Erploring a maze: There is an n x n grid that has n2 distinct integers, labeled 1 to n2 in each cell. You can choose any cell to start, and in each step you can jump to a cell in the same row or column that has a greater number than the current cell. The route needs to be alternating, i.e. if you jump horizontally in the previous step, you need to jump vertically in the next step, and vice versa. The length of the route is defined as the number of cells visiteod on the route. First, suppose there are 2n people, each charting a specific route. There is one person per row, and one person per column Itcrate over the numbers in increasing order. When a number is sclected, the two pcople in that row and column wil use that number in their route, and swap places. Prove that one of these people will find a route of length n, and also prove that it is not always possible to find a route of length n1