import logging
import os
import sys
from collections import defaultdict

VERBOSE = os.getenv("AOC_VERBOSE") == "True"
logging.basicConfig(level=logging.INFO if VERBOSE else logging.WARNING)

Direction = {
    ">": (0, +1),
    "<": (0, -1),
    "^": (-1, 0),
    "v": (+1, 0),
}

Neighbors = {".": ((+1, 0), (-1, 0), (0, +1), (0, -1)), "#": ()} | {
    k: (v,) for k, v in Direction.items()
}


def neighbors(
    grid: list[str], node: tuple[int, int], ignore: set[tuple[int, int]] = set()
):
    """
    Compute neighbors of the given node, ignoring the given set of nodes and considering
    that you can go uphill on slopes.
    """
    i, j = node

    for di, dj in Neighbors[grid[i][j]]:
        ti, tj = di + i, dj + j

        if ti < 0 or ti >= n_rows or tj < 0 or tj >= n_cols:
            continue

        if (ti, tj) in ignore:
            continue

        v = grid[ti][tj]

        if (
            v == "#"
            or (v == "v" and di == -1)
            or (v == "^" and di == 1)
            or (v == ">" and dj == -1)
            or (v == "<" and dj == 1)
        ):
            continue

        yield ti, tj


def reachable(
    grid: list[str], start: tuple[int, int], target: tuple[int, int]
) -> tuple[tuple[int, int], int]:
    """
    Compute the next 'reachable' node in the grid, starting at the given node.

    The next 'reachable' node is the first node after a slope in the path starting from
    the given node (not going uphill).
    """
    distance, path = 0, {start}
    while True:
        i, j = start

        if (i, j) == target:
            return (target, distance)

        if grid[i][j] != ".":
            di, dj = Direction[grid[i][j]]
            return ((i + di, j + dj), distance + 1)

        start = next(neighbors(grid, start, path := path | {(i, j)}))
        distance += 1


def compute_direct_links(
    grid: list[str], start: tuple[int, int], target: tuple[int, int]
) -> dict[tuple[int, int], list[tuple[tuple[int, int], int]]]:
    if start == target:
        return {}

    direct: dict[tuple[int, int], list[tuple[tuple[int, int], int]]] = {start: []}
    for neighbor in neighbors(grid, start):
        i, j = neighbor
        di, dj = Direction[grid[i][j]]

        reach, distance = reachable(lines, (i + di, j + dj), target)
        direct[start].append((reach, distance + 2))

        direct.update(compute_direct_links(grid, reach, target))

    return direct


def longest_path_length(
    links: dict[tuple[int, int], list[tuple[tuple[int, int], int]]],
    start: tuple[int, int],
    target: tuple[int, int],
) -> int:
    max_distance: int = -1
    queue: list[tuple[tuple[int, int], int, frozenset[tuple[int, int]]]] = [
        (start, 0, frozenset({start}))
    ]

    nodes = 0
    while queue:
        node, distance, path = queue.pop()

        nodes += 1

        if node == target:
            max_distance = max(distance, max_distance)
            continue

        queue.extend(
            (reach, distance + length, path | {reach})
            for reach, length in links.get(node, [])
            if reach not in path
        )

    logging.info(f"processed {nodes} nodes")

    return max_distance


lines = sys.stdin.read().splitlines()
n_rows, n_cols = len(lines), len(lines[0])
start = (0, 1)
target = (len(lines) - 1, len(lines[0]) - 2)


direct_links: dict[tuple[int, int], list[tuple[tuple[int, int], int]]] = {
    start: [reachable(lines, start, target)]
}
direct_links.update(compute_direct_links(lines, direct_links[start][0][0], target))

# part 1
answer_1 = longest_path_length(direct_links, start, target)
print(f"answer 1 is {answer_1}")

# part 2
reverse_links: dict[tuple[int, int], list[tuple[tuple[int, int], int]]] = defaultdict(
    list
)
for origin, links in direct_links.items():
    for destination, distance in links:
        if origin != start:
            reverse_links[destination].append((origin, distance))

links = {
    k: direct_links.get(k, []) + reverse_links.get(k, [])
    for k in direct_links.keys() | reverse_links.keys()
}

answer_2 = longest_path_length(links, start, target)
print(f"answer 2 is {answer_2}")