Given an undirected graph with v vertices and e edges, you are asked to determine if itβs a star graph. A star graph is a graph that has a central vertex that is connected to all the other vertices, while all the other vertices are only connected to the central one and no other vertex.
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Input
The first line of the input contains two integers v (1 β€ v β€ 100 000) and e (1 β€ e β€ 100 000).
The following e 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 a star graph and No otherwise.