CF1705F.Mark and the Online Exam

Mark is administering an online exam consisting of $n$ true-false questions. However, he has lost all answer keys. He needs a way to retrieve the answers before his client gets infuriated.

Fortunately, he has access to the grading system. Thus, for each query, you can input the answers to all $n$ questions, and the grading system will output how many of them are correct.

He doesn't have much time, so he can use the grading system at most $675$ times. Help Mark determine the answer keys.

Note that answer keys are fixed in advance and will not change depending on your queries.

马克正在组织一场包含 $n$ 道判断题的在线考试。然而，他丢失了全部标准答案。他必须在客户暴怒之前找回正确答案。

幸运的是，他可以访问自动阅卷系统。因此，对于每次查询，你可以输入全部 $n$ 道题的答案，阅卷系统将返回其中答对的题目数量。

时间紧迫，他最多只能使用阅卷系统 $675$ 次。请帮助马克确定所有题目的标准答案。

注意：标准答案是预先固定好的，不会因你的查询而改变。

The first line of the input consists of an integer $n$ ($1\leq n\leq 1000$) — the number of questions.

输入的第一行包含一个整数 $n$（$1\leq n\leq 1000$）——问题的数量。

The empty lines in the example are just for you to better understand the interaction process. You're not required to print them.

In the first example, there are $3$ questions, and the answer to each question is 'true', 'true', and 'false', respectively.

• The first query, guessing the answers to be 'false', 'true', and 'true', respectively, guesses only one question — the $2$-nd question — correctly.
• Then, in the second query, the program correctly guesses the answer key. The interaction ends here.

In the second example, there are $4$ questions, and the answer to each question is 'true', 'false', 'true', and 'true', respectively.

• The first query guessed none of the questions correctly, resulting in the answer $0$.
• The second query guessed the $1$-st, $3$-rd, and $4$-th question correctly, resulting in the answer $3$.
• In the third query, the program correctly guesses the answer key. Then, the interaction ends.

示例中的空行仅用于帮助你更好地理解交互过程，你无需输出这些空行。

在第一个示例中，共有 $3$ 道题目，各题的正确答案依次为“true”、“true”和“false”。

• 第一次查询猜测的答案依次为“false”、“true”、“true”，仅第 $2$ 题猜对，因此返回结果为 $1$。
• 接着，在第二次查询中，程序成功猜出了全部正确答案。此时交互结束。

在第二个示例中，共有 $4$ 道题目，各题的正确答案依次为“true”、“false”、“true”和“true”。

• 第一次查询未猜对任何一题，因此返回结果为 $0$。
• 第二次查询猜对了第 $1$、$3$ 和 $4$ 题，因此返回结果为 $3$。
• 在第三次查询中，程序成功猜出了全部正确答案，交互随即结束。