Prime Ring Problem

Problem Description 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 6
1 6 5 2 3 4

Case 2:
1 2 3 8 5 6 7 4
1 2 5 8 3 4 7 6
1 4 7 6 5 8 3 2
1 6 7 4 3 8 5 2

Source Asia 1996, Shanghai (Mainland China)

題外話：

省賽的失利也不能阻擋我前進的腳步，經歷過就是一件好事，正如老師所說的，結果誰也沒法預測，但這個過程是實實在在的，自己可以在其中收獲很多東西。人生中需要經歷很多事情，有些事情，只有親身經歷過才會懂。

解題思路：

素數環要求任何相鄰的兩個數相加的和必須為素數。用DFs，從一年前期末考試兩個多小時也沒做出來這個題到現在的一次Ac，自己真的進步了。

代碼：

#include 
#include 
#include 
#include 
using namespace std;
const int maxn=25;
bool visit[maxn];
int num[maxn];
int n;

bool prime(int n)
{
    if(n==1)
        return false;
    if(n==2)
        return true;
    if(n%2==0)
        return false;
    for(int i=3;i<=(int)sqrt(n);i+=2)
        if(n%i==0)
        return false;
    return true;
}

void dfs(int step)
{
    if(step>n&&prime(num[n]+num[1]))
    {
        for(int i=1;i<=n-1;i++)
            cout<>n)
    {
        cout<<"Case "<