There are N cities in a country, and there is one and only one simple path between each pair of cities. A merchant has chosen some paths and wants to earn as much money as possible in each path. When he move along a path, he can choose one city to buy some goods and sell them in a city after it. The goods in all cities are the same but the prices are different. Now your task is to calculate the maximum possible profit on each path.
Input
The first line contains N, the number of cities.
Each of the next N lines contains wi the goods’ price in each city.
Each of the next N-1 lines contains labels of two cities, describing a road between the two cities.
The next line contains Q, the number of paths.
Each of the next Q lines contains labels of two cities, describing a path. The cities are numbered from 1 to N.
1 ≤ N, wi, Q ≤ 50000
Output
The output contains Q lines, each contains the maximum profit of the corresponding path. If no positive profit can be earned, output 0 instead.
Sample Input
4
1
5
3
2
1 3
3 2
3 4
9
1 2
1 3
1 4
2 3
2 1
2 4
3 1
3 2
3 4
Sample Output
4
2
2
0
0
0
0
2
0
这个题做了一个上午加一个下午，自己边玩边学，以后还是不要这样了，主要就是这个题需要维护起点u到lca，和lca到终点v之间的信息，有Max区间最大值，Min区间最小值，Up上升区间内最优解，Down下降区间最优解。想清楚了还是很容易的，竟然耗费了一整天。加油吧，下次周赛不能再垫底了
vj突然登不上了