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{
    FastScanner in;
    PrintWriter out;

    long[][] sum = new long[2000][2000];
    int[][] a = new int[2000][2000];
    long S[][] = new long[2000][2000];

    public void solve()
    {
        int n = in.nextInt();
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                a[i][j] = in.nextInt();
                S[i][j] = a[i][j];
            }
        }

        for (int i = 0; i < n; i++)
            for (int j = 0; j < n; j++) {
                sum[i][j] = a[i][j];
                if(i > 0 && j > 0)
                    sum[i][j] += sum[i-1][j-1];

                S[i][j] += sum[i][j] - a[i][j];
            }
        for (int i = 0; i < n; i++)
            for (int j = n-1; j >= 0; j--) {
                sum[i][j] = a[i][j];
                if(i > 0 && j + 1 < n)
                    sum[i][j] += sum[i-1][j+1];

                S[i][j] += sum[i][j] - a[i][j];
            }
        for (int i = n-1; i >= 0; i--)
            for (int j = 0; j < n; j++) {
                sum[i][j] = a[i][j];
                if(i + 1 < n && j > 0)
                    sum[i][j] += sum[i+1][j-1];

                S[i][j] += sum[i][j] - a[i][j];
            }
        for (int i = n-1; i >= 0; i--)
            for (int j = n-1; j >= 0; j--) {
                sum[i][j] = a[i][j];
                if(i + 1 < n && j + 1 < n)
                    sum[i][j] += sum[i+1][j+1];

                S[i][j] += sum[i][j] - a[i][j];
            }


        long mx1 = -1, mx2 = -1;
        int ax = 0, ay = 0, bx = 0, by = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if ((i+j)%2 == 0) {
                    if (mx1 < S[i][j]) {
                        mx1 = S[i][j];
                        ax = i;
                        ay = j;
                    }
                }
                else {
                    if (mx2 < S[i][j]) {
                        mx2 = S[i][j];
                        bx = i;
                        by = j;
                    }
                }
            }
        }


        out.println(mx1 + mx2);
        out.println((ax+1) + " " + (ay+1) + " " + (bx+1) + " " + (by+1));
    }


    public void run()
    {
        in = new FastScanner();
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }


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

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

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

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

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}