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
N=int(input())

if N==2:
  print(1)
  sys.exit(0)

answer_set=set()
for i in range(2,int(N**0.5)+1):
  N2=N
  while N2%i==0:
    N2//=i
  if N2%i==1:
    answer_set.add(i)
#print(answer_set)

for i in range(1,int(N**0.5)+1):
  if (N-1)%i==0:
    answer_set.add((N-1)//i)    
#print(answer_set)

answer_set.add(N)
print(len(answer_set))