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문제

You are given $n$ strings, each a permutation of the first $k$ upper-case letters of the alphabet.

String $s$ is a subsequence of string $t$ if and only if it is possible to delete some (possibly zero) characters from the string $t$ to get the string $s$.

Compute the length of the longest common subsequence of all $n$ strings.

입력

The first line of input contains two integers $n$ ($1 \le n \le 10^5$) and $k$ ($1 \le k \le 26$), where $n$ is the number of strings, and the strings are all permutations of the first $k$ upper-case letters of the alphabet.

Each of the next $n$ lines contains a single string $t$. It is guaranteed that every $t$ contains each of the first $k$ upper-case letters of the alphabet exactly once.

출력

Output a single integer, the length of the longest subsequence that appears in all $n$ strings.

예제 입력 1

2 3
BAC
ABC

예제 출력 1

2

예제 입력 2

3 8
HGBDFCAE
ADBGHFCE
HCFGBDAE

예제 출력 2

3

예제 입력 3

6 8
AHFBGDCE
FABGCEHD
AHDGFBCE
DABHGCFE
ABCHFEDG
DGABHFCE

예제 출력 3

4