Mike is the president of country What-The-Fatherland. There are $*n*$ bears living in this country besides Mike. All of them are standing in a line and they are numbered from $1$ to $*n*$ from left to right. $*i*$-th bear is exactly $*a*_{*i*}$ feet high.

A group of bears is a non-empty contiguous segment of the line. The size of a group is the number of bears in that group. The strength of a group is the minimum height of the bear in that group.

Mike is a curious to know for each $*x*$ such that $1 ≤ *x* ≤ *n*$ the maximum strength among all groups of size $*x*$.

Input

The first line of input contains integer $*n*$ ($1 ≤ *n* ≤ 2 × 10^{5}$), the number of bears.

The second line contains $*n*$ integers separated by space, $*a*_{1}, *a*_{2}, ..., *a*_{*n*}$ ($1 ≤ *a*_{*i*} ≤ 10^{9}$), heights of bears.

Output

Print $*n*$ integers in one line. For each $*x*$ from $1$ to $*n*$, print the maximum strength among all groups of size $*x*$.