Description

Input

The first line contains two integers $n$ and $m$ ($3 \le n \le 200\ 000$ and $1 \le m \le 200\ 000$).

The $i$-th of the next $m$ lines contains two integers $u_i$ and $v_i$ ($1 \le u_i, v_i \le n$, $u_i \neq v_i$), that mean that there's an edge between nodes $u$ and $v$.

It is guaranteed that the given graph is simple (there is no self-loop, and there is at most one edge between every pair of nodes).

Output

Print the minimum number of edges we have to add to the graph to make it harmonious.

14 8
1 2
2 7
3 4
6 3
5 7
3 8
6 8
11 12

1

200000 3
7 9
9 8
4 5

0

Note

In the first example, the given graph is not harmonious (for instance, $1 < 6 < 7$, node $1$ can reach node $7$ through the path $1 \rightarrow 2 \rightarrow 7$, but node $1$ can't reach node $6$). However adding the edge $(2, 4)$ is sufficient to make it harmonious.

In the second example, the given graph is already harmonious.