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>

/*                    ॐ Shree ॐ                     */
/* ॐ ॐ ॐ
ॐ भूर् भुवः स्वः
तत् सवितुर्वरेण्यं
भर्गो देवस्य धीमहि
धियो यो नः प्रचोदयात्
*/
using namespace std;
typedef long long int ll;
vector<int> ve(3006, 0);
int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cout.tie(NULL);
#ifndef ONLINE_JUDGE
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
#else
// online submission
#endif
	int n;
	cin >> n;
	ll a = 7;
	for (int i = 0; i < 10000000; i++) {
		if (a%n == 0) {
			cout << i + 1;
			return 0;
		}
		else {
			a = ((a * 10) % n + 7) % n;
		}
	}
	cout << -1;
}