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2018-03-24 09:00 AKDT

## NAIPC 2018

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2018-03-24 14:00 AKDT
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# Problem ACut It Out!

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

You would like to make a sequence of cuts to cut out $B$ from $A$. To do this, you draw a straight line completely through $A$ that is incident to one of the edges of $B$, which separates $A$ into two pieces. You cut along this line and discard the piece that doesn’t contain $B$. You repeat this until the piece that you have left is exactly B. The cost of making a cut is equal to the length of the cut (i.e. the length of the line through the remainder of $A$). Given $A$ and $B$, find the minimum cost needed to cut $B$ out.

## Input

Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. Each test case will begin with a line containing a single integer $a$ ($3 \le a \le 200$), which is the number of points in polygon $A$. Each of the next $a$ lines will contain two integers $x$ and $y$ ($-10^6 \le x,y \le 10^6$), which are the vertices of polygon $A$, in clockwise order. It is guaranteed that polygon $A$ will be convex.

The next line will contain a single integer $b$ ($3 \le b \le 200$), which is the number of points in polygon $B$. Each of the next $b$ lines will contain two integers $x$ and $y$ ($-10^6 < x,y < 10^6$), which are the vertices of polygon $B$, in clockwise order. It is guaranteed that polygon $B$ will be convex. It is also guaranteed that polygon $B$ will reside entirely within the interior of polygon $A$.

No three points, within a polygon or across polygons, will be collinear.

## Output

Output a single floating point number, which is the minimum cost to cut $B$ out of $A$. To be considered correct, this number must be within a relative error of $10^{-6}$ of the judges’ answer.

Sample Input 1 Sample Output 1
4
0 0
0 14
15 14
15 0
4
8 3
4 6
7 10
11 7

40.0000000000

Sample Input 2 Sample Output 2
4
-100 -100
-100 100
100 100
100 -100
8
-1 -2
-2 -1
-2 1
-1 2
1 2
2 1
2 -1
1 -2

322.1421356237