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)

n = gets.to_i
a = Array.new(10000000)
for i in 0..9999999
  x = 0
  r = n * (i+1)
  m = 10
  while m > 0 
    x = x + r%10
    r = r/10
    m -= 1
  end
  a[i] = x
end
puts a.min