Maximize the Intersections

题意翻译

在一个圆上有 $2n$ 个不同的点，具有以下性质：无论你如何选择 $3$ 条连接 $3$ 对互不相干的点的弦，在圆内没有一个点严格属于所有 $3$ 条弦。这些点按顺时针顺序被编号为 $1,2, \ldots ,2n$。 最初，$k$ 条和弦连接了 $k$ 对点，其方式是这些和弦的所有 $2k$ 个端点是不同的。 你想画出 $n-k$ 条额外的和弦，连接剩余的 $2(n-k)$ 个点（每个点必须正好是一个和弦的端点）。 最后，让 $x$ 成为所有 $n$ 条弦的交叉点的总数。计算如果你以最佳方式选择 $n - k$ 条弦，$x$ 能达到的最大值。 请注意，$2n$ 个点的确切位置并不重要，只要第一段中所述的属性成立即可。

题目描述

On a circle lie $ 2n $ distinct points, with the following property: however you choose $ 3 $ chords that connect $ 3 $ disjoint pairs of points, no point strictly inside the circle belongs to all $ 3 $ chords. The points are numbered $ 1, \, 2, \, \dots, \, 2n $ in clockwise order. Initially, $ k $ chords connect $ k $ pairs of points, in such a way that all the $ 2k $ endpoints of these chords are distinct. You want to draw $ n - k $ additional chords that connect the remaining $ 2(n - k) $ points (each point must be an endpoint of exactly one chord). In the end, let $ x $ be the total number of intersections among all $ n $ chords. Compute the maximum value that $ x $ can attain if you choose the $ n - k $ chords optimally. Note that the exact position of the $ 2n $ points is not relevant, as long as the property stated in the first paragraph holds.

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 100 $ ) — the number of test cases. Then $ t $ test cases follow. The first line of each test case contains two integers $ n $ and $ k $ ( $ 1 \le n \le 100 $ , $ 0 \le k \le n $ ) — half the number of points and the number of chords initially drawn. Then $ k $ lines follow. The $ i $ -th of them contains two integers $ x_i $ and $ y_i $ ( $ 1 \le x_i, \, y_i \le 2n $ , $ x_i \ne y_i $ ) — the endpoints of the $ i $ -th chord. It is guaranteed that the $ 2k $ numbers $ x_1, \, y_1, \, x_2, \, y_2, \, \dots, \, x_k, \, y_k $ are all distinct.

输出格式

For each test case, output the maximum number of intersections that can be obtained by drawing $ n - k $ additional chords.

输入输出样例

输入样例 #1

4
4 2
8 2
1 5
1 1
2 1
2 0
10 6
14 6
2 20
9 10
13 18
15 12
11 7

输出样例 #1

4
0
1
14

说明

In the first test case, there are three ways to draw the $ 2 $ additional chords, shown below (black chords are the ones initially drawn, while red chords are the new ones): We see that the third way gives the maximum number of intersections, namely $ 4 $ . In the second test case, there are no more chords to draw. Of course, with only one chord present there are no intersections. In the third test case, we can make at most one intersection by drawing chords $ 1-3 $ and $ 2-4 $ , as shown below: 

题意翻译

在一个圆上有 $2n$ 个不同的点，具有以下性质：无论你如何选择 $3$ 条连接 $3$ 对互不相干的点的弦，在圆内没有一个点严格属于所有 $3$ 条弦。这些点按顺时针顺序被编号为 $1,2, \ldots ,2n$。 最初，$k$ 条和弦连接了 $k$ 对点，其方式是这些和弦的所有 $2k$ 个端点是不同的。 你想画出 $n-k$ 条额外的和弦，连接剩余的 $2(n-k)$ 个点（每个点必须正好是一个和弦的端点）。 最后，让 $x$ 成为所有 $n$ 条弦的交叉点的总数。计算如果你以最佳方式选择 $n - k$ 条弦，$x$ 能达到的最大值。 请注意，$2n$ 个点的确切位置并不重要，只要第一段中所述的属性成立即可。