Description:
You are given an array $$$a$$$ of $$$n$$$ points in $$$k$$$-dimensional space. Let the distance between two points $$$a_x$$$ and $$$a_y$$$ be $$$\sum \limits_{i = 1}^{k} |a_{x, i} - a_{y, i}|$$$ (it is also known as Manhattan distance).
You have to process $$$q$$$ queries of the following two types:
- $$$1$$$ $$$i$$$ $$$b_1$$$ $$$b_2$$$ ... $$$b_k$$$ — set $$$i$$$-th element of $$$a$$$ to the point $$$(b_1, b_2, \dots, b_k)$$$;
- $$$2$$$ $$$l$$$ $$$r$$$ — find the maximum distance between two points $$$a_i$$$ and $$$a_j$$$, where $$$l \le i, j \le r$$$.
Input Format:
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 Format:
Print the answer for each query of the second type.
Note:
None