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())

def divisors(n):
    ret1 = []
    ret2 = []
    i = 1
    while i**2 <= N:
        if n%i == 0:
            ret1 += [i]
            ret2 += [n//i]
        i += 1
    return ret1 + ret2

ans1 = len(set(divisors(N-1))) - 1
ans2_cand = set(divisors(N))
ans2 = 0
for k in ans2_cand:
    if k == 1: continue
    n = N
    while n%k == 0:
        n = n//k
    if n%k == 1:
        ans2 += 1


print(ans1 + ans2)