Time Limit: 4000/2000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 25156    Accepted Submission(s): 11234

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

#include
      
       #include
       
        #include
        
         #include
         
          #include
          
           using namespace std;int date[25]= {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20};int ans[25];int n, cnt;int flag;void dfs(int step){    int temp;    if(step==n)       //深搜究竟时注意推断首尾是否符合要求    {        flag=1;        temp = ans[0]+ans[n-1];        if(flag)        {            for(int i=2; i*i<=temp; i++)                if(temp%i==0)                {                    flag=0;                    break;                }        }        if(flag)        {            printf("%d", ans[0]);            for(int i=1; i