Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

6

Sample Output 1

3

There are three choices of K in which N becomes 1 in the end: 2, 5, and 6.

In each of these choices, N will change as follows:

When K=2: 6 \to 3 \to 1

When K=5: 6 \to 1

When K=6: 6 \to 1

Sample Input 2

3141

Sample Output 2

13

Sample Input 3

314159265358

Sample Output 3

9

Solution in PyPy2 (5.6.0) (judge verdict: Wrong Answer)

n = input()

m = n - 1
sqm = int(m ** 0.5) + 1

ans = set([m])
for i in xrange(2, sqm):
    if m % i == 0:
        ans.add(i)
        if i * i != m: ans.add(m // i)

divs = [n]
sqn = int(n ** 0.5) + 1
for i in xrange(2, sqn):
    if n % i == 0:
        divs.append(i)
        if i * i != n: divs.append(n // i)

for d in divs:
    N = n
    while N % d == 0: N //= d

    if N % d == 1: ans.add(d)

print len(ans)