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.Arrays;
import java.util.StringTokenizer;

public class GargaryAndBishops {

    public static void main(String[] args) throws Exception{
        // TODO Auto-generated method stub
        
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        
        StringTokenizer st=new StringTokenizer(br.readLine());
        
        int N=Integer.parseInt(st.nextToken());
        
        int [] [] mat=new int[N][N];
        
        long [] principles=new long[2*N-1];
        long [] secondaries=new long[2*N-1];
        
        
        for(int i=0;i<N;i++){
            
            st=new StringTokenizer(br.readLine());
            
            for(int j=0;j<N;j++){
                
                mat[i][j]=Integer.parseInt(st.nextToken());
                
                principles[getPrincpleDiagIndex(i, j, N)]+=mat[i][j];
                secondaries[getSecondaryDiagIndex(i, j)]+=mat[i][j];
                
            }
            
        }
        

        long bestWhite=Integer.MIN_VALUE;
        long bestBlack=Integer.MIN_VALUE;
        
        int y1=-1,x1=-1,y2=-1,x2=-1;
        
        for(int i=0;i<N;i++){
            for(int j=0;j<N;j++){
                
                long res=principles[getPrincpleDiagIndex(i, j, N)]+secondaries[getSecondaryDiagIndex(i, j)] - mat[i][j];
                
                //System.out.println("i: "+i +" j: "+j+" "+ " score: " + res + " princ: "+ getPrincpleDiagIndex(i, j, N) + " sec: "+getSecondaryDiagIndex(i, j) );
                
                
                
                
                if((i+j)%2 ==0){
                    
                    
                    
                    if(res>bestWhite){
                        bestWhite=res;
                        y1=i+1;
                        x1=j+1;
                    }
                    
                }
                else{
                    if(res>bestBlack){
                        
                        bestBlack=res;
                        y2=i+1;
                        x2=j+1;
                        
                    }
                    
                }
                
            }
            
            
            
            
        }
        System.out.println(bestBlack+bestWhite);
        System.out.println(y1 + " "+x1 + " "+y2 + " "+x2);
        
    }
    
    public static int getPrincpleDiagIndex(int i, int j,int N){
        
        if(i>j){
            
            return N + (i-j-1);
            
        }
        
        else{
            
            return j-i;
        }
        
    }
    
    public static int getSecondaryDiagIndex(int i, int j){
        return i+j;
    }

}
