CodeForces - 274B Zero Tree — 树形DP

A tree is a graph with n vertices and exactly n - 1 edges; this graph should meet the following condition: there exists exactly one shortest (by number of edges) path between any pair of its vertices.

A subtree of a tree T is a tree with both vertices and edges as subsets of vertices and edges of T.

You're given a tree with n vertices. Consider its vertices numbered with integers from 1 to n. Additionally an integer is written on every vertex of this tree. Initially the integer written on the i-th vertex is equal to v_i. In one move you can apply the following operation:

1. Select the subtree of the given tree that includes the vertex with number 1.
2. Increase (or decrease) by one all the integers which are written on the vertices of that subtree.

Calculate the minimum number of moves that is required to make all the integers written on the vertices of the given tree equal to zero.

Input

The first line of the input contains n (1 ≤ n ≤ 10⁵). Each of the next n - 1 lines contains two integers a_i and b_i (1 ≤ a_i, b_i ≤ n; a_i ≠ b_i) indicating there's an edge between vertices a_i and b_i. It's guaranteed that the input graph is a tree.

The last line of the input contains a list of n space-separated integersv₁, v₂, ..., v_n (|v_i| ≤ 10⁹).

Output

Print the minimum number of operations needed to solve the task.

Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Example

Input

3
1 2
1 3
1 -1 1

Output

3

题目大意：给你一个n。给你n-1条边使得这1-n这n个点连成一个树形的结构。

再给你n个数，是这n个点分别代表的权值。。

每次的操作是在整棵树中挑出一棵以1为根结点的子树。然后将所有在这棵子树中的点的权值 + 1  or - 1；

问最少需要几步可以将所有点的权值都变为0。

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