There are two machines in a factory. Both machines can do one job in a day, and they can work simultaneously.

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