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 Problem Description

A ring is composed of n (even number) circles as shown in diagram. Put natural numbers 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 ≤ 16)

 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. You are to write a program that completes above process.

 Sample Input

6

8

 Sample Ouput

Case 1:

1 4 3 2 5 6

1 6 5 2 3 4

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

代码如下：

#include 
   
    #include 
    
     #include 
     
      #include 
      
       #include 
       
        using namespace std;int n;int pri[35];int vis[20];int ans[20];void judge(){    for (int i=2;i<35;i++)    {        if(!pri[i])        {            for (int j=2*i;j<35;j+=i) pri[j]=1;        }    }}void dfs (int num){    if(num==n)    {        for (int i=0;i
       
      
     
    
   

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