allocation_binary_decision_v3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3b60f21c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from cvxopt import matrix, solvers, log, exp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib\n",
    "plt.style.use('ggplot')\n",
    "matplotlib.rcParams.update({\"axes.grid\" : False})\n",
    "\n",
    "from PyomoSolver import PyomoSolver"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c055c2ad",
   "metadata": {},
   "source": [
    "### set up problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0981d0e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 80\n",
    "M = 50\n",
    "T = 500\n",
    "\n",
    "# noise sub-gaussianity parameter\n",
    "eta = 1\n",
    "# maximum value of R\n",
    "max_R = 1\n",
    "\n",
    "R_true = np.random.beta(8, 8, size=(N, M))\n",
    "\n",
    "plt.hist(R_true.flatten(), bins=np.int32(np.sqrt(N * M)))\n",
    "plt.show()\n",
    "# _, s, _ = np.linalg.svd(R_true)\n",
    "# plt.yscale(\"log\")\n",
    "# plt.plot(s)\n",
    "# plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65f6eca7",
   "metadata": {},
   "source": [
    "### set static capacities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3ed84059",
   "metadata": {},
   "outputs": [],
   "source": [
    "# capacities\n",
    "C = np.ones(M)\n",
    "# demands\n",
    "D = np.ones(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7617babe",
   "metadata": {},
   "source": [
    "### ILP Solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c1b7931f",
   "metadata": {},
   "outputs": [],
   "source": [
    "solver = PyomoSolver(N, M, C, D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "39519467",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_offerings_and_prices(R):\n",
    "    x = solver.solve_system(R)\n",
    "    p = solver.get_prices()\n",
    "    p = p - np.min(p)\n",
    "    return x, p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7a26a928",
   "metadata": {},
   "outputs": [],
   "source": [
    "def filter_decisions(x, p):\n",
    "    accepted = np.int32(R_true >= p)\n",
    "    x_accepted = x * accepted\n",
    "    # print(np.sum((R_true - p) * x, axis = 0))\n",
    "    return x_accepted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cfbb3d89",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_surplus(x):\n",
    "    return np.sum(x * R_true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ba4fbcfd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_dissatisfaction(x, p):\n",
    "    current_surplus = np.sum(x * (R_true - p), axis = 1)\n",
    "    best_surplus = np.maximum(np.max(R_true - p, axis = 1), 0)\n",
    "    return np.sum(best_surplus - current_surplus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "881e8398",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_proxy(R_lower, R_upper, alpha):\n",
    "    R_proxy = R_lower + alpha * (R_upper - R_lower)\n",
    "    return R_proxy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "979eb56e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_intervals(R_lower, R_upper, p, x_accepted, x_rejected):\n",
    "    p_extended = np.tile(p,(N, 1))\n",
    "    R_lower = np.maximum(R_lower, x_accepted * p_extended + (1 - x_accepted) * R_lower)\n",
    "    R_upper = np.minimum(R_upper, x_rejected * p_extended + (1 - x_rejected) * R_upper)\n",
    "    return R_lower, R_upper"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee4516c7",
   "metadata": {},
   "source": [
    "### get the optimum solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "44637fe9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "38.643064948420204\n",
      "[0.0431996  0.02618232 0.13185342 0.01404526 0.10300523 0.00249305\n",
      " 0.12313194 0.04336495 0.08486758 0.05332387 0.11538022 0.06985717\n",
      " 0.06582636 0.04423174 0.08586184 0.14508755 0.07489243 0.1324831\n",
      " 0.10613653 0.1231863  0.05530721 0.11316181 0.06807094 0.07477207\n",
      " 0.01892386 0.07534036 0.09389915 0.         0.07217618 0.06526049\n",
      " 0.0679916  0.07906    0.09730129 0.14121164 0.06428971 0.09317236\n",
      " 0.06458888 0.06872382 0.07649879 0.07615973 0.12127033 0.05746395\n",
      " 0.05685477 0.11071951 0.00501003 0.10243961 0.03161089 0.00265569\n",
      " 0.05173616 0.10218818]\n"
     ]
    }
   ],
   "source": [
    "x_opt, p_opt = get_offerings_and_prices(R_true)\n",
    "surplus_opt = get_surplus(x_opt)\n",
    "print(surplus_opt)\n",
    "print(p_opt)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72a944b7",
   "metadata": {},
   "source": [
    "### set the experiment history arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "5ca4e186",
   "metadata": {},
   "outputs": [],
   "source": [
    "exp_names = [\"UCB with halving\", \"UCB with comp pricing\"]\n",
    "num_of_exp = len(exp_names)\n",
    "\n",
    "rewards = np.zeros((num_of_exp, T))\n",
    "acceptance = np.zeros((num_of_exp, T))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8e48eab",
   "metadata": {},
   "source": [
    "### UCB with halving"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d93b5065",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 14.23859846886592 18.771403290401118 0.48\n",
      "7.0710678118654755\n",
      "10 11.777956510060198 17.559932077223024 0.38\n",
      "6.224949798994366\n",
      "20 11.062457552086684 18.071282722012285 0.36\n",
      "6.254998001598402\n",
      "30 10.03055125973437 18.21765356385378 0.34\n",
      "6.284902544988268\n",
      "40 9.714833427495261 18.104892770525048 0.32\n",
      "6.041522986797286\n",
      "50 11.707928927691999 18.70846801854224 0.4\n",
      "6.519202405202649\n",
      "60 8.55877804890862 17.94916892099194 0.28\n",
      "5.916079783099616\n",
      "70 8.14439563407898 17.90095304435176 0.26\n",
      "6.0878978309429606\n",
      "80 11.804648065218178 18.390687723530963 0.4\n",
      "6.284902544988268\n",
      "90 8.08341802546111 18.903131085982594 0.26\n",
      "6.190971248519896\n",
      "100 10.355619885880394 16.774300808748606 0.32\n",
      "5.029530201656756\n",
      "110 12.579658102356891 16.133435908106776 0.38\n",
      "4.725396449355773\n",
      "120 15.341946287126571 42.0424536231324 0.42\n",
      "4.079411916125633\n",
      "130 15.38911128093356 43.21081614240313 0.44\n",
      "4.271316518482914\n",
      "140 15.943651338102873 45.08359175082009 0.44\n",
      "3.442940031546512\n",
      "150 19.50803957806665 39.55258893296971 0.52\n",
      "2.940325818467619\n",
      "160 29.020030930970645 34.15544808028247 0.76\n",
      "1.6286770433838826\n",
      "170 28.15486939748259 33.56861917054224 0.72\n",
      "0.48450810027793983\n",
      "180 28.887935123530433 30.669008514360065 0.74\n",
      "0.5590717974926017\n",
      "190 35.65128054730044 23.723607950804535 0.92\n",
      "0.35493715074901055\n",
      "200 35.06180792580898 23.053794344348958 0.9\n",
      "0.03125095482683837\n",
      "210 37.14980971925415 21.09990533552902 0.96\n",
      "0.27950849718787407\n",
      "220 37.96994304653746 19.99830797355134 0.98\n",
      "0.0009765625891304767\n",
      "230 38.643064948420204 19.999315617357222 1.0\n",
      "1.9524501984309195e-06\n",
      "240 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "250 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "260 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "270 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "280 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "290 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "300 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "310 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "320 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "330 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "340 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "350 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "360 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "370 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "380 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "390 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "400 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "410 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "420 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "430 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "440 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "450 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "460 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "470 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "480 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "490 38.643064948420204 19.37845848394104 1.0\n",
      "4.2146848510894033e-07\n",
      "done\n"
     ]
    }
   ],
   "source": [
    "exp_id = 0\n",
    "\n",
    "delta = 1e-7\n",
    "\n",
    "R_lower = np.zeros((N, M))\n",
    "R_upper = max_R * np.ones((N, M))\n",
    "\n",
    "for t in range(T):\n",
    "        \n",
    "    # get a point in each interval\n",
    "    R_proxy = get_proxy(R_lower, R_upper, 1)\n",
    "    x_offered, p_w = get_offerings_and_prices(R_proxy)\n",
    "    \n",
    "    p_learn = np.max(get_proxy(R_lower, R_upper, 0.5) * x_offered, axis = 0)\n",
    "        \n",
    "    R_length = R_upper - R_lower\n",
    "    to_learn = np.max(x_offered * (R_length > delta), axis = 0) > 0\n",
    "    p = to_learn * p_learn + (1 - to_learn) * p_w\n",
    "         \n",
    "#     p = np.minimum(p_learn, p_w)\n",
    "    \n",
    "    x_accepted = filter_decisions(x_offered, p)\n",
    "    x_rejected = x_offered - x_accepted\n",
    "    R_lower, R_upper = update_intervals(R_lower, R_upper, p, x_accepted, x_rejected)\n",
    "\n",
    "    acceptance[exp_id, t] = np.sum(x_accepted) / np.sum(x_offered)\n",
    "    rewards[exp_id, t] = get_surplus(x_accepted)\n",
    "    diss = get_dissatisfaction(x_accepted, p)\n",
    "    \n",
    "    if t % 10 == 0:\n",
    "        print(t, rewards[exp_id, t], diss, acceptance[exp_id, t])\n",
    "        # print(to_learn)\n",
    "        print(np.linalg.norm(np.sum(R_length * x_offered, axis = 1 )))\n",
    "\n",
    "        # print(R_length)\n",
    "        # print(np.linalg.norm(p - p_opt), np.linalg.norm(p_w - p_opt))\n",
    "\n",
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dc60827",
   "metadata": {},
   "source": [
    "### UCB with competetive prices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d1693398",
   "metadata": {},
   "outputs": [],
   "source": [
    "# def find_comp_prices(R_lower, R_upper, x, p):\n",
    "#     p_extended = np.tile(p,(N, 1))\n",
    "#     B = R_upper - p_extended\n",
    "#     A = R_lower - p_extended\n",
    "#     A_max = np.max(A, axis = 1)\n",
    "#     A_max_exc = np.max(A * (1 - x), axis = 1)\n",
    "#     is_valid = (B.T > A_max).T\n",
    "#     B_min = np.min(B * is_valid + 10 * max_R * (1 - is_valid), axis = 1)\n",
    "        \n",
    "#     A_curr = np.sum(A * x, axis = 1)\n",
    "#     B_curr = np.sum(B * x, axis = 1)\n",
    "  \n",
    "#     p_shift = np.zeros(N)\n",
    "    \n",
    "#     for n in range(N):\n",
    "#         if A_max_exc[n] < A_curr[n] and B_min[n] < B_curr[n]:\n",
    "#             p_shift[n] = B_min[n]\n",
    "#         else:\n",
    "#             p_shift[n] = (B_min[n] + A_max[n]) / 2\n",
    "            \n",
    "# #     print(np.sum(is_valid))\n",
    "\n",
    "# #     print(p_shift)\n",
    "    \n",
    "#     p = p + x.T @ p_shift\n",
    "    \n",
    "        \n",
    "#     return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "440e3ca2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# def find_comp_prices(R_lower, R_upper, x, p, last_accepted_offers):\n",
    "#     p_extended = np.tile(p,(N, 1))\n",
    "#     B = R_upper - p_extended\n",
    "#     A = R_lower - p_extended\n",
    "#     A_max = np.max(A, axis = 1)\n",
    "#     offer_next_price = np.sum(last_accepted_offers * x, axis = 1)\n",
    "    \n",
    "#     is_valid = (B.T > A_max).T\n",
    "#     B_min = np.min(B * is_valid + 10 * max_R * (1 - is_valid), axis = 1)\n",
    "    \n",
    "#     B_max_exc = np.max(B * (1 - x), axis = 1)\n",
    "    \n",
    "#     A_curr = np.sum(A * x, axis = 1)\n",
    "#     B_curr = np.sum(B * x, axis = 1)\n",
    "  \n",
    "#     p_shift = np.zeros(N)\n",
    "#     for n in range(N):\n",
    "#         if A_curr[n] >= B_max_exc[n] - 1e-7:\n",
    "#             p_shift[n] = A_curr[n]\n",
    "#         elif offer_next_price[n]:\n",
    "#             p_shift[n] = B_min[n]\n",
    "#         else:\n",
    "#             p_shift[n] = (B_min[n] + A_max[n]) / 2\n",
    "            \n",
    "#     ratio = (p_shift - A_curr)/(B_curr - A_curr + 1e-12)\n",
    "#     ratio = np.minimum(np.maximum(ratio, 0.01), 0.99)\n",
    "#     p_shift = ratio * (B_curr - A_curr) + A_curr\n",
    "            \n",
    "# #     print(np.sum(is_valid))\n",
    "\n",
    "# #     print(p_shift)\n",
    "        \n",
    "#     p = p + x.T @ p_shift\n",
    "    \n",
    "        \n",
    "#     return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "0677cd16",
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_comp_prices(R_lower, R_upper, x, p_w):\n",
    "    p_extended = np.tile(p_w,(N, 1))\n",
    "    B = R_upper - p_extended\n",
    "    A = R_lower - p_extended\n",
    "    A_max = np.max(A, axis = 1)\n",
    "    \n",
    "    other_and_valid = (1-x) * (B.T > A_max).T\n",
    "    B_other_min = np.min(B * other_and_valid + 10 * max_R * (1 - other_and_valid), axis = 1)\n",
    "    \n",
    "    B_second_max = np.max(B * (1 - x) - 10 * max_R * x, axis = 1)\n",
    "\n",
    "    other_best_surplus = np.max((R_upper - p_w) * (1 - x), axis = 1)\n",
    "    current_worst_surplus = np.sum((R_lower - p_w) * x, axis = 1)\n",
    "    \n",
    "    current_best_surplus = np.sum((R_upper - p_w) * x, axis = 1)\n",
    "\n",
    "    current_R_lower = np.sum(R_lower * x, axis = 1)\n",
    "    current_R_upper = np.sum(R_upper * x, axis = 1)\n",
    "\n",
    "    opt_found = np.bitwise_and(current_worst_surplus - other_best_surplus + 1e-8 > 0, current_worst_surplus + 1e-8 > 0)\n",
    "        \n",
    "    p_w_user = x @ p_w\n",
    "    p_user = np.zeros(N)\n",
    "    for n in range(N):\n",
    "        if opt_found[n]:\n",
    "            p_user[n] = p_w_user[n] - 1e-8\n",
    "        else:\n",
    "            smallest_price = current_R_lower[n] + 0.3 * (current_R_upper[n] - current_R_lower[n])\n",
    "            largest_price = current_R_lower[n] + 0.7 * (current_R_upper[n] - current_R_lower[n])\n",
    "            p_user[n] = p_w_user[n] + A_max[n] + 0.5 * (B_other_min[n] - A_max[n])\n",
    "            p_user[n] = np.minimum(np.maximum(p_user[n], smallest_price), largest_price)\n",
    "\n",
    "    print()\n",
    "    print( x.T @ (p_user - current_R_lower)/( x.T @ (current_R_upper - current_R_lower)))\n",
    "    \n",
    "   # print(x.T @ current_R_lower, x.T @ current_R_upper)\n",
    "    \n",
    "    p = x.T @ p_user\n",
    "    \n",
    "#     print(current_best_surplus - other_best_surplus)\n",
    "            \n",
    "#     print(np.sum(opt_found) / len(opt_found))\n",
    "\n",
    "    # print(p)\n",
    "        \n",
    "    return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e5f1df08",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5\n",
      " 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5\n",
      " 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5]\n",
      "0 14.23859846886592 18.771403290401118 0.48\n",
      "3.5355339059327378\n",
      "\n",
      "[0.7 0.7 0.3 0.7 0.3 0.3 0.7 0.3 0.3 0.3 0.5 0.3 0.3 0.5 0.5 0.3 0.3 0.5\n",
      " 0.3 0.3 0.5 0.5 0.5 0.5 0.3 0.3 0.3 0.3 0.3 0.3 0.5 0.5 0.5 0.3 0.3 0.5\n",
      " 0.7 0.3 0.5 0.5 0.7 0.3 0.7 0.3 0.5 0.5 0.5 0.3 0.3 0.5]\n",
      "\n",
      "[0.6   0.3   0.3   0.4   0.3   0.3   0.5   0.3   0.3   0.625 0.3   0.625\n",
      " 0.3   0.3   0.4   0.625 0.625 0.4   0.625 0.3   0.3   0.625 0.625 0.4\n",
      " 0.625 0.4   0.4   0.4   0.4   0.625 0.4   0.625 0.625 0.3   0.3   0.4\n",
      " 0.625 0.3   0.625 0.625 0.4   0.3   0.6   0.3   0.625 0.625 0.4   0.625\n",
      " 0.5   0.5  ]\n",
      "\n",
      "[0.3    0.4    0.575  0.3    0.4    0.575  0.4    0.55   0.5625 0.4\n",
      " 0.3    0.4    0.5625 0.3    0.3    0.3    0.5625 0.4    0.5625 0.6875\n",
      " 0.3    0.6875 0.35   0.5625 0.5625 0.3    0.3    0.35   0.3    0.3\n",
      " 0.6875 0.5625 0.7    0.5625 0.5625 0.4    0.6875 0.3    0.575  0.7\n",
      " 0.6875 0.3    0.5625 0.3    0.575  0.5625 0.5625 0.3    0.3    0.3   ]\n",
      "\n",
      "[0.35    0.5375  0.3     0.5375  0.7     0.7     0.3     0.45    0.45\n",
      " 0.4     0.5     0.3     0.53125 0.53125 0.53125 0.53125 0.7     0.3\n",
      " 0.3     0.59375 0.35    0.7     0.65625 0.53125 0.3     0.3     0.45\n",
      " 0.7     0.3     0.5     0.53125 0.605   0.53125 0.65625 0.3     0.3\n",
      " 0.65625 0.5     0.605   0.5375  0.65625 0.7     0.53125 0.55    0.53125\n",
      " 0.5375  0.53125 0.4     0.5     0.4    ]\n",
      "\n",
      "[0.3      0.685    0.3      0.425    0.51875  0.45     0.51875  0.45\n",
      " 0.7      0.3      0.45     0.6325   0.3      0.685    0.45     0.515625\n",
      " 0.375    0.515625 0.3      0.515625 0.3      0.375    0.7      0.3\n",
      " 0.3      0.546875 0.6325   0.425    0.685    0.45     0.3      0.45\n",
      " 0.3      0.59375  0.640625 0.5575   0.5575   0.640625 0.6325   0.525\n",
      " 0.51875  0.640625 0.515625 0.3      0.6325   0.45     0.51875  0.546875\n",
      " 0.515625 0.3     ]\n",
      "\n",
      "[0.528125   0.4375     0.6325     0.675      0.375      0.509375\n",
      " 0.475      0.7        0.475      0.7        0.475      0.5234375\n",
      " 0.57125    0.425      0.375      0.3625     0.5078125  0.5835\n",
      " 0.425      0.3        0.7        0.7        0.3        0.3\n",
      " 0.3        0.640625   0.7        0.3        0.6328125  0.6325\n",
      " 0.475      0.4375     0.425      0.57125    0.7        0.509375\n",
      " 0.53375    0.578125   0.3        0.3        0.46416667 0.3\n",
      " 0.57125    0.5390625  0.5125     0.3        0.45       0.509375\n",
      " 0.5078125  0.5078125 ]\n",
      "\n",
      "[0.3        0.3        0.7        0.3        0.6625     0.3\n",
      " 0.3875     0.3        0.51171875 0.4875     0.4375     0.6859375\n",
      " 0.52734375 0.540625   0.4625     0.3        0.54675    0.7\n",
      " 0.3        0.3        0.5234375  0.3        0.7        0.6785\n",
      " 0.60625    0.4625     0.5390625  0.6328125  0.6859375  0.62890625\n",
      " 0.60625    0.3        0.3        0.3        0.3        0.6859375\n",
      " 0.66775    0.6328125  0.5703125  0.3        0.5046875  0.5140625\n",
      " 0.53375    0.51171875 0.7        0.50625    0.3        0.3\n",
      " 0.3        0.601875  ]\n",
      "\n",
      "[0.60625    0.7        0.5328125  0.3        0.3        0.3\n",
      " 0.65625    0.43125    0.6925     0.3        0.4875     0.3\n",
      " 0.3        0.7        0.5253125  0.46875    0.3        0.7\n",
      " 0.696875   0.53515625 0.65673077 0.51953125 0.528375   0.619375\n",
      " 0.3        0.3        0.62890625 0.3875     0.67890625 0.545625\n",
      " 0.3        0.593125   0.3        0.51640625 0.601875   0.62695312\n",
      " 0.4375     0.521875   0.503125   0.56640625 0.53515625 0.7\n",
      " 0.62890625 0.3        0.475      0.6171875  0.6575     0.50976562\n",
      " 0.50234375 0.51171875]\n",
      "\n",
      "[0.44375    0.49375    0.3        0.7        0.5        0.653125\n",
      " 0.67828125 0.593125   0.7        0.3        0.50976562 0.68875\n",
      " 0.48125    0.67890625 0.434375   0.53296875 0.7        0.6953125\n",
      " 0.3        0.3        0.62695312 0.6653125  0.51757812 0.5375625\n",
      " 0.3        0.44375    0.39375    0.48884615 0.5515625  0.3\n",
      " 0.3        0.56445312 0.5865625  0.67890625 0.51523438 0.3\n",
      " 0.3        0.662375   0.50351562 0.5865625  0.51074219 0.53320312\n",
      " 0.7        0.62695312 0.5159375  0.3        0.5015625  0.5\n",
      " 0.5        0.3       ]\n",
      "\n",
      "[0.7        0.3        0.440625   0.484375   0.67539063 0.671875\n",
      " 0.3        0.66742188 0.6515625  0.5996875  0.3        0.3\n",
      " 0.686875   0.3        0.3        0.3        0.69453125 0.50878906\n",
      " 0.5        0.64875    0.53710938 0.662375   0.3        0.46875\n",
      " 0.53296875 0.3        0.3        0.3        0.62597656 0.67539063\n",
      " 0.54859375 0.59421875 0.446875   0.3        0.3        0.7\n",
      " 0.62792969 0.7        0.6596875  0.50410156 0.56347656 0.3\n",
      " 0.3        0.51296875 0.62597656 0.4875     0.3        0.50078125\n",
      " 0.5        0.3       ]\n",
      "10 7.498389477980593 20.42064749089127 0.24\n",
      "3.4767011438734614\n",
      "\n",
      "[0.496875   0.4859375  0.3        0.67363281 0.7        0.7\n",
      " 0.3        0.6171875  0.66199219 0.65078125 0.60296875 0.623125\n",
      " 0.32975207 0.3        0.3        0.3        0.52914063 0.53613281\n",
      " 0.50830078 0.62548828 0.396875   0.6128125  0.3        0.7\n",
      " 0.69414062 0.53067188 0.62841797 0.3        0.6596875  0.3\n",
      " 0.653125   0.465625   0.56298828 0.4453125  0.68242187 0.31731771\n",
      " 0.67363281 0.50039062 0.3        0.53417969 0.50976562 0.3\n",
      " 0.63625    0.7        0.3        0.62548828 0.51148437 0.3\n",
      " 0.3        0.4       ]\n",
      "\n",
      "[0.48515625 0.67275391 0.4953125  0.64875    0.3        0.471875\n",
      " 0.60460938 0.3        0.3        0.3        0.66640625 0.7\n",
      " 0.3        0.7        0.7        0.52952344 0.3        0.3\n",
      " 0.3        0.6859375  0.6103125  0.3        0.4671875  0.3\n",
      " 0.7        0.3        0.67275391 0.3        0.6296875  0.62524414\n",
      " 0.65834375 0.51582031 0.3        0.7        0.7        0.68066406\n",
      " 0.3        0.50380859 0.5        0.3        0.3        0.56274414\n",
      " 0.49375    0.60953125 0.45       0.51222656 0.62524414 0.3\n",
      " 0.50019531 0.53369141]\n",
      "\n",
      "[0.3        0.623125   0.3        0.4734375  0.68546875 0.67231445\n",
      " 0.7        0.65117188 0.5        0.64453125 0.3        0.66476563\n",
      " 0.4421875  0.7        0.68115234 0.7        0.7        0.36330645\n",
      " 0.53105469 0.3984375  0.65767188 0.60390625 0.6938125  0.5\n",
      " 0.46796875 0.5        0.52894922 0.67978516 0.56262207 0.61796875\n",
      " 0.62512207 0.61609375 0.58847656 0.7        0.7        0.3\n",
      " 0.3        0.67231445 0.54710938 0.7        0.3        0.50366211\n",
      " 0.3        0.625625   0.3        0.3        0.34283854 0.62512207\n",
      " 0.53344727 0.50009766]\n",
      "\n",
      "[0.67209473 0.47265625 0.5        0.3        0.6103125  0.67790527\n",
      " 0.68523438 0.66394531 0.63085938 0.7        0.65097656 0.7\n",
      " 0.3        0.69071875 0.7        0.7        0.62506104 0.53009766\n",
      " 0.68740234 0.3        0.61773437 0.7        0.60070313 0.67172852\n",
      " 0.7        0.7        0.54636719 0.52866211 0.68764648 0.65733594\n",
      " 0.56268311 0.3        0.65820312 0.62506104 0.51259766 0.7\n",
      " 0.6793457  0.62817383 0.67209473 0.61210937 0.58751953 0.3\n",
      " 0.475      0.7        0.7        0.3        0.4        0.3\n",
      " 0.3        0.3671875 ]\n",
      "\n",
      "[0.60390625 0.68511719 0.48554688 0.7        0.47226563 0.68530273\n",
      " 0.67198486 0.40040323 0.66353516 0.44296875 0.7        0.62402344\n",
      " 0.65087891 0.52851855 0.7        0.7        0.39921875 0.3\n",
      " 0.3        0.52961914 0.6553125  0.46757812 0.3        0.68917187\n",
      " 0.6670166  0.7        0.60917969 0.62805176 0.3        0.3\n",
      " 0.61691406 0.62503052 0.7        0.51241211 0.62503052 0.7\n",
      " 0.50004883 0.67912598 0.3        0.67198486 0.54599609 0.58704102\n",
      " 0.65738281 0.496875   0.7        0.4625     0.3        0.3\n",
      " 0.5        0.5       ]\n",
      "\n",
      "[0.47207031 0.66685791 0.67192993 0.68505859 0.67335937 0.48535156\n",
      " 0.60070313 0.68425293 0.7        0.66333008 0.62744141 0.7\n",
      " 0.7        0.65083008 0.44257812 0.68146973 0.3        0.62501526\n",
      " 0.65750391 0.3        0.46777344 0.7        0.3        0.60230469\n",
      " 0.68839844 0.66466064 0.7        0.7        0.58728027 0.56265259\n",
      " 0.65697266 0.3        0.62501526 0.33830986 0.7        0.51231934\n",
      " 0.3        0.54618164 0.67901611 0.62799072 0.67192993 0.51025391\n",
      " 0.7        0.3        0.4        0.7        0.3        0.3\n",
      " 0.7        0.65251221]\n",
      "\n",
      "[0.3        0.68477783 0.59910156 0.66133423 0.48525391 0.3818892\n",
      " 0.60310547 0.6850293  0.44277344 0.34815574 0.7        0.3\n",
      " 0.7        0.66322754 0.65080566 0.67190247 0.5        0.65741992\n",
      " 0.67838135 0.7        0.5298584  0.3        0.3        0.62179688\n",
      " 0.67907104 0.68801172 0.66348267 0.7        0.7        0.58716064\n",
      " 0.7        0.62502289 0.62500763 0.7        0.50002441 0.3\n",
      " 0.7        0.53356934 0.62796021 0.54608887 0.60771484 0.67190247\n",
      " 0.56263733 0.45625    0.64       0.35       0.3        0.3\n",
      " 0.5        0.3       ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[0.68501465 0.60270508 0.3        0.68451538 0.65857239 0.3\n",
      " 0.3        0.66289368 0.3        0.68781836 0.3        0.65079346\n",
      " 0.62573242 0.7        0.66317627 0.65337891 0.7        0.67188873\n",
      " 0.62500381 0.65737793 0.47704016 0.52973877 0.7        0.7\n",
      " 0.61621094 0.4640625  0.5626297  0.67683716 0.68493125 0.7\n",
      " 0.58710083 0.7        0.46787109 0.50001221 0.65248657 0.62501907\n",
      " 0.53363037 0.51049805 0.3        0.3        0.62794495 0.60698242\n",
      " 0.67188873 0.65676758 0.7        0.7        0.3        0.51227295\n",
      " 0.459375   0.61      ]\n",
      "\n",
      "[0.65995331 0.66259918 0.47216797 0.60250488 0.68438416 0.68500732\n",
      " 0.68772168 0.3        0.67739688 0.7        0.5        0.44287109\n",
      " 0.66315063 0.40848633 0.62487793 0.65078735 0.3        0.65004883\n",
      " 0.48520508 0.67188187 0.3        0.67904358 0.61341797 0.3\n",
      " 0.62793732 0.67188187 0.7        0.54613525 0.63202148 0.67606506\n",
      " 0.62501717 0.65735693 0.7        0.62500191 0.53359985 0.50001831\n",
      " 0.65247375 0.7        0.60661621 0.51037598 0.60378906 0.3\n",
      " 0.375      0.56262589 0.65666504 0.595      0.7        0.7\n",
      " 0.51224976 0.3       ]\n",
      "\n",
      "[0.68431854 0.68767334 0.68500366 0.66245193 0.3        0.60240479\n",
      " 0.47211914 0.67362969 0.7        0.7        0.44291992 0.64838379\n",
      " 0.7        0.62445068 0.7        0.66313782 0.6507843  0.7\n",
      " 0.3        0.59990234 0.67187843 0.6279335  0.6503849  0.3\n",
      " 0.67187843 0.67902985 0.7        0.32525476 0.3        0.65661377\n",
      " 0.67567902 0.3        0.65734644 0.3        0.62500095 0.65246735\n",
      " 0.51031494 0.3        0.7        0.60283203 0.3        0.61765625\n",
      " 0.60643311 0.3        0.56262398 0.3        0.7        0.7\n",
      " 0.62501621 0.51223816]\n",
      "20 1.9480251864015585 13.269672359078708 0.06\n",
      "4.059203014053843\n",
      "\n",
      "[0.60235474 0.67174609 0.65926285 0.68764917 0.66237831 0.7\n",
      " 0.68428574 0.47209473 0.7        0.68500183 0.32866908 0.3\n",
      " 0.3        0.7        0.67187672 0.7        0.62423706 0.66313141\n",
      " 0.65078278 0.7        0.59950195 0.67187672 0.7        0.67902298\n",
      " 0.54611206 0.62793159 0.65658813 0.60634155 0.7        0.65830566\n",
      " 0.7        0.67548599 0.47490365 0.65734119 0.7        0.62500048\n",
      " 0.61132324 0.3        0.3        0.7        0.61632813 0.3\n",
      " 0.636      0.5        0.575      0.56262302 0.3        0.41071429\n",
      " 0.5        0.62501574]\n",
      "\n",
      "[0.6623415  0.3        0.68426933 0.7        0.60232971 0.68763708\n",
      " 0.7        0.3        0.6755825  0.65891762 0.68500092 0.62500024\n",
      " 0.64713501 0.44289551 0.7        0.62413025 0.7        0.65078201\n",
      " 0.6631282  0.48522949 0.7        0.67187586 0.59970215 0.62793064\n",
      " 0.3        0.7        0.3        0.67187586 0.6250155  0.3\n",
      " 0.51223236 0.7        0.50002136 0.7        0.65733856 0.67401123\n",
      " 0.3        0.60235352 0.7        0.67901955 0.5        0.3\n",
      " 0.7        0.60629578 0.3        0.3        0.56262255 0.3\n",
      " 0.7        0.7       ]\n",
      "\n",
      "[0.68763104 0.7        0.6023172  0.67268789 0.7        0.66232309\n",
      " 0.67553425 0.658745   0.62500012 0.68426113 0.67144775 0.65733725\n",
      " 0.61167236 0.64692688 0.3        0.7        0.6631266  0.7\n",
      " 0.62407684 0.65078163 0.48521729 0.7        0.67187629 0.59960205\n",
      " 0.47210693 0.68500046 0.52967896 0.56262231 0.65660095 0.7\n",
      " 0.3        0.50001984 0.3        0.65072632 0.3        0.68674927\n",
      " 0.7        0.7        0.7        0.61566406 0.67901783 0.62793016\n",
      " 0.54612366 0.67187543 0.60627289 0.7        0.3        0.5375\n",
      " 0.7        0.61325   ]\n",
      "\n",
      "[0.67221699 0.7        0.66231389 0.67551012 0.68762802 0.62500006\n",
      " 0.7        0.3        0.60231094 0.66487671 0.61184692 0.7\n",
      " 0.65733659 0.48522339 0.3        0.599552   0.7        0.62405014\n",
      " 0.7        0.6631258  0.65078182 0.64682281 0.7        0.67187607\n",
      " 0.3        0.6586587  0.68500023 0.7        0.7        0.7\n",
      " 0.50001907 0.51223526 0.65246414 0.6801239  0.63908386 0.67858887\n",
      " 0.60211426 0.61599609 0.7        0.62375    0.7        0.67901697\n",
      " 0.62792993 0.54611786 0.67187521 0.60626144 0.65659454 0.56262219\n",
      " 0.3        0.7       ]\n",
      "\n",
      "[0.7        0.67549806 0.68762651 0.7        0.67198154 0.66159119\n",
      " 0.66230929 0.60230782 0.61175964 0.62500003 0.68425703 0.63326263\n",
      " 0.7        0.3        0.5        0.48522034 0.64677078 0.7\n",
      " 0.7        0.7        0.62403679 0.6631254  0.65078173 0.47211304\n",
      " 0.67187597 0.54612076 0.65861554 0.68500011 0.51223381 0.7\n",
      " 0.65246254 0.68343658 0.3        0.6678833  0.7        0.65733627\n",
      " 0.61583008 0.628125   0.60199463 0.7        0.58375    0.6596875\n",
      " 0.67901654 0.62792981 0.7        0.67187511 0.60626717 0.65659134\n",
      " 0.56262213 0.5835    ]\n",
      "\n",
      "[0.7        0.52970886 0.67186382 0.62500004 0.7        0.67549202\n",
      " 0.65994843 0.68762576 0.66230699 0.60230625 0.6573361  0.61180328\n",
      " 0.63035202 0.3        0.6467968  0.7        0.48521881 0.47210999\n",
      " 0.7        0.62403011 0.7        0.65078168 0.6631252  0.7\n",
      " 0.65859396 0.67187591 0.68425498 0.65658974 0.68500006 0.51223454\n",
      " 0.68178024 0.65246174 0.7        0.7        0.66253052 0.7\n",
      " 0.6303125  0.63953125 0.61574707 0.307      0.579125   0.54611931\n",
      " 0.55625    0.67901633 0.62792975 0.3        0.67187505 0.7\n",
      " 0.3        0.3       ]\n",
      "\n",
      "[0.67548901 0.62500004 0.7        0.61178146 0.65912704 0.67180496\n",
      " 0.65733602 0.7        0.68762538 0.3        0.66230584 0.7\n",
      " 0.67901622 0.7        0.48521957 0.3        0.7        0.62889671\n",
      " 0.64678379 0.7        0.30990072 0.62402678 0.3        0.6631251\n",
      " 0.65078166 0.47210846 0.67187589 0.65860475 0.68425601 0.68500003\n",
      " 0.65985413 0.7        0.5122349  0.65246134 0.60193481 0.3\n",
      " 0.62945312 0.3        0.581875   0.3        0.546875   0.5620625\n",
      " 0.54675    0.3        0.575      0.62792972 0.3        0.67187503\n",
      " 0.7        0.56262216]\n",
      "\n",
      "[0.62500003 0.61177055 0.7        0.65871635 0.6754875  0.65733598\n",
      " 0.67177552 0.7        0.7        0.66230526 0.60230703 0.68762519\n",
      " 0.7        0.62816906 0.3        0.3        0.3171582  0.7\n",
      " 0.3        0.3        0.66312505 0.7        0.62402511 0.7\n",
      " 0.7        0.68425549 0.3        0.67187587 0.65859936 0.3\n",
      " 0.68500001 0.65851593 0.68095207 0.60190491 0.61570557 0.3\n",
      " 0.5809375  0.5421875  0.62921875 0.62441406 0.565125   0.7\n",
      " 0.4        0.7        0.67901617 0.54611858 0.6279297  0.60627003\n",
      " 0.67187501 0.65658894]\n",
      "\n",
      "[0.6117651  0.65851101 0.67548675 0.65733596 0.62500003 0.7\n",
      " 0.7        0.62780523 0.7        0.67176081 0.68762509 0.66230498\n",
      " 0.60230664 0.7        0.5        0.67901614 0.3        0.7\n",
      " 0.67187587 0.47210922 0.7        0.7        0.7        0.62402594\n",
      " 0.66312503 0.65078164 0.7        0.68425524 0.3        0.67500641\n",
      " 0.3        0.60188995 0.3        0.3        0.62867187 0.7\n",
      " 0.54453125 0.58046875 0.62189453 0.55353125 0.45       0.3\n",
      " 0.3        0.5375     0.54611822 0.65658854 0.7        0.62792969\n",
      " 0.6062686  0.67187501]\n",
      "\n",
      "[0.65840834 0.65733595 0.62500003 0.7        0.61176237 0.62762332\n",
      " 0.7        0.67548637 0.67901613 0.62792969 0.67175345 0.7\n",
      " 0.66230483 0.7        0.50286948 0.671875   0.47500078 0.5461184\n",
      " 0.7        0.64679029 0.4721096  0.7        0.3        0.7\n",
      " 0.3        0.66312501 0.65078164 0.7        0.67187586 0.68425511\n",
      " 0.60230645 0.68762505 0.7        0.61568481 0.3        0.60188248\n",
      " 0.3        0.54926562 0.3        0.58023438 0.3        0.5\n",
      " 0.55625    0.5559375  0.5        0.5        0.5        0.5\n",
      " 0.3        0.7       ]\n",
      "30 4.93503135168716 12.816056996977139 0.16\n",
      "3.96065930761828\n",
      "\n",
      "[0.65733594 0.7        0.61176101 0.62753236 0.3        0.7\n",
      " 0.67901612 0.658357   0.62792969 0.67548618 0.7        0.67174977\n",
      " 0.68762502 0.671875   0.7        0.54611849 0.67187586 0.68469699\n",
      " 0.7        0.7        0.64678704 0.47210941 0.7        0.65078164\n",
      " 0.7        0.62402552 0.66312501 0.60230635 0.7        0.65860206\n",
      " 0.68425504 0.66230476 0.7        0.7        0.6231543  0.3\n",
      " 0.54713281 0.3        0.55134375 0.3        0.565625   0.58011719\n",
      " 0.3        0.7        0.7        0.7        0.7        0.5\n",
      " 0.65658834 0.60626931]\n",
      "\n",
      "[0.3        0.62748688 0.65833133 0.7        0.7        0.61176033\n",
      " 0.62500003 0.67901612 0.671875   0.54611854 0.7        0.67548609\n",
      " 0.67174793 0.62792969 0.60626895 0.56262214 0.7        0.7\n",
      " 0.47210951 0.65860071 0.7        0.66217535 0.64678542 0.68425501\n",
      " 0.62402532 0.7        0.7        0.663125   0.65078164 0.7\n",
      " 0.67187586 0.6023063  0.66230472 0.68762501 0.7        0.7\n",
      " 0.54904688 0.475      0.54606641 0.54570312 0.62894531 0.60188622\n",
      " 0.3        0.58017578 0.3        0.3        0.3        0.3\n",
      " 0.3        0.7       ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[0.7        0.3        0.65733595 0.67901611 0.7        0.62792969\n",
      " 0.61175998 0.62500003 0.6583185  0.671875   0.67548604 0.7\n",
      " 0.3        0.54611856 0.56262214 0.60626878 0.3        0.65658844\n",
      " 0.7        0.3        0.32187802 0.7        0.65860138 0.6467846\n",
      " 0.7        0.7        0.7        0.62402521 0.663125   0.65078164\n",
      " 0.66230471 0.67187586 0.684255   0.60230628 0.68762501 0.61567444\n",
      " 0.7        0.55019531 0.3        0.4875     0.3        0.3\n",
      " 0.575      0.3        0.675      0.54511719 0.5609375  0.575\n",
      " 0.575      0.7       ]\n",
      "\n",
      "[0.62750962 0.7        0.7        0.62792969 0.65733594 0.67901611\n",
      " 0.671875   0.61175981 0.54611855 0.3        0.60626869 0.65831208\n",
      " 0.7        0.30378777 0.67548602 0.7        0.47210946 0.56262214\n",
      " 0.65658839 0.3        0.3        0.3        0.7        0.64528411\n",
      " 0.6467842  0.7        0.62402526 0.7        0.60230629 0.663125\n",
      " 0.7        0.65078164 0.687625   0.68425499 0.6623047  0.7\n",
      " 0.7        0.3        0.54482422 0.3        0.6125     0.62908203\n",
      " 0.6125     0.54659961 0.6125     0.55859375 0.3        0.7\n",
      " 0.5        0.5       ]\n",
      "\n",
      "[0.7        0.67901611 0.62749825 0.671875   0.62792969 0.7\n",
      " 0.54611854 0.65733594 0.3        0.60626873 0.62500003 0.56262214\n",
      " 0.7        0.67548603 0.67174839 0.65830887 0.3        0.7\n",
      " 0.7        0.5        0.68425498 0.7        0.64246891 0.7\n",
      " 0.7        0.64678399 0.3        0.3        0.7        0.7\n",
      " 0.663125   0.7        0.67187586 0.3        0.7        0.66230469\n",
      " 0.687625   0.3        0.55742187 0.55076953 0.59375    0.3\n",
      " 0.3        0.54467773 0.3        0.7        0.54633301 0.6625\n",
      " 0.5        0.5       ]\n",
      "\n",
      "[0.67901611 0.62792969 0.7        0.54611854 0.62749257 0.671875\n",
      " 0.60626871 0.7        0.65733594 0.61175973 0.56262214 0.7\n",
      " 0.37473958 0.62500003 0.3        0.7        0.65658836 0.65830727\n",
      " 0.7        0.68425498 0.7        0.3        0.7        0.3\n",
      " 0.7        0.6410613  0.64678389 0.7        0.62402524 0.7\n",
      " 0.65078164 0.663125   0.7        0.67187586 0.7        0.687625\n",
      " 0.66230469 0.67174816 0.7        0.55683594 0.65625    0.54460449\n",
      " 0.7        0.636875   0.7        0.55048242 0.59375    0.3\n",
      " 0.7        0.625     ]\n",
      "\n",
      "[0.3        0.671875   0.62792969 0.3        0.3        0.6062687\n",
      " 0.56262214 0.7        0.7        0.65733594 0.7        0.65658835\n",
      " 0.67548602 0.65830647 0.62500003 0.61175969 0.7        0.7\n",
      " 0.7        0.51223508 0.7        0.7        0.47210948 0.52969391\n",
      " 0.6403575  0.7        0.7        0.65078164 0.7        0.3\n",
      " 0.62402522 0.64678384 0.663125   0.7        0.67187586 0.68425498\n",
      " 0.60230628 0.66230469 0.687625   0.67174828 0.7        0.7\n",
      " 0.653125   0.3        0.5        0.3        0.54456787 0.6346875\n",
      " 0.584375   0.584375  ]\n",
      "\n",
      "[0.62792969 0.69114149 0.67901611 0.60626869 0.671875   0.56262214\n",
      " 0.62749541 0.7        0.7        0.7        0.7        0.7\n",
      " 0.62500003 0.65733594 0.65830607 0.3        0.7        0.51223517\n",
      " 0.66250961 0.65658834 0.65246114 0.68425498 0.47499896 0.7\n",
      " 0.60230628 0.7        0.7        0.64678382 0.6400056  0.62402522\n",
      " 0.7        0.7        0.65078164 0.663125   0.7        0.67187586\n",
      " 0.47210947 0.687625   0.66230469 0.7        0.67174822 0.67548602\n",
      " 0.7        0.5796875  0.5625     0.63359375 0.55062598 0.3\n",
      " 0.6515625  0.5796875 ]\n",
      "\n",
      "[0.671875   0.60626869 0.3        0.3        0.67901611 0.7\n",
      " 0.7        0.56262214 0.62749399 0.7        0.3        0.7\n",
      " 0.65830627 0.61175971 0.65733594 0.62500003 0.7        0.3\n",
      " 0.65246104 0.65626122 0.65658834 0.68053799 0.68425498 0.7\n",
      " 0.7        0.3        0.63982965 0.7        0.6467838  0.67187586\n",
      " 0.7        0.7        0.62402521 0.65078164 0.663125   0.7\n",
      " 0.7        0.60230628 0.67174819 0.66230469 0.687625   0.7\n",
      " 0.67548602 0.7        0.7        0.57734375 0.3        0.55654297\n",
      " 0.57734375 0.47578125]\n",
      "\n",
      "[0.68671223 0.7        0.3        0.56262214 0.60626869 0.7\n",
      " 0.65658834 0.671875   0.3        0.67901611 0.7        0.67928231\n",
      " 0.3        0.7        0.3        0.65733594 0.7        0.7\n",
      " 0.68033094 0.65246099 0.65313702 0.7        0.52970139 0.30297644\n",
      " 0.68425498 0.60230628 0.3        0.63974168 0.7        0.6467838\n",
      " 0.47210947 0.62402521 0.7        0.7        0.65078164 0.663125\n",
      " 0.7        0.67187586 0.7        0.687625   0.66230469 0.67174818\n",
      " 0.7        0.67548602 0.7        0.62500003 0.63332031 0.57617188\n",
      " 0.3        0.65078125]\n",
      "40 4.884702250486203 10.353467569665465 0.14\n",
      "4.216603500942502\n",
      "\n",
      "[0.60626869 0.56262214 0.5        0.7        0.68449761 0.65658834\n",
      " 0.7        0.7        0.3        0.3        0.67901611 0.65157492\n",
      " 0.7        0.66892346 0.3        0.7        0.6117597  0.7\n",
      " 0.65830617 0.68043447 0.7        0.65246096 0.7        0.3\n",
      " 0.60188808 0.61566925 0.47210947 0.7        0.66230469 0.7\n",
      " 0.6467838  0.63969769 0.7        0.7        0.62402521 0.65078164\n",
      " 0.663125   0.7        0.67187586 0.7        0.68425498 0.60230628\n",
      " 0.687625   0.67174817 0.7        0.7        0.7        0.67548602\n",
      " 0.62500003 0.3       ]\n",
      "\n",
      "[0.7        0.3        0.671875   0.7        0.65658834 0.68339029\n",
      " 0.7        0.60626869 0.7        0.7        0.7        0.67901611\n",
      " 0.66374404 0.65079387 0.61175969 0.7        0.65733594 0.7\n",
      " 0.3        0.7        0.7        0.60188715 0.65246095 0.61566666\n",
      " 0.52969765 0.62901367 0.3        0.66230469 0.7        0.3\n",
      " 0.6396757  0.7        0.6467838  0.62402521 0.7        0.7\n",
      " 0.65078164 0.663125   0.7        0.67187586 0.60230628 0.68425498\n",
      " 0.67174817 0.687625   0.7        0.7        0.7        0.62500003\n",
      " 0.67548602 0.65830612]\n",
      "\n",
      "[0.56262214 0.7        0.68283664 0.65658834 0.7        0.7\n",
      " 0.7        0.7        0.60626869 0.66115433 0.7        0.671875\n",
      " 0.65040334 0.67901611 0.3        0.65246096 0.7        0.6803827\n",
      " 0.7        0.7        0.60188762 0.61566536 0.7        0.62897949\n",
      " 0.54454956 0.52969578 0.3        0.47210947 0.687625   0.3\n",
      " 0.7        0.7        0.6396647  0.7        0.7        0.7\n",
      " 0.62402521 0.65078164 0.663125   0.7        0.67187586 0.66230469\n",
      " 0.60230628 0.7        0.67174816 0.7        0.67548602 0.7\n",
      " 0.65830609 0.62500003]\n",
      "\n",
      "[0.7        0.65658834 0.60626869 0.7        0.56262214 0.7\n",
      " 0.7        0.68255981 0.65985947 0.65020808 0.7        0.65246095\n",
      " 0.671875   0.68035682 0.7        0.7        0.3035     0.61175969\n",
      " 0.67901611 0.60188785 0.61566601 0.7        0.6289624  0.7\n",
      " 0.62252441 0.54454041 0.60230628 0.3        0.7        0.6396592\n",
      " 0.7        0.7        0.7        0.6467838  0.68425498 0.62402521\n",
      " 0.7        0.7        0.65078164 0.663125   0.7        0.67187586\n",
      " 0.66230469 0.7        0.687625   0.67174816 0.62500003 0.65830608\n",
      " 0.7        0.67548602]\n",
      "\n",
      "[0.65658834 0.7        0.7        0.7        0.7        0.65921205\n",
      " 0.65011045 0.65246095 0.3        0.30030496 0.671875   0.7\n",
      " 0.56262214 0.7        0.7        0.68034388 0.67901611 0.7\n",
      " 0.61175969 0.7        0.3        0.3        0.54454498 0.62283936\n",
      " 0.62895386 0.58020508 0.3        0.687625   0.47210947 0.3\n",
      " 0.7        0.68425498 0.7        0.63965645 0.6467838  0.7\n",
      " 0.7        0.7        0.62402521 0.65078164 0.663125   0.7\n",
      " 0.7        0.66230469 0.67548602 0.65830607 0.67174816 0.7\n",
      " 0.65733594 0.7       ]\n",
      "\n",
      "[0.3        0.7        0.56262214 0.65888833 0.7        0.65006163\n",
      " 0.65246095 0.68033741 0.7        0.7        0.68235219 0.60626869\n",
      " 0.7        0.7        0.7        0.7        0.7        0.67901611\n",
      " 0.671875   0.61175969 0.54454727 0.3        0.61566568 0.3\n",
      " 0.58021973 0.54619971 0.687625   0.52969484 0.62894958 0.7\n",
      " 0.3        0.7        0.3        0.66230469 0.3        0.63965508\n",
      " 0.67187586 0.62402521 0.7        0.7        0.65078164 0.663125\n",
      " 0.7        0.7        0.68425498 0.60230628 0.7        0.67174816\n",
      " 0.7        0.65733594]\n",
      "\n",
      "[0.7        0.65872648 0.3        0.65003723 0.7        0.65246095\n",
      " 0.3        0.7        0.68033418 0.7        0.3        0.68231758\n",
      " 0.7        0.7        0.67901611 0.7        0.671875   0.60188797\n",
      " 0.7        0.61566552 0.7        0.54454613 0.62299683 0.5802124\n",
      " 0.54613306 0.55069775 0.62894745 0.3        0.63345703 0.47210947\n",
      " 0.3        0.67174816 0.7        0.7        0.63965439 0.6467838\n",
      " 0.68425498 0.7        0.7        0.7        0.62402521 0.65078164\n",
      " 0.663125   0.7        0.67187586 0.66230469 0.60230628 0.687625\n",
      " 0.7        0.7       ]\n",
      "\n",
      "[0.7        0.65002502 0.7        0.65246095 0.65864555 0.68033256\n",
      " 0.7        0.65658834 0.56262214 0.7        0.7        0.7\n",
      " 0.68230028 0.60626869 0.7        0.60188791 0.61566544 0.671875\n",
      " 0.7        0.7        0.67901611 0.3        0.58020874 0.54616638\n",
      " 0.3        0.63352539 0.55066187 0.62894638 0.52969531 0.3\n",
      " 0.687625   0.7        0.60230628 0.7        0.7        0.3\n",
      " 0.63965405 0.7        0.3        0.62402521 0.7        0.7\n",
      " 0.67187586 0.663125   0.7        0.68425498 0.66230469 0.3\n",
      " 0.7        0.61175969]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[0.65860508 0.65246095 0.65658834 0.68033175 0.65001892 0.7\n",
      " 0.7        0.7        0.7        0.56262214 0.7        0.7\n",
      " 0.60626869 0.60188788 0.54421387 0.30001913 0.5445467  0.6156654\n",
      " 0.62894585 0.67901611 0.4000494  0.62291809 0.671875   0.55064392\n",
      " 0.3        0.3        0.63349121 0.55639648 0.3        0.5\n",
      " 0.3        0.7        0.67174816 0.7        0.7        0.7\n",
      " 0.6467838  0.63965387 0.7        0.68425498 0.7        0.7\n",
      " 0.62402521 0.65078164 0.663125   0.7        0.67187586 0.60230628\n",
      " 0.66230469 0.687625  ]\n",
      "\n",
      "[0.65001587 0.68033135 0.7        0.7        0.65246095 0.7\n",
      " 0.65858485 0.7        0.65658834 0.54454641 0.3        0.60188787\n",
      " 0.3        0.7        0.671875   0.3        0.7        0.3\n",
      " 0.62287872 0.3        0.7        0.62894558 0.54614972 0.3\n",
      " 0.63347412 0.55632324 0.58020691 0.57558594 0.57851562 0.60230628\n",
      " 0.67174816 0.7        0.7        0.7        0.67548602 0.3\n",
      " 0.7        0.6467838  0.63965379 0.7        0.7        0.62402521\n",
      " 0.7        0.7        0.65078164 0.663125   0.7        0.68425498\n",
      " 0.687625   0.66230469]\n",
      "50 3.434916596215502 9.427883378955705 0.1\n",
      "4.2251857302374995\n",
      "\n",
      "[0.65246095 0.7        0.7        0.54454627 0.68033115 0.60188786\n",
      " 0.61566542 0.65857473 0.3        0.65658834 0.65001434 0.3\n",
      " 0.7        0.62894545 0.68229596 0.62285904 0.60626869 0.7\n",
      " 0.7        0.5        0.671875   0.58020599 0.3        0.7\n",
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      " 0.7        0.33007813 0.66523832 0.67174816 0.60230628 0.7\n",
      " 0.7        0.7        0.6467838  0.63965374 0.7        0.687625\n",
      " 0.3        0.62402521 0.7        0.3        0.3        0.7\n",
      " 0.65078164 0.68425498]\n",
      "\n",
      "[0.68033105 0.5445462  0.65856968 0.7        0.7        0.61566541\n",
      " 0.60188785 0.65001358 0.65246095 0.7        0.65658834 0.62894538\n",
      " 0.7        0.56262214 0.7        0.58020645 0.68229379 0.60626869\n",
      " 0.7        0.671875   0.7        0.54615805 0.7        0.6334613\n",
      " 0.3        0.6228492  0.55635986 0.57792969 0.57514648 0.687625\n",
      " 0.7        0.3        0.3        0.65830607 0.67174816 0.60230628\n",
      " 0.7        0.7        0.7        0.6467838  0.63965372 0.7\n",
      " 0.7        0.7        0.62402521 0.67187586 0.663125   0.65078164\n",
      " 0.7        0.7       ]\n",
      "\n",
      "[0.7        0.7        0.3        0.60188786 0.54454616 0.62894535\n",
      " 0.68033099 0.61566541 0.6500132  0.65246095 0.3        0.62284428\n",
      " 0.65658834 0.7        0.3        0.54615388 0.7        0.30002166\n",
      " 0.60626869 0.7        0.58020622 0.7        0.55065738 0.671875\n",
      " 0.55637817 0.57521973 0.57763672 0.65019531 0.3        0.67174816\n",
      " 0.65830607 0.52969554 0.3        0.67548602 0.7        0.61175969\n",
      " 0.3        0.68425498 0.60230628 0.7        0.6467838  0.63965371\n",
      " 0.65078164 0.3        0.7        0.7        0.7        0.663125\n",
      " 0.67187586 0.7       ]\n",
      "\n",
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      " 0.62894533 0.58020611 0.5461518  0.68033097 0.65857221 0.7\n",
      " 0.65246095 0.65658834 0.3        0.7        0.3        0.55065514\n",
      " 0.68229217 0.60626869 0.7        0.7        0.7        0.3\n",
      " 0.57518311 0.57749023 0.3        0.7        0.7        0.7\n",
      " 0.52969543 0.65830607 0.67548602 0.7        0.61175969 0.67174816\n",
      " 0.62500003 0.3        0.7        0.60230628 0.7        0.6467838\n",
      " 0.63965371 0.67187586 0.7        0.7        0.62402521 0.7\n",
      " 0.663125   0.65078164]\n",
      "\n",
      "[0.7        0.6156654  0.65246095 0.62894532 0.60188785 0.54454614\n",
      " 0.62284059 0.3        0.55065401 0.7        0.68033096 0.54615076\n",
      " 0.63346344 0.7        0.7        0.65658834 0.6938355  0.3\n",
      " 0.3        0.6822919  0.60626869 0.65001291 0.7        0.7\n",
      " 0.57741699 0.65009766 0.7        0.7        0.55636902 0.52969537\n",
      " 0.57516479 0.5        0.7        0.3        0.7        0.67548602\n",
      " 0.67174816 0.7        0.68425498 0.3        0.7        0.7\n",
      " 0.6467838  0.6396537  0.60230628 0.62402521 0.7        0.67187586\n",
      " 0.7        0.663125  ]\n",
      "\n",
      "[0.60188785 0.3        0.68033095 0.62283997 0.39946289 0.58020617\n",
      " 0.54454613 0.62894532 0.63346451 0.54615024 0.65246095 0.55065345\n",
      " 0.7        0.55636444 0.65658834 0.7        0.7        0.3\n",
      " 0.57515564 0.7        0.68229176 0.60626869 0.7        0.7\n",
      " 0.65001287 0.7        0.65004883 0.3        0.53125    0.3\n",
      " 0.57738037 0.7        0.7        0.7        0.3        0.7\n",
      " 0.67548602 0.3        0.7        0.7        0.62500003 0.7\n",
      " 0.7        0.6467838  0.6396537  0.65078164 0.7        0.7\n",
      " 0.62402521 0.67187586]\n",
      "\n",
      "[0.6156654  0.62894531 0.5296954  0.58020619 0.62283966 0.54614998\n",
      " 0.3        0.7        0.54454613 0.55065373 0.7        0.68033095\n",
      " 0.3        0.63346397 0.7        0.7        0.65001284 0.55636673\n",
      " 0.6938355  0.7        0.7        0.6822917  0.60626869 0.65658834\n",
      " 0.7        0.4        0.7        0.546875   0.3        0.57739868\n",
      " 0.65002441 0.7        0.7        0.3        0.5        0.7\n",
      " 0.65733594 0.7        0.67548602 0.62500003 0.7        0.7\n",
      " 0.3        0.7        0.3        0.6396537  0.65078164 0.62402521\n",
      " 0.7        0.7       ]\n",
      "\n",
      "[0.62894531 0.62283951 0.7        0.54614985 0.6156654  0.3\n",
      " 0.3        0.54454613 0.7        0.63346424 0.55065359 0.55636559\n",
      " 0.5        0.57516022 0.7        0.65001283 0.68033095 0.3\n",
      " 0.57740784 0.6938355  0.7        0.65658834 0.68229166 0.60626869\n",
      " 0.7        0.7        0.45       0.7        0.7        0.65001221\n",
      " 0.7        0.5390625  0.52969538 0.7        0.7        0.3\n",
      " 0.3        0.7        0.7        0.67548602 0.7        0.62500003\n",
      " 0.7        0.68425498 0.7        0.6467838  0.6396537  0.7\n",
      " 0.3        0.7       ]\n",
      "\n",
      "[0.62283943 0.58020618 0.54454613 0.55065352 0.3        0.63346411\n",
      " 0.54614978 0.7        0.62894531 0.7        0.55636616 0.57515793\n",
      " 0.68033095 0.7        0.7        0.7        0.57740326 0.65001282\n",
      " 0.6500061  0.7        0.6938355  0.7        0.65658834 0.68229165\n",
      " 0.60626869 0.7        0.3        0.6        0.3        0.7\n",
      " 0.7        0.5        0.7        0.52969538 0.5        0.7\n",
      " 0.7        0.67548602 0.62500003 0.7        0.7        0.65733594\n",
      " 0.7        0.7        0.6467838  0.7        0.3        0.66230469\n",
      " 0.3        0.62402521]\n",
      "\n",
      "[0.58020619 0.54614982 0.3        0.63346404 0.5        0.55065349\n",
      " 0.55636587 0.62283939 0.7        0.62894531 0.7        0.3\n",
      " 0.57740555 0.39180666 0.65001282 0.7        0.3        0.7\n",
      " 0.7        0.7        0.65000916 0.6938355  0.7        0.3\n",
      " 0.65658834 0.60626869 0.7        0.7        0.7        0.7\n",
      " 0.7        0.55       0.53515625 0.3        0.5        0.3\n",
      " 0.7        0.62500003 0.65733594 0.7        0.7        0.7\n",
      " 0.68425498 0.3        0.7        0.687625   0.7        0.6467838\n",
      " 0.6396537  0.60230628]\n",
      "60 5.576131885621159 17.453266594174217 0.16\n",
      "4.070267360383651\n",
      "\n",
      "[0.3        0.55065347 0.7        0.55636601 0.62894531 0.7\n",
      " 0.3        0.3        0.7        0.7        0.62283937 0.63346401\n",
      " 0.6575     0.5774044  0.3        0.65000763 0.7        0.7\n",
      " 0.7        0.51000372 0.68033095 0.7        0.6938355  0.3\n",
      " 0.7        0.65658834 0.7        0.3        0.525      0.53710938\n",
      " 0.6        0.7        0.3        0.7        0.52969538 0.5\n",
      " 0.7        0.7        0.7        0.65733594 0.30150856 0.7\n",
      " 0.3        0.3        0.66230469 0.7        0.6467838  0.7\n",
      " 0.68425498 0.6396537 ]\n",
      "\n",
      "[0.5461498  0.3        0.7        0.3        0.55065346 0.63625\n",
      " 0.63346399 0.7        0.62283937 0.7        0.54454613 0.57740498\n",
      " 0.7        0.65000687 0.7        0.62894531 0.7        0.7\n",
      " 0.7        0.53613281 0.7        0.7        0.7        0.6938355\n",
      " 0.7        0.65001282 0.68033095 0.7        0.55       0.5125\n",
      " 0.4        0.4        0.3        0.5        0.3        0.5\n",
      " 0.3        0.65733594 0.7        0.7        0.67548602 0.7\n",
      " 0.62500003 0.60230628 0.7        0.7        0.7        0.6396537\n",
      " 0.7        0.6467838 ]\n",
      "\n",
      "[0.55065346 0.63346398 0.7        0.646875   0.58020619 0.55636609\n",
      " 0.7        0.54614979 0.57740469 0.62283936 0.3        0.65000648\n",
      " 0.7        0.7        0.68033095 0.7        0.7        0.7\n",
      " 0.53662109 0.62894531 0.7        0.7        0.65001282 0.7\n",
      " 0.6938355  0.7        0.7        0.3        0.45       0.525\n",
      " 0.50625    0.4        0.3        0.3        0.5        0.52969538\n",
      " 0.5        0.3        0.7        0.7        0.7        0.61175969\n",
      " 0.7        0.3        0.62500003 0.3        0.68425498 0.7\n",
      " 0.6467838  0.7       ]\n",
      "\n",
      "[0.63346398 0.55636605 0.62894531 0.7        0.54614979 0.3\n",
      " 0.58020619 0.55065346 0.65000629 0.57740455 0.7        0.54454613\n",
      " 0.7        0.62283936 0.7        0.7        0.7        0.53686523\n",
      " 0.7        0.7        0.509375   0.5125     0.7        0.7\n",
      " 0.7        0.6938355  0.65001282 0.7        0.68033095 0.45\n",
      " 0.475      0.3        0.3        0.3        0.7        0.3\n",
      " 0.52969538 0.7        0.61175969 0.7        0.7        0.5\n",
      " 0.65733594 0.7        0.30001961 0.67548602 0.687625   0.7\n",
      " 0.3        0.7       ]\n"
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    {
     "name": "stdout",
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      "[0.55636607 0.6415625  0.3        0.57740448 0.63346398 0.6500062\n",
      " 0.55065345 0.7        0.58020619 0.7        0.7        0.7\n",
      " 0.54454613 0.54614979 0.7        0.53674316 0.7        0.62283936\n",
      " 0.7        0.5109375  0.50625    0.475      0.3875     0.7\n",
      " 0.68033095 0.7        0.7        0.65001282 0.7        0.4875\n",
      " 0.45       0.4        0.4        0.4        0.7        0.6\n",
      " 0.5        0.7        0.52969538 0.61175969 0.65733594 0.7\n",
      " 0.7        0.62500003 0.7        0.7        0.7        0.68229165\n",
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      " 0.7        0.63346398 0.7        0.58020619 0.62894531 0.7\n",
      " 0.3        0.55065345 0.7        0.3        0.54614979 0.7\n",
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      " 0.62894531 0.54454613 0.7        0.63346397 0.62283936 0.51210937\n",
      " 0.7        0.3        0.3        0.3        0.545      0.7\n",
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      " 0.475      0.3        0.35       0.55       0.5        0.4\n",
      " 0.3        0.52969538 0.5        0.3        0.61175969 0.625\n",
      " 0.7        0.7        0.65733594 0.7        0.7        0.7\n",
      " 0.60230628 0.67174816]\n",
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      "  0.62283936  0.7         0.54454613  0.55065345  0.62894531  0.58020619\n",
      " -8.88435385  0.40500001  0.496875    0.5275      0.46875     0.68033095\n",
      "  0.7         0.7         0.7         0.7         0.54614979  0.4875\n",
      "  0.375       0.525       0.575       0.7         0.64640625  0.4\n",
      "  0.3         0.50890625  0.63346397  0.7         0.52969538  0.5109375\n",
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      "  0.7         0.7       ]\n",
      "\n",
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      "  0.3         0.65453094  0.7         0.63859344 -8.28038144  0.51171875\n",
      "  0.55065345  0.3         0.3         0.7         0.51181641  0.62894531\n",
      " -8.88435385  0.62283936  0.3         0.3         0.7         0.3\n",
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      "  0.61175969  0.3         0.7         0.7         0.7         0.7\n",
      "  0.7         0.7       ]\n",
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      "  0.64227158  0.55636606  0.3         0.51176758 -8.28038144  0.48714912\n",
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      "  0.7         0.68033095  0.7         0.7         0.58020619  0.7\n",
      "  0.51875     0.58480469  0.7         0.62894531  0.475       0.4\n",
      "  0.3         0.63923828 -6.39564484  0.39375     0.53625     0.3\n",
      "  0.52969538  0.7         0.61175969  0.7         0.7         0.7\n",
      "  0.7         0.7       ]\n",
      "70 8.859006047630206 43.99355627321616 0.26\n",
      "3.818109099606484\n",
      "\n",
      "[ 0.7         0.65980469  0.55065345  0.62263579  0.3         0.51179199\n",
      "  0.6772377   0.63907227  0.55636606  0.65000611 -8.28038144  0.46484375\n",
      "  0.54614979  0.49765625  0.3         0.67522469  0.63346397  0.7\n",
      " -8.88435385  0.3         0.3         0.3         0.51113281  0.4625\n",
      "  0.531875    0.3         0.7         0.7         0.51000318  0.7\n",
      "  0.55625     0.7         0.7         0.55400391  0.3         0.62894531\n",
      "  0.3         0.4953125  -6.39564484  0.3         0.595      -6.33418121\n",
      "  0.3         0.7         0.515625    0.7         0.7         0.7\n",
      "  0.7         0.7       ]\n",
      "\n",
      "[ 0.65310547  0.67647896  0.3         0.51177979  0.6500061   0.60883425\n",
      "  0.3         0.51123047  0.63898926  0.55636606 -8.28038144  0.7\n",
      "  0.3         0.46523437  0.3         0.7         0.49804688  0.66908777\n",
      " -8.88435385  0.3         0.63346397  0.49453125  0.5875      0.5296875\n",
      "  0.5140625   0.7         0.62283936  0.7         0.55281635  0.53860352\n",
      "  0.3         0.7         0.62894531  0.61939833  0.58020619  0.54614979\n",
      "  0.54503271  0.57740445 -6.39564484  0.45        0.7        -6.33418121\n",
      "  0.3         0.7         0.46875     0.67672698  0.7         0.65733594\n",
      "  0.7         0.7       ]\n",
      "\n",
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      "  0.3         0.57740445  0.3         0.64975586 -8.28038144  0.3\n",
      "  0.3         0.3         0.7         0.52859375  0.3         0.3\n",
      " -8.88435385  0.7         0.62894531  0.6500061   0.7         0.3\n",
      "  0.52459962  0.7         0.7         0.58020619  0.7         0.55140818\n",
      "  0.471875    0.475       0.7         0.3         0.7         0.62283936\n",
      "  0.49414062  0.3        -6.39564484  0.7         0.51177368 -6.33418121\n",
      "  0.58375     0.3         0.7         0.43887111  0.68836349  0.51328125\n",
      "  0.7         0.7       ]\n",
      "\n",
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      "   0.49785156   0.3          0.6759099    0.7          0.63903076\n",
      "  -8.28038144   0.3          0.3          0.62586563   0.62894531\n",
      "   0.585625     0.3          0.3         -8.88435385   0.47619048\n",
      "   0.7          0.7          0.55636606   0.49394531   0.55070409\n",
      "   0.3          0.52804688   0.62283936   0.7          0.7\n",
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      "   0.3         -6.33418121   0.4875     -10.8223576    0.52390137\n",
      "   0.3          0.62219917   0.68539338   0.7          0.7       ]\n",
      "\n",
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      "  0.57740445  0.46533203  0.49794922  0.52777344 -8.28038144  0.63901001\n",
      "  0.55636606  0.6119302   0.3         0.49384766  0.7         0.3\n",
      " -8.88435385  0.5         0.3         0.69272871  0.6500061   0.7\n",
      "  0.5846875   0.3         0.7         0.7         0.5242505   0.58020619\n",
      "  0.7         0.62283936  0.3         0.3         0.62359958  0.3\n",
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      "  0.3         0.42783944]\n",
      "\n",
      "[  0.51119385   0.46538086   0.3          0.49790039   0.7\n",
      "   0.52791016   0.3          0.51177444   0.3          0.52407593\n",
      "  -8.28038144   0.58020619   0.7          0.3          0.3\n",
      "   0.3          0.65000305   0.69115242  -8.81536539   0.41780885\n",
      "   0.48779865   0.63899963   0.56651138   0.3          0.7\n",
      "   0.3          0.6690625    0.68545742   0.62283936   0.7\n",
      "   0.7          0.36426536   0.7        -32.82751291   0.7\n",
      "   0.58421875   0.67576764   0.7         -6.39564484   0.3\n",
      "   0.47619048  -6.33418121   0.55035204   0.7          0.3\n",
      "   0.67443842   0.3          0.49375      0.62289937   0.7       ]\n",
      "\n",
      "[  0.3          0.4979248    0.3          0.46535645   0.67261259\n",
      "   0.58398438   0.7          0.5278418    0.3          0.49399414\n",
      "  -8.28038144   0.67574393   0.7          0.58020619   0.3\n",
      "   0.55636606   0.63899445   0.7         -8.88435385   0.5\n",
      "   0.68672864   0.7          0.7          0.3          0.7\n",
      "   0.7          0.55052807   0.66390625   0.68545742   0.7\n",
      "   0.3          0.7          0.62283936 -32.82751291   0.7\n",
      "   0.7          0.47265625   0.6500061   -6.39564484   0.52398865\n",
      "   0.45454545  -6.33418121   0.7          0.33796296   0.62254927\n",
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      "\n",
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      "   0.51119995   0.3          0.52403229   0.3          0.7\n",
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      "   0.68545742   0.7          0.7        -86.34478026   0.47226563\n",
      "   0.42081307   0.7          0.68451674   0.66132812   0.7\n",
      "   0.62237422   0.7          0.3        -32.82751291   0.3\n",
      "   0.55044006   0.65000153   0.55636606  -6.39564484   0.57740445\n",
      "   0.7         -6.2741957    0.3          0.7          0.7\n",
      "   0.3          0.67169968   0.49406738   0.52132353   0.63899185]\n"
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    {
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      "\n",
      "[   0.7           0.52779053 -294.53150064    0.3          -5.43399865\n",
      "    0.3           0.3           0.49403076    0.52401047    0.45539793\n",
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      "    0.7           0.55636606    0.7          -6.39564484    0.55039605\n",
      " -134.51760472   -6.27042391    0.45407767 -123.67906223    0.51177483\n",
      "    0.3           0.63899055    0.7           0.67124322    0.3       ]\n",
      "\n",
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      "    0.49404907  -18.4400263     0.62224293    0.7           0.66326172\n",
      "   -8.28038144    0.7           0.65000076    0.6389912     0.68266824\n",
      "    0.57740445    0.55636606    0.7           0.3           0.54285162\n",
      "    0.7           0.7           0.7           0.3           0.7\n",
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      "    0.58020619    0.7           0.7         -32.82751291    0.51054688\n",
      "    0.68545742    0.7           0.7          -6.39564484    0.7\n",
      " -134.51760472   -6.27042391    0.46536255    0.5           0.3\n",
      "  -24.23488627    0.511203      0.55037405    0.56644147    0.67101499]\n",
      "80 16.49914553412747 47.40062161915179 0.44\n",
      "3.1908752286366493\n",
      "\n",
      "[   0.3           0.52399411 -294.53150064    0.35127152   -5.43399865\n",
      "    0.7         -18.4400263     0.67090088    0.3           0.3\n",
      "   -8.28038144    0.3           0.7           0.7           0.68545742\n",
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      "    0.5           0.7           0.3           0.65242188    0.3\n",
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      " -134.51760472   -6.27042391    0.7           0.5           0.51120148\n",
      "  -24.23488627    0.51177502    0.7           0.4653656     0.55036305]\n",
      "\n",
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      "  3.00000000e-01  3.25718349e-01  3.00000000e-01  3.00000000e-01\n",
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      "  4.94039917e-01 -2.42348863e+01  7.00000000e-01  7.00000000e-01\n",
      "  3.00000000e-01  5.11200714e-01]\n",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "140 33.12783421667042 29.11703530633713 0.86\n",
      "0.29639458576484984\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "170 36.37701543967362 22.596316252614937 0.94\n",
      "0.1763084469887084\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "\n",
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      " -4.59635631e+06 -7.17318755e+05]\n",
      "180 38.643064948420204 20.086976024364727 1.0\n",
      "0.021722861567363184\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "190 38.643064948420204 19.39591748574781 1.0\n",
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      "200 38.643064948420204 19.39591748574781 1.0\n",
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      "\n",
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      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "210 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "220 38.643064948420204 19.39591748574781 1.0\n",
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      "230 38.643064948420204 19.39591748574781 1.0\n",
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      "\n",
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      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "240 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "\n",
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      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "250 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "260 38.643064948420204 19.39591748574781 1.0\n",
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      "270 38.643064948420204 19.39591748574781 1.0\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
      "[-2.39851423e+03 -1.03336686e+08 -7.73781354e+03 -1.50222016e+03\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "280 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "\n",
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      "\n",
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      "290 38.643064948420204 19.39591748574781 1.0\n",
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      "300 38.643064948420204 19.39591748574781 1.0\n",
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      "\n",
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      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "310 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "\n",
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      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "320 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "330 38.643064948420204 19.39591748574781 1.0\n",
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      "340 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "350 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "\n",
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      "\n",
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      "360 38.643064948420204 19.39591748574781 1.0\n",
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      "370 38.643064948420204 19.39591748574781 1.0\n",
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      "380 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
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     "name": "stdout",
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     "text": [
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      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "390 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "400 38.643064948420204 19.39591748574781 1.0\n",
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      "410 38.643064948420204 19.39591748574781 1.0\n",
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      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "\n",
      "[-2.39851423e+03 -1.03336686e+08 -7.73781354e+03 -1.50222016e+03\n",
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      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "\n",
      "[-2.39851423e+03 -1.03336686e+08 -7.73781354e+03 -1.50222016e+03\n",
      " -3.87390554e+03 -9.02091970e+07 -8.31971792e+07 -1.22767805e+08\n",
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      " -6.74402146e+03 -8.55060163e+07 -9.73790825e+07 -8.82411407e+02\n",
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      " -3.44998646e+01 -4.09660247e+05 -9.17033795e+07 -1.90366921e+02\n",
      " -8.99643868e+02 -1.22119860e+08 -9.86626102e+07 -9.99215650e+07\n",
      " -6.02859209e+03 -1.41308718e+03 -1.06167927e+08 -4.05436472e+03\n",
      " -8.36698465e+07 -1.47184518e+05 -2.83691006e+03 -1.30532329e+08\n",
      " -1.19464393e+08 -1.30710706e+03 -1.17096550e+08 -1.11957983e+08\n",
      " -2.50190471e+04 -3.90976700e+03 -3.23722467e+03 -6.95760509e+05\n",
      " -4.59635631e+06 -7.17318737e+05]\n",
      "420 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "\n",
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      "430 38.643064948420204 19.39591748574781 1.0\n",
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      "440 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "450 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "\n",
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      "\n",
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      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "460 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "470 38.643064948420204 19.39591748574781 1.0\n",
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      "480 38.643064948420204 19.39591748574781 1.0\n",
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      "\n",
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      "\n",
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      " -4.59635631e+06 -7.17318737e+05]\n",
      "490 38.643064948420204 19.39591748574781 1.0\n",
      "0.021722861567352002\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
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      "\n",
      "[-2.39851423e+03 -1.03336686e+08 -7.73781354e+03 -1.50222016e+03\n",
      " -3.87390554e+03 -9.02091970e+07 -8.31971792e+07 -1.22767805e+08\n",
      " -6.46267465e+05 -1.05702417e+08 -2.89659964e+04 -9.34176120e+07\n",
      " -6.74402146e+03 -8.55060163e+07 -9.73790825e+07 -8.82411407e+02\n",
      " -8.68538218e+06 -2.07426269e+02 -2.97418669e+04 -2.07682127e+06\n",
      " -7.34358049e+01 -6.77543773e+03 -1.11486320e+08 -1.04268132e+08\n",
      " -3.44998646e+01 -4.09660247e+05 -9.17033795e+07 -1.90366921e+02\n",
      " -8.99643868e+02 -1.22119860e+08 -9.86626102e+07 -9.99215650e+07\n",
      " -6.02859209e+03 -1.41308718e+03 -1.06167927e+08 -4.05436472e+03\n",
      " -8.36698465e+07 -1.47184518e+05 -2.83691006e+03 -1.30532329e+08\n",
      " -1.19464393e+08 -1.30710706e+03 -1.17096550e+08 -1.11957983e+08\n",
      " -2.50190471e+04 -3.90976700e+03 -3.23722467e+03 -6.95760509e+05\n",
      " -4.59635631e+06 -7.17318737e+05]\n",
      "\n",
      "[-2.39851423e+03 -1.03336686e+08 -7.73781354e+03 -1.50222016e+03\n",
      " -3.87390554e+03 -9.02091970e+07 -8.31971792e+07 -1.22767805e+08\n",
      " -6.46267465e+05 -1.05702417e+08 -2.89659964e+04 -9.34176120e+07\n",
      " -6.74402146e+03 -8.55060163e+07 -9.73790825e+07 -8.82411407e+02\n",
      " -8.68538218e+06 -2.07426269e+02 -2.97418669e+04 -2.07682127e+06\n",
      " -7.34358049e+01 -6.77543773e+03 -1.11486320e+08 -1.04268132e+08\n",
      " -3.44998646e+01 -4.09660247e+05 -9.17033795e+07 -1.90366921e+02\n",
      " -8.99643868e+02 -1.22119860e+08 -9.86626102e+07 -9.99215650e+07\n",
      " -6.02859209e+03 -1.41308718e+03 -1.06167927e+08 -4.05436472e+03\n",
      " -8.36698465e+07 -1.47184518e+05 -2.83691006e+03 -1.30532329e+08\n",
      " -1.19464393e+08 -1.30710706e+03 -1.17096550e+08 -1.11957983e+08\n",
      " -2.50190471e+04 -3.90976700e+03 -3.23722467e+03 -6.95760509e+05\n",
      " -4.59635631e+06 -7.17318737e+05]\n",
      "\n",
      "[-2.39851423e+03 -1.03336686e+08 -7.73781354e+03 -1.50222016e+03\n",
      " -3.87390554e+03 -9.02091970e+07 -8.31971792e+07 -1.22767805e+08\n",
      " -6.46267465e+05 -1.05702417e+08 -2.89659964e+04 -9.34176120e+07\n",
      " -6.74402146e+03 -8.55060163e+07 -9.73790825e+07 -8.82411407e+02\n",
      " -8.68538218e+06 -2.07426269e+02 -2.97418669e+04 -2.07682127e+06\n",
      " -7.34358049e+01 -6.77543773e+03 -1.11486320e+08 -1.04268132e+08\n",
      " -3.44998646e+01 -4.09660247e+05 -9.17033795e+07 -1.90366921e+02\n",
      " -8.99643868e+02 -1.22119860e+08 -9.86626102e+07 -9.99215650e+07\n",
      " -6.02859209e+03 -1.41308718e+03 -1.06167927e+08 -4.05436472e+03\n",
      " -8.36698465e+07 -1.47184518e+05 -2.83691006e+03 -1.30532329e+08\n",
      " -1.19464393e+08 -1.30710706e+03 -1.17096550e+08 -1.11957983e+08\n",
      " -2.50190471e+04 -3.90976700e+03 -3.23722467e+03 -6.95760509e+05\n",
      " -4.59635631e+06 -7.17318737e+05]\n",
      "done\n"
     ]
    }
   ],
   "source": [
    "exp_id = 1\n",
    "\n",
    "delta = 1e-7\n",
    "\n",
    "R_lower = np.zeros((N, M))\n",
    "R_upper = max_R * np.ones((N, M))\n",
    "\n",
    "x_accepted = np.zeros((N, M))\n",
    "\n",
    "for t in range(T):\n",
    "        \n",
    "    # get a point in each interval\n",
    "    R_proxy = get_proxy(R_lower, R_upper, 1)\n",
    "    x_offered, p_w = get_offerings_and_prices(R_proxy)\n",
    "        \n",
    "    p = find_comp_prices(R_lower, R_upper, x_offered, p_w)\n",
    "        \n",
    "    x_accepted = filter_decisions(x_offered, p)\n",
    "    x_rejected = x_offered - x_accepted\n",
    "    R_lower, R_upper = update_intervals(R_lower, R_upper, p, x_accepted, x_rejected)\n",
    "    R_length = R_upper - R_lower\n",
    "\n",
    "    acceptance[exp_id, t] = np.sum(x_accepted) / np.sum(x_offered)\n",
    "    rewards[exp_id, t] = get_surplus(x_accepted)\n",
    "    diss = get_dissatisfaction(x_accepted, p)\n",
    "    \n",
    "    if t % 10 == 0:\n",
    "        print(t, rewards[exp_id, t], diss, acceptance[exp_id, t])\n",
    "        # print(to_learn)\n",
    "        print(np.linalg.norm(np.sum(R_length * x_offered, axis = 1 )))\n",
    "\n",
    "        # print(R_length)\n",
    "        # print(np.linalg.norm(p - p_opt), np.linalg.norm(p_w - p_opt))\n",
    "\n",
    "print(\"done\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "206047fd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(num_of_exp):\n",
    "    plt.plot(np.arange(T), rewards[i], label = exp_names[i])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0232c455",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mQBG39Avkpl71d04pa1F9Lz96OFr4YJ0rFEJ0Nk329K1WK0lJSTgcDpRSjBgxgqFDhzJw4EASExNJTU2le/fuJCQkANC3b19GjBhBQkICBoOBOXPmYDDU/22ZO3cuy5cvx2azERUVRXR0dPu2zoUppXgjIw9Po8bcX+7JB9Rn74O9DsN9D+tYnRCis9JUSwbbdZKTk6N3CZ3Ol8dKSEzPZV5sT6YMPDeWn5+L4//+B9rYqRgeeETnCoUQeurVq/FFkuSJ3C6ostbOP/bmExHiw8Twbs7tauMaMHrI1MlCiEuS0O+C1hwowlpt59GYnhgN9bdjqoI81K7taGMmonVr/AK5EEJI6HcxOaU21v1sYdyAYAZ293VuVxvXgGZAm3SPjtUJITo7Cf0u5u29Z/E0GPh9VKhzmyo8i/om9VwvX5ZBFEJcmoR+F7I3p5yMMxXMiAzB5Hv+xqv6Xr4mY/lCiCZJ6HcRtXbFqu/y6RXoye2Dzo/Zq8KzqPRtaKNvQzNJL18IcXkS+l3ExiwrZ0ptzBnaE0/j+bl01KaPz/Xyp+tYnRCiq5DQ7wJKq+tY/UMhN13lT0zv84uaq4I81NcpaKNuQzN317FCIURXIaHfBXz4QyFVdQ5mD+3RYLta9wEYjWhTZ+hUmRCiq5HQ7+ROFNew+XAxkyK60S/4/KLmKvcU6ts0tLFT5b58IUSzSeh3Ykop/nfPWfw9DTx4Q2jD1zauAU8vtIlyx44Qovkk9Duxr0+WceBsJb+9MZQg7/PLHar8XNS3O9BunYwWGKRfgUKILkdCv5OqqXPw9t58+pu8ue2C+XUA1OZP6sfyJ9ylS21CiK5LQr+T+vyQlaLKOuYOPT+/DoAqKkClp6KNniBj+UKIFpPQ74TKaux8crCImF7+DOnp1+A1teVTQMlYvhCiVST0O6FPDhZRWevgd1G/unhbYkXt3Io2YhxaSOgljhZCiEuT0O9kCipq+fyQlVv7B3GNyafBa2rrWrDb0SZLL18I0ToS+p3Mv38oRAEP/foWzbJS1Jeb0IaNQevR+Io4QgjRFAn9TuRkSQ2pR0uYMrAbPQI8G7ymUtZBrQ1tssyxI4RoPQn9TuS9zAJ8PAzc95uGs2WqynLU9s/hphFovfrpVJ0QwhVI6HcSPxVU8u3pcu4ebCbIx6PBayr1c6iqxDD1fp2qE0K4Cgn9TuLdzAJMPkbuuK7hvfequhKVsh5uvBmtb3+dqhNCuAoJ/U7gp/xKDuZXMX1ICD4eDf9J1JeboKIMg8ykKYRoAxL6ncAnP1oI8jYy4dpuDbarmhrU1mQYHI3Wf6AutQkhXIuEvs5OltSQcaacqYNMeP+6l79zM5SVYJgmY/lCiLYhoa+z5B8teBs1pgw0Ndiuam2ozWthUCRaxGCdqhNCuBoJfR0VVtaSdryE+PBuDaZOBlBfpUCJRcbyhRBtSkJfR+t/tuJQcOd1v+rl19WiNn8M114H192gU3VCCFckoa+TcpudLYeLGXV1ED0DvBq8pr7ZDpZCDNPuR9O0S5xBCCFaTkJfJ5sPF1NV5+Du6391X77djtr0MVwdDr+5SafqhBCuSkJfBza7g89/thB1lT8DzL+aSfPbNCjIk16+EKJdSOjr4KsTZVir7Rf38h32+gXP+1wDN96sT3FCCJcmoa+DjVlW+gR5cWPYr1bF2vM1nD2DYeoM6eULIdqFhH4HO1xUxeGiaiYP7NYg2JXDUd/Lv6ov3DRSxwqFEK5MQr+DbcoqxsdDY2z/4IYv7NsFZ06gTbkPzSD/LEKI9uHR1A6FhYUkJSVRXFyMpmnEx8czZcoUysvLSUxMpKCggNDQUObPn09AQAAAa9euJTU1FYPBwOzZs4mKigLg6NGjJCUlYbPZiI6OZvbs2W41jFFaY2fniVLGDQjG3+v8w1jKYcfx2fsQ1gft5tE6ViiEcHVNdimNRiO/+93vSExMZNGiRWzZsoXTp0+TnJxMZGQky5YtIzIykuTkZABOnz5Neno6S5cuZeHChbz11ls4HA4AVq5cybx581i2bBl5eXlkZma2Z9s6nW1HirHZFZMjujXYrnbvgNxTGO58CM1gbPxgIYRoA02GvslkYsCAAQD4+vrSu3dvLBYLGRkZxMXFARAXF0dGRgYAGRkZjBw5Ek9PT3r06EFYWBjZ2dlYrVaqqqoYOHAgmqYxZswY5zHuwKEUmw8XMzjUt8GC58rhQG04d8eOjOULIdpZk8M7F8rPz+fYsWOEh4dTUlKCyVQ/fYDJZKK0tBQAi8VCRESE8xiz2YzFYsFoNBIScn4ZwJCQECwWS6Pvk5KSQkpKCgCLFy9uWYs6qb05FeSV1zLzxoYLnrNvF+SdRnv0GRnLF0K0u2aHfnV1NUuWLGHWrFn4+fldcj+lVIu2NyY+Pp74+Phm798VbMqyYvIxMrxvoHObUgrHxo+gRy+0odLLF0K0v2Z1Levq6liyZAmjR49m2LBhAAQHB2O1WgGwWq0EBQUB9T34oqIi57EWiwWz2XzR9qKiIszmhg8nuaqz5Ta+y6ngtohueBovuHC9fw+cPHrujh0ZyxdCtL8mQ18pxYoVK+jduzfTpk1zbo+JiSEtLQ2AtLQ0YmNjndvT09Opra0lPz+f3NxcwsPDMZlM+Pr6kpWVhVKKHTt2EBMT007N6lw2ZRWjaTAxvJtzm1IKx+f/hu490YbF6VecEMKtNDm8c+jQIXbs2EG/fv145plnAHjwwQe56667SExMJDU1le7du5OQkABA3759GTFiBAkJCRgMBubMmYPh3Fj13LlzWb58OTabjaioKKKjo9uxaZ1DTZ2DlCPFDOsTSIif5/kXDu6F44fRfvefaB4turQihBCtpqmWDLbrJCcnR+8SWi31aAl//yaXv47vyw1h/sC5Xv7/exashRgWvYnm4dnEWYQQomV69erV6Ha5XaSdbTo3z05kzwsufv+8H478jDZ5ugS+EKJDSei3o2PWarKKqpkU0XCeHcfnq6GbGe0W17pDSQjR+Unot6Mth4vxMmrcesE8O+rQAcg6gDbpXjRPr8scLYQQbU9Cv51U1zlIO17KyH6BBF6w6Lljw2oI6oY2+jYdqxNCuCsJ/Xby1YlSKmsdDW/TzP4JfvoebeLdaF7e+hUnhHBbEvrtZPPhYvoGe3F9qK9zm2PDaggIQoubrGNlQgh3JqHfDo5aqjlcVM3E8PMXcNWxLDiwF+22u9G8fZo4gxBCtA8J/XawNfviC7iODR+BfyDaWOnlCyH0I6HfxqrrHHx5rOEFXHXyCHy/Gy3+DjSfS09WJ4QQ7U1Cv419daKUqrqGF3Adn68GX3+0cdMufaAQQnQACf02tjW7mD5B5y/gqtPHYd8utPG3o/n561ucEMLtSei3oRPFNRwqrOa2Cy/gbvgIfHzR4m/XuTohhJDQb1Nbs4vxMGiM7V+/toDKPYX67mu0sVPR/AObOFoIIdqfhH4bsdkdfHmshOF9AwjyqZ8qWW34CLy80SbcpW9xQghxjoR+G0k/WUa5zcFt5y7gqrwzqN070W6djBYYpGttQgjxCwn9NvJFdjFhAZ7OKZTVxjXg6YF22136FiaEEBeQ0G8DZ0ptHMivYsK13TBoGqogD/Xtl2hjJqEFmfQuTwghnCT028DW7GIMGoy7tv4JXLXpYzAY0SberXNlQgjRkIT+Faq1O0g9WsKwPgGYfT1QRfmo9G1ooyegdQvRuzwhhGhAQv8KfXOqnNIaOxMj6odx1OZPAA1t0r36FiaEEI2Q0L9CWw5bCQvw5MYwP5SlEPXVF2i3xKOZQ/UuTQghLiKhfwVOl9RwIL+K28LPXcDd8ikohTZZevlCiM5JQv8KbM4uxsMA468NRhVbUDu3og0fi9a9p96lCSFEoyT0W6mmzsH2oyUM6xNINx8P1Na1YK9Dm3Kf3qUJIcQlSei30i9P4E6K6IYqLUalbUK7OQ6tx1V6lyaEEJckod9KW7KL6RVY/wSu+uIzqK1Fmyq9fCFE5yah3wonimv4qaD+Ai7lZajtG9BiR6OF9dG7NCGEuCwJ/VbYlGXF06Ax/tpuqJR1UFONNmWG3mUJIUSTJPRbqKq2fg3cW64OJLCuCrX9cxg6Eq13P71LE0KIJknot1Da8RKq6hxMjjChtq2HqkoMU+/XuywhhGgWCf0WUEqx+XAx/U3eDPR3oLatg6hhaH37612aEEI0i4R+CxwqrOaYtYZJEd1g+waorMAwTXr5QoiuQ0K/BTYdtuLrYWDMVZ71t2lGxqBdHa53WUII0WwS+s1UWl3H1yfKuLV/ED5fbYGKMunlCyG6HAn9Ztp6pIRah2LyNf6orckwOBptwCC9yxJCiBbxaGqH5cuXs3fvXoKDg1myZAkA5eXlJCYmUlBQQGhoKPPnzycgIACAtWvXkpqaisFgYPbs2URFRQFw9OhRkpKSsNlsREdHM3v2bDRNa7+WtSG7Q7Epy8oNYX70/WotqqwEw+3SyxdCdD1N9vRvvfVWnn/++QbbkpOTiYyMZNmyZURGRpKcnAzA6dOnSU9PZ+nSpSxcuJC33noLh8MBwMqVK5k3bx7Lli0jLy+PzMzMNm9Me/n2dBmFlXVM7V0/lq8NH4sWPljvsoQQosWaDP3Bgwc7e/G/yMjIIC4uDoC4uDgyMjKc20eOHImnpyc9evQgLCyM7OxsrFYrVVVVDBw4EE3TGDNmjPOYruDzQ1Z6+HsydP9msNvRpJcvhOiimhzeaUxJSQkmU/3ygCaTidLSUgAsFgsRERHO/cxmMxaLBaPRSEjI+fViQ0JCsFgslzx/SkoKKSkpACxevLg1JbaZ49ZqDuZXMWtwIIZVG9FuHo3Wo5euNQkhRGu1KvQvRSnVou2XEh8fT3x8fFuUdMU+P2TF26gxPjsVam1o8vStEKILa9XdO8HBwVitVgCsVitBQUFAfQ++qKjIuZ/FYsFsNl+0vaioCLPZfCV1d4jSGjtpx0uJ6+OLf9r6+pk0r5KZNIUQXVerQj8mJoa0tDQA0tLSiI2NdW5PT0+ntraW/Px8cnNzCQ8Px2Qy4evrS1ZWFkopduzYQUxMTNu1op2kZBdjsyum5H0Ltho0uS9fCNHFaaqJsZfXXnuNH3/8kbKyMoKDg5kxYwaxsbEkJiZSWFhI9+7dSUhIcF7s/fTTT9m+fTsGg4FZs2YRHR0NwJEjR1i+fDk2m42oqCgefvjhZt+ymZOTc4XNbDm7Q/HYuiP08DXyl88XoEXGYHj0mQ6vQwghWqNXr8avPTYZ+p2BHqG/50w5f/3yNE/7HmPkpjcwvPR3tD4ysZoQomu4VOjLE7mXsCnLisnHyM07P4Abb5bAF0K4BAn9Rpwtt/FdTgXxhrN4lJdgmDxd75KEEKJNSOg3Ymt2CRowYdcHcN0NaNdep3dJQgjRJiT0f6XWrvjiSDFDjcV0t5zGcM/v9S5JCCHaTJs+nOUKvjlVRkm1nYk/rUMbegta/4F6lySEEG1Gevq/svmwlZ5UE5X/E9qdv9W7HCGEaFMS+hc4WVzDwfwqbjuehvHmUfL0rRDC5UjoX2DzYSseOBiXsxtt2gN6lyOEEG1OQv+cqloH24+WMLJgP91uikEL6613SUII0ebkQu45O0+UUlmnmHj6G7Sn/0vvcoSLUkpRXV2Nw+HoMivHic5LKYXBYMDHx6fZP08S+tR/4zb9VMDVFXlcP2SA9PJFu6mursbT0xMPD/nVE22jrq6O6upqfH19m7W/DO8AWUXVHC21MzH3Wwwyli/akcPhkMAXbcrDw8O5LG1zSOgDmw7k4VNXw60DgtG699S7HOHCZEhHtIeW/Fy5feiX1dj5+kwlcfn78Jt0l97lCCFEu3L70N/2Yx42jEzqXocWGqZ3OUK0q1OnTjFu3LgG25YsWcKKFSucX69YsYIxY8Ywbtw44uPjWbNmDQDTp09n9OjRTJgwgbi4ON57771W1fDKK6+wY8cOAFauXElVVZXztQvX2L6UX9fbHMOGDbvsutx5eXk88sgjLTpnV+XWg4sOpdj8Uz6DSs7S/55JepcjhO7+9a9/sWPHDjZs2EBgYCClpaVs3rzZ+fr//M//cOONN2K1WrnllluYMWMGXl5eLXqPZ545vxjRqlWruPfee5t9EbK9hIWFsXLlSl1r6ChuHfp7jxWSq3y537sILUyevhUdy/HvlahTx9r0nFrf/hgeaH2P9fXXX2fNmjUEBgYCEBQUxIwZMy7ar7KyEl9fX4xGY4Pt+/btIykpiVWrVrFlyxb++Mc/8tNPP+FwOBg7dizffPMNTz31FPHx8Zw9e5azZ89y3333YTKZ+PjjjwFYvHgxKSkp+Pj48M477xAaGnrR+2dlZTF9+nTOnDnD3LlzmTNnDgAPP/wwOTk51NTUMGfOHGbOnNnguEWLFtG7d29mzZoF1H9q8Pf3Z+rUqfzhD38gNTWV1atX88UXX1BVVcXx48eZPHkyL7zwAgAffvghSUlJhIWF0b9/f7y8vFi0aFGrv996cOvhnXW7j2OuKeGWCSP0LkUI3ZWXl1NRUcE111xzyX0ef/xx4uPjGTNmDE899dRFoR8ZGcmBAwcA+Pbbbxk0aBDff/89+/btcy6d+os5c+bQs2dP1qxZ4wz8yspKbrrpJlJSUhg+fDjvv/9+o3VkZ2fz/vvvs2HDBpYuXUptbS1QH+KbN29m48aNvP322xcN6dx5552sX7/e+fX69eu5/fbbLzr/wYMHeeONN9i2bRvr1q3jzJkz5OXl8dprr7F+/Xo+/PBDsrOzL/l96szctqd/7Gwx39sDmWn/Aa9+w/QuR7ihK+mRt9bl7vJQSjV5F8gvwztFRUXccccdjB07lj59zn9K9vDw4JprruHw4cNkZmby6KOPsmvXLux2OzfffHOT9Xl5eTFhwgSg/g/Izp07G91v/PjxeHt74+3tTffu3SkoKKBXr168/fbbbNq0CahfZvXYsWOYzWbncUOGDKGwsJC8vDyKiooIDg6md+/enDp1qsH5R40aRVBQEAADBw7kzJkzWCwWhg8fjslkAmDatGkcPXq0yTZ1Nm7b01+38ye87TYm3XqD3qUI0WFMJhMlJSUNthUXF2M2mwkMDMTX15cTJ040eZ6QkBAiIyPZu3fvRa8NGzaM1NRUPDw8GD16NLt37yYjI4Phw4c3eV4PDw/nHx6j0UhdXV2j+3l7ezv/32g0YrfbSU9PZ+fOnaxfv56UlBSGDBlCTU3NRcdOnTqVDRs2sG7dOu68885Gz3/hdQqDwUBdXR1dYDnxZnHL0C8qqWBHVRDjao4RGDFI73KE6DD+/v706NHD2YO2Wq1s377d2Qt//PHHWbhwIWVlZQCUlZU1epdOVVUVBw4caHQoaNiwYaxatYqhQ4cSEhKC1WolOzubQYMu/l0LCAigvLy8TdpWVlZGcHAwvr6+ZGdnN/oHCeqHeD777DM2bNjA1KlTm33+qKgodu3aRXFxMXV1dWzcuLFN6u5objm8s+nL77Fr3bjj5mv1LkWIDvf3v/+d559/nr/85S8AJCQkOMP7D3/4A5WVlUyZMsU5XcS8efOcxz7++OP4+Phgs9mYMWMGN9xw8Sfl6OhoCgsLnT37wYMHk5+f3+jQ0W9/+1tmzpxJjx49nOP6rXXrrbfy7rvvEh8fz4ABA7jpppsa3W/QoEFUVFQQFhZGz57Nfxjzqquu4oknnmDatGmEhYURERHhvODdlWiqC3xmycnJabNzVVfXMHf1Qa6vLeD5ObfJE5KiQ1VWVuLn56d3GaKVKioq8Pf3p66ujjlz5vDAAw8wefJkvctq9OeqV69eje7rdj391O3fUeZh5s5BPSTwhRAtsmTJEnbu3ElNTQ1xcXFMmtT1nu9xq9C32+tYnwvXqnwG3zxK73KEEF3Miy++qHcJV8ytLuTuSdtDjreZOwf4YTC4VdOFEAJwo56+cjhYd6ScEE8jI0c3foFHCCFcndt0d3/etZcDfn2YFqbw9DA2fYAQQrggt+jpK6X46EcrgZ5GJt0a3fQBQgjhotyip5/93Q/s9e3LnSHV+Pl46l2OELpxhamVu4J//etfzu9bY/Scytktevqrvz9LgEd3poyTsXwhLsddp1ZuS3V1dfz+97+/7D56TuXs8qF/5EAWGT59edCvAH8/76YPEKKDrNpzlmPW6jY9Z3+TD3NjWr/kZ1eYWrmiooIXXniB/fv3o2ka8+fPZ+rUqSQnJ/P666+jlGL8+PEsXLgQqP/0MGvWLHbu3ElwcDALFixg0aJFnDlzhj//+c/cdtttrF69ms2bN2Oz2Th58iR33303CQkJF7U7IiKCmTNnkp6eTnBwMG+88QYhISFMnz6doUOHsmfPHiZMmOB8iOuxxx7j2LFjLFiwgKKiIoxGI2+++SZGo1G3qZxdfnjn33tO41dXzdRxMpYvxOV0lamVX3vtNQIDA9m2bRspKSnccsst5OXlsWjRIj766CO2bt1KZmam8xNKZWUlI0aMYPPmzQQEBPDyyy/z4YcfsmrVKl555RXneTMzM3n99dfZunUrn3/+Od9///1F711ZWUlkZCRbtmxhxIgRLF261PlaaWkpn3zyCY899liDY5544glmzZpFSkoKn332WaNTP3TkVM4u3dM/nHWC3Z69eMDzDIHBUXqXI0QDV9Ijby1XmFp5586dLF++3Pl1t27dnCEcEhICwD333MOuXbuYNGkSXl5ejB07FoDrrrsOLy8vPD09uf766zl9+rTzPKNHj3ZOwzx58mR2797NjTfe2OC9DQYDd9xxh/M95s6d63ztl+0XKi8vJzc31zlVg4+PT6Pt7sipnF26p//vb44RUFvJ7eOlly8EuMbUyo39cbrcFGIXntNgMDinZf5lyuRf/PqczZmm5cJ9GptTqblTm3XkVM4dHvqZmZn86U9/4oknniA5Obnd3udQxvfs8QjjzoASAkLMTR8ghBtwhamV4+LieOedd5xfFxcXEx0dza5du7BYLNjtdpKTkxkxomUr4u3cuROr1UpVVRVbtmwhNjb2on0cDgcbNmwAYO3atU1+egkMDOSqq65yDjXV1NQ0uFvpctprKucOHd5xOBy89dZbvPDCC4SEhPDcc88RExPT4ONhW/nwQBGBhm5Mu3tkm59biK6sq0+t/Kc//Ynnn3+ecePGYTAYSEhIYMqUKTz33HPcd999KKUYN24cEydObNH3JTY2lieffJLjx49z9913XzS0A/W9+UOHDjFp0iQCAwMb3Op6KcuWLePZZ5/l1VdfxcPDgzfffLNZ08C011TOHTq1clZWFmvWrHFeVV+7di0Ad99992WPa+nUynV1dv615ku6+3tyxx1jWlesEO1AplbunFavXs3+/fubvDMmIiKCw4cPd1BVzZ/KudNOrWyxWJwXWqB+XLCxb2BKSgopKSlA/e1bLeXhYeThB8e3vlAhhOgE2mMq5w4N/cY+VDT2kS8+Pp74+PiOKEkIIbj//vu5//77m9yvI3v50D5TOXfohdyQkBCKioqcXxcVFTlvRxLCHXSBhepEF9SSn6sODf1rr72W3Nxc8vPzqaurIz09nZiYmI4sQQhd/fo2QSGuVF1dXYvWB+nQ4R2j0cjDDz/MokWLnI9l9+3btyNLEEJXPj4+VFdXU1NTI8t1iiumlMJgMFzyoa/GuN3C6EII4Q4udfeOSz+RK4QQoiEJfSGEcCMS+kII4Ua6xJi+EEKItuHSPf0FCxboXUKHkza7B2mze2iPNrt06AshhGhIQl8IIdyIS4e+O87fI212D9Jm99AebZYLuUII4UZcuqcvhBCiIQl9IYRwIx064VpHyczM5J133sHhcDB+/HjuuusuvUtqE8uXL2fv3r0EBwezZMkSAMrLy0lMTKSgoIDQ0FDmz59PQEAAUL8yWWpqKgaDgdmzZxMVFaVj9a1TWFhIUlISxcXFaJpGfHw8U6ZMcel222w2XnrpJerq6rDb7QwfPpwZM2a4dJt/4XA4WLBgAWazmQULFrh8m//zP/8THx8fDAYDRqORxYsXt3+blYux2+3q8ccfV3l5eaq2tlY9/fTT6tSpU3qX1SYOHjyojhw5ohISEpzb3n33XbV27VqllFJr165V7777rlJKqVOnTqmnn35a2Ww2dfbsWfX4448ru92uR9lXxGKxqCNHjiillKqsrFRPPvmkOnXqlEu32+FwqKqqKqWUUrW1teq5555Thw4dcuk2/2L9+vXqtddeU3/729+UUq7/8/3HP/5RlZSUNNjW3m12ueGd7OxswsLC6NmzJx4eHowcOZKMjAy9y2oTgwcPdv7F/0VGRgZxcXEAxMXFOduakZHByJEj8fT0pEePHoSFhZGdnd3hNV8pk8nEgAEDAPD19aV3795YLBaXbremac6pcu12O3a7HU3TXLrNUL+o0t69exk//vxSp67e5sa0d5tdLvQbW4fXYrHoWFH7Kikpca4+ZjKZKC0tBS7+PpjN5i7/fcjPz+fYsWOEh4e7fLsdDgfPPPMMc+fOJTIykoiICJdv8z/+8Q9mzpzZYJ0BV28zwKJFi3j22Wed64K3d5tdbkxfNXMdXlfX2PehK6uurmbJkiXMmjULPz+/S+7nKu02GAy88sorVFRU8Oqrr3Ly5MlL7usKbf7uu+8IDg5mwIABHDx4sMn9XaHNAH/9618xm82UlJTw3//935ecAx/ars0uF/rutg5vcHAwVqsVk8mE1WolKCgIuPj7YLFYMJvNepV5Rerq6liyZAmjR49m2LBhgHu0G8Df35/BgweTmZnp0m0+dOgQe/bsYd++fdhsNqqqqli2bJlLtxlw1hwcHExsbCzZ2dnt3maXG95xt3V4Y2JiSEtLAyAtLY3Y2Fjn9vT0dGpra8nPzyc3N5fw8HA9S20VpRQrVqygd+/eTJs2zbndldtdWlpKRUUFUH8nzw8//EDv3r1dus0PPfQQK1asICkpiaeeeoohQ4bw5JNPunSbq6urqaqqcv7//v376devX7u32SWfyN27dy///Oc/nevw3nPPPXqX1CZee+01fvzxR8rKyggODmbGjBnExsaSmJhIYWEh3bt3JyEhwXmx99NPP2X79u0YDAZmzZpFdHS0zi1ouZ9//pkXX3yRfv36OYfpHnzwQSIiIly23SdOnCApKQmHw4FSihEjRjB9+nTKyspcts0XOnjwIOvXr2fBggUu3eazZ8/y6quvAvUX7EeNGsU999zT7m12ydAXQgjROJcb3hFCCHFpEvpCCOFGJPSFEMKNSOgLIYQbkdAXQgg3IqEvhBBuREJfCCHcyP8P2z1l0Uh29mUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(num_of_exp):\n",
    "    plt.plot(np.arange(T), np.cumsum(surplus_opt - rewards[i]), label = exp_names[i])\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "11eb646c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "06121f31",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "raw",
   "id": "ce056e1f",
   "metadata": {},
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}