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.*;
import java.util.*;


public class sugar {

    /**
     * @param args
     */
    public static long[]main_dig = new long[4500];
    public static long[]secd_dig = new long[4500];
    public static void main(String[] args) throws IOException {
        // TODO Auto-generated method stub
        BufferedReader k=new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(k.readLine());
        long[][]array = new long[n][n];
        for (int i = 0; i < array.length; i++) {
            StringTokenizer str=new StringTokenizer(k.readLine());
            
            for (int j = 0; j < array.length; j++) {
                array[i][j] = Long.parseLong(str.nextToken());
                main_dig[i+j] += array[i][j];
                secd_dig[i-j+n] += array[i][j];
            }
            
        }
        
        long even = -1 , odd = -1;
        int x_even = -1 , y_even = -1 , x_odd = -1 , y_odd = -1;
        for (int i = 0; i < array.length; i++) {
            for (int j = 0; j < array.length; j++) {
                
                if ((i+j) % 2 == 0) {
                    
                    if (even < main_dig[i+j]+secd_dig[i-j+n]-array[i][j]) {
                        even = main_dig[i+j]+secd_dig[i-j+n]-array[i][j];
                        x_even = i;
                        y_even = j;
                    }
                    
                }
                else {
                    if (odd < main_dig[i+j]+secd_dig[i-j+n]-array[i][j]) {
                        odd = main_dig[i+j]+secd_dig[i-j+n]-array[i][j];
                        x_odd = i;
                        y_odd = j;
                    }
                }
                
                
            }
        }
        x_even++;
        y_even++;
        x_odd++;
        y_odd++;
        System.out.println(even+odd);
        System.out.println(x_even+" "+y_even+" "+x_odd+" "+y_odd);
        
    }

}
