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)

k = gets.to_i

node  = Array.new(k){Float::INFINITY} # nodes initial value
deque = []

deque.push(1)  # start node      = 1
node[1] = 0    # start node cost = 0

while !deque.empty?
  break if node[0] != Float::INFINITY  # goal
  u = deque.shift
  #-----------------
  # x10 move
  #-----------------
  n = (u*10) % k
  if node[n] > node[u]
    node[n] = node[u]
    deque.unshift(n)
  end
  #-----------------
  # +1 move
  #-----------------
  n = (u+1) % k
  if node[n] > node[u] + 1
    node[n] = node[u] + 1
    deque.push(n)
  end
end

p node[0] + 1