### Problem Statement

You are given a simple directed graph with $N$ vertices numbered $1$ to $N$ and $M$ edges numbered $1$ to $M$. Edge $i$ is a directed edge from vertex $u_i$ to vertex $v_i$.

You may perform the following operation zero or more times.

-   Choose distinct vertices $x$ and $y$ such that there is no directed edge from vertex $x$ to vertex $y$, and add a directed edge from vertex $x$ to vertex $y$.

Find the minimum number of times you need to perform the operation to make the graph satisfy the following condition.

-   For every triple of distinct vertices $a$, $b$, and $c$, if there are directed edges from vertex $a$ to vertex $b$ and from vertex $b$ to vertex $c$, there is also a directed edge from vertex $a$ to vertex $c$.

### Input

The input is given from Standard Input in the following format:

```
$N$ $M$
$u_1$ $v_1$
$\vdots$
$u_M$ $v_M$
```

### Output

Print the answer.

### Constraints

-   $3 \leq N \leq 2000$
-   $0 \leq M \leq 2000$
-   $1 \leq u_i ,v_i \leq N$
-   $u_i \neq v_i$
-   $(u_i,v_i) \neq (u_j,v_j)$ if $i \neq j$.
-   All values in the input are integers.

3

Initially, the condition is not satisfied because, for instance, for vertices 2, 4, and 3, there are directed edges from vertex 2 to vertex 4 and from vertex 4 to vertex 3, but not from vertex 2 to vertex 3.
You can make the graph satisfy the condition by adding the following three directed edges:

• one from vertex 2 to vertex 3,
• one from vertex 2 to vertex 1, and
• one from vertex 4 to vertex 1.

On the other hand, the condition cannot be satisfied by adding two or fewer edges, so the answer is 3.