Similar Chocolates
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## Data Structures, Hash Maps, Hash Tables, Implementation

Problem
Editorial
Analytics

There are $N$ chocolates denoted by array $A$ where $A[i]$ is the length of the $i$-th chocolate. Alice can melt each chocolate and then convert it into a chocolate whose length is any divisor of the number $A[i]$. So, a chocolate of length $A[i]$ can be converted into $X$ different types of chocolate where $X$ is the count of divisors of the number $A[i]$. So you need to count the total unordered pair of chocolates such that their $X$ value is same.

Input Format
The first line contains an integer $N$ as input denoting the total number of elements in the array $A$.
The next line contains $N$ space-separated integers that denote the elements of the array $A$.

Output Format
In the output, print the total number of ways as mentioned in the statement.

Constraints
$1 \le N \le 10^5$
$1 \le A[i] \le 10^6$

SAMPLE INPUT
3
2 3 4
SAMPLE OUTPUT
1

Explanation

There is only one possible value i.e. to pick the chocolates $2$ and $3$ as both of them have $2$ divisors hence their $X$ value is same.

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

## This Problem was Asked in

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