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 codeforces;

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

public class C {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter writer = new PrintWriter(System.out);
    StringTokenizer stringTokenizer;

    C() throws IOException {
//        reader = new BufferedReader(new FileReader("bridges.in"));
//        writer = new PrintWriter(new FileWriter("bridges.out"));
    }

    String next() throws IOException {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(reader.readLine());
        }
        return stringTokenizer.nextToken();
    }

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

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

    final int MOD = 1000 * 1000 * 1000 + 7;
    int sum(int a, int b) {
        a += b;
        return a >= MOD ? a - MOD : a;
    }
    int product(int a, int b) {
        return (int)(1l * a * b % MOD);
    }
    int pow(int x, int k) {
        int result = 1;
        while(k > 0) {
            if(k % 2 == 1) {
                result = product(result, x);
            }
            x = product(x, x);
            k /= 2;
        }
        return result;
    }
    int inv(int x) {
        return pow(x, MOD - 2);
    }

    void solve() throws IOException {
        int n = nextInt();
        int[][] a = new int[n][n];
        long[] u = new long[2 * n];
        long[] v = new long[2 * n];
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < n; j++) {
                a[i][j] = nextInt();
                u[i + j] += a[i][j];
                v[n + i - j] += a[i][j];
            }
        }
        long[] s = {-1, -1};
        int[] r = new int[2];
        int[] c = new int[2];
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < n; j++) {
                long f = u[i + j] + v[n + i - j] - a[i][j];
                if(s[i + j & 1] < f) {
                    s[i + j & 1] = f;
                    r[i + j & 1] = i + 1;
                    c[i + j & 1] = j + 1;
                }
            }
        }
        writer.println(s[0] + s[1]);
        writer.println(String.format("%d %d %d %d", r[0], c[0], r[1], c[1]));
        writer.close();
    }

    public static void main(String[] args) throws IOException {
        new C().solve();
    }
}
