Problem: Gerald has n younger brothers and their number happens to be even. One day he bought n2 candy bags. One bag has one candy, one bag has two candies, one bag has three candies and so on. In fact, for each integer k from 1 to n2 he has exactly one bag with k candies. 

Help him give n bags of candies to each brother so that all brothers got the same number of candies.

Input

The single line contains a single integer n (n is even, 2 ≤ n ≤ 100) — the number of Gerald's brothers.

Output

Let's assume that Gerald indexes his brothers with numbers from 1 to n. You need to print n lines, on the i-th line print n integers — the numbers of candies in the bags for the i-th brother. Naturally, all these numbers should be distinct and be within limits from 1 to n2. You can print the numbers in the lines in any order. 

It is guaranteed that the solution exists at the given limits.

Examples

Input

2


Output

1 4
2 3

Note

The sample shows Gerald's actions if he has two brothers. In this case, his bags contain 1, 2, 3 and 4 candies. He can give the bags with 1 and 4 candies to one brother and the bags with 2 and 3 to the other brother.

Solution (in JAVA):

Solution:


import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;
import java.lang.*;

public class P334A {
    //static long m=1000000007;
    static BigInteger ways(int N,  int K) {
        BigInteger ret = BigInteger.ONE;
        for(int i=N;i>=N-K+1;i--)
        {
             ret = ret.multiply(BigInteger.valueOf(i));
            
        }
        for (int j = 1; j<=K; j++) {
            ret = ret.divide(BigInteger.valueOf(j));
        }
       
            ret=ret.mod(BigInteger.valueOf(1000000007));
        
        return ret;
    }
    public static int prime(int n)
    {
        int f=1;
        if(n==1)
            return 0;
        for(int i=2;i<=(Math.sqrt(n));)
        {
            if(n%i==0)
            {
                f=0;
                break;
            }
            if(i==2)
                i++;
            else
                i+=2;
        }
        if(f==1)
            return 1;
        else 
            return 0;
    }
/*public static long gcd(long x,long y)
{
    if(x%y==0)
        return y;
    else return gcd(y,x%y);
}*/
    public static BigInteger fact(int n)
    {
        BigInteger f=BigInteger.ONE;
        for(int i=1;i<=n;i++)
        {
            f=f.multiply(BigInteger.valueOf(i));
        }
        //f=f.mod(BigInteger.valueOf(m));
        return f;
    }
public static int gcd(int x,int y)
{
    if(x%y==0)
        return y;
    else return gcd(y,x%y);
}
public static int max(int a,int b)
{
    if(a>b)
        return a;
    else
        return b;
}
public static int min(int a,int b)
{
    if(a>b)
        return b;
    else 
        return a;
}



    public static void main(String[] args) throws Exception{
        
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder("");
        //int t=Integer.parseInt(br.readLine());
    //  while(t-->0)
        //{
        //int n=Integer.parseInt(br.readLine());
        //long n=Long.parseLong(br.readLine());
        //String l[]=br.readLine().split(" ");
        //int m=Integer.parseInt(l[0]);
        //int k=Integer.parseInt(l[1]);
        //l=br.readLine().split(" ");
        //long m=Long.parseLong(l[0]);
        //long n=Long.parseLong(l[1]);
        //char ch=a.charAt();
    //  char c[]=new char[n];
        //String l[]=br.readLine().split(" ");
        //l=br.readLine().split(" ");
        /*int a[]=new int[n];
        for(int i=0;i<n;i++)
        {
            a[i]=Integer.parseInt(l[i]);
        }*/
        /*long a[]=new long[n];
        for(int i=0;i<n;i++)
        {
            a[i]=Long.parseLong(l[i]);
        }*/
        /*int a[][]=new int[n][n];
        for(int i=0;i<n;i++)
        {
        l=br.readLine().split(" ");
            for(int j=0;j<n;j++)
            {
                a[i][j]=Long.parseLong(l[j]);
            }
        }*/
        
        //  String a=br.readLine();
        
        // char a[]=c.toCharArray();
        //char ch=l[0].charAt(0);
        
        //HashMap<Integer,Integer>hm=new HashMap<Integer,Integer>();
        //HashMap<Integer,String>hm=new HashMap<Integer,String>();
        //HashMap<Integer,Long>hm=new HashMap<Integer,Long>();
        //hm.put(1,1);
        //HashSet<Integer>hs=new HashSet<Integer>();
        //HashSet<Long>hs=new HashSet<Long>();
        //HashSet<String>hs=new HashSet<String>();
        //hs.add(x);
        //Stack<Integer>s=new Stack<Integer>();
        //s.push(x);
        //s.pop(x);
        //Queue<Integer>q=new LinkedList<Integer>();
        //q.add(x);
        //q.remove(x);
        //ArrayList<Integer>ar=new ArrayList<Integer>();
        //long x=Long.parseLong(l[0]);
        
        //int min=100000000;
    
        //long c1=(long)Math.ceil(n/(double)a);
        //Arrays.sort(a);
          // int f1[]=new int[26];
           //int f2[]=new int[26];
        /*for(int i=0;i<n;i++)
        {
        int x=a.charAt(0);
            f1[x-97]++;
        }*/
        /*for(int i=0;i<n;i++)
        {
            
        }*/
        /*for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                
            }
        }*/
        /*while(q--)
          {
                l=br.readLine().split(" ");
                int n=Integer.parseInt(l[0]);
                int k=Integer.parseInt(l[1]);
          }
         */
        /*if(f==1)
            System.out.println("Yes");
        else
            System.out.println("No");*/
        //System.out.print("");
        //sb.append("");
        //sb.append("").append("\n");
        
        int n=Integer.parseInt(br.readLine());
        int e=0;
        int f=0;
        for(int i=1;i<=n;i++)
           {
            for(int j=1+f,c=1;c<=n/2;j++,c++)
            {
                System.out.print((j)+" "+(n*n-e)+" ");
                e++;
            }
            f+=n/2;
            System.out.println();
           }
        
        //}
    }
}