Tree destruction

Tarjan and Dijkstra are playing a game. Both of them have a tree each, and each edge of their respective trees has some weight. The trees are both rooted at the node with index 1(1-indexed). The cost of travelling from a node u to a node v is the sum of the weights of the edges on the path between them. The mobilisation cost for a tree is defined as follows. Now, Tarjan and Dijkstra both have