


'''simple docstring'''

from __future__ import annotations

import os
from collections.abc import Mapping

lowercase__				     =		tuple[int, int]





class 						__SCREAMING_SNAKE_CASE					:






     def __init__(			self     ,							__UpperCamelCase     ,							__UpperCamelCase		)       ->    None:
          _a						=		vertices
          _a						=		{
              (min(__UpperCamelCase		), max(__UpperCamelCase		)): weight for edge, weight in edges.items()
          }






     def  a_					(			self     ,							__UpperCamelCase     ,							__UpperCamelCase		)       ->    None:
          self.vertices.add(edge[0]		)
          self.vertices.add(edge[1]		)
          _a						=		weight






     def  a_					(			self		)       ->    Graph:
          _a						=		Graph({min(self.vertices		)}     ,							{}		)
          _a						=		42
          _a						=		42
          _a						=		42
          _a						=		42

          while len(subgraph.vertices		) < len(self.vertices		):
               _a						=		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						=		edge
                              _a						=		weight

               subgraph.add_edge(__UpperCamelCase     ,							__UpperCamelCase		)

          return subgraph







def __UpperCamelCase   (			__lowerCamelCase		: str = "p107_network.txt"				)      ->     int:







     '''simple docstring'''






     _a						=		os.path.abspath(os.path.dirname(__lowerCamelCase				)				)
     _a						=		os.path.join(__lowerCamelCase      ,  __lowerCamelCase				)
     _a						=		{}
     _a						=		42
     _a						=		42
     _a						=		42

     with open(__lowerCamelCase				) as f:
          _a						=		f.read().strip().split("\n"				)

     _a						=		[line.split(","				) for line in data]

     for edgea in range(1      ,  len(__lowerCamelCase				)				):
          for edgea in range(__lowerCamelCase				):
               if adjaceny_matrix[edgea][edgea] != "-":
                    _a						=		int(adjaceny_matrix[edgea][edgea]				)

     _a						=		Graph(set(range(len(__lowerCamelCase				)				)				)      ,  __lowerCamelCase				)

     _a						=		graph.prims_algorithm()

     _a						=		sum(graph.edges.values()				)
     _a						=		sum(subgraph.edges.values()				)

     return initial_total - optimal_total


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





'''simple docstring'''

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
lowercase__				     =		object()

# For specifying empty leaf dict `{}`
lowercase__				     =		object()






def __UpperCamelCase   (			__lowerCamelCase		: Tuple      ,  __lowerCamelCase		: Tuple				)      ->     Union[str, Any]:







     '''simple docstring'''






     _a						=		tuple((re.compile(x + "$"				) for x in qs)				)
     for i in range(len(__lowerCamelCase				) - len(__lowerCamelCase				) + 1				):
          _a						=		[x.match(__lowerCamelCase				) for x, y in zip(__lowerCamelCase      ,  ks[i:]				)]
          if matches and all(__lowerCamelCase				):
               return True
     return False






def __UpperCamelCase   (			__lowerCamelCase		: int				)      ->     Union[str, Any]:







     '''simple docstring'''






     def replace(__lowerCamelCase		: Tuple      ,  __lowerCamelCase		: Any				):
          for rule, replacement in rules:
               if _match(__lowerCamelCase      ,  __lowerCamelCase				):
                    return replacement
          return val

     return replace






def __UpperCamelCase   (			)      ->     Tuple:







     '''simple docstring'''






     return [
         # embeddings
         (("transformer", "wpe", "embedding"), P("mp"      ,  __lowerCamelCase				)),
         (("transformer", "wte", "embedding"), P("mp"      ,  __lowerCamelCase				)),
         # atention
         (("attention", "(q_proj|k_proj|v_proj)", "kernel"), P(__lowerCamelCase      ,  "mp"				)),
         (("attention", "out_proj", "kernel"), P("mp"      ,  __lowerCamelCase				)),
         (("attention", "out_proj", "bias"), None),
         # mlp
         (("mlp", "c_fc", "kernel"), P(__lowerCamelCase      ,  "mp"				)),
         (("mlp", "c_fc", "bias"), P("mp"				)),
         (("mlp", "c_proj", "kernel"), P("mp"      ,  __lowerCamelCase				)),
         (("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   (			__lowerCamelCase		: Dict				)      ->     Tuple:







     '''simple docstring'''






     _a						=		_get_partition_rules()
     _a						=		_replacement_rules(__lowerCamelCase				)
     _a						=		{k: _unmatched for k in flatten_dict(__lowerCamelCase				)}
     _a						=		{k: replace(__lowerCamelCase      ,  __lowerCamelCase				) for k, v in initd.items()}
     assert _unmatched not in result.values(), "Incomplete partition spec."
     return freeze(unflatten_dict(__lowerCamelCase				)				)

