Problem: There are N persons, conveniently numbered 1 through N. They will take 3y3s Challenge for N-1 seconds.

During the challenge, each person must look at each of the N-1 other persons for 1 seconds, in some order.

If any two persons look at each other during the challenge, the challenge ends in failure.

Find the order in which each person looks at each of the N-1 other persons, to be successful in the challenge.

Constraints

* 2 \leq N \leq 100

Input

The input is given from Standard Input in the following format:


N


Output

If there exists no way to be successful in the challenge, print `-1`.

If there exists a way to be successful in the challenge, print any such way in the following format:


A_{1,1} A_{1,2} ... A_{1, N-1}
A_{2,1} A_{2,2} ... A_{2, N-1}
:
A_{N,1} A_{N,2} ... A_{N, N-1}


where A_{i, j} is the index of the person that the person numbered i looks at during the j-th second.

Judging

The output is considered correct only if all of the following conditions are satisfied:

* 1 \leq A_{i,j} \leq N
* For each i, A_{i,1}, A_{i,2}, ... , A_{i, N-1} are pairwise distinct.
* Let X = A_{i, j}, then A_{X, j} \neq i always holds.

Examples

Input

7


Output

2 3 4 5 6 7
5 3 1 6 4 7
2 7 4 1 5 6
2 1 7 5 3 6
1 4 3 7 6 2
2 5 7 3 4 1
2 6 1 4 5 3


Input

2


Output

-1

Solution (in JAVA):

Solution:
import java.io.IOException; 
import java.io.InputStream; 
import java.io.PrintWriter; 
import java.util.*; 
 

class Main{ 

	static void solve(){
		int n=ni();
		int[][] A = new int[n][n-1];
		if(n==2){
			out.println(-1);return;
		}
		if(n%2==1){
			for(int i=0;i<n;++i){
				for(int j=1;j<=n-1;++j)A[i][j-1]=(i+j)%n;
			}
		}else{
			for(int i=0;i<n;++i)A[i][0]=(i+1)%n;
			for(int i=0;i<n-1;++i){
				for(int j=2;j<=n-2;++j)A[i][j-1] = (i+j)%(n-1);
			}
			for(int j=1;j<n-1;++j)A[n-1][j]=j;
			for(int i=0;i<n-2;++i)A[i][n-2]=n-1;
		}
		for(int i=0;i<n;++i){
			for(int j=0;j<n-1;++j)out.print((A[i][j]+1)+" ");
			out.println();
		}
 
	} 
 
 
 
 
	 public static void main(String[] args){ 
		 solve(); 
		 out.flush(); 
	 } 
	 private static InputStream in = System.in; 
	 private static PrintWriter out = new PrintWriter(System.out); 
 
	 static boolean inrange(int y, int x, int h, int w){ 
		 return y>=0 && y<h && x>=0 && x<w; 
	 } 
	 @SuppressWarnings("unchecked") 
	 static<T extends Comparable> int lower_bound(List<T> list, T key){ 
		 int lower=-1;int upper=list.size(); 
		 while(upper - lower>1){ 
		 int center =(upper+lower)/2; 
		 if(list.get(center).compareTo(key)>=0)upper=center; 
		 else lower=center; 
		 } 
		 return upper; 
	 } 
	 @SuppressWarnings("unchecked") 
	 static <T extends Comparable> int upper_bound(List<T> list, T key){ 
		 int lower=-1;int upper=list.size(); 
		 while(upper-lower >1){ 
		 int center=(upper+lower)/2; 
		 if(list.get(center).compareTo(key)>0)upper=center; 
		 else lower=center; 
		 } 
		 return upper; 
	 } 
	 @SuppressWarnings("unchecked") 
	 static <T extends Comparable> boolean next_permutation(List<T> list){ 
		 int lastIndex = list.size()-2; 
		 while(lastIndex>=0 && list.get(lastIndex).compareTo(list.get(lastIndex+1))>=0)--lastIndex; 
		 if(lastIndex<0)return false; 
		 int swapIndex = list.size()-1; 
		 while(list.get(lastIndex).compareTo(list.get(swapIndex))>=0)swapIndex--; 
		 T tmp = list.get(lastIndex); 
		 list.set(lastIndex++, list.get(swapIndex)); 
		 list.set(swapIndex, tmp); 
		 swapIndex = list.size()-1; 
		 while(lastIndex<swapIndex){ 
		 tmp = list.get(lastIndex); 
		 list.set(lastIndex, list.get(swapIndex)); 
		 list.set(swapIndex, tmp); 
		 ++lastIndex;--swapIndex; 
		 } 
		 return true; 
	 } 
	 private static final byte[] buffer = new byte[1<<15]; 
	 private static int ptr = 0; 
	 private static int buflen = 0; 
	 private static boolean hasNextByte(){ 
		 if(ptr<buflen)return true; 
		 ptr = 0; 
		 try{ 
			 buflen = in.read(buffer); 
		 } catch (IOException e){ 
			 e.printStackTrace(); 
		 } 
		 return buflen>0; 
	 } 
	 private static int readByte(){ if(hasNextByte()) return buffer[ptr++]; else return -1;} 
	 private static boolean isSpaceChar(int c){ return !(33<=c && c<=126);} 
	 private static int skip(){int res; while((res=readByte())!=-1 && isSpaceChar(res)); return res;} 
 
	 private static double nd(){ return Double.parseDouble(ns()); } 
	 private static char nc(){ return (char)skip(); } 
	 private static String ns(){ 
		 StringBuilder sb = new StringBuilder(); 
		 for(int b=skip();!isSpaceChar(b);b=readByte())sb.append((char)b); 
		 return sb.toString(); 
	 } 
	 private static int[] nia(int n){ 
		 int[] res = new int[n]; 
		 for(int i=0;i<n;++i)res[i]=ni(); 
		 return res; 
	 } 
	 private static long[] nla(int n){ 
		 long[] res = new long[n]; 
		 for(int i=0;i<n;++i)res[i]=nl(); 
		 return res; 
	 } 
	 private static int ni(){ 
		 int res=0,b; 
		 boolean minus=false; 
		 while((b=readByte())!=-1 && !((b>='0'&&b<='9') || b=='-')); 
		 if(b=='-'){ 
			 minus=true; 
			 b=readByte(); 
		 } 
		 for(;'0'<=b&&b<='9';b=readByte())res=res*10+(b-'0'); 
		 return minus ? -res:res; 
	 } 
	 private static long nl(){ 
		 long res=0,b; 
		 boolean minus=false; 
		 while((b=readByte())!=-1 && !((b>='0'&&b<='9') || b=='-')); 
		 if(b=='-'){ 
			 minus=true; 
			 b=readByte(); 
		 } 
		 for(;'0'<=b&&b<='9';b=readByte())res=res*10+(b-'0'); 
		 return minus ? -res:res; 
	} 
}