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 sys
input = sys.stdin.readline
from math import sqrt

x=int(input())

DIV=[]

for i in range(1,int(sqrt(x))+2):
    if x%i==0:
        DIV.append(i)
        DIV.append(x//i)

ANS=[]
for d in DIV:
    if d==1:
        continue
    k=x
    while k%d==0:
        k//=d
    if k%d==1:
        ANS.append(d)

t=x-1
for i in range(1,int(sqrt(t))+2):
    if t%i==0:
        ANS.append(i)
        ANS.append(t//i)

print(len(set(ANS))-1)