Problem:
Score: 600 points

Problem Statement

AtCoder's head office consists of N rooms numbered 1 to N. For any two rooms, there is a direct passage connecting these rooms.

For security reasons, Takahashi the president asked you to set a level for every passage, which is a positive integer and must satisfy the following condition:

For each room i\ (1 \leq i \leq N), if we leave Room i, pass through some passages whose levels are all equal and get back to Room i, the number of times we pass through a passage is always even.

Your task is to set levels to the passages so that the highest level of a passage is minimized.

Constraints

N is an integer between 2 and 500 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print one way to set levels to the passages so that the objective is achieved, as follows:

a_{1,2} a_{1,3} ... a_{1,N}
a_{2,3} ... a_{2,N}
.
.
.
a_{N-1,N}

Here a_{i,j} is the level of the passage connecting Room i and Room j.

If there are multiple solutions, any of them will be accepted.

Sample Input 1

3

Sample Output 1

1 2
1

The following image describes this output:

For example, if we leave Room 2, traverse the path 2 \to 3 \to 2 \to 3 \to 2 \to 1 \to 2 while only passing passages of level 1 and get back to Room 2, we pass through a passage six times.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.math.*;
import java.io.*;

class Main
{
	
	public static void main(String[] args)
	
	{
		new Main().run();
	}
	
	void run(){
		Scanner sc=new Scanner(System.in);
		int N=sc.nextInt();
		int sz=0;
		while((1L<<sz)<=N)++sz;
		int[][] a=new int[N][N];
		for(int i=0;i<N;++i)for(int j=0;j<N;++j)a[i][j]=-1;
		for(int shift=0;shift<sz;++shift){
			for(int i=0;i<N;++i){
				for(int j=0;j<N;++j){
					if((((i>>shift)%2)^((j>>shift))%2)==0)continue;
					if(a[i][j]!=-1)continue;
					a[i][j]=shift+1;
					a[j][i]=shift+1;
				}
			}
		}
		for(int i=N-1;i>=0;--i){
			for(int j=0;j<i;++j){
				System.out.print(a[i][j]+(j==i-1?"\n":" "));
			}
		}
		
	}
	
	
	void tr(Object...objects){
		System.out.println(Arrays.deepToString(objects));
	}
}