user: In this task, you are given an input stream, and your task is to produce a grammatically correct version of the input sentence. The input to this task is a stream of words, possibly from captions generated by a speech-to-text engine, and the output is a grammatically correct version of the input stream. Stream words are in [] and have been separated with a comma. The sentence can contain words that have case, punctuation, stem-based, intra-word, and digit punctuation errors that need to be corrected. For example, the text should be uppercased/lowercased as per necessity (like the beginning of a sentence, proper nouns, etc.), and digits need to be normalized (6 as six and so on). Note that you don't need to normalize the years. You don't need to fully edit the sentences, if end of the input stream contains sentence fragments, keep them as is.

Example Input: ['if', 'you', 'know', 'the', 'explanation', 'for', 'why', 'the', 'sky', 'is', 'blue', "you've", 'heard', 'that', 'sunlight', 'is', 'white', 'light', 'composed', 'of', 'many', 'frequencies', 'and', 'that', 'higher', 'frequency', 'bluer', 'light', 'scatters', 'in', 'the', 'air', 'more', 'than', 'lower', 'frequency', 'redder', 'light', 'so', 'you', 'might', 'ask', 'why', "isn't", 'the', 'sky', 'violet', 'since', 'violet', 'is', 'an', 'even', 'higher', 'frequency', 'than', 'blue', 'first', 'off', 'ultraviolet', 'light', 'and', 'x-rays', 'are', 'also', 'higher', 'frequency', 'than', 'blue', 'and', 'that', "doesn't", 'mean', 'the', 'sky', 'is', 'the', 'color', 'of', 'x-rays', 'both', 'because', 'we', "can't", 'see', 'them', 'and', 'also', 'because', 'the', 'Sun', "doesn't", 'make', 'very', 'many', 'of', 'them', 'and', 'then', 'the', 'atmosphere']
Example Output: ['If', 'you', 'know', 'the', 'explanation', 'for', 'why', 'the', 'sky', 'is', 'blue', "you've", 'heard', 'that', 'sunlight', 'is', 'white', 'light', 'composed', 'of', 'many', 'frequencies', 'and', 'that', 'higher', 'frequency,', 'bluer,', 'light', 'scatters', 'in', 'the', 'air', 'more', 'than', 'lower', 'frequency,', 'redder,', 'light.', 'So,', 'you', 'might', 'ask', '"why', "isn't", 'the', 'sky', 'violet,', 'since', 'violet', 'is', 'an', 'even', 'higher', 'frequency', 'than', 'blue?".', 'First', 'off,', 'ultraviolet', 'light', 'and', 'x-rays', 'are', 'also', 'higher', 'frequency', 'than', 'blue,', 'and', 'that', "doesn't", 'mean', 'the', 'sky', 'is', 'the', 'color', 'of', 'x-rays…', 'Both', 'because', 'we', "can't", 'see', 'them', 'and', 'also', 'because', 'the', 'sun', "doesn't", 'make', 'very', 'many', 'of', 'them', 'and', 'then', 'the', 'atmosphere']

Example Input: ['I', 'have', 'triangle', 'ABC', 'here', 'and', 'in', 'the', 'last', 'video', 'we', 'started', 'to', 'explore', 'some', 'of', 'the', 'properties', 'of', 'points', 'that', 'are', 'on', 'angle', 'bisectors', 'and', 'now', 'what', 'I', 'want', 'to', 'do', 'in', 'this', 'video', 'is', 'to', 'see', 'what', 'happens', 'when', 'we', 'apply', 'some', 'of', 'those', 'ideas', 'to', 'triangles', 'or', 'the', 'angles', 'and', 'triangles', 'so', "let's", 'bisect', 'this', 'angle', 'right', 'over', 'here', 'angle', 'BAC', 'and', 'let', 'me', 'draw', 'an', 'angle', 'bisector', 'so', 'the', 'angle', 'bisector', 'might', 'look', 'something', 'I', 'want', 'to', 'make', 'sure', 'I', 'get', 'that', 'angle', 'right', 'into', 'pretty', 'close', 'so', 'that', 'looks', 'pretty', 'close', 'so', "that's", 'the', 'angle']
Example Output: ['I', 'have', 'triangle', 'ABC', 'here.', 'And', 'in', 'the', 'last', 'video,', 'we', 'started', 'to', 'explore', 'some', 'of', 'the', 'properties', 'of', 'points', 'that', 'are', 'on', 'angle', 'bisectors.', 'And', 'now,', 'what', 'I', 'want', 'to', 'do', 'in', 'this', 'video', 'is', 'just', 'see', 'what', 'happens', 'when', 'we', 'apply', 'some', 'of', 'those', 'ideas', 'to', 'triangles', 'or', 'the', 'angles', 'in', 'triangles.', 'So', "let's", 'bisect', 'this', 'angle', 'right', 'over', 'here--', 'angle', 'BAC.', 'And', 'let', 'me', 'draw', 'an', 'angle', 'bisector.', 'So', 'the', 'angle', 'bisector', 'might', 'look', 'something--', 'I', 'want', 'to', 'make', 'sure', 'I', 'get', 'that', 'angle', 'right', 'into', 'pretty', 'close', 'so', 'that', 'looks', 'pretty', 'close.', 'So', "that's", 'the', 'angle']

Example Input: ['so', 'we', 'want', 'to', 'evaluate', 'the', 'definite', 'integral', 'from', 'negative', '1', 'to', '2', 'from', 'negative', '1', 'to', 'negative', '2', 'of', '16', 'minus', 'X', 'to', 'the', 'third', 'over', 'X', 'to', 'the', 'third', 'DX', 'now', 'at', 'first', 'this', 'might', 'seem', 'daunting', 'I', 'have', 'this', 'rational', 'expression', 'I', 'have', "X's", 'in', 'the', 'numerators', 'and', "X's", 'in', 'the', 'denominators', 'but', 'we', 'just', 'have', 'to', 'remember', 'we', 'said', 'to', 'do', 'some', 'algebraic', 'manipulation', 'and', 'this', 'is', 'going', 'to', 'seem', 'a', 'lot', 'more', 'tractable', 'this', 'is', 'the', 'same', 'thing', 'as', 'the', 'definite', 'integral', 'from', 'negative', '1', 'to', 'negative', '2', 'of', '16', 'over', 'X', 'to', 'the', '3rd']
Example Output:

assistant: so we want to evaluate the definite integral from negative 1 to 2 from negative 1 to negative 2 of 16 minus x to the third over x to the third dx. Now at first this might seem daunting, I have this rational expression, I have xs in the numerators and xs in the denominators, but we just have to remember, we said to do some algebraic manipulation, and this is going to seem a lot more attractable. This is the same thing as the definite integral from negative one to negative two of 16 over x to the third