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 Ruby (2.7.1) (judge verdict: Accepted)

# https://atcoder.jp/contests/abc174/tasks/abc174_c

K = gets.to_i

K /= 7 if (K % 7).zero?

if K.even? || (K % 5).zero?
  puts(-1)
  exit 0
end

ws = 10.times.map { |i| K * i }
n = m = 1
v = 1

K.times do
  # p [n, m, v]
  w = ws.find { |a| a % 10 == v % 10 }
  while v < w
    v += 10**m
    n += 1
    m += 1
    # p [' ', n, m, v]
  end
  v -= w
  if v.zero?
    puts n
    exit 0
  end
  v /= 10
  m -= 1
end

puts(-1)