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Problem

Submissions

Rectangles In N x N Board

Contributed by

Shivam Mehla

Medium

0/80

Avg time to solve 20 mins

Success Rate 80 %

7 upvotes

Problem Statement

You are given a positive integer N. Your task is to find the number of possible rectangles, excluding squares, in a N x N chessboard.

Example:

Let’s assume that we have a chessboard of dimension 4x4, i.e. N = 4. Then the rectangles can have the following possible dimensions: {1*2, 1*3, 1*4, 2*1, ……, 2*4, ………,4*4}. So, the total number of rectangles in the chessboard is 70.

Detailed explanation ( Input/output format, Notes, Constraints, Images )

Input format:

The very first line of input contains an integer T’ denoting the number of test cases. 

The first line of every test case contains an integer ‘N’ denoting the dimension of the chessboard.

Output format:

For each test case, print the number of possible rectangles, excluding squares, in a N x N chessboard.

Output for each test case is printed on a separate line.

Note:

The result can be very large. So, print the answer modulo 1000000007.

You do not need to print anything, it has already been taken care of. Just return the number of possible rectangles.

Constraints:

1 <= T <= 10 
1 <= N <= 5 * 10^4

Time Limit: 1 sec

Sample Input 1:

2
4
1

Sample Output 1:

70
0

Explanation For Sample Input 1:

For the first test case refer to the example explained above.

For the second test case we have, a chessboard of dimension 1x1, i.e. N = 1. There are no possible rectangles. Hence, the answer is zero.

Sample Input 2:

2
2
5

Sample Output 2:

4
170

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