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)

K=gets.to_i
q=[]
cost=[Float::INFINITY]*K

q<<1
cost[1]=1
while !q.empty?
    x=q.shift
    if x==0
        puts cost[x]
        break
    end
    
    t=x*10%K
    if cost[t]>cost[x]
        cost[t]=cost[x]
        q.unshift t
    end

    t=(x+1)%K
    if cost[t]>cost[x]+1
        cost[t]=cost[x]+1
        q << t
    end
end