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())

def sum_keta(num):
  ans = 0
  for i in str(num):
    ans = ans + int(i)
  return ans

min_sum_keta = float("inf")
limit = k*10**len(str(k))
add = k
while k < limit:
  min_sum_keta = min(min_sum_keta,sum_keta(k))
  k += add
print(min_sum_keta)