Multiples/Divisors Blob Game

This game is for 2 players.

Start with an n-by-n grid drawn on paper. (n should be at least 8, I suggest.)

The first player fills in any one of the grid's squares to start.

Thereafter, players continue to take turns each filling in one empty square each turn.
After the first move, each square that is filled in must be immediately next to (in the direction of above, below, left of, or right of) at least one square that is already filled in.

After both players have each filled in floor(n^2/4) squares (for 2*floor(n^2/4) squares filled in total), the game is over.

Player 1 gets as a score the number of ROWS of the grid meeting this condition: Every run-length (of runs each of either all filled in squares or all empty squares) in that particular row is either a multiple or divisor of every other run length in that row.

Player 2 gets as a score the number of COLUMNS of the grid meeting this condition: Every run-length (of runs each of either all filled in squares or all empty squares) in that particular column is either a multiple or divisor of every other run length in that column.

The player with the largest score wins.

Example: (n=12)

o o * o o o o o o o o o
o o * * o o * * o o o o
o o o * * o * * o * * *
o o o o * * * * * * o *
o o o * * * * o o * * *
o o o * o o * o * * * o
o * * * * * * * o o * o
o * o o * * o * * o * *
* * o o * * * * o o * *
* o o o * o o * * o * o
* * o * * * o o o * * *
o o o o o * * o * * * o

Run-lengths of rows:
(2,1,9)
(2,2,2,2,4) Point!
(3,2,1,2,1,3)
(4,6,1,1)
(3,4,2,3)
(3,1,2,1,1,3,1)
(1,7,2,1,1)
(1,1,2,2,1,2,1,2) Point!
(2,2,4,2,2) Point!
(1,3,1,2,2,1,1,1)
(2,1,3,3,3)
(5,2,1,3,1)

Run-lengths of columns:
(8,3,1)
(6,3,1,1,1) Point!
(2,4,1,5)
(1,2,1,3,3,1,1)
(2,3,1,5,1)
(3,2,1,3,1,2)
(1,6,1,1,2,1) Point!
(1,3,2,4,2)
(3,1,1,1,1,1,1,1,1,1) Point!
(2,4,4,2) Point!
(2,1,1,8) Point!
(2,3,2,2,1,1,1)

Player 2 wins, 5 to 3.

Thanks,
Leroy Quet