Signed graph P38073

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”.