Description

Students should learn to make more good friends. Friendship is mutual: if $A$ is a good friend of $B$, then $B$ is also a good friend of $A$. Friendship is not transitive: if $A$ is a good friend of $B$, and $B$ is a good friend of $C$, $A$ and $C$ are not necessarily good friends. Given the friendship relations among some students in a primary school, write a program to count how many good friends the student with the most friends has.

Input Format

The input consists of $m+1$ lines.
The first line contains two integers $n$ and $m$, representing the total number of students and the number of friendship pairs.
Lines $2$ to $m+1$ each describe a friendship pair, with two different student names separated by a single space. Each name consists only of lowercase letters, and $1 \leq$ name length $\leq 10$.

Output Format

A single integer, representing the maximum number of good friends any student has.

Sample

4 3
lucy lily
jam lily
jam peter

2