You are given a chessboard made up of N squares by N squares with equal size. Some of the squares are colored black, and the others are colored white. Please write a program to calculate the number of rectangles which are completely made up of white squares.
There are multiple test cases. Each test case begins with an integer N (1 <= N <= 100), the board size. The following N lines, each with N characters, have only two valid character values:
# - (sharp) representing a black square; . - (point) representing a white square.
Process to the end of file.
For each test case in the input, your program must output the number of white rectangles, as shown in the sample output.