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[编程题]travel
White Cloud has a tree with n nodes.The root is a node with number 1. Each node has a value.
White Rabbit wants to travel in the tree 3 times. In Each travel it will go through a path in the tree.
White Rabbit can't pass a node more than one time during the 3 travels. It wants to know the maximum sum value of all nodes it passes through.



输入描述:
The first line of input contains an integer n(3 <= n <= 400001)
In the next line there are n integers in range [0,1000000] denoting the value of each node.
For the next n-1 lines, each line contains two integers denoting the edge of this tree.


输出描述:
Print one integer denoting the answer.
示例1

输入

13
10 10 10 10 10 1 10 10 10 1 10 10 10
1 2
2 3
3 4
4 5
2 6
6 7
7 8
7 9
6 10
10 11
11 12
11 13

输出

110

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