Description

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 consisting 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

The first line of the input file contains a single integer number n (1 ≤ n ≤ <nobr>5 000</nobr>) — the number of words in the language. It is followed by n lines with a word on each line. Each word consists of 1 to 30 lowercase Latin letters from “a” to “z”. All words in the input file are different.

Output

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.

<table style="border-color: black; border-collapse: collapse;" border="1"><tbody><tr><th>#1</th><td>3<br>fix<br>foo<br>ox</td></tr><tr><th>#2</th><td>4<br>a<br>ab<br>ac<br>ad</td></tr></tbody></table>

<table style="border-color: black; border-collapse: collapse;" border="1"><tbody><tr><th>#1</th><td>5</td></tr><tr><th>#2</th><td>3</td></tr></tbody></table>

Source