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;
struct node {
  int x, y, z;
} ob[100010];
bool cmp(node a, node b) { return a.z < b.z; }
int n, f[100010], size[100010], sum, x[100010];
int find(int x) {
  if (f[x] == x) return x;
  return f[x] = find(f[x]);
}
void ini() {
  scanf("%d", &n);
  for (int i = 1; i < n; i++) scanf("%d%d%d", &ob[i].x, &ob[i].y, &ob[i].z);
  for (int i = 1; i <= n; i++) scanf("%d", &x[i]);
  sort(ob + 1, ob + n, cmp);
  for (int i = 1; i <= n; i++) f[i] = i, sum += x[i], size[i] = 1;
}
int main() {
  ini();
  for (int i = 1; i < n; i++) {
    int tx = find(ob[i].x);
    int ty = find(ob[i].y);
    x[ty] += x[tx];
    size[ty] += size[tx];
    f[tx] = ty;
    if (sum - x[ty] < size[ty]) {
      printf("%d", ob[i].z);
      return 0;
    }
  }
  printf("0");
  return 0;
}