Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

When a radio station is broadcasting over a very large area, repeaters are
used to retransmit the signal so that every receiver has a strong signal. However,
the channels used by each repeater must be carefully chosen so that nearby repeaters
do not interfere with one another. This condition is satisfied if adjacent repeaters
use different channels.

Since the radio frequency spectrum is a precious resource, the number of channels
required by a given network of repeaters should be minimised. You have to write
a program that reads in a description of a repeater network and determines the
minimum number of channels required.

The input consists of a number of maps of repeater networks. Each map begins
with a line containing the number of repeaters. This is between 1 and 26, and
the repeaters are referred to by consecutive upper-case letters of the alphabet
starting with A. For example, ten repeaters would have the names A,B,C,...,I
and J. A network with zero repeaters indicates the end of input.

Following the number of repeaters is a list of adjacency relationships. Each line has the form:

A:BCDH

which indicates that the repeaters B, C, D and H are adjacent to the repeater A. The first line describes those adjacent to repeater A, the second those adjacent to B, and so on for all of the repeaters. If a repeater is not adjacent to any other, its line has the form

A:

The repeaters are listed in alphabetical order.

Note that the adjacency is a symmetric relationship; if A is adjacent to B, then B is necessarily adjacent to A. Also, since the repeaters lie in a plane, the graph formed by connecting adjacent repeaters does not have any line segments that cross.

Following the number of repeaters is a list of adjacency relationships. Each line has the form:

A:BCDH

which indicates that the repeaters B, C, D and H are adjacent to the repeater A. The first line describes those adjacent to repeater A, the second those adjacent to B, and so on for all of the repeaters. If a repeater is not adjacent to any other, its line has the form

A:

The repeaters are listed in alphabetical order.

Note that the adjacency is a symmetric relationship; if A is adjacent to B, then B is necessarily adjacent to A. Also, since the repeaters lie in a plane, the graph formed by connecting adjacent repeaters does not have any line segments that cross.

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