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 java.util.StringTokenizer;

// http://codeforces.com/contest/463/problem/C
public class GargariAndBishops {

	public static void main(String[] args) throws IOException {
		try (BufferedReader reader = new BufferedReader(new InputStreamReader(System.in))) {
			String input;

			while ((input = reader.readLine()) != null && input.length() > 0) {
				int n = Integer.parseInt(input);
				int[][] field = new int[n][n];
				long[] diag1 = new long[2 * n];
				long[] diag2 = new long[2 * n];

				for (int i = 0; i < n; i++) {
					StringTokenizer data = new StringTokenizer(reader.readLine());

					for (int j = 0; j < n; j++) {
						field[i][j] = Integer.parseInt(data.nextToken());
						diag1[i + j] += field[i][j];
						diag2[n + i - j] += field[i][j];
					}
				}
				long max1 = 0;
				int x1 = 0;
				int y1 = 0;

				long max2 = 0;
				int x2 = 0;
				int y2 = 0;

				for (int i = 0; i < n; i++) {
					for (int j = 0; j < n; j++) {
						long currentMax = diag1[i + j] + diag2[n + i - j] - field[i][j];

						if ((i + j) % 2 == 0 && currentMax >= max1) {
							max1 = currentMax;
							x1 = i;
							y1 = j;
						} else if ((i + j) % 2 != 0 && currentMax >= max2) {
							max2 = currentMax;
							x2 = i;
							y2 = j;
						}
					}
				}
				System.out.println(max1 + max2);
				System.out.printf("%d %d %d %d\n", x1 + 1, y1 + 1, x2 + 1, y2 + 1);
			}
		}
	}
}