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())
ans=1
s=set()
for i in range(1,int(n**0.5)+1):
  if n%(i+1)==0:
    k=n
    cnt=1
    c=0
    while k%(i+1)==0:
      k//=(i+1)
      cnt*=(i+1)
      if cnt not in s:
        s.add(cnt)
        c+=1
    for j in range(1,c+1):
      if k%((i+1)**j)==1:
        ans+=1
d=dict()
k=n-1
for i in range(1,int((n-1)**0.5)+1):
  t=0
  while k%(i+1)==0:
    k//=(i+1)
    t+=1
  if t>0:
    if i+1 not in d:
      d[i+1]=t
    else:
      d[i+1]+=t
if k>1:
  if k not in d:
    d[k]=1
  else:
    d[k]+=1
d=list(d.items())
m=1
for p,root in d:
  m*=(root+1)
print(ans+m-1)