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 proconio::marker::Chars;
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused)]
const ALPHA_SMALL: [char; 26] = [
    'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's',
    't', 'u', 'v', 'w', 'x', 'y', 'z',
];
#[allow(unused)]
const ALPHA: [char; 26] = [
    'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M', 'N', 'O', 'P', 'Q', 'R', 'S',
    'T', 'U', 'V', 'W', 'X', 'Y', 'Z',
];
#[allow(unused)]
const N: usize = 1_000_000 + 10;
fn main() {
    input!(K: usize);
    if K % 2 == 0 || K % 5 == 0 {
        println!("-1");
        return;
    }

    let mut m = 7;
    let mut ans: usize = 1;
    for i in 0..N {
        if m % K == 0 {
            break;
        }
        ans += 1;
        m = 10 * m + 7;
        m %= K;
    }
    println!("{}", ans);
}