A graph is complete if all the vertices are connected to all the other vertices.
Given an undirected graph with n vertices and m edges, you are asked to check if itβs a complete graph.
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Input
The first line of the input contains two integers n(1 β€ v β€ 500) and m (1 β€ e β€ 100 000).
The following m lines contain pairs of integers v1, v2 (1 β€ v1, v2 β€ v) which means that the vertex v1 is connected to the vertex v2 and vice versa.
Output
The program should print Yes if the graph is complete and No otherwise.