There are $n$ cities with airports but no flight connections. You are given $m$ requests which routes should be possible to travel.

Your task is to determine the minimum number of one-way flight connections which makes it possible to fulfil all requests.

Input

The first input line has two integers $n$ and $m$: the number of cities and requests. The cities are numbered $1,2,\dots,n$.

After this, there are $m$ lines describing the requests. Each line has two integers $a$ and $b$: there has to be a route from city $a$ to city $b$. Each request is unique.

Output

Print one integer: the minimum number of flight connections.

Constraints

• $1 \le n \le 10^5$
• $1 \le m \le 2 \cdot 10^5$
• $1 \le a, b \le n$

Example

Input:

4 5
1 2
2 3
2 4
3 1
3 4

Output:

4

Explanation: You can create the connections $1 \rightarrow 2$, $2 \rightarrow 3$, $2 \rightarrow 4$ and $3 \rightarrow 1$. Then you can also fly from city $3$ to city $4$ using the route $3 \rightarrow 1 \rightarrow 2 \rightarrow 4$.