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)

N = int(input())
N_tmp = N
pf={}
for i in range(2,int(N**0.5)+1):
    while N%i==0:
        pf[i]=pf.get(i,0)+1
        N//=i
if N>1:pf[N]=1

kouho = [1]
for k in pf.keys():
    new_kouho = []
    for v in range(0, pf[k] + 1):
        for val in kouho:
            new_kouho.append(val * k ** v)
        kouho.extend(new_kouho)

cnt = 0
new_kouho = []
for v in sorted(list(set(kouho)))[1:]:
    for base in range(-1, 1):
        new_kouho.append(v + base)

for K in sorted(list(set(new_kouho))):
    tmp_N = N_tmp
    if K <= 1: continue
    if tmp_N % K == 0:
        tmp_N = (tmp_N // K) % K
    else:
        tmp_N = tmp_N % K
    if tmp_N == 1:
        cnt += 1

print(cnt)