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CSES Problem Set

Building II


Task | Statistics


CSES - Building II

Time limit:1.00 s Memory limit:512 MB

You are given a map of a forest where some squares are empty and some squares have trees.

You want to place a rectangular building in the forest so that no trees must be cut down. For each building size, your task is to calculate the number of ways you can do this.

Input

The first input line contains integers $n$ and $m$: the size of the forest.

After this, the forest is described. Each square is empty (.) or has trees (*).

Input

Print $n$ lines that each contain $m$ integers.

Constraints
Example

Input:
4 7
...*.*.
.*.....
.......
......*


Output:
24 17 13 9 6 3 1
16 9 7 5 3 1 0
9 3 2 1 0 0 0
3 0 0 0 0 0 0


Explanation: For example, there are $5$ possible places for a building of size $2 \times 4$.