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
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;

public class c {
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        long n = Long.parseLong(in.readLine());
        long[][] grid = new long[(int) n][(int) n];
        for (int i = 0; i < n; i++) {
            String[] s = in.readLine().split(" ");
            for (int j = 0; j < n; j++) {
                grid[i][j] = Long.parseLong(s[j]);
            }
        }
        long[][] ss_right = new long[(int) n][(int) n];
        long[][] ss_left = new long[(int) n][(int) n];
        // right
        for (int i = 0; i < n; i++) {
            long sum = 0;
            for (int j = 0, k = i; j < n && k < n; j++, k++)
                sum += grid[j][k];
            ss_right[0][i] = sum;
        }
        for (int i = 0; i < n; i++) {
            long sum = 0;
            for (int j = 0, k = i; j < n && k < n; j++, k++)
                sum += grid[k][j];
            ss_right[i][0] = sum;
        }
        // left
        for (int i = 0; i < n; i++) {
            long sum = 0;
            for (int j = (int) n - 1, k = i; j >= 0 && k < n; j--, k++)
                sum += grid[j][k];
            ss_left[i][(int) (n - 1)] = sum;
        }
        for (int i = 0; i < n; i++) {
            long sum = 0;
            for (int j = 0, k = i; j < n && k >= 0; j++, k--)
                sum += grid[j][k];
            ss_left[0][i] = sum;
        }
        long a = -1, b = -1;
        int x1 = 0, x2 = 0, y1 = 0, y2 = 0;
        for (int i = 0; i < n; i++) {
            for (int j = (i % 2); j < n; j += 2) {
                int min = Math.min(i, j);
                long temp1 = ss_right[i - min][j - min];
                int x = Math.min(i, (int) n - j - 1);
                temp1 += ss_left[i - x][j + x];
                if ((temp1 - grid[i][j] > a)) {
                    a = temp1 - grid[i][j];
                    x1 = i + 1;
                    y1 = j + 1;
                }
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = (i % 2) + 1; j < n; j += 2) {
                int min = Math.min(i, j);
                long temp1 = ss_right[i - min][j - min];
                int x = Math.min(i, (int) n - j - 1);
                temp1 += ss_left[i - x][j + x];
                if ((temp1 - grid[i][j] > b)) {
                    b = temp1 - grid[i][j];
                    x2 = i + 1;
                    y2 = j + 1;
                }

            }
        }
        System.out.println(a + b);
        System.out.println(x1 + " " + y1 + " " + x2 + " " + y2);
    }
}
