{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing Clamped Mean Bounds with the Sparse Vector Technique #\n",
    "\n",
    "In [Computing Bounds for Clamped Means](clamped-mean-bounds.ipynb), we determined the clamping parameters for a dataset of unknown range by issuing a `PrivateQuantile` query against a dataset. While simple, this approach depends on the assumption that clamping to the 99th percentile of a dataset will result in negligble error in downstream analytics. Sometimes it is desirable to determine clamping bounds with an error expression that is closer to the eventual use case.\n",
    "\n",
    "This notebook demonstrates how a clamping bound can be chosen with an error expression based on the result of a query of a population, choosing a clamping bound that results in population-level error less than a small threshold. We use a sum query for demonstration, but it could easily be a more complex calculation, like the average load shape.\n",
    "\n",
    "The approach employed here is adapted from [Applying the Sparse Vector Technique](https://uvm-plaid.github.io/programming-dp/notebooks/ch10.html#applying-the-sparse-vector-technique) in _Programming Differential Privacy_ [Near, 2020].\n",
    "\n",
    "\n",
    "## Sparse Vector Technique for Clamping Bounds ##\n",
    "\n",
    "With SVT, we will issue a series of queries with different choices of clamping bounds, seeking a bound that provides acceptable accuracy against a queries similar to those that will be issued later.\n",
    "\n",
    "We will issue a sequence of clamped sum queries against the entire pool of meters, looking for the first result that returns error less than a threshold. The threshold will be error less than 0.01 kWh average across 24 hours (or 0.24 kWh total across 24 hours).\n",
    "\n",
    "**How do you choose epsilon for the SVT query?**\n",
    "\n",
    "For SVT to return accurate results, the difference between \"good\" responses and \"bad\" response should be \"large\". This is what the \"Sparse\" in \"Sparse Vector Technique\" refers to. For our use case, we use a synthetic population to dial in the SVT privacy parameter.\n",
    "\n",
    "Residential energy consumption values are closely approximated by a log-normal distribution. With `b` values (the clamping bound) spaced widely enough apart, each step will decrease error by an order of magnitude.\n",
    "\n",
    "ε should be chosen to distinguish the correct clamping bound in almost every cases (say, 999/1000). \n",
    "\n",
    "A demonstration with a synthetic population of 5,000 meters is shown below, resulting in a required ε of 0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "\n",
    "from eeprivacy.mechanisms import LaplaceMechanism\n",
    "from eeprivacy.operations import PrivateAboveThreshold\n",
    "\n",
    "np.random.seed(1234)  # Fix seed for deterministic documentation\n",
    "\n",
    "mpl.style.use(\"seaborn-white\")\n",
    "\n",
    "MD = 28\n",
    "LG = 36\n",
    "plt.rcParams.update(\n",
    "    {\n",
    "        \"figure.figsize\": [25, 7],\n",
    "        \"legend.fontsize\": MD,\n",
    "        \"axes.labelsize\": LG,\n",
    "        \"axes.titlesize\": LG,\n",
    "        \"xtick.labelsize\": LG,\n",
    "        \"ytick.labelsize\": LG,\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1800x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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t2jSNHz++wu+vxWLRmDFjjP00pOKljWr6PH5+fpo9e7bOOeccBQUFqW3btrr55psr/PeilM1m07vvvusRGkhSaGioHnzwQaPvcrnk7++vt99+u0JwGxkZqUcffdToJyUlKS0trdo6AQCAbyM4AAAAQL0ovwZ4RESElyo5Ns2bN9fDDz9c5fmOHTvqxhtvNPrl1w4vz2az6amnnqp0rfLS+913331G/7vvvlNhYaHHmPfee89o33nnnRXeSCjLZDLpwQcfNJZH+emnn5ScnOwxpuya87feemuVDygl6aGHHqp2I+jays/PN9put7vaMOCcc87RPffco2effVbvvvvuSd+49e67767ynoMGDfLo33LLLVWO7devn9Gu6eFxdcr+/Y8bN85jY+bK3HHHHQoPD5ckbdu2rcJa+OWNHTv2mB661zT+o48+Mtrnn39+jfs7TJ061fgdLCws1Mcff1zt+NGjR6tZs2a1rvd4zZ071/jvWf/+/StdQqisc845x3jLw+FwaM6cOdWOP++88xQdHV3rei655BJ16NCh0nN9+vTx+Lu54IILKl12SZJ69OjhEX4cz+8oAABo+ggOAAAAUC/Kr+t9sr81XleXXnqpgoODqx1z+eWXG+3SDXOrMmzYMLVq1ara+UaMGGEsd5STk+PxoHf//v3asWOH0a/NcixRUVEey8ysXLnSaCclJWnPnj0e965OSEiIhg8fXuM9axIZGWm8dXLkyBHdcsstxjrt5VmtVk2YMEGXXXaZ+vXrd8K+SV6ZwMDACt/kLqtsaGO1Wj3CgfJKH95LqnQN+9ooXbu+VG3+/gMCAoy1+iXPv//KxMXFHVNN1Y3Pzc3VunXrjH7Zty6q4u/vr8suu8zo//rrr3W+/4lQujyTVLufvyQNHTrUaNf08+/fv/8x1VPdpucWi8UjpK1ubpPJ5BHAlA97AQAAymKPAwAAANSL0NBQj37Z/Q4asto8xGvbtq1atGih9PR0ScXf6q7qW721mc/f318xMTHGckTbtm3TWWedJUnGsVKvvvpqjfNJnj/vrVu3Vtpu2bJlrTbs7dmzZ41vVtTG2LFj9dJLL0kqXrrnsssuU9u2bXXWWWdp0KBBGjRoUIXlgU62tm3bymyu+vtUZQOx8PDwakONqt4yORZbt271CN0++OADY9+M6pQNh8r+nZdntVqr/N2ty/jt27cbe2eYTCb16dOnVvP269dPb731liRp8+bNcrvdVb7J0blz51rXWx9K9wyQikOE8m/wVOavv/4y2tX9/CWpU6dOx1RPTW8nlP29i4qKqnaszWYz2jUtaQUAAHwbwQEAAADqRdu2bWUymYyHUaVr6jd0p556aq3G2e12Izgo/bMyp5xySq3nK1V2rfHyc3/22We1mq+ssiFC2flqExpIxX+X9eGWW27Rjh079PXXXxvH9u3bp88++0yfffaZTCaTunfvrqFDh+rCCy+scUmeE6H8XgXVqWyPhvpW/u+/7M+utqoL7cLCwo5pKaiaxmdkZBjt0NDQCvuEVKV169ZG2+l06tChQ1UuR3QylynKzc31+Cb+qlWralz6qbzDhw+rqKiowltYpcq+mVIbx/L5T8bvKAAA8A0sVQQAAIB6ERAQ4PEQfuPGjcc1X9k18k+k2j7oLF1aSJIOHTpUr/MdPny40nZdlV0mJzs7u9J7VqempZtqy2w2a/r06Zo5c6bOOOOMCt/Id7vd2rBhg1599VWNGDFCEyZM0P79++vl3rVVH28J1Kf6/vsvLzAw8Jjmqml8Tk6O0T6WvTHKz1vdv+/HWvPxKPt56srtdle7DFBt/z0sVVUAAQAAcCI1rP+VDAAAgEZtwIABxpIpK1asqHb5kepkZGTo7LPPVkxMjAYMGKBRo0adsOVKarsXQ9kHgdU9yCy/0fGxzle23aJFixrXf69J2aV1ahvG1PYz1NawYcM0bNgwZWVl6bffftNvv/2mVatWKSkpyWPcf//7X23fvl1z5849rs21i4qKjrdkryn/u7V+/foG/S3ysmHBsayZXz7cOJnhQHXKP9R/6623ar3PAQAAQFPCGwcAAACoN2U31c3IyPBYK/xYJCQkyOFwaMOGDfrPf/5zQvdLKLtMUHUOHDhgtKtbyud45yu7jEl2dracTmet5qtK2Y2ay96zOgcPHjyue1YlPDxcI0aM0JNPPqkffvhB//3vf/XII494bOy8d+9ezZ492+O6suFTbUKB+vjWuLeUD0yqWxarISi7R8Xhw4dr/bMvuyeAv7//MS0ZdSKFhYV5vIVyov5dAAAAaOgIDgAAAFBvzjrrLLVp08bov/POO8c8h8vl0vvvv2/027Rpo379+tVLfZX5448/ahyzZ88ej/CiR48exzVfXl6etm3bVul83bp1M9oOh6PWSz59//33SkhI0JYtWzy+zV32oXxGRob+/PPPGufasGFDre5Zk5ycHP3xxx/avXt3pefbtm2rMWPGaO7cuRowYIBxfOXKlR7jyi7VUpu3Jvbu3VvHir2va9euHps1l98suyrLli3TDz/8oI0bN1a7lFZ969q1q/Gg3e12a+3atbW6bs2aNUb7tNNOq9ObSSeCyWRSTEyM0V+3bl2trtu6dasWLlyotWvXKiUl5QRVBwAAcPIQHAAAAKDeWCwW3XLLLUb/+++/1/fff39Mc7z33nseD9XHjx/v8SC1vtVm89nPP//caHft2tVjY9fyFi1aJIfDUe18CxcuNMZERESoV69exrnOnTurZcuWRn/evHk11rdv3z7de++9uu2223TppZdq4cKFxrkOHTp47D1R9rNUxuFw6LvvvqvxnjWZNm2a+vXrp9GjR+uFF16odqzNZtP5559v9MsvY1N2z4Wy31SvTH5+vhITE+tQccMQEhKi008/3ejX5u8/JydHkyZN0p133qlRo0bprbfeOpEleggKClLPnj2N/ty5c2u85siRIx6/o2ecccYJqa0ytQkoytazaNGiWi3B9Mwzz2jSpEm65pprdNdddx1XjQAAAA0BwQEAAADq1ejRoz0ehN9///1KSEio1bXffPONnn/+eaPfrVs3jR49ut5rLOuPP/6o9mHn1q1bPZbOGTNmTLXzpaWl6fXXX6/yfEpKil566SWjf9VVV8lmsxl9k8mka6+91ujPnz9fy5cvr3I+t9utxx9/3FjSKCQkRBdeeKHHmOuuu85ov/vuux7BTHmvvfZarZdbqk7fvn2N9rJly7Rjx45qx5d9s+K0007zONe+fXujvWnTJu3atavKeV5++eVGvVSR5Pk79uuvv9YY9kyfPt14I8ZisWjUqFEnsrwKyv5+/fDDDzWGhc8995zxO2Y2m0/4v+Nllf13raqA7+qrrzbeosjOztYTTzxR7ZyLFi3Sb7/9ZvRP5ucBAAA4UQgOAAAAUK+sVqumT59ufGv+yJEjuu2223T//fdX+cD6zz//1EMPPaR7773XWMM+PDxcL730kseDvhPl0Ucf1fvvvy+Xy+VxfNmyZRo3bpyxgXK3bt30f//3fzXON3PmTL344osVNhlev369rrvuOmVkZEgq3n/gpptuqnD99ddfr1NOOUVS8Zr+t956qz799NMK6/sfOHBA99xzj3766Sfj2K233qpmzZp5jBszZoyxHFJBQYHGjRtXYdPlwsJCvfTSS5o1a1aNn6824uPjjb0bjhw5oltuuUUrVqyoMM7lcmn27Nn64osvjGNXX321x5iBAwcabx243W7dfffd2rdvn8eYrKwsPfbYY3r33XfrpX5vGjlypPr06WP0H374Yc2cObPCRt5ZWVl64okn9PHHHxvHrrzyygrBy4l2wQUXeARF9913n2bPnl1hf47s7GxNmTJFH374oXHs9ttvV8eOHU9araGhoUZ769atle4h0q5dO91www1G//PPP9fEiRMrBGoOh0OffPKJHnzwQeNYly5ddPnll5+AygEAAE4ua81DAAAAgGMTHR2t9957TxMmTFBSUpIk6auvvtJXX32lU089VV27dlVoaKhyc3O1Y8cO7dixQ26327i+VatWevvttz2W2DlRQkJClJOTo6eeekpvv/224uLiZLVatXnzZo+gw2636+WXX/ZYb7+6+d544w3NmTNHAwYMUFBQkHbu3OmxWXRISIheffVVjweZ5c+NGzdOmZmZKigo0L/+9S+9+uqr6tu3r4KDg7Vv3z6tW7fOI5w477zzKg0iLBaLnnvuOY0bN06pqak6ePCg/vGPf6hr167q2rWrCgoKtGrVKiPQiIuLO+7lfqxWq5566inddNNNcjqdSk5O1g033KCOHTuqffv2ioiIUHZ2ttatW+fxQPaKK66osHSNv7+/brnlFr344ouSpG3btun8889X//79FRUVpbS0NCUmJqqgoEAmk0k333yz3nzzzeOq35usVqtefvllXXvttUpOTlZRUZFeeukl/ec//1G/fv0UERGh/fv3a/369R7LOvXp00cPPfTQSa/XYrHo5Zdf1pgxY/Tnn3/K4XBo2rRpmjVrluLi4hQaGqrU1FTj76jUueeeq9tuu+2k1lo2VNm+fbuuvvpqxcTEKDg4WFOmTDHO3XvvvdqxY4eWLl0qSfr222+1ePFi9e3bV23btlVmZqY2bdrksZ9B8+bN9corr3hsrgwAANBY8b9oAAAAcEJ07NhRn3/+uV5++WV9+umnxgPupKQkI0woz2q1atSoUZo0aVKFb82fKPfee6+WLVumH3/8USkpKfrmm28qjOnfv7+ee+45j42fqzJ27FgdPHhQc+bMUWZmZqXLtnTp0kUvvPCCxyas5XXt2lXz5s3T/fffb2w4m56erh9++KHCWIvFohtuuEGTJk2qcg33jh07as6cOZowYYI2b94sSdqyZYu2bNniMW7MmDEaMmRIvewTMHjwYL322muaMmWKEUrs3LlTO3furDDWZrPpH//4h+65555K5xo/frwOHjyo999/X263Ww6Hw2N5GKl4L4RHHnlE3bp1a9TBgSRFRUV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\n",
      "text/plain": [
       "<Figure size 1800x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 6000\n",
    "synthetic = np.random.lognormal(mean=-0.6, sigma=1.2, size=N * 24)\n",
    "plt.hist(synthetic, bins=30)\n",
    "plt.title(\"Distribution of hourly consumption values\")\n",
    "plt.xlabel(\"Hourly consumption (kWh)\")\n",
    "plt.ylabel(\"Count\")\n",
    "plt.show()\n",
    "\n",
    "clipped_sums = []\n",
    "bs = np.linspace(start=1, stop=20, num=20)\n",
    "for b in bs:\n",
    "    clipped_sums.append(\n",
    "        np.sum(np.clip(synthetic, 0, b)) - np.sum(np.clip(synthetic, 0, b - 1))\n",
    "    )\n",
    "\n",
    "plt.plot(clipped_sums)\n",
    "plt.title(\"Clipped sum error term\")\n",
    "plt.xlabel(\"Clipping Upper Bound (kWh)\")\n",
    "plt.ylabel(\"delta\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AgaVAsaysLOecc04OP/zwJZ7DPG3atHqt36xZs+yyyy7ZZZddkiSfffZZhg0blvvuu6+0q3fOnDn53e9+lzvuuKPWr3/hhReWwtiWLVvmwgsvzN57773Ym2QuqL8yDR8+vFrYfcwxx+TMM89cYedg18TC58IvuMHosowaNarU7tq163KvYcyYMfnhD3+Yjz76qNrr3njjjVl33XWX+/UBAKhO4A0AQCHcddddpfaPf/zjHH300UsdP2bMmGr92p7hXV5eng8//DAzZszI1ltvvcjzbdq0yT777JN99tmn2s7nl19+OeXl5bUKgqdOnZpHH3201D/77LOz7777LnXO4t5ffZ0hvjj33ntvqb3lllvm3HPPTePGjWs8/+CDD87BBx9cr2vadtttS+2RI0dm+vTpS7155rRp0zJy5MhSf3mPGvnoo49yzDHHVNs1/o1vfCMDBw7M6quvvlyvDQDA4tX8b6AAAPAlNWnSpGo3pezRo8cy5zz00EPV+ks78/uLhg4dmq233jr77rtvevfunblz5y51/MLh9Lx58xY563tZPvzww9KNMZNlv7+qqqo88sgj1R5b3BrrMwBfeAfzDjvsUKuwe0Xp1KlTunXrliSpqKhY5N/5Fz3wwAOlf05du3bNhhtuWOfaM2fOzPHHH18t7O7Vq1cGDRok7AYAWIEa/m+hAACwnL64W3rhs5IX5/77718kEK6oqKhxvW222aYU6E6ZMmWZN1t84403Su0111yz2s0Ua6K27++GG27Iq6++Wu2xxb2/pk2bLvX52mjbtm2pvfAu6S/67LPPcsEFF2T8+PHLVa+mFj7T++qrr86ECRMWO+6TTz7JtddeW+ofeeSRy1X3wgsvrHY8ygEHHJDLL7+8QY94AQD4KhB4AwCwylt99dWrnbd8/fXX55lnnllk3KRJk3LxxRenT58+izw3c+bMGtdbe+2106tXr1L/ggsuyF133VVtF/YCTz/9dAYMGFDqH3HEETWus8DGG2+cNdZYo9S/+OKLFxt6f/TRRzn77LNzxRVXLPLc4t7fwjuN33777cWuv6Z23XXXUvvpp5/ODTfcsMiu8ieeeCKHHHJI/vznP+eQQw7J8OHD61yvpo444oh06dIlyfybRx533HHVguhk/vnexx57bCZNmpQk2WijjXLYYYct9vXGjh2bTTfdtPTnmmuuWWTMiy++mLvvvrvU32677XLRRRd9KXa9AwAUnTO8AQAohJ/+9Kf5+c9/nmR+uPvDH/4wW2yxRTp37pxGjRrl448/zquvvloKdcvKytKsWbNSELwg7Kyps88+O88880w+/fTTlJeX51e/+lWuuuqqdO3aNR07dsycOXMyYsSIvPfee6U5W265ZY4//vhav7emTZumd+/eueSSS5LMD24POuigbLPNNtlggw1SWVmZsWPH5vXXXy+dRd6yZcuUl5eX3u+kSZOy1lprVXvdzp07l9rvvPNOvv/972fTTTdNq1atcu6559Zqjfvtt19uvvnmUhB/+eWX56677kr37t1TWVmZ1157rdqxJzNmzFgpN9Zs2rRpLrroovzwhz/MzJkz884772S//fbLDjvskPXXXz9jx47NCy+8UDrSpmXLlrniiiuq7X6vrRtuuKFav3Xr1vnNb35T4/mdO3fOscceW+f6AABfZQJvAAAKYe+9906fPn1y+eWXl3YWjxgxIiNGjFhk7EYbbZQBAwbkxhtvzD//+c8k828mufvuu9e43tprr53bb789p556at5+++0k84PoJR2Zseeee+aCCy5Y6k0Tl+a4447LuHHjcttttyWZf073Sy+9lJdeemmRsVtttVUuvvjinHbaaaXjRV555ZVqu+CT+Wdtd+/evXT8yWuvvZbXXnstq622Ws4666w0adKkxusrKyvL73//+5xwwgl55513ksw/e/zDDz9cZOy2226b888/P5tvvnmNX395dO/ePTfddFN++ctfZty4cZk3b16effbZRcats846ufLKK7PFFlvUudbnn3+eYcOGVXvsySefrNVr7LjjjgJvAIA6EngDAFAYP/nJT7LLLrvkz3/+c55//vl88sknKS8vT8uWLdOxY8d07do13/rWt9KrV680bdo0u+22Wynwvu+++3LKKaekrKzmf0XeaKONcs8992To0KF59NFH88Ybb2TChAmZM2dO2rRpkw4dOqRnz57ZZ599ss022yzXe2vUqFH69u2bvffeO3/961/z0ksvZcKECamsrEzr1q2z7rrrZvPNN893v/vd7L777mnUqFF22223UuB99913L3JMR1lZWW6++eYMHDgwQ4cOzYQJE9KoUaN07NgxEydOTMeOHWu1xvXWWy933XVX7rnnnvzjH//I22+/nc8//zwtWrRI+/bt06NHj3z3u9/NN7/5zeX6Z1EXPXr0yIMPPpg777wzQ4cOzahRozJt2rS0atUqXbp0yR577JHDDjuszh9ILPD+++8v19EwAAAsn0ZVC77zCAAAAAAAq7DC3zXl1FNPzaabbppLL720oZcCAAAAAMAKVOjAe8iQIXnkkUcaehkAAAAAAKwEhQ28x40blwsvvLChlwEAAAAAwEpSyMC7qqoqZ599dukGOQAAAAAAFF8hA+9bbrklzzzzTPbaa69stdVWDb0cAAAAAABWgrKGXkB9GzVqVC6//PKstdZa+Z//+Z/8/Oc/X+ac2bNn5/XXX0/79u3TpEmTlbBKAAAAAABqa+7cufn000/TrVu3NG/efJHnCxV4V1RUpE+fPpkzZ04uv/zytGvXrkbzXn/99Rx11FEreHUAAAAAANSHP/3pT9l+++0XebxQgfe1116bN954IwcddFD22GOPGs9r3759kvn/kNZZZ50VtTwAAAAAAJbDJ598kqOOOqqU6X5RYQLvV155JTfeeGPWWWed9O3bt1ZzFxxjss4662SDDTZYEcsDAAAAAKCeLOlo6kLctHLWrFk588wzM2/evFx00UVZffXVG3pJAAAAAACsZIUIvC+++OKMHj06Rx55ZP7rv/6roZcDAAAAAEADWOUD7yeffDJ33HFHNtxww/Tp06ehlwMAAAAAQANZ5c/wfvDBB5MkH374Ybbddtsljhs0aFAGDRqU9ddfP48//vjKWh4AAAAAACvJKh94b7TRRtluu+2W+PzIkSMzffr0rLPOOllvvfWWePdOAAAAAABWbat84H3iiSfmxBNPXOLzxxxzTJ577rnsv//+OeOMM1biygAAAAAAWJlW+TO8AQAAAAAgEXgDAAAAAFAQ9XakyaxZs9KrV6+MGzcuAwYMyMEHH1yr+cOGDcvdd9+dl19+ORMnTkyLFi3SsWPH7Lrrrjn00EPz9a9/vb6WCgAAAABAAdVb4N2/f/+MGzeu1vNmzpyZM888M48++mi1x8vLyzNt2rSMHDkyt956a0499dSccMIJtX792267rdZzAAAAAABY9dRL4H3jjTfmzjvvrPW8ysrK9O7dO88991zpsa5du2bzzTfP7Nmz88wzz2TatGmpqKjIZZddlsrKypx88sn1sWQAAAAAAApmuQLvqqqqDBw4MAMHDqzT/Ouvv74Udrdo0SKXXHJJ9txzz9Lzs2fPzkUXXZTBgwcnSa6++ur07NkzPXr0WJ5lAwAAAABQQHW+aeXUqVPTu3fvOofdkydPzk033VTq9+vXr1rYnSTNmzdPv379cuCBByaZH7BfccUVdV0yAAAAAAAFVuvAu6qqKkOGDMkBBxyQJ554ovR4ixYtavU699xzT2bNmpVk/jEm+++//xLHnnvuuaXXf/755/POO+/UdtkAAAAAABRcrQLvOXPm5OCDD85ZZ52V8ePHJ5m/C/uSSy7JVlttVavCQ4cOLbX32WefNGrUaIlj27Ztm29+85ul/kMPPVSrWgAAAAAAFF+tA+8RI0aU+j169MiQIUNKR47U5nVee+21Un+nnXZa5pztt9++1H766adrVQ8AAAAAgOKr000rO3XqlNNOOy377rvvUndmL8l7772XysrKUn+TTTZZ5pyFx7z99tu1rgkAAAAAQLHVKvBu1qxZrrzyyuy5555p0qRJnYuOHTu21G7btm1at269zDkdO3YstWfOnJnJkyenXbt2dV4DAAAAAADFUqsjTZo3b55evXotV9idJBMnTiy111prrRrN+WK4PWXKlOVaAwAAAAAAxVKrwLu+zJgxo9Ru3rx5jea0atWqWn/69On1uiYAAAAAAFZtDRJ4l5eXl9qrrbZajeaUlVU/faWioqJe1wQAAAAAwKqtQQLvxo3/U3Z5j0cBAAAAAICkgQLvFi1alNqVlZU1mvPFcc2aNavXNQEAAAAAsGprkMC7ZcuWpfbMmTNrNGfhc7+TRc/0BgAAAADgq61BAu8111yz1J4yZUqN5kyePLlav3379vW6JgAAAAAAVm0NEnhvvPHGpfakSZNqdAPKTz75pNRu06ZN2rRps0LWBgAAAADAqqlBAu8NN9ywdAb33Llz89577y1zzrvvvltqd+nSZYWtDQAAAACAVVODBN5NmjTJ1ltvXeoPHz58mXNeeOGFUnvHHXdcIesCAAAAAGDV1SCBd5L06tWr1L7//vuXOnbKlCl58sknS/099thjha0LAAAAAIBVU4MF3nvvvXdatGiRJHnxxRczZMiQJY7t379/Zs+enSTp3r17unXrtjKWCAAAAADAKqTBAu+11lorJ554Yqnft2/f3Hnnnamqqio9Nnv27Jx33nmlHeCNGjXKGWecsdLXCgAAAADAl19ZQxY/7rjj8uSTT2b48OGpqKhI3759M2jQoHTv3j3l5eV59tlnM3Xq1NL43r17p2fPng23YAAAAAAAvrQaNPBu1qxZBg0alD59+uSxxx5LknzwwQf54IMPqo1r0qRJTjrppJxyyikNsUwAAAAAAFYBDRp4J0mrVq1y3XXX5amnnsq9996bF198MRMnTkzjxo2z7rrrpmfPnvnBD36Qrl27NvRSAQAAAAD4Equ3wPu2225brvm77rprdt1113paDQAAAAAAXzUNdtNKAAAAAACoTwJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCAJvAAAAAAAKQeANAAAAAEAhCLwBAAAAACgEgTcAAAAAAIUg8AYAAAAAoBAE3gAAAAAAFILAGwAAAACAQhB4AwAAAABQCGUNvYD69NFHH2XQoEF56qmnMn78+LRu3TpbbrllDjnkkOyzzz4NvTwAAAAAAFagwgTeL7zwQnr37p3p06enWbNm6dy5c6ZPn55hw4Zl2LBhefjhh3PFFVekSZMmDb1UAAAAAABWgEIcaTJ9+vScdtppmT59enbfffc88cQTuf/++/PPf/4zN998c1q1apVHHnkkf/jDHxp6qQAAAAAArCCFCLyHDBmSTz/9NO3atctll12Wdu3alZ7beeedc+KJJyZJ/vKXvzTUEgEAAAAAWMEKcaTJOuusk/333z8bbrhhWrVqtcjzm266aZLkk08+SVVVVRo1arSylwgAAAAAwApWiMB7jz32yB577LHE51977bUkSadOnYTdAAAAAAAFVYjAe0lmzZqVO++8MzfccEOS5KSTTmrgFQEAAAAAsKIUMvB++umnM2DAgIwZMyazZs1K27Ztc9555+Wggw5q6KUBAAAAALCCFOKmlV80YsSIjBw5MrNmzUqSzJw5M88880wmTJjQwCsDAAAAAGBFKWTgfcABB2T48OH597//nauvvjrt27fPAw88kCOPPDLTpk1r6OUBAAAAALACFDLw7tChQ1q3bp127dplr732yu23357WrVtn7NixufXWWxt6eQAAAAAArACFDLy/aL311sv++++fJHnuuecaeDUAAAAAAKwIhQi8p02blhEjRmTixIlLHLPRRhslST799NOVtCoAAAAAAFamQgTeRx11VL73ve/l9ttvX+KYcePGJUk6duy4spYFAAAAAMBKVIjAe9ddd02S3H333Zk1a9Yiz0+ePDn33ntvkmT33XdfqWsDAAAAAGDlKETg/aMf/SitW7fOhAkT8rOf/Szjx48vPTdq1Kj8+Mc/zpQpU/L1r389Rx55ZAOuFAAAAACAFaWsoRdQHzp27Jhrr702P/vZzzJs2LB85zvfyUYbbZR58+blvffeS1VVVTbZZJPccMMNWW211Rp6uQAAAAAArAD1FnjPmjUrvXr1yrhx4zJgwIAcfPDBtZo/bNiw3H333Xn55ZczceLEtGjRIh07dsyuu+6aQw89NF//+teXOv8b3/hG7r///vzhD3/IE088kdGjR6dZs2bp3r17evXqle9///tp0aLF8rxFAAAAAAC+xOot8O7fv3/pxpC1MXPmzJx55pl59NFHqz1eXl6eadOmZeTIkbn11ltz6qmn5oQTTljqa6277rrp27dv+vbtW+t1AAAAAACwaquXwPvGG2/MnXfeWet5lZWV6d27d5577rnSY127ds3mm2+e2bNn55lnnsm0adNSUVGRyy67LJWVlTn55JPrY8kAAAAAABTMcgXeVVVVGThwYAYOHFin+ddff30p7G7RokUuueSS7LnnnqXnZ8+enYsuuiiDBw9Oklx99dXp2bNnevTosTzLBgAAAACggBrXdeLUqVPTu3fvOofdkydPzk033VTq9+vXr1rYnSTNmzdPv379cuCBByaZH7BfccUVdV0yAAAAAAAFVuvAu6qqKkOGDMkBBxyQJ554ovR4bW8Iec8992TWrFlJ5h9jsv/++y9x7Lnnnlt6/eeffz7vvPNObZcNAAAAAEDB1epIkzlz5uT73/9+RowYUXpswS7su+66q9pZ3MsydOjQUnufffZJo0aNlji2bdu2+eY3v5lHHnkkSfLQQw+lS5cutVk6AAB8JW109t8begk0kNG/3behlwAAsNLVaof3nDlzqoXdPXr0yJAhQ0pHjtTmdV577bVSf6eddlrmnO23377Ufvrpp2tVDwAAAACA4qvTTSs7deqU0047Lfvuu+9Sd2YvyXvvvZfKyspSf5NNNlnmnIXHvP3227WuCQAAAABAsdUq8G7WrFmuvPLK7LnnnmnSpEmdi44dO7bUbtu2bVq3br3MOR07diy1Z86cmcmTJ6ddu3Z1XgMAAAAAAMVSqyNNmjdvnl69ei1X2J0kEydOLLXXWmutGs35Yrg9ZcqU5VoDAAAAAADFUqvAu77MmDGj1G7evHmN5rRq1apaf/r06fW6JgAAAAAAVm0NEniXl5eX2quttlqN5pSVVT99paKiol7XBAAAAADAqq1BAu/Gjf9TdnmPRwEAAAAAgKSBAu8WLVqU2pWVlTWa88VxzZo1q9c1AQAAAACwamuQwLtly5al9syZM2s0Z+Fzv5NFz/QGAAAAAOCrrUEC7zXXXLPUnjJlSo3mTJ48uVq/ffv29bomAAAAAABWbQ0SeG+88cal9qRJk2p0A8pPPvmk1G7Tpk3atGmzQtYGAAAAAMCqqUEC7w033LB0BvfcuXPz3nvvLXPOu+++W2p36dJlha0NAAAAAIBVU4ME3k2aNMnWW29d6g8fPnyZc1544YVSe8cdd1wh6wIAAAAAYNXVIIF3kvTq1avUvv/++5c6dsqUKXnyySdL/T322GOFrQsAAAAAgFVTgwXee++9d1q0aJEkefHFFzNkyJAlju3fv39mz56dJOnevXu6deu2MpYIAAAAAMAqpMEC77XWWisnnnhiqd+3b9/ceeedqaqqKj02e/bsnHfeeaUd4I0aNcoZZ5yx0tcKAAAAAMCXX1lDFj/uuOPy5JNPZvjw4amoqEjfvn0zaNCgdO/ePeXl5Xn22WczderU0vjevXunZ8+eDbdgAAAAAAC+tBo08G7WrFkGDRqUPn365LHHHkuSfPDBB/nggw+qjWvSpElOOumknHLKKQ2xTAAAAAAAVgENGngnSatWrXLdddflqaeeyr333psXX3wxEydOTOPGjbPuuuumZ8+e+cEPfpCuXbs29FIBAAAAAPgSq7fA+7bbbluu+bvuumt23XXXeloNAAAAAABfNQ1200oAAAAAAKhPAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIZQ29gPr0ySef5Oabb85TTz2Vjz76KEmy/vrrZ7fddstxxx2X9u3bN/AKAQAAAABYUQoTeL/wwgs56aST8tlnn6VJkybp1KlTkmT06NEZNWpUhgwZkkGDBqVbt24NvFIAAAAAAFaEQhxp8tlnn+WUU07JZ599ll133TX/93//l0ceeaT0Z7vttsvkyZPz05/+NDNnzmzo5QIAAAAAsAIUIvC+5557Mnny5HTo0CFXXnllOnToUHquU6dOufbaa7PGGmvkk08+yd///vcGXCkAAAAAACtKIQLvZ599Nkmy++67p3Xr1os8365du2y77bZJktdee22lrg0AAAAAgJWjEGd4n3TSSdlrr73SuXPnJY6pqqpKksydO3dlLQsAAAAAgJWoEIF39+7d07179yU+P3ny5Dz33HNJkq5du66sZQEAAAAAsBIV4kiTZenfv39mzZqV5s2bp1evXg29HAAAAAAAVoDCB97XXXddHnjggSTJiSeeWO2GlgAAAAAAFEchjjRZkoEDB+aaa65JknzrW99K7969G3hFAAAAAACsKIUMvCsrK9OvX78MHjw4SbLzzjvnqquuSuPGhd/QDgAAAADwlVW4wHv69Ok59dRT869//StJstdee+XSSy9Ns2bNGnhlAAAAAACsSIUKvD/55JMcf/zxGTlyZJLk2GOPzZlnnmlnNwAAAADAV0BhAu/x48fnmGOOyYcffpjGjRvnV7/6VY4++uiGXhYAAAAAACtJIQLv8vLynHTSSfnwww/TtGnTXHbZZdlrr70aelkAAAAAAKxEhTjrY9CgQXnjjTeSJL/+9a+F3QAAAAAAX0Gr/A7v8vLy3HLLLUmSsrKyDBkyJEOGDFni+J133jmnnHLKSlodAAAAAAArS70F3rNmzUqvXr0ybty4DBgwIAcffHCt5g8bNix33313Xn755UycODEtWrRIx44ds+uuu+bQQw/N17/+9cXOGzlyZKZNm5YkqayszIsvvrjUOuuss06t1gUAAAAAwKqh3gLv/v37Z9y4cbWeN3PmzJx55pl59NFHqz1eXl6eadOmZeTIkbn11ltz6qmn5oQTTlhkfrdu3fL222/Xed0AAAAAABRDvQTeN954Y+68885az6usrEzv3r3z3HPPlR7r2rVrNt9888yePTvPPPNMpk2bloqKilx22WWprKzMySefXB9LBgAAAACgYJYr8K6qqsrAgQMzcODAOs2//vrrS2F3ixYtcskll2TPPfcsPT979uxcdNFFGTx4cJLk6quvTs+ePdOjR4/lWTYAAAAAAAXUuK4Tp06dmt69e9c57J48eXJuuummUr9fv37Vwu4kad68efr165cDDzwwyfyA/YorrqjrkgEAAAAAKLBaB95VVVUZMmRIDjjggDzxxBOlx1u0aFGr17nnnnsya9asJPOPMdl///2XOPbcc88tvf7zzz+fd955p7bLBgAAAACg4GoVeM+ZMycHH3xwzjrrrIwfPz7J/F3Yl1xySbbaaqtaFR46dGipvc8++6RRo0ZLHNu2bdt885vfLPUfeuihWtUCAAAAAKD4ah14jxgxotTv0aNHhgwZUjpypDav89prr5X6O+200zLnbL/99qX2008/Xat6AAAAAAAUX51uWtmpU6ecdtpp2XfffZe6M3tJ3nvvvVRWVpb6m2yyyTLnLDzm7bffrnVNAAAAAACKrVaBd7NmzXLllVdmzz33TJMmTepcdOzYsaV227Zt07p162XO6dixY6k9c+bMTJ48Oe3atavzGgAAAAAAKJZaHWnSvHnz9OrVa7nC7iSZOHFiqb3WWmvVaM4Xw+0pU6Ys1xoAAAAAACiWWgXe9WXGjBmldvPmzWs0p1WrVtX606dPr9c1AQAAAACwamuQwLu8vLzUXm211Wo0p6ys+ukrFRUV9bomAAAAAABWbQ0SeDdu/J+yy3s8CgAAAAAAJA0UeLdo0aLUrqysrNGcL45r1qxZva4JAAAAAIBVW4ME3i1btiy1Z86cWaM5C5/7nSx6pjcAAAAAAF9tDRJ4r7nmmqX2lClTajRn8uTJ1frt27ev1zUBAAAAALBqa5DAe+ONNy61J02aVKMbUH7yySeldps2bdKmTZsVsjYAAAAAAFZNDRJ4b7jhhqUzuOfOnZv33ntvmXPefffdUrtLly4rbG0AAAAAAKyaGiTwbtKkSbbeeutSf/jw4cuc88ILL5TaO+644wpZFwAAAAAAq64GCbyTpFevXqX2/fffv9SxU6ZMyZNPPlnq77HHHitsXQAAAAAArJoaLPDee++906JFiyTJiy++mCFDhixxbP/+/TN79uwkSffu3dOtW7eVsUQAAAAAAFYhZQ1VeK211sqJJ56YK664IknSt2/fVFRU5NBDD02jRo2SJLNnz85FF11U2gHeqFGjnHHGGfW+lrlz5yapfmNMAAAohBmTG3oFNJCxY8c29BIAAOrdggx3Qab7RQ0WeCfJcccdlyeffDLDhw9PRUVF+vbtm0GDBqV79+4pLy/Ps88+m6lTp5bG9+7dOz179qz3dXz66adJkqOOOqreXxsAABrSag29ABrMd/5xYUMvAQBghfn000/zta99bZHHGzTwbtasWQYNGpQ+ffrkscceS5J88MEH+eCDD6qNa9KkSU466aSccsopK2Qd3bp1y5/+9Ke0b98+TZo0WSE1AAAAAABYPnPnzs2nn366xGOvGzTwTpJWrVrluuuuy1NPPZV77703L774YiZOnJjGjRtn3XXXTc+ePfODH/wgXbt2XWFraN68ebbffvsV9voAAAAAANSPxe3sXqBRVVVV1UpcCwAAAAAArBANvsMbqJ25c+fmoYceysMPP5zXX389kydPTpMmTdKhQ4dsu+22Ofjgg7PjjjvWe91Zs2bl3nvvzdChQ/Puu+9m0qRJadasWTbYYIPsvPPO+cEPfpBOnTrVe134qmuoa/6JJ57Ifffdl5dffjmTJk1KVVVV1lprrWy99dbZb7/98u1vf7t0k2mgfs2ZMyd33XVXHn/88bz99tuZOnVqWrRoka9//ev55je/mcMOOywdOnSo97qvvPJK/vKXv+SFF17I+PHjU1ZWlnXWWSc9e/bMoYcemi233LLeawLzNcR1P3fu3Dz22GN55JFH8uqrr2bixImpqKhI27Zts8kmm2SXXXbJYYcdljXWWKNe6wIN97N+cWbOnJnvfe97GT16dJLk7bffXil1YUWywxtWIaNHj87Pf/7zvPXWW0sdt8cee2TAgAFp06ZNvdR98sknc/755+fjjz9e4pimTZvmjDPOyI9+9KN6qQk0zDU/ceLE/PKXv8wzzzyz1HHbbbddrrzyynTs2HG5awL/8cwzz+TMM8/M+PHjlzimZcuWOfXUU3PsscfWS83KyspceOGFueOOO5Y4plGjRvnhD3+YM844I02bNq2XusB8DXHdv/XWWznjjDPyzjvvLHVc69atc/755+eAAw6ol7pAw1zzS3Peeedl8ODBpb7AmyIQeMMq4uOPP87hhx+eTz/9tPRYly5dsuWWW6aysjIvvfRSPvroo9Jz3bt3z6233poWLVosV90HH3wwffr0SWVlZZL5wXaPHj2y3nrrZcKECXn++eczZ86c0vizzz57pfxQhqJriGv+888/z5FHHlntl99OnTplm222SePGjfP6669n1KhRpec23HDD/OUvf8laa61V55rAf/zjH//I6aefXvqZm8y/zrp3755GjRrl9ddfz/vvv1967tBDD82FF1643N+26NOnT+67775Sv1OnTtl6660zd+7cDB8+PBMmTKhWs3///stVD/iPhrju33zzzRx99NGZPn166bGNN944m2++eZo1a5YPPvggr7zySrU1nXfeeTnqqKPqXBOYr6F+1i/JE088kRNOOKHaYwJvikDgDauI448/Pk8++WSS+Td7veSSS7LHHnuUnp83b15uv/32DBgwIPPmzUuSHHfccTnrrLPqXHP06NE54IADSoH2rrvumgsvvDDrrLNOacz48ePTp0+fPPvss0nmB+L3339/OnfuXOe6QMNc8//zP/9T2uHZtGnTnH/++Tn00EOr/QX7wQcfzLnnnptZs2YlSfbaa69cffXVda4JzPfee+/lkEMOycyZM5Mkq6++en7zm9+kV69e1cY98sgjOffcc0tB1VlnnZXjjjuuznWHDBlS+v9G48aN07dv32qhVmVlZa6//vpcc801pccuu+yy7LfffnWuCczXENd9RUVF9ttvv9LRBR06dMgll1ySnXbaqdq4MWPG5Jxzzsnzzz+fJGnSpEnuvvvubL755nWqCzTcz/olmTx5cg444IBqG2wSgTfF0LihFwAs2/vvv18KvpLkt7/9bbXgK5n/S+p///d/56c//WnpsT//+c+lUKouLrjgglLYvdtuu+W6666rFnYnSceOHXPdddeVjjWoqKjIn/70pzrXBBrmmp8+fXruvvvuUv+Xv/xlDjvssEV2k+yzzz75n//5n1L/kUceyZgxY+pUE/iPq666qvQLcPPmzXPLLbcs8gtwMv9DphtvvDFlZWWleQvvwK6NioqKXH755aX+qaeeusgOzrKysvzsZz/LSSedVG2tC+9MA+qmIa77IUOGlMLuli1b5o9//OMiYXcy/5seN910UzbbbLMk88/7XviDL6D2GuKaX5rzzz9/kbAbikLgDauABTsrkmTdddfNnnvuucSxP/rRj0o/GGfPnp2XX365TjXfeuutPP3000nm7y7t379/mjVrttixrVu3ztFHH13qLxzUAbXXENf8K6+8kvLy8iRJs2bNcuSRRy5x7IEHHpi111671F/wDQ+gbqZNm5ZHH3201D/ppJOWeoPIHj165NBDD00y/7qv6wfNQ4cOLZ0futZaay31Phw//elPSx96f/jhhxk2bFidagLzNdR1/8ADD5Tahx9+eDbeeOMljm3evHl+/vOfl/rDhg1brs008FXWUNf8ktxzzz35xz/+UaoFRSPwhlXAlClTSu0v7rD+otatW2fNNdcs9SdPnlynmguf5Xncccelffv2Sx2/77775sQTT8w555yTk08+uU41gfka4ppfuGbbtm3TvHnzJY5t1KhROnXqtNw1gfmef/75zJ07N8n8b28cccQRy5yz//77l9oPPfRQneoOHTq01P72t7+91HsANG3aNPvss89y1wTma4jrvqqqKq+88kqp/61vfWuZc3bcccdSe86cORk7dmyt6wIN97N+cT766KPS/Tg6duyYvn371ttrw5dFWUMvAFi2Dh06lNrL+kvm7NmzM3Xq1FJ/wVEjtfX444+X2jU5p3P99dfP6aefXqdaQHUNcc0vXHPKlCmZMWNGWrVqtcTxn3zyyWLnArU3bty4UvtrX/tatQ+xlqRr166l9gcffJDJkyenXbt2taq78LdJFnekwRdtv/32+d///d8kyb/+9a9a1QKqa4jrfsaMGfnOd76TCRMm5JNPPskGG2ywzDmNG1ffIzdjxowa1wP+o6F+1n/RvHnzctZZZ5XOB7/ooovSpk2b5XpN+DKywxtWAdtss03pL5uffvppHnnkkSWO/etf/5qKiookSZs2bUrn7tXG7Nmz88EHHyRJ1lxzzWy00Ua1XzRQZyv7mk+SzTbbLC1btkwy/1zfwYMHL3HsY489VvpLe1lZma9BwnJa8Etnkhr9Apxkkd3Ytb3B1LRp00rHmSRZ6rEGC2yyySal9qeffurbHbAcGuK6b926dS677LLcdtttefTRR6t9W2tJRowYUa2/1lpr1aomMF9DXPOL84c//KH0gfeRRx6ZXXbZZblfE76MBN6wCujcuXO1rxGfe+65+b//+79Fxg0ZMiSXXHJJqX/CCSekdevWta73zjvvZN68eUlSLex+9dVXc8EFF6RXr17Zdttts/322+d73/terrzyykyaNKnWdYDFW9nXfDI/LD/mmGNK/csvvzx33313qqqqqo176qmncvbZZ5f6hx12WI1+YQaWbOGdVZ9//nmN5iz8zY4k1cLrmvjoo4+q9Wuy0/OLRyw52gDqriGu+7r461//Wmq3b9++Rv+vABb1Zbjm33rrrVx11VVJ5u8yP/PMM5fr9eDLzJEmsIq44IILMmHChDz33HOZPn16evfuna5du2aLLbYonce34I7rjRs3zgknnJDjjz++TrXGjBlTaq+99tqZNWtWfvvb32bw4MGLhF8jRozIiBEjcuutt+aCCy6ods4YUHcr85pf4JRTTsmYMWPy4IMPpqKiIueee26uv/76bL311ikrK8tbb72VN998szT+4IMPzq9//evlqgnM/6Vzgffeey/Tpk3LGmussdQ5C5/Dmyz6S/GyTJw4sdRu3rx5jT4sW2211dKyZcvMnDkzSfWz/4HaaYjrvrZefvnl3H///aX+3nvvnUaNGq3QmlBUDX3Nl5eXp0+fPqmoqEiTJk1y8cUXl77dCUUk8IZVROvWrXPLLbfk7rvvzoABAzJjxoyMHDkyI0eOrDZuzTXXzPXXX59tttmmzrUW/rpVWVlZfv7zn+eJJ55IMn9nx3bbbZdWrVpl9OjReeWVVzJ37tzMmDEjffr0yaxZs3L44YfXuTYw38q85hdo2rRprrjiiuyzzz654IIL8umnn+bDDz/Mhx9+WG1cixYtcvnll+fb3/72ctcE5p+N3bx588yePTtz587NLbfcklNPPXWpc/70pz9V68+ZM6dWNRc+h3dpN6n9olatWpUCb2f5Qt01xHVfG5MnT84vfvGL0rc+W7RokRNOOGGF1YOia+hr/vLLLy/9HvHjH/842267bZ1fC1YFjjSBVcTcuXPzhz/8IZdddtlSf8GcMmVKjjvuuNx4442lv6DW1oJfZJNk6NCheeKJJ9K0adP8+te/zhNPPJGrr746AwYMyB133JH7778/W265ZZL5d37v16/fImf9AbW3Mq/5hd15553p379/Pv300yWOmTVrVk499dRcfPHFKS8vX+6a8FXXvHnzHHbYYaX+DTfckKFDhy5x/A033JCnn3662mOVlZW1qrnwtbvaaqvVeF5Z2X/2yyy4fwBQew1x3dfU9OnTc8IJJ1Q7+qhPnz5uUg3LoSGv+WeffTZ//OMfk8y/b88pp5xSp9eBVYnAG1YB5eXl6d27dy699NJMmTIlZWVlOeaYY3LPPffklVdeyfDhw/PnP/85Bx10UBo1apQZM2bksssuq7YrozYWDrwrKirSqFGjXHHFFTn66KPTpEmTamM33njj3HrrraWvaFVUVOTKK69crvcLX3Ur+5pP5n9g9atf/Sp9+/Yt3ZDywAMPzB133JHhw4fn5Zdfzj333JNjjjkmTZs2TUVFRf73f/83xx57bGbPnl2fbx++kk4++eSst956Seb/QnvKKafkvPPOy6uvvprZs2dnxowZeeGFF3LKKafk8ssvT1lZWbWzdJs1a1aregtujJtkkZ/twMqxsq/7mpg2bVp+/OMf57XXXis9tt9+++Woo46q91rwVdMQ1/znn3+es88+O1VVVWnatGkuueSSFfL/DviycaQJrAKuueaaPPXUU0nm/5C78cYbs9NOO1Ub06NHj/To0SO77bZbfvnLX2bevHl56KGH0q1bt/zkJz+pVb0v/gD87ne/m+9+97tLHN+6dev06dMnP/vZz5IkTz75ZCZNmuQu7lBHK/uaT5LBgwfnrrvuSpI0atQov/3tb3PQQQdVG7Pllltmyy23zJ577pkTTjghs2bNygsvvJCLL744559/ft3eLJAkadeuXa6//vr85Cc/yYQJEzJv3rwMHjw4gwcPXmRsWVlZ+vXrl8cff7x048jaHEuSzD+eYIHa7BhbeKxfmGH5rOzrflnGjx+fn/zkJ9WOT9t5550zYMCAeq0DX1UNcc3369cvH3/8cZLk1FNPzaabbrp8bwJWEXZ4w5fc559/nttuu63UP/300xcJvha2zz77VDtf74YbbsisWbNqVfOLN6844IADljnnW9/6VukHcFVVVZ5//vla1QTma4hrft68ebn++utL/aOOOmqRsHthO+64Y371q1+V+oMHDy7tCgfqbtNNN81dd92VffbZZ4k3httyyy1zxx135JBDDslnn31Werxdu3a1qtWqVatSe+Fvdi3LwkcsLfwaQN2szOt+ad58880cfvjh1cLuXXbZJb///e99uAX1aGVe8w8//HDuu+++JMl2221Xp00xsKqywxu+5J599tlSeLXaaqvlyCOPXOacH//4x7nppptSWVmZzz77LM8991x22223GtdcffXVq/W7dOmyzDlNmzbNRhttlLfeeivJ/B0iQO01xDX/9ttvVwusf/SjHy1zziGHHJIrrrgikyZNyty5c/P444/7ujPUg44dO+aKK67IGWeckaeeeipjxozJ3Llzs84662THHXfMFltsURq78Pm6tT1bd8011yy1p0+fnvLy8mWGWnPmzKkWjrdv375WNYHFW1nX/ZL885//zC9+8Ytq1/dee+2VSy+9VNgNK8DKuOYnTJhQ+gZmy5Ytc/HFF1c7zgyKTuANX3IffPBBqb3xxhtX+wrykrRp0yZf//rXSzs03nvvvVqFXwvO416gpmd7Lry22uwWA/6jIa75hWuuscYa6dSp0zLnNG7cON27d88///nPJMn7779f43rAsq2//vr5/ve/v8TnP/vss2q/BG+88ca1ev2NNtoojRs3Lp37P378+GVe+1/8Jsf6669fq5rA0q3o635xbr/99vTv37/aPUCOOeaYnHvuucIxWMFW5DU/bNiwTJ06Ncn8382XdkTpFy187MnPfvYzN7lkleQnGHzJzZ07t9SuzV86Fz6WpKKiolY1u3btWq1WTXdrL/x1qzXWWKNWNYH5GuKar4+a5eXltaoJLJ9nnnmm1F5//fVr/TXn5s2bVwu433nnnWXOeffdd0vtddZZJ23atKlVTWD5LO91/0VXX311fvOb35TC7kaNGuWss85K3759hd3wJVDf1zx8ldjhDV9yC9/4ccFXnWqy43rhT4Jr+5Xj5s2bZ7PNNsuIESOSzP9Bu/322y91zowZMzJ69OhSvybHoACLaohrfuGaU6ZMydSpU9O2bdta1ayvr1XDV9WFF16Y8ePHZ+LEiRk4cOAyb/z86KOPltq77rprnWpuu+22pW94DB8+PN/+9reXOv6FF14otXfcccc61QT+oyGu+wWuuuqqXHfddaV+s2bN8rvf/S577733cr0usGQr85rv3LlzjjjiiBqNnTFjRh544IFSf+F53bp1q1Vd+LIQeMOXXI8ePUrtadOm5amnnsq3vvWtpc554YUX8umnny72NWpqv/32KwXeQ4YMyQknnLDUM/z+/ve/l3aJrr766tlmm21qXRNomGt+q622SrNmzUq7tP/+978v8zzusWPH5rXXXqtzTaC6559/vnQfjGHDhuXAAw9c4thx48bloYceKvVrcnPpxenVq1eGDBmSJHnooYdy+umnp6xs8b8elJeX58EHHyz199hjjzrVBP6jIa77JLnrrruqhd2tW7fO9ddfnx122KHOrwks28q85rfddttsu+22NRo7duzYaoF3v379alULvox8Twm+5DbaaKNqP6guuuiiTJ8+fYnjZ86cmd/85jelfo8ePbLhhhvWuu4BBxxQOq5gzJgxueKKK5Y4dsKECbnyyitL/UMPPTRNmzatdU2gYa75Vq1aZc899yz1r7766nzyySdLHD937tycf/75pQ+5NthgA78kw3Ja+IOtW265pdp5ugubO3duzjnnnNLRRdtvv32dP3D6r//6r9I3Qj766KNcf/31Sxx77bXXlo4469ix4zJ3gwPL1hDX/ahRo3LhhReW+q1bt84f//hHP8dhJWiIax6+qgTesAo4++yzSzuuPvjggxxxxBF55ZVXFhk3cuTIHH300aVPjZs2bZqzzz57sa+36aablv4sTvv27fOLX/yi1P/f//3fnH/++Zk2bVq1cW+++WaOOeaYTJo0KUmy3nrr5Wc/+1nd3iiQpGGu+dNOOy2tWrVKkkydOjVHHHFEnnrqqUXGffTRRznhhBMybNiw0mPnnHPOEneFAjVzxBFHpHnz5kmSN954I3369CndbGqBjz76KD/+8Y/z73//O0my2mqr5fzzz1/s69Xkum/atGnOOuusUn/gwIH5/e9/X+1c/8rKygwcOLBaGP6LX/zCB9tQDxriuu/fv39mzZpV6l922WXZaqut6uHdAMvSENc8fFX57RRWAdtss00uuOCC/PrXv868efPy7rvv5vDDD0+XLl3SpUuXNGvWLKNGjcrrr7+eqqqqJPNvPHfhhReme/fuda579NFH5+23386dd96ZJPnLX/6S++67Lz169Ej79u0zevTovPzyy6VPplu0aJGLL744rVu3Xv43DV9hDXHNd+rUKVdddVVOPvnklJeX55NPPslPfvKTdOrUKVtssUVatWqVDz/8MC+//HIqKytL80477TRHG0A9WG+99XLmmWeWvkb8wAMP5Mknn0z37t2z9tpr5+OPP87w4cNLYXRZWVkuvvjidO3adbnq7r///nnsscfy0EMPpaqqKldeeWXuuOOO0r07nn/++UyYMKE0fr/99stBBx20XDWB+Vb2df/aa6/lX//6V6nfrl27PP7443n88cdr/BrHHntsOnfuXKf68FXXUD/r4atI4A2riEMPPTTt27fPr371q9JZve+8807eeeedRcZ27NgxAwYMyH/9138tV81GjRrlwgsvzIYbbpjrrrsus2bNysyZMxe763O99dbLtddemy222GK5agLzNcQ1v+uuu+ZPf/pT+vTpU7oJ7ZgxYzJmzJhFxq6xxhrp27fvcp0hClR31FFHZe7cubnkkktSUVGRzz77rNq3KRZYf/31079//+y00071UvfSSy/N6quvnjvvvDNVVVUZP358/v73vy8y7ogjjsh5551XLzWB+Vbmdb/wOfxJMnny5AwePLhWr7HvvvsKvGE5NNTPeviqEXjDKmS33XbLY489lnvvvTf/93//lxEjRmTKlClJ5u/Q2GKLLfKtb30rBx544FJvMFlbJ5xwQvbff//cc889eeKJJzJ27NhMmzYtrVu3zqabbpo999wzhxxySFq0aFFvNYGGuea7d++eBx98MA8//HCGDh2aV199NZMnT05lZWXWXHPNdO3aNbvuumsOOeQQ3+aAFeC///u/s/vuu+dPf/pT/vWvf2Xs2LGpqKhI27Zts/nmm2fPPffM/vvvX/pKdH0oKyvLb37zmxxyyCG5++6789xzz2XChAmZO3duOnTokO233z5HHHFEjW9+BdTOyrruR40aVU8rBpZHQ/ysh6+aRlULvgsNAAAAAACrMDetBAAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAApB4A0AAAAAQCEIvAEAAAAAKASBNwAAAAAAhSDwBgAAAACgEATeAAAAAAAUgsAbAAAAAIBCEHgDAAAAAFAIAm8AAAAAAArh/wGNyskiu5UUlwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1800x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "trials = []\n",
    "\n",
    "qs = -np.array(clipped_sums)\n",
    "\n",
    "threshold = 0.01 * N * 24\n",
    "\n",
    "epsilon = 0.2\n",
    "\n",
    "above_threshold = PrivateAboveThreshold()\n",
    "\n",
    "for t in range(1000):\n",
    "    trials.append(\n",
    "        above_threshold.execute(queries=qs, threshold=-threshold, epsilon=epsilon)\n",
    "    )\n",
    "\n",
    "plt.hist(trials)\n",
    "plt.yscale(\"log\")\n",
    "plt.title(f\"Trials at ε={epsilon}\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}