Problem: 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.

Examples

Input

3 3
...
.#.
...


Output

2


Input

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


Output

3

Solution (in PYTHON):

Solution:
def main():
    h, w = map(int, raw_input().split())
    aa = []
    for _ in xrange(h):
        aa.append(raw_input())
    q = []
    dist = [[False] * w for _ in xrange(h)]
    for y in xrange(h):
        row = aa[y]
        for x in xrange(w):
            if row[x] == '#':
                dist[y][x] = True
                q.append([x, y])
    m = 0
    nexts = []
    while True:
        for x, y in q:
            for dx, dy in [[1, 0], [-1, 0], [0, 1], [0, -1]]:
                xx = x + dx
                yy = y + dy
                if 0 <= xx < w and 0 <= yy < h:
                    if aa[yy][xx] == '.' and not dist[yy][xx]:
                        dist[yy][xx] = True
                        nexts.append([xx, yy])
        if nexts:
            m += 1
            q = nexts
            nexts = []
        else:
            break
    print m


if __name__ == '__main__':
    main()