




"""simple docstring"""







def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->List[str]:






		"""simple docstring"""


		return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase=0				)			->List[str]:






		"""simple docstring"""


		return sorted(_lowerCamelCase,  key=lambda _lowerCamelCase				: x[column]				)

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase=float("inf"				)				)			->Tuple:






		"""simple docstring"""


		for i in range(points_counts - 1				):
				for j in range(i + 1,  _lowerCamelCase				):
						__lowercase				:		Optional[Any]												=				euclidean_distance_sqr(points[i],  points[j]				)
						if current_dis < min_dis:
								__lowercase				:		str												=				current_dis
		return min_dis

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase=float("inf"				)				)			->int:






		"""simple docstring"""


		for i in range(min(6,  points_counts - 1				),  _lowerCamelCase				):
				for j in range(max(0,  i - 6				),  _lowerCamelCase				):
						__lowercase				:		Dict												=				euclidean_distance_sqr(points[i],  points[j]				)
						if current_dis < min_dis:
								__lowercase				:		int												=				current_dis
		return min_dis

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase				)			->str:






		"""simple docstring"""


		if points_counts <= 3:
				return dis_between_closest_pair(_lowerCamelCase,  _lowerCamelCase				)

		# recursion
		__lowercase				:		Dict												=				points_counts // 2
		__lowercase				:		Tuple												=				closest_pair_of_points_sqr(
		    _lowerCamelCase,  points_sorted_on_y[:mid],  _lowerCamelCase				)
		__lowercase				:		Optional[Any]												=				closest_pair_of_points_sqr(
		    _lowerCamelCase,  points_sorted_on_y[mid:],  points_counts - mid				)
		__lowercase				:		List[str]												=				min(_lowerCamelCase,  _lowerCamelCase				)
		__lowercase				:		Optional[Any]												=				[]
		for point in points_sorted_on_x:
				if abs(point[0] - points_sorted_on_x[mid][0]				) < closest_pair_dis:
						cross_strip.append(_lowerCamelCase				)

		__lowercase				:		List[str]												=				dis_between_closest_in_strip(
		    _lowerCamelCase,  len(_lowerCamelCase				),  _lowerCamelCase				)
		return min(_lowerCamelCase,  _lowerCamelCase				)

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->Tuple:






		"""simple docstring"""


		__lowercase				:		Optional[Any]												=				column_based_sort(_lowerCamelCase,  column=0				)
		__lowercase				:		Union[str, Any]												=				column_based_sort(_lowerCamelCase,  column=1				)
		return (
		    closest_pair_of_points_sqr(
		        _lowerCamelCase,  _lowerCamelCase,  _lowerCamelCase				)
		) ** 0.5


if __name__ == "__main__":
						__A   :  List[str]					=      [(2, 3), (1_2, 3_0), (4_0, 5_0), (5, 1), (1_2, 1_0), (3, 4)]
						print('Distance:', closest_pair_of_points(points, len(points)))






"""simple docstring"""







from __future__ import annotations

import math

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->list:






		"""simple docstring"""


		if len(_lowerCamelCase				) != 2 or len(a[0]				) != 2 or len(_lowerCamelCase				) != 2 or len(b[0]				) != 2:
				raise Exception("Matrices are not 2x2"				)
		__lowercase				:		Tuple												=				[
		    [a[0][0] * b[0][0] + a[0][1] * b[1][0], a[0][0] * b[0][1] + a[0][1] * b[1][1]],
		    [a[1][0] * b[0][0] + a[1][1] * b[1][0], a[1][0] * b[0][1] + a[1][1] * b[1][1]],
		]
		return new_matrix

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->Dict:






		"""simple docstring"""


		return [
		    [matrix_a[row][col] + matrix_b[row][col] for col in range(len(matrix_a[row]				)				)]
		    for row in range(len(_lowerCamelCase				)				)
		]

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->Tuple:






		"""simple docstring"""


		return [
		    [matrix_a[row][col] - matrix_b[row][col] for col in range(len(matrix_a[row]				)				)]
		    for row in range(len(_lowerCamelCase				)				)
		]

def 						snake_case__       (					_lowerCamelCase				)			->tuple[list, list, list, list]:






		"""simple docstring"""


		if len(_lowerCamelCase				) % 2 != 0 or len(a[0]				) % 2 != 0:
				raise Exception("Odd matrices are not supported!"				)

		__lowercase				:		Tuple												=				len(_lowerCamelCase				)
		__lowercase				:		Any												=				matrix_length // 2

		__lowercase				:		Dict												=				[[a[i][j] for j in range(_lowerCamelCase,  _lowerCamelCase				)] for i in range(_lowerCamelCase				)]
		__lowercase				:		List[str]												=				[
		    [a[i][j] for j in range(_lowerCamelCase,  _lowerCamelCase				)] for i in range(_lowerCamelCase,  _lowerCamelCase				)
		]

		__lowercase				:		Union[str, Any]												=				[[a[i][j] for j in range(_lowerCamelCase				)] for i in range(_lowerCamelCase				)]
		__lowercase				:		List[str]												=				[[a[i][j] for j in range(_lowerCamelCase				)] for i in range(_lowerCamelCase,  _lowerCamelCase				)]

		return top_left, top_right, bot_left, bot_right

def 						snake_case__       (					_lowerCamelCase				)			->tuple[int, int]:






		"""simple docstring"""


		return len(_lowerCamelCase				), len(matrix[0]				)

def 						snake_case__       (					_lowerCamelCase				)			->None:






		"""simple docstring"""


		print("\n".join(str(_lowerCamelCase				) for line in matrix				)				)

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->list:






		"""simple docstring"""


		if matrix_dimensions(_lowerCamelCase				) == (2, 2):
				return default_matrix_multiplication(_lowerCamelCase,  _lowerCamelCase				)

		__lowercase						,__lowercase						,__lowercase						,__lowercase				:		Optional[Any]												=				split_matrix(_lowerCamelCase				)
		__lowercase						,__lowercase						,__lowercase						,__lowercase				:		Any												=				split_matrix(_lowerCamelCase				)

		__lowercase				:		str												=				actual_strassen(_lowerCamelCase,  matrix_subtraction(_lowerCamelCase,  _lowerCamelCase				)				)
		__lowercase				:		Dict												=				actual_strassen(matrix_addition(_lowerCamelCase,  _lowerCamelCase				),  _lowerCamelCase				)
		__lowercase				:		Union[str, Any]												=				actual_strassen(matrix_addition(_lowerCamelCase,  _lowerCamelCase				),  _lowerCamelCase				)
		__lowercase				:		Any												=				actual_strassen(_lowerCamelCase,  matrix_subtraction(_lowerCamelCase,  _lowerCamelCase				)				)
		__lowercase				:		List[Any]												=				actual_strassen(matrix_addition(_lowerCamelCase,  _lowerCamelCase				),  matrix_addition(_lowerCamelCase,  _lowerCamelCase				)				)
		__lowercase				:		Optional[int]												=				actual_strassen(matrix_subtraction(_lowerCamelCase,  _lowerCamelCase				),  matrix_addition(_lowerCamelCase,  _lowerCamelCase				)				)
		__lowercase				:		Optional[Any]												=				actual_strassen(matrix_subtraction(_lowerCamelCase,  _lowerCamelCase				),  matrix_addition(_lowerCamelCase,  _lowerCamelCase				)				)

		__lowercase				:		str												=				matrix_addition(matrix_subtraction(matrix_addition(_lowerCamelCase,  _lowerCamelCase				),  _lowerCamelCase				),  _lowerCamelCase				)
		__lowercase				:		Dict												=				matrix_addition(_lowerCamelCase,  _lowerCamelCase				)
		__lowercase				:		int												=				matrix_addition(_lowerCamelCase,  _lowerCamelCase				)
		__lowercase				:		Union[str, Any]												=				matrix_subtraction(matrix_subtraction(matrix_addition(_lowerCamelCase,  _lowerCamelCase				),  _lowerCamelCase				),  _lowerCamelCase				)

		# construct the new matrix from our 4 quadrants
		__lowercase				:		Optional[int]												=				[]
		for i in range(len(_lowerCamelCase				)				):
				new_matrix.append(top_left[i] + top_right[i]				)
		for i in range(len(_lowerCamelCase				)				):
				new_matrix.append(bot_left[i] + bot_right[i]				)
		return new_matrix

def 						snake_case__       (					_lowerCamelCase,  _lowerCamelCase				)			->list:






		"""simple docstring"""


		if matrix_dimensions(_lowerCamelCase				)[1] != matrix_dimensions(_lowerCamelCase				)[0]:
				__lowercase				:		int												=				(
				    "Unable to multiply these matrices, please check the dimensions.\n"
				    F'Matrix A: {matrixa}\n'
				    F'Matrix B: {matrixa}'
				)
				raise Exception(_lowerCamelCase				)
		__lowercase				:		List[Any]												=				matrix_dimensions(_lowerCamelCase				)
		__lowercase				:		Tuple												=				matrix_dimensions(_lowerCamelCase				)

		if dimensiona[0] == dimensiona[1] and dimensiona[0] == dimensiona[1]:
				return [matrixa, matrixa]

		__lowercase				:		int												=				max(*_lowerCamelCase,  *_lowerCamelCase				)
		__lowercase				:		Any												=				int(math.pow(2,  math.ceil(math.loga(_lowerCamelCase				)				)				)				)
		__lowercase				:		Dict												=				matrixa
		__lowercase				:		str												=				matrixa

		# Adding zeros to the matrices so that the arrays dimensions are the same and also
		# power of 2
		for i in range(0,  _lowerCamelCase				):
				if i < dimensiona[0]:
						for _ in range(dimensiona[1],  _lowerCamelCase				):
								new_matrixa[i].append(0				)
				else:
						new_matrixa.append([0] * maxim				)
				if i < dimensiona[0]:
						for _ in range(dimensiona[1],  _lowerCamelCase				):
								new_matrixa[i].append(0				)
				else:
						new_matrixa.append([0] * maxim				)

		__lowercase				:		Dict												=				actual_strassen(_lowerCamelCase,  _lowerCamelCase				)

		# Removing the additional zeros
		for i in range(0,  _lowerCamelCase				):
				if i < dimensiona[0]:
						for _ in range(dimensiona[1],  _lowerCamelCase				):
								final_matrix[i].pop()
				else:
						final_matrix.pop()
		return final_matrix


if __name__ == "__main__":
						__A   :  int					=      [
						    [2, 3, 4, 5],
						    [6, 4, 3, 1],
						    [2, 3, 6, 7],
						    [3, 1, 2, 4],
						    [2, 3, 4, 5],
						    [6, 4, 3, 1],
						    [2, 3, 6, 7],
						    [3, 1, 2, 4],
						    [2, 3, 4, 5],
						    [6, 2, 3, 1],
						]
						__A   :  Union[str, Any]					=      [[0, 2, 1, 1], [1_6, 2, 3, 3], [2, 2, 7, 7], [1_3, 1_1, 2_2, 4]]
						print(strassen(matrixa, matrixa))
