Sunny Graph#3291
The Sun is a great heavenly body that is worshiped by various religions. Bob loves the Sun and loves any object that is similar to the Sun. He noticed that he can find the shape of the Sun in certain graphs, which he calls "Sunny".
A graph G=(V,E) with a vertex v \in V is called "Sunny" when there exists a subgraph G'=(V,E'), where E' \subseteq E, that satisfies the following two properties (note that the set of vertices must remain the same):
The connected component containing vertex is a cycle that consists of three or more vertices.
Every other component has exactly two vertices.
The following picture is an example of a subgraph that satisfies these properties.
Your task is to write a program that determines whether a given simple graph has a vertex that is "Sunny" or not. A simple graph means that each edge connects two different vertices, and there is at most one edge between any pair of vertices.
The first line contains two integers and , separated by a space, where 1 \leq N \leq 200 is the number of vertices, and 0 \leq M \leq 20\,000 is the number of edges.
The following lines describe the edges. Each line contains two integers u_i and v_i (1 \leq u_i, v_i \leq N), which indicate an edge that connects vertices u_i and v_i. Vertices u_i and v_i are always different, and each pair of vertices is connected by at most one edge.
Print a line containing "Yes" if the graph is "Sunny". Otherwise, print "No".
Example 1