RectangleArea

Your friend has drawn a rectangle on the coordinate plane consisting of points (x, y) such that 0 <= x <= W, 0 <= y <= H, where W and H are positive numbers (not necessarily integer). Then she has divided it into a grid of NxM smaller rectangles. In order to do it, she has chosen numbers (X[0], X[1], ..., X[N]) and (Y[0], Y[1], ..., Y[M]) such that 0 = X[0] < X[1] < ... < X[N] = W and 0 = Y[0] < Y[1] < ... < Y[M] = H. The small rectangle in row i, column j of the grid consists of points (x, y) such that Y[i] <= y <= Y[i+1] and X[j] <= x <= X[j+1]. Note that rows are numbered from 0 to M-1 and columns are numbered from 0 to N-1.

Now, you and your friend play the following game. Initially, you only know the values of N and M, but do not know the values of W, H, X and Y. Your goal is to determine the area of the initial large rectangle, i.e., W * H, but since you don't know W and H, it's not so easy to do. In order to achieve the goal, you can ask questions to your friend. Each question is of the form: "What is the area of the small rectangle in row i, column j?" Your friend always gives true answers, i.e., she responds with the value of (Y[i+1] - Y[i]) * (X[j+1] - X[j]).

You have already asked some questions, the information about them is contained in a String[] known. It contains M elements, each element consists of N characters. The j-th character in i-th element is 'Y' if you already know the area of the small rectangle in row i, column j, and it is 'N' if you haven't yet asked the question about this small rectangle.

Return the minimum number of additional questions that you need to ask in order to determine the area of the initial large rectangle. If you can determine the area without asking additional questions, return 0.