There are n writing samples that are generated either by humans $($H$)$ or a GAI program $($G$).$ A testing program takes $2$ writing samples, evaluates their similarities, and outputs either a $$high$$ or $$low$$ evaluation. It is assumed all samples that generated by humans have a high level of similarity, and all samples generated by GAI also have a high level of similarity. However, there should be a low level of similarity between a sample generated by humans and another sample generated by GAI. The testing program has generated m evaluations for m pairs of samples. We consider the m evaluations to be consistent if it is possible to label each sample either H or G in such a way that for each pair $($i$,$j$)$ labeled $$high$,$ it is the case that i and j have the same label; and for each pair $($i$,$j$)$ labeled $$low$,$ it is the case that i and j have different labels. a$)$ Model this problem by defining input and output using appropriate notations for formulation and present an efficient algorithm in pseudo$-$code, to determine whether the m evaluations are consistent. b$)$ Show how this algorithm works on a problem instance with $6$ samples and $7$ evaluations and present the output and present the output. c$)$ Analyze the time complexity of your algorithm: determine the closest bound of the running time function using Big$-$O notations