



import numpy as np


def       UpperCamelCase(  __UpperCamelCase							:		List[Any]			):
		lowerCAmelCase_ ,  lowerCAmelCase_      :					List[Any]     =			a.shape
		lowerCAmelCase_      :					Dict     =			min(_A					,_A			)
		lowerCAmelCase_      :					List[Any]     =			np.eye(_A			)
		lowerCAmelCase_      :					Union[str, Any]     =			a.copy()

		for k in range(t - 1			):
				# select a column of modified matrix A':
				lowerCAmelCase_      :					Any     =			r[k:, [k]]
				# construct first basis vector
				lowerCAmelCase_      :					List[str]     =			np.zeros_like(_A			)
				lowerCAmelCase_      :					Optional[int]     =			1.0
				# determine scaling factor
				lowerCAmelCase_      :					Union[str, Any]     =			np.linalg.norm(_A			)
				# construct vector v for Householder reflection
				lowerCAmelCase_      :					Dict     =			x + np.sign(x[0]			) * alpha * ea
				v /= np.linalg.norm(_A			)

				# construct the Householder matrix
				lowerCAmelCase_      :					List[Any]     =			np.eye(m - k			) - 2.0 * v @ v.T
				# pad with ones and zeros as necessary
				lowerCAmelCase_      :					List[str]     =			np.block([[np.eye(_A			), np.zeros((k, m - k)			)], [np.zeros((m - k, k)			), q_k]]			)

				lowerCAmelCase_      :					Optional[int]     =			q @ q_k.T
				lowerCAmelCase_      :					Tuple     =			q_k @ r

		return q, r


if __name__ == "__main__":
						import doctest

						doctest.testmod()










def       UpperCamelCase(  __UpperCamelCase							:		list			):
		for i, _ in enumerate(__UpperCamelCase			):
				if (i % 2 == 1) == (nums[i - 1] > nums[i]):
						lowerCAmelCase_ ,  lowerCAmelCase_      :					Union[str, Any]     =			nums[i], nums[i - 1]

		return nums


if __name__ == "__main__":
						print('''Enter the array elements:''')
						A__  :  str       = list(map(int, input().split()))
						print('''The unsorted array is:''')
						print(array)
						print('''Array after Wiggle sort:''')
						print(wiggle_sort(array))





