O Canada

In this problem a grid is an $N \times N$ array of cells, and each cell is either red or white.

Grid $A$ is similar to grid $B$ if and only if $A$ can be turned into $B$ by some sequence of changes. One change picks a $2 \times 2$ square in the grid and flips the colour of all four cells inside it. Red cells in the square become white, and white cells in the square become red.

You are given $G$ grids. Count the pairs of grids that are similar. Number the grids from $1$ to $G$, then count the pairs $(i, j)$ with $1 \le i < j \le G$ such that grid $i$ and grid $j$ are similar.

The first line contains the grid size $N$ ($2 \le N \le 10$). The second line contains the number of grids $G$ ($2 \le G \le 10000$). The next $N \times G$ lines each contain $N$ characters, and each character is R or W, giving the colour of that cell. R is red and W is white. After the first two lines, the next $N$ lines describe the first grid, the following $N$ lines describe the second grid, and so on.

Print the number of pairs of grids that are similar.