3. [20 Points] PCFG: Consider the following simple PCFG S ->NP VP S-VP NP > Pronoun NP-> PlurNourn VP -> Verb VP- Verb NP VP -> VP PP PP> Prep NEP 0.6 0.4 0.4 0.6 0.2 0.2 0.6 1.0 Pronoun>I Pronoun YOU PlurNoun>FLIES PlurNoun>ARROWS VerbLIKE Verb-FLIES Prep-> LIKE Prep-> WITH 0.5 0.5 0.5 0.5 0.6 0.4 0.4 0.6 Use the probabilistic CKY algorithm tofind the most probable parse tree for the sentence: "FLIES LIKE ARROWS a. Show the triangular CKY table with each cell filled with s constituents together with their probabilities, showing your work FLIES LIKE AR ROWS b. Finally, showafinal parse trees for this sentence (in the original grammar) with their probabilities