Flight Route Requests

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.