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)

#![allow(non_snake_case)]
use proconio::input;
// use std::collections::HashMap;

fn main() {
    input! {
        K: i64,
    }

    // 数学的性質として、この数列を素因数分解しても2と5は現れない
    if K % 2 == 0 || K % 5 == 0 {
        println!("-1");
        return;
    }

    // 出現の順番がバラバラなので、「実際にやってみた」としたい
    // しかし、数が10^999999くらいなので実際にやってみることができない (これが気のせい)

    // 表現方法はさておき、O(K)ではあるのでは?
    // 初めからmodで表現すればいけるのでは?

    let mut d = 1;
    let mut val = 7;
    while true {
        if val % K == 0 {
            println!("{}", d);
            return;
        }
        val = (val * 10) % K;
        val = (val + 7) % K;
        d += 1;
    }
}