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
#!/usr/bin/env python3


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


n = int(input())
ans = len(divisors(n - 1)) - 1
for k in divisors(n)[1:]:
    t = n
    while t % k == 0:
        t //= k
    if t % k == 1:
        ans += 1
print(ans)
