Cyclically Shifted Maze

Let's call a maze a rectangular grid of cells, where each cell is either empty or a wall. From an empty cell, you can move in four directions to an adjacent empty cell.

A maze is connected if every empty cell can be reached from every other empty cell by moving in four directions.

A connected maze of size $n \times m$ was cyclically shifted: some rows were moved down and some columns were moved right. The exact shifts are unknown. Find all possible shifts.

The first line contains two integers $n$ and $m$ ($1 \le n, m \le 200$), the size of the maze. Each of the next $n$ lines contains $m$ characters, either '.' for an empty cell or '#' for a wall. The maze has at least one empty cell.

On the first line, print the number of possible shifts $k$ ($0 \le k \le n \cdot m$). Each of the next $k$ lines contains two integers $r_i$ and $c_i$ ($0 \le r_i < n$, $0 \le c_i < m$): the original maze was shifted down by $r_i$ rows and right by $c_i$ columns. The original maze must be connected for each listed pair. Print the pairs $(r_i, c_i)$ in lexicographical order.