CodeChef: June Challenge | Minimum Dual Area DAREA| Python, Java, C++ Solutions

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Given NN points in a 2D2D space, find the minimum sum of areas of rectangles required to cover all the points given that we can use at most 22 non-overlapping rectangles whose sides can touch. The rectangles must be axis-aligned, meaning the sides are vertical and horizontal.

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Input

  • The first line contains an integer TT, the number of test cases. Then the test cases follow.
  • Each test case contains N+1N+1 lines of input.
  • The first line contains a single integer NN, the number of points.
  • The next NN lines each contains two integers xixi, yiyi, the coordinates of the ii-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≤1051≤T≤105
  • 1≤N≤1051≤N≤105
  • 0≤xi,yi≤1090≤xi,yi≤109
  • The sum of NN over all test cases is at most 105105.

Subtasks

Subtask #1 (100 points): original constraints

Sample Input

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

0
0
4851

Explanation

Case 1: Since there is only one point, the minimum area of a rectangle to cover this point is 00.

Case 2: We can have rectangles as 22 opposite sides of the square. Since the width of the rectangles is 00, the total area is also 00.

Case 3: The optimal solution is with the rectangles having endpoints {(1,1),(100,1),(1,50),(100,50)}{(1,1),(100,1),(1,50),(100,50)} and {(1,100),(1,100),(100,100),(100,100)}{(1,100),(1,100),(100,100),(100,100)}. Therefore the total area is 49⋅99+0⋅99=485149⋅99+0⋅99=4851

Solution

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