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: Time Limit Exceeded)

# 高橋くんが好きな整数の入力
K = gets.to_i

# 判定の計算を簡単にするため、Lを定義
if K % 7 == 0
  # Kが7の倍数ならLを9K/7と定義
  L = 9 * K / 7
else
  # そうでなければLを9Kと定義
  L = 9 * K
end

mod = 10 % L
# Lと10が互いに素でなければ
if L % 2 == 0 || L % 5 == 0
  # 数列にKの倍数は見つからない
  puts -1
elsif mod == 1
  puts 1
else
  for i in 2..9000000 do
    mod *= 10
    if mod % L == 1
      puts i
      break
    end
  end
end