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
import copy

n = int(input())
m = int(math.sqrt(n)+.1)+1

def f(x):
    a = copy.copy(n)
    while a%x == 0:
        a /= x
    return a%x == 1

ans = {n}
if n > 2:
    ans.add(n-1)

for k in range(2,m):
    if (n-1)%k == 0:
        ans.add(k)
        ans.add((n-1)//k)
    elif f(k):
        ans.add(k)
print(len(ans))