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

Difficulty: competition

Starter code:

Solutions:
n = int(input())
if n%4 > 1:
  print(-1)
else:
  a = [n+1>>1]*n
  for i in range(n//4):
    j = i*2
    a[j], a[j+1], a[-2-j], a[-1-j] = j+2, n-j, j+1, n-1-j
  print(' '.join(map(str, a)))

n=int(input())

L=[0]*(n+1)

X=[False]*(n+1)

if(n%4!=0 and n%4!=1):
    print(-1)

else:
    for i in range(1,n+1):
        if(X[i]):
            continue
        X[i]=True
        X[n-i+1]=True
        for j in range(i+1,n+1):
            if(X[j]):
                continue
            X[j]=True
            X[n-j+1]=True
            L[i]=j
            L[n-i+1]=n-j+1
            L[j]=n-i+1
            L[n-j+1]=i
            break
        if(n%4==1):
            L[n//2+1]=n//2+1
    for i in range(1,n):
        print(L[i],end=" ")
    print(L[n])
        


n = int(input())
if n % 4 > 1: print(-1)
else:
    k = n // 2
    t = [0] * n
    for i in range(0, k, 2):
        t[i] = str(i + 2)
    for i in range(1, k, 2):
        t[i] = str(n - i + 1)
    if n & 1:
        k += 1
        t[k - 1] = str(k)
    for i in range(k, n, 2):
        t[i] = str(n - i - 1)
    for i in range(k + 1, n, 2):
        t[i] = str(i)
    print(' '.join(t))

'''
Created on

@author: linhz
'''
import sys
usedNum=0
n=int(input())
p=[0 for i in range(n+1)]
usedNum=0
if n%4==3 or n%4==2:
    print(-1)
else:
    i=1
    j=n
    a=1
    b=n
    while j>i:
        p[i]=a+1
        p[i+1]=b
        p[j]=b-1
        p[j-1]=a
        i+=2
        j-=2
        a+=2
        b-=2
    if j==i:
        p[i]=a
    ans=""
    for i in range(1,n+1):
        ans+=str(p[i])+" "
    print(ans)

from itertools import permutations
from sys import stdin


def checkit(vector, upto=-1):
    if upto == -1:
        upto = len(vector)
    for i in range(0, upto):
        if vector[vector[i] - 1] != len(vector) - (i + 1) + 1:
            return False
    return True


def calculate(n):
    numbers = list(range(1, n + 1))
    result = [0] * n
    for i in range(0, n):
        if result[i] != 0: continue
        if i > 0 and checkit(result, i): continue

        expected = n - i

        for v in numbers:
            if v - 1 == i and expected != v:
                continue

            if v == expected:
                result[v-1] = v
                numbers.remove(v)
                break
            elif result[v - 1] == expected:
                numbers.remove(v)
                result[i] = v
                break
            elif result[v - 1] == 0:
                assert expected in numbers
                result[i] = v
                result[v - 1] = expected
                numbers.remove(v)
                numbers.remove(expected)
                break

    return result

def calculate_v2(n):
    result = [0] * n
    first_sum = n + 2
    second_sum = n

    nf = n
    i = 0
    while nf > first_sum // 2:
        result[i] = first_sum - nf
        result[i + 1] = nf
        nf -= 2
        i += 2

    if n % 2 == 1:
        result[i] = i + 1

    i = n - 1
    while i > n // 2:
        result[i] = i
        result[i-1] = second_sum - i
        i -= 2

    return result


def main():
        number = int(stdin.readline())
        result = calculate_v2(number)
        if not checkit(result):
            print(-1)
        else:
            print(" ".join([str(v) for v in result]))


def __starting_point():
    main()
__starting_point()

n = int(input())



if n % 4 > 1:

    print(-1)

    return



a = [i for i in range(0, n+1)]

for i in range(1, n//2+1, 2):

    p, q, r, s = i, i+1, n-i,n-i+1

    a[p], a[q], a[r], a[s] = a[q], a[s], a[p], a[r]



def check(arr):

    for i in range(1, n+1):

        k = arr[i]

        if arr[arr[k]] != n-k+1:

            return False

    return True



# print(check(a))

print(*a[1:])



n=int(input())
if n%4==2 or n%4==3:
        print(-1);return
res,i=[0]*n,0
for i in range(0,n//2,2):
    res[i],res[i+1]=i+2,n-i
    res[n-i-1],res[n-i-2]=n-i-1,i+1
    i+=2
if n%4==1:res[n//2]=n//2+1
print(*res)

n = int(input())
if n%4 > 1:
    print(-1)
    return
a = [(n+1) // 2] * n
for i in range(n//4):
    j = 2*i
    a[j], a[j+1], a[-j-2], a[-j-1] = j+2, n-j, j+1, n-j-1
print(' '.join(map(str, a)))


import sys
from collections import deque
n = int(input())
if n % 4 == 2 or n % 4 == 3:
    print('-1')
    return

arr = [None] * (n + 1)
qt = deque([i for i in range(1, n + 1)])
mark = set()
while qt:
    while qt and qt[0] in mark:
        qt.popleft()
    if not qt:
        break
    a = qt.popleft()
    while qt and qt[0] in mark:
        qt.popleft()
    if not qt:
        break
    b = qt.popleft()
    for i in range(4):
        mark.add(a) 
        mark.add(b)
        arr[a] = b
        arr[b] = n - a + 1
        a = b
        b = arr[b]

for i in range(1, n + 1):
    if not arr[i]:
        arr[i] = a
        break
print(' '.join(map(str, arr[1:])))


n=int(input())
if n==1:
	print (1)
	return
if n%4>1:
	print (-1)
	return
ans=[-1]*n
left=n
start=n-2
nums=1
nume=n
while left>=4:
	ans[start]=nums
	ans[nums-1]=nums+1
	ans[nums]=nume
	ans[nume-1]=nume-1
	start-=2
	nums+=2
	nume-=2
	left-=4
	# print (ans)
if left==1:
	ans[start+1]=start+2
print (*ans)

n=int(input())
if (n//2)&1:
	print(-1)
else:
	ans=[0]*(n+1)
	for i in range(1,(n//2)+1,2):
		ans[i]=i+1
		ans[i+1]=n-i+1
		ans[n-i+1]=n-i
		ans[n-i]=i
	if n%2:
		ans[(n//2)+1]=(n//2)+1
	print(*ans[1:])


n=int(input())
if(n%4>1):
    print(-1)
else:
    ans=[0]*(n+1)
    i,j,a,b=1,n,1,n
    while(i<j and a<=n and b>=1):
        ans[i],ans[j]=a+1,b-1
        ans[i+1],ans[j-1]=b,a
        i+=2
        j-=2
        a+=2
        b-=2
    if(i==j):
        ans[i]=a
    for i in range(1,n+1):
        print(ans[i],end=' ')