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=gets.to_i
a=[] << (0..9).map{|i|n*i}
(1..18).each{|i|a[i]=a[i-1].map{|x|x*10}}
res = 999
(0..15).each{|i|
  (0..15).each{|j|
    a[i].product(a[j]).map{|x,y|
      m=x+y
      tmp=m%10
      tmp+=m%10 while (m/=10) > 0
      if res > tmp && tmp != 0
        res = tmp
      end
    }
  }
}

p res