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())

if N==2:
  print(1)
  exit()

ans = 2 # N and N-1
for K in range(2, N):
    if K*K>N: break
    n = N
    if n%K!=0: continue
    while n%K==0: n//=K
    if n%K==1: ans +=1

y = 0
N_ = N-1
for K in range(2, N):
    if K*K>=N_: break
    if N_%K==0: y +=2
if K*K==N_: y += 1

print(ans+y)