A race report lists n runners in bib order, each with a performance value. For every runner, count how many of the runners listed after them (to their right in the list) have a strictly smaller value than they do.

Output these counts, one per runner, in the original bib order. The intended approach obtains all counts together while performing a single merge sort that remembers each value's original position.

Input format

Line 1: an integer n, the number of runners. Line 2: n space-separated integers, the performance values in bib order.

Output format

A single line of n space-separated integers: for each runner (in bib order), the number of strictly-smaller values that appear later in the list.

Constraints

• 1 <= n <= 100000
• 0 <= each value <= 1000000000

5
5 2 6 1 3

3 1 2 0 0

4
1 2 3 4

0 0 0 0