Problem:
Score : 200 points

Problem Statement

You are given an H × W grid.

The squares in the grid are described by H strings, S_1,...,S_H.

The j-th character in the string S_i corresponds to the square at the i-th row from the top and j-th column from the left (1 \leq i \leq H,1 \leq j \leq W).

. stands for an empty square, and # stands for a square containing a bomb.

Dolphin is interested in how many bomb squares are horizontally, vertically or diagonally adjacent to each empty square.

(Below, we will simply say "adjacent" for this meaning. For each square, there are at most eight adjacent squares.)

He decides to replace each . in our H strings with a digit that represents the number of bomb squares adjacent to the corresponding empty square.

Print the strings after the process.

Constraints

1 \leq H,W \leq 50

S_i is a string of length W consisting of # and ..

Input

Input is given from Standard Input in the following format:

H W
S_1
:
S_H

Output

Print the H strings after the process.

The i-th line should contain a string T_i of length W, where the j-th character in T_i corresponds to the square at the i-th row from the top and j-th row from the left in the grid (1 \leq i \leq H, 1 \leq j \leq W).

Sample Input 1

3 5
.....
.#.#.
.....

Sample Output 1

11211
1#2#1
11211

For example, let us observe the empty square at the first row from the top and first column from the left.

There is one bomb square adjacent to this empty square: the square at the second row and second column.

Thus, the . corresponding to this empty square is replaced with 1.

Sample Input 2

3 5
#####
#####
#####

Sample Output 2

#####
#####
#####

It is possible that there is no empty square.

Sample Input 3

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

Sample Output 3

#####3
#8#7##
####5#
4#65#2
#5##21
#4#310

Solution in Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

program bomb
  implicit none
  integer :: h, w, i, c, j
  character(len=55), allocatable :: s(:), ans(:)
  
  read(*,*) h, w
  allocate(s(h),ans(h))
  do i = 1, h
     read(*,'(a)') s(i)
  end do

  call bombcount(s, h, w, ans)

  do i = 1, h
     write(*,'(a)') trim(ans(i))
  end do
  deallocate(s, ans)

  stop
contains
  
  subroutine bombcount(s, h, w, ans)
    implicit none
    character(len=55) :: s(h), ans(h)
    integer :: i, j, h, w, num(0:h+1,0:w+1)
    integer :: a, c

    num = 0
    do i = 1, h
       do j = 1, w
          ans(i)(j:j) = '0'
       end do
    end do

    do i = 1, h
       do j = 1, w
          if ( s(i)(j:j) == '#' ) then
             do a = i-1, i+1
                do c = j-1, j+1
                   num(a,c) = num(a,c) + 1
                end do
             end do
          end if
       end do
    end do

    do i = 1, h
       do j = 1, w
          if ( s(i)(j:j) == '#' ) then
             write(ans(i)(j:j),'(a)') '#'
          else
             write(ans(i)(j:j),'(i1)') num(i,j)
          end if
       end do
    end do
    
  end subroutine bombcount
end program bomb