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())
if n==2: print(1); exit()
Ans = set([n-1])
for i in range(2, int((n-1)**(1/2))+1):
    if (n-1)%i == 0: Ans.add(i); Ans.add((n-1)//i)
Div = set([n])
for i in range(2, int(n**(1/2))+1):
    if n%i == 0: Div.add(i); Div.add(n//i)
for d in Div:
    m = n
    while m%d == 0: m//=d
    if m%d == 1: Ans.add(d)
print(len(Ans))