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.*;

public class Main {
	
	public static void main(String[] args) throws IOException {
		input = new BufferedReader(new InputStreamReader(System.in));
//		input = new BufferedReader(new FileReader("input.txt"));

		output = new PrintWriter(System.out);
		tokenizer = new StreamTokenizer(input);
		
			int n = nextInt() - 1;
			int[][] array = new int[n + 1][n + 1];
			for(int i = 0; i < n; i++)
				for(int j = 0; j < n; j++)
					array[i][j] = 1 + (i + j) % n;
			
			for(int i = 0; i < n; i++) {
				array[i][n] = array[n][i] = array[i][i];
				array[i][i] = 0;
			}
			
			for(int i = 0; i <= n; i++) {
				for(int j = 0; j <= n; j++) { 
					output.print(array[i][j]);
					output.print(' ');
				}
				
				output.println();
			}
			
		input.close();
		output.close();
	}
	
	static BufferedReader input;
	static PrintWriter output;
	static StreamTokenizer tokenizer;
	
	static int nextInt() throws IOException {
		tokenizer.nextToken();
		return (int)tokenizer.nval;
	}
	
	static double nextDouble() throws IOException {
		tokenizer.nextToken();
		return tokenizer.nval;
	}
	
	static String nextWord() throws IOException {
		tokenizer.nextToken();
		return tokenizer.sval;
	}
	
	static String nextLine() throws IOException {
		return input.readLine();
	}
}