Warehouse Tree Compatible Pairs

A network of warehouses is an undirected rooted weighted tree with warehouse_nodes nodes rooted at warehouse 1. Each node has a value val[v]. A pair (u, v) is compatible iff:

• u is an ancestor of v in the tree.
• distance(u, v) ≤ val[v].

Count compatible pairs.

Example: with the input from the OA, the answer is 5.

Constraints

• 1 ≤ warehouse_nodes ≤ 1.5·10⁵
• 1 ≤ warehouse_weight[i] ≤ 10⁴
• 1 ≤ val[i] ≤ 10⁹