Number and sum of divisors

You are given a natural number $n$. Find the number and the sum of all its divisors (including $1$ and $n$ itself).

A single integer $n$ ($1 \le n \le 10^{12}$).

A single line with two numbers: the number of divisors and their sum.

It is enough to search for divisors up to $\sqrt{n}$ (d * d <= n): for $n = 10^{12}$ that is steps, while going up to would take — too slow. For every divisor found, also count its pair , but if (a perfect square), do not count it twice.