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.awt.Point;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Hashtable;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.Vector;


public class Main {	
	
	static long mat[][] ;
	static HashMap<Integer,Long> l = new HashMap<Integer,Long>(),r = new HashMap<Integer, Long>();

	public static void main(String[] args) {
			MyScanner sc = new MyScanner() ;
			long wmax = Integer.MIN_VALUE,bmax = Integer.MIN_VALUE ;
			int n = sc.nextInt(),temp,x1=0,x2=0,y1=0,y2=0;
			mat = new long[n][n] ;
			for(int i = 0; i < n ; i++)
				for(int j = 0 ; j < n ; j++ ){
					mat[i][j] = sc.nextInt() ;
						if(l.containsKey(i-j))
							l.put(i-j,l.get(i-j) + mat[i][j]);
						else
							l.put(i-j,mat[i][j]);
						if(r.containsKey(i+j))
							r.put(i+j,r.get(i+j) + mat[i][j]);
						else
							r.put(i+j,mat[i][j]);
				}
			
			for(int i = 0; i < n ; i++)
				for(int j = 0 ; j < n ; j++ ){
					mat[i][j] = l.get(i-j) + r.get(i+j) - mat[i][j] ;
					if(getC(i, j)){
						if( wmax < mat[i][j] ){
							wmax = mat[i][j] ;
							x1 = i+1;
							y1 = j+1;
						}
					}else{
						if( bmax < mat[i][j] ){
							bmax = mat[i][j] ;
							x2 = i+1;
							y2 = j+1;
						}
					}
				}
			
			System.out.println(wmax+bmax+"\n"+x1+" "+y1+" "+x2+" "+y2);
	}

	private static boolean getC(int i, int j) {
		// TODO Auto-generated method stub
		if( ( i % 2 == 0 && j % 2 == 0 ) || ( i % 2 != 0 && j % 2 != 0 ) )
			return true;
		return false ;
	}
	
	static boolean getC(int i,int j,int a,int b){
		if( getC(i,j) && !getC(a,b) || !getC(i,j) && getC(a,b) )
			return true ;
		return false;
	}

}


class MyScanner {
	BufferedReader br;
	StringTokenizer st;

	public MyScanner() {
		br = new BufferedReader(new InputStreamReader(System.in));
	}

	String next() {
		while (st == null || !st.hasMoreElements()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (IOException e) {
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}
	
	int nextInt() {
		return Integer.parseInt(next());
	}

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

	double nextDouble() {
		return Double.parseDouble(next());
	}

	String nextLine(){
		String str = "";
		try {
			str = br.readLine();
		} catch (IOException e) {
			e.printStackTrace();
		}
		return str;
	}
	
}



