|Codeforces Round #264 (Div. 2)|
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 ≤ 109) — 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.
1 1 1 1
2 1 1 0
1 1 1 0
1 0 0 1
2 2 3 2