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 (3.4.3) (judge verdict: Accepted)

import math
def divs(n):
    res = []
    for i in range(1, n+1):
        if i * i > n:
            break
        if n % i == 0:
            res.append(i)
            if i != n//i:
                res.append(n//i)
    return res

def one(n, k):
    if k == 1:
        return False
    while n % k == 0:
        n //= k
    n %= k
    return n == 1


n = int(input())

ans = sorted(set(divs(n) + divs(n-1)))

ok = 0
for x in ans:
    if one(n, x):
        ok += 1

print(ok)