Done problem set and solution for day 6

diff --git a/06-tour-shapes/06-tours.txt b/06-tour-shapes/06-tours.txt
new file mode 100644 (file)
index 0000000..c6946e8
--- /dev/null
+++ b/06-tour-shapes/06-tours.txt
@@ -0,0 +1,226 @@
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diff --git a/06-tour-shapes/tour-shape-plots.py b/06-tour-shapes/tour-shape-plots.py
index a32f4cd00db4594f2965bdbec488998f0dc6b821..af9e3564113f635008007f6f67177f8a8847f0af 100644 (file)
--- a/06-tour-shapes/tour-shape-plots.py
+++ b/06-tour-shapes/tour-shape-plots.py
@@ -497,10 +497,20 @@ def heart_tour_func(): return heart_tour
 #         meta.add_text('Description', tour)
 #         im.save(filename, 'PNG', pnginfo=meta)
 
-with open('tours-open.txt') as f:
+# with open('tours-open.txt') as f:
+#     for i, tour_s in enumerate(f.readlines()):
+#         tour = tour_s.strip()
+#         filename = 'tour-{:03}-s{:04}-m{:03}-open.png'.format(i, len(tour), len(mistake_positions(trace_tour(tour))))
+#         plot_trace(trace_tour(tour), filename=filename)
+#         im = Image.open(filename)
+#         meta = PngImagePlugin.PngInfo()
+#         meta.add_text('Description', tour)
+#         im.save(filename, 'PNG', pnginfo=meta)
+
+with open('tours-random-walk.txt') as f:
     for i, tour_s in enumerate(f.readlines()):
         tour = tour_s.strip()
-        filename = 'tour-{:03}-s{:04}-m{:03}-open.png'.format(i, len(tour), len(mistake_positions(trace_tour(tour))))
+        filename = 'tour-{:03}-s{:04}-m{:03}-walk.png'.format(i, len(tour), len(mistake_positions(trace_tour(tour))))
         plot_trace(trace_tour(tour), filename=filename)
         im = Image.open(filename)
         meta = PngImagePlugin.PngInfo()

diff --git a/06-tour-shapes/tour-shapes-build-problem-set.ipynb b/06-tour-shapes/tour-shapes-build-problem-set.ipynb
new file mode 100644 (file)
index 0000000..05df310
--- /dev/null
+++ b/06-tour-shapes/tour-shapes-build-problem-set.ipynb
@@ -0,0 +1,1190 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "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",
+    "1. which tours are closed?\n",
+    "2. what is the area enclosed by the tour?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import collections\n",
+    "import enum\n",
+    "import random\n",
+    "import os\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class Direction(enum.Enum):\n",
+    "    UP = 1\n",
+    "    RIGHT = 2\n",
+    "    DOWN = 3\n",
+    "    LEFT = 4\n",
+    "    \n",
+    "turn_lefts = {Direction.UP: Direction.LEFT, Direction.LEFT: Direction.DOWN,\n",
+    "              Direction.DOWN: Direction.RIGHT, Direction.RIGHT: Direction.UP}\n",
+    "\n",
+    "turn_rights = {Direction.UP: Direction.RIGHT, Direction.RIGHT: Direction.DOWN,\n",
+    "               Direction.DOWN: Direction.LEFT, Direction.LEFT: Direction.UP}\n",
+    "\n",
+    "def turn_left(d):\n",
+    "    return turn_lefts[d]\n",
+    "\n",
+    "def turn_right(d):\n",
+    "    return turn_rights[d]\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "Step = collections.namedtuple('Step', ['x', 'y', 'dir'])\n",
+    "Mistake = collections.namedtuple('Mistake', ['i', 'step'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def advance(step, d):\n",
+    "    if d == Direction.UP:\n",
+    "        return Step(step.x, step.y+1, d)\n",
+    "    elif d == Direction.DOWN:\n",
+    "        return Step(step.x, step.y-1, d)\n",
+    "    elif d == Direction.LEFT:\n",
+    "        return Step(step.x-1, step.y, d)\n",
+    "    elif d == Direction.RIGHT:\n",
+    "        return Step(step.x+1, step.y, d)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def step(s, current):\n",
+    "    if s == 'F':\n",
+    "        return advance(current, current.dir)\n",
+    "    elif s == 'L':\n",
+    "        return advance(current, turn_left(current.dir))\n",
+    "    elif s == 'R':\n",
+    "        return advance(current, turn_right(current.dir))\n",
+    "    else:\n",
+    "        raise ValueError"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def trace_tour(tour, startx=0, starty=0, startdir=Direction.RIGHT):\n",
+    "    current = Step(startx, starty, startdir)\n",
+    "    trace = [current]\n",
+    "    for s in tour:\n",
+    "        current = step(s, current)\n",
+    "        trace += [current]\n",
+    "    return trace    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def positions(trace):\n",
+    "    return [(s.x, s.y) for s in trace]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def valid(trace):\n",
+    "    return (trace[-1].x == 0 \n",
+    "            and trace[-1].y == 0 \n",
+    "            and len(set(positions(trace))) + 1 == len(trace))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def valid_prefix(tour):\n",
+    "    current = Step(0, 0, Direction.RIGHT)\n",
+    "    prefix = []\n",
+    "    posns = []\n",
+    "    for s in tour:\n",
+    "        current = step(s, current)\n",
+    "        prefix += [s]\n",
+    "        if (current.x, current.y) in posns:\n",
+    "            return ''\n",
+    "        elif current.x == 0 and current.y == 0: \n",
+    "            return ''.join(prefix)\n",
+    "        posns += [(current.x, current.y)]\n",
+    "    if current.x == 0 and current.y == 0:\n",
+    "        return ''.join(prefix)\n",
+    "    else:\n",
+    "        return ''"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def mistake_positions(trace, debug=False):\n",
+    "    mistakes = []\n",
+    "    current = trace[0]\n",
+    "    posns = [(0, 0)]\n",
+    "    for i, current in enumerate(trace[1:]):\n",
+    "        if (current.x, current.y) in posns:\n",
+    "            if debug: print(i, current)\n",
+    "            mistakes += [Mistake(i+1, current)]\n",
+    "        posns += [(current.x, current.y)]\n",
+    "    if (current.x, current.y) == (0, 0):\n",
+    "        return mistakes[:-1]\n",
+    "    else:\n",
+    "        return mistakes + [Mistake(len(trace)+1, current)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def returns_to_origin(mistake_positions):\n",
+    "    return [i for i, m in mistake_positions\n",
+    "           if (m.x, m.y) == (0, 0)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "sample_tours = ['FFLRLLFLRL', 'FLLFFLFFFLFFLFLLRRFR', 'FFRLLFRLLFFFRFLLRLLRRLLRLL']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def random_walk(steps=1000):\n",
+    "    return ''.join(random.choice('FFLR') for _ in range(steps))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bounds(trace):\n",
+    "    return (max(s.x for s in trace),\n",
+    "            max(s.y for s in trace),\n",
+    "            min(s.x for s in trace),\n",
+    "            min(s.y for s in trace))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n",
+    "           Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def chunks(items, n=2):\n",
+    "    return [items[i:i+n] for i in range(len(items) - n + 1)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None, filename=None):\n",
+    "    plt.axis('on')\n",
+    "    plt.axes().set_aspect('equal')\n",
+    "    for s, t in chunks(trace, 2):\n",
+    "        w, h = plot_wh[t.dir]\n",
+    "        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",
+    "    xh, yh, xl, yl = bounds(trace)\n",
+    "    if xybounds is not None:    \n",
+    "        bxh, byh, bxl, byl = xybounds\n",
+    "        plt.xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
+    "        plt.ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
+    "    else:\n",
+    "        plt.xlim([xl-1, xh+1])\n",
+    "        plt.ylim([yl-1, yh+1])\n",
+    "    if filename:\n",
+    "        plt.savefig(filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def trim_loop(tour, random_mistake=False):\n",
+    "    trace = trace_tour(tour)\n",
+    "    mistakes = mistake_positions(trace)\n",
+    "    if random_mistake:\n",
+    "        end_mistake_index = random.randrange(len(mistakes))\n",
+    "    else:\n",
+    "        end_mistake_index = 0\n",
+    "#     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",
+    "    # while this mistake extends to the next step in the trace...\n",
+    "    while (mistakes[end_mistake_index].i + 1 < len(trace) and \n",
+    "           end_mistake_index + 1 < len(mistakes) and\n",
+    "           mistakes[end_mistake_index].i + 1 == \n",
+    "           mistakes[end_mistake_index + 1].i):\n",
+    "#         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",
+    "        # push this mistake finish point later\n",
+    "        end_mistake_index += 1\n",
+    "    mistake = mistakes[end_mistake_index]\n",
+    "    \n",
+    "    # find the first location that mentions where this mistake ends (which the point where the loop starts)\n",
+    "    mistake_loop_start = max(i for i, loc in enumerate(trace[:mistake.i])\n",
+    "                             if (loc.x, loc.y) == (mistake.step.x, mistake.step.y))\n",
+    "#     print('Dealing with mistake from', mistake_loop_start, 'to', mistake.i, ', trace has len', len(trace))\n",
+    "    \n",
+    "    # direction before entering the loop\n",
+    "    direction_before = trace[mistake_loop_start].dir\n",
+    "    \n",
+    "    # find the new instruction to turn from heading before the loop to heading after the loop\n",
+    "    new_instruction = 'F'\n",
+    "    if (mistake.i + 1) < len(trace):\n",
+    "        if turn_left(direction_before) == trace[mistake.i + 1].dir:\n",
+    "            new_instruction = 'L'\n",
+    "        if turn_right(direction_before) == trace[mistake.i + 1].dir:\n",
+    "            new_instruction = 'R'\n",
+    "#     if (mistake.i + 1) < len(trace):\n",
+    "#         print('turning from', direction_before, 'to', trace[mistake.i + 1].dir, 'with', new_instruction )\n",
+    "#     else:\n",
+    "#         print('turning from', direction_before, 'to BEYOND END', 'with', new_instruction )\n",
+    "    return tour[:mistake_loop_start] + new_instruction + tour[mistake.i+1:]\n",
+    "#     return mistake, mistake_loop_start, trace[mistake_loop_start-2:mistake_loop_start+8]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def trim_all_loops(tour, mistake_reduction_attempt_limit=10):\n",
+    "    trace = trace_tour(tour)\n",
+    "    mistake_limit = 1\n",
+    "    if trace[-1].x == 0 and trace[-1].y == 0:\n",
+    "        mistake_limit = 0\n",
+    "    mistakes = mistake_positions(trace)\n",
+    "    \n",
+    "    old_mistake_count = len(mistakes)\n",
+    "    mistake_reduction_tries = 0\n",
+    "    \n",
+    "    while len(mistakes) > mistake_limit and mistake_reduction_tries < mistake_reduction_attempt_limit:\n",
+    "        tour = trim_loop(tour)\n",
+    "        trace = trace_tour(tour)\n",
+    "        mistakes = mistake_positions(trace)\n",
+    "        if len(mistakes) < old_mistake_count:\n",
+    "            old_mistake_count = len(mistakes)\n",
+    "            mistake_reduction_tries = 0\n",
+    "        else:\n",
+    "            mistake_reduction_tries += 1\n",
+    "    if mistake_reduction_tries >= mistake_reduction_attempt_limit:\n",
+    "        return ''\n",
+    "    else:\n",
+    "        return tour"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def reverse_tour(tour):\n",
+    "    def swap(tour_step):\n",
+    "        if tour_step == 'R':\n",
+    "            return 'L'\n",
+    "        elif tour_step == 'L':\n",
+    "            return 'R'\n",
+    "        else:\n",
+    "            return tour_step\n",
+    "        \n",
+    "    return ''.join(swap(s) for s in reversed(tour))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def wander_near(locus, current, limit=10):\n",
+    "    valid_proposal = False\n",
+    "    while not valid_proposal:\n",
+    "        s = random.choice('FFFRL')\n",
+    "        if s == 'F':\n",
+    "            proposed = advance(current, current.dir)\n",
+    "        elif s == 'L':\n",
+    "            proposed = advance(current, turn_left(current.dir))\n",
+    "        elif s == 'R':\n",
+    "            proposed = advance(current, turn_right(current.dir))\n",
+    "        if abs(proposed.x - locus.x) < limit and abs(proposed.y - locus.y) < limit:\n",
+    "            valid_proposal = True\n",
+    "#     print('At {} going to {} by step {} to {}'.format(current, locus, s, proposed))\n",
+    "    return s, proposed"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def seek(goal, current):\n",
+    "    dx = current.x - goal.x\n",
+    "    dy = current.y - goal.y\n",
+    "\n",
+    "    if dx < 0 and abs(dx) > abs(dy): # to the left\n",
+    "        side = 'left'\n",
+    "        if current.dir == Direction.RIGHT:\n",
+    "            s = 'F'\n",
+    "        elif current.dir == Direction.UP:\n",
+    "            s = 'R'\n",
+    "        else:\n",
+    "            s = 'L'\n",
+    "    elif dx > 0 and abs(dx) > abs(dy): # to the right\n",
+    "        side = 'right'\n",
+    "        if current.dir == Direction.LEFT:\n",
+    "            s = 'F'\n",
+    "        elif current.dir == Direction.UP:\n",
+    "            s = 'L'\n",
+    "        else:\n",
+    "            s = 'R'\n",
+    "    elif dy > 0 and abs(dx) <= abs(dy): # above\n",
+    "        side = 'above'\n",
+    "        if current.dir == Direction.DOWN:\n",
+    "            s = 'F'\n",
+    "        elif current.dir == Direction.RIGHT:\n",
+    "            s = 'R'\n",
+    "        else:\n",
+    "            s = 'L'\n",
+    "    else: # below\n",
+    "        side = 'below'\n",
+    "        if current.dir == Direction.UP:\n",
+    "            s = 'F'\n",
+    "        elif current.dir == Direction.LEFT:\n",
+    "            s = 'R'\n",
+    "        else:\n",
+    "            s = 'L'\n",
+    "    if s == 'F':\n",
+    "        proposed = advance(current, current.dir)\n",
+    "    elif s == 'L':\n",
+    "        proposed = advance(current, turn_left(current.dir))\n",
+    "    elif s == 'R':\n",
+    "        proposed = advance(current, turn_right(current.dir))\n",
+    "        \n",
+    "#     print('At {} going to {}, currently {},  by step {} to {}'.format(current, goal, side, s, proposed))\n",
+    "\n",
+    "    return s, proposed"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def guided_walk(loci, locus_limit=5, wander_limit=10, seek_step_limit=20, return_anyway=False):\n",
+    "    trail = ''\n",
+    "    current = Step(0, 0, Direction.RIGHT)    \n",
+    "    l = 0\n",
+    "    finished = False\n",
+    "    while not finished:\n",
+    "        if abs(current.x - loci[l].x) < locus_limit and abs(current.y - loci[l].y) < locus_limit:\n",
+    "            l += 1\n",
+    "            if l == len(loci) - 1:\n",
+    "                finished = True\n",
+    "        s, proposed = wander_near(loci[l], current, limit=wander_limit)\n",
+    "        trail += s\n",
+    "        current = proposed\n",
+    "#     print('!! Finished loci')\n",
+    "    seek_steps = 0\n",
+    "    while not (current.x == loci[l].x and current.y == loci[l].y) and seek_steps < seek_step_limit:\n",
+    "#         error = max(abs(current.x - loci[l].x), abs(current.y - loci[l].y))\n",
+    "#         s, proposed = wander_near(loci[l], current, limit=error+1)\n",
+    "        s, proposed = seek(loci[l], current)\n",
+    "        trail += s\n",
+    "        current = proposed\n",
+    "        seek_steps += 1\n",
+    "    if seek_steps >= seek_step_limit and not return_anyway:\n",
+    "        return ''\n",
+    "    else:\n",
+    "        return trail"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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FIBNJl6SFQEV+muMwZFu3buWGG25QGDKRAEKHIVsFPOHufxk9LykEWfRehSETqYDQYcgs\n+ouVHIIMNIFIpBKC3V7MzB4E/g+4xMyOmdmtwF3A9WZ2mFwUorvOt424Y1ARiETCSdrxXkoYsn8o\n8lJJIcjyJb2EISLh6H4CItNEqucO6H4CIuGleiqxiISX6pqAhg2LpJdmEYpUuYreWUgdgyLhDAwM\nJFqvIoVA3FbROAGRcLLZbKL1KloIaJyASPqoY1Bkmkj11QF1DIqEp3ECIlUu1TUBDRsWCS/VhYCG\nDYuEl+pbjseZUzgykXBSPU4gPvmTdlyIyPhSPU4gHiSk5oBI+qhjUKTKqWNQZJq4IOMEzOxGM3vV\nzI6Y2e2T2ZaITE7SuTmJCwEzywD/Si5E2Z8DnzSzSwu9V8OGRdJrMjWBK4Hfufsf3H0A+Am58GRj\naNiwSHpN5qxcDryZ9/w4uYJhjPgS4bXXXktHRwdz584FoL+/n9mzZ9Pd3c1FF13E6dOn6ezsZO3a\ntbS2ttLT08PChQvp7Oxk3rx5dHR00NPTw6pVq2htbaWzs5MlS5bQ0dHBzJkz6e/vp6+vj4svvpiW\nlhY6OjpoaGg4p0+it7eX5cuX09raSnt7O2vWrOHtt99mcHCQ+vp6enp6aGpq4u2336a9vZ1169Zx\n8uRJ+vr6mDt3Lt3d3SxcuJCzZ8/S1dXFmjVraG1tpauri2w2S21tLXPmzKGrq4ve3l5Wrlw5ktdl\ny5bR1tZGNptleHiY3t5eVqxYQWtrKx0dHaxcuZIzZ84wPDxMNpult7eXZcuWcfLkSdra2li3bh2n\nTp1iYGCAgYEB6urqRvLa0dHBunXrRvbbggUL6OzspLGxkfb2drq7u1m9evVIXpuamujo6KC+vp6+\nvr4x+23FihW0tbVhZnR0dDBjxoyRvLS3t7N69WpOnz7N0NAQM2fOpKenh6VLl468Hu+3/v5+5syZ\nQ3d3N4sWLeLMmTPnHON4eXyMjx8/Tl1dHatXr6alpYXOzk6WLl1Ke3s7dXV1DA4OjslrvN/cnWw2\nS09PT9Fj3NDQQHd3N01NTRw9epRMJsPatWs5efIkvb29zJ8/n66uLhYsWEBbW9s5+y3+nra3tzNr\n1ix6enrGHOPly5dz9uzZke9cX18fM2fOZGhoiI6ODlatWsXp06cZHh6mrq6Onp6ec/br2rVrOXXq\nVNFzY926dbS0tBQ8N06cOJHsTHb3RH/Ax4H78p5/CrinwPt8y5YtvmzZMgcc8Lq6upHH8V9DQ8PI\n4wULFox5Pf9v8eLFk3p94cKFI4/r6+vHvD5v3ryRx/Pnzx/z+owZMwpua7J5zWazY17P3xezZ88e\n83r+ssbGxjGv19TUjDxetGjRpPKav/7MmTPHvJ6/r+bOnTvm9fx9Xc5jnP8ZCx2X/O9WofwVOsb5\nx2Kyxzj/cxf67ucftzlz5ox5fSLnxvz58725udmbm5sd8JLO5UkUAlcDT+U9vwO4vVAhMFpzc/OY\nZaEoLaV1odO6UJ+p1EJgMn0CvwH+xMxWmVkd8PfkwpOJyBRSUkDSoiub3QjcQ66D8X53HxOOzMyS\nJyAik+IlBCSdVCEgIlOfbioiUuVUCIhUuYoXAiGHGpvZ/WbWYmb78pY1mtkzZnbYzJ42s3llSGeF\nmT1rZgfNbL+Z3RYwrRlm9isz2xOl1RwtX21mL0RpPWRmZRuJZWYZM3vJzB4PmZaZ/d7MXo4+26+j\nZWXfh9F255nZdjM7ZGYHzOyqQMfrkujzvBT9bzOz2wJ+ri+b2Stmts/MfmxmdRM+XqVcQijXH7lC\n5zVgFZAF9gKXlnH7fwtcBuzLW3Y38LXo8e3AXWVIZwlwWfR4NnAYuDREWtG2GqL/NcALwFXAw8Dm\naPm9wD+VcT9+Gfhv4PHoeZC0gKNA46hlofbhfwK3Ro9rgXmh0spLMwO8BVwc6Hu4LNqHdXnH6ZaJ\nHq+yfeASM301sDvvecGxBZNMY9WoQuBVoCl6vAR4NcDnegxYHzotoAF4kdzIzFYgk7dfnypTGiuA\nnwPX5RUCJwOl9QawcNSysu9DYA7weoHloY/XDcD/BPxcy4A/AI1RwfY4cP1EvxuVbg4UGmq8PHCa\nF7l7C4C7nwAWl3PjZraaXO3jBXIHuexpRdXzPcAJcifo68BZd4/njh4n94Uoh+8BXyU3Ag0zWwic\nCZSWA0+b2W/M7PPRshD7cC1wysweiKrp95lZQ6C08n0CeDB6XPa03P0t4LvAMeCPQBvwEhP8blS6\nECh0zXLKXqM0s9nADuBL7t5JoM/i7sPufjm5X+krgXcVettk0zGzjUCLu+/lnWNljD1u5fqc73X3\nvwY2AF80s/eVcdv5aoErgB+6+xVAF7laaLDvnpllgZuB7dGisqdlZvPJTdpbRe5EnwXcVOCt5027\n0oXAcWBl3vMV5NpMIbWYWROAmS0hV1WatKizZQfwX+6+M2RaMXdvB54nV8WbH03nhvLtx2uAm83s\nKPAQ8AHg+8C8AGnFv4i4+0lyTaorCbMPjwNvuvuL0fNHyBUKIY/XTcBv3f1U9DxEWuuBo+5+2t2H\ngEeB9zLB70alC4FKDDUe/cv1OPCZ6PEtwM7RKyT0I+Cgu98TMi0zWxT3JJtZPbkDfxB4DthczrTc\n/RvuvtLd15I7Ns+6+6dCpGVmDVFNCjObRa79vJ8A+zCqhr9pZpdEiz4IHAiRVp5PkitIYyHSOgZc\nbWYzzcx453NN7HiVsyOkxM6MG8n1pv8OuKPM236QXKnXF+2gW8l1mvwiSvPnwPwypHMNMETu6sYe\ncu2wG4EFAdL6i2j7e4F9wL9Ey9cAvwKOkOsNzpZ5X17LOx2DZU8r2ma8//bH34UQ+zDa7rvJ/Qjt\nBX5G7upAqLTqyXWmzslbFiqtZuBQ9N3YRu6q24SOl4YNi1Q5jRgUqXIqBESqnAoBkSqnQkCkyqkQ\nEKlyKgREqpwKAZEqp0JApMr9P8nYgJi0MFyGAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7ffba4edcf60>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def square_tour(a=80):\n",
+    "    \"a is width of square\"\n",
+    "    return ('F' * a + 'L') * 4\n",
+    "\n",
+    "plot_trace(trace_tour(square_tour()))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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k6yMEKDzGmzHGPSUtKopIo4g8KSJxEXlbRG4WkWYReU5E+kXkuIg0rvT+6urqghdbGGPc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\nybOEYIzJ+/+3mLJIMXCXRQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7ffba4b355c0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def cross_tour(a=50, b=40):\n",
+    "    \"a is width of cross arm, b is length of cross arm\"\n",
+    "    return ('F' *  a + 'L' + 'F' * b + 'R' + 'F' * b + 'L') * 4\n",
+    "\n",
+    "plot_trace(trace_tour(cross_tour()))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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Ukpa9WWhgqFF+bEHHGFQ509PTzM7Out0MR2hgqJGOMahqqqVkbyYaGJRySDgcrno7c7PQ\nwKCUQ5aWlpibm3O7GY7QwFAjHWNQ1czPz5NOp91uhiM0MFwiHWNQ5egYg1KqRDgcZvfu3W43wxEa\nGJRyyMLCQtPkYqhGA0ON8ocQOsagykmn09tmGgQNDDXKBwQdY1DlBAIBt5vgGA0MNdKAoKoJhUI6\nxrDT6OlKVU0qlWJ0dNTtZjhCA0ON9JJoVc3q6qrbTXCMU1PUhUTkuyIyIiJPi8j1ItInIiesKep+\nKiKV58RSqsl1dXXR2upItkTXOdVj+BLwkDHmSuCPgGfIJYN92Jqi7hRwl0PrUsqTgsEgAwMDbjfD\nEU7MXdkNvNYY8w0AY8y6MSZFbhKaB61iDwK32V2XF+gYgypnZmZG08cXOAhMicg3ROQJEfmaiHQA\nMWNMAsAYMwFsi1CqYwyqnO1yDQM4kz6+FXgl8D5jzK9E5H5yhxE1f4PuueeejcdenaJOewqqmt7e\nXrq6utxuRlmFU9RV48QUdTHg/xpjDlrP/4RcYDgEHDPGJEQkDjxijUEUv78ppqhbXV0lEAjoFHWq\nrLe97W089thjJBIJt5tSk7pOUWcdLpwXkSPWovwUdceBO61lOkWd2va2U/p4p86tfAD4poi0AS8A\n7wZagO+IyHvIzW/59grv97zC6xg0OKitbKf9wqkp6n4D/IstXrrRifq9YDv90VV9hMNhPV250zTD\nOIhyVyaTYX193e1mOEIDQ430XglVzczMjKaP32n0XglVjaZ2U0qV6OvrY3Bw0O1mOEIDg1IOWVlZ\nIZVKud0MR2hgqJGOMahqUqmUpo/fqXSMQZXj9/vdboJjNDAo5ZC+vj5N7aaU2mxxcVHTx+80mj5e\nVbO4uLhtbr3WwFAjTR+vqtH08TuQBgRVjaaP34H0dKWqRtPH70B6SbSqRtPHK6VKdHV10dLS4nYz\nHKGBQSmHBINBYrGY281whAaGS6RjDKqc2dlZvY5hp9IxBlVOJpNxuwmOcSwwiIjPmlfiuPV8v4ic\ntqao+5aINPXcXdpTUNV4PX38pXCyx/BBYLjg+ReAe60p6uaAv3RwXUp5js/no7Oz0+1mOMKpSW13\nA28C/mvB4tcD37cePwi81Yl1uU17DqqcmZmZpplTohqnegz3Ax/Fmn1KRCLArDEmf+H4KLDLoXW5\nQq9jUNVspx8N28f9IvJnQMIY86SIHMsvtv4VKvuN0inq1HYQDofp7+93uxllNXqKuv8EvAtYB9qB\nbuAfgTcCcWNMVkRuAO42xty6xfubYoq6lZUVgsGgTlGnynrrW9/Ko48+yvT0tNtNqUm9p6j7pDFm\nrzV35TuAU8aYdwGP8PLsU00/RZ3eK6GqmZ6eZmZmxu1mOKKe1zF8AviwiPweCANfr+O66k7HGFQ1\n2ym1m6PXFhhjfg783Hr8InC9k/Ur5WXhcFjTxyulNlteXtb08TuNjjGoajR9/A6mYwyqHJ2iTilV\nIhKJcNlll7ndDEdoYFDKIRcvXmRiYsLtZjhCA0ONNH28qiadTm+bW681MNRI08erarbTdQwaGGqk\nAUFV09vbq+njdxo9Xamq0fTxO5BeEq2q0fTxSqkSnZ2dmj5eKbVZe3u7po/fqXSMQZWj6eN3MB1j\nUOVks9nqhZqEBoYaaU9BVdPT06NZopVSm7W0tOi8EjuV9hxUOZo+fgfS6xhUNdvpR8N2YBCR3SJy\nSkSGReS3IvIBa3mfiJywpqj7qYiE7DfXPdvpj67qIxwOE4lE3G6GI5zoMawDHzbGXAX8MfA+EbmC\nXDLYh60p6k4BdzmwLtdoT0FVk8lkts1+4kT6+AljzJPW4wVgBNgNvIXc1HRY/99md11u0nslVDUz\nMzPbJn28o1miRWQ/cC1wGogZYxKQCx4iMlDufel0moWFhXwdGGPIZrObLi/NZDK0trZuTPiSfz1/\n7tgYg4hsvD//vKh9NdVd+Dxf99ra2qb1KFWstTX3dUomkxv7qM/nK+lFbPVafp8sfp5XWL5c3fn9\nslrdQNUZsxwLDCLSBXwP+KAxZkFEau5TbZdzv2pnu/nmmzl16lRTXBZdLQWd7SnqAESkFfjfwI+N\nMV+ylo0Ax4wxCRGJA48YY67c4r0GYHR0dNvky1PKy2644QYuXLjA6Oho/aaos/wdMJwPCpbjwJ3W\n46pT1G2XQRulvC6RSFTNG+HE6crXAP8OeL2I/FpEnhCRW4AvADeJyLPAjcDnKzbEp5dUKNUIHR0d\nBIPBimVsjzEYY34BlLsJ/cZLqMduU5RSNYjFYhhjGBkZKVvGMz/TOtKvVGOkUimmpqYqlvFMYNhO\nt6wq5WVzc3NMTk5WLOOZwKA9BqUao729vepdoBoYlNphotEoe/bsqVhGA4NSO8zU1BTj4+MVy3gm\nMKyvr7vdBKV2hHQ6zdzcXMUyngkM2yXttlJeFwqFqt4r4ZnAoJRqjJ6enuYJDDrGoFRjJJNJzp07\nV7GMZwKDjjEo1Rirq6uk0+mKZTwTGHSMQanGiEQiVe9k9kxg0HsllGqMQCBQNQeKZwKDjjEo1RgT\nExO88MILFct4JjBkMhm3m6DUjpDNZqt+3zwTGDQfg1KNMTg4yIEDByqW8cy3UQ8llGqMWu5kdjRL\ntFLK+8bGxnjxxRcrlvFMj0HzMSjVGH6/fyPVfTl1DwwicouIPCMivxeRj5dtiI4xKNUQ8XicgwcP\nVixT12+jiPiAvwVuBq4G3mlNX1dCr2NQqjGWl5ddv/LxOuCMMeasMWYN+Da5qetKaGBQqjEakj6+\nisuA8wXPR61lpQ3RQ4kS+WCZn3Kv8LHTz7d73epl7e3t9U8fX8VW5yC3/CvpH28zPX3rnJtuuokT\nJ0643QzPiMfjABXTx9c7MIwCewue7wbGtip433330d3dzbFjxzh27Fidm9Uczp8/z8DAy3MB5yfl\nLX5eGES2er3weaFKZbd6z6XWXdg+t+p+1atexalTp0pe34mGhoYYGhpiZGSE+fn5imUdmbuybOUi\nLcCzwBuAceBx4J3GmJGCMgZyX4Ldu3fXrS3NRkRIJBJEo1G3m9LUDh8+zHPPPac90gKHDh3auFei\n3NyVde0xGGMyIvJ+4AS58YyvFwaFQtp1LqWfiX2Dg4OsrKy43QxPyaePX1hYKFum7lc+GmN+Ahyt\nVk6/BKoeWltbaWtrc7sZnhKNRslmszpFXbPSq0HtSyaTVW8x3mk0fXyT01O49unt/KVqSR/vmZuo\nNLVbKR0wsy8ej+sYQ5F8luhKE9t65idJvwSl9PDKvmw2q73RIk01r4T2GEppN9i+ZDLJ+fPnqxfc\nQRKJRPOkj19bW3O7CZ6jwdK+1tZW/RyLrK2tVb2JSscYPEwPr+yLRqM6xlAkEomwtLTEhQsXypbx\nTI9BqXpYWloilUq53QxPaar08aqUXsdg3+zsLMlk0u1meIqmj29y1dJvqeoCgQDt7e1uN8NTakkf\n75k9T8cYSukYg30DAwMsLS253QxPicfjZDKZiglhPdNjUKU0MNg3OzvLxMSE283wlOJb9beigcHD\nNDDYt7CwUDX3wE4zPj7ePGMMOtBWSu+VsK+7u5tQKOR2MzyltbXV/fTxtdIvgaqH3t7ejVRmKmdw\ncNDd9PGXQrvNqh6SySQvvfSS283wlOXl5aoDshoYPEwPr+xbXl7WKx+LJBKJqvePeCYw6KFEKf1M\n7AuHw5o3s0gt6eNt7Xki8tciMiIiT4rI90Wkp+C1u0TkjPX6G6vVpT2GUvqZ2NfZ2Ulvb6/bzfCU\neDzOgQMHKpax+5N0ArjaGHMtcAa4C0BErgL+HLgSuBX4ilQ5caq5B0rpZ2JfIpHg+eefd7sZnjI/\nP8/09HTFMrYCgzHmYWNM/kD4NLl5IwDeDHzbGLNujHmJXNC4rlJdejxdSnsM9i0vL+vl9kVquX/E\nyYPY9wAPWY+Lp6a7QJmp6fL017GUfib2DQ4O6nwlRfLp4yupeq+EiJwEYoWLyE0z9yljzI+sMp8C\n1owx3yooU6ziz59+CUppj8G+1tZW/H6/283wlGg0ijGG4eHhsmWqBgZjzE2VXheRO4A3Aa8vWDwK\n7Cl4XnZqurx7771Xp6grooHBPk0f/7L8FHVPP/101RwVtqaoE5FbgHuBf2WMmS5YfhXwTeB6cocQ\nJ4HDZouV5aeoO3fuHHv27Cl+eccSEZLJ5Ka5K9Wlu/LKK3nmmWc0yBZoxBR1DwB+4KR1KHDaGPNe\nY8ywiHwHGAbWgPduFRQK6W3XpXRntk/Tx5cKhUJEIpGKZyZsBQZjzOEKr30O+Nwl1GWnKduSjrvY\nZ4zR9PFFQqEQAwMDFQODZy6t0x5DKT3NZp+mjy+VTCY1fXwz02Bpn8/n00vLi6yurjZP+nj945XS\nwyv7YrGYjjEUiUQipNNpxsbKnyj0zLdRj6dVPSwvL2sGpyKBQKDqBU6eCQyqlF4mbt/MzIymjy8y\nMTFRMREseCgw6MhxKU0fb18gEKh6i/FOU8uZGs/sefolKKU9Bvs0fXypWCzG+vp6c6SP14E2VQ+a\nPn5r1Qb7PRMY7A4+Dg0NOdMQD63LGLMtt6uR62p0+vhm+AzHxsaq5qjwTP99fHycTCaDz+dDRBAR\n1tfXaWlpwRiDz+djbW2N1tbWjQkzstnsRtnjx49z+PDhjQCTzWbx+Xwb781kMhtly9Xd0tJS8v78\n4/z7AI4fP86RI0f+4LozmczG63lbrdfn8zE0NNSwm8q247q6u7vx+/2MjY2V/bwL/7bF+836+vqm\nfbJwHyx+3Rizad/I76d/SN0isun7kK8v/35jDD/60Y829vnC/Sa/D5b7LkHuGpmKF9DlV+LWP3K3\nY+u/Lf4tLi6au+++2zTKdlzX+9//ftf/jl78d9tttxnAmDLfS08cSpRr3KX8u/vuuxsWzBq1ro6O\nDrf/NE3vgQce2Jb7ht11/eAHP6j4udm67doJ+duulVKNZ8rcdu16YFBKeY8nDiWUUt6igUEpVWJb\nBAYR+YiIZEUkXLDsb6wJb54UkWsdWIdjk+vUuL5bROQZEfm9iHzciToL6t4tIqdEZFhEfisiH7CW\n94nICRF5VkR+KiKOTRMtIj4ReUJEjlvP94vIaWtd3xIRR06di0hIRL5r/S2eFpHr67VdIvIhEfmd\niDwlIt8UEb+T2yUiXxeRhIg8VbCs7LY4us83agS1Xv/IJZr9CfAiELaW3Qr8H+vx9eRSztldz42A\nz3r8eeBz1uOrgF+TuyZkP/Ac1tiNjXX5rHr2AW3Ak8AVDn5mceBa63EX8CxwBfAF4GPW8o8Dn3dw\nnR8C/idw3Hr+D8Dbrcf/Bfgrh9bz34B3W49bgVA9tgvYBbwA+Au25w4ntwv4E+Ba4KmCZVtui9P7\nvCN/dDf/Ad8FrikKDF8F/k1BmREg5uA6bwP+h/X4E8DHC177MXC9zfpvAH5c8HzTOurwGf6jFfie\nyX9OVvB4xqH6d5NLCHysIDBMFgTaG4CfOLCebuD5LZY7vl1WYDgL9FkB6DhwE5B0crvI/TgUBobi\nbRmxHju6zzf1oYSI/GvgvDHmt0UvXfKEN5fI1uQ6NSiuc9SBOrckIvvJ/SqdJrcjJQCMMROAUymq\n7wc+Su7iGkQkAsyal2cxGyX3RbPrIDAlIt+wDlu+JiId1GG7jDFj5DKknyP3N08BTwBzddiuQtGi\nbcnP2OvofuiZS6LLqTDhzaeBT5KL0iVv22JZ1fOyjZpcpwb1qLN0JSJdwPeADxpjFupxTYmI/BmQ\nMMY8KSLH8osp3UYn1t0KvBJ4nzHmVyJyP7neVj22qxd4C7lf9BS5nuutWxRt1PUAju4zng8MpsyE\nNyLyz8gd0/9Gchej7waeEJHr+AMmvKm0roJ13oEDk+vUYBTY63Cdm1iDYt8jd0j0Q2txQkRixpiE\niMTJdYvteg3wZhF5E9BOrrv/n4GQiPisX1entm+UXA/yV9bz75MLDPXYrhuBF4wxMwAi8gPgXwK9\nddiuQuW2xdH9sGkPJYwxvzPGxI0xB40xB8h9MP/cGJMkd7z3FwAicgO57l3CzvokN7nOx4A3G2MK\nkwgeB95hjUgfAC4HHrezLuD/AZeLyD4R8QPvsNbjpL8Dho0xXypYdhy403p8B/DD4jddKmPMJ40x\ne40xB8khgmMMAAAA+ElEQVRtxyljzLuAR4C3O7yuBHBeRI5Yi94APE0dtovcIcQNIhK0fpjy63J6\nu4p7V4XbcmdB/c7u83YHYbzyj9wIcbjg+d+SG9n/DfBKB+o/Q26w6Qnr31cKXrvLWtcI8EaHtucW\ncmcLzgCfcPizeg2QIXe249fW9twChIGHrfWeBHodXu+f8vLg4wHgn4DfkxvJb3NoHX9ELrA+Cfwv\ncmcl6rJdwN3W3/wp4EFyZ5Ac2y7g78n96q+QC0TvJjfYueW2OLnP6yXRSqkSTXsooZSqHw0MSqkS\nGhiUUiU0MCilSmhgUEqV0MCglCqhgUEpVUIDg1KqxP8Hcqx+SW6w/jsAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7ffba4bf1278>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def quincunx_tour(a=60, b=30, c=50):\n",
+    "    \"a is length of indent, b is indent/outdent distance, c is outdent outer length\"\n",
+    "    return ('F' * a + 'R' + 'F' * b + 'L' + 'F' * c + 'L' + 'F' * c + 'L' + 'F' * b + 'R') * 4\n",
+    "plot_trace(trace_tour(quincunx_tour()))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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ZZ57hwIED7Nu3r84N3FRGpzCGuczMTFJSUjx/7Pv27aN79+6WU6lgVv6cyBEj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\nVBW0UCqlVBW0UCqlVBX+P0VFnoIKajtRAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7ffba49b3710>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "heart_points = [Step(60, 50, Direction.UP), Step(50, 90, Direction.UP),\n",
+    "                Step(20, 70, Direction.UP), \n",
+    "                Step(-40, 90, Direction.UP), Step(-60, 80, Direction.UP), \n",
+    "                Step(0, 0, Direction.RIGHT)]\n",
+    "\n",
+    "heart_tour = ''\n",
+    "current = Step(0, 0, Direction.RIGHT)\n",
+    "\n",
+    "for hp in heart_points:\n",
+    "    while not (current.x == hp.x and current.y == hp.y):\n",
+    "        s, proposed = seek(hp, current)\n",
+    "        heart_tour += s\n",
+    "        current = proposed\n",
+    "\n",
+    "plot_trace(trace_tour(heart_tour))\n",
+    "\n",
+    "def heart_tour_func(): return heart_tour"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def trim_some_mistakes(tour, mistake_limit):\n",
+    "    trimmed_tour = rw\n",
+    "    mistake_count = len(mistake_positions(trace_tour(trimmed_tour)))\n",
+    "    while len(mistake_positions(trace_tour(trimmed_tour))) > mistake_limit:\n",
+    "        trimmed_tour = trim_loop(trimmed_tour, random_mistake=True)\n",
+    "    return trimmed_tour"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "cross.txt\t   small-squares.txt\t  tours.txt\r\n",
+      "large-squares.txt  tours-open.txt\t  tours-with-mistakes.txt\r\n",
+      "quincunx.txt\t   tours-random-walk.txt\r\n"
+     ]
+    }
+   ],
+   "source": [
+    "!ls *txt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "113"
+      ]
+     },
+     "execution_count": 46,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "valid_tours = [t.strip() for t in open('tours.txt').readlines() if valid(trace_tour(t.strip()))]\n",
+    "valid_tours += [t.strip() for t in open('tours-with-mistakes.txt').readlines() if valid(trace_tour(t.strip()))]\n",
+    "valid_tours += [t.strip() for t in open('tours-open.txt').readlines() if valid(trace_tour(t.strip()))]\n",
+    "valid_tours += [t.strip() for t in open('tours-random-walk.txt').readlines() if valid(trace_tour(t.strip()))]\n",
+    "\n",
+    "len(valid_tours)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "all(valid(trace_tour(t)) for t in valid_tours)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(87, 0)"
+      ]
+     },
+     "execution_count": 47,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tours_with_mistakes = [t.strip() for t in open('tours-with-mistakes.txt').readlines() \n",
+    "                       if not valid(trace_tour(t.strip()))]\n",
+    "len(tours_with_mistakes)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "100"
+      ]
+     },
+     "execution_count": 48,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tours_open = [t.strip() for t in open('tours-open.txt').readlines() \n",
+    "                       if not valid(trace_tour(t.strip()))]\n",
+    "len(tours_open)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(84, 116)"
+      ]
+     },
+     "execution_count": 50,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "tours_walks_loops = [t.strip() for t in open('tours-random-walk.txt').readlines() \n",
+    "                       if len(mistake_positions(trace_tour(t.strip()))) > 1]\n",
+    "tours_walks_unloops = [t.strip() for t in open('tours-random-walk.txt').readlines() \n",
+    "                       if len(mistake_positions(trace_tour(t.strip()))) == 1]\n",
+    "len(tours_walks_loops), len(tours_walks_unloops)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAAEACAYAAADBWvbHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\no9BKcBRaCY5CK8FRaCU4/wdDXVwAkfqwLwAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7ffba4647c18>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(tours_with_mistakes[31]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "65"
+      ]
+     },
+     "execution_count": 54,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum(1 for t in valid_tours if len(t) > 100)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 92,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "48"
+      ]
+     },
+     "execution_count": 92,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "problem_set = [t for t in valid_tours if len(t) <= 100]\n",
+    "len(problem_set)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 93,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(48, 65)"
+      ]
+     },
+     "execution_count": 93,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# problem_set += [t for t in valid_tours if len(t) > 100][0::2]\n",
+    "valids_to_split = [t for t in valid_tours if len(t) > 100]\n",
+    "len(problem_set), len(valids_to_split)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 94,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "148"
+      ]
+     },
+     "execution_count": 94,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "problem_set += random.sample(tours_with_mistakes + tours_open + tours_walks_loops + tours_walks_unloops, 100)\n",
+    "len(problem_set)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 95,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2284"
+      ]
+     },
+     "execution_count": 95,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "max(len(t) for t in valids_to_split)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 96,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1680"
+      ]
+     },
+     "execution_count": 96,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum(len(t) for t in problem_set if valid(trace_tour(t)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 85,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[]"
+      ]
+     },
+     "execution_count": 85,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[(i, j) \n",
+    " for i in range(len(problem_set)) \n",
+    " for j in range(len(problem_set))\n",
+    " if i != j\n",
+    " if valid(trace_tour(problem_set[i] + problem_set[j]))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 87,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "attempting 0\n",
+      "** found split for 0\n",
+      "attempting 1\n",
+      "attempting 2\n",
+      "attempting 3\n",
+      "attempting 4\n",
+      "attempting 5\n",
+      "attempting 6\n",
+      "attempting 7\n",
+      "attempting 8\n",
+      "attempting 9\n",
+      "attempting 10\n",
+      "attempting 11\n",
+      "** found split for 11\n",
+      "attempting 12\n",
+      "attempting 13\n",
+      "attempting 14\n",
+      "attempting 15\n",
+      "attempting 16\n",
+      "attempting 17\n",
+      "** found split for 17\n",
+      "attempting 18\n",
+      "attempting 19\n",
+      "attempting 20\n",
+      "attempting 21\n",
+      "attempting 22\n",
+      "attempting 23\n",
+      "attempting 24\n",
+      "attempting 25\n",
+      "attempting 26\n",
+      "attempting 27\n",
+      "attempting 28\n",
+      "attempting 29\n",
+      "** found split for 29\n",
+      "attempting 30\n",
+      "attempting 31\n",
+      "attempting 32\n",
+      "attempting 33\n",
+      "attempting 34\n",
+      "** found split for 34\n",
+      "attempting 35\n",
+      "attempting 36\n",
+      "attempting 37\n",
+      "attempting 38\n",
+      "** found split for 38\n",
+      "attempting 39\n",
+      "attempting 40\n",
+      "attempting 41\n",
+      "** found split for 41\n",
+      "attempting 42\n",
+      "attempting 43\n",
+      "attempting 44\n",
+      "attempting 45\n",
+      "attempting 46\n",
+      "attempting 47\n",
+      "attempting 48\n",
+      "** found split for 48\n",
+      "attempting 49\n",
+      "** found split for 49\n",
+      "attempting 50\n",
+      "** found split for 50\n",
+      "attempting 51\n",
+      "attempting 52\n",
+      "attempting 53\n",
+      "attempting 54\n",
+      "attempting 55\n",
+      "attempting 56\n",
+      "attempting 57\n",
+      "** found split for 57\n",
+      "attempting 58\n",
+      "attempting 59\n",
+      "** found split for 59\n",
+      "attempting 60\n",
+      "attempting 61\n",
+      "attempting 62\n",
+      "** found split for 62\n",
+      "attempting 63\n",
+      "attempting 64\n"
+     ]
+    }
+   ],
+   "source": [
+    "split_valids = []\n",
+    "unsplit_valids = []\n",
+    "i = 0\n",
+    "for v in valids_to_split:\n",
+    "    can_add = False\n",
+    "    attempts_remaining = 500\n",
+    "    print('attempting', i)\n",
+    "    while not can_add and attempts_remaining > 0:\n",
+    "        # print('splitting', i, 'attempt', attempts_remaining)\n",
+    "        attempts_remaining -= 1\n",
+    "#         split_pos = len(v) // 2 + random.randrange(10)\n",
+    "        split_pos = random.randint(20, len(v) - 40)\n",
+    "        vl = v[:split_pos]\n",
+    "        vr = v[split_pos:]\n",
+    "        can_add = True\n",
+    "        if valid(trace_tour(vr + vl)): can_add = False\n",
+    "        for other in problem_set:\n",
+    "            if can_add and valid(trace_tour(other + vl)): can_add = False\n",
+    "            if can_add and valid(trace_tour(other + vr)): can_add = False\n",
+    "            if can_add and valid(trace_tour(vl + other)): can_add = False\n",
+    "            if can_add and valid(trace_tour(vr + other)): can_add = False\n",
+    "        for other in split_valids:\n",
+    "            if can_add and valid(trace_tour(other + vl)): can_add = False\n",
+    "            if can_add and valid(trace_tour(other + vr)): can_add = False\n",
+    "            if can_add and valid(trace_tour(vl + other)): can_add = False\n",
+    "            if can_add and valid(trace_tour(vr + other)): can_add = False\n",
+    "    if can_add:\n",
+    "        split_valids += [vl, vr]\n",
+    "        print('** found split for', i)\n",
+    "    else:\n",
+    "        unsplit_valids += [v]\n",
+    "    i += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['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',\n",
+       " 'LLRRLFFFFFFFLFFFRFFFFFFFLLRFFRFFFRFFFLLFFRLRFFFLFRFFRFLFRFFFRFLLFFLFFFFFFRRFLRFRLFFFLFFFFFFFFLFFRLFFFFRFFFRFFFLFFFRLR',\n",
+       " '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',\n",
+       " 'FLFFRRFFFFRLLFFFLFLLRRFFFRFFFLRFFFLFLFFRRFFFFLLFRFFLFRFFRFFFRFLFFFFRLFFFLRFFFFRFRLFFRLLFFFFFF']"
+      ]
+     },
+     "execution_count": 97,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "split_valids[:4]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 98,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(0, 1),\n",
+       " (2, 3),\n",
+       " (4, 5),\n",
+       " (6, 7),\n",
+       " (8, 9),\n",
+       " (10, 11),\n",
+       " (12, 13),\n",
+       " (14, 15),\n",
+       " (16, 17),\n",
+       " (18, 19),\n",
+       " (20, 21),\n",
+       " (22, 23),\n",
+       " (24, 25)]"
+      ]
+     },
+     "execution_count": 98,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[(i, j) \n",
+    " for i in range(len(split_valids)) \n",
+    " for j in range(len(split_valids))\n",
+    " if i != j\n",
+    " if valid(trace_tour(split_valids[i] + split_valids[j]))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 99,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "226"
+      ]
+     },
+     "execution_count": 99,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "problem_set += (split_valids + unsplit_valids)\n",
+    "len(problem_set)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 100,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "with open('06-tours.txt', 'w') as f:\n",
+    "    f.writelines(t + '\\n' for t in random.sample(problem_set, len(problem_set)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

diff --git a/06-tour-shapes/tour-shapes-build-raw-tours.ipynb b/06-tour-shapes/tour-shapes-build-raw-tours.ipynb
new file mode 100644 (file)
index 0000000..7903070
--- /dev/null
+++ b/06-tour-shapes/tour-shapes-build-raw-tours.ipynb
@@ -0,0 +1,3282 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "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",
+    "1. which tours are closed?\n",
+    "2. what is the area enclosed by the tour?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import collections\n",
+    "import enum\n",
+    "import random\n",
+    "import os\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class Direction(enum.Enum):\n",
+    "    UP = 1\n",
+    "    RIGHT = 2\n",
+    "    DOWN = 3\n",
+    "    LEFT = 4\n",
+    "    \n",
+    "turn_lefts = {Direction.UP: Direction.LEFT, Direction.LEFT: Direction.DOWN,\n",
+    "              Direction.DOWN: Direction.RIGHT, Direction.RIGHT: Direction.UP}\n",
+    "\n",
+    "turn_rights = {Direction.UP: Direction.RIGHT, Direction.RIGHT: Direction.DOWN,\n",
+    "               Direction.DOWN: Direction.LEFT, Direction.LEFT: Direction.UP}\n",
+    "\n",
+    "def turn_left(d):\n",
+    "    return turn_lefts[d]\n",
+    "\n",
+    "def turn_right(d):\n",
+    "    return turn_rights[d]\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "Step = collections.namedtuple('Step', ['x', 'y', 'dir'])\n",
+    "Mistake = collections.namedtuple('Mistake', ['i', 'step'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def advance(step, d):\n",
+    "    if d == Direction.UP:\n",
+    "        return Step(step.x, step.y+1, d)\n",
+    "    elif d == Direction.DOWN:\n",
+    "        return Step(step.x, step.y-1, d)\n",
+    "    elif d == Direction.LEFT:\n",
+    "        return Step(step.x-1, step.y, d)\n",
+    "    elif d == Direction.RIGHT:\n",
+    "        return Step(step.x+1, step.y, d)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def step(s, current):\n",
+    "    if s == 'F':\n",
+    "        return advance(current, current.dir)\n",
+    "    elif s == 'L':\n",
+    "        return advance(current, turn_left(current.dir))\n",
+    "    elif s == 'R':\n",
+    "        return advance(current, turn_right(current.dir))\n",
+    "    else:\n",
+    "        raise ValueError"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def trace_tour(tour, startx=0, starty=0, startdir=Direction.RIGHT):\n",
+    "    current = Step(startx, starty, startdir)\n",
+    "    trace = [current]\n",
+    "    for s in tour:\n",
+    "        current = step(s, current)\n",
+    "        trace += [current]\n",
+    "    return trace    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# def trace_tour(tour, startx=0, starty=0, startdir=Direction.RIGHT):\n",
+    "#     current = Step(startx, starty, startdir)\n",
+    "#     trace = [current]\n",
+    "#     for s in tour:\n",
+    "#         if s == 'F':\n",
+    "#             current = advance(current, current.dir)\n",
+    "#         elif s == 'L':\n",
+    "#             current = advance(current, turn_left(current.dir))\n",
+    "#         elif s == 'R':\n",
+    "#             current = advance(current, turn_right(current.dir))\n",
+    "#         trace += [current]\n",
+    "#     return trace    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "k = Step(1, 2, 3)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Step(x=1, y=2, dir=3)"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "k"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "__main__.Step"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Step"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Direction.UP: 1>"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "d = Direction.UP\n",
+    "d"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<Direction.RIGHT: 2>"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "turn_right(d)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{<Direction.RIGHT: 2>: <Direction.DOWN: 3>,\n",
+       " <Direction.UP: 1>: <Direction.RIGHT: 2>,\n",
+       " <Direction.LEFT: 4>: <Direction.UP: 1>,\n",
+       " <Direction.DOWN: 3>: <Direction.LEFT: 4>}"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "turn_rights"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
+       " Step(x=2, y=1, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=2, y=2, dir=<Direction.UP: 1>)]"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "trace_tour('FLRL')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=2, y=1, dir=<Direction.UP: 1>),\n",
+       " Step(x=3, y=1, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=3, y=2, dir=<Direction.UP: 1>),\n",
+       " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=1, y=1, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
+      ]
+     },
+     "execution_count": 14,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "trace_tour('FFLRLLFLRL')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
+       " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-1, y=1, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-2, y=-1, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-2, y=-2, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-2, y=-3, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-1, y=-3, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=0, y=-3, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=-3, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=-2, dir=<Direction.UP: 1>),\n",
+       " Step(x=1, y=-1, dir=<Direction.UP: 1>),\n",
+       " Step(x=0, y=-1, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=0, y=-2, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-1, y=-2, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-1, y=-1, dir=<Direction.UP: 1>),\n",
+       " Step(x=-1, y=0, dir=<Direction.UP: 1>),\n",
+       " Step(x=0, y=0, dir=<Direction.RIGHT: 2>)]"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "trace_tour('FLLFFLFFFLFFLFLLRRFR')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=2, y=-1, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=3, y=-1, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=3, y=0, dir=<Direction.UP: 1>),\n",
+       " Step(x=3, y=1, dir=<Direction.UP: 1>),\n",
+       " Step(x=4, y=1, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=4, y=2, dir=<Direction.UP: 1>),\n",
+       " Step(x=3, y=2, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=0, y=2, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=0, y=3, dir=<Direction.UP: 1>),\n",
+       " Step(x=0, y=4, dir=<Direction.UP: 1>),\n",
+       " Step(x=-1, y=4, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-1, y=3, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-2, y=3, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-2, y=2, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-1, y=2, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=-1, y=1, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-1, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=-1, y=-1, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=0, y=-1, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=0, y=0, dir=<Direction.UP: 1>)]"
+      ]
+     },
+     "execution_count": 16,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def positions(trace):\n",
+    "    return [(s.x, s.y) for s in trace]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(0, 0),\n",
+       " (1, 0),\n",
+       " (2, 0),\n",
+       " (2, -1),\n",
+       " (3, -1),\n",
+       " (3, 0),\n",
+       " (3, 1),\n",
+       " (4, 1),\n",
+       " (4, 2),\n",
+       " (3, 2),\n",
+       " (2, 2),\n",
+       " (1, 2),\n",
+       " (0, 2),\n",
+       " (0, 3),\n",
+       " (0, 4),\n",
+       " (-1, 4),\n",
+       " (-1, 3),\n",
+       " (-2, 3),\n",
+       " (-2, 2),\n",
+       " (-1, 2),\n",
+       " (-1, 1),\n",
+       " (-2, 1),\n",
+       " (-2, 0),\n",
+       " (-1, 0),\n",
+       " (-1, -1),\n",
+       " (0, -1),\n",
+       " (0, 0)]"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "positions(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def valid(trace):\n",
+    "    return (trace[-1].x == 0 \n",
+    "            and trace[-1].y == 0 \n",
+    "            and len(set(positions(trace))) + 1 == len(trace))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 20,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "False"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLLFF'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "False"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "valid(trace_tour('FFLLLFRR'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "False"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "valid(trace_tour('F'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "valid(trace_tour('LLLL'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def chunks(items, n=2):\n",
+    "    return [items[i:i+n] for i in range(len(items) - n + 1)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['abcdefg',\n",
+       " 'bcdefgh',\n",
+       " 'cdefghi',\n",
+       " 'defghij',\n",
+       " 'efghijk',\n",
+       " 'fghijkl',\n",
+       " 'ghijklm',\n",
+       " 'hijklmn',\n",
+       " 'ijklmno',\n",
+       " 'jklmnop',\n",
+       " 'klmnopq',\n",
+       " 'lmnopqr',\n",
+       " 'mnopqrs',\n",
+       " 'nopqrst',\n",
+       " 'opqrstu',\n",
+       " 'pqrstuv',\n",
+       " 'qrstuvw',\n",
+       " 'rstuvwx',\n",
+       " 'stuvwxy',\n",
+       " 'tuvwxyz']"
+      ]
+     },
+     "execution_count": 26,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import string\n",
+    "chunks(string.ascii_lowercase, 7)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Using the [Shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def shoelace(trace):\n",
+    "    return abs(sum(s.x * t.y - t.x * s.y for s, t in chunks(trace, 2))) // 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "4"
+      ]
+     },
+     "execution_count": 28,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "shoelace(trace_tour('FFLRLLFLRL'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "9"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "shoelace(trace_tour('FLLFFLFFFLFFLFLLRRFR'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "15"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "shoelace(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def valid_prefix(tour):\n",
+    "    current = Step(0, 0, Direction.RIGHT)\n",
+    "    prefix = []\n",
+    "    posns = []\n",
+    "    for s in tour:\n",
+    "        current = step(s, current)\n",
+    "        prefix += [s]\n",
+    "        if (current.x, current.y) in posns:\n",
+    "            return ''\n",
+    "        elif current.x == 0 and current.y == 0: \n",
+    "            return ''.join(prefix)\n",
+    "        posns += [(current.x, current.y)]\n",
+    "    if current.x == 0 and current.y == 0:\n",
+    "        return ''.join(prefix)\n",
+    "    else:\n",
+    "        return ''"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def mistake_positions(trace, debug=False):\n",
+    "    mistakes = []\n",
+    "    current = trace[0]\n",
+    "    posns = [(0, 0)]\n",
+    "    for i, current in enumerate(trace[1:]):\n",
+    "        if (current.x, current.y) in posns:\n",
+    "            if debug: print(i, current)\n",
+    "            mistakes += [Mistake(i+1, current)]\n",
+    "        posns += [(current.x, current.y)]\n",
+    "    if (current.x, current.y) == (0, 0):\n",
+    "        return mistakes[:-1]\n",
+    "    else:\n",
+    "        return mistakes + [Mistake(len(trace)+1, current)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def returns_to_origin(mistake_positions):\n",
+    "    return [i for i, m in mistake_positions\n",
+    "           if (m.x, m.y) == (0, 0)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "sample_tours = ['FFLRLLFLRL', 'FLLFFLFFFLFFLFLLRRFR', 'FFRLLFRLLFFFRFLLRLLRRLLRLL']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'FFLRLLFLRL'"
+      ]
+     },
+     "execution_count": 35,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "valid_prefix(sample_tours[0])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 36,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "all(valid_prefix(t) == t for t in sample_tours)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 37,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "valid_prefix(sample_tours[0] + 'FLLLL') == sample_tours[0]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Mistake(i=10, step=Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
+       " Mistake(i=13, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
+      ]
+     },
+     "execution_count": 38,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mistake_positions(trace_tour(sample_tours[0] + 'F'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Mistake(i=10, step=Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
+       " Mistake(i=13, step=Step(x=1, y=0, dir=<Direction.UP: 1>)),\n",
+       " Mistake(i=14, step=Step(x=0, y=0, dir=<Direction.LEFT: 4>)),\n",
+       " Mistake(i=15, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>)),\n",
+       " Mistake(i=17, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mistake_positions(trace_tour(sample_tours[0] + 'FLLLL'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'FFLRLLFLRL'"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(sample_tours[0] + 'FLLLL')[:10]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def random_walk(steps=1000):\n",
+    "    return ''.join(random.choice('FFLR') for _ in range(steps))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "''"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "valid_prefix(random_walk(1000))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'FFRRFR'"
+      ]
+     },
+     "execution_count": 45,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "valid_prefix(random_walk(1000))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "collapsed": true,
+    "scrolled": true
+   },
+   "outputs": [],
+   "source": [
+    "walks = []\n",
+    "while len(walks) < 10:\n",
+    "    w = valid_prefix(random_walk())\n",
+    "    if len(w) > 30: walks += [w]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['RLFFLRFFFFRRLFFFRFFFFRFFLFFFRFRF',\n",
+       " 'FFFFFLLFFRRLFFFFLLFFRLRFFLFFLRLL',\n",
+       " 'LRLRLFFFFLLRLRLRFLFFFRLFLFFFLRLL',\n",
+       " 'FLFFFFLFRLFFFFRLRFLLFFFFFFLRFLFLFLRFRFFRFFFFLRFFFLFRLRFLLFFFFRLFLFFR',\n",
+       " 'LLFRLRFFLLRFRFLFFFLRLFFLFRFFFLFFRFFLFFFFLLFFFRFRFFLFRF',\n",
+       " 'FLLFLFFFRLFFLLRFFFFLRFLFFLFFFFLRRF',\n",
+       " 'FFLFRLLFFRFFFLRLFRLFLFFRLFFFLFFFRFRLRLFFLRRFFLLRLRFLFFLFFRFLFLLRRFFFRL',\n",
+       " 'RFFFFFLLRLFFFRLFLRFLLFRFFFFFFFLLFFFFRLLR',\n",
+       " 'LLFFFRLLFFFRFLLFRFFLLRFFLRLFLRRFLL',\n",
+       " 'FLLRFLRFFRRFLFFRRLFFFFFFRFFRFFRL']"
+      ]
+     },
+     "execution_count": 47,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "walks"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
+       " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
+      ]
+     },
+     "execution_count": 48,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "trace_tour('FLLL')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(-1, 3)"
+      ]
+     },
+     "execution_count": 49,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fdf356d8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline\n",
+    "plt.axis('on')\n",
+    "plt.arrow(0, 0, 0.8, 0, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
+    "plt.arrow(0.2, 0, 0, 1, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
+    "plt.xlim([-1, 2])\n",
+    "plt.ylim([-1, 3])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bounds(trace):\n",
+    "    return (max(s.x for s in trace),\n",
+    "            max(s.y for s in trace),\n",
+    "            min(s.x for s in trace),\n",
+    "            min(s.y for s in trace))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(0, 2, -13, -13)"
+      ]
+     },
+     "execution_count": 51,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "bounds(trace_tour('RFRFFLRFLFFRRFFRRRRLLLRRRRRRFRLFRFFRFFRRFRLRRFLLFRLLFRFLFLFRFRLLFRLFRFLRRLLFRRRFRRRRLLFLFRFRRFFRRLLLRLRRFRLRRFFRRFLFRRLLRRFFRFRRRRRFLLLLLRRFFFLLFFFRRLFLFFLRRRFRFLLFFRRLLRFLLRRF'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n",
+    "           Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None, filename=None):\n",
+    "    plt.axis('on')\n",
+    "    plt.axes().set_aspect('equal')\n",
+    "    for s, t in chunks(trace, 2):\n",
+    "        w, h = plot_wh[t.dir]\n",
+    "        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",
+    "    xh, yh, xl, yl = bounds(trace)\n",
+    "    if xybounds is not None:    \n",
+    "        bxh, byh, bxl, byl = xybounds\n",
+    "        plt.xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
+    "        plt.ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
+    "    else:\n",
+    "        plt.xlim([xl-1, xh+1])\n",
+    "        plt.ylim([yl-1, yh+1])\n",
+    "    if filename:\n",
+    "        plt.savefig(filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None):\n",
+    "#     plt.ioff()\n",
+    "#     if fig is None:\n",
+    "#         fig = plt.figure()\n",
+    "#         ax = fig.gca()\n",
+    "#     if subplot_details is not None:\n",
+    "#         ax = fig.add_subplot(*subplot_details)\n",
+    "#     plt.axis('on')\n",
+    "# #     plt.axes().set_aspect('equal')\n",
+    "#     ax.set_aspect('equal')\n",
+    "#     for s, t in chunks(trace, 2):\n",
+    "#         w, h = plot_wh[t.dir]\n",
+    "#         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",
+    "#     xh, yh, xl, yl = bounds(trace)\n",
+    "#     if xybounds is not None:    \n",
+    "#         bxh, byh, bxl, byl = xybounds\n",
+    "#         ax.set_xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
+    "#         ax.set_ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
+    "#     else:\n",
+    "#         ax.set_xlim([xl-1, xh+1])\n",
+    "#         ax.set_ylim([yl-1, yh+1])\n",
+    "#     plt.close(fig)\n",
+    "#     return fig"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def pqr(p, q, r):\n",
+    "    return '{}:{};{}'.format(p, q, r)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'1:2;3'"
+      ]
+     },
+     "execution_count": 55,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pqrt = (1, 2, 3)\n",
+    "pqr(*pqrt)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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kP1LxyGazsUcYkVKbFzRzMckrBu6+2d37wsMXgIb8RyoepfafXmrzgmYuJkleM/gnYGOC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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fdc55b70>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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mVpXUYCKSX7muDH4DjHX3I4HVwA25j1Q4MplM7BH6pdjmBc1cSHKKgbsvcPeO8PRFoCb3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\nAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fdcc74a8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'), colour='g')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 58,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAADqCAYAAAChr/4gAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fdb35b00>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour('FFFLLFFL'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 59,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
+       " Step(x=1, y=2, dir=<Direction.UP: 1>),\n",
+       " Step(x=1, y=3, dir=<Direction.UP: 1>),\n",
+       " Step(x=1, y=4, dir=<Direction.UP: 1>),\n",
+       " Step(x=1, y=5, dir=<Direction.UP: 1>),\n",
+       " Step(x=0, y=5, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-1, y=5, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-1, y=6, dir=<Direction.UP: 1>),\n",
+       " Step(x=-2, y=6, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-3, y=6, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-4, y=6, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-5, y=6, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-6, y=6, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-6, y=7, dir=<Direction.UP: 1>),\n",
+       " Step(x=-7, y=7, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-7, y=8, dir=<Direction.UP: 1>),\n",
+       " Step(x=-7, y=9, dir=<Direction.UP: 1>),\n",
+       " Step(x=-8, y=9, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-8, y=8, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-8, y=7, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-8, y=6, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-8, y=5, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-8, y=4, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-8, y=3, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-8, y=2, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-7, y=2, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=-7, y=1, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-7, y=0, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-6, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=-5, y=0, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=-5, y=1, dir=<Direction.UP: 1>),\n",
+       " Step(x=-5, y=2, dir=<Direction.UP: 1>),\n",
+       " Step(x=-6, y=2, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=-6, y=3, dir=<Direction.UP: 1>),\n",
+       " Step(x=-6, y=4, dir=<Direction.UP: 1>),\n",
+       " Step(x=-5, y=4, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=-4, y=4, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=-3, y=4, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=-3, y=3, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-3, y=2, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-3, y=1, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-3, y=0, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-3, y=-1, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-2, y=-1, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=-2, y=-2, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-2, y=-3, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-2, y=-4, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-2, y=-5, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=-1, y=-5, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=0, y=-5, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=0, y=-6, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=1, y=-6, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=1, y=-7, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=1, y=-8, dir=<Direction.DOWN: 3>),\n",
+       " Step(x=2, y=-8, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=2, y=-7, dir=<Direction.UP: 1>),\n",
+       " Step(x=2, y=-6, dir=<Direction.UP: 1>),\n",
+       " Step(x=2, y=-5, dir=<Direction.UP: 1>),\n",
+       " Step(x=2, y=-4, dir=<Direction.UP: 1>),\n",
+       " Step(x=2, y=-3, dir=<Direction.UP: 1>),\n",
+       " Step(x=3, y=-3, dir=<Direction.RIGHT: 2>),\n",
+       " Step(x=3, y=-2, dir=<Direction.UP: 1>),\n",
+       " Step(x=3, y=-1, dir=<Direction.UP: 1>),\n",
+       " Step(x=2, y=-1, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=1, y=-1, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=0, y=-1, dir=<Direction.LEFT: 4>),\n",
+       " Step(x=0, y=0, dir=<Direction.UP: 1>)]"
+      ]
+     },
+     "execution_count": 59,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "trace_tour(walks[3])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 60,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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1i6VuWDnP4Z1ztwWsNQ/4TWcDZs6c2XG9urqa6urqgKUFYOHChQwfPrxjXkpn6urq+Nzn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\nVxR48cr/AwOlW67H9WljAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fda79780>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(walks[3]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10"
+      ]
+     },
+     "execution_count": 61,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "long_walks = [w for w in walks if len(w) >= 30]\n",
+    "len(long_walks)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 62,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAADkCAYAAABXPKW7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nirCFtp8KBQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fdbb2710>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(long_walks[0]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 63,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['RLFFLRFFFFRRLFFFRFFFFRFFLFFFRFRF',\n",
+       " 'FFFFFLLFFRRLFFFFLLFFRLRFFLFFLRLL',\n",
+       " 'LRLRLFFFFLLRLRLRFLFFFRLFLFFFLRLL',\n",
+       " 'FLFFFFLFRLFFFFRLRFLLFFFFFFLRFLFLFLRFRFFRFFFFLRFFFLFRLRFLLFFFFRLFLFFR',\n",
+       " 'LLFRLRFFLLRFRFLFFFLRLFFLFRFFFLFFRFFLFFFFLLFFFRFRFFLFRF',\n",
+       " 'FLLFLFFFRLFFLLRFFFFLRFLFFLFFFFLRRF',\n",
+       " 'FFLFRLLFFRFFFLRLFRLFLFFRLFFFLFFFRFRLRLFFLRRFFLLRLRFLFFLFFRFLFLLRRFFFRL',\n",
+       " 'RFFFFFLLRLFFFRLFLRFLLFRFFFFFFFLLFFFFRLLR',\n",
+       " 'LLFFFRLLFFFRFLLFRFFLLRFFLRLFLRRFLL',\n",
+       " 'FLLRFLRFFRRFLFFRRLFFFFFFRFFRFFRL']"
+      ]
+     },
+     "execution_count": 63,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "walks"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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2WNK1JH91f1tmDqEfEWwFZpvZQUlfA54luWXzZJK/7PZ0qzHcGDbMMoXjPGNmp0g6GnhW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\n8v89qQ80wuYWhQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd986160>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour('FLFFLRFRLFRRRR'))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 65,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(313, [])"
+      ]
+     },
+     "execution_count": 65,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "w = random_walk()\n",
+    "ms = mistake_positions(trace_tour(w))\n",
+    "len(ms), returns_to_origin(ms)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 66,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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Sd+7cGatWrcK6desAtK0+paWlyR/Fu+++i7Nnz2LatGkA3B7djY2N6Nq1q5wO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\nQREEYVr+H+clU6giyaiIAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd8c0898>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(w))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 67,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def trim_loop(tour, random_mistake=False):\n",
+    "    trace = trace_tour(tour)\n",
+    "    mistakes = mistake_positions(trace)\n",
+    "    if random_mistake:\n",
+    "        end_mistake_index = random.randrange(len(mistakes))\n",
+    "    else:\n",
+    "        end_mistake_index = 0\n",
+    "#     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",
+    "    # while this mistake extends to the next step in the trace...\n",
+    "    while (mistakes[end_mistake_index].i + 1 < len(trace) and \n",
+    "           end_mistake_index + 1 < len(mistakes) and\n",
+    "           mistakes[end_mistake_index].i + 1 == \n",
+    "           mistakes[end_mistake_index + 1].i):\n",
+    "#         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",
+    "        # push this mistake finish point later\n",
+    "        end_mistake_index += 1\n",
+    "    mistake = mistakes[end_mistake_index]\n",
+    "    \n",
+    "    # find the first location that mentions where this mistake ends (which the point where the loop starts)\n",
+    "    mistake_loop_start = max(i for i, loc in enumerate(trace[:mistake.i])\n",
+    "                             if (loc.x, loc.y) == (mistake.step.x, mistake.step.y))\n",
+    "#     print('Dealing with mistake from', mistake_loop_start, 'to', mistake.i, ', trace has len', len(trace))\n",
+    "    \n",
+    "    # direction before entering the loop\n",
+    "    direction_before = trace[mistake_loop_start].dir\n",
+    "    \n",
+    "    # find the new instruction to turn from heading before the loop to heading after the loop\n",
+    "    new_instruction = 'F'\n",
+    "    if (mistake.i + 1) < len(trace):\n",
+    "        if turn_left(direction_before) == trace[mistake.i + 1].dir:\n",
+    "            new_instruction = 'L'\n",
+    "        if turn_right(direction_before) == trace[mistake.i + 1].dir:\n",
+    "            new_instruction = 'R'\n",
+    "#     if (mistake.i + 1) < len(trace):\n",
+    "#         print('turning from', direction_before, 'to', trace[mistake.i + 1].dir, 'with', new_instruction )\n",
+    "#     else:\n",
+    "#         print('turning from', direction_before, 'to BEYOND END', 'with', new_instruction )\n",
+    "    return tour[:mistake_loop_start] + new_instruction + tour[mistake.i+1:]\n",
+    "#     return mistake, mistake_loop_start, trace[mistake_loop_start-2:mistake_loop_start+8]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 68,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF'"
+      ]
+     },
+     "execution_count": 68,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "w = 'RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF'\n",
+    "w"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 69,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd29a710>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "w_short = w[:100]\n",
+    "plot_trace(trace_tour(w_short))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 70,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n",
+      "RFFRRFFFRFFRFLLRFLFFFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd244b70>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "trimmed = trim_loop(w_short)\n",
+    "print('{}\\n{}'.format(w_short, trimmed))\n",
+    "plot_trace(trace_tour(trimmed))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 71,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "RFFRRFFFRFFRFLLRFLFFFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n",
+      "RFFRRFFFRFFRFLLRFLFFLLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd00c9b0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "trimmed2 = trim_loop(trimmed)\n",
+    "print('{}\\n{}'.format(trimmed, trimmed2))\n",
+    "plot_trace(trace_tour(trimmed2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 72,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Mistake(i=104, step=Step(x=-4, y=6, dir=<Direction.DOWN: 3>)),\n",
+       " Mistake(i=105, step=Step(x=-5, y=6, dir=<Direction.LEFT: 4>)),\n",
+       " Mistake(i=106, step=Step(x=-5, y=7, dir=<Direction.UP: 1>)),\n",
+       " Mistake(i=107, step=Step(x=-5, y=8, dir=<Direction.UP: 1>)),\n",
+       " Mistake(i=108, step=Step(x=-5, y=9, dir=<Direction.UP: 1>)),\n",
+       " Mistake(i=115, step=Step(x=-5, y=12, dir=<Direction.LEFT: 4>)),\n",
+       " Mistake(i=116, step=Step(x=-5, y=11, dir=<Direction.DOWN: 3>)),\n",
+       " Mistake(i=127, step=Step(x=2, y=11, dir=<Direction.LEFT: 4>)),\n",
+       " Mistake(i=130, step=Step(x=3, y=11, dir=<Direction.UP: 1>)),\n",
+       " Mistake(i=132, step=Step(x=3, y=11, dir=<Direction.UP: 1>))]"
+      ]
+     },
+     "execution_count": 72,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mistake_positions(trace_tour(w[:130]))[-10:]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 73,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Step(x=40, y=36, dir=<Direction.UP: 1>)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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4BuzPuLRMdHS0Ko21u+j1enndOp1OtUsMQEC/aDqdzqUt3PqaEhISwtJ+rkXS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\nRK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fcecd470>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "w_tour_start = w #[:250]\n",
+    "print(trace_tour(w_tour_start)[-1])\n",
+    "plot_trace(trace_tour(w_tour_start))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 74,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF\n",
+      "RFFRRFFFRFLRFRFLLRFLLRLRRLFRLRRFFLLRLLRRFRFLRLFFLFLRRLRRLRLFLLRRFFLRLLFFFFFRRFFLFRLFFRLLRRFLFFFLRFLRRLRFLFLFFRLLFFRRFFLRLFRFFRLFFLRRFLRFLRRLFRRLFFFFRLFLFFLRFFLFRFLRRFFFFFLFRLRRFRLLRLLFRFLFFFRLFRFLFLRLRFFFFFLFFRFFFFLRFLFRFLRLRLFFLRRFFFRLLFRLFLRRFLRLLRLFFRFLRRLFLLRFLFFRFLFRLRFFFFFLRLLFRFLLRRFLRRFLRLRFLRRLFFFRFLRRLF\n",
+      "Step(x=40, y=36, dir=<Direction.UP: 1>)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd292eb8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "w_tour = w_tour_start\n",
+    "w_trace = trace_tour(w_tour)\n",
+    "mks = mistake_positions(w_trace)\n",
+    "while len(mks) > 1:\n",
+    "#     print(len(mks))\n",
+    "    w_tour = trim_loop(w_tour)\n",
+    "    w_trace = trace_tour(w_tour)\n",
+    "    mks = mistake_positions(w_trace)\n",
+    "print('{}\\n{}\\n{}'.format(w_tour_start, w_tour, trace_tour(w_tour)[-1]))\n",
+    "plot_trace(trace_tour(w_tour))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 75,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def trim_all_loops(tour, mistake_reduction_attempt_limit=10):\n",
+    "    trace = trace_tour(tour)\n",
+    "    mistake_limit = 1\n",
+    "    if trace[-1].x == 0 and trace[-1].y == 0:\n",
+    "        mistake_limit = 0\n",
+    "    mistakes = mistake_positions(trace)\n",
+    "    \n",
+    "    old_mistake_count = len(mistakes)\n",
+    "    mistake_reduction_tries = 0\n",
+    "    \n",
+    "    while len(mistakes) > mistake_limit and mistake_reduction_tries < mistake_reduction_attempt_limit:\n",
+    "        tour = trim_loop(tour)\n",
+    "        trace = trace_tour(tour)\n",
+    "        mistakes = mistake_positions(trace)\n",
+    "        if len(mistakes) < old_mistake_count:\n",
+    "            old_mistake_count = len(mistakes)\n",
+    "            mistake_reduction_tries = 0\n",
+    "        else:\n",
+    "            mistake_reduction_tries += 1\n",
+    "    if mistake_reduction_tries >= mistake_reduction_attempt_limit:\n",
+    "        return ''\n",
+    "    else:\n",
+    "        return tour"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 76,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'RFFRRFFFRFLRFRFLLRFLLRLRRLFRLRRFFLLRLLRRFRFLRLFFLFLRRLRRLRLFLLRRFFLRLLFFFFFRRFFLFRLFFRLLRRFLFFFLRFLRRLRFLFLFFRLLFFRRFFLRLFRFFRLFFLRRFLRFLRRLFRRLFFFFRLFLFFLRFFLFRFLRRFFFFFLFRLRRFRLLRLLFRFLFFFRLFRFLFLRLRFFFFFLFFRFFFFLRFLFRFLRLRLFFLRRFFFRLLFRLFLRRFLRLLRLFFRFLRRLFLLRFLFFRFLFRLRFFFFFLRLLFRFLLRRFLRRFLRLRFLRRLFFFRFLRRLF'"
+      ]
+     },
+     "execution_count": 76,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "w_trimmed = trim_all_loops(w)\n",
+    "w_trimmed"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 77,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fcfd4358>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(trim_all_loops(w)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def reverse_tour(tour):\n",
+    "    def swap(tour_step):\n",
+    "        if tour_step == 'R':\n",
+    "            return 'L'\n",
+    "        elif tour_step == 'L':\n",
+    "            return 'R'\n",
+    "        else:\n",
+    "            return tour_step\n",
+    "        \n",
+    "    return ''.join(swap(s) for s in reversed(tour))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 79,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk\nMvwPf/iDldyCwSBf/vKX2bRpk5UUT548ycqVK63i78aNG1m0aJEmO6WiaA+KsAsuuIA5c+YAsHbt\nWlatWhWzzZVXXklVVVWHx1i8eHFS5/T5QjfPf//3f9/pdpdddlmn/9+nTx++8pWvWMuR2cWUUonx\nTDFWKeVteZns2trauP3226msrKSystIazy26we3x48fj7jtp0iRrv4kTJ7J161br/yId6rtTdBQR\n67jTp0/nwIEDncYPMHPmTGsfEWHs2LHW8uzZs5OOQSlPS7bdVrKv0Cmya//+/QaIeX388cfWNnfd\ndZdpH9sll1wSd7+Il19+OWafrgSDQTNy5MiYY06ZMqXT/ebNmxezT3l5uW159uzZScWiVL4L/37G\nzUV5+cwu0h7NdHIH1n6uBoD//u//ti2LCH369LGWIxUVyRARaz7Y6HWDBw/udL+lS5eydOnSpM+n\nlIovL4uxSinVXl7e2SXi1KnYOb3r6uo4fPhwh/sEAgEAtm/fbq0zxnRae6uUcoe8THYNDQ1AaKSQ\n6EqJaIMHD7a1c2tra6N///4x2915553Wz2PGjAGISW5r1qzhiiuuSCrG7nQXU0p1X14mu3i1r+35\n/X5ruCTAmpFry5YtTJo0CQglwMh6gMmTJ8c8BxQRtm3blnSyq6urS2p7pVRq9JldO9FDKUUnunSL\nngJRKZV5nk12wWAwbcfqrNZXKeUOeZHsXnzxRVsH+YEDB3a5T2SkkfYd9KMnqk7Ut7/97ZgBAzp7\nAVb/W6VUduTFM7u5c+cC8M1vfhMIDXN+8cUXd7rPkiVLGDduHB999BEQeoZ33nnnWZUQidq2bRtL\nliyxktixY8cYMmSIVXN75swZ+vfvb+t90dDQwCOPPJLUeZRSqcmLUU8uuOACduzYocVJpTxOh2VX\nSnleXhRjI8MdffnLX7aKk3PmzOHmm292MiyllIvkRTG2pqaGyy+/PGa93+/vtK2dUiq/dFaMzYtk\n196xY8cYOHCgPsNTymP0mZ1SyvNcn+xMeKb7aM3NzQ5Fo5TKVa5LdlVVVTGzbLWf9aukpIT33nuv\nw2NEGga3b8wbmWxHKeU9rkt2keGTjh49ytGjRzly5Aj79++3lo8ePQrAH//4xw6PUV5ezpEjR6it\nrbXtE2+CHaWUN7iy6cnAgQMZMGBASscYNGhQzLrKysqUjqmUyl2uu7NTSqlMyGqy27FjB4MHD7Y9\nRysqKorEudifAAAGQ0lEQVTpJH/uued2eaympibr57Vr11JSUmI7Tr9+/WKOq3d2SnlXSsVYEbkG\neIxQ0nzOGPPjzra///77qa2tZcKECUCow/6wYcNsQ6R//PHH/PrXv+7y3NGNha+77jpaWlqs4x47\ndoyJEydSW1sLhIZT9/v9/Pu//3uS71AplS+6nexExAf8DLgCOAxsEpHlxpidHe0TGXrpr3/9a3dP\na/H5PrkpHTVqFDt27EjLcZVS+SmVYuxUYLcx5iNjTAD4DXB9esJSSqn0SqUYew5wMGr5EKEEmJSG\nhoZuDVH+zjvvWHd39fX1Se+vlPKWVJJdvP5ncTujLly4EIANGzbE/F+vXr04cOAAw4YNS/jEo0aN\n4rXXXuO1116z1v3Lv/xLwvsrpfJDTU0NNTU1CW3b7YEAROSzwEJjzDXh5fmAaV9JET0QwNy5c/nl\nL39p66AvIrz//vucf/753YpDKaUiMjUQwCZgtIgMF5Ei4CvAis52iIw7p5RS2dbtYqwxpk1Evgms\n4pOmJ++nLTKllEqjlNrZGWNWAuMS3b6srIwePXpYy5FJqv1+fyphKKVUl7Lag+Kjjz6yZt0CKCwM\n5druTF+olFLJyGqy69+/fzZPp5RSFh0IQCnlCVlNdtFdvOCTZ3btRyJWSql0y2qyO3bsmG25oKAg\nFIRPbzCVUpmV1SzTr18/23Jk6KXoGlqllMoEvaVSSnlCVodlj3QT27Vrl219MBjMZhhKKQ/K6iTZ\nq1at4uqrr47Z5tChQ5xzzjkZjUMplf9cM0n2rFmzCAQCGGNsr927d2czjJQkOsKCW2i8mZVL8eZS\nrJD+eLP+zC7SayJaLn0JuRQraLyZlkvx5lKskAfJTimlnKDJTinlCVmpoMjoCZRSKkpHFRQZT3ZK\nKeUGWoxVSnmCJjullCc4muxE5BoR2SkiH4jIvU7GEo+IPCcitSKyLWpdXxFZJSK7RORtEalwMsZo\nIjJURNaKyA4R2S4id4bXuy5mESkWkQ0isjkc64Ph9SNE5E/hWF8Skaz28umKiPhE5D0RWRFedm28\nIrJfRLaGP+ON4XWuuxYiRKRCRF4RkfdF5K8iMi2d8TqW7ETEB/wMuBq4ALhJRNw2xdgvCMUXbT6w\nxhgzDlgL3Jf1qDrWCtxtjJkATAf+T/gzdV3MxpgW4HJjzGTgIuBaEZkG/BhYHI71JPBPDoYZz13A\njqhlN8cbBKqNMZONMZE5nV13LUR5HHjLGDMemATsJJ3xtu/NkK0X8Fngd1HL84F7nYqnkziHA9ui\nlncCg8I/DwZ2Oh1jJ7G/Dlzp9piBUuDPhCZZPwr4oq6RlU7HFxXnUGA1UA2sCK875uJ49wH92q1z\n5bUA9AL2xFmftnidLMaeAxyMWj4UXud2A40xtQDGmCPAAIfjiUtERhC6Y/oToYvFdTGHi4SbgSOE\nksge4KQxJjIyxCFgiFPxxfEo8B3Ck8GLSD/ghIvjNcDbIrJJROaF17nyWgBGAsdF5BfhxwTPiEgp\naYzXyWQXry2MtoNJAxEpB5YBdxljGnDp52qMCZpQMXYoobu68fE2y25U8YnI54BaY8wWPrl2hdjr\n2BXxhs0wxkwBriP0SONS3BVftELg74CnjDF/BzQSKu2lLV4nk90h4Nyo5aHAYYdiSUatiAwCEJHB\nhIpdrhF+QL4MeNEYszy82tUxG2NOA38gVAzsE36eC+66Ji4GviAie4GXgJnAY0CFS+ON3AlhjDlG\n6JHGVNx7LRwCDhpj/hxefpVQ8ktbvE4mu03AaBEZLiJFwFeAFQ7G05H2f71XAN8I//x1YHn7HRz2\nPLDDGPN41DrXxSwi/SM1ayJSQujZ4g7g98AN4c1cESuAMWaBMeZcY8xIQtfqWmPMLbg0XhEpDd/h\nIyJlwCxgOy68FgDCRdWDIjI2vOoK4K+kM16HH0peA+wCdgPznX5IGie+XxP6S90CHADmAn2BNeG4\nVwN9nI4zKt6LgTZgC7AZeC/8GVe6LWbgwnB8W4BtwP3h9ecBG4APgJeBHk7HGif2y/ikgsKV8Ybj\nilwH2yO/X268FqJinkToJmgL8P+AinTGq93FlFKeoD0olFKeoMlOKeUJmuyUUp6gyU4p5Qma7JRS\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd7e2940>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(w_trimmed))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 80,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+P07WWIriKKEW4snJycEYw7Zt2xKlVrvotBElKTh69ChdunQJec1aLtzj8dCr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\ngjJMbcJZvAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fcf89198>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(reverse_tour(w_trimmed)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 81,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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QN910kywvL5enPvlEyaioUH+1liJUrAb7c+aEJysWCdV4YvpqN1ecefPmyRQv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\nH6uGZnvGhXMvAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fdaa1ef0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "w1 = random_walk()\n",
+    "w2 = random_walk()\n",
+    "plot_trace(trace_tour(w1))\n",
+    "w1bounds = bounds(trace_tour(w1))\n",
+    "plot_trace(trace_tour(w2), colour='r', xybounds=w1bounds)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 82,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "w1 = 'RLFFFLFFLRFLFLRFFFFFFLLFFFLFLFLFFLLLFFFFFRFFLRFLFFLFFFFLLFLLRFFFFLRLFRRLLFLRFLFLLFFLFFRFFFFLRFLLRFFLRFFRFRLFRFRFFLFLRFRLLFRLFFLLLFFFRFLFFLFLLRFRFLFRRFRFLLFRFFFFLFFFRLFFFFRFRFRFLFFRFFFLFRFFRRLRFRFFLFFFRRFLFFRRRFLFFLRFFLLFFLFRFFRFRRFFRRLLLFFFFFFFRFLFLFLLFRFFFLFFFRRFFLFFRRFFLRFRLRFFFRFRLFRLFRRFLLLFLRFLFRFFRLFLFRFFFFLFRLFFRRFFRFRFFFFFFLFLRLFFFFRLRFFRLFFLFFFLRFFFFLRFFRFFRFRFFRFFRRRFFRFLRLLLFLFFFLFRFFRLFRLLFLFLFLLRFLFLFLFLFFRFFRRLLFRRLRLFFFFLRLRRRFFRFFRRFFRLLFFLLLLFLLLLFFRLFFRRRRFFRRRRLFFLFFFRLLRLFRLRFLFRFRRFLLLFFFFFLFFRRRFRLRLFRLLLRFLFFFFFFFFRRFFFFRLRRFFRLFFRLFFLLLFFLFFFFFLFFLFRRRFLFLFFFFLFLFLLLRFRFLFRLFLFFLRFLLFLRLLLFLFRRLFFRLFLRLFFRFLFLFFFRFRFRFFRFFRRFFRFRFFFFFRRFFLFFRFLRFFFLFFFFRFRLFRFFRRFFFFLFFFFLRFRFFLLLRLRRLLFFLRLLFFFRFFFFFFLFRFFFLRFRLRFFLLFFRLRFFFFRRFRFFLRFRFRFLFFFRFFFFRLFLRLFFLRLFFFFFRLFLRFFRLLFFRLFRFFFLRLRFLFLFFFLFFFFLFLRRFFRLLFFLFFLFRLFFFRLFRFRFFLFFLFLLFRLLFFRFLFLFFFFLFLRFRFRLFRRFLLRRRRFFRFLFRFFLLFRRRFRLRRLRFFLRLFLLFLLFFFRLLFLRFRLFLRFLRFFRLLRLRRFFFLLFFLLFLFRFLLLRFRRLFLLLRRFFFRFFFF\n",
+      "w2 = 'LFLFFFFFFRFFFRRLLFFFFLFFFLFFLFFLLFFFLFLLFFRFRRLFFRLLLRFRLRLRRFFFFLRFLFLLLLRRFFRFLFFFFRFFFLLLRFRFFFLFRRFRLFFLLFLRFFFRFRLFFLFFFRLFFFRFFFRFRFRFFRFRRRLFRFRRFFRFRLRLFLFFFRLFRLRFLRFFFLFFRRFFRLLLLFRFFRFLRFFRFLLLRRFLFFFLLRLLFFFFLRFLLLLFRRFLRFFFLFFFLFRLLFRRLLLLFRLRRLRLFFFRFFFFFLRRFFLFFRFLRFLLFFFLFRLLLFRRRFFLLLLRFFLFFFRLRRFFFFLLRFFLFRFLRFRFLLFFRRLLFFRLRFFFRLFLRFLLFRLLLRRRFRFRRFFFRFFFFFLRFFRLFFLFFRRRRLFFRFRLFFRLRLFFLRFFRLLFFRFFLLRRLRRLRLLFLLFRRFLFFLLFFFLFFRFRFLFRFLFFFFLFLRRFLRLRLFLFRFFLFLFFFFLRLLFRFLLRFLRRFFFLRFFLLRFFRRFLFFRFRFFFFFFFFLFLRLFLFFFFLLRFRFLFFLRFFRFFFLLFRLFLRLFFLRFFLLLFFRFLFFRFFFFLRRFRLFFFLFLLLLFFFFLRFFRFFFRFRLRRLRFFRFFLLFLFRFFFRRFFFFFFFRFRLFFFLFRFFFFFFRFRLRFFLLLFFLRFRLLLLLLRFFFFLFFLFFLFRLFRLFFFLLFFFFRRRFRFRFLFLFFRLFFFLLRRFFFFLLFFFFFRRFFLRFLFFFFFLLFFFRFFLFLRFRFFFLFFFFRLRRFFRRFLRFLLLRRLRFLLFFRRLFFFFLFFRFFLRLLRRRLLLFFFLLFFLFFFFFFFRFFLLFFLRLFFFRFLFFFLLFRRFLRRFLLRFFLRFFFLFFFFLRFRRFRLLFFFFFFFFFLFFFFFRFRFLLLFFLRLFLFRLLFLFFRFFRRFLFFRRRFLFLLLFRFLFLFFFFLLLLLFFFRFFFLRFRLRFFLFFLFFFRFFRLFLFRFRFLFF\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"w1 = '{}\".format(w1))\n",
+    "print(\"w2 = '{}\".format(w2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 83,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def wander_near(locus, current, limit=10):\n",
+    "    valid_proposal = False\n",
+    "    while not valid_proposal:\n",
+    "        s = random.choice('FFFRL')\n",
+    "        if s == 'F':\n",
+    "            proposed = advance(current, current.dir)\n",
+    "        elif s == 'L':\n",
+    "            proposed = advance(current, turn_left(current.dir))\n",
+    "        elif s == 'R':\n",
+    "            proposed = advance(current, turn_right(current.dir))\n",
+    "        if abs(proposed.x - locus.x) < limit and abs(proposed.y - locus.y) < limit:\n",
+    "            valid_proposal = True\n",
+    "#     print('At {} going to {} by step {} to {}'.format(current, locus, s, proposed))\n",
+    "    return s, proposed"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 84,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def seek(goal, current):\n",
+    "    dx = current.x - goal.x\n",
+    "    dy = current.y - goal.y\n",
+    "\n",
+    "    if dx < 0 and abs(dx) > abs(dy): # to the left\n",
+    "        side = 'left'\n",
+    "        if current.dir == Direction.RIGHT:\n",
+    "            s = 'F'\n",
+    "        elif current.dir == Direction.UP:\n",
+    "            s = 'R'\n",
+    "        else:\n",
+    "            s = 'L'\n",
+    "    elif dx > 0 and abs(dx) > abs(dy): # to the right\n",
+    "        side = 'right'\n",
+    "        if current.dir == Direction.LEFT:\n",
+    "            s = 'F'\n",
+    "        elif current.dir == Direction.UP:\n",
+    "            s = 'L'\n",
+    "        else:\n",
+    "            s = 'R'\n",
+    "    elif dy > 0 and abs(dx) <= abs(dy): # above\n",
+    "        side = 'above'\n",
+    "        if current.dir == Direction.DOWN:\n",
+    "            s = 'F'\n",
+    "        elif current.dir == Direction.RIGHT:\n",
+    "            s = 'R'\n",
+    "        else:\n",
+    "            s = 'L'\n",
+    "    else: # below\n",
+    "        side = 'below'\n",
+    "        if current.dir == Direction.UP:\n",
+    "            s = 'F'\n",
+    "        elif current.dir == Direction.LEFT:\n",
+    "            s = 'R'\n",
+    "        else:\n",
+    "            s = 'L'\n",
+    "    if s == 'F':\n",
+    "        proposed = advance(current, current.dir)\n",
+    "    elif s == 'L':\n",
+    "        proposed = advance(current, turn_left(current.dir))\n",
+    "    elif s == 'R':\n",
+    "        proposed = advance(current, turn_right(current.dir))\n",
+    "        \n",
+    "#     print('At {} going to {}, currently {},  by step {} to {}'.format(current, goal, side, s, proposed))\n",
+    "\n",
+    "    return s, proposed"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 85,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def guided_walk(loci, locus_limit=5, wander_limit=10, seek_step_limit=20, return_anyway=False):\n",
+    "    trail = ''\n",
+    "    current = Step(0, 0, Direction.RIGHT)    \n",
+    "    l = 0\n",
+    "    finished = False\n",
+    "    while not finished:\n",
+    "        if abs(current.x - loci[l].x) < locus_limit and abs(current.y - loci[l].y) < locus_limit:\n",
+    "            l += 1\n",
+    "            if l == len(loci) - 1:\n",
+    "                finished = True\n",
+    "        s, proposed = wander_near(loci[l], current, limit=wander_limit)\n",
+    "        trail += s\n",
+    "        current = proposed\n",
+    "#     print('!! Finished loci')\n",
+    "    seek_steps = 0\n",
+    "    while not (current.x == loci[l].x and current.y == loci[l].y) and seek_steps < seek_step_limit:\n",
+    "#         error = max(abs(current.x - loci[l].x), abs(current.y - loci[l].y))\n",
+    "#         s, proposed = wander_near(loci[l], current, limit=error+1)\n",
+    "        s, proposed = seek(loci[l], current)\n",
+    "        trail += s\n",
+    "        current = proposed\n",
+    "        seek_steps += 1\n",
+    "    if seek_steps >= seek_step_limit and not return_anyway:\n",
+    "        return ''\n",
+    "    else:\n",
+    "        return trail"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 86,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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FIBNJl6SFQEV+muMwZFu3buWGG25QGDKRAEKHIVsFPOHufxk9LykEWfRehSETqYDQYcgs\n+ouVHIIMNIFIpBKC3V7MzB4E/g+4xMyOmdmtwF3A9WZ2mFwUorvOt424Y1ARiETCSdrxXkoYsn8o\n8lJJIcjyJb2EISLh6H4CItNEqucO6H4CIuGleiqxiISX6pqAhg2LpJdmEYpUuYreWUgdgyLhDAwM\nJFqvIoVA3FbROAGRcLLZbKL1KloIaJyASPqoY1Bkmkj11QF1DIqEp3ECIlUu1TUBDRsWCS/VhYCG\nDYuEl+pbjseZUzgykXBSPU4gPvmTdlyIyPhSPU4gHiSk5oBI+qhjUKTKqWNQZJq4IOMEzOxGM3vV\nzI6Y2e2T2ZaITE7SuTmJCwEzywD/Si5E2Z8DnzSzSwu9V8OGRdJrMjWBK4Hfufsf3H0A+Am58GRj\naNiwSHpN5qxcDryZ9/w4uYJhjPgS4bXXXktHRwdz584FoL+/n9mzZ9Pd3c1FF13E6dOn6ezsZO3a\ntbS2ttLT08PChQvp7Oxk3rx5dHR00NPTw6pVq2htbaWzs5MlS5bQ0dHBzJkz6e/vp6+vj4svvpiW\nlhY6OjpoaGg4p0+it7eX5cuX09raSnt7O2vWrOHtt99mcHCQ+vp6enp6aGpq4u2336a9vZ1169Zx\n8uRJ+vr6mDt3Lt3d3SxcuJCzZ8/S1dXFmjVraG1tpauri2w2S21tLXPmzKGrq4ve3l5Wrlw5ktdl\ny5bR1tZGNptleHiY3t5eVqxYQWtrKx0dHaxcuZIzZ84wPDxMNpult7eXZcuWcfLkSdra2li3bh2n\nTp1iYGCAgYEB6urqRvLa0dHBunXrRvbbggUL6OzspLGxkfb2drq7u1m9evVIXpuamujo6KC+vp6+\nvr4x+23FihW0tbVhZnR0dDBjxoyRvLS3t7N69WpOnz7N0NAQM2fOpKenh6VLl468Hu+3/v5+5syZ\nQ3d3N4sWLeLMmTPnHON4eXyMjx8/Tl1dHatXr6alpYXOzk6WLl1Ke3s7dXV1DA4OjslrvN/cnWw2\nS09PT9Fj3NDQQHd3N01NTRw9epRMJsPatWs5efIkvb29zJ8/n66uLhYsWEBbW9s5+y3+nra3tzNr\n1ix6enrGHOPly5dz9uzZke9cX18fM2fOZGhoiI6ODlatWsXp06cZHh6mrq6Onp6ec/br2rVrOXXq\nVNFzY926dbS0tBQ8N06cOJHsTHb3RH/Ax4H78p5/CrinwPt8y5YtvmzZMgcc8Lq6upHH8V9DQ8PI\n4wULFox5Pf9v8eLFk3p94cKFI4/r6+vHvD5v3ryRx/Pnzx/z+owZMwpua7J5zWazY17P3xezZ88e\n83r+ssbGxjGv19TUjDxetGjRpPKav/7MmTPHvJ6/r+bOnTvm9fx9Xc5jnP8ZCx2X/O9WofwVOsb5\nx2Kyxzj/cxf67ucftzlz5ox5fSLnxvz58725udmbm5sd8JLO5UkUAlcDT+U9vwO4vVAhMFpzc/OY\nZaEoLaV1odO6UJ+p1EJgMn0CvwH+xMxWmVkd8PfkwpOJyBRSUkDSoiub3QjcQ66D8X53HxOOzMyS\nJyAik+IlBCSdVCEgIlOfbioiUuVUCIhUuYoXAiGHGpvZ/WbWYmb78pY1mtkzZnbYzJ42s3llSGeF\nmT1rZgfNbL+Z3RYwrRlm9isz2xOl1RwtX21mL0RpPWRmZRuJZWYZM3vJzB4PmZaZ/d7MXo4+26+j\nZWXfh9F255nZdjM7ZGYHzOyqQMfrkujzvBT9bzOz2wJ+ri+b2Stmts/MfmxmdRM+XqVcQijXH7lC\n5zVgFZAF9gKXlnH7fwtcBuzLW3Y38LXo8e3AXWVIZwlwWfR4NnAYuDREWtG2GqL/NcALwFXAw8Dm\naPm9wD+VcT9+Gfhv4PHoeZC0gKNA46hlofbhfwK3Ro9rgXmh0spLMwO8BVwc6Hu4LNqHdXnH6ZaJ\nHq+yfeASM301sDvvecGxBZNMY9WoQuBVoCl6vAR4NcDnegxYHzotoAF4kdzIzFYgk7dfnypTGiuA\nnwPX5RUCJwOl9QawcNSysu9DYA7weoHloY/XDcD/BPxcy4A/AI1RwfY4cP1EvxuVbg4UGmq8PHCa\nF7l7C4C7nwAWl3PjZraaXO3jBXIHuexpRdXzPcAJcifo68BZd4/njh4n94Uoh+8BXyU3Ag0zWwic\nCZSWA0+b2W/M7PPRshD7cC1wysweiKrp95lZQ6C08n0CeDB6XPa03P0t4LvAMeCPQBvwEhP8blS6\nECh0zXLKXqM0s9nADuBL7t5JoM/i7sPufjm5X+krgXcVettk0zGzjUCLu+/lnWNljD1u5fqc73X3\nvwY2AF80s/eVcdv5aoErgB+6+xVAF7laaLDvnpllgZuB7dGisqdlZvPJTdpbRe5EnwXcVOCt5027\n0oXAcWBl3vMV5NpMIbWYWROAmS0hV1WatKizZQfwX+6+M2RaMXdvB54nV8WbH03nhvLtx2uAm83s\nKPAQ8AHg+8C8AGnFv4i4+0lyTaorCbMPjwNvuvuL0fNHyBUKIY/XTcBv3f1U9DxEWuuBo+5+2t2H\ngEeB9zLB70alC4FKDDUe/cv1OPCZ6PEtwM7RKyT0I+Cgu98TMi0zWxT3JJtZPbkDfxB4DthczrTc\n/RvuvtLd15I7Ns+6+6dCpGVmDVFNCjObRa79vJ8A+zCqhr9pZpdEiz4IHAiRVp5PkitIYyHSOgZc\nbWYzzcx453NN7HiVsyOkxM6MG8n1pv8OuKPM236QXKnXF+2gW8l1mvwiSvPnwPwypHMNMETu6sYe\ncu2wG4EFAdL6i2j7e4F9wL9Ey9cAvwKOkOsNzpZ5X17LOx2DZU8r2ma8//bH34UQ+zDa7rvJ/Qjt\nBX5G7upAqLTqyXWmzslbFiqtZuBQ9N3YRu6q24SOl4YNi1Q5jRgUqXIqBESqnAoBkSqnQkCkyqkQ\nEKlyKgREqpwKAZEqp0JApMr9P8nYgJi0MFyGAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fdaa1f98>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def square_tour(a=80):\n",
+    "    \"a is width of square\"\n",
+    "    return ('F' * a + 'L') * 4\n",
+    "\n",
+    "plot_trace(trace_tour(square_tour()))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 87,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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k6yMEKDzGmzHGPSUtKopIo4g8KSJxEXlbRG4WkWYReU5E+kXkuIg0rvT+6urqghdbGGPc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\nybOEYIzJ+/+3mLJIMXCXRQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fcf938d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def cross_tour(a=50, b=40):\n",
+    "    \"a is width of cross arm, b is length of cross arm\"\n",
+    "    return ('F' *  a + 'L' + 'F' * b + 'R' + 'F' * b + 'L') * 4\n",
+    "\n",
+    "plot_trace(trace_tour(cross_tour()))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 88,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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Ukpa9WWhgqFF+bEHHGFQ509PTzM7Out0MR2hgqJGOMahqqqVkbyYaGJRySDgcrno7c7PQ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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fda6aeb8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def quincunx_tour(a=60, b=30, c=50):\n",
+    "    \"a is length of indent, b is indent/outdent distance, c is outdent outer length\"\n",
+    "    return ('F' * a + 'R' + 'F' * b + 'L' + 'F' * c + 'L' + 'F' * c + 'L' + 'F' * b + 'R') * 4\n",
+    "plot_trace(trace_tour(quincunx_tour()))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 89,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fc91f7f0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(('F' * 10 + 'R' + 'F' * 5 + 'L' + 'F' * 10 + 'L' + 'F' * 10 + 'L' + 'F' * 5 + 'R') * 4))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 90,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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ZZ57hwIED7Nu3r84N3FRGpzCGuczMTFJSUjx/7Pv27aN79+6WU6lgVv6cyBEj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\nVBW0UCqlVBW0UCqlVBX+P0VFnoIKajtRAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd7f34e0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "heart_points = [Step(60, 50, Direction.UP), Step(50, 90, Direction.UP),\n",
+    "                Step(20, 70, Direction.UP), \n",
+    "                Step(-40, 90, Direction.UP), Step(-60, 80, Direction.UP), \n",
+    "                Step(0, 0, Direction.RIGHT)]\n",
+    "\n",
+    "heart_tour = ''\n",
+    "current = Step(0, 0, Direction.RIGHT)\n",
+    "\n",
+    "for hp in heart_points:\n",
+    "    while not (current.x == hp.x and current.y == hp.y):\n",
+    "        s, proposed = seek(hp, current)\n",
+    "        heart_tour += s\n",
+    "        current = proposed\n",
+    "\n",
+    "plot_trace(trace_tour(heart_tour))\n",
+    "\n",
+    "def heart_tour_func(): return heart_tour"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'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'"
+      ]
+     },
+     "execution_count": 91,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# lc = trace_tour(('F' * 50 + 'L') * 4)\n",
+    "# lc = trace_tour(('F' * 50 + 'L' + 'F' * 20 + 'R' + 'F' * 20 + 'L') * 4)\n",
+    "# lc = trace_tour(('F' * 60 + 'R' + 'F' * 30 + 'L' + 'F' * 60 + 'L' + 'F' * 60 + 'L' + 'F' * 30 + 'R') * 4)\n",
+    "lc = trace_tour(heart_tour)\n",
+    "rw = guided_walk(lc, wander_limit=8)\n",
+    "rw"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 92,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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Nm9mxYwdnzpypvTPuJKevNrx8gk6YMEGT7qGhoV4dK/GclJSUGp+sc+fOdblI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\nZiANwzAiYAbSMAwjAmYgDcMwIvB/2ZiakzGZzHoAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd0eab00>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(rw))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 93,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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LWi2pR9JvJJ3ejj5G2dOlkl6tH5v1kr7R5n7ultQraeMQNSvrx2iDpHnt7GekfUlaIGlX\nw3G6oc39zJK0TtILkp6TdE2LutEdq4go7Qv4EDAHWAd8pEXNBOAPwGxgErABOKvNfd0KXFdfXgIs\nb1H35zb3MexzB64Cvl9f/iq108Wye7oUWDmGv0d/A8wDNrbYvhD4WX35E8BvO6SvBcCaMTxOpwDz\n6svvAbY0+dmN+liVOhOJzr1ZbTFwT335HuCLLerafSF4JM+9sdcHgM92QE/Q/mMzICJ+CbwxRMli\n4N567ZPAVEkzhqgfq75gbI/TzojYUF/uA17k8Hu2Rn2sjob/gFfGzWonR0Qv1A488P4Wde+W9DtJ\nv5bUjmAbyXMfqInaRexdkk5sQy+j6QngS/Xp8P2SZrWxn5EY3PMf6ZwbHufXT4d/JumcsRpU0hnU\nZklPDto06mNV5Fu8TXXqzWpD9DWa89LTI2KnpA8A6yRtjIit2d4G9TTY4Oc+uEZNaoo0kp7WAPdF\nRL+kK6nNlNo9QxpKp97w+AwwOyL+Imkh8CAwt92DSnoPtVnrt+ozkndsbvItQx6rtodIRHwuuYvt\nQOPFwlnAjuQ+h+yrfjFsRkT0SjoFeLXFPnbW/90qqQp8GCgyREby3LcBpwE7JL0LeG9EDDeFbmtP\ng8b/AbVrTGXaTu0YHVLI71BW4x9wRDws6fuSToyI19s1pqSJ1ALkxxHx0yYloz5WnXQ6M+zNapIm\nU7tZbU2be1kDXFZfvhQ47GBLmlbvB0knAX8NvFBwHyN57mvrPQJ8hdpF6nYatqd68B6ymOKPSzOi\n9e/QGuDrMHAH9a5Dp6tl9tV4rUHS+dRuuWhbgNT9EHghIr7XYvvoj9VYXRlucbX4i9ReSfdSu5v1\n4frjM4GHGuouonYluQdYOgZ9nQj8d33MXwDT6o9/FLirvvxJYCPwLPB74LI29XLYcweWAYvqy+8G\n7q9v/y1wxhgcn+F6+ldgU/3YPA7MbXM/91F7tdwHvAJcDlwJfLOh5g5q7yr9nhbvBI51X8A/NByn\nXwOfaHM/nwIOUHtH7Vlgff1nmTpWvtnMzFI66XTGzI5CDhEzS3GImFmKQ8TMUhwiZpbiEDGzFIeI\nmaU4RMws5f8Az4SYkuCKQGwAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fc90abe0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "rw_trimmed = trim_all_loops(rw)\n",
+    "plot_trace(trace_tour(rw_trimmed))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 94,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "4"
+      ]
+     },
+     "execution_count": 94,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "len(rw_trimmed)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 95,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(250,\n",
+       " 92,\n",
+       " 'LFLRRFFFFRFRFRLLFFFFLFFFFLFLRFFRFRLLFRFLRFFLFFFLFRLRFFLFLFRLFRFFFFRFLFFFFFLFFFLRRLFFFFLLRFRL')"
+      ]
+     },
+     "execution_count": 95,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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hk4tOP/10AL75zW9muJLco6ARkeAUNCISnIJGRIJT0IhIcAoaEQlOQSMiwaUcNGZ2vJk9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\nBPf/AaHHidH8UAAMAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fcf7c438>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "lc = trace_tour(square_tour(a=10))\n",
+    "rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
+    "rw_trimmed = trim_all_loops(rw)\n",
+    "plot_trace(trace_tour(rw_trimmed))\n",
+    "len(rw), len(rw_trimmed), rw_trimmed"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 96,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# success_count = 0\n",
+    "# while success_count <= 20:\n",
+    "#     lc = trace_tour(square_tour(a=10))\n",
+    "#     rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
+    "#     if rw:\n",
+    "#         rw_trimmed = trim_all_loops(rw)\n",
+    "#         if len(rw_trimmed) > 10:\n",
+    "#             with open('small-squares.txt', 'a') as f:\n",
+    "#                 f.write(rw_trimmed + '\\n')\n",
+    "#                 success_count += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 97,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# success_count = 0\n",
+    "# while success_count <= 20:\n",
+    "#     lc = trace_tour(square_tour())\n",
+    "#     rw = guided_walk(lc)\n",
+    "#     if rw:\n",
+    "#         rw_trimmed = trim_all_loops(rw)\n",
+    "#         if len(rw_trimmed) > 10:\n",
+    "#             with open('large-squares.txt', 'a') as f:\n",
+    "#                 f.write(rw_trimmed + '\\n')\n",
+    "#                 success_count += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 98,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# success_count = 0\n",
+    "# while success_count <= 20:\n",
+    "#     lc = trace_tour(cross_tour())\n",
+    "#     rw = guided_walk(lc)\n",
+    "#     if rw:\n",
+    "#         rw_trimmed = trim_all_loops(rw)\n",
+    "#         if len(rw_trimmed) > 10:\n",
+    "#             with open('cross.txt', 'a') as f:\n",
+    "#                 f.write(rw_trimmed + '\\n')\n",
+    "#                 success_count += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 99,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# success_count = 0\n",
+    "# while success_count <= 20:\n",
+    "#     lc = trace_tour(quincunx_tour())\n",
+    "#     rw = guided_walk(lc)\n",
+    "#     if rw:\n",
+    "#         rw_trimmed = trim_all_loops(rw)\n",
+    "#         if len(rw_trimmed) > 10:\n",
+    "#             with open('quincunx.txt', 'a') as f:\n",
+    "#                 f.write(rw_trimmed + '\\n')\n",
+    "#                 success_count += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 100,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd7d8a20>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(rw_trimmed), filename='test.png')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 101,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
+    "# tours_filename = 'tours.txt'\n",
+    "\n",
+    "# try:\n",
+    "#     os.remove(tours_filename)\n",
+    "# except OSError:\n",
+    "#     pass\n",
+    "\n",
+    "# success_count = 0\n",
+    "# while success_count < 100:\n",
+    "#     lc = trace_tour(random.choice(patterns)())\n",
+    "#     rw = guided_walk(lc)\n",
+    "#     if rw:\n",
+    "#         rw_trimmed = trim_all_loops(rw)\n",
+    "#         if len(rw_trimmed) > 10:\n",
+    "#             with open(tours_filename, 'a') as f:\n",
+    "#                 f.write(rw_trimmed + '\\n')\n",
+    "#                 success_count += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 102,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Found mistakes: 1867\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(5242,\n",
+       " 1244,\n",
+       " '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')"
+      ]
+     },
+     "execution_count": 102,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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PldVqpWfPnqSnpzN27Fhuv/125yYyv0X7iuq9JMGYl1YogkWHDh28zrbWqVMn\nhgwZ4ncdImJpuDv27NlTIRFM5QPsXTOFor5hNBoDlhQpYnsYzgjMzgAhzq6XlBKdTkdcXBwpKSmh\nVFGhCChLly7l/vvv57LLLuPMmTNs376d9PR0ysvLeeSRRzCZTNx7771+lRmxPQxnxqdmzZrRrFkz\nmjZtSrNmzcjKyqJp06bKWCiintGjR3PhwgXMZjMnTpzg0Ucf5eLFi0yZMgWz2cx9993nd5kR28OI\niYlRO1gV9ZrMzEz69u3LihUraNGiBQsXLmThwoXa9Xbt2vldZkQajGeffZapU6eGWg2FIqScPn2a\nixcvAnD8+PGgyIwYg1FcXMzu3buRUjJ16lQSEhICEoJMoYgkcnNz2bJlC1JKbDabtoXCarVy+eWX\n+33Le9gHAXbq17t37woRhWbNmsWDDz4YKtUUipBzww03sHbtWo/X9Xo9FoulVm17CgIcMQYjJiYG\ns9nMlVdeGZRQZApFJHPvvffy2muv+T1qeMTMkuzevZshQ4awbdu2UKuiUIQ9gdoWETEGo23btsya\nNSvUaigUEUGgwvVFjMFQKBTe47ri2Z9ElMFQe0MUCu8oKCgIyObLiDIYer0+1CooFBFBTExMQNqN\nKIMRzjM6CkU4ERMTQ4MGDfzerjIYCkUUUlhYGJAo4hFlMBQKhXcEavgeUQZDZW9XKLwjISGBpKQk\nv7cbkb/ALl260K5dOxUVXKHwwKVLl7R4nv4kogxGdnY2vXv35qeffuLAgQP87W9/0/wayr+hUNiR\nUgYs9EPADIYQ4nIhxGYhxA4hxPdCiF4u1+Y4kjHvFEJ097bN2NhYbWfepk2bgF8THAUjiYtCEc58\n8sknCCHQ6XQsXLiQli1b+l1GIHsYzwHTpZQ9gOmO1wghbgTaSCnbAvcAtcpR37dvX0pLSykuLmba\ntGkqWbOi3uMMW1lcXExxcTGHDh3yu4xAxsOwAcmO84bYc6gC3AK8DSCl3CKESBZCZEgpfc647Fyc\n4nSGHj16VBuaxMfH07hx47ror1BEFM7fQSBzrAbSYEwBPhVCvIA9n2o/R7mnZMy1TtHuzLnQunXr\nCuUHDhzwWwIXhSLcMZlMAZdRJ4MhhPgMcM2OLLCnZXscGAJMllKuFEKMAhYCQ6llMubqGDFiRBWn\npxCCnJwcZTAU9Qaz2RxwGYFMxvyOlHKyo95yIcTrjku/AM1dqlabjPmpp57SzgcOHMjAgQO91i8Y\nb6BCES4a2AvPAAAciklEQVTUZabQ22TMgRySnBRCXCul/EoIMRg44Cj/CLgfWCqE6APkV+e/cDUY\nvmIwREzIUoWiztRlSFL5n/GMGTPc1gvkL2o8MEcIoQdKsWdzR0q5WghxoxDiIFAE/ClQCqg0BIr6\nRDDCPwQyGfMmwG0GWCnlxEDI/P777/niiy+0NHG1DYCqqH/s3r2bTz75BJ1Oh8lkwmw2Y7PZiI2N\npby8nLvvvpuGDRuGWs1qcSb3CiRR1We/6qqrtHOj0Ujnzp1DqI0ikujatavbcoPBgMViYc2aNaxf\nvz7IWvlGMGZJImppuDc4IyWbzWYaNWoUanUUEcTy5cu1/LzOo7y8nEaNGnH27NlQq1cjwRiCR1UP\nA2DhwoXs2LGDzMxM/va3v4VaHUUEUVZW5rY8Nzc3IvxhrvqXl5czefJksrOzmTJlit/0jyqDMWzY\nMNauXcuWLVsAGD58OD179gyxVopIwen7qkzLli0jorfqqv+TTz7JK6+8AkD37t0ZNGiQX2RE1ZBk\nzZo1rFy5UnsdjDGdIvLYunWrFlXbNbp2VlaW2/qB3P3pT/R6PUIIOnTowLPPPquV+9MZGlU9DIB3\n330XgJtuuokuXbqEWBtFOPLdd98B9t2dVqsVg8FAw4YN6du3r9v6x48fJycnh5EjR3Lu3DmWLl1K\nRkaG27qhxGKxIKVk3759/OlPf2LWrFk0bNjQvwsYKzt5wumwq+cbmzZtkgkJCRKQmzdv9vl+RfTz\nyiuvSF++W876zZs3l4C89dZbA6hd7cnLy5NCCJmZmSkPHz4spZQSkGvXrvW5Lcf7U+U3GVVDErBv\ney8oKACiZx1GQkJClS6084iWZwwmHTp0AOyzCh9//HGN9e+9916klBw/fpz09PSwHeqmpaVhs9k4\ndeoU69ev14ZRzZs3r+FO74kqgzF9+nQaNWpEq1atgOhZ6VlUVMS//vUvDh8+zJEjRzhy5AgHDthX\n2iuD4Tvdu3fXhh8//PCDT/fm5eWxcuVK+vbtS+vWrUlNTaV379506tSJlJQUXnvttTrrN2PGDFJT\nU+nWrRu9e/emUaNGtGvXjpEjR3rdhjNhec+ePRk8eDDNmzfn6quvpkWLFmRmZjJ27NjaKeeu2xEu\nBz4OSQAphJDJycmyf//+sqioyKf7wxVA/t///V+FMpvNJgFZXFwcIq0iF+cQIyMjQ168eNGne+fP\nny+NRqPs0qWLTElJkYDs0KGDbNq0qcS+67rO+jnbadGihWzfvr0UQsjGjRtLQJaUlHjVxsmTJ2VK\nSors2rWrNJlMMj4+Xnbr1k0mJiZKo9FY43cHD0OSkBuF6g5f33y9Xi9ff/11n+6JBAC5ePHiCmXK\nYNSe+fPnSyGE39udMGGCbNiwYZ3bCfTnbTabNaN05513etRBRrsPw2q1Rm0XvbKn2zncipZhVzAp\nKytz/kPyK5cuXSI/P9+ne3JycujUqRPx8fEIIbQ4nJU/V39+3kajEZvNRoMGDfjxxx99ujfqplWj\nIQbGwYMHuXjxIlJK2rVrB1RNTOP8wgfiix/pnDlzhjNnzlBWVobJZEKv19OpUyct3EE45bdZtWoV\ne/fupXv37ly4cIEWLVrQpk0bRo0aVaGe83N2+lxMJhNCCMxms/ZcVqtV+57YbDZ0Oh1JSUlug0gJ\nISguLiY3N5cdO3Zgs9kAuOyyy0hJSfGob1QZDJ1OF9B4hsFgzZo13Hjjjdrr5GR7WFRPmaxUD6Mq\nmZmZVcrGjx/PvHnzgMDFSUlKSvJ5R6tTlx07dnhVv0+fPj7rtWvXLreb60aOHMmKFSu44oorKpRX\n908ofEytH7DZbBViAnzwwQcIIWjRokVQYgV4Q69evbQpUedu2oKCAlq0aIEQQjMWUkoeeeQRLl68\nCHjOxh0XF8eiRYuCo3wEkZub6+oLY+fOndq12NhYwG6M9+zZ43PbBQUFGI1G4uLitM8yLS2NU6dO\nuR2SLFiwoMLn7Yq3qzCFELX1A/LLL7+4bbPyZru33nqrRj2iqocBv34A+/fv54EHHgDgxIkTXLhw\ngfT09FCqBsC2bdsYMmQIRqORNWvWAPDjjz9y4sQJbr75ZiwWC7///e8Be7SxCxcuYLPZuPXWWyu0\nI4Rg1qxZTJkyhQkTJqDT6ZBSMmrUqLBdJxBI9u/fz5YtW7SudWXOnj3L4sWLsdlsWCwW+vfvz8aN\nG1m6dKnH6FKeWLduHRaLhVGjRnHhwgUSExNZvnw527dvd1v/wQcfBHBrnIIxpFy3bh25ubma7+KG\nG24gNTW1drrUxmoF66AW06rz58/XznF4gQGZm5vrU1uBApAnT56U+fn52hTcpk2baj0dN2HCBAlI\nnU4nATlu3Dh/qhsxOD9v51FaWqpdu/3226tcdx47d+70WdYHH3xQ5fPq3LmzBOSgQYOq1O/YsaNs\n2bKl28/4jTfe8MtUrCeaNWtW5Zl79erltu6iRYs0XagP06qV35jt27dXKH/++ed9ai8QOA3GpUuX\nqujrK+np6dq9BoNBAvL6668PgNbhDyA3btwYFFkrVqzQPq8dO3Zon8Hx48fd1r/88stl+/btK3zW\ncXFxdfrsa0vr1q1lWlqa22vvvvtujQYjqoYk27dv55133sFoNNK0aVN69OgB/OpInDZtGn/5y18C\nJv/QoUPMmzePuLg4bDYbZrOZ3/3ud1WcSv/617+YMWMG77//Pps2bcJqtTJgwACf5eXl5fHAAw9o\n42m9Xs/jjz/ur8eJOILlp3IOex5//HG++uorrfyuu+6iX79+6PV6ysrKEELQtm1b9u/fT0lJSYXP\nOz4+ntLSUqxWK8OGDQuK3gDnz5/n4sWLPP3005r8+Ph4ysrKvHO8urMi4XLgR8vbtWtX2a1bN7+1\n5w7cdHkNBkOFOpmZmRKQzZo1q5MstXCrIoD8+uuvgyLrxIkT2mpJQA4dOlQOHDjQ47CnefPmskmT\nJkHRrSaef/75Kj2c2NhY7bx3795SynoyJKmO7Oxs2bZtW7+15w6TySSnTJmivR4/fnyFXY6ux1VX\nXVUnWU6D4e1S4WjH+b6OGTMm1KpUAJDdunWTXbt2DbUqPuHJYNQ189ko4CmgI9BLSrnd5dpjwFjA\ngj0D2jpH+TBgNvYp3QVSymcrtxsIjh8/jhCCF154gU2bNiGl5Prrr+fee++lvLycadOmcfbsWd54\n441aL+wxm80UFxdrr4uKigD7LM2UKVPo2LEjJpMJq9VaZdbDV5zrL0aPHo1er6d///6aN74+snXr\nVm677Tbefvttr6YHg8mePXs8rqOJONxZEW8PoD3QFvgCuMKlvCOwA/u0bSvgIPYUiTrHeUvACOwE\nOlTTvt8sZtu2bWWbNm3cOhrnz5+vvX7xxRdrLQOQEyZM0F5/9dVXUgghTSaTLCwsrPMzuGKz2TTP\nvOuz1Gd69eoVdu/DFVdcIQE5d+7cUKviEwRiL4mUcp+U8gBV86WOAJZIKS1SyqPYs571dhwHpJTH\npJTlwBJH3YBjMpm0mIdSSnbt2gXY/1OPHz9e61WUlpa6vf8vf/lLhTgU06ZNq1InPj6+wkrTAQMG\nYLPZKCsrIz4+3q/PI4Rg9+7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xRqgO7LMnbYEvqLgQrCOwA/usTivgIPZ1HzrHeUvACOwE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\nvEYZDIVC4TXKYCgUCq9RBkOhUHjN/wcaO9HUZ2T8GQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fdb72e48>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "lc = trace_tour(cross_tour())\n",
+    "rw = guided_walk(lc)\n",
+    "print('Found mistakes:', len(mistake_positions(trace_tour(rw))))\n",
+    "rw_trimmed = trim_all_loops(rw)\n",
+    "plot_trace(trace_tour(rw_trimmed))\n",
+    "len(rw), len(rw_trimmed), rw_trimmed"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 103,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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ElJycTERk8RxNEXoBlaXc3NxqvbasrCxed/PmzYnIqKZ36NCB76/KoroGLTCU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\nG1NhmJiY+I2pMExMTPzm/wGejUjhDTUtvQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fdba0cf8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(rw))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 104,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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PldVqpWfPnqSnpzN27Fhuv/125yYyv0X7iuq9JMGYl1YogkWHDh28zrbWqVMn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\nvEYZDIVC4TXKYCgUCq9RBkOhUHjN/wcaO9HUZ2T8GQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd5f98d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_trace(trace_tour(trim_all_loops(rw)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 105,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[Mistake(i=8, step=Step(x=0, y=0, dir=<Direction.RIGHT: 2>)), Mistake(i=30, step=Step(x=0, y=-8, dir=<Direction.LEFT: 4>)), Mistake(i=31, step=Step(x=-1, y=-8, dir=<Direction.LEFT: 4>))]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "'RFFRLFFLRFRFLLFFFFLLFFFFFLRRFRFFFFFFLFFFFFLFFRLLFFFLRRRFFFFRRLFFFFFLFFRFRFFRFRLRLRFFFFFFFRFFRFRRFRFFFFRFFFFLLLFRRRFFFRFFFRFFFFRFFFLLFFFLFFFFLRFRLFFLFFLFRRLFFFFRRFFRFLLLFFFRFLFFFRLFLFRFFFLLRLRLFRFFFRRFFLFFLLRLLFFFFFFRLFFFRLLLFFFRLLFRFFFFRFRFFRFLFFFLFFLFFFFRLFLLRRFFFFFFRLLFFLFFFLFFFRFLFRFFLLRFRRFLFRLLFLFFLLFRFLFLFRFFFFLLFFFFFFFFRLLLFLFLFFRFLFFFLFFFLLRFFFFFLFFFFFFFFRFFFRLLLLLFFFLFFFFLFFLRFFRFLFFFFRRRFRLLRRFLRRLFFFFRFFFFFFFRRFFFFFLLLRFFRFFFFRFFFFLRRFFFFFFFLLFFFLFRRLLFFRFRFFFRRFFFRFFFRRFRFFFFFFFFLLFLRRLLRFFFRLFRFFLLFLLFFFLRRRFFFFFFFLFLLFLLRLLLLLFFFFFFFLFLLLRLFFLLFFFRFFLRFFRLFFFFRLLFRLFLLRLFFFFFLFFLLFFRFLRFRFLFLFRFFFFFRFRRRRFRFFFFFFRRFLFLLFLFFFFLFRFRFFFFFFFFFFFRFFLLRFLFLFLFFFFRFFLFFFRFFFRFFFRFLFFFLLLRFLRRFFLFLRRRFFFFFFFRFFFFRFFFFFFRLFFFLRLLFLRRLFFFFFLFFFRFFRFRFFLRFFRFFRFRRLRFFLFFFFFFLLFLFFRLFRLLFRRRFFRFRFFRFLFFLFFFFRRRRFFFFFFRLFLRRRFRFFFFLFFFLLRFFRFFFFLLFFFFFFFFLFFFFFFFFFFFFFFRFFRFFRFFFLLFFFFLFFRRFRFLFFFRFRLFRLFFRRFFFLLFLFLRFFFLRLLFLFFFFLRRFFRFFRFLLRRFFFFFFFFRRLFRRFRFFFFFLRFFFLLFFFFRRLFFFLLLLFFLLLLRFLRRFRLFFFFRFRRFFFFLRRFFFFLFRFLFFFRLFRLFFLRFFLFLFFFLRLFRFFFFFFFFRFRFRRLRFFRFFLFLFFLFFFFFLRFFFFLFFFRRFRRFFLFFFLLLFRFFLFFFRFRLFFFLFFFRRRFFFRFFRFLFLFLFFLRLFRFFFFFFLLLFFFRFFRLRLLRLRRLLLLFFFLFRFFLLFLFFRFFFFLFFLFFRFFRFRRRFFLFLRRRFFRFFRFFFLFRRFLLLLRFLFFFLFFFFFLFFFLLRRFFRRFFFRFFFFFFFRRFFRLFFFFFFFLFRLLRRFFFRFLFFLLFFRRFFLFLRFLFFRFLFFRRFRLLFRLRRLLFFFRLFLRRLFLRLFFFFFFFRFLFFLFFFFLRFFFFLRFFLFLFFFFFFRLLFFFLRFFRRLFFFLLFLRFLFFFFFFLFFLFRRRLRRLFLFFFLFFFRLFRFRFRRRRFRFLFFLLLFRLFFRLRFFRRLFFFFRFRFFLRRFRFFLFLRRLFFRRFFFFFFRFLRFFFFFFRFFLFFRFFFLFFFRLRFFFFFFFFRFFFFFFFLFFLFFFLFRFRLFRFRRLFLLFFLFFFFFFFFFFLRFFFLRLRFLFFFFFFFFFLFFRLRFLLRFFFFFFLFFFLRLFRRFLFFFFFFLFRRRLLLFRLLFLFFLFRFRLFLRFFFRFLFLFRFFFRFFFFFFFFFFFRFLRRRFFRRRFFFRRFFFFFRRFRLFFLFFFFRLFFFLRLRFRFLLFFFLLFRFRFFFLFLFFFRFRFFRFFFRFFFFFRFFFLFFFFFLRLRRFFRRLRFRRFFFLRRFRFRFLLFRFRRFFFFFFFFRRFFFFFFFRRLRFFRFLFRFFFFFLFRFLLLFFRFLFFFFLFFLFLFRRLLRFFFFLRFFRFLFFLFLFFFLFRFFLLFRRRFFLLFFRRFFFFLLFFFLFFFFFLFLRLRRFLRFFFFLLFRFRLFLRFLFLFLRRFFRFRFFFFFFLFFFFLFRFRLFRLFFFLFFFFFLRLRRRFFFFLFRFFRFFRFFFFRFFLFFLFFFFFRFFRFLFFFLFRFFRRRFLFLFRFFRLRFLLLFFRFRLFFFFLFLLFLFRFFLFFRFRFFFLFFFLFFFRRLRFLRRFRLFFFRRRFLLFFFLLRRFFFRFFFFFRFFFRFFFFFFFRFRFLFFFFLRRRFFFRFRFLRFRLLFFFFRFLFRFFLFRFFFFRFLRRFLRRLLFRLRFLRRRLLFFFFRFRRFRLLLFFLLLFRFFFRRFFRLRFFRFFFFRLLLRRFRLLLLFFFFRRFRFFFRFRLLFRRFFFFRFFFFFFFFRRFFLFFLFRLFFLFFRRFRRFRRFLFRFRFRLRFLLFLFFRFFLFFLFFLLFFFRFFFFLFRRFRFFFFFFRFFFFRFFLFFFLLFFFFFRLRRFFRFRFLRLLFFFLFFRLLFFFFFFFFFLLFFFFFRFRRRRRFFFFRLRFRRFRLFFFFLFRFFFFFFRFRFFRFRFFFLLFFFRFFFRFFFLFRFLFFFLFFRFFFLLRRFFFLRFFLFFFRFFFFFFFRRFFFFFLLFFLFFFFFRFLRFLFRLFFFRFFFLLFFFFFRFFFRFFFLLFFFLFFFRFFFFRFFFRFFFFFFFFLLRFFRFFFFRRFRLFRRLFFFFLFLLFLFFFFFFFFFFFRFLLFFRFLFFLLFRFFLFFFFFFFLLFRFFFFFRFLFFLLRLFFRFFLFLFLFLFFRRLRFFRFRFLFFLFFLFFLLLRFRFRFRFRFRFFRFFFFFFLFLFRRFFFFFFRFLFFFFLFFFRLLFRFFRLRLLFFFRFLFRRLFFRFRRFFRLLFFFLFLLLFLRFFFLFFFFRFFRFFFLRRFFFFRFFRRFFRFFFLFFRFFFLLFFLLRFFFFFFFLFFFFFFFLLLLFFLFFFFFFFFFRLFRLFFFLFFFRRFLLLRRRFRFRFLFFFFFLFLRLFFLFFLLFLFFFFLFLLLRFFFFFRFFRRRFFFFFFFRLFFRRFFLFFFFFFLRFRFRFRFFFFFLFFFFFLFLFRRFFRFFLRFFLFRFFFRRFFFLFLFFLLLRFLFRFRRFFFRFFRFLFFFLFFRLFFLFLLFFFRFRLRLFRRLRFFFRLLRFRFFFFFRFFFLRRFLFFFRFLLFFLLFFRFFFFFFFFFRRFRRFFFRFFFFRFFFLFRFLFFFFRFFFFRLLRRFFRFRFLLFFLFFLFLRRLFFFRLLFFLFRFFFFFRRFLRFRFRFRLFFFRFRFFRLFFLRRFLLLFLFFRFFFFRLFLLFFLFRFLFLLFFFRFRFFFFRFFRFRFFFLRRLFRFFFRLLLFFFFFFLFLRFLFFFLFLLLLFFRFFFRRFRLFLRFFFLFFFFFFFFLFRFFLFLFFFFFFFLFFLFRRFFFRRFFFFFFFFFFLLLRFLLFFFLLFFFFLRRRLRFLFFFFRRRFFFFRFFLFFFFFRFFFFRLLLFFFFFFLFFLLLRLFRFFLLFFFFFLFLFRLFFFRFFRRFFFLRFRRRRLLFFFFFRLFFFLRFLRLLFFLFLFFFFFFFLFFLLLLLFLLRLLFLLRLRFFFRRLRFFFFRRFRRFRFFFFRLFFFFFFFFFFFRFLLFFLFFFLFFRFRFRRFFRFFRFFLLFFLFFFLFFFLFFFLFRRLRLFFFLFRFFRFRRFFLLFFLFLFFFFLFFRFFFFFFLRLRFFRFFRFLLFRLLFFFFFLFFFFFFRFFFFRFRFRFFFFFFFFFFRFLFFRFLFFFFLFFFLFLFFRFRFFFFFFRFFLFLRFRFLLFLFFLFRFFFRRLFRLLLFLFFRRLRFFRFLFRRFFFFFFFLRLLFFFLFFFRLLFLFLLLRRRLFFRFFFLLLFLFFFFFFFFFFFLLFFFLLRFFLLFFFLFFLFRLRFFFFRFRFRFFFRRFFFRFFRRLFFLFFFFRFLFRFLFFLFFFFLFLRFFFFRFRFFFFRFRFFFFFFRRLRFRFLFLFLFFLFFFFFFFFFRFLFFFFFFFFRRRRLRFFFLLFFLFLFFLFLRLLFFFRLFRRFFFFFFFRFFRFRLFFFLRFRFFRRRFFFRLLLFFFFRFFRRRLFRFFFFFLLFFFLFFLRFFFLRFFRRLFFRFRFRLFFFFRFFLFFFLFLFFRRFFLFLFLRFFFRLFFFFLLFFFLRFFFFFRRFFLLFFFRRFLRRFLFFLFFFFLFFFFRRFFFFRFRRFFFFFLFFFLFRLFLFFFFFFFFFFFFLFRFFRFLLLRLFFLFRFFFRFRFLFFFLFFFRFLFFFLRLFFLFFLFLFFFFLFLFLFRFFFFRFRFFFRFLLFLFFFFFFFFLFFLFFFRFRFFRFFFLFRLLFFLRFFFFFRFRFFFFFFFFRFFFFFFFFRFFFFFFFFFRRLFLLFFFFFFFRRLRFFLFFFFFLFLFFRFFLFFRRLLLLLLFLLFFFFFFRFRFLRRFFRFLFFRRFRLRRFFRLLFFFLRFFFFFFFRFFLFLFFFLFLLFRFFRLLFFRFFFFLLFFFFFFFFFLFLFFFFFFLLRRFRFFLFFFFFFRFRLFFFFFFLRRFFRFFRLFFFFFFFRRLRFFFFRFLFRRLRFFFFFFFFRFRRFRRRFRLFLFFFRRFRFFLLLFLFLFFRRFFFRRRLFFLFFLFFRFRFRFFFFLLFLFRFRFLLFFFFFLFRFLFFLFFFFFLFLFRFFRLFFLRRFRFFFFRFFFFRLFFFRLFRFRRRFFFLRFRFFLLFFFLLRRLFLRFLRRFRFFRFLFFFLFRRFRFRRFFFFFFFLLFLFFFFLLLRFRRFFFLRFFFFFRFLFFLFLFFFFFLRRRFFFFFRFLFRLFLLRLFFLFFFFFRRFFFLFRFFRRFFFFRRFFFFRFRRFRRRFFFFFRFRRLFFFFRRFFRFRFLFFLFLFLFRLLFFLLFRLFFFRLLLFLFRLRFFLFFRLFFFLRRRRFFFFRFFRFFFLFFLFFFFFFFFLRRRFFFFFFFRLFLLLFFLLLFFFFFFFFFFFLFLLFFRFFFRFFFFFFLRFFFLFFLLFLFFRLRLFLFFFLFFFLFRRLLLFRFFRLRRFLFFLRFFFFFFLRLLFLFFRLLLFFRFRRFFFFRRRFRFFFFFRRRRFRLLLFFFFRFLLFFRRRRFLLFFLFFLFFFFLLLFFFFRFFFRFFFFFRFRRFRFFRFLLFLFFFLFFLLRLFLFFFLFLFRLRFRLFRFLLFLFFFRRFRRRRRLFFFLRFLLRRRFFFFFLFRFLFFFFLRFFRLFLFFFRFRFFFRFFFRFFFFFFFFFLRFFFLFLRFRFFLLFFRFLFFFFFFFFFFFFLFFFLFRLFLFRFRLFFRFFFFFFRLFFFFLRL'"
+      ]
+     },
+     "execution_count": 105,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "w_tour = rw\n",
+    "w_trace = trace_tour(w_tour)\n",
+    "mks = mistake_positions(w_trace)\n",
+    "print(mks[:3])\n",
+    "trim_loop(w_tour)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 106,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1867\n",
+      "1863\n",
+      "1860\n",
+      "1859\n",
+      "1850\n",
+      "1843\n",
+      "1837\n",
+      "1833\n",
+      "1831\n",
+      "1829\n",
+      "1821\n",
+      "1816\n",
+      "1814\n",
+      "1799\n",
+      "1793\n",
+      "1788\n",
+      "1784\n",
+      "1778\n",
+      "1777\n",
+      "1772\n",
+      "1764\n",
+      "1760\n",
+      "1758\n",
+      "1755\n",
+      "1752\n",
+      "1748\n",
+      "1736\n",
+      "1731\n",
+      "1726\n",
+      "1717\n",
+      "1705\n",
+      "1700\n",
+      "1695\n",
+      "1692\n",
+      "1686\n",
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+      "8\n",
+      "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF\n",
+      "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\n",
+      "Step(x=0, y=0, dir=<Direction.LEFT: 4>)\n"
+     ]
+    },
+    {
+     "data": {
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PldVqpWfPnqSnpzN27Fhuv/125yYyv0X7iuq9JMGYl1YogkWHDh28zrbWqVMn\nhgwZ4ncdImJpuDv27NlTIRFM5QPsXTOFor5hNBoDlhQpYnsYzgjMzgAhzq6XlBKdTkdcXBwpKSmh\nVFGhCChLly7l/vvv57LLLuPMmTNs376d9PR0ysvLeeSRRzCZTNx7771+lRmxPQxnxqdmzZrRrFkz\nmjZtSrNmzcjKyqJp06bKWCiintGjR3PhwgXMZjMnTpzg0Ucf5eLFi0yZMgWz2cx9993nd5kR28OI\niYlRO1gV9ZrMzEz69u3LihUraNGiBQsXLmThwoXa9Xbt2vldZkQajGeffZapU6eGWg2FIqScPn2a\nixcvAnD8+PGgyIwYg1FcXMzu3buRUjJ16lQSEhICEoJMoYgkcnNz2bJlC1JKbDabtoXCarVy+eWX\n+33Le9gHAXbq17t37woRhWbNmsWDDz4YKtUUipBzww03sHbtWo/X9Xo9FoulVm17CgIcMQYjJiYG\ns9nMlVdeGZRQZApFJHPvvffy2muv+T1qeMTMkuzevZshQ4awbdu2UKuiUIQ9gdoWETEGo23btsya\nNSvUaigUEUGgwvVFjMFQKBTe47ri2Z9ElMFQe0MUCu8oKCgIyObLiDIYer0+1CooFBFBTExMQNqN\nKIMRzjM6CkU4ERMTQ4MGDfzerjIYCkUUUlhYGJAo4hFlMBQKhXcEavgeUQZDZW9XKLwjISGBpKQk\nv7cbkb/ALl260K5dOxUVXKHwwKVLl7R4nv4kogxGdnY2vXv35qeffuLAgQP87W9/0/wayr+hUNiR\nUgYs9EPADIYQ4nIhxGYhxA4hxPdCiF4u1+Y4kjHvFEJ097bN2NhYbWfepk2bgF8THAUjiYtCEc58\n8sknCCHQ6XQsXLiQli1b+l1GIHsYzwHTpZQ9gOmO1wghbgTaSCnbAvcAtcpR37dvX0pLSykuLmba\ntGkqWbOi3uMMW1lcXExxcTGHDh3yu4xAxsOwAcmO84bYc6gC3AK8DSCl3CKESBZCZEgpfc647Fyc\n4nSGHj16VBuaxMfH07hx47ror1BEFM7fQSBzrAbSYEwBPhVCvIA9n2o/R7mnZMy1TtHuzLnQunXr\nCuUHDhzwWwIXhSLcMZlMAZdRJ4MhhPgMcM2OLLCnZXscGAJMllKuFEKMAhYCQ6llMubqGDFiRBWn\npxCCnJwcZTAU9Qaz2RxwGYFMxvyOlHKyo95yIcTrjku/AM1dqlabjPmpp57SzgcOHMjAgQO91i8Y\nb6BCES4a2AvPAAAciklEQVTUZabQ22TMgRySnBRCXCul/EoIMRg44Cj/CLgfWCqE6APkV+e/cDUY\nvmIwREzIUoWiztRlSFL5n/GMGTPc1gvkL2o8MEcIoQdKsWdzR0q5WghxoxDiIFAE/ClQCqg0BIr6\nRDDCPwQyGfMmwG0GWCnlxEDI/P777/niiy+0NHG1DYCqqH/s3r2bTz75BJ1Oh8lkwmw2Y7PZiI2N\npby8nLvvvpuGDRuGWs1qcSb3CiRR1We/6qqrtHOj0Ujnzp1DqI0ikujatavbcoPBgMViYc2aNaxf\nvz7IWvlGMGZJImppuDc4IyWbzWYaNWoUanUUEcTy5cu1/LzOo7y8nEaNGnH27NlQq1cjwRiCR1UP\nA2DhwoXs2LGDzMxM/va3v4VaHUUEUVZW5rY8Nzc3IvxhrvqXl5czefJksrOzmTJlit/0jyqDMWzY\nMNauXcuWLVsAGD58OD179gyxVopIwen7qkzLli0jorfqqv+TTz7JK6+8AkD37t0ZNGiQX2RE1ZBk\nzZo1rFy5UnsdjDGdIvLYunWrFlXbNbp2VlaW2/qB3P3pT/R6PUIIOnTowLPPPquV+9MZGlU9DIB3\n330XgJtuuokuXbqEWBtFOPLdd98B9t2dVqsVg8FAw4YN6du3r9v6x48fJycnh5EjR3Lu3DmWLl1K\nRkaG27qhxGKxIKVk3759/OlPf2LWrFk0bNjQvwsYKzt5wumwq+cbmzZtkgkJCRKQmzdv9vl+RfTz\nyiuvSF++W876zZs3l4C89dZbA6hd7cnLy5NCCJmZmSkPHz4spZQSkGvXrvW5Lcf7U+U3GVVDErBv\ney8oKACiZx1GQkJClS6084iWZwwmHTp0AOyzCh9//HGN9e+9916klBw/fpz09PSwHeqmpaVhs9k4\ndeoU69ev14ZRzZs3r+FO74kqgzF9+nQaNWpEq1atgOhZ6VlUVMS//vUvDh8+zJEjRzhy5AgHDthX\n2iuD4Tvdu3fXhh8//PCDT/fm5eWxcuVK+vbtS+vWrUlNTaV379506tSJlJQUXnvttTrrN2PGDFJT\nU+nWrRu9e/emUaNGtGvXjpEjR3rdhjNhec+ePRk8eDDNmzfn6quvpkWLFmRmZjJ27NjaKeeu2xEu\nBz4OSQAphJDJycmyf//+sqioyKf7wxVA/t///V+FMpvNJgFZXFwcIq0iF+cQIyMjQ168eNGne+fP\nny+NRqPs0qWLTElJkYDs0KGDbNq0qcS+67rO+jnbadGihWzfvr0UQsjGjRtLQJaUlHjVxsmTJ2VK\nSors2rWrNJlMMj4+Xnbr1k0mJiZKo9FY43cHD0OSkBuF6g5f33y9Xi9ff/11n+6JBAC5ePHiCmXK\nYNSe+fPnSyGE39udMGGCbNiwYZ3bCfTnbTabNaN05513etRBRrsPw2q1Rm0XvbKn2zncipZhVzAp\nKytz/kPyK5cuXSI/P9+ne3JycujUqRPx8fEIIbQ4nJU/V39+3kajEZvNRoMGDfjxxx99ujfqplWj\nIQbGwYMHuXjxIlJK2rVrB1RNTOP8wgfiix/pnDlzhjNnzlBWVobJZEKv19OpUyct3EE45bdZtWoV\ne/fupXv37ly4cIEWLVrQpk0bRo0aVaGe83N2+lxMJhNCCMxms/ZcVqtV+57YbDZ0Oh1JSUlug0gJ\nISguLiY3N5cdO3Zgs9kAuOyyy0hJSfGob1QZDJ1OF9B4hsFgzZo13Hjjjdrr5GR7WFRPmaxUD6Mq\nmZmZVcrGjx/PvHnzgMDFSUlKSvJ5R6tTlx07dnhVv0+fPj7rtWvXLreb60aOHMmKFSu44oorKpRX\n908ofEytH7DZbBViAnzwwQcIIWjRokVQYgV4Q69evbQpUedu2oKCAlq0aIEQQjMWUkoeeeQRLl68\nCHjOxh0XF8eiRYuCo3wEkZub6+oLY+fOndq12NhYwG6M9+zZ43PbBQUFGI1G4uLitM8yLS2NU6dO\nuR2SLFiwoMLn7Yq3qzCFELX1A/LLL7+4bbPyZru33nqrRj2iqocBv34A+/fv54EHHgDgxIkTXLhw\ngfT09FCqBsC2bdsYMmQIRqORNWvWAPDjjz9y4sQJbr75ZiwWC7///e8Be7SxCxcuYLPZuPXWWyu0\nI4Rg1qxZTJkyhQkTJqDT6ZBSMmrUqLBdJxBI9u/fz5YtW7SudWXOnj3L4sWLsdlsWCwW+vfvz8aN\nG1m6dKnH6FKeWLduHRaLhVGjRnHhwgUSExNZvnw527dvd1v/wQcfBHBrnIIxpFy3bh25ubma7+KG\nG24gNTW1drrUxmoF66AW06rz58/XznF4gQGZm5vrU1uBApAnT56U+fn52hTcpk2baj0dN2HCBAlI\nnU4nATlu3Dh/qhsxOD9v51FaWqpdu/3226tcdx47d+70WdYHH3xQ5fPq3LmzBOSgQYOq1O/YsaNs\n2bKl28/4jTfe8MtUrCeaNWtW5Zl79erltu6iRYs0XagP06qV35jt27dXKH/++ed9ai8QOA3GpUuX\nqujrK+np6dq9BoNBAvL6668PgNbhDyA3btwYFFkrVqzQPq8dO3Zon8Hx48fd1r/88stl+/btK3zW\ncXFxdfrsa0vr1q1lWlqa22vvvvtujQYjqoYk27dv55133sFoNNK0aVN69OgB/OpInDZtGn/5y18C\nJv/QoUPMmzePuLg4bDYbZrOZ3/3ud1WcSv/617+YMWMG77//Pps2bcJqtTJgwACf5eXl5fHAAw9o\n42m9Xs/jjz/ur8eJOILlp3IOex5//HG++uorrfyuu+6iX79+6PV6ysrKEELQtm1b9u/fT0lJSYXP\nOz4+ntLSUqxWK8OGDQuK3gDnz5/n4sWLPP3005r8+Ph4ysrKvHO8urMi4XLgR8vbtWtX2a1bN7+1\n5w7cdHkNBkOFOpmZmRKQzZo1q5MstXCrIoD8+uuvgyLrxIkT2mpJQA4dOlQOHDjQ47CnefPmskmT\nJkHRrSaef/75Kj2c2NhY7bx3795SynoyJKmO7Oxs2bZtW7+15w6TySSnTJmivR4/fnyFXY6ux1VX\nXVUnWU6D4e1S4WjH+b6OGTMm1KpUAJDdunWTXbt2DbUqPuHJYNQ189ko4CmgI9BLSrnd5dpjwFjA\ngj0D2jpH+TBgNvYp3QVSymcrtxsIjh8/jhCCF154gU2bNiGl5Prrr+fee++lvLycadOmcfbsWd54\n441aL+wxm80UFxdrr4uKigD7LM2UKVPo2LEjJpMJq9VaZdbDV5zrL0aPHo1er6d///6aN74+snXr\nVm677Tbefvttr6YHg8mePXs8rqOJONxZEW8PoD3QFvgCuMKlvCOwA/u0bSvgIPYUiTrHeUvACOwE\nOlTTvt8sZtu2bWWbNm3cOhrnz5+vvX7xxRdrLQOQEyZM0F5/9dVXUgghTSaTLCwsrPMzuGKz2TTP\nvOuz1Gd69eoVdu/DFVdcIQE5d+7cUKviEwRiL4mUcp+U8gBV86WOAJZIKS1SyqPYs571dhwHpJTH\npJTlwBJH3YBjMpm0mIdSSnbt2gXY/1OPHz9e61WUlpa6vf8vf/lLhTgU06ZNq1InPj6+wkrTAQMG\nYLPZKCsrIz4+3q/PI4Rg9+7dSCnJycnRyjwdntYIRAsJCQls3brVY7qAUPHf//4XKSUTJkwItSp+\nIVArPT1laK9c/oujLOAcPnyYffv2aa+7du3KgQMH2Lx5Mxs3buTMmTOA58jRK1euRAihhXd7/vnn\nGTZsGD169NBW0hUVFVFYWBjgJ6lK48aNOXz4MM899xwtWrSgR48e9OjRg+bNm2urC8M9p0ZdKSoq\n4qWXXmLTpk2hViWqqdGHUV2Gdimlp3BFnjK0uzNQ1S4vq0syZlcWLlzI7bffXuH+7Oxsr7O7O1dS\nXnXVVbz55pvcddddHDp0iIMHD3LfffdpkZtCtbGpdevWPPLIIwCUlJSg1+s5c+YM8fHxXHbZZdrq\n0WimR48eJCQkhFqNiMTbZMz+ms3YQEUfxlTgUZfXa4GrgD7AWk/13LQbiOGZR2JiYjxOjQHyuuuu\nq3JPZb/IO++8E1SdXcnMzJT/8z//EzL5oYQgLtyqDxCEhVuuvYqPgEVCiFnYhxzZwPfYexjZQoiW\nwGlgNHC7H3WoE4WFhdrMhpRS2/Dj9AO480Ps379fiyGq1+v9+h8uPz+fjh07kpGRwb59+2jQoAEt\nW7bk0KFDSClp06YNJ0+epKCggLZt23L69Glyc3P9Jj8S+PnnnxkxIihuMAV13HwmhLgV+A+QDqwS\nQuyUUt4gpdwjhHgP2AOUAxMcVssqhJgIrOPXadW9dXsE/2EwGLTt5N6i0+l8vsdbnn32Wc6cOUNG\nRgYxMTHo9XqklNrmspiYGGJjY7FYLMTExNC+fXvmzp0bEF3ClenTp7N//3769etHv379Qq1O1FMn\ngyGlXAms9HDtn8A/3ZSvxT4dq6iBbt26ARUD1Tp7EP369ePbb78NiV7hRHJyMklJSeq9CBJRFQ8j\n2rj99tvd+nY6duyoZgMcFBcXc+nSpVCrUW9QBiMCCZdgQOFANIRkjCSiardqfaFZs2bOWaR6T1JS\nUvQsu44AVA8jAsnNzeXIkSOhViMssFgsqscVRFQPI8yZN28e5eXllJaWYjQaMRqNnDlzJmrTKfhK\nKFbW1meUwQhjXnrpJSZNmlShzGAwYLFYomZvQl1RKzuDizIYYYxzj4ryV3jGYDBoUcAVgUcZjDDk\nySefpLCwkM8++yzUqoQlVquVZ555hrNnz/LFF1943GGs8D/KYIQZK1asYObMmdrr+rBpzFeee+45\nnnjiCe313XffHUJt6hfKYIQZzn0pahjiGSkler1eOX5DgJpWDTPUj6BmiouL1VRqiFAGI8xQPYua\ncUZOUwQfZTDCDPVjqBmTyeQx16wisCiDEWY4u9odOnSgUaNGXHXVVfTt21cNVVwoLi52G0pxz549\ntG7dmgEDBpCdnU3z5s2ZOHFiCDSMXpTBCDNGjBjB5ZdfTk5ODnl5eZw7d47vvvuOZcuWhVq1sMG5\nd8S5LNxisWCxWLj77rs5evQo58+fJycnh19++YW5c+dWqefp3N3hKblzfUXNkoQZ6enp7Ny5s0KZ\nTqfT8pAo4OqrrwbcD9+uvPJKtm7dCtgDAyckJNR5mGe1WkMWqzXcUAYjApBSqv90LgwdOlR7P5xh\nFJ3nrsTHx3usV9O5E2fwZ4UdZTYjBLPZzL59+zhx4kTNlesBzjirlc+9rVfTeeUyhR1lMCIAIQTL\nli2jQ4cOtGjRguPHj4dapXqBs2ehehi/ogxGBCClZPXq1drr8+fPh1AbRX2mTgZDCDFKCLFbCGEV\nQlzhUj5ECLFNCPGDEGKrEOI6l2tXCCF2CSH2CyFm10V+fWHJkiUMGjSITz/9FFCrQYOFGpJURdSl\nuyWEaA/YgNeAh6Uje7sQ4nIgR0p5RgjRGfhUSpnluLYFmCSl/F4IsRr4t5TyUw/tS9UdrIgQgh07\ndtC9e/dQqxL1SCnR6XRYLJZ6FwbQ4QCuYikDkoxZSvmDlPKM4/wnIEYIYRRCNAESpZTfO6q+Ddxa\nFx3qI8qIKkJFwH0YQohRwA5pz9beDHsCZidBS8YcTcydO1fF9AwCakhSlUAlY3be2xl7MqOhLvdW\nJijJmKOFtm3bsmDBAjZs2MChQ4dCrU5UU59mSbxNxlwnH4bWiBAbgL84fRiOsixgPXCnlPI7R1kT\nYIOUsqPj9WjgWinlfR7aVT4MN/Tp04cDBw5w7ty5UKsS1Sgfhp99GJVluAhLBlYBU53GAsDh17gk\nhOgt7P28McCHftShXnDmzBk1tRoE1JCkKnWdVr1VCHEC6IM9GfMax6WJQBvgSSHEDiHEdiFEuuPa\nBGABsB844Mi1qvCBzMxMMjIyaq6oqBP1aUjiLX4ZkgQKNSRxz0033cQnn3zi9trLL7/Mffe5HeEp\nfEQNSaoOSZTBiECklGzatAkpJUIISktLMZlMDBgwgD59+rB58+ZQqxi2fPTRRzzxxBM0bdqUS5cu\ncfHiRZo2bYrNZuPs2bOkpaURFxfHmTNniIuLY/PmzfVyt6ong6F2q0YgQghti3dlVGKf6hkxYgQA\n+fn5nD59GovFQl5eHmVlZVy8eJHExEQSExM5deoUer2enj17Kh+GC8pgRBGZmZkkJSWFWo2wJjU1\nld/+9re8+uqroVYlIqlf/awo5/Tp05w9e9YvbS1YsICEhASuuOIKmjVrhslkolu3bnTu3NlteLxI\n4fz588yfP5/s7Gy6d+9OTEwMs2erLU3eogxGlGEw+KfTePfdd7vNKLZnzx4WL17sFxmh4D//+U+F\n98hisTBlypQQahRZKIMRRWRlZZGWluaXtlJTU/njH//I9u3bOXnyJGazmV27dqHX6yPaAThx4kTK\nyso4ePAgO3fu5JFHHlG5WX0gcj95RRV++eUXVqxYQatWrbSIUVlZWcTFxXHhwgWf2jp//ryWhc0V\nq9UaVeECi4uLVW5WH1AGI4r4/PPP6d69O506daJ379506dKFLl26UFpaysKFC31uz5OvIpJ9GJWJ\nJuMXDNQsSRQxePBgduzYUaXcYDD47NuIjY0lJSXF47VooUGDBqFWIaJQPYx6gNVq5cEHH/RpBWhZ\nWRlms9nttWj6r1xeXh5qFSIKZTDqAevXr6dly5Zerz1Yv349UkouXbrk9no0/cg8GUWFe5TBqAcM\nGjSIm266yauhxL59+xgyZAiAxx5JNOU1jabhVTBQBqOeoNfrKS0t1WZPPBmDwsJCwL5f5ZZbbnFb\nJ5qGJGrZt28op2c9Yfbs2bRp04aCggJefvllXn31VRo2bEhRURFgzxJWXFzM8OHDa2wrmqKWO5//\n448/5tNPP0Wv19OgQQNKS0uZOnWqCiNQCWUw6glCCB544AEA2rRpw+23386LL76ojeETEhIoLCz0\naqdrXXOVhhPO4ZVrb8r5Xrz++utu16LUZ9SQpB4yevRopJSUlZUhpURKSUFBAY0aNfLKCfjNN99U\nSSkohIhIZ2jbtm21888++0x7LwYMGEDTpk1DqFl4onoYCo3c3FxMJlON9ZYuXQrAe++9h5QSq9XK\nHXfcwQ033MCcOXPo1KlToFWtllmzZrF27Vr0ej0pKSmcO3cOKSVpaWnk5+djNptJT0/HYrGwdOlS\nsrKySE1N5ZprrtHaOHbsGMeOHQvhU4Qpzv8w4XjY1VMEi9TUVNm5c2dZ3fs+cuRICchHH320QnnP\nnj0lIDt16hRoNWsEeyR6CcgmTZpo5xkZGdp5WlqaBOTzzz/vto127dpJg8EQZM3DB8d3oMpvUvUw\nFBqJiYk1TjMuX77cbfm2bdvo06cPW7ZsCcjMw2uvvcaf//xnn+/LycnxGJNTCOFxCJaZmRnRm+wC\nhQrRp9AQQmAwGLBYLLUKfGuz2fjpp58q+DScS9KtVqsWF9Nms1X4MTpf63Q6ysrKMBqNFc67du3K\n0KFDWbdunVd65OTkcPLkSQoKChg4cGC1BiMxMZEuXbpgtVo5deoUjRs3pkGDBnz33XdIKaNqRsgX\nPIXoq+uQYRSwG7ACV7i53gIoAB5yKRsG/Iw9avijNbQfqB6Xwg1vvfWW1Ol0cuTIkaFWpQKAHD58\neJVym82m/XV3npOTU+3waurUqRKQLVu2lJmZmRKQjRs3lpdddpkE5DvvvBOAp4kM8DAkCUgyZpfr\nyx3GZIuU8kUhhM5hKAYDp4CtwGgp5c8e2pd10U8RHWRkZDBkyBAWLVoE2J2tv//9772+X32HfCcg\nQYCllPscjVcNRy7ECOAQUORS3Bt7LpJjjjpLgBHYexwKhVvOnj1bIXHT7t27AfueFscXG6DCuRO1\nktO/BMTpKYRoADyCPafqX10uNQNOuLz+BbsRUShq5OTJkxQVFWkpIv0VjlDhPYFKxjwDmCWlLK5k\n4VUyZoXPZGRkYLFYyMrK0spat24dQo2iD2+TMftrvcQGXJyewNfAYcdxAcjDniKxD7DWpd5UqnF8\nAnLDhg3+9+jUQH2RGSq5vsoEZLdu3ap1YPpbpj+IZJl4cHoGJBmzlHKAlPIyKeVlwGzgf6WUL2N3\ncmYLIVoKIUzAaOCj6hr1yur5mfoiM1RyayMzPz8/6DLrSjTKDFQyZrdIKa3YEzWvA34Clkgp99ZF\nB0X085vf/Ibjx4/TvHnzUKtS76nrLMlKYGUNdWZUer0WaF8XuYr6xdq1a0OtgsJB2K/0DLUOCkV9\nRUZa9naFQhFeqN01CoXCa5TBUCgUXhNWBkMIMUoIsVsIYRVCXFHp2mNCiANCiL1CiOtdyocJIX4W\nQuwXQjxaR/mXCyE2CyF2CCG+F0L0crk2xyF/pxCie13kuJE7yfEMPwohnnEpd/vMfpT7sBDCJoRI\ndSkLyHMKIZ5zPMdOIcQKIUSSy7WAPac/vx81yMkSQnwhhNjj+BwfcJSnCCHWCSH2CSE+FUIk+1mu\nTgixXQjxkeN1KyHEdw55i4UQ/l0O625xRqgO7LMnbYEvqLgQrCOwA/usTivgIPZ1HzrHeUvACOwE\nOtRB/qfA9Y7zG4ANjvMbgU8c51cB3/nxmQdin2Y2OF6nV/fMfpSbBawFjgCpLs8cqOccAugc588A\n/3ScdwrUc/r7+1GDrCZAd8d5ArAP6AA8CzziKH8UeMbPcqcA7wIfOV4vBX7rOH8FuMef8sKqhyGl\n3CelPEDVJeQjsK/ZsEgpjwIHsO9B0TazSSnLAedmttpiA5z/ARoCJx3ntwBvO3TcAiQLIfwVTvo+\n7F8ii6P9PEe5p2f2F7OouM/HKTMgzyml/FxK6cxP8B12gwX29zZQz+nv74dHpJRnpJQ7HeeFwF7s\nzzgCeMtR7S3gVn/JFEJkYf9n9rpL8SBghYu82/wlD8JsSFINlTetnXSUudvM1qwOcqYAzwshjgPP\nAY/VIN8ftAMGOLqRG4QQPQMtUwhxM3BCSvljpUuBfE5XxgKrgyDT398PrxBCtAK6YzeMGVLKHLAb\nFaCRH0U5jb50yE0DLrgY5l8Av0YyDvp2v1puZvO0ac2dwat2nrg6+di7zZOllCuFEKOAhdh33Pq8\nac5LmU9g/wwaSin7OHwmy4DLAixzGvbnqnJbgGRqn60Q4nGgXEq52B8ya1IpgG27FyhEArAc+/eo\nMFBriYQQw4EcKeVOIcRAZzFVn9mv8oNuMKSU7r6oNfEL4LouOAt7AB6BPapX5fJayRdCvCOlnOyo\nt1wI4ezqeZLvFTXIvBd431Fvq8Phm+aQ6dOzeSNTCNEFu6/gB0cckyxguxCiNwF8TofsO7F3oQe5\nFNdJZg3U6T30FYeDcTnwjpTyQ0dxjhAiQ0qZI4RoApz1k7irgVuEEDcCcUAi9n1byUIInaOX4f/n\nDYQDyA+OnA1AT5fXTseYCWjNr05PPb86tUzYnVod6yD3J+Bax/lgYKvj3NXp2Qf/OgP/DMxwnLcD\njlX3zAF4r48AKUF4zmGO9zetUnnAntPf3w8v5L0NvFip7FkcO7IJgNPT0e61VHR6/t5x/gpwr19l\nBerNq+WD34p9zFkCnAbWuFx7zPHh78Uxk+HyRdyH3Vk2tY7y+wHbHF/gzUAPl2svOeT/gJv4pXWQ\naQTeAX50yL62pmf283t+GMcsSYCf8wBwDNjuOF4OxnP68/tRg5yrsYej3On4/mx3yE4FPnfo8Bn2\n4ae/ZbsajNbAFuyhMJcCRn/KUkvDFQqF10TKLIlCoQgDlMFQKBReowyGQqHwGmUwFAqF1yiDoVAo\nvEYZDIVC4TXKYCgUCq9RBkOhUHjN/wcaO9HUZ2T8GQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fdaa1860>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "w_tour = rw\n",
+    "w_trace = trace_tour(w_tour)\n",
+    "mks = mistake_positions(w_trace)\n",
+    "while len(mks) > 3:\n",
+    "    print(len(mks))\n",
+    "    w_tour = trim_loop(w_tour)\n",
+    "    w_trace = trace_tour(w_tour)\n",
+    "    mks = mistake_positions(w_trace)\n",
+    "print('{}\\n{}\\n{}'.format(w_tour_start, w_tour, trace_tour(w_tour)[-1]))\n",
+    "plot_trace(trace_tour(w_tour))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 107,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[]"
+      ]
+     },
+     "execution_count": 107,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mks"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 108,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "IndexError",
+     "evalue": "list index out of range",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-108-982d2ade068b>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtrim_loop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw_tour\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-67-102a8e4a5818>\u001b[0m in \u001b[0;36mtrim_loop\u001b[0;34m(tour, random_mistake)\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0;31m#     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))\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m     \u001b[0;31m# while this mistake extends to the next step in the trace...\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m     while (mistakes[end_mistake_index].i + 1 < len(trace) and \n\u001b[0m\u001b[1;32m     11\u001b[0m            \u001b[0mend_mistake_index\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmistakes\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     12\u001b[0m            \u001b[0mmistakes\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mend_mistake_index\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mi\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m==\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mIndexError\u001b[0m: list index out of range"
+     ]
+    }
+   ],
+   "source": [
+    "trim_loop(w_tour)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 109,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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pfBdZq+FGgxMnTkQ6BV86efKkUZyuW467srLSy3QaJYXvgi1btgCwYMGCCGdy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\nED4khS+ED0nhC+FD/x8fErW+FPwE4wAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd0eab38>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "lc = trace_tour(square_tour(a=10))\n",
+    "rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
+    "plot_trace(trace_tour(rw))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 110,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(292,\n",
+       " 10,\n",
+       " 'RFLLFFLFLL',\n",
+       " [Step(x=-1, y=0, dir=<Direction.DOWN: 3>),\n",
+       "  Step(x=0, y=0, dir=<Direction.RIGHT: 2>)])"
+      ]
+     },
+     "execution_count": 110,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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XwMXArjyPX0Pu5BrAx4FnEpp7ObChF3nPAy6Org8FXu3muSg5c5/t2dz95+7+wYfczwBj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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd712198>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "rw_trimmed = trim_all_loops(rw)\n",
+    "plot_trace(trace_tour(rw_trimmed))\n",
+    "len(rw), len(rw_trimmed), rw_trimmed, trace_tour(rw_trimmed)[-2:]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 111,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(1, Step(x=0, y=0, dir=<Direction.RIGHT: 2>))"
+      ]
+     },
+     "execution_count": 111,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd6c24a8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "rw_trimmed = rw\n",
+    "mks = len(mistake_positions(trace_tour(rw_trimmed)))\n",
+    "while mks >= 4:\n",
+    "    rw_trimmed = trim_loop(rw_trimmed, random_mistake=True)\n",
+    "    mks = len(mistake_positions(trace_tour(rw_trimmed)))\n",
+    "    \n",
+    "# rw_trimmed = trim_all_loops(rw)\n",
+    "plot_trace(trace_tour(rw_trimmed))\n",
+    "mks, trace_tour(rw_trimmed)[-1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 112,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def trim_some_mistakes(tour, mistake_limit):\n",
+    "    trimmed_tour = rw\n",
+    "    mistake_count = len(mistake_positions(trace_tour(trimmed_tour)))\n",
+    "    while len(mistake_positions(trace_tour(trimmed_tour))) > mistake_limit:\n",
+    "        trimmed_tour = trim_loop(trimmed_tour, random_mistake=True)\n",
+    "    return trimmed_tour"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 113,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(3, Step(x=0, y=0, dir=<Direction.RIGHT: 2>))"
+      ]
+     },
+     "execution_count": 113,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fdb2d6d8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "rw_trimmed = trim_some_mistakes(rw, 4)\n",
+    "\n",
+    "plot_trace(trace_tour(rw_trimmed))\n",
+    "len(mistake_positions(trace_tour(rw_trimmed))), trace_tour(rw_trimmed)[-1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 114,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
+    "# tours_filename = 'tours-with-mistakes.txt'\n",
+    "\n",
+    "# try:\n",
+    "#     os.remove(tours_filename)\n",
+    "# except OSError:\n",
+    "#     pass\n",
+    "\n",
+    "# success_count = 0\n",
+    "# while success_count < 100:\n",
+    "#     lc = trace_tour(random.choice(patterns)())\n",
+    "#     rw = guided_walk(lc)\n",
+    "#     if rw:\n",
+    "#         rw_trimmed = trim_some_mistakes(rw, random.randint(0, 15) + random.randint(1, 3))\n",
+    "#         if len(rw_trimmed) > 10:\n",
+    "#             with open(tours_filename, 'a') as f:\n",
+    "#                 f.write(rw_trimmed + '\\n')\n",
+    "#                 success_count += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 115,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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ffzFhwgSuuuoqjEYjb731FgkJCbzzzjscOXKEjIyMOpaCFixYAMBbb72lypy2AqAt1bq7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\nEPGGH0ccYxDxhh9HHGMQ/w87It8NbHAcAQAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fd276ac8>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "lc = trace_tour(square_tour())\n",
+    "rw = guided_walk(lc, seek_step_limit=0, return_anyway=True)\n",
+    "plot_trace(trace_tour(rw))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 116,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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hLSISIYW3iEiEFN4iIhFSeIuIREjhLSISIYW3iEiEFN4iIhFSeIuIREjhLSISoUyHMZSZ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\niEiEFN4iIhFSeIuIREjhLSISof8HrbA0eP/SgKEAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f03fc718f28>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "rw_trimmed = trim_some_mistakes(rw, 1)\n",
+    "plot_trace(trace_tour(rw_trimmed))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 117,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[Mistake(i=32, step=Step(x=10, y=4, dir=<Direction.RIGHT: 2>))]"
+      ]
+     },
+     "execution_count": 117,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "mistake_positions(trace_tour(rw_trimmed))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
+    "# tours_filename = 'tours-open.txt'\n",
+    "\n",
+    "# try:\n",
+    "#     os.remove(tours_filename)\n",
+    "# except OSError:\n",
+    "#     pass\n",
+    "\n",
+    "# success_count = 0\n",
+    "# while success_count < 100:\n",
+    "#     lc = trace_tour(random.choice(patterns)())\n",
+    "#     rw = guided_walk(lc, seek_step_limit=0, return_anyway=True)\n",
+    "#     if rw:\n",
+    "#         rw_trimmed = trim_some_mistakes(rw, random.randint(0, 15) + random.randint(1, 3))\n",
+    "#         if len(rw_trimmed) > 10:\n",
+    "#             with open(tours_filename, 'a') as f:\n",
+    "#                 f.write(rw_trimmed + '\\n')\n",
+    "#                 success_count += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 119,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "tours_filename = 'tours-random-walk.txt'\n",
+    "\n",
+    "try:\n",
+    "    os.remove(tours_filename)\n",
+    "except OSError:\n",
+    "    pass\n",
+    "\n",
+    "success_count = 0\n",
+    "while success_count < 200:\n",
+    "    rw = random_walk()\n",
+    "    if rw:\n",
+    "        if random.choice([True, False]):\n",
+    "            rw_trimmed = trim_some_mistakes(rw, random.randint(0, 15) + random.randint(1, 3))\n",
+    "        else:\n",
+    "            rw_trimmed = trim_all_loops(rw)\n",
+    "        if len(rw_trimmed) > 10:\n",
+    "            with open(tours_filename, 'a') as f:\n",
+    "                f.write(rw_trimmed + '\\n')\n",
+    "                success_count += 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

diff --git a/06-tour-shapes/tour-shapes-problem-creation.ipynb b/06-tour-shapes/tour-shapes-problem-creation.ipynb
deleted file mode 100644 (file)
index ddfcbdf..0000000
--- a/06-tour-shapes/tour-shapes-problem-creation.ipynb
+++ /dev/null
@@ -1,3198 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "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",
-    "1. which tours are closed?\n",
-    "2. what is the area enclosed by the tour?"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "import collections\n",
-    "import enum\n",
-    "import random\n",
-    "import os\n",
-    "\n",
-    "import matplotlib.pyplot as plt\n",
-    "%matplotlib inline\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "class Direction(enum.Enum):\n",
-    "    UP = 1\n",
-    "    RIGHT = 2\n",
-    "    DOWN = 3\n",
-    "    LEFT = 4\n",
-    "    \n",
-    "turn_lefts = {Direction.UP: Direction.LEFT, Direction.LEFT: Direction.DOWN,\n",
-    "              Direction.DOWN: Direction.RIGHT, Direction.RIGHT: Direction.UP}\n",
-    "\n",
-    "turn_rights = {Direction.UP: Direction.RIGHT, Direction.RIGHT: Direction.DOWN,\n",
-    "               Direction.DOWN: Direction.LEFT, Direction.LEFT: Direction.UP}\n",
-    "\n",
-    "def turn_left(d):\n",
-    "    return turn_lefts[d]\n",
-    "\n",
-    "def turn_right(d):\n",
-    "    return turn_rights[d]\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "Step = collections.namedtuple('Step', ['x', 'y', 'dir'])\n",
-    "Mistake = collections.namedtuple('Mistake', ['i', 'step'])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def advance(step, d):\n",
-    "    if d == Direction.UP:\n",
-    "        return Step(step.x, step.y+1, d)\n",
-    "    elif d == Direction.DOWN:\n",
-    "        return Step(step.x, step.y-1, d)\n",
-    "    elif d == Direction.LEFT:\n",
-    "        return Step(step.x-1, step.y, d)\n",
-    "    elif d == Direction.RIGHT:\n",
-    "        return Step(step.x+1, step.y, d)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def trace_tour(tour, startx=0, starty=0, startdir=Direction.RIGHT):\n",
-    "    current = Step(startx, starty, startdir)\n",
-    "    trace = [current]\n",
-    "    for s in tour:\n",
-    "        if s == 'F':\n",
-    "            current = advance(current, current.dir)\n",
-    "        elif s == 'L':\n",
-    "            current = advance(current, turn_left(current.dir))\n",
-    "        elif s == 'R':\n",
-    "            current = advance(current, turn_right(current.dir))\n",
-    "        trace += [current]\n",
-    "    return trace    "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "k = Step(1, 2, 3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Step(x=1, y=2, dir=3)"
-      ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "k"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "__main__.Step"
-      ]
-     },
-     "execution_count": 9,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Step"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<Direction.UP: 1>"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "d = Direction.UP\n",
-    "d"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<Direction.RIGHT: 2>"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "turn_right(d)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{<Direction.RIGHT: 2>: <Direction.DOWN: 3>,\n",
-       " <Direction.UP: 1>: <Direction.RIGHT: 2>,\n",
-       " <Direction.DOWN: 3>: <Direction.LEFT: 4>,\n",
-       " <Direction.LEFT: 4>: <Direction.UP: 1>}"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "turn_rights"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
-       " Step(x=2, y=1, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=2, y=2, dir=<Direction.UP: 1>)]"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "trace_tour('FLRL')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=2, y=1, dir=<Direction.UP: 1>),\n",
-       " Step(x=3, y=1, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=3, y=2, dir=<Direction.UP: 1>),\n",
-       " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=1, y=1, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "trace_tour('FFLRLLFLRL')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
-       " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-1, y=1, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-2, y=-1, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-2, y=-2, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-2, y=-3, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-1, y=-3, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=0, y=-3, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=1, y=-3, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=1, y=-2, dir=<Direction.UP: 1>),\n",
-       " Step(x=1, y=-1, dir=<Direction.UP: 1>),\n",
-       " Step(x=0, y=-1, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=0, y=-2, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-1, y=-2, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-1, y=-1, dir=<Direction.UP: 1>),\n",
-       " Step(x=-1, y=0, dir=<Direction.UP: 1>),\n",
-       " Step(x=0, y=0, dir=<Direction.RIGHT: 2>)]"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "trace_tour('FLLFFLFFFLFFLFLLRRFR')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=2, y=-1, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=3, y=-1, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=3, y=0, dir=<Direction.UP: 1>),\n",
-       " Step(x=3, y=1, dir=<Direction.UP: 1>),\n",
-       " Step(x=4, y=1, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=4, y=2, dir=<Direction.UP: 1>),\n",
-       " Step(x=3, y=2, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=2, y=2, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=1, y=2, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=0, y=2, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=0, y=3, dir=<Direction.UP: 1>),\n",
-       " Step(x=0, y=4, dir=<Direction.UP: 1>),\n",
-       " Step(x=-1, y=4, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-1, y=3, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-2, y=3, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-2, y=2, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-1, y=2, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=-1, y=1, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-2, y=1, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-2, y=0, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-1, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=-1, y=-1, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=0, y=-1, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=0, y=0, dir=<Direction.UP: 1>)]"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def positions(trace):\n",
-    "    return [(s.x, s.y) for s in trace]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[(0, 0),\n",
-       " (1, 0),\n",
-       " (2, 0),\n",
-       " (2, -1),\n",
-       " (3, -1),\n",
-       " (3, 0),\n",
-       " (3, 1),\n",
-       " (4, 1),\n",
-       " (4, 2),\n",
-       " (3, 2),\n",
-       " (2, 2),\n",
-       " (1, 2),\n",
-       " (0, 2),\n",
-       " (0, 3),\n",
-       " (0, 4),\n",
-       " (-1, 4),\n",
-       " (-1, 3),\n",
-       " (-2, 3),\n",
-       " (-2, 2),\n",
-       " (-1, 2),\n",
-       " (-1, 1),\n",
-       " (-2, 1),\n",
-       " (-2, 0),\n",
-       " (-1, 0),\n",
-       " (-1, -1),\n",
-       " (0, -1),\n",
-       " (0, 0)]"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "positions(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def valid(trace):\n",
-    "    return (trace[-1].x == 0 \n",
-    "            and trace[-1].y == 0 \n",
-    "            and len(set(positions(trace))) + 1 == len(trace))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 21,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "False"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "valid(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLLFF'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 22,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "False"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "valid(trace_tour('FFLLLFRR'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 23,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "False"
-      ]
-     },
-     "execution_count": 23,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "valid(trace_tour('F'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 24,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "valid(trace_tour('LLLL'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def chunks(items, n=2):\n",
-    "    return [items[i:i+n] for i in range(len(items) - n + 1)]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['abcdefg',\n",
-       " 'bcdefgh',\n",
-       " 'cdefghi',\n",
-       " 'defghij',\n",
-       " 'efghijk',\n",
-       " 'fghijkl',\n",
-       " 'ghijklm',\n",
-       " 'hijklmn',\n",
-       " 'ijklmno',\n",
-       " 'jklmnop',\n",
-       " 'klmnopq',\n",
-       " 'lmnopqr',\n",
-       " 'mnopqrs',\n",
-       " 'nopqrst',\n",
-       " 'opqrstu',\n",
-       " 'pqrstuv',\n",
-       " 'qrstuvw',\n",
-       " 'rstuvwx',\n",
-       " 'stuvwxy',\n",
-       " 'tuvwxyz']"
-      ]
-     },
-     "execution_count": 26,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "import string\n",
-    "chunks(string.ascii_lowercase, 7)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Using the [Shoelace formula](https://en.wikipedia.org/wiki/Shoelace_formula)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 27,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def shoelace(trace):\n",
-    "    return abs(sum(s.x * t.y - t.x * s.y for s, t in chunks(trace, 2))) // 2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 28,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "4"
-      ]
-     },
-     "execution_count": 28,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "shoelace(trace_tour('FFLRLLFLRL'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 29,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "9"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "shoelace(trace_tour('FLLFFLFFFLFFLFLLRRFR'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 30,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "15"
-      ]
-     },
-     "execution_count": 30,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "shoelace(trace_tour('FFRLLFRLLFFFRFLLRLLRRLLRLL'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 31,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def step(s, current):\n",
-    "    if s == 'F':\n",
-    "        return advance(current, current.dir)\n",
-    "    elif s == 'L':\n",
-    "        return advance(current, turn_left(current.dir))\n",
-    "    elif s == 'R':\n",
-    "        return advance(current, turn_right(current.dir))\n",
-    "    else:\n",
-    "        raise ValueError"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 32,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def valid_prefix(tour):\n",
-    "    current = Step(0, 0, Direction.RIGHT)\n",
-    "    prefix = []\n",
-    "    posns = []\n",
-    "    for s in tour:\n",
-    "        current = step(s, current)\n",
-    "        prefix += [s]\n",
-    "        if (current.x, current.y) in posns:\n",
-    "            return ''\n",
-    "        elif current.x == 0 and current.y == 0: \n",
-    "            return ''.join(prefix)\n",
-    "        posns += [(current.x, current.y)]\n",
-    "    if current.x == 0 and current.y == 0:\n",
-    "        return ''.join(prefix)\n",
-    "    else:\n",
-    "        return ''"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 33,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def mistake_positions(trace, debug=False):\n",
-    "    mistakes = []\n",
-    "    current = trace[0]\n",
-    "    posns = [(0, 0)]\n",
-    "    for i, current in enumerate(trace[1:]):\n",
-    "        if (current.x, current.y) in posns:\n",
-    "            if debug: print(i, current)\n",
-    "            mistakes += [Mistake(i+1, current)]\n",
-    "        posns += [(current.x, current.y)]\n",
-    "    if (current.x, current.y) == (0, 0):\n",
-    "        return mistakes[:-1]\n",
-    "    else:\n",
-    "        return mistakes + [Mistake(len(trace)+1, current)]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 34,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def returns_to_origin(mistake_positions):\n",
-    "    return [i for i, m in mistake_positions\n",
-    "           if (m.x, m.y) == (0, 0)]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 35,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "sample_tours = ['FFLRLLFLRL', 'FLLFFLFFFLFFLFLLRRFR', 'FFRLLFRLLFFFRFLLRLLRRLLRLL']"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'FFLRLLFLRL'"
-      ]
-     },
-     "execution_count": 36,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "valid_prefix(sample_tours[0])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 37,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 37,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "all(valid_prefix(t) == t for t in sample_tours)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "True"
-      ]
-     },
-     "execution_count": 38,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "valid_prefix(sample_tours[0] + 'FLLLL') == sample_tours[0]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 39,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Mistake(i=10, step=Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
-       " Mistake(i=13, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
-      ]
-     },
-     "execution_count": 39,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "mistake_positions(trace_tour(sample_tours[0] + 'F'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 40,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Mistake(i=10, step=Step(x=0, y=0, dir=<Direction.DOWN: 3>)),\n",
-       " Mistake(i=13, step=Step(x=1, y=0, dir=<Direction.UP: 1>)),\n",
-       " Mistake(i=14, step=Step(x=0, y=0, dir=<Direction.LEFT: 4>)),\n",
-       " Mistake(i=15, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>)),\n",
-       " Mistake(i=17, step=Step(x=0, y=-1, dir=<Direction.DOWN: 3>))]"
-      ]
-     },
-     "execution_count": 40,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "mistake_positions(trace_tour(sample_tours[0] + 'FLLLL'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 41,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'FFLRLLFLRL'"
-      ]
-     },
-     "execution_count": 41,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "(sample_tours[0] + 'FLLLL')[:10]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 42,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def random_walk(steps=1000):\n",
-    "    return ''.join(random.choice('FFLR') for _ in range(steps))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 43,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "''"
-      ]
-     },
-     "execution_count": 43,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "valid_prefix(random_walk(1000))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 44,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "''"
-      ]
-     },
-     "execution_count": 44,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "valid_prefix(random_walk(1000))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 45,
-   "metadata": {
-    "collapsed": true,
-    "scrolled": true
-   },
-   "outputs": [],
-   "source": [
-    "walks = []\n",
-    "while len(walks) < 10:\n",
-    "    w = valid_prefix(random_walk())\n",
-    "    if len(w) > 30: walks += [w]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 46,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['FFFFRFFLRLRRFFFFFFFLRFFFFRFFFRFFFFFLFR',\n",
-       " 'RFLFFFLFFFFLFRFRFLRFLLFRLFFFFFFLFFFFFLFRFL',\n",
-       " 'FFRFLFFRFFFLRFRFFFFFRFFFLFRFRFLF',\n",
-       " 'FFRLFLFFFLRRLLFLRFFFFFLFLRFFLFFL',\n",
-       " 'FFFFFRFFFFRFLFRFRFFFLFFFFRFFRFFF',\n",
-       " 'RRLFFLRRLFLFRRFLFLFRFLLFFFFFFLRFFFFL',\n",
-       " 'LFFFRRLLRFLFLLRFFFRLFFFLFFRFFLFLFFFLRFRLRFLFLL',\n",
-       " 'FRFLFLRFLRFLFLLRFRFFFFLLFRFFLFFF',\n",
-       " 'RFFFRLRFFRFFFFLLFFFRFRFFFFFFRFRFLFFRLF',\n",
-       " 'LLFRFRLFFFFLFLFFFRFFLFFFLLRRFLFLRF']"
-      ]
-     },
-     "execution_count": 46,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "walks"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 47,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=1, y=1, dir=<Direction.UP: 1>),\n",
-       " Step(x=0, y=1, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=0, y=0, dir=<Direction.DOWN: 3>)]"
-      ]
-     },
-     "execution_count": 47,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "trace_tour('FLLL')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 48,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(-1, 3)"
-      ]
-     },
-     "execution_count": 48,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1034b579e8>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "import matplotlib.pyplot as plt\n",
-    "%matplotlib inline\n",
-    "plt.axis('on')\n",
-    "plt.arrow(0, 0, 0.8, 0, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
-    "plt.arrow(0.2, 0, 0, 1, head_width=0.1, head_length=0.1, fc='k', ec='k', length_includes_head=True)\n",
-    "plt.xlim([-1, 2])\n",
-    "plt.ylim([-1, 3])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 49,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def bounds(trace):\n",
-    "    return (max(s.x for s in trace),\n",
-    "            max(s.y for s in trace),\n",
-    "            min(s.x for s in trace),\n",
-    "            min(s.y for s in trace))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 50,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(0, 2, -13, -13)"
-      ]
-     },
-     "execution_count": 50,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "bounds(trace_tour('RFRFFLRFLFFRRFFRRRRLLLRRRRRRFRLFRFFRFFRRFRLRRFLLFRLLFRFLFLFRFRLLFRLFRFLRRLLFRRRFRRRRLLFLFRFRRFFRRLLLRLRRFRLRRFFRRFLFRRLLRRFFRFRRRRRFLLLLLRRFFFLLFFFRRLFLFFLRRRFRFLLFFRRLLRFLLRRF'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 51,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n",
-    "           Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 52,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None, filename=None):\n",
-    "    plt.axis('on')\n",
-    "    plt.axes().set_aspect('equal')\n",
-    "    for s, t in chunks(trace, 2):\n",
-    "        w, h = plot_wh[t.dir]\n",
-    "        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",
-    "    xh, yh, xl, yl = bounds(trace)\n",
-    "    if xybounds is not None:    \n",
-    "        bxh, byh, bxl, byl = xybounds\n",
-    "        plt.xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
-    "        plt.ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
-    "    else:\n",
-    "        plt.xlim([xl-1, xh+1])\n",
-    "        plt.ylim([yl-1, yh+1])\n",
-    "    if filename:\n",
-    "        plt.savefig(filename)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 53,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None):\n",
-    "#     plt.ioff()\n",
-    "#     if fig is None:\n",
-    "#         fig = plt.figure()\n",
-    "#         ax = fig.gca()\n",
-    "#     if subplot_details is not None:\n",
-    "#         ax = fig.add_subplot(*subplot_details)\n",
-    "#     plt.axis('on')\n",
-    "# #     plt.axes().set_aspect('equal')\n",
-    "#     ax.set_aspect('equal')\n",
-    "#     for s, t in chunks(trace, 2):\n",
-    "#         w, h = plot_wh[t.dir]\n",
-    "#         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",
-    "#     xh, yh, xl, yl = bounds(trace)\n",
-    "#     if xybounds is not None:    \n",
-    "#         bxh, byh, bxl, byl = xybounds\n",
-    "#         ax.set_xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
-    "#         ax.set_ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
-    "#     else:\n",
-    "#         ax.set_xlim([xl-1, xh+1])\n",
-    "#         ax.set_ylim([yl-1, yh+1])\n",
-    "#     plt.close(fig)\n",
-    "#     return fig"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 54,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def pqr(p, q, r):\n",
-    "    return '{}:{};{}'.format(p, q, r)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 55,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'1:2;3'"
-      ]
-     },
-     "execution_count": 55,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "pqrt = (1, 2, 3)\n",
-    "pqr(*pqrt)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 56,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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kP1LxyGazsUcYkVKbFzRzMckrBu6+2d37wsMXgIb8RyoepfafXmrzgmYuJkleM/gnYGOC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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10348a6358>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 57,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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mVpXUYCKSX7muDH4DjHX3I4HVwA25j1Q4MplM7BH6pdjmBc1cSHKKgbsvcPeO8PRFoCb3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\nAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10347d76a0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(sample_tours[0] + 'FLLLL'), colour='g')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 58,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAADqCAYAAAChr/4gAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1034735828>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour('FFFLLFFL'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 59,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Step(x=0, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=1, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=2, y=0, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=2, y=-1, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=3, y=-1, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=4, y=-1, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=4, y=0, dir=<Direction.UP: 1>),\n",
-       " Step(x=4, y=1, dir=<Direction.UP: 1>),\n",
-       " Step(x=4, y=2, dir=<Direction.UP: 1>),\n",
-       " Step(x=4, y=3, dir=<Direction.UP: 1>),\n",
-       " Step(x=3, y=3, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=3, y=4, dir=<Direction.UP: 1>),\n",
-       " Step(x=4, y=4, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=4, y=5, dir=<Direction.UP: 1>),\n",
-       " Step(x=3, y=5, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=2, y=5, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=2, y=4, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=1, y=4, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=0, y=4, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-1, y=4, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-2, y=4, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-3, y=4, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-4, y=4, dir=<Direction.LEFT: 4>),\n",
-       " Step(x=-4, y=3, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-4, y=2, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-3, y=2, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=-3, y=1, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-3, y=0, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-3, y=-1, dir=<Direction.DOWN: 3>),\n",
-       " Step(x=-2, y=-1, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=-1, y=-1, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=0, y=-1, dir=<Direction.RIGHT: 2>),\n",
-       " Step(x=0, y=0, dir=<Direction.UP: 1>)]"
-      ]
-     },
-     "execution_count": 59,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "trace_tour(walks[3])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 60,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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DLgDu6nT/X4H6LvbzEL333nteXl7uEydOTLuVILS2tvp3vvMdB2LfqqqqvLq62keOHJlI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\nCZYCTkSC9X9HKanR5sBgvwAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10347d5630>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(walks[3]))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 61,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "10"
-      ]
-     },
-     "execution_count": 61,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "long_walks = [w for w in walks if len(w) >= 30]\n",
-    "len(long_walks)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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BPoAyYF0zv+8h7dmzxzt27OgFBQU+bty4oNmSG4BfccUVfs899/i8efOCZtfV1fnTTz/t\nY8aMCZrr7r5ixQofMWKE79ixI2jutm3b/K677vKFCxcGzU2lUv6LX/zCx48fHzTX3X3ZsmU+YsQI\n3717d9DcDz74wL/3ve/5smXLgubW1tb6k08+6Q899FDQ3GxKd+eXOrXFM+/mmNkp7r49/fk9wDfc\n/TtN3NczOdahtm7dSmlpKQC33nor06dPD5YtuWFmDBgwgMWLFyc9iki7ZWaHPfPO9Bx/spmtM7M1\nQD/gngzzWq179+4HrjGpuEXkWJPRNyzdfXioQUREpPX0DksRkQipvEVEIqTyFhGJkMpbRCRCKm8R\nkQipvEVEIqTyFhGJkMpbRCRCKm8RkQipvEVEIqTyFhGJkMpbRCRCKm8RkQhlXN5mdpeZbTSzt81s\nUoihRESkeRn9SFgz6w8MBs529/1mdlKQqeSot3PnTgA2bNhAXV0dhYWFCU8kEpdMz7xHApPcfT+A\nu4dfe91K2dj9l83c+vp6Qm4WOlgMj8XEiROBxg3vCxYsCJYrcqzIdHt8L+AqM/sJ8AVwn7u/mflY\nbXP11Vezbt06qqurMfvyns4j8fHHH/Poo48ybdo0fvvb33LZZZcFyd2/fz/PP/8848aNY8iQITz+\n+ONBcgFWr17N2LFj2bJlC++9916w3F27dlFZWcmvfvUrFixYQN++fTPOHDZsGNOmTaNjx44MHDgw\nwJQix5ZMtsePBx4GXnb3fzWzbwCz3b1HEznBt8e/9tprXHnllQBZO4uVRuk9esFzJ0+ezH333Rc8\nVyRWOdkeD/wBuOqg21VA5ybum43Fyr5+/XofPHiwd+3a1RsaGoLl1tTU+Pjx472kpMRfe+21YLn1\n9fU+e/ZsLysr83vvvTdYrrv72rVrfdCgQd6jR4+gubt37/YxY8Z4SUmJv/XWW0GzRaR5ZGl7/HeB\nru5eYWa9gJfcvayJ+3omx2qJuwe7ZBJzbjazszmziBxeU9vjMy3vQuBpoA+QAn7g7kubuG9Wy1tE\n5GiUlfJu4wAqbxGRNmqqvPUOSxGRCKm8RUQipPIWEYmQyltEJEIqbxGRCKm8RUQipPIWEYmQyltE\nJEIqbxGRCKm8RUQipPIWEYmQyltEJEIqbxGRCKm8RUQilFF5m9ksM1uV/thiZqtCDdYeHLyKKAax\nzQuaORdimxfimzmJeTMqb3cvd/e+7t4X+A3wQpix2gc9gbJPM2dfbPNCfDMnMW+m2+MPdgMwIGCe\niIg0Icg1bzO7Etju7v8TIk9ERJrX4ho0M3sJOPngXwIcGOfu89L3+Tmw2d1/2kyOdqCJiByBrOyw\nNLN84EOgr7t/lFGYiIi0SojLJt8CNqi4RURyJ0R53wjMDJAjIiKtlPFlExERyb2cvsPSzM4zs+Vm\nttrM/tvMLszl8Y+Emd1lZhvN7G0zm5T0PK1lZqPNrMHMTkx6lpaY2WQz22Bma8zsN2bWKemZDsfM\nrkk/F94zs/uTnqclZtbNzBab2bvp5+/dSc/UGmaWl37j39ykZ2kNMzvBzJ5LP4fXm9nFuThurt8e\nPxmocPfzgQpgSo6P3yZm1h8YDJzt7ucAjyY7UeuYWTdgIFCd9CyttBA4y937AJuBBxKe50vMLA94\nChgEnAXcZGZnJjtVi/YD97r73wOXAqMimBng+8C7SQ/RBj8D/uDuvYHzgA25OGiuy7sBOCH9eQmN\nr1Jpz0YCk9x9P4C770p4ntb6KXBf0kO0lrsvcveG9M0VQLck52nCRTS+HLba3euAWcCQhGdqlrtv\nd/c16c8/o7FUuiY7VfPSJx7/APxn0rO0hpl9BbjS3acDuPt+d/80F8fOdXnfAzxqZn+m8Sy83Z1h\nHaIXcJWZrTCzVyK5zDMY2Orubyc9yxG6DXgx6SEOoyuw9aDbH9DOi/BgZnYa0Ad4I9lJWvTXE49Y\nvhnXA9hlZtPTl3r+w8yOy8WBQ749Hmj+TT00fin/fXefY2bXA0/T+FLDxDQz73gaH58Sd7/EzL4B\nPEvjX1aiWpj5Qf72Mf3Si/uT0Mo3e40D6tz9mQRGbMnhHscoCsbMOgLP0/j/3mdJz9MUM7sW2OHu\na9KXLNvFc7cFBUBfYJS7v2lmTwBjabwsnFU5fbWJmf2vu5ccdPsTdz+huT+TJDP7A42XTZalb1cB\nF7v77mQnOzwzOxtYBHxO4xO/G42Xpi5y951JztYSM7sF+C5wtbunkp7nUGZ2CTDB3a9J3x4LuLtX\nJjtZ88ysAPgd8KK7/yzpeZpjZj8BhtF4rf444CvAC+4+PNHBmmFmJwPL3b1H+vYVwP3uPjjbx871\nZZMPzawfgJl9E3gvx8dvqznANwHMrBdQ2F6LG8Dd33H3U9y9h7ufTuOX9udHUNzXAGOAf2yPxZ22\nEuhpZmVmVgSUAzG8GuJp4N32XtwA7v6gu5emi7AcWNyeixvA3XcAW9P9AI19kZNvtga/bNKC24F/\nT7+lvpbGM632bDrwtJm9DaSAdv1EOgwnji89nwSKgJfMDGCFu9+R7Eh/y93rzexOGl8Zkwf80t1z\n8qqCI2VmlwM3A2+b2Woanw8Puvv8ZCc76twN/JeZFQLvAyNycVC9SUdEJEJagyYiEiGVt4hIhFTe\nIiIRUnmLiERI5S0iEiGVt4hIhFTeIiIR+j+lRtB3jPdEdgAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1034735710>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(long_walks[0]))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "['FFFFRFFLRLRRFFFFFFFLRFFFFRFFFRFFFFFLFR',\n",
-       " 'RFLFFFLFFFFLFRFRFLRFLLFRLFFFFFFLFFFFFLFRFL',\n",
-       " 'FFRFLFFRFFFLRFRFFFFFRFFFLFRFRFLF',\n",
-       " 'FFRLFLFFFLRRLLFLRFFFFFLFLRFFLFFL',\n",
-       " 'FFFFFRFFFFRFLFRFRFFFLFFFFRFFRFFF',\n",
-       " 'RRLFFLRRLFLFRRFLFLFRFLLFFFFFFLRFFFFL',\n",
-       " 'LFFFRRLLRFLFLLRFFFRLFFFLFFRFFLFLFFFLRFRLRFLFLL',\n",
-       " 'FRFLFLRFLRFLFLLRFRFFFFLLFRFFLFFF',\n",
-       " 'RFFFRLRFFRFFFFLLFFFRFRFFFFFFRFRFLFFRLF',\n",
-       " 'LLFRFRLFFFFLFLFFFRFFLFFFLLRRFLFLRF']"
-      ]
-     },
-     "execution_count": 63,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "walks"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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2WNK1JH91f1tmDqEfEWwFZpvZQUlfA54luWXzZJK/7PZ0qzHcGDbMMoXjPGNmp0g6GnhW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\n8v89qQ80wuYWhQAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10345119b0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour('FLFFLRFRLFRRRR'))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(383, [])"
-      ]
-     },
-     "execution_count": 66,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "w = random_walk()\n",
-    "ms = mistake_positions(trace_tour(w))\n",
-    "len(ms), returns_to_origin(ms)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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YpX2bzYaLLmJ9dH/xi1/g2LFj2Lt3ryhrb2/HiBEj4HA4/Aqp4Q8lJSWmGLOV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\n+wAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10345996a0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(w))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def trim_loop(tour, random_mistake=False):\n",
-    "    trace = trace_tour(tour)\n",
-    "    mistakes = mistake_positions(trace)\n",
-    "    if random_mistake:\n",
-    "        end_mistake_index = random.randrange(len(mistakes))\n",
-    "    else:\n",
-    "        end_mistake_index = 0\n",
-    "#     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",
-    "    # while this mistake extends to the next step in the trace...\n",
-    "    while (mistakes[end_mistake_index].i + 1 < len(trace) and \n",
-    "           end_mistake_index + 1 < len(mistakes) and\n",
-    "           mistakes[end_mistake_index].i + 1 == \n",
-    "           mistakes[end_mistake_index + 1].i):\n",
-    "#         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",
-    "        # push this mistake finish point later\n",
-    "        end_mistake_index += 1\n",
-    "    mistake = mistakes[end_mistake_index]\n",
-    "    \n",
-    "    # find the first location that mentions where this mistake ends (which the point where the loop starts)\n",
-    "    mistake_loop_start = max(i for i, loc in enumerate(trace[:mistake.i])\n",
-    "                             if (loc.x, loc.y) == (mistake.step.x, mistake.step.y))\n",
-    "#     print('Dealing with mistake from', mistake_loop_start, 'to', mistake.i, ', trace has len', len(trace))\n",
-    "    \n",
-    "    # direction before entering the loop\n",
-    "    direction_before = trace[mistake_loop_start].dir\n",
-    "    \n",
-    "    # find the new instruction to turn from heading before the loop to heading after the loop\n",
-    "    new_instruction = 'F'\n",
-    "    if (mistake.i + 1) < len(trace):\n",
-    "        if turn_left(direction_before) == trace[mistake.i + 1].dir:\n",
-    "            new_instruction = 'L'\n",
-    "        if turn_right(direction_before) == trace[mistake.i + 1].dir:\n",
-    "            new_instruction = 'R'\n",
-    "#     if (mistake.i + 1) < len(trace):\n",
-    "#         print('turning from', direction_before, 'to', trace[mistake.i + 1].dir, 'with', new_instruction )\n",
-    "#     else:\n",
-    "#         print('turning from', direction_before, 'to BEYOND END', 'with', new_instruction )\n",
-    "    return tour[:mistake_loop_start] + new_instruction + tour[mistake.i+1:]\n",
-    "#     return mistake, mistake_loop_start, trace[mistake_loop_start-2:mistake_loop_start+8]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 69,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF'"
-      ]
-     },
-     "execution_count": 69,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "w = 'RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF'\n",
-    "w"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 70,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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iIm2AD0RkharuCGDbxpizSHpPrKr7VXVL7PpxYDtwXrLbNd5s2rQJ8NZNlCxtsCRJw+th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\nrC2Hf85MaAAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1033e45b38>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "w_short = w[:100]\n",
-    "plot_trace(trace_tour(w_short))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 71,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n",
-      "RFFRRFFFRFFRFLLRFLFFFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1033e457f0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "trimmed = trim_loop(w_short)\n",
-    "print('{}\\n{}'.format(w_short, trimmed))\n",
-    "plot_trace(trace_tour(trimmed))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 72,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "RFFRRFFFRFFRFLLRFLFFFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n",
-      "RFFRRFFFRFFRFLLRFLFFLLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLR\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1033c33940>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "trimmed2 = trim_loop(trimmed)\n",
-    "print('{}\\n{}'.format(trimmed, trimmed2))\n",
-    "plot_trace(trace_tour(trimmed2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Mistake(i=104, step=Step(x=-4, y=6, dir=<Direction.DOWN: 3>)),\n",
-       " Mistake(i=105, step=Step(x=-5, y=6, dir=<Direction.LEFT: 4>)),\n",
-       " Mistake(i=106, step=Step(x=-5, y=7, dir=<Direction.UP: 1>)),\n",
-       " Mistake(i=107, step=Step(x=-5, y=8, dir=<Direction.UP: 1>)),\n",
-       " Mistake(i=108, step=Step(x=-5, y=9, dir=<Direction.UP: 1>)),\n",
-       " Mistake(i=115, step=Step(x=-5, y=12, dir=<Direction.LEFT: 4>)),\n",
-       " Mistake(i=116, step=Step(x=-5, y=11, dir=<Direction.DOWN: 3>)),\n",
-       " Mistake(i=127, step=Step(x=2, y=11, dir=<Direction.LEFT: 4>)),\n",
-       " Mistake(i=130, step=Step(x=3, y=11, dir=<Direction.UP: 1>)),\n",
-       " Mistake(i=132, step=Step(x=3, y=11, dir=<Direction.UP: 1>))]"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "mistake_positions(trace_tour(w[:130]))[-10:]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 74,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Step(x=40, y=36, dir=<Direction.UP: 1>)\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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4BuzPuLRMdHS0Ko21u+j1enndOp1OtUsMQEC/aDqdzqUt3PqaEhISwtJ+rkXS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\nRK5CYII=\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1033a7d6a0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "w_tour_start = w #[:250]\n",
-    "print(trace_tour(w_tour_start)[-1])\n",
-    "plot_trace(trace_tour(w_tour_start))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 75,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF\n",
-      "RFFRRFFFRFLRFRFLLRFLLRLRRLFRLRRFFLLRLLRRFRFLRLFFLFLRRLRRLRLFLLRRFFLRLLFFFFFRRFFLFRLFFRLLRRFLFFFLRFLRRLRFLFLFFRLLFFRRFFLRLFRFFRLFFLRRFLRFLRRLFRRLFFFFRLFLFFLRFFLFRFLRRFFFFFLFRLRRFRLLRLLFRFLFFFRLFRFLFLRLRFFFFFLFFRFFFFLRFLFRFLRLRLFFLRRFFFRLLFRLFLRRFLRLLRLFFRFLRRLFLLRFLFFRFLFRLRFFFFFLRLLFRFLLRRFLRRFLRLRFLRRLFFFRFLRRLF\n",
-      "Step(x=40, y=36, dir=<Direction.UP: 1>)\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1033a7dfd0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "w_tour = w_tour_start\n",
-    "w_trace = trace_tour(w_tour)\n",
-    "mks = mistake_positions(w_trace)\n",
-    "while len(mks) > 1:\n",
-    "#     print(len(mks))\n",
-    "    w_tour = trim_loop(w_tour)\n",
-    "    w_trace = trace_tour(w_tour)\n",
-    "    mks = mistake_positions(w_trace)\n",
-    "print('{}\\n{}\\n{}'.format(w_tour_start, w_tour, trace_tour(w_tour)[-1]))\n",
-    "plot_trace(trace_tour(w_tour))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 76,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def trim_all_loops(tour, mistake_reduction_attempt_limit=10):\n",
-    "    trace = trace_tour(tour)\n",
-    "    mistake_limit = 1\n",
-    "    if trace[-1].x == 0 and trace[-1].y == 0:\n",
-    "        mistake_limit = 0\n",
-    "    mistakes = mistake_positions(trace)\n",
-    "    \n",
-    "    old_mistake_count = len(mistakes)\n",
-    "    mistake_reduction_tries = 0\n",
-    "    \n",
-    "    while len(mistakes) > mistake_limit and mistake_reduction_tries < mistake_reduction_attempt_limit:\n",
-    "        tour = trim_loop(tour)\n",
-    "        trace = trace_tour(tour)\n",
-    "        mistakes = mistake_positions(trace)\n",
-    "        if len(mistakes) < old_mistake_count:\n",
-    "            old_mistake_count = len(mistakes)\n",
-    "            mistake_reduction_tries = 0\n",
-    "        else:\n",
-    "            mistake_reduction_tries += 1\n",
-    "    if mistake_reduction_tries >= mistake_reduction_attempt_limit:\n",
-    "        return ''\n",
-    "    else:\n",
-    "        return tour"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 77,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'RFFRRFFFRFLRFRFLLRFLLRLRRLFRLRRFFLLRLLRRFRFLRLFFLFLRRLRRLRLFLLRRFFLRLLFFFFFRRFFLFRLFFRLLRRFLFFFLRFLRRLRFLFLFFRLLFFRRFFLRLFRFFRLFFLRRFLRFLRRLFRRLFFFFRLFLFFLRFFLFRFLRRFFFFFLFRLRRFRLLRLLFRFLFFFRLFRFLFLRLRFFFFFLFFRFFFFLRFLFRFLRLRLFFLRRFFFRLLFRLFLRRFLRLLRLFFRFLRRLFLLRFLFFRFLFRLRFFFFFLRLLFRFLLRRFLRRFLRLRFLRRLFFFRFLRRLF'"
-      ]
-     },
-     "execution_count": 77,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "w_trimmed = trim_all_loops(w)\n",
-    "w_trimmed"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 78,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1033a3d908>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(trim_all_loops(w)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 79,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def reverse_tour(tour):\n",
-    "    def swap(tour_step):\n",
-    "        if tour_step == 'R':\n",
-    "            return 'L'\n",
-    "        elif tour_step == 'L':\n",
-    "            return 'R'\n",
-    "        else:\n",
-    "            return tour_step\n",
-    "        \n",
-    "    return ''.join(swap(s) for s in reversed(tour))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 80,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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nAaEhk3w+Hz169ABg/fr1LF68OKkEc+LECSorK3n11VetRNfa2sqcOXMoLPyk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\nnqDJTinlCZrslFKeoMlOKeUJ/x9O8a6mC0FDEQAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1033accef0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(w_trimmed))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 81,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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+P07WWIriKKEW4snJycEYw7Zt2xKlVrvotBElKTh69ChdunQJec1aLtzj8dCr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\ngjJMbcJZvAAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1033cf2eb8>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(reverse_tour(w_trimmed)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 82,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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Mst8dQoCICPk8MNB0zC8khA1R2NOfmzpVToO7/V+1ijWxAwOBxYvluOYWW7XWPYmTEH1I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\nkAKBF/H/E7cUOhxnMSgAAAAASUVORK5CYII=\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f103452c198>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "w1 = random_walk()\n",
-    "w2 = random_walk()\n",
-    "plot_trace(trace_tour(w1))\n",
-    "w1bounds = bounds(trace_tour(w1))\n",
-    "plot_trace(trace_tour(w2), colour='r', xybounds=w1bounds)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 83,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "w1 = 'FRRFRRFFLFRRRLFFFLRFFFRLRFRRFLFLFFFFLRLFFFFFFLRRFLRLLFLLRFLFLLFFFLRLLFRFFFLFLFFRRLFRFRFFFRLFFFFRFFFRFFLRFRRRRFLLFFFRFFLLFLFLRFLFFLFFFRFLRLFRFLFFLLFFFLFFFFLFFFFFLRFFRRRFFLFRFFRFRRRRLLRFFFRFFRFRRFRLLRLLRFRFFLFLFRFRRLFLFLFLFFFFFLLLRRRFRFFRLLRRLRFLFLLLFFFLLFLLFLRFRLRLFFFRLLFLFRFRFRRLFRLFFLFFFFLFFFFRRRLFFFRLLLLFFRFRLRFFFFRFFRFFLLLFFFLRFRLFFFRFFFFRLLFFLRRFFLFRFFFFFFFFRLRLFFLFFLLFFLRFLRFFFFFFFFFLFFFLFRRRRFRFLLLRRFFRFRLFRFLFFFLLRFLLFLFRFLFFRFFFFFRLFRLLRRFFLRRFFFFFFRRFFFFFFRFFLRFFFLFLRRFLLLFFRFLFFFFFLFLLLRFRLFFFLFRFLRLLFRFRFFLFLFLRLFLFFFFFFFFFRFRLFRRRLFLRFLFFFFLLLLFFLFFFFFFFLLFLLLRRRLFLLLRLLFFFFFLFFFFRFFFLLRLRRLFFRFRLLRRFFFFFLFRFFRFLLFFFLRRRFFLLRLLFFFLLRFLFFLFRFFFRLRFFLRFLFFRFFRFFLFRRFFRFRLFLFRRRFRFFRFFFFFRFFFLRRFRFFRRFFFRFRFLFRLRLFLRLFFRFFFFFRRFRFLFFRLFRRFLFFLFRFLFLLLFLRFLLFLFRRRRFFRFFRFFFRLFFFLFRFRLRRFFFLRFRFFLFRRRFFRFFFFRFLRFFRFRFRRFFLFLFLRLFLFLFLLFLFFRFFFFFFFLFRFFLRLFRRLFFRRRFFRFRFRRLRLFFRFFRRFFFRFRFRLLRLFFLLLRFFRRFRFRFRFLLFFFFFLFFLFFFLLFFFFFLRFLFFFFLFRRFFFLFLFLLFFLFFFFFFFRFFLLFFLLLLFFRFFLL\n",
-      "w2 = 'FLFFFRLRLFFFLRLRRFFFFFFLFFFFLRFFFFRLFLFFLLRFLRLLFLFRLRRFFLFFRRLLRFRLRRLRRLRFFFFFRLFLRLFFFFLFFFFFRRLFFLFRFRFLFFRRLFFLRLLFRFFRFRFFLLFLRFRRFLFFRRFFFLRLFFRLLFFFFFFFRFFRFFFFRFRFLRFFLFLFLFLFRRRRFFFRFRRFFFFRFFLFFLRLFLFFFRLFFFRRLFFFFFLFRFRFFFFRRFRRFRLFRFFLRRRFFFLFLFFRRRFFFFRFFFFFLRLLLFRFLFLRFRLLFFFRFRLRLFRFFLLFFLFFRLFLLLFRRFRLFRFLLRRRFFLFLLFRFFFFFLLLRRLFLLRLLFFFFRRFLFFFLFFLLFFFRFRFFFRFFRFRLFFFLFLRRRLRFLLLRFLLFFRRFRFRFRFFFFLFLFLFFFFFRFFLLLRRFLLLRFRFFFFFFFLLFLFLFLFFLRFLFRLLFFFFRLFRFFLLFFLFLLRFRRLFFRFFRFFRFFLLLFFFFLLLFRRLFRFLLRLRFLLFLRFRFFFFLFLFLRFFLLLLLRRRLFRFFFLFRFRLLFRFFLRFFLFFFFFLRFRFFFFRLFLFRLRRRFLRFFFFLFRRRRFRFFLLRRFRFFRFFFLLRFFFLFLLLFRFLRLRFLRFFRFRFLRRFRFLLRFFLLRLRFFFRLFFFRFLRRRLRRFFLRFLLLLFFFLFRLRLRLLLRFFLFRRFRRLRFRFRLLLFRFFLFLFFLFLFLFFRLRFRFFLLLLRFFLFRFLFLRRRRRFFFFFLFRFRFLLRFRFLFFFFFLRLFLFLFFRLFFFLRRFLRFLFFFFRLFRFLLRFFRFFRFLRFFLLFFRLLRFFLLRRRLFLLFFFLLFFFRRLLRFLFFLLLLFFFFRFFRFRFRLFFFRLRFRLFFFRLLRFFFFFFFFFRLLFFFRRFFRFRFRRFRLFRLLRFRRLRFRFRFFFLFFFFRRFFFLRFRLFRFFFRFRFFLFFFRLLFRRRRFRLFFFFFRFFL\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(\"w1 = '{}\".format(w1))\n",
-    "print(\"w2 = '{}\".format(w2))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 84,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def wander_near(locus, current, limit=10):\n",
-    "    valid_proposal = False\n",
-    "    while not valid_proposal:\n",
-    "        s = random.choice('FFFRL')\n",
-    "        if s == 'F':\n",
-    "            proposed = advance(current, current.dir)\n",
-    "        elif s == 'L':\n",
-    "            proposed = advance(current, turn_left(current.dir))\n",
-    "        elif s == 'R':\n",
-    "            proposed = advance(current, turn_right(current.dir))\n",
-    "        if abs(proposed.x - locus.x) < limit and abs(proposed.y - locus.y) < limit:\n",
-    "            valid_proposal = True\n",
-    "#     print('At {} going to {} by step {} to {}'.format(current, locus, s, proposed))\n",
-    "    return s, proposed"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 85,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def seek(goal, current):\n",
-    "    dx = current.x - goal.x\n",
-    "    dy = current.y - goal.y\n",
-    "\n",
-    "    if dx < 0 and abs(dx) > abs(dy): # to the left\n",
-    "        side = 'left'\n",
-    "        if current.dir == Direction.RIGHT:\n",
-    "            s = 'F'\n",
-    "        elif current.dir == Direction.UP:\n",
-    "            s = 'R'\n",
-    "        else:\n",
-    "            s = 'L'\n",
-    "    elif dx > 0 and abs(dx) > abs(dy): # to the right\n",
-    "        side = 'right'\n",
-    "        if current.dir == Direction.LEFT:\n",
-    "            s = 'F'\n",
-    "        elif current.dir == Direction.UP:\n",
-    "            s = 'L'\n",
-    "        else:\n",
-    "            s = 'R'\n",
-    "    elif dy > 0 and abs(dx) <= abs(dy): # above\n",
-    "        side = 'above'\n",
-    "        if current.dir == Direction.DOWN:\n",
-    "            s = 'F'\n",
-    "        elif current.dir == Direction.RIGHT:\n",
-    "            s = 'R'\n",
-    "        else:\n",
-    "            s = 'L'\n",
-    "    else: # below\n",
-    "        side = 'below'\n",
-    "        if current.dir == Direction.UP:\n",
-    "            s = 'F'\n",
-    "        elif current.dir == Direction.LEFT:\n",
-    "            s = 'R'\n",
-    "        else:\n",
-    "            s = 'L'\n",
-    "    if s == 'F':\n",
-    "        proposed = advance(current, current.dir)\n",
-    "    elif s == 'L':\n",
-    "        proposed = advance(current, turn_left(current.dir))\n",
-    "    elif s == 'R':\n",
-    "        proposed = advance(current, turn_right(current.dir))\n",
-    "        \n",
-    "#     print('At {} going to {}, currently {},  by step {} to {}'.format(current, goal, side, s, proposed))\n",
-    "\n",
-    "    return s, proposed"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 124,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def guided_walk(loci, locus_limit=5, wander_limit=10, seek_step_limit=20, return_anyway=False):\n",
-    "    trail = ''\n",
-    "    current = Step(0, 0, Direction.RIGHT)    \n",
-    "    l = 0\n",
-    "    finished = False\n",
-    "    while not finished:\n",
-    "        if abs(current.x - loci[l].x) < locus_limit and abs(current.y - loci[l].y) < locus_limit:\n",
-    "            l += 1\n",
-    "            if l == len(loci) - 1:\n",
-    "                finished = True\n",
-    "        s, proposed = wander_near(loci[l], current, limit=wander_limit)\n",
-    "        trail += s\n",
-    "        current = proposed\n",
-    "#     print('!! Finished loci')\n",
-    "    seek_steps = 0\n",
-    "    while not (current.x == loci[l].x and current.y == loci[l].y) and seek_steps < seek_step_limit:\n",
-    "#         error = max(abs(current.x - loci[l].x), abs(current.y - loci[l].y))\n",
-    "#         s, proposed = wander_near(loci[l], current, limit=error+1)\n",
-    "        s, proposed = seek(loci[l], current)\n",
-    "        trail += s\n",
-    "        current = proposed\n",
-    "        seek_steps += 1\n",
-    "    if seek_steps >= seek_step_limit and not return_anyway:\n",
-    "        return ''\n",
-    "    else:\n",
-    "        return trail"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 87,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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FIBNJl6SFQEV+muMwZFu3buWGG25QGDKRAEKHIVsFPOHufxk9LykEWfRehSETqYDQYcgs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\nEKlyKgREqpwKAZEqp0JApMr9P8nYgJi0MFyGAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10342c3b00>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "def square_tour(a=80):\n",
-    "    \"a is width of square\"\n",
-    "    return ('F' * a + 'L') * 4\n",
-    "\n",
-    "plot_trace(trace_tour(square_tour()))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 88,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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k6yMEKDzGmzHGPSUtKopIo4g8KSJxEXlbRG4WkWYReU5E+kXkuIg0rvT+6urqghdbGGPc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\nybOEYIzJ+/+3mLJIMXCXRQAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10345c7fd0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "def cross_tour(a=50, b=40):\n",
-    "    \"a is width of cross arm, b is length of cross arm\"\n",
-    "    return ('F' *  a + 'L' + 'F' * b + 'R' + 'F' * b + 'L') * 4\n",
-    "\n",
-    "plot_trace(trace_tour(cross_tour()))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 90,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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Ukpa9WWhgqFF+bEHHGFQ509PTzM7Out0MR2hgqJGOMahqqqVkbyYaGJRySDgcrno7c7PQ\nwKCUQ5aWlpibm3O7GY7QwFAjHWNQ1czPz5NOp91uhiM0MFwiHWNQ5egYg1KqRDgcZvfu3W43wxEa\nGJRyyMLCQtPkYqhGA0ON8ocQOsagykmn09tmGgQNDDXKBwQdY1DlBAIBt5vgGA0MNdKAoKoJhUI6\nxrDT6OlKVU0qlWJ0dNTtZjhCA0ON9JJoVc3q6qrbTXCMU1PUhUTkuyIyIiJPi8j1ItInIiesKep+\nKiKV58RSqsl1dXXR2upItkTXOdVj+BLwkDHmSuCPgGfIJYN92Jqi7hRwl0PrUsqTgsEgAwMDbjfD\nEU7MXdkNvNYY8w0AY8y6MSZFbhKaB61iDwK32V2XF+gYgypnZmZG08cXOAhMicg3ROQJEfmaiHQA\nMWNMAsAYMwFsi1CqYwyqnO1yDQM4kz6+FXgl8D5jzK9E5H5yhxE1f4PuueeejcdenaJOewqqmt7e\nXrq6utxuRlmFU9RV48QUdTHg/xpjDlrP/4RcYDgEHDPGJEQkDjxijUEUv78ppqhbXV0lEAjoFHWq\nrLe97W089thjJBIJt5tSk7pOUWcdLpwXkSPWovwUdceBO61lOkWd2va2U/p4p86tfAD4poi0AS8A\n7wZagO+IyHvIzW/59grv97zC6xg0OKitbKf9wqkp6n4D/IstXrrRifq9YDv90VV9hMNhPV250zTD\nOIhyVyaTYX193e1mOEIDQ430XglVzczMjKaP32n0XglVjaZ2U0qV6OvrY3Bw0O1mOEIDg1IOWVlZ\nIZVKud0MR2hgqJGOMahqUqmUpo/fqXSMQZXj9/vdboJjNDAo5ZC+vj5N7aaU2mxxcVHTx+80mj5e\nVbO4uLhtbr3WwFAjTR+vqtH08TuQBgRVjaaP34H0dKWqRtPH70B6SbSqRtPHK6VKdHV10dLS4nYz\nHKGBQSmHBINBYrGY281whAaGS6RjDKqc2dlZvY5hp9IxBlVOJpNxuwmOcSwwiIjPmlfiuPV8v4ic\ntqao+5aINPXcXdpTUNV4PX38pXCyx/BBYLjg+ReAe60p6uaAv3RwXUp5js/no7Oz0+1mOMKpSW13\nA28C/mvB4tcD37cePwi81Yl1uU17DqqcmZmZpplTohqnegz3Ax/Fmn1KRCLArDEmf+H4KLDLoXW5\nQq9jUNVspx8N28f9IvJnQMIY86SIHMsvtv4VKvuN0inq1HYQDofp7+93uxllNXqKuv8EvAtYB9qB\nbuAfgTcCcWNMVkRuAO42xty6xfubYoq6lZUVgsGgTlGnynrrW9/Ko48+yvT0tNtNqUm9p6j7pDFm\nrzV35TuAU8aYdwGP8PLsU00/RZ3eK6GqmZ6eZmZmxu1mOKKe1zF8AviwiPweCANfr+O66k7HGFQ1\n2ym1m6PXFhhjfg783Hr8InC9k/Ur5WXhcFjTxyulNlteXtb08TuNjjGoajR9/A6mYwyqHJ2iTilV\nIhKJcNlll7ndDEdoYFDKIRcvXmRiYsLtZjhCA0ONNH28qiadTm+bW681MNRI08erarbTdQwaGGqk\nAUFV09vbq+njdxo9Xamq0fTxO5BeEq2q0fTxSqkSnZ2dmj5eKbVZe3u7po/fqXSMQZWj6eN3MB1j\nUOVks9nqhZqEBoYaaU9BVdPT06NZopVSm7W0tOi8EjuV9hxUOZo+fgfS6xhUNdvpR8N2YBCR3SJy\nSkSGReS3IvIBa3mfiJywpqj7qYiE7DfXPdvpj67qIxwOE4lE3G6GI5zoMawDHzbGXAX8MfA+EbmC\nXDLYh60p6k4BdzmwLtdoT0FVk8lkts1+4kT6+AljzJPW4wVgBNgNvIXc1HRY/99md11u0nslVDUz\nMzPbJn28o1miRWQ/cC1wGogZYxKQCx4iMlDufel0moWFhXwdGGPIZrObLi/NZDK0trZuTPiSfz1/\n7tgYg4hsvD//vKh9NdVd+Dxf99ra2qb1KFWstTX3dUomkxv7qM/nK+lFbPVafp8sfp5XWL5c3fn9\nslrdQNUZsxwLDCLSBXwP+KAxZkFEau5TbZdzv2pnu/nmmzl16lRTXBZdLQWd7SnqAESkFfjfwI+N\nMV+ylo0Ax4wxCRGJA48YY67c4r0GYHR0dNvky1PKy2644QYuXLjA6Oho/aaos/wdMJwPCpbjwJ3W\n46pT1G2XQRulvC6RSFTNG+HE6crXAP8OeL2I/FpEnhCRW4AvADeJyLPAjcDnKzbEp5dUKNUIHR0d\nBIPBimVsjzEYY34BlLsJ/cZLqMduU5RSNYjFYhhjGBkZKVvGMz/TOtKvVGOkUimmpqYqlvFMYNhO\nt6wq5WVzc3NMTk5WLOOZwKA9BqUao729vepdoBoYlNphotEoe/bsqVhGA4NSO8zU1BTj4+MVy3gm\nMKyvr7vdBKV2hHQ6zdzcXMUyngkM2yXttlJeFwqFqt4r4ZnAoJRqjJ6enuYJDDrGoFRjJJNJzp07\nV7GMZwKDjjEo1Rirq6uk0+mKZTwTGHSMQanGiEQiVe9k9kxg0HsllGqMQCBQNQeKZwKDjjEo1RgT\nExO88MILFct4JjBkMhm3m6DUjpDNZqt+3zwTGDQfg1KNMTg4yIEDByqW8cy3UQ8llGqMWu5kdjRL\ntFLK+8bGxnjxxRcrlvFMj0HzMSjVGH6/fyPVfTl1DwwicouIPCMivxeRj5dtiI4xKNUQ8XicgwcP\nVixT12+jiPiAvwVuBq4G3mlNX1dCr2NQqjGWl5ddv/LxOuCMMeasMWYN+Da5qetKaGBQqjEakj6+\nisuA8wXPR61lpQ3RQ4kS+WCZn3Kv8LHTz7d73epl7e3t9U8fX8VW5yC3/CvpH28zPX3rnJtuuokT\nJ0643QzPiMfjABXTx9c7MIwCewue7wbGtip433330d3dzbFjxzh27Fidm9Uczp8/z8DAy3MB5yfl\nLX5eGES2er3weaFKZbd6z6XWXdg+t+p+1atexalTp0pe34mGhoYYGhpiZGSE+fn5imUdmbuybOUi\nLcCzwBuAceBx4J3GmJGCMgZyX4Ldu3fXrS3NRkRIJBJEo1G3m9LUDh8+zHPPPac90gKHDh3auFei\n3NyVde0xGGMyIvJ+4AS58YyvFwaFQtp1LqWfiX2Dg4OsrKy43QxPyaePX1hYKFum7lc+GmN+Ahyt\nVk6/BKoeWltbaWtrc7sZnhKNRslmszpFXbPSq0HtSyaTVW8x3mk0fXyT01O49unt/KVqSR/vmZuo\nNLVbKR0wsy8ej+sYQ5F8luhKE9t65idJvwSl9PDKvmw2q73RIk01r4T2GEppN9i+ZDLJ+fPnqxfc\nQRKJRPOkj19bW3O7CZ6jwdK+1tZW/RyLrK2tVb2JSscYPEwPr+yLRqM6xlAkEomwtLTEhQsXypbx\nTI9BqXpYWloilUq53QxPaar08aqUXsdg3+zsLMlk0u1meIqmj29y1dJvqeoCgQDt7e1uN8NTakkf\n75k9T8cYSukYg30DAwMsLS253QxPicfjZDKZiglhPdNjUKU0MNg3OzvLxMSE283wlOJb9beigcHD\nNDDYt7CwUDX3wE4zPj7ePGMMOtBWSu+VsK+7u5tQKOR2MzyltbXV/fTxtdIvgaqH3t7ejVRmKmdw\ncNDd9PGXQrvNqh6SySQvvfSS283wlOXl5aoDshoYPEwPr+xbXl7WKx+LJBKJqvePeCYw6KFEKf1M\n7AuHw5o3s0gt6eNt7Xki8tciMiIiT4rI90Wkp+C1u0TkjPX6G6vVpT2GUvqZ2NfZ2Ulvb6/bzfCU\neDzOgQMHKpax+5N0ArjaGHMtcAa4C0BErgL+HLgSuBX4ilQ5caq5B0rpZ2JfIpHg+eefd7sZnjI/\nP8/09HTFMrYCgzHmYWNM/kD4NLl5IwDeDHzbGLNujHmJXNC4rlJdejxdSnsM9i0vL+vl9kVquX/E\nyYPY9wAPWY+Lp6a7QJmp6fL017GUfib2DQ4O6nwlRfLp4yupeq+EiJwEYoWLyE0z9yljzI+sMp8C\n1owx3yooU6ziz59+CUppj8G+1tZW/H6/283wlGg0ijGG4eHhsmWqBgZjzE2VXheRO4A3Aa8vWDwK\n7Cl4XnZqurx7771Xp6grooHBPk0f/7L8FHVPP/101RwVtqaoE5FbgHuBf2WMmS5YfhXwTeB6cocQ\nJ4HDZouV5aeoO3fuHHv27Cl+eccSEZLJ5Ka5K9Wlu/LKK3nmmWc0yBZoxBR1DwB+4KR1KHDaGPNe\nY8ywiHwHGAbWgPduFRQK6W3XpXRntk/Tx5cKhUJEIpGKZyZsBQZjzOEKr30O+Nwl1GWnKduSjrvY\nZ4zR9PFFQqEQAwMDFQODZy6t0x5DKT3NZp+mjy+VTCY1fXwz02Bpn8/n00vLi6yurjZP+nj945XS\nwyv7YrGYjjEUiUQipNNpxsbKnyj0zLdRj6dVPSwvL2sGpyKBQKDqBU6eCQyqlF4mbt/MzIymjy8y\nMTFRMREseCgw6MhxKU0fb18gEKh6i/FOU8uZGs/sefolKKU9Bvs0fXypWCzG+vp6c6SP14E2VQ+a\nPn5r1Qb7PRMY7A4+Dg0NOdMQD63LGLMtt6uR62p0+vhm+AzHxsaq5qjwTP99fHycTCaDz+dDRBAR\n1tfXaWlpwRiDz+djbW2N1tbWjQkzstnsRtnjx49z+PDhjQCTzWbx+Xwb781kMhtly9Xd0tJS8v78\n4/z7AI4fP86RI0f+4LozmczG63lbrdfn8zE0NNSwm8q247q6u7vx+/2MjY2V/bwL/7bF+836+vqm\nfbJwHyx+3Rizad/I76d/SN0isun7kK8v/35jDD/60Y829vnC/Sa/D5b7LkHuGpmKF9DlV+LWP3K3\nY+u/Lf4tLi6au+++2zTKdlzX+9//ftf/jl78d9tttxnAmDLfS08cSpRr3KX8u/vuuxsWzBq1ro6O\nDrf/NE3vgQce2Jb7ht11/eAHP6j4udm67doJ+duulVKNZ8rcdu16YFBKeY8nDiWUUt6igUEpVWJb\nBAYR+YiIZEUkXLDsb6wJb54UkWsdWIdjk+vUuL5bROQZEfm9iHzciToL6t4tIqdEZFhEfisiH7CW\n94nICRF5VkR+KiKOTRMtIj4ReUJEjlvP94vIaWtd3xIRR06di0hIRL5r/S2eFpHr67VdIvIhEfmd\niDwlIt8UEb+T2yUiXxeRhIg8VbCs7LY4us83agS1Xv/IJZr9CfAiELaW3Qr8H+vx9eRSztldz42A\nz3r8eeBz1uOrgF+TuyZkP/Ac1tiNjXX5rHr2AW3Ak8AVDn5mceBa63EX8CxwBfAF4GPW8o8Dn3dw\nnR8C/idw3Hr+D8Dbrcf/Bfgrh9bz34B3W49bgVA9tgvYBbwA+Au25w4ntwv4E+Ba4KmCZVtui9P7\nvCN/dDf/Ad8FrikKDF8F/k1BmREg5uA6bwP+h/X4E8DHC177MXC9zfpvAH5c8HzTOurwGf6jFfie\nyX9OVvB4xqH6d5NLCHysIDBMFgTaG4CfOLCebuD5LZY7vl1WYDgL9FkB6DhwE5B0crvI/TgUBobi\nbRmxHju6zzf1oYSI/GvgvDHmt0UvXfKEN5fI1uQ6NSiuc9SBOrckIvvJ/SqdJrcjJQCMMROAUymq\n7wc+Su7iGkQkAsyal2cxGyX3RbPrIDAlIt+wDlu+JiId1GG7jDFj5DKknyP3N08BTwBzddiuQtGi\nbcnP2OvofuiZS6LLqTDhzaeBT5KL0iVv22JZ1fOyjZpcpwb1qLN0JSJdwPeADxpjFupxTYmI/BmQ\nMMY8KSLH8osp3UYn1t0KvBJ4nzHmVyJyP7neVj22qxd4C7lf9BS5nuutWxRt1PUAju4zng8MpsyE\nNyLyz8gd0/9Gchej7waeEJHr+AMmvKm0roJ13oEDk+vUYBTY63Cdm1iDYt8jd0j0Q2txQkRixpiE\niMTJdYvteg3wZhF5E9BOrrv/n4GQiPisX1entm+UXA/yV9bz75MLDPXYrhuBF4wxMwAi8gPgXwK9\nddiuQuW2xdH9sGkPJYwxvzPGxI0xB40xB8h9MP/cGJMkd7z3FwAicgO57l3CzvokN7nOx4A3G2MK\nkwgeB95hjUgfAC4HHrezLuD/AZeLyD4R8QPvsNbjpL8Dho0xXypYdhy403p8B/DD4jddKmPMJ40x\ne40xB8khgmMMAAAA+ElEQVRtxyljzLuAR4C3O7yuBHBeRI5Yi94APE0dtovcIcQNIhK0fpjy63J6\nu4p7V4XbcmdB/c7u83YHYbzyj9wIcbjg+d+SG9n/DfBKB+o/Q26w6Qnr31cKXrvLWtcI8EaHtucW\ncmcLzgCfcPizeg2QIXe249fW9twChIGHrfWeBHodXu+f8vLg4wHgn4DfkxvJb3NoHX9ELrA+Cfwv\ncmcl6rJdwN3W3/wp4EFyZ5Ac2y7g78n96q+QC0TvJjfYueW2OLnP6yXRSqkSTXsooZSqHw0MSqkS\nGhiUUiU0MCilSmhgUEqV0MCglCqhgUEpVUIDg1KqxP8Hcqx+SW6w/jsAAAAASUVORK5CYII=\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10346c3cf8>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "def quincunx_tour(a=60, b=30, c=50):\n",
-    "    \"a is length of indent, b is indent/outdent distance, c is outdent outer length\"\n",
-    "    return ('F' * a + 'R' + 'F' * b + 'L' + 'F' * c + 'L' + 'F' * c + 'L' + 'F' * b + 'R') * 4\n",
-    "plot_trace(trace_tour(quincunx_tour()))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 91,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10346ee208>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(('F' * 10 + 'R' + 'F' * 5 + 'L' + 'F' * 10 + 'L' + 'F' * 10 + 'L' + 'F' * 5 + 'R') * 4))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 92,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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ZZ57hwIED7Nu3r84N3FRGpzCGuczMTFJSUjx/7Pv27aN79+6WU6lgVv6cyBEj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\nVBW0UCqlVBW0UCqlVBX+P0VFnoIKajtRAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10341de518>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "heart_points = [Step(60, 50, Direction.UP), Step(50, 90, Direction.UP),\n",
-    "                Step(20, 70, Direction.UP), \n",
-    "                Step(-40, 90, Direction.UP), Step(-60, 80, Direction.UP), \n",
-    "                Step(0, 0, Direction.RIGHT)]\n",
-    "\n",
-    "heart_tour = ''\n",
-    "current = Step(0, 0, Direction.RIGHT)\n",
-    "\n",
-    "for hp in heart_points:\n",
-    "    while not (current.x == hp.x and current.y == hp.y):\n",
-    "        s, proposed = seek(hp, current)\n",
-    "        heart_tour += s\n",
-    "        current = proposed\n",
-    "\n",
-    "plot_trace(trace_tour(heart_tour))\n",
-    "\n",
-    "def heart_tour_func(): return heart_tour"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 93,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'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'"
-      ]
-     },
-     "execution_count": 93,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# lc = trace_tour(('F' * 50 + 'L') * 4)\n",
-    "# lc = trace_tour(('F' * 50 + 'L' + 'F' * 20 + 'R' + 'F' * 20 + 'L') * 4)\n",
-    "# lc = trace_tour(('F' * 60 + 'R' + 'F' * 30 + 'L' + 'F' * 60 + 'L' + 'F' * 60 + 'L' + 'F' * 30 + 'R') * 4)\n",
-    "lc = trace_tour(heart_tour)\n",
-    "rw = guided_walk(lc, wander_limit=8)\n",
-    "rw"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 94,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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A0caxrWrln376qZnmb8/UHZPJ1KxszZGYM6NirZUxY8aM9r1anEBrsircR1M3E1s0vv/a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\n0guCoKWIpBcEQUvxN5buseIr1WPNAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10339959b0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(rw))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 95,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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wy84dlknySA6HY8DH8GeL2S9+8QsAtm/f3uW4drud1tZWysrKOHDgAFlZWcyd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\nUimleqBJUimleqBJUimlevD/A80VXGG6+r+KAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f103350d470>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "rw_trimmed = trim_all_loops(rw)\n",
-    "plot_trace(trace_tour(rw_trimmed))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 96,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "764"
-      ]
-     },
-     "execution_count": 96,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "len(rw_trimmed)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 97,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(284, 22, 'FFRRLLRRFFFFFRFFFRFFRL')"
-      ]
-     },
-     "execution_count": 97,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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HP/xh7CidMpmMnn76ad18882xo3zMSy+9pGuvvVYfffRR7CidkrCf33///aqoqJAklZeX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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10346f29b0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "lc = trace_tour(square_tour(a=10))\n",
-    "rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
-    "rw_trimmed = trim_all_loops(rw)\n",
-    "plot_trace(trace_tour(rw_trimmed))\n",
-    "len(rw), len(rw_trimmed), rw_trimmed"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 98,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# success_count = 0\n",
-    "# while success_count <= 20:\n",
-    "#     lc = trace_tour(square_tour(a=10))\n",
-    "#     rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
-    "#     if rw:\n",
-    "#         rw_trimmed = trim_all_loops(rw)\n",
-    "#         if len(rw_trimmed) > 10:\n",
-    "#             with open('small-squares.txt', 'a') as f:\n",
-    "#                 f.write(rw_trimmed + '\\n')\n",
-    "#                 success_count += 1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 99,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# success_count = 0\n",
-    "# while success_count <= 20:\n",
-    "#     lc = trace_tour(square_tour())\n",
-    "#     rw = guided_walk(lc)\n",
-    "#     if rw:\n",
-    "#         rw_trimmed = trim_all_loops(rw)\n",
-    "#         if len(rw_trimmed) > 10:\n",
-    "#             with open('large-squares.txt', 'a') as f:\n",
-    "#                 f.write(rw_trimmed + '\\n')\n",
-    "#                 success_count += 1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 100,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# success_count = 0\n",
-    "# while success_count <= 20:\n",
-    "#     lc = trace_tour(cross_tour())\n",
-    "#     rw = guided_walk(lc)\n",
-    "#     if rw:\n",
-    "#         rw_trimmed = trim_all_loops(rw)\n",
-    "#         if len(rw_trimmed) > 10:\n",
-    "#             with open('cross.txt', 'a') as f:\n",
-    "#                 f.write(rw_trimmed + '\\n')\n",
-    "#                 success_count += 1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 101,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# success_count = 0\n",
-    "# while success_count <= 20:\n",
-    "#     lc = trace_tour(quincunx_tour())\n",
-    "#     rw = guided_walk(lc)\n",
-    "#     if rw:\n",
-    "#         rw_trimmed = trim_all_loops(rw)\n",
-    "#         if len(rw_trimmed) > 10:\n",
-    "#             with open('quincunx.txt', 'a') as f:\n",
-    "#                 f.write(rw_trimmed + '\\n')\n",
-    "#                 success_count += 1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 102,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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HP/xh7CidMpmMnn76ad18882xo3zMSy+9pGuvvVYfffRR7CidkrCf33///aqoqJAklZeX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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10342e2390>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(rw_trimmed), filename='test.png')"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 103,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
-    "# tours_filename = 'tours.txt'\n",
-    "\n",
-    "# try:\n",
-    "#     os.remove(tours_filename)\n",
-    "# except OSError:\n",
-    "#     pass\n",
-    "\n",
-    "# success_count = 0\n",
-    "# while success_count < 100:\n",
-    "#     lc = trace_tour(random.choice(patterns)())\n",
-    "#     rw = guided_walk(lc)\n",
-    "#     if rw:\n",
-    "#         rw_trimmed = trim_all_loops(rw)\n",
-    "#         if len(rw_trimmed) > 10:\n",
-    "#             with open(tours_filename, 'a') as f:\n",
-    "#                 f.write(rw_trimmed + '\\n')\n",
-    "#                 success_count += 1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 104,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Found mistakes: 1916\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "(5540, 14, 'LFFFFLLRLFFLRL')"
-      ]
-     },
-     "execution_count": 104,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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23wCPFrOWvH0uBe7p4L44FRgFrCpw+9nAb5PtU4ClneWox46g7t6Yd/EbQLad3c4CFrn7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\nx0SoEAAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1033d81390>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "lc = trace_tour(cross_tour())\n",
-    "rw = guided_walk(lc)\n",
-    "print('Found mistakes:', len(mistake_positions(trace_tour(rw))))\n",
-    "rw_trimmed = trim_all_loops(rw)\n",
-    "plot_trace(trace_tour(rw_trimmed))\n",
-    "len(rw), len(rw_trimmed), rw_trimmed"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 105,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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GjEBoaCjefPNNvk9wr1gVioqKUFBQgClTpsBgMMDNzQ1OTk6SZ/nyyy/j1q1b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\nQmCC\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f103402bef0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(rw))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 106,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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23wCPFrOWvH0uBe7p4L44FRgFrCpw+9nAb5PtU4ClneWox46g7t6Yd/EbQLad3c4CFrn7\ndnf/jFwb8QnJ+GfdvXXMUmBYgVJGO88ERY4v+B1PXfgQolD9YsZ39B1T5wO/TrZ/DVzQQf3O5mqV\nP+dj5L5XoJi1tFdvL+7+MvBpoduT+X6T7PsaMNDMajvYv2ffqDezfzazDcAPgZvb2WUo8GHe5Y3J\ndW39GCh0AubAM2a2zMyuLLBPofFt639UoH5HiqlfSEf1D3b3LQDuvhk4qMAc1clLi3/n63/P9n6X\nPfXcfTfwmZkNLmIt+S5Mnp7nm1mhg0Yhxf699yjpbabO3sR395uAm5LXM9cAt7SZYjLwTTP7QXL5\nYCBrZu958iGAmf0c+NLd5xao3wxUARXAPUmtfyxmPLkHzbDkq3Qg95Kjv5kt9iI+hCimficK1X+2\niLGtvuXum83sJ8AsMxvu7u8nt7U9A2579LO8fYr5vqsngbnu/qWZTSZ3ND5z72EFFf2dWq1KCqi7\njy9y13nAb9k7oDcDY939HwDM7H7g+bxwXQqcA3ynmPpmNgPYUex4cg+Q9r7jqahPyDqrX4RC9Z9M\nTjZq3X1LcoL5xwJr2JxsLgc+B04A3if3kmZTm90/BA4DNlnu64MGuHvrU/JHQP5J017j8/YFeIjc\n6+Su+CipX7DGXjp7kdrdH+DIvO1rgPnt7JN/ktS6PSi5bQLwB+DADmrUkJyMkXud+3vge10YX8FX\nJwZV5E4MRrTZ53lgdFfrFzm+YH1yf/zp3sFJErkTy6pk+2Dg/8g9GAv9Lj/hq5OkH/D1k6Ri7otD\n8ra/D7zSzpqOAFYX+H3P4auTpHqKOEnqyYA+BqxKftEngEOT60cDD+bt9/fAe8Ba4Ed5178HrCd3\nZFied8ceCixItocn868g90//ru/K+Lwgv5vsnz/+AnJHnCZyX1D2dBfrdzq+k/qDgWeT2xbz1QN3\nz/0HjEnu4xXASuDutnMBM4G/TLargfnJ7UuBI9r8zfZaS5vxvwDeSur9N3BUm/FzyR0RW4ANwGXk\nniUm5e0zm9wDYSUdvDvS+qM36iVq+ud2EjUFVKKmgErUFFCJmgIqUVNAJWoKqERNAZWo/T9ydJit\nx0SoEAAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1034757358>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plot_trace(trace_tour(trim_all_loops(rw)))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 108,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[Mistake(i=9, step=Step(x=0, y=5, dir=<Direction.RIGHT: 2>)), Mistake(i=29, step=Step(x=5, y=6, dir=<Direction.DOWN: 3>)), Mistake(i=33, step=Step(x=5, y=2, dir=<Direction.DOWN: 3>))]\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "'LFFFFRFFRFFLFFLFFFLFFRRFRFFFFFFFFFFFRFRLRRLLRFFFFRFLFFLLFLRFFFFFLFFFFFLFFLFRLFRFRLFFFFLLFFFFLFFFRLFRRFFFLFFFFFFFFFLFLRFFFRLRLLFRRFLLFFFLFFFFFRLFFFRRLFFFLLFFLRLFLFLRFRFFFFLFFFRRFFLLLFLLLRLFFFFFLLFFFFFFLFFLRLLFFFRRLFLLLFRRFLFLLFFRFFLFFRFFFFFFFFFFFFFRFRRRRRFFRRRFFFLRRFLRFFFLLFFLRFLFLFFFLFFFLFLFRFFFFFRLFFFFFLFFLFFRRRRFLFFFFFFFFFFFFLFFFFLFRFLLLFFRRFFLLFFLFFLFFFFFFRRFFRLFLLFFFFFFLFFLLFFRFRRLLFRFFRRFLRLFLLFFFRFRFFFFFFFFFFFFFFFFRFFFFRFLFFFFFFFRFFLFFFFRRFFFLLFRFFFRRFFFFRRFFFFFFLLFLFFFFLRRLLFRFFLRFRFLFFFFRRRFFFRRFFRRRRRRFLRRFRFRFRFLFFFFLLLLFFLRRRFFFFFFRFFRFFLLFFFRFFRRFFFLFFFFFLFLFFFFLFLLFFFFFRFFLLFFFLFRFFLLRLFFFFFFLFFLRRLFFRFFFLLFLFFFRRFRRFRFFRFFRFRRRFFRFFFRFRRLRFFFFLFLFFFRFFFFFFFFRFFRFFFRLFRFRFRRRRFRFLRFFFLRLRFRFLFFFFFFLRRFFLLFFFLFLFFFFRFRFRFFLFFRRFFFFFRLRFFFFFRFFFFRFFFFFRFFLLFFRFFLRRLFLFLFFFFFFFFFFFLFFFFFRFFLRLFLLFFFRFRFFFRFFRFFRFLFFLRFFRRLRRFFLLRRLFFFLFFFFFFFRRRLRFFLFRFFRLFRFFRFFFFFLFFFFLFFFFLFFFRRFRFRFLFLFRFFLFFLRFRFFFFRFFFFLFLFFFRRRLFLFFLFRFRFFLFLFFLFLFLLFFFFFFLFFFRFFFLFFRFFFFRFFFLLFLFFRFRFFRFRFFFFFFFFLLLFFLFFFLFFFFFLFRRFFFFLFFFFRRRFRFRFFLLFRFLFRLFLLLRFFLFFLFFFFFRRLFFLFFFFRRFFFLFRFRRRRFRLFLFRFFFLFLRFFFFLFLFLRFFLFRFRFRFLFLFLFRFLRFFRFRLFFFRFLLFFRRFFFFFFFRLFLLFLFFFLFRLRRFFFFLFFLLRFFLFRRRFLFLLFFFFFFLFFLLLFFFFFFLLRRFRFFFRRFLLFFFLLFFFFFRFRRLFFFFLRRLRRFFLRRFFFLFLFFFFLRLFLLRFFRFRFRFRFFLLRRLRLRFRFFFFFFFFFFFFFFFRFFLFRRFFRFFFLRLLLRRFFLFRFRRLFRFRFFRFFFRLFFFRRLFRFFFFRFFFRFFFFFRFFFRLLFFRLFRFFFRFRRRRFFFRRLLFFLFFFFFFFFRFFFRFFFLFFLFFFFFFFFLFLFFRFFFFFFRFFRFFFFLLLLFFFFLLLFRFLFRFRFFFRFFFLRFFRRLFFLFLLRFFRRRLLRFRFRFLFFFFLRRLRRLLFFFFFFRFFRRRFFLFFFFFLFFFFLRFFRLFFFLFFLFLFFLFFFLFFFLLLFFFFLFFFFFLRFFFRLFFFFLFLRRRRFFRFFFLRRLFFFRFLFFLFFFFFLRRFRLFLFLLFRLFRLFLFRFRFRLLFFRFLRFFRFFLRRLRFFFLRFRFFFFFLFFRLRFFFRFRFLRFRFLFFFRRRRRLFFFFFLFFFRFLFFFLFRFFFFFFFRFLFLFLLLRRFFFFFFFFRLFLRFRFFLLLFFFLFLFFRFLFFFRRFFRLFFRLFRFRFFLRFRFFFFFFFFRFFFRLFFRFFFLFLRFFFFLFFLFFFRFFFRFFFLFLLLLFLFFFLFLFFRFLLFLFFLFRFFFFLFFFRFFFFFFFFFFFFLLFFFFFFRLLFRRRFFFFLRFFFFRFFFFRFLFRLFFRFFFLFLFRFRLFFFRRLFRFLRFFFFFFFFRLFRFFFFFRRFRFRRFLFRFRFFFLFFFFFLRRLFLRFRRFRFFRFRRFFFFFFFLFRFFFRFRRLRRFFFFFFRLLLLFRFLLFFLFFLFFFFFFFFFFFFFFFFFLFFLRFFLRFFLFRFLRRLFLFFFLFFRFLRFFFFLRFFRFFFFFFFFRFRFFFRRFFFLLFFFFFFLRFFRRFRFLFFLFLFFLFLFRFLFFFLRFFRFLLFLFRFRFFFFLLFFFFFFFFLFRRRRFFFFFFFFRFFLFFRRFRRFLFFRRFFRRFFFRRFRFRFFFFFRFFFFFRRFFRRFFLFFLFRFLRRRFFFLLFFFFFFFFFLLLFRFFFFRRFLFLFFLRRFFFFRFFLRRFLFRFFFFRLLFLLFFFFRFRFFRFLFLRFLRFLFRFLFFRRRLFFRLFLRLFRFFRFFLFLFRFFFFRFFFFFFFRFFLFRLFLLRLFFFFFFRFFFRFFFFRFFRFFFRFFRLRFFFRLFRRRRRFFRRRRRFFRLRFFRFFLRLFFLRFRRFFRFFFFRFFFFFRFFFFRFFFFFRFRFLLFRFFFFFRFLLFRFRFRFRLFFRRRRRRFFFRRFFFLLFRFRFFRRLFFLLFFFFLFFLRRRFFFFRLLFRFFRFLRRRFRLFFLLFRFFFRFFFFFRFFFFRFFRFRFFFFFFRFLFLFFFFFRRFLLFFFFFLFFLFFFLFFFLRLFFLFFFFFFFLFRFLLFLFFLFFRFFFLFFLLRLFFRFFRFRLFRFFRFFRLRFFLLFRLFFFFRFFLFFLFRRFRFFFLFFLRFRLFFLFLRFFLFLFFFFLFFFLFFFFFFFFFLFFFFFLFFFFRLRFFFFFFFFFFRRFFFFFRRRRFFLLFFLRFFFFRFFFFRFFFFLFFFRFFFFFFRLFFLFFRFFRFRFFLLRFLFLFLFFLFLFFLFLRFFFFRRRFFFRFFLFLRFLFFRRFLFLFLLFFFFRLLLLLRLRRFFRRFFLRLFFRLLFRRLFFRFLLFFFLRLFFFFFFFFFLFRLFRLFLFFFFFRLRLRFFFRFRFFFRFFFFFFRFRFFFLFLFLLRRFRFLRFRFLFRRFRLFFFFFLFLFFFFFFFFLFRFFFFFFRRFFRLFFRFLLFLRFFFFLFRFFFLFFLFLFLFFFRRFRFFLRFLFRLFFFRFFFLFFFFFFRFLFFLFFRFRFFRFFFFFFFFFFFFRFFFFFFRRRFFFRFFFFRFFFLLRFFRLRFRFFLFFFRFFLFLFFFFLLRFFRRRFRLLRRLFFFLFLLFRFFFFRFFFFRFLFFLLFFFLFFFFLFFFFLFLLFRFLFFLRLFFFFLRFRLFRFFRFFFRLFFFRFLFFLLRFRRFFFFFFFFFFFFFFFFRRFLLFFLLRLFFFFFFFFFFFFFFLRFRRFFFRRFLLRFFFRFFLFLFRLRFFFFFRFFRFFFRLRRFFFFFRRRRRLFLLFFLLFFRRFRFFFFFLFFFFLFLFFRFFLFFFFLRLLFFFLFLFFFLLFLFLFFLRRRFFFFFRLFFFRLFFFFRFRFFFFRFFLFLLFLFRRFFRRRFFFLFRFFFRFFFFFFFFRRLFFFFFFRFLLFFFFRLFFFLFFLFFRLFFLFRFFFLFFFFLLFFFRFRLRFRFFRFLFFFLLLRFFFRFFFFFFFFLRLLFRRFLRFRRRLLRFRFFLLRFFLFLLRFFFFFLLFRRRRRRFFFFFRFFRRFLFFFFFRLFFFLFLFFLFLLFFLFFRFFRRRFFLRRRFLFFRFFFFFLFFLLFFRFRRRFFRFRRFRFRFFLRFRFFRRFRFFFRFFLFRFLRFFLFFRLRFFFFFFLRFFFFRLLLFLFLFLFLLFFLRFFRFFRFFLFFFRFFRRRFRLFLFFFLFFLFFFLFFFFFLLRLFFLFLFFFFFFFFLLFFFRRFFLRLFFFLLFLLFFFFLFFFRFFFFLFRFFRFRFRFRLLFFFLLFFFLRRFFRFRFLFLFFFLLRRRRFRRLLLRLFLFFLFFFLFFFFFFFFFLRRRFFFFRFFFRRLFFFFFFFLRFLRLFLFFFFFLFFLFFRFRRFFRRLFFFLFFFFFRLRFFLFRFFFRFFRRRRRLFFFRFFRFRRRLFFFFLFFLLFFRRRRLFLFRRFRRLFFFRFFFLLFRLLLRLFFFRFFRFFFLRRFFFFFFFFFRRRLFFFFLRFFFRRFFFFFRLFFFFRRRLFFFFRRFRLFFFFFFRLLLRLLFFFFFRFLLFFRFFFFRFRFFFLFRFFFFFFFRRRLFFLRFRLFFFFFFFFLFFFFLFRFLRLRFLFFFFFFFFFLFFLLFFFFLFLFFFFFLFFFFLFLFFFLLFFRRFFFRFFFRFFFFRLRFFLFFFFFLRFLLLFRRLLRFFFFFFFFFRFLLLFRLFFFLFRFFRFRFFFFFFFRFLLLFFFFFFLFFFFFRFRLFFFRFLRLFLFLLRFFLRFFFRFFRFFFLRFFLFFLFLFFFFRFFFFFFFFFRFLRRFFFFRRLFRFFFFFRRFRLLFFRRRLLFFRLFFFLLFFFFRFFFFFFRRFRFFLRFFRFFFFFFFFFFFFFFFFRRFLFFFRRFRFFLLFFLRLFLFFFRFFFFRFFRLFFFFFFLFFLFFRLRFFFFRFFFRRLFFFFLLFLRFFLFFFFFFFFFFFRRFRFLFLFRRFFLLFFRFRFFFFLRLRFLLRLLFRFLFRRFLFFRFRFFFRFFFFLFFFRFFRRFFFLFFFFLFFRFLLLFRRLFLRLLLFLFFLLFFFFFFRRFFLLFLLRFRFRFFRFFFFFRFFRRFLFLRFLFFRLFFFLRRRRRFFFRRFFRLFFFRFRLFRFRFLRFRLRFRRFRLFFFLFRFFLRLRFFFRFFFRFFFFFFFFRFLFFFFRFFFFRFFFFLFRRFLFFFFRLLFFFFFLFLFFFRFRFLRLRRFRFLLFLFFFRRLFRFRLFFFLFRFRFLFFFFFFRRFLRRLRLFLLFFFFFFRRFRFFRLFFRFLFFLFFRFFFLFFLFFLFRFRFFFFLLRRRRFFFFFFFFLFFFFFFFFFLFLFRRFFFFRFRFFFFRFFRRFRFFFFLLLRLFFFRFFFFFFRFRLFFFLFFFFFFFFFFLRFFFRRRFRRFRFRFFFFLFLFFLRFLFFLFLFFFLFLFFFLFFFFFLFFFFFRFFFFLLRFFRFFFRFRFLLLFFFLFFFFLFFFFLRRFRFFLRLLFFFRFFFFLLLLRFFFRFFFFFFFFFFFRFRLLFFLFLFRLFFFFFFFFFFFLFFFFFFFFFFFFLRFFFFLFLFFLFLFFRRFRLRFFFFFFFLFLFFRFLRFFFFFRFRFFLLFRLFRFFRRFRLLFFRFLRFFFFRRFRFLFFLFFLFLRFFRFFRRFLLLLFLRFFFFLFFRRFRLFFFFLRFFLFFLFFLFRLFFLFRFFLFFFFLFFFFRRFLFRFFFFRFFFLFLLLRFFFFFFRFFFLLFRFFRRFRFLFFLFFRFLFFFFRFFLRFRFFRFFFLRRFLFFFLRFFLRRFLFRLFFRFFFFRLRLLLRLFFFFFFFFFLFLFFFFRFFFLLFFFFFRFRFFFFFFFLFFLRFFRFRRRLFFLLLRFRFFFLFFFLFRLRFLLFLFFFLFFLRFLFFFLFFLLFLLFRFRFLRLFFLFFFRFFFLLLFRFFFFFFFRLFFLFFLFLFFRLFFFFFRRLRLFFLRL'"
-      ]
-     },
-     "execution_count": 108,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "w_tour = rw\n",
-    "w_trace = trace_tour(w_tour)\n",
-    "mks = mistake_positions(w_trace)\n",
-    "print(mks[:3])\n",
-    "trim_loop(w_tour)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 109,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1916\n",
-      "1912\n",
-      "1909\n",
-      "1903\n",
-      "1900\n",
-      "1896\n",
-      "1894\n",
-      "1892\n",
-      "1883\n",
-      "1881\n",
-      "1878\n",
-      "1872\n",
-      "1860\n",
-      "1855\n",
-      "1854\n",
-      "1849\n",
-      "1846\n",
-      "1845\n",
-      "1839\n",
-      "1835\n",
-      "1833\n",
-      "1828\n",
-      "1825\n",
-      "1821\n",
-      "1819\n",
-      "1810\n",
-      "1800\n",
-      "1793\n",
-      "1784\n",
-      "1783\n",
-      "1763\n",
-      "1737\n",
-      "1735\n",
-      "1729\n",
-      "1719\n",
-      "1716\n",
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-      "RFFRRFFFRFFRFLLRFLFFLLLLFRRRFLFFFFRRFFFRLLLRRFLLFRLLLFRLLRFLRRLFLFFRLLRFLLFRRLLRLFRFFFLLFFLFLRRLFRLRRLRRRRFFFFFFRRRLLFFFFFFLRRRLLLRLLLLRFRLRFRRRFRLRLLRFRLFLLRFRFLRRRRLRFLLRLRRLFFFRLRRFFRFLRFLLFLFRLRLRLRRRLFFRLRRFFRRFFLLRLLFLLLFRFRFLRLFFLFRRRRLRRLRRLRFRRLRRRFRRRRLLRFLLRRFFRLRFFLFLFRRLLLRLFFFRFRLRLLFRRFLLRLFFFLLRLLRRLRFRFFFFFRRFFLFRFLRFRFLFLFRLFLFLRFFLFRLRRRLRRRRFFFRFLLRLFRFRRRLRFFFFFLLFRRLFRRFRFRFLRLLFRFFFLLRRFRRRRLFFFLFLLLFFLRRLRFLFLFFRLLFFRRFFLRLLRFLRLLFLFRLLLRFFFFFFFFLFLRLLRLRLRFLLFFFLFLFFLFRRRRRFFRLLFFFRLFFLFRLFFRFFFFRLRRRLLFLRRFLRFFLRRFRRFLRFLRRLFRRLFFFFRLFLFFLRFFFFFRLFLFLRFFFLLLFLLLFFLRRLFLFRRFRRFFRRRFFRFLFLLFLFRFRFLLLRRRLFRRFFRLRFLFLFLRRLFFFLFRLRFRFFRFLRRFFFFFLFRLRRFRLLRLLFFLLLFFLFFFRLFRFRRRRLFLFLLLLRLFRFRLRLLFLFLLLRRRLLLFRRFRLRFFRRRLLLFRLRLLFFLLRFFFFRLLRLRLLLRLFFFRRLRFRFFRRRFFFRFFFFLRFLFRFLRFRRLLLRLLFRRLFFLRRFFFRLLFRLFLRRFLRLLRRFFLLFLLLFFFFRRFFRLFFLLFLLFRFRLRFLRFFRFRLRLLLFFFLFLRFRFRFLRRLLLLLRFRRLFLLLLRRFFFLLRFLFFRLLLLFLFRLRFFFFFLRLLFFLLLFFLLRRFLRRFLRLRRLLLRRRRRLLLFLRRLFFFRFLRRLF\n",
-      "LFFFFRFFRFLRFFFFLFFFRLFFLFLRFRFFFFLFFFRRFLLFFRFFLFFRFFFFFFFFFFFFFRFRFLFFRFFFLFFFLFLFRFFFFFRLFRFFFFFFFFFLFFFFFFLFRLFFFLRLRFFRFLFFRFFFLFFLRFFFRLFLFFFFFRFLRFFFLRLRFFRLRRFFLLRRLFFFLFFFFFLFFLFRFFRLFRFFRFFFFFLFFRLFFLRFRFFFFRFFFFLFLRFFLFRFRFLLFRFFFLRFRFFLLFRFLFRRFLFFLFFFFFRRLFLRFFFFFFFLFRRLFLLRFFFFFFFRLLFFRLFRFFFRFFFFRRLLFFLFFFFFFFFRFFFRFFFLFFLFFFFFFFFFRFFFLFFFFFLFFFFFFFFRLFLRFRFLRFFFFRLLFFRFFFFFFFFFFFFFFFFLFFLRFFLRFFLFRFLRFLRFFFFFRFFFFFLFFLRFFLFRFFRFLFLRFLRFLFRFRRLFLRLFRFFRFFLFLFRFFFFRFFFLFRFLRFFFFLRLFLFRFLLFRFFRFFFFRRLLFLRFFFFFRFFLFFFRFLFLFFFFFRRFLLFRLRLFFLFFFFFFFFRRLFFFFRFFFFFLRFRLFFFLFFFFFFFFFLFFFFFLFFFFRLRFFFFFFFFFFRFFFFFRFFFFLFFFRFFFFFFRLFFRFLFFLFLRFFFLFFRFFLFLRFLFFRRFLRFFRFFLFRLFRLFLFFFFFRLRLFRFFFFFFFLFRFFLFFFFFFRFFFFFFFFLRFLLRFLFFFFFRRLFFFFFFRFFLFLFRFFFFFLRFFLRFRLFFRFFLFRRFFFLFFFRFFFRFLFFFLFFFFFLFFFRRLFFFFFFLFRRLFFFLFFFFFRLRFFLFRFFLRFFFFRFLLFFRFFFFRFRFFFLFLFFFFFFLFFFFLFRLRLLRFFFFFFFFFRRFFFFFLFFFRFFLLFFFFRFFFFLFLRFFRFFFFFFFFFFFFFFFFRRFLRLRLFLFFFRFFFFRLRFLLRRFLFLRFLFFRLFFFFFFLFLFFFFRFFFFRFFFFLFRRFLFFFFRLLFFFFFLFLFFFRFRFRLFLFFFRRLFRFRLFFFLFRFRFLRLFFFFLFRLFFRFLFFFFFFFFFFLLFRLFRFFFRFFFFFFRFRLFFFLFFFFFFFFFFFFFFFFRRFFLFFFLFFFRRLFFRFLFFFLFFFLRFFLRRFLFRLRRFFFLLFFFFFRFRFFFFFFFLFRFFFLFRRFLFFLRFLFFFLFFRLFFFFFFRRLRLFFLRL\n",
-      "Step(x=0, y=0, dir=<Direction.RIGHT: 2>)\n"
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d+BSY4WMdPnPkyBHOnDkTbDE0Gp+Ij4+v02OWq+1FZGSkz34v6sLrHoaIJACX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\nDI1G4zH/D8E8vVutsQ6KAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10540d85c0>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "w_tour = rw\n",
-    "w_trace = trace_tour(w_tour)\n",
-    "mks = mistake_positions(w_trace)\n",
-    "while len(mks) > 3:\n",
-    "    print(len(mks))\n",
-    "    w_tour = trim_loop(w_tour)\n",
-    "    w_trace = trace_tour(w_tour)\n",
-    "    mks = mistake_positions(w_trace)\n",
-    "print('{}\\n{}\\n{}'.format(w_tour_start, w_tour, trace_tour(w_tour)[-1]))\n",
-    "plot_trace(trace_tour(w_tour))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 110,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Mistake(i=1219, step=Step(x=0, y=5, dir=<Direction.DOWN: 3>))]"
-      ]
-     },
-     "execution_count": 110,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "mks"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 111,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'LFFFFLLRLFFLRL'"
-      ]
-     },
-     "execution_count": 111,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "trim_loop(w_tour)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 112,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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mrKXbR44caTx2VFSU0ccsay7I1KlTjca95ZZbgMY3lmAIu8IXQjhPCl8IF5LCF8KFpPCF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\nRK5CYII=\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1033a4ae10>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "lc = trace_tour(square_tour(a=10))\n",
-    "rw = guided_walk(lc, wander_limit=4, locus_limit=2)\n",
-    "plot_trace(trace_tour(rw))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 113,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(326,\n",
-       " 80,\n",
-       " 'RFLLRFFLFRFFLFFFRFLFRFFLRLLFLRRFFFFFLFFFFFLFRFRLFLRFFRLLFFLFFFRFFFRFFLFFRLFLRLFF',\n",
-       " [Step(x=-1, y=0, dir=<Direction.RIGHT: 2>),\n",
-       "  Step(x=0, y=0, dir=<Direction.RIGHT: 2>)])"
-      ]
-     },
-     "execution_count": 113,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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QVFTkbSHka4GALwcUpzRfBUVBQQGAXxf2IeqvoaEBAPD+++97XEn68VVQcCEfOpfYL5Kc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\nRU5ErkJggg==\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10345d82e8>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "rw_trimmed = trim_all_loops(rw)\n",
-    "plot_trace(trace_tour(rw_trimmed))\n",
-    "len(rw), len(rw_trimmed), rw_trimmed, trace_tour(rw_trimmed)[-2:]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 114,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(1, Step(x=0, y=0, dir=<Direction.RIGHT: 2>))"
-      ]
-     },
-     "execution_count": 114,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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IQAw+kYF8FfyO6+OfPHnS40qI0puvmp6PHj0KAJg1a5altt3S0lLMnz8fr7zyCrv+fOD4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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1033d95908>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "rw_trimmed = rw\n",
-    "mks = len(mistake_positions(trace_tour(rw_trimmed)))\n",
-    "while mks >= 4:\n",
-    "    rw_trimmed = trim_loop(rw_trimmed, random_mistake=True)\n",
-    "    mks = len(mistake_positions(trace_tour(rw_trimmed)))\n",
-    "    \n",
-    "# rw_trimmed = trim_all_loops(rw)\n",
-    "plot_trace(trace_tour(rw_trimmed))\n",
-    "mks, trace_tour(rw_trimmed)[-1]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 132,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "def trim_some_mistakes(tour, mistake_limit):\n",
-    "    trimmed_tour = rw\n",
-    "    mistake_count = len(mistake_positions(trace_tour(trimmed_tour)))\n",
-    "    while len(mistake_positions(trace_tour(trimmed_tour))) > mistake_limit:\n",
-    "        trimmed_tour = trim_loop(trimmed_tour, random_mistake=True)\n",
-    "    return trimmed_tour"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 116,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(3, Step(x=0, y=0, dir=<Direction.RIGHT: 2>))"
-      ]
-     },
-     "execution_count": 116,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f1034745a20>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "rw_trimmed = trim_some_mistakes(rw, 4)\n",
-    "\n",
-    "plot_trace(trace_tour(rw_trimmed))\n",
-    "len(mistake_positions(trace_tour(rw_trimmed))), trace_tour(rw_trimmed)[-1]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 117,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "# patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
-    "# tours_filename = 'tours-with-mistakes.txt'\n",
-    "\n",
-    "# try:\n",
-    "#     os.remove(tours_filename)\n",
-    "# except OSError:\n",
-    "#     pass\n",
-    "\n",
-    "# success_count = 0\n",
-    "# while success_count < 100:\n",
-    "#     lc = trace_tour(random.choice(patterns)())\n",
-    "#     rw = guided_walk(lc)\n",
-    "#     if rw:\n",
-    "#         rw_trimmed = trim_some_mistakes(rw, random.randint(0, 15) + random.randint(1, 3))\n",
-    "#         if len(rw_trimmed) > 10:\n",
-    "#             with open(tours_filename, 'a') as f:\n",
-    "#                 f.write(rw_trimmed + '\\n')\n",
-    "#                 success_count += 1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 138,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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pbQWEhISQn5/PokWLuP322xk2bBiHDx+mQ4cOHDhwAIAlS5ZgNpspKSmRdvzX\nrl3LoEGDyMnJQVEUNm/ezKBBgzwyQOOzDX/lypXs2LEDsL7JTp8+jdFoJD8/n7CwMN544w2HNOpw\ny1aHv6ysTO6McoaqEmmr/qih4YqSkhKqqqpkg1frle1ynq3efkVFBUVFRQQFBXH69GkCAgI4efIk\neXl5DkYxx40bR1hYGN999x1grZOqGa3KykoCAwN5//33+eSTTwBHdV71tzODpLXx2Yav9uju5k4W\ni4U33niDs2fPYjQa5Z9w9913YzQa5R9RWVnJ3r17Abj++utp06YNqampgFXnWo2joeEp//3vfwF4\n9dVXAcehfrt27Zg8eTL33XefR6awhgwZwnfffWdnR09FURSGDBnCddddx2+//Sbr8vLly+3yUH97\npNTmSqXPW4EGquy+/vrrdTq3sHWX3djw5z//uUHl1Li0WLRokUPdiYyMtFPZ/b//+z+7857w+9//\nXoSFhYnVq1c7pHFXb2NiYhzirF69Wh4TLc3KrrokUVpa6rI3Vm2Lubo529CuXTsAfvzxRwCys7MB\nWLFiBUIIp/7VNDRqM23aNEpKSqR/vpKSEo4dO0ZZWRklJSWUlpby2muvUVxc7NTAhivy8/PlnB+s\n9T4/P18O9fv16yfr8oQJEwBrvVfVegHefvtthBCMHj26zuv57FC/Q4cOAFKQYev1VSU6OtrOCoo7\navs8VxWAGmPRRePS45ZbbmH16tXyt1o/XXHllVd6lG9sbCyRkZGkpKQ4zdfWfXdISIhTmVR9VhZ8\ntuGPGDFCNlJXN5SbmyudFtaFOu9R81Lfnr7kHVfD9/nmm28AePrpp6UVXbUe1f4Ez9f38/PzOXPm\nDD169LCr95mZmSQmJtp1eqpb7tp4ei3wwXX8N954w6klUj8/P4fj6oYFZ0o6tYPqKEN1j6SuiToz\n16yh4YqBAwcCViu7KrW192rbzfcEdUSakZFhV+8DAwNlo7/33ntRFIV3333XqUkur/f4iqKEA28C\n3QAL8AfgIPAxkAIcA24XQhR5fGUXLFq0CLBKKNW3Z1ZWFseOHUOn00lVSfXt1q1bNzt3ybafNTU1\nWCwW/P39uffee6muruaPf/wjHTt2JDY2lkmTJnH06FE7U8gaGu745JNPWLVqFQDXXXed1/JVR6Sq\nxdzly5eTlJRkVzeXLVuGn58frVq1cupPoj49vqeS+RXApHPf/YFwYB7w2LljjwN/c5HWI6mmSteu\nXe0kloDD27TIAAAgAElEQVSIjY2Vx4qLi2XcHTt2yON6vV4AIj4+XgDCaDTKc1OnTpVukAHRunVr\nB+loRkZGvcqpoeFNRowYYVcfLRaLuOqqqxzqabdu3aSLbVts47zzzjvymHDVpl2dEOcbbihwxMnx\n/UDcue/xwH4X6ev1ALKyssS1114runfvLm688UbRs2dPcdNNN4nevXsLQPz973+XcVWnhFdccYW4\n5pprRO/evcXo0aNFz549BSB0Op18GKrf8x49eojRo0eLXr16CUCkp6cLQPzhD3+oVzk1NLxJXl6e\nuOmmm8Tll18uXnjhBSGEteFefvnlYuDAgaJfv36iR48eYt++faJdu3ZOG77a+SUnJ8tjohEWeNoD\n+YqiLAcuB3YA0881+pxzLfu0oigxHuRVJ4mJiXz55ZdOz9Xea6wq+Wzfvt1p3Pj4eE6dOgUgd/Pp\n9XpGjhzJ/fffj6IoLF++nAEDBrh0zKGh0RxER0ezZs0ah+Nr1qwhOTnZaZrg4GBCQkKkv0d13u/M\nLVhtPBHu+QO9gCVCiF5AGfAE1p7UI2bPni3D5s2bPU3mFFvdaHfWRP/0pz/JRg/n1Xi3b98utfXg\n/MaGupZlNDSaE+FmReuVV14BrHKB3NxcKR9Q6/jAgQOZPXu22/w96fGzgBNCiB3nfn+KteHnKIoS\nJ4TIURQlHsh1lUFdhXDFxo0bOXnypBTYAXz44Yfs3bsXk8nE999/D1idGuj1ervRgNFo5J133pGj\nBFWKf+jQIebMmcPKlSsB+Pe//w243/SjodHcqA1+1apVxMTE2AmqLRYLK1asQFEU+vfvT8eOHZ3m\n8eyzz7rOX32z1FGIb4F7hBAHFUV5BlB3AZwRQsxTFOVxIEII8YSTtMKTa9Tmo48+Yty4cfVO11AG\nDBjA1q1bm+16Ghp1Ubszc4Wr9nVuVczpGp+n6/jTgPcVRfkV6zz/eaxS/WsURTkAjAD+5mFeHqHa\nzBfC6uLY2efVV18t44jzwkQ553/iiScwm82YzWaEEJjNZqmyq8bdtm0bgGbRR8PnMJlMDvXe9vtP\nP/3U4Lw96vEbQ0N7/B9//JEBAwbUGS8+Pl7q3VssFo/sjTnj+uuvZ926dQ1Kq6HhLf73v/9JDz2e\n0pAe32dVdvv3709JSYl8y9kq5pjNZukmOSQkRKZRpZr79u2jc+fO9OzZk88++0xq85nNZvz8/Cgt\nLbXuUNLpCA4Oxt/fXxru0NC4kBw7dgyAoqIiWd+FjQpw7bbgiQTfGT7b8AG7Ru0J6ptPldAHBATI\nTQ8aGhcai8VCZGQkRUV1K7g2tV9In2749aX20kdTT2M0NOqDTqejqKiIuXPn4ufnJ+fqYH0p6PV6\nzGYzgwYNavrCuNLs8Vagnpp7W7dudVBTVNVv27ZtKwDRqlUrsWnTJoe0FotFAOLYsWN26WfPnl2v\nMmhoNAVms1kAwmQyeSW/kpIS0adPHztVdUBkZmYKIdxr7vnc7rzp06cD5y2I6nQ6qqqqiImJoU2b\nNkRGRlJYWMg999zjkFbt8Y1GIxMnTpSCPtudVBoaFwq1fjrbWdcQDhw4wPbt24mLi6Nt27YkJCQA\n8Nxzz9WZ1meG+t999x0vvPCCtCemrl/GxMSQk5NDv379iIqKIjQ0lHXr1rkVatx1110kJCRwzTXX\n8OWXX2I2m7nuuut4+OGH7Uxua2g0J55um50yZQrZ2dlERERQUFBAREQEubm5REVF8eKLL0ojMqqN\nSdVKj3oNVYXXLa6GAt4KeDjUNxgMLu2KKYoiABESEiKPGQwGp/m0b99egL3bYNugoXGh8GSo//XX\nX8u62qpVK4edprGxsTLutm3bnG7Wue++++R30YhNOs2CyWSia9euLFq0iOrqar744gsWL17Mhg0b\n5PJFSUkJBw8e5Mknn6SmpoaNGzfSo0cPoqKi2LFjB2fPnmXdunV06tTJIf/x48fz/vvv89VXX8n8\noqOj6dmz5wW4W41LAVWtXFUZF+eEze6G+qobbjWuLYqi2G0mcxYHPFQ/d/VG8FbAw1520KBBLnt8\ndyExMdFuXz4gCgoKHPJfvny50/RHjhzxqHwaGvXlT3/6k9M6V1pa6jKNMyu7KklJSaJbt27yt7Me\nPzg4WEydOlUI0UKEe1u2bLErmGqvXNi/RKSFnrS0NIYPH87Jkyc5ceKEjAs43WJ79913O3spObVk\noqHhDbZs2QI41mF3nm7UOM7IysoiIyPDbVzV2m9d+EzDr01iYiLg6BDw9OnT9OzZk8OHD7Nx40YA\nxowZI+MCbm/89OnTdvn17dsXRVGYOnVqk92LxqXJ5ZdfDjjWYSEEoaGhTm1D3nLLLQ5pbNOWl5fL\n3/369XO4pk6n80jxzWfm+LUZPXo0J06csJuvpKens3//fr7//ntOnjzJhAkT+OGHH1i8eDEPPPAA\n+/fvJz093a1U8/jx4wDs37+f4uJi8vPzueGGG9iwYUOT35PGpcVHH33E3Llz7dxWp6en4+/vT2lp\nKU8++SSTJk2iurpa7sT75ptvuP/++9m/f79Dfunp6RgMBnbv3o3FYkFRFGJi7O3fWCwWj+b4Ptvw\nAZKSkrBYLLRp00Ya1QgNDeXpp5/m5ZdflvHat28PWB8MQJ8+ferMu7YA0BPXwhoa9SUtLU1+t9XS\nA0hISJD+I1RUJ5nOBNSpqamEh4e73H9fH3y+tut0Ok6dOsX999/PkiVL6NWrF9OnTycyMpI777yT\nmTNnkpSUxBtvvMGuXbvIz88nKiqKoKAgioqKCAgIoLq6WirzCCG49dZbHa5j62hTQ6MpUKX56md9\n/TUeOXLEI+Ufj/QFXEn9vBWo59r5jh07pGput27dHCSiqgFN9XPJkiX1yt+WyZMny3w7dOjQ4Hw0\nNDyldn1WjcCGhoaKwMBAt/omERERIjU1tc78x40bJ78LX5fqq9x5551ya6LaS6u77fR6vRySq2++\n+++/v8HXeu2112Q+ffv2bXA+GhqeUtsWv+ooxs/PT4aZM2c6TXv27Fny8vLqvEZgYGCdcXyu4as+\nwYQQ/PrrrwghpDNBk8kkh+QJCQnSL9l9990nnRzUlx9++AHATgCjoeFNhBAsWLCAyZMn06VLFyZP\nngzAwoULycjIwGKxcPbsWUpKSqipqWH+/Pku8zKZTEyZMoWDBw+6jNOiFHhUevToUadqbWxsrBg2\nbJj417/+1Sh1XEAqQUyZMqXe6TU0POGtt95y2GkKiOzs7HrlM3fu3Drru21dpiWo7KqoPfrq1atJ\nSEggKChIqjuGhISQkpJCbm4uer1eLt1t2LDBzptofThy5AigWdnV8D5ms5nDhw/LqeuePXvsnGoW\nFBSQk5OD0WjEbDbToUMHDAaDy/z+/Oc/8+c//5mJEyeycuVKuaGtNi1qk45Kv3793Krorlq1ys5D\nTtu2bd2qObpD3fwDiNdff73e6TU03DF16tR6qZ+HhIR4lK9a310FtS7TkoR7qlkiVyq7J0+elNZK\nhg8fzrFjx+S6aH1RLZYKIbj33nu9cwMaGudQXWovXboUcN/JjhgxwrOeGqtym7u8PKnLPtfwVcUF\nVYW2tsriQw89BFj3Im/cuBG9Xu81wwYaGt5EVbSZMmUKcL4uO+uooqOj3XqG8jY+12I+++wztmzZ\nwrBhwwBYsGABcP7hDRo0iAcffJCvv/6ab775Rloj1dDwNdS6rHZW6ghAHb3akpub27wbxtwNGbwR\naKDxi3vuucfp/MVWYWfLli2akQ0Nn+fNN990qMdBQUEu5+hDhgzxynVpSVJ9lSVLlrB9+3Zyc3OJ\nj4+nbdu2pKen281fVFt6Y8eOZdKkSReqqBoabjGZTIB1x2lKSgrx8fG0atWK/Px8QkNDKSkpYevW\nreTn5zNgwAC+/fbbpi+UqzeCtwIN7Imrq6tFjx49RExMjBg0aJCIjIwUAwcOFGFhYaJ79+4iKipK\nmteKi4sTPXr0ENHR0WLw4MEiIiJCDBgwQISEhIiuXbuKmJgY0aZNG7Fy5coGlUVDozEsWbJEACIy\nMlLcdtttTuOMGjVKAFJiHx0dLSZMmCCqq6sbfF3c9Pg+2/DffvttOfRJTU0VgLSnFxkZ6TA8ioqK\nEoBIS0uTy3yACAsL06YDGheU06dPi65du8o6WFNT4xBn2LBhAhBVVVV2prKzsrIafF13Dd9nh/qq\nQs1zzz2HwWDAZDKh1+uprKzEz88Ps9nMihUrOH78uFNhSW0mTJjAu+++29TF1tDgwIEDfPDBB9Jp\nhk6n44477kAIwV/+8heuueYaoqKi6N69uxRMq0o+L7zwAtOnT8dkMvGXv/ylyQTXPus0c+rUqXL9\nUzWO6QpP8p80aRIrVqzwKK6GRmOIjIyU3p4bgm19r6iokPtX6ssFd5pZU1PDiRMnsFgsBAcHYzAY\nEMKqtmgwGJyaClIfXEFBgYyrfoK1saemplJUVMSRI0eIjo4mPDyciooKKioqZFzVWWZ5eXlz3KqG\nBmfPnmXQoEHS5p4zFEVh4cKFcqlv5MiRfPXVV83WMTVLw+/UqZOdkcDa/PDDD/Tv39/umOo0wBOl\nBtXKicViISgoyGW82tZONDSagujoaFl/3WFr9SkqKorw8PCmLJYdzaLAozb6WbNmAdbeWlWXBav1\n0NqojdQ2bu3P4cOHA/DEE08A5y2PZGVl2cVVv6tmjTQ0mpL8/HxycnLqjKd6iwLIy8vzyIuut2iW\nOb4qjGsuTpw4QVJSUrNdT0PDFkVRGDVqFGvXrnUbZ/HixWzevFnakoiNjfXohVGfclzQOb7a6CdP\nnkx6ejoxMTFSgHHnnXcybdo0+vXrh9lslhL7jRs38s477/D+++/LY7bz/Orqal588UX27NnDQw89\nxKJFi5g6dSqvvvqqxz7KNDSaCk9s25tMJlatWkV0dDQLFy6UaurNgqt1Pm8FQPj7+7s1HFA7vPDC\nC+LVV1+tc919+PDh9dr2qKpJ9u/f322+GhqeUlNTIxISEgQgkpKSRHZ2ttO6p+qZxMTENJmKbm1w\ns47v8VBfURQdsAPIEkKMVhSlLfAREAH8AtwlhKhxkk6oPbWzaymKQuvWrWnXrh16vZ4dO3ZQVlbG\nP/7xDx588EG3Us6CggLuuecesrKyOHXqFEVFRSQkJBAdHY3BYKCmpgaTyURYWBhnzpwhMTGRjIwM\n9u7dqy3raXiF3Nxc4uLi6N+/Pz/++CP//Oc/ad26NbNmzaK8vJyoqCjy8/OlifiEhARycnLYunUr\nbdu2JT4+nk8++aRJpqbuhvr1afgzgN5A2LmG/zGwSgjxiaIoS4FfhRCvO0knL2A0GgkICKCqqkrq\nKFdWVqLT6QgPD6esrIzq6mqEECQlJZGVlcXll1/OjTfeyJw5c7wyhN++fTt9+/ale/fuxMfHk5ub\ni8FgYNOmTQQHBzc6f41Li/z8fGJiYuQUNDExkfT0dLKzs+XysqIohIaGUlRURGJiIidOnGD37t38\n7W9/4/HHH2+ysrlr+J4O15OAr4ChwJpzx/IA3bnv/YEvXaQVjz76qMPwxtb6jSfBnWvh+lBcXCzS\n09Md1HmnTZvmlfw1Li1OnTolAGGxWGRdsjWTXTvYquOOGTOmScuGFyzwLABmniswiqJEAWeFEKo6\nXRaQ4Crxiy++6HBhW+s3zsLixYsBWLZsGXDe1HZjCQ0NZd++fQghWL9+PW+88QagOc/UaBhqvXzr\nrbcAGDFiBM888wx33nkn//d//8f8+fNZtmyZVC3Pzs6W08yjR4/y/vvvXxB7EnUO9RVFGQVcL4R4\nQFGUocDDwB+AH4QQHc7FSQK+EEJc7iS9eOaZZ+TvoUOHMnTo0DoLtnPnTnr16iV/q77CvIltfqtW\nreJ3v/udV/PXuPiprKwkLCyM6urqOuPatjXbunfllVfy3XffNbosmzdvZvPmzfL3s88+2/ChPvA8\nkAlkANlAKfAekIv9UP8/LtI31Uim0YDVvLaGhjcAxIwZMwQgBg8eLKeUS5cudVihAsTChQvljtKm\nKo9o6FBfCPGUECJZCNEeuAPYJIQYD3wD3HYu2kRgtcevJh9CW/PX8Caqqbh+/fpJ45lTpkxx2Gij\nKAr+/v60adOGtm3bNncxG6Wy+wTwsKIoB4FI4C3vFKl5EdqynoYXee+996isrOSll14iNzcXsO6w\nKy4utosnhJCb11TfDs1JvRq+EOJbIcToc9+PCiH6CSE6CiF+L4Soe5LTjFx55ZV2FnqdBUBbwtPw\nKkajEaPRCCA3jAUGBmIwGBzqXnJyMomJibRv355169Y51E9/f3/53Xbu7g181hBHY9myZQtDhw5l\n1KhRdtt5VQeFZrOZbt260aVLlwtcUo2LCdsRZGRkJIWFhcyfP18qlOn1eqqrqwkLC2PMmDGMHTsW\nnU7HwoULAXjppZekOru/vz/V1dXMnDmTL774wiOhuKf4rCEOL1yXmTNnunVAqKHhTTyRF9W1Yc1Z\nW1EUhSeffJLnn3++3uURLqT6PmdX35togjuN5mTBggW0bduW1NRUunTpQnx8PAaDAZ1OR0hICH5+\nfoSGhuLn50dwcDB+fn4YDAbi4uJIT09n9WrX8nHVUq+3uGiH+oDmaEPD62RnZzN9+nTy8/OJj4+n\noKCAmJgYCgoKCA4OpnPnzlZjlv7+tG7dmlatWlFUVMT48eOZOHFig6/rbW9RF3XDb6itMg0NV1xx\nxRWcOnUKsAqGy8rKiIiIqNPG3tdff92ohu/t0WuLaviZmZns2rULs9mMwWCguroaf39/acnUYrHY\nGSr0RJtKQ6M+qG7c6yO3Wrp0qfQF2VAu6YafkpJSr/hXXXVVE5VE41IlMTHRzlaeJ9Q3flPlYUuL\nE+4tWrTIYyMgN9xww4UursZFRmZmZr3NY3nD7JytfT5v0OIavrd26WloNIQuXbpI99e1sVW4UUP/\n/v3t6mxdSmWqnokt4eHhzJs3zy5OY/VPWlzDb06jnRoatdm9ezcHDx50es5sNvOPf/wDsG7/bteu\nHT/99JNDnT106BAZGRlkZGRw8OBBjh8/zpEjR8jIyOD11193WI3Kzs62M08/duxY9u3b17gb8XTY\n3NCAF3bn2boUfu211xqdn4ZGQ+nbt69o166d03M4MbzhLDgzKrNq1SqHeEajsV7GatSwePFiWR7R\nWJt7DcUbmnuKojBjxgw6duzI5MmTvVQyDY36ExgYSGVlpVOp/tq1a9m0aRMLFizAYDAQGBhIUVER\nI0aM4Ouvv+aRRx5h2LBhjBo1yiHtVVddxX//+19Gjx7NmjVreOSRRwgMDKS8vJzAwECKi4vlaKJV\nq1YUFhbSu3dvjEYjVVVV8vPnn38mJSWFY8eOecfmXkNpbMMX55bq1KU7DY0LSefOncnOzqawsBCw\nLhnfcsstrFu3jsTERE6ePOk2fVBQkDTCWVBQIO3x1d69B9CxY0cOHjwoncY6Q9X9Vz8BUlNTOXz4\n8MWhsqup32r4Arm5uXYebwoLC1m3bh16vZ6goCACAwPt4sfFxQFI/5Dl5eUYDAaCg4MJCQkhJCSE\n4OBgdDqd1M6Lj4/Hz8+PoKAgjEajW3VdVRCofvr7+/Ppp5/WeR8+34Xa7qrT0LjQqNqgf/zjH/Hz\n85PGNsaPH09ISAglJSWsWLGCvn378tNPPzmkVxSF8vJyvvjiC1atWkVQUBBlZWUYDAapgKYO20NC\nQujZsyfLly/n0Ucf5cUXXwSgXbt2HDt2rHG2JFxN/r0VaKRwz2w2C0BUV1c3Kh8NDW/w9ttvuxSq\nBQQEyO+ffvqpQ1q1LptMJo+EdMHBwfK7rROYjh07OpjycgZesLJ7wVCHP97epKCh0RAmTZpk14BU\nZR4hhHTPLoRg7NixDmlr1+UFCxbY5bVnzx5++eUX8vLyEEKQkZHBL7/8IvMvKyvjn//8p5Qv7Ny5\nU14/Pz+fnTt3euwsxueH+uqaptls1hq/hs+hNjJhY+zFFWpdVof0er1enps6dSpLly61i6vKB8Aq\nVIyJiaGiokIeU61QCyGIiYmRxxcvXsz999/vtiw+35LUxq5p7Gn4IvWRQdn2+BaLxU4N99ChQwB8\n/vnndvllZmYCViGh2ujvuusuAAcZgvp727ZtdZalxfT46ltSQ8OXaGiPD/admSokvOWWW+zyBTAY\nDBiNRvz9/dHr9YSFhRESEiKX79Tr9uvXD0Aa+XSHz7ckbY6v4cs0tMcHe/XzAwcOAOd7c9v8TCYT\nlZWV1NTUUFFRQVFREaWlpXKq8Nprr/Hhhx/y/fffA7hUKbYrtyeCgMbQWAUei8WCn58fJpPJbk6k\noeELnD59mtatW3vk6Umty01NeHg4hYWFbhV4fH6or83xNXwZtX562uOvWLGC9evXc+bMGfbt24fF\nYkGv11NZWYler6esrIyCggKCgoIICAggNDSU48ePExISQlBQEAUFBXKkoMoKkpOTyczMlL9tFYxc\nlqVxt930NPWIREPDG4SGhjJq1CjKysrcxps4cSIffPAB/fv3Jzc3l7CwMAoKCvDz86OqqorKykrA\nquFnMpk4fvy4/B0REUFoaKjUDvzvf/8LIOOosgNPVNtbTMPXDGdq+CIxMTH07NmT0tJS1q1bx5df\nfulRumeffZbKykry8vIoLi7m5MmT5OTk2L04VDNfer0ei8VCbm4uhYWFVFRU8Pzzz0vHHbXp06dP\nndf36aH+Sy+9JIctmnBPwxdRFEUq2SiKUq8O6uWXX+aWW25h2bJl6HQ6FEXhm2++YevWrQwePBiw\ndnxRUVF89tlnDm2g9rLdpEmTWL58OWlpaXVe22cb/ueff87MmTMBq0cSbcivcbFhNBoZOnQoJ06c\ncDi3ZcsWu9833XQTX3zxhcu82rdvz/LlywGYNm1andf22YafnZ0NWN94paWl5OXlYTAYiIyMvMAl\n09BwTWFhIadOncLf35+amhrZSxcWFmIymezW+8+cOcOJEydITEzkyy+/pLKyku+//57p06eTnZ1N\n69atWbt2LTfeeCPZ2dnk5ORQU1ODn58fFouFgoICed36Ot702eW8N954g8mTJ8sbVfnuu++48sor\nvVlEDQ2vEBAQIOflzYmr9tUi9+ObzWZphEP9DdaNCRoavoi6ScdisciNNxaLRergCyFkvVbj2MZV\nz7mKUztf9bMh+GzDVxu87SYd2+MaGr6GMy2+2lZza6/728atrdlXO07tfGsfqw8+24rUBl9bgUdb\n1tNoafiiRyefbfi11+/VT026r9HS8EXrUT7b8Gv3+Oqn1vA1Whq+WGd9tuHXfkt27twZ4IJITTU0\nPOG1116jS5cudO/e3c7NljpN7dKlC4899phvvAhc2eRSA5AEbAJ+A3YD084djwA2AAeA9UC4i/R1\n2gZzxuLFi6VdsW7duknbY2PHjm1QfhoaTQ029vJuvvlmeby0tFTodDq3DjWaqjzCRbv2RIGnBnhY\nCPGroighwM+KomwAJgFfCyHmK4ryOPAk8IQ3Xka2vPrqq1x99dV07dqVjz/+2DfelhqXLDU1Nbzz\nzjuUl5djNBqpqamRyjoA//znP7n99tvtevzg4GC5KqUoik+sTNXZ8IUQp4HT576XKoqyD+so4GZg\nyLlo7wCb8WLDV3WVa9sO+8Mf/uCtS2ho1JuePXuyZ88eu2PqdliAQYMGERkZSWJiokNaW0H1hd5m\nXi+VXUVR2gI9gB+BOCFEDlhfDoqixLhJWm8uv/xyaWBTURTN2KaGT6B6yhFCyN5eNQunfp45c8ap\nK21fsiblcQnODfNXAQ8JIUqxzleajO3bt+Pn5yeFfNr6vYYvEBsbC1iH7Hq9Xiro2H6CdZONoih0\n7dpVpq29NH0h8ajHVxTFH2ujf1cIsfrc4RxFUeKEEDmKosQDLi38zZ49W34fOnQoQ4cOrfOaO3bs\nAM4/JF9cC9W49FB7crPZjMlkorCwUJreUnt8nU7HVVddRU5ODr/99ptM29Q9/ubNm9m8ebNHcT0d\n6r8N/CaEWGRzbA1wNzAPmAisdpIOsG/4nqK5ztLwRRISEigsLMTPz4++ffuyZs0aea59+/bSHHZk\nZCSBgYGUlJTI87bq500xx6/dqT777LMu49bZ8BVFGQTcCexWFGUn1iH+U1gb/D8VRfkDkAnc1qhS\n10KT3mv4Ir/++ivLly/n008/ZcOGDXYdVGZmJnfffTdDhw7lrrvuolOnTpw6dUqm9SX7kZ5I9b8H\nXJV0hHeLo6Hh2+j1eu69915OnDjBhg0b7LzdAIwaNYpbb70VsI4ObI1stFipfnNia3NcQ8PXmDlz\nJrt372b37t1cd9118rjthpzTp0/baZqqowNfkOr7bMPX5vYavkxYWJh0d2WLrYXb0NBQu3O+VKcv\n/KvHBb7wVtTQqC+2sqna+0pa3HLehcD24fzyyy8cP35cWjE1Go3ccMMNPvUG1dAAq+Vbg8FATU2N\ndGf9r3/9S9rJA9/o1Hza5t59993n0hnhNddcw4YNG7xRRA0NrxATE0N+fn6d8ZpLC9UnbO6pjb/2\np7Phjzhnd8wWs9ksbZEBHDt2zGl+GhoXiry8PLsdcF26dAEcd8D6Qo/fLEP9hx56iL///e8NSqv2\n9rWXPw4dOuRyqF9cXOwgWNHQaG5SUlIoLi6+0MVwSrMM9SMiIjh79ixZWVnyuDqET0pK4oUXXmDI\nkCEEBgZy8803k5mZSVZWFmfOnKGqqoo+ffpIryHnhi8kJibaeSi1zS8rK8vp7igNjeYkPT2dAwcO\nXLDR6AX3lhsWFkZZWZnLxpiamsqAAQMA6NSpE1VVVSQmJsrGDdC3b18At41aG/Zr+BIpKSlSwOdr\nNMtko7KyEpPJ5PK87ZD98OHDdlsadTod69ev58knnwTg008/rTMfTdqv4QvUrsu+RLM0fNU6iStu\nu+02FEXBYDBw9OhRh4Y7cuRInn/+ecB5b15YWEi/fv20Bq/hU8THx/tsnWyWhh8REUFwcLDTc88+\n+5kRblgAACAASURBVCzh4eFER0cTGxtLcHAwH3/8scu8nCk/fPvtt2zbto3AwECuueYaEhISvFZ2\nDY2GUlBQ4LPTzmYR7gUGBkr3Qo3Mi969e9OxY0f+/ve/Ex0dDVgVJH73u9/57EPWuDTp2bMnv/76\nq9t6uWvXLunr/qmnnqJTp05eu/4FF+516dKFvLy8RuczcuRINmzYwM8//0xBQQHr168HfGObo4ZG\nbTzpiK655hpyc602bFauXNlsnVezNPz9+/dTVlZmd+zIkSPk5+cTGRlJhw4dPMpHbeiKorBnzx62\nb99OTU0NBw4c8HqZNTQaS12yLYDc3Fzatm1Lhw4d+Oqrr5qhVFaapeF3796dM2fOyN9FRUWkpaXJ\n35s3b2bIkCHOkjrl6quvZtOmTXKJDyAkJMQ7hdXQ8BJxcXHSOKcrkpOTSUtLIzw8HIPB0Ewla6aG\nv3fvXjsNpsrKSuC80k19pwEbN270avk0NJqC7OzsOtfxMzMz0ev1tGvXzu2St7dpFql+jx49AOsQ\nXVEU4uPjgfNzIF/QXdbQ8DYpKSkkJSW5jRMdHU1SUhIxMTFERUU1U8maqcffvHkzO3fulEtxhw8f\nZty4cXKNU7O2o3ExkpGRYaem7oz8/HxOnTqFn58fBQUFzVQy6vad19gAiOXLl9v5FasrPProo/Vz\nEqbhwD333COf56xZs9zG7dmzZ73+n9ohODhYAEJRlEbl40lYtWpVkz+7EydONMu9NCakpKTUeR+4\n8Z3XLOv4rVu3Jjs7m+7du7Nr1y7atGnDiRMnaN++PRkZGcTGxpKbm0tUVBQmk4mSkhJtTb6RKIpC\nQkICpaWlFBcXu32e6sjLaDRSVVUl/4/27dsTFBRERUUFR44coWfPnnTp0gWDwUBFRQXh4eGUl5cT\nHh5OcXExwcHBlJeX88477xAWFiblOqGhoZSUlHDLLbfw+eefk5qaypEjR+xcTwUHB1NWVibLkJqa\nKo8dOXKEQYMG8f3339OjRw927tzZpM9u1apV3HbbbbKcUVFRFBQUkJyczPDhwzGZTPzvf/9jz549\npKamouqpHDlyhICAACnDqs2ECRNYuXIlISEhlJaWynZgi5pe9ccXHBwsp8IlJSXSbn9NTU2dbcTd\nOn6z9PgRERECENOmTROA8Pf3d/oWMxgMdm/aVq1aicDAQNGnTx9hMBhE7969hU6nE506dRK//vpr\n417rFzmAGDNmjIiJiZG9cUhIiN1z7dy5s6iurnbZqwQEBIg+ffoIvV4vj3Xo0EEEBgaKmJgYsXz5\ncpfXDggIkGnU0Yefn5/La8XFxdn9rp1fYGCgwygjNDRUpKamioCAABEdHS0AWVZFUcTHH3/s9hm9\n+OKLAhDt27cXwcHBIjIyUixdulSsXLlSlgEQRqNR5h0UFCTWrVsnZsyYIY/16dNH3q/6qSiK3XNr\naDh27JjdcwgNDRXJyckOz8jV/yBctUtXJ7wVAJGeni5atWolBg0aJG/I1m2wGlw9qPT0dAGITp06\nyWNpaWl13vilDCCuvfbaOivfu+++6/Z8586dnTZQ9QXtjL/+9a92aY4ePSr/Q4PBYJdePbZ582YR\nGxvrtOE/9NBDLsunvtjUYJuvXq+v8xkB8qWhhn/96192Db92CA8PFwMHDpS/u3Tp4jSe+sJoTDh6\n9Kgsb1RUlEhLSxMdOnRodMNvFnH60aNHKSws5MiRI2AtjbSmYxtMJpP8rhruEEKwb98+hBDs379f\nDm+ac82zpaLX66XgdP78+QBSkWrmzJkAvPfee4B1Q4mqAn3DDTcA8Nhjj3Hrrbfy2GOPATBgwADG\njx/PzJkzSU1NdbjeJ598wmOPPUZISIjdnopFixZx2223MXPmTB5//HEee+wxnnrqKZmvEIIhQ4aQ\nk5PD3LlzHfJduHCh3QqQ0WgE4JFHHmHKlCnyXsrLy7FYLDKuJ0Lj+++/X1rOmTRpkrxvgMcffxyA\nzp07AxAeHg5Y9VC2b98OWLeLR0VFSZ2Sm266SR7Pzc1l5syZUg1XjfPII48AVn0UgI4dOxIRESGf\nhTjfadpppRYUFJCRkeFyKlEvXL0RvBUA8dJLL9m9xTzhtddecxkXEJdffrlH+VyqAGL06NFyiDxv\n3jwBiPz8/Hr1OM5GZmoYN26cwzXV8PDDDzsVkKk9vm1ITEyUecydO9fl/672dLZBvYZerxc1NTV2\nZQkMDKzzGT355JPy99SpUxvdQ6vhww8/FGPGjPEobmhoqIiPj7e7b4vFIgCRmZkpj6WlpYlevXqJ\nrl27towe/+GHHyYzM5MHHngAsCotFBUVuU1T19u6oqLCa+W7WFEdOwLSp7tqyWjr1q0APPXUU4DV\nAEp6ejoA7777LgDHjx/n6NGjHD9+HIA5c+bYVZ4PPvjA4ZqLFlndK+bm5speyzZNVVWVQ69WXV1N\nVlYWGRkZbhVeDh48iBCCgIAAWb5jx45x/PhxDh06xMmTJzl+/Lj0X+eJQoxtPVLNYc+bN0/mD7Bk\nyRIAbrzxRhl32rRpDvdmG+644w7pMPOvf/2rjAvnVXkXLlwIWEcqai+emZlJaWmp0+28hw8fZvfu\n3Xb++BqMq4J7K4B1romTN507Xn/9daHT6Zyei4+PF1dffXWdb7xLmeDgYDF+/Hi3PbazYDQaZa9b\nO6xZs8btNZ2liYyMdJvG2aggLi7ObRpP587Jyclu8wkICBBPPfWU/D19+nQRFBQk3nzzTbt8Pvnk\nE9G2bdt61+Hp06fLeOHh4cJsNgtAmEwmAYh//OMfTmUwiqI47fFtBZznrFe7hQvd46u9y6xZswCr\na6G6MJvNLh0PnD59Wr6NNZxTVlbGmTNn5DNU/3BVPVqc633efvttwKpd2bdvX6qqqqTSSe3Kos5f\n3fHvf/8bsHqLBez2aDhDCMHYsWPtrlNX/VB7cleVWr039dMVlZWVdj1+aWkp5eXl0lCrmj4+Pp6j\nR4/a5X/llVe6zRtgwYIFMn5hYaGDm2yz2Ux1dTXt27eXz+vzzz9HCOcm5dWyTpgwoc57q4tmafiq\n615VcFNeXg6cV+F1FqZOneoyDkD//v09uvb48eNlukGDBnn5zurHb7/95vae3YWzZ8/W61qtWrUi\nKipKCofUfGJiYuRvgD/84Q+A1Qvstm3b0Ov1jVKhVl8OAQEBtGvXjnbt2tWZJigoqF7XUAW7ts/H\nz8/Pzm9dZGQkJ06ccPk81eGyXq+XaVShYe37d9YIbdPVF9XN1vTp0wGrhp/6grzlllvsrpmcnGxX\n78G6fVeN48rATZ1laFjR68fHH3/Mpk2bsFgsDBgwQL7R16xZI73j3HzzzSQlJTFhwgR5k+np6YSH\nh0vLuio6nY4RIzxz1Pv+++/j7+/PlVdeyTfffOP9m6sHu3fvBqz3PXr0aGbMmEFQUBCKoqDT6ais\nrJSV+tixY7z33nsybmZmppT8ekJhYSG5ubmyx1+9ejU6nY6ioiLGjx8v8502bRp///vfadeuHYsW\nLWLEiBHMmDGjwfe4ZMkS7r//fiIiIuQcty7UjsBT1Lqg1h8hBKNHj6ampkY2yOzsbLmNW42verMZ\nPXq03ANv+7JQ5/i1R5rOeteGbqjZ+f/tnXts1NeVxz937PmNzXiMbbAxwdiBJrtgTKDQQHYDCVqw\nyCot1C0k0KYlUSJqCmy026QlSVUgUhMlStWtAorZpKzQCmzCGypCjENKQS2wiHfMI4sTMC8/MLge\nm7HH9t0/xvfym/HMePzAHoffV7qy5zf3d3/nd+Y+zjn33HOOH6e8vJzKykrKysp46623GDhwIPn5\n+cTGxnLhwgU2bdrEr3/9a6qqqvSE39rayubNmzEMg1deeYWxY8dy9epVXnnllS7R0Ss6fiBOnz4d\nVF965plnOtRbOovhw4fLnJwc+dxzz3Wok/3xj3/UtCg31JSUlA51ycTExIh0ysLCQglo/e369esh\n6x44cEDTC8hTp06FrNvQ0CBHjBihdb/6+noJyGeffVY6nU4/ffD69esS0Prm2rVrJSAnTpyo6/zs\nZz+LyGocCECePXtWAvLb3/62dDqd0ul0dnhPXl5ep56jHJEUFD/dbnfEdPZU6S6Uc1uwMmjQIL++\nCD6fA4W//e1vYWkgjI7fJ7nz1Cmk3NxcXC4XbrcbgIKCgh5/lppdJ0yY0GHdRYsWAfDEE0/wwAMP\nUF1dTVpaGlVVVSQmJmpXYrvdzu7duwGfGpOenk5lZSX79u0L235gFGBzZtVABO5qhAvqcOPGDb76\n6ityc3PZu3cvf/nLXwCfft3Q0OC3YinR36xngr/o2p2kjqq9hoaGiCMjheNDuGcodDb99Jo1a9iy\nZQvFxcVkZWUxcuRIXC4XR44c4caNG9q1XPFz0qRJJCcnY7PZaGxsxOVycfz4cb170B188sknvP76\n68TFxeH1eqmsrOTkyZPk5uaSlpZGRUUFgwcP5vr16wwaNEjvmkDn+WZGnwx8RXBP5b5rbGzkhRde\n4NChQzz44IOUl5cTHx+P1+tFCEFaWlpEotmQIUO4desW+/fv77CuYRh4vV5KSkqYMmWKn9EsVGTV\nYGnBQiFQhwynUypxtbi4WKsN4PN/NwyDxsZGRo0ahdPp1KKj0r2Vs0pghKSuQtFpGIb21c/IyGDl\nypW8+OKLQe/p7tasmtjME1w4LFy4kIULFyKE4Hvf+x4LFiwgPz9fbzFfu3YNuMvPr7/+GofDQVlZ\nGUOGDOHSpUs9xq/Jkyf7xZfYtWsXs2bNimhsdOf8fp8MfLNVtifCD3/66acUFhYCPkvt9evX/b5f\ntWoVO3fu7LCduro6LX10BDW41q5dy6FDhwB48sknw76TGhSqg4ZboQJTLAd+DtauguKvx+Nh4MCB\nVFZWtgtPpnIP3rp1C5fLxfvvv9/u3boCRWdLSwuFhYX8+Mc/5urVq7z00kshB35iYmKnntGT8Rvi\n4uKYNGmS36QRmPhS2Uqqq6v9IuqovfyeRGcGszJGdgV9uuL3VMxx85ZVKKiJAaCkpIQzZ87o02Eq\nFZdyonjvvfeYOXMmY8eODdmeWq2VdTiS1UbVUe+9Zs0akpKS8Hg8fp1ZCEFZWRlw18mjqKiI/fv3\na2OWKg6Ho932lxKxY2JitNVXPbu6uprU1FQ9QX300UchB6QZJ06c4LPPPsNms/n2gW02fvKTn7QL\nHqF+25qaGq1qLF26lA8//DBk2511SAlUe7qTSOXw4cNIKXE6ncyZM4d169Zx4sQJxo8fr3m/evVq\nvct0rxGJeiSlZP369Rw9erTrDwql/EdSgKeAc8AF4Fch6rQzOigDU2tra2QWkA6wffv2Dg0tixYt\nkoZhyDNnzvSI4UYZmFavXh2xkWfjxo1+xr2eLMqIBsg9e/ZIQP7gBz+Q48aN8zuscuPGDT/j3rp1\n69rRqVxXzYiER4AsLS31+37YsGHyF7/4RUhnrAEDBsgXXnghIv4pKIOYguJnfX19p9oxHxp76623\n5MsvvyxjY2NlbW2t3zvs2rWrU+12Bzt37uywPy1ZssTPABgKhDHudVlmEkLYgFXATGAMMF8IMSrC\newHfzN3Y2IjX66WxsZGmpia8Xi8ejwev1xtxZB7Ztpqpdsx/lf5bV1dHU1OTFuWDMUPtJ6tDH+Gg\npAPzdpBCc3MzXq9Xv4/X6/VbpdT7nzx5UqcX83g8+oCJlFIb6NS7qfjsoYpZRVH3eDweampqNI1N\nTU1aOlL0B+OxqmPmI/j8MNTz8vLywvJHOaRcvXoVt9sd0mDY0NDQaR+FQJtAV1f8gwcP6vd57bXX\ncLvdNDc3k5iY6OcIlJSU1Kl2uwrVZ0JBSonX69VuzfX19Xz11Vc0NDTgdrv9+ntH6I6yNAn4Ukp5\nSUrpBYqA2ZHcqMRPwzCIi4vTfx0OB4ZhEB8fj2EYPProoxERonzMA9szDAPDMJg9ezYulwun0xm2\nc2RnZzNq1Cji4+M7dNBwuVzYbLagllWXy4VhGPp9DMNg4sSJWpxXg2DcuHF+9C5cuFC3EUhnZzq1\nzWYjOzub3bt3U15eTmxsLAcOHMDhcOgsQ+o3CHZmIisrC/DnJ9zlM/hOqgVLRa7otNvtzJs3D/Cp\nNKHgcrn0JBEpXC6XHz/UAO3ObgT4IjXHx8e3u94babCWLVuGYRjMmTMnZJ0pU6ZgGIY+Uel0OklM\nTMTpdOo+ZxgG7733XofP687AHwaYw4dcabvWIRISEvSMqo7nmo/pqv8j1WFGjRrVrh31F3zWWbfb\nTX19fVhd/PTp05w7d05LHOFQV1dHa2tr0G02j8ejtyYNw2Dq1KmcOnVKd0w1AVRWVvrRuXXrVt1G\nIJ3h6A5Ea2srp0+f1rp4c3OzNkAqa7RqTx01NUMFiAz8XX74wx/qOrdu3Qqqm5ulrw0bNtDa2sqY\nMWNC0lpXV9fpjLKBEZo6u50XCvX19UF3GDrD+65C9XWVHDYY/vrXvxIXF8fIkSM1XV6vV9N3+PBh\nwJedpyN0h1PBpsFOcyjQfznUtWC4ePGin8tmsL8Ajz/+uBbXwrn6KpdedXZdbY2pZ5iNaGq1U26X\ngS7F5eXl2Gw2XC6XPuf+7LPP+j0vLS3Nj86amhrdxhNPPKHbhc5bvocMGaK9Is10Kau7+tyRmB3q\nN0hOTiYhIYGqqiq/9rOzs/W7qDBRX3zxBeAbsMHcryP1SPz+97/vZ4RV6KkVX/UR8+8OdFoi6QpS\nU1NJSkrSklgoV3WPx6MNv+C/lz958mTgbvyAcOiOVf8KkGn6nAFcC1ZxxYoV+v9p06Zp3/3uYuTI\nkWzYsIHa2lrsdjvNzc3ExMToVUoxa/78+bhcLqZOncrNmzcZN25c0Pa2bt1KUVERmzdvpqSkhIKC\nAt1efn4+R44cYdasWYCvM9y6dYu5c+eyadMmCgoKdJy0/Px8ysrKaG1tpba2li1btlBYWEhtba0O\nxvD5559z/vx5YmJiaGpqYvHixYBvclCW3dGjR5OamsrQoUMj8nk3o7q6WsevM+urSqcvKCggPz9f\nuxF3FtXV1bjdbr26FBQUUFFRwfnz59mwYQN2u11LTSr+njr8o3jl9XpJTk7mmWeeieiZO3bsIDMz\nEymlX6y6nlrx3333XR577DGqqqqIjY2lpaWF9PR0PZndS6gY/Dk5OQB+fU/15fz8fOLj48nJydGB\nQBRKS0v58MMPuXjxInfu3PEbc0ERzmAUrgAxwP8BWYABnABGB6kX2jwZpXjttdeCWqx37dolV6xY\n4WfxXb58eVhre1JSUkTPDLwHkBkZGRLwc+s0H9MM1Y6y6qenp2t3TxWII9Bld8GCBe3aUOG4wuFH\nP/qRBOS+ffs63AHIyckJy6OzZ89GxCMhhJw5c6YcP358yGdmZGT4havqL1BBO8JZ9VVfeOmllyLa\nSeJeWPWllC3AEqAY+AIoklKe7Wp70YRQoY2amppYsWIFCQkJTJ48mQMHDmhjkDKAKacKZUTrjJho\ns9l4+OGH+c53vsOoUaMYO3YsY8aMYeLEidqn4O233+6wHbXStrS06AMwSgxWomG41TGS3RRlFIzE\niqzcpbOzs8nMzNQ8UlLM8uXLO2wDfItUdXV1UAPcz3/+c7Kzs7ly5UrYNOvRCnU6L5xVPy4uTkce\n7i665cAjpdwD9Fxe3yhBKCcKNWjU92+//bbWX2tra4mPj9fiteqcnTlRZ7fbycjIoKmpidTUVOx2\nO8nJySQlJekBHIl7q9qRMBvNVIdS8fSUUS/YBBCJyKzeL5S/uBJT4a7zVEpKCsOHDyczM5ODBw9q\nfbYj496qVatYv369fjdzOjYFFSUn8CRnf4HixW9+8xsApk6dSnp6OteuXSM9PZ3y8nI8Hg9Xrlxh\n8+bNgO9MSUpKCjdv3tR1s7KyWLNmTdAdFz+EEgV6qtAPRf1XX301qCi5bdu2oKJqXl6ebGpqChpN\npaSkJKJnvv/+++3uVaGaVfTZhIQEefTo0bDtAPJPf/pTu7aefvrpiMXsdevWdShKzp49WwKyuLg4\nYmefUKWjiMnmugkJCXLGjBkyLi4uZN133nknbHvRiCNHjrTji/rd1enPYGXAgAF+dQH505/+VEoZ\nXtTvE5fdaEeofVuzFTpYZJnuHJpYsmSJjknYXagV2zAMTZMy4tXX1+N0OsOuipHsW6tnhKprFkkz\nMjK4cuUKv/zlL3n33XcpKipi3rx5vPHGG/z2t7+lsrKSjz/+GK/Xi81mIyYmBiklX375pT78tHjx\nYlavXo3X6+Xs2bN4PB6Kior0GXuzhNEb++49jUcffRQpJdu3bycvL6/LUkuk724N/CAIJ74CXY56\n0ltQg9Kssly+fJnY2FjdoaQMfZgoEn9xJeqHqmvWQ5U1X22TKsceFYTy73//e7utzkAoUb6xsVEf\nlJk/f37QuuagmP0NkR5lDodIDu9YaWqDwOyUY555lYGssxFjehuKZrORTrY5e0Ti3hrJfriyNZjr\nmv83GzWVA4+Kx6foU8dRhw4d2k4UVf4Fqq6KleB0OnnkkUf0d8FKJPvY0Yru+iJA+JOcCtaKHwTK\nkSdwcMye7fNIVnHrohWK7mCqh/kkY6jBH4lxLykpiaSkpJDitVkVUgZQFY9P1Z0+fXrI9s1xGQE+\n+OADwCdJnDp1ql+K85Ggq+9lvk85f4WDteIHwaxZs6ipqaGyspKKigodn00FOewo53lfQ62SwSLB\ndqSbQ2SrTk1NDbdv39aiqYqvp/zIzYd4HnroIQDy8/P96oZz3FHbhIr3Ktb96NGjcTgc/dJyHwm6\n81579uzh5s2bOoBqhw+6l4V+aNUPBkyW1EWLFvU1OSFBCOtvYAl3JNqcNDIUnn/+eRkXFyc/++wz\nXRfuxtzrjfJNxN69ezvFA/NOUmlpqV9bWFb97uPEiRNs27YNIQTLli3ra3JC4vjx42zfvp2VK1cS\nExPD5MmTycnJYejQoXqPe9q0aWFX/EjEzcrKSjweT7sVSkrJpUuXWLt2LW+++SZSSp12W6VLN1vg\nFVRQlKysLC5dukRmZiYPP/wwU6ZMYeXKlcyePZvMzEyOHTuG3W7no48+6hqDohwzZsxg48aNlJaW\nardn2aaWtbS06ENXKrScw+GgqamJYcOGdc62EWpG6KnCN3RmjnZA8Iw0Xq9X5ubmSvBFEPZ4PO3q\nfPDBB3oV+da3vuXnU9ATRdG3cOFCfW3s2LHS5XLJN998U18z58rrKOW1hfYgzIpv6fjfYATT1b1e\nL3v37iUlJYWamhqKiora1Tl27Bjg8+5LS0tj0KBBZGRkkJ6eHvJZZikh0kzG5lW/oqKCuro6Fi9e\nzPTp0xk4cCCpqamkpKQwYcIEvyPBFroPS9T/BqO2tpa8vDxWrlzptwUGvpTLQghWrVrFrl27sNvt\n3LlzRyfRhOCutCp7y3e/+11aW1u5cOECJ0+eZO7cuXz88cfk5uYSHx/P0aNHdbTahIQE3G43SUlJ\n3L59m8xM36HOP//5z7pdFf0oJSWFkpKSe8IPCyaEEgV6qmCJ+n0CTKJ1enq6vu52u7VxT4n85pKQ\nkCDz8/NDGs9CJdTsThFC6KSUFnoOWKL+/YnY2FhSUlK4ceMGBw4c4ODBgzqBqRCC4uJiv84wYcIE\n3G63lgpWrVrlF/Md4I033vC7R3njqXvUVp2KLwB3/R9UHAYVylvliYPOR9q10D1Yov43GM3NzdqR\nJtCpo7W1tZ2jzvDhw7l69aoexEuXLgV8FvxQTkuhEkw6HA69i7Bjxw7grmiv2t2+fTvgmzRu3rzZ\nrcwwFjqHfr/im/XE/oDepDc1NZVhw3xhENUKrQ69BPPOu3btGhUVFfo7NQGESw0WKsGkivwD6Jj0\ngS675qCQQoiwacI6A6tPRIBQOkBPFe6x3rZ8+fJ72n5Po7fopQd18FdffTXkczZt2tRjz3E4HD3y\n7laf8AHLgef+Q1VVFfv376elpYXLly/7bbe1tLToo69CCO0I0traytChQzEMQ6sCI0aM0Ct1MMyZ\nM4dDhw5RXl5ObW0tt2/f5s6dO9TU1NDU1ITdbkcIweDBg3E4HHz99dfU1tZqhx2Hw8HMmTOx2Wzk\n5ub2BmssYOn431gMHjy4x/a+ww188EV3VRFeLfQPCBngctnjDxDi3j7AggULISGlDOp/fc8HvgUL\nFqIP/d6qb8GChc7DGvgWLNyH6NcDXwjxlBDinBDighDiV31NTyCEEBlCiH1CiFIhxGkhxL+1XU8W\nQhQLIc4LIT4VQrRPYNeHEELYhBDHhBA72z4/KIQ41EZvoRAiaozCQoiBQohNQoizQogvhBCTo5m/\nQoh/F0KcEUKcEkKsF0IYfcHffjvwRTfSdPcimoH/kFJmA/8ELG6jcRlQIqX8R2AfEDpTYt/gZaDU\n9Pkd4Hdt9N4GXuwTqoLjD8BuKeVoYBxwjijlrxDiAWApMEFK+Qi+XbX59AV/Q23wR3sBHgM+MX1e\nBvyqr+nqgObtwAx8nXNI27V04Fxf02aiMQPYC0wDdrZdqwJsJr7v6Ws622hxAReDXI9K/gIPAJeA\nZHyDfieQC1T2Nn/77YpPN9J09wWEEA8C44FD+DplBYCU8gYQTdE7fw+8is+bDiHEIOCWlFL55l7B\n14GjASOBaiHEf7epJv8lhBhAlPJXSnkN+B1wGbgK1ALHgNu9zd/+PPB7JE13b0AIkQBsBl6WUrqJ\nXjqfBiqklCe4y19Be15HC/2xwARgtZRyAlCPT/KLFvr8IIRIAmbjSzT7AOAE/jVI1XtOf38e+BGn\n6e5LtBlqNgP/I6Xc0Xa5QggxpO37dHyiXjTgcWCWEKIMKAT+BfhPYGCbTQWii89XgHIp5dG2z1vw\nTQTRyt8ZQJmUskb6ks5uA/4ZSOpt/vbngf+/wENCiCwhhAHMw6czRRvWAqVSyj+Yru0Enm/7fwGw\nI/CmvoCU8nUpZaaUciQ+fu6TUj4HfA7MbasWTfRWAOVCiH9ouzQdX+bmqOQvPhH/MSFEnPAdiww2\nHwAAAKBJREFUnlD09j5/+9rg0U1jyVPAeeBLYFlf0xOEvseBFuAEcByfPvcUkAKUtNG+F0jqa1qD\n0P4kd417I4DDwAVgI2Dva/pMdI7DtwicALYCA6OZv8By4CxwClgH2PuCv5bLrgUL9yH6s6hvwYKF\nLsIa+BYs3IewBr4FC/chrIFvwcJ9CGvgW7BwH8Ia+BYs3IewBr4FC/chrIFvwcJ9iP8HKYL1vSUC\nA8MAAAAASUVORK5CYII=\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10348f8470>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "lc = trace_tour(square_tour())\n",
-    "rw = guided_walk(lc, seek_step_limit=0, return_anyway=True)\n",
-    "plot_trace(trace_tour(rw))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 139,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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3Dzu2nsOsWbMoLy8HYO7cuV201mjsixOrl9laOZSXl5Ofn8+BAwesFkWjCQvD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\nDhqNxi9aOWg0Gr/8f+oSxfuPC6HEAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x7f10341ba780>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "rw_trimmed = trim_some_mistakes(rw, 1)\n",
-    "plot_trace(trace_tour(rw_trimmed))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 140,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Mistake(i=702, step=Step(x=-1, y=1, dir=<Direction.RIGHT: 2>))]"
-      ]
-     },
-     "execution_count": 140,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "mistake_positions(trace_tour(rw_trimmed))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 141,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": [
-    "patterns = [square_tour, cross_tour, quincunx_tour, heart_tour_func]\n",
-    "tours_filename = 'tours-open.txt'\n",
-    "\n",
-    "try:\n",
-    "    os.remove(tours_filename)\n",
-    "except OSError:\n",
-    "    pass\n",
-    "\n",
-    "success_count = 0\n",
-    "while success_count < 100:\n",
-    "    lc = trace_tour(random.choice(patterns)())\n",
-    "    rw = guided_walk(lc, seek_step_limit=0, return_anyway=True)\n",
-    "    if rw:\n",
-    "        rw_trimmed = trim_some_mistakes(rw, random.randint(0, 15) + random.randint(1, 3))\n",
-    "        if len(rw_trimmed) > 10:\n",
-    "            with open(tours_filename, 'a') as f:\n",
-    "                f.write(rw_trimmed + '\\n')\n",
-    "                success_count += 1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "collapsed": true
-   },
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.5.2+"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}

diff --git a/06-tour-shapes/tour-shapes-solution.ipynb b/06-tour-shapes/tour-shapes-solution.ipynb
new file mode 100644 (file)
index 0000000..9a0a4e1
--- /dev/null
+++ b/06-tour-shapes/tour-shapes-solution.ipynb
@@ -0,0 +1,674 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "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",
+    "1. which tours are closed?\n",
+    "2. what is the area enclosed by the tour?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import collections\n",
+    "import enum\n",
+    "import random\n",
+    "import os\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "class Direction(enum.Enum):\n",
+    "    UP = 1\n",
+    "    RIGHT = 2\n",
+    "    DOWN = 3\n",
+    "    LEFT = 4\n",
+    "    \n",
+    "turn_lefts = {Direction.UP: Direction.LEFT, Direction.LEFT: Direction.DOWN,\n",
+    "              Direction.DOWN: Direction.RIGHT, Direction.RIGHT: Direction.UP}\n",
+    "\n",
+    "turn_rights = {Direction.UP: Direction.RIGHT, Direction.RIGHT: Direction.DOWN,\n",
+    "               Direction.DOWN: Direction.LEFT, Direction.LEFT: Direction.UP}\n",
+    "\n",
+    "def turn_left(d):\n",
+    "    return turn_lefts[d]\n",
+    "\n",
+    "def turn_right(d):\n",
+    "    return turn_rights[d]\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "Step = collections.namedtuple('Step', ['x', 'y', 'dir'])\n",
+    "Mistake = collections.namedtuple('Mistake', ['i', 'step'])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def advance(step, d):\n",
+    "    if d == Direction.UP:\n",
+    "        return Step(step.x, step.y+1, d)\n",
+    "    elif d == Direction.DOWN:\n",
+    "        return Step(step.x, step.y-1, d)\n",
+    "    elif d == Direction.LEFT:\n",
+    "        return Step(step.x-1, step.y, d)\n",
+    "    elif d == Direction.RIGHT:\n",
+    "        return Step(step.x+1, step.y, d)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def step(s, current):\n",
+    "    if s == 'F':\n",
+    "        return advance(current, current.dir)\n",
+    "    elif s == 'L':\n",
+    "        return advance(current, turn_left(current.dir))\n",
+    "    elif s == 'R':\n",
+    "        return advance(current, turn_right(current.dir))\n",
+    "    else:\n",
+    "        raise ValueError"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def trace_tour(tour, startx=0, starty=0, startdir=Direction.RIGHT):\n",
+    "    current = Step(startx, starty, startdir)\n",
+    "    trace = [current]\n",
+    "    for s in tour:\n",
+    "        current = step(s, current)\n",
+    "        trace += [current]\n",
+    "    return trace    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def positions(trace):\n",
+    "    return [(s.x, s.y) for s in trace]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def valid(trace):\n",
+    "    return (trace[-1].x == 0 \n",
+    "            and trace[-1].y == 0 \n",
+    "            and len(set(positions(trace))) + 1 == len(trace))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def valid_prefix(tour):\n",
+    "    current = Step(0, 0, Direction.RIGHT)\n",
+    "    prefix = []\n",
+    "    posns = []\n",
+    "    for s in tour:\n",
+    "        current = step(s, current)\n",
+    "        prefix += [s]\n",
+    "        if (current.x, current.y) in posns:\n",
+    "            return ''\n",
+    "        elif current.x == 0 and current.y == 0: \n",
+    "            return ''.join(prefix)\n",
+    "        posns += [(current.x, current.y)]\n",
+    "    if current.x == 0 and current.y == 0:\n",
+    "        return ''.join(prefix)\n",
+    "    else:\n",
+    "        return ''"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def mistake_positions(trace, debug=False):\n",
+    "    mistakes = []\n",
+    "    current = trace[0]\n",
+    "    posns = [(0, 0)]\n",
+    "    for i, current in enumerate(trace[1:]):\n",
+    "        if (current.x, current.y) in posns:\n",
+    "            if debug: print(i, current)\n",
+    "            mistakes += [Mistake(i+1, current)]\n",
+    "        posns += [(current.x, current.y)]\n",
+    "    if (current.x, current.y) == (0, 0):\n",
+    "        return mistakes[:-1]\n",
+    "    else:\n",
+    "        return mistakes + [Mistake(len(trace)+1, current)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def returns_to_origin(mistake_positions):\n",
+    "    return [i for i, m in mistake_positions\n",
+    "           if (m.x, m.y) == (0, 0)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "sample_tours = ['FFLRLLFLRL', 'FLLFFLFFFLFFLFLLRRFR', 'FFRLLFRLLFFFRFLLRLLRRLLRLL']"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def bounds(trace):\n",
+    "    return (max(s.x for s in trace),\n",
+    "            max(s.y for s in trace),\n",
+    "            min(s.x for s in trace),\n",
+    "            min(s.y for s in trace))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "plot_wh = {Direction.UP: (0, 1), Direction.LEFT: (-1, 0),\n",
+    "           Direction.DOWN: (0, -1), Direction.RIGHT: (1, 0)}"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def chunks(items, n=2):\n",
+    "    return [items[i:i+n] for i in range(len(items) - n + 1)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def plot_trace(trace, colour='k', xybounds=None, fig=None, subplot_details=None, filename=None):\n",
+    "    plt.axis('on')\n",
+    "    plt.axes().set_aspect('equal')\n",
+    "    for s, t in chunks(trace, 2):\n",
+    "        w, h = plot_wh[t.dir]\n",
+    "        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",
+    "    xh, yh, xl, yl = bounds(trace)\n",
+    "    if xybounds is not None:    \n",
+    "        bxh, byh, bxl, byl = xybounds\n",
+    "        plt.xlim([min(xl, bxl)-1, max(xh, bxh)+1])\n",
+    "        plt.ylim([min(yl, byl)-1, max(yh, byh)+1])\n",
+    "    else:\n",
+    "        plt.xlim([xl-1, xh+1])\n",
+    "        plt.ylim([yl-1, yh+1])\n",
+    "    if filename:\n",
+    "        plt.savefig(filename)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Part 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "226"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "with open('06-tours.txt') as f:\n",
+    "    tours = [t.strip() for t in f.readlines()]\n",
+    "len(tours)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "61762"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "sum(len(t) for t in tours if valid(trace_tour(t)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 209 ms per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "sum(len(t) for t in tours if valid(trace_tour(t)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Part 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 1min 29s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "[(i, j) \n",
+    " for i, pi in enumerate(tours) \n",
+    " for j, pj in enumerate(tours)\n",
+    " if i != j\n",
+    " if not valid(trace_tour(pi))\n",
+    " if not valid(trace_tour(pj))\n",
+    " if valid(trace_tour(pi + pj))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(16, 125),\n",
+       " (70, 48),\n",
+       " (91, 128),\n",
+       " (110, 134),\n",
+       " (116, 194),\n",
+       " (123, 51),\n",
+       " (136, 9),\n",
+       " (142, 193),\n",
+       " (152, 63),\n",
+       " (168, 150),\n",
+       " (201, 83),\n",
+       " (208, 204),\n",
+       " (212, 113)]"
+      ]
+     },
+     "execution_count": 31,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[(i, j) \n",
+    " for i, pi in enumerate(tours) \n",
+    " for j, pj in enumerate(tours)\n",
+    " if i != j\n",
+    " if not valid(trace_tour(pi))\n",
+    " if not valid(trace_tour(pj))\n",
+    " if valid(trace_tour(pi + pj))]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "80622"
+      ]
+     },
+     "execution_count": 42,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(sum(len(t) for t in tours if valid(trace_tour(t)))\n",
+    "    +\n",
+    "    sum(len(pi + pj) \n",
+    "     for i, pi in enumerate(tours) \n",
+    "     for j, pj in enumerate(tours)\n",
+    "     if i != j\n",
+    "     if not valid(trace_tour(pi))\n",
+    "     if not valid(trace_tour(pj))\n",
+    "     if valid(trace_tour(pi + pj)))\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 1\n",
+      "2 1\n",
+      "3 4\n",
+      "4 5\n",
+      "5 7\n",
+      "6 3\n",
+      "7 1\n",
+      "8 2\n",
+      "9 2\n",
+      "11 2\n",
+      "18 1\n",
+      "19 1\n"
+     ]
+    }
+   ],
+   "source": [
+    "l1s = {}\n",
+    "for t in tours:\n",
+    "    tr = trace_tour(t)\n",
+    "    l1 = abs(tr[-1].x) + abs(tr[-1].y)\n",
+    "    if l1 > 0:\n",
+    "        if l1 not in l1s:\n",
+    "            l1s[l1] = []\n",
+    "        l1s[l1] += [t]\n",
+    "\n",
+    "for l1 in l1s:\n",
+    "    if l1 < 20:\n",
+    "        print(l1, len(l1s[l1]))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(0, 124),\n",
+       " (1, 1),\n",
+       " (2, 1),\n",
+       " (3, 4),\n",
+       " (4, 5),\n",
+       " (5, 7),\n",
+       " (6, 3),\n",
+       " (7, 1),\n",
+       " (8, 2),\n",
+       " (9, 2),\n",
+       " (11, 2),\n",
+       " (18, 1),\n",
+       " (19, 1)]"
+      ]
+     },
+     "execution_count": 30,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[(l1, len(l1s[l1])) for l1 in l1s if l1 < 20]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 1min 28s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "(sum(len(t) for t in tours if valid(trace_tour(t)))\n",
+    "    +\n",
+    "    sum(len(pi + pj) \n",
+    "     for i, pi in enumerate(tours) \n",
+    "     for j, pj in enumerate(tours)\n",
+    "     if i != j\n",
+    "     if not valid(trace_tour(pi))\n",
+    "     if not valid(trace_tour(pj))\n",
+    "     if valid(trace_tour(pi + pj)))\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "good_is = []\n",
+    "goods = []\n",
+    "tried = []\n",
+    "for l1 in l1s:\n",
+    "    possible_l1s = [i for i in range(l1-1, l1+1) if i in l1s]\n",
+    "    candidates = [t for i in possible_l1s for t in l1s[i]]\n",
+    "    for t1 in candidates:\n",
+    "        for t2 in candidates:\n",
+    "            if t1 != t2:\n",
+    "                t12 = t1 + t2\n",
+    "                if (t12) not in tried:\n",
+    "                    tried += [(t12)]\n",
+    "                    if valid(trace_tour(t12)):\n",
+    "                        good_is += [(tours.index(t1), tours.index(t2))]\n",
+    "                        goods += [t12]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "80622"
+      ]
+     },
+     "execution_count": 51,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(sum(len(t) for t in tours if valid(trace_tour(t)))\n",
+    "    +\n",
+    "    sum(len(t12) for t12 in goods)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1 loop, best of 3: 1.16 s per loop\n"
+     ]
+    }
+   ],
+   "source": [
+    "%%timeit\n",
+    "\n",
+    "l1s = {}\n",
+    "for t in tours:\n",
+    "    tr = trace_tour(t)\n",
+    "    l1 = abs(tr[-1].x) + abs(tr[-1].y)\n",
+    "    if l1 > 0:\n",
+    "        if l1 not in l1s:\n",
+    "            l1s[l1] = []\n",
+    "        l1s[l1] += [t]\n",
+    "\n",
+    "goods = []\n",
+    "tried = []\n",
+    "for l1 in l1s:\n",
+    "    possible_l1s = [i for i in range(l1-1, l1+1) if i in l1s]\n",
+    "    candidates = [t for i in possible_l1s for t in l1s[i]]\n",
+    "    for t1 in candidates:\n",
+    "        for t2 in candidates:\n",
+    "            if t1 != t2:\n",
+    "                t12 = t1 + t2\n",
+    "                if (t12) not in tried:\n",
+    "                    tried += [(t12)]\n",
+    "                    if valid(trace_tour(t12)):\n",
+    "                        goods += [t12]\n",
+    "\n",
+    "(sum(len(t) for t in tours if valid(trace_tour(t)))\n",
+    "    +\n",
+    "    sum(len(t12) for t12 in goods)\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.2+"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

diff --git a/06-tour-shapes/tours-random-walk.txt b/06-tour-shapes/tours-random-walk.txt
new file mode 100644 (file)
index 0000000..ffb1608
--- /dev/null
+++ b/06-tour-shapes/tours-random-walk.txt
@@ -0,0 +1,200 @@
+RFFLFFRRFLFFFFFFLRFLFFFRFRFFLRFLFRLFFLFFRFRLRRFLFFFFLFFLRFFRFLFFLRRLRFFFLLRFLFRFRLFFFRFLLFRFFFFFRLRLFRFLFFRFLFFLFFFFFLRRFRFFFLRFFFLFFLFFRLFLFRFRFLRFLRFLFFFRFLFFLLRLRRFFFFLFRFFF
+FLFFLLRLRFLFFFRFRLRFFLRLFLFFRFFFRFFFFLFFLRFRFLRFFLFRFLRFFFFLFLFFFFFFFLLFRRFFRLFRFLRFFLRFRLLRLFFFLRFFFRFLFFFF
+FRLLFLRFFFFFRRFLFFLLFRFRFFFLFRRFLFFFFFLLFRLRFFFRFFLLFFFRLFRFFRFFFLLFFRFRFFLLRFLFRRFFFFFRFLFFRFFFLFFFFLRRFLFFLRRFFFFFRFFLRFLFFFLRRLRFFLFLFFFLFRFFFFFLFFLRRLRFFFFRLRLLFLRRFRLFFLRFRFRLLFFRFFLRFRRLFLFFLFLRFFRFLFFRFRFFLFRFRR
+FFFRLFFRLLFRRLFRLRLFRFFRFFLLRRLFFFLFFFLRLRFFFRLLFFFFLFRFLFRFFRFLFFFRLRLFFFFFFFLLRLRLRFFFRLLRFLRRFLLFRFLRFLRFRLFRFFFRFLFFLFRLFRFFLLRFFFRLFFLRFFRFLFLFFRLFFRFFLFLFFRLLFRFRLRFFRLFFFLFLFR
+RRLRFFLRFFLLRFFRFLFRLFFFLFFRFLFFFFFRLFRLFFLFFRRFLFFRLLRFFRRFLLRFFFLFFRLFLFFRFFRLLFLRRLFLFRFRFFFLLRFFRLFFRLRFFFFFFLFLFFLRFFFFRFFFLFFRFFFRFFFFLRFFLFLFFRFFLFFFRFFFRLRFFFLRLLFRRLRFFLFFFLRL
+FFRFFRLFRFLRRLRFLRFFFRFFFFFFLFLRFFRFFLFRLLRFRFFLLFFRFFRFFRLFLFRFFFLFFRLFRRLFFLFFFFFFFFLRFFFFRLRFFLFFFFFFFFRFFRLRRLFLFFLLRFRFFLRLRLFFFFLRFFLFLRLFRFFRFFFFLFRFRLLFFFLRFFFFFLRFLFRFLRFFFFFFLFLFFRFFRFLFRFLLRRFLFFLFFFFFRFFLFFFRLRFLRRLLFFLRFRRL
+FLRFFRFFLFFFFFFLFFRRLFFLFFFRFRFFFFLFLRRFFFLRRFFLLFRFLFRFLFFFFFRFFRLFLLRFFLRFFFLRLLFFFRFFFRFFFFFRRRRFLRFFLFLRFFFFRLLFFRLFLRLFFFFF
+FLLFFLLRRFRFLFRFRFFRFLFRFLRFRFFLFRFFLFRLFFFRLLRFRFFFRFFRLLFRFFLFFFFRFFRFFFFRLFLFFFLFFFFRLFRFLRFFFFLFFFFLFRLRFRRFFRFRFLFRRLFLRLFLRFFFRLFLFRRLFLFFLFLRLRFFFFLFRLFRLLRRLFRLLFFFRLLRFLFFRFRRLFFLFRLFLFFFFFRRFFFFFFLFRFFFFFFLRFLRLFLFLFRFFFRFFFFRLLFFLLRFFFLFFFLFFRFFFFRLFRLRFLFFLFRFFRLFFFRFFFFRLRFFLFLRLFF
+LLFFFFFLLFRFFLFRLRFFFLRLFRFFFRLLFFFFFRRLFFFFRFFFFLRLFLRLRLFFLFRFLRFFFLRLFFRRLLRRLFLFFFRFRFLLFFFRFFFFFRRFFFFRFRFFFFLFRFFFFLFFFFRFFRLLFRFLFRFRFFLFRLRFFLFRFFFFLFLRFRRLFFFFFRLFFLFFRRLFLLRFLFFFFFRFLRRLFLLFRFFFFLRFRFFRFFLFLFFFFFFLFRLFLRFFFFRFFLFRRFFLLFFRFRLFRRFFRFFRFFFFRFLLRFFRLRRFRRFFRLFRLFFFLRRFLFLRFFRRLRLRFFFFRLFRFFFRFLFLFFLLFFFFRLFLFFFFRFFRFLLFFFRFRLLRRLRFRFFF
+LLFFFRRLFFFRFLLFFFFRRFLFLFFRLFLLRRFFRFFFFFLFFFFLFFRFLRRFRLFFLLRFFFFRFRLFRLFRFRLFFFFFRFFLFRLFRFFLLRLFRFFFFRFFLFFRFFLFFFLRFFFRFFLFRLRRFFFLRLLFFRRLRFLFFFFLFFRRFLLFRFFRLRFFFLLFRFFRLLRLLRFFRFFFLLRRLLRLFFRFFRLRFLFRLRLFFFRRLFFRFFLFFLFRFFRFLFRFRFFRLLFRFRLFFLRLLFRLFF
+RFLRRLRFLLFRFFFLRFRFFFFFLFRLFFRRFFFFLFFFFFFFLFFRFFFRFFFRFRRLFFFFFFRFFLLRFRRFFFFFFFLRFLLLRRLRRLLFFFFFFFFRFRLFRLFRRFLFFFFFFLLF
+FRRFRFRLFRLFRFRFLLFFFRLFRLFLFLRFFFFFRRLFFLFFFLFRRFFLFRFLFFLRFFLFFFRRLFLFFFFFFRLLRFFFFLFFFFFLLRRLFLRFFFFFFFRFRFFFFFFLFRFFFFFFFFLRLLFRFFRLFRLRFFFFRFLRRLLFFFRRLLFFFRFFLFFLFRRFFLFLFFFRFRFFFLLFFFFFRLRFFFFFFLLRRLLFRFFFFLFFRRLFLRRLFL
+RRLLFRLRLFFFLFRFRFLLFRRLFRFLRLFFFFFFFRLLFFFRFRLRFFFFFFLLFRFRFRLFFFRLFFFRLFRFLFLRRFLFRLRFFLLRLFFRFFLFFRLLRFLFRRLLFRFRLFFRLFRRLFRLRFFFFLFLFRFFFFFLRFFLFFFLFLRFRFFFFFRFFLFRRLFRLFFFFRLFFFLRFLFLLRRLRLFFLRRLFRRLFRLFFFRF
+FRFFFRFLFLRFFFFFFFLFLRFRFFLFRRFFFLRLFFFLFFRFFFRFRFLLRFFFFLFRFFFFFFRFLFFFFRFLFFFLRRLFFFFFFFRLFRFFFFFFFRLFFRRLFFLLFRFLLRFFRFFLFRLLFRFFFFFFFRFFLRFRFLLFRFLRFRRLFFRFFFLFFFLF
+RFFRLLFFLLRFFFRLRLRFLFRFLFFLFFFFLRFRRLLFRFFLFFFRLFFRRFFFFRLFFLFLFFRFRFFFFFLLRRLRRFFLLRRLLRLFFRLRLFFRRLLFFLFFFFFRFFLFRFFFRLLRFLFFFFFFRRFRFFFFFFRLRFFFRFLLFFRFRLFFRLFFFRLLFRFRFLFRLFFFFFFRFFFFFRFFLFFFLFLFRFFRLLFFFRRFFLRLFFFLLLFFRLFFLFFLRFRFFLLRRFRFRLFFRRRFFFFFLRRFLFFLFLRFRFFFFRFFLFLRRFLFFRRLFFFLLRRFLFRFFLFFRLFRFFFFFFFFFFFRFLRFLFFRFFRFLRFFRFFF
+LLFFFFFRLFLFRRFFLFFRRLFFRFFRLFFFRLFFFFLFRFFLFLRRFFLLFFRRFFFLRFLLFRLRFLFFRFFFLFFFFFFRLRRLFRLFLRFFRFFLRFFRLLFFLLRFRLLRFFFRLRFFLFRLRLFFRRFLFFRFFFFFLRLRFRFLFFFLLFRLRLRFLFFFRFRLFLRFFFRLLFFLLRRFFFFRFFFFLRFLLFRFFFFFFLFRLRFLFFFFLRRLFLRFFRLFFFRFFFFRLLFLFFRLFFFRLLRFFRFFRFFFRLLFFFFFLFFFFFRFLFFRLRFFFRFLRLLFRFFRLLFRFFFF
+LFLRFRFLFFRFFLRFFFFRFLRRLLFRFFLRLRRFLLRFFFFFRFLLRFLFFFLFLRRRLFFRFFLRRLRFFLLFRLFFRLFRRLFFFLFFRFFLFRFFLRFFFRFLFFLFFFFLLRRLFRRFFFLRRLLRFFLFFFLRFRFFFFRFLRRLLFRLFLRLFLRFFFFLFLRLLLLRLRFFFLFRFRFRFFLRLFLRLFRRFLFFFFFRFFLFLFFFFL
+RLLFLRLFRFFFLFFLFRFFRRLFLFRFFFLRFFFLFFFRLLRFRLFFFFFFLRLRFRFFFRLRLFLFRLRLLRFFFFFRFLFFFLFFRRFLRFRLFLFLRFRFRFFFFFRFLFFFRFLLFFFFFRLFLRRLFRFFLFFFFRRFLFLRFFFLFFRFFFFFLLFRFRFFFFRRLLRLRRLFLFRLRLRFFLLRFRFRFFLFFFF
+FRFFFFFRLFFFFLRFFFFLRLFRFLFRFFFLRRRRF
+RFFFFRFFLFFFFFFRLLRFFFRRLFFFRFLRLFLRFFFLFRLRFFLRFFRLFRLFLFRRFLFRFLFFLRFRLRLFFFFFFRFFLFLRRRFRFLFLRLRFFFLFFLFFFFLRRFFLRFFFRLRFFLFLRFRLFFFLFRLFFFFFLLRFFLLFLFFFFFFRFFRLLFFFRFRLFLFLLLFFFRFLFFFFFRFFFFFFLFFFFFFLRRFFFFFFLLRF
+FRLRLRFLRFLFFFFLFRLLFFFFRFFFFRLFFFRFRFRFRFFLFLRFRLFFFLFLLFFFFFFFFRFFLFFRFFFFFFFFRFFF
+LLLFFRFLRFFFFFFFFLLFRFFFLFFFFFLFRFLLFRFFFFFFFFRLFLFRFFFLLFRFLFFFFLFFRFFFFRRFLFFFLFFFFFLRFF
+FRLRLFLFRRLLRLLRRFFRFRLLFFRFFRFLLFFFLFFFLRFFLFRFRFFFFFFFFFLFFRRFFFFLFLFFFFFFRLFRFFFLFFLFFRFFFRLFFFFFLFRFFLLRLFFFFFFRFFRFFRLFLRFLRLRRFLFLFFFFRLLRFFLFRFLRRFFFFRLFLFFFFRLRFLRLFRFLRFFFFLFFLRFLFRRFFFFFFFLFLFRFLFFFRFRLRFFRLFFLRFFFRLLFRFLFFFRFLFFFFLFRRFFLLFFFLF
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+FFFFLFFFFRLFFFRRLLFFFRFRFFLLFFRFLRFFFFFLRRLRLRLFLRLFFRFFFRFFFFFRLFLFFLRFLRFFFFLFRFRLFFFLRFFFFRFFLRFFFFRLFRLFFFFFFFRLLRFFRFFLLFRLFFFFLRFFFFRLFRRLLFFRFFFFLFRFRFLFFRLFLRFLFFFLRFFFFFLFRRFLRLFLRLFRRFFLLRFLRRFFFFLFFLFRFFRLFFLRFFLRFRLRLRFFLFRFLLFFFRRFFFLFFFFFFRFRFRLFFLFFFFRFRF
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+RFFFFFFFFRFLRLLFRLLRLFRLRFFRLFRRFFFLLRLFFFRRLRFFFLRFLRLFLFFRFLRFFFFLFLLFLFRFFFFFRFFLFFFFFLFRFRFFFFLLFRLFFFFLRFFRRFLFFFRRFLFLFFLRFFLFFRFFRRLFLFFFLFFRFFFRLLFFFFFRFLRLLRRFRLRLRFLFRFFFRLFFFFFLFRFFFFLFFFRRFFFLFFLLRRLRLFFFRFLFLLFFF
+FLFLRLLFFRLFFRFLFLFFFFRRLLFLRFFFFLRFLFFFFFLFFFRLFL
+FRRFFFFFLLRFLRLFFRRFFFFLLRFRFFFLLRRFFRFFLLFLFRFFFFRLRLFRLLRFRFRFLFRFLRFRFFLFRFRFRFFFRLLRLFRFFRFRFRLRFFRLFFRLRLRFFRFRRRLFFFRFRLRFFLRLRFLFLFRFFFFFRFFFFFFFLFRLFFRFLFFLFRFFFFRFFRFFFLFFFRFFFRFFLFFLRLLFFLFRRLFRLFRFFFLRLFRFFRLRFRLLFFRLLFRRFFFLFFFFFRFLLLFFLL
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+FLFRFFRFFFLRLFFFFRFFLFFFFLRLRLFRFRFFFFFFFRFLFLFFFFRFFLRRLFFLFFFRFRFFRRFFFLFFRRRLFLFLFRLFRRFRRRLLRRRLRFLFRFFLLRFFLFFFLLLLFFLRFRFFLFFRFFFLFRLRRLRLRFLFFFFLLLFFFLLFF
+FFFFFFFFFFRFRLRRLFFLFRLLRRFFRLFFLFRFRFRRFLRRFFFLFFRLFLFFRFFRRFRLFRFFFFFRFLFRFFFFFFLRFLFRLRFFRFFRRRFLRFFFFFFFLFLRRFFLFRLFFFFRLLFFRRFLLFFFF
+RLLRFFFLLLFLFFRLFFRLFRLLRFRLLFRLFRLFFFRLFLFFLFRLLFLFFRRFLLRFLRFFFFRFFFFFFLLRFRFFLLFRFFRFLFFRRLLFRFRFFFLRFFLFRFLFLRFLFLFRFRFLFLFFLLFLFRFRLRLRLFRFFFLFFFFFRFRFFFLFRRFFRF
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+RFLFRFFLFLFFFFFFFLRFFRFFRRFLFRFRFFFLRRFFLFFFFFRFFFLFRRLFFFFRRFLFRRLLFFRRLFFFFFRLFFLFFFRLRFFRFFLFLFFFRRLFFFRLFFLFRFLRFFFRLRLRFLFFLRRLFFRFFFLLRFLRFLFRFFFRFFRRLLFRLFRFLFFFRFLFRLFLFFFFLRRFRFLLRRLRFLFLRRFFLLRFFFRLRFFFFRLRFFFRLFLLRLRFRRRFFFFFFFFFLFRFRFLFFLFFRFRFFFRFLRLFFRFRLFFRFFLFLRLFFLFFRRFFFRFLLRFFRRFRRFRLRLFLFFLFLLLFFRFFLFFFFFLFFLRRLFLRFFFFRFRFRFLFRFFRFFRF
+FFFLLRFRFFLFRLFFFFFRLFFLRRFFFLRLRRFLLFRLFFFFLLFRFFRFFFFFFRLFLRFLLRRFFFLFFRRFFRLLFRLLFRFFFRFFLRLRFRFRLFRRFRLFFLLLFFLRRLRLLRFFFLLRRLLFRLRRFFFFRLFFFFRFRLRLFLFRFRFLRLFFF
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+RFLFRLRFLFLFRFLFRRFLLRFRFRLFFLFFLFRLFLRFRFRFLLRFFLFFRLRLRLFFFRFFRRFLRFFFRFFRRFLLFRLRFLRFFFFLRRFFFLLFRRFLFFFRLLFFFFRRFLFFFRFRFFLFFLFFRLFFFFFFFLRFRFFRFLFLFFFFRFLFRLRFFFLFRFFFFLRRFFFFFLLRFFRFFLFFRFFFLLFFLFFFFFFFFRFFLR
+FFFFLRLLFFFRFRFLFRFFFFRFFFFFLFFFRRLFLRFRLFRLRLFFRFFFLRFRFLFLFRRFFLLFFFFRFLFFLRFFFRFFFLLFFFFRFFFLFRFFFFRLLFRFLLFFRFFFFFFFRFFFLLRFFFFLFFFRRLRLRLLFFFLFRRFFLFRFRLFRFFFFFFFLFFRRFLFFRFFFFLRFLFFFLLRRFFFLLRLRFFFLRFFRFLFFLFFFFRFFRLFFLFFFLRFFFFFFRRFFLLFFFLRFFRFFLRRFF
+RFLFLRFFFFRLLFFFFLRLFFRFLFRFRFFFFLFFFRLLFFFFFFFRFRFFLFFRLLFFLFFRFFRLRFLFFFRLLFRLFFLRFLFFFRLRFRLFFFRFRFLFFLRFRLLRFFFRFRLFFLFLFFFFFRFRLRFLFRFRFRLFLL
+RFRFFFRFFRFFRRFFLRRFFFFFFFFFRLRFLFRFLFLFFRFFLRLRLLRRFLRLFLFRFFFFFFFFFRLFFFFFFRLFFFRFFFFFLFRLFFLFLFRFFFFRFFFFRRFRFRLRFFFFRFLLRFFFFRFLRRLFFFFFFFLRLFFFLFFRFFFRRLLRLFFLFRRFLFFFFLFFFFFRRLFLRFLFFFRFFRFFFFLFFFFRFFFFFFF
+LFLRLFLFFFFFRLFFLFFFFFLRFRLFRRLFFFFFLLRFLFFFRFFFFFLFFRFFFRFRFFLFFLRRFLFLFRFRFLFRFFLFFLFFRFLFRFRFLFRLRFLFFFRFFRLLFFRFFFFFFRLFFFRFFFFFRLFFFRFFRLLFFFRLLRLLRFRFFFLFFRRLFFLFFRFRLFLFLRFFRFLFLRLFRFFRFFFFLRLRLLFFLRFRLFRRFLFRRLFFLFFFFFFR
+FFFRLFLLLFFRRLFFLRLFLFFFFFRLRFLFFRFFRLFRLFFLLFLFLFRLRFLRLRFFFLFLRLRLFLRRFLFFFFFRFFFRLFFLLFLFFLFRFFRLFFLFLFRRLLRLLFRFLRFFRFRLFRFLFRFRLFFFFFLRLRFLRFRLLFLFRFRFFFFLFLFFFF
+FFFFFFRFFRLFRLFLFFRFFRLLFFFFRRLFFFFFFFLFRLFFLFRFRFLRFLFRFLLFFFRFFLLRFRFFFFFLFFFFRFFLFFFLLRLFRRFFFRFLLRF
+FRFFLFFRFRLFLFRFRLLFFLLRRFRFLLFFRRFLFFLLRLRRLRFLLRRFFLFFRFFRFLRFFFLFLFFFRRLRFLRLRFLFFRRLFFLRLFRRLFLFFRLFLFRFFFLRRLFFFRFRFLFFRFLFFFLRFLFFFFFRFRFLFFFRLFFFLFFFFFFLRFFRFRLLRRFLFFFFRFFFRLFLLRFLRFFFFFRFRFLL
+FFFRFFLLFRRLRLFFRRLFLLRRFLLRFLRFFFRRFLRFFLFRFLLRFRFFFRFFFFFFLFLRFLRFLFLFFRLRFLRFRLFFFFLRLFRFLFFLFFLRFFFRFFRLLFFLFRRLFFRRLFFRLFFFFLFRFLRFFFRFLFFFFFRRLRLLRFLFFLRFFRFFFFFFRFFRLFLFLFFRFFFRFFRRLFLF
+FFLLRRFFFFFLRFFFLFFFRFFRLFFFRFFFRLLFRFLFFRLFLFLRLRRFRLFRLFRRLRFLFRFLLFRLRFFRLRFFFFFLFFRFFFFFFFLRFLLRFF
+RFLRRFLFFRFFRFRFFRLFFFRLLRLRLFLFRFFLFRLLRFFLFRLFFFFFRLLFLRFRFFLFFRFRRFRFFFFFFLFFRFFFFFLLFFFFLFFLLRLLFRFFFRFFFLFFRFFLFLRRFFFFRLFFFFFFLRLLFRFRLRRLFLFFFRFLFRRRLLLRRLFRFLLRLLRRLFF
+FFLRFRLRFLFRFFLFRFFFFLRFFFLRFLRRFFLLRFRFLLRFRFFFFLFFFRFFRLFLRRFLFFLFFFRRFFFFFFFFFRLLFLFFFFFRFFFRLFRRLLFRFFFFLFFFFFFFRLFFRLFRFFLRRFFLFFFFFLRFRFRLLFRLLFRLFFFFFLFFRLRLRFRLRFRLFRFLFFLRRLFRLFLRLFFRFRLLRRFRLFFRFLFFFLFFRRFLFFFFFRFFFFFLFLRFFRFFLLFRFLFFFRFLLRFFFFFLRFFLFRLRFLFFRFFFFFLFFLRLRLRRFFFLRFRRLLFRLRFLFRFLRFLRFLFRFFFFLF
+LFFFLFLLLFFFFRLFRLFFFLFLRFFLFFFFRLLFLFRRFFRFFFFFFRFFLFLRFLFFRLLFRFRFFLRLFFFFFFFRFFFFFRFRFFFLRLLFRFRLLFFFFFFRLFFRLRFFLFLFFFLFRRLFFLRRFLFFFFFFFRFLFFFRFLFLRLFRLLFRFLRFLRFFRFFRFLLFLRLFRFFRFLFRFLFFFFFFLRRRFRLFRLFLLLFLFFFFFLFFFFFLRFLFFLLFFFLFLRFLRFFLFLFFFRRLFFFFLRFRFRLRLFRFFLLRRFRLFFFLFLRFLLF
+LLRFFRFFFLFLLFLFFFLFRLFLFLRRFFLFFRLFLRFFFFFRFRFFLFFRRLFRLFLRFLRFFFFFFFFFFFLFFFFFFLRLFRRLRLFRFLRFLFFFLFRFFLLRRFFFFRLFLFRFLFRFRLLFRFFFRLFFFFFFFLFFFFFFRRFFFFFF
+FLFRFFLLFFRFFFRFFFFLFRRRLFFFLLFRLFLFFFFRRFFFLFFRLFLFFLFLFLFFRLRLRRLFLLFFFFFFLFFFFRFRLFFFLRRFFLLFFRRFLFFFRFRLLF
+FFRFLRLFRLFLLRFFFLFRFFRFRLRLFFLRFFFFFFFRFRLFLFRFFRFLFRFFLFFLFRFFFFRLFFFRFFLLFFFFFRRLLFFFFFRFFFLFFFRFFRLLFRLRFRFFFFFLLFRFLFRFFFLLFFFRFLFFRFLFLFRRFFRFFFFFFFFLFRLFFFRRFLFLFFLLRRLFFFLFRFRFLFFFRFFFFFFFFRLFFFRFFLFFLRLLFRFFRFFRLLRLRFRRLFLRFLFFLRRFFRFRLLRLFFFRFLRLRFLFRRFFLFFFFLRFLLFFFRFFFFLFRLFRFLLFFFFFRFFRFFFLFLFFFFRFRLFFRRFFFLFFFLFFRFFLFFFFFFFRRFFRFRFFLFFFRFLFFFFLRRFLFFRLRFFFFRLFRFLFFFLFFLRFFLFRFFFFRRRFLRFRFLRLFFFFRLRFFFFFF
+FLFFFFLFLRFFFLLRFFFRRLLLFFRFFFLFFFLFFRRLLFRRLRFLFLFLRFFFFFFLLLFFRLLRLRFLRFFLFFFFFRFFFRLFLLRFFFFRFFRLFLLLFLFRFFRFFFFLFFFFFRFFFRFFFFFFFLRLRFRLFFFRLRFRLFFFFLRFRFLFFLFLFRLLFRFRRLFFFFLRRF
+FFRLRFFFFLRLRRFLLRFFFRFFRFFFFFLFRLFRRLFRRFRFRFLRRFFLLRFLFRFFFFLLRRFFLRFFFLFRFFFLFRLFLRFFFFLFFFLRRFFFFLFFFFFFRFFFFLRRRRFFLRFLFFRRFFFFFFRLRFLFFRFRFLRFFLLFRFLRFLFFFRFLLRFFFFRFFRLFLRFFLRFFLRLRLRRLFFFLFRFRFFFLRFRFLFLRFRFLFFLLRFFFFFRFLFLRF
+FFLLFFFFFFFFRFFFRFLRFRFRFFRLFLRFFFRRLFFLRFLFRRFFLRRLLFLRFFFFFLRFFFFFFFFRFFFFFLFRFFFFFFFRFFFLFRFFFFRFFFRFFRFLRLFFFFFFLFFFLFLFLFFFRLRRLFRFLFFFLFFFFLRRFLFRFLFFFFFLFFRR
+LFRLRRFLFRRLFFLRRFLFRFFLLRFLFRFRFFFLFFLRFFFFFLRFFRFLFLRFFFLFFLRFLFFRFL
+LFFLLRFRFFFLFRLFFFFFLRFFFFRFFFLFFRFLRLFRLFFFLFFFRFFFLRLRFFFRFLFFRFFLFFFLFFFRFFFRLRFLFRLFFFFFFFFLRFFRLRRLLFLRFFFLFLRRFFFFFLFFFFLRFLFRFFLRFFRFLFLFFRFFFLFFFRFRFLRFFLFFFRLFRFFLFRFFRFLFLFFFLFRLRFFRFLLFFRFLFRFLRFLFLRLRLRFFFFFRRFFFLLRFFFRLLFFL
+RLFLFRFRFLRFRFRFRLFFFFFLLFLLRFFRRFFFFFRFFLRFFFLRRRLFLFLFRRLLFRRLRLFLLRFLFRRRFLFFLRFFFFRLFFRLRLRFRLLFLRRLLFLRLFRFRFLLRRLRFRFLRFLRLFFLFRFLRFLFFFFFLLFFLF
+FFFLRFRFFFFRLLFLFRFFFLLRFRLRFFFLFRFLRLRRLRLFFLRRFFFFFFLFRFFLFFFRRFLFFFFLLFRRFLLRFRLFLRFFRFFLRFFRFLFLFLRRFLFFFFFRFLLRRFFFFFFFRFLLFFFRFRFFFRLFFFFFRLFFRLLFFFFFFFRFLRFLRRLFFFFFFRLLRRFRFLRLRFLFFFFFFRRLLRRFLLFFF
+RRRRRFFFRFFLFLFFLFRFRFRLFLRFRRLFRLLRFRRRFFLRLFRLFFFFFFLFRFFFRRLFFFFFFFFFFLFFRFLFRFLFFFLRFFLFRFLFFFLLRLRFFFLFFRRRLFLLRFFFLRFFLFFLLFFRRFLRFRLFLFRRFFLFRLFFRLFFLFRFFRLR
+RRLRFLFFFRFLLFFFLRFFFFFLFFFFLRRFFFRFFLFFFFFLFFFFRRLFFFRLRLLRFFFFFLFRFLRLFRFLFFRFFRFLRRFFLFFFFRLFFFFFFFFFFRLFRLFRFFFFRRLFLFFFFRFLFFLFRFFRFRLFFLFFLRFFFFLLRRFFFFLLFRFLRLRLLFRFRFLFLRFFFFRFFFFFFFFFLRFFFFFFRLFLRFFRFFLFFRFLFFFFFFFFRFLLRLRLRFFFLFFRFLFRFFRRLFFLRLFFFFRFRFLFLRFRFLFFFLFRLFRFLFRLLFLFRFRRLFLRFRLFFLFRFFFLFF
+RLLRLFFFFLFLFRFFFFLLRLFRFFFLFFRLRFLFFFRLLRFFFFFFLRLFFRFLFFFLRFRFFLRFLFLFRLFLFRFLRRFLRFLRFFLLRFFRFFFLFFRFFLFRFFFLFRLLFFLF
+RRFRLRLFFLRRLLFFFFRFFFFLLFRLRRLRLFFRFFLFRLLFLRFFFFRFFRLFRFFLFLRFRLFLRFLRFLFRFFFRFRFLLRLFRLRFFFLRLFLRLFRLFRFLFLFFLFRFRFFFLRRFRFLLRLLRRFFFRLRFLLRRFFFRFR
+LFRFLFLFRFRFFFLLFRLFFLFRFLFRFRFFFLRFLFRFLRRFLFLFRFFRFLFRFFLFRRFFFFLFFFLFFLFRFRFLFFFRFFFFRFFFLFFLFFFFFFLFFRFFRRLFFFFLRFRFFFRFLFFFFFFFFLRLFLRRFFRFLFFRRLLFLRFLFFRLFLFRFRFLFLRFFRFLFFFLLRLRLFRRLFFFLFFFRRLFRFFLRFLRFFRLFFFFLFFFRFFLFRLRFFFLFFFLFRFLRFFFLRFFLFFFFFLFRFLRRFLFRLFRLLFFF
+FLFFRFLFRLRFLLFFFFFLRRLRFLRFFLFFRFFLRLFRRLFFFLRFLRRLRLRFFRFFFLFFLRLLRRLRFL
+LLFRFFLLFFFFFFRLFFRLLRRFFLRRFLFRLFFFFLLFRLRRLRFFFRRLFFFRLRFLFLRRLLFFFFFFLLRFFFFFRFLFLFFRFLFFFRFFFFFFFRFLFFFFRRFLLFFRRFFLLFFFFFFRLFFFFRLLFFFLRFFFFFLRFFFLFFFLRRLFRFLLRFRLLRLFRFRLRRLFFRFLFRFFLRFRLFRFFRRL
+FRRFFFRFFFRLFRRLLFLFFFRRFFLFFFFFFFRFLFLRLRFRFFLFFFFLRFRFLFRRFLFRRLFFFRLFFFFFFFLFFLRFFLRLFFFRLFFRFLFRFFFRFLFFFFFFFFLLFFRLRFRLFFFLLRFRLFFRFFFFFLFLFRLRFRFFFFFRLFRFRLRFLFFFFFFRFFFLFFLRFLRLFRFFFLFFFFFFFFFFFLRFFRLFRFFFFRFLRF
+FRRFFRFRFLRFLFRRFLRFRLLFFFLFLRRLLRFFFFRFFLRFLFFRFLFFRFLFRLLRFLFFRLRFFFRLLFFRLF
+FFFFRRLRFFFRFFFLRFFLFFRLFLRFFFFRFFFRLLFRFLRLRLFRLLRRLFRFFFFRRLFLFLFFRFLFFFFFFFLFRFRFLRRFLFRFLRLRFFLLFRFRLFFFFRFLFFLRRLLRFFFFFFFR
+RRFFLRFRLFFFFLFFLFRRLLFFLFLRFRLLFRFRRLFLFFFFFFFLRLFRFFFLFFFRFLFFFFFFFFLRFRFLFFRFFFFFFRRLRFFFFLFFRLFFFFFLRLRLRRLFLFFFRFFFFFFLFFFFLLRFFLRRLFFFFRFFRLFRFFRFRL
+LLFFFLFRFFRLRFLRLFRRFFFFRLFLLRRFFFFFFRFFLFRLRLFRLFFRLRLLRRFFFLFLLRRFLFRFFFFFRLFRFLFFLFFFFRLFRLFFLFRFFRRLFLFRFLRFLRFFRLFLRFLFFFFFFFFFFFLFFRFFRFFLLRRFFLLRLFFRFFFFLRFRFLRFFF
+LLFFFFLFLFFFFFLFRFFRLFFRFLRRFFLFFFLFRFFFRLFFFFRFLRFFLLFFRRLFFFFFRFRFLFRLRLFFRLFLRLFFFFFLLFFRFFRLRRFFLFRFFFFFRLFLRFLRLRLFLRRFLFLFRRLFFFFFRFLFLFFRFLRRFFFFFFFFFFFRLFFLRFFFRFFLFFFFRFLRFRLFFRFRLFLRFFLRFFRLRFLFFFFLFLRFFLFFFFFLRFFFRLFRFFRLLFFLFFFFFRFFFLFFFFFRFFRL
+FFLLFFFFRFRFFFFLFRFLFFFRLRLRRFFFFFFRFFLFFFFRFLFFLRLFRFFRLFFRLRFFLRLFLFLRRLRFFFRFRFLLRRLLFFRFFFLRFFLLFFRRFFFFLFFFRFLRLRFFFFFFFFFFFLLRFRLRFLRFLFRFFLFFFRFLFLFRRLFRFFLFLRRFFFFFFRLRLLRFFFLFFFRFFFRFLFLFFLFRLFFFFRFRFFFFFFFFFFFLFRFRFRLRLLRFFFFFFFRLLRFFFFFFLFLFFFRRFFFFFFFLRFFLRFRLRFFLFFLFFRFRFFFFFRFLFLFRFFLFRFFFRFLFFRLFFF
+FFFRRLFLRFFFFRRLFFLFRLFLRRLFFFFLFFLRRLFFFFFLLRLFFLLRFFFFFFRRRFFFRLLRFFFLFFLLFFFRLLRFFRFLRFFRRRFFFRLLRFLRFRFFLFLRFFFFFRFRFLFFFRFFFFLFLFRRLFLFRFRLLFFLFFRFFFFFFFFFFLFRLFFFFRLRFRFLFFFFLLRFLFFRFLFRFLLRRFFFLLRFRFLFFFFRRLFRRFRFFLRRRRRFFLRLRFRFFRFFRRRFFR
+LRFRLRRFLRFLRFFFFFLFFFFFLFRLFFFFRFFFLRFFRLLRFRFFRLLFRFLFRFLLRFLFLFFFRFFRLLRFFFLFLFRFFRFFLRLRFRLFRFFLFRFFFLFLRFFLRFRLFLFFFFRFLFFLFFLRRFLFRRLFFFFRRLLFLRFRFFFLFLFFFRFFFFLLFRFRRLFFFLFRFFLLFFFRFFFRFFLRFFLFFRFRLRLFFFFRFLFFFRFFFRLLRFFLFFFRRFFLLRFFRFFFFFRFFLLF
+FRRFLRFFLFLRFFRFRFFFFFRLLRFRLRLFRFFRFFLLRFLRFFLLRFFFFLFRLFFFFFFRFLLRFFRFFLLFFFRLFFFRFFFLFFRFLLFRRLFR
+FLFLRFLFFFRLRLLRFLFRLFFFFLFRRFFLRFFFLLRFFRFLFFFRFFLFFLLRRLRRLLFRFFRFFLRFFFFFFLFLFRFLLRFRFLLRFRRRFRFFFFFRLRLLRFRFRLLLFLFLRLFRFLFFRFLFLFFRFFFLFFRFRFLRRLLFRRFFRRFFLRLFFFFFFLLRFFFRFFRLRFLRFLFFFF
+LLFFFLFLRFFFFRLRLLRRLRFLFFRFFLFRFFFLFFRLFFFFFFRFLFFFFFFFFFRLFRLRLFRFLRRFLRFRLLRFFLLFRRFFRFFFFLFFFFFLFLRFFLFRFLRFFFFLFFFFRLFRFFFLFRFLRLRRLLRLFFFFLFRRLLRFLRFFFFFLFRFRLFLFFLRFFFFFFLLRFRFFFRLFFLFFRLFFFFRRLFLFLRRFFFLFLFRFFRRLRLFFFFFFFFFLFFFFFFFFFRFLLRRFRFLFFFRFFLRLFLLRFFRFFFFRFFFLRLRLRRFFLRRF
+FRFLRFRLFRFRFFLFFFFFFFRFLFLRRLFFLRFFFFFRLRLRFFLFLRFFFFFFFRFFFFFFRLFLFRRFFRFLFFLFLRFFFFFFFFRFLLRRLFFLFRFLRLRFFFFFRFRFFFFLFFFRLRFLRRFLFLFRFLFLLRFRFLRFLFFRFRFLFFFFFFLRLFLFRFLFFFFRRLRFFFFFLFFFFFFLFFFRFFLRLFRFLR
+RRFLFRRFFFRLFRLFRFLLRLFRFFLFFRFRFLLRLFRRLFLRFRFRLLFFRLFFFLFRFRFRLFFLRLFFFLRFRFLRLRLRRFLLFRLFLFRFRFRLLRRLLRFLFRRFFFRFLFRLFRLFFFFLFFRLFLFRFLRFRLRLFLRFFFFFF
+LLFRRFFFRFLRRFFLFFLFFFRFFFLFRLFFLFFFRFFFFRRLFFFFFRFLFRFFFFFFLFFRLLFFRFFLFFRFLFFFRFFLFFRLFRLFRRFFFFLRLFRLFFFFRLFFRLRFFF
+FLFLRFFRRFLRLFFRLFFFFFRLFLFFRFRLLFLFFFFRLRFLFFFFFFRRFFLFFFFRFFFFFLFFRFLFFRFFFRLRRLLRFLRLFRLFLLRL
+FRLRFFFFRLFRLFLFRRLRFLRFRRRFLFRFFFFRFLFFLFFFRFFFFFFFLFRFFLFFFRLFFRRFLFFRFLFFFFRLLFRFRFLRFLFFLFRLFFRFFFRLFLRFFFFLFFFFFLRFFFLLLFLFFRRLFFLRRLFFRLRFFFRLLFRFFLFLFRFFFF
+FRFLFFFFFFFFLFLRFFRFFLFFFFRFFRFLLRFFLRFFFFFFFFRFLFLFFFFFFRFFFRLFRLLRFRFFFFFLLRFRRLFFRLFFFLFFFLLRFFFFFFFFFLRLRFFFRFLRFLRLRLLRFRFFRLLFFLRFRLRLRRFFFFFLFLFL
+LFRLLRRLFFRLFFLFRFFFFFLRFFFLRFLFFFRFRLRRLLFFFFRLFRFFFFFRFFFLFFLRRLFLFFFFFFFFRLFRLFFFLFFFLRFFFRFLLRFFFFFFRFLFFFFFFLLRLFFRLRFLRFLRFLRFFRFFFLRFFLRRFFLFLFFRLRFLFLLRFFRFFFFFFFFFFLRFLFFRFFRFLFFRFFFLFLFRFRLFFRFRFLRLLRLRRLLFRLFFLFLF
+RRFLRLFRLRFFFFLRLLLLRLFLFRFRFFLLRRLFFLFRFLRLFFFFFFLLLFFRLFFFLFLFRLRRLFFFLRLLFFRFFFFFRLFLRFFFFRRLFL
+FRFRRFFFFFLRFLFFRFRLFLLFFLRRFFLFFRFFFLFFLFFRFFFFLFRFRFFFFLRLRFFRFLRFFLFFLLLFFLFFFFFFFFRRFFFRFLFFRFRLFRFLFFFRFFFRFFRRFFFRFFRRRFFFRF
+RLFLFRFFRLFFFRLLFLRRFFFFFFFRLFRFRF
+FRLRLFFRFRLFLRFRLRFLFFLLRFRFFFFFLFFFLLFFRFRFLFRLFLFFFRRFLRLFFFRFRLFFFFFFLFFLFRFLFFRFFFRRFLLFFFLLRFRFFRFLFFRFFFFFRLFFFLLRLFFRFFFFLFFFFFFFFRLFFFFFRRLFFFRRLLRRLFFFFLFFLRLFFFFFFFLRLFRFFRLRFLLRFFFFFRFFLFRFLFFFRRLLRFRLFRFRLRLFLLRFFFRFLLRFFFLFRLRFFLFFFFLFRLFRLRRFFLFFFLRFFLFFFLFFLFLFFFFFFFFFFFFRLFLFRFFRLLFFFRLRFFFLLRFLRLFRFFLRFFFRFFFFFFFFFRFF
+LRFFLRLLRRLLFFLFFFFLRFFFFFFLRLFFRLFRLLFLFLFFFFFFRLRRRFLLFFFLLFLRRFFRFLFFFFRFFRFFLFFLRRFFFLFFLFFFLRRLFFRLFRFRLFFFRLFFLRFFLRFRFLFF
+FFFLLRFFFFFRFLRFFFRFRFRLLFRLFRFFFFFFFFLFLFRRF
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+RLLFLFFRFLFFRLFLFRFFRLFLFFFFLFFRRFLLRFFFLFFFFRFLFLFRFFFRFRFFLRFFLFRFLRLFFFFRFFFFLFFFFRFLFFLFRLRFFLFFFRFRFRLFFLFRLFLRFLRLFFLFFRFRFFFFFFFLFRLFFRLFFRFLFLFRLRFRFFLFFFFRFRFFLRLLRFFFFFRRFFFFLFLFFRFFRLLRRFLRFLFFFLLFFRFFRFLFFFFFFFFFFFFFFFFRFFFFFFLFFFRFFFLFFFRFLRLFFFLFRLFFFRFFRFRLRLFFFFLRFFFLLFFRFFFFRLFFLLRFFRFLFFLRFFFFFLF
+RRFLFFFFRRLRLFFRFRLRFLLFFFLFFRFLRLRLRFLRFFFFRFRFFLFFRFFLRLFLRFLFFFFFFFLFFRLRFFFFLRFLFFRFLFLRFFRLRRFLLRFFRRLFFFRFFLFFLRLFFFRLFRFRFFFFLFRRLLRFFLRRLLFFFFFFFLFFFRRLLFFLFRRLRFRLFFFRLRRFLFLRLFFFFRFRLFLFFRLFFFFLRFRFLRFFRFLLFRFRLLFLRFFFLRLLRFLRFFFFFRFFFLFFFLFLFRRFFFRFLRFFFFFFFRFFFFRLFRLLRFFFFLRFLRFFLFLFFFRRFLFFRFRLRLFFFFFFFFFRRFLLFFFRLFRLRFLRFLLRLFFFFFRFFLFFLRFFFFFFFFFFFLFFRLFFFRFFFFRFLFFFFLLRRFFLRFLRRFLFRRFLFFFFLF
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+RLFLFRFFFFRRFLFFLFLFRLRFRLLFFRFRFFFLFFLRFFFFFRLLFFFRLRLFFFLRRFFLRRFFLFRRLFFFRFRFRFFFFRFLFFRFFFFFFFFLLRLRFRLFFRLFFRFLLRFFLFFFFFRLFFLFRFRLFFFLRFRLFFFFRLLLRFRFRLLFRLRFRFFLLFRFFRFF
+FFLFFLRRFLFRFLFLRRFFFRFLLLLLFLRLRLRLRFRFFFFFFFFFFLFFFFFFFFFFFFRLRLFLFFFRLRFFLRRLFFLFLFFFFRFLRFRFFFLFLFLLFRFFFLRFLLFFFRFRLFFFFRFFLFRFFFRFLRFLFRFFRRRFFLRFFFFFFLFFRLFRFFFFFFLRFLLFFLFRRLRLFRFFRFFLFRFLRFFLLLRLFLFFFFFRLRFLFFFLRFLRRLRFFFLRLFFRLRFFLFFFFFFRFFLFLRRLLFRFLFRFRLFFLFFRFRFLFFLRFFLRFFF
+LFFFFFFLFRFLFFFLFRRFFFFFFFLRFFRLFLFRLRFRFFFFFFLLRFFRFRFLLFRLFRFFFFRFLFFFFFFLRFFLRFFFFFFRFLFFFFRLFFLRRLRLLFFFFLRFFFFFFFLFFFRFLFFLFFFRLRFRLRFFRFLFLRLFFRRLLFFRLRFFRFFLRLLFFFRLLRFFRFLLFFFRFLFFFRFFFFFFLLRFLRRFFFFFLRFLFFRRFLFFFFLRLRLFFFFRRLFFLFFLRFFFRFFLRFFRLFFFFLRFFFFFLRFFFRLLRFRRLFFLRFFFFFFFFFRFLFFRLFLFFRFLFFLRFF
+FLLLFFFFLRFFFFLFRLFFRFRRFFLFRFLFFRLRFFFLRFLLRLFRFFLFFFFFLFRRFRLFLRLLRFFFFLRRRLRFLFLRRLRFLRFFRFLRRFRFFLFFRRLLRFFFFFFRFFLFFLRFFFLFFFFFFRFFFFFLRFLFFLFFRRLFFFLRFFRFLFFFFFLFFFFFFRFFFLFFRFFLFRLFFFRFLFFRRFFFFFLFRFFLFFRLRFRFLFLRFFLLLFLRLLFRFLFRLRLFFFFRFFLFRLLFFFFFRRLRLFLFFRLFLLRFRFRLRFRLRFFFFL
+FRFFFRLRFLRFRFFLLFRFFLRFFFLRFFFFLFLFFRFRRFLLFR
+FRFFFLLFFRFLFRFFFRFFLRRFFFFRRFFFFFLLLLFRLFFRLFRFFLFFLRFRLRLFFFFFFFLFRFFRRLFFLRRFFFRRFLFFLLRRLFRFFFRLFFFFLFFFFFFRLFFFRFRLFFLFRFFFFLRFLFLRFRFFLRLLFRRFLLFFFFFRFFFFFFFFFRFFFR
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+LFRRLFRFFFLRFFRFFFLLFFRRFLFFFLLLFLFFRRLFLLLRFFRLFRFRLFFFFFLLFFRFLRFFFFRLFFFFFRRLLFLFLFFRRRFFFLLLRLFFFFFLFFLFFFFRLFFRFFFRFLLRRLFFRFFLFFFLLRFFFFFLFFFFFRLL
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+FFFFFFFFFRLRFLRFLFRFLLRRFRLFFFFFLFRFLRFFRFFFLLFFFRLRLRFRLRFFLRFFLFFFFLRLRLRFLFFFLLFRFRFFFRRLFLFFFRRFFFFFFLFFFFFFLFRFLFFRFRLLFFLRFFFLRFFFFFLFLFFRFLFLRFLL
+RRFFFRFFFLFFFFLFLFRFLRLRFRLFFRFFFFLFFFFLRFFFFRFFFFFLFRLFLRFFLFRRFFLLRFRFFLFFFRLFLFFRFFFFLFFFFRRLFLRFFLRFLRLFFRLFFFFFLFRFRLRFFLRFFFFFLFFFFRRLFFRFFLRFRLFFFFRRLFFLFRFFLRFLFFFFLFRLFFRFLRLFFFRFRFLRLFFFFFFFRFLFRRLRFRFLLRFFRLLRFFFF
+FLFRFLFFLRFLLFRRFLLRRFFRLRFLLFFFLRFFFFFRFLLFFFRRLR
+FLFFFFFFRFRRRLRFFLFFRLRFLFLLLFFFLFFLRRFLFLRFFFLRFLFFFRLFFLLFLFRLRLFFLFFFLRFFFFFLLRLLFFLLRRFFLRFFFLRLLRLFRFRLFFLLRFFFFFFFFLRFFLFFLRLLRFRLFRRFFFFFFLFRFFLRFLRFRLFFLFLLF
+LLFRFLLRLRRFFLFFFFLRLRFFFRFRLRFFFLLFFRFFFFFFFFRRFFFLLRFLRRLLFRFFFRFLFFFLFFRLRLFFFFFLRFLFLRRLFFLLRRFFFFRFFFRFRLFLRFFFFFFLLRRLFLRFFFFLFFRFRFRLLFLF
+RFRRFFFFFRFFFFFFRRLLRFLFFFFLFRRLRFFFLFRFFRFFLFRRLLFFLLRFFFRFFLFLRFRFLRRFLFLRFFFRLFRLFFFFRLFLRFFFRRLLRLFRFRFFFFFLLFFFFFFFFFRFRFRLLRRLLFFLFFFFFLRFRFLFFRLRFRLFFFFFFLFFRFLFFRLLFLFRRLFFLRLFFFRRLFRLFRLLRLRFLLRLRRLRRLLRFRLFFFFRFLFFRFFLFFFFRLFFFLFLRRF
+FFRFFFLFFLRLFFFFRLRRLLFRLRFRFLFFLFLRFFFLFFRFLLFRRFFLFFLLFLFRRRLFFRFFFLFFRLFRRFLFFFRLFFRFFFLFFLRRRRRFFFFFFFFFFFFFLFRRFFFFFRLRFFFLLFFLFFLFFRFLLFFLRRFFFFFFLFLFRLFFRFLRFFFRFLLRFFFLLRLFRRLFFRRFLLFLLRFFFRLFRLFRFFRFFFLFFLLLRFFLRLRLLFFFRRLFLFRRLFRFFLFFRRLLFF
+RLFLFRFFLFLLRFFRLRRLRLRFFFLFRLFRFLLFFFFFFRFFRLFFFFLRLLRLLRRFFFRFLRFFLFFFFFFLFFRLFFFFRRFFFLRFFFFRFFFLFRFFFLLRLFFFFRLFRLFFFFFRLFRFLLFRFFRLRFLRFFLRFRLRFLFFRLFRFRLLFRLFFRLLRRFLFRFLRLLFFRRFLFFFFRLLRFRLRFFFFLRFFFLFFFFFLLFFRFRLFRRLLRRLRLRFFFLFFFFRFRFFLRFFLFLRFLFRFFFFLRFFFLRFRRLFLRFRLFFFLFFFFFFFFFRFLRFLFLFFFFFRFFLRRFFFLFFLFFFFFFFFFFRRLFFFRFLFLFFRFRLLRLFR
+LRLLFLRFLFFLFRFFLRRFLFFFRFFFRFFLFLFRLRFFFLFRFRLFFRLFFFRLFLFLFFRFLFRLRFFFLRRLFRLLFRFLFFRLLRFFFLFFFRRLFFRRFLLRFRLFFFRLFLRFRFLFFF
+FFLFLFRRFLRLRFRLFFLRLRFFFRFFLLFFFFFFRLRLFFFFRFLLFRLRRLFLRR
+RRLRRLRLLFFFFFFFRLLRFRLLFFFRFFFFFLLFRLFFRFFFFRLLFFFRLRFFFLRFFFRFRLFRFFFRLLFFFRLLRFRFLFFRFRRLFLFFFFFLF
+LFFFLRFRFRLFRFFFFFFFFFLLFFRFFFLFLFRFRRLFLRLRFFFFFFFFLFFFFFLRLFFRFFFLFFFRFFFFLFLRFFRFLFRFFFLFFLFFRFFLRLLRFRFRFLLRRFFFFFLRFFRLFLFFFFFLLRFFLRLRRLRRFLRFLFLFRFFFFFRRLFRRLFLFRFLFFLRFFRFLLRFRFFFLRLRFLFLFRFLL
+FFFLFRFFFLFFFRFFFFFFRLLFLRFFRFFFFLFRLRLRFFFRRLLRFLFFFLFRLLRFFFLRRLFFLRFFFLRLFFFFRFLRFFLRRFFFFLFLFRRFLFLRRFFLFFFFFRLRFFLFLRLFFFRFRLRFRLFFLFFRLRFLFFLRFFFRFLRFFFFFRLFFLFFLF
+FRLRFLFFFFRFFRFRLFLFFRFFFRLRRLRRRLLFLFFFFLLRLLFLFFFLRLFLR
+FFLFRLFFFFRRFFLRFLFFFFFFLFFFLRRFFFLFRLRLLRLRRFFRLRFFRFLFLRLRLLRFRLLFRRLFRLRFFLFFLRLFFFLRFFFFFFFFFLFRRFFLFLFRFFRFLFFFRRFLFFFFLFLFRFFFLFRFRFLRRLFLFRLFFLLRFRFFFFFFLFRFRLFFRFLFRFRFLFRLRLFFFFFLFFRLFFFFFFRRFFFFFFLRFLFRRLLRFFFFRFLRRLFLFLFRRLFFFLLF
+FFLLFFFFRRFLFRLFRFLLFFFFRLLLFLFRFFRRRRFLRFFFRLFFLLRFFFFLFRFFFLFLLLRLLFFRLFLLRRFRFFLLRRFFLFRFFFFLRRLRFLFRFFLFLRFLFRRFFFFFFFFLRFFFFFLFLLLFLRFFLLRRFRFFLRRLFFFFLRLFRLRRLFLFRFLLFLRFFRFFFFLRFLRFFFLFRLFLRFFFFLFFLRFRFFFRLRFLFFFFLFFFFRFFLFRFRRFFFRFLRFRFLFLFFRFLFRFFFFFLLFFRF
+LRFFLFFFRLFFFFLLRFFFFFLFFFFFFFRFRLLFFLRRLRFFFRFFFFLFFFFLFFLFFFRFRFFFLFFFFRFFRLFRFLLFFLRFRFRFFLFFFFRLRLLRFLFRRFFLFRFFLFFFFFFFRFRFFFFFLLRFFLFRFFRLRFLFFLFLRFLFRLRRF
+FLFFFFFLRFFLRFFFLFFRFFFFRFLFFRFLFFRFFFFRFRFRFFFRFLFFFRFFFFLLRLRRLRLFLFFRFFLFFFLLRFRFRFFLFFFLFRFFFFRLFLRFFFFFRFFLLFFRRFFFFFFRLRRFFLFFFLRFFFFFFFFFFFFFFFFFFLRLRFF
+FLLFFRLFFLRFRFFFLFRRFLRRLLRFFFRLLFLRRLRFRLLFFLRFFLFFFRFLRFRFRLLFFFFFRLLFRFRRLLFRLRFLLRFFLFLRFFFFFFRFFLFFRLLRLFRRLFFRRFRLRFFRFLFFFFLRRRLFFFFFLFFLRFRLFLFFRFLFFFFLFFRFLRF
+FLFLFLFFFFLFRFRFLFFLFFFRFFLRFFFLFFLRFRFLLRLRLRFLFFRFFFLRLFRLFLFFRLFFLRRFFFFFFLFRFRLFFLRFFFFFFRFLFLFFFLRFLFLRFFRFRFLRFFFRLFLRLFFLFRFRFRLLRFFFFRLFFFFFFRFFFFFRFFRF
+FFFFRFFRFLRRLFRLFLFLFFRFRFFFFRFLLRRLLFRFFFLLFFFRLRFFFFFFFFFFLFFFLRFFFFFLRFFFFFFLFRFLRLRLFRFFFFFLLRFFRFLRLLFFFRRFFFFFFRFFRFLLRFLRFFRFFFLFLFRFFFFFRFLFFLRFFFLRRLFLRFRRLFLFFRLLFFRFLFRLFFRFLFFFLRFRLRFFRFFRLLFLFFFFFRFFLLFFRFLFRRLLRFRFFFFFFFLRLFFFLFFRFLFFFFFFRLRFFLFRFFLFFFRFRLFFLFLFRFFFRLRLFRFLLFRRFFLFRLFLRLRLFRFRFLFFFLRLRLLRLFFRLRFLFLRFFRFL
+FFLFLFLRFRLFFRRFLRLLFFFLFFRRFLRFFFFFRFLFF
+FFFLFLFRLLFFRLFFFFFLFRFRFFRRFLFLFFLRFFFFLFRLFFFRFFFFFRFRFRRLRRFLLRFFLFFFRLFFLRLFRRLFFRLLRLRFFLRLFFRFFRLFFFRLFLFRFFFFFLFRFFFFFFFLLRLFFFRFFFFFRFFFFFFLLRFFFFFFFFFFFFRLFLFFRLFFRFFFFFRFFRFFFRLLFLRFLFLFFLLFFFFLRFFLRFFRFFRFLFFFFFLFRFFLFFLRFFRFLFFRRFFLRLFFLFRFFFRFLLRFFFFFFLFRFLLFFRFLRLFRFFLFFFLFLFLFFLFFRFFFRRF
+FFRFLFLRRFLFLRFLFRRFFLRFFFLFFLRFFRLLRFLLFFRFRFFLRFLRFFFFLRLFRFLFFRFRLFFFFFFLRRLFFLFRRFRRLFRFRFRLFLLFRFLRFFRFLFLRRFFFFRRFFLFFLLFFFFFFFFFFFFRFRLFLRLLFFFFFFFRFLRLRLFFFFFRLLLRLFFFFRRFLFRLLRFFLF
+RFFRLFFLFLRLRFLFLFFFFFRFFRLFFFFRFLRRFRLFFFLLLLFFFFRLFLRFFFFLRRFFFFLFFLRFFFFFFLFRFLRFLFRFRLRFLFLLFFFFFLLRFRLRFRFFLFFFFFFFFRRLFFRFLLRFLF
+RFFFFFLRFRLFFRFFRLFRLLFRLFFLFFFFFRFRFFLFFRLFLFFFFFFRLLRRFLFFFLFFRLLRFFFLRFFFLLFRRLRLRFRFFLRFFLFRLFRLFFFFLFRLFFRRFFFFLLRFFLRFLFFFLRRFFFFFLRLRFRFFFFFRFLRLRLFLRLFLRRLRFFFFFFFFRLLFFRRLFLFFFFFRRLFFLFFRFFLFFFRFRFFLRFFFFFRFLLRFLFLFFRLFFRFRLRFFLFFFRRLLFRFRLLFRRFFFFRLRFLFFLFLRRFFFFRFFLLFFFFFRFLLRFFFRLFRFFLRLRF
+LFFLFFFLFRFRFFRFFLRFFFRLLRFFFFFRFFLFLRFFRFLFRFLLRFFFFLFFFLRRFFRFLFFRLFFRFFFRLLRFRLFLRLFFFRFFLLFRLFFFFRLLFFFRLFRRFFRLLFFFLRRLFFRFLRLRRLRFFLFFFFFFFRFLRFFFFLRFLRFFRFLFLFRFLFRFFFRRLFFLLLRRFFFFLFFRFFFRFFFFFRFFLLFFFRLFRFFRFFFLLRLRFFFLFFLRFLRFFFFLFRLLFRFFFLRLLFF
+FRRFFLRFFFFLLRFRFRLFFFFFFFFFRFRLRLRLFFFRFLFLFLRFLRFFRFFLRFFLRLRLRLRLFRRLFFRLRFLRLFFFRLFLRFLRRFFLFFRFLFFFFFFFFLLRRFLFFLFFRLLRRFFFFRLFFFLFRFLFFFFFLLRLRFLLF
+FFRFFFFFLLRFLRFFRFRFLFRLFLFFFFLFFFRLRFFFLLFFRFRFRLFFRRLLFLRFFFFFFRLFRLFRFFLFFFLFRFFLLRLRRLFFFFRLFFFLFLLFFFFFLFFRRLFFFRLFRLFFFFRRLFLFFRFRFLLFRFFLFLFFRFRLFFRLFFFLFRLRFFLFRFFFRFLFFFFRLFFFRLLLFFLLFRLFFFFRLLRRFRLFLFRFRFRLFRLFFRLLF
+FFFLRFFFFFFLFRFLFRFRFFLFFFLRRLFFLFFLRFFFFFLRFFRFFFFRLFFRLLFFFFRLLFFLRFFFLRFFRFFFRFLLRFFLFFFRRFFLFFFLRFRFLLRFFFLRFFFFLFFRFFFFRLFLFFFRFFFFRLFLRRLFFLRRFRLRFLLRFFFRRFLFFLFRFFLFRFRFFLFFFFFFLFRLLRFFRRLLFLRRLFRFFLFRLFFFFFLFFLFFRFFFFFRFLFFRFFRFLFFFRFFFFFFFRFFLLFFFRLRRLFFLFRLFFRLFFFFFFFRLFFFFFFFRLFFRF
+LFLRLRFFFFFRRLFLLRLRFFFFRFFFFLFFRLRFFFLFFFFRLFFLRRLLRRFFRFLFRLFLRFLFFFFFFLFRFRFFLFFLRFRFFFFLLRFFFFLRFRFFLFFFLRFFFFFFFRFFLFRLFFFRFLRFFLLRLFFFFRFRFFLFFRFFRFLFFFRFFRLFRLRFLFLFRRFFLLFFFFFFLRRFLRLRRFFRLLFFFFFFLFFR
+FRRFLFFFRLFLFRFFFLRFFRFLFLLRRFLRFLFFFFFFLFFRFFFRLRRLFFFLFRFRLFFFFLRFRLFRLFLFFRLFRFRLFRRFLFFFFRLLFFFLRFFFFFFFFLFRRFFLRLLFRRFFLRLL
+FRRFLRRFFLFFRFRFRRFFRLFRRLRFFLRFLRRLLFFRFFFFFFRFFFFFFFRLRFLRLLLRFFFFFFLRLLRFLFFFFLRFFRLLFFFFRLLRRFLFFFFFLFFRFRLLFFLLLFLRLFRFRFLFFRLRLLRFFRLFLFFFFFLRLRFRLLLFLFLFFLFRRLRFLFRLRFFFLFFRFLFRFRFRLRFLRFFLFLFFRLRRFLLRFRLFFFFFFFLFFFFFLLFFLLLFRLRFFFFLLRRFFLRFFFFRFFLFFRRFFFLLFRLLRRFRLRFFRFFLFFFL
+RLLFLRLRFRLRFFLFRFLFLRFFLLFFRLRRFFLRFFFFLLFRFLFRFLFFFFRLRLLFFRFFFLFRFFRLRLFFFLRLFLRFFFFFRFLFLRLLFRRLRFFLRFFFLFLRFFRFFFFFLFFFFFRFRFLFRLFFRFRFLLFFLRLRFFRFLFFFRLRFLRLFRFLFLFRRFFLFFFFRFFFFRLLFFFRLLRFFLRRFLFFRFFFFRFLFFFRLRLFLFF
+FLFRFFLRLRLFFFLFRFFFRFFLFFFRRFFFFFLRRLLFFRFFRLFFRLRRLFLFLFFFFFRFFLFRFFFRLLFLRFLFRFLFFFRFRFFFLFLFFRFFFFLFFRFFFLFRFFFRLLRFLRLFFLFFLLFR
+FRFRLLRFRLFRFLFFFFFRFRFRFFFFLFRFFRLFFLLFLFRLFRRFLLLFFRLLRFLLFRFRFFFRFLFFLRFFRFFFLRRFFLRLFFRRFFFFRFFFFLRLFFLRFRFRRFRFLFRLRFFRFLLFFRLRFLFLFRLRLFLLRFLFFFLFFRFFLLFLFFFRLLFFRLRFFLLRLRRLFRFFFRFFFFLFRLFRLFLRFRFFLRFFLRFFLFFFLL
+FRFFFFLFFFLLFFFFRLFRRLFFRFFFFFLFLLFFRLFRFRFFFFFFFLFRLRRRLFLFRFFFLFRLFFLFRLLLRRFFFLRLFRFLFFRFLRRFFFLFRFFFFFFFLLFFRFLLFRFFFFFRFLFFFFFFLFLFFL
+FLRLRLRFLLRFFLFRFFLLRRFFLFLRFFFRLRFLFFFFFLLRFFLFRLRLFRFLRFFLRLFRFRLRFFLFFLRFFFFFFLFFLRRFFFFLFFRFLFRFRLFRFFLLFFRLFRRLRFLFFLLRRFRFFFLFFFFLFRFFFFFLFFFRLRFRFFLRLLRFFLFLRLFRFFFFFFLFFRFFRLFFRFFLFFRRFLLRLF
+RFLFRLRLRFFLLFFFFRRLLFFFFLRFFRRLFLRFFFFLFFRFLFRRLLFFLRRFFRFLRFLFFRLLRFFLFFFFFFFRLLRRLRFFLLRLRLRRLLFFRFRL
+RFLFRFFRFFFFRFFFFFFRRLFFRLLFFF
+FFLLRRFLFFRLFFFFFRFFFRFFFFLRRLFFFLRRFLRFLFLFRRFLRFFLRLFFRLFLFRRLFFLLRFRRLLRLFFFFFRFFRFLRLLFFLRLFFRFFFFRLRFRLFRLFLFRRFFFFLRFFFRLFLFLFFFRRRFFF
+FFLLRFFLRFFRRFLFRFFLFRLLRLRFLRRFRLFFLFFFRFFFLFFRFFFLRFLFRRFFRFLRFFLLRLFRFLFFRFFFLFRFFLFFRFFFLFFLFFFRFFFFFFRFLRLFFFFFLRFFRFRLFFFFLFFLRFRFFFFLRFFFLFLFRRLFFFFFFRRFFFFFFLFLRFRLRLLFRFFRFFFLFLFFLRFLRFFFFLFFFRFRFLFFFFLRFLFRRLRRLFFRFFRLLFLFRFFFFLLRRLRF
+RRLFRLRLLRRFFFFFLFFFFFLFFRLFRFLFFFFLRLRFFFFFLRRLFFFRLRLFLFRRFFLRFRFLFFRLFLFRFLRFFFFLRFFRLFFFLRRFLFFRRLFFRLLFFRRLFRLFLRFFFLFFRLRLRFFFFFFFFFFFFFRFFLLFFFFFRFFFLRRLFLLR
+FLFRFFLFRFFFFFFFFRFLFLFRFLFLFFFRFRFFFFFFFRFLRFFLLFFFRLFFFRFFLLFFFFFFRLFFFFFFRFRFFFFLFRLLFFLRRFFLLRFFFLFFRFFLFRFFFRLLRFFFFRFFFLFFLFFFRFFRFLLFRRFFFFFLLFRRLFLRLFLFFRRFFLFFFFFFFFRFFLFRLFFFFFRFLRFRLRFLFLFFRLRFLRRFF
+FLFFFLRLRLFLRFFFLRLRFFLRLFFFFRFFFLFFFFRRFLRFFFLFFLRFFFFFLFFFFRRLLRRLRFLLRRFFFFLLRRFFLLFFRFLRRLRRLRFLFFFFLFFFFFRLFFFLFFRFLFRRFLRFFFFLLRFRRLFFLRLRFFRFLFRFFRLFLFFF
+FFRLRLRFLRLFFRLFRFRFLFLRRFFLRFFRLRFRFRLLRLFFFFRLFRFFFFLFFFFFRRLFFFRRRFRFRFFLFFRLRFFFLRLFFRRLLLRRFRLRFRLRFLLRLFFFFFLRFFFFFFLFFRFFFLLFRFLFFRFRLFFLRLFRLFFFLFRFRRLLFRRLFFFLFFRFFRFLLRRLLFRLRFFFFFLRFRFFFFRFFLFFFFRFLFFFRFFLRFFLFLLRFFFRFLLFFRLFRRLFFLRFRRRFLFRLRFRRFRLFFFFLFFRFFLFFRFFLFLFRFLRFRFLLRLRLRFRLFFFFRLFRRLFLRLRRLFFLFRFRLFFFLFLFFFRRLFFRFFFLFLFFLLLFFF
+RFRFFFFFRLRFLLFFFFLFFRLFLRRFRFFFFFRLFRLRLRFLFLRFRLLFFFFFRFLRRFFFFRLFLFRFLRLFFLRFRFFFFRLFLFFFFFFRFLLFRFFRFFFFFFRFLFRFLRFLFFLFFLRRLFLRFFFFFRLFLFFLRRLFFRFLFFFLFRFLFRLRRFLR
+FFFFRRFFFFFLFFFRFRFFFFLFFFFFFFFFFRLLFRRLFLLRFRLFFFFFLRLRRFRLRFLFFFFFFFLFRLRLFRRFLLFFFFFFFFRLLRFFFLFRLRRFRLFFLFFL
+LFFLFFLLFRFFFFRLFFLRLFFRFLLRLRFLLFRFFLRFFRFLFFLRRLLFRLFRFFLRFLRRLLRLRLFRFLLRFFFFLRFFFLLFFFFF
+LFLLRRLFLRFFRLFFLRFFLLRRLRRFLFRLRFFFFRLLFRFLFRFFFFFFFRFFLFRLRRFLFFFFRFLFFFFRLLRFFRRRRRFLRLRLLFRFFFFFLFRRLFLFLFFRFFRLLFLFRFFLFFRFFRFFRLFLFRRFLLFRLFLFRFRRLLFRRLLFFFLFFRRLFFFLFFFLFFFLFFFRFLFLRFRLRF
+FFFFFFFFFFFFFFFFFFFLFLFRFFFFLFRLRFFRLLFFFFRLFFRLFLRFRFFRRRFRFLFLFLLRLLFFRFRLFFFFLLLLFFRRLFLFLFRFRLFRFRRFFFFFFFRFLFFRLFFFFLRFFFRFFLFFLLFFFFLFLRLFRLFFFFRLFRFFFFLLFFRLFRFFLRFFFLFFRLRLFLRFRLRRLFFFFRFFFRRRFFLRFRLFRLLFLRRFFFFLFFFFFFFFFRFLLFFFFFLFRFFRFFLFFFRRLFLFFFFFLFFRFFFLRFFLLRFRFFRRFLFFFRFFLFFFFFLLFF
+FFFLRLLFFRFFFFRLFLRFLRRFFLFFFRLRRFFLRLFLRLLRFFLFFFFRRFLLRF
+FLFFLFFLFLRFRFLRLFRRFLFLFRFLFRFFFRRLFLLRFLRFFFFFFFFFFLFFRLRFFFRFFFLFFFRFRFLRLFFLFFRFLLFRFFRFRLFFLFFFFRFFFFFFLRFLFFFRLFFFFRLRFFFFFRLFFFFFRFLRFRFLFRLLRRFFFLLFFRFRFLFRLFFLFFRFFLFFFFRFRFLFFFFRFLRRLFFFFLLRFRFFLFRFRRLFFLFFRFFFLFFFFFFRFFFLRLFLFLFRFFFLFFRRFLF
+LFFFFRFRFFLFFFRLFRFFLFFFFFRFLFFRRLRFFFLRRLFLFFLFRLFLRFRFFFLFRRLLFLLLFLFFFRFRLRLLRFLFFRFFRFFRLFFLFRFFLFFFLRLFRFFRFFLFFRLRRLLRRFFFRRLFRFFL
+FFRLFFFLLFRRLFRFLFFRFFLFLRFFFFFFFFLFLRRLRFFFRLFFRLFLRRFFFFLLFFFRLFLFFRFRFFFFLFFFFLRLFFRFLFRFFFFRLLFRRLFFLFFRRFFFLFFRRFLFLFFFFRFFLFRRFFLFRFRLFLFLRLFRRLFFFRRFFLFFFFLFLFFRFFFFFRLFFFFFFRLFFLFFRFLFFLFFFFRFLFLRRLFRLRFFFFRFFLRRLFFLLRFFFRFFFRLFFLFFFRFLRFFFFLRFFLRLFFRLRLFFLLRRLFRLFFFFFRFFFRLRLRFFFLFRFFLFRFFFLLFFFRLFLRLRRLFF
+FFLLRFFFFLFFLFFFRFFFLFRFFLFRLRFFFFFFRFLLFFRRFFLFFFRFFLFFLFRLRLRFLFFFRRFFFFLRLFFRLLRRFRLFFLFFLFFFRLLRRFFFLRFFFLRLRLFFFFFLF
+LLRFLRFFFLFLFFFRFFLRFRFLFFFLLRLRFRFLFFLFRFFRRFRFFLFRFFFFFLRFRFRFFLFRFLFLFFLRRLRFRFLFRFLFFRRFFFFLFFLRLRFFRLLFFFLFRFRFFRLFFLFFFLFRFFFFLLFLFFFRLFFFLRLFRLFRFRFRLFFLFFFRFFFLRLFRFLFFRRRFRFFRLFLFFRFLFFRFLFRFLLRLRLLFFRFRFFFFRLFLLRRLRLFRFFFFLFFRRFLLLRFFFFLFLFFFRFFLRRLFFLRRLFFLF
+FFFRLLRFLLRLRFFFLRFRLFRFFFLFFRLLFRRLFFFFRFLLFFRFRLLFRFFFLFFFRFRFLRFFLFFLFRLFRLFRLRLFFRLFFFFFRFFLRFLRRLFLRLFLRRLFFLFFFFLRFLFRRLFRLFFLRFFFRFRLFRLFLFRFRLLFLRFLFFFRFRLFFFLRFRFRRRFRFFRLFFLFFFRLLFFFFFFLRFFFFFRRLFFRLFRRLLRLFFFFFFRFLFRFFFLFRFFFFFFFF
+RRFLRRLFFFFFFLRRLFLFFRFLFFFLRFFRFFRFRRFFRFFFFFLRRFLFFRFLFFFLFFRLFLRFLFFRFFFFFRLFFFRLFRFFLFLRRFFFRRRFFRFFLRFLFLRRFFFFRFRRRFRFFFLLFRRFFFFFLRFFFLRFFFFFFFLLRFFFFLLLFRFLFFRFLFLFFFFFRFFFLLLFLFRLFLRLRRLLFFLFLRRLLLRLFRFFLFFFFFFRLFFFFFLFRFFLFFLLLFFFFFFFFFRFLFFRRFLFFFFLFLFFRFLFRFLRFFRLFFRFRFLLFRRFFLFFFLRLFRLFFLFFRFRLLFRLRRLFFFFRFRLRLFFFRRFLRFLLRLLRFR
+FRRFLFFLFFRFFLLRRLLRFFFLRLRLFFLLRFFFRRFFFLFFFFLRFFFRRLFLFFRFFFFRLLRFLFFFFRFFLFLFFFRFLFRLFFFFFFFRFFLRFFRFFLRFFFFRFLFRFFFFLLRFFRFLLFFRFLRFRFLFLFFRFFFFRFFLLLLRRFFRRLFRFLFFRRFLRLFFFFFFLFFFRLLRLLLFFRFFFLFFRFFFLFFLFFFRFFFRLRRFFRRLFFRLFFFRRRFFFRLRRLFFFLRFLFRFLFFRFLRLRFFFRFLLRRLLLRRFLLFRFFRFFRFFRLFLFFFLFLFRFRFFRFLLFRFFLFFFLFFFFFFRLLFLFRRFRFLLFRF
+FFRFFFRLLRFFFRLFLFRRLLFRRLFLLRFFRFFRFFLFFFFRLFRFLRLFFFFRLFRLRLLFLRLFRFFFLRLRFFFLFRFLLRRFFRFFFRLRFLFRFFFFLFFRLFFRFLFLFFRFLFFFFFFRFRFFFLRFFFLFFFFFFLRFRLRLRLFFFRFRLLFFRFFFLRFLFFFFLRRFFFFFLFLFF
+FLFRLFRFFRLFRLLFFFFRLFRLFFRFRFFFFFLRLFFFFRFLFFFLRFRFFRFFFLFFLRFRFFLRFFFFFLFRLLFFRRFLFLRFFLRFRLFFFFFRLFRFLFLRFFRLFLLRLRFFRFFLLRFFFFFLFFRLFFFRRLLRFLFRLFFFFLFRFFFLFLRFFLF
+FFLFRLRFFLRFFFLFFFLFFFFFLRFFRRFRFRLFFFRLRFFFFLRLFLRRFRFFLFFLRFFRFLFFFRFLFFFRLLFFFRFFFFFFRLRFFFRFFFLFFRFRLFFFFFLLRLFFRLRLRFFLFRFLFFFFRFFLFLRFFRFFRFFFLLFFRFFRFLRFLLFRRFFLFLFRFFFLLFLFRRFFFRFRLLFRFFLFFFRLRLFRLFFRLLFLFLFFFFLFFLFFLFRLFFFFFLRLFLFFRLRFRRRRLLRFRFFFFRFFFFFFLFRFRLLRLFFFRFRLFLLRFFFFRFLFLLRRFFLFRFFRRF
+RRFLFFRFLFRFLRFFFFLFRLFRFFFRLFFFFFFLFFFFLFRRLRFFLFFRRLRLFRFLRFFRFFFR
+FFFFRFFFLRFFFRFFFLFLRFLFLRFFLRFFFLLRFFRFLRRLFFFLRRLLFFRFLRFFFFLFFFFFFFFFLRRLFFLRLFLFRFFFFLRFRFFLFFLRFLFFFRRLFRLFRFFFFFFLLFRRFFLFFLFFRLFFFRLRFFFFFFFFFFLFFRFRLFFLRFFFRFFLFFLRFFLFRRLFRFLFFLFFFFLLFRFRFFFRFFLLRFLRRLRLLRFFLRLLRRFLFFFRRLFFFLFFFRFFFLRRFFFFLRFRLLFFRFLRLLRRFFFFFFFRRFLFFLLRLRFLFFRFLFFFFRFFRR
+LFFFLLRFRFFFFFLFLFFRLLRFFFRLFLLRFFRFFLLRFFFFFRLFFLLFLLRRFFLRFLFFLFLRFFFFFLRFRFRRFFFFFLFRLFRLRFFLLFLLFRLFRLFLFLLFLFRLRLFFFFFFFLFRRFFLLFRFRLLRRLLRFFFRFLFFRLRRRFLLRFFFFLFLRFLFFFLRRFLFLLFFLFLFFRLFFFRFFFLFFRRLFFFLFFFRLFRFLFFFLLLLFFFRRF
+FFFFLFLFRFFLRFRFFLFRFLRLFRFFFFLFLRFFFRLFLRFRFFFFFLRFFRFFFFFLLFRFRFLLFFRRFLRFLRLFFFFLFFRLFFFFFLFRLFRLFLRRLFFLRRFLFFRLFFFRFFLRFLRFRFRLFFRLLFRLFFLFRFLRFRLFRFFFFFF
+LFFFLFFFLRFFFFRLFFRRLFLFFFLFLRRFLFFRRFFFLRRFLFRFLFFFFLFLFRFLRRLRFRLLRLFFLRRFLLFRFLLFFRFRFFLLFRFLRFRFFFRFFFFLFFFRLFFLRFFFFFFRFLFLFFFRLFRRFLRLRFFFLRFRFLFFFLFLRFFRFLFRFLRFLLFRLRFFRLLRFFFFF
+RFFRFLFRRFLLRFFRFFFFFFRLLFLFFFFRFFFFLFLRLRFFRLFRFFFLLFFFFFFRFLFLFRFFFFFRFRLFFFFFFLRLRFFLFFFLFFRFLRFRFLRFFLRLRFLLFRRFFRLFFFLRFRFFFLFRLRLFFLLFRL
+LFFLFFFFRFRFLFLFFFFFRLLRRFLFRFLFRFFFRFLRFFFLFRRFFFFFFLFFFFFLRFFLFFLFRFLFFFRRLRFFFFLRLFRLRRLFLFLFRFRFFFFFLRLRFLRLLRFFLFFRLFFFRLFLFRFRRLFFFLLRFFRRLFFLFFLRFFFFFFFLLFRFFRLRFRFFFLFFFFFRLFRFFLFRFFFLFFRRFLFFFFFRFFLFLFRFRFLFFLRFFLFFFFRLFFFFRLFFFLFFLRFFRLFFRLFLFRRFFFFFFFFFFFRRFLFFLFFFFRFLLFFRFLFLRFFRRLLRLLRFFFFRFRFLFLLRRFFFFFFRFLFFFRFLLFFFLFFRFLRFLFRFRFFFLFFFLFFFRFFFRFFRLFFFFFRFFFFLFLFFFRLFFFFRFLFFFLRLFLFRFFRFLFFFRFFFFFLFLRLR
+FLRRFFRLFLRFFFRFLRFLFFLFRLRFFFRLFLFRRFFLFFRFFRFFRLLFLFFFRRFLRFRLRLFFLFLRLRFLFRFFLFRFRFRLFFLRFFFFFLRRLLRFFLRRFLFFFRLLFRFFFLFFFRFRLRLRFLRFFFRLLFFFFRFLFRFRLFFRLRLFRLFFRLFFRFLFRLFFLRFLRFLFRLFRFFFLLRRFRLLFFRLFRLFFFRRFLFFLFFFLRRFLFLFFFRRFLRLFFLRFRLLFRLRLFLRFFFLRRLFFRLFLFRFFFFFLFLRRLLFFRFFRFLLFFLRFRFFFFFFF
+FLFRFLFFRLFRFRLLRFFFFFFFFLFFFFFFFLRFFFFLRFFFRFFLLRRLFRFFLLFFFRRLRFFRFLFFFLRLFFRFFFFRRFLFLFLLFLFFLLLFRFFFFRFFFFFRRFLFFFLFFRRFFFFLFLFFLFRRFFRLFLFFFFRFFFFLFRRLFLFFFFFFFRFFRLFFFFLFRRFFLFRFFRRFLLFLRFFLRLFRFFRLFFRLFFFFFFLFFLRLFLFFRRFFFLRLFRFFFFFFFRRRFFRFFFFFFFRLFFFLFRFFRFFRFFFFLLFFFRRFFFFLFFRLLFFFFFLFRRFFFRRFLLRLLRFFLFFFRFFLLFRFFFFLFFFLLLFLFLFRFRFLLRFFFF
+RFRFFFRFLLFRLFLFLFFFFRFFFFLFLRFFRLFFFRFLFFLFFFRFLRRLFFLLLLFRRFLFLFLRFFRFFLFFRFFLFRFFLRFFFLFRFFRLFFRFRFFLRLFLLLFFFFLRRFFLRFFFFFFFFRFFFFRLRFFRFFLFFLRFRLFFRLFLRRLRLFRFRFLLFFFLFFFRFFLFFFLRLFFRFFFLRFRLLRFFLFFFRFLFFRFFFFFFLRLFRRFFFLF
+LFFRLRRFFFFFFFLRLRRFFRLRFFFLFFFLRFRFFLFLLRRLFFRFFLFFFRFFRFLRFFLRFLRRRLFRFLFFFRFRFLFFFFLFFLFFFRFLFLLFFLLRRFFFFFRLFLFFFRRRFFLRRFFFRFFFFFRLRRLRLFFFLLRRLFFFRFFFLRFFFLRFLFLLFFLFFFRLLFRFFRLFFLRLLRLFFLLRLLFFRFFFLRLFFFFRLRFLFRFRLFFFLFFFFLRRFFFFFFLLFRRLFFFFFFFFLFLLRFLFLFFFRLLFRLRLFRLLFFFFFFFF
+FLLFLRRFFFLRFFFRFFLFFLRFRLFLFFRLRLLFFFFFRLFFFFRRLLFFFRLFFFFFRLFFFLFFRFRFFLLRFRLRFLFFFFFLRFRLLFFFLFRFLRLLFRLRFRRLLFFRRLRFFLFFRRLFLRRFFLFFFFLLFFFRRFFFLFFFFFRFRFLRFRLFFL
+FRLFRLFFFLRFFRFLFRFRFFLLRFFFLFFRFLRLFLRFRFFFLFFRRFLFFFFFFLFFFFFFFRLRFRLFLRLFFFFFRFLLFRFFFFLRRRLFFLFFRFFFLFLLFLFLFRFRFLFFLRFRRLFFLFFRFLFFFLFRFLFFFFRLRFRLFFFFFRLLFFLFFFFFFRFFFFFRFFLRRLLRFRFLFFFLFLRFLFRLLRLFFFFRLFFLLRFFFFFFFLRFFRFLRLFLFFFFRFLLFFRLRRLFFFRLFLRFFFFLLRFFFFRFFFLFFFFRFRLFLFFFFRLLFRLRRRFFFFRL
+RRFLRFRLRRLFFFLRFFFFFFRRLFLFFFRFFFFRRRRFLFRFFFFLFLFRFRRLFRLRFLFFFLRFFFFRFLFLFRLFLFRLLLFFFFLRRFFFLFLRFLFRFFRFFLFFFFRFLRLRFFFFFLLRRRLRFFFFFRLFFFFRLLRLFLRFRRLFLFFFFFFFFFRFFLRFRFFRFFFFRRLLFRFRRLFLRFRFFLLRFLFFLRFLFFRRLFLFFRFFFFFFFFRLLLRF
+FRFFRLFLFFFFRFRFFLRFFRLFFFRFFRFLFFRLFFFFLFFFLRLRFRFLFFRFFLFLFFFFFFFRFLFLFFFRLRFRFFFRFLFFFFRFLRRLFRFFFLLFFFFFRFLFLFRFFLFFFFFLFFRFFLFRLFFFLLFFRF
+FRFFRFLRFLFFLLRFFRFFFFFFFFFFRLFRFFFRLFFRFLFFFFFLFFRLRFLRFFFRRLFLRRLFLFLRLF
+FRRLRLLRFFLFFFF
+LLLFLFFFLRLRFFLFRLRLFLFRFFLLRFRLRFLFFFLFRRLFLLRRFFLLRRFRFLRLFFFFFRLFRFLRRFFFFFFFLFLFFRFFFRFRFLFLRFRFLFLLRFFLRRFLRFFFFLRFFFFFFFFFRFFLFLFFFFRFRFLFFFRFFFFFLFFFFLRFLFFFRLFRFFLFFFRLLFFFFFFFRFFRLFFFRFFRLFFRFLRLLFRFFFRLRFFRFLFRLFFRLFLRLFFFFLFRLLFFRRFLRR