



'''simple docstring'''

import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)

class 	__magic_name__						(    unittest.TestCase   ):







							def 							__lowercase			(							self					:       Any		):
									_a     :      str        =							Vector([1, 2, 3]		)
									self.assertEqual(x.component(0		)	,1		)
									self.assertEqual(x.component(2		)	,3		)
									_a     :      Union[str, Any]        =							Vector()







							def 							__lowercase			(							self					:       int		):
									_a     :      List[Any]        =							Vector([0, 0, 0, 0, 0, 1]		)
									self.assertEqual(str(_UpperCAmelCase		)	,'(0,0,0,0,0,1)'		)







							def 							__lowercase			(							self					:       Union[str, Any]		):
									_a     :      Tuple        =							Vector([1, 2, 3, 4]		)
									self.assertEqual(len(_UpperCAmelCase		)	,4		)







							def 							__lowercase			(							self					:       Optional[int]		):
									_a     :      Dict        =							Vector([1, 2]		)
									_a     :      Optional[Any]        =							Vector([1, 2, 3, 4, 5]		)
									_a     :      Tuple        =							Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]		)
									_a     :      Union[str, Any]        =							Vector([1, -1, 1, -1, 2, -3, 4, -5]		)
									self.assertAlmostEqual(x.euclidean_length()	,2.2_36	,3		)
									self.assertAlmostEqual(y.euclidean_length()	,7.4_16	,3		)
									self.assertEqual(z.euclidean_length()	,0		)
									self.assertAlmostEqual(w.euclidean_length()	,7.6_16	,3		)







							def 							__lowercase			(							self					:       Any		):
									_a     :      Dict        =							Vector([1, 2, 3]		)
									_a     :      Union[str, Any]        =							Vector([1, 1, 1]		)
									self.assertEqual((x + y).component(0		)	,2		)
									self.assertEqual((x + y).component(1		)	,3		)
									self.assertEqual((x + y).component(2		)	,4		)







							def 							__lowercase			(							self					:       Tuple		):
									_a     :      str        =							Vector([1, 2, 3]		)
									_a     :      int        =							Vector([1, 1, 1]		)
									self.assertEqual((x - y).component(0		)	,0		)
									self.assertEqual((x - y).component(1		)	,1		)
									self.assertEqual((x - y).component(2		)	,2		)







							def 							__lowercase			(							self					:       Dict		):
									_a     :      Tuple        =							Vector([1, 2, 3]		)
									_a     :      int        =							Vector([2, -1, 4]		)  # for test of dot product
									_a     :      Dict        =							Vector([1, -2, -1]		)
									self.assertEqual(str(x * 3.0		)	,'(3.0,6.0,9.0)'		)
									self.assertEqual((a * b)	,0		)







							def 							__lowercase			(							self					:       List[Any]		):
									self.assertEqual(str(zero_vector(10		)		).count('0'		)	,10		)







							def 							__lowercase			(							self					:       Tuple		):
									self.assertEqual(str(unit_basis_vector(3	,1		)		)	,'(0,1,0)'		)







							def 							__lowercase			(							self					:       Optional[Any]		):
									_a     :      Optional[Any]        =							Vector([1, 2, 3]		)
									_a     :      Any        =							Vector([1, 0, 1]		)
									self.assertEqual(str(axpy(2	,_UpperCAmelCase	,_UpperCAmelCase		)		)	,'(3,4,7)'		)







							def 							__lowercase			(							self					:       Optional[Any]		):
									_a     :      Union[str, Any]        =							Vector([1, 0, 0, 0, 0, 0]		)
									_a     :      Union[str, Any]        =							x.copy()
									self.assertEqual(str(_UpperCAmelCase		)	,str(_UpperCAmelCase		)		)







							def 							__lowercase			(							self					:       Tuple		):
									_a     :      Union[str, Any]        =							Vector([1, 0, 0]		)
									x.change_component(0	,0		)
									x.change_component(1	,1		)
									self.assertEqual(str(_UpperCAmelCase		)	,'(0,1,0)'		)







							def 							__lowercase			(							self					:       List[Any]		):
									_a     :      Dict        =							Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]	,3	,3		)
									self.assertEqual('|1,2,3|\n|2,4,5|\n|6,7,8|\n'	,str(_UpperCAmelCase		)		)







							def 							__lowercase			(							self					:       Dict		):
									_a     :      List[Any]        =							Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]	,3	,3		)
									_a     :      Optional[int]        =							[[-3, -14, -10], [-5, -10, -5], [-2, -1, 0]]
									for x in range(a.height()		):
											for y in range(a.width()		):
													self.assertEqual(minors[x][y]	,a.minor(_UpperCAmelCase	,_UpperCAmelCase		)		)







							def 							__lowercase			(							self					:       List[str]		):
									_a     :      List[Any]        =							Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]	,3	,3		)
									_a     :      List[str]        =							[[-3, 14, -10], [5, -10, 5], [-2, 1, 0]]
									for x in range(a.height()		):
											for y in range(a.width()		):
													self.assertEqual(cofactors[x][y]	,a.cofactor(_UpperCAmelCase	,_UpperCAmelCase		)		)







							def 							__lowercase			(							self					:       List[str]		):
									_a     :      Any        =							Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]	,3	,3		)
									self.assertEqual(-5	,a.determinant()		)







							def 							__lowercase			(							self					:       List[str]		):
									_a     :      Union[str, Any]        =							Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]	,3	,3		)
									_a     :      Any        =							Vector([1, 2, 3]		)
									self.assertEqual('(14,32,50)'	,str(a * x		)		)
									self.assertEqual('|2,4,6|\n|8,10,12|\n|14,16,18|\n'	,str(a * 2		)		)







							def 							__lowercase			(							self					:       List[Any]		):
									_a     :      Optional[int]        =							Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]	,3	,3		)
									a.change_component(0	,2	,5		)
									self.assertEqual('|1,2,5|\n|2,4,5|\n|6,7,8|\n'	,str(_UpperCAmelCase		)		)







							def 							__lowercase			(							self					:       List[str]		):
									_a     :      str        =							Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]	,3	,3		)
									self.assertEqual(7	,a.component(2	,1		)	,0.01		)







							def 							__lowercase			(							self					:       Tuple		):
									_a     :      Union[str, Any]        =							Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]	,3	,3		)
									_a     :      Dict        =							Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]	,3	,3		)
									self.assertEqual('|2,4,10|\n|4,8,10|\n|12,14,18|\n'	,str(a + b		)		)







							def 							__lowercase			(							self					:       Dict		):
									_a     :      List[Any]        =							Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]	,3	,3		)
									_a     :      int        =							Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]	,3	,3		)
									self.assertEqual('|0,0,-4|\n|0,0,0|\n|0,0,-2|\n'	,str(a - b		)		)







							def 							__lowercase			(							self					:       Dict		):
									self.assertEqual(
									    '|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n'	,str(square_zero_matrix(5		)		)	,)


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






def     __lowerCAmelCase			(			a__  )       ->  str:
				__a										=    []
				__a										=    set({'''(''', '''[''', '''{'''}  )
				__a										=    set({''')''', ''']''', '''}'''}  )
				__a										=    {'''{''': '''}''', '''[''': ''']''', '''(''': ''')'''}

				for i in range(len(a__  )  ):
								if s[i] in open_brackets:
												stack.append(s[i]  )

								elif s[i] in closed_brackets and (
								    len(a__  ) == 0 or (len(a__  ) > 0 and open_to_closed[stack.pop()] != s[i])
								):
												return False

				return len(a__  ) == 0


def     __lowerCAmelCase			(			)       ->  Dict:
				__a										=    input('''Enter sequence of brackets: '''  )
				if is_balanced(a__  ):
								print(a__						,    '''is balanced'''  )
				else:
								print(a__						,    '''is not balanced'''  )


if __name__ == "__main__":
					main()