From 09676bf1605311f08554ab791d50783e4d7c2639 Mon Sep 17 00:00:00 2001 From: Peter Norvig Date: Sun, 8 Aug 2021 18:25:54 -0700 Subject: [PATCH] Add files via upload --- ipynb/RaceTrack.ipynb | 545 +++++++++++++++++++++++++++++------------- 1 file changed, 373 insertions(+), 172 deletions(-) diff --git a/ipynb/RaceTrack.ipynb b/ipynb/RaceTrack.ipynb index 8168cfa..6a2ff4a 100644 --- a/ipynb/RaceTrack.ipynb +++ b/ipynb/RaceTrack.ipynb @@ -8,23 +8,33 @@ "\n", "# RaceTrack\n", "\n", - "From 538's [The Riddler](https://fivethirtyeight.com/features/can-you-zoom-around-the-race-track/) on 6 August 2021:\n", + "From 538's [The Riddler](https://fivethirtyeight.com/features/can-you-zoom-around-the-race-track/) on 6 August 2021 (slightly edited):\n", "\n", - "> The game of [RaceTrack](https://link.springer.com/chapter/10.1007/978-3-642-13122-6_26) was published by recreational mathematician Martin Gardner in 1973. There have been a few modifications and even some neat [digital versions](https://harmmade.com/vectorracer/#) since then, and it’s high time we had a race here on The Riddler. So without further ado, welcome to the Riddler-opolis 500!\n", + "> The game of [RaceTrack](https://link.springer.com/chapter/10.1007/978-3-642-13122-6_26) was published by recreational mathematician [Martin Gardner](http://www.martin-gardner.org/) in [1973](https://www.scientificamerican.com/article/mathematical-games-1973-01/). There have been some neat [digital versions](https://harmmade.com/vectorracer/#) since then, and it’s high time we had a race here on The Riddler: the Riddler-opolis 500!\n", ">\n", - "> You begin at the midpoint of the starting line at the bottom (the thicker border), and your goal is to circumnavigate the race track shown below in a single counterclockwise loop. You’ll be moving from point to point on the grid, without ever venturing into the gray surrounding square or the central circle. If the center is at the origin (with radius 3), the starting point in blue is at (0, -5). The starting line is between (0, -3) and (0, -7).\n", + "> You begin at the blue point on the starting line below the circle (diagram shown below) with a velocity vector of zero, and your goal is to circumnavigate the track in a counterclockwise loop. You’ll be moving from point to point on the grid, without ever venturing into the outer wall or the central circle. (Moving tangent to the circle is allowed, as is being on a grid point along a wall.)\n", ">\n", - "> For your first move, you can choose among nine grid points surrounding and including the starting position. From there, you have inertia. So for your second move, you again have nine possible destinations, but they are determined by your current velocity vector. That is, you can maintain your current direction and speed, or you can alter your destination by one point in any direction (horizontally, vertically or diagonally). For example, if your first move was up and to the right, then your possible second moves are shown below, although two of them will cause you to crash into the wall.\n", + "> For each move you have a choice of nine possible destinations, corresponding to the 3x3 grid that surrounds the point formed by adding your current velocity vector to your current position. That is, you can maintain your current velocity, or you can alter your velocity (and hence your destination) by one grid point in any direction (horizontally, vertically or diagonally). For example, if your first move was up and to the right, then your possible second moves are shown below, although two of them will cause you to crash into the central circle.\n", ">\n", "> ![](https://fivethirtyeight.com/wp-content/uploads/2021/08/Screen-Shot-2021-08-04-at-10.44.11-PM.png?w=400)\n", ">\n", - "> How quickly can you navigate the track? At no time can your path venture into the wall. (Being tangent to the wall is allowed, as is being on a grid point along a wall.)\n", + "> How quickly can you navigate the track? \n", ">\n", "\n", "\n", "# Defining Points and the Track\n", "\n", - "First some imports: " + "I will define the following:\n", + "- `Point`: a point in the 2-D plane, implemented as a complex number. `X(p)` and `Y(p)` give coordinates\n", + "- `Path`: a list of points representing the car's moves\n", + "- `track`: all the legal grid points\n", + "- `start`: the single starting point\n", + "- `finish`: a Path defining the finish line\n", + "- `zero`: a vector (your starting velocity vector)\n", + "- `radius`: the radius of the central circle, whose center is defined as the origin\n", + "- `deltas`: the nine possible changes to the car's velocity on each move\n", + "- `X(point)`, `Y(point)`: the x- and y-coordinates of a point, respectively\n", + "- `velocity(path)`: the car's velocity when it has just made the last move in a path" ] }, { @@ -34,33 +44,23 @@ "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", - "from typing import List, Tuple, Iterator\n", - "import math" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now define a `Point` in the 2-D plane as a complex number (with functions to extract the `X` and `Y` components), and a `Path` as a list of points. Then define some global variables: the points in the `track`; the `finish` line; the `start` point; the `zero` vector; and the allowable `deltas` (the nine possible changes on each move)." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "Point = Vector = complex\n", - "Path = List[Point]\n", + "from typing import List, Tuple\n", + "\n", + "Point = Vector = complex\n", + "Path = List[Point]\n", + "track = {Point(x, y) for x in range(-7, 8) for y in range(-7, 8) if abs(Point(x, y)) >= 3}\n", + "start = Point(0, -5)\n", + "finish = [Point(0, -3), Point(0, -7)]\n", + "zero = Vector(0, 0)\n", + "radius = 3\n", + "deltas = [Vector(x, y) for y in (1, 0, -1) for x in (-1, 0, 1)]\n", + "\n", "def X(point) -> float: return point.real\n", "def Y(point) -> float: return point.imag\n", "\n", - "track = {Point(x, y) for x in range(-7, 8) for y in range(-7, 8) if abs(Point(x, y)) >= 3}\n", - "finish = [Point(0, -3), Point(0, -7)]\n", - "start = sum(finish) / 2 # midpoint of finish line\n", - "zero = Vector(0, 0)\n", - "deltas = [Vector(x, y) for y in (1, 0, -1) for x in (-1, 0, 1) ]" + "def velocity(path) -> Vector:\n", + " \"\"\"Velocity of the car at the end of the path.\"\"\"\n", + " return zero if len(path) == 1 else path[-1] - path[-2] " ] }, { @@ -69,16 +69,16 @@ "source": [ "# Visualization\n", "\n", - "I think it will be helpful to introduce a way to visualize the track and the path(s) on it:" + "I think it will be helpful now to introduce a way to visualize the racetrack and the path(s) on it:" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ - "def plot(paths=(), track=track, start=start, finish=finish):\n", + "def plot(paths=()):\n", " \"\"\"Plot the track and any paths, along with the start and finish line.\"\"\"\n", " fig, ax = plt.subplots()\n", " plt.xticks([]); plt.yticks([])\n", @@ -87,29 +87,30 @@ " ax.plot(*XY(track), 'k,' ) # grid points\n", " for path in paths:\n", " ax.plot(*XY(path), 'o-') # paths\n", - " ax.plot(*XY([start]), 'bD') # start\n", - " ax.plot(*XY(finish), 'b:') # finish\n", - " lengths = {len(path) - 1 for path in paths}\n", - " plt.title(f'{len(paths)} paths, lengths {lengths}')\n", - "\n", - "def XY(points): return [X(p) for p in points], [Y(p) for p in points]" + " ax.plot(*XY([start]), 'bD') # start point\n", + " ax.plot(*XY(finish), 'b:') # finish line\n", + " plt.title(f'{len(paths)} paths of {set(len(path) - 1 for path in paths)} moves')\n", + " \n", + "def XY(points) -> Tuple[List[float], List[float]]: \n", + " \"\"\"A tuple of: (the x-coordinates of points, the y-coordinates of points).\"\"\"\n", + " return [X(p) for p in points], [Y(p) for p in points]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Here is a single path consisting of the first move from the start point:" + "Below is my replication of the diagram above: nine paths for the second move (two of which crash)." ] }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [ { "data": { - "image/png": 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+ "image/png": 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fGs3O6/aC6Nj+krfboX2z1g2Ml/7NoHK3l9Kq675edcV0gKnBuru7AxPYld2lv2Kl3O0FU50rS9/Rc1TZmoHxASJWevNb3alf6StFYV0AQQnsFRvW0BadPlxLxIwrNqyZtS67/P3M6DfiHbDpppLTD4wPcPm2y4lalLbI9CPn7dF2rj756vk2fVFQWBdId3c3S5cubemvMTn7uGV8dv2qw/+v6o7zpU3vnfXgUiR9gMT+Z8iuPJH8kqMAg573wOY74IT/NGP6QlCH08Pce8693HzqzfR19mEYfZ19bN2wVQeXytDR4AWUTCaJRqMcPHiwZd/W+fDRS/j2MwN844K1bDhm7gNknbu/g2VTRD7xTSJ9H5x12uKg3n3W3Zy44kROXHGiwlkh9awLLJFI0NvbG4oPTkTSB+j6xwfgAxcRqyKoMj8KaxNEo1GWL18e6I/gRSIRlr/2IJadwE6/YdZpFdT60DC4SQqn1SUSCUZGRpicnGx2kyrW3t5OTzxH9IX74AOfgJXHl51WQa2fYL6sh0g8Hqe3t5elS5e2/Ans8XicZcuWsWzZMqLP3AWT43D69WWnV1Drq7W3jkWk8GH3iYkJxsbGWuoAVCwWo6ur650vORsfgp/eM2uvqqDWn8LaQsyMzs5OkskkqVSKiYmJpg2PDaO9vZ1kMjnza1h23Tlrr6qgNobC2oLMjGQySTKZJJvNkkqlSKfT5HK5hs+3a9cOvrPtL1n58AhDfX1Er72G9s2b35moTK/62jMD7Hr4F4wNZ5hoH2HJ0e/hq5/56pxBfWXHdnY8dD+jQ4N0L+/ltEs/y/GnndGopxhoCmuLi8fjxONxlixZQjabJZPJkMlkyGaz5PP5mh7bzIhEIsTjcRKJBJkfPcGSe/6Cnoz34fpcfz/7/8j7FFJPIbAletXXnhlg+wN7yE167Ummezh97yV07F0FK8rP/5Ud2/m7e+4kN5kBYHTwbf7unjsBFNgSGhJWM6vqg8uqm72uENzCt1Hkcjmy2Sy5XI58Ps/U1BT5fJ58Po9zjtWrVzMwMHA4lNFo9PB1LBYjHo9P+87j/jvuwDLTz4Jx6TRv3XqbF9Yyvequh39xOKgF+ax3+69/qPznfHc8dP/hoBbkJjPseOj+isMatHVYi4aENShnNAS9LhaLlT2CvHEjnH66Y9WqkneXlNtf+uyZw7eX2VcdG86UqCp/u3OON176OaODb5e8f3RosMIWt866aFRdMQ2DQ+qyy+ZfE+vrI9c/89zVWF9f2V517743ydsUETfzVwm6lk3/DdtCSHf94Hvs2/MyFongSgzlu5f3zr/xi4DCGlLVhHXltdew78YvY9l3jkBbezsrr72mZK+6d9+b/OAbPyVBJ9FYFFd0/CvWFuEjF64DZoa0a9lyNl1+JbFEgif/513ThsKxtgSnXfrZ+Td+EVBYQyrrny8en/1U1Gl6Nm/mjRdfI3b/t3FAfM0aVl57DT0f2wC3XzGtVy0ENT7Zwcm/08uq7FGHjwZ3LUvwkQvXcey/X8XrL/5sRkg/+LGPE/MbFo1GdTS4QgprSJ11lnf94x/Pry5/yofh/m9z4Mtf49TPXODd+MQfT+tVi4O6/rdXctrJ6wEOH0wq9KTf3/rnZUNacPxpZyicFVJYQ+pzn6vTAx2xr1ouqFB+uFsqpDJ/CmtIfeYzdXqgon3VckFVSBeGwhpSExPedU2/WVzUq+7Nds0IqkK6sBTWkDrvPO96vvus0/i96t73XT4tqB/9d78x54EjqT+FNaSuvLK2+lhuFH56D3v/zaf5wb1vEZ/s4DcuX8F74zG+v/UGhbQJFNaQuuSS2upXvPkj9k4l+cHPziaWaefYM8fo/9sf86xC2jQKa0iNjHjX8/1RgH/d/V3if95GW2IHk5kufu3lp3h7/xSvfv+NWUO6e/dunnzySUZGRujp6WHTpk2ccMIJc85v/8DD7P3FN0hn9tOe6GPtuuvoW33h/Bq9SCisIXWhv73PZ5/14Vs/T8cJTxKNeie+J9rHiJ24Ddx/4EMfL9+T7t69m0ceeYSs/0mMkZERHnnkEYBZA7t/4GH27PlD8vkUAOlMP3v2/CGAAluCzecDxuvXr3fPPffc3A8akDMawlz3wx/CxRd/Eud+WHHNY4+dSKJ9bMbtU1NRctljy9aNT4zj8jPbF4vHWbduXdm64eF/IJ9Pz7i9PbGGU0/dUVGbg7Au5lNnZs8759aXuk9n3YS07pOfZF5BBWhLzAwqQCQyhWO4fF1b+d/CSafL/6hVqaACpDOlz/4pJQjropa6YhoGh9Sgf5ZZb4UnsGx/8G7cCsNs5kY1meni/PN2la299dZbGSnsJBfp6enhwguuLVv39NOnkc7MDHN7oq+yRi8y+nbDkPrUp7xLJbY/eDepJd/COSM/NX2TmJqKkn311FnrN23aRPyIfdl4PM6mTZtmrVu77joikem/iB6JdLB23XWVNXyRUc8aUl/4QmXTFYIajacYffECYpYiftzTtCXGmMx0kX31VC689puzPkbhINJ8jwYXDiLpaHBlGnKASYKhOKhjL53PxX/wP5rdpEVvtgNMGgaH1MCAdylHQQ0eDYND6tJLvetS77MqqMGksIbUl75U+nYFNbgU1pA655yZtymowaZ91pB6803vUqCgBp961pDavBn27IHHHwcGFNQwUM8aQjdd+TVefjlDJgPnnpvimTd2KaghoLCGzE1Xfo2v33cV2az3BduZTAdbv/JNdj1+qYIacA0Jq5mprgl127fD1++7ikxm+kf4Mpkkt9x1A9u313+eqmtsXbGGhDUoZzSErW7LFmYEtSCT6WDLlvrPU3WNrSumYXCI3HcfJBKpkvclEinuu2+BGyR1pbCGyBlnwPVb7pgR2EQixfVb7uAMffF9oCmsIXPzXTdw/ZY7iMe9E7sLQb35rhua3DKplc66CamTTnrnfVb1qMGx4F/rIs33Tf8U1A0bmtsOqR+FNaQU0vDRPmtIvfSSd5HwUM8aUr/3e951Tb91Iy1FYQ2pP/uzZrdA6k1hDalTTml2C6TetM8aUj/7mXeR8FDPGlLXXONda581PHTWTUjrbrsNnnrqpKrmV+08VVf/umI66yakdSedBM5VPw4OwnNcDHXFtM8aUs8+610kPLTPGlJf/KJ3rX3W8FBYQ+rOO5vdAqk3hTWkPvjBZrdA6k37rCG1c6d3kfBQzxpSN97oXWufNTwU1pC6++5mt0DqTWENqeOOa3YLpN60zxpSTz3lXSQ81LOG1Fe+4l1rnzU8FNaQuvfeZrdA6k1hDam1a5vdAqk3nXUT0ronngCzM6uaX7XzVF3964rprJuQ1p15Jjj3RFXzq3aeqqt/XTEdDRYJCIVVJCAUVpGAUFhFAkJhFQkIhVUkIBRWkYBQWEUCQmEVCYh5/fK5mb0NvN645ogsekc751aUumNeYRWR5tEwWCQgFFaRgFBYRQJCYRUJCIVVJCAUVpGAUFhFAkJhFQkIhVUkIP4/Al6h7HZ5O64AAAAASUVORK5CYII=\n", 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" ] @@ -120,14 +121,53 @@ ], "source": [ "path = [start, Point(1, -4)]\n", - "plot([path])" + "paths = [path + [Point(path[-1] + velocity(path) + d)] \n", + " for d in deltas]\n", + "plot(paths)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Here are nine paths for the second move (two of which crash into the circle in the center):" + "# Navigating Regions\n", + "\n", + "The goal of the race is to circumnavigate the center circle. I can describe that in a way that's generalizable to different tracks by saying that `is_complete(path)` is true if the path enters *regions* of points in a prescribed order. For our track a path is complete if it travels from the fourth [quadrant](https://mathworld.wolfram.com/Quadrant.html) to the first, second, third, and back to the fourth. A *region* is defined by a predicate that is true of any point in the region." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def Q1(p: Point) -> bool: \"upper right quadrant\"; return X(p) >= 0 and Y(p) >= 0\n", + "def Q2(p: Point) -> bool: \"upper left quadrant\"; return X(p) < 0 and Y(p) >= 0\n", + "def Q3(p: Point) -> bool: \"lower left quadrant\"; return X(p) < 0 and Y(p) < 0 \n", + "def Q4(p: Point) -> bool: \"lower right quadrant\"; return X(p) >= 0 and Y(p) < 0\n", + "\n", + "circumnavigate = (Q4, Q1, Q2, Q3, Q4)\n", + " \n", + "def is_complete(path, regions=circumnavigate) -> bool:\n", + " \"\"\"Does the path go through all the regions in the prescribed order?\"\"\"\n", + " current = 0\n", + " for p in path:\n", + " if regions[current](p):\n", + " current += 1\n", + " if current == len(regions):\n", + " return True\n", + " return False" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Possible and Legal Moves\n", + "\n", + "I'm thinking about how to solve for our specific track, and also how to make the code general enough that it could handle other tracks. I'll do that by splitting up responsibility:\n", + "- `possible_moves(path)` is general; it returns up to 9 points that are on the track and have the right velocity. \n", + "- `legal_moves(path)` is specific; it won't cross into the center circle, and it won't pass from the fourth quadrant backwards into the third (while that is not technically illegal, it was causing problems, and no fast path should do that)." ] }, { @@ -136,19 +176,120 @@ "metadata": {}, "outputs": [], "source": [ - "def velocity(path) -> Vector:\n", - " \"\"\"Velocity of the car at the end of the path.\"\"\"\n", - " return zero if len(path) == 1 else path[-1] - path[-2] " + "def possible_moves(path) -> List[Point]:\n", + " \"\"\"All moves with the right velocity that end up on the track.\"\"\"\n", + " p, v = path[-1], velocity(path)\n", + " return {(p + v + Δ) for Δ in deltas} & track\n", + " \n", + "def legal_moves(path) -> List[Point]:\n", + " \"\"\"What points can be reached in one step from this path?\"\"\"\n", + " p = path[-1]\n", + " return [p2 for p2 in possible_moves(path)\n", + " if not (Q4(p) and Q3(p2)) # Don't go backwards over the finish line\n", + " and not intersects_circle(p, p2)]\n", + "\n", + "def intersects_circle(p: Point, p2: Point, radius=radius, N=20):\n", + " \"\"\"Are any of N+1 points on the line segment [p, p2] inside the circle's radius?\"\"\"\n", + " linepoints = (p + (i / N) * (p2 - p) for i in range(N + 1))\n", + " return any(abs(q) < radius for q in linepoints)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The math for solving for the intersection of a line segment and a circle looked [complicated](https://stackoverflow.com/questions/6091728/line-segment-circle-intersection), so instead I just define N+1 points along the line from point *p* to point *p2* and ask if any of those points is within the radius of the circle. If N is too small this could miss an intersection, but on the small grid for this race track, it shouldn't be a problem." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# A Frontier of Possible Paths\n", + "\n", + "Now I want to expand paths by adding legal moves to the end until I find complete path(s). I could keep all my paths in a `list`, but there will be an exponential number of them (up to 9n paths of length *n* and it looks like *n* will be around 10 to 13).\n", + "\n", + "Instead I will keep track of a `frontier`, which I define as a mapping of `{(endpoint, velocity): path}`. The idea is that there may be many paths that arrive at the some endpoint with the same velocity in the same number of moves, but if so, the best continuation of all of them will be the same, so I only need to keep one of them. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, + "outputs": [], + "source": [ + "def expand(frontier) -> dict:\n", + " \"\"\"The {(endpoint, velocity): path} mapping extended one move in all legal ways.\"\"\"\n", + " return {(p, velocity([path[-1], p])): path + [p] \n", + " for path in frontier.values() \n", + " for p in legal_moves(path)}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I will show how the frontier expands over the first few steps:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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\n", 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hqmRcdDFxVevChc0scGtZ9UzZ3wiaWDW+t0Taq4mJSVEtcLSs6qytofiD91GFYOAvbobdnxxngaNl1TNpfyNoYtX4XtK8vVpRaD/OAkfLqqqq8uWLzxJvd2Do0xtdsA6OscCtZdUzaX8jaLduNDoln8z/kEEhQWWdm5/c+wZ3jTIze9ZlTcubt1ebW+CtS/5I5oaXcKfJBLpZCVTrm2L2fLWM4k0b6O32ETt+POz5JLyg/2xuW/goH5lG0LsklkvL3ZQOPYCQRgHf2N9r+l5znP29d0U+76w8RMgTQjbLXDmxK49M6t2uc9Yyq0an45P5H/LHdQIVAQhKlAT+uE7wyfwPm9aJtFdzcnKbLPDu1ffRZ82/SQr5OdLFTGKtn4Fr3mfrkj/irK1h+Wsv0D0xDaEo4fmrjRb4ttVv877lPEJSMhP2eKiKlXm5+2BuW/hom/b33hX5vPXFQRRPCAEonhBvfXGQe1fkt+u8tVk3WtxZsc9TiXt8gwcPLZ9q78HI4xs8Td8j7dWgXddkgTM3vIRZVSnJNBMwSHQrdmNWVTLWv8SXLz5LKBBkcHa38POWuiY3WeCPTCNQJSP9jvpJaVD4qr8JVTbxkWlEm/b3nZWHQDlmgoKihsvbwRmxwWfzjI3vU5yqqgSDQYLBIIqiEAqFUBQFRVFQVZXq6mpqamoQQiBJErIsI0kSkiSh1+vR6Vr/7z9bzjEapUr0AfmlSlzTtiLt1YNbqpsssO5/foISFDdm1ThHEIDq6ngKyzYx6bqbUN54N/y8peIvwhvtP5vg1jqEojJhdzir7sk2ACACla3aX4BQY0aNVt4etDZrJ0JVVbxeL36/n0Ag0CTS9hIRrV6vx2AwYDQaTysbf1tkSvWUKAlRysMvmIq0V3Nzc9n9wTe9wBV6A940uSmrAjgDBpZXdiezdz8GTzyPA/f8maSfXd+iF1gXOkDv0lhSGhQ+HGMFIUDxYqt9oc3eX8koo/qOF6ZsbvsdOa2htVnPchRFwe12U1tbS0VFBXV1dbhcLvx+/2kJNbJtn8+H0+lssX23231ac2HPNHeNMmOm5ZvYzPi4a1TYhkbaq1YpqUUvcNmIOS2yqqrCZ+U9CaLngl/djnf7jvDzlvrmNVngTeWbsNZ+eFxWjal7CzlU22rvb365A11I4bhalARXTuzarvPWxHqW4vf7qa+vp7Kykvr6erxe72mL80QoioLH42nab0NDA8Fg8Izusz3MnnUZj45RGy2mSpZUx6Nj1Kbe4Eh7tfpAsMVAiHhTDQGDROJRLwqw3pVJsTORc+fcSEJGVtP8VbOhEIDtqd24ZcktDD3ShZQGhVV9w2+7MbnWYnYtb9X+5pc7uOrF9Sg6Cal3LJJZRgUks8zV07q3uzdYs8FnGV6vF6fTid/vP/HKZ5BQKITT6cTlcmE0GomJicFgMHynx9Sc2bMuo3DJR1ikEGseuaapPNJezc3No/DrqiYLHHRXcti7BuEOseXCF0hKOpfNv7+FzN65DJ3xI+Cb+aty4WJcKb24adNfSXEZGFg6mrpYhecn7CQr9yYuXXAvciv2N7/cwdUvrsenqrhHJPHq6F5MT277lZIni5ZZzxL8fj81NTXU1tZ+50JtTqSdXF1dTV1d3VmZaZsTaa8mWlNbWOCSTb8joBcscpiYnD25qff3gl/djiTJTfNXrYP6QOkWXlZqSRNxTNk0jXi3hKH/SjLSZ7TZ+xsRqirAPjyBy7qldphQQRPrd46iKNTX11NdXY3P1743Yn9beDweqqqqaGhoOGvbtJH2aqDa0mSBg+5Kir1rkO0KrszJlGzYTOGWTYy/8joSMrKAb+avuizh2yo7Urpy72t+vHHjqY9VGdtzE3sc9a2O/Y0IVZYFljFpJMabeahnVoeemybW75DIj9/tdn/Xh3LSqKqK0+mkurr6rHIAESLt1bLd3iYLHMmqnzTomJIwnuWvvUBm735N9he+mb/qdnxOgTmGO3YNZkvmVOJdAn3/FSSkTOX+tfeTG5t7nP2NCFUnC6bO6E6BpPB472wS9B3bytTE+h0QyaZ1dXWEQu275/ZdEwgEqKmpweFwfNeH0kSkvZqWlImnIUCP4alNWdXs1LGSGNTP97WwvxEq1yzjSLpKf8VLUvqPUD78DHvSeOrjBEO6vMN75RWUOkt5cOyDLexvc6E+cPUQXrfb+XFaQofa3wiaWL9lgsEgNTU1nSqbtoaqqjgcDmpra894T/XJEGmv6nzxTRY4klW/9MQy1TWAI9u3tbC/AJsOrUbdcwBdVlgO9W9uZ/W0XxDnVIkZsocSkcVHhZ8dZ3+bC/X1G0fx98pqEvW6Dre/ETSxfov4fD5qamoIBALf9aF0KJEOqO/6vCLtVWeRjtwBSUhKLcXeNcR5LCyqD5C5wXWc/d1Uvonn3rgNnQLDu1jxKyk4S93UGQdjj5fplvw0b1T6jrO/zYX69k2jme9yssflPSP2N4J26+Zbwu12Y7fbz9qOmdMl4hgSEhIwGo0nDmhk/4Zy1s0/2Oa7Z6KxdtkNpHMhqhpiyZLuWKRJlNdfiNlkxl+uo8fw1KasekgaxrhdJQgFDvWdyZDPtlNlEiQ37EG2P8lNpWaQfNikfKp3xLDh+r8TV6BgmOFlcYNElc/FrYd/xN5715MsZDarAe6X3Fhizbx902hcJolndldEtb8vvDaPsoLDqFIAoejJ6JHDL3567alWL6Bl1m8Ft9tNfX3991aoERRFoa6u7qR7tfdvKGf5m/vafPdMNNYuuwG3uqLpu5DApawgf98WbPoUdHqZLt0Vir1rSPTaWLyjki6VJryDpvGflDgqzRI63z7Uhn/i1yUxsDABU04Ssl7FpetPZVUS9ngdhrjnWe3UM6FhGFNqJpAq6SgSCg9IPgyqzK8DZXRJsnD73sNR7e8Lr82jtPAQqhwAAaocoLTwEC+8Nu/UKrYRbdbNGY6LCPWHwqkIdt38gyd890w03MoKjv0v8Pli8Pl1BGss5A5IonLH3QT0AmIvo+cWMOak8XbfEfhkgd67l7iqJwjJyXjif0fCkSJMpgo8tXpWX/5X4uwhMifZePnoQTLNsVxz9CpMQlBIiNtwowP+T1jo7+rCU8UVrdrfsoLDII5pywslXN4OtHfdnME4r9eL3W5v1z46MxHBnqgNG8moJ1veRJRrpb0+bJ1VewzdBuqbsuqyRQXIiuDiX99NpUVuIdT6tHvpV1yOTglhS6vDlzGZo1s82ON17JOfpC4kuH/k3WRhbiHUZ7CQg0xNrJ5niqPbXwBVin7+rZWfCM0GnyGCweAPwvq2RkSwbfUSR94xc7LlTUSpUrs9DRkVg2RF530knFWDs6GwhrqRCeTk9ia5YU8LoapyHOfs3g6omJP9fNn3d8TZg1jHBFhUupXzEmIYlzeLzWrgOKEGBNw/0NR2768avUtIKPqo5SdCE+sZ4GR+qD8EIhes1hgzqzs6Q8ufYOTdM21hkSbR/BqoqlBfn4ben0hePyMlgdXEuW189dFuKhK8jJx5KZvKNyHb/9lCqADTNqzGEBdESe7NgXV+7HESi/yPkaJT+GXfy/l8Vzn3SF506jdCBXihm4FDsbpWe38LygsISv7jLyyqREaPnDbPrzU0sZ4B6uvrv/PbGGcLXq+31YETvUalM3lOn6bvzd890xajzn2e2r2JTd897hj8fis6TxKpGa8Q0AtK8wcTDPhYP7ieBHMityy5BZuaRH3avcQGbQhV5cL160lw2rFlelll+zlx9iC1/XZQ7i7nqkQ/Bx0TuPmNzQhUnhEW4lVQVJV1MSqvdzO0an8Lygt46eWXkFUZsysbEdKDCiKkJ7Nb13b3Bmu3bjoYt9uN95gX/f7QcTqdGI3GqLN2eo1KZ+m8vQyZksOYS9rOqBEO79zOkVVpjGh8uGBW1its3rwAs2TGaV6GoT6GbRtryB8SIiunJ/esuofUUBJHku/B1GDmj2kJXDswiYJ7b0FBYEoN8PX+HgRig3yuvsS05CQsajq/ea8KgcrL1NHFHcSQVUDiXb/l31/vJykQjGp/I0I1+I0k1A5m2pUj6Tcu87TqL4KWWTuQUChEQ0PDd30YZx2qqnboPeb89asxmC1N3w8dKkJSDfTov4KgHvavzSS+Wx7rM46SX5tPmi6V8c7fUmlNIFTYwMyBGVQ8+hiK3Q4CCjIvwdog2J29kJzYLPoGgzy45gqEgFd1H5FLHv78RcTNnN5m729EqLqAjiT7ULr3yqPv2OjvjG0Pmlg7ELvd/oNvp7ZGIBDokHHEoWCAg5vW031E+DGgKiqFBwsxBswYMr8gWBGDs8LCgdEyqoBMSyYPHbyNd3ukYHEGGWWzYtm6AfvHH6NLTcSYGGCdfSZ1MQ522b7i/NhxPL3514RUHa/Ev04fMQk15IRQMQdyu7Xa+9tkfYMyufpRWNQEJs3p06GPydHE2kF4vV7N/p4Al8t12vNhD+/cjtflpPeY8eFtyiFcbieZWftQDEEK1yWRM3Mii+uXY9aZedL7J1bGx1JuEAT21TOru42y++7H0L07wapaarMHgzuGrzM+YHzabF5Y0Rsh4L8D9zPKWYk/0BXf7vmYpk/jjn1Hovb+Nhfq4J4T8B+2Mu7yntgSTdFOod1oYu0gzqbZJ2crkYH/p0PEAucOCg+orzYGkKQA6d1W4TxqRWfpzSPB11FR+WX6z9DtCvJqHwtZqoRc62PsZ/MI1tSQcPXVqArsSPgxtZYq7JlVfLZqMAbZz8Pn7ubc/IdpMN6OMIQIHFrN6xPOj2p/mwt1wpTJ1K0zkdM/sUPtbwRNrB2A2+3Wen9PEo/H0+55sM0tsE4fvldZZQyRmVGAZPRRvjWNt7tuw6g3ISMxbn0vFvWPoUwoGAodzFGP4vvfApJuupHg4f1Upg7Fo6axOWsRh/dfhEEI7hrxf0wu/B8+0/n4nUmE6jZxaOgwnvOqx9nf5kKdMmsKnvWJSJLocPsbQRNrB+B0Or/rQ+hUtLe+jrXAKiq1ZhddsnfRcMTKqgQ/trRUzLKZ4WIQRo+Rl3P1DDAbse8p44oV8zD27EnyLbfgXL2SQ91mUGsuYy8WVG8ef528iG4WH9aSQhoMtyLH6alf/S6PzbnpOPvbXKhTL5lKcm0vSg/UnxH7G0G7dXOaeL3es/65RGcbPp+PYDCITqfDu+AlCGajrvonwe1fEBx2D6aLb4wa19wCv/34dcTN2MYwowshoMHRD8cAwd3n3M3NS27mqtLz+fK8VEqDbib4ZC7eNR+Do55PBw9D/8v5BLr8GYRA9a8kUDOdl67pgVqxgrRiN77u9+DfI2HMq+WNKTPYb7Hxy6/X8eabRaCYCens1CdtRZbDQh2WPop3XtwY1f7e8cTtJOw6gNUjcJlV6gb05KnfP92uetMy62nyfZhE/m2jqmr4fvSClzBsvhcIPzdbRyWGzfeGBXwMzS3w+0/dQNKQ9RhNrqYB/fG98/nJwXjWH16HrMqMsY3heVOAEbEWWLSU8w9/zbKxE5GUGQSMSUQCU/yjub1mJb1i1gIqKZ54GuzTkeONbDu0ljcvmM055UdJ2ZuHUCwokp+G+P2gGsgL6pjUfxLLXt8X1f7e8cTtZGw5QIxHQiCI8UhkbDnAHU/c3q5602bdnEZcMBg86x9ydrbi8XjQbfkbkmhZf5Lwodvyt+PWb26B4/pvQ5ZbPg5HlkPE99/G5/s/Zai7N+undKfUF+AancSPl8/DnZWHPjgJRW457liRjZj946g48AIWVxB9v3/hL3FjGJ3EXwaOJCEU5Nz1AoFMSPJhT9yOIgWIqxuIr/ocdq4sadX+Juw6gC50zHDKkETCrgPtqjNt1s1pxHk8nh/sQP3TJRQKIatVUZdFK29ugQ1GV9Q4g9FFGZWc1+V8nq2rY0SshaR/PkmCz0nGIw8TMCRGjQsYEqkXFaTq+9KwOwE53si/XIcpzMrhkSQzZp/pOKHqA7GgmFn3cUGrvb9WT/Rk0Fr5idBs8Gmg3Vc9PUIi5aTKj+0F9vusUeP8PiuyKuMacB4lvgD3lh2ky4ZlrD5nJpmjhqH310aN0/trQQgS0v6E/4iDwxPT+Y8plim7tqKvKiGocxwvVECRfFHtr9fpZPk7rU8wd5m6nBAAACAASURBVJnbd4HXOpjaSeTtbRrtp6Hvr4nf83CLMkU1Ehx+T4sf5rG9wPbdQ0geuhZJ+uZHHwrJ1O8ezDl9TbxY7mG8rJDw2KMcik3HcsNNbP1yG0F1KzC1xf6kkI+AZTkWXQbBtTaUBD93K3YsXg959lI2rSuFeAlVCrYQqkqIkORj3OVDmuyv1+lk8+L5bFz0CYrXQ1WsQqJToFO+yYlBWaFuQM921Zcm1nbi8/k0C3yaeCdcjtdggs/D09yCpBIcfnxv8LEDIezjRpDo2IiqKkhSCL/Pin33EB5N3coFaXdT4gzw4sK3UGprePLc27jf3sCdq3YzRwwh5LcjqSEChgT0/lqCxhX0ufRzksw34T/i4B8jJfL9Bi4o2Ek3s5mjPi9IQXp53NSEdKioqJKXkOylR6/u9B2b0STSzYvnE/C42Z/Xm705+dRbSxlwuDe9C50d0husibWdaB1LHUNwylXw+TpCtkHo5v7ruB/ksRbYHXCjW74Z3ZgANV+PZYy0FNnzJi+nfYIsdrLU24trCvdgXryIz4fOoF96Gr9ZU8GtVYfxG8fgMn7CzwcOJvn6C+H5CRyNc5IvILAqm62xQd6Pi2N4ySGuXbaC1YMGoQqF8aHdTLaspWH01cRfMoBPntxK9REHY2Z3Ye37b7Fl8Xz8HjeHuw9gxZCRGN3P41PLGV05muvOu47x94/vkLrSxNpOtBFLHcOJ6vFYC/xO/jskZtYRCsn0cW0BG4S8AVbHbyXHMozdDUGuf+V56NqdVUmDOejRc6H7K/ym6Ri8X9GjcD+xd/8Blj+Co6aUvT17E3I5sVTl8NeJJhL1Mre98l/WjBmDKhTSVC9T9Z9SH/g5lqHZ7FxZQkl+Odm9D/P2ff/C73Hj6TuEd/uPIzYjiYS9d1Onq2F87QSGJAxlzJgxHVZXmljbQeQN4xqnz4nE2twCuwNu3tj0Cnel1+GuzqG7aQu1mCid4KekohTZdjF/+fgt5Lpa1p33Uw76kklSqslzDgcqqElxMsUZh891iKVrd7DDcA3D9R+SWHERL/c1U2zUce+BLWwaPQZFUrAZLVzkWYoixeMxzcIn/KyY9xoh7xYKNvqIH3IOH/cby77YFK5P0bFpzc1UGuxcGJiB2W1j1rWzkOX2vTg5GppY24Hf79faqx1EWxe9iAXu0WiBX981jytLumLILcVRkg1sAWBN0nakSpm8/RLnfLWM4PTZPONLR4fKlVXF+I1jabAsZMDuArZPnsjut78gxGBGDHIiBNTUTOSVoTomSW7shaUoskJ6kpWUAhNdkrZS6buePcad7PjTsyghL9mDR7J57FQeVy30tBiZl2Xmb/+bQ6WxgZ/ZrqZ+l4/JUyeTmpraoXWlibUddNb303Q2Iha415jxuANuXt31KndkxRMKyXTXT4PAfFTgi8NfYKYPf3jnDZSMbH6mH40OlSuCq5rsL5mJbBs2FMXlYjB7OXf2zzikvElDRS6P9MrFRoiuK1ajyAoD62qorJ3A6LSHWVPVm81VRwgoB5H0Pcj80aU8lpdEuS/Ar3NS+Wm8yg3vX0GFsYE7s35JxVYXWVlZHWp/I2hibQeaWL8dmlvg1/Pn4bLXYc6pxV2dQ7+yLhAHB3QyJc4SbvzSRKy9nj8Nug5kme6eYhIcYftb3MWHTjHQy13DBbGfkjh8Fr6+I6lfczuL3fdxIFHigh2bMIV8jFq/A9+AWRgdC/h4j4xPSSXd1pV6/SjcOTncmW6kpyzxv2E9yVYamPPu5VQYG7g791Z0VQn4/XXMmtWx9jeCNiiiHWjt1TNPcwvsJ8Cru17lN9UjMBg9+I5ko8+KAWCV0cjQApj2dT6f9JjMkfguDNG7mNpQi9+QSHX8eqwWGxd+uoifJH5JYlwMnP8QlVWfUUQe78QPolf5UfJqyhlSfBivZKeg5GNqG/aTHetmes41eFIvwa9L4aVBen6dm8aXI3o3CvXHVBgbuCf31wxKGcfevXuZPLnj7W8ETaztQMusZ57mFvid/Heo89URm1lDKCSTU3MuiZf3QgU2qSZ+8ZmgODad+b2mcl1OPT0ca/CbxmHwrcYXl8Bkm41uXUuRg1Vw8TNgiuXIoUX8R7kDY8DH2AM7yVDrKHKVcDDOQGJSKtd23cLkqRfwdkoXfLV+to2M5e3xffhz90wcDRUthHrxyDksXrz4jNnfCJoNbgdaZu04CrY9B0zAKfbw2cJ+pNiuZfikPzZZ4NS+fXh1wV2Mjx+F2bAed3UOo6dP4bmHL2b4hjQebwgBIbYNEZwbs5+qUjs5DeOBCuz9LaRYrGRvmE9iHxcMv57bV+1gSZFCjbgHZMGouk0kFe/E6WwgzeFGzbiUq89ZSqjSxExpIhcW+wjkWUlo2MmVK504LDKJ5Y8hm5z8IefXXDX5F7z33nv4/f6o9vehJ95mYZWNKgQpqFyU4uC+31/VrrrSMms70HqCO4aCbc/hk98Bwm/E0Ft91Pr/y6alDzdZ4PcLP6TOV8fEvXKTBX7l458xcXkpSQ3hOAGM31VGZvVn5JSY8BsScWfvwOlyM75fL5KTN6PoErijOo+Pc0ZTIyU3TZHbmjSQ0jEDGBOIpV9FkJFXdkMuXsGj6VcwdnMQkxCUGvP5oGc/HFYdcVWPI0JHcSTeyua9Bnbt2tWq/X3oibd5oyqWSiFQBVQKwRtVsTz0xNvtqi9tilw7SE8/8SsJNU6MO/QRkr7lhU/SqRQd+Aivy0nuOefw6q5XGZc1DkNaGaGQzMAhVzB8QynGY4ZlG4Og9+TgN41D71uNnJpFSkoKPTc/izE2iHL+3/kyZyB+0XIam1+Y+KLrSOL27qBkyFhqDzxNtT4eS+BS0mpDjJuazSfdcwnJAeIq/47OX0xD8m14bCNZmN2tVfurBhUWVsXiO/YFWgIWVtnaVV/aFLl2UF7e9isJNU4OnSX6kE1HiRmD2cI6Yz51vjp+Ebocc3phuBd42gwSojyauTQpDqMyE4OvgsQfn0N1dTUXDEjC7FjB0dqe/J9jCDUiKer+akQikhpi0fBkxtRspGbA77BtcZFiFDjU7Tgscguh+i3hMcoNMbEt7K8aVPDsq6Xi3X28MHclla3kgqpob9Y6mfpqV9QPnDPxMKwfIkG3Eb21pWCVEDQU2eg+cgSP75vH+SnnUbDhQ5LGe3CW5LB3207qbZB4zEMSD/WYid+QSFnscnxFGaQnx5P49VP8w3M5r1pn0XvdKqTxg1Gi/OST1FrKklL4vX45ijmFXftGoSoNVNa/w+4FtcSdr6ALtBQqgM1pZ/LESdhqddSuyMexu5pPfV5ew0cZKjoVglF+KinR3qx1Emht1nagibVjsMiXogRa1mXD4RhCfpmSrAB1vjpurbgSXfZRQiGZpJzzsN94A4e7tBTcijGj8JnHY/CtwjrqQkqq6qj2q5xb9TuelS5hUlIZB8Z1QSaEXm35ZEWD6uWiA+vJGD+YHuVrWR36JeWHXPhcSyky6fh4shddoBhn4q0thKoPBvnZQQddl8lUvLqL93eUcbXq5DG8VJmOMt63kB837MF4jC6NKlyU0r7HsWqZtR3IsqwN5O8Aegy5hYJt4c8qEHAZ8R4ejsHs4B3P59ygu5LAtjrM54UtcPo/nqEmzkTOUQeVcSAr4DXEoWMm+Cp4LqUn3fYVsds/CG+ljinBnQzWV/PS0PNxCBtX712G22RiWd5AakQiSWot04q28tOn3iR5diwV/mx2lA1EqOVkp/fi5YHvo6hljHFfhyiOZdVQF/VWC6lehV/vD3B+XQKfZ+h5ucbNUacPa0w1luSFzDmqw1TqZOqNs7Bur++w3mBNrO3gTIxO+aHSY8gt7F6wEzkQx5QZ23n+42uhRwpB71EuPTqR9ba3SDJ6aCjOJKTzUNwTuq2AJZf2ptvYw5R+ELa/hy3LsOvGsdkJ0wy7uN3yGV8f7cI/ZlyDQ9j46YGveKVsMEOmd6Um6CNblZi6RPDjrSvxm3QkGfJ5reZJgkJmSHIid/R5FkUp4yKu5qIDw+lilpHWKCgGF/uCJWzLSeZaq+BIsZ30RD8xOe+QHFfOnAODaCg+xNQbb2Xw+TMYfD7c10F1pdngdiBJWrWdCSIDIb6y7uO+hluQ/DRZYOuqcuS/z2Xw5iqKMwQ3/vktDq4Zgt80Hr1vNe8ax5Gk8/EP23u8ID3CDt0Q/nFJWKg3FX7FCuMkguPT2BT08fO4WK5+awlZRf/GVHwQa26Qrz2zcIdy0Wcr3Nnn3wSVo1zmuIlb944hQy8w90/GcEVX/iLv4W7JxHNFXsxGhV59l+BMvZ+ZfbK55fAEGvZ+I9SORsus7UCn06rtTJC/fjUYdSRLWfQvy6Ouh7epF3jAE8/y5TM3MskBm6f0YtPHX5FefgFQwSe9+kMD/FRayqWBBXyUeh2P9r4Ah7BxQ+FX7Bx4KfvcbtIQ3O0uofKlR1GCLnoYYpFUsGVLfOGcQ0wsPJX9HAGlmMscN3GzbRKrnZVkTO5CSY6Rv32ylVp/Fn3SLEztXcyS6qeJM8byzxGP4/pgA4XbNp0xoYKWWduFXt++18xrHE/EpSiqQsGmdVSnwh3V1xFKkNlVNC88EOJoF0xWhUFfh7Pqf+Sfk/7lJvyGRFzpSwmYUulmsDNH9xn/izmfub1/hEPYuCZ/OR/1u4jlLhddDxzixnf/SfnrzwFJ5E37DZQGwCKzRtyKhMyLvV4ioBZzqe965t78K7Z4FVYYQ/zhwBHu+XAnIuDhxkEBbN3/zedV/2Ba7vl8OPP9sFC3nFmhgpZZ24VOp0OSJG3YYQcQcSkutwOfy8U5XaZhDhipXPwYxuvDD0LrPfpqFjz8CyY7YNW5vbjCtw6/6XwM3pWkDS5j/zYnzxjeZp2uL38aegMOYeOyfSt4se+FpDkcXLb4bbqVHyS550D08kWkx6WRtMsJpXuoHTqSskAfVvb4nHr9Hn7c8Et+P+MnvLL8IE8XHMGuV+lvtjEoWERmTD0fBT/E5rHx5KQnmZQ5kYX/fORbESpoYm03er1eew5TBxB5G3qds550Wy9G+odiL1iM3V+FOd2BuzqHW3ZV8fiWcFbte+FvqZxXDlRgPX8ZqhrLULEf2azyh5G/wSFsXFi4njd7X8C4PRsYveZzYuKGMfO8q1AOBdDbwBFSqXfvxmBMZGfsFRyJL2RP8ufM9l9HZnVfZny4jSN1HjKExGNXDObork85Ul/BYusSpuZO5Y+j/ohNjvlWhQqaWNuN0WjUxNoB6PV6VDWE1+Pj3Kzz8Tccpv7oKkovHEym8Utqj+Qwp/o/JDpgy/m9ML2+Ar9xLFLuKuLiXLgdNq60reOPjUK9oGgjKxIGcNuni5is605C9m1YhYyvKECFT2GJVWHaTweS+dC/WNPvaryyyvJubzAoeDnLDvalFBf94mxc6jRw2ZRcNpa9h73QzqGUQzw47UGm5k4lGAh860IFEKcy5G7EiBHq119/fQYPp/MQCASoqor+RHmNk0OSJNY8+CIDLMOwyOHxskWl63ggJYNbBn1ATNY+fLV/IvGJx3DECArOnY2omIrB+xVxWTEUywFcwodVNWKW09mdbUfx9eDOIgMxwoxbwDo5yB4dZJUrBNNMHMpZyrK8sU33WScUbWBdtR57XX/6IHHnBb1R8l0U76lmzZjX6LI/A51VR560jPTu1RitQfxOHWUbUhkx+d4TCvWuZ97ks6x0qhMSSK6r44KSch6/bU6r6wshNquqOiJqfZ1GXf+g0ev1Wq/wabLmgRcYHjMOqy4WIQRCCLIzzuF6137MaeFe4KMr/kuiA7aPHIDx8BAMvgpiM2PI17lxST4Q4JJ81ClHOPdggDsLFHDks39MDJeFKvibrwZLjRvZ6KcwZwnzu05rnHUjUSMls7jrVEan+ngk18TjsYLs1BD79hSyOW0xtlIzep2OLN06kvvbUWN0eIUJxaYjeWId6/Y8gTMYavXv9mff5r3ePahKTEIVElWJSbzXqwd3PfNmu+rrjGRWIUS7Bsl3triGhgbt3ayngeOfW7HqYo8rX2N6i+Rzv6B68wS6vLcBR4zgSO6VTfbX6TWFhXqKvDdhPLVSckcc+mmRUlvDzsumRF3WVmY9I6mhs8yeOd04k8mkibWdSJLUZH2PRZ9XQigkU11cwSAHrB0zHot/PAbvV9x07wPM/cvc6BtVIbtgH1tTeuKX9eTEmjHUBpDjBPt6e6htZdYNqsrVpSup0tkx+mKRzSqBoBchBLLsJyapjqgTZVTo2fPeFgWV/iC7HR6qDhayNzGlad5sc6oTEtqsm9bQfNxpYDAYMBgM+P3+E6+s0QKTyYQ95MSqaylYZ8jRaIFzGbKhiG0944l3TAUqmHjfT3ju708gEKhRZq5YVSPJB2tY3/cGjLLEaATLxy9hS9JEakQashogxPH3yJPUGq7f24PFhlpsVZnUpW0gGPLTt99KYuOPojpljLbj32vkdemYmf0k+1xeFlTWs7Cyjtgtm7l+0YcMPJjPT/76DJVJx798K7murl11pon1NLFYLJpY24HFYqHGW4E1pqVYt8f8j2Sjh/rDGSQ6jrKn/wz8hkSk3FUs+bAElzOAECCpgpD4RrCyKpEb0qM7byp2dz2jh2/lHwkTqRFXkB0q4JId+6mPFSzoNqLFBHSD6uW8orUc0XfHVtYFb+pmgqEAeV23YosrZd2CHuTGusieWIbcbKJ8KCA4cKgLEzbuo8DlZcS+Xfz584/Jzd+L22Jld/8ZzNh4lHfOi8Vn/OadsEafjwtK2jcfWhPraWI2m3E4HNpD1E4Bg8HA/q2bSTVnUuerxiAbsMg23CEH+tzwWGDbigK+nDAKWQ7b34DOhssZwC+CpBqDpPkNFCi6pt7g3JCeLp/O4//unYkhMZYvxRVkKwVMLV/BsE/74jL3ZkJgM4gvWN6sN3hy0RruOXAeG/WVqHonHkMtNrOT1NR8NizoTVy1ikckU77cTtJYH0ZrEJ9Lx9fFPfjPwL9yTf5u/rngPWy7duK32dg8bBiuvEsI1iZyybhclPz1fNbl5HuD20IT62kihCAmJga73f5dH0qnISYmhiOvrWNg7Dls0W9inz5EbiiG2XddS+Gme3BX52JrcGAOzoRgBa7uBgKNQo3XQc/Rb1FUMIHLStexU87DOOsZ3t37Ihun/J0akUa2UsCYkpXcmzGb1Z96cJrT6C22sts0Aqf9I+Qjv6WLYuBCwwyucY8iqHdTWhWPL2cloYCObt13sHFRH2KrQzC0B5PnLWHF5GncbbsOCRjbxcocDrLyxccJbt2KmpjI9tGjKMzrSjfbJIIHQgyfkcuoi7sxWnTn8Q6qN02sHYDFYsHlcmnvaz0JjEYjBdu30tPan3L3Ea545s88+JcHAPjyvw+QcI6HhuIMqnpMwG9IJGD9gkAgAb8IEiPpGDjkJVSX4OHCSxhi2cyHfQeyubqImtRryFYKGF66kuGrJzFxwoWsfi0fpzmN7MBqVqSmsSr3H9RYSxgdP5o7B03BWfo2xj0TKdM1ELC6cfglevVqYMvSROKrAmwc2YcRe9wEheDrS37C33pmMbVwH4EnHsezZQtKagpHZsxgfYyVzNw8hjKcwq9rm4Ta0Q8p0MTaAUSya319/Xd9KGc9NpuNjY1ZtTBmE83vUUhpRwiFZCoP6pHM4zEFV+GOCQvVJumIydhDwArrd45l/Mj1XBf/RFMmnVzwMXt2jGOUMpW4mGp2fFaB05xGpv8rFo2zs063AKscwwNDriPLs5yyQ38iqfZCJMXIgVorjpQdKHFWNm3YTpfKAMtH9iZ9wGxmvnwz5ssv51mLQtU9d9KweTO6tDQCP/8ZnwUC+FWVqeedh/dgAnvXlJ0xoYIm1g7DYrHgdru1zqY2sFgs7N+6uUVWjeAPujGnFVJa2AtTcDqSeojaTENTRv3YOIzfprzOvPpZbBo4vUmkE8oX8ut3izhS7SdxyGXofdUoDh9Ocxq50npeuWQf+fX59Pd248YBXkT18yiWrnTv9gfsuyy4RZAi2wECSDiKN5NdHqBm9ABeufUhAg8+gB0Qu3dz+J130KWlEXf3XazU6cgvLCQ7O5tZF89i5+fV7F1TekaFCppYO5S4uDhqamq02ThRkGWZ2NjYprbqsVnVbDmCweghsG4kIbPAnlLZJNRnfV0ZPeBL/hD3VJNIJ9au5Pad75Ov64qcf4SvR/yGbK8Doz8s1DTdGv48ZgFWp5FrTFZGZO/CLHUl2PVpFtYLlh+AeeWxbA2VErRUo7pKyS51YhszmN/e/lfsCxdS/cGHAAQrK0m77z4O9+rJh0uXEgwGmT59OiPPGclX7xxgz+ozL1TQxNqh6PV6YmJiaGiI8qzMHzixsbHs2bQhalYFsOSUs/vLCRjM/XCmHMAngph1Muv71GNISuBLEW6Tjq9aQvcjqbidBvRCQgAuSxppxjSMfjdOcxomaQlzR33KyBgLF8dUUekbxvLER1nuSeRgkYpQQ9xQW42i+NhnOgABN/HFpdjGDGLOqB9RfM21eDZvBiDljjvQ//gyFn3xBfsXLSI7O5vZs2eTmJDIirfyvzWhgibWDsdqteL1ejU73AyLxYLZbG41q6p+Hz59Ddaq2dRlHsAjByjvZWRF2pCmTHpu3cecc+QIRxtG0aVHFv369YNP3gZUdvW+CpPfg9OcCmIxL41fzkXxNuwxs7nPNZZKawxSnUpfdnKj2MLVPScTV5DDZ7rVhEQAy+FCUrpnM3HTYQ4//3Pk5GSQJOKuuJyjo0fx2UsvNWXTUaNGIRDfulBBm3VzRgiFQlRXV2v3Xgm7jeTkZHZvXI/pgwbqfTWMeObqpuW/++/DfJY3ihqRSKJaS093AQct3aiWUslWChhYtpo5MQvQywJrxtv06z8Qs9nM5Mde51B9EvE+L7dUewiaU1HFYj6cuo/6xF9QKnVDqCpda4JMy1jGIP87dE8eybzl1WyN2UeVLEgJqQxy9mbSMhe98g+jS0sj6Ze/wLtrF/aF/2PXrbewu7yc7OxsDvkXsNJ6kHoV4gWcV9WPGT0ePaFQP/3bTMa4txOHEzsxrLMMZsY9i1tdX5t18y0jyzLx8fE/+OcLy7JMQkICQgiOvLYOk2yhMKawafnv/vsw73ed0jQLplZKZkPMaEBlZslr/LrEzexABcQK/K6JDB8xskmohfVJJDQT6s7AIT7oOox9yY/SLXEg9yYkcOf8eu6seZ3JyruM7TeXecurWRm7j0qdhCoElTqJ1bH5rJ5oJe3+++j+5RdYJ0ygfv4CCrt3J7+6munTp1PkX8Biy0Hq1fCbdepVwcLkPSwq/e0JhTrFvYF4EX7DerxwMsW9gU//NrNd9anNujmDcW63+wd7O0cIQWJiIkajkV0b1kXNqv2XLgkL9RiSlGrmfLUeVQ0y4Zx5gGDVpusQIpxbXvANJcHn5VfNhPppWhdUQDctrtVjyj30S6p0x+cnoarY2ugUdEhhcR9LejDIgiO1rcYZVS9SFC3XqzHEP1ASNUabdfMdxVksFkKhEA5H+57A3pmJi4vD2Dgm9shr6xkYO6KprWp3unn46RepGXNu1NgakUi2Lh5T/DICVqjdNYgcfSKqqlIbdBEfRagRhrp2gKqgqhJCNF5YFYXUho2skqNnQRUYHwBVURGqGp4pI0uoanjZZ8aoYVTIMhVpE1tuSw0RDDrw+xro59wbvW5o30wtrYPpDGOzhQeq/5AEGx8fj8ViAWDXhnX0tPaj3H2E6Y/8lrsffhrLnvXE90lHYlyr7575yd0/Z/0XT4ILZt7wGg8tehVvwWFsAWsL69tcqAL4lfUflK97EG9dF666/xze+vccltjyWWWVkYBo+TM1pGIuu4Jzd+8hbe9eHnvqRb6Uw4P9haLQo+Q66qNcn+MkyPvVewQCdVRWfUFl5aeUFW6ifHMidQVJZPWJIT6KMO3EEN+OetXE+i3wQxGsEIK4uLgmocI3WXWbtIL//XIhaUEHvgG9eGfsdGRCyKpCQBia1jeoXi4o2sDKynlIaVBwcDgfPf0g8X4riiqTXdwjqlBVoFt8DekxT7G72ICU+SQ/f2M/u9NlUgJwRWU61SYra2MO4G32kHaTojDU0YeGzK6kvPcBn5w7hXUGC4QUbC4nL33lY1NmP95K2EOg2aRWPSoTPTls3XY9dXVr8dTKVG//f/bOOzCO6tr/n5nZXrQradVlFVuyLVuyLffeu40NmOYQegsEAoZACAnVobcAprcQisGAK+42tnGXm9wkWdVWsfpqpdX23ZnfHwJhRTJ5j5eXl5/R9z/d0bkzuzOfvfece87cZBpOpYIocDZeYp3Yg8vkIjTCj2mofkXVFmT6Gd9vN6z/JpnNZiRJorm5+YLcjFkURaxWKzrdj+VnOTt2tI+qzbXH8Wsj8fVtA9UpmLkldw3NFn17NDhSsTPz9H4eu/K35GwbiddloroqA0ntodUMvY9mEtRFU689TF7PeHC0QSrQBuqaOybx7nN3sX9QISeNbZAurDBj9M2nSfLQr7kX6tAqjpjz26PB2c6+rElfxKJVX6CIAktnzEfyuLlp3SoWSJOJ1uiw1V+JS/06W8x17dHg8f44JqWfwl7lpeHoWCqP1SNIEr5IGyUZfnLCjqDrNY/w3RH/rWjwT6l76ebfLJ/Ph8PhuKCWddRqNeHh4e3vpPrBJ51UGSLLMowNrauo7j8AqSG3HdQbctdxY90M6gbsYvuKXfTQGpj34ac8uuJtEhr20K9vDifzR3AmfCij1dE0roGgLppm3SHeNgzgcqGSdT2XovJH883cy9n4+WdsMZ/6HtIQU2ssXH3xElZ+sZsmyU4PMRXP2UQq+jgRXScRZZkzfQYQO2AQ9jPlLLr3djaOm0JzeATztm5AM+kpIkUVdn2IiJhfU58aR5OmGUUJodcnoWciZ/YGKMk5iqRSI0fF4TRaaRnkZZNrydhdugAAIABJREFUE/N6zeOJ0U8gif+9fZF+KsDUDev/gUKhEE1NTRdE4oROp8NqtSKKYjukhrx9GDVBLrHdjMPXyKCXruC5px/oAOp8+zBaJTujHr6GFxfOp3RAMlrJiNWvZ9iQVWjxM3ziPrZvXk/NyiBBXTROwwFWi5m0SiLPTnqA+85EcvFZFSVxde2QTqwM59br3sdojuGDVz6mSbJjlNIpF2KJcZ8kqLEjRceSNn0Wa90htjS28NCn7zJ5zw58ajXhab1w9rmLSFnkrLEK58g/g6Sg18QRHTcfTWgIxzccomDPd6jUGsLSMyj3K4RHx+Ae6ObT05/+bFDh/yAa3K2fliRJREZG4nK5aG1t/f8yl1gURcLCwjAYDB0gjQk6adRGMkI37Pt11QNs+gdQJ2ggMhiBu+8JHlr+Jt7sfsT4jThFN7EJeeiMrSh1EzqCajyAFB1GVbOKK4I5lOcmkWWtYHVa23T3qgoT5opFDLx4KKvdIq4PPqZZsqOWepOXGkZK4V5krULPqTPZZIri9YomwlUSf6opY8qub0EjYLh/FPbC6cT6RcpNp1Am/J3kMh/RlrEEhjzLvuVfULDnZVQaDb3HT6HY5eeMy83IsSMpiS7h0+P/M1D/mbph/T/SD2V1Wq2W5ubm/69GWZ1Oh8ViodXja4/u/gCpe+wVXDmoJ8blLmrcFRRH2TuA+uAtizj27A5ejtlOqLwFqz9AQC1QrW7g2bue4NiOYeACuzSRunNAnXTVEe757Aqu1r9NSc9i1n/vk15yRs9V13zI9i9d+PRufhOs59bP99Ms2YmQeqJPCREoPojdmEjVxDG84fYR3uLmD7EWpv/9FUK714MkUvNICNPx8cT7I6kx2ul35zAsOWXYC4rZGd6bgqW/RaXRMHj2fFqMVg4dP0FERAQ3XHEl6x3reSv3rf9VUKF7GvwfI7fbTWtr6390AbtarcZsNuMLyu0jqfl7SPWjpvDHW36FSqVi/R0vkxU2lL8bV3QA9Q93PcIDbz+M2KJg8Rtwqt2QGkv0yq301BiwzjEgxuyiLm8kzpxZ7aAOnvkxR7YncLhHdft0d0qNhdVhGpyqZAxRd3HDVid5A3Wknz2IQ7ITJ/SgSVtPldbIobiBlMaEEa6SuCXBzNTij3CWfU4gzE/0YjXeiWaIfIzoQBh2o4r+Dw3HUXqSfc/fRkFzJCqtluwZc4keMIQNW7/F4XAwcuRIJk+ezAf5H/B67uv/MlC7fdb/T6QoSju0/0kBKJVKhclkIiDzk5AC7dlKy8I28fno6e2guhNj8Rafweo3tkGaEs3iy+7EoNXx0uVzSNTpib3iCD6nibIN97eBqt+PMeIbdkU52yGdVG3h5Mgn2K6KIqJ4EYq/B3e0/hZdnQe34RhNkh2rHE+hxc3JPoM4ZbSi98tcF93A1MBSfC07QVRQNWuI3piMsrua4NzXiFAEmoxqYq+LI2flMgp270AlhMieOo0B83/N7pwDHDhwgIiICObPn09ycjJvHX3rXwoqdPus/99IEASMRiMGgwGPx/N/WswuCAJarRaDwYAvKPPYy+92mu4+cQ6kP6jio30ciavqAKrd68Oa10BALeAJM7AgWsXoq3/fwU7qV48vqKd8430EddH4Nas50ufb9iWYi0+bKXFezetzxpBh1PFAtJX3i0EnCEhlTrxReTRJdtRKAksHJnEmIoYwIcj85s3MNX2MoclFqFHCdFhFXO+FRE+8ltKHL8Y/9SlsikCdJkB12D42PfAdKrWaYbZqho7JpnbUJfzt0886jKYajeZ/BdR/ek+6R9b/bAUCATweD16v9788Rf7b4qVY5AHwfc5Os3iM6x9e+E/tBEHg8Fv3UN9wCa6QDaPUgC1yFQdLOO9I+oPeW/QYdrOGoLrxHFDXI7dIONVu5GQbvypIwy81M+rhaxC/t1960x24lEn41BEIShAFEbvxPZYNyiMqEGJCdRi7Gm6hThPDr67tz6U940g36lhx9VUk5Rejd7vwGIyc7juIQ/3H88HoAZjxMIuVTFPWom41YzsbjvrrEsxhmWxNjMVZ34ASciFIRmyxqaQofThQvRyVRkP2jLkMNZ1Cn/s2OzKfZ/vxSiIiIjjeeoSIYBQ6WY9X9FCmzSd9zIB/CuqexZfjz8glFC4jNYlo8gcx+uEvf+oedE+DLwQFAgF8Ph8+n49AINBlFLkN1EEd3wSvKDSLuZ2AFQQBURRRq9VotVq2P3cjlXXXEVR+TGxQCV4Soj7hSNzMLiGFNlCrw0QkVXMHUIUmCUdGGIsX3MGBd/9Cr8q2ddXBv/oj0AaqQ7wIWfox+VaQA5jlFZQm53J46BMk57pZ3axmgeDhxacvA2DF1VeRlnsC1TmuQlCSKB6UxbabEpmnO06MYRz7P48n/lQpqcWriPrtb1mRf4yWmirg3B89FcaYePqNGMbQiy7FIPqRX86kQOzDssBkRo4cyddHlhHjj0el/PjZg0KQGk017/3x/fPerz2LL8c79DDKObnFgg90BwefF9h/O6z/qVUwF5pdMBgkEAgQDAaRZZlQKMTSPx4CoYtfejlEav69P3meugF/whWK7tQuEsCoPnteu5rw6i5HVIOswR86v6cVW52KT9N5Swutv5FW96rzX+j5vkIBlJ9w7ORAC11lBwuSkfTLC89vJ4l0tX+GIMuE/8S2n/5wb5eOpmQXmXhZUZc23VU3F6idSqXqYqRry3v96+psAO6Zd6StWRCpN2v4KblCnbd6AJBRIajOv+VDV6ACuAU/2qCu8//7faR4ymhRD+myP586AonzlLoAonKe4JsCAZUaQex63VoOdN2uhFwE3D+c74fvWmj/K6g+/7VEB/7hmAJKwI/i88N59sAKhf+8dfXuANMFJxmQGNmnulP7desOndfqg/ffgQM/ZNp2lFGqR3VbHJemX4pW6vhwPrX43nOWZ34EFcCgaLh3aiv5O3rTInmIv2oku195EdkznBb9CCAEdJ4FaAN2fNar8SNTqpa5/df9qJWcbNi6DZ2rlnnfrMXgdnWycxkMfDPvIkRZQBOwMevy8ZhaajnyWR61Qj9C0rsooc52AIXb0xkd38hYYS9PzFrJpy4ZpWkVutYdzCkZj142dLLxiG6ufOQ5lGAQ1/79ODdswLl9D5JtIppekymJuoNQRGcwpaaf986Hbp/1AtNTt7/Ypc8qCwHm3zWMpP6dp50fvP8OvqMxCCEBQmpC54xqKsFLbMxH/Dk1j2hDNDdn3dwO7U+BKikicS0yN1texuHW803LXGTPcJz6NDT+JsLYiUwAhzS3g88qhnxY5TUknGqkJmow9VEDQdQgCwE82ka0umYSyw/R++i+Tj5r7cCJmFOmUCrWU6aqw08QZBGt10pySyMuTQMttZ19VkkTQzBUixAKYIgS+GRoMk5xD8gyg/OiCFciMJp6d/JZm+XTPCSn4ty8BdkdRNN3FprUiYBEvaGISmUbxhH7/rN91m793+qp21/EFBwEiEhikBbxFGH0QwDm3jmwA7DtoAohGsPKGS3spLzhclrltmhwrO1rxkpb2DT1AVY1F3C47jDRhmimFAzsAGp8hYTdrMEt+DEoGiKcfp4UM1ns2tAJ0upgGSFfCMESTVxI1x4N1gbsGIVtPDV+JyknJ3HRoUZGVh/HHtmPst5TcauTABUIQeKbvqL30V0IioLHYKQ8rTelQgtxthH0VAYQY7ZQKzooEMupUdXjFSQkZIz1HrCXo8ht0WCdOQNFGI9gzSez5R32OhKQQgKNFj9OjZHU+iB1PRSabFbC/Qnt0WBDTQFXfFuEaInCOP460KRDCPTSbnYl1PGbjGuZEG7mrjV/JNAdDe7WTympRwHaUAwP/+kLyhpqyUoZTfU+qQOw54Lq61GDpjSDONvTXCzuZ2sog1unvcM8VRW/33491qCfqouX4IhKZ8t7n3cA9cvIlbw48DWubbLyO3s1Vw9IY+eLz3aCtEdcLqPVR/CEVOR6+3Gw0sj03/2JzX/zIGvL+d2rN7P54HGe2v1HGqxn6FU6nmlhg5hSeBj5ux0EJA0l/ach+yJpjM1m6P6ncJh74Bu7gMhMM0fWfYUrUIlKM4Q+EZEMHDyKUL4LGZlqTQFvRutIcFSjDgZQAKfehNI/HVtJNdb83hjNu9gauZN+x9SoZBFRAY9eZFhmFQmlYWgOewk5HIgGA8ZJM9CkTSNQrUHxy+hNxwnzv8HXQ65mUdgsJoSb+TArFb3035vydsP6C9RFs94lwjeaWQv3oY6wUlBQwCVTr2Xb34oQAKlfEXJRLIIQQpfdgudgMn1HxdFceDcXC/vYGsog54YVvHqmltUpPuKXzsMa9POKcEMnUDWihmt7/oan7X14Ye3HyJ5hHSB9z9qLy8dm4lr2CjZtE+MSG0hRV+JTNGgm38/rnw3Cr6mgNtGHrrWWze4snCnLICyfRb3vpGWDg5CzliF5hcScLgEgJKqw6yy4zT0o7XsjiiChyDKyaz2B4CmGXrSA/qUbsYZyKBMeQvL1QVIUTklVHDRWo40z4Tx7FgIgECC51YKrdSiCUEpR5B4Si+rw6GRMbggJAnGtHgal9Sd+xjxQUnHl1KEEQujjGglregK1ronPp7zNImf0zwYVut9u+ItU/4x9DO9dC8D48eMJBoNUtRQw67ZMBF1hO6jG4U5StaNAhiEzkzv0cVuPKAySyHvuGNQ3buwEasK0FADiZBsRH+/nua8KaGYhPikSm381UdYTxE+Kg+h0ntnvpFifSGvEQLyz3+DjskEEogchbHsSSVCI09Ri8FTjdCdxVq1navWljI4cwcuFSzgcdhKTJY7+8+a0X5uohLC5G7G1VKP2NhEpliEqIVTWOUiaLA6u+ZoNZwxsFK7hxgEp/M18iAKpkr5yAr92DsFSZ2dPzHcI6U0MUgqoNthxmU6jKD3p0TQeZ4SOi/LqGK2rJLWnigZbBOtrT7N5xSaqth1Dl6oiJnEJkfbrUPftx+dXbvsfg/rP1B0NvkAVCGjwB9oemKioKDIzM8nJyaEsugRCcQhCCFm0MzxtDt9+XEDfMXGEReo79BGhVnFzYhSvnqklefnfO4C6YHIvrt30In8oGvF9dDcNjdSEzb+ar/ufYLg8jKGueMypvZmybgktMbNYHz2DedcMYe8Hi6mMGcPi1gR6koaCQApVXKldw7veacSHZvC7a4awfFkpZTHlHLEdYYzbQ8OrJ2hOiKEidT6tvmiGHn4eg6eWsblPcbbfNJrConhnTiQv7QlxuspGbWsdDWUpXF4TpMUczY6sSl70v88l9knMdoxjetMoAr7vSDKvpd/OEpaln8CjnoE+1B+zbgFr5p0i3FrJ4LB5ZEo6ShoOUOg8RLkznz7ORkbGN2G77AM+j5jIolMV/6ugQvc0+ILVDz7r4seXc9UtN1FfX88bby4humEwghBC6t2C/0RS+7LiNU+OIixSz8pHZ7RPg6cs3oc9EOStZx7oAOoVDW9yyH4xoX/wSV+fOJyBRoUKx7uUqBqxyDoy8k2kVRjQxvZhW9oCTlQ2MZjT9Nc24EeFNSUTw14jOl0+E20rSAsdxq0YOMIwvhP6Y8HMAWEZB1NCzMofRnLTrxDlAInGPEw7V1AREUMgKpxRh/cQUKnR97bQs/dxKszzWVGtRamvojU8HbM4Fa2sR9YEiAt3Yzq+jTSdDV3SWFAECgLHKardR3FMgAUTn+LIugpUphqaDGV4xQBqQUV6jzh6N62npaSI3OYeBEIC+kHDeSN9OJm90v4loHYn8v8ClT1gO5G+se1/r1m9oh1U3eBmrr/uBk7uqmL7J6cAcNS4O42swD+Auo6ehTXkeJ5qg/T7kVQ7oSf9xt1D4RkHMxrOcFPZPRzQHeYL43r29W/geLqW2SnTSD50mCqiOaQkY4tMZPG1U7FZTCzZuwmXbOC6pntIVZfxuO4Txgg7GKLsp+60FZu4kPqwAtZnHGDmGQ3y6Bt4UTONN3evolWrxznkVnIMUxlbsYRAfh2Fp+I40bueE+O1qHQu+lQUQVItA4JZ1FaoaHD3ozb6Yipw09u3C682lb7qLNITB2AYFI1KFvAYBApaY+mni6fPnAgKj31DfnkheWSijhtAr9Gp1NdU0Zybw/VHckgfORZX5FXoeyR3+g7/VeqG9QJVRp8D9HD3Bjouz9REHmVMfBvEDRU/vibzmyVHmXvnwA59/OM6asrRJJr1k9shTbJtZYCpkrODX2/P+2lx1hHmS8FTepKZoWjq0sLZl1LHl2ffRxelJz7YH4t4GVtqJC6pbGW6xQSA26enwSiyQBPkY2Eug3xNDAvuIim1mGj5HeIrhnN3ZAYbkncT8vVhXuICBBS0oRBKUSsp4VWkJR5n04DB1J9yMaiglD6FUGkz0aKHs+XQULcWq8dHVOoEYmddQ/k3OznuHo7g0VIu+BhmMyPmNoKgkGptwpvcxOn8VAyrvmWO+nlmZ8zhdNYi8krPknvyJCGvF6VXFpH4KTu8n+L9u+gzciwjF1yF7X8B2u5p8AWo1x76PaGmMQS94ZjC7ISCWiSVD+NwJwadiYKCAm6+7naWP3OUvqPiSO4fwfq3TyAAJUP3fv+2wUhEQkiEuCX3GyILJ7VPd3cllxIYE88Tmb8h8MEMrEE/j0S8xJbULOr0EtGeEFNLjhJeepSgNQIfEt4UAyddK6g2NROpTSRYeTu1TSquUG8mrmYuAG5NEy0RO+nT3JsWdx9EOYBJv48eyXuY6MyhSR3Gfb36ccB3loWH1Mzb4kGUoSkMCoZYOdI3hMPuYdQphbGFIhp32xKNIggcTImlIcyApNEguT34JRFNSEaICCfcNAWT3Isan4xKgD5GgSRV2w51Zf5ijrtT0eJDELR4FdAJgNbJ7tmRXOS1U1RQgLulBX1zPWp7LUowRPrIMYy+bCHvL/kQsfI4QtCHotIiJ2bxh2cfO++96166+QXptYd+j9Q8hZdXjAR+yA1WECK2csdTT7X5rm+8QY/wvvgKorl68UjCIvWU5tbx+qF3+TJ1Cn7hx3xeteLnirLNDN9dz/qMcKrGjKOm6G4+mf0JA6MGUleTy6vL9vBJxii8qh+zpnRBhQUFucSYw7nxkqk0nDjEN68+R+qtl7Dav5ND1SeZWz6euLppqOQfU3yCoo/66I2E1WWyZlofsqNMDH3xaWZP74/Nko+/cD3POGK5aIuI7pxEJJ8KDo21Mnq7Awx6pPETeDi5H+GeZi5b8wVxDhf7U2NpMndMGxRlGYstkfnj78UwLoGquib2bfqcYFUWPVV6UjQiB1qD1PxDOrIEhKubufK1SwiFQpw+fZq8vDzyjx8jWHkaTVMtfF8VdW4CpyKIhJIHnxfY7qqbX5Dd2/d8SdAbSW5pW1L+oJ71AKh0jXw296cTyBuEyPPuPTOg8IHz2rXtA9PF1hSKgorzvfFCISv/YUz+iE5HXBo7W2Z3ncOb3lrOr577jIgutsBtDINnHnukS7uougaGrFqLT9PZ89MEQ2gMl/3D1Qkokh6txoQiGfF28fXrBKixqv7BTkYRHChUYijbhNBFGaOs0nL/p193eZ3dVTe/ILugt+3h/wHSc9udoucnbRvpnDcMbXvPtEqB81/fT/Qp/sRRoz+8y3aDP5wmlbrLYzlWK3e0fNblsfAWaFAb6eqHoyHBRKa66yJxvySiEzsH11AUgj4nAb2xSzuvAoK74wsB2s5sRlF6g7yhSzsheP6yup9Sd4DpApNKZyfojaTV0/awm/SB9vbDky/HaffyySN7UVJP0+Q9yz333IPRaOSpxYtYMubq8+49k5X0V3bYH0OKuYEicTDbhvehr1HPoX2bubExnFpDZztJVriouoXBh5ehERSue34Jq15fzemaShyqBtyaJoxdjKytmiYmF3zMYdsNDDt+guvu/S02ewNbP/2UvKCMI4wuR1ZHGOzbfQ3VUiQr4qdz+ZSbUKkE/r7pTj4TnGhCSfhVnYFVhxSqp55gtrCO5ngnxaYrWXPmGNqzWno39yatOva8I+tvX5kMgMtVSl3dOqprNlBaEqSiIgulUdslmIrq/CV3P6VuWC8w+Q37kQJTeG/zj/WsguTDb9hL3t4e1J8OBxlmz5vGR5+9z549eziwbx2fj57ZFlA6z94zH/ScQ4rpeQa7G6g0wcuna7nVWcShNz5j6tCxfJ0xuIPPqg4pmPw+ViZYWGu9numnyrE/8gYtUgOSSiTcF019xC60dTM6+KwB0U9R/GpyzKVEuf6EEtuLv3wRSWpdHYQUcr1DicveyojddrT/4LPmZ1tZGZjLHGU/t1YsQ/W3pVSpJMwGA/NEC2JkOGKTA/mcvW5EWaYuJZUPEi7jPeaRHdgEB0rIbspGCkoEe45CsLcieU0dJvQSYFI5KCtbQl39elpaCqmt6UVl5RC8XjUJCTHUxerRVuUiKD9OhRVBRE7M+ln3tjvAdAHqtYd+T96xy1CCegb1KSFg3MNHqRuJdEpcVHwP/ceMZNLVffn66685lbeLz0fPpEUwc2Puui73nrnx1GBe6GPnSFxvavRqUp1e4uynmPHtdly+RsxpKRRED2RL2sD2aPCtxa3MrvPzZmw565MzqDcbsbpbGVtSQ/bRtXhb64lOjeaULoww+1gM/nDcmiaqLYdZHRzGQtvfKTEWcUIvEBWUGd/cg9y6m8lFz3BRw/SmR8g45MDa0jainhwawSOXv06Wq5nGI8cJuaKYrtrDlZpNZMs1SMg0CDGsqsnAXedvjwarErX0nn+c/b5EDmkvZQ/jkGSZse4mhuhjeEkKMcojcOWGMlqDlvZosFnVSOQlDyLLIi3NkyktTcTlCpGYmMjEiRPp1asXgiDw7B8e644Gd+untegPfyWteQD7E3P5+5/vZekrz/Ci4VMinRJPDVjCkKljeWrxog6gPnLvX1h7x630/HYnJSP6M/ejr1i/fiNp34KMzJ6xDg6LNnaIZuoMOmLqzzKl4iTP3b2Ibz/9hOPrvsKkT+K2v73Bx088x2i5F6qAma2m3RzQ9WNzajKtFh3hjnqGFxXzxp03YjRo2bi1F/YWIwsvOcaWlZ/wxHEXVe5Y5hp3ki5Vsjv8BCf0AragzMDGNCqH3s9uwcSVOZtxajRoe6Twq37hPFB2hlJDFqbGD5lYXYBLuY29Z7VYaOVa3RFuSjhM2NkDiN+PdKdVKlakjSHZAhbtSdxuM0Wtf+R4WhYbnH4URSE+KLB0oAGNexN19etpbS0AwGQaSrNjDCdO+Glpae0E6c9VN6y/QN3623dIdfYjv3cOf//zvTjtXt599HE+G/ANkU6JCa5JHUC977Y/YjQaO8HqDri59+0/cN+ZucjIHO1fReO2veQkJ5AzfBqNRjOpTi8TKvKJ+u5rNNokQj364VA1EKGSmRMaiCpgZn/EDlpOHuZAVCZbR86j1WpG7Qow1+HhoribcDQZUZ24mAJZJqD42aFJpcody/yovZw5Ox6/dTN62xby9RAVlJnqiMbfMpwGk5Vm204KOYNbUCPb7qXROIBneidSt7aMN0rriJAU7CEBreDiHmkFv1J/ixxmw9JSjaiEaJZ0FGZpaQlTk5J8O7tqL+EP3hYigzJ2tYBG8TOVDSw0n6ZX1HhqqpPZu/coLS0t/zJIf1B31c0vUOvWzOaDLf3b/z688Qz60HTubl7YCVTFqWbPnj1d9vP5qc/Zbd7OvlF2JEFk8MlEpGCQUSEHfqOB8Y3VeFQSy1LSAaiIMNKishPui4a8Cg7HFhFUOxlhn4AhIpGxQiN5s0dyTU0rYkhhRUIYDwmvsE+Zy0lFobfPx/y1m3nUVE+CoYZV9aMIROZja5nFMyM+5PaqnsQEBZbaGvguaQ1a9UrylDMMCmoJs95Bo3EAAA8WVvJXS5DeFjcpyQ/ylvVZxgkFPBv8NaMD73Nb8308Kd/G3ugrCFoEhhxtIb7aw+kzb6Krvo2rag7wItfxpvEdJoe5WS9czE2td3P3vkhWfrufsLAwfv3rX3PTTTeRlpb2LwH1n6k7wHSBatiIA8S7UnECTruXvN1n6Tsmjr2l9R1AvWzUXPLPVpGTk8Po0aM79OEOuPnbib8xJmEM/Uw2chrWMTxyBpMTf0XZJDU3JsdTsfskI7ylHP1+K+9jaWnYE7MYWJPHyICOqZdezzd/uZvREVcwhsvJse1Co1Xz4NAYsj/5lI22WPL6x7LMdhmaYX6m55XSz7Cf0dfdRfyz61BMtZxsSeOiqM2sfPYU+hgNA60aBI+TkKBhU7ibqKBCSms4OVHx9Glegr9+FmVJKcjReo5Fp9PHtZiT+n1c3seC9WQR+902crwx5GvjCdoqaLTuIVpro74wHl1jPrbIMu4qf5SUk+EI/WykS9XEF5ziO1siB6KTOBabzI2JUViSov8tkP6g7mnwBapzfdabes0hb+dZmuJWdwB1tXkVkU6JxzOfZ+PePYwePRr/ii/bp8F198/m5UMv82T8Imo+3kmrr5Go1P6MDE1EEUS+U5VRqT6LhIipWY9cvYPGxGzWTZnXHogad3Al0adOEJUazVjdHFQBM98Zt1HmbVta6iOIhI37hC2NC/hKtwBfmAZ1a4DUIhdn6l1MlpspMTmpcscyM3oVB6378QgCM/wQXjYV0VzG0cgSTujaAlHTmmNYUXcds6wS+ZlqvjP2IcnXQLkmEgSBmICXuTaRNE8+3xxo4VBNTwwqFwPiZXakpTMyoPBE4mfUNa4itsFCn7wyVMi0SBGE+lxEw7AbeMUTwfLaJrSiyA0JNm5PiiJK0/W68H9X3T7rL1A33/4eKc4MCvvuZ1RNNk0xqzsFk84NOl2pvZFqh5OBVWfo9T2sz82qY7gnid7b1LR+H/WNip2MvbqecXJPZBR2cYblSTau1zVRvrEtwCTbBPb1GcnBmCQazRaSmhxMEtykHf+OyfKwdmBnXXodtr592wNMw9cM46V3e+2lAAAgAElEQVT4Eawflo07TI2+Ncjw/EP0ED5iv+9azrrimBK7goyesDlQx4S9GeC38/XMCVxSsIVjhtx2aGc6bFzhsnNL/8c5HtGTOc4SkmM8bPcayQ8lowgiPYSz9HEcprx0KOV1ISSVwO1jUxlqdlBX9RSRtjyc9mGMNA0lpmEvQul2kINgTaa4/6/5a8Q0lrcI/1Jou2H9BSoquh5HYwSTrlvOxNQ9nUD9QecCO6p+Gll2O/127KFgRD/+Pugss470pdXXiCZ2MEGTDYeqAQmRBF8C40NJhAhyT7aGUc2nMW5fgUnXg1ZvFRFGH/UeLWeGTWdb3yHY9XpsTgezzpzgtsY41AEzObZdXL7oiTZYHToy/ySyePZz7NfIZEV5KczQ06KPRwpUM/DsBpwV/TjrjmV25A58A1rptdmMOtTKS/NuZ0CRG2/xEX4d/g2bwyvOGWmj2d3/Wg5qsrlBeYcFlgaEiIvYLw9hWflxCugNCOgcfmLLmqmp86MhyOgIF7eM24PXs56U5Nvp2fM+BE8TFKyFvJXwPbjFMSP4a+87WS72QCtK/2Nou2H9heny+z/hq1cWQkBC0IaIe/I46mx3J1B/0LnAXpOjYUiuEwWwh8GxAfH4Yy7GoWpEQiTMH8WY8dkMnTWyw7JOTuMO6lwnANBLJvTaBBzRQZxaC0FB4ExCT3ITM6jVaxjU0MJLeS0Y/Rr2RpeR3tSXKK9IvU5mV8wRityrOBBRh1sQSRKHURB+PS5TGJpmN7YTZTS7TCTZqjnt7IHsBVEH/SJOs8L+KCFBYqc5lTIi2G4sb4c2XclgQ8o9zDrzFkUcoV4SiAopZAUH8F3SIoSgmyqjBaElQFipE1+dlzCdyCPj1xLOegocA7DpKojUNtHoC+dAzUxeGNSnHdxibRx/Tbud5eGj0YpwQ2I0tydF88o7L7Cu52CqdVHEeeuZXXqYv9z5x/Peu25Yf0G6/P5P+Pq1hSi+c9LqtCFmPrCC9U9cdl67pa88w3cVf+c36xU056Tq+FSwa1QsIdsV7ZCeq/XrN2JYU8wR+2ZCyo8pRZKgwmzOwBSvZcrCq7D17YvD4+HhLbvYKVmRBYlP9jgJD4gdMnk9IqxJ2ccR+V3sKomEpHFMSphGTm4Uy00GfHoVuj3VKN5/qGYRITP2NA/2fgG/RsRiGUy4ZRq7N+9mvXiIEzoBc0jGIwoEzwkK6WSZid4M+qhnkjluPCcN4aypd5BT3oRU4kRV7+beIa/TL7Ljdhe+kJp1Fdew5MY/gdvePuIWVxfz1x5Xszx66vc7BwgExR/juPqQl6sLtp0X2O6qm1+I3bZtMGVWqCOoP/ShDfGbBatIT646r/2wLW8QeZ5qlo9/1XWSP8DAnB54Qs5O7XrJxLHhnc8nI1IRPownS+cT3UVOe61OZoe0o7OdDLnWTHba9Qi+Lvas0cEjylFCfjWK/COQMkHkiMO8G51HQOwcvY0Oysz+bnoH+J16PUXJyZyITuaPsX/Gpu+8fUiDNxzvto4/Xhp8JKkqUMx+rhn2JB5V5wKBeE8th2fP6PzB6a66+cXY3XADXYIKbe1L107m/ruXnNc+vAtQf2g/EXb+vW56h6xdtntCrRwPs3dtFFqPzTe/y0NRXpEWfRCN3Hlvnn72PHb6sru0k71QohExaDr/AsjeTIJCXpd29ZIAvvIO9UEmH2Q7TpENRN7S9WeP1DZxtPx0p/azqAAV3pFdJ+xX67reU+ifqXud9QLShx/+9Mi6fIWVSZP+3KXt2fxKytZ9SkTnAZKmMBhT8SjPPXpFp2P+Vi/vbbkeT6i10zG9ZOKW6De4fu6E9rbmxjPs+OJZiveUUZ8mE+PtnJdTp1NYmbySUQljmJE6g0k9JqH3Baj9/AFsFat5V/cRirfzdQo6gU99WQxPiWDugDhmZMZilgIs2f4Jf9OmE3v6C+pUnUfWqJDCuHv/QHZ2NgGPQmluPUUHa6g4sZ+gZx+NvnBsus7ANvrCue+LbwCQvUE8eY24j9WzvbCeD2Qvcd56zupjOtnFees7tf1X1A3rBaRJk2DBXUs7+ayCNsSCu5aSd/gokyY938nubH4lrW/sxh5hJsLZkVavCg4NjCW52sa9i7agstrbofW3eql8eh8aVWQnWCVBhdWQzr1GCx99uJyFZjWxdesp2XOaUABysvxoI48wvWII+nNmtB4RXkvXEae5klOVX7Hr7C5UisAIt4eZbhcRJQn0G3maEzUpCOfYKSIE0i0oZg0H8x3sX3WSR1adQAgX8cVmkRxey+BABtvFfLxixx+IiGAs69atY/P6b9E2x6N2OFECBwj5G6gbMIqj9v5cGfMh2nNqen0hNTtrLmHu4Vo8xxvwnLKzTw7woRQgTw6SYNYyoegAK/tPwiP9+OYNfcjL7NLDQNfT4J9Sd4DpAtQ/RoMX3LWUD033UmrqwU4m89v7fgT2B1B16jCcW/+MXR9CkH2Et7SNqJ+NFyhJ0JJ69n7SW2PQKQIlehmtpZFbAjGoggIb6j7E5XGiFdV4Qq3oJRP9rWNJsqXwlrWGVT3TcFis9CkpYuSZg1TpizmaUMiEyhFkRGQy78xgQKBOJ3O05x6+jYet4gwSfTXcXfIiZ8QytujMNEgyUkghoT4MRX81edUpKEpbNHhkymFsSU6WC1chK6B4ZVRVbjTVTmQ3CAr00moYEPMeR3UnqJcEYoIhdIqG0xqZGRVziPBa8Kt8CAE/4SEfYbMu4VHFTG+jjvTjXzEhdkV7NHjv2Uv5fdl4lJDMAYPAB6KfE61eEqx67pqcxqWDE9GoRP685OnuaHC3flrxseU02GO45LbV7Lg0nYur1rKk+AXyzD3bgf0BVL0+mprKlZgOb2LljEm8rZ/DFcJKntN9xfJQBk/1cGJrlZjQsICywHAynCrGGVTEqkXWuQ7irNtK4qTpNORm4tDkYm7eS3hEMuNMk0EIscO+lm2x6ezLGoIjzIrae5Ihebl8dffTqFQqzjy4g9PWJg5pSkGsJ6HnZqp0PfggeDsN+miuqVnJo0VvUeAWWKaP4Ui/KGrcNQjH/0C4YGdOshdVwEfmgE+pIo5nhT/jECLRE8KjiFhrfaRV+XHJIcrsbgQgMSjykvoVMjS53BkzlkPGU1xUNIAefhtyQir1TQ5cWh01af15YeokTGUuPMcb8BY2QUhBDNNwOFHPOw0OjtU5O0H6c/VTsEqPPfbYf7mjd95557Fbb731Z19It/59Kjv1GguvfZNUyYM/ayQnTOnoHKeZ2nwYg9bBiq1lJGwPoNdHU2Y4i+3gSgzDhrE1LoqCQCIR1HBpdk8yHDl4q8awN+4s9aoCpmlNjFYSiZE0HHD7qWvYSEAykC9mEukx41XbiQw7S2NlJS1UkajvR4ohjZheJupLP6XOWIagGsrppOGs/24fVNWRWg7NWheR6qMUN5tJrzmDJqqJKeqN1DqT2RA5ka8t05joO8Wt/nwuam0gVT+MHfUZqIUWzkRuIKaxBxtCFsaGn2CWsJYoyyAO+WyoAwpqjURpkg7ZpGaYQ6BXSKLRILAzGMNNqvXYG5Np1cWwK+4kEzPn0nPmr3nHpyKhtYW4ihLy9h0icNKO1WvANCSWowOsPOpw8GFJHSq1xJ9mZ/DsggEM7GFF6iLa/N/R448/Xv3YY4+909Wx7qqbC1QpScX0738YAfh9aiw1/gDKpW+xNHw8fVtqmenLRGeIodTSSP9ED6GmJqJ+e0fHTsbfD0Evv5uWzMKCUTSYQyw3f4tKCuDpIeJOK0SRG1HrRpJmb3vRmlcVTlN5M4IoIMZZyO/lBEWib6EGos8yK9/B/hEDuaq4iJqISB40WtrO5alhUvPHmHBTGjYPSbOQoE/N7Ybn+f2qV3GjZeGQl7k161kCqLmkfCMiMmpBT0HybTTp/fSstfFMlQZZDjHB8SA3Vb6F1RXEoRdJcYQwmtR8O8bCyakWBhuPM7hyLznBflyp20dR1XzSnZk8X/cabyxbgioYxk32AcxVDyfcbGGPupCPpV38/tQBbl97nIZWP89cmsW230/kquFJ/6PR9L+qblgvUNXUJlBW1vaS7zFWEyMtRl47U8fYaUsoll9CFYzHZfmAfGk3je9/gHHcOPSDBnXsJKo3ZF4GB97jrgce5g9nbqBO7+KB2MVsd28kcOY44XFx0KOaAlNb8CXCp6cqfhHOiCwqTp4ie9xgPgpbBorEk6cXMTd5FtGR4Tx35SSWV/2dhwvfAKDImMys1LfRJg+ittnDoLR5lK7PwO0z0nf2fq5tWMotiTbWRIxk3NCvuDHzMQAiA80cPHEfsw1N6IN65tX8jlVHJ+NXBMbFb2amcCN9/PupsIq0SEHGF+fibajjyyGT2XrT3dgvfx4jHlZG7iWy8XrSWzMpNH5ObMk6nogSOTkxA9vkeRRZhlDuEujRWsAN1nyen2hkQXbcvwXSH9QN6wWqFWuv4bXXHgXakip+GF0/35iH2RfFsfBvSPevYWze1q5H1R80/n6UoBf3kocZFRjGHYWzqde52OXYTGNlOY66Ksg/RJK2bQmjSaOQ4BWIDIxFRsWrzzzNV9GHWGZahaCo6Fuo4eALtxB6vi8ZdV+xoGYfAOFuN5XWGJ5O6otXUvPhR58wf9sB6r5IxuUzkpW0i9ac5zHLDppFPesiJ9GqM+OR9JhDLqY3fkasUEPAfYb+hQvwHH8VQdQyzeJhivdNwqofwuUr57u0QURb4XGNBr1P5Hq7iS3hE7C5lrNvpA5n/wcYFszmVNzXaAPbeHRNHouWHeVAowpt38nMvvQq4qNtbNqwnldffZWcnBwCgfO/+fFfqW5YL1DNnfEFt976TPvfqdUOBjS4+axvFAVWO7P/8BJfmMaiOepDThT5YOunXfbj1yfRGhpHmLgOf0ILC35/MwvzR5BcbaZVH0CKieaKxQ8yYFxbgoM2VE36LIFjVhWiNpvIljpmHniIRs9E6s0rEBQRW8tcqnSDqZ/+HrGPHgPAptewe+JgrigtITcxDbUED/zuj4iX3cRB30xagmFMidpCZsshHmrMY1K9jE+jJT+mLy9ovyLXMoaxqv34UJOd9Azp5mXYlMdQgiKjTU7+5PVwXeNOopvWclKK4nFPA8aGlVzvLOKd9BvRKW5uqfqSq9MSuXL4YjJcWeTaljHGdogpfaPpEa5n1bFqrlpawqZAX+KGzsAUZmHdunX/Nmi7Yb1A1SOhjL59jwNtyzOuN/fwm5IQ9TqR8mvHAzDTOp+QTySpbz3j+JbXX7y/Qx8/rKO6AlchCAFkz2I+uPt2qKrG4tKQm+ZgfVIuG1dv6WA3a8ZYfOF/Y/nQHEKCmtjmAyTXxPJ59RXs0ewDRY3KdxeHT3dM3oiwmInN2cVTLz9FAIEkdyNPWGL52LaAt5Xf0uozcqPhfRqL1jD3pJ8wlxNBgDezw3l78Mtsrnkcq9jKgcBg+lWuIvnAnRiO9UKUtcQlV7DAE2TDqam87HRgExWOxF/MUrGR440vssHamxurvubZvDyuP1NHkepmsv2DOBb1JRNic9ly7wQ23jOeOyen0+AK8PQuO8+WxlIeOZSApP+3QNu9dHMB6q3bXkJvisTb50sG116Fvikci8pAiaWRv84ayGmPnz1ZSVTOmIEuM5MdmbUsbPqOPHNPvvDN4NOWMTyLnmGCgkbRUCoeJMr3OmnGRlaKE3A0WFBrjTQqAZZm7MPWKjHjzCA03mtxmgsRhRK0ocMkmV1Ya30ctsdTGX8lid4EdIqA31bDJYIVhBAbrHuYVTeT49IZjhlPYJJcFJmsnLb0ZUhxCd/160e5OZ5WnYmBpQe4IfodTBoX23dOYrNnNFH+Buht4ET/oUR4/VxxcBPIIQaqi5kursfoC1IbpuVElgUkmRZ7JBGGRrxakXWhS/hSdSUoAYZUvs6astW8EdmXF/r+Bbcqil4qhbSilzksHWFm8wyuaJxHjE+gViuz0nKKyKyJrDteTXGdk3jRyVhTLQa/A6PJzITx48jOzuaJF5/E51GhJ4gHFVp9kMUPPnbee9f9DqZfkN667SWmWofy+qrJvPHGn4kQJCxqMwdbS5j4p8vafdcd737Q7qtec/cqloaPp8WdyqiWiUDbg6FRNAQIUmwpozisLyoJsmITaalvZNRlv+K+l95lYcEo6sJkvkmvbLsAQcBtMNKiH0VcvYqeNgWVWs3k5Lbp8dGwAHJjDHt9LcghNZPqJ39/5QJ+vwGHLxyN2kSTzYgiqJh2soo3Wyxcnn+KcltvnlA9icenY/rYTYiSgqgozNq1istXf4gvFOCtsXMJaK0UBzNpTt/M8chxmHwhRh9oQJAVwsIbCOpAJcjMU33N06H7sHkdHEi6j21R47jJUUZ24zOE1f+VM+4Kvk26k/6eLDZYNnJYvxMRiPOJXN+QQcupTWxeNJ6N90zgsklDOKwdxAZ/H0pbFNatW8fjTz4JHgGDEEQQwCAEUTwCDz/z2M+6t/8r6Yb/qVUpvwS7YdZsdILAgxdvp773F1B3NYIgkGTuxas3z0QB0sZfT/hnn1AfrmfzkgfbbbNib8CNBvhxGqdGxWDnZN5PMxNTV8vJPXkEjVaWFKyDU+shK4qJp4exN75tn9eA0GYbUqnYYRzNqV6RRIdOE9i7kxLJRbCfkfygRENNDHYlh+muMYgIaJW2R1GWVUQ2NKGv11MqJNJLOM27hSdwiFYSmt00Rhso3JdC9uw81MYAktxWz5dSXcqVX77Fupk3sym9L3NO7OOe0r20+GYiKtOZoj3JcP9G/LqOU+9EqYKXhd/xaf2NLE66jm/rd3JnrZ9jujJOtDzFAXM/fldzMx/Y3mNJ3OcAzHGMRy/DnIYBFHx1GwCzgJk94EyUmZ32OA47ejBQqUQSOt43laDg9vw87Lqrbi4wuyjaHsaMhHosaflQ92N7wNl2u2/8+jMsrlY+HDOdmNqSdtsIWwR1dC49iwhG8GXy5dS1RjLc9y36Pia+TPkxqf83ZSsYVt+2XlpsKSYuqEMn6/Do9axLnoEuxs1t5S8QrPazLvPSNqNe8JsdxazVHGaBfwS95FiOy+W0iB78fj1FXpkSIonRnsUWqCTHbwYEaG5F2+KneE0yJAmY410YfB7cdXoifA4cx1zIFjW1Ris9gq0s6zEKsaiVPHcv3tdu7vpL0wa5Wvcu5SSxxTaUEU15fNB3EQvUn3GlsoNE7w08VHUzTyV0BDbGK1AUubVDVxpgSiJMVmDnd9d0eTo9wS7b/5m6E/kvMNUTIgYVx8tjqNdmkXJO++3vf4TsdlM173LyBmSz8Yqb2T4gDq0o4HG6qXj9EAQ7l7vZVXYeK91L8PgJdAaF64LryWydhl9tIaQonPS4EeS2ele/6Oe7uBzGV48nojXEX4JF9DLbqBqYjebgfi4aUUiBysBOuxONxoPDLyCjICAwxz+YtZrDeHWNPBK9CUtSFO6WOEoKK3h5vBZ/QOZU4SmcFSbCXK34W1XIRoFec8opWZtEjT2KKFUTw21WMiwpNOTlkq5upHZqAj3rvkblEwjqOn08VD6BdNNnZKXoUCxFmNfcxNDK0zwQu4T5ewuwaBXifOpOwA72jGPc0LalJ0WWqS4upOTQPnKKS9nZcyCZNGDoAkzPz8Su22e9wHTAcQSvovDCmvG8807bFNerKBxwHEEdkvCt3ojsaCburjupDYT+X3tnHh5FnebxT1VXH+kjCQkJCbmAcCRcQuQOR8SHQ4ZjBCIDyIIggq4zoqJ4D+OBiiOrou5wiqCDMNwjKIccQgANJBwBQkhCEnKHzt2ddHd11f6RlWOS4DOz67MbrM9/9at8u/pJ17fe+h3v72VbtYqqmNj5wgFSbAdx477t8+oFF6m2g8RfXIursoK2fXqjR2a4MYMRI8ewX12JvzsfnbfhpoyujsYpOTkacgSDksMHhW+ypGoXIZPGIhhNHEg+wzJzOA/QBcGkIIoNuiyxGBGR33ji8JV8yCttRfkZgQB1B0ajk4zz+yjI3ka8mEqJf2c8ggSqQE2BBblOR/Rv8nB3CKAoOIxv83T8OUXCrlrok51GVV01ycFT+dC1ELf3H3JMVZXSyiiUPW7cn16j5pXd2IsCmZ+7hdBaFxvu78OCOCdFRgGD2mDY/jU9+Dj0K5a3/YqS/GKObtnCZ4sW8pc163hDH8aHY+aRHtMf2SQjq7cvP5RVAaPPvxZZtdHgu5C/zFuG1bcV9TGb6Vk4nZT8UhyVB4l0OelZXIdPjx5ErFzBg6mZXHXW88Ta08iGSFoHFJNhucSamgG8iw9dpGpSbAcprbJjK6zAotQxJTqNcr0fIXIVf7ynFzsri0mM6EnoDiNu98PU2DIosyRzMDIZf6OCyW8I18p/ANXLPdnd6J1ezcCxzxF1QcQcF8yK/FVMKx3LeV0euaYcRjkH4VB1nDLnUezNwyN48RUkqlWZ7t0PEGwtINjdmg/2PsBxUyxtXCUkuL6n27hsrNYasoPe4n17J2pKPUTlXGaU8ypJcjuutG9HfXs/AuQKnlQ+oIs+DZ1LwIkJvb4e2+5ehDALyeRPnZJDJ/OT5IdN4r1OYWxVJyDJCgvSZSYWeMk3uvljxDKK9XkMSAsg2NWV1ITxpLQKxaoTmRsexGMRQbTSS7z6zuL/tdFgzax3Kas/eZT2sYdwehYzbtQMDs+ZTEV2ETFF5YSvXoVt8GD255cx40oBo087eKA8lylLprF81Zu8n9UbX2o5984UnvvTIoIvXkRExb9XNO0sFxlSnoyEyjo/Gykh9/LRlO1kHj/F/i9q8TUXM2PZND5JepK1WYfx16nUBs7FWV+E4foBEg+2oSzYwohBTzBqcgKCKJC76BDpfnZGvTSZI1uPEJis4kXloHgGq0GiRK1AFhT0CAyKvAQd0lCUOh4/9CrBPoXsmp8AgpHU1KmoqpeNFT6kmqZQax3N/aeP41tby9Xq1pwL60hVFz9Us0TUpRxmb99In/ocip+swxDgJP/og4TWjyfWLBHkfROT7hTnu45GTniNZy/XkC5Dt9x0Eg5tw6J6ODjMTa6UR02rWUj+I24z6b+KNnXzKyQzO5oLF+JuHA/96HM6l1VRavNhz7LFVBYUkvfy10SWejjRzcCEN37X5Oe8++oSvEYDKnA5v47AAS8zp0Mf9ljMzKiq4b2MJL79ZCyXsm4+xD8vuM5a4XG6t+5DpVfAal/FZ3EJrIhYRUG71oQWOXmz9DlGfvMMSaWZAKgqnD9/nvNF5zkgpqBDYLjSi273xvF4QiRtFAEPKkfyYsj4fi5Wd8NSSlWRST0zg+Mp0zjjVFGBqQF17OgVzXGxntCCInxUD2VxbWhnLWP2xi9ofyGb3JgoFi94jinj3uKz5JdwllsJH7KdNuPO4P+UhZwOVkTqaX/OiHHpWR5du46hpw+RHtGZ9bNeZP/v3+ZU+8V4zXHYKtbxSusLLOoQ+j8y6s+hmfUuZfuuiaxZ8+yN44qNGxFlL1L7EPL1Fja//HfqfaIYl1dAlUnPl0X2Jj8n42QSepeLyvBwWtuLeOnIm5xRS8iN7YeEQKkxkJH2EwzNXgaAW6xmUUY+oUY9jwz4iDnRCVR6BRYdXUh52lFejF2AZDQxOD+GIvsR5n0zCYBqRzVbt25FEARGTB+Fva+ADgFLkpuMA/uZ2/EsVosFk85ImbeKb05mA+BVdXx23UCu28Q9Fh2i0LDr4ZXLr5Kzfg6T9/6dVvZyhl1OpSAsgjVzZhHYO5bEAhWLIlDbtzXJPSN4Je15asqtXK//kM1bF5DV6iJXnIH4iNuwGFQS2kxiqW4w02QDNSqk1tbT2WJl2+jlJIQn8H7yEjZf3vyL/qaaWe9SZkxdz9NPN+y3pDgcNzJreq3+GwHmMXhMnbBUfcOiucNuZOTUe2+ftlEULye3fkVgeCSL3/2IQ/FergWXEF0YzuDgZxF6JBLprWZdp4X86NdQBCtO9z1r017iuZpzJAT48kT8x8wKHEClV+DdkJUUDi2hz5gJBOVUsTjoZfylhvo6HqWQQ/eUcs/kEXTr1o1hk4ZR0SELHQJm76Mk+y0g4b77qPe66DyoC4GSpeFLqgLxFx8j3rCCvuJyws7F43NUAi9UTfVS8raHrsNkEAXeEzw8VAjpVXX8LVykvdnAmAAb7ggL7sHRrMl7lJpyK+2i8vj24n1saPsietGDedAZdgwMoLjaxVOHKtid4uH3ZhtX69xMOpvH/V1fJSE8gTdOvvGLGlYz611KSJsSIiKuAg1R1VtRgXXWbDb9fjNOYyeCnPuxK5fYPjuRBcFWit2eRtE142QS9vw8+k+awsJ9D5Lve40OldEMOivx5fov2ST1R/HU46rLY2fwHACyfMIZaT9B/+8fZ8/yMexft5YHj85kpm//hgh7bCElwTUgimRu3cHUyu4AiJI/9pqTzP82kRG7nyYp6S8MKXyWCv8DDYY94SU7IwuPwcPRlGN83aVhPbKIQLlay46j37Jx3xmKDyu02iTRZkMoCCKK1YtHfxaDKvHjiRN0O1XIClc1T/koXFPq2FNeQ1BZIYq3ntN9BrMrYCr11b78tu8eKtzpfO3tjzl5FWtyMtkwOBDdhA60VQRmbi9kY4ZCqCowP72QuuA/MChs6C9qWM2sdymXr3Tm7Nl+CC439jVrMQ0cxI6Vl6jziaJ1QDEPrX+be60m8vUmiv8wg35WI8tzS5H/e/dcQVVuRNUVFUv5riyPxIiebPr3LZTGdiXoehGn9yfzo18/5hfv5OnQhv1x66p78W3c2yT592Kk/QRD8hZxLuxteviNZmpoQx/206JPUdr5o6+pJHHsGAACzCFsGb+bTqETGl6PM/+TETGjEWf8jotdS9Eh0OVcMKogE+gK5E+p9wIgyh4eOHKETrIfdqmew706cnzcw3inv0O7kHWoig6DtZhgiwdF58Lt9wVpu97B8B+vMfuLt5mUm4wcFD+yv5MAAAdcSURBVESNjx+BVLBXGsVbwZ9S4QxkfO+dpIS1xybU8XjFDnbvz2bk3jTej5Ioim9DhwoPq/eU82SJyt7rDo4ZHyU2OP4XM6xm1ruUXbsn8PnnT+F37DTeigqSqzrcMOqUJdMASFizhXutJgr0Jvpu+JBit4czpnAAohx52PPzuBydy3fX85gY3pPIzh8Q/+Nlvhg6leKYGIKuF3EsJwBRdmHL2XXj2mPHz6dv19VsE565YdqBR5+ga3opD7ijqfQKfNcpBZ1R4oftN2/qGP9Qtgd1ZktBFR2NPShyZzDvwHRe02/iK/M36BBIrBqJwS2T7HAAIBgM9Nq3hwmj+jD2m730KBcpNslsP3mAfV+mUnx0FqgiUXFfYFArqfC0I6RTF3pODCLu4UwmRr7D++pM/k34Eq/OFxXIkU0ssi2jWA5jYPR3VLbpzlzDfjZM7ciobiHsu1RKYtIVxjgrOBBpYlqmiw1JDoJr4HvjHFr59ftFDKtN3dyFbHpsOr7JpYhVKhHGAhx+fvzYa8ltRr2Vw3Mmc6q2nu3jZuOTVUj85WPYvLUoiHwXG0Xr/h4u+j5JkVumj6+Zhe1DGNbKxvOvv0DwpUvc3y4HUY4lqXYeoGIWr4PlLLGdEzjlyqC26iJ9bVcYVn4KWZRY3boHay1l9L/ix32FAxgYNB4Ah7eKk+JBortfYIWvP86LeVxvHUm5MRPwEld6H8/bf0umroCtgp1jcntUBKx4iBeyeSwri2v9ZlJ4OR2jfznF5lo8gpdIYw2RfXdRURnChbT7kSQXsmzAaHTgG3UVW6iDrfyWHxiAHjc6ROqR8FEdvKIsJtZxhUGpFbh1InqvgtMo8bXfYJKDXmffhWIc9TLjJSMzdSZ2hulZ1UHAv/wThLoUgulHqZiFqtgRxEC6KKPZMvOFRr/BT2jzrL8iNj02ne4nUhBvSalUJUjv35eJa9Y3qzs8ZzLLQ3rTNysZ/S01azyCxLnInlRPefiGSW8tIPzcnxYxqKiUEh7Cy83VQRL16G1HqWsXTkJCArGxsez5eiU+OVsZVn6KH3x8OFI7gWmuRCTxZsU1WXFzmK/pvn8fljoF0WqlZOxw/tzDTbbjCBHVXRiQ/yDrMeHl5qJ8HV6G6zKJzf4BVXGg0xuI7N4Hp9efXLcdo62Y0LbpXMkYzK1VckRRpr6Tg81hjzC1VRWj1R3U2g+yXx3CDuEhvKrKhpJ5DLpccNtrqCwK7AoeythHd5CUeZ3d54v4Lq2YAS6B4TYfPu6qp6TuTfSe3Nv+z6pgIEZNbNawWq2bX5Hu/ICuSJUqxx0DARhkOQGA7C8wd2zz+9UCjLq0G1+58c761ZKVkbaezeoyxGicSuOSEGaxjHzrYf6xOLjJx0mvgALC857CKjVei1wrV5LSej1evYRXd3PeUkHFi4cPi39HLY1La1hxk9D+GLJFj+wj8dOFdYqIzWkmsKAMl8vaSGc01uLnG4bZ+9NDSgG1Fpk6kgLb8/G117C4Gi8RdBgldg5cfuNYViDLLnGhSE9IiZlDMUsQlSbKh4iBnJ9xuHE7Wq2bX5VOV6kAwg2T3tpeqA+5o9bWhFF/ao/yH9Ks7kxlE9WlAKcSiDn3WpPnzmKiSzu/Js9ZdH5Mq98HTZTIAHiLprNZatGzpXPT5wiE+dnbmzzlclkoLav6h1YdYCWqoqzJxfgAZpdMxuGM29oEoDvglQSEpowKqErTc9o/h5Z1c5fh9ReRKhub2+svsnpG5B21SeesTUbWGsmK2q9x6txPmA/Ym4msdvwHDGhC0YCjoKrJyOrwVvF52FPN6qxZnmYiq4d5nh+a1WF0NBNZHdzbvX+zMmea1GRkdRolxiaObVa348QhaMKYgth8Rb47oZn1LuNiz96N+qyKvqF9Stsud9SuC+tMz7xzjfqsV8I6EzFxWPPCEy8h1QxG5mb+mUQ9WM4y/eklzV/v+WdIUH6DJN40nqy4OSkeYtbcZc3qjr28jIPejo36rAN1V3lx5DPN6j4omo0n14Si3LztRVHGp205I8clNqvbVrCB8aXfIyk3H4KyKLC3VTwTOzb5xgpAl6TRpAt/Q1BvZjKpgoEYZXSzmjuhTd3cZUxZ+SVpA+OQ/QVUVGR/gbSBcUxZ2fTuhbfy16WvNwwmSVZUGvqq5yJ78telr99R98h7SzDYjmEWywAFs1iGwXaMR95r3qgAs5Yu4zC7qZUrUVWVWrmSw+xm1tLmjQqw6q1nGK7LxIobULHiZrguk1VvNW9UgAUz1+IbVYjRWAuoGI21+EYVsmDm2jvqJs7fxa7goTiMEioNfdVdwUOZOH/XHXVbZr5AjJoIYmBDOUkx8I6DSz+HNhqsofH/CC3rRkPjLkAzq4ZGC0Ezq4ZGC0Ezq4ZGC0Ezq4ZGC+GfGg0WBKEMyP3ZP9TQ0PhXiVJVtfEKE/5Js2poaPzfob0Ga2i0EDSzami0EDSzami0EDSzami0EDSzami0EDSzami0EDSzami0EDSzami0EDSzami0EP4L7pFpliE3T6cAAAAASUVORK5CYII=\n", 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\n", 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\n", 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" ] @@ -158,46 +299,23 @@ } ], "source": [ - "plot([path + [Point(path[-1] + velocity(path) + d)] for d in deltas])" + "frontier = {(start, zero): [start]}\n", + "\n", + "for i in range(6):\n", + " frontier = expand(frontier)\n", + " plot(frontier.values())\n", + " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "# Complete Paths and Legal Moves\n", + "(Note that the growth is much slower then 9n.)\n", "\n", - "For our circle-in-the-middle track, I can say that a path `is_complete` if the path goes from the fourth quadrant to the first, second, third, and back to the fourth:" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [], - "source": [ - "def Q1(p) -> bool: return X(p) >= 0 and Y(p) >= 0 # upper right\n", - "def Q2(p) -> bool: return X(p) < 0 and Y(p) >= 0 # upper left\n", - "def Q3(p) -> bool: return X(p) < 0 and Y(p) < 0 # lower left \n", - "def Q4(p) -> bool: return X(p) >= 0 and Y(p) < 0 # lower right\n", - " \n", - "def is_complete(path, regions=(Q4, Q1, Q2, Q3, Q4)) -> bool:\n", - " \"\"\"Does the path complete a tour of the regions, in order?\"\"\"\n", - " for p in path:\n", - " if regions[0](p):\n", - " regions = regions[1:]\n", - " return not regions" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now I'll define the `legal_moves` that can be made. Given a path, `legal_moves(path)` yields all points that can follow on to the end of the path. Each point must be a point on the track (not inside the circle), the velocity vector can differ from the previous velocity vector only by an allowable delta, and the line from the previous final point on the path to the new point must not intersect the circle. \n", + "# Searching for Fastest Complete Paths\n", "\n", - "I have inserted a hack here: to make sure that paths start off going counterclockwise, for the first two steps I insist that the deltas be either up or to the right or zero.\n", - "\n", - "I got the calculation for `intersects_circle` from several posts on math overflow." + "Now all I have to do to solve the problem is repeatedly expand the frontier until some path(s) are complete. The first completed paths are guaranteed to be the fastest (i.e., have the fewest moves), because we are expanding one move at a time. In the end, I return a list of all the completed paths in the frontier, but there may be many other paths that are not returned, because I only kept one path for each `(endpoint, velocity)` pair along the way. " ] }, { @@ -205,42 +323,6 @@ "execution_count": 8, "metadata": {}, "outputs": [], - "source": [ - "def legal_moves(path, track=track, deltas=deltas) -> Iterator[Point]:\n", - " \"\"\"What points can be reached in one step from this path?\"\"\"\n", - " if len(path) <= 2: # Make sure we start counterclockwwise\n", - " deltas = [Point(x, y) for y in (0, 1) for x in (0, 1)]\n", - " p, v = path[-1], velocity(path)\n", - " for d in deltas:\n", - " new_p = p + v + d\n", - " if new_p in track and not intersects_circle(p, new_p, 3, zero):\n", - " yield new_p\n", - " \n", - "def intersects_circle(p, q, r, c):\n", - " \"\"\"Does a line from p to q intersect a circle of radius r at center c?\"\"\"\n", - " if p == q:\n", - " return abs(c - p) < r\n", - " norm = (q - p) / abs(q - p)\n", - " v = abs(X(norm) * Y(c - p) - Y(norm) * X(c - p)) # Norm of the 2D cross-product\n", - " return (v < r)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Finding a Fastest Path\n", - "\n", - "I can use a breadth-first search, adding each legal move to each path until I find path(s) that are complete. \n", - "\n", - "I keep track of a `frontier`, which is a mapping of `{(point, velocity): path}` for all paths of the longest length explored so far. The reason for this is that there may be an exponential number of paths that arrive at the some position with the same velocity in the same number of moves. But none of them will have any advantage in reaching the finish line ahead of the others, so I only need to keep one of them. In the end, I return the completed paths I have found, but there may be many other paths that are not returned, because I only kept one for each `(point, velocity)` pair along the way. " - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], "source": [ "def search(path=[start]) -> Path:\n", " \"\"\"Find the shortest possible complete path(s).\"\"\"\n", @@ -248,24 +330,18 @@ " completed = []\n", " while not completed:\n", " frontier = expand(frontier)\n", - " completed = [path for path in frontier.values() if is_complete(path)]\n", - " return completed\n", - "\n", - "def expand(frontier) -> dict:\n", - " \"\"\"The {(point, velocity): path} mapping extended one step in all legal ways.\"\"\"\n", - " return {(p, velocity(path + [p])): path + [p] \n", - " for path in frontier.values() \n", - " for p in legal_moves(path)}" + " completed = list(filter(is_complete, frontier.values()))\n", + " return completed" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -282,36 +358,78 @@ "cell_type": "markdown", "metadata": {}, "source": [ + "We see that the fastest path takes 12 moves, and there are several ways to get there.\n", + "\n", "# Submitting your Answer\n", "\n", - "I'll need some help to put my answers into the form requested by The Riddler:\n", + "I'll need a bit of work to put my answers into the form requested by The Riddler:\n", "\n", "> Finally, submitting your answer can be tricky work. Please be sure to submit both your total time, as well as your sequence of moves. Each move should be assigned a digit from 1 through 9, corresponding to the nine possible destinations of the move:\n", ">\n", "> 1 2 3\n", "> 4 5 6\n", - "> 7 8 9" + "> 7 8 9\n", + "\n", + "I will define two functions to translate back and forth between my path and The Riddler's list of digits: " + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "Digits = List[int]\n", + "\n", + "def digits_from_path(path) -> Digits:\n", + " \"\"\"The digits that the path represents.\"\"\"\n", + " return [deltas.index(velocity(path[:i + 1]) - velocity(path[:i])) + 1\n", + " for i in range(1, len(path))]\n", + "\n", + "def path_from_digits(digits, start=start) -> Path:\n", + " \"\"\"The path that the digits represent.\"\"\"\n", + " velo = zero # Velocity\n", + " path = [start]\n", + " for d in digits:\n", + " velo += deltas[d - 1]\n", + " path.append(velo + path[-1])\n", + " return path" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[3, 3, 1, 7, 7, 8, 4, 8, 9, 9, 6, 3]\n", + "[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 6, 6]\n", + "[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 6, 3]\n", + "[3, 3, 1, 7, 7, 8, 4, 8, 9, 9, 3, 3]\n", + "[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 9]\n", + "[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 6]\n", + "[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 3]\n" + ] + } + ], "source": [ - "def encode_path(path) -> List[int]:\n", - " \"\"\"The digits representing the moves (as coded changes in acceleration).\"\"\"\n", - " return [deltas.index(velocity(path[:i + 1]) - velocity(path[:i])) + 1\n", - " for i in range(1, len(path))]\n", + "for path in search([start]):\n", + " digits = digits_from_path(path)\n", + " assert path == path_from_digits(digits_from_path(path)) # Inverses\n", + " assert digits == digits_from_path(path_from_digits(digits)) # Inverses\n", + " print(digits)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Alternative Paths\n", "\n", - "def decode_path(digits, start=start) -> Path:\n", - " \"\"\"The points that the digits represent.\"\"\"\n", - " velocity = zero\n", - " path = [start]\n", - " for d in digits:\n", - " velocity += deltas[d - 1]\n", - " path.append(velocity + path[-1])\n", - " return path" + "Here we search from several different opening move sequences and get different results, but all of 12 moves:" ] }, { @@ -320,38 +438,48 @@ "metadata": {}, "outputs": [ { - "name": "stdout", - "output_type": "stream", - "text": [ - "[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 6]\n", - "[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 9]\n", - "[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 3, 3]\n", - "[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 6, 3]\n", - "[3, 3, 1, 7, 7, 5, 7, 8, 9, 9, 6, 6]\n" - ] - } - ], - "source": [ - "for path in search():\n", - " print(encode_path(path))\n", - " assert path == decode_path(encode_path(path)) " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To get an idea of some of the paths that were discarded by the `frontier`, here we start with a path that is tighter around the circle, and search for completions:" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ + "data": { + "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", 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/IvOyJE+yQer99VqIWBMk3rwsn7o3ZKhG5sfj8SRlcfrrHDki1gQJzcviC7SH56z5d+uHTLztmkxXzbQEAoGk3rmGrkVA+3s0f5DZkZnPe8iauX+lwFbI4DumyPDCFFBUVERJSedpHxNhy6+WUu89zOkPzk5tpTJIn8983h+QEUupQc5j4ohYk0Sia1KDiDVxRKxJ0l+/rZRqAoFAWueAzSVErELGEeuaGCJWIeNIkyIxRKxCxhGxJoaIVcg4uTr/T6oRsQoZRyxrYohYhYwjPeuJISFyQlbQ19fCjPeahMgJWUFfXwsz3mviBgsZRzycxBCxChnHYpHbMBHkLAkZR8SaGHKWhIxjtVozXQVTIGIVMo5Y1sSQsyRknGS+H9wfEbEKGcVisYhYE0TEmiTiuqUGm80mr24SRO64JLHb7d0nErolLy8v01UwDSLWJHE4HJmuQk4gD73EEbH2gGV3PkC1czCl9kr2zX+L9X94LtNVMjUWiwWn05npapgGEWuCLLvzAca2nYjNYj86GZLnJBFsL8jLy5P2ag+QqJsEGdkyMubEVKPbjk+qbIEOVlWibrpHom4SRCamSi3RLrBE3XSPuMEJ0l8nQ0oXTqdTXn/1EDlbCbKzcGenyZD8AR/bC3dmqEbmpqCgINNVMB0i1gSZftdcNudvosXXiNaagPbT5m/hov/8mQxE7yF5eXnyfjUJRKw9YPpdc9m27Wl2vHsHr/AWRfZSNjz1NkVFRZmumqmQ85UcItYk8OPg3ZFLaW5vwL65AYfDIeNbE8ThcMi71SQRsSbJeYNqeMO2nnK7S6xrDygult7zZBGxJskFp1zH48e/3MG6SjusawoKCuQc9QIRa5IMHXo6o6yaNdaPKLe7+PeitygtLZXXEXGwWq1JT5osGMid1QsucI3j96NfpNlnWFeLxSLucBxKSkrkQdZL5Oz1ggtOuQ6v3cd2x7awdS0sLBRXL4qCggLy8/MzXQ3TI2LtAa8/uJihOzcy+PAXvDN+Mtte3s7YgJXnhj8Ttq6BQIDy8nJ59xrEbrdTWlqa8v0unbuAQlsxxxQcx9YbX2Hp3AUpLyPbELEmyOsPLqbi0ftw+NtRgKvlCBWP3seMrQP42OHmUGVT2LparVbKysr6fUSJ1WqlvLw85edh6dwF1DgnYVHWoxFQzkk5L1iJukmQvEWP4vR3HG7o9LczauURAHaMWRW2rn6/H4fDkRaLYhaUUpSVlSX8/rkn12J0Xk3sCKi8mh7VLxkk6sYE+SpajsRcX9rSxNiAlZUN62gYRNi6gtFW66/vFUtLS3v0NY2+joDK5nstHuIGJ0hdYXnc9Re4xrHR4mPg5eUdrCsYgwD6m2DLysrSOlC/v0ZAiVgTxDv7J7itHV0vr8WGd/ZPuOCU6wB449MnO1lX6D+CDbm+6Y6o+aLls07rfIF2tnk3prXcTCNiTZDzr59F3U9upLawnADgR+EbOIjzr5/F0KGnMzZgZcWh9Zzy06mdrCsYgs3lTieLxUJ5eXnaher1eHA5B+D2tYYjoFp8jWx0r+HSB25Ja9mZRsTaA86/fhZnrX8f25trePzESynYv5fWtWsBwq5w7ZENMa0rGG3YioqKnHutY7fbcblcfTJA/9U77qfSMYBt7g2MuW8GQ+89mzH3zch5oYKINSlGDyhi66SpNBWWcujhRwDCrvDKj/4Y17qCEXXicrlyZuCE0+mksrKyT6KOvB4Pw3wjafE1ctptV6e9vGxDxJoESimmjRvOM8dNoXX1alrXru3gCjsKnHGtKxjvHysrK009BM9isVBWVkZFRUWfHUPIqu50b6Zy8KA+KTObMOedkgXMqBnEKyNOx1taftS6Bl3hffvXdmldwRB8UVERlZWVprOyTqeTqqqqPv00S3+3qiBiTZrRA4oYNqicVeMuDFvXo67wY91a1xCh9l5PBhBkCrvdTkVFRUba3f3dqoKINWmUUkyvGcRjJSejKl0cevgRhg49nRMCVlYcXA/QrXWNpKCggKqqKkpLS7OuA8pms1FWVkZVVVVGvvIgVtVAxNoLZtQMwm2xs+eCK8LW9cIIVzhR6xpCKUVhYSHV1dWUlZVl1D1WSuF0OqmoqKC6ujqjXyMUq2ogYu0FowcUMaq6iL+4TsVaZVjXSFcYDOvq9rVSuU2x9+a32XrjMtb+flmX+1VKUVBQgMvloqqqiqKioj5xkZVS2O12iouLqaqqoqKiIuPfSxKrehQRay8IucLvf9GM4+rZtK5eTeUBWwdXeMOfVmG35mFVtmCESDFV+5zdCjaE3W6npKSE6upqqqqqKCkpweFwpKQHVimF1WrF6XRSWlpKVVUVVVVVFBcXZ037WazqUdJyRZRSSQ1cNmO+GTWDeOD17bzztTOZVLWIQw8/woXfHMf9devYt38tJXvBGnXj2yx2Sva6e1ye3W7HbreHv0bh8/lob2/H5/MRCATw+/0EAgECgQBaawYOHMiBAwdQSmGxWLBareG/NpsNu90et32cDdcibFV1fKuaDfVMZ75IJOqml/lCrvA/ttbhuvZaWlev5nzLFMBwhQussT/zEm99T+pps9nIz8+nuLiY0tJSKioqcLlcVFdXM3PmAKZM0QwYMIDq6mpcLhfl5eWUlpZSVFSE0+nssiMrG65FIlY1G+qZznyRiBvcS0Ku8JrddbRPvxxrlQv1/FthV7jV3xw336E/bsCzqyEt9Zo921jMirRVOyNiTQEzagYR0LBiR33Yun67cSQbLT4OVjd2miPHF2hnr2cH7QdbOfTHDWkRrdnFKm3VzohYU0DIFX5l45eUzZyJtcrFyR8Ybs/Or7/GoSFuWnxNwQiRJtbVb+aDL1/iXe/fKbpwKO2HUi/a9nZjMSNiVWOTHV1+JifkCj+0aju17eC69lq+umcBF421syKwntm/eDycVmvNzkc3krfexhfbl7Fc/YH/uPHXeP9dT9Nbezn0xw04jiulZOpwHMcl/1mYadOMv2++2cuDywCv3nE/4xyT2dC8mjGDZ2S6OlmDWNYUEXKFX910IGxdr1iTHx4gEUIpxZQrx+AsHUvl8CvYv20LL933GxwTKhh000RKLzkuJZb22muNxWyIVY2PiDVFRLrCFqcT17XXUrajkRM+1+EBEiEKSx2c/d3RNNcPY+yU2ezftoUX75lPu99L8ZlDUiLaq682FrMhbdX4iFhTRGSv8KEmT9i6XvNuIDxAIpLjJwzg2JNdfLapginfnxsWrNfdhrJbey3a1lZjMRNiVbtGxJpCQq7w8k8OhK3rcXs0vi/aO7jCcNQdtjks7N5YxsU/v7GDYIFeiXb6dGMxE2JVu0bEmkJGDyhiZFUhr2zYD0DZzJmoilK+9W6gkysMR93hr3Y30tYynBlz53USLCQn2p/+1FjMgljV7hGxphClFDNOGhx2hS1OJ9VzfkrNHs2n69fGzBNyh9cs2U3ViFPjChZ6JtqZM43FLIhV7R4Ra4qJdIXBsK6ePPje37x88rUTeG/SCbx57zXh9JHu8KrFWzj+tDO7FCx0L9qWjw6ydf56Nt/wPl8uWEPLRwf77Ph7ytK5C9h64yucYjmdgA7gp+u43/6MiDXFRLvCb/9+DlYf5PmNk13RCGV/WdNBsJHu8Mevfc6Y08/qVrAQX7RHntvK7D+P5EcvjMVf76H+xe1ZKdjQnDWFthIj2EBZqCnI/TlrkkXmuklxvmhX2P7CGmyBjmkcPrC/sKbDukh3uO7Llg6CvWH6eXEFCx1Fq/JtoOGH4/fzw/HGA0O3B2h89bOUHWOq8vWnOWtkrpsszRfpCpc1xk5THrU+2h0OBHRYsCMHVHVpYcP7sFvRbT4ALh5zmIvHHA5v89d7uj+wCNJ9Tl9/+PF+NWeNRN1kKZGucH1J/HT7b70N75494f+j3WEgYZc4hLXMmAyqrtVGXaut0/pM8/rDj/P+9YsY/fnouGlyfc6aZBGxpoFIV7jlGxPwRI3A9thgxygHjcuWsXP6jA6ijXaHoWeCLblwBMpuYc7LJzDn5ROM+tgtlFw4Ii3HmiiRIh2cP4ztzZvY0LQ6ZkRSrs9Zkywi1jQRcoW/Ou9u6r8/iboSCAB1JfDhuV5u/7afv/xmMqVXfa+DaNs//7yTOwyJC7ZwXDVlVxzPT849yHWT9mEtc1B2xfEUjqvuw6M/SiyRNkz1c97DP2PGIzex0b2m381ZkyyqJ770hAkT9Lp169JYndxBa83U371FVbGDZ687/eiGQACeuoTFTdtYWJrPtOHT+O0JN9L456c48uzf0D4fpZddRv1ZV/LGkoOcfsVITr1geDj71g/e4ZUHFjJ49Alccet88pz5GTi67nn94cfJ/9TG0ILj8Gsfu1o+pfLy4zn5gmmZrlpWo5Rar7WeEGubWNY0Ed0rHMZigcsfYlZTC/Ms1azcs5Lbt9xHxc03MnLlCiquvorGZctg3ncZZD/Imr/vCrvDkLiFPXDAWPqariypCLV3iFjTSPQAiTAVx8HU+czauY55g85j5Z6V3Pz2zeAqZ8CttzJy5Qoqr76KkR88jHI3s/zuFbh3fxbOnohgv/tdY+krRKTpR9zgNBLXFYawO8yBTSy+8CYWbnyMacOnce/Z92IPvntsP3iQjx94mTW1oxi562VOGl+E6ydzyBtuuMVducTLlxt/L7oovcco7m5q6coNFrGmmd+t3MZDq7bz4W1TqSqOen1Stwv+cAaMOJPFp1zKwnULOwlWa82yB9bx+ZYGJn383xQ07af0ssvCos1UG1ZEmh6kzZpB4rrCEHaH2b6CWV4r8ybMC7vE7cFXGkopzpl9EvbCPHZdchflV13Voff42MHDYrrEe/caS6oRdzdziFjTTPRY4U5M/DEMPwOW38qsoVNjCjY0WOLgF23sn3Blh46ondNnULzkn1z4vdkdBHvppXD88fDGG6k5DhFp5hE3uA+Ys3gdr27+CgUMLstn3oVj+Ma4IUcTRLjDXPkcizf/pZNLrLXmn49u5PNP6vjO7ROpGFRI+8GD1D3xRPiVT8N5Z/N+7Rc01M/gnhXX0h6w4rT5uH3aYu5Y9sOE6rp07gJG59VQYC2m1d/ErpatlNoqxN3tI8QNziAvf7SPN7cdAkAD++rbuPXFjbz80b6jiSLcYT5+mllfn9XJwsYaO2yvrg73HldcfRVlb79PW+0MFr5mCBXA7bPxXyuv4e7pf+62rtFRMIW2Ek4smcCQ/OFiSbOAtFhWs8wj0hf5zliwin31nV+tDCnL571bzju6IqJ3mP+9GkoGs/iTxSxct5CGtQ3sfGAndoudbWsPsPKJzZ0GSwCsfPEIl80sxu3r/IVZp83PPTOWMW7Il3HrOqxwJHZL52kmW31NjL4vsW/EZPO1MEO+PresZolo6It8+2MINeb64GAJ/F5Y+gvQOmxhSyeWhi1srLHDIX78y/KYQgVw+6wsfGMqxxSMiLvYlD1m3vwUzMsj+XofdSMf+U4zg8vyY1rWwWUx5j0NucPLb4aPn4ZxVzHr67MAWLhuIbwN9559L1OuHMMzv/mQVYu3cMW88VgsRqzkk0/C9At8cSyrj7++nM/Icy+IW9etN75Coa1zmJBEwWQH0mZNM/MuHEO+vfNsbSOrimI/bSddF+4dptHoQY5uw+YVWzqF0gGcey7cPm0x+baOn0bJt/m5fdpizj2367pu826UKJgsRsSaZr4xbgj3XFHDkLJ8FDCkzMmU0S7e3l7Lb/6xubNgY7jD0FmwI06tiOkO37Hsh9w27SnyrEYQutPm47ZpTyXUG3zpA7dIFEw2o7VOeBk/frwWek8gENC/WfqJHn7zP/T8JZt0IBDonOiDP2h9Z4nW//prh9VPbXpKn7joRH3DGzfo+rpm/adfvqWfX7BW+/0d93HyyVo7HFqvWpXOIxFSDbBOx9GftFkzgFKKO2YYgeFPvLsbgF9fMrbjd3omXQdblhju8MhzoWQwQMc2LPDj7/yKVU9u5ePXPu/QO/zII8bfyZPTfTRCXyFizRDdCjbkDj8y2XCHr3wOgts6CHYYnH/yNaxZspsRNS4qBhUCItJcRNqsGSQk2B+deSxPvvdZ5zZs1GCJSMJt2M9X8uaIZzt9WWLTJmMRcgexrBmmWwsbx6TalnIAAAN1SURBVB2GjhY2/6RKPB+cGnaHf/5zI40Z52cVYiNizQK6FGykO7xkLlz1fNgdhgjBrl3I1UMGs2aJYkSNi4ULC/v+QIS0Im5wltClSxxyh3es7OQOQ9AlnjiPFwY+hNfi4fWnNjN+vGbixD49BCHNiGXNIrq0sF24w3DUwr7U+AxTt1/DTd97F5s/j8pj9jNsaj4zL0nzJyOEtCOWNcuIa2EjB0ssmRseLBHJrK/PYpxrHAEC/P2dE3nh/dEUuEs5sAz+9o/lGTgaIZXIXDdZmC9asJXT5hiC7cYdBsj/aDgWLHxr8na+NXk7ALZAHp+/1vWX/JOtq+RLb75IJOomS/NFCrZkwuVHLWyMscOR5LuNgfjHuJo5xtXcaX066ir50pcvEnGDs5iYLrFSXbrDbU5jxqs9B4vZc7C403rBvIhYs5yYgi0/Nq47PGxqPj6Ll5dWj+Kl1aMA8Fm8DJuanV/uFxJHeoNNQMxe4hk/Rm3+e6fe4ZmXXMTfWM5ljetxeItodTZIb3COIB9MMxFaa+5+ZQtPvLubH5wxgl9PdqJCH1qLGiwhmBP5YFqO0Mklft+NnnpnTHf4/feNRcgdxA02GZ1c4sln8uthp6Oi3OHbbjPSy9jg3EHEakKiBVs+/gau338NKmLs8GOPZbiSQsoRN9ikRLrEv1vvY/mgOR3c4TFjjEXIHcSymphIC/uzdwO86TqZYctvQY08l7c+MtzhKVMyWUMhlYhYTU6kYGe9dw2vOW/FtmQudz7+PKCkzZpDiBucA4QEO/WM0/mtdyZqx0ruP/kMHj/pZA7MH8XaJdKAzQVErDlCSLADBwzErxWnlH/CqIrPGMghTlx/hwg2B5ComxzKp5TiG3VPYlWa13adw2u7zgEgX3kZ+q+FaSlT8qU3XyRpabOaJaIhF/NV60OgYOpxb0atr01bmZIvffkiETc4xzioquKsd/VxTYRUI2LNMfaeOo823XHaxjadx95T52WoRkKqELHmGBMvm8Om8XdzgCoCWnGAKjaNv5uJl83JdNWEXiJRN4KQRUjUjSDkACJWQTAJIlZBMAkiVkEwCSJWQTAJPeoNVkodAvakrzqC0O8ZrrWOObKlR2IVBCFziBssCCZBxCoIJkHEKggmQcQqCCZBxCoIJkHEKggmQcQqCCZBxCoIJkHEKggm4f8D87ETlGtEAVsAAAAASUVORK5CYII=\n", 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" ] @@ -361,7 +489,80 @@ } ], "source": [ - "plot(search(decode_path([3, 5, 2, 4, 4])))" + "for opening in ([3, 3], [3, 5], [3, 6], [6, 2], [6, 3]):\n", + " plot(search(path_from_digits(opening)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Tests\n", + "\n", + "The code that I have the least confidence in is `intersects_circle`. Here are some tests and visualizations for it:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "def test_intersects(expected: bool, segments: List[Path]):\n", + " \"\"\"Test if segments do the expected thing with `intersects_circle`.\"\"\"\n", + " plot(segments)\n", + " for p, q in segments:\n", + " assert intersects_circle(p, q) is expected" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "test_intersects(True, [ # Line segments that intersect the circle\n", + " [Point(-2, 3), Point(5, 2)], \n", + " [Point(-1, 5), Point(4, 0)], \n", + " [Point(2, 4), Point(2, -4)],\n", + " [Point(-3, -1),Point(1, -4)],\n", + " [Point(-6, 0), Point(7, 7)]])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "test_intersects(False, [ # Line segments that do not intersect the circle\n", + " [Point(-2, 3), Point(5, 3)], \n", + " [Point(-1, 5), Point(4, 1)], \n", + " [Point(3, 4), Point(3, -4)],\n", + " [Point(-3, -2),Point(1, -4)],\n", + " [Point(-7, 0), Point(7, 7)]])" ] } ],