**Time limit:**1.00 s**Memory limit:**512 MB

There are a total of $n$ jobs to be done. For some jobs $a$ and $b$ it is known that $a$ must be done before $b$.

What is the minimum number of days needed to do all the jobs?

**Input**

The first input line contains two integers $n$ and $m$: the number of jobs and the number of relations. The jobs are numbered $1,2,\ldots,n$.

After this, there are $m$ lines that describe the relations. Each line contains two integers $a$ and $b$: job $a$ must be done before job $b$.

**Output**

Print one integer: the minimum number of days needed to do all the jobs.

You can assume that there is a way to do all the jobs.

**Constraints**

- $1 \le n \le 500$

- $0 \le m \le \frac{n(n-1)}{2}$

**Example**

Input:

`3 2`

1 2

1 3

Output:

`2`