A14597 | Training Session

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.

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 $2 \cdot 10^5$ .

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