You are given an undirected graph with $n$ nodes labeled from $0$ to $n - 1$, represented by an integer array nums of length $n$ and a $2 ext{D}$ integer array edges where edges[i] $= [u_i, v_i]$ represents an edge connecting node $u_i$ and node $v_i$. Each node $i$ has an assigned value nums[i].

A subset of nodes forms a connected subgraph if it is nonempty and every pair of nodes in the subset is connected by a path using only nodes and edges within the subset.

Return the total number of nonempty connected subgraphs where the sum of the node values is even.

Constraints:

• $1 \le n =$ nums.length $\le 13$

• nums[i] is $0$ or $1$.

• $0 \le$ edges.length $\le \frac{n imes (n - 1)}{2}$

• edges[i] $= [u_i, v_i]$

• $0 \le u_i < v_i < n$

• All edges are distinct.

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.