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 = input()
a = [[0 for i in xrange(n)] for j in xrange(n)]

for i in xrange(n):
    a[i] = map(int, raw_input().strip().split())

d1 = [0 for i in xrange(2 * n - 1)] # sum
d2 = [0 for i in xrange(2 * n - 1)] # diff

for i in xrange(n):
    x, y = 0, i
    while x < n and y < n and x >= 0 and y >= 0:
        d1[i] += a[x][y]
        x, y = x + 1, y - 1
    
    x, y = 0, i
    while x < n and y < n and x >= 0 and y >= 0:
        d2[i + n - 1] += a[x][y]
        x, y = x + 1, y + 1

for i in xrange(1, n):
    x, y = i, n - 1
    while x < n and y < n and x >= 0 and y >= 0:
        d1[i + n - 1] += a[x][y]
        x, y = x + 1, y - 1

    x, y = i, 0
    while x < n and y < n and x >= 0 and y >= 0:
        d2[i - 1] += a[x][y]
        x, y = x + 1, y + 1

eve = odd = -1
p0 = [0, 0]
p1 = [0, 0]
for r in xrange(n):
    for c in xrange(n):
        s = r + c
        diff = r - c
        if diff <= 0: diff = n - 1 - diff
        else: diff -= 1
        earn = d1[s] + d2[diff] - a[r][c]
        if s & 1:
            if earn > odd:
                odd = earn
                p1 = [r, c]
        else:
            if earn > eve:
                eve = earn
                p0 = [r, c]

ans = eve + odd
print ans
print p0[0] + 1, p0[1] + 1, p1[0] + 1, p1[1] + 1