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())
if n==2:
    count=1
else:
    count=2
for i in range(2,int(n**0.5)+1):
    if n%i==0:
        k=n//i
        while k>0:
            if k%i==0:
                k=k//i
            else:
                if k%i==1:
                    count+=1
                break
    elif (n-1)%i==0:
        count+=1
        if i!=(n-1)//i:
            count+=1
print(count)
