0-1 MST
Description
Ujan has a lot of useless stuff in his drawers, a considerable part of which are his math notebooks: it is time to sort them out. This time he found an old dusty graph theory notebook with a description of a graph.
It is an undirected weighted graph on $n$ vertices. It is a complete graph: each pair of vertices is connected by an edge. The weight of each edge is either $0$ or $1$; exactly $m$ edges have weight $1$, and all others have weight $0$.
Since Ujan doesn't really want to organize his notes, he decided to find the weight of the minimum spanning tree of the graph. (The weight of a spanning tree is the sum of all its edges.) Can you find the answer for Ujan so he stops procrastinating?
The first line of the input contains two integers $n$ and $m$ ($1 \leq n \leq 10^5$, $0 \leq m \leq \min(\frac{n(n-1)}{2},10^5)$), the number of vertices and the number of edges of weight $1$ in the graph.
The $i$-th of the next $m$ lines contains two integers $a_i$ and $b_i$ ($1 \leq a_i, b_i \leq n$, $a_i \neq b_i$), the endpoints of the $i$-th edge of weight $1$.
It is guaranteed that no edge appears twice in the input.
Output a single integer, the weight of the minimum spanning tree of the graph.
Input
The first line of the input contains two integers $n$ and $m$ ($1 \leq n \leq 10^5$, $0 \leq m \leq \min(\frac{n(n-1)}{2},10^5)$), the number of vertices and the number of edges of weight $1$ in the graph.
The $i$-th of the next $m$ lines contains two integers $a_i$ and $b_i$ ($1 \leq a_i, b_i \leq n$, $a_i \neq b_i$), the endpoints of the $i$-th edge of weight $1$.
It is guaranteed that no edge appears twice in the input.
Output
Output a single integer, the weight of the minimum spanning tree of the graph.
Samples
6 11
1 3
1 4
1 5
1 6
2 3
2 4
2 5
2 6
3 4
3 5
3 6
2
3 0
0
Note
The graph from the first sample is shown below. Dashed edges have weight $0$, other edges have weight $1$. One of the minimum spanning trees is highlighted in orange and has total weight $2$.
In the second sample, all edges have weight $0$ so any spanning tree has total weight $0$.