Prime Ring Problem

A ring is compose of n circles as shown in diagram. Put natural number 1, 2, ..., n into each circle separately, and the sum of numbers in two adjacent circles should be a prime.

Note: the number of first circle should always be 1.


Input

n (0 < n < 20).

Output

The output format is shown as sample below. Each row represents a series of circle numbers in the ring beginning from 1 clockwisely and anticlockwisely. The order of numbers must satisfy the above requirements. Print solutions in lexicographical order.

You are to write a program that completes above process.

Print a blank line after each case.

Sample Input

6
8

Sample Output

Case 1:1 4 3 2 5 61 6 5 2 3 4Case 2:1 2 3 8 5 6 7 41 2 5 8 3 4 7 61 4 7 6 5 8 3 21 6 7 4 3 8 5 2

简单的dfs，每次检查相邻两个是否满足，满足条件后输出

#include<iostream>
#include <cstring>
#include<cmath>
using namespace std;
int n,a[21],b[21],num=0;
int check(int i,int j)
{
    int k=i+j,n;
    for (n=2;n<=sqrt(k);n++)
        if ((k%n)==0) return 0;
    return 1;
}
void dfs(int k)
{
    int i,j;
    for (i=1;i<=n;i++)
        if ((check(a[k-1],i))&&(b[i]==0))
        {
            a[k]=i;
            b[i]=1;
            if ((k+1)<=n)
                dfs(k+1);
            if ((a[n]!=0)&&(check(a[n],a[1])))
            {
                cout<<a[1];
                for(j=2;j<=n;j++) cout<<" "<<a[j];
                cout<<endl;
            }
            a[k]=0;
            b[i]=0;
        }

}
int main()
{
    while(cin>>n)
    {
        num++;
        memset(a,0,sizeof(a));
        memset(b,0,sizeof(b));
        a[1]=1;b[1]=1;
        if (n>1)
        {
            cout<<"Case "<<num<<":"<<endl;
            dfs(2);
        }
        else
        {
            cout<<"Case "<<num<<":"<<endl;
            cout<<a[1]<<endl;
        }
        cout<<endl;
    }
}