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Given $N$ points in a $2D$ space, find the minimum sum of areas of rectangles required to cover all the points given that we can use at most $2$ non-overlapping rectangles whose sides can touch. The rectangles must be axis-aligned, meaning the sides are vertical and horizontal.

------ Input ------

The first line contains an integer $T$, the number of test cases. Then the test cases follow.
Each test case contains $N + 1$ lines of input.
The first line contains a single integer $N$, the number of points.
The next $N$ lines each contains two integers $x_{i}$, $y_{i}$, the coordinates of the $i$-th point.

Note: Points need not be distinct.

------ Output ------
For each test case, output in a single line the answer to the problem.

------ Constraints ------
$1 ≤ T ≤ 10^{5}$
$1 ≤ N ≤ 10^{5}$
$0 ≤ x_{i}, y_{i} ≤ 10^{9}$
The sum of $N$ over all test cases is at most $10^{5}$.

------ Subtasks ------
Subtask #1 (100 points): original constraints

----- Sample Input 1 ------
3

1

100 100

4

1 100

100 100

100 1

1 1

5

1 100

100 100

100 1

1 1

50 50
----- Sample Output 1 ------
0

0

4851
----- explanation 1 ------
Case 1: Since there is only one point, the minimum area of a rectangle to cover this point is $0$.

Case 2: We can have rectangles as $2$ opposite sides of the square. Since the width of the rectangles is $0$, the total area is also $0$.

Case 3: The optimal solution is with the rectangles having endpoints $\{(1, 1), (100, 1), (1, 50), (100, 50)\}$ and $\{(1, 100), (1, 100), (100, 100), (100, 100)\}$. Therefore the total area is $49 \cdot 99 + 0 \cdot 99 = 4851$

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