Z. Nearest Smaller Values
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Constraints:

  • $$$1 \le n \le 2\cdot 10^5$$$
  • $$$1 \le x,a_i \le 10^9$$$
Output

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

Example
Input
8
2 5 1 4 8 3 2 5
Output
0 1 0 3 4 3 3 7