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G. Multidimensional Queries
time limit per test
6 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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

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.

Example
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

Output
8
4
4
12
10