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.

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.

#include<iostream>
using namespace std;

int N;
int PrimeCycle[20];
int visited[20];
bool IsPrime(int num)
{
    for (int i = 2; i*i <= num; i++)
    {
        if (num%i == 0)
            return false;
    }
    return true;

}
void dfs(int current,int size)
{
    if (size == N+1)
    {
        if (IsPrime(current + 1))
        {
            for (int i = 1; i < N; i++)
            {
                cout << PrimeCycle[i] << " ";
            }
            cout << PrimeCycle[N];
            cout << endl;
        }
        return;
    }
    else
    {
        for (int i = 2; i <= N; i++)
        {
            
            if (visited[i]==0 && IsPrime(current + i))
            {
                PrimeCycle[size] = i;
                visited[i] = 1;
                dfs(i,size+1);
                visited[i] = 0;
            }
        }
    }
}
int main()
{
    int Case = 1;
    PrimeCycle[1] = 1;
    while (cin >> N)
    {
        cout << "Case " << Case++ << ":" << endl;
        dfs(1, 2);
        cout << endl;
    }
    
    
    return 0;

}