Problem Statement

Given the width and height of a rectangular grid, return the total number of rectangles (NOT counting squares) that can be found on this grid.

For example, width = 3, height = 3 (see diagram below):

__ __ __
|__|__|__|
|__|__|__|
|__|__|__|

In this grid, there are 4 2x3 rectangles, 6 1x3 rectangles and 12 1x2 rectangles. Thus there is a total of 4 + 6 + 12 = 22 rectangles. Note we don't count 1x1, 2x2 and 3x3 rectangles because they are squares.

Definition

 Class: RectangularGrid Method: countRectangles Parameters: int, int Returns: long Method signature: long countRectangles(int width, int height) (be sure your method is public)

Notes

-rectangles with equals sides (squares) should not be counted.

Constraints

-width and height will be between 1 and 1000 inclusive.

Examples

0)

 3 3
Returns: 22
 See above
1)

 5 2
Returns: 31
 __ __ __ __ __ |__|__|__|__|__| |__|__|__|__|__| In this grid, there is one 2x5 rectangle, 2 2x4 rectangles, 2 1x5 rectangles, 3 2x3 rectangles, 4 1x4 rectangles, 6 1x3 rectangles and 13 1x2 rectangles. Thus there is a total of 1 + 2 + 2 + 3 + 4 + 6 + 13 = 31 rectangles.
2)

 10 10
Returns: 2640
3)

 1 1
Returns: 0
4)

 592 964
Returns: 81508708664

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=1589

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4535&pm=1589