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())

if n == 2:
    print(1)
    exit()
num = n - 1
cnt = 1
lst = [n]
for i in range(2, int(n ** 0.5) + 1):
    if num % i == 0:
        cnt += 2
        if num == i ** 2:
            cnt -= 1
    if n % i == 0:
        lst.append(i)
        if n != i ** 2:
            lst.append(n // i)
for num in lst:
    n2 = n
    while n2 % num == 0:
        n2 //= num
    if n2 % num == 1:
        cnt += 1
print(cnt)