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.InputStreamReader;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Lokesh Khandelwal
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n = in.nextInt(), i, j;
        long a[][] = new long[n][n];
        for(i=0;i<n;i++) {
            for(j=0;j<n;j++) {
                a[i][j] = in.nextInt();
            }
        }
        long left[] = new long[2 * n - 1], right[] = new long[2 * n - 1];
        for(i=0;i<n;i++) {
            for(j=0;j<n;j++) {
                left[i - j + n - 1] += a[i][j];
                right[i + j] += a[i][j];
            }
        }

        long x1 = -1, y1 = -1, x2 = -1, y2 = -1, max1 = -1, max2 = -1;
        for(i=0;i<n;i++) {
            for(j=0;j<n;j++) {
                if((i + j) % 2 == 0) {
                    if(left[i - j + n - 1] + right[i + j] - a[i][j] > max1) {
                        max1 = left[i - j + n - 1] + right[i + j] - a[i][j];
                        x1 = i;
                        y1 = j;
                    }
                } else {
                    if(left[i - j + n - 1] + right[i + j] - a[i][j] > max2) {
                        max2 = left[i - j + n - 1] + right[i + j] - a[i][j];
                        x2 = i;
                        y2 = j;
                    }  
                }
            }
        }
        
        
        out.printLine(max1 + max2);
        out.printLine((x1 + 1)+" "+(y1 + 1)+" "+(x2 + 1)+" "+(y2 + 1));
    }
}

class InputReader
{
    BufferedReader in;
    StringTokenizer tokenizer=null;

    public InputReader(InputStream inputStream)
    {
        in=new BufferedReader(new InputStreamReader(inputStream));
    }
    public String next()
    {
        try{
            while (tokenizer==null||!tokenizer.hasMoreTokens())
            {
                tokenizer=new StringTokenizer(in.readLine());
            }
            return tokenizer.nextToken();
        }
        catch (IOException e)
        {
            return null;
        }
    }
    public int nextInt()
    {
        return Integer.parseInt(next());
    }
}

class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}

	public OutputWriter(Writer writer) {
		this.writer = new PrintWriter(writer);
	}

	public void print(Object...objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}

	public void printLine(Object...objects) {
		print(objects);
		writer.println();
	}

	public void close() {
		writer.close();
	}
}

