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)

require 'prime'

def div(x,d)
    z = 0
    while x%d == 0
        z += 1
        x /= d
    end
    z
end

kei = gets.to_i

f5 = div(kei, 5)
f2 = div(kei, 2)

if f5 < f2
    kei *= 5**(f2-f5)
elsif f2 < f5
    kei *= 2**(f5-f2)
end

p (kei).to_s.chars.map(&:to_i).reduce(:+)