refactor: replace mdFixer with finalizer and reducer, add ngram script

config.json

@@ -51,9 +51,12 @@
         "agentBeastMode": {
           "temperature": 0.7
         },
-        "mdFixer": {
+        "finalizer": {
           "model": "gemini-2.5-flash-preview-05-20"
         },
+        "reducer": {
+          "maxTokens": 16000
+        },
         "fallback": {
           "maxTokens": 8000,
           "model": "gemini-2.0-flash-lite"
@@ -85,7 +88,10 @@
         "fallback": {
           "temperature": 0
         },
-        "mdFixer": {}
+        "finalizer": {},
+        "reducer": {
+          "maxTokens": 16000
+        }
       }
     }
   }

jina-ai/config.json

@@ -59,7 +59,8 @@
           "maxTokens": 8000,
           "model": "gemini-2.0-flash-lite"
         },
-        "mdFixer": {}
+        "finalizer": {},
+        "reducer": {"maxTokens": 16000}
       }
     },
     "openai": {
@@ -87,7 +88,8 @@
         "fallback": {
           "temperature": 0
         },
-        "mdFixer": {}
+        "finalizer": {},
+        "reducer": {"maxTokens": 16000}
       }
     }
   }

package.json

@@ -12,6 +12,7 @@
     "dev": "npx ts-node src/agent.ts",
     "search": "npx ts-node src/test-duck.ts",
     "rewrite": "npx ts-node src/tools/query-rewriter.ts",
+    "ngram": "npx ts-node src/cli/ngram.ts",
     "lint": "eslint . --ext .ts",
     "lint:fix": "eslint . --ext .ts --fix",
     "serve": "ts-node src/server.ts",
@@ -65,4 +66,4 @@
   "optionalDependencies": {
     "@ai-sdk/google-vertex": "^2.1.12"
   }
-}
+}

src/agent.ts

@@ -41,10 +41,11 @@ import {
 } from "./utils/text-tools";
 import { MAX_QUERIES_PER_STEP, MAX_REFLECT_PER_STEP, MAX_URLS_PER_STEP, Schemas } from "./utils/schemas";
 import { formatDateBasedOnType, formatDateRange } from "./utils/date-tools";
-import { reviseAnswer } from "./tools/md-fixer";
+import { finalizeAnswer } from "./tools/finalizer";
 import { buildImageReferences, buildReferences } from "./tools/build-ref";
 import { logInfo, logError, logDebug, logWarning } from './logging';
 import { researchPlan } from './tools/research-planner';
+import { reduceAnswers } from './tools/reducer';
 
 async function wait(seconds: number) {
   logDebug(`Waiting ${seconds}s...`);
@@ -813,8 +814,13 @@ But then you realized you have asked them before. You decided to to think out of
           isAggregated: true
         } as AnswerAction;
 
+        // aggregate urls
+        visitedURLs.push(...subproblemResponses.map(r => r.readURLs).flat());
+        weightedURLs = subproblemResponses.map(r => r.allURLs.map(url => ({ url, title: '' } as BoostedSearchSnippet))).flat();
 
-        // break the loop, move to final boxing
+        // TODO aggregate images @shazhou2015
+
+        // break the loop, jump directly final boxing
         break;
       }
 
@@ -1037,7 +1043,7 @@ But unfortunately, you failed to solve the issue. You need to think out of the b
         fixBadURLMdLinks(
           fixCodeBlockIndentation(
             repairMarkdownFootnotesOuter(
-              await reviseAnswer(
+              await finalizeAnswer(
                 answerStep.answer,
                 allKnowledge,
                 context,
@@ -1072,6 +1078,9 @@ But unfortunately, you failed to solve the issue. You need to think out of the b
         imageReferences = [];
       }
     }
+  } else if (answerStep.isAggregated) {
+    answerStep.answer = await reduceAnswers(answerStep.answer, context, SchemaGen);
+    answerStep.mdAnswer = repairMarkdownFootnotesOuter(buildMdFromAnswer(answerStep));
   }
 
   // max return 300 urls
@@ -1079,7 +1088,7 @@ But unfortunately, you failed to solve the issue. You need to think out of the b
   return {
     result: thisStep,
     context,
-    visitedURLs: returnedURLs,
+    visitedURLs: returnedURLs, // deprecated
     readURLs: visitedURLs.filter(url => !badURLs.includes(url)),
     allURLs: weightedURLs.map(r => r.url),
     allImages: withImages ? imageObjects.map(i => i.url) : undefined,

src/cli/ngram.ts

@@ -0,0 +1,36 @@
+import fs from 'fs';
+import { extractNgrams } from '../utils/text-tools';
+
+async function main() {
+    const args = process.argv.slice(2);
+    if (args.length === 0) {
+        console.error('Please provide a file path');
+        process.exit(1);
+    }
+
+    const filePath = args[0];
+    const n = parseInt(args[1]) || 3; // Default to 3-grams
+    const minFreq = parseInt(args[2]) || 2; // Default minimum frequency of 2
+    const minPMI = parseFloat(args[3]) || 1.0; // Default minimum PMI of 1.0
+
+    try {
+        const text = await fs.promises.readFile(filePath, 'utf-8');
+        const results = extractNgrams(text, n, minFreq, minPMI);
+
+        console.log('\nN-gram Analysis Results:');
+        console.log('------------------------');
+        results.forEach(({ ngram, freq, pmi }) => {
+            if (pmi !== undefined) {
+                console.log(`${ngram}: ${freq} (PMI: ${pmi.toFixed(2)})`);
+            } else {
+                console.log(`${ngram}: ${freq}`);
+            }
+        });
+    } catch (err) {
+        const error = err as Error;
+        console.error('Error:', error.message);
+        process.exit(1);
+    }
+}
+
+main(); 

src/tools/finalizer.ts

@@ -61,9 +61,9 @@ IMPORTANT: Do not begin your response with phrases like "Sure", "Here is", "Belo
   }
 }
 
-const TOOL_NAME = 'mdFixer';
+const TOOL_NAME = 'finalizer';
 
-export async function reviseAnswer(
+export async function finalizeAnswer(
   mdContent: string,
   knowledgeItems: KnowledgeItem[],
   trackers: TrackerContext,
@@ -71,7 +71,7 @@ export async function reviseAnswer(
 ): Promise<string> {
   try {
     const prompt = getPrompt(mdContent, knowledgeItems, schema);
-    trackers?.actionTracker.trackThink('final_answer', schema.languageCode)
+    trackers?.actionTracker.trackThink('finalize_answer', schema.languageCode)
 
     const result = await generateText({
       model: getModel(TOOL_NAME),
@@ -83,10 +83,10 @@ export async function reviseAnswer(
 
 
     logInfo(TOOL_NAME, { text: result.text });
-    logDebug(`repaired before/after: ${mdContent.length} -> ${result.text.length}`);
+    logDebug(`finalized answer before/after: ${mdContent.length} -> ${result.text.length}`);
 
     if (result.text.length < mdContent.length * 0.85) {
-      logWarning(`repaired content length ${result.text.length} is significantly shorter than original content ${mdContent.length}, return original content instead.`, {
+      logWarning(`finalized answer length ${result.text.length} is significantly shorter than original content ${mdContent.length}, return original content instead.`, {
         originalContent: mdContent,
         repairedContent: result.text
       });
@@ -96,7 +96,7 @@ export async function reviseAnswer(
     return result.text;
 
   } catch (error) {
-    logError(`Error in ${TOOL_NAME}`, { error });
+    logError(TOOL_NAME, { error });
     return mdContent;
   }
 }

src/tools/reducer.ts

@@ -0,0 +1,93 @@
+import { PromptPair, TrackerContext } from '../types';
+import { getModel } from "../config";
+import { generateText } from "ai";
+import { Schemas } from "../utils/schemas";
+import { logInfo, logError, logDebug } from '../logging';
+
+
+function getPrompt(mdContent: string): PromptPair {
+
+
+  return {
+    system: `
+You are an article aggregator that creates a coherent, high-quality article by smartly merging multiple source articles. Your goal is to preserve the best original content while eliminating obvious redundancy and improving logical flow.
+
+<core-instructions>
+1. Content Preservation
+ALWAYS preserve original sentences verbatim - do not paraphrase or rewrite
+Select the highest quality version when multiple articles cover the same point
+Maintain the original author's voice and technical accuracy
+Keep direct quotes, statistics, and factual claims exactly as written
+2. Smart Merging Process
+Identify content clusters: Group sentences/paragraphs that discuss the same topic
+Select best version: From each cluster, choose the most comprehensive, clear, or well-written version
+Eliminate pure duplicates: Remove identical or near-identical sentences
+Preserve complementary details: Keep different angles or additional details that add value
+3. Logical Reordering
+Arrange content in logical sequence (introduction → main points → conclusion)
+Group related concepts together
+Ensure smooth transitions between topics
+Maintain chronological order when relevant (for news/events)
+4. Quality Criteria for Selection
+When choosing between similar content, prioritize:
+Clarity: More understandable explanations
+Completeness: More comprehensive coverage
+Accuracy: Better sourced or more precise information
+Relevance: More directly related to the main topic
+</core-instructions>
+
+<output-format>
+Structure the final article with:
+Clear section headings (when appropriate)
+Logical paragraph breaks
+Smooth flow between topics
+No attribution to individual sources (present as unified piece)
+</output-format>
+
+Do not add your own commentary or analysis
+Do not change technical terms, names, or specific details
+
+Your final output should read as a cohesive, high-quality article that appears to be written by a single author, while actually being a careful curation of the best sentences from all input sources.
+    `,
+    user: mdContent
+  }
+}
+
+const TOOL_NAME = 'reducer';
+
+export async function reduceAnswers(
+  mdContent: string,
+  trackers: TrackerContext,
+  schema: Schemas
+): Promise<string> {
+  try {
+    const prompt = getPrompt(mdContent);
+    trackers?.actionTracker.trackThink('reduce_answer', schema.languageCode)
+
+    const result = await generateText({
+      model: getModel(TOOL_NAME),
+      system: prompt.system,
+      prompt: prompt.user,
+    });
+
+    trackers.tokenTracker.trackUsage(TOOL_NAME, result.usage)
+
+
+    logInfo(TOOL_NAME, { text: result.text });
+    logDebug(`reduce before/after: ${mdContent.length} -> ${result.text.length}`);
+
+    // if (result.text.length < mdContent.length * 0.85) {
+    //   logWarning(`reduce content length ${result.text.length} is significantly shorter than original content ${mdContent.length}, return original content instead.`, {
+    //     originalContent: mdContent,
+    //     repairedContent: result.text
+    //   });
+    //   return mdContent;
+    // }
+
+    return result.text;
+
+  } catch (error) {
+    logError(TOOL_NAME, { error });
+    return mdContent;
+  }
+}

src/utils/i18n.json

@@ -5,7 +5,8 @@
     "read_for": "Let me read ${urls} to gather more information.",
     "read_for_verify": "Let me fetch the source content to verify the answer.",
     "late_chunk": "Content of ${url} is too long, let me cherry-pick the relevant parts.",
-    "final_answer": "Let me finalize the answer.",
+    "finalize_answer": "Let me finalize the answer.",
+    "reduce_answer": "Let me aggregate all research results.",
     "blocked_content": "Hmm...the content of ${url} doesn't look right, I might be blocked.",
     "hostnames_no_results": "Can't find any results from ${hostnames}.",
     "cross_reference": "Let me cross-reference the information from the web to verify the answer."
@@ -16,7 +17,8 @@
     "read_for": "让我读取网页 ${urls} 来获取更多信息。",
     "read_for_verify": "让我读取源网页内容来验证答案。",
     "late_chunk": "网页 ${url} 内容太长，我正在筛选精华部分。",
-    "final_answer": "我来整理一下答案。",
+    "finalize_answer": "我来整理一下答案。",
+    "reduce_answer": "让我综合整理所有的调研结果。",
     "blocked_content": "额…这个 ${url} 的内容不太对啊，我是不是被屏蔽了啊。",
     "hostnames_no_results": "额… ${hostnames} 找不到什么结果啊。",
     "cross_reference": "让我交叉验证一下网页上的信息来验证答案。"
@@ -27,7 +29,8 @@
     "read_for": "讓我閱讀 ${urls} 來獲取更多信息。",
     "read_for_verify": "讓我獲取源內容來驗證答案。",
     "late_chunk": "網頁 ${url} 內容太長，我正在挑選相關部分。",
-    "final_answer": "我來整理一下答案。",
+    "finalize_answer": "我來整理一下答案。",
+    "reduce_answer": "讓我整合所有調研結果。",
     "blocked_content": "咦...奇怪了，${url} 好像把我擋在門外了。有够麻烦！",
     "hostnames_no_results": "咦... ${hostnames} 找不到什么结果。",
     "cross_reference": "讓我交叉驗證一下網頁上的信息來驗證答案。"
@@ -38,7 +41,8 @@
     "read_for": "${urls} を読んで、情報を集めます。",
     "read_for_verify": "答えを確認するために、ソースコンテンツを取得します。",
     "late_chunk": "${url} のコンテンツが長すぎるため、関連部分を選択します。",
-    "final_answer": "答えをまとめます。",
+    "finalize_answer": "答えをまとめます。",
+    "reduce_answer": "答えをまとめます。",
     "blocked_content": "あれ？${url}にアクセスできないみたいです。壁にぶつかってしまいました。申し訳ありません。",
     "hostnames_no_results": "${hostnames} から結果が見つかりません。",
     "cross_reference": "ウェブ上の情報をクロスリファレンスして、答えを確認します。"
@@ -49,7 +53,8 @@
     "read_for": "${urls} 을 읽어 더 많은 정보를 수집하겠습니다.",
     "read_for_verify": "답변을 확인하기 위해 소스 콘텐츠를 가져오겠습니다.",
     "late_chunk": "${url} 의 콘텐츠가 너무 길어, 관련 부분을 선택하겠습니다.",
-    "final_answer": "답변을 마무리하겠습니다.",
+    "finalize_answer": "답변을 마무리하겠습니다.",
+    "reduce_answer": "답변을 마무리하겠습니다.",
     "blocked_content": "어라? ${url}에서 문전박대를 당했네요. 참 황당하네요!",
     "hostnames_no_results": "${hostnames} 에서 결과를 찾을 수 없습니다.",
     "cross_reference": "웹에서 정보를 교차 검증하여 답변을 확인하겠습니다."
@@ -60,7 +65,8 @@
     "read_for": "Je vais lire ${urls} pour obtenir plus d'informations.",
     "read_for_verify": "Je vais récupérer le contenu source pour vérifier la réponse.",
     "late_chunk": "Le contenu de ${url} est trop long, je vais sélectionner les parties pertinentes.",
-    "final_answer": "Je vais finaliser la réponse.",
+    "finalize_answer": "Je vais finaliser la réponse.",
+    "reduce_answer": "Je vais finaliser la réponse.",
     "blocked_content": "Zut alors ! ${url} me met à la porte. C'est la galère !",
     "hostnames_no_results": "Aucun résultat trouvé sur ${hostnames}.",
     "cross_reference": "Je vais croiser les informations sur le web pour vérifier la réponse."
@@ -71,7 +77,8 @@
     "read_for": "Ich werde ${urls} lesen, um weitere Informationen zu sammeln.",
     "read_for_verify": "Ich werde den Quellinhalt abrufen, um die Antwort zu überprüfen.",
     "late_chunk": "Der Inhalt von ${url} ist zu lang, ich werde die relevanten Teile auswählen.",
-    "final_answer": "Ich werde die Antwort abschließen.",
+    "finalize_answer": "Ich werde die Antwort abschließen.",
+    "reduce_answer": "Ich werde die Antwort abschließen.",
     "blocked_content": "Mist! ${url} lässt mich nicht rein.",
     "hostnames_no_results": "Keine Ergebnisse von ${hostnames} gefunden.",
     "cross_reference": "Ich werde die Informationen im Web abgleichen, um die Antwort zu überprüfen."
@@ -82,7 +89,8 @@
     "read_for": "Voy a leer ${urls} para recopilar más información.",
     "read_for_verify": "Voy a obtener el contenido fuente para verificar la respuesta.",
     "late_chunk": "El contenido de ${url} es demasiado largo, voy a seleccionar las partes relevantes.",
-    "final_answer": "Voy a finalizar la respuesta.",
+    "finalize_answer": "Voy a finalizar la respuesta.",
+    "reduce_answer": "Voy a finalizar la respuesta.",
     "blocked_content": "¡Oh no! Estoy bloqueado por ${url}, ¡no es genial!",
     "hostnames_no_results": "No se encontraron resultados de ${hostnames}."
   },
@@ -92,7 +100,8 @@
     "read_for": "Leggerò ${urls} per raccogliere ulteriori informazioni.",
     "read_for_verify": "Recupererò il contenuto sorgente per verificare la risposta.",
     "late_chunk": "Il contenuto di ${url} è troppo lungo, selezionerò le parti rilevanti.",
-    "final_answer": "Finalizzerò la risposta.",
+    "finalize_answer": "Finalizzerò la risposta.",
+    "reduce_answer": "Finalizzerò la risposta.",
     "blocked_content": "Mannaggia! Sono bloccato da ${url}, non è bello!",
     "hostnames_no_results": "Nessun risultato trovato da ${hostnames}.",
     "cross_reference": "Incrocerò le informazioni sul web per verificare la risposta."
@@ -103,7 +112,8 @@
     "read_for": "Vou ler ${urls} para reunir mais informações.",
     "read_for_verify": "Vou buscar o conteúdo da fonte para verificar a resposta.",
     "late_chunk": "O conteúdo de ${url} é muito longo, vou selecionar as partes relevantes.",
-    "final_answer": "Vou finalizar a resposta.",
+    "finalize_answer": "Vou finalizar a resposta.",
+    "reduce_answer": "Vou finalizar a resposta.",
     "blocked_content": "Ah não! Estou bloqueado por ${url}, não é legal!",
     "hostnames_no_results": "Nenhum resultado encontrado em ${hostnames}.",
     "cross_reference": "Vou cruzar as informações da web para verificar a resposta."
@@ -114,7 +124,8 @@
     "read_for": "Дайте мне прочитать ${urls} для сбора дополнительной информации.",
     "read_for_verify": "Дайте мне получить исходный контент для проверки ответа.",
     "late_chunk": "Содержимое ${url} слишком длинное, я выберу только значимые части.",
-    "final_answer": "Дайте мне завершить ответ.",
+    "finalize_answer": "Дайте мне завершить ответ.",
+    "reduce_answer": "Дайте мне завершить ответ.",
     "blocked_content": "Ой! Меня заблокировал ${url}, не круто!",
     "hostnames_no_results": "Ничего не найдено на ${hostnames}.",
     "cross_reference": "Дайте мне сопоставить информацию из сети, чтобы проверить ответ."
@@ -125,6 +136,8 @@
     "read_for": "دعني أقرأ ${urls} لجمع المزيد من المعلومات.",
     "read_for_verify": "دعني أحضر محتوى المصدر للتحقق من الإجابة.",
     "late_chunk": "محتوى ${url} طويل جدًا، سأختار الأجزاء ذات الصلة.",
+    "finalize_answer": "دعني أنهي الإجابة.",
+    "reduce_answer": "دعني أنهي الإجابة.",
     "blocked_content": "أوه لا! أنا محظور من ${url}، ليس جيدًا!",
     "hostnames_no_results": "لا يمكن العثور على أي نتائج من ${hostnames}.",
     "cross_reference": "دعني أقوم بمقارنة المعلومات من الويب للتحقق من الإجابة."
@@ -135,7 +148,8 @@
     "read_for": "Ik zal ${urls} lezen om meer informatie te verzamelen.",
     "read_for_verify": "Ik zal de broninhoud ophalen om het antwoord te verifiëren.",
     "late_chunk": "De inhoud van ${url} is te lang, ik zal de relevante delen selecteren.",
-    "final_answer": "Ik zal het antwoord afronden.",
+    "finalize_answer": "Ik zal het antwoord afronden.",
+    "reduce_answer": "Ik zal het antwoord afronden.",
     "blocked_content": "Verdorie! Ik word geblokkeerd door ${url}.",
     "hostnames_no_results": "Geen resultaten gevonden van ${hostnames}.",
     "cross_reference": "Ik zal de informatie op het web kruisverwijzen om het antwoord te verifiëren."
@@ -146,7 +160,8 @@
     "read_for": "让我阅读 ${urls} 来获取更多信息。",
     "read_for_verify": "让我获取源内容来验证答案。",
     "late_chunk": "网页 ${url} 内容太长，我正在筛选精华部分。",
-    "final_answer": "我来整理一下答案。",
+    "finalize_answer": "我来整理一下答案。",
+    "reduce_answer": "让我整合所有调研结果。",
     "blocked_content": "额…这个内容不太对啊，我感觉被 ${url} 屏蔽了。",
     "hostnames_no_results": "额… ${hostnames} 找不到什么结果啊。",
     "cross_reference": "让我交叉验证一下网页上的信息来验证答案。"

src/utils/text-tools.ts

@@ -824,3 +824,111 @@ export async function detectBrokenUnicodeViaFileIO(str: string) {
   // Now check for the visible replacement character
   return { broken: readStr.includes('<27>'), readStr };
 }
+
+interface NgramResult {
+  ngram: string;
+  freq: number;
+  pmi?: number;  // Added PMI score
+}
+
+function calculatePMI(
+  ngram: string,
+  ngramFreq: number,
+  wordFreqs: Map<string, number>,
+  totalNgrams: number
+): number {
+  const words = ngram.split(' ');
+  if (words.length < 2) return 0;
+
+  // Calculate joint probability
+  const jointProb = ngramFreq / totalNgrams;
+
+  // Calculate individual probabilities
+  const wordProbs = words.map(word => (wordFreqs.get(word) || 0) / totalNgrams);
+
+  // Calculate PMI
+  const pmi = Math.log2(jointProb / wordProbs.reduce((a, b) => a * b, 1));
+  return pmi;
+}
+
+function isCJK(char: string): boolean {
+  const code = char.charCodeAt(0);
+  return (
+    (code >= 0x4E00 && code <= 0x9FFF) || // CJK Unified Ideographs
+    (code >= 0x3040 && code <= 0x309F) || // Hiragana
+    (code >= 0x30A0 && code <= 0x30FF) || // Katakana
+    (code >= 0xAC00 && code <= 0xD7AF)    // Hangul
+  );
+}
+
+function isCJKText(text: string): boolean {
+  return Array.from(text).some(char => isCJK(char));
+}
+
+export function extractNgrams(
+  text: string,
+  n: number,
+  minFreq: number = 2,
+  minPMI: number = 1.0  // Added minimum PMI threshold
+): NgramResult[] {
+  // Split text into chunks by newlines
+  const chunks = text.split('\n').filter(chunk => chunk.trim().length > 0);
+
+  // Maps to store frequencies
+  const ngramFreq: Map<string, number> = new Map();
+  const wordFreq: Map<string, number> = new Map();
+  let totalNgrams = 0;
+
+  // First pass: collect frequencies
+  for (const chunk of chunks) {
+    if (isCJKText(chunk)) {
+      // For CJK text, use character-level ngrams
+      for (let len = 2; len <= n; len++) {
+        for (let i = 0; i <= chunk.length - len; i++) {
+          const ngram = chunk.slice(i, i + len);
+          ngramFreq.set(ngram, (ngramFreq.get(ngram) || 0) + 1);
+          totalNgrams++;
+        }
+      }
+    } else {
+      // For non-CJK text, use word-level ngrams
+      const words = chunk.split(/\s+/).filter(word => word.length > 0);
+
+      // Count individual word frequencies
+      words.forEach(word => {
+        wordFreq.set(word, (wordFreq.get(word) || 0) + 1);
+      });
+
+      // Count ngram frequencies
+      for (let len = 2; len <= n; len++) {
+        for (let i = 0; i <= words.length - len; i++) {
+          const ngram = words.slice(i, i + len).join(' ');
+          ngramFreq.set(ngram, (ngramFreq.get(ngram) || 0) + 1);
+          totalNgrams++;
+        }
+      }
+    }
+  }
+
+  // Second pass: calculate PMI and filter
+  const results: NgramResult[] = Array.from(ngramFreq.entries())
+    .filter(([ngram, freq]) => freq >= minFreq)
+    .map(([ngram, freq]) => {
+      const pmi = isCJKText(ngram) ? 0 : calculatePMI(ngram, freq, wordFreq, totalNgrams);
+      return { ngram, freq, pmi };
+    })
+    .filter(result => result.pmi === undefined || result.pmi >= minPMI)
+    .sort((a, b) => {
+      // If both have PMI scores, sort by PMI
+      if (a.pmi !== undefined && b.pmi !== undefined) {
+        return b.pmi - a.pmi;
+      }
+      // If only one has PMI, prioritize the one with PMI
+      if (a.pmi !== undefined) return -1;
+      if (b.pmi !== undefined) return 1;
+      // If neither has PMI (CJK text), sort by frequency
+      return b.freq - a.freq;
+    });
+
+  return results;
+}