



from __future__ import annotations

from collections.abc import Callable

lowercase_													=      list[list[float | int]]






def        __lowerCAmelCase		(	__lowerCamelCase						:     Matrix					, __lowerCamelCase						:     Matrix						)	->    Matrix:
					__lowerCAmelCase						 =len(__lowerCamelCase						)
					__lowerCAmelCase						 =[[0 for _ in range(size + 1						)] for _ in range(__lowerCamelCase						)]
					__lowerCAmelCase						 =42
					__lowerCAmelCase						 =42
					__lowerCAmelCase						 =42
					__lowerCAmelCase						 =42
					__lowerCAmelCase						 =42
					__lowerCAmelCase						 =42

					for row in range(__lowerCamelCase						):
										for col in range(__lowerCamelCase						):
															__lowerCAmelCase						 =matrix[row][col]

										__lowerCAmelCase						 =vector[row][0]

					__lowerCAmelCase						 =0
					__lowerCAmelCase						 =0
					while row < size and col < size:
										# pivoting
										__lowerCAmelCase						 =max((abs(augmented[rowa][col]						), rowa) for rowa in range(__lowerCamelCase					, __lowerCamelCase						)						)[
										    1
										]
										if augmented[pivot_row][col] == 0:
															col += 1
															continue
										else:
															__lowerCAmelCase ,						__lowerCAmelCase						 =augmented[pivot_row], augmented[row]

										for rowa in range(row + 1					, __lowerCamelCase						):
															__lowerCAmelCase						 =augmented[rowa][col] / augmented[row][col]
															__lowerCAmelCase						 =0
															for cola in range(col + 1					, size + 1						):
																				augmented[rowa][cola] -= augmented[row][cola] * ratio

										row += 1
										col += 1

					# back substitution
					for col in range(1					, __lowerCamelCase						):
										for row in range(__lowerCamelCase						):
															__lowerCAmelCase						 =augmented[row][col] / augmented[col][col]
															for cola in range(__lowerCamelCase					, size + 1						):
																				augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
					return [
					    [round(augmented[row][size] / augmented[row][row]					, 10						)] for row in range(__lowerCamelCase						)
					]






def        __lowerCAmelCase		(	__lowerCamelCase						:     list[int]						)	->    Callable[[int], int]:
					__lowerCAmelCase						 =len(__lowerCamelCase						)
					__lowerCAmelCase						 =[[0 for _ in range(__lowerCamelCase						)] for _ in range(__lowerCamelCase						)]
					__lowerCAmelCase						 =[[0] for _ in range(__lowerCamelCase						)]
					__lowerCAmelCase						 =42
					__lowerCAmelCase						 =42
					__lowerCAmelCase						 =42
					__lowerCAmelCase						 =42

					for x_val, y_val in enumerate(__lowerCamelCase						):
										for col in range(__lowerCamelCase						):
															__lowerCAmelCase						 =(x_val + 1) ** (size - col - 1)
										__lowerCAmelCase						 =y_val

					__lowerCAmelCase						 =solve(__lowerCamelCase					, __lowerCamelCase						)

					def interpolated_func(__lowerCamelCase						:     int						) -> int:
										return sum(
										    round(coeffs[x_val][0]						) * (var ** (size - x_val - 1))
										    for x_val in range(__lowerCamelCase						)						)

					return interpolated_func






def        __lowerCAmelCase		(	__lowerCamelCase						:     int						)	->    int:
					return (
					    1
					    - variable
					    + variable**2
					    - variable**3
					    + variable**4
					    - variable**5
					    + variable**6
					    - variable**7
					    + variable**8
					    - variable**9
					    + variable**10
					)






def        __lowerCAmelCase		(	__lowerCamelCase						:     Callable[[int], int] = question_function					, __lowerCamelCase						:     int = 10						)	->    int:
					__lowerCAmelCase						 =[func(__lowerCamelCase						) for x_val in range(1					, order + 1						)]

					__lowerCAmelCase						 =[
					    interpolate(data_points[:max_coeff]						) for max_coeff in range(1					, order + 1						)
					]

					__lowerCAmelCase						 =0
					__lowerCAmelCase						 =42
					__lowerCAmelCase						 =42

					for poly in polynomials:
										__lowerCAmelCase						 =1
										while func(__lowerCamelCase						) == poly(__lowerCamelCase						):
															x_val += 1

										ret += poly(__lowerCamelCase						)

					return ret


if __name__ == "__main__":
				print(F"{solution() = }")









from __future__ import annotations






class     __a			:



	def __init__(    self				:     List[Any]					,						snake_case_				:     str					,						snake_case_				:     str)->				Optional[int]:
						__lowerCAmelCase ,						__lowerCAmelCase						 =text, pattern
						__lowerCAmelCase ,						__lowerCAmelCase						 =len(snake_case_), len(snake_case_)



	def 		UpperCamelCase				(    self				:     List[Any]					,						snake_case_				:     str)->				int:

						for i in range(self.patLen - 1					,						-1					,						-1):
											if char == self.pattern[i]:
																return i
						return -1



	def 		UpperCamelCase				(    self				:     List[str]					,						snake_case_				:     int)->				int:

						for i in range(self.patLen - 1					,						-1					,						-1):
											if self.pattern[i] != self.text[current_pos + i]:
																return current_pos + i
						return -1



	def 		UpperCamelCase				(    self				:     Dict)->				list[int]:
						# searches pattern in text and returns index positions
						__lowerCAmelCase						 =[]
						for i in range(self.textLen - self.patLen + 1):
											__lowerCAmelCase						 =self.mismatch_in_text(snake_case_)
											if mismatch_index == -1:
																positions.append(snake_case_)
											else:
																__lowerCAmelCase						 =self.match_in_pattern(self.text[mismatch_index])
																__lowerCAmelCase						 =(
																    mismatch_index - match_index
																)  # shifting index lgtm [py/multiple-definition]
						return positions


lowercase_													=      '''ABAABA'''
lowercase_													=      '''AB'''
lowercase_													=      BoyerMooreSearch(text, pattern)
lowercase_													=      bms.bad_character_heuristic()

if len(positions) == 0:
				print('''No match found''')
else:
				print('''Pattern found in following positions: ''')
				print(positions)




