Given is a positive integer N.

We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K.

* Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.



In how many choices of K will N become 1 in the end?

Constraints

* 2 \leq N \leq 10^{12}
* N is an integer.

Input

Input is given from Standard Input in the following format:


N


Output

Print the number of choices of K in which N becomes 1 in the end.

Examples

Input

6


Output

3


Input

3141


Output

13


Input

314159265358


Output

9
def main():
    n = int(input())
    count = 2
    sqrt = int(n ** (1/2))
    for i in range(2,sqrt + 1):
        if n % i == 1:
            count += 2
        elif n % i == 0:
            ins = n
            while ins % i == 0:
                ins = ins // i
            if ins % i == 1:
                count += 1
    if sqrt ** 2 == n - 1:
        count -= 1

    print(count)


if __name__ == "__main__":
    main()
