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.*;
import java.util.*;

public class c {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int N = Integer.parseInt(br.readLine());
		long a[][] = new long[N][N], h[] = new long[4100], v[] = new long[4100];
		Arrays.fill(h, 0);
		Arrays.fill(v, 0);
		for(int i = 0; i < N; i++) {
			StringTokenizer st = new StringTokenizer(br.readLine());
			for(int j = 0; j < N; j++) {
				a[i][j] = Long.parseLong(st.nextToken());
				h[2000+i-j] += a[i][j];
				v[i+j] += a[i][j];
			}
		}
		long max1 = 0, max2 = 0;
		int x1 = 2, y1 = 2, x2 = 2, y2 = 1;
		for(int i = 0; i < N; i++) {
			for(int j = i%2; j < N; j+=2) {
				long val = h[2000+i-j] + v[i+j] - a[i][j];
				if(val > max1) {
					max1 = val;
					x1 = i+1;
					y1 = j+1;
				}
			}
		}
		for(int i = 0; i < N; i++) {
			for(int j = (i+1)%2; j < N; j+=2) {
				long val = h[2000+i-j] + v[i+j] - a[i][j];
				if(val > max2) {
					max2 = val;
					x2 = i+1;
					y2 = j+1;
				}
			}
		}
		System.out.println(max1 + max2);
		System.out.println(x1 + " " + y1 + " " + x2 + " " + y2);
		br.close();
	}
}
