code: def enumerate(self, edge, lengths=None):
      semiring = self.semiring
      edge, batch, N, M, lengths = self._check_potentials(edge, lengths)
      d = {}
      d[0, 0] = [([(0, 0)], edge[:, :, 0, 0, 1])]
      # enum_lengths = torch.LongTensor(lengths.shape)
      for i in range(N):
          for j in range(M):
              d.setdefault((i + 1, j + 1), [])
              d.setdefault((i, j + 1), [])
              d.setdefault((i + 1, j), [])
              for chain, score in d[i, j]:
                  if i + 1 < N and j + 1 < M:
                      d[i + 1, j + 1].append(
                          (
                              chain + [(i + 1, j + 1)],
                              semiring.mul(
                                  score, edge[:, :, i + 1, j + 1, 1]
                              ),
                          )
                      )
                  if i + 1 < N:
                      d[i + 1, j].append(
                          (
                              chain + [(i + 1, j)],
                              semiring.mul(
                                  score, edge[:, :, i + 1, j, 2]
                              ),
                          )
                      )
                  if j + 1 < M:
                      d[i, j + 1].append(
                          (
                              chain + [(i, j + 1)],
                              semiring.mul(
                                  score, edge[:, :, i, j + 1, 0]
                              ),
                          )
                      )
      all_val = torch.stack([x[1] for x in d[N - 1, M - 1]], dim=-1)
      return semiring.unconvert(semiring.sum(all_val)), None
  
imports: import torch_struct
  import torch
  from torch_struct import LogSemiring
  import itertools
  from hypothesis.strategies import integers, composite, floats
  from hypothesis.extra.numpy import arrays
  import numpy
label_desc: Use image node_id 3 for calling the AlignmentTest obj's underlying member method code with example usage: obj.enumerate(edge, lengths) and returns: semiring,  None