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())

divisors = set()
for i in range(1, int(-(-n**.5//1))+1):
    if n % i == 0:
        divisors |= {i, n//i}

ans = set()
for div in divisors:
    x = n
    if div == 1:
        continue
    while x % div == 0:
        x = x//div
    if x % div == 1:
        ans |= {div}


n -= 1
for i in range(1, int(-(-n**.5//1))+1):
    if n % i == 0:
        ans |= {i, n//i}

ans ^= {1}
print(len(ans))
