hp_test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-10T23:02:37.972334Z",
     "start_time": "2019-08-10T23:02:37.962501Z"
    }
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "\n",
    "import math\n",
    "import sys\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as patches\n",
    "import random\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import torch.optim as optim\n",
    "import torchvision.transforms as T\n",
    "\n",
    "from hp import HP\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "dev = \"cuda:0\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-10T23:02:39.855597Z",
     "start_time": "2019-08-10T23:02:39.694100Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('SSSSLSSS', 'SSSSSSSS')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hp = HP(\"HHHPPPHHH\")\n",
    "hp.conformation, hp.coordinates()\n",
    "hp.show(plt.gca())\n",
    "hp.energy()\n",
    "hp.random_move(), hp.conformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-10T23:02:42.043206Z",
     "start_time": "2019-08-10T23:02:41.846747Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LLSRSRRL -2\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "conformation, energies, _ = hp.minimize(n=1000)\n",
    "print(conformation,hp.energy())\n",
    "hp.conformation = conformation\n",
    "hp.show(plt.gca())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-10T23:02:44.473565Z",
     "start_time": "2019-08-10T23:02:44.247518Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hp2 = HP(\"HHHHHPPPPPPHHHHHHPHPHPHHHHHHPPPPPPHHHHHHPHPHPH\")\n",
    "hp2.show(plt.gca())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-10T02:00:41.484998Z",
     "start_time": "2019-08-10T02:00:16.658898Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(1,2,figsize=(10,5))\n",
    "c,e,l = hp2.minimize(t=1,n=25000)\n",
    "hp2.show(ax[0])\n",
    "ax[0].set_title(\"energy = %d\" % hp2.energy())\n",
    "ax[1].plot(e);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-10T02:01:24.262757Z",
     "start_time": "2019-08-10T02:00:41.486100Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hp3 = HP(\"\".join([\"H\" if random.random() < 0.5 else \"P\" for _ in range(30)]))\n",
    "fig,ax = plt.subplots(1,2,figsize=(10,5))\n",
    "c,e,l = hp3.minimize(t=10,n=100000)\n",
    "hp3.show(ax[0])\n",
    "ax[0].set_title(\"energy = %d\" % hp3.energy())\n",
    "ax[1].plot(e);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-10T02:01:24.281299Z",
     "start_time": "2019-08-10T02:01:24.264177Z"
    }
   },
   "outputs": [
    {
     "data": {
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       "  0,\n",
       "  0,\n",
       "  0,\n",
       "  0,\n",
       "  0,\n",
       "  0,\n",
       "  -1,\n",
       "  ...],\n",
       " ['SSSSSSSSSSSSSSSSSSSSSSSSSSSSS',\n",
       "  'SSSSSSSSSSSSSSSSSSSSSSSSSSSSL',\n",
       "  'SSSSSSSSSSSSSSRSSSSSSSSSSSSSL',\n",
       "  'SSSSSSSSSSSSSSRSSSSLSSSSSSSSL',\n",
       "  'SSSSSSSSLSSSSSRSSSSLSSSSSSSSL',\n",
       "  'SSSSSSSSLSSSSLRSSSSLSSSSSSSSL',\n",
       "  'SSSSSSSSLSSSSLRSSSSLSSSSSSSSR',\n",
       "  'SSSSSSSSLSSSSLRSSSSLSSSRSSSSR',\n",
       "  'SSSSSSSSLSSSSLRSSSSLSSSRSRSSR',\n",
       "  'SSSSSSSSLSSSSLRSSSSLSSSRSSSSR',\n",
       "  'SSSSSSSSLSSSSLRSSSSLSSSRSSSSL',\n",
       "  'SSSSLSSSLSSSSLRSSSSLSSSRSSSSL',\n",
       "  'SSSSLSSSLSSSRLRSSSSLSSSRSSSSL',\n",
       "  'SSSSLSSSLSSSRLRSSSSLSSSRSSRSL',\n",
       "  'SSSSSSSSLSSSRLRSSSSLSSSRSSRSL',\n",
       "  'SSSSSSSSLSRSRLRSSSSLSSSRSSRSL',\n",
       "  'SSSSSSSSLSRSRLSSSSSLSSSRSSRSL',\n",
       "  'SSSSSSSLLSRSRLSSSSSLSSSRSSRSL',\n",
       "  'SSSSSSSLLSRSRLSSSSSLSSSRLSRSL',\n",
       "  'SSSSSSSLLSRSRLSSSSSLSLSRLSRSL',\n",
       "  'SSSSSSSLLSRSRLSSSSSLSLSRSSRSL',\n",
       "  'SSSSSSSLLSRSRLSSSSSLSLSRSLRSL',\n",
       "  'SRSSSSSLLSRSRLSSSSSLSLSRSLRSL',\n",
       "  'SRSSSSSLLSRSRLSSSSSLSLSRRLRSL',\n",
       "  'SRSSSSSLSSRSRLSSSSSLSLSRRLRSL',\n",
       "  'SRSRSSSLSSRSRLSSSSSLSLSRRLRSL',\n",
       "  'SRLRSSSLSSRSRLSSSSSLSLSRRLRSL',\n",
       "  'SRLLSSSLSSRSRLSSSSSLSLSRRLRSL',\n",
       "  'RRLLSSSLSSRSRLSSSSSLSLSRRLRSL',\n",
       "  'RRRLSSSLSSRSRLSSSSSLSLSRRLRSL',\n",
       "  'RLRLSSSLSSRSRLSSSSSLSLSRRLRSL',\n",
       "  'RLRLRSSLSSRSRLSSSSSLSLSRRLRSL',\n",
       "  'RLRLRSSLSSRSRLSSSSSLSLSRRLRLL',\n",
       "  'RLRLRSSLSSRSRLSSSSSLSLSRSLRLL',\n",
       "  'RLRSRSSLSSRSRLSSSSSLSLSRSLRLL',\n",
       "  'RSRSRSSLSSRSRLSSSSSLSLSRSLRLL',\n",
       "  'RSRSRSSLSSRSRLSRSSSLSLSRSLRLL',\n",
       "  'RSRSSSSLSSRSRLSRSSSLSLSRSLRLL',\n",
       "  'RSRSSLSLSSRSRLSRSSSLSLSRSLRLL',\n",
       "  'RSRSRLSLSSRSRLSRSSSLSLSRSLRLL',\n",
       "  'RSRSRLSLSSLSRLSRSSSLSLSRSLRLL',\n",
       "  'RSRSRLSLSSLSRSSRSSSLSLSRSLRLL',\n",
       "  'RSLSRLSLSSLSRSSRSSSLSLSRSLRLL',\n",
       "  'RSLSRLSLSSLRRSSRSSSLSLSRSLRLL',\n",
       "  'RSLSRLSLSSLRRSSRSSSLSLSRSLRLR',\n",
       "  'RSLSRLRLSSLRRSSRSSSLSLSRSLRLR',\n",
       "  'RSLSRLRLSSLRRSSRSSSLSLRRSLRLR',\n",
       "  'RSLSRLRLSSLRRSSRSSRLSLRRSLRLR',\n",
       "  'RSLSRLRLSSLRRLSRSSRLSLRRSLRLR',\n",
       "  'RSLSRLRLSSLRRLSRSSRLSLRLSLRLR',\n",
       "  'RSLSRLRLSSLRRLSRSSRSSLRLSLRLR',\n",
       "  'RSLLRLRLSSLRRLSRSSRSSLRLSLRLR',\n",
       "  'RSLLRLRLSSLRRLSRSLRSSLRLSLRLR',\n",
       "  'RSLLRLRLSSLRRLSRSLRSSLRRSLRLR',\n",
       "  'RSRLRLRLSSLRRLSRSLRSSLRRSLRLR',\n",
       "  'RSRLSLRLSSLRRLSRSLRSSLRRSLRLR',\n",
       "  'RSRLSLRLSSLRRLSRSLSSSLRRSLRLR',\n",
       "  'RSRLSLRLSSLRRLSSSLSSSLRRSLRLR',\n",
       "  'RSSLSLRLSSLRRLSSSLSSSLRRSLRLR',\n",
       "  'SSSLSLRLSSLRRLSSSLSSSLRRSLRLR',\n",
       "  'SSSLSLRLSSLRRLSSRLSSSLRRSLRLR',\n",
       "  'SSSLSSRLSSLRRLSSRLSSSLRRSLRLR',\n",
       "  'SSSLSSRLSSLRRLSRRLSSSLRRSLRLR',\n",
       "  'SSSLRSRLSSLRRLSRRLSSSLRRSLRLR',\n",
       "  'SSSLRSRLSSLRRLSRRLSSSLLRSLRLR',\n",
       "  'SSSLRSRLSSLRRLSRRSSSSLLRSLRLR',\n",
       "  'RSSLRSRLSSLRRLSRRSSSSLLRSLRLR',\n",
       "  'RSLLRSRLSSLRRLSRRSSSSLLRSLRLR',\n",
       "  'RSLLRSRLSSLRLLSRRSSSSLLRSLRLR',\n",
       "  'RSLLRSRLSSLRLLSRRSLSSLLRSLRLR',\n",
       "  'RSLLRSRLSSLRLLSRRSLSSSLRSLRLR',\n",
       "  'RSLLRSRLSSLRLLSRRSLSSSLRRLRLR',\n",
       "  'RSLLRSRLSSLRLLSRRSLSSSLRRSRLR',\n",
       "  'SSLLRSRLSSLRLLSRRSLSSSLRRSRLR',\n",
       "  'SSLLRSRLSSLRLLSRRSLSSSLRRSLLR',\n",
       "  'SSLLSSRLSSLRLLSRRSLSSSLRRSLLR',\n",
       "  'SSLLSSRLSSLRLLSRRSLSRSLRRSLLR',\n",
       "  'SSLLSSRLSSLRSLSRRSLSRSLRRSLLR',\n",
       "  'RSLLSSRLSSLRSLSRRSLSRSLRRSLLR',\n",
       "  'RSLLSSRLSSSRSLSRRSLSRSLRRSLLR',\n",
       "  'RSLLSSRLSSSRSLSRRSLSRSLLRSLLR',\n",
       "  'RSLLSSRLLSSRSLSRRSLSRSLLRSLLR',\n",
       "  'RSLLSSRLLSSRSLSRRSLSRSLRRSLLR',\n",
       "  'RSLLSSRLLRSRSLSRRSLSRSLRRSLLR',\n",
       "  'RSSLSSRLLRSRSLSRRSLSRSLRRSLLR',\n",
       "  'RSSLSSRLLRSRSLSLRSLSRSLRRSLLR',\n",
       "  'RSSLSSRLLRSRSLSLRSLSRSLRSSLLR',\n",
       "  'RSSLSSRLLRSSSLSLRSLSRSLRSSLLR',\n",
       "  'RSSLSSRLLRSSSLSLRSLSRRLRSSLLR',\n",
       "  'RSSLSSRLLRSSSLSLRLLSRRLRSSLLR',\n",
       "  'RSRLSSRLLRSSSLSLRLLSRRLRSSLLR',\n",
       "  'RSRLSSRLLRSSSLSLRLSSRRLRSSLLR',\n",
       "  'RSRLSSRLLRSSSLSLRLSSRRLRSSLRR',\n",
       "  'RRRLSSRLLRSSSLSLRLSSRRLRSSLRR',\n",
       "  'RRRLSRRLLRSSSLSLRLSSRRLRSSLRR',\n",
       "  'RRRLSRRLLRSSSLSLRLSSRRLRSSLLR',\n",
       "  'RRRLSRRLSRSSSLSLRLSSRRLRSSLLR',\n",
       "  'RRRLSRRLLRSSSLSLRLSSRRLRSSLLR',\n",
       "  'RRRLSRRLLRSSSLSLRLSSSRLRSSLLR',\n",
       "  'RRRLSRRLLRSSSLSLRLRSSRLRSSLLR',\n",
       "  'RRRLSRRLLRLSSLSLRLRSSRLRSSLLR',\n",
       "  'RRRLLRRLLRLSSLSLRLRSSRLRSSLLR',\n",
       "  'RRRLLRRLLRLSSLSLRLRSSRLSSSLLR',\n",
       "  'RRRLLRRLLRLSSLSLRLRSSRLSSRLLR',\n",
       "  'RRRLLRRLLRLSSLRLRLRSSRLSSRLLR',\n",
       "  'RRRLLRRLLRLSSLRLRLRSRRLSSRLLR',\n",
       "  'RRRLLRRLLRLSSLRLRLLSRRLSSRLLR',\n",
       "  'RRRLLRRLLRLSSLRLRLLSRRLSSRLRR',\n",
       "  'RRRLLRRLLRLSSLRSRLLSRRLSSRLRR',\n",
       "  'RSRLLRRLLRLSSLRSRLLSRRLSSRLRR',\n",
       "  'RSRLLRRLLRLRSLRSRLLSRRLSSRLRR',\n",
       "  'RSRLLRRLLRLRSLRSRLLSLRLSSRLRR',\n",
       "  'SSRLLRRLLRLRSLRSRLLSLRLSSRLRR',\n",
       "  'SSRLLRRLLRLSSLRSRLLSLRLSSRLRR',\n",
       "  'SSRLLRRLRRLSSLRSRLLSLRLSSRLRR',\n",
       "  'SSRLLRRLRRLSSLRSRLSSLRLSSRLRR',\n",
       "  'SSRLLRRLRRLSSLRSRLSSLRLSRRLRR',\n",
       "  'SSRLLRRLRRLSSLRSRLSSLRLLRRLRR',\n",
       "  'SSRLLRRLRRLSSSRSRLSSLRLLRRLRR',\n",
       "  'SSRLLRRLRRLLSSRSRLSSLRLLRRLRR',\n",
       "  'SSRLLRRLRRLLSSRSRLSSSRLLRRLRR',\n",
       "  'SSRLLRRLRRLLSSRSRLSSSRLLRRLRS',\n",
       "  'SSRLLRRLRRLLSSRSRLSSSRLLRRLLS',\n",
       "  'SSRLLRRLRRLLSSRSRLSSSRLLRSLLS',\n",
       "  'SSRLLRRLRRLLSSRSRSSSSRLLRSLLS',\n",
       "  'SSRLLRRLRRLLSSRSRSSSSRLLRSLRS',\n",
       "  'SSRLLSRLRRLLSSRSRSSSSRLLRSLRS',\n",
       "  'RSRLLSRLRRLLSSRSRSSSSRLLRSLRS',\n",
       "  'RSRLLSRLRRLLSSRSRSSSLRLLRSLRS',\n",
       "  'RSRLSSRLRRLLSSRSRSSSLRLLRSLRS',\n",
       "  'SSRLSSRLRRLLSSRSRSSSLRLLRSLRS',\n",
       "  'SSRLSSRLRRLLSSRSRSSSLRLLRSLRL',\n",
       "  'SSRLSSRLRRLLSSRSRSSSLRLLRRLRL',\n",
       "  'LSRLSSRLRRLLSSRSRSSSLRLLRRLRL',\n",
       "  'LSRLSSRLRRLLSSRSLSSSLRLLRRLRL',\n",
       "  'LSRLSSRLRRLSSSRSLSSSLRLLRRLRL',\n",
       "  'LSSLSSRLRRLSSSRSLSSSLRLLRRLRL',\n",
       "  'LSSLSSRLRRLSSSSSLSSSLRLLRRLRL',\n",
       "  'LSSLSLRLRRLSSSSSLSSSLRLLRRLRL',\n",
       "  'LSSLSLRLRRLSSSSSLSSSLRLLRSLRL',\n",
       "  'LSSLSLRLRRLSSSSRLSSSLRLLRSLRL',\n",
       "  'LSSLSLRLRRLSSSRRLSSSLRLLRSLRL',\n",
       "  'LSSLSLRLRRLSSSSRLSSSLRLLRSLRL',\n",
       "  'LSSLSLRLRRLSSSSRLSSSRRLLRSLRL',\n",
       "  'LSSLSLRSRRLSSSSRLSSSRRLLRSLRL',\n",
       "  'LSSLSLRSRRLSSSSRLSSSRRLLRSLRR',\n",
       "  'LSSLSLRSRRLSSSSRLSSSRRLLRRLRR',\n",
       "  'LSSRSLRSRRLSSSSRLSSSRRLLRRLRR',\n",
       "  'LSSRSLRSRRLSSSSRLSSSRRLLRSLRR',\n",
       "  'LSSRSLRSRRLSSSSRLLSSRRLLRSLRR',\n",
       "  'SSSRSLRSRRLSSSSRLLSSRRLLRSLRR',\n",
       "  'SSSRSLRSRRLSSSSRLLSSRSLLRSLRR',\n",
       "  'SSSRSLRSRRLSSSSRLLSSRSSLRSLRR',\n",
       "  'SSSRSLRSRRLSSSSRLLRSRSSLRSLRR',\n",
       "  'SSSRSLRSRRLSSSSRLLSSRSSLRSLRR',\n",
       "  'SSSRSLRSRSLSSSSRLLSSRSSLRSLRR',\n",
       "  'SSSRSLRSRSLSSLSRLLSSRSSLRSLRR',\n",
       "  'SSLRSLRSRSLSSLSRLLSSRSSLRSLRR',\n",
       "  'SSLRLLRSRSLSSLSRLLSSRSSLRSLRR',\n",
       "  'SSLRLLRSRSLSSSSRLLSSRSSLRSLRR',\n",
       "  'SSLRLLRSRSLSSSSRLLSSRSRLRSLRR',\n",
       "  'SSLRLLRSRSLSSSSRLLSSRSRLLSLRR',\n",
       "  'SSLRLLRSRSLSSSSRLLSSRLRLLSLRR',\n",
       "  'SSLRLLRSRSLSSRSRLLSSRLRLLSLRR',\n",
       "  'SSLRLLSSRSLSSRSRLLSSRLRLLSLRR',\n",
       "  'SSLRLLRSRSLSSRSRLLSSRLRLLSLRR',\n",
       "  'SSSRLLRSRSLSSRSRLLSSRLRLLSLRR',\n",
       "  'SSLRLLRSRSLSSRSRLLSSRLRLLSLRR',\n",
       "  'SSLRLLRSRSLSSRSRLLSSRSRLLSLRR',\n",
       "  'RSLRLLRSRSLSSRSRLLSSRSRLLSLRR',\n",
       "  'RSLRLLRSRSLSSRSRLSSSRSRLLSLRR',\n",
       "  'RSLRLLRSRSLSSRSRLSSSLSRLLSLRR',\n",
       "  'RSLRLLRSRSLSSRSRLSSSLSRLLSLSR',\n",
       "  'RRLRLLRSRSLSSRSRLSSSLSRLLSLSR',\n",
       "  'RRLRLLRSRSLSSRSRLRSSLSRLLSLSR',\n",
       "  'RRLRLLRSRSLSSRSRLRSSLSRLSSLSR',\n",
       "  'RRLRLLRSRSLSSRSRLRSSLSRLSSRSR',\n",
       "  'RRLRLLRSLSLSSRSRLRSSLSRLSSRSR',\n",
       "  'RRLRLLRSLSLSSRSRLRSSLSRLRSRSR',\n",
       "  'RRLRLLRSLSLSSRSRLRSSSSRLRSRSR',\n",
       "  'RRLRLLRSLSLSSRSRLRSLSSRLRSRSR',\n",
       "  'RRSRLLRSLSLSSRSRLRSLSSRLRSRSR',\n",
       "  'RRSRLLRSLSLSSRSRLRSLRSRLRSRSR',\n",
       "  'RRSRLLRSLSLSSRSRLRSLRSRLRSLSR',\n",
       "  'RRLRLLRSLSLSSRSRLRSLRSRLRSLSR',\n",
       "  'RRLRLLRSLSLRSRSRLRSLRSRLRSLSR',\n",
       "  'RRLRLLRSLSLRSRSRLRSLRLRLRSLSR',\n",
       "  'RRLRSLRSLSLRSRSRLRSLRLRLRSLSR',\n",
       "  'RRLRSLRSLSLRSRSRLRSLRLRLRSLLR',\n",
       "  'RRLRSLRLLSLRSRSRLRSLRLRLRSLLR',\n",
       "  'RRLRSLRLLSLRSRSRLRSSRLRLRSLLR',\n",
       "  'RRSRSLRLLSLRSRSRLRSSRLRLRSLLR',\n",
       "  'RRSRSLRLLSLRSRSRLRSSLLRLRSLLR',\n",
       "  'LRSRSLRLLSLRSRSRLRSSLLRLRSLLR',\n",
       "  'LSSRSLRLLSLRSRSRLRSSLLRLRSLLR',\n",
       "  'SSSRSLRLLSLRSRSRLRSSLLRLRSLLR',\n",
       "  'SSSRSLRLLSLRSRSRLRSSLLRLRSLRR',\n",
       "  'SSSRSLRLLSLRSRSLLRSSLLRLRSLRR',\n",
       "  'SSSRSLRLLRLRSRSLLRSSLLRLRSLRR',\n",
       "  'SSSRSLRSLRLRSRSLLRSSLLRLRSLRR',\n",
       "  'SSSRSLRSLRLRSRSLLRSSLLRLRRLRR',\n",
       "  'SSSRSLRSLRLRSSSLLRSSLLRLRRLRR',\n",
       "  'SSSRSLRSLRLRSSSLLRSSLLRLRRLLR',\n",
       "  'SSSSSLRSLRLRSSSLLRSSLLRLRRLLR',\n",
       "  'SSSSSLRSLRLRSSSLLRSSRLRLRRLLR',\n",
       "  'SSSSSLRSLRLRSSSLLRSSRLRLRSLLR',\n",
       "  'SSSRSLRSLRLRSSSLLRSSRLRLRSLLR',\n",
       "  'SSSRSLRSLRLRSSSLLRLSRLRLRSLLR',\n",
       "  'SSSRSLRSLRLRSSSLSRLSRLRLRSLLR',\n",
       "  'SSSRSLRSLRLRSSSLRRLSRLRLRSLLR',\n",
       "  'SSSRSLRSLRLRLSSLRRLSRLRLRSLLR',\n",
       "  'SSSRSLRSLRLRLSSLRRLRRLRLRSLLR',\n",
       "  'SSSRSLRLLRLRLSSLRRLRRLRLRSLLR',\n",
       "  'SSSRSLRLLRLRLSSLRRLRRLRLRRLLR',\n",
       "  'SSSRSLRRLRLRLSSLRRLRRLRLRRLLR',\n",
       "  'SSLRSLRRLRLRLSSLRRLRRLRLRRLLR',\n",
       "  'LSLRSLRRLRLRLSSLRRLRRLRLRRLLR',\n",
       "  'RSLRSLRRLRLRLSSLRRLRRLRLRRLLR',\n",
       "  'RSLRSLRRLRLRLSSLRRLRRLSLRRLLR',\n",
       "  'LSLRSLRRLRLRLSSLRRLRRLSLRRLLR',\n",
       "  'LSLRSLRRLRLRLSSLRSLRRLSLRRLLR',\n",
       "  'LSLRSLRRLRLRLSSLRSLRRLRLRRLLR',\n",
       "  'LSRRSLRRLRLRLSSLRSLRRLRLRRLLR',\n",
       "  'SSRRSLRRLRLRLSSLRSLRRLRLRRLLR',\n",
       "  'SSRRSLRRLRLRLSSLRSLRRLRLSRLLR',\n",
       "  'SSRSSLRRLRLRLSSLRSLRRLRLSRLLR',\n",
       "  'SSRSSLRRLRLRLSSLRSLRRLRLSRLSR',\n",
       "  'SSRSSLRRLRLRLSSLRSLRRSRLSRLSR',\n",
       "  'SSRSSLRRLRLRLSSLRSLRRSRLSRLRR',\n",
       "  'SSRSSLRRLRLRLSSLRSLRRSRLSRLRS',\n",
       "  'SSRSSLRRSRLRLSSLRSLRRSRLSRLRS',\n",
       "  'SSRSSLRRSRLRLSSLRSLRRSSLSRLRS',\n",
       "  'SSLSSLRRSRLRLSSLRSLRRSSLSRLRS',\n",
       "  'SSLSSLRRSRLRLSSLRSLRRSSLRRLRS',\n",
       "  'SSLSSLRRSRLRLSSLRSLRRSSLRSLRS',\n",
       "  'SSLSSLRRSSLRLSSLRSLRRSSLRSLRS',\n",
       "  'SSLRSLRRSSLRLSSLRSLRRSSLRSLRS',\n",
       "  'SSLRSLRRSSSRLSSLRSLRRSSLRSLRS',\n",
       "  'SSLRSLRRSSSRLSSLRSLRRSLLRSLRS',\n",
       "  'SSLRSLRRSSSRLSSLRSLRRSLLRSLLS',\n",
       "  'SSLRSLRRSSSRLRSLRSLRRSLLRSLLS',\n",
       "  'SSLRSLRSSSSRLRSLRSLRRSLLRSLLS',\n",
       "  'SSLRSLRSSSSRLRSLRSLRRSSLRSLLS',\n",
       "  'SSLRSLRSSSSRLRSLRSLRSSSLRSLLS',\n",
       "  'SSLRSLRSSSSRLRSLRSLRSSLLRSLLS',\n",
       "  'SSLRSLRSSSSLLRSLRSLRSSLLRSLLS',\n",
       "  'SSLRSLRSSSSLLRSLRSLRSSLLRSLLR',\n",
       "  'SSLRSLRSSSSLLRSLRSLRSRLLRSLLR',\n",
       "  'SSLRSLRSLSSLLRSLRSLRSRLLRSLLR',\n",
       "  'SSLRSLRSSSSLLRSLRSLRSRLLRSLLR',\n",
       "  'SSLRSLRSSSSLLRRLRSLRSRLLRSLLR',\n",
       "  'SSLRSLRSSSSLLRRLLSLRSRLLRSLLR',\n",
       "  'SSRRSLRSSSSLLRRLLSLRSRLLRSLLR',\n",
       "  'SSRRSLRRSSSLLRRLLSLRSRLLRSLLR',\n",
       "  'SSRRSLRRSSSLLRRLLSLRSRLLRSRLR',\n",
       "  'SSRRSLSRSSSLLRRLLSLRSRLLRSRLR',\n",
       "  'SSRRSLSRSSSLSRRLLSLRSRLLRSRLR',\n",
       "  'SSSRSLSRSSSLSRRLLSLRSRLLRSRLR',\n",
       "  'SSSRSLSRSSSLSRRLLSLSSRLLRSRLR',\n",
       "  'SSSRSLSRSSSLSRRLSSLSSRLLRSRLR',\n",
       "  'SSSRSLSRSSSLSRRLSRLSSRLLRSRLR',\n",
       "  'SSSRSLSRSSSSSRRLSRLSSRLLRSRLR',\n",
       "  'LSSRSLSRSSSSSRRLSRLSSRLLRSRLR',\n",
       "  'LSSRSLSRSSSSSRRLSRLSSRLLRSRLS',\n",
       "  'LSSRSLSRSSSSSRRLLRLSSRLLRSRLS',\n",
       "  'LLSRSLSRSSSSSRRLLRLSSRLLRSRLS',\n",
       "  'LLSRSLSRSSSSSRRLLRLSSRLLSSRLS',\n",
       "  'LLSRLLSRSSSSSRRLLRLSSRLLSSRLS',\n",
       "  'LLSRLLSRSSSSLRRLLRLSSRLLSSRLS',\n",
       "  'LLSRLLSRSSSSLRRLLRSSSRLLSSRLS',\n",
       "  'LRSRLLSRSSSSLRRLLRSSSRLLSSRLS',\n",
       "  'LRSRLLSRSSSSLRRLLRRSSRLLSSRLS',\n",
       "  'LRSRLLSRSRSSLRRLLRRSSRLLSSRLS',\n",
       "  'LRSRLLSRSRSSLRRLLRRSSRLLRSRLS',\n",
       "  'LRSRLLSRSRSSLRSLLRRSSRLLRSRLS',\n",
       "  'LRSRLLSRSRSSLRSLLRRSSRSLRSRLS',\n",
       "  'LRSRLLSRSRLSLRSLLRRSSRSLRSRLS',\n",
       "  'LRSRLLSRSRLSLRSSLRRSSRSLRSRLS',\n",
       "  'LRSRLLSLSRLSLRSSLRRSSRSLRSRLS',\n",
       "  'LRSRLRSLSRLSLRSSLRRSSRSLRSRLS',\n",
       "  'RRSRLRSLSRLSLRSSLRRSSRSLRSRLS',\n",
       "  'RRSSLRSLSRLSLRSSLRRSSRSLRSRLS',\n",
       "  'RRSSLRSLLRLSLRSSLRRSSRSLRSRLS',\n",
       "  'RRSSLRRLLRLSLRSSLRRSSRSLRSRLS',\n",
       "  'LRSSLRRLLRLSLRSSLRRSSRSLRSRLS',\n",
       "  'LRSSLRRLLRLSLRSSLRRSSRSLRSLLS',\n",
       "  'LRSSLRRLLRLRLRSSLRRSSRSLRSLLS',\n",
       "  'LRSSLRRLLRLRLLSSLRRSSRSLRSLLS',\n",
       "  'LRLSLRRLLRLRLLSSLRRSSRSLRSLLS',\n",
       "  'LRLSLRRLLRLRLLSSLRSSSRSLRSLLS',\n",
       "  'LRLSLRRLLRLRLLSSRRSSSRSLRSLLS',\n",
       "  'LRLSLRRLLRLRLLSSRSSSSRSLRSLLS',\n",
       "  'LRLSLRRLLRLRRLSSRSSSSRSLRSLLS',\n",
       "  'LRLSLRRLLRLRRLSSRSSSSRSLRSSLS',\n",
       "  'LRLSLRRLLRLSRLSSRSSSSRSLRSSLS',\n",
       "  'LRLSLRRLLRLSRLSSRSSSSRSLRLSLS',\n",
       "  'LRLSLRRLLRSSRLSSRSSSSRSLRLSLS',\n",
       "  'LRLSLRRLLSSSRLSSRSSSSRSLRLSLS',\n",
       "  'LRLSLRRLLSSSRLSSRSSSSLSLRLSLS',\n",
       "  'LRLSLRRLLSSSRLSSRSSSSLSLRLSRS',\n",
       "  'LRLSLRRLLSSSRLSSRSSSRLSLRLSRS',\n",
       "  'LRLSSRRLLSSSRLSSRSSSRLSLRLSRS',\n",
       "  'LRLSSRRLLSSSRLSSRSSSRLSLRLSRR',\n",
       "  'LRLSSLRLLSSSRLSSRSSSRLSLRLSRR',\n",
       "  'LRLSSLRLLSSSRLSLRSSSRLSLRLSRR',\n",
       "  'SRLSSLRLLSSSRLSLRSSSRLSLRLSRR',\n",
       "  'SRLSSLRLLSSSRLSSRSSSRLSLRLSRR',\n",
       "  'SLLSSLRLLSSSRLSSRSSSRLSLRLSRR',\n",
       "  'SLLSSLRLLSSSRLLSRSSSRLSLRLSRR',\n",
       "  'SLLSSLRLLSSSRLLSRSSSRLRLRLSRR',\n",
       "  'SLLSSLRLLSSSRLLSRSSLRLRLRLSRR',\n",
       "  'SLLSSLRLLSSSRLLSRLSLRLRLRLSRR',\n",
       "  'SLLSSLRRLSSSRLLSRLSLRLRLRLSRR',\n",
       "  'SLLSSLRRLSSRRLLSRLSLRLRLRLSRR',\n",
       "  'SLLSSLRRLRSRRLLSRLSLRLRLRLSRR',\n",
       "  'SLLSSLRRLRSRRLLSRLSLRSRLRLSRR',\n",
       "  'SLLSSLRRLRSRRLLSRLSLRSRLSLSRR',\n",
       "  'LLLSSLRRLRSRRLLSRLSLRSRLSLSRR',\n",
       "  'SLLSSLRRLRSRRLLSRLSLRSRLSLSRR',\n",
       "  'SLLSSLRRLRSRRLLSRLSLRLRLSLSRR',\n",
       "  'SLSSSLRRLRSRRLLSRLSLRLRLSLSRR',\n",
       "  'SSSSSLRRLRSRRLLSRLSLRLRLSLSRR',\n",
       "  'SSSSSLRRLRSSRLLSRLSLRLRLSLSRR',\n",
       "  'SSSSSLRRLRSSRLLSRLSLRLRLSLSSR',\n",
       "  'SSSSSLRSLRSSRLLSRLSLRLRLSLSSR',\n",
       "  'SSSSSLRSLRSSRLRSRLSLRLRLSLSSR',\n",
       "  'SSSSSLRSLRSSLLRSRLSLRLRLSLSSR',\n",
       "  'SSSSSLRSLRSSLLRSRLSLRLRLSSSSR',\n",
       "  'SSSSSLRSLRSSRLRSRLSLRLRLSSSSR',\n",
       "  'RSSSSLRSLRSSRLRSRLSLRLRLSSSSR',\n",
       "  'RSSSSLRSLRSSRLRSRLSLRLRLLSSSR',\n",
       "  'RSSLSLRSLRSSRLRSRLSLRLRLLSSSR',\n",
       "  'RSSLSLRSLRLSRLRSRLSLRLRLLSSSR',\n",
       "  'RSSLSLRSSRLSRLRSRLSLRLRLLSSSR',\n",
       "  'SSSLSLRSSRLSRLRSRLSLRLRLLSSSR',\n",
       "  'SSSLSLRSSRLRRLRSRLSLRLRLLSSSR',\n",
       "  'SSRLSLRSSRLRRLRSRLSLRLRLLSSSR',\n",
       "  'SSSLSLRSSRLRRLRSRLSLRLRLLSSSR',\n",
       "  'SSSLSLRSSRLRRLRSRLSLRLRLRSSSR',\n",
       "  'SSSLSLRSSRLRRLRSRLSLRLRLRSSRR',\n",
       "  'SSSLSLRLSRLRRLRSRLSLRLRLRSSRR',\n",
       "  'SSSLSLRLSRLRRLRSRLSLRSRLRSSRR',\n",
       "  'SSSLSLRLSRLRRLSSRLSLRSRLRSSRR',\n",
       "  'SLSLSLRLSRLRRLSSRLSLRSRLRSSRR',\n",
       "  'SLSRSLRLSRLRRLSSRLSLRSRLRSSRR',\n",
       "  'SLSRSLRLSSLRRLSSRLSLRSRLRSSRR',\n",
       "  'SLSRSLRSSSLRRLSSRLSLRSRLRSSRR',\n",
       "  'SLSRSLSSSSLRRLSSRLSLRSRLRSSRR',\n",
       "  'SLSRSLSSSSLRRLLSRLSLRSRLRSSRR',\n",
       "  'SLSRSLSSSSLRSLLSRLSLRSRLRSSRR',\n",
       "  'SLSRSLSSSSLRSLSSRLSLRSRLRSSRR',\n",
       "  'SLSRSLSSSSLRSLSLRLSLRSRLRSSRR',\n",
       "  'SLSRSLSSSRLRSLSLRLSLRSRLRSSRR',\n",
       "  'SLSRSLSSSRLRSLSLRLSLRSRLRSSRL',\n",
       "  'SLSRSLSSLRLRSLSLRLSLRSRLRSSRL',\n",
       "  'SLSRSLSSLRLRSLSRRLSLRSRLRSSRL',\n",
       "  'SLSRSLSSLRLRSLSRRSSLRSRLRSSRL',\n",
       "  'SLSRSRSSLRLRSLSRRSSLRSRLRSSRL',\n",
       "  'SLSRSRSSLRLRSLSLRSSLRSRLRSSRL',\n",
       "  'SSSRSRSSLRLRSLSLRSSLRSRLRSSRL',\n",
       "  'SSSRSRSSLRLRSLSLRSRLRSRLRSSRL',\n",
       "  'SSSRSRSSLRLRSLSLRSRLRLRLRSSRL',\n",
       "  'SSSRSRSSLRLRRLSLRSRLRLRLRSSRL',\n",
       "  'SSSRSRSSLRLRRLSLRSRSRLRLRSSRL',\n",
       "  'SSSRSLSSLRLRRLSLRSRSRLRLRSSRL',\n",
       "  'SSSRSLSSLRLRRLSLRSSSRLRLRSSRL',\n",
       "  'SSSRSLSSSRLRRLSLRSSSRLRLRSSRL',\n",
       "  'SSSRSLSSSRLRRLSLRSSSRLRLSSSRL',\n",
       "  'SSSRSLRSSRLRRLSLRSSSRLRLSSSRL',\n",
       "  'SSSRSLRSSRLRRLSLRSSSLLRLSSSRL',\n",
       "  'SSSRLLRSSRLRRLSLRSSSLLRLSSSRL',\n",
       "  'SSSRLLRSSRLRRSSLRSSSLLRLSSSRL',\n",
       "  'SLSRLLRSSRLRRSSLRSSSLLRLSSSRL',\n",
       "  'SLSRLLRSSSLRRSSLRSSSLLRLSSSRL',\n",
       "  'SLSRLLRSSRLRRSSLRSSSLLRLSSSRL',\n",
       "  'SRSRLLRSSRLRRSSLRSSSLLRLSSSRL',\n",
       "  'SRSRLLRSSRLRRSSLRSSSLLRLSSLRL',\n",
       "  'SRSRLLRSSRLRRSSLRSSSLLRLSRLRL',\n",
       "  'SRSRLLRSSLLRRSSLRSSSLLRLSRLRL',\n",
       "  'SRSRLLRSSRLRRSSLRSSSLLRLSRLRL',\n",
       "  'SRSRLLRSSRLRLSSLRSSSLLRLSRLRL',\n",
       "  'SRSRLLRSSRLRLSSLRSSSLLRRSRLRL',\n",
       "  'SRSRLLRSSRLRLSSSRSSSLLRRSRLRL',\n",
       "  'SRSRLLRRSRLRLSSSRSSSLLRRSRLRL',\n",
       "  'SRSRLLRRSRLRLSSSRSRSLLRRSRLRL',\n",
       "  'SRSRLLRRLRLRLSSSRSRSLLRRSRLRL',\n",
       "  'SRSRLLRRLRLRLSSSRSRSLLSRSRLRL',\n",
       "  'SRSRLLRRLRLRLSSSLSRSLLSRSRLRL',\n",
       "  'SRSRSLRRLRLRLSSSLSRSLLSRSRLRL',\n",
       "  'SRSRSLRRLRLRLSRSLSRSLLSRSRLRL',\n",
       "  'SRSRSLRRLRLRLSRSSSRSLLSRSRLRL',\n",
       "  'SSSRSLRRLRLRLSRSSSRSLLSRSRLRL',\n",
       "  'SSSRSLRRLRLRLSSSSSRSLLSRSRLRL',\n",
       "  'LSSRSLRRLRLRLSSSSSRSLLSRSRLRL',\n",
       "  'LSSSSLRRLRLRLSSSSSRSLLSRSRLRL',\n",
       "  'LSSSSLRLLRLRLSSSSSRSLLSRSRLRL',\n",
       "  'LSSSSLRLLRLRLSSSSSRSLLSRLRLRL',\n",
       "  'LSSSSLRLLRLRLSSSSSRSLLSRLRLRR',\n",
       "  'LSSSSLRLLRLRLSSSSSRSLLSRLRLRS',\n",
       "  'LSSSSLRLLRLRLSSSSSRSLLSRSRLRS',\n",
       "  'LSSSSLRLLRLRLSSSSSRSRLSRSRLRS',\n",
       "  'LSSLSLRLLRLRLSSSSSRSRLSRSRLRS',\n",
       "  'LSSLSLRLLRLRLSSSSSRSRLSRSRLRR',\n",
       "  'LSSLSLRLLRLRLSSSSSRSSLSRSRLRR',\n",
       "  'LSSLSLRLLRLRLSSSSSRSSLSRSRLRS',\n",
       "  'LSSLSLRLLRLRLSSSSSRSSLSRSSLRS',\n",
       "  'LSSLSLRRLRLRLSSSSSRSSLSRSSLRS',\n",
       "  'LSSLSLRRLRLRLSSSSSRRSLSRSSLRS',\n",
       "  'LSSLSLRRLRLRLSSSSSRRSLSRSSLRL',\n",
       "  'LSSLSLRRLRLRLSSSSSRRSLSRSSLRS',\n",
       "  'LSSLSLRRLRLRLSSSSSRRSLSRSSLLS',\n",
       "  'LSSLSLRRLRLRLSSSSSRRSLLRSSLLS',\n",
       "  'LSSLSLRRLRLRLSSSSSRRSLLRSSLSS',\n",
       "  'LSSLSLRRLRLRLSSSSSRRSLLSSSLSS',\n",
       "  'LSSLSSRRLRLRLSSSSSRRSLLSSSLSS',\n",
       "  'LSSLSSRLLRLRLSSSSSRRSLLSSSLSS',\n",
       "  'LSSLSSRLLRLRSSSSSSRRSLLSSSLSS',\n",
       "  'LSSLSSSLLRLRSSSSSSRRSLLSSSLSS',\n",
       "  'LSSLSSSLLRLRSSSSSSRRSLRSSSLSS',\n",
       "  'LSRLSSSLLRLRSSSSSSRRSLRSSSLSS',\n",
       "  'LSRLSSSLLRLSSSSSSSRRSLRSSSLSS',\n",
       "  'LSRLSSSLLRLSSSSSSSRRSLRLSSLSS',\n",
       "  'LSRRSSSLLRLSSSSSSSRRSLRLSSLSS',\n",
       "  'LSRRSSSLLRLSSSSSSSRRSLRLSRLSS',\n",
       "  'LSRRSSSLLRLSSSSSLSRRSLRLSRLSS',\n",
       "  'LSRRSSSLLRLSSSSSLSRRLLRLSRLSS',\n",
       "  'LSRRSSSLLRLSSSSSLSRRLLSLSRLSS',\n",
       "  'LSRRSSSLLRLSSSSSLSRRLRSLSRLSS',\n",
       "  'LSRRSSSLLRLSSSSSLSRRLSSLSRLSS',\n",
       "  'LSRRLSSLLRLSSSSSLSRRLSSLSRLSS',\n",
       "  'LSRRLSSLLRLSSSRSLSRRLSSLSRLSS',\n",
       "  'LSRRLSSLLRLSSSRSLSSRLSSLSRLSS',\n",
       "  'LSRRLSSLLRLSSRRSLSSRLSSLSRLSS',\n",
       "  'LSRRLSSLLRLSSRRSLSSRLSSLRRLSS',\n",
       "  'LSRRLSSLLRLSSSRSLSSRLSSLRRLSS',\n",
       "  'LSRRLSSRLRLSSSRSLSSRLSSLRRLSS',\n",
       "  'LSRRLSSRLRLSSSRSLSSRLSSLRRLRS',\n",
       "  'LSRRLSSRLRLSSSRSLSSRLSSLRRSRS',\n",
       "  'LSLRLSSRLRLSSSRSLSSRLSSLRRSRS',\n",
       "  'LSLRLSSRLRLSSSRSLSSRLSLLRRSRS',\n",
       "  'LSLRLSSRLRSSSSRSLSSRLSLLRRSRS',\n",
       "  'LSLRLSSRLRSSSSRSLRSRLSLLRRSRS',\n",
       "  'LSLRLSSRLRSSSSRSLRLRLSLLRRSRS',\n",
       "  'LSRRLSSRLRSSSSRSLRLRLSLLRRSRS',\n",
       "  'LSRRLLSRLRSSSSRSLRLRLSLLRRSRS',\n",
       "  'LSRRLLSRLRSSSSRSLRLRLRLLRRSRS',\n",
       "  'LSRRLLSRLRSSSSRSLRLRLRLLRLSRS',\n",
       "  'LSRRLLSRLRSSSSRSLRLRLRLSRLSRS',\n",
       "  'LSRRLLSRLRSSSSRSLRLRLRLSRLSRL',\n",
       "  'LSRRLLSRLRSSSSRSLRLRLRRSRLSRL',\n",
       "  'LSRRLLSRLRSSSLRSLRLRLRRSRLSRL',\n",
       "  'LSRRLLSRLRSSSLRSLRLRLRSSRLSRL',\n",
       "  'LSRRLLSRLRSSSLRSLRLRSRSSRLSRL',\n",
       "  'LSRRLLSRLRSSSLRSLRLRSRLSRLSRL',\n",
       "  'LSRRLLSRLRSSSLRSLRLRSRLSRLSRS',\n",
       "  'LSRRLLSRLRSSSLRSLRLSSRLSRLSRS',\n",
       "  'LSRRLLSRLRSSSLRSLRLSSRSSRLSRS',\n",
       "  'LSRRLLRRLRSSSLRSLRLSSRSSRLSRS',\n",
       "  'LSRRLLRSLRSSSLRSLRLSSRSSRLSRS',\n",
       "  'LSRRLLRLLRSSSLRSLRLSSRSSRLSRS',\n",
       "  'LSRRLLRRLRSSSLRSLRLSSRSSRLSRS',\n",
       "  'LSRRLLRRLRSSSLRRLRLSSRSSRLSRS',\n",
       "  'LSRRLLRRLRSSSLRRLRLLSRSSRLSRS',\n",
       "  'LSRRLLRRLRSSSLRRLRLLSRSSSLSRS',\n",
       "  'LSRRLLRRLLSSSLRRLRLLSRSSSLSRS',\n",
       "  'LSRRLLRRLLSSSLRRLRLLSRSSSLSLS',\n",
       "  'LSRRLLRRLLSSSLRRLRRLSRSSSLSLS',\n",
       "  'LSRRLLRRLLSSSLRRLRLLSRSSSLSLS',\n",
       "  'LLRRLLRRLLSSSLRRLRLLSRSSSLSLS',\n",
       "  'LLRRLLRRLLSSSLRRLRLLSRSSSRSLS',\n",
       "  'SLRRLLRRLLSSSLRRLRLLSRSSSRSLS',\n",
       "  'SLRRLLRRLSSSSLRRLRLLSRSSSRSLS',\n",
       "  'SLRRLLRRLSSSSLRRLRLLSRSSSRSRS',\n",
       "  'SLRRLLRRLSLSSLRRLRLLSRSSSRSRS',\n",
       "  'SLRRLLRRLSLSSLRRLRLLSRSSSRLRS',\n",
       "  'SLRRLLRRLSLSSLRRSRLLSRSSSRLRS',\n",
       "  'SLRRSLRRLSLSSLRRSRLLSRSSSRLRS',\n",
       "  'SLRRSLRRLSLSSLRRSSLLSRSSSRLRS',\n",
       "  'SLRRSLRRLSLSSLRRSSLLSRSSSRLRL',\n",
       "  'SSRRSLRRLSLSSLRRSSLLSRSSSRLRL',\n",
       "  'SSRRSLRRLSLSRLRRSSLLSRSSSRLRL',\n",
       "  'SSLRSLRRLSLSRLRRSSLLSRSSSRLRL',\n",
       "  'SSLRSLRRLSLSRLRSSSLLSRSSSRLRL',\n",
       "  'SSLRSLRRLSLSRLRSRSLLSRSSSRLRL',\n",
       "  'LSLRSLRRLSLSRLRSRSLLSRSSSRLRL',\n",
       "  'LSLRSLRRLSLSRLRSRSLLSRSSSRLRS',\n",
       "  'LSSRSLRRLSLSRLRSRSLLSRSSSRLRS',\n",
       "  'LSLRSLRRLSLSRLRSRSLLSRSSSRLRS',\n",
       "  'LSLRSLRRLSRSRLRSRSLLSRSSSRLRS',\n",
       "  'RSLRSLRRLSRSRLRSRSLLSRSSSRLRS',\n",
       "  'RSLRSLRRLSRSSLRSRSLLSRSSSRLRS',\n",
       "  'RSLRSLRRLSRSSLRSRSLLSRSSSSLRS',\n",
       "  'RSSRSLRRLSRSSLRSRSLLSRSSSSLRS',\n",
       "  'RSSRSLRRLSRLSLRSRSLLSRSSSSLRS',\n",
       "  'RSSRSLLRLSRLSLRSRSLLSRSSSSLRS',\n",
       "  'RSSRSLRRLSRLSLRSRSLLSRSSSSLRS',\n",
       "  'RRSRSLRRLSRLSLRSRSLLSRSSSSLRS',\n",
       "  'RRSRSLRRSSRLSLRSRSLLSRSSSSLRS',\n",
       "  'RRSRLLRRSSRLSLRSRSLLSRSSSSLRS',\n",
       "  'RRSSLLRRSSRLSLRSRSLLSRSSSSLRS',\n",
       "  'RRSSLLRRSSRLSLRSRSLLRRSSSSLRS',\n",
       "  'RRSSLLRRSSRLSLSSRSLLRRSSSSLRS',\n",
       "  'RRSSLLRRSSRLSLSSRSLLRSSSSSLRS',\n",
       "  'RRSSLLRRSSRLSLSSRSLLRSSSSRLRS',\n",
       "  'RRSSLLRRSSRLSLSSRSLLRSSRSRLRS',\n",
       "  'RRSSLLRRSSRLSLSSRRLLRSSRSRLRS',\n",
       "  'RRSSLLRSSSRLSLSSRRLLRSSRSRLRS',\n",
       "  'RRSSLLRSSSRLSLSSRRLLRSLRSRLRS',\n",
       "  'RRLSLLRSSSRLSLSSRRLLRSLRSRLRS',\n",
       "  'RRSSLLRSSSRLSLSSRRLLRSLRSRLRS',\n",
       "  'LRSSLLRSSSRLSLSSRRLLRSLRSRLRS',\n",
       "  'LRSSLLSSSSRLSLSSRRLLRSLRSRLRS',\n",
       "  'LRSRLLSSSSRLSLSSRRLLRSLRSRLRS',\n",
       "  'LRSRLLSSSSSLSLSSRRLLRSLRSRLRS',\n",
       "  'SRSRLLSSSSSLSLSSRRLLRSLRSRLRS',\n",
       "  'SRSRLLSSSSSLSLSSRRLLRLLRSRLRS',\n",
       "  'SRSRLLSSSSSLSLSSRRLLRLLRSRSRS',\n",
       "  'SRSRLLSSSSSLSLSSRRSLRLLRSRSRS',\n",
       "  'SRSRLLSSSSSRSLSSRRSLRLLRSRSRS',\n",
       "  'SRSRLLSSSSSRSLSSRRSLRLLRSRSSS',\n",
       "  'SRSRLLSSSSSSSLSSRRSLRLLRSRSSS',\n",
       "  'SRSRLLSSSSSSSLSSRRSLRLLRSRSSR',\n",
       "  'SRSRLLSSSSSLSLSSRRSLRLLRSRSSR',\n",
       "  'SRSRLLSSSSSLSLSSRRSLRLLSSRSSR',\n",
       "  'RRSRLLSSSSSLSLSSRRSLRLLSSRSSR',\n",
       "  'RRSRLLSSSSSLRLSSRRSLRLLSSRSSR',\n",
       "  'RRSRLLSSSSSLRLSSRLSLRLLSSRSSR',\n",
       "  'RRSRLLRSSSSLRLSSRLSLRLLSSRSSR',\n",
       "  'RRSRLLRSSSSLRLSSRLSLRLLSSRLSR',\n",
       "  'RRSSLLRSSSSLRLSSRLSLRLLSSRLSR',\n",
       "  'RRLSLLRSSSSLRLSSRLSLRLLSSRLSR',\n",
       "  'RRLSLLRSSSSLRLSSRLSRRLLSSRLSR',\n",
       "  'RRLSLLRSSSSLRLSSRLSRRLLSSRLSL',\n",
       "  'RRLSLLRSSSSLSLSSRLSRRLLSSRLSL',\n",
       "  'RRLSLLRRSSSLSLSSRLSRRLLSSRLSL',\n",
       "  'RRLSLLRRSSSLSLSSRLSRRLRSSRLSL',\n",
       "  'RRLSLLRRSSSLRLSSRLSRRLRSSRLSL',\n",
       "  'RRLSLLRRSSLLRLSSRLSRRLRSSRLSL',\n",
       "  'RRLSLLRRSSLLRLSSRLSRRLLSSRLSL',\n",
       "  'RRLRLLRRSSLLRLSSRLSRRLLSSRLSL',\n",
       "  'RRLRLLRRSSLLRLSSRLSRRLLSSRRSL',\n",
       "  'RRLRLLRRSSLLRLSLRLSRRLLSSRRSL',\n",
       "  'RRLRLLRRSSLLRLSLRLSRRLLSSRLSL',\n",
       "  'RRLRLLRRSSLLRLSLRLSRRLLSSRLRL',\n",
       "  'RRLRLLRRSSLLRLSSRLSRRLLSSRLRL',\n",
       "  'RRLRLLRRSSLLRSSSRLSRRLLSSRLRL',\n",
       "  'RRLRSLRRSSLLRSSSRLSRRLLSSRLRL',\n",
       "  'RRLRSLRRSSLLSSSSRLSRRLLSSRLRL',\n",
       "  'RRLRSLRRSSLLSSSSRLSRSLLSSRLRL',\n",
       "  'RRLRSLRRSRLLSSSSRLSRSLLSSRLRL',\n",
       "  'RRLRSLSRSRLLSSSSRLSRSLLSSRLRL',\n",
       "  'RRLRSLSRSRLSSSSSRLSRSLLSSRLRL',\n",
       "  'RRLRSLSRSRLSSLSSRLSRSLLSSRLRL',\n",
       "  'RRLRSLSRSRLSSLSSRLSRSLLRSRLRL',\n",
       "  'RRLRRLSRSRLSSLSSRLSRSLLRSRLRL',\n",
       "  'RRLRRLSRSRLSSLSSRLSRSLLSSRLRL',\n",
       "  'RRLRRLSRSRLSSLSSRLSRSLRSSRLRL',\n",
       "  'RRLRRLSRSRLSSLSSRLRRSLRSSRLRL',\n",
       "  'RRLRRLSRSRLSSLSSRLRRLLRSSRLRL',\n",
       "  'RRLRRLSRSSLSSLSSRLRRLLRSSRLRL',\n",
       "  'RRLRRLSRSSLSSLSLRLRRLLRSSRLRL',\n",
       "  'RRLRRLSRSSLSSLSLRLRRLLRSSRLRR',\n",
       "  'RRLRRLSRSSLSSLSLRLRRLSRSSRLRR',\n",
       "  'RRLRRLSRSSLSSLSLRLRSLSRSSRLRR',\n",
       "  'RRSRRLSRSSLSSLSLRLRSLSRSSRLRR',\n",
       "  'RRSRRLSRSRLSSLSLRLRSLSRSSRLRR',\n",
       "  'RRSRRLSRSRLSSLSLRLRSLSRSSRSRR',\n",
       "  'RSSRRLSRSRLSSLSLRLRSLSRSSRSRR',\n",
       "  'RSSRRLSRSRLSSLRLRLRSLSRSSRSRR',\n",
       "  'RSSRRLSRSRLSSLRLRLRSLSRSSRSLR',\n",
       "  'RSSRRLSRSRLSSLRLRLRRLSRSSRSLR',\n",
       "  'RSSRRLSRSRLSLLRLRLRRLSRSSRSLR',\n",
       "  'RSSRRLSRSRLSLLRLRLRSLSRSSRSLR',\n",
       "  'RSSRRLSRSRLSLSRLRLRSLSRSSRSLR',\n",
       "  'RSSRRLSRSRLSLSRLSLRSLSRSSRSLR',\n",
       "  'RSSRRLSRSRLSLSRLSLRSLLRSSRSLR',\n",
       "  'LSSRRLSRSRLSLSRLSLRSLLRSSRSLR',\n",
       "  'LSSRRLSRSRLSLSRLSRRSLLRSSRSLR',\n",
       "  'LRSRRLSRSRLSLSRLSRRSLLRSSRSLR',\n",
       "  'LRSRRLSRSRLSLSRLSRRSLLRSSRRLR',\n",
       "  'LRSRRLSRSRLSLRRLSRRSLLRSSRRLR',\n",
       "  'LRLRRLSRSRLSLRRLSRRSLLRSSRRLR',\n",
       "  'LRLRSLSRSRLSLRRLSRRSLLRSSRRLR',\n",
       "  'LRLRSLSRSRLSLRRLSSRSLLRSSRRLR',\n",
       "  'LRLRSLSRSRLSLLRLSSRSLLRSSRRLR',\n",
       "  'LRLRSLSRSRLSLLRLSSRSLLRSLRRLR',\n",
       "  'LRLRSLSRSRLRLLRLSSRSLLRSLRRLR',\n",
       "  'LRLRLLSRSRLRLLRLSSRSLLRSLRRLR',\n",
       "  'SRLRLLSRSRLRLLRLSSRSLLRSLRRLR',\n",
       "  'SRLRLLSRSRLRLLRLSSRSRLRSLRRLR',\n",
       "  'SRLRLLSSSRLRLLRLSSRSRLRSLRRLR',\n",
       "  'SRLRLLSSSRLRLLRLSSRSRLRSLRSLR',\n",
       "  'SRLRLLSSSRLRLLRLSSRSRLLSLRSLR',\n",
       "  'SRLRLLSSSRLRLLRLSSRSRLLSRRSLR',\n",
       "  'SRLRLLSSSRLRRLRLSSRSRLLSRRSLR',\n",
       "  'SRLRLLSSLRLRRLRLSSRSRLLSRRSLR',\n",
       "  'SRLRLLSSLRLRRSRLSSRSRLLSRRSLR',\n",
       "  'SRLRLLSSLRLRSSRLSSRSRLLSRRSLR',\n",
       "  'SRLRLLSSLRLRSSRLSSRSRLLSRLSLR',\n",
       "  'SRLRLLSSLRLRSSRLSSRSRLLSRLSSR',\n",
       "  'SRLRLLSSLRLRSSRLSSRSRLLSSLSSR',\n",
       "  'SRLRLLSSLRLRSSRLSSRSRLLSSSSSR',\n",
       "  'SRLRLLSSLRLRSSRLSSRSRLLSSRSSR',\n",
       "  'SRLRLLSSLRLRSSRLSSSSRLLSSRSSR',\n",
       "  'SRLRLLSSLRLRSSRLSSLSRLLSSRSSR',\n",
       "  'RRLRLLSSLRLRSSRLSSLSRLLSSRSSR',\n",
       "  'LRLRLLSSLRLRSSRLSSLSRLLSSRSSR',\n",
       "  'LRLRLLSSLRLRSSRLSSLSRLRSSRSSR',\n",
       "  'LRLRLLSSLRSRSSRLSSLSRLRSSRSSR',\n",
       "  'LRLRLLSSLRSRSSRLLSLSRLRSSRSSR',\n",
       "  'LRLRLLSRLRSRSSRLLSLSRLRSSRSSR',\n",
       "  'LRLRLLSRLRSRSSRLLSRSRLRSSRSSR',\n",
       "  'LRLRLLSRLLSRSSRLLSRSRLRSSRSSR',\n",
       "  'LRLRLLSRLLSRSSRLLSRSRLSSSRSSR',\n",
       "  'LRLRSLSRLLSRSSRLLSRSRLSSSRSSR',\n",
       "  'LRLRSLSRSLSRSSRLLSRSRLSSSRSSR',\n",
       "  'LRLSSLSRSLSRSSRLLSRSRLSSSRSSR',\n",
       "  'LRLSSLSRLLSRSSRLLSRSRLSSSRSSR',\n",
       "  'LRLSSLSRLLSRSSRLLSRSRLSSSRSSL',\n",
       "  'LRLSSLSRLLSRSSSLLSRSRLSSSRSSL',\n",
       "  'LRLSSLSRLLSRSSSLLSRSRLSRSRSSL',\n",
       "  'LRLSSRSRLLSRSSSLLSRSRLSRSRSSL',\n",
       "  'LRLSSRSRLLSRSSSRLSRSRLSRSRSSL',\n",
       "  'LRLSSRSRLLSRSSSRLSRSRLSRSRSSS',\n",
       "  'LRLSSRSRLLSRSSSLLSRSRLSRSRSSS',\n",
       "  'LRLSSSSRLLSRSSSLLSRSRLSRSRSSS',\n",
       "  'LRLSSSSRLLSRSSSLLSRSRLSSSRSSS',\n",
       "  'LRLSSSSRLLSRSSSLLSRSRLSLSRSSS',\n",
       "  'LRLSSSSRLLSRSSSLLSRSRSSLSRSSS',\n",
       "  'LRLSSSSRLLSSSSSLLSRSRSSLSRSSS',\n",
       "  'LRSSSSSRLLSSSSSLLSRSRSSLSRSSS',\n",
       "  'LRSSSSSRLLSSSSRLLSRSRSSLSRSSS',\n",
       "  'LRSSSSSRLLSSSSRLLSLSRSSLSRSSS',\n",
       "  'LRSSSSSRLLSSSSRLLRLSRSSLSRSSS',\n",
       "  'LRSSSSSRLLSSSSRLLRSSRSSLSRSSS',\n",
       "  'LRSSSLSRLLSSSSRLLRSSRSSLSRSSS',\n",
       "  'LRSSSLSRLLSSSSRLLRSSRSSLSRSLS',\n",
       "  'LRSSSLSRLLSSSRRLLRSSRSSLSRSLS',\n",
       "  'LRSRSLSRLLSSSRRLLRSSRSSLSRSLS',\n",
       "  'LRLRSLSRLLSSSRRLLRSSRSSLSRSLS',\n",
       "  'LRLRSLSRSLSSSRRLLRSSRSSLSRSLS',\n",
       "  'LRLRSLSRSLSSSRRLLRSSRSSLSSSLS',\n",
       "  'LRLRSLSRSLRSSRRLLRSSRSSLSSSLS',\n",
       "  'LRLLSLSRSLRSSRRLLRSSRSSLSSSLS',\n",
       "  'LRLLSLSRSLRSLRRLLRSSRSSLSSSLS',\n",
       "  'LRLLSLSRSLRSLRRLLRSLRSSLSSSLS',\n",
       "  'LRLLSLSRSLRSLRRLLRSLRSRLSSSLS',\n",
       "  'LRLLRLSRSLRSLRRLLRSLRSRLSSSLS',\n",
       "  'LRLLRLSRSLRSLSRLLRSLRSRLSSSLS',\n",
       "  'LRSLRLSRSLRSLSRLLRSLRSRLSSSLS',\n",
       "  'LRSLRLLRSLRSLSRLLRSLRSRLSSSLS',\n",
       "  'LRSLRLLRSLRSLSRLLRSLRSRLSLSLS',\n",
       "  'LRSRRLLRSLRSLSRLLRSLRSRLSLSLS',\n",
       "  'LRSRRLLRSLRSLSRLLRSLRSRLSLSSS',\n",
       "  'LRSRRLLRSLRSLRRLLRSLRSRLSLSSS',\n",
       "  'LRSRRLLRSLRSLRRLLRSLRSRLSLSSL',\n",
       "  'RRSRRLLRSLRSLRRLLRSLRSRLSLSSL',\n",
       "  'RRSRRLLRSLRSLRRLLRSLRSRLSLSRL',\n",
       "  'RRLRRLLRSLRSLRRLLRSLRSRLSLSRL',\n",
       "  'RRLRRLLRSLRSLRRLLRSLRLRLSLSRL',\n",
       "  'RRLLRLLRSLRSLRRLLRSLRLRLSLSRL',\n",
       "  'RRRLRLLRSLRSLRRLLRSLRLRLSLSRL',\n",
       "  'RRRLRLLRSLRSLRRLLRSLRLRLSRSRL',\n",
       "  'RRRLRLLRSLRSLRRLLRSLRLRLSRSRR',\n",
       "  'RRRLRLLRSLRSLRRLRRSLRLRLSRSRR',\n",
       "  'SRRLRLLRSLRSLRRLRRSLRLRLSRSRR',\n",
       "  'SRRLSLLRSLRSLRRLRRSLRLRLSRSRR',\n",
       "  'SRRSSLLRSLRSLRRLRRSLRLRLSRSRR',\n",
       "  'SRRSSLLRSLRSLRRLRRSLSLRLSRSRR',\n",
       "  'LRRSSLLRSLRSLRRLRRSLSLRLSRSRR',\n",
       "  'LRRSSLLRSLRSLRRLRRSLSLRLSRSRS',\n",
       "  'LRRSSLLRSLRSLRRLRRSLSLRLSSSRS',\n",
       "  'LRRSSLRRSLRSLRRLRRSLSLRLSSSRS',\n",
       "  'LRRLSLRRSLRSLRRLRRSLSLRLSSSRS',\n",
       "  'LRRLSLRRSLRSLRRLRLSLSLRLSSSRS',\n",
       "  'LRRLSLRRSLRSLRRLRLSLSLRLSSRRS',\n",
       "  'LRRLSLRRSLRSLRRLRLSLRLRLSSRRS',\n",
       "  'LRRLSLSRSLRSLRRLRLSLRLRLSSRRS',\n",
       "  'LRRLSLRRSLRSLRRLRLSLRLRLSSRRS',\n",
       "  'LRRLSLLRSLRSLRRLRLSLRLRLSSRRS',\n",
       "  'LRRLSLLRSLRSLRRLRSSLRLRLSSRRS',\n",
       "  'LRRLSLLRSLRSLSRLRSSLRLRLSSRRS',\n",
       "  'LRRLRLLRSLRSLSRLRSSLRLRLSSRRS',\n",
       "  'LRRLRLLRRLRSLSRLRSSLRLRLSSRRS',\n",
       "  'LRRLRLLRRLRSLSRSRSSLRLRLSSRRS',\n",
       "  'LRRLRLLRRLRSLSRSRSSLRLRSSSRRS',\n",
       "  'LRRLRLLRRLRSLSRSRSSLRLSSSSRRS',\n",
       "  'LRSLRLLRRLRSLSRSRSSLRLSSSSRRS',\n",
       "  'LRSLRLLRRLRSLSRSRSSLRLSLSSRRS',\n",
       "  'LRSLRLLRRLRSLSRSRLSLRLSLSSRRS',\n",
       "  'LRSLRLLRRLRSLSRSRLSLRLSLSSLRS',\n",
       "  'LRSLRLLRRLRSLSRSRLSLRLSLRSLRS',\n",
       "  'LRSLRLLRRLRSLSRSRLSLRLRLRSLRS',\n",
       "  'LRSLRLLRRLRSLSRSRLSLRSRLRSLRS',\n",
       "  'LRSLRLLRRLRSLSRSRLSLRSRLSSLRS',\n",
       "  'LRSLRLLRRLRSLSLSRLSLRSRLSSLRS',\n",
       "  'LRSLRLLRRSRSLSLSRLSLRSRLSSLRS',\n",
       "  'LRSLRLLRRSRSSSLSRLSLRSRLSSLRS',\n",
       "  'LLSLRLLRRSRSSSLSRLSLRSRLSSLRS',\n",
       "  'SLSLRLLRRSRSSSLSRLSLRSRLSSLRS',\n",
       "  'SLSLRLLRRSRSSSLSSLSLRSRLSSLRS',\n",
       "  'SLSLRLLRRSRSSSLSSLSLRSRLSSLLS',\n",
       "  'SLSLRLLRRSRSSSLSRLSLRSRLSSLLS',\n",
       "  'SLSLRLLRRSRSSSLRRLSLRSRLSSLLS',\n",
       "  'SLSLRLLSRSRSSSLRRLSLRSRLSSLLS',\n",
       "  'SLSLRLLSRSRSSSLRRLSLRSRLSSSLS',\n",
       "  'SLSLRLLSRSRSSRLRRLSLRSRLSSSLS',\n",
       "  'SLSLRLLSRSRSSRLRRLSLRSRLSSSSS',\n",
       "  'SLSLRLLSRSRSSRLRRLSLRSRLLSSSS',\n",
       "  'SLSLRLLSRSRSSRLRRLSLRSRRLSSSS',\n",
       "  'SLSLRLLSRSRSSRLRSLSLRSRRLSSSS',\n",
       "  'SLSRRLLSRSRSSRLRSLSLRSRRLSSSS',\n",
       "  'SLSRRLLSRSRSSRLRSLSLRSRRLSSSL',\n",
       "  'SLSRRLLSRSRSSRLRSLSLRSRRLSSRL',\n",
       "  'SLSRRLLSRSRSSRLRSLSLRSRRLSSRR',\n",
       "  'SLSRRLLSRSRSSRLRSLSLRSRRLSSRS',\n",
       "  'SSSRRLLSRSRSSRLRSLSLRSRRLSSRS',\n",
       "  'SSSRRLLSRSRSSLLRSLSLRSRRLSSRS',\n",
       "  'SSSRRLLSRSSSSLLRSLSLRSRRLSSRS',\n",
       "  'SSSRRLLSRSSRSLLRSLSLRSRRLSSRS',\n",
       "  'SSSRRLLSRSSRSLLRSLSLSSRRLSSRS',\n",
       "  'SSSRRLLSRSSRSLLRRLSLSSRRLSSRS',\n",
       "  'SSSRRLLSRSSRSLLRRLSSSSRRLSSRS',\n",
       "  'SSSSRLLSRSSRSLLRRLSSSSRRLSSRS',\n",
       "  'SSSSRLLSRSSSSLLRRLSSSSRRLSSRS',\n",
       "  'SSSSRLLSRSSSSLLRRLSSSSRRLLSRS',\n",
       "  'SSSSRLLSRSRSSLLRRLSSSSRRLLSRS',\n",
       "  'SSLSRLLSRSRSSLLRRLSSSSRRLLSRS',\n",
       "  'SSLSRLLSRSRSSLLRRLSLSSRRLLSRS',\n",
       "  'SSLSRLLSRSRSSSLRRLSLSSRRLLSRS',\n",
       "  'SSLSRLLSRSRSSSLRRLSLSSRRLLSLS',\n",
       "  'SSLSRLLSRSRSSSLRRLSLSSRRSLSLS',\n",
       "  'RSLSRLLSRSRSSSLRRLSLSSRRSLSLS',\n",
       "  'RSLSRLLSRSRSSRLRRLSLSSRRSLSLS',\n",
       "  'RSLSRLLSRSRSSRLSRLSLSSRRSLSLS',\n",
       "  'RSLSRLLSRSRSSRLSRLSLSSLRSLSLS',\n",
       "  'RSLSRLLSRSRSLRLSRLSLSSLRSLSLS',\n",
       "  'RSLSRLLSRSRSLRLRRLSLSSLRSLSLS',\n",
       "  'RSLSRLLSRSLSLRLRRLSLSSLRSLSLS',\n",
       "  'RSLSRLLSRSLSSRLRRLSLSSLRSLSLS',\n",
       "  'RSLSRLLSRSLSSRLRRLSLSSLRSLRLS',\n",
       "  'RSLSRLLSRSLSSRLRRLSLSSLRSLSLS',\n",
       "  'RSLSRLLSSSLSSRLRRLSLSSLRSLSLS',\n",
       "  'RSSSRLLSSSLSSRLRRLSLSSLRSLSLS',\n",
       "  'SSSSRLLSSSLSSRLRRLSLSSLRSLSLS',\n",
       "  'SSSSRLLSSSLSSRLRRLSLSSLRSSSLS',\n",
       "  'SSSSRLLSSSLSSRLRRLSLRSLRSSSLS',\n",
       "  'SSSSRLLSSSLSSRSRRLSLRSLRSSSLS',\n",
       "  'SSSSRLLSSSLSSRSRRLSLRSLRSSSSS',\n",
       "  'SSSSRLLSSSLSSRSRRLSLSSLRSSSSS',\n",
       "  'SLSSRLLSSSLSSRSRRLSLSSLRSSSSS',\n",
       "  'SLSSRLLSSSLLSRSRRLSLSSLRSSSSS',\n",
       "  'SLSSRLLSSSLLSRSRRLSLSSLRSSSSL',\n",
       "  'SLSSRLLRSSLLSRSRRLSLSSLRSSSSL',\n",
       "  'SLSSRLLRSSLLSRSRRLSLRSLRSSSSL',\n",
       "  'SLSSSLLRSSLLSRSRRLSLRSLRSSSSL',\n",
       "  'SLSSSLLRSSLLSRSRRLSLRSLRSSRSL',\n",
       "  'SLSSSLLRSSLLSRSRRLSLRSLSSSRSL',\n",
       "  'SLSSSSLRSSLLSRSRRLSLRSLSSSRSL',\n",
       "  'SLSSSSLRSSLLSRSRRLSLRRLSSSRSL',\n",
       "  'SLSSSSLRSSLLSRSRRLSLLRLSSSRSL',\n",
       "  'SLSSSLLRSSLLSRSRRLSLLRLSSSRSL',\n",
       "  'SLSSSLLRSSLLSRSRRLSLLRRSSSRSL',\n",
       "  'RLSSSLLRSSLLSRSRRLSLLRRSSSRSL',\n",
       "  'RLSSSLRRSSLLSRSRRLSLLRRSSSRSL',\n",
       "  'RLSSSLRRSSLLSSSRRLSLLRRSSSRSL',\n",
       "  'RLSSSLRRSSLLSSSRRLSLLRRSSSLSL',\n",
       "  'RLSSSLRRSSLLSSSRRLRLLRRSSSLSL',\n",
       "  'RLSSSLRRSSLLSSSRRLRLLRLSSSLSL',\n",
       "  'RLLSSLRRSSLLSSSRRLRLLRLSSSLSL',\n",
       "  'RLLSSLRRSSLLSSSRRLRLLRSSSSLSL',\n",
       "  'RLLSSLRRSSLLSSSRRLRLLRLSSSLSL',\n",
       "  'RLLSSLRRSSLLSSSRRLRLLRRSSSLSL',\n",
       "  'RLLSSLRRSSLLSSSRRLRLLRRLSSLSL',\n",
       "  'RLLSSLRRSSLLSSSRRLRLSRRLSSLSL',\n",
       "  'RLLSSLRRSSLLSSSRSLRLSRRLSSLSL',\n",
       "  'RLLSSLRRSSLLSSSSSLRLSRRLSSLSL',\n",
       "  'RLLSSLRRSSLLSRSSSLRLSRRLSSLSL',\n",
       "  'RLLRSLRRSSLLSRSSSLRLSRRLSSLSL',\n",
       "  'RLLRSLRRSSLLSRSSRLRLSRRLSSLSL',\n",
       "  'RLLRSLRRSSLLSSSSRLRLSRRLSSLSL',\n",
       "  'RSLRSLRRSSLLSSSSRLRLSRRLSSLSL',\n",
       "  'RSLRSLRRSSLLSSSSRLRLLRRLSSLSL',\n",
       "  'RSLRRLRRSSLLSSSSRLRLLRRLSSLSL',\n",
       "  'RSLRRLLRSSLLSSSSRLRLLRRLSSLSL',\n",
       "  'RSLRRLLRSSLLSSSSRLRLLRRLRSLSL',\n",
       "  'RSLRRLRRSSLLSSSSRLRLLRRLRSLSL',\n",
       "  'RSLRRLRRSSLLSSRSRLRLLRRLRSLSL',\n",
       "  'RSLRRLRRSSLLSSRSRLRLLRLLRSLSL',\n",
       "  'RSLRRLRRSSLLSSSSRLRLLRLLRSLSL',\n",
       "  'RSLRRLRRSSLLSSSSRLRLLRLLRSSSL',\n",
       "  'RSLRRLSRSSLLSSSSRLRLLRLLRSSSL',\n",
       "  'RSLRRLSRSRLLSSSSRLRLLRLLRSSSL',\n",
       "  'RSLRRLSRSRLLSSRSRLRLLRLLRSSSL',\n",
       "  'RSLRRLSRSRLLRSRSRLRLLRLLRSSSL',\n",
       "  'RLLRRLSRSRLLRSRSRLRLLRLLRSSSL',\n",
       "  'RLLRRLSRSRLLRSRSRLRLLRLLRRSSL',\n",
       "  'RLLRRLSRSRLLRSRSRLRLLRLSRRSSL',\n",
       "  'RLLRRSSRSRLLRSRSRLRLLRLSRRSSL',\n",
       "  'RLLRRLSRSRLLRSRSRLRLLRLSRRSSL',\n",
       "  'RLLRRLSRSRLLRSRSRLRLLRLSRSSSL',\n",
       "  'RLLRRLSRSRLLRSSSRLRLLRLSRSSSL',\n",
       "  'RLLRRLSRSRLLRSSSRLRRLRLSRSSSL',\n",
       "  'RLLRRLSRSRLLRSSSRLRRLRLLRSSSL',\n",
       "  'RLLRRLSSSRLLRSSSRLRRLRLLRSSSL',\n",
       "  'RLLRRLSSSRLLRRSSRLRRLRLLRSSSL',\n",
       "  'RLLRRLSSSRLLRRSSRLSRLRLLRSSSL',\n",
       "  'RLLRRLSSSRLLRRSSRLSRLRLLRSSSR',\n",
       "  'RLLRRLSSSRLLRRSSRLSSLRLLRSSSR',\n",
       "  'RLLRRLSSSRLLSRSSRLSSLRLLRSSSR',\n",
       "  'RLLRRLSSSRLRSRSSRLSSLRLLRSSSR',\n",
       "  'RLLRRLSSLRLRSRSSRLSSLRLLRSSSR',\n",
       "  'RLLRRLSSLRLRSRSSRLSSLRSLRSSSR',\n",
       "  'RLLRRLSSLRLRSRSSRLSSLRSSRSSSR',\n",
       "  'RLLRRLLSLRLRSRSSRLSSLRSSRSSSR',\n",
       "  'LLLRRLLSLRLRSRSSRLSSLRSSRSSSR',\n",
       "  'LLLRRLLSLRLSSRSSRLSSLRSSRSSSR',\n",
       "  'LLLRRLLSLRLSSSSSRLSSLRSSRSSSR',\n",
       "  'LLLRRLLSLRLSSSSSRLSSLRSSRSRSR',\n",
       "  'LLLRRLLSLRLSSSSLRLSSLRSSRSRSR',\n",
       "  'LLLRRLLSLRLSSSSLRLSSLRSSRLRSR',\n",
       "  'LLLRRLLSLRLSRSSLRLSSLRSSRLRSR',\n",
       "  'LLLRRLLSLRLSRSSLRLSLLRSSRLRSR',\n",
       "  'LLLRRLLSLRLSRSSLRLSLLRSSRSRSR',\n",
       "  'LLLRRLLSRRLSRSSLRLSLLRSSRSRSR',\n",
       "  'SLLRRLLSRRLSRSSLRLSLLRSSRSRSR',\n",
       "  'SLLRRLLSRRLSRSSLRLSLSRSSRSRSR',\n",
       "  'SLLRRSLSRRLSRSSLRLSLSRSSRSRSR',\n",
       "  'SLLRRSLSRRLSRSSLRLSLSRSSRSSSR',\n",
       "  'SLLRRSLLRRLSRSSLRLSLSRSSRSSSR',\n",
       "  'SRLRRSLLRRLSRSSLRLSLSRSSRSSSR',\n",
       "  'SRLRRSLLRRLSRSSSRLSLSRSSRSSSR',\n",
       "  'SRLRRSLLRRSSRSSSRLSLSRSSRSSSR',\n",
       "  'SRLRRSLLRLSSRSSSRLSLSRSSRSSSR',\n",
       "  'LRLRRSLLRLSSRSSSRLSLSRSSRSSSR',\n",
       "  'LRLRRSLLRLSSRSSLRLSLSRSSRSSSR',\n",
       "  'LRLRRSLLRLSSRRSLRLSLSRSSRSSSR',\n",
       "  'LRLRRSLLRLSSRRSLRLSSSRSSRSSSR',\n",
       "  'LSLRRSLLRLSSRRSLRLSSSRSSRSSSR',\n",
       "  'LSLRRSLLRLSSRRSLSLSSSRSSRSSSR',\n",
       "  'LSLRRSLLRLSSRRSLSLSSSSSSRSSSR',\n",
       "  'LSLRRSLLRLSSRSSLSLSSSSSSRSSSR',\n",
       "  'SSLRRSLLRLSSRSSLSLSSSSSSRSSSR',\n",
       "  'SSLRRSLLRLSSRSSLSLSSSSSLRSSSR',\n",
       "  'SSLRRSLLRLSSRSSLSLSSSSRLRSSSR',\n",
       "  'SSLRRSLLRLSSRSSLSLSSSSRLRSRSR',\n",
       "  'SSLRRSLLRLSSRSSLSLSSSSSLRSRSR',\n",
       "  'SSLRRSLLRLSSRSSLSLSSSSSLRLRSR',\n",
       "  'SSLRRSLLRLSSRSSRSLSSSSSLRLRSR',\n",
       "  'SSLRRSLLRLSLRSSRSLSSSSSLRLRSR',\n",
       "  'SSLRRSLLRLSLRSSRSLSSLSSLRLRSR',\n",
       "  'SSLRRSLLRSSLRSSRSLSSLSSLRLRSR',\n",
       "  'SSLRRSLLRSSLRSSRSLSSLSSLRSRSR',\n",
       "  'SSLRRSLLRLSLRSSRSLSSLSSLRSRSR',\n",
       "  'SSLRRSLLRLSLSSSRSLSSLSSLRSRSR',\n",
       "  'SSLRRSLLRLSLSSSRSLSSLSSSRSRSR',\n",
       "  'SSLRRSLLRLRLSSSRSLSSLSSSRSRSR',\n",
       "  'SSLRRSLLRLRLSSSRSLSSLSSSRSRSL',\n",
       "  'SSLRRSLLRLRLSSSRSLSSSSSSRSRSL',\n",
       "  'SSLRRSLLRLRLSSSRSLSSSSSSRSLSL',\n",
       "  'SSLRRSLLRLRLSSRRSLSSSSSSRSLSL',\n",
       "  'SSLSRSLLRLRLSSRRSLSSSSSSRSLSL',\n",
       "  'SSLSRSLLRLRLSSRRSLSSSSSSRSSSL',\n",
       "  'SSLSRSLLRLRSSSRRSLSSSSSSRSSSL',\n",
       "  'SSLSRSLLRLRSSSSRSLSSSSSSRSSSL',\n",
       "  'SSLSRSLLRLRSSSSRSLSSSSLSRSSSL',\n",
       "  'SSLSRSLLRLRSLSSRSLSSSSLSRSSSL',\n",
       "  'SSLSRSLLRLRSLSSRSLSSSSLSRSRSL',\n",
       "  'SSLSRSLLRLRSLSSRSLSSSSSSRSRSL',\n",
       "  'SLLSRSLLRLRSLSSRSLSSSSSSRSRSL',\n",
       "  'SLLSRSLLRLRSLSSSSLSSSSSSRSRSL',\n",
       "  'SLLRRSLLRLRSLSSSSLSSSSSSRSRSL',\n",
       "  'SLLRRSLLRLRRLSSSSLSSSSSSRSRSL',\n",
       "  'SSLRRSLLRLRRLSSSSLSSSSSSRSRSL',\n",
       "  'SLLRRSLLRLRRLSSSSLSSSSSSRSRSL',\n",
       "  'SLLRRSLLRLRRLSSLSLSSSSSSRSRSL',\n",
       "  'SLLRRSLLRLRRLSSLSRSSSSSSRSRSL',\n",
       "  'SSLRRSLLRLRRLSSLSRSSSSSSRSRSL',\n",
       "  'SRLRRSLLRLRRLSSLSRSSSSSSRSRSL',\n",
       "  'SRLRRSRLRLRRLSSLSRSSSSSSRSRSL',\n",
       "  'LRLRRSRLRLRRLSSLSRSSSSSSRSRSL',\n",
       "  'LRLRRSRLSLRRLSSLSRSSSSSSRSRSL',\n",
       "  'LRLRRSRLSLRRLSSLSRSSSSSSRSLSL',\n",
       "  'LRLRRSRLSLRRLSSLSSSSSSSSRSLSL',\n",
       "  'LRLRRSRLSLRRLSSLSSSSSSSSRRLSL',\n",
       "  'LRLRRSRLSLRRLLSLSSSSSSSSRRLSL',\n",
       "  'LRLRRSRLSLRRLLSLSSSSSSSSRRLSR',\n",
       "  'LRLRRSRLSLRRLLSLSSSSSSSLRRLSR',\n",
       "  'LRLRRSRLSLRRLLSLSSSSSRSLRRLSR',\n",
       "  'LRLRRSRLSLRRLLSLSSSSSRLLRRLSR',\n",
       "  'LRLRRSRLSLRRLLSLSSSSSRLLRRSSR',\n",
       "  'LRLRSSRLSLRRLLSLSSSSSRLLRRSSR',\n",
       "  'LRLRRSRLSLRRLLSLSSSSSRLLRRSSR',\n",
       "  'LRLRRSRLSLRRLLSLSSSSSRLLRRSLR',\n",
       "  'LRLRRSRLSLRRLLSLSSSSSRSLRRSLR',\n",
       "  'LRLRRSRLSLRRLLSLSSSSSRLLRRSLR',\n",
       "  'LRLRRSRLSLRRLLSLSSSSSRLLRRSSR',\n",
       "  'SRLRRSRLSLRRLLSLSSSSSRLLRRSSR',\n",
       "  'SRLRRSRLSLRRSLSLSSSSSRLLRRSSR',\n",
       "  'SRLRRSRLSLRRSLSLRSSSSRLLRRSSR',\n",
       "  'SRLRRSRLSLSRSLSLRSSSSRLLRRSSR',\n",
       "  'SRLRRSRLSLSRSLSLRSSSLRLLRRSSR',\n",
       "  'SRLSRSRLSLSRSLSLRSSSLRLLRRSSR',\n",
       "  'SRLSRSRLSLSSSLSLRSSSLRLLRRSSR',\n",
       "  'SRLSRSRLSLRSSLSLRSSSLRLLRRSSR',\n",
       "  'SRLLRSRLSLRSSLSLRSSSLRLLRRSSR',\n",
       "  'SRLLRSRLSLRSSLSLRSSSLRLLRSSSR',\n",
       "  'SRLLRSRLSLRSSLSLRSSSLRLLRSSLR',\n",
       "  'SRLLRSRLSLRSSLSLRSSSLRRLRSSLR',\n",
       "  'SRLLRSRLSLRSSLSLRSSSLRRLRSSLS',\n",
       "  'SRLLRSRLSLRSSLSLRSSSLRRLRSSRS',\n",
       "  'SRLRRSRLSLRSSLSLRSSSLRRLRSSRS',\n",
       "  'SRLRRSRLSLRSSLSLRSSSLSRLRSSRS',\n",
       "  'SRLRRSRLSLRLSLSLRSSSLSRLRSSRS',\n",
       "  'SRLRRSRLSLRLSLRLRSSSLSRLRSSRS',\n",
       "  'SRLRRSRLSLRLRLRLRSSSLSRLRSSRS',\n",
       "  'RRLRRSRLSLRLRLRLRSSSLSRLRSSRS',\n",
       "  'RRLRRSSLSLRLRLRLRSSSLSRLRSSRS',\n",
       "  'RRLRRSSLSLRLRLRLRSSSLSRLRSSLS',\n",
       "  'RRLRRSSSSLRLRLRLRSSSLSRLRSSLS',\n",
       "  'RRLRRSSSSLRLRLRLRSSSLSRLRRSLS',\n",
       "  'RRLRRSSSSLRLRLRLRSSSLSRLRRSSS',\n",
       "  'RRLRRSSSSRRLRLRLRSSSLSRLRRSSS',\n",
       "  'RRLRRLSSSRRLRLRLRSSSLSRLRRSSS',\n",
       "  'RRLRRLSSSRLLRLRLRSSSLSRLRRSSS',\n",
       "  'RLLRRLSSSRLLRLRLRSSSLSRLRRSSS',\n",
       "  'RLLRRLSSSRLLRLRLSSSSLSRLRRSSS',\n",
       "  'RLLRLLSSSRLLRLRLSSSSLSRLRRSSS',\n",
       "  'RLLRLLSSLRLLRLRLSSSSLSRLRRSSS',\n",
       "  'RLLRRLSSLRLLRLRLSSSSLSRLRRSSS',\n",
       "  'RLLRRLSSLRRLRLRLSSSSLSRLRRSSS',\n",
       "  'RLLRSLSSLRRLRLRLSSSSLSRLRRSSS',\n",
       "  'RLLRSLSSLRRLRLRLSLSSLSRLRRSSS',\n",
       "  'RLLRSLSSLRSLRLRLSLSSLSRLRRSSS',\n",
       "  'RLLRSLSSLRSLRLRLSLSSLRRLRRSSS',\n",
       "  'RLLRLLSSLRSLRLRLSLSSLRRLRRSSS',\n",
       "  'RLLRLLSSLRSRRLRLSLSSLRRLRRSSS',\n",
       "  'RLLRLLRSLRSRRLRLSLSSLRRLRRSSS',\n",
       "  'SLLRLLRSLRSRRLRLSLSSLRRLRRSSS',\n",
       "  'SLRRLLRSLRSRRLRLSLSSLRRLRRSSS',\n",
       "  'LLRRLLRSLRSRRLRLSLSSLRRLRRSSS',\n",
       "  'LLRRLLRSLRSRRLRLSLSSLSRLRRSSS',\n",
       "  'LLRRLLRSLRSRRLRLSLSSLSRLRRSSR',\n",
       "  'LLRRLLRSLRSRRLRLSLSSSSRLRRSSR',\n",
       "  'LLRRLLRSLRSRRLRLSLSSSSRLRRSSL',\n",
       "  'LLRRLLRSLRSRRLRLSSSSSSRLRRSSL',\n",
       "  'LLRRLLRSLRSRRLRLSSSSSSRLRRSLL',\n",
       "  'LLRRLLRSLRSRRLRLSSSSLSRLRRSLL',\n",
       "  'LLRRLLRSLRSRRLRLSRSSLSRLRRSLL',\n",
       "  'LLRRLLRSLSSRRLRLSRSSLSRLRRSLL',\n",
       "  'LLRRLLRSLSSRRLRLSRSSSSRLRRSLL',\n",
       "  'LLRRLLRSLSSLRLRLSRSSSSRLRRSLL',\n",
       "  'LLRRLLRSLSSLRSRLSRSSSSRLRRSLL',\n",
       "  'LLRRLSRSLSSLRSRLSRSSSSRLRRSLL',\n",
       "  'LLRRLSRSLSSLRSRLSRSSSSRLRSSLL',\n",
       "  'LLRRLSRSLRSLRSRLSRSSSSRLRSSLL',\n",
       "  'LLRRLSRSLSSLRSRLSRSSSSRLRSSLL',\n",
       "  'LLRRLSRSLSSLRSRLSRSSSSRLRSSLR',\n",
       "  'LLRRLSRSLSSLRLRLSRSSSSRLRSSLR',\n",
       "  'LLRRLSRSLSSLRLRLSRRSSSRLRSSLR',\n",
       "  'LLRRLSRSLSSLRLRLSRRSSSRLSSSLR',\n",
       "  'LLRRLSRSLSSLRLRLSRRSSSRLSSRLR',\n",
       "  'LLRRLSRSLSSLRLRLSRSSSSRLSSRLR',\n",
       "  'LLRRLSRSLSSLRSRLSRSSSSRLSSRLR',\n",
       "  'LLRRLSRRLSSLRSRLSRSSSSRLSSRLR',\n",
       "  'LLRRLSRRLSSLRSRLSRSSSSRLLSRLR',\n",
       "  'LLRRLSRRLSSLRSRLSRSRSSRLLSRLR',\n",
       "  'LLRRLLRRLSSLRSRLSRSRSSRLLSRLR',\n",
       "  'LSRRLLRRLSSLRSRLSRSRSSRLLSRLR',\n",
       "  'LSRRLLRRLSSLRSLLSRSRSSRLLSRLR',\n",
       "  'LSRRLLRRLSSLRSSLSRSRSSRLLSRLR',\n",
       "  'LSRRLLRRLSSSRSSLSRSRSSRLLSRLR',\n",
       "  'LSRRLLRRLSSSRSSLSRSRSSRLLSSLR',\n",
       "  'LSRRLLRRLSSSRSSLSRSLSSRLLSSLR',\n",
       "  'LSRRLLRRLSSSRSSLSRRLSSRLLSSLR',\n",
       "  'LSRRLLRRLRSSRSSLSRRLSSRLLSSLR',\n",
       "  'LLRRLLRRLRSSRSSLSRRLSSRLLSSLR',\n",
       "  'SLRRLLRRLRSSRSSLSRRLSSRLLSSLR',\n",
       "  'SLRRLLRRLRSSRSSLSRRLSSRRLSSLR',\n",
       "  'SLSRLLRRLRSSRSSLSRRLSSRRLSSLR',\n",
       "  'SLSRRLRRLRSSRSSLSRRLSSRRLSSLR',\n",
       "  'SLSRRLRRLRSSRSSLLRRLSSRRLSSLR',\n",
       "  'SLSRRLRRLRSSRSSLLRRLRSRRLSSLR',\n",
       "  'SLSRRLRRLSSSRSSLLRRLRSRRLSSLR',\n",
       "  'SLSRRLRRLSSSRSSLLRRLRSRLLSSLR',\n",
       "  'SLSRRLRRLSSSSSSLLRRLRSRLLSSLR',\n",
       "  'RLSRRLRRLSSSSSSLLRRLRSRLLSSLR',\n",
       "  'RLSRRLRRLSSSSSSLLRSLRSRLLSSLR',\n",
       "  'RLSRRLRRLSSSSSSLLRSLRSRLLSSRR',\n",
       "  'RLSRRLRRLSSSSSSLLRSLRSRLRSSRR',\n",
       "  'RLSRRLLRLSSSSSSLLRSLRSRLRSSRR',\n",
       "  'LLSRRLLRLSSSSSSLLRSLRSRLRSSRR',\n",
       "  'LLSRRLLRLSSSSSSRLRSLRSRLRSSRR',\n",
       "  'LLSRRLSRLSSSSSSRLRSLRSRLRSSRR',\n",
       "  'LLSRRLSRLSSSSSLRLRSLRSRLRSSRR',\n",
       "  'LLSRRLSRLSRSSSLRLRSLRSRLRSSRR',\n",
       "  'LLSRRLSRLSRSSSLRLRSLRSSLRSSRR',\n",
       "  'LLSRSLSRLSRSSSLRLRSLRSSLRSSRR',\n",
       "  'LLSRSLSRLSRSSSLRLRSSRSSLRSSRR',\n",
       "  'LLSRSLSRLSRRSSLRLRSSRSSLRSSRR',\n",
       "  ...])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e,l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-10T23:02:48.427091Z",
     "start_time": "2019-08-10T23:02:48.399055Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('HHPHHHHHHPHHHPHHHHHH', tensor([[1., 0.],\n",
       "         [1., 0.],\n",
       "         [0., 1.],\n",
       "         [1., 0.],\n",
       "         [1., 0.],\n",
       "         [1., 0.],\n",
       "         [1., 0.],\n",
       "         [1., 0.],\n",
       "         [1., 0.],\n",
       "         [0., 1.],\n",
       "         [1., 0.],\n",
       "         [1., 0.],\n",
       "         [1., 0.],\n",
       "         [0., 1.],\n",
       "         [1., 0.],\n",
       "         [1., 0.],\n",
       "         [1., 0.],\n",
       "         [1., 0.],\n",
       "         [1., 0.],\n",
       "         [1., 0.]]))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hp = HP.random(20,h_prob=0.75)\n",
    "hp.sequence, hp.one_hot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-08-10T23:02:53.562230Z",
     "start_time": "2019-08-10T23:02:50.563904Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1., 0.],\n",
       "        [0., 1.],\n",
       "        [0., 1.],\n",
       "        [0., 1.],\n",
       "        [0., 1.],\n",
       "        [1., 0.],\n",
       "        [0., 1.],\n",
       "        [0., 1.],\n",
       "        [1., 0.],\n",
       "        [0., 1.],\n",
       "        [1., 0.],\n",
       "        [1., 0.],\n",
       "        [0., 1.],\n",
       "        [0., 1.],\n",
       "        [0., 1.],\n",
       "        [0., 1.],\n",
       "        [0., 1.],\n",
       "        [0., 1.],\n",
       "        [1., 0.],\n",
       "        [0., 1.]], device='cuda:0')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = HP.random(20).one_hot().to(dev)\n",
    "t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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