P10126 "Daily OI Round 3" Pigeon

> Recently, are you busy? You did not even call me. Oh, really? Hehe, turns out I never gave you my number. But still, that is not an excuse for you not to look for me. Next time, I will punish you to keep me company until the sun comes up. —— recollect_i's blog.

recollect_i gives you a sequence $x$ of length $n$. You need to find a real number $y$ such that for all $1\leq i\vert x_i-y\vert$, or report that there is no solution.

The first line contains an integer $n$, representing the length of the sequence. The second line contains $n$ integers $x$, representing the sequence.

If there is a solution, output the string `lovely` on the first line, and output a real number $y$ on the second line. To avoid precision issues, if your output satisfies that for all $ 1\leq i10^{-6}$, then your answer is considered correct. You also need to ensure that $-2\times 10^9\leq y\leq 2\times 10^9$, and that $y$ has no more than $10$ digits after the decimal point. Otherwise, the correctness of judging cannot be guaranteed. If there is no solution, output the string `pigeon` in one line.

#### [Hint] In the output format, $>10^{-6}$ is only to avoid precision issues. You may treat it as requiring $\vert x_j-y\vert>\vert x_i-y\vert$. It can be proven that if there is a solution, then there must exist a $y$ satisfying $-2\times 10^{9}\leq y\leq2\times 10^{9}$ and for all $1\leq i0.2$, and the number of digits after the decimal point does not exceed $3$. #### [Constraints] For all testdata: $5\leq n\leq10^5$, $-10^9\leq x_i\leq10^9$. Translated by ChatGPT 5