# Path: opt_einsum/parser.py
# def get_symbol(i: int) -> str:
#     """Get the symbol corresponding to int ``i`` - runs through the usual 52
#     letters before resorting to unicode characters, starting at ``chr(192)``.
# 
#     **Examples:**
# 
#     ```python
#     get_symbol(2)
#     #> 'c'
# 
#     get_symbol(200)
#     #> 'Ŕ'
# 
#     get_symbol(20000)
#     #> '京'
#     ```
#     """
#     if i < 52:
#         return _einsum_symbols_base[i]
#     return chr(i + 140)
# 
# Path: opt_einsum/typing.py



from typing import Any, Collection, Dict, FrozenSet, Iterable, List, Optional, Tuple, Union, overload
from .parser import get_symbol
from .typing import ArrayIndexType, PathType
import numpy as np
    size_dict : dict[str, int]
        The dict of index sizes, only returned if ``return_size_dict=True``.

    Examples
    --------
    >>> eq, shapes = rand_equation(n=10, reg=4, n_out=5, seed=42)
    >>> eq
    'oyeqn,tmaq,skpo,vg,hxui,n,fwxmr,hitplcj,kudlgfv,rywjsb->cebda'

    >>> shapes
    [(9, 5, 4, 5, 4),
     (4, 4, 8, 5),
     (9, 4, 6, 9),
     (6, 6),
     (6, 9, 7, 8),
     (4,),
     (9, 3, 9, 4, 9),
     (6, 8, 4, 6, 8, 6, 3),
     (4, 7, 8, 8, 6, 9, 6),
     (9, 5, 3, 3, 9, 5)]
    """

    if seed is not None:
        np.random.seed(seed)

    # total number of indices
    num_inds = n * reg // 2 + n_out
    inputs = ["" for _ in range(n)]
    output = []


# Path: opt_einsum/parser.py
# def get_symbol(i: int) -> str:
#     """Get the symbol corresponding to int ``i`` - runs through the usual 52
#     letters before resorting to unicode characters, starting at ``chr(192)``.
# 
#     **Examples:**
# 
#     ```python
#     get_symbol(2)
#     #> 'c'
# 
#     get_symbol(200)
#     #> 'Ŕ'
# 
#     get_symbol(20000)
#     #> '京'
#     ```
#     """
#     if i < 52:
#         return _einsum_symbols_base[i]
#     return chr(i + 140)
# 
# Path: opt_einsum/typing.py



# Path: opt_einsum/helpers.py
from typing import Any, Collection, Dict, FrozenSet, Iterable, List, Optional, Tuple, Union, overload
from .parser import get_symbol
from .typing import ArrayIndexType, PathType
import numpy as np

    size_dict : dict[str, int]
        The dict of index sizes, only returned if ``return_size_dict=True``.

    Examples
    --------
    >>> eq, shapes = rand_equation(n=10, reg=4, n_out=5, seed=42)
    >>> eq
    'oyeqn,tmaq,skpo,vg,hxui,n,fwxmr,hitplcj,kudlgfv,rywjsb->cebda'

    >>> shapes
    [(9, 5, 4, 5, 4),
     (4, 4, 8, 5),
     (9, 4, 6, 9),
     (6, 6),
     (6, 9, 7, 8),
     (4,),
     (9, 3, 9, 4, 9),
     (6, 8, 4, 6, 8, 6, 3),
     (4, 7, 8, 8, 6, 9, 6),
     (9, 5, 3, 3, 9, 5)]
    """

    if seed is not None:
        np.random.seed(seed)

    # total number of indices
    num_inds = n * reg // 2 + n_out
    inputs = ["" for _ in range(n)]
    output = []


    size_dict = {get_symbol(i): np.random.randint(d_min, d_max + 1) for i in range(num_inds)}