题目描述

Little Lev is learning how to draw letters $\tt{Q}$ and $\tt{F}$. 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 $\tt{Q}$ and letters $\tt{F}$ drawn by Lev.

输入格式

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 $\tt{.}$, a black cell is denoted by $\tt{\#}$.

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

输出格式

Print two integers --- the number of letters $\tt{Q}$ and the number of letters $\tt{F}$ drawn by Lev, respectively.

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

1 0

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

0 1

5 8
###..###
#.#..#..
###..##.
..#..#..
..#..#..

1 1

8 8
.....###
###..#.#
#.######
###.####
#.###.##
#.#.###.
..#...#.
......#.

2 2

提示

Illustration for the fourth example test: