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
_data = iter(map(int, stdin.read().split()))
n = next(_data)
b = n - 1
m = 2 * n
a = [[0] * n for _ in range(n)]
rs = [0] * m
cs = [0] * m
for i in range(n):
    for j in range(n):
        x = next(_data)
        u, v = i + j, i - j + b
        a[i][j] = x
        rs[u] += x
        cs[v] += x
ans = [-1] * 2
pos = [0] * 4
for i in range(n):
    for j in range(n):
        u, v = i + j, i - j + b
        t = rs[u] + cs[v] - a[i][j]
        p = (i + j) & 1
        if t > ans[p]:
            ans[p] = t
            pos[p << 1], pos[(p << 1) + 1] = i + 1, j + 1
print(sum(ans))
print(' '.join(map(str, pos)))


