There is an undirected tree with n nodes labeled from 0 to n - 1, and rooted at node 0. You are given a 2D integer array edges of length n - 1, where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree.

You are also given a 0-indexed integer array values of length n, where values[i] is the value associated with the ith node.

You start with a score of 0. In one operation, you choose a node i, add values[i] to your score, and then set values[i] to 0. All three steps happen together as a single operation.

A tree is healthy if, for every leaf node, the sum of the current values on the path from the root to that leaf is not equal to 0.

Return the maximum score you can obtain by performing this operation on the tree any number of times, so that the tree remains healthy at the end.

 

Example 1:

Input: edges = [[0,1],[0,2],[0,3],[2,4],[4,5]], values = [5,2,5,2,1,1]
Output: 11
Explanation: We apply the operation to nodes 1, 2, 3, 4, and 5, so the values become [5,0,0,0,0,0]. The leaves are nodes 1, 3, and 5.
- The sum of values on the path from 0 to 1 is equal to 5.
- The sum of values on the path from 0 to 3 is equal to 5.
- The sum of values on the path from 0 to 5 is equal to 5.
Every leaf has a non-zero path sum, so the tree is healthy. The score is the sum of the original values of the chosen nodes: 2 + 5 + 2 + 1 + 1 = 11.
It can be shown that 11 is the maximum score obtainable by performing any number of operations on the tree.

Example 2:

Input: edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [20,10,9,7,4,3,5]
Output: 40
Explanation: We apply the operation to nodes 0, 2, 3, and 4, so the values become [0,10,0,0,0,3,5]. The leaves are nodes 3, 4, 5, and 6.
- The sum of values on the path from 0 to 3 is equal to 10.
- The sum of values on the path from 0 to 4 is equal to 10.
- The sum of values on the path from 0 to 5 is equal to 3.
- The sum of values on the path from 0 to 6 is equal to 5.
Every leaf has a non-zero path sum, so the tree is healthy. The score is the sum of the original values of the chosen nodes: 20 + 9 + 7 + 4 = 40.
It can be shown that 40 is the maximum score obtainable by performing any number of operations on the tree.

 

Constraints:

• 2 <= n <= 2 * 104
• edges.length == n - 1
• edges[i].length == 2
• 0 <= ai, bi < n
• values.length == n
• 1 <= values[i] <= 109
• The input is generated such that edges represents a valid tree.