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 (3.4.3) (judge verdict: Wrong Answer)

K = int(input())
def count(n):
  return sum(map(int, list(str(n))))
while K%2 == 0:
  K = K//2
while K%5 == 0:
  K = K//5
r = count(K)
for i in range(1, 10):
  n = K*i
  c = count(n)
  if c < r:
    r = c
print(r)