Color the Map

You have obtained a map of a mysterious world you are about to explore. The map shows the whole region, divided into several countries whose borders are intricate. Because it is drawn in a single ink color, it is hard to tell at a glance which region belongs to which country, so you decide to color the map before setting out.

Each country consists of one or more territories, each of which is a simple polygon. The territories of one country need not touch one another, so a country may have disconnected territories. All territories of the same country must be given the same color. Two different countries may share a color, but two adjacent countries must be given different colors. Two countries are adjacent when any of their territories share a border of non-zero length; territories that meet only at a single point do not count as sharing a border.

Write a program that determines the least number of colors needed to color the map under these rules.

The input consists of several maps. Each map begins with a line containing the total number of territories $n$, a positive integer with $n \le 100$. The data for the $n$ territories follow.

A territory with $m$ vertices is given in the following format:

String
x1 y1
x2 y2
...
xm ym
-1

String is the name of the country the territory belongs to: a sequence of alphanumeric characters, at least 1 and at most 20 characters long. When a country has several territories, the same name appears in each of them.

The remaining lines list the vertices of the territory. Each vertex line contains two nonnegative integers, the $x$- and $y$-coordinates, separated by a single space; neither coordinate exceeds 1000. The edges of the territory are obtained by connecting consecutive vertices, and by connecting the last vertex back to the first. A line containing only -1 marks the end of the vertex list. The number of vertices satisfies $m \le 100$.

You may assume that every polygon is simple (its boundary neither crosses nor touches itself) and that no two polygons share a region of non-zero area. Each map contains at most 10 countries.

The end of the input is a line containing a single zero.

For each map, output one line containing the least number of colors needed to color it under the stated rules.