Competitions

Maximum sum on a tree

Given a tree of n nodes, where each node i (1in) has ci coins attached with it. You have to choose a subset of nodes such that no two adjacent nodes (i.e. nodes connected directly by an edge) are chosen and sum of coins attached with nodes in chosen subset is maximum.

Input

The first line contains the number of vertices n (1n105) in a tree. Each of the next n - 1 lines gives two integers u and v (1u, vn) and describes an edge in a tree. The last line contains n positive integers c1, ... cn - the number of coins in tree nodes.

Output

Print the maximum sum of coins in a chosen subset of tree nodes.

Time limit 1 second
Memory limit 128 MiB
Input example #1
5
1 2
1 3
2 4
2 5
1 5 7 1 2

Output example #1
12

Input example #2
5
1 2
1 3
2 4
2 5
3 7 5 10 1

Output example #2
16