from collections import defaultdict

n, k = map(int,input().split())

graph = [[".XO".find(v) for v in input()] for _ in range(n)]

ships = [int(input()) for _ in range(k)]

poss = defaultdict(lambda: {})
def place(ships, board):
    # print(len(ships))
    if len(ships) == 0:
        if any(v==2 for row in board for v in row):
            return 0
        return 1

    key = tuple(tuple(v) for v in board)

    if key in poss[len(ships)]:
        return poss[len(ships)][key]

    c=ships.pop()
    total_poss = 0
    for x in range(n):
        for y in range(n):
            for dx, dy in ([(1, 0), (0, 1)] if c>1 else [(1, 0)]):
                if 0 <=x + dx*(c-1) < n and 0<=y+dy*(c-1)<n and all(board[y+dy*d][x+dx*d] in [0, 2] for d in range(c)):
                    # print(x, y, dx, dy)
                    new_board = [[v for v in row] for row in board]
                    for d in range(c):
                        new_board[y+dy*d][x+dx*d] = 3
                    total_poss += place(ships, new_board)


    ships.append(c)
    poss[len(ships)][key] = total_poss
    return total_poss



print(place(ships, graph))