Signed graph

An undirected graph is signed if each edge has a positive or negative sign. A signed graph is called balanced if the product of all signs around every cycle is positive.

Given a signed graph, can you tell if it is balanced or not?

Input

Input consists of several cases, each one with the number of vertices $n$ , followed by the number of edges $m$ , followed by $m$ triples $x$ $y$ $s$ to indicate an edge between $x$ and $y$ with sign $s \in \{ -1, 1 \}$ . Assume $1 \le n \le 10^5$ , $0 \le m \le 5n$ , that vertices are numbered between 0 and $n-1$ , $x \ne y$ , and that there is no more than one edge between $x$ and $y$ .

Output

For every graph, print “yes” if it is balanced; otherwise print “no”.

Problem information

Author: Conrado Martínez

Generation: 2026-01-25T10:35:59.874Z