
import numpy as np
from numpy import floataa
from numpy.typing import NDArray




def 				lowerCamelCase__				(						a__  :  NDArray[floataa]	,      a__  :  NDArray[floataa]     )		->	NDArray[floataa]:
       UpperCamelCase_       ,				UpperCamelCase_							       =       np.shape(a__     )

       UpperCamelCase_							       =       np.zeros((rows, 1)	,      dtype=a__     )
       for row in reversed(range(a__     )     ):
              UpperCamelCase_							       =       0
              for col in range(row + 1	,      a__     ):
                     total += coefficients[row, col] * x[col]

              UpperCamelCase_							       =       (vector[row] - total) / coefficients[row, row]

       return x




def 				lowerCamelCase__				(						a__  :  NDArray[floataa]	,      a__  :  NDArray[floataa]     )		->	NDArray[floataa]:
       UpperCamelCase_       ,				UpperCamelCase_							       =       np.shape(a__     )
       if rows != columns:
              return np.array(()	,      dtype=a__     )

       # augmented matrix
       UpperCamelCase_							       =       np.concatenate((coefficients, vector)	,      axis=1     )
       UpperCamelCase_							       =       augmented_mat.astype("""float64"""     )

       # scale the matrix leaving it triangular
       for row in range(rows - 1     ):
              UpperCamelCase_							       =       augmented_mat[row, row]
              for col in range(row + 1	,      a__     ):
                     UpperCamelCase_							       =       augmented_mat[col, row] / pivot
                     augmented_mat[col, :] -= factor * augmented_mat[row, :]

       UpperCamelCase_							       =       retroactive_resolution(
           augmented_mat[:, 0:columns]	,      augmented_mat[:, columns : columns + 1]     )

       return x


if __name__ == "__main__":
      import doctest

      doctest.testmod()





def 				lowerCamelCase__				(						a__  :  list     )		->	list:
       UpperCamelCase_							       =       1.3
       UpperCamelCase_							       =       len(a__     )
       UpperCamelCase_							       =       False

       while not completed:
              # Update the gap value for a next comb
              UpperCamelCase_							       =       int(gap / shrink_factor     )
              if gap <= 1:
                     UpperCamelCase_							       =       True

              UpperCamelCase_							       =       0
              while index + gap < len(a__     ):
                     if data[index] > data[index + gap]:
                            # Swap values
                            UpperCamelCase_       ,				UpperCamelCase_							       =       data[index + gap], data[index]
                            UpperCamelCase_							       =       False
                     index += 1

       return data


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      _A	  =					input('''Enter numbers separated by a comma:\n''').strip()
      _A	  =					[int(item) for item in user_input.split(''',''')]
      print(comb_sort(unsorted))



