2021: d20: ex2: add solution

2021/d20/ex1/ex1.py

@@ -0,0 +1,82 @@
+#!/usr/bin/env python
+
+import itertools
+import sys
+from typing import List, NamedTuple, Set, Tuple
+
+
+class Point(NamedTuple):
+    x: int
+    y: int
+
+
+Algorithm = List[bool]
+Image = Set[Point]
+
+
+def solve(input: List[str]) -> int:
+    def parse() -> Tuple[Algorithm, Image]:
+        algo_str, blank, *image_str = input
+
+        assert blank == ""  # Sanity check
+        assert len(algo_str) == 512  # Sanity check
+
+        algo = [c == "#" for c in algo_str]
+        image = {
+            Point(i, j)
+            for i in range(len(image_str))
+            for j in range(len(image_str[0]))
+            if image_str[i][j] == "#"
+        }
+
+        return algo, image
+
+    def do_step(algo: Algorithm, image: Image, step: int) -> Image:
+        min_x, max_x = min(p.x for p in image), max(p.x for p in image)
+        min_y, max_y = min(p.y for p in image), max(p.y for p in image)
+
+        def color(p: Point) -> bool:
+            # Always return true if we *know* that it is lit
+            if p in image:
+                return True
+            # Return early if the rules don't lead to a flashing infinity case
+            flashes_infinity = algo[0] and not algo[-1]
+            if not flashes_infinity:
+                return False
+            # Pixels in proximity to the image are assumed to change their state normally
+            if min_x <= p.x <= max_x and min_y <= p.y <= max_y:
+                return False
+            # Odd indices have a "lit infinity" which turns off, and vice versa
+            return (step % 2) == 1
+
+        def bits(p: Point) -> int:
+            x, y = p
+            res = 0
+            for dx, dy in itertools.product(range(-1, 1 + 1), repeat=2):
+                res = (res << 1) + color(Point(x + dx, y + dy))
+            return res
+
+        # We know the image we care for cannot grow by more than 1 per turn
+        xs, ys = range(min_x - 1, max_x + 1 + 1), range(min_y - 1, max_y + 1 + 1)
+
+        res: Image = set()
+        for p in map(Point._make, itertools.product(xs, ys)):
+            if algo[bits(p)]:
+                res.add(p)
+
+        return res
+
+    rules, image = parse()
+    for i in range(2):
+        image = do_step(rules, image, i)
+
+    return len(image)
+
+
+def main() -> None:
+    input = [line.strip() for line in sys.stdin.readlines()]
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()

2021/d20/ex1/input

@@ -0,0 +1,102 @@
+##..#######.#.#...##..#.#....#..#####..###...#..#.#..##....#.###..#.###..#.#.#.##.######.#.##.#.#..#######.####..#.#.#.##..##.#.#######...#..#...........###.#.........#..#....#.#..##.##....#.##.#...#.##..##....##..#####......#.#.##....#...#########...#..##...####.#####.##.#.###..##.##..#.#..#.......#..##....#.##.######.#.##..##......####...#.##..#...#.###.##..##...#..#####..#.#.###.#.##..##..#####...#.#.#...###..#.##.####.#.#..#####..##.##...#.#.#....####.##..#.##.###.....##.#....#####....###...##.#.#......
+
+##.##...#.##...####.#.#..######......#.##.#.#.###......#.#...##..##.###.###.##.#..#..#.....#..####..
+#######...##..#....#..####..##.##.#.##.##.##..#...##.##..##..#..##....#########....##........###...#
+##.#.###...#...###.#####..#..#.##..#....#####..##.#..#..#....##.#..#.#..#...#.##....##.##......#####
+..#...##..##..#.###..###.#.###.##.#.###.##.####..#.#.##....#..##.###.##..##......#.#####.##..#.#.#.#
+#.........#.##.#.#....#..#..##..###..###.#...##.#.#.###.##..#.##.......###.###...#..##.#####.#...#.#
+.##..####.#.###.#..#.......####.....#.###...####.#.###..####..#.......##.##.##########..#.#.#..#.#..
+#..#.###..#.##..######.....#######.##.#.#...##..#.##...##..#.##..###..######..#.##.....##...#.#.#.#.
+###..#..###.#.#.#...#####...#.#..#.##....##.#.##..#..###.#..##..####.######.#.#...#.#..#.####...##.#
+#....#...#####.###.######..#....##.#....#####..#.#####...#.#...#.#.#.######...##...##.##..####.##..#
+.###..####.#..##.#####.#...#....####.#.##..##..###....#.#..##...#..#..####.####...#...#....###..##.#
+..#...####.##.#.#.##.#..##.....#.#.###.#.#.##....##........#...##...#.#.####.##..#...#.#.....#..#..#
+.##....#....#.##.##.......####.#.###.#..##..#.#..#..#.....#.##.###..##.##..#.####.######.#.##..#.##.
+..##.#..#.#..#.#....######.....#..##...#......##....#...#..#.#...#..#.#.#####....####.###.#.#####...
+#.#...#.####.###..#.#.####.####...###.###.#.#..##........#..#...##.###....##..#..##.#.####.#.##..##.
+###.###.#.#.......###.#....####..##.#....#.####...#..#.#.##.....##..##......#####...#..##.....##.#.#
+#...###.#.#..#.#.#..####.######..#..##.###..#....#..#..##.##..##.###...####..#..#..####..#.#####.##.
+..#.##....#.###...#######..##.#.##..###...#...#....####.#.##.####....##..###...##.#.####..#..#..#.#.
+#######..#.#.#.#.###..###..###.....#####..######.#.#..#.#.#..#.#.#.#...#.#..##....#.####.###.##.#.#.
+..###...##.#.#######.....###..##.#..###....##........##..#..#.##.#.####.##....#####.##..##...##....#
+.#..#..#...##.#.##..#.#.##.##.######..#.####...#.......####....#.###..#....#.#........####.#...#.##.
+##..#.#...#.#.##.#..#.##.......##.#..#.#.#.#.####.##....#.#...#....######.#......#.##.#.##...#.##..#
+#.#.#.#########...#.##..#...###....#..#..#.###.##...#.#..#...#.#...#.###.#.#.##..##....###...#.#...#
+##..###.#.####.##..##.##.###.##.#.#..##..#######...#...#.###.#.##.##.#...#.....#.#.#####..##.#.##.#.
+...#..##...###########.#.#####.###.#.......#....#####..#.#.###..#....#...###...#..##.###...##.###.##
+##.......#....####..#...##.####..#.#..#..####......#.....#.##.#.##..#...#.####.#.#.#.##...#...#..#..
+#.....##.#......##.####.##.#....#.####..#..##.#..#.##.#.#..###.##..#.#..####......##.#..##..####....
+.#.##.##..#...########.#.#.......#...#.###..#...#..#..##.#.#...#####..#..######..#..#.#...###..##.#.
+##.##..##...#.##.##.#.###.#.....##.#...####.###.#.#..#...##.#.#...###..###..#...#.#..##......#..###.
+####..#.#..#...##.###....#..##.##.##.#..#..#.##..##...#.#.#.#...#.#......####.#.#..#......##.##.....
+##.....##..#...##.######.#....#.###....####.##.##.###.#.##..####.#...##.##.#.##.....#..###.#.....###
+#.#..#..#.#....##.#.##.#...##.#.#..##.#.##...#...###.#...#####.#.....##.#.#...##.....######..#.#.###
+...#.#..##.....####.#.#..#.#.###.....##..#.#..#.##..#.#.##..##...##...#.####.#.#.##...####.#.#.#.#.#
+...##.##...#####.#.#..###.####.#.#.#.#.#####.#.######.####.#.#.##.####.####..###.#...###..#.#.#.####
+#..##.#.##.#..#.##.##...#.#.##.#.##..#.###.###..#.##....##.####....##..#.#.##.####.#....##..#.#..#..
+#.######.##.###.#.#...##...##...#.###..###.#.......#.###...#..##.....#..#.......##.###.....#.##..#.#
+..#.##.#...##.#..#...###.#.##.###...#...#...#..###...#..#...######.###.#.....#.###.#..###.....#...#.
+##.#.#.......###.#.#....#..#.#.#..#..#.###.##.#..#..###.###.#....#.......###....##.#.###.###.###...#
+...##.###..#...#.#...##..##..#.#.#...#.##..#.....#..#...###..##.##.##.....####..#.#.#..##..##..#..#.
+#......#####..#.###.....##...######.......#..####....#.#.#...#.#..#.####.#...###...#..#.#.##...#.#..
+#.##...#.##.##...##....#....####.##..#....#..##....#..#.##.......######.#.##.###.##....#.#.#.....##.
+#####.#.....###....##..#####..#.#.##.##.#.#.#...####.###.###..#....#...##.#.#....#..####.#...###..##
+#.#####..##...######.######....#.#.#..##.##.######..##...#...####..##.##.#.#....#.#.#.#..#...#...#..
+.###.#.##.#.#.##.##....#..####.#..##.#.##....###.##...#....#..###..##.#########..##.......##.....#.#
+##..#.##..#..#.#.#..#...##...##########...##.##..#..#.#.###########.....#######....#....#.###.#...#.
+...##.#..##...#..#.##...###...####.#...#####.####..#.###..###....###..#..#####.#.##.#.##....#......#
+..##..##...###.#.#.#..#.#####..#.##..#..#...###.###..##....#.#.##...###..#.###..#.#.##.###.##....###
+.#.#.#######.#..#.....#.##.###...##.##.###.##..##...###..#.##...###.#..##..###.#.####.#..##..##...#.
+#.####.#.#....###...###....##...##.....#.###.#.....#..#...#..####.#...#..#######...###.#........#...
+..##...#.#..###..##..#.#..####.#...#.##.#...#.#..###..#.##.#.#.#...###..######....#.###.#.#.#..##.#.
+###.#.#.....###..#....###.#.......##...#..#.###..###.#......#...##..#.#..###..#.##.#.##.######.#.#.#
+#...###.#.#....#.####....##.###...##..##....#####....#......#.#.......###...#.#..#.#....#....####.#.
+#.#.##.######..#.#.######.#...#..###.#..####..#.##..###.#.#.#.###..#..#.#....#..#.##.#..##.####.##.#
+#.##.#.###...#.##.#..#.#....#.####...#.###...#..###......#.########....#.#####..#.#.#..#...#.####.#.
+####...#.#.##.###...##.#....#.#..######.#.######.#.##.#.#.#..#...#.###.#..#.####.#..#.#....#....#.##
+##.##.....#.##..#......#....###.#..#######.#...##..#.#...##..##.#.#..##.###.######.....###.##.##..##
+..####.##.#####....#.#..#.#.#.########.#.###........#..###...###........####.##.##.#.#..#.##.....#.#
+...#.#..#.#.###.....##.#.##.#.##..#.##..#..####........###..####..##..#.####..#...#.####.##.#.#.##.#
+.##.#.#..#####..#####.#.....##.#.####.#.###..#..##.#..####.###.##.###.###.#..#..##....#.##.....#.#..
+.#...####..##.###....##..#..##.###..#..##....#...##.###.###.#...##..###.#..##.#.##...##.##.#..##.#..
+.#.##.##.####.###.#.#..##.....####.##..######.###..#.#.##..##.#.#.....#.#############..#..#..###..##
+.#.#..###...###..###.#....###.....##.#.#..###..####..##.##.#.##...########..##..####.##.##.##.#.#...
+...#.##.###.#..#..##...#..##..#.....##..#.#..###..#...#...##.#.#..#.###.#####..#.....##...###.######
+##...#..##.#.##.##...#.....#....#...##.###...#####..#..##.##.###..#.###.##..#.#..##.##..#.#...######
+.##.#..###.###....#.###.#..#..#..##...############...#########.#..#.###...###....#..#.########.#.##.
+.........###..##.####.#.#...#..##.#...###....###.##.######.#..#.#..###.###.#.###.##.##.##..#.#.#.#..
+.##....###.#.###.#.#..##...#.#...#.##....###...##.#..#######....##..#...#...#....##.##..####.######.
+###.####...##.#.###.....#..######....###..#.#.#..#######..#..#.##.#.####.###.#....#..#.#...##..#.#..
+##..#.#####.###...#..#.......###.###..##.....##...#.##.##..###.####..#...#.#.##.#.#...##....#.##.###
+#...####......###.##..#..####.##.#.###.##.#.#....#.....#..#...###..##..##..#.##..###.#.##.###....#..
+#..##.#..####...##.##.####..#....#......###...##.#.#..#.#.....#..##..###..#.##.##.#..####..##.#.####
+....#..#......##....###...#.##..##.#...#.....#..##.#.###..#...#...........##..#####....#..#.##...#..
+...#..####.#.#####.####...#..#..#..###.#.#.#.##.##......#.####........##.#.....#..###.#..#..##..###.
+#######.#.#..#.##..#.#.##.#..#..#......#.#..####....#####.#.....###.#.#..##.#..#..##.#..###..#.###.#
+#....#.#.##.##...#..##.####....###....#...#..###..##.######...#.##.##.##.#.#.#.#####.##.#.####.###.#
+...#.#..#..#....#...###..#.#..#...#..##...#..##.#.###.#.##...#####......#.##.#..#.###..##.##...#.#.#
+.#.##.....#####.#.#####..###.#.###....##...#.....##...###.##.#.#.#...##.......###....##..##...##....
+####.#...##.#####.##..####.########...#..#..#....#.##.###..###.##.##..###.###.######..##...#......##
+.##...###..###..#.####.##.##...#.....####.###.##.#.##..#.#.#.#.#....##.#######.##.##..#...#....#####
+.###.##....#.#......#.##....#..###.##..##..##..##..#.......#..#.#.###...#..####.##.#.##..###..##.##.
+....######.#..#.##.##.#####..#.##.#.#.#.##..#..#.########.#####..###.###.#...#..##.#......##.#.#.#..
+.#.#.#...###.#.#.#....###.####..#.##....#......#...#.#.##.##.#..###.....#.#.##..##.#..###.#.#.####..
+##....########.#..#####...#.....##.#.....##.#...####..####..#......##...#..#..##..#..#.##..###..##.#
+##..####.#####.#.#.#.#.###.###..#..#...##.#.#....#.#..#.#.###..#.##...#.#.##.#.##.##....#..######.##
+#..#.....#.#..#.#.#..##..#....#.#.###.#.#..#..###..#.#...###..##...####.##..#..#...#.#...###.##..##.
+...#..#...####.##.###.#####.###.##..###.#....##..##...#.###.#...#...#.............##...####.####.#.#
+.###.##...##.#.###.#.#...##.#..#...#####..##.#.#...##.#######.####....####....#######.#...#.#.###...
+....#.#...##.#.####.#####.#.######.#####.##...####...###.#.##.####..##.###.###....#.....#####.....#.
+......##.#.#....#.#..##..#.#.###...##.##.####.#....##...##...##...#...#.###.#.##...#..####....##....
+.#####..#.#####...##.#...###.#.#..#.#..##..#.#.#.##..#.##....###..###..#..##...##..#.###.#.##....###
+#####....#.#...##.###.#....###.##.........#..##..###.#...######.#..#.#.########.....###.#.#...#.....
+.##.#.#####.#..#.#.#.###...########.###..##.#..#.####.#...##.#....#...##.######..##....##....##.##..
+###...##.##..####...#.#.#..##.....###..#..##..#.####.###..#.#.##.######...#.#...###.##..#....##.#.##
+##..##.#..#..#.###.#..#..#....#..#....###.####.###...#.##.##.##......##.####...#.....#...#.#...#..#.
+....#.##...#..##.##......#.#.#..####....#..#######.#...#...##..#......#.#........##.##....###....##.
+##.#...#...##.###.###..####.#...#..##...##.###..#..###..#.....#...###..###.##..#..#####.....####.##.
+.##.#...#..####..#.....##..###.#.#.#..#...##...###...#..##.....#..##...##..###.#..#####...##.#..###.
+.#.#.#..####...#.###.###....##....#.#..#.#..#..#####.#..#...#.###.........##.####.####..#.##..##..#.
+#..##.####.#..##....#.####.###...#.#..#####.##.#..#......###.##...#....#.##..#....##.#.....#.##.##.#
+#..#..#.###.#..#.#.####.####..#.#.#..#.#...#....#######.####.............####..###.#..####.######.##
+.#....####...#...#...#..#..##......#######.###.##..####.##.####.#####....##.###.#.###..#.#....#...#.

2021/d20/ex2/ex2.py

@@ -0,0 +1,82 @@
+#!/usr/bin/env python
+
+import itertools
+import sys
+from typing import List, NamedTuple, Set, Tuple
+
+
+class Point(NamedTuple):
+    x: int
+    y: int
+
+
+Algorithm = List[bool]
+Image = Set[Point]
+
+
+def solve(input: List[str]) -> int:
+    def parse() -> Tuple[Algorithm, Image]:
+        algo_str, blank, *image_str = input
+
+        assert blank == ""  # Sanity check
+        assert len(algo_str) == 512  # Sanity check
+
+        algo = [c == "#" for c in algo_str]
+        image = {
+            Point(i, j)
+            for i in range(len(image_str))
+            for j in range(len(image_str[0]))
+            if image_str[i][j] == "#"
+        }
+
+        return algo, image
+
+    def do_step(algo: Algorithm, image: Image, step: int) -> Image:
+        min_x, max_x = min(p.x for p in image), max(p.x for p in image)
+        min_y, max_y = min(p.y for p in image), max(p.y for p in image)
+
+        def color(p: Point) -> bool:
+            # Always return true if we *know* that it is lit
+            if p in image:
+                return True
+            # Return early if the rules don't lead to a flashing infinity case
+            flashes_infinity = algo[0] and not algo[-1]
+            if not flashes_infinity:
+                return False
+            # Pixels in proximity to the image are assumed to change their state normally
+            if min_x <= p.x <= max_x and min_y <= p.y <= max_y:
+                return False
+            # Odd indices have a "lit infinity" which turns off, and vice versa
+            return (step % 2) == 1
+
+        def bits(p: Point) -> int:
+            x, y = p
+            res = 0
+            for dx, dy in itertools.product(range(-1, 1 + 1), repeat=2):
+                res = (res << 1) + color(Point(x + dx, y + dy))
+            return res
+
+        # We know the image we care for cannot grow by more than 1 per turn
+        xs, ys = range(min_x - 1, max_x + 1 + 1), range(min_y - 1, max_y + 1 + 1)
+
+        res: Image = set()
+        for p in map(Point._make, itertools.product(xs, ys)):
+            if algo[bits(p)]:
+                res.add(p)
+
+        return res
+
+    rules, image = parse()
+    for i in range(50):
+        image = do_step(rules, image, i)
+
+    return len(image)
+
+
+def main() -> None:
+    input = [line.strip() for line in sys.stdin.readlines()]
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()

2021/d20/ex2/input

@@ -0,0 +1,102 @@
+##..#######.#.#...##..#.#....#..#####..###...#..#.#..##....#.###..#.###..#.#.#.##.######.#.##.#.#..#######.####..#.#.#.##..##.#.#######...#..#...........###.#.........#..#....#.#..##.##....#.##.#...#.##..##....##..#####......#.#.##....#...#########...#..##...####.#####.##.#.###..##.##..#.#..#.......#..##....#.##.######.#.##..##......####...#.##..#...#.###.##..##...#..#####..#.#.###.#.##..##..#####...#.#.#...###..#.##.####.#.#..#####..##.##...#.#.#....####.##..#.##.###.....##.#....#####....###...##.#.#......
+
+##.##...#.##...####.#.#..######......#.##.#.#.###......#.#...##..##.###.###.##.#..#..#.....#..####..
+#######...##..#....#..####..##.##.#.##.##.##..#...##.##..##..#..##....#########....##........###...#
+##.#.###...#...###.#####..#..#.##..#....#####..##.#..#..#....##.#..#.#..#...#.##....##.##......#####
+..#...##..##..#.###..###.#.###.##.#.###.##.####..#.#.##....#..##.###.##..##......#.#####.##..#.#.#.#
+#.........#.##.#.#....#..#..##..###..###.#...##.#.#.###.##..#.##.......###.###...#..##.#####.#...#.#
+.##..####.#.###.#..#.......####.....#.###...####.#.###..####..#.......##.##.##########..#.#.#..#.#..
+#..#.###..#.##..######.....#######.##.#.#...##..#.##...##..#.##..###..######..#.##.....##...#.#.#.#.
+###..#..###.#.#.#...#####...#.#..#.##....##.#.##..#..###.#..##..####.######.#.#...#.#..#.####...##.#
+#....#...#####.###.######..#....##.#....#####..#.#####...#.#...#.#.#.######...##...##.##..####.##..#
+.###..####.#..##.#####.#...#....####.#.##..##..###....#.#..##...#..#..####.####...#...#....###..##.#
+..#...####.##.#.#.##.#..##.....#.#.###.#.#.##....##........#...##...#.#.####.##..#...#.#.....#..#..#
+.##....#....#.##.##.......####.#.###.#..##..#.#..#..#.....#.##.###..##.##..#.####.######.#.##..#.##.
+..##.#..#.#..#.#....######.....#..##...#......##....#...#..#.#...#..#.#.#####....####.###.#.#####...
+#.#...#.####.###..#.#.####.####...###.###.#.#..##........#..#...##.###....##..#..##.#.####.#.##..##.
+###.###.#.#.......###.#....####..##.#....#.####...#..#.#.##.....##..##......#####...#..##.....##.#.#
+#...###.#.#..#.#.#..####.######..#..##.###..#....#..#..##.##..##.###...####..#..#..####..#.#####.##.
+..#.##....#.###...#######..##.#.##..###...#...#....####.#.##.####....##..###...##.#.####..#..#..#.#.
+#######..#.#.#.#.###..###..###.....#####..######.#.#..#.#.#..#.#.#.#...#.#..##....#.####.###.##.#.#.
+..###...##.#.#######.....###..##.#..###....##........##..#..#.##.#.####.##....#####.##..##...##....#
+.#..#..#...##.#.##..#.#.##.##.######..#.####...#.......####....#.###..#....#.#........####.#...#.##.
+##..#.#...#.#.##.#..#.##.......##.#..#.#.#.#.####.##....#.#...#....######.#......#.##.#.##...#.##..#
+#.#.#.#########...#.##..#...###....#..#..#.###.##...#.#..#...#.#...#.###.#.#.##..##....###...#.#...#
+##..###.#.####.##..##.##.###.##.#.#..##..#######...#...#.###.#.##.##.#...#.....#.#.#####..##.#.##.#.
+...#..##...###########.#.#####.###.#.......#....#####..#.#.###..#....#...###...#..##.###...##.###.##
+##.......#....####..#...##.####..#.#..#..####......#.....#.##.#.##..#...#.####.#.#.#.##...#...#..#..
+#.....##.#......##.####.##.#....#.####..#..##.#..#.##.#.#..###.##..#.#..####......##.#..##..####....
+.#.##.##..#...########.#.#.......#...#.###..#...#..#..##.#.#...#####..#..######..#..#.#...###..##.#.
+##.##..##...#.##.##.#.###.#.....##.#...####.###.#.#..#...##.#.#...###..###..#...#.#..##......#..###.
+####..#.#..#...##.###....#..##.##.##.#..#..#.##..##...#.#.#.#...#.#......####.#.#..#......##.##.....
+##.....##..#...##.######.#....#.###....####.##.##.###.#.##..####.#...##.##.#.##.....#..###.#.....###
+#.#..#..#.#....##.#.##.#...##.#.#..##.#.##...#...###.#...#####.#.....##.#.#...##.....######..#.#.###
+...#.#..##.....####.#.#..#.#.###.....##..#.#..#.##..#.#.##..##...##...#.####.#.#.##...####.#.#.#.#.#
+...##.##...#####.#.#..###.####.#.#.#.#.#####.#.######.####.#.#.##.####.####..###.#...###..#.#.#.####
+#..##.#.##.#..#.##.##...#.#.##.#.##..#.###.###..#.##....##.####....##..#.#.##.####.#....##..#.#..#..
+#.######.##.###.#.#...##...##...#.###..###.#.......#.###...#..##.....#..#.......##.###.....#.##..#.#
+..#.##.#...##.#..#...###.#.##.###...#...#...#..###...#..#...######.###.#.....#.###.#..###.....#...#.
+##.#.#.......###.#.#....#..#.#.#..#..#.###.##.#..#..###.###.#....#.......###....##.#.###.###.###...#
+...##.###..#...#.#...##..##..#.#.#...#.##..#.....#..#...###..##.##.##.....####..#.#.#..##..##..#..#.
+#......#####..#.###.....##...######.......#..####....#.#.#...#.#..#.####.#...###...#..#.#.##...#.#..
+#.##...#.##.##...##....#....####.##..#....#..##....#..#.##.......######.#.##.###.##....#.#.#.....##.
+#####.#.....###....##..#####..#.#.##.##.#.#.#...####.###.###..#....#...##.#.#....#..####.#...###..##
+#.#####..##...######.######....#.#.#..##.##.######..##...#...####..##.##.#.#....#.#.#.#..#...#...#..
+.###.#.##.#.#.##.##....#..####.#..##.#.##....###.##...#....#..###..##.#########..##.......##.....#.#
+##..#.##..#..#.#.#..#...##...##########...##.##..#..#.#.###########.....#######....#....#.###.#...#.
+...##.#..##...#..#.##...###...####.#...#####.####..#.###..###....###..#..#####.#.##.#.##....#......#
+..##..##...###.#.#.#..#.#####..#.##..#..#...###.###..##....#.#.##...###..#.###..#.#.##.###.##....###
+.#.#.#######.#..#.....#.##.###...##.##.###.##..##...###..#.##...###.#..##..###.#.####.#..##..##...#.
+#.####.#.#....###...###....##...##.....#.###.#.....#..#...#..####.#...#..#######...###.#........#...
+..##...#.#..###..##..#.#..####.#...#.##.#...#.#..###..#.##.#.#.#...###..######....#.###.#.#.#..##.#.
+###.#.#.....###..#....###.#.......##...#..#.###..###.#......#...##..#.#..###..#.##.#.##.######.#.#.#
+#...###.#.#....#.####....##.###...##..##....#####....#......#.#.......###...#.#..#.#....#....####.#.
+#.#.##.######..#.#.######.#...#..###.#..####..#.##..###.#.#.#.###..#..#.#....#..#.##.#..##.####.##.#
+#.##.#.###...#.##.#..#.#....#.####...#.###...#..###......#.########....#.#####..#.#.#..#...#.####.#.
+####...#.#.##.###...##.#....#.#..######.#.######.#.##.#.#.#..#...#.###.#..#.####.#..#.#....#....#.##
+##.##.....#.##..#......#....###.#..#######.#...##..#.#...##..##.#.#..##.###.######.....###.##.##..##
+..####.##.#####....#.#..#.#.#.########.#.###........#..###...###........####.##.##.#.#..#.##.....#.#
+...#.#..#.#.###.....##.#.##.#.##..#.##..#..####........###..####..##..#.####..#...#.####.##.#.#.##.#
+.##.#.#..#####..#####.#.....##.#.####.#.###..#..##.#..####.###.##.###.###.#..#..##....#.##.....#.#..
+.#...####..##.###....##..#..##.###..#..##....#...##.###.###.#...##..###.#..##.#.##...##.##.#..##.#..
+.#.##.##.####.###.#.#..##.....####.##..######.###..#.#.##..##.#.#.....#.#############..#..#..###..##
+.#.#..###...###..###.#....###.....##.#.#..###..####..##.##.#.##...########..##..####.##.##.##.#.#...
+...#.##.###.#..#..##...#..##..#.....##..#.#..###..#...#...##.#.#..#.###.#####..#.....##...###.######
+##...#..##.#.##.##...#.....#....#...##.###...#####..#..##.##.###..#.###.##..#.#..##.##..#.#...######
+.##.#..###.###....#.###.#..#..#..##...############...#########.#..#.###...###....#..#.########.#.##.
+.........###..##.####.#.#...#..##.#...###....###.##.######.#..#.#..###.###.#.###.##.##.##..#.#.#.#..
+.##....###.#.###.#.#..##...#.#...#.##....###...##.#..#######....##..#...#...#....##.##..####.######.
+###.####...##.#.###.....#..######....###..#.#.#..#######..#..#.##.#.####.###.#....#..#.#...##..#.#..
+##..#.#####.###...#..#.......###.###..##.....##...#.##.##..###.####..#...#.#.##.#.#...##....#.##.###
+#...####......###.##..#..####.##.#.###.##.#.#....#.....#..#...###..##..##..#.##..###.#.##.###....#..
+#..##.#..####...##.##.####..#....#......###...##.#.#..#.#.....#..##..###..#.##.##.#..####..##.#.####
+....#..#......##....###...#.##..##.#...#.....#..##.#.###..#...#...........##..#####....#..#.##...#..
+...#..####.#.#####.####...#..#..#..###.#.#.#.##.##......#.####........##.#.....#..###.#..#..##..###.
+#######.#.#..#.##..#.#.##.#..#..#......#.#..####....#####.#.....###.#.#..##.#..#..##.#..###..#.###.#
+#....#.#.##.##...#..##.####....###....#...#..###..##.######...#.##.##.##.#.#.#.#####.##.#.####.###.#
+...#.#..#..#....#...###..#.#..#...#..##...#..##.#.###.#.##...#####......#.##.#..#.###..##.##...#.#.#
+.#.##.....#####.#.#####..###.#.###....##...#.....##...###.##.#.#.#...##.......###....##..##...##....
+####.#...##.#####.##..####.########...#..#..#....#.##.###..###.##.##..###.###.######..##...#......##
+.##...###..###..#.####.##.##...#.....####.###.##.#.##..#.#.#.#.#....##.#######.##.##..#...#....#####
+.###.##....#.#......#.##....#..###.##..##..##..##..#.......#..#.#.###...#..####.##.#.##..###..##.##.
+....######.#..#.##.##.#####..#.##.#.#.#.##..#..#.########.#####..###.###.#...#..##.#......##.#.#.#..
+.#.#.#...###.#.#.#....###.####..#.##....#......#...#.#.##.##.#..###.....#.#.##..##.#..###.#.#.####..
+##....########.#..#####...#.....##.#.....##.#...####..####..#......##...#..#..##..#..#.##..###..##.#
+##..####.#####.#.#.#.#.###.###..#..#...##.#.#....#.#..#.#.###..#.##...#.#.##.#.##.##....#..######.##
+#..#.....#.#..#.#.#..##..#....#.#.###.#.#..#..###..#.#...###..##...####.##..#..#...#.#...###.##..##.
+...#..#...####.##.###.#####.###.##..###.#....##..##...#.###.#...#...#.............##...####.####.#.#
+.###.##...##.#.###.#.#...##.#..#...#####..##.#.#...##.#######.####....####....#######.#...#.#.###...
+....#.#...##.#.####.#####.#.######.#####.##...####...###.#.##.####..##.###.###....#.....#####.....#.
+......##.#.#....#.#..##..#.#.###...##.##.####.#....##...##...##...#...#.###.#.##...#..####....##....
+.#####..#.#####...##.#...###.#.#..#.#..##..#.#.#.##..#.##....###..###..#..##...##..#.###.#.##....###
+#####....#.#...##.###.#....###.##.........#..##..###.#...######.#..#.#.########.....###.#.#...#.....
+.##.#.#####.#..#.#.#.###...########.###..##.#..#.####.#...##.#....#...##.######..##....##....##.##..
+###...##.##..####...#.#.#..##.....###..#..##..#.####.###..#.#.##.######...#.#...###.##..#....##.#.##
+##..##.#..#..#.###.#..#..#....#..#....###.####.###...#.##.##.##......##.####...#.....#...#.#...#..#.
+....#.##...#..##.##......#.#.#..####....#..#######.#...#...##..#......#.#........##.##....###....##.
+##.#...#...##.###.###..####.#...#..##...##.###..#..###..#.....#...###..###.##..#..#####.....####.##.
+.##.#...#..####..#.....##..###.#.#.#..#...##...###...#..##.....#..##...##..###.#..#####...##.#..###.
+.#.#.#..####...#.###.###....##....#.#..#.#..#..#####.#..#...#.###.........##.####.####..#.##..##..#.
+#..##.####.#..##....#.####.###...#.#..#####.##.#..#......###.##...#....#.##..#....##.#.....#.##.##.#
+#..#..#.###.#..#.#.####.####..#.#.#..#.#...#....#######.####.............####..###.#..####.######.##
+.#....####...#...#...#..#..##......#######.###.##..####.##.####.#####....##.###.#.###..#.#....#...#.