def compute_compatible_dim_mapping(dim_mapping_list):
    """Compute the compatible dim mapping given a list of dim mapping."""
    if not dim_mapping_list:
        return None

    def _compute_compatible_dim_mapping_two(dm1, dm2):
        if dm1 == -1:
            return True, dm2
        if dm2 == -1:
            return True, dm1
        if dm1 == dm2:
            return True, dm1
        return False, None

    compatible_result = -1
    for mapping in dim_mapping_list:
        compatible, compatible_result = _compute_compatible_dim_mapping_two(
            compatible_result, mapping)
        if not compatible:
            return None
    return compatible_result