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
import queue

N = int(input())

def common_divisors(n):
    i = 1
    res = []
    while i*i <= n:
        if n % i == 0:
            res.append(i)
            res.append(n//i)
        if i*i == n:
            res.pop()
        i += 1
    return res

ans = 0
ans += len(common_divisors(N-1))-1

for i in common_divisors(N):
    if i == 1:
        continue
    n = N
    while n % i == 0:
        n /= i
    if n % i == 1:
        ans += 1
print(ans)

