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)

# coding: utf-8
N = int(input())
array = [100000000]
X = int(10000000/N)
     
for i in range(X):
    if i == 0:
        i +=1
    else:
        Y = str(N*i)
        a_list = list(map(int,Y))
        ddd = sum(a_list)
        if ddd < array[0]:
            array.pop(0)
            array.append(ddd)

print(int(array[0]))