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

Example Output

0 1 0 3 4 3 3 7