Minimum Cost to Connect All Points Problem Statement

Given an array COORDINATES representing the integer coordinates of some points on a 2D plane, determine the minimum cost required to connect all points. The cost to connect two points, (x1, y1) and (x2, y2), is defined by their Manhattan distance: |x1 - x2| + |y1 - y2|.

Input:

The first line of input contains an integer 'T' representing the number of test cases. The first line of each test case contains an integer ‘N’ representing the number of points in the ‘COORDINATES’ array. The next ‘N’ lines of each test case contain two space-separated integers representing the ‘X’ and ‘Y’ coordinates of a point.

Output:

For each test case, output a single integer denoting the minimum cost to connect all points. Each test case's result should be printed on a new line.

Example:

Consider the input:

2
3
0 0
2 2
3 10
4
0 0
10 10
20 20
5 5

Expected output:

12
30

Constraints:

• 1 ≤ T ≤ 5
• 1 ≤ N ≤ 1000
• 10^{-6} ≤ X, Y ≤ 10^{6}
• All points are distinct.

Note:

You do not need to implement input/output handling. The focus should be on the function logic to compute the minimum cost.

Ensure all points are connected with one simple path only, as defined by path terminology in graph theory.