{"raw_statement":[{"iden":"problem statement","content":"This is an **interactive task**, where your program and the judge interact via Standard Input and Output.\nThe judge has a string of length $N$ consisting of $0$ and $1$: $S = S_1S_2\\ldots S_N$. Here, $S_1 = 0$ and $S_N = 1$.\nYou are given the length $N$ of $S$, but not the contents of $S$. Instead, you can ask the judge at most $20$ questions as follows.\n\n*   Choose an integer $i$ such that $1 \\leq i \\leq N$ and ask the value of $S_i$.\n\nPrint an integer $p$ such that $1 \\leq p \\leq N-1$ and $S_p \\neq S_{p+1}$.  \nIt can be shown that such $p$ always exists under the settings of this problem."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 2 \\times 10^5$"},{"iden":"input and output","content":"First, receive the length $N$ of the string $S$ from Standard Input:\n\n$N$\n\nThen, you get to ask the judge at most $20$ questions as described in the problem statement.\nPrint each question to Standard Output in the following format, where $i$ is an integer satisfying $1 \\leq i \\leq N$:\n\n? $i$\n\nIn response to this, the value of $S_i$ will be given from Standard Input in the following format:\n\n$S_i$\n\nHere, $S_i$ is $0$ or $1$.\nWhen you find an integer $p$ satisfying the condition in the problem statement, print it in the following format, and immediately quit the program:\n\n! $p$\n\nIf multiple solutions exist, you may print any of them."},{"iden":"notes","content":"*   **Print a newline and flush Standard Output at the end of each message. Otherwise, you may get a TLE verdict.**\n*   **If there is malformed output during the interaction or your program quits prematurely, the verdict will be indeterminate.**\n*   After printing the answer, immediately quit the program. Otherwise, the verdict will be indeterminate.\n*   The string $S$ will be fixed at the start of the interaction and will not be changed according to your questions or other factors."},{"iden":"sample input and output","content":"In the following interaction, $N = 7$ and $S = 0010011$.\n\nInput\n\nOutput\n\nDescription\n\n`7`\n\n$N$ is given.\n\n`? 1`\n\nAsk the value of $S_1$.\n\n`0`\n\nThe judge responds with $S_1 = 0$.\n\n`? 6`\n\nAsk the value of $S_6$.\n\n`1`\n\nThe judge responds with $S_6 = 1$.\n\n`? 5`\n\nAsk the value of $S_5$.\n\n`0`\n\nThe judge responds with $S_5 = 0$.\n\n`! 5`\n\nPresent $p = 5$ as an integer satisfying the condition.\n\nFor the presented $p = 5$, we have $1 \\leq p \\leq N-1$ and $S_p \\neq S_{p+1}$. Thus, if the program immediately quits here, this case will be judged as correctly solved."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}