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.IOException;
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[][] ar = new int[n + 1][n + 1];
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= n; j++) {
                    ar[i][j] = in.nextInt();
                }
            }

            long[] left = new long[2 * n];
            long[] right = new long[2 * n + 1];
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= n; j++) {
                    right[i + j] += ar[i][j];
                    left[j - i + n] += ar[i][j];
                }
            }

            long odd = 0;
            long even = 0;
            long oddX = 1;
            long oddY = 1;
            long evenX = 1;
            long evenY = 2;
            for (int i = 1; i <= n; i++) {
                for (int j = 1; j <= n; j++) {
                    long score = right[i + j] + left[j - i + n] - ar[i][j];
                    if ((i + j) % 2 == 0) {
                        if (score > even) {
                            even = score;
                            evenX = i;
                            evenY = j;
                        }
                    } else {
                        if (score > odd) {
                            odd = score;
                            oddX = i;
                            oddY = j;
                        }
                    }
                }
            }
            out.println(odd + even);
            out.print(oddX + " " + oddY + " " + evenX + ' ' + evenY);


        }

    }

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

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }
}

