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;
int n, k, q, i, a[15], j, p, s, tree[1000005][35], t, l, r;
void Push(int i, int l, int r, int x, int y, int p) {
  if (l == r) {
    tree[i][y] = p;
    return;
  }
  int mid = (l + r) / 2;
  if (mid >= x)
    Push(i * 2, l, mid, x, y, p);
  else
    Push(i * 2 + 1, mid + 1, r, x, y, p);
  tree[i][y] = max(tree[i * 2][y], tree[i * 2 + 1][y]);
}
int Query(int i, int l, int r, int ll, int rr, int y) {
  if (l >= ll && r <= rr) return tree[i][y];
  int mid = (l + r) / 2, s = -1000000000;
  if (mid >= ll) s = max(s, Query(i * 2, l, mid, ll, rr, y));
  if (mid < rr) s = max(s, Query(i * 2 + 1, mid + 1, r, ll, rr, y));
  return s;
}
int main() {
  scanf("%d %d", &n, &k);
  for (i = 1; i <= n; i++) {
    for (j = 0; j < k; j++) scanf("%d", &a[j]);
    for (j = 0; j < (1 << k); j++) {
      s = 0;
      for (p = 0; p < k; p++)
        if ((j >> p) & 1)
          s -= a[p];
        else
          s += a[p];
      Push(1, 1, n, i, j, s);
    }
  }
  scanf("%d", &q);
  while (q--) {
    scanf("%d", &t);
    if (t == 2) {
      scanf("%d %d", &l, &r);
      s = -1000000000;
      for (i = 0; i < (1 << (k - 1)); i++)
        s = max(s, Query(1, 1, n, l, r, i) +
                       Query(1, 1, n, l, r, (1 << k) - i - 1));
      printf("%d\n", s);
    } else {
      scanf("%d", &l);
      for (j = 0; j < k; j++) scanf("%d", &a[j]);
      for (j = 0; j < 1 << k; j++) {
        s = 0;
        for (p = 0; p < k; p++)
          if ((j >> p) & 1)
            s -= a[p];
          else
            s += a[p];
        Push(1, 1, n, l, j, s);
      }
    }
  }
}
