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 Python (2.7.6) (judge verdict: Accepted)

import collections


dq=collections.deque()
n=input()
dis=[100000]*100005
# print(dis[100])
dis[1]=1
dq.append(1)

while len(dq):
    a=dq[0]
    dq.popleft()
    if a==0:
        break
    b=(a*10)%n
    c=(a+1)%n
    if dis[b]> dis[a]:
        dis[b]=dis[a]
        dq.appendleft(b)
    if dis[c]>dis[a]+1:
        dis[c]=dis[a]+1
        dq.append(c)

print (dis[0])