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.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
import java.util.Arrays;

public class Solution {
//    ----------------------------------------------------------------------------

    public static void main(String[] args) throws IOException {

        //IF INPUT-OUTPUT is via files. uncomment use the below 3 lines of code. comment out the next 4
        //     File file = new File("input.txt"); // here input.txt and output.txt being the file names 
        //   InputReader in = new InputReader(new FileInputStream(file));
        //    PrintWriter out = new PrintWriter(new FileOutputStream("output.txt"));
        //ELSE 
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }

    static class Task {

        static final int mod = 1000000007;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int start = 1;
            int m = n * n;
            for (int k = 0; k < n; k++) {
                for (int i = 0; i < n / 2; i++) {
                    out.print(start + " ");
                    start++;
                }
                for (int i = 0; i < n / 2; i++) {
                    out.print(m + " ");
                    m--;
                }
                out.println();

            }
        }

    }

//    ----------------------------------------------------------------------------
    // MAIN - INPUT - OUTPUT 
    static class InputReader {

        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public Double nextDouble() {
            return Double.parseDouble(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int[] nextIntArray(int arraySize) {
            int array[] = new int[arraySize];

            for (int i = 0; i < arraySize; i++) {
                array[i] = nextInt();
            }

            return array;
        }
//need to review this again
//        public char[][] nextMatrix(int row, int col) {
//
//            char[][] m = new char[row][col];
//            
//            return m;
//        }

    }
}