School of Engineering \ Material Science and Nanotechnology Engineering
	
	
	
 
				
	Course Credit
	ECTS Credit
	Course Type
	Instructional Language
 
				
				
	Programs that can take the course
	
	
	
 
	Can be taken as faculty elective course by the other engineering departments
	
	
	
 
				
	Definition of Solid-State Physics and Classification of Solids; Crystal Structure and Crystal Dynamics, Energy Band Theory, Semiconductors, Electrical Conduction Theory, Metal-Semiconductor Contacts, Semiconductor Devices, Dielectric Properties, Superconductivity, Nanostructures. 
	
	
	
 
				
	Textbook and / or References
	
	
	
 
	Katıhal Fiziği, J. R. Hook, H. E. Hall, Literatür Yayınları, ISBN: 975-7860-93-X
Katıhal Fiziğine Giriş, Charles Kittel, Palme Yayıncılık
Katıhal Fiziği, Şakir Aydoğan, Nobel Yayın, ISBN: 978-605-395-431-6
Katıhal Fiziği, Mustafa Dikici, Seçkin Yayıncılık
Katıhal Fiziği Temelleri, Ercüment Akat, Papatya Yayıncılık
	
	
	
 
				
	Introducing students to the fundamental properties of solids and their application areas. In this context, the course aims to first provide an understanding of solid-state physics and the fundamental approaches used in the classification of solids. Key topics such as lattice structures, lattice vibrations, and energy band theory, which form the basis of electrical, thermal, magnetic, and optical properties in solids, will be covered. Additionally, widely used semiconductors and semiconductor devices will be introduced. Finally, dielectric properties and superconductors will be discussed, and the course will conclude by establishing a connection between these topics and nanostructures. 
	
	
	
 
				
	
					
						1. Understanding the crystal structures of solids, particularly metals and semiconductors widely used in technology.
					
						2. Examining lattice vibrations in one-dimensional solids for monoatomic and diatomic systems and defining phonon dispersion relations.
					
						3. Calculating heat capacity arising from lattice vibrations (learning the Einstein and Debye models).
					
						4. Understanding wave diffraction by crystals, reciprocal lattice, and the definition of Brillouin zones.
					
						5. Learning the Kronig-Penney Model and determining energy levels in solids.
					
						6. Defining energy band levels in semiconductors.
					
						7. Understanding the Fermi energy level and carrier concentration in semiconductors.
					
						8. Doping in semiconductors.
					
						9. Understanding the electrical conductivity theory (Drude model) and learning drift and diffusion current densities.
					
						10. Metal-semiconductor contacts (Ohmic and Schottky contacts) and devices based on these contacts.
					
						11. pn junctions and examples of pn junction devices (LEDs, solar cells, and transistors) along with their basic principles and applications.
					
						12. Understanding bipolar transistors, field-effect transistors, junction field-effect transistors, MOSFETs, and CMOS examples.
					
						13. Learning about dielectrics, ferroelectric, and piezoelectric properties.
					
						14. Understanding superconductivity and the role of nanostructured solids in technological applications.
					
				
	
	
	
 
				
	Week 1: What is Solid-State Physics? Classification of Solids 
Week 2: Crystal Structure & Crystal Dynamics 
Week 3: Crystal Dynamics 
Week 4: Energy Band Theory 
Week 5: Energy Band Theory 
Week 6: Semiconductors 
Week 7: Electrical Conduction Theory 
Week 8: Metal-Semiconductor Contacts 
Week 9: Semiconductor Devices 
Week 10: Dielectric Properties 
Week 11: Superconductivity 
Week 12: Nanostructures 
	
	
	
 
				
				
					
					
						
							
								
									| Tentative Assesment Methods | 
								
								
									| Activities | 
									Number | 
									Weight (%) | 
								
							
							
								
									
										| Course Attendance/Participation | 
										1 | 
										5% | 
									
								
									
										| Laboratory | 
										- | 
										- | 
									
								
									
										| Application | 
										- | 
										- | 
									
								
									
										| Homework | 
										- | 
										- | 
									
								
									
										| Project | 
										- | 
										- | 
									
								
									
										| Presentation | 
										- | 
										- | 
									
								
									
										| Field Work | 
										- | 
										- | 
									
								
									
										| Internship | 
										- | 
										- | 
									
								
									
										| Course Boards | 
										- | 
										- | 
									
								
									
										| Quiz | 
										5 | 
										10% | 
									
								
									
										| Midterm Exam | 
										2 | 
										50% | 
									
								
									
										| Final Exam | 
										1 | 
										35% | 
									
								
							
							
								
									 | 
									Total | 
									100% | 
								
							
						
						
						
							
								
									| Tentative ECTS-Workload Table | 
								
								
									| Activities | 
									Number/Weeks | 
									Duration (Hours) | 
									Workload | 
								
							
							
								
									
										| Course Hours (first 6 weeks) | 
										6 | 
										4 | 
										24 | 
									
								
									
										| Course Hours (last 6 weeks) | 
										6 | 
										3 | 
										18 | 
									
								
									
										| Laboratory | 
										- | 
										- | 
										- | 
									
								
									
										| Application | 
										- | 
										- | 
										- | 
									
								
									
										| Homework | 
										- | 
										- | 
										- | 
									
								
									
										| Project | 
										- | 
										- | 
										- | 
									
								
									
										| Presentation | 
										- | 
										- | 
										- | 
									
								
									
										| Field Work | 
										- | 
										- | 
										- | 
									
								
									
										| Internship | 
										- | 
										- | 
										- | 
									
								
									
										| Course Boards | 
										- | 
										- | 
										- | 
									
								
									
										| Preparation for Quiz | 
										5 | 
										12 | 
										60 | 
									
								
									
										| Preparation for Midterm Exam | 
										2 | 
										20 | 
										40 | 
									
								
									
										| Final Exam | 
										1 | 
										2 | 
										2 | 
									
								
									
										| Preparation for Final Exam | 
										1 | 
										20 | 
										20 | 
									
								
									
										| Study Hours Out of Class (preliminary work, reinforcement, etc.) | 
										12 | 
										1 | 
										12 | 
									
								
							
							
								
									| Total Workload |  |  | 
									176 | 
								
								
									| Total Workload / 30 |  |  | 
									176 / 30 | 
								
								
									 |  |  | 
									5.866667 | 
								
								
									| ECTS Credits of the Course |  |  | 
									6 | 
								
							
						
					
				
			
				
					
						
							 | 
							
								Program Outcome
								**
							 | 
						
						
							
								| 1 | 
							
								2 | 
							
								3 | 
							
								4 | 
							
								5 | 
							
								6 | 
							
								7 | 
							
								8 | 
							
								9 | 
							
								10 | 
							
								11 | 
							
						
					
					
						| 
							Course Outcome
						 | 
						
							
								| 1 | 
								
									
									
									
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
											
										
										
										
											
										
											
										
											
												
											
										
									
									
									
										
										
											
												B, C
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
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											 | 
										
									
								
							
						
							
								| 2 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
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											 | 
										
									
								
							
						
							
								| 3 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
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											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 4 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
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											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
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											 | 
										
									
								
							
						
							
								| 5 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
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											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 6 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 7 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 8 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 9 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 10 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
									
									
										
										
											
												A
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 11 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
									
									
										
										
											
												A
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 12 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
									
									
										
										
											
												A
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 13 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
									
									
										
										
											
												A
											 | 
										
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
							
						
							
								| 14 | 
								
									
									
									
									
										
										
											
										
										
										
											
												
											
										
											
										
											
										
									
										
										
											
										
										
										
											
										
											
												
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
											
												A, B
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											 | 
										
									
								
									
									
									
									
										
										
										
										
									
										
										
										
										
									
										
										
										
										
									
									
									
										
										
										
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											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
									
										
										
										
										
											
										
											
										
									
										
										
											
										
										
										
											
												
											
										
											
										
									
									
									
										
										
											
												A
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											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
											 | 
										
									
								
									
									
									
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
										
										
										
										
											
										
											
										
											
										
									
									
									
										
										
										
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											 |