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;
const int MAXN = 8e5 + 10, M = 35;
int n, k, q, seg[M][MAXN], a[MAXN];
void add(int ind, int val, int t, int b = 0, int e = n, int id = 1) {
  if (b + 1 == e) {
    seg[t][id] = val;
    return;
  }
  int mid = (b + e) / 2;
  if (ind < mid)
    add(ind, val, t, b, mid, id * 2);
  else
    add(ind, val, t, mid, e, id * 2 + 1);
  seg[t][id] = max(seg[t][id * 2], seg[t][id * 2 + 1]);
  return;
}
int get(int l, int r, int t, int b = 0, int e = n, int id = 1) {
  if (r <= b || e <= l) return -INT_MAX / 2;
  if (l <= b && e <= r) return seg[t][id];
  int mid = (b + e) / 2;
  return max(get(l, r, t, b, mid, id * 2), get(l, r, t, mid, e, id * 2 + 1));
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  for (int i = 0; i < (1 << k); i++)
    for (int j = 0; j < MAXN; j++) seg[i][j] = -INT_MAX / 2;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < k; j++) cin >> a[j];
    for (int m = 0; m < (1 << k); m++) {
      int x = 0;
      for (int j = 0; j < k; j++) {
        if ((m >> j) & 1)
          x += a[j];
        else
          x -= a[j];
      }
      add(i, x, m);
    }
  }
  cin >> q;
  while (q) {
    q--;
    int ty;
    cin >> ty;
    if (ty == 1) {
      int ind;
      cin >> ind, ind--;
      for (int i = 0; i < k; i++) cin >> a[i];
      for (int i = 0; i < (1 << k); i++) {
        int x = 0;
        for (int j = 0; j < k; j++) {
          if ((i >> j) & 1)
            x += a[j];
          else
            x -= a[j];
        }
        add(ind, x, i);
      }
    } else {
      int l, r, ans = -INT_MAX / 2;
      cin >> l >> r, l--;
      for (int mask = 0; mask <= (1 << k) / 2; mask++) {
        ans = max(ans, get(l, r, mask) + get(l, r, (1 << k) - 1 - mask));
      }
      cout << ans << endl;
    }
  }
  return 0;
}
