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 solve1(kei)
    def div(x,d)
        z = 0
        while x%d == 0
            z += 1
            x /= d
        end
        z
    end
    
    
    f5 = div(kei, 5)
    f2 = div(kei, 2)
    
    if f5 < f2
        kei *= 5**(f2-f5)
    elsif f2 < f5
        kei *= 2**(f5-f2)
    end
    
    return (kei).to_s.chars.map(&:to_i).reduce(:+)
end

def solve2(kei)
    best = 1e9
    2.step(100000) do |x|
        best = [solve1(kei*x), best].min
    end
    best
end

p solve2(gets.to_i)