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
n=int(input())
ns=int(n**0.5)
nms=int((n-1)**0.5)
p=[n]
for i in range(2,ns+1):
  if n%i==0:
    p.append(i)
    if i!=n//i:
      p.append(n//i)

def chd(x,k):
  while x%k==0:
    x=x//k
  return int((x%k)==1)

count=0
for i in p:
  count+=chd(n,i)
for i in range(2,nms+1):
  if (n-1)%i==0:
    count+=1
    if i!=(n-1)//i:
      count+=1
print(count+1-(n==2))