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.InputStreamReader;
import java.util.HashMap;
import java.util.StringTokenizer;

public class P463C
{
	public static void main(String[] args)
	{
		FastScanner scan = new FastScanner();
		int n = scan.nextInt();
		int[][] grid = new int[n][n];
		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++)
				grid[i][j] = scan.nextInt();
		HashMap<Integer, Long> sum = new HashMap<>();
		HashMap<Integer, Long> diff = new HashMap<>();
		for (int i = 0; i < n; i++)
		{
			for (int j = 0; j < n; j++)
			{
				Long s = sum.get(i+j);
				if (s == null)
					s = 0L;
				sum.put(i+j, s+grid[i][j]);
				
				Long d = diff.get(i-j);
				if (d == null)
					d = 0L;
				diff.put(i-j, d+grid[i][j]);
			}
		}
		long max0 = -1, max1 = -1;
		long x0 = -1, y0 = -1, x1 = -1, y1 = -1;
		for (int i = 0; i < n; i++)
		{
			for (int j = 0; j < n; j++)
			{
				long s = sum.get(i+j);
				long d = diff.get(i-j);
				long score = s+d-grid[i][j];
				if (((i+j) & 1) == 0)
				{
					if (score > max0)
					{
						max0 = score;
						x0 = i+1;
						y0 = j+1;
					}
				}
				else
				{
					if (score > max1)
					{
						max1 = score;
						x1 = i+1;
						y1 = j+1;
					}
				}
			}
		}
		System.out.println(max0 + max1);
		System.out.println(x0 + " " + y0 + " " + x1 + " " + y1);
	}
	
	static class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner()
		{
			try
			{
				br = new BufferedReader(new InputStreamReader(System.in));
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
		}

		public String next()
		{
			if (st.hasMoreTokens())
				return st.nextToken();
			try
			{
				st = new StringTokenizer(br.readLine());
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return st.nextToken();
		}

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

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

		public String nextLine()
		{
			String line = "";
			try
			{
				line = br.readLine();
			} catch (Exception e)
			{
				e.printStackTrace();
			}
			return line;
		}
	}
}
