Problem: Before the start of the football season in Berland a strange magic ritual is held. The most experienced magicians have to find a magic matrix of the size n × n (n is even number). Gods will never allow to start the championship without it. Matrix should contain integers from 0 to n - 1, main diagonal should contain only zeroes and matrix should be symmetric. Moreover, all numbers in each row should be different. Magicians are very tired of the thinking process, so they ask you to write a program to find such matrix.

Input

The first line contains one integer n (2 ≤ n ≤ 1000), n is even.

Output

Output n lines with n numbers each — the required matrix. Separate numbers with spaces. If there are several solutions, output any.

Examples

Input

2


Output

0 1
1 0


Input

4


Output

0 1 3 2
1 0 2 3
3 2 0 1
2 3 1 0

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.UnsupportedEncodingException;
import java.util.StringTokenizer;

public class Main implements Runnable {

    /////////////////////////////////////////////////////////////////
    // Solution

    private void solve() throws Throwable {
        int n = nextInt();
        int[][] a = new int[n][n];
        boolean[][] hor = new boolean[n][n], ver = new boolean[n][n];
        for (int k = 1; k < n; k++) {
            for (int i = 1; i <= k; i++) {
                int j = k - i;
                if (i == j)
                    continue;
                a[i][j] = a[j][i] = k;
                hor[i][k] = hor[j][k] = ver[i][k] = ver[j][k] = true;
            }
        }
        
        for (int i = 0; i < n - 1; i++) {
            for (int j = i + 1; j < n; j++) {
                if (a[i][j] != 0)
                    continue;
                
                for (int k = 1; k < n; k++) {
                    if (!hor[i][k] && !ver[j][k]) {
                        a[i][j] = a[j][i] = k;
                        hor[i][k] = hor[j][k] = ver[i][k] = ver[j][k] = true;
                        break;
                    }
                }
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                pw.print(a[i][j]);
                pw.print(' ');
            }
            pw.println();
        }
    }

    /////////////////////////////////////////////////////////////////
    // Utility functions

    PrintWriter pw;
    BufferedReader in;
    StringTokenizer st;

    void initStreams() throws FileNotFoundException,
            UnsupportedEncodingException {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            System.setIn(new FileInputStream("1"));
        }
        pw = new PrintWriter(System.out);
        in = new BufferedReader(new InputStreamReader(System.in, "ISO-8859-9"));
    }

    String nextString() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    int nextInt() throws NumberFormatException, IOException {
        return Integer.parseInt(nextString());
    }

    double nextDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(nextString());
    }

    long nextLong() throws NumberFormatException, IOException {
        return Long.parseLong(nextString());
    }

    static Throwable sError;

    public static void main(String[] args) throws Throwable {
        Thread t = new Thread(new Main());
        t.start();
        t.join();
        if (sError != null)
            throw sError;
    }

    public void run() {
        try {
            initStreams();
            solve();
        } catch (Throwable e) {
            sError = e;
        } finally {
            if (pw != null)
                pw.close();
        }
    }

}