D. Training Sessiontime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputMonocarp 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.InputThe 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.OutputPrint the number of ways to select three training problems that meet either of the requirements described in the statement.ExampleInput
2
4
2 4
3 4
2 1
1 3
5
1 5
2 4
3 3
4 2
5 1
Output
3
10
NoteIn 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.
2
4
2 4
3 4
2 1
1 3
5
1 5
2 4
3 3
4 2
5 1

3 10 
['combinatorics', 'data structures', 'geometry', 'implementation', 'math', '*1700']