P10671 BZOJ1278 Vector vector

The weight of a two-dimensional vector $(x, y)$ is defined as $x^2 + y^2$. Given a set consisting of $n$ two-dimensional vectors, find a subset such that the weight of the sum of the vectors in this subset is as large as possible.

The first line contains a positive integer $n$, indicating that there are $n$ vectors. The next $n$ lines each contain $2$ real numbers, representing the $n$ vectors $(x_i, y_i)$.

Output $1$ real number, i.e., the maximum possible weight of the vector sum, accurate to $3$ digits after the decimal point.

Constraints: it is guaranteed that $1 \leq n \leq 100000$. Translated by ChatGPT 5