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)

def solve(x)
    res = 0
    while x > 0
        res += x % 10
        x /= 10
    end
    return res
end

k = gets.to_i
hoge = 0
digit = 1
ans = 114514
1000.times do |i|
    bar = hoge
    1.upto(9) do |j|
        foo = hoge + digit * j;
        aha = solve(foo * k)
        if ans > aha
            ans = aha
            bar = foo
        end
    end
    hoge = bar
    digit *= 10
end
p ans