Given a permutation of the first $N$ positive integers and the ability to swap any two adjacent integers, compute the minimum number of swaps needed to sort the list in decreasing order.

Constraints

$1\le N\le {10}^3$

$v_i$ form a permutation of the first $N$ positive integers.

Input Specification

The first line of the input consists of a single integer, $N$.

The next line contains $N$ space-separated integers, the permutation of the first $N$ integers.

Output Specification

Output, on a single line, the minimum number of swaps needed.

Sample Input

3
2 1 3

Sample Output

2