Triball Ranking

Triball is a sport proposed for the Youth Olympic Games in Singapore. It is played by $k$ players numbered $1$ through $k$. Every match puts three distinct players on the court, and the result names either the one player who won or the one player who lost.

Say match $i$ is played by $p_{i1}$, $p_{i2}$, $p_{i3}$. A result written as $p_{i1} > p_{i2}, p_{i3}$ means $p_{i1}$ won, so $p_{i1}$ is better than $p_{i2}$ and better than $p_{i3}$. A result written as $p_{i2}, p_{i3} > p_{i1}$ means $p_{i1}$ lost, so $p_{i2}$ is better than $p_{i1}$ and $p_{i3}$ is better than $p_{i1}$.

You are given the results of $n$ matches. Line up all $k$ players so that a better player always comes before a worse one. When more than one lineup satisfies every result, answer with the lexicographically smallest one, comparing lineups as sequences of player numbers. When no lineup satisfies every result, print $0$.

The first line contains the number of players $k$ and the number of matches $n$, separated by a space. ($1 \le k \le 1000$, $1 \le n \le 10000$)

Each of the next $n$ lines holds one match result. A line is written without spaces as p1>p2,p3 or as p2,p3>p1, and the three players in a match are distinct.

If a lineup satisfying every result exists, print the $k$ player numbers of the lexicographically smallest such lineup on one line, separated by single spaces. Otherwise print $0$.