Problem:
Score : 700 points

Problem Statement

Find the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Constraints

2 \leq K \leq 10^5

K is an integer.

Input

Input is given from Standard Input in the following format:

K

Output

Print the smallest possible sum of the digits in the decimal notation of a positive multiple of K.

Sample Input 1

6

Sample Output 1

3

12=6×2 yields the smallest sum.

Sample Input 2

41

Sample Output 2

5

11111=41×271 yields the smallest sum.

Sample Input 3

79992

Sample Output 3

36

Solution in Ruby (2.3.3) (judge verdict: Wrong Answer)

K = gets.to_i
keta = K.to_s.size
ret = K.to_s.each_char.map(&:to_i).inject(:+)
n = ret - keta
while n >= 0
  ones = ("1"*(n)).to_i * (10**(keta))
  (0..("9" * keta).to_i).each do |x|
    kouho = ones + x
    break if kouho == 0
    # puts kouho
    if kouho % K == 0
      kouho = kouho.to_s.each_char.map(&:to_i).inject(:+)
      if kouho < ret
        ret = kouho
        n = ret - keta + 1
        break
      end
    end
  end
  n -= 1
end
puts ret