Inversion Count

Once upon a time in a mystical land, there lived a wise sorcerer named Merlin. Merlin possessed a unique power to perceive the hidden patterns in permutations. He was particularly intrigued by the concept of inversions in a permutation.
An inversion in a permutation is a pair of elements `(``)` such that `i < j` and . The number of inversions in a permutation represents how far the permutation is from being sorted in ascending order.
Merlin decided to challenge the talented programmers by posing the following problem: Given a permutation of integers from `1` to `n`, your task is to calculate the number of inversions present in the permutation.

Input

The first line contains a single integer `n` (1 β€ n β€ 100 000), representing the size of the permutation. The second line contains `n` space-separated integers, representing the elements of the permutation.

Output

Print a single integer, representing the number of inversions in the given permutation.

Examples

 Input Output 5 3 1 4 2 5 3 4 1 2 3 4 0

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB