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.util.*;
import java.io.*;

public class Codeforces {

    static boolean arr[];

    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        int n = Reader.nextInt();
        int arr[][] = new int[n][n];
        long rDiag[] = new long[n + n], lDiag[] = new long[n + n];

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                arr[i][j] = Reader.nextInt();
                rDiag[i + (n - 1) - j] += arr[i][j];
                lDiag[i + j] += arr[i][j];
            }
        }

        long maxOdd = -1, maxEven = -1;
        int x1 = 0, y1 = 0, x2 = 0, y2 = 0;

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                long x = lDiag[i + j] + rDiag[i + (n - 1) - j] - arr[i][j];

                if ((i + j) % 2 == 0) {

                    if (maxEven < x) {
                        maxEven = x;
                        x1 = i + 1;
                        y1 = j + 1;
                    }
                }
                
                else if (maxOdd < x) {
                    maxOdd = x;
                    x2 = i + 1;
                    y2 = j + 1;
                }
            }
        }

        System.out.println(maxEven + maxOdd);
        System.out.println(x1 + " " + y1 + " " + x2 + " " + y2);
    }
}

class Reader {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /**
     * call this method to initialize reader for InputStream
     */
    public static int pars(String x) {
        int num = 0;
        int i = 0;
        if (x.charAt(0) == '-') {
            i = 1;
        }
        for (; i < x.length(); i++) {
            num = num * 10 + (x.charAt(i) - '0');
        }

        if (x.charAt(0) == '-') {
            return -num;
        }

        return num;
    }

    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    static void init(FileReader input) {
        reader = new BufferedReader(input);
        tokenizer = new StringTokenizer("");
    }

    /**
     * get next word
     */
    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return pars(next());
    }

    static byte nextByte() throws IOException {

        return Byte.parseByte(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}
