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)

a=int(input())
 
y=10000000000000
for j in range(1,100000):
  b=sum([int(i) for i in list(str(a*j))])
  y=min(y,b)
 
x=0
for j in range(1,18):
  if a % 2**j==0:
    x = j

c = sum([int(i) for i in list(str(a * (5**x)))])    
print(min(y,c))