Watershed#868
Given the map of rivers of a certain continent. Each river is represented as a polyline, which starts at the source of the river and ends either at the point where the river flows into another river or at the estuary. The vertices of the polyline are either turning points of the river or points where tributaries join.
We will consider the basin of a river as the convex polygon of minimal area that contains the river and all its tributaries.
Note: According to this definition, the same area can belong to the basins of different rivers.
Example: A continent with three rivers is shown. The coordinates of the rivers and the area of the basin are given in the table.
It is required to find the largest area of a river basin located on the given continent.
The first line contains the number of rivers . The following lines contain blocks describing each river. The -th block consists of:
one line with k_i — the number of vertices of the polyline describing the river;
k_i lines each containing two real numbers x_j and y_j (1 \leq j \leq k_i), separated by a space — the coordinates of the points describing the river.
1 \leq N \leq 10, \sum k_i \leq 1000, -1000 \leq x_j, y_j \leq 1000.
Output one number — the area of the largest river basin, rounded to two decimal places.
Example 1