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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

function is_dark(A){
  var darks = [];
  for(var i=0;i<A.length;i++){
    line_set = new Set(A[i])
    darks.push
    if(line_set.size==2 || line_set.size==1 && A[i][0]=='.'){return false;}
  }
  return true;
}

function get_darken_blacks(A, blacks){
  var darken_blacks=[]
  for(var i=0;i<blacks.length;i++){
    var c_black = blacks[i];
    x = c_black[1];
    y = c_black[0];

    if(y>0                            && A[y-1][x]=='.'){darken_blacks.push([y-1, x])}
    if(x>0                            && A[y][x-1]=='.'){darken_blacks.push([y, x-1])}
    if(x<A[0].length-1 && A[y][x+1]=='.'){darken_blacks.push([y, x+1])}
    if(y<A.length-1       && A[y+1][x]=='.'){darken_blacks.push([y+1, x])}
  }
  return darken_blacks;
}

function darken(A, blacks){

  for(var i=0;i<blacks.length;i++){
    var c_black = blacks[i];
    x = c_black[1];
    y = c_black[0];
    A[y][x]='#';
  }
  return A;
}

function get_blacks(A){
  blacks = [];
  for(var i=0;i<A.length;i++){
    for(var j=0;j<A[0].length;j++){
      if(A[i][j]=='#'){blacks.push([i,j])}
    }
  }
  return blacks;
}

function main(input){
  const lines = input.split('\n');
  const H = lines[0].split(' ').map(x => parseInt(x))[0];
  const W = lines[0].split(' ').map(x => parseInt(x))[1];
  var A=[];
  for(var i=0;i<H;i++){
    var line = lines[1+i].split('');
    A.push(line);
  }

//  console.log([H,W,A]);

  var result = 0;

  var blacks = get_blacks(A);
  while(!is_dark(A)){
    blacks = get_darken_blacks(A, blacks)
    A=darken(A, blacks);
    //console.log('==');
    //console.log(blacks);
    //console.log(A);
    result++;
  }

  console.log(result);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'));