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);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }

    static class Task {
        public void solve(InputReader in, PrintWriter out) {
            int n = in.nextInt();
            long[] posDiagonal = new long[5 * n];
            long[] negDiagonal = new long[5 * n];
            int[][] g = new int[n][n];
            long max1 = Long.MIN_VALUE;
            long max2 = Long.MIN_VALUE;
            int[] ans = new int[4];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    g[i][j] = in.nextInt();
                    posDiagonal[i + j + 2] += g[i][j];
                    negDiagonal[i - j + n] += g[i][j];
                }
            }
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (((i + 1) % 2 != 0 && (j + 1) % 2 != 0) || ((i + 1) % 2 == 0 && (j + 1) % 2 == 0)) {
                        if ((posDiagonal[i + j + 2] + negDiagonal[i - j + n] - g[i][j]) > max1) {
                            max1 = posDiagonal[i + j + 2] + negDiagonal[i - j + n] - g[i][j];
                            ans[0] = i + 1;
                            ans[1] = j + 1;
                        }
                    } else {
                        if ((posDiagonal[i + j + 2] + negDiagonal[i - j + n] - g[i][j]) > max2) {
                            max2 = posDiagonal[i + j + 2] + negDiagonal[i - j + n] - g[i][j];
                            ans[2] = i + 1;
                            ans[3] = j + 1;
                        }
                    }
                }
            }
            out.println(max1 + max2);
            Arrays.stream(ans).forEach(e -> out.printf("%d ", e));
            out.println();
        }
    }

    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());
        }
    }
}
