


from __future__ import annotations

import os
from collections.abc import Mapping

lowerCAmelCase__      		= tuple[int, int]







class      lowerCAmelCase__       :




     '''simple docstring'''


     def __init__(						self ,						__lowerCamelCase ,						__lowerCamelCase)			->				None:
            _A      :       set[int]				    = vertices
            _A      :       dict[EdgeT, int]				    = {
                (min(__lowerCamelCase), max(__lowerCamelCase)): weight for edge, weight in edges.items()
            }


     def  _lowerCamelCase (						self ,						__lowerCamelCase ,						__lowerCamelCase)			->				None:
            self.vertices.add(edge[0])
            self.vertices.add(edge[1])
            _A      :       int				    = weight


     def  _lowerCamelCase (						self)			->				Graph:
            _A      :       Graph				    = Graph({min(self.vertices)} ,						{})
            _A      :       EdgeT
            _A      :       int
            _A      :       EdgeT
            _A      :       int

            while len(subgraph.vertices) < len(self.vertices):
                   _A      :       Any				    = max(self.edges.values()) + 1
                   for edge, weight in self.edges.items():
                          if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
                                 if weight < min_weight:
                                        _A      :       int				    = edge
                                        _A      :       int				    = weight

                   subgraph.add_edge(__lowerCamelCase ,						__lowerCamelCase)

            return subgraph




def 							_UpperCAmelCase				(UpperCamelCase__     :  str = "p107_network.txt"						):
       _A      :       str				    = os.path.abspath(os.path.dirname(UpperCamelCase__						)						)
       _A      :       str				    = os.path.join(UpperCamelCase__				,							UpperCamelCase__						)
       _A      :       dict[EdgeT, int]				    = {}
       _A      :       list[str]
       _A      :       int
       _A      :       int

       with open(UpperCamelCase__						) as f:
              _A      :       Dict				    = f.read().strip().split("\n"						)

       _A      :       List[str]				    = [line.split(","						) for line in data]

       for edgea in range(1				,							len(UpperCamelCase__						)						):
              for edgea in range(UpperCamelCase__						):
                     if adjaceny_matrix[edgea][edgea] != "-":
                            _A      :       List[Any]				    = int(adjaceny_matrix[edgea][edgea]						)

       _A      :       Graph				    = Graph(set(range(len(UpperCamelCase__						)						)						)				,							UpperCamelCase__						)

       _A      :       Graph				    = graph.prims_algorithm()

       _A      :       int				    = sum(graph.edges.values()						)
       _A      :       int				    = sum(subgraph.edges.values()						)

       return initial_total - optimal_total


if __name__ == "__main__":
    print(f"{solution() = }")




import re

from flax.core.frozen_dict import freeze
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.experimental import PartitionSpec as P


# Sentinels
lowerCAmelCase__      		= object()

# For specifying empty leaf dict `{}`
lowerCAmelCase__      		= object()
def 							_UpperCAmelCase				(UpperCamelCase__     :  str				,							UpperCamelCase__     :  Union[str, Any]						):
       _A      :       str				    = tuple((re.compile(x + "$"						) for x in qs)						)
       for i in range(len(UpperCamelCase__						) - len(UpperCamelCase__						) + 1						):
              _A      :       Tuple				    = [x.match(UpperCamelCase__						) for x, y in zip(UpperCamelCase__				,							ks[i:]						)]
              if matches and all(UpperCamelCase__						):
                     return True
       return False
def 							_UpperCAmelCase				(UpperCamelCase__     :  str						):
       def replace(UpperCamelCase__     :  List[str]				,							UpperCamelCase__     :  Optional[int]						):
              for rule, replacement in rules:
                     if _match(UpperCamelCase__				,							UpperCamelCase__						):
                            return replacement
              return val

       return replace
def 							_UpperCAmelCase				():
       return [
           # embeddings
           (("transformer", "wpe", "embedding"), P("mp"				,							UpperCamelCase__						)),
           (("transformer", "wte", "embedding"), P("mp"				,							UpperCamelCase__						)),
           # atention
           (("attention", "(q_proj|k_proj|v_proj)", "kernel"), P(UpperCamelCase__				,							"mp"						)),
           (("attention", "out_proj", "kernel"), P("mp"				,							UpperCamelCase__						)),
           (("attention", "out_proj", "bias"), None),
           # mlp
           (("mlp", "c_fc", "kernel"), P(UpperCamelCase__				,							"mp"						)),
           (("mlp", "c_fc", "bias"), P("mp"						)),
           (("mlp", "c_proj", "kernel"), P("mp"				,							UpperCamelCase__						)),
           (("mlp", "c_proj", "bias"), None),
           # layer norms
           ((r"ln_\d+", "bias"), None),
           ((r"\d+", r"ln_\d+", "scale"), None),
           (("ln_f", "bias"), None),
           (("ln_f", "scale"), None),
       ]






def 							_UpperCAmelCase				(UpperCamelCase__     :  List[str]						):
       _A      :       int				    = _get_partition_rules()
       _A      :       Optional[int]				    = _replacement_rules(UpperCamelCase__						)
       _A      :       Optional[int]				    = {k: _unmatched for k in flatten_dict(UpperCamelCase__						)}
       _A      :       List[str]				    = {k: replace(UpperCamelCase__				,							UpperCamelCase__						) for k, v in initd.items()}
       assert _unmatched not in result.values(), "Incomplete partition spec."
       return freeze(unflatten_dict(UpperCamelCase__						)						)
