A13003. Harmonious Graph

You're given an undirected graph with $n$ nodes and $m$ edges. Nodes are numbered from $1$ to $n$ .

The graph is considered harmonious if and only if the following property holds:

- For every triple of integers $(l, m, r)$ such that $1 \le l < m < r \le n$ , if there exists a path going from node $l$ to node $r$ , then there exists a path going from node $l$ to node $m$ .

In other words, in a harmonious graph, if from a node $l$ we can reach a node $r$ through edges ( $l < r$ ), then we should able to reach nodes $(l+1), (l+2), \ldots, (r-1)$ too.

What is the minimum number of edges we need to add to make the graph harmonious?

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).

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

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.