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
I = lambda : list(map(int,input().split()))

n,=I()
l=[]
for i in range(n):
	l.append(I())
d={};su={};s=0;an=[1,1,2,1]
for i in range(n):
	for j in range(n):
		d[i-j]=d.get(i-j,0)+l[i][j]
		su[i+j]=su.get(i+j,0)+l[i][j]
x=0;y=0
for i in range(n):
	for j in range(n):
		l[i][j]=d[i-j]+su[i+j]-l[i][j]
		if (i+j)%2:
			if l[i][j]>x:
				an[0],an[1]=i+1,j+1
				x=l[i][j]
		else:
			if l[i][j]>y:
				an[2],an[3]=i+1,j+1
				y=l[i][j]
s=x+y
print(s)
print(*an)
