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. 

 [Image] 

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.


-----Examples-----
Input
10
1 2 3 4 5 4 3 2 1 6

Output
6 4 4 3 3 2 2 1 1 1

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '__author__ = \'kitkat\'\nimport sys\n\n#sys.stdin = open("in.txt")\nMAXN = int(2e5+10)\ntry:\n    while True:\n        S = [0] * MAXN\n        ans = [0] * MAXN\n        L = [0] * MAXN\n        R = [0] * MAXN\n        n = int(input())\n        val = list(map(int, input().split(" ")))\n        top = -1\n        for i in range(n):\n            while ~top and val[i] <= val[S[top]]:\n                top -= 1\n            L[i] = S[top] if ~top else -1\n            top += 1\n            S[top] = i\n        top = -1\n        for i in range(n-1, -1, -1):\n            while ~top and val[i] <= val[S[top]]:\n                top -= 1\n            R[i] = S[top] if ~top else n\n            top += 1\n            S[top] = i\n        for i in range(n):\n            ans[R[i] - L[i] - 1] = max(ans[R[i] - L[i] - 1], val[i])\n        for i in range(n-1, 0, -1):\n            ans[i] = max(ans[i], ans[i+1])\n        for i in range(1, n+1):\n            sys.stdout.write(\'%d \'%ans[i])\n        print("")\nexcept EOFError:\n    pass\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 8007128