P9508 "STA - R3" Existence

Description

Construct a sequence of length $n$ such that every subarray of length at least $2$ has a majority element. Based on this, maximize the number of distinct values in the sequence. The majority element of a sequence is defined as a number whose occurrence count is at least half of the sequence length. Each element in your constructed sequence must be an integer between $0$ and $10^9$.

Input Format

One line containing a positive integer $n$.

Output Format

One line containing $n$ integers, representing the sequence you constructed. If there are multiple answers, output any one of them.

Explanation/Hint

**This problem uses bundled tests.** Constraints: - Subtask 1 (10pts): $n \le 5$. - Subtask 2 (40pts): $n$ is a multiple of $3$. - Subtask 3 (50pts): No special restrictions. For all data, $1 \le n \le 10^3$. Translated by ChatGPT 5