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;

fn main() {
    input! {
        k: u128,
    }
    let div = if k % 7 == 0 {
        9 * k / 7
    } else {
        9 * k
    };

    if div % 2 == 0 || div % 5 == 0 {
        println!("{}", -1);
        return;
    }
    let mut count = 0;
    let mut remain = 10 % div;
    let ans = loop {
        count+=1;
        if remain == 1 {
            break count;
        }
        remain = remain * 10 % div;
    };
    println!("{}", ans);

}