Nearest Smaller Values

Given an array 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 input line has an integer n: the size of the array. The second line has n integers x_1,x_2,\dots,x_n: the array values.

Output

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

Constraints

$1 \le n \le 2$ \cdot 10^5$

$1 \le x_i \le 10^9$

Example

Input

8
2 5 1 4 8 3 2 5

Output

0 1 0 3 4 3 3 7