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:print(1);exit()
a = [n]
for i in range(2,int(n**0.5+1)):
    if n%i==0:
        a.append(i)
        if i!=n//i:
            a.append(n//i)
cnt =0
for v in a:
    s = n
    while v<=s and s%v==0:
        s = s//v
    if s%v==1: cnt += 1
b = [n-1]
m = n-1
for i in range(2,int(m**0.5+1)):
    if m%i==0:
        b.append(i)
        if i!=m//i:
            b.append(m//i)
print(cnt + len(b))