Unique Count In Rows/Columns

This game is for 2 players.
Start by drawing an n-by-n grid on paper. (I suggest an n of about 12
for beginners.)
Players take turns filling in the grid's squares, one empty square
being filled in on each move.
Each player fills in a total of floor(n^2 /4) squares.
(So a total of 2*floor(n^2 /4) squares are filled in all together.)
Scoring is as follows:
Player 1 gets a point for every ROW with a unique number of filled-in
squares in it. In other words, every row that counts does not have a
number of filled-in squares that any other row also has.
Player 2 gets a point for every COLUMN with a unique number of filled-
in squares in it.

Variation:
Players on their moves each draw cards from a regular card deck (no
jokers).
The cards are not placed back, unless n is big enough that the card
would run out -- in which case just reshuffle and reuse the deck as
needed.
The player moving then writes down the number of the card in the empty
square, instead of simply filling the square in.
(Ace = 1, jack = 11, queen = 12, king = 13.)
Then, as before, each player fills in floor(n^2/4) squares. Scoring is
as follows:
Player 1 gets a point for every ROW with a unique SUM of the values of
the filled-in squares in it. In other words, every row that counts
does not have a SUM of the values of filled-in squares that any other
row also has.
Player 2 gets a point for every COLUMN with a unique sum of the values
of the filled-in squares in it.
Thanks,
Leroy Quet