The Treasure of The Segments

题意翻译

$Polycarp$有$n$个数字区间，每个区间有两个参数$l[i]$（起始），$r[i]$（结束）。 $Polycarp$对一个好集合的定义是： 你在所有元素中选取部分元素组成这个集合。 你可以在这个集合中找到一个元素$p[i]$，使这个集合中每个元素都至少含有$p[i]$左右区间涵盖的数字之一。 题目给的样例$[[1,4],[2,3],[3,6]]$是一个好集合。$[[1,2],[2,3],[3,5],[4,5]]$则不是一个好集合。 现在给你$n$个数字区间，让你求从中至少删去多少个元素，才能使该集合为一个好集合。 输入格式： 第一行一个数字，测试数据组数。 每组数据第一行为一个数字$n$，表示一共有多少个区间。 接下来$n$行每行两个正整数$l[i]$和$r[i]$。 输出格式： 对于每组数据，输出一个整数，为答案。

题目描述

Polycarp found $ n $ segments on the street. A segment with the index $ i $ is described by two integers $ l_i $ and $ r_i $ — coordinates of the beginning and end of the segment, respectively. Polycarp realized that he didn't need all the segments, so he wanted to delete some of them. Polycarp believes that a set of $ k $ segments is good if there is a segment $ [l_i, r_i] $ ( $ 1 \leq i \leq k $ ) from the set, such that it intersects every segment from the set (the intersection must be a point or segment). For example, a set of $ 3 $ segments $ [[1, 4], [2, 3], [3, 6]] $ is good, since the segment $ [2, 3] $ intersects each segment from the set. Set of $ 4 $ segments $ [[1, 2], [2, 3], [3, 5], [4, 5]] $ is not good. Polycarp wonders, what is the minimum number of segments he has to delete so that the remaining segments form a good set?

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \leq t \leq 2 \cdot 10^5 $ ) — number of test cases. Then $ t $ test cases follow. The first line of each test case contains a single integer $ n $ ( $ 1 \leq n \leq 2 \cdot 10^5 $ ) — the number of segments. This is followed by $ n $ lines describing the segments. Each segment is described by two integers $ l $ and $ r $ ( $ 1 \leq l \leq r \leq 10^9 $ ) — coordinates of the beginning and end of the segment, respectively. It is guaranteed that the sum of $ n $ for all test cases does not exceed $ 2 \cdot 10^5 $ .

输出格式

For each test case, output a single integer — the minimum number of segments that need to be deleted in order for the set of remaining segments to become good.

输入输出样例

输入样例 #1

4
3
1 4
2 3
3 6
4
1 2
2 3
3 5
4 5
5
1 2
3 8
4 5
6 7
9 10
5
1 5
2 4
3 5
3 8
4 8

输出样例 #1

0
1
2
0