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: Time Limit Exceeded)


kei = gets.to_i

best = [(kei).to_s.chars.map(&:to_i).reduce(:+), 1]

2.step(1000000,2) do |x|
    s = (kei*x).to_s.chars.map(&:to_i).reduce(:+)
    best = [best, [s,x]].min
end

p best[0]