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)

KS = gets.chomp
K = KS.to_i
L = KS.length
P = 10**L

def digitsum(a)
    sum = 0
    ai = a
    while ai > 0 do
        sum += ai % 10
        ai /= 10
    end
    return sum
end

min = 60

(1..(P*P/K)).each do |t|
    sum = digitsum(t*K)
    min = sum if min > sum
end

print min