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)

import sys
import math
import time
sys.setrecursionlimit(int(1e6))
if False:
    dprint = print
else:
    def dprint(*args):
        pass

k = list(map(int, input().split()))[0]

if (k % 7 == 0):
    l = 9*k/7
else:
    l = 9*k
dprint('k, l = ', k, l)

i = 1
n = 10
while(i < k):
    m = n % l
    if (m == 1): # (10^i mod L = 1)
        print(i)
        exit()
    dprint('i, n, m = ', i, n, m)

    i = i + 1
    n = m * 10
else:
    print(-1)