Basic Complete Search

In many problems (especially in Bronze) it suffices to check all possible cases in the solution space, whether it be all elements, all pairs of elements, or all subsets, or all permutations. Unsurprisingly, this is called complete search (or brute force), because it completely searches the entire solution space.

Example

You are given $N$ $(3\le N\le 5000)$ integer points on the coordinate plane. Find the square of the maximum Euclidean distance (aka length of the straight line) between any two of the points.

Input Format

The first line contains an integer $N$.

The second line contains $N$ integers, the $x$-coordinates of the points: $x_1,x_2,\dots ,x_N$ ($-1000\le x_i\le 1000$).

The third line contains $N$ integers, the $y$-coordinates of the points: $y_1,y_2,\dots ,y_N$ ($-1000\le y_i\le 1000$).

Output Format

Print one integer, the square of the maximum Euclidean distance between any two of the points.

Problems