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 PyPy3 (7.3.0) (judge verdict: Accepted)

from sys import stdin
from sys import setrecursionlimit
from collections import Counter, deque, defaultdict
from math import floor, ceil
from bisect import bisect_left
from fractions import Fraction
from itertools import combinations
from math import gcd
setrecursionlimit(100000)

INF = int(1e10)
MOD = int(1e9 + 7)

def main():
    from builtins import int, map
    K = int(input())
    ss = set({})
    mod = 7 % K
    count = 1
    while True:
        if mod == 0:
            print(count)
            exit()
        if mod in ss:
            print(-1)
            exit()
        ss.add(mod)
        mod = (mod * 10 + 7) % K
        count += 1

if __name__ == '__main__':
    main()