You are given an undirected graph with n nodes labeled from $1$ to n, and an array edges where each edges[i] = [u_i, v_i] represents an undirected edge between node u_i and node v_i. The graph may contain multiple edges connecting the same pair of nodes.

You are also given an integer array queries. The answer for query queries[j] is the total number of pairs of nodes $(a, b)$ satisfying $1 \leq a < b \leq$ n such that the number of edges incident to node $a$ or node $b$ is strictly greater than queries[j].

An edge is incident to node $a$ or node $b$ if at least one of its endpoints is node $a$ or node $b$.

Return an array answers where answers[j] is the answer for queries[j].

Note: An edge directly connecting node $a$ and node $b$ is counted only once when determining the total number of incident edges for the pair $(a, b)$.

Constraints:

• $2 \leq$ n $\leq 2 imes 10^4$

• $1 \leq$ edges.length $\leq 10^5$

• $1 \leq$ u_i, v_i $\leq$ n

• u_i $\neq$ v_i

• $1 \leq$ queries.length $\leq 20$

• $0 \leq$ queries[j] $<$ edges.length

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.