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
def divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n%i == 0:
            divisors.append(i)
            if i != n//i:
                divisors.append(n//i)
    return sorted(divisors)

N = int(input())

ans = len(divisors(N-1)) -1

for k in divisors(N)[1:]:
    N_ = N
    while N_ % k == 0:
        N_ = N_//k
    if N_ % k == 1:
        ans += 1

print(ans)

