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There is a board of size $NM($represented by an array board consisting of strings$).$ Rows are numbered from $0$ to $N-1($from top to bottom$)$ and columns are numbered from $0$ to $M-1($from left to right$).$ Each cell is either empty $($denoted by $\text{'}.\text{'})$ or contains a letter A or B$.$ The cell in the R$-$th row and C$-$th column is represented by board $[R][C].$

Calculate the number of rectangles inside the board with a corner at position $(0,0)($board $[0][0])$ which cover an equal number of letters A and $B.$

For example, for board $=["$AB$.","$BY$.","..$ A$"],$ there are five such rectangles:

the first row without the last element $($marked in the picture below$)$;

the whole first row;

symmetrically, the whole first column $($marked below$)$ and the first column without the last element;

the whole board.

$\backslash$table$[[,0,1,2],[,$A$,B,],[,$B$,.,*$