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)

// template version 1.15
using namespace std;
#include <bits/stdc++.h>

// varibable settings
#define int long long
const int INF=1e18;

// define basic macro {{{
#define _overload3(_1,_2,_3,name,...) name
#define _rep(i,n) repi(i,0,n)
#define repi(i,a,b) for(int i=(int)(a);i<(int)(b);++i)
#define rep(...) _overload3(__VA_ARGS__,repi,_rep,)(__VA_ARGS__)
#define _rrep(i,n) rrepi(i,0,n)
#define rrepi(i,a,b) for(int i=(int)((b)-1);i>=(int)(a);--i)
#define rrep(...) _overload3(__VA_ARGS__,rrepi,_rrep,)(__VA_ARGS__)
#define each(i,a) for (auto&& i : a)
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define pb(a) push_back(a)
#define mp(a, b) make_pair(a, b)
#define mt(a, b, c) make_tuple(a, b, c)
#define ub upper_bound
#define lb lower_bound
#define posl(A, x) (lower_bound(all(A), x)-A.begin())
#define posu(A, x) (upper_bound(all(A),x)-A.begin())
template<class T> inline void chmax(T &a, const T &b) { if((a) < (b)) (a) = (b); }
template<class T> inline void chmin(T &a, const T &b) { if((a) > (b)) (a) = (b); }

#define divceil(a,b) ((a)+(b)-1)/(b)
#define is_in(x, a, b) ((a)<=(x) && (x)<(b))
#define uni(x) sort(all(x));x.erase(unique(all(x)),x.end())
#define slice(l, r) substr(l, r-l)

typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef long double ld;
typedef pair<int,int> pii;
typedef tuple<int,int,int> iii;

template<typename T> using PQ = priority_queue<T, vector<T>, greater<T>>;
struct Fast { Fast(){ std::cin.tie(0); ios::sync_with_stdio(false); } } fast;

#if defined(PCM) || defined(LOCAL)
    #include "lib/dump.hpp"
#else
    #define dump(...) 42
    #define dump_1d(...) 42
    #define dump_2d(...) 42
    #define cerrendl 42
#endif
//}}}

signed main() {
    int k;cin>>k;

    if (1<=k && k<=9){
        cout << k << endl;
        return 0;
    }

    vector<vector<string>> x(10);
    rep(i, 10) x[i] = {to_string(i)};
    dump(x);
    vector<string> y;
    rep(i, 1, 10) y.pb(to_string(i));

    int c = 9;

    rep(d, 13){
        vector<vector<string>> tmp(10);
        rep(i, 10){
            // i-1
            if (i-1>=0){
                each(el, x[i-1]){
                    string t = to_string(i);
                    t += el;
                    tmp[i].pb(t);
                }
            }
            // i
                each(el, x[i]){
                    string t = to_string(i);
                    t += el;
                    tmp[i].pb(t);
                }
            // i+1
            if (i+1<=9){
                each(el, x[i+1]){
                    string t = to_string(i);
                    t += el;
                    tmp[i].pb(t);
                }
            }
        }
        x = tmp;
        rep(i, 1, 10){
            each(el, x[i]){
                y.pb(el);
                c++;
                if (c==k){
                    cout << el << endl;
                    return 0;
                }
            }
        }
        // dump(y);
    }

    return 0;
}