D. Mike and Feet

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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 ai 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 × 105), the number of bears.

The second line contains n integers separated by space, a1, a2, ..., an (1 ≤ ai ≤ 109), 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.

Examples

input

10 1 2 3 4 5 4 3 2 1 6

output

6 4 4 3 3 2 2 1 1 1 学些数据结构才可以拯救自己吧，数据结构是省时的好东西哦，本来n^2可以变为nlgn甚至n，简直爆炸，单调栈就算能把复杂程度降到n的，太强辣，强行学习一波 其实我只是为了做出我们平台那道题，大佬讲让我用单调栈类似物，但是我并不了解这种数据结构啊，先mark下

#include 
         
          using namespace std;const int N=2e5+5;struct node{    int L, num;}S;stack 
          
            sta;int a[N], ans[N];int main (){    int n;    while (scanf ("%d", &n) != EOF)    {        for (int i=0; i
           
            =1; i--)            ans[i] = max (ans[i], ans[i+1]);        for (int i=1; i