Problem G
Forest Highway

Task

You are given a description of the forest and the highway. The forest is a simple polygon, i.e. its sides do not cross, and the highway can be considered a straight line of width zero. You are also given $d$, the safe distance from the highway. Calculate the size of the inhabitable area of the forest.

Figure 1: Drawing of the sample input

Input

The first line of the input contains one integer $N$ $(3\leq N\leq 250\, 000)$ denoting the number of vertices of the polygon. $N$ lines follow with two floating point numbers $x_ i$ and $y_ i$, denoting that the $i$-th point of the polygon is $(x_ i, y_ i)$.

Next line contains 4 floating point numbers $x_ a, y_ a, x_ b, y_ b$, denoting that the highway passes through points $(x_ a, y_ a)$ and $(x_ b, y_ b)$. The last line of the input contains one positive floating point number $d$, the safe distance from the highway.

All floating point numbers will be at most $100\, 000$ in absolute value and will have at most 4 digits after the decimal point.

Output

Output one line with one number – the size of the inhabitable area of the forest. Results with relative or absolute error $10^{-7}$ will be considered correct.

7
0.0 0.0
2.0 4.0
4.0 0.0
5.0 5.0
1.0 6.0
1.0 4.0
-1.0 3.0
-2.0 4.0 6.0 1.0
0.6

13.082798910