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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

from collections import deque
K = int(input())

q = deque()
q.append((1, 1, 1))
used = set()
while True:
    x, y, k = q.popleft()
    if (x, y, k) in used:
        continue
    else:
        used.add((x, y, k))
    # print(x, y, k)
    if k % K == 0:
        print(x)
        break
    q.appendleft((x, 0, k*10%K))
    if (y + 1) % 10 == 0:
        q.appendleft((x, 0, k+1))
    else:
        q.append((x+1, y+1, k+1))