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
def f(x):
    s=set()
    for i in range(1,int(x**(0.5))+6):
        if x%i==0: s.add(i);s.add(x//i)
    return s 


ans=set()
n=int(input())
ans=f(n-1)
ans1=f(n)
ans1.remove(1)

for x in ans1:
    p=n
    while p>=x:
        if p%x==0: p//=x
        else: p%=x
    if p==1: ans.add(x)

if 1 in ans: ans.remove(1)
print(len(ans))