



'''simple docstring'''





def        _SCREAMING_SNAKE_CASE  (	UpperCamelCase      ):



				"""simple docstring"""





				lowerCAmelCase__			:  List[str]											= len(UpperCamelCase      )
				lowerCAmelCase__			:  Union[str, Any]											= len(matrix[0]      )
				lowerCAmelCase__			:  int											= min(UpperCamelCase							,   UpperCamelCase      )

				for row in range(UpperCamelCase      ):
								# Check if diagonal element is not zero
								if matrix[row][row] != 0:
												# Eliminate all the elements below the diagonal
												for col in range(row + 1							,   UpperCamelCase      ):
																lowerCAmelCase__			:  Union[str, Any]											= matrix[col][row] / matrix[row][row]
																for i in range(UpperCamelCase							,   UpperCamelCase      ):
																				matrix[col][i] -= multiplier * matrix[row][i]
								else:
												# Find a non-zero diagonal element to swap rows
												lowerCAmelCase__			:  int											= True
												for i in range(row + 1							,   UpperCamelCase      ):
																if matrix[i][row] != 0:
																				lowerCAmelCase__			:  str											= matrix[i], matrix[row]
																				lowerCAmelCase__			:  int											= False
																				break
												if reduce:
																rank -= 1
																for i in range(UpperCamelCase      ):
																				lowerCAmelCase__			:  Tuple											= matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
												row -= 1

				return rank


if __name__ == "__main__":
	import doctest

	doctest.testmod()







'''simple docstring'''





class 	lowerCAmelCase_:
  '''simple docstring'''




  def __init__(   self  ,__UpperCAmelCase				)   ->		Tuple:
      lowerCAmelCase__			:  Union[str, Any]											= n
      lowerCAmelCase__			:  int											= [None] * self.n
      lowerCAmelCase__			:  Union[str, Any]											= 0  # index of the first element
      lowerCAmelCase__			:  Union[str, Any]											= 0
      lowerCAmelCase__			:  Union[str, Any]											= 0




  def __len__(   self				)   ->		int:
      return self.size




  def 							UpperCAmelCase_     (   self				)   ->		bool:
      return self.size == 0




  def 							UpperCAmelCase_     (   self				)   ->		Optional[Any]:
      return False if self.is_empty() else self.array[self.front]




  def 							UpperCAmelCase_     (   self  ,__UpperCAmelCase				)   ->		Union[str, Any]:
      if self.size >= self.n:
          raise Exception("""QUEUE IS FULL"""				)

      lowerCAmelCase__			:  str											= data
      lowerCAmelCase__			:  List[str]											= (self.rear + 1) % self.n
      self.size += 1
      return self






  def 							UpperCAmelCase_     (   self				)   ->		int:
      if self.size == 0:
          raise Exception("""UNDERFLOW"""				)

      lowerCAmelCase__			:  int											= self.array[self.front]
      lowerCAmelCase__			:  Optional[Any]											= None
      lowerCAmelCase__			:  int											= (self.front + 1) % self.n
      self.size -= 1
      return temp


