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;

#define eb emplace_back
#define ii pair<int, int>
#define OK (cerr << "OK" << endl)
#define debug(x) cerr << #x " = " << (x) << endl
#define ff first
#define ss second
#define int long long
#define tt tuple<int, int, int>
#define all(x) x.begin(), x.end()
#define vvi vector<vector<int>>
#define vvii vector<vector<pair<int, int>>>
#define Mat(n, m, v) vector<vector<int>>(n, vector<int>(m, v))
#define endl '\n'

constexpr int INF = 2e18;
constexpr int MOD = 1e9 + 7;
constexpr int MAXN = 2e5 + 3;

// #define MULTIPLE_TEST_CASES
void solve() {
  int n;
  cin >> n;
  int cur = 0;
  for (int i = 0; i < 1e7; ++i) {
    cur = (cur * 10 + 7) % n;
    if (cur == 0) {
      cout << i + 1 << endl;
      return;
    }
  }
  cout << -1 << endl;
}

signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);

  int t = 1;
#ifdef MULTIPLE_TEST_CASES
  cin >> t;
#endif
  while (t--)
    solve();
}