You are given $$$n$$$ points in 4-dimensional space: $$$p_1, ~p_2, ~\ldots, ~p_n$$$, where each point $$$p_i$$$ has coordinates $$$(x_i, ~y_i, ~z_i, ~w_i)$$$.
Your task is to find a point $$$o = (o_x, ~o_y, ~o_z, ~o_w)$$$ in 4-dimensional space such that the maximum distance from $$$o$$$ to any point $$$p_i$$$ is minimized. Formally, you need to minimize the value: $$$$$$ \max_{1 \leq i \leq n} \sqrt{(o_x - x_i)^2 + (o_y - y_i)^2 + (o_z - z_i)^2 + (o_w - w_i)^2} $$$$$$
The first line contains a single integer $$$n$$$ $$$(1 \leq n \leq 10^4)$$$ — the number of points.
The next $$$n$$$ lines each contain four integers $$$x_i, ~y_i, ~z_i, ~w_i$$$ $$$(-10^4 \leq x_i, ~y_i, ~z_i, ~w_i \leq 10^4)$$$ — the coordinates of the $$$i$$$-th point. All given points are unique.
Print four real numbers $$$o_x, ~o_y, ~o_z, ~o_w$$$ — the coordinates of the optimal point.
Your answer will be correct if it has an absolute or relative error of at most $$$10^{-6}$$$.
30 0 0 04 0 0 03 2 0 0
2 0.25 0 0
160 0 0 00 0 0 40 0 4 00 0 4 40 4 0 00 4 0 40 4 4 00 4 4 44 0 0 04 0 0 44 0 4 04 0 4 44 4 0 04 4 0 44 4 4 04 4 4 4
2 2 2 2