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.io.IOException;
import java.util.StringTokenizer;

public class GargariAndBishops {
	public static void main(String[] args) {
		MyScanner sc = new MyScanner();
		
		int N = sc.nextInt();
		
		long[] mins = new long[5000];
		long[] plus = new long[5000];
		int[][] board = new int[N][N];
		
		for (int r = 0; r < N; r++) {
			for (int c = 0; c < N; c++) {
				int a = sc.nextInt();
				board[r][c] = a;
				mins[r - c + 2000] += a;
				plus[r + c] += a;
			}
		}
		
		long black = 0;
		int br = -1, bc = -1;
		for (int r = 0; r < N; r++) {
			for (int c = r % 2; c < N; c += 2) {
				long score = mins[r - c + 2000] + plus[r + c] - board[r][c];
				if (score >= black) {
					br = r;
					bc = c;
					black = score;
				}
			}
		}
		
		long white = 0;
		int wr = -1, wc = -1;
		for (int r = 0; r < N; r++) {
			for (int c = (r + 1) % 2; c < N; c += 2) {
				long score = mins[r - c + 2000] + plus[r + c] - board[r][c];
				if (score >= white) {
					wr = r;
					wc = c;
					white = score;
				}
			}
		}
		
		System.out.println(black + white);
		System.out.println((br + 1) + " " + (bc + 1) + " " + (wr + 1) + " " + (wc + 1));
	}

	public static class MyScanner {
		BufferedReader br;
		StringTokenizer st;

		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		String nextLine() {
			String str = "";
			try { str = br.readLine(); }
			catch (IOException e) { e.printStackTrace(); }
			return str;
		}
	}
}