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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import static java.lang.System.out;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Solution {

    public static void main(String[] args) throws IOException {
        InputReader in = new InputReader();

        int n =in.nextInt();
        int x1 = 0, x2 = 0, y1 = 0, y2 = 0;
        long[][] a = new long[n+1][n+1];
        long max1 = 0;
        long max2 = 0;
        long tot = 0;
        
         for (int i = 1; i <= n; i++) {
         for (int j = 1; j <= n; j++) {
         a[i][j] = in.nextInt();
         }
         }
        long[] d1 = new long[2 * n];
        long[] d2 = new long[2 * n];
        for (int i = 1, x = 1, y = 1; i < 2 * n; i++) {
            //go left and down

            d1[i] = a[x][y];
            int k = x + 1;
            int l = y - 1;
            while (k <= n && l > 0) {
                d1[i] += a[k][l];
                k++;
                l--;
            }
            if (i < n) {
                y++;
            } else {
                x++;
            }
        }
        for (int i = 1, x = 1, y = n; i < 2 * n; i++) {
            //go right and down
            d2[i] = a[x][y];
            int k = x + 1;
            int l = y + 1;
            while (k <= n && l <= n) {
                d2[i] += a[k][l];
                k++;
                l++;
            }

            if (i < n) {
                y--;
            } else {
                x++;
            }
        }
        /*
         long d1e = 0;
         long d2e = 0;
         long d1o = 0;
         long d2o = 0;
         int i1e = 0;
         int i1o = 0;
         int i2e = 0;
         int i2o = 0;
         for (int i = 1; i < 2 * n; i++) {
         if (i % 2 == 0) { //even
         if (d1[i] > d1o) {
         d1o = d1[i];
         i1o = i;
         }
         if (d1[i] > d2o) {
         d2o = d1[i];
         i2o = i;
         }

         } else {       //odd
         if (d1[i] > d1e) {
         d1e = d1[i];
         i1e = i;
         }
         if (d1[i] > d2e) {
         i2e = i;
         d2e = d1[i];
         }

         }
         }
         */
        long maxeven = 0;
        long maxodd = 0;
        for (int i = 1; i <= n; i++) {
            int x = i;
            int y = n + i - 1;
            for (int j = 1; j <= n; j++) {

               long m = d1[x] + d2[y] - a[i][j];
                x++;
                y--;
                if ((i + j) % 2 == 0 && m >= maxeven) {
                    maxeven = m;
                    x1 = i;
                    y1 = j;
                } else if ((i + j) % 2 != 0 && m >= maxodd) {
                    maxodd = m;
                    x2 = i;
                    y2 = j;
                }
            }
        }
        out.println(maxodd + maxeven);
        out.println(x1 + " " + y1 + " " + x2 + " " + y2);
    }

}

class InputReader {

    private BufferedReader reader;

    private StringTokenizer tokenizer;

    public InputReader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = null;

    }

    public String nextLine() {
        try {
            return reader.readLine();
        } catch (IOException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
            return 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() throws IOException {
        return Integer.parseInt(next());
    }

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

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

}
