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 = "def read_data():\n    n = int(input())\n    hs = list(map(int, input().split()))\n    return n, hs\n\n\ndef solve(n, hs):\n    left = get_left_index(n, hs)\n    right = get_right_index(n, hs)\n    vals = [[] for i in range(n)]\n    for h, l, r in zip(hs, left, right):\n        vals[r - l - 2].append(h)\n    min_hs = []\n    min_h = - float('inf')\n    for val in vals[::-1]:\n        for v in val:\n            min_h = max(min_h, v)\n        min_hs.append(min_h)\n    print(* min_hs[::-1])\n\n\ndef get_left_index(n, hs):\n    left = []\n    stack = []\n    for i, h in enumerate(hs):\n        while stack and hs[stack[-1]] >= h:\n            del stack[-1]\n        if stack:\n            left.append(stack[-1])\n        else:\n            left.append(-1)\n        stack.append(i)\n    return left\n\n\ndef get_right_index(n, hs):\n    hs.reverse()\n    tmp = get_left_index(n, hs)\n    hs.reverse()\n    tmp.reverse()\n    right = [n - 1 - a for a in tmp]\n    return right\n\nn, hs = read_data()\nsolve(n, hs)"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13789