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 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);
        mysolver mysol = new mysolver();
        mysol.solve(in, out);
        out.close();
    }

}
class node {
	long tl;
	long tr;
	long bl;
	long br;
}
class mysolver {
	node nodes[][];
	long A[][];
    public void solve(InputReader in,OutputWriter out)
    {
    	PrintWriter pout = new PrintWriter(new BufferedOutputStream(System.out));
    	int n = in.readInt();
    	A = new long[n][n];
    	nodes = new node[n][n];
    	long d1[] = new long[4001];
    	long d2[] = new long[4001];
    	for(int i=0;i<n;i++)
    		for(int j=0;j<n;j++)
    		{
    			A[i][j] = in.readInt();
    			d1[i+j] += A[i][j];
    			d2[i-j+n] += A[i][j];
    		}
    	long sum1=-1;
    	long sum2=-1;
    	int x1=0,y1=0,x2=0,y2=0;
    	for(int i=0;i<n;i++)
    	{
    		for(int j=0;j<n;j++)
    		{
    			if((i+j)%2==0)
    			{
    				if(sum1 < d1[i+j] + d2[i-j+n]-A[i][j])
    				{
    					sum1 = d1[i+j] + d2[i-j+n]-A[i][j];
    					x1 = i+1;
    					y1 = j+1;
    				}
    			}
    			else
    			{
    				if(sum2 < d1[i+j] + d2[i-j+n]-A[i][j])
    				{
    					sum2 = d1[i+j] + d2[i-j+n]-A[i][j];
    					x2 = i+1;
    					y2 = j+1;
    				}
    			}
    		}
    	}
    	pout.println((sum1+sum2));
    	pout.println(x1+" "+y1+" "+x2+" "+y2);
    	pout.close();
    }

}
class InputReader {
 
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
 
    public InputReader(InputStream stream) {
        this.stream = stream;
    }
 
    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }
 
    public int readInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
 
    public String readString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }
 
    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return isWhitespace(c);
    }
 
    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
 
    public String next() {
        return readString();
    }
 
    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}
 
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 close() {
        writer.close();
    }
 
    public void printLine(int i) {
        writer.println(i);
    }
}
 
class IOUtils {
 
    public static void readIntArrays(InputReader in, int[]... arrays) {
        for (int i = 0; i < arrays[0].length; i++) {
            for (int j = 0; j < arrays.length; j++)
                arrays[j][i] = in.readInt();
        }
    }
 
    }