B"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 <= q n <= q 10^5 , 0 <= q m <= q 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 <= q a_i, b_i <= q 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. 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 . "...