{"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"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc154_d"},"statements":[{"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 $(i,j,k)$ such that $1 \\le i,j,k \\le N$ and ask whether $P_i + P_j > P_k$.\n\nFind all of $P_1,P_2,\\dots,P_N$.\n\n## Constraints\n\n*   $1 \\le N \\le 2000$\n*   $P$ is decided before the start of the interaction of your program and the judge.\n\n## Input And Output\n\n**This is an interactive task**, where your program and the judge interact via input and output.\nFirst, your program is given $N$, the length of the permutation, from Standard Input:\n\n$N$\n\nThen, you get to ask questions. Print your question to Standard Output in the following format: (There should be a newline at the end.)\n\n? $i$ $j$ $k$\n\nIf the question is valid, the answer $ans$ will be given from Standard Input:\n\n$ans$\n\nHere, $ans$ is `Yes` or `No`.\nIf the question is malformed or judged invalid because you have asked more questions than allowed, `-1` will be given from Standard Input:\n\n\\-1\n\nHere, the submission has already been judged incorrect. The judge will end the interaction at this point; preferably, your program should also quit.\nOnce 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.)\n\n! $P_1$ $P_2$ $\\dots$ $P_N$\n\n## Judging\n\n*   **Each time you print something, end it with a newline and flush Standard Output. Otherwise, you might get a TLE verdict.**\n*   After printing the answer (or receiving `-1`), immediately terminate the program normally. Otherwise, the verdict will be indeterminate.\n*   Note that unnecessary newlines will be considered as malformed output.\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc154_d","tags":[],"sample_group":[],"created_at":"2026-03-03 11:01:13"}}