Programming Question 1- Generating Lattice Paths: Generating all possible paths to go from one point to another in a lattice (that is, a grid) is a popular problem in mathematics and has several applications, for example, in game design. Consider a 1x1 grid. To get to the top right corner starting from the bottom left corner, there are exactly 2 possible paths. Here we assume that one can move either up (North direction) or right (East direction) only (diagonal movement is not allowed). 1x1 Grid (Paths are North-East and East-North) For a 2 x2 grid,there are 6 paths as shown below: For a 3 x 3 grid, there are 20 paths: For a 4x4 grid, there are 70 paths, and so on. The number of paths increases rapidly with the grid size, and is given by the formula (2n)