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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		int n = int.Parse(Console.ReadLine());
    int answer = 1;
    int ansMemo = 2;
    int[][] answers = new int[n][];
    int[] pairs = new int[n];
    for(int i = 0; i < n; i++)
    {
      answers[i] = new int[n];
    }
    while(true)
    {
      if(ansMemo >= n) break;
      ansMemo *= 2;
      answer++;
    }
    //Console.WriteLine(2);
    for(int i = 0; i < n; i++)
    {
      if(i % 2 == 1) pairs[i] = 1;
    }
    

    for(int i = 0; i < answer; i++)
    {
      for(int j = 0; j < n; j++)
      {
        for(int k = j+1; k < n; k++)
        {
          //Console.WriteLine(k);
          if(pairs[j] + pairs[k] == 1 && answers[j][k] == 0)
          {
            answers[j][k] = i+1;
            //Console.WriteLine(i+" "+j+" "+k);
          }
        }
      }

      for(int j = 0; j < n; j++)
      {
        if(j%Math.Pow(2,(i+2)) <= Math.Pow(2,i+1)-1)
        {
          pairs[j] = 1-pairs[j];
        }
      }
    }
    //Console.WriteLine("aa");

    
    int[][] answersSub = new int[n-1][];
    for(int i = 0; i < n-1; i++)
    {
      answersSub[i] = new int[n-1-i];
      for(int j = 0; j < n-1-i; j++)
      {
        answersSub[i][j] = answers[i][j];
      }
    }
    //Console.WriteLine("aaa");
    
    for(int i = 0; i < n-1; i++)
    {
      Console.WriteLine(string.Join(" ", answersSub[i]));
    }
	}
}