How many balloons do I need in each corner? You have a square board with a bunch of items laid out on it in one of a \$3 \times 3\$ grid of cells and you want to lift it up using balloons, but you can only attach balloons to the corners of the board. Your task is to determine the minimum number of balloons in each corner to make sure the board won't tip over in flight, but can still lift all its contents.

"Physics" Model


Each balloon can lift 0.25kg (these are very strong balloons)
The board itself weighs 1kg, so you would need 1 balloon in each corner to lift an empty board
Items in each corner cell only exert force on their respective corners (i.e. 4 balloons are needed in the corresponding corner per kg)
Items on each edge cell split their force evenly between their neighboring corners (i.e. 2 balloons on each of the two corresponding corners per kg)
Items in the center cell split their force evenly across all corners (i.e. 1 balloon is needed in each corner per kg)


Example Test Cases

1

Input:
0 0 0
0 0 0
0 0 0

Output:
1 1
1 1


2

Input:
1 2 1
2 4 2
1 2 1

Output:
17 17
17 17


3

Input:
5 0 0
0 0 2
0 1 0

Output:
21 5
 3 7


4

Input:
12  9 35
 1 32  2
 4  6 18

Output:
101 195
 63 121


5

Input:
9999 9999 9999
9999 9999 9999
9999 9999 9999

Output:
89992 89992
89992 89992


6

Input:
9999    2 9001
   0 9999 9999
9999  999 9999

Output:
50000 66006
51994 71992


Rules and Assumptions


You may assume each cell is filled with a whole number between \$0\$ and \$9999\$ kg weight worth of items
Use any convenient format for I/O
Shortest code wins!
Jelly, 14 bytes

3Ḷ×þ`ZU$Ƭ×µ§§‘


Try it online!

Takes input as a 3x3 matrix and outputs a list going clockwise starting from the bottom-right.

Explanation

3Ḷ×þ`ZU$Ƭ×µ§§‘     Main Link
3Ḷ                 [0, 1, 2]
  ×þ`              outer product by multiplication with itself ([0, 0, 0], [0, 1, 2], [0, 2, 4])
        Ƭ          (include the original, plus) rotate clockwise until results are no longer unique (4 results total)
     ZU$           zip and upend (clockwise rotation)
         ×         vectorized multiply with original (gets the workload distributions to each balloon)
           §§      sum results for each balloon (vectorized-sum rows in the matrix; sum the results)
              ‘    increment