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)

mod = 1000000007
eps = 10**-9


def main():
    import sys
    input = sys.stdin.readline

    K = int(input())
    seen = [0] * K
    d = 0
    for i in range(1, 10**6+1):
        d = (d * 10 + 7) % K
        if d == 0:
            print(i)
            exit()
        if seen[d]:
            break
        seen[d] = 1
    print(-1)


if __name__ == '__main__':
    main()