#include <bits/stdc++.h>
using namespace std;
long long int binomialCoeff(long long int n, long long int k) {
  long long int C[n + 1][k + 1];
  long long int i, j;
  for (i = 0; i < n + 1; i++) {
    for (j = 0; j < (min(i, k) + 1); j++) {
      if (j == 0 || j == i)
        C[i][j] = 1;
      else
        C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
    }
  }
  return C[n][k];
}
vector<bool> natural_nos(100001, true);
vector<long long int> prime;
void precompute() {
  long long int i, j;
  for (i = 2; i < 100001; i++) {
    prime.push_back(i);
    for (j = 2; (j * i < 100001) && (natural_nos[i]); j++) {
      natural_nos[j * i] = false;
    }
  }
}
long long int dfs_leading(vector<vector<long long int> > A, long long int a,
                          long long int b, long long int n) {
  long long int sum, i, j, temp1, temp2, temp3;
  sum = A[a][b];
  i = a + 1;
  temp3 = i;
  temp2 = 0;
  for (j = b + 1; j < n && i < n; j++) {
    temp2 += A[i][j];
    i++;
  }
  sum += temp2;
  i = temp3;
  i = a - 1;
  temp3 = i;
  temp2 = 0;
  for (j = b - 1; j >= 0 && i >= 0; j--) {
    temp2 += A[i][j];
    i--;
  }
  sum += temp2;
  i = temp3;
  return sum;
}
long long int dfs_following(vector<vector<long long int> > A, long long int a,
                            long long int b, long long int n) {
  long long int sum, i, j, temp1, temp2, temp3;
  sum = A[a][b];
  i = a - 1;
  temp3 = i;
  temp2 = 0;
  for (j = b + 1; j < n && i >= 0; j++) {
    temp2 += A[i][j];
    i--;
  }
  sum += temp2;
  i = temp3;
  i = a + 1;
  temp3 = i;
  temp2 = 0;
  for (j = b - 1; j >= 0 && i < n; j--) {
    temp2 += A[i][j];
    i++;
  }
  sum += temp2;
  i = temp3;
  return sum;
}
void mark(vector<vector<long long int> > &A, long long int a, long long int b,
          long long int n) {
  long long int sum, i, j, temp1, temp2, temp3;
  i = a + 1;
  temp3 = i;
  temp2 = 0;
  for (j = b + 1; j < n && i < n; j++) {
    A[i][j] = 1;
    i++;
  }
  i = temp3;
  i = a - 1;
  temp3 = i;
  temp2 = 0;
  for (j = b - 1; j >= 0 && i >= 0; j--) {
    A[i][j] = 1;
    i--;
  }
  i = temp3;
  i = a - 1;
  temp3 = i;
  temp2 = 0;
  for (j = b + 1; j < n && i >= 0; j++) {
    A[i][j] = 1;
    i--;
  }
  i = temp3;
  i = a + 1;
  temp3 = i;
  temp2 = 0;
  for (j = b - 1; j >= 0 && i < n; j--) {
    A[i][j] = 1;
    i++;
  }
  i = temp3;
}
int main(void) {
  ios_base::sync_with_stdio(0);
  long long int test, i, j, x1, x2, y1, y2, k, n, m, a, b, temp1, temp2, temp3,
      ans;
  cin >> n;
  vector<vector<long long int> > A;
  vector<long long int> leading_diagonal(4 * n, 0);
  vector<long long int> following_diagonal(4 * n, 0);
  for (i = 0; i < n; i++) {
    vector<long long int> B;
    for (j = 0; j < n; j++) {
      cin >> temp1;
      B.push_back(temp1);
      leading_diagonal[i - j + n] = 0;
      following_diagonal[i + j + n] = 0;
    }
    A.push_back(B);
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      leading_diagonal[i - j + n] += A[i][j];
      following_diagonal[i + j + n] += A[i][j];
    }
  }
  ans = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      temp1 = leading_diagonal[i - j + n];
      temp2 = following_diagonal[j + i + n];
      temp3 = temp1 + temp2 - A[i][j];
      if (temp3 >= ans) {
        ans = temp3;
        x1 = i;
        y1 = j;
      }
    }
  }
  bool flag = ((x1 + y1) % 2 == 1) ? false : true;
  long long int ans1 = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if ((((i + j) % 2 == 0) != flag)) {
        temp1 = leading_diagonal[i - j + n];
        temp2 = following_diagonal[j + i + n];
        temp3 = temp1 + temp2 - A[i][j];
        if (temp3 >= ans1) {
          ans1 = temp3;
          x2 = i;
          y2 = j;
        }
      }
    }
  }
  cout << ans + ans1 << endl;
  cout << x1 + 1 << " " << y1 + 1 << " " << x2 + 1 << " " << y2 + 1 << endl;
  return 0;
}

### Prompt

Please formulate 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;
long long int binomialCoeff(long long int n, long long int k) {
  long long int C[n + 1][k + 1];
  long long int i, j;
  for (i = 0; i < n + 1; i++) {
    for (j = 0; j < (min(i, k) + 1); j++) {
      if (j == 0 || j == i)
        C[i][j] = 1;
      else
        C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
    }
  }
  return C[n][k];
}
vector<bool> natural_nos(100001, true);
vector<long long int> prime;
void precompute() {
  long long int i, j;
  for (i = 2; i < 100001; i++) {
    prime.push_back(i);
    for (j = 2; (j * i < 100001) && (natural_nos[i]); j++) {
      natural_nos[j * i] = false;
    }
  }
}
long long int dfs_leading(vector<vector<long long int> > A, long long int a,
                          long long int b, long long int n) {
  long long int sum, i, j, temp1, temp2, temp3;
  sum = A[a][b];
  i = a + 1;
  temp3 = i;
  temp2 = 0;
  for (j = b + 1; j < n && i < n; j++) {
    temp2 += A[i][j];
    i++;
  }
  sum += temp2;
  i = temp3;
  i = a - 1;
  temp3 = i;
  temp2 = 0;
  for (j = b - 1; j >= 0 && i >= 0; j--) {
    temp2 += A[i][j];
    i--;
  }
  sum += temp2;
  i = temp3;
  return sum;
}
long long int dfs_following(vector<vector<long long int> > A, long long int a,
                            long long int b, long long int n) {
  long long int sum, i, j, temp1, temp2, temp3;
  sum = A[a][b];
  i = a - 1;
  temp3 = i;
  temp2 = 0;
  for (j = b + 1; j < n && i >= 0; j++) {
    temp2 += A[i][j];
    i--;
  }
  sum += temp2;
  i = temp3;
  i = a + 1;
  temp3 = i;
  temp2 = 0;
  for (j = b - 1; j >= 0 && i < n; j--) {
    temp2 += A[i][j];
    i++;
  }
  sum += temp2;
  i = temp3;
  return sum;
}
void mark(vector<vector<long long int> > &A, long long int a, long long int b,
          long long int n) {
  long long int sum, i, j, temp1, temp2, temp3;
  i = a + 1;
  temp3 = i;
  temp2 = 0;
  for (j = b + 1; j < n && i < n; j++) {
    A[i][j] = 1;
    i++;
  }
  i = temp3;
  i = a - 1;
  temp3 = i;
  temp2 = 0;
  for (j = b - 1; j >= 0 && i >= 0; j--) {
    A[i][j] = 1;
    i--;
  }
  i = temp3;
  i = a - 1;
  temp3 = i;
  temp2 = 0;
  for (j = b + 1; j < n && i >= 0; j++) {
    A[i][j] = 1;
    i--;
  }
  i = temp3;
  i = a + 1;
  temp3 = i;
  temp2 = 0;
  for (j = b - 1; j >= 0 && i < n; j--) {
    A[i][j] = 1;
    i++;
  }
  i = temp3;
}
int main(void) {
  ios_base::sync_with_stdio(0);
  long long int test, i, j, x1, x2, y1, y2, k, n, m, a, b, temp1, temp2, temp3,
      ans;
  cin >> n;
  vector<vector<long long int> > A;
  vector<long long int> leading_diagonal(4 * n, 0);
  vector<long long int> following_diagonal(4 * n, 0);
  for (i = 0; i < n; i++) {
    vector<long long int> B;
    for (j = 0; j < n; j++) {
      cin >> temp1;
      B.push_back(temp1);
      leading_diagonal[i - j + n] = 0;
      following_diagonal[i + j + n] = 0;
    }
    A.push_back(B);
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      leading_diagonal[i - j + n] += A[i][j];
      following_diagonal[i + j + n] += A[i][j];
    }
  }
  ans = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      temp1 = leading_diagonal[i - j + n];
      temp2 = following_diagonal[j + i + n];
      temp3 = temp1 + temp2 - A[i][j];
      if (temp3 >= ans) {
        ans = temp3;
        x1 = i;
        y1 = j;
      }
    }
  }
  bool flag = ((x1 + y1) % 2 == 1) ? false : true;
  long long int ans1 = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if ((((i + j) % 2 == 0) != flag)) {
        temp1 = leading_diagonal[i - j + n];
        temp2 = following_diagonal[j + i + n];
        temp3 = temp1 + temp2 - A[i][j];
        if (temp3 >= ans1) {
          ans1 = temp3;
          x2 = i;
          y2 = j;
        }
      }
    }
  }
  cout << ans + ans1 << endl;
  cout << x1 + 1 << " " << y1 + 1 << " " << x2 + 1 << " " << y2 + 1 << endl;
  return 0;
}

```