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
#!/usr/bin/python3

def calcDivisors(x):
    divs = []
    for i in range(1, int(x ** 0.5)+1):
        if x % i == 0:
            divs.append(i)
            if i * i != x:
                divs.append(x // i)
    return divs

n = int(input())
c = 0

#n = ak + 1
c += len(calcDivisors(n - 1)) - 1

#n = k^n(ak + 1)
divs = calcDivisors(n)
divs.sort()
for k in divs[1:]:
    r = n
    while r % k == 0:
        r //= k
    if r % k == 1:
        c += 1

print(c)