408115: GYM102992 C Certain Scientific Railgun

Misaka Mikoto is the third-ranked Level 5 esper in Academy City and has been nicknamed Railgun due to her signature move. One day, several evil robots invade Academy City and Misaka is planning to terminate all of them.

Consider Academy City as a 2-dimensional plane. There are $$$n$$$ robots in total and the position of the $$$i$$$-th robot is $$$(x_i, y_i)$$$. Misaka will start moving from $$$(0, 0)$$$ and her railgun ability will terminate all robots sharing the same $$$x$$$- or $$$y$$$-coordinate with her. More formally, if Misaka is now located at $$$(x_m, y_m)$$$, all robots whose $$$x_i = x_m$$$ or $$$y_i = y_m$$$ will be terminated.

As Misaka hates decimals and Euclidean geometry, she will only move from one integer point to another integer point and can only move horizontally (parallel to the $$$x$$$-axis) or vertically (parallel to the $$$y$$$-axis). As moving among the city is quite tiresome, Misaka asks you to calculate the minimum distance she has to move to terminate all robots.

Recall that an integer point is a point whose $$$x$$$-coordinate and $$$y$$$-coordinate are both integers.

There are multiple test cases. The first line of the input contains an integer $$$T$$$ indicating the number of test cases. For each test case:

The first line contains an integer $$$n$$$ ($$$1 \leq n \leq 10^5)$$$ indicating the number of robots.

For the following $$$n$$$ lines, the $$$i$$$-th line contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$-10^9 \le x_i, y_i \le 10^9$$$) indicating the position of the $$$i$$$-th robot.

It is guaranteed that the sum of $$$n$$$ of all test cases will not exceed $$$10^5$$$.

For each test case output one line containing one integer indicating the minimum distance Misaka needs to move to terminate all robots.

3
2
0 1
1 0
4
1 1
-3 -3
4 -4
-2 2
4
1 100
3 100
-100 1
3 -100

0
8
4

For the second sample test case, Misaka should first go to $$$(0, 1)$$$, then to $$$(0, 2)$$$, then to $$$(0, -3)$$$, then to $$$(0, -4)$$$.

For the third sample test case, Misaka should first go to $$$(1, 0)$$$, then to $$$(1, 1)$$$, then to $$$(3, 1)$$$.