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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <fstream>
#include <iomanip>
#include <math.h>
#include <limits.h>
#include <algorithm>
#include <vector>
#include <list>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <bitset>
#include <string>
#include <string.h>
#include <sstream>
#include <ctime>

using namespace std;

#define eps 1e-12
#define pi 3.14159265358979323846
#define pb push_back
#define mp make_pair
#define st first
#define nd second
#define bgn begin
#define ll long long
#define ld long double
#define ull unsigned long long
#define ii pair<ll,ll>




const ll N=1e7;
ll n,t,mn;




ll f(ll i)
{
	ll ret=0;
	for(;i;)
	{
		ret+=i%10;
		i/=10;
	}
	return ret;
}





void solve()
{
	cin>>n;
	while(n%2==0)n/=2;
	while(n%5==0)n/=5;
	for(ll i=1;i<=N;i++)
	{
		t=f(n*i);
		if(i==1||mn>t)mn=t;
	}
	cout<<mn<<"\n";
}

int main()
{
	std::ios::sync_with_stdio(0);
	cin.tie(0);
#ifdef localProject
	freopen("in.txt","r",stdin);
#endif
	solve();
	return 0;
}