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
n = int(input())
set_ans = {n}
for x in range(2, int(n ** 0.5) + 1):
    if n % x == 0:
        tmp = n
        while tmp % x == 0:
            tmp //= x
        if tmp % x == 1:
            set_ans.add(x)
for x in range(1, int((n-1) ** 0.5) + 1):
    if (n - 1) % x == 0:
        if x > 1:
            set_ans.add(x)
        if (n - 1) // x != x:
            set_ans.add((n - 1) // x)
print(len(set_ans))