





"""simple docstring"""
def 		_SCREAMING_SNAKE_CASE			():
 return [list(range(1000 - i  ,     -1000 - i  ,     -1			)			) for i in range(1000			)]


__UpperCamelCase     :						Union[str, Any]						       =  generate_large_matrix()
__UpperCamelCase     :						Tuple						       =  (
    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
    [[3, 2], [1, 0]],
    [[7, 7, 6]],
    [[7, 7, 6], [-1, -2, -3]],
    grid,
)

def 		_SCREAMING_SNAKE_CASE			(_UpperCAmelCase					:    list[list[int]]			):
 assert all(row == sorted(_UpperCAmelCase  ,     reverse=_UpperCAmelCase			) for row in grid			)
 assert all(list(_UpperCAmelCase			) == sorted(_UpperCAmelCase  ,     reverse=_UpperCAmelCase			) for col in zip(*_UpperCAmelCase			)			)

def 		_SCREAMING_SNAKE_CASE			(_UpperCAmelCase					:    list[int]			):
 lowerCAmelCase    				= 0
 lowerCAmelCase    				= len(_UpperCAmelCase			) - 1

 # Edge cases such as no values or all numbers are negative.
 if not array or array[0] < 0:
  return 0

 while right + 1 > left:
  lowerCAmelCase    				= (left + right) // 2
  lowerCAmelCase    				= array[mid]

  # Num must be negative and the index must be greater than or equal to 0.
  if num < 0 and array[mid - 1] >= 0:
   return mid

  if num >= 0:
   lowerCAmelCase    				= mid + 1
  else:
   lowerCAmelCase    				= mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
 return len(_UpperCAmelCase			)

def 		_SCREAMING_SNAKE_CASE			(_UpperCAmelCase					:    list[list[int]]			):
 lowerCAmelCase    				= 0
 lowerCAmelCase    				= len(grid[0]			)

 for i in range(len(_UpperCAmelCase			)			):
  lowerCAmelCase    				= find_negative_index(grid[i][:bound]			)
  total += bound
 return (len(_UpperCAmelCase			) * len(grid[0]			)) - total

def 		_SCREAMING_SNAKE_CASE			(_UpperCAmelCase					:    list[list[int]]			):
 return len([number for row in grid for number in row if number < 0]			)

def 		_SCREAMING_SNAKE_CASE			(_UpperCAmelCase					:    list[list[int]]			):
 lowerCAmelCase    				= 0
 for row in grid:
  for i, number in enumerate(_UpperCAmelCase			):
   if number < 0:
    total += len(_UpperCAmelCase			) - i
    break
 return total

def 		_SCREAMING_SNAKE_CASE			():
 from timeit import timeit

 print('Running benchmarks'			)
 lowerCAmelCase    				= (
     'from __main__ import count_negatives_binary_search, '
     'count_negatives_brute_force, count_negatives_brute_force_with_break, grid'
 )
 for func in (
     "count_negatives_binary_search",  # took 0.7727 seconds
     "count_negatives_brute_force_with_break",  # took 4.6505 seconds
     "count_negatives_brute_force",  # took 12.8160 seconds
 ):
  lowerCAmelCase    				= timeit(F'{func}(grid=grid)'  ,     setup=_UpperCAmelCase  ,     number=500			)
  print(F'{func}() took {time:0.4f} seconds'			)


if __name__ == "__main__":
       import doctest

       doctest.testmod()
       benchmark()












'''simple docstring'''






from __future__ import annotations

import math







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase ) ->				int:



			"""simple docstring"""


			if depth < 0:
						raise ValueError("""Depth cannot be less than 0""" )

			if not scores:
						raise ValueError("""Scores cannot be empty""" )

			if depth == height:
						return scores[node_index]

			return (
			    max(
			        minimax(depth + 1    ,	node_index * 2    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	minimax(depth + 1    ,	node_index * 2 + 1    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	)
			    if is_max
			    else min(
			        minimax(depth + 1    ,	node_index * 2    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	minimax(depth + 1    ,	node_index * 2 + 1    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	)
			)







def 					_a						(       ) ->				None:



			"""simple docstring"""


			__snake_case					:      Union[str, Any]							      =     [90, 23, 6, 33, 21, 65, 123, 3_4423]
			__snake_case					:      Optional[int]							      =     math.log(len(_lowerCamelCase )    ,	2 )
			print(F'''Optimal value : {minimax(0    ,	0    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )}''' )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()


