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.*;

public class Main {
    private static void solve(int n, int[][] a) {
        int l = 2*n-1;
        long[] lds = new long[l];
        long[] rds = new long[l];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                lds[i+j] += a[i][j];
                rds[i+(n-1-j)] += a[i][j];
            }
        }
        long[][] res = new long[2][3];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                long v = lds[i+j]+rds[i+(n-1-j)]-a[i][j];
                int d = (i+j)%2;
                if (v >= res[d][0]) {
                    res[d][0] = v;
                    res[d][1] = i;
                    res[d][2] = j;
                }
            }
        }
        System.out.println(res[0][0]+res[1][0]);
        for (int i = 0; i < 2; i++) {
            for (int j = 1; j < 3; j++) {
                System.out.print((res[i][j]+1)+" ");
            }
        }
        System.out.println();
    }
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int[][] a = new int[n][n];
        for (int i = 0; i < n; i++) {
            String[] p = br.readLine().split(" ");
            for (int j = 0; j < n; j++) {
                a[i][j] = Integer.parseInt(p[j]);
            }
        }
        solve(n, a);
    }
}