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

a = set(divisor(n-1))

for k in divisor(n):
    if k < 2:
        continue
    if k in a:
        continue
    m = n
    while m%k == 0:
        m //= k
    s = m%k
    if s == 1:
        a.add(k)

print(len(a)-1)

