Description

You are given $n$ strings and required to find the length of the longest perfect word.

A string $t$ is called a perfect word, if and only if every non-empty substring of $t$ appears in the given strings.

A string $s$ is called a substring of $t$ if and only if it can be obtained by removing several (possibly zero) characters from the beginning or end of $t$.

Input Format

The first line contains a single integer $n$ ($1 \leq n \leq 10 ^ 5$).

Each of the next $n$ lines contains a string consisting of lowercase English letters.

It is guaranteed that the total length of the given strings is no more than $10 ^ 5$.

Output Format

Output an integer, representing the length of the longest perfect word.

4
a
t
b
ab

2

Hint

Source: The 2022 ICPC Asia Xi'an Regional Contest Problem G.

Author: MonkeyKing.