A permutation of integers from 1 to n is a sequence a₁, a₂, ..., a_n, such that each integer from 1 to n is appeared in the sequence exactly once.</p>

Two integers in а permutation form an inversion, when the bigger one is before the smaller one.

As an example, in the permutation 4 2 7 1 5 6 3, there are 10 inversions in total. They are the following pairs: 4–2, 4–1, 4–3, 2–1, 7–1, 7–5, 7–6, 7–3, 5–3, 6–3.

Write program invcnt that computes the number of the inversions in a given permutation.

입력 형식

The value for the number n is written on the first line of the standard input. The permutation is written on the second line: n numbers, delimited by spaces.

출력 형식

Write the count of inversions on the standard output.

예제 입력

7
4 2 7 1 5 6 3

예제 출력

10