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())

div = []
for i in range(1, int(n**0.5)+1):
    if n % i == 0:
        div.append(i)
        if i ** 2 != n:
            div.append(n // i)

cnt = 0
for i in range(1, int((n-1)**0.5)+1):
    if (n - 1) % i == 0:
        if i ** 2 == n - 1:
            cnt += 1
        else:
            cnt += 2

res = cnt - 1
for v in div[1:]:
    tmp = n
    while tmp % v == 0:
        tmp //= v
    if tmp % v == 1:
        res += 1

print(res)