Difference Matrix Sum

You are given a positive integer N. Your task is to compute the sum of all elements in an N x N matrix where the element at the intersection of the i-th row and j-th column is defined as \(|i - j|\) (with 0-based indices). This problem tests your ability to implement algorithms and correctly handle basic arithmetic operations.

Problem Details:

• The matrix is defined as: \(A[i][j] = |i - j|\) for all \(0 \leq i, j < N\).
• You need to compute the total sum of all the elements in this matrix.

Example:

Input: 3
Output: 8
Explanation: For N = 3, the matrix is:
[ [0, 1, 2],
[1, 0, 1],
[2, 1, 0] ]
The sum is 0+1+2+1+0+1+2+1+0 = 8.

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inputFormat

The input consists of a single integer N (1 \leq N \leq 10^4 or based on constraints) provided via standard input.

outputFormat

Output a single integer, which is the sum of all elements in the difference matrix, printed to standard output.

## sample

3

8