You are given a network of $n$ nodes labeled from $0$ to $n - 1$, represented by an $n \times n$ adjacency matrix graph, where graph[i][j] = 1 indicates a direct connection between node i and node j, and graph[i][j] = 0 indicates no connection.

You are also given an array initial containing the nodes initially infected with malware. When two nodes are directly connected and at least one of them is infected, the malware spreads to the other node. This infection process continues until no additional nodes can be infected.

Suppose $M(\text{initial})$ denotes the total number of nodes infected after the spread terminates.

You must remove exactly one node from initial, completely removing that node and all edges connected to it from the network.

Return the node that should be removed to minimize $M(\text{initial})$. If multiple nodes result in the same minimum value, return the node with the smallest index.

Constraints:

• n $==$ graph.length

• n $==$ graph[i].length

• $2 \leq$ n $\leq 300$

• graph[i][j] is $0$ or $1$.

• graph[i][j] $==$ graph[j][i]

• graph[i][i] $== 1$

• $1 \leq$ initial.length $< n$

• $0 \leq$ initial[i] $\leq n - 1$

• All the integers in initial are unique.

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.