{

 "cells": [

  {

   "cell_type": "markdown",

   "id": "opened-florist",

   "metadata": {},

   "source": [

    "import time\n",

    "seconds = time.time()\n",

    "print(\"Time in seconds since beginning of run:\", seconds)\n",

    "local_time = time.ctime(seconds)\n",

    "print(local_time)\n",

    "# Pegasos Quantum Support Vector Classifier\n",

    "\n",

    "There's another SVM based algorithm that benefits from the quantum kernel method. Here, we introduce an implementation of a another classification algorithm, which is an alternative version to the `QSVC` available in Qiskit Machine Learning and shown in the [\"Quantum Kernel Machine Learning\"](./03_quantum_kernel.ipynb) tutorial. This classification algorithm implements the Pegasos algorithm from the paper \"Pegasos: Primal Estimated sub-GrAdient SOlver for SVM\" by Shalev-Shwartz et al., see: https://home.ttic.edu/~nati/Publications/PegasosMPB.pdf.\n",

    "\n",

    "This algorithm is an alternative to the dual optimization from the `scikit-learn` package, benefits from the kernel trick, and yields a training complexity that is independent of the size of the training set. Thus, the `PegasosQSVC` is expected to train faster than QSVC for sufficiently large training sets.\n",

    "\n",

    "The algorithm can be used as direct replacement of `QSVC` with some hyper-parameterization."

   ]

  },

  {

   "cell_type": "code",

   "execution_count": 12,

   "id": "759a01c7-b426-4ebe-8a4e-c9b9a1104603",

   "metadata": {},

   "outputs": [

    {

     "name": "stdout",

     "output_type": "stream",

     "text": [

      "Time in seconds since beginning of run: 1696472962.5317466\n",

      "Thu Oct  5 02:29:22 2023\n"

     ]

    }

   ],

   "source": [

    "import time\n",

    "seconds = time.time()\n",

    "print(\"Time in seconds since beginning of run:\", seconds)\n",

    "local_time = time.ctime(seconds)\n",

    "print(local_time)"

   ]

  },

  {

   "cell_type": "markdown",

   "id": "thirty-painting",

   "metadata": {},

   "source": [

    "Let's generate some data:"

   ]

  },

  {

   "cell_type": "code",

   "execution_count": 13,

   "id": "impressed-laser",

   "metadata": {},

   "outputs": [],

   "source": [

    "from sklearn.datasets import make_blobs\n",

    "\n",

    "# example dataset\n",

    "features, labels = make_blobs(n_samples=20, n_features=2, centers=2, random_state=3, shuffle=True)"

   ]

  },

  {

   "cell_type": "markdown",

   "id": "moderate-yugoslavia",

   "metadata": {},

   "source": [

    "We pre-process the data to ensure compatibility with the rotation encoding and split it into the training and test datasets."

   ]

  },

  {

   "cell_type": "code",

   "execution_count": 14,

   "id": "adolescent-composer",

   "metadata": {},

   "outputs": [],

   "source": [

    "import numpy as np\n",

    "\n",

    "from sklearn.model_selection import train_test_split\n",

    "from sklearn.preprocessing import MinMaxScaler\n",

    "\n",

    "features = MinMaxScaler(feature_range=(0, np.pi)).fit_transform(features)\n",

    "\n",

    "train_features, test_features, train_labels, test_labels = train_test_split(\n",

    "    features, labels, train_size=15, shuffle=False\n",

    ")"

   ]

  },

  {

   "cell_type": "markdown",

   "id": "central-poverty",

   "metadata": {},

   "source": [

    "We have two features in the dataset, so we set a number of qubits to the number of features in the dataset.\n",

    "\n",

    "Then we set $\\tau$ to the number of steps performed during the training procedure. Please note that, there is no early stopping criterion in the algorithm. The algorithm iterates over all $\\tau$ steps.\n",

    "\n",

    "And the last one is the hyperparameter $C$. This is a positive regularization parameter. The strength of the regularization is inversely proportional to $C$. Smaller $C$ induce smaller weights which generally helps preventing overfitting. However, due to the nature of this algorithm, some of the computation steps become trivial for larger $C$. Thus, larger $C$ improve the performance of the algorithm drastically. If the data is linearly separable in feature space, $C$ should be chosen to be large. If the separation is not perfect, $C$ should be chosen smaller to prevent overfitting."

   ]

  },

  {

   "cell_type": "code",

   "execution_count": 15,

   "id": "dying-dispatch",

   "metadata": {},

   "outputs": [],

   "source": [

    "# number of qubits is equal to the number of features\n",

    "num_qubits = 2\n",

    "\n",

    "# number of steps performed during the training procedure\n",

    "tau = 50\n",

    "\n",

    "# regularization parameter\n",

    "C = 1000"

   ]

  },

  {

   "cell_type": "markdown",

   "id": "improving-wilderness",

   "metadata": {},

   "source": [

    "The algorithm will run using:\n",

    "\n",

    "- The default fidelity instantiated in `FidelityQuantumKernel`\n",

    "- A quantum kernel created from `ZFeatureMap`"

   ]

  },

  {

   "cell_type": "code",

   "execution_count": 16,

   "id": "automated-allergy",

   "metadata": {},

   "outputs": [],

   "source": [

    "from qiskit import BasicAer\n",

    "from qiskit.circuit.library import ZFeatureMap\n",

    "from qiskit.utils import algorithm_globals\n",

    "\n",

    "from qiskit_machine_learning.kernels import FidelityQuantumKernel\n",

    "\n",

    "algorithm_globals.random_seed = 12345\n",

    "\n",

    "feature_map = ZFeatureMap(feature_dimension=num_qubits, reps=1)\n",

    "\n",

    "qkernel = FidelityQuantumKernel(feature_map=feature_map)"

   ]

  },

  {

   "cell_type": "markdown",

   "id": "attractive-stationery",

   "metadata": {},

   "source": [

    "The implementation `PegasosQSVC` is compatible with the `scikit-learn` interfaces and has a pretty standard way of training a model. In the constructor we pass parameters of the algorithm, in this case there are a regularization hyper-parameter $C$ and a number of steps.\n",

    "\n",

    "Then we pass training features and labels to the `fit` method, which trains a models and returns a fitted classifier.\n",

    "\n",

    "Afterwards, we score our model using test features and labels."

   ]

  },

  {

   "cell_type": "code",

   "execution_count": 17,

   "id": "representative-thumb",

   "metadata": {},

   "outputs": [

    {

     "name": "stdout",

     "output_type": "stream",

     "text": [

      "PegasosQSVC classification test score: 1.0\n"

     ]

    }

   ],

   "source": [

    "from qiskit_machine_learning.algorithms import PegasosQSVC\n",

    "\n",

    "pegasos_qsvc = PegasosQSVC(quantum_kernel=qkernel, C=C, num_steps=tau)\n",

    "\n",

    "# training\n",

    "pegasos_qsvc.fit(train_features, train_labels)\n",

    "\n",

    "# testing\n",

    "pegasos_score = pegasos_qsvc.score(test_features, test_labels)\n",

    "print(f\"PegasosQSVC classification test score: {pegasos_score}\")"

   ]

  },

  {

   "cell_type": "markdown",

   "id": "sustainable-empire",

   "metadata": {},

   "source": [

    "For visualization purposes we create a mesh grid of a predefined step that spans our minimum and maximum values we applied in MinMaxScaler. We also add some margin to the grid for better representation of the training and test samples."

   ]

  },

  {

   "cell_type": "code",

   "execution_count": 18,

   "id": "judicial-pottery",

   "metadata": {},

   "outputs": [],

   "source": [

    "grid_step = 0.2\n",

    "margin = 0.2\n",

    "grid_x, grid_y = np.meshgrid(\n",

    "    np.arange(-margin, np.pi + margin, grid_step), np.arange(-margin, np.pi + margin, grid_step)\n",

    ")"

   ]

  },

  {

   "cell_type": "markdown",

   "id": "marine-constitution",

   "metadata": {},

   "source": [

    "We convert the grid to the shape compatible with the model, the shape should be `(n_samples, n_features)`.\n",

    "Then for each grid point we predict a label. In our case predicted labels will be used for coloring the grid."

   ]

  },

  {

   "cell_type": "code",

   "execution_count": 19,

   "id": "competitive-outdoors",

   "metadata": {},

   "outputs": [],

   "source": [

    "meshgrid_features = np.column_stack((grid_x.ravel(), grid_y.ravel()))\n",

    "meshgrid_colors = pegasos_qsvc.predict(meshgrid_features)"

   ]

  },

  {

   "cell_type": "markdown",

   "id": "former-constraint",

   "metadata": {},

   "source": [

    "Finally, we plot our grid according to the labels/colors we obtained from the model. We also plot training and test samples."

   ]

  },

  {

   "cell_type": "code",

   "execution_count": 20,

   "id": "monetary-knife",

   "metadata": {

    "tags": [

     "nbsphinx-thumbnail"

    ]

   },

   "outputs": [

    {

     "data": {

      "image/png": 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0HmO+u+1CCHHr1i0xc+ZM0apVK2Fvby8CAgLE1KlTxY0bN2rUOSEhoUZbevXqpfd4PBHJA98NRFZBq9XCy8sLgwcPxhdffGHp6hARUSPimBWSnRs3btQY1/LVV1/h8uXLetPtExGRbWDPCslOZmYm3njjDTzzzDPw9PREdnY2UlJSEBoaikOHDtV4kR4RETVtHGBLshMUFISAgAB88sknuHz5Mjw8PDBq1Ch88MEHDCpERDaIPStEREQkaxyzQkRERLLGsEJERESyZhVjVrRaLS5cuABnZ2ejpt8mIqKmQwiBq1evokWLFnrvHrtfWq0WN2/eNNnx6N7s7e0Nvp+rNlYRVi5cuICAgABLV4OIiGTg/Pnz8Pf3N8mxbt68iTNnztz3CzTJeG5ubvD19a1XJ4RVhJXqKcD/hpZQmfDO1dedeprsWETmNvLoLktXgZooa/lZKDS3oDnxjUleCwFU9dTk5+dDqVQiICDApL01ZJgQAteuXUNRUREAwM/P7577WEVYqU5dKihMGlYkJR+DJethyn/7RHeytp+FphoOUFlZiWvXrqFFixa6l2ZS43B0dAQAFBUVwdvb+563hPjTj4iIbFL1W8w5f5NlVAfE+rztnWGFiIhsGh/csAxjvu4MK0RERCRrDCtERERkNEmSsGHDhkY5F8MKERGRFcrKyoJSqURCQkK9ygcFBWHevHkmO39+fj769etnsuPVxSqeBiIiIpKdX38Frl41vN3ZGQgONtvpU1JS8OqrryIlJQUXLlxAixYt7vuYGo0GkiTV6zFuX1/f+z5ffbFnhYiIyFi//gq0bQtERhpe2ratKmcGZWVlWLNmDV555RUkJCQgNTW1zvIxMTE4e/Ys3njjDUiSpBvcmpqaCjc3N2zatAnt27eHWq3GuXPncODAATzxxBN44IEH4Orqil69eiE7O1vvmHfeBsrLy4MkSUhLS0Pv3r3RrFkzhIWFISsryyTtZVghIiIyVnWPyooVwKFDNZcVK/TLmdg333yDdu3aISQkBCNGjMCyZcsghDBYPi0tDf7+/pg1axby8/ORn5+v23bt2jV8+OGHWLp0KY4fPw5vb29cvXoVo0ePxu7du/HTTz8hODgY/fv3x9V7tGfatGmYPHkycnJy0LZtWwwbNgyVlZX33V7eBiIiImqo0FAgIqLRT5uSkoIRI0YAAPr27YuSkhLs3LkTMTExtZb38PCAUqmEs7Nzjds3t27dwqJFixAWFqZbFxsbq1dmyZIlcHNzw86dOzFgwACD9Zo8ebJuDM3MmTPRoUMH/Pbbb2jXrl1DmqnDnhUiIhvljVsIQAXCr12qdWlTUWLpKlItTp48if3792PYsGEAADs7OwwdOhQpKSkNOp5KpULnzp311hUWFmL8+PEIDg6Gq6srXFxcUFZWhnPnztV5rDuPUz2NfvW0+veDPStERDbIG7cwCxcAANNO/Z/Bcu1DB+M3tWtjVYvqISUlBZWVlXoDaoUQUKvVWLBgAVxdjbtejo6ONSZoGz16NP7880/Mnz8fgYGBUKvViIqKuufbqe3t7XV/rz6mKV4SybBCRGSD1Lj9H8iKFVW3Mu6WmwuMGAEnzb2nQqfGU1lZia+++gpz5sxBnz599LYlJiZi1apVePnll2vdV6VS6V4xcC979uzBokWL0L9/fwBVb7q+dOnS/VX+PjCsEBHZMguNuaCG2bx5M65cuYIXXnihRg/K008/jZSUFINhJSgoCLt27cJzzz0HtVqNBx54wOB5goOD8fXXX6Nr164oLS3Fm2++qXv5oCVwzAoREVFD5eYC2dk1l9xcs5wuJSUFcXFxtd7qefrpp3Hw4EEcOXKk1n1nzZqFvLw8tG7dGl5eXvc8z5UrVxAREYGRI0fitddeg7e3t0na0BDsWSEiIjKWs3PVn7efyLlnORP5v/8zPL6oW7dudT6+3L17d/z8889668aMGYMxY8bUKNulSxccOHBAb92QIUP0Pt95rqCgoBrndnNzq7M+xmBYISIiMlZwMHDqlEVnsLUlDCtEREQNwSDSaBhWiIhsmaGxFWYac0HUEAwrREQ2qKL6+Yp7jLkoU9rXuZ2oMdh0WBmbs8Msx10WHnvvQkREFlQEe0xHi7/mW6lFBRTomXsIPRt4Dv4sJFOx6bBCRGTLisBeE7IOnGeFiIiIZI1hhYiIiGSNYYWIiIhkjWGFiIiIjBYUFIR58+Y1yrmMCiufffYZOnfuDBcXF7i4uCAqKgr/+c9/6tzn22+/Rbt27eDg4IBOnTphy5Yt91VhIiIiWzZmzBhIkqRbPD090bdvX4PvBKoWExODiRMnmqweBw4cwIsvvmiy49XFqLDi7++PDz74AIcOHcLBgwcRGxuLJ598EsePH6+1/N69ezFs2DC88MILOHz4MBITE5GYmIhjx46ZpPJERESWptEAmZnAqlVVf2o05j9n3759kZ+fj/z8fGzfvh12dnYYMGDAfR9XCIHKysp6lfXy8kKzZs3u+5z1YVRYGThwIPr374/g4GC0bdsWs2fPhpOTE3766aday8+fPx99+/bFm2++idDQULz77ruIiIjAggULTFJ5IiIiS0pLA9q0AXr3BoYPr/qzTZuq9eakVqvh6+sLX19fhIeHY8qUKTh//jwuXrxYa/kxY8Zg586dmD9/vq5HJi8vD5mZmZAkCf/5z38QGRkJtVqN3bt34/Tp03jyySfh4+MDJycnPPzww/j+++/1jnn3bSBJkrB06VI89dRTaNasGYKDg7Fp0yaTtLfBY1Y0Gg1Wr16N8vJyREVF1VomKysLcXFxeuvi4+ORlZVV57ErKipQWlqqtxAREclJWhowZAjQqROQlVX1TsOsrKrPQ4aYP7BUKysrw4oVK9CmTRt4enrWWmb+/PmIiorC+PHjdT0yAQEBuu1TpkzBBx98gNzcXHTu3BllZWXo378/tm/fjsOHD6Nv374YOHAgzp07V2ddZs6ciWeffRZHjhxB//798be//Q2XL1++7zYaPSnc0aNHERUVhRs3bsDJyQnr169H+/btay1bUFAAHx8fvXU+Pj4oKCio8xzJycmYOXOmsVUjIiJqFBoN8I9/AAMGABs2AIrbv/p37171OTERmDwZePJJQKk0/fk3b94MJycnAEB5eTn8/PywefNmKBS190G4urpCpVKhWbNm8PX1rbF91qxZeOKJJ3SfPTw8EBYWpvv87rvvYv369di0aRMmTJhgsF5jxozBsGHDAADvv/8+PvnkE+zfvx99+/ZtUDurGd2zEhISgpycHOzbtw+vvPIKRo8ejRMnTtxXJe42depUlJSU6Jbz58+b9PhERET348cfgbw84O23/woq1RQKYOpU4MyZqnLm0Lt3b+Tk5CAnJwf79+9HfHw8+vXrh7NnzzboeF27dtX7XFZWhsmTJyM0NBRubm5wcnJCbm7uPXtWOnfurPt78+bN4eLigqKiogbV6U5G96yoVCq0adMGABAZGYkDBw5g/vz5+Pzzz2uU9fX1RWFhod66wsLCWlPdndRqNdRqtbFVIyIiahT5+VV/duxY+/bq9dXlTK158+a6/4sBYOnSpXB1dcUXX3yB9957r0HHu9PkyZORkZGBf/3rX2jTpg0cHR0xZMgQ3Lx5s87j2Nvrv8JBkiRotYbfP1Vf9z3PilarRUVFRa3boqKisH37dr11GRkZBse4EBERWQM/v6o/DT3cWr2+upy5SZIEhUKB69evGyyjUqmgqeejSnv27MGYMWPw1FNPoVOnTvD19UVeXp6Jams8o3pWpk6din79+uHBBx/E1atXsXLlSmRmZmLbtm0AgFGjRqFly5ZITk4GALz++uvo1asX5syZg4SEBKxevRoHDx7EkiVLTN8SIiKiRtKjBxAUBLz/vv6YFQDQaoHkZKBVq6py5lBRUaEb/3nlyhUsWLAAZWVlGDhwoMF9goKCsG/fPuTl5cHJyQkeHh4GywYHByMtLQ0DBw6EJEn4f//v/5mkh6ShjOpZKSoqwqhRoxASEoLHH38cBw4cwLZt23SDcs6dO4f8O/q8oqOjsXLlSixZsgRhYWFYu3YtNmzYgI6G+s2IiIisgFIJzJkDbN5cNZj2zqeBEhOr1v/rX+YZXAsAW7duhZ+fH/z8/PDII4/gwIED+PbbbxETE2Nwn8mTJ0OpVKJ9+/bw8vKqc/zJ3Llz4e7ujujoaAwcOBDx8fGIiIgwQ0vqRxJCCIudvZ5KS0vh6uqK5xEAlRW8IWBZeKylq0BN0NicHZauApFRTP2zUGhuovLov1FSUgIXF5f7Pt6NGzdw5swZtGrVCg4ODg06Rlpa1VNBd94hadWqKqgMHnzfVWzSjPn6Gz3AloiIiKoMHlz1ePKPP1YNpvXzq7r1Y64eFVvFsEJERHQflEqgjrsvZALyv6dCRERENo1hhYiIiGSNt4GIiMgsTD0o/Ca0WG7SI5K1YM8KERERyRrDChEREckawwoRERHJGsesEJHseOMW1DA8tXcFFCiCvcHtRNS0MKwQkax44xZm4cI9y01HCwYWIhvB20BEJCu6HpUVK4BDh2ouK1bolyOyUVlZWVAqlUhISKhX+aCgIMybN8+kdYiJicHEiRNNeszasGeFiOQpNBSw4IvTiO7p11+r3l5oiLMzEBxsttOnpKTg1VdfRUpKCi5cuIAWLVqY7VyWxp4VIiIiY/36K9C2LRAZaXhp27aqnBmUlZVhzZo1eOWVV5CQkIDU1NQ6y8fExODs2bN44403IEkSJEnSbdu9ezd69OgBR0dHBAQE4LXXXkN5eblu+6JFixAcHAwHBwf4+PhgyJAhAIAxY8Zg586dmD9/vu6YeXe+0dGEGFaIiIiMVVePSkPKGembb75Bu3btEBISghEjRmDZsmUQQhgsn5aWBn9/f8yaNQv5+fnIz88HAJw+fRp9+/bF008/jSNHjmDNmjXYvXs3JkyYAAA4ePAgXnvtNcyaNQsnT57E1q1b0bNnTwDA/PnzERUVhfHjx+uOGRAQYJb28jYQERGRlUlJScGIESMAAH379kVJSQl27tyJGANvVPTw8IBSqYSzszN8fX1165OTk/G3v/1NN+4kODgYn3zyCXr16oXPPvsM586dQ/PmzTFgwAA4OzsjMDAQXbp0AQC4urpCpVKhWbNmesc0B/asEBERWZGTJ09i//79GDZsGADAzs4OQ4cORUpKitHH+vnnn5GamgonJyfdEh8fD61WizNnzuCJJ55AYGAgHnroIYwcORL//ve/ce3aNVM36Z7Ys0JE8pSba9x6IhuRkpKCyspKvQG1Qgio1WosWLAArq6u9T5WWVkZXnrpJbz22ms1tj344INQqVTIzs5GZmYmvvvuO0yfPh3vvPMODhw4ADc3N1M0p14YVohIViqqO3xvd3HfsxyRDamsrMRXX32FOXPmoE+fPnrbEhMTsWrVKrz88su17qtSqaDRaPTWRURE4MSJE2jTpo3Bc9rZ2SEuLg5xcXGYMWMG3NzcsGPHDgwePLjWY5oDwwoRyUoR7DEdLTiDLVEtNm/ejCtXruCFF16o0YPy9NNPIyUlxWBYCQoKwq5du/Dcc89BrVbjgQcewFtvvYXu3btjwoQJGDduHJo3b44TJ04gIyMDCxYswObNm/H777+jZ8+ecHd3x5YtW6DVahESEqI75r59+5CXlwcnJyd4eHhAoTD9LxL81YSIZKcI9jgPtcGFQYVsVUpKCuLi4mq91fP000/j4MGDOHLkSK37zpo1C3l5eWjdujW8vLwAAJ07d8bOnTtx6tQp9OjRA126dMH06dN1t5jc3NyQlpaG2NhYhIaGYvHixVi1ahU6dOgAAJg8eTKUSiXat28PLy8vnDt3ziztlkRdzzrJRGlpKVxdXfE8AqCygny1LDzW0lWgJmhszg5LV4HIom5Ci+U4j5KSEri4uNz38W7cuIEzZ86gVatWcHBwMG7n6nlW7uXUKbNODGfNjPn68zYQERGRsYKDq4KIBWewtSUMK0RERA3BINJo5H9PhYiIiGwawwoRERHJGm8DmYE5BkJy0C4REdkq9qwQERGRrDGsEBERkawxrBAREZGsMawQERGRrDGsEBERkawxrBAREVmRMWPGQJIk3eLp6Ym+ffsafCdQtZiYGEycONHkdUlMTDTpMWvDsEJERHQfNBogMxNYtarqT43G/Ofs27cv8vPzkZ+fj+3bt8POzg4DBgww/4kthGGFiIiogdLSgKAgoHdvYPjwqj+DgqrWm5NarYavry98fX0RHh6OKVOm4Pz587h48WKt5ceMGYOdO3di/vz5uh6ZvLw8AMCxY8fQr18/ODk5wcfHByNHjsSlS5d0+65duxadOnWCo6MjPD09ERcXh/Lycrzzzjv48ssvsXHjRt0xMzMzzdJehhUiIjILb9xCACoMLt64Zekq3pe0NGDIEOCPP/TX//e/VevNHViqlZWVYcWKFWjTpg08PT1rLTN//nxERUVh/Pjxuh6ZgIAAFBcXIzY2Fl26dMHBgwexdetWFBYW4tlnnwUA5OfnY9iwYRg7dixyc3ORmZmJwYMHQwiByZMn49lnn9Xr5YmOjjZLGzmDLRERmZw3bmEWLtyz3HS0QBHsG6FGpqXRAK+/DghRc5sQgCQBEycCTz4JKJWmP//mzZvh5OQEACgvL4efnx82b94MhaL2PghXV1eoVCo0a9YMvr6+uvULFixAly5d8P777+vWLVu2DAEBATh16hTKyspQWVmJwYMHIzAwEADQqVMnXVlHR0dUVFToHdMcGFaIiMjk1NBW/WXFCiA0tGaB3FxgxIi/ylmZH3+s2aNyJyGA8+erysXEmP78vXv3xmeffQYAuHLlChYtWoR+/fph//79ulBRHz///DN++OEHXfC50+nTp9GnTx88/vjj6NSpE+Lj49GnTx8MGTIE7u7uJmtLfTCsEBGR+YSGAhERlq6FyeXnm7acsZo3b442bdroPi9duhSurq744osv8N5779X7OGVlZRg4cCA+/PDDGtv8/PygVCqRkZGBvXv34rvvvsOnn36KadOmYd++fWjVqpVJ2lIfHLNCRERkJD8/05a7X5IkQaFQ4Pr16wbLqFQqaO56VCkiIgLHjx9HUFAQ2rRpo7c0b95cd+xHH30UM2fOxOHDh6FSqbB+/XqDxzQHhhUiIiIj9egB+PtXjU2pjSQBAQFV5cyhoqICBQUFKCgoQG5uLl599VVdL4khQUFB2LdvH/Ly8nDp0iVotVokJSXh8uXLGDZsGA4cOIDTp09j27ZteP7556HRaLBv3z68//77OHjwIM6dO4e0tDRcvHgRobdv7QUFBeHIkSM4efIkLl26hFu3zDNommGFiIjISEolMH9+1d/vDizVn+fNM8/gWgDYunUr/Pz84Ofnh0ceeQQHDhzAt99+i5g6BshMnjwZSqUS7du3h5eXF86dO4cWLVpgz5490Gg06NOnDzp16oSJEyfCzc0NCoUCLi4u2LVrF/r374+2bdvif/7nfzBnzhz069cPADB+/HiEhISga9eu8PLywp49e8zSXo5ZISIiaoDBg4G1a6ueCrpzsK2/f1VQGTzYPOdNTU1Famqq0fu1bdsWWVlZNdYHBwcjzcBz1qGhodi6davBY3p5eeG7774zui7GMiqsJCcnIy0tDb/88gscHR0RHR2NDz/8ECEhIQb3SU1NxfPPP6+3Tq1W48aNGw2rMRERWY/cXOPWW5nBg6seT/7xx6rBtH5+Vbd+zNWjYquMCis7d+5EUlISHn74YVRWVuLtt99Gnz59cOLECd1AnNq4uLjg5MmTus+SoZt8RETUJFRUjzIYMaJ+5ayYUmmex5PpL0aFlbu7glJTU+Ht7Y1Dhw6hZ8+eBveTJMnsE8YQEZF8FMEe09GiznlUKqCwygnhqPHd15iVkpISAICHh0ed5crKyhAYGAitVouIiAi8//776NChw/2cmoiIZI5BhEylwf1vWq0WEydOxKOPPoqOHTsaLBcSEoJly5Zh48aNWLFiBbRaLaKjo/FHHVP/VVRUoLS0VG8hIiIyB1HbnPlkdsZ83RscVpKSknDs2DGsXr26znJRUVEYNWoUwsPD0atXL6SlpcHLywuff/65wX2Sk5Ph6uqqWwICAhpaTSIiolopb4+CvXnzpoVrYpuuXbsGALC3v3cPXINuA02YMAGbN2/Grl274O/vb9S+9vb26NKlC3777TeDZaZOnYpJkybpPpeWljKwEBGRSdnZ2aFZs2a4ePEi7O3tDb4EkExLCIFr166hqKgIbm5uutBYF6PCihACr776KtavX4/MzMwGvRdAo9Hg6NGj6N+/v8EyarUaarXa6GMTERHVlyRJ8PPzw5kzZ3D27FlLV8fmuLm51fvhG6PCSlJSElauXImNGzfC2dkZBQUFAKpePe3o6AgAGDVqFFq2bInk5GQAwKxZs9C9e3e0adMGxcXF+Oijj3D27FmMGzfOmFMTERGZnEqlQnBwMG8FNTJ7e/t69ahUMyqsVL+O+u7pfJcvX44xY8YAAM6dO6fXlXblyhWMHz8eBQUFcHd3R2RkJPbu3Yv27dsbc2oiIiKzUCgUcHBwsHQ1qA6SsIJh0KWlpXB1dcXzCICqCUwg1BDLwmMtXQWysLE5OyxdBSKLugktluM8SkpK4OLiYunqUCPiu4GIyCp44xYnGCOyUQwrRCR73riFWbhwz3LT0YKBhagJYlghItnT9aisWAGEhtYskJsLjBhRZ88LEVkvhhUish6hoUBEhKVrQUSNzDZHqxIREZHVYFghIiIiWeNtICKiBuITSkSNg2GFiKgB+IQSUeNhWCEi65Gba9x6M7qfJ5TYI0NkHIYVIpK9iurhdSNG1K9cYzLyCSX2yBAZj2GFiGSvCPaYjhZNojeivnPBcM4Yor8wrBCRVbCGIGLInbd9fHHLwrUhsj4MK0REZuSOSvwdlyxdDSKrxnlWiIjMSA3Zv9ieSPbYs0JEdD9k9IQSUVPFsEJE1AD1fULpJqRGqA1R08awQkTUAPV9QolP9RDdP4YVIqIGutcTSt641eCnfywyZwyRTDGsEBGZQX0nf6uWAk8U3A4/1jJnDFFjYVghIjIDY2//FMAe56E2U22IrBv7GYmIZIC3fYgMY88KEZEFpcATZ6HmbR+iOjDKExFZUAHsGVSI7oFhhYiIiGSNYYWIiIhkjWGFiIiIZI1hhYjIDOr7dA+fAiK6Nz4NRERkBvWdjp+Da4nujWGFiMhMGESITIP9j0RERCRrDCtEREQkawwrREREJGsMK0RERCRrDCtEREQkawwrREREJGsMK0RERCRrDCtEREQka5wUjoiIAADeuMUZd0mWGFaIiAjeuIVZuHDPctPRgoGFGh3DChER/dWjsmIFEBpas0BuLjBiRJ09L0TmwrBCRER/CQ0FIiIsXQsiPRxgS0RERLLGsEJERESyZlRYSU5OxsMPPwxnZ2d4e3sjMTERJ0+evOd+3377Ldq1awcHBwd06tQJW7ZsaXCFiYiIyLYYFVZ27tyJpKQk/PTTT8jIyMCtW7fQp08flJeXG9xn7969GDZsGF544QUcPnwYiYmJSExMxLFjx+678kRERNT0GTXAduvWrXqfU1NT4e3tjUOHDqFnz5617jN//nz07dsXb775JgDg3XffRUZGBhYsWIDFixc3sNpERGQWubnGrSdqBPf1NFBJSQkAwMPDw2CZrKwsTJo0SW9dfHw8NmzYYHCfiooKVFRU6D6XlpbeTzWJiOgeKqo72keMqF85okbU4LCi1WoxceJEPProo+jYsaPBcgUFBfDx8dFb5+Pjg4KCAoP7JCcnY+bMmQ2tGhERGakI9piOFpzBlmSpwWElKSkJx44dw+7du01ZHwDA1KlT9XpjSktLERAQYPLzEBHRXxhESK4aFFYmTJiAzZs3Y9euXfD396+zrK+vLwoLC/XWFRYWwtfX1+A+arUaarW6IVUjIiKiJsaom49CCEyYMAHr16/Hjh070KpVq3vuExUVhe3bt+uty8jIQFRUlHE1JSIiIptkVM9KUlISVq5ciY0bN8LZ2Vk37sTV1RWOjo4AgFGjRqFly5ZITk4GALz++uvo1asX5syZg4SEBKxevRoHDx7EkiVLTNwUIiIiaoqM6ln57LPPUFJSgpiYGPj5+emWNWvW6MqcO3cO+fn5us/R0dFYuXIllixZgrCwMKxduxYbNmyoc1AuERERUTWjelaEEPcsk5mZWWPdM888g2eeecaYUxEREREB4LuBiIiISOYYVoiIiEjW7msGWyKipsYbtzgxGpHMMKwQEd3mjVuYhQv3LDcdLRhYiBoRwwoR0W26HpUVK4DQ0JoFcnOBESPq7HkhItNjWCEiultoKBARYelaENFtHGBLREREssawQkRERLLGsEJERESyxrBCREREssYBtkREd8vNNW49EZkVwwoR0W0V1Z3NI0bUrxwRNQqGFSKi24pgj+lowRlsiWSGYYWI6A4MIkTyw75MIiIikjWGFSIiIpI1hhUiIiKSNYYVIiIikjWGFSIiIpI1Pg1EsiaEBFHWFqh0A+yKITmdgiQJS1eLiIgaEcMKyZa2OAJS4XBornvo1tk5XobWZyUUbtkWrBkRETUm3gYiWdIWR0CTl4S+j7sjKwu4ehXIygLiY92gyUuCtjjC0lUkIqJGwrBCsiOEBKlwOAYMADZulNC9O+DkBHTvDmzapEBCgoBUOAxCSJauKhERNQKGFZIdUdYWldc9MG2aBMVd/0IVCmDaNAUqr3tWjWUhIqImj2GF5KfSDQDQsWPtm3Xrb5cjIqKmjQNszWBZeKylq2Dd7IoBAMeOVd36uduxY/rlbIW5/l2NzdlhluMSEZkKe1ZIdiSnU7BzvIz33tNCe9fLb7VaYPZsLewc/4TkdMoyFSQiokbFsEKyI0kCwmcl0tMlDBqk1XsaaNAgLdLTJQifVZxvhYjIRvA2EMmSwi0bCFqIbTuGIz39znlWrkAZtIrzrBAR2RCGFZIthVs2hOthKO+YwRZOp6BgjwoRkU1hWCFZkyQByfmkpatBREQWxDErREREJGsMK0RERCRrDCtEREQkawwrREREJGsMK0RERCRrDCtEREQkawwrREREJGsMK0RERCRrDCtEREQkawwrREREJGsMK0RERCRrRoeVXbt2YeDAgWjRogUkScKGDRvqLJ+ZmQlJkmosBQUFDa0zERER2RCjw0p5eTnCwsKwcOFCo/Y7efIk8vPzdYu3t7expyYiIiIbZPRbl/v164d+/foZfSJvb2+4ubkZvR8RERHZtkYbsxIeHg4/Pz888cQT2LNnT2OdloiIiKyc0T0rxvLz88PixYvRtWtXVFRUYOnSpYiJicG+ffsQERFR6z4VFRWoqKjQfS4tLTV3NYmIiEimzB5WQkJCEBISovscHR2N06dP4+OPP8bXX39d6z7JycmYOXOmuauGZeGxZj8HEZGtMvXPWKG5CRz9t0mPSdbBIo8ud+vWDb/99pvB7VOnTkVJSYluOX/+fCPWjoiIiOTE7D0rtcnJyYGfn5/B7Wq1Gmq1uhFrRERERHJldFgpKyvT6xU5c+YMcnJy4OHhgQcffBBTp07Ff//7X3z11VcAgHnz5qFVq1bo0KEDbty4gaVLl2LHjh347rvvTNcKIiIiarKMDisHDx5E7969dZ8nTZoEABg9ejRSU1ORn5+Pc+fO6bbfvHkT//jHP/Df//4XzZo1Q+fOnfH999/rHYOIiIjIEEkIISxdiXspLS2Fq6srnkcAVCYcZsMBtkTA2Jwdlq4CNVHmGGBbefTfKCkpgYuLi0mPTfLGdwMRERGRrDGsEBERkawxrBAREZGsMawQERGRrDGsEBERkawxrBAREZGsMawQERGRrDGsEBERkawxrBAREZGsMawQERGRrDGsEBERkawxrBAREZGsMawQERGRrDGsEBERkawxrBAREZGs2Vm6Asb4ulNPSEqVpatB1KQsC481y3HH5uwwy3HJ9Mz1b4DIVNizQkRERLLGsEJERESyxrBCREREssawQkRERLLGsEJERESyxrBCREREsmZVjy5bghASRFlboNINsCuG5HQKkiQsXS0iIiKbwbBSB21xBKTC4dBc99Cts3O8DK3PSijcsi1YMyIiItvB20AGaIsjoMlLQt/H3ZGVBVy9CmRlAfGxbtDkJUFbHGHpKhIREdkEhpVaCCFBKhyOAQOAjRsldO8OODkB3bsDmzYpkJAgIBUOgxCSpatKRETU5DGs1EKUtUXldQ9MmyZBcddXSKEApk1ToPK6Z9VYFiIiIjIrhpXaVLoBADp2rH2zbv3tckRERGQ+DCu1sSsGABw7Vvtm3frb5YiIiMh8GFZqITmdgp3jZbz3nhZarf42rRaYPVsLO8c/ITmdskwFiYiIbAjDSi0kSUD4rER6uoRBg7R6TwMNGqRFeroE4bOK860QERE1As6zYoDCLRsIWohtO4YjPf3OeVauQBm0ivOsEBERNRKGlToo3LIhXA9DeccMtnA6BQV7VIiIiBoNw8o9SJKA5HzS0tUgIiKyWRyzQkRERLLGsEJERESyxrBCREREssYxK0RkFsvCY01+zLE5O0x+THMxR/uJbBV7VoiIiEjWGFaIiIhI1hhWiIiISNYYVoiIiEjWGFaIiIhI1owOK7t27cLAgQPRokULSJKEDRs23HOfzMxMREREQK1Wo02bNkhNTW1AVYmIiMgWGR1WysvLERYWhoULF9ar/JkzZ5CQkIDevXsjJycHEydOxLhx47Bt2zajK0tERES2x+h5Vvr164d+/frVu/zixYvRqlUrzJkzBwAQGhqK3bt34+OPP0Z8fLyxpyciIiIbY/YxK1lZWYiLi9NbFx8fj6ysLIP7VFRUoLS0VG8hIiIi22T2sFJQUAAfHx+9dT4+PigtLcX169dr3Sc5ORmurq66JSAgwNzVJCIiIpmS5dNAU6dORUlJiW45f/68patEREREFmL2dwP5+vqisLBQb11hYSFcXFzg6OhY6z5qtRpqtdrcVSMiIiIrYPaelaioKGzfvl1vXUZGBqKiosx9aiIiImoCjA4rZWVlyMnJQU5ODoCqR5NzcnJw7tw5AFW3cEaNGqUr//LLL+P333/HP//5T/zyyy9YtGgRvvnmG7zxxhumaQERERE1aUaHlYMHD6JLly7o0qULAGDSpEno0qULpk+fDgDIz8/XBRcAaNWqFdLT05GRkYGwsDDMmTMHS5cu5WPLREREVC9Gj1mJiYmBEMLg9tpmp42JicHhw4eNPRURERGR+QfYElmSEBJEWVug0g2wK4bkdAqSZDhsExGR/DCskKyYMlxoiyMgFQ6H5rqHbp2d42VofVZC4ZZtohoTEZG5yXKeFbJN2uII4NRH0Jx+C5qzL0Fz+i3g1EdV6xtwLE1eEvo+7o6sLODqVSArC4iPdYMmL6lBxyQiIstgWCFZMGW4EEKCVDgcAwYAGzdK6N4dcHICuncHNm1SICFBQCocBiEkM7aIiIhMhbeBrEhTHX9xd7hQ3I7Q1eFi0CAttu0YBuF6uF7tFWVtobnugWnToDtWNYUCmDZNgfR0TyjL2kJyPmmGFpG5LAuPtXQViMgCGFashLY4Apr/Dgdu/TX+AvaXoWxp/eMvTB4uKt0AAB071r5Zt/52OSIikjfeBrIC1bdIcMtdf8OtJjL+wtThwq4YAHDsWO2bdetvlyMiInljWJE5IaSqHhUAwN1jLBQABDT/tfLxFyYOF5LTKdg5XsZ772mh1epv02qB2bO1sHP8E5LTqQZVl4iIGhfDisyJsra3b/0YCiMK4JZnVTkrZepwIUkCwmcl0tMlDBqk1RuwO2iQFunpEoTPqiYx3oeIyBYwrMhdfW99WPH4C3OEC4VbNpRBC7FtRzGiowEXFyA6Gti24wqUQQutfpwPEZEt4QBbuavvuAorH3+hcMsGghZi247hSE+/cxK3K1AGrWpQuFC4ZUO4Hobyjieo4HQKCvaoEBFZFYYVmZOcTgH2l4Fbbqi9I0wL2F9pEuMvzBEuJEnw8WQiIivH20AyJ0kCypYrUTVm5a4BHdACkKBs2XTGX0iSgML5JBTu+6BwPtlk2kVERA3HsGIFqsdfwL5Yf4M9x18QEVHTx9tAVkLhlg3J9XCTnMGWiIioLgwrVoTjL4iIyBbxNhARERHJGsMKERERyRrDChEREckawwoRERHJGsMKERERyRqfBjIjISQ+akxERHSfGFbMRFscAalwODTX73zPzWVofVZyEjciIiIj8DaQGWiLI6DJS0Lfx9313iAcH+sGTV4StMURlq4iERGR1WBYMTEhJEiFwzFgALBxo4Tu3QEnJ6B7d2DTJgUSEgSkwmEQQtKV114NgfbKI9BeDdGtJyIioiq8DWRioqwtNNc9MG0aoLgrCioUwLRpCqSne0JZ1hZC05y3iqjJGpuzw9JVqLdl4bGWrgIR1YE9K6ZW6QYA6Nix9s3V60VpF94qIiIiqgeGFVOzKwYAHDtW++bq9Yqr3et9q4iIiMiWMayYmOR0CnaOl/Hee1potfrbtFpg9mwtFKoSVN5wwbRpksFbRZXXPaseeyYiIrJxDCsmJkkCwmcl0tMlDBqk1bvFM2iQFunpEoTLTwDufauo+pYSERGRLeMAWzNQuGUDQQuxbcdwpKffOXj2CpRBqwBlOTSX4nHsWNWtn7vpbiHdvqVERERkyxhWzEThlg3hehjKO2awhdMpKCQBIaTbt4rcsGmTQu9WUPWtIjvHK4DTKUtVn4iISDZ4G8iMJElA4XwSCvd9UDif1E21X69bRT6rODU/ERER2LNiMfe6VcR5VoiIiKowrFhQXbeKiIiIqArDioVJkoDkfNLS1SAiIpItjlkhIiIiWWPPiswIIVVNBnf7tpDkdIoDbYmIyKYxrMiItjgCmv8OB279NeAW9pehbMkXGxIRke3ibSCZ0BZHQJOXBNxy199wiy82JCIi28awIgNCSFU9KgCAu19eqAAgoPkvX2xIRES2iWFFBkRZ29u3fgyFEQVwiy82JCIi29SgsLJw4UIEBQXBwcEBjzzyCPbv32+wbGpqKiRJ0lscHBwaXOEmqb4vLOSLDYmIyAYZHVbWrFmDSZMmYcaMGcjOzkZYWBji4+NRVFRkcB8XFxfk5+frlrNnz95XpZuc+r6wkC82JCIiG2R0WJk7dy7Gjx+P559/Hu3bt8fixYvRrFkzLFu2zOA+kiTB19dXt/j4+NxXpZsayekUYH8ZgNZACS1g/2dVOSIiIhtjVFi5efMmDh06hLi4uL8OoFAgLi4OWVlZBvcrKytDYGAgAgIC8OSTT+L48eMNr3ETJEkCypYrUTVm5e7AogUgQdmSLzYkIiLbZFRYuXTpEjQaTY2eER8fHxQUFNS6T0hICJYtW4aNGzdixYoV0Gq1iI6Oxh9//GHwPBUVFSgtLdVbmjqFWzaUQQsB+2L9DfZXoAxayHlWiIjIZpl9UrioqChERUXpPkdHRyM0NBSff/453n333Vr3SU5OxsyZM81dNdlRuGVDcj3MGWypUY3N2WHpKlicOb4Gy8JjTX5MIltlVM/KAw88AKVSicLCQr31hYWF8PX1rdcx7O3t0aVLF/z2228Gy0ydOhUlJSW65fz588ZU06pJkoDC+SQU7vugcD7JoEJERDbPqLCiUqkQGRmJ7du369ZptVps375dr/ekLhqNBkePHoWfn5/BMmq1Gi4uLnoLERER2SajbwNNmjQJo0ePRteuXdGtWzfMmzcP5eXleP755wEAo0aNQsuWLZGcnAwAmDVrFrp37442bdqguLgYH330Ec6ePYtx48aZtiVERETUJBkdVoYOHYqLFy9i+vTpKCgoQHh4OLZu3aobdHvu3DkoFH912Fy5cgXjx49HQUEB3N3dERkZib1796J9+/amawURERE1WZIQQvaDIkpLS+Hq6gq7Tn+DpFRZujpETQoH2JoHB9iantDcROXRf6OkpITDA2wM3w1EREREssawQkRERLLGsEJERESyxrBCREREssawQkRERLLGsEJERESyxrBCREREssawQkRERLLGsEJERESyxrBCREREssawQkRERLLGsEJERESyxrBCREREssawQkRERLJmZ+kKUOMSQoIoawtUugF2xZCcTkGShKWrRUREZBDDig3RFkdAKhwOzXUP3To7x8vQ+qyEwi3bgjWj+hibs8PSVSAjWNP1WhYea+kqENWJt4FshLY4Apq8JPR93B1ZWcDVq0BWFhAf6wZNXhK0xRGWriIREVGtGFZsgBASpMLhGDAA2LhRQvfugJMT0L07sGmTAgkJAlLhMAghWbqqRERENTCs2ABR1haV1z0wbZoExV1XXKEApk1ToPK6Z9VYFiIiIplhWLEFlW4AgI4da9+sW3+7HBERkZwwrNgCu2IAwLFjtW/Wrb9djoiISE4YVmyA5HQKdo6X8d57Wmi1+tu0WmD2bC3sHP+E5HTKMhUkIiKqA8OKDZAkAeGzEunpEgYN0uo9DTRokBbp6RKEzyrOt0JERLLEeVZshMItGwhaiG07hiM9/c55Vq5AGbSK86wQEZFsMazYEIVbNoTrYSjvmMEWTqegYI8KERHJGMOKjZEkAcn5pKWrQUREVG8cs0JERESyxrBCREREssawQkRERLLGsEJERESyxrBCREREssawQkRERLLGsEJERESyxrBCREREssawQkRERLLGsEJERESyxrBCREREsmZV7wYaeXQXVCbMV8vCY012LCIiazU2Z4dZjsufsWQq7FkhIiIiWWNYISIiIlljWCEiIiJZY1ghIiIiWbOqAba2SggJoqwtUOkG2BVDcjoFSRKWrhYREVGjaFDPysKFCxEUFAQHBwc88sgj2L9/f53lv/32W7Rr1w4ODg7o1KkTtmzZ0qDK2iJtcQRw6iNoTr8FzdmXoDn9FnDqo6r1RERENsDosLJmzRpMmjQJM2bMQHZ2NsLCwhAfH4+ioqJay+/duxfDhg3DCy+8gMOHDyMxMRGJiYk4duzYfVe+qdMWR0CTl4S+j7sjKwu4ehXIygLiY92gyUtiYCEiIpsgCSGMup/wyCOP4OGHH8aCBQsAAFqtFgEBAXj11VcxZcqUGuWHDh2K8vJybN68Wbeue/fuCA8Px+LFi+t1ztLSUri6uuJ5BNjMPCtCSMCpj9D3cXds3ChBcUeztVpg0CAttu24ArT9J28J2QhzzYVBZC6m/hkrNDdRefTfKCkpgYuLi0mPTfJm1P/8N2/exKFDhxAXF/fXARQKxMXFISsrq9Z9srKy9MoDQHx8vMHyAFBRUYHS0lK9xdaIsraovO6BadP0gwoAKBTAtGkKVF73rBrLQkRE1IQZFVYuXboEjUYDHx8fvfU+Pj4oKCiodZ+CggKjygNAcnIyXF1ddUtAQIAx1WwaKt0AAB071r5Zt/52OSIioqZKlo8uT506FSUlJbrl/Pnzlq5S47MrBgAYGtqjW3+7HBERUVNlVFh54IEHoFQqUVhYqLe+sLAQvr6+te7j6+trVHkAUKvVcHFx0VtsjeR0CnaOl/Hee1potfrbtFpg9mwt7Bz/hOR0yjIVJCIiaiRGhRWVSoXIyEhs375dt06r1WL79u2IioqqdZ+oqCi98gCQkZFhsDxVkSQB4bMS6ekSBg3S6j0NNGiQFunpEoTPKg6uJSKiJs/oSeEmTZqE0aNHo2vXrujWrRvmzZuH8vJyPP/88wCAUaNGoWXLlkhOTgYAvP766+jVqxfmzJmDhIQErF69GgcPHsSSJUtM25ImSOGWDQQtxLYdw5Ge7qFbb+d4BcqgVVXbiYiImjijw8rQoUNx8eJFTJ8+HQUFBQgPD8fWrVt1g2jPnTsHxR2Pr0RHR2PlypX4n//5H7z99tsIDg7Ghg0b0NHQyFHSo3DLhnA9DOUdM9jC6RQU7FEhIiIbYfQ8K5Zgi/OsEN2N86yQteE8K2QqsnwaiIiIiKgawwoRERHJGsMKERERyRrDChEREcma0U8DNSXmGrDIgbtERKb/GXsTWiw36RHJWrBnhYiIiGSNYYWIiIhkjWGFiIiIZI1hhYiIiGSNYYWIiIhkjWGFiIiIZI1hhYiIiGSNYYWIiIhkjWGFiIiIZI1hhYiIiGSNYYWIiIhkjWGFiIiIZI1hhYiIiGSNYYWIiIhkjWGFiIiIZI1hhYiIiGSNYYWIiIhkjWGFiIiIZI1hhYiIiGTNztIVqA8hBADgJrQWrkn9CM1NS1eBmiBr+fdPZC7V3wPV/yeQ7ZCEFVz1P/74AwEBAZauBhERycD58+fh7+9v6WpQI7KKsKLVanHhwgU4OztDkqRGP39paSkCAgJw/vx5uLi4NPr5zYXtsh5NsU0A22VtLN0uIQSuXr2KFi1aQKHgKAZbYhW3gRQKhSxStIuLS5P6wVON7bIeTbFNANtlbSzZLldXV4uclyyL0ZSIiIhkjWGFiIiIZI1hpR7UajVmzJgBtVpt6aqYFNtlPZpimwC2y9o01XaR/FnFAFsiIiKyXexZISIiIlljWCEiIiJZY1ghIiIiWWNYISIiIlljWLlt4cKFCAoKgoODAx555BHs37+/zvLffvst2rVrBwcHB3Tq1AlbtmxppJoax5h2paamQpIkvcXBwaERa3tvu3btwsCBA9GiRQtIkoQNGzbcc5/MzExERERArVajTZs2SE1NNXs9jWVsuzIzM2tcK0mSUFBQ0DgVrofk5GQ8/PDDcHZ2hre3NxITE3Hy5Ml77if3762GtMsavrc+++wzdO7cWTfhW1RUFP7zn//UuY/crxU1HQwrANasWYNJkyZhxowZyM7ORlhYGOLj41FUVFRr+b1792LYsGF44YUXcPjwYSQmJiIxMRHHjh1r5JrXzdh2AVUzU+bn5+uWs2fPNmKN7628vBxhYWFYuHBhvcqfOXMGCQkJ6N27N3JycjBx4kSMGzcO27ZtM3NNjWNsu6qdPHlS73p5e3ubqYbG27lzJ5KSkvDTTz8hIyMDt27dQp8+fVBeXm5wH2v43mpIuwD5f2/5+/vjgw8+wKFDh3Dw4EHExsbiySefxPHjx2stbw3XipoQQaJbt24iKSlJ91mj0YgWLVqI5OTkWss/++yzIiEhQW/dI488Il566SWz1tNYxrZr+fLlwtXVtZFqd/8AiPXr19dZ5p///Kfo0KGD3rqhQ4eK+Ph4M9bs/tSnXT/88IMAIK5cudIodTKFoqIiAUDs3LnTYBlr+d66U33aZW3fW9Xc3d3F0qVLa91mjdeKrJfN96zcvHkThw4dQlxcnG6dQqFAXFwcsrKyat0nKytLrzwAxMfHGyxvCQ1pFwCUlZUhMDAQAQEBdf5WZS2s4Vrdj/DwcPj5+eGJJ57Anj17LF2dOpWUlAAAPDw8DJaxxutVn3YB1vW9pdFosHr1apSXlyMqKqrWMtZ4rch62XxYuXTpEjQaDXx8fPTW+/j4GLz/X1BQYFR5S2hIu0JCQrBs2TJs3LgRK1asgFarRXR0NP7444/GqLJZGLpWpaWluH79uoVqdf/8/PywePFirFu3DuvWrUNAQABiYmKQnZ1t6arVSqvVYuLEiXj00UfRsWNHg+Ws4XvrTvVtl7V8bx09ehROTk5Qq9V4+eWXsX79erRv377WstZ2rci6WcVbl6lxREVF6f0WFR0djdDQUHz++ed49913LVgzultISAhCQkJ0n6Ojo3H69Gl8/PHH+Prrry1Ys9olJSXh2LFj2L17t6WrYlL1bZe1fG+FhIQgJycHJSUlWLt2LUaPHo2dO3caDCxEjcXme1YeeOABKJVKFBYW6q0vLCyEr69vrfv4+voaVd4SGtKuu9nb26NLly747bffzFHFRmHoWrm4uMDR0dFCtTKPbt26yfJaTZgwAZs3b8YPP/wAf3//Ostaw/dWNWPadTe5fm+pVCq0adMGkZGRSE5ORlhYGObPn19rWWu6VmT9bD6sqFQqREZGYvv27bp1Wq0W27dvN3ivNioqSq88AGRkZBgsbwkNadfdNBoNjh49Cj8/P3NV0+ys4VqZSk5OjqyulRACEyZMwPr167Fjxw60atXqnvtYw/VqSLvuZi3fW1qtFhUVFbVus4ZrRU2IpUf4ysHq1auFWq0Wqamp4sSJE+LFF18Ubm5uoqCgQAghxMiRI8WUKVN05ffs2SPs7OzEv/71L5GbmytmzJgh7O3txdGjRy3VhFoZ266ZM2eKbdu2idOnT4tDhw6J5557Tjg4OIjjx49bqgk1XL16VRw+fFgcPnxYABBz584Vhw8fFmfPnhVCCDFlyhQxcuRIXfnff/9dNGvWTLz55psiNzdXLFy4UCiVSrF161ZLNaFWxrbr448/Fhs2bBC//vqrOHr0qHj99deFQqEQ33//vaWaUMMrr7wiXF1dRWZmpsjPz9ct165d05Wxxu+thrTLGr63pkyZInbu3CnOnDkjjhw5IqZMmSIkSRLfffedEMI6rxU1HQwrt3366afiwQcfFCqVSnTr1k389NNPum29evUSo0eP1iv/zTffiLZt2wqVSiU6dOgg0tPTG7nG9WNMuyZOnKgr6+PjI/r37y+ys7MtUGvDqh/ZvXupbsfo0aNFr169auwTHh4uVCqVeOihh8Ty5csbvd73Ymy7PvzwQ9G6dWvh4OAgPDw8RExMjNixY4dlKm9Abe0BoPf1t8bvrYa0yxq+t8aOHSsCAwOFSqUSXl5e4vHHH9cFFSGs81pR0yEJIUTj9eMQERERGcfmx6wQERGRvDGsEBERkawxrBAREZGsMawQERGRrDGsEBERkawxrBAREZGsMawQERGRrDGsEBERkawxrBAREZGsMawQERGRrDGsEBERkawxrBAREZGs/X9iAnoyZwKRMAAAAABJRU5ErkJggg==\n",

      "text/plain": [

       "<Figure size 500x500 with 1 Axes>"

      ]

     },

     "metadata": {},

     "output_type": "display_data"

    }

   ],

   "source": [

    "import matplotlib.pyplot as plt\n",

    "\n",

    "plt.figure(figsize=(5, 5))\n",

    "meshgrid_colors = meshgrid_colors.reshape(grid_x.shape)\n",

    "plt.pcolormesh(grid_x, grid_y, meshgrid_colors, cmap=\"RdBu\", shading=\"auto\")\n",

    "\n",

    "plt.scatter(\n",

    "    train_features[:, 0][train_labels == 0],\n",

    "    train_features[:, 1][train_labels == 0],\n",

    "    marker=\"s\",\n",

    "    facecolors=\"w\",\n",

    "    edgecolors=\"r\",\n",

    "    label=\"A train\",\n",

    ")\n",

    "plt.scatter(\n",

    "    train_features[:, 0][train_labels == 1],\n",

    "    train_features[:, 1][train_labels == 1],\n",

    "    marker=\"o\",\n",

    "    facecolors=\"w\",\n",

    "    edgecolors=\"b\",\n",

    "    label=\"B train\",\n",

    ")\n",

    "\n",

    "plt.scatter(\n",

    "    test_features[:, 0][test_labels == 0],\n",

    "    test_features[:, 1][test_labels == 0],\n",

    "    marker=\"s\",\n",

    "    facecolors=\"r\",\n",

    "    edgecolors=\"r\",\n",

    "    label=\"A test\",\n",

    ")\n",

    "plt.scatter(\n",

    "    test_features[:, 0][test_labels == 1],\n",

    "    test_features[:, 1][test_labels == 1],\n",

    "    marker=\"o\",\n",

    "    facecolors=\"b\",\n",

    "    edgecolors=\"b\",\n",

    "    label=\"B test\",\n",

    ")\n",

    "\n",

    "plt.legend(bbox_to_anchor=(1.05, 1), loc=\"upper left\", borderaxespad=0.0)\n",

    "plt.title(\"Pegasos Classification\")\n",

    "plt.show()"

   ]

  },

  {

   "cell_type": "code",

   "execution_count": 21,

   "id": "fddca436-0531-4f77-9c54-71a0ed4dc462",

   "metadata": {},

   "outputs": [

    {

     "name": "stdout",

     "output_type": "stream",

     "text": [

      "Time in seconds since end of run: 1696472984.9916549\n",

      "Thu Oct  5 02:29:44 2023\n"

     ]

    }

   ],

   "source": [

    "seconds = time.time()\n",

    "print(\"Time in seconds since end of run:\", seconds)\n",

    "local_time = time.ctime(seconds)\n",

    "print(local_time)"

   ]

  },

  {

   "cell_type": "code",

   "execution_count": 22,

   "id": "imperial-promise",

   "metadata": {

    "tags": []

   },

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