A9466 | Lightbulb for Minister

The first line contains integer $n$ $(2<=n<=10^{5})$ — the number of generators. Each of the next $n$ lines contains a pair of integers $x_{i}$ , $y_{i}$ , representing the coordinates of the $i$ -th generator in the plane of the class ceiling. It's guaranteed that no two generators have the same location.

The next line contains integer $m$ $(3<=m<=10^{5})$ — the number of vertexes in the convex polygon that describes the ceiling of the class. Each of the following $m$ lines contains a pair of integers $p_{i},q_{i}$ , representing the coordinates of the $i$ -th point of the polygon in the clockwise order. It's guaranteed that the polygon is strictly convex.

The absolute value of all the coordinates don't exceed $10^{6}$ .

Print a single real number — the minimum value of the sum of squares of distances from the generators to the point of the lightbulb's optimal position. The answer will be considered valid if its absolute or relative error doesn't exceed $10^{-4}$ .

We'll define a strictly convex polygon as a convex polygon with the following property: no three vertices of the polygon lie on the same line.