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())

cnt = 0

def check(d):
    tmp = n
    while tmp % d == 0:tmp //= d
    tmp %= d
    return tmp == 1

d = 1
while d * d <= n:
    if n % d != 0:
        d+=1
        continue
    if d != 1:
        cnt += check(d)
    if n // d > d:
        cnt += check(n // d)
    d += 1

n -= 1
d = 1
while d * d <= n:
    if n % d != 0:
        d+=1
        continue
    if d != 1:
        cnt += 1
    if n // d > d:
        cnt += 1
    d += 1

print(cnt)
