D. Come a Little Closertime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe game field is a matrix of size $$$10^9 \times 10^9$$$, with a cell at the intersection of the $$$a$$$-th row and the $$$b$$$-th column denoted as ($$$a, b$$$).There are $$$n$$$ monsters on the game field, with the $$$i$$$-th monster located in the cell ($$$x_i, y_i$$$), while the other cells are empty. No more than one monster can occupy a single cell.You can move one monster to any cell on the field that is not occupied by another monster at most once .After that, you must select one rectangle on the field; all monsters within the selected rectangle will be destroyed. You must pay $$$1$$$ coin for each cell in the selected rectangle.Your task is to find the minimum number of coins required to destroy all the monsters.InputThe first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of monsters on the field.The following $$$n$$$ lines contain two integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \le x_i, y_i \le 10^9$$$) — the coordinates of the cell with the $$$i$$$-th monster. All pairs ($$$x_i, y_i$$$) are distinct.It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$2 \cdot 10^5$$$.OutputFor each test case, output a single integer — the minimum cost to destroy all $$$n$$$ monsters.ExampleInput731 11 22 151 12 66 43 38 241 11 10000000001000000000 11000000000 100000000011 151 24 24 33 13 231 12 52 244 33 14 41 2Output3 32 1000000000000000000 1 6 4 8 NoteBelow are examples of optimal moves, with the cells of the rectangle to be selected highlighted in green. Required move for the first example. Required move for the fifth example.