from pathlib import Path

FILE = "input.txt"

def main():
    raw_lines = Path(FILE).read_text().splitlines()
    position = raw_lines[0].index('S')
    return traverse(position, raw_lines[1:], 0, dict())

def traverse(position: int, grid: list[str], level: int, memo: dict[tuple[int, int], int]) -> int:
    if (position, level) in memo.keys():
        return memo[(position, level)]
    if not len(grid):
        return 1
    if grid[0][position] == '^':
        memo[(position, level)] = (
            traverse(position-1, grid[1:], level+1, memo) +
            traverse(position+1, grid[1:], level+1, memo)
        )
        return memo[(position, level)]
    memo[(position, level)] = traverse(position, grid[1:], level+1, memo)
    return memo[(position, level)]

if __name__ == "__main__":
    print(main())