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

N = int(input())


def f(x):
    n = N
    while n % x == 0:
        n //= x
    return n % x == 1


ans = 1
for k in range(2, int(sqrt(N)) + 1):
    res = N % k
    if res == 0:
        k1, k2 = k, N // k
        ans += 1 if f(k1) else 0
        ans += 1 if k1 != k2 and f(k2) else 0
    elif res == 1:
        ans += 1 if k == (N - 1) // k else 2
if N >= 3:
    ans += 1

print(ans)
