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.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.JSC_2019_qual
{
    class D
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            SetOut(sw);

            Method(args);

            Out.Flush();
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            bool odd = n % 2 == 1;
            int[,] levels = new int[n, n];
            int now = 1;
            bool inMax = false;
            for (int i = 0; i < n; i++)
            {
                int x = odd ? n - i - 2 : n - i - 1;
                if (x >= 0) levels[i, x] = i + 1;
            }
            for(int i = 1; i < n; i++)
            {
                for (int j = 0; j < n; j++)
                {
                    if (j+i >= n) break;

                    if (levels[j, j + i] > 0 && levels[j, j + i] <= now)
                    {
                        inMax = true;
                    }
                    else
                    {
                        levels[j, j + i] = now;
                    }
                }
                if (!inMax) now++;
            }
            if (odd)
            {
                int val = 0;
                for (int i = 0; i < n-1; i++) val = Max(val, levels[0, i]);
                val++;
                for(int i = 0; i < n - 1; i++)
                {
                    levels[i, n - 1] = val;
                }
            }

            for (int i = 0; i < n - 1; i++)
            {
                for (int j = i+1; j < n; j++)
                {
                    Write(levels[i, j]);
                    if (j < n -1) Write(" ");
                }
                WriteLine();
            }
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}