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 P463C {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
//        int test = in.nextInt();
        int test = 1;
        while(test-->0) {
            int n = in.nextInt();
            long[][] grid = new long[n][n];
            for (int i = 0; i < n; i++) {
                grid[i] = in.nextLongArray(n);
            }
            long[] dp = new long[2 * n];
            long[] dp2 = new long[2 * n];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    dp[i + j] += grid[i][j];
                    dp2[n - (i - j)] += grid[i][j];
                }
            }
            int even_row = 0, even_col = 0;
            long maxEven = 0;
            int odd_row = 0, odd_col = 1;
            long maxOdd = 0;
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if ((i + j) % 2 == 0) {
                        if (dp[i + j] + dp2[n - (i - j)] - grid[i][j] > maxEven) {
                            even_row = i;
                            even_col = j;
                            maxEven = dp[i + j] + dp2[n - (i - j)] - grid[i][j];
                        }
                    } else {
                        if (dp[i + j] + dp2[n - (i - j)] - grid[i][j] > maxOdd) {
                            odd_row = i;
                            odd_col = j;
                            maxOdd = dp[i + j] + dp2[n - (i - j)] - grid[i][j];
                        }
                    }
                }
            }

            pw.println(maxEven + maxOdd);
            pw.println((even_row + 1) + " " + (even_col + 1) + " " + (odd_row + 1) + " " + (odd_col + 1));
        }
        pw.close();
    }

    private static int[][] flip(int[][] grid) {
        int[][] g = new int[grid.length][grid.length];
        for (int i = 0; i < grid.length; i++) {
            for (int j = 0; j < grid.length; j++) {
                g[i][grid.length - 1 - j] = grid[i][j];
            }
        }
        return g;
    }

    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;

        public InputReader(InputStream st) {
            this.stream = st;
        }

        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int [] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }
        public long[] nextLongArray(int n) {
            long [] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextLong();
            }
            return a;
        }

        public static int[] shuffle(int[] a, Random gen)
        { for(int i = 0, n = a.length;i < n;i++)
        { int ind = gen.nextInt(n-i)+i;
            int d = a[i];
            a[i] = a[ind];
            a[ind] = d;

        }
            return a;
        }


        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
}
