Alob and Bice inherited from their parents a piece of land
represented by a simple polygon. There is a canal represented
by a straight line. Each brother inherited the lands on one
side of the canal. It is possible that the land of each person
consists of several disconnected pieces of land. It is also
possible that one person does not inherit any land at all.
Alob decided to grow corn fields on his land while Bice
decided to grow rice fields. However, they both agree that
their fields are symmetrical about the canal.
Your task is to help Alob identify the largest possible area
of land to grow corn fields.
Note that a simple polygon is a nonintersecting polygon,
and does not have any $3$
consecutive vertices that are collinear.
Input

The first line contains $N$  the number of vertices
representing the simple polygon land ($3 \leq N \leq 100$).

In the next $N$
lines, the $i^\textrm
{th}$ one contains two integers $x_ i$, $y_ i$  the coordinate of the
$i^\textrm {th}$
vertex ($1\, 000 \leq x_ i,
y_ i \leq 1\, 000$).

The last line contains four spaceseparated integers
$x_ a$, $y_ a$, $x_ b$, $y_ b$ representing the
coordinates of two distinct points in the straight line
canal ($1\, 000 \leq x_ a,
y_ a, x_ b, y_ b \leq 1\, 000$).
Output
Output a single real number  the largest possible area of
land to grow corn fields for Alob. Your answer will be
considered correct if its relative or absolute error doesn’t
exceed $10^{6}$.
Namely: let’s assume that your answer is $a$, and the answer of the jury is
$b$. The checker program
will consider your answer correct, if $\frac{ab}{max(1,b)} \leq
10^{6}$.
Sample Clarification
These are visualization of the samples below:
First sample:
Second sample:
Third sample:
Sample Input 1 
Sample Output 1 
4
0 0
2 0
2 2
0 2
0 1 0 3

0.0000000000

Sample Input 2 
Sample Output 2 
6
0 1
0 4
3 6
7 5
4 2
7 0
5 7 2 0

9.476048311178

Sample Input 3 
Sample Output 3 
6
5 0
3 2
0 1
3 2
5 0
0 5
0 0 1 0

8.0000000000
