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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class GargariAndBishops {
    private void solve() {
        int n = in.nextInt();
        long[][] chessboard = new long[n][n];
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                chessboard[i][j] = in.nextInt();
            }
        }
        Map<Integer, Long> pdiags = new HashMap<>();
        Map<Integer, Long> ndiags = new HashMap<>();
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                pdiags.put(i - j, pdiags.getOrDefault(i - j, 0L) + chessboard[i][j]);
                ndiags.put(i + j, ndiags.getOrDefault(i + j, 0L) + chessboard[i][j]);
            }
        }
        long odd = 0;
        long even = 0;
        int[] epos = new int[2];
        int[] opos = new int[2];
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                if (Math.abs(i - j) % 2 == 0) {
                    if (even <= pdiags.get(i - j) + ndiags.get(i + j) - chessboard[i][j]) {
                        even = pdiags.get(i - j) + ndiags.get(i + j) - chessboard[i][j];
                        epos[0] = i;
                        epos[1] = j;
                    }
                } else {
                    if (odd <= pdiags.get(i - j) + ndiags.get(i + j) - chessboard[i][j]) {
                        odd = pdiags.get(i - j) + ndiags.get(i + j) - chessboard[i][j];
                        opos[0] = i;
                        opos[1] = j;
                    }
                }
            }
        }
        out.println(odd + even);
        out.println((epos[0] + 1) + " " + (epos[1] + 1) + " " + (opos[0] + 1) + " " + (opos[1] + 1));
    }

    private class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in), 327680);
            st = new StringTokenizer("");
        }

        String next() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        char nextChar() {
            String s = next();
            if (s.length() > 1)
                throw new RuntimeException("character expected but string provided");
            return s.charAt(0);
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return str;
        }
    }

    private FastScanner in;
    private PrintWriter out;

    private void run() {
        try {
            in = new FastScanner();
            out = new PrintWriter(new BufferedOutputStream(System.out));
            solve();
        } finally {
            out.close();
        }
    }

    public static void main(String[] arg) {
        new GargariAndBishops().run();
    }
}

