Sum of Subset

Duration: 7 min

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Inside: a video lesson and guided study material.

Module outline

  1. About Course: UPPSC Course Overview
  2. Interview Preparation & Guidance: Interview Preparation
  3. Paper 1 | General Hindi: 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, वर्णमाला, समास, संधि, 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), शब्द-भंडार, वर्ण-विचार, हिन्दी की ध्वनि और स्वनिम व्यवस्था, प्राचीन और मध्यकालीन भारतीय आर्यभाषाएँ, काव्य के लक्षण, हेतु और प्रयोजन, अशुद्धि-शोधन, शब्द-रचना, शब्द-भेद, हिन्दी की रूप रचना, रूप-रचना, हिन्दी शब्द रचना, हिन्दी साहित्येतिहास दर्शन, भक्तिकालीन काव्यधाराएँ, भारतीय काव्यशास्त्र की परंपरा, भारतीय नवजागरण और स्वाधीनता आंदोलन, अन्य गद्य विधाएँ एवं प्रवासी साहित्य, निर्धारित उपन्यासों का तुलनात्मक अध्ययन, गोदान, हिन्दी कहानी का विकास, स्वातंत्र्योत्तर और नयी कहानी, हिन्दी निबंध का विकास, शुक्लोत्तर निबंध, द्विवेदी और शुक्ल युग के निबंध, हिन्दी की संवैधानिक स्थिति, आधुनिक भारतीय आर्यभाषाएँ और हिन्दी का उद्भव, हिन्दी भाषा प्रयोग के विविध रूप, रीतिकाल, जीवनी, द्विवेदी युग और छायावाद, रीति, वक्रोक्ति और औचित्य सिद्धान्त, शब्दशक्ति और ध्वनि सिद्धान्त, रस सिद्धान्त और साधारणीकरण, उत्तर आधुनिकतावाद, लोहिया दर्शन, हिन्दी उपन्यास का विकास, हिन्दी नवजागरण, अंबेडकर दर्शन, आदिकाल, प्रयोगवाद और नयी कविता, छायावादी काव्य: प्रसाद और निराला, प्रगतिवाद से समकालीन कविता, निर्गुण भक्ति काव्य, द्विवेदीयुगीन काव्य, रीतिकालीन काव्य, आरंभिक हिन्दी उपन्यास, स्वातंत्र्योत्तर उपन्यास, आत्मकथा, स्वाधीनता-पूर्व प्रेमचंदोत्तर उपन्यास, निर्धारित कहानियों का तुलनात्मक अध्ययन, साठोत्तरी नाटक, प्रसाद और प्रसादोत्तर युग के नाटक, भारतेन्दु युगीन नाटक, स्वातंत्र्योत्तर नाटक, भारतेन्दु युगीन निबंध, संस्मरण और रेखाचित्र, व्यंग्य, एक साहित्यिक की डायरी, संस्कृति के चार अध्याय, सगुण भक्ति काव्य, हिन्दी नाटक, एकांकी और रंगमंच, आधुनिक गद्य और हिन्दी नवजागरण, अलंकार सिद्धान्त, हिन्दी आलोचना का विकास, भक्ति आंदोलन, कल्पना, बिम्ब, प्रतीक, मिथक और फंतासी, नयी कविता का विस्तार और साठोत्तरी कविता, उत्तर-छायावादी और प्रगतिवादी काव्य, काव्यगुण और काव्यदोष, प्लेटो, अरस्तू और पाश्चात्य परंपरा, मार्क्सवाद, स्वच्छन्दतावादी काव्यशास्त्र, आधुनिक पाश्चात्य आलोचना, भाषा और भाषा परिवार, देवनागरी लिपि
  4. Paper 2 | General Studies: State Wise GK, Polity, Geography, History, GK- Current Affairs
  5. Paper 1 | Programming Language: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++
  6. Paper 1 | Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, ORDBMS, NoSQL
  7. Paper 1 | Cyber Security: Society, Law & Ethics, Cyber Threats and Malware Attacks, Role of Internet and Web Services, Security in Mobile and Wireless Computing, Electronic Data Interchange and E-Commerce, Physical Security and Cryptography Basics, Intrusion Detection Systems (IDS), Cyber Safety and Security, Ethical Hacking
  8. Paper 1 | Computer Organization and Architecture: Basics of COA, Programming the Basic Computer, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design
  9. Paper 1 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security
  10. Paper 1 | Design and Analysis of Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
  11. Paper 1 | Data Structures: Introduction to DS, Array, Linked List, Stack, Queue, Tree, Graphs, Hashing
  12. Paper 1 | Discrete Structures and Theory of Logic: Permutation and Combination, Set Theory, Relations, Functions, Propositional and Predicate Logic, Graph Theory, Group Theory
  13. Paper 1 | Software Project Management: Software Project Management
  14. Paper 2 | Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS, Security
  15. Paper 2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment, Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Pushdown Automata & CFG, Complexity Theory
  16. Paper 2 | Artificial Intelligence & High Performance Computing: Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Natural Language Processing, Emerging Tech Trends
  17. Paper 2 | Image Processing: Digital Image Fundamentals, Image Enhancement, Image Restoration, Color Image Processing, Image Compression
  18. Paper 2 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  19. Paper 2 | Computer Graphics: Basics of Computer Graphics, 2-D Geometrical Transforms and Viewing, 3-D Object Representation, Geometric Transformations and Viewing
  20. Paper 2 | Web Technologies: Website, Browser & Services, Internet Fundamentals, Web Design & Development, Protocols & Services, Web Publishing & Hosting, Server Side & Security, Emerging Technologies, HTML Basics, JavaScript-Basics, Java
  21. Paper 2 | Soft Computing: Fuzzy Sets, Artificial Neural Networks, Genetic Algorithms
  22. Paper 2 | Distributed System: Distributed Systems
  23. UPPSC Live Class Recordings: UPPSC Polytechnic Lecturer 2025 (CS)
  24. Previous Year Papers:
  25. Mock Test:
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+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? No. 2+3+? 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+?

  3. 5:00 – 7:01 05:00-07:01

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