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())
k = 2
count = set()
while k * k <= n:
    if n % k == 1:
        count.add(k)
        count.add((n-1)//k)
    elif n % k == 0:
        n_copy = n
        while n_copy % k == 0:
            n_copy //= k
        if n_copy % k == 1:
            count.add(k)
    k += 1
if n > 2:
    count.add(n-1)
count.add(n)
print(len(count))
