Problem:
Score : 300 points

Problem Statement

Takahashi loves the number 7 and multiples of K.

Where is the first occurrence of a multiple of K in the sequence 7,77,777,\ldots? (Also see Output and Sample Input/Output below.)

If the sequence contains no multiples of K, print -1 instead.

Constraints

1 \leq K \leq 10^6

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print an integer representing the position of the first occurrence of a multiple of K. (For example, if the first occurrence is the fourth element of the sequence, print 4.)

Sample Input 1

101

Sample Output 1

4

None of 7, 77, and 777 is a multiple of 101, but 7777 is.

Sample Input 2

2

Sample Output 2

-1

All elements in the sequence are odd numbers; there are no multiples of 2.

Sample Input 3

999983

Sample Output 3

999982

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
using Graph = vector<vector<int>>;
#define rep(i,m,n) for(int (i)=(m);(i)<(n);++(i))
#define rREP(i,m,n) for(int (i)=(n)-1;(i)>=(m);--(i))
#define all(x) (x).begin(),(x).end()
#define out(y,x,h,w) (y)<0||(x)<0||(y)>=(h)||(x)>=(w)
constexpr int INF = 1000000001;
constexpr ll mod = 1000000007;
constexpr double PI = 3.1415926535897932;
template<class T>inline bool chmin(T& a, T b) {
	if (a > b) {
		a = b;
		return true;
	}
	return false;
}
template<class T>inline bool chmax(T& a, T b) {
	if (a < b) {
		a = b;
		return true;
	}
	return false;
}
inline void init() {
	cin.tie(nullptr); cout.tie(nullptr);
	ios::sync_with_stdio(false);
	cout << fixed << setprecision(15);
}

int main() {
	init();

	int K; cin >> K;
	int cnt = 7;
	cnt %= K;
	int ans = 1;
	while (cnt) {
		cnt *= 10;
		cnt += 7;
		cnt %= K;
		++ans;
		if (ans >= 100000000) {
			ans = -1;
			break;
		}
	}
	cout << ans << "\n";

	return 0;
}