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