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())
div = []
ans = []

for i in range(1,int(n**0.5)+2):
    if n%i == 0:
        div.append(i)
        div.append(n//i)

for i in div:
    if i == 1:
        continue
    k = n
    while k%i == 0:
        k//=i
    if k%i== 1:
        ans.append(i)
        
n -= 1

for i in range(1,int(n**0.5)+2):
    if n%i == 0:
        ans.append(i)
        ans.append(n//i)
        
print(len(set(ans)) - 1)