Welcome Party

The annual welcome party of the Department of Computer Science and Technology is coming soon! Many students have been applying to show up at the welcome party, and every one of them can choose to sing a song or play crosstalk. This troubles the chief director a lot: how to arrange the program list, such that every student can have a chance to show up on the stage, and the satisfactory value of audiences is maximized?

To cope with this problem, the director proposes a model. In this model, every student has two attributes: the singing ability and crosstalking ability. The satisfactory value of audiences to singings is the maximum singing ability among all students that choose to sing a song; similarly, the satisfactory value to crosstalks is the maximum crosstalking ability among all students that choose play crosstalk. The strange thing is, the overall satisfactory value to the whole party is negatively related to the absolute difference between the satisfactory values to singings and crosstalks. The problem is, what is the minimum possible absolute difference between the satisfactory values of the two types of programs?

Note that:
- every student should choose exactly one type of programs to play;
- at least one student should sing a song, and at least one student should play crosstalk.

The first line of input consists of a single integer $T~(1 \leq T \leq 70)$, the number of test cases.

Each test case starts with a line of a single integer $n~(2 \leq n \leq 100\,000)$, denoting the number of students applying to show up on the stage. Then follow $n$ lines, each containing two integers $x$ and $y~(0 \leq x, y \leq 10^{18})$, denoting the singing ability and crosstalking ability of a student.

It is guaranteed that the sum of $n$ over all test cases never exceeds $1\,000\,000$.

For each test case, output a single integer, denoting the minimum possible absolute difference between the satisfactory values of the two types of programs.

2
5
27 46
89 13
55 8
71 86
22 35
3
3 5
4 7
6 2

3
1

2019 Multi-University Training Contest 10