A KLA process planner records n projects in execution order. Each project has a positive completion time and belongs to one of three groups, represented by labels 0, 1, or 2. For a target time d, count the number of non-empty subsequences whose selected completion times sum to exactly d, with no two consecutively selected projects belonging to the same group.
A subsequence preserves the original project order, but projects may be skipped. Projects are identified by their indices, so selecting different projects with equal completion times produces different subsequences. Return the count as an integer. The answer will fit within a signed 64-bit integer.
Implement count_valid_sequences(times, groups, d), where times[i] is the completion time of project i, groups[i] is its group, and d is the required total time. Return the number of valid non-empty subsequences.
def count_valid_sequences(times, groups, d):