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