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.*;
import java.util.*;

public class CF {

	void realSolve() {
		int n = in.nextInt();
		int[][] a = new int[n][n];
		for (int i = 0; i < n - 1; i++)
			for (int j = 0; j < n - 1; j++)
				a[i][j] = 1 + (i + j) % (n - 1);
		for (int i = 0; i < n; i++) {
			a[i][i] = 0;
			boolean[] used = new boolean[n];
			for (int j = 0; j < n - 1; j++)
				used[a[i][j]] = true;
			for (int j = 0; j < n; j++)
				if (!used[j])
					a[i][n - 1] = a[n - 1][i] = j;
		}
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				out.print(a[i][j] + " ");
			}
			out.println();
		}
	}

	private class InputReader {
		StringTokenizer st;
		BufferedReader br;

		public InputReader(File f) {
			try {
				br = new BufferedReader(new FileReader(f));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
		}

		public InputReader(InputStream f) {
			br = new BufferedReader(new InputStreamReader(f));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				String s;
				try {
					s = br.readLine();
				} catch (IOException e) {
					return null;
				}
				if (s == null)
					return null;
				st = new StringTokenizer(s);
			}
			return st.nextToken();
		}

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

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

		boolean hasMoreElements() {
			while (st == null || !st.hasMoreElements()) {
				String s;
				try {
					s = br.readLine();
				} catch (IOException e) {
					return false;
				}
				st = new StringTokenizer(s);
			}
			return st.hasMoreElements();
		}

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

	InputReader in;
	PrintWriter out;

	void solve() {
		in = new InputReader(new File("object.in"));
		try {
			out = new PrintWriter(new File("object.out"));
		} catch (FileNotFoundException e) {
			e.printStackTrace();
		}

		realSolve();

		out.close();
	}

	void solveIO() {
		in = new InputReader(System.in);
		out = new PrintWriter(System.out);

		realSolve();

		out.close();

	}

	public static void main(String[] args) {
		new CF().solveIO();
	}
}