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.util.*;
import java.io.*;
import java.math.*;

public class Main {
	public static boolean bg = true;

	public static void main(String[] args) throws Exception {
		ST in = new ST();
		//LR in = new LR();
		int n1 = in.ni();
		for (int i = 0; i<n1; i++){
			StringBuilder fin = new StringBuilder();
			for (int j = 0; j<n1/2; j++){
				fin.append((i*n1+j+1)+" ");
			}
			for (int j = 0; j<n1/2; j++){
				fin.append((n1*n1 +1 -(i*n1+j+1))+" ");
			}
			pn(fin);
		}
	}

	private static BigInteger bi(long n1) {
		return BigInteger.valueOf(n1);
	}

	private static void p(Object o1) {
		System.out.print(o1);
	}

	private static void pn(Object o1) {
		System.out.println(o1);
	}

	private static void px(Object... o1) {
		System.out.println(Arrays.deepToString(o1));
	}

	private static void ex() {
		System.exit(0);
	}

	private static class LR {
		BufferedReader k1 = null;

		public LR() throws Exception {
			k1 = new BufferedReader(new InputStreamReader(System.in));
		}

		public String nx() throws Exception {
			return k1.readLine();
		}
	}

	private static class ST {
		StreamTokenizer k1 = null;

		public ST() throws Exception {
			k1 = new StreamTokenizer(System.in);
		}

		public int ni() throws Exception {
			k1.nextToken();
			return (int) k1.nval;
		}

		public double nd() throws Exception {
			k1.nextToken();
			return (double) k1.nval;
		}

		public long nl() throws Exception {
			k1.nextToken();
			return (long) k1.nval;
		}
	}
}