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: Accepted)

from math import log10

K = int(input())
  
def find(K):
  if K % 2 == 0 or K % 5 == 0:
    return -1
  
  if K % 7 == 0:
    L = K * 9 // 7
  else:
    L = K * 9

  count = max(int(log10(L)), 1)
  
  quotient = 10**count % L
  
  while True:
    if quotient == 1:
      return count
    quotient = quotient * 10 % L
    count += 1
    
    
print(find(K))