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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Scanner;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author sagimbekov_ma
 */
public class C463 {

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
        int n = Integer.parseInt(in.readLine());
        int[][] m = new int[n][n];
        long[] rSum = new long[2 * n - 1];
        long[] lSum = new long[2 * n - 1];
        for (int i = 0; i < n; i++) {
            int j = 0;
            for (String line : in.readLine().split(" ")) {
                m[i][j] = Integer.parseInt(line);
                rSum[i + j] += m[i][j];
                lSum[n - 1 + i - j] += m[i][j];
                j++;
            }
        }

        long maxSum1 = Long.MIN_VALUE;
        long maxSum2 = Long.MIN_VALUE;
        int x1 = 0;
        int y1 = 0;
        int x2 = 0;
        int y2 = 0;

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                long sum = (long) rSum[i + j] + (long) lSum[n - 1 + i - j] - (long) m[i][j];
                if ((i + j) % 2 == 0) {
                    if (sum > maxSum1) {
                        maxSum1 = sum;
                        x1 = i + 1;
                        y1 = j + 1;
                    }
                } else {
                    if (sum > maxSum2) {
                        maxSum2 = sum;
                        x2 = i + 1;
                        y2 = j + 1;
                    }
                }
            }
        }

        out.write(((long) maxSum1 + (long) maxSum2) + "\n");
        out.write(x1 + " " + y1 + " " + x2 + " " + y2 + "\n");
        out.flush();
    }
}
