Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

Solution in C++14 (Clang 3.8.0) (judge verdict: Accepted)

#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#include <climits>

#define rep(i, m, n) for(int i=int(m);i<int(n);i++)
#define EACH(i, c) for (auto &(i): c)
#define all(c) begin(c),end(c)
#define EXIST(s, e) ((s).find(e)!=(s).end())
#define SORT(c) sort(begin(c),end(c))
#define pb emplace_back
#define MP make_pair
#define SZ(a) int((a).size())

//#define LOCAL 0
//#ifdef LOCAL
//#define DEBUG(s) cout << (s) << endl
//#define dump(x)  cerr << #x << " = " << (x) << endl
//#define BR cout << endl;
//#else
//#define DEBUG(s) do{}while(0)
//#define dump(x) do{}while(0)
//#define BR
//#endif


//改造
typedef long long int ll;
using namespace std;
#define INF (1 << 30)
#define INFl (ll)5e15
#define DEBUG 0 //デバッグする時1にしてね
#define dump(x)  cerr << #x << " = " << (x) << endl
#define MOD 1000000007

//ここから編集する
struct BFS01 {
    struct edge {
        ll to, cost;
    };
    typedef pair<ll, ll> P;//firstは最短距離、secondは頂点の番号

    int V;//超点数
    vector<vector<edge> > G;//グラフ,G[i]はiから出る辺の集合,G[i][j]はiから出る辺のj番目の辺
    vector<ll> d; //最短距離

    BFS01(int N) {
        V = N;
        G = vector<vector<edge> >(N);
        d = vector<ll>(N);
    };

    void addEdge(int from, int to, int cost) {
        edge e;
        e.to = to;
        e.cost = cost;
        G[from].push_back(e);
    }

    void calc(int s) {
//        priority_queue<P,vector<P>,greater<P> > que;
        deque<P> que;
        fill(d.begin(), d.end(), INFl);
        d[s] = 0;
        que.push_back(P(0, s));

        while (!que.empty()) {
            P p = que.front();
            que.pop_front();
            ll v = p.second;
            if (d[v] < p.first) continue;
            for (int i = 0; i < G[v].size(); i++) {
                edge e = G[v][i];
                if (d[e.to] > d[v] + e.cost && !(d[e.to] == INFl && d[v] == INFl)) {
                    d[e.to] = d[v] + e.cost;
                    if (e.cost == 0) {
                        que.push_front(P(d[e.to], e.to));
                    }else{
                        que.push_back(P(d[e.to],e.to));
                    }
                }
            }
        }

    }
};

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int K;
    cin >> K;
    BFS01 bfs01(K);
    rep(i, 0, K) {
        bfs01.addEdge(i, (i + 1) % K, 1);
        bfs01.addEdge(i, i * 10 % K, 0);
    }
    bfs01.calc(1);
    cout << bfs01.d[0] + 1 << endl;


    return 0;
}