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 acc;
import java.util.*;
import java.io.*;

   public  class ACC { 
//************Main*****************//
         
         public static void main(String[] args) throws IOException
			 {
             //   PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
              //  Scanner in=new Scanner (System.in);
               InputStream inputStream = System.in;
                OutputStream outputStream = System.out;
                InputReader in = new InputReader(inputStream);
                PrintWriter out = new PrintWriter(outputStream);
                int n=in.nextInt();
                int m=n;
                long arr1[]=new long[n+m];
                long arr_1[]=new long[n+m+n];
                int arr[][]=new int[n][n];
                for(int i=n-1;i>=0;i--){
                    for(int j=0;j<m;j++){
                        int a=in.nextInt();
                        arr[i][j]=a;
                        arr1[j+n-i]+=a;
                        arr_1[j+n+i]+=a;
                    }
                }
                long mod=-1000000000;
                mod*=10000;
                int ans[][]=new int [2][2];
                long sum[]=new long[2];
                sum[0]=-1;
                sum[1]=-1;
                for(int t=0;t<2;t++){
                    
                for(int i=n-1;i>=0;i--){
                    for(int j=0;j<m;j++){
                        if(arr1[j+n-i]+arr_1[j+n+i]-arr[i][j]>sum[t]){
                            ans[t][0]=i;
                            ans[t][1]=j;
                            sum[t]=arr1[j+n-i]+arr_1[j+n+i]-arr[i][j];
                        }
                    }
                }
                int i1=ans[t][0];
                int j1=ans[t][1];
                
                for(int i=n-1;i>=0;i--){
                    for(int j=0;j<m;j++){
                        if((j+n-i)==(j1+n-i1)||(j+n+i)==(j1+n+i1)){
                           arr1[j+n-i]=mod;
                           arr_1[j+n+i]=mod;
                        }
                    }
                }
                }
                out.println(sum[0]+sum[1]);
                out.print((n-ans[0][0])+" "+(ans[0][1]+1)+" "+(n-ans[1][0])+" "+(ans[1][1]+1));
                out.close();
         }
         
   }
    class Pair implements Comparable<Pair>{
    int x,y;
    public  Pair(int X,int Y){
        super();
x=X;
y=Y;
}
    @Override
      public int compareTo(Pair p){
       return Integer.compare(x, p.x);
}
  }
class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }
    public long nextLong(){
        return Long.parseLong(next());
    }
}