P11192 [COTS 2021] Dish Jelo

Translated from [Izborne Pripreme 2021 (Croatian IOI/CEOI Team Selection)](https://hsin.hr/pripreme2021/) D1T1。$\texttt{1s,0.5G}$。 Due to the special SPJ of this problem, the TL and ML of this problem are changed to $\texttt{10s,2G}$ respectively. However, for contestants' programs, the time and memory limits are the same as in the original problem. If you upload your answer using a zip package, name the files as $\texttt{jelo-1.out}\sim \texttt{jelo-5.out}$ respectively.

Given a positive even integer $N$, construct a largest possible set $S\subseteq \{0,1,\cdots,2^{N}-1\}$ such that $\left|\bigcup_{i,j\in S,i\lt j} \{i\oplus j\}\right|={|S|\choose 2}$。In other words, for any two chosen pairs $(a,b),(c,d)$ in $S$ ($a,b,c,d\in S$, $a\lt b$, $c\lt d$, $(a,b)\neq (c,d)$), it holds that $a\oplus b\neq c\oplus d$. Here, $\oplus$ denotes the bitwise XOR operation.

One line containing a positive integer $N$.

The first line contains an integer $|S|$. Then output $|S|$ numbers describing $S$.

For $100\%$ of the testdata, it is guaranteed that $1\le N\le 30$. This problem has $5$ test points. Each test point has three scoring parameters $t_1,t_2,t_3$. Let $t=|S|$. The score is computed as: $$\mathrm{score}(t)= \begin{cases} 2.4\cdot \frac{t}{t_1} & t\in [0,t_1) \\ 2.4+3.6\cdot \frac{t-t_1}{t_2-t_1} & t\in [t_1,t_2) \\ 6+12\cdot \frac{t-t_2}{t_3-t_2} & t\in [t_2,t_3) \\ 20 & t\in [t_3,2^N] \\ \end{cases}$$ | Test Point ID | $N=$ | $t_1=$ | $t_2=$ | $t_3=$ | Score | | :--: | :--: | :--: | :--: | :--: | :--: | | $ 1 $ | $ 18 $ | $ 267 $ | $ 283 $ | $ 512 $ | $ 20 $ | | $ 2 $ | $ 20 $ | $ 444 $ | $ 462 $ | $ 1024 $ | $ 20 $ | | $ 3 $ | $ 26 $ | $ 2019 $ | $ 2040 $ | $ 8192 $ | $ 20 $ | | $ 4 $ | $ 28 $ | $ 3295 $ | $ 3327 $ | $ 16384 $ | $ 20 $ | | $ 5 $ | $ 30 $ | $ 5377 $ | $ 5430 $ | $ 32768 $ | $ 20 $ | [Hint] Please pay attention to the code length limit. Translated by ChatGPT 5