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. 题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1016

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace::std;

int n,bj=0;
int map[25];
int a[100];
bool sushu(int n)
{
    for(int i = 2;i<=sqrt(n);i++)
    {
        if(n%i == 0)
            return false;
    }
    return true;
}
void dfs(int k)
{
    if(k == n+1 && sushu(map[1]+map[k-1]))
    {
        for(int i=1;i<=n;i++)
        {
            if(i != 1)
                printf(" ");
            printf("%d",map[i]);
        }
        printf("\n");
        bj = 1;
        return ;
    }
    for(int i = 2;i<=n;i++)
    {
        if(sushu(map[k-1]+i))
        {
            if(a[i] == 0)
            {
                a[i] = 1;
                map[k] = i;
                dfs(k+1);
                a[i] = 0;
                map[k] = 0;
            }
        }
    }
}
int main()
{
    int j=1;
    while(~scanf("%d",&n))
    {
        map[1]=1;
        printf("Case %d:\n",j++);
        dfs(2);
        printf("\n");
    }


}