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

n = int(input())
ans=2

def go(n,k):
	aux=1
	while(n%k==0):
		n/=k
	if n%k==1:
		return True
	return False

for i in range(2,n):
	if(i*i>n): 
		break
	if n%i==0:
		if(go(n,i)): 
			ans+=1
		if(i!=n/i and go(n,n/i)):
			ans+=1
n-=1

for i in range(2,n):
	if(i*i>n): 
		break
	if n%i==0: 
		ans+=1
		if(i!=n/i):
			ans+=1
if n==1:
	print("1")
else:
	print(ans)