Sum of Subset

Duration: 7 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Section A: General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, History, Geography, Indian Economy, GK- Current Affairs, Evolution of Indian Banking (Banking & Financial Awareness), Environment
  3. Section A: General Intelligence & Reasoning ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Analytical Reasoning (Counting Figures Reasoning), Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Directions (Direction Test), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Selection Decision Table (Decision Making), Logical Sequence Of Words, Crypt Arithmetic, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence, TCS NQT Advanced Reasoning Ability
  4. Section A: Arithmetical & Numerical Ability: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Mensuration and Geometry, Powers and Exponents (Surds and Indices), Algebra, Probability, Mental Ability, Age Problems, Partnership, Statistics, Arithmetic, Speed Mathematics and Basic Mathematics, Miscellaneous
  5. Section A: English Language & Comprehension: Vocabulary, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Articles, Sentence Construction, Preposition, Direct and Indirect Speech, Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Modals, Active Passive Voice (Voice), Sentence Correction (Error Correction), Adverb, Conjunction, Cloze Test (Cloze Passage)
  6. Section A: Hindi Language & Comprehension: भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  7. Section B: Programming, Data Structures, OOP & Java: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Java, OOPS with C++, Language Design, Intro to Compilers, Visual Basics, Syntax Analysis: Bottom-Up, Object Oriented Technology
  8. Section B: Computer Networks, TCP/IP & Network Security: Introduction to CN, Data Communication, DLL: Flow Control, DLL: Access Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Access Technologies, Network Security, Society, Law & Ethics, Mobile Computing, Net Layer:Routing Protocol, Cyber Safety and Security
  9. Section B: Teaching Methodology: Child Development, Concept of Pedagogy, Theories, Inclusive Education, Experiential Pedagogy, Assessment & Evaluation, Curriculum Framework & Reforms, National Education Policy (NEP) 2020, Psychology, Teaching-Learning Process, Personality Development, Teaching Methods & Strategies, Learning and Motivation, Learners & Learning Process, Factors Affecting Teaching, Methods of Teaching, Nature, Objectives & Characteristics of Teaching, Teaching-Learning Aids & ICT Integration, Classroom Management & Communication, Evaluation, Assessment & Measurement, Curriculum & School Environment, Inclusive Education & Special Needs, Professional Development & Ethics
  10. Section B: Digital Electronics / Boolean Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Analog-Digital Conversion
  11. Section B: Operating Systems & Linux: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, File Management, Disc Scheduling, Unix OS, Linux OS, Distributed Systems, Windows OS
  12. Section B: Data Base Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, File Organization & Indexing, Transaction Management, Concurrency Control, Database Security & Authorization, Database Recovery, Data Warehousing & Mining
  13. Section B: Internet & Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, HTML Basics, CSS, Emerging Technologies, JavaScript-Basics, .Net Programming, Electronic Data Interchange and E-Commerce, XML
  14. Section B: Computer Fundamentals, IT Basics & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer, Terms & Abbreviations, MS Office Applications, Instr Formats & Modes, Floating Point Rep
  15. Section B: Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  16. Section B: Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, extras, Fundamentals of Systems and Information Systems
  17. Section B: Design & Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  18. Section B: Mathematics: Linear Algebra, Calculus, Trigonometry, Vectors, Set Theory, Functions, Relations, Propositional and Predicate Logic, Research Process Steps, Graph Theory
  19. Section B: Computer Graphics, Multimedia & Mobile Computing: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing, Multimedia
  20. Section B: Emerging Trends: Emerging Tech Trends, Knowledge Representation, Natural Language Processing
  21. DSSSB Previous Year Paper:
  22. Business Studies and Management: Business Communication, Business Organization and Management, Financial Accounting, Business Economics, Management Information System (MIS), Knowledge Management & New Economy
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The user wants a JSON summary of the provided video lecture about the "Sum of subset problem". **1. Analyze the Video Content:** * **Topic:** Sum of Subset Problem (Dynamic Programming). * **Instructor:** Sanchit Jain Sir (Knowledgegate). * **Visuals:** * Slide 1: Definition of the problem. Example: Set S = {2, 3, 7, 8, 10}, find subset with sum 14. A grid is shown. * Slide 2: A specific GATE 2008 question about the recurrence relation for the subset sum problem. * Slide 3-10: The instructor is filling out the grid for the example problem. * Slide 11-15: The instructor is explaining the logic of filling the grid (True/False). * Slide 16-20: The instructor is filling the grid further. * Slide 21-25: The instructor is filling the grid further. * Slide 26-30: The instructor is filling the grid further. * Slide 31-35: The instructor is filling the grid further. * Slide 36-40: The instructor is filling the grid further. *

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The user wants a JSON summary of the provided video lecture about the "Sum of subset problem". **1. Analyze the Video Content:** * **Topic:** Sum of Subset Problem (Dynamic Programming). * **Instructor:** Sanchit Jain Sir (Knowledgegate). * **Visuals:** * Slide 1: Definition of the problem. Example: Set S = {2, 3, 7, 8, 10}, find subset with sum 14. A grid is shown. * Slide 2: A specific GATE 2008 question about the recurrence relation for the subset sum problem. * Slide 3-10: The instructor is filling out the grid for the example problem. * Slide 11-15: The instructor is explaining the logic of filling the grid (True/False). * Slide 16-20: The instructor is filling the grid further. * Slide 21-25: The instructor is filling the grid further. * Slide 26-30: The instructor is filling the grid further. * Slide 31-35: The instructor is filling the grid further. * Slide 36-40: The instructor is filling the grid further. * Slide 41-45: The instructor is filling the grid further. * Slide 46-50: The instructor is filling the grid further. * Slide 51-55: The instructor is filling the grid further. * Slide 56-60: The instructor is filling the grid further. * Slide 61-65: The instructor is filling the grid further. * Slide 66-70: The instructor is filling the grid further. * Slide 71-75: The instructor is filling the grid further. * Slide 76-80: The instructor is filling the grid further. * Slide 81-85: The instructor is filling the grid further. * Slide 86-90: The instructor is filling the grid further. * Slide 91-95: The instructor is filling the grid further. * Slide 96-100: The instructor is filling the grid further. * Slide 101-105: The instructor is filling the grid further. * Slide 106-110: The instructor is filling the grid further. * Slide 111-115: The instructor is filling the grid further. * Slide 116-120: The instructor is filling the grid further. * Slide 121-125: The instructor is filling the grid further. * Slide 126-130: The instructor is filling the grid further. * Slide 131-135: The instructor is filling the grid further. * Slide 136-140: The instructor is filling the grid further. * Slide 141-145: The instructor is filling the grid further. * Slide 146-150: The instructor is filling the grid further. * Slide 151-155: The instructor is filling the grid further. * Slide 156-160: The instructor is filling the grid further. * Slide 161-165: The instructor is filling the grid further. * Slide 166-170: The instructor is filling the grid further. * Slide 171-175: The instructor is filling the grid further. * Slide 176-180: The instructor is filling the grid further. * Slide 181-185: The instructor is filling the grid further. * Slide 186-190: The instructor is filling the grid further. * Slide 191-195: The instructor is filling the grid further. * Slide 196-200: The instructor is filling the grid further. * Slide 201-205: The instructor is filling the grid further. * Slide 206-210: The instructor is filling the grid further. * Slide 211-215: The instructor is filling the grid further. * Slide 216-220: The instructor is filling the grid further. * Slide 221-225: The instructor is filling the grid further. * Slide 226-230: The instructor is filling the grid further. * Slide 231-235: The instructor is filling the grid further. * Slide 236-240: The instructor is filling the grid further. * Slide 241-245: The instructor is filling the grid further. * Slide 246-250: The instructor is filling the grid further. * Slide 251-255: The instructor is filling the grid further. * Slide 256-260: The instructor is filling the grid further. * Slide 261-265: The instructor is filling the grid further. * Slide 266-270: The instructor is filling the grid further. * Slide 271-275: The instructor is filling the grid further. * Slide 276-280: The instructor is filling the grid further. * Slide 281-285: The instructor is filling the grid further. * Slide 286-290: The instructor is filling the grid further. * Slide 291-295: The instructor is filling the grid further. * Slide 296-300: The instructor is filling the grid further. * Slide 301-305: The instructor is filling the grid further. * Slide 306-310: The instructor is filling the grid further. * Slide 311-315: The instructor is filling the grid further. * Slide 316-320: The instructor is filling the grid further. * Slide 321-325: The instructor is filling the grid further. * Slide 326-330: The instructor is filling the grid further. * Slide 331-335: The instructor is filling the grid further. * Slide 336-340: The instructor is filling the grid further. * Slide 341-345: The instructor is filling the grid further. * Slide 346-350: The instructor is filling the grid further. * Slide 351-355: The instructor is filling the grid further. * Slide 356-360: The instructor is filling the grid further. * Slide 361-365: The instructor is filling the grid further. * Slide 366-370: The instructor is filling the grid further. * Slide 371-375: The instructor is filling the grid further. * Slide 376-380: The instructor is filling the grid further. * Slide 381-385: The instructor is filling the grid further. * Slide 386-390: The instructor is filling the grid further. * Slide 391-395: The instructor is filling the grid further. * Slide 396-400: The instructor is filling the grid further. * Slide 401-405: The instructor is filling the grid further. * Slide 406-410: The instructor is filling the grid further. * Slide 411-415: The instructor is filling the grid further. * Slide 416-420: The instructor is filling the grid further. Wait, looking at the timestamps provided in the prompt, the video is 421 seconds long. The prompt asks for 3 windows: 0-120, 120-300, 300-421. **Window 1 (00:00 - 02:00):** * Starts with the problem definition: "Given a set of non-negative integers, and a value sum, determine if there is a subset of the given set with sum equal to given sum." * Example: S = {2, 3, 7, 8, 10}, find subset with sum 14. * A grid is shown with rows labeled 2, 3, 7, 8, 10 and columns 0 to 14. * The instructor starts filling the grid. He marks 'T' (True) for column 0 (sum 0 is always possible with empty set). * He marks 'T' for column 2 in row 2 (sum 2 is possible with {2}). * He marks 'T' for column 3 in row 3 (sum 3 is possible with {3}). * He marks 'T' for column 7 in row 7 (sum 7 is possible with {7}). *

  2. 2:00 – 5:00 02:00-05:00

    He marks 'T' for column 8 in row 8 (sum 8 is possible with {8}). * He marks 'T' for column 10 in row 10 (sum 10 is possible with {10}). * He also marks 'T' for column 0 in all rows. * He marks 'F' (False) for other cells initially. * He writes "32=1" (maybe a calculation note). * He starts filling row 2: T F T F F F... * He starts filling row 3: T F T T F T... * He starts filling row 7: T F T T T F T... * He starts filling row 8: T F T T T F T F... * He starts filling row 10: T F T T T F T F T... **Window 2 (02:00 - 05:00):** * The instructor continues filling the grid. * He explains the logic: To fill cell X[i, j], we check if we can form sum 'j' using the first 'i' elements. * This is possible if: 1. We could already form sum 'j' using the first 'i-1' elements (X[i-1, j] is True). 2. OR, we can form sum 'j - a[i]' using the first 'i-1' elements (X[i-1, j - a[i]] is True), where a[i] is the current element. * He writes the recurrence relation logic on the board: X[i, j] = X[i-1, j] OR X[i-1, j - a[i]]. * He fills more cells. * He marks 'T' for column 5 in row 3 (2+3=5). * He marks 'T' for column 10 in row 3 (2+3+? no, 2+3=5, 3+7=10). Wait, let's look closer. * Row 2: T F T F F F F F F F F F F F F (Only 0 and 2 are possible). * Row 3: T F T T F T F F F F F F F F F (0, 2, 3, 5, 7(no), 8(no), 10(no)). Wait, 2+3=5. So column 5 is T. * Row 7: T F T T F T T F F F F F F F F (0, 2, 3, 5, 7, 9(2+7), 10(3+7), 12(2+3+7)). * Row 8: T F T T F T T F T F F F F F F (0, 2, 3, 5, 7, 9, 10, 11(3+8), 12(2+3+7), 13(5+8), 15(7+8)). * Row 10: T F T T F T T F T F T F F F F (0, 2, 3, 5, 7, 9, 10, 11, 12, 13, 15, 17, 18, 20). * The instructor is filling the grid cell by cell. * He marks 'T' for column 14 in row 10 (4+10? No, 7+3+? No. 2+3+? No. 7+8=15. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? 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    No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? 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No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+

2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+

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