



def 							A			(  _UpperCAmelCase       :     list[list[int | float]]					)       ->				int:







			'''simple docstring'''
			_UpperCAmelCase	 =     len(_UpperCAmelCase					)
			_UpperCAmelCase	 =     len(matrix[0]					)
			_UpperCAmelCase	 =     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					):
												_UpperCAmelCase	 =     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
									_UpperCAmelCase	 =     True
									for i in range(row + 1							,     _UpperCAmelCase					):
												if matrix[i][row] != 0:
															_UpperCAmelCase ,  _UpperCAmelCase	 =     matrix[i], matrix[row]
															_UpperCAmelCase	 =     False
															break
									if reduce:
												rank -= 1
												for i in range(_UpperCAmelCase					):
															_UpperCAmelCase	 =     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()





import unittest

from knapsack import knapsack as k







class     __lowerCAmelCase					(    unittest.TestCase		):



			def 					_lowerCamelCase (		self     :						Optional[Any])     ->					Any:



						"""simple docstring"""






						_UpperCAmelCase	 =     0
						_UpperCAmelCase	 =     [0]
						_UpperCAmelCase	 =     [0]
						_UpperCAmelCase	 =     len(A)
						self.assertEqual(k.knapsack(A				,	A				,	A				,	A)				,	0)

						_UpperCAmelCase	 =     [60]
						_UpperCAmelCase	 =     [10]
						_UpperCAmelCase	 =     len(A)
						self.assertEqual(k.knapsack(A				,	A				,	A				,	A)				,	0)



			def 					_lowerCamelCase (		self     :						str)     ->					List[str]:



						"""simple docstring"""






						_UpperCAmelCase	 =     3
						_UpperCAmelCase	 =     [1, 2, 3]
						_UpperCAmelCase	 =     [3, 2, 1]
						_UpperCAmelCase	 =     len(A)
						self.assertEqual(k.knapsack(A				,	A				,	A				,	A)				,	5)



			def 					_lowerCamelCase (		self     :						Tuple)     ->					Tuple:



						"""simple docstring"""






						_UpperCAmelCase	 =     50
						_UpperCAmelCase	 =     [60, 1_00, 1_20]
						_UpperCAmelCase	 =     [10, 20, 30]
						_UpperCAmelCase	 =     len(A)
						self.assertEqual(k.knapsack(A				,	A				,	A				,	A)				,	2_20)


if __name__ == "__main__":
							unittest.main()
