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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N=5e6;
const int X[4]={0,1,0,-1},Y[4]={1,0,-1,0};

  int n,m,l,r;
  int q[N],v[N];
#define C getchar()
void in()
{
  cin>>n>>m;
  C;
  for (int i=0;++i<=n;C)
    for (int j=0;++j<=m;)
      if (C=='#')
			  v[q[++r]=i*m+j]=1;
}

  int d[N];
void wor()
{
  while (++l<=r)
    {
      int x=(q[l]-1)/m,y=(q[l]-1)%m+1;
      for (int i=4;~--i;)
        if (x+X[i]&&x+X[i]<=n&&y+Y[i]&&y+Y[i]<=m)
          {
            int p=(x+X[i])*m+(y+Y[i]);
            if (!v[p])
              v[p]=1,
              q[++r]=p,
              d[p]=d[q[l]]+1;
          }
    }
}

void out()
{
  cout<<d[q[r]];
}

int main()
{
  in();
  wor();
  out();
  exit(0);
}