



"""simple docstring"""
def    A_  (			_lowercase	):







						'''simple docstring'''


						snake_case_ :int						=			len(_lowercase	)
						snake_case_ :List[Any]						=			len(matrix[0]	)
						snake_case_ :Optional[int]						=			min(_lowercase,					_lowercase	)

						for row in range(_lowercase	):
												# 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,					_lowercase	):
																								snake_case_ :int						=			matrix[col][row] / matrix[row][row]
																								for i in range(_lowercase,					_lowercase	):
																														matrix[col][i] -= multiplier * matrix[row][i]
												else:
																		# Find a non-zero diagonal element to swap rows
																		snake_case_ :Any						=			True
																		for i in range(row + 1,					_lowercase	):
																								if matrix[i][row] != 0:
																														snake_case_,       snake_case_ :int						=			matrix[i], matrix[row]
																														snake_case_ :Dict						=			False
																														break
																		if reduce:
																								rank -= 1
																								for i in range(_lowercase	):
																														snake_case_ :Dict						=			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"""
from __future__ import annotations

__a      =				10
def    A_  (			_lowercase	):







						'''simple docstring'''


						snake_case_ :Union[str, Any]						=			1
						snake_case_ :List[str]						=			max(_lowercase	)
						while placement <= max_digit:
												# declare and initialize empty buckets
												snake_case_ :list[list]						=			[[] for _ in range(_lowercase	)]
												# split list_of_ints between the buckets
												for i in list_of_ints:
																		snake_case_ :Any						=			int((i / placement) % RADIX	)
																		buckets[tmp].append(_lowercase	)
												# put each buckets' contents into list_of_ints
												snake_case_ :Optional[Any]						=			0
												for b in range(_lowercase	):
																		for i in buckets[b]:
																								snake_case_ :Union[str, Any]						=			i
																								a += 1
        # move to next
												placement *= RADIX
						return list_of_ints


if __name__ == "__main__":
						import doctest

						doctest.testmod()
