Meet over Grid

There are $N$ people standing on an infinite grid. The coordinates of the $i^{th}$ person is given by $(X_i,Y_i)$. In one move, a person can move to any of its adjacent cell. Note that two cells are adjacent if they share an edge. A group of size $M$ can be formed by selecting any $M$ out of the $N$ people. The *cost* of such a group is defined as the **minimum** number of total moves require