#!/usr/bin/env python3

from collections import defaultdict
from functools import reduce

import numpy as np


lines = (x.strip() for x in open("input.txt"))
rotations = [(t, r) for t in (True, False) for r in range(4)]
tiles = {}
borders = defaultdict(set)


def add_tile(num, tile):
    global tiles, borders
    tiles[num] = tile
    for transpose, rotate in rotations:
        view = np.rot90(tile.T if transpose else tile, rotate)
        edge = np.packbits(view[0])
        edge = edge[0] * 4 + edge[1] // 64
        borders[edge].add(num)


for line in lines:
    if line.startswith("Tile"):
        num = int(line[5:-1])
        tile = np.zeros((10, 10), dtype=np.int16)
        lnr = 0
    elif line == "":
        add_tile(num, tile)
    else:
        a = np.array([(0 if x == '.' else 1) for x in line], dtype=np.int16)
        tile[lnr] = a
        lnr += 1
add_tile(num, tile)

# every border matches only once
print("sum    joints", sum(1 for key, val in borders.items() if len(val) > 1))
print("should joints", (len(tiles)-np.sqrt(len(tiles))) * 2)
print("sum    outer", sum(1 for key, val in borders.items() if len(val) == 1))
print("should outer", np.sqrt(len(tiles)) * 4)
print("cnt tiles", len(tiles))
print("multi matches", sum(1 for key, val in borders.items() if len(val) > 2))

# find corners
edges = defaultdict(int)
for key, val in borders.items():
    if len(val) == 1:
        for item in val:
            edges[item] += 1

print(reduce(lambda a, b: a*b, (key for key, val in edges.items() if val == 4), 1))