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
a=int(input())
x = [list(map(int, raw_input().split(' '))) for i in range(a)]
s = [0] * (5*a)
t = [0] * (5*a)
for i in range(a):
    for j in range(a):
        s[i-j] += x[i][j]
        t[i+j] += x[i][j]


e1 = 0
e2 = 0
emax = 0
o1 = 0
o2 = 0
omax = 0
for i in range(a):
    for j in range(a):
        if ((i+j)%2==0):
            diag1 = s[i-j]
            diag2 = t[i+j]
            
            if diag1 + diag2 - x[i][j] >= emax:
                e1 = i
                e2 = j
                emax = diag1 + diag2 - x[i][j]
        if (i+j)%2==1:
            diag1 = s[i-j]
            diag2 = t[i+j]
            if diag1+diag2-x[i][j]>=omax:
                o1=i
                o2=j
                omax = diag1+diag2-x[i][j]

print(emax+omax)
print(str(o1+1)+' '+str(o2+1)+' '+str(e1+1)+' '+str(1+e2))