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())

def y(n):
    yaku = set()
    for i in range(1, 10 ** 6 + 1):
        if n % i == 0:
            yaku.add(i)
            yaku.add( n // i)
    yaku.remove(1)
    return yaku

ans = len(y(n - 1))

for i in y(n):
    nn = n
    while nn % i == 0:
        nn //= i
    if nn % i == 1:
        ans += 1
print(ans)
        
