Chef and Finding Direction

Chef has a grid of size N * N with its rows numbered from 1 to N, and the columns also numbered from 1 to N. The cell at the ith row and the jth column is cell (i,j). From cell (i,j), you can go in one of the four directions U L D R (corresponding to up, left, down, right) to cells (i-1,j), (i,j-1), (i+1,j), (i,j+1) respectively, and of course you cannot go outside of the grid. However, with each