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