Problem: 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 <image>. 

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].

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n;
const int N = 5000;
struct edge {
  int a, b, c;
} E[N];
int xi[N], yi[N], fa[N], sum, ans;
int comp(edge u, edge v) { return u.c < v.c; }
int get_f(int a) { return fa[a] == a ? a : fa[a] = get_f(fa[a]); }
int main() {
  scanf("%d", &n);
  for (int i = 1; i < n; ++i) scanf("%d%d%d", &E[i].a, &E[i].b, &E[i].c);
  sort(E + 1, E + n, comp);
  for (int i = 1; i <= n; ++i)
    scanf("%d", &xi[i]), yi[i] = 1, fa[i] = i, sum += xi[i];
  for (int i = 1; i < n; ++i) {
    ans = E[i].c;
    xi[get_f(E[i].a)] += xi[get_f(E[i].b)];
    yi[get_f(E[i].a)] += yi[get_f(E[i].b)];
    fa[get_f(E[i].b)] = get_f(E[i].a);
    if (yi[get_f(E[i].a)] > sum - xi[get_f(E[i].a)]) break;
  }
  printf("%d\n", ans);
}