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
def check(i):
	tot=k
	while(tot%i==0):
		tot//=i
	if(tot%i==1):
		setl.add(i)
import math
k=int(input())
setl = set()
setl.add(k); setl.add(k-1)
for x in range(2,int(math.sqrt(k))+1):
	check(x)
	check(k//x)
if(setl.__contains__(1)):
	setl.remove(1)
print(len(setl))