CF 286A(Lucky Permutation-数列找规律)

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A permutation p of size n is the sequence p₁, p₂, ..., 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 ≤ 10⁵) — 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 p₁, p₂, ..., p_n (1 ≤ p_i ≤ n) after a space — the required permutation.

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

Sample test(s)
input
1
output
1 
input
2
output
-1
input
4
output
2 4 1 3 
input
5
output
2 5 3 1 4 

找规律

如图所示

#include<cstdio>#include<cstring>#include<cstdlib>#include<cctype>#include<iostream>using namespace std;int n;int main(){cin>>n;if (n%4>1) {cout<<"-1\n";return 0;}for (int i=1;i<=n/2;i++){if (i%2) cout<<i+1<<' ';else cout<<(n-i+2)<<' ';}int m=n/2;if (n%4==1){cout<<m+1;if (m+1<n) cout<<' ';m++;}for (int i=m+1;i<n;i++){if ((i-m)%2) cout<<n-i<<' ';else cout<<i-1<<' ';}if (m+1<n) cout<<(n-1);cout<<endl;return 0;}