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
from math import sqrt

n = int(input())

ans = 0

for i in range(2,int(sqrt(n))+1):
    if n%i==0:
        x = i
        y = n//i
        while y%x==0:
            y//=x
        if (y-1)%x==0:
            ans += 1
    elif (n-1)%i==0:
        if i**2==n-1:
            ans += 1
        else:
            ans += 2

if n>2:
    ans += 2
else:
    ans += 1

print(ans)
