#include <bits/stdc++.h>
using namespace std;
void testcase() {
  int n;
  cin >> n;
  long long int a[n][n];
  map<int, long long int> mp1;
  map<int, long long int> mp2;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> a[i][j];
      mp1[i - j] += a[i][j];
      mp2[i + j] += a[i][j];
    }
  }
  long long int me = 0, mo = 0;
  int x1 = 1, y1 = 1, x2 = 1, y2 = 2;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      long long int val = mp1[i - j] + mp2[i + j] - a[i][j];
      if ((i + j) % 2) {
        if (mo < val) {
          x1 = i + 1;
          y1 = j + 1;
          mo = val;
        }
      } else {
        if (me < val) {
          x2 = i + 1;
          y2 = j + 1;
          me = val;
        }
      }
    }
  }
  cout << me + mo << "\n";
  cout << x1 << " " << y1 << " " << x2 << " " << y2 << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t = 1;
  while (t--) {
    testcase();
  }
  return 0;
}

### Prompt

Construct a CPP code solution to the problem outlined:

Gargari is jealous that his friend Caisa won the game from the previous problem. He wants to prove that he is a genius.

He has a n × n chessboard. Each cell of the chessboard has a number written on it. Gargari wants to place two bishops on the chessboard in such a way that there is no cell that is attacked by both of them. Consider a cell with number x written on it, if this cell is attacked by one of the bishops Gargari will get x dollars for it. Tell Gargari, how to place bishops on the chessboard to get maximum amount of money.

We assume a cell is attacked by a bishop, if the cell is located on the same diagonal with the bishop (the cell, where the bishop is, also considered attacked by it).

Input

The first line contains a single integer n (2 ≤ n ≤ 2000). Each of the next n lines contains n integers aij (0 ≤ aij ≤ 109) — description of the chessboard.

Output

On the first line print the maximal number of dollars Gargari will get. On the next line print four integers: x1, y1, x2, y2 (1 ≤ x1, y1, x2, y2 ≤ n), where xi is the number of the row where the i-th bishop should be placed, yi is the number of the column where the i-th bishop should be placed. Consider rows are numbered from 1 to n from top to bottom, and columns are numbered from 1 to n from left to right.

If there are several optimal solutions, you can print any of them.

Examples

Input

4
1 1 1 1
2 1 1 0
1 1 1 0
1 0 0 1


Output

12
2 2 3 2

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void testcase() {
  int n;
  cin >> n;
  long long int a[n][n];
  map<int, long long int> mp1;
  map<int, long long int> mp2;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      cin >> a[i][j];
      mp1[i - j] += a[i][j];
      mp2[i + j] += a[i][j];
    }
  }
  long long int me = 0, mo = 0;
  int x1 = 1, y1 = 1, x2 = 1, y2 = 2;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      long long int val = mp1[i - j] + mp2[i + j] - a[i][j];
      if ((i + j) % 2) {
        if (mo < val) {
          x1 = i + 1;
          y1 = j + 1;
          mo = val;
        }
      } else {
        if (me < val) {
          x2 = i + 1;
          y2 = j + 1;
          me = val;
        }
      }
    }
  }
  cout << me + mo << "\n";
  cout << x1 << " " << y1 << " " << x2 << " " << y2 << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t = 1;
  while (t--) {
    testcase();
  }
  return 0;
}

```