0-1 MST

有一张完全图，n个节点 有m条边的边权为1，其余的都为0 这m条边会给你 问你这张图的最小生成树的权值 ------By zrmpaul

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.

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

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 $ .