Hypertransmission

There are $N$ planets in a galactic federation. On every planet exactly one of two political movements --- industrialism or ecologism --- holds the majority. Each planet is equipped with an identical hyper-radio transmitter of range $R$: a planet's broadcast is received by every planet lying within Euclidean distance $R$ of it, and every planet always receives its own broadcast.

For a planet $A$, let $N^+(A)$ be the number of planets that receive $A$'s broadcast and share $A$'s majority movement (this count includes $A$ itself), and let $N^-(A)$ be the number of planets that receive $A$'s broadcast but hold the opposite movement. Planet $A$ is called destabilizing when $N^+(A) < N^-(A)$.

Choose the range $R$ so that the number $D$ of destabilizing planets is as large as possible. Among all ranges that attain this maximum $D$, the range must be the smallest one.

The first line contains the integer $N$ --- the number of planets ($1 \le N \le 1000$). Each of the next $N$ lines contains four integers $x_i$, $y_i$, $z_i$, and $p_i$ describing one planet: $(x_i, y_i, z_i)$ are its coordinates in space and $p_i$ is its majority movement, with $p_i = 0$ for industrialists and $p_i = 1$ for ecologists. Every coordinate satisfies $|x_i|, |y_i|, |z_i| \le 10^4$. No two planets occupy the same point.

On the first line output $D$ --- the maximum possible number of destabilizing planets. On the second line output $R^2$ --- the square of the smallest range that achieves $D$ destabilizing planets. Because all coordinates are integers, the optimal range is either $0$ or the distance between two planets, so $R^2$ is always a non-negative integer; recover the range itself as $R = \sqrt{R^2}$.