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>
struct nod {
  int v, k;
} d[1111111];
struct edg {
  int x, y, l;
} e[1111111];
bool operator<(const edg x, const edg y) { return x.l < y.l; }
nod operator+(nod x, nod y) {
  x.v += y.v, x.k += y.k;
  return x;
}
int n, fa[1111111];
int rt(int x) { return fa[x] ? fa[x] = rt(fa[x]) : x; }
int main() {
  scanf("%d", &n);
  if (n == 1) return puts("0"), 0;
  register int i;
  for (i = 1; i < n; i++) scanf("%d%d%d", &e[i].x, &e[i].y, &e[i].l);
  std::sort(e + 1, e + n);
  int S = 0;
  for (i = 1; i <= n; i++) scanf("%d", &d[i].v), d[i].k = 1, S += d[i].v;
  for (i = 1; i < n; i++) {
    int a = rt(e[i].x), b = rt(e[i].y);
    fa[a] = b, d[b] = d[a] + d[b];
    if (d[b].k + d[b].v > S) return printf("%d\n", e[i].l), 0;
  }
}