




from __future__ import annotations




def 			__magic_name__				( A		:					list[list[int]]   ):






			'''simple docstring'''







			a    =			len(A   )
			# We need to create solution object to save path.
			a    =			[[0 for _ in range(A   )] for _ in range(A   )]
			a    =			run_maze(A,  0,  0,  A   )
			if solved:
						print("\n".join(str(A   ) for row in solutions   )   )
			else:
						print("No solution exists!"   )
			return solved




def 			__magic_name__				( A		:					list[list[int]],  A		:					int,  A		:					int,  A		:					list[list[int]]   ):






			'''simple docstring'''







			a    =			len(A   )
			# Final check point.
			if i == j == (size - 1):
						a    =			1
						return True

			a    =			(not i < 0) and (not j < 0)  # Check lower bounds
			a    =			(i < size) and (j < size)  # Check upper bounds

			if lower_flag and upper_flag:
						# check for already visited and block points.
						a    =			(not solutions[i][j]) and (not maze[i][j])
						if block_flag:
									# check visited
									a    =			1

									# check for directions
									if (
									    run_maze(A,  i + 1,  A,  A   )
									    or run_maze(A,  A,  j + 1,  A   )
									    or run_maze(A,  i - 1,  A,  A   )
									    or run_maze(A,  A,  j - 1,  A   )
									):
												return True

									a    =			0
									return False
			return False


if __name__ == "__main__":
		import doctest

		doctest.testmod()












from bisect import bisect
from itertools import accumulate




def 			__magic_name__				( A		:					Optional[Any],  A		:					List[str],  A		:					Tuple,  A		:					Optional[Any]   ):






			'''simple docstring'''







			a    =			sorted(zip(A,  A   ),  key=lambda A   : x[0] / x[1],  reverse=A   )
			a    ,		a    =			[i[0] for i in r], [i[1] for i in r]
			a    =			list(accumulate(A   )   )
			a    =			bisect(A,  A   )
			return (
			    0
			    if k == 0
			    else sum(vl[:k]   ) + (w - acc[k - 1]) * (vl[k]) / (wt[k])
			    if k != n
			    else sum(vl[:k]   )
			)


if __name__ == "__main__":
		import doctest

		doctest.testmod()






