{"raw_statement":[{"iden":"statement","content":"There is a full binary tree with $n$ levels(so it has exactly $2^n-1$ nodes). Each node has an integer ID from $1$ to $2^n-1$, and the $2^n-1$ IDs form an arrangement from $1$ to $2^n-1$, but you don't know.\n\nYou need to find the IDs of the $2^n-1$ nodes using at most $4800$ queries."},{"iden":"input","content":"The first line contains one integer $n(1\\leq n\\leq 10)$, the levels of the full binary tree.\n\nTo ask a query, you need to pick two nodes with IDs $u,v(1\\leq u,v\\leq 2^n-1)$, and print the line of the following form:\n\n> \"? u v\"\n\nAfter that, you will receive:\n\n> \"t\"\n\nThe lowest common ancestor's ID of $u$ and $v$.\n\nYou can ask at most $4800$ queries.\n\nIf you have found the structure of the tree, print a line of the following form:\n\n\"! $f_1\\ f_2\\ f_3\\ f_4$ ... $f_{2^n-1}$\"\n\n$f_i$ means the i-th node's father's ID. If it has no father, then $f_i=-1$.\n\nAfter printing a query or the answer for a test case, do not forget to output the end of line and flush the output. Otherwise, you will get the verdict 'Idleness Limit Exceeded'. To do this, use:\n\n`fflush(stdout)` or `cout.flush()` in C++;\n\n`System.out.flush()` in Java;\n\n`stdout.flush()` in Python.\n\nThe interactor in this task is not adaptive."},{"iden":"note","content":"In this case, the tree's root is $3$, it's two sons are $1$ and $2$.\n\nFor any query \"? a b\",if $a\\neq b$, the jury will return answer $3$.\n\nSo we found the tree's root is $3$ ."}],"translated_statement":null,"sample_group":[["2\n\n3\n\n3\n\n3","\n? 1 2\n\n? 2 3\n\n? 1 3\n\n! 3 3 -1"]],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}