# Path: opt_einsum/typing.py



import itertools
import numpy as np
from typing import Any, Dict, Iterator, List, Tuple
from .typing import ArrayType, TensorShapeType
    """
    rename: Dict[str, str] = {}
    for name in equation:
        if name in ".,->":
            continue
        if name not in rename:
            rename[name] = get_symbol(len(rename))
    return "".join(rename.get(x, x) for x in equation)


def find_output_str(subscripts: str) -> str:
    """
    Find the output string for the inputs ``subscripts`` under canonical einstein summation rules.
    That is, repeated indices are summed over by default.

    Examples
    --------
    >>> oe.parser.find_output_str("ab,bc")
    'ac'

    >>> oe.parser.find_output_str("a,b")
    'ab'

    >>> oe.parser.find_output_str("a,a,b,b")
    ''
    """
    tmp_subscripts = subscripts.replace(",", "")
    return "".join(s for s in sorted(set(tmp_subscripts)) if tmp_subscripts.count(s) == 1)



# Path: opt_einsum/typing.py



# Path: opt_einsum/parser.py
import itertools
import numpy as np
from typing import Any, Dict, Iterator, List, Tuple
from .typing import ArrayType, TensorShapeType

    """
    rename: Dict[str, str] = {}
    for name in equation:
        if name in ".,->":
            continue
        if name not in rename:
            rename[name] = get_symbol(len(rename))
    return "".join(rename.get(x, x) for x in equation)


def find_output_str(subscripts: str) -> str:
    """
    Find the output string for the inputs ``subscripts`` under canonical einstein summation rules.
    That is, repeated indices are summed over by default.

    Examples
    --------
    >>> oe.parser.find_output_str("ab,bc")
    'ac'

    >>> oe.parser.find_output_str("a,b")
    'ab'

    >>> oe.parser.find_output_str("a,a,b,b")
    ''
    """
    tmp_subscripts = subscripts.replace(",", "")
    return "".join(s for s in sorted(set(tmp_subscripts)) if tmp_subscripts.count(s) == 1)



def find_output_shape(inputs: List[str], shapes: List[TensorShapeType], output: str) -> TensorShapeType: