Longest Concatenated Word Length

You are given a list of words. Your task is to find the maximum length among all words that can be formed by concatenating at least two other words from the list.

A word is considered to be formed by concatenation if it can be split into two or more parts, each of which is a word present in the list. Note that the parts used for concatenation must be non-empty, and a word cannot be used as its own component in the formation.

If no such word exists, print 0.

Note: The input will be read from standard input (stdin) and the output should be printed to standard output (stdout).

inputFormat

The first line contains an integer N representing the number of words. The next N lines each contain a word.

Example:

6
cat
bat
rat
catbat
batcat
catrat

outputFormat

Print a single integer which is the length of the longest word that can be formed by concatenating other words from the list. If no such word exists, print 0.

## sample

1
cat

0

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