# Path: opt_einsum/helpers.py
# @overload
# def compute_size_by_dict(indices: Iterable[int], idx_dict: List[int]) -> int:
#     ...
# 
# def flop_count(
#     idx_contraction: Collection[str],
#     inner: bool,
#     num_terms: int,
#     size_dictionary: Dict[str, int],
# ) -> int:
#     """
#     Computes the number of FLOPS in the contraction.
# 
#     Parameters
#     ----------
#     idx_contraction : iterable
#         The indices involved in the contraction
#     inner : bool
#         Does this contraction require an inner product?
#     num_terms : int
#         The number of terms in a contraction
#     size_dictionary : dict
#         The size of each of the indices in idx_contraction
# 
#     Returns
#     -------
#     flop_count : int
#         The total number of FLOPS required for the contraction.
# 
#     Examples
#     --------
# 
#     >>> flop_count('abc', False, 1, {'a': 2, 'b':3, 'c':5})
#     30
# 
#     >>> flop_count('abc', True, 2, {'a': 2, 'b':3, 'c':5})
#     60
# 
#     """
# 
#     overall_size = compute_size_by_dict(idx_contraction, size_dictionary)
#     op_factor = max(1, num_terms - 1)
#     if inner:
#         op_factor += 1
# 
#     return overall_size * op_factor
# 
# Path: opt_einsum/typing.py



import functools
import heapq
import itertools
import operator
import random
import re
import numpy as np
from collections import Counter, OrderedDict, defaultdict
from typing import Any, Callable
from typing import Counter as CounterType
from typing import Dict, FrozenSet, Generator, List, Optional, Sequence, Set, Tuple, Union
from .helpers import compute_size_by_dict, flop_count
from .typing import ArrayIndexType, PathType
    from .path_random import random_greedy_128
    ```

    where `path` is a list of int-tuples specifying a contraction order.
    """

    def _check_args_against_first_call(
        self,
        inputs: List[ArrayIndexType],
        output: ArrayIndexType,
        size_dict: Dict[str, int],
    ) -> None:
        """Utility that stateful optimizers can use to ensure they are not
        called with different contractions across separate runs.
        """
        args = (inputs, output, size_dict)
        if not hasattr(self, "_first_call_args"):
            # simply set the attribute as currently there is no global PathOptimizer init
            self._first_call_args = args
        elif args != self._first_call_args:
            raise ValueError(
                "The arguments specifying the contraction that this path optimizer "
                "instance was called with have changed - try creating a new instance."
            )

    def __call__(
        self,
        inputs: List[ArrayIndexType],
        output: ArrayIndexType,
        size_dict: Dict[str, int],
        memory_limit: Optional[int] = None,

# Path: opt_einsum/helpers.py
# @overload
# def compute_size_by_dict(indices: Iterable[int], idx_dict: List[int]) -> int:
#     ...
# 
# def flop_count(
#     idx_contraction: Collection[str],
#     inner: bool,
#     num_terms: int,
#     size_dictionary: Dict[str, int],
# ) -> int:
#     """
#     Computes the number of FLOPS in the contraction.
# 
#     Parameters
#     ----------
#     idx_contraction : iterable
#         The indices involved in the contraction
#     inner : bool
#         Does this contraction require an inner product?
#     num_terms : int
#         The number of terms in a contraction
#     size_dictionary : dict
#         The size of each of the indices in idx_contraction
# 
#     Returns
#     -------
#     flop_count : int
#         The total number of FLOPS required for the contraction.
# 
#     Examples
#     --------
# 
#     >>> flop_count('abc', False, 1, {'a': 2, 'b':3, 'c':5})
#     30
# 
#     >>> flop_count('abc', True, 2, {'a': 2, 'b':3, 'c':5})
#     60
# 
#     """
# 
#     overall_size = compute_size_by_dict(idx_contraction, size_dictionary)
#     op_factor = max(1, num_terms - 1)
#     if inner:
#         op_factor += 1
# 
#     return overall_size * op_factor
# 
# Path: opt_einsum/typing.py



# Path: opt_einsum/paths.py
import functools
import heapq
import itertools
import operator
import random
import re
import numpy as np
from collections import Counter, OrderedDict, defaultdict
from typing import Any, Callable
from typing import Counter as CounterType
from typing import Dict, FrozenSet, Generator, List, Optional, Sequence, Set, Tuple, Union
from .helpers import compute_size_by_dict, flop_count
from .typing import ArrayIndexType, PathType
    from .path_random import random_greedy_128

    ```

    where `path` is a list of int-tuples specifying a contraction order.
    """

    def _check_args_against_first_call(
        self,
        inputs: List[ArrayIndexType],
        output: ArrayIndexType,
        size_dict: Dict[str, int],
    ) -> None:
        """Utility that stateful optimizers can use to ensure they are not
        called with different contractions across separate runs.
        """
        args = (inputs, output, size_dict)
        if not hasattr(self, "_first_call_args"):
            # simply set the attribute as currently there is no global PathOptimizer init
            self._first_call_args = args
        elif args != self._first_call_args:
            raise ValueError(
                "The arguments specifying the contraction that this path optimizer "
                "instance was called with have changed - try creating a new instance."
            )

    def __call__(
        self,
        inputs: List[ArrayIndexType],
        output: ArrayIndexType,
        size_dict: Dict[str, int],
        memory_limit: Optional[int] = None,

    ) -> PathType: