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=input()
res=2

if n==2:
    print 1
    exit(0)
if n==3:
    print 2
    exit(0)
for i in xrange(2, int(math.sqrt(n)+1)):
    k=n
    while k>1:
        if k%i==0:
            k=k/i
        else:
            k=k%i
            break
        
    if k==1:
        res+=1

for i in xrange(2, int(math.sqrt(n))):
    if (n-1)%i==0:
        res+=1

print res