Problem:
Score : 400 points

Problem Statement

A positive integer X is said to be a lunlun number if and only if the following condition is satisfied:

In the base ten representation of X (without leading zeros), for every pair of two adjacent digits, the absolute difference of those digits is at most 1.

For example, 1234, 1, and 334 are lunlun numbers, while none of 31415, 119, or 13579 is.

You are given a positive integer K. Find the K-th smallest lunlun number.

Constraints

1 \leq K \leq 10^5

All values in input are integers.

Input

Input is given from Standard Input in the following format:

K

Output

Print the answer.

Sample Input 1

15

Sample Output 1

23

We will list the 15 smallest lunlun numbers in ascending order:

1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
21,
22,
23.

Thus, the answer is 23.

Sample Input 2

1

Sample Output 2

1

Sample Input 3

13

Sample Output 3

21

Sample Input 4

100000

Sample Output 4

3234566667

Note that the answer may not fit into the 32-bit signed integer type.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

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

namespace ProgrammingContestTemplateByDotNetCore
{
    #region "Input and Output Classes"

    class Scanner : IDisposable
    {
        private readonly Queue<string> _buffer;
        private readonly char[] _sep;
        private readonly TextReader _reader;

        public Scanner(TextReader reader = null, char[] sep = null)
        {
            _buffer = new Queue<string>();
            _sep = sep ?? new[] { ' ' };
            _reader = reader ?? Console.In;
        }

        public Scanner(string path, char[] sep = null)
            : this(new StreamReader(path), sep) { }

        private void CheckBuffer()
        {
            if (_buffer.Any() || _reader.Peek() == -1)
                return;

            string str = string.Empty;
            for (;
                string.IsNullOrWhiteSpace(str);
                str = _reader.ReadLine()) { }

            var values = str.Split(_sep).Where(s => !string.IsNullOrWhiteSpace(s));
            foreach (var item in values)
            {
                _buffer.Enqueue(item);
            }
        }

        public string Next()
        {
            CheckBuffer();
            return _buffer.Dequeue();
        }
        public string[] GetStringArray(int count)
            => Enumerable.Range(0, count)
                .Select(e => Next())
                .ToArray();

        public int NextInt() => int.Parse(Next());
        public int[] GetIntArray(int count)
            => Enumerable.Range(0, count)
                .Select(e => NextInt())
                .ToArray();

        public long NextLong() => long.Parse(Next());
        public long[] GetLongArray(int count)
            => Enumerable.Range(0, count)
                .Select(e => NextLong())
                .ToArray();

        public double NextDouble() => double.Parse(Next());
        public double[] GetDoubleArray(int count)
            => Enumerable.Range(0, count)
                .Select(e => NextDouble())
                .ToArray();

        public decimal NextDecimal() => decimal.Parse(Next());
        public decimal[] GetDecimalArray(int count)
            => Enumerable.Range(0, count)
                .Select(e => NextDecimal())
                .ToArray();

        public BigInteger NextBigInt() => BigInteger.Parse(Next());
        public BigInteger[] GetBigIntArray(int count)
            => Enumerable.Range(0, count)
                .Select(e => NextBigInt())
                .ToArray();

        public T GetT<T>(Func<Scanner, T> func) => func(this);
        public T[] GetTArray<T>(int count, Func<Scanner, T> func)
            => Enumerable.Range(0, count)
                .Select(e => GetT(func))
                .ToArray();

        public bool IsEnd
        {
            get
            {
                CheckBuffer();
                return !_buffer.Any();
            }
        }

        public void Dispose()
        {
            if (!_reader.Equals(Console.In))
                _reader.Dispose();
        }
    }

    class Writer : IDisposable
    {
        private readonly TextWriter _writer;
        private readonly StringBuilder _cache;
        private readonly bool _isReactive;

        public Writer(TextWriter writer = null, bool isReactive = false)
        {
            _writer = writer ?? Console.Out;
            _isReactive = isReactive;
            if (!_isReactive)
                _cache = new StringBuilder();
        }

        public Writer(string path)
            : this(new StreamWriter(path)) { }

        public Writer(bool isReactive)
            : this(null, isReactive) { }

        public void Write(object value)
        {
            if (_isReactive)
            {
                _writer.Write(value);
                _writer.Flush();
            }
            else
            {
                _cache.Append(value);
            }
        }

        public void WriteFormat(string format, params object[] values)
        {
            var value = string.Format(format, values);
            Write(value);
        }

        public void WriteLine(object value = null)
        {
            Write($"{value}{Environment.NewLine}");
        }

        public void WriteLine(string format, params object[] values)
        {
            WriteFormat($"{format}{Environment.NewLine}", values);
        }

        public void Dispose()
        {
            if (!_isReactive)
            {
                _writer.Write(_cache);
                _writer.Flush();
            }
            if (!_writer.Equals(Console.Out))
            {
                _writer.Dispose();
            }
        }
    }

    public static class Extensions
    {
        public static void Set<TKey, TValue>(
            this IDictionary<TKey, TValue> source,
            TKey key, TValue value)
        {
            if (source.ContainsKey(key))
                source[key] = value;
            else
                source.Add(key, value);
        }

        public static void Update<TKey, TValue>(
            this IDictionary<TKey, TValue> source,
            TKey key, Func<TValue, TValue> update)
        {
            if (!source.ContainsKey(key))
                source.Add(key, default(TValue));
            source[key] = update(source[key]);
        }
    }

#endregion

    class MainClass : IDisposable
    {
#region "Template"

        /// <summary> 入力を受け取る </summary>
        private readonly Scanner sc;
        /// <summary> 出力を行う </summary>
        private readonly Writer wr;
        private const string _inputFile = "input.txt";
        private const string _outFile = "output.txt";

        static void Main(string[] args)
        {
            using (new MainClass()) { }
        }

        public MainClass()
        {
            wr = new Writer(_isReactive);
            // TODO: ファイルに出力したい場合はこっち → wr = new Writer(_outFile);

#if DEBUG
            // 手元では、ファイルから入力を受け取る
            sc = new Scanner(_inputFile);
#else

            // 提出時、標準入力から受け取る
            sc = new Scanner();
#endif

            Solve();
        }

        public void Dispose()
        {
            sc?.Dispose();
            wr?.Dispose();
        }

        #endregion

        void Solve()
        {
            int K = sc.NextInt();
            Queue<long> que = new Queue<long>(
                Enumerable.Range(1, 9).Select(x => (long)x));
            for (int i = 0; i < K - 1; i++)
            {
                var cur = que.Dequeue();
                for (int j = -1; j < 2; j++)
                {
                    var nxt = cur % 10 + j;
                    if (nxt < 0 || nxt >= 10)
                        continue;
                    que.Enqueue(cur * 10 + nxt);
                }
            }

            wr.WriteLine(que.Dequeue());
        }

        /// <summary>
        /// TODO: リアクティブ問題か否かを指定してね♪
        /// </summary>
        private const bool _isReactive = false;
    }
}