06-tour-shapes/tour-shapes-problem-creation.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "markdown",
   5    "metadata": {},
   6    "source": [
   7     "Given a sequence of {F|L|R}, each of which is \"move forward one step\", \"turn left, then move forward one step\", \"turn right, then move forward one step\":\n",
   8     "1. which tours are closed?\n",
   9     "2. what is the area enclosed by the tour?"
  10    ]
  11   },
  12   {
  13    "cell_type": "code",
  14    "execution_count": 1301,
  15    "metadata": {
  16     "collapsed": true
  17    },
  18    "outputs": [],
  19    "source": [
  20     "import collections\n",
  21     "import enum\n",
  22     "import random\n",
  23     "import os\n",
  24     "\n",
  25     "import matplotlib.pyplot as plt\n",
  26     "%matplotlib inline\n"
  27    ]
  28   },
  29   {
  30    "cell_type": "code",
  31    "execution_count": 2,
  32    "metadata": {
  33     "collapsed": true
  34    },
  35    "outputs": [],
  36    "source": [
  37     "class Direction(enum.Enum):\n",
  38     "    UP = 1\n",
  39     "    RIGHT = 2\n",
  40     "    DOWN = 3\n",
  41     "    LEFT = 4\n",
  42     "    \n",
  43     "turn_lefts = {Direction.UP: Direction.LEFT, Direction.LEFT: Direction.DOWN,\n",
  44     "              Direction.DOWN: Direction.RIGHT, Direction.RIGHT: Direction.UP}\n",
  45     "\n",
  46     "turn_rights = {Direction.UP: Direction.RIGHT, Direction.RIGHT: Direction.DOWN,\n",
  47     "               Direction.DOWN: Direction.LEFT, Direction.LEFT: Direction.UP}\n",
  48     "\n",
  49     "def turn_left(d):\n",
  50     "    return turn_lefts[d]\n",
  51     "\n",
  52     "def turn_right(d):\n",
  53     "    return turn_rights[d]\n"
  54    ]
  55   },
  56   {
  57    "cell_type": "code",
  58    "execution_count": 82,
  59    "metadata": {
  60     "collapsed": true
  61    },
  62    "outputs": [],
  63    "source": [
  64     "Step = collections.namedtuple('Step', ['x', 'y', 'dir'])\n",
  65     "Mistake = collections.namedtuple('Mistake', ['i', 'step'])"
  66    ]
  67   },
  68   {
  69    "cell_type": "code",
  70    "execution_count": 4,
  71    "metadata": {
  72     "collapsed": true
  73    },
  74    "outputs": [],
  75    "source": [
  76     "def advance(step, d):\n",
  77     "    if d == Direction.UP:\n",
  78     "        return Step(step.x, step.y+1, d)\n",
  79     "    elif d == Direction.DOWN:\n",
  80     "        return Step(step.x, step.y-1, d)\n",
  81     "    elif d == Direction.LEFT:\n",
  82     "        return Step(step.x-1, step.y, d)\n",
  83     "    elif d == Direction.RIGHT:\n",
  84     "        return Step(step.x+1, step.y, d)"
  85    ]
  86   },
  87   {
  88    "cell_type": "code",
  89    "execution_count": 489,
  90    "metadata": {
  91     "collapsed": true
  92    },
  93    "outputs": [],
  94    "source": [
  95     "def trace_tour(tour, startx=0, starty=0, startdir=Direction.RIGHT):\n",
  96     "    current = Step(startx, starty, startdir)\n",
  97     "    trace = [current]\n",
  98     "    for s in tour:\n",
  99     "        if s == 'F':\n",
 100     "            current = advance(current, current.dir)\n",
 101     "        elif s == 'L':\n",
 102     "            current = advance(current, turn_left(current.dir))\n",
 103     "        elif s == 'R':\n",
 104     "            current = advance(current, turn_right(current.dir))\n",
 105     "        trace += [current]\n",
 106     "    return trace    "
 107    ]
 108   },
 109   {
 110    "cell_type": "code",
 111    "execution_count": 490,
 112    "metadata": {
 113     "collapsed": true
 114    },
 115    "outputs": [],
 116    "source": [
 117     "k = Step(1, 2, 3)"
 118    ]
 119   },
 120   {
 121    "cell_type": "code",
 122    "execution_count": 491,
 123    "metadata": {},
 124    "outputs": [
 125     {
 126      "data": {
 127       "text/plain": [
 128        "Step(x=1, y=2, dir=3)"
 129       ]
 130      },
 131      "execution_count": 491,
 132      "metadata": {},
 133      "output_type": "execute_result"
 134     }
 135    ],
 136    "source": [
 137     "k"
 138    ]
 139   },
 140   {
 141    "cell_type": "code",
 142    "execution_count": 8,
 143    "metadata": {},
 144    "outputs": [
 145     {
 146      "data": {
 147       "text/plain": [
 148        "__main__.Step"
 149       ]
 150      },
 151      "execution_count": 8,
 152      "metadata": {},
 153      "output_type": "execute_result"
 154     }
 155    ],
 156    "source": [
 157     "Step"
 158    ]
 159   },
 160   {
 161    "cell_type": "code",
 162    "execution_count": 9,
 163    "metadata": {},
 164    "outputs": [
 165     {
 166      "data": {
 167       "text/plain": [
 168        "<Direction.UP: 1>"
 169       ]
 170      },
 171      "execution_count": 9,
 172      "metadata": {},
 173      "output_type": "execute_result"
 174     }
 175    ],
 176    "source": [
 177     "d = Direction.UP\n",
 178     "d"
 179    ]
 180   },
 181   {
 182    "cell_type": "code",
 183    "execution_count": 10,
 184    "metadata": {},
 185    "outputs": [
 186     {
 187      "data": {
 188       "text/plain": [
 189        "<Direction.RIGHT: 2>"
 190       ]
 191      },
 192      "execution_count": 10,
 193      "metadata": {},
 194      "output_type": "execute_result"
 195     }
 196    ],
 197    "source": [
 198     "turn_right(d)"
 199    ]
 200   },
 201   {
 202    "cell_type": "code",
 203    "execution_count": 11,
 204    "metadata": {},
 205    "outputs": [
 206     {
 207      "data": {
 208       "text/plain": [
 209        "{<Direction.RIGHT: 2>: <Direction.DOWN: 3>,\n",
 210        " <Direction.DOWN: 3>: <Direction.LEFT: 4>,\n",
 211        " <Direction.LEFT: 4>: <Direction.UP: 1>,\n",
 212        " <Direction.UP: 1>: <Direction.RIGHT: 2>}"
 213       ]
 214      },
 215      "execution_count": 11,
 216      "metadata": {},
 217      "output_type": "execute_result"
 218     }
 219    ],
 220    "source": [
 221     "turn_rights"
 222    ]
 223   },
 224   {
 225    "cell_type": "code",
 226    "execution_count": 494,
 227    "metadata": {},
 228    "outputs": [
 229     {
 230      "data": {
 231       "text/plain": [
 232        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 233        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 234        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
 235        " Step(x=2, y=1, dir=<Direction.RIGHT: 2>),\n",
 236        " Step(x=2, y=2, dir=<Direction.UP: 1>)]"
 237       ]
 238      },
 239      "execution_count": 494,
 240      "metadata": {},
 241      "output_type": "execute_result"
 242     }
 243    ],
 244    "source": [
 245     "trace_tour('FLRL')"
 246    ]
 247   },
 248   {
 249    "cell_type": "code",
 250    "execution_count": 13,
 251    "metadata": {},
 252    "outputs": [
 253     {
 254      "data": {
 255       "text/plain": [
 256        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 257        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 258        " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
 259        " Step(x=2, y=1, dir=<Direction.UP: 1>),\n",
 260        " Step(x=3, y=1, dir=<Direction.RIGHT: 2>),\n",
 261        " Step(x=3, y=2, dir=<Direction.UP: 1>),\n",
 262        " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
 263        " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
 264        " Step(x=1, y=1, dir=<Direction.DOWN: 3>),\n",
 265        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
 266        " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
 267       ]
 268      },
 269      "execution_count": 13,
 270      "metadata": {},
 271      "output_type": "execute_result"
 272     }
 273    ],
 274    "source": [
 275     "trace_tour('FFLRLLFLRL')"
 276    ]
 277   },
 278   {
 279    "cell_type": "code",
 280    "execution_count": 14,
 281    "metadata": {},
 282    "outputs": [
 283     {
 284      "data": {
 285       "text/plain": [
 286        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 287        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 288        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
 289        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
 290        " Step(x=-1, y=1, dir=<Direction.LEFT: 4>),\n",
 291        " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
 292        " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
 293        " Step(x=-2, y=-1, dir=<Direction.DOWN: 3>),\n",
 294        " Step(x=-2, y=-2, dir=<Direction.DOWN: 3>),\n",
 295        " Step(x=-2, y=-3, dir=<Direction.DOWN: 3>),\n",
 296        " Step(x=-1, y=-3, dir=<Direction.RIGHT: 2>),\n",
 297        " Step(x=0, y=-3, dir=<Direction.RIGHT: 2>),\n",
 298        " Step(x=1, y=-3, dir=<Direction.RIGHT: 2>),\n",
 299        " Step(x=1, y=-2, dir=<Direction.UP: 1>),\n",
 300        " Step(x=1, y=-1, dir=<Direction.UP: 1>),\n",
 301        " Step(x=0, y=-1, dir=<Direction.LEFT: 4>),\n",
 302        " Step(x=0, y=-2, dir=<Direction.DOWN: 3>),\n",
 303        " Step(x=-1, y=-2, dir=<Direction.LEFT: 4>),\n",
 304        " Step(x=-1, y=-1, dir=<Direction.UP: 1>),\n",
 305        " Step(x=-1, y=0, dir=<Direction.UP: 1>),\n",
 306        " Step(x=0, y=0, dir=<Direction.RIGHT: 2>)]"
 307       ]
 308      },
 309      "execution_count": 14,
 310      "metadata": {},
 311      "output_type": "execute_result"
 312     }
 313    ],
 314    "source": [
 315     "trace_tour('FLLFFLFFFLFFLFLLRRFR')"
 316    ]
 317   },
 318   {
 319    "cell_type": "code",
 320    "execution_count": 15,
 321    "metadata": {},
 322    "outputs": [
 323     {
 324      "data": {
 325       "text/plain": [
 326        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 327        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 328        " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
 329        " Step(x=2, y=-1, dir=<Direction.DOWN: 3>),\n",
 330        " Step(x=3, y=-1, dir=<Direction.RIGHT: 2>),\n",
 331        " Step(x=3, y=0, dir=<Direction.UP: 1>),\n",
 332        " Step(x=3, y=1, dir=<Direction.UP: 1>),\n",
 333        " Step(x=4, y=1, dir=<Direction.RIGHT: 2>),\n",
 334        " Step(x=4, y=2, dir=<Direction.UP: 1>),\n",
 335        " Step(x=3, y=2, dir=<Direction.LEFT: 4>),\n",
 336        " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
 337        " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
 338        " Step(x=0, y=2, dir=<Direction.LEFT: 4>),\n",
 339        " Step(x=0, y=3, dir=<Direction.UP: 1>),\n",
 340        " Step(x=0, y=4, dir=<Direction.UP: 1>),\n",
 341        " Step(x=-1, y=4, dir=<Direction.LEFT: 4>),\n",
 342        " Step(x=-1, y=3, dir=<Direction.DOWN: 3>),\n",
 343        " Step(x=-2, y=3, dir=<Direction.LEFT: 4>),\n",
 344        " Step(x=-2, y=2, dir=<Direction.DOWN: 3>),\n",
 345        " Step(x=-1, y=2, dir=<Direction.RIGHT: 2>),\n",
 346        " Step(x=-1, y=1, dir=<Direction.DOWN: 3>),\n",
 347        " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
 348        " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
 349        " Step(x=-1, y=0, dir=<Direction.RIGHT: 2>),\n",
 350        " Step(x=-1, y=-1, dir=<Direction.DOWN: 3>),\n",
 351        " Step(x=0, y=-1, dir=<Direction.RIGHT: 2>),\n",
 352        " Step(x=0, y=0, dir=<Direction.UP: 1>)]"
 353       ]
 354      },
 355      "execution_count": 15,
 356      "metadata": {},
 357      "output_type": "execute_result"
 358     }
 359    ],
 360    "source": [
 361     "trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL')"
 362    ]
 363   },
 364   {
 365    "cell_type": "code",
 366    "execution_count": 16,
 367    "metadata": {
 368     "collapsed": true
 369    },
 370    "outputs": [],
 371    "source": [
 372     "def positions(trace):\n",
 373     "    return [(s.x, s.y) for s in trace]"
 374    ]
 375   },
 376   {
 377    "cell_type": "code",
 378    "execution_count": 17,
 379    "metadata": {},
 380    "outputs": [
 381     {
 382      "data": {
 383       "text/plain": [
 384        "[(0, 0),\n",
 385        " (1, 0),\n",
 386        " (2, 0),\n",
 387        " (2, -1),\n",
 388        " (3, -1),\n",
 389        " (3, 0),\n",
 390        " (3, 1),\n",
 391        " (4, 1),\n",
 392        " (4, 2),\n",
 393        " (3, 2),\n",
 394        " (2, 2),\n",
 395        " (1, 2),\n",
 396        " (0, 2),\n",
 397        " (0, 3),\n",
 398        " (0, 4),\n",
 399        " (-1, 4),\n",
 400        " (-1, 3),\n",
 401        " (-2, 3),\n",
 402        " (-2, 2),\n",
 403        " (-1, 2),\n",
 404        " (-1, 1),\n",
 405        " (-2, 1),\n",
 406        " (-2, 0),\n",
 407        " (-1, 0),\n",
 408        " (-1, -1),\n",
 409        " (0, -1),\n",
 410        " (0, 0)]"
 411       ]
 412      },
 413      "execution_count": 17,
 414      "metadata": {},
 415      "output_type": "execute_result"
 416     }
 417    ],
 418    "source": [
 419     "positions(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 420    ]
 421   },
 422   {
 423    "cell_type": "code",
 424    "execution_count": 18,
 425    "metadata": {
 426     "collapsed": true
 427    },
 428    "outputs": [],
 429    "source": [
 430     "def valid(trace):\n",
 431     "    return (trace[-1].x == 0 \n",
 432     "            and trace[-1].y == 0 \n",
 433     "            and len(set(positions(trace))) + 1 == len(trace))"
 434    ]
 435   },
 436   {
 437    "cell_type": "code",
 438    "execution_count": 19,
 439    "metadata": {},
 440    "outputs": [
 441     {
 442      "data": {
 443       "text/plain": [
 444        "True"
 445       ]
 446      },
 447      "execution_count": 19,
 448      "metadata": {},
 449      "output_type": "execute_result"
 450     }
 451    ],
 452    "source": [
 453     "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 454    ]
 455   },
 456   {
 457    "cell_type": "code",
 458    "execution_count": 20,
 459    "metadata": {},
 460    "outputs": [
 461     {
 462      "data": {
 463       "text/plain": [
 464        "False"
 465       ]
 466      },
 467      "execution_count": 20,
 468      "metadata": {},
 469      "output_type": "execute_result"
 470     }
 471    ],
 472    "source": [
 473     "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLLFF'))"
 474    ]
 475   },
 476   {
 477    "cell_type": "code",
 478    "execution_count": 21,
 479    "metadata": {},
 480    "outputs": [
 481     {
 482      "data": {
 483       "text/plain": [
 484        "False"
 485       ]
 486      },
 487      "execution_count": 21,
 488      "metadata": {},
 489      "output_type": "execute_result"
 490     }
 491    ],
 492    "source": [
 493     "valid(trace_tour('FFLLLFRR'))"
 494    ]
 495   },
 496   {
 497    "cell_type": "code",
 498    "execution_count": 22,
 499    "metadata": {},
 500    "outputs": [
 501     {
 502      "data": {
 503       "text/plain": [
 504        "False"
 505       ]
 506      },
 507      "execution_count": 22,
 508      "metadata": {},
 509      "output_type": "execute_result"
 510     }
 511    ],
 512    "source": [
 513     "valid(trace_tour('F'))"
 514    ]
 515   },
 516   {
 517    "cell_type": "code",
 518    "execution_count": 23,
 519    "metadata": {},
 520    "outputs": [
 521     {
 522      "data": {
 523       "text/plain": [
 524        "True"
 525       ]
 526      },
 527      "execution_count": 23,
 528      "metadata": {},
 529      "output_type": "execute_result"
 530     }
 531    ],
 532    "source": [
 533     "valid(trace_tour('LLLL'))"
 534    ]
 535   },
 536   {
 537    "cell_type": "code",
 538    "execution_count": 24,
 539    "metadata": {
 540     "collapsed": true
 541    },
 542    "outputs": [],
 543    "source": [
 544     "def chunks(items, n=2):\n",
 545     "    return [items[i:i+n] for i in range(len(items) - n + 1)]"
 546    ]
 547   },
 548   {
 549    "cell_type": "code",
 550    "execution_count": 25,
 551    "metadata": {},
 552    "outputs": [
 553     {
 554      "data": {
 555       "text/plain": [
 556        "['abcdefg',\n",
 557        " 'bcdefgh',\n",
 558        " 'cdefghi',\n",
 559        " 'defghij',\n",
 560        " 'efghijk',\n",
 561        " 'fghijkl',\n",
 562        " 'ghijklm',\n",
 563        " 'hijklmn',\n",
 564        " 'ijklmno',\n",
 565        " 'jklmnop',\n",
 566        " 'klmnopq',\n",
 567        " 'lmnopqr',\n",
 568        " 'mnopqrs',\n",
 569        " 'nopqrst',\n",
 570        " 'opqrstu',\n",
 571        " 'pqrstuv',\n",
 572        " 'qrstuvw',\n",
 573        " 'rstuvwx',\n",
 574        " 'stuvwxy',\n",
 575        " 'tuvwxyz']"
 576       ]
 577      },
 578      "execution_count": 25,
 579      "metadata": {},
 580      "output_type": "execute_result"
 581     }
 582    ],
 583    "source": [
 584     "import string\n",
 585     "chunks(string.ascii_lowercase, 7)"
 586    ]
 587   },
 588   {
 589    "cell_type": "markdown",
 590    "metadata": {},
 591    "source": [
 592     "Using the [Shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula)"
 593    ]
 594   },
 595   {
 596    "cell_type": "code",
 597    "execution_count": 26,
 598    "metadata": {
 599     "collapsed": true
 600    },
 601    "outputs": [],
 602    "source": [
 603     "def shoelace(trace):\n",
 604     "    return abs(sum(s.x * t.y - t.x * s.y for s, t in chunks(trace, 2))) // 2"
 605    ]
 606   },
 607   {
 608    "cell_type": "code",
 609    "execution_count": 27,
 610    "metadata": {},
 611    "outputs": [
 612     {
 613      "data": {
 614       "text/plain": [
 615        "4"
 616       ]
 617      },
 618      "execution_count": 27,
 619      "metadata": {},
 620      "output_type": "execute_result"
 621     }
 622    ],
 623    "source": [
 624     "shoelace(trace_tour('FFLRLLFLRL'))"
 625    ]
 626   },
 627   {
 628    "cell_type": "code",
 629    "execution_count": 28,
 630    "metadata": {},
 631    "outputs": [
 632     {
 633      "data": {
 634       "text/plain": [
 635        "9"
 636       ]
 637      },
 638      "execution_count": 28,
 639      "metadata": {},
 640      "output_type": "execute_result"
 641     }
 642    ],
 643    "source": [
 644     "shoelace(trace_tour('FLLFFLFFFLFFLFLLRRFR'))"
 645    ]
 646   },
 647   {
 648    "cell_type": "code",
 649    "execution_count": 29,
 650    "metadata": {},
 651    "outputs": [
 652     {
 653      "data": {
 654       "text/plain": [
 655        "15"
 656       ]
 657      },
 658      "execution_count": 29,
 659      "metadata": {},
 660      "output_type": "execute_result"
 661     }
 662    ],
 663    "source": [
 664     "shoelace(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
 665    ]
 666   },
 667   {
 668    "cell_type": "code",
 669    "execution_count": 30,
 670    "metadata": {
 671     "collapsed": true
 672    },
 673    "outputs": [],
 674    "source": [
 675     "def step(s, current):\n",
 676     "    if s == 'F':\n",
 677     "        return advance(current, current.dir)\n",
 678     "    elif s == 'L':\n",
 679     "        return advance(current, turn_left(current.dir))\n",
 680     "    elif s == 'R':\n",
 681     "        return advance(current, turn_right(current.dir))\n",
 682     "    else:\n",
 683     "        raise ValueError"
 684    ]
 685   },
 686   {
 687    "cell_type": "code",
 688    "execution_count": 31,
 689    "metadata": {
 690     "collapsed": true
 691    },
 692    "outputs": [],
 693    "source": [
 694     "def valid_prefix(tour):\n",
 695     "    current = Step(0, 0, Direction.RIGHT)\n",
 696     "    prefix = []\n",
 697     "    posns = []\n",
 698     "    for s in tour:\n",
 699     "        current = step(s, current)\n",
 700     "        prefix += [s]\n",
 701     "        if (current.x, current.y) in posns:\n",
 702     "            return ''\n",
 703     "        elif current.x == 0 and current.y == 0: \n",
 704     "            return ''.join(prefix)\n",
 705     "        posns += [(current.x, current.y)]\n",
 706     "    if current.x == 0 and current.y == 0:\n",
 707     "        return ''.join(prefix)\n",
 708     "    else:\n",
 709     "        return ''"
 710    ]
 711   },
 712   {
 713    "cell_type": "code",
 714    "execution_count": 267,
 715    "metadata": {
 716     "collapsed": true
 717    },
 718    "outputs": [],
 719    "source": [
 720     "def mistake_positions(trace, debug=False):\n",
 721     "    mistakes = []\n",
 722     "    current = trace[0]\n",
 723     "    posns = [(0, 0)]\n",
 724     "    for i, current in enumerate(trace[1:]):\n",
 725     "        if (current.x, current.y) in posns:\n",
 726     "            if debug: print(i, current)\n",
 727     "            mistakes += [Mistake(i+1, current)]\n",
 728     "        posns += [(current.x, current.y)]\n",
 729     "    if (current.x, current.y) == (0, 0):\n",
 730     "        return mistakes[:-1]\n",
 731     "    else:\n",
 732     "        return mistakes + [Mistake(len(trace)+1, current)]"
 733    ]
 734   },
 735   {
 736    "cell_type": "code",
 737    "execution_count": 84,
 738    "metadata": {
 739     "collapsed": true
 740    },
 741    "outputs": [],
 742    "source": [
 743     "def returns_to_origin(mistake_positions):\n",
 744     "    return [i for i, m in mistake_positions\n",
 745     "           if (m.x, m.y) == (0, 0)]"
 746    ]
 747   },
 748   {
 749    "cell_type": "code",
 750    "execution_count": 34,
 751    "metadata": {
 752     "collapsed": true
 753    },
 754    "outputs": [],
 755    "source": [
 756     "sample_tours = ['FFLRLLFLRL', 'FLLFFLFFFLFFLFLLRRFR', 'FFRLLFRLLFFFRFLLRLLRRLLRLL']"
 757    ]
 758   },
 759   {
 760    "cell_type": "code",
 761    "execution_count": 35,
 762    "metadata": {},
 763    "outputs": [
 764     {
 765      "data": {
 766       "text/plain": [
 767        "'FFLRLLFLRL'"
 768       ]
 769      },
 770      "execution_count": 35,
 771      "metadata": {},
 772      "output_type": "execute_result"
 773     }
 774    ],
 775    "source": [
 776     "valid_prefix(sample_tours[0])"
 777    ]
 778   },
 779   {
 780    "cell_type": "code",
 781    "execution_count": 36,
 782    "metadata": {
 783     "scrolled": true
 784    },
 785    "outputs": [
 786     {
 787      "data": {
 788       "text/plain": [
 789        "True"
 790       ]
 791      },
 792      "execution_count": 36,
 793      "metadata": {},
 794      "output_type": "execute_result"
 795     }
 796    ],
 797    "source": [
 798     "all(valid_prefix(t) == t for t in sample_tours)"
 799    ]
 800   },
 801   {
 802    "cell_type": "code",
 803    "execution_count": 37,
 804    "metadata": {},
 805    "outputs": [
 806     {
 807      "data": {
 808       "text/plain": [
 809        "True"
 810       ]
 811      },
 812      "execution_count": 37,
 813      "metadata": {},
 814      "output_type": "execute_result"
 815     }
 816    ],
 817    "source": [
 818     "valid_prefix(sample_tours[0] + 'FLLLL') == sample_tours[0]"
 819    ]
 820   },
 821   {
 822    "cell_type": "code",
 823    "execution_count": 89,
 824    "metadata": {},
 825    "outputs": [
 826     {
 827      "data": {
 828       "text/plain": [
 829        "[Mistake(i=1, step=Step(x=0, y=0, dir=<Direction.RIGHT: 2>)),\n",
 830        " Mistake(i=11, step=Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
 831        " (13, Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
 832       ]
 833      },
 834      "execution_count": 89,
 835      "metadata": {},
 836      "output_type": "execute_result"
 837     }
 838    ],
 839    "source": [
 840     "mistake_positions(trace_tour(sample_tours[0] + 'F'))"
 841    ]
 842   },
 843   {
 844    "cell_type": "code",
 845    "execution_count": 90,
 846    "metadata": {},
 847    "outputs": [
 848     {
 849      "data": {
 850       "text/plain": [
 851        "[Mistake(i=1, step=Step(x=0, y=0, dir=<Direction.RIGHT: 2>)),\n",
 852        " Mistake(i=11, step=Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
 853        " Mistake(i=14, step=Step(x=1, y=0, dir=<Direction.UP: 1>)),\n",
 854        " Mistake(i=15, step=Step(x=0, y=0, dir=<Direction.LEFT: 4>)),\n",
 855        " Mistake(i=16, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>)),\n",
 856        " (17, Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
 857       ]
 858      },
 859      "execution_count": 90,
 860      "metadata": {},
 861      "output_type": "execute_result"
 862     }
 863    ],
 864    "source": [
 865     "mistake_positions(trace_tour(sample_tours[0] + 'FLLLL'))"
 866    ]
 867   },
 868   {
 869    "cell_type": "code",
 870    "execution_count": 91,
 871    "metadata": {},
 872    "outputs": [
 873     {
 874      "data": {
 875       "text/plain": [
 876        "'FFLRLLFLRL'"
 877       ]
 878      },
 879      "execution_count": 91,
 880      "metadata": {},
 881      "output_type": "execute_result"
 882     }
 883    ],
 884    "source": [
 885     "(sample_tours[0] + 'FLLLL')[:10]"
 886    ]
 887   },
 888   {
 889    "cell_type": "code",
 890    "execution_count": 574,
 891    "metadata": {
 892     "collapsed": true
 893    },
 894    "outputs": [],
 895    "source": [
 896     "def random_walk(steps=1000):\n",
 897     "    return ''.join(random.choice('FFLR') for _ in range(steps))"
 898    ]
 899   },
 900   {
 901    "cell_type": "code",
 902    "execution_count": 42,
 903    "metadata": {},
 904    "outputs": [
 905     {
 906      "data": {
 907       "text/plain": [
 908        "''"
 909       ]
 910      },
 911      "execution_count": 42,
 912      "metadata": {},
 913      "output_type": "execute_result"
 914     }
 915    ],
 916    "source": [
 917     "valid_prefix(random_walk(1000))"
 918    ]
 919   },
 920   {
 921    "cell_type": "code",
 922    "execution_count": 44,
 923    "metadata": {},
 924    "outputs": [
 925     {
 926      "data": {
 927       "text/plain": [
 928        "''"
 929       ]
 930      },
 931      "execution_count": 44,
 932      "metadata": {},
 933      "output_type": "execute_result"
 934     }
 935    ],
 936    "source": [
 937     "valid_prefix(random_walk(1000))"
 938    ]
 939   },
 940   {
 941    "cell_type": "code",
 942    "execution_count": 45,
 943    "metadata": {
 944     "collapsed": true,
 945     "scrolled": true
 946    },
 947    "outputs": [],
 948    "source": [
 949     "walks = []\n",
 950     "while len(walks) < 10:\n",
 951     "    w = valid_prefix(random_walk())\n",
 952     "    if len(w) > 30: walks += [w]"
 953    ]
 954   },
 955   {
 956    "cell_type": "code",
 957    "execution_count": 46,
 958    "metadata": {},
 959    "outputs": [
 960     {
 961      "data": {
 962       "text/plain": [
 963        "['RFLFFLFFFFFFLRRLLRLFFFLFFFLRFRLLFFRR',\n",
 964        " 'FLRLFLFFLFRLLRRFLFRFLLFFFLLRRFLF',\n",
 965        " 'LRFLFRFRLLRLRLRRLRRFLFRLRLFRLRRFLLRRLFFRFRRL',\n",
 966        " 'RFLLRFLFFFFLRFFLFLFLRFRFLRRLLFLFRL',\n",
 967        " 'LFFRLFRLLRFFLLRFLFFLRFRFFLLRLRLF',\n",
 968        " 'LRFRLFRFFLRRLRLFFRFFFRFLRFFFFRLR',\n",
 969        " 'LRFLFFFRRLLRFFFRRLFRFFRLLFLRFRFLRRLR',\n",
 970        " 'LLRRLFLFRLFFFFFFLLRLFRLRFLFFRFRLRFLLRFLFLRFLFFFF',\n",
 971        " 'FLFRFFRFLRFLLRFRFRLFRRLLRRFLFLRRFFLR',\n",
 972        " 'FRFFFRFFRRLLFRFLRFRLFLRRFRFLFFRFRL']"
 973       ]
 974      },
 975      "execution_count": 46,
 976      "metadata": {},
 977      "output_type": "execute_result"
 978     }
 979    ],
 980    "source": [
 981     "walks"
 982    ]
 983   },
 984   {
 985    "cell_type": "code",
 986    "execution_count": 47,
 987    "metadata": {},
 988    "outputs": [
 989     {
 990      "data": {
 991       "text/plain": [
 992        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
 993        " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
 994        " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
 995        " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
 996        " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
 997       ]
 998      },
 999      "execution_count": 47,
1000      "metadata": {},
1001      "output_type": "execute_result"
1002     }
1003    ],
1004    "source": [
1005     "trace_tour('FLLL')"
1006    ]
1007   },
1008   {
1009    "cell_type": "code",
1010    "execution_count": 48,
1011    "metadata": {},
1012    "outputs": [
1013     {
1014      "data": {
1015       "text/plain": [
1016        "(-1, 3)"
1017       ]
1018      },
1019      "execution_count": 48,
1020      "metadata": {},
1021      "output_type": "execute_result"
1022     },
1023     {
1024      "data": {
1025       "image/png": 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aZghIUsMMAUlqmCEgSQ3rFAJJPpzkn5McTXLeceo2J9mb5IdJru3SpiSpP11nAnuA/wz8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\n",
1026       "text/plain": [
1027        "<matplotlib.figure.Figure at 0x7f40411df278>"
1028       ]
1029      },
1030      "metadata": {},
1031      "output_type": "display_data"
1032     }
1033    ],
1034    "source": [
1035     "import matplotlib.pyplot as plt\n",
1036     "%matplotlib inline\n",
1037     "plt.axis('on')\n",
1038     "plt.arrow(0, 0, 0.8, 0, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
1039     "plt.arrow(0.2, 0, 0, 1, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
1040     "plt.xlim([-1, 2])\n",
1041     "plt.ylim([-1, 3])"
1042    ]
1043   },
1044   {
1045    "cell_type": "code",
1046    "execution_count": 49,
1047    "metadata": {
1048     "collapsed": true
1049    },
1050    "outputs": [],
1051    "source": [
1052     "def bounds(trace):\n",
1053     "    return (max(s.x for s in trace),\n",
1054     "            max(s.y for s in trace),\n",
1055     "            min(s.x for s in trace),\n",
1056     "            min(s.y for s in trace))"
1057    ]
1058   },
1059   {
1060    "cell_type": "code",
1061    "execution_count": 50,
1062    "metadata": {},
1063    "outputs": [
1064     {
1065      "data": {
1066       "text/plain": [
1067        "(0, 2, -13, -13)"
1068       ]
1069      },
1070      "execution_count": 50,
1071      "metadata": {},
1072      "output_type": "execute_result"
1073     }
1074    ],
1075    "source": [
1076     "bounds(trace_tour('RFRFFLRFLFFRRFFRRRRLLLRRRRRRFRLFRFFRFFRRFRLRRFLLFRLLFRFLFLFRFRLLFRLFRFLRRLLFRRRFRRRRLLFLFRFRRFFRRLLLRLRRFRLRRFFRRFLFRRLLRRFFRFRRRRRFLLLLLRRFFFLLFFFRRLFLFFLRRRFRFLLFFRRLLRFLLRRF'))"
1077    ]
1078   },
1079   {
1080    "cell_type": "code",
1081    "execution_count": 51,
1082    "metadata": {
1083     "collapsed": true
1084    },
1085    "outputs": [],
1086    "source": [
1087     "plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n",
1088     "           Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}"
1089    ]
1090   },
1091   {
1092    "cell_type": "code",
1093    "execution_count": 1198,
1094    "metadata": {
1095     "collapsed": true
1096    },
1097    "outputs": [],
1098    "source": [
1099     "def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None, filename=None):\n",
1100     "    plt.axis('on')\n",
1101     "    plt.axes().set_aspect('equal')\n",
1102     "    for s, t in chunks(trace, 2):\n",
1103     "        w, h = plot_wh[t.dir]\n",
1104     "        plt.arrow(s.x, s.y, w, h, head_width=0.1, head_length=0.1, fc=colour, ec=colour, length_includes_head=True)\n",
1105     "    xh, yh, xl, yl = bounds(trace)\n",
1106     "    if xybounds is not None:    \n",
1107     "        bxh, byh, bxl, byl = xybounds\n",
1108     "        plt.xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
1109     "        plt.ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
1110     "    else:\n",
1111     "        plt.xlim([xl-1, xh+1])\n",
1112     "        plt.ylim([yl-1, yh+1])\n",
1113     "    if filename:\n",
1114     "        plt.savefig(filename)"
1115    ]
1116   },
1117   {
1118    "cell_type": "code",
1119    "execution_count": 995,
1120    "metadata": {
1121     "collapsed": true
1122    },
1123    "outputs": [],
1124    "source": [
1125     "# def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None):\n",
1126     "#     plt.ioff()\n",
1127     "#     if fig is None:\n",
1128     "#         fig = plt.figure()\n",
1129     "#         ax = fig.gca()\n",
1130     "#     if subplot_details is not None:\n",
1131     "#         ax = fig.add_subplot(*subplot_details)\n",
1132     "#     plt.axis('on')\n",
1133     "# #     plt.axes().set_aspect('equal')\n",
1134     "#     ax.set_aspect('equal')\n",
1135     "#     for s, t in chunks(trace, 2):\n",
1136     "#         w, h = plot_wh[t.dir]\n",
1137     "#         ax.arrow(s.x, s.y, w, h, head_width=0.1, head_length=0.1, fc=colour, ec=colour, length_includes_head=True)\n",
1138     "#     xh, yh, xl, yl = bounds(trace)\n",
1139     "#     if xybounds is not None:    \n",
1140     "#         bxh, byh, bxl, byl = xybounds\n",
1141     "#         ax.set_xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
1142     "#         ax.set_ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
1143     "#     else:\n",
1144     "#         ax.set_xlim([xl-1, xh+1])\n",
1145     "#         ax.set_ylim([yl-1, yh+1])\n",
1146     "#     plt.close(fig)\n",
1147     "#     return fig"
1148    ]
1149   },
1150   {
1151    "cell_type": "code",
1152    "execution_count": 967,
1153    "metadata": {
1154     "collapsed": true
1155    },
1156    "outputs": [],
1157    "source": [
1158     "def pqr(p, q, r):\n",
1159     "    return '{}:{};{}'.format(p, q, r)"
1160    ]
1161   },
1162   {
1163    "cell_type": "code",
1164    "execution_count": 968,
1165    "metadata": {},
1166    "outputs": [
1167     {
1168      "data": {
1169       "text/plain": [
1170        "'1:2;3'"
1171       ]
1172      },
1173      "execution_count": 968,
1174      "metadata": {},
1175      "output_type": "execute_result"
1176     }
1177    ],
1178    "source": [
1179     "pqrt = (1, 2, 3)\n",
1180     "pqr(*pqrt)"
1181    ]
1182   },
1183   {
1184    "cell_type": "code",
1185    "execution_count": 1002,
1186    "metadata": {},
1187    "outputs": [
1188     {
1189      "data": {
1190       "image/png": 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kP1LxyGazsUcYkVKbFzRzMckrBu6+2d37wsMXgIb8RyoepfafXmrzgmYuJkleM/gnYGOC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\n",
1191       "text/plain": [
1192        "<matplotlib.figure.Figure at 0x7f4026af4b00>"
1193       ]
1194      },
1195      "metadata": {},
1196      "output_type": "display_data"
1197     }
1198    ],
1199    "source": [
1200     "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'))"
1201    ]
1202   },
1203   {
1204    "cell_type": "code",
1205    "execution_count": 1003,
1206    "metadata": {},
1207    "outputs": [
1208     {
1209      "data": {
1210       "image/png": 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mVpXUYCKSX7muDH4DjHX3I4HVwA25j1Q4MplM7BH6pdjmBc1cSHKKgbsvcPeO8PRFoCb3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\nAABJRU5ErkJggg==\n",
1211       "text/plain": [
1212        "<matplotlib.figure.Figure at 0x7f4026adc278>"
1213       ]
1214      },
1215      "metadata": {},
1216      "output_type": "display_data"
1217     }
1218    ],
1219    "source": [
1220     "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'), colour='g')"
1221    ]
1222   },
1223   {
1224    "cell_type": "code",
1225    "execution_count": 1004,
1226    "metadata": {},
1227    "outputs": [
1228     {
1229      "data": {
1230       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAADqCAYAAAChr/4gAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAEs9JREFUeJzt3HuM1eWdx/HPZ4Y6MzAFL1zacNOlVlubha5VsbbxrKuW\nS5VLJUq7va2NdrtE0qKVuk2Y/UOTEtta1m4vkbqrKSXUbgultlVLD6YiYIqIcpe0wsCKKNCKAsXh\nu3/MYRjGGeYM5zC/M/O8X8kv/i7P+T3fPIHP7+E556cjQgCA3q8q6wIAAN2DwAeARBD4AJAIAh8A\nEkHgA0AiCHwASETJgW97mO1ltjfYft72bR20m2d7q+21tseU2i8AoGv6lOEeb0n6SkSstV0v6Y+2\nH4uITcca2B4vaVREnG/7MknflzS2DH0DAIpU8gw/Il6OiLWF/QOSNkoa2qbZJEkPFdqskjTA9pBS\n+wYAFK+sa/i2z5U0RtKqNpeGStrR6nin3v5QAACcRmUL/MJyziOSZhZm+idcbucj/D8dAKAblWMN\nX7b7qDnsH46Ixe00aZQ0vNXxMEm72rkPDwEAOAUR0d7E+gTlmuH/SNKGiPhOB9eXSPqMJNkeK2l/\nROxur2FEsEVozpw5mddQKRtjwVgwFiffilXyDN/2FZI+Jel528+qeanmLkkjm/M7fhgRj9qeYPtF\nSW9I+nyp/QIAuqbkwI+IpyRVF9FuRql9AQBOHW/aVqhcLpd1CRWDsTiOsTiOseg6d2X953SzHZVU\nDwD0BLYV3filLQCgwhH4AJAIAh8AEkHgA0AiCHwASASBDwCJIPABIBEEPgAkgsAHgEQQ+ACQCAIf\nABJB4ANAIgh8AEgEgQ8AiSDwASARBD4AJILAB4BEEPgAkAgCHwASQeADQCIIfABIBIEPAIkg8AEg\nEWUJfNvzbe+2va6D61fa3m97TWH7ejn6BQAUr0+Z7vOgpP+U9NBJ2jwZEdeXqT8AQBeVZYYfEX+Q\ntK+TZi5HXwCAU9Oda/hjbT9r+1e239+N/QIAVL4lnc78UdLIiHjT9nhJv5D03vYaNjQ0tOzncjnl\ncrnuqA8Aeox8Pq98Pt/lzzkiylKA7ZGSfhkRf19E2z9Jujgi9rY5H+WqBwBSYVsR0emyeTmXdKwO\n1ultD2m1f6maHzR722sLADg9yrKkY3uBpJykc2xvlzRH0hmSIiJ+KOkG2/8q6Yikg5JuLEe/AIDi\nlW1JpxxY0gGArstiSQcAUMEIfABIBIEPAIkg8AEgEQQ+ACSCwAeARBD4AJAIAh8AEkHgA0AiCHwA\nSASBDwCJIPABIBEEPgAkgsAHgEQQ+ACQCAIfABJB4ANAIgh8AEgEgQ8AiSDwASARBD4AJILAB4BE\nEPgAkAgCHwASUZbAtz3f9m7b607SZp7trbbX2h5Tjn4BAMUr1wz/QUkf6+ii7fGSRkXE+ZJulfT9\nMvWblBUrVuiKK67QvHnzsi4lc8uXL9fYsWM1f/78rEvJVEToiSee0MUXX6yf/OQnWZeDCleWwI+I\nP0jad5ImkyQ9VGi7StIA20PK0XcKjgX9NddcoxUrVmjlypVZl5SZ5cuX65JLLtHEiRO1atUqrV69\nOuuSMnEs6MeMGaPJkydrzZo1WrNmTdZlocL16aZ+hkra0ep4Z+Hc7m7qv0dasWKF7rjjDq1du1Zv\nvvlm1uVkavny5br99tu1ceNGvfHGG1mXk5mI0O9+9zvNmjVL27ZtS3oscAoioiybpJGS1nVwbamk\nD7c6fkLSB9tpF4g4ePBgjB49Ompra0NS8tu5557LWBS2kSNHRl1dXeZ1VML2hS98Ieu/qhVDUkQR\nOd1dM/xGScNbHQ+TtKu9hg0NDS37uVxOuVzudNZVkbZs2aLnnntO9fX1qqur08GDB9/W5iMf+UgG\nlWVj+PDhWrx4sWpra3Xo0KG3XU9pLIYNG6YlS5aopqZGhw8fftv1VMZi69ateuCBBzRz5kx94AMf\nyLqcbpfP55XP57v+wWKeCsVsks6V9HwH1yZI+lVhf6yklR20O43PwJ7jueeeC0mxf//+mDNnTtTX\n158wq5s+fXrWJXa7vXv3xte+9rXo27fvCbP9W265JevSut2ePXti1qxZ0bdv36ipqWkZi9tvvz3r\n0rrFjh07ora2NmzHxIkTsy6nIqjIGX65fpa5QNIKSe+1vd32523favuWQoo/KulPtl+U9ANJXypH\nv73dgAED1NDQoMbGRn31q19VfX29+vTprn+UVZazzjpL99xzjxobG/XlL39Zffv2VXV1ddZlZWLg\nwIG699579dJLL2nGjBnq27evqqrSeaVmzpw5ampqUkRo2bJleuGFF7Iuqcdw88OhMtiOSqonK+vW\nrdPo0aPVdiz+8pe/6L777tPll1+ua6+9NqPqKsO+ffv0rW99S1dffbWuvPLKrMvJ1KuvvqpvfvOb\nmjx5si677LKsyzmtGhsbdf7557cs7VVVVWn8+PFaunRpxpVly7Yiwp22q6SAJfCbdRT4QOpuvvlm\nPfzwwzpy5EjLubq6Oq1evTrJtfxjig38dP4dCKBHa2xs1IIFC04Ie0k6fPiwZs+enVFVPQuBD6BH\nePLJJ3X48GHV1NS0nKupqVGfPn301FNP6a233sqwup6BwAfQI9x0003as2ePdu7cqbvvvluStHPn\nTu3atUvbt29P9gcNXcEIAegRqqqqdM4550hq/gWbpJZjFIcZPgAkgsAHgEQQ+ACQCAIfABJB4ANA\nIgh8AEgEgQ8AiSDwASARBD4AJILAB4BEEPgAkAgCHwASQeADQCIIfABIBIEPAIkg8AEgEQQ+ACSC\nwAeARBD4AJAIAh8AElGWwLc9zvYm21ts39nO9c/afsX2msL2L+XoFwBQvD6l3sB2laT7Jf2TpF2S\nnrG9OCI2tWm6MCJuK7U/AMCpKccM/1JJWyPipYg4ImmhpEnttHMZ+gIAnKJyBP5QSTtaHTcWzrU1\n1fZa24tsDytDvwCALih5SUftz9yjzfESSQsi4ojtWyX9j5qXgN6moaGhZT+XyymXy5WhRADoPfL5\nvPL5fJc/54i22dzFG9hjJTVExLjC8WxJERHf6KB9laS9EXFmO9ei1Hp6g3Xr1mn06NFiLID2ffe7\n39WMGTP4O1JgWxHR6bJ5OZZ0npH0HtsjbZ8h6SY1z+hbF/OuVoeTJG0oQ78AgC4oeUknIppsz5D0\nmJofIPMjYqPt/5D0TEQslXSb7eslHZG0V9LnSu0XANA15VjDV0T8RtIFbc7NabV/l6S7ytEXAODU\n8KYtACSCwAeARBD4AJAIAh8AEkHgA0AiCHwASASBDwCJIPABIBEEPgAkgsAHgEQQ+ACQCAIfABJB\n4ANAIgh8AEgEgQ8AiSDwASARBD4AJILAB4BEEPgAkAgCHwASQeADQCL6ZF0Amv3tb3/TT3/6U0nS\ntm3bJEk//vGPJUn19fWaNGlSZrUB6B0I/Arx9NNP69Of/rT69evXcu6LX/yijh49qoMHD+qVV17R\nwIEDM6wQQE/Hkk6F+OhHP6rzzjtPBw4c0IEDByRJBw4c0OHDhzVlyhTCHkDJyhL4tsfZ3mR7i+07\n27l+hu2Ftrfaftr2iHL025tUVVVp7ty5qq+vP+H8O97xDt1zzz0ZVQWgNyk58G1XSbpf0sckXSRp\nuu0L2zS7WdLeiDhf0n2S5pbab280ZcoUDR48uOW4urpaEyZM0AUXXJBhVd1j6tSpuu6667R+/fqs\nS8nc+PHj9YlPfEKbN2/OupTM5XI5TZ8+veV7LZQoIkraJI2V9OtWx7Ml3dmmzW8kXVbYr5a0p4N7\nReoeeeSRqK+vD0lRW1sbmzZtyrqkbjFixIioqqqKurq6+PjHPx7r16/PuqTMDBo0KKqqqqK2tjam\nTp0amzdvzrqkzPTv3z+qq6ujtrY2pk+fHtu2bYuIiPvvvz/Ii+MKY9FpXpdjSWeopB2tjhsL59pt\nExFNkvbbPrsMffc6x2b5tpOZ3R9z7AvqRx99VB/60Id0/fXXa8OGDVmXlYmjR4/q0KFDWrx4sUaP\nHq0bbrhBW7ZsybqsTDQ1NenQoUNatGiRLrroIn3yk5/Uq6++mnVZPZKbHw4l3MC+QdK1EXFL4fif\nJV0SETNbtXmh0GZX4fjFQpt9be4VpdbTGyxatEg33nhj1mVkrqqqeT5y5plnau/evRlXk63q6mpF\nhPr166fXX38963IyVV1draNHj7ZeGUiebUWEO2tXjp9lNkpq/SXsMEm72rTZIWm4pF22qyX1bxv2\nxzQ0NLTs53I55XK5MpTYs0ybNk1//vOftXLlyqxL6TY///nP33aurq5OZ599tsaPH689e/ZkUFU2\nOhqLwYMH66qrrtJrr72WQVXZ6Ggshg4dqrvvvjuDiipDPp9XPp/v+geLWfc52abmNfkXJY2UdIak\ntZLe16bNlyT9V2H/JkkLO7hX+Re30COMGDEiJIWk6NevX4wYMSIWLlwYTU1NWZfW7QYNGtQyFvX1\n9TFq1Kj42c9+luRY9O/f/4SxuPDCC2Pp0qVx9OjRrEurKCpyDb/kGX5ENNmeIekxNf/qZ35EbLT9\nH5KeiYilkuZLetj2VkmvFUIfOEFNTY2GDBmiuXPnatq0aS1LOimqra3V0KFDNXfuXE2ePDnpsair\nq9PIkSN17733asKECbI7XblAB0pewy8n1vDTNX/+fNXX1ycf9JL0ve99T0OGDEk+6CVp3rx5GjVq\nFEHfiWLX8Al8AOjhig38tKcPAJAQAh8AEkHgA0AiCHwASASBDwCJIPABIBEEPgAkgsAHgEQQ+ACQ\nCAIfABJB4ANAIgh8AEgEgQ8AiSDwASARBD4AJILAB4BEEPgAkAgCHwASQeADQCIIfABIBIEPAIkg\n8AEgEQQ+ACSCwAeARJQU+LbPsv2Y7c22f2t7QAftmmyvsf2s7V+U0icA4NQ4Ik79w/Y3JL0WEXNt\n3ynprIiY3U67v0ZE/yLuF6XUAwApsq2IcKftSgz8TZKujIjdtt8lKR8RF7bT7vWIeGcR9yPwAaCL\nig38UtfwB0fEbkmKiJclDeqgXY3t1bZX2J5UYp8AgFPQp7MGth+XNKT1KUkh6etd6GdERLxs+zxJ\ny2yvi4g/tdewoaGhZT+XyymXy3WhGwDo/fL5vPL5fJc/V+qSzkZJuVZLOr+PiPd18pkHJf0yIv63\nnWss6QBAF3XXks4SSZ8r7H9W0uJ2CjnT9hmF/YGSPixpQ4n9AgC6qNQZ/tmSFkkaLmm7pGkRsd/2\nxZJujYhbbF8u6QeSmtT8gPl2RPx3B/djhg8AXdQtv9IpNwIfALquu5Z0AAA9BIEPAIkg8AEgEQQ+\nACSCwAeARBD4AJAIAh8AEkHgA0AiCHwASASBDwCJIPABIBEEPgAkgsAHgEQQ+ACQCAIfABJB4ANA\nIgh8AEgEgQ8AiSDwASARBD4AJILAB4BEEPgAkAgCHwASQeADQCJKCnzbN9h+wXaT7X84SbtxtjfZ\n3mL7zlL6BACcmlJn+M9LmiJpeUcNbFdJul/SxyRdJGm67QtL7LfXy+fzWZdQMRiL4xiL4xiLrisp\n8CNic0RsleSTNLtU0taIeCkijkhaKGlSKf2mgD/MxzEWxzEWxzEWXdcda/hDJe1oddxYOAcA6EZ9\nOmtg+3FJQ1qfkhSS/j0ifllEH+3N/qO48gAA5eKI0rPX9u8lzYqINe1cGyupISLGFY5nS4qI+EY7\nbXkQAMApiIiTLa1LKmKG3wUddfaMpPfYHinp/yTdJGl6ew2LKRgAcGpK/VnmZNs7JI2VtNT2rwvn\n3217qSRFRJOkGZIek7Re0sKI2Fha2QCArirLkg4AoPJV3Ju2xb7M1Zvxoloz2/Nt77a9LutasmZ7\nmO1ltjfYft72bVnXlBXbNbZX2X62MBZzsq4pa7arbK+xveRk7Sou8FXEy1y9GS+qneBBNY8DpLck\nfSUi3i/pckn/luqfi4g4LOkfI+KDksZIGm/70ozLytpMSRs6a1RxgV/ky1y9GS+qFUTEHyTty7qO\nShARL0fE2sL+AUkblfD7LBHxZmG3Rs0/Pkl2bdr2MEkTJD3QWduKC3zwohpOzva5ap7Zrsq2kuwU\nljCelfSypMcj4pmsa8rQtyXdoSIeepkEvu3Hba9rtT1f+O91WdRTYXhRDR2yXS/pEUkzCzP9JEXE\n0cKSzjBJl9l+f9Y1ZcH2REm7C//6szpZGSnn7/CLFhHXZNFvD9EoaUSr42GSdmVUCyqI7T5qDvuH\nI2Jx1vVUgoj4q+28pHEqYg27F7pC0vW2J0iqk/RO2w9FxGfaa1zpSzopruO3vKhm+ww1v6h20m/e\ne7lOZy0J+ZGkDRHxnawLyZLtgbYHFPbrJF0taVO2VWUjIu6KiBER8XdqzoplHYW9VIGB39HLXKng\nRbXjbC+QtELSe21vt/35rGvKiu0rJH1K0lWFnyOusT0u67oy8m5Jv7e9Vs3fY/w2Ih7NuKYegRev\nACARFTfDBwCcHgQ+ACSCwAeARBD4AJAIAh8AEkHgA0AiCHwASASBDwCJ+H/mh3TR5lLJjgAAAABJ\nRU5ErkJggg==\n",
1231       "text/plain": [
1232        "<matplotlib.figure.Figure at 0x7f4027cd51d0>"
1233       ]
1234      },
1235      "metadata": {},
1236      "output_type": "display_data"
1237     }
1238    ],
1239    "source": [
1240     "plot_trace(trace_tour('FFFLLFFL'))"
1241    ]
1242   },
1243   {
1244    "cell_type": "code",
1245    "execution_count": 1005,
1246    "metadata": {},
1247    "outputs": [
1248     {
1249      "data": {
1250       "text/plain": [
1251        "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
1252        " Step(x=0, y=-1, dir=<Direction.DOWN: 3>),\n",
1253        " Step(x=0, y=-2, dir=<Direction.DOWN: 3>),\n",
1254        " Step(x=1, y=-2, dir=<Direction.RIGHT: 2>),\n",
1255        " Step(x=1, y=-1, dir=<Direction.UP: 1>),\n",
1256        " Step(x=2, y=-1, dir=<Direction.RIGHT: 2>),\n",
1257        " Step(x=3, y=-1, dir=<Direction.RIGHT: 2>),\n",
1258        " Step(x=3, y=0, dir=<Direction.UP: 1>),\n",
1259        " Step(x=3, y=1, dir=<Direction.UP: 1>),\n",
1260        " Step(x=3, y=2, dir=<Direction.UP: 1>),\n",
1261        " Step(x=3, y=3, dir=<Direction.UP: 1>),\n",
1262        " Step(x=3, y=4, dir=<Direction.UP: 1>),\n",
1263        " Step(x=2, y=4, dir=<Direction.LEFT: 4>),\n",
1264        " Step(x=2, y=5, dir=<Direction.UP: 1>),\n",
1265        " Step(x=2, y=6, dir=<Direction.UP: 1>),\n",
1266        " Step(x=2, y=7, dir=<Direction.UP: 1>),\n",
1267        " Step(x=1, y=7, dir=<Direction.LEFT: 4>),\n",
1268        " Step(x=0, y=7, dir=<Direction.LEFT: 4>),\n",
1269        " Step(x=0, y=6, dir=<Direction.DOWN: 3>),\n",
1270        " Step(x=0, y=5, dir=<Direction.DOWN: 3>),\n",
1271        " Step(x=1, y=5, dir=<Direction.RIGHT: 2>),\n",
1272        " Step(x=1, y=4, dir=<Direction.DOWN: 3>),\n",
1273        " Step(x=1, y=3, dir=<Direction.DOWN: 3>),\n",
1274        " Step(x=0, y=3, dir=<Direction.LEFT: 4>),\n",
1275        " Step(x=-1, y=3, dir=<Direction.LEFT: 4>),\n",
1276        " Step(x=-1, y=2, dir=<Direction.DOWN: 3>),\n",
1277        " Step(x=-2, y=2, dir=<Direction.LEFT: 4>),\n",
1278        " Step(x=-2, y=3, dir=<Direction.UP: 1>),\n",
1279        " Step(x=-3, y=3, dir=<Direction.LEFT: 4>),\n",
1280        " Step(x=-3, y=2, dir=<Direction.DOWN: 3>),\n",
1281        " Step(x=-3, y=1, dir=<Direction.DOWN: 3>),\n",
1282        " Step(x=-2, y=1, dir=<Direction.RIGHT: 2>),\n",
1283        " Step(x=-1, y=1, dir=<Direction.RIGHT: 2>),\n",
1284        " Step(x=-1, y=0, dir=<Direction.DOWN: 3>),\n",
1285        " Step(x=0, y=0, dir=<Direction.RIGHT: 2>)]"
1286       ]
1287      },
1288      "execution_count": 1005,
1289      "metadata": {},
1290      "output_type": "execute_result"
1291     }
1292    ],
1293    "source": [
1294     "trace_tour(walks[3])"
1295    ]
1296   },
1297   {
1298    "cell_type": "code",
1299    "execution_count": 1006,
1300    "metadata": {},
1301    "outputs": [
1302     {
1303      "data": {
1304       "image/png": 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HOHDgQOIsd+fVV19l+vTplJaWcvvtt0f5nJtKZ4x2yN05//zz2bFjBxdccEHivClTpkQY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\nFUMk4P8ANAvxgu/mStQAAAAASUVORK5CYII=\n",
1305       "text/plain": [
1306        "<matplotlib.figure.Figure at 0x7f4027bb3e80>"
1307       ]
1308      },
1309      "metadata": {},
1310      "output_type": "display_data"
1311     }
1312    ],
1313    "source": [
1314     "plot_trace(trace_tour(walks[3]))"
1315    ]
1316   },
1317   {
1318    "cell_type": "code",
1319    "execution_count": 57,
1320    "metadata": {},
1321    "outputs": [
1322     {
1323      "data": {
1324       "text/plain": [
1325        "10"
1326       ]
1327      },
1328      "execution_count": 57,
1329      "metadata": {},
1330      "output_type": "execute_result"
1331     }
1332    ],
1333    "source": [
1334     "long_walks = [w for w in walks if len(w) >= 30]\n",
1335     "len(long_walks)"
1336    ]
1337   },
1338   {
1339    "cell_type": "code",
1340    "execution_count": 58,
1341    "metadata": {},
1342    "outputs": [
1343     {
1344      "data": {
1345       "image/png": 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4CWaPBUT+ElgA3KeqV3wm+uoZ0wVVZfny5dxzzz3ceeedoWrV19ezevVqFixYwNChQ0PV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\nLJjGS/8Hemre+Ei14dEAAAAASUVORK5CYII=\n",
1346       "text/plain": [
1347        "<matplotlib.figure.Figure at 0x7f4027d30588>"
1348       ]
1349      },
1350      "metadata": {},
1351      "output_type": "display_data"
1352     }
1353    ],
1354    "source": [
1355     "plot_trace(trace_tour(long_walks[0]))"
1356    ]
1357   },
1358   {
1359    "cell_type": "code",
1360    "execution_count": 59,
1361    "metadata": {},
1362    "outputs": [
1363     {
1364      "data": {
1365       "image/png": 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tW7fSo0cPrrjiiqD1R44cyaZNm7j33ntj3UQFYNiwYezdu5ennnqKo446qvUfaIfCwkLu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\n",
1366       "text/plain": [
1367        "<matplotlib.figure.Figure at 0x7f4027d86518>"
1368       ]
1369      },
1370      "metadata": {},
1371      "output_type": "display_data"
1372     }
1373    ],
1374    "source": [
1375     "plot_trace(trace_tour(long_walks[1]))"
1376    ]
1377   },
1378   {
1379    "cell_type": "code",
1380    "execution_count": 60,
1381    "metadata": {},
1382    "outputs": [
1383     {
1384      "data": {
1385       "image/png": 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DoH///uzduzfhjqS5tIqQnD17NmPGjIk+tnXlypWMGjWKsrKyqHW3bt3K2LFjef7556PW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\nEZGA/wZbNepTD8ADbQAAAABJRU5ErkJggg==\n",
1386       "text/plain": [
1387        "<matplotlib.figure.Figure at 0x7f4027c0a8d0>"
1388       ]
1389      },
1390      "metadata": {},
1391      "output_type": "display_data"
1392     }
1393    ],
1394    "source": [
1395     "plot_trace(trace_tour(long_walks[2]))"
1396    ]
1397   },
1398   {
1399    "cell_type": "code",
1400    "execution_count": 61,
1401    "metadata": {},
1402    "outputs": [
1403     {
1404      "data": {
1405       "image/png": 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HOHDgQOIsd+fVV19l+vTplJaWcvvtt0f5nJtKZ4x2yN05//zz2bFjBxdccEHivClTpkQY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\nFUMk4P8ANAvxgu/mStQAAAAASUVORK5CYII=\n",
1406       "text/plain": [
1407        "<matplotlib.figure.Figure at 0x7f4027d86518>"
1408       ]
1409      },
1410      "metadata": {},
1411      "output_type": "display_data"
1412     }
1413    ],
1414    "source": [
1415     "plot_trace(trace_tour(long_walks[3]))"
1416    ]
1417   },
1418   {
1419    "cell_type": "code",
1420    "execution_count": 62,
1421    "metadata": {},
1422    "outputs": [
1423     {
1424      "data": {
1425       "image/png": 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MHDmSXr16JapVVVXF8OHDefzxx6OMg968eTMVFRX89re/TVyrK8t5WV4zmwhc7O7XZR5/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\n",
1426       "text/plain": [
1427        "<matplotlib.figure.Figure at 0x7f4027d88ac8>"
1428       ]
1429      },
1430      "metadata": {},
1431      "output_type": "display_data"
1432     }
1433    ],
1434    "source": [
1435     "plot_trace(trace_tour(long_walks[4]))"
1436    ]
1437   },
1438   {
1439    "cell_type": "code",
1440    "execution_count": 63,
1441    "metadata": {},
1442    "outputs": [
1443     {
1444      "data": {
1445       "image/png": 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twFH5y4OB7YF5UqKmTZsGwFVXXcXevXsLPE3xCS3adcD3zew1cke3kj5F+ZZbbuGUU07h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\nKppIAiqaSAIqmkgCKppIAiqaSAL/C/h8KF2f/R1oAAAAAElFTkSuQmCC\n",
1446       "text/plain": [
1447        "<matplotlib.figure.Figure at 0x7f4027db4390>"
1448       ]
1449      },
1450      "metadata": {},
1451      "output_type": "display_data"
1452     }
1453    ],
1454    "source": [
1455     "plot_trace(trace_tour(long_walks[5]))"
1456    ]
1457   },
1458   {
1459    "cell_type": "code",
1460    "execution_count": 64,
1461    "metadata": {},
1462    "outputs": [
1463     {
1464      "data": {
1465       "image/png": 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kKwhxJDMa2ODuG929EVgATApQV9LQkiVLMDOysrJYvnx5qtuRLiBEyJQAm/d7vKXla9IN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\n",
1466       "text/plain": [
1467        "<matplotlib.figure.Figure at 0x7f4027d1fcf8>"
1468       ]
1469      },
1470      "metadata": {},
1471      "output_type": "display_data"
1472     }
1473    ],
1474    "source": [
1475     "plot_trace(trace_tour(long_walks[6]))"
1476    ]
1477   },
1478   {
1479    "cell_type": "code",
1480    "execution_count": 65,
1481    "metadata": {},
1482    "outputs": [
1483     {
1484      "data": {
1485       "image/png": 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vXtr7V1VVcd999zF58mSmTZtGt27d4m5R2hBlRdh/A6YBow/5t1ZpRdj4DBkyhO9///u8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\nr2s6ANnE1QAAAABJRU5ErkJggg==\n",
1486       "text/plain": [
1487        "<matplotlib.figure.Figure at 0x7f4027ca70b8>"
1488       ]
1489      },
1490      "metadata": {},
1491      "output_type": "display_data"
1492     }
1493    ],
1494    "source": [
1495     "plot_trace(trace_tour(long_walks[7]))"
1496    ]
1497   },
1498   {
1499    "cell_type": "code",
1500    "execution_count": 66,
1501    "metadata": {},
1502    "outputs": [
1503     {
1504      "data": {
1505       "image/png": "iVBORw0KGgoAAAANSUhEUgAAARkAAAEACAYAAACHyQJEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
1506       "text/plain": [
1507        "<matplotlib.figure.Figure at 0x7f402c0d3588>"
1508       ]
1509      },
1510      "metadata": {},
1511      "output_type": "display_data"
1512     }
1513    ],
1514    "source": [
1515     "plot_trace(trace_tour(long_walks[8]))"
1516    ]
1517   },
1518   {
1519    "cell_type": "code",
1520    "execution_count": 67,
1521    "metadata": {},
1522    "outputs": [
1523     {
1524      "data": {
1525       "text/plain": [
1526        "['RFLFFLFFFFFFLRRLLRLFFFLFFFLRFRLLFFRR',\n",
1527        " 'FLRLFLFFLFRLLRRFLFRFLLFFFLLRRFLF',\n",
1528        " 'LRFLFRFRLLRLRLRRLRRFLFRLRLFRLRRFLLRRLFFRFRRL',\n",
1529        " 'RFLLRFLFFFFLRFFLFLFLRFRFLRRLLFLFRL',\n",
1530        " 'LFFRLFRLLRFFLLRFLFFLRFRFFLLRLRLF',\n",
1531        " 'LRFRLFRFFLRRLRLFFRFFFRFLRFFFFRLR',\n",
1532        " 'LRFLFFFRRLLRFFFRRLFRFFRLLFLRFRFLRRLR',\n",
1533        " 'LLRRLFLFRLFFFFFFLLRLFRLRFLFFRFRLRFLLRFLFLRFLFFFF',\n",
1534        " 'FLFRFFRFLRFLLRFRFRLFRRLLRRFLFLRRFFLR',\n",
1535        " 'FRFFFRFFRRLLFRFLRFRLFLRRFRFLFFRFRL']"
1536       ]
1537      },
1538      "execution_count": 67,
1539      "metadata": {},
1540      "output_type": "execute_result"
1541     }
1542    ],
1543    "source": [
1544     "walks"
1545    ]
1546   },
1547   {
1548    "cell_type": "code",
1549    "execution_count": 68,
1550    "metadata": {},
1551    "outputs": [
1552     {
1553      "data": {
1554       "image/png": 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2WNK1JH91f1tmDqEfEWwFZpvZQUlfA54luWXzZJK/7PZ0qzHcGDbMMoXjPGNmp0g6GnhW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\n8v89qQ80wuYWhQAAAABJRU5ErkJggg==\n",
1555       "text/plain": [
1556        "<matplotlib.figure.Figure at 0x7f402c0babe0>"
1557       ]
1558      },
1559      "metadata": {},
1560      "output_type": "display_data"
1561     }
1562    ],
1563    "source": [
1564     "plot_trace(trace_tour('FLFFLRFRLFRRRR'))"
1565    ]
1566   },
1567   {
1568    "cell_type": "code",
1569    "execution_count": 69,
1570    "metadata": {},
1571    "outputs": [
1572     {
1573      "data": {
1574       "text/plain": [
1575        "(310, [])"
1576       ]
1577      },
1578      "execution_count": 69,
1579      "metadata": {},
1580      "output_type": "execute_result"
1581     }
1582    ],
1583    "source": [
1584     "w = random_walk()\n",
1585     "ms = mistake_positions(w)\n",
1586     "len(ms), returns_to_origin(ms)"
1587    ]
1588   },
1589   {
1590    "cell_type": "code",
1591    "execution_count": 70,
1592    "metadata": {},
1593    "outputs": [
1594     {
1595      "data": {
1596       "image/png": 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4BuzPuLRMdHS0Ko21u+j1enndOp1OtUsMQEC/aDqdzqUt3PqaEhISwtJ+rkXS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\nRK5CYII=\n",
1597       "text/plain": [
1598        "<matplotlib.figure.Figure at 0x7f402c0b97f0>"
1599       ]
1600      },
1601      "metadata": {},
1602      "output_type": "display_data"
1603     }
1604    ],
1605    "source": [
1606     "plot_trace(trace_tour(w))"
1607    ]
1608   },
1609   {
1610    "cell_type": "code",
1611    "execution_count": 1216,
1612    "metadata": {},
1613    "outputs": [],
1614    "source": [
1615     "def trim_loop(tour, random_mistake=False):\n",
1616     "    trace = trace_tour(tour)\n",
1617     "    mistakes = mistake_positions(trace)\n",
1618     "    if random_mistake:\n",
1619     "        end_mistake_index = random.randrange(len(mistakes))\n",
1620     "    else:\n",
1621     "        end_mistake_index = 0\n",
1622     "#     print('end_mistake_index {} pointing to trace position {}; {} mistakes and {} in trace; {}'.format(end_mistake_index, mistakes[end_mistake_index].i, len(mistakes), len(trace), mistakes))\n",
1623     "    # while this mistake extends to the next step in the trace...\n",
1624     "    while (mistakes[end_mistake_index].i + 1 < len(trace) and \n",
1625     "           end_mistake_index + 1 < len(mistakes) and\n",
1626     "           mistakes[end_mistake_index].i + 1 == \n",
1627     "           mistakes[end_mistake_index + 1].i):\n",
1628     "#         print('end_mistake_index {} pointing to trace position {}; {} mistakes and {} in trace'.format(end_mistake_index, mistakes[end_mistake_index].i, len(mistakes), len(trace), mistakes))\n",
1629     "        # push this mistake finish point later\n",
1630     "        end_mistake_index += 1\n",
1631     "    mistake = mistakes[end_mistake_index]\n",
1632     "    \n",
1633     "    # find the first location that mentions where this mistake ends (which the point where the loop starts)\n",
1634     "    mistake_loop_start = max(i for i, loc in enumerate(trace[:mistake.i])\n",
1635     "                             if (loc.x, loc.y) == (mistake.step.x, mistake.step.y))\n",
1636     "#     print('Dealing with mistake from', mistake_loop_start, 'to', mistake.i, ', trace has len', len(trace))\n",
1637     "    \n",
1638     "    # direction before entering the loop\n",
1639     "    direction_before = trace[mistake_loop_start].dir\n",
1640     "    \n",
1641     "    # find the new instruction to turn from heading before the loop to heading after the loop\n",
1642     "    new_instruction = 'F'\n",
1643     "    if (mistake.i + 1) < len(trace):\n",
1644     "        if turn_left(direction_before) == trace[mistake.i + 1].dir:\n",
1645     "            new_instruction = 'L'\n",
1646     "        if turn_right(direction_before) == trace[mistake.i + 1].dir:\n",
1647     "            new_instruction = 'R'\n",
1648     "#     if (mistake.i + 1) < len(trace):\n",
1649     "#         print('turning from', direction_before, 'to', trace[mistake.i + 1].dir, 'with', new_instruction )\n",
1650     "#     else:\n",
1651     "#         print('turning from', direction_before, 'to BEYOND END', 'with', new_instruction )\n",
1652     "    return tour[:mistake_loop_start] + new_instruction + tour[mistake.i+1:]\n",
1653     "#     return mistake, mistake_loop_start, trace[mistake_loop_start-2:mistake_loop_start+8]"
1654    ]
1655   },
1656   {
1657    "cell_type": "code",
1658    "execution_count": 299,
1659    "metadata": {},
1660    "outputs": [
1661     {
1662      "data": {
1663       "text/plain": [
1664        "'RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF'"
1665       ]
1666      },
1667      "execution_count": 299,
1668      "metadata": {},
1669      "output_type": "execute_result"
1670     }
1671    ],
1672    "source": [
1673     "w = 'RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF'\n",
1674     "w"
1675    ]
1676   },
1677   {
1678    "cell_type": "code",
1679    "execution_count": 238,
1680    "metadata": {},
1681    "outputs": [
1682     {
1683      "data": {
1684       "image/png": 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1685       "text/plain": [
1686        "<matplotlib.figure.Figure at 0x7f4027310390>"
1687       ]
1688      },
1689      "metadata": {},
1690      "output_type": "display_data"
1691     }
1692    ],
1693    "source": [
1694     "w_short = w[:100]\n",
1695     "plot_trace(trace_tour(w_short))"
1696    ]
1697   },
1698   {
1699    "cell_type": "code",
1700    "execution_count": 214,
1701    "metadata": {},
1702    "outputs": [
1703     {
1704      "name": "stdout",
1705      "output_type": "stream",
1706      "text": [
1707       "turning from Direction.UP to Direction.UP with F\n",
1708       "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n",
1709       "RFFRRFFFRFFRFLLRFLFFFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n"
1710      ]
1711     },
1712     {
1713      "data": {
1714       "image/png": 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1715       "text/plain": [
1716        "<matplotlib.figure.Figure at 0x7f40274ccbe0>"
1717       ]
1718      },
1719      "metadata": {},
1720      "output_type": "display_data"
1721     }
1722    ],
1723    "source": [
1724     "trimmed = trim_loop(w_short)\n",
1725     "print('{}\\n{}'.format(w_short, trimmed))\n",
1726     "plot_trace(trace_tour(trimmed))"
1727    ]
1728   },
1729   {
1730    "cell_type": "code",
1731    "execution_count": 215,
1732    "metadata": {},
1733    "outputs": [
1734     {
1735      "name": "stdout",
1736      "output_type": "stream",
1737      "text": [
1738       "turning from Direction.UP to Direction.LEFT with L\n",
1739       "RFFRRFFFRFFRFLLRFLFFFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n",
1740       "RFFRRFFFRFFRFLLRFLFFLLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n"
1741      ]
1742     },
1743     {
1744      "data": {
1745       "image/png": 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kBnQDtgATW/l3X4t4TWJmzpyp+fn5vhZ3X3LJJUm1Mw0YMMDXnC+99NK0tF8BumDBAs/z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\n",
1746       "text/plain": [
1747        "<matplotlib.figure.Figure at 0x7f40271e3240>"
1748       ]
1749      },
1750      "metadata": {},
1751      "output_type": "display_data"
1752     }
1753    ],
1754    "source": [
1755     "trimmed2 = trim_loop(trimmed)\n",
1756     "print('{}\\n{}'.format(trimmed, trimmed2))\n",
1757     "plot_trace(trace_tour(trimmed2))"
1758    ]
1759   },
1760   {
1761    "cell_type": "code",
1762    "execution_count": 250,
1763    "metadata": {},
1764    "outputs": [
1765     {
1766      "data": {
1767       "text/plain": [
1768        "[Mistake(i=104, step=Step(x=-4, y=6, dir=<Direction.DOWN: 3>)),\n",
1769        " Mistake(i=105, step=Step(x=-5, y=6, dir=<Direction.LEFT: 4>)),\n",
1770        " Mistake(i=106, step=Step(x=-5, y=7, dir=<Direction.UP: 1>)),\n",
1771        " Mistake(i=107, step=Step(x=-5, y=8, dir=<Direction.UP: 1>)),\n",
1772        " Mistake(i=108, step=Step(x=-5, y=9, dir=<Direction.UP: 1>)),\n",
1773        " Mistake(i=115, step=Step(x=-5, y=12, dir=<Direction.LEFT: 4>)),\n",
1774        " Mistake(i=116, step=Step(x=-5, y=11, dir=<Direction.DOWN: 3>)),\n",
1775        " Mistake(i=127, step=Step(x=2, y=11, dir=<Direction.LEFT: 4>)),\n",
1776        " Mistake(i=130, step=Step(x=3, y=11, dir=<Direction.UP: 1>)),\n",
1777        " (132, Step(x=3, y=11, dir=<Direction.UP: 1>))]"
1778       ]
1779      },
1780      "execution_count": 250,
1781      "metadata": {},
1782      "output_type": "execute_result"
1783     }
1784    ],
1785    "source": [
1786     "mistake_positions(trace_tour(w[:130]))[-10:]"
1787    ]
1788   },
1789   {
1790    "cell_type": "code",
1791    "execution_count": 288,
1792    "metadata": {},
1793    "outputs": [
1794     {
1795      "name": "stdout",
1796      "output_type": "stream",
1797      "text": [
1798       "Step(x=40, y=36, dir=<Direction.UP: 1>)\n"
1799      ]
1800     },
1801     {
1802      "data": {
1803       "image/png": 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4BuzPuLRMdHS0Ko21u+j1enndOp1OtUsMQEC/aDqdzqUt3PqaEhISwtJ+rkXS\n0tJU7711KnpSsrbQzzpBEESAIUVLOIVzjttvvx2MMXkAQK9evUIiCwCMHTtWJY/yECYFa3m9cXsL\nZ1auXGlzb5KTkx3eN3HExMSoytHR0Tb3MjMzM8RXF34wT1dwPR7A4hge0DGIwGE2m6HT6TBgwABp\nHjh//jw2bNgQkgWPjz76CEuWLJFf+oKCAvTu3Rt1dXUALKl8iouLZdCSpqYm6HQ6/Pe//21VpgNx\nf8R9KC4uxoABA1BWVgbA4inT3NyMpKQkuYvr5MmTGDFihNwdWFlZia5du6K6uhqA5YfuwoULyMnJ\nQXp6erAvSfO0BI2yuwpLipZwCWMMW7duDQtvii1btiArK6vVhzhMSEjwyhWO8B5nipZMBwRBEAGG\nvA4It3jnnXewefNmAJbtldOnT7dZbdYCynxUWkhX884776C4uFjG6W3bti3q6+ulbFVVVUhJSZFu\naY2NjTJ+q3ATbGxsxJYtW+T9bmxsxNChQ3HZZZcBsFxzamqqzKIM2A+Q/d577+H8+fPSIyMjIwNT\np07VxH2KdMh0QLgkMTERNTU1qnOxsbEy44SW+P7773HjjTfCbDaHXIEcPHhQBr8OBj///DNGjx4N\n4NJ7Jr57x44ds5syfubMmZg/f37QZIxkyHRA+IR1wBVAu7nR3E0lFAyUi0jKezd06FBXEe9QXl6u\nKvfv31+WhcK010YgFgcF4ofSuo0/gwgRjiFFS3hFuKZ91gLeeD8odxu68yPi7hbj1uSJEUpI0RIR\nhT0zlfU5b+v4QxZ/9OWoX2fjkfkutNC0hPCY3r17e7VtNxi4k0DTXT766CPcd999XrcX8RbMZrMq\ntsLOnTtV8vXt21fG1RUZOZSZHgBg9+7dDq9JKFFlFDnh3mXdxro8dOhQj66J8A5StITHHD16NNQi\nOGTkyJE4cOAACgsL5bmGhgZV0ByxiUGYP0wmE8xms2qlfvz48Vi0aJFPilY87lsHsLn11lsxc+ZM\nAMCf/vQnHD58WL7WoUMHbN68Gdu3b5fnZs+ejZiYGKxbtw4AMGvWLOzbt0++LpSn0gukqKgIAPDd\nd98BsKT8+ctf/iLLgEVBjx8/3uvrI9yHFC3hFVq20V511VW46qqrfO4nUAtqAwYMwE033QTAspXZ\nOjdZVlaWKjrZ7NmzodPpZJvMzEyVonWGaJOamqoqE8GFbLQEQRABhvxoCZfcc889+PTTT+WjtfWj\nNmMM2dkTSjNoAAAfgklEQVTZePHFF0Mppl9hjCEqKkquyhsMBgwaNEjaUg0GA7p27Yr8/HxZZ/v2\n7Rg9erTNfdLr9WCMySwP0dHR0q6qzPygHNub74zS9GGvX4AWxQIJxTogfMLdR2gtbBLwFx9//DH+\n+Mc/qvxRe/fubWOf3rhxI2688UYAQM+ePXHq1CmXfXurSP0BfRcDB21YIHxm69atKkd3vV4vy2KB\nJVKULADcd999MiiLOI4cOWLj8K/MrnH+/HkAlzYFPP3006qyaPPUU0/J8i233GK3Tn19vao8bNgw\nWb7tttvstlm3bp2qrKyza9eugN0rwjWkaAmCIAKMdpeOiZBx4MAB1ZZNANi7d69qxhpJs1d3OXjw\noGpbLaDewir8WLdt2wYAOHfunKpsD9GPqCPK//znP1W7wWpqamQdEVPWmgMHDtj434o2wrZMhAhn\ne65b3vRMAD8AOARgP4C/tJxPAfAdgKMAvgWQ5KA9J8KH119/nQNweTz77LOyzbp16zgAbjabQyh5\nYFmyZInd+7B48WJZ5+6773br3u3YsUO2+fTTT91qY+8QmM1mrtPp3GpjNBqDet9aEy3viV096o7p\nwAjgSc55PwCjATzGGOsDIBvAJs557xZFPNuNvgiNIxz9uZX9T2mjNZlMeOWVV2QbsUsskme5xcXF\nAGzvS1VVlazzySefqF7funWrTRuTyYQRI0bINpMnT4bJZLKpY11WnlPee8By341Go6qNyEhs/YWn\n2AahwaWi5ZwXc87zWv6vBXAYllnuRAArWqqtAPDrQAlJBA93ttZa73SKZAUrsBff1RX27ou9NOfW\n5+yVlee8kYUILR4thjHGugMYDGA7gI6c8xLAoowBXOZv4QiC8A4txgpuzbitaBlj7QB8DuCJlpkt\nOeRFIOILap35VDwq20Mk93NWJ9wRmV+t78uzzz7rMKNsoHKsZWRk2MgSExOD06dPyzo069UWbnkd\nMMb0sCjZDznna1pOlzDGOnLOSxhj6QBKHbV/4YUX5P/W+7gJbZGTkwMAePrpp+Xj6tChQzFmzBiH\nbZS+pJHKgw8+iKNHj8JoNEo7Z1JSkspGK1LQCKqrq+VmBn9y33334dChQ2huboZOpwPnHK+++ipy\nc3PRvXt3AEB8fLxmg7NHCjk5OfL74gq3doYxxj4AcIFz/qTi3KsAKjjnrzLGngGQwjnPttOWR/JM\nJ9IYPXo0tm/f7tHsdOPGjRg/fnxEz2i1DmMM69atw4QJEwBQFtxQ4GxnmMsZLWNsDID7AexnjOXC\nYjJ4FsCrAD5ljP0ewFkAk/0nMkEQROTgUtFyzrcCcOQT4v/nIsIuBw8exL333ivtc4AlDUlNTY1M\nW9K+fXvs3r0b3bp1A2DZJltcXIzU1FRpBkhISMC5c+fkI25SUhLy8vLQo0cPAJcc28eNGyc9EFJT\nU3H48GF07NhR9vHmm2+ic+fOAC7ZaInQ8pe//AWLFy8GANTW1oZYGkIJBZUJEy6//HKbuKXWxMfH\n2yTls0an03msGNu1a2f3iyve13Xr1uHOO++MqKAy4cbAgQOxf/9+1bmFCxeqUpATgcUn0wGhDfLz\n8xEXF+dSkQYDa2UqtoqSkg0d7gYCJ0IDBZUhvELLGRYIQmuQog0j6uvr5f+cc1UZQFBnu0pzUGtw\n7yIIX6BpSZjQp08fHDlyxOXj+datW/3qKG82m+3ujzeZTDaycM7JfEAQdqAZbZhw6NAh1NfXy6O2\nthZlZWWqcwDw008/+XVc4a2wadMm1TgAUFBQgIKCAsyaNQsA2WgJwhE0ow0TGGOqlNmAxcsgWLRt\n21Y1vl6vl65m1jFQCYJQQzNagiCIAEMz2jBh6dKleOSRR1zWu3jxYkDGt451YDQayUZLEG5CijZM\nEEpWBI0+ceIEKioq0LZtW0RFRcFsNqOhoQGJiYl+HVd4FOh0OukvK7wbhOmiubkZEyZMICVLEA4g\nRRtGxMXFYceOHQCAr776ChMmTFAtTjHG/B5BXyyG/fjjj9KbgTEGvV5P2zwJwk3IRksQBBFgaEYb\nRiiDORsMBrt1RPZaR/z000/Yvn27LNfV1SE2NlbOhKuqqpCWliazu4pxPvroI5kDizHmVsobJY2N\njfjf//1flecCYwyNjY2IiYkBACQnJ+Phhx+2m+6FIMIZUrRhhHI3llBG1gtQKSkpDttfuHAB1113\nnVdjv/3226ryP/7xD4/az5gxA++++67LeitXrsQPP/zgUd8EoXVI0YYR1dXV8n8xA7VegBIzUXuI\nxStPo6kxxnzecXbw4EGXYzPGKNcVEZHQM1oYIeLORjLCs4EgIglStGGKo5mhckYbyDjA1n27Kmsh\nvCNBhApStGHCddddh/r6epn19I477gBgq9DmzJkj60RFRWHy5EsZhoSys4765QzhR6tcfMvOzkZU\nVJQqC6urcm5ursuxkpKS0L59e7dlI4hwgTIshAnV1dXYuHGj6tF68ODBqtQ2ZWVl2LlzpyzPnDkT\nx48fl8q4rq4O7dq18zgTAmMMP/74I6699lpZ1uv1+PLLL2WdpqYmREdHy35NJhPMZrPKU2Ls2LFO\nzR+MMVx55ZU4duyY27IRhFZwlmGBFG0EM3LkSOzcuVMq2oaGBsTFxfm8GCYUrSMXM29hjCErKwub\nN2/2a78EEQycKVoyHRAEQQQYUrQRzNmzZwFYkiu2a9fO7mP7Bx98AMaYrJOWloa4uDjodDp5DrAE\nlRH2VuBSUBlxdO7cWdbX6XRITk5GU1OTQ9k453j00UdlG2ESEeMRRCRBpoMIJjc3FxMnTsS5c+fk\nuUGDBiEvL0+WAxkI5rXXXpNBwa2prKy0u7kiPz9fpj4niHCCTAetlKuvvhpnz54F51weSiUrGD9+\nvKqO9QEA77zzjqoMQJa/++47VVlpE3ZEQkKCTRvOOSlZIiIhRUsQBBFgQr4Ft7S0VPVo29TUhGHD\nhnkctITwntOnT2P37t0ALLbX/Px8mEwmAJf8aD/88EO7s2Elu3btUpkiaJMCQVgIqY3WaDSq/CwF\nU6dOxfLlywMqF2GhR48eOH36tMftdDqd3IVWUFCALl262NSZOHGiytdWycWLF5GamoqamhpaACMi\nAs3aaPV6y4T68OHDKtve119/HUqxWhWnTp1S2Ug7duwIwNbeumTJElVZOXPNzMyE0Wi0aVNZWelw\nXJEJgpQs0RogGy2hwlGGBlfeCfba+TvbA0GEK5pUtI2NjaEWodXirinJWThGT/siiEgnpIpWLLj0\n7dtX5QwfjAj7W7duVTncOzrefPPNgMuiJcTGAeU9UJ5X4uy+AcDmzZsdvi7MRgTRGgjpp118IW+6\n6SYMGDAAgMW/cvbs2QEfWyjQJ598EoBlFv32229j3LhxGDRoEABg/vz5mDlzJmbMmBFwebTC2LFj\ncerUKVx99dWIioqC0WhE3759MXXqVJu6Q4cOBQAUFRWhsLBQ3kuTyYTq6mokJyfL97isrAydOnWS\nM+G6ujoMGTIkSFdFECHGmaO6Pw7LEI4BwL/66iundQLB9OnTubVsAPhnn32mKicnJwdbtJCSnZ1t\nc1+sAcD1er0sf/fddy7bEESk0/IdsKsHNWmjJQiCiCRC6kdrMpmg1+sxYsQIpKenAwBKSkqQmZkp\nQ/CdP38e/fv3x8WLFwFYHvH1er3Kxnfu3Dn06dNHOsiXl5ejR48eMseWeJRNS0uTDvg//fQTLl68\niFtvvRVt2rSB2WzG+vXrkZSUJDO1FhcXo0OHDigpKQnAnQk8VVVVePLJJ3HhwgUAFt/Vrl27yky5\nZrMZFy9eRIcOHaS9fNu2bSgrK3O6kBUXFweDwYDbbrsNgOU927FjB8aNGyfzkvXu3Rtz586ljSdE\nq8GZH607j/7vAygBsE9xLgXAdwCOAvgWQJKT9g6n2s3NzRyAyyM+Pt6tesojJibG4zb2jl69evn5\nASN4XHnllTbX06ZNG5fX/Jvf/MZpv8uWLXPr3j377LNBulKCCD3w0XSwDMDNVueyAWzinPcG8AMA\nr1avxK4w5YYFe0dtba3HtuHGxkanr0+fPh2ArWP+3r17VeXS0lJvLk0T2Avc0tzc7PLeffHFF077\nfeihh1T1HQWViYmJCewFEkSY4FLRcs7/C+Ci1emJAFa0/L8CwK/9LBfhB0LtQhXIEIwEEU54uxjW\ngXNeAgCc82IAl/lPJFuchdvzFncDnjjbRhqOWN9Lk8lkE6Dbuk5DQ4PKZss5V9UR9l2CIOwT0imP\n8Kl0thPs8OHD6Nevn835DRs24NZbb/V6bOG3az3ruuyyS78ZHTt2VJXDjQkTJmDnzp1Bm1lajyNy\njBFEa8dbRVvCGOvIOS9hjKUDcGrIfOGFF+T/WVlZyMrKsgze8mjrbGV63759ANQzy+TkZBw5csQn\nRTtz5kw88sgjqtlYU1MTOnToIMslJSVO07FonTlz5uDhhx+WngAAUFtbi/j4eKkUDQYDzGazyp5a\nW1urCvZSV1eHuLg4VYbbxsZG2e+mTZtw1113qd6jhoYG6UlCEJFITk4OcnJy3KrrrqJlLYdgLYCH\nALwKYCqANc4aKxWtPdzZcpuUlKQq+8NtKNIjR4lcXkqs76M9rOu4aiMicSnruTMOQYQzykkjALz4\n4osO67rUcIyxjwH8DKAXY+wsY+x3AOYBuIkxdhTAjS3liET43RIEQXiNp25Tnh5w4kdrNpvd9me1\n9ldzdcTGxrr0H3300UdV/fbr18/l2Nb88Y9/tKn/xhtvyNebmpr4qFGjbOocP37cab9a5oMPPvD4\nPhFEpAMnfrSayLCQkpKCbt26AbDYX/Py8tC9e3fAIjmefvpp3HfffbLdwoUL8dxzz8lEfnFxccjP\nz0fHjh2lHTElJQWnTp1CcnIyACAvLw9RUVEYOHAgAODAgQMyWLVCVqSlpclsAWlpaVi6dKmUxcH1\noVOnTjJg9v79+2EymWS/JSUlSE9Px6BBg8AYg9FoxIEDBzBp0iSsXr3ao3upFcQ9Hjx4MABLhoVp\n06Y5fXQiiEjHp51hvh7QSFAZALxz586y7CiozN69ez3ud/78+bI8ePBgVb+VlZV2x5kwYYJH42gJ\nQB1UhiAI33eGEQRBED4QUj9a3vJ4/eWXX+L48eMALK5EsbGxMg1KXV0dsrKy/OKTWVNTgwULFgCw\nBJUBLHFpW6b8AFw732/YsEHKam+h7MSJEwAgxxEuT6+99prKU0KZ+ddfnDlzRpUMsaamBvfff780\nsdjj4sWL+OCDD1RtkpOT5X0wGo1gjNmkpbGXVJMgCPuE1Ebb2NgoI2W5wlc53XHa1+v1OHfunEP/\nz7Vr12LixIk25/Pz86UyS0pKklHDnPHxxx/j3nvvdVnPE+xdY+fOnXH+/HmP2rhDVFQU7QgjCAWa\nzYIr0qM4CyqzatUqv413++23Ow0qYzAYnDrZi51s1jIqZ4xig4N4Tcxordv4W8kK/v73v8sxRowY\ngcLCQpdtrrvuOk/t7uT2RhAe0KpstL5Gk3Jn9heMfGf+Ht9ePjCCIPyH5hStctYkyv7sW9Dc3Oy3\nfpV4kx3W+pr9RW1trcux/YX1DNfeOIE2UxGEVolIG21FRQUuu+wytx5vPen3888/x+TJk2E2m1UZ\ne50plYMHD6J///4u+x4yZAh2797ttixHjhxB37593a5vTzbAYsMtKipSvd6lSxecPXvWYXu9Xu8X\n+6xOp0NVVZUqFgNBhCvObLQh9ToQq/CzZ8/G8OHDAQCTJk0CY0zlzC9ecxcRKGX16tVSIU6aNAnD\nhw9XZdi9/vrrPepXKG6lCYFzjm7duuGee+4BALzxxhsqJSTiKShlaWxsRHR0tHzMX7p0KTZs2OCR\nLEePHgUAGaSbc47f/va3mDx5srT/PvXUUzh58qSsU19fjwceeEDVz65du7BlyxZpPnj33Xfx7bff\nOh27tLQUr7zyigwKdPLkSaxevVp1jSaTCSaTSb7HJpMJRqNRmm+MRiPuvvtut39oCSKs8WQRxJsD\nHm5YAMBbZsFeU1paaneTwKRJk3zq94svvrDb78SJE2W5bdu2qjpnzpxxuT31ySef9HgL6/r16+3K\nMm/ePFkeMWKEqk59fb3LcdzJgmuNN1lwjUYjbdslIgrQhgWCIIjQEVRFW1RUhOuvvx6pqalITU2V\nTvC33367PAdYZtmizBjDjBkzPBqHt9ggGWOIioqSj+inT5/2Sf6qqipVv+Ixec2aNVJekXkgOTkZ\nqampqgDjos7o0aNVNtDy8nKPZRFjR0dHq+5ddnY2GGNgjGHnzp2qNiKrhKifmJgIxhi6du0qz82b\n53kgNqVLmyPy8/MxfPhwOY4wOyjvy4gRI3Dq1CmPxycIzeNoquuvA4rHw9/+9rc2EZ/0er2q3K5d\nOx4dHe1TZKiSkhK70aWGDBni2bOAFbfffrvb0cZcHcOGDZP9zpo1y+NrbG5ulmYKV4cgPz/frfoz\nZ870SJavvvrKpfw9e/Z0a+zevXt7NDZBaAVoxXSQlpYGwHaTgLJcU1ODpqYmWfZmw4KY7XG1wnca\nhcsdxLZT637nz58vy2JxR5TPnDljt41yY4Q3zv9t2rRBfX29Tb+9evVy6C4mgnE7+jCIY/78+R7L\n4goRgFyMYW/zBwB06tTJo7EJIhwgGy1BEESACap7l5i17N+/X55LTU1FRkaGwzYGg8GmTX19PeLi\n4mS5qakJffr0ka5U9sZRnnfE2bNnUVFRIW3H1vm03MmIK+yVwj2tpKQEgCX3maOdZSI2gpCXc442\nbdp45SdbU1NjE+dWlIWNmXPu14SN7mzSsEa8F87uC0FEDK4eI309oLDdCTcg6+PEiRMO7R47d+50\ny7antL+WlZXZrXP11Vc7HIdbhHXrMBqNqjbKjAqJiYlu9fHJJ5/INitXrrRb5/Tp007l9Vb+2tpa\nj/p1xYYNGzgAbjabHda5+eabVXZcEafX+li+fLlfZSOIYAGt2GhvuukmmdWAX1LETrfDDh8+3EZo\n6z769euHPXv2yDbt27e3p/CdRrES7N271+FYs2bNAgCbkIHKGZ2YgYs29oLKCGd9wZQpU+zKW1ZW\n5lJea1588UWn98poNPp9J5bSg8ARxcXFqnJSUpLd93Xq1Kl+lY0gtEDQbbTWSgrwPFSfvT7cQSgE\nb8dyFLDF09is3srvDtaBc6zHCuTYzkhISHBZJ1SyEUSgiYjFMGEXdYWYKQYSitFKEIQ1IQ0q0/K6\nyz5GjRqFbdu2yfKQIUOQm5vrtE3Pnj1x9OhRp4+1HTp0kItVJpPJqxmvu3hyn92VpU2bNtJUIVi+\nfHnQH7+/++473HzzzS7rJSYmygU5gog0NBtUBgBWrFiBTZs2SR9PvV6P4uJitG/fHoAlKPj333+v\napObm4uhQ4di9OjRAICVK1eivLwcjz32GBhjqKurw7Jly2zGioqKwlVXXSX7LS0tla/pdDps3rwZ\nn3/+uVTKixYtAgC5u6uoqAgXLlyQ4xgMBrz77rsYNGgQrr32WgAWhRoTEyPtzjU1NRg1apRH90Sn\n02HLli349NNPpSwVFRVIS0uTCruiogIZGRlyJ5rIKPzggw96NJY/uOmmm7Bs2TIZfcxoNMJgMKgC\nxpSWlmLOnDlBl40gNIGjVTJ/HfBwx5M1q1atstl1BIAvWrRIlvv166eq4yiojDIL7oABA1zuZgLA\nk5OTZdlRUBllFlyCIFon0IrXAUEQRGsk5KYDd5kwYYLqUVSZPeDYsWOqurzl8frmm29GYmKiPF9c\nXIzJkycDuJStVsmCBQvw5ZdfSrMFYNmkIMYVC13WstTU1Hh9XQRBRD4hXwxzRVVVFZKTk1XnEhIS\nkJubi8svvxwAMG7cOOzZswcXL14EYLHhDhkyxK3+lbJ5s0MpPj4eu3fvRu/evT1uSxBE5KDZLLju\nYM+xvbq6WipZwDJTVW6PFdkCuNpWjE6dOsnyY489Znc85YYFgSj/+te/tum3traWlCxBEE7RvKL1\nJ8oZK+2vJwgiWESEorUO9uLIVKHcKusoNGGgTSkEQbQ+wmYxzBk9e/ZUKVsR08B61lpaWmpzzro8\nePBgm/5dtVm/fj1uv/12zwUnCKJVEBEz2oqKCtTX18uy8AgoKSlBaWmp3JiQmJgoy+fPn8eOHTtw\n6NAheQDAe++9p2qTkJAgy++99x4AyLKoYx2OkSAIQklEzGitETPODh06qM63a9cOl112mSyLqP9K\nUlJSVHV0Op0sC7cv5euAbSAXgiAIJRExow2kXZVstgRB+EpEzGgLCgoAuLalFhYWqs499thjMp6B\nWChTmiAAix+vq379Hd+VIIjIwqcNC4yxWwC8CcvM+H3O+at26vi0YcEdoqOjYTAY5CN8U1MT9Hq9\n3Mklxu/bt69UkocPH1b5y4qIWR9++CEeeOABITsAoF+/fgCAkydPoqmpSZYbGhqQkJCAPXv2UCxV\ngmjlBCR6F2MsCsAiAOMAFAL4hTG2hnN+xNs+veXKK6/EoUOH0NjY6Habxx9/XM5mgUtBp8VmBwFj\nDAcPHgQA/Oc//8GkSZNkmSAIwh18sdGOAHCcc36Gc24AsArARP+IRRAEETn4YqPNAHBOUS6ARfkG\nHXu7vGpra2VWXHtcuHBBVRYmhGeeeQbz5s1TnV+yZAkAYOfOnf4QlyCIVoYvitaeLcKuMfaFF16Q\n/2dlZSErK8uHYV0jAtE4sw137dpVlQOsrq4OAJCfn29Td9q0afJ/ZWQvgiBaLzk5OcjJyXGrri+K\ntgBAV0U5ExZbrQ1KRRsIhJIUOMuqK6ivr1dtwxWz39dffx3/8z//A8AyU2aMOdyuSxBE68V60vji\niy86rOuLjfYXAFcwxroxxqIBTAGw1of+vCYuLi4UwxIEQbiF1zNazrmJMTYdwHe45N512G+SBRh3\nZr0AbVggCMJ3fNoZxjn/hnPem3N+Jed8nusWgSEjIwMdO3aUZWFKcObuJYKJC/OAWFCbNWuWqkz+\nsQRB+IrmMyy4Q7t27VBXVydnn2VlZejQoYPL2ejGjRtRUVEBwLIz7IEHHsDcuXNxxRVXAACmTJmC\nlJQUWYcgCMIRzjYsRISiveqqq3Do0CGPFa01jDHs3bsXAwcOlOXk5GSZIocgCMIRYZ3KhiAIItyJ\niKAyCQkJqrKwzTY1NXkcwnDQoEEqe6919gaCIAhPiYgZ7ZEj6vAKer3l9yM6OtqjfkaNGgXAEjC8\npKQEiYmJ2Lhxo3+EJAii1RIRM9qMjAxUVVXJslC0niZg3LZtm1/lIgiCACJkRksQBKFlImJGKzh6\n9CgAoLy8PMSSEARBXCIiZrR/+MMfAAB9+vRBnz59MGbMGADONywQBEEEi4hQtDNnzoTBYJAZEzjn\n2Lx5s00Qby3jbhQgrUDyBpZwkjecZAVCI29EKFrg0gKYgN78wELyBpZwkjecZAVI0RIEQUQkpGgJ\ngiACTFBiHQR0AIIgCI0QsqAyBEEQrR0yHRAEQQQYUrQEQRABJiIVLWPsFsbYEcbYMcbYM6GWxxrG\n2PuMsRLG2D7FuRTG2HeMsaOMsW8ZY0mhlFHAGMtkjP3AGDvEGNvPGPtLy3mtyhvDGNvBGMttkff5\nlvPdGWPbW+RdyRjT1K5IxlgUY2wPY2xtS1mz8jLGTjPG9rbc450t57T6eUhijH3GGDvMGDvIGBsZ\nClkjTtEyxqIALAJwM4CrANzLGOsTWqlsWAaLfEqyAWzinPcG8AOA2UGXyj5GAE9yzvsBGA3gsZb7\nqUl5OedNAMZyzq8GMBjArYyxkQBeBfBGi7yVAB4OoZj2eALAIUVZy/KaAWRxzq/mnI9oOafJzwOA\nBQA2cM77AhgE4AhCIatyN1UkHABGAfhaUc4G8Eyo5bIjZzcA+xTlIwA6tvyfDuBIqGV0IPeXAG4M\nB3kBxAHYBWAEgFIAUYrPyDehlk8hZyaAjQCyAKxtOVemYXlPAUizOqe5zwOABAAn7ZwPuqwRN6MF\nkAHgnKJc0HJO63TgnJcAAOe8GMBlIZbHBsZYd1hmidth+aBqUt6Wx/BcAMWwKLCTACo55+aWKgUA\nOodKPjv8H4CnAHAAYIylAbioYXk5gG8ZY78wxv7Qck6Ln4eeAC4wxpa1mGXeY4zFIQSyRqKitefH\nRj5sPsIYawfgcwBPcM5roeF7yjk3c4vpIBOW2Wxfe9WCK5V9GGO3AyjhnOfh0meXwfZzrAl5W7iG\ncz4MwG2wmJKuhbbkE+gBDAGwmHM+BEAdLE+4QZc1EhVtAYCuinImgMIQyeIJJYyxjgDAGEuH5VFX\nE7QsxHwO4EPO+ZqW05qVV8A5rwawBZZH7+QW+z2grc/EGAB3MsbyAawEcAOANwEkaVReMQsE57wM\nFlPSCGjz81AA4BznfFdLeTUsijfoskaiov0FwBWMsW6MsWgAUwCsDbFM9rCetawF8FDL/1MBrLFu\nEEL+BeAQ53yB4pwm5WWMtReryIyxtrDYkw8B2Axgcks1zcjLOX+Wc96Vc94Tls/qD5zzB6BReRlj\ncS1PN2CMxQMYD2A/NPh5aDEPnGOM9Wo5NQ7AQYRC1lAbrANkBL8FwFEAxwFkh1oeO/J9DMsMpQnA\nWQC/A5ACYFOL3BsBJIdazhZZxwAwAcgDkAtgT8v9TdWovANaZMwDsA/AX1vO9wCwA8AxAJ8AaBNq\nWe3Ifj0uLYZpUt4WucRnYb/4fmn48zAIlslXHoAvACSFQlbagksQBBFgItF0QBAEoSlI0RIEQQQY\nUrQEQRABhhQtQRBEgCFFSxAEEWBI0RIEQQQYUrQEQRABhhQtQRBEgPn/Hr9Pu8XImnAAAAAASUVO\nRK5CYII=\n",
1804       "text/plain": [
1805        "<matplotlib.figure.Figure at 0x7f4027beb4a8>"
1806       ]
1807      },
1808      "metadata": {},
1809      "output_type": "display_data"
1810     }
1811    ],
1812    "source": [
1813     "w_tour_start = w #[:250]\n",
1814     "print(trace_tour(w_tour_start)[-1])\n",
1815     "plot_trace(trace_tour(w_tour_start))"
1816    ]
1817   },
1818   {
1819    "cell_type": "code",
1820    "execution_count": 289,
1821    "metadata": {},
1822    "outputs": [
1823     {
1824      "name": "stdout",
1825      "output_type": "stream",
1826      "text": [
1827       "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF\n",
1828       "RFFRRFFFRFLRFRFLLRFLLRLRRLFRLRRFFLLRLLRRFRFLRLFFLFLRRLRRLRLFLLRRFFLRLLFFFFFRRFFLFRLFFRLLRRFLFFFLRFLRRLRFLFLFFRLLFFRRFFLRLFRFFRLFFLRRFLRFLRRLFRRLFFFFRLFLFFLRFFLFRFLRRFFFFFLFRLRRFRLLRLLFRFLFFFRLFRFLFLRLRFFFFFLFFRFFFFLRFLFRFLRLRLFFLRRFFFRLLFRLFLRRFLRLLRLFFRFLRRLFLLRFLFFRFLFRLRFFFFFLRLLFRFLLRRFLRRFLRLRFLRRLFFFRFLRRLF\n",
1829       "Step(x=40, y=36, dir=<Direction.UP: 1>)\n"
1830      ]
1831     },
1832     {
1833      "data": {
1834       "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
1835       "text/plain": [
1836        "<matplotlib.figure.Figure at 0x7f4026fcb9b0>"
1837       ]
1838      },
1839      "metadata": {},
1840      "output_type": "display_data"
1841     }
1842    ],
1843    "source": [
1844     "w_tour = w_tour_start\n",
1845     "w_trace = trace_tour(w_tour)\n",
1846     "mks = mistake_positions(w_trace)\n",
1847     "while len(mks) > 1:\n",
1848     "#     print(len(mks))\n",
1849     "    w_tour = trim_loop(w_tour)\n",
1850     "    w_trace = trace_tour(w_tour)\n",
1851     "    mks = mistake_positions(w_trace)\n",
1852     "print('{}\\n{}\\n{}'.format(w_tour_start, w_tour, trace_tour(w_tour)[-1]))\n",
1853     "plot_trace(trace_tour(w_tour))"
1854    ]
1855   },
1856   {
1857    "cell_type": "code",
1858    "execution_count": 950,
1859    "metadata": {},
1860    "outputs": [],
1861    "source": [
1862     "def trim_all_loops(tour, mistake_reduction_attempt_limit=10):\n",
1863     "    trace = trace_tour(tour)\n",
1864     "    mistake_limit = 1\n",
1865     "    if trace[-1].x == 0 and trace[-1].y == 0:\n",
1866     "        mistake_limit = 0\n",
1867     "    mistakes = mistake_positions(trace)\n",
1868     "    \n",
1869     "    old_mistake_count = len(mistakes)\n",
1870     "    mistake_reduction_tries = 0\n",
1871     "    \n",
1872     "    while len(mistakes) > mistake_limit and mistake_reduction_tries < mistake_reduction_attempt_limit:\n",
1873     "        tour = trim_loop(tour)\n",
1874     "        trace = trace_tour(tour)\n",
1875     "        mistakes = mistake_positions(trace)\n",
1876     "        if len(mistakes) < old_mistake_count:\n",
1877     "            old_mistake_count = len(mistakes)\n",
1878     "            mistake_reduction_tries = 0\n",
1879     "        else:\n",
1880     "            mistake_reduction_tries += 1\n",
1881     "    if mistake_reduction_tries >= mistake_reduction_attempt_limit:\n",
1882     "        return ''\n",
1883     "    else:\n",
1884     "        return tour"
1885    ]
1886   },
1887   {
1888    "cell_type": "code",
1889    "execution_count": 306,
1890    "metadata": {},
1891    "outputs": [
1892     {
1893      "data": {
1894       "text/plain": [
1895        "'RFFRRFFFRFLRFRFLLRFLLRLRRLFRLRRFFLLRLLRRFRFLRLFFLFLRRLRRLRLFLLRRFFLRLLFFFFFRRFFLFRLFFRLLRRFLFFFLRFLRRLRFLFLFFRLLFFRRFFLRLFRFFRLFFLRRFLRFLRRLFRRLFFFFRLFLFFLRFFLFRFLRRFFFFFLFRLRRFRLLRLLFRFLFFFRLFRFLFLRLRFFFFFLFFRFFFFLRFLFRFLRLRLFFLRRFFFRLLFRLFLRRFLRLLRLFFRFLRRLFLLRFLFFRFLFRLRFFFFFLRLLFRFLLRRFLRRFLRLRFLRRLFFFRFLRRLF'"
1896       ]
1897      },
1898      "execution_count": 306,
1899      "metadata": {},
1900      "output_type": "execute_result"
1901     }
1902    ],
1903    "source": [
1904     "w_trimmed = trim_all_loops(w)\n",
1905     "w_trimmed"
1906    ]
1907   },
1908   {
1909    "cell_type": "code",
1910    "execution_count": 304,
1911    "metadata": {},
1912    "outputs": [
1913     {
1914      "data": {
1915       "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
1916       "text/plain": [
1917        "<matplotlib.figure.Figure at 0x7f40271d91d0>"
1918       ]
1919      },
1920      "metadata": {},
1921      "output_type": "display_data"
1922     }
1923    ],
1924    "source": [
1925     "plot_trace(trace_tour(trim_all_loops(w)))"
1926    ]
1927   },
1928   {
1929    "cell_type": "code",
1930    "execution_count": 309,
1931    "metadata": {
1932     "collapsed": true
1933    },
1934    "outputs": [],
1935    "source": [
1936     "def reverse_tour(tour):\n",
1937     "    def swap(tour_step):\n",
1938     "        if tour_step == 'R':\n",
1939     "            return 'L'\n",
1940     "        elif tour_step == 'L':\n",
1941     "            return 'R'\n",
1942     "        else:\n",
1943     "            return tour_step\n",
1944     "        \n",
1945     "    return ''.join(swap(s) for s in reversed(tour))"
1946    ]
1947   },
1948   {
1949    "cell_type": "code",
1950    "execution_count": 308,
1951    "metadata": {},
1952    "outputs": [
1953     {
1954      "data": {
1955       "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
1956       "text/plain": [
1957        "<matplotlib.figure.Figure at 0x7f4027562b38>"
1958       ]
1959      },
1960      "metadata": {},
1961      "output_type": "display_data"
1962     }
1963    ],
1964    "source": [
1965     "plot_trace(trace_tour(w_trimmed))"
1966    ]
1967   },
1968   {
1969    "cell_type": "code",
1970    "execution_count": 310,
1971    "metadata": {},
1972    "outputs": [
1973     {
1974      "data": {
1975       "image/png": 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ZmUHGpTOGE4saVopgjOGFF15g9OjRAFxwwQUJ1ii9UcNKIc4991wuuuiiRKuhoH2slECd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\ngjJMbcJZvAAAAABJRU5ErkJggg==\n",
1976       "text/plain": [
1977        "<matplotlib.figure.Figure at 0x7f40275594e0>"
1978       ]
1979      },
1980      "metadata": {},
1981      "output_type": "display_data"
1982     }
1983    ],
1984    "source": [
1985     "plot_trace(trace_tour(reverse_tour(w_trimmed)))"
1986    ]
1987   },
1988   {
1989    "cell_type": "code",
1990    "execution_count": 575,
1991    "metadata": {},
1992    "outputs": [
1993     {
1994      "data": {
1995       "image/png": 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3QD61kj8AsmTJkrAi4sSJE0PW5+fnRxVjw4mIgVNH2rVrZ9ONRkSsS2nKDPba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\nAAAAAElFTkSuQmCC\n",
1996       "text/plain": [
1997        "<matplotlib.figure.Figure at 0x7f4026efc4e0>"
1998       ]
1999      },
2000      "metadata": {},
2001      "output_type": "display_data"
2002     }
2003    ],
2004    "source": [
2005     "w1 = random_walk()\n",
2006     "w2 = random_walk()\n",
2007     "plot_trace(trace_tour(w1))\n",
2008     "w1bounds = bounds(trace_tour(w1))\n",
2009     "plot_trace(trace_tour(w2), colour='r', xybounds=w1bounds)"
2010    ]
2011   },
2012   {
2013    "cell_type": "code",
2014    "execution_count": 562,
2015    "metadata": {},
2016    "outputs": [
2017     {
2018      "name": "stdout",
2019      "output_type": "stream",
2020      "text": [
2021       "w1 = 'FFRFFRRFFFRRFRFRFRLFRRLLFFLRFFLLRFLLRRLFFLLLFLRRFFLLLFLFLRFRRLRRFLLLFFRRFRFRRRRFRRRFLRLLRRRFRFFFLFLRLFFLRFLRLFLRRFFRRFFLFLRFLLFRFLLRRRLLFFRLLRRLFRRFLLLRLRLLLLRRRRRRFFLRRRFLLLLRFRRFRFLRLFRFLFLLLLLFFFLFRLLLRLRFRRFRRRRLRFFRRFRLRFFRLRFLLFLLLRLRFFRLRFFRFLRRLLRRRFFRLRLFLRFLLRLFFRFFLFFFFFLFFLFLLLFLFRFLLFRLFRFRFLFFRRLLFRLRFRFFLRFRFFLRFFLFFLFRLRFRLLRFRRRRFRFRRFRRRRFLFRFLFFLFLFFRFLFFFFLLRRFFLLRFRRFLFRFLLRLRLRRFFLFFLFFRLFLLRFFLRRFLFLRRRRFLFFLFRLFFFRRLFRLFLLFRRLFLFFRRLRLRFFFFFFRFRRRRFLLLFRFRFRFLRFFRFRRRRFFFFRLFRRLLFLLLRRLFLFRLRLLRRFFLRRFRLFLLFRLLRRLLRLFLRRFLLLRFLRFRFFFFRFLLLRRFRFFFFFRFRLRFFLFFLRLLRFRLRFLRLRLRFRFRLLLLFFLFRLRLLRFRRLRLFLLRFLLRRLRRFRLLFRFRLFLLRFRLFLRLLLLLFRFFRLLFFLLFRLFLRFRFLFFRRRFRFRRFRFFRLFFRRLRRRLLLFLFRFRRRFFFRFFFFRRFLRLLLRFFFFFRLRLRLLLLFRRRLFRLFRRLRFFFLFFLRFRFRFFFFFRLFLLRFRRRFFLFLFFFLRRFLLLLFLFFLRRLLLRLRRFFRLRLLRFRLRRLRRRFRFLLRLFFLLFFLLLLRRLRFLLRFRRRRRRRLRFFRFLFLRLLFFRFRRRLRLRLLFLRLFLFRLRLRRRLLLLFFFRFFRFFFFLLFLLLLRRLFFRLLFFFFRRRLFRFLRFLLFRLLRLRFLRRFFRRRRLRLFFFFLLFLFFFLRFFLRLRFRFLL\n",
2022       "w2 = 'FFFLRFFLLFFRFRFLFLRLLLRRRLRRLFFFLFRFLRRFFRLFRRLFRRFRRLLFLLFFFFRFLLFRFFFFLFRFFRFLFRRLFRRLFRRRRLLFRRLFRRRLFFFFFLFLRLFFLRLLRFFLFLRLFLRLLRLLLRLLRFLFFRFRFLRRLLLRFLFFFLFRFFRLFRFLLLRLFFLFFLFRFRFFFFFRLLRLFLLRRFLFFFLRFLFFLLLFFRRRRFLLRFFRFLRRFLLFFFFRFLLRRLRFRLRLRLRLRRLRFLRLFLLRLFLFRLFRFRLLRFFLRLRRLFRLRFFRRFLLLRFFLLFRRLRRRFRLRLRRLFFRLFRRRRRFLFRFLLRLFFRFLFRLFRLRFRFRFLLRLRLFLRLFLLFRFRRFRFLLLFFFRLLLLFFFRFLLLFRLRFRLRRLLFLLLRFLLFRFFRRRRLRFRLFLRLRLLRFLRLRFRLRFRLLRFLFRRLRRLFRFLRLRRFLRRLRFLRRRRLFLFLFLFLRRFFFLLFRFRLLFLFRRLLLRRRLLLRFRFFRFRFFLLFFLFRFLRFRRLLLLLRFRLLRRRFRRRLRLRLFRRRRLRFRFRLLRLRFLLFLLFFLFLFRRLLLLLFFFRFRFRFRRLRFLFLLRRFLLLFFRLRRLLFRRLLRLFLLLFFLRFFLLFRLLRRLFFFRLRFLRLFRRLRRLRRFRFFRLLLFRLLFLLRFFRLFLLFFFRLFRFFLRRLFLFRLLRLRFFLRLFFRFRFRRFFRFFLFFFFFFFRFRFFRLLLRFLFRLRLLLLRFFRLLFFFLLLLRFRFFLFRFFRRFFFRFRRLFLLFFRRLFLFFRFRFRLFFRLRFFLLFFFLLRRFFFFFFLRFLLRRRFFLFFFRFLFFFRLFFRLRRFFRRRRLFFLRFLLFRFFRLFFRRLFRRRFFFRFLFRFFRFFFRFRRRRRLRLLLLFFFRLRLLLFRLRRLFRFRFLFLRRLRFRFFRFRLLRLRFLLLRLRFLFFRLRLLRFLLLFFRRFFFLLLFRRRLFFRL\n"
2023      ]
2024     }
2025    ],
2026    "source": [
2027     "print(\"w1 = '{}\".format(w1))\n",
2028     "print(\"w2 = '{}\".format(w2))"
2029    ]
2030   },
2031   {
2032    "cell_type": "code",
2033    "execution_count": 725,
2034    "metadata": {
2035     "collapsed": true
2036    },
2037    "outputs": [],
2038    "source": [
2039     "def wander_near(locus, current, limit=10):\n",
2040     "    valid_proposal = False\n",
2041     "    while not valid_proposal:\n",
2042     "        s = random.choice('FFFRL')\n",
2043     "        if s == 'F':\n",
2044     "            proposed = advance(current, current.dir)\n",
2045     "        elif s == 'L':\n",
2046     "            proposed = advance(current, turn_left(current.dir))\n",
2047     "        elif s == 'R':\n",
2048     "            proposed = advance(current, turn_right(current.dir))\n",
2049     "        if abs(proposed.x - locus.x) < limit and abs(proposed.y - locus.y) < limit:\n",
2050     "            valid_proposal = True\n",
2051     "#     print('At {} going to {} by step {} to {}'.format(current, locus, s, proposed))\n",
2052     "    return s, proposed"
2053    ]
2054   },
2055   {
2056    "cell_type": "code",
2057    "execution_count": 1192,
2058    "metadata": {},
2059    "outputs": [],
2060    "source": [
2061     "def seek(goal, current):\n",
2062     "    dx = current.x - goal.x\n",
2063     "    dy = current.y - goal.y\n",
2064     "\n",
2065     "    if dx < 0 and abs(dx) > abs(dy): # to the left\n",
2066     "        side = 'left'\n",
2067     "        if current.dir == Direction.RIGHT:\n",
2068     "            s = 'F'\n",
2069     "        elif current.dir == Direction.UP:\n",
2070     "            s = 'R'\n",
2071     "        else:\n",
2072     "            s = 'L'\n",
2073     "    elif dx > 0 and abs(dx) > abs(dy): # to the right\n",
2074     "        side = 'right'\n",
2075     "        if current.dir == Direction.LEFT:\n",
2076     "            s = 'F'\n",
2077     "        elif current.dir == Direction.UP:\n",
2078     "            s = 'L'\n",
2079     "        else:\n",
2080     "            s = 'R'\n",
2081     "    elif dy > 0 and abs(dx) <= abs(dy): # above\n",
2082     "        side = 'above'\n",
2083     "        if current.dir == Direction.DOWN:\n",
2084     "            s = 'F'\n",
2085     "        elif current.dir == Direction.RIGHT:\n",
2086     "            s = 'R'\n",
2087     "        else:\n",
2088     "            s = 'L'\n",
2089     "    else: # below\n",
2090     "        side = 'below'\n",
2091     "        if current.dir == Direction.UP:\n",
2092     "            s = 'F'\n",
2093     "        elif current.dir == Direction.LEFT:\n",
2094     "            s = 'R'\n",
2095     "        else:\n",
2096     "            s = 'L'\n",
2097     "    if s == 'F':\n",
2098     "        proposed = advance(current, current.dir)\n",
2099     "    elif s == 'L':\n",
2100     "        proposed = advance(current, turn_left(current.dir))\n",
2101     "    elif s == 'R':\n",
2102     "        proposed = advance(current, turn_right(current.dir))\n",
2103     "        \n",
2104     "#     print('At {} going to {}, currently {},  by step {} to {}'.format(current, goal, side, s, proposed))\n",
2105     "\n",
2106     "    return s, proposed"
2107    ]
2108   },
2109   {
2110    "cell_type": "code",
2111    "execution_count": 1145,
2112    "metadata": {
2113     "collapsed": true
2114    },
2115    "outputs": [],
2116    "source": [
2117     "def guided_walk(loci, locus_limit=5, wander_limit=10, seek_step_limit=20):\n",
2118     "    trail = ''\n",
2119     "    current = Step(0, 0, Direction.RIGHT)    \n",
2120     "    l = 0\n",
2121     "    finished = False\n",
2122     "    while not finished:\n",
2123     "        if abs(current.x - loci[l].x) < locus_limit and abs(current.y - loci[l].y) < locus_limit:\n",
2124     "            l += 1\n",
2125     "            if l == len(loci) - 1:\n",
2126     "                finished = True\n",
2127     "        s, proposed = wander_near(loci[l], current, limit=wander_limit)\n",
2128     "        trail += s\n",
2129     "        current = proposed\n",
2130     "#     print('!! Finished loci')\n",
2131     "    seek_steps = 0\n",
2132     "    while not (current.x == loci[l].x and current.y == loci[l].y) and seek_steps < seek_step_limit:\n",
2133     "#         error = max(abs(current.x - loci[l].x), abs(current.y - loci[l].y))\n",
2134     "#         s, proposed = wander_near(loci[l], current, limit=error+1)\n",
2135     "        s, proposed = seek(loci[l], current)\n",
2136     "        trail += s\n",
2137     "        current = proposed\n",
2138     "        seek_steps += 1\n",
2139     "    if seek_steps >= seek_step_limit:\n",
2140     "        return ''\n",
2141     "    else:\n",
2142     "        return trail"
2143    ]
2144   },
2145   {
2146    "cell_type": "code",
2147    "execution_count": 896,
2148    "metadata": {},
2149    "outputs": [
2150     {
2151      "data": {
2152       "image/png": 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FIBNJl6SFQEV+muMwZFu3buWGG25QGDKRAEKHIVsFPOHufxk9LykEWfRehSETqYDQYcgs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\nEKlyKgREqpwKAZEqp0JApMr9P8nYgJi0MFyGAAAAAElFTkSuQmCC\n",
2153       "text/plain": [
2154        "<matplotlib.figure.Figure at 0x7f4027b86898>"
2155       ]
2156      },
2157      "metadata": {},
2158      "output_type": "display_data"
2159     }
2160    ],
2161    "source": [
2162     "def square_tour(a=80):\n",
2163     "    \"a is width of square\"\n",
2164     "    return ('F' * a + 'L') * 4\n",
2165     "\n",
2166     "plot_trace(trace_tour(square_tour()))"
2167    ]
2168   },
2169   {
2170    "cell_type": "code",
2171    "execution_count": 898,
2172    "metadata": {},
2173    "outputs": [
2174     {
2175      "data": {
2176       "image/png": 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k6yMEKDzGmzHGPSUtKopIo4g8KSJxEXlbRG4WkWYReU5E+kXkuIg0rvT+6urqghdbGGPc\nUV1dXfImw7eAZ1W1C/gNoI/cvR1fUNUjwAngoZXenMlkrB+CMWWSyWRK12QQkTDwr1X1cQBVXVDV\nceBu4AlntieA311pGY2NjdZT0ZgyKuUAKdcBwyLyuIi8JiLfEZF6oF1VEwCqegloW2kB4+PjVlQ0\npowWFhZWfX0jCSEA3Ah8W1VvBKbJNRe0mIWcPHmSnp4eYrHYBkIxxqwkFovR09MDwIsvvrjqvKJa\n1Pf3n98o0g78P1W9znn+r8glhANAVFUTItIBvOjUGK58v9bX1/OJT3yC733ve+uKwRizdjU1NXzt\na1/jwQcfRFWXPd2w7iMEp1lwXkQOO5M+DLwNPAPc70y7D3h6pWXMzMzYvR2NKZNUKlWwqLh6haGw\nzwHfF5EgcBr4DFAN/EhEHgDOAfes9OaGhgYrKhpTRoX6/WwoIajqG8BNy7x0x1rePz09zcTExEZC\nMMYUodBtDzzvqVio55Qxxj2FaoaeJoTt27fT2LhiR0ZjjItqamoKDmrsaUKYmJhgcHDQyxCM2TLm\n5+f9faOW2tpau/zZmDLy9TDsc3NzTE1NeRmCMVuK74dQs5u9GlM+pey6vGEtLS3WZDCmTEKhkL/v\n7TgyMkIikfAyBGO2jFQqxczMzKrzeJoQqqqqaGpq8jIEY7aUUl7+vGHZbLbgaRBjjHt8X1QsVOQw\nxrgnnU6v+rrd29GYLSIQCFBXV7fqPJ7f29F6KhpTHgsLC/7uqQgQDoe9DsGYLaPQ5c+eJ4RCbRpj\njHt8fZYBLCEYU05zc3Orvu5pQohEIlZUNKaMfN1TcXh42MZUNKaMfF9ULHQaxBjjHt8XFdc7DLwx\npni+LyoWKnIYY9yTSqVWfd16Khqzhfh6TMVkMkkymfQyBGO2FN8XFQvdr94Y456SFxVFpMq5+/Mz\nzvP9IvKKiPSLyA9EZNUqRqEAjTHuCQaDq76+0Vu5AXwe6AW2O88fBR5T1SdF5K+A3wf+60pvPnPm\nDM8//zyZTAbIDZqSyWQIBAJkMhlUNX8Nd3V1NapKOp0mGAySyWTyCSWdThMIBMhms/lK6vz8PKFQ\nKL+8xWk1NTUsLCwQCARQVVKpFDU1NflliAipVIpQKMTCwkJ+pNpMJpNfL+SuLV9cXzabzcejqpfF\nulxcwWCQbDZLdXU1IsL8/Dzt7e3cdNNyN8Iy65FOpzlx4gRVVVW+/LyX7psiwuzsLLW1tfn9e3F5\ni3Et3dcX3wvk/7/FWFWVqqqqq2JdjGVVqrruP2AP8DwQBZ5xpg0BVc7jW4CfrfBeve2225Tc7ePt\nz/l7/fXX1bjjwIEDnn+efvt79dVXFVBd4Tu90SOEbwJ/DDQCiEgrMKqqi0MpDwC7VnrzSy+9tMHV\nby4iYmNMuujSpUscPnyY/v5+r0OpGOtOCCLyMSChqq+LSHRxsvO3lK60jJ6envzjaDRKNBpdadYt\no+AhnVmz6elpG6IPiMVixGKxNc0rus6egiLyX4BPAwtAHRAG/h44BnSoalZEbgEeUdU7l3m/rnfd\nm5WIcPz4cY4dO+Z1KJtCZ2cnkUiEX/7yl16H4isigqouO7jius8yqOrDqrpXVa8D7gVOqOqngReB\ne5zZ7gOeXu86tqLF4o/ZuP7+fuLxuNdhVJRS9EN4EPiiiJwEWoDvlmAdm1ahvuZm7To6Oti3b5/X\nYVQUV/Y+VX0JeMl5fAa42Y3lbkWFhsk2azc7O2vXyhTJfo58xnZg94yPj9PQ0OB1GBXFEoLPhEIh\nr0PYNLq6uuziuSJZQvAZKyq6Jx6PW0IokucXN5nLWVHRPa2trXR0dHgdRkWxhGCMybOfI5+xnoru\nSSaTBa/uM5ezhOAzNj6Ee7q6umhra/M6jIpiCcFn7G7Y7onH4zYiV5GshuAzNmCMe8LhMM3NzV6H\nUVEsIZhNq76+vuCgouZy1mTwGbvXpXsSiYTd96NIlhB8xnoqusd6KhbPEoLPWFHRPfF43DomFclq\nCD6zOMCn2bj6+nq2bdvmdRgVxfY+n7HLn93T3NzM9u3bC89o8qzJ4DNWVHTPhQsX7HLyIllC8Bkr\nKrqns7PTeioWyRKCz9jlz+7p6+tjcnLS6zAqitUQzKYVCoXsiKtIlhB8xs4yuGfnzp3WD6FI1mTw\nGWsyuOfs2bNMTEx4HUZFsYTgMzZiknuOHDliRcUi2d7nM3aE4J7+/n67lVuRrMHqM3YxjnsCgYDV\nZIq07q0lIntE5ISI9IrIWyLyOWd6s4g8JyL9InJcRBrdC3fzs56K7tm7d69dy1CkjaTPBeCLqtoN\n3Ap8VkQ6yd3K7QVVPQKcAB7aeJjGFO/06dP09vZ6HUZFWXcNQVUvAZecx1MiEgf2AHcDv+XM9gQQ\nI5ckzBrYiEnuOXjwIDt27PA6jIriSlFRRPYDNwCvAO2qmoBc0hARK/MWwWoI7nnvvfesSFukDScE\nEdkGPAV83jlSWPMe3dPTk38cjUaJRqMbDafi2cVN7slkMmSzWa/D8FwsFiMWi61pXtnIL5KIBID/\nDfxUVb/lTIsDUVVNiEgH8KKqdi3zXrVfw8uJCMePH+fYsWNeh7IpHDp0iLa2Nl5++WWvQ/EVEUFV\nl61eb/SczN8AvYvJwPEMcL/z+D7g6Q2uY0uxQ1z3nDp1ing87nUYFWXdTQYR+RDw74G3RORXgAIP\nA48CPxKRB4BzwD1uBLpVWFHRPfv27bPTjkXayFmG/wustPfesd7lGuOWRCJht3IrknXj8hkrKrpn\nbm7O7pVZJLuWwWfs4ib3HD582C5uKpLtfT5jp8ncc/LkSYaGhrwOo6JYQvAZO0Jwz+7du9m5c6fX\nYVQU2/vMpjUxMWH3ZSiSFRV9xopg7pmcnGRqasrrMCqKHSH4jA0K6p7Ozk4bU7FIlhB8xnoquqev\nr4/W1lavw6golhB8xoqK7mlvb7eeikWyGoLP2IhJ7kmlUtbRq0j2c+Qzdi9C94yOjlJXV+d1GBXF\nEoLP1NTUeB3CptHV1WVFxSJZQvCZhYUFr0PYNOLxuHVdLpLVEHzGioruaWlpsTEVi2QJwWdsFCn3\nVFdX230ZimQ/Rz6TSqW8DmHTGBoasgFnimQJwWesqOie7u5u65hUJEsIPmPnzd3T29tLe3u712FU\nFGtg+YwVFd2zbds2GhvtToLFsITgM9ZT0T3hcJj6+nqvw6go9nPkM1ZUdM/7779v/TqKZAnBZ+zy\nZ/dYT8XiWULwGftFc088HmfXrl1eh1FRrIbgM9aRxj11dXV2cVORSrb3ichHRaRPRE6KyJdLtR5j\nVtLa2kpTU5PXYVSUkjQZRKQK+Avgw8BF4J9E5GlV7SvF+jYTGzHJPQMDA8zOznodRkUp1RHCB4F3\nVPWsqqaBHwJ3F3rTWm9ZXUpexxAMBj2PAbzfDm7E0NXVRXd3t6cxuKVccZSqqLgbOL/k+QC5JLGq\nWCxGNBotUUhr43UMDz/8MPPz8+zbt4/q6mrC4TBDQ0NEIhEmJycBaGxsZHBwkNbWVqampshms7S0\ntDA4OEhTUxOzs7MsLCwQiUQYHBwkHA6TTqdJp9P5afX19agqs7OzRCIRRkZGqKmpobq6mqmpKQYG\nBrjmmmsIBoPU1dUxOjpKW1sbo6OjBAIBGhoaSCaTRCIRxsfHqaqqyse6GJeq0tTUxODgIC0tLczM\nzFwW6/bt25mfn2dhYYGWlhaGh4dpaGhgYWGBVCrFwMAAu3fvpq6ujqqqKqanp4lEIiSTSWpqaggG\ng0xMTNDW1sbIyAiBQCAfayQSIR6Ps3v37g19Hl7vD+WOo1QJYbneNVddxtfT05N/7IeN7rXbb7+d\nEydOEAqFeOuttwCor69nZmaGhoYGpqengVxCGB8fp7a2Nj/CUktLCyMjI1RVVeXv/hSJRBgeHr5s\nHW1tbVfdzai1tZVkMnnZtNraWt58883LpjU1NTE2NgbkjmTS6TTbt29nYmICyPUMnJqayse89D2L\n8y+NVUTyV3cuF2tdXR1vvPFGwVgXlwfkl7lYO3jssceW29RbSiwWW/MRRqkSwgCwd8nzPeRqCZdZ\nmhDAP4dnXvn5z38O5LbLldum3CyGzSMajV72g/vVr351xXmlFNffi0g10E+uqPg+8I/Ap1Q1vmQe\nu/DfGI+o6rJ95EtyhKCqGRH5I+A5coXL7y5NBqsFZIzxTkmOEIwxlcm6xRlj8nyVEETkP4lIVkRa\nlkz7cxF5R0ReF5EbSrjuPxWRuLOeH4vI9iWvPeTEEBeRY6WKwVlX2Xt4isgeETkhIr0i8paIfM6Z\n3iwiz4lIv4gcF5GSDy4gIlUi8pqIPOM83y8irzgx/EBESnr9jYg0isiTzmf9tojcXO7tICJfEJFf\ni8ibIvJ9EQmVbTuoqi/+yJ2J+BlwBmhxpt0J/B/n8c3AKyVc/x1AlfP4G8DXncfdwK/I1Vv2A6dw\nmloliKHKWf4+IAi8DnSWYdt3ADc4j7eRKwh3Ao8Cf+JM/zLwjTLE8gXgfwDPOM//J3CP8/ivgD8o\n8fr/G/AZ53EAaCzndgB2AaeB0JL//75ybYeSfrhFbogngeuvSAh/DXxyyTxxoL0Msfwu8D3n8YPA\nl5e89lPg5hKt9xbgp0ueX7buMn4Wf+8kyL7F7e0kjb4Sr3cP8DwQXZIQhpYk6luAn5Vw/WHg3WWm\nl207OAnhLNDsJKRngI8Ag+XYDr5oMojIvwHOq+pbV7x0ZY/HC860UnsAeNaDGJbr4VmO/zdPRPYD\nNwCvkPsSJABU9RJQ6ruefBP4Y5xObCLSCoyqatZ5fYDcF6ZUrgOGReRxp9nyHRGpp4zbQVUvAo8B\n58jta+PAa8BYObZD2cZDEJHngaUjXgq5D/4/Aw+Ty4JXvW2Zaes+LbJKDF9R1Z8483wFSKvqD0oR\nQ6EQy7iuq1cusg14Cvi8qk6Vs6+IiHwMSKjq6yISXZzM1duklDEFgBuBz6rqqyLyTXJHaeXcDk3k\nrvvZRy4ZPEmu6XylksRUtoSgqst94RGRD5Brm78huQEF9wCvicgHyWXCa5bMvmyPx43GsCSW+4C7\ngNuXTHY1hgLW1MOzFJwi1VPkmkpPO5MTItKuqgkR6SB32FoqHwI+LiJ3AXXkDt//DGgUkSrn17HU\n22OA3JHqq87zH5NLCOXcDncAp1V1BEBE/g74TaCpHNvB8yaDqv5aVTtU9TpVvZbch/IvVXWQXPvp\nPwCIyC3kDpsSpYhDRD4K/AnwcVWdX/LSM8C9TqX3WuAguZ6XpfBPwEER2SciIeBeZ/3l8DdAr6p+\na8m0Z4D7ncf3AU9f+Sa3qOrDqrpXVa8j93+fUNVPAy8C95QphgRwXkQOO5M+DLxNGbcDuabCLSJS\n6/xALsZQnu1QquLIBooqp3GKis7zvyBXeX8DuLGE632HXDHnNefvL5e89pATQxw4VuL//6Pkqvzv\nAA+WaZt/CMiQO6vxK+f//yjQArzgxPM80FSmeH6Lfy4qXgv8A3CSXKU9WOJ1/wa5xPw68L/InWUo\n63YAHnH2tTeBJ8idcSrLdrCeisaYPM+bDMYY/7CEYIzJs4RgjMmzhGCMybOEYIzJs4RgjMmzhGCM\nybOEYIzJ+/+3mLJIMXCXRQAAAABJRU5ErkJggg==\n",
2177       "text/plain": [
2178        "<matplotlib.figure.Figure at 0x7f4027da7048>"
2179       ]
2180      },
2181      "metadata": {},
2182      "output_type": "display_data"
2183     }
2184    ],
2185    "source": [
2186     "def cross_tour(a=50, b=40):\n",
2187     "    \"a is width of cross arm, b is length of cross arm\"\n",
2188     "    return ('F' *  a + 'L' + 'F' * b + 'R' + 'F' * b + 'L') * 4\n",
2189     "\n",
2190     "plot_trace(trace_tour(cross_tour()))"
2191    ]
2192   },
2193   {
2194    "cell_type": "code",
2195    "execution_count": 1181,
2196    "metadata": {},
2197    "outputs": [
2198     {
2199      "data": {
2200       "image/png": 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Ukpa9WWhgqFF+bEHHGFQ509PTzM7Out0MR2hgqJGOMahqqqVkbyYaGJRySDgcrno7c7PQ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\n",
2201       "text/plain": [
2202        "<matplotlib.figure.Figure at 0x7f402c0cc5c0>"
2203       ]
2204      },
2205      "metadata": {},
2206      "output_type": "display_data"
2207     }
2208    ],
2209    "source": [
2210     "def quincunx_tour(a=60, b=30, c=50):\n",
2211     "    \"a is length of indent, b is indent/outdent distance, c is outdent outer length\"\n",
2212     "    return ('F' * a + 'R' + 'F' * b + 'L' + 'F' * c + 'L' + 'F' * c + 'L' + 'F' * b + 'R') * 4\n",
2213     "plot_trace(trace_tour(quinqux_tour()))"
2214    ]
2215   },
2216   {
2217    "cell_type": "code",
2218    "execution_count": 792,
2219    "metadata": {},
2220    "outputs": [
2221     {
2222      "data": {
2223       "image/png": 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iqnu92C4RrS2vFgeNIrZGYOlMl0rkA15dAoiH2yKiAvHqDEABvCYiCuC/VPWpbDM+8cQT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\nWKIAAAAASUVORK5CYII=\n",
2224       "text/plain": [
2225        "<matplotlib.figure.Figure at 0x7f4026e9cc18>"
2226       ]
2227      },
2228      "metadata": {},
2229      "output_type": "display_data"
2230     }
2231    ],
2232    "source": [
2233     "plot_trace(trace_tour(('F' * 10 + 'R' + 'F' * 5 + 'L' + 'F' * 10 + 'L' + 'F' * 10 + 'L' + 'F' * 5 + 'R') * 4))"
2234    ]
2235   },
2236   {
2237    "cell_type": "code",
2238    "execution_count": 1205,
2239    "metadata": {},
2240    "outputs": [
2241     {
2242      "data": {
2243       "image/png": 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ZZ57hwIED7Nu3r84N3FRGpzCGuczMTFJSUjx/7Pv27aN79+6WU6lgVv6cyBEj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\nVBW0UCqlVBW0UCqlVBX+P0VFnoIKajtRAAAAAElFTkSuQmCC\n",
2244       "text/plain": [
2245        "<matplotlib.figure.Figure at 0x7f401d61d860>"
2246       ]
2247      },
2248      "metadata": {},
2249      "output_type": "display_data"
2250     }
2251    ],
2252    "source": [
2253     "heart_points = [Step(60, 50, Direction.UP), Step(50, 90, Direction.UP),\n",
2254     "                Step(20, 70, Direction.UP), \n",
2255     "                Step(-40, 90, Direction.UP), Step(-60, 80, Direction.UP), \n",
2256     "                Step(0, 0, Direction.RIGHT)]\n",
2257     "\n",
2258     "heart_tour = ''\n",
2259     "current = Step(0, 0, Direction.RIGHT)\n",
2260     "\n",
2261     "for hp in heart_points:\n",
2262     "    while not (current.x == hp.x and current.y == hp.y):\n",
2263     "        s, proposed = seek(hp, current)\n",
2264     "        heart_tour += s\n",
2265     "        current = proposed\n",
2266     "\n",
2267     "plot_trace(trace_tour(heart_tour))\n",
2268     "\n",
2269     "def heart_tour_func(): return heart_tour"
2270    ]
2271   },
2272   {
2273    "cell_type": "code",
2274    "execution_count": 882,
2275    "metadata": {},
2276    "outputs": [
2277     {
2278      "data": {
2279       "text/plain": [
2280        "'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'"
2281       ]
2282      },
2283      "execution_count": 882,
2284      "metadata": {},
2285      "output_type": "execute_result"
2286     }
2287    ],
2288    "source": [
2289     "# lc = trace_tour(('F' * 50 + 'L') * 4)\n",
2290     "# lc = trace_tour(('F' * 50 + 'L' + 'F' * 20 + 'R' + 'F' * 20 + 'L') * 4)\n",
2291     "# lc = trace_tour(('F' * 60 + 'R' + 'F' * 30 + 'L' + 'F' * 60 + 'L' + 'F' * 60 + 'L' + 'F' * 30 + 'R') * 4)\n",
2292     "lc = trace_tour(heart_tour)\n",
2293     "rw = guided_walk(lc, wander_limit=8)\n",
2294     "rw"
2295    ]
2296   },
2297   {
2298    "cell_type": "code",
2299    "execution_count": 883,
2300    "metadata": {},
2301    "outputs": [
2302     {
2303      "data": {
2304       "image/png": 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cPHmSs2fPsnfvXr744osGnJVKY+CqME0NwR1iP1qj1ummECJVkqTlQCJQAuwCjgJ5QgjZ\nmjWZasmv0ZBF+xdffBFPT09l8HCnxXvZ6HPHjh2MGzfOrmn1HXfcQWlpKfPmzWPZsmWMGjWKvXv3\n1qv9qqoqwHQ6L0lSrXHvVFxPY4ZpchT1FTJyc3N59913KS0t5fHHH6d79+4O7pkdA50kScHAH4AY\nIB/YAtxl4VCrT/Frr72mfB45ciQjR46sYzfNkV1k3nnnHZP9U6ZMaXDdjqIhb+XHHnuMZcuW1XuQ\ns4WHh4fD61RxHD4+PrRp08bV3agz9b2vwsLClJfxP//5TzIyMuwqt3//fvbv32/XsfYoEEYDF4UQ\nOQCSJH0DDAGCJUnSXJPqoqiezlrEeKCrK8XFxRw/fpyKigq0Wi1CVGfSku187JGSXEVJSQkAJ0+e\nrHPZzp07I4TgwIEDjBgxgu+//57o6Gg6depkV/lffvmF48ePA/D9998rxsaguo9ZY/fu3Zw5c4bQ\n0FAl364kSVRWVuLj40N5eTkeHh4meVQt5Vc1GAwIIdBqtUiSxNChQ+sk7ZSWlpoY7DYVSktLKSoq\nYv369VRUVNCtWzd8fX2Va9W+fXtFaQjVM57Tp08jhCAsLIyAgABFyWgPNYWm119/3frB1hbvxHVl\nwiDgFOANSMA64GmqlRFTxHVlxCwr5Ru0wHjrrbdaDQSo1WobVLez+eKLL5S++vv716uOtLQ0k3Mu\nLi6utczWrVttBlCcPXt2vfrS3LF1zRqyDRo0qE79CA0NFffff7+TztI5hISEiOHDh9vMsQyIiooK\npYyscDPebrvttnr3gYYoI4QQh4GvgGPAiWuD3SfAfOB5SZLigVDg09rqqg/79u2T+2G2yWtQ7sqU\nKVOUvtbXpadt27bGLw27pLG4uDgAfv31V6D62slSBpgaKKuYIge83LJli6PsSOss0efk5LjUqb8u\nyOeYm5tLSkqKklBn9uzZyu9VVVUmMy/5Hs7Pz+fRRx8Frt/ne/bscUo/7bJ9E0K8DtSUCy8Bgx3e\noxr06tVLXVPi+g1lfMNYQ35YBwwYAFxX0MiDrU7XZD3/nIY8rZdfno4Kg9WjRw+TkEf2EBQURHh4\nuEPadzbR0dGKZYBxPLoPPvgAMFcOyrajMp9+Wi0fpaenmxzr7+/vUH9f97HFsMLp06eVtaaWjHwT\n2KNVDgsLAyAtLY2rV68qN4z8190lYVcgr6HJLwFHrWOePXu2zvdvfn5+k1mjS0lJ4emnnwYgKipK\nuY4JCQkcPXqUVatWKd8BJX3j2rVrAZg2bRrJyckUFhZSUFBAQUEBc+fOdbhlgNsPdHVZgG8JBAYG\nmoRskrcXXnhBOaZbt25AdUDE1q1bExAQAEBkZLUFkPzd0Rw9etRi3+Rt3rx5ZmX27Nljs0xjbnD9\nJdGuXTuHXJMePXooEXjrghzMoSnw0UcfAZCcnKxIxp07d+bGG2/kySefBFBCOMmO//IzHRISQrt2\n7fD39ycgIEDZHG0P6/ZzmKSkJHXqeo3Dhw9z8eJFtFotVVVVijZr6tSprF69WjG1mTx5Mr6+vhQX\nFyvawPvuu49Vq1bx5JNP0rdvX6f075dffgGqQ0099dRTzJ49mw8++IAhQ4bw008/8dVXX/H222+b\nlPnHP/4BwBdffGGmwZTPU/4rhECn01FZWYmnpyd6vR6NRmNR+3nfffdx7733MnnyZJOyVVVViuZU\nxrjMmjVriI6OdlgYrLNnz9ZrqaC4uNgh7TubzMxM9u7dy3333UdYWBgffvgh5eXleHp6otPp0Ov1\n9OnTB4D//e9/XLp0iejoaIYMGQJcT3JlTFlZmdWAs/XGEQuutSzG1luLIoQQ/v7+IiQkpEF1NHc6\ndOhgpr0aP3688rvshJ2amioA8emnnzqk3Y8++siiZk1ORSm3e/z4cQGIzp07m9Vx//33OyVoAdiX\n6jIzM9PEYT07O9uh/ejSpYtS99NPP21XGUCMHTvWof1wNq1atRIjRoyoUxlL907Nzd/fXwDC29vb\n6jFr1qxR6hNWxiG3l+jkt7aKdXbu3Mkbb7yBh4cHer2eU6dOsX37duV3eVomrikyHLVG99JLL6HR\naJg+fToGg4Eff/yRS5cumbVbc6HfGGd6ssjna4uTJ0+Sl5fH9OnT+fzzz/Hx8XFoH3bs2MFrr73G\nnj17+Oijj/jwww/tKudOHj72kJmZafK/t4djx46xcuVK9Ho9Hh4elJeX4+/vz4EDB/jtt9+YPn06\ngYGBFBQUEBAQQFFREV5eXiZS4Pr161mwYIGivbWKtRHQURsNfFtrtVrh4+PToDpaGm+88YaJlCRL\nVrJN3scff1xrHXq9XvTq1UsAomvXropEBojIyEjlbarRaJQyDz/8sMmb1jicj1y+JlOmTHGYRFdV\nVSXuvPNOpb2lS5fWWmbnzp0mfbXHTrE+jB071u7zBNeGaaoPnp6edbYXtMaCBQvqdK1CQ0OVz6K+\ndnSuJiQkhODgYFd3o0lRU2MoSwfyfntMJxISEjh9+jTBwcGEh4cTGBhIeHg4fn5+tGnThsDAQLp1\n62bigjNo0CAAQkNDmT17tqKAkBf4o6KizNpxdDiinTt3KhFx5QCRtmiscEh1tV10tGTpbCoqKhyW\ndLsuMw5/f3+7XC3dduq6bds2XnnlFbKyspqcGO8uDB48mFatWim+g/KiuK0byWAwMH78eFJTqz36\n6uJcLtcfGxuraC3feust3nrrLRPNpjGym9yNN97Igw8+yJw5c+xurybi2lQ1JycHSZLsiuVXMxiE\ns+41OVz+TTfdpCiKWrduTXp6OqNGjWLJkiUmSzRNMfBCfTXFR48eZe7cuWRlZZGenl6ne87u62RN\n1HPURj2nJRhNef7xj3/Uq46WivH0LSAgQACid+/eory8vFZlxCeffKKUHTlyZJ3aLSgoMJu6yoDl\nGGuHDx9WFpzre6/IVFRUCEDo9XoBiB07dtRaZt++fSZT18LCwgb1wRr/+9//zBbRjV2grly5ohwL\niEmTJjmlH84CEN27d693WUubPURERIhevXop9YimqIwYM2YMO3fudHU3mhxlZWWA9cV4a/vh+hTr\ntddeo3///na1ZzAYWLVqFZmZmSxZsoSsrCxWrFhhJh1ZMhn43e9+R2FhIRs2bGD69Ol2tWcNWSKS\n/xq3n5+fr5g+6HQ6Kioq8PPz49y5cybHGk/rU1JS+PTTT5V+CyPzFl9fX8rLyxk4cKBdiYsGDRpk\n9bpLkmS23NBUDIYdRVBQEN7e3mRkZBAdHU1SUpKiYJPNicrLy/Hy8qKsrExRXqSlpdk1ZXbbgc7X\n15fWrVu7uhtNkobYHY4ePRq4HnHG1qAoM336dDZu3Giyz1JeUlv2ZI5wS5MHJPmv8VTQ1jpv+/bt\nLbrYWVpTtIQ916guyOugTY36ris+//zzrFixQnnJyol5Xn31VeUY2QbSEq+88kqtbbh8oLty5Yqy\nDieEwM/Pj+7du1NSUtLi3mqOQr4hfv31V+W6hoWF0aFDh1rL9uvXDyEE8fHxdOvWTQkMACj/m5rI\n6yRHjhxR2qvZPth2q3KEy1VNiU4IQVFREb/99htQbY1v7I9pCUmSyMnJUUwlHn74YcWouSaHDx9m\n8ODBZucJ1T6dvXv3rteaX3FxscMW9huT7Oxsfv31V/r27VunF9fy5ctZvny5E3vm4oHuypUrFh++\n/fv3ExISomjrVOpGTEwMAAMHDjTZLy/y2mOXKAc2rVnH7t27FalP5r777uP//u//zI6tSfv27a3+\n5ggneksSnbG72yOPPGK1rLFEZ3zf3XvvvVbLyBKftfN+9913mTt3rp29v05oaKhy/ZsKWq2WxMRE\nBg4cSLt27UzywroDLjUvkUVVIUzDCJ07d47c3FxVoqsnsh+h8WIsXI/pb497TUhIiCXFEqdPnzY7\ndurUqfYopRR/R0s01OVHCGEm0cl1PvPMMwghWLBggdXyNbWucpgmW+tvkZGRNs/3559/rte5NKUw\nTTJ6vR6dTkfHjh0blOfEWbhUopND0dQU72fNmgVA7969G71PzQHZnq3mdZWd+htyXeu7lqbT6Wyu\nHTbE+yUhIYEuXboo3+Wpu0ajwcfHRzHtsIU8OMmDY0MlTB8fn3qH0g8ICGhysxmNRkNgYCCdOnVy\nvJ+qA3CpRBcZGUleXh5paWmkpqaSlpYGwNtvv83Vq1dZunSpK7vXZBkzZgxZWVmKu5F8XY8fP052\ndjaDB9c/jGB93ceqqqoUmzVLNOThOHPmDIAS9FEejA0GA6WlpXY5yMsvBXnAbeiaYWlpqdVMdbVR\nWFjY5GYzBoOBgoICEhISlP+DO9EoA91jjz1mNTROSEgIERERREZGEhERAcC8efNo3bq11TJyGCKV\nah599FGzaxQeHs4zzzwDoGjwWrduTWhoqMU6tm7davV6azQaZSBoiJdKzaCLxsjSj7U+nDp1qtay\n8tqk3Ne77qrO4SSHBrKFLNHJ0p98LzaEunhddOrUycSouqmt0UH1y+zKlStu6ZveKFPXNWvWoNPp\nlCB8Qgg8PDyoqqpSQrnMnDmTPn36cOrUKTp27MilS5eIiIggLS0NrVbLqlWr0Gg07NmzR81LWoO1\na9fi5eWlSHCyvdfFixdZvHixXZo/OabYmjVrFA2iVqtFr9crYZKioqK48847691PSyF5ZMaNG8fu\n3bu5cuWK0q4cPmnmzJls3LjRqoQ/YsQI/vvf/xIfH8+sWbNYs2YNM2fOZM6cOQwcOJBp06bV2jdJ\nkjh69ChHjx4lNDSUoUOH1vs8ZWR7xtr48ccfOXfuHFqtlsrKSoKDg20qQdwdd5y6NopnhKUwQvKm\n0+nM9i1evFgAYtq0acLX11cEBQUpltDvv/++U8L6NGWioqLEjTfeaLb/l19+MbH6T0lJsVrHqFGj\nnHpdAbFkyZJ6l503b16tx5WWlprcR3v37q1Xe47AuB9r1651WT8aC0D4+PgISZJc9nzias+I7du3\n8/LLL+Pl5aUEjJSTTgcEBFBQUKBIDt98840yTcnOzjbzkRQONs5sDiQnJ1t0GpcX1O2R6ByVI8EW\nttboHIGs7Jg4cSL9+/d3SP7g+nLkyBGWLl3K1q1bmTdvHjNmzHBZXxqLyspK930+rY2AjtqwMLoX\nFxeLsLAwASiBCe+8807FV9HS5u3tLby8vBziE9ncCAoKsuhnePToUZNrmJ6ebrWOESNGOOy6VlRU\niLvuuksAom/fvorvqa1AmBUVFSImJkYAokePHop/rtz3F1980a52qeFj62q45m/c3AGEl5eXTYlO\nTl0qh/+Sn/3IyEhx4MABh/RBWBmHXLJq+Le//Y3s7Gy8vLzw9vZGp9Oxc+dOMjMzlbURjUajbFCt\ncvf19cXf358lS5a4ottuS35+PlevXjXb369fP26++WZ0Oh2TJk2yabJQ10xVtsjKyuK7775Dp9Nx\n4sQJJd2fsPG237p1K1euXMHT0xMfHx+0Wi3e3t5IksTgwYPtMrx1x0XwlmT4Lq4LNxbZt28fGo1G\n+b/KLmOpqancd999Tu2bS+zoZMNV48VaSZK45557aN++Pbfccgvh4eFkZmby448/Alh8kFWuY2mg\nkiSJn376ya7ydTGFOHToEK+++irl5eV89NFHZnZ5smlGZWUlkiTxxBNPALanx7LZii2Fhb04O6xX\nWVkZs2fP5vz587Rp04aMjAz69+/PihUrzI7Nzc1VQlE1dyorK5XPt99+OxqNhqqqKoKCgsjLywOq\nBZa8vDxGjBiBh4cHo0ePZs+ePeTl5TF8+HAWL17M8OHDHd85a6KeozYsiLFLliwxE2979uwpABES\nEiIAodVqlWnLJ5980mCxtjkDiIiIiAbVMXHiRLunrhhNhzt16mT2e3JysjKFHDZsmHJsZmam1To/\n//xzh4Zpciavvfaack7h4eHK56ysLLNjo6OjRc+ePZ3aH3fA09PT6rKT8bNc2+br61vvPuBqZURN\nLBljWnItaun87W9/o6ysTDGzkEPWyGGGWrdurYQ2qquBa1ZWFuvXr1dc744dO1an8rfffju7d+/m\n4sWLLFu2TMlXMXz4cCXo5sqVK5k0aRITJkzA29ub9evXI4RQsnVNmzbNIfZqMjVdwBxNaWkpq1ev\n5uDBgwAy4ToCAAAgAElEQVTcfffddO/enTZt2jB37lyLZhVJSUluOaV2NBUVFYSEhCj+1G+99Rbj\nxo2jd+/ebNiwgatXrzJ37ly6d+/OuXPnePjhh+nbty8VFRXMmzePwMBAvLy8yMzMZMWKFQghkCSJ\n0aNHc8MNNzS8g9ZGQEdtWHhLv/POO6pCoRZWr15t9rbTaDRm+5566inh7+8vunbtWqf6a9YDCEmS\n7C77+9//Xrz00ksW6zE287D1Nu/du7dS56ZNm9xeops+fbrVc/Hx8RFlZWVmZbp37y4GDBjglP64\nEw899JDF63LkyBG7pTlrm73gbhKds80MmgNyOKFvv/1WydkQHBxsEqdMkiQKCgooKioycwK/cuUK\nZWVlZuGD/Pz8lKgbEydOZOPGjSQnJzNgwACr63TZ2dlm9ZeVlbFkyRITxdAnn3zCE088gbe3t9mi\ntCRJ3HzzzaxZswZPT09uuOEG4uLiEEJw6dIlJQaZHFIJqmPa2SvxJScnK/0/f/68sr+kpIT09HSE\nEHTp0gWDwUBsbGy9fHZlsyf53OQwTTXP1Zhz5861iLzE69atY926dcr66J/+9Cf++te/KuGm5ACn\nAN27d+ebb75hwoQJQPW9ERkZSWhoKHFxcZw7d4527dpx8uRJhg4dym+//abcx/JfT09POnbsaHf/\nXDLQycltVawj+zqOHTvWZH9paaniWqTVavHz86NDhw4mLkM7duxg/PjxVuv+7rvv8PLyIjAwkLvv\nvpvdu3fb7IscfMEYS6ntdDqdTUXAoUOH6NWrl/Ldw8ODVatW8fTTTyv7asa7O3v2rMUYeMacPHnS\nJCl3bce3b9++Xv6Y7du3V/JvgH1Kj549ezpUo+3uyF4tvr6+eHt7c/HiRcD8f2I8HY2KiiImJoah\nQ4cSFxdH9+7d8ff3Jz4+3mJZmYULF/LGG2/Y1S+XLB5UVlY6LLdoc0U2Sfj++++B61KEsWZLr9dT\nVFTE5cuXlZsCqpONyGVqblAdIry8vJz8/Hx2796NVqut9cVz/vx5kzosOZ3r9Xqb0s3ixYtN6qis\nrFTWu/75z3+a9RmwK1zR5cuXgeua25p1yD6/MTExdO7cmcTExFrrtERSUpISIEFupzbOnDnDiRMn\n6tVeU0ReKy4tLaWsrExZs6t5H8qhxKBaGk9ISODtt99GCMHLL79MUVERERERtpbETCT3WrFWkaM2\njObYr7zySoPm4C2JrVu3mlyjmjlS7dkyMjLqXGbXrl0NXlOpbVu4cKHw8/MTOp1OPPHEE8LDw8Pi\nGh0gfvzxx1qvlaXEM8bbihUrRExMjBg1apS44447RPv27ev1Pxk7dqwICwsTP/74o8V2LGmVO3fu\nLPr371+v9poi3t7edX7GY2NjxfDhw5XvslbbFoGBgeKJJ54w2YeNNbpGleh27doFoBh/GmeTVzFl\n4sSJJCYmkpCQQH5+vhLiOyEhQdkAfv/73wPV61nx8fFcuHCBhIQESkpKlCivNcu8+eabwPX8EDqd\nTsnxIK9DydPZvXv3AtUZ0Y3r6N+/P3v27GHPnj3cfPPNQLXEVrM94zLPP/88AP/5z38oLi6mqqqK\noqIiKisrrTqCCzukpkGDBpGenq6s7xm3m5SUxHPPPceVK1eU61NfiS4jI4Ps7GzlPk5ISODnn39W\nrlFmZqZZmYSEBJN1x+aOnOdl4sSJQPX9I6+/WuPChQucPXtW+W7PGn5BQUHdcuVaGwEdtQHi6aef\nVkb2Nm3aiKVLlwpAnD9/3mTULykpsTmKq5hi/PaUU74Zc+7cOYtv1507dyppEJ29WdIUW9q2bdtm\nsUxcXJzd18OWC6E9m+y+VNu2fPnyOp1fly5dHPlvd0sef/xxm5KcwWAwSWtZczO2x/zLX/5Sq0Tn\n6+trMkMQwrZEJwk73pgN4drNg06nY9myZUyYMIEvvviCl19+GSEE+/bt49SpUzz77LMkJiYSHR3t\n1P40J+Lj49m+fTv+/v7MmDHDonbvv//9L3FxccoicVBQEA899BAJCQls27aNqqoqDh8+rDhkazQa\nkpKSqKysVNyXfHx8KCkpUTIxaTQaBg8ejIeHB5IkUVVVxaFDhxBC0Lt3b8LCwpT25PSARUVFHDly\nhNLSUlJSUtBoNEyYMIGwsDCmTZtGeHg4O3bs4MKFC0o7bdu2ZfLkyXW6Jj///DOHDx9WbA/l+zsv\nL0+xFezfvz8hISFKGeO+yqHDKisr0Wq1VFRUKPH4NBoNDz/8MAEBAXz99dckJycr4cZycnIIDQ1V\nbBzl0Fa+vr488sgjzV7zKkkSrVu3VtZ+33//fSZNmmSiNZckiRUrVuDp6ams5QkhmDNnDpIkKVL9\nggULWLJkiU1p/vz582zbto25c+cqKRCvaWQtaogaZaCLiooiJCRE8XlcsmQJCxYsMDkRSZLUgU5F\npYkiSRI9evRAkiQl4rOtY4UQeHl52XT5s2dsio6OVsYWWwOdXTYekiQFAWuA3oABeASIBzYDMcBl\nYLIQwuKkOTk52URLZ+0EnD3oqqioOA+dTqdoyUNCQvDy8qK4uJjCwkJ0Oh2+vr7odDpycnLo3bs3\nPXv2JCMjQ7EsGDduHOXl5UiSxAsvvGBXmzXHFmvYJdFJkrQO+F4I8Q9JknSAH/AykC2EWCZJ0jwg\nRAgx30JZERQUREFBAWFhYZSXl1NWVmYWu0qSJFJSUpQELioqKk0HSZKUJQAZOWK4TL9+/Thx4oTy\n3BsfLy8X2Mvq1auZN28eBQUFxMbGkpCQYFOiq1XrKklSAHCLEOIfAEKIqmuS2x+Az64d9hkwwVod\n69atQwhBeXk5lZWV6PV6Xn/9dbPjHBG5QkVFpfHZuHGjormXqWkrW1VVhRBCMaA21rTLaQDs5ckn\nn6S4uBhJkvj0009rPb5WiU6SpL7AJ8AZoC9wBJgDpAghQoyOyxZCmAXeuuY/WXtHJImkpCTFPUlF\nRaXp0atXL86cOcOECROQJIn09HRFUeVIJEli2rRpiqG5vK8ha3Q64EbgaSHEEUmSVgLzqVbt2sVr\nr72mfB45cqTVENcNTTGnoqLiWpYuXcof/vAH/vWvfyn7nBJfDkhPTzcZW2xhj0TXBjgkhOh07fsw\nqge6WGCkECJDkqS2wD4hhFleubpIdBMnTsTPzw8hqjNQDRo0SFHfyyp+cc2hVw5XZJwtytiB3Xg/\nVK8HyKGO9Ho9Xbt2dWlOARUVlfojSRJTp05l48aNJvvqLdFdG8iSJEnqKoSIB0YBp69tDwNvAw8B\n/25o57/55huT7+vXr7d5vPFAVh9ULa+KStPFy8vL7mPtdQGbDfxTkqTjVK/TLaF6gLtdkqTfgNHA\nW3Xspxn/+9//SEpKUlxGRo0aRVJSkmL4WXOTncjruqWnpze0qyoqKi6mLspLu+zohBAngN9Z+Gm0\n3S3ZweDBg02+7927l+joaEaMGMH+/fsd2RRQLdE5O7+AioqK4/Hy8iIgIMDu490mxnNNqQtQYqrJ\nBoWORh3kVFSaJuXl5XVK6OTSgc44QXXNDa5HN6kZfLKhyAOpukanotI0CQgIIDg42O7jXRrmNyUl\nBYDjx48rGtN+/foxc+ZMxo8fT/v27fHw8KBz584ObVceSFWJTkWlaVJYWKikULSHRnHqt9aGHAK7\npivY3//+d2bOnFnvNmNiYuyKOSabpKioqLgvQghatWql5J+oyYoVK3juueca7tTf2DQ0eU5iYiI6\nnY4RI0YAKPZzycnJnDlzhjfffJORI0eqg5yKShNAkiSys7P5y1/+gp+fHwaDgQULFtCzZ0/OnDnD\n4sWLee6552xXUh/zjLps2Aigd/LkSbMAe4BYtWqV1TK2mDRpkhKMLywszOz3tWvX1hrQT0VFxf2Q\nn+tWrVqZBe309vZWjhHuEEq9Jo52+dqyZYsSzy42Ntbp7amoqDQO8+fP56abbmLYsGH87nemlm5l\nZWW1lnfpQCdHXfX39+d3v/sdQUFBAA1KhSjHpjJO/yej1WrrXa+KiorrWLp0KYcOHWLgwIFKDpK6\n4NKBrlOnTowYMYLi4mLy8vIoKCggPDycBx54oF71vfjiixQXFwPw7rvvmv2uSnQqKk2bBQsWKCkU\nZSzlHa6JS5URPj4+DvF4WLVqFT/88AOBgYFMmjSJNm3aEBMT0/AOqqioNAiDwcDy5cs5duwYgYGB\nFBYW0rZtW5YvX17vOj/77DMeeugh2rdvT2JiIkVFRbWWcUuta1156qmnAExi0MfHx/Of//zH5Dh1\n6qqi0rj88MMPvPjiiwD4+vpSUlICVIdNv+222+pVp0aj4ZFHHmHt2rVAtXlJbTSLgQ7g7NmzBAYG\nsm/fPh544AGLJioNiXSioqJSO6WlpfzrX/9Cr9cjSZISSn3Dhg1K6PQHHnigbjlZLfDpp5/aFVlY\nptkMdADt2rVTPstSnjHNPeWcioqrmTFjBps3bzbbX3PdvU+fPvVuQ6Opu2qhWQ10AIsWLeKpp55C\nq9WSk5OjBNyEarcRqM7xKa5FLpH/GiOuBf6Uc3vKx/j4+NQpBpaKSkvj559/BiA3N1fJ23zPPfco\n342fudzcXOXZMxgMSi5c42fO0nNan5mZS13AHNgGZ8+e5eabb66T/1tdkf8RKioqlnniiSf45JNP\nnNrGqVOn6N27t9n+BmUBa0rk5OQghFACdRoMBpPP8uJlzWMs/a25b/Pmzap5iopKLXz88ccmz4+s\nEKzPM2ftr6VBrjaa1UBXMyqJHPJp1apViqbG1rHGf2vuq8+6gIpKS6bmc1PXZ662Y+tCi3h6d+/e\nDVSruusbRl3V2Kqo1B13mQU1G2VEjx5mCchM8PLyYtiwYY3UGxUVFaifhtQZNIuB7ocffuDbb79V\nsoLJyg8hBBqNhqqqKu6//34X91JFpeXhLjOhZjHQDRs2zOnSmhq7TkWl7rjLQOcecmUToLKy0tVd\nUFFpcriLkb460NmJu/zDVFTckR07dhAZGUnPnj0V5R/ULfeqM2kWU9fGQDUUVlGxzr333ktZWRlp\naWnccccdyjq5t7e3i3tWjTrQ2Ym7aI9UVOqDEIL333+f06dPM2DAAGbNmuXQ+svKyggICECj0ZCf\nn89DDz3E8ePHrSa0aWyahQtYY7BlyxYmT56s5oJVaZJs3ryZ++67T/nu6Pv4hRdesBjs1lntWaLJ\nZQFzJwwGA7t27eLw4cMA/Pvf/1bMWFq1asWQIUNc3EMVldqRw5ZlZWXZFZG3rrzzzju88847xMbG\ncvHiRcaOHcu3337Lf/7zH8aMGWPy3Mg+48HBwYwcOdLhfbGItaw5jtpo4lm33n33XbOsQ8bb6dOn\nXd1FFZVa+fzzzwUgMjMzBSAMBoNT2lm5cqXybPTq1UukpqbafH4WLlzosLZx1yxgTYETJ04AsHHj\nRqDazKS8vFwxN0lLS6OyspKqqioqKipMPldVVbmNC4xKy0ZcmzrKWtDy8nK7smfVlTlz5iiDS1xc\nHBEREVRVVVFZWUllZWVNIYiUlBTlWamsrFQ+y787CnWgq4ULFy4AMG3aNKDazMTLy0sxNxk9ejSe\nnp7KfuPPHh4eSvpFFRVXIsdRjIqKAqrztfj4+HDw4EGntnv69Gl0Oh0eHh54eHiYvPijo6NZu3at\n8qx4enoqnx2trVUHulqQgwDIUVOFEOj1euWNs2/fPuW7cVgovV7PU089RVpamsv6rqIiI0tyWVlZ\nwHUJ7+zZs05tNyUlxaQ9Y0+Jy5cvmzw3BoMBvV7Pyy+/bDEVQkNQB7pakN8scmKdiooKdDqd4hKW\nk5OjmJ7IYaGg2hzl6tWrJvutbZZCT6uoOBL5vpQHHPmvo1wbx40bp9zPU6dOtdqup6encpxWq1VC\nOcmbVqtlyZIleHp6OqRfMqrWtRbkdQzZYFheZ9i5cyd33nkniYmJVsvKb8udO3cq4aBlzZNGo0Gv\n13PXXXexb98+pkyZ4vyTUWmx1BzYag5ADeXbb7+lTZs2aLVavvjiCzZt2gRcl+AkSeL8+fNcuHDB\nJDS6wWBAp9NRVlaGl5cXlZWVaDQa+vXr55B+yagDnRX++te/Mnv2bOV7WFgYAP7+/gDceeedADz3\n3HM899xzNusaM2aMzd99fX0b0lUVlVqpOaA5erG/bdu29OjRg6tXr5KamqrsNza079y5M507d3Zo\nu/Zi90AnSZIGOAIkCyHuliSpA/AFEAIcBaYLIZqNn9RLL70EQNeuXYmPj2f06NEsWrSIlJQUVq9e\nzTPPPMOHH37I0KFDGTp0KPn5+fj6+lJWVoZOp0Ov13PgwAHi4uJqbauhqd9UVOqKoyW69PR0PDw8\n8PPzM9nv6AG1vtRFonsWOAMEXvv+NrBcCLFFkqRVwKPAxw7un8vo1KkTqampDBo0iPj4eCRJ4t57\n72XdunWsXr2aDz/8EIAJEybw5z//2WIdTz75JHFxcUiSRExMDFeuXCE6OpqkpCSCgoKUAS40NLTR\nzkulZSJLVvJSjDzQNXQt7M9//jPLly8HoH379mRkZJj87i4+4nYpIyRJigLGAmuMdt8GfH3t82fA\nRMd2zbWkpqaSnZ3NihUrGD16NGFhYXz11Vf4+fnxwAMPEBMTA1w3P7HE4sWLGTNmDNHR0cTGxhIT\nE0OXLl3o2LEjvXr1olOnTvTp04fXX3+9sU5LpYUi233K2swOHToAEBsb26B6ly9fTkhICLGxsXz2\n2WdmEp3bpAe1Zklcw7BvC9APGAH8HxAGxBv9HgWctFLWYZbPjUlsbKzQ6XTK902bNglAdOnSRYwe\nPVrExsYKQAQEBIjx48eLvLw8F/ZWpaVx3333idjYWPH444+LysrKWo//7LPPBCCio6NlDwIBiMOH\nDzeoH4CYM2eO8r1Dhw5KO7feeqto27ataKwxABueEbVOXSVJGgdkCCGOS5I0Ut59bTMZM63V8dpr\nrymfR44c2Xj+bQ2guLjYROz+5ZdfADh//jwlJSWKfVBhYSHbt29n8eLFvPPOOy7pq0rLIikpiS++\n+AKonlE899xzdO/e3WaZO+64gy5dunD+/HnA3FOiIQijdbhVq1YxceJEkpKSqKioICMjg7Fjxza4\nDUvs37+f/fv323VsrdFLJElaAjwAVAE+QADwL+AOoK0QwiBJ0k3Aq0KIuyyUF7W14Y5ERUWRkpKi\n/BNnz57NX//6V4QQbNu2jX379rFy5Ur69u3LiRMnGDBgAMOGDUOSJPR6PX/605/o0qWLi89CpTly\n5coVOnTooJhonDp1Co1Gw5o1axTTpaqqKjw8PKioqMDX15fy8nJ8fX3JyclRcq9KksR9991HZGSk\nYrgrl/X09KS8vBx/f39KS0vx9fU1+evp6UlFRQUrV66kf//+jBgxgldffZXg4GCXXRdb0Uvq6qA/\nAvi/a583A1OufV4FzLJSxnmyqhPp0KGD0Gg0yvfnn39eAKK4uNimk7K8RUdHu7D3Ks2ZS5cumUw/\n4+Li7LontVqtAERwcLAQQoiePXvaVQ4QHh4eAhBeXl5Wjxk3bpwrL4vTnPrnA89LkhQPhAKfNqAu\nt6GsrIy9e/eSm5tr4q4iT2PFNQlvz549ANx8880ATJo0ie+//x6DwUC7du1ISkpq5J6rtBRqejPI\n9+Rbb71lU1CRneVzc3OBaj9UW8cbbxUVFQghKCsrM3PM/+Mf/6jU567UyWBYCPE98P21z5eAwc7o\nlCsJDw+nuLgYgIceekjZr9NVXypZHT969GgADh06BFQH5tyyZQu///3v6dq1q5pjQqXRkd0UG5M+\nffqwdetWABPXL3dD9YyoQXFxMQMHDlSUDzKydOfh4YHBYFD89VauXMmzzz6rfI+Pj6ekpESV6FQa\nHTm4hOxiBc5P03ny5Emn1u8oVKf+GrRp04Z27dqZ7W/VqhWA4oQs30DPPfecyffx48cTGxtL+/bt\nG6/TKi0K+SUq33N9+vQBYP78+Wg0GpYtW8bMmTOV+zIiIsJlfXUXVImuBhkZGRalMdlHr7S0VNFO\nyX+N36Le3t507NjRprO/ikpDkL0PcnNzEUIoseUWLVrEwoUL2bZtG0ePHgXgnnvu4euvv7ZVXYtA\nHehq0LZtW4vBMkNCQoDqgIVg24evbdu2yoKvioqjkb0N5HtSZuHChQD8+OOPQHVgy7CwMCUQRUtG\nnbrWID09nStXrpjtv/322zl06BAbNmyotY6rV69SUFDgjO6pqCgD3FdffcU333zDli1bgOtRsHv0\n6MHWrVu5cOECOTk5FBUVuayv7oKa7rAGQUFBDBs2jB07dlj8vbCwkMDAQEUhYYmIiAglMrFMv379\nOHbsmMP7q9Ly+PHHH7nlllsQQtCnTx+7IuQADB8+nO+//97JvXMdtgyGVYmuBgUFBTY1psbRhK0h\nRxZ+4IEHeOaZZxg9ejTHjx93bEdVVIC4uDgmTqyOp3HjjTcC1UsnDz74II899phyv95yyy0cOHDA\nZf10OfYaDNZ3o4l5RgDitttus/p7UVFRrenidDqdYi3evn17E+vxTp06CUC0atVK2Zeenu6MU1Fp\n4mzdulX4+voKQERERJjcP7a2vn37KnX4+PiY/NacQU13WDdsKRKEHdNw2YsiMDCQyMhIJXRNWFgY\nkZGRtGrViujoaNq2bQvAkiVLHNBrlebGvffeS0lJCaGhobRr147g4GAiIiIICAgAqmcVQUFBtGnT\nBkDZn5ycrNQh+54GBwfzl7/8pZHPwH1QBzoLxMfHM3z4cEVFb4ylqetnn31Gr169GDVqFH379lX2\n5+fnc+jQIWWxOCoqiqSkJIqKirhy5Qp5eXlA9bqfikpNgoODCQkJITs7m19++YXc3Fx+/PFHTp06\nBUDfvn2ZMWOGEklHjoqdl5dHv379GDlypLKMEh0dzbFjx+jXrx/PP/+8a07IlVgT9Ry10cTE5Tff\nfNOmqF9QUGA2dZWPlZ2ma5bNyspS4tdZ2mbMmNEo56bStPDz8xPe3t5m+ysrK0W7du2U++fs2bMC\nEEuXLrU5pZVjwzW1Z9JeaEg8upZCQkIC69evJysriyFDhnDkyBEqKipYuHChIr3pdDpKSkoAc2XE\ns88+y3vvvQdUu4lVVVWZlH3wwQepqqpi0aJFJhpb2dNCRaUmer3eJLCEjE6nU6ankiQpSyW7du0C\n4He/+x2HDx8GoF27dqSmprJw4UK0Wi2FhYVK6POWhDrQXcNa7LjFixeb7WvVqpXiDSEjr49AtRtZ\nSkqKxbJhYWFmZYOCghrSdZVmimzGVBuSJHHzzTezb98+ABOvnAEDBpCamsqiRYtMyshePS2FlnOm\ndjBz5kwA+vfvb3M6fvXqVTOJ7uLFi/zyyy8cPHhQUVj8/PPP5OTkmJTNysoyu8EuXryoSJAqKjKZ\nmZlkZWXVepwQgp9++km570pLS5Xf5ATs8v0XHx8PVEfMlj+3CGw90I7YaCLrAR07dlTWL15//fU6\nla1pQmK8BQYG2ixrbC5w//33N+QUVJoZ3bt3F127drV5DCBOnTpl8j0iIkL5/vjjj5vcg4mJiSb3\nZ0JCguM77iJQ1+hq5+LFi/UuW9NlLCYmhsTERJ588klWrVpl8pswCgAgSRIJCQlKiCd749+rNE9q\n3hvnzp2rVz1yPEWo1sAauyPKydLlNjIzMxucCawpoE5dHcjAgQORJInExESGDBmCn5+fErBTRg6d\nU/MvwNChQ13RbRUXI7/oLN0Tf/jDH+pcl/F6cWBgoBKIAq7bgcp/W8o6nSrROZBff/2V2NhYDh8+\nTEBAAHPmzLGYwNd4jU9+s0qSRFhYWGN3WcVNOHLkiJIrGKrvC41GU2dFlRDCxC6zsLDQZM3OWNsP\n2KXsaA6oA50DiYqKIjY2ltDQUMA8C7p8U7Vu3dpmPQ888ACff/65czqp4pYMHDjQ5Pu//vWvOktz\nMgUFBVZ9sWtKdM6OQOwuqAOdA0lOTjbJTF5Ti6rRaDh27BgnTpxQAnfC9bd3VVUVr776Khs2bFAH\nuhbGSy+9xNKlSxk4cCBHjhxh9erV9R7ounTpwrx58/D09MRgMHD33Xcrv9WU6OQBr9ljTUvhqI0m\nonV1BN7e3hY1r3WhX79+Sjk5OEBgYKAAFAdvezZPT0+TssZ9y8nJcdIVUKkPlv5/48ePt7vsyZMn\nTb6PGDHC6vFpaWkW75UTJ0409DRcDqrWtXEoKytDkiSmTp1KeXk5Wq2WuXPn1qmO77//nrlz55KZ\nmUl4eDj5+fmEhISQl5dHcHAw+fn5+Pj4UFpaqryVKysr8fLyorS0lMDAQAoKCggLCzMpGxgYSGFh\nIV9++SVbt27l0UcfdcYlUKkn3t7eeHl5cdtttxEREcE777xjd9maCgVbCgZ5/W7SpEls2bKFW2+9\nlX379rFp0yZuuOGG+nW+CaAOdA5GCMG2bduUG6pfv34MGjTI7vKBgYH8/e9/d1b3+PLLL51Wt0r9\nOXHiBF27drXrWCEEAwcOVIJO9O7dmxtuuIGdO3cCUF5eXmsdcqAJ2ZtCdm1srrQM3XIjIkkSwcHB\nBAcH4+3tzcsvv+zqLplhSROs4lpkDwZ7SExM5OjRo8p6sE6n4+TJk6xbtw7AZo4IvV5v8l2W/o4c\nOVLHHjct1IHOwfj4+BAVFcWQIUOUWGDuhisSHavY5p577uHee+9lyJAhTJ482WZMRHlwkmcKcoj+\n1atXA9XhwawhJ1a/5ZZbgOvZ7Zq9PZ21xTtHbbQgZcSiRYvMFnofe+wxV3fLBEB88sknru6GihF9\n+vQRgAgNDVXum7vuusvq8WVlZaJbt24CEMHBwaK8vFxMnjxZAEKSJLFr1y6rZVNSUiyGFZszZ44z\nTq1RQVVGNA5/+ctfWnQUV5X6UTPbfW22bV5eXmbuYZs3b2bz5s21tiVPd99++220Wi16vZ558+Y1\n+5SI6kDXApGnLyrui7E9piMJCAjAz8+PefPmmex/4IEHnNKeu6AOdC0QVRnhnhQWFiqx5MrKypzS\nhudS868AABf2SURBVKenZ4vM86oOdC0MSZLMAg2ouAeBgYHK5ylTpriwJ82PZq5qUamJEMLMxEDF\nffjwww8RQvDwww+7uivNCnWga8L06tVLiXxSc7Nl2tLsTQmaKBqNRpW2nYR6xzdhzpw5w8SJE0lI\nSCApKYmLFy9y+fJlnnvuOZu2VC0lNE9Tw2AwqOunTkJ9fTRxQkJCzCLEDhgwADA1UzCOlqIm43E+\nt99+O3v27LF5TEBAgEn0X0CV6JxErVdVkqQoYD3QFtADfxdCfCBJUgiwGYgBLgOThRDWxQgVp2Ap\noc79999PZWUlJSUliq2UTqejqqqKDh06MHbsWBf0tGWxZ88e+vbty2OPPaakt9RoNOj1ejw9PUlK\nSuLNN980K6cmSHIOkqglHpUkSW2BtkKI45Ik+QO/An8AZgDZQohlkiTNA0KEEPMtlBe1taFSP4wl\nto0bNzJ16lQX9kbFGEmSeOihhxT/05qcOXOGXr16mcSDkySJDz/8kKeffrqRetm8uJZvw6K1da1r\ndEKIdCHE8Wufi4CzQBTVg91n1w77DJjgmO6q2MvBgwcZN24cAC+++KKLe6NSk7y8PKu/WVsnVddP\nnUOdlBGSJHUA+gE/A22EEBlQPRgCrRzdORXbDBkyhO3btwPOMzBVqT/+/v589913REREIEmSSfgt\nOcy+JEkMGzbMLMS5imOxe+Xz2rT1K+BZIUSRJEl2/0dee+015fPIkSMZOXJkHbqoUhsBAQFqYh03\npLi4mLFjxypLDI8//jiPPfYYgLJW+u2333Lw4EEuX74MqJFl6sL+/fvtThFq10AnSZKO6kHucyHE\nv6/tzpAkqY0QIuPaOt5Va+WNBzoVx1NYWEhaWpqru6ECLFiwgE8++QSo1qBqtVo0Gg3+/v7k5uYy\nbtw4vL29KS0tZdKkSezYsUNRVIB5vDgV69QUml5//XWrx9or0a0Fzggh3jfa93/Aw8DbwEPAvy2U\nU2kEIiMja80sptI4LFmyRPksa1n1er0SX+7bb79Vfv/uu++YMWMGUB0OXy6j4njsMS8ZCtwPnJIk\n6RjV8atepnqA+1KSpEeARGCSMzuqYp3U1FSbBsIqjcvMmTNZs2aNiamIt7c3ZWVl3HPPPXh5eZGd\nnc1//vMf/va3vwEwZ84cAA4cOKAMkHA94fnUqVMJCQlp/JNpJtRqXtLgBlTzEqfTpUsXwsPDOXTo\nkKu70uKRJImZM2eyceNGpk2bxpo1axxWt/oc2caWeYlqht0MSEhIICMjo05lKioqSEtLQ6vVUl5e\njqenJ5WVlWi1WsLDw/Hz81OOLSgoMAvtLYRAp9NRXl6Oh4cHVVVVJgvpQggkScLPz4/w8PCGnWAT\no7CwkJKSEpNrJmduu3z5MkII9u7dy8yZM7l8+TIdOnRg8+bNDBo0yCTfqlarpaKigscff5z//ve/\nrjqdZoEq0TUDunXrRnh4OAcPHrS7TEBAgNW4ZF5eXibmKg3N5p6cnEy7du0aVEdTwfharVy5kpde\neskhpj8DBgxo9glsGkqDDIZV3J/4+HhOnz5dpzJFRUVMmDDBLLb+ihUrLKbLO3/+fH1zhpCZmemQ\n82wqrFu3DiEEc+bMobS01CG5V9RBrmGoA10TxNvb2yQkE9Q9PHpwcDChoaFm+xtix3X69GmzcFFy\nW80ZeZoun2+3bt1c3COVmqgDXROkvLycZcuWAShTwqysrDrVkZeXR3Z2ttn+hthx/fTTTwDExcUp\nW0pKCh06dKh3nU0BeYA7cOAAly5d4qabbnJxj1Rqoq7RNUEsrZnJRqj24ufnx+TJk4mKimLx4sV2\nlzt69Cj9+/c32bd3715Gjx6tfG9p/28hBBqNhoyMDNWe0YWoWtdmyA033MDJkyfx8PCgsrKyzoam\nJSUlZGVlsW7dOjw9PXn99deVOk6cOEF8fDxHjhzhrrvuIjw8nF69ejF//nz27dtnNtB98MEHQHUK\nvYkTJzrmBJsQ8ounoUobFeehDnRNlJdeeompU6fi6elJeHh4vSSJoKAgPDw88PX1Zf786ghb+/fv\nZ/78+YpUZmzJP3/+fItrePKxLTWCinz+qvuW+6IOdE0U44cqLS2NkpKSOteRn5+Ph4eHiSLj3Xff\nRQiBr6+vxTotPcwtPU+sLMmp0YHdF1UZ0USRo2AUFxcD1eYiPj4+/POf/7S7DnkwKywsNPtt27Zt\nFsu88MIL9OnTBy8vL2JjYwkKCmLHjh31OIPmgyrRuT/qQNcEefbZZ80UD3q9nrKysjplXC8tLaVN\nmzZEREQo++R1OkuD3zPPPIPBYKCgoICKigpyc3MpKChAr9fz/vvvmx3f0lBDLLkvqta1CSOH95Gj\n0sqKCeMgjitXruTnn38mMDCQwsJCvLy8KC8v58svv+SPf/wjW7duBWDChAkEBQWxa9cu0tLSGD58\nOAcOHGhxGtS6IBtY/+9//2PLli1cvXqVVq3U+LOuwpbWVR3omjCWtHxarVZJmRcXF0efPn2A69Ez\njDly5Aj//e9/bSoR1P+ddY4fP65ooAMDA8nOzlbX6VyIal7SjAkNDSUnJweAG2+8kaNHj/KPf/wD\ng8FAUlISYHuwGjBgAC+88ILZ/vj4eNXCvxbkMEzqy8D9UQe6JoxGo1EGufDwcB588EGOHj3KI488\nohzj7+9fr7pVmzCV5oSqjGjCGAwG7r//fgCqqqqYNm0aV69eZdiwYUC1pGFJqWAPlqSU8vJysrKy\nyMjIIDs7W/mblZWlZphXcWtUia4J4+/vT1BQEH/4wx/497//7XT3o+DgYKshh0JCQhTpsqWgSr1N\nB1Wia8IUFRVRUFDAN998o4TzMRgMvPHGG05pr6ysjPfeew+DwaC0ZTAYuPvuu80Cc7YE1LW5poMq\n0TVxNmzYwIYNG8z2y3lD60tAQABwXWqRkzFrtVoz387Q0NBmH4rJEqpE13RQB7omTFFREXFxcUo4\ndNlGTqfT0blz5wbVHRERwaVLl8jIyOCmm25Sgmdasv7Pzs62mZW+uaJKdE0HdaBrwvj5+TF48GCn\n1d+hQwe7YsmFhITg7e3ttH64C2vXruXRRx8FYPjw4bzyyitA/SW71q1b1znXh0r9UAc6lQaTmZnp\nkLwI7s6KFSsAGDp0KAcOHCAxMRGAhQsX4unpSUVFBVqtFr1ebxIGXU5f6OXlRUVFBT4+PiQnJ/Px\nxx+78nRaFOpAp2IXxtmpatJY63Nvv/22Ek7KuO28vDwiIiJIS0ujW7dunDt3zintR0ZGEh8fz6hR\nozh48KBir7ho0SKl/bZt25Kenk5AQEC9TXtUHI860KnYhbw2J/vVGtNYybPnz5+Pr68vnTt3Jiws\njIyMDGJiYkhOTiYmJobExEROnjzptPYzMjKorKzkxRdfVBISGQwGPDw8iI6OJjExkaioKBITE4mM\njCQ5OZnw8HDy8/Px8fGhoqICSZLw8fGhuLiYqVOnOq2vKqaoA52KXcgx5yytR/n6+jZaP2644QYl\nUXdhYSH9+/enuLgYnU5HWloacD1ZjTG7du3iT3/6Ezk5OURFRXHhwgV69+7NuXPn6NWrF2fPnuXW\nW29ly5YtVtuWNdmRkZH07t2blJQUpk6dyocffuiks1VxFOpAp2IXttbgGnN9zng6+Oqrr3LhwgWg\nWuLMzMxkzJgxFssZ7zcYDBQWFpKamkpubi7p6elkZ2fz1VdfUVpaio+Pj8U64uLigOqE3qmpqeTk\n5PDRRx+pA10TQB3oVEzQ6/UsW7aM8+fPm6wzyRrGTZs2cfLkSTQaDVVV/9/e2cZGVaVx/Pe00zda\nRGAJlZZSsMOyhCiLCkTc3SJIEF3RD0Y/rCsqxiXqria+AIKYJihqDLjiaja7C+omarCmdrObCiit\n8kFEpcQVxKLyUulqsS2C7bTT8uyH+8Kd6dRO6UzvtJxfcjPnnrn3nv89nT73ueflOZ1kZWUl9XUx\nGm/vrjNIecmSJW4Yqry8PJYuXUooFCIrKyvCs+ut/U5EuOuuuxg5ciQ//PADBQUFrFmzxvVmnXhz\nTjvl7t27mTlzZsLv0ZAEErG4bi8LGKth8PDcc88poIDm5ua66d6222+/PenaAJ0xY4a7//7777vl\n5+TkRHzG2l5//fUer3369Olu1wL0zjvvdI9x6sNh165dan7fqYP9t4hph4xHZ4ggHA4Dkb2rIkJd\nXR3BYJDS0lIuv/xyVq9e7cvYOUcfwBVXXNHjoF0RoaysjNWrVwPWoOaamhrKy8u55ppruml3PL+7\n776bzs5OGhoaqKysZOfOnSxfvpzW1lba29sBeOCBBxARjh07BkB5ebkbAPX8889n3rx5Cb9vQz/p\nyQImasM88QYVGzZs6OalAHrw4MEI7+iyyy4bcG3Z2dk6d+7cuI4FdO3ate7+1KlTXe3Dhw/vdnxX\nV1fc3mtvW3V1dcLu2RA//IRHZyb1GyKINXwEznh4Tz/9NGAF5mxra6O1tZVQKJTQME0dHR2EQiHa\n2toIhUKuJxUKhdypaPHgvZd9+/ZRVFTE5MmTY45vS0tL8z6c2bx5M42NjTQ3N7ufTU1Nbvr777+n\nubmZlpYW2tra+PHHH911PA4dOtSPuzckA/Pqaoigt1DgTjTiEydORAwrKSkpoa6urt/lh0KhmL2e\nmzdv5oILLmD8+PFxX8u7WE1RURHBYJC0tDR35bSfYsmSJXGXE82FF1541ucakoPx6AwR9OaZ3XDD\nDYAVscQbpungwYMJKd/x3tQOA+V4WJ9//jkNDQ0cPnw47mt5AxAcOXKEL7/8kq+//ppvvvmm13O3\nbNniTuXq6uqKSDufu3bt6qZVVd3Ap4bUwXh0hggCgcBPTlJ3PL7s7Gz3OCekUyJwDJt6Bv1mZGSQ\nlZVFYWEhEyZMiPtaztKNYAUeKCgoIDc3113rAazFv8eNG9ft3BtvvLFPuk3IptSmX4ZORBYCG7A8\nw7+r6pMJUWXwDe9yiT19D5GDhE+dOpWw8qNj3TllhkIh6uvr+7QGhteja25udmdOOJPxAfbv3w/A\n9u3b3Z7T+fPns2rVKkpLS93ys7Oz6ejoIBAIuEZYVZkyZcpZ36th4DhrQyciacBGYB5wDNgtIm+p\nanJmVBsGhJ7a6BzjV1FRAUBTUxMiwtq1ayM8p77y8ccfc+mllwIwc+ZM3n77bbc8r7HLzs5mzJgx\nffLoHn30UXegM8BXX33lpqM9sOghIdOnTzfDRIYQ/fHoZgJ1qnoYQEReAxYDxtANYpw2smi80YSX\nLl1KOBzm+eefZ82aNVx77bVnXd769esBWLhwIVVVVTE9OrCmfjU2NrpTvuLh+uuvp6Kiwl0SMjMz\nk6lTp3LRRRcxevRo1yuL9ZoaK8CoYfDSH0NXABz17NdjGT/DIOa8884DLEMzduxYNzCk04PZ1NTE\nU0895R4fCATOamjJm2++yU033eSeW1VVBZwJ+SQijBw50p3mNWrUKDIzMykoKIi7jGXLllFRUcEt\nt9zCs88+S0dHB7W1tRw4cIC2tjY3pFJ5eTlHjhyhoKDA7ajoab6rYXDSH0MXq/U1ZuPOY4895qZL\nS0vdtg9D6nHHHXfw8ssvc/z4cQoLC8nLy+Oqq66iqKgIcFdDJycnh2nTpvHCCy/wxBNP9Lmc2267\njc7OTsaPH8/Jkyc5efIkxcXFdHV1cejQIUpKSigoKKChoYHhw4fz4IMPsmrVKr777ru4y3A6Hdrb\n26mpqeH++++npaWF/Px8jh49SjAYJCcnh5KSEjIyMpg4cSLDhg2juLi4X16qYWCorq6muro6voN7\nGknc2wbMBqo8+8uBh2Mcl+gB0AafAPSZZ55RIGKGwqJFixTQwsJCffzxxyPOKSsr00mTJunFF1+s\nwWBQg8GgTps2TTMyMjQrK6tbGSdOnOhx/iigs2bNilvr1q1bFdB77rmnD3dpGKyQpLmuu4ESEZkA\nNAA3AyaS4BDHeYUdMWKEm1dWVsaHH35IfX09K1euZMWKFe533s6AaDZt2tQtz2kb0xgx5QBaW1vj\n1uq0N/Y028Nw7nDWhk5Vu0TkHmArZ4aX7E+YMkNKonbvq3ex6ksuuYTGxkZefPFFli1bxr333ktu\nbq5rlPbs2cP06dPjur7Tg9vTuLTeZm54cYyyGeNm6Nc4OlWtAn6eIC2GQcKwYcPIz8/vlj9v3jwC\ngQAbN24kJyfHnfsZDAbjvrZjSHvy6LzTunqjN6NpOHcwU8AMfUJEaG1t5cCBA2zbti1isHAwGHQH\nHLe2trrtI7m5uX26vvczmp6Gv8TCvLIaHIyhM/SJtLQ05syZw969e1mwYEHCeye9Hl00eXl5jBkz\nJu5rOd5fVlZWYsQZBi3G0Bn6xOnTp3nvvfdcQ1RTU5PQ63s9Oscjcz5PnTrVp+Elznl98QINQxNj\n6Axxk5uby3333Ud6erprkObOnZvQMpyVtkTELSc9PZ2tW7cybty4PoVpuvrqqwG48sorE6rRMPjw\n3dDFPeAvBTjXtba0tBAOh2lvbyccDhMOh3nnnXf6fV2v1pycHDo7OyPKAdixYwfHjh2LO0xTV1eX\new0ntFQiONd/A8ki2VqNoesD57rWQCBAIBAgMzPTTSeiRzNaa3p6ekQ5AOvWrQNg9uzZcV0zLS3N\nvUYiOdd/A8ki2VpNPDpDynP8+HF27txJeno6CxYs8FuOYRBiDJ0h5Rk9ejSLFy/2W4ZhECOxuvET\nWoBIcgswGAwGG1WN2ZaSdENnMBgMfuN7Z4TBYDAkG2PoDAbDkMdXQyci94rI5yLyqYis8+SvEJE6\nEdkvIinTzSYiD4jIaREZ5cn7s621VkTiC9GRRETkKbveakWkXETO83yXcvUqIgvt38AXIvKw33q8\niEihiLwrIvvs3+gf7fyRIrJVRA6IyNsiMqK3aw0EIpImIp+ISKW9XywiH9g6XxWRlOh8FJERIrLF\n/h1+JiKzkl6nPQWqS/YGlGKFeArY+z+zP38B7MHqES4GDmK3Jfq5AYVAFfA1MMrOuxr4t52eBXyQ\nAjrnA2l2eh3whJ2emmr1ivWgPQhMADKAWmCK33Xo0ZcPTLfTecABYArwJPCQnf8wsM5vrbaW+4F/\nApX2/uvAjXb6BeAuvzXaWjYDt9npADAi2XXqp0e3zL6ZTgBVPW7nLwZeU9VOVT0E1JEaa1GsBx6M\nylsMvAygqruAESIydqCFeVHV7arqhO34AMtAA1xH6tWru8CSqoYBZ4GllEBV/6eqtXb6FLAfqz4X\nAy/Zh70EXO+PwjOISCGwCPibJ/tKoNxOvwQkborIWSIiw4FfqeomAPv3eIIk16mfhm4y8Gvbtd4h\nIpfY+dGL7nxj5/mGiPwWOKqqn0Z9lXJao7gd+I+dTkWtsRZY8ltTTESkGJiO9fAYq6rfgmUMgfhD\nqiQP50GsACIyGmj2PPTqge4rdQ88k4DjIrLJfs3+q4gMI8l1mtR3dhHZBng9HMH6Q6yyyz5fVWeL\nyGXAFqxKiHvRnQHUuhK4KtZpMfL81PqIqv7LPuYRIKyqr3qOicbvsUWpqKkbIpIHvAH8SVVPpdrY\nUBG5BvhWVWtFpNTJpnv9poLuADADuFtVPxKR9VjrzSRVW1INnarGMg4AiMgfgDft43aLSJf9FKoH\nijyHFmItkJ1UetIqItOw2rT2ijWxsxD4RERmYmn1htPwVauDiNyK9RrjDdvhi9Ze8OVv3RfsBvw3\ngFdU9S07+1sRGauq34pIPhB/7KjkMAe4TkQWATnAcGADVlNKmu3VpUrd1mO9HX1k75djGbqk1qmf\nr64VwDwAEZkMZKrq90AlcJOIZIrIRKAE+NAvkar6X1XNV9VJqjoR6w/1S1X9ztb6ewARmQ20OO63\nX4jIQuAh4DpV9QZiqwRuTpV6tXEXWBKRTKwFlip91hTNP4B9qvqsJ68SWGKnbwXeij5pIFHVlapa\npKqTsOrwXVX9HbADcFbn9l0ngP3/cdT+nwfLBnxGsuvUx56XDOAV4FPgI+A3nu9WYPXG7QcW+KWx\nB91fYfe62vsbba17gRkpoK8OOAx8Ym9/SeV6BRZi9WbWAcv91hOlbQ7QhdUbvMeuz4XAKGC7rXsb\nVhOM73ptzb/hTK/rRGAX8AVWD2yG3/psXRdjPeRqsd7qRiS7Ts0UMIPBMOQxMyMMBsOQxxg6g8Ew\n5DGGzmAwDHmMoTMYDEMeY+gMBsOQxxg6g8Ew5DGGzmAwDHmMoTMYDEOe/wNMCtJO4nIQxgAAAABJ\nRU5ErkJggg==\n",
2305       "text/plain": [
2306        "<matplotlib.figure.Figure at 0x7f402c1a68d0>"
2307       ]
2308      },
2309      "metadata": {},
2310      "output_type": "display_data"
2311     }
2312    ],
2313    "source": [
2314     "plot_trace(trace_tour(rw))"
2315    ]
2316   },
2317   {
2318    "cell_type": "code",
2319    "execution_count": 884,
2320    "metadata": {},
2321    "outputs": [
2322     {
2323      "data": {
2324       "image/png": 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gmSDHZxrub6Xly5cbHIkQ/ktNdX5cgzEiwG63c9lll/H+++8D3w6fapvYBg0a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\nktiEEFFHEpsQIur8f/yi651PnLLMAAAAAElFTkSuQmCC\n",
2325       "text/plain": [
2326        "<matplotlib.figure.Figure at 0x7f40271d9320>"
2327       ]
2328      },
2329      "metadata": {},
2330      "output_type": "display_data"
2331     }
2332    ],
2333    "source": [
2334     "rw_trimmed = trim_all_loops(rw)\n",
2335     "plot_trace(trace_tour(rw_trimmed))"
2336    ]
2337   },
2338   {
2339    "cell_type": "code",
2340    "execution_count": 885,
2341    "metadata": {},
2342    "outputs": [
2343     {
2344      "data": {
2345       "text/plain": [
2346        "760"
2347       ]
2348      },
2349      "execution_count": 885,
2350      "metadata": {},
2351      "output_type": "execute_result"
2352     }
2353    ],
2354    "source": [
2355     "len(rw_trimmed)"
2356    ]
2357   },
2358   {
2359    "cell_type": "code",
2360    "execution_count": 1180,
2361    "metadata": {},
2362    "outputs": [
2363     {
2364      "name": "stdout",
2365      "output_type": "stream",
2366      "text": [
2367       "At Step(x=-2, y=0, dir=<Direction.DOWN: 3>) going to Step(x=0, y=0, dir=<Direction.RIGHT: 2>), currently left,  by step L to Step(x=-1, y=0, dir=<Direction.RIGHT: 2>)\n",
2368       "At Step(x=-1, y=0, dir=<Direction.RIGHT: 2>) going to Step(x=0, y=0, dir=<Direction.RIGHT: 2>), currently left,  by step F to Step(x=0, y=0, dir=<Direction.RIGHT: 2>)\n"
2369      ]
2370     },
2371     {
2372      "data": {
2373       "text/plain": [
2374        "(204,\n",
2375        " 80,\n",
2376        " 'RLLRFRFLFFFLFRFFRFLFFLFFFFFLLFRFFRFFFLFRFLFFFFRFRFFFLFLFFFFFFLFFFFRFLRLLRFLRFFLF')"
2377       ]
2378      },
2379      "execution_count": 1180,
2380      "metadata": {},
2381      "output_type": "execute_result"
2382     },
2383     {
2384      "data": {
2385       "image/png": 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UIuI9BZWIeK/fBdW+ffuA8POTtNW2SDPnHKWlpQBUVVXF3E0zb7d076n0nb/5+fnMmDEj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\nRU5ErkJggg==\n",
2386       "text/plain": [
2387        "<matplotlib.figure.Figure at 0x7f4027412588>"
2388       ]
2389      },
2390      "metadata": {},
2391      "output_type": "display_data"
2392     }
2393    ],
2394    "source": [
2395     "lc = trace_tour(square_tour(a=10))\n",
2396     "rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
2397     "rw_trimmed = trim_all_loops(rw)\n",
2398     "plot_trace(trace_tour(rw_trimmed))\n",
2399     "len(rw), len(rw_trimmed), rw_trimmed"
2400    ]
2401   },
2402   {
2403    "cell_type": "code",
2404    "execution_count": 1194,
2405    "metadata": {},
2406    "outputs": [],
2407    "source": [
2408     "success_count = 0\n",
2409     "while success_count <= 20:\n",
2410     "    lc = trace_tour(square_tour(a=10))\n",
2411     "    rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
2412     "    if rw:\n",
2413     "        rw_trimmed = trim_all_loops(rw)\n",
2414     "        if len(rw_trimmed) > 10:\n",
2415     "            with open('small-squares.txt', 'a') as f:\n",
2416     "                f.write(rw_trimmed + '\\n')\n",
2417     "                success_count += 1"
2418    ]
2419   },
2420   {
2421    "cell_type": "code",
2422    "execution_count": 1195,
2423    "metadata": {
2424     "collapsed": true
2425    },
2426    "outputs": [],
2427    "source": [
2428     "success_count = 0\n",
2429     "while success_count <= 20:\n",
2430     "    lc = trace_tour(square_tour())\n",
2431     "    rw = guided_walk(lc)\n",
2432     "    if rw:\n",
2433     "        rw_trimmed = trim_all_loops(rw)\n",
2434     "        if len(rw_trimmed) > 10:\n",
2435     "            with open('large-squares.txt', 'a') as f:\n",
2436     "                f.write(rw_trimmed + '\\n')\n",
2437     "                success_count += 1"
2438    ]
2439   },
2440   {
2441    "cell_type": "code",
2442    "execution_count": 1196,
2443    "metadata": {
2444     "collapsed": true
2445    },
2446    "outputs": [],
2447    "source": [
2448     "success_count = 0\n",
2449     "while success_count <= 20:\n",
2450     "    lc = trace_tour(cross_tour())\n",
2451     "    rw = guided_walk(lc)\n",
2452     "    if rw:\n",
2453     "        rw_trimmed = trim_all_loops(rw)\n",
2454     "        if len(rw_trimmed) > 10:\n",
2455     "            with open('cross.txt', 'a') as f:\n",
2456     "                f.write(rw_trimmed + '\\n')\n",
2457     "                success_count += 1"
2458    ]
2459   },
2460   {
2461    "cell_type": "code",
2462    "execution_count": 1197,
2463    "metadata": {
2464     "collapsed": true
2465    },
2466    "outputs": [],
2467    "source": [
2468     "success_count = 0\n",
2469     "while success_count <= 20:\n",
2470     "    lc = trace_tour(quincunx_tour())\n",
2471     "    rw = guided_walk(lc)\n",
2472     "    if rw:\n",
2473     "        rw_trimmed = trim_all_loops(rw)\n",
2474     "        if len(rw_trimmed) > 10:\n",
2475     "            with open('quincunx.txt', 'a') as f:\n",
2476     "                f.write(rw_trimmed + '\\n')\n",
2477     "                success_count += 1"
2478    ]
2479   },
2480   {
2481    "cell_type": "code",
2482    "execution_count": 1203,
2483    "metadata": {},
2484    "outputs": [
2485     {
2486      "data": {
2487       "image/png": 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MmTOnQXUOGDDA6fvs2bOVzxERETzxxBMNlFbD3xFCNPglE6io+mqsnDEpMTGR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\nNDQATRloaGhUoCkDDQ0NAP4/oI3jTPrjMJgAAAAASUVORK5CYII=\n",
2488       "text/plain": [
2489        "<matplotlib.figure.Figure at 0x7f40276510b8>"
2490       ]
2491      },
2492      "metadata": {},
2493      "output_type": "display_data"
2494     }
2495    ],
2496    "source": [
2497     "plot_trace(trace_tour(rw_trimmed), filename='test.png')"
2498    ]
2499   },
2500   {
2501    "cell_type": "code",
2502    "execution_count": 1206,
2503    "metadata": {},
2504    "outputs": [],
2505    "source": [
2506     "patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
2507     "tours_filename = 'tours.txt'\n",
2508     "\n",
2509     "try:\n",
2510     "    os.remove(tours_filename)\n",
2511     "except OSError:\n",
2512     "    pass\n",
2513     "\n",
2514     "success_count = 0\n",
2515     "while success_count < 100:\n",
2516     "    lc = trace_tour(random.choice(patterns)())\n",
2517     "    rw = guided_walk(lc)\n",
2518     "    if rw:\n",
2519     "        rw_trimmed = trim_all_loops(rw)\n",
2520     "        if len(rw_trimmed) > 10:\n",
2521     "            with open(tours_filename, 'a') as f:\n",
2522     "                f.write(rw_trimmed + '\\n')\n",
2523     "                success_count += 1"
2524    ]
2525   },
2526   {
2527    "cell_type": "code",
2528    "execution_count": 1190,
2529    "metadata": {},
2530    "outputs": [
2531     {
2532      "name": "stdout",
2533      "output_type": "stream",
2534      "text": [
2535       "At Step(x=2, y=3, dir=<Direction.DOWN: 3>) going to Step(x=0, y=0, dir=<Direction.RIGHT: 2>), currently above,  by step F to Step(x=2, y=2, dir=<Direction.DOWN: 3>)\n",
2536       "At Step(x=2, y=2, dir=<Direction.DOWN: 3>) going to Step(x=0, y=0, dir=<Direction.RIGHT: 2>), currently above,  by step F to Step(x=2, y=1, dir=<Direction.DOWN: 3>)\n",
2537       "At Step(x=2, y=1, dir=<Direction.DOWN: 3>) going to Step(x=0, y=0, dir=<Direction.RIGHT: 2>), currently right,  by step R to Step(x=1, y=1, dir=<Direction.LEFT: 4>)\n",
2538       "At Step(x=1, y=1, dir=<Direction.LEFT: 4>) going to Step(x=0, y=0, dir=<Direction.RIGHT: 2>), currently above,  by step L to Step(x=1, y=0, dir=<Direction.DOWN: 3>)\n",
2539       "At Step(x=1, y=0, dir=<Direction.DOWN: 3>) going to Step(x=0, y=0, dir=<Direction.RIGHT: 2>), currently right,  by step R to Step(x=0, y=0, dir=<Direction.LEFT: 4>)\n",
2540       "Found mistakes: 2052\n"
2541      ]
2542     },
2543     {
2544      "data": {
2545       "text/plain": [
2546        "(5348,\n",
2547        " 1210,\n",
2548        " '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')"
2549       ]
2550      },
2551      "execution_count": 1190,
2552      "metadata": {},
2553      "output_type": "execute_result"
2554     },
2555     {
2556      "data": {
2557       "image/png": 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8FxpNdyTYVgFx29AopeKA8SLyGoCINIrIUWAqtlUrsf+d5rGWGo3GoE+fPnz2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\noC4AAAAASUVORK5CYII=\n",
2558       "text/plain": [
2559        "<matplotlib.figure.Figure at 0x7f402c03b908>"
2560       ]
2561      },
2562      "metadata": {},
2563      "output_type": "display_data"
2564     }
2565    ],
2566    "source": [
2567     "lc = trace_tour(cross_tour())\n",
2568     "rw = guided_walk(lc)\n",
2569     "print('Found mistakes:', len(mistake_positions(trace_tour(rw))))\n",
2570     "rw_trimmed = trim_all_loops(rw)\n",
2571     "plot_trace(trace_tour(rw_trimmed))\n",
2572     "len(rw), len(rw_trimmed), rw_trimmed"
2573    ]
2574   },
2575   {
2576    "cell_type": "code",
2577    "execution_count": 1187,
2578    "metadata": {},
2579    "outputs": [
2580     {
2581      "data": {
2582       "image/png": 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+/v5IT08X1el0Ojz33HP46aefHChdzVNYWGiV011D+x7aYodRf8wBGxBEhF69ekGv1/N0\nAjk5OUhISEC7du0AOD7KVk2zd+9e+Pn5AQAePHiAnJwcXlasWAEAojoJ65A6jDpGSUkJTp48iSNH\njgAAQkNDAQD5+fn4+uuved6PHj16OExGRzB27FhoNBpMmDAB3t7e8PLy4kVIGG1cN3PmTMk+wwok\nb9U6xuDBg/Hbb78BAMLCwhAZGYkbN24gLCwMABAcHIzU1FSefrGhEB4ejkaNGmHTpk3ljplaVl2z\nZg0AICYmptplq09II4w6wC+//ALGGJydnXln0bhxY6SkpCA2NhZDhw7lSqn79+8DaHhTkqSkJFy/\nfh2PPfYYdzxr1KgRGGO4ffu2yWu+++67emngVp1II4w6wKxZswAYLBtVKhXCwsIQGBiI27dvQ6VS\n4ZdffkFsbCx0Oh2Pnt3QQtfp9XpotVrEx8cjJiYGRISgoCAkJyebzAwHSCbjVmHt8oqtBQ1wOcta\nli5danZJcd68eSbrz54962ixa5TJkyfzpVhjvL29udOaMYDpTGsNAUjLqvUfIoJMJkNhYSFPpixR\nOULYPiESuXH9tm3bMHLkSAdK5xikZdUGQEObYtiTe/cM7kxbt24V1dsrG11DQuow6gjSaMw6hg0b\nxjuMUaNGYfXq1fyYpMOoOlKHUceQOo6q8fPPP2PDhg18v6CggG+PHDkSr7zyiiPEqrNIHUYdID09\nHdOmTQMgTU2swThuhhAb4/Dhw2jSpAm+/vprR4lVJ5GWVesAo0aNwoEDBxAeHg5nZ2dHi1PnMDbc\nEpade/fujejoaNy8edNRYtVJpBFGHUCj0SAoKAh37tyR5t1WIPiYAIagTYJh186dO6UOuIpIHUYd\n4P79+0hLS3O0GHWWF154gfvePP/889i+fTt27NgBNze3epUhriaQpiR1AH9/f8nD0kYEZ7w2bdpg\n+PDhAABXV1eRElSicqQRRi1HoVDg5MmTCA4OdrQodZK2bduKkhoJ7v8A4OLiIimRq4hk6VnLYYxh\n+/bteOaZZyT9RRVQq9UYNWoUfv75Z16nUqng4uICZ2dnKJVK3LlzB0DDW6q2xdJTmpLUAUJDQ012\nFjqdDjqdjtv5y2Qy6HQ6yGQyKJVKB0jqOIiIJ6TW6/U4ceIEfv75Zzg7O3M9hVqtllIO2Ig0JakD\nmAuT7+7uDqVSyX85lUolXF1doVKpsHTp0hqW0rEMHToUcrkcSqUSLi4u6NOnD2QyGTQaDcaOHQsA\nUCqVPG4IYNANSVOSqiF1GHWAjh078jyigMEHomPHjvzXMjQ0FB4eHqJr/vjjjxqV0dGcPXuWRx8D\ngA4dOvDscDqdDoBheTolJYWfo1arG9x0xFaszd7uwxjbxxhLYIztZYx5GR1bW5q9/SxjrH11Cd5Q\nWLhwIRQKBcaNGwfA8KWPjY3FmTNn0KRJEwQHB6Nx48Y8tqdA165dHSCtY0hLS0NWVhays7N5naDo\nVKvVoo7EOKu91FlYQWX+7wB6AmgPo2TMAJYDeKt0ez6AZaXbTwHYWbrdFcAfFbRrXyf/eky/fv14\nnpEnnnjCZNwHZ2dn6tatG4+H0a9fP0eI6hBgIh5IaGgoERG5u7ubjSUSHBxMpcr3BgWqOy8JymRv\nB3AVQFDpdjCAK6XbGwC8aHTeFeE8E21W82uxD8bZsjw9Penxxx8v98Xz9vYmAJSRkWHTve7cuUMA\nyN/fn7dtnJtDyKNhSYmOjrbTG6j9WPpOjIuzs7PFiYwePnxISqWS5HJ5pe0af3atW7eugaevOrZ0\nGNbqMAKJKK30vz4VQGBpfb3L3i7kLQUM+UoPHz4sOu7i4oIBAwYAAL755hub7rV27VoAQL9+/bg5\ns16vR2RkJPz9/flcHBAPrY3rmjRpAgAi5V59Z/Xq1ejWrRt8fX1F9RW9g+LiYri6uvJgwBWxb98+\naDQarhMxRaNGjRAZGYnGjRtj4MCB6N+/Py5evGj5Q9QR7L2sWqXs7bU9GTOVznGjoqLAGMOVK1fK\nnRMVFYX/+7//A2PM5qS/SqUSCoUCW7duxZgxY7B7927odDokJSUhJCQEKpWKKzpNBX/R6/Xcmaoh\nWYbOnDkTM2fOREZGBgIDA8EYg4+PD5KTk8utgri7uyM/Px8AcOXKFTRq1KjS9k197mURbDqSkpKQ\nmJiIwMBAeHt7W/E09scRyZjLTkn4VAMVT0n41MVEm3YZXu3evbvcsNDd3Z2Ki4ur3Na+ffsIMOTz\nLNumJWXDhg1ERNSuXTuRLMK2i4sLAaBNmzbxe16/fp3nETVViIh69epFYWFhFBgYSACoadOmRESk\nVCpF506bNo2IDEPOVq1a2fpqaz3btm0r946F4urqSkTmpytVYcaMGVZ9H4xL+/btq+MVWAVsmJJY\nOsJgEI8efgEwDgbl5zgAO4zqXwewjTEWAyCHSqcu1cWXX34JAHjrrbeQk5ODc+fO4cSJE8jJyUFA\nQECV2hJsF6ZPn45169ahsLAQzz77LPz8/HDkyBFcvXoVPXr0QH5+Ps6dOwcAiI6OxlNPPYWwsDBM\nmjQJAHDu3Dk888wziIyMhKurK/Lz88EYg5ubG5YtW4Y333wTqamp0Gq1+PPPP3m8BplMxkcOrVq1\nwq+//goAuH37Nl8OnDlzJj788EMAhhUT42vy8/N5Xg7jGBD1lQ8++ACAYdm5qKgIRUVFfBpQWFgo\n8lK1haSkJL6tUqmg1+tFTmullpN8v0mTJvD29kZ8fDxCQ0Oh0Whw9uxZfPDBB9DpdFAqlfDz88Pk\nyZPrnh1IZT0KTGdv9wEQCyABwG8AvI3O/ycM2dvPAehYQbt26S3/9re/8V+M4cOHcyWkNSOMESNG\nkJeXFxERtWnThm8TERUUFPBfi+bNm/Pt6dOnl2sHAMXGxpq8Byr4FWrVqlW50QIR0RdffEEAyM/P\nT5R0GGV+XYXo2EDDWCUR3oslysiypSpMmzbN5hGGqbJkyZJqejMVg+pUehLRy0QUSkRKImpERF8R\n0QMi6k9ELYloABHlGJ0/nYiaEVE7IoqvrH1bUSqVPBVeTk4O3Nzc8ODBA6v0CSUlJcjNzQUAeHt7\ni0Yorq6uICIEBwfj2rVrAAwWmObu079/f4wfPx4A8O6774p0HL6+vvwD+OqrrwAYOm5jJZ1KpeLb\nEydOBBEhMzNTZCIuk8n4fBwAd+EGgEceqdO6ZosQ3otWqxV9qcPDwzFo0CD+q9+7d2+b7uPlZTAz\nGjhwoEXnZ2ZmWvJDbJNr/eDBg7mtiVAGDRpkdXuWUqd9SX777Tfs3r0b+fn5mDhxIuLj421yVxY6\nC8AwDRAUWcZs3rwZU6dOxc2bN6HVakX/sAKXLl3Ck08+if/85z/46quvsG7dOjDG0L17d8TFxUGt\nVuO1116DRqPhQ+gJEybgxo0bvI1NmzYhISEBISEhyMvLg5OTEzw8PJCTkwPGGLy8vKDX60W+El26\ndMGjjz6KwMBALFu2zOr3UNdJTk6Gj48P37958yb69++PvLw8JCUlISMjo0rtCdO7ffv2wcPDgxvJ\nPfvssxg4cCCcnJzw4YcfIiUlBYcPH7Z4KlRUVFQlOYzZvXs3unbtivHjx4Mxhn//+9/Yt28fACA7\nOxvTp09H586dMWvWLPtOe6wdmthaYIcpCYyGd4Li0BZDnGeffZYUCgUREUVFRZFSqazwngBo6tSp\nJtsaMGAAeXp6EhHRl19+yadKwnVlFZbGdgHGRaVS8W0fHx++7evry7cFY66JEyda/ez1CQDUuXNn\nIiJ64403yk3dJkyYUKX2FixYwK8NDw/n22vXruXnGH/elsq4cOHCKslR9vopU6bw/YkTJ5abmgOg\n5ORkk9eStf+31l5oa7FHh8EYI+Avq0c/Pz+bOgwhe1bZMn78eJP1xh2AqRIcHFzuHiEhIdS3b1++\n/9VXX5nsMB599FEKCAioUF4fHx8aOnQoERF5enrSzJkzrX72+sSjjz5KAMjDw8Mu7S1btkz0mZr7\nvIUfG0twdXXlequKMDYcLFs++OADft6MGTN4hzV27Fh+zoULF8q12WA7jNTUVL7UGBYWJvrgGGP0\n4YcfVrnN48ePEwAKCgqilStX8jb9/PwoLi6OAFBERAQBoOzsbDp48CDFxcVRXFwcHThwgOLi4ujw\n4cN06NAhUqvV5doHxFaYn3/+Ob+Hk5MTtWjRggDwpdmKAEDdunXj2+PHj6/y89ZH8vLy6NNPP62y\nctMcP/30k9nRX4cOHeixxx7jdePGjbOozczMTHrhhRe4jOnp6dSlSxcaMmQIdezYkR577DEaMmSI\n6H4HDx6kw4cPU1xcHP3555+i9oQfNSIivV5Px44dIwAUFRVFHTp0oCFDhlDPnj0pMTGx4XYYREQ7\nd+6s8FfeGgYMGCBqw8/Pjx599FEig+DUunVrq9t2c3Ojrl278v2NGzeWk7lZs2ZchooAQP379+fb\nr776qlUy1Ud+//33au8whO9GQECAqO7evXsWtTt37lwu44svvkgAKDIykrdjvN2nT58K23r11VfL\nPa+xTMKPXHR0tE0dRp13bx88eLDQAZkMY2eNwmffvn3cOxQAsrKyuKIsNDSUa82toWnTpjhx4gTX\nbE+ePJkfmzdvHogI165dQ0hICAIDAytoCWjWrBliY2P5M3br1s1queobwnfCHoSHh5us79OnDzIz\nM7myXEhhYGkKRldXV7i5uQEAN+k3tvkw3q7MUlP47I1XTYC/VmySkpLQokUL21fPrO1pbC2oYu+f\nmZlJbm5uJJfLSaFQUNu2balp06bk7OxM69atI8BgAQk7jTJ0Oh1lZmaK2hEsNW1tNz09nTIyMggA\neXl58fYYY9S6dWtq0aIFdzqriJKSEkpPT6f09HTKzs4mvV5vlUz1hZKSEho2bBj5+vpyJae16PV6\n6t27NzVt2pRUKhXXMQm/0IBBdxYUFESAWBlq6Qhj9uzZIhkzMzP5dyMtLY3S09MpMzOTT5MBg/K2\nY8eOFBISQmlpaSJ5s7OzKT09ndLS0igjI4MePnwoup+TkxO1adOmYYwwlixZgoKCApSUlECn00Gr\n1UKn06G4uBhvvPEGgL8cskaMGGHz/WQyGXdmmj9/PgDDL4cQ/m7evHlWtxsQEAB/f38AQFBQEK83\nHg0pFApRij9TODk5ISAgAAEBAfDx8al7VoN2JicnBzt2GIyO5XI5t7ytCgUFBUhLS8Mff/yBuLg4\nAODfM0A8ejB2AExPTwdgiPxlqYVxWQdCPz8/uLu7g4jg7++PgIAA+Pr6is4TlmLv37+Pv//977xe\n8J8JCAhAYGAg/P39uX2SgE6ng0ajsUg2s1jb09haUMXef9WqVRXqKoQil8uJiKhTp04WKQ4rQq/X\nEwCKiYmxaVRhjvbt2/ORi4TtpKen2/wZlf0+ERHt2LGDGGN8VU4on332Gb/G3d2dnJycqnSv9957\nr9zSvdB2x44diYhE1rthYWH0/PPPExGRl5cXzZo1q0r3a9q0KfXt27dhjDBM6Q2ICE899ZSorqSk\nBCqVCjdu3OD+HrZy/fp1NGvWzC5tGXPmzBkQEQoLC+3edkNg7969UKlUaNy4MRhjlep8KoNK9R7G\nlqPAX74iRITu3bvz819//XUsWrQIgMFq0zj8QGXMnj0bH330ETQaDdzc3ER6BwCIj4+HSqXCkSNH\nEBISAiJCSkoKT2iVm5uLvLy8Kj1fRkaGyDjRGhzaYaSnp+Pw4cMWPfipU6dM1hvHHBBMrzUaDb78\n8ktER0djxIgROHr0qE3OWJmZmXjw4IHV10vYn9TUVEybNg0ajQatW7dGhw4d0KVLF8yePdvu9xo4\ncCD+9re/oVu3bujXrx+vVygU3BFQ+H6tX7/eojZXr17Nv6/mfjCE6cP9+/dx8OBBABB1SkKHZil5\neXm2hz2wdmhia4HR0K5JkyaVDqeEdXWULh+idLjYq1cvXv/4449zuwxBuSMUa2wUhClJZGQktW3b\n1u5TEgnrET5XYYhuD4TPW6vVmj3nzz//5Pc2jq5lXM6cOVPpvSoyyKqoREZGEpF1hnphYWE8YhzV\n1SlJ27ZtRRm09Xo9WrRoAcYYtm7dCsCw3DhnzhwAhg7OOOiJ4LBFZMjLIfT0Fy5cQHR0NB+mCgos\na0hKSqooUhvvAAAgAElEQVRyby5hf5555hkwxjBjxgxe16ZNG6vbi4uLA2MMfn5+YIxx5WJFy6Iu\nLi5wcXEBYBh5msISX5WrV6/irbfeAmD47hoHKq6IpKQk9O3bF3l5eSb9mCpCq9XankvW2p7G1gKI\nfSrmzp1L//jHP2jEiBG8N1WpVDRmzBi+hDVkyBD6+OOP+dLWxo0bueKwefPmIv+MYcOGiZajTPmF\nWMLGjRvpxRdfpNjYWGmE4WBgtLQ9a9Ysbpq/a9cuq9rr168fAaDXXntNtGS+YcMGs+ERPvzwQ9Ey\nuLBtHHTpxIkTFt1fWFb9/PPP+YgjKiqKt2PsL2SqvPLKK5XeQ6PR0MaNG7lFcaNGjWwaYTi8w6iu\nkpaWRjdu3OD7QpQqa0lISJA6DAdT9jP29PTk2zk5OVVu78UXXyQ/Pz8iMkxtmzVrxp0YO3XqZPIa\nwa+kQ4cOIln69etHoaGhBKCc2bY5zpw5U+6ZjIM+mysRERGkUqno9ddfr/Qewg+qEEBasPuhujol\ncXV1Fe0L9glCPERTVnavvPIKf4DWrVubbDcoKAirV6/m+1WNr7hmzRowxqBSqcAYQ8uWLat0vUT1\nYLwSYqwsr2h4fufOHZEF5LBhwwAYhvdZWVlQqVT4/fffcf36dT4tEewqyiKsZMTHx6N9e0PaHYVC\ngf379+PevXsAxLFMKqJ9+/b8ezxlyhQAlVuJPvXUU0hKSoJarbZIkS+Xy9GyZUs4OzsDsM2lHoDj\nRxjGw7rRo0dz68rs7GyaOnUqP2Yc99Lb25tmz55N8+bNE9nbt2jRgrp06WKyV27WrBmtXLmSZs+e\nTdOnT6e5c+fSm2++SVOnTqVZs2bRW2+9RW+88QYlJSUREfFfi8cff5w6d+7Mo2xJOI6yn6nxd2fc\nuHH04MEDIiK6ePEivf7663Tw4EEiIvrnP/9JAGjx4sXcUezo0aP8O7V06VJuGWrsGl6WK1euUOfO\nnfkxYfrcu3dv0ZTGlEt5ZajVaj7diY6OJg8PD5E39JNPPknLly+nkpISPsoZO3ZshW1+8803ZsMm\nUH2Ykuzdu5e0Wi0BIL1eTxcuXCAA9Prrr5t86Krk6ahsqGes/yAi2rRpEwHlAwJLOI6yn5mxhzIA\neuSRR4iIuLm28Hlt2LCBb8+aNcvUPw+tX79eVGfKVb3sNSdPniSgvMvAgQMHbHpGwWNZcIE3vqfg\nVAeA9u/fX6X3BfwVzpDq6pQkMjKSbwvDf8BgNitowD/77DPRNYsXLwYRoaSkBBMnToSnp2el9zG8\nP/MdpFqtxosvvsjNeidMmAAiQn5+PogIiYmJdnleCdsRTPaN86QCwN27d8EYQ1pamijcobFBlLOz\ns8nM9lOmTOHTAYVCYXJa4eLigoiICL5//fp1AIZhvnHKjKoaVJVFkKOsfQZjDL169QJg+B737du3\n0rZ69uzJt+VyeTlz8ari8BB9OTk56NSpE06dOoUFCxbAx8cHAwYMQGpqKp5++ml8/PHHaNeuHbKz\ns5GcnIy9e/eid+/emDhxIrKzs3HkyBH+AQUFBSEsLAynT58udx+hw6gIwSv15ZdfxoMHD6DX6+Hv\n74+cnBybLeQk7IOTk5PJJE5lEToTlUrFlxJDQ0ORnZ0NjUaDwYMHY8+ePdDr9Rg1ahQyMzN5R6LV\nak0mLSoqKuJ6ChcXF54jBhDn2LH1u3Lr1i0AEIUDBIDvvvsOMpnMZN7c1NRUboXapEkT7gWr0+nQ\noUMHhIaGYufOnVVeii2HtUOT0n/A2QAuAjgP4FsAzgAiAPwBQ0Tx7wHIzVxrdnogDCk7duwo8kAd\nMmQIEYmXtqpSBgwYUOEQTliGNY6qZLzds2fPCq+XqF7KTkFsKcYxLIx1BcKQ3ZSfhhDur7Ii6FKs\nQQi3CKCc70pFGC/HmirC91h4h1TTOgwAoQBuAnAu3d8G4JXSvyNK69YDmGzmepMP9vLLL1f5wzeX\ncFdQUFnywiUk6jJ9+vQRfdcFi05BiU9E1KJFC+rfv79DdRhOANwYY3IALjDkL3kCwE+lxzcDeLYq\nDX733Xd8Ozg4GBcuXABgmFc++uijJq8xN8z6888/q3JrCYk6i7FupWnTpjwHsLH+JjExEXfv3rXp\nPlZ3GER0D8A/YEhudBdALoB4GLKdCYvJKTCMRExiLq+lm5sb3N3d8Z///AetW7fG2rVrodVqodVq\neVSjqmKJgkhCoi4ixGkREGwugPIZ8MgCXV5FMGsbYIx5wzCSGAFDZ/EDgP8C+DsRtSg9JwzATiJq\nZ+L6Cm+s1+sbfEAYCYmK+N///odnnnnG5DG5XI6SkhIkJSXx0UeLFi3QuHFjxMbGgois+ueyZUrS\nH8BNIsomIh2A7QC6A/BmjAnthsEwTamU2NhYaLVarnkWHIJGjx5tg4gSEvWXy5cvl6sTRu3CKk9U\nVBS3VL558yaf4luLLR3GHQAxjDEVMwwF+gG4BOAgDKMOwKAE3WHmegCGZa/vvvsO/fr1g1wuh1Kp\nxEsvvYSgoCAEBATgu+++w9WrV5GQkIBr167h9u3bNogsIVF/MJ6GqFQqREZGIigoSDRt9/T0RFBQ\nEBITE6HT6eDh4WHbTa3VlpZOZRYBuALDsupmAAoAkQBOAEiEYcVEYeZaAirO/iQEyi1b1qxZY6Uu\nWUKi/rB69WoCDFapq1ev5vXmki1FRETwZVtyxCoJEX1ARNFE1JaIXiEiLRElEVFXImpBRC8SUYUe\nMkuWLOGxCATnIBcXFxAZAqGWFRgQh1+XkGioCAZpwoKAgLFBmYBcLsetW7dM5guuCg639BTw9PTk\nFnJqtRq5ubk4dOgQZDIZnJ2dMWjQIJw4cQJAec2vhERDRPgBBcT/E02aNEF8fDyAv+KRCjoN42BV\n1lBrOoyy5rR9+/bFmTNn+P6gQYOwd+9eAMCoUaNqVDYJidqIEBMUAI8CBhhM4BMSElBQUFBuGbXs\nflVxeIfh7OzMh1Zt27bFw4cPkZSUxDsLwZ5e6CxsfWAJifqC8f+CEBy4R48eOHbsGLfF8PHxsWsA\na4d7qwo8/fTTuH79OpKSkkRBcTp27AjAYPX5008/mbtcQqLBYRyf87PPPkOrVq1w7Ngx0TFbPWfL\nYrXhls03rsRwS0AYgfz66694+umnq1ssCYk6w40bN6qcL8fX1xfZ2dkOMdyyG0FBQSAiUc4Hf39/\ndOjQARqNBkQkdRYSEjCEDhRWE5s1awY3NzcQEaZPnw6lUlluRfHmzZt8PzIy0qYo60At6DCaNGmC\nzz77DNu2bYOvry86deoEwBDCXcjyJCEhAZw8eRIjR44U1RUUFAAwTD0qypv6xRdfICkpCcnJyTbJ\n4FCl5xNPPIGDBw9i7NixouhCQkp6m1PTS0jUI/r37y8KqGOMqShiAmq1Gq+99hoAYOnSpXjppZes\nlsGhIwwhzaFgypqYmAgiQw5JmUxmtWeqhER9RCaTYejQoeVWChlj+OKLL/g2YwzDhw8HYBjBC0uu\nRIQXX3zRNhlsutpGMjIy8Pe//x2pqakAIAqLlpycjNOnT2PYsGHo3r07OnfujE8//dRRokpIOJzc\n3FwcOHAAy5cvBwCu8Pztt9/w5JNPAgC6desGpVKJHTt2YMCAAWjVqhXWrVuHK1eu2EcIa23KbS0o\ntW//8ccfiQwVlJiYyO3hhSjOQqYmoUhINFRWrFgh+l/o1KkT/5+4fv06AaDw8HB+vHHjxgQYoo8b\nAwdG3LKZstMOnU4HxhimTp2K2bNn4/bt24iJiXGQdBIStYd58+Zxk28AOHXqFA/227RpUxAR7ty5\ng6lTpwIA9+zu0aOH3WRwuB2Gi4sLwsPDkZiYiKtXr6JZs2bl3HPz8vLg5OSE9u3bIz09HdnZ2WjR\nogUKCwuRkpKCiIgIeHl54ffff7coorSERF0mOzsbfn5+GDFiBLZs2WJS4Xn//n0QERhjCAgIEP1P\nlfqX1D07jFmzZqG4uBgajQbdu3dH8+bNIZPJMGjQIH5OXl4eGGM8gpBGo0FhYSG/rrCwEBqNBseO\nHcPRo0cd+DQSEjWDkJfFw8PD7OpISEgIQkNDERISYtfFA4cuQ6xatQqrVq0qV79nzx70798f+/fv\nB1B5vkngL+2whERDwN3d3aIEXvam1q5bxsbGVvkaqcOQaCjk5+ebtcmoTurVhD8+Pt72zE4SEnUE\nS0be9qbedBhubm6YMWMGunXr5mhRJCSqHScnJ9vjc1pBvekw8vPz0blzZ249KiFRn9HpdBX6jlQX\n9abDAOCQFygh4ShMxe6sbmzqMBhjXoyxHxhjVxhjlxhjXRljPoyxfYyxBMbYXsaYl72ErYyQkBCE\nh4fX1O0kJByKYLRVk9g6wlgDYBcRRQNoB+AqgAUAYomoJYADAN628R4WERUVhb1799qcO1JCoi7g\nKDMCqzsMxpgHgF5E9BUAEFEJEeUCGAZDjhKU/h1us5RGJCYmYvbs2YiLixPVJyQkYPTo0bh//749\nbychUSshIoesCNpih9EEQCZj7CsYRhenAMwCEEREaQBARKmMsQDbxfyLli1bAgBWr15dzs33tdde\nQ2BgoD1vJyFRazFOulxT2DIlkQPoCOAzIuoIoACG6Ui1OqcYm8IyxkTOOBISDQVXV9cKg+ZUF7aM\nMFIAJBPRqdL9n2DoMNIYY0FElMYYCwaQbq6B999/n2/36dMHffr0qfSmV69excyZM/HLL78AAI4e\nPcojizvKkU5CoqYpLCzEzz//jNTUVDg7OyM7OxtKpRJRUVFYvHixyH/k0KFDOHTokH1ubK1ffOk/\n52EALeivPKvLS8v80rr5AJaZudbquACLFi3iPv/r16/nPv6HDh2yuk0JibrEG2+8wf8HPD09RXEy\n9u3bV+G1cGA8jBkAvmWMnYVBj7G0tMMYwBhLANAfwDIb71EO47nb1KlTuba4T58+eOqpp+x9OwmJ\nWsfatWv5P3Fubq4oUrhx5Dp7Y5PzGRGdA9DZxKH+trRbGaYMtFq1aoXr169jz5491XlrCYlaT3Ua\nMNZJS89x48ahSZMmfN/d3R15eXkoLi7Ghg0bJF2GRINGpVJVW9t1ssOIjIzEjRs3eLTkhw8fIjk5\nGUSEyZMnQyaTgTGG5557ztGiSkjUONX5g+nQEH223lvQXcjlcshkMjx8+BDOzs5gjCEwMBCMMbRv\n3x5xcXGIi4vjSZIkJOorQnS6jRs3YsKECWbPoboYos9Wli5dCoVCgZKSEhQXF2Px4sU88Gl+fj7y\n8/Oxd+9eFBUVYdq0aQ6WVkKi+pkzZw4YY3j11Verpf06PcIADNadW7duLRd9qE2bNiAiXLx4EZGR\nkWjVqhX+97//2Xw/CYnaznPPPYfjx4+bdZOwZYRRa0P0WUJkZCRu3bpl8tiFCxf4dlJSkhRNXKJB\n8Nxzz2H79u1wcnKqlvbrdIdhrrMo7UFFdSkpKTUgkYREzXLixAlkZWVBr9eDMYbt27cjKioKa9as\nqZb71ekOwxxCZzFp0iSec9J4GVZCoj6wZcsWjB07tlx9bGxstSUyr1fj9ObNm8Pf359bvS1ZsoQf\nc0T8QwmJ6qS4uBiAOFq+u7s7wsLC8NZbb1XLPeu00nPHjh344YcfcP78eVy4cAFBQUFIS0vjI4yM\njAzu7t6mTRucP3/eZrklJCZMmMAziykUCsjlchQUFCA5ORl+fn7Q6/U4d+4cZDIZiAjOzs7w8/OD\nTqdDXl4eNwNwd3eHQqHAgwcPkJubi6ioKDRu3Bh5eXkAgMGDB2POnDlm5SAivPnmm/j0008hk8mg\n1+vRq1cvxMfHo6CgwKw9hi1KT4cmY7YnAKhJkyakUql4XUZGBgGgRx55hAYNGmTX+0k0TEaPHi1y\n9KrukpubW6lM3bt3L3fd+PHjzZ6PupyM2Z7cvHkTQUFBfJ9Ke9isrCwUFhY6SiyJekRNh8WzxJHs\n6NGjeP3116FQKBAVFQUA+Oqrr3gYP8YYN2jcsGGDTfLUqw5j8uTJOHz4MN8XOgy1Wo2srCxHiSVR\nj9iyZQvGjx8PwOCz0aZNGwCAj48PAgJMB5czTmmoUCgAAM8//zyWLVuGTz75BIC4I7JmSTQ/Px9a\nrRZXr17FuHHjsGLFCgDAlClTsGzZMqxcuRIA8PHHH1e5bRHWDk1sLaiGKcnhw4dFdcKUxN/fn/r2\n7WvX+0k0bGDhlCIoKIjat29PAMjJyYm6du1KZb/7ACgwMNDk9Xfv3rVInkmTJvFrdu7cyduNi4vj\n54SGhlKPHj0a9pRkx44dvHf29vYWHRPiZmRmZjokca1E/Wbo0KGVnpOWloazZ88CMCQfOnHiBACI\npgsAkJ6ejpCQEAAQpcqwNPO6MBUBgCFDhvB2jT1XicjmKVWdt8P45ptvAABnzpxB27ZtRcc8PT1x\n5swZZGRkoH//ag3RYREzZsxAYmIiNm7ciMaNGztanAbHjz/+iOXLl3M9V2ZmJry9vREWFoYvv/zS\nojZ0Oh2GDRsGADh9+jSio6OhVCpx//595Ofno6CggJ/bpk0bFBQUQKfT4fbt2/DyMqToyc3NxYcf\nfoji4mIoFAosWrQIc+bMwTvvvAN/f3+R3sLd3R16vR7z58/HiRMnoNfr8eyzz2Lu3LkoKirC5MmT\nkZOTg+3bt6Ndu3bo378/wsLC4OXlhUuXLuH111+HUqlEYGAg7t+/DxcXF9teorVDE1sL7DQlEbTW\ntZ3c3Fw+ZGzXrp2jxWmQCO/fx8eHXF1dCQA5OzsTALp8+bJFbaxatarctMHLy4tvy2Qyvv3II4/w\nbcYY33755ZfLybV582a+3apVK95mYWEh3blzp9w9iYj+8Y9/8P1//vOfREQ0ZMgQk1MbQZbt27c3\n7CmJq6trnTDKolIFbNOmTREcHMzrjx8/LhqeCmkUJOyPSqXC0qVLkZ2dze0UhOhUOp3OojZMpbHI\nzc3l28YZ1Y2Tagmf//Lly/Htt99CLpeLpiSvvPIK3/by8oKPjw+/TpCNiLBr1y7eplwu59Pu6dOn\ngzGGnTt3imTLzMwEESElJQVEhOHDbUsTVOenJLm5ueU8VWsT06ZNw3//+1++nHXjxg1RB3fu3DkA\nBge5xYsXY9OmTQ6RsyGgVquRmpqKmJgY3L59GyUlJVi3bh0AWOyc+PLLL+OJJ55AaGgoRo8ejfnz\n58PDwwN6vR737t0DYDC4Ki4uxtWrV8EYQ0lJCWQyGRQKBTfZ1ul0iI6OxsaNG6FSqeDv7w/AMAXp\n0aMH95MSri9LZGQk0tPTUVxcjFatWuGnn34S6Sv0ej08PT3h5+dn9fsyRZ3vMGraC1Wv15uMmSiT\nyUzmiVi/fj0AiOITFBcXo6SkRPQLERERwee4EvZH+Mz++OMPnDx5ktePGjVKdLwihM9eUK536dKF\nL6sCf/kreXt7Q61WIyIiosL2vLy80KtXr3L1X375JUaMGIHo6GgQEe8wsrKyEB0djU6dOiExMZHb\nFl2+fBl79uzBrFmzKn0GW7G5w2CMyWDIepZCREMZYxEAtgLwARAPYAwRVVsYY09PT/j6+lZX8+WI\niorCtWvXTB47fPgwevfuXa6+Q4cO0Gq1yM7ORt++fXHgwAEoFArDnNCow3N1dYWrq2u1yd5QOXr0\nKHr27AlAHHG+bdu2SEtLQ1paGrePqIiAgABkZ2fz/c6dTcW/BkJDQy3qgMwpIHv37o3U1FTIZDJR\nwmVhFFIWhUJRcwZl1io/hAJgNoBvAPxSur8NwIjS7fUAJpu5ziIlU2W8+OKLVVJ6fvzxxwSAIiMj\nyd3dnbKysiq9ZsuWLQSAWrRoQQBoyJAhpNfrSa/XExGRXq8nALR27dpy1wIgPz+/StfrGzVqJFJo\nSdiHJUuWlHvXSqWSAFDnzp153ZUrVyptCwBNmTJF9NmbwsPDgwDQ448/XmFbMTExREQ0btw4rhjt\n1KkTFRYW8u9UQUEB6fV60ul0pNPpiIj49urVq7n8n3zyicXvBDYoPW0aYTDGwgAMBrAEgOAl0xfA\nqNLtzQDeB7DRlvtUBJUqk9LT05GUlASlUgkiQnFxMZRKJYKDg0VKxrfffhvu7u5o3LgxkpKSsGDB\nAkyZMoXH0KDStWqZTIbi4mLI5XKMGTMGcrkcjRo1glwux7/+9S9Rjy5s37x5E6dPn+ZOR4KyasuW\nLXjzzTdx+fJlREREcIejgoICFBcXIzQ0FBEREWCMibLBSdjOwoUL4ebmhtmzZ2Px4sVwcnJCeHg4\nGjVqhDfeeAMLFy7EY489hqZNm1rUnvD9qAhBp2ZsdWyOq1ev4j//+Q/8/Pzg6emJU6dO4erVq+jQ\noQOA8vYawF/T8GnTpmHbtm3w8fHBpEmTLJLfZqztaUr/UX8A0B7A4wB+AeAHINHoeBiA82autbhH\nrIhJkyaRr69vhb/exqhUKpo4cSIRETVu3Nhii7233nqrQjmCg4PNXpufn08ajYbvjxs3zi7PLlE5\nvr6+NHDgQLOfjZ+fn8VtyWQymjt3bqXnGY8ozQGAmjVrZlKm//3vf3yEUVhYaLF8lgJHLKsyxoYA\nSCOiswCE7o8ZbfM+ydp7WMLDhw/5vDIuLk70cOnp5dO6qtVqPr+8deuWxS9q+fLlFcohuDubKm5u\nbnB2duajoTNnztj5LUiYIzs7W+RH9P777/PPZfjw4SKdRGXo9Xqo1epKzzMe0VbE9evXRfvz588H\nADz99NP4xz/+YbFcNYktU5IeAIYyxgYDcAHgAWA1AC/GmIyI9DCMMO6Za8DSZMz37t3D/v37IZfL\nodfrUVJSAicnJ6SmpuKPP/7g5+3cuRM3b96Es7MzdDqd2S9DUVFRFR/Vvmi1Wofev6GRkZHBt0+f\nPo1vv/0WPj4+ePjwIe/ELcWSz+7HH3/EzJkzsW/fPnz77bcoLi6GSqWCTqdDSUkJX02LiIjAqlWr\ncOfOHSxcuJD/KMlkMsybN69KclVErUnGLBSUTknoL6Xni/SX0nOKmWssHkJVNNyvrBjHxxCGYxXF\nCqhuIiIiqH///g67f0NjwIABBICio6OpY8eOou9G7969SSaTWdwWAJo1a5ZF5xYXF3MrUnMlPj6e\nt2uulJSUWPXclT0H1fSUpAIWAJjDGEsE4AvAZkuk1NRUAKh06evQoUOihysuLoaHhwcYY9i6dStv\nIzc3F05OTlyZNGLECFtFrBS1Wg3GGG7duoXY2FiRMqus01xFLFmyBIwxvpRmXPbv31+NT1A32bdv\nH4gIly9fxunTp41/sFBcXCxatrQnCoUCGo2mwn8+QbEJGHyiBLkA4J133gERVVv0b2uxi+EWER0G\ncLh0OwlAV3u0K3Dnzh2sXbsWSqUSxcXF/IO+f/8+zp49i1mzZuGVV14pN7zMycnhw9E33ngDiYmJ\n0Gq12L17N/R6Pbp3747ExET8+OOP9hTXJKb0KQK5ubno1asXNBoNpkyZYjZjFQC8++67UCqVmDdv\nHtRqNfR6PVxcXLBkyRJ8/fXX6NevX3WIX2/Q6/VYvHgxACAvL69SK+H79+/jn//8J7ffsKdVMRFx\nWb7//ntcuXIFI0eOxI4dO7B06VJRTNpag7VDE1sL7GxvAJiPhzFr1izR+nvZ8uyzz9pVFlNkZmZa\nPI2qiJYtW1KnTp3K1QOg1157rbrErzcsW7aMAJBcLqe+fftW+r6Fz0QulxMAOnPmjN1k+fTTT81+\nB+bPn2+3+5QFtWxK4jDKro9T6Yhj1apVICKo1WqTL+G///1vtcsmyAKII5ibitJUdqohFFdXVxQU\nFJjU1Lu4uIisGCVMk5mZCcCgvAwICDBrPSkQGBiI559/HlqtFkSE9u3b200Wc9agDx48wLJly+x2\nH3tS531JjBk2bBjc3NygUqlQUFAg8hx0NMZxEry9vfnQNiYmBlFRUcjOzoZarYazszNkMhnUajXk\ncjnkcjm2bduG/Px8FBUVISUlRdSWQFFREXbs2IFnnnkGAwcOrLHnqo1cunQJixYtgqenJx4+fIji\n4mL4+PhArVbzADZjx47FgQMHeAdSFipdSk9PTxetstiT2bNnIy4uDrt378b48ePRvXt3TJo0CTdu\n3MBjjz1WLfe0GWuHJrYWVMOUxFypDdy+fZvLY2ywUzY2giliYmIoICCAX7dp06Zy50ybNq1WPa8j\nEd6DsQGVp6dnlYb+N2/e5OccPHiwWuScP38+v0d2djaX/dSpU9VyPwFIUxIDlhhuOQpjpzJjgx0h\nLFtFBAQEICMjg1/36quvlpuu/Otf/7K/0HWUiIgIDB48mMeCICLk5uaCiLhxlFBvbugveIgSkcg+\n6LfffuPvXAhNYC2PPvoo3/b19eVTaiEWRm2kXk1JXnnlFXh4eCAkJAQZGRl86N6jRw9s3rwZzZo1\nc5hs/v7+iIuLQ+/evREcHIxNmzYhJCREtLRmjh07duDPP/8EkcGPQa1Wc+MfrVbLPV/nzJmD48eP\nY/jw4diyZUudCCxUHdy6dcusB7PwnXj88ceRlpYGf39/qFQq3Lt3D25ubvDz88Pdu3d5VrEOHTrg\nhx9+wHvvvYfjx4/zJEOAYRm/Xbt2Vss5ZswYtGnTBmq1GiUlJVAoFPD396/daT2tHZrYWmDnofPw\n4cP58K5p06blhp6PPfaYXe9nLS4uLtS1a9dqaXvRokX8eavivVjfAEAdO3Y0eezy5cv0yCOP8OmK\nt7c3hYeHE2AI12fqu9OpU6dydU2bNqXk5OQafjL7ABumJPVmhLF9+/ZydQUFBXB3dwcAk4FKHEFw\ncHC1Bcox/rWzZORSX4mMjDQ71YuOjkZKSkqlbRin2Tx16pTomJeXVzk/kIZCnc6taglFRUXQarXc\n4tPRCPPfMWPGYPPmzXZvXxhyV5cFY12AMYauXbuK/IysoaioCEVFRcjPz4eLiwvPierm5mZx+P/a\niC25Vet9h1GbyM3NFZmBN7TnrykYY+jQoQPi4+MdLUqtxJYOo16tktRmioqKeGdhycqIhPWEh4dL\n75m8/2gAABeWSURBVLiakDqMGiI/P59v379/34GS1H8yMjJM+nwIofjnzp3rAKnqB9KUpIa4ePGi\nKMI0ABw5cgQ9evRwkET1F8YY2rZtW85OgjEGpVIJjUaD2NhY6HQ69OzZs8EFXpamJHUAU51jz549\nayQ0fEMjICCAp0M0pmXLltx/o3///hg0aJDJ8yTMI3UYNYSpFRrGmFlfBgnr0ev1JjOZXb16lXfQ\nRITnnntOin5WRaQOo4YoO8Lo0aMHiAjx8fHl1vklbCMrKwtpaWkmjwkdxNWrV3H+/HmL8odI/EXd\nXUyuY5SdJx89ehQAcOXKFXTu3FlaYrUjrq6uZlMEurq6QiaTITo6uoalqh9II4wawjjvpSlMxb/4\n29/+VkPS1Q+Ki4vh5eWFwsJCkx1Gv379sHLlyloV9qCuIa2S1BCC0dZHH33EtfXFxcXQ6XS4fPky\nHjx4AI1GA6VSib1798LFxQVFRUXlRh7Xr1/HJ598And3d27F+tJLL6Fv374OerLaQ3p6OoKCgrB0\n6VJMnz69nPMdYwy9evWCv78/GGM4c+YMkpKSGtzozpZVknrjfFbbycnJsThWBUodnKZNm1buWMuW\nLU2GG5QgSk9Pr/BdAKD333+f7z///PPk6upaE6LVKuCIeBiMsTDG2AHG2GXG2AXG2IzSeh/G2D7G\nWAJjbC9jTEpJbgXTpk3DZ599Vq6+uLgY7dq14+EGd+3a5QDpaieV+Qo5OTmJIs8zxnjcCwnLsEXp\nWQJgDhGdZYy5AzjNGNsHYDyAWCJawRibD+BtGFIPSFQBIR4DYIiaPm3aNLi5uSEpKQlyuRwjR45E\nVlZWrQoS5GiodGrx1FNPobCwEAEBASguLsaDBw/g4+MDnU6H9evX49ChQ/Dy8sL+/ftF71micqzu\nMIgoFUBq6XY+Y+wKDJnOhsGQ2AgwJGM+BKnDqPI82TgfxeDBg3Hp0iXuH1FSUoJjx47h7t27AIAn\nn3zSfoLWYXx9fREZGYk9e/YAMLihazQaqNVqnsA4JSUFKSkpCAoKwoMHD7Bo0SJHilznsMuyKmMs\nAoakzH8ACCKiNMDQqTDGyofFboCYGi536NABZ8+ehZ+fHzIzM3HgwAGeV8Q4mnVwcDC0Wi0SEhLQ\nqlUreHp62uy6XR9xcnLCzZs3ARiibkVGRvJjwsrI9u3bMXz4cIfIVx+wucMonY78CGBm6UijYamc\nLUToMCIiIgAYPCrPnj2LRx99FJcuXUJUVBRu377Nz1+6dClWrFgBlUrFHal69+6NK1eumExNICFG\nCHCTkJAAvV4PmUwGlUqFRo0aOViyuo1NHQZjTA5DZ7GFiHaUVqcxxoKIKI0xFgzA7CTb0mTM9QE3\nNzcMGDAABw8eBGMMbm5ucHV1xb///W9MnDgRt2/f5vlGhCVVY7NlmUyG7OxseHp6VkvgnfqGYPfS\nokULB0vieOyZjNkmOwzG2NcAMolojlHdcgDZRLS8VOnpQ0TldBgNzQ7DHH/++Se6dOnC9319fZGV\nleVAieoHv//+O3r37t3gbCwswSHeqoyxHgBGA+jLGDvDGItnjD0JYDmAAYyxBAD9AdTOFE41DBEh\nJiYGPj4+IivO8+fPAzDMsYlI6iyqwJo1ayCTyaBUKsEYw44dO/gxYQoYHh5uczoACSOsNeCwtaCB\nGRsJhltt27al4OBgbmC0fv16yfDKSlQqlch4zc3Njc6fP09ERHq9nnr37k0AaOTIkQ6WtHYBKZFR\n3eHcuXP4+eef+b6Liwtf8pOoGmUVmAUFBWjbti0A4Nq1a4iLiwMAJCYm1rhs9RXpm1pDCEPkwYMH\nIyYmhtfrdDrJGcpKwsPDTdaXnZ7k5ubWlEj1Hsn5rIbIyckplwJv27Zt2LdvHzZt2iQp56zg7t27\nmDhxIjfUAoCgoCCkpaXx9JKAIfXg4MGDUVJSgqFDh+LcuXPIzs5GcnIyFi1ahG7dujnqERyClGag\nDiB4qwoxJY1p0qQJbty44SDJ6j5ljeLkcnmVfEQa0vcQkGJ61il8fX15VjJBkSR1FrYhvMfs7GwA\nkBzKqhGpw6hh7t+/bzZ8nIRt+Pj4cA9f48xkjDF4eXnBz88PXl5ecHNzg7u7O/z8/PDll186Stw6\nidRh1BDGeUkmTJjgQEnqN9OmTYNcLkdUVBSvGz16NHJycpCZmYmcnBzk5+fj4cOHyMzMxKuvvupA\naeseUodRQxjPs/Py8vj2pUuXeEg+wYhLwjZCQkJEcS/MraZIVB0pCHANYRwEWFjyGzVqFK5du8br\nv/vuO25HIGE9ycnJfIXkiy++wLhx4xwrUD1CGmHUEMZTksWLFyM4OBhbt27F6dOn8dRTTwFAnc4I\nXpv44IMPuCPfxIkTpfdqR6Rl1Rrizp07aNy4sWgJr2fPnjzdgED79u1x5syZmhav3iE5n5nHlmVV\nqeutIYy/uFqtFlOnTsXRo0fh5OTEs3S1bNkSZ8+eRb9+/ZCeng4/Pz+oVCrcv38fq1atkiKDwxAZ\nfOzYsSAipKamwsPDA15eXrh//z4UCgUCAgKQmpoq0hNJ2BFrnVBsLWhgDle3bt3iTmYnT54UOU0J\nZdKkSRQSEkJeXl4EgDw9PSkkJIRvSxCNGjWKAFBgYCCPnt6oUSP+DiMjI/n2008/7WhxayWwwflM\nGmHUEMarJILviL+/P6Kjo/H7779DoVAgLCwM9+7d4/k08vLy+C9ls2bNal7oWoiHhwd8fX0lWxYH\nIekwaojk5GQ0atQIMpkMzs7OXClXltatW+PixYuiutjYWDzxxBOSVysMK0tbt26VdBM2IJmG1wFC\nQkIQGBgIvV5vsrOQy+Um82R0795d6iyMkDx7HYv0Lawh5HI50tLSMGjQIJPHS0pKQES4evUqr2vd\nujWOHj0qdRZGeHt7w8tLyo3lKKRvYg2zZ88enDx5slx9aGgoEhISREPtl156qSZFqxLdu3cHYwzb\ntm2ze9sff/wxGGMYM2ZMuWMFBQVSfAsHIukwHAAR4aWXXsKVK1dw+fJlvqy6YMECfPzxx1i/fj0W\nLFiAvLw8s3P1K1euIC0tDTKZDIwxuLi4oFOnTlbJk5CQgPT0dGi1WkRFRSE0NBQAcObMGeTn5/Np\ngDDS0Wq1PH+Kq6srfv31VyiVSnTp0kVkkl0Zer0ex44dAxGBMQa1Wg2lUonevXtzF/UNGzagefPm\nvN2///3vOHTokKTDsAEpGXMd5s8//+TLgMePH+f1Y8aMoYCAAJPXCEmHy5YPPvigyve/ceNGuXaI\niD777DOT96ioTP7/9s4+uIoqS+C/k+S9fBKCRkJJwiAfMgtDJQ6wULIgtaDyUZlFKQTjKiCW/OHo\nOlXZmcBoAfrHwhYUrDW1Y1kOI7XymWFAYIDABhUsimWCCfIRAoqwsGBYa0NCJAlJ3t0/uvva7+Ul\nvBdehwD3V9VV3ffd7tOnX/fpe+85fe6CBVHJnjhxYtQyADVu3Lio9TT8CN0xp6eITBaR0yJyxp5u\nwBCGkSNH6j/DnbqvtrZWfw8Ryg8//AAQaoC5cuVK1PKvXbumj7Vx40bAegO99tprbWSEyhs4cGDQ\nsaKZ+2LUqFGUlpbq6FelFA0NDaSlpYWt//zzz+t6Tq5OQ9fjSRyGiMQBvwMmApeBv4rIJ0qp0x3v\naXBwJjE6dOgQZWVl+P1+4uPjaWxspKamBrBctTt27NDN9Rs3btzyuDdv3uSjjz7SHhlnakGAGTNm\n8Pbbb3Pu3DkaGxuZM2dOh8eaMWMG27Zt00l23TO33YqysjKmTJnC8uXLddnZs2epr69n5syZHDly\nRB8vKSmJDRs2sH79el338OHDVFRUUFBQQHp6esRyDbdJZ5smHS3AGGC3a7sI+E1InVi1sO5JXnjh\nBZWRkRHUFI+Pjw/a7tu3b9B2Xl7eLY+bl5fX5li9e/eO+vycaFT3kpubG/H+gKqqqgoqO378eIdd\nkdD9AdWjR4+oz/1+h27YJekLXHRtX7LLDBHS2tqquwsHDhxAKaVdr3v37gXQs7c7X2NG8lWmk1zG\nOZZSqlNRk9euXQu6kZysVp1l4cKFDB8+vMM6Tt4Qd9SscbF2LV6FhocbgTXD2lGwbt06Ro4cSWFh\nIe+88w5Dhw5l2LBhvPrqq0FjGykpKYwYMYKDBw9SW1tLeXm5zhkajm+++UZ3aWKJUorKykqKiopo\namri5s2bpKam0traSmNjIwUFBYwdOzZoH8c7BLBs2TJSUlK4ceMGU6dOZdeuXUF1Bw8ezKBBgxgx\nYgQ+n4/Fixfz4osvsnjx4pjrYmgfT9yqIjIGWKKUmmxvF2E1g5a76ij3n32vT8bcWUIzYjc0NLBm\nzRo9KBmOjv7TAQMGUFtbG/MpGQsLC1m5cqWeSBosN6w7MtN9XiJCVVWVniy5f//+9OzZ85ZZx9as\nWcO8efMQEQ4cOMC4ceNiqse9SOhkzEuXLu1eblUgHvga+AngByqAvwmpE8tu2T0LYfrykydP1lMD\nusvz8/N1X3/z5s1h9x01apQaNmyY5+ddWVl5yzEI9xhGTk5Ou2MXkyZNCnstysvLPdfjXoTu9rWq\nUqpVRH4J7MWKJv2DUqrSC1n3Ih988AGbN2/G5/Mxbdo0Ll68iFKK48ePA/Dpp58CUF1dzc6dO4mP\nj8fn83Hy5El27NgBoJv0xcXFena1goICKioqOmyBxIrdu3dr+c3NzTz11FNt6ri7JOvWrWP+/PlB\nKQsdTpw4wXPPPUd+fj6zZ8/G5/ORk5NDXl6edwoYwtNZS3O7C6aF0S643qLOxM2AGjZsmMrJyVFZ\nWVlt3thKKbVixQpd/sorr7TrWXj//fc912HVqlVhz9F9Lu4WhqNTe4vjlVm7dq3n536vQzf0khhu\nk/Xr16OU4sqVK/rPOnHiBKmpqfj9/rD7JCQk6JiM1NRU7UFYvXq1Hgs5evQoCxYs8Pz8z58/DwR7\nNkSE/fv36zpDhgzR5dXV1TokPZy3x/l+JHS6SUPXYgxGN8XdXHdTVVXF999/D1hRou6ZyRsaGnTA\nV11dnX7IiouLdZ2OgpxaWloYP348Y8eOpW/fvgwfPpxp06YFJTCOFGc2t8cee4ykpCRdPn36dJ01\nfeXKlWzfvp0nn3wS+PFblaFDh5KamgpYgWvPPvssAN9++y35+flRn4shdhiD0U1pb7q/zMxMHT59\n9OjRoIl4Qmf7cnA/sO21TpRSFBcXc/DgQa5cucLly5e5cOECu3btori4OFyXskMuXrTCcOrq6oLy\nf1y/fp3p06cD8PTTTzNlyhT27dsHoHX57rvvdPj7mDFjdHxG//79bynX4C3GYHRT3A+5mz59+ugU\nfgBffPGFNg5+v193SXr06KFbExkZGWRnZwPtu1xzc3MpKCgA4Ny5cyilqKurIzk5mZdffpm4uLig\nxfm6tD2c1sLXX3/dxsg4cSI+ny8o14fj+quurmbFihX6OEuXLm1XjqFrMQajm9JRl8T9/cfgwYP1\nemNjo+6S1NfX63ygV69e5dKlSwA8+uijiAiJiYl6/MDv92sPzJAhQ+jZsyciwuDBg/U4yMMPP6zf\n8M44Qugs9A7Lly8PO1VCa2srLS0tlJWVaVmbNm3SHhRHr+TkZAoLCwHrm5rQgC+HI0eO4Pf7mTRp\nUrvXyxBbTBLgbsqFCxeoqqrSD3VzczMPPfQQe/bsYebMmWEDr9xva+eNXldXpwOpZs2axebNmwFI\nTEwkEAgQCARISkpCRMjIyCAzMxOlFImJiTz44IOkpaURCATIysoiMTGRpqYmevXqxcSJE8OGZZeX\nl1NUVKS3165dS2ZmJgkJCaSkpJCVlUUgEGDBggV8+OGHzJ07l5s3b9KvXz/effdd5syZQ3p6Oqmp\nqRQUFNDc3KwN05kzZwgEAlrP+fPn09zcTGlpKTU1NWRmZsbo6hvapbPuldtdMG7VdklPT2/XvdjU\n1KQ2bdqkAJWdna0ef/xx7b5cvXq1Xn/jjTdUUlJSh67KQCAQ0/PeunVrRPksnOWll14KCurauHFj\nmzo+ny+iY924cSOmutzLcD+7VaPJwXC3yKytrW3zRznuyJaWFv2GvXTpEocOHdL7OfkwRIT33nuv\nzRiDUors7GztgbgV0eoZLugKrLwZym7xbNmyRa+/9dZbQeMbjvfHTXNzM2+++WbYm3f8+PGkpqai\nlCI5OTmqcw3lXryPvJB513dJPvvssy7/BuVOyPz8888B2LlzZ9A0BAkJCTzxxBMUFRXpBDgDBw6k\noaGB0aNHc/36dU6fPs2ECRNYtGgRNTU12pCEfqcSSrR6ur829fl85ObmUlZWRmJiItu2bWsjs6Sk\nhGPHjuH3+1FKaRdx7969qa+v1/k9KisrtSs2EAggIsTFxXH+/HntTbld7pf76L43GPcLSin8fj+z\nZs0KKm9paaG0tJTS0lJd5sRAbN26VZd9/PHHQfvdylh0BneodnNzsx7cPHXqFM888wyAzjualpbG\n66+/HvY4V69eDdouKSmhpKQkbF3Hs2PoGozBuEsQkXa9Et2FPn36RBSjAVY8RjiWLFnCkiVLYnhW\nhlhyR7OG3xHBBoMB1cnP2++YwTAYDHcfd72XxGAwdB3GYBgMhoi5qw2GiBSKSEBEHnCVvSciZ0Wk\nQkRilmFFRP5VRCrt424RkXTXbwttmZUi0jZTzO3L9nyOFxHJFpH9InJKRI6LyBt2eS8R2SsiVSJS\nIiIxz7orInEi8qWIbLe3+4vIYVvmBhGJ6eC8iPQUkWL7/zopIqO91lNEfiUiJ0TkKxFZJyJ+L/QU\nkT+ISLWIfOUqa1e3qJ+XzkZ83ekFyAb2AN8CD9hlU4C/2OujgcMxlDcJiLPXlwH/Yq8PBcqxPE79\nsVITSgzlxvFjukMfVrrDn3pwPfsAefZ6GlAF/BRYDvzaLv8NsMwD2b8CPga229ubgJn2+u+BBTGW\n9xEwz15PAHp6qSfwMHAO8Lv0m+OFnsDfAXnAV66ysLp15nmJ6R/flQtQDAwPMRjvA7NcdSqBLA9k\nTwf+w14PmnMF2A2MjqGsW87x4tH13WYbydPONbSNyukYy8kG9gETXAbjf13GeQywJ4byegDfhCn3\nTE/bYFwAetkGajvwJHDVCz2xXi5ugxGqW6W9HvXzcld2SUQkH7iolDoe8lPofCj/gzfzobwMOHnw\nvZbZ5XO8iEh/rLfUYawbqBpAKfUd8FCMxa0C/hl7GgoReRCoUUo56cYvYT1wsWIA8L2I/NHuBn0g\nIil4qKdS6jKwEvhvrPujFvgSuOahnm56h+jW2y6P+t7ttoFbIrIPyHIXYd1UbwGLsCx0m93ClEXs\nN+5A5m+VUjvsOr8FmpVSG2IhM5LT8vj4wcJE0oA/Af+klKr3Ml5GRKYB1UqpChGZ4BTTVudYnkMC\n8HPgNaVUmYiswmq1ealnBvAPWG/+WqzW8ZQwVbs6xiHqe6vbGgylVDiDgIj8DGus4JhY8c3ZwJci\n8rdYVjrHVT0ba27X25Lpkj0HmAr8vav4tmRGwCWgn4fH19iDbn/C6m59YhdXi0iWUqpaRPpgNaNj\nxVjgFyIyFUjG6i6sBnqKSJz99vXiel5USpXZ21uwDIaXek4Cziml/g9ARLYCjwMZHurppj3dor53\n77ouiVLqhFKqj1JqgFLqESylH1NKXcXqG74EejKla05T7HYRkcnAr4FfKKXcMdrbgdn2qPcjwCDg\nSCxk2vwVGCQiPxERPzDblukFa4BTSql/c5VtB+ba63OAT0J36ixKqUVKqX5KqQFYeu1XSv0j8Ckw\n0yOZ1cBFEXnULpoInMRDPbG6ImNEJMl+yTkyvdIztJXm1m2uS070z0usBnbu1II1+vyAa/t3WF6F\nY8DPYyjnLNbA1Zf28u+u3xbaMiuBpzzQcTKW1+IsUOTRdRwLtGJ5YcptHScDDwD/acvfB2R4JP8J\nfhz0fAT4L+AMlifBF2NZuViGuAL4M5aXxFM9gcX2/fEVsBbL4xVzPYH1WK2EJixDNQ9rsDWsbtE+\nLyY03GAwRMxd1yUxGAx3DmMwDAZDxBiDYTAYIsYYDIPBEDHGYBgMhogxBsNgMESMMRgGgyFijMEw\nGAwR8//9Y6WTlqlWbwAAAABJRU5ErkJggg==\n",
2583       "text/plain": [
2584        "<matplotlib.figure.Figure at 0x7f4026f76c18>"
2585       ]
2586      },
2587      "metadata": {},
2588      "output_type": "display_data"
2589     }
2590    ],
2591    "source": [
2592     "plot_trace(trace_tour(rw))"
2593    ]
2594   },
2595   {
2596    "cell_type": "code",
2597    "execution_count": 1037,
2598    "metadata": {},
2599    "outputs": [
2600     {
2601      "data": {
2602       "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQMAAAEACAYAAAC3RRNlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nf+gzCYz9KNTkAAAAAElFTkSuQmCC\n",
2603       "text/plain": [
2604        "<matplotlib.figure.Figure at 0x7f402c0e22e8>"
2605       ]
2606      },
2607      "metadata": {},
2608      "output_type": "display_data"
2609     }
2610    ],
2611    "source": [
2612     "plot_trace(trace_tour(trim_all_loops(rw)))"
2613    ]
2614   },
2615   {
2616    "cell_type": "code",
2617    "execution_count": 1013,
2618    "metadata": {},
2619    "outputs": [
2620     {
2621      "name": "stdout",
2622      "output_type": "stream",
2623      "text": [
2624       "[Mistake(i=20, step=Step(x=8, y=0, dir=<Direction.UP: 1>)), Mistake(i=38, step=Step(x=10, y=2, dir=<Direction.UP: 1>)), Mistake(i=42, step=Step(x=8, y=4, dir=<Direction.LEFT: 4>))]\n"
2625      ]
2626     },
2627     {
2628      "data": {
2629       "text/plain": [
2630        "'FFFFFLLRRFRFLFLLRFFRRFLFFFFRRFFRFFLFFRFFFFRRRRRRFLRRFLLFFFLRFRRFFFFFRRFRRFRFFRFLLFLLLFLLFFLFLFFFFFLFFFFRRFFFFRRFFFFRRFFFFFRFRFFFFLFLRFRRRLLRFFRRFFRFRFLRLFFFFRRRFLFFRFRLFRRFRFLFFLLFLRFFFRFRFLRFLLFFFFRLLLLFLFFFLFLFRRFFLR'"
2631       ]
2632      },
2633      "execution_count": 1013,
2634      "metadata": {},
2635      "output_type": "execute_result"
2636     }
2637    ],
2638    "source": [
2639     "w_tour = rw\n",
2640     "w_trace = trace_tour(w_tour)\n",
2641     "mks = mistake_positions(w_trace)\n",
2642     "print(mks[:3])\n",
2643     "trim_loop(w_tour)"
2644    ]
2645   },
2646   {
2647    "cell_type": "code",
2648    "execution_count": 1014,
2649    "metadata": {},
2650    "outputs": [
2651     {
2652      "name": "stdout",
2653      "output_type": "stream",
2654      "text": [
2655       "74\n",
2656       "73\n",
2657       "72\n",
2658       "70\n",
2659       "66\n",
2660       "54\n",
2661       "47\n",
2662       "45\n",
2663       "41\n",
2664       "37\n",
2665       "25\n",
2666       "22\n",
2667       "15\n",
2668       "14\n",
2669       "13\n",
2670       "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF\n",
2671       "FFFFFLLRRFRFLFLLRFFFFFRFLFFFFLFFLFRFRFLRLFFFLLFRLRFFFRFRFLRFLLFFFFRLLLLFLFFFLFLFRRFFLR\n",
2672       "Step(x=0, y=0, dir=<Direction.DOWN: 3>)\n"
2673      ]
2674     },
2675     {
2676      "data": {
2677       "image/png": 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iP3FOpkjgBCk3ANPMrBWwCvhphreXqNTJL84///yEJ5F8kvp+aA7fF5nu/lwM/CBLs4hI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\nCgQRCSgQRCSgQBCRgAJBRAL/C3NK901rmAdaAAAAAElFTkSuQmCC\n",
2678       "text/plain": [
2679        "<matplotlib.figure.Figure at 0x7f40276002e8>"
2680       ]
2681      },
2682      "metadata": {},
2683      "output_type": "display_data"
2684     }
2685    ],
2686    "source": [
2687     "w_tour = rw\n",
2688     "w_trace = trace_tour(w_tour)\n",
2689     "mks = mistake_positions(w_trace)\n",
2690     "while len(mks) > 3:\n",
2691     "    print(len(mks))\n",
2692     "    w_tour = trim_loop(w_tour)\n",
2693     "    w_trace = trace_tour(w_tour)\n",
2694     "    mks = mistake_positions(w_trace)\n",
2695     "print('{}\\n{}\\n{}'.format(w_tour_start, w_tour, trace_tour(w_tour)[-1]))\n",
2696     "plot_trace(trace_tour(w_tour))"
2697    ]
2698   },
2699   {
2700    "cell_type": "code",
2701    "execution_count": 1015,
2702    "metadata": {},
2703    "outputs": [
2704     {
2705      "data": {
2706       "text/plain": [
2707        "[Mistake(i=70, step=Step(x=-2, y=6, dir=<Direction.UP: 1>)),\n",
2708        " Mistake(i=71, step=Step(x=-3, y=6, dir=<Direction.LEFT: 4>))]"
2709       ]
2710      },
2711      "execution_count": 1015,
2712      "metadata": {},
2713      "output_type": "execute_result"
2714     }
2715    ],
2716    "source": [
2717     "mks"
2718    ]
2719   },
2720   {
2721    "cell_type": "code",
2722    "execution_count": 1016,
2723    "metadata": {},
2724    "outputs": [
2725     {
2726      "data": {
2727       "text/plain": [
2728        "'FFFFFLLRRFRFLFLLRFFFFFRFLFFFFLFFLFRFRFLRLFFFLLFRLRFFFRFRFLRFLLFFFFRFLFFFLFLFRRFFLR'"
2729       ]
2730      },
2731      "execution_count": 1016,
2732      "metadata": {},
2733      "output_type": "execute_result"
2734     }
2735    ],
2736    "source": [
2737     "trim_loop(w_tour)"
2738    ]
2739   },
2740   {
2741    "cell_type": "code",
2742    "execution_count": 1212,
2743    "metadata": {},
2744    "outputs": [
2745     {
2746      "data": {
2747       "image/png": 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WL0S5ubl8/PHHAcnRQzr3AsTfHvo+ffpw5MgRy1ZjgOuvv55vvvmG6upqo+W+xaXt2bOH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\n",
2748       "text/plain": [
2749        "<matplotlib.figure.Figure at 0x7f4027ba30b8>"
2750       ]
2751      },
2752      "metadata": {},
2753      "output_type": "display_data"
2754     }
2755    ],
2756    "source": [
2757     "lc = trace_tour(square_tour(a=10))\n",
2758     "rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
2759     "plot_trace(trace_tour(rw))"
2760    ]
2761   },
2762   {
2763    "cell_type": "code",
2764    "execution_count": 1247,
2765    "metadata": {},
2766    "outputs": [
2767     {
2768      "data": {
2769       "text/plain": [
2770        "(254,\n",
2771        " 20,\n",
2772        " 'RLLFLRRFLLFFFFLFLFRL',\n",
2773        " [Step(x=-1, y=0, dir=<Direction.DOWN: 3>),\n",
2774        "  Step(x=0, y=0, dir=<Direction.RIGHT: 2>)])"
2775       ]
2776      },
2777      "execution_count": 1247,
2778      "metadata": {},
2779      "output_type": "execute_result"
2780     },
2781     {
2782      "data": {
2783       "image/png": 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ubBEp0ujRo7F+/XoAQGVlJZ566ikkk8nAqc4PKigRcUsFJSJuqaBExC0VlIi4pYISEbdU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\npss0Ar0AAAAASUVORK5CYII=\n",
2784       "text/plain": [
2785        "<matplotlib.figure.Figure at 0x7f402c1a5cf8>"
2786       ]
2787      },
2788      "metadata": {},
2789      "output_type": "display_data"
2790     }
2791    ],
2792    "source": [
2793     "rw_trimmed = trim_all_loops(rw)\n",
2794     "plot_trace(trace_tour(rw_trimmed))\n",
2795     "len(rw), len(rw_trimmed), rw_trimmed, trace_tour(rw_trimmed)[-2:]"
2796    ]
2797   },
2798   {
2799    "cell_type": "code",
2800    "execution_count": 1281,
2801    "metadata": {},
2802    "outputs": [
2803     {
2804      "data": {
2805       "text/plain": [
2806        "(1, Step(x=0, y=0, dir=<Direction.RIGHT: 2>))"
2807       ]
2808      },
2809      "execution_count": 1281,
2810      "metadata": {},
2811      "output_type": "execute_result"
2812     },
2813     {
2814      "data": {
2815       "image/png": 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lImGpoEQkLBWUiIRVVEGZ2TQzW2dmrWZ2elahRAaSt99+m+nTpwPw5ptvcvnll/P+++8n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\nL6Qd6rXaC/YAAAAASUVORK5CYII=\n",
2816       "text/plain": [
2817        "<matplotlib.figure.Figure at 0x7f40275e2908>"
2818       ]
2819      },
2820      "metadata": {},
2821      "output_type": "display_data"
2822     }
2823    ],
2824    "source": [
2825     "rw_trimmed = rw\n",
2826     "mks = len(mistake_positions(trace_tour(rw_trimmed)))\n",
2827     "while mks >= 4:\n",
2828     "    rw_trimmed = trim_loop(rw_trimmed, random_mistake=True)\n",
2829     "    mks = len(mistake_positions(trace_tour(rw_trimmed)))\n",
2830     "    \n",
2831     "# rw_trimmed = trim_all_loops(rw)\n",
2832     "plot_trace(trace_tour(rw_trimmed))\n",
2833     "mks, trace_tour(rw_trimmed)[-1]"
2834    ]
2835   },
2836   {
2837    "cell_type": "code",
2838    "execution_count": 1282,
2839    "metadata": {
2840     "collapsed": true
2841    },
2842    "outputs": [],
2843    "source": [
2844     "def trim_some_mistakes(tour, mistake_limit):\n",
2845     "    trimmed_tour = rw\n",
2846     "    mistake_count = len(mistake_positions(trace_tour(trimmed_tour)))\n",
2847     "    while len(mistake_positions(trace_tour(trimmed_tour))) >= mistake_limit:\n",
2848     "        trimmed_tour = trim_loop(trimmed_tour, random_mistake=True)\n",
2849     "    return trimmed_tour"
2850    ]
2851   },
2852   {
2853    "cell_type": "code",
2854    "execution_count": 1299,
2855    "metadata": {},
2856    "outputs": [
2857     {
2858      "data": {
2859       "text/plain": [
2860        "(1, Step(x=0, y=0, dir=<Direction.RIGHT: 2>))"
2861       ]
2862      },
2863      "execution_count": 1299,
2864      "metadata": {},
2865      "output_type": "execute_result"
2866     },
2867     {
2868      "data": {
2869       "image/png": 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2870       "text/plain": [
2871        "<matplotlib.figure.Figure at 0x7f402c0c5f98>"
2872       ]
2873      },
2874      "metadata": {},
2875      "output_type": "display_data"
2876     }
2877    ],
2878    "source": [
2879     "rw_trimmed = trim_some_mistakes(rw, 4)\n",
2880     "\n",
2881     "plot_trace(trace_tour(rw_trimmed))\n",
2882     "len(mistake_positions(trace_tour(rw_trimmed))), trace_tour(rw_trimmed)[-1]"
2883    ]
2884   },
2885   {
2886    "cell_type": "code",
2887    "execution_count": 1300,
2888    "metadata": {
2889     "collapsed": true
2890    },
2891    "outputs": [],
2892    "source": [
2893     "patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
2894     "tours_filename = 'tours-with-mistakes.txt'\n",
2895     "\n",
2896     "try:\n",
2897     "    os.remove(tours_filename)\n",
2898     "except OSError:\n",
2899     "    pass\n",
2900     "\n",
2901     "success_count = 0\n",
2902     "while success_count < 100:\n",
2903     "    lc = trace_tour(random.choice(patterns)())\n",
2904     "    rw = guided_walk(lc)\n",
2905     "    if rw:\n",
2906     "        rw_trimmed = trim_some_mistakes(rw, random.randint(0, 15) + random.randint(1, 3))\n",
2907     "        if len(rw_trimmed) > 10:\n",
2908     "            with open(tours_filename, 'a') as f:\n",
2909     "                f.write(rw_trimmed + '\\n')\n",
2910     "                success_count += 1"
2911    ]
2912   },
2913   {
2914    "cell_type": "code",
2915    "execution_count": null,
2916    "metadata": {
2917     "collapsed": true
2918    },
2919    "outputs": [],
2920    "source": []
2921   }
2922  ],
2923  "metadata": {
2924   "kernelspec": {
2925    "display_name": "Python 3",
2926    "language": "python",
2927    "name": "python3"
2928   },
2929   "language_info": {
2930    "codemirror_mode": {
2931     "name": "ipython",
2932     "version": 3
2933    },
2934    "file_extension": ".py",
2935    "mimetype": "text/x-python",
2936    "name": "python",
2937    "nbconvert_exporter": "python",
2938    "pygments_lexer": "ipython3",
2939    "version": "3.5.2+"
2940   }
2941  },
2942  "nbformat": 4,
2943  "nbformat_minor": 2
2944 }