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)

def sum_of_digits(n)
  sum = 0
  begin
    n, b = n.divmod(10)
    sum += b
  end until n == 0 and b == 0
  sum
end

def make_ten?(n)
  
  while n%5 == 0 do
    n /= 5
  end
  
  while n%2 == 0 do
    n /= 2
  end
  
  n == 1
end

K = gets.to_i

ans = 10**20

(1..(10**6)).each do |i|
  v = sum_of_digits K*i
  ans = v if ans > v
end

# (2..10**5).each do |i|
#   p [i, sum_of_digits(i)]
# end

ans = 1 if make_ten?(K)
ans = 14 if ans > 14 and K % 3 != 0

puts ans