Multidimensional Queries

Description:

Input:

The first line contains two numbers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 2 \cdot 10^5$$$, $$$1 \le k \le 5$$$) — the number of elements in $$$a$$$ and the number of dimensions of the space, respectively.

Then $$$n$$$ lines follow, each containing $$$k$$$ integers $$$a_{i, 1}$$$, $$$a_{i, 2}$$$, ..., $$$a_{i, k}$$$ ($$$-10^6 \le a_{i, j} \le 10^6$$$) — the coordinates of $$$i$$$-th point.

The next line contains one integer $$$q$$$ ($$$1 \le q \le 2 \cdot 10^5$$$) — the number of queries.

Then $$$q$$$ lines follow, each denoting a query. There are two types of queries:

• $$$1$$$ $$$i$$$ $$$b_1$$$ $$$b_2$$$ ... $$$b_k$$$ ($$$1 \le i \le n$$$, $$$-10^6 \le b_j \le 10^6$$$) — set $$$i$$$-th element of $$$a$$$ to the point $$$(b_1, b_2, \dots, b_k)$$$;
• $$$2$$$ $$$l$$$ $$$r$$$ ($$$1 \le l \le r \le n$$$) — find the maximum distance between two points $$$a_i$$$ and $$$a_j$$$, where $$$l \le i, j \le r$$$.

There is at least one query of the second type.

Output:

Print the answer for each query of the second type.

Sample Input:

5 2
1 2
2 3
3 4
4 5
5 6
7
2 1 5
2 1 3
2 3 5
1 5 -1 -2
2 1 5
1 4 -1 -2
2 1 5

Sample Output:

8
4
4
12
10