



from __future__ import annotations

from queue import Queue

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :Optional[Any]  ,      _snake_case  :Optional[Any]							)     ->    tuple[int, int]:
			a ^= b
			b ^= a
			a ^= b
			return a, b

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :Tuple  ,      _snake_case  :Union[str, Any]							)     ->    list[list[int]]:
			_A						     =					1
			while (1 << j) < max_node:
						for i in range(1  ,      max_node + 1							):
									_A						     =					parent[j - 1][parent[j - 1][i]]
						j += 1
			return parent

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :Dict  ,      _snake_case  :Dict  ,      _snake_case  :Dict  ,      _snake_case  :Dict							)     ->    int:
			# u must be deeper in the tree than v
			if level[u] < level[v]:
						_A						     =					swap(_snake_case  ,      _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]:
									_A						     =					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]]:
									_A						     =					parent[i][u], parent[i][v]
    # returning longest common ancestor of u,v
			return parent[0][u]

def   SCREAMING_SNAKE_CASE_       (  _snake_case  :List[Any]  ,      _snake_case  :Optional[Any]  ,      _snake_case  :Optional[Any]  ,      _snake_case  :Union[str, Any]  ,      _snake_case  :Any = 1  ,      )     ->    tuple[list[int], list[list[int]]]:
			_A						     =					0
			_A						     =					Queue(maxsize=_snake_case							)
			q.put(_snake_case							)
			while q.qsize() != 0:
						_A						     =					q.get()
						for v in graph[u]:
									if level[v] == -1:
												_A						     =					level[u] + 1
												q.put(_snake_case							)
												_A						     =					u
			return level, parent

def   SCREAMING_SNAKE_CASE_       (  )     ->    None:
			_A						     =					13
			# initializing with 0
			_A						     =					[[0 for _ in range(max_node + 10							)] for _ in range(20							)]
			# initializing with -1 which means every node is unvisited
			_A						     =					[-1 for _ in range(max_node + 10							)]
			_A						     =					{
			    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: [],
			}
			_A						     =					breadth_first_search(_snake_case  ,      _snake_case  ,      _snake_case  ,      _snake_case  ,      1							)
			_A						     =					create_sparse(_snake_case  ,      _snake_case							)
			print('''LCA of node 1 and 3 is: '''  ,      lowest_common_ancestor(1  ,      3  ,      _snake_case  ,      _snake_case							)							)
			print('''LCA of node 5 and 6 is: '''  ,      lowest_common_ancestor(5  ,      6  ,      _snake_case  ,      _snake_case							)							)
			print('''LCA of node 7 and 11 is: '''  ,      lowest_common_ancestor(7  ,      11  ,      _snake_case  ,      _snake_case							)							)
			print('''LCA of node 6 and 7 is: '''  ,      lowest_common_ancestor(6  ,      7  ,      _snake_case  ,      _snake_case							)							)
			print('''LCA of node 4 and 12 is: '''  ,      lowest_common_ancestor(4  ,      12  ,      _snake_case  ,      _snake_case							)							)
			print('''LCA of node 8 and 8 is: '''  ,      lowest_common_ancestor(8  ,      8  ,      _snake_case  ,      _snake_case							)							)


if __name__ == "__main__":
			main()








from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_sentencepiece_available, is_torch_available


UpperCAmelCase_		   =				{
    """configuration_xlm_prophetnet""": ["""XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP""", """XLMProphetNetConfig"""],
}

try:
   if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase_		   =				["""XLMProphetNetTokenizer"""]

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase_		   =				[
       """XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST""",
       """XLMProphetNetDecoder""",
       """XLMProphetNetEncoder""",
       """XLMProphetNetForCausalLM""",
       """XLMProphetNetForConditionalGeneration""",
       """XLMProphetNetModel""",
       """XLMProphetNetPreTrainedModel""",
   ]


if TYPE_CHECKING:
   from .configuration_xlm_prophetnet import XLM_PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, XLMProphetNetConfig

   try:
      if not is_sentencepiece_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_xlm_prophetnet import XLMProphetNetTokenizer

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_xlm_prophetnet import (
          XLM_PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
          XLMProphetNetDecoder,
          XLMProphetNetEncoder,
          XLMProphetNetForCausalLM,
          XLMProphetNetForConditionalGeneration,
          XLMProphetNetModel,
          XLMProphetNetPreTrainedModel,
      )

else:
   import sys

   UpperCAmelCase_		   =				_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



