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: Accepted)

use proconio::input;
use std::collections::HashSet;

fn main() {
    input! {
        k: usize,
    }

    println!("{}", sevens(k as i64));
}

fn sevens(k: i64) -> i64 {
    let (mut sevens, mut modulo) = (HashSet::new(), 7 % k);
    for i in 1.. {
        if modulo == 0 {
            return i;
        } else if sevens.contains(&modulo) {
            break;
        }
        sevens.insert(modulo);
        modulo = (modulo * 10 + 7) % k;
    }
    -1
}