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: Accepted)

D=[1<<99]*K=gets.to_i
D[1]=1
q=[1]
while n=q.shift
	[[n*10%K,0,:unshift],[(n+1)%K,1,:<<]].each{|e,d,m|
		if D[e]>D[n]+d
			D[e]=D[n]+d
			q.send(m,e)
		end
	}
end
p D[0]