CF1242B.0-1 MST

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?

乌詹的抽屉里堆满了各种无用的东西，其中相当一部分是他的数学笔记：是时候整理一下了。这次他发现了一本陈旧积灰的图论笔记，上面描述了一个图。

这是一个含有 $n$ 个顶点的无向带权图。该图是完全图：任意两个顶点之间都有一条边相连。每条边的权重为 $0$ 或 $1$；其中恰好有 $m$ 条边的权重为 $1$，其余所有边的权重均为 $0$。

由于乌詹并不真的想整理自己的笔记，他决定计算该图的最小生成树（MST）的权重。（生成树的权重定义为其中所有边的权重之和。）你能帮乌詹算出这个答案，好让他停止拖延吗？

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.

输入的第一行包含两个整数 $n$ 和 $m$（$1 \leq n \leq 10^5$，$0 \leq m \leq \min(\frac{n(n-1)}{2},10^5)$），分别表示图中顶点的数量以及权值为 $1$ 的边的数量。

接下来的 $m$ 行中，第 $i$ 行包含两个整数 $a_i$ 和 $b_i$（$1 \leq a_i, b_i \leq n$，$a_i \neq b_i$），表示第 $i$ 条权值为 $1$ 的边的两个端点。

保证输入中不会出现重复的边。

Output a single integer, the weight of the minimum spanning tree of the graph.

输出一个整数，表示该图的最小生成树的权重。

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 $0$.

第一个样例的图如下所示。虚线边的权重为 $0$，其余边的权重为 $1$。其中一棵最小生成树以橙色高亮显示，其总权重为 $2$。

在第二个样例中，所有边的权重均为 $0$，因此任意一棵生成树的总权重均为 $0$。