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
n = int(raw_input())

ns = []

for i in xrange(n):
    line = map(int, raw_input().split())
    ns.append(line)

d1, d2 = {}, {}
for i in xrange(-n + 1, n):
    tot = 0
    for j in xrange(n):
        y = j
        x = i + j
        if y < 0 or x < 0 or y >= n or x >= n:
            continue
        tot += ns[y][x]
    d1[i] = tot

for i in xrange(0, n + n):
    tot = 0
    for j in xrange(n):
        y = j
        x = i - j
        if y < 0 or x < 0 or y >= n or x >= n:
            continue
        tot += ns[y][x]
    d2[i] = tot

#print d1
#print d2

maxi1, maxi2 = 0, 0
p1, p2 = (0, 0), (0, 1)
for i in xrange(-n + 1, n):
    for j in xrange(0, n + n):
        if i % 2 == 0 and j % 2 == 0:
            y = abs(i - j) / 2
            x = i + y
            if 0 <= x < n and 0 <= y < n:
                tot = d1[i] + d2[j] - ns[y][x]
                if tot > maxi1:
                    maxi1 = tot
                    p1 = (y, x)
        elif i % 2 == 1 and j % 2 == 1:
            y = abs(i - j) / 2
            x = i + y
            if 0 <= x < n and 0 <= y < n:
                tot = d1[i] + d2[j] - ns[y][x]
                if tot > maxi2:
                    maxi2 = tot
                    p2 = (y, x)
        else:
            continue
print maxi1 + maxi2
print p1[0] + 1, p1[1] + 1, p2[0] + 1, p2[1] + 1

