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: Runtime Error)

import heapq as hq

INF = 10_0000_0007
K = int(input())

dist = [INF for _ in range(K)]

h = []
hq.heappush(h, (1, 1))

while h:
    v, c = hq.heappop(h)
    if dist[v] <= c:
        continue
    dist[v] = c
    
    if dist[(v+1)%K] > c+1:
        hq.heappush(h, ((v+1)%K, c+1))
    if dist[(v*10)%K] > c:
        hq.heappush(h, ((v*10)%K, c))

print(dist[0])