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 $*a*_{*ij*}$ $(0 ≤ *a*_{*ij*} ≤ 10^{9})$ — 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: $*x*_{1}, *y*_{1}, *x*_{2}, *y*_{2}$ $(1 ≤ *x*_{1}, *y*_{1}, *x*_{2}, *y*_{2} ≤ *n*)$, 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.