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.Generic;
using System.IO;
using System.Linq;
using static ABC161D.Input;

namespace ABC161D
{
    static class Input
    {
        private static Func<string, T[]> Cast<T>() => _ => _.Split(' ').Select(Convert<T>()).ToArray();

        private static Func<string, T> Convert<T>()
        {
            Type t = typeof(T);
            if (t == typeof(string)) return _ => (T) (object) _;
            if (t == typeof(int)) return _ => (T) (object) int.Parse(_);
            if (t == typeof(long)) return _ => (T) (object) long.Parse(_);
            if (t == typeof(double)) return _ => (T) (object) double.Parse(_);
            if (t == typeof(string[])) return _ => (T) (object) _.Split(' ');
            if (t == typeof(int[])) return _ => (T) (object) Cast<int>()(_);
            if (t == typeof(long[])) return _ => (T) (object) Cast<long>()(_);
            if (t == typeof(double[])) return _ => (T) (object) Cast<double>()(_);

            throw new NotSupportedException(t + "is not supported.");
        }

        private static T Convert<T>(string s) => Convert<T>()(s);

        private static string String() => Console.ReadLine();

        private static string[] String(long rowNumber) => new bool[rowNumber].Select(_ => String()).ToArray();

        public static void Cin<T>(out T a) => a = Convert<T>(String());

        public static void Cin<T1, T2>(out T1 a1, out T2 a2)
        {
            var v = String().Split(' ');
            set(v[0], out a1);
            set(v[1], out a2);
        }

        public static void Cin<T1, T2, T3>(out T1 a1, out T2 a2, out T3 a3)
        {
            var v = String().Split(' ');
            set(v[0], out a1);
            set(v[1], out a2);
            set(v[2], out a3);
        }

        public static void Cin<T1, T2, T3, T4>(out T1 a1, out T2 a2, out T3 a3, out T4 a4)
        {
            var v = String().Split(' ');
            set(v[0], out a1);
            set(v[1], out a2);
            set(v[2], out a3);
            set(v[3], out a4);
        }

        public static void Cin<T1, T2, T3, T4, T5>(out T1 a1, out T2 a2, out T3 a3, out T4 a4, out T5 a5)
        {
            var v = String().Split(' ');
            set(v[0], out a1);
            set(v[1], out a2);
            set(v[2], out a3);
            set(v[3], out a4);
            set(v[4], out a5);
        }

        public static void Cin<T1, T2, T3, T4, T5, T6>(out T1 a1, out T2 a2, out T3 a3, out T4 a4, out T5 a5, out T6 a6)
        {
            var v = String().Split(' ');
            set(v[0], out a1);
            set(v[1], out a2);
            set(v[2], out a3);
            set(v[3], out a4);
            set(v[4], out a5);
            set(v[5], out a6);
        }

        private static void set<T1>(string s, out T1 o1) => o1 = Convert<T1>(s);

        public static void Cin<T>(long n, out T[] l) => l = String(n).Select(Convert<T>()).ToArray();

        public static void Cin<T1, T2>(long n, out T1[] l1, out T2[] l2)
        {
            l1 = new T1[n];
            l2 = new T2[n];
            for (int i = 0; i < n; i++) Cin(out l1[i], out l2[i]);
        }

        public static void Cin<T1, T2, T3>(long n, out T1[] l1, out T2[] l2, out T3[] l3)
        {
            l1 = new T1[n];
            l2 = new T2[n];
            l3 = new T3[n];
            for (int i = 0; i < n; i++) Cin(out l1[i], out l2[i], out l3[i]);
        }

        public static void Cin<T1, T2, T3, T4>(long n, out T1[] l1, out T2[] l2, out T3[] l3, out T4[] l4)
        {
            l1 = new T1[n];
            l2 = new T2[n];
            l3 = new T3[n];
            l4 = new T4[n];
            for (int i = 0; i < n; i++) Cin(out l1[i], out l2[i], out l3[i], out l4[i]);
        }

        public static void Cin<T>(out T[] a) => a = Convert<T[]>(String());

        public static void Cin<T>(long h, out T[][] map) => map = String(h).Select(Convert<T[]>()).ToArray();
    }

    class Program
    {
        public static void Main(string[] args)
        {
            StreamWriter streamWriter = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            Console.SetOut(streamWriter);
            new Solver().Solve();
            Console.Out.Flush();
        }

        public static void Debug()
        {
            new Solver().Solve();
        }
    }

    class Solver
    {
        public void Solve()
        {
            long k;
            Cin(out k);
            dfs("1");
            dfs("2");
            dfs("3");
            dfs("4");
            dfs("5");
            dfs("6");
            dfs("7");
            dfs("8");
            dfs("9");
            runrun.Sort();
            Console.WriteLine(runrun[(int) k - 1]);
        }

        void dfs(string cur)
        {
            runrun.Add(long.Parse(cur));
            if (cur.Length > 10) return;
            var last = cur.Last();
            switch (last)
            {
                case '0':
                    dfs(cur + '0');
                    dfs(cur + '1');
                    break;
                case '1':
                    dfs(cur + '0');
                    dfs(cur + '1');
                    dfs(cur + '2');
                    break;
                case '2':
                    dfs(cur + '1');
                    dfs(cur + '2');
                    dfs(cur + '3');
                    break;
                case '3':
                    dfs(cur + '2');
                    dfs(cur + '3');
                    dfs(cur + '4');
                    break;
                case '4':
                    dfs(cur + '3');
                    dfs(cur + '4');
                    dfs(cur + '5');
                    break;
                case '5':
                    dfs(cur + '4');
                    dfs(cur + '5');
                    dfs(cur + '6');
                    break;
                case '6':
                    dfs(cur + '5');
                    dfs(cur + '6');
                    dfs(cur + '7');
                    break;
                case '7':
                    dfs(cur + '6');
                    dfs(cur + '7');
                    dfs(cur + '8');
                    break;
                case '8':
                    dfs(cur + '7');
                    dfs(cur + '8');
                    dfs(cur + '9');
                    break;
                case '9':
                    dfs(cur + '8');
                    dfs(cur + '9');
                    break;
            }
        }

        List<long> runrun = new List<long>();
    }
}