G. Multidimensional Queriestime limit per test6 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputPrint the answer for each query of the second type.ExampleInput
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

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

8 4 4 12 10 
['bitmasks', 'data structures', '*2300']