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 edge {
  int fr, to, val;
  bool operator<(const edge &o) const { return val < o.val; }
} e[2000100];
int n, m, x, y, z, fa[2000100], cnt[2000100], sum, siz[2000100], ans, flag = 1;
int gf(int u) { return u == fa[u] ? u : fa[u] = gf(fa[u]); }
int main() {
  scanf("%d", &n);
  for (int i = 1; i < n; i++) scanf("%d %d %d", &e[i].fr, &e[i].to, &e[i].val);
  for (int i = 1; i <= n; i++)
    scanf("%d", &cnt[i]), sum += cnt[i], fa[i] = i, siz[i] = 1;
  sort(e + 1, e + n);
  for (int i = 1; i < n; i++) {
    if (flag) ans = e[i].val;
    int f1 = gf(e[i].fr), f2 = gf(e[i].to);
    fa[f1] = f2, siz[f2] += siz[f1], cnt[f2] += cnt[f1];
    if (siz[f2] > sum - cnt[f2]) flag = 0;
  }
  printf("%d\n", ans);
  return 0;
}