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.*;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(in, out);
        out.close();
    }
}


class TaskA {

    void solve(InputReader in, OutputWriter out) {
        int n = in.nextInt();
        List<Integer> tab[] = new List[n];
        for(int k=0;k<n;k++) {
            tab[k] = new ArrayList<>();
        }
        int i = 1;
        int j = n*n;
        int number = 0;
        while(i < j) {
            tab[number].add(i);
            tab[number].add(j);
            i++;
            j--;
            number++;
            if(number == n) number = 0;
        }
        for(int k=0;k<n;k++) {
            for(int val : tab[k]) {
                out.print(val + " ");
            }
            out.printLine();
        }
    }


}
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 boolean hasNext() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                String line = reader.readLine();
                if ( line == null ) {
                    return false;
                }
                tokenizer = new StringTokenizer(line);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return true;
    }
    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong() {
        return Long.parseLong(next());
    }
    public double nextDouble() { return Double.parseDouble(next());}
}
class OutputWriter {
    private final PrintWriter writer;
    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }
    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }
    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if ( i != 0 ) {
                writer.print(' ');
            }
            writer.print(objects[i]);
        }
    }
    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }
    public void close() {
        writer.close();
    }
}