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?

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.

Constraints

• $2 \leq N \leq 10^{12}$
• N is an integer.

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

见题面 Input 部分

见题面 Output 部分