Problem Statement

We have a grid with H horizontal rows and W vertical columns. We denote by (i, j) the cell at the i-th row from the top and j-th column from the left of the grid.
Each cell in the grid has a symbol # or . written on it. Let C[i][j] be the character written on (i, j). For integers i and j such that at least one of $1 \leq i \leq H$ and $1 \leq j \leq W$ is violated, we define C[i][j] to be ..
(4n+1) squares, consisting of (a, b) and $(a+d,b+d),(a+d,b-d),(a-d,b+d),(a-d,b-d) (1 \leq d \leq n, 1 \leq n)$, are said to be a cross of size n centered at (a,b) if and only if all of the following conditions are satisfied:

• C[a][b] is #.
• C[a+d][b+d],C[a+d][b-d],C[a-d][b+d], and C[a-d][b-d] are all #, for all integers d such that $1 \leq d \leq n$,
• At least one of C[a+n+1][b+n+1],C[a+n+1][b-n-1],C[a-n-1][b+n+1], and C[a-n-1][b-n-1] is ..

For example, the grid in the following figure has a cross of size 1 centered at (2, 2) and another of size 2 centered at (3, 7).

The grid has some crosses. No # is written on the cells except for those comprising a cross.
Additionally, no two squares that comprise two different crosses share a corner. The two grids in the following figure are the examples of grids where two squares that comprise different crosses share a corner; such grids are not given as an input. For example, the left grid is invalid because (3, 3) and (4, 4) share a corner.

Let $N = \min(H, W)$, and S_n be the number of crosses of size $n. Find S_1, S_2, \dots, S_N$.

Input

The input is given from Standard Input in the following format:
H W
$C[1][1]C[1][2]\dots C[1][W]$
$C[2][1]C[2][2]\dots C[2][W]$
$\vdots$
$C[H][1]C[H][2]\dots C[H][W]$

Output

Print $S_1, S_2, \dots$, and S_N, separated by spaces.

Constraints

• $3 \leq H, W \leq 100$
• C[i][j] is # or ..
• No two different squares that comprise two different crosses share a corner.
• H and W are integers.

Sample Input 1

5 9

.#.#...

.#...#.#.

.#...#..

.....#.#.
....#...#

Sample Output 1

1 1 0 0 0

As described in the Problem Statement, there are a cross of size 1 centered at (2, 2) and another of size 2 centered at (3, 7).

Sample Input 2

3 3
...
...
...

Sample Output 2

0 0 0

There may be no cross.

Sample Input 3

3 16

.#.....#.#..#.

.#.......#....#.

.#.....#.#..#.

Sample Output 3

3 0 0

Sample Input 4

15 20

.#..#.............

.#....#....#.#....#.

.#....#....#....#..

........#..#.#..#...

.....#..#.....#....

.#...#....#...#..#.#
..#.#......#.#....#.
...#........#....#.#
..#.#......#.#......
.#...#....#...#.....

.....#..#.....#....

........#.......#...

.#....#....#.#..#..

.#....#......#....#.

.#..#......#.#....

Sample Output 4

5 0 1 0 0 0 1 0 0 0 0 0 0 0 0

见题面 Input 部分

见题面 Output 部分