import sys

# PART 1

def spiral(nth):
	length = 1
	nth -= 1
	x = 0
	y = 0
	while True:
		x += min(length, nth)
		nth -= min(length, nth)
		if nth == 0: return x, y
		y += min(length, nth)
		nth -= min(length, nth)
		if nth == 0: return x, y

		length += 1

		x -= min(length, nth)
		nth -= min(length, nth)
		if nth == 0: return x, y
		y -= min(length, nth)
		nth -= min(length, nth)
		if nth == 0: return x, y

		length += 1

def manhattan(x, y):
	return abs(x) + abs(y)

# PART 2

def store(cap):
	stored = {(0, 0): 1}
	nth = 2
	while True:
		x, y = spiral(nth)
		adjacent = 0
		adjacent += stored.get((x-1, y-1), 0)
		adjacent += stored.get((x  , y-1), 0)
		adjacent += stored.get((x+1, y-1), 0)
		adjacent += stored.get((x-1, y  ), 0)
		adjacent += stored.get((x+1, y  ), 0)
		adjacent += stored.get((x-1, y+1), 0)
		adjacent += stored.get((x  , y+1), 0)
		adjacent += stored.get((x+1, y+1), 0)
		stored[(x, y)] = adjacent
		nth += 1

		if adjacent > cap:
			return adjacent

def main():
	nth = 277678
	print(f"Solutions")
	x, y = spiral(nth)
	dist = manhattan(x, y)
	print(f"Part 1: {dist}")
	adjacent = store(nth)
	print(f"Part 2: {adjacent}")

if __name__ == "__main__":
	main()