University Rankings

A rating agency publishes one ranking list per department. Every university in the survey runs the same $M$ departments, and each department list places all $N$ universities in a strict order from best to worst.

Because there are many lists, two universities often cannot be ordered against each other. The agency therefore uses a relation it calls absolutely better: university $X$ is absolutely better than university $Y$ when $X$ comes before $Y$ in every one of the $M$ department rankings.

Take three universities $X$, $Y$, $Z$ and three departments CS, EE, FLS with these rankings:

• CS: $X$, $Y$, $Z$
• EE: $X$, $Z$, $Y$
• FLS: $Z$, $X$, $Y$

$X$ comes before $Y$ in all three lists, so $X$ is absolutely better than $Y$. $X$ and $Z$ cannot be ordered: $X$ leads in CS, $Z$ leads in FLS.

Find universities $U_1, \dots, U_k$ such that $U_i$ is absolutely better than $U_j$ for every $i < j$. Report the largest possible $k$. Universities are given as numbers.

The first line holds one integer $C$, the number of test cases ($1 \le C \le 10$).

Each test case begins with a line holding two integers $N$ and $M$ ($1 \le N, M \le 400$), the number of universities and the number of departments. $M$ lines follow. The $k$-th of them holds $N$ integers, a permutation of $1$ through $N$, listing the universities of the $k$-th department's ranking from best to worst. If university $U$ appears before university $V$ on that line, the $k$-th department of $U$ is better than the $k$-th department of $V$.

Print $C$ lines, one per test case in the order given, each holding the largest possible $k$. Print no extra spaces.