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문제

Let's call a maze a rectangular field of cells, where cells can either be empty or contain a wall, and one can move from an empty cell to its empty neighbour cells in four directions.

Let's call a maze connected if it's possible to reach any its empty cell from any other empty cell by moving in four directions.

There was a connected maze of size $n \times m$. It was cyclically shifted some rows down and some columns right, but nobody knows the exact shifts. Find all possible shifts.

입력

The first line contains two integers $n$ and $m$ ($1 \le n, m \le 200$) --- the sizes of maze.

Each of the next $n$ lines contains $m$ characters "." or "#" --- empty cells and walls, correspondingly.

There is at least one empty cell in the maze.

출력

In the first line output a single integer $k$ ($0 \le k \le n \cdot m$) --- the number of possible shifts.

In each of the next $k$ lines output two integers $r_i$ and $c_i$ ($0 \le r_i < n, 0 \le c_i < m$) --- the number of rows the original maze was shifted down and the number of columns it was shifted right. Pairs ($r_i$, $c_i$) should be output in lexicographical order. Original maze must be connected for each of these cases.

예제 입력 1

5 6
..####
.###..
...#.#
##...#
.###..

예제 출력 1

9
0 2
0 3
0 4
1 2
1 3
1 4
4 2
4 3
4 4

예제 입력 2

8 10
##########
..........
#.####..##
..###..##.
#....##...
######..##
....###...
....###...

예제 출력 2

2
0 5
1 5