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())


def factor(n):
    res=set()
    for i in range(2,int(n**(1/2))+10):
        if n%i == 0:
            res.add(i)
            res.add(n//i)

    res.add(n)
    res.discard(1)
    return list(res)

ans = 0

ans += len(factor(n-1))


for k in factor(n):
    n2=n
    if k==1:
        continue
    while n2%k==0:
        n2//=k
    if n2%k == 1:
        ans +=1
        

print(ans)
