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
n = int(input())
mod0 = set()
mod1 = set()

for i in range(1, int(n**0.5)+1):
    if n%i==0:
        mod0.add(i)
        mod0.add(n//i)
    if (n-1)%i==0:
        mod1.add(i)
        mod1.add((n-1)//i)
mod0.remove(1)
mod1.remove(1)
ans = 0
for i in mod0:
    nn = n
    while nn%i==0:
        nn//=i
    if nn%i==1:
        ans += 1
ans += len(mod1)
print(ans)