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 N = 2 * 1e5 + 5;
int it_max[32][4 * N], it_min[32][4 * N], a[10], n, k, q;
void update(int st, int p, int l, int r, int id, int val) {
  if (l > id || r < id) return;
  if (l == r) {
    it_max[st][p] = it_min[st][p] = val;
    return;
  }
  int m = (l + r) / 2;
  update(st, p * 2, l, m, id, val);
  update(st, p * 2 + 1, m + 1, r, id, val);
  it_max[st][p] = max(it_max[st][p * 2], it_max[st][p * 2 + 1]);
  it_min[st][p] = min(it_min[st][p * 2], it_min[st][p * 2 + 1]);
}
pair<int, int> get(int st, int p, int l, int r, int ql, int qr) {
  if (ql > r || l > qr) return make_pair(-1e9, 1e9);
  if (ql <= l && r <= qr) return make_pair(it_max[st][p], it_min[st][p]);
  int m = (l + r) / 2;
  auto tmp1 = get(st, p * 2, l, m, ql, qr);
  auto tmp2 = get(st, p * 2 + 1, m + 1, r, ql, qr);
  return make_pair(max(tmp1.first, tmp2.first), min(tmp1.second, tmp2.second));
}
void add(int id) {
  for (int i = 0; i < k; i++) cin >> a[i];
  for (int st = 0; st < (1 << k); st++) {
    int val = 0;
    for (int i = 0; i < k; i++)
      if ((st >> i) & 1)
        val += a[i];
      else
        val -= a[i];
    update(st, 1, 1, n, id, val);
  }
}
int main() {
  ios_base ::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  for (int i = 1; i <= n; i++) add(i);
  cin >> q;
  for (int i = 1; i <= q; i++) {
    int type, id, l, r;
    cin >> type;
    if (type == 1) {
      cin >> id;
      add(id);
    } else {
      cin >> l >> r;
      int res = 0;
      for (int st = 0; st < (1 << k); st++) {
        auto tmp = get(st, 1, 1, n, l, r);
        res = max(res, tmp.first - tmp.second);
      }
      cout << res << '\n';
    }
  }
}
