The Lost Cows

On a sunny day, farmer John was kidnapped by the cows of his neighbor, farmer Marcus. The forced holiday does not bother him, but he wants to be sure that his own cows can end up together.

John's pastures are numbered $1$ through $N$, and one cow stands in each pasture. The barn is pasture $1$. Every pasture has $M$ signs, and sign $j$ at pasture $i$ points along a path to pasture $S_{i,j}$. A sign sometimes points back to the pasture it stands in.

Marcus's cows let John write one list of instructions and hand it to all of his cows. An instruction is a single sign number. A cow reads the first number on the list, finds that sign in the pasture where she stands, and walks the path it points to. In the new pasture she reads the second number on the list and walks again the same way. She repeats this until the list runs out. Every cow follows the same list in the same order, so one instruction moves every cow one step.

John starts by working out how many instructions it takes to bring two cows into one pasture. For pastures $a$ and $b$, let $d(a, b)$ be the smallest length of a list such that the cow starting at $a$ and the cow starting at $b$ stand in the same pasture after the whole list has been followed. The two cows may be in different pastures along the way; only their positions after the last instruction have to match.

A list that gathers every cow at the barn is guaranteed to exist, so $d(a, b)$ is defined for every pair $a$, $b$.

The first line contains the number of pastures $N$ and the number of signs $M$ ($3 \le N \le 200$, $1 \le M \le 200$).

Line $j$ of the next $M$ lines contains $N$ integers $S_{1,j}, S_{2,j}, \dots, S_{N,j}$ ($1 \le S_{i,j} \le N$), where $S_{i,j}$ is the pasture that sign $j$ at pasture $i$ points to.

Print the largest value of $d(a, b)$ over all pairs of pastures $a < b$.