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 itertools   import *
from collections import *
from operator    import *
from bisect      import *
from fractions   import *

Ii = lambda: map(int, raw_input().split())
Is = lambda: raw_input().split()
ri = raw_input

n = input()
A = [Ii() for _ in xrange(n)]

plusDiag = []
for i in xrange(n):
  plusDiag.append(sum(A[i-j][j] for j in xrange(i+1)))
for i in xrange(n,2*n-1):
  plusDiag.append(sum(A[i-j][j] for j in xrange(i-n+1,n)))

minusDiag = []
for i in xrange(n-1,0,-1):
  minusDiag.append(sum(A[-i+j][j] for j in xrange(i,n)))

for i in xrange(0,-n,-1):
  minusDiag.append(sum(A[-i+j][j] for j in xrange(n+i)))

ex=ey=ox=oy=0
evenBest = -1
oddBest  = -1

for x in xrange(n):
  for y in xrange(n):
    value = plusDiag[x+y] + minusDiag[x-y+n-1] - A[x][y]
    if (x+y)%2==1:
      if value>oddBest:
        oddBest = value
        ox = x+1
        oy = y+1
    else:
      if value>evenBest:
        evenBest = value
        ex = x+1
        ey = y+1

print evenBest + oddBest
print ex,ey,ox,oy