Maximal polygon brightness

A convex polygon $P$ lies in the plane. Put a light source at a point $T$ outside $P$, and some edges of $P$ become lit. If $A$ and $B$ are two consecutive vertices of $P$, the edge $AB$ is lit when the area of triangle $TAB$ is not zero and that triangle does not meet the interior of $P$.

The brightness of the polygon is the sum of the lengths of the lit edges. The maximal brightness is the largest brightness you can reach by choosing the best point $T$. The distance between $T$ and the polygon is unrestricted, and the coordinates of $T$ do not have to be integers.

The polygons $P$, $P_1$, $P_2$ and $P_3$ from the second example. The figure also marks the maximal brightness.

The vertices of $P$ are, in order, $A_1, A_2, \dots, A_n$. The polygon changes over $q$ steps. In step $j$ you delete one vertex that is still present and obtain a new polygon $P_j$. The vertices of $P_j$ are the vertices of $P$ that have not been deleted, in the order they had in $P$. Every $P_j$ is convex as well.

Compute the maximal brightness of $P$ and of each polygon $P_1, P_2, \dots, P_q$.

The first line contains the number of vertices $n$ of the initial polygon $P$.

The $j$-th of the next $n$ lines contains two integers $x_j$ and $y_j$, the coordinates of vertex $A_j$ ($-10^9 \le x_j, y_j \le 10^9$).

The next line contains the number of steps $q$ ($0 \le q \le n - 3$).

The $j$-th of the next $q$ lines contains an integer $k_j$ ($1 \le k_j \le n$), meaning that step $j$ deletes vertex $A_{k_j}$.

The vertices of $P$ are given counter-clockwise, no two consecutive edges are parallel, and all $k_j$ are distinct.

Print $q + 1$ lines.

The first line holds the maximal brightness of the initial polygon $P$. The $j$-th of the next $q$ lines holds the maximal brightness of the polygon $P_j$ obtained after step $j$.

Round every value to six decimal places and print all six digits, trailing zeros included. In every test the answer stays far from a rounding boundary, so double precision arithmetic prints the same digits.