463_C. Gargari and Bishops
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
```python
import sys
input=sys.stdin.buffer.readline
t=1    
for __ in range(t):
    a=[]
    n=int(input())
    for i in range(n):
        b=list(map(int,input().split()))
        a.append(b)
    dr={}
    di={}
    for i in range(n):
        for j in range(n):
            dr[i+j]=dr.get(i+j,0)+a[i][j]
            di[i+n-j+1]=di.get(i+n-j+1,0)+a[i][j]
    ind1=[0]*2
    ind2=[0]*2
    maxi1=0
    maxi2=0
    for i in range(n):
        for j in range(n):
            #if maxi<(dr[i+j]+di[i+n-j+1]-a[i][j]):
            if ((i+j)&1)==1:
                if maxi1<=(dr[i+j]+di[i+n-j+1]-a[i][j]):    
                    maxi1=(dr[i+j]+di[i+n-j+1]-a[i][j])
                    ind1[0]=i+1
                    ind1[1]=j+1
            else:
                if maxi2<=(dr[i+j]+di[i+n-j+1]-a[i][j]):    
                    maxi2=(dr[i+j]+di[i+n-j+1]-a[i][j])
                    ind2[0]=i+1
                    ind2[1]=j+1
                    
    
    
    print(maxi1+maxi2)
    print(ind1[0],ind1[1],ind2[0],ind2[1])
```