


def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case      ,							snake_case					)  ->    Union[str, Any]:
       # Return True if there is node that has not iterated.
       lowercase__:       str        =       [False] * len(snake_case					)
       lowercase__:       Any        =       []
       queue.append(snake_case					)
       lowercase__:       Optional[int]        =       True

       while queue:
              lowercase__:       List[Any]        =       queue.pop(0					)
              for ind in range(len(graph[u]					)					):
                     if visited[ind] is False and graph[u][ind] > 0:
                            queue.append(snake_case					)
                            lowercase__:       str        =       True
                            lowercase__:       Tuple        =       u

       return visited[t]




def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case					)  ->    Optional[Any]:
       # This array is filled by BFS and to store path
       lowercase__:       List[str]        =       [-1] * (len(snake_case					))
       lowercase__:       Optional[int]        =       0
       while bfs(snake_case      ,							snake_case      ,							snake_case      ,							snake_case					):
              lowercase__:       str        =       float('Inf'					)
              lowercase__:       Optional[Any]        =       sink

              while s != source:
                     # Find the minimum value in select path
                     lowercase__:       Dict        =       min(snake_case      ,							graph[parent[s]][s]					)
                     lowercase__:       Dict        =       parent[s]

              max_flow += path_flow
              lowercase__:       Dict        =       sink

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


__lowerCAmelCase			=							[
    [0, 16, 13, 0, 0, 0],
    [0, 0, 10, 12, 0, 0],
    [0, 4, 0, 0, 14, 0],
    [0, 0, 9, 0, 0, 20],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

__lowerCAmelCase	,__lowerCAmelCase			=							0, 5




print(ford_fulkerson(graph, source, sink))






from math import pow




def        snake_case_					(  snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							snake_case      ,							)  ->    tuple[int, int]:
       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

       lowercase__:       int        =       int(pow(snake_case      ,							snake_case					)					)
       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
              lowercase__      ,						lowercase__:       Any        =       backtrack(
                  snake_case      ,							snake_case      ,							current_number + 1      ,							snake_case      ,							snake_case					)
              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.
              lowercase__      ,						lowercase__:       Optional[int]        =       backtrack(
                  snake_case      ,							snake_case      ,							current_number + 1      ,							snake_case      ,							snake_case					)
       return current_sum, solutions_count




def        snake_case_					(  snake_case      ,							snake_case					)  ->    int:
       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(snake_case      ,							snake_case      ,							1      ,							0      ,							0					)[1]  # Return the solutions_count


if __name__ == "__main__":
 import doctest

 doctest.testmod()


