Mikileaks has posted thousands of blurry images purportedly stolen from a secrect government database of UFO sitings. You believe each potentially belongs to one of two different groups, perhaps Romulans vs Dragons (R and D for simplicity), but its hard to directly label any one image in isolation. Instead, you study each pair i and j side-by-side; label the pair (i, j) either same (meaning you believe them both to come from the same group) or different (they represent different groups ). As a third alternative, you may offer no opinion on a given pair; call the pair ambiguous. Given the collection of n images, as well as a collection of m judgments (either same or different for the non-ambiguous pairs), youd like to know if this data is consistent with the idea that each image is from one of only two groups. More concretely, well declare the m judgments to be consistent if it is possible to label each image either R or D in such a way that for each pair (i, j) labeled same, it is the case that i and j have the same label; and for each pair (i, j) labeled different, it is the case that i and j have opposite labels. For example, if 1 and 2 are same, and 1 and 3 are same, but 2 and 3 are different, then there is no consistent labeling, whereas if 2 and 3 are same, then there is a consistent labeling. Give an algorithm with running time O(m + n) that determines whether the m judgments are consistent