




from __future__ import annotations

from queue import Queue







def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int	):
					a ^= b
					b ^= a
					a ^= b
					return a, b







def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							list[list[int]]	):
					__lowerCAmelCase							  =			1
					while (1 << j) < max_node:
										for i in range(1 , max_node + 1	):
															__lowerCAmelCase							  =			parent[j - 1][parent[j - 1][i]]
										j += 1
					return parent







def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							list[int] , SCREAMING_SNAKE_CASE_				:							list[list[int]]	):
					# u must be deeper in the tree than v
					if level[u] < level[v]:
										__lowerCAmelCase  ,				__lowerCAmelCase							  =			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							  =			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  ,				__lowerCAmelCase							  =			parent[i][u], parent[i][v]
    # returning longest common ancestor of u,v
					return parent[0][u]







def       _a (		SCREAMING_SNAKE_CASE_				:							list[int] , SCREAMING_SNAKE_CASE_				:							list[list[int]] , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							dict[int, list[int]] , SCREAMING_SNAKE_CASE_				:							int = 1 , ):
					__lowerCAmelCase							  =			0
					__lowerCAmelCase							  =			Queue(maxsize=SCREAMING_SNAKE_CASE_	)
					q.put(SCREAMING_SNAKE_CASE_	)
					while q.qsize() != 0:
										__lowerCAmelCase							  =			q.get()
										for v in graph[u]:
															if level[v] == -1:
																				__lowerCAmelCase							  =			level[u] + 1
																				q.put(SCREAMING_SNAKE_CASE_	)
																				__lowerCAmelCase							  =			u
					return level, parent







def       _a (		):
					__lowerCAmelCase							  =			13
					# initializing with 0
					__lowerCAmelCase							  =			[[0 for _ in range(max_node + 10	)] for _ in range(20	)]
					# initializing with -1 which means every node is unvisited
					__lowerCAmelCase							  =			[-1 for _ in range(max_node + 10	)]
					__lowerCAmelCase							  =			{
					    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  ,				__lowerCAmelCase							  =			breadth_first_search(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_ , 1	)
					__lowerCAmelCase							  =			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()










from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCamelCase__            =     {
    """configuration_marian""": ["""MARIAN_PRETRAINED_CONFIG_ARCHIVE_MAP""", """MarianConfig""", """MarianOnnxConfig"""],
}

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

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase__            =     [
					    """MARIAN_PRETRAINED_MODEL_ARCHIVE_LIST""",
					    """MarianForCausalLM""",
					    """MarianModel""",
					    """MarianMTModel""",
					    """MarianPreTrainedModel""",
					]

try:
					if not is_tf_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase__            =     ["""TFMarianModel""", """TFMarianMTModel""", """TFMarianPreTrainedModel"""]

try:
					if not is_flax_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					UpperCamelCase__            =     ["""FlaxMarianModel""", """FlaxMarianMTModel""", """FlaxMarianPreTrainedModel"""]

if TYPE_CHECKING:
					from .configuration_marian import MARIAN_PRETRAINED_CONFIG_ARCHIVE_MAP, MarianConfig, MarianOnnxConfig

					try:
										if not is_sentencepiece_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .tokenization_marian import MarianTokenizer

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_marian import (
										    MARIAN_PRETRAINED_MODEL_ARCHIVE_LIST,
										    MarianForCausalLM,
										    MarianModel,
										    MarianMTModel,
										    MarianPreTrainedModel,
										)

					try:
										if not is_tf_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_tf_marian import TFMarianModel, TFMarianMTModel, TFMarianPreTrainedModel

					try:
										if not is_flax_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_flax_marian import FlaxMarianModel, FlaxMarianMTModel, FlaxMarianPreTrainedModel

else:
					import sys

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




