Training Session
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.
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.
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.
Samples
2
4
2 4
3 4
2 1
1 3
5
1 5
2 4
3 3
4 2
5 1
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.