Problem Statement

You are given a tree T with N vertices.
Edge $i (1\leq i\leq N-1) connects vertices u _ i$ and v _ i, and has a weight of w _ i.
Process Q queries in order. There are two kinds of queries as follows.

• 1 i w : Change the weight of edge i to w.
• 2 u v：Print the distance between vertex u and vertex v.

Here, the distance between two vertices u and v of a tree is the smallest total weight of edges in a path whose endpoints are u and v.

Input

The input is given from Standard Input in the following format:
N
u _ 1 v _ 1 w _ 1
u _ 2 v _ 2 w _ 2
$\vdots$
u _ {N-1} v _ {N-1} w _ {N-1}
Q
$\operatorname{query} _ 1$
$\operatorname{query} _ 2$
$\vdots$
$\operatorname{query} _ Q$

Here, $\operatorname{query} _ i$ denotes the i-th query and is in one of the following format:
1 i w

2 u v

Output

Print q lines, where q is the number of queries of the second kind.
The $j-th line (1\leq j\leq q)$ should contain the answer to the j-th query of the second kind.

Constraints

• $1\leq N\leq 2\times10^5$
• $1\leq u _ i,v _ i\leq N$\ $(1\leq i\leq N-1)$
• $1\leq w _ i\leq 10^9$\ $(1\leq i\leq N-1)$
• The given graph is a tree.
• $1\leq Q\leq 2\times10^5$
• For each query of the first kind,
• $1\leq i\leq N-1$, and

• $1\leq w\leq 10^9$.

• For each query of the second kind,

• $1\leq u,v\leq N$.

• There is at least one query of the second kind.

• All values in the input are integers.

Sample Input 1

5
1 2 3
1 3 6
1 4 9
4 5 10
4
2 2 3
2 1 5
1 3 1
2 1 5

Sample Output 1

9
19
11

The initial tree is shown in the figure below.

Each query should be processed as follows.

• The first query asks you to print the distance between vertex 2 and vertex 3. Edge 1 and edge 2, in this order, form a path between them with a total weight of 9, which is the minimum, so you should print 9.
• The second query asks you to print the distance between vertex 1 and vertex 5. Edge 3 and edge 4, in this order, form a path between them with a total weight of 19, which is the minimum, so you should print 19.
• The third query changes the weight of edge 3 to 1.
• The fourth query asks you to print the distance between vertex 1 and vertex 5. Edge 3 and edge 4, in this order, form a path between them with a total weight of 11, which is the minimum, so you should print 11.

Sample Input 2

7
1 2 1000000000
2 3 1000000000
3 4 1000000000
4 5 1000000000
5 6 1000000000
6 7 1000000000
3
2 1 6
1 1 294967296
2 1 6

Sample Output 2

5000000000
4294967296

Note that the answers may not fit into 32-bit integers.

Sample Input 3

1
1
2 1 1

Sample Output 3

0

Sample Input 4

8
1 2 105
1 3 103
2 4 105
2 5 100
5 6 101
3 7 106
3 8 100
18
2 2 8
2 3 6
1 4 108
2 3 4
2 3 5
2 5 5
2 3 1
2 4 3
1 1 107
2 3 1
2 7 6
2 3 8
2 1 5
2 7 6
2 4 7
2 1 7
2 5 3
2 8 6

Sample Output 4

308
409
313
316
0
103
313
103
525
100
215
525
421
209
318
519

见题面 Input 部分

见题面 Output 部分