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: Wrong Answer)

use num_bigint::{BigInt, ToBigInt};
fn main() {
    let timer = std::sync::Arc::new(std::time::Instant::now());
    proconio::input! {
        k: BigInt,
    }
    let mut s = ToBigInt::to_bigint(&7).unwrap();
    if &k % 2 == ToBigInt::to_bigint(&0).unwrap() {
        println!("-1");
        return;
    }
    for i in 1.. {
        if &s % &k == ToBigInt::to_bigint(&0).unwrap() {
            println!("{}", i);
            return;
        } else if timer.elapsed().as_millis() > 1900 {
            println!("-1");
            return;
        }
        s *= 10;
        s += 7;
    }
}