2759: DZY Loves Planting
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
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Description
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.
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).
Print a single integer representing the answer.
4
1 2 1
2 3 2
3 4 3
1
1
1
1
2
4
1 2 1
2 3 2
3 4 3
4
4
4
4
3
In the first sample, one of the optimal p is [4,3,2,1].