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


def divisors(x):
    for i in range(1, int(sqrt(x)) + 1):
        if x % i == 0:
            yield i
            if x // i != i:
                yield x // i


n = int(input())

ans = 0
for e in divisors(n):
    if e == 1:
        continue

    r = n
    while r % e == 0:
        r //= e

    if r % e == 1:
        ans += 1

ans += len(list(divisors(n - 1))) - 1

print(ans)
