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.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.StringTokenizer;

public class C463 {

    public static BufferedReader in;
    public static PrintWriter out;
    public static StringTokenizer tokenizer;

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        in = new BufferedReader(new InputStreamReader(inputStream), 32768);
        out = new PrintWriter(outputStream);
        solve();
        out.close();
    }

    public static void solve() {
        int n = nextInt();
        long[] d1 = new long[2 * n];
        long[] d2 = new long[2 * n];
        long[][] map = new long[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                long x = nextLong();
                d1[i + j] += x;
                d2[n + i - j - 1] += x;
                map[i][j] = x;
            }
        }
        int[][] result = new int[2][2];
        long[] sum = new long[2];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                int r = (i + j) % 2;
                if (d1[i + j] + d2[n + i - j - 1] - map[i][j] >= sum[r]) {
                    sum[r] = d1[i + j] + d2[n + i - j - 1] - map[i][j];
                    result[r][0] = i + 1;
                    result[r][1] = j + 1;
                }
            }
        }
        out.println(sum[0] + sum[1]);
        out.println(result[0][0] + " " + result[0][1] + " " + result[1][0] + " " + result[1][1]);
    }

    public static String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(in.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

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

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

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