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())
if N==2:
  print(1)
  exit()
def yaku(n):
    a=set()
    s=int(math.sqrt(n))
    for i in range(2,s+1):
        if n%i==0:
            a.add(i)
            a.add(n//i)
    return a
ans=len(yaku(N-1))+1
a=yaku(N)
for i in a:
    n=N
    while n%i==0:
        n=n//i
    if n%i==1:
        ans+=1
print(ans+1)