class GameBoard:

def $\_\_$init$\_\_($self$,$ size$)$:

self.size $=$ size

self.num$\_$disks $=[0]*$ size

self.items $=[[0]*$ size for $\_$ in range$($size$)]$

self.points $=[0]*2$ # points$[0]$ for player $1,$ points$[1]$ for player $2$

def num$\_$free$\_$positions$\_$in$\_$column$($self$,$ column$)$:

$"""$Returns the number of free positions in the given column."""

if column $<0$ or column $>=$ self.size:

return $0$

return self.size $-$ self.num$\_$disks$[$column$]$

def game$\_$over$($self$)$:

$"""$Returns True if the game is over $($no free positions$),$ otherwise False."""

return all$($disk$\_$count $>=$ self.size for disk$\_$count in self.num$\_$disks$)$

def display$($self$)$:

$"""$Displays the current state of the game board."""

for row in range$($self$.$size $-1,-1,-1)$:

for col in range$($self$.$size$)$:

if self.items$[$col$][$row$]==0$:

print$("",$ end$="")$

elif self.items$[$col$][$row$]==1$:

print$("$o$",$ end$="")$

elif self.items$[$col$][$row$]==2$:

print$("$x$",$ end$="")$

print$()$

print$("-"*($self$.$size $*2-1))$

print$("".$join$($str$($col$)$ for col in range$($self$.$size$)))$

print$($f$"$Points player $1$: $\{$self$.$points$[0]\}")$

print$($f$"$Points player $2$: $\{$self$.$points$[1]\}")$

def num$\_$new$\_$points$($self$,$ column, row, player$)$:

$"""$Calculates the number of newly created $4-$in$-$a$-$row sequences after adding a disk."""

directions $=[$

$(1,0),$ # Horizontal

$(0,1),$ # Vertical

$(1,1),$ # Diagonal down$-$right

$(1,-1)$ # Diagonal down$-$left

$]$

total$\_$points $=0$ # To count newly created $4-$in$-$a$-$row sequences

for dx$,$ dy in directions:

count $=1$ # Start counting with the current disk

# Check in the positive direction

for step in range$(1,4)$: # Check $3$ steps in the positive direction

new$\_$col $=$ column $+$ step $*$ dx

new$\_$row $=$ row $+$ step $*$ dy

if $0<=$ new$\_$col $<$ self.size and $0<=$ new$\_$row $<$ self.size:

if self.items$[$new$\_$col$][$new$\_$row$]==$ player:

count $+=1$

else:

break # Stop if we hit a different disk

else:

break # Stop if out of bounds

# Check in the negative direction

for step in range$(1,4)$: # Check $3$ steps in the negative direction

new$\_$col $=$ column $-$ step $*$ dx

new$\_$row $=$ row $-$ step $*$ dy

if $0<=$ new$\_$col $<$ self.size and $0<=$ new$\_$row $<$ self.size:

if self.items$[$new$\_$col$][$new$\_$row$]==$ player:

count $+=1$

else:

break # Stop if we hit a different disk

else:

break # Stop if out of bounds

# If count is $4,$ we've created a new $4-$in$-$a$-$row

if count $>=4$:

total$\_$points $+=1$ # Count this as a new point

return total$\_$points

def add$($self$,$ column, player$)$:

$"""$Inserts a disk into the specified column for the given player."""

if column $<0$ or column $>=$ self.size or self.num$\_$disks$[$column$]>=$ self.size:

return False # Invalid column or column is full

# Determine the first available row

row $=$ self.num$\_$disks$[$column$]$

# Place the disk on the board

self.items$[$column$][$row$]=$ player

# Increment the number of disks in this column

self.num$\_$disks$[$column$]+=1$

# Calculate new points created by this move

new$\_$points $=$ self.num$\_$new$\_$points$($column$,$ row, player$)$

self.points$[$player $-1]+=$ new$\_$points # Update the player's points

return True