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)

def mizu(x):
    temp=0
    while x>0:
        temp+=x%10
        x//=10
    return temp 

def main():
    K=int(input())
    ans=10**9
    for i in range(1,10**8):
        ans=min(ans,mizu(i*k))
    print(ans)

if __name__ == '__main__':
    main()