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())
n_ = n-1
a = [n]
if n_ == 1:
    a_ = []
else:
    a_ = [n_]
    
for i in range(2,int(n**0.5//1+1)):
    if n%i == 0:
        a.append(i)
        if n/i != i:
            a.append(n/i)
    if n_%i == 0:
        a_.append(i)
        if n_/i != i:
            a_.append(n_/i)

ans = len(a_)
for i in a:
    num = n
    while num%i == 0:
        num /= i
    if num % i == 1:
        ans += 1
    
print(ans)