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
import sys

input = sys.stdin.readline

def pluss(i, j):
    return plus[i + j]


def minuss(i, j):
    return minus[n - i + 1 + j]


n = int(input())
plus = [0] * (2 * n + 1)
minus = [0] * (2 * n + 1)

arr = [0]
for i in range(n):
    k = [0] + map(int, input().split(' '))
    arr.append(k)

for i in range(1, n + 1):
    for j in range(1, n + 1):
        k = arr[i][j]

        plus[i + j] += k
        minus[n - i + 1 + j] += k

m = -1
x1 = 0
y1 = 0
x2 = 0
y2 = 0
s1 = -1
s2 = -1
for i in range(1, n + 1):
    for j in range(1, n + 1):
        k = pluss(i, j) + minuss(i, j) - arr[i][j]
        if (i + j) % 2 == 0:
            if k > s1:
                s1 = k
                x1 = i
                y1 = j
        else:
            if k > s2:
                s2 = k
                x2 = i
                y2 = j

print(s1 + s2)
print x1,y1,x2,y2