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.util.*;
import java.io.*;
import java.math.BigInteger;

public class Solution{	

	public static void main(String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int[][] arr = new int[n][n];
		long[] p = new long[2*n];
		long[] s = new long[2*n];

		for(int i = 0; i < n; i++){
			StringTokenizer token = new StringTokenizer(br.readLine());
			for(int j = 0; j < n; j++){
				arr[i][j] = Integer.parseInt(token.nextToken());
				p[n + j - i] += (long)arr[i][j];
				s[i + j] += (long)arr[i][j];
			}
		}

		long black = Integer.MIN_VALUE;
		long white = Integer.MIN_VALUE;

		int x1 = -1, y1 = -1, x2 = -1, y2 = -1;	
		for(int i = 0; i < n; i++)
			for(int j = 0; j < n; j++){
				if((i + j) % 2 == 0){
					long sum = (long)p[n + j - i] + (long)s[i + j] - (long)arr[i][j];
					if(sum >= black){
						black = sum;
						x1 = i;
						y1 = j;
					}
				}			

				else{	

					long sum = (long)p[n + j - i] + (long)s[i + j] - (long)arr[i][j];
					if(sum >= white){
						white = sum;
						x2 = i;
						y2 = j;
					}
				}
			}
		
		x1++;x2++;y1++;y2++;
		System.out.println(black+white);
		System.out.print(x1+" "+y1+" "+x2+" "+y2);	
	}	
}