgiW1A7gpiTr6+sA4M5k4kJkHniXzWaRTCYHjFuWEYvtr7WbnZ11ZxeRB2hg22wEjWRpZHMYz9LTz75WoOjTOVaWKbBQ0McyaZhrZEbHm5EDTX8l8XBCpoCRVD6yD/XMG9bL97FjzPm0ubmJjY0N5ygkmGHfjcLnpGMBC2tkW4NKla9PICupQRRlMEcBC/u8739LvrpY8OBTrD6mtCFhlmEVOHB4Fxqt/1HAwJah99q+UCPTGv16X1T7jlIW2j7+zwmjgJO/cUJq+QoqooCMMrq9Pgz8qCIHDoxp/R5lQPjKGnbNgknLO76xHDYXfHWLAopafhTPaz+pUtdno3jStpd/aRBvbW05YVmtVrG8vOx2/qDBpjm9fLZYLCIejw+cNs22z8zM4MSJE7j99tvRbDbdORa2PdYAs+3x9YVtjyU7D9lnWrY1YPQe33t8/ZtIJNwiTVWQVumocakfGkB6xoMaWCqDaLxSUTGK5DNSRzESRyU9p0ANEV10P8yA9ZFvbNhuNXi1z9Sg0Pv5+1EgX/sUwMBWwMPGncaO7tai5wtwzMjbNAZoEGt7NKXNB67Ytz4QosaWlTvad+S5qIP6fG08CoTovfa9PvBFQ1DvGVamGnFKPsDDcjmWOi5cu6DPKni3QMwXkdC+HLU/LI/admgUSiOUJNWrvvRYKz+0nvr+KFIZYmUt+VJ5j7/zf42e8j2NRsNtZ05vORdPc7Ex5wqfoxNGD4mrVqvuzJDZ2VnMzMy4zUIIYIMgOHRatI5rEBysHVBZZUHIMFtDQYzV1T5iP9ktcDnGmUwGW1tbzqDXsjRCEaUXfH8pa+hc0jNYyDdhGLr1O91u1+26RYch6Th8Tjo2sIgSVLYj+ddn9Ohffh82OL5y9DlrwA4rh3X2ITef8rMeSjKferzVkLZMYIWxrattW9TvUULdChmtr4ZhWf+oPrxVZMGFHedhz+mEtQA2yviznjxVECoENWWNytoXtRhGashbL6/1OFs+t/XU36ziUL7ygYdhfarPWLBn22D/t/WxRnQYhk4hZLNZt1CR/R0EwYBB1Ov1kM/nceHCBdx1111Owayurrp7Y7EYpqencfr0aUxMTKDb7SKbzbpDAlkPO7eGAYphANr2la+tfJ/yox0j/WvfETX2XHitaRy2XpzL2lZrOJIINmz/kLizim77qwsFb+W8t6SGxShe7qMMWysfVO9o+zUFSoEFeU1/i5KLOpd9aRBRZI0senK17mq82NQLvc/OPftebacaqOQTbQfbyDYrD0ZFg+zzbN+oNEx+6zxhfSirj9LhPh3Id6h9wufZVh1L4GBbVz7LMukA0Db7+MS2T+sXRcofHCefXiAvsM5K6iTzyR99l3VY8bp1zOg91Il6TfvA2klqE/H3fr+PiYkJ5PN555HnFutMa9K0SfXkcw5zHBhVCsPQnZIei8WcPNN3ck7phhg2GsH6WmcE2xM1jlGGtsoYdVpYWWwdLCTWlQce0ilHHuE87/f77oBbgiQLTK3cssS2s0xeI9ADDsAs56R+1Fl4FB0bWEQZSJbRfV6hKIFhr9kBjnrOZ6xH1d3WS/+3gkGFvK+Oypy+cnXSar0sItbfrIE3zPDT9iv40Her8WONJl95o3isLLE8jQ4oKaPbd1sAoh9th97vM+i0TAUOPmHBZzXN5LjtPooXreLTvo9StsOMVh//RwFkNYB9AkcNiWHl2jrF43G3kJr/T0xM4MSJE0458pRUbWMqlcLJkydx9uxZTE5O4o477nC5tyyDByyVy2UX4qZiigIUPnAUJWfsdSUrv5TI13yfT6D6eMfXnwos+C7rqFHvswUWqrjVyLFeaps6E4ahO4SRe8JHecBvBTGqpWs82P4oT6mNPviI/WRTE2xUS9vOvrPOMNaNY8p56OsTzlm2Y1TPdBAcRC/ooWVKGvlJgQ8NXP6uxoPysq4PoAGmgEedMj4D0vK/giDfmNwq4thom3xOAvW4An7ZTYMnCuCxDylfrAOQz/EMBOa4c+conuOgh+Fpf6rsZfRDfxsGvnzAxyefVN7YKFmUjozqd+1bjWZa/tCImeoL/lVZpB/tU/WWl0olt816vV53W+VyYbFuGdvv990ZDHo+CPUDPydPnkS5XEYQBMhms06e6iGSfD/rpREgBRnqtffJ/qPmhfaRgn/Kdp9DkKTl8l7yE+VaoVBAqVRCLBZDs9lEs9kEAOTzeddGKzcpO4CD07qZTkxZs7m5iVQq5VKrMpkMJiYmUCwW3dlJ3L3SOik+L6lQisa0Q6mANYxrO9Q3iXzl8x7rydMJonVQJXJUuVHXVID66u/zWFjgYT2aKmR0YkeBCpahwENRp7ZRvV62T3mfInjtUx2zKIa3Rrs1+LWvVAFouar8tF95jwUV1gPJaIKS9b5ZPqBXSsdKoxa+Ph0GHK2Xzd7r61v9zWek2Hb4yI6Ljil/1/5mm1TAqPeE/aCpN9of6mHhXxt98QnLbreLarXqdvegV0MNq7m5OZw/fx65XA6NRsN5mqamphCP729hWC6X8bjHPQ75fB7NZnPA0Ov3+07xUInpnGd6jx7+xmeoRHxjENXXVs6oZ9DOLTUwlBS46XO8xrNP+v0+MpmMU34cRzWOLVC2AFHz49nnejprLBYbSCeYmJhwOd58nxoaN0v09HLbXM0VtvLvOAYS4N+yVWWiz0jVeWjXEliA5jMK1cgaxdC2TgEFDza/2sebWneCCyXlKU2Ls+BnWN/qO4DDqTEsnzw2DPANI/seNehsnZTHVbZGRQq0jVbu8ruP3+x6HM4hNZosKLX59FZ3q6yxYNeS7vwWxfM6LnZxvm/uRJVhDWO+U6OlvswNrQP7kR/ysy4K1oXS2g9caF0sFt3aq263i2Kx6IAFz8Lo9/c3ArFOAPI4d9OKxWLuIEON1Pnmr9pT2t9sE9N2lZ+0n3iv9gd/13L0Gq8rr+h4Wr7We+LxOFKpFHK5HNLpNEqlkjsJnWmtql/5Xt88YB8lEgmXaqnnYdBxp84o8q3yB/tP5fiosuBYEQtbODuIDbaMoeRDf7xuB9IKCXtNr/O7Gq76Tp+hpm1Qha1EA9lHakAr8+g7lNGHgQp91v4W1Xa9FgXkVAmxnlH32/99zBN1v510OgYquCzz+yaFlmMNqaNI28l3KJBgORp5U3719Z+vvT5gZv9XgGjL1vb62m3fGVUXVfo6vnw/cDhkSwGv3hEfX1DoKljT8DL7kQfzdLtdVw4VTSaTcYvzALh85lOnTmF5eRn9fh/nzp3DmTNnnFeGoIBggcJPFyxru+0OGbqzCu/TeXic1A7lC8urytM+uaiK2c4TGvjMN+baFHqYVHYo0GaddLcWTdPh/ayfKguVBQR3ykt2h6MbJYImvp+GG6MX5FvKTutljyJbR809t55WBZ+60481QIfJP72m9T3Ka2cdJAAG6mz1kwIM9kVU/dgeCzzYBypz1SBlWZwP/G6NR9s+O69uJIKh48Y+pJESpc+s7FIQzL8TExOHdrRS2aDjwec0918XgStw4IYTBPsqOxV867xT2euzN5TUmPWN8bC+s30zbL2Pzj9gMNJlZb2VUaqzmDbj2y3JGrjcxYnGPykejyOfz7tdAYvFott+lid8kyfoMed1ykkuIm61WqjX6+j3++6AOPaHlSOsnwWy/K5ONtV3LE/5J0o2DJObfIbvZ/30ozolCAIHKgA4QBCGods6VmWojoeWbW0P22ZGTgk6AKDdbqPVaiGRSKBUKmFqampgEwRmKxxHTxwbWPgMQXoVVekeRcqg9q8P0StTq8HgQ4RKdhLrxLLl2/spOHwedG2D77oKGv1offlenwEaVZavzj5lpP9zfHyRFeCwwRUl8KLaRbLAQoU+f/cZaj7jYhio03J03Pi7pqlZfqWxrGPr4zff2Eb1n33WN7mVtD5R37W9dlxZd5sKYoUM04n0oCE1vKKMV84vCjbLv+w3hlGTyaQTQgQhmUwGU1NTLk+WbTh58iQajQYSiQRmZmbQ7XZdeVoHel1YbwIbn2eT/3NXDN0FTg1/6008yutH0nFXsGs9VUcZGHqd6y10LKwX3vKlAmE7t/id4xYEwUCkwhoC1lt5I4ZjFLEeExMTh7ZfVCVLsmPJa9bQUQPLKnyVI1qWdSQNM+Z8ZPUBMMgDVh7oPLNRESVrIKjxOkyHqrNEedA3llbn2XnjI9t31hmk5OMZnyzXMbfvV31o541vfvqAt6231dU6fgrANbWOpOkz2gcWnKqMp06xvOrrG2v42utK6lCJKs/XTk1VAg5kp/YhgAFZwnan02nnEFI+03Ve+n56wXXNA+c8gSR3B+QYEKhsbW25FE1uOZ7NZt1hetlsFvl8HrlcDslk0h0Gp46rVCrlxonGMPWdjZLZfhzFztMxVV6wdoeP+H6WrxsAWPuFctvOf9XjGh3iOOsOdzof1KFDRxLBC/tNd+Pi2sZUKoViseichow+U4/ccmChjbXC5qhJZJ/js/b7MAPbZyBEGRhqXCkzWYHtm5j2Hj6rxqoKbhW+vrbxf1897XfWSSeBz3i1YCRKUfgE+FG/DYs4WeVk62aBAq/pX991a1xHRZB8/RwlXH0KivXnXwIuW5avTymo7Lt891vhcBTAiFLQ+qwFoqrYrKeGHj37rP5le9TIpAJRwaWL3sMwdCBCwb3uBhWL7W8RePr0aZw4cWKgv7vdLiqVCu6++26n2LkVqW2fnR9qHGkbtL7WeLHA66hx8F3Xcbd86pNh9ru2gb8lEgmXAmB5hW1QY0V5VPuCipveQI6Legz1fZlMxuWnU2GQVL7dKGl+NN/N1CzrqdMcZ1sPK498Bi35n/dTufp0DvtT7x+V9Fkqf3qArYOL0QI1bvWeYfJDAaHPkFS56UtptLpL2zoqoLCRDN5vPZUqo63sUsNHy1bgzPpo2p/9zc4Zfbcl9okF/Tr2wIGhx2gf+ZVlcs5Z45llqCPA5uir11x5QutOg5dyjG0m32pf8h2cy/b8Djt2On5sJx0L7GfdopV9xjQbni1RqVRw7tw5LCwsoN/vuxOd0+m0W3StYJ0H4fFMo3a7jXa77eTS7u6uu0anU7FYxN7eHpaXl3H9+nVsb2+jVCphenoa+XzetSudTqNYLLr3ZjIZzMzMOPnBNjIFdGtrC5ubm2g0Gm69nq6/0Ai3jq2NHigv8y+/ayR2WNTIjo/ytc9A99ktfDc34VA5pDqJ/KnnFAFwJ3MTMHLHJzr77LxR3cLt4BuNxiGH6ig0MrDwTSQyKAWJDUMOU+RRv/kMaf7vAyA+AwQ4fBjcMNDiM6x9IEj/qhET1Q5lFqsE7Me2U4WTrx+GDbQ1SrVOvr5Xo9rnCbJG97D36sd6RqImjj47rEwfWXAxjE/Yr9ZLZcuySvooI9LXzz4F7SOtiwVh9h2W10k0SFTBac4kDctcLod2u40gCNw2fYlEAtls1p2GurW15dqvBr9GSBjJoKCmsRWPxzE1NYWLFy/i5MmTAA6iNzSkuasHlbrOByrlVCqFqakpV/b6+rpb+FcoFJxgpXCv1+tui1qWx/oo0BjG97b/+Zu9FjX3La8rH/jmOMeGZA1vjTBaQ0RlsN37XfPGaWyz/vQ66cmwVsneDA0z2LU+Nm9d3607lqgxpWOo6Q12vus4+QyD44AKkspjGnBRckZ3+omKnkS9w+oIJWusKuDRvlQjU/PQfQDNvl//+q5b+W7rBxxeT6d1IulvysvA4A5BVveofLN0lI6w9bCL6ynr6C3XlEPKJY3uck6y3bqGjf1hx1EBtl0XQF5RcGDTQHUc2VYLyMIwdDsy5XK5Qw5ZGtr9ft9FAGKxg/M70uk0CoUCKpWK23Sg2+06YFEoFAbmaCaTcYfXJZNJtxYgnU5jcnLSRS0p70ulEsrlMgCgVqthe3sbjUbDAYiZmRnXZ9zYg5FxtlNtBhsV5GdiYsK9KwgCt0if+o76T0+ttmBUZbKNZFC36HN2bvj0vp3jo8hd1cd8J6PyvnnJtDSCA27vHovFBtKtyEsEXTZrgXwXBbyG0bEjFtpp/G5DnKqYfWQjCVFGm5blE+QkGxa3330G2zBjT39XZTWs7Sosh4EK6z32GTx2GzqtU5RC0/7ytcPXLt/9FJgcI5JVzHYyHKV4bJv13cOY1Zblu1f7l8Ldjodtly7stuWzLN87fcakr52+8R0GqG0dlNcsj1j+Ag5yRrPZLEqlEoIgQLvdRjqdxuzsLAqFAnK5nOuHVCqFjY0N9Pt9FAoF9Pv7O3OsrKw4QavnUVBhtVotAHBCWkPuhUIBFy9exOnTpweEp3p3ma+pAIAh2UwmgwsXLrj1Ftvb2zh58iTS6bQTgOq5KRaLyGazOPX/8fZezY1lyXp2boAWngBd2e7p6Z7R0dGcOCGFdKNfoT+qX6A7RUihS4U0Rz1zpl0ZehIeNHDfBeNJvshaGwCrar4VwSAJ7L38ynzTrtev7f3799Zut12gQNhKzV/cOzr/uv76mZ53s/RlUwqE4hqlBFVdO9VGqr99ngsqz/GsuqPCMAHggIb7+/uFW4WjsLSKJq4qMX+8Fvqr4EljBHQcOma9jVxdGlJzjyuc2aexBp87Pt3f2hafK7PXcSko+RoFIRuAhQtDXn8jMH2OhjWvMM5YD0AY+sqc6Forv2efqsCoRec3tWbrjkG1xAA49gQgG1pHX9CAY9VTPhjBZJZlubw6VdS6puNWeoiLCm2pwK3jQBBiT5iZ31lQqVTs+PjYjo+PzezxHonBYODxDsQ8QMsfHh4WfPrv7u78biIyEtG3nZ2dBRejvb09q1arDuC73a4NBgN78+aN/fGPf7RXr14tzBvrjzKo0+ksAF7NWKSZnqbTqVs+dN8XCgV/j7EUi0Wr1Wr29u1be/PmjT08PNjp6amdn5/b1taWNZtNe/HihY3HY7fIYDlHmMK1V/dQah/qeuhPVEqx9+Bj0BR9PrXnWWP+vru7czquVjTmjXoRpJbRH84Z1gt4JmcBvourGi5u65TPcoXifyYPiTflLpQqeSbhvJIHrvS7lPSWKlFQ0X6uAuX6fvx+HaEiPpNqQ7Vh9E83d55AkCdYRYYa/48CUwRGlJQlSYlubAPGAgGMQYGfw+CWrWne2KOQpN+rKxTjoaTcX7ToGqVAqe7XuN7xHf2dsoLp2UvtLcZ3cHBgP/zwg21ublqj0fA6NzY2PEiYOqbTqb148cLPLHX97ne/WyB02sbu7u4CMxoMBnZzc2M//vijvXv3zmazmWupzJ60j2jIEOb4DiCZZZlVq1U7PDy0ra0t+zf/5t/499vb21av161YfIzpaLfbVi6XrVB4dK1qt9vWbDbtm2++sf39fZtOp3Z2dmb39/fOAKOQnFdUGxrXSdciD6RG2qB1sBf1WSwO6hcMmGbd8rRzADPdF8rAVIAj//vt7e0CUOdsfC3wq7npKcpsFeTF2JKo5dO9oaCdEs+qjinSf9Xcp0q0JihgWFV0fVXbzm+1NOlnOgalGylNN89EK4XeiqtzGQN3IzCO8/ecEhWM1JuieTqWyEtSAkVqvKl10fVVr4nUmJR+8RyfoYDQ+B898wiJSqOZf95RmhF9+VM4J2qqtU7mS5MOMCaAI66Fql2GVlJfpVKxZrNpjUbDNjY2rFwuf3KbOGl1eZb7bsjkRB9qtZpbOTS70N3dnfeVPVer1ZyGv3371l68eGHHx8cLe3EwGLjVvFwu29HRkd8uTapx1qlYLLp1gcBiQO5gMPAMR7PZbOFyTi7XK5fLVqvVFnjJ1taWtVotq1arbs3f2dlxED6ZTGw4HFq323WlF8Hjk8nEbm9vPS4wxRtSe08xoH6uZ4f3UVbQTiqZgCp5lecobYC38IOlGsFJzxT7gfp4hsts2et/lxiLVOCjai6UwOozqwhYZCjx85RAk3qedyLhhqHnCRspYB/7vgyIQ9j0We2DEtcUw4hjihsx5fucAi+puUuBo1T7KQEi1hGJcySaKgDFQ0RRApjX5yjoRUEh7q9UifMTx6Rro4dVxxRBYRRItY3YXyUaqT4wl+qqo4JYsfiYihVArloFZVpokF68eGHNZtNv1YQQYMbWMTDGuG9hELPZUwYowC7aveFwaJPJxP1kYUr7+/tubv348aPt7Oy4Vmw8HluxWLR+v2/n5+dWqVTs7u7OKpWKWyVgTP1+38rlsv3444/2+9//3gqFgvV6Pbu8vLTpdGrff/+9bW1t2f39vY/z9evXtrOzY69fvzYzs9FoZI1Gw3755Re3qjCvjF8D2/S8811qPSMxTykwIm2gjnju9RxhGcISoyBZhTBlBupLi5ubtqmWIpjh/f29M+Ise7orQZ9dBvTWKSnBAs1fdGeKNI6/VftHH5UOsGfjvtWx61oxVjT9vKvrphp31iS6Piwreub1vWjt4NzqnCvtyRMqGDdWLeolj79aBKP1gLFq22rVfU5RASXFt/k7YoU4njgPeSX1nWq+FbxHLfG69amAETFNaizqhqIWECwd0U1Pi2qk1dKFoBL5Fv0BwAP6y+WyVSoVm8/n1u/3bTAYLFiQuQMBzX+j0XB6AmAFgDNu3A5jqVarlmXZAkhVjTmuYwD0V69e2eHhofOjqAx9eHhwC8rW1pYdHx97WlUNRIb3lEolOzw8dH4xmz3GfVxdXdnFxYULKYo9VBjIskcr/tbWlrtZYW1hPcrl8sL+arfb3tdqteqCSL/ft+vra7dkqTVfz0PcM3mf63lXGob3wNXVlfX7fV8bzjyCFvuTcUcLxd3dnbum4fKFgBn3pmavAjdgIWJtoDfrlM+2WERNa55goRqFWJYBwzwwnCJSeQBbQUAKZK8CqVGztGxSU9Ko/k5pafg8arRV25M3/rwxa8kTpHTtVgkn2qYy7VT91Bf3hpaU9SAlVMS+xr7EtmIfFcwr0FABSN/N0zZEopHaY3FsKljEutCOKIifTqcecA2DQkh4eHiwWq1mL1688HSeu7u7Vq1W3fSpVge0PtPp1IEkfQPkQ7zRagOk7u/v3X2qWCzaaDSydrttk8nE75nY2Niw77//3q0gmKt3d3dtNpvZv/t3/86yLHOGhOl6MpnYn/70JzMzZ1DD4dDMzK0pm5ubNhwO7fDw0M7Pz+3h4cF9d/v9vv2///f/zMz8cr6zszP7n//zf9o333xjf/rTn2w0GtnGxoYdHR3Z999/74SV/dLtds3sERy0223r9/t+YRCMLO6DaCWI+43P4xnNo1l6hgApaOFYHwQ59ojGGqiQAXPhsi/eVXCkAoya4uMeXgXK1ikp4RvQzD5nPiLgiMIb/+cBxpjAQ3+rm5LZooV8GZhNCR2ryjILVt78qIJD+4bQlOqjjk2BkYJrHasKLbzLfHzuWusc01dV5jG2VXOYp3BUOsyejZ/Hs6XuNcuKzh+F86DKB7S60ZpGf3S+ddysS55VjDGl7qbQdQQ40gbPIxSoIoE7HqiXuUERhWDBWBBKUVLpOQU0qqbazBbGp9nmUHoxL1ikm82mA/vd3d1P6CAAFcFoe3vbwS6CGcLKzs6O88vBYLDApwqFglWr1YVb0nUv7uzseH85LzyjVg4sxvS5VCr5utdqNee16m6VZZn1ej233EQlhdIvxZ/6jK5VxB/w00aj4TEqeuEoPI35wJoAz9B2mJ+dnR0bj8d2fX3te4I9C+ZgbtQdTJVzea6JqfJsi4UeYGVIKeYUQWgKiKZK1FCZ5QPp+FkEjXkEZ5lQE0tKwFAiGkGq/ugmyuu//q0bU9vJE1jySkqY0jpSQkX8LvaRdV5GxPU7rSPFVPPeyyup/qWED0BFPLAQ1sgU8xgd9cf9FcemQo0+Hy0jgH4Ov641QkepVLI3b964CRrQjcYVhkGaPc6V+lTiC7m5uWmlUslub2/dtKtaegUaMAwEAuYEIo/m4/7+3v7617+6YLO7u2tXV1e2vb3tAHh3d9fjPGA8nU7HzeKz2cyFnmq1arVazcdRrVbt5ubGSqWSdbtd63Q6VqvV7NWrV/bu3TsbDAbWaDSs3W5bq9Wy/f19ZxSTycROT0+t3W67FePly5e2u7vrzGs0GvmNsKPRyH799Ve7urpyt6NisejAXTW/y/Zjai/GsxlpGnOpGVkQOHElY66icIhwgCYJn2z6qv63yhCUVquGXPv4JQVwo5pZ+mi2GIAa50bPa3RvUfCYp9nXtiL9jwBbGaS2o0BgHXpEiYJaXonjYe0KhYJbdei30gjGF7XiqoBSHsUYdM+pRSrFX3UeU5/znabPpF7dT6m4tVgUkGrdOlZdD/aDjpUzFDXGy0oUWPV8FItFV4CoQEqfUhYsdbGL5z3F32hTx6t7h6DrWq3mQgPAkrlF64yll5gMFAcop3B1QgBgrIBnBAjoIqBU94ve3UFfNbNSlmVuAYFPlUqlBV9/DRxGiCuVSs7LCKKGhgHgAcRYc7GSkHgC8E3coNkixtzd3fVzolZQPeukuyXVKvODVQjQHsE/c9tuty3LsoU9o3Oj+1P3OXsuKleU7hB8jwIQpR8xIQRlM+88r0HuuMGheJrNZtbtdp0HqmCqygJNmBFp5brlWfdYqEYvToQSM/6Pz8ai78aijJD/lwHpCPh4PzIyrXeZpikFDFJ1qcYqD6znCRUp5pgaa7Ro5PU5NVf8Hec6PhPB+rLCmPPazysRyC/T7iyrOyWw6DhgRlG4UKCrLjCrGJN+xz7IExD1c9VsmZlbINRFAoK0s7NjP/zwgzWbTatWqwsmdtqDKAOCAZCFwmO8Qb/f97HhlsJclMvlhaA3fFJ5H8ajFxbV63U7PDz0+rFSXF5e2ng8tt3dXet0OjYcDu3k5MRTFN7e3i6szWQysZOTE6tUKq6B6vf7zhyx2LCvRqORTadT29/ft263a/P53K6vrz1V3sPDg3W7XXt4ePDsUZPJxLa3t+3w8NDH+eHDB/v55589fWKWPQZ8c6lfsVi0b7/91u7u7ty8jZsDAgZjwBKwjmZ02b5QIQjNkLoZ4A6AYKhauEKh4AwYbROaOdYQDRPWj5R1gs/R6EXlyOcWBAjV3sazHs9daj4VfDFeVeLANBlzHo9QGs97+kwEpbG/zxEuYok8RmlGtFjl8Q4VoKJlQ4U3BcBKX9cpUeiK/DEleOiz6r6n/HCd+Vn2P0Xrpn19fl2hQseqY1P6B/BMAT7dY2rN0LmPFpzYP10rzoiC1t3dXdvb27NWq2WlUsmBv1o5AIulUumTmAQKsRMqLMR10/7SZz1LqhDgf97Vv+kD606wt9bFJXfFYtEFBZRf8Cnq3NjYWLAcIEjj+qoxW9BQ2uJ9gD+8hQvgSHnLumEp5g4OgDwWe8Uns9nM7x6C7tbrdY9doy7tX54SRYUbVQhRB23xgxCdZY8uacwxyimEx+l06m5fOgbdb/ygpOAMx1ThWI6UnqZc5fLKZ12Qp5OU0vLEZ1J/m+VnGKKolkWJXmSCCu5jyRMIUgAgD1Ar401ZL7QO/a3EPn4Wn8+TZJcJJnkl9VzKopT3bOwnRechMi8l9LHeFBNZh3GvwzCUAcQ2FZDo+BWQ6B5b1QcVWlaVCGII/oI4mT0ygOPjY9vf37e9vT3b2tpyFyaAH8QHAlosPmVGUm1sv9/3uAyzJ+sMREa1xZhwmT/VNDLOCNx2d3c9FW2r1bLBYOApBQ8ODqzT6dhgMHCmAJFGcKpUKnZ/f+/zCWNAE4Pbkl6YVy6X7e7uznZ2duz+/t7Oz8+97uvra9vY2LDb29uFuA0EqPF4bPv7+9ZoNGw4HNr/+l//y/75n//ZNjc37eXLl2ZmNhgM7OTkxP74xz/a9fW1ffz4ccFiYfYEbKLvdd5eSdED6mHMjFXvnkAzpSZomCPgGkYAI4GxK4ifTqcuvPK9amChMTAXBL8vAdEUYnMUcMHwVEjQuVCLjNliMCrAgvlXrSBjielotR7qVc2w0h3mS+mugv4vKdStSoxoHdLzwRpG/hA1pnEt1adf21hHaROVgKyNani1pNqJAs+XFBVyImin/shj1xWIofUxLtTMXEFD/XqhXJ7rUhQsUhYcwDp7QC07GvQMyCPdKnEHEfjHH91DhULBA7vV75531QrI+NULhfPIeYiJTXQe1dpTKBQ8xqLf71uv13PQS7/IGrW7u+tB4iimUIyowoU5RGGiVg6zRytGt9u1brfrlnRisiqVyoJrD9mvrq6u7OrqymazmVv8VTmHqxDzkEr6gUUF3gT96ff7fp8H44O/rtrn7CkEoF6v567Hs9nMMyZiYSL2AdcwhKvIa5SWMB6wANYKPetYljT2BMFGXcbW5ROfnW6WvyOh1o2rz+Z1SMG6fpbS4FAiMYnf532nmqhVwDZFRONmWAZMVbqPmgJtI7azrtCT6v86gofOXYpQx76n5lIZfJ7gmEfwVTBMCR+pMTxHoIKYL5vDOP5UP6PguK4GU4XJlMWCA0vWjEKhYHt7e3Z/f+/CAWeC4DH6CdBst9uuYR+NRmb2pKVSBmr2uFaYqhmXmqfNnnw2IeIIQTAeiD3EGIJOqkDG1Gw2nTnc3t46qMXtqVAouAYGTVytVjMzs2636+5Td3d3TlCr1ap1u11nCKwDBHIwGCwITC9fvrTvv//eTk9P7ePHj3Z7e+uWjKurK3v79q0/XyqV7O3bt56i8fvvv7eTkxM7Pz93BgGjVUb6OSAcEIBlaTgceuDlcDh00zbrALOEaSvYUktGBDD08f7+3rIsc4aggmme8uJLiwaDR5pOX9VtK1oceI75Ug0zwInvzJ7uVqFN1QBHS4ZaI1RJpHVGuqHzFM9VfIaxxPGodlf7wh6Krl38rcCVMakiT4HYl5aYmjnyqij8rVuUn2nflz2v+yYKN3FvYd1TJUvsP5+rcKlFNczaN43tiThm3blICaxRocVdDXt7e37vAu4puBmh2CEgmYICCKEhZvyJRfengmYVYOIei0HdrCfWEEApwhMusjpHuNOyvqoAMXsS3jjPjIMMVP1+38bjsQNd1h7XHx1PlmUuTNzd3bmQg0WCdUUJR/xErVazer3ulvMoKM7nj5Z00uly30ekZ59LR4vFosdVDodD63Q69uuvv9pkMvF7QhAg2DOMBfdo7vxgruPaYx1lHeEzKPSgz2olUoE4KpOXlWe7QsXO0kmzRbNf/J3SmCvBiSUKF1rXOoJFBI1KkPKEi2XCjAJh/TtPMxS1C6m+KtFdVvI26yqLT15dOj+xfgXGqf6mrA3L+p8SPKI2RetO9VX7EQUSfVb/jgBBwYjuhbgn4zzonsjbw3l9id9xc+jh4aEf2larZaPRyDqdjhNT2vjmm2+cIJiZE1l88QuFgpVKpWT/NSuGaochLhqspxo0TNTK+CB2FxcXVqlU/PKkdrttxWLRBaJCoeDtovFRDdR8PrdyuWyDwcBqtZpbIobDoWuX0FRhCidmA1ek6+trT0E7n8+t1Wo5qNzZ2bGLiwur1+tWr9cXgu0QWD58+GCVSsV9exEednd3bT6f26tXr+zly5fW7/ft8vLSzs7ObDQaLTDEZcwjniXV2j88PHg8Rb/f979xDYBxqKKG/atACSEzCtK8H13lGCMCGX+zFxRYfElR0KP9V8CMljY1Xyo8MWeavQvGrZp+5llBHPs58iUdpwJ31pVzov1RMBTHRduqWdd5XGU1gHnnWSmiYKExUZytCGby1jC1ZxU0xPc5h6uEgby2+En1fdnzKsgpLeQ5tf7oezzL/6oU4fO4L8yeYglUkDCzBWFFMQo0KWKTyO8jPuCcqQDEOHd3d/1WZJRHKCFwBZ3P5wt3Vuh8sH+xeurZyBNGoytWxG7UibZa22Ruif9A+FBX3dRcYMGAJqorr54B5YOaialSqVi1WnXwD4imv4yfmARdc+IQoPkor0qlkjWbTSuVSk5TVbBRlyFu9r6+vva7n7hc1mzx/rHngHD2CUqkyWRivV7Pfv75ZxsOh44ZNDWyuogSk6IXCULHdL5jHBf8/+7uzobDoVs1dN8rvUSQX6c8S7BQQQLtF5No9inATQkZ+nck/PH5WN86Lijx0EbBhvpVuIh9yxOU8kBkHtCMBCzPIhE1WlpvnoATzXTLCmNdBuJjP3TeUgJgStsY+xn/T81lHmNMgfM4H6n1UCYS10X7nzfPca+uai8lHCpYMzPPlvEP//APVq/XzcwcsJOTGw0+fSTAbjQaeVYMtCwQFIg6ddE24JEYAcrm5qa7I3EGICgwnPF4bOVy2YPCYAAIDmQsIcguyx4D3kajkWVZ5pmZdnd3bX9/303Fo9HIc4fjFrW9ve0WF+ItHh4ebGdnx0ajkd/4Sl8PDw89daL6xpJ+tlQqmZnZL7/84gKQ0i0z83o3Njbc/azT6Vin07Fiseh51bMss5cvX9r+/r799NNPdnV1tcAodZ9GmgPzBbhpHAXB2vobE7O6ALFvEEgUMMNcFKADPHS9dU3JpMKaRsVAyvXluUWFH7WgwJxpS/d5ir6p5QUgFel0itfEM8f8aDB7PNcpEEgfdFy6vrpWqfGvmiPWCYCg1o5Y6LPys0iTIt1OuTClLEk6dgWezF9qbVaNTd22FKCoq03sV9Rkp9aDfqnLUnSVWrfEceXNgfZLhQIAlq5ftGymeDxtsQewMu/v79vBwYHV6/WF80pb0JNlSkzOtioyoN0A7tg3XS89s/H8Kp2hqDBm9oTNVJGkF1bGMp/PFyzp3NOBMoj+aeKSuCc5E9BW7Q8CM/xSY010rXHHnc/n7upLau77+3tP8bu7u+t0l4sVb29v/f+dnR1rtVo2m82cZz9HWUOcw+3trfV6PReMZrPH9LekfaXv9Hs8Hruizezpzijcruv1ulWrVV8ftcSoGy5zBN+azWYL3hM6h+uUZ7lCrQLWUdBQ6T+WPGFDf8dNmUfoIrFNAci8ManlYl0itazOuPFT/+c9kydopQiVWdpSsWoMWnfeOPL6o99r3/S7VYJGClAsm7NUv1JlmfWGPuozUWBax/qTmrO8ddne3nbC/N1339kPP/xgjUbDBQbMtBAwCDmMamtry+9vQCOkFhOIIfMF00CTAdgG1G5vb9tgMFjIwW725A+PhmM6nfoleN1u95Nc+b1ez8weBYH9/X1P1bqxseEuVRBXiLSZeZ2dTsfK5bKb0fFNxUJxeXlp29vbrqGCQN7d3dm//Mu/OAO9v7+3Wq1mw+HQ79UgCBwtPQIXmUPQQCGMtNttt1QgLE2nU+v1er4/9vf3P7HKROFX95gCaQAIzB0GjzsUlzwhBEaNuq47a0BaQawPOzs7n/hUK9NEe/fw8LCQsx6anGVPFq0YwPelRYEj+yJqbClKl1Q5oEH97M8oWEQeosBTQXnqHbVgsg/Qoir9izTxc2iUfq/WiFRbcW4oeUoo5jhPONS1SI0hgknARqTn6gabN16lSbFu3XdR+RO/A9BEa0ee1TACRz2ncez6DuNRHqWCmAqscf50f+uYtbCm0COyIZEB6vDw0Pb29qxUKvlN4GZPLmpos6OQk+JHqrxUQSFq1eOe0zWK2YyU78T2tT2dP5REgFWCgdVPv9fr2XA4XEililJKebKuaxTA1arCO2q5TJ1xtdLhCgT/Q8BAccW8MY9YPoglGY/HVqvVrFQqWbVaXQi45++4f3XO6CsWqk6nYzc3N65oKxQK7tFgZgv0HyUZ+6RYLDruYI7gEQgLnCf6yLziAo1gAZ1VoWMZNovlWYKFEu9lhCUSIwUyvJOneYrv6+GJADcKFrrRU4xE29e+KROK/dQDkwealdBE0K2Eax1QmiIWzxF6UoUxpeZP+6oEdVnRMUHk49zEdcvTMFJPZKTrbOCofeOzuIZqrYlWI2XK/K/EaNm44pzo+gPsvvnmG/vjH/9otVrNbzSdz+cLfvVobdSFqNPpOMCBQKPlYs6jxp660U5TJwAfYlEsFh3s4qOqMRUQaYApJu9SqeQErlKp2MXFhe3v77tWGSHpzZs3trm5abe3t3Z9fe2Wkr/97W92cXFhh4eHHoy9tbVl9XrdNjc3rdfreRAjmbEIckabdXNz4/Ecg8HAgTEA+uLiwjY3N63ZbLrb1fv37+3ly5cuQMF0SGNYKpX8kj+CwDc3N208Hlun07F+v+9MX5mUMncFjKqhV4aNZi0KGspYFRQojcT6xOcAhOhaZLaooceqlVLeRIa9zD/7OYU5oB36DXOKPsnz+aKfvAq9qkFj7FHLH8G0AgfaQ/hSJk+bCu55V92AYhyDgq6vVXQulB7pPEVBVscRlVGx0Gcdb17RfRaFNt3zAI7Uewr+4a3wC7VSRH7N+6yZ9iP2Ua0XZp8GI1NU8I4ly55cB1O8QX90PRRsA9DYO5HvMWZceWq1mjUaDecJxE8ADM1sIYUsc6gxDSij8gSmPLyxubnpcQrwDl1ntSzpnKeUAgigPIfQBH8hPoS4C40VGI1Gdnp66m4/AF2UP9Vq1czM3UfpZ9y37BW9QJb+IjAgmDG3KJGiRVMLaXzhGcPh0PckLklaP/uo0WjY5uamNRoN63Q61u12rdfrLdC1GL8AXbq/v3fBgsyKKOw08YmOkXOG5wFxecQgggey7ClGUxVVqtxQoVPPdeqzVWVtwSJqVPRz/U6fTb3P36pZiiWaS1N/a3t5BDWCzPhuitikNNcpgKzEh/fiZ1rytHTMhf7WduPcpoq+s2y8KmCk5jK2pYLasrZj35b1Ie8ZNfOtI0RFwTbVj7y5XfYOfUi5+em+zRuXtlcqlezg4MA1VWgluJwNywUEulgsLtyUyTt6L4USGkyg+Faixeh2uy5kKMAtlUo2GAxsMBgsuA4Rx7Czs2OdTsdGo5FbKugHQlGlUlkgMA8PD/bTTz9Zs9l05np6emqtVsum06m/98MPPzihRqA6Ojpy31Yzc9Ptx48f7fe//719+PDBhsOhNRoNu7+/91SMEN7t7W17+fKl/frrr26l+eabb+zh4cFOTk7s7u7O09FubW3ZL7/8YrVazarVqltZAPakwz0+PrZer+e+wpubm/bq1Su7ubmxy8tL33vqQqACNkQYRgIIQAsGkyT7k2rb4r5Gw6sgPRXQqmsMg1KAAyPT3PapLERfQ7BQwMm8RJAXAZxqwSNwjfRH61fgFgUmBX/ql492MAVY6RtAFNAUBQmlk1EJkceHUiBPQWreXOpztBkL+yJVIj9bxk/5LKVgU+2vWTrmkhLXUNvXccU5U/CFoBv7G/cO76b2RAT7CqCj0JDCAil+rkA+Bo0vcxVBsDg6OrJWq+WKEr0Ik7YAgKotV2UVbpSqJGGcKuyp0hR3ItoEcEb3IeYdYUkFPAQO5pXP2Xuc15iClsvnyuWy70fiyviNJQPlDkAeV1EsAFE5FPeU0hB14aWfnHHNiIfgFwVu/kbwIH6QO5vgIfGW793dXQ82h+ep5djMXIiiXxqozz6mDd5FocR+U2FP6WCWZZ4JEqEoWsEixlNXqChk5OGkZeVZFgvV/OqCrvNuJLpR+loF2FIAWw9jihiqpj9qoHUDpdplvCnhJAVQ15mHVInjiYQ0RZDzSp7gxd8p4M13/K3tqZVqWf+Xacry2qZN1SAyvpSFJo8J5jHsPOEmjjnuzSh0RKFt1RwriCAVqx5mXI00U48S6fv7e9eW0yZBe6PRyK6vr61cLru2C9cfCCTvm9kCQCoUCk4I6Sc/pK9Di4LGfTabucCRZY/xE9ymSrq78Xhsr1+/tv39fTs5ObFut2vNZtOm06ln0Gi1WnZ7e2uNRsMuLy/d/N/r9dzNaTAYWKVSMTOzw8NDOzk5sXa7bYeHh+7fenBw4MwFjU6hULCjoyPP582cYa5WzeYf//hHu7m5WXCJYq64X+Py8tIajYaZmbczHo/t+++/t0qlYmdnZx5oH8GeglnmBoGC3OOk1sVMrvtA9x31IVzGvc07ah2ACROYyHqqKwKxMco4VOP29yrUr6Z29q2ePc2CBbPM81eGIeq6q+VH50wBqYLCVDyCavBS7epFamoJUEFD+xg12do/+p0q0RqgezlaC1LzrVpGdY9QMBzfUSuBWufUPSIlpGibSjsjD6P9KAzxrCp0VNBgLnVfx7bzCuuncxCF1vh+FPpUKRfnj/rVtUTbZl7K5fJCCmyy1tXrdb+UTa1l+NtDt3FlxEUHKyaAk7stogUO7XVcS3UV5PP5fO6WXEAzab/NnjII6ryzt1WhUi6X/eZobV/f297e9ng+FUan06ldXl763APWcXE1M0+ZqnQijoOEHggsKMmwXsBvx+Pxwk3lKABR3pHsQ/cL92+QGQoeydg2NjasXq+7dZ04PngivADPhfl87vE29XrdL269ublxlyfGBu1GOIEGVioVF3I0bfls9pS0g73P39BOdaeKlyAyv3l0KlW+OMYiBT7zQKYS6QjI8iwEEfBFQkNJCQEqDLFhU8BRNVJxjMowmPg8rREbO74fx58C9PpM6m/6FrUry6TJlGCRR0hhVtrfFMB/TtG1zpsztJpRA5FifBT9PI5J1yElqMW+qYaDZ1JjTlmy4jjYS1n2GFfxH//jf/QL2brdrgc5A6ogaqRRZX8iHEBINBhM/eTR9vAc5mfcmiAg9BltCZmk8M9kXGRnajQabi43M9c4EVTI82iXuEQP3+Gbmxs35SvxJwBtNpu5eXg8Hi/cBHt9fW2Xl5dWLBYd4KN9YuzMw83NjbtPFYtFr38ymbgp2+yR4b9//97u7u6sVCot5E7v9/tWKBQ8EJ0c6QgOSmCPjo6ciWK90L3K2AgkJOMVOddhJvjvQvgj4FGAitYqlphTXOMpYgCsCheRhqimTgMnP6dE8M5nZk8ARF0lVDvHMwAoBOJUUVqmQCIvgFbB17KisRWqcFCQHGlICiQvK8vofV5/KKqdpCwDxyn6mUeLde2gRdQRBeZ1yzJek/pfgW7qOe1/Kg5Gx6brmOKR0fVw1RhU4IlzFPcKBZoIgG42m+76xJ0PpOzWS+Q49xpErPfVINgqGFfBTPd53p5X3qxnk2BgBA/mSpVRjBOFlbo2Uidxb+VyeWF9YlFrD7QVWma2KEDAN7Uv0b1SBXie0QtIdR6ZP51LBDZ4q1quWXN4oGr5U4Iu1iGEFSwxzCnrOxgMfB7gm/CO4XDoOIF5gJbzjiqM9P4OlFuMD+GM86NWJerVOYy0R/fNqvJZWaEoCraiZSAPiEVire+sI6DkPcfGU0EHjZ7Wpe/St5SGm827jpSWEn6UsPGZmrDyiJnOJWOij9pGbFvnQecoEpDU9yqZatGNFYn9MoEm9i0Cd/2bNdK10BKFsDyhQp+PQl5KaI0CRwqIxHqVUbEuymjRgH/33Xf2pz/9yXZ3d+3jx4/222+/2eHhoQ0GA5vP505c0OwQjwDBglCamWeCglhjDYCoIVigWSezBBoWZaC7u7t+iRwuUWRxQgDKssyJ8Gw28xtgMclubW25UIMWZT6f24cPH/x56kb7AeAjKBsNUa1W8zp3d3d9Xn73u9+Z2SNTASgDxrHezGZPOc/J6Y3GEMZ8d3fnDLPRaFi5XLZer2dnZ2euiUJLaPZ0GzmCD4T69vbW00EWCgUP+L65ufG1YE/g+0z7g8HA/WzJAqUpGtEGUQ8aNQA4e0wFSoA5gp3uP927KVeivD1tZgvC5OcUtF96lhR0KHjVdIlaFDirwEeBKarZP9IiBSqA/5RlAosEbUaXCGXAWifWDLOnLDh5fOK5DFkL659ysVFgkFpnnSf9LK9Ey8vn9FnnWi2xqXGpIiaCHRUY47hns5nv+QhozZ72XkqIVoFR6UWsI86Hlmjh0/3DD/O2tbVlrVbLDg8PrdVqueZb6WG1WrVKpeLZewCFemmfAkX6Bv1D+855WtcPHm29uk2ieeeiOVyuyJjH9/AZkoIouE7hE11b1mw2m3ndnU7H62YsWASgpaxXxFXF4lOGQh37dDr1+DxV0tBHDVYmOyHB5GZPbpHj8dhdiaAz8/nT3RFks1LLsfYBcK8ur2SQqlarLjygfPzxxx+t1+tZt9v1vlD39va2lUolt4QoDaRt5T9R0I7WCPaoXpjHd9GdlTrWLc8SLKKGQEFa1FBRVMI1SwsRAMsUSI4lgr48ABgBsxIV3ouCUSq2Q4WLZYRW+xoJXZ7AlAeSU0xKpctl7ev8rOqv9mMV+EiNJRLtKLSpEBn7pHtJrU3L+hIFEp2PKChEzZGClTjvUQBVwBPHqwQKn001Mf7bf/tv7Q9/+IO1Wi07PT21d+/eLbgRANo1riEyufF47G5C7AtSxhUKBb9Eqdvt2sXFhRNhXGzIqgERRfiYTCZurej1eg5myXikWiM9E1gr0H5cXV3ZZDKxer1urVbL6vW63d/f2+npqWdayrLM/UwvLy+9X+122wkja41p2Mzs4ODArS7z+dyfe//+vX38+NGOjo5sY2PD2u22vXv3zr755hvr9/vWaDRsOp16tqXBYGCvXr1ygQ4NoZm5eZ97L8jOwhpo1iQIuuaTLxaL9t1333lg+t3dnQMoGC4Cnt7EqilnNWgbWgTjUJcG9eNWbSQMi8sHVZtVKBQWMlOxjxVEpcDol1gnmasUkONHwZcKz/q8WnCiwB/PYx6P0LYVICoNiNo4rEIpWpfXD+Ux6jYV6fc6yikFZQrGlHbQlwgeo0AQx5FHT2NJKVSoO/JRVa5EHqG/qSPWqXUrQDJ7wgyqoKPOyE94RgF/nkCteEB5QsQvSv/j2ulzul4qxFEflop6vW57e3tmZgtKGs48YJ5sd2iyibeLljsF1ghvq6xxuqfgQ8R+MRe4iOJCFAW/KODwvWrUETCwzKONZ3/yDAHcqmChrVKp5NngoJPqfmj2lNiB+ELoNGNF+NRbo9WNECCuQi2CFOcLIWoyeUz3Dk3VS/nifkztN9aLdVIBSc+TWqrUKsUPyip4EUlOisWizyMW7hiQrhcLophjHhHWtY8IIJwHdZFcp6wtWOA6oBuVyYuHjN9KnBVQaj1K7FmgPGtHHnjmJ+WPHN+P4D0S4xRxjn/nMTStNxJ/NRNGpqX1LmsrztUyhpG30Zf9v+p5/Sw1T8rA9eClGKsKf4wtCqGr+pOyckSGGqV29mqe4BEZY0o4Ii5A33n9+rV99913dnx8bDs7O/bnP//ZTk9PbWdnx46Pj93MDICmH1ySRnuA8fF47ASQvYxZeTp9vChuNBq5poZ7LhBYbm9vXTsCcMICcHt76y4529vbtr+/75oZ3JJonxiBDx8+2GQy8RtKOafT6dROT0+dkTK3jUbD52tra8vOzs6s2+1atVq1g4MDKxQKHjz+888/+0WBvV7PA7/NzC8KKpVKdnp6aj/99JPHZ0ynj+lq6/X6wrkrl8tWqVQsyzLrdDr29u1be//+vU2nU3dN+PDhg/3jP/6j+7Oq+V8JPQLey5cv7ccff7Sff/7ZarWavX792n744Qf7y1/+YoVCwZkrgIAf5pu/NTOUukBtb2973AzmdzNz6xBCD/0yMxcG2R8wPhi4jkX/V8GCvRhdKD6nqJ9uNKcrLUAwp91o1YBBKhCiqIUHkJDSlOr/CGHQG4Qv/V6BstaBwKD10Qd4jQpOqlVep6glWoV6rSe6QWiBLmmsitmnN3p/bmHd1DVGNfW4DMa9FvuYqlMBOYKzKhlVUwroUa28gl59ZpUwpXtUP2PeEOZUS/2cotphtX4B5BEe9JzSJmnIyZR0e3u7VLBkDlICZ5z76fQpM53SIvpmZm5VIakGCTsGg4HHA9DW7u6uPTw8uEYfLf7m5qYrPFQoKRQKriE3M9fIwxtxP1JewjlTRQ0KPSwr/NZzypjwBGCcSnMUrJOVijmmfoS88XhslUrFLQ0IM2oBQPDWeac9BEj4ArwO/g+wr9frDuKJxWQOEBq63a7t7e3ZN9984woy6tG7KZRGoXxUoRH+/fDw4AKgWo1SVrx1y7MsFss0NjqZCsIigIwaJ9VU6/MqYPB5bJt6FeClNEcKWGN/IrDN2xxqacnThKwqCp6pS9vLKzqXqr1MlQim80qqzVWCTWoN+T+15suKMnFllrqWeQJUXt9T2jLmjP2bV5e6TcQS9yag28xsb2/P/vmf/9nNw5PJxK6vr+3Dhw92dnZm//iP/+haFVLIsg9IA6eWCfwxyT/NOZhMJh6ofX197eDfzJxRAA652yHLMo9lQAtOkHO5XPZ5QZtRKpX88rhKpeLCBlmScK8ql8seRNfr9fy+CeriDNI3hJ3RaOT9evnypX348MHN7BDV7e1tj7GAiDJ2TM7tdtv7C1MiWxXuXZVKxWazmXW7XfvXf/1Xm81mbvKez+d2dnZmu7u79o//+I9WLBbtL3/5i71+/do1Zgr42u22nZ6e2t7e3kLAPGlqf/vtN2dgysg0o4e6P0VhlfSKzWbTb4GF6OPzDNOA8eraQffYkwAsFRjQFKolQ4Gn0tHPLQRowrhh3tESrD9mtkCvOQcKMFPKH34UIEb+E11y9HvVvvOj9Cu2kyoqmMUxrVNU+FJgmFJoqfUiZVlKWbNV0aP1PbevOm/sm6iYSdWnQkMK/MZ1iHxHn4lrruczJSzzbuRLy8atn2v9sSwT1tTyqDdFqyCm6cWxUHe7XSsUnhJpAKC139TPGeZnmctjdMVRv3vN8sS5UyCvc6B4Jc6vKg8UpKuFgfXRjFMoY6Bl6v5JKnHWTl2teBYQPJ/PFwQw+qGXjyJwqiDHs2qdRqhBwHp4eFjI8kS2JbV6quuwCvpqneb5zc1Ne3h4sMvLSzs7O3MFH5iCM46wpAoL3ccIfQiwlUrFdnZ2PDaDe6OwUKAQ1OQYurY8Z2YLfYlKgnXLs4O39cDTMf6PjEI/j4RIgTolJVzkFX1GD51ufP7XzyMAjQcjRaAhXmqeXzVXOkdaVNiJ44+CmtYRhRoYTJz/VJvxu2VChRILPmNe9Pu88cVn1ikQFl2rPIEzzoPOQYoh84x+nmK0sb+p9rW/k8nEjo+P7Z/+6Z+s2+3a3d2dNZtNa7fbdnJyYrPZzGq1mhWLRSe0EBjiBmazmZt80bhgdQMEAgz5nMtztM8QTualXC5bv99fyAqFlowANsz0qsXiBysIFgq0M/SZ2AKzR8GK2AKELsy1zGO/33dgBJFst9uuPdEsKJ1OxxmO2SOR44bsyWTi1gzGwTPdbteZxebmpmvR+v2+X7bXbDbdde13v/udtdttu7m5sf39fRd6zMwzWAHiC4WCVatV63Q69uLFCyuVSlYul+38/NwBxNXVlVuN1BqhGjvVKvPZxsaGVatVazQatre3Z81m083baPEADrhVqYadswqzTWmPATAav6Gm7jyFwXOLWtfUR1ktDGgttUQTO/s4BZYiDeZ86DvqVgHTRAuowC7SYKUpnLcIbPV7LSmwnbKoUuhrBMN8l7IepSwrCqwj39D9p3QstvkcYUh5roKrWAf7XYEkwIqiQkXk2/xW4Uh5uAoTOp6UcKnC6rpjVQH5OQXlUL1et3q97hp1xhv3EOccmqpuPxS1wnDOUQ5Qh66nziX3QKCY0H4or1d+M51OPX6OosIQ51mVScpnojU20hg+V2UcVmYUY91u1zXoxDLoOYUGQ/OgjWpNJGaOZwqFwkJqWN0rWGDMzC+7gycjIDFfmgZ5Pp/7HOPFAD/s9/vW6XTs9vbWDg8P7ejoyLLs0Uvh4uLC3r175zEWKBMB/tPp1FOjRyzDHqtUKj7PWJgmk4l1u90Fa1O1WvWkJSgRWcPNzU23enDehsOhzWYzF1ZS9GtV+aLgbQV6uui6cSMgpOjnKZNLHoBfJsAo0KINrU8/0/r4PAUmFeSq76WWyJi173nMJjWu2L/IbOP4lzGuZUXryPsfApASuvR77XMkWKl2lbBSIoPReYqEfZm1hr7ENY5MJ08Aob0ofKTq393dte+++84eHh7s/Pzc3rx5Y9Vq1X799VcXDMrlsmVZ5oHMZuYmWdpBI835iqAUoD+bzdx0bGYLmUJIiwfRA0ijyRmNRh77gEXEzOzi4sIeHh48iLpUKlmWZe6aBTjMsszjCPgf4ENgcq/Xsyx7igXhncFg4ALV0dGR94k6qtWqXV9fO/ggNR/uYM1m08bjsTUajYUbUdF4lctl63a71m63rdVq2ebm5sLFebVazWazmQsvpBxEy3NycmIvXrywarXqhPbPf/6zff/99wvAiTszaKtYfMxCtbW15elxSQuo2qVoltaYCXyEsVTgClWtVm1jY2MhPTDgAdN9ak+iLVXQl9JORSGE/f6lFgsFmREEqgKHeUkpKXTOlcak2op8RS0PGqjJ5+rbrO42KTqqtE3dJhSsq6Y+pbyIPC5Fl3S865RlyqqUYKHfqRJFFVPrgm2tM08wUUCve17HGtc+hQHylH30IfJzjXHQfqXWZ53yHGErFvYKihrOmvr7o9zBiqyuUfjA6y3OGmSrvJJnOOuqTALgYkXV+dE10LOgFs2I11BGqNUVYVHPFzwpBqDTXwB41IyzzprdkLVWawLKCXhqjEVAiYXlQRUGzCNnVC05agHgOb6jz7q/oTEIMSrEojSrVqtuxSemBBenKATh9hoDy3GjQvBAaNCiiqpareYKO1L1Ml/FYtEFoYeHB08FzJ5TKw+8ROnluuWL0s0yiWhSKNGMHYULJQx5bZl96ruvn/G3MnBtR//m2SiQRECtbWudfB6FGu2HFm0/75llJTLbVHtR+Il9j/1J1b1MuIj9iQKcbrS46XT8CjC0DjXzphgH36UYIMxmmYCQ6gu/lWnpftF3FKSk9iy+kMQllEolu7q68tgGDjTm1MFg4MwGBoBfK5qeaLXBPK4ZJV6+fGmnp6feb/qFZaRYLHrmEYgzwclmT6ZxzixEkNgKBcExB7leyoeJF5D69u1br593yc+OH/Z05zR44gABAABJREFUOvUsTAgqNzc3TsTMzDqdjk0mj+lim82mVSoVe//+vX348MGm06lrZZSRIKzA0GEqMO7J5PEGdC65QytXrVbtD3/4g2vzzs/P7eDgwH73u99Zp9PxGIZms2n1et263a5tbW25JmpjY8NarZbN53P7p3/6J7u6unKhTK0z6hagYK9UKvkNvI1GwxqNhpvgzZ608dvb2y64wbzUtSRqb1UAhCnO50+B8Gih0FAq2PwahfGxNhE8K/DkfwrjiPXo2VTXp1S8RdSMx7oBAwA/5przzhlhDlEoIbCk+qOCH+dSXbFSlomvUXTN8rTWUauvigsVPHVMqcLeZV/F+nUf6bpogZbSh6gMjOOgP8vSpkbrIHVAm/Q8/D1KFNoeHh6s3+/7XmE8GjMBcMS9E3oBsJ/NZn6HgQoW8d4iBBW08Wjd1QKtyirFL+qqxpzt7Oy4K6Yq8NR9iPd17Gbm7qrT6dRdaHWfqKADjQcAw+c05kH7i1ClAgVnN6V8QLEHv1GBWJUPmllPaQtjvL+/97TmZuY0U4E6e79UKi3QY/bcfD636+tru7q6suvra78lu16ve1ukFeZ+JvguQgZJAOCpKLY0ff1oNHKezcW0KZrD/gS74BpNDChCLu7SkV6vU54lWDDZsTB5KSISP9dDGDUXsUSNRupZPbgKGlVwUCC5rD4VBrTt+HcKqOsc8b0yJH1GN3kUQOLfUVqMwlOegJEi1FHIUvCvGrhlGsPU/3lrqMBhmaVGNWHRz5hx6WHlebUk6Tvxb507bTOWKLzEZ7RP8/mjyfD09NS+/fZbD7h7//69lUolD9iez+fu3oN/pWqcGB+3XatJGmGEW0gnk4l9/PjRx49GG6KMgKPMRAkLVotCoeAXGLXbbet0Ora/v+/PY9m4v7+3g4MDd10qFAoL909QuG8C96etrS3b3993AIIw1el07Orqyubzue3u7lq9XrdGo2G9Xs/v1NDboYfDod3c3Nh4/HjXR61W86A3XFsIIByNRvbjjz9auVx2hlCtVu3u7s729vas3+/7RXoXFxc2nU7t6urKut2u/ft//+/NzKxcLtvPP/9slUrFDg4OnMn+8ssvNhqNrNFoWL/ft2Kx6O5v4/HY6vW6vX792v7Lf/kv9l//63/1uzGwkCgdYE9xoRHuTzAMQD97RANWVVOG1Un3KQwOjSWBlVi6yEAG8yfQm3e+9B6LZf64USHB2FIAx2wRXOYBcmV6/K+/U31AaxkVH5yjaMlAIGaeFEDzbATxvMNvpalxXJGOa715fDHVrpnlMn7GnQKGMejbbFGxkvo8jj/yUOW3SjNjn1SbrXXwnr4TLS9RacW5YF+l4oieU1LKrLx9xdlRq4H6p2Oxnc/nCxeSocHXuwZ072lyAAWsOheqHNC9qmcByzG8EiFNFTMU+ExqjPo7bx74zRqg/cZSr8ITwDnLMndRhG9BB5UfRAHZ7ElRBhhmHhAYoNcaG4QQyg/xearI0ZgMFD0aN6cKQtX60x8zc8FJvRPu7u7cooIgpuvPGjUaDU9RrOPnniWEsegqxbyzz/IwMwIcfSVwngsZ9/f3bWdnxwWzPEVBXnmWK1QkAqodiIQugvmomUgRH33OLO1ilBpYtCzoZ1HLHd/RMeln1KUANtUHBe2RGGpbtBFNyCniqSU1H/o5h0kBQh4BTL27bG7jWLRefVe1RfqTmrc8wUk1rGaL/s95+4v3OaipPufNZd4Y457msyisTadTv2n66urKptOpXVxc2M7Ojv3+97+33d3dhZR39BFrAm49aGIgjJgt5/Mndw76wRxj6SiVSq7RItCr0+nYfP4YnNxsNv15iKTZE/jBAvLbb7/Z5eWlZ0bC2oH2fDAYWKlUsnfv3lm9Xvf7LnZ2djwGYDweW61WcyHnt99+s/l8bldXV5Zlme3t7blwoILr3d2dZ9t4eHiwdrvtDGY2e4xToT9k2Wq1Wu5uBvHr9XoeV/Lq1St79+6du0LBCNQ/GRP50dGRffz40arVql1dXdkf/vAHm8/n9vHjR9cK/ulPf7Ji8TFonHGjcarVatbtdu36+tpqtZr9h//wH+y///f/7uA+yzI3p7MGBHfiAkUOe/x/o3WUcRIkb2YLbnHKLOfzuXW7XWesZHPB2oOlSMGPguYvKauySilDV40ozDoqTFSgylNcMK/QjTwNvtliXIMqM2gLiwOMN4JXpVGqNAEIUocKeMusyKosoehZX2cuV9F6M3OfbU1sEpUzsV/8HZU1gEbeiVanaOWJfVSBhHFokK/ZE30C3CE08B3tR8GCMQLEUtaYvBKfi4os+pr3LgAUAUP3MdZmgDL1atBvnCfAuFrZ4l7S+lgLtaixtgBslAm4uKSUZ9CD+Lnumzysw/cqlEe3qM3Np7symDuUT2Rf0sDslOtPxEyaOU/PE3uEtUGxgjvt7u6uVatV9z6gXqXBm5ubnh693+9bu912i0O8AwLruLqdRauB0iBoMPQYxc7Ozo4dHh7amzdvrF6vL8TdsJZbW1vWbDY99XxKqYqQoxkFFdOwx8bjsbXbbc8WiWsWcS8ITH8Xi4US+CgsKLDVzxX08o66Sekk8PwqiSgKNpEoRyAO41ACYfapAKJ91Xoi4Y39jgcsMucI4vOECwXQ8T36GQWjVD2RmSlw1890vaJQsUrAUOYQ1yMyrtTnsS6dUxUEY0mttY5jWYnPpASplOATixJMgPK7d+88M9E333zjgb7T6dQuLy9tPB5btVp1Iqj7kvpgnBDc+XzugMDM3O+U4Dl8JfHh7ff79uHDBxsMBlar1VxIyLLMBQuyM2FK3djYsG6361mUOOPEScznc3v//r2bac0eNZzEYhQKBTebo30hgBmGQVsAx4eHB4+b2N3ddZ/TVqvlbgJ6LwdgCPBRqVScGHa7XXvz5o3d399bs9m04+Nj+/XXX21vb8/evXvn7ghoBzFDb25u+r0Vs9lj7Mr29rY1Gg07OztzQaff79u//uu/2mAwsP/0n/6TvX792k5PT92q0+/37f3799ZsNt2l4fj42CqViq8/68f6IiAQsE1cBYGIce9xJrjVXM8UKVQVmMM4uc+DVIa0XSw+Ze5iz+K//KUlVYcKLOp+xxige4BB1S5HOhOBkApEKeYdgZhq6qgTwKJWIs53yjobtfBqVeJ7BcGqFKG/KfAT21lVVPGSKqqNBriinVTfdTP7BIDnafiZs5TQpWCSH1wSVRBQN57oDqXtRFoZ8QVjjwotrAAIQNof5j6CsDyrho51GS7RtuN4NM2xtq9zpD8qqKlwpf3T/U697GsANmU6nToIZW03NjYcyONypNaQ1JpQN0kzcLtSfk0aVeJCVMvNetD3FD/mDMU9xfd6VlSAJb5QrSLz+ZNrpIJ7FcYQWiJmAlirwIr7EDGFe3t77sqqd2kgZM5mM28Xnhm9GAaDwUJmSIL+uTiRucKlWvtWLBb9ct08hdDd3Z11Oh3r9XpWLBZdEVYoFDxQXmM9sGAMh0P3LiBw/rmunGsLFgqAFYArcYsMQzdEishDdKOAsqxEIKt1RyHB7FPLiY6Hzad1aRs6RhUwYl3KKCL4TWmF+C51uKI0Hg9a/F77oJ+rVljXgL/jO7Qf+5gqUaiIzH7VGqbaUAuTrmEU9lRQTGlNUiVPu7KqX6lnAHlcvnZ+fu4BvBCa+fzxAjo0GprqlXSvs9nMzb3KCPQsAKKxSlAgXDBpNEKYfQuFgj/DvtnZ2Vnwu2Xv39zc2M3NjftakpIVpqH+mwQ4A8p7vZ4LKxqcNhwObW9vzwqFgmtA8IetVqvW7XZdMMOkDIPTQMZisei3oWZZ5n2D+GHZIObh6OjIWq2WnZ+f22z26K51cnLizJXsF9wqe3p6and3d1ar1Tzl32w2s3fv3vl6bm9v28ePH+1f/uVf7MWLF65hhNhDpEnz9+LFC/vP//k/23/7b//NUx5y3mgbAl+tVq1cLi9cCKUadFVuqPCGKxSCmLoBaI50/GXNnqwJ3W7XTfcEUqLdhXl9jaIgSF01+E5BpYItPQdK+xSYxqJzxVkHUOi5RyAFLKp1gQLwot1UXxSIoqmESasvexwze1rpcNTWP2d+l9G+QqGwAOw4D2ZPfCVaV2K9Sv8UyMei4I+21IKsc6NZwlS40TWMiks+i9YrFZx0rRC2eUd/UvMY90EUaPN4gX4GHdb9TB9V6NK+sNc0zsBsuUubjlHHwF5ij1MA0CiD9B36qziCtdFEBbPZo6suAb8aQM0YURCh0IhWliggxbOtWCvOrc6jCmqsJ+AbHqtuwNSnwjRrZGZOH7Fo61wC4lHcqEa/UCi4tVyzfsV9RLsIdxsbGwvxcrgtMZ9YQnCB4nPN2MX4U3dNaHl4eLCbmxu7uLjwLHfsOfgv7tlYx3BTm0wmHkdYqVScd66rgHqWYJH3f0rDoounWocohOjfKQFlWV+UwEThIjILno+AXg+rCjqpjZ/qR+qH9+LfCAbLNFIKpFUo0X6m2khZNHSuokARv48lCgvxu6iliT+pca1Tb5wHxhIFjCj4LSvPEXTyis7d69ev7eXLl9bpdKxardqbN28W3CBOTk78oKJ54D4GrBC6FwAn4/HYBoOBA3iIKWAWTXOWZQ4q8YklcAxtxnz+aG3gvWaz6RmsyHE9nU7tw4cP9vLlS48nGI/H1ul0nKixpw4PD71/BJPd3d1Zr9ez4+PjBT/Q4XDogoIKxASbYZput9s2Go2s2Wz6baJkwGKcNzc3dnd35z6fXJKEteTq6sqOj4/t+vra3r17Z1tbW3Z1deWp8lqtls1mM8+AcXh46KkM5/O5r9XW1pbd3Ny4AHRzc2PVatX+9Kc/2fv37+2nn36yjx8/+oWCW1tb1mq17Orqyi89vLu7s48fP1qtVrMffvjB/sf/+B82nz+6oiFUcBcGgoVm7GDf6289D7gpwPipW5mgWinUBYO9dnt7a+122+bzR5epcrnsQlK1Wv3ic0JfFUArXYLGqsZdlTIqcEQgkge4Ir3X92LbAJ4Un4h9py9KW6GdmjUnCkr6Q5vqC0+bmrbyuUXbUq08ReeKPRMFHlUcxDWLc5lnxYh9inye9jXzjfIz2qUvUZjQorxY14P9oTxN5yPy0zg+/V/7QD15Wnzlf5zB6Gqowh0JPdTvXvcoe5x6USrRFzTgmnQA5RUAlLmO66JrwvzBM2JiCc3axD0LAF4NLseCoZfu6f0bzEPeGtIm4B1LIoBX3dnm86fbwlVwgi7qRXWMOWZYZJ9H2qBKm6id54I8dVWGt0ynU4+no3DezeyTmBFofalUsnq9bre3twufK33SGCGdo5S7ZV5R1yn2T7SiciaJ1zw4OLAXL1447jg5OXHei4J0nfKs4G2IfSQaKcuD/lbrhIJlBYs8r1qMVFup7/idsopoP/IEF/0dwTcbUJ9JgQD+jsQsWkyiVoYS5yKOIfUZ86HzrH1ICTxRsFEGvwykx3VQohoFjPi8/h8FJ+2HPqv/qyaM/+OeW1WWjU33En/HNqljY2PDjo6O7Pr62s7Ozhwckvr08vLSNQP41usBZly4KhHMDRMC0Jg9aVjROqGRwp0FYqv7H4JNLAcgnnNHlovJZGKNRsO++eYb29/ft2Kx6Fmt6ONwOLTz83PXqkPsLy8v7fLy0n1hf/zxR3v58qX7e97c3Fij0bCtrS07OTmxwWBgv/vd77yve3t77h51eHi4ENC4ubnpQeBo0QuFx7iNXq/nGrNGo2HFYtFjJTY3N+38/NzG47ELEFhw5vO51Wo1vzSPOJGjoyNrt9t2fn6+kPUDjQ1xJ//8z/9s5+fn9ttvv9m3335rR0dHNps9ulZtbGx4OkcsFoVCwZrNps83sTXq/qRChe7DqM2LChLNCgPDxDKCCxQZsijsP/YYVp/t7W13jSOW5UsKfYUhqhY6Kg1S30X3mCicKB1epx+pz9UX2uxTi3Zk1roGCpKUhil4jHQJIYSgStrQ9yPoi/OVKvpuSlkVlT86BwAMaAWAKxXsvI5AoUXnQ4uuLf2IQg79UcVXrFvnV60QtEf/sVil5i3igPidClqR/6eeVXdVNNlohnUPQwNIoEE9mq6UfqlgkWWZA1/OMpp2FQhRUChfVq27urApIMfqibCCJRNQirKr0WgsXN6pdAeaE3GCWmqyLPO+R+uZJhGIc628WOdKLQQRk+nYNTuWCuK0b/ZkTcZKrXOD0IjVG8uuWtejoBz3GuvDOeMeqVqt5vGHtKM0RwUA6ldFQkrhynvsJ3gtcTapuuHLrVbLGo2GjUYju7q6sk6n422nBMW88izBYl1NO//rd/xWIhi1Rix6JOz6W+tUEJjXVqr/UTiJwDK+EwWlWEf8LPYPIohWRtumHe0Hf6vpK8V89G8l0CpgROFDtXXRtSoKF6l1yPtf+6DrG5/PEwa0z6l1XVaWPZ+3Pqvq0XWnQMBns5kNBgObTh8DYiHEzWbT74nodDoLPqiqISkWH4OIiUWYz+cetIbGn/ZhVhAmsydfdfYVRJP3CUSGEZEZaG9vz96+fevBZ8Vi0S4vL204HNrh4aELLxDU7e1tq9VqnmmKgDcC2QCnOzs79uHDB7/HgTkkXgJ/zkKh4Hd7QEg1VqRQKPjlejAxNL1odzATA9Tm88dAa4B9v9+3t2/feiau4XBoBwcHVigU/BKjVqvlZwsNFWb2fr9vL1++tMlkYtVq1YbDob1//96q1aq9fv3atre3fW4PDg48PSDCXrVadVcAXMuUKZH6lzHomVDaxxxGGkS9qtEjrgJXBJh5ZJ4wLkA15nH2j2oCP6eokKTACfDAeNRqF7WXCnyiu4zGMiwrKWsFnwM41S1G29MSeQE/qkShLfWP1zEpPdHgUgAGAE+11XmxB1qUFqmAQ9F5p0+8t6pEUP0cwSI190qb4+c6TylBKJa8cSiAT/mDR0Esukbp+YrzuqpPKiBpQgk077rnUnsPrTjCv1omdY50/xBXAMiPfVUArlp7wDCxCQp2zZ7AMgCXWAosAgQmaxpfBOYoxKhlmexCKIg0cQkxG6Rfvb299VTr1WrVeR/zom6+UVDW/rAeXK6qQi/Wfu0DawVugj9haQJYZ1m2YCXWv1kv0t1Wq1W/fZ3YFiz9nU5nQVHEZ3d3dwvrrK5IuleVV6h1hHOP23KhULDBYGCDwcBOT0/N7EmBpngNN1pwxMHBgbVaLW+30+l8cq7yytqCBQulloY4uEiI+TyCyRSxUiFDn80DhpFQ8Jm2DUGPmnwt2l7UOCnYh4mkSmrccVwKFJRQKSNdBuRTn6fAfgTZSoiVedJPDk+0cmidKaFgHaKrQk4sqc8jsIp7SrOaKOBIzSFrmWozdTC1z9ofsydtGITh/PzcL3ErFAr222+/2R/+8Af3M4WgQpzMnnw4AV9k7IERIUBwsOmTuk/hn48LEe9wIZ5qbcjhfXV1ZbPZzNOw0ge0U4eHhwtWk0ajYePx+JMYjWLxMVis3W67FYRbRZvNps1mM/v111+tUCjY27dvXROC3+vZ2ZlfwofAUy6X7fT01BkX48EfWN1HyOSxsbHhbj6np6e+Jmim9vf3bX9/3zNEoX3BHF0ulxdS/v7xj3+0//N//o/t7+9bpVKxm5sb6/f7TtwPDg4809Z3331nxWLRBUnmAleCra0t+/Of/2ydTseazaYdHh5ar9dzczfMQV3alC6k9mIU9NGAa9AejAkLGesVNaC0i8ATL1360pICrZFOc8ZVaErRkZSihTlKuVcwTv0sziV7PPZrmRIjKqqiska/hz4B7CL9i8oTwC3AAMASBcJI56M1N+VepM9Gi0UcX1SCMYZoVVIekZr/vHZUCRLnGiCUSnH63JJSiKUwgyp4UvyE+Vgm4KkAw75AKABIY5mAhqUEBBUCCIw2s4U+Utgj8RxRr5YIorGOa4a8SFf4HyULvIKYQPoeU7+qggTlhArI6oKk54N3syxz6zdKO9x14TvqKpRaZ1XOKB9UaxP8GMEJ3quuaUqHoaOsI2PBBUzjL/jNvsAajNCk72s/VRmMwIF7FcIJaeTxPNB6WGtdb/hRsfgUsE0ykXa77XOgma00xo+5IfYP69RwOFyq7NDybFcoDmMkIpGQa0lpMKgz1sFEPadPvK916zMqHOiz2p/IyCKRXWWx0bbiZ4xJiUJqnClQQbux/TxAr+2nLAZ5giDfLRMqzBZ9d5Ux61zF72NZJmxE5hUFKRWYVmnforCxCjxE4Rfiiqap2Wza9va2ffjwwYOayCg0mz0GuA0GA/v111/t+Ph4QZCbTqeusYYQkS3l48ePdnh4aKPRyH1e1XqA+RiBg/+JDTAzv72ai24QUNAqZVnmbcK8IBa7u7tOdBEoLi8vzcz8PgsEAYgb4Buh54cffvCUt6S5JV4Doolw0+v1bD5/1Ia9ePHC1x0/W+5ZKBQKnsWp1WrZr7/+6oIEt3ezzpPJxI6OjqxUKi1oBXElwDLRarXs4uLCzfisx/X1te3u7tr+/r7NZo9uCCo4jUYjq9frbgU5PDy0q6srBxDqR037r1+/trOzM3fdqlarTqw161DqHOp51X0PzUPjpBlPopaVOlSYQIuG5YnP6PfXLgqqYNaRFqvfsII5BQmqkVetf/xcgTogRxk48wUTJsh3VcmbW7VkINxFoK/uGikeoWALgQS6E0HEOvOtPHqZe5v2if5qespoAeB3HIOCyFQ/+V6F3nUsJ88pjJW1jXNu9iTE5PUtxfuWYRqCoqEtZk9acvYyQBENPVYCzp4Ca+rgHOKSw/lXvsF6pPYUWnuSYmCpZX5wo4WPRCGZ7EZYU7BCM27oDwKHau5pn75jEVCLNS6s7FF4JxmtSAISMSPaftY3tQ+XrRn91zgBLCv0MS9D3nw+d9cw0nczXhWeuOiUO4mwLCHMcL/S999/b69fv/Y1xPqPgpA+4C6rihHOIPsZi44qNhgrc6QX4d3c3Fi73bbBYOCX6R0eHjofAA+MRiPrdrsLwtNXFyxUOjb7NIsD368Cu7pQWt867aeKEsUIjDnc0Xwe213W78hE8jTtPB/7EK0lMEwVGigR/OeNObab0vTF/9VyoWNTUJ0S/vTv1Gf8rRs6ChuUddabgxLnQutI9SF+lpq7lACRtzcpHMyjoyN349nY2LCXL1/a7e2t+913Oh0bjUZ2cnJihULBXX0AHGgAMCuOx2MPYDYzd4GCGKBhRzONhuHdu3cO/vnc7DHYGCIwnz8GQQ8GA8uyzFqtlr19+9bevHljJycndnJy4lYBCCT3UZiZE8N6ve5BzWQRwmQLA4UQY3K9uLiw4XDol+/1+33XjnPZnmYIQZB6+/attdttu7y89FzrOvZOp2N7e3uuMarX626eRlPP2sHMG42G1et1F4Y0pe7m5qZdX1/bv/zLv3jQ+rt376zVatnd3Z1resjvXS6X/XzUajUXMND2417A2m9tbdnr1689xW2z2bRqterasWX7L34e/4Y5RqadB87RzOGGhXsbrmVo1lbRm1Ulz2IB/YnW7jimlDCVAg/6mSpq8izKqrBQWqbARoUYLSqIAEKVziu9j3RFwYAKgKrIUmWTgne1RjGGZXQ2znnsj36XspDH7/IUWqk9ohrTvPnn++coJJeV1Fzkta3P0y7gTfuQt66pdjmDnCvde/yNoNnr9azb7bolAx996BDzrNYwsycBIwrkWC6Ul+se0rMU9znvoZzRTFbQCn7TlgqMnAV1e+JHx6FByXo+1Gqvmn/WCe04F8qqFp4+T6fTBVeevP2RKjpXKszrvoQ/5WENlHAoEfScs8/VhRnFGj8as6BKkO3tbWs2m96f2WzmvDDPUqNtmy3eCxPXp1gsLij9wCB4QsCbeBcvAbDGcxRPn50VSgUDJT4RsMZ39XDHQ83f61gyIvNRAK/PqQCUAs5xsVIbMmoDUt/pb60rBYyfI1SxadA2REK8DriOAkRKqFgFsPNKJPCpoox9naJrmbePYh9T86+/oyS/CkQBzieTib169coF1G6365mGSDtbKpWs3+/b3/72N7/4jDSmaMwhFpeXl56mFcLJzdAQ0CzLPCAcAlAoFDzoGvc1+jQej63Valmr1bKPHz/a+fm5ZVnmubaxqJB5iaxGAHIsCaQURMg4Pz93QQAix3nCl5//uQtjOBzaYDCw6+trz4akoB/BinJ/f+/B4/jvXl5e2suXL61cLtv29rZf+DYYDOzq6spzh8MoJ5OJ3dzcuEWCzFWDwcA18rhroaEbj8f28uVLy7LMXafoOxo/LEQbGxsuTGhciJk5YIDhcl7JpHF8fGyj0chBBUyCfRvd++K+V7CmZ0gDghUMAFTQpmkWEmI7sLLA+NWK9SVFYyzMFgGlCglqMdCSEiQYs/o+RysFDC+CVz7nvKu7gPqeK6DXovVq9hS1Uihog3fpXLIf1DIQLS9qTYl8lO+0v2ZP2vcIrPWzVNH+5n2nPufU+TngP9ZNXfp//Hvdwtln/Zhn1pI5i4KUavoZn8by6Pupkrdv457Vfatj1H0AMNXPU/xOP9Mx8b6mCtUL88ye0qxG4IliBO07beBywxwpaNWxTadTtywAZCNNUuGNtonzuL299VTiKM04b+rrj/BRKBT88+l06vGLkeasW5S+phTTkR4gLOGaRTzE/f29z32xWPTPi8XF27OJ/xsMBjYajWw4HLrHAYo30tWjLCPOBSWbFqWlWsAMw+HQbm5u7Orqym5ubmxjY8P29vZsb2/PyuWy7e/vu9WauzP0fTJwPTw8WLVatb29PavX62tbGp9t+45CQgTIedobfd7siTDEulMaZyWylKhN4W8VNJSh6ISoNK8bCfAeia4C8dRh5/+UUJXSzqXeTz2rmvuU5ihaQ3RMq4CzlqhJjICceqP2ZxXD0bmNn61Tls0VJU8o0jryhLHUXlXA9/Dw4K5F3W7XswRx8zO3UmqWC/Vj5zO0BbjXnJycOKAGgF5cXCxoYIhPgLBjVaCPtIFfbqVSscFgYN9++60dHx/7+ADSs9nMYwUI8sqybEFztbW1Zfv7+7ax8ZRrWzVOaFsajYanb8UlSYO56SOap0aj4e5UWZZ5+kLW7vT0dMGnt91uW6HwGDvSaDTs7u7OdnZ27Ndff7X7+3srlUp2c3PjMS5Z9nTBEIIfghFWIIKq8d1FE9Rutx1k1Go1y7LMBoOBr12tVjMzs59//tn29/c9k9Xu7q6nqtVAQ4Sjm5sbKxQKfqmepplkfhSc5ilUdJ7i55p1hu9U61gsFp1x1Ot1N9NjFkeoAAw8R/hPlTylC9+p1j2Phqj1Qb9T+qr1sP4pGp03HuYpNWbejwoifiuQ1T6uo7SIdIg69CcKC6o80/e1j9ovnffYX/18mYtUXAvlv6v2SNynKZ4W+/IcnqAFkK3gNwpvcZ/wmT4T+X2KZ+sPIA8Qr7FMKsBo9h8UUQg8tKtzqvs3zok+o/79qnhSiwQldYa0f/EM6DypUIxAohp56tfzqHtVtfk8GzNg6RzHMSCY4P7FOxoPoZp58JuOY9neUuEvBmbDr+ANKijxv76jig/WSeMd4KXcJ8Uz8Dzi/4gn0VvZUzQ+b231eX1OsTGKMPgAd2bofqRf0+nUM1dx2e065dkxFilCwMFV4srnWqIQogwmBdoj2NW2aS8KFwrEY0kxKUoE17HfWneeUKFzZZZ/0U3ePKSei31QIqgaM+1HnMuUkKdt5zEBLcuIb2o+dE1TzGVZ3bFvqXdSz0bGu6rkrYHuSfxIX79+bcPh0N68eeMp9rIss59++sn29/ft97//ve3s7HjecSwJSlTu7+9tb2/P5vO5DYdDK5VK9uLFC78PQ9OjEmxHf9D+o6EajUY2nz9aCvb39+3i4sJdrkajkW1sbFi9Xl+I8SC4nPgQApQvLi5cmzGdTt33t1wu22AwcOJYLpet2+36/QcAauJAuEQPF69qtWrz+dxv4/7LX/7it4K/evXKarWav/fu3Ttnvi9fvrR37975DaB7e3seMH94eOjMqV6vu9ChwXhm5mlne72e/fzzz34x3N3dnW1vb9vR0ZHHVJycnDiz6PV6PkfKhCuVirunIfRkWWYvX760w8ND114Vi0XPFnV/f2+1Ws3u7u4WGI8y2hSApaTOlT4XtZx8zh0kCFswBuI88KEFJMCgP0dznCopQYH+L2uHuVaN87r9grkr4IhCS5Y9BVgr3QScaGxBZKBqGXluUSCfNxaAmLpmKFCLRQUR5TPRsqPAW/mSjj/VF/qjQGNVYS/TllpVIn9k366ysCwrUYCIY9C+R4CbshZon1NjAmSqG44KFmrpYN53d3et1Wq5ayzaYAX1zAF9XTbfgHMSWKSUZilFGWOhfugYAdMUnS99V/dmXhvsNxVAIuZSgWZ3d9fMzJVR7Fu1AKhVCUUJihXa6Pf7rthCAMB6s7u7mzuXxWLRLci6duPx2JVQWle8x2NjY8NpKXOLeyk/3OyNyxHZBrkHCgsRPFcFlWjB1H3InKg1mDEgXKjCbDabeRvz+Xyhn/yt51LxI2POw8ep8tnRenqAdENE4SKvqASum08BPJ9FwUPryNO2x+dSdfKT0jisM3b9PwLgPGCtCxYFB95LjV1BiR7k6GakQCPWHRlUFBJZw9R4U5YcLSmhJ8/cnlrHGDwXSwRh1JV6Jq/oHC9j8Pp9oVBwFxZMse/evbM3b944wNzc3LRer2dnZ2cLGY6obzZ7vExIBYC9vT3b3t72C4i4ARmCpWvP7/v7excIMKdubm560DftctGPmTk4GI1Gtre35yZX3i2Xy3ZwcOA+lWgxEH52dnZcuOB/CBeCwfX1tWvjuMWblLHsgXK57GZeTKrs1Y2Nx7Snu7u7Hpx3cHBgFxcXzjSIF9na2vLYhqurK2c0WZa5MEHObg0YvLi48BSvXE6EOxoEnsA6LiisVCru6oT2hjM3Go2sUCjYhw8fXHBgrNwKTupG+q17NKUAicw6RSN0b0Ygw94haJA4CvLn4+Iwnz8F6RYKT0kK1hHGV5UI2rVAR5bRaxhkik7oM3H+4pnWduhPStkS3WTy2lXeoDRCLQIK5vPej+NQhR1AKeWmRV+X0ehUnTpmHd+qtY58McVnqTM1b6rF5vkI8COtXdWf1HPqrqOCg45Zg5Hj2qlbYvytc6tCOHXGvcd70V0KOotgof1jnvlMb1leNRcp3BH3n55F3QsIyRqTBQ+Owp7SG7VexPTJ2gcEKFxHAc08y2eaQh1FHGPT2DHmXJ9VJRvWdOpHcIp4KloVsHaoBUKfVSF0Mpks3D5NwL22EWPf4jlCmNEEGqRV1/0bvWx4P4VRdf8j7OBmPRgMfC2xQqir03w+d96t6XZ1jvMUBMvKF6UBiWA4AtBIiCKhS2kZUkxnmdDA58vqj+8vE1DixssDyPFAp9qNgkWqLj5LzVMk1pGpxTrzGEZKCo3zACiJ7cTxxvaj8BO1PXFNY7vUye/YpzgPkWjGfqb2UEoYWTU+ZeLj8djev39v8/nc3r17Z9VqdQFoVyoV+/nnn83MHKxSF0xGMzEBpIvFx0vpcLtSgs8Fetp3JcpoOgC8WZa56RSilmWPWt9er+cxDLPZzGMnDg4OXODgds5yuWybm5vudsV6bm9vuyVkb2/PBRHu3MAPlixSuGYVCo8ZK3q9nufzRkNTqVTs9vbWrTyFQsFevXplP/74ozUaDev3+25lubu7s0ajsQA8KQSwc/kfrmMESRJ4z3ptbDxeasflPzDL+fzpUjbiLXq9njUaDbdGIdRgqp5Op/b+/XtrNBp2dHRk8/mjCxhzp4wygqoUvYklnhU9D5p2FkaND7Cmt0VThUZeAw+hX19LsGDcUZNOG+qykuevnjcXfA/QiHOiVgra0rOsddI/ZZjR7UxLfDe6F6hgGek5WloFonyX4oNxLpftD+YyKpfWcXXKqyvSS/YNRcfM/5qRJs9axJqoJWodoULdcChqPdC9m+qnurjkCX7LStwnZGpK8aL4vL63u7vrt9sD7HCdxDrNPMU6taiwFLEN4FrnblWBfmu6VD1T0+l0QbOOxQSlSdT4s2eYB03GkcIJ8/ncU3irsMI4YrYmeG+/31+4KFCtGKk9qPNbKDzFbBDPUalUPHaDsWrAuNYHrU0JpXq3BdYNpUH0QbOEaQyF0s+4n/UnukiZPVnfUHYOh0O7vr72fcv6jUYja7fbbtGpVCoL7fM96dLr9fpCApNV5YuCt5/zXgR8ERRGoeC5JQ9U63epTaYM3iwNZvNAvr4Xx5ACE6l29bNYR3w2NUer1kE3Xl572o6ORUve3MXPYBzaZqqPqXf1u2V7IM6z/h+l6rxxpIg2nxGIhtsOl8rMZo/Bv99//72Nx2O7urqyvb09u7m5sZOTE9vd3V1I28kleuPx2F68eGHdbtfTygLyceNRRgExji4LaIIA8GQcIWAZ4eDq6sozEJ2fn3uQ7mw2W/gNA7i5ubHBYGClUsmJTr/ft4ODA2c43W7XptOpNZtNNxVDDOv1ugs2ZEg6PT11htTr9TzN4Obmptc5GAzs7OzMTbLdbtdub29dAGk0Gra5uWn9ft/29vY8qLzX69nW1pYHyZdKJRdO0L4UCo+XOWG5QRvV7/f9f7RlWZa5xkvdoKbTqbVaLWu32579aWNjw9rtth0fH9vp6albe3AdU5M8YF61TwpGWdfnAh3eYQxqdodhkX0GE7dejGVmrh38GkHbqQItyFMSrassyvsuVSJwV4ULwB+XQM6VavNUoRIVDKpVVnej2FYE5hEMKMCItFkFG3XLWWUp1jaVXlD0s6g0oa083pbic3Gc8V11ydBxMk+pvmpbuvbQPF1X/k7R8vg+a5cSOFJjT5UU/zZ7cg+az+d+bwECPmPTuw4QIKC70f8e8Keacs14p2NVnqCuWCrgrltYMxWY2Hsx25POdbQoaB/hL9AYzgzxC6pwQfOPuxhjIgZM51uFASzD6j5Gn6CFCtDj3uAd5px1MXuyOulY1KKhY9ZYF90rCIsAfRR+6lKl7k/6rion19mL2h9oBm541LG3t+fWeAQg8FqKbmD9ns/n1u12nXeuU54tWCwDn6vez9PIrQNao/YjVY+61EQwHgWbZf1ISdUpzWLeIuv7/B0XTp+JQk2qb3l9zvsuthXLc+Z8XUFv2RrHepWJL+sX85YSxqJ5nqJBXDq/KUYU32XecM0pFAqeWvb+/t5doG5ubtwdhmxNL1688AMLgDF7BN60iQaevnNXwsHBwYI53Mw8oxAWB72/gTiHg4MDJ471et01dIDtw8NDd1ki+xHuU7PZzF68eOFCChk3Pn786OljJ5OJZ1SqVCr27t07u7q68ttMW62WbW1t2enpqc1mj36c4/HY9vb23ApWrVatXq/7PL169cr6/b799a9/tWLxMQUet4E3m01/jnngN9q+zc1Nj7soFAp2fX1t5XLZgTyZLGBaV1dXbplhDbh7QgWd3d1dF9Devn1r5+fn3j6asY2NDW93Pn+89fsf/uEf7PXr156Ny+yJmVxfX9vr16/doqMa+7w9r2ckfh+ZD8Ghu7u73kalUnE3KEAOcUGqtYUBYx1jv35JAaSkxrNMk5h6/rn8BYChWnPoLMGf2gcK68K7+n7qedXQRuuPahG1bzomdXNSn+oUOF6l2Wd86nedApZ51iHA2Kp51TXN4zu69jp3665jav5Yj7g3+RyhQ4U0BfcKKrUdBLllPFTHxRwBXOkTmZFQEqkVBc0vgoUKCiqA4eOu/SFZh2rl6btmrMPl0uwptmpdfq11AnbZzxp4jPCE26+6+zA/cb4Azfo9wtJoNPokI5L68SM8MCbA7/39vWfvow76qKAdVyCzpzjX1B6GT6pyBd5NBkC9cyRaxqiPLFej0chpcqFQcBdnEp6QIh0rhd5PEddD548Sraz6fIy9gF9vbm66JZ0xkzwlRZd0vrBSdLtda7fbrlxcp3zxjUgpjXfK5SdP8loHvC4TCPKeje/o/ylGreaqlEAS605peGKbURhRzY9qavheTaBxflToSB1k1bJpvVryQH8K+K96L1UPv1Prv45wEz/Xd1LPpsCZrmfUsOizy7Q68/ncDg4OPCCYDE2VSsXdd05PT21nZ8fOzs5sMBjY4eGhB0NDQHHJmc1m1uv17Obmxg9mqVTylKzcuEn9EK3t7W1P64rplXrJyESbZrZw0Q85qhEOCISeTqd2fHxsm5ubnhav0+lYp9OxwWDg5nCzx7sxiNsgA1aj0bCtrS2/XG5jY8PvrZhMJnZ5eekZLq6vr/1ypXa7bVmW2cHBgQc1aypaMqcAINCyow28uLiw169fW5Y9akL/+te/2vb2tr19+9ZN8qTN5SfLMresfP/9974nLi8vPasVQhfMDV/oy8tLOzw8tG636/E1BKSXy2V7//69B8ZdXl5aqVSyk5MTvwODMSDY6I3bUUBmv2pRASV+x3qTR59L77jDBNcBGDWaUm6Fn0wmLlAoHXoOkF9WVp31lDCfOpPP1bzSdp5AhlYPa6B+F/3/1RKQouvqQgaIjNaDvL6tYymgPsCA7mt1sYnzplYa3s9bV20/z8Uhj1bqfOqzsY95QnNeif1BAFYgpPXgpqX8VTXPfKdro79VkExp32PftH9YMM2e/O0JMtYYMopaBXAlms1mnrVNM/DlzbNq5RlzSlnxnKK8m7pjGtfnWHjiXFGm08c7KjqdjluauQMkBmszJhXSmHNoHPcTMT/qEpral3l9VKEenIUVg/VV6xP0EwEG91O1QADUce9CIch+Y38ojdH+qlWVkkcn4zpCy+7v763X63nmQ/aZxvDA11Q4UwFsPp87f8V6sU75rHSzkTGmAHtkiJ8jHKTKqjpSTGWd75YBYRUmUqBABYYIcPOEFLVixHfjeCGM9DNFQNTEnupj3lxEZqd9Xrek5ipaY7SfSuxh8Dy/bA5ifepiEoVJDnEETHkCb4ppZVnmrkeDwcBev35tt7e3flB3dnas3++76w6mTwquJycnJ9bpdKxcLlun0zGzR7//SqVirVbLer2ej52g483NTfv1118dbDNufpNtAq0NlgHAMX3BckGwNjeeQiiYp9vbW4+PwIVmNpv5HR1cdEf+7f39fSuXy9Zut61Wq9nV1ZW3YfYYwGz2KDBwxwUEs1AoWKfTccZwe3vrlg5Ss06nU3djGo/HVqvVXDtF9iluQUfjzl0guGDVajU7OzuzyWTiQfO4CQ2HQzs4OHBm9fDwYMPh0F2HSOn4xz/+0T58+GAHBwdWqVTcNaBSqbj2zMwcKGB5wtVB0xETPB3dQczSl8tR8r4DABBPQR8onG00WGhYo5JD3Qm+dlGGveyZlEZd3/+S9qPCZdlYAVfxM60jT8O4TgFM5AlaUXkUNYvMk36mmnnVTKYEjrw+xbFq32KbkV8o/1dLRV5RRZxaGnReUwKSrgv9inFCcayARgWREXTmxYSkiu4B0smqUAogZPyafYp9Mp/PXcMNj0BIifsDcMu+VcWZWuRWKeH0O+WnsQAs1b1IsQprqzEUyptTgplal4jLw2Ie9wJ/q5uqWvhQlqRAbt64UviUfqUstdGiBU7BYwCLDmOFX1cqFZ8PeDKKOTwVUP4wxyqMqCIAes0+0n0X5zdiNxWWuM+CLFy4yqJ44j4TrFGsf1SSFAqFhTiMVeWzLBYRLK961my1FlzB8DKhYJ1+pdqN30VmgbYhCgARpKc0TMv6pm3xv0q00aoRC5uMOjRgLkXY86Tz1Fjy+vuckrcHVJOi/dSASkBt1DYt62eeW1QctxLgWPLmWQ8nbjGkC93b27Pr62v7+eefbTabeZAX9wJAOBkPbikQhvF4bDc3N5ZlmZsoCbZWLQd+mlqXHu6trS0bDAY2HA6dIZmZXV1dOWG7vb213d1dNyfPZjPb29tzsHF1dWXT6dT29/ft+vrag7KLxaKD37u7O9d6cMM1wof6XaLFMXvSppmZM04AOikWzcw6nY5bLCB01EGmDCwzZo/CEXNFnm9ce7jordfrObOazWbuYsbNoQhY3EjOszAwxos712g0suvra3cb63Q6nmmkWCy6hYYgTAQSLkQ0M9d6oWWLYGqZljiWFG2EZu3u7vo+VYGdOeQM4DNLn+kLzC5eXvg1irryRBO+ji2l/V6m9X5OUUtYSjgAYFAUICm9SYGWdawqyqR1XHF88ZnYX30ufsb/EfDHtvKKvps3Vt2/ee0oqF42H/pbCzw4zoXyjJTWXAG4jjXunTx+rfwjb544V/QHdxnoCFZPBAYsEqn9CxDFSoHLE25GKI30ngpVQMY51rnMoyuAaE2zG5UWCnbV6oJySmlMofAUu4UShaBn5b+3t7fOD6CPuF0RV0eMH3yVdnVfPRebUJivuA64psXbx+Fj/NY9Aw/Gdc1s0Q0TtyhV7JVKJb91G9e4wWDgMZm4sqpVm3ahTUoH8lxNtY8IAoeHh+6axe3apVLJWq2WK+k0xkITwKjV+7mKp7UFCxiUHpRIpPNAckoLkgKkeQwkD+TTJiWlCdRNoURTiTRjUqtAqv7YzxSR0sMfn4sCjTKu+I7ORZ5FI86LCkbrzG2UfiPDStWTEryW9U3/ju8qo4iMLAJ9/TvWz1xGJpxHiOL41JSsxGE+n/vvQqFgZ2dndnl5ad99951lWWYnJycezDyfzz3tK0CGwOwsy+ybb76x29tbJ1xm5uAPbb2ZOTOBuShRRGOFQDqdTt2FCl/Vu7s7u7i48NSpuC4Bejc3N61arfrcQwCJXwCoov0niBsGQkA0FoWdnR3XeEOICFDsdrs2Go2sXq/b8fGxM0O0ObPZzDUmGmzHM7h56U3l8/mjGwExJnd3d54OGKsIQgPZPDY3N+3q6sozYkynU7daIOgjoLFnqtWqtdtt+/Of/2ytVssZPlaK3d1de/HihX348MHMzLNnFAqPFw/hloa/LjEpCBm0ta7gG88SBWZOqmBM74CaQqHgYAIGEc89jP5zb7HNKwrUouYtjikyy1Ug77l9WNY+RbXyke5zDlX7TFnVR9X80g8FvqyTKl1U6ZRSmqT4EvOo50jjSpaNPwpT0VWMNlU7r/xM34m0ObajlmflufP50x0IqoTSuiJ/Uy23avS139qPlBeF8jC1lMQShRziBbDyMj9k4oGuAbZVAMMdBeUE4Jvni8XiAmjX/sT4IY0PUgCoY2cPwF+iAKHzS51qFbm9vbVut+uZ/nADQih4eHjwOVBXJManyhyUSYBtM3MapgHwrBdrAphnrHHv6j7VMet6617gZmmsvMwdvFddsMyeUskqXlGFRbH4eHcVcRVkAeM+JYQo3J+73a5VKhWr1+seVK3YhbOs55k9Ht2VdKzMBfuItO+sd6lUsmazaVmWecZF+qWCM+uk53zd8tVv3taF+1pl3fpUSPicktIAaR9SRCuC8Twmoxs+ap+UmK3qg/6Oz0ZrQCwpYYf3ohZoGXNI1Rvfy6srfq/asUgwYj+X9W2VUJoqMPr5/OmGY6wR8/ncOp2OnZ+f2/HxsY3HY7u4uHDXFmIMDg8P7fLy0trttmvGzcyBc5Zltr+/7wQCrTn3UQBuYapoftCIqT8kblTqS6+p93BFIgUtggcWgbu7Oyd0hcKTOxJm+FKpZIeHh3Zzc+NB3s1m04rFortCXV9fu5UFoQThC6LPbeWbm5t+u/jh4aF9/PjRXUYuLi5se3vb9vb2rF6ve4YrvQGUGALm++zszHq9nhNA1gIB6Pb21mq1mtVqNbu9vfV+mtkC2K/X657FiaBx1ubbb7+109NTm0wmHvdB+lxMytzGXSqV7Pj42Jku6W5///vfe6Aht4BfXFy4+xzaKGhB6syvOnM8g1CE9gvNomaTmU6fcsSzN1WYIBXksiDezyl6NpeNRwFbypXiSwp0V8FAisZomxGgxqIgXMsyy4CCX94FMCJE8AyWLugB7jWxvlSJPCjl1pD3nioxaE+1t0qzowY98jC1HKSEi/hslmUL8wE9ZM6gz9wFoZYN6tNA7RjnMJ/PXXmjz8S+q/AU9w1gi89xL+EMRVetLMv8zoJyuex0DJql7kS0SawGvAnhIgp1jCuCcKwbfI4ApIHOxIFMp9NPALzGZ+k+pw+4z9I+ggS8jngCFXDUEh4t2awZ76fq5vMYOK9WbrUgwDsRevR86VhpI2Zg0v2K4EHCD1J4qysbfAo62mq1XEBhX7APNIg/CpgkAlD3KHVN0/NHuvqUEKlKQ4QGXQss17hM9/t963a7ZmaOA7CeoHBbZfGMZW1OkqdpilqEPE3TKmaZAqfrCgjLwPyy/vOMMndlMgrQIziOxHGZhnyZ4KUSsX62DhOg/Tj+ZZtN640MUr+Lmh0teWupc5kSCOIYeAZGkrIYab1x/Iw9JbDF93VelKikQB4gbTweu48iZu5isej/b2xs2I8//ujAHfcYnUMlVru7u55ZQbUQKlAxFnyHsyzz26WxDtD/YrHoF+2Q8rXf79t8PrdGo2HD4dCm06lrgl69euWBc2RJmkwmdnp66i5dzWbTRqORDQYDq9frNplMPMj89vbWvvnmmwXrAfdwcLHd0dGRM4FvvvnGL7br9/uexrZcLturV69c49dsNl2jZfYoQEHguHOjUHjMzjWbzdxKYfaoEXv37p0Vi0W/PXw+f8zWRJzFdDp1Iqnrc319bbVazfr9vnU6HXepevv2rb1//95ms5nVajX3k0UrO5vNrN1u22g0srdv31qn0/H5yLLMA7rxKWbNo4WONdR9Hf9epViAMRIIydqqiV/fg+HBtHZ2dtydjJtwv3ZZRgtgWMxPKkj3c9tToKLnLc8CoFbPZYyUZyOz19/6rNIl1dQriNL54PxQ/3OUZQqa1NVF950W/tdsM9EiANhUbb3Wr0KA9h3wvKz/KvTo2gOSAdtoTkk+oO8qXdd51boBowBZdXOhqEChoE7dUTSOo1gsuusOFgDGgfsoVmNNRU1foJmagpTfrIFaG2lT3XRYA+YaZY9mRdI7Ilg/3mH9VMDRH7VoMCe6d1SrDR/DBVPrwKqO+w2CDmvGeYLH6vzHYGxiFnRPRUEfIYdxK05jrAiGCEsay8G+0CxWZuaZIs2erDGaPatWq7kgqYIt/EoFPb3vQteaeYhpxFkzxT8Rl6qgjOKSG8QRDHmWMfNcsVh0V2PwBhfiMv516dCzVFRReKCDscE87XOcgGXtfEnRPi1jzPp8fEeBbl79cVHN0llcUuPVNiIjVRNw7H8UEKgjJQhEwJwaswpJkUBTIgDW8Wjd+ju2Fw99DEDUNmI/UyXOz7I9GdcJ7ZfOPUwXs/bNzY0TH8Ax76GJJ+6g0+lYo9H45NATHEUaUojl3d2dnZ6eup+l2ZMvepY9BYzD+I6Ojmw8HtvZ2ZkzIb3M6P7+3gaDwYJGFhNzlmVOTLBeoIFHY3R3d+cxGoPBwC4vL52oA5q5N4KsT2aPhBUXKsZrZtZut10oww3ql19+sfl87nEVxK/MZjM7OztzlyXGBdFmXh8eHtwlaTAYWLvd9hu/sT7MZjP7+PHjAqAB1EDEsyxz4YmLf2hnPB7bycmJZVlmL1++dIZK4PXDw4Odn5/b7e2tVSoVzy7F3Pz+97+3v/71r/bq1St79+6dzyf9R1Op2bBS9Cm1d5VpxPOHRgzhCW2nxulEcADDQqCAif29itIa6IiCPB2nCl6f25ZmzoFpR95FUeAY1yDOM7RZNeCp56OlIDUWBcFYmNSfmvoisFpW1CWCtaftaJHie8Atz6kvPvOmtxqvuy4IvSo4QnejBlkFbeZDgSBnt1AoeLpO5WFxDVRZte7ccbY0ha1qi1kXtM26Z4kr4KI14tA4ZzqvpIjlfPIMdbBfsXByXnSO9G6IuB7sAeLG6Be8AiCsoJ2xqlC1ysqlRQV4rB0pzIGQipUjFY+jbloa6xG/R/k3Ho9d465nivgGhKvIE+BZ2nf928w8PSxYAPdW6OZsNnPLSLfbXVCUsKZKV2kTBY+esSgop+Y4WimYY3WH46zlrc1wOLR2u21nZ2fu8qzWeU0Ig2CNkLau1eKrpJuNwC1OzDIt8pcKEXllWf0KuPk/Bc6VwKeEiBQo0LpSByv+n3dwVcJe9lnUdK9iyCmBIK6X1mX2FF+jbar2K6+9dYQEBRxqkk49t4xB5PUlzkkUqPQ9CHKWPaZFxb1ld3fXbm5u3JJxeHhorVbLfvvtN5tOH9O3AgwwGaMdjzmuFSyrMKNzrkBL3QAABhC1h4cHOzk5sclkYvV63depWHwMvlb/zIeHB7u8vHRBAK0a76K1h3hxPwa3jGPmZRy6HtzgSdulUsndghACYJTKeDABz2aPLmQAZ7REZNIAZPR6PTs8PPQYDrJX8YP71Xg8ds1Lu9329xH07u7uPN/49fW1B71PJhPr9Xr27t07K5fLvs4wl3q9bqenp34RYaVScSENa8vLly/tl19+WQhAx3KBHys3mMJMUkJyit7omdJ9jdZQtUz4M6sAo1YKnkdj9/dwhaLkadi0RJqaJwSsW/R8A6S0D9BRpfH6jPbdbJGWqQCQ6mPU+mo9q8YcLQasryqb4vuRT636nIIAqvQQ90qzxUyDymcU8CsPgW4pyNG1oC/RkkAbCqo0wQnP6XdxfXRsKlBDdyLfzFsD6lQljYJV6lRBlX4B3hEQVBDTANno96/jVm02PEKFM13bKESqQhdFCmuq4DZapuJe5f2UZU7nkT6pVYVnVFhX4QC6iztvzMika0H7KvSyl9kDuAJrEhEzc5qIsmtjY8PnMyWo6xlgD2kfNGuXmbkSJ8syu7m58ZTtCHHwy7jnWDd1TVU3OARGtXCrAKkCm9IJPU8U5po5vr+/9/socJdFYCoUCj6Huj80biMKeMvKszhJCrQpSNe/8w6xEpsImtdhJMsEmby6l40lBdzzxpZ6f50xa9/zvsv7LA8oa1EhZlUbq4SBvH7Hg5fnrrVMyxEBUhSKtC0l2lEoSJVowsxrX3/MnpjU3d2d39MAYe10Oh54dnl5aS9evPBAu59//tljEXDnAUTSD4ju1taWXV5e2t3dnX377bcLvq2Y+7mDwewp2w/v393dOThWYk+Qt2plZrOZa1jm87ln38BV6OrqyorFx5zWAGrNIf7ixQsrFh9jAnD3YWwQqkKhYNVq1fr9vt3d3dmrV69sMBjY/f29dTod9xeF+HIT+NnZmVtosuzxkj+0Sur60ev1FnxrC4WCB/q9f//emeb+/r7t7Oy49Ye5QXiaz+c+r1xS2Gw2XRjAUnN0dGTffPONvXv3ztPHFotFu76+9j3IJYAEjXOh3nw+d+Hn559/tr29Pfvb3/7maX/ZB6TvVTeEKFAvK3kAiIL1AcECIZbnYOqaalBB4t9LwaN9VU2htqmM7Dka5lUlxWOUOapmLwXkU9q/+Ewezed7aJtaIijqfmS2mC5VNe7xczNb+DyCEA0U1jZiH1gD1oT9wNhVgaCKDxU0AGAKXJlfjYfgcxVKdK4iXdb7C7Rd5T86H1GTy/hQGOieS+GHyDtUiFBNMu1q+1n2ZK3Vc7WMD2q8QJZlHgPHBZ3j8ditkKlUpNB6xqfuM/AWXXuNr1ChS8eiQvhsNluwhKoFTutEcRYTjjAelEZkwIL+K4CPwgUCAHPPmulZZM/gMru9ve194QeBh7GZPWXG08xVtMncArDph1pIcD1WhR/CTbfb9dTzuH5xRrWdwWDgWQvJhIWLFX2L5yx1VvTc853OFXyLS+7Oz8/t8vLSsuzR3fvo6MhjLOC5tVptQZBDkVgqlazRaKzEjZS1BYvIACOY1gMb/2ZSUqA39Y6+lyqpeiLRWfZ8/C72gzpjG3EcKWafV0f8OxL4VFt5/Y19X2ZtiX1URpYntWv9Cgh4PzXP0Ty37lryjjLP2B8VaJYVdROJwogyB+qK2glub+50OjabzRZcVn744Qd3w/nLX/5ig8HABoOBvXr1ymq1mrVaLfdvh/CrYLC3t2eFQsGazaZ1u13P1oQbEEIAhIrMHWbmZnOCsiGaCEIEPk+nU6tUKq5hb7fbHjBNQHitVvPgLPyDER5YZ72hmcve/va3v1mtVrNisWivXr2yV69e2dXVlV1cXDihLJVK1m63bT6fe+yB2SPAeP/+vZVKJQ/Qns/nfo8EIFjdpJi3+XxulUrFms2mu56VSqUFjUuWZe5ucH9/b5eXl7a/v+9MnnUkuBvNPSlwsUYVCo/ZTj58+OBxJtfX114H/roIjwTit1ot6/f7LjAQwG/2lI0IH1bSEOt3urfzBHb2cl5BK4ngEOmZarwAvfr839NiQd8V2CmNiEBQP2NOdSyrivKkqBFXBryuWT8WzmWe0uc5AlK0KkU6qPVEISn1d6pd5RGRvuqYVDMKaKPOLFvUQusc014EUcxx1LymrBSxzyrc6Y9aU1JCn46XosG7qpihPyqUpPaOzlWKr0Gz7+/v3XKZEiJRQmkWIgQy3CU1RirLnu5z0P7FvtEv6kOAiDEDrClKDh2HWh4A1RpXE+eI+lVwVGEWv314KzRJg5fNbCG2JNZfKBQWxoIlB0EO4QBhINJT+qcWLKxK8TJCfVZjJtT9ETdmaBJWK9aLz/jNPlW6MB6PrdfrWa/X83eYXwLcWXNda1XKpOiO4i+1HELbwSWj0cgFjqhMiEIXY1Ar91cXLBgAC5ciUimwnAfYdbKZMCVCWq/WmTcwBb6p/uQ9H9taJiTws67gwsJp3xT4Rkab6qNqirS/uhZRuEsRPyWMqg2Odel7kbAqSOfvCOL12bx5UiavxCi17soM1hlTqh9xDPyt80t/uF15f3/fAe6bN29sY2PDrq+v3VLQ7/fNzBzQEqyr4B+CRtA1Wm0unQNM4xqjQXpZljmhRIjY3Ny009NTT8NarVY9N/jm5qY1Gg3b2Niwjx8/ejo/3LSwDuzs7Pg4Tk9P/RZsM3OAj7YJVyPG9eHDB6vX6+6G9fr1azs7O7N2u207OzvW6XRsb2/PBQQufyoWi3Z0dOQZlXZ2dlww29rasuFw6Glnmd9Go+FBdaTp29nZsYuLCyuVSpZlmZ2dndnd3Z1tbGx4v+r1ult49vb27JdffvEbwol3wYKkgsfNzY1nz2g2m3Z6eurMFcY3HA6tUqn43qhUKn6x3uXlpZXLZavX61Yqlezq6soZGVq/qD1TjbYCrVSJZ9UsP8mBMtv4rAIqmDPa4XWB+7plmeJFtcTqEqdgMYLRlNY/r6i29jnjUkZulp8YRF1H8tqMmnLq57d+vk5ReqbaSgUdqc9TGvlUvfwd+8eY8uoAgMSAWtWOR3qetzdSfWMPUB8gUudP+4iwEMcVXdRUkGLMqj1PrbH2B40169Htdt1nPeKj2Wy2oEknk1CsH+DP+UxZUmKfU8oDzXSkQjq/dR/Cm1CG8R1gnjWMIJk2AbBqxVOLBmD27u7OMxBpQhK1ysSzAuCfzWY2HA5tOBxaoVBwnmlm1u12XRmIsgTLwnw+90v5SGaSOnMq2LHGAH3dB6PRyLMLInj3+32bzWauMNNMjzEblwrIhULB3WSxvEQBQjGXnkVdi3juWX9tc2Njw/b29szM/D4Skoro3mHO4Vm6j0gGsk75LBVVHkFcBub1uzhxqc/y6o/9WKesEjJWvZsCrLG+ZePm+5SQlKpfn1kmTOUJRSnQnzeWvPq0f2qyVdOkCjWpNqLQo88o01LgrxpK6lhH+NM+pcYV66BezMho/Qle+vnnn+13v/udzWYzu7m5cSKxvb3tLji4GSmQU80P/a9UKlatVu309NRjNyAOEEhiOWCOEF4IBJfrNRoNB/1oVwimHgwGbolQX36ILNryRqPhF+Mx17g7QThZF4SDarXqggYEmJSxr169sn6/7+lOG42GtdtttwARW4DGbjqdeuA28wSzvru782xUxDBkWeZ3WdRqNf9sb2/Px6ya91arZZPJxDNQ7e/v2/39vTMwrDvc9ZFlmd/sPZlMPFge4Q8N393dnWf2gnkwjlarZdfX17axseFZOLCKmJm1Wi2fN4034W89F8uKPpPa67PZYtYRsyd3P9VkqQYSxrMK5K0qeUJRVCKllDrMgdKEyFS/tCgI5P+855bNRR5PiFrg2EacgzyhRelYbCc1F6l5V+WV1rnKSk1RMJk3Xv1cheaoPaWP8d11yzLeGuvRPaMKMOWJEbxGhRf95QeBAzAYBQ54A5prFYJ1LeEtrHsqWYKOFeElWo7oF5ZxvbNGAeI6QluWZR5/kAL3qoGP7kGq+Ue4SM2zuhlhib67u/PAZlx3mWMCu/kMOsmN3bFoRkEzW9hzzLNaxKMwZ/Z0iSaeAhrADm2kT9Pp1IbDoe8LzcB3d3dnvV7PY0jUshHdGxU34JWg2Ceuk85pxM56VnlHf2N1QBnW7/ddCGZP6X5kDlLna53y7BiLz2F8zzE5fy5zS/UtBerznllWbx7g/hyNU6qvqcWLDCklhOl49LA8dw5TAgyEK9X/FDCI/8c5Swli65ix43fLmFJkIqvAgZl5sC8gHWBWrVbtl19+sel06pI+PvNo/wuFgrv3oB2JmuLpdGrn5+d2dXVl4/HYs2JMJhN78eKFmT3ONaAfrQe+srgDqUa3WCz6Ta0wFAgh/YeAEbBdqVTMzOz09NQv7lFtPASQutAusVYEe9NPCD0xFfSFS+T0UqQse4wh4TLBSqVie3t7trm56X64Wfbo9/n69WvXqKjgNJ8/putl/Lu7uzYejxfS8HLXBcwSQeLXX3/1sTabTTN7ci/DPMwt4tVq1bNnNRoNq9VqroViHyP0YWlhDbCoFAoFOzg4MDPzeBOEErPFe2NSyoBlNEUBY955ZA9qVhiYWcpfOwrzn1vQbmnRcSpjjpYE5Rl5dGTdAtBRSwftxbiKFEhnrqLlkKKCj4KEdfqr/VlG/1IgfFlcRywKZOK4daxRa699VO1u5Ff6LvQpzp+C83XmJm8ccc7ywGEsKkSn6tEzxLPQZ+VBeumZuoXoOSIL3mg0WjiPMZ6Jz/PwCCBzMnm8Rwf/9sibsyxzd014i8ZYaLsU6DTKDl17NNS69gBdLBpo3zUmT9c3b6+oZZTxIZSogET6XbXmKO1Q1yGUVLyPqy8xDHEfkKxC96XusWUlxoDAA1DCRcsc9Je10EtRFcuxplhLlM7kKWxVIURRuqqKGdqC5sOLNC6Ke1VQvJFERfulAuBXFyzyJCEt6wDtvAOl3y+rI/V9BN7L3olMeVl7kfFHLVB8P2oboluXPrMO8I195u/Us/yOloW8kvouBVSWtRf7lAJJPBfnLSW0KLjI61/enEXtlL6TB1ZYIw71bDaz/f19B8+dTsdB8O3trYPmwWDgRLLf79v+/r51Oh2/zA3tD9od3KWKxaK1220zMxdEer2etVot98vf3d31C+cgJASWb24+3nQK2EFzj///bDbzi+0qlYqdnJxYpVKxV69eOfEgr3qpVPIAMlLTaupbTL1ok7jUj3swEDZ2dnbcvUhv/ibzBy4AED18ZE9OTjz2gbFyiRTAnlS3CDswj8lkYt1u1wldv993psE8sn9wVwAM3Nzc+FoAJAaDgQ2HQyuVSu6eVS6XfW6q1arHVUCAERawIKmQMxwObTabucsbc0rfSV+LkBTpUR5NiucoRYvQPFGvKh5iHnq0dKto7rplGR1Vq4wKNXnjTNH4z+2PAkD9ySspmhHfi8qYOMYoNMV31bVIhS6do1S/9Pc6Y1/F31L1qTCaV1RoYOwpi03K3W+dvvMTXT+W9Sk1PuWF0QoT10DjjhQs6xyqS47eMYBLC5eUkmpU5wgXFYSjKPAp4GMvjcfjhbgNhAC924A6zWxBwFMLpSoK1aWMPvHDGKFNWAwQVuBtPA//BMAyZl0zhBPmguDnLMs+SWusYDt1hlhXjWNgrLpf9F3WFQ38fD7/JCYCCy9rkMJ06+w1VerMZjNPF7wMu8Rzo1YM9gN7IlWP4h49L/o9c4/LFbyXhAEozgqFwsK+iJbtry5YrDPReUKDguw8gpcH1pcVBfv8rQcorz/LhIPUmFPCQ17/lCAu67P2L6/9+OwqxpJi4HEscVx59cS/9eCm6tTnUxtficY6eyiPsWodqWfyJP0odOh+gdBCrNvtth0eHlqxWLRWq+WAfTKZuNYcDQw3N2NSRLiAoJLOFb9/3JTIfU0wNWZkwOf9/b01m033u+TeBghzo9Hw9iGUpVLJg8QRLmq1mg0GA3f/IYXrfD73uIRut+vEbzAYuPZrOn28zKhSqdj19bVdX1/7vBJzMh6PrdlsupvP1taW7e/v29XVld8Nwc/l5aUdHx+7sMWdGKSn7Xa7dnl56S5hBKKTsYIbsbGwwFSJn+j3+9ZsNj37FVmr0MyYmRN7tHb1et22t7ddkwPjRFjh2fv7e9fqsbbNZtM1V2QRa7VaVq1WbTgcLqQsRqCADtLmuoQ6dY70M9akVCpZuVy2SqXiwZMKAlVTCIOez+dfJXibOc0r6u6Edi6CAPULjmVdJs8ZUjO/ulesa51RgYQ+LXtXn9e+5L0XXSIY+9coCijXUZzlvZv3Hr+joKXAXS0LKSvVsvK15yOvKODnDACozMzPBqm5O52OXV5euptlq9Wycrnsih5SWVcqFc+6h+VVz1gEuOxNrA5m5u6cGsBMLB17mmQUWGBR3KhLF6AarTWWAeZY7+DgHepnDuL6si4aN4LLKPczsN7EodE3AoR5F5rL3DM/cZ1UQFLr0zp7C+HB7Mmiq1mkGLe2kYcxsixzSxJ8Mp5xFDbsI816mFfo/3Q69ViU2ewxgQrp5FOFdlh3aF/8fnt72y+NRbjABZx0851Ox4Xjra0tz6aI4Lzu+X02J9GJSRGtVQByGdjXknLF0WdXgePYp7x+LHtnlcCRqvtzNX95Wq6UEKT9i/O5TDLOa3fZZyqtRoEtJQSsEhZVi6gapM/pe+yvtqdgKvUT20F4aLfbdnR0ZGdnZ/by5Uvr9/vuf1+tVu3h4cEPXbVatel0av/6r/9q1WrVNfkAGn6j0QHYw4hgWJqqEO0BTEgZBEJMuVy2X3/9dcEFyuzpAjx8KMmMdHp6arPZzAOdsZowd6VSyd2g0B6p69D29rZ9/PjRCdfh4aFVq1XrdrtWq9W8XjRYHz58cPP9bDazRqNhHz9+tOPjYyfcuGKZPWrl9vf3F1K9jkYjT+uqZmVA+vfff+8ar7OzM7/EkDzdZO+oVCrW7XZtZ2fHzs7OnKnBRK+urqxer9vBwYHfvs0+wjKBpYf7RugXlzIRR3JwcGDz+dz7eX197YAApoBPLoHieWdnmdAfn1PhH5cz9mIM0GO/xFzuqTPx3JISTFIMf5ViQWnOqufzSmpsy3iKukdo+0qfqEddDXhumUInag+jiwfP/T1A9CqamgI7ecox1Qgzn/yOFguzRSvyMmVbbFPbifXkuZDF8dIvXVNoWlRGmpnTauYCIKgCFiAdQJZlmQNj4tJUmIra89RaYDXEJx/QamaurAGsE+NmZg6GNW4DpQGCNS5MKDDUFQrljp5ZkmdoIHYsuv7EQ1CPxmig5NDshuxvXC/VxYybyqOLku4bde3jexVAdS/yvK6r4gQEDXUNU4sN86euo3GfaTA8wpF+b/ZkQaKvecJBHFtKGbqqQN90HWgbbwSUp2pp413mjrUgcYvO5bKzp+VZrlAKJDEjxoVOESkFjutYDyKA1e+WvbeMAeUx7WWCwzLhIj7H75RWPwpbnwue4xosey6v5IGSVD36m7VW61N8Js7DqvHE/uh+Wibw6PdRq5bHWFIHFeLIYefwAUrv7u7sp59+sh9++MGJ/NnZmZk9EiECrgGOuMkUCgWX7mezmXW7XY9RoBBYjTlSxzSdTt2ywa3a9PPFixd2dnbmIJFAbvpxeHhoZma//PKL30g6n8/dwtLpdBa0ioDsSqVihULBM05RNzeQc+Ec2Y0Ish4MBg6kAf8wHwKur6+v3UUJZoT2vlgs2u3traepRVgzM3exYi4QSMzMfv31VyeijI+brtvttmfEyrLM9vf33QKBSRlf6L29Pev1emZm7saEkIiv7t7ennU6Hd/7av3Y3t62fr/vMRkXFxcLKf7u7+/doqWBfGZPF0+uokd5e1+ZEJ/v7OxYq9VyJpBlj4Hv6gqlQYkpQP25JQoW9ClmC8obm9mnN8h+DtiOZ39VyQMOqg2lTuKjImhcV/gBkABGUq4L/38VBRNa8iwsUbCgjix7ysqXNw/rjE/nm/ag1yoAreIvqnnWM6L7E3CpY1JNOK6ncW+gUMJlBCUBbq+4ZE4mEwf/y/pLe+wpdcEC+GZZ5tbn7e1t50WAcoQctNDz+dzjv/SmbZ1X7g8ql8vu0osbLffh5BWdMwQUCnsAOqNxGxTONeNDkZVSQADydY7YE9B+lDUqlJk9XTYYBUl+Ux97Jq4Jwl6MS4trqkKGzoO2EwXnWNgzKlwS76CueauK4jSdRwQF+Cv9Ulfk7e1t29vb83bn87nPwXNp1LNjLFKCQepzvlv2uf6mDjVBRWbK8yli/hzJLvY9Vde679M3Jj0lVMT/49jyihIZ2ls2p8sEMe1DFAjyBAT6oP2O/nbL2ohrlSKwkVksm48IwlJzwO/Yt9QYzGwBbHFTMsSOK+/7/b6dn5+7ZobDSbYoM3OXE7MnlxAYN5I/BHw2m9nx8bHHIRSLT/cbAOx5vtfr2XA4dEDe6XSsXq/7zdQw0Ha7bVn2GKdgZu5ORN8QTl69emXj8diurq6cmAwGAx8bgJ8sGrgdqTIBqwgm1Gaz6URagRfzTjzBzz//bJubm7a/v2+TycSD2mLQOEyNLBbz+dxjV/b29nw+NK1sqVRyRrK7u+sB94PBwOr1uruaESczn8+t1WotxJggoLAP2B+kxiVInLnlPg3mDdcuBVuaelA1u1mWuUAaNdrrKF8iDYS5YVHZ29tbiJ9Qtxs0khGwfWmJYDRF/1TbH8F/ZL5f0q8UT4nCQOr5WOIYoB9aD64VebRQtX1R8UGdrNPXFDBSPtkRJNA/fWaZW0kEYLqW7Gn1f9d211E2pfajzs2q+Ym0n/HRb3VxYjwqZDOuddpJ1cO6KpiMey9iBM3gBp2KLovwBGizuphyVnDH4hl1zwW4IpDgtoXgz+e6FzTQWfc9qcFJ/crcsfbQUQ1yT3koYIVBQRPBOcAWfkxBwEdAV+zFOwgGerFsVKQgmMS1QeiBn6EAYy/Br9hnqmhQK5cqOHRvqWub7ifWEmGNOUvNzTp7U8ekv0kBzI8KqWphVy8EdV1dp3zRzdtfoyiTVGCYB27XEQDU5L0OU15F8CiRSVJShEj7G/u5rL2UsLVq3vX7vGfzhIhUf2If+EytFTrHeeNJCVWUSFxTz+QJSnkMPO+dlKChjEZT2qFhwddwd3fX73sg6BYQf3d35zds4r4EMcqyzIOv8LW9vr72FLIKnngfdx6zR5BGlhGIKkQaYeDu7s6azaadnZ25v+fp6alnQ1JND20h2AA05/P5grkdpogVYzgc2v7+vmvw0UJBXHXvd7tdu7m5cXetyWTigH8ymdje3p4LcQgnWDh2dnbc5Yw4jyx7jPmAuG5sbNjJyYnNZjP3M4YIoh2cTqceY4C15t27d+5HjOCh2kbGNZ8/Bnnf3t5apVJx1wFSDA+HQw/kZ9xqhTo8PPRc9piTYXwwYdUQ0d9I91JnP0XHIi3j2c3NTatWq/4dGk4VLpTh5Z2d5xbAUR69U61wnqVEhVId67o0OhYFC3Gcn1NnChhGYK51q2ARBTwAJM9+TVcoXd88Wv9cLWS0WqNN1nZQFKT4odly2k398Rldv1Vrpnw3JUxSv4JN3E4B5ykrotal2n+skbEoeFRtu1p8mC++p08KLrEGTKdTp4WpeTMzB4YIurjncLMzYJm0uL1ez2m/gneUSIB35oZ1v729tV6v55Z4ftQyUq1Wnc6r0kPnTi3cKphScMslRkUtUbqvsUQhTKiVQ3kd/YxuXipM6B0pqtFnfPANXMCYK97Vy/5oR90k6RuKMuaVPQCvxuqdwi/PoVsqyFD3aDTyS/rAGKSB53wQ+4jrneK+dcoXX7W6CiRrZ+gcnc8j9FEjtE5bUfCIwkVev1fVueyZPEAciVsEAHy2ziKlCFzq+2VCltniTa559awjAC0DH3lAJ/6tAklqDlN7Y1VZJpzoPtT68DFUDRFBwBAhDtfV1ZVNp1P74x//aH/5y1/M7BHAYcngEjYAXKHwlEKWmAaCq+knAJ57D8j+QRpWDXqbzWZ+ZwKuUOVy2Xq9nmv2zZ4YULFYtOFw6LeCw0iur69te3vb74NAWCL4m0Bu4giur6/dulGv1/02bbRGCEmAc9UWXVxc+FyTRQuhpNPpWLlcdmFqY2PDRqORZ23Sm0ExZyMEmZm12237h3/4B3v37p2nemS91MK0tbVlL1++tHa77e5YXJREqtzb21sPbGMdsdiYPbpkEcRPikPWlX1Tq9Vsb2/Prq+vXaiEIcec5spII51b53ylFCVRKCHrx/39vdXr9QX3Ir3fgve+pqbc7AnYRmCnYBp+wHyYfRq0C2hYZm1YVSJfUI3eOuNWwUhdA1LP8HeelSQFfPW5r1miEEtRoMe+XLdQl1pb4nieA0DiHKTm9rlzo0obpfv0FYFCQarujxhbocAMJRQulbPZ7JPEAPq8utToHCroVGFDlREqFGswNHEQKgjRd93bvKeWcngSe1ktK3yuGZOwwFIPAkiWZZ5+nffJhlUsFl25FfcOY2JOdO+nzneWZZ9kRWJ83AlEv9QqgYKQfaACUkxMkBJoFTtGawXjR9jRNcfFMQrccc/zg/BYLpfd/Rp+FGNg9CysQwf1HNIHPAVqtZrPKS5zxFfA90hIohaidfHYZwkW62iQ8jRty8oyAB+BZ94zZulUpvpbidi6/Um1v4wYRsaZkjaj0KGfxb6nwEPsTyTmEUTH+clrN3W4VdjT9lRYTM2bzp1+HjUv68xBat0VlMSi70Wpnz4DIgHTAOqPHz/6LdFXV1dWKBQ8FSwE9fLy0g4PDx34KtFGwKA0Gg377rvv7P/+3//rRHVvb8+JO4SJoGUz++TyI7IwHRwceJvb29seh4GmvVwu29XVle3u7lqWZXZxceFxI6SsxfKAqfjVq1eeDanVatnW1pZ9/PjRM0/hc4zmC6aGGdXs8RI4TOQfP350LT/ar729PWu32zYajez4+NiZWaPRcAYHEzF7tPSUSiU7OTnx7Es8O5lM7H//7/9thULB6vW6ry053RHGWq3WgrCHa9LR0ZHHXdTrdX+HOW40Gm4p4VkYJ4yxWq1ap9Oxra0tu729tZ9++sl2d3ft3bt3Pvf4DqPx0iwwq4T5FO1c5zP2HQwLS1C/37fhcOipkwlkhzZ8DmiPBVqh7gCMC6sQTBpAq+dEGbhmUnlO4GCqT7QDmEOwzxt3pOnrAPBIw1IuQTrWKER9zULf45wpoKWPnyNYArjMFrXznOlll7/pnkCxoyA6r++UqCzTz6IQyVj1rKlSRPsftcz0C222BknjFhnjpugXz6tgoXVrytY4r4xDYxAosW+0xbhUWYB2XYE3dBylGlpzzpoKI5zZzc3NBQsHvIPgbOZle3vbrSN5tE0tA2pV0P3DeeA+C01wwnrhwgOPJNCay2BTd+qsC4p1T0F7UphRXRwVW+l+UKGVOaAv7CMyiGXZYzKAbrfr2Qp1HMzNumdVhSgV+Le3t61er/uakVmSjGP1et1ub2/t+vraU75zQe7fxWKxzsJEcJoi2lHLFj/XyV/FaGNJAfznbKg8JqP90t+pDRc1VPG39idvPOvOtRLLFBjXdlbNXwqw6LsRAOhh0rr1b527KNDod3Gdl5U4h6qxSZWoteJvNE2aSWM4HNr29ra9ffvWLi4unAmYPWq6T09PFwgpt0pDtJWwj0YjKxaLVqvVbDgc2vn5+UKQGmn50JpnWebagtns0d3nxYsXdnV1Zb1ezw4ODuzu7s4+fvxo1WrVhQpiKEhBO5k8psUtl8uuyZ/P556NamNjw25ubjyd6tbWlp2enlqWZQ48Cah7+fKlX5aHS5MG/Y1GI3cf+vDhg2vwEE4UTKP92Nvbs/l8boPBwMrlspthC4WCByC22227ubnxGAi9XRzGhoUEa8Rs9uhSVS6XXRjD3EvmplarZePx2G5ubha0igD/QqFgrVbLwfjNzY2NRiOr1+vuAofQYmb+HHuADFLsKRg/QE73X96ZS9G8VTQjnlX2F4webRhB65ubm+4yhj/vl5Zoutdx5lkvKGphTo0NMLVMu7nq3RTYiQWQE2nWqqLPKz0iBaf+mH2aBeZrlZhZJxalg7pOEfwwD+uUaBGIFoY4N+oGBwAG4AKE0NBrH9QKpv0EtOv7utbqZsT76opi9qk7sQq/nKmYWlQBbtxnquXVeyYojA9aAg/VoHG1rKhyD7qr9CvLMs9YyDmBb+G2Y/YkmEDL6bumuU3RJKyyCFRY9pk3BBXWEwVRDJiHH0CHFPDSPkIZfv9RSafzi7IL/hEtG88t4AJ+lI7RRsrSp2cdF+hltCOeGaxKCEtY379GUewWz7/Oo8agaJIC9jtWr3XKF7tCpRgfRQnKKq1yrCOC03WECrPlt30vE3a0v/F5JWRRgIjfR+Eo1pX6bNkhWEfwiBkzlmlClUDFz1P90PFo3fq3SsSpPq/aG6m1SgUrpcDVMmEqvhu/V79rxnN7e+vZfAqFgmcGUs3Q69evPQYDoot/ZaFQcOsAd1qQlhSzI6Xb7XpwNOBfNUVmT64ghcLjLdrT6dQajYa7PGH2nc8fL9tjnPhN6oV7CDEAXbRG33777UIsgwYEXl1dWblcdqEFzf3m5qZbH4ghwd1pY2PDGo2G3x9RLD6mt6tWqy4YIER8+PDB54A7OC4uLtwKwN0ZxLCoFouMTMTHjMdjOzo6ssFg4FofXKqw5rCO7IV6vb6wPwi4JhsLMRm0j/UGAqxZrtgDWKx2dna8nel0umBOVmClv/P2Lr/zFBQ6BoCFMkWE18Fg4CZ7BD69R+VLSiq7kNmi1k4/08/z5iEqmpbR97yi7yn4zQP2ETTk0bXIKyIQjZmJ6Heq7s8pKTqrAFefWUbf6aPS5Of0S/ed0tTY1xjnwmdoedUfHb6gc0X/1FKiAia0Mu4TgLfOifrfQ7fVRSZPCabvA7DhFVj/EAjMFl2PaVN5ngpxqnyAH+h4dNwolHT8JAJBGYbLVqrwLm6R9FXHDo2AXiMoaMAvFg3GqXEeul58T5say4BCTYUi6DlWcfrH3KIUY57XwVI631EZmTonUVClfei+ZqlSOqvurgijqqTQuphvtX6hoFpmsUt5nSwrjEX5hvadvYX7ta4d2EEVaqvK3zXGwmzxkPN/HiiMn+cRxajR+5K+rRICUoRFJzdaJyIBWtbfPAC+7vOpeVWwr+1HBreq7lUl1qebPY4jb45TnykQ0wMdQVXeOFJlGQDTegHjMEgIxGg0cg0QFg7AJAQOIKoaIQ5loVDwexCYI3KGZ1lmjUbDL+CDwe7s7NhgMPA82zyLjySCAcSBS+YI9sZkr4CZm6LRwKPBvrq6ckBcrVY9nkTvW0AbMxqNrNvtel9qtZrV63W/O4M9eXNz42Z8hK1Xr16ZmXnAoNmjlpt7JgC6aJ34DMGBQEncq3B7gvBhqlVGpXeLEFsBWCE9MIHfpVJpwae/WCx6kDgCpgoGmmEKszX9T9E4mAnMM48u5n2mwr3WnXeOFCAqoNE5wJ8bX+ovKQpSUiUPyCvggpkp8Izgcl1rhT6feifFJCMwT9UT69D6ea5QKCSBpFpEYOjPFS7yxgQIiuA8JXDE+hT4RsHqSwvnRbPwqOZf50Z5KGNTOsZZ1+cjH0vVA13Wy+/MbCF4Gw210v+Uuw6fK61O4RwzW3g+b15VqAFIK+hUUMrz1WrV+xTdadWtK29v8T1zQXvUB9iFR6DU4TmUERqnogV6iyKmVCotPAv/UjcuXE3VGq33dGAFoS86vnXOEHsHSwh8ES8C+oXybTAYuNVX6aPS1FT2L+Zf96GuEX3XNL3wE+I1yeSVWrcolD8Huy2bp16vZ51O5xMFAG6zz0l7+2xXqKhxSIHIvBLBZwTQqTqWgW8lPlFISfU7xbxjO6tAcTTx6t+r/k8B+VXPRKFq2f/8joufWjf9jnGlmGmqqBYmJQTq+FPzEJmwPqfjgUHHvqfaWkdTof3nM4goRGU+f/RtJe0ot1+jNcEncTwe2/HxsftE7uzs+C3POkf0i3S0MEUIAzEP+L0D2CFEZraQWrVWq3k2Dr47Pj52rRwEEyBu9siY0ewD6nd3d+34+Nh+/vln6/f7VqlUXBPGXpjP53Z4eGjj8djOzs4WGMloNLJqtep+twDvLMv8bo1CoWCdTsf6/b5tb2/bb7/95taZLHu0htRqNddUETANw9abTc0eA5J7vZ67T6nlAberk5MTGw6H1mw2fX13dnbs+vraLSNq5Wm32y4oEkxP2kXWe3t7203BaPAqlYrd3NwspOOlML8QYlzLWPcUw9D9naJleXRXP4t1qZJBmbq65xAXpK4In1uWKRLic3yvwg6fqetBnkVzVb3xszx6lCqAcK0jT4vPdzGWIs9iHgWRSM9TfVkmDCjd1LqVVrLnnkMnlYesmv84pxFk84zuXdVWR5qvYEmVS9o/PQ95IFz7kOofwg7Zi1jzFLZRjS3txDPDPPAsPwDj2A/aMntKpGC2aElXoUu14GQkwkLMLdKcZz7PK0oXtB8pwU+tSWqRgW6nwCY8C4so/dZzEttUxYIGW1NQ4ql7jronMU/Q7oil4O38cGb0Gc4yAs18Pv9E8IC3q5cBghhzo0KK3orOvOIZQB1Y8KvVqtVqNQ/m1r7rvK1zllcV1o79hFUbNznmsVwuL1im1imfdfM2g8rTgqeAq9lyTbMSCj2EeWByVVEh5rklj0Fpv5YJUsu+j4A8PhP/ZiEhsJRVrkLLBCTWLprmlhUl/qkxp+rUEucuJVTo3KT6kxJSUmNN9ZkStQ6AfXwc0bpzsPk8yx5Ttb548cL9UolHKBaLHjCNCZr+wHw6nY49PDz4jdPc7UAWCCWGZGgAXG9tbVm323WrCMyrXq/bdDq1s7Mz29ra8hSvCB4Q2Sx7zOBxf39vnU7HhYubmxvr9/ve13q9bldXVwvz2m63XVjRNLOkM2V+Njc3rdVqeaYk0hxiMUBAIGtTuVz2oOsXL17YxsaGdbtde3h4sEqlYh8/fjSzp9Sp/X7fer2eE27WjIsG6TPPDIdDt1pMp1MXnMxswbrz5s0bd8fCOmFmHrS2s7Nj3W7XM3YhsHW7XbeWwMzRIqpGjX6pywdjUAC4SqhfJkQvYzIKnlTLpz7seRr95xYYcNTSp4q2qXRAyzLLQXS5QVCP44AGaOaeZWPVevQz/Z1657klTyDRouAv0nbAVIrXcub13WUCDJ+rK5D2EUFg1Vh4VgErRfeZ8jIVftU9ie8ir1CrH0WtLDo3qT6qNl9pNfuJ/xUcIhgocIyFsQGoURblCaTaL8aq65USipQ3ar2a6hUeUSg8uWatalfpB/xKv0eAwXKP4B2tPVr0TgTcf9VKgYKJ/kE7iIeB/6EpV4EDazpj1SBnFHCz2dOdEpE2sI/AmuqWxf+8H/cac6IZptgjfK5p28fj8UJ6cvbKdDr1rE/Q5XK5bPv7++52zJzkWSY+F99q2dzctEql4u1SLwpTsiDC51ZZpSlfnBUqpS3T58zSTHIZmFaikwLGn8sA13kv9kUJW14/1hE0Ut/pOJe9kwIfcZ4i44htKTHKEwxS49HvU/3k87x3+B1Ng3Gs8ZDAYJSAxnlcJkil+hnHEUFGsVhcyASF1aBer9v5+bkTC+IEbm9vnQDgl3h3d7cQ5EdpNBoL2uHpdOomdH7QklBwRQJw0w79v7u788BktDC0VSgU7Pz83MeIRj/LMtvb27PBYGCj0cj29/f9Xe59KJVKC0HXmi4VYohvMUHVCDhoNX777TcH4aTFnc8fb4St1+ue7u7q6sozFhEX0el0PCsT2pNWq/WJMIcpGSYzGo2sVCq5wILGSbWKzANrR79gVsR0wEx7vZ779DJ/Gkw+nz/efUGgPiZsmBtAQxl8ymVC/19Gp1Z9T590r6tGFmEQQMvnyuQ/t6ggpX2J5xWgugzkK9jVelL0g6ICh55zBaNKJ/JoEfshr0ReoEAwxSe0XQXSPBfrjf1MgdPUWPgbf30d+6oS6eJzi85FrE/7pWMkJkvHqbwgtVYpfABAVMthSiDVbD2AwthPPtf/OTMofPQuBAXeFBUyzBZvk4/ANq6P9is1x/yOKWz1HCnd0bSnfGdmC2Ba1yb2S/m7arH1vWjJgL+pcIFQpmtIOzpWjTVB0ErFbhHcres5m8089mM2mzloV2GBfZeid7r36GseTVSLF3/D7/TuB72IUAUV+M3Dw4Nbvc3M+4WlI75HP5+DffIK849gSOwi2SGj0L2uUGH2lWIsUkQ6TkIe4M4Do88pquVQQKrtLPs7Eub4s0qoyCvLmNcyISDvu2WAOtW2PhPbXPbOqg2aJ+g8pygTUfOl2WL2jwhWUntMGWLKihaf17pi2wgO+OcfHR3ZycmJp4AFROIiA7Pp9XpWKpVse3vber2eMyAIHO5CELbf//73trGxYR8/frRisWjVatXdrehDo9GwXq/nggoZOSBYZo/Bx1gduKyt3+/bYDCwarXq89Jut61cLnugOWZlLnPDjxLgbPZoAm02m27ZIEsWtzoTPK5aejNbyAhC39GM4Gr1yy+/2GQysWazaefn5+721Ov1/AJA5m8ymdjl5aXvmVqtZtPp40V4WJmwLpiZBxXOZjPrdrv+3v7+vu3s7NhwOPTn1FKEcAhQmM1m7l9cr9c9voU5nE6nCyl+dS/N53O/NVxN6BDzVWdtlcIm77tlIB3moBcifg69XVYUGKFdZP4VtOnZX6eo68O6fYjabQUyKbpDWUdwUwEG5gywVTeSuP4RSKV4DM+py0eke1qXAnZ11ficov3JUwTFovOtNFUtFxprgLBrtuhZwFmP7jLUT19SVp511kzHQx+hWzE9KcCPjHuDwcDj4sigBI1jLIwRGg89VmCuAbB6Md8q4U/3f8oiiAUAq/VkMvEsfBHsYq3UvaUJO1hLxqkxAZwX1lpT2qJUwa0GBQ77QLNk8b7Wx1zpmqW09aoYQcgwM1eGadyGrjcuXVmWfRIvoKmwY3C59kcLfWUNmWPonhbwAvwQIRd63Ov1nA/jjkR8YaPRsEaj4XdzULdaGFN0YlVhT+olsfQ1KkafW75YsPjcsgz45hEzZRBKjPR3/DvVXkpA0M/zBIJV9cTvlFmk6lgH7Ou4V5VUfSkwnXqPZ9cFLFFjto6AwxzFQ5c3b6rl0fqjhidqN6PgpYxan48aNLQLSOyAfQAmAc+42kCw0YQQBAyTor1Op+M5tiHYm5ubfpjv7+/9Mrlms2mj0cgGg4HHL6gpHmEL4s2NzsVi0ftPJqNyuWw3NzcO6pl3CCDEEzMu75LKEBeuRqPhLkPqRoCZl7zYw+HQ4xTK5bJ1u90Fc3i1WnXwzwVuEFRdo+l0as1m0y0OpLudzWZWqVRcU0WqX9Ipop3r9/veB1IR8t3Dw4MdHx/bYDCwi4sLB3I8Y/Z4f0ax+HRxFQAAjRjgwczcHQ0m8PDw4EIopmxM+VmWLbgnpM7m5wjsem5TZziCKfoftbVfqygQ1D6o9nPZuyng/bl9eG4d0ZqQouv85tyjtWR+9Tfj1vWJGsY8MB/BsPZRS8ryQ5ufM3cKxMyeAn2VNsc5o08apLyMF1EP9CECGQXOqsGPAqmeFwVasQ9RW84aAQKjAEqfAHjQVp6nH9xrw7lS0BeFFYCc9m0+f9KKL7MY6l7RGA79TnnddDp1K6r2IyUwRoFN5033Nj9KqxkzPIR5xKKNBZ91UT7MHpvP5wvxFBE7qTDEukQBXMcD7eYdxoSSj3dS861zwZoC/lkveAJ8MM/1TgUj5lLTQdNf+Cgp0HHDxp047oFY1PqThzm1MI/wf/AB7XFvyTqWzryytmAR3VJiYaOkAOgqRhKFivheSuBQgkFZJWFFRhEPVkrYyKsnvhffiVaO2Hd9noOWJ3Aoc1Lil1oLZeB5/Y4lJSAsm/t1S9QQaR3RYqFzlGJIOiYVPCgpjYe+lwJSmBwB6+Px2LNYAFi17zc3N65V4PObmxurVCqejpS+aKA0BfMtGm/WvVwuW6fTsfl87ulAzWwhDqNQKCxk0QDQkPdaM0VBeLGm8BtGOpvNHNjTl2azaRsbG3ZxcWG7u7tOULEwIEhkWWYvX770wO3ffvvNer2ea6ZgPGr+R9OvKWB5jmDpjx8/egaOwWDghP3g4MAKhccAaPoM44cAYsHhedUgcZdHp9NxYE/wvfrD4obG5Ye4uiEUIfihqcTawX5lzAR3ExujGUh4X4MeUwAs7uNVJU8YAVyrtjzVjlpSvmZRoAOThdGqW4o+r64PqoWLVpB1LBdmi8AkJXCl+sy5VyFh1Xv0VxUAKVoW+6WAlPaUxit40nfjHNAnPte7ED638G4UnNade4qej7gPIiDnOQWGWIPiWKhH3Tk4U7G+2J+oOde2IiDUQp+hO9Axs/S+0PaVl0wmE49Z0KDkvKLnQgPDtZ+0lbdGagWLggJzQr3UCa9Dqz4ajTzLE3cZ6UV+8BpckiaTiVs+VIGkFhP2vFq3IkCmD1jTyaCkAglzhGswijKzxexfq2gre09TwGqcxGw288t089zWdJ11vRi/utLOZjNXknU6HavVavbmzRs7OjryFOwIcTonuv85A2ZPd6Tk0SnGg9fD/v6+HR0dOcZk/nu93tJ5WlbWFiz0kC3T5JgtaktWgVmtP08oSWlrlGiniE4sqf5Qv5pwYz8i6M0TKvKEFf07EiploCntpWr4IAAqCS/zxYyasdi/KOHq3K6zflpX/Fv7oOPOm7/Ud7FfCoC0jdTYljFU6tJ1heERqEtpt9sOVOfzuQewVSoVv73a7FEAQMIHYJMBg7VVoJFlmWcK2t/fX+gfhHM+nzvQRWMynz/GP1xeXjoRJT3dfP6U8pS9wuV1aNX29vas0+kspEucz+eeChcBYXd3192w7u/vrd1u22w28yDyX3/91f2ju92uu43t7e3Z8fGxZ2ziNvDNzU1rNpueOYt4EZgF81MsFj0DF5fk9Xo9q1QqfpeECiyMEaK7vb1tHz9+tEKh4P03Mw/iZjxm5poh3IE0JSLCFEH2KqQNh0O/uEgtP1n2dEEVMSrD4dDXjWfxYaUwbt2fcb/qfs/b09QVlQNZ9uSWgatCBEOrFDJfUrT/2maedlbXN0XDltGjWKdqltcdY6SBee9FugY4VkEzKlbi+1GgiP3UvqTaT/U9KlCeI6DmlXW0oKnvUxhBf6Jlx+zTNOaAvJTFOQrFcZ7VuqrPRU1zdFNTHKAKCpQruOKgeIkWcV1XpfkqtOq8MjfRdU6/oz9RaNLCOHTf0z6W+Limum7LrBnUjzCmwcuaNQkFl7oqKf/S88w86fql9lLcM7wbBTZdd+YmWnVY+1hU0NWsSPQ5KkLVbTmFNeDf9It5QJnGGqtCR8cZheU8eqR7jzlEEGefpHA184DlAt5FhqgvdZP9Kq5QkZHlEb1VdawiXKlnWAT9P/YpVZYRPLP0Dd7rChPxoOa1rc9F0Jw3ntT30ZqhY4sa/FivChfL2ohMQpmBHjg9/KlxpAS3SMz0O/rI9xyKZfssJaSlntN55xI5bikuFAp2cHDgeZ3JQFQqlWwwGPgFbdfX167BQMNh9khwANL7+/sOVre3t117zl0VBAbzntmTH6kGHqOZr9frNhgMPN7h5OTEfVy5OTzLMms2mwuWETTzs9nMtfZZ9niZHi5ZqgGBAGqGLLTyaj1pNpueivX6+toZ7vb2tmtcuCiwWCx6vQSqocEZj8fuNkY2qslkYqenp67hYR4A+KwDgh0BdPijwvh0jrGYROaHf+vBwYELTWZm33zzjZ2dnbmLGNYlLFRYeMi/Tt1YKygoAxDK0KClaFbe+XluQbDY2dnxGCDGzPfLXDC+RlFao1r4PCtJSpiI7jIpZqkMWIHd36OoMIcCgfbZA9r3FD9RN6DUmOLz6zB6zpUCl+fw40g/FRitKssEGnUrYTypkmclYH5Vc68AcjabLVzmBm3RQGt+VFEFPeIsAy51HNytAN3p9XpOP1lnTZAAbQR0QofAKmqxZFzQIJ1LHX+0QqSUZ1EhqO5DqoRUC0XqvKjABZ9UxYjyBtrCHRXFCbQYVzIF4IxZ21EwnEcTNG5xPp+7qxV7C9rKM7yHsMD8qfJN51fXLcbxqHCIVYjYm7gvzRaFHYQxaIWOZXd3192PGP/29rYVCgW3BGmci/IttUZrH1U4TdFB1mdra8t6vZ71ej1rt9tWqVSs1Wp55krOzjLrR175qjEWzwHzPK9MNBLBdYUEs7QgsKxNvkuZ3PKECiWyKbAdJWt9NhYOrPY/HjzqjAQjChOR6aQAyrI5jMAiNQf6HfXF9Us9F+dG/9a5j/Okc6Hj4/P4W+dsVaEuiD3ZF6ijVCq5oJFlmX+/ufl42zSH/PXr11YoFNwKgJ9plmULQgaa+729vYXbmLEOAKA5yNPp010PMFU0CdwXMZk8XgjX6/VsNptZrVazQuEx9qPdbtvu7q71+323oCjxUWAH4KbN3d1dq9frVq1W7fLy0m9ZBQBrJqbDw0O7vLy009NTd/9h7K1WyyaTyUK6Wk17amYLvquYy/V81mo1297etvl8bp1OZ2ENibXY3d21+fwpkxVCHzeJa+509YvFxWw6nfocAEyYJ7J1qNsUhFqD/ViP6KOszE2Zb0r4Te3RlIJgGQ2M2nb+3t7etnK57PnRb25uFlzmnuva8pySUq4o2M6jMwqmVHOYCoykMK/RQqr7fxltW6couDB7iimI39OOApRI71SpEtvQ/kZgoCBH95GCNEBhytVOaUHeGKM2Nb6ft2/03ZSmN45V+6L7UQWklFAZ66ZARwBcKkTob10b5QdmT+lbocFq4VVttgZjQ9NQ0KBU4MxH8EdR5Rl15s1t5OXs6+jeo3PPOdd9q4BU58fsiXbN508ad735mnaglfQzek8oP9D1YYyp+nA7VbDMuKEH+hnzpG5GuAHqftCYNp7RDIzUzRrrmCJ4jzhsNlu8M0axoe53dU9SulYqlfxHb3HHVY6AfA3y18QHka6l8GgsSr+YD1y0oZdY6YgzZd+vK2B8drpZ7bx+9hyh4jnPf05ZVncEtssAcupHv+PvuPGXMQ4VCCJDNFvMcKR/x029iknEkgIsSuwUxK9iwCmhRr/L0xhq/fEgxue0b2pdoV4OdhSO1pWyWTeAJAcaX1Ke2d7edp9RAtIGg4EDXj10ECwIEn6mXBZHBg6IsaYm1TkB6GdZ5iln0czx3u3t7YL2i4vfarWazedzv78CgK1pCnGTUmKaZY/Zkbrdrtc9mz36Hu/t7blloFKpeCapUqnkDBaBB3O4Cr/MDRocPQek3aM/9Xrdrq+v/UI8BAzcpHSuCBoHVGF1wC/WzBZ8c9Xvl+8QbngfEGFmdn5+vnDe0IjR/wgG0Dzq+JlDiLdq9aIbQOpcRTob97C+qwWBrlwuW6PRsL29Pb9ZXc9Jnk/5lxQFBLFu9kuekECfmEPVoDLn+mxeUWY8nz/lyU8pPtYtKWAfaagKRsondEyxXRWeIk/QeYoAg8/Mnlw9oAdReGM/5FnIeSaCuzhX9Ceun7pkpIRDHTPjVVBLfxGIAcdRGKX+mAITWq6Cf+TtCkr1M72TAcCFooR01ggMyt9VC21m/jx9U2UKbfGeunnxriqlomCk70OzmHedA+WTJMHIsix5ozP104YKTqwdbjKMhX2mcwtvQjAslUrOj1QIwOKtY8Lv3+xJONQ9rPQv0sVIZ2ifPRSFrvn8UZkY36Mu3f8qqLNm+kz8iWc+YiDonvJhLsaDpxOrgutvsVh0d96oJGTeU2dB5yhVWHfiX5gr6O3Ozo4rLFNjWVa+yGKhG/25gkCKuOtn+nceOM0TBJ7zP5+lmGqeUJH60c0ftTSxbgVVkWgwtih4pdqE8aQIhY4hzqt+nmKQbCzGkpqTdeZU5yUS9ijUaTv6vx4i+qV9V4AXx5zqj45T50s1NdwPQeAvn6u518w8LRzEUxkqfvgQUg4uqWxJVdvr9bx9ZQ4QNLRnEELcfhS80h/mGmYD4yLwbmdnx122JpOJVSoVe/XqlX348MGur6+tWq3adDr1+BGI58bGxsJN11n2GHAOI8C8XywWbTAY+K2iw+FwQdtMLAeuAAQvbm9v2+3trWd+ms/n7lY0mUzs5ubGZrOn26wh3pjZFeRUq9UF0AnTUMCFBUXPLARWfaiZQyxb+h6uT2rp0f3Ku6wldEAZpp6zvLJMeH8OzSXzR6PRsGazuRAImNL8fu0SQSTALdIGBaa8l3oXd4ZIe2NJ0bdY8sa/yqKizDZFv1LChv7gusH51/lIgXBtB1CnShf6FcetAC0KsXlzlpqrqAjSelJBsfGuBB1LSqnEOVYtrP6OnykgpCCsA/ahq9AZnlEBK7pMReEu7j8F/gpA9VmsJqoxp6/0TwOlU3xQcUEePtHsUNSDwgk6Rl8jTY880OzpxmylgXyve0nnR5/Rfa+B8CiCyDqIIkkvglN3MZ3vuGcivmJstEWGvrwEBhGb6PwrH46K29R8aZ3RXU3HoAIZ74InyF44HA7dkgLYj0qBVNu0r7/XKQhetVptwS0ZXsyltChUn1P3ZwsWq7Q+qYk3+5QApurLA4nrCBjLBI74Oc/qdxEIR2aQEiioP36vzDtvUVKBm3qAOWSx3Ti2vBKZm2q2YrsK2PVZHaN+lrdeKUEiMpN4mFPvQqh0HKpZSc3ZOptf50C1YWip8eevVCrW6/UWbtJEewPAB2TWajXr9Xr+DMFqEAdckmgL9yLajCAT4HVxceGERuMazMw1evP53O/IoJ7xeOzfExdRKDzeDn11dWXF4uPdGzBJNCaYROkjYzs6OjIz88Bxbraez+eeShYLASbefr+/QGjpE6bV7e1tK5VKPlZM6/iukt0DSwbrgPUHE/FwOLSHhwe/84PbWrmFmzo4UxD50Wjk91AwVsAH4ED3FmtLHewfYmH0Ai0YKwSZddH0gc8FelpW0bx4VnFNIB4GjRjfq4vC36NwfhVkxfYAaMojlAZEHsJ3KdCldGEZ/6CoNnJZURCsGt2ouWe91Sdc+8Bc4P63zAUmtqt0UseJ4Kr1o0WN85HaU6uKand1zhWU6Fyn3LCUF8T50yBqBaPPsaapFUH5mbpXqRChf0cAyuckZKjVah4fxdnR+xAYK4A5nkHGiVChqWzhQ2oZUIFF54C+AtRVgKBuhBfdb9Snwk4suAmNRiMzM08IomtMPXHO6J8KiGjSGWev17PBYGAPDw9WqVQ8zanWrf8rDmO+GB/0Qe8hUYvPqtgx6me/RYGFz1PCSdxzKeFXsQr8S62MeAwgAOEtcXd353GN+v3XLlmWeR8ajYZn3er3+3Zzc2NXV1d2fX294Eq3bnlWulmKgj2z5aYWvl9XOFj2zjoMYlVZBsqj1ikKEKnf8VnVZFGnMoE4FhiFauJ1/KoBUNC9DEjEwvvUlfo+738Ohmp+tM74Th7jinOnGkvmQZ9L9UstAkp4okCybC7yCkIAmZ+KxaLd3t4uXIYG8EWzAGEkgAtiR0rTra0tJ9AwtPl87oRTLQMUNC7RTAxh5i4I+kKbjUbDzMw6nY5Vq1Xr9/tOKAA3o9HI3r17565Mk8nENRLlcnnBvYK0qmZPF+xRDg8P7e7uztrtthM/dfPZ2tqydrvt5nAEHNLvwtyUEe3s7Lh/qWbZQkjIsqdMWgrCEIQgkuPx2IUas0cmrBlRuH+EenARQ5jCClOv1/2iQyw1WI4ouH3NZo8X8SH04EJGQB7ngWBzPe95yg7dl6mSooXL6CVz2Wg03NWNcaEE+XswLy2RLtJH1VCmFDQ8n2LgefxENarLNH3ah1S2GNoBrCoYVjCHT766Ienz8T2AJi4htLGqjzo+1ZLrWdILwhSc6jhVwKPdqCGPYJ7vVeEVfyswS/EB7bsqVmgzzg20nP7q/lhG49nztAWNUm+B6DmwbO75TcY8lDeRHul+VWWV7o8oZJjZQmwXYFxdeqLgpm4/iiFU0MFqo7FtWMjyCnPFMxroq0KP7iH6oy5gtKfxAAjS8BU9J9o+zzKnKlTp+LBWR0Woumqt2iNqKWPfRmsVZzf2TffhKuFD69JxnZ6eOn/qdrvWbrd9bqvVqu3t7fneXadoXyImXTYH8/njvVDX19fWbrc9aLzVarkFg7jFdcragoUyPDXl5zW0juZH/049v4xxRICtoDdVv5aUAJH6PyVU8H78jp/ot8lnqm1Qxq/1pjam1hm1m2qqoy19Rol9rF9BB4dDmTtFTZ8qXKiwkidkpeaXz3hPNWBx7qKAo/Ok8x+ZYRQ4eIa51/FSAPq4Dc3nc08XCuiCSZG5iAwYx8fH9uHDhwUmM5/P3SRrZq59RzOgBFK1W3FNAYSFwmN2JtyHAMFowTudjltQYATEKSDsYKWo1Wret1qt5syPW1uPjo68D2SK4p35/PE+D7JLURAsut2uXV5eLmhx0fYNBgNP3wuA1zstuDdid3fXqtWqM27NR846Y2Wh7clk4ndQIETBuLUNBCjWSFPGslaTycT6/b7XhXCC5l/3Fa5SZuZzrK5x7An1k6VOPYdadG+mzk4UJuJZ0b8RZPnNxYlY49gHf09rhfYFEKQgTJlypJf62brm+GXKjbznOdspvqHAQ+8OUKFB6Qq0KmXZ4H0+V7qroCXSUAqgB3Bn9gQg6St1R4FC22BPaIntRyGXNVKAFQE/RfliXBfVdOu5BoADGJl3dWlRL4CUKx3f8ROFCp2ryO9SOCDyCoJas+zRugsdi/1iDXgGCy2gXWMNdE4UM8Bv8/z4lV/q+qqmPcsyB/PRFSdVNjY2nE7pfKhgkodTHh4ePGEI1mjGi9KFGDo+Q5BkPdhPtME8Qavhm3quNPlJFGh0LeM+VFoTLYU615xvBKPU2YlnQduisF+hIyj+rq+vF87dzs6OJ1EhxmHZmun+1P2CILOs6H5DgCBrZbVadQzR7XZtMBjkxnHE8lmuUEpAlPikNEMpYg7QW8YkVtWRav+5ZR0pLgoOqslRUJ0iSnyvki2ba5kr0jr9XvasrkNksHG9Yl15zyqTVevKMk1Pqs86JzrHyiRSFgudPzQRqmFICTJxfaN2ju8xs5o9MbFKpWKdTsf29/et3W67Nh5Cs7m56ZaLcrlsrVbLhYtUgdhdXFx40HO9Xl8Q2hAUptOpxx2wVwqFgnW7XcuyzDNLoeWHEMTUtOfn5w5sS6WSMw3cs/r9vlsi0PZvbm7azc2NM8P5/DGu4+Liwl2FACZkqEIIQ7u/s7OzIFQh/Jg9ggesGXxOnAhB4Ny/oeuPhQUNL65MCvRZl62tLe87liWED/pDRiisUmZP4AAhBKvJbPYY38GYGCfMbDZbvIkV7ZZeokd8Q555/jl0bNWzkRbFc8rcw+A4f7p/vkZRrXBKeRDdnpTORhqc5yK0qn2tI2X1SL1DSVkZzJ5AD2uu1jf2KG1EX/SoZFILhypZtM+6b9UFBeFVQQ19YCxKN1Uby/f8r5aHdeY6ro9qz+MPfVdFmvJEABvPcVYVXKeEtOjuY/ZpMgLq56wzB7iAcDldtOCgfYemALZHo5Hd3Nx4tru4r9R1BvdDjZNDmI8X0bEX6I/edaBrrHuaPqL8ihaSlAIjT+COgnDkYwhJhULB5y0CXgWpSjs5I7GgtKIwB1xux16M3gycCZ07pSPML59HYVszEOq7Go+ilr7YbhRM4QEoaOgbfCrS/BT92d7etlarZc1m01qtlu3v7y/EWKwSLlAm6hqvgycZ+8bGhtVqNTMzK5fLrswjHe1oNPLzsE75aulmPxfgp8BrrOtLhAdKSguUp+2IFokUU4rMmw0QD2keUDb7NA83ADkF+GOfte9KQHTOlv2tv2lHtf/6XRwv5keeicQqJWhF4KAmzijEqeVBha7UQacu9TuNbcd+RC0VwW5mTwFV3W7XA6yZG0yWvD8cDm1vb8+m06lbBiAyZk/aONYYQoNGW4nufD531ylALSZlxs19GOpfipaGPtK/0WhkzWbTBoOBBxICorlzYmNjwyqVijNSxgUD3th4vNk7unMxFmWAo9HIiaqaexFYbm5unGCREx53AtyL1DqEhYNnbm9vFwSVQqFgg8HA0+EhuGl+ddXawhDK5bLvX10r1dqzJ6hzMpl4MGS5XPb9tLGx4cKYnlX2Jq5GnOtms7mgmf8cuqbnNfWuChKqADJ7clfQe0jIlqUg52sWFWZ0jlS7p3SAd1JAXOvTsmoOlRbHOiJPiHRRNejaFn1U7a26xjDGuGd5XkEJ5525oA0F1Dp+BZcppZDS2AiYo9VaxxBp/ypQou0o4Nc11fr4nVK4QRuZIx2LKvJSrmjKtxCiOHe6Hgh9KCOUhgJ8+fz+/t7dSVFyUN9oNPLsfimQztprClro3O3trQ2Hw0/OGjQTmopVRIU+tVCxL3iGOdF7GHQeIyDXfRD5cXQ/4n3WFndO3Tt6ftXaMJ8/JRNRrwPaVV6mbavArUX3AnOi/VBBRPEC+0XrTSk2mCN1TVNLdnR71PazLPskxmM+f3J95hlVhKpbIArK/f19F0gjJkuVdZW7qb2qwpXeUUJGxqurK2u3254y/+8mWOQxn1XEPcUIVwkQqxivEp91+5QnYKhgkPpJCRvKCLS+qH3i88jw9XBHYmq2eHFeSiBSxpJijqvmJD6XEjpSv/k7T3jReUgJDHF+otChxEOJQGrNlCjFNdQ6orDDd6qhMnsKXgOUFgoFvyMBLXSz2bR2u+3zDjiDEGg/IPAwoSzLXIgxe7q9uVgs2u7urrvwaAYivi8Wi1apVNwsSRsKRpRB8QzPoWXSTFbz+dwDpRFumHNiSO7u7mwwGHiMAJaaWq1m/X7fNW2aihaGoVo/1gIBgvlEgIm+ucRm6FoVi8UFBtTpdBYuvFMmSfxEv9+3YvHxMkEsUSpMs+4wADJwKUihTVyisNyoWxvrzFxQL3ujUql8QgP07EZ6l0fXlgkV+n0E0AhIg8HAXRZW3SD7pSV1xumj9pmiAFy/i8A8RYvzirardSjt5m9AQnRL0XHk9Ze2Is1XLXCkdZwDfU/nRS0U2h7vKm1GUFGrRNTca115fAKe81wrEe2zx8lwg4umzndcvzi3WC7RPEdtfeTjaiWIrj+MVYN8UTYgnMzn84V5Q5FEQg4sqgRyo9BAmExhG+YfgQagTT/14jQUORrgy9yZmaf1NjMXTohnUEFAhVq1Fuo44z5nvPyOe5FxqBug8jbmTdPr6nvsJawHqsknDs3s6bzEPRzPhQqDKpxEOqNzoUonLFjM+TJlhboNsn6Mk7rYrzo/uu4o4bgIz2zR/Xk+f1TmnZ2dWb/ft4uLC3v9+rW9efPG7wL50sL5j4Km7tvxeOwp9C8vL+3s7MwuLi6s3+/bcDi04XC4EudTvjjdbB5TNFt02VGgl6qH56PGiM9jm6n2VMJNPZMSKrToRCsgjqY4/leLhI4rauJjH1K+eKpFWHfx4pzllTwmHtcv9RwECOaUEjZWCTIpoS3+H0FCCviZLabqVStNSkBRUBhBE4RyOBx6WjXMvABbnkHjD2HnLgSYV6vVcrccMi3BDGez2cL9E8pgZrPHLC6AU/oPISI1KyAZ4E3wNuZ47nXQOaP/ZCtSH2Pu4MCCUalUzMx8PtCsjUYje/v2rfuD0hZzBNMFHN3f3/v3mpMclwDWAYaEexEEWNPmkqqW//lNvVyOR6C0AmPGqxYWGA1uXuwl3Jrm87kzet2LaqExe7JCwWxwo4DhRJrAGrRaLddCcm4QlPLO5KrPGFf8XmmRajQfHh785uB+v+/ADdc7hIyvVfRcs5ZR2IkFesM5UI2/gmLej3sk0nbmR2mG+jMrX1LtoAoMaJx5LgJaDQrmnah8UkDGu1G7r/NFfzVDUB5/1XmlD8wbQE5dsrSdOPf6s0zQjPPHXJjZghCgrkx59UT+yWfQBYR+XafIoxg/64sQQV9Ua8ycQ4s1257uMxXieAaaoLRqmRZXQSaAWoULnRvmD1pOm7iK8ZzeqaHtmNknLkfQPbVIQodVYNPn6Uvcv/xkWebWWBUmqRcFG+uIwklLjIFgjvhumctopANx/+geV8UOgetKj1QxybgjPlPhi3oQXhFSNAWx9isKW7HvzClW/ZubG7+76fj4OHcelpWIrxgDY4s4l9+46l1dXS38cMv8c6zaX+wKlScUaKdXvR/BcSRY6/YjTwBJTUYEtKk2U6A4At0IlFMaFd20Kc2+goMI2JXx6SZLCUWrNmGexSG2FedQn+Fgq5mdfi9jILFEYSIy1xQw0HfUTUDXmM8icYggAp9R/DwhgGi4C4XHW6y5wRpNe6FQsOvrawcbNzc3NhqNrNfreYyEmmDNnuIXADQEQquZHc0+AHd3d9d99Jl/XK640A2mre5E5L8GzAO8syyzTqdjlUrF3bv29/d9LtCU3d7euqCytbVlFxcX7k6FD+bu7q61223b2dnx9KVm5haE2WzmggQMo9Pp2N7enu8f3Js0XmQymbglBdcjpSX39/cuTJTLZc/aZPZEuBHUzBYTDyCYweBxcUJYm06nrolU31/ct+ibmtP1LDCnxIkouNza2rI3b954Kls953ng+rn0L+99/iZ/fL/fd4uXupKk3Dq+ZlHaEZk7ReknRQF77J9+rgKM/uY51kzbinWlCntFxwCI0L3A95xxVS7pGMyetNgKiBTMKx2EnkRlCaBZ50VpjxaljYCjqGxRwLZqH2hfFEDyOXQMiwp91QvvUK5EdxX6xVkhhgBLblSAqZAGHdW5jgoobWs6ndpoNPL9SHA1dwsUi0Wr1+ver5ubGw+4JQYt7uHIY9kfkTdjPYQ+oNRAmEC5VK1WPficdcOVVGOidP+rgEtaaVX04PKyzHKFYAOPpKhVRemgnkXahadFJU8sUViIgiL16llTtzvdL3r+dS9j3YnnjLHCI0g1b/bk2mj2RIe4x0r3FfuJdWNPRyUoc57aI6xNsVi0RqNh5XI5GZeyqug+UIy67FnFQygUB4OBr73yiXXLZ2WF+pzveWbZu3l1rKPlWvb8On2LADT1fNQ0qfZEN2nUPlEgmimhQ+MrlpVlDDDveSXEqg2MgqC+E4EJkn3UnGn9+n8ETrG+lPC1at5Vo8jc6w/1pNymKMy3Br7hEjKZTPxGadUGbW5uuvuQMmnmEWCNsKF9NDOr1Wqu5VFTKIF6xDBg+sYCoP7BpEkF6BAjoaAZQG/2uEe73a77w47HY2s2m5+4dUD4ISBZljmIxkWpVqs5E5zNZnZ6evqJVon2CZzWy/Q0EwprCJjnLDEv+HHyjIIvbhHXPs7nc880EjWHaJdwt0LjqJcyRUGUrFuqpWL/KGOEWURwETWj7MHDw0P/W8Hmc2gTf69DJ/UZ4gQQLNBAaVHt2t+7KHOPNDKOS89yHmPLmw9VeKgAkqI3ERiZLWr59BkFz6oYSdF+3T/aF4RrDbKlbl3HqF1V4BgVOyneoPtYn41znWcRWjXfykN0v7PH0dLrHDF/9Et/UmBRXaoicNO+Kq1QwSwF0NQiQWC1CpEIGNPp1N1Dut2u00l1e4l4Q0GYYobIQ3XtoZGcVcavgcY6r/Hyt5TABg9RXq8uQami85jCNyhStF49L3EPRv6rZyMKN3nYRnETAgHzZGYeWE8f4DOqQOIdxqCxR/oZfEGtjNQL8Gc9EEgp+jx7VN0PeUeza2nAOEHx9Xo9eUP6uiXOecQjYB+9F2Q8Htvl5aWdn5/b5eWldTodjzHSQPl1y7MsFlHS04HkPc/3kfivo93OY55MnC5ufHaVMJLXXvyJ36Wej8QsEjn9TgULiEqsM4L+PAEg1X8F9inAb2af1M9n2t/U2mm9UcDQNvSZvH6u+j8y/Th3qfVIMfXIfObzp2Dt0Wjk2hyYBf60PMedFjAFXIJwcVFQDECFOZrZAtOifuZGA4Rns5lrhhgvN3/P53Or1+tWKpVca8Z4IZwIFDAlTaP68PBgpVJpQYuk++/u7m7BpLu9ve0WmmKx6G5eZo8EEwtMt9v1i6Ig2qVSaUFgANzDpBHeiP8oFArOvGkDQjuZTFx7iMaJPsznj1aNN2/e+ByjFYPws8+n06mPhf5gZWAuWO/oMoBm38y8jwhF7Emzxfzq1I0wStq+CADXESpSJQrry56ZzWZ+kzyXU6H9jbTruT71zy0qjEctpZ7XaNVQRr+qj8xxSgOaAgx8j2ubPq8lWqi03+wPVQykFCUR7Kpgy08E+ClXr/n8ye1On4+xGLEejcmIhedjv/IKz6qWnRJTkiroVeEVmgdN1TOb2tt6LlUwYF7Ur12twQgoFGgAl3PyWcrfnrkeDAbW7XYXrCZqbWH/MhfcOxQtaLqHmSd12WJeWTOs1goOYzIBzgpWcLVy8z3xXSmLlhZ4AOuJCzBZguA91IO1RecPTKPxIpwvFcr0vVRh7umLuoNpql7FfzGBgtLoKADBD1AGRU+DWPKEk9hnzr+uL25YxeLj/RSNRsN2dnb8hmsUZcTyLBP+lhWlfToOzsZkMvEYO7I94VZ3fX1t5+fndnNzs2CxYM6e05/PcoWKIFQPd96ipEBgXvkcZmv2JPisqj++E9tdJlREjfWqd2NbAFQFvcrgFTxr/1KLmpJM84QJrWsZc4nzlmo/ah1UoxDbZU0UbCrT1TGkBDsljrxL/QD5lPVCv9MC6OMwAQQgNoD1+fwxkHkwGDih514LtOBcRIfbDwcasyIEk1SsHHrGD6FU8IT1gQvXKApw6W+pVLL5fO6B1FdXVwsXvQGgYeb9ft99QzUwkPpU4FCgMJ1O7ejoyBm2BiZDcLDWwNhYcwUMjFuDhs3MtTSqvWHd1H+3VCrZaDRyxopGjjkkWJu1KJfL3ubDw4O7oHFfxmw2W3BT29nZ8f1B3TAK9QGmz9pP3fO4cVG+/fbbhVgPfTZqPFeVZcoafYb9dH9/b4PBwNrttrXbbet2uz6Hqomivr9X0TM+nT6ljFYtvio88uhopIMppZLZojCh9CoqK7R/UWBTBYHWpwCYPihwZp+kxhLnWy0P+k58V4UZPte9x9xAZ5WWURT4KYiK87BMKRTnN45B11OVa/pc1LQrrV8ldCv/jX76/Fb3FbUsREtUdI+jbVUM3N3duevgaDRyVyISYfA8AdX/X3tv8hxpcqR3e2YCyH3FDtTW1dVsNoecmSY5HBtpJI2ZZJKu0lEH6U/TSXedpJNOMq2zaIYcDptNsqura8EO5IbEnvkdYL/Ak17xvpkJoJrD+eBmMACZ7xuLR4S7P+4eERhjvO+jVlo/fyOfKAuZgGdZ56ECY/qAvmIeqo706wre6fjRPp++56MuKsd1zxHr2c8vjOrYXNbnYsQ4KkhAJvv3tH/oV9qJPlFApZ/H7BcljTSgF3He8Z1f8/od81gdVsViMYwjTjEi/BphuYsd7GWffoezCVCDg7XdbgdH62h0cwu8HooyLd3bcbPa8CQCPcaM/lm9d74e/T/GgGkBzyRw5NvuoxJJ76nixihKq8vs/dSGNJoEKPSzWMgyCUDE+qWgQseURaV99XV7YaVlJoENfscWiwruSfxHoODtwKAm8lAqlaxQKIR9CdygrWOMt7pcLodNv2okY0iz6Q5BgSBk/wMXzOGVwquvQhvFUa1WbW9vL4CNcrlsFxcX1u12bX5+fix/lP0QbKQmAtPpdEJKAl70Xq8X5iJ3ZLCRWwXd+fm5vXr1ysxuNgdSL7zlsjoMVvgNT/UEEXhRqVRCJIMIEsrI7Gad4Fmcn5+3drs9BqxIQzO7iRoQdQG4VavVMF4KDmiPgh8FeGY3Z5szz1XhERXStITR6DoNgVvVi8WiPX/+fEy+eUXr12KS8asU+07XgKY/tdttOzg4sIODA+v1esFY8RsObxt6n0STZJyOOfNGDUiz8dOQvGxIU8K67ikHQ0wNKXV8TGq7pk14T7Qa0hhXfK8gWKM3t7k/RI10NXy0HjMLckg3M/tcdfqpaVbwKUnvKN/QBR4UIWuJlCBPMPIymcyYPPHvTjJkaIMHNzoOyFMPIrQu/lb9QPpTu90OZ/hfXFyEyz5brdbY6U17e3shIqjrSiM7kBrYGmVRLzt9ASx6x5nZza3Yfo5mMjeRBLzs3omg80frV7CCgwyAxLz3a4W/NRqv93Eozc1dn/anPFDSdenrUblINErXmdlNlARj3ffJAxacSKQmsykfuaFA2O850fnD/CdirmmKHIZidu1kpO5CoRDuibi4uLBqtWqXl5fBcXnXCDK8hNe0jei92mTooUKhEPZSElHSFNpp23Qvm7djBmHSs2bJaVDeW6EKOFZnUhuUvJLWd5k8+p4awd6Tk2Rox+rTRRxDjVq/zyNWZQG/Yv2Z5FlSz5o+6439tPeTDB8EWpJSuS153vtIjvfGTJpzlEU53gNSLpdDqBxhyMkIvg2ZTCYctzoaXXuZ+B9vOMrHCwY1WlVAc/ITi53Qrwp2NgNfXFwELzzCTT1Fg8EgRCOazWYoZzi8vuANr0m32w37JzRcfXZ2Fgx9hCneGQSUekPIDda0K+YD7VXBDd/xcC0sLFi1WrVutxv6zx4Knu92u4HfREUuLi7C97qhmsv2yE/V1AUzC5vrAXBqXF9dXe9JgWeqhFQBao6yGj+6ltXQffTokTUajfeMmCRQoXN20uceYKtxq3sq9vf3bW9vzw4PD0PYHeARSxm4b5rkZIA0SgRvvLHo26lre1Ld+k5MLmtULcmZ4pW1yifmmpat/9Pn2OkqyhfdQ4Bs1T5jFGKk63zzXlr1jqvu0M80dSam/2KOKOVLEiBV3aZAxOzGwKQvOu6MNbKQ73xbVP/oGCtw0fH2ANTbGBp50oM9mIc4ORqNhjWbzTDmXFKKEekjSTrWtJ81qAcBeN3m55KCCjXk+VyNXp2bCmA0JY75o2kyzCfknxrMfk1opIK1w1ihd7ydoZEqPS5Xo2geDCmA0Sgyz6sjTkG/RoG8Q0mjXbyDTve8hgfMX93MriBcj2r388qPHY7LxcXFMJdwwtXrdavX61M7HHTtx5zIqs+JzNdqtTC3sTM0koFNoeD0t3JBXhJ5ITWt4Rl7zpeRpHwVuHhPoQcXSeQVR+w7BRqTFJzvg76vCinWbwS0J508sff8olYlGzMivALSBeKNAw0hegGSBFz8uMTa65Ww8iCmLKAYSFTyoJAFRp0IhoWFBSuVSra1tWWdTmcs1er8/DyAEFKWTk9PAzghbQrjFY8+xClN/h6LVqsVbs/GUIZfeEWLxWJIaykWi1atVm04HFqtVgtAgb5zY2axWAwRDICKem65b4IQP4IEIYq3k9OYdAxGo+tN08vLy3Z2dhb2fxwdHQWDnXO7ubEW/nIG/Pn5eYhAEAFhfwS8QcHk8/kg9JnvHFc7HA7De4AjgJZGkPCkASzwFME7wCCnY+neGrMbEIfAV4+WRiA5RWxhYcGePHkylibi57uXRdPOX95T757mF3NfxeHhoe3v74fNp6RBYUBpeuJdnQJpRF99XnqS0aeGtdn792F4WZVWr0Y7FKAoUFZDSIEDpHz2HmazmztsWF/qbfX9wDDy0RhNIdF3YoQxw1pQJwZ99kfVJqWgKI8wuDQaQH3eQExzbOmazGazwYPMeiR6ou1QYKyHa2BMajppkr5VkKF9j80TP989+CHdSQ3cRqNh1Wo1pKH6fSNats439fib3ewRUFmvJ0gBHH2/AAKUqeuYE6sABv7UJp7BMFZjnj5rpIexw2Gj8kUjVegXQKBGjJIIPYUHn43Luo48YFb9BU/UHsC5RAaCEu1WGa7zifoUGJrZmF7VetWO0b0aKot1DvJesVi0crlsjUbDVldXrVqtWrVaDZkM7P9BV05DrIXY+lb+wcNs9voCWmyVk5MTOzg4CLfKHx4eWjabtXq9Hk6nxMF37xGLSQJcyXuHkr7Tz5LKTwIR+nnaM9N8puSVfKzcmOEbe4+/dWL6/se8Wt7blcSztM/837oIVdhou/y4eV55EOH/j4EJbYMHBp6SFIB+P+s7SghtFC7tMrOxEzhyuZy1Wi07PDwMi0+PhDs+Pg4br1GYLOrhcBjSTRAuGBJ4idV4KRaL1m63g6fezN4zci4vL0Nb2EOB4Y9XRk+GUi9UNpsNGxk9aGMfiBoIvV7PyuVyEHCAndFoFE6vIsx+dXVlOzs7oS2j0Sjcv4FCNhs/uxuPD/zRSAYeHw1Va7qB37RIdAae8Y6OlwfTgAWUIEBEIzSqFLQM3ejHM1yeOBqNgpeMdi8tLdnq6upYmo+WlzSnY9/FvIXMJ5/fr0cGHh4e2sHBgbXb7QDm9DQilM2HBhYxWUp9KEUPNtJAls6DaepVWR1zuHhDhnf5UY8vBhXePL6POTr4Hv7GHCvKezXsFHCoZ17bpm1WowLjG7nkjRzq0ed5xzuIfHuT+Kj9RuYRddBIhfJc7/jRKJrKVIxXjVxo/5UvtIe+cKy1mYVy0gg+YaRqv1jvGIJ4gnGMKICFNx6sqCMCPvm54PuifeV//zy/kctq/CrYUsCi4FU/S5IDapcAGjXFDkL+paVW0h/miGZt+HnI8wqofMQNMOXnrm74Vl54vipvFcT5dcl89HvEAEqUQd3oUahYLFqlUrFarWa1Ws2q1apVKpWwYVvTqKYlbQf/m1m4PV5PdwLEVSqVMFd6vZ7t7e1Zv98PkROz8b1D7MOYxnludouIxSTDPOl5NWQZPN9Inbj6P38nUey9pHemNdL1c6/oYiDAt8HXHwMJaWDCg5EkYOLbO8k4UFCR9LyOlVe2vg2+rNh3Sl4oemATMwSS+kp/1CPg20edlK9Grtm4YkUQ5HI5e/Tokb169cpyudyY8a45/ZpKQkoTUQzaj0dcT5PihA4FB7RZUwLYWJzN3mxCNLvxokCXl5ch4oH3rFAoBEBBGwEsRCngMwaHel2IziwvL1u327WDg4NgPOumLgwqwAL9Biip4ru8vD6RgqgAnh02TSPoELC0kf77CBqRFviip8tQN0BSPeUY1poyAa9RdGY3ucNs1tTN7rTXe9EAVQsLC7ayshL2nkwDgGPrzMtO6mdjKR5IAAOf93q9kCfOHSsoF/WyemP+QxLGpoI8sxs5oG3ic1X4rF01MGJ883XiCadelYFmNyfJ+EiFvqvpImpYqBGsYA3ycow5zJpT7y5jrdEMDGEMUbOb/QC0hXc16qBOieFwGCJ1zCNNP9EInKZNeD5NM770h/QK7nvQCIrnJ4dpcJISMo934IkC6Gm84jhPcHp4I9OTRozUa6zRhBhf6JfKEz2sgTlP2RqZ0DHSKBdl6OWnfKeRBm07ckqja2pz0EY9Nj0GyiBdZ35Oqq7kPRxOo9Eo6BJ4EBubtLXhjWscUjo3FDzTVuY3PCYrQcthTJSvRDHUecT4IJs0QkP9OjfRKTrGCwsLIfIFMK1UKlapVEIkiH08Gr2YhXRuIb8uLi6s3W7bmzdv7O3bt8GxdHp6aouLi/bo0SNbWlqyw8ND29rasm+++cYymYxVq1VbWVkJoIRIBadHfTBgMUtnzZKFPkI+Bi48eIl9Nk3dMYM8rT1p//vvksrx7da/1cPiFWasbTzLe7rYPEhJMug9gk96J40v/rskwKbI2XvmVGFPCvMnUdoYpYEY3zY+ox14CRAW2WzW1tfXrVKpjG10mp+fD6ctIZgoB4XnDR4FCaQMqWJE6aN8ASEIRTzPpBZh9OvNr2Y3mx/V24/xreFfPfvbzMY2TCMM8WqcnJzY3t5e2JyOga7HtJrdeM/xhnmghAeL1CqzGyUHkIFPlKMh+piyhg8+RQA+sLdDx9xHQRDIZuOb72JzCMOTSBVgolKpBB6SumFm1mw27eOPP7ZyuZy4XtIAu5+76vnmwrB+vx9Oq1FPL5di6bGCABCMBPoTS/v50EQ/lA/wXtePjp16Fn3ENeb8gLQMSD2eaqSo11SfjUVRfEQRz7t3JlGG9l1/tH4vq1kPyH71Jqu88u1VWaLA2gM25pVGndU4nlZG69jQfmSO5uprahJ1smmW909PT98rLzYnkmwCL+vhAUZjTGd4oECZ8A7+IecHg0FINWR9dTqdsL+OteiNV7Obk/R8NMv30cyCI0bbp9Err+90vLTM2Nwyu3GM+Si+Es4fndsKYD2pvIrpRP1eU8yoR8v3/fDrSNN6NSrAWgRIxwATdSmQ8SBKo5gKhHXMkAGet7SRqHy1WrVarWaLi4u2tLRkKysrIX344ODAhsOhra+vh1PHbkuDwSDcmM1dFBztDqhhvyWAZmFhwZaXl8NcwVHI/B4MBmO2zjQ0M7BIU0BphmqS982/y6KLAYKk8mPlaZqOIjme90awN7xvo2hVUMfaFQMrqhz9377vMeVG++mjtl15Gltgvh2+30ljpryCh2oAxvqa9l2MPOj0E9rXH2uTggf9Ww0J/VF+cffAwcFBMFrNxi9JU88Ggki9LTo+mUzGarVaMD5RspyQgacJw//8/NwODw9tbm7O6vW6dTodOzk5CfsT9EInfnNMHIIQYASoYE+CputUq9UAekajUdjQzfG2gAi/90M9JCgm2s1z9J9oDuFzD8p4Xr13enIRkZeFhQU7Pj4eM9joO+PjjwLUNvOOAiI8YdSta4C5RJs0h1ZlCnWyRiqVilWrVVtaWhpbP0q6VmPf6ecKuvAkHR8f2+HhYVAOtJFN2wAM9pnwvf79bYIKLwvVMDB7f48CxqiPamBc8f0kzzXPsw41eqGGJsZJzHjxjhJ1HKR50NUQ0z7QBvWQx9qsANps/Ox8nCHeuIvlkuP19/nRajBpWybpCk8YYwoQM5mb+yM0tVP5gsGv3ns9hYhnFQTzHv2J5XzTF07a48ffDYDs8qma6vTR9TEaXR+V3W637fDw0Pb29mx3d9eOjo6CLC+Xy2Z2c2O4zglNpUtyqKo+AbCaWQA4ZsmX4WpZKs+UZ9oWPNhzc3NWKpXGnmHuqUzW8U5bc9Sv603lMO3X43gvLi7CetKUPR3/GLEG1HkE72KRHZ5B/7Cvg34p4ND+wA+NWkLoIL04z2z8TpBisWgbGxu2vr5uzWbTqtWqZTIZ29rasu3t7eAAbDabiXydRMPh0Dqdjv3qV7+yv/u7vwv3V2HL1Ot1q9VqdnFxEY6X5QJcdH6n0wk/nFjF2o4ByST6IBGLNEXlDfwkihmyMSWoxu80nkFfZlL79EfLSmqzgoIkUo+RKigFB4qCdRF68OHbFzNGtG18Ni3A0Odpo36unif/XhKoSAIkSXxKKkPr0N+KqP2zvl5VKDHvz2g0sidPntjOzk4ADMPh9YZE0qHw3tMPzw8iBGqcasqFRgf0jgaMCo6TRWhhFPo0CryCgAPSifjOpwzxPgYp+wzU+6nKXlOfeJ9+ovgUMGi6CEY/7VbPpHotzSwYaYwToIa2nJ6eBuXLmGDI5HK5cDu5Ui6XG2s3iob1pkfhwhc9qxxiw7dGXMxsrE6iW6VSyV68eBGO7ZtESXKN7+AfF92xwQ6vlB77y6ZXxoE0Hb9HQNedOiXuk/x6VINEDVgFDcoTb8zHZJqOJ++kyQ8tXz2m8EuJ+an51GrQYgx5j6d6Pb232TtgJhlp8Eq9xJSj60O/p81mFtoIsKdOBQHqJNCUsWkBRgwke6+2RskU1DI2CgZUTqjhCT9jEShtp98AC7iKGZkQfcU41LQ7tTEA62w6xiinDNrCBmL6GQN1/nsFneoR189j+yNifdExJVWH8VZnFGk6jLfqKNrE/jU+43nK1P7omPl+q/HPuPnIh0YKdN4wrl6+K2hXOafzWdOb/Bj4I8hVPqmT2ztB/LM6d332Qy53ffz4zs6ODQYDK5VK4WCT8/Nza7Vatrq6asvLy7eKVuCIYzO8ygWiJOyT7HQ6IeJNeix6lwgF97Hoepskozzdeo9FrLJJgGKaz7QObyR7sDGpzjSKlRMDE7clD2Z8uQokaIePQMQUri8zVl9SW2bxQk0iLTMWMeBzNdpVUXkjwLc/Fq3w7U+qd9Z+at0qqNbW1mxpacl2dnYsk8kEwxZSMKGCByODtCYEkRraaihns9mQx4iHnnbgTfc3nKIASPnBgNbN3Xj6NX3p6upqbD8Bygblo0epwg/vdaMvKGGMLM2RR0YAHFAQKEsPUtRgA3BhyKMQNJ1ADSpC3nyXyVzfx4GR7ecL40sZfMYGUb2XRN+jzWz2Vm8ixgTh5hcvXox52yeBeW808z9RrJOTE+v1etbpdOzg4MD29vbs4OBgzKOEolRFqOtMjRbvBLnNupmGNFqonm2NRjD2njxIiIEvX/a0pE4eTXPwzyg4ok6MNf5n4y7ri98q92JGLQZYkjfWR1b5H34BfjWvGzmhERoFxOqo4l3kE8/eJmqhPFMnmObBqyc7BgIxznCimN14oPU9rQtS2UE/Nd3Se+Nj7fU3SDNGmvapY5vP561Wq4UTAPVUJiJgzBed63ymToNMJjPmtUdHaCSUeXJ5eRmiazGwrg4kABmySk9M8o4k1oCeVqXA2svd2D4I79FXUK38Vv3iAb+uBx8t8YDKzy2e14iXRp78WosZzGq7aBsUwCs4gpcKaP2enMvLy7DXjf7m83lbXV211dVVW1xcTN1f4W04wLae1IW+Y73Pz1/fLl8uly2TyYSUPaKC/uAPbBDABmtY5+y0dCtgoR2NfT5rIybV4wFFkkcq1i4+i72fpKiS3p0GdKgh5p/3CyhWj/ZXBZD/PwlsxPrBRIvVOYtHirJiNKthP02ZSWV7QKHP6e9YXbGyecYDoFKpZCsrK7a1tTXmPdJ2Y4wqeOAkEn8kZbPZDAuYd/zC9cpSDUzqVCVFvZovqwocJaTzh028HH87Go2CAU6d+o4PYwNE+v3+e54q/s7lcmGjHYYYJyjxPQpHU6FUIamC5+SQq6sry+fzVq/XwwV/aoiQ02pmYbNfPp+Phtd5hmiE8pd+qBLT9DXarWlyo9F1StsPfvADa7VaY3NPf/s5q+OvigPjkbA1kQrupCA9Tj2camQQyfIAPubo+FDAgrK1TXw2TaRkWj0ya/tjxgPE52qoeA+7B0aU4yNDyA3GxaeWqKfYf6ZGsTo8dJ54faDtUkBJ5FRBCvNZeecNwlnJgwd4Rrt0XqvxynrXtejnrK4z+pfk3PS6gnWgssw7hfSOHAUZjNtodO29r9Vq4XAMjDFSEjHKdIypX50vCmAw/OGJ7xN90LkwHA7DxnjADCcbqkzyERC8296xoBFlvVhO57XyHV6rQ0cj1jp3lccx417nP2WiH3xURqMZSgocfQSaPquTSdeA6gY/d/RAEtVvCmA0go9uAUwyHtVq1RqNRjhVEodQJpMJUQWcAn4+e9mQzV4fEbu7u2u7u7uWyWSs2WxarVazUqkUHAtXV1chon55eWlHR0chwu3HT9PGVGaw5wm+TEszAQs1vLxSihnpSc/o395rr5QEUqap3wunWfvpF17Mw5L0Ls975e2NFf3bAxgtJ2bUptWfpBRiRnQMXPjvlTQ8rGX6v2PvJvEkRl6gpNXnwUYSeYDiQSYCjj7m83nb3Ny0L7/8MuRA8lw2mw3RiH6/Hy6Wy+fzIQVFhTOCqNFohBOc1NOKwiOFSY0ZFSpEKTjtQg0iNST15A8tH+U4Go3CZXBsKic8ms1mg8df56iGmjWKQD9LpZINh0Pr9/thzpLapR5+BF0+nw/gQ71C6tWGEOAAN/inKQ5LS0u2v78flD1eSMCfloEixetLhGc4HIZ9LHpcsIJIIkEYHQjiUqlk9XrdfvCDH4zN99ha0rnn5Z+mPg0GA+t0Ora/vx8UCWeOs6nfG1jlcjl4zeiTtiUGZj4UqND+mk3OD//Q5B0UGiH2xrmCc5X9GD5m7xu5MT3ButG/AbBaF+VQvo/4xsAHz/O9Ahf1eOPhZF3pd5D/f1byThAPCDDk8MjrCT8YznjU6atPWU2K7sTaorJTAZ43+BkP2qXjg2FMGdy3MBqNwqZYIsX8ACxVTpnZ2ImB7HlDFgEsdB2r7FVgAY9xUnGB6OXlZUht4n3mBLpETxeEdE8H5WjKkx9DjVR4Xe5Tl/Q7Dwy9jcN7OHZYp7rWYuMPQPPOU+abB0saYdZTm2JziHkBP3VsYjYmPNT5w6WKa2trls/n7fDwMIDMfD5vxWLRisVi4vrTecycPTs7s93dXfvVr35luVzOHj9+PHbUMJfudrvdAHg7nY4dHR2FAxPYt8iYMj/IpLi6ugogNGm/ShLNBCymNap51gMRr2AnGct8HzNEvSGuihPhqUJ32v6p4tGJqhOcBa8DrkI0yaD2SFv/V4GhwsxPePrkeefb5IGDLsgk0BFDpklGURqgoN1pBlVsXGN88tEJr2yVR96ASopsaH1JgAQlVi6XbWlpyV6/fv1emkkmk7GTk5Nw03Y2mw0eAjZl00c2R3GmOp6xfr9vtVrNlpeX7fXr10HAVqvVYKDrHRfcvM3+CIACXorj4+OQS53N3hxTSwoWm7wxuHu9Xsj1xHOjOblq8Cjv2FuSyWSCkGLDt/eKkiLUbrcD0CAVbDS6OQZS94FwdK/OId4xs+CBVY8L+aW0FyCB4tZLkTKZTDhxhXp4hxAx80j3gACWlFe8u7i4aE+ePAkXD/pUK/qha1idBvAbI0P3U+zu7trW1pYdHR2FeaSnrphdn/TVbDat2WwGXp6entrBwUEAUBgNMUfMLJvzZiU1FtXo/TYJGa4yyKeHKVBQYO9/vLziWY0U+XQ0BR4xUuOBOaNpOAp8kBN4honKmdnYGtLTkDBOdU7SbuSlT2+5LWFkIn90DdBe9JU3nDCMvH7jd1rKG3xn/enxp/RPj8ymTuak7s3Q/Soe0LFOu91u2Ly9ublpjx8/Dmv18PAwzC3mHqfxARLUhonZBzEjXcEGG+SR7foevNd5TX886fjoGmHeeieO1uUdYYy98kv5rGWmzTe1p5LsRG+HKYjX9D/GU8Gv6vE0O5Gxpix+dK8KdSHXiKo3m01rNBphczz6rtFomNn1qYLqrPXtUJml/dV5fnx8bK9evbKjo6Ngk2AntNvtsWjaycmJLS8v28bGhm1sbATnE05SDjzI5a6P2e/1emFsk+RWjO6kSTTakEaTAESMYsb5beuJDdY07Uqb0OqZij3nP1MAEotUqJcLcMF7AA2dePqehntVUCUBOm1jjAdahqdZJlfs+WnGMWle6bjdhwfU84uy4bnZ9RFty8vLtru7Gwxq0nzgPZ4mBKV6hRBCbK5SoY1h0O12g2FNasv29vaYca3CRQUzR9AiyHlHPfGQPkcbyNVVw9PsJjXEC2k8Imo8Ifz1mFlIT3nBU6eGD2lZtC2TyYylWdHOQqFgtVrN5ubmgpDM5XJWLpft6urKOp1OqAPlzbqAT81mM5yapP3UfFnqw0ulJ7H4tIqrq6vQh7m5OVtcXLTPP/889BeDRMEuvNe/dT7SPtKf9vb2bHt7O6Q/AZ7Ye8McrVQq1mg0bGVlxRqNxphiQDHqxvjYGp9VRs9K3gj34OK29XtQkETqnFBPbsygUx55A1g/V1BCHchr5AHgQIFGTI4rj2grxoPZzX0Jfv5gEACiqU/vwFCnjNkNoNCIDaSG6yyk+savE+rnOT2pKjYG8E73SSAjJtkdMTDowRNlMm6aPqMpR+pkVCMY/iG7arWara2tWbVatYWFhZAmRYQCnY4DiHYC9GOkcl73UWk5sRO/PLDQ8fH98nzTua1rVR046shT2a26QPWBvqPrgHq8DNT1EGuD55FS7FmNTFK/Gsu6fnX+eieoB2c6V3x9RAVIgQKEsC5rtVrQS8iLJPkFD/X/bDYbyr+4uLD9/X178+aNzc3NhdOfzs7OwpHxOBMLhYK1Wi3b2Niwjz76yObm5sIlev1+P9xcfnZ2ZgcHB2NjMos8uFcX1V3BQxr5yRf7ftby7qJIJ70bU9g6QN4rbzZ+yoAiWP725Xhw4T+PgYtYO7XsmLCZhWLjFGtvUlt8GQqc9HesrbE28H9a/z04gf8Ig42NDfv666+DgaY8574HhD8bmmm72U3qj9m4Z0k3X5JeUygUxu7K8CdQxCJaKoQxSug3yhPe8oxGO3yqh/e4IoAxsjW64CMcGpbWaIeGoofDYbhplAgEbaTPmtM8HA5D6Fd5gaDkHgnGBB7grcTw73a7ZjYOJszGNzHyvTd4Na0NhUJk4fz83Gq1mn322Wfh0iP1cmpkwjsAtO+ckd/r9ezo6Cjsp9jb27Ojo6NgqGgueKlUsqWlJVteXralpSVbWlqyer0ewCxhdz0tROm+QPqspPN5GlCQRBgz06bIQDGDR4EH3zPugF7vZaYMH/lgnlAX5arxpe2ORUj4nLqZd3qvgv5PmeT4Y9wRrQNw+xxw3ZzLGpolehEz4jwP+dF0yqSxZ70zZ+EnTpA0A4c61Yvs9wtom1nbOH3gNwdCJKV/zM1dHw3KnQDI7mw2a41Gw1qtlh0fHweDjfQS7xzSPTxJpKDT62vGW99XOe5BCfzXPW4eiCnpe/BK39XUu5hx7Oczn6Xp4xjQ9Os11tZM5uZUL9aLBxTeQYDuGg6HY9F9jidm3apO0iNpmTPe4UAqa6fTMTMLUYt8Pm/Hx8dBH+rcniXVqFAo2OPHj61Wq9nr16/tiy++sFevXgWe1Ov1EH0rFArWaDTs448/tufPn1uz2Qz3WWSzWavX6zYajcLxyRz56x0Ss+iHe499T6MgJoEE/6x/3oOCWUGCR6CzvDeJFBQkveMNaF28/K/58oAGvlPh6v/3/fOLOA0Vx4RCrH9eSMSe02fUAzANee+BfnYbI2iasfZeQDU4yI9st9sBzZvd9BFh6w0QjpvVvFqzm5OQhsNhOFFEowYQQAXBjYEaC4vrpjnfj1iOs+5p4Fn14HiQ4vmneacehGh+uqYOaH3q5UJYM++LxWJIq6JtCkh1g6OGwgETgCVNw8hms9bv98fmoDcSVYHEALn+rWkGRAwWFxfHgJGCfR9V9Ov38vIy7Kc4OjoKkYqDgwPrdDoBVGBoFQoFq9frtrq6auvr67a0tGTNZjOcVw6wIN3t4ODAer3e2PHA/vd9pcFMS8p72qBrT5/zz/J3zKOZJnuVVJZ4hwVzSAFrLEqX5JDxfGXtUpdGyRToqyHGc9o3NfhVxqvuoE36rjoYvJPHp4Sojp1WZivvvCylLDXi0lIrFCCp80WBSlIbvJ7xaVjKD+Sxn/ueR2l9RobQP7Nr+d5oNIKBRkoiZamjZVJaF+1Vp4nul4NHPKeAzjt3fGRP9YifB5DyU8GzynGVzb7t/O2jvVqvphGl8WASKSD2csTbiwrE0c96nDv80JRYH6HUvsTsJxyR7JVD95pZ2KNXLpdDWiDt9DJB2+2jaYxzLKI2Pz9vy8vLViqVrNls2ne/+1375JNPLJfLhaNms9nrvZGcFNlut8fS97xzZFq6E7BIEgwx8gJLSY1V/31MoSSV79/5EBQTNl5QMwhpi04XGW1HEKhAoG++bAyXpO9j9cW8PR7c3JV3SUZAjJImq84FLUcFmq8z1gbfp0ljR53wC8N+fn7enj9/bl988cWYEETwqPFOXm82mw2gAE+xnjKihko2mw0eaDU01Uui/KB+BCPfKwBVXmo6k3phaS9/K29jURFNg9INop54jpOctHx/HC7P8z3gDAClHmDK0z7qPoNsNmvlcjnst9CI0Wh0nfYFiGMNUb83TBHu1OcFt9lN2lmxWLRKpTJmoGh51BdbG3hnz87OrNvt2uHhoe3s7Nj29rbt7u6Gm7U54Wo0GlmxWLR6vW5ra2u2ublpa2tr1mq1rFarBUWlyqNarVq5XA7zUuWLN+q/LVIDwHv6vfPCzMaeiVHMo6lrw5Ma1WlKVFORFCSzrjWywG8FH+po8KBfPaWxMmgn80/bzbzP5XLhHhzmqkYNkTkKTPQUHMpTg3vWeaDATNvHnCUNT9O00nSDAkzdB5HkTGIuKei6uroKF3OqkYisZr8DUWdSinQPhj8tSOny8tIODg4C+M/n82GdmVlIiULe6hHWKg/SgIXOTdYucpAUUi1Po0/KSx9RS4uOKBDWviuYVj2sBq5/hnp0r4o6ZDz41nlOv3QdezDqAYdGdmL9iOlHBbu6bvUEKUj7ihygXz6SyFwk8tHpdGxvb8/m5+dtfX3dHj9+bKurq+HyRnQOMoN9Dzo/iFBz0MqbN2/G9lY8e/YsrBnk/sbGhjUaDWs0Glar1axardrx8bGdnJxYp9MJ84rDXjgUhD2UXJ6ra3camhpYTOsFmuaZmOEbUyax8mLAZBL5tt+nAtUyvSJjosae17b5nEP/jnosdGGrgNLyPdDRZzH6vCExiSdeGUzr1fHPxuqjX0mg04NG+oXxqzmKsf4ntdELJjUEvQdraWnJnj17Zr/5zW/GjBAzs2KxGI6QpRzGTMtWgxnC2zQajcLRp3pSEt+pocO80o2YCF1vAGvfMYZYb5qe5evgJnDmjwplbvQ+PT0NghCloCCW9qjiUXBLxAbPHoqHPQqUh5BmnDUKwZ4UrePk5CTshWFO9fv9ANxYD9TB/7yvzgD+5kdPlSLEjGJQgO+jFjGir4PBIICK7e1t297etp2dHet2u2MRL7xLS0tLtrm5aaurq7a2tmaLi4vhCExO1cHQmJ+ft3K5bOVyOcwX2pVmqH8bRDvVwIA0RSPNUaFgzq9l76CJgW7vyfUOML43u9lwy7saOeMzNd60f2osq4zXdRcD6f471j4GGnONdCdkkzqd/G/WkhpS1KEyLMbTNACq5QEk9Kx9Xf/Irdgc9HqG3+ro8Ck8us68U4D39ahX+KdGJ6BL+adRYN9vfQdHCeNBNMT3h/8pT8Gm2kDqWIHUk61RCvrEM8obyqU+NVTVPtH5GRtfXU+000fYY7aN8l/ngNeDyt80fR373DvAtG5dU9o3L9djfFbdRz9Vp3jZAIACWFN/Lnd9j1S73bZsNhuOna1Wq2PlIevZZI1uI+V3OBza8fGxXVxcWLfbDbqC/YaAm3K5bMVi0crlcjh+djgchvLQrzhNNcVZbatSqWSLi4shUs6cm4ZufUFeEgiAYpMs9rmW6Z+N/X8bkOGVRZoR7ZVY0rNe8HpjLbYI9DM1wFTRqHFndqNgY0Ah6bd6j8ze9/T7/7U9SbzjmTRjRJ9LAh1J88IDDf0+TZFNS7G2JBk11I9gRyB99tln9vXXX7/nnSGUyelGGNqxs9DPz8/H8ncR0NSPQKIdyke8n3jcRqPr/QPkUXJChOZ9a98ox+/xYH+EnqGtAAWPP2k0ZjfhfDXSVYEpPzH8mZdqlCmP6Z96b8xsLGXBh7oRdngc8Qxi2ANeCPUyTnqxoJ6pjxJRWcFz8I0x53hZTomiXlX6Ola6PpgLepwskYq9vT1rt9tjd1TgEW21Wvbo0SNbWVmxpaWlMVDhHQYKLpK8r96Y/7YIHnjgr6DTeyz1ex0bdbho9EvXQZq+Ym15IDBrfzD4dN2p4ahtVPme5BVXogz1GsYiNIy1fuadHL7dlKdpQxhFXi5qGgakgArjEQ+nr9evYTU0lSgTMKBtVWcKz6pe8sakbnhXPaqyNjaX+BxeaL/n5uas1WpZpVIJ65joIhu3T05OQgoi9wVBGOh+bcbAroIJ/U6Bqge8rC/qQIZp9MKDD/SXAg7lo4IoBWbe8cQYaJ/g9SRnhsoFde6kUWx90x4ccF62wTueVdmhc4H/6RPAXZ9HN+Ako6/++GA/lqenp2EfBIZ/t9sNe4vYG1gsFq1Wq9nJyYm9evXKfv3rX1u73bZCoRAiHr1ezwaDQThh8vnz53Z5eWl7e3v28uVLM7OQJlutVq1arVqz2QzHzcIPQHGlUrH5+fkxJ6Kul0k0M7BQo2cSuIC8ceopLTSndcXAhwqLadseK8d7SbynRpWOLsiYAc33akj59/3zygcmtjfoEfwKGPitIMULDO2TvutzdXUhpfHVfx7ziqn3Iwlk6LP+bwVRsbZ570MaqbEwjcGgXgh4a2a2srJiL168sL/7u78LbdBQKsarvxhOvUWkV2Hgq8GAMEPZkJfrFSe8QLjzLmlYGongeXhInbRLeaRzhAiM3gNBPw4PD0P7PaDQ8fCABiBF+wAyCGRIN5ZrFIS7O3q93hgvUMzn5+fBM398fBzaoCF5eIty1U3lyltNqdBxwmhbWlqyarVqV1dXYzele++p/q3r/OTkJJz8dHBwMHZEJaACwInnaHl52VZWVgKoaDQaVq1WQzjb858xRwGVSqVw9j6yRKM9XOr3oUiVOeTlkv/Og1bfPy+TvUE4rSJUma0REPWOx2SHymBNf1LjWeW37pcyS05f1N88p/JfAa8HJ8h2TdvUNiofFeR4+ZgkL5UXMT3gjWNP3skQ+16jlEl7EVQn0BfmNGPA3+pR1qNuFbTquCBTvINOeY4BZmbhRJ1ut2v9fj94ltEPtN+n5yjP4KfyTeeJjnEsO8LzVZ0k3ohGd6mdoFEaX7+fB7ruNLIdc2Ao8NQ16qMdarf4upLWcZpd6euIletTr/jcg13KwRDXNYDTp1arhfHOZDJWqVTGojLeceF5Shoe85M5WywWbX5+3gaDgQ0GAzs6OrJerxf22TGn+/2+VSoVq1Qq4TLaYrEY7l3x4BOdy5ycn5+3VqtlFxcXdnh4GG7qVptyWpv/gxxcrgxLGnAVTLOAFE8x5eEnYppw08nkwUpSXX5CJC2KGABRoaFleUGNkPPeOl2UHlgkKQgfIkzqowpWv2Bjbfd98uXF+qwUG3cVWH4BTvLsJdWR9EwSyFAlrvzI5XL22Wef2TfffBPOLs9ms2MpTP5SOd5Vb08MlHphRg4wedz6rEYKeE9PXUFpUI7yfzAYhD4RCUD50nc/33wKk7ZZlRmeMfWaUQ7pTqRPYTAoKNE5Cv80dY92YuwDqHhuNBqF/QoYW4Az1obmi6pDQ3kJ3zKZm0uUGAfGZWlpyXK5nO3t7Vmv17NyuRwFaspH1sLZ2Zn1+307OjqynZ0d29nZsa2tLWu32+FyP/hVLpdtbW3N1tbWwulPi4uLVq1WQ5jbz1PqZkyKxWKIdHBjsG4ezWQyoZ4PReoM8Kl6MUM69q6OtZcp/m81mP33SXXESJ0vMb2mdcU89Gb2nnGpoMOnppjF94foHBqNRmGtYXyoV5Z3SXVgLeBxVCOBtqvnO4kXOoeV1Cj1nt80wzSJMplrrzCnWOlt1r5eNZYgBU/IItIE2agKGMf5o/0j8sOPghb13KvjrFwuh+M/2+227e/vh0gm/MexwVjwo0Z3zFCmXtJh9FJMTYGlPf4OkDReK+nY8o6moKp+wuGkOk8NY5VHqu9I/4wBXMrXfQo6n6al2DhpH5PsN0jXhZJeXgvlcrkgX1dWVsbK0jWJ3CMyxKV4qj+Zl/V6faxtRO5IeapWq1YoFMLBHdge8JSTp/L5vD169MieP38+5uA4OzsLAGVubs5KpZIVi8Xw/PLysm1tbdmrV6/s+PjYrq6uwjvTjsW9AouYcpv2HY/G9X2PnpOM/jSahHiTUKRvq1cu03rEfBt8xEA/V4Nb0bEau1q3Gp38aAhchWzMCEkz2KcBGGnv+r550oUVE4YYSPpc2lh5b0/suWmErjcGMQIajYY9ffo05PEPh9d5j8VicaxcvXVVjSnCoCxmFBuGNmWcn59boVAYM8DZlKuggTJjhojOHQUbeOzNrj3vbOTyYJZ5yL4Ms5t1itDW43d1oyrCmedIDQCgKWk/tF7WCGXrJUUoLwUXsTLUeND+6wk/Oi+8UWJmYxsvM5mMLS8v28XFhfX7fXv79m0wzHXzb0w2DIfDsUjF3t6ebW1t2c7Oju3t7QVAAahoNpu2urpqGxsbtrKyEi6/Q7FoJMUDPXiAV3VjY8Py+bwtLy8HYIFBkMlcR0W+jYiFX28qE2KOCl3vKt9iZSvNIpd5PzaPfLu9LuIz1swkPaNGOP1ToJTk7feGGoaPnjSnIEeNMp7hN3MMuaDGr/7ofPI8iOkbs/FoL4a/OgFUB8WMvBgBkLVu5asCT410AJLgpUaDtU/IEvUS+9QnNVZVrvOd7s04PDy0fr9vh4eHQXaoEUmf/D4RTSHzaUY6PugD7bvyUdOxlZijmgbFM7o5l89ZD2qP8Dzj7ceQ+ef7yXc+CqRzx9sifj14/U/5SXNGdRLEWCkQVp5o3TrX0IvwHh2Uz+etXC5bpVKxarU69r6OZbVatXq9bqVSyTY2NqxarQanJGlRJycnwfHXaDQCwODYcVJluT17bm7OarWa5fN563a7Ya5xWWapVAqAV9O3SbFSfcXhMXrk/cHBQYiILy8vzyRT7w1YTAskeNZ7YWPhMbP3vbqz1kUZ05KfhNMIPr9IY9/772JhQPW+sPhUYPNZ7Md/D48R5qrM/KL0IT99xit6/z/vx0CO8jMGRGKKK8anmEDxQIPPvJCddgw94VXCI6zj9emnn9rh4aFtbW2Z2U1Kj+ZeorzwWtVqtbF7D7iBG4WnAlsFqtbNb4wIP+/4XtMtNA8U/iLsOE8bDx2Gh4ICHUc1vPH+0U4MpPPz83DHBd599fTghRwMBqE8nbfD4c2mPvqBlw+hTiqZyg28ZboBjtQpBLwajhhWzHXNS/c52SgiDPPl5WUbDAb2+vXr8MzGxkbom5ZLO/E49ft9a7fbtru7a+/evbN3797Z/v5+OPlpOLzeT8ERxxsbG7a+vm6tViukPnHaDPPHry1v8FQqFcvlciFfVjfVav9J6/htkRrGZu8b4ZpL7eXErEBCSY0djJG0iMis9WGwpjlC1PscK1t5g7F0cnIS5hxyCvliZsGA4DhknsX7j7eVS7ogL2c1rUrb7SM1yBz/PG1H7vCT1lcdh1wuF4wlrVeNWL0t2zsOkiJho9HovZu2WesqgxUgTdoTMxwOrdvt2rt37+zrr78O8qNer4+dkEW5uq/t8vLSTk5Oxo49jbVZx0k985Sh/E7qt/72cw+ZwJzym3t5FtnNeCPnaHss+uXXljqj1CnFc+o009Q+BY5JfUQfKbEXgj7p3NUxTCpTI2BskMZ41zVOlAH9urm5aRsbG9ZqtcLz6OB2u21HR0e2u7tre3t7lslk7MWLF/bixQvL5XL25s0b+8UvfmFv374N96IsLi7a06dPrVQqWSaTsW63ay9fvgwnWCp4oe30nRQqDnMhSq6giWg57V1eXg4Xr05D9wIsFNFOojQjDybEDMw0z7LZdKHuJOOWz2LeEG9Ep7VdUbwaPfq/N+K1HerNUaDglY8+o5Q0BspXnWgKOCaV4Q1Z71WLAZDY+zHeeyCgpMJTvf8ekCQBD+qOgZhY/Z4PivQxmFutlq2vr9v+/n64KwCBo6BMyyakqOlAhMa1nwom1DOFElReK1+VP2YWBBrl0H59d25uLlzGp+lOlKVpAJ5PXOamDgHeJ/2i1+uNGTt+jsSiLOr9g0+0FZ5pNIJ1AABRQyCfz9tweHOsrc4H9o8wn/CqUibt0rzsJ0+e2Orqqo1GIzs8PAwRmGfPntl3vvOdsVx8ymDNEqnodDrhmMqdnZ0AKtjoR57rxsaGra2t2crKShDqHCVLH2JrRg0DxoWUmGKxGHium2zpJ4bnhyAvPxQ0JPUDYg36PQtJPJiGVI6oXFZZkmQAa/tp2zT1QdSnp+RQJuVP0qesMz0YgrYjj1grzD91UiFPdK2rgUq7kB8xmctaBbxTtj8RR2U0fVNHxfn5eUhh1B8FSfBFx0QNTAxZjTRo6hHgITbnVHaq0axy10d2YvNQHUDZ7HVqS7lctsXFRatUKra/v2+7u7vW7XbH7hJSQsYjk9XwVUegrh9AlI9cJzmfvF2hMsPz5+rqaix9VnlmNp2RrwQfFQD5/kBJ9kSSvaC6SsvW+UefeE/tGOWJOpu0Lm93wUsMdG07Tq6rqyvb3d0Nt1lz/Ov8/LwdHh6GCNfc3Jxtbm6amVm327U///M/D5fs8X2xWLS5ubngZCoWi2Gt694fdej5cVN+4nhgbyZgY25uzlZXV0OUpVarhSOtp6F7v3k75kGbRLEJnQQY/ASbpg7vQaQcb3zOYhRPKj+pzUo+ksBnsQngJ4gqQA9atF++nfo973qAE1Pwnj8xwOUBlH6vho4qTh/SjSlUDwR8eUmAwbfL88z33ZNu3lZDOJvN2pMnT2xraysseLPr/H0Em25GVq8ZXgPyhjGWNVqF15r9AZ7vKhgRgF75YOTqBkidpzyPYeC91z70PhrdeO4RQJSp3jWdgxhd2jatB956wK3gWYEEBoTOy1wuF4wP+oshpMfjYcipZ4yohRpGzCmUNXOm0WjY8+fPrVwuhyP+Go2GNZtN+6M/+iNrNptRJcd5/v1+3w4ODuzg4CDsqdBIxWg0Crm66+vrIf1pcXHRWq3WmFCHb7oOdJ2pLGLc4FWSQo0p0vsm9Yxq7vE0pM6RSc6eSXpBeeV5wmc8l7YfR48vpjwF2DE5qoarGslmN0aaTwWO9Q9PO0avepBZ02qsYbzTLk1zoU9qeGuf9R31UHtjkHcwmgE+mhqpBrsCC4609MBC16WWoSBK55Ia0EQxiUbgSPC8hFRWeTkGX5VfuoZ0HWLcVSoVW1passePH1uj0Qhe6svLy3ABqE+5Q8aRsuI3rut8VSMPviDzfGTF2w+qpz24oh/Mf5WDqm+VL7MAC54jckP/1K7RaLmS14V+jXlw4fWIzu/Ye5quFTOiY7YFxjgADP7q5n1AZaFQsJWVFXv06JHVajXrdDohDZnjw6+uruxnP/uZ/e3f/q3t7e2FNKparRbSo5rNZjjqnAgKm8XZq6GHlPi+6iZzADCnUpF1UK1WQ6RwUqTO00z3WHjjWReZPpP0Ph3znyn59/3E0XbE2qf/e0PVG7ne8E1bGHgzkhTaNB60NOPZtye2eGIgwoecYwvPG/GxOpP6HwMWHuH79vq/+d6DAT+Oyh/lk7ZNBZsqdP87NsZ+fGL9jUWRVBjy99LSkn3yySe2vb0dToEC9XvPIGXhfcrn82PeKDXo6PPCwkLIhed50qcgTdlRcIFwpB0IB42AYDhTZ8wQUg9+TOHyjM4v9kLwOcIrZgwrv71RpwqXy4oAJkoaxdF8Wm2f1qNGJHxmbaMkEcichsX/X3/9tf3BH/yBPX36NISznz59asvLy+/JGfrOMZRHR0djoEJvwh6NRmFDOKlPq6ur4eQp3aStfUma20nz3INvwCfvzKI47kJpRj9zWY0ZM0uUK/oea5A14OvyslM/98au2TgI8O9qXax/s/eP7KWtGh3Sea7P6XGOMR0X46Nvt6YPkVudNK46jzTFyhvwOg68p3JfQZLaBmo40y413FTvqNGKUcc88HJUDT+VTzhpeE6Bjd/Eq/yDKNsDc/3e67gYHzOZTEg5MbuOVtPe5eVly+fztre3Z3t7e+HuC5V/2k7qUDDn5TxtANDQft3DofrBO1G07THyzggdJy9XtVwvpzwY03b6cfEA1H+m4FJ/wyvffp1zMdkAAZDURlG+eDDNPMOw18sWkf3Hx8ehHD3gxMxC1CGXy1mtVrNKpWKDwSCMMwCA1F5ScZvNptVqtQDk8/m8tVqtcI+F2gYxXqhjQR0apVIp9FEPOZiV7t1FlSQMVTDEFivPqMDS8mKIO2bIxwz/GCiKlZHUXn0vppTMbgSp/9wb5p7Uy8xzKsC0DWoA8ndMGHgDJBYNUpARMzRi/fBKOQaCYkAkxgvPV29sYmBo+1QJeWESAxn+uzR+p/En6Znnz5/bu3fv7Ne//vWYgY0RzxhpP5SH8EaPp0UB0G4MZ7+xlGc0ekEZXhhjmDNX9LQVAIj2UcseDodhMxftVM85baMchKYHhx7Uxuak9k+9kLlcLtwE6jcsozQBNApMYqS80Tp9n/ibCEiv17PNzU179OiRVSoVe/78eVBCSR4hLr47OjoK91Ps7OzY0dFR2MyeydwcJ7u5uWnr6+shUlGv10Po2wPtSXIrJm+VbzFKcnjcN3kAqzLCO0rM4p7kWB/8HPOykfUQAyYxB4k+541tNUBYEyqTNDqjP95oUbmJU8IbWzHHifZNn+fUMwxqDB01iLyXXY1N33/VC14XUAYAwvfRn3zEj0YPKIP2+X0UCly83Fc+0h7voND+eXCi32uqnYLTWJ9VvnljH3nE3pXLy+sbutvtdkhRyWazIcUlZmx7h606PDKZm+iypoaiZ3TPhp/7GKnMHW9s+/US6x9tjNkKOn94X3nswYUHJ7yva9TLMe/c4n0Fo0kRD68X+YyyfOqe2bjs0brUIOckLA5kAShw0lKxWAx9XFhYCGBiYWEh3EFEhH0wGNjh4WG48LJcLgcwUiwWbXV11V68eGGNRmNsnxyAgL1yagvAf9UhmiUBb0mLIt02BkympamBRZIymuX9NEMeovPTKM+kZ2Kfe4NTfyjTK1ad3FqeV95p5N/3Sg0lRN95x4MZbyjrRFFDWIWr/k0d/j0VsrpgfV99X1TQJv3E+p80B7ROP6EV+HhhosIvCXB4gyrpt/Inbf4haObn5+3zzz8Pm6684GXR66YohJoqA9qshuzp6WlY4KoIzG5SDlAsqowVtMU8RqPRKIRPUYKAAj/OtEfHxwvl0WgUbvpst9uBZxxrqmOnhr+Ore5NIIKgkYYY/9hoThqU9wbrPFB+a94tY+nD+GpQAKYKhYL9yZ/8iTWbzbH3lTfqnWajduxIWU4UQyFwkzZH/XHpHaDCz9FpZd4sdFsFMgt5R4dGAnwbvCGnv2PkwYCOYexZv+Z9+oR6e/17utaYP5wVHytf5RTpKiorABPqzaR8L9t0n4k3EJHzrBeNQvi+MQYYJ5orrzKVujDM+dFyPCjTSI+ZvcdLBSI4BBSEqOMkJsfUmUL/1QM7Gl3nvLN21Qicm5sLB0/gkGBMFhYWQqQBPUAf2Fit+gTSNuIxbrValslkwmbbwWAQnj07O7Nut2u9Xu+9NCfvDY+ls9B/3aDO/z4yo+vB8wieJnnw1WagPap//Xplvqm8pT6/Dph7zBMPMmLAIIli9sIkGaC882AjBnj0c90EzYEhBwcH1ul0wnHGpVLJqtWqLS8vW7lcDvM6k8mE70k9JDVub2/Pdnd3g77Y3d01M7P19XV7+vRpSI9tNBpWKpVCmYAa5iy6UTfKo1PTeMp3vt+3oVtfkDct3UbhqbCiDPXw+HJh3KR28KxfKEnPJlFM4SQ9p7+9Rz+tntgge6ChgMQDBv1OQ6aUo3nEvs+xOpP+9gDD93Fa5U4b1Iul7VHFymdeyHlhl7ZAVEF6ihmbvt8oy1arZT/84Q/tv//3/x424fo0Aq8M9eQSsxsvI3Xqme0oQgUNpOioQWB2kz6khq6CRv4ndxfhzd/UZza+L+T4+DjwZDQa96ghsDDwqZsTjhCeGBHqVdIN3Yyfgg812k5OTgIg4jsVmLHx8t5t7ZPOI5SueqtUvmSzWfvJT35iq6urY4DHOyKoQyMVHBEIqNDTn8rlsq2srITzyAlx49FSUOHbFJuTk+guwOOu5PmqnsAYqbJPStHwz3vPdOyZNNITajDwMYSY96wXNaDwWirg9yCIMtR41vkFsOAZBcDqFFOAjOHggQWk/KBdpMvoHTaaBsj38EDHSoFFLH1FIw0x0MPfuoeCZ5Fn9B2jE94p4IoZuj51ykcsFVzgBVbewC890EGdGYytAhTv7EMulstlM7tJszw/P7d2u239fj+ADE2Z9Y4Q+KkOF/L4zWwMPOg8o49JcpA2EpHRCBn81PFU3uh+Cj/mCmLZcO9BCHxjXxBjpYeMeIfYrKTzk/+9TgSAAfJpO+/4aLkS77Jvh+NcAQakK3GqH/J9c3MzAMyLi4twj0Uul7Pj42Pr9Xp2eHho33zzjb1+/dp2dnbs5OTETk9Prdls2tramn3/+9+3zc3NwB+ciswxHWfGAh7o76RI/n3TTMDiNqAi9jf/xwxL/SzpGd+WaYCATiwVwAyUj5L4z9PKNns/jcADoySjXNuvHmK+9wY87VIjXvuk/PHle6PQ7H3vBd/FhIyCB//dtIAiBub8mHplmvSefk6/9BnvcffCW40d712JzcPYOI1G16cC7ezs2E9/+tNg9MNr9ciY2Zhy4ntOQCJCQfnwFMMfDxvggr0MnHqkhgiGCsabfuc3UKvHS+vVuWV2I3TL5bINh8NwCgbtUD4htGm/epOV99o+FPvS0pL1+30bDodWKpWs1+uFPNLRaBT4YGZWKpXCuNE3eIWRpl47HWM/H3Rt0HbC0c1mc2ze6dqDN4wFZ9jv7u4GUMEpUuwRqdVqtry8bOvr67a2tmarq6vh4jtyZGPrgbpnoWnk9ocGHcgInQdqEKl3fBog4WmSDkh7Rg1J2sY4+UsfSS3ktBdV5hwv6ee7blLVd9RZwjqBV8gXNRT9MzHdqAagGmtqvMbK4RmMPn2XcfFjyI96qv06izmAFFB6HhG90P0ZtM33VcGQ9o+bi72BqoY17dDNrmzy9hFlJX/6lO8TefTcNVOpVGx1ddUeP34c5MHR0dFYHxVQJc1ZbxeoTuAeDgWBuvF90uZqlf06p3SMk0iBtOoZoj/Mt1jfVE6rjNNol46jtiUWNdH2KK94VnW7AlctL+0Z5Rfpq4uLi6GfuVwupEOVSiWr1+vWaDRsNBrZ8fGx7ezs2GAwsFqtZq1WyxYWFuzw8ND29/dDtB/nElSv1+3p06fWaDTM7NrJ1+/3LZPJWLVatUqlMqbn4aWeAOmdHN8GffBUqCQj0xv4SXV4Yz9W5iRAooJR644J5mkUlG/vpN+zUKzd3kPj0z5YuPq/Ri5Y3NpnH9nwhrw+78GNeqe8gtHvk/irPwreYryPKSYN08dAgRc4/rlJ46zCy3/Ou/B7OLzejP2DH/zAjo6O7OXLl8H4Vf75tKV+v2+j0WjMQ4YBgzdFlYfmchJKpw38ht/UBTEuGr3S99RTT1sVhPq5oN+rkeLzwtXgQHkxfzWqo2OdzWbt6OgogJh2ux3SFGi3el1IK1GwrfNdj9HT8ceo0Pmtxk42ex1S5kQm8tQ9r3keUHF8fDy2UXtvb8+Ojo5CaobZtUeTKAURC/ZUcB56kqxKkyleTqY9H3v2Q5N3TGjbdE7GKGnNqsNjGlLj2pcB6ZxVb6s6CtSgZD3oPQU6p5gfmuJDWzS1yctNdV4keZZ9+xUgxAwvnldZpoantsUbfDG5r2lPPqXG9y8WyYmBegVffBfzYuu46GdJR8uqLvHpl+S5j0ajEDXVaLDXN54nOg8AL8Vi0SqVSkiNxDFC1AYwygZfnxoIf5h36AX4hIzS+3pUHqs88zyO1ROziVTu+HnD5z76yLgD1GiPN/hpkwIaBSp+jijgUPvBywBtWxJ5R6jOCw+Qza7BWblcDicBcscQqU5cLMeP7iE6PT21o6Mje/v2rXU6HavX6+FS3YODA9vf3w8b/LPZrFUqFavVauGSvHK5bJlMJkS8er1esAuIfHjQBU+/bUAR+PUhC0/rFEz3xmva877c2ETy5cbq8wLUl38XUsNL23jbshRc+MiKLjKtT70PHnHrgoy1z/NH26ICyf+tXsiY4eDr8G3xiiRmcCqoYPGowI+9Szu0bWmhVm2HN1J1TOAPBnypVLIf/ehHdn5+bi9fvjSzGw+/Cl4PplAEajBjWM7NzYUL9vAksjlP+0BZynOMG/jEd8ViMaTiaHuoX8GoemrVSMBIxlNCPZrbTXuom0iNr1PbzLgSSscQI23DzMIxvLxLOpg32q6urk+4QKlzmzV1+JQv6s3lbi7jqlar9vHHH9toNLJarTY2Zszf4XAYPI4nJyfhoiNyZI+OjkL9mcz1Dd16+hM5s5wX7r2GHsDApyRP2jT021A2OubMEZUZkzzxzEevB2bxyKnjQUkNQyWAsdcbtCmN0ry8HkSojIcXng/UncQDjbB4Lz7fI480HQUZij45OTkZO0EoJkvhTUzPes+15tPrRVw4BJgHpPqwTjTdx8sKv85xpMSAhPJP9Yamo/K5rmUFFvBIwZeZjfFYx5V2KXAjr55jPXF4AEQ58Q9e0H5NC9X0OG07/9MmTobSFDP46wGAzj0//7U/CiC87vWgO2lNU49G9LyjcpKeRtdoVE4dTfBC7TCVE8ovDx5iRP+KxaI9efLEvve979l3v/tdq1QqYxfjxcA56X7dbte2trbs1atXtr29Hfbh5PP5MIcuLy+t0+lYu922QqFg3//+9+3Jkye2uLho/X7f3rx5E3QYqVSsU3VAqnxSu+XbppmOmzWLKzr/TIySPNix8pPKiXk6+NyDBDVWtK1JoCRGXpnE6tayqZdF5ie1b6e239eTJLRRFH5BsLjVaxQDGDEkG/Nmx/iiyo//fZ8mgQmeUePaK4AYCDQbD1fGvE8qkFThegCD0Y1hDE+T+q398nOWds7Pz9vq6qp9+umnQUBoREAFsipC9fYj6BB8mUwmnB50eXlplUoleMZ1Xwbed9pEWYT1dX7qfgoVtso7vlfgqt+NRjepGgAGFKUaIwpe+cGbl8/nbTAYBGFJHdwWDG8QpJRFn7lAinrY46HeaDVezMZzk+fm5sJFQDwPqMALyOlM3W43GP16tCgEeOl0OuEEqHfv3tnh4WG43dzMxjZqAyqWlpbCMYUxsMXfzN+Y/PDk5UZsHif9/yHJe0xj8kNJZYPyXP/2OkG9urEyY8aK55fymfmjskbTjdSDrHn+fqw0xTC2P8HLezUAPS/4Xx0TKp9U5rD+uU9FU52Yb6qjNArq2wlvvPNG17vKbTXc/IZt/VFjU4342HpQg1N5pPqHz9WwRe6ojKe/yFR4iYNBDUbmlY6DOlVi9ogS94icnp4GRwPtLBQK1mq1wiVr/X5/TJ5RpgIOPx/MbvbH6clQHGeLvlDQpzIlFk1SUrvMg2I/PxRYxGw2rS9WD+V4XU8ZCmZ4VvWTpj9720v5FwPNalflcjmrVCrWaDRscXHRPv30U/vBD35gn3322RiPiTxpn7yzgj0ZxWLRBoNBSH1qtVrhmFj0Dg7Fo6MjGw6HY1EKNm6TAqU2Usyp+tuiO0UskjxnMYopTF9OmpLznkJfVpLx75WG/j9JSacBmdiz96GkFVX7hauGp1c6kF9UZslefBamKoaYp0CFugoVFeIx4KSAxgsGbXvsO/Uw0S/1sHkD2IMLP86qNP1ihBcxD5ef317IUT5gAGDxl3/5l++964WzmY15/bXdqsRQfngT9XuMbwW1fI+i0ZON1NCgP37cdcx4j/QQD4TwmujFTKoEtd/8KLjzPId0YyqA18sIDH3Akgcymu+uioj2Am6YV4Scl5aW7F/+y39pxWLRzs/Pw82jeiywtpML8NrtdohWcJsqfCFSsbq6Gm7TVlChY5gmK5ViMskDkt9V8qBC1y+f+ec1z36SoZRWp/6OGXDZ7E0ev6Zu8Kye5KPrCoMdcKxj5tsbA4AqJ9T4VuOasq6ursKhD2YWPOMKJK6urkJKDvxTL7zXP3yelK+vzhpkgO5xKhaLNj8/b4PBYMzTmgSavdHrjTUPQBQwEGXVMeB99SyTvqaOEvqhQFXBvZclMbDKd3pBJg6H3d3dMF8WFhas2Wzao0ePbDQa2fb2tr158ybsm9Px1HlAvUnHy8bagRzVFFAfOUwi+q089s970AU48tGhpPJjNpzOR/YNUK/qIr8viDIZdwWZHpBSHjxWx8Hjx4/ts88+s08++SSkrLLvijYMBgPr9XrW7XaDY4pURDZzLyws2Obmpu3t7dlXX31lv/71r21vb8+y2ZuU28ePH1upVLLRaGT7+/v2s5/9zC4uLqxWq1m1WrWlpSUrl8vhvgtdizGg9NukO2/eTgIXMQE5CdXP0g5fvnpJvAdF0XUMZU8Ljj4kJYEmL2j1+bQfBDD/q1EHH7wRowAi1j6v3Dyo8L896VzxhrsHOXymXkIWtM/b9e3X8n1/ND0gZvjr+94gTlKm+vfCwoL95Cc/sZOTE/vbv/3bsMkTJeeBGXNU9814UKXKGUDAu+q9z2Qy4dz64+Pj8KwKQYAI/CXsj2BWvqihRgRBFamuKZ2vhGq5GCi2DtXbp7zAYOOODdpNuZlMJpwqo6Ff3y6dm0lGGGlm/FxdXdmjR4/sP/yH/2B/8id/Ym/fvrX/+T//p21sbETnNMrz+PjYOp2OHR4ehn0VnBIyHA6D8UBe7trami0uLlqlUgnnj8fWYdo8iynh2Oe/y+DC0zSASwG2WbIsm6U+Xw7v63zS9FcPRmiPeop13ahc0HJi7VYD13+nhjegRyMXAIuzs7OxCDdOCHXe0Gc/nzC007yj2jc99Yc0HdIofaqKRn/0c8975aO/wCsW5eBv5Kj2NQZUFFgCRLRsb9zHKDY+emGmOk2azWbIle90Ou+BHJWVKocAbji1YjaD3/PjZUSSntbvVQ9q5E29+woOVTfrfPXyl7kXa4PO8dj33mmqNsEs9pzyU410dNjS0pJ99NFH9umnn1qlUjGzmwtbzSyAcz3hUOUDc5SN3o1Gw87Ozmx7e9sODg6Cw/D8/Nw2Njbs6dOnlsvl7IsvvrC9vT07OTkJt2yzD0/vmtAx8rpjVl7cJ93r5u1pBL4aArzj30sqJ+bRU8+0/1v/92Xcti+TkKE3HCcNrgcUSeSFgS4ivksyfEejURAIZjYmNGNGs/7vhVUSuIhNbF+ettMDCA90/LuqMNRoQECpd9MvNIQ4hqi+r0aur1sjIwqEYnOAfqPMf/KTn1g2m7W/+7u/s263+57hC6EY8vn8mGcltj7oG54bDG6fA8yzamQov1CupVIpeA+pywMb6lHjwM8P+KMnMcU24KnBQVs0AqVHQGqUQT3V2jed26qMVWEpb1RR87mmFzx69Mj+3b/7d/bZZ5/Z69ev7csvv7TFxUVrtVrvjR18YcN2u922w8NDOzo6CkfKXl5e2sLCgjUaDVtaWhq7NZVTY2KGkJcJXll4miR3p3n275O3y2w8ysgcixl4k55Xjy7fJzk+1NDnBzCtz/M5hp0/OtVHRlnXWhbzh7WieiJJjsaItcoa8KcWaTmspZOTk7AGSI3SfRe02d9yr33ynnv4C3/4wZhXo9Ps5ihWeAMP2OOgesUDKTVyFQjxnT8FCd7qHRnkx+vRuso3bReyKZ/Pj409bfCkHm822HICUKPRsH6/H/Y7XF1dhUvRMpnrey/w9Ps0VjXO+Tk9PR27yyfNqccYeU+/znkdV/18GtK6VZ/rupxkM8BTlfG+T8pbv69Bo+pKKlN9JEP3KJCOxD0U1Wo1nLp1fn4e+K3lzc/PBxmvfad89gxms9kgJ3gXB9T5+bk1Gg3b3Ny0Wq1mT58+DXdVNJtNazabIf1J9xwq7xUkx/r+bdKdN2/HvL4x5ByjJEAxLcqKAY1YO9LqNLsRuNNQmtBP628Sqpyk0GPGhuexb7sqNA8glHzoUHkZ82r4PniQEeubN8a9gZYU8fJtZeFkMjdHiurpQpTljwdUBartixlznrcq5LwASyL62Gg07A//8A9tOBzaT3/6U+t2u0GQZzI3IXoV5hqi1nHQXG76pOAQMJPJZEKuMPsF2GegyphUDDaD+/sktB71TsY8md6zF1McHhTyt89nVePD8wOjQ/vBs4y5zgcFD7RbjTcI46LRaNif/umfWrFYtK+//trOz8+tXq+PARYdezxVJycnIQxO+hMeqGw2a9Vq1VZXV211ddWWlpas0WiEI2XVy8ZY+zmYRPetLGLA+kORNxTTZLWOmco1/d6/m+ScMIvrFtrDCTa6FtRREWuXAhVvSOv4xowqbat3vGhd0+rDmC7Qd0nv0YglRrOCCcrRd72Dhef9OPo+KgjEuFSeJfUtyRGh4+WdYbTTjx/j4D3k3nFC9IMcd76jj1pv0hzTecb/gIvFxUV7/Pixzc/PW7vdtm63axcXF8GQzWaz1uv1AtjR8fObzAERGNKqT5IMde9Q0/ntx9nP+6QIVex5r7907vh5Mmnt+rnk+e/nT+zgA/9/rH/a3mq1ahsbG7a5uWlPnjyxRqMxNge0XWbX64pTwE5PT4P813Z2u13rdrt2cHBg7969C6dCkmbLhYpHR0dBf29sbITICWmESaTj6R2l6lT+tkDGrYDFNMIuCTQoeQE6yWjjHX3WK+akOrxC4rM0QzqJphH0SeAqZsh6w957t70RHAMKaUBDhb+Wi9HoBU5SX3gmqW8xSjJWtO8+ROpBFO1CaAAEVZhqezA6MbjN7D0jFR6r98ADKISP8o/vvUeM33rXxOLiov3whz+04+Nj+8UvfjF2jKW2j7LwwuAF1XZns9mQM819CJnM+F0VCrDU6NbvEYJmFm6A5h0dr5hSUSWkz3neYqx3Op33hJyOuY7vcDgMt1HrPiGAGMLRRxk0zUsNhxhY07mOQVUoFGxpacn+8T/+x/bpp58GAIpXKJvNhk2vzMOrq6uxFCjSoI6Ojqzf74d0s0qlEqIUKysr1mq1rFarhVt/dS34tefnlv9c5+IkmlaZfFtKR40NjawlyVWdI0nfx+aUnu7j17BvjxpfrF9vNCmp4cpYTtsPPWkqn88HT3js3Zih5Mv0nm1tF3IDJwJrQj2+OC44lcmvfe/RZw7GPMO0yWz8sAT2IuHB5W/VaeoMUH7pPQ+atkm5vKdpX3xGJEYdI+gH5KzeYEy6C2ucqI16x3VeKKDhe22vyrClpSWrVqu2ublpr1+/tpcvX1qn07Hl5WV7/vx5ADadTse63e6YIal7FBhr0mg0AhWb597ITwK1Knf1cy3HgxY9sTAGSOG3B7PoXr/BO1YGshtvvUZTYusiZnOpblAQqOuE55rNpn3ve9+zP/zDP7R6vR6iVfCoUCiEuYNOGg6v02LRBScnJ1apVKzZbNr8/Lzt7u7aL37xC3v16pW1223r9Xo2Nzdnm5ub9nu/93u2tLRk7Xbb3r17Z+/evQvAptFoTC2/6I+ekOjXyrQO9LvSrYDFtB6UJIoBgiQDVCkJiMTAhU4u0iD4fFoFqu3yiDdNeST97Q3yWNsVXNB2v9AVCGh7VMgBGpJAoNZFHeoF9n1SgxzSnNjbkAcXHiBo/fRPeYYA0vpV+alA8woryfOkhjBloLAw0jEy6QOkix+A0Wq17E/+5E/s6urKvvrqK+v3+2NKSr3tc3PXZ2WzoVL3RMADlCXvMLdpG2OO4tY2Mr7K09gRdcoHL9RUgJnZ2DyDZyrYdO7wPWOnBpl6WniX3ygF9o9Qht5A7ueK8sx7O1UhVioV+2f/7J/Z9773vdAG7Q/jzf8YRmzYa7fbdnR0ZIeHh9Zut8OxkdxVsbm5acvLy9ZqtcKZ5CgpXbNpMimm0JOeV9kxqdxvk2LyQz+PASgFC7EImHcW6fwys7E5kFSP1ufbZDbuqfUgWdupbTUbT2PR9YBM8bKOdsYUv5f3sbZ7w0PbSLnwRscCuUEbaJvyTPuoMkT55b3PSQapOjzgjZ8XSQasepmVT95Lq+96x5OOj15cCIDRiO9odHOyIm31+kLLVh7reCCHMVDn5uas3++HU390g2+j0bDV1VUbjUY2GAzCiYCk6SCPkUXIsRjI8xENs3GAEiPkm6ZLabqX13sY/NzRocBZ01HhI7LaO0d1jsVInUJatp+L6gTTNuuag3iOjAb0AQdrLC0tWbFYDHWen58HZxx94shYjSSxBxD9BH9qtZotLS1ZoVCwRqNhCwsL9vjxY9vc3LRWqxUccpeXl1av10MK3bSk+ivmqPWOlw+pG+5tj4UuWl1YOhFVqCUhzaR3+T/N8PV16HeU4yecb78id6+0piEVyEoq/HyZflGpsR3jkY9oxPpq9v5Z47H+eAWUFPL0IMkr66TxpO9+XLXPGjXQ59WY9spnNLoJYWu6jubjI3SpGyGX5gHwCg1vjJIqRg9YaIuO0dramv3rf/2v7b/9t/9mv/nNb+zy8tJ6vV5oG8J/MBgE4VKpVMImPwS1bsLDc5PNZsP+DJ7hHHP4oalSamhzSlQmk7FCoRD2W6gXlj4yLhoxgD94RTVtgFAwXlJtv849IjTMVY2wUBYgDYGey+XCSSvKawwElITKA9qPUi0UCra8vGz/6l/9K3vx4sWYjKFt3uhjLAaDgXW73ZD2RJibXOdisWjLy8sh/WllZSXkyLLpTtflJMPQz8u072PPqfzzz8wi2+5KacZzrN2qsBVc6Jpjjvt166Mh/pSySW0kIojh4UEv9XhSw1UdHzoGundIDVs16H0/tK9+HGmjziGNNNAeUkj9XgzkpN4yrqdIpfXXLL53RdeeHyPdg6AOkKQycabQLtI7ta9+buhekdi+Ne+k4lkMx3w+Hy47Q36xvqlTHTpeJuJdx1BHBiMry+Wy1et1Gw6HViwWwzypVCq2ublpxWLR9vb2bHd3105OTkLkRaMvo9HI8vm8FYvF90ATbcIJgg7kyNOksRwMBiFao0a3zjk9TEQjYCpDdZ+Izjedv8xv5LcHMTrHeT7mNNHyfFRNn4tFUninXC5bs9m0Vqtla2trVqvV3gOy7KXr9XpWrVat0WgEYKFt8w6G0WgUbtBuNpvhuPhcLhf2VFQqFSsWi7aysmKj0Wgss+Au5PfOMG/S9uPcB90qYpHksb9tI2d9L+l5/3mSwRuj2ET05PvtjfrYM1DaIE5rNOh3HlyoB9SjVm98qddZF6caVUngjbq1XTHjJfY37fQeO4+0VYlrJEMJRYlXH1KPBcqIsjRsGxsDD/pIEdD9Gcoj5V+sz1pepVKxf/Ev/oVtbm7aT3/6UxsOb1J/MKjNzPr9vq2vr9vCwoLl8/kgxNkQrHVww2yhUAh7ODAMUAZ4sxDuPnzLuHBCkn7uoyD0x4fk4TmKU89LV+NCc7w9rzGgdB3h2VfvmRphalD4S60YOy0fr1qhULCPP/7Y/vk//+e2vr4eeIDQ9Wvag3U8l5VKJdzDQfrD/Py8NZvNsFmbfRV6IVKMvKd1FrmlBlIaqfGh46Jz6kOTrhttQ2wfjHe4eIPEbLoT7JIiobG2qXNJ5Z16fnVOqbGEEQZ5g1vfQ976dBAvA/nMO708nyAfYfGyms/U4FMQRPtZpzFdkDSmMVLDLAng6W8F8R7Ead/8WvHyWfnCmGm5/CioQo5cXV0Fw9/MxvSF6peYwws55m8+hwfIyHq9bo8fPw5HiFYqleABJ+8eednr9cacftTBmOm+HkgPC+B59AVy1Y8HPFMDnfx+7QP8Qt4pqPBgV9ur80T55Hmr46rrgPnqbSkFE0lzVZ9Xh1yxWBy7tHRtbS3cL5TL5cK9I6enp8FxRjqrBxVE1Tm5CTB1dnZm3W7X9vf3rd/vW7lctuXlZavVamPPMv53IXisqWlKqt8/JH2Qm7dji38SxYzU30Y7tD3apmk8N7F6ZgEUlK1AIbbYYvWrZyjWTq+c1QumEQRVfr4fWleaQe099kl/+9BxzLOgi0DLQCiSNuTzJ73xilDX41a13T4CQxkYo/oc7ykPk8AgwjGTuY4K/OAHP7DFxUX7i7/4C3v58mU4jpbnuYUVLx3eKAUZpP9wqhCRjrm5uRCFgF/e0FdD6PT0NNxRgYeJ/3U/i24cVB6oUahrjf7qmCpfVbErD3kOA43xyuWuN6Iz1t5I0nbSd5Qu7dac8k8//dT+7M/+zFZXV8fa6Pfb6LzTOaFeTLyBeCXz+XzwZnFMYLVaDcojTb7dVvZ5+eBBvparc9zTfcndpDaqccGaNRvfGKzrUEkNaigGKnjGp0lO018PKhTE6g9tRsawpjAaY/JN91VgTKkhq7zhHTWs1Jil79pH2qJpLshI2qTvenmeyWRCJECfnwZ4qiEa4yn1eSeQH2cFIGl1eUeH54fqLpXb8IOUltPT0xA9KBQKZmYhIqJOnBiwyGQyY1EEvmNeeL2vIAfjtFqtmtn4wRW0KZvNhjYiBxUgwS9OKuIEOn9IiQKKubm5ELEgqgBfdK4hf+FNuVwOc5g1ofsFY3rZ88PbE/DV75nwRH2sG1KD9GQmwKHOISWdVxqx0z1wa2tr4eLScrkc9jOenp6GFFfSmQCB2m/6jqMPwEdkfW9vz7755hsbDAb2+PFjW19fDw5EMgxic31WUiDHPGFd6Fqc1TZP0hlJdC/AwguH29KsijWts7N48malJCXlEbZvy33WHzNktb/esFWkygQze//MaiamV9rTjLE3yGL99l5HBQ7ekPNGgXqd8BDz471+6k1C8GSz2eCZV++f9xJiqCqIQMnyHYIqBsKSQChCfmNjw/7pP/2nVqvV7Je//KX1+/1gYHCEKRvENNWI6IOGNXu9XlCKmo9J2xG4mvONwAOMDIfDAKDMbow43QeiIIU5RL8x2FWoq7Lwxxsqv9UQgzR9AwIQkv+r46SGFH3X+Q2omJ+ft88//9x+9KMf2crKSoju8L4CDD8nFbCivDlqttvthgutCoVCuJ+iVCoFo8XX4cvXz9OUzDRyxEdekkidCR8SVJiNex+9YavrLEl+Kml+dZqSnOTUoR1paxgjijbqnGH++ZQjlUMY/AosvF7S55PAYKxtMZkcA2TMW58iom3nb9ZTbF2myf0YX/UzjdzE+A3vfDn6PkQkWiNSpO/gPFGQBi9Ju+I0Ny4cxUmDbOI3aY/aViLlRDVqtVowROEpgFGBpHrmFYhpBPP09DQYoQcHB7a/v29HR0cBbBSLxaB7mE96XDBgxR+mofWqrOSYZG4CVyANn5F3/ujhmMPTAxp1GEwigBrvQqw/+Kj78hh71tc0lM1mQ5RifX3dnj59ak+ePAlHuXKik+q0ubm5cDw48jwmf1RPXlxcWL/ft/39/bCZG53AfRTlcjnwjvnCnKf+2DqZhpf8Vlnhgf20xNrycyCN7jVicRuA8aGM/lmUpR+I2yBF34ZY/bHPYyABmnZR+rJ8BMLsZgMTixEFST2xdt4WMVOmKhJvbHvl4pUxwkT5pR57vEqc6kEfvbFKXxHuXoF64ch7XOBEdEC9fRr5mHYsFYQsLCzY4uKi/dmf/Zk9evTI/tf/+l+2u7sbogVmFk4XUu8hyrlWq9l3v/tdW19ft/Pzc/vVr35lBwcHYwYL/SW0Cj/xwjD+sbxLzYcdDq/TsEjFov147eGXKnEMeXKQFfBkMuObuxW4qMfY55LrpUSx6BfzDcUDL9gQn8/n7Yc//KH98R//sVUqlbFxQzkpr9XQVyCk6XdHR0f2+vXrcJMuKQz1et3q9bpVKpWwZ8ZHZjxNcj7EHAlJpGsmpvxZQ0le5g9FagTGPp+2DDVU+ewubWHOxVIkvQPBR1v4XPcG6XxCVmhkDEqTr7fRn96IZGzVS6t1xvZaIOeS5qOuy1hbNMLjP1d9o6krqg/47Z0ECuxUFiMvOeZTZZrKeTWk+Q1AQCaSklQul8MBHXoD9nB4vQej3++HeweQtSq/NEWJk+fQJ2lg9+zszPb39+3ly5f27t07Oz4+tuPjY8tms2GzL3VQ5A0AAFrCSURBVBcMogs5UaxQKIRjrUulUnRsdGMx/QdkDQaD0FcPtjWNTff5pckkBU/8H1v3rA119vG/jrGu0eFwOKZTMHyZH36eq14plUpWr9dtaWnJnj17Zt/5znfs+fPndnl5Gfa0jEajcFpbpVKxRqMRohSQRsiY06onzs7OrNPphAtTC4WCLS4uhjQoACBl6H5ReHMbUJFEfl36NYc9oNEN1iiHGnDh6zR0a2DhvdoxQXQbgT+NgvUTOO3/ab12/K2fx+g2BvckkDOpzCSwowAitsiTPGRaZ8wYp1x93ntc/d/aVvVKxUCKtpeJrWhdwYXZjbedBYhxp95BVV4KRNQLqikHnlB2nM5BmRohoCyEH5shVTB6QAfhbVcvyNzcnH3/+9+3fD5vf/mXfxk8G8PhMIAMBDmGtRrAa2tr9kd/9Ef2H//jfwxRj1KpFJ7BC6TGDyeN0D72ecBbboZlw2Cz2bR+vx+AS7VaHSsTBToa3VzC6EPhKF71EJO3S7s0hSmW7qTzUsPQ/gg9BRSZTCZ4mf7JP/kn9uMf/ziAFpSEGoTqLaI+futFaKenp9btdu3du3d2cHBg2WzWVlZWQgqUbtYGVEzrtUuSE7qutK9KXuEzrhcXFyHSo2tofn5+LBf4rg6VWUiVmvf8TXqP8fVeS33G16OyLaYcY14+5IGCbOYb4BLe+hOG+NvvN4rxWPuPjJnmGW98+Lmh6w05HItQx6ItMUIWIve8cwj+JukFPU1Po8OeVG7wrD6v/GGtqheZdzE4+dGN1Pxg+BeLxXBiE/IEgxYwcnp6OhYdQEZ3Oh07Pj4eA2c8Vy6Xw986Z2MyYWFhwVqtll1cXFi1Wg1zjg3Y/MAjP+Yq5z1h7J6cnFin0wmAiPsRCoWCnZ+fW7/ft16vFxxb3W7XOp3OWJSEKAZ6gPIBLhwgosaptlHlk84tHIQ6JxlvxpS/NbpEKpjKAo2YzM3dXFK4vLxsT548sadPn9ra2potLi5aqVQKgLlarYa5Sh8ZO12DusbRmRx+goHO/rvFxUU7PDy07e1ty2Qy9vz5cysWi+GeJAU+qoPuCiyU/6rnuHOp1+tZPp8PKbuHh4e2tbVlR0dHVi6XbWVlxZaXly2bzYYTGaelmYBFbEL472NGfpKnJg0QTFu+p5incRqFxbPTgItJNI13MSlaoO9rlOE27fHgQkP46jFGUc3iQUsCGPq3V5AKRlWRKy+8J1uBg3qF1DDRvur7CENVnDyvKTs8z3F+6mFGWOmJR3q6Cj9ERpIIL4vmXdOnZ8+eWa/Xs5///OcBNBWLRet2u2MATE8gOTs7s8FgYP/jf/wP++u//mtrtVpWrVZD/iyK8OzsLIRgLy8vbXt72zqdTlA+COzj4+OQGkBqFUKJE1KKxWK4yIl2kJbg5waGlrYdYYniVYMWcAKg1Ps1KIf9I/yo8GW+mFlQ5IVCwR4/fmw/+clPwslPamghyFXZq7HLuKHc4SmgYnd31zKZjK2urlqhULB6vR4uO+LGVs2f9jTNevOOj5jM5LeOi94VwGkmKF/2qhQKBWs2mxM3ln8IUsWfZmTGSGVizAnC38wNHYOYLtL16EGAOhHUy63AQj3Imq/Oc8hdbZMfx2k8gUmAw/9NXzQ9lM89EPGGehJ5Q5Y1Pc2c8Y4kdRQljQdywuxmr4j+Nhu/W0LLQSbrfgndi6fONMAjEVj16jI3SVE6OTkJzgOe1z0yyA6MUp7BicJ8SgKY3OA8Pz9vy8vLoQ29Xs9evXoVDH5kJ/zz0ZkkIuLS6/Usk8lYqVQK0XyMb9WbGMuAGdqjF/j58lkT2Wz2vf2M3gmg814dUtSj5OW8T89l7Pxcgv/I5sePH9uLFy/s448/tmq1GvrOmHEaFHUomNC1TbuRp51Oxw4ODsb2nhABq1Qq4UhyImNra2vWarVC32irnsB1F0eP8ljHivYfHx/b7u5umMMXFxf29u1b+/LLL+3Nmze2uLho3/nOd8bAp7ZtEs0csVCBnvZ9jDygmFXZ3oa80vV1eMGb1Ka0wY4Z/irskgCW2Xg6hy+TRa5Cywvpafilgswb4rH2xvof+1v7ngQe9W/1GvrPvZKJ8dx7rjAuNWwe86CZvQ8kEBJ4ttX404WOAaHl6ud4xjy4iM0J2ucNxbm5Ofvoo49sa2vLOp1OSGEqFAp2fHw8ZhBks9mQ/rS3txf4cHBwYNVqdSzCwQlQeIIODg6s1+uNGXXZbDZsMMNTxrnqgC1yT7mBlJC5rilNF4EnfK65uyhAPalKDUB+66kWPk0FLyJK1ezGw4PwKxQK9umnn9qPf/xj29jYGNvUmORthdRjCdDDsDw+Prb9/X1rt9s2HA6t1WqFDY7lctlKpVJIp8BY1/UXW2Pe0Eha0zGnil9LV1dXIU8bT+NgMLD9/f2wdlDgtVrNLi4uQupHzNP5oUg9f9Mat2bvRyaTjFNN01Mnkz6jxpmCYfXOQj6KhkeS9atGpkYqzMZPFeJdytO0nmmdYL6vyhufIhaTiRjUyDzeUe+yRjvgXRJAnrW9rD8fKdQ2KeDz0R9POIPgpY67OiUUnLCuM5lM2NfG2kDn6r48eIGHmjL5wbONnEHu+nnkx8yPC3s92GCupwGyRpFD6skn3SrNHlDApqljpPyUy2XL5W4ugIPnem+D/vi65ubmxi6Sg1cq++CjGu18pil5etAFY0jkQO0IBZn+h7KWl5ft8ePH9vjx47GLSjXigjMGUKQRGdVPmrnAmuHY2VarFeYPY8N8XltbC3yvVCp2cHBg5+fn4ZSufD4f9MddTobyPNX2I3M41rZQKNjBwYG9fPnS/s//+T9hX0+327Ver2ej0chOTk7ChnWcitPQ1JpkGm/JJKFzV6GUVGZauWmedrMbD4qn2wCcSe+kGe9K3rMU88rdJnrhwY7/PtbeaQwer9w8YPDPJn2OcPF5vLyjikXHHaPAgxwWt0ZjWFyaa4iw8MJTvZXeS6GpERgokxadB4YKkGq1mj19+tR2dnbMzEKaip7zjpfZ7HoPxunpafA6mZm12+2xaASe9n6/b6PRzZGyKvjwyJGmZXbjCVReorhRCpov7D2+lKH7Ougn/de8XZSFn6MoFwUvqkx9e+F/pVKxH//4x/ajH/3IqtXqWF98lEtTBzAGMBr1okKUfLvdtsPDQ7u4uLBGoxGABaetoCh0T4+fAzGg4Y2p2FpT3niQilHUbrdte3vbvvnmGzs8PAxGEV4q/l9YWAgpBJVKJTGF4kORrl+/JmLP8pu+MKemkVsejPCMOpy0XJ3b/l0f0VLljUHKd34fgZmNpaRpRA9SGXMbmgag+X0KtEH75sdHvZ7e6NfPpiF1rGjffXl8pmuD8VLe0v5YOxgz7yDQ59l/oREojGTWsN5poTYD0VEcQXppZxpPYvMf/iPPYg4ts+s5hOGnx8GenZ1Zr9ezs7OzsXmnzhx0IQ6Hs7OzcCiIRhyojwg24E1lhDrrNBKtcyMWRaCfHmCrsyuWCqRRBI1cqz7AKVcsFgNYarVatry8HDZMI6cBigqivHNQ7QEF5Fr33Nz1aVsqP/y+lLm5OWu1WiFV7OLiwo6Pj8fucIpF/2clBeK0V2UJQLLValmpVAqpcb/85S+t2+0GINzr9ezt27c2GAys1WrZ4uKiNZvNqaPa96ZJ0hSC/2wSGIgZ4JP+TyOvCLxxjfGSZHTPWp/3pMXq9u1LqtcsOTKhqHRaihnACG5vrMT6NYmS+Ou/9xEkH6JXxUsfMeCT6lXw4L+j/brwzMYvf9PUJhSGpi758mIUMwr9+/4Z/t7c3LRqtWrffPONmVnI+dX8UZ6dm5sLEQrN7ybn1As/D6Q0HQAvGcLT83I0ur77gXHSKJE3/nV+ec+h8l09VhhyKOOYIEfwa9upgw2MuVzOPvroI/tH/+gf2ZMnT94Tgt4gurq6GjvuUA0Poj1XV9cXI+nN2ldXV9ZoNGxxcdEajYaVSqUQ5dH0DG9UxuZPEoBgnvj/k2QFwOHdu3f26tUr297etv39/bBRv1gsWq/Xs+Pj48B/ToM5Pz8P+0F+G6TGRpLnXo19Hf9JpE4A5qyW4SMftAVjFOOAdpLn7aM/rBM1DBWc0A7WhG+D1nvb6MVtyesEbYuux5gcpU+stUm6yPdb17hGjPR5+I4BrGCDZzAOzW48+xr55Dnaq7JAx9CncJIKwvrWqGqhUAhrX50b8Mqne3oexIxqle/szzCzEH3kNCuNotAvoqnqAOI0KaIQOJGol8tVe71euC9DQUY2mw2nUXkAHLMlFMyk2RF+jDVFTY1xIgeMqUbZ1NEE6OHZVqsVTny6vLy03d1d+3//7/9Zq9Wy7373u1atVm00Glm73Q53QAE6PIhWwDSNfaTzgL0/3nGhII+xYh7dlbzzyex9XYxNwB7EWq02FilhPvV6vZChAHCbhr61U6GmFZK3FaYxZZxk0KtQiZWhz8S86/fZdp+WoR6jpImcBHxm+TzpOfXua30xIyepnBipQZQELnTzku+3Gq9qhKiXS59FWWh/Ysr86uoqCC39QUCpQFUFivBISn2ij94QVCXnvUr1et2ePHliv/zlL+309DScRqFGNcb3J598Yp9++qn9zd/8TUjLUSNIDRRtD+ljGrJnPwL84h1N40EB+bGhPB0rhKo/no55rekBjKNuxjOzcBIXxi7RF4Qi4WM2Yy4vL9tPfvIT+/73vx9OffIKTseeuQNYw8AmHI736vT01A4PD21nZyfcL0Kkgovv8ICpcZAmf+6D/LwaDq/zp3d3d217eztsKCRlAg+ornNuLkdx3sdNr7P2QY1Y7U+MdK2rgZ7m1PIRCCU17ny7/DPUqR5V5pfmVSs4YP2ovKEcHbdZjfM0mgRkqVN1ju5TULnEd5oCYhYHa2kGV4yU5z5VQ6M2HuSow0TLwiDFSFMDPfYMfFDdoTKBdgEsOMqVdCO+i+WeqyzTiLK2Q731OhbKE6IkOIx07xlOtuFwGKItanwzPnjvSZVSzzkHeSigu7q6ClE15K/XDfBRHV3U6dezZgMwxn7fkZKW7w8BAaQpQFddwDydn5+3arVqm5ub9t3vftc6nU6I5l9dXdnS0lK4AG8wGNj5+XmIylCO6k11iDGGCq4VNKhcJooS6yfl6FzWSOJdSO1GXZfexvQ2mdo/ZER0u13LZrMh1ffegUXMwNYFmmZoTqNU04R7jLyyTqonqRyv/OmfGnue8dO0S8vhf7M4j3wYOMkAiYG0uygfyvDGcFJ90DQG0qRnvOLz8yoGYrzC1tNC+O0NjbQIgb6L4lFFgfdDN8lBCii8d38aHsR4joAZjUb24sUL+/nPf26vXr0KXgPARTabtdXVVfv000/t3/ybf2PLy8v2n/7Tf7K/+Zu/sb29vbH9CKS5IDCy2WwQoMozDZHDB+81QVhzpJ8aQb7f+hsPo36vxok+r2NZq9XGFBF5r5xcwudnZ2dWr9ft+fPn9sMf/tCePn0a+MgcQVh7QGFmIdoDmND/B4OBHR8fW7/ft263a+fn52ETYLPZDLevak6sH1N+khSL8mVW4KFyRr26XCTI3RoYCgq0GF++Ozk5CcdaflvkFa6mNsV4oYYK5D2/+rk3fKcl/64CFDWIkBfqgRyNRmMbvBU0eEMdYK9RFP37NoSc9N5ir8/UU657a/D863vTzN/btNG3jXo0h12BhsrgmK3AvFY5jmxTHYwcw8Hh50fMiciYYcACwpN0gAIOv+/Cy6Bp9TjvZ7PZcPQpexgGg4HNzV2fPsT9PGz01lOxms1m2GtwdHRkX331lb1+/doWFhbChZ6dTicc8MFm8nq9Hhw7ekQvxr86vpC1ergBPNNINPpI54KmP8EXymHMmCOkMqnco24//2u1mn3nO9+xZrMZItFffvmlVatVazabtrm5GcAh8of5w4W1vKdt9elaaqck2QZKzFuiMLOC8xhRRpodqQC63+/b1taW/epXv7LhcBgicOzj4RREjlmeNqJy64hFUsO9Z3bWMmdl7DT1ecHk302bAJMmhr6vA+oVnf6thnDMU+SVgq8jjdQjOWmixjzq01DSszEPrY9KaF+0DfBFFY/yhfc0tK0RCxXWagwktR8Pi3qMUE6aCqXjg9BSJUYffSg7xmPfd0iFQbPZtB/96EfW6/Xs5OQknM6xtLRkn3/+uf37f//v7dGjRzYajezVq1f29OlTK5fL9uWXX9rr168tk8lYr9cLufMo0EwmM3acop7YoWOkf/v17I0qndfwUMdQ+eM9dGpImd144EjLyWQydnR0FMZRjbpM5vpYwOfPn9tnn31mz58/D2e3k6eqESt1GKjnfjgcjgELDKvBYGAHBwfW6XRCKlG5XLZmsxmOkcULGNvEqHM9af4lyQd91z/n5YsafXNzc1ar1Wx1ddXK5bJ98803Ie1BN6Tmcten5aCQMYDVG/qhSMdA14v3VCe95w1c1nySkykWjfDlotSVYnJBjSU1HNXbrvNe87ZVPvhyNWVq2si454k6OjS64J1HafM0Nrf43Htj0wDgLO3XcihLozYqi+BRkvNQDVbAEu2lHB1r78yCYrKctYIBy5HkSfzkOY0gwDcfRZ5Gp7O2V1ZWAqCZm5uzs7MzOzo6CnVy50KpVLKVlRUbDofW6XTChXtXV1dWLBZtaWnJ5ufnx47JXVlZsdXVVTs8PLRsNhv2jZBfj4HJXQaMx+npafD609ZMJhNSti4vr0845JhyoiS6P4GIte6RIEIOcCK9N5PJhH0li4uLISo4Go3G9rvU63U7Pz+3t2/fBjm9vr4evPD9fj/oQy7HUx2l+kAdT6xpPaJY9ZzKNk9+3P3f90XevkKv6oEuZhZkvu4roZ2aFtzv9213dzdkJ0xDt968neZlm/VzyvPkvdkxBZwkaNI8Av4d/T9W5zTtTgMZWk5MQfr3JpEKTMqe9L4KahWySUbNJJA3jZLxgt1/7slHe+ChPo8gwqugYchJkTPqQEmiNDF2FFjo/9pPNYx4JuadmBawKWDh+U8//dT6/b797//9v4MReHR0ZG/fvrX/+3//r3355Zehv3Nzc7a2tmalUsmePHlixWLRjo+P7W//9m/DvRbD4TBEMFTIUAZ3WZiN316NwgaEeGXqNxea2dgzGpZHiWQymeD1gtT4z+VyIULAjbOMazZ7fVEURwZubGwEhYViUe8PUQ34hLJSoemVBp6aTqcTUp84YrLRaFitVgvH76mQTZNFsb+TaNIzfO9TCRir5eVlW15eti+++CJsFARk+eMcURT0eVbv/iyE/PH8uItxetf24KTQNsBXBZ+j0c09Mj4lgjmGsTQ3d3NsJ4ZVzLEFPzR6NAkIKWkevTo6VK5pxASjzUcacTyoUa7v8n2Mbus8TJPXrF01zliz+l6MF/49viOFlNOfOAFK+UaKDe1ToAKfkYFELJIiOdMYX5Oi3krlctmePXtma2tr4dI8IqkcAY5O63a7Vq1W7dNPP7VPPvnEDg8P7c///M/tr/7qr2w0ut6Uu729bWZmrVbLisViMK65QZz7HhYWFsIxrXisT05OApBBViMrubdjYWHBut2udbtdOzs7C4Bnfn7ednd3bWtrK6Rhwk/GqVQq2fLysq2urtpoNLJ3797Z27dvrd1uh+PTzcw2Njbs2bNnVigU7PDw0I6OjqxYLNrGxoatrq7acDi0d+/e2a9+9SsrFAq2trZma2trAVitrKyENDEFRXNz13c9dTod6/f7trCwYKVSycrlcgAlnApGRErBPWPrSde3Ty38UMQ6vri4CId6MPakNV1eXtr6+nrQA2QIcPBHt9sNp0m+fft26jbfa8TCG5t85r0hH4I8mEjypsbarwawhqM9OJmWqR4xprXVtyH2flK900Ql/PP+XUjr8RGVWQyAJC+rBw1J/U8DIdpXQpeqtNUj4D9X451nVLgjVDAY8UqpktD5oO8kRStiRmXSHFWeF4tF+9GPfmTFYtH++q//2jqdjmUyGXv16pX91//6X+33fu/37NGjR1Yul0Mf6/V6SMnBa4UBDD8QHOq94FxzvNts4gOIaGQDzwYKmbQbDBL11sBbjKxOpxO850oYcZeXN3dicDoFhOdsY2MjXGyEtwnBCU/VW8vcJeLBBXcYKIALDETOqyfik8/nrVar2eLiolWr1XD6kxpxjKmun2nkxSyyBPLrysu8bPY6TWJ1ddUeP35sZhbSIeADY5DP58McIZ3rPvJ7k8g7ID6kUoU3Po1RyUc5aSPEWiSioHOfOcaPRjU08sB89DrFG9fTRiq8TNY2+zmon/mIseeDymYdHzV+NK/9LhRzwGlbY9/RlhgvtFwvg/UZNscyjrGjYHE46Cbu4XAY7gYirclHLLTt+lujWL6tOncmUS6XC4Z/tVoNaZocDV4qlazf79vZ2ZkdHh7awsKCra+vhxOflpeX7eOPP7arqytrNptBL9RqtdAG9B51cLAD6biDwcB6vV5Ip+VYbdXHeqEcc+7q6soWFxdtdXU18KzT6Vin0xkbWwVZgNm5uTmr1+tmdq3fuEcIMKT8ZvwGg4F1u127uroKegw9TeREN/drSiZ94V6Kvb29cKogezB0/6Uvg3Wke9kU6Pq1+aGBBfXAI06a7Ha74cQn9qN89tln1u12bXd31w4ODiyXy4U7PWaJpEJ33rw9jcF5W8+Gp2kM3KTBSjPyIG/QxjwJk7wLSe2e1PakiRYziCfVHXsmbSLzXdr7/rNZgGISuIg9p4pOSRcoxjLGktahz2t0Q5Wk5vFq2FyjEHrjZoxfPsIxSWiosetJN+KZXQvjUqlkn3/+ub148cK2t7eDQF1dXQ0C3UesEOjD4dAWFxfDaUl8z63ctIe2aK6xemAJQ3c6nZCzqyCFIxYRtuw7ODg4sG+++cZqtZr923/7b+173/ueffHFF/af//N/tp2dneBJR3nRBzxYjB05w0tLS7axsfFemsNweL1hOZu9PrlET/pSoZ7NZsdyjRG2HClL1IYQOZEeBRVspKTuGFBMo1mMsrSUoNjftIE88I8++sjy+bwdHR0FkHR6emr7+/u2tbVl3W7XSqWSNRqNMY/hhyaMLTXSp1Wus+gQNURj79EO9YSn1aWOBL9JP5vNBkBP39jbwnwlNUr7T926eTOtj2qIauQZgAKwT9ssmkTIXNqijgF1+NwXUX4sWqRgK+YIjKWZwFdSPpUHlIEhXS6Xw7pn07PKBR/lGwwGYQM1UR+/YVvnk0a5NMLt9wbNSgpU9L6cYrFo5XLZ9vb2bHt7O3j2zcy63a7V63VbWFiwP/iDPxhznvm5Qpvpx/n5ue3t7dnr16+DEToYDGw0uk7XJcoBYKPfRH+vrq6CAb66umpPnz61YrFop6entru7a4eHh9Go9cnJie3v71u/37dyuWyNRsOePXtmc3Nz1ul0rNvthmd3dnYsk7m5GZ2LQL/66itbWFiwSqVia2trtry8bOvr67aysmKlUmnMtlPwqm3gwjvSxzgZCx2gxwurHmY+EfXSA2Ducw3NQpnMdepwqVSyzc1N++KLL+ybb76xX/ziF9ZsNu0P//APwz1au7u74TLVZrNpGxsbU9ndnm61eTuGzpPIe1T857HvoGmRku+49yB4o9l/FmtvrA79+zYpU2kDlBbBuC1548NHKSZRzAvG50meVN8PzxfvHfNl8z25k74f6pnixCCUlHog+U5D5x5YsPD50Y2VCGFVCMo7jXak8XTSOCLQ8Hiqh3A4HIYUHJ6j/3rmNgKNNnFMLoqWdwFJqvgwmFRRViqV0D54h8LAACHCkMlkwkZpBG6/37enT5/az3/+c/v5z39uKysrIVUEPnOPQqfTsXK5HELYGGl4z/gfEIcnUfdKzM/PW6/XC3my6iHyaVbqgdbNj6QYZLPZcPY5qU+6aRPStaE8TprXSbIsNnf8Z7F3NVqpBk4mk7HFxcWw4R8jamdnx7755hubm5uzo6MjKxQKVq1WzcxCJCsp5eU+SY3jWUCFet6hNG+/GgwxikUXeNZ/59N2GGvaZnaT9qfzjfmi+drIKrPx3H8/d7zBp7zTdsb+1vlHO1ROqUz2BrjyQtvhP1eaNa0jNjZ+fGN6MknO+gg7Mo1+KnijHOQJjheiFKovtA3KewV3aSldfux8GbPyzGcYkKbD93jWs9lsWNuZTCacaqUn+qgjjbZ6/YnzB2OblNlKpWLLy8vWarXCXUo8p04OQAenMC0sLNjTp08DOGm32+EIbPiIkwjwBChH7jOXibSq3iIie3FxYYVCwZrNZtiUzr0NSUdqwwPAW7FYDNEdHFNmFuaI6gLABPIzybH42yCfWZHL5YJuazQalsvlrN1u28uXLwMoZZ8KJx7ibIQH09C3ciNSGqiYlpKMcj5XsODBjApz3pm2rbdt86T2TqIk77ZSmkGblOaURjGlkQYuYv/7MUhqWyxyoUo1yWvoy8EjEFOMZjaW+uLfRfj5s7KTgIVXrEmgIs2o0Xnq5y7fq8EfWzt8b/b+hjAUJAa5es00uhMzEmIgkHrw2OtzSWlH+XzePv74Y2u1WvbmzRv7L//lv9ibN29C1ANFXiwWbXl52TY2NkKEhb4pwNSTM1B4XOiHx8rs5gQRlKQqb1UopEX1er2QP4rSQuDW63WrVqsh7O5PDYmN66wUC5HHyopF8DzY1t/M7aurqwCaSG0rFAohLUGVNrnnH5IYD91PNC3fWMNJ6+G25HlGWWpw6uEBfMc7sXFh/sJj1oWe0qaGPXVoufx4ozjWduWFzn1kiK5T2q/y18sxLVf7p8ZJzHD6bRlPZuM8Q17ACyJIEDISg5AUGwCgyhx0g5mFdzSigqGZBsR8G2clBSKZzM3R2MisSqVi+Xw+bLLGs07KVlKaY1JUyOwaGDQaDSsWi7a5uRkMSxxKOH04tpa9D8w5vPl6K3k2m7VHjx7Z4uKivXjxwl6/fm1v3ryx/f39ECnK5XK2uLgYNma32207ODgI+93m5q7vb+LSu1qtFuSz2U30PZPJhP4TcVCHgCecMBznziEd9EkvUGQd4yTjsjs1yuH5baMUSTphms+TnNSMN3t2cDJ1u137q7/6q8Cber0e5hypcAoAp6E73bztOziNYEkySO+LvMK9DxCT5Km5r/rS6pg0MSfxPGlC6veT2j1pbKdB5zHvjxrFsSiI/zzmKUNY68ZcnlXPvO+Heng44QchqOkuMYWbZBCm8cAbQ97Dhvdd88LVYI/xx3vDUIoY4XraA5/5sU4COAp09DMFNvCYOjQyMBqNbGlpyRqNhvV6PVteXg6b+eAxp2rQVt1EqjnMlIdBpJssiUDgdTcb9yrBD7xVKAFOfuIOkEqlYvV63VqtllWrVatUKuHsd+Vv2npJA5SQn08x4K7l87c3Yum3Hyv6T2rA4eGhbW9v297enh0fHwcAbWYhWkPa24cEFp43Pu1lGrkJD+DZtA4a5gplMJ4YKsxbLy9oo7+ZV+WXN+bz+fxY+Vqn9t/s5pJIH53whiRzwI93zOut4EF5r8av54PyV+v2PGRvjneCxEDuXSnWPt9PeBKT0do2fzITP3qIBHICj786o87Pz21/f9+Gw2HwvjcajSCnvFNL/04a+1lJeUFUfTgcjkUhfL36M8l5ESuDSL7ZuNNGASvAS0EzKYPIeeU5jsCFhYVwMEa32w1jkc1mrVarWa1Ws/Pzc5ufnw+b7ZHLzWbTFhcXrdVqhUsEdR+g7nGgL5eXl2HjuafR6HpTO5flsWm9Wq0G8Ejf4YuZhTRe7xTQ/Re3BZJqe8Tkl9n7UUbV+0Rv4IceVHJ+fh72ZLbbbdvb27O9vb0ArOkz+y71ZK5ps4juFLFQxXgXir0/bQe0LUl/pxm+k0LB0wqDpOe8RznJING6JgnUaQSVF7gxQ12NQp7x5SYZtvp9EijwClHfMRvnvedNUrm85wU2Jxyo4qduBIH3LM3PzwfPDscD+pM6fJ9jSnfSeCQpX1WCXjniTdb9BLFyY3zUtvJ5LGrnDVL65te0GlG+7xj9Ct60b3Nzc9ZsNoMXBPCAAOSMbAwX3sUr6oW2brocDofBkwZYoJzRaBSMaLz31Wo1pD/1ej0bDAZhkxpRCja+63Gi1OXXsAp/5X8aENd1mSQLkoCGB+P6P8oA4HR0dDR2W/hoNAqnx8AzLtDjHotZQt2zku9rWhpJjJBTrOFZTlBS0MqcZY4xX9SQ1HJ5V8/vZ/zUANUUCt3b5C+JhLR+1jfGWYy8IZ208dT3W73rvMu89nPM7wUwu/FyksZI/xXoY2jeFVR4/aeyOKlvXlbRLgiwoN/rpXBmNxuPNQ2WY6eJ5G1vb9vBwUHYDExqEUBLeex5eluvdYzUcE2jNJvnNsTc8PpO2xI73MDsZu+BRuZGo5G1Wi1bWlp6Tzcxv/v9fpiPg8EgRDKIJOP4oS2q/zSyRIRaZbf+vrq6sp2dHXvz5o1tbW3Z4uJiOMJcx5YUXo5aRy4wznpUroLZ2xA8MBtPh/RRLw+MaRd9JsVXfzg6fXV11VqtlrVaLVtZWbF2ux1O2OJQl+Pj4zFeTitzZ4pYJBmWsQHzRkvMaPVeOf08FmaOUUxhaZmqlM3ez5f13i/CP749MVIB6D1CfB/zssV4lGacxnimfFJjUBWDTwdRfkyqS43RmFEcM1b9M+o18u2OGdVJuaoxPun/ehmSnvShAo928Q4hUk640FQofYfnFczoWvB9TAKyk+aTzkcMJ+WvB4mez2rk+rnEHNS5AnmDWcvWsU4aj7S55HlgNn4UI4YYoFCFl3pO1HjWXF+AhZ5gpcqL07RYnwpWzK4Ninq9HrxTeMTwgHkA7Pvi+ZE2RlDMUFJZlwZK9FmN2uBdAiD0+/0AKgDW8JgN6tzMzXnzp6enIX3uPilNIel68gaiJ28w6n6ZNIWn5SqPzeIpTawj1oMCWz0MAoMF4MHmXl2HAGWMBL03xINTjHPq8tEpb/AneaLT+s971Kuf6XqPOXy0zwq2pzU0piF44I0+bZ+PEkExY1aNfQVO8Jx9Wio3OOgAw2w0GoWLMUmTnJ+ft8FgEBw/CoD4rfXc1aj3FNMxH5qS7JNYW5JsQDMbGwMihkkGeLlctrW1tbB5nn0XGO4qzxlvjqRlzJmrOn/1IlQ28SMXFTxoarS2XfelqA0WA/y3JZ371A1Rr+6LG41GYe3AWyJtOzs74R6QXC4XnHDv3r0LcomTz5SXABN1ntw7sEjqfNr/05A3dO6jHUnPzFKPPjuN8J6GkgTCJO9CkkGd9s59kjecvRE8zTyIPZcEWHy9fJ9ktPNbFbcazCgsyiQFClDhvQw+iuPBxKQ+xGja52ahGKD3f09qz7RtSZtvScA37X2zGy+L32ipBqD+T66096Jq3RgG7Oc4Pj42MwuAEyU1Pz9vS0tL4fSncrkcoldqHE5L3hESAw+xz70xFwNtnuCLhql1A3qn0wkne7Hfhnxh9WT1ej3LZDJWr9ft448/tqWlpZn6PIlQUDFjWtMY1TiIlcG4eu+cf2aa9sRyhD2YVkNeDVme0xuI1TBFucecS75MX7/KHVXiaogppc3PtDXto9R8prLEy2AtczQavXdj8n2QyncFdPBUjTmVCfquggs1vDDQcBhgLBYKhWBgnp6eBoOr3++Ppb00Gg178uSJbW5uhrmKgyO2T8/P7W8bBPy2iHXKWJi9nwY4TaQNyufztrS0ZIuLi4lOOz7XO5rwsvsTBAEejDPy8uTkxMyuHU148NlDwgV4s4zlXcebeW52s141yq1A2DviVJ+cn5/b7u6uffXVV3Z1dRXuODo+Pra9vT3rdDrhjo/V1dUQodE9OTjz9BLZaehWwCJmzPjvbvPuXWkarxWUZJTxnTeE1UjVkLmWkdYnb8glGd/ek+Q/17+9sXsfE9ob8/pdEghMe26ad/xnujgm8VT5Qd6ppiaohxzlRH4/EQu9JVWjGzH+TGrLJPJetdj3/E4z0mMA766UVMa0oGJSOVBsXUHqsTQbN3LI283n88EgoDxySLmLgguaOI4Wg/vi4iJsPgRQoETSUi+SSNdiLMo6jQKN8cR/rqk1bJg8Pj62brcbFCX7JRRwXF1dhXxaFC8XPK2trdnKyoptbm7a0tKSNZvNqfs9DSlAU+WO0TcNGPbrwL97H15zTW1SmYL88NEJPkd5o+w9qcL3G8AVrCCvNMdZ3/XrG57E0pl8qoR+DlEPn1MGfNXPNarkPbZqAN0X0RbdcO6j8jFHFu1QIzCXywWHkQce/qQs9WZzyAH7rmq1mlUqlRD903f5UeCoDhF95v+vBL9jc24S+VRTdSqpjaEnH41Go3CZHYd8ABJOTk7s6OjIjo6OzMzC6Ud6o3mj0Qi3cetR9N8WxdZxLILpIxd60a3Z9XHDHDHOfSbat3K5bNns9QlbON3q9brlcjl79uxZiGz7Y7GnoZmAhTfEY94M/+w0lGbk35UQirN+p8/o30lGfgyM+PeTjIckozQGbpR04k0ybLV90xjB3iMYMy4ngQNVAtMYoL6vMZCS1G4EinqlEEJ6vwP/674KPQFKFURSfb5Pk3iZBhKSeDvpmUnlTqJJ790WqMRkQdIaSCKdezHPtBp6eN8xqkkFwmvFqSmVSsWy2WwIk3OUHpEK9QpPGi/fTwUXsXbH+JM05vpbDVKAE142IjK9Xi+kM3E6i262Y0/JcHh9gszl5aVVq1VbXFy0p0+f2vr6+sSjGGclL8sBbD56MSmFid/eg+6Ny2kAv0838894WWp2Y6RiFOlpSton0oPMxjdy+jbq/8oPf5pZErBO0z9arkZNVN4rD7TNAAXaHwNayEXkpLb1PpwaSgouoEmOO9qDka/gwkdoaDM6QvsGAK/VagFs47WGd3rKEaS88g6fD+FE/ftCk5xR09ga01ASSM9kblKhNRpyeXkZ9gwoWBgMBnZ0dGR7e3vBucQt3LRXTwM0szFH5X2CxJizIPY9/da+m92kWHKxLWlL2DZEGXgeZxyX4hGdJ+2Lu424GE9l76xz+N6Om1VD8rYT6UMswNjiTpv0SQLMG0x+Uujfmten5epvfT7Gr0mG/bSE4Ewy8Gcx/Gc1srXdaX3Qd32+s68nRni1WGgABU2d4DkMLJSD7q1QcDELv6cdn5jRzecxwKefx+r05cb+j3n3PFhLenea/9MoDRAlUVJ96qVSDw1GNpvN+BsPTK1WC6eIzM/Ph43Lg8HAMplMAJfUpXPvPuVRGoD0+cC6Yfj09HRsPwQK5OzszPr9fvickP75+XlI0+BIypOTE7u8vLSVlRVbWVmxtbU1e/TokS0tLYU9LvelLJF7jJV6kNVg9TnyMdJ8X29wTzs2MRCQpsSTyqAc5Ap7f1DabPjV40epF48pBo+CFKVJ0Rd4SNlJoAJgAe/4XMGP31SuZfOuntKmoEaf9b/vi2JG1TTRKU0h8dECBYY+UqPzlZPgLi4uwklCbMr3F0pqlIf54ftx38Dr7xv51EQPgO+DdA1CrGWdn2ygxonEDd+kyJ6enob7M9D/jUbDCoVCmF+cDAZ4OTs7s6urq3CMbrFYvLd+xdJBkSvav1wuFy453d3dDZe4lkolOzk5CSc7zc/P2+bmpm1sbIQLAi8uLsK+u7/4i7+wSqUSAAT7VvQ3d3fchW4FLNTgmWTw6e8PTWntiX3njbNYKkPS8/5zDyS8EFbvziSexRRGTKjH6uJzn0Y1i+Gb1u9JwMr3Y1KftX0IdhX4MdJnKFe9VarQ9W/KZIOWggoPKHRMYwahtvkuvJ307rTCOQ206Oc6F/SzafrhwWPSnPfvzMqfGPjVsC/pQHjpiVJ0u107PT21TOb6lnGOJOQY2Xw+H/JLASRcPujrm6bdsyjOtGcBFEQmUICACqITAAifI6zRieHwZsM7Sqvf79vc3Jytr6/bxx9/bB999JFVq9X3wvyzhLpjpF5FbwQqqJjkfday1ADXNTeLTlGZqAdtUE+s7th38Er5rN5v2spFeGoMYaySSousoz2a7hNbC+qJ1xTR2PfUpeWyBwBDif75ujQ1SD2WusdB3/k2UkR0TvF/GvnnYm3UvnogzFHXnCSUy+UCAGfNqBE4Go2fNOb13T9kYKF6dhawftu6+K2AUXmvJz0CDtlbwWb90WgUQEK5XLZqtRqOIlfvvtnN5XdEAhYWFm7l6PV6N8kWVZCr8nQ0uj4Sd2dnx7a2tuzi4iIcPDIYDGxnZ8e2t7fHHA9zc3PWarWsUCiEY8d3dnbs4uIipP+WSqVwzL6eFhfLFJiFPsgFebfxLM36vF+40ygq/TvGLM1tTXrfh6Y9TTIgvNBL8/ib3XgDYt4hfcencvg2pSnSJIpN/qT2ap2zeBO1fR7YqTKb1EZVsB5c4WUyuxk/PfkhthnU90f5F1P8STxOGpP7oKSoQ4xicyLp80le07Q60z6fJJCT6iZagTdeje1ut2vtdjtcUMQFSvV6Pdy4igDGw9Pv98PFeOfn5+HyJDU0JrVx0jr3/UkC36PRKIAJIhKc0uQ3ZuszbEJkQzvKslgs2srKirVaLWs2mzYcDm1ra8sKhYJ98skn9ujRI2s2m2ObK9V4vAux50VlFOvXg5ZZlZX37E27t8LXDwgws2i7fA63/gBqdTOw1oMMIJ0mNp8BkJrOwPGVAAbkuRpQPm2JdgIavHMEg8//zcEVSf2jfh2/0WgUDLQYuJh2M+5tibbMErnwlMlkQqqfGqh6mpd3RCnIgnRu0Fe/bnR+6lj+QybvVPDz9r5J9by3gwANtVrNFhcX7erqKuylMzOrVqt2dXUVjlmtVqs2Go2CswqgiAMyn8+Ho231pu9pifUUm8d6dLqmOeEIODk5sXfv3tnbt2/t5OQk3GSOLiuXy3Z2dmalUsmazaYdHR3Z9va2ffHFF9ZoNOz58+f26NEje/LkSXBEFYtFq1arViqV7Pz83Nrttm1vb1uj0QibuPVQFC8Pp6GpgUUSwqLi2DNJ78a+ixn5Zu8b4yxW723l+5g3Nq0PMQM/yQgwG7+YSstXw3gS+FCh4w1T3WCmnvbYQtVnYyDD9ylm8Kpi0TJUOMQM6ST++LLVEIuNiR8vH91RY4Lv0wx7FIieCa+eJvjPwlWFHEPpyhfSynz/0kCFKuck/vnntE+xtZP2/TQAz889fS/W/ti7Wn8aSElrS9pc0vYAKhD8bMQ+Ojqyg4ODkBo0Nzdn9XrdFhcXrdFohBzparUajtQrFovhcryDgwNbX18PR8wy56fdd+UBBu/CF6JjXm5heJDuREpTt9sN92uwZ0Q3agMsuCWY+Vgul21xcdEePXpka2trtrS0NLbhlM3ahMDVo610VyNA16jKoGnSnpJI5aCmNE6j5NQQBgyowaxl8bcqeHUmecVv9v4RkP6SrtjeCX+aixq52mc+0zQmL8fVcI3l/MdOuaPdgBl/ZKXKBoCOeud1U7Ifp/sEFV6meJnlwUWsbg/MYmmufKabd/Uo02w2O7YB3PPAnwLmgWnMk/+7Tl5vKDDV9fEhQGZsHbHGOGoWHWF2LfOQw/wm1YmUJk6FQp5qlJS/efc+SG0G5oveBM8zHEaDvjo7O7PV1VWrVCpWq9VCBIWfZrNp7969C/cYMeeXl5fHTvzTk9DYp3d4eGjZbNZarZaZvZ+KT6R1WrrTqVDTPDctqIgZoGbvg5YkIyatbb4dKjgxBFSQavlJ7U8ztr2BoXVp/R5AqOLz6U/6bOw76tV31VhPI69QYvz0qVVJFBM6Sd/5seR5b9zRJ/9sbC4oPylDlQV91c88gPJGRwzExv5P4kPaZ0nfpz0bWydp5U1SwGnkjeckUOffuS1p3zBmEISDwWDsEp+DgwM7PDy04XAYcmUXFxfDzbjcoq23s2YymXDs3u7urvV6PWu1WtFNnpPIgwqNePg5i6HB3hAAA0qQKIwHF/QbYMWJNeTIrq2theMCV1ZWrF6vB8Wp6X9m455llUUxh8hdiH56UD0LYTCzjr1Mm1S/j1LggfPATgGE2Y13Tj/Xd8zGo8hEMTAMdLM985ZyfJpDEqnxlM1mw8k2HGs67RomrSdpXqt8U++pX+N6og/lfkhSHcbc1M2zapDFxgRiDWjKn+cdoIz+qaEGv/WyTNpH+apDkFVmyfd+/UMgBWsecH4o0nr01Ds9GQ8HDaCClKjz83PrdDrhGGE9ar5cLlulUrHFxUVbXV219fX1ENkaDofWbrdtf3/fer2eVatVW11dDZf6zdJ2PRFOD5hBDnCxqa5D5tLKyorVarVwZxNOKBymxWIxHJterVbt0aNH9sd//MdWLBat2WwGZxK0t7dnL1++tDdv3tjV1fXFsRzru7CwEHis7Z9Vjt97KtRtlYj3UqY9O+kZ74WCpp34SQbrpHpj7eC3elg8SPA/XrCave99gTzIiAlP/5nvg+eLXzT++TSwECP/uRoIMV5P8m57QBX7HxBBqgEeKcaB/2+zWTutb9M8M8tcSnp2lnl43wouCSDeR70+hQZDfDAYWLfbDZEKzuEeDofhNAsiFK1WK9ykXSwWx7y53Jq7trZmh4eHtr+/H04FwWMVi1rE0iJipN5cNX78vhCUIn+jHHXfCPss8JZVq1VrtVq2trZmz549s1arFW6iJVSPDPCnmMQ89NrXmNy4zdjdN3l+TyvDvdNqmufVE6qghN/IlUnOFZ7XNaryTnmdlNqD7FJHiTpD/AlVfkyJyLJfQPsUS1FhvngDPqmfamwkjbt/fxbjhH75SI46wWKOQX3W61RkCm3RSBZ8Vb7hEfZj7sclxs/fVfLADEpad99WNMYDGObB5eXl2L0MOGWy2Wy48FRBI/3Su2cAz0S1OXo8k7neo9HtdqfW2Qp2dU6enp7a+fm5XV1dhTmWzWbHLurjdD+cEdgplUolOMh6vV4AHSoXSG/K5/O2uroa2gu/NBKiICefz1u1Wg0pYZyOpetqGnnnaWZgMY2BEzM804xF74FVoRF73tczTWRkVkCQZAyaJd+vEBuEWKTEbHzDkRdS/hkPNCZFLLwy9O2Ptd1HCFSAK0/S+p1GMX4mATj6mRQdiIEZFe4YSspjTQvQTY2xds+6iNLmyizvKaVFCqaJVNxF4E8DFHx7pgGYaeXFwC6ggn0F7KfY39+3w8NDM7Nw6hNGNoCCIwNVScAXLsdrNpt2cHBgnU7H6vX6WN1QksGg8smn6KjHSZUGUQn2SHBOOJELNmEToRiNRiHNaX193TY3N21tbc2Wl5etVqtZoVB4bwO2GpjaZz4HPOmz9wU8/XG1aqjfZj76lJJZIkrIUjVI4Adpb2YWQFjsnHaN+mBA+1QmysWjzUlKjIle2kk0g+/ZFMq+DcpUcJDL5d47FlvHmnXC+wsLC2P54PCA1AfGyZ8EprqESId6OT35KE5MlqoMnmVfjG+TjiX817KVF0n6SdclY0Gb1FCFn758n5Ls9zRqO5lHH9KD/yEJmeLls/IrFimCdx+acLJwuS2nPwEMMJ4x1BuNhq2vr9vq6qqNRqOwP69arQaZymbvk5MTu7q6Cpv1a7Wazc3N2fLycjiOOA1Ekt6KnGUN00ZuwCYVsd1u29HRkZ2cnIR5qKcBzs/P2/r6um1sbFitVrP5+XlbWVl572RLgBHzNJPJjB09rk6zfD5vL168sI8++ii0RWUL43mXvUG33mMxy/dpi93/Hfs/6TP/fVo7YsbfLG2e5LVXL6GvR4GBelv8AKr33P/oAlZhp0DEC4OktniDIgakYmBskvfPC6JJYFL/T5rA3iiK9SdWh4atY1EJbYdv67RezmkAVewdT9PW58tImr+zGnF+HtyXoTlNnZ4YYxWuvV7POp2OHR4eBiBgZsGDz3GybNQm/1T3znhgXKlUbGVlxfb29uzw8NBWVlbGjtlLAxTwSPNwMUoUTLDButfrjQEkjozVC+145+LiItwAu7q6ak+fPrWPPvrIlpeXQ5oTBp83nlFMOoZ+o6kapepxvisYpWwt9z68mTHnwyzveAeJWTyiHfPO+ne9w0OBiBq9GLB4wmNGLf/znO5JQTcADhRA0g7mNoaIHk3p+a9zg7p8BJcytXw1orVcTTNL4r0am7qmdN3EdLzqRn1G++MjBvTRe7N1nPg85lGG7xoVihnKutZic83z/9uQox+CmCeeYnLCOzr1/Q/V/6urq7G0oNFoFE6545ht5O3p6aktLCxYrVazVqsV9iJwaMfi4mK4GJR1xBzBCAdg6Nwi1dEDiIuLi3CfkKbD40QiAq0ATdcu/7fbbTs4OAgX2a2vr4cLfVUm4CQ5OTkJqV6ADCIVqhOy2WxwuPn0UKW7jt1MwCLJiJvWQE8zhLygn4T2kzoeAykq7KbJfYwZ3GnePQUA3tupBk1MCGnEwt8GmhSd0BCvX8D6t3rw+Z+2+LzlGLCIjUESbydRDOQk8dEbP9oO39ZJwMLzUBeZF4ZJ4Er7PMnj68v0457Gm1mNJz83bwMophkXyK+HpHbfRqnqvBwOh+9tLDs4OLD9/X1rt9tmZiH1qdFoBGDBudzek8+61HZxE+ni4mLwGuHFVVDq+8Xvq6urcMQrP/zPJmvAUbvdtn6/b6enp8FbRmgcr3U2mw3RicePH9uTJ09sdXXVFhcXrV6vv+epVu+5GlwYm2os+bYnjfVdlYnnjyri25AaN7c1VNRIVqNYQQDl6+ZrBWYKUNQI5xn2WDCeWqbOawWdakwoAKHN1EE6DtGQi4sLy2QywcDAGDa7ifLRhqurqxBFymRu0j3IMWcOqX5Q4yYW5VHeqEz1vKa9ykN4hvHm56KCGD7jfdUB3qPu26iRLh8pUeCm5bNW8ADzLG33AFHnAfzXMfxdplj0Tp2fnnSdKji9b2IdHR8f2+7uru3t7dnp6akVi8WQLsTcVf2hm7QXFhZC+igygeOXab/KWp8uisw4OzsLDiNuaS8Wi+HGbz3dDxnPu6S5mlnYI1epVEJUsdPp2GAwCFH5UqlkS0tLtrKy8p4zeTQa2WAwsP39fTs6OgonYCkIKZfLwRGhBxOobvAHUTDHbxuBuvMeC298pYGHacrit6YazNIWJTUk+Z1UbtJC8MI+TRl7JA+p4NayfBqUeta9F8Abyh6AUK6vw/eB/9XAZtF4EOhBWpJRMg3gjL2rffO8TSozre6kiIYHFrE2KY+mAQyxeaDrwLd12nlzF/L9m/TsXeuKlaNreBaQYmZjxhf7Dtisvb+/b91u14bDoVUqlZD6RMSiVquF0DiGhyo5eKPrktzS3/zmN7a3t2eNRsOy2awVCoXQHvX2+vSsfr8fPGRqVI5Go6A4zMz6/X7YAKh5tGYWjglcW1uzx48f2+bmpi0vL4ez1TEq/fpReabAyctjPwbq7ID3dzH+lTBGbpP2MolY27cpN8YT/6PeeT01y6fLqENGDVT0CsYD/NUUGk9qSPvN4XgjSXPwkSmNGviIgm4Qp71+D4HfBI7xTKqol51atwIFb2gqT7npXctR41TndUwexhxLsU3a+rzODz/GPm9cj/lVT6+CKPUqe4eXzy7QOmPf/S5QTE/HDjjRqI931t2VYmN4dXUVNmijE9rtdgDpHGqxsLBglUrFCoXCWMQ6k8mEPQ4cfpHJZEKU2K89b0fRBl0Xegkvd9ocHBzY1taWHR0djfHO3000GAxsNBqNRR2KxWK4ITyfz4c0rKdPn1qz2bRSqRT4zW3b3G90cXHx3h4hLgv0OjHNFuF/dajchqYGFl4IJSmjmDEbM1KnIe9xj9Ekpei/9140P4G1HzED1telXjAPXjwo0LJUqajXKgYsFDCogNZ2esGW1J+Y4NDwsO+XhgV95CDJeOF7zzMVQFBsM6S20ysZBUW+H/BHeR/jRZLiwtvrDdAkSgIXWscsFAPG+tsL87R3k9rqx1/L5Psk5TBJICV9lvY5BKggxM2eCk5/6na7ZnYNBjj9CWDBfgoiFV546nzQ/udyOWu1Wra1tWWHh4chT1eNjb29PWu322Gt4lXqdrsBWBDeRsFlszeb8nK5XOgPinA0GlmxWLTl5eWQ67q2tmaNRsNKpVLYcAvF5pSu55hDwL+b9H9SObchTjG5D0ChctXLnVnL0b0NXu76ean7G5iP6Ay/D0KNSIwEf6M1cwmlT7/UMGcdYqSoQaAeccpBJp+dnY0ZE5QJaFAvs+oYvZk7RhhWpFOMRqMQwcCAUiNcDW6vM+izymB1iimfdK8I5HUln+l7vOt1u76rzgsl5kAsXZYy1KmgbdGjymPz4UN67z80wTuN5CkvAN3a//sgnUOsnWz2+hZtjPZerxcid7lczrrdru3v7weZSsoT97WYjd//wlxg7nLrtkau1GETS6MDxOilpu122968eWMvX760drttjUbDNjY2rNVq2e7uboiMA4aGw6G9efPG9vb2rNls2scff2wff/yxLS0t2dOnT8fSsQqFwth6PTk5se3tbXv9+rXlcjlbXV21zc1Nq1QqYzalrrlp5yF85b3b0L2cCpXU4Bi48N/57+/Ty5XUnljdaUZyrBxvuJiN5y/HBsQPshf8sT0WvJc2MdKARBLQ0L4raFAeqRfMj08spcwbODFPa5JC1/boT1I6FuX6aI0HdlqX/01ZMTCsfaQdMU9ZEuDUcmLG+rTzLQlApT2XVnYSuJy1DbE60tZvzMD1ShtvjnqlABWXl5fhbgaUB0eucnuoHimsbUmSO1ymt7q6al999ZW9fv06eLrm5ubs+PjYfvOb39jbt28DcCFvlYgFIXc2/WnY/PT0NCglPGNcYPfs2TP76KOP7NmzZ9ZsNkO9KLM08ByTX0ljmbZG/XN3NYA+hOz2RqvZeGTWGwuxNsWMSl3T3iBFRvnoRNJ4qMGhxj/RKwWdanDr+9pXXRe0VWU1z2jkQNODeEbv6fF8w+BKmjuqv9RpRrsVHNAGbTeOghhQSJpn2exN+pTqrKQoBT9+D4Ufc78XJqYP/I8HMl5Hx0DbtLL6LkS5aijTr9gzSpPWSoxiESs1wu97zTNHKZu9DNw6/fbtWzs+Pg77j66uroLOuLy8tHq9PgYmLy8vQxSDyDZ76fihLtatyhb29/X7fZubm7NKpWKlUmkMcLXbbdvd3bWdnR3rdruWzWatUqnY/Px8uEPo+Pg4RO+oh5uxFxcXbXl52TY2NkIbVQadnZ1Zv983MwsOh/n5eatWq2FTeavVCn27r3HQ37PSne6xmAQE0oyu2LOTvG33RTEDPO17bY+2iUmpiF0Fni/DAwv19iQBCw3fKnlDd5JQSwMXk/pJfSq01YvHO75c9c5p+dpuD/b0t5btvc6ev8pb7Y/3Gvkx0DbxvSpVVfoxgOAp6fukd28zx2dZV/492jGrEryNgEkyWvz/nJuNsc7ldUQRLi8vw+VuzWYz7K2oVCpWLpfHTrmJrc+kujOZ61z1lZUV29rast3d3VBeuVy24+NjOz8/D8aU7o04Pj62w8PDsCEPYOEvM8M7VSqV7KOPPrLvfOc79uLFC9vc3LRarTZ2kpJvO+vfU4yfd5WVH8oQui2hgM3Gc+wxrnXTbsxhFCNkis8fV+NfPdE6f9Wg1P0ZGFl48hVYkB6ne2GQL5TjU5pU7p+fn4/JLdqGfKI9egKUGi/szwCEqGGYpiOSSA1q5RmAQzeYj0bXud8AKuVhEulcV6M9SW7qRtvYGPv15FONkwidrmtZeaBRUc+zaXTEXYk2JM1nM0uM3M56SpsHaPrufTgjYgTPiRiSSrq7u2vb29t2cnJilUolXACqJygNh8MwzqyhQqFgzWbTnjx5YpVKZUy20A8ze29+Xl1d2dHRkf3617+2nZ0dq9Vq9ujRI9vY2BjbrN1ut+3ly5f28uVLq9Vq1mg0rFgshsM6tre3Q5maolUoFOzFixf22Wef2ebm5tgR+NDl5WUAN2YWgFOxWAwnWjGfbxtd+BB07/dYTEveOJpVOcaen/T/pPenqVN/87eCCn4neYW9R0Q9YjoxeJ/n1MClDFVUk7wwnrzxrPUnpZ55QKEe/Zi3iLq1n/qZNwjUePB/x7xQ3qOk/fHePd8PfV95QD13FZgfynsVK/e2RuVd25Xk/UsCffqeKkU9/YlIxd7eXgh5l0ola7VaY5u1Oddbj5PV+pM8Lp5XuVzOGo2GPX361H7xi1/Yq1evrFQqWb1et36/b/l83lqtVkh/wnvF3wANyiZXdjQahdzZVqtl3//+9+33f//37dmzZwFQqPHq5WASKEuiaR0yaeV9KEfObcgbc2bjR/yqjNIUxjSPrMpKlTFmcdmN80flDyCCVDc1trzsoBz2SvCZpgppu/jxKVL+sj7knabiqCzzsj9JTnq9o6CBNqqho3XBh8vLy/dSeilDU65of9JpUpDXiTGHF23zdxHoe8p/bbvyDOM8SV/7E9X8PFGQwrPeuPsQRh+gyvfRE+3WaE4MVCjvYvKS9D7Wg9Jd+qbrStugTkzucbi4uLB6vR5OxqtWq1av14MdwuVytLNUKtnGxoYtLy9bsVgMBjnpW35ck+TiwsKCVatVOz09tfn5eTs5ObGdnZ0QObi8vAxpsf1+3xYWFuzi4sIWFhbG+E5UJZvNWqPRCJeaPnr0yFqtVoiCmNlY2iHOhVKpFJwFPrXx7yN90FZNo6hUCE8y9u/qmbutp08Vmvcgafv1mSTj1AMJFU5pHgBVDl5Z+Hdjf2u5HohMqlsFlBr1usFHz+7m+VgbffsgFdgeVHivpD8nXIGKCive8ePklbQ3BmJj59uXBlqmBRXTAINJIGeWd6dZY7PQJKPXK3gdFzXQOJK10+mEaEW73bbRaBQ22jWbzXCLKCdw6NGrHmwn9dPzPJu9zmFdWVmx7e1t+/rrr+3rr7+2ZrMZ2sbNrbu7uyGKcn5+HlJayLFFTuDpHA6Htry8bJ9//rn9+Mc/to2NjbENeGbjF+r5fiTxetL4zfLs7wp5xwHrXI1q74DwffeGL+948sYOm5AxZlH4bPrUZxl3/seAxaDV9zD0FUxoxCSTyYxdloUc0yiFBxWxKJ323esB1UEq52PPqEET26BuNh7x1TqniSxplIKy/JhgdPlN9V6/eONRI05+P4XXGaqDvANK3/POKw9WY+DoruTr0Lr4Pvb8JCASmx+q73Xstc5p++Y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+ }
+ ]
+ },
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+ },
+ "source": [
+ "## **Authors**\n",
+ "\n",
+ "* Miguel Ángel Hernández Tapia [Github](https://github.com/MiguelAngel-ht)\n",
+ "* David Ángel Alba Bonilla [Github](https://github.com/DavidAlba2627) -- [Blog](https://datasciencelifelonglearn.blogspot.com/)"
+ ]
+ },
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+ "# **Bibliography**\n",
+ "\n",
+ "1. Orts, F., Filatovas, E., Garzón, E. G., & Ortega, G. (2023). A quantum circuit to generate random numbers within a specific interval. EPJ Quantum Technology, 10(1). https://doi.org/10.1140/epjqt/s40507-023-00174-1"
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diff --git a/hackathon/Solution_Jingle_Bell_States/readme.md b/hackathon/Solution_Jingle_Bell_States/readme.md
new file mode 100644
index 0000000..ae1a55a
--- /dev/null
+++ b/hackathon/Solution_Jingle_Bell_States/readme.md
@@ -0,0 +1,8 @@
+# Challenges
+1. Quantum Universal Education
+2. IBM Hackathon
+# Equipo
+Jingle Bell States
+# Integrantes
+* David Angel Alba Bonilla
+* Miguel Angel Hernandez Tapia