983. Grid

Let `M` be a grid of `n` rows and `n` columns. The rows are numbered from 1 to `n` and the columns are numbered from 1 to `n`. A cell `(i,\ j)` denotes the cell in row `i` and column `j` in the grid. Each cell is colored in black or white. Let `C_{ij}` denote the color of the cell `(i,\ j)`. All cells of the form `(i,\ i)` for `1\ ≤\ i\ ≤\ n` are called diagonal cells.

Swapping rows `i` and `j` of the grid `M` denotes the following action: we swap the values of `C_"ik"` and `C_"jk"` for `k\ =\ 1,\ 2,\ …,\ n`. Swapping two columns is defined analogously.

We say that `M` is white-colorable if it is possible to swap some of the pairs of rows and some of the pairs of columns (in any sequence) so that, after all the swappings, all the diagonal cells of `M` are white.

Your task is to write a program that determines whether given grid `M` is white-colorable.

The first line contains a single positive integer `n` (`n\ ≤\ 1000`) – the size of the grid. The `i`-th line of the following `n` lines contains `n` characters `C_{ij}` (`i=1,\ 2,\ …,\ n`; `j=1,\ 2,\ …,\ n`) specifying color pattern of the grid. Character `C_{ij}` is 'B' or 'W' indicating that the color of cell `(i,\ j)` is black or white respectively.

Write "YES" if given grid is white-colorable or "NO" otherwise.

3
WWW
WBB
WBB

NO

3
BWB
BWW
WWB

YES