



'''simple docstring'''




lowerCamelCase							:Union[str, Any]				    =					[
    [0, 1_6, 1_3, 0, 0, 0],
    [0, 0, 1_0, 1_2, 0, 0],
    [0, 4, 0, 0, 1_4, 0],
    [0, 0, 9, 0, 0, 2_0],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]



def 	a			( lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__    ):
			'''simple docstring'''





			A_	:						Tuple	=     [False] * len(lowerCamelCase__    )
			A_	:						List[str]	=     [s]
			A_	:						List[str]	=     True

			while queue:
						A_	:						Dict	=     queue.pop(0    )
						for ind in range(len(graph[u]    )    ):
									if visited[ind] is False and graph[u][ind] > 0:
												queue.append(lowerCamelCase__    )
												A_	:						Optional[Any]	=     True
												A_	:						Optional[Any]	=     u

			return visited[t]



def 	a			( lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__    ):
			'''simple docstring'''





			A_	:						Tuple	=     [-1] * (len(lowerCamelCase__    ))
			A_	:						Tuple	=     0
			A_	:						int	=     []
			A_	:						List[Any]	=     [i[:] for i in graph]  # Record original cut, copy.
			while bfs(lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__    ):
						A_	:						Union[str, Any]	=     float("""Inf"""    )
						A_	:						Optional[int]	=     sink

						while s != source:
									# Find the minimum value in select path
									A_	:						Optional[Any]	=     min(lowerCamelCase__						,      graph[parent[s]][s]    )
									A_	:						Any	=     parent[s]

						max_flow += path_flow
						A_	:						Optional[int]	=     sink

						while v != source:
									A_	:						str	=     parent[v]
									graph[u][v] -= path_flow
									graph[v][u] += path_flow
									A_	:						Optional[Any]	=     parent[v]

			for i in range(len(lowerCamelCase__    )    ):
						for j in range(len(graph[0]    )    ):
									if graph[i][j] == 0 and temp[i][j] > 0:
												res.append((i, j)    )

			return res


if __name__ == "__main__":
						print(mincut(test_graph, source=0, sink=5))




'''simple docstring'''




from math import pow



def 	a			( lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__						,      lowerCamelCase__						,      ):
			'''simple docstring'''





			if current_sum == needed_sum:
						# If the sum of the powers is equal to needed_sum, then we have a solution.
						solutions_count += 1
						return current_sum, solutions_count

			A_	:						Optional[int]	=     int(pow(lowerCamelCase__						,      lowerCamelCase__    )    )
			if current_sum + i_to_n <= needed_sum:
						# If the sum of the powers is less than needed_sum, then continue adding powers.
						current_sum += i_to_n
						A_,    A_	:						int	=     backtrack(
						    lowerCamelCase__						,      lowerCamelCase__						,      current_number + 1						,      lowerCamelCase__						,      lowerCamelCase__    )
						current_sum -= i_to_n
			if i_to_n < needed_sum:
						# If the power of i is less than needed_sum, then try with the next power.
						A_,    A_	:						int	=     backtrack(
						    lowerCamelCase__						,      lowerCamelCase__						,      current_number + 1						,      lowerCamelCase__						,      lowerCamelCase__    )
			return current_sum, solutions_count



def 	a			( lowerCamelCase__						,      lowerCamelCase__    ):
			'''simple docstring'''





			if not (1 <= needed_sum <= 10_00 and 2 <= power <= 10):
						raise ValueError(
						    """Invalid input\n"""
						    """needed_sum must be between 1 and 1000, power between 2 and 10."""    )

			return backtrack(lowerCamelCase__						,      lowerCamelCase__						,      1						,      0						,      0    )[1]  # Return the solutions_count


if __name__ == "__main__":
						import doctest

						doctest.testmod()