from pathlib import Path
from functools import cache

FILE = "input.txt"

class Foo:
    def __init__(self, grid: list[str]) -> None:
        self.grid: list[str] = grid

    def timelines(self) -> int:
        start = self.grid[0].index('S')
        return self.traverse(start, 1)

    @cache
    def traverse(self, position: int, level: int) -> int:
        grid = self.grid[level:]
        if not len(grid):
            return 1
        if grid[0][position] == '^':
            return (
                self.traverse(position-1, level + 1) +
                self.traverse(position+1, level + 1)
            )
        return self.traverse(position, level + 1)

def main():
    raw_lines = Path(FILE).read_text().splitlines()
    return Foo(raw_lines).timelines()


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