Students scoring lower

Problem

Exam marks are whole numbers from 0 to 1000. For each student, print how many students scored strictly lower. The students are listed in input order.

Input: One line: the marks, separated by spaces.
Output: For each student in input order, the count of lower marks, separated by single spaces.
Constraints: 1 ≤ number of students ≤ 100000
0 ≤ each mark ≤ 1000

Example 1

Input

8 1 2 2 3

Output

4 0 1 1 3

Example 2

Input

5 5

Output

0 0

Try the problem first. Open one hint at a time.

Hint 1

The range is small, so counting works better than sorting.

Hint 2

A running total of the counts gives the number of lower marks.

Write your Python code, run it on the examples and submit it to hidden tests.