The Islands

Byteotia is an island surrounded by the ocean. Byteotia contains lakes; on those lakes there are isles that themselves contain lakes, on which there are further isles, and so on.

We assign a degree to every body of water and every piece of land:

• the ocean has degree $0$;
• Byteotia, the outermost island, has degree $1$;
• a lake lying on an island of degree $i$ has degree $i+1$;
• an island lying on a lake of degree $l$ has degree $l+1$.

Consequently every island has an odd degree, while every lake (and the ocean) has an even degree.

Every lake and every island is bounded by a coastline shaped like a rectilinear polygon: each edge is perpendicular to its neighbours (all edges are parallel to the $x$- or $y$-axis) and every vertex has integer coordinates. No two coastlines touch or cross.

Given all of the coastlines, compute the maximum degree that occurs among the islands and lakes.

Write a program that:

• reads the coastlines of the islands and lakes from standard input,
• computes the maximum degree of any island or lake,
• writes the result to standard output.

The first line contains one integer $n$, the number of coastlines, $1 \le n \le 40000$.

Each of the next $n$ lines describes one coastline. A line begins with an even integer $k$, the number of vertices of that coastline, $4 \le k \le 10000$, followed by $k$ integers $x_1, x_2, \dots, x_k$ with $0 \le x_i \le 10^8$. The vertices of the coastline are

$(x_1,x_2),(x_3,x_2),(x_3,x_4),(x_5,x_4),\dots,(x_{k-1},x_k),(x_1,x_k),$

given in Cartesian coordinates in anticlockwise order (so when walking from one vertex to the next the interior always lies on the left).

The coastlines are listed so that:

• the coastline of every lake appears after the coastline of the island it lies on,
• the coastline of every island appears after the coastline of the lake it lies on.

The whole map is described using at most $200000$ vertices in total.

Output a single integer: the maximum degree of any island or lake.