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())

if N == 2:
    # K = 2
    print(1)
    exit()

result = 2 # K = N - 1, N
for K in range(2, int(N ** 0.5 + 1)):
    t = N
    while t >= K and t % K == 0:
        t //= K
    if t % K == 1:
        result += 1

    if (N-1) % K == 0 and (N-1) // K > K:
        result += 1
print(result)
