Letters Q and F

Little Lev is learning how to draw letters Q and F. Initially, he has a white grid of size $n\times m$. Then he will draw several letters of one of the following two shapes:

Lev will not rotate or mirror these two shapes. Every time he draws a new letter, he will choose a position for the letter inside the grid and paint all cells of the shape black. Lev will only draw letters in such a way that before drawing all black cells of the letter are white — that is, he will never paint a cell twice.

You are given the final coloring of the grid. Count the number of letters Q and letters F drawn by Lev.

Input

The first line contains two integers $n$ and $m$ — the height and the width of the grid ($5\le n\le 300$; $3\le m\le 300$).

The next $n$ lines contain $m$ characters each, denoting the final state of the grid. A white cell is denoted by '.', a black cell is denoted by '#'.

It is guaranteed that the grid is a valid result of Lev's drawing.

Output

Print two integers — the number of letters Q and the number of letters F drawn by Lev, respectively.

Examples

Note

Illustration for the fourth example test: