NN-RL.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import gym_2048\n",
    "import gym\n",
    "import numpy as np\n",
    "import random\n",
    "import copy\n",
    "\n",
    "from itertools import permutations\n",
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def push_up(bb):\n",
    "    s = 0\n",
    "    s1 = 0\n",
    "\n",
    "    b = copy.deepcopy(bb)\n",
    "    b_new = copy.deepcopy(bb)\n",
    "\n",
    "    for i in [0, 1, 2, 3]:\n",
    "        l = []\n",
    "        for j in range(0, 4):\n",
    "            l.append(b[j][i])\n",
    "\n",
    "        l = list(filter((0).__ne__, l))\n",
    "\n",
    "        l_n = []\n",
    "        while len(l) > 1:\n",
    "            if l[0] == l[1] and l[0] != 0:\n",
    "                l_n.append(2 * l[0])\n",
    "                s = s + (2 * l[0])\n",
    "                s1 = s1 + 1\n",
    "                l.pop(0)\n",
    "                l.pop(0)\n",
    "\n",
    "            else:\n",
    "                l_n.append(l[0])\n",
    "                l.pop(0)\n",
    "        if len(l) == 1:\n",
    "            l_n.append(l[0])\n",
    "            l.pop(0)\n",
    "\n",
    "        for k in range(4 - len(l_n)):\n",
    "            l_n.append(0)\n",
    "\n",
    "        for j in range(0, 4):\n",
    "            b_new[j][i] = l_n[j]\n",
    "    return b_new, s, s1 * 16\n",
    "\n",
    "\n",
    "def push_down(bb):\n",
    "    s = 0\n",
    "    s1 = 0\n",
    "\n",
    "    b = copy.deepcopy(bb)\n",
    "    b_new = copy.deepcopy(bb)\n",
    "\n",
    "    for i in [0, 1, 2, 3]:\n",
    "        l = []\n",
    "        for j in [3, 2, 1, 0]:\n",
    "            l.append(b[j][i])\n",
    "\n",
    "        l = list(filter((0).__ne__, l))\n",
    "\n",
    "        l_n = []\n",
    "        while len(l) > 1:\n",
    "            if l[0] == l[1] and l[0] != 0:\n",
    "                l_n.append(2 * l[0])\n",
    "                s = s + (2 * l[0])\n",
    "                s1 = s1 + 1\n",
    "                l.pop(0)\n",
    "                l.pop(0)\n",
    "\n",
    "            else:\n",
    "                l_n.append(l[0])\n",
    "                l.pop(0)\n",
    "        if len(l) == 1:\n",
    "            l_n.append(l[0])\n",
    "            l.pop(0)\n",
    "\n",
    "        for k in range(4 - len(l_n)):\n",
    "            l_n.append(0)\n",
    "\n",
    "        for j in range(0, 4):\n",
    "            b_new[j][i] = l_n[3 - j]\n",
    "    return b_new, s, s1\n",
    "\n",
    "\n",
    "def push_left(bb):\n",
    "    s = 0\n",
    "    s1 = 0\n",
    "\n",
    "    b = copy.deepcopy(bb)\n",
    "    b_new = copy.deepcopy(bb)\n",
    "\n",
    "    for i in [0, 1, 2, 3]:\n",
    "        l = []\n",
    "        for j in [0, 1, 2, 3]:\n",
    "            l.append(b[i][j])\n",
    "\n",
    "        l = list(filter((0).__ne__, l))\n",
    "\n",
    "        l_n = []\n",
    "        while len(l) > 1:\n",
    "            if l[0] == l[1] and l[0] != 0:\n",
    "                l_n.append(2 * l[0])\n",
    "                s = s + (2 * l[0])\n",
    "                s1 = s1 + 1\n",
    "                l.pop(0)\n",
    "                l.pop(0)\n",
    "\n",
    "            else:\n",
    "                l_n.append(l[0])\n",
    "                l.pop(0)\n",
    "        if len(l) == 1:\n",
    "            l_n.append(l[0])\n",
    "            l.pop(0)\n",
    "\n",
    "        for k in range(4 - len(l_n)):\n",
    "            l_n.append(0)\n",
    "\n",
    "        for j in range(0, 4):\n",
    "            b_new[i][j] = l_n[j]\n",
    "\n",
    "    return b_new, s, s1\n",
    "\n",
    "\n",
    "def push_right(bb):\n",
    "    s = 0\n",
    "    s1 = 0\n",
    "\n",
    "    b = copy.deepcopy(bb)\n",
    "    b_new = copy.deepcopy(bb)\n",
    "    for i in [0, 1, 2, 3]:\n",
    "        l = []\n",
    "        for j in [3, 2, 1, 0]:\n",
    "            l.append(b[i][j])\n",
    "\n",
    "        l = list(filter((0).__ne__, l))\n",
    "\n",
    "        l_n = []\n",
    "        while len(l) > 1:\n",
    "            if l[0] == l[1] and l[0] != 0:\n",
    "                l_n.append(2 * l[0])\n",
    "                s = s + (2 * l[0])\n",
    "                s1 = s1 + 1\n",
    "                l.pop(0)\n",
    "                l.pop(0)\n",
    "            else:\n",
    "                l_n.append(l[0])\n",
    "                l.pop(0)\n",
    "        if len(l) == 1:\n",
    "            l_n.append(l[0])\n",
    "            l.pop(0)\n",
    "\n",
    "        for k in range(4 - len(l_n)):\n",
    "            l_n.append(0)\n",
    "\n",
    "        for j in range(0, 4):\n",
    "            b_new[i][j] = l_n[3 - j]\n",
    "\n",
    "    return b_new, s, s1\n",
    "\n",
    "\n",
    "def is_done(bb):\n",
    "    b = copy.deepcopy(bb)\n",
    "\n",
    "    if b == push_down(b)[0] and b == push_up(b)[0] and b == push_left(b)[0] and b == push_right(b)[0]:\n",
    "        return True\n",
    "    else:\n",
    "        return False\n",
    "\n",
    "\n",
    "def is_monotonic(L):\n",
    "    return all(x >= y for x, y in zip(L, L[1:])) or all(x <= y for x, y in zip(L, L[1:]))\n",
    "\n",
    "def get_total_merges(bb):\n",
    "    b = copy.deepcopy(bb)\n",
    "    count = push_down(b)[2] + push_left(b)[2]\n",
    "    # print(\"Merges : \",push_down(b)[2]+push_left(b)[2])\n",
    "    return count\n",
    "\n",
    "\n",
    "\n",
    "def generate_monotonic_data():\n",
    "    a = [True, False, True, False, True, False, True, False]\n",
    "\n",
    "    b = list(permutations(a, 4))\n",
    "\n",
    "    c = list(set(b))\n",
    "\n",
    "    d = list(permutations(c + c, 2))\n",
    "\n",
    "    return list(set(d))\n",
    "\n",
    "\n",
    "def get_monotonicity_index(a):\n",
    "    l = []\n",
    "    for MN in [a, a.T]:\n",
    "        k = []\n",
    "        for i in MN:\n",
    "            k.append(is_monotonic(i))\n",
    "\n",
    "        l.append(tuple(k))\n",
    "\n",
    "    return Monotonicity_master_data.index(tuple(l)), Counter(l)[True], Counter(l)[False]\n",
    "\n",
    "\n",
    "def get_empty_cells(bb):\n",
    "    count = 0\n",
    "    b = copy.deepcopy(bb)\n",
    "\n",
    "    for i in range(4):\n",
    "        for j in range(4):\n",
    "            if b[i][j] == 0:\n",
    "                count = count + 1\n",
    "    return count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 \t0 \t0 \t2\n",
      "0 \t0 \t0 \t2\n",
      "0 \t0 \t0 \t0\n",
      "0 \t0 \t0 \t0\n"
     ]
    }
   ],
   "source": [
    "Monotonicity_master_data = generate_monotonic_data()\n",
    "\n",
    "env = gym.make('2048-v0')\n",
    "# env.seed(42)\n",
    "\n",
    "Q = np.zeros((256, 16, 9, 4))\n",
    "\n",
    "env.reset()\n",
    "env.render()\n",
    "\n",
    "done = False\n",
    "\n",
    "moves = 0\n",
    "episodes = 100\n",
    "\n",
    "explore_rate = 0.02\n",
    "discount_factor = 0.8\n",
    "learning_rate = 0.8\n",
    "\n",
    "total_reward = 0\n",
    "\n",
    "state = (0, 0, 0)\n",
    "\n",
    "dump = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Iteration :  1\n",
      "[[ 2  8  4  2]\n",
      " [16  4 64  8]\n",
      " [ 8 16  2 16]\n",
      " [ 2  4 32  4]]\n",
      "Unique Q: 86\n",
      "\n",
      "Iteration :  2\n",
      "[[  4   2  16   4]\n",
      " [  2  16  64   8]\n",
      " [ 64   8 128   2]\n",
      " [  4  64   2   8]]\n",
      "Unique Q: 208\n",
      "\n",
      "Iteration :  3\n",
      "[[  2   4  16   4]\n",
      " [128   8  32  16]\n",
      " [ 16  64  16   4]\n",
      " [  4   2  32   2]]\n",
      "Unique Q: 330\n",
      "\n",
      "Iteration :  4\n",
      "[[ 2  4  8  2]\n",
      " [ 4  8 32  4]\n",
      " [16  2 64 16]\n",
      " [ 2  4  8  4]]\n",
      "Unique Q: 386\n",
      "\n",
      "Iteration :  5\n",
      "[[ 4  8  4  2]\n",
      " [32  4  2  4]\n",
      " [ 2 64 32  8]\n",
      " [ 4 32  4  2]]\n",
      "Unique Q: 447\n",
      "\n",
      "Iteration :  6\n",
      "[[ 2  8  4  2]\n",
      " [ 8 16 64  8]\n",
      " [ 4  8 16 64]\n",
      " [ 2  4  8  2]]\n",
      "Unique Q: 530\n",
      "\n",
      "Iteration :  7\n",
      "[[  4   2  16   4]\n",
      " [ 16 128  64   8]\n",
      " [  4   8  16   2]\n",
      " [  2  64   4   8]]\n",
      "Unique Q: 617\n",
      "\n",
      "Iteration :  8\n",
      "[[ 2  8  2  4]\n",
      " [16 64  8 16]\n",
      " [ 4 16 64  4]\n",
      " [ 2  4  8  2]]\n",
      "Unique Q: 666\n",
      "\n",
      "Iteration :  9\n",
      "[[ 2 16  8  2]\n",
      " [ 8 64 16  4]\n",
      " [ 2 16  8  2]\n",
      " [ 4  2 16  8]]\n",
      "Unique Q: 714\n",
      "\n",
      "Iteration :  10\n",
      "[[ 4  8  4  8]\n",
      " [ 2 32  8  4]\n",
      " [ 4 64 32  2]\n",
      " [ 2  8 16  4]]\n",
      "Unique Q: 772\n",
      "\n",
      "Iteration :  11\n",
      "[[ 4 16  8  4]\n",
      " [16 64 16  8]\n",
      " [ 4 32  8  4]\n",
      " [ 2  4 16  2]]\n",
      "Unique Q: 823\n",
      "\n",
      "Iteration :  12\n",
      "[[ 2  8  2  4]\n",
      " [16 32  8  2]\n",
      " [ 8 64 16  4]\n",
      " [ 4  8  4  8]]\n",
      "Unique Q: 878\n",
      "\n",
      "Iteration :  13\n",
      "[[ 4  2  8  4]\n",
      " [ 2 16  4 32]\n",
      " [ 4  2 64  4]\n",
      " [ 2  4  8  2]]\n",
      "Unique Q: 932\n",
      "\n",
      "Iteration :  14\n",
      "[[ 2  4  8  4]\n",
      " [ 4  8  4 32]\n",
      " [ 2  4 32  4]\n",
      " [ 4  8  4  2]]\n",
      "Unique Q: 969\n",
      "\n",
      "Iteration :  15\n",
      "[[  2  32   4   2]\n",
      " [  8  16 128   4]\n",
      " [  2  32  16   8]\n",
      " [  8   4   2   4]]\n",
      "Unique Q: 1022\n",
      "\n",
      "Iteration :  16\n",
      "[[  8   4   8   2]\n",
      " [  4   8  64   8]\n",
      " [  8 128   8   2]\n",
      " [  4  64   2   4]]\n",
      "Unique Q: 1089\n",
      "\n",
      "Iteration :  17\n",
      "[[  4  16   4   2]\n",
      " [ 32 256   2   8]\n",
      " [  8  32   8   4]\n",
      " [  2   4  16   2]]\n",
      "Unique Q: 1166\n",
      "\n",
      "Iteration :  18\n",
      "[[  2   4   2   8]\n",
      " [  4  32   8   2]\n",
      " [128  16 128   8]\n",
      " [  2   8   2   4]]\n",
      "Unique Q: 1235\n",
      "\n",
      "Iteration :  19\n",
      "[[ 2 32  2  4]\n",
      " [ 4  2  4 16]\n",
      " [ 8  4 64  8]\n",
      " [ 2  8 16  2]]\n",
      "Unique Q: 1267\n",
      "\n",
      "Iteration :  20\n",
      "[[ 4 32  2  8]\n",
      " [16 64  8  4]\n",
      " [ 8 32  4  2]\n",
      " [ 2  4 16  4]]\n",
      "Unique Q: 1306\n",
      "\n",
      "Iteration :  21\n",
      "[[  2   4  32   2]\n",
      " [  4  16 256   4]\n",
      " [  8  32  64  16]\n",
      " [  4   8   4   8]]\n",
      "Unique Q: 1380\n",
      "\n",
      "Iteration :  22\n",
      "[[  4   8   4   2]\n",
      " [  2  16  32   8]\n",
      " [ 32 128   8   2]\n",
      " [  2   8  16   4]]\n",
      "Unique Q: 1421\n",
      "\n",
      "Iteration :  23\n",
      "[[  2  16   8   2]\n",
      " [ 16 128  32  16]\n",
      " [  4   8  16   8]\n",
      " [  2  16   8   2]]\n",
      "Unique Q: 1480\n",
      "\n",
      "Iteration :  24\n",
      "[[ 2  4  8  2]\n",
      " [ 8  2  4  8]\n",
      " [ 4 16 32 16]\n",
      " [ 2  8 16  4]]\n",
      "Unique Q: 1507\n",
      "\n",
      "Iteration :  25\n",
      "[[ 8  4  2  4]\n",
      " [ 4 16  4  2]\n",
      " [ 2  4 16 64]\n",
      " [ 4 16  4  2]]\n",
      "Unique Q: 1553\n",
      "\n",
      "Iteration :  26\n",
      "[[64  2 16  2]\n",
      " [ 8  4 64 16]\n",
      " [32 16  8  4]\n",
      " [ 2  8  4  2]]\n",
      "Unique Q: 1606\n",
      "\n",
      "Iteration :  27\n",
      "[[  4   2   8   2]\n",
      " [  2   8  64   4]\n",
      " [ 32   4  32   2]\n",
      " [  4   8   2 128]]\n",
      "Unique Q: 1665\n",
      "\n",
      "Iteration :  28\n",
      "[[ 2  4 64  2]\n",
      " [ 4 32 16  4]\n",
      " [ 2  8  2 32]\n",
      " [ 8 16  4  2]]\n",
      "Unique Q: 1708\n",
      "\n",
      "Iteration :  29\n",
      "[[ 2 32  4  2]\n",
      " [ 4 16  2  8]\n",
      " [ 8 64  4 16]\n",
      " [ 2  4  8  2]]\n",
      "Unique Q: 1737\n",
      "\n",
      "Iteration :  30\n",
      "[[ 2  8  4  2]\n",
      " [ 4 16  8  4]\n",
      " [16 64 16  2]\n",
      " [ 8  2  4  8]]\n",
      "Unique Q: 1761\n",
      "\n",
      "Iteration :  31\n",
      "[[32  2  4 16]\n",
      " [ 2  4 16  4]\n",
      " [ 4 32  8 32]\n",
      " [ 2  8  4  2]]\n",
      "Unique Q: 1792\n",
      "\n",
      "Iteration :  32\n",
      "[[  2   4   8   2]\n",
      " [  4   8  32   4]\n",
      " [128  32  16   2]\n",
      " [  4   8   4   8]]\n",
      "Unique Q: 1863\n",
      "\n",
      "Iteration :  33\n",
      "[[  2   8 128   2]\n",
      " [ 16  32   8   4]\n",
      " [  2  64  16   8]\n",
      " [ 16   2   8   2]]\n",
      "Unique Q: 1911\n",
      "\n",
      "Iteration :  34\n",
      "[[ 4 16  4  2]\n",
      " [16  4 64  4]\n",
      " [ 8 64  4  2]\n",
      " [ 2  4 16  4]]\n",
      "Unique Q: 1953\n",
      "\n",
      "Iteration :  35\n",
      "[[  2   8   2   4]\n",
      " [  4  32   4   8]\n",
      " [  8   4 128   2]\n",
      " [  4   2  16   8]]\n",
      "Unique Q: 1983\n",
      "\n",
      "Iteration :  36\n",
      "[[  2 128   8   4]\n",
      " [ 32  64  16   2]\n",
      " [  2   8  32   8]\n",
      " [  4   2   8   4]]\n",
      "Unique Q: 2048\n",
      "\n",
      "Iteration :  37\n",
      "[[  2   8  64   4]\n",
      " [  4  16   4 128]\n",
      " [  8   4  64   8]\n",
      " [  2  16   4   2]]\n",
      "Unique Q: 2113\n",
      "\n",
      "Iteration :  38\n",
      "[[  4   8   4   2]\n",
      " [  2  16  32 128]\n",
      " [ 64   2   4   2]\n",
      " [  2   4   2  64]]\n",
      "Unique Q: 2158\n",
      "\n",
      "Iteration :  39\n",
      "[[ 4  2  8 16]\n",
      " [16 64  4  2]\n",
      " [ 2  4  8  4]\n",
      " [ 4  8  2  8]]\n",
      "Unique Q: 2187\n",
      "\n",
      "Iteration :  40\n",
      "[[  2   4   8   2]\n",
      " [  4 128  16   4]\n",
      " [  8  16  64   2]\n",
      " [  4   8  16   8]]\n",
      "Unique Q: 2220\n",
      "\n",
      "Iteration :  41\n",
      "[[  2  16   4   2]\n",
      " [  8  64   8  16]\n",
      " [ 16  32 128   2]\n",
      " [  4   8  16   4]]\n",
      "Unique Q: 2256\n",
      "\n",
      "Iteration :  42\n",
      "[[ 16   2   4   2]\n",
      " [ 32  64 256  16]\n",
      " [  4  16   4   2]\n",
      " [  2   4  16   4]]\n",
      "Unique Q: 2331\n",
      "\n",
      "Iteration :  43\n",
      "[[ 2  8 16  2]\n",
      " [ 4 16  8  4]\n",
      " [ 8 32  4 16]\n",
      " [ 4 16  2  4]]\n",
      "Unique Q: 2361\n",
      "\n",
      "Iteration :  44\n",
      "[[ 2 32  2  4]\n",
      " [ 8 16 32  2]\n",
      " [ 2  4 16  4]\n",
      " [ 4  8  4  2]]\n",
      "Unique Q: 2403\n",
      "\n",
      "Iteration :  45\n",
      "[[ 4 16  8  2]\n",
      " [16  4  2 32]\n",
      " [ 4  8 32  8]\n",
      " [ 2  4  8  4]]\n",
      "Unique Q: 2420\n",
      "\n",
      "Iteration :  46\n",
      "[[  2   4   8   2]\n",
      " [  8 128  64  16]\n",
      " [  4  16   4   8]\n",
      " [  2   4   8   2]]\n",
      "Unique Q: 2450\n",
      "\n",
      "Iteration :  47\n",
      "[[ 4  8  4  2]\n",
      " [ 8 64 16  8]\n",
      " [ 4 16 32 16]\n",
      " [ 2  8  4  2]]\n",
      "Unique Q: 2472\n",
      "\n",
      "Iteration :  48\n",
      "[[ 2  4 32  8]\n",
      " [ 8 64  8  4]\n",
      " [ 4  8 16  2]\n",
      " [ 2  4 64  4]]\n",
      "Unique Q: 2507\n",
      "\n",
      "Iteration :  49\n",
      "[[ 2  4 32  2]\n",
      " [16  8  2 32]\n",
      " [ 4 64 16  4]\n",
      " [ 2  4  8  2]]\n",
      "Unique Q: 2540\n",
      "\n",
      "Iteration :  50\n",
      "[[ 4 32  2  4]\n",
      " [ 2  4 64 16]\n",
      " [ 4 64 16 32]\n",
      " [ 2  4  8  2]]\n",
      "Unique Q: 2578\n",
      "\n",
      "Iteration :  51\n",
      "[[  2   4   2   8]\n",
      " [  8 128   8   2]\n",
      " [  4   8  16   8]\n",
      " [  2  64   4   2]]\n",
      "Unique Q: 2616\n",
      "\n",
      "Iteration :  52\n",
      "[[ 2 16  8  4]\n",
      " [16  8 16  8]\n",
      " [ 4 64  2  4]\n",
      " [ 2 16  4  2]]\n",
      "Unique Q: 2638\n",
      "\n",
      "Iteration :  53\n",
      "[[  2  32   4   2]\n",
      " [  4   8  16 128]\n",
      " [  8  32   2   8]\n",
      " [  4   2  16   4]]\n",
      "Unique Q: 2677\n",
      "\n",
      "Iteration :  54\n",
      "[[  8   2  32   4]\n",
      " [  2   8   4  16]\n",
      " [  4 256  16   8]\n",
      " [  2  16   8   2]]\n",
      "Unique Q: 2714\n",
      "\n",
      "Iteration :  55\n",
      "[[ 4 64  2  8]\n",
      " [ 2 32  8  4]\n",
      " [32  4 32  2]\n",
      " [ 4  8  2  4]]\n",
      "Unique Q: 2746\n",
      "\n",
      "Iteration :  56\n",
      "[[  8   2   4   2]\n",
      " [  2  32   2   8]\n",
      " [  4   2 256   4]\n",
      " [  2   8   4   2]]\n",
      "Unique Q: 2788\n",
      "\n",
      "Iteration :  57\n",
      "[[ 2 16  4  2]\n",
      " [ 8 64 16  4]\n",
      " [16 32 64  8]\n",
      " [ 8  2  8  2]]\n",
      "Unique Q: 2812\n",
      "\n",
      "Iteration :  58\n",
      "[[  4   2  16   4]\n",
      " [ 32  16 128  32]\n",
      " [  4  32   4   2]\n",
      " [  2   4   8   4]]\n",
      "Unique Q: 2839\n",
      "\n",
      "Iteration :  59\n",
      "[[  2   4   2  16]\n",
      " [  8  32 128   2]\n",
      " [  4   8   4  16]\n",
      " [  2  16   2   8]]\n",
      "Unique Q: 2862\n",
      "\n",
      "Iteration :  60\n",
      "[[ 8  4 16  8]\n",
      " [16 64  4  2]\n",
      " [ 4 32  2 32]\n",
      " [ 2  4 16  2]]\n",
      "Unique Q: 2885\n",
      "\n",
      "Iteration :  61\n",
      "[[ 8  2 16  2]\n",
      " [ 4 32  8  4]\n",
      " [ 2 16 32  8]\n",
      " [ 4  2 16  4]]\n",
      "Unique Q: 2904\n",
      "\n",
      "Iteration :  62\n",
      "[[  2  32   8   4]\n",
      " [  4   8  16  32]\n",
      " [ 32 128   8   2]\n",
      " [  2   8  32   4]]\n",
      "Unique Q: 2936\n",
      "\n",
      "Iteration :  63\n",
      "[[ 4  2  4  2]\n",
      " [ 2  4 32 16]\n",
      " [ 8 64 16  8]\n",
      " [ 2  4  8  4]]\n",
      "Unique Q: 2958\n",
      "\n",
      "Iteration :  64\n",
      "[[  4   8   4   2]\n",
      " [ 16 128  64   8]\n",
      " [  2  64   8   4]\n",
      " [  4   8   4   2]]\n",
      "Unique Q: 2991\n",
      "\n",
      "Iteration :  65\n",
      "[[ 16   2   4   2]\n",
      " [  2   4  32  64]\n",
      " [128  16   4   2]\n",
      " [  2   8   2   8]]\n",
      "Unique Q: 3024\n",
      "\n",
      "Iteration :  66\n",
      "[[ 2  4 64  4]\n",
      " [ 8 32  4  2]\n",
      " [ 2  4  8 16]\n",
      " [16  2  4  2]]\n",
      "Unique Q: 3052\n",
      "\n",
      "Iteration :  67\n",
      "[[  4  32   4   2]\n",
      " [  8 128  64   4]\n",
      " [  2   4  32  16]\n",
      " [  4  32   4   2]]\n",
      "Unique Q: 3090\n",
      "\n",
      "Iteration :  68\n",
      "[[  4   2  32   2]\n",
      " [  2   8 128  16]\n",
      " [  4  64  32   2]\n",
      " [  2  16   4  16]]\n",
      "Unique Q: 3131\n",
      "\n",
      "Iteration :  69\n",
      "[[ 2  4 16  2]\n",
      " [ 8  2 32  8]\n",
      " [ 4 16 64 16]\n",
      " [ 2  4  8  2]]\n",
      "Unique Q: 3147\n",
      "\n",
      "Iteration :  70\n",
      "[[  2   4   8   2]\n",
      " [  4   8  32   8]\n",
      " [128  64   8   4]\n",
      " [  8   4  16   2]]\n",
      "Unique Q: 3183\n",
      "\n",
      "Iteration :  71\n",
      "[[ 2 64 32  4]\n",
      " [16  4  8 16]\n",
      " [ 2  8 16  4]\n",
      " [ 4 32  4  2]]\n",
      "Unique Q: 3203\n",
      "\n",
      "Iteration :  72\n",
      "[[ 4  2  8  2]\n",
      " [16 64 32 16]\n",
      " [ 2 32 16  4]\n",
      " [ 8  2  4  2]]\n",
      "Unique Q: 3228\n",
      "\n",
      "Iteration :  73\n",
      "[[ 2  4 16  2]\n",
      " [ 4 32 64  4]\n",
      " [ 2  4 32  2]\n",
      " [16  2  8  4]]\n",
      "Unique Q: 3250\n",
      "\n",
      "Iteration :  74\n",
      "[[  4  32   8   2]\n",
      " [  2 128  64  32]\n",
      " [  8  32  16   8]\n",
      " [  2   4   8   4]]\n",
      "Unique Q: 3277\n",
      "\n",
      "Iteration :  75\n",
      "[[ 4  8  4  2]\n",
      " [16 64 32 16]\n",
      " [ 4 32  2  4]\n",
      " [ 2  4  8  2]]\n",
      "Unique Q: 3296\n",
      "\n",
      "Iteration :  76\n",
      "[[ 2 64  8  2]\n",
      " [16  2 64  8]\n",
      " [ 8  4  8  4]\n",
      " [ 2 16  4  2]]\n",
      "Unique Q: 3319\n",
      "\n",
      "Iteration :  77\n",
      "[[ 2  8  2  4]\n",
      " [ 8 32  8  2]\n",
      " [16  8 16  4]\n",
      " [ 4 64  4  2]]\n",
      "Unique Q: 3339\n",
      "\n",
      "Iteration :  78\n",
      "[[ 2  4  8  2]\n",
      " [ 4  8 16  8]\n",
      " [16 64  8  4]\n",
      " [ 8 16  4  2]]\n",
      "Unique Q: 3355\n",
      "\n",
      "Iteration :  79\n",
      "[[ 16   8  16   8]\n",
      " [  8  64   8   4]\n",
      " [128  32  16   2]\n",
      " [  4   8   2   4]]\n",
      "Unique Q: 3381\n",
      "\n",
      "Iteration :  80\n",
      "[[ 2  4 16  2]\n",
      " [16 64  8 16]\n",
      " [ 8  4 16  4]\n",
      " [16  2  8  2]]\n",
      "Unique Q: 3399\n",
      "\n",
      "Iteration :  81\n",
      "[[  2 128   2   8]\n",
      " [ 16   4  16   4]\n",
      " [  8  32   8   2]\n",
      " [  2   4   2   4]]\n",
      "Unique Q: 3416\n",
      "\n",
      "Iteration :  82\n",
      "[[  2  16   4   2]\n",
      " [ 16   4  16  32]\n",
      " [  4 128   4   8]\n",
      " [ 16   2  16   2]]\n",
      "Unique Q: 3438\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Iteration :  83\n",
      "[[ 2  4  8 16]\n",
      " [ 8 32 16  2]\n",
      " [ 2  8 64  4]\n",
      " [ 8 16  4  2]]\n",
      "Unique Q: 3459\n",
      "\n",
      "Iteration :  84\n",
      "[[ 8  2  4  2]\n",
      " [ 4 64 16  4]\n",
      " [32  2 32  8]\n",
      " [ 4 16  8  2]]\n",
      "Unique Q: 3482\n",
      "\n",
      "Iteration :  85\n",
      "[[  2  16   8   2]\n",
      " [  4   8 256   8]\n",
      " [ 32   4  32   2]\n",
      " [  8   2   8   4]]\n",
      "Unique Q: 3531\n",
      "\n",
      "Iteration :  86\n",
      "[[ 8 16  4  2]\n",
      " [ 4  8 64 16]\n",
      " [ 2 32  4  8]\n",
      " [ 4 16  8  2]]\n",
      "Unique Q: 3550\n",
      "\n",
      "Iteration :  87\n",
      "[[  2  32  16   4]\n",
      " [ 32   2  32  64]\n",
      " [  4 128   4  16]\n",
      " [  2   4  32   2]]\n",
      "Unique Q: 3583\n",
      "\n",
      "Iteration :  88\n",
      "[[  2   8   4   8]\n",
      " [  4 256  16   4]\n",
      " [  8  64   8   2]\n",
      " [  4   8   2   4]]\n",
      "Unique Q: 3614\n",
      "\n",
      "Iteration :  89\n",
      "[[16  2  4  2]\n",
      " [ 4 64 16  8]\n",
      " [ 8 32  4  2]\n",
      " [ 2  4  8  4]]\n",
      "Unique Q: 3632\n",
      "\n",
      "Iteration :  90\n",
      "[[  2   4   2   8]\n",
      " [  8  32  64  32]\n",
      " [  2  16 128   8]\n",
      " [  4   8   4   2]]\n",
      "Unique Q: 3656\n",
      "\n",
      "Iteration :  91\n",
      "[[  4   2   4   2]\n",
      " [  8   4   8 128]\n",
      " [  4   2 128  16]\n",
      " [  2  32   8   2]]\n",
      "Unique Q: 3678\n",
      "\n",
      "Iteration :  92\n",
      "[[ 4  2  8  2]\n",
      " [ 2  8 16  4]\n",
      " [16 32  8 64]\n",
      " [ 2 16  4  2]]\n",
      "Unique Q: 3700\n",
      "\n",
      "Iteration :  93\n",
      "[[ 2  4  8  2]\n",
      " [ 4 64  2 16]\n",
      " [ 2  8 16  2]\n",
      " [ 8  2 32  4]]\n",
      "Unique Q: 3722\n",
      "\n",
      "Iteration :  94\n",
      "[[  2  16   8   2]\n",
      " [  4 128  16   8]\n",
      " [  8  32   4   2]\n",
      " [  4   8   2   4]]\n",
      "Unique Q: 3745\n",
      "\n",
      "Iteration :  95\n",
      "[[  2  16   2   4]\n",
      " [  8  32 128   8]\n",
      " [  4   8  16   4]\n",
      " [  2   4   8   2]]\n",
      "Unique Q: 3766\n",
      "\n",
      "Iteration :  96\n",
      "[[  2   4   8   4]\n",
      " [  4 128  32  16]\n",
      " [  2   8  64  32]\n",
      " [  4  16   4   2]]\n",
      "Unique Q: 3798\n",
      "\n",
      "Iteration :  97\n",
      "[[ 2  4 16  2]\n",
      " [ 4  8  4 16]\n",
      " [16  4 16  4]\n",
      " [ 4  8  4  2]]\n",
      "Unique Q: 3810\n",
      "\n",
      "Iteration :  98\n",
      "[[  4  32   4   2]\n",
      " [  2   4 128   4]\n",
      " [  4  32   8  16]\n",
      " [  2   8  16   8]]\n",
      "Unique Q: 3827\n",
      "\n",
      "Iteration :  99\n",
      "[[ 4 16  4  2]\n",
      " [ 8  4 64  4]\n",
      " [16 64 32  8]\n",
      " [ 4 16  4  2]]\n",
      "Unique Q: 3841\n",
      "\n",
      "Iteration :  100\n",
      "[[ 4  2 16  2]\n",
      " [ 2 16  8  4]\n",
      " [16 32 16  8]\n",
      " [ 2  4  8  2]]\n",
      "Unique Q: 3855\n"
     ]
    }
   ],
   "source": [
    "for iteration in range(1, episodes + 1):\n",
    "    \n",
    "    prev_state = np.array([[0,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]])\n",
    "    \n",
    "    env.reset()\n",
    "\n",
    "    # print(\"Iteration : \", iteration)\n",
    "\n",
    "    counter = 0\n",
    "\n",
    "    while True:\n",
    "\n",
    "        # print(\"\")\n",
    "        counter += 1\n",
    "\n",
    "        # env.render()\n",
    "\n",
    "        p = 0\n",
    "        p = random.random()\n",
    "\n",
    "        if p < explore_rate:\n",
    "            action = env.action_space.sample()\n",
    "        else:\n",
    "            count = 0\n",
    "            for i in (Q[state[0], state[1], state[2]]):\n",
    "                if i == 0.0:\n",
    "                    count = count + 1\n",
    "            if count == 4:\n",
    "                action = random.randint(0, 3)\n",
    "            else:\n",
    "                action = np.argmax(Q[state[0], state[1], state[2]])\n",
    "            pass\n",
    "        \n",
    "        observation, reward, done, _ = env.step(action + 1)\n",
    "        # print(\"Action : \", action + 1)\n",
    "\n",
    "        merges = get_total_merges(observation)\n",
    "        empty_cells = get_empty_cells(observation)\n",
    "        monotonicity = get_monotonicity_index(np.array(observation))\n",
    "\n",
    "#         print(reward)\n",
    "        reward = merges + 10 * empty_cells + 10 * monotonicity[1] - 5 * monotonicity[2]\n",
    "\n",
    "        act=[]\n",
    "        if action == 0:\n",
    "            act = [1,0,0,0]\n",
    "        elif action==1:\n",
    "            act = [0,1,0,0]\n",
    "        elif action==2:\n",
    "            act = [0,0,1,0]\n",
    "        else:\n",
    "            act = [0,0,0,1]\n",
    "\n",
    "        p = []\n",
    "\n",
    "        for m in prev_state:\n",
    "            p += list(m)\n",
    "            \n",
    "        dump.append((p, reward, act))\n",
    "        \n",
    "        prev_state = observation\n",
    "\n",
    "#         print(reward)\n",
    "        total_reward = total_reward + reward\n",
    "\n",
    "        q_alpha = np.max(Q[monotonicity[0], empty_cells, merges])\n",
    "\n",
    "        Q[state][action] += learning_rate * (reward + discount_factor * q_alpha - Q[state][action])\n",
    "\n",
    "        state = (monotonicity[0], empty_cells, merges)\n",
    "\n",
    "        if done:\n",
    "            print(\"\\nIteration : \", iteration)\n",
    "            print(observation)\n",
    "            print(\"Unique Q:\", (np.count_nonzero(Q)))\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# dump=[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20446"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(dump)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 131, [1, 0, 0, 0]),\n",
       " ([2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 130, [0, 1, 0, 0]),\n",
       " ([2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 131, [0, 1, 0, 0]),\n",
       " ([0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 121, [0, 0, 1, 0]),\n",
       " ([2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 4], 121, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 4, 4], 111, [1, 0, 0, 0]),\n",
       " ([2, 0, 4, 4, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 110, [0, 1, 0, 0]),\n",
       " ([0, 0, 2, 8, 2, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0], 100, [0, 0, 1, 0]),\n",
       " ([0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 2, 0, 4, 2], 91, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 8, 2, 2, 4, 2], 82, [1, 0, 0, 0]),\n",
       " ([2, 2, 2, 2, 0, 0, 4, 8, 4, 0, 0, 2, 0, 0, 0, 0], 70, [0, 0, 1, 0]),\n",
       " ([0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 8, 4, 2, 4, 2], 72, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 8, 4, 4, 4, 2], 80, [0, 1, 0, 0]),\n",
       " ([0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 8, 0, 4, 8, 2], 72, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 4, 8, 0, 4, 8, 2], 63, [1, 0, 0, 0]),\n",
       " ([2, 2, 2, 2, 0, 4, 4, 8, 2, 0, 8, 2, 0, 0, 0, 0], 63, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 4, 8, 4, 4, 8, 2], 71, [0, 0, 0, 1]),\n",
       " ([0, 0, 0, 0, 4, 2, 0, 0, 2, 4, 8, 2, 8, 8, 2, 0], 71, [0, 1, 0, 0]),\n",
       " ([0, 0, 2, 0, 0, 0, 4, 2, 2, 4, 8, 2, 0, 0, 16, 2], 70, [0, 0, 1, 0]),\n",
       " ([0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 8, 2, 2, 4, 16, 4], 73, [1, 0, 0, 0]),\n",
       " ([4, 4, 2, 2, 0, 0, 4, 4, 0, 0, 8, 0, 0, 2, 16, 0], 91, [0, 0, 0, 1]),\n",
       " ([8, 4, 0, 0, 8, 0, 0, 4, 8, 0, 0, 0, 2, 16, 0, 0], 83, [0, 1, 0, 0]),\n",
       " ([0, 0, 8, 4, 0, 0, 8, 4, 0, 0, 0, 8, 0, 2, 2, 16], 93, [1, 0, 0, 0]),\n",
       " ([0, 2, 16, 8, 0, 2, 2, 8, 0, 0, 0, 16, 0, 0, 0, 0], 90, [0, 0, 0, 1]),\n",
       " ([2, 16, 8, 0, 4, 8, 0, 0, 16, 2, 0, 0, 0, 0, 0, 0], 81, [0, 1, 0, 0]),\n",
       " ([0, 2, 16, 8, 0, 0, 4, 8, 2, 0, 16, 2, 0, 0, 0, 0], 71, [0, 1, 0, 0]),\n",
       " ([0, 2, 16, 8, 0, 0, 4, 8, 0, 2, 16, 2, 2, 0, 0, 0], 80, [0, 0, 1, 0]),\n",
       " ([0, 0, 2, 0, 0, 0, 16, 0, 0, 0, 4, 16, 2, 4, 16, 2], 71, [0, 0, 1, 0]),\n",
       " ([0, 0, 2, 2, 0, 0, 16, 0, 0, 0, 4, 16, 2, 4, 16, 2], 61, [0, 0, 1, 0]),\n",
       " ([0, 2, 2, 0, 0, 0, 16, 2, 0, 0, 4, 16, 2, 4, 16, 2], 61, [0, 0, 0, 1]),\n",
       " ([4, 0, 0, 0, 16, 2, 2, 0, 4, 16, 0, 0, 2, 4, 16, 2], 53, [1, 0, 0, 0]),\n",
       " ([4, 2, 2, 2, 16, 16, 16, 0, 4, 4, 2, 0, 2, 0, 0, 0], 73, [0, 0, 0, 1]),\n",
       " ([4, 4, 2, 0, 32, 16, 0, 0, 8, 2, 0, 0, 2, 2, 0, 0], 80, [0, 1, 0, 0]),\n",
       " ([2, 0, 8, 2, 0, 0, 32, 16, 0, 0, 8, 2, 0, 0, 0, 4], 70, [0, 0, 1, 0]),\n",
       " ([2, 0, 0, 2, 0, 0, 8, 16, 0, 0, 32, 2, 2, 0, 8, 4], 70, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 2, 2, 0, 8, 16, 0, 0, 32, 2, 4, 0, 8, 4], 62, [0, 0, 0, 1]),\n",
       " ([2, 0, 0, 0, 2, 8, 16, 0, 32, 2, 2, 0, 4, 8, 4, 0], 61, [0, 0, 0, 1]),\n",
       " ([2, 0, 2, 0, 2, 8, 16, 0, 32, 4, 0, 0, 4, 8, 4, 0], 60, [1, 0, 0, 0]),\n",
       " ([4, 8, 2, 0, 32, 4, 16, 2, 4, 8, 4, 0, 0, 0, 0, 0], 51, [1, 0, 0, 0]),\n",
       " ([4, 8, 2, 2, 32, 4, 16, 0, 4, 8, 4, 0, 0, 0, 0, 2], 50, [1, 0, 0, 0]),\n",
       " ([4, 8, 2, 4, 32, 4, 16, 0, 4, 8, 4, 0, 2, 0, 0, 0], 40, [0, 0, 0, 1]),\n",
       " ([4, 8, 2, 4, 32, 4, 16, 0, 4, 8, 4, 0, 2, 0, 0, 2], 42, [0, 0, 0, 1]),\n",
       " ([4, 8, 2, 4, 32, 4, 16, 0, 4, 8, 4, 0, 4, 0, 4, 0], 51, [1, 0, 0, 0]),\n",
       " ([4, 8, 2, 4, 32, 4, 16, 0, 8, 8, 8, 2, 0, 0, 0, 0], 50, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 4, 0, 32, 4, 16, 0, 8, 16, 2, 0, 2, 0, 0], 42, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 4, 0, 32, 4, 16, 0, 8, 16, 2, 0, 0, 2, 2], 40, [1, 0, 0, 0]),\n",
       " ([4, 8, 2, 4, 0, 32, 4, 16, 0, 8, 16, 4, 2, 0, 2, 0], 41, [0, 0, 0, 1]),\n",
       " ([4, 8, 2, 4, 32, 4, 16, 0, 8, 16, 4, 0, 4, 4, 0, 0], 33, [0, 0, 1, 0]),\n",
       " ([4, 8, 0, 2, 32, 4, 2, 0, 8, 16, 16, 0, 4, 4, 4, 4], 23, [0, 0, 1, 0]),\n",
       " ([4, 8, 4, 0, 32, 4, 2, 0, 8, 16, 16, 2, 4, 4, 4, 4], 42, [0, 1, 0, 0]),\n",
       " ([0, 4, 8, 4, 0, 32, 4, 2, 2, 8, 32, 2, 0, 0, 8, 8], 44, [0, 0, 1, 0]),\n",
       " ([0, 0, 8, 2, 0, 4, 4, 4, 0, 32, 32, 4, 2, 8, 8, 8], 45, [0, 0, 1, 0]),\n",
       " ([0, 0, 8, 2, 0, 4, 4, 2, 0, 32, 32, 8, 2, 8, 8, 8], 62, [0, 1, 0, 0]),\n",
       " ([2, 0, 8, 2, 0, 0, 8, 2, 0, 0, 64, 8, 0, 2, 8, 16], 72, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 4, 0, 0, 16, 4, 0, 0, 64, 8, 2, 2, 8, 16], 73, [1, 0, 0, 0]),\n",
       " ([2, 2, 16, 8, 2, 0, 64, 8, 0, 0, 8, 16, 0, 0, 0, 0], 71, [0, 1, 0, 0]),\n",
       " ([0, 4, 16, 8, 0, 2, 64, 8, 0, 0, 8, 16, 2, 0, 0, 0], 73, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 16, 0, 2, 4, 64, 16, 2, 2, 8, 16], 80, [0, 0, 1, 0]),\n",
       " ([0, 2, 0, 0, 0, 0, 16, 0, 0, 4, 64, 0, 4, 2, 8, 32], 70, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 2, 0, 2, 16, 0, 0, 4, 64, 0, 4, 2, 8, 32], 60, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 2, 16, 0, 2, 4, 64, 2, 4, 2, 8, 32], 50, [0, 0, 1, 0]),\n",
       " ([2, 0, 0, 0, 0, 2, 16, 0, 2, 4, 64, 2, 4, 2, 8, 32], 53, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 2, 2, 16, 0, 4, 4, 64, 2, 4, 2, 8, 32], 50, [0, 0, 1, 0]),\n",
       " ([0, 0, 2, 0, 0, 2, 16, 0, 2, 4, 64, 2, 8, 2, 8, 32], 41, [0, 0, 0, 1]),\n",
       " ([2, 0, 2, 0, 2, 16, 0, 0, 2, 4, 64, 2, 8, 2, 8, 32], 40, [0, 1, 0, 0]),\n",
       " ([2, 0, 0, 4, 0, 0, 2, 16, 2, 4, 64, 2, 8, 2, 8, 32], 41, [1, 0, 0, 0]),\n",
       " ([4, 4, 2, 4, 8, 2, 64, 16, 0, 0, 8, 2, 0, 0, 2, 32], 42, [0, 0, 0, 1]),\n",
       " ([8, 2, 4, 0, 8, 2, 64, 16, 8, 2, 0, 0, 2, 32, 2, 0], 31, [0, 1, 0, 0]),\n",
       " ([0, 8, 2, 4, 8, 2, 64, 16, 2, 0, 8, 2, 0, 2, 32, 2], 25, [0, 0, 0, 1]),\n",
       " ([8, 2, 4, 0, 8, 2, 64, 16, 2, 8, 2, 0, 2, 32, 2, 2], 51, [0, 0, 1, 0]),\n",
       " ([0, 2, 0, 0, 0, 4, 4, 0, 16, 8, 64, 16, 4, 32, 4, 2], 41, [0, 0, 1, 0]),\n",
       " ([0, 2, 0, 0, 2, 4, 4, 0, 16, 8, 64, 16, 4, 32, 4, 2], 40, [0, 1, 0, 0]),\n",
       " ([0, 0, 0, 2, 0, 4, 2, 8, 16, 8, 64, 16, 4, 32, 4, 2], 30, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 2, 2, 4, 2, 8, 16, 8, 64, 16, 4, 32, 4, 2], 22, [1, 0, 0, 0]),\n",
       " ([2, 4, 2, 2, 16, 8, 64, 8, 4, 32, 4, 16, 0, 0, 2, 2], 12, [0, 0, 1, 0]),\n",
       " ([0, 2, 2, 2, 2, 4, 64, 8, 16, 8, 4, 16, 4, 32, 2, 2], 3, [1, 0, 0, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 3, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 2, 2], 23, [0, 0, 0, 1]),\n",
       " ([4, 4, 0, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 32, 4, 0], 21, [0, 1, 0, 0]),\n",
       " ([0, 0, 8, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 2, 32, 4], 20, [0, 1, 0, 0]),\n",
       " ([0, 0, 8, 2, 16, 4, 64, 8, 4, 8, 4, 16, 2, 4, 32, 4], 11, [0, 0, 0, 1]),\n",
       " ([8, 2, 2, 0, 16, 4, 64, 8, 4, 8, 4, 16, 2, 4, 32, 4], 2, [1, 0, 0, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 2, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 8, 16, 4, 64, 16, 4, 8, 4, 4, 2, 4, 32, 2], 12, [0, 1, 0, 0]),\n",
       " ([2, 8, 4, 8, 16, 4, 64, 16, 0, 4, 8, 8, 2, 4, 32, 2], 11, [0, 0, 0, 1]),\n",
       " ([2, 8, 4, 8, 16, 4, 64, 16, 4, 16, 0, 2, 2, 4, 32, 2], 3, [0, 1, 0, 0]),\n",
       " ([2, 8, 4, 8, 16, 4, 64, 16, 4, 4, 16, 2, 2, 4, 32, 2], 2, [0, 0, 0, 1]),\n",
       " ([2, 8, 4, 8, 16, 4, 64, 16, 8, 16, 2, 2, 2, 4, 32, 2], 0, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 131, [1, 0, 0, 0]),\n",
       " ([0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 122, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2], 132, [0, 1, 0, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4], 130, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 8, 4], 120, [1, 0, 0, 0]),\n",
       " ([0, 0, 8, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0], 110, [0, 0, 0, 1]),\n",
       " ([8, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0], 100, [1, 0, 0, 0]),\n",
       " ([8, 2, 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0], 91, [1, 0, 0, 0]),\n",
       " ([8, 2, 2, 2, 4, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0], 100, [0, 1, 0, 0]),\n",
       " ([0, 8, 2, 4, 0, 0, 0, 8, 2, 0, 0, 2, 0, 0, 0, 0], 101, [0, 0, 0, 1]),\n",
       " ([8, 2, 4, 0, 8, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0], 101, [0, 1, 0, 0]),\n",
       " ([0, 8, 2, 4, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 2, 0], 110, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 8, 4, 16], 100, [0, 0, 0, 1]),\n",
       " ([0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 8, 4, 16, 0], 90, [1, 0, 0, 0]),\n",
       " ([2, 4, 2, 0, 4, 0, 16, 0, 8, 0, 2, 0, 0, 0, 0, 0], 80, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 4, 2, 0, 2, 0, 4, 0, 16, 0, 8, 4, 2, 0], 70, [1, 0, 0, 0]),\n",
       " ([2, 4, 2, 4, 4, 0, 16, 0, 8, 0, 2, 0, 0, 0, 0, 2], 62, [0, 0, 1, 0]),\n",
       " ([2, 0, 0, 0, 2, 0, 2, 0, 4, 0, 16, 4, 8, 4, 2, 2], 73, [0, 0, 0, 1]),\n",
       " ([2, 0, 0, 0, 4, 0, 0, 2, 4, 16, 4, 0, 8, 4, 4, 0], 72, [0, 1, 0, 0]),\n",
       " ([2, 0, 0, 2, 0, 0, 4, 2, 0, 4, 16, 4, 0, 0, 8, 8], 73, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 2, 0, 4, 4, 0, 0, 16, 4, 2, 4, 8, 8], 81, [0, 0, 0, 1]),\n",
       " ([0, 0, 0, 0, 2, 8, 0, 0, 16, 4, 2, 0, 2, 4, 16, 0], 81, [1, 0, 0, 0]),\n",
       " ([2, 8, 2, 4, 16, 8, 16, 0, 2, 0, 0, 0, 0, 0, 0, 0], 71, [0, 0, 0, 1]),\n",
       " ([2, 8, 2, 4, 16, 8, 16, 0, 2, 0, 0, 0, 0, 0, 0, 2], 70, [1, 0, 0, 0]),\n",
       " ([2, 16, 2, 4, 16, 0, 16, 2, 2, 0, 0, 0, 0, 0, 2, 0], 73, [0, 0, 0, 1]),\n",
       " ([2, 16, 2, 4, 32, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0], 72, [0, 0, 0, 1]),\n",
       " ([2, 16, 2, 4, 32, 4, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0], 81, [1, 0, 0, 0]),\n",
       " ([2, 16, 4, 4, 32, 4, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0], 81, [0, 0, 1, 0]),\n",
       " ([0, 2, 0, 0, 2, 0, 0, 0, 32, 16, 0, 0, 4, 4, 8, 4], 82, [0, 0, 0, 1]),\n",
       " ([2, 0, 0, 0, 2, 0, 0, 0, 32, 16, 0, 2, 8, 8, 4, 0], 81, [0, 0, 1, 0]),\n",
       " ([0, 0, 2, 0, 4, 0, 0, 0, 32, 16, 0, 0, 8, 8, 4, 2], 80, [0, 0, 0, 1]),\n",
       " ([2, 0, 2, 0, 4, 0, 0, 0, 32, 16, 0, 0, 16, 4, 2, 0], 81, [0, 1, 0, 0]),\n",
       " ([0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 32, 16, 0, 16, 4, 2], 71, [0, 1, 0, 0]),\n",
       " ([0, 0, 0, 4, 0, 2, 0, 4, 0, 4, 32, 16, 0, 16, 4, 2], 61, [0, 1, 0, 0]),\n",
       " ([0, 0, 0, 4, 0, 0, 2, 4, 0, 4, 32, 16, 2, 16, 4, 2], 52, [0, 0, 0, 1]),\n",
       " ([4, 4, 0, 0, 2, 4, 0, 0, 4, 32, 16, 0, 2, 16, 4, 2], 50, [0, 0, 0, 1]),\n",
       " ([8, 0, 0, 0, 2, 4, 2, 0, 4, 32, 16, 0, 2, 16, 4, 2], 41, [0, 0, 1, 0]),\n",
       " ([8, 0, 0, 0, 2, 4, 2, 2, 4, 32, 16, 0, 2, 16, 4, 2], 40, [1, 0, 0, 0]),\n",
       " ([8, 4, 2, 4, 2, 32, 16, 0, 4, 16, 4, 2, 2, 0, 0, 0], 31, [0, 0, 0, 1]),\n",
       " ([8, 4, 2, 4, 2, 32, 16, 2, 4, 16, 4, 2, 2, 0, 0, 0], 21, [0, 0, 0, 1]),\n",
       " ([8, 4, 2, 4, 2, 32, 16, 2, 4, 16, 4, 2, 2, 0, 0, 2], 21, [0, 0, 1, 0]),\n",
       " ([8, 2, 0, 0, 2, 4, 2, 4, 4, 32, 16, 2, 2, 16, 4, 4], 22, [0, 0, 0, 1]),\n",
       " ([8, 2, 2, 0, 2, 4, 2, 4, 4, 32, 16, 2, 2, 16, 8, 0], 21, [1, 0, 0, 0]),\n",
       " ([8, 2, 4, 4, 2, 4, 16, 2, 4, 32, 8, 0, 2, 16, 2, 0], 11, [0, 0, 1, 0]),\n",
       " ([8, 2, 4, 0, 2, 4, 16, 2, 4, 32, 8, 4, 2, 16, 2, 2], 12, [0, 1, 0, 0]),\n",
       " ([2, 8, 2, 4, 2, 4, 16, 2, 4, 32, 8, 4, 0, 2, 16, 4], 22, [0, 0, 1, 0]),\n",
       " ([0, 8, 2, 2, 0, 4, 16, 4, 4, 32, 8, 2, 4, 2, 16, 8], 21, [0, 0, 0, 1]),\n",
       " ([8, 4, 2, 0, 4, 16, 4, 0, 4, 32, 8, 2, 4, 2, 16, 8], 21, [0, 0, 1, 0]),\n",
       " ([0, 4, 2, 0, 8, 16, 4, 2, 4, 32, 8, 2, 8, 2, 16, 8], 13, [0, 1, 0, 0]),\n",
       " ([0, 4, 4, 2, 8, 16, 4, 2, 4, 32, 8, 2, 8, 2, 16, 8], 21, [1, 0, 0, 0]),\n",
       " ([8, 4, 8, 4, 4, 16, 8, 2, 8, 32, 16, 8, 0, 2, 0, 4], 11, [0, 1, 0, 0]),\n",
       " ([8, 4, 8, 4, 4, 16, 8, 2, 8, 32, 16, 8, 2, 0, 2, 4], 12, [0, 1, 0, 0]),\n",
       " ([8, 4, 8, 4, 4, 16, 8, 2, 8, 32, 16, 8, 2, 0, 4, 4], 14, [0, 0, 1, 0]),\n",
       " ([8, 0, 2, 4, 4, 4, 16, 2, 8, 16, 16, 8, 2, 32, 4, 4], 33, [0, 1, 0, 0]),\n",
       " ([2, 8, 2, 4, 0, 8, 16, 2, 0, 8, 32, 8, 0, 2, 32, 8], 25, [0, 0, 0, 1]),\n",
       " ([2, 8, 2, 4, 8, 16, 2, 2, 8, 32, 8, 0, 2, 32, 8, 0], 52, [0, 0, 1, 0]),\n",
       " ([0, 0, 2, 0, 2, 8, 0, 0, 16, 16, 4, 4, 2, 64, 16, 2], 42, [1, 0, 0, 0]),\n",
       " ([2, 8, 2, 4, 16, 16, 4, 2, 2, 64, 16, 2, 0, 0, 0, 0], 43, [1, 0, 0, 0]),\n",
       " ([2, 8, 2, 4, 16, 16, 4, 4, 2, 64, 16, 0, 0, 2, 0, 0], 53, [0, 0, 0, 1]),\n",
       " ([2, 8, 2, 4, 32, 8, 0, 0, 2, 64, 16, 0, 2, 2, 0, 0], 61, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 2, 16, 2, 0, 32, 64, 2, 0, 4, 2, 16, 4], 51, [0, 1, 0, 0]),\n",
       " ([0, 0, 0, 0, 0, 2, 16, 2, 2, 32, 64, 2, 4, 2, 16, 4], 41, [0, 1, 0, 0]),\n",
       " ([0, 0, 0, 2, 0, 2, 16, 2, 2, 32, 64, 2, 4, 2, 16, 4], 31, [0, 1, 0, 0]),\n",
       " ([2, 0, 0, 2, 0, 2, 16, 2, 2, 32, 64, 2, 4, 2, 16, 4], 32, [0, 0, 0, 1]),\n",
       " ([4, 0, 2, 0, 2, 16, 2, 0, 2, 32, 64, 2, 4, 2, 16, 4], 21, [0, 1, 0, 0]),\n",
       " ([2, 0, 4, 2, 0, 2, 16, 2, 2, 32, 64, 2, 4, 2, 16, 4], 33, [0, 0, 1, 0]),\n",
       " ([0, 0, 4, 2, 0, 2, 16, 2, 4, 32, 64, 4, 4, 2, 16, 4], 51, [1, 0, 0, 0]),\n",
       " ([8, 2, 4, 4, 0, 32, 16, 8, 0, 2, 64, 2, 0, 0, 16, 0], 41, [0, 0, 1, 0]),\n",
       " ([0, 4, 4, 0, 0, 2, 16, 4, 0, 32, 64, 8, 8, 2, 16, 2], 40, [0, 0, 0, 1]),\n",
       " ([8, 0, 2, 0, 2, 16, 4, 0, 32, 64, 8, 0, 8, 2, 16, 2], 30, [0, 0, 1, 0]),\n",
       " ([8, 0, 2, 0, 2, 16, 4, 2, 32, 64, 8, 0, 8, 2, 16, 2], 21, [0, 0, 0, 1]),\n",
       " ([8, 2, 0, 0, 2, 16, 4, 2, 32, 64, 8, 2, 8, 2, 16, 2], 22, [1, 0, 0, 0]),\n",
       " ([8, 2, 4, 4, 2, 16, 8, 2, 32, 64, 16, 0, 8, 2, 2, 0], 12, [1, 0, 0, 0]),\n",
       " ([8, 2, 4, 4, 2, 16, 8, 2, 32, 64, 16, 0, 8, 2, 2, 2], 21, [0, 0, 0, 1]),\n",
       " ([8, 2, 8, 0, 2, 16, 8, 2, 32, 64, 16, 0, 8, 4, 2, 4], 11, [0, 1, 0, 0]),\n",
       " ([2, 8, 2, 8, 2, 16, 8, 2, 0, 32, 64, 16, 8, 4, 2, 4], 1, [0, 1, 0, 0]),\n",
       " ([2, 8, 2, 8, 2, 16, 8, 2, 2, 32, 64, 16, 8, 4, 2, 4], 1, [0, 0, 1, 0]),\n",
       " ([2, 8, 2, 8, 2, 16, 8, 2, 4, 32, 64, 16, 8, 4, 2, 4], 1, [0, 0, 1, 0]),\n",
       " ([2, 8, 2, 8, 4, 16, 8, 2, 4, 32, 64, 16, 8, 4, 2, 4], 2, [0, 0, 1, 0]),\n",
       " ([2, 8, 2, 8, 2, 16, 8, 2, 8, 32, 64, 16, 8, 4, 2, 4], 11, [1, 0, 0, 0]),\n",
       " ([4, 8, 2, 8, 16, 16, 8, 2, 2, 32, 64, 16, 0, 4, 2, 4], 12, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 0, 4, 2, 4], 2, [0, 0, 0, 1]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 0, 0, 1]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 0, 0, 1]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 0, 0, 1]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 2, [0, 1, 0, 0]),\n",
       " ([4, 8, 2, 8, 2, 32, 8, 2, 2, 32, 64, 16, 4, 2, 4, 2], 13, [0, 0, 1, 0]),\n",
       " ([2, 0, 2, 8, 4, 8, 8, 2, 4, 64, 64, 16, 4, 2, 4, 2], 13, [0, 0, 1, 0]),\n",
       " ([2, 0, 2, 8, 2, 8, 8, 2, 4, 64, 64, 16, 8, 2, 4, 2], 13, [0, 0, 1, 0]),\n",
       " ([0, 4, 2, 8, 4, 8, 8, 2, 4, 64, 64, 16, 8, 2, 4, 2], 13, [0, 0, 1, 0]),\n",
       " ([0, 4, 2, 8, 2, 8, 8, 2, 8, 64, 64, 16, 8, 2, 4, 2], 13, [0, 0, 1, 0]),\n",
       " ([4, 4, 2, 8, 0, 8, 8, 2, 2, 64, 64, 16, 16, 2, 4, 2], 4, [1, 0, 0, 0]),\n",
       " ([4, 4, 2, 8, 2, 8, 8, 2, 16, 64, 64, 16, 2, 2, 4, 2], 32, [0, 0, 0, 1]),\n",
       " ([8, 2, 8, 0, 2, 16, 2, 2, 16, 128, 16, 0, 4, 4, 2, 0], 41, [0, 0, 0, 1]),\n",
       " ([8, 2, 8, 0, 2, 16, 4, 4, 16, 128, 16, 0, 8, 2, 0, 0], 30, [1, 0, 0, 0]),\n",
       " ([8, 2, 8, 4, 2, 16, 4, 0, 16, 128, 16, 0, 8, 2, 0, 2], 21, [0, 0, 1, 0]),\n",
       " ([8, 2, 0, 0, 2, 16, 8, 2, 16, 128, 4, 4, 8, 2, 16, 2], 22, [0, 0, 0, 1]),\n",
       " ([8, 2, 2, 0, 2, 16, 8, 2, 16, 128, 8, 0, 8, 2, 16, 2], 32, [0, 0, 1, 0]),\n",
       " ([8, 2, 0, 0, 2, 16, 2, 2, 16, 128, 16, 0, 8, 2, 16, 4], 31, [0, 0, 0, 1]),\n",
       " ([8, 2, 0, 0, 2, 16, 4, 0, 16, 128, 16, 2, 8, 2, 16, 4], 22, [0, 0, 0, 1]),\n",
       " ([8, 2, 0, 0, 2, 16, 4, 2, 16, 128, 16, 2, 8, 2, 16, 4], 32, [1, 0, 0, 0]),\n",
       " ([8, 2, 4, 4, 2, 16, 32, 4, 16, 128, 2, 0, 8, 2, 0, 0], 30, [1, 0, 0, 0]),\n",
       " ([8, 2, 4, 8, 2, 16, 32, 0, 16, 128, 2, 0, 8, 2, 0, 2], 21, [0, 0, 1, 0]),\n",
       " ([8, 2, 0, 2, 2, 16, 4, 0, 16, 128, 32, 8, 8, 2, 2, 2], 12, [0, 0, 1, 0]),\n",
       " ([8, 2, 2, 0, 2, 16, 4, 2, 16, 128, 32, 8, 8, 2, 2, 2], 20, [0, 1, 0, 0]),\n",
       " ([0, 0, 8, 4, 2, 16, 4, 2, 16, 128, 32, 8, 2, 8, 2, 4], 11, [0, 0, 0, 1]),\n",
       " ([8, 4, 0, 2, 2, 16, 4, 2, 16, 128, 32, 8, 2, 8, 2, 4], 3, [0, 1, 0, 0]),\n",
       " ([2, 8, 4, 2, 2, 16, 4, 2, 16, 128, 32, 8, 2, 8, 2, 4], 23, [1, 0, 0, 0]),\n",
       " ([4, 8, 8, 4, 16, 16, 32, 8, 2, 128, 2, 4, 0, 8, 2, 0], 31, [0, 1, 0, 0]),\n",
       " ([0, 4, 16, 4, 0, 32, 32, 8, 2, 128, 2, 4, 0, 2, 8, 2], 32, [0, 0, 0, 1]),\n",
       " ([4, 16, 4, 0, 64, 8, 0, 2, 2, 128, 2, 4, 2, 8, 2, 0], 42, [1, 0, 0, 0]),\n",
       " ([4, 16, 4, 2, 64, 8, 4, 4, 4, 128, 0, 0, 2, 8, 0, 0], 41, [0, 1, 0, 0]),\n",
       " ([4, 16, 4, 2, 0, 64, 8, 8, 0, 0, 4, 128, 2, 0, 2, 8], 52, [0, 0, 0, 1]),\n",
       " ([4, 16, 4, 2, 64, 16, 2, 0, 4, 128, 0, 0, 4, 8, 0, 0], 42, [0, 0, 0, 1]),\n",
       " ([4, 16, 4, 2, 64, 16, 2, 0, 4, 128, 0, 0, 4, 8, 2, 0], 62, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 2, 4, 32, 0, 0, 64, 128, 4, 0, 8, 8, 4, 2], 60, [0, 0, 0, 1]),\n",
       " ([2, 0, 4, 0, 4, 32, 0, 0, 64, 128, 4, 0, 16, 4, 2, 0], 51, [0, 0, 0, 1]),\n",
       " ([2, 4, 0, 0, 4, 32, 0, 0, 64, 128, 4, 4, 16, 4, 2, 0], 42, [1, 0, 0, 0]),\n",
       " ([2, 4, 4, 4, 4, 32, 2, 2, 64, 128, 0, 0, 16, 4, 0, 0], 51, [0, 0, 0, 1]),\n",
       " ([2, 8, 4, 2, 4, 32, 4, 0, 64, 128, 0, 0, 16, 4, 0, 0], 51, [1, 0, 0, 0]),\n",
       " ([2, 8, 8, 2, 4, 32, 0, 0, 64, 128, 2, 0, 16, 4, 0, 0], 51, [0, 0, 0, 1]),\n",
       " ([2, 16, 2, 2, 4, 32, 0, 0, 64, 128, 2, 0, 16, 4, 0, 0], 51, [0, 0, 0, 1]),\n",
       " ([2, 16, 4, 0, 4, 32, 0, 0, 64, 128, 2, 2, 16, 4, 0, 0], 40, [1, 0, 0, 0]),\n",
       " ([2, 16, 4, 2, 4, 32, 2, 0, 64, 128, 0, 0, 16, 4, 0, 2], 41, [0, 0, 1, 0]),\n",
       " ([2, 16, 0, 0, 4, 32, 4, 0, 64, 128, 4, 0, 16, 4, 2, 4], 31, [0, 1, 0, 0]),\n",
       " ([2, 0, 2, 16, 0, 4, 32, 4, 0, 64, 128, 4, 16, 4, 2, 4], 32, [0, 0, 0, 1]),\n",
       " ([4, 16, 0, 0, 4, 32, 4, 2, 64, 128, 4, 0, 16, 4, 2, 4], 40, [1, 0, 0, 0]),\n",
       " ([8, 16, 8, 2, 64, 32, 2, 4, 16, 128, 0, 0, 0, 4, 0, 2], 32, [0, 0, 1, 0]),\n",
       " ([0, 16, 0, 2, 8, 32, 0, 2, 64, 128, 8, 4, 16, 4, 2, 2], 31, [0, 0, 0, 1]),\n",
       " ([16, 2, 0, 2, 8, 32, 2, 0, 64, 128, 8, 4, 16, 4, 4, 0], 40, [0, 1, 0, 0]),\n",
       " ([2, 0, 16, 4, 0, 8, 32, 2, 64, 128, 8, 4, 0, 0, 16, 8], 30, [0, 0, 0, 1]),\n",
       " ([2, 16, 4, 0, 8, 32, 2, 0, 64, 128, 8, 4, 16, 8, 0, 2], 21, [0, 0, 1, 0]),\n",
       " ([2, 16, 2, 0, 8, 32, 4, 0, 64, 128, 2, 4, 16, 8, 8, 2], 12, [0, 0, 1, 0]),\n",
       " ([2, 16, 2, 2, 8, 32, 4, 0, 64, 128, 2, 4, 16, 8, 8, 2], 24, [0, 0, 0, 1]),\n",
       " ([2, 16, 4, 0, 8, 32, 4, 0, 64, 128, 2, 4, 16, 16, 2, 2], 31, [1, 0, 0, 0]),\n",
       " ([2, 16, 8, 4, 8, 32, 4, 2, 64, 128, 0, 0, 16, 16, 2, 0], 31, [0, 0, 0, 1]),\n",
       " ([2, 16, 8, 4, 8, 32, 4, 2, 64, 128, 0, 2, 32, 2, 0, 0], 22, [0, 0, 0, 1]),\n",
       " ([2, 16, 8, 4, 8, 32, 4, 2, 64, 128, 2, 0, 32, 2, 2, 0], 22, [0, 0, 0, 1]),\n",
       " ([2, 16, 8, 4, 8, 32, 4, 2, 64, 128, 2, 2, 32, 4, 0, 0], 22, [0, 0, 0, 1]),\n",
       " ([2, 16, 8, 4, 8, 32, 4, 2, 64, 128, 4, 2, 32, 4, 0, 0], 13, [0, 0, 0, 1]),\n",
       " ([2, 16, 8, 4, 8, 32, 4, 2, 64, 128, 4, 2, 32, 4, 4, 0], 12, [0, 1, 0, 0]),\n",
       " ([2, 16, 8, 4, 8, 32, 4, 2, 64, 128, 4, 2, 0, 2, 32, 8], 22, [0, 0, 1, 0]),\n",
       " ([0, 16, 0, 4, 2, 32, 8, 4, 8, 128, 8, 4, 64, 2, 32, 8], 13, [0, 1, 0, 0]),\n",
       " ([2, 0, 16, 4, 2, 32, 8, 4, 8, 128, 8, 4, 64, 2, 32, 8], 32, [0, 0, 1, 0]),\n",
       " ([0, 2, 0, 0, 4, 32, 16, 4, 8, 128, 16, 8, 64, 2, 32, 8], 22, [0, 1, 0, 0]),\n",
       " ([0, 2, 0, 2, 4, 32, 16, 4, 8, 128, 16, 8, 64, 2, 32, 8], 23, [0, 1, 0, 0]),\n",
       " ([2, 0, 0, 4, 4, 32, 16, 4, 8, 128, 16, 8, 64, 2, 32, 8], 41, [0, 0, 1, 0]),\n",
       " ([2, 0, 0, 0, 4, 32, 4, 0, 8, 128, 32, 8, 64, 2, 32, 16], 40, [0, 0, 1, 0]),\n",
       " ([2, 0, 2, 0, 4, 32, 0, 0, 8, 128, 4, 8, 64, 2, 64, 16], 30, [0, 0, 1, 0]),\n",
       " ([2, 0, 0, 2, 4, 32, 2, 0, 8, 128, 4, 8, 64, 2, 64, 16], 31, [0, 0, 0, 1]),\n",
       " ([4, 2, 0, 0, 4, 32, 2, 0, 8, 128, 4, 8, 64, 2, 64, 16], 32, [0, 0, 1, 0]),\n",
       " ([2, 2, 0, 0, 8, 32, 2, 0, 8, 128, 4, 8, 64, 2, 64, 16], 31, [0, 0, 0, 1]),\n",
       " ([4, 0, 0, 2, 8, 32, 2, 0, 8, 128, 4, 8, 64, 2, 64, 16], 31, [1, 0, 0, 0]),\n",
       " ([4, 32, 2, 2, 16, 128, 4, 8, 64, 2, 64, 16, 0, 0, 4, 0], 32, [0, 0, 0, 1]),\n",
       " ([4, 32, 4, 0, 16, 128, 4, 8, 64, 2, 64, 16, 4, 2, 0, 0], 22, [0, 0, 0, 1]),\n",
       " ([4, 32, 4, 2, 16, 128, 4, 8, 64, 2, 64, 16, 4, 2, 0, 0], 32, [0, 0, 1, 0]),\n",
       " ([4, 0, 2, 0, 16, 32, 0, 2, 64, 128, 8, 8, 4, 4, 64, 16], 42, [0, 1, 0, 0]),\n",
       " ([0, 2, 4, 2, 0, 16, 32, 2, 0, 64, 128, 16, 0, 8, 64, 16], 32, [0, 0, 0, 1]),\n",
       " ([2, 4, 2, 0, 16, 32, 2, 0, 64, 128, 16, 0, 8, 64, 16, 2], 42, [1, 0, 0, 0]),\n",
       " ([2, 4, 4, 2, 16, 32, 32, 0, 64, 128, 4, 0, 8, 64, 0, 0], 32, [1, 0, 0, 0]),\n",
       " ([2, 4, 4, 2, 16, 32, 32, 0, 64, 128, 4, 0, 8, 64, 2, 0], 41, [0, 1, 0, 0]),\n",
       " ([0, 2, 8, 2, 0, 2, 16, 64, 0, 64, 128, 4, 0, 8, 64, 2], 40, [1, 0, 0, 0]),\n",
       " ([0, 4, 8, 2, 0, 64, 16, 64, 0, 8, 128, 4, 0, 2, 64, 2], 31, [1, 0, 0, 0]),\n",
       " ([0, 4, 8, 2, 0, 64, 16, 64, 0, 8, 128, 4, 2, 2, 64, 2], 20, [1, 0, 0, 0]),\n",
       " ([2, 4, 8, 2, 0, 64, 16, 64, 2, 8, 128, 4, 0, 2, 64, 2], 12, [0, 0, 0, 1]),\n",
       " ([2, 4, 8, 2, 64, 16, 64, 2, 2, 8, 128, 4, 2, 64, 2, 0], 21, [0, 0, 1, 0]),\n",
       " ([0, 4, 8, 0, 2, 16, 64, 2, 64, 8, 128, 4, 4, 64, 2, 4], 20, [0, 0, 1, 0]),\n",
       " ([0, 4, 8, 0, 2, 16, 64, 4, 64, 8, 128, 2, 4, 64, 2, 8], 11, [0, 0, 0, 1]),\n",
       " ([4, 8, 0, 4, 2, 16, 64, 4, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 1, 0, 0]),\n",
       " ([4, 4, 8, 4, 2, 16, 64, 4, 64, 8, 128, 2, 4, 64, 2, 8], 1, [0, 0, 1, 0]),\n",
       " ([4, 4, 8, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 0, 1]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [1, 0, 0, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [1, 0, 0, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [1, 0, 0, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 2, [0, 0, 1, 0]),\n",
       " ([8, 8, 2, 2, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 11, [0, 1, 0, 0]),\n",
       " ([2, 0, 16, 4, 2, 16, 64, 8, 64, 8, 128, 2, 4, 64, 2, 8], 0, [0, 1, 0, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 131, [1, 0, 0, 0]),\n",
       " ([0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0], 130, [0, 0, 0, 1]),\n",
       " ([4, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 121, [1, 0, 0, 0]),\n",
       " ([4, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0], 121, [1, 0, 0, 0]),\n",
       " ([4, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2], 121, [1, 0, 0, 0]),\n",
       " ([8, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 111, [1, 0, 0, 0]),\n",
       " ([8, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 102, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 0, 2, 8, 0, 0, 0, 2, 2, 2, 2], 112, [0, 0, 0, 1]),\n",
       " ([2, 0, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 4, 4, 0, 0], 112, [0, 0, 0, 1]),\n",
       " ([2, 0, 4, 0, 2, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0], 101, [0, 1, 0, 0]),\n",
       " ([0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 0, 8], 93, [0, 1, 0, 0]),\n",
       " ([0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 2, 8, 0, 0, 0, 8], 92, [0, 1, 0, 0]),\n",
       " ([0, 0, 2, 4, 0, 0, 0, 4, 0, 0, 2, 8, 0, 0, 4, 8], 111, [0, 0, 1, 0]),\n",
       " ([2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 4, 16], 110, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 2, 0, 8, 16], 100, [0, 1, 0, 0]),\n",
       " ([0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 8, 0, 2, 8, 16], 90, [0, 1, 0, 0]),\n",
       " ([0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 8, 0, 2, 8, 16], 92, [0, 0, 0, 1]),\n",
       " ([0, 0, 0, 0, 4, 0, 0, 2, 2, 8, 0, 0, 2, 8, 16, 0], 102, [1, 0, 0, 0]),\n",
       " ([4, 16, 16, 2, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0], 101, [0, 0, 0, 1]),\n",
       " ([4, 32, 2, 0, 4, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0], 100, [1, 0, 0, 0]),\n",
       " ([8, 32, 2, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 90, [1, 0, 0, 0]),\n",
       " ([8, 32, 2, 0, 4, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0], 91, [0, 1, 0, 0]),\n",
       " ([0, 8, 32, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0], 82, [0, 0, 0, 1]),\n",
       " ([8, 32, 2, 2, 2, 4, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0], 81, [0, 0, 0, 1]),\n",
       " ([8, 32, 4, 0, 2, 4, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0], 71, [1, 0, 0, 0]),\n",
       " ([8, 32, 4, 2, 2, 4, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0], 72, [1, 0, 0, 0]),\n",
       " ([8, 32, 4, 2, 2, 4, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0], 70, [0, 0, 0, 1]),\n",
       " ([8, 32, 4, 2, 2, 8, 0, 0, 4, 2, 0, 0, 0, 0, 0, 4], 60, [0, 1, 0, 0]),\n",
       " ([8, 32, 4, 2, 2, 0, 2, 8, 0, 0, 4, 2, 0, 0, 0, 4], 61, [0, 0, 0, 1]),\n",
       " ([8, 32, 4, 2, 4, 8, 0, 0, 4, 2, 0, 0, 4, 0, 4, 0], 61, [0, 1, 0, 0]),\n",
       " ([8, 32, 4, 2, 0, 0, 4, 8, 0, 0, 4, 2, 0, 2, 0, 8], 60, [1, 0, 0, 0]),\n",
       " ([8, 32, 8, 2, 0, 2, 4, 8, 0, 0, 0, 2, 0, 0, 2, 8], 52, [1, 0, 0, 0]),\n",
       " ([8, 32, 8, 2, 0, 2, 4, 8, 0, 2, 2, 2, 0, 0, 0, 8], 52, [0, 0, 1, 0]),\n",
       " ([0, 0, 2, 2, 0, 0, 8, 8, 0, 32, 4, 2, 8, 4, 2, 8], 44, [1, 0, 0, 0]),\n",
       " ([8, 32, 2, 2, 0, 4, 8, 8, 0, 4, 4, 2, 0, 0, 2, 8], 60, [0, 1, 0, 0]),\n",
       " ([2, 8, 32, 4, 0, 0, 4, 16, 0, 0, 8, 2, 0, 0, 2, 8], 50, [1, 0, 0, 0]),\n",
       " ([2, 8, 32, 4, 0, 0, 4, 16, 0, 0, 8, 2, 2, 0, 2, 8], 51, [1, 0, 0, 0]),\n",
       " ([4, 8, 32, 4, 0, 0, 4, 16, 0, 0, 8, 2, 0, 2, 2, 8], 41, [1, 0, 0, 0]),\n",
       " ([4, 8, 32, 4, 2, 2, 4, 16, 0, 0, 8, 2, 0, 0, 2, 8], 42, [0, 0, 0, 1]),\n",
       " ([4, 8, 32, 4, 4, 4, 16, 0, 8, 2, 4, 0, 2, 8, 0, 0], 43, [1, 0, 0, 0]),\n",
       " ([8, 8, 32, 4, 8, 4, 16, 0, 2, 2, 4, 0, 4, 8, 0, 0], 42, [0, 0, 1, 0]),\n",
       " ([2, 8, 0, 0, 16, 4, 32, 0, 2, 2, 16, 0, 4, 8, 4, 4], 31, [1, 0, 0, 0]),\n",
       " ([2, 8, 32, 4, 16, 4, 16, 2, 2, 2, 4, 0, 4, 8, 0, 0], 32, [0, 1, 0, 0]),\n",
       " ([2, 8, 32, 4, 16, 4, 16, 2, 4, 0, 4, 4, 0, 0, 4, 8], 32, [0, 0, 1, 0]),\n",
       " ([0, 0, 2, 4, 2, 0, 32, 2, 16, 8, 16, 4, 4, 4, 8, 8], 23, [0, 0, 1, 0]),\n",
       " ([0, 2, 2, 4, 2, 0, 32, 2, 16, 8, 16, 4, 4, 4, 8, 8], 13, [1, 0, 0, 0]),\n",
       " ([2, 2, 2, 4, 16, 8, 32, 2, 4, 4, 16, 4, 0, 2, 8, 8], 31, [0, 0, 0, 1]),\n",
       " ([4, 2, 4, 0, 16, 8, 32, 2, 8, 16, 4, 0, 2, 16, 2, 0], 22, [0, 1, 0, 0]),\n",
       " ([2, 4, 2, 4, 16, 8, 32, 2, 0, 8, 16, 4, 0, 2, 16, 2], 12, [0, 0, 0, 1]),\n",
       " ([2, 4, 2, 4, 16, 8, 32, 2, 8, 16, 4, 2, 2, 16, 2, 0], 24, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 0, 16, 4, 32, 0, 8, 8, 4, 4, 2, 32, 2, 4], 22, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 0, 16, 4, 32, 2, 8, 8, 4, 0, 2, 32, 2, 8], 13, [0, 0, 1, 0]),\n",
       " ([2, 2, 2, 0, 16, 4, 32, 2, 8, 8, 4, 2, 2, 32, 2, 8], 24, [0, 0, 0, 1]),\n",
       " ([4, 2, 0, 2, 16, 4, 32, 2, 16, 4, 2, 0, 2, 32, 2, 8], 50, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 0, 4, 2, 0, 2, 32, 8, 32, 4, 2, 32, 4, 8], 52, [0, 1, 0, 0]),\n",
       " ([4, 0, 0, 0, 0, 0, 4, 4, 32, 8, 32, 4, 2, 32, 4, 8], 50, [0, 1, 0, 0]),\n",
       " ([0, 0, 0, 4, 0, 2, 0, 8, 32, 8, 32, 4, 2, 32, 4, 8], 40, [0, 1, 0, 0]),\n",
       " ([0, 4, 0, 4, 0, 0, 2, 8, 32, 8, 32, 4, 2, 32, 4, 8], 31, [1, 0, 0, 0]),\n",
       " ([32, 4, 2, 4, 2, 8, 32, 8, 0, 32, 4, 4, 2, 0, 0, 8], 31, [0, 0, 0, 1]),\n",
       " ([32, 4, 2, 4, 2, 8, 32, 8, 32, 8, 4, 0, 2, 8, 0, 0], 21, [0, 0, 0, 1]),\n",
       " ([32, 4, 2, 4, 2, 8, 32, 8, 32, 8, 4, 0, 2, 8, 2, 0], 22, [0, 0, 1, 0]),\n",
       " ([32, 0, 2, 2, 2, 4, 32, 0, 32, 8, 4, 4, 2, 16, 2, 8], 12, [0, 0, 1, 0]),\n",
       " ([32, 2, 2, 0, 2, 4, 32, 2, 32, 8, 4, 4, 2, 16, 2, 8], 2, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 8, 4, 8, 2, 16, 2, 2], 13, [0, 0, 0, 1]),\n",
       " ([32, 4, 2, 2, 2, 4, 32, 4, 32, 8, 4, 8, 2, 16, 4, 0], 23, [1, 0, 0, 0]),\n",
       " ([32, 8, 2, 2, 2, 8, 32, 4, 32, 16, 8, 8, 2, 0, 2, 0], 22, [0, 0, 1, 0]),\n",
       " ([32, 0, 2, 0, 2, 2, 32, 2, 32, 16, 8, 4, 2, 16, 2, 8], 21, [0, 0, 1, 0]),\n",
       " ([32, 2, 2, 0, 2, 0, 32, 2, 32, 2, 8, 4, 2, 32, 2, 8], 24, [1, 0, 0, 0]),\n",
       " ([32, 4, 2, 2, 2, 32, 32, 4, 32, 0, 8, 8, 2, 0, 2, 2], 13, [0, 0, 1, 0]),\n",
       " ([32, 2, 2, 2, 2, 0, 32, 4, 32, 4, 8, 8, 2, 32, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [0, 0, 1, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 5, [1, 0, 0, 0]),\n",
       " ([32, 2, 2, 2, 2, 4, 32, 4, 32, 32, 8, 8, 2, 2, 2, 2], 42, [0, 0, 0, 1]),\n",
       " ([32, 4, 2, 0, 2, 4, 32, 4, 64, 16, 0, 0, 4, 4, 2, 0], 42, [0, 0, 0, 1]),\n",
       " ([32, 4, 2, 0, 2, 4, 32, 4, 64, 16, 0, 0, 8, 2, 2, 0], 41, [0, 0, 0, 1]),\n",
       " ([32, 4, 2, 0, 2, 4, 32, 4, 64, 16, 0, 0, 8, 4, 0, 2], 30, [0, 1, 0, 0]),\n",
       " ([0, 32, 4, 2, 2, 4, 32, 4, 0, 0, 64, 16, 2, 8, 4, 2], 31, [0, 0, 1, 0]),\n",
       " ([0, 0, 4, 2, 2, 32, 32, 4, 0, 4, 64, 16, 4, 8, 4, 2], 33, [0, 0, 0, 1]),\n",
       " ([4, 2, 0, 0, 2, 64, 4, 0, 4, 64, 16, 2, 4, 8, 4, 2], 23, [0, 0, 0, 1]),\n",
       " ([4, 2, 0, 0, 2, 64, 4, 2, 4, 64, 16, 2, 4, 8, 4, 2], 43, [0, 0, 1, 0]),\n",
       " ([0, 2, 0, 0, 4, 2, 4, 0, 2, 128, 16, 2, 8, 8, 4, 4], 51, [0, 1, 0, 0]),\n",
       " ([0, 2, 0, 2, 0, 4, 2, 4, 2, 128, 16, 2, 0, 0, 16, 8], 51, [0, 0, 0, 1]),\n",
       " ([4, 0, 2, 0, 4, 2, 4, 0, 2, 128, 16, 2, 16, 8, 0, 0], 43, [0, 0, 0, 1]),\n",
       " ([4, 2, 0, 0, 4, 2, 4, 0, 2, 128, 16, 2, 16, 8, 0, 2], 60, [0, 0, 1, 0]),\n",
       " ([2, 0, 0, 0, 8, 4, 0, 0, 2, 128, 4, 0, 16, 8, 16, 4], 52, [1, 0, 0, 0]),\n",
       " ([2, 4, 4, 4, 8, 128, 16, 4, 2, 8, 0, 0, 16, 0, 0, 0], 51, [1, 0, 0, 0]),\n",
       " ([2, 4, 4, 8, 8, 128, 16, 0, 2, 8, 0, 0, 16, 2, 0, 0], 51, [0, 1, 0, 0]),\n",
       " ([0, 2, 8, 8, 0, 8, 128, 16, 2, 0, 2, 8, 0, 0, 16, 2], 61, [0, 1, 0, 0]),\n",
       " ([0, 0, 2, 16, 0, 8, 128, 16, 2, 0, 4, 8, 0, 0, 16, 2], 50, [0, 0, 0, 1]),\n",
       " ([2, 16, 2, 0, 8, 128, 16, 0, 2, 4, 8, 0, 16, 2, 0, 0], 41, [0, 0, 0, 1]),\n",
       " ([2, 16, 2, 2, 8, 128, 16, 0, 2, 4, 8, 0, 16, 2, 0, 0], 31, [0, 0, 1, 0]),\n",
       " ([2, 16, 2, 0, 8, 128, 2, 0, 2, 4, 16, 0, 16, 2, 8, 2], 22, [0, 0, 0, 1]),\n",
       " ([2, 16, 2, 0, 8, 128, 2, 0, 2, 4, 16, 2, 16, 2, 8, 2], 13, [0, 0, 0, 1]),\n",
       " ([2, 16, 2, 2, 8, 128, 2, 0, 2, 4, 16, 2, 16, 2, 8, 2], 21, [1, 0, 0, 0]),\n",
       " ([2, 16, 4, 4, 8, 128, 16, 2, 2, 4, 8, 0, 16, 2, 0, 2], 32, [0, 1, 0, 0]),\n",
       " ([2, 2, 16, 8, 8, 128, 16, 2, 0, 2, 4, 8, 0, 0, 16, 4], 32, [1, 0, 0, 0]),\n",
       " ([2, 2, 32, 8, 8, 128, 4, 2, 2, 2, 16, 8, 0, 0, 0, 4], 41, [0, 0, 0, 1]),\n",
       " ([4, 32, 8, 0, 8, 128, 4, 2, 4, 16, 8, 0, 4, 2, 0, 0], 41, [1, 0, 0, 0]),\n",
       " ([4, 32, 8, 2, 8, 128, 4, 0, 8, 16, 8, 2, 0, 2, 0, 0], 50, [0, 0, 1, 0]),\n",
       " ([0, 32, 0, 0, 0, 128, 8, 0, 4, 16, 4, 2, 16, 2, 8, 4], 40, [0, 0, 0, 1]),\n",
       " ([32, 0, 0, 4, 128, 8, 0, 0, 4, 16, 4, 2, 16, 2, 8, 4], 32, [1, 0, 0, 0]),\n",
       " ([32, 8, 4, 4, 128, 16, 8, 2, 4, 2, 2, 4, 16, 0, 0, 0], 43, [0, 0, 0, 1]),\n",
       " ([32, 8, 8, 0, 128, 16, 8, 2, 4, 4, 4, 0, 16, 0, 0, 2], 50, [0, 1, 0, 0]),\n",
       " ([0, 0, 32, 16, 128, 16, 8, 2, 2, 0, 4, 8, 0, 0, 16, 2], 43, [0, 0, 0, 1]),\n",
       " ([32, 16, 0, 0, 128, 16, 8, 2, 2, 4, 8, 0, 16, 2, 2, 0], 43, [0, 0, 0, 1]),\n",
       " ([32, 16, 0, 0, 128, 16, 8, 2, 2, 4, 8, 0, 16, 4, 0, 2], 34, [0, 0, 0, 1]),\n",
       " ([32, 16, 0, 2, 128, 16, 8, 2, 2, 4, 8, 0, 16, 4, 2, 0], 22, [0, 1, 0, 0]),\n",
       " ([2, 32, 16, 2, 128, 16, 8, 2, 0, 2, 4, 8, 0, 16, 4, 2], 13, [0, 1, 0, 0]),\n",
       " ([2, 32, 16, 2, 128, 16, 8, 2, 2, 2, 4, 8, 0, 16, 4, 2], 13, [0, 1, 0, 0]),\n",
       " ([2, 32, 16, 2, 128, 16, 8, 2, 2, 4, 4, 8, 0, 16, 4, 2], 13, [0, 1, 0, 0]),\n",
       " ([2, 32, 16, 2, 128, 16, 8, 2, 0, 2, 8, 8, 2, 16, 4, 2], 12, [0, 1, 0, 0]),\n",
       " ([2, 32, 16, 2, 128, 16, 8, 2, 2, 0, 2, 16, 2, 16, 4, 2], 12, [0, 0, 0, 1]),\n",
       " ([2, 32, 16, 2, 128, 16, 8, 2, 4, 16, 2, 0, 2, 16, 4, 2], 21, [1, 0, 0, 0]),\n",
       " ([2, 32, 16, 4, 128, 32, 8, 2, 4, 16, 2, 4, 2, 0, 4, 0], 21, [1, 0, 0, 0]),\n",
       " ([2, 64, 16, 4, 128, 16, 8, 2, 4, 0, 2, 4, 2, 2, 4, 0], 13, [0, 0, 1, 0]),\n",
       " ([2, 0, 16, 2, 128, 64, 8, 4, 4, 16, 2, 2, 2, 2, 4, 4], 31, [0, 1, 0, 0]),\n",
       " ([0, 2, 16, 2, 128, 64, 8, 4, 0, 4, 16, 4, 2, 0, 4, 8], 22, [0, 1, 0, 0]),\n",
       " ([2, 2, 16, 2, 128, 64, 8, 4, 0, 4, 16, 4, 0, 2, 4, 8], 20, [0, 0, 0, 1]),\n",
       " ([4, 16, 2, 0, 128, 64, 8, 4, 4, 16, 4, 0, 2, 4, 8, 2], 13, [0, 1, 0, 0]),\n",
       " ([0, 4, 16, 2, 128, 64, 8, 4, 2, 4, 16, 4, 2, 4, 8, 2], 31, [0, 0, 1, 0]),\n",
       " ([0, 0, 16, 0, 2, 4, 8, 2, 128, 64, 16, 8, 4, 8, 8, 2], 31, [0, 0, 0, 1]),\n",
       " ([16, 0, 0, 0, 2, 4, 8, 2, 128, 64, 16, 8, 4, 16, 2, 2], 31, [0, 1, 0, 0]),\n",
       " ([0, 2, 0, 16, 2, 4, 8, 2, 128, 64, 16, 8, 0, 4, 16, 4], 32, [0, 0, 1, 0]),\n",
       " ([0, 2, 0, 16, 2, 4, 0, 2, 2, 64, 8, 8, 128, 4, 32, 4], 32, [0, 1, 0, 0]),\n",
       " ([0, 0, 2, 16, 2, 2, 4, 2, 0, 2, 64, 16, 128, 4, 32, 4], 32, [1, 0, 0, 0]),\n",
       " ([2, 4, 2, 16, 128, 4, 4, 2, 2, 0, 64, 16, 0, 0, 32, 4], 30, [0, 0, 1, 0]),\n",
       " ([0, 0, 2, 16, 2, 0, 4, 2, 128, 2, 64, 16, 2, 8, 32, 4], 22, [1, 0, 0, 0]),\n",
       " ([2, 2, 2, 16, 128, 8, 4, 2, 2, 2, 64, 16, 0, 0, 32, 4], 31, [0, 1, 0, 0]),\n",
       " ([0, 2, 4, 16, 128, 8, 4, 2, 2, 4, 64, 16, 0, 0, 32, 4], 30, [1, 0, 0, 0]),\n",
       " ([128, 2, 8, 16, 2, 8, 64, 2, 0, 4, 32, 16, 2, 0, 0, 4], 31, [0, 0, 1, 0]),\n",
       " ([0, 0, 2, 16, 0, 2, 8, 2, 128, 8, 64, 16, 4, 4, 32, 4], 22, [1, 0, 0, 0]),\n",
       " ([128, 2, 2, 16, 4, 8, 8, 2, 0, 4, 64, 16, 2, 0, 32, 4], 31, [0, 0, 0, 1]),\n",
       " ([128, 4, 16, 0, 4, 16, 2, 0, 4, 64, 16, 2, 2, 32, 4, 0], 31, [1, 0, 0, 0]),\n",
       " ([128, 4, 16, 2, 8, 16, 2, 0, 2, 64, 16, 0, 2, 32, 4, 0], 23, [0, 1, 0, 0]),\n",
       " ([128, 4, 16, 2, 2, 8, 16, 2, 0, 2, 64, 16, 0, 2, 32, 4], 40, [0, 0, 1, 0]),\n",
       " ([0, 0, 0, 2, 0, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 30, [0, 0, 1, 0]),\n",
       " ([2, 0, 0, 2, 0, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 21, [0, 0, 1, 0]),\n",
       " ([0, 0, 2, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 20, [0, 0, 0, 1]),\n",
       " ([4, 2, 0, 0, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 10, [0, 0, 0, 1]),\n",
       " ([4, 2, 0, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 12, [0, 1, 0, 0]),\n",
       " ([0, 2, 4, 4, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 11, [0, 0, 0, 1]),\n",
       " ([2, 8, 2, 0, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 2, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ([2, 4, 8, 2, 2, 4, 32, 4, 128, 8, 64, 16, 2, 4, 32, 4], 2, [0, 1, 0, 0]),\n",
       " ...]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dump"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using Theano backend.\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "os.environ['KERAS_BACKEND'] = 'theano'\n",
    "\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Activation\n",
    "from keras.utils import np_utils\n",
    "\n",
    "# import tensorflow as tf\n",
    "import numpy\n",
    "import pandas as pd\n",
    "import theano"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Sequential()\n",
    "model.add(Dense(100, input_dim=16, activation='relu'))\n",
    "model.add(Dense(100, activation='relu'))\n",
    "\n",
    "model.add(Dense(10, activation='relu'))\n",
    "\n",
    "model.add(Dense(4, activation='softmax'))\n",
    "# model.add(Activation(tf.nn.softmax))\n",
    "\n",
    "# Compiling model\n",
    "# model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])\n",
    "model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_1 (Dense)              (None, 100)               1700      \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 100)               10100     \n",
      "_________________________________________________________________\n",
      "dense_3 (Dense)              (None, 10)                1010      \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (None, 4)                 44        \n",
      "=================================================================\n",
      "Total params: 12,854\n",
      "Trainable params: 12,854\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_vectors(dump):\n",
    "    d = np.array(dump)\n",
    "    l=d[:,0]\n",
    "    x=list(l)\n",
    "    x = np.array(x)\n",
    "    p = d[:,2]\n",
    "    y = list(p)\n",
    "    y = np.array(y)\n",
    "    return x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "x, y = get_vectors(dump)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  0,  0, ...,  0,  0,  0],\n",
       "       [ 2,  0,  2, ...,  0,  0,  0],\n",
       "       [ 2,  0,  2, ...,  0,  0,  0],\n",
       "       ...,\n",
       "       [ 4,  2, 16, ...,  4,  8,  2],\n",
       "       [ 4,  2, 16, ...,  4,  8,  2],\n",
       "       [ 4,  2, 16, ...,  4,  8,  2]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/100\n",
      "20446/20446 [==============================] - 0s 24us/step - loss: 1.3858 - acc: 0.2873\n",
      "Epoch 2/100\n",
      "20446/20446 [==============================] - 1s 28us/step - loss: 1.3228 - acc: 0.3057\n",
      "Epoch 3/100\n",
      "20446/20446 [==============================] - 1s 28us/step - loss: 1.3032 - acc: 0.3204\n",
      "Epoch 4/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.3016 - acc: 0.3135\n",
      "Epoch 5/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2971 - acc: 0.3184\n",
      "Epoch 6/100\n",
      "20446/20446 [==============================] - 1s 31us/step - loss: 1.2955 - acc: 0.3148\n",
      "Epoch 7/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2917 - acc: 0.3183\n",
      "Epoch 8/100\n",
      "20446/20446 [==============================] - 1s 31us/step - loss: 1.2904 - acc: 0.3191\n",
      "Epoch 9/100\n",
      "20446/20446 [==============================] - 1s 29us/step - loss: 1.2881 - acc: 0.3190\n",
      "Epoch 10/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2851 - acc: 0.3220\n",
      "Epoch 11/100\n",
      "20446/20446 [==============================] - 1s 33us/step - loss: 1.2826 - acc: 0.3216\n",
      "Epoch 12/100\n",
      "20446/20446 [==============================] - 1s 33us/step - loss: 1.2821 - acc: 0.3235\n",
      "Epoch 13/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2802 - acc: 0.3223\n",
      "Epoch 14/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2807 - acc: 0.3248\n",
      "Epoch 15/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2784 - acc: 0.3252\n",
      "Epoch 16/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2737 - acc: 0.3229\n",
      "Epoch 17/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2692 - acc: 0.3324\n",
      "Epoch 18/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2691 - acc: 0.3267\n",
      "Epoch 19/100\n",
      "20446/20446 [==============================] - 1s 31us/step - loss: 1.2685 - acc: 0.3353\n",
      "Epoch 20/100\n",
      "20446/20446 [==============================] - 1s 31us/step - loss: 1.2663 - acc: 0.3251\n",
      "Epoch 21/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2661 - acc: 0.3390\n",
      "Epoch 22/100\n",
      "20446/20446 [==============================] - 1s 33us/step - loss: 1.2672 - acc: 0.3263\n",
      "Epoch 23/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2651 - acc: 0.3287\n",
      "Epoch 24/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2653 - acc: 0.3343\n",
      "Epoch 25/100\n",
      "20446/20446 [==============================] - 1s 33us/step - loss: 1.2676 - acc: 0.3238\n",
      "Epoch 26/100\n",
      "20446/20446 [==============================] - 1s 33us/step - loss: 1.2645 - acc: 0.3281\n",
      "Epoch 27/100\n",
      "20446/20446 [==============================] - 1s 37us/step - loss: 1.2621 - acc: 0.3323\n",
      "Epoch 28/100\n",
      "20446/20446 [==============================] - 1s 41us/step - loss: 1.2634 - acc: 0.3302\n",
      "Epoch 29/100\n",
      "20446/20446 [==============================] - 1s 50us/step - loss: 1.2684 - acc: 0.3264\n",
      "Epoch 30/100\n",
      "20446/20446 [==============================] - 1s 39us/step - loss: 1.2677 - acc: 0.3279\n",
      "Epoch 31/100\n",
      "20446/20446 [==============================] - 1s 44us/step - loss: 1.2653 - acc: 0.3300\n",
      "Epoch 32/100\n",
      "20446/20446 [==============================] - 1s 38us/step - loss: 1.2613 - acc: 0.3373\n",
      "Epoch 33/100\n",
      "20446/20446 [==============================] - 1s 33us/step - loss: 1.2613 - acc: 0.3349\n",
      "Epoch 34/100\n",
      "20446/20446 [==============================] - 1s 33us/step - loss: 1.2630 - acc: 0.3292\n",
      "Epoch 35/100\n",
      "20446/20446 [==============================] - 1s 33us/step - loss: 1.2584 - acc: 0.3419\n",
      "Epoch 36/100\n",
      "20446/20446 [==============================] - 1s 31us/step - loss: 1.2437 - acc: 0.3691\n",
      "Epoch 37/100\n",
      "20446/20446 [==============================] - 1s 31us/step - loss: 1.2310 - acc: 0.3740\n",
      "Epoch 38/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2296 - acc: 0.3735\n",
      "Epoch 39/100\n",
      "20446/20446 [==============================] - 1s 33us/step - loss: 1.2282 - acc: 0.3733\n",
      "Epoch 40/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2320 - acc: 0.3707\n",
      "Epoch 41/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2225 - acc: 0.3789\n",
      "Epoch 42/100\n",
      "20446/20446 [==============================] - 1s 31us/step - loss: 1.2126 - acc: 0.3860\n",
      "Epoch 43/100\n",
      "20446/20446 [==============================] - 1s 34us/step - loss: 1.2030 - acc: 0.3902\n",
      "Epoch 44/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2145 - acc: 0.3844\n",
      "Epoch 45/100\n",
      "20446/20446 [==============================] - 1s 31us/step - loss: 1.2123 - acc: 0.3852\n",
      "Epoch 46/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.2078 - acc: 0.3890\n",
      "Epoch 47/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.1991 - acc: 0.3931\n",
      "Epoch 48/100\n",
      "20446/20446 [==============================] - 1s 35us/step - loss: 1.1996 - acc: 0.3935\n",
      "Epoch 49/100\n",
      "20446/20446 [==============================] - 1s 36us/step - loss: 1.1962 - acc: 0.3950\n",
      "Epoch 50/100\n",
      "20446/20446 [==============================] - 1s 39us/step - loss: 1.1966 - acc: 0.3955\n",
      "Epoch 51/100\n",
      "20446/20446 [==============================] - 1s 33us/step - loss: 1.1943 - acc: 0.3959: 0s - loss: 1.1844 - \n",
      "Epoch 52/100\n",
      "20446/20446 [==============================] - 1s 39us/step - loss: 1.1939 - acc: 0.3959\n",
      "Epoch 53/100\n",
      "20446/20446 [==============================] - 1s 45us/step - loss: 1.1923 - acc: 0.3984\n",
      "Epoch 54/100\n",
      "20446/20446 [==============================] - 1s 40us/step - loss: 1.1869 - acc: 0.4001\n",
      "Epoch 55/100\n",
      "20446/20446 [==============================] - 1s 34us/step - loss: 1.1833 - acc: 0.4070\n",
      "Epoch 56/100\n",
      "20446/20446 [==============================] - 1s 35us/step - loss: 1.1813 - acc: 0.4117\n",
      "Epoch 57/100\n",
      "20446/20446 [==============================] - 1s 36us/step - loss: 1.1965 - acc: 0.3986\n",
      "Epoch 58/100\n",
      "20446/20446 [==============================] - 1s 40us/step - loss: 1.1901 - acc: 0.4053\n",
      "Epoch 59/100\n",
      "20446/20446 [==============================] - 1s 36us/step - loss: 1.1858 - acc: 0.4072\n",
      "Epoch 60/100\n",
      "20446/20446 [==============================] - 1s 45us/step - loss: 1.1776 - acc: 0.4134\n",
      "Epoch 61/100\n",
      "20446/20446 [==============================] - 1s 38us/step - loss: 1.1804 - acc: 0.4099\n",
      "Epoch 62/100\n",
      "20446/20446 [==============================] - 1s 41us/step - loss: 1.1782 - acc: 0.4126\n",
      "Epoch 63/100\n",
      "20446/20446 [==============================] - 1s 40us/step - loss: 1.1763 - acc: 0.4138\n",
      "Epoch 64/100\n",
      "20446/20446 [==============================] - 1s 40us/step - loss: 1.1750 - acc: 0.4140\n",
      "Epoch 65/100\n",
      "20446/20446 [==============================] - 1s 41us/step - loss: 1.1749 - acc: 0.4147\n",
      "Epoch 66/100\n",
      "20446/20446 [==============================] - 1s 42us/step - loss: 1.1754 - acc: 0.4159\n",
      "Epoch 67/100\n",
      "20446/20446 [==============================] - 1s 41us/step - loss: 1.1723 - acc: 0.4169\n",
      "Epoch 68/100\n",
      "20446/20446 [==============================] - 1s 41us/step - loss: 1.1733 - acc: 0.4160\n",
      "Epoch 69/100\n",
      "20446/20446 [==============================] - 1s 46us/step - loss: 1.1697 - acc: 0.4174\n",
      "Epoch 70/100\n",
      "20446/20446 [==============================] - 1s 44us/step - loss: 1.1702 - acc: 0.4188\n",
      "Epoch 71/100\n",
      "20446/20446 [==============================] - 1s 45us/step - loss: 1.1709 - acc: 0.4172\n",
      "Epoch 72/100\n",
      "20446/20446 [==============================] - 1s 46us/step - loss: 1.1725 - acc: 0.4191\n",
      "Epoch 73/100\n",
      "20446/20446 [==============================] - 1s 46us/step - loss: 1.1697 - acc: 0.4182\n",
      "Epoch 74/100\n",
      "20446/20446 [==============================] - 1s 34us/step - loss: 1.1663 - acc: 0.4212\n",
      "Epoch 75/100\n",
      "20446/20446 [==============================] - 1s 31us/step - loss: 1.1664 - acc: 0.4215\n",
      "Epoch 76/100\n",
      "20446/20446 [==============================] - 1s 30us/step - loss: 1.1637 - acc: 0.4230\n",
      "Epoch 77/100\n",
      "20446/20446 [==============================] - 1s 30us/step - loss: 1.1651 - acc: 0.4215\n",
      "Epoch 78/100\n",
      "20446/20446 [==============================] - 1s 30us/step - loss: 1.1678 - acc: 0.4208\n",
      "Epoch 79/100\n",
      "20446/20446 [==============================] - 1s 29us/step - loss: 1.1609 - acc: 0.4237\n",
      "Epoch 80/100\n",
      "20446/20446 [==============================] - 1s 40us/step - loss: 1.1648 - acc: 0.4222\n",
      "Epoch 81/100\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20446/20446 [==============================] - 1s 37us/step - loss: 1.1686 - acc: 0.4192\n",
      "Epoch 82/100\n",
      "20446/20446 [==============================] - 1s 49us/step - loss: 1.1594 - acc: 0.4243\n",
      "Epoch 83/100\n",
      "20446/20446 [==============================] - 1s 35us/step - loss: 1.1604 - acc: 0.4234\n",
      "Epoch 84/100\n",
      "20446/20446 [==============================] - 1s 43us/step - loss: 1.1599 - acc: 0.4244\n",
      "Epoch 85/100\n",
      "20446/20446 [==============================] - 1s 37us/step - loss: 1.1591 - acc: 0.4260\n",
      "Epoch 86/100\n",
      "20446/20446 [==============================] - 1s 33us/step - loss: 1.1592 - acc: 0.4271\n",
      "Epoch 87/100\n",
      "20446/20446 [==============================] - 1s 29us/step - loss: 1.1555 - acc: 0.4286\n",
      "Epoch 88/100\n",
      "20446/20446 [==============================] - 1s 29us/step - loss: 1.1400 - acc: 0.4394\n",
      "Epoch 89/100\n",
      "20446/20446 [==============================] - 1s 29us/step - loss: 1.1396 - acc: 0.4386\n",
      "Epoch 90/100\n",
      "20446/20446 [==============================] - 1s 29us/step - loss: 1.1343 - acc: 0.4412\n",
      "Epoch 91/100\n",
      "20446/20446 [==============================] - 1s 29us/step - loss: 1.1362 - acc: 0.4423\n",
      "Epoch 92/100\n",
      "20446/20446 [==============================] - 1s 29us/step - loss: 1.1364 - acc: 0.4408\n",
      "Epoch 93/100\n",
      "20446/20446 [==============================] - 1s 28us/step - loss: 1.1361 - acc: 0.4401\n",
      "Epoch 94/100\n",
      "20446/20446 [==============================] - 1s 29us/step - loss: 1.1317 - acc: 0.4432\n",
      "Epoch 95/100\n",
      "20446/20446 [==============================] - 1s 28us/step - loss: 1.1324 - acc: 0.4421\n",
      "Epoch 96/100\n",
      "20446/20446 [==============================] - 1s 31us/step - loss: 1.1313 - acc: 0.4442\n",
      "Epoch 97/100\n",
      "20446/20446 [==============================] - 1s 32us/step - loss: 1.1301 - acc: 0.4440\n",
      "Epoch 98/100\n",
      "20446/20446 [==============================] - 1s 28us/step - loss: 1.1303 - acc: 0.4438: 0s - loss: 1.1248 - acc: \n",
      "Epoch 99/100\n",
      "20446/20446 [==============================] - 1s 31us/step - loss: 1.1339 - acc: 0.4426\n",
      "Epoch 100/100\n",
      "20446/20446 [==============================] - 1s 29us/step - loss: 1.1290 - acc: 0.4451\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x1c25df1400>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(x, y, epochs=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# y_dash = model.predict(x.reshape(len(x),16))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import keras.utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# y_dash"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# np.argmax(y_dash, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Iteration :  0\n",
      "[[ 4  2  4  2]\n",
      " [ 2  8 16  4]\n",
      " [ 4 16 64 16]\n",
      " [ 8 32  2 32]]\n",
      "\n",
      "Iteration :  1\n",
      "[[  2   8   2   4]\n",
      " [  4  16   4   2]\n",
      " [  8 128  16   8]\n",
      " [ 32  16   4  16]]\n",
      "\n",
      "Iteration :  2\n",
      "[[  2   4   2   4]\n",
      " [  4   8   4   8]\n",
      " [ 16 128  64  16]\n",
      " [ 32   2   4  64]]\n",
      "\n",
      "Iteration :  3\n",
      "[[  2   4   2   8]\n",
      " [  4   8   4  16]\n",
      " [ 16  64  16  32]\n",
      " [128  16 128   2]]\n",
      "\n",
      "Iteration :  4\n",
      "[[ 2  4  2  4]\n",
      " [ 4  8  4  2]\n",
      " [16  2 16  8]\n",
      " [ 2  4 32 16]]\n",
      "\n",
      "Iteration :  5\n",
      "[[  4   2   4   2]\n",
      " [  2  32   8   4]\n",
      " [ 32  64  32  16]\n",
      " [ 64 128   4  32]]\n",
      "\n",
      "Iteration :  6\n",
      "[[ 4  2  4  2]\n",
      " [ 8  4  2  8]\n",
      " [16  2  8 16]\n",
      " [32  4 16  2]]\n",
      "\n",
      "Iteration :  7\n",
      "[[  2   8   4   2]\n",
      " [  4  16   8   4]\n",
      " [  8  64  32   8]\n",
      " [ 32 128  64  32]]\n",
      "\n",
      "Iteration :  8\n",
      "[[ 4  2  8  4]\n",
      " [16  4 16  8]\n",
      " [ 2  8 32 16]\n",
      " [ 4 32 64  2]]\n",
      "\n",
      "Iteration :  9\n",
      "[[ 2  4  2  4]\n",
      " [ 4  8  4  2]\n",
      " [ 8 32  8  4]\n",
      " [32 64 32  8]]\n"
     ]
    }
   ],
   "source": [
    "explore_rate = 0.05\n",
    "\n",
    "for iteration in range(10):\n",
    "\n",
    "    env.reset()\n",
    "\n",
    "    action = env.action_space.sample()\n",
    "    observation, reward, done, _ = env.step(action + 1)\n",
    "\n",
    "\n",
    "    while True:\n",
    "#         env.render()\n",
    "\n",
    "        counter += 1\n",
    "\n",
    "        rand_action = env.action_space.sample()\n",
    "\n",
    "        max_action = np.argmax(model.predict(np.ravel(np.array(list(observation))).reshape(1,16)), axis=1)[0]\n",
    "\n",
    "        action = int(np.random.choice([rand_action, max_action], 1, p=[explore_rate, 1 - explore_rate]))\n",
    "\n",
    "#         print(\"\\nAction\",action)\n",
    "\n",
    "        observation, reward, done, _ = env.step(action + 1)\n",
    "\n",
    "        if done:\n",
    "            print(\"\\nIteration : \", iteration)\n",
    "            print(observation)\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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