GoToBedBellman.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import clear_output\n",
    "from random import randint, random\n",
    "from time import sleep"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Utilities</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_board(agent_position):\n",
    "    fields = list(range(16))\n",
    "    board = \"-----------------\\n\"\n",
    "    for i in range(0, 16, 4):\n",
    "        line = fields[i:i+4]\n",
    "        for field in line:\n",
    "            if field == agent_position:\n",
    "                board += \"| A \"\n",
    "            elif field == fields[0] or field == fields[-1]:\n",
    "                board += \"| X \"\n",
    "            else:\n",
    "                board += \"|   \"\n",
    "        board += \"|\\n\"\n",
    "        board += \"-----------------\\n\"     \n",
    "    print(board)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-----------------\n",
      "| X |   |   |   |\n",
      "-----------------\n",
      "|   |   |   |   |\n",
      "-----------------\n",
      "| A |   |   |   |\n",
      "-----------------\n",
      "|   |   |   | X |\n",
      "-----------------\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print_board(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_state_to_state_prime_verbose_map():\n",
    "    l = list(range(16))\n",
    "    state_to_state_prime = {}\n",
    "    for i in l:\n",
    "        if i == 0:\n",
    "            state_to_state_prime[i] = {'N': 0, 'E': 0, 'S': 0, 'W': 0}\n",
    "        elif i == 15:\n",
    "            state_to_state_prime[i] = {'N': 15, 'E': 15, 'S': 15, 'W': 15}\n",
    "        elif i % 4 == 0:\n",
    "            state_to_state_prime[i] = {'N': i - 4 if i - 4 in l else i, 'E': i + 1 if i + 1 in l else i, 'S': i + 4 if i + 4 in l else i, 'W': i}\n",
    "        elif i % 4 == 3:\n",
    "            state_to_state_prime[i] = {'N': i - 4 if i - 4 in l else i, 'E': i, 'S': i + 4 if i + 4 in l else i, 'W': i - 1 if i - 1 in l else i}\n",
    "        else:\n",
    "            state_to_state_prime[i] = {'N': i - 4 if i - 4 in l else i, 'E': i + 1 if i + 1 in l else i, 'S': i + 4 if i + 4 in l else i, 'W': i - 1 if i - 1 in l else i}\n",
    "\n",
    "    return state_to_state_prime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'N': 0, 'E': 0, 'S': 0, 'W': 0}\n",
      "{'N': 1, 'E': 2, 'S': 5, 'W': 0}\n",
      "{'N': 2, 'E': 3, 'S': 6, 'W': 1}\n",
      "{'N': 3, 'E': 3, 'S': 7, 'W': 2}\n",
      "{'N': 0, 'E': 5, 'S': 8, 'W': 4}\n",
      "{'N': 1, 'E': 6, 'S': 9, 'W': 4}\n",
      "{'N': 2, 'E': 7, 'S': 10, 'W': 5}\n",
      "{'N': 3, 'E': 7, 'S': 11, 'W': 6}\n",
      "{'N': 4, 'E': 9, 'S': 12, 'W': 8}\n",
      "{'N': 5, 'E': 10, 'S': 13, 'W': 8}\n",
      "{'N': 6, 'E': 11, 'S': 14, 'W': 9}\n",
      "{'N': 7, 'E': 11, 'S': 15, 'W': 10}\n",
      "{'N': 8, 'E': 13, 'S': 12, 'W': 12}\n",
      "{'N': 9, 'E': 14, 'S': 13, 'W': 12}\n",
      "{'N': 10, 'E': 15, 'S': 14, 'W': 13}\n",
      "{'N': 15, 'E': 15, 'S': 15, 'W': 15}\n"
     ]
    }
   ],
   "source": [
    "l = list(range(16))\n",
    "state_to_state_prime = {}\n",
    "for i in l:\n",
    "    if i == 0:\n",
    "        state_to_state_prime[i] = {'N': 0, 'E': 0, 'S': 0, 'W': 0}\n",
    "    elif i == 15:\n",
    "        state_to_state_prime[i] = {'N': 15, 'E': 15, 'S': 15, 'W': 15}\n",
    "    elif i % 4 == 0:\n",
    "        state_to_state_prime[i] = {'N': i - 4 if i - 4 in l else i, 'E': i + 1 if i + 1 in l else i, 'S': i + 4 if i + 4 in l else i, 'W': i}\n",
    "    elif i % 4 == 3:\n",
    "        state_to_state_prime[i] = {'N': i - 4 if i - 4 in l else i, 'E': i, 'S': i + 4 if i + 4 in l else i, 'W': i - 1 if i - 1 in l else i}\n",
    "    else:\n",
    "        state_to_state_prime[i] = {'N': i - 4 if i - 4 in l else i, 'E': i + 1 if i + 1 in l else i, 'S': i + 4 if i + 4 in l else i, 'W': i - 1 if i - 1 in l else i}\n",
    "\n",
    "for i in l:\n",
    "    print(state_to_state_prime[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_random_policy():\n",
    "    return {i: {'N': 0.0, 'E': 0.0, 'S': 0.0, 'W': 0.0} if i == 0 or i == 15 else {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25} for i in range(16)} # [N, E, S, W]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: {'N': 0.0, 'E': 0.0, 'S': 0.0, 'W': 0.0},\n",
       " 1: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 2: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 3: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 4: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 5: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 6: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 7: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 8: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 9: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 10: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 11: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 12: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 13: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 14: {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25},\n",
       " 15: {'N': 0.0, 'E': 0.0, 'S': 0.0, 'W': 0.0}}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{i: {'N': 0.0, 'E': 0.0, 'S': 0.0, 'W': 0.0} if i == 0 or i == 15 else {'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25} for i in range(16)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_probability_map():\n",
    "    states = list(range(16))\n",
    "    state_to_state_prime = create_state_to_state_prime_verbose_map()\n",
    "    \n",
    "    probability_map = {}\n",
    "    \n",
    "    for state in states:\n",
    "        for move in [\"N\", \"E\", \"S\", \"W\"]:\n",
    "            for prime in states:\n",
    "                probability_map[(prime, -1, state, move)] = 0 if prime != state_to_state_prime[state][move] else 1\n",
    "            \n",
    "    return probability_map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{(0, -1, 0, 'N'): 1,\n",
       " (1, -1, 0, 'N'): 0,\n",
       " (2, -1, 0, 'N'): 0,\n",
       " (3, -1, 0, 'N'): 0,\n",
       " (4, -1, 0, 'N'): 0,\n",
       " (5, -1, 0, 'N'): 0,\n",
       " (6, -1, 0, 'N'): 0,\n",
       " (7, -1, 0, 'N'): 0,\n",
       " (8, -1, 0, 'N'): 0,\n",
       " (9, -1, 0, 'N'): 0,\n",
       " (10, -1, 0, 'N'): 0,\n",
       " (11, -1, 0, 'N'): 0,\n",
       " (12, -1, 0, 'N'): 0,\n",
       " (13, -1, 0, 'N'): 0,\n",
       " (14, -1, 0, 'N'): 0,\n",
       " (15, -1, 0, 'N'): 0,\n",
       " (0, -1, 0, 'E'): 1,\n",
       " (1, -1, 0, 'E'): 0,\n",
       " (2, -1, 0, 'E'): 0,\n",
       " (3, -1, 0, 'E'): 0,\n",
       " (4, -1, 0, 'E'): 0,\n",
       " (5, -1, 0, 'E'): 0,\n",
       " (6, -1, 0, 'E'): 0,\n",
       " (7, -1, 0, 'E'): 0,\n",
       " (8, -1, 0, 'E'): 0,\n",
       " (9, -1, 0, 'E'): 0,\n",
       " (10, -1, 0, 'E'): 0,\n",
       " (11, -1, 0, 'E'): 0,\n",
       " (12, -1, 0, 'E'): 0,\n",
       " (13, -1, 0, 'E'): 0,\n",
       " (14, -1, 0, 'E'): 0,\n",
       " (15, -1, 0, 'E'): 0,\n",
       " (0, -1, 0, 'S'): 1,\n",
       " (1, -1, 0, 'S'): 0,\n",
       " (2, -1, 0, 'S'): 0,\n",
       " (3, -1, 0, 'S'): 0,\n",
       " (4, -1, 0, 'S'): 0,\n",
       " (5, -1, 0, 'S'): 0,\n",
       " (6, -1, 0, 'S'): 0,\n",
       " (7, -1, 0, 'S'): 0,\n",
       " (8, -1, 0, 'S'): 0,\n",
       " (9, -1, 0, 'S'): 0,\n",
       " (10, -1, 0, 'S'): 0,\n",
       " (11, -1, 0, 'S'): 0,\n",
       " (12, -1, 0, 'S'): 0,\n",
       " (13, -1, 0, 'S'): 0,\n",
       " (14, -1, 0, 'S'): 0,\n",
       " (15, -1, 0, 'S'): 0,\n",
       " (0, -1, 0, 'W'): 1,\n",
       " (1, -1, 0, 'W'): 0,\n",
       " (2, -1, 0, 'W'): 0,\n",
       " (3, -1, 0, 'W'): 0,\n",
       " (4, -1, 0, 'W'): 0,\n",
       " (5, -1, 0, 'W'): 0,\n",
       " (6, -1, 0, 'W'): 0,\n",
       " (7, -1, 0, 'W'): 0,\n",
       " (8, -1, 0, 'W'): 0,\n",
       " (9, -1, 0, 'W'): 0,\n",
       " (10, -1, 0, 'W'): 0,\n",
       " (11, -1, 0, 'W'): 0,\n",
       " (12, -1, 0, 'W'): 0,\n",
       " (13, -1, 0, 'W'): 0,\n",
       " (14, -1, 0, 'W'): 0,\n",
       " (15, -1, 0, 'W'): 0,\n",
       " (0, -1, 1, 'N'): 0,\n",
       " (1, -1, 1, 'N'): 1,\n",
       " (2, -1, 1, 'N'): 0,\n",
       " (3, -1, 1, 'N'): 0,\n",
       " (4, -1, 1, 'N'): 0,\n",
       " (5, -1, 1, 'N'): 0,\n",
       " (6, -1, 1, 'N'): 0,\n",
       " (7, -1, 1, 'N'): 0,\n",
       " (8, -1, 1, 'N'): 0,\n",
       " (9, -1, 1, 'N'): 0,\n",
       " (10, -1, 1, 'N'): 0,\n",
       " (11, -1, 1, 'N'): 0,\n",
       " (12, -1, 1, 'N'): 0,\n",
       " (13, -1, 1, 'N'): 0,\n",
       " (14, -1, 1, 'N'): 0,\n",
       " (15, -1, 1, 'N'): 0,\n",
       " (0, -1, 1, 'E'): 0,\n",
       " (1, -1, 1, 'E'): 0,\n",
       " (2, -1, 1, 'E'): 1,\n",
       " (3, -1, 1, 'E'): 0,\n",
       " (4, -1, 1, 'E'): 0,\n",
       " (5, -1, 1, 'E'): 0,\n",
       " (6, -1, 1, 'E'): 0,\n",
       " (7, -1, 1, 'E'): 0,\n",
       " (8, -1, 1, 'E'): 0,\n",
       " (9, -1, 1, 'E'): 0,\n",
       " (10, -1, 1, 'E'): 0,\n",
       " (11, -1, 1, 'E'): 0,\n",
       " (12, -1, 1, 'E'): 0,\n",
       " (13, -1, 1, 'E'): 0,\n",
       " (14, -1, 1, 'E'): 0,\n",
       " (15, -1, 1, 'E'): 0,\n",
       " (0, -1, 1, 'S'): 0,\n",
       " (1, -1, 1, 'S'): 0,\n",
       " (2, -1, 1, 'S'): 0,\n",
       " (3, -1, 1, 'S'): 0,\n",
       " (4, -1, 1, 'S'): 0,\n",
       " (5, -1, 1, 'S'): 1,\n",
       " (6, -1, 1, 'S'): 0,\n",
       " (7, -1, 1, 'S'): 0,\n",
       " (8, -1, 1, 'S'): 0,\n",
       " (9, -1, 1, 'S'): 0,\n",
       " (10, -1, 1, 'S'): 0,\n",
       " (11, -1, 1, 'S'): 0,\n",
       " (12, -1, 1, 'S'): 0,\n",
       " (13, -1, 1, 'S'): 0,\n",
       " (14, -1, 1, 'S'): 0,\n",
       " (15, -1, 1, 'S'): 0,\n",
       " (0, -1, 1, 'W'): 1,\n",
       " (1, -1, 1, 'W'): 0,\n",
       " (2, -1, 1, 'W'): 0,\n",
       " (3, -1, 1, 'W'): 0,\n",
       " (4, -1, 1, 'W'): 0,\n",
       " (5, -1, 1, 'W'): 0,\n",
       " (6, -1, 1, 'W'): 0,\n",
       " (7, -1, 1, 'W'): 0,\n",
       " (8, -1, 1, 'W'): 0,\n",
       " (9, -1, 1, 'W'): 0,\n",
       " (10, -1, 1, 'W'): 0,\n",
       " (11, -1, 1, 'W'): 0,\n",
       " (12, -1, 1, 'W'): 0,\n",
       " (13, -1, 1, 'W'): 0,\n",
       " (14, -1, 1, 'W'): 0,\n",
       " (15, -1, 1, 'W'): 0,\n",
       " (0, -1, 2, 'N'): 0,\n",
       " (1, -1, 2, 'N'): 0,\n",
       " (2, -1, 2, 'N'): 1,\n",
       " (3, -1, 2, 'N'): 0,\n",
       " (4, -1, 2, 'N'): 0,\n",
       " (5, -1, 2, 'N'): 0,\n",
       " (6, -1, 2, 'N'): 0,\n",
       " (7, -1, 2, 'N'): 0,\n",
       " (8, -1, 2, 'N'): 0,\n",
       " (9, -1, 2, 'N'): 0,\n",
       " (10, -1, 2, 'N'): 0,\n",
       " (11, -1, 2, 'N'): 0,\n",
       " (12, -1, 2, 'N'): 0,\n",
       " (13, -1, 2, 'N'): 0,\n",
       " (14, -1, 2, 'N'): 0,\n",
       " (15, -1, 2, 'N'): 0,\n",
       " (0, -1, 2, 'E'): 0,\n",
       " (1, -1, 2, 'E'): 0,\n",
       " (2, -1, 2, 'E'): 0,\n",
       " (3, -1, 2, 'E'): 1,\n",
       " (4, -1, 2, 'E'): 0,\n",
       " (5, -1, 2, 'E'): 0,\n",
       " (6, -1, 2, 'E'): 0,\n",
       " (7, -1, 2, 'E'): 0,\n",
       " (8, -1, 2, 'E'): 0,\n",
       " (9, -1, 2, 'E'): 0,\n",
       " (10, -1, 2, 'E'): 0,\n",
       " (11, -1, 2, 'E'): 0,\n",
       " (12, -1, 2, 'E'): 0,\n",
       " (13, -1, 2, 'E'): 0,\n",
       " (14, -1, 2, 'E'): 0,\n",
       " (15, -1, 2, 'E'): 0,\n",
       " (0, -1, 2, 'S'): 0,\n",
       " (1, -1, 2, 'S'): 0,\n",
       " (2, -1, 2, 'S'): 0,\n",
       " (3, -1, 2, 'S'): 0,\n",
       " (4, -1, 2, 'S'): 0,\n",
       " (5, -1, 2, 'S'): 0,\n",
       " (6, -1, 2, 'S'): 1,\n",
       " (7, -1, 2, 'S'): 0,\n",
       " (8, -1, 2, 'S'): 0,\n",
       " (9, -1, 2, 'S'): 0,\n",
       " (10, -1, 2, 'S'): 0,\n",
       " (11, -1, 2, 'S'): 0,\n",
       " (12, -1, 2, 'S'): 0,\n",
       " (13, -1, 2, 'S'): 0,\n",
       " (14, -1, 2, 'S'): 0,\n",
       " (15, -1, 2, 'S'): 0,\n",
       " (0, -1, 2, 'W'): 0,\n",
       " (1, -1, 2, 'W'): 1,\n",
       " (2, -1, 2, 'W'): 0,\n",
       " (3, -1, 2, 'W'): 0,\n",
       " (4, -1, 2, 'W'): 0,\n",
       " (5, -1, 2, 'W'): 0,\n",
       " (6, -1, 2, 'W'): 0,\n",
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       " (11, -1, 2, 'W'): 0,\n",
       " (12, -1, 2, 'W'): 0,\n",
       " (13, -1, 2, 'W'): 0,\n",
       " (14, -1, 2, 'W'): 0,\n",
       " (15, -1, 2, 'W'): 0,\n",
       " (0, -1, 3, 'N'): 0,\n",
       " (1, -1, 3, 'N'): 0,\n",
       " (2, -1, 3, 'N'): 0,\n",
       " (3, -1, 3, 'N'): 1,\n",
       " (4, -1, 3, 'N'): 0,\n",
       " (5, -1, 3, 'N'): 0,\n",
       " (6, -1, 3, 'N'): 0,\n",
       " (7, -1, 3, 'N'): 0,\n",
       " (8, -1, 3, 'N'): 0,\n",
       " (9, -1, 3, 'N'): 0,\n",
       " (10, -1, 3, 'N'): 0,\n",
       " (11, -1, 3, 'N'): 0,\n",
       " (12, -1, 3, 'N'): 0,\n",
       " (13, -1, 3, 'N'): 0,\n",
       " (14, -1, 3, 'N'): 0,\n",
       " (15, -1, 3, 'N'): 0,\n",
       " (0, -1, 3, 'E'): 0,\n",
       " (1, -1, 3, 'E'): 0,\n",
       " (2, -1, 3, 'E'): 0,\n",
       " (3, -1, 3, 'E'): 1,\n",
       " (4, -1, 3, 'E'): 0,\n",
       " (5, -1, 3, 'E'): 0,\n",
       " (6, -1, 3, 'E'): 0,\n",
       " (7, -1, 3, 'E'): 0,\n",
       " (8, -1, 3, 'E'): 0,\n",
       " (9, -1, 3, 'E'): 0,\n",
       " (10, -1, 3, 'E'): 0,\n",
       " (11, -1, 3, 'E'): 0,\n",
       " (12, -1, 3, 'E'): 0,\n",
       " (13, -1, 3, 'E'): 0,\n",
       " (14, -1, 3, 'E'): 0,\n",
       " (15, -1, 3, 'E'): 0,\n",
       " (0, -1, 3, 'S'): 0,\n",
       " (1, -1, 3, 'S'): 0,\n",
       " (2, -1, 3, 'S'): 0,\n",
       " (3, -1, 3, 'S'): 0,\n",
       " (4, -1, 3, 'S'): 0,\n",
       " (5, -1, 3, 'S'): 0,\n",
       " (6, -1, 3, 'S'): 0,\n",
       " (7, -1, 3, 'S'): 1,\n",
       " (8, -1, 3, 'S'): 0,\n",
       " (9, -1, 3, 'S'): 0,\n",
       " (10, -1, 3, 'S'): 0,\n",
       " (11, -1, 3, 'S'): 0,\n",
       " (12, -1, 3, 'S'): 0,\n",
       " (13, -1, 3, 'S'): 0,\n",
       " (14, -1, 3, 'S'): 0,\n",
       " (15, -1, 3, 'S'): 0,\n",
       " (0, -1, 3, 'W'): 0,\n",
       " (1, -1, 3, 'W'): 0,\n",
       " (2, -1, 3, 'W'): 1,\n",
       " (3, -1, 3, 'W'): 0,\n",
       " (4, -1, 3, 'W'): 0,\n",
       " (5, -1, 3, 'W'): 0,\n",
       " (6, -1, 3, 'W'): 0,\n",
       " (7, -1, 3, 'W'): 0,\n",
       " (8, -1, 3, 'W'): 0,\n",
       " (9, -1, 3, 'W'): 0,\n",
       " (10, -1, 3, 'W'): 0,\n",
       " (11, -1, 3, 'W'): 0,\n",
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       " (9, -1, 10, 'S'): 0,\n",
       " (10, -1, 10, 'S'): 0,\n",
       " (11, -1, 10, 'S'): 0,\n",
       " (12, -1, 10, 'S'): 0,\n",
       " (13, -1, 10, 'S'): 0,\n",
       " (14, -1, 10, 'S'): 1,\n",
       " (15, -1, 10, 'S'): 0,\n",
       " (0, -1, 10, 'W'): 0,\n",
       " (1, -1, 10, 'W'): 0,\n",
       " (2, -1, 10, 'W'): 0,\n",
       " (3, -1, 10, 'W'): 0,\n",
       " (4, -1, 10, 'W'): 0,\n",
       " (5, -1, 10, 'W'): 0,\n",
       " (6, -1, 10, 'W'): 0,\n",
       " (7, -1, 10, 'W'): 0,\n",
       " (8, -1, 10, 'W'): 0,\n",
       " (9, -1, 10, 'W'): 1,\n",
       " (10, -1, 10, 'W'): 0,\n",
       " (11, -1, 10, 'W'): 0,\n",
       " (12, -1, 10, 'W'): 0,\n",
       " (13, -1, 10, 'W'): 0,\n",
       " (14, -1, 10, 'W'): 0,\n",
       " (15, -1, 10, 'W'): 0,\n",
       " (0, -1, 11, 'N'): 0,\n",
       " (1, -1, 11, 'N'): 0,\n",
       " (2, -1, 11, 'N'): 0,\n",
       " (3, -1, 11, 'N'): 0,\n",
       " (4, -1, 11, 'N'): 0,\n",
       " (5, -1, 11, 'N'): 0,\n",
       " (6, -1, 11, 'N'): 0,\n",
       " (7, -1, 11, 'N'): 1,\n",
       " (8, -1, 11, 'N'): 0,\n",
       " (9, -1, 11, 'N'): 0,\n",
       " (10, -1, 11, 'N'): 0,\n",
       " (11, -1, 11, 'N'): 0,\n",
       " (12, -1, 11, 'N'): 0,\n",
       " (13, -1, 11, 'N'): 0,\n",
       " (14, -1, 11, 'N'): 0,\n",
       " (15, -1, 11, 'N'): 0,\n",
       " (0, -1, 11, 'E'): 0,\n",
       " (1, -1, 11, 'E'): 0,\n",
       " (2, -1, 11, 'E'): 0,\n",
       " (3, -1, 11, 'E'): 0,\n",
       " (4, -1, 11, 'E'): 0,\n",
       " (5, -1, 11, 'E'): 0,\n",
       " (6, -1, 11, 'E'): 0,\n",
       " (7, -1, 11, 'E'): 0,\n",
       " (8, -1, 11, 'E'): 0,\n",
       " (9, -1, 11, 'E'): 0,\n",
       " (10, -1, 11, 'E'): 0,\n",
       " (11, -1, 11, 'E'): 1,\n",
       " (12, -1, 11, 'E'): 0,\n",
       " (13, -1, 11, 'E'): 0,\n",
       " (14, -1, 11, 'E'): 0,\n",
       " (15, -1, 11, 'E'): 0,\n",
       " (0, -1, 11, 'S'): 0,\n",
       " (1, -1, 11, 'S'): 0,\n",
       " (2, -1, 11, 'S'): 0,\n",
       " (3, -1, 11, 'S'): 0,\n",
       " (4, -1, 11, 'S'): 0,\n",
       " (5, -1, 11, 'S'): 0,\n",
       " (6, -1, 11, 'S'): 0,\n",
       " (7, -1, 11, 'S'): 0,\n",
       " (8, -1, 11, 'S'): 0,\n",
       " (9, -1, 11, 'S'): 0,\n",
       " (10, -1, 11, 'S'): 0,\n",
       " (11, -1, 11, 'S'): 0,\n",
       " (12, -1, 11, 'S'): 0,\n",
       " (13, -1, 11, 'S'): 0,\n",
       " (14, -1, 11, 'S'): 0,\n",
       " (15, -1, 11, 'S'): 1,\n",
       " (0, -1, 11, 'W'): 0,\n",
       " (1, -1, 11, 'W'): 0,\n",
       " (2, -1, 11, 'W'): 0,\n",
       " (3, -1, 11, 'W'): 0,\n",
       " (4, -1, 11, 'W'): 0,\n",
       " (5, -1, 11, 'W'): 0,\n",
       " (6, -1, 11, 'W'): 0,\n",
       " (7, -1, 11, 'W'): 0,\n",
       " (8, -1, 11, 'W'): 0,\n",
       " (9, -1, 11, 'W'): 0,\n",
       " (10, -1, 11, 'W'): 1,\n",
       " (11, -1, 11, 'W'): 0,\n",
       " (12, -1, 11, 'W'): 0,\n",
       " (13, -1, 11, 'W'): 0,\n",
       " (14, -1, 11, 'W'): 0,\n",
       " (15, -1, 11, 'W'): 0,\n",
       " (0, -1, 12, 'N'): 0,\n",
       " (1, -1, 12, 'N'): 0,\n",
       " (2, -1, 12, 'N'): 0,\n",
       " (3, -1, 12, 'N'): 0,\n",
       " (4, -1, 12, 'N'): 0,\n",
       " (5, -1, 12, 'N'): 0,\n",
       " (6, -1, 12, 'N'): 0,\n",
       " (7, -1, 12, 'N'): 0,\n",
       " (8, -1, 12, 'N'): 1,\n",
       " (9, -1, 12, 'N'): 0,\n",
       " (10, -1, 12, 'N'): 0,\n",
       " (11, -1, 12, 'N'): 0,\n",
       " (12, -1, 12, 'N'): 0,\n",
       " (13, -1, 12, 'N'): 0,\n",
       " (14, -1, 12, 'N'): 0,\n",
       " (15, -1, 12, 'N'): 0,\n",
       " (0, -1, 12, 'E'): 0,\n",
       " (1, -1, 12, 'E'): 0,\n",
       " (2, -1, 12, 'E'): 0,\n",
       " (3, -1, 12, 'E'): 0,\n",
       " (4, -1, 12, 'E'): 0,\n",
       " (5, -1, 12, 'E'): 0,\n",
       " (6, -1, 12, 'E'): 0,\n",
       " (7, -1, 12, 'E'): 0,\n",
       " (8, -1, 12, 'E'): 0,\n",
       " (9, -1, 12, 'E'): 0,\n",
       " (10, -1, 12, 'E'): 0,\n",
       " (11, -1, 12, 'E'): 0,\n",
       " (12, -1, 12, 'E'): 0,\n",
       " (13, -1, 12, 'E'): 1,\n",
       " (14, -1, 12, 'E'): 0,\n",
       " (15, -1, 12, 'E'): 0,\n",
       " (0, -1, 12, 'S'): 0,\n",
       " (1, -1, 12, 'S'): 0,\n",
       " (2, -1, 12, 'S'): 0,\n",
       " (3, -1, 12, 'S'): 0,\n",
       " (4, -1, 12, 'S'): 0,\n",
       " (5, -1, 12, 'S'): 0,\n",
       " (6, -1, 12, 'S'): 0,\n",
       " (7, -1, 12, 'S'): 0,\n",
       " (8, -1, 12, 'S'): 0,\n",
       " (9, -1, 12, 'S'): 0,\n",
       " (10, -1, 12, 'S'): 0,\n",
       " (11, -1, 12, 'S'): 0,\n",
       " (12, -1, 12, 'S'): 1,\n",
       " (13, -1, 12, 'S'): 0,\n",
       " (14, -1, 12, 'S'): 0,\n",
       " (15, -1, 12, 'S'): 0,\n",
       " (0, -1, 12, 'W'): 0,\n",
       " (1, -1, 12, 'W'): 0,\n",
       " (2, -1, 12, 'W'): 0,\n",
       " (3, -1, 12, 'W'): 0,\n",
       " (4, -1, 12, 'W'): 0,\n",
       " (5, -1, 12, 'W'): 0,\n",
       " (6, -1, 12, 'W'): 0,\n",
       " (7, -1, 12, 'W'): 0,\n",
       " (8, -1, 12, 'W'): 0,\n",
       " (9, -1, 12, 'W'): 0,\n",
       " (10, -1, 12, 'W'): 0,\n",
       " (11, -1, 12, 'W'): 0,\n",
       " (12, -1, 12, 'W'): 1,\n",
       " (13, -1, 12, 'W'): 0,\n",
       " (14, -1, 12, 'W'): 0,\n",
       " (15, -1, 12, 'W'): 0,\n",
       " (0, -1, 13, 'N'): 0,\n",
       " (1, -1, 13, 'N'): 0,\n",
       " (2, -1, 13, 'N'): 0,\n",
       " (3, -1, 13, 'N'): 0,\n",
       " (4, -1, 13, 'N'): 0,\n",
       " (5, -1, 13, 'N'): 0,\n",
       " (6, -1, 13, 'N'): 0,\n",
       " (7, -1, 13, 'N'): 0,\n",
       " (8, -1, 13, 'N'): 0,\n",
       " (9, -1, 13, 'N'): 1,\n",
       " (10, -1, 13, 'N'): 0,\n",
       " (11, -1, 13, 'N'): 0,\n",
       " (12, -1, 13, 'N'): 0,\n",
       " (13, -1, 13, 'N'): 0,\n",
       " (14, -1, 13, 'N'): 0,\n",
       " (15, -1, 13, 'N'): 0,\n",
       " (0, -1, 13, 'E'): 0,\n",
       " (1, -1, 13, 'E'): 0,\n",
       " (2, -1, 13, 'E'): 0,\n",
       " (3, -1, 13, 'E'): 0,\n",
       " (4, -1, 13, 'E'): 0,\n",
       " (5, -1, 13, 'E'): 0,\n",
       " (6, -1, 13, 'E'): 0,\n",
       " (7, -1, 13, 'E'): 0,\n",
       " (8, -1, 13, 'E'): 0,\n",
       " (9, -1, 13, 'E'): 0,\n",
       " (10, -1, 13, 'E'): 0,\n",
       " (11, -1, 13, 'E'): 0,\n",
       " (12, -1, 13, 'E'): 0,\n",
       " (13, -1, 13, 'E'): 0,\n",
       " (14, -1, 13, 'E'): 1,\n",
       " (15, -1, 13, 'E'): 0,\n",
       " (0, -1, 13, 'S'): 0,\n",
       " (1, -1, 13, 'S'): 0,\n",
       " (2, -1, 13, 'S'): 0,\n",
       " (3, -1, 13, 'S'): 0,\n",
       " (4, -1, 13, 'S'): 0,\n",
       " (5, -1, 13, 'S'): 0,\n",
       " (6, -1, 13, 'S'): 0,\n",
       " (7, -1, 13, 'S'): 0,\n",
       " (8, -1, 13, 'S'): 0,\n",
       " (9, -1, 13, 'S'): 0,\n",
       " (10, -1, 13, 'S'): 0,\n",
       " (11, -1, 13, 'S'): 0,\n",
       " (12, -1, 13, 'S'): 0,\n",
       " (13, -1, 13, 'S'): 1,\n",
       " (14, -1, 13, 'S'): 0,\n",
       " (15, -1, 13, 'S'): 0,\n",
       " (0, -1, 13, 'W'): 0,\n",
       " (1, -1, 13, 'W'): 0,\n",
       " (2, -1, 13, 'W'): 0,\n",
       " (3, -1, 13, 'W'): 0,\n",
       " (4, -1, 13, 'W'): 0,\n",
       " (5, -1, 13, 'W'): 0,\n",
       " (6, -1, 13, 'W'): 0,\n",
       " (7, -1, 13, 'W'): 0,\n",
       " (8, -1, 13, 'W'): 0,\n",
       " (9, -1, 13, 'W'): 0,\n",
       " (10, -1, 13, 'W'): 0,\n",
       " (11, -1, 13, 'W'): 0,\n",
       " (12, -1, 13, 'W'): 1,\n",
       " (13, -1, 13, 'W'): 0,\n",
       " (14, -1, 13, 'W'): 0,\n",
       " (15, -1, 13, 'W'): 0,\n",
       " (0, -1, 14, 'N'): 0,\n",
       " (1, -1, 14, 'N'): 0,\n",
       " (2, -1, 14, 'N'): 0,\n",
       " (3, -1, 14, 'N'): 0,\n",
       " (4, -1, 14, 'N'): 0,\n",
       " (5, -1, 14, 'N'): 0,\n",
       " (6, -1, 14, 'N'): 0,\n",
       " (7, -1, 14, 'N'): 0,\n",
       " (8, -1, 14, 'N'): 0,\n",
       " (9, -1, 14, 'N'): 0,\n",
       " (10, -1, 14, 'N'): 1,\n",
       " (11, -1, 14, 'N'): 0,\n",
       " (12, -1, 14, 'N'): 0,\n",
       " (13, -1, 14, 'N'): 0,\n",
       " (14, -1, 14, 'N'): 0,\n",
       " (15, -1, 14, 'N'): 0,\n",
       " (0, -1, 14, 'E'): 0,\n",
       " (1, -1, 14, 'E'): 0,\n",
       " (2, -1, 14, 'E'): 0,\n",
       " (3, -1, 14, 'E'): 0,\n",
       " (4, -1, 14, 'E'): 0,\n",
       " (5, -1, 14, 'E'): 0,\n",
       " (6, -1, 14, 'E'): 0,\n",
       " (7, -1, 14, 'E'): 0,\n",
       " (8, -1, 14, 'E'): 0,\n",
       " (9, -1, 14, 'E'): 0,\n",
       " (10, -1, 14, 'E'): 0,\n",
       " (11, -1, 14, 'E'): 0,\n",
       " (12, -1, 14, 'E'): 0,\n",
       " (13, -1, 14, 'E'): 0,\n",
       " (14, -1, 14, 'E'): 0,\n",
       " (15, -1, 14, 'E'): 1,\n",
       " (0, -1, 14, 'S'): 0,\n",
       " (1, -1, 14, 'S'): 0,\n",
       " (2, -1, 14, 'S'): 0,\n",
       " (3, -1, 14, 'S'): 0,\n",
       " (4, -1, 14, 'S'): 0,\n",
       " (5, -1, 14, 'S'): 0,\n",
       " (6, -1, 14, 'S'): 0,\n",
       " (7, -1, 14, 'S'): 0,\n",
       " (8, -1, 14, 'S'): 0,\n",
       " (9, -1, 14, 'S'): 0,\n",
       " (10, -1, 14, 'S'): 0,\n",
       " (11, -1, 14, 'S'): 0,\n",
       " (12, -1, 14, 'S'): 0,\n",
       " (13, -1, 14, 'S'): 0,\n",
       " (14, -1, 14, 'S'): 1,\n",
       " (15, -1, 14, 'S'): 0,\n",
       " (0, -1, 14, 'W'): 0,\n",
       " (1, -1, 14, 'W'): 0,\n",
       " (2, -1, 14, 'W'): 0,\n",
       " (3, -1, 14, 'W'): 0,\n",
       " (4, -1, 14, 'W'): 0,\n",
       " (5, -1, 14, 'W'): 0,\n",
       " (6, -1, 14, 'W'): 0,\n",
       " (7, -1, 14, 'W'): 0,\n",
       " (8, -1, 14, 'W'): 0,\n",
       " (9, -1, 14, 'W'): 0,\n",
       " (10, -1, 14, 'W'): 0,\n",
       " (11, -1, 14, 'W'): 0,\n",
       " (12, -1, 14, 'W'): 0,\n",
       " (13, -1, 14, 'W'): 1,\n",
       " (14, -1, 14, 'W'): 0,\n",
       " (15, -1, 14, 'W'): 0,\n",
       " (0, -1, 15, 'N'): 0,\n",
       " (1, -1, 15, 'N'): 0,\n",
       " (2, -1, 15, 'N'): 0,\n",
       " (3, -1, 15, 'N'): 0,\n",
       " (4, -1, 15, 'N'): 0,\n",
       " (5, -1, 15, 'N'): 0,\n",
       " (6, -1, 15, 'N'): 0,\n",
       " (7, -1, 15, 'N'): 0,\n",
       " (8, -1, 15, 'N'): 0,\n",
       " (9, -1, 15, 'N'): 0,\n",
       " (10, -1, 15, 'N'): 0,\n",
       " (11, -1, 15, 'N'): 0,\n",
       " (12, -1, 15, 'N'): 0,\n",
       " (13, -1, 15, 'N'): 0,\n",
       " (14, -1, 15, 'N'): 0,\n",
       " (15, -1, 15, 'N'): 1,\n",
       " (0, -1, 15, 'E'): 0,\n",
       " (1, -1, 15, 'E'): 0,\n",
       " (2, -1, 15, 'E'): 0,\n",
       " (3, -1, 15, 'E'): 0,\n",
       " (4, -1, 15, 'E'): 0,\n",
       " (5, -1, 15, 'E'): 0,\n",
       " (6, -1, 15, 'E'): 0,\n",
       " (7, -1, 15, 'E'): 0,\n",
       " (8, -1, 15, 'E'): 0,\n",
       " (9, -1, 15, 'E'): 0,\n",
       " (10, -1, 15, 'E'): 0,\n",
       " (11, -1, 15, 'E'): 0,\n",
       " (12, -1, 15, 'E'): 0,\n",
       " (13, -1, 15, 'E'): 0,\n",
       " (14, -1, 15, 'E'): 0,\n",
       " (15, -1, 15, 'E'): 1,\n",
       " (0, -1, 15, 'S'): 0,\n",
       " (1, -1, 15, 'S'): 0,\n",
       " (2, -1, 15, 'S'): 0,\n",
       " (3, -1, 15, 'S'): 0,\n",
       " (4, -1, 15, 'S'): 0,\n",
       " (5, -1, 15, 'S'): 0,\n",
       " (6, -1, 15, 'S'): 0,\n",
       " (7, -1, 15, 'S'): 0,\n",
       " ...}"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "create_probability_map()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'N': 15, 'E': 15, 'S': 15, 'W': 15}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{(0, -1, 15, 'W'): 0}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "states = list(range(16))\n",
    "state_to_state_prime = create_state_to_state_prime_verbose_map()\n",
    "\n",
    "probability_map = {}\n",
    "state = 15\n",
    "print(state_to_state_prime[state])\n",
    "move = \"W\"\n",
    "prime = 0\n",
    "probability_map[(prime, -1, state, move)] = 0\n",
    "probability_map[(prime, -1, state, move)]\n",
    "probability_map"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " key (0, -1, 0, 'N'), prob 1\n",
      " key (0, -1, 0, 'E'), prob 1\n",
      " key (0, -1, 0, 'S'), prob 1\n",
      " key (0, -1, 0, 'W'), prob 1\n",
      " key (1, -1, 1, 'N'), prob 1\n",
      " key (2, -1, 1, 'E'), prob 1\n",
      " key (5, -1, 1, 'S'), prob 1\n",
      " key (0, -1, 1, 'W'), prob 1\n",
      " key (2, -1, 2, 'N'), prob 1\n",
      " key (3, -1, 2, 'E'), prob 1\n",
      " key (6, -1, 2, 'S'), prob 1\n",
      " key (1, -1, 2, 'W'), prob 1\n",
      " key (3, -1, 3, 'N'), prob 1\n",
      " key (3, -1, 3, 'E'), prob 1\n",
      " key (7, -1, 3, 'S'), prob 1\n",
      " key (2, -1, 3, 'W'), prob 1\n",
      " key (0, -1, 4, 'N'), prob 1\n",
      " key (5, -1, 4, 'E'), prob 1\n",
      " key (8, -1, 4, 'S'), prob 1\n",
      " key (4, -1, 4, 'W'), prob 1\n",
      " key (1, -1, 5, 'N'), prob 1\n",
      " key (6, -1, 5, 'E'), prob 1\n",
      " key (9, -1, 5, 'S'), prob 1\n",
      " key (4, -1, 5, 'W'), prob 1\n",
      " key (2, -1, 6, 'N'), prob 1\n",
      " key (7, -1, 6, 'E'), prob 1\n",
      " key (10, -1, 6, 'S'), prob 1\n",
      " key (5, -1, 6, 'W'), prob 1\n",
      " key (3, -1, 7, 'N'), prob 1\n",
      " key (7, -1, 7, 'E'), prob 1\n",
      " key (11, -1, 7, 'S'), prob 1\n",
      " key (6, -1, 7, 'W'), prob 1\n",
      " key (4, -1, 8, 'N'), prob 1\n",
      " key (9, -1, 8, 'E'), prob 1\n",
      " key (12, -1, 8, 'S'), prob 1\n",
      " key (8, -1, 8, 'W'), prob 1\n",
      " key (5, -1, 9, 'N'), prob 1\n",
      " key (10, -1, 9, 'E'), prob 1\n",
      " key (13, -1, 9, 'S'), prob 1\n",
      " key (8, -1, 9, 'W'), prob 1\n",
      " key (6, -1, 10, 'N'), prob 1\n",
      " key (11, -1, 10, 'E'), prob 1\n",
      " key (14, -1, 10, 'S'), prob 1\n",
      " key (9, -1, 10, 'W'), prob 1\n",
      " key (7, -1, 11, 'N'), prob 1\n",
      " key (11, -1, 11, 'E'), prob 1\n",
      " key (15, -1, 11, 'S'), prob 1\n",
      " key (10, -1, 11, 'W'), prob 1\n",
      " key (8, -1, 12, 'N'), prob 1\n",
      " key (13, -1, 12, 'E'), prob 1\n",
      " key (12, -1, 12, 'S'), prob 1\n",
      " key (12, -1, 12, 'W'), prob 1\n",
      " key (9, -1, 13, 'N'), prob 1\n",
      " key (14, -1, 13, 'E'), prob 1\n",
      " key (13, -1, 13, 'S'), prob 1\n",
      " key (12, -1, 13, 'W'), prob 1\n",
      " key (10, -1, 14, 'N'), prob 1\n",
      " key (15, -1, 14, 'E'), prob 1\n",
      " key (14, -1, 14, 'S'), prob 1\n",
      " key (13, -1, 14, 'W'), prob 1\n",
      " key (15, -1, 15, 'N'), prob 1\n",
      " key (15, -1, 15, 'E'), prob 1\n",
      " key (15, -1, 15, 'S'), prob 1\n",
      " key (15, -1, 15, 'W'), prob 1\n"
     ]
    }
   ],
   "source": [
    "states = list(range(16))\n",
    "state_to_state_prime = create_state_to_state_prime_verbose_map()\n",
    "\n",
    "probability_map = {}\n",
    "\n",
    "for state in states:\n",
    "    for move in [\"N\", \"E\", \"S\", \"W\"]:\n",
    "        for prime in states:\n",
    "            probability_map[(prime, -1, state, move)] = 0 if prime != state_to_state_prime[state][move] else 1\n",
    "            if (probability_map[(prime, -1, state, move)] == 1):\n",
    "                print(\" key {}, prob {}\".format((prime, -1, state, move), probability_map[(prime, -1, state, move)]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Agent</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def agent(policy, starting_position=None, verbose=False):\n",
    "    l = list(range(16))\n",
    "    state_to_state_prime = create_state_to_state_prime_verbose_map()\n",
    "    agent_position = randint(1, 14) if starting_position is None else starting_position\n",
    "        \n",
    "    step_number = 1\n",
    "    action_taken = None\n",
    "    \n",
    "    if verbose:\n",
    "        print(\"Move: {} Position: {} Action: {}\".format(step_number, agent_position, action_taken))\n",
    "        print_board(agent_position)\n",
    "        print(\"\\n\")\n",
    "        sleep(2)\n",
    "    \n",
    "    while not (agent_position == 0 or agent_position == 15):\n",
    "        if verbose:\n",
    "            clear_output(wait=True)\n",
    "            print(\"Move: {} Position: {} Action: {}\".format(step_number, agent_position, action_taken))\n",
    "            print_board(agent_position)\n",
    "            print(\"\\n\")\n",
    "            sleep(1)\n",
    "        \n",
    "        current_policy = policy[agent_position]\n",
    "        next_move = random()\n",
    "        lower_bound = 0\n",
    "        print(\"-\")\n",
    "        print(current_policy)\n",
    "        for action, chance in current_policy.items():\n",
    "            if chance == 0:\n",
    "                continue\n",
    "            if lower_bound <= next_move < lower_bound + chance:\n",
    "                agent_position = state_to_state_prime[agent_position][action]\n",
    "                action_taken = action\n",
    "                break \n",
    "            lower_bound = lower_bound + chance\n",
    "                \n",
    "        step_number += 1   \n",
    "                \n",
    "    if verbose:\n",
    "        clear_output(wait=True)\n",
    "        print(\"Move: {} Position: {} Action: {}\".format(step_number, agent_position, action_taken))\n",
    "        print_board(agent_position)\n",
    "        print(\"Win!\")\n",
    "    \n",
    "    return step_number"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Random Policy test</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100.0%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.25, 'E': 0.25, 'S': 0.25, 'W': 0.25}\n",
      "Average steps to finish: 18.778\n"
     ]
    }
   ],
   "source": [
    "data = []\n",
    "\n",
    "for i in range(1000):\n",
    "    clear_output(wait=True)\n",
    "    print(\"{}%\\n\".format((i + 1) / 10))\n",
    "    data.append(agent(create_random_policy()))\n",
    "    \n",
    "print(\"Average steps to finish: {}\".format(sum(data)/len(data)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Move: 9 Position: 0 Action: N\n",
      "-----------------\n",
      "| A |   |   |   |\n",
      "-----------------\n",
      "|   |   |   |   |\n",
      "-----------------\n",
      "|   |   |   |   |\n",
      "-----------------\n",
      "|   |   |   | X |\n",
      "-----------------\n",
      "\n",
      "Win!\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "agent(create_random_policy(), verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Create greedy policy based on V(s)</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_greedy_policy(V_s):\n",
    "    s_to_sprime = create_state_to_state_prime_verbose_map()\n",
    "    print(s_to_sprime)\n",
    "    policy = {}\n",
    "        \n",
    "    for state in range(16):\n",
    "        \n",
    "        state_values = {a: V_s[s_to_sprime[state][a]] for a in ['N', 'S', 'E', 'W']}\n",
    "        \n",
    "        if state == 0 or state == 15:\n",
    "            policy[state] = {'N': 0.0, 'E': 0.0, 'S': 0.0, 'W': 0.0}\n",
    "        else:\n",
    "            max_actions = [k for k, v in state_values.items() if v == max(state_values.values())]\n",
    "            policy[state] = {a: 1 / len(max_actions) if a in max_actions else 0.0 for a in ['N', 'S', 'E', 'W']}\n",
    "    return policy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Iterative policy evaluation</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def iterative_policy_evaluation(policy, theta=0.01, discount_rate=0.5):\n",
    "    V_s = {i: 0 for i in range(16)} # 1.\n",
    "    probablitiy_map = create_probability_map() # 2.\n",
    "\n",
    "    delta = 100 # 3.\n",
    "    while not delta < theta: # 4.\n",
    "        delta = 0 # 5.\n",
    "        for state in range(16): # 6.\n",
    "            v = V_s[state] # 7.\n",
    "            \n",
    "            total = 0 # 8.\n",
    "            for action in [\"N\", \"E\", \"S\", \"W\"]:\n",
    "                action_total = 0\n",
    "                for state_prime in range(16):\n",
    "                    action_total += probablitiy_map[(state_prime, -1, state, action)] * (-1 + discount_rate * V_s[state_prime])\n",
    "                total += policy[state][action] * action_total   \n",
    "                \n",
    "            V_s[state] = round(total, 1) # 9.\n",
    "            delta = max(delta, abs(v - V_s[state])) # 10.\n",
    "    return V_s # 11."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: {'N': 0, 'E': 0, 'S': 0, 'W': 0}, 1: {'N': 1, 'E': 2, 'S': 5, 'W': 0}, 2: {'N': 2, 'E': 3, 'S': 6, 'W': 1}, 3: {'N': 3, 'E': 3, 'S': 7, 'W': 2}, 4: {'N': 0, 'E': 5, 'S': 8, 'W': 4}, 5: {'N': 1, 'E': 6, 'S': 9, 'W': 4}, 6: {'N': 2, 'E': 7, 'S': 10, 'W': 5}, 7: {'N': 3, 'E': 7, 'S': 11, 'W': 6}, 8: {'N': 4, 'E': 9, 'S': 12, 'W': 8}, 9: {'N': 5, 'E': 10, 'S': 13, 'W': 8}, 10: {'N': 6, 'E': 11, 'S': 14, 'W': 9}, 11: {'N': 7, 'E': 11, 'S': 15, 'W': 10}, 12: {'N': 8, 'E': 13, 'S': 12, 'W': 12}, 13: {'N': 9, 'E': 14, 'S': 13, 'W': 12}, 14: {'N': 10, 'E': 15, 'S': 14, 'W': 13}, 15: {'N': 15, 'E': 15, 'S': 15, 'W': 15}}\n",
      "{0: 0.0, 1: -1.7, 2: -1.9, 3: -1.9, 4: -1.7, 5: -1.9, 6: -1.9, 7: -1.9, 8: -1.9, 9: -1.9, 10: -1.9, 11: -1.7, 12: -1.9, 13: -1.9, 14: -1.7, 15: 0.0}\n",
      "{0: {'N': 0, 'E': 0, 'S': 0, 'W': 0}, 1: {'N': 1, 'E': 2, 'S': 5, 'W': 0}, 2: {'N': 2, 'E': 3, 'S': 6, 'W': 1}, 3: {'N': 3, 'E': 3, 'S': 7, 'W': 2}, 4: {'N': 0, 'E': 5, 'S': 8, 'W': 4}, 5: {'N': 1, 'E': 6, 'S': 9, 'W': 4}, 6: {'N': 2, 'E': 7, 'S': 10, 'W': 5}, 7: {'N': 3, 'E': 7, 'S': 11, 'W': 6}, 8: {'N': 4, 'E': 9, 'S': 12, 'W': 8}, 9: {'N': 5, 'E': 10, 'S': 13, 'W': 8}, 10: {'N': 6, 'E': 11, 'S': 14, 'W': 9}, 11: {'N': 7, 'E': 11, 'S': 15, 'W': 10}, 12: {'N': 8, 'E': 13, 'S': 12, 'W': 12}, 13: {'N': 9, 'E': 14, 'S': 13, 'W': 12}, 14: {'N': 10, 'E': 15, 'S': 14, 'W': 13}, 15: {'N': 15, 'E': 15, 'S': 15, 'W': 15}}\n",
      "{0: 0.0, 1: -1.0, 2: -1.5, 3: -1.8, 4: -1.0, 5: -1.5, 6: -1.8, 7: -1.5, 8: -1.5, 9: -1.8, 10: -1.5, 11: -1.0, 12: -1.8, 13: -1.5, 14: -1.0, 15: 0.0}\n"
     ]
    }
   ],
   "source": [
    "policy = create_random_policy()\n",
    "V_s = iterative_policy_evaluation(policy)\n",
    "policy = create_greedy_policy(V_s)\n",
    "print(V_s)\n",
    "\n",
    "V_s = iterative_policy_evaluation(policy)\n",
    "policy = create_greedy_policy(V_s)\n",
    "print(V_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: {'N': 0.0, 'E': 0.0, 'S': 0.0, 'W': 0.0},\n",
       " 1: {'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0},\n",
       " 2: {'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0},\n",
       " 3: {'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5},\n",
       " 4: {'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0},\n",
       " 5: {'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5},\n",
       " 6: {'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25},\n",
       " 7: {'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0},\n",
       " 8: {'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0},\n",
       " 9: {'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25},\n",
       " 10: {'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0},\n",
       " 11: {'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0},\n",
       " 12: {'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0},\n",
       " 13: {'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0},\n",
       " 14: {'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0},\n",
       " 15: {'N': 0.0, 'E': 0.0, 'S': 0.0, 'W': 0.0}}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "100.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "Average steps to finish: 2.997\n"
     ]
    }
   ],
   "source": [
    "data = []\n",
    "\n",
    "for i in range(1000):\n",
    "    clear_output(wait=True)\n",
    "    print(\"{}%\\n\".format((i + 1) / 10))\n",
    "    data.append(agent(policy))\n",
    "    \n",
    "print(\"Average steps to finish: {}\".format(sum(data)/len(data)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Move: 2 Position: 15 Action: S\n",
      "-----------------\n",
      "| X |   |   |   |\n",
      "-----------------\n",
      "|   |   |   |   |\n",
      "-----------------\n",
      "|   |   |   |   |\n",
      "-----------------\n",
      "|   |   |   | A |\n",
      "-----------------\n",
      "\n",
      "Win!\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "agent(policy, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h1>Value iteration</h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def value_iteration(V_s, theta=0.01, discount_rate=0.5):\n",
    "    probablitiy_map = create_probability_map()\n",
    "\n",
    "    delta = 100\n",
    "    while not delta < theta:\n",
    "        delta = 0\n",
    "        for state in range(1, 15):\n",
    "            v = V_s[state]\n",
    "            \n",
    "            totals = {}\n",
    "            for action in [\"N\", \"S\", \"E\", \"W\"]:\n",
    "                total = 0\n",
    "                for state_prime in range(16):\n",
    "                    total += probablitiy_map[(state_prime, -1, state, action)] * (-1 + discount_rate * V_s[state_prime])\n",
    "                totals[action] = total\n",
    "            \n",
    "            V_s[state] = round(max(totals.values()), 4)\n",
    "            delta = max(delta, abs(v - V_s[state]))\n",
    "    return V_s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: {'N': 0, 'E': 0, 'S': 0, 'W': 0}, 1: {'N': 1, 'E': 2, 'S': 5, 'W': 0}, 2: {'N': 2, 'E': 3, 'S': 6, 'W': 1}, 3: {'N': 3, 'E': 3, 'S': 7, 'W': 2}, 4: {'N': 0, 'E': 5, 'S': 8, 'W': 4}, 5: {'N': 1, 'E': 6, 'S': 9, 'W': 4}, 6: {'N': 2, 'E': 7, 'S': 10, 'W': 5}, 7: {'N': 3, 'E': 7, 'S': 11, 'W': 6}, 8: {'N': 4, 'E': 9, 'S': 12, 'W': 8}, 9: {'N': 5, 'E': 10, 'S': 13, 'W': 8}, 10: {'N': 6, 'E': 11, 'S': 14, 'W': 9}, 11: {'N': 7, 'E': 11, 'S': 15, 'W': 10}, 12: {'N': 8, 'E': 13, 'S': 12, 'W': 12}, 13: {'N': 9, 'E': 14, 'S': 13, 'W': 12}, 14: {'N': 10, 'E': 15, 'S': 14, 'W': 13}, 15: {'N': 15, 'E': 15, 'S': 15, 'W': 15}}\n",
      "{0: 0, 1: -1.0, 2: -1.5, 3: -1.75, 4: -1.0, 5: -1.5, 6: -1.75, 7: -1.5, 8: -1.5, 9: -1.75, 10: -1.5, 11: -1.0, 12: -1.75, 13: -1.5, 14: -1.0, 15: 0}\n"
     ]
    }
   ],
   "source": [
    "V_s = {i: 0 for i in range(16)}\n",
    "V_s = value_iteration(V_s)\n",
    "policy = create_greedy_policy(V_s)\n",
    "\n",
    "print(V_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "0.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "0.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "0.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "0.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "0.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "0.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "0.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "0.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "1.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "1.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "1.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "1.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "1.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "1.5%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "1.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "1.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "1.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "1.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "2.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "2.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "2.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "2.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "2.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "2.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "2.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "2.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "2.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "2.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "3.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "3.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "3.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "3.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "3.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "3.5%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "3.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "3.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "3.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "3.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "4.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "4.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "4.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "4.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "4.4%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "4.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "4.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "4.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "4.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "4.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "5.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "5.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "5.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "5.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "5.4%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "5.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "5.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "5.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "5.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "5.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "6.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "6.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "6.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "6.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "6.4%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "6.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "6.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "6.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "6.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "6.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "7.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "7.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "7.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "7.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "7.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "7.5%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "7.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "7.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "7.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "7.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "8.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "8.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "8.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "8.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "8.4%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "8.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "8.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "8.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "8.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "8.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "9.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "9.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "9.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "9.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "9.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "9.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "9.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "9.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "9.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "9.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "10.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "10.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "10.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "10.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "10.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "10.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "10.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "10.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "10.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "10.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "11.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "11.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "11.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "11.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "11.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "11.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "11.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "11.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "11.8%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "11.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "12.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "12.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "12.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "12.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "12.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "12.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "12.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "12.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "12.8%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "12.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "13.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "13.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "13.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "13.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "13.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "13.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "13.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "13.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "13.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "13.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "14.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "14.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "14.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "14.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "14.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "14.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "14.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "14.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "14.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "14.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "15.0%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "15.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "15.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "15.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "15.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "15.5%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "15.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "15.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "15.8%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "15.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "16.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "16.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "16.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "16.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "16.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "16.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "16.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "16.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "16.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "16.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "17.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "17.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "17.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "17.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "17.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "17.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "17.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "17.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "17.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "17.9%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "18.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "18.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "18.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "18.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "18.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "18.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "18.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "18.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "18.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "18.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "19.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "19.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "19.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "19.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "19.4%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "19.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "19.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "19.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "19.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "19.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "20.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "20.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "20.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "20.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "20.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "20.5%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "20.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "20.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "20.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "20.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "21.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "21.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "21.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "21.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "21.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "21.5%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "21.6%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "21.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "21.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "21.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "22.0%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "22.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "22.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "22.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "22.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "22.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "22.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "22.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "22.8%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "22.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "23.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "23.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "23.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "23.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "23.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "23.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "23.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "23.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "23.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "23.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "24.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "24.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "24.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "24.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "24.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "24.5%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "24.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "24.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "24.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "24.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "25.0%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "25.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "25.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "25.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "25.4%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "25.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "25.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "25.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "25.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "25.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "26.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "26.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "26.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "26.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "26.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "26.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "26.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "26.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "26.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "26.9%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "27.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "27.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "27.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "27.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "27.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "27.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "27.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "27.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "27.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "27.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "28.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "28.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "28.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "28.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "28.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "28.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "28.6%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "28.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "28.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "28.9%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "29.0%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "29.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "29.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "29.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "29.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "29.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "29.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "29.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "29.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "29.9%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "30.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "30.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "30.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "30.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "30.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "30.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "30.6%\n",
      "\n",
      "-\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "30.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "30.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "30.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "31.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "31.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "31.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "31.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "31.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "31.5%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "31.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "31.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "31.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "31.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "32.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "32.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "32.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "32.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "32.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "32.5%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "32.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "32.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "32.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "32.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "33.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "33.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "33.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "33.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "33.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "33.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "33.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "33.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "33.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "33.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "34.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "34.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "34.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "34.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "34.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "34.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "34.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "34.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "34.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "34.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "35.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "35.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "35.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "35.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "35.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "35.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "35.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "35.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "35.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "35.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "36.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "36.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "36.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "36.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "36.4%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "36.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "36.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "36.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "36.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "36.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "37.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "37.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "37.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "37.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "37.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "37.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "37.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "37.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "37.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "37.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "38.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "38.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "38.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "38.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "38.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "38.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "38.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "38.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "38.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "38.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "39.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "39.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "39.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "39.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "39.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "39.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "39.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "39.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "39.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "39.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "40.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "40.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "40.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "40.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "40.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "40.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "40.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "40.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "40.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "40.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "41.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "41.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "41.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "41.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "41.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "41.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "41.6%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "41.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "41.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "41.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "42.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "42.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "42.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "42.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "42.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "42.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "42.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "42.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "42.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "42.9%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "43.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "43.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "43.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "43.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "43.4%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "43.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "43.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "43.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "43.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "43.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "44.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "44.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "44.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "44.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "44.4%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "44.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "44.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "44.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "44.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "44.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "45.0%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "45.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "45.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "45.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "45.4%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "45.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "45.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "45.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "45.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "45.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "46.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "46.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "46.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "46.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "46.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "46.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "46.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "46.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "46.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "46.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "47.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "47.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "47.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "47.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "47.4%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "47.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "47.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "47.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "47.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "47.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "48.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "48.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "48.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "48.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "48.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "48.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "48.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "48.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "48.8%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "48.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "49.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "49.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "49.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "49.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "49.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "49.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "49.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "49.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "49.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "49.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "50.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "50.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "50.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "50.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "50.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "50.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "50.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "50.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "50.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "50.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "51.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "51.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "51.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "51.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "51.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "51.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "51.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "51.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "51.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "51.9%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "52.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "52.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "52.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "52.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "52.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "52.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "52.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "52.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "52.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "52.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "53.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "53.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "53.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "53.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "53.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "53.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "53.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "53.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "53.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "53.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "54.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "54.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "54.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "54.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "54.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "54.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "54.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "54.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "54.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "54.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "55.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "55.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "55.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "55.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "55.4%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "55.5%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "55.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "55.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "55.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "55.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "56.0%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "56.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "56.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "56.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "56.4%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "56.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "56.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "56.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "56.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "56.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "57.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "57.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "57.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "57.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "57.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "57.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "57.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "57.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "57.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "57.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "58.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "58.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "58.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "58.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "58.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "58.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "58.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "58.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "58.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "58.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "59.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "59.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "59.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "59.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "59.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "59.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "59.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "59.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "59.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "59.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "60.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "60.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "60.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "60.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "60.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "60.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "60.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "60.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "60.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "60.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "61.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "61.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "61.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "61.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "61.4%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "61.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "61.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "61.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "61.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "61.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "62.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "62.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "62.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "62.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "62.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "62.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "62.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "62.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "62.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "62.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "63.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "63.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "63.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "63.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "63.4%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "63.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "63.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "63.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "63.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "63.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "64.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "64.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "64.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "64.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "64.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "64.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "64.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "64.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "64.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "64.9%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "65.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "65.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "65.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "65.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "65.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "65.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "65.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "65.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "65.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "65.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "66.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "66.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "66.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "66.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "66.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "66.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "66.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "66.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "66.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "66.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "67.0%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "67.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "67.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "67.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "67.4%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "67.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "67.6%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "67.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "67.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "67.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "68.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "68.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "68.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "68.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "68.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "68.5%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "68.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "68.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "68.8%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "68.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "69.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "69.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "69.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "69.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "69.4%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "69.5%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "69.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "69.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "69.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "69.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "70.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "70.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "70.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "70.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "70.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "70.5%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "70.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "70.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "70.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "70.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "71.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "71.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "71.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "71.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "71.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "71.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "71.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "71.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "71.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "71.9%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "72.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "72.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "72.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "72.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "72.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "72.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "72.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "72.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "72.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "72.9%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "73.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "73.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "73.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "73.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "73.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "73.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "73.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "73.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "73.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "73.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "74.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "74.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "74.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "74.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "74.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "74.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "74.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "74.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "74.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "74.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "75.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "75.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "75.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "75.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "75.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "75.5%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "75.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "75.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "75.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "75.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "76.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "76.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "76.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "76.3%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "76.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "76.5%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "76.6%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "76.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "76.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "76.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "77.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "77.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "77.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "77.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "77.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "77.5%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "77.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "77.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "77.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "77.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "78.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "78.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "78.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "78.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "78.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "78.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "78.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "78.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "78.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "78.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "79.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "79.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "79.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "79.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "79.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "79.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "79.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "79.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "79.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "79.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "80.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "80.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "80.2%\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "80.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "80.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "80.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "80.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "80.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "80.8%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "80.9%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "81.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "81.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "81.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "81.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "81.4%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "81.5%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "81.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "81.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "81.8%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "81.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "82.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "82.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "82.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "82.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "82.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "82.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "82.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "82.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "82.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "82.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "83.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "83.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "83.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "83.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "83.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "83.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "83.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "83.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "83.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "83.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "84.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "84.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "84.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "84.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "84.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "84.5%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "84.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "84.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "84.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "84.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "85.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "85.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "85.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "85.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "85.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "85.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "85.6%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "85.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "85.8%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "85.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "86.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "86.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "86.2%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "86.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "86.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "86.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "86.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "86.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "86.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "86.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "87.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "87.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "87.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "87.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "87.4%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "87.5%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "87.6%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "87.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "87.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "87.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "88.0%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "88.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "88.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "88.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "88.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "88.5%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "88.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "88.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "88.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "88.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "89.0%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "89.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "89.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "89.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "89.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "89.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "89.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "89.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "89.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "89.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "90.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "90.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "90.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "90.3%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "90.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "90.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "90.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "90.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "90.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "90.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "91.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "91.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "91.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "91.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "91.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "91.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "91.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "91.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "91.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "91.9%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "92.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "92.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "92.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "92.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "92.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "92.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "92.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "92.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "92.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "92.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "93.0%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "93.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "93.2%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "93.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "93.4%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "93.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "93.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "93.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "93.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "93.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "94.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "94.1%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "94.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "94.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "94.4%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "94.5%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "94.6%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "94.7%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "94.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "94.9%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "95.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "95.1%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "95.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "95.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "95.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "95.5%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "95.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "95.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "95.8%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "95.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "96.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "96.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "96.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "96.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "96.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "96.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "96.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "96.7%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "96.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "96.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "97.0%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "97.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "97.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "97.3%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "97.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "97.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "97.6%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "97.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "97.8%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "97.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "98.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "98.1%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "98.2%\n",
      "\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "98.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "98.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "98.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "98.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "98.7%\n",
      "\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "98.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "98.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "99.0%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 0.5, 'S': 0.0, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "99.1%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.5, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "99.2%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "99.3%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.5, 'E': 0.0, 'W': 0.5}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "99.4%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 1.0, 'W': 0.0}\n",
      "99.5%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "99.6%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "99.7%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "99.8%\n",
      "\n",
      "-\n",
      "{'N': 0.25, 'S': 0.25, 'E': 0.25, 'W': 0.25}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "-\n",
      "{'N': 1.0, 'S': 0.0, 'E': 0.0, 'W': 0.0}\n",
      "99.9%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 1.0, 'E': 0.0, 'W': 0.0}\n",
      "100.0%\n",
      "\n",
      "-\n",
      "{'N': 0.0, 'S': 0.0, 'E': 0.0, 'W': 1.0}\n",
      "Average steps to finish: 3.008\n"
     ]
    }
   ],
   "source": [
    "data = []\n",
    "\n",
    "for i in range(1000):\n",
    "    #clear_output(wait=True)\n",
    "    print(\"{}%\\n\".format((i + 1) / 10))\n",
    "    data.append(agent(policy))\n",
    "    \n",
    "print(\"Average steps to finish: {}\".format(sum(data)/len(data)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Move: 4 Position: 15 Action: E\n",
      "-----------------\n",
      "| X |   |   |   |\n",
      "-----------------\n",
      "|   |   |   |   |\n",
      "-----------------\n",
      "|   |   |   |   |\n",
      "-----------------\n",
      "|   |   |   | A |\n",
      "-----------------\n",
      "\n",
      "Win!\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "agent(policy, verbose=True)"
   ]
  }
 ],
 "metadata": {
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   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
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