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 sys
def input(): return sys.stdin.readline().rstrip()


def main():
    n = int(input())
    ans = 2-(n==2)
    for k in range(2,int(n**0.5)+1):
        if n % k == 1:
            ans += 2
            ans -=k**2+1==n
        elif n % k == 0:
            g = n//k
            while g % k == 0:
                g = g//k
            ans += g % k == 1
    
    print(ans)


if __name__ == '__main__':
    main()