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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <numeric>
#include <string>
#include <cstdio>
#include <cstring>
#include <queue>
#include <stack>
#include <set>
#include <cmath>
#include <bitset>

typedef long long ll;
typedef unsigned long long ull;
using namespace std;

#define FALSE printf("false\n");
#define TRUE printf("true\n");
#define all(x) (x).begin(),(x).end()
#define rep(i,n) for(int (i) = 0;(i) < ((int)(n));++(i))
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() );
#define test(a) cout<<"line:"<<__LINE__<<"["<<(#a)<<": "<<(a)<<"]"<<endl

const int INF = 1e9+7;
const ll INFL = 9*1e18;

const int dx[4] = { 1, 0, -1, 0 };
const int dy[4] = { 0, 1, 0, -1 };

// const int dx[8] = {1, 1, 0,-1,-1,-1, 0, 1};
// const int dy[8] = {0, 1, 1, 1, 0,-1,-1,-1};

#define SUM(vec) accumulate(all(vec),0LL) // 配列の中身を全部足す
template<typename T>void print(T&& x){cout<<x<<endl;}// 改行付き出力
ll inline digit(ll num){int tmp = 0;while(num){tmp++;num/=10;}return tmp;} // 桁数
template<typename T>inline T digitSum(T num){T sum = 0;while(num){sum+=num%10;num/=10;}return sum;} // 各桁の和
template<typename T>inline T gcd(T a,T b){if(b == 0)return a;return gcd(b,a%b);} // 最大公約数
template<typename T>inline T lcm(T a, T b){T g = gcd(a,b);return a/g*b;} // 最小公倍数
template<typename T>inline T power(T a,T b){T tmp=1;rep(i,b){tmp*=a;}return tmp;} // 累乗
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
int ctoi(char c){return c-'0';}

// TODO: write
int main() {
  int n;cin>>n;
  queue<ll> que;
  rep(i,9)que.push(i+1);
  rep(i,n-1){
    ll x = que.front();que.pop();
    if(x%10 != 0){
      que.push(10*x+x%10-1);
    }
    que.push(10*x+x%10);
    if(x%10 != 9){
      que.push(10*x+1+x%10);
    }
  }
  print(que.front());
  return 0;
}