I have a grid containing $$$10^5$$$ rows and $$$10^5$$$ columns. I also have coordinates of $$$N$$$ cells of this grid each of which has either a red ball, or a blue ball, or both. When a person visits a cell, he/she can collect all the balls from that cell. The target is to reach the bottom-right cell from the top-left cell by collecting at least one ball of each color. From one cell, it's only possible to visit the cell on its right or the cell below it. Upper bound of $$$N$$$ is $$$1000$$$.