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

很經(jīng)典的深搜，啟發(fā)
1，預(yù)處理非常重要，
（1），先求出所有的prime數(shù)最大 16+16，bool isprime[32],
（2）由于已經(jīng)給出范圍，我們可以先求出1-19的每個(gè)數(shù)下一個(gè)可能的取值，例如15，下一個(gè)可以取2,4,------兩重for循環(huán)，可以避免搜索時(shí)重復(fù)判斷。
2，用一個(gè)數(shù)組記錄使輸出的有序，op[n]與dfs(int begin,int n)中n對(duì)應(yīng)
 if( bp[t] )
       {
        op[o] = t ;
        o ++ ;
        bp[t] = false ; 
        dfs( t , n );//
        o -- ;
        bp[t] = true ;
       }