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
// package april2020;

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

public class Main {
	static int MAX = 2020;
	static long[] d1, d2, sol;
	static int[][] a;
	static Pair[] v;
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		FastReader scn = new FastReader();
		
		int n = scn.nextInt();
		a = new int[MAX][MAX];
		d1 = new long[MAX*2];
		d2 = new long[MAX*2];
		sol = new long[2];
		sol[0]=sol[1]=-1;
		v = new Pair[2];
		v[0] = new Pair(-1,-1);
		v[1] = new Pair(-1,-1);
		for(int i =1;i<=n;i++) {
			for(int j=1;j<=n;j++) {
				a[i][j] = scn.nextInt();
				d1[i+j] +=a[i][j];
				d2[i-j+n]+=a[i][j];
			}
		}
		
		for(int i=1;i<=n;i++) {
			for(int j=1;j<=n;j++) {
				update((i+j)&1, i,j,d1[i+j]+d2[i-j+n]-a[i][j]);
			}
		}
		System.out.println(sol[0]+sol[1]);
		
		if(v[0].compareTo(v[1])>0) {
			Pair temp = v[0];
			v[0] = v[1];
			v[1] = temp;
		}
		
		System.out.println(v[0].x+" "+v[0].y+" "+v[1].x+" "+v[1].y);
	}
	static void update(int c, int i, int j, long val) {
		if(val>sol[c]) {
			sol[c]= val;
			v[c].x = i;
			v[c].y = j;
		}
	}
	private static class Pair implements Comparable<Pair>{
		int x;
		int y;
		public Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}
		@Override
		public int compareTo(Pair o) {
			// TODO Auto-generated method stub
			if(this.x==o.x) {
				return this.y-o.y;
			}else {
				return this.x-o.x;
			}
		}
	}
	static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            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; 
        } 
    }

}
