Painting polygon outlines

Adrian paints convex polygons on the coordinate plane with watercolors. He has no time to fill their interiors, but he still wants the drawing order to show, so the shade of each point on a polygon boundary depends on how many polygons cover that point. Say Adrian draws the polygons $p_1, p_2, \dots, p_n$ in this order. He paints a segment of polygon $p_j$ with shade $t$ if that segment, except possibly its endpoints, lies inside exactly $t$ of the later polygons $p_{j+1}, \dots, p_n$.

Painting a segment with shade $t$ costs $\frac{1}{t+1}$ units of black paint per unit of length. Compute the total amount of paint Adrian needs in order to draw all the polygons.

The first line contains the number of polygons $n$ ($1 \le n \le 10$). Then $n$ blocks follow, and the $k$-th block describes polygon $p_k$. The first line of a block contains the number of vertices $m$ ($3 \le m \le 20$). Each of the next $m$ lines contains two integers $x$ and $y$ ($0 \le x, y \le 100$), the coordinates of one vertex. The vertices are given counterclockwise, every polygon is convex, and no two consecutive sides are parallel.

Two different polygons never touch at a vertex or along a side. More precisely, if $A$ and $B$ are sides of different polygons $p_i$ and $p_j$, then $A$ and $B$ either have no common point at all, or they meet in exactly one point that lies in the interior of $A$ and in the interior of $B$.

Print the total amount of paint on one line, rounded to exactly six digits after the decimal point.

The picture for the first example.

The picture for the second example.