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: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Reflection;
using System.Text;

namespace A
{
    class StartingPoint
    {
        static void Main(string[] args)
        {
            if (args?.Any() == true)
            {
                var assembly = Assembly.GetEntryAssembly();
                var resourceName = "AtCoderCSharp.In.txt";
                var stream = assembly.GetManifestResourceStream(resourceName);
                var streamReader = new StreamReader(stream, Encoding.UTF8);
                var str = streamReader.ReadToEnd();
                var textReader = new StringReader(str);
                Console.SetIn(textReader);
            }

            try
            {
                foreach (var s in new Program().Solve())
                {
                    Console.WriteLine(s);
                }
            }
            catch (Exception e)
            {
                Console.WriteLine(e);
                if (args?.Any() != true)
                    throw e;
            }

            if (args?.Any() == true)
                Console.ReadKey();
        }
    }

    class Program
    {
        public List<int> ScanInts(int count) => Enumerable.Range(0, count).Select(_ => ScanInt).ToList();
        public List<int> ScanInts(long count) => ScanInts((int)count);
        public List<long> ScanLongs(int count) => Enumerable.Range(0, count).Select(_ => Scan).ToList();
        public List<long> ScanLongs(long count) => ScanLongs((int)count);
        public int ScanInt => int.Parse(Str);
        public long Scan => long.Parse(Str);
        public double ScanDouble => (double)Scan;

        StringBuilder sb = new StringBuilder();

        public string Str => ScanStr();
        public string ScanStr()
        {
            sb.Clear();

            int r = 0;
            bool? b = null;
            do
            {
                r = Console.Read();
                b = IsBreak(r);
            } while (b == true);

            if (b == null)
                throw new Exception("input error: unexpected end of stream");

            do
            {
                sb.Append((char)r);
                r = Console.Read();
                b = IsBreak(r);
            } while (b == false);

            return sb.ToString();
        }

        bool? IsBreak(int c)
        {
            switch (c)
            {
                case -1:
                    return null;
                case (int)' ':
                case (int)'\n':
                case (int)'\r':
                    return true;
                default:
                    return false;
            }
        }

        public IEnumerable<int> Loop(int count) => Enumerable.Range(0, count);
        public IEnumerable<int> Loop(int from, int to) => Enumerable.Range(from, to - from + 1);

        public IEnumerable<long> Loop(long count) => Loop(0, count - 1);
        public IEnumerable<long> Loop(long from, long to)
        {
            for (long i = from; i <= to; i++)
                yield return i;
        }

        public string YesNo(bool isYes) => isYes ? "Yes" : "No";

        public HashSet<T> ToHashSet<T>(IEnumerable<T> ts) => new HashSet<T>(ts);

        struct Mint
        {
            public static long Divider { set { divider = value; } }
            private static long divider = 1000000007;
            public static void Set998244353() { divider = 998244353; }

            public long Value { get; }

            public Mint(long value)
            {
                this.Value = value % divider;
            }

            public static Mint operator +(Mint a, Mint b) => new Mint((a.Value + b.Value) % divider);

            public static Mint operator -(Mint a, Mint b)
            {
                var t = (a.Value - b.Value) % divider;
                if (t < 0)
                    t += divider;
                return new Mint(t);
            }

            public static Mint operator *(Mint a, Mint b) => new Mint((a.Value * b.Value) % divider);

            public static Mint operator /(Mint a, Mint b) => new Mint((a.Value * InvImpl(b.Value)) % divider);

            public Mint Pow(long p) => new Mint(PowImpl(Value, p));
            private static long PowImpl(long a, long p)
            {
                if (p == 0)
                    return 1L;

                if (p == 1)
                    return a;

                var halfP = p / 2;
                var halfPowered = PowImpl(a, halfP);
                var powered = halfPowered * halfPowered % divider;
                return p % 2 == 0 ? powered : powered * a % divider;
            }

            public static Mint Inv(long a) => new Mint(InvImpl(a));
            private static readonly Dictionary<long, long> invCache = new Dictionary<long, long>();
            private static long InvImpl(long a)
            {
                long cache = 0L;
                if (invCache.TryGetValue(a, out cache))
                    return cache;

                var result = PowImpl(a, divider - 2);
                invCache.Add(a, result);
                return result;
            }

            public static Mint Fac(long a) => new Mint(FacImpl(a));
            private static readonly List<long> facCache = new List<long>() { 1L };
            private static long FacImpl(long a)
            {
                if (a >= divider)
                    return 0;

                if (a < facCache.Count)
                    return facCache[(int)a];

                var val = facCache.Last();
                var start = facCache.Count;
                for (int i = start; i <= a; i++)
                {
                    val = (val * i) % divider;
                    facCache.Add(val);
                }

                return val;
            }

            public static Mint Perm(long n, long r) => new Mint(PermImpl(n, r));
            private static long PermImpl(long n, long r)
            {
                if (n < r)
                    return 0L;

                if (r <= 0)
                    return 1L;

                var nn = FacImpl(n);
                var nr = FacImpl(n - r);
                return (nn * InvImpl(nr)) % divider;
            }

            public static Mint Comb(long n, long r) => new Mint(CombImpl(n, r));
            private static long CombImpl(long n, long r)
            {
                if (n < r)
                    return 0L;

                if (n == r)
                    return 1L;

                var nn = FacImpl(n);
                var nr = FacImpl(n - r);
                var rr = FacImpl(r);

                var nndnr = (nn * InvImpl(nr)) % divider;
                return (nndnr * InvImpl(rr)) % divider;
            }
        }

        public IEnumerable<string> Solve()
        {
            var n = Scan;

            var memo = new Dictionary<int, Dictionary<int, bool>>();
            var lvs = new List<List<int>>();
            foreach (int i in Loop(n))
            {
                memo.Add(i, new Dictionary<int, bool>());

                var l = new List<int>();
                foreach (var j in Loop(n))
                {
                    l.Add(0);
                }
                lvs.Add(l);
            }



            foreach (int i in Loop(n))
            {
                var reg = new HashSet<int>();
                var lv = 1;

                while (reg.Count < i)
                {
                    var ts = memo.Where(x => x.Key < i && !reg.Contains(x.Key) & x.Value.ContainsKey(lv) && x.Value[lv]).Count();
                    var fs = memo.Where(x => x.Key < i && !reg.Contains(x.Key) & x.Value.ContainsKey(lv) && !x.Value[lv]).Count();
                    bool b = ts < fs;

                    var ads = memo.Where(x =>
                        x.Key < i &&
                        !reg.Contains(x.Key) &&
                        (x.Value.ContainsKey(lv) == false || x.Value[lv] != b))
                        .Select(x => x.Key)
                        .ToArray();

                    memo[i].Add(lv, b);

                    foreach (var a in ads)
                    {
                        lvs[i][a] = lv;
                        lvs[a][i] = lv;

                        if (memo[a].ContainsKey(lv))
                            memo[a][lv] = !b;
                        else
                            memo[a].Add(lv, !b);
                        reg.Add(a);
                    }

                    lv++;
                }
            }



            foreach (var i in Loop(n))
            {
                yield return string.Join(" ", lvs[(int)i].Skip((int)i + 1).Select(x => x.ToString()));
            }
        }
    }
}