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 ∑ _{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, ..., b_k);
  * 2 l r — find the maximum distance between two points a_i and a_j, where l ≤ i, j ≤ r.

Input

The first line contains two numbers n and k (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ k ≤ 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 ≤ a_{i, j} ≤ 10^6) — the coordinates of i-th point.

The next line contains one integer q (1 ≤ q ≤ 2 ⋅ 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 ≤ i ≤ n, -10^6 ≤ b_j ≤ 10^6) — set i-th element of a to the point (b_1, b_2, ..., b_k);
  * 2 l r (1 ≤ l ≤ r ≤ n) — find the maximum distance between two points a_i and a_j, where l ≤ i, j ≤ 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
#include <bits/stdc++.h>
using namespace std;
void buildSegTre(vector<int>& x) {
  for (int i = x.size() >> 1; i--;) x[i] = max(x[i << 1], x[i << 1 | 1]);
}
void updateSegTre(vector<int>& x, int a) {
  for (a += x.size() >> 1; a; a >>= 1) x[a >> 1] = max(x[a], x[a ^ 1]);
}
int querySegTre(const vector<int>& x, int a, int b) {
  int ret = -5000000;
  for (a += x.size() >> 1, b += x.size() >> 1; a < b; a >>= 1, b >>= 1) {
    if (a & 1) ret = max(ret, x[a++]);
    if (b & 1) ret = max(ret, x[--b]);
  }
  return ret;
}
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  vector<vector<int> > a(n, vector<int>(k));
  for (auto& i : a)
    for (int& j : i) scanf("%d", &j);
  vector<vector<int> > trees(1 << k, vector<int>(n * 2));
  for (int j = 0; j < 1 << k; j++) {
    for (int i = 0; i < n; i++) {
      trees[j][i + n] = 0;
      for (int I = 0; I < k; I++)
        trees[j][i + n] += (j >> I & 1 ? a[i][I] : -a[i][I]);
    }
    buildSegTre(trees[j]);
  }
  int q;
  scanf("%d", &q);
  while (q--) {
    int t;
    scanf("%d", &t);
    if (t == 1) {
      int i;
      scanf("%d", &i);
      i--;
      for (int& j : a[i]) scanf("%d", &j);
      for (int j = 0; j < 1 << k; j++) {
        trees[j][i + n] = 0;
        for (int I = 0; I < k; I++)
          trees[j][i + n] += (j >> I & 1 ? a[i][I] : -a[i][I]);
        updateSegTre(trees[j], i);
      }
    } else if (t == 2) {
      int l, r;
      scanf("%d%d", &l, &r);
      l--;
      int ans = 0;
      for (int i = 0; i < 1 << k >> 1; i++) {
        ans = max(ans, querySegTre(trees[i], l, r) +
                           querySegTre(trees[(1 << k) - 1 - i], l, r));
      }
      printf("%d\n", ans);
    }
  }
}
