Description:

Bobo has a tree,whose vertices are conveniently labeled by 1,2,...,n.Each node has a weight wi. All the weights are distrinct.

A set with m nodes v1,v2,...,vm is a Bobo Set if:

- The subgraph of his tree induced by this set is connected.

- After we sort these nodes in set by their weights in ascending order,we get u1,u2,...,um,(that is,wui<wui+1 for i from 1 to m-1).For any node x in the path from ui to ui+1(excluding ui and ui+1),should satisfy wx<wui.

Your task is to find the maximum size of Bobo Set in a given tree.

Input:

The input consists of several tests. For each tests:

The first line contains a integer n (1≤n≤500000). Then following a line contains n integers w1,w2,...,wn (1≤wi≤109,all the wi is distrinct).Each of the following n-1 lines contain 2 integers ai and bi,denoting an edge between vertices ai and bi (1≤ai,bi≤n).

The sum of n is not bigger than 800000.

Output:

For each test output one line contains a integer,denoting the maximum size of Bobo Set.

Sample Input:

7 3 30 350 100 200 300 400 1 2 2 3 3 4 4 5 5 6 6 7

Sample Output:

5

Source:

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