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>
const int MAXN = 3000 + 1000;
int n, sum;
int in[MAXN], out[MAXN];
struct Union_Find_Set {
  int f[MAXN];
  void Init(int N) {
    for (int i = 1, _ = N; i <= _; i++) f[i] = i;
  }
  int Find(int x) { return x == f[x] ? x : f[x] = Find(f[x]); }
  bool Union(int x, int y) {
    x = Find(x);
    y = Find(y);
    if (x == y) return 0;
    in[x] += in[y];
    out[x] += out[y];
    f[y] = x;
    if (in[x] + out[x] > sum) return 1;
    return 0;
  }
} t;
struct Edge {
  int u, v, w;
  Edge() {}
  Edge(int u, int v, int w) : u(u), v(v), w(w) {}
  bool operator<(const Edge &a) const { return w < a.w; }
} G[MAXN];
void Init() {
  int u, v, w;
  scanf("%d", &n);
  t.Init(n);
  for (int i = 1, _ = n - 1; i <= _; i++) {
    scanf("%d%d%d", &u, &v, &w);
    G[i] = Edge(u, v, w);
  }
  for (int i = 1, _ = n; i <= _; i++) {
    scanf("%d", &out[i]);
    sum += out[i];
    in[i] = 1;
  }
}
void Solve() {
  if (n == 1) {
    puts("0");
    return;
  }
  int u, v;
  std::sort(G + 1, G + n);
  for (int i = 1, _ = n - 1; i <= _; i++) {
    if (t.Union(G[i].u, G[i].v)) {
      printf("%d\n", G[i].w);
      return;
    }
  }
}
int main() {
  Init();
  Solve();
}