RandLeastSquaresAnalysis (Copy).ipynb

{"cells":[{"cell_type":"markdown","id":"af8a42ea-8ab4-4fe7-a945-10043f9f02bf","metadata":{"id":"af8a42ea-8ab4-4fe7-a945-10043f9f02bf"},"source":["# RandLeastSquares Algorithm"]},{"cell_type":"code","execution_count":1,"id":"7ca239fd-8346-418f-a441-a3356f956ded","metadata":{"id":"7ca239fd-8346-418f-a441-a3356f956ded","executionInfo":{"status":"ok","timestamp":1733200144549,"user_tz":300,"elapsed":333,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}}},"outputs":[],"source":["# imports\n","import numpy as np\n","from scipy.linalg import hadamard\n","from tqdm import tqdm"]},{"cell_type":"code","execution_count":2,"id":"3272c794-2789-407e-ad09-a342cd7cba35","metadata":{"id":"3272c794-2789-407e-ad09-a342cd7cba35","executionInfo":{"status":"ok","timestamp":1733200145499,"user_tz":300,"elapsed":103,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}}},"outputs":[],"source":["def randLeastSquares(A: np.matrix, b: np.array, epsilon: float, mode=\"linear\"):\n","    \"\"\"\n","    Solves the least squares problem using a randomized algorithm.\n","\n","    Parameters:\n","    A (np.matrix): The input matrix of shape (n, d).\n","    b (np.array): The target vector of shape (n).\n","    epsilon (float): The error tolerance for the approximation.\n","    mode (str): \"log\" or \"linear\" to determine how r is set.\n","\n","    Returns:\n","    np.array: The solution vector of shape (d).\n","    \"\"\"\n","    n, d = A.shape\n","\n","    # Ensure n is a power of 2 by padding with zeros if necessary\n","    if not (n > 0 and ((n & (n - 1)) == 0)):\n","        next_power_of_2 = 2 ** int(np.ceil(np.log2(n)))\n","        A = np.pad(A, ((0, next_power_of_2 - n), (0, 0)), mode='constant')\n","        b = np.pad(b, (0, next_power_of_2 - n), mode='constant')\n","        n = next_power_of_2\n","\n","    # Determine r based on the mode\n","    if mode == \"log\":\n","        r = max(\n","            48**2 * d * np.log(40 * n * d) * np.log(100**2 * d * np.log(40 * n * d)),\n","            (40 * d * np.log(40 * n * d)) / epsilon\n","        )\n","        r = int(np.ceil(r))\n","    elif mode == \"linear\":\n","        r = max(48**2 * d, (40 * d) / epsilon)\n","        r = int(np.ceil(r))\n","    else:\n","        raise ValueError(\"Invalid mode. Choose 'log' or 'linear'.\")\n","\n","    # Create sampling-and-rescaling matrix S\n","    S = np.zeros((r, n))\n","    for t in range(r):\n","        i_t = np.random.choice(range(n))\n","        S[t, i_t] = np.sqrt(n / r)\n","\n","    # Generate Hadamard and diagonal matrices\n","    H = hadamard(n) / np.sqrt(n)\n","    D_diags = np.random.choice([-1, 1], size=n)\n","    D = np.diag(D_diags)\n","\n","    # Compute HDA and HDb\n","    HDA = H @ D @ A\n","    HDb = H @ D @ b\n","\n","    # Compute the solution vector x_opt\n","    x_opt = np.linalg.pinv(S @ HDA) @ (S @ HDb)\n","\n","    return x_opt"]},{"cell_type":"code","execution_count":3,"id":"a514b35b-915b-4ee4-9964-c1faa5f607c0","metadata":{"id":"a514b35b-915b-4ee4-9964-c1faa5f607c0","executionInfo":{"status":"ok","timestamp":1733200148117,"user_tz":300,"elapsed":109,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}}},"outputs":[],"source":["def relative_err(x_opt, x_true):\n","    return np.linalg.norm(x_opt - x_true) / np.linalg.norm(x_opt)"]},{"cell_type":"code","execution_count":4,"id":"5b0d9801-2972-4d38-b51d-07d2249ea4c9","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"5b0d9801-2972-4d38-b51d-07d2249ea4c9","executionInfo":{"status":"ok","timestamp":1733200153535,"user_tz":300,"elapsed":4708,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}},"outputId":"6bbb3d27-855a-438b-f7bb-4d75f75590b8"},"outputs":[{"output_type":"stream","name":"stderr","text":["100%|██████████| 5/5 [00:04<00:00,  1.16it/s]"]},{"output_type":"stream","name":"stdout","text":["Average error over 5 tests: 0.019226181985947742\n"]},{"output_type":"stream","name":"stderr","text":["\n"]}],"source":["# Parameters\n","num_tests = 5\n","matrix_size = (2**5, 8)\n","epsilon = 0.01\n","\n","# Run multiple tests\n","err = []\n","A = np.random.randn(*matrix_size)\n","b = np.random.randn(matrix_size[0])\n","x_true = np.linalg.lstsq(A, b, rcond=None)[0]\n","for _ in tqdm(range(num_tests)):\n","\n","\n","    x_opt = randLeastSquares(A, b, epsilon)\n","    # print(x_opt)\n","    # print(x_true)\n","\n","    acc = relative_err(x_opt, x_true)\n","    err.append(acc)\n","\n","# Compute average accuracy\n","average_err = np.mean(err)\n","print(\"Average error over {} tests: {}\".format(num_tests, average_err))"]},{"cell_type":"markdown","id":"f75ec4b2-5853-4bc3-ac55-81fb851aed42","metadata":{"id":"f75ec4b2-5853-4bc3-ac55-81fb851aed42"},"source":["# Analysis"]},{"cell_type":"code","execution_count":5,"id":"4675e3a8-bbb9-4480-9645-8229e073d55b","metadata":{"id":"4675e3a8-bbb9-4480-9645-8229e073d55b","executionInfo":{"status":"ok","timestamp":1733200153536,"user_tz":300,"elapsed":4,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}}},"outputs":[],"source":["# imports\n","import time\n","import matplotlib.pyplot as plt"]},{"cell_type":"code","execution_count":8,"id":"0927fccb-dab5-40b6-8258-b8605b5bd039","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":936},"id":"0927fccb-dab5-40b6-8258-b8605b5bd039","executionInfo":{"status":"ok","timestamp":1733188723694,"user_tz":300,"elapsed":148702,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}},"outputId":"e817b29c-cd0d-404e-a17a-4f175ad029c9"},"outputs":[{"output_type":"stream","name":"stderr","text":["Processing epsilons:   0%|          | 0/3 [00:00<?, ?it/s]\n","Matrix sizes for epsilon=0.1:   0%|          | 0/6 [00:00<?, ?it/s]\u001b[A\n","Matrix sizes for epsilon=0.1:  17%|█▋        | 1/6 [00:00<00:01,  2.56it/s]\u001b[A\n","Matrix sizes for epsilon=0.1:  33%|███▎      | 2/6 [00:00<00:02,  1.97it/s]\u001b[A\n","Matrix sizes for epsilon=0.1:  50%|█████     | 3/6 [00:01<00:01,  1.57it/s]\u001b[A\n","Matrix sizes for epsilon=0.1:  67%|██████▋   | 4/6 [00:02<00:01,  1.16it/s]\u001b[A\n","Matrix sizes for epsilon=0.1:  83%|████████▎ | 5/6 [00:04<00:01,  1.24s/it]\u001b[A\n","Matrix sizes for epsilon=0.1: 100%|██████████| 6/6 [00:08<00:00,  1.95s/it]\u001b[A\n","Processing epsilons:  33%|███▎      | 1/3 [00:08<00:16,  8.24s/it]\n","Matrix sizes for epsilon=0.01:   0%|          | 0/6 [00:00<?, ?it/s]\u001b[A\n","Matrix sizes for epsilon=0.01:  17%|█▋        | 1/6 [00:00<00:04,  1.17it/s]\u001b[A\n","Matrix sizes for epsilon=0.01:  33%|███▎      | 2/6 [00:01<00:03,  1.22it/s]\u001b[A\n","Matrix sizes for epsilon=0.01:  50%|█████     | 3/6 [00:02<00:02,  1.01it/s]\u001b[A\n","Matrix sizes for epsilon=0.01:  67%|██████▋   | 4/6 [00:04<00:02,  1.18s/it]\u001b[A\n","Matrix sizes for epsilon=0.01:  83%|████████▎ | 5/6 [00:07<00:01,  1.91s/it]\u001b[A\n","Matrix sizes for epsilon=0.01: 100%|██████████| 6/6 [00:12<00:00,  3.01s/it]\u001b[A\n","Processing epsilons:  67%|██████▋   | 2/3 [00:20<00:10, 10.85s/it]\n","Matrix sizes for epsilon=0.001:   0%|          | 0/6 [00:00<?, ?it/s]\u001b[A\n","Matrix sizes for epsilon=0.001:  17%|█▋        | 1/6 [00:08<00:43,  8.68s/it]\u001b[A\n","Matrix sizes for epsilon=0.001:  33%|███▎      | 2/6 [00:18<00:37,  9.45s/it]\u001b[A\n","Matrix sizes for epsilon=0.001:  50%|█████     | 3/6 [00:30<00:31, 10.52s/it]\u001b[A\n","Matrix sizes for epsilon=0.001:  67%|██████▋   | 4/6 [00:48<00:27, 13.58s/it]\u001b[A\n","Matrix sizes for epsilon=0.001:  83%|████████▎ | 5/6 [01:20<00:20, 20.06s/it]\u001b[A\n","Matrix sizes for epsilon=0.001: 100%|██████████| 6/6 [02:07<00:00, 29.14s/it]\u001b[A\n","Processing epsilons: 100%|██████████| 3/3 [02:28<00:00, 49.34s/it]\n"]},{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"iVBORw0KGgoAAAANSUhEUgAAAjIAAAHHCAYAAACle7JuAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAAB9Q0lEQVR4nO3dd1hT1x8G8DchIWEPEYIKiFsR96JuiyCOOltnVRy/WmeLtdatVavV1lm1rVsrrraOWrXi3qNWFByoFcXBcLFXSO7vD0okAgoxEALv53nySO785qDycu6554oEQRBAREREZITEhi6AiIiISFcMMkRERGS0GGSIiIjIaDHIEBERkdFikCEiIiKjxSBDRERERotBhoiIiIwWgwwREREZLQYZIiIiMloMMkSlzIYNGyASiXD//n1Dl1KqHT9+HCKRCMePHy/yc4tEIsycObPIz0tUGBhkiHSUFQiyXhKJBOXLl8fgwYPx+PHjIq2lTZs2WrXk9SqNP7zu37+v+fxz5szJdZv+/ftDJBLB0tJSp3MEBgZiyZIl71Clfpw+fRp+fn4oX7485HI5XF1d0aVLFwQGBhq6NKJCI+Kzloh0s2HDBvj7++Prr7+Gu7s7UlNTcf78eWzYsAEVK1ZEaGgo5HJ5kdQSFBSE6OhozftLly5h2bJlmDx5MmrWrKlZXqdOHXh4eECpVEImk0EkEhVJfYZ0//59uLu7Qy6Xo1KlSrh+/brW+qSkJDg5OUGlUsHExASJiYkFPkfnzp0RGhpaoF4utVqN9PR0mJqaQix+998pd+7cid69e6NevXro06cP7OzsEB4ejpMnT0IqleLYsWOabVNTUyGRSCCRSN75vESGxr/FRO/Iz88PjRo1AgAMGzYMDg4O+Pbbb7F371589NFHRVJD+/bttd7L5XIsW7YM7du3R5s2bXJsb2JiUiR1FScdO3bE77//jqtXr6Ju3bqa5Xv27EF6ejo6dOiAo0ePFnodqampmvCiz6A7c+ZM1KpVC+fPn4epqanWupiYGK33RRWwiYoCLy0R6VnLli0BAP/++69mWZs2bXINFIMHD0bFihU177Mug3z33Xf4+eefUblyZchkMjRu3BiXLl3SS325jZGpWLEiOnfujOPHj6NRo0YwMzODp6enZvzG77//Dk9PT8jlcjRs2BBXrlzJcdxbt26hV69esLe3h1wuR6NGjbB379431qJUKmFvbw9/f/8c6+Lj4yGXy/HFF19oli1fvhweHh4wNzeHnZ0dGjVqlO/LJl5eXnB3d8+x/ZYtW9ChQwfY29vn2GfPnj3o1KkTypUrB5lMhsqVK2P27NlQqVSabdq0aYM///wTDx480FzCyvqeZo2D2bZtG6ZOnYry5cvD3Nwc8fHxOcbI3Lx5E2ZmZhg4cKBWDadPn4aJiQkmTpz4xs/377//onHjxjlCDAA4Ojpqvc9+mTH7pbfcXtlduHABHTp0gI2NDczNzdG6dWucOXPmjXURFTb2yBDpWVZAsLOz0/kYgYGBSEhIwCeffAKRSIQFCxagR48euHfvHqRSqZ4q1Xb37l3069cPn3zyCQYMGIDvvvsOXbp0wY8//ojJkydj5MiRAIB58+bho48+QlhYmOaSyPXr19G8eXOUL18eX331FSwsLLBjxw5069YNv/32G7p3757rOaVSKbp3747ff/8dP/30k9YP4d27dyMtLQ19+vQBAKxevRpjx45Fr169MG7cOKSmpuLatWu4cOEC+vXrl6/P2LdvX/zyyy+YP38+RCIRnj17hkOHDmHz5s04ePBgju03bNgAS0tLBAQEwNLSEkePHsX06dMRHx+PhQsXAgCmTJmCuLg4PHr0CIsXLwaAHGNtZs+eDVNTU3zxxRdIS0vLNWzUrFkTs2fPxoQJE9CrVy988MEHSEpKwuDBg1GjRg18/fXXb/xsbm5uOHLkCB49eoQKFSrkqz0AoGzZsti8ebPWMqVSic8//1yrzqNHj8LPzw8NGzbEjBkzIBaLsX79erRr1w6nTp1CkyZN8n1OIr0SiEgn69evFwAIhw8fFp4+fSo8fPhQ+PXXX4WyZcsKMplMePjwoWbb1q1bC61bt85xjEGDBglubm6a9+Hh4QIAoUyZMsKLFy80y/fs2SMAEP7444981bZz504BgHDs2LE86w4PD9csc3NzEwAIZ8+e1Sz766+/BACCmZmZ8ODBA83yn376Kcex33//fcHT01NITU3VLFOr1cJ7770nVK1a9Y21Zp3n9c/WsWNHoVKlSpr3Xbt2FTw8PN720XPIatOFCxcKoaGhAgDh1KlTgiAIwooVKwRLS0shKSlJGDRokGBhYaG1b3Jyco7jffLJJ4K5ubnWZ+3UqZPW9zHLsWPHBABCpUqVchwra132dlSpVEKLFi0EJycn4dmzZ8KoUaMEiUQiXLp06a2fc+3atQIAwdTUVGjbtq0wbdo04dSpU4JKpcqxLQBhxowZeR5r5MiRgomJiXD06FFBEDK/l1WrVhV8fX0FtVqt2S45OVlwd3cX2rdv/9b6iAoLLy0RvSNvb2+ULVsWLi4u6NWrFywsLLB3794C/Vb8ut69e2v16GRdrrp3794715uXWrVqwcvLS/O+adOmAIB27drB1dU1x/KsWl68eIGjR4/io48+QkJCAp49e4Znz57h+fPn8PX1xZ07d954F1e7du3g4OCA7du3a5a9fPkSQUFB6N27t2aZra0tHj169E6X2Dw8PFCnTh1s3boVQGbPV9euXWFubp7r9mZmZpqvsz5by5YtkZycjFu3buX7vIMGDdI6Vl7EYjE2bNiAxMRE+Pn5YeXKlZg0aZJmDNabDBkyBAcPHkSbNm1w+vRpzJ49Gy1btkTVqlVx9uzZfNe6adMmrFy5EgsWLEDbtm0BAMHBwbhz5w769euH58+fa77HSUlJeP/993Hy5Emo1ep8n4NInxhkiN7RihUrEBQUhF9//RUdO3bEs2fPIJPJ3umY2YMD8Ooy1cuXLwEAKSkpiIqK0nq9q9fPaWNjAwBwcXHJdXlWLXfv3oUgCJg2bRrKli2r9ZoxYwaAnINNs5NIJOjZsyf27NmDtLQ0AJljcpRKpVaQmThxIiwtLdGkSRNUrVoVo0aN0ml8Rr9+/bBz507cvXsXZ8+efeNlqevXr6N79+6wsbGBtbU1ypYtiwEDBgAA4uLi8n1Od3f3fG9buXJlzJw5E5cuXYKHhwemTZuW7319fX3x119/ITY2FidPnsSoUaPw4MEDdO7c+Y3fgyzBwcEYMWIE+vbti4CAAM3yO3fuAMgMZK9/j9esWYO0tLQCtQeRPnGMDNE7atKkieY35m7duqFFixbo168fwsLCNGMlRCIRhFxmOsg+aDS7vO4qyjrG9u3bcwyQze34BZHXOd9WS9Zv4l988QV8fX1z3bZKlSpvPHefPn3w008/4cCBA+jWrRt27NiBGjVqaN1dVLNmTYSFhWHfvn04ePAgfvvtN6xcuRLTp0/HrFmz3vr5svTt2xeTJk3C8OHDUaZMGfj4+OS6XWxsLFq3bg1ra2t8/fXXqFy5MuRyOf755x9MnDixQD0Q+emNye7QoUMAgCdPnuD58+dQKBQF2t/c3BwtW7ZEy5Yt4eDggFmzZuHAgQMYNGhQnvu8fPkSPXv2RLVq1bBmzRqtdVmfdeHChahXr16u++s6Bw/Ru2KQIdIjExMTzJs3D23btsUPP/yAr776CkBmj0pul4UePHig03l8fX0RFBT0TrXqS6VKlQBkDtz19vbW6RitWrWCs7Mztm/fjhYtWuDo0aOYMmVKju0sLCzQu3dv9O7dG+np6ejRowfmzp2LSZMm5fuWYldXVzRv3hzHjx/Hp59+mudcKsePH8fz58/x+++/o1WrVprl4eHhObbV53w8P/74I4KCgjB37lzMmzcPn3zyCfbs2aPz8bJCdmRkZJ7bqNVq9O/fH7GxsTh8+HCOS22VK1cGAFhbW+v8PSYqLLy0RKRnbdq0QZMmTbBkyRKkpqYCyPxBcOvWLTx9+lSz3dWrV3W+ddXZ2Rne3t5aL0NxdHREmzZt8NNPP+X6wzL7Z86LWCxGr1698Mcff2Dz5s3IyMjQuqwEAM+fP9d6b2pqilq1akEQBCiVygLVPGfOHMyYMQNjxozJc5usnqjsPV3p6elYuXJljm0tLCz0cmklPDwcEyZMQM+ePTF58mR899132Lt3LzZt2vTWfY8cOZLr8v379wMAqlevnue+s2bNwl9//YWtW7fmehmsYcOGqFy5Mr777rtcJwzMz/eYqLCwR4aoEEyYMAEffvghNmzYgBEjRmDIkCFYtGgRfH19MXToUMTExODHH3+Eh4cH4uPjDV3uO1uxYgVatGgBT09PDB8+HJUqVUJ0dDTOnTuHR48e4erVq289Ru/evbF8+XLMmDEDnp6eWjMSA4CPjw8UCgWaN28OJycn3Lx5Ez/88AM6deoEKyurAtXbunVrtG7d+o3bvPfee7Czs8OgQYMwduxYiEQibN68OddLeA0bNsT27dsREBCAxo0bw9LSEl26dClQTYIgYMiQITAzM8OqVasAAJ988gl+++03jBs3Dt7e3ihXrlye+3ft2hXu7u7o0qULKleujKSkJBw+fBh//PEHGjdunGc9ISEhmD17Nlq1aoWYmBj88ssvWusHDBgAsViMNWvWwM/PDx4eHvD390f58uXx+PFjHDt2DNbW1vjjjz8K9HmJ9IVBhqgQ9OjRQ/Mb7PDhw1GzZk1s2rQJ06dPR0BAAGrVqoXNmzcjMDDQIA8N1LdatWrh77//xqxZs7BhwwY8f/4cjo6OqF+/PqZPn56vY7z33ntwcXHBw4cPc/TGAJk/1Lds2YJFixYhMTERFSpUwNixYzF16lR9fxwAQJkyZbBv3z6MHz8eU6dOhZ2dHQYMGID3338/x1igkSNHIjg4GOvXr8fixYvh5uZW4CCzfPlyHD9+HL/99hvKli2rWb527VrUrl0bw4cPx59//pnn/mvWrMGePXuwY8cOPHnyBIIgoFKlSpgyZQomTpyY5yW058+fQxAEnDhxAidOnMixPmtwc5s2bXDu3DnMnj0bP/zwAxITE6FQKNC0aVN88sknBfqsRPrEZy0RERGR0eIYGSIiIjJaDDJERERktBhkiIiIyGgxyBAREZHRYpAhIiIio8UgQ0REREarxM8jo1ar8eTJE1hZWel1GnEiIiIqPIIgICEhAeXKlYNYnHe/S4kPMk+ePMnx9F4iIiIyDg8fPkSFChXyXF/ig0zW1OUPHz6EtbV1jvVKpRKHDh2Cj48PpFJpUZdXqrCtiw7buuiwrYsO27poFJd2jo+Ph4uLy1sfQVLig0zW5SRra+s8g4y5uTmsra35D6OQsa2LDtu66LCtiw7bumgUt3Z+27AQDvYlIiIio8UgQ0REREaLQYaIiIiMVokfI5NfKpUKKpXK0GWUaEqlEhKJBKmpqSW6raVSKUxMTAxdBhFRqVDqg4wgCLCyssK9e/c4z0whEwQBCoUCDx8+LPFtbWtrC4VCUeI/JxGRoZX6IBMTEwM7OzuULVsWlpaW/MFTiNRqNRITE2FpafnGyY2MmSAISE5ORkxMDADA2dnZwBUREZVspTrIqFQqxMfHw8HBAWXKlCmxP1yLC7VajfT0dMjl8hLd1mZmZgAyQ7KjoyMvMxERFaKS+9MkH5RKJQDA1NTUwJVQSWNubg7g1d8xIiIqHKU6yGTh5STSN/6dIiIqGgwyREREZLQYZChXIpEIu3fvBgDcv38fIpEIwcHBBq2JiIjodQwyRmrw4MEQiUQ5Xh06dNDL8SMjI+Hn56eXY+nLtWvX0LJlS8jlcri4uGDBggVv3Wfs2LFo2LAhZDIZ6tWrV/hFEhFRkSrVdy0Zuw4dOmD9+vVay2QymV6OrVAo9HIcfYmPj4ePjw+8vb3x448/IiQkBEOGDIGtrS3+97//vXHfIUOG4MKFC7h27VoRVUtEVDqoBTXOPzmPZuWaQSwyTN8Ie2SMmEwmg0Kh0HrZ2dkByLw0tGrVKvj5+cHMzAyVKlXCr7/+qtk3PT0do0ePhrOzM+RyOdzc3DBv3jzN+uyXlnJz4sQJNGnSBDKZDM7Ozvjqq6+QkZGhWd+mTRuMHTsWX375Jezt7aFQKDBr1iydP+uWLVuQnp6OdevWwcPDA3369MHYsWOxaNGiN+63bNkyjBo1CpUqVdL53EREpC1DnYF99/ah596e+OTwJzj+8LjBamGPTDaCICBFaZip882kJnq/02XatGmYP38+li5dis2bN6NPnz4ICQlBzZo1sWzZMuzduxc7duyAq6srHj58iIcPH+bruI8fP0bHjh0xePBgbNq0Cbdu3cLw4cMhl8sxc+ZMzXYbN25EQEAALly4gHPnzmHw4MGoV68eunbtCgDw8/PDqVOn8jyPm5sbrl+/DgA4d+4cWrVqpXWrvK+vL7799lu8fPlSE+CIiKjwpKnSsOfuHqwLXYfHiY8BABZSCzxLeWawmhhksklRqlBr+l8GOfeNr31hblqwb8e+fftgaWmptWzy5MmYPHkyAODDDz/EsGHDAACzZ89GUFAQli9fjpUrVyIiIgJVq1ZFixYtIBKJ4Obmlu/zrly5Ei4uLvjhhx8gEolQo0YNPHnyBBMnTsT06dM1k93VqVMHM2bMAABUrVoVP/zwA06cOKEJMmvWrEFKSkqe55FKpZqvo6Ki4O7urrXeyclJs45Bhoio8CQpk7AjbAc23dikCS12MjsMqDUAfWr0gbWptcFqY5AxYm3btsWqVau0ltnb22u+9vLy0lrn5eWlufNo8ODBaN++PapXr44OHTqgc+fO8PHxydd5b968CS8vL60epObNmyMxMRGPHj2Cq6srgMwgk51CocCzZ69Se/ny5fN1PiIiMoyXqS/xy81fsPXWViSkJwAAFBYKDPYYjB5Ve8BMYmbgChlktJhJTXDja1+DnbugLCwsUKVKFZ3O16BBA4SHh+PAgQM4fPgwPvroI3h7e2uNo3lX2XtUgMxxN2q1WvO+IJeWFAoFoqOjtdZnvS9uA5OJiIxdrDoWCy8vxO5/dyMlI7PnvKJ1RQz1HIpO7p0gNZG+5QhFh0EmG5FIVODLO8XZ+fPnMXDgQK339evX17y3trZG79690bt3b/Tq1QsdOnTAixcvtHp1clOzZk389ttvEARB0ytz5swZWFlZoUKFCvmuryCXlry8vDBlyhQolUrN8qCgIFSvXp2XlYiI9CQ8Lhxrrq3Bn/F/QhWfOWa0VplaGOY5DO1c2sFEXPyeHVdyfmqXQmlpaYiKitJaJpFI4ODgAADYuXMnGjVqhBYtWmDLli24ePEi1q5dCwBYtGgRnJ2dUb9+fYjFYuzcuRMKhQK2trZvPe/IkSOxZMkSjBkzBqNHj0ZYWBhmzJiBgICAAj0MsiCXlvr164dZs2Zh6NChmDhxIkJDQ7F06VIsXrxYs82uXbswadIk3Lp1S7Ps7t27SExMRFRUFFJSUjSX1mrVqsVnbBER/efG8xtYE7IGhx8chgABANDIsRGG1xkOr3JexfqxKwwyRuzgwYNwdnbWWla9enXND/JZs2Zh27ZtGDlyJJydnbF161bUqlULAGBlZYUFCxbgzp07MDExQePGjbF///58BZHy5ctj//79mDBhAurWrQt7e3sMHToUU6dO1f+H/I+NjQ0OHTqEUaNGoWHDhnBwcMD06dO15pCJi4tDWFiY1n7Dhg3DiRMnNO+zeqTCw8NRsWLFQquXiKi4EwQBf0f/jbUha3HmyRnN8lblW6FGXA2M8B6RY4hAcSQSBEEwdBGFKT4+HjY2NoiLi4O1tfao6tTUVNy7dw8ODg5wcHAoUG9CcScSibBr1y5069bN0KVoqNVqxMfHw9raukS1dW5SU1MRHh4Od3d3yOXyIj+/UqnE/v370bFjR6P4j8iYsa2LDttaPwRBwMlHJ7E6ZDWuPr0KABCLxPBz98OQ2kPgbuleLNr5TT+/s2OPDBERUSmQoc7AX/f/wtrQtbjz8g4AwFRsim5VumFw7cFwsXIBkBkYjQmDDBERUQmWNYnd+tD1eJT4CABgLjFH7xq98XHNj1HWvKyBK3w3DDIlVAm/YkhERG+RpEzCzrCd2Hhjo9Ykdv1r9kefGn1gI7MxcIX6wSBDRERUgrxMfYktN7dg662tiE+PBwA4mTtpJrEzl5obuEL9YpAhIiIqAaKSorDx+kb8duc3rUnshtQegs6VOherSez0iUGGiIjIiN2Pu491oevwx70/kKHOAADUtK+JYZ7D8L7r+8VyEjt9YpAhIiIyQjef38SakDUIehD0ahI7p0YY5jkM75V7r1hPYqdPDDJERERGQhAEXI6+jDWha3Dm8atJ7FpXaI1hnsNQz7Ge4YozEAYZIiKiYk4QBJx6fAqrr61G8NNgAJmT2HWo2AFDPYeiml01wxZoQAwylKvsMwPfv38f7u7uuHLlCurVq2fo0oiISo0MdQYO3T+EtaFrcfvlbQCAVCxFtyrd4O/hDxdrFwNXaHgle574Emzw4MEQiUQ5Xh06dNDL8SMjI+Hn56eXY+nLtWvX0LJlS8jlcri4uGDBggVv3SciIgKdOnWCubk5HB0dMWHCBGRkZGjWR0ZGol+/fqhWrRrEYjE+++yzQvwERET5k65Kx87bO/HB7g8w8dRE3H55G+YScwz2GIyDPQ9iutd0hpj/sEfGiHXo0AHr16/XWiaTyfRybIVCoZfj6Et8fDx8fHzg7e2NH3/8ESEhIRgyZAhsbW21HhyZnUqlQqdOnaBQKHD27FlERkZi4MCBkEql+OabbwBkPkG8bNmymDp1qtaTtImIDCFrErtNNzbhacpTAICtzBb9a/ZH3xp9S8wkdvrEHhkjJpPJoFAotF52dnYAMi8NrVq1Cn5+fjAzM0OlSpXw66+/avZNT0/H6NGj4ezsDLlcDjc3N8ybN0+zXiQSYffu3Xme+8SJE2jSpAlkMhmcnZ3x1VdfafV0tGnTBmPHjsWXX34Je3t7KBQKzJo1S+fPumXLFqSnp2PdunXw8PBAnz59MHbsWCxatCjPfQ4dOoQbN27gl19+Qb169eDn54fZs2djxYoVSE9PBwBUrFgRS5cuxcCBA2Fjw/8giMgwYlNjsSJ4BXx+9cH3l7/H05SncDR3xJeNv8RfPf/CiLojGGLywCCTnSAA6UmGeRXCIwWmTZuGnj174urVq+jfvz/69OmDmzdvAgCWLVuGvXv3YseOHQgLC8OWLVtQsWLFfB338ePH6NixIxo3boyrV69i1apVWLt2LebMmaO13caNG2FhYYELFy5gwYIFmD17No4dO6ZZ7+fnB0tLyzxfHh4emm3PnTuHVq1awdTUVLPM19cXYWFhePnyZa51njt3Dp6ennByctLaJz4+HtevX8/XZyUiKkzRSdFYcGkBfH7zwY9Xf0R8ejzcrN3w9Xtf42CPg/i41sclbiZefeOlpeyUycA35Qxz7slPAFOLAu2yb98+WFpaah9m8mRMnjwZAPDhhx9i2LBhAIDZs2cjKCgIy5cvx8qVKxEREYGqVauiRYsWEIlEcHNzy/d5V65cCRcXF/zwww8QiUSoUaMGnjx5gokTJ2L69OkQizPzcZ06dTBjxgwAQNWqVfHDDz/gxIkT6Nq1KwBgzZo1SElJyfM82R8fHxUVBXd3d631WQElKipK0xOVXVRUlFaIeX0fIiJDeRD/AOtD12PPv3s0k9jVsK+BYZ7D4O3qXeInsdMnBhkj1rZtW6xatUprmb29veZrLy8vrXVeXl4IDg4GkDlYuH379qhevTo6dOiAzp07w8fHJ1/nvXnzJry8vLQmW2revDkSExPx6NEjuLq6AsgMMtkpFAo8e/ZM8758+fL5Oh8RUUlx68UtzSR2akENAGjo1BDDPIehebnmpWYSO31ikMlOap7ZM2KocxeQhYUFqlSpotPpGjRogPDwcBw4cACHDx/GRx99BG9vb61xNO8qe48KkDnuRq1Wa977+fnh1KlTee7v5uamuQSkUCgQHR2ttT7rfV4DkxUKBS5evFigfYiICsPl6MtYE7IGpx+f1ixrVaEVhnkOQ33H+gaszPgxyGQnEhX48k5xdv78eQwcOFDrff36r/7BWFtbo3fv3ujduzd69eqFDh064MWLF1q9OrmpWbMmfvvtNwiCoPnt4cyZM7CyskKFChXyXV9BLi15eXlhypQpUCqVmuVBQUGoXr16rpeVsvaZO3cuYmJi4OjoqNnH2toatWrVynedRES6yJrEbk3IGlyJuQIgcxI734q+GFp7KKrbVzdwhSUDg4wRS0tLyzHWQyKRwMHBAQCwc+dONGrUCC1atMCWLVtw8eJFrF27FgCwaNEiODs7o379+hCLxdi5cycUCgVsbW3fet6RI0diyZIlGDNmDEaPHo2wsDDMmDEDAQEBmvEx+VGQS0v9+vXDrFmzMHToUEycOBGhoaFYunSp1i3Tu3btwqRJk3Dr1i0AgI+PD2rVqoWPP/4YCxYsQFRUFKZOnYpRo0Zp3aaedbktMTERT58+RXBwMExNTRl2iEgnKrUKhx4cwtqQtQh7GQYgcxK7rlW6wt/DH67WrgausGRhkDFiBw8ehLOzs9ay6tWra36Qz5o1C9u2bcPIkSPh7OyMrVu3an44W1lZYcGCBbhz5w5MTEzQuHFj7N+/P19BpHz58ti/fz8mTJiAunXrwt7eHkOHDsXUqVP1/yH/Y2Njg0OHDmHUqFFo2LAhHBwcMH36dK05ZOLi4hAWFqZ5b2Jign379uHTTz+Fl5cXLCwsMGjQIHz99ddax87eS3X58mUEBgbCzc0N9+/fL7TPQ0QlT7oqHXv/3Yv1oesRkRABADCTmOGjah9hoMdAOJo7GrjCkkkkCIVw328xEh8fDxsbG8TFxcHa2lprXWpqKu7duwcHBwc4ODgUqDehuMv+iIHiQq1WIz4+HtbW1iWqrXOTmpqK8PBwuLu7Qy6XF/n5lUol9u/fj44dO+YYq0T6xbYuOsW1rZOVydh5eyc2Xd+EmJQYAICNzAb9a/ZHvxr9jG7+l+LSzm/6+Z0de2SIiIh0EJsai8BbgQi8FYi4tDgAgKO5IwbVGoRe1Xpx/pciwiBDRERUANFJ0dh0YxN23t6JlIzMGxZcrVwx1HMoOlfqDFMT07ccgfSJQaaEKuFXDImIilxEfATWha7D3n/3QqlWAsicxG6o51C0d23PSewMhEGGiIjoDcJehGFNyBocenBIM4ldA8cGGOY5DC3Kt+AkdgbGIENERJSLf6L/wZqQNTj1+NXEnS3Lt8Qwz2Fo4NTAgJVRdgwyRERE/xEEAacfn8aakDX4J+YfAP9NYufmi6GenMSuOGKQISKiUk+lViHoQRDWhq7FrReZc3FJxVJ8UPkDDKk9hJPYFWMMMkREVGqlq9Lxx79/YP319XgQ/wBA5iR2H1b7EANrDYSThZOBK6S3YZAhIqJSRzOJ3Y1NiEnOnMTO2tQaA2oOQN8afWErtzVsgZRvDDKUq+wzA9+/fx/u7u64cuUK6tWrZ+jSiIh0FpcWh8Cbgdhya8urSezMHDHQYyA+rPYhJ7EzQiV7nvgSbPDgwRCJRDleHTp00MvxIyMj4efnp5dj6cu1a9fQsmVLyOVyuLi4YMGCBW/dJyIiAp06dYK5uTkcHR0xYcIEZGRkaG1z/PhxNGjQADKZDFWqVMGGDRu01p88eRJdunRBuXLlIBKJsHv3bj1+KiIqCjHJMfju0ndo/2t7rLy6EnFpcXC1csUMrxk40PMABnkMYogxUuyRMWIdOnTA+vXrtZZlf6rzu1AoFHo5jr7Ex8fDx8cH3t7e+PHHHxESEoIhQ4bA1tZW68GR2alUKnTq1AkKhQJnz55FZGQkBg4cCKlUim+++QYAEB4ejk6dOmHEiBHYsmULjhw5gmHDhsHZ2Rm+vr4AgKSkJNStWxdDhgxBjx49iuwzE9G7exj/EOuur8Oeu3s0k9hVt6uOYZ7D0N6Nk9iVBOyRMWIymQwKhULrZWdnByDz0tCqVavg5+cHMzMzVKpUCb/++qtm3/T0dIwePRrOzs6Qy+Vwc3PDvHnzNOvf1vNw4sQJNGnSBDKZDM7Ozvjqq6+0ejratGmDsWPH4ssvv4S9vT0UCgVmzZql82fdsmUL0tPTsW7dOnh4eKBPnz4YO3YsFi1alOc+hw4dwo0bN/DLL7+gXr168PPzw+zZs7FixQqkp6cDAH788Ue4u7vj+++/R82aNTF69Gj06tULixcv1hzHz88Pc+bMQffu3XWun4iKVtiLMHx54kt03t0Zv97+FUq1Eg0cG2DF+yuws8tOdHDvwBBTQjDIZCMIApKVyQZ5FcYjBaZNm4aePXvi6tWr6N+/P/r06YObN28CAJYtW4a9e/dix44dCAsLw5YtW1CxYsV8Hffx48fo2LEjGjdujKtXr2LVqlVYu3Yt5syZo7Xdxo0bYWFhgQsXLmDBggWYPXs2jh07plnv5+cHS0vLPF8eHh6abc+dO4dWrVrB1PTVM0x8fX0RFhaGly9f5lrnuXPn4OnpCScnJ6194uPjcf36dc023t7eWvv5+vri3Llz+WoLIipersRcwagjo9Drj144cP8A1IIaLcq3wIYOG7DRbyNaVWjFmXhLGF5ayiYlIwVNA5sa5NwX+l0o8PXZffv2wdLSUmvZ5MmTMXnyZADAhx9+iGHDhgEAZs+ejaCgICxfvhwrV65EREQEqlatihYtMqfXdnNzy/d5V65cCRcXF/zwww8QiUSoUaMGnjx5gokTJ2L69OkQizPzcZ06dTBjxgwAQNWqVfHDDz/gxIkT6Nq1KwBgzZo1SElJyfM82R8fHxUVBXd3d631WQElKipK0xOVXVRUlFaIeX2fN20THx+PlJQUmJmZvb1BiMigBEHAmSdnsPraas0kdiKI4FPRB0NrD0XNMjUNXCEVJgYZI9a2bVusWrVKa5m9vb3may8vL611Xl5eCA4OBpA5WLh9+/aoXr06OnTogM6dO8PHxydf57158ya8vLy0fqtp3rw5EhMT8ejRI7i6Zk4cVadOHa39FAoFnj17pnlfvnz5fJ2PiCg3KrUKQRFBWBeyDjdfZPY2S8QSdK3cFf61/eFmnf9f0Mh4FZsgM3/+fEyaNAnjxo3DkiVLAACpqakYP348tm3bhrS0NPj6+mLlypU5foPWFzOJGS70u1Aox87PuQvKwsICVapU0el8DRo0QHh4OA4cOIDDhw/jo48+gre3t9Y4mneVvUcFyBx3o1arNe/9/Pxw6tSp13fTcHNz01wCUigUiI6O1lqf9T6vgckKhQIXL1584z55Hdfa2pq9MUTFlFKlxB/3/8C60HVak9j1qtYLA2sNhMKieN2sQIWrWASZS5cu4aeffsrxG/znn3+OP//8Ezt37oSNjQ1Gjx6NHj164MyZM4VSh0gkKlG3350/fx4DBw7Uel+/fn3Ne2tra/Tu3Ru9e/dGr1690KFDB7x48UKrVyc3NWvWxG+//QZBEDS9MmfOnIGVlRUqVKiQ7/oKcmnJy8sLU6ZMgVKp1CwPCgpC9erVc72slLXP3LlzERMTA0dHR80+1tbWqFWrlmab/fv3a+0XFBSUozeLiAwvJSMFZ1PPYtneZYhJeTWJXf+a/dGvRj9OYldKGTzIJCYmon///li9erXWYNG4uDisXbsWgYGBaNeuHQBg/fr1qFmzJs6fP49mzZoZquRiIy0tTTPWI4tEIoGDgwMAYOfOnWjUqBFatGiBLVu24OLFi1i7di0AYNGiRXB2dkb9+vUhFouxc+dOKBQK2NravvW8I0eOxJIlSzBmzBiMHj0aYWFhmDFjBgICAjTjY/KjIJeW+vXrh1mzZmHo0KGYOHEiQkNDsXTpUq27i3bt2oVJkybh1q3M56T4+PigVq1a+Pjjj7FgwQJERUVh6tSpGDVqlOY29REjRuCHH37Al19+iSFDhuDo0aPYsWMH/vzzT81xExMTcffuXc378PBwBAcHw97eXnMZjYgKT1xaHAJvBSLwZiBi02IBAGXNymKQxyD0qtYLFlILwxZIBmXwIDNq1Ch06tQJ3t7eWkHm8uXLUCqVWneU1KhRA66urjh37lyeQSYtLQ1paWma9/Hx8QAApVIJpVKpta1SqdTcLSQIgtZlj+JOEAQcPHgQzs7OWsurV6+OGzduAABmzpyJrVu3YuTIkXB2dsaWLVtQo0YNqNVqWFhYYMGCBbhz5w5MTEzQuHFj7Nu3DwA07aBWqzWv7O+dnZ2xb98+TJw4EXXr1oW9vT2GDBmCyZMna7VhXm2qS1tbWVnh4MGDGDNmDBo2bAgHBwdMmzYNw4YN0xzr5cuXCAsL07wXiUTYu3cvRo4cCS8vL1hYWGDgwIGYOXOmZhs3Nzf88ccfGD9+PJYuXYoKFSrg559/Rvv27TXbXLx4Ee+//76mloCAAADAwIEDc8zjk0WtVkMQBCiVSpiYFP0tnll/11//O0/6x7YuPE9TnuKXW7/gtzu/ITkjGQBgL7bH/+r/D92qdIOpSeZdjGx7/Souf6fze36RUBj3/ebTtm3bMHfuXFy6dAlyuRxt2rRBvXr1sGTJEgQGBsLf318rlABAkyZN0LZtW3z77be5HnPmzJm5zlcSGBgIc3Pty0YSiQQKhQIuLi5at/WWBHZ2dvjll1/QqVMnQ5dSKqWnp+Phw4eIiorKMZMwEb3Zc9VznEo7hSvpV6CCCgCgECvQSt4KHlIPmIg4/0tpkJycjH79+iEuLg7W1tZ5bmewHpmHDx9i3LhxCAoKglwu19txJ02apPmNGcjskXFxcYGPj0+OhkhNTUVERASAzN/4S9rcAmZmZm/85hc1QRCQkJBQItv6dampqTAzM0OrVq30+vc7v5RKJYKCgtC+ffscg65Jv9jW+nP75W1suLEBhyIOQS1k9ojWK1sP/rX80aJcC2RkZLCti0Bx+TuddUXlbQwWZC5fvoyYmBg0aNBAs0ylUuHkyZP44Ycf8NdffyE9PR2xsbFa4zaio6PfOH2+TCbLdZp+qVSa4xuiUqk0P1BFIlGBxncYA7FYXKw+U/ZLPsWprsIgFoshEoly/XtXlAx9/tKEba274JhgrAlZgxOPTmiWNS/fHMM9h6OhU0PNsqz/r9nWRcPQ7ZzfcxssyLz//vsICQnRWubv748aNWpg4sSJcHFxgVQqxZEjR9CzZ08AQFhYGCIiInhHST4Y8IohEdFbCYKAs0/OYnXIalyOvgwgcxK79m7tMcxzGCexo3wzWJCxsrJC7dq1tZZZWFigTJkymuVDhw5FQEAA7O3tYW1tjTFjxsDLy4t3LBERGSmVWoXDEYexNmSt1iR2H1T+AP4e/qhoU9GwBZLRMfhdS2+yePFiiMVi9OzZU2tCPH1j7wXpG/9OEWlTqpTYd28f1oWuw/34+wAyJ7HrWbUnBnkM4iR2pLNiFWSOHz+u9V4ul2PFihVYsWJFoZwv6/pb1pOQifQlOTnzVlFex6fSLlmZjN/v/I4N1zcgOjlzFm0rUyvNJHZ28twntCTKr2IVZIqaiYkJrK2t8fTpU8jlclhaWpb4u2kMSa1WIz09HampqSV2sK8gCEhOTkZMTAxsbW0NMocMUXEQlxaHrbe2YsvNLVqT2A2sNRAfVv+Qk9iR3pTqIAMAjo6OuH37NmQymdYDDUn/BEHQPFG6pAdGW1vbN95dR1RSPU1+is03NmN72HbNJHYVLCvAv7Y/ulbpCplJzrtKid5FqQ8yIpEICQkJeO+99wxdSomnVCpx8uRJtGrVqkRfcpFKpeyJoVLnYcJDrA9djz139yBdnXm5vqpdVQyrPQw+FX0gEZf6HzdUSPg36z8mJiYl+odrcWBiYoKMjAzI5XK2NVEJcfvlbawNWYuD9w9qTWI3zHMYWlVoVeJ7X8nwGGSIiKjAgmOCsTZkLY4/Oq5Z1rxccwzzHIaGTg0ZYKjIMMgQEVG+CIKAc0/OYU3oGlyKugTg1SR2Qz2HolaZWgaukEojBhkiInojlVqFIxFHsDZ0LW48vwEAkIgk6FK5C/xr+8Pdxt3AFVJpxiBDRES5ym0SO7mJHL2q9eIkdlRsMMgQEZGWlIwUzSR2UUlRADInsetboy/61+wPe7m9gSskeoVBhoiIAGROYrft1jZsubkFL9NeAgAczBwyJ7Gr9iEsTS0NXCFRTgwyRESl3LOUZ9h0YxN2hO1AkjIJAFDesjyG1B7CSeyo2GOQISIqpR4lPMKG6xuw684uzSR2VWyrYJjnMPhW9OUkdmQU+LeUiKiUufPyDtaGrsXB8INQCSoAQJ2ydTDcczhaVWgFsahkPguNSiYGGSKiUuLq06tYE7IGxx8e1yx7r9x7GOY5DI2cGnESOzJKDDJERCWYIAg4F3kOa0PW4mLURQCZk9h5u3ljqOdQeJTxMHCFRO+GQYaIqARSC2ocjTiK1SGrtSax61y5M/xr+6OSTSUDV0ikHwwyREQliFKtxJ/3/sS60HUIjwsHkDmJXc9qPTGo1iA4WzobuEIi/WKQISIqAXKdxE5qhT41+mBArQGcxI5KLAYZIiIjFp8er5nE7kXqCwBAGXkZDPQYiI+qfcRJ7KjEY5AhIjJCz1KeYfONzdgetl1rEjt/D390q9qNk9hRqcEgQ0RkRB4nPsb60PU5JrEb6jkUHSp24CR2VOrwbzwRkRG4+/Iu1oauxYHwA68msXOog2Gew9DapTUnsaNSi0GGiKgYu/b0GtaErMGxh8c0y7ycvTDMcxgaKxpzEjsq9RhkiIiKGUEQcD7yPNaGrMWFqAsAMiexe9/1fQzzHAYPB05iR5SFQYaIqJhQC2ociziG1SGrcf35dQCZk9h1qtQJQzyHcBI7olwwyBARGZhSrcT+e/uxLnQd7sXdA5A5iV2Pqj0w2GMwJ7EjegMGGSIiA0nJSMGuO7uw4foGRCZFAng1iV3/mv1RxqyMgSskKv4YZIiIilh8ejy239qOX27+opnEzl5uj4G1BuKj6h/BytTKwBUSGQ8GGSKiIvIs5Rl+ufELtodtR6IyEUDmJHaDPQajW5VukEvkBq6QyPgwyBARFbLHiY+xIXQDdt3dhTRVGgCgsk3lzEns3DtAKpYauEIi48UgQ0RUSP6N/RdrQ9Zif/h+zSR2ng6eGOY5DG1c2nASOyI9YJAhItKzkKchWBOyBkcfHtUsa+bcDMM8h6GJogknsSPSIwYZIiI9yJrEbs21NZpJ7ABoJrGr7VDbgNURlVwMMkRE70AtqHEj/Qa2/rUV11+8msSuY6WOGFp7KCrZchI7osLEIENEpAOlWokD4QewNmQt7iXfA5IBmYlMM4ldOctyhi6RqFRgkCEiKoDUjFTsursLG0I34EnSEwCADDL0q9UPg2oP4iR2REWMQYaIKB8S0hOwPWw7Nt/YrDWJXf/q/WFz3wY96vWAVMrbqImKGoMMEdEbPE95jl9u/oJtt7ZpJrErZ1EOg2sPRvcq3WEimGD/g/0GrpKo9GKQISLKxZPEJ9hwfQN+v/O7ZhK7SjaVMNRzKPzc/TST2CmVSkOWSVTqMcgQEWVzL/Ye1oauxf57+5EhZADInMRuqOdQtHVpy0nsiIoZBhkiIgChz0IzJ7GLOAoBAgCgqXNTDPMchqaKppzEjqiYYpAholJLEARcjLqINSFrcD7yvGZ5O5d2GOY5DJ5lPQ1YHRHlB4MMEZU6akGNYw+PYW3IWoQ8CwEAmIhM0KlSJwypPQSVbSsbuEIiyi8GGSIqNZRqJQ6GH8TakLX4N+5fAJmT2HWv0h2Daw9GecvyBq6QiAqKQYaISrzUjFTsvrsbG65vwOPExwAAS6kl+tTog/41+8PBzMHAFRKRrhhkiKjESkxP1Exi9zz1OYDMSew+rvUxelfvDStTKwNXSETvqsBBRq1W48SJEzh16hQePHiA5ORklC1bFvXr14e3tzdcXFwKo04ionx7nvIcW25uwbZb25CgTAAAOFs4Y7DHYHSv2h1mEjMDV0hE+pLvIJOSkoLvv/8eq1atwosXL1CvXj2UK1cOZmZmuHv3Lnbv3o3hw4fDx8cH06dPR7NmzQqzbiKiHCITIzWT2KWqUgEA7jbuGFp7KDpW6qiZxI6ISo58B5lq1arBy8sLq1evRvv27XN9psiDBw8QGBiIPn36YMqUKRg+fLheiyUiyk1uk9jVLlMbwzyHoa0rJ7EjKsnyHWQOHTqEmjVrvnEbNzc3TJo0CV988QUiIiLeuTgioje5/uw61oSswZGII68msVM0xVDPoWjm3IyT2BGVAvkOMm8LMdlJpVJUrsx5GIhI/wRBwKWoS1gTsgbnIs9plrd1aYthnsNQp2wdA1ZHREVNp7uWDh48CEtLS7Ro0QIAsGLFCqxevRq1atXCihUrYGdnp9ciiYjUghrHHx7H2pC1uPbsGoDMSew6unfEkNpDUMWuimELJCKD0OnC8YQJExAfHw8ACAkJwfjx49GxY0eEh4cjICBArwUSUemWoc7AH//+gZ57e2LcsXG49uwaTMWm6F29N/Z134dvWn7DEENUiunUIxMeHo5atWoBAH777Td07twZ33zzDf755x907NhRrwUSUen1T/Q/mHx6smYSOwupBXpX742Pa33MSeyICICOQcbU1BTJyckAgMOHD2PgwIEAAHt7e01PDRHRu9h1Zxe+Pv81MtQZsJfbY0DNAehdozesTa0NXRoRFSM6BZkWLVogICAAzZs3x8WLF7F9+3YAwO3bt1GhQgW9FkhEpUuGOgOLLi/C5hubAQDt3dpjTvM5MJeaG7gyIiqOdBoj88MPP0AikeDXX3/FqlWrUL585oPWDhw4gA4dOui1QCIqPRLSEzD66GhNiBlZdyS+a/0dQwwR5UmnHhlXV1fs27cvx/LFixe/c0FEVDo9iH+AMUfHIDwuHHITOea0mAPfir6GLouIirl8B5mCjH2xtuY1bCLKv/OR5zH++HjEp8fDydwJy9otQ60ytQxdFhEZgXwHGVtb23zPkqlSqXQuiIhKl223tmH+xflQCSrUcaiDJW2XoKx5WUOXRURGIt9B5tixY5qv79+/j6+++gqDBw+Gl5cXAODcuXPYuHEj5s2bp/8qiajEUaqV+Pbit9gelnmzQOdKnTHzvZmQmcgMXBkRGZN8B5nWrVtrvv7666+xaNEi9O3bV7Psgw8+gKenJ37++WcMGjQoX8dctWoVVq1ahfv37wMAPDw8MH36dPj5+QEAUlNTMX78eGzbtg1paWnw9fXFypUr4eTklN+yiagYik2NxfgT43Ex6iJEEGFcg3EYUnsIn41ERAWm011L586dQ6NGjXIsb9SoES5evJjv41SoUAHz58/H5cuX8ffff6Ndu3bo2rUrrl+/DgD4/PPP8ccff2Dnzp04ceIEnjx5gh49euhSMhEVE//G/ot++/vhYtRFmEvMsazdMgz1HMoQQ0Q60SnIuLi4YPXq1TmWr1mzBi4uLvk+TpcuXdCxY0dUrVoV1apVw9y5c2FpaYnz588jLi4Oa9euxaJFi9CuXTs0bNgQ69evx9mzZ3H+/HldyiYiAzv56CT67++PhwkPUd6yPH7p+AvauLQxdFlEZMR0uv168eLF6NmzJw4cOICmTZsCAC5evIg7d+7gt99+06kQlUqFnTt3IikpCV5eXrh8+TKUSiW8vb0129SoUQOurq44d+4cmjVrlutx0tLSkJaWpnmfdbeVUqmEUqnMsX3WstzWkX6xrYtOcWtrQRDwy61fsOTKEggQ0MCxARa2WAg7uV2xqVFXxa2tSzK2ddEoLu2c3/OLBEEQdDnBo0ePsHLlSty6dQsAULNmTYwYMaJAPTJA5kMnvby8kJqaCktLSwQGBqJjx44IDAyEv7+/VigBgCZNmqBt27b49ttvcz3ezJkzMWvWrBzLAwMDYW7OSbWIilqGkIE9KXtwJf0KAKChaUN0MesCiUin36OIqJRITk5Gv379EBcX98ZpXXQOMvqSnp6OiIgIxMXF4ddff8WaNWtw4sQJBAcH6xRkcuuRcXFxwbNnz3JtCKVSiaCgILRv3x5SqVS/H460sK2LTnFp6+cpz/HFqS9w9dlViEVijG8wHn2q9SlR42GKS1uXBmzrolFc2jk+Ph4ODg5vDTI6/0oUGxuLixcvIiYmBmq1Wmtd1kMk88PU1BRVqlQBADRs2BCXLl3C0qVL0bt3b6SnpyM2Nha2traa7aOjo6FQKPI8nkwmg0yW8/ZNqVT6xm/I29aT/rCti44h2zrsRRjGHB2DyKRIWEmt8F3r7/Be+fcMUktR4N/rosO2LhqGbuf8nlunIPPHH3+gf//+SExMhLW1tdZvVyKRqEBB5nVqtRppaWlo2LAhpFIpjhw5gp49ewIAwsLCEBERoZm7hoiKpyMPjmDS6UlIyUiBm7UblrdbDncbd0OXRUQlkE5BZvz48RgyZAi++eabdxp3MmnSJPj5+cHV1RUJCQkIDAzE8ePH8ddff8HGxgZDhw5FQEAA7O3tYW1tjTFjxsDLyyvPgb5EZFiCIODnaz/jh+AfAABezl5Y2HohbGQ2Bq6MiEoqnYLM48ePMXbs2HcePBsTE4OBAwciMjISNjY2qFOnDv766y+0b98eQObdUWKxGD179tSaEI+Iip/UjFRMPzMdB+4fAAD0r9kfXzT6AhIxB/USUeHR6X8YX19f/P3336hUqdI7nXzt2rVvXC+Xy7FixQqsWLHinc5DRIUrOika446Nw/Xn1yERSTC52WR8WO1DQ5dFRKWATkGmU6dOmDBhAm7cuAFPT88cA3I++OADvRRHRMVfyNMQjDs2Dk9TnsJWZotFbRahsaKxocsiolJCpyAzfPhwAJnPXHqdSCTi06+JSon99/Zj+tnpSFOloYptFSxrtwwuVgWbS4qI6F3oFGRev92aiEoXtaDGD1d+wOqQzEeVtK7QGvNbzoelqaWBKyOi0oaj8IioQJKVyZh0ahKOPjwKAPCv7Y9x9cfBRGxi4MqIqDTS6aGRAHDixAl06dIFVapUQZUqVfDBBx/g1KlT+qyNiIqZJ4lP8PGBj3H04VFIxVJ80+IbBDQMYIghIoPRKcj88ssv8Pb2hrm5OcaOHYuxY8fCzMwM77//PgIDA/VdIxEVA/9E/4O+f/bF7Ze3UUZeBut816FL5S6GLouISjmdLi3NnTsXCxYswOeff65ZNnbsWCxatAizZ89Gv3799FYgERnerju78PX5r5GhzkBN+5pY1m4ZFBZ5PyqEiKio6NQjc+/ePXTpkvM3sQ8++ADh4eHvXBQRFQ8qtQoLLy3E9LPTkaHOQHu39tjQYQNDDBEVGzr1yLi4uODIkSOahz1mOXz4MFxceOslUUmQkJ6ACScn4MzjMwCAT+t+ihF1R0As0nloHRGR3un8rKWxY8ciODgY772X+TTbM2fOYMOGDVi6dKleCySiohcRH4HRR0cjPC4cchM55rSYA9+KvoYui4goB52CzKeffgqFQoHvv/8eO3bsAADUrFkT27dvR9euXfVaIBEVrQuRFxBwPADx6fFwNHfE8nbLUatMLUOXRUSUK53nkenevTu6d++uz1qIyMC23dqG+RfnQyWoUMehDpa0XYKy5mUNXRYRUZ50CjKXLl2CWq1G06ZNtZZfuHABJiYmaNSokV6KI6KioVQr8e3Fb7E9bDsAoHOlzpj53kzITGQGroyI6M10GrU3atQoPHz4MMfyx48fY9SoUe9cFBEVndjUWIwIGoHtYdshggifNfgM37T4hiGGiIyCTj0yN27cQIMGDXIsr1+/Pm7cuPHORRFR0bgXew+jj47Gw4SHMJeYY37L+Wjr2tbQZRER5ZtOPTIymQzR0dE5lkdGRkIi4eObiIzBqUen0H9/fzxMeIjyluWxueNmhhgiMjo6BRkfHx9MmjQJcXFxmmWxsbGYPHky2rdvr7fiiEj/BEHAxusbMfroaCQqE9HQqSECOwWiml01Q5dGRFRgOnWffPfdd2jVqhXc3NxQv359AEBwcDCcnJywefNmvRZIRPqTrkrH1+e+xp5/9wAAelbtiSlNp0BqIjVwZUREutEpyJQvXx7Xrl3Dli1bcPXqVZiZmcHf3x99+/aFVMr/EImKo+cpz/HZsc8Q/DQYYpEYExpNQP+a/SESiQxdGhGRznQe0GJhYYH//e9/+qyFiApJ2IswjDk6BpFJkbCSWmFh64VoXr65ocsiInpnOj80ZfPmzWjRogXKlSuHBw8eAAAWL16MPXv26K04Inp3Rx4cwccHPkZkUiTcrN2wpdMWhhgiKjF0CjKrVq1CQEAA/Pz88PLlS6hUKgCAnZ0dlixZos/6iEhHgiBgTegafHb8M6RkpKCZczNs6bgF7jbuhi6NiEhvdAoyy5cvx+rVqzFlyhSt260bNWqEkJAQvRVHRLpJzUjFjuQdWHltJQCgX41+WOW9CjYyGwNXRkSkXzqNkQkPD9fcrZSdTCZDUlLSOxdFRLqLTorG2KNjcUN5AxKRBJObTcaH1T40dFlERIVCpx4Zd3d3BAcH51h+8OBB1KxZ811rIiIdhT4LRd8/++LGixswE5lhZbuVDDFEVKLp1CMTEBCAUaNGITU1FYIg4OLFi9i6dSvmzZuHNWvW6LtGIsqH/ff2Y/rZ6UhTpaGyTWV0VXdFIyc+wJWISjadgsywYcNgZmaGqVOnIjk5Gf369UO5cuWwdOlS9OnTR981EtEbqAU1VgSvwM/XfgYAtK7QGrO9ZuNk0EkDV0ZEVPh0nkemf//+6N+/P5KTk5GYmAhHR0d91kVE+ZCsTMbk05NxJOIIAMC/tj/G1R8HtUpt4MqIiIqGTmNkUlJSkJycDAAwNzdHSkoKlixZgkOHDum1OCLK25PEJ/j4wMc4EnEEUrEUc1vMRUDDAJiITQxdGhFRkdEpyHTt2hWbNm0CkPmwyCZNmuD7779H165dsWrVKr0WSEQ5XYm5gr5/9sXtl7dRRl4G63zX4YPKHxi6LCKiIqdTkPnnn3/QsmVLAMCvv/4KhUKBBw8eYNOmTVi2bJleCyQibbvu7MKQv4bgReoL1LCvga2dtqKeYz1Dl0VEZBA6jZFJTk6GlZUVAODQoUPo0aMHxGIxmjVrpnlcARHpl0qtwqLLi7DpRmZvaHu39pjTfA7MpeYGroyIyHB06pGpUqUKdu/ejYcPH+Kvv/6Cj48PACAmJgbW1tZ6LZCIgIT0BIw+OloTYkbUHYHvWn/HEENEpZ5OQWb69On44osvULFiRTRt2hReXl4AMntncpvxl4h0FxEfgQH7B+D049OQm8ixsPVCjKo3CmKRzs98JSIqMXS6tNSrVy+0aNECkZGRqFu3rmb5+++/j+7du+utOKLS7kLkBQQcD0B8ejwczR2xrN0yeJTxMHRZRETFhs7zyCgUCigUCq1lTZo0eeeCiCjT9lvbMe/iPKgEFTwdPLG07VKUNS9r6LKIiIqVfPdNjxgxAo8ePcrXttu3b8eWLVt0LoqoNFOqlZhzfg7mXJgDlaBCp0qdsL7DeoYYIqJc5LtHpmzZsvDw8EDz5s3RpUsXNGrUCOXKlYNcLsfLly9x48YNnD59Gtu2bUO5cuXw888/F2bdRCVSXFocxh8fjwtRFyCCCGMbjMXQ2kMhEokMXRoRUbGU7yAze/ZsjB49GmvWrMHKlStx48YNrfVWVlbw9vbGzz//jA4dOui9UKKS7l7sPYw+OhoPEx7CXGKO+S3no61rW0OXRURUrBVojIyTkxOmTJmCKVOm4OXLl4iIiEBKSgocHBxQuXJl/tZIpKNTj07hy5NfIlGZiPKW5bGs3TJUs6tm6LKIiIo9nQf72tnZwc7OTp+1EJU6giBg041NWHR5EdSCGg0cG2Bx28Wwl9sbujQiIqOgc5AhoneTrkrH7POzsfvubgBAz6o9MaXpFEhNpIYtjIjIiDDIEBnA85Tn+Pz457gScwVikRgTGk1A/5r9eXmWiKiAGGSIiljYizCMOToGkUmRsJJaYWHrhWhevrmhyyIiMkoMMkRF6EjEEUw6NQkpGSlwtXLF8veXo5JNJUOXRURktHR+WEtGRgYOHz6Mn376CQkJCQCAJ0+eIDExUW/FEZUUgiBg9bXV+OzYZ0jJSEEz52YI7BTIEENE9I506pF58OABOnTogIiICKSlpaF9+/awsrLCt99+i7S0NPz444/6rpPIaKVmpGL62ek4EH4AANCvRj9MaDwBEjE7RImI3pVOPTLjxo1Do0aN8PLlS5iZmWmWd+/eHUeOHNFbcUTGLiY5Bv4H/XEg/AAkIgmmNZuGSU0nMcQQEemJTv+bnjp1CmfPnoWpqanW8ooVK+Lx48d6KYzI2IU+C8W4o+MQkxIDG5kNFrdZjMaKxoYui4ioRNEpyKjVaqhUqhzLHz16BCsrq3cuisjYHQg/gGlnpiFNlYbKNpWx/P3lcLFyMXRZREQljk6Xlnx8fLBkyRLNe5FIhMTERMyYMQMdO3bUV21ERkctqLH8ynJ8efJLpKnS0KpCK/zS8ReGGCKiQqJTj8z3338PX19f1KpVC6mpqejXrx/u3LkDBwcHbN26Vd81EhmFZGUyJp+ejCMRmePE/D38Ma7BOJiITQxcGRFRyaVTkKlQoQKuXr2Kbdu24dq1a0hMTMTQoUPRv39/rcG/RKXFk8QnGHt0LMJehkEqlmLmezPxQeUPDF0WEVGJp/OtExKJBAMGDNBnLURG6UrMFXx27DO8SH0Be7k9lrZdinqO9QxdFhFRqaBzkHny5AlOnz6NmJgYqNVqrXVjx45958KIjMHuu7sx69wsZKgzUMO+Bpa1XQZnS2dDl0VEVGroFGQ2bNiATz75BKampihTpozWg+5EIhGDDJV4KrUKiy8vxsYbGwEA7d3aY07zOTCXmhu4MiKi0kWnIDNt2jRMnz4dkyZNglis81MOiIxSQnoCJp6ciFOPTwEARtQdgU/rfgqxiP8WiIiKmk5BJjk5GX369GGIoVInIj4CY46Owb24e5CbyDG7xWx0qNjB0GUREZVaOiWRoUOHYufOnfquhahYuxh5Ef3298O9uHtwNHfEBr8NDDFERAamU4/MvHnz0LlzZxw8eBCenp6QSqVa6xctWqSX4oiKix1hOzDvwjxkCBnwdPDE0rZLUda8rKHLIiIq9XQOMn/99ReqV68OADkG+xKVFEq1Et9e/Bbbw7YDADpV6oSZXjMhl8gNXBkREQHvMLPvunXrMHjwYD2XQ1R8xKXFYfzx8bgQdQEiiDC2wVgMrT2UYZ2IqBjRaYyMTCZD8+bN3/nk8+bNQ+PGjWFlZQVHR0d069YNYWFhWtukpqZi1KhRKFOmDCwtLdGzZ09ER0e/87mJ3uRe7D30+7MfLkRdgJnEDEvaLsEwz2EMMURExYxOQWbcuHFYvnz5O5/8xIkTGDVqFM6fP4+goCAolUr4+PggKSlJs83nn3+OP/74Azt37sSJEyfw5MkT9OjR453PTZSXU49Oof/+/ohIiEA5i3LY7LcZ7VzbGbosIiLKhU6Xli5evIijR49i37598PDwyDHY9/fff8/XcQ4ePKj1fsOGDXB0dMTly5fRqlUrxMXFYe3atQgMDES7dpk/SNavX4+aNWvi/PnzaNasmS7lE+VKEARsvrEZ31/+HmpBjQaODbC47WLYy+0NXRoREeVBpyBja2tbKL0icXFxAAB7+8wfHJcvX4ZSqYS3t7dmmxo1asDV1RXnzp3LNcikpaUhLS1N8z4+Ph4AoFQqoVQqc2yftSy3daRfxbmt01XpmHdpHvbc2wMA6Fa5GyY1mgSpibRY1vs2xbmtSxq2ddFhWxeN4tLO+T2/SBAEoZBryRe1Wo0PPvgAsbGxOH36NAAgMDAQ/v7+WsEEAJo0aYK2bdvi22+/zXGcmTNnYtasWTmWBwYGwtyc08dTTonqRGxN2ooHqgcQQQQ/Mz94mXpxPAwRkQElJyejX79+iIuLg7W1dZ7b6fzQSH0bNWoUQkNDNSFGV5MmTUJAQIDmfXx8PFxcXODj45NrQyiVSgQFBaF9+/Y5LpGRfhXHtr798jY+P/k5IlWRsJRaYn7z+Xiv3HuGLuudFce2LqnY1kWHbV00iks7Z11ReZt8B5kGDRrgyJEjsLOzQ/369d/42+o///yT38MCAEaPHo19+/bh5MmTqFChgma5QqFAeno6YmNjYWtrq1keHR0NhUKR67FkMhlkMlmO5VKp9I3fkLetJ/0pLm19JOIIJp2ahJSMFLhauWL5+8tRyaaSocvSq+LS1qUB27rosK2LhqHbOb/nzneQ6dq1qyYgdOvWTaeiXicIAsaMGYNdu3bh+PHjcHd311rfsGFDSKVSHDlyBD179gQAhIWFISIiAl5eXnqpgUofQRCwJmQNll1ZBgBo6twU37f+HjYyGwNXRkREBZXvIDNjxgwMGTIES5cuxYwZM/Ry8lGjRiEwMBB79uyBlZUVoqKiAAA2NjYwMzODjY0Nhg4dioCAANjb28Pa2hpjxoyBl5cX71ginaRmpGLG2RnYH74fANC3Rl9MaDwBUjF/uyMiMkYFmkdm48aNSElJ0dvJV61ahbi4OLRp0wbOzs6a1/bt2zXbLF68GJ07d0bPnj3RqlUrKBSKfN/eTZRdTHIM/A/6Y3/4fkhEEkxrNg2Tm05miCEiMmIFGuyr7xuc8nM8uVyOFStWYMWKFXo9N5Uu159dx9ijYxGTEgMbmQ0Wt1mMxorGhi6LiIjeUYHvWkpISIBc/uYH5r3pNimionYw/CCmnpmKNFUaKttUxvJ2y+Fi7WLosoiISA8KHGSqVauW5zpBECASiaBSqd6pKCJ9UAtqrAhegZ+v/QwAaFWhFb5t+S0sTS0NXBkREelLgYPMr7/+qpl5l6i4SlYmY8rpKTgccRgA4O/hj3ENxsFEbGLgyoiISJ8KHGSaN28OR0fHwqiFSC8iEyMx5ugYhL0Mg1QsxQyvGehapauhyyIiokJQbGb2JdKH4JhgjDs2Di9SX8Bebo+lbZeinmM9Q5dFRESFpEC3X7u5ucHERLtrvlOnToiMjNRrUUS6+PX2r/D/yx8vUl+ghn0NbOu0jSGGiKiEK1CPTHh4eI5lJ0+e1OvcMkQFpVQpMf/ifOy4vQMA0N6tPeY0nwNzKR8SSkRU0vHSEhm1ZynPEHA8AFdirkAEEcY2GIuhtYfyydVERKXEOwcZNzc3PryLDCLkaQg+O/4ZYpJjYCW1wvxW89GqQitDl0VEREXonYNMaGioPuogKpDdd3dj9rnZSFeno5JNJSxtuxQVbSoauiwiIipiOgeZ2NhYXLx4ETExMVCr1VrrBg4c+M6FEeVGqVbi+7+/x5abWwAAbV3a4psW33CSOyKiUkqnIPPHH3+gf//+SExMhLW1tdZ4BJFIxCBDheJF6gt8ceILXIq6BAAYWXckPqn7CcSiAt18R0REJYhOQWb8+PEYMmQIvvnmG5ib884QKnw3n9/EuGPjEJkUCXOJOea1nId2ru0MXRYRERmYTkHm8ePHGDt2LEMMFYk/7/2JmWdnIlWVCjdrNyxtuxSVbSsbuiwiIioGdOqT9/X1xd9//63vWoi0ZKgz8P3f3+OrU18hVZWKFuVbILBTIEMMERFp6NQj06lTJ0yYMAE3btyAp6dnjtuvP/jgA70UR6VXXFocJpyYgHOR5wAAwz2HY1S9UXzoIxERadEpyAwfPhwA8PXXX+dYJxKJoFKp3q0qKtXCXoRh3LFxeJz4GGYSM8xuPhu+FX0NXRYRERVDOgWZ12+3JtKXQ/cPYeqZqUjJSEF5y/JY2nYpqttXN3RZRERUTPERBVQsqNQqrAhegdUhqwEAzZybYWGrhbCV2xq2MCIiKtZ0CjK5XVLKbvr06ToVQ6VTfHo8vjr5FU49PgUAGOwxGOMajINEzJxNRERvptNPil27dmm9VyqVCA8Ph0QiQeXKlRlkKN/uxd7D2GNj8SD+AWQmMsx6bxY6Vepk6LKIiMhI6BRkrly5kmNZfHw8Bg8ejO7du79zUVQ6HI04ismnJyNJmQRnC2csabsEtcrUMnRZRERkRPQ2t7u1tTVmzZqFadOm6euQVEKpBTVWBa/CuGPjkKRMQmNFY2zrvI0hhoiICkyvgxDi4uIQFxenz0NSCZMqpOKLU1/g+KPjAID+NftjfKPxkIqlb96RiIgoFzoFmWXLlmm9FwQBkZGR2Lx5M/z8/PRSGJU8D+If4KeEn/A07ilMxaaY5jUN3ap0M3RZRERkxHQKMosXL9Z6LxaLUbZsWQwaNAiTJk3SS2FUspx8dBITT05EojoRjmaOWNJ2CTzLehq6LCIiMnI6BZnw8PA816WkpOhcDJU8giBgbehaLPtnGQQIcDVxxZoOa+Bs7Wzo0oiIqATQ22DftLQ0LFq0CO7u7vo6JBm5ZGUyxp8Yj6X/LIUAAT2r9MQQyyFwMHMwdGlERFRCFCjIpKWlYdKkSWjUqBHee+897N69GwCwbt06uLu7Y/Hixfj8888Lo04yMg8THmLAgQEIehAEiViCac2mYUqTKZCIOMkdERHpT4F+qkyfPh0//fQTvL29cfbsWXz44Yfw9/fH+fPnsWjRInz44YcwMeHTiUu7s0/OYsKJCYhPj4eDmQMWtVmE+o71oVQqDV0aERGVMAUKMjt37sSmTZvwwQcfIDQ0FHXq1EFGRgauXr0KkUhUWDWSkRAEAZtubMKiy4ugFtTwdPDE4jaL4WThZOjSiIiohCpQkHn06BEaNmwIAKhduzZkMhk+//xzhhhCSkYKZp6dif3h+wEA3ap0w9RmUyEzkRm4MiIiKskKFGRUKhVMTU1f7SyRwNLSUu9FkXF5kvgEnx37DDdf3IREJMGXTb5En+p9GHCJiKjQFSjICIKAwYMHQybL/C07NTUVI0aMgIWFhdZ2v//+u/4qpGLtUtQljD8+Hi/TXsJOZofv23yPxorGhi6LiIhKiQIFmUGDBmm9HzBggF6LIeMhCAICbwVi4aWFUAkq1LSviaVtl8LZkvPDEBFR0SlQkFm/fn1h1UFGJE2VhtnnZmPPv3sAAJ0qdcIMrxkwk5gZuDIiIiptOKkHFUhUUhQ+P/Y5Qp+HQiwSI6BhAAbWGsjxMEREZBAMMpRvV2Ku4PNjn+N56nPYyGywsNVCeJXzMnRZRERUijHIUL7sCNuBeRfnIUOdgap2VbG07VK4WLkYuiwiIirlGGTojZQqJb65+A1+vf0rAMDHzQezm8+GudTcwJURERExyNAbPE1+ioDjAQh+GgwRRBjXYByG1B7C8TBERFRsMMhQrq49vYbPj32OmJQYWEmt8G2rb9GyQktDl0VERKSFQYZy2HVnF2afnw2lWolKNpWwrN0yuFm7GbosIiKiHBhkSEOpVmLhpYXYemsrAKCdSzt80/IbWEgt3rInERGRYTDIEADgecpzjD8xHpejLwMARtYbiU/qfAKxSGzgyoiIiPLGIEO4/vw6Pjv2GaKSomAhtcC8FvPQ1rWtocsiIiJ6KwaZUm7fvX2YeXYm0lRpcLN2w7K2y1DJtpKhyyIiIsoXBplSKkOdgcWXF2PTjU0AgJblW2J+q/mwNrU2cGVERET5xyBTCsWmxmLCyQk4H3keADDcczhG1RsFE7GJgSsjIiIqGAaZUibsRRjGHRuHx4mPYSYxw5zmc+BT0cfQZREREemEQaYUOXj/IKafmY6UjBRUsKyApe2WoppdNUOXRUREpDMGmVIgKikKa0PWYlvYNgCAl7MXFrZeCBuZjYErIyIiejcMMiXYrRe3sPH6RhwMP4gMIQMA4O/hj7ENxkIi5reeiIiMH3+alTCCIOD049PYeGMjLkRe0CxvrGiMobWHonn55gasjoiISL8YZEqIdFU6/rz3Jzbd2IS7sXcBACYiE/hU9MEgj0HwKONh4AqJiIj0j0HGyMWmxmLH7R3YemsrnqU8AwBYSC3Qs2pPDKg5AM6WzgaukIiIqPAwyBiph/EPsenGJuz5dw9SMlIAAE7mThhQcwB6VusJK1MrA1dIRERU+BhkjExwTDA2Xt+IIxFHIEAAANS0r4lBHoPgU9EHUrHUwBUSEREVHQYZI6BSq3D04VFsvL4RV59e1SxvWb4lBnsMRmNFY4hEIgNWSEREZBgMMsVYsjIZu+/uxuYbm/Eo8REAQCqWokvlLhhYayAq21Y2cIVERESGxSBTDD1Nfoqtt7Zie9h2xKfHAwBsZDboXb03+tboCwczBwNXSEREVDyIDXnykydPokuXLihXrhxEIhF2796ttV4QBEyfPh3Ozs4wMzODt7c37ty5Y5hii8Cdl3cw9fRU+P7mi9UhqxGfHg9XK1dMbToVQb2CMKb+GIYYIiKibAzaI5OUlIS6detiyJAh6NGjR471CxYswLJly7Bx40a4u7tj2rRp8PX1xY0bNyCXyw1Qsf4JgoDzkeex8fpGnHlyRrO8gWMDDPQYiDYV2vCp1ERERHkwaJDx8/ODn59frusEQcCSJUswdepUdO3aFQCwadMmODk5Yffu3ejTp09Rlqp3SpUSB+8fxMbrGxH2MgwAIBaJ4e3qjUEeg1CnbB0DV0hERFT8FdsxMuHh4YiKioK3t7dmmY2NDZo2bYpz587lGWTS0tKQlpameR8fnznGRKlUQqlU5tg+a1lu6wpDhjoD229vx6abm/A05SkAwExihm6VuqFfjX4ob1m+SOspSkXd1qUZ27rosK2LDtu6aBSXds7v+YttkImKigIAODk5aS13cnLSrMvNvHnzMGvWrBzLDx06BHNz8zz3CwoK0rHS/IvMiMSulF14onoCALASWaGZrBmamDaBWYwZrsZcxVVcfctRjF9RtDVlYlsXHbZ10WFbFw1Dt3NycnK+tiu2QUZXkyZNQkBAgOZ9fHw8XFxc4OPjA2tr6xzbK5VKBAUFoX379pBKC2cyuTRVGlaHrsbGGxuhElSwNrXG2Hpj0cW9C6QmpWcCu6Joa8rEti46bOuiw7YuGsWlnbOuqLxNsQ0yCoUCABAdHQ1n51fPC4qOjka9evXy3E8mk0Emk+VYLpVK3/gNedt6XV2JuYLpZ6bjfvx9AICPmw8mNZ1Uqu8+Kqy2ppzY1kWHbV102NZFw9DtnN9zF9sg4+7uDoVCgSNHjmiCS3x8PC5cuIBPP/3UsMXlQ5IyCUv/WYptt7ZBgAAHMwdMbToV77u9b+jSiIiISgyDBpnExETcvXtX8z48PBzBwcGwt7eHq6srPvvsM8yZMwdVq1bV3H5drlw5dOvWzXBF58OZx2cw69wsRCZFAgB6VO2BgIYBsJHZGLgyIiKiksWgQebvv/9G27ZtNe+zxrYMGjQIGzZswJdffomkpCT873//Q2xsLFq0aIGDBw8W2zlkYlNjsfDvhdj7714AQHnL8pjhNQNe5bwMXBkREVHJZNAg06ZNGwiCkOd6kUiEr7/+Gl9//XURVlVwgiDg0IND+ObCN3iR+gIiiDCg1gCMrjca5tK875QiIiKid1Nsx8gYi5jkGMw9PxdHHx4FAFS2qYxZzWehbtm6Bq6MiIio5GOQ0ZEgCNh1dxe+u/QdEpQJkIgkGFZnGIZ7DoepiamhyyMiIioVGGR0FHA8AIcjDgMAapepjVnNZ6GaXTUDV0VERFS6MMjoyKucF04/Po3R9UdjQM0BfLAjERGRATDI6KhXtV5oWb4lnC2d374xERERFQqxoQswVmKRmCGGiIjIwBhkiIiIyGgxyBAREZHRYpAhIiIio8UgQ0REREaLQYaIiIiMFoMMERERGS0GGSIiIjJaDDJERERktBhkiIiIyGgxyBAREZHRYpAhIiIio8UgQ0REREaLQYaIiIiMFoMMERERGS0GGSIiIjJaDDJERERktBhkiIiIyGgxyBAREZHRYpAhIiIio8UgQ0REREaLQYaIiIiMlsTQBRAREVExplYBafFAajyQGvff13GZ77O+rtYBcK5jkPIYZIiIiEoqQQCUKbkEkLhXX7+2ziQlFm2fPYbk30mZ69MT3n4ei7IMMkRERPQaVcZ/ISNWuwckt96R1Njce07UGQU6pRiANQCkvrZCIgdk1oDcBpD/96fMOvPrMlX08nF1wSBDRERUGAQBSE/MI4Dk1iOSSzhRJumnFpH4VeiQ2wCy18PIq/cZEgtcvHoLTVp5Q2JR5tU6iUw/tegZgwwREVFuMtKzhYq4XHpAcgsgsdneJwCCSj+1SM1zho5ce0dsc/aWyG0AU0tAJMrXqQSlEk/DJRDKNQCkUv3UX4gYZIiIqORRqzPHduR6CSarRySvdf/9mfH6tRUdiSV5hA6bXHtEcu05MSn+gcJQGGSIiKj4Uaa+FjLiIEp+CbdnpyE+fy/zks3bekcg6KcWU6s8QsYbekSyr5Oa57s3hAqOQYaIiPRLc7vua7fo5ugBicvj8kwcoErPcVgJgHoA8LAAtZiYvuGSTH56RKwBsYl+2oUKBYMMERG9IgiAMjmXABKbj/Ehcfm/XTdfRFohQy2zQnRsKpxcq0Bsbpe/yzVSuZ5qoeKKQYaIqCR5/XbdNw5Qjc19XQFv182TxCz3yzBaAcQ273WmVoD41QT0KqUSF/fvR8eOHSE2gkGoVDQYZIiIiovst+vmd46Q198rk/VTi0icz0Gpb+gRkZjqpxaiN2CQISLSl4z0nLfhvnECs9fmE0mLBwS1fmqRWrx53EeOHpHX1placIAqGQUGGSIiINvtunkNUM19AjNJaix8455CEvI//d6uq9ULkv1W3Dx6RF7vDTHhf+9UOvBvOhEZP0HIDBG53RWT3wGqOt6uKwKQYzipzPoNY0JyuyTz2jqpGXtDqNhQqwWkKFVISs9ASroKSWkqpCgzkJzt6/oudqjoYGGQ+hhkiKh4UauAxBgg/gkQ/xhIiAJSXr49nORyu65OTGRvuSRjq/U+Q2KOU5dC0MK7I6SWZQCZFW/XpSInCALSVWqkpKuQnK5Ccrp20EhOVyE57b/lyqyvX22nvY8Sz+NMMOvaMSSnq5CqfPvlzvk9PBlkiKgUyEgHEiKzhZRsX8c/yXwlRL3DtO6ifD1LRru3xEa756SAt+sKSiXir8cBtq5GMZ07GdbrvRt5hQlN0FBm5AgdKena+2d9naHW0wSAAAARkKbUXiICzKUmMDOVwNzUJNtLAgdLwz2HiUGGiPQjPQmIj3wVShKevAon8Y8z1yXF5O9YIhPAyhmwLgdYKQBz+5x3xeTWW2JqqXW7LpGu0jPU2QJGLkEjXYXkNO3ejRRlBpLeEjpSlHp69tIbmJqIYfZa0Mj1a5nkv2BiAgtZ5nIzqQlkJkDw3xfg3aYlrM3lmetNJZBLxRAVw0ueDDJE9GaCkHn5RtNj8iRnL0r8k8y7dPLDRJYZULRe5f8LLf+9t3Tk5Rl6q6zeDe2AkTN0ZI3ryN67kRU6Ul7r9Sic3o3c5QwZ2u/NTCWwyB46/gsaFjJJZlDJ9rWFqUQTXqQm7xbmlUolYsOAak5WkBpBLyODDFFpplYDyc/f0IvyJLMnRZmUv+OZWuYMJ9kDinX5zN6VYvhbHRUe7d6NnL0V2Xs3sg8mTXq9pyMtQzN2IyVdbbDejczgkHvoMPtvuYXstdCRLWwU594NY8QgQ1RCiQRVZhBJjsk2HuW1XpSEyPwPkjWzz9mLknX5Jyu0yK0L90NRocneu6EVMHK5RJLVu/H6HSzJabmP6SjssRsA8ryMkhU6svdumGULGuamEpjLtHs3sh/nXXs3qPAxyBAZo4w07TCiCSiZf0rin6BLQhREwfn5ASLKvJSjdYnHWbtHxbpc5i3BZHDpGWqtoKEVMPIIHa/fKptb6CiK3g2piUgTEMy0eihyho7sYSQrdJiaAFf/voD3W7eEjYVcEzrkEhOIxezdKK0YZIiKm7TE1+7qea0XJf4JkPzsjYfI+i9dEEsg0vSaZL/Ekz20KACT4n8d3Jio1QJSM1SaMRh5hY7X7zrJcdfK67fNFunYDZM8Q0dW0MgtdGT1bmi+NjWBuTRzX1PJu4/diAsDqiuMY+wGFQ0GGaKiIgiZ86Hk0YuSecfPk8wZZPNDIs+zFyXD3BGHL93E+x/0gdTUcLdFFndZvRvJ2QZ+vjVgvDbWIyktA9HPTLDw1imkKrN6PYqmd8Msj8Ge2b/O846V14JG1tfs3SBjwyBDpA9qNZD0NO+5UbJeGSn5O57M+g29KP8FFjO7PAfNCkol0qSRmQ/+M3Kv927kFTpyv0U2r/k5MpCiVEGp0lfvhghIyf17+2owqPZgz3wFjdfHesj017tBVFIwyBC9jUqZOUlbXnOjZC1XZ+TveOZlct7Jk30sipWz0Q2aFQQBqcqcd6ZoQobyv7tS/huLoT2AVIWUbPu9fjtsUfRuSMSizJ6MXAZ7an+dc5nMBAi5chltWnjB2kKmCRoWMvZuEBUFBhkq3ZQp2S715NGLkhiN/D2DR5Q53uT1O3k0vSj/hRQDDZoVBAFpGer/Bn1maM2/kVuvRq7LlHlP8iUU/tCN/y6lmOSzV0N7fEeOXhE99W4olUqkhwuo72rLcRtEBsAgQyVXavyb50aJfwykvMjfscTSbAEll8s81uUAS6d3HjSbPWxoB4zXJvBKfzXnRm4BJClNiejnJvju1imkKNVI+e9SShGME4VcKs68FCLNOcmX2euXSl4bLGqWxyBR9m4QUV4YZKjoCQKgTM0cL5L1Z0ZaZu9IRmrmK7flyv/ea/ZLfW35f1+nxWcGlfSE/NUjMct9Erfsy8wdNFPfZz2cLfOukv8uiySokPw8PscdKsnZLptkv4TyqjdE+zJLcnqGHsOGCEjOfdyGTCLWChSvj8Uwl+Y+ydfrYST7+I+s8GLCsEFERYhBprRTZeQSCHILCm8IGNmX5xowMpdLMlLROS0JJldyTmZVWASZNTIsnZFu7ow0MwWS5WWRKHNCvNQRLyUOeCkpi1i1OZKV6lcziz5XITkyK1ykICk9DCnp17ON31BBVQRdG6ZZYUOqHSReDyCvXzoxNzWBqRgIDf4HbVp4wcpMliNwMGwQUUnBIFNSqNWZc4skRGW+EqOAhOj//ozKHOeREpszeOR3gKoeiADkeHqOSJzZIyKRQZCaQW0ig9pEBpVYBqVYBqVIBqXIFGkiU6TBFKmCFCmCFMnqzFeSWoIElQSJKgniMySIV0rwIkOKB+m2eKy2Q3KqHMjzbuZUAA/f6TNln748154K6X9f/zceQ3u713s5sn0tNYHkHWYUVSqVyLgvoAHHbRBRCccgU9yplEBiTLZw8l8oef3PxBhAeMe7O0xMM+cmkcgBqVwTMCA1y3N5hokM6ZAhDVKkwRQpkCJFnRk2ElVSJKlMkKiSIkElQWyaCLcfP4e8TDnEKSV4mS5GXBqQmK5GUmJGod2dkjXfhiZgZBvkmT1YWGj1ckg0l1eyP6zt9d4QTl9ORGRYDDK6un0IiLz63w92+asf9q//mf2Hf/YQkJGadyjJ/mfyc+TvjhkAEAEWDoClArBy+u/P/16WToC5PQSJHCmCKVLUEiSqJUhSmSI+Q4yEDAmSlAIS0zIn+Er875WUljnANCEtA0nJOdcVfB4OJ+ClCkDeoUVqIoKFTAILUwms5JLMr2USWMoyw4alXAJL2avlVpqvTTTL9TmbKBERFV8MMroK2w9cXq/jziLkP5xkTjOvNi8Lpbkj0uWOSJE7IEnqgHhpGcSZlMFLsR2ewg7PBRvEK6EJH0kxGUh69CqMJKUlISk9rlDuXJFLxbCUSTPDRo6AkRlCzCRiRNy7jcb1PGFtLoOlLDOUWJhmBRMTWMolkElyXIAiIiLKFYOMrly9Mi/lvD7I9bUBsEK2O3NEgvq/nTOTRIbIFPGSMog1KYMX/4WRGMEWUWobPM6wwSOlFR6kW+MFrCAkv61XIQ5vGAySg0gEWJpm68mQS1/1eGQFDNl/AeO/icK0e0ey9YqY5m88h1KpxP7UMHRsVIHjNoiISC+MIsisWLECCxcuRFRUFOrWrYvly5ejSZMmBq0ppWYvPK3QBU8TU/E0IQ1PE9Mz/8x6JabhWXrmn+kZagACpFBBjnTIkY40SBAPC7x6vN+biUWARbbgkXXpJft7y/8uqWT++epSi3n2Ho9sl15EeUxvT0REZCyKfZDZvn07AgIC8OOPP6Jp06ZYsmQJfH19ERYWBkdHR4PVNXlXCHZdeZzv7a3kUpS1skRZSxnKWslgay7NDB+vhxNNQNEOIXKpmMGDiIjoNcU+yCxatAjDhw+Hv78/AODHH3/En3/+iXXr1uGrr74yWF0OlqaQScRwtJZpwklZKxkcsr5+bZlcynEfRERE+lasg0x6ejouX76MSZMmaZaJxWJ4e3vj3LlzBqwMmNihBiZ3rMleEiIiIgMq1kHm2bNnUKlUcHJy0lru5OSEW7du5bpPWloa0tLSNO/j4+MBZA40VSpzziibtSy3dW+ToX77NvTKu7Q1FQzbuuiwrYsO27poFJd2zu/5i3WQ0cW8efMwa9asHMsPHToEc3PzPPcLCgoqzLIoG7Z10WFbFx22ddFhWxcNQ7dzcnJyvrYr1kHGwcEBJiYmiI6O1loeHR0NhUKR6z6TJk1CQECA5n18fDxcXFzg4+MDa2vrHNsrlUoEBQWhffv2vCW4kLGtiw7buuiwrYsO27poFJd2zrqi8jbFOsiYmpqiYcOGOHLkCLp16wYAUKvVOHLkCEaPHp3rPjKZDDKZLMdyqVT6xm/I29aT/rCtiw7buuiwrYsO27poGLqd83vuYh1kACAgIACDBg1Co0aN0KRJEyxZsgRJSUmau5iIiIio9Cr2QaZ37954+vQppk+fjqioKNSrVw8HDx7MMQCYiIiISp9iH2QAYPTo0XleSiIiIqLSi48FJiIiIqPFIENERERGi0GGiIiIjBaDDBERERktBhkiIiIyWgwyREREZLQYZIiIiMhoGcU8Mu9CEAQAeT+zQalUIjk5GfHx8ZzyupCxrYsO27rosK2LDtu6aBSXds76uZ31czwvJT7IJCQkAABcXFwMXAkREREVVEJCAmxsbPJcLxLeFnWMnFqtxpMnT2BlZQWRSJRjfdbTsR8+fJjr07FJf9jWRYdtXXTY1kWHbV00iks7C4KAhIQElCtXDmJx3iNhSnyPjFgsRoUKFd66nbW1Nf9hFBG2ddFhWxcdtnXRYVsXjeLQzm/qicnCwb5ERERktBhkiIiIyGiV+iAjk8kwY8YMyGQyQ5dS4rGtiw7buuiwrYsO27poGFs7l/jBvkRERFRylfoeGSIiIjJeDDJERERktBhkiIiIyGgxyBAREZHRKtVBZsWKFahYsSLkcjmaNm2KixcvGrokozNv3jw0btwYVlZWcHR0RLdu3RAWFqa1TWpqKkaNGoUyZcrA0tISPXv2RHR0tNY2ERER6NSpE8zNzeHo6IgJEyYgIyOjKD+KUZk/fz5EIhE+++wzzTK2s/48fvwYAwYMQJkyZWBmZgZPT0/8/fffmvWCIGD69OlwdnaGmZkZvL29cefOHa1jvHjxAv3794e1tTVsbW0xdOhQJCYmFvVHKdZUKhWmTZsGd3d3mJmZoXLlypg9e7bWs3XY1ro5efIkunTpgnLlykEkEmH37t1a6/XVrteuXUPLli0hl8vh4uKCBQsWFPZHy0kopbZt2yaYmpoK69atE65fvy4MHz5csLW1FaKjow1dmlHx9fUV1q9fL4SGhgrBwcFCx44dBVdXVyExMVGzzYgRIwQXFxfhyJEjwt9//y00a9ZMeO+99zTrMzIyhNq1awve3t7ClStXhP379wsODg7CpEmTDPGRir2LFy8KFStWFOrUqSOMGzdOs5ztrB8vXrwQ3NzchMGDBwsXLlwQ7t27J/z111/C3bt3NdvMnz9fsLGxEXbv3i1cvXpV+OCDDwR3d3chJSVFs02HDh2EunXrCufPnxdOnTolVKlSRejbt68hPlKxNXfuXKFMmTLCvn37hPDwcGHnzp2CpaWlsHTpUs02bGvd7N+/X5gyZYrw+++/CwCEXbt2aa3XR7vGxcUJTk5OQv/+/YXQ0FBh69atgpmZmfDTTz8V1ccUBEEQSm2QadKkiTBq1CjNe5VKJZQrV06YN2+eAasyfjExMQIA4cSJE4IgCEJsbKwglUqFnTt3ara5efOmAEA4d+6cIAiZ/+DEYrEQFRWl2WbVqlWCtbW1kJaWVrQfoJhLSEgQqlatKgQFBQmtW7fWBBm2s/5MnDhRaNGiRZ7r1Wq1oFAohIULF2qWxcbGCjKZTNi6dasgCIJw48YNAYBw6dIlzTYHDhwQRCKR8Pjx48Ir3sh06tRJGDJkiNayHj16CP379xcEgW2tL68HGX2168qVKwU7Ozut/z8mTpwoVK9evZA/kbZSeWkpPT0dly9fhre3t2aZWCyGt7c3zp07Z8DKjF9cXBwAwN7eHgBw+fJlKJVKrbauUaMGXF1dNW197tw5eHp6wsnJSbONr68v4uPjcf369SKsvvgbNWoUOnXqpNWeANtZn/bu3YtGjRrhww8/hKOjI+rXr4/Vq1dr1oeHhyMqKkqrrW1sbNC0aVOttra1tUWjRo0023h7e0MsFuPChQtF92GKuffeew9HjhzB7du3AQBXr17F6dOn4efnB4BtXVj01a7nzp1Dq1atYGpqqtnG19cXYWFhePnyZRF9mlLw0MjcPHv2DCqVSus/dABwcnLCrVu3DFSV8VOr1fjss8/QvHlz1K5dGwAQFRUFU1NT2Nraam3r5OSEqKgozTa5fS+y1lGmbdu24Z9//sGlS5dyrGM768+9e/ewatUqBAQEYPLkybh06RLGjh0LU1NTDBo0SNNWubVl9rZ2dHTUWi+RSGBvb8+2zuarr75CfHw8atSoARMTE6hUKsydOxf9+/cHALZ1IdFXu0ZFRcHd3T3HMbLW2dnZFUr9ryuVQYYKx6hRoxAaGorTp08bupQS5+HDhxg3bhyCgoIgl8sNXU6Jplar0ahRI3zzzTcAgPr16yM0NBQ//vgjBg0aZODqSpYdO3Zgy5YtCAwMhIeHB4KDg/HZZ5+hXLlybGvKt1J5acnBwQEmJiY57uiIjo6GQqEwUFXGbfTo0di3bx+OHTuGChUqaJYrFAqkp6cjNjZWa/vsba1QKHL9XmSto8xLRzExMWjQoAEkEgkkEglOnDiBZcuWQSKRwMnJie2sJ87OzqhVq5bWspo1ayIiIgLAq7Z60/8fCoUCMTExWuszMjLw4sULtnU2EyZMwFdffYU+ffrA09MTH3/8MT7//HPMmzcPANu6sOirXYvL/ymlMsiYmpqiYcOGOHLkiGaZWq3GkSNH4OXlZcDKjI8gCBg9ejR27dqFo0eP5uhmbNiwIaRSqVZbh4WFISIiQtPWXl5eCAkJ0fpHExQUBGtr6xw/UEqr999/HyEhIQgODta8GjVqhP79+2u+ZjvrR/PmzXNMIXD79m24ubkBANzd3aFQKLTaOj4+HhcuXNBq69jYWFy+fFmzzdGjR6FWq9G0adMi+BTGITk5GWKx9o8hExMTqNVqAGzrwqKvdvXy8sLJkyehVCo12wQFBaF69epFdlkJQOm+/VomkwkbNmwQbty4Ifzvf/8TbG1tte7ooLf79NNPBRsbG+H48eNCZGSk5pWcnKzZZsSIEYKrq6tw9OhR4e+//xa8vLwELy8vzfqs24J9fHyE4OBg4eDBg0LZsmV5W/BbZL9rSRDYzvpy8eJFQSKRCHPnzhXu3LkjbNmyRTA3Nxd++eUXzTbz588XbG1thT179gjXrl0Tunbtmuutq/Xr1xcuXLggnD59WqhatWqpvyX4dYMGDRLKly+vuf36999/FxwcHIQvv/xSsw3bWjcJCQnClStXhCtXrggAhEWLFglXrlwRHjx4IAiCfto1NjZWcHJyEj7++GMhNDRU2LZtm2Bubs7br4vS8uXLBVdXV8HU1FRo0qSJcP78eUOXZHQA5Ppav369ZpuUlBRh5MiRgp2dnWBubi50795diIyM1DrO/fv3BT8/P8HMzExwcHAQxo8fLyiVyiL+NMbl9SDDdtafP/74Q6hdu7Ygk8mEGjVqCD///LPWerVaLUybNk1wcnISZDKZ8P777wthYWFa2zx//lzo27evYGlpKVhbWwv+/v5CQkJCUX6MYi8+Pl4YN26c4OrqKsjlcqFSpUrClClTtG7nZVvr5tixY7n+3zxo0CBBEPTXrlevXhVatGghyGQyoXz58sL8+fOL6iNqiAQh2xSKREREREakVI6RISIiopKBQYaIiIiMFoMMERERGS0GGSIiIjJaDDJERERktBhkiIiIyGgxyBAREZHRYpAhIiIio8UgQ0QGUbFiRSxZsqRQzzF48GB069atUM8BAK1atUJgYGC+t79x4wYqVKiApKSkQqyKqHRgkCEqpQYPHgyRSIQRI0bkWDdq1CiIRCIMHjw438e7f/8+RCIRgoOD87X9pUuX8L///S/fx8/N6tWrUbduXVhaWsLW1hb169fXPDkZAJYuXYoNGza80zneZu/evYiOjkafPn3yvU+tWrXQrFkzLFq0qBArIyodGGSISjEXFxds27YNKSkpmmWpqakIDAyEq6troZwzPT0dAFC2bFmYm5vrfJx169bhs88+w9ixYxEcHIwzZ87gyy+/RGJiomYbGxsb2NravmvJb7Rs2TL4+/vneIrz2/j7+2PVqlXIyMgopMqISgcGGaJSrEGDBnBxccHvv/+uWfb777/D1dUV9evX19r24MGDaNGiBWxtbVGmTBl07twZ//77r2a9u7s7AKB+/foQiURo06YNgFeXd+bOnYty5cqhevXqALQvLR0/fhympqY4deqU5ngLFiyAo6MjoqOjc6197969+OijjzB06FBUqVIFHh4e6Nu3L+bOnavZJvulpaweo9dfWXUCwOnTp9GyZUuYmZnBxcUFY8eOfePln6dPn+Lo0aPo0qWL1nKRSIQ1a9age/fuMDc3R9WqVbF3716tbdq3b48XL17gxIkTeR6fiN6OQYaolBsyZAjWr1+veb9u3Tr4+/vn2C4pKQkBAQH4+++/ceTIEYjFYnTv3h1qtRoAcPHiRQDA4cOHERkZqRWOjhw5grCwMAQFBWHfvn05jt2mTRt89tln+PjjjxEXF4crV65g2rRpWLNmDZycnHKtW6FQ4Pz583jw4EG+PqeLiwsiIyM1rytXrqBMmTJo1aoVAODff/9Fhw4d0LNnT1y7dg3bt2/H6dOnMXr06DyPefr0aZibm6NmzZo51s2aNQsfffQRrl27ho4dO6J///548eKFZr2pqSnq1aunFd6ISAdF/rxtIioWBg0aJHTt2lWIiYkRZDKZcP/+feH+/fuCXC4Xnj59KnTt2lUYNGhQnvs/ffpUACCEhIQIgiAI4eHhAgDhypUrOc7j5OQkpKWlaS13c3MTFi9erHmflpYm1KtXT/joo4+EWrVqCcOHD39j/U+ePBGaNWsmABCqVasmDBo0SNi+fbugUqlyfMbXpaSkCE2bNhU6d+6s2X7o0KHC//73P63tTp06JYjFYiElJSXXGhYvXixUqlQpx3IAwtSpUzXvExMTBQDCgQMHtLbr3r27MHjw4Dd+TiJ6M/bIEJVyZcuWRadOnbBhwwasX78enTp1goODQ47t7ty5g759+6JSpUqwtrZGxYoVAQARERFvPYenpydMTU3fuI2pqSm2bNmC3377DampqVi8ePEbt3d2dsa5c+cQEhKCcePGISMjA4MGDUKHDh00vUR5GTJkCBISEhAYGKgZ23L16lVs2LABlpaWmpevry/UajXCw8NzPU5KSgrkcnmu6+rUqaP52sLCAtbW1oiJidHaxszMDMnJyW+slYjeTGLoAojI8IYMGaK5hLJixYpct+nSpQvc3NywevVqlCtXDmq1GrVr19YM3n0TCwuLfNVx9uxZAMCLFy/w4sWLfO1Xu3Zt1K5dGyNHjsSIESPQsmVLnDhxAm3bts11+zlz5uCvv/7CxYsXYWVlpVmemJiITz75BGPHjs2xT14Dnx0cHPDy5ctc10mlUq33IpEoR8B68eIFKleu/MbPR0RvxiBDROjQoQPS09MhEong6+ubY/3z588RFhaG1atXo2XLlgAyx4dkl9XjolKpdKrh33//xeeff47Vq1dj+/btGDRoEA4fPlygu4Fq1aoFAHkO0P3tt9/w9ddf48CBAzkCRIMGDXDjxg1UqVIl3+erX78+oqKi8PLlS9jZ2eV7vyyhoaHo1atXgfcjold4aYmIYGJigps3b+LGjRswMTHJsd7Ozg5lypTBzz//jLt37+Lo0aMICAjQ2sbR0RFmZmY4ePAgoqOjERcXl+/zq1QqDBgwAL6+vvD398f69etx7do1fP/993nu8+mnn2L27Nk4c+YMHjx4gPPnz2PgwIEoW7YsvLy8cmwfGhqKgQMHYuLEifDw8EBUVBSioqI0A3AnTpyIs2fPYvTo0QgODsadO3ewZ8+eNw72rV+/PhwcHHDmzJl8f9Ys9+/fx+PHj+Ht7V3gfYnoFQYZIgIAWFtbw9raOtd1YrEY27Ztw+XLl1G7dm18/vnnWLhwodY2EokEy5Ytw08//YRy5cqha9eu+T733Llz8eDBA/z0008AMse//Pzzz5g6dSquXr2a6z7e3t44f/48PvzwQ1SrVg09e/aEXC7HkSNHUKZMmRzb//3330hOTsacOXPg7OysefXo0QNA5piWEydO4Pbt22jZsiXq16+P6dOno1y5cnnWbWJiAn9/f2zZsiXfnzXL1q1b4ePjAzc3twLvS0SviARBEAxdBBGRsYqKioKHhwf++eeffIeS9PR0VK1aFYGBgWjevHkhV0hUsrFHhojoHSgUCqxduzZfd29liYiIwOTJkxliiPSAPTJERERktNgjQ0REREaLQYaIiIiMFoMMERERGS0GGSIiIjJaDDJERERktBhkiIiIyGgxyBAREZHRYpAhIiIio8UgQ0REREbr/3fLMQbs3jIqAAAAAElFTkSuQmCC\n"},"metadata":{}}],"source":["from tqdm import tqdm\n","import numpy as np\n","import time\n","import matplotlib.pyplot as plt\n","\n","# Matrix sizes and error tolerances\n","matrix_sizes = [2**i for i in range(5, 11)]  # Sizes: 32, 64, ..., 1024\n","epsilons = [0.1, 0.01, 0.001]  # Different error tolerances\n","\n","run_times = []\n","\n","# Measure run-time for each matrix size and epsilon with tqdm progress bars\n","for epsilon in tqdm(epsilons, desc=\"Processing epsilons\"):\n","    times = []\n","    for size in tqdm(matrix_sizes, desc=f\"Matrix sizes for epsilon={epsilon}\", leave=False):\n","        A = np.random.randn(size, 8)  # Fix d=8 for simplicity\n","        b = np.random.randn(size)\n","        start_time = time.time()\n","        x_opt = randLeastSquares(A, b, epsilon)\n","        end_time = time.time()\n","        times.append(end_time - start_time)\n","    run_times.append(times)\n","\n","# Plot results\n","for i, epsilon in enumerate(epsilons):\n","    plt.plot(matrix_sizes, run_times[i], label=f\"Epsilon={epsilon}\")\n","\n","plt.xlabel(\"Matrix Size (n)\")\n","plt.ylabel(\"Run-Time (seconds)\")\n","plt.title(\"Run-Time vs Matrix Size\")\n","plt.legend()\n","plt.grid()\n","plt.show()\n"]},{"cell_type":"code","execution_count":7,"id":"ed810ef5-de43-4118-85a1-7f0b27c1d3a0","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":603},"id":"ed810ef5-de43-4118-85a1-7f0b27c1d3a0","executionInfo":{"status":"ok","timestamp":1733187748391,"user_tz":300,"elapsed":276611,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}},"outputId":"18407b12-2bfb-4486-eecc-a146c444c27d"},"outputs":[{"output_type":"stream","name":"stdout","text":["Testing for epsilon=0.1\n"]},{"output_type":"stream","name":"stderr","text":["Epsilon=0.1: 100%|██████████| 5/5 [00:14<00:00,  2.85s/it]\n"]},{"output_type":"stream","name":"stdout","text":["Testing for epsilon=0.01\n"]},{"output_type":"stream","name":"stderr","text":["Epsilon=0.01: 100%|██████████| 5/5 [00:24<00:00,  4.85s/it]\n"]},{"output_type":"stream","name":"stdout","text":["Testing for epsilon=0.001\n"]},{"output_type":"stream","name":"stderr","text":["Epsilon=0.001: 100%|██████████| 5/5 [03:56<00:00, 47.38s/it]\n"]},{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["from tqdm import tqdm\n","\n","accuracies = []\n","\n","# Measure accuracy for each epsilon\n","for epsilon in epsilons:\n","    err = []\n","    print(f\"Testing for epsilon={epsilon}\")  # Optional: Display current epsilon\n","    for _ in tqdm(range(num_tests), desc=f\"Epsilon={epsilon}\"):  # Add tqdm here\n","        x_opt = randLeastSquares(A, b, epsilon)\n","        acc = relative_err(x_opt, x_true)\n","        err.append(acc)\n","    accuracies.append(np.mean(err))\n","\n","# Plot results\n","plt.plot(epsilons, accuracies, marker='o')\n","plt.xlabel(\"Epsilon\")\n","plt.ylabel(\"Relative Error\")\n","plt.title(\"Accuracy vs Epsilon\")\n","plt.xscale('log')  # Log scale for epsilon\n","plt.grid()\n","plt.show()\n"]},{"cell_type":"code","execution_count":9,"id":"5552968f-ce98-41f8-8b00-c3b5c7075b6f","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":377},"id":"5552968f-ce98-41f8-8b00-c3b5c7075b6f","executionInfo":{"status":"error","timestamp":1733188942813,"user_tz":300,"elapsed":183659,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}},"outputId":"5f64a845-451a-46cc-fa2e-7a75c75303ad"},"outputs":[{"output_type":"stream","name":"stderr","text":["Processing mode: log:   0%|          | 0/5 [03:03<?, ?it/s]\n"]},{"output_type":"error","ename":"KeyboardInterrupt","evalue":"","traceback":["\u001b[0;31m---------------------------------------------------------------------------\u001b[0m","\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)","\u001b[0;32m<ipython-input-9-25e480d03502>\u001b[0m in \u001b[0;36m<cell line: 6>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     10\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtqdm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum_tests\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdesc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34mf\"Processing mode: {mode}\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m         \u001b[0mstart_time\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m         \u001b[0mx_opt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrandLeastSquares\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mepsilon\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0mt\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 39\u001b[0;31m         \u001b[0mi_t\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mchoice\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     40\u001b[0m         \u001b[0mS\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi_t\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     41\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n","\u001b[0;31mKeyboardInterrupt\u001b[0m: "]}],"source":["modes = [\"log\", \"linear\"]\n","mode_accuracies = []\n","mode_run_times = []\n","\n","# Measure accuracy and run-time for each mode\n","for mode in modes:\n","    err = []\n","    times = []\n","    # Use tqdm to wrap the range for progress tracking\n","    for _ in tqdm(range(num_tests), desc=f\"Processing mode: {mode}\"):\n","        start_time = time.time()\n","        x_opt = randLeastSquares(A, b, epsilon, mode=mode)\n","        end_time = time.time()\n","\n","        acc = relative_err(x_opt, x_true)\n","        err.append(acc)\n","        times.append(end_time - start_time)\n","\n","    mode_accuracies.append(np.mean(err))\n","    mode_run_times.append(np.mean(times))\n","\n","# Plot Accuracy Comparison\n","plt.bar(modes, mode_accuracies)\n","plt.xlabel(\"Mode\")\n","plt.ylabel(\"Average Relative Error\")\n","plt.title(\"Accuracy: Log vs Linear Mode\")\n","plt.show()\n","\n","# Plot Run-Time Comparison\n","plt.bar(modes, mode_run_times)\n","plt.xlabel(\"Mode\")\n","plt.ylabel(\"Average Run-Time (seconds)\")\n","plt.title(\"Run-Time: Log vs Linear Mode\")\n","plt.show()"]},{"cell_type":"code","source":["# Analysis with smaller size matrices\n","# Example usage\n","modes = [\"log\", \"linear\"]\n","mode_accuracies = []\n","mode_run_times = []\n","\n","num_tests = 5\n","matrix_size = (32, 8)  # Example size\n","epsilon = 0.01\n","\n","A = np.random.randn(*matrix_size)\n","b = np.random.randn(matrix_size[0])\n","x_true = np.linalg.lstsq(A, b, rcond=None)[0]\n","\n","# Measure accuracy and run-time for each mode\n","for mode in modes:\n","    err = []\n","    times = []\n","\n","    for _ in tqdm(range(num_tests), desc=f\"Processing mode: {mode}\"):\n","        start_time = time.time()\n","        x_opt = randLeastSquares(A, b, epsilon, mode=mode)\n","        end_time = time.time()\n","\n","        acc = relative_err(x_opt, x_true)\n","        err.append(acc)\n","        times.append(end_time - start_time)\n","\n","    mode_accuracies.append(np.mean(err))\n","    mode_run_times.append(np.mean(times))\n","\n","# Plot Accuracy Comparison\n","plt.bar(modes, mode_accuracies)\n","plt.xlabel(\"Mode\")\n","plt.ylabel(\"Average Relative Error\")\n","plt.title(\"Accuracy: Log vs Linear Mode\")\n","plt.show()\n","\n","# Plot Run-Time Comparison\n","plt.bar(modes, mode_run_times)\n","plt.xlabel(\"Mode\")\n","plt.ylabel(\"Average Run-Time (seconds)\")\n","plt.title(\"Run-Time: Log vs Linear Mode\")\n","plt.show()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":983},"id":"NsnwpMgMHImN","executionInfo":{"status":"ok","timestamp":1733189284521,"user_tz":300,"elapsed":322987,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}},"outputId":"974305c6-98b0-4320-d1da-d7e78d32f3e0"},"id":"NsnwpMgMHImN","execution_count":10,"outputs":[{"output_type":"stream","name":"stderr","text":["Processing mode: log: 100%|██████████| 5/5 [05:18<00:00, 63.62s/it]\n","Processing mode: linear: 100%|██████████| 5/5 [00:04<00:00,  1.20it/s]\n"]},{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 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\n"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":["<Figure 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\n"},"metadata":{}}]},{"cell_type":"code","source":["# Line Chart Example\n","plt.figure(figsize=(10, 5))\n","plt.plot(modes, mode_accuracies, marker='o', label='Accuracy')\n","plt.plot(modes, mode_run_times, marker='x', label='Run-Time')\n","plt.xlabel(\"Mode\")\n","plt.title(\"Performance Metrics by Mode\")\n","plt.legend()\n","plt.grid(True)\n","plt.show()\n","\n","# Box Plot Example\n","data = [np.random.rand(10), np.random.rand(10)]  # Replace with actual relative error/run-time data\n","plt.figure(figsize=(10, 5))\n","plt.boxplot(data, labels=modes)\n","plt.xlabel(\"Mode\")\n","plt.ylabel(\"Value\")\n","plt.title(\"Distribution of Performance Metrics\")\n","plt.show()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":977},"id":"aKmMF4Q0I3-1","executionInfo":{"status":"ok","timestamp":1733189407238,"user_tz":300,"elapsed":592,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}},"outputId":"4b034c36-6ddf-4ae9-ab1b-10169dd8894c"},"id":"aKmMF4Q0I3-1","execution_count":11,"outputs":[{"output_type":"display_data","data":{"text/plain":["<Figure size 1000x500 with 1 Axes>"],"image/png":"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\n"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":["<Figure 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\n"},"metadata":{}}]},{"cell_type":"code","execution_count":null,"id":"0da36f77-9bd8-4841-b021-f3c05a3ac0f9","metadata":{"id":"0da36f77-9bd8-4841-b021-f3c05a3ac0f9"},"outputs":[],"source":["# Additional Analysis"]},{"cell_type":"code","execution_count":8,"id":"88006146-ede3-4131-91e2-5ef56ca96a53","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":1000},"id":"88006146-ede3-4131-91e2-5ef56ca96a53","executionInfo":{"status":"ok","timestamp":1733195762793,"user_tz":300,"elapsed":1841989,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}},"outputId":"926ec74a-339b-46a7-aceb-7164007fc101"},"outputs":[{"output_type":"stream","name":"stdout","text":["Testing mode: log\n"]},{"output_type":"stream","name":"stderr","text":["log Mode Progress: 100%|██████████| 10/10 [30:29<00:00, 182.92s/it]\n"]},{"output_type":"stream","name":"stdout","text":["Testing mode: linear\n"]},{"output_type":"stream","name":"stderr","text":["linear Mode Progress: 100%|██████████| 10/10 [00:12<00:00,  1.21s/it]\n"]},{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 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\n"},"metadata":{}},{"output_type":"display_data","data":{"text/plain":["<Figure 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\n"},"metadata":{}}],"source":["# Parameters for testing\n","num_tests = 10\n","\n","\n","# Initialize results storage\n","mode_accuracies = []\n","mode_run_times = []\n","\n","# Compare log vs linear modes\n","modes = [\"log\", \"linear\"]\n","for mode in modes:\n","    err = []\n","    times = []\n","\n","    print(f\"Testing mode: {mode}\")\n","\n","    for _ in tqdm(range(num_tests), desc=f\"{mode} Mode Progress\"):\n","        # Generate random test data\n","        # n, d = 128, 32  # Example size; adjust as needed\n","        n, d = 64, 16\n","        A = np.random.randn(n, d)\n","        x_true = np.random.randn(d)\n","        b = A @ x_true + 0.01 * np.random.randn(n)\n","        epsilon = 0.1\n","\n","        start_time = time.time()\n","        x_opt = randLeastSquares(A, b, epsilon, mode=mode)\n","        end_time = time.time()\n","\n","        acc = np.linalg.norm(x_opt - x_true) / np.linalg.norm(x_true)  # Relative error\n","        err.append(acc)\n","        times.append(end_time - start_time)\n","\n","    mode_accuracies.append(np.mean(err))\n","    mode_run_times.append(np.mean(times))\n","\n","# Plot Accuracy Comparison\n","plt.bar(modes, mode_accuracies)\n","plt.xlabel(\"Mode\")\n","plt.ylabel(\"Average Relative Error\")\n","plt.title(\"Accuracy: Log vs Linear Mode\")\n","plt.show()\n","\n","# Plot Run-Time Comparison\n","plt.bar(modes, mode_run_times)\n","plt.xlabel(\"Mode\")\n","plt.ylabel(\"Average Run-Time (seconds)\")\n","plt.title(\"Run-Time: Log vs Linear Mode\")\n","plt.show()\n","\n"]},{"cell_type":"code","execution_count":9,"id":"11d690a3-9c27-491e-94dd-7e83a429e344","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":510},"id":"11d690a3-9c27-491e-94dd-7e83a429e344","executionInfo":{"status":"ok","timestamp":1733197057317,"user_tz":300,"elapsed":228403,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}},"outputId":"7bab61f4-59a9-478b-be94-3062edd6ef22"},"outputs":[{"output_type":"stream","name":"stderr","text":["Size vs Run-Time Analysis: 100%|██████████| 3/3 [03:47<00:00, 75.99s/it]\n"]},{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}],"source":["# Additional Analysis: Size vs Run-Time and Accuracy vs Epsilon\n","size_run_times_log = []\n","size_run_times_linear = []\n","\n","dimensions = [8, 16, 32] # dimensions = [64, 128, 256]  # Example sizes for analysis\n","# Compare log vs linear modes\n","modes = [\"log\", \"linear\"]\n","\n","for size in tqdm(dimensions, desc=\"Size vs Run-Time Analysis\"):\n","    A = np.random.randn(size, size // 2).astype(np.float32)\n","    b = A @ np.random.randn(size // 2) + 0.01 * np.random.randn(size).astype(np.float32)\n","\n","    for mode in modes:\n","        start_time = time.time()\n","        randLeastSquares(A, b, epsilon=0.1, mode=mode)\n","        end_time = time.time()\n","\n","        if mode == \"log\":\n","            size_run_times_log.append(end_time - start_time)\n","        else:\n","            size_run_times_linear.append(end_time - start_time)\n","\n","plt.plot(dimensions, size_run_times_log, label=\"Log Mode\")\n","plt.plot(dimensions, size_run_times_linear, label=\"Linear Mode\")\n","plt.xlabel(\"Matrix Size\")\n","plt.ylabel(\"Run-Time (seconds)\")\n","plt.title(\"Size vs Run-Time\")\n","plt.legend()\n","plt.show()"]},{"cell_type":"code","source":["epsilons = [0.01, 0.1, 1]   # Example epsilon values for analysis\n","\n","\n","# Additional Analysis: Accuracy vs Epsilon Analysis\n","modes = [\"log\", \"linear\"]\n","epsilon_accuracies_log = []\n","epsilon_accuracies_linear = []\n","\n","for eps in tqdm(epsilons, desc=\"Accuracy vs Epsilon Analysis\"):\n","    A = np.random.randn(32, 18)# A = np.random.randn(128, 64)\n","    x_true = np.random.randn(18)\n","    b = A @ x_true + eps * np.random.randn(32)\n","\n","    for mode in modes:\n","        x_opt = randLeastSquares(A, b, epsilon=eps, mode=mode)\n","\n","        acc = np.linalg.norm(x_opt - x_true) / np.linalg.norm(x_true)  # Relative error\n","\n","        if mode == \"log\":\n","            epsilon_accuracies_log.append(acc)\n","        else:\n","            epsilon_accuracies_linear.append(acc)\n","\n","plt.plot(epsilons, epsilon_accuracies_log, label=\"Log Mode\")\n","plt.plot(epsilons, epsilon_accuracies_linear, label=\"Linear Mode\")\n","plt.xlabel(\"Epsilon\")\n","plt.ylabel(\"Relative Error\")\n","plt.title(\"Accuracy vs Epsilon\")\n","plt.legend()\n","plt.show()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":510},"id":"_fiQgBmsW1oo","executionInfo":{"status":"ok","timestamp":1733200678881,"user_tz":300,"elapsed":518525,"user":{"displayName":"Jesus Rodriguez","userId":"11168746376106142982"}},"outputId":"0f9712aa-3c1b-4bc6-9730-f6952ef23ca9"},"id":"_fiQgBmsW1oo","execution_count":6,"outputs":[{"output_type":"stream","name":"stderr","text":["Accuracy vs Epsilon Analysis: 100%|██████████| 3/3 [08:38<00:00, 172.69s/it]\n"]},{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}]}],"metadata":{"kernelspec":{"display_name":"Python 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