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 $S_1, S_2, \\dots, S_N$.

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.

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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.

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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 $(3, 7)$.

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Sample Input 2

3 3
...
...
...

Sample Output 2

0 0 0

There may be no cross.

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Sample Input 3

3 16
#.#.....#.#..#.#
.#.......#....#.
#.#.....#.#..#.#

Sample Output 3

3 0 0

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Sample Input 4

15 20
#.#..#.............#
.#....#....#.#....#.
#.#....#....#....#..
........#..#.#..#...
#.....#..#.....#....
.#...#....#...#..#.#
..#.#......#.#....#.
...#........#....#.#
..#.#......#.#......
.#...#....#...#.....
#.....#..#.....#....
........#.......#...
#.#....#....#.#..#..
.#....#......#....#.
#.#..#......#.#....#

Sample Output 4

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