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
def div(x):
    D = set()
    d = 1
    while d*d <= x:
        if x % d == 0:
            D.add(d)
            D.add(x//d)
        d += 1
    return D


n = int(input())
cnt = 0
for d in div(n) | div(n-1):
    if d == 1:
        continue
    tmp = n
    while tmp % d == 0:
        tmp = tmp // d
    if tmp % d == 1:
        cnt += 1
print(cnt)
