M found two papers and a pencil in his room (as you know it's so valuable for a prisoner). a weighted (weights are either \(0\) or \(1\)) graph is drawn on the first paper.

M is forced to draw a spanning tree of the graph (which is drawn on the first paper) on the second paper which includes odd number of \(1\) weighted edges.

Can M draw a spanning tree with the conditions described above?

Input

First line contains two integers \(n, m\), number of first paper graph's vertices and number of first paper graph's edges.

Each of the following \(m\) lines contains \(v_i, u_i\) and \(w_i\) separated space describing graph's \(i\)th edge's vertices(\(v_i, u_i\)) and its weight (\(w_i\)).

Output

In the only line of output print YES if M can draw a spanning tree of the first paper's graph with odd number of \(1\) weighted edges and otherwise print NO.

Constraints

\(1 \leq n, m \leq 3 \times 10^5\)

\(1 \leq v_i, u_i \leq n \\ 0 \leq w_i \leq 1\)

It is guaranteed that there is no multiple edges or self loops in the graph.