Training Session

题意翻译

多组询问，每次给定 $n$ 个二元组 $(a_i,b_i)$，保证任意两个二元组的 $a_i$ 或者 $b_i$ 至少一个不同。求从这 $n$ 个二元组中选三个满足 $a_i$ 或者 $b_i$ 至少一个两两不同的方案数。 $\sum n\leq 2\cdot 10^5,a_i,b_i\leq n$。 Translated by LinkZelda.

题目描述

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.

输入输出格式

输入格式

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 $ .

输出格式

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

输入输出样例

输入样例 #1

2
4
2 4
3 4
2 1
1 3
5
1 5
2 4
3 3
4 2
5 1

输出样例 #1

3
10

说明

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.