Write a Graph client AllPaths whose constructor takes a Graph as argument and supports operations to count or print all simple paths between two given vertices \(\mathrm{s}\) and \(\mathrm{t}\) in the graph. A simple path is a path that does not repeat any vertices. In two-dimensional grids, such paths are referred to as self-avoiding walks (see Section 1.4). Enumerating paths is a fundamental problem in statistical physics and theoretical chemistry—for example, to model the spatial arrangement of linear polymer molecules in a solution. Warning: There might be exponentially many paths.