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: Wrong Answer)

import sys
n = sys.stdin.readline()
c = 0
K = 2
N = int(n)
M = N
if K <= N/2:
  M = N
  while M % K == 0:
    M //= K
  else:
    M %= K
  if M == 1:
    c += 1
K += 1
while K <= N/2:
  M = N
  while M % K == 0:
    M //= K
  else:
    M %= K
  if M == 1:
    c += 1
  K += 2
print(c + 2)