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)

K = input()
keta = len(K)
K = int(K)
ans = float('inf')
for i in range(1, 10**keta):
    n = K * i
    n = str(n)
    kakui_sum = 0
    for kakui in n:
        kakui_sum += int(kakui)
    ans = min(ans, kakui_sum)
print(ans)