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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

#!/usr/bin/env python3
def modpow(a, n, p):
    '''aをn乗した値のmod(p)を求める
    '''
    if n == 0:
        return 0
    if n == 1:
        return a % p
    if n % 2 == 1:
        return (a * modpow(a, n - 1, p)) % p
    else:
        t = modpow(a, n // 2, p)
        return (t * t) % p

K = int(input())
ans = 0
if K % 2 == 0:
    ans = -1
else:
    seven = 7
    for i in range(1000000):
        seven = seven + 7 * modpow(10, i, K)
        seven %= K
        if seven == 0:
            ans = i+1
            break
print(ans)