Nearest Smaller Values

Given an array of $nn$ 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 $nn$: the size of the array.

The second line has $nn$ integers $x_1,x_2,\dots ,x_{n}x\_1,x\_2,\backslash dots,x\_n$: the array values.

Output

Print $nn$ integers: for each array position the nearest position with a smaller value. If there is no such position, print $00$.