5590: DZY Loves Planting
内存限制：256 MB
时间限制：2 S
题面：传统
评测方式：文本比较
上传者：
提交：1
通过：1
题目描述
E. DZY Loves Planting
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
DZY loves planting, and he enjoys solving tree problems.
DZY has a weighted tree (connected undirected graph without cycles) containing n nodes (they are numbered from 1 to n). He defines the function g(x,y) (1≤x,y≤n) as the longest edge in the shortest path between nodes x and y. Specially g(z,z)=0 for every z.
For every integer sequence p1,p2,...,pn (1≤pi≤n), DZY defines f(p) as
.
DZY wants to find such a sequence p that f(p) has maximum possible value. But there is one more restriction: the element j can appear in p at most xj times.
Please, find the maximum possible f(p) under the described restrictions.
DZY has a weighted tree (connected undirected graph without cycles) containing n nodes (they are numbered from 1 to n). He defines the function g(x,y) (1≤x,y≤n) as the longest edge in the shortest path between nodes x and y. Specially g(z,z)=0 for every z.
For every integer sequence p1,p2,...,pn (1≤pi≤n), DZY defines f(p) as
. DZY wants to find such a sequence p that f(p) has maximum possible value. But there is one more restriction: the element j can appear in p at most xj times.
Please, find the maximum possible f(p) under the described restrictions.
Input
The first line contains an integer n(1≤n≤3000). Each of the next n-1 lines contains three integers ai,bi,ci(1≤ai,bi≤n;1≤ci≤10000), denoting an edge between ai and bi with length ci. It is guaranteed that these edges form a tree.
Each of the next n lines describes an element of sequence x. The j-th line contains an integer xj(1≤xj≤n).
Output
Print a single integer representing the answer.
Examples
Input
4 1 2 1 2 3 2 3 4 3 1 1 1 1
Output
2
Input
4 1 2 1 2 3 2 3 4 3 4 4 4 4
Output
3
Note
In the first sample, one of the optimal p is [4,3,2,1]. 输入样例 复制
输出样例 复制