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())

def divisor(n):
    if n==1:return []
    ret = [n]
    for i in range(2,n+1):
        if i*i==n:
            ret.append(i)
        elif i*i > n:
            break
        elif n%i==0:
            ret.append(i)
            ret.append(n//i)
    ret.sort()
    return ret

ans = len(divisor(N-1))

for k in divisor(N):
    M = N
    while M%k==0:
        M//=k
    if M%k==1:
        ans += 1
print(ans)