write a go solution for Description:
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.

Input Format:
The first line of the input consists of an integer n (1<=n<=1000) — the number of questions.

Output Format:
None

Note:
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.. Output only the code with no comments, explanation, or additional text.