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
def pluss(i,j):
    return plus[i+j]

def minuss(i,j):
    return minus[n-i+1+j]


n=input()
plus=[0]*(2*n+1)
minus=[0]*(2*n+1)

arr=[0]
for i in range(n):
    k=[0]+map(int,raw_input().split())
    arr.append(k)
for i in range(1,n+1):
    for j in range(1,n+1):
        #print i,j
        k=arr[i][j]
        plus[i+j]+=k
        minus[n-i+1+j]+=k
ans=0
m=0
oth=[]
for i in range(1,n+1):
    for j in range(1,n+1):
        k=pluss(i,j)+minuss(i,j)-arr[i][j]
        if k>=m:
            m=k
            oth=[i,j]
ans+=m
#print m
a=oth[0]+oth[1]
b=n-oth[0]+1+oth[1]
m=0
sec=[]
for i in range(1,n+1):
    for j in range(1,n+1):
        if abs(i+j-a)%2==1 and abs(n-i+1+j-b)%2==1  :
            k=pluss(i,j)+minuss(i,j)-arr[i][j]
            if k>=m:
                m=k
                sec=[i,j]
ans+=m
print ans
a,b=oth
c,d=sec
print a,b,c,d

