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: Wrong Answer)

from collections import defaultdict

k = int(input())

def prime_factorize(n):
    a = defaultdict(int)
    while n % 2 == 0:
        a[2] += 1
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a[f] += 1
            n //= f
        else:
            f += 2
    if n != 1:
        a[n] += 1
    return a

def f(k):
  if k % 2 == 0 or k % 5 == 0:
    return -1    

  val = 7
  cnt = 1
  while True:
    if val % k == 0:
      break
    cnt += 1
    val = val * 10 + 7
  return cnt
    
li = prime_factorize(k)

li = {343:1}

ans = 1
for k, v in li.items():
  if k ** v <= 10000:
    ans *= f(k) * k ** (v - 1)
  else:
    ans *= (k - 1) * k ** (v - 1)
    
if ans < 0:
  print(-1)
else:
  print(ans)