You are given an integer n, representing the number of vertices in an undirected graph numbered from $0$ to n $- 1$. You are also given a $2$D integer array edges, where edges[i] $= [u_i, v_i, w_i]$ denotes a prospective undirected edge between vertex $u_i$ and vertex $v_i$ with weight $w_i$.

Initially, the graph contains no edges. You process the edges in edges one by one in the given order. An edge is added to the graph if and only if adding it does not form any cycle with an odd total weight.

Return the total number of edges successfully added to the graph.

Constraints:

• $3 \leq$ n $\leq 5 imes 10^4$

• $1 \leq$ edges.length $\leq 5 imes 10^4$

• edges[i] $= [u_i, v_i, w_i]$

• $0 \leq u_i < v_i <$ n

• All elements in edges are distinct.

• $w_i = 0$ or $w_i = 1$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.