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
a = []
n = int(raw_input())
for _ in xrange(n):
    a.append(map(int, raw_input().split()))
l, r = {}, {}
for i in xrange(n):
    for j in xrange(n):
        r[i - j] = a[i][j] + r[i - j] if i - j in r else a[i][j]
        l[i + j] = a[i][j] + l[i + j] if i + j in l else a[i][j]
black, white = (-1, -1, -1), (-1, -1, -1)
for i in xrange(n):
    for j in xrange(n):
        t = l[i + j] + r[i - j] - a[i][j]
        if (i + j) % 2:
            black = max(black, (t, i, j))
        else:
            white = max(white, (t, i, j))
a1, x1, y1 = black
a2, x2, y2 = white
print (a1 + a2)
print x1 + 1, y1 + 1, x2 + 1, y2 + 1
