CF1598D.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.

Monocarp 是贝尔兰国立大学编程队的教练。他决定为自己的队伍设计一场训练赛的题目集。

Monocarp 手中有 $n$ 道题目，他的所有学生都尚未见过这些题。第 $i$ 道题有一个主题 $a_i$（取值范围为 $1$ 到 $n$ 的整数）和一个难度 $b_i$（取值范围也为 $1$ 到 $n$ 的整数）。所有题目互不相同，即不存在两道题同时具有相同主题和相同难度。

Monocarp 决定从这 $n$ 道题中恰好选出 3 道题组成题目集。所选的三道题必须满足以下两个条件中的至少一个（也可能同时满足）：

• 所选三道题的主题互不相同；
• 所选三道题的难度互不相同。

你的任务是计算出满足上述要求的、选出三道题的方案总数。

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 $2 \cdot 10^5$.

第一行包含一个整数 $t$（$1 \le t \le 50000$）—— 测试用例的数量。

每个测试用例的第一行包含一个整数 $n$（$3 \le n \le 2 \cdot 10^5$）—— Monocarp 拥有的题目数量。

接下来的 $n$ 行中，第 $i$ 行包含两个整数 $a_i$ 和 $b_i$（$1 \le a_i, b_i \le n$）—— 第 $i$ 道题的主题和难度。

保证不存在两道题具有完全相同的话题和难度。

所有测试用例的 $n$ 值之和不超过 $2 \cdot 10^5$。

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

输出满足题目描述中任一要求的三道训练题的选取方案数。

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.

在第一个例子中，你可以选择以下三道题的组合：

• 第 $1$、$2$、$4$ 题；
• 第 $1$、$3$、$4$ 题；
• 第 $2$、$3$、$4$ 题。

因此，方案数等于三。