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
```