


from __future__ import annotations

from queue import Queue

def  lowercase_						(						_A     :       int       ,   _A     :       int		):

      """simple docstring"""




      a ^= b
      b ^= a
      a ^= b
      return a, b

def  lowercase_						(						_A     :       int       ,   _A     :       list[list[int]]		):

      """simple docstring"""




      lowerCamelCase__						:							str       =    1
      while (1 << j) < max_node:
            for i in range(1       ,   max_node + 1		):
                  lowerCamelCase__						:							Dict       =    parent[j - 1][parent[j - 1][i]]
            j += 1
      return parent

def  lowercase_						(						_A     :       int       ,   _A     :       int       ,   _A     :       list[int]       ,   _A     :       list[list[int]]		):

      """simple docstring"""




      if level[u] < level[v]:
            lowerCamelCase__						:							Tuple       =    swap(__SCREAMING_SNAKE_CASE       ,   __SCREAMING_SNAKE_CASE		)
      # making depth of u same as depth of v
      for i in range(18       ,   -1       ,   -1		):
            if level[u] - (1 << i) >= level[v]:
                  lowerCamelCase__						:							Any       =    parent[i][u]
    # at the same depth if u==v that mean lca is found
      if u == v:
            return u
      # moving both nodes upwards till lca in found
      for i in range(18       ,   -1       ,   -1		):
            if parent[i][u] not in [0, parent[i][v]]:
                  lowerCamelCase__						:							str       =    parent[i][u], parent[i][v]
    # returning longest common ancestor of u,v
      return parent[0][u]

def  lowercase_						(						_A     :       list[int]       ,   _A     :       list[list[int]]       ,   _A     :       int       ,   _A     :       dict[int, list[int]]       ,   _A     :       int = 1       ,   ):

      """simple docstring"""




      lowerCamelCase__						:							Tuple       =    0
      lowerCamelCase__						:							Queue[int]       =    Queue(maxsize=__SCREAMING_SNAKE_CASE		)
      q.put(__SCREAMING_SNAKE_CASE		)
      while q.qsize() != 0:
            lowerCamelCase__						:							List[str]       =    q.get()
            for v in graph[u]:
                  if level[v] == -1:
                        lowerCamelCase__						:							Union[str, Any]       =    level[u] + 1
                        q.put(__SCREAMING_SNAKE_CASE		)
                        lowerCamelCase__						:							List[Any]       =    u
      return level, parent

def  lowercase_						(						):

      """simple docstring"""




      lowerCamelCase__						:							List[str]       =    13
      # initializing with 0
      lowerCamelCase__						:							Optional[Any]       =    [[0 for _ in range(max_node + 10		)] for _ in range(20		)]
      # initializing with -1 which means every node is unvisited
      lowerCamelCase__						:							Optional[int]       =    [-1 for _ in range(max_node + 10		)]
      lowerCamelCase__						:							dict[int, list[int]]       =    {
          1: [2, 3, 4],
          2: [5],
          3: [6, 7],
          4: [8],
          5: [9, 10],
          6: [11],
          7: [],
          8: [12, 13],
          9: [],
          10: [],
          11: [],
          12: [],
          13: [],
      }
      lowerCamelCase__						:							Union[str, Any]       =    breadth_first_search(__SCREAMING_SNAKE_CASE       ,   __SCREAMING_SNAKE_CASE       ,   __SCREAMING_SNAKE_CASE       ,   __SCREAMING_SNAKE_CASE       ,   1		)
      lowerCamelCase__						:							List[Any]       =    create_sparse(__SCREAMING_SNAKE_CASE       ,   __SCREAMING_SNAKE_CASE		)
      print("LCA of node 1 and 3 is: "       ,   lowest_common_ancestor(1       ,   3       ,   __SCREAMING_SNAKE_CASE       ,   __SCREAMING_SNAKE_CASE		)		)
      print("LCA of node 5 and 6 is: "       ,   lowest_common_ancestor(5       ,   6       ,   __SCREAMING_SNAKE_CASE       ,   __SCREAMING_SNAKE_CASE		)		)
      print("LCA of node 7 and 11 is: "       ,   lowest_common_ancestor(7       ,   11       ,   __SCREAMING_SNAKE_CASE       ,   __SCREAMING_SNAKE_CASE		)		)
      print("LCA of node 6 and 7 is: "       ,   lowest_common_ancestor(6       ,   7       ,   __SCREAMING_SNAKE_CASE       ,   __SCREAMING_SNAKE_CASE		)		)
      print("LCA of node 4 and 12 is: "       ,   lowest_common_ancestor(4       ,   12       ,   __SCREAMING_SNAKE_CASE       ,   __SCREAMING_SNAKE_CASE		)		)
      print("LCA of node 8 and 8 is: "       ,   lowest_common_ancestor(8       ,   8       ,   __SCREAMING_SNAKE_CASE       ,   __SCREAMING_SNAKE_CASE		)		)


if __name__ == "__main__":
    main()



import warnings

from .generation import FlaxGenerationMixin







class      SCREAMING_SNAKE_CASE__					(  __UpperCamelCase    ):
       # warning at import time
       warnings.warn(
           "Importing `FlaxGenerationMixin` from `src/transformers/generation_flax_utils.py` is deprecated and will "
           "be removed in Transformers v5. Import as `from transformers import FlaxGenerationMixin` instead."   ,							__UpperCamelCase   ,							)



