Little Sub likes Math. Now he has a simple counting problem for you.
Given an positive integer sequence A, for each Ai, Please calculate how many elements Aj in the sequence satisfied Ai^Aj > Aj^Ai.
The first line contains one positive integer n(1 ≤ n ≤ 100000).
The following line contains n positive integers Ai(1 ≤ Ai ≤ 2^31 − 1).
Please output n integer in one line and separate them by a single space. The ith integer indicates the answer concerning Ai.