Problem:
Score : 300 points

Problem Statement

You are given a grid of squares with H horizontal rows and W vertical columns, where each square is painted white or black.
HW characters from A_{11} to A_{HW} represent the colors of the squares.
A_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.

We will repeatedly perform the following operation until all the squares are black:

Every white square that shares a side with a black square, becomes black.

Find the number of operations that will be performed.
The initial grid has at least one black square.

Constraints

1 \leq H,W \leq 1000

A_{ij} is # or ..

The given grid has at least one black square.

Input

Input is given from Standard Input in the following format:

H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}

Output

Print the number of operations that will be performed.

Sample Input 1

3 3
...
.#.
...

Sample Output 1

2

After one operation, all but the corners of the grid will be black. After one more operation, all the squares will be black.

Sample Input 2

6 6
..#..#
......
#..#..
......
.#....
....#.

Sample Output 2

3

Solution in PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import queue

def resolve():
    # ★get input
    h, w = map(int, input().split())

    grid = [["" for i in range(w)] for j in range(h)]

    for i in range(h):
        line = input()
        for j in range(w):
            grid[i][j] = line[j:j+1]

    # ★exec
    # BFSにて最短経路を求める
    # 準備
    distance = [[-1 for i in range(w)] for j in range(h)]
    que = queue.Queue()

    # スタート地点の情報を設定
    # 多点スタートの設定
    for i in range(h):
        for j in range(w):
            if grid[i][j] == "#":
                que.put([i, j])
                distance[i][j] = 0

    # BFS開始
    while not que.empty():

        now = que.get()

        # 上下左右のマスを確認
        for move_y, move_x in ((1, 0), (-1, 0), (0, 1), (0, -1)):

            # 盤の範囲外なら何もしない
            target = [now[0] + move_y, now[1] + move_x]
            if not h > target[0] >= 0 or not w > target[1] >= 0:
                continue

            # 黒塗りされているなら何もしない
            if grid[target[0]][target[1]] == '#':
                continue

            # 距離が設定済みなら何もしない
            if not distance[target[0]][target[1]] == -1:
                continue

            # キューに追加
            que.put(target)

            # 最短距離を設定
            distance[target[0]][target[1]] = distance[now[0]][now[1]] + 1

    # 距離が最大の点 = 答えになる。
    ans = 0
    for i in range(h):
        ans = max(ans, max(distance[i]))

    print(ans)


if __name__ == "__main__":
    resolve()