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 get_divisors(n):
    result = []
    for i in range(1, int(n**.5)+1):
        if n % i == 0:
            result.append(i)
            if n != i ** 2:
                result.append(n // i)
    result.sort()
    return result

c = 0
for number in get_divisors(n)[1:]:
    tmp = n
    while tmp % number == 0:
        tmp //= number
    if tmp % number == 1:
        c += 1

c += len(get_divisors(n-1)) - 1
print(c)
