Coloring the Flag

Problem Background

Special for beginners, ^_^

Problem Description

A country's law states that a flag made of $N \times M$ small squares is legal as long as it satisfies the following rules (a certain bear: achoo—):

• The top several rows (at least one row) are entirely white;
• The next several rows (at least one row) are entirely blue;
• The remaining rows (at least one row) are entirely red.

Now there is a chessboard-like cloth divided into $N$ rows and $M$ columns of cells, each cell being white, blue, or red. Xiao a wants to turn this cloth into a legal flag of that country, by painting some cells to cover their previous colors.

Xiao a is lazy and wants to paint the fewest cells so that the cloth becomes a legal flag.

Input Format

The first line contains two integers $N, M$.

The next $N$ lines form a matrix where each cell is one of W (white), B (blue), R (red).

Output Format

One integer: the minimum number of cells that must be painted.

Sample Input

4 5
WRWRW
BWRWB
WRWRW
RWBWR

Sample Output

11

Sample Explanation

The target state is:

WWWWW
BBBBB
RRRRR
RRRRR

which requires changing $11$ cells in total.

Constraints

For $100\%$ of the data, $N, M \le 50$.