A permutation p of size n is the sequence p_1, p_2, ..., p_{n}, consisting of n distinct integers, each of them is from 1 to n (1 ≤ p_{i} ≤ n).

A lucky permutation is such permutation p, that any integer i (1 ≤ i ≤ n) meets this condition p_{p}_{i} = n - i + 1.

You have integer n. Find some lucky permutation p of size n.


-----Input-----

The first line contains integer n (1 ≤ n ≤ 10^5) — the required permutation size.


-----Output-----

Print "-1" (without the quotes) if the lucky permutation p of size n doesn't exist.

Otherwise, print n distinct integers p_1, p_2, ..., p_{n} (1 ≤ p_{i} ≤ n) after a space — the required permutation.

If there are multiple answers, you can print any of them.


-----Examples-----
Input
1

Output
1 

Input
2

Output
-1

Input
4

Output
2 4 1 3 

Input
5

Output
2 5 3 1 4

```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 = 'from itertools import permutations\nfrom sys import stdin\n\n\ndef checkit(vector, upto=-1):\n    if upto == -1:\n        upto = len(vector)\n    for i in range(0, upto):\n        if vector[vector[i] - 1] != len(vector) - (i + 1) + 1:\n            return False\n    return True\n\n\ndef calculate(n):\n    numbers = list(range(1, n + 1))\n    result = [0] * n\n    for i in range(0, n):\n        if result[i] != 0: continue\n        if i > 0 and checkit(result, i): continue\n\n        expected = n - i\n\n        for v in numbers:\n            if v - 1 == i and expected != v:\n                continue\n\n            if v == expected:\n                result[v-1] = v\n                numbers.remove(v)\n                break\n            elif result[v - 1] == expected:\n                numbers.remove(v)\n                result[i] = v\n                break\n            elif result[v - 1] == 0:\n                assert expected in numbers\n                result[i] = v\n                result[v - 1] = expected\n                numbers.remove(v)\n                numbers.remove(expected)\n                break\n\n    return result\n\ndef calculate_v2(n):\n    result = [0] * n\n    first_sum = n + 2\n    second_sum = n\n\n    nf = n\n    i = 0\n    while nf > first_sum // 2:\n        result[i] = first_sum - nf\n        result[i + 1] = nf\n        nf -= 2\n        i += 2\n\n    if n % 2 == 1:\n        result[i] = i + 1\n\n    i = n - 1\n    while i > n // 2:\n        result[i] = i\n        result[i-1] = second_sum - i\n        i -= 2\n\n    return result\n\n\ndef main():\n        number = int(stdin.readline())\n        result = calculate_v2(number)\n        if not checkit(result):\n            print(-1)\n        else:\n            print(" ".join([str(v) for v in result]))\n\n\ndef __starting_point():\n    main()\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14237