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
from math import sqrt, ceil

def factors_set(number):
    factors = set()
    for i in range(1, ceil(sqrt(number))+1):
        if number % i == 0:
            factors.add(i)
            factors.add(number // i)
    return factors

N = int(input())

Ks = factors_set(N-1) | factors_set(N)
Ks.remove(1)

ans = 0
for K in Ks:
    N_tmp = N
    while N_tmp % K == 0:
        N_tmp //= K
    if N_tmp % K == 1:
        ans += 1

print(ans)
