Place the delivery hub

Choose one node for the brewery delivery hub. The link between node i and parent[i] has length lengths[i] and can be traveled in either direction. Each node needs demand[i] deliveries. A hub costs the sum, over all nodes, of demand[i] times the total link length on the unique path from the hub to i. Return [hubIndex, minimumCost]. If several nodes have the same minimum cost, choose the smallest index. A delivery to the hub itself has distance zero. The tree has nodes numbered 0 through n - 1. parent[0] is -1; every other parent[i] is the parent of node i. The tree is connected and has no cycles. Node numbers do not imply traversal order: a parent may have a larger number than its child.

Keep in mind

• 1 <= n = parent.length <= 20,000
• parent[0] = -1; all other parent entries are valid node indices describing one rooted tree.
• lengths.length = demand.length = n; lengths[0] = 0.
• Each non-root link length is an integer from 1 to 1,000.
• Each demand is an integer from 0 to 1,000.
• All costs fit exactly in a JavaScript Number; no modulo is required.