code: def size_hint(
      self, expr: Expr, *, fallback: Optional[int] = None
  ) -> int:
      out = self.symbolic_hint(expr)
      if (
          not isinstance(out, (int, sympy.Integer))
          and fallback is not None
      ):
          # Use the provided heuristic fallback hint
          sym_vrs = {
              s: self.shape_env.var_to_range.get(s, None)
              for s in expr.free_symbols
          }
          if all(vr is not None for vr in sym_vrs.values()):
              expr_vr = bound_sympy(expr, sym_vrs)
              lower = self.size_hint(expr_vr.lower)
              upper = self.size_hint(expr_vr.upper)
              fallback = min(max(fallback, lower), upper)
          return fallback
      try:
          return int(out)
      except Exception:
          log.debug("failed on: %s", out)
          raise
  
imports: import functools
  import itertools
  import logging
  from typing import Any, Callable, Dict, Iterable, List, Optional, Set, Tuple, Union
  import sympy
  from sympy import Expr
  from torch.fx.experimental.symbolic_shapes import ShapeEnv
  from torch.utils._sympy.functions import FloorDiv, ModularIndexing
  from torch.utils._sympy.value_ranges import bound_sympy
  from .utils import sympy_subs, sympy_symbol, VarRanges
  from .virtualized import V
label_desc: Use image node_id 26 for calling the SizeVarAllocator obj's underlying member method code with example usage: obj.size_hint(expr) and returns: fallback, int