The Balanced Timber Cut

You are managing a logging operation. A tree is represented by N nodes, where each node has a weight (the amount of timber). You must cut exactly one edge to split the tree into two separate components. Your goal is to find the edge that, when removed, results in the minimum absolute difference between the total timber weights of the two components. Input Format: - Line 1: An integer N, the number of nodes. - Line 2: N space-separated integers, where the i-th integer is the weight of node i+1. - Next N-1 lines: Two integers u and v, representing an edge between node u and node v. Output Format: - A single integer: the minimum possible absolute difference. Example: Input: 3 10 20 15 1 2 2 3 Output: 5 (Removing 2-3 gives {10,20} and {15}, diff 15. Removing 1-2 gives {10} and {20,15}, diff 25. Min is 15? Wait, sum(1,2)=30, sum(3)=15, diff=15. Sum(1)=10, sum(2,3)=35, diff=25. Answer is 15.)