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 = 'n = list(map(int, input().split()))[0]\nlst = list(map(int, input().split()))\n\n\nsorted_index = sorted(range(n), key=lambda k: lst[k], reverse=True)\n\nlookup = [(0, 0)] * n\n\nres = []\nres_pos = 1\nfor index in sorted_index:\n    seq_len = lookup[index][0] + lookup[index][1] + 1\n    if seq_len >= res_pos:\n        step = seq_len - res_pos + 1\n        res += [lst[index]] * step\n        res_pos += step\n\n    step_back = lookup[index][0] + 1\n    if index - step_back >= 0:\n        lookup[index - step_back] = (lookup[index - step_back][0],\n                                     lookup[index - step_back][1] + 1 + lookup[index][1])\n\n    step_forward = lookup[index][1] + 1\n    if index + step_forward < n:\n        lookup[index + step_forward] = (lookup[index + step_forward][0] + 1 + lookup[index][0],\n                                        lookup[index + step_forward][1])\n\n\nres = list(map(str, res))\nprint(" ".join(res))'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13579