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: Runtime Error)

a=int(input())
x1=0
x2=0
for j in range(1,17):
  if a % 2**j==0:
    x1 = j
for j in range(1,17):
  if a % 5**j==0:
    x2 = j
c = str(a * (5**(x1-x2)))

for j in range(len(c),0,-1):
  if c[j-1]=='0':
    c=c[:j]

y=10000000000000
for j in range(1,1000):
  b=sum([int(i) for i in list(str(c * j))])
  y=min(y , b)

print(y)