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.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
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();
	}
}

class TaskC {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int[][] board = new int[n][n];
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j)
                board[i][j] = in.nextInt();
        long[] dia1 = new long[2 * n - 1];
        long[] dia2 = new long[2 * n - 1];
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j) {
                dia1[i + j] += board[i][j];
                dia2[i - j + n - 1] += board[i][j];
            }
        long[] maxSum = new long[2];
        Arrays.fill(maxSum, -1);
        int[][] position = new int[2][];
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j) {
                int parity = (i + j) % 2;
                long sum = dia1[i + j] + dia2[i - j + n - 1] - board[i][j];
                if (sum > maxSum[parity]) {
                    maxSum[parity] = sum;
                    position[parity] = new int[]{i, j};
                }
            }
        out.println(maxSum[0] + maxSum[1]);
        for (int x = 0; x < 2; ++x)
            for (int y = 0; y < 2; ++y) {
                out.print(position[x][y] + 1);
                out.print(" ");
            }
    }
}

class InputReader {
    private BufferedReader reader;
    private 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());
    }

}

