Maximum Sum of Edge Values in an Undirected Graph

Given an undirected graph, you need to assign each of the N nodes a value from 1 to N. The value of each edge equals the sum of the values of the two nodes it connects. Find the maximum possible sum of all edge values. Input Format: First line contains two integers, N (number of nodes) and M (number of edges). The next M lines each contains two integers u and v, indicating there is an undirected edge between node u and node v. Output Format: Output an integer, representing the maximum possible sum of all edge values. Constraints: 1 ≤ N ≤ 100000 1 ≤ M ≤ 200000 Example: Input: 4 3 1 2 2 3 3 4 Output: 14 Example Input 4 3 1 2 2 3 3 4