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())
count = 1
for i in range(int(n ** 0.5)):
    test = i + 1
    n2 = n
    if test == 1:
        continue
    while n2 % test == 0:
        n2 //= test
    else:
        n2 %= test
    if n2 == 1:
        count += 1
n3 = n - 1
a = []
for i in range(1, int(n3 ** 0.5) + 1):
    if n3 % i == 0:
        temp = n3 // i
        if temp > int(n ** 0.5):
            a.append(temp)
count += len(a)
print(count)