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

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

    static class TaskC {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[][] a = new int[n][n];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    a[i][j] = in.nextInt();
                }
            }
            long[] d1 = new long[2 * n - 1];
            long[] d2 = new long[2 * n - 1];
            for (int y = 0; y < n; y++) {
                for (int x = 0; x < n; x++) {
                    d1[x + y] += a[y][x];
                    d2[n - 1 - x + y] += a[y][x];
                }
            }
            long oddMin = -1;
            long evenMin = -1;
            int x1 = -1;
            int x2 = -1;
            int y1 = -1;
            int y2 = -1;
            for (int y = 0; y < n; y++) {
                for (int x = 0; x < n; x++) {
                    long cost = d1[x + y] + d2[n - 1 - x + y] - a[y][x];
                    if ((x + y) % 2 == 0) {
                        if (cost > oddMin) {
                            oddMin = cost;
                            x1 = x;
                            y1 = y;
                        }
                    } else {
                        if (cost > evenMin) {
                            evenMin = cost;
                            x2 = x;
                            y2 = y;
                        }
                    }
                }
            }
            out.println(oddMin + evenMin);
            out.println((y1 + 1) + " " + (x1 + 1) + " " + (y2 + 1) + " " + (x2 + 1));
        }

    }

    static class InputReader {
        private StringTokenizer tokenizer;
        private BufferedReader reader;

        public InputReader(InputStream inputStream) {
            reader = new BufferedReader(new InputStreamReader(inputStream));
        }

        private void fillTokenizer() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (Exception e) {
                    throw new RuntimeException(e);
                }
            }
        }

        public String next() {
            fillTokenizer();
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

