Cycle with Even Weight Sum

You are given an undirected graph with n vertices and m edges. Each edge is described by three integers u, v, and w denoting an edge between vertices u and v with weight w.

Your task is to determine whether there exists a cycle in the graph such that the sum of the weights of the edges in the cycle is even. In other words, if a cycle is composed of edges with weights \(w_1, w_2, \ldots, w_k\), you need to check whether:

\(w_1 + w_2 + \cdots + w_k \equiv 0 \pmod{2}\)

It is guaranteed that self-loops and multiple edges will not appear in the input. If such a cycle exists, print YES; otherwise, print NO.

Note: The cycle must consist of at least three vertices and no edge or vertex (except the starting/ending vertex) is repeated.

inputFormat

The input is read from stdin and has the following format:

1. The first line contains two integers n and m — the number of vertices and the number of edges, respectively.
2. Each of the next m lines contains three integers u, v, and w, representing an edge between vertices u and v with weight w.

outputFormat

Output a single line to stdout containing either YES if there exists a cycle with an even total weight, or NO otherwise.

5 5
1 2 3
2 3 4
3 4 5
4 5 6
5 1 7

NO