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)

N = 1000
K = gets.to_i
def f(k)
  n = 0
  res = 10**8
  k.times{
    n += k
    x = "#{n}".chars.map{|c|c.to_i}.inject:+
    res = x if x < res
  }
  res
end

p f(K)