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 (3.4.3) (judge verdict: Accepted)

from collections import deque

K = int(input())

G = [None]*K
for i in range(K):
    G[i] = ((10*i % K, 0), ((i+1) % K, 1))
s = 1

dist = [10**9] * K
S = deque([s])
T = deque()
dist[s] = 0

d = 0
while S:
    while S:
        v = S.popleft()
        for w, c in G[v]:
            if d+c < dist[w]:
                dist[w] = d+c
                if c:
                    T.append(w)
                else:
                    S.append(w)
    S, T = T, S
    d += 1

print(dist[0]+1)