Suppose we are given an n×n grid, some of whose cells are marked; the grid is represented by an array m[1 .. n,1 .. n] of booleans, where m[i, j] = true if and only if cell (i, j) is marked. a monotone path through the grid starts at the top-left cell, moves only right or down at each step, and ends at the bottom-right cell. our goal is to cover the marked cells with as few monotone paths as possible.