Given an array $A$ of $n$ integers, your task is to find for each array position the nearest position to its left having a smaller value.

Input

• The first line contains an integer $n$.
• The second line contains $n$ integers $A_i$.

Output

• Print $n$ integers: for each array position the nearest position with a smaller value. If there is no such position, print $0$.

Constraints

• $1 \le n \le 10^5$.
• $1 \le A_i \le 10^9$.

Example

Input:

8
2 5 1 4 8 3 2 5

Output:

0 1 0 3 4 3 3 7