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 sys

input = sys.stdin.readline

n = int(input())

matrix = []
diagonal_main = [0] * (2 * n + 1)
diagonal_secondary = [0] * (2 * n + 1)
secondary_corresponds_main = {}

for i in range(n):
    matrix.append(map(int, input().split(' ')))

for i in range(n):
    for j in range(n):
        node = matrix[i][j]
        diagonal_main[i - j] += node
        diagonal_secondary[i + j] += node

max_odd = 0
x_odd = 0
y_odd = 0
max_even = 0
x_even = 0
y_even = 0

for i in range(n):
    for j in range(n):
        node = diagonal_secondary[i + j] + diagonal_main[i - j] - matrix[i][j]

        if (i + j) % 2 == 0:
            if node > max_odd:
                max_odd = node
                x_odd = i
                y_odd = j
        else:
            if node > max_even:
                max_even = node
                x_even = i
                y_even = j

print(max_odd + max_even)

if x_odd == x_even and y_odd == y_even:
    print x_odd + 1, y_odd + 1, x_even + 1, y_even + 2
else:
    print x_odd + 1, y_odd + 1, x_even + 1, y_even + 1
