yet another mst problem

There are $N$ distinct integer points on the coordinate plane. The distance between $(x_1,y_1)$ and $(x_2,y_2)$ is their Manhattan distance $|x_1-x_2|+|y_1-y_2|$.

You must choose exactly one of the given points and move it to any integer point. After the move, consider a minimum spanning tree whose vertices are the resulting $N$ points.

Find the minimum possible total weight of this minimum spanning tree. You may move the chosen point to its original position or to the same coordinates as another point.

The input is given from Standard Input in the following format:

$T$ case$_1$ case$_2$ $\vdots$ case$_T$

Each case is given in the following format:

$N$ $x_1\ y_1$ $x_2\ y_2$ $\vdots$ $x_N\ y_N$

For each test case, print the minimum possible total weight of the Manhattan minimum spanning tree on one line.

• $1 \leq T \leq 70$.
• $1 \leq N \leq 70$.
• $1 \leq x_i,y_i \leq 10^9$ ($1 \leq i \leq N$).
• $(x_i,y_i) \neq (x_j,y_j)$ ($1 \leq i < j \leq N$).
• The sum of $N$ over all test cases does not exceed $70$.