A. Optimal Point
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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: $$$$$$ \max_{1 \leq i \leq n} \sqrt{(o_x - x_i)^2 + (o_y - y_i)^2 + (o_z - z_i)^2 + (o_w - w_i)^2} $$$$$$

Input

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.

Output

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 $$$10^{-6}$$$.

Examples
Input
3
0 0 0 0
4 0 0 0
3 2 0 0
Output
2 0.25 0 0
Input
16
0 0 0 0
0 0 0 4
0 0 4 0
0 0 4 4
0 4 0 0
0 4 0 4
0 4 4 0
0 4 4 4
4 0 0 0
4 0 0 4
4 0 4 0
4 0 4 4
4 4 0 0
4 4 0 4
4 4 4 0
4 4 4 4
Output
2 2 2 2