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 Rust (1.42.0) (judge verdict: Time Limit Exceeded)

use proconio::*;

fn main() {
    input! {
        k: i64,
    };

    let mut ans = 0;
    let mut seven = 7;
    let a = 7i64.rem_euclid(k);

    for i in 1.. {
        if seven % k == 0 {
            ans = i;

            break;
        }

        seven = (seven * 10 + 7) % k;
        if a == seven {
            ans = -1;
            break;
        }
    }

    println!("{}", ans);
}