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
import math
n = int(input())


cnt=0
for i in range(2,int(math.sqrt(n))+1):
    
    if (n-1)%i==0:
       
        
        cnt=cnt+2
    if (n)%i==0:
        s=n
        while s%i==0:
            s=s//i
        if s%i==1:
            
            cnt=cnt+1
if int(math.sqrt(n-1)) == math.sqrt(n-1):
    
    cnt=cnt-1

if n==2:
    print(1)
else:
    print(cnt+2)
        