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 divisior(n):
    a = []
    i = 1
    while (i*i <= n):
        if n%i == 0:
            a.append(i)
            if (i*i != n): a.append(n//i)
        i += 1
    return a

ans = 0
a = divisior(n)

for x in a[1:]:
    tmp = n
    while (tmp%x == 0): tmp = tmp//x
    if (tmp%x == 1) : ans += 1

b = divisior(n-1)

ans = ans + len(b) -1

print(ans)


