Problem L. Language Recognition

Author:ACM ICPC 2007-2008, Northeastern European Regional Contest   Time limit:3 sec
Input file:language.in   Memory limit:64 Mb
Output file:language.out  

Statement

Deterministic Final-State Automaton (DFA) is a directed multigraph whose vertices are called states and edges are called transitions. Each DFA transition is labeled with a single letter. Moreover, for each state s and each letter l there is at most one transition that leaves s and is labeled with l. DFA has a single starting state and a subset of final states. DFA defines a language of all words that can be constructed by writing down the letters on a path from the starting state to some final state.

Given a language with a finite set of words it is always possible to construct a DFA that defines this language. The picture on the left shows such DFA for the language cosisting of three words: fix, foo, ox. However, this DFA has 7 states, which is not optimal. The DFA on the right defines the same language with just 5 states.

Your task is to find the minimum number of states in a DFA that defines the given language.

Input file format

The first line of the input file contains a single integer number n — the number of words in the language. It is followed by n lines with a word on each line.

Output file format

Write to the output file a single integer number — the minimal number of states in a DFA that defines the language from the input file.

Constraints

1 ≤ n ≤ 5000

Each word in the input file consists of 1 to 30 lowercase Latin letters from a to z. All words are different.

Sample tests

No. Input file (language.in) Output file (language.out)
1
3
fix
foo
ox
5
2
4
a
ab
ac
ad
3

0.108s 0.018s 15