Training Session

2000ms

262144K

Description:

Monocarp is the coach of the Berland State University programming teams. He decided to compose a problemset for a training session for his teams.

Monocarp has $$$n$$$ problems that none of his students have seen yet. The $$$i$$$-th problem has a topic $$$a_i$$$ (an integer from $$$1$$$ to $$$n$$$) and a difficulty $$$b_i$$$ (an integer from $$$1$$$ to $$$n$$$). All problems are different, that is, there are no two tasks that have the same topic and difficulty at the same time.

Monocarp decided to select exactly $$$3$$$ problems from $$$n$$$ problems for the problemset. The problems should satisfy at least one of two conditions (possibly, both):

the topics of all three selected problems are different;
the difficulties of all three selected problems are different.

Your task is to determine the number of ways to select three problems for the problemset.

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 50000$$$) — the number of testcases.

The first line of each testcase contains an integer $$$n$$$ ($$$3 \le n \le 2 \cdot 10^5$$$) — the number of problems that Monocarp have.

In the $$$i$$$-th of the following $$$n$$$ lines, there are two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \le a_i, b_i \le n$$$) — the topic and the difficulty of the $$$i$$$-th problem.

It is guaranteed that there are no two problems that have the same topic and difficulty at the same time.

The sum of $$$n$$$ over all testcases doesn't exceed $$$2 \cdot 10^5$$$.

Output:

Print the number of ways to select three training problems that meet either of the requirements described in the statement.

Sample Input:

Sample Output:

3
10

Note:

In the first example, you can take the following sets of three problems:

problems $$$1$$$, $$$2$$$, $$$4$$$;
problems $$$1$$$, $$$3$$$, $$$4$$$;
problems $$$2$$$, $$$3$$$, $$$4$$$.

Thus, the number of ways is equal to three.

Informação

Provedor Codeforces

Código CF1598D