F - Division or Subtraction /

### 問題文

2 以上 N 以下の整数 K を決めて、NK 未満になるまで次の操作を繰り返し行います。

• 操作：NK で割り切れるとき、NN/K に置き換える。そうでないとき、NN-K に置き換える。

### 制約

• 2 \leq N \leq 10^{12}
• N は整数

### 入力

N


### 入力例 1

6


### 出力例 1

3


それぞれのとき、N は次のように変化します。

• K=2 のとき：6 \to 3 \to 1
• K=5 のとき：6 \to 1
• K=6 のとき：6 \to 1

### 入力例 2

3141


### 出力例 2

13


### 入力例 3

314159265358


### 出力例 3

9


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