A12348 | Multidimensional Queries

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 $l \le i, j \le r$ .

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.

Print the answer for each query of the second type.