Problem

An inversion of an array $A[1..n]$ is a pair of indices $(i,j)$ such that $1 \le i < j \le n$ and $A[i] > A[j]$. The number of inversions shows how far the array is from being sorted: if it is already sorted then there are no inversions, whereas if it is sorted in reverse order then the number of inversions is maximal.

Given: A positive integer $n \le 10^5$ and an array $A[1..n]$ of integers from $-10^5$ to $10^5$.

Return: The number of inversions in $A$.

Sample Dataset

5
-6 1 15 8 10

Sample Output

2