Given a permutation of the integers ~1~ to ~N~, print out the number of inversions in the array.

An inversion is defined as a pair of indices, ~i, j~ such that ~i \neq j, i < j, a_i > a_j~.

Input Specification

The first line will contain the integer ~N~ ~(1 \le N \le 10^5)~.

The second line will contain ~N~ integers, ~a_1, a_2, \ldots a_N~ ~(1 \le a_i \le N)~.

It is guaranteed the second line will contain a valid permutation of the integers from ~1~ to ~N~.

Output Specification

Output the number of inversions in the permutation.

Sample Input

4
3 2 1 4

Sample Output

3