Given an unsorted array arr[] of integers, Print Count of number of smaller elements on right of each element in the array.

Input

An array of integers where each element of array abs(value)<=10^6

The size of the array is of the order of 10^6

Output

Print the space separated list of number of smaller elements on right of each element in the array.

Example

Input:
12 1 2 3 0 11 1
Output:
6 1 2 2 0 1 0