E. Delete a Segmenttime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere are n segments on a Ox axis [l_1, r_1], [l_2, r_2], ..., [l_n, r_n]. Segment [l, r] covers all points from l to r inclusive, so all x such that l \le x \le r.Segments can be placed arbitrarily  — be inside each other, coincide and so on. Segments can degenerate into points, that is l_i=r_i is possible.Union of the set of segments is such a set of segments which covers exactly the same set of points as the original set. For example:  if n=3 and there are segments [3, 6], [100, 100], [5, 8] then their union is 2 segments: [3, 8] and [100, 100];  if n=5 and there are segments [1, 2], [2, 3], [4, 5], [4, 6], [6, 6] then their union is 2 segments: [1, 3] and [4, 6]. Obviously, a union is a set of pairwise non-intersecting segments.You are asked to erase exactly one segment of the given n so that the number of segments in the union of the rest n-1 segments is maximum possible.For example, if n=4 and there are segments [1, 4], [2, 3], [3, 6], [5, 7], then:  erasing the first segment will lead to [2, 3], [3, 6], [5, 7] remaining, which have 1 segment in their union;  erasing the second segment will lead to [1, 4], [3, 6], [5, 7] remaining, which have 1 segment in their union;  erasing the third segment will lead to [1, 4], [2, 3], [5, 7] remaining, which have 2 segments in their union;  erasing the fourth segment will lead to [1, 4], [2, 3], [3, 6] remaining, which have 1 segment in their union. Thus, you are required to erase the third segment to get answer 2.Write a program that will find the maximum number of segments in the union of n-1 segments if you erase any of the given n segments.Note that if there are multiple equal segments in the given set, then you can erase only one of them anyway. So the set after erasing will have exactly n-1 segments.InputThe first line contains one integer t (1 \le t \le 10^4) — the number of test cases in the test. Then the descriptions of t test cases follow.The first of each test case contains a single integer n (2 \le n \le 2\cdot10^5) — the number of segments in the given set. Then n lines follow, each contains a description of a segment — a pair of integers l_i, r_i (-10^9 \le l_i \le r_i \le 10^9), where l_i and r_i are the coordinates of the left and right borders of the i-th segment, respectively.The segments are given in an arbitrary order.It is guaranteed that the sum of n over all test cases does not exceed 2\cdot10^5.OutputPrint t integers — the answers to the t given test cases in the order of input. The answer is the maximum number of segments in the union of n-1 segments if you erase any of the given n segments.ExampleInput
3
4
1 4
2 3
3 6
5 7
3
5 5
5 5
5 5
6
3 3
1 1
5 5
1 5
2 2
4 4
Output
2
1
5

3
4
1 4
2 3
3 6
5 7
3
5 5
5 5
5 5
6
3 3
1 1
5 5
1 5
2 2
4 4

2 1 5 
['brute force', 'constructive algorithms', 'data structures', 'dp', 'graphs', 'sortings', 'trees', 'two pointers', '*2300']