{"raw_statement":[{"iden":"problem statement","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 $P_1,P_2,\\dots,P_N$."},{"iden":"constraints","content":"*   $1 \\le N \\le 2000$\n*   $P$ is decided before the start of the interaction of your program and the judge."},{"iden":"input and output","content":"**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! $P_1$ $P_2$ $\\dots$ $P_N$"},{"iden":"judging","content":"*   **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."},{"iden":"sample interaction","content":"Below is an interaction with $N = 4$ and $P=(3,1,2,4)$.\n\nInput\n\nOutput\n\nDescription\n\n`4`\n\n$N$ is given.\n\n`?` `1` `2` `3`\n\nAs the first question, you ask whether $P_1 + P_2 > P_3$.\n\n`Yes`\n\nWe have $P_1 + P_2=4$ and $P_3=2$, so the answer is `Yes`.\n\n`?` `2` `3` `3`\n\nAs the second question, you ask whether $P_2 + P_3 > P_3$.\n\n`Yes`\n\nWe have $P_2 + P_3=3$ and $P_3=2$, so the answer is `Yes`.\n\n`?` `2` `3` `4`\n\nAs the third question, you ask whether $P_2 + P_3 > P_4$.\n\n`No`\n\nWe have $P_2 + P_3=3$ and $P_4=4$, so the answer is `No`.\n\n`!` `3` `1` `2` `4`\n\nYou print $P_1,P_2,P_3,P_4$. We do have $P=(3,1,2,4)$, so you get an AC."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}