5232: Superhero's Job
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
上传者：
提交：0
通过：0
题目描述
D. Superhero's Job
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
It's tough to be a superhero. And it's twice as tough to resist the supervillain who is cool at math. Suppose that you're an ordinary Batman in an ordinary city of Gotham. Your enemy Joker mined the building of the city administration and you only have several minutes to neutralize the charge. To do that you should enter the cancel code on the bomb control panel.
However, that mad man decided to give you a hint. This morning the mayor found a playing card under his pillow. There was a line written on the card:
The bomb has a note saying "J(x)=A", where A is some positive integer. You suspect that the cancel code is some integer x that meets the equation J(x)=A. Now in order to decide whether you should neutralize the bomb or run for your life, you've got to count how many distinct positive integers x meet this equation.
However, that mad man decided to give you a hint. This morning the mayor found a playing card under his pillow. There was a line written on the card:
The bomb has a note saying "J(x)=A", where A is some positive integer. You suspect that the cancel code is some integer x that meets the equation J(x)=A. Now in order to decide whether you should neutralize the bomb or run for your life, you've got to count how many distinct positive integers x meet this equation.
Input
The single line of the input contains a single integer A (1≤A≤1012).
Output
Print the number of solutions of the equation J(x)=A.
Examples
Input
3
Output
1
Input
24
Output
3
Note
Record x|n means that number n divides number x.
is defined as the largest positive integer that divides both a and b.
In the first sample test the only suitable value of x is 2. Then J(2)=1+2.
In the second sample test the following values of x match:
- x=14, J(14)=1+2+7+14=24
- x=15, J(15)=1+3+5+15=24
- x=23, J(23)=1+23=24
输入样例 复制
输出样例 复制