




from __future__ import annotations



def 						lowerCAmelCase		(		_lowerCAmelCase							:   int = 4	):




 """simple docstring"""







 UpperCAmelCase__							 =						abs(_lowerCAmelCase	) or 4
 return [[1 + x + y * row_size for x in range(_lowerCAmelCase	)] for y in range(_lowerCAmelCase	)]



def 						lowerCAmelCase		(		_lowerCAmelCase							:   list[list[int]]	):




 """simple docstring"""







 return reverse_row(transpose(_lowerCAmelCase	)	)
 # OR.. transpose(reverse_column(matrix))



def 						lowerCAmelCase		(		_lowerCAmelCase							:   list[list[int]]	):




 """simple docstring"""







 return reverse_row(reverse_column(_lowerCAmelCase	)	)
 # OR.. reverse_column(reverse_row(matrix))



def 						lowerCAmelCase		(		_lowerCAmelCase							:   list[list[int]]	):




 """simple docstring"""







 return reverse_column(transpose(_lowerCAmelCase	)	)
 # OR.. transpose(reverse_row(matrix))



def 						lowerCAmelCase		(		_lowerCAmelCase							:   list[list[int]]	):




 """simple docstring"""







 UpperCAmelCase__							 =						[list(_lowerCAmelCase	) for x in zip(*_lowerCAmelCase	)]
 return matrix



def 						lowerCAmelCase		(		_lowerCAmelCase							:   list[list[int]]	):




 """simple docstring"""







 UpperCAmelCase__							 =						matrix[::-1]
 return matrix



def 						lowerCAmelCase		(		_lowerCAmelCase							:   list[list[int]]	):




 """simple docstring"""







 UpperCAmelCase__							 =						[x[::-1] for x in matrix]
 return matrix



def 						lowerCAmelCase		(		_lowerCAmelCase							:   list[list[int]]	):




 """simple docstring"""







 for i in matrix:
  print(*_lowerCAmelCase	)


if __name__ == "__main__":
  _lowerCAmelCase						:   Optional[int]		=   make_matrix()
  print("\norigin:\n")
  print_matrix(matrix)
  print("\nrotate 90 counterclockwise:\n")
  print_matrix(rotate_aa(matrix))

  _lowerCAmelCase						:   Union[str, Any]		=   make_matrix()
  print("\norigin:\n")
  print_matrix(matrix)
  print("\nrotate 180:\n")
  print_matrix(rotate_aaa(matrix))

  _lowerCAmelCase						:   Optional[int]		=   make_matrix()
  print("\norigin:\n")
  print_matrix(matrix)
  print("\nrotate 270 counterclockwise:\n")
  print_matrix(rotate_aaa(matrix))











import math



def 						lowerCAmelCase		(		_lowerCAmelCase							:   int	):




 """simple docstring"""







 UpperCAmelCase__							 =						math.loga(math.sqrt(4 * positive_integer + 1	) / 2 + 1 / 2	)

 return exponent == int(_lowerCAmelCase	)



def 						lowerCAmelCase		(		_lowerCAmelCase							:   float = 1 / 1_2345	):




 """simple docstring"""







 UpperCAmelCase__							 =						0
 UpperCAmelCase__							 =						0

 UpperCAmelCase__							 =						3
 while True:
  UpperCAmelCase__							 =						(integer**2 - 1) / 4
  # if candidate is an integer, then there is a partition for k
  if partition_candidate == int(_lowerCAmelCase	):
   UpperCAmelCase__							 =						int(_lowerCAmelCase	)
   total_partitions += 1
   if check_partition_perfect(_lowerCAmelCase	):
    perfect_partitions += 1
  if perfect_partitions > 0:
   if perfect_partitions / total_partitions < max_proportion:
    return int(_lowerCAmelCase	)
  integer += 1


if __name__ == "__main__":
  print(F'''{solution() = }''')





