A9631 | Gargari and Bishops

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).

The first line contains a single integer $n$ $(2<=n<=2000)$ . Each of the next $n$ lines contains $n$ integers $a_{ij}$ $(0<=a_{ij}<=10^{9})$ — description of the chessboard.

On the first line print the maximal number of dollars Gargari will get. On the next line print four integers: $x_{1},y_{1},x_{2},y_{2}$ $(1<=x_{1},y_{1},x_{2},y_{2}<=n)$ , where $x_{i}$ is the number of the row where the $i$ -th bishop should be placed, $y_{i}$ 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.