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
from sys import stdin
 
def empty_list(length):
    return [0] * (2 * length - 1)
 
def read_input():
    n = int(stdin.readline())
    nw_diagonals, se_diagonals = empty_list(n), empty_list(n)
    matrix = [[0] * n for _ in range(n)]
    for rnb in range(n):
        row = [int(x) for x in stdin.readline().split()]
        for cnb, el in enumerate(row):
            nw_diagonals[(n - 1) - rnb + cnb] += el
            se_diagonals[rnb + cnb] += el
            matrix[rnb][cnb] = el
 
    return n, nw_diagonals, se_diagonals, matrix
 
if __name__ == "__main__":
    n, nw_diagonals, se_diagonals, matrix = read_input()
 
    # max, x-coord, y-coord for white and black bishops
    mw = xw = yw = mb = xb = yb = 0
    for i in range(n):
        for j in range(n):
            cur_sum = (nw_diagonals[(n - 1) - i + j] +
                      se_diagonals[i + j] -
                      matrix[i][j])
 
            if (i + j) % 2:
                if cur_sum > mw:
                    mw, xw, yw = cur_sum, i, j
            else:
                if cur_sum > mb:
                    mb, xb, yb = cur_sum, i, j
 
    print(mw+mb)
    if xb==xw and yb == yw:
        print ' '.join(map(str, (1,1,1,2)))
    else:
        print ' '.join(map(str, (xb+1, yb+1, xw+1, yw+1)))