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.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;

public class ladder13 {

	
	public static void main(String[] args) {
	
		FastScanner s = new FastScanner();
		int n = s.nextInt();
		
		int[][] grid = new int[n][n];
		long[] d1 = new long[2*n+1];
		long[] d2 = new long[2*n+1];
		
		for(int i=0;i<n;i++)
			for(int j=0;j<n;j++)
			{
				grid[i][j] = s.nextInt();
				d1[i+j]+=grid[i][j];
				d2[i-j+n-1]+=grid[i][j];
			}
		
		int x1=-1,x2=-1,y1=-1,y2=-1;
		long max1 = -1,max2 = -1;
		
		for(int i=0;i<n;i++)
		{
			for(int j=0;j<n;j++)
			{
				if((i+j)%2==0)
				{
					long c = d1[i+j]+d2[i-j+n-1]-grid[i][j];
					if(max1<c)
					{
						x1 = i+1;
						y1 = j+1;
						max1 = c;
					}
				}
				else
				{
					long c = d1[i+j]+d2[i-j+n-1]-grid[i][j];
					if(max2<c)
					{
						x2 = i+1;
						y2 = j+1;
						max2 = c;
					}
				}
			}
		}
		max1+=max2;
		System.out.println(max1+" "+x1+" "+y1+" "+x2+" "+y2);
		
	}

static class FastScanner {
		
	    private InputStream mIs;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public FastScanner() {
			this(System.in);
		}

		public FastScanner(InputStream is) {
			mIs = is;
		}

		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = mIs.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		
		}	

	}

}
