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;
const int N = 3050;
struct node {
  int x, y, c;
} E[N];
bool cmp(node x, node y) { return x.c < y.c; }
int fa[N], s[N], x[N];
int getf(int v) {
  if (v == fa[v]) return v;
  return fa[v] = getf(fa[v]);
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i < n; i++) scanf("%d%d%d", &E[i].x, &E[i].y, &E[i].c);
  sort(E + 1, E + n, cmp);
  int sum = 0;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &x[i]);
    sum += x[i];
    fa[i] = i;
    s[i] = 1;
  }
  for (int i = 1; i < n; i++) {
    int u = getf(E[i].x), v = getf(E[i].y);
    fa[u] = v;
    s[v] += s[u];
    x[v] += x[u];
    if (s[v] > sum - x[v]) {
      printf("%d\n", E[i].c);
      return 0;
    }
  }
  printf("0");
}