transaction transaction transaction

Kelukin is a businessman. Every day, he travels around cities to do some business. On August 17th, in memory of a great man, citizens will read a book named "the Man Who Changed China". Of course, Kelukin wouldn't miss this chance to make money, but he doesn't have this book. So he has to choose two city to buy and sell.
As we know, the price of this book was different in each city. It is $a_i$ $yuan$ in $i$$t$ city. Kelukin will take taxi, whose price is $1$$yuan$ per km and this fare cannot be ignored.
There are $n-1$ roads connecting $n$ cities. Kelukin can choose any city to start his travel. He want to know the maximum money he can get.

The first line contains an integer $T$ ($1\leq T \leq 10$) , the number of test cases.
For each test case:
first line contains an integer $n$ ($2\leq n\leq 100000$) means the number of cities;
second line contains $n$ numbers, the $i$$th$ number means the prices in $i$$th$ city; $(1 \leq Price \leq 10000)$
then follows $n-1$ lines, each contains three numbers $x$, $y$ and $z$ which means there exists a road between $x$ and $y$, the distance is $z$$km$ $(1\leq z\leq 1000)$.

For each test case, output a single number in a line: the maximum money he can get.

1  
4  
10 40 15 30  
1 2 30
1 3 2
3 4 10

8

2017 ACM/ICPC Asia Regional Shenyang Online