instruction:
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.
question:
['solve', 'for', 'a', 'and', 'check', 'your', 'solution', 'we', 'have', 'a', 'plus', 'five', 'is', 'equal', 'to', '54', 'now', 'all', 'this', 'is', 'saying', 'is', 'that', 'we', 'have', 'some', 'number', 'some', 'variable', 'a', 'and', 'if', 'I', 'add', '5', 'to', 'it', 'I', 'will', 'get', '54', 'and', 'you', 'might', 'be', 'able', 'to', 'do', 'this', 'in', 'your', 'head', 'but', "we're", 'going', 'to', 'do', 'it', 'a', 'little', 'bit', 'more', 'systematically', 'because', "that'll", 'be', 'helpful', 'for', 'you', 'when', 'we', 'do', 'more', 'complicated', 'problems', 'so', 'in', 'general', 'whenever', 'you', 'have', 'an', 'equation', 'like', 'this', 'we', 'want', 'to', 'have', 'the', 'variable', 'we', 'want', 'this', 'a', 'all', 'by', 'itself', 'on', 'one']
answer:
['Solve', 'for', 'a', 'and', 'check', 'your', 'solution', 'we', 'have', 'a', 'plus', '5', 'is', 'equal', 'to', '54.', 'Now,', 'all', 'this', 'is', 'saying', 'is', 'that', 'we', 'have', 'some', 'numbers,', 'some', 'variable', 'a.', 'And', 'if', 'I', 'add', '5', 'to', 'it,', 'I', 'will', 'get', '54.', 'And', 'you', 'might', 'be', 'able', 'to', 'do', 'this', 'in', 'your', 'head.', 'But', "we're", 'going', 'to', 'do', 'it', 'a', 'little', 'bit', 'more', 'systematically.', 'Because', "that'll", 'be', 'helpful', 'for', 'you', 'when', 'we', 'do', 'more', 'complicated', 'problems.', 'So', 'in', 'general,', 'whenever', 'you', 'have', 'an', 'equation', 'like', 'this,', 'we', 'want', 'to', 'have', 'the', 'variable.', 'We', 'want', 'this', 'a', 'all', 'by', 'itself', 'on', 'one']

question:
["we're", 'told', 'to', 'solve', 'for', 'y', 'and', 'we', 'have', 'this', 'inequality', 'that', 'says', 'that', 'the', 'absolute', 'value', 'of', 'y', 'plus', '22', 'is', 'less', 'than', 'or', 'equal', 'to', '13', 'and', 'a', 'half', 'or', 'thirteen', 'point', 'five', 'so', 'a', 'good', 'place', 'to', 'start', 'is', 'maybe', 'they', 'just', 'isolate', 'the', 'absolute', 'value', 'of', 'y', 'on', 'the', 'left', 'hand', 'side', 'of', 'this', 'inequality', 'and', 'the', 'best', 'way', 'to', 'do', 'that', 'we', 'can', 'subtract', '22', 'from', 'both', 'sides', 'so', "let's", 'subtract', '22', 'from', 'both', 'sides', 'the', 'left', 'hand', 'side', 'these', 'guys', 'cancel', 'out', 'that', 'was', 'the', 'whole', 'point', 'so', "you're", 'just', 'left', 'with', 'the', 'absolute']
answer:
["We're", 'told', 'to', 'solve', 'for', 'y,', 'and', 'we', 'have', 'this', 'inequality', 'that', 'says', 'that', 'the', 'absolute', 'value', 'of', 'y', 'plus', '22', 'is', 'less', 'than', 'or', 'equal', 'to', '13', 'and', 'a', 'half', 'or', 'thirteen', 'point', 'five', 'so', 'a', 'good', 'place', 'to', 'start', 'is', 'maybe', 'to', 'just', 'isolate', 'the', 'absolute', 'value', 'of', 'y', 'on', 'the', 'left', 'hand', 'side', 'of', 'this', 'inequality.', 'And', 'the', 'best', 'way', 'to', 'do', 'that,', 'we', 'can', 'subtract', '22', 'from', 'both', 'sides.', 'So', "let's", 'subtract', '22', 'from', 'both', 'sides', 'the', 'left', 'hand', 'side', 'these', 'guys', 'cancel', 'out,', 'that', 'was', 'the', 'whole', 'point,', 'so', "you're", 'just', 'left', 'with', 'the', 'absolute']

question:
["let's", 'take', 'a', 'little', 'bit', 'of', 'a', 'hiatus', 'from', 'our', 'more', 'rigorous', 'math', 'where', "we're", 'building', 'the', 'mathematics', 'of', 'vector', 'algebra', 'and', 'just', 'think', 'a', 'little', 'bit', 'about', 'something', 'that', "you'll", 'probably', 'encounter', 'if', 'you', '', 'have', 'to', 'have', 'to', 'write', 'a', 'three-dimensional', 'computer', 'program', '', 'have', 'to', 'do', 'any', 'mathematics', 'dealing', 'with', 'three', 'dimensions', 'if', "that's", 'the', 'idea', 'of', 'just', 'the', 'equation', 'of', 'a', 'plane', 'equation', 'of', 'a', 'plane', 'in', 'r3', 'and', 'you', 'know', 'what', 'a', 'plane', 'is', 'I', 'mean', 'we', 'live', 'in', 'a', 'three-dimensional', 'world', 'and', 'we', 'see', 'planes', 'all', 'around', 'us', 'the', 'the', 'surface', 'of', 'your', 'monitor']
answer:
Let's take a little bit of a hiatus from our more rigorous math where we're building the mathematics of vector algebra and just think a little bit about something that you'll probably encounter if you have to have to write a three-dimensional computer program have to do any mathematics dealing with three dimensions. And that's the idea of just the equation of a plane equation of a plane in R3. And you know what a plane is. I mean we live in a three-dimensional world and we see planes all around us the the surface of your monitor,