Given a tree with N (N <= 100000) nodes. Each node has a interger value x_i (|x_i| <= 10000).

You have to apply Q (Q <= 100000) operations:

1. 1 a b : answer the maximum contiguous sum (maybe empty,will always larger than or equal to 0 ) from the path a->b ( inclusive ).

2. 2 a b c : change all value in the path a->b ( inclusive ) to c. (|c| <= 10000)

Input

first line consists one interger N.

next line consists N interger x_i.

next N-1 line , each consists two interger u,v , means that node u and node v are connected

next line consists 1 interger Q.

next Q line : 1 a b or 2 a b c .

Output

For each query, output one line the maximum contiguous sum.

Example

Input:
5
-3 -2 1 2 3
1 2
2 3
1 4
4 5
3
1 2 5
2 3 4 2
1 2 5
Output:
5
9