In image$-$processing applications, such as for optical character recognition, it is often useful to group together contiguous sets of similarly colored pixels in an image. $($See figure below$)$ For instance, in a black$-$and$-$white image, we might say that a black pixel, $p.$ is adjacent with another black pixel, $q,$ if $q$ shares a boundary with $p\text{'}$s North, East, South, or West boundary. Typically, the way an image is represented imposes constraints on an algorithm for finding the contiguous parts of similarly colored pixels, and, as an image$-$processing algorithm designer, we often don't get to dictate the order in which pixels are presented. Design an efficient algorithm that can take a sequence of black or white pixels, given in an arbitrary order, taken from some image, and output all the contiguous shapes in that image. You may assume that each time a pixel is given, you are told its $(x,y)-$coordinates and the colors of its North, East, South, and West neighbors.