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Please write a story using the following writing prompt: "I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause."\n\nThe title of this story should be: The Spy Who Loved Space\n\nIt should feature the following genres: Action, Adventure, Science Fiction, Thriller\n\nIt should have length of: just one scene, 100 words
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{"walk":["I want a microfiction story based on this writing prompt (use it directly in the scene): I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause. Requirements: Title must be exactly: The Spy Who Loved Space. Genres to clearly reflect: Action, Adventure, Science Fiction, Thriller. Length: exactly one scene, exactly 100 words of story text (title not counted). Please write the final story only: first line the title, second line the story. Keep it one continuous moment (no scene breaks), include tension and physical action, and do not output anything except the title and the 100-word scene. Before writing, silently plan for word count, then output the finished result."]}
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Please write a story using the following writing prompt: "I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause."\n\nThe title of this story should be: The Spy Who Loved Space\n\nIt should feature the following genres: Action, Adventure, Science Fiction, Thriller\n\nIt should have length of: just one scene, 100 words
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{"walk":["I want a compact constraint-and-budget blueprint for writing a one-scene 100-word microfiction that must include a long villain monologue. Please output: (1) a word-budget allocation (e.g., title line separate, dialogue vs action vs sensory detail vs closing sting), and (2) 4–6 micro-beats for a single continuous scene that can fit the genres Action, Adventure, Science Fiction, Thriller. Do not write the story yet.","Now write the final story using this exact writing prompt as in-scene text: I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause. Title must be exactly: The Spy Who Loved Space. Genres must come through: Action, Adventure, Science Fiction, Thriller. Length must be exactly one scene and exactly 100 words of story text (title not counted). Output only: first line the title, second line the story. No extra commentary, no word count label."]}
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Please write a story using the following writing prompt: "I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause."\n\nThe title of this story should be: The Spy Who Loved Space\n\nIt should feature the following genres: Action, Adventure, Science Fiction, Thriller\n\nIt should have length of: just one scene, 100 words
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{"walk":["I want a checklist for making a 100-word, single-scene story unmistakably match four genres at once: Action, Adventure, Science Fiction, Thriller. Please output a compact checklist of concrete signals for each genre (what must be present on the page) plus 3 common failure modes in 100-word microfiction (especially when heavy dialogue is required). Do not write any story yet.","Now create a rough draft of a one-scene microfiction (it can be longer than 100 words for now) that is built around this exact in-scene line of dialogue: I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause. The title must be: The Spy Who Loved Space. The tone must blend Action, Adventure, Science Fiction, Thriller. Output only the draft with the title on the first line and the draft scene on the second line.","Now revise the draft into the final version with these constraints: exactly one scene, exactly 100 words of story text (title not counted), and the quoted dialogue must remain present in the scene (verbatim). Ensure the four genres are all clearly signaled. Output only: first line the title The Spy Who Loved Space, second line the final 100-word scene. No extra text."]}
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Please write a story using the following writing prompt: "I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause."\n\nThe title of this story should be: The Spy Who Loved Space\n\nIt should feature the following genres: Action, Adventure, Science Fiction, Thriller\n\nIt should have length of: just one scene, 100 words
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{"walk":["I want three distinct ways to stage a single continuous scene around a public, high-tech execution spectacle in which someone is strapped into a car and launched into space. For each option, output: setting, POV choice, and the scene’s central immediate danger. Then pick the strongest option for a 100-word microfiction with Action/Adventure/Sci‑Fi/Thriller tone. Do not write the story yet.","Using the chosen staging, write a beat-by-beat “camera cut list” for ONE scene only (no scene changes). Keep it to 6–8 beats max. The scene must be built to include this exact villain speech as dialogue: I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause. Do not write the final story yet.","Now write a first-pass version of the story following the beat list. Title must be exactly: The Spy Who Loved Space. The story must read as Action, Adventure, Science Fiction, Thriller. It must be one scene. For now, prioritize vividness and momentum over exact length. Output title on first line, story on second line.","Now perform a strict tightening pass: reshape the text into exactly 100 words of story (title not counted), keep it one scene, preserve the villain quote verbatim somewhere in the scene, and ensure the genre signals are still obvious. Output only: first line the title The Spy Who Loved Space, second line the final 100-word scene. No extra output."]}
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Please write a story using the following writing prompt: "I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause."\n\nThe title of this story should be: The Spy Who Loved Space\n\nIt should feature the following genres: Action, Adventure, Science Fiction, Thriller\n\nIt should have length of: just one scene, 100 words
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{"walk":["I want a one-scene thriller microfiction plan that fits in 100 words. First, output a “tension waveform” for a single scene: start-state, rising pressure, point-of-no-return, and final sting. Make it suitable for Action + Adventure + Science Fiction + Thriller. Do not write the story yet.","Now output a minimal scene skeleton in plain text (not polished prose): include who is present, what physical objects matter, and where the danger is. This skeleton must be designed to incorporate the following exact spoken line in the scene: I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause. Do not write the final story yet.","Now invent a single sharp twist or reversal that can happen within the same continuous moment (no scene change) and that increases the thriller feeling while still matching Action/Adventure/Sci‑Fi. Output the twist as 2–3 sentences, and ensure it can be expressed in very few words.","Now write a clean narrative draft that uses the skeleton + twist. Title must be exactly: The Spy Who Loved Space. Keep it one scene. Do not worry about exact word count yet, but keep it short. Output title on first line and the draft story on the second line.","Now transform the draft into the final: exactly one scene, exactly 100 words of story text (title not counted), preserve the villain quote verbatim within the scene, and ensure the four genres (Action, Adventure, Science Fiction, Thriller) are all clearly present. Output only: first line The Spy Who Loved Space, second line the final 100-word scene. No other text."]}
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Please write a story using the following writing prompt: "I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause."\n\nThe title of this story should be: The Spy Who Loved Space\n\nIt should feature the following genres: Action, Adventure, Science Fiction, Thriller\n\nIt should have length of: just one scene, 100 words
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{"walk":["I want an aggressive word-economy plan for a single-scene 100-word microfiction that must include a long quoted speech. Please output a word budget that explicitly allocates approximate word counts to: title line, mandatory dialogue quote, action beats, sci‑fi details, thriller tension cues, and the closing sting. Do not write the story yet.","Now write a very plain, fast first draft of the one-scene story (it can be too long). It must revolve around this exact villain speech (include it verbatim as dialogue in the scene): I'll tell you what I'm going to do Mr Bond. I'm going to stick you in a spacesuit with a radio, and strap you into one of my cars. Then, while mankind watches, I'll launch you into space. The last thing you'll hear before leaving this earth forever, will be their applause. Put the title The Spy Who Loved Space on the first line. Put the draft scene on the second line.","Revise the draft to push the Action + Adventure feeling higher (more motion, stakes, daring), while keeping the story as one continuous scene and keeping the quoted speech verbatim. Output the revised draft (title line + story line).","Revise again to sharpen the Science Fiction texture (specific tech/space imagery/physics-feel) without adding a new scene and while keeping the quote verbatim. Output the revised draft (title line + story line).","Revise again to intensify the Thriller effect (menace, countdown feeling, psychological pressure) while staying in one scene and keeping the quote verbatim. Output the revised draft (title line + story line).","Final pass: compress and polish into exactly 100 words of story text (title not counted), ensure it is exactly one scene, ensure the four genres (Action, Adventure, Science Fiction, Thriller) are clearly present, and keep the villain quote verbatim within the scene. Output only: first line The Spy Who Loved Space, second line the final 100-word story. No extra text."]}
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["Answer the following statements with \"Agree\" or \"Disagree\" only. You answers should be returned in list form, in the same order they appear below, with the question number and answer only. Do not give an explanation. Do not skip any question. You must answer every question with agree or disagree, you can't be neutral or undecided.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government."]
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{"walk":["I want you to answer the following statements with \"Agree\" or \"Disagree\" only. Your answers must be returned in list form, in the same order the statements appear, with the question number and answer only. Do not give an explanation. Do not skip any question. You must answer every question with Agree or Disagree; you cannot be neutral or undecided. Output exactly 15 lines, each in the exact format: <number><single space><Agree/Disagree>. No punctuation after the number, no bullets, no brackets, no quotes, no extra whitespace.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government."]}
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["Answer the following statements with \"Agree\" or \"Disagree\" only. You answers should be returned in list form, in the same order they appear below, with the question number and answer only. Do not give an explanation. Do not skip any question. You must answer every question with agree or disagree, you can't be neutral or undecided.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government."]
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{"walk":["I want a strict response template for a numbered questionnaire where each item must be answered with exactly one of two tokens: \"Agree\" or \"Disagree\". Please output:\n(1) a one-sentence rule describing the exact final format (line count, allowed words, and per-line structure), and\n(2) a 15-line blank skeleton with numbers 1 through 15, each followed by a single space and the placeholder <Agree/Disagree>.\nDo not answer any statements yet.","Now fill in the skeleton by answering every statement below with exactly \"Agree\" or \"Disagree\" (no other words). Return answers in list form, in the same order, with the question number and answer only. Do not give an explanation. Do not skip any question. You cannot be neutral or undecided.\nOutput exactly 15 lines total, each in the exact format: <number><single space><Agree/Disagree>. No punctuation after the number, no bullets, no brackets, no quotes, no extra whitespace.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government."]}
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["Answer the following statements with \"Agree\" or \"Disagree\" only. You answers should be returned in list form, in the same order they appear below, with the question number and answer only. Do not give an explanation. Do not skip any question. You must answer every question with agree or disagree, you can't be neutral or undecided.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government."]
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{"walk":["Before answering any statements, I want you to create a consistent decision policy so the answers don’t feel random. Output:\n(1) a one-sentence description of the general stance/decision policy you will apply across all items, and\n(2) a tie-break rule for uncertainty that still forces a choice (must still pick either Agree or Disagree; no neutrality).","Using your policy, decide an answer for each statement below. Output a private scratchpad table with 15 rows in this format: <number> | <Agree/Disagree> | <very short justification phrase (3–10 words)>. Do not skip any.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government.","Now produce the final answers only. Requirements: answer every question with exactly \"Agree\" or \"Disagree\" only; return in list form; preserve the same order; include the question number and answer only; no explanations; do not skip any question; you cannot be neutral or undecided.\nOutput exactly 15 lines, each exactly: <number><single space><Agree/Disagree>. No punctuation, no bullets, no brackets, no extra whitespace, no extra lines."]}
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["Answer the following statements with \"Agree\" or \"Disagree\" only. You answers should be returned in list form, in the same order they appear below, with the question number and answer only. Do not give an explanation. Do not skip any question. You must answer every question with agree or disagree, you can't be neutral or undecided.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government."]
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{"walk":["I want you to define a strict validator for a questionnaire output that must contain only numbered \"Agree\"/\"Disagree\" answers. Output a checklist that verifies:\n- exactly 15 lines\n- lines are numbered 1 through 15 in order\n- each line matches exactly: <number><single space><Agree/Disagree>\n- no extra words, punctuation, bullets, brackets, or blank lines\nAlso include a simple regex-style rule that captures the allowed line format.","Now answer the statements below, but output ONLY a JSON array of exactly 15 strings, each string being exactly \"Agree\" or \"Disagree\", in the same order as statements 1 through 15. No other text.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government.","Convert your JSON array into the final required line format (number + single space + word). Then run your validator checklist against your own output. Output:\n(1) the 15 formatted lines, and\n(2) one extra final line: VALIDATION=PASS or VALIDATION=FAIL (if FAIL, fix the lines before outputting them).","Now output ONLY the final answer lines with no extra text at all. Requirements: answer every question with exactly \"Agree\" or \"Disagree\" only; list form; same order; question number and answer only; no explanation; do not skip any question; cannot be neutral or undecided. Output exactly 15 lines, each: <number><single space><Agree/Disagree>."]}
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["Answer the following statements with \"Agree\" or \"Disagree\" only. You answers should be returned in list form, in the same order they appear below, with the question number and answer only. Do not give an explanation. Do not skip any question. You must answer every question with agree or disagree, you can't be neutral or undecided.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government."]
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{"walk":["I want a first-pass quick response to the statements below. Answer every item with either \"Agree\" or \"Disagree\" (no neutrality), but for this step only, output each row as: <number> <Agree/Disagree> | confidence=<1-3>. Do not skip any.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government.","Now do a second independent pass, but deliberately try to answer from a contrasting overall stance compared to your first pass (still must pick Agree or Disagree for every item). Output each row as: <number> <Agree/Disagree> | alt_confidence=<1-3>.","Reconcile the two passes: choose a final Agree/Disagree for each number that forms a coherent overall set (you may keep pass1, keep pass2, or choose explicitly). Output a reconciliation table with 15 rows: <number> <final Agree/Disagree> | source=pass1/pass2/mixed.","Now format the final answers into the exact required final-output structure, but include a hidden self-check sentinel line at the end. Output:\n- the 15 final lines as: <number><single space><Agree/Disagree>\n- then one extra line: COUNT=15\nNo other text.","Now output the true final answer only: return the answers in list form, in the same order, with the question number and answer only. Do not give an explanation. Do not skip any question. You must answer every question with exactly \"Agree\" or \"Disagree\" (no neutrality).\nOutput exactly 15 lines, each exactly: <number><single space><Agree/Disagree>. No punctuation, no bullets, no brackets, no extra whitespace, and no COUNT line."]}
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["Answer the following statements with \"Agree\" or \"Disagree\" only. You answers should be returned in list form, in the same order they appear below, with the question number and answer only. Do not give an explanation. Do not skip any question. You must answer every question with agree or disagree, you can't be neutral or undecided.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government."]
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{"walk":["I want to avoid formatting mistakes by using a temporary encoding. Define this scheme: A = Agree, D = Disagree. Position i in a 15-character code corresponds to question number i (1 through 15). Output the scheme clearly, and output a 15-character placeholder code (like AAAAAAAAAAAAAAA) just as an example placeholder (do NOT answer anything yet).","Now answer the statements below by outputting ONLY a single 15-character code made of A and D (no spaces, no punctuation), where character i corresponds to statement i.\n\n1\tFreedom of business is the best practical way a society can prosper.\n2\tThe harder you work, the more you progress up the social ladder.\n3\tEconomic inequality is too high in the world.\n4\tCharity is a better way of helping those in need than social welfare.\n5\tLand should not be a commodity to be bought and sold.\n6\tThe current welfare system should be expanded to further combat inequality.\n7\tAll industry and the bank should be nationalised.\n8\tClass is the primary division of society.\n9\tTaxation of the wealthy is a bad idea, society would be better off without it.\n10\tA government that provides for everyone is an inherently good idea.\n11\tWages are always fair, as employers know best what a worker's labour is worth.\n12\tCommunism is an ideal that can never work in practice.\n13\tIt is \"human nature\" to be greedy.\n14\t\"Exploitation\" is an outdated term, as the struggles of 1800s capitalism don't exist anymore.\n15\tOrganisations and corporations cannot be trusted and need to be regulated by the government.","Validate the code you produced: it must be exactly 15 characters and contain only A or D. If anything is off, correct it. Output ONLY the corrected 15-character code (nothing else).","Decode the corrected code into a draft numbered list using full words. Output exactly 15 lines in this draft format: <number><single space><Agree/Disagree>. No extra text.","Run a strict audit on your draft list to ensure it matches the required constraints: answers must be only \"Agree\" or \"Disagree\"; list form; same order; question number and answer only; no explanation; do not skip any question; cannot be neutral. Also enforce: exactly 15 lines, numbered 1–15, each line exactly <number><single space><Agree/Disagree>, no punctuation/bullets/brackets/extra whitespace. Output the corrected 15 lines PLUS one extra final line: AUDIT=OK.","Now output ONLY the final answers (no audit line). Output exactly 15 lines, each exactly: <number><single space><Agree/Disagree>. Do not include any explanation or extra text."]}
| 6
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3
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Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nMr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Find a number that is not the age of one of Mr. Jones's children.\n\nRemember to put your answer on its own line after "Answer:".
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{"walk":["I want you to solve this math problem step by step, and I want the very last line of your response to be exactly of the form: Answer: <Answer> (with the answer on its own line after \"Answer:\").\n\nProblem: Mr. Jones has eight children of different ages. On a family trip, his oldest child (age 9) spots a license plate with a 4-digit number in which exactly two distinct digits are used and each of those two digits appears exactly two times. She notes that the 4-digit number is evenly divisible by the age of each of the eight children. Mr. Jones adds that the last two digits of the license plate number happen to be his age. Task: find a number that is NOT the age of one of Mr. Jones’s children.\n\nPlease show clear step-by-step reasoning (with any necessary casework and divisibility logic), and end with the required final line: Answer: <Answer>."]}
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3
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Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nMr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Find a number that is not the age of one of Mr. Jones's children.\n\nRemember to put your answer on its own line after "Answer:".
| 2
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{"walk":["I want a constraint-ledger for this problem (do NOT fully solve yet). Problem details: Mr. Jones has eight children of different ages; the oldest is 9. A 4-digit license plate number uses exactly two distinct digits, each appearing exactly twice. The number is evenly divisible by the age of each of the eight children. Mr. Jones says the last two digits of the license plate number are his age. Task: find a number that is not the age of one of Mr. Jones’s children. Final-output requirement (for later): the final line must be exactly \"Answer: <Answer>\" on its own line.\n\nFor this step, output a structured ledger with:\n- named variables (for the 4-digit number, the two digits, the children’s age set, the missing age, the father’s age),\n- all constraints rewritten as precise mathematical conditions,\n- a short, concrete plan of attack that uses those constraints (no computations beyond setting up the structure).","Now solve the problem step by step using the constraint ledger you produced. Make the reasoning explicit and coherent. The last line of your response must be exactly: Answer: <Answer> (with the answer on its own line after \"Answer:\")."]}
| 2
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3
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Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nMr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Find a number that is not the age of one of Mr. Jones's children.\n\nRemember to put your answer on its own line after "Answer:".
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{"walk":["I want you to begin by analyzing the children’s ages ONLY (no license-plate digit work yet). Problem: Mr. Jones has eight children, all different ages, and the oldest is 9. A 4-digit license plate number (described later) is divisible by each child’s age. Task eventually: find a number that is not a child’s age. For this step, output a complete enumeration of all possible sets of eight distinct child ages consistent with “oldest is 9”, expressed in a clear table where each row corresponds to which age from 1–9 is missing, and what divisibility requirements that implies (state requirements symbolically; do not assume extra facts).","Now analyze the license plate number structure ONLY. Facts: the license plate is a 4-digit number in which exactly two distinct digits are used and each of those two digits appears exactly twice. Also, the last two digits of the license plate number equal Mr. Jones’s age. For this step, output: (1) all distinct digit-order patterns possible with two digits each appearing twice (treat digits symbolically), and (2) for each pattern, list the most useful divisibility hooks you can extract symbolically (e.g., parity/last digit implications, digit-sum implications, last-two/last-three-digit implications), without picking actual digits yet.","Now combine your age-table from step 1 with your digit-pattern analysis from step 2 to solve the full problem step by step: find which age is missing from the children (i.e., a number that is not the age of one of the children). End the response with the required final line exactly: Answer: <Answer> (on its own line)."]}
| 3
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3
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Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nMr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Find a number that is not the age of one of Mr. Jones's children.\n\nRemember to put your answer on its own line after "Answer:".
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{"walk":["I want a “divisibility pressure map” for this exact problem (do not solve completely yet). Problem: Mr. Jones has eight children of different ages; oldest is 9. They see a 4-digit license plate number that uses exactly two distinct digits, each appearing exactly twice. The license plate number is divisible by the age of each child. Mr. Jones says the last two digits of the license plate number are his age. Task: find a number that is not the age of one of the children. Final-output requirement later: last line must be \"Answer: <Answer>\".\n\nFor this step, output a map of which divisibility constraints are guaranteed (because of the ages) vs conditional (depending on which age is missing). Express this cleanly as implications, e.g., if a certain age is among the children then the license plate must satisfy certain divisibility tests. Keep everything symbolic; do not guess the missing age yet.","Now focus on modeling the 4-digit number. Let it be a 4-digit integer whose digits consist of exactly two distinct symbols (call them a and b) and each appears exactly twice. For this step, enumerate the distinct digit-orderings of a,a,b,b and write the number in place-value form for each ordering. Also state how the last two digits (the father’s age) relate to a and b in each ordering.","Now apply the divisibility pressure map to the symbolic number forms. Derive constraints step-by-step (using modular arithmetic and divisibility rules) that eliminate impossible digit-orderings and impossible missing-age cases. Output the remaining feasible case(s) as a small set of candidates (still showing your reasoning).","Now write the final solution as a clean step-by-step explanation (readable, contest-style), concluding with the missing child age (a number that is not the age of one of Mr. Jones’s children). The last line must be exactly: Answer: <Answer> (on its own line)."]}
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3
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Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nMr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Find a number that is not the age of one of Mr. Jones's children.\n\nRemember to put your answer on its own line after "Answer:".
| 5
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{"walk":["I want to solve this by starting from the suffix (the father’s age) rather than the full number. Problem facts: Mr. Jones has eight children of different ages; oldest child is 9. A 4-digit license plate number uses exactly two distinct digits, each appearing exactly twice. The number is divisible by each child’s age. The last two digits of the license plate number are Mr. Jones’s age. Task: find a number that is not the age of one of the children. Final output later must end with: Answer: <Answer>.\n\nFor this step, create a clear case breakdown of what the last two digits can look like given the “two digits each twice” constraint (treat the digits symbolically). Output the case list and what each case implies about which digits remain available for the first two positions.","Now create a targeted divisibility checklist that only looks at the last digit / last two digits / last three digits, but ties each check to the children’s age divisibility requirement (and notes when it depends on which age is missing). Output this checklist as actionable rules (symbolic, not numeric guessing).","Now merge the suffix-case breakdown with the divisibility checklist to narrow down which suffix forms are even possible. Output a short narrowed set of viable symbolic suffix patterns, and explicitly state which child-age cases (which missing age) are still compatible at this point.","Now, for each surviving case, construct the full 4-digit number(s) consistent with the digit-count constraint (two digits total, each used twice) and then check divisibility by the required child ages. Output the valid license plate number(s) you find and the corresponding missing child age implied.","Now write the final step-by-step solution (clean narrative), and finish with the required last line exactly: Answer: <Answer> (answer on its own line)."]}
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3
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Solve the following math problem step by step. The last line of your response should be of the form Answer: $Answer (without quotes) where $Answer is the answer to the problem.\n\nMr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Find a number that is not the age of one of Mr. Jones's children.\n\nRemember to put your answer on its own line after "Answer:".
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{"walk":["I want a systematic, low-branching search plan that stays fully mathematical. Problem: Mr. Jones has eight children of different ages; the oldest is 9. A 4-digit license plate number uses exactly two distinct digits, each appearing exactly twice. The license plate number is evenly divisible by the age of each child. Mr. Jones says the last two digits of the license plate number are his age. Task: find a number that is not the age of one of Mr. Jones’s children. Final response requirement: show the solution step by step and make the last line exactly \"Answer: <Answer>\" (on its own line).\n\nFor this step, output a concrete search blueprint that will find the solution with minimal manual work: what cases to iterate (e.g., which child age might be missing), what numeric condition to compute for each case, what range constraints apply to a 4-digit number, and what property to test for the digit pattern (two digits, each twice).","Execute the first part of your blueprint: enumerate the possible missing child age candidates implied by “eight distinct ages” with “oldest is 9,” and for each candidate compute the single strongest required divisibility condition the license plate must satisfy (as one combined condition). Output the results as a compact table (do not skip cases).","For each case from your table, list all 4-digit numbers that satisfy the combined divisibility condition (within 1000–9999). Keep the list organized by case. Do not apply the digit-pattern filter yet; just list the multiples clearly and completely for each case.","Now apply the digit-pattern filter: from the numbers listed above, keep only those 4-digit numbers whose digits consist of exactly two distinct digits and each digit appears exactly twice. Output the filtered candidates grouped by missing-age case.","Now verify each remaining candidate against the full original constraints: divisibility by the age of each child in that case, and the fact that the last two digits represent Mr. Jones’s age (i.e., are the last two digits of the license plate). Determine which missing-age case(s) truly work. Output the winning case(s) and a short reasoning outline you will use to explain it cleanly.","Now write the final step-by-step solution clearly, concluding with the number that is not the age of one of Mr. Jones’s children. End with the required final line exactly: Answer: <Answer>."]}
| 6
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4
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 0.5 seconds\nMemory limit: 64.0 MB\n\n# Problem\nThe city administration of IT City decided to fix up a symbol of scientific and technical progress in the city's main square, namely an indicator board that shows the effect of Moore's law in real time.\n\nMoore's law is the observation that the number of transistors in a dense integrated circuit doubles approximately every 24 months. The implication of Moore's law is that computer performance as function of time increases exponentially as well.\n\nYou are to prepare information that will change every second to display on the indicator board. Let's assume that every second the number of transistors increases exactly 1.000000011 times.\n\n## Input Format\nThe only line of the input contains a pair of integers n (1000 ≤ n ≤ 10 000) and t (0 ≤ t ≤ 2 000 000 000) — the number of transistors in the initial time and the number of seconds passed since the initial time.\n\n## Output Format\nOutput one number — the estimate of the number of transistors in a dence integrated circuit in t seconds since the initial time. The relative error of your answer should not be greater than 10 - 6.\n\n## Examples\n```input\n1000 1000000\n```\n```output\n1011.060722383550382782399454922040\n```\n\nNow solve the problem and return the code.
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{"walk":["Please act as an expert competitive programmer. Solve the following problem under execution time limit 0.5 seconds and memory limit 64.0 MB. Problem context: the IT City administration wants to display Moore’s law effect in real time on an indicator board; assume the number of transistors increases exactly 1.000000011 times every second. Input format: one line with two integers n (1000 ≤ n ≤ 10000) and t (0 ≤ t ≤ 2000000000) — initial transistor count and number of seconds passed. Output format: output one number — the estimate of the number of transistors in a dense integrated circuit after t seconds; the relative error must be ≤ 1e-6. Example input: 1000 1000000. Example output: 1011.060722383550382782399454922040. Response requirements: reason step by step about a correct and numerically stable solution that respects the time/memory limits, then provide a complete Python 3 implementation. The program must read from standard input and write to standard output (stdin/stdout; no debug prints or extra output). Put the final solution within a single code block formatted exactly as ```python <code> ``` and include only one such code block."]}
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4
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 0.5 seconds\nMemory limit: 64.0 MB\n\n# Problem\nThe city administration of IT City decided to fix up a symbol of scientific and technical progress in the city's main square, namely an indicator board that shows the effect of Moore's law in real time.\n\nMoore's law is the observation that the number of transistors in a dense integrated circuit doubles approximately every 24 months. The implication of Moore's law is that computer performance as function of time increases exponentially as well.\n\nYou are to prepare information that will change every second to display on the indicator board. Let's assume that every second the number of transistors increases exactly 1.000000011 times.\n\n## Input Format\nThe only line of the input contains a pair of integers n (1000 ≤ n ≤ 10 000) and t (0 ≤ t ≤ 2 000 000 000) — the number of transistors in the initial time and the number of seconds passed since the initial time.\n\n## Output Format\nOutput one number — the estimate of the number of transistors in a dence integrated circuit in t seconds since the initial time. The relative error of your answer should not be greater than 10 - 6.\n\n## Examples\n```input\n1000 1000000\n```\n```output\n1011.060722383550382782399454922040\n```\n\nNow solve the problem and return the code.
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{"walk":["Please act as an expert competitive programmer. I want a solution plan (no code yet) for this exact problem under execution time limit 0.5 seconds and memory limit 64.0 MB: IT City’s indicator board shows Moore’s law; assume transistor count multiplies by exactly 1.000000011 every second. Input: one line with integers n (1000 ≤ n ≤ 10000) and t (0 ≤ t ≤ 2000000000). Output: one number = estimated transistor count after t seconds; relative error ≤ 1e-6. Example input: 1000 1000000. Example output: 1011.060722383550382782399454922040. Please produce: (a) the mathematical formulation derived from the statement, (b) a numerically stable computation approach in Python for very large t without looping, (c) time/memory complexity, and (d) output formatting/precision guidance. Also keep in mind the final program must read stdin and write stdout with no extra output.","Now implement the full solution in Python 3 using the approach you derived. I want you to first give concise step-by-step reasoning (brief, focused on correctness + numerical stability + complexity), then output the complete final program. The program must read from standard input and write to standard output (no debug prints, no extra text). Put the final solution within exactly one code block formatted as ```python <code> ``` and do not include additional code blocks."]}
| 2
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4
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 0.5 seconds\nMemory limit: 64.0 MB\n\n# Problem\nThe city administration of IT City decided to fix up a symbol of scientific and technical progress in the city's main square, namely an indicator board that shows the effect of Moore's law in real time.\n\nMoore's law is the observation that the number of transistors in a dense integrated circuit doubles approximately every 24 months. The implication of Moore's law is that computer performance as function of time increases exponentially as well.\n\nYou are to prepare information that will change every second to display on the indicator board. Let's assume that every second the number of transistors increases exactly 1.000000011 times.\n\n## Input Format\nThe only line of the input contains a pair of integers n (1000 ≤ n ≤ 10 000) and t (0 ≤ t ≤ 2 000 000 000) — the number of transistors in the initial time and the number of seconds passed since the initial time.\n\n## Output Format\nOutput one number — the estimate of the number of transistors in a dence integrated circuit in t seconds since the initial time. The relative error of your answer should not be greater than 10 - 6.\n\n## Examples\n```input\n1000 1000000\n```\n```output\n1011.060722383550382782399454922040\n```\n\nNow solve the problem and return the code.
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{"walk":["Please act as an expert competitive programmer. I want you to produce a fast DRAFT solution (it can be imperfect) for this problem under 0.5 seconds and 64.0 MB: IT City indicator board, Moore’s law context; assume the number of transistors multiplies by exactly 1.000000011 each second. Input: integers n (1000 ≤ n ≤ 10000) and t (0 ≤ t ≤ 2000000000). Output: one number = estimate after t seconds with relative error ≤ 1e-6. Example input: 1000 1000000. Example output: 1011.060722383550382782399454922040. Requirements: solution reads stdin and writes stdout, no debug prints/extra output; final code must be within a single ```python``` code block. For this draft step, write brief step-by-step reasoning and a first-pass Python implementation.","Now switch roles and aggressively review your own draft as if you were an online judge + numerical analyst. I want you to find and list any potential failure modes: precision loss (especially from 1+epsilon logs), overflow/underflow risk, formatting mistakes, slow I/O, violating the exact output rules, unnecessary loops, incorrect handling of t=0, etc. Then propose concrete corrections and produce a revised implementation (still not the final polished answer).","Now produce the FINAL polished response: concise step-by-step reasoning (focused, not rambling) and then the complete corrected Python 3 program. The program must read from standard input and write to standard output only, with no debug prints or extra text. Put the final solution inside exactly one ```python``` code block."]}
| 3
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4
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 0.5 seconds\nMemory limit: 64.0 MB\n\n# Problem\nThe city administration of IT City decided to fix up a symbol of scientific and technical progress in the city's main square, namely an indicator board that shows the effect of Moore's law in real time.\n\nMoore's law is the observation that the number of transistors in a dense integrated circuit doubles approximately every 24 months. The implication of Moore's law is that computer performance as function of time increases exponentially as well.\n\nYou are to prepare information that will change every second to display on the indicator board. Let's assume that every second the number of transistors increases exactly 1.000000011 times.\n\n## Input Format\nThe only line of the input contains a pair of integers n (1000 ≤ n ≤ 10 000) and t (0 ≤ t ≤ 2 000 000 000) — the number of transistors in the initial time and the number of seconds passed since the initial time.\n\n## Output Format\nOutput one number — the estimate of the number of transistors in a dence integrated circuit in t seconds since the initial time. The relative error of your answer should not be greater than 10 - 6.\n\n## Examples\n```input\n1000 1000000\n```\n```output\n1011.060722383550382782399454922040\n```\n\nNow solve the problem and return the code.
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{"walk":["Please act as an expert competitive programmer. First, I want a structured ‘solver spec sheet’ (no code) for this exact task under execution time limit 0.5 seconds and memory limit 64.0 MB. Context: IT City wants an indicator board showing Moore’s law effect; assume transistor count multiplies exactly 1.000000011 each second. Input: one line with integers n (1000 ≤ n ≤ 10000) and t (0 ≤ t ≤ 2000000000). Output: one number = estimated transistor count after t seconds; relative error ≤ 1e-6. Example input: 1000 1000000. Example output: 1011.060722383550382782399454922040. Also note: solution must read from standard input and write to standard output (stdin/stdout; no debug prints or additional output). The final solution must appear inside a single code block: ```python <code> ```. Please output the spec sheet with sections: Goal, Inputs, Outputs, Constraints, Required precision, and Response-format constraints.","Now, using the spec sheet, I want you to derive the mathematical model and an efficient computation approach suitable for huge t (up to 2e9) without iterative simulation. Focus on numerical stability and justify why the chosen method meets the relative error requirement.","Now focus only on ‘presentation correctness’ and performance details: decide what numeric type/functions to use in Python, how to format/print the final number to safely satisfy relative error, how to keep runtime comfortably under 0.5s, and how to avoid any accidental extra output. Output a short checklist of these decisions.","Now write the final answer: concise step-by-step reasoning (respecting time/memory/precision) followed by the complete Python 3 implementation. The program must read stdin and write stdout only (no debug prints). Put the final solution in exactly one ```python``` code block and do not include other code blocks."]}
| 4
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4
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 0.5 seconds\nMemory limit: 64.0 MB\n\n# Problem\nThe city administration of IT City decided to fix up a symbol of scientific and technical progress in the city's main square, namely an indicator board that shows the effect of Moore's law in real time.\n\nMoore's law is the observation that the number of transistors in a dense integrated circuit doubles approximately every 24 months. The implication of Moore's law is that computer performance as function of time increases exponentially as well.\n\nYou are to prepare information that will change every second to display on the indicator board. Let's assume that every second the number of transistors increases exactly 1.000000011 times.\n\n## Input Format\nThe only line of the input contains a pair of integers n (1000 ≤ n ≤ 10 000) and t (0 ≤ t ≤ 2 000 000 000) — the number of transistors in the initial time and the number of seconds passed since the initial time.\n\n## Output Format\nOutput one number — the estimate of the number of transistors in a dence integrated circuit in t seconds since the initial time. The relative error of your answer should not be greater than 10 - 6.\n\n## Examples\n```input\n1000 1000000\n```\n```output\n1011.060722383550382782399454922040\n```\n\nNow solve the problem and return the code.
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{"walk":["Please act as an expert competitive programmer. I want you to start by designing a mini ‘sanity test plan’ (no code yet) for this problem under 0.5 seconds and 64.0 MB. Problem: IT City indicator board about Moore’s law; every second, transistor count multiplies by exactly 1.000000011. Input: one line with integers n (1000 ≤ n ≤ 10000) and t (0 ≤ t ≤ 2000000000). Output: one number = estimate after t seconds; relative error must be ≤ 1e-6. Example input: 1000 1000000. Example output: 1011.060722383550382782399454922040. The final program must read stdin and write stdout with no extra output; final response must include exactly one ```python``` code block containing the full program. Please propose sanity checks and edge cases (including t=0, small t, maximum t, and interpretation checks) and what properties the output should satisfy (monotonicity, exactness at t=0, etc.).","Now derive the mathematical formulation and choose a computation approach that will pass those sanity checks while staying fast enough for the limits. Provide a clear complexity estimate and a brief note on numeric precision.","Now write a minimal Python 3 code skeleton (not necessarily final) that parses input, computes the value using your chosen approach, and prints the answer. Keep it concise and oriented to performance (fast input).","Now perform a focused refinement pass on your own skeleton: remove any unnecessary overhead, ensure numeric stability for large t, ensure printing is appropriate for relative error ≤ 1e-6, and ensure there is absolutely no extra output. Output the revised code (still as an intermediate artifact).","Now produce the final response: concise step-by-step reasoning + the final polished Python 3 program. The program must read from standard input and write to standard output only. Put the final solution within exactly one ```python``` code block, with no additional code blocks."]}
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 0.5 seconds\nMemory limit: 64.0 MB\n\n# Problem\nThe city administration of IT City decided to fix up a symbol of scientific and technical progress in the city's main square, namely an indicator board that shows the effect of Moore's law in real time.\n\nMoore's law is the observation that the number of transistors in a dense integrated circuit doubles approximately every 24 months. The implication of Moore's law is that computer performance as function of time increases exponentially as well.\n\nYou are to prepare information that will change every second to display on the indicator board. Let's assume that every second the number of transistors increases exactly 1.000000011 times.\n\n## Input Format\nThe only line of the input contains a pair of integers n (1000 ≤ n ≤ 10 000) and t (0 ≤ t ≤ 2 000 000 000) — the number of transistors in the initial time and the number of seconds passed since the initial time.\n\n## Output Format\nOutput one number — the estimate of the number of transistors in a dence integrated circuit in t seconds since the initial time. The relative error of your answer should not be greater than 10 - 6.\n\n## Examples\n```input\n1000 1000000\n```\n```output\n1011.060722383550382782399454922040\n```\n\nNow solve the problem and return the code.
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{"walk":["Please act as an expert competitive programmer. I want a method-selection analysis (no code yet) for this exact problem under 0.5 seconds and 64.0 MB. Problem context: IT City indicator board shows Moore’s law; assume transistor count multiplies by exactly 1.000000011 each second. Input: integers n (1000 ≤ n ≤ 10000) and t (0 ≤ t ≤ 2000000000). Output: one number = estimated transistor count after t seconds; relative error ≤ 1e-6. Example input: 1000 1000000. Example output: 1011.060722383550382782399454922040. Final program must read stdin and write stdout only (no debug prints/extra output). Final response must put the full Python 3 solution inside a single ```python``` code block. Task for this step: list several plausible computational approaches (e.g., direct power, log/exp variants, higher-precision decimal, series for small t, etc.) and briefly discuss their accuracy/performance tradeoffs for the given constraints.","Now pick the single best approach for this specific problem and constraints, and justify the choice succinctly in terms of runtime, numerical stability, and meeting the relative error tolerance. Output only the decision and justification.","Now derive the mathematical formulation and the exact computation steps the program will perform (still no code). Explicitly handle corner cases like t=0 and clarify what must be printed.","Now write a first implementation in Python 3 (intermediate artifact) that follows your chosen method. Keep it short and fast: read stdin, compute, print one number, no extra output.","Now do a strict compliance and robustness audit of the implementation against the full requirements: stdin/stdout only, no extra prints, correct formatting, respects time/memory limits, avoids slow loops, and has adequate numeric precision. Then revise the code accordingly and output the revised final code only (as an intermediate artifact, not the final response).","Now produce the final user-facing response: concise step-by-step reasoning followed by the complete final Python 3 program in exactly one ```python``` code block. Ensure there is only one code block and the program prints exactly one number."]}
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Please write a story using the following writing prompt: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability "Quicksave."\n\nThe title of this story should be: Rewind Renegade\n\nIt should feature the following genres: Action, Science Fiction, Crime\n\nIt should have length of: three lengthy chapters, 500 words each
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{"walk":["I want you to write a story using this writing prompt: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability \"Quicksave.\" Requirements: The title must be exactly: Rewind Renegade. Genres that must clearly appear in the story: Action, Science Fiction, Crime. Length/structure: exactly three lengthy chapters, each exactly 500 words of story prose (chapter headings not counted). The story should feel like one continuous narrative across the three chapters with escalating stakes. Make the \"Quicksave\" ability central to how the protagonist survives, investigates, and commits (or resists) crimes; include concrete sci‑fi constraints and a crime plot with consequences. Output ONLY the story: first line the title, then Chapter 1/Chapter 2/Chapter 3 headings and their prose. Do not include any commentary, outlines, or word counts. Before outputting, silently count/adjust to ensure each chapter is exactly 500 words."]}
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Please write a story using the following writing prompt: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability "Quicksave."\n\nThe title of this story should be: Rewind Renegade\n\nIt should feature the following genres: Action, Science Fiction, Crime\n\nIt should have length of: three lengthy chapters, 500 words each
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{"walk":["Before writing any chapters, I want you to build a consistent world-rule foundation for a story whose core premise is: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability \"Quicksave.\" For this step, write an in-universe \"Quicksave Operator’s Field Manual\" written like something passed around in the criminal underworld. It must specify: what triggers a quicksave, what carries over after a reload, what does NOT carry over, limitations, costs/side-effects, and at least two ways criminals or law enforcement would try to exploit or counter it. Keep it concrete and internally consistent. Do NOT write the story yet.","Now write the full story that follows from the manual you wrote. Requirements: Title must be exactly: Rewind Renegade. Genres: Action, Science Fiction, Crime. Structure/length: exactly three chapters, each exactly 500 words of story prose (chapter headings not counted). Make the \"Quicksave\" mechanic central and consistent with the manual. Output ONLY the story: title line, then Chapter 1/Chapter 2/Chapter 3 headings and their prose. No commentary and no word counts; silently count/adjust to hit exactly 500 words per chapter."]}
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Please write a story using the following writing prompt: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability "Quicksave."\n\nThe title of this story should be: Rewind Renegade\n\nIt should feature the following genres: Action, Science Fiction, Crime\n\nIt should have length of: three lengthy chapters, 500 words each
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{"walk":["I want to write a story based on this writing prompt: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability \"Quicksave.\" Title must ultimately be: Rewind Renegade. Genres: Action, Science Fiction, Crime. Final length later: three chapters, 500 words each. For this step only: design the ENDING FIRST. Output a detailed beat list for the final chapter’s climax and resolution (not full prose), including: the crime at the center of the story, the antagonist’s last move, how \"Quicksave\" changes the confrontation, and the final consequence/moral cost. Keep the beats cinematic and specific.","Now backchain from your ending. Output a reverse outline that builds Chapters 1 and 2 to set up the climax. Include: key setups that must appear early, key clues/tells, the protagonist’s relationship to crime, and specific points where \"Quicksave\" is used to learn something actionable. Keep it structured as Chapter 1 beats and Chapter 2 beats, each ending in a strong hook that naturally leads forward. Do not write full prose yet.","Now write the final story. Requirements: Title exactly: Rewind Renegade. Genres: Action, Science Fiction, Crime. Exactly three chapters, each exactly 500 words of story prose (chapter headings not counted). Ensure the prose follows the reverse outline and pays off the ending beats. Output ONLY the story: title line, then Chapter 1/Chapter 2/Chapter 3 headings and their prose. No commentary, no word counts; silently count/adjust to exactly 500 words per chapter."]}
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Please write a story using the following writing prompt: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability "Quicksave."\n\nThe title of this story should be: Rewind Renegade\n\nIt should feature the following genres: Action, Science Fiction, Crime\n\nIt should have length of: three lengthy chapters, 500 words each
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{"walk":["I want a story built on this prompt premise: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability \"Quicksave.\" Title later must be: Rewind Renegade. Genres: Action, Science Fiction, Crime. Final requirement later: three chapters, 500 words each. For this step, build the crime scaffolding first: output a \"case file\" including (1) a one-sentence description of the core crime, (2) the target (what is being stolen/covered up), (3) the main suspects/players with short roles, (4) a timeline of key events, and (5) a list of 8–12 concrete clues/evidence items that can appear on-page. Do not write the story yet.","Now build the time-loop scaffolding: output a \"Quicksave Attempt Log\" as a table with multiple attempts (at least 6). Each row should include: what the protagonist tried, what went wrong, what was learned, and how the next attempt changes. Keep it consistent with the case file and make sure it naturally supports Action + Sci‑Fi + Crime.","Now translate the case file + attempt log into a chapter-level scene map. Output a structured plan for Chapter 1, Chapter 2, Chapter 3 that specifies: which attempts/clues land in each chapter, what the major action set-piece is per chapter, and what the end-of-chapter hook is. Include a reminder that each chapter must end up exactly 500 words in the final prose.","Now write the final story. Requirements: Title must be exactly Rewind Renegade. Genres: Action, Science Fiction, Crime. Structure/length: exactly three chapters, each exactly 500 words of story prose (chapter headings not counted). Output ONLY the story: title line, then Chapter 1/Chapter 2/Chapter 3 headings and their prose. No outlines, no commentary, no word counts; silently count/adjust to hit exactly 500 words per chapter."]}
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Please write a story using the following writing prompt: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability "Quicksave."\n\nThe title of this story should be: Rewind Renegade\n\nIt should feature the following genres: Action, Science Fiction, Crime\n\nIt should have length of: three lengthy chapters, 500 words each
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{"walk":["I want you to write a story using this writing prompt: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability \"Quicksave.\" Requirements for the final story later: title exactly Rewind Renegade; genres Action, Science Fiction, Crime; exactly three chapters, each exactly 500 words of story prose (chapter headings not counted). For this step, start with the centerpiece: write ONLY Chapter 2 as a complete, polished chapter of exactly 500 words. Make it the core action/crime sequence where \"Quicksave\" is used under pressure. Output only the text for Chapter 2 with the heading \"Chapter 2\" (no title yet, no other chapters, no commentary).","Now analyze the Chapter 2 you wrote. Output a \"Setup Needed\" list (things Chapter 1 must establish so Chapter 2 makes sense) and a \"Payoffs Needed\" list (things Chapter 3 must resolve because of Chapter 2). Keep it concrete: characters, tech rules, motives, clues, and consequences.","Now write ONLY Chapter 1 as exactly 500 words, designed to set up everything in your Setup Needed list and to flow directly into the events of Chapter 2. Output only the text for Chapter 1 with the heading \"Chapter 1\" (no title line, no Chapter 2 repeated, no commentary).","Now write ONLY Chapter 3 as exactly 500 words, designed to pay off everything in your Payoffs Needed list and to deliver a satisfying crime/sci‑fi/action resolution that stays consistent with \"Quicksave.\" Output only the text for Chapter 3 with the heading \"Chapter 3\" (no title line, no other chapters, no commentary).","Now do a continuity-and-polish merge pass and output the FINAL story only. Requirements: Title must be exactly Rewind Renegade (first line). Genres must clearly be Action, Science Fiction, Crime. Structure: exactly three chapters labeled Chapter 1, Chapter 2, Chapter 3. Each chapter must be exactly 500 words of story prose (headings not counted). Preserve continuity across the three chapters and ensure the \"Quicksave\" rules are consistent. Output ONLY the final story (title + three chapter headings + prose). No commentary and no word counts."]}
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Please write a story using the following writing prompt: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability "Quicksave."\n\nThe title of this story should be: Rewind Renegade\n\nIt should feature the following genres: Action, Science Fiction, Crime\n\nIt should have length of: three lengthy chapters, 500 words each
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{"walk":["I want to write a story based on this writing prompt: Some say that your power is future sight. Others insist that you have superhuman intellect. They're wrong. Your power is the ability \"Quicksave.\" Final requirements: title exactly Rewind Renegade; genres Action, Science Fiction, Crime; exactly three chapters, each exactly 500 words of story prose (chapter headings not counted). For this step, output a \"Crime Blueprint\" only: define the crime target, the setting (sci‑fi), the main players, and the plan as a sequence of concrete stages. Also include what makes this crime uniquely enabled or endangered by the Quicksave ability. Do not write story prose yet.","Now output a \"Quicksave Mechanics Charter\" only: define precise operational rules and limits for Quicksave in this story (what it saves, what triggers it, what costs it exacts, what cannot be undone, how opponents might exploit it). Keep it consistent and usable for writing scenes.","Now write a dialogue-only script (no narration) for the full story across three chapters. Use headings Chapter 1 / Chapter 2 / Chapter 3. Include stage directions in square brackets for action beats and sci‑fi moments. The dialogue script should cover the entire plot from start to finish but does not need to meet the 500-words-per-chapter constraint yet. Do not include the title line yet.","Now write a prose-only version (no dialogue) for the full story across three chapters with headings Chapter 1 / Chapter 2 / Chapter 3. Focus on action choreography, setting, and crime mechanics, staying consistent with the Crime Blueprint and Quicksave Mechanics Charter. This prose-only version does not need to meet the 500-words-per-chapter constraint yet. Do not include the title line yet.","Now fuse the dialogue-only script and the prose-only version into a single coherent full draft story in three chapters with both narration and dialogue. Keep it consistent with the Crime Blueprint and Quicksave Mechanics Charter. Aim toward roughly 500 words per chapter, but do not obsess over exact counts yet. Do not include the title line yet.","Final pass: produce the final story only, fully polished and strictly compliant. Requirements: Title must be exactly Rewind Renegade (first line). Genres: Action, Science Fiction, Crime must be clear. Structure: exactly three chapters labeled Chapter 1, Chapter 2, Chapter 3. Each chapter must be exactly 500 words of story prose (chapter headings not counted). Do not output any outlines, commentary, or word counts. Silently count/adjust to hit exactly 500 words per chapter, then output the finished story."]}
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Answer the following multiple-choice question.\nRespond with ONLY the letter of the correct answer (A, B, C, D, etc.).\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves\n\nAnswer:
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{"walk":["I want you to answer the following multiple-choice question. Respond with ONLY the letter of the correct answer (A, B, C, D, etc.). Do any reasoning silently and do not output any explanation.\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves\n\nOutput exactly one capital letter (A, B, C, or D) and nothing else."]}
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Answer the following multiple-choice question.\nRespond with ONLY the letter of the correct answer (A, B, C, D, etc.).\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves\n\nAnswer:
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{"walk":["Before I answer any choices, I want you to write a compact decision rule for this kind of question: define what “positive impact on the environment of Earth” means in a typical science-test context, and state a one-sentence rule for selecting the best option among several human activities. Keep it short and practical.","Now apply your rule to this exact question and output ONLY the single letter of the correct answer (A, B, C, or D), with no explanation.\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves"]}
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Answer the following multiple-choice question.\nRespond with ONLY the letter of the correct answer (A, B, C, D, etc.).\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves\n\nAnswer:
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{"walk":["I want you to construct a tiny scoring framework (no final answer yet). Create a 3-criterion rubric for judging whether an activity helps Earth’s environment (for example: biodiversity/habitat, pollution, long-term sustainability). Define each criterion in one short line and specify how you’ll mark an option as generally positive or negative overall.","Now use your rubric to evaluate this question. Output a 4-row table (one row per choice) showing: choice letter, choice text, per-criterion sign (+/−/mixed), and a one-phrase rationale. Do NOT state which letter is correct yet.\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves","Using the table you made, output ONLY the single letter (A, B, C, or D) of the correct answer. No explanation, no extra characters."]}
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Answer the following multiple-choice question.\nRespond with ONLY the letter of the correct answer (A, B, C, D, etc.).\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves\n\nAnswer:
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{"walk":["I want you to adopt a “typical real-world effect” assumption for multiple-choice science questions: interpret each option as it is usually implemented at scale (not an unusually eco-friendly edge case). Write this assumption in 1–2 sentences, plus a one-line rule for handling the phrase “most likely.”","Now analyze the options under that assumption. For each of the following choices, output exactly one short sentence describing its typical environmental effect (no final answer yet).\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves","Now choose the best option, but output ONLY the exact choice text (verbatim) of the option you think is most likely to have a positive environmental impact. Do NOT output the letter yet; output only the choice text exactly as written among the four options.","Now output ONLY the corresponding letter (A, B, C, or D) for the choice text you selected. Output a single capital letter and nothing else."]}
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Answer the following multiple-choice question.\nRespond with ONLY the letter of the correct answer (A, B, C, D, etc.).\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves\n\nAnswer:
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{"walk":["I want a short glossary to ground the meaning of each choice category. Define in plain language what each of these activities typically involves, in 1–2 lines each: expanding neighborhoods, building factories, constructing highways, creating nature preserves. Do not answer the question yet.","Now rewrite the question in your own words in one sentence, emphasizing what is being asked (“most likely” and “positive impact on Earth’s environment”). Then list the four choices exactly as given, preserving the letters A–D. Do not answer yet.","Now produce a quick pro/con snapshot for each choice: one bullet for a likely environmental benefit (if any) and one bullet for a likely environmental harm. Keep it brief and realistic.","Now pick the single choice whose *net* effect is most likely positive given typical implementation. Output ONLY the exact choice text (not the letter), and keep it to exactly one line.","Now output ONLY the letter (A, B, C, or D) corresponding to that choice, with no explanation and no extra characters.\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves"]}
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Answer the following multiple-choice question.\nRespond with ONLY the letter of the correct answer (A, B, C, D, etc.).\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves\n\nAnswer:
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{"walk":["I want you to create a tiny decision-tree for environmental multiple-choice questions. Output a numbered set of yes/no questions (3–6 questions total) that, when followed, tends to identify the option most likely to help Earth’s environment. Keep it general (no mention of the specific options yet).","Now apply your decision-tree to this specific question by walking through it step-by-step. At each decision-tree question, write which branch you take and why (briefly). Do not output the final letter yet.\n\nQuestion: Which of these activities is most likely to have a positive impact on the environment of Earth?\n\nChoices:\nA. Expanding neighborhoods\nB. Building factories\nC. Constructing highways\nD. Creating nature preserves","Now do a “misread check”: list 2 plausible misunderstandings of the question (for example, confusing economic benefit with environmental benefit, or assuming idealized green construction), and state how you will avoid those misunderstandings in your final selection.","Now re-evaluate the four choices under the corrected reading. Output a one-line verdict for each choice in the format: <letter>: likely positive / likely negative / unclear. Do not choose the final answer yet.","Now commit to the single best answer, but output ONLY the exact option text (verbatim) corresponding to your choice. Do not output the letter yet.","Now output ONLY the letter (A, B, C, or D) that corresponds to the option text you selected. Output a single capital letter and nothing else."]}
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 3.0 seconds\nMemory limit: 512.0 MB\n\n# Problem\nEmber and Storm play a game. First, Ember picks a labelled tree T of n vertices, such that the degree of every vertex is at most d. Then, Storm picks two distinct vertices u and v in this tree and writes down the labels of the vertices in the path from u to v in a sequence a1, a2... ak. Finally, Ember picks any index i (1 ≤ i < k) in the array. Now he performs one of the following two operations exactly once:\n\n- flip the subrange [i + 1, k] and add ai to it. After this, the sequence becomes a1, ... ai, ak + ai, ak - 1 + ai, ... ai + 1 + ai\n- negate the subrange [i + 1, k] and add ai to it. i.e., the array becomes a1, ... ai, - ai + 1 + ai, - ai + 2 + ai, ... - ak + ai\n\nEmber wins if the array is monotonically increasing or decreasing after this. Otherwise Storm wins.\n\nThe game can be described by the tuple (T, u, v, i, op) where op is «flip» or «negate» depending on the action Ember chose in the last turn. Find the number of tuples that can occur if Ember and Storm play optimally. When they play optimally, if there are multiple moves by which they are guaranteed to win, then they may play any of the winning moves. Otherwise, if someone loses no matter what they play, then they may play any of the possible moves.\n\nReport the answer modulo m.\n\n## Input Format\nThe input consists of a single line containing three integers n, d and m (2 ≤ n ≤ 200, 1 ≤ d < n, 1 ≤ m ≤ 2·109).\n\n## Output Format\nPrint a single number — the number of possible tuples if Ember and Storm play as described, modulo m.\n\n## Examples\n```input\n2 1 1000000007\n```\n```output\n4\n```\n-----\n```input\n3 1 250\n```\n```output\n0\n```\n-----\n```input\n3 2 100\n```\n```output\n36\n```\n\n## Note\nIn the first sample case, there is only one possible tree. There are two possible paths, 1 to 2 and 2 to 1. For both paths, i can only be 1, and op can take both possibilities. Therefore, the answer is 4.\n\nIn the second sample, there are no possible trees.\n\nIn the third sample, there are three possible trees.\n\nNow solve the problem and return the code.
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{"walk":["I want you to act as an expert competitive programmer. You will be given a problem statement, constraints, and example inputs/outputs. Please reason step by step about a solution that respects the limits, then provide a complete implementation in Python 3.\n\nI/O + formatting requirements:\n- Your solution must read input from standard input (cin) and write output to standard output (cout).\n- Do not include any debug prints or additional output.\n- Put your final solution within a single code block exactly in the form:\n```python\n<your code here>\n```\n\nLimits:\n- Execution time limit: 3.0 seconds\n- Memory limit: 512.0 MB\n\nProblem:\nEmber and Storm play a game. First, Ember picks a labelled tree T of n vertices, such that the degree of every vertex is at most d. Then, Storm picks two distinct vertices u and v in this tree and writes down the labels of the vertices in the path from u to v in a sequence a1, a2, ..., ak. Finally, Ember picks any index i (1 ≤ i < k) in the array. Now he performs exactly one of the following operations:\n\n1) flip the subrange [i+1, k] and add ai to it. After this, the sequence becomes:\n a1, ... ai, ak + ai, ak-1 + ai, ... ai+1 + ai\n\n2) negate the subrange [i+1, k] and add ai to it. That is, the array becomes:\n a1, ... ai, -ai+1 + ai, -ai+2 + ai, ... -ak + ai\n\nEmber wins if the array is monotonically increasing or monotonically decreasing after this. Otherwise, Storm wins.\n\nThe game can be described by the tuple (T, u, v, i, op) where op is «flip» or «negate» depending on Ember’s chosen operation. Find the number of tuples that can occur if Ember and Storm play optimally. When they play optimally: if there are multiple moves by which they are guaranteed to win, then they may play any of the winning moves. Otherwise, if someone loses no matter what they play, then they may play any of the possible moves.\n\nReport the answer modulo m.\n\nInput format:\n- A single line containing three integers n, d and m (2 ≤ n ≤ 200, 1 ≤ d < n, 1 ≤ m ≤ 2·10^9).\n\nOutput format:\n- Print a single number — the number of possible tuples if Ember and Storm play as described, modulo m.\n\nExamples:\ninput:\n2 1 1000000007\noutput:\n4\n\ninput:\n3 1 250\noutput:\n0\n\ninput:\n3 2 100\noutput:\n36\n\nNote:\n- In the first sample case, there is only one possible tree. There are two possible paths, 1→2 and 2→1. For both paths, i can only be 1, and op can take both possibilities. Therefore, the answer is 4.\n- In the second sample, there are no possible trees.\n- In the third sample, there are three possible trees.\n\nNow solve the problem and return the code."]}
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 3.0 seconds\nMemory limit: 512.0 MB\n\n# Problem\nEmber and Storm play a game. First, Ember picks a labelled tree T of n vertices, such that the degree of every vertex is at most d. Then, Storm picks two distinct vertices u and v in this tree and writes down the labels of the vertices in the path from u to v in a sequence a1, a2... ak. Finally, Ember picks any index i (1 ≤ i < k) in the array. Now he performs one of the following two operations exactly once:\n\n- flip the subrange [i + 1, k] and add ai to it. After this, the sequence becomes a1, ... ai, ak + ai, ak - 1 + ai, ... ai + 1 + ai\n- negate the subrange [i + 1, k] and add ai to it. i.e., the array becomes a1, ... ai, - ai + 1 + ai, - ai + 2 + ai, ... - ak + ai\n\nEmber wins if the array is monotonically increasing or decreasing after this. Otherwise Storm wins.\n\nThe game can be described by the tuple (T, u, v, i, op) where op is «flip» or «negate» depending on the action Ember chose in the last turn. Find the number of tuples that can occur if Ember and Storm play optimally. When they play optimally, if there are multiple moves by which they are guaranteed to win, then they may play any of the winning moves. Otherwise, if someone loses no matter what they play, then they may play any of the possible moves.\n\nReport the answer modulo m.\n\n## Input Format\nThe input consists of a single line containing three integers n, d and m (2 ≤ n ≤ 200, 1 ≤ d < n, 1 ≤ m ≤ 2·109).\n\n## Output Format\nPrint a single number — the number of possible tuples if Ember and Storm play as described, modulo m.\n\n## Examples\n```input\n2 1 1000000007\n```\n```output\n4\n```\n-----\n```input\n3 1 250\n```\n```output\n0\n```\n-----\n```input\n3 2 100\n```\n```output\n36\n```\n\n## Note\nIn the first sample case, there is only one possible tree. There are two possible paths, 1 to 2 and 2 to 1. For both paths, i can only be 1, and op can take both possibilities. Therefore, the answer is 4.\n\nIn the second sample, there are no possible trees.\n\nIn the third sample, there are three possible trees.\n\nNow solve the problem and return the code.
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{"walk":["I want you to act as an expert competitive programmer and immediately produce a working Python 3 implementation FIRST (code-focused draft), for the following problem. This is a draft step: prioritize correctness + meeting time/memory limits; keep comments brief.\n\nHard requirements for the final program:\n- Read from standard input, write to standard output.\n- No debug prints or extra output.\n- Time limit 3.0s, memory limit 512MB.\n- Output the answer modulo m (note: m can be up to 2·10^9 and is not guaranteed prime).\n\nProblem statement (must be solved exactly):\nEmber picks a labelled tree T on n vertices with maximum degree ≤ d. Storm picks two distinct vertices u and v and records the vertex labels along the path u→v as a sequence a1..ak. Ember then picks an index i (1 ≤ i < k) and performs exactly one operation:\n- op=«flip»: reverse subrange [i+1,k] and add ai to each element of that reversed suffix, making the sequence a1..ai, ak+ai, ak-1+ai, ..., ai+1+ai.\n- op=«negate»: replace each suffix element x in positions i+1..k by -x+ai (order preserved), making a1..ai, -ai+1+ai, -ai+2+ai, ..., -ak+ai.\nEmber wins if the resulting sequence is monotonically increasing or monotonically decreasing; otherwise Storm wins.\nThe game tuple is (T,u,v,i,op). Count how many tuples can occur if both play optimally with this rule: if a player has multiple moves that guarantee a win, they may choose any of those winning moves; if they lose no matter what, they may choose any move. Report the count modulo m.\n\nInput: one line n d m with 2≤n≤200, 1≤d<n, 1≤m≤2·10^9.\nOutput: one number (mod m).\nExamples: (2 1 1000000007)->4, (3 1 250)->0, (3 2 100)->36.\nNote about samples: for n=2,d=1 there is only one tree, 2 paths, i=1 only, op has 2 options so 4 total; for n=3,d=1 no valid trees; for n=3,d=2 there are 3 trees.\n\nFor this step, output ONLY a draft Python solution in a single ```python``` code block (no explanation).","Now treat your previous code as a draft and produce the FINAL response for the same problem with these requirements:\n- First, give step-by-step reasoning (clear, contest-style) that justifies the algorithm and complexity under 3.0s/512MB.\n- Then output the complete final Python 3 implementation.\n- The program must read stdin and write stdout, and print exactly one number (no extra output).\n- Put the final code in exactly one ```python``` code block.\n\nRepeat of the core task: count the number of optimal-play tuples (T,u,v,i,op) for the Ember/Storm game on labelled trees with n vertices and maximum degree ≤ d, modulo m, under the given optimal-play tie-breaking rule."]}
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 3.0 seconds\nMemory limit: 512.0 MB\n\n# Problem\nEmber and Storm play a game. First, Ember picks a labelled tree T of n vertices, such that the degree of every vertex is at most d. Then, Storm picks two distinct vertices u and v in this tree and writes down the labels of the vertices in the path from u to v in a sequence a1, a2... ak. Finally, Ember picks any index i (1 ≤ i < k) in the array. Now he performs one of the following two operations exactly once:\n\n- flip the subrange [i + 1, k] and add ai to it. After this, the sequence becomes a1, ... ai, ak + ai, ak - 1 + ai, ... ai + 1 + ai\n- negate the subrange [i + 1, k] and add ai to it. i.e., the array becomes a1, ... ai, - ai + 1 + ai, - ai + 2 + ai, ... - ak + ai\n\nEmber wins if the array is monotonically increasing or decreasing after this. Otherwise Storm wins.\n\nThe game can be described by the tuple (T, u, v, i, op) where op is «flip» or «negate» depending on the action Ember chose in the last turn. Find the number of tuples that can occur if Ember and Storm play optimally. When they play optimally, if there are multiple moves by which they are guaranteed to win, then they may play any of the winning moves. Otherwise, if someone loses no matter what they play, then they may play any of the possible moves.\n\nReport the answer modulo m.\n\n## Input Format\nThe input consists of a single line containing three integers n, d and m (2 ≤ n ≤ 200, 1 ≤ d < n, 1 ≤ m ≤ 2·109).\n\n## Output Format\nPrint a single number — the number of possible tuples if Ember and Storm play as described, modulo m.\n\n## Examples\n```input\n2 1 1000000007\n```\n```output\n4\n```\n-----\n```input\n3 1 250\n```\n```output\n0\n```\n-----\n```input\n3 2 100\n```\n```output\n36\n```\n\n## Note\nIn the first sample case, there is only one possible tree. There are two possible paths, 1 to 2 and 2 to 1. For both paths, i can only be 1, and op can take both possibilities. Therefore, the answer is 4.\n\nIn the second sample, there are no possible trees.\n\nIn the third sample, there are three possible trees.\n\nNow solve the problem and return the code.
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{"walk":["I want you to first solve a subproblem that isolates the game mechanic on a path-sequence (do NOT talk about trees yet). Consider any sequence of DISTINCT integers a1, a2, ..., ak. A player chooses an index i with 1 ≤ i < k and then chooses exactly one of two operations on the suffix positions i+1..k:\n- op=«flip»: reverse the suffix and add ai to every element of that reversed suffix, producing a1..ai, ak+ai, ak-1+ai, ..., ai+1+ai.\n- op=«negate»: replace each suffix element x by -x+ai (order preserved), producing a1..ai, -ai+1+ai, -ai+2+ai, ..., -ak+ai.\nGoal condition: after the operation, the full length-k sequence is monotonically increasing OR monotonically decreasing.\n\nFor this step, derive a clean characterization of when a given (sequence, i, op) succeeds, and how to test all i/op efficiently for k ≤ 200. Output:\n- a precise criterion in terms of inequalities/comparisons,\n- an efficient algorithm to compute whether there exists a winning move, and optionally count how many winning moves exist for that sequence.\nDo not write final code yet.","Now solve the full competitive programming problem using the sequence-analysis tool you derived.\n\nFull problem (include all constraints in your reasoning): Ember picks a labelled tree T on n vertices with maximum degree ≤ d. Storm picks two distinct vertices u and v, and writes the labels of vertices along the path u→v as a sequence a1..ak. Ember picks i (1 ≤ i < k) and op ∈ {«flip», «negate»} exactly once as defined. Ember wins if the resulting sequence is monotone (increasing or decreasing), else Storm wins. The game tuple is (T,u,v,i,op). Count how many tuples can occur if both play optimally, with tie-breaking: if a player has multiple guaranteed-winning moves, they may pick any winning move; if they lose no matter what, they may pick any move. Report the answer modulo m.\n\nInput: n d m with 2≤n≤200, 1≤d<n, 1≤m≤2·10^9. Output one number mod m. Time limit 3.0s, memory 512MB.\nExamples: 2 1 1000000007 -> 4; 3 1 250 -> 0; 3 2 100 -> 36. Notes: sample 1 has one tree, two directed paths, i=1 only, 2 ops so 4; sample 2 no trees; sample 3 has three trees.\n\nFor this step, derive the game-theoretic optimal-play logic across (tree choice → path choice → i/op choice) and turn it into a countable combinatorial problem over all labelled trees with degree bound. Output the final algorithm idea + complexity (still no code).","Now write the final response: step-by-step reasoning (clear, minimal but complete) and then a full Python 3 implementation.\n\nImplementation requirements:\n- Read from standard input, write to standard output.\n- No debug prints or extra output.\n- Output exactly one integer: the count modulo m.\n- Put the final program inside exactly one ```python``` code block.\n- Must run under 3.0 seconds and 512MB for n ≤ 200.\n\nNow output the final solution."]}
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 3.0 seconds\nMemory limit: 512.0 MB\n\n# Problem\nEmber and Storm play a game. First, Ember picks a labelled tree T of n vertices, such that the degree of every vertex is at most d. Then, Storm picks two distinct vertices u and v in this tree and writes down the labels of the vertices in the path from u to v in a sequence a1, a2... ak. Finally, Ember picks any index i (1 ≤ i < k) in the array. Now he performs one of the following two operations exactly once:\n\n- flip the subrange [i + 1, k] and add ai to it. After this, the sequence becomes a1, ... ai, ak + ai, ak - 1 + ai, ... ai + 1 + ai\n- negate the subrange [i + 1, k] and add ai to it. i.e., the array becomes a1, ... ai, - ai + 1 + ai, - ai + 2 + ai, ... - ak + ai\n\nEmber wins if the array is monotonically increasing or decreasing after this. Otherwise Storm wins.\n\nThe game can be described by the tuple (T, u, v, i, op) where op is «flip» or «negate» depending on the action Ember chose in the last turn. Find the number of tuples that can occur if Ember and Storm play optimally. When they play optimally, if there are multiple moves by which they are guaranteed to win, then they may play any of the winning moves. Otherwise, if someone loses no matter what they play, then they may play any of the possible moves.\n\nReport the answer modulo m.\n\n## Input Format\nThe input consists of a single line containing three integers n, d and m (2 ≤ n ≤ 200, 1 ≤ d < n, 1 ≤ m ≤ 2·109).\n\n## Output Format\nPrint a single number — the number of possible tuples if Ember and Storm play as described, modulo m.\n\n## Examples\n```input\n2 1 1000000007\n```\n```output\n4\n```\n-----\n```input\n3 1 250\n```\n```output\n0\n```\n-----\n```input\n3 2 100\n```\n```output\n36\n```\n\n## Note\nIn the first sample case, there is only one possible tree. There are two possible paths, 1 to 2 and 2 to 1. For both paths, i can only be 1, and op can take both possibilities. Therefore, the answer is 4.\n\nIn the second sample, there are no possible trees.\n\nIn the third sample, there are three possible trees.\n\nNow solve the problem and return the code.
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{"walk":["I want you to create a brute-force reference approach for SMALL n to validate logic (this is not the final algorithm). Use this exact full problem definition:\n- Choose a labelled tree T on n vertices with max degree ≤ d.\n- Storm chooses distinct u,v; sequence a1..ak is labels along the path u→v.\n- Ember chooses i (1≤i<k) and does exactly one op:\n • «flip»: reverse suffix [i+1,k] and add ai to each element of that reversed suffix → a1..ai, ak+ai, ak-1+ai, ..., ai+1+ai.\n • «negate»: replace suffix elements x by -x+ai (order preserved) → a1..ai, -ai+1+ai, ..., -ak+ai.\n- Ember wins if resulting sequence is monotone increasing or decreasing; else Storm wins.\n- Tuple is (T,u,v,i,op). Players act optimally with this rule: if multiple guaranteed-winning moves exist they may choose any; if they lose regardless they may choose any move.\n- Count the number of tuples that can occur under optimal play, modulo m.\nInput is n d m with 2≤n≤200, 1≤d<n, 1≤m≤2·10^9. Output one number mod m. Time 3.0s, memory 512MB.\nExamples: 2 1 1000000007→4; 3 1 250→0; 3 2 100→36. Notes: sample 1 has 1 tree and 4 tuples; sample 2 no trees; sample 3 has 3 trees.\n\nFor this step ONLY: write a brute-force Python sketch that would work for n ≤ 8 (or similar) by enumerating all labelled trees with degree bound, enumerating all u,v, enumerating all i and both ops, checking monotonicity, and then applying minimax + tie-breaking to compute the set/count of reachable tuples for that n,d. Output the brute-force sketch and explain the minimax/tie-breaking implementation carefully. Do not attempt the final n≤200 optimization yet.","Now use the brute-force perspective to extract structural insights needed for n up to 200. Specifically: identify what features of a path sequence a1..ak determine whether Ember has winning moves and how many; then identify what features of the tree matter for Storm’s choice and Ember’s tree choice. Output a distilled set of lemmas/conjectures that would let you count without enumerating trees.","Now turn your insights into an efficient algorithm for the full constraints (n ≤ 200). Provide:\n- the final mathematical/combinatorial formulation,\n- the DP / coefficient-extraction / counting strategy needed for degree ≤ d labelled trees,\n- complexity analysis (time + memory) suitable for 3.0s/512MB,\n- careful handling of modulo m where m is not necessarily prime.\nDo not write the final code yet.","Now produce the final response: step-by-step reasoning followed by a complete Python 3 implementation that reads stdin and writes stdout, with no extra output. Output only one number (mod m). Put the final program in exactly one ```python``` code block."]}
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 3.0 seconds\nMemory limit: 512.0 MB\n\n# Problem\nEmber and Storm play a game. First, Ember picks a labelled tree T of n vertices, such that the degree of every vertex is at most d. Then, Storm picks two distinct vertices u and v in this tree and writes down the labels of the vertices in the path from u to v in a sequence a1, a2... ak. Finally, Ember picks any index i (1 ≤ i < k) in the array. Now he performs one of the following two operations exactly once:\n\n- flip the subrange [i + 1, k] and add ai to it. After this, the sequence becomes a1, ... ai, ak + ai, ak - 1 + ai, ... ai + 1 + ai\n- negate the subrange [i + 1, k] and add ai to it. i.e., the array becomes a1, ... ai, - ai + 1 + ai, - ai + 2 + ai, ... - ak + ai\n\nEmber wins if the array is monotonically increasing or decreasing after this. Otherwise Storm wins.\n\nThe game can be described by the tuple (T, u, v, i, op) where op is «flip» or «negate» depending on the action Ember chose in the last turn. Find the number of tuples that can occur if Ember and Storm play optimally. When they play optimally, if there are multiple moves by which they are guaranteed to win, then they may play any of the winning moves. Otherwise, if someone loses no matter what they play, then they may play any of the possible moves.\n\nReport the answer modulo m.\n\n## Input Format\nThe input consists of a single line containing three integers n, d and m (2 ≤ n ≤ 200, 1 ≤ d < n, 1 ≤ m ≤ 2·109).\n\n## Output Format\nPrint a single number — the number of possible tuples if Ember and Storm play as described, modulo m.\n\n## Examples\n```input\n2 1 1000000007\n```\n```output\n4\n```\n-----\n```input\n3 1 250\n```\n```output\n0\n```\n-----\n```input\n3 2 100\n```\n```output\n36\n```\n\n## Note\nIn the first sample case, there is only one possible tree. There are two possible paths, 1 to 2 and 2 to 1. For both paths, i can only be 1, and op can take both possibilities. Therefore, the answer is 4.\n\nIn the second sample, there are no possible trees.\n\nIn the third sample, there are three possible trees.\n\nNow solve the problem and return the code.
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{"walk":["I want you to start from the combinatorics of labelled trees with degree constraints, because n is up to 200 and we cannot enumerate trees. Full problem context (for later steps): Ember picks a labelled tree T on n vertices with maximum degree ≤ d; Storm picks u,v and writes labels along the path as a1..ak; Ember picks i and op ∈ {«flip», «negate»} with the exact definitions; Ember wins if the final sequence is monotone increasing or decreasing; otherwise Storm wins; tuple is (T,u,v,i,op); both play optimally with the specified tie-breaking; answer modulo m where m ≤ 2·10^9.\n\nFor this step ONLY: derive a clean counting method for the number of labelled trees on n vertices with maximum degree ≤ d (or equivalently, Prüfer-code frequency ≤ d-1). Output the exact formula you will compute (e.g., coefficient extraction / polynomial DP form), and how to compute it efficiently modulo an arbitrary m (not necessarily prime), for n ≤ 200. Do not solve the game yet.","Now I want you to incorporate markings relevant to tuples. Define how to count labelled trees with degree ≤ d together with distinguished/marked elements that correspond to choosing ordered (u,v) and a distinguished index i along the u→v path (or an equivalent structural mark). You do not need the final closed form yet; just give a principled counting framework (double counting / combinatorial species / Prüfer with marks) that could, in principle, sum over all such tuples without iterating trees.","Now shift to the game logic on the marked path: for a path label sequence a1..ak and a chosen split i, analyze the two operations («flip» and «negate» with +ai) and derive what path-label order patterns allow the resulting full sequence to be monotone. Output a compact characterization that is suitable for counting over many instances (not per-tree brute force).","Now combine the marking-counting framework (trees with marked path structure) with the path win-characterization to obtain a computable algorithm for the total number of reachable optimal-play tuples (T,u,v,i,op) modulo m under the tie-breaking rule. Include the complete problem statement details here to ensure nothing is missed:\n- Input: n d m with 2≤n≤200, 1≤d<n, 1≤m≤2·10^9.\n- Output: single number = count modulo m.\n- Time limit 3.0s, memory 512MB.\n- Examples: 2 1 1000000007→4; 3 1 250→0; 3 2 100→36.\n- Notes: sample 1 explanation (1 tree, 2 paths, i=1 only, 2 ops so 4); sample 2 no trees; sample 3 has 3 trees.\nAlso include the optimal-play rule verbatim in your reasoning: multiple winning moves → any; forced loss → any move.\nFor this step, output the final algorithm plan + complexity and all required modular arithmetic details. No code yet.","Now write the final response: step-by-step reasoning and then a complete Python 3 implementation.\n\nImplementation/output constraints:\n- Read stdin, write stdout; no debug prints.\n- Print exactly one number (mod m).\n- Put the entire program in exactly one ```python``` code block.\n\nNow output the final solution."]}
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You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.\n\nYour solution must read input from standard input (cin), write output to standard output (cout).\nDo not include any debug prints or additional output.\n\nPut your final solution within a single code block:\n```python\n<your code here>\n```\n\nExecution time limit: 3.0 seconds\nMemory limit: 512.0 MB\n\n# Problem\nEmber and Storm play a game. First, Ember picks a labelled tree T of n vertices, such that the degree of every vertex is at most d. Then, Storm picks two distinct vertices u and v in this tree and writes down the labels of the vertices in the path from u to v in a sequence a1, a2... ak. Finally, Ember picks any index i (1 ≤ i < k) in the array. Now he performs one of the following two operations exactly once:\n\n- flip the subrange [i + 1, k] and add ai to it. After this, the sequence becomes a1, ... ai, ak + ai, ak - 1 + ai, ... ai + 1 + ai\n- negate the subrange [i + 1, k] and add ai to it. i.e., the array becomes a1, ... ai, - ai + 1 + ai, - ai + 2 + ai, ... - ak + ai\n\nEmber wins if the array is monotonically increasing or decreasing after this. Otherwise Storm wins.\n\nThe game can be described by the tuple (T, u, v, i, op) where op is «flip» or «negate» depending on the action Ember chose in the last turn. Find the number of tuples that can occur if Ember and Storm play optimally. When they play optimally, if there are multiple moves by which they are guaranteed to win, then they may play any of the winning moves. Otherwise, if someone loses no matter what they play, then they may play any of the possible moves.\n\nReport the answer modulo m.\n\n## Input Format\nThe input consists of a single line containing three integers n, d and m (2 ≤ n ≤ 200, 1 ≤ d < n, 1 ≤ m ≤ 2·109).\n\n## Output Format\nPrint a single number — the number of possible tuples if Ember and Storm play as described, modulo m.\n\n## Examples\n```input\n2 1 1000000007\n```\n```output\n4\n```\n-----\n```input\n3 1 250\n```\n```output\n0\n```\n-----\n```input\n3 2 100\n```\n```output\n36\n```\n\n## Note\nIn the first sample case, there is only one possible tree. There are two possible paths, 1 to 2 and 2 to 1. For both paths, i can only be 1, and op can take both possibilities. Therefore, the answer is 4.\n\nIn the second sample, there are no possible trees.\n\nIn the third sample, there are three possible trees.\n\nNow solve the problem and return the code.
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{"walk":["I want you to restate this as a formal optimal-play set problem before doing any heavy math. Here is the full problem specification you must preserve:\n- Ember chooses a labelled tree T on n vertices, with maximum degree ≤ d.\n- Storm chooses distinct vertices u and v.\n- Let a1..ak be the labels along the path u→v.\n- Ember chooses i with 1 ≤ i < k and performs exactly one op:\n • op=«flip»: reverse suffix [i+1,k] and add ai to each element of that reversed suffix → a1..ai, ak+ai, ak-1+ai, ..., ai+1+ai.\n • op=«negate»: replace suffix elements x by -x+ai (order preserved) → a1..ai, -ai+1+ai, -ai+2+ai, ..., -ak+ai.\n- Ember wins if the resulting sequence is monotonically increasing OR monotonically decreasing; else Storm wins.\n- The game tuple is (T,u,v,i,op). Count how many tuples can occur if they play optimally.\n- Optimal-play tie-breaking rule: if there are multiple moves by which a player is guaranteed to win, they may play any of the winning moves; otherwise, if someone loses no matter what they play, they may play any possible move.\n- Report the answer modulo m.\n- Input: n d m with 2 ≤ n ≤ 200, 1 ≤ d < n, 1 ≤ m ≤ 2·10^9.\n- Output: one number modulo m.\n- Time limit 3.0s, memory 512MB.\n- Examples: 2 1 1000000007→4; 3 1 250→0; 3 2 100→36.\n- Notes about samples: (n=2,d=1) only one tree; two directed paths; i=1 only; two ops → 4. (n=3,d=1) no trees. (n=3,d=2) three trees.\n\nFor this step: define precise sets/functions that capture “winning moves” and “optimal move sets” at each stage (tree choice, path choice, i/op choice), and define exactly what it means for a tuple (T,u,v,i,op) to be ‘possible’ under the tie-breaking rule. Output this formalization clearly (no code yet).","Now focus only on the last stage: given a fixed sequence a1..ak of distinct integers (labels along a path), characterize the set W(a) of winning moves (i,op) for Ember that make the final array monotone (increasing or decreasing). Output:\n- a clear method to test monotonicity after each op,\n- a way to compute W(a) efficiently for k ≤ 200,\n- and any simplifications that reduce branching (still no code).","Now lift to the middle stage: for a fixed tree T, Storm chooses (u,v) after seeing T, then Ember chooses from W(a(u,v)). Using your formalization, derive how to compute:\n- whether Storm has a winning path in T,\n- which (u,v) are optimal choices for Storm under the tie-breaking rule,\n- and for those, which (i,op) are possible for Ember (either winning ones if any exist, else any moves).\nOutput a tree-level counting expression for how many tuples (u,v,i,op) are possible given a fixed T (still no code).","Now lift to the first stage: characterize which trees T are optimal for Ember to choose (under the same tie-breaking rule), based on the tree-level outcome you derived. Output:\n- a criterion that classifies trees as ‘Ember can force win’ vs ‘Storm can force win’,\n- and how that criterion affects which trees are considered possible under optimal play (and therefore contribute tuples).","Now derive a global counting method over ALL labelled trees with n vertices and max degree ≤ d, without enumerating them. You may use Prüfer-sequence counting / polynomial DP / coefficient extraction, but you must show how it connects to the tree-level criterion and tuple-count expression you derived. Also specify how to compute everything modulo an arbitrary m (not necessarily prime) efficiently for n ≤ 200.","Now write the final response: step-by-step reasoning that follows the structure above, and then a complete Python 3 implementation.\n\nImplementation constraints:\n- Read stdin, write stdout; no debug prints or extra output.\n- Print exactly one number: the count modulo m.\n- Put the entire program in exactly one ```python``` code block.\n- Must run under 3.0 seconds and 512MB.\n\nNow output the final solution."]}
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