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.

n (0 < n < 20).

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.

6
8

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

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<pre name="code" class="html">#include<stdio.h>
#include<string.h>
bool prim[44],visit[22]; 
int b[22];
int n;
void f(){
	prim[2]=prim[3]=prim[5]=prim[7]=prim[11]=prim[13]=prim[17]=prim[19]=1;
	prim[23]=prim[29]=prim[31]=prim[37]=prim[41]=1;
}
void dfs(int op){
	if(op==n){
		if(!prim[b[op-1]+b[0]])	return;
		printf("%d",b[0]);
		for(int i=1;i<n;++i)
		   printf(" %d",b[i]);
		printf("\n");
		return;
	}
	for(int i=2;i<=n;++i){
		if(!visit[i]){	    
			if(prim[b[op-1]+i]){
				b[op]=i;visit[i]=1;dfs(op+1);
			} 
			visit[i]=0;
	   }
	}
}
int main(){	
	f();
	int ncas=0;
	while(~scanf("%d",&n)){
		printf("Case %d:\n",++ncas);
		memset(visit,0,sizeof(visit));
		b[0]=1;dfs(1);
		printf("\n");
	}
	return 0;
}