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 math
N = int(input())

k = 2
res = 0

ts = set()
kn = {N}
kn_1 = {N-1}
while k <= math.sqrt(N):
    if N % k == 0:
        nk = N//k
        while nk % k == 0:
            nk //= k

        if nk % k == 1:
            kn.add(k)
        if k % nk == 1:
            kn.add(nk)

        ts.add(k)
        ts.add(nk)

    if (N-1) % k == 0:
        kn_1.add(k)
        kn_1.add((N-1)//k)

    k+=1

kn_1 -= {1}
print(len(kn)+len(kn_1))