A9503. DZY Loves Planting

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 .

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.

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 $x_{j} (1<=x_{j}<=n)$ .

Print a single integer representing the answer.

In the first sample, one of the optimal $p$ is $[4,3,2,1]$ .