Crazy Bobo

Time Limit: 6000/3000 MS (Java/Others) Memory Limit: 131072/65536 K (Java/Others)
Total Submission(s): 612 Accepted Submission(s): 189

Problem 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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