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 p 1, p 2, ..., p n (1 ≤ p i ≤ 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 x j times. Please, find the maximum possible f(p) under the described restrictions.

输入描述:

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).

输出描述:

Print a single integer representing the answer.

备注:

In the first sample, one of the optimal p is [4, 3, 2, 1].