Pick a Pair

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문제 설명

예제2

문제

Friends play an interesting game with words. The goal of this game is arranging words in pairs.

Friends have $n$ words of the same length. They are choosing the largest number $k$ such that it is possible to divide the words into pairs so that words in each pair have common prefix of length at least $k$ .

Find the maximum possible value of $k$ .

입력

The first line of input contains an even integer $n$ --- number of words ( $1 \leq n \leq 2\cdot 10^5$ ).

The following $n$ lines contain words that the friends have. All words have same length. Total words length is less or equal to $2 \cdot 10^6$ .

출력

Output maximal possible value of $k$ .