Counting Inversions in an Array

Given an array of integers, you are required to count the number of inversions needed to sort the array in ascending order. An inversion is a pair of indices \( (i, j) \) such that \( i arr[j] \). In other words, the total number of inversions is given by the formula:

\( I = \sum_{i arr[j]\}} \)

For example, for the array [2, 3, 8, 6, 1], the inversion count is 5. Your task is to implement an efficient algorithm to compute this inversion count.

inputFormat

The first line contains an integer \( N \), representing the number of elements in the array. The second line contains \( N \) space-separated integers representing the array elements.

outputFormat

Output a single integer representing the number of inversions in the array.

## sample

5
2 3 8 6 1

5

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