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 p_1, p_2, ..., p_{n} (1 ≤ p_{i} ≤ n), DZY defines f(p) as $\operatorname{min}_{i = 1}^{n} g(i, p_{i})$. 

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 x_{j} 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 a_{i}, b_{i}, c_{i} (1 ≤ a_{i}, b_{i} ≤ n; 1 ≤ c_{i} ≤ 10000), denoting an edge between a_{i} and b_{i} with length c_{i}. 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 x_{j} (1 ≤ x_{j} ≤ 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].

Source: codeforces | Difficulty: VERY_HARD
Tags: Tree algorithms

Sorting

Spanning trees


Solutions:
n = int(input())
edges = [[int(x) for x in input().split()] for i in range(n - 1)]
edges = sorted(edges)
use_count = [0] + [int(input()) for i in range(n)]
(lo, hi) = (0, 10000)

def getpar(par, u):
	if par[par[u]] == par[u]:
		return par[u]
	par[u] = getpar(par, par[u])
	return par[u]

def unite(par, sz, use, u, v):
	u = getpar(par, u)
	v = getpar(par, v)
	par[u] = v
	sz[v] += sz[u]
	use[v] += use[u]

def solve(fp):
	par = [i for i in range(n + 1)]
	sz = [1 for i in range(n + 1)]
	use = [use_count[i] for i in range(n + 1)]
	for edge in edges:
		if edge[2] < fp:
			unite(par, sz, use, edge[0], edge[1])
	total_use = sum(use_count)
	for i in range(n + 1):
		p = getpar(par, i)
		if p == i:
			if total_use - use[p] < sz[p]:
				return False
	return True
while lo < hi:
	mid = (lo + hi + 1) // 2
	if solve(mid):
		lo = mid
	else:
		hi = mid - 1
print(lo)