Rectangle Counting on an N x N Chessboard
Given a positive integer N, determine the number of possible rectangles that can be formed on an N x N chessboard, excluding squares.
Input:
The first line contains an integer T, the number of test cases.
Each of the following T lines contains a single integer N, the dimension of the chessboard.
Output:
For each test case, output the number of rectangles (excluding squares) that can be formed on the chessboard.
Example:
Input:
2
3
4
Output:
20
70
Constraints:
- 1 <= T <= 10
- 1 <= N <= 5 * 10^4
- Results should be returned modulo 1000000007.
Note:
Calculate the total number of rectangles possible and subtract the number of squares from it. Return the count modulo 1000000007 for each test case.
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Count the number of rectangles (excluding squares) that can be formed on an N x N chessboard.
Calculate total rectangles using formula N*(N+1)*M*(M+1)/4 where M = N-1
Subtract the number of squares (N*(...read more
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