A + B > C ?

AtCoder

IDarc154_d

Time2000ms

Memory256MB

Difficulty—

PCT has a permutation $(P_1,P_2,\dots,P_N)$ of $(1,2,\dots,N)$. You are only informed of $N$. You can ask him at most $25000$ questions of the following form. * Specify a triple of integers $(i,j,k)$ such that $1 \le i,j,k \le N$ and ask whether $P_i + P_j > P_k$. Find all of $P_1,P_2,\dots,P_N$. ## Constraints * $1 \le N \le 2000$ * $P$ is decided before the start of the interaction of your program and the judge. ## Input And Output **This is an interactive task**, where your program and the judge interact via input and output. First, your program is given $N$, the length of the permutation, from Standard Input: $N$ Then, you get to ask questions. Print your question to Standard Output in the following format: (There should be a newline at the end.) ? $i$ $j$ $k$ If the question is valid, the answer $ans$ will be given from Standard Input: $ans$ Here, $ans$ is `Yes` or `No`. If the question is malformed or judged invalid because you have asked more questions than allowed, `-1` will be given from Standard Input: \-1 Here, the submission has already been judged incorrect. The judge will end the interaction at this point; preferably, your program should also quit. Once you have identified all of $P_1, P_2, \dots, P_N$, print them to Standard Output in the following format: (There should be a newline at the end.) ! $P_1$ $P_2$ $\dots$ $P_N$ ## Judging * **Each time you print something, end it with a newline and flush Standard Output. Otherwise, you might get a TLE verdict.** * After printing the answer (or receiving `-1`), immediately terminate the program normally. Otherwise, the verdict will be indeterminate. * Note that unnecessary newlines will be considered as malformed output. [samples]

API Response (JSON)

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  "problem": {
    "name": "A + B > C ?",
    "description": {
      "content": "PCT has a permutation $(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$. You are only informed of $N$. You can ask him at most $25000$ questions of the following form. *   Specify a triple of integers $(i,j,k",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
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    "sign": "arc154_d"
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      "statement_type": "Markdown",
      "content": "PCT has a permutation $(P_1,P_2,\\dots,P_N)$ of $(1,2,\\dots,N)$. You are only informed of $N$.\nYou can ask him at most $25000$ questions of the following form.\n\n*   Specify a triple of integers $(i,j,k...",
      "is_translate": false,
      "language": "English"
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