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.lang.*;
import java.io.*;
import java.math.*;
     
public class Main{
    public static int mod=(int)Math.pow(10,9)+7;
    public static void main (String[] args) throws java.lang.Exception{
        //BufferedReader in=new BufferedReader(new InputStreamReader(System.in));
        InputReader in=new InputReader(System.in);
        PrintWriter out=new PrintWriter(System.out);
        int n=in.readInt();
        //0-2*n-2  -n+1  n-1
        long[] a=new long[2*n-1];
        long[] b=new long[2*n-1];
        int[][] xyz=new int[n][n];
        long maxeven=0,maxodd=0,evenx=0,eveny=0,oddx=0,oddy=1;
        for(int i=0;i<n;i++)
            for(int j=0;j<n;j++){
                int x=in.readInt();
                xyz[i][j]=x;
                a[i+j]+=x;
                b[n-1+i-j]+=x;
            }
        for(int i=0;i<n;i++)
            for(int j=0;j<n;j++){
                int x=xyz[i][j];
                if((i+j)%2==0){
                    if(maxeven<a[i+j]+b[n-1+i-j]-x){
                        evenx=i;
                        eveny=j;
                        maxeven=a[i+j]+b[n-1+i-j]-x;
                    }
                }else{ 
                    if(maxodd<a[i+j]+b[n-1+i-j]-x){
                        oddx=i;oddy=j;
                        maxodd=a[i+j]+b[n-1+i-j]-x;
                    }
                }
            }
        out.println(maxeven+maxodd);
        out.println((evenx+1)+" "+(eveny+1)+" "+(oddx+1)+" "+(oddy+1));
        out.close();
    }
    static final class InputReader{
        private final InputStream stream;
        private final byte[] buf=new byte[1024];
        private int curChar;
        private int numChars;
        public InputReader(InputStream stream){this.stream=stream;}
        private int read()throws IOException{
            if(curChar>=numChars){
                curChar=0;
                numChars=stream.read(buf);
                if(numChars<=0)
                    return -1;
            }
            return buf[curChar++];
        }
        public final int readInt()throws IOException{return (int)readLong();}
        public final long readLong()throws IOException{
            int c=read();
            while(isSpaceChar(c)){
                c=read();
                if(c==-1) throw new IOException();
            }
            boolean negative=false;
            if(c=='-'){
                negative=true;
                c=read();
            }
            long res=0;
            do{
                if(c<'0'||c>'9')throw new InputMismatchException();
                res*=10;
                res+=(c-'0');
                c=read();
            }while(!isSpaceChar(c));
            return negative?(-res):(res);
        }
        public final int[] readIntBrray(int size)throws IOException{
            int[] arr=new int[size];
            for(int i=0;i<size;i++)arr[i]=readInt();
            return arr;
        }
        public final String readString()throws IOException{
            int c=read();
            while(isSpaceChar(c))c=read();
            StringBuilder res=new StringBuilder();
            do{
                res.append((char)c);
                c=read();
            }while(!isSpaceChar(c));
            return res.toString();
        }
        public final String readLine()throws IOException{
            int c=read();
            while(isSpaceChar(c))c=read();
            StringBuilder res=new StringBuilder();
            do{
                res.append((char)c);
                c=read();
            }while(!isSpaceChar(c));
            return res.toString();
        }
        private boolean isSpaceChar(int c){
            return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
        }
    }
}