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
num = int(input())
n = num
num -= 1
result = 1
for i in range(2, int(pow(num, 0.5))+1):
    c = 0
    while num%i==0:
        num //= i
        c += 1
    if c>0:
        result *= c+1

if num > 1:
    result *= 2
result -= 1

r = set()
for i in range(2, int(pow(n, 0.5))+1):
    num = n
    if num%i==0:
        r.add(i)
        r.add(n//i)
r.add(n)
for i in r:
    num = n
    while num%i==0:
        num //= i
    if num%i == 1:
        result += 1

print(result)