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)

k = gets.to_i

inf = 10**9
d = Array.new(k, inf)

d[1] = 1
q = [1]
while d[0] == inf
  x = q.shift
  
  if d[x*10%k] > d[x%k]
    d[x*10%k] = d[x%k]
    q.unshift(x*10)
  end
  
  if d[(x+1)%k] > d[x%k]+1
    d[(x+1)%k] = d[x%k]+1
    q.push(x+1)
  end
end

p d[0]