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.

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.

• $1 \le n \le 2 \cdot 10^5$
• $1 \le x_i \le 10^9$

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