p02722 AtCoder Beginner Contest 161 - Division or Subtraction
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
```python
N = int(input())
ans = set()

def check(N, k):
    if k<2:
        return False
    N //= k
    while N:
        if (N-1)%k==0:
            return True
        if N%k:
            return False
        N //= k

for k in range(1, int(N**0.5)+1):
    if (N-1)%k==0:
        ans.add(k)
        ans.add((N-1)//k)
    if N%k==0:
        if check(N, k):
            ans.add(k)
        if check(N, N//k):
            ans.add(N//k)

ans.remove(1)
print(len(ans))
```