def write_predictions(all_examples, all_features, all_results, n_best_size,
                      max_answer_length, do_lower_case, output_prediction_file,
                      output_nbest_file, output_null_log_odds_file, verbose_logging,
                      version_2_with_negative, null_score_diff_threshold):
    """Write final predictions to the json file and log-odds of null if needed."""
    logger.info("Writing predictions to: %s" % (output_prediction_file))
    logger.info("Writing nbest to: %s" % (output_nbest_file))

    example_index_to_features = collections.defaultdict(list)
    for feature in all_features:
        example_index_to_features[feature.example_index].append(feature)

    unique_id_to_result = {}
    for result in all_results:
        unique_id_to_result[result.unique_id] = result

    _PrelimPrediction = collections.namedtuple(  # pylint: disable=invalid-name
        "PrelimPrediction",
        ["feature_index", "start_index", "end_index", "start_logit", "end_logit"])

    all_predictions = collections.OrderedDict()
    all_nbest_json = collections.OrderedDict()
    scores_diff_json = collections.OrderedDict()

    for (example_index, example) in enumerate(all_examples):
        features = example_index_to_features[example_index]

        prelim_predictions = []
        # keep track of the minimum score of null start+end of position 0
        score_null = 1000000  # large and positive
        min_null_feature_index = 0  # the paragraph slice with min null score
        null_start_logit = 0  # the start logit at the slice with min null score
        null_end_logit = 0  # the end logit at the slice with min null score
        for (feature_index, feature) in enumerate(features):
            result = unique_id_to_result[feature.unique_id]
            start_indexes = _get_best_indexes(result.start_logits, n_best_size)
            end_indexes = _get_best_indexes(result.end_logits, n_best_size)
            # if we could have irrelevant answers, get the min score of irrelevant
            if version_2_with_negative:
                feature_null_score = result.start_logits[0] + result.end_logits[0]
                if feature_null_score < score_null:
                    score_null = feature_null_score
                    min_null_feature_index = feature_index
                    null_start_logit = result.start_logits[0]
                    null_end_logit = result.end_logits[0]
            for start_index in start_indexes:
                for end_index in end_indexes:
                    # We could hypothetically create invalid predictions, e.g., predict
                    # that the start of the span is in the question. We throw out all
                    # invalid predictions.
                    if start_index >= len(feature.tokens):
                        continue
                    if end_index >= len(feature.tokens):
                        continue
                    if start_index not in feature.token_to_orig_map:
                        continue
                    if end_index not in feature.token_to_orig_map:
                        continue
                    if not feature.token_is_max_context.get(start_index, False):
                        continue
                    if end_index < start_index:
                        continue
                    length = end_index - start_index + 1
                    if length > max_answer_length:
                        continue
                    prelim_predictions.append(
                        _PrelimPrediction(
                            feature_index=feature_index,
                            start_index=start_index,
                            end_index=end_index,
                            start_logit=result.start_logits[start_index],
                            end_logit=result.end_logits[end_index]))
        if version_2_with_negative:
            prelim_predictions.append(
                _PrelimPrediction(
                    feature_index=min_null_feature_index,
                    start_index=0,
                    end_index=0,
                    start_logit=null_start_logit,
                    end_logit=null_end_logit))
        prelim_predictions = sorted(
            prelim_predictions,
            key=lambda x: (x.start_logit + x.end_logit),
            reverse=True)

        _NbestPrediction = collections.namedtuple(  # pylint: disable=invalid-name
            "NbestPrediction", ["text", "start_logit", "end_logit"])

        seen_predictions = {}
        nbest = []
        for pred in prelim_predictions:
            if len(nbest) >= n_best_size:
                break
            feature = features[pred.feature_index]
            if pred.start_index > 0:  # this is a non-null prediction
                tok_tokens = feature.tokens[pred.start_index:(pred.end_index + 1)]
                orig_doc_start = feature.token_to_orig_map[pred.start_index]
                orig_doc_end = feature.token_to_orig_map[pred.end_index]
                orig_tokens = example.doc_tokens[orig_doc_start:(orig_doc_end + 1)]
                tok_text = " ".join(tok_tokens)

                # De-tokenize WordPieces that have been split off.
                tok_text = tok_text.replace(" ##", "")
                tok_text = tok_text.replace("##", "")

                # Clean whitespace
                tok_text = tok_text.strip()
                tok_text = " ".join(tok_text.split())
                orig_text = " ".join(orig_tokens)

                final_text = get_final_text(tok_text, orig_text, do_lower_case, verbose_logging)
                if final_text in seen_predictions:
                    continue

                seen_predictions[final_text] = True
            else:
                final_text = ""
                seen_predictions[final_text] = True

            nbest.append(
                _NbestPrediction(
                    text=final_text,
                    start_logit=pred.start_logit,
                    end_logit=pred.end_logit))
        # if we didn't include the empty option in the n-best, include it
        if version_2_with_negative:
            if "" not in seen_predictions:
                nbest.append(
                    _NbestPrediction(
                        text="",
                        start_logit=null_start_logit,
                        end_logit=null_end_logit))
                
            # In very rare edge cases we could only have single null prediction.
            # So we just create a nonce prediction in this case to avoid failure.
            if len(nbest)==1:
                nbest.insert(0,
                    _NbestPrediction(text="empty", start_logit=0.0, end_logit=0.0))
                
        # In very rare edge cases we could have no valid predictions. So we
        # just create a nonce prediction in this case to avoid failure.
        if not nbest:
            nbest.append(
                _NbestPrediction(text="empty", start_logit=0.0, end_logit=0.0))

        assert len(nbest) >= 1

        total_scores = []
        best_non_null_entry = None
        for entry in nbest:
            total_scores.append(entry.start_logit + entry.end_logit)
            if not best_non_null_entry:
                if entry.text:
                    best_non_null_entry = entry

        probs = _compute_softmax(total_scores)

        nbest_json = []
        for (i, entry) in enumerate(nbest):
            output = collections.OrderedDict()
            output["text"] = entry.text
            output["probability"] = probs[i]
            output["start_logit"] = entry.start_logit
            output["end_logit"] = entry.end_logit
            nbest_json.append(output)

        assert len(nbest_json) >= 1

        if not version_2_with_negative:
            all_predictions[example.qas_id] = nbest_json[0]["text"]
        else:
            # predict "" iff the null score - the score of best non-null > threshold
            score_diff = score_null - best_non_null_entry.start_logit - (
                best_non_null_entry.end_logit)
            scores_diff_json[example.qas_id] = score_diff
            if score_diff > null_score_diff_threshold:
                all_predictions[example.qas_id] = ""
            else:
                all_predictions[example.qas_id] = best_non_null_entry.text
            all_nbest_json[example.qas_id] = nbest_json

    with open(output_prediction_file, "w") as writer:
        writer.write(json.dumps(all_predictions, indent=4) + "\n")

    with open(output_nbest_file, "w") as writer:
        writer.write(json.dumps(all_nbest_json, indent=4) + "\n")

    if version_2_with_negative:
        with open(output_null_log_odds_file, "w") as writer:
            writer.write(json.dumps(scores_diff_json, indent=4) + "\n")