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.Linq;
using System.Collections.Generic;

namespace AtCoder
{
	class Program
	{
		public static void Main()
		{
			var inputNumber = IO.ReadInt();
			if(inputNumber < 13)
			{
				IO.Write(inputNumber);
				return;
			}
			
			var list = new List<long>(Enumerable.Range(1 , 9).Select(iNumber => (long)iNumber));
			var index = 0;
			while(list.Count < inputNumber)
			{
				var top = list[index];
				var checkNumber = top % 10;
				var baseNumber = top * 10;
				if(checkNumber > 0) { list.Add(baseNumber + (checkNumber - 1)); }
				list.Add(baseNumber + checkNumber);
				if(checkNumber < 9) { list.Add(baseNumber + (checkNumber + 1)); }

				++ index;
			}

			IO.Write(list[inputNumber - 1]);
		}
	}

	public static class IO
	{
		public static string   Read()							   { return Console.ReadLine(); }
		public static string[] ReadArray(char iSplitter = ' ')	   { return Read().Split(iSplitter); }
		public static int	   ReadInt()						   { return int.Parse(Read()); }
		public static int[]	   ReadIntArray(char iSplitter = ' ')  { return ReadArray().Select(iText => int.Parse(iText)).ToArray(); }
		public static long	   ReadLong()						   { return int.Parse(Read()); }
		public static long[]   ReadLongArray(char iSplitter = ' ') { return ReadArray().Select(iText => long.Parse(iText)).ToArray(); }
		public static char[]   ReadCharArray()					   { return Read().ToCharArray(); }

		public static void Write(string iValue)			  { Console.WriteLine(iValue); }
		public static void Write(int iValue)			  { Console.WriteLine(iValue); }
		public static void Write(IEnumerable<int> iValue) { Console.WriteLine(string.Join(" " , iValue)); }
		public static void Write(long iValue)			  { Console.WriteLine(iValue); }
		public static void Write(decimal iValue)		  { Console.WriteLine(iValue); }
		public static void Write(bool iValue)			  { Console.WriteLine(iValue ? "Yes" : "No"); }
	}

	public static class Util
	{
		public static long Gcd(long i0 , long i1)	{ return (i0 > i1) ? _Gcd(i0 , i1) : _Gcd(i0 , i1); }
		public static long ModPow(long iBaseNumber , long iPow , long iModNumber)
		{
			var num = 1L;
			while(iPow != 0)
			{
				if((iPow & 0x1) != 0)
				{
					num = (num * iBaseNumber) % iModNumber;
				}
				iBaseNumber = (iBaseNumber * iBaseNumber) % iModNumber;
				iPow >>= 1;
			}
			return num;
		}

		private static long _Gcd(long i0 , long i1)	{ return (i1 == 0) ? i0 : _Gcd(i1 , i0 % i1); }
	}
}