#include <bits/stdc++.h>
using namespace std;
int n;
int isvalid(int i, int j) {
  if (i < 0 || i >= n || j >= n || j < 0) return 0;
  return 1;
}
int mod(int x) {
  if (x < 0) return -x;
  return x;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  cin >> n;
  long long int a[n][n], i, j, sj, si;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) cin >> a[i][j];
  }
  long long int ul[n][n], ur[n][n], lwl[n][n], lwr[n][n];
  for (j = 0; j < n; j++)
    ul[0][j] = a[0][j], ur[0][j] = a[0][j], lwl[n - 1][j] = a[n - 1][j],
    lwr[n - 1][j] = a[n - 1][j];
  for (i = 1; i < n; i++) ul[i][0] = a[i][0], ur[i][n - 1] = a[i][n - 1];
  for (i = 0; i < n; i++) lwr[i][n - 1] = a[i][n - 1], lwl[i][0] = a[i][0];
  for (sj = 0; sj < n; sj++) {
    i = 1;
    j = sj + 1;
    while (j < n) {
      ul[i][j] = ul[i - 1][j - 1] + a[i][j];
      i++;
      j++;
    }
  }
  for (si = 1; si < n; si++) {
    i = si + 1;
    j = 1;
    while (i < n) {
      ul[i][j] = ul[i - 1][j - 1] + a[i][j];
      i++;
      j++;
    }
  }
  for (sj = n - 1; sj >= 0; sj--) {
    i = 1;
    j = sj - 1;
    while (j >= 0) {
      ur[i][j] = ur[i - 1][j + 1] + a[i][j];
      i++;
      j--;
    }
  }
  for (si = 1; si < n; si++) {
    i = si + 1;
    j = n - 2;
    while (i < n) {
      ur[i][j] = ur[i - 1][j + 1] + a[i][j];
      i++;
      j--;
    }
  }
  for (sj = 0; sj < n; sj++) {
    i = n - 2;
    j = sj - 1;
    while (j >= 0) {
      lwr[i][j] = lwr[i + 1][j + 1] + a[i][j];
      i--;
      j--;
    }
  }
  for (si = n - 2; si >= 0; si--) {
    i = si - 1;
    j = n - 2;
    while (i >= 0) {
      lwr[i][j] = lwr[i + 1][j + 1] + a[i][j];
      i--;
      j--;
    }
  }
  for (sj = 0; sj < n; sj++) {
    i = n - 2;
    j = sj + 1;
    while (j < n) {
      lwl[i][j] = lwl[i + 1][j - 1] + a[i][j];
      i--;
      j++;
    }
  }
  for (si = n - 2; si >= 0; si--) {
    i = si - 1;
    j = 1;
    while (i >= 0) {
      lwl[i][j] = lwl[i + 1][j - 1] + a[i][j];
      i--;
      j++;
    }
  }
  long long int mx = INT_MIN, x1, y1, x2, y2, ans = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      long long int v = 0;
      if (isvalid(i - 1, j - 1)) v += ul[i - 1][j - 1];
      if (isvalid(i - 1, j + 1)) v += ur[i - 1][j + 1];
      if (isvalid(i + 1, j + 1)) v += lwr[i + 1][j + 1];
      if (isvalid(i + 1, j - 1)) v += lwl[i + 1][j - 1];
      v += a[i][j];
      if (v > mx) {
        mx = v;
        x1 = i;
        y1 = j;
      }
    }
  }
  ans += mx;
  mx = INT_MIN;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if ((mod(i - x1) + mod(j - y1)) % 2 == 0) continue;
      long long int v = 0;
      if (isvalid(i - 1, j - 1)) v += ul[i - 1][j - 1];
      if (isvalid(i - 1, j + 1)) v += ur[i - 1][j + 1];
      if (isvalid(i + 1, j + 1)) v += lwr[i + 1][j + 1];
      if (isvalid(i + 1, j - 1)) v += lwl[i + 1][j - 1];
      v += a[i][j];
      if (v > mx) {
        mx = v;
        x2 = i;
        y2 = j;
      }
    }
  }
  ans += mx;
  cout << ans << "\n";
  cout << x1 + 1 << " " << y1 + 1 << " " << x2 + 1 << " " << y2 + 1;
  return 0;
}

### Prompt

In CPP, your task is to solve 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;
int n;
int isvalid(int i, int j) {
  if (i < 0 || i >= n || j >= n || j < 0) return 0;
  return 1;
}
int mod(int x) {
  if (x < 0) return -x;
  return x;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  ;
  cin >> n;
  long long int a[n][n], i, j, sj, si;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) cin >> a[i][j];
  }
  long long int ul[n][n], ur[n][n], lwl[n][n], lwr[n][n];
  for (j = 0; j < n; j++)
    ul[0][j] = a[0][j], ur[0][j] = a[0][j], lwl[n - 1][j] = a[n - 1][j],
    lwr[n - 1][j] = a[n - 1][j];
  for (i = 1; i < n; i++) ul[i][0] = a[i][0], ur[i][n - 1] = a[i][n - 1];
  for (i = 0; i < n; i++) lwr[i][n - 1] = a[i][n - 1], lwl[i][0] = a[i][0];
  for (sj = 0; sj < n; sj++) {
    i = 1;
    j = sj + 1;
    while (j < n) {
      ul[i][j] = ul[i - 1][j - 1] + a[i][j];
      i++;
      j++;
    }
  }
  for (si = 1; si < n; si++) {
    i = si + 1;
    j = 1;
    while (i < n) {
      ul[i][j] = ul[i - 1][j - 1] + a[i][j];
      i++;
      j++;
    }
  }
  for (sj = n - 1; sj >= 0; sj--) {
    i = 1;
    j = sj - 1;
    while (j >= 0) {
      ur[i][j] = ur[i - 1][j + 1] + a[i][j];
      i++;
      j--;
    }
  }
  for (si = 1; si < n; si++) {
    i = si + 1;
    j = n - 2;
    while (i < n) {
      ur[i][j] = ur[i - 1][j + 1] + a[i][j];
      i++;
      j--;
    }
  }
  for (sj = 0; sj < n; sj++) {
    i = n - 2;
    j = sj - 1;
    while (j >= 0) {
      lwr[i][j] = lwr[i + 1][j + 1] + a[i][j];
      i--;
      j--;
    }
  }
  for (si = n - 2; si >= 0; si--) {
    i = si - 1;
    j = n - 2;
    while (i >= 0) {
      lwr[i][j] = lwr[i + 1][j + 1] + a[i][j];
      i--;
      j--;
    }
  }
  for (sj = 0; sj < n; sj++) {
    i = n - 2;
    j = sj + 1;
    while (j < n) {
      lwl[i][j] = lwl[i + 1][j - 1] + a[i][j];
      i--;
      j++;
    }
  }
  for (si = n - 2; si >= 0; si--) {
    i = si - 1;
    j = 1;
    while (i >= 0) {
      lwl[i][j] = lwl[i + 1][j - 1] + a[i][j];
      i--;
      j++;
    }
  }
  long long int mx = INT_MIN, x1, y1, x2, y2, ans = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      long long int v = 0;
      if (isvalid(i - 1, j - 1)) v += ul[i - 1][j - 1];
      if (isvalid(i - 1, j + 1)) v += ur[i - 1][j + 1];
      if (isvalid(i + 1, j + 1)) v += lwr[i + 1][j + 1];
      if (isvalid(i + 1, j - 1)) v += lwl[i + 1][j - 1];
      v += a[i][j];
      if (v > mx) {
        mx = v;
        x1 = i;
        y1 = j;
      }
    }
  }
  ans += mx;
  mx = INT_MIN;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if ((mod(i - x1) + mod(j - y1)) % 2 == 0) continue;
      long long int v = 0;
      if (isvalid(i - 1, j - 1)) v += ul[i - 1][j - 1];
      if (isvalid(i - 1, j + 1)) v += ur[i - 1][j + 1];
      if (isvalid(i + 1, j + 1)) v += lwr[i + 1][j + 1];
      if (isvalid(i + 1, j - 1)) v += lwl[i + 1][j - 1];
      v += a[i][j];
      if (v > mx) {
        mx = v;
        x2 = i;
        y2 = j;
      }
    }
  }
  ans += mx;
  cout << ans << "\n";
  cout << x1 + 1 << " " << y1 + 1 << " " << x2 + 1 << " " << y2 + 1;
  return 0;
}

```