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())

ans = [n]
if n != 2:
    ans.append(n - 1)
for k in range(2, min(n - 1, 1000001)):
     tmp = n
     while tmp % k == 0:
         tmp //= k
     tmp %= k
     if tmp == 1:
         ans.append(k)
if 1000000 < n:
    ks = [k for k in ans]
    for k in ks:
        if k < n - 1 and (n - 1) % k == 0:
            ans.append((n - 1) // k)
ans = set(ans)
print(len(ans))