Cut It Out!

You are given two convex polygons $A$ and $B$. It is guaranteed that $B$ lies strictly inside $A$.

You want to cut $B$ out of $A$. Each cut is a straight line that passes completely through $A$ and runs along one edge of $B$. The line splits $A$ into two pieces. You cut along it and discard the piece that does not contain $B$. Repeat until the remaining piece is exactly $B$.

The cost of a cut is the length of the cut, that is, the length of the line segment that runs through the remaining part of $A$. Given $A$ and $B$, find the minimum cost to cut $B$ out.

The first line contains an integer $a$ ($3 \le a \le 200$), the number of vertices of $A$. The next $a$ lines each contain two integers $x$ and $y$, the vertices of $A$ in clockwise order. $A$ is guaranteed to be convex.

The next line contains an integer $b$ ($3 \le b \le 200$), the number of vertices of $B$. The next $b$ lines each contain two integers $x$ and $y$, the vertices of $B$ in clockwise order. $B$ is guaranteed to be convex and to lie entirely inside $A$. The coordinates of $A$ satisfy $-10^6 \le x, y \le 10^6$, and the coordinates of $B$ satisfy $-10^6 < x, y < 10^6$.

No three points are collinear, whether within one polygon or across both polygons.

Print a single floating point number, the minimum cost to cut $B$ out of $A$. The answer is accepted if its relative error is within $10^{-6}$ of the judges' answer.