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: Accepted)

k = gets.to_i
dist = Array.new(k,50)
que = [1]
dist[1] = 1
while que.any?
  f = que.shift
  if dist[(f*10)%k] > dist[f]
    dist[(f*10)%k] = dist[f]
    que.unshift((f*10)%k)
  end
  if dist[(f+1)%k] > dist[f]
    dist[(f+1)%k] = dist[f]+1
    que.push((f+1)%k)
  end
end

puts dist[0]