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
input = stdin.buffer.readline

n = int(input())
board = [list(map(int, input().split())) for i in range(n)]
d1 = [0] * (2 * n - 1)
d2 = [0] * (2 * n - 1)
for r in range(n):
    for c in range(n):
        d1[n - 1 + r - c] += board[r][c]
        d2[r + c] += board[r][c]
best = [-1] * 2
bestv = [None] * 2
for r in range(n):
    for c in range(n):
        p = (r + c) % 2
        cur = d1[n - 1 + r - c] + d2[r + c] - board[r][c]
        if cur > best[p]:
            best[p] = cur
            bestv[p] = [str(r + 1), str(c + 1)]
print(sum(best))
print(" ".join(sum(bestv, [])))
