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
init=int(input())

ans=[]
for K in range(2,int(init**0.5)+1):
    N=init
    while N%K==0:
        N/=K
    if N-(N//K)*K==1:
        ans.append(K)
        
tgt=init-1
cand=[]
for i in range(1,int(init**0.5)+1):
    if tgt%i==0:
        cand.append(i)
        if i!=tgt//i:
            cand.append(tgt//i)
ans=list(set(ans+cand))
print(len(ans))

    