Problem Statement

You are given a tree with N vertices. The vertices are numbered 1 to N, and the i-th edge connects vertices A_i and B_i.
You are also given a sequence of positive integers $C = (C_1, C_2, \ldots ,C_N)$ of length N. Let d(a, b) be the number of edges between vertices a and b, and for $x = 1, 2, \ldots, N$, let $\displaystyle f(x) = \sum_{i=1}^{N} (C_i \times d(x, i)). Find \displaystyle \min_{1 \leq v \leq N} f(v)$.

Input

The input is given from Standard Input in the following format:
N
A_1 B_1
A_2 B_2
$\vdots$
A_{N - 1} B_{N - 1}
$C_1 C_2 \cdots C_N$

Output

Print the answer in one line.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq A_i, B_i \leq N$
• The given graph is a tree.
• $1 \leq C_i \leq 10^9$

Sample Input 1

4
1 2
1 3
2 4
1 1 1 2

Sample Output 1

5

For example, consider calculating f(1). We have d(1, 1) = 0, d(1, 2) = 1, d(1, 3) = 1, d(1, 4) = 2.
Thus, $f(1) = 0 \times 1 + 1 \times 1 + 1 \times 1 + 2 \times 2 = 6$.
Similarly, f(2) = 5, f(3) = 9, f(4) = 6. Since f(2) is the minimum, print 5.

Sample Input 2

2
2 1
1 1000000000

Sample Output 2

1

f(2) = 1, which is the minimum.

Sample Input 3

7
7 3
2 5
2 4
3 1
3 6
2 1
2 7 6 9 3 4 6

Sample Output 3

56

见题面 Input 部分

见题面 Output 部分