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
import sys 
input=sys.stdin.readline 
n=int(input())
mat=[]

for i in range(n):
    mat.append([int(i) for i in input().split()])
pri=[0]*(2*n+1)
sec=[0]*(2*n+1)
for i in range(n):
    for j in range(n):
        pri[i-j+n]+=mat[i][j]
        sec[i+j]+=mat[i][j]
resw=-1 
resb=-1 
indw=[]
indb=[]
for i in range(n):
    for j in range(n):
        curr=pri[i-j+n]+sec[i+j]-mat[i][j]
        if (i+j)&1:
            #i am blck 
            if curr>resb:
                resb=curr 
                indb=[i+1,j+1]
        else: 
            if curr>resw:
                resw=curr 
                indw=[i+1,j+1]
print(resw+resb)
print indb[0],indb[1],
print indw[0],indw[1]