White Rectangles

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.

2
.#
..
4
..#.
##.#
.#..
.#.#

5
15

JIANG, Ming

ZOJ Monthly, January 2004