Connecting Dots

You have 2m dots on X-axis. The dots are colored in m different colors such that there are exactly 2 dots of each color. The dots are placed at the coordinates (1,0), (2,0), ..., (2m, 0). Your task is to draw a path for each color that joins the two dots of that color. Each path should be composed of vertical or horizontal line segments between grid points. No two paths can intersect or touch eac