Cycle XOR Consistency

Given an undirected graph G with n nodes and m edges. Each edge is described by three integers A_i, B_i and C_i, where C_i is the weight of the edge between nodes A_i and B_i. Determine whether the following property holds:

For every cycle C in the graph, the XOR sum of the weights of its edges is 0, i.e., $$\bigoplus_{e\in C} C_e = 0.$$

Hint: The property holds if and only if one can assign a number x_v to each vertex v such that for every edge (u, v) with weight w, the relation below is satisfied:

$$x_u \oplus x_v = w.$$

inputFormat

The input is given as follows:

• The first line contains two integers n and m (1 ≤ n ≤ 10⁵, 0 ≤ m ≤ 10⁵), representing the number of nodes and the number of edges, respectively.
• Each of the following m lines contains three integers A_i, B_i and C_i (1 ≤ A_i, B_i ≤ n, 0 ≤ C_i ≤ 10⁹), describing an undirected edge between nodes A_i and B_i with weight C_i.

outputFormat

Output a single line containing Yes if the property holds, or No otherwise.

sample

3 3
1 2 1
2 3 2
3 1 3

Yes