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: Wrong Answer)

K = int(input())

while K % 2 == 0 :
    K //= 2
    
while K % 5 == 0 :
    K //= 5

m = float('inf')
for i in range(1, 100001) :
    KK = list(str(K * i))
    ret = sum(map(int, KK))
    if ret < m :
        m = ret
print(m)