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.io.StreamTokenizer;
import java.util.Scanner;

public class C {

    /**
     * @param args
     */
     static StreamTokenizer st = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        static int nextInt() throws IOException
        {
           st.nextToken();
           return (int)st.nval;
        }
        static char nextChar() throws IOException
        {
             st.nextToken();
             return st.sval.charAt(0);
        }
    public static void main(String[] args) throws IOException {
        // TODO Auto-generated method stub
        int n = nextInt();
        int[][] a = new int[n][n];
        long[] b = new long[2 * n - 1];
        long[] c = new long[2 * n - 1];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                a[i][j] = nextInt();
                b[i + j] += a[i][j];
                c[n - 1 + i - j] += a[i][j];
            }
        }
        long[][] mas = new long[n][n];
        long max1 = -1;
        long max2 = -1;
        int x1=0, x2=0, y1=0, y2=0;

        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++) {
                mas[i][j] = b[i + j] + c[n - 1 + i - j] - a[i][j];
                if ((i + j) % 2 == 0) {
                    if (mas[i][j] > max1){
                        max1 = mas[i][j];
                        x1=i;
                        y1=j;
                    }
                } else {
                    if (mas[i][j] > max2){
                        max2 = mas[i][j];
                        x2=i;
                        y2=j;
                    }
                }
            }
        x1++;
        x2++;
        y2++;
        y1++;
        System.out.println(max1+max2);
        System.out.println(x1+" "+y1+ " "+x2+" "+y2);
        
    }

}
