2242 - Maximum Score of a Node Sequence\.

Hard

There is an undirected graph with n nodes, numbered from 0 to n - 1.

You are given a 0-indexed integer array scores of length n where scores[i] denotes the score of node i. You are also given a 2D integer array edges where <code>edgesi = a_i, b_i</code> denotes that there exists an undirected edge connecting nodes <code>a_i</code> and <code>b_i</code>.

A node sequence is valid if it meets the following conditions:

• There is an edge connecting every pair of adjacent nodes in the sequence.

• No node appears more than once in the sequence.

The score of a node sequence is defined as the sum of the scores of the nodes in the sequence.

Return the maximum score of a valid node sequence with a length of 4. If no such sequence exists, return -1.

Example 1:

Input: scores = 5,2,9,8,4, edges = \[\[0,1],1,2,2,3,0,2,1,3,2,4]

Output: 24

Explanation: The figure above shows the graph and the chosen node sequence 0,1,2,3.

The score of the node sequence is 5 + 2 + 9 + 8 = 24.

It can be shown that no other node sequence has a score of more than 24.

Note that the sequences 3,1,2,0 and 1,0,2,3 are also valid and have a score of 24.

The sequence 0,3,2,4 is not valid since no edge connects nodes 0 and 3.

Example 2:

Input: scores = 9,20,6,4,11,12, edges = \[\[0,3],5,3,2,4,1,3]

Output: -1

Explanation: The figure above shows the graph.

There are no valid node sequences of length 4, so we return -1.

Constraints:

• n == scores.length

• <code>4 <= n <= 5 * 10⁴</code>

• <code>1 <= scoresi<= 10⁸</code>

• <code>0 <= edges.length <= 5 * 10⁴</code>

• edges[i].length == 2

• <code>0 <= a_i, b_i<= n - 1</code>

• <code>a_i != b_i</code>

• There are no duplicate edges.