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 (3.8.2) (judge verdict: Wrong Answer)

K = int(input())
ans = 10**18

for i in range(1, 10**5 + 100):
  i *= K
  cnt = 0
  while i > 0:
    i, r = divmod(i, 10)
    cnt += r
  ans = min(ans, cnt)
print(ans)