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.*;

/**
 *
 * @coder myrza
 */
public class C {

        String inputFileName = "";

        void solution() throws Exception {
                int n = in.nextInt();
                long[][] arr = new long[n][n];
                for (int i = 0; i < n; i++) {
                        for (int j = 0; j < n; j++) {
                                arr[i][j] = in.nextLong();
                        }
                }
                long[][] dp = new long[n][n];
                for (int i = 0; i < n; i++) {
                        int x = i, y = 0;
                        long sum = 0;
                        do {
                                sum += arr[x][y];
                                x++;
                                y++;
                        } while (x < n && y < n);
                        x--;
                        y--;
                        while (x >= 0 && y >= 0) {
                                dp[x][y] = sum;
                                x--;
                                y--;
                        }
                }
                for (int j = 0; j < n; j++) {
                        int x = 0, y = j;
                        long sum = 0;
                        do {
                                sum += arr[x][y];
                                x++;
                                y++;
                        } while (x < n && y < n);
                        x--;
                        y--;
                        while (x >= 0 && y >= 0) {
                                dp[x][y] = sum;
                                x--;
                                y--;
                        }
                }
                for (int i = 0; i < n; i++) {
                        int x = i, y = n - 1;
                        long sum = 0;
                        do {
                                sum += arr[x][y];
                                x++;
                                y--;
                        } while (x < n && y >= 0);
                        x--;
                        y++;
                        while (x >= 0 && y < n) {
                                dp[x][y] += sum - arr[x][y];
                                x--;
                                y++;
                        }
                }
                for (int j = 0; j < n - 1; j++) {
                        int x = 0, y = j;
                        long sum = 0;
                        do {
                                sum += arr[x][y];
                                x++;
                                y--;
                        } while (x < n && y >= 0);
                        x--;
                        y++;
                        while (x >= 0 && y < n) {
                                dp[x][y] += sum - arr[x][y];
                                x--;
                                y++;
                        }
                }
                long max1 = -1, max2 = -1;
                int x1 = 0, y1 = 0, x2 = 0, y2 = 0;
                for (int i = 0; i < n; i++) {
                        for (int j = 0; j < n; j++) {
                                if ((i + j) % 2 == 0) {
                                        if (max1 < dp[i][j]) {
                                                max1 = dp[i][j];
                                                x1 = i + 1;
                                                y1 = j + 1;
                                        }
                                } else {
                                        if (max2 < dp[i][j]) {
                                                max2 = dp[i][j];
                                                x2 = i + 1;
                                                y2 = j + 1;
                                        }
                                }
                        }
                }
                out.println(max1 + max2);
                out.println(x1 + " " + y1 + " " + x2 + " " + y2);
        }

        public static void main(String[] args) throws Exception {
                new C().run();
        }

        Scanner in;
        PrintWriter out;

        void run() throws Exception {
                if (inputFileName.equals("")) {
                        in = new Scanner(System.in);
                        out = new PrintWriter(System.out);
                } else {
                        in = new Scanner(new File(inputFileName + ".in"));
                        out = new PrintWriter(new File(inputFileName + ".out"));
                }
                solution();
                out.flush();
        }

        class Scanner {

                private final BufferedReader reader;
                private StringTokenizer tokenizer;

                Scanner(InputStream streamReader) {
                        reader = new BufferedReader(new InputStreamReader(streamReader));
                }

                Scanner(File file) throws Exception {
                        reader = new BufferedReader(new FileReader(file));
                }

                String next() throws Exception {
                        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                                tokenizer = new StringTokenizer(reader.readLine());
                        }
                        return tokenizer.nextToken();
                }

                Integer nextInt() throws Exception {
                        return Integer.parseInt(next());
                }

                Long nextLong() throws Exception {
                        return Long.parseLong(next());
                }

                Double nextDouble() throws Exception {
                        return Double.parseDouble(next());
                }
        }
}
