# Longest Common Subsequence

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.

## Input

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.

## Output

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

Sample Input 1 | Sample Output 1 |
---|---|

2 3 BAC ABC |
2 |

Sample Input 2 | Sample Output 2 |
---|---|

3 8 HGBDFCAE ADBGHFCE HCFGBDAE |
3 |

Sample Input 3 | Sample Output 3 |
---|---|

6 8 AHFBGDCE FABGCEHD AHDGFBCE DABHGCFE ABCHFEDG DGABHFCE |
4 |