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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Deque;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class GargariAndElefants {

	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		
		int n = in.nextInt();

		// check long
		
		long[][] board = new long[n][n];
		for (int i = 0; i < board.length; i++) {
			for (int j = 0; j < board.length; j++) {
				board[i][j] = in.nextInt();
			}
		}
		
		
		long[][] values = new long[n][n];
		for (int i = 0; i < board.length; i++) {
			long diag = 0;
			for (int j = 0; j <= i; j++) {
				diag += board[j][i - j];
			}
			for (int j = 0; j <= i; j++) {
				values[j][i - j] += diag;
			}
		}
		for (int i = 1; i < board.length; i++) {
			long diag = 0;
			for (int j = n - 1; j >= i; j--) {
				diag += board[j][i + (n - 1 - j)];
			}
			for (int j = n - 1; j >= i; j--) {
				values[j][i + (n - 1 - j)] += diag;
			}
		}
		
		
		for (int i = 0; i < board.length; i++) {
			long diag = 0;
			for (int j = 0; j <= n - 1 - i; j++) {
				diag += board[i + j][j];
			}
			for (int j = 0; j <= n - 1 - i; j++) {
				values[i + j][j] += diag;
			}
		}
		for (int i = 0; i < board.length - 1; i++) {
			long diag = 0;
			int dec = 0;
			for (int j = n - 1; j >= n - 1 - i; j--) {
				diag += board[i - dec][j];
				dec++;
			}
			dec = 0;
			for (int j = n - 1; j >= n - 1 - i; j--) {
				values[i - dec][j] += diag;
				dec++;
			}
		}
		
		long maxOdd = -1;
		long max = -1;
		int x1 = 0;
		int y1 = 0;
		int x2 = 0;
		int y2 = 0;
		for (int i = 0; i < board.length; i++) {
			for (int j = 0; j < board.length; j++) {
				if ((i + j) % 2 == 0) {
					if (max < values[i][j] - board[i][j]) {
						x1 = i + 1;
						y1 = j + 1;
						max = values[i][j] - board[i][j];
					}
				} else {
					if (maxOdd < values[i][j] - board[i][j]) {
						x2 = i + 1;
						y2 = j + 1;
						maxOdd = values[i][j] - board[i][j];
					}
				}
			}
		}
		
		out.println(max + maxOdd);
		out.print(x1 + " " + y1 + " " + x2 + " " + y2);
		out.close();
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream));
			tokenizer = 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() {
			return Integer.parseInt(next());
		}

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