Counting Inversions

Given a sequence of integers, your task is to compute the number of inversions in the sequence.

An inversion is defined as a pair of indices \( (i, j) \) such that \( i a_j \). The number of inversions in the sequence gives a measure of how far the sequence is from being sorted.

For example, for the sequence [5, 3, 2, 4, 1], there are 8 inversions.

inputFormat

The input is given via standard input. The first line contains an integer \( n \) representing the number of elements in the sequence. The second line contains \( n \) space-separated integers representing the sequence.

outputFormat

Output a single integer representing the number of inversions in the given sequence. The output should be printed to standard output.

## sample

5
5 3 2 4 1

8

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