#include <bits/stdc++.h>
using namespace std;
const int MAXN = 2000;
long long int board[MAXN + 10][MAXN + 10];
long long int n;
long long int NEXT_FREE, curr_x, curr_y, curr_sum;
long long int diagonal[10 * MAXN];
map<long long int, long long int> M1;
map<long long int, long long int> M2;
int main() {
  std::ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  for (long long int i = (1); i <= (n); i++) {
    for (long long int j = (1); j <= (n); j++) {
      cin >> board[i][j];
    }
  }
  for (long long int i = (n - 1); i >= (1); i--) {
    curr_x = n;
    curr_y = n - i;
    curr_sum = 0;
    while (curr_y > 0) {
      curr_sum += board[curr_x][curr_y];
      --curr_y;
      --curr_x;
    }
    diagonal[NEXT_FREE] = curr_sum;
    M1[i] = NEXT_FREE++;
  }
  curr_sum = 0;
  for (long long int i = (1); i <= (n); i++) {
    curr_sum += board[i][i];
  }
  diagonal[NEXT_FREE] = curr_sum;
  M1[0] = NEXT_FREE++;
  for (long long int i = (-1); i >= (1 - n); i--) {
    curr_x = 1;
    curr_y = 1 - i;
    curr_sum = 0;
    while (curr_y < n + 1) {
      curr_sum += board[curr_x][curr_y];
      ++curr_y;
      ++curr_x;
    }
    diagonal[NEXT_FREE] = curr_sum;
    M1[i] = NEXT_FREE++;
  }
  for (long long int i = (n + 2); i <= (2 * n); i++) {
    curr_x = i - n;
    curr_y = n;
    curr_sum = 0;
    while (curr_x <= n) {
      curr_sum += board[curr_x][curr_y];
      --curr_y;
      ++curr_x;
    }
    diagonal[NEXT_FREE] = curr_sum;
    M2[i] = NEXT_FREE++;
  }
  curr_sum = 0;
  curr_x = n;
  curr_y = 1;
  for (long long int i = (1); i <= (n); i++) {
    curr_sum += board[curr_x][curr_y];
    --curr_x;
    ++curr_y;
  }
  diagonal[NEXT_FREE] = curr_sum;
  M2[n + 1] = NEXT_FREE++;
  for (long long int i = (2); i <= (n); i++) {
    curr_x = 1;
    curr_y = i - 1;
    curr_sum = 0;
    while (curr_y >= 1) {
      curr_sum += board[curr_x][curr_y];
      --curr_y;
      ++curr_x;
    }
    diagonal[NEXT_FREE] = curr_sum;
    M2[i] = NEXT_FREE++;
  }
  long long int x1, y1, x2, y2;
  long long int max1 = 0, max2 = 0;
  for (long long int i = (1); i <= (n); i++) {
    for (long long int j = (1); j <= (n); j++) {
      if ((i + j) & 1) {
        long long int temp_l =
            diagonal[M1[i - j]] + diagonal[M2[i + j]] - board[i][j];
        if (max1 <= temp_l) {
          max1 = temp_l;
          x1 = i;
          y1 = j;
        }
      } else {
        long long int temp_l =
            diagonal[M1[i - j]] + diagonal[M2[i + j]] - board[i][j];
        if (max2 <= temp_l) {
          max2 = temp_l;
          x2 = i;
          y2 = j;
        }
      }
    }
  }
  cout << fixed;
  cout << max1 + max2 << endl;
  cout << x1 << " " << y1 << " " << x2 << " " << y2 << endl;
}

### Prompt

Generate a CPP solution to the following problem:

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;
const int MAXN = 2000;
long long int board[MAXN + 10][MAXN + 10];
long long int n;
long long int NEXT_FREE, curr_x, curr_y, curr_sum;
long long int diagonal[10 * MAXN];
map<long long int, long long int> M1;
map<long long int, long long int> M2;
int main() {
  std::ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  for (long long int i = (1); i <= (n); i++) {
    for (long long int j = (1); j <= (n); j++) {
      cin >> board[i][j];
    }
  }
  for (long long int i = (n - 1); i >= (1); i--) {
    curr_x = n;
    curr_y = n - i;
    curr_sum = 0;
    while (curr_y > 0) {
      curr_sum += board[curr_x][curr_y];
      --curr_y;
      --curr_x;
    }
    diagonal[NEXT_FREE] = curr_sum;
    M1[i] = NEXT_FREE++;
  }
  curr_sum = 0;
  for (long long int i = (1); i <= (n); i++) {
    curr_sum += board[i][i];
  }
  diagonal[NEXT_FREE] = curr_sum;
  M1[0] = NEXT_FREE++;
  for (long long int i = (-1); i >= (1 - n); i--) {
    curr_x = 1;
    curr_y = 1 - i;
    curr_sum = 0;
    while (curr_y < n + 1) {
      curr_sum += board[curr_x][curr_y];
      ++curr_y;
      ++curr_x;
    }
    diagonal[NEXT_FREE] = curr_sum;
    M1[i] = NEXT_FREE++;
  }
  for (long long int i = (n + 2); i <= (2 * n); i++) {
    curr_x = i - n;
    curr_y = n;
    curr_sum = 0;
    while (curr_x <= n) {
      curr_sum += board[curr_x][curr_y];
      --curr_y;
      ++curr_x;
    }
    diagonal[NEXT_FREE] = curr_sum;
    M2[i] = NEXT_FREE++;
  }
  curr_sum = 0;
  curr_x = n;
  curr_y = 1;
  for (long long int i = (1); i <= (n); i++) {
    curr_sum += board[curr_x][curr_y];
    --curr_x;
    ++curr_y;
  }
  diagonal[NEXT_FREE] = curr_sum;
  M2[n + 1] = NEXT_FREE++;
  for (long long int i = (2); i <= (n); i++) {
    curr_x = 1;
    curr_y = i - 1;
    curr_sum = 0;
    while (curr_y >= 1) {
      curr_sum += board[curr_x][curr_y];
      --curr_y;
      ++curr_x;
    }
    diagonal[NEXT_FREE] = curr_sum;
    M2[i] = NEXT_FREE++;
  }
  long long int x1, y1, x2, y2;
  long long int max1 = 0, max2 = 0;
  for (long long int i = (1); i <= (n); i++) {
    for (long long int j = (1); j <= (n); j++) {
      if ((i + j) & 1) {
        long long int temp_l =
            diagonal[M1[i - j]] + diagonal[M2[i + j]] - board[i][j];
        if (max1 <= temp_l) {
          max1 = temp_l;
          x1 = i;
          y1 = j;
        }
      } else {
        long long int temp_l =
            diagonal[M1[i - j]] + diagonal[M2[i + j]] - board[i][j];
        if (max2 <= temp_l) {
          max2 = temp_l;
          x2 = i;
          y2 = j;
        }
      }
    }
  }
  cout << fixed;
  cout << max1 + max2 << endl;
  cout << x1 << " " << y1 << " " << x2 << " " << y2 << endl;
}

```