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 p1, p2, ..., pn (1 ≤ pi ≤ 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 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].

inputFormat

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).

outputFormat

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].

样例

4
1 2 1
2 3 2
3 4 3
1
1
1
1

2

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