Task $1$

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 $[][]$ which cover an equal number of letters A and $B.$

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$[[,0,1,2],[0,A,B,.],[1,$B$,*,.],[2,,.,A$