Letters Q and F

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시간 제한2초메모리 제한512 MB

요약

겹치지 않게 Q와 F 모양을 그려 만든 격자가 주어질 때, 그려진 Q와 F의 개수를 각각 센다.

난이도: 보통10점 중 5점
유형: 구현, 시뮬레이션, 완전 탐색
정답자: 아직 제출이 없습니다

문제

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.

입력

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.

출력

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

힌트

Illustration for the fourth example test:

예제4

예제 1
입력
```
5 3
###
#.#
###
..#
..#
```
예상 출력
```
1 0
```
예제 2
입력
```
5 3
###
#..
##.
#..
#..
```
예상 출력
```
0 1
```

예제 3

입력

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

예상 출력

1 1

예제 4

입력

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

예상 출력

2 2