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 Python (2.7.6) (judge verdict: Runtime Error)


def solve1(n):
    # n = k ^ a
    res = []
    for i in xrange(1, 100):
        u = int(pow(n, 1.0 / i) + 0.1)
        if u ** i == n:
            res.append(u)
    return set(res)

def solve2(n):
    # n = a * k + 1
    m = n - 1

    i = 1
    res = set()
    while i * i <= m:
        if m % i == 0:
            res.add(i)
            res.add(m / i)
        i += 1
    return res ^ set([1])

def solve3(n):
    i = 2
    res = set()
    while i * i <= n:
        if n % i == 0:
            m = n / i
            while m and m % i == 0:
                m /= i
            if m % i == 1:
                res.add(i)
        i += 1
    return res

def brute_force(n):
    res = []
    for i in xrange(2, n + 1):
        m = n
        while m % i == 0:
            m /= i
        m %= i
        if m == 1:
            res.append(i)
    # print res
    return len(res)

def solve(n):
    s1 = solve1(n)
    s2 = solve2(n)
    s3 = solve3(n)
    # print sorted(s1 | s2 | s3)
    return len(s1 | s2 | s3)

assert solve(6) == 3
assert solve(3141) == 13
assert solve(314159265358) == 9

assert solve(10 ** 12)

import random
for i in xrange(100):
    n = random.randint(1, 1000)
    assert brute_force(n) == solve(n)

n = int(raw_input())
print solve(n)