2. Max-Flow and Min-Cut Problem

In this problem, we need to decide whether there is a feasible plan for all the persons in a building to escape when they meet some emergency issues. More specifically, a building is described as an n by n grid and the position of p persons are represented as the integer points (x1, y1), . . . , (xp, yp) in the building. Note that to ensure safety, we dont allow any intersection between the paths of any two persons. Therefore, your task is to decide whether there exist p vertex-disjoint paths from their starting points to any p different points on the boundary of the grid. Give an algorithm polynomial in n and prove the correctness of it.