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)

from datetime import datetime
K = int(input())
start = datetime.now()
def KSum(n):
    k = 0
    for i in str(n):
        k += int(i)
    return k

m = KSum(K)
j = 1
while((datetime.now()-start).total_seconds() < 1.8):
    for x in range(100):
        P = KSum(K*j)
        if m > P:
            m = P
        j += 1
print(m)