



import heapq as hq
import math
from collections.abc import Iterator





class 		UpperCAmelCase						:





			def __init__(	self       ,     _lowerCAmelCase			):
									_lowerCAmelCase 			=  str(id_			)
									_lowerCAmelCase 			=  None
									_lowerCAmelCase 			=  None
									_lowerCAmelCase 			=  []
									_lowerCAmelCase 			=  {}  # {vertex:distance}





			def __lt__(	self       ,     _lowerCAmelCase			):
									return self.key < other.key





			def __repr__(	self			):
									return self.id





			def 	__lowerCAmelCase							(	self       ,     _lowerCAmelCase			):
									self.neighbors.append(UpperCamelCase__			)





			def 	__lowerCAmelCase							(	self       ,     _lowerCAmelCase       ,     _lowerCAmelCase			):
									_lowerCAmelCase 			=  weight






def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	Optional[int]     ,				_SCREAMING_SNAKE_CASE   :	Any     ,				_SCREAMING_SNAKE_CASE   :	Any     ,				_SCREAMING_SNAKE_CASE   :	Tuple				)->Optional[Any]:
						# add the neighbors:
						graph[a - 1].add_neighbor(graph[b - 1]				)
						graph[b - 1].add_neighbor(graph[a - 1]				)
						# add the edges:
						graph[a - 1].add_edge(graph[b - 1]     ,				_SCREAMING_SNAKE_CASE				)
						graph[b - 1].add_edge(graph[a - 1]     ,				_SCREAMING_SNAKE_CASE				)
def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	list     ,				_SCREAMING_SNAKE_CASE   :	Vertex				)->Optional[int]:
						_lowerCAmelCase 			=  []
						for u in graph:
												_lowerCAmelCase 			=  math.inf
												_lowerCAmelCase 			=  None
						_lowerCAmelCase 			=  0
						_lowerCAmelCase 			=  graph[:]
						while q:
												_lowerCAmelCase 			=  min(_SCREAMING_SNAKE_CASE				)
												q.remove(_SCREAMING_SNAKE_CASE				)
												for v in u.neighbors:
																		if (v in q) and (u.edges[v.id] < v.key):
																								_lowerCAmelCase 			=  u
																								_lowerCAmelCase 			=  u.edges[v.id]
						for i in range(1     ,				len(_SCREAMING_SNAKE_CASE				)				):
												a.append((int(graph[i].id				) + 1, int(graph[i].pi.id				) + 1)				)
						return a
def 							UpperCAmelCase__		(				_SCREAMING_SNAKE_CASE   :	list     ,				_SCREAMING_SNAKE_CASE   :	Vertex				)->int:
						for u in graph:
												_lowerCAmelCase 			=  math.inf
												_lowerCAmelCase 			=  None
						_lowerCAmelCase 			=  0

						_lowerCAmelCase 			=  list(_SCREAMING_SNAKE_CASE				)
						hq.heapify(_SCREAMING_SNAKE_CASE				)

						while h:
												_lowerCAmelCase 			=  hq.heappop(_SCREAMING_SNAKE_CASE				)
												for v in u.neighbors:
																		if (v in h) and (u.edges[v.id] < v.key):
																								_lowerCAmelCase 			=  u
																								_lowerCAmelCase 			=  u.edges[v.id]
																								hq.heapify(_SCREAMING_SNAKE_CASE				)

						for i in range(1     ,				len(_SCREAMING_SNAKE_CASE				)				):
												yield (int(graph[i].id				) + 1, int(graph[i].pi.id				) + 1)
def 							UpperCAmelCase__		(				)->Optional[int]:
						pass


if __name__ == "__main__":
				import doctest

				doctest.testmod()




from typing import TYPE_CHECKING

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


UpperCAmelCase_									=							{"processing_layoutxlm": ["LayoutXLMProcessor"]}

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

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

if TYPE_CHECKING:
    from .processing_layoutxlm import LayoutXLMProcessor

    try:
        if not is_sentencepiece_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_layoutxlm import LayoutXLMTokenizer

    try:
        if not is_tokenizers_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .tokenization_layoutxlm_fast import LayoutXLMTokenizerFast

else:
    import sys

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