Discuss the salient features of the genetic algorithms. Explain its applications in business. How do they differ from artificial neural networks?
Algorithms (GAs) are adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetic. The basic concept of GAs is designed to simulate processes in natural system necessary for evolution, specifically those that follow the principles first laid down by Charles Darwin of survival of the fittest. As such they represent an intelligent exploitation of a random search within a defined search space to solve a problem.
GAs as a number of different things:
*GAs as problem solvers
*GAs as challenging technical puzzle
*GAs as basis for competent machine learning
*GAs as computational model of innovation and creativity
*GAs as computational model of other innovating systems
*GAs as guiding philosophy
GAs were introduced as a computational analogy of adaptive systems. They are modelled loosely on the principles of the evolution via natural selection, employing a population of individuals that undergo selection in the presence of variation-inducing operators such as mutation and recombination (crossover). A fitness function is used to evaluate individuals, and reproductive success varies with fitness.
The Algorithms
1. Randomly generate an initial population M(0)
2. Compute and save the fitness u(m) for each individual m in the current population M(t)
3. Define selection probabilities p(m) for each individual m in M(t) so that p(m) is proportional to u(m)
4. Generate M(t+1) by probabilistically selecting individuals from M(t) to produce offspring via genetic operators
5. Repeat step 2 until satisfying solution is obtained.
The paradigm of GAs descibed above is usually the one applied to solving most of the problems presented to GAs. Though it might not find the best solution. more often than not, it would come up with a partially optimal solution.
everyone can gain benefits from Algorithms, once he can encode solutions of a given problem to chromosomes in GA, and compare the relative performance (fitness) of solutions. An effective GA representation and meaningful fitness evaluation are the keys of the success in GA applications. The appeal of GAs comes from their simplicity and elegance as robust search algorithms as well as from their power to discover good solutions rapidly for difficult high-dimensional problems. GAs are useful and efficient when
**The search space is large, complex or poorly understood.
**Domain knowledge is scarce or expert knowledge is difficult to encode to narrow the search space.
**No mathematical analysis is available.
**Traditional search methods fail.
The advantage of the GA approach is the ease with which it can handle arbitrary kinds of constraints and objectives; all such things can be handled as weighted components of the fitness function, making it easy to adapt the GA scheduler to the particular requirements of a very wide range of possible overall objectives.
GAs have been used for problem-solving and for modelling. GAs are applied to many scientific, engineering problems, in business and entertainment, including:
Optimization: GAs have been used in a wide variety of optimisation tasks, including numerical optimisation, and combinatorial optimisation problems such as traveling salesman problem (TSP), circuit design, job shop scheduling and video & sound quality optimisation.
Automatic Programming: GAs have been used to evolve computer programs for specific tasks, and to design other computational structures, for example, cellular automata and sorting networks.
Machine and robot learning: GAs have been used for many machine- learning applications, including classificationa and prediction, and protein structure prediction. GAs have also been used to design neural networks, to evolve rules for learning classifier systems or symbolic production systems, and to design and control robots.
Economic models: GAs have been used to model processes of innovation, the development of bidding strategies, and the emergence of economic markets.
Immune system models: GAs have been used to model various aspects of the natural immune system, including somatic mutation during an individual's lifetime and the discovery of multi-gene families during evolutionary time.
Ecological models: GAs have been used to model ecological phenomena such as biological arms races, host-parasite co-evolutions, symbiosis and resource flow in ecologies.
Population genetics models: GAs have been used to study questions in population genetics, such as "under what conditions will a gene for recombination be evolutionarily viable?"
Interactions between evolution and learning: GAs have been used to study how individual learning and species evolution affect one another.
Models of social systems: GAs have been used to study evolutionary aspects of social systems, such as the evolution of cooperation , the evolution of communication, and trail-following behaviour in ants.
---------------------------------
Applications of Algorithms
GA on optimisation and planning: Travelling Salesman Problem
The TSP is interesting not only from a theoretical point of view, many practical applications can be modelled as a travelling salesman problem or as variants of it, for example, pen movement of a plotter, drilling of printed circuit boards (PCB), real-world routing of school buses, airlines, delivery trucks and postal carriers. Researchers have tracked TSPs to study biomolecular pathways, to route a computer networks' parallel processing, to advance cryptography, to determine the order of thousands of exposures needed in X-ray crystallography and to determine routes searching for forest fires (which is a multiple-salesman problem partitioned into single TSPs). Therefore, there is a tremendous need for algorithms.
In the last two decades an enormous progress has been made with respect to solving travelling salesman problems to optimality which, of course, is the ultimate goal of every researcher. One of landmarks in the search for optimal solutions is a 3038-city problem. This progress is only party due to the increasing hardware power of computers. Above all, it was made possible by the development of mathematical theory and of efficient algorithms. Here, the GA approach is discussed.
There are strong relations between the constraints of the problem, the representation adopted and the genetic operators that can be used with it. The goal of traveling Salesman Problem is to devise a travel plan (a tour) which minimises the total distance travelled. TSP is NP-hard (NP stands for non-deterministic polynomial time) - it is generally believed cannot be solved (exactly) in time polynomial. The TSP is constrained:
*The salesman can only be in a city at any time
*Cities have to be visited once and only once.
When GAs applied to very large problems, they fail in two aspects:
1. They scale rather poorly (in terms of time complexity) as the number of cities increases.
2. The solution quality degrades rapidly.
Failure of Standard Algorithm
To use a standard GA, the following problems have to be solved:
A binary representation for tours is found such that it can be easily translated into a chromosome.
An appropriate fitness function is designed, taking the constraints into account.
Non-permutation matrices represent unrealistic solutions, that is, the GA can generate some chromosomes that do not represent valid solutions. This happens:
*in the random initialisation step of the GA.
*as a result of genetic operators (mutation and crossover).
Thus, permutation matrices are used. Two tours including the same cities in the same order but with different starting points or different directions are represented by different matrices and hence by different chromosomes, for example:
tour (23541) = tour (12354)
An proper fitness function is obtained using penalty-function method to enforce the constraints.
However, the ordinary genetic operators generate too many invalid solutions, leading to poor results. Alternative solutions to TSP require new representations ( Position Dependent Representations) and new genetic operators.
GAs as guiding philosophy
Evolutionary Divide and Conquer (EDAC)
This approach, EDAC, has potential for any search problem in which knowledge of good solutions for subproblems can be exploited to improve the solution of the problem itself. The idea is to use the Algorithm to explore the space of problem subdivisions rather than the space of solutions themselves, and thus capitalise on the near linear scaling qualities generally inherent in the divide and conquer approach.
The basic mechanisms for dissecting a TSP into subproblems, solving the subproblems and then patching the subtours together to form a global tour, have been obtained from the cellular dissection algorithms of Richard Karp. Although solution quality tends to be rather poor, Karp`s algorithms possess an attractively simple geometrical approach to dissection, and offer reasonable guarantees of performance. Moreover, EDAC approach is intrinsically parallel.
The EDAC approach has lifted the application of GAs to TSP an order or magnitude larger in terms of problem sizes than permutation representations. Experimental results demonstrate the successful properties for EDAC on uniform random points and PCB problems in the range 500 - 5000 cities.
GA in Business and Their Supportive Role in Decision Making
Algorithms have been used to solve many different types of business problems in functional areas such as finance, marketing, information systems, and production/ operations. Within these functional areas, GAs have performed a variety of applications such as tactical asset allocation, job scheduling, machine-part grouping, and computer network design.
Finance Applications
Models for tactical asset allocation and international equity strategies have been improved with the use of GAs. They report an 82% improvement in cumulative portfolio value over a passive benchmark model and a 48% improvement over a non-GA model designed to improve over the passive benchmark.
algorithms are particularly well-suited for financial modelling applications for three reasons:
1. They are payoff driven. Payoffs can be improvements in predictive power or returns over a benchmark. There is an excellent match between the tool and the problems addressed.
2. They are inherently quantitative, and well-suited to parameter optimisation (unlike most symbolic machine learning techniques).
3. They are robust, allowing a wide variety of extensions and constraints that cannot be accommodated in traditional methods."
Information Systems Applications
Distributed computer network topologies are designed by a GA, using three different objective functions to optimise network reliability parameters, namely diameter, average distance, and computer network reliability. The GA has successfully designed networks with 100 order of nodes.
GA has also been used to determine file allocation for a distributed system. The objective is to maximise the programs' abilities to reference the file s located on remote nodes. The problem is solved with the following three different constraint sets:
1. There is exactly one copy of each file to be distributed.
2. There may be any number of copies of each file subject to a finite memory constraint at each node.
3. The number of copies and the amount of memory are both limited.
Production/Operation Applications
Algorithm has been used to schedule jobs in a sequence dependent setup environment for a minimal total tardiness. All jobs are scheduled on a single machine; each job has a processing time and a due date. The setup time of each job is dependent upon the job which immediately precedes it. The GA is able to find good, but not necessarily optimal schedules, fairly quickly.
GA is also used to schedule jobs in non-sequence dependent setup environment. The jobs are scheduled on one machine with the objective of minimising the total generally weighted penalty for earliness or tardiness from the jobs' due dates. However, this does not guarantee that it will generate optimal solutions for all schedules.
GA is developed for solving the machine-component grouping problem required for cellular manufacturing systems. GA provides a collection of satisfactory solutions for a two objective environment (minimising cell load variation and minimising volume of inter cell movement), allowing the decision maker to then select the best alternative.
Role in Decision Making
Applying the well established decision processing phase model of Simon (1960), Algorithms appear to be very well suited for supporting the design and choice phases of decision making.
*In solving a single objective problem, GA designs many solutions until no further improvement (no increase in fitness) can be achieved or some predetermined number of generations have evolved or when the allotted processing time is complete. The most fit solution in the final generation is the one that maximises or minimises the objective (fitness) function; this solution can be thought of as the GA has recommended choice. Therefore with single objective problems the user of GA is assisted in the choice phase of decision processing.
*When solving multi-objective problems, GA gives out many satisfactory solutions in terms of the objectives, and then allows the decision maker to select the best alternative. Therefore GAs assist with the design phase of decision processing with multi-objective problems.
GAs can be of great assistance for examining alternatives since they are designed to evaluate existing potential solutions as well to generate new (and better) solutions for evaluation. Thus GAs can improve the quality of decision making.
What is an artificial neural network?
An artificial neural network is a system based on the operation of biological neural networks, in other words, is an emulation of biological neural system. Why would be necessary the implementation of artificial neural networks? Although computing these days is truly advanced, there are certain tasks that a program made for a common microprocessor is unable to perform; even so a software implementation of a neural network can be made with their advantages and disadvantages.
Advantages:
• A neural network can perform tasks that a linear program can not.
• When an element of the neural network fails, it can continue without any problem by their parallel nature.
• A neural network learns and does not need to be reprogrammed.
• It can be implemented in any application.
• It can be implemented without any problem.
Disadvantages:
• The neural network needs training to operate.
• The architecture of a neural network is different from the architecture of microprocessors therefore needs to be emulated.
• Requires high processing time for large neural networks.
Another aspect of the artificial neural networks is that there are different architectures, which consequently requires different types of algorithms, but despite to be an apparently complex system, a neural network is relatively simple.
Artificial neural networks are among the newest signal processing technologies nowadays. The field of work is very interdisciplinary, but the explanation I will give you here will be restricted to an engineering perspective.
In the world of engineering, neural networks have two main functions: Pattern classifiers and as non linear adaptive filters. As its biological predecessor, an artificial neural network is an adaptive system. By adaptive, it means that each parameter is changed during its operation and it is deployed for solving the problem in matter. This is called the training phase.
A artificial neural network is developed with a systematic step-by-step procedure which optimizes a criterion commonly known as the learning rule. The input/output training data is fundamental for these networks as it conveys the information which is necessary to discover the optimal operating point. In addition, a non linear nature make neural network processing elements a very flexible system.
Basically, an artificial neural network is a system. A system is a structure that receives an input, process the data, and provides an output. Commonly, the input consists in a data array which can be anything such as data from an image file, a WAVE sound or any kind of data that can be represented in an array. Once an input is presented to the neural network, and a corresponding desired or target response is set at the output, an error is composed from the difference of the desired response and the real system output.
The error information is fed back to the system which makes all adjustments to their parameters in a systematic fashion (commonly known as the learning rule). This process is repeated until the desired output is acceptable. It is important to notice that the performance hinges heavily on the data. Hence, this is why this data should pre-process with third party algorithms such as DSP algorithms.
In neural network design, the engineer or designer chooses the network topology, the trigger function or performance function, learning rule and the criteria for stopping the training phase. So, it is pretty difficult determining the size and parameters of the network as there is no rule or formula to do it. The best we can do for having success with our design is playing with it. The problem with this method is when the system does not work properly it is hard to refine the solution. Despite this issue, neural networks based solution is very efficient in terms of development, time and resources. By experience, I can tell that artificial neural networks provide real solutions that are difficult to match with other technologies.
Fifteen years ago, Denker said: “artificial neural networks are the second best way to implement a solution” this motivated by their simplicity, design and universality. Nowadays, neural network technologies are emerging as the technology choice for many applications, such as patter recognition, prediction, system identification and control.
3. What are integrated software applications? Discuss their advantages and business utility. “Every component of a computer such as hardware software and network should be protected”. Justify and elaborate.
Integrated software combines the functions of several programs into one interface. Such a program is usually designed for the beginning or casual user.
Many advanced features are omitted that might be found in stand-alone products. For example, the word processor in an integrated software package would not likely have a way to automatically generate a table of contents and would have fewer options on how to handle footnotes, headers, and footers.
Microsoft Works is an example of integrated software.
Suites
A software suite is a set of applications which can each stand alone. They are packaged together for a lower price than if all were bought separately. There are usually enhancements that help the applications communicate with each other, also.
Some popular suites of office software include MS Office, Lotus Smart Suite, WordPerfect Office, OpenOffice, and iWork (for Mac computers). These include several programs, such as:
• word processing
• spreadsheet
• presentations
• e-mail client
• address book
• database
Other Examples of Software Suites
An example of a graphics suite is Corel Draw Suite, which includes programs for:
• vector illustration
• layout
• bitmap creation
• image-editing
• painting
• animation software
An example of a publishing suite is Adobe Publishing Collections, which includes:
• Adobe PageMaker - desktop publishing
• Adobe Photoshop - bitmap graphics
• Adobe Illustrator - vector graphics
• Adobe Acrobat - converts documents to Portable Document Format for sharing
Purpose: Linking different applications together for better work
(integrated software) Simplifying things for new users
Major Advantage: Costs less than a set of similar stand alone applications bought separately
Major Disadvantage: (integrated software) Lacks many features of the stand-alone versions of the same software.
(suites) You may not need all the parts or the advanced features in the collection.
Integrated software is a single program that contains "modules" or "tools" to complete many popular business applications. These applications include word processing, spreadsheets, database management, graphics, and communications.
These tools are sufficient for the typical tasks performed by a small business, a student, or a home user. The word processing module might be used to type a letter or report. The spreadsheet module might be used to do financial analysis or to record comparisons. The database module can be used in a variety of ways, such as to organize an inventory; to compile a list of customers' (or friends') names, street or e-mail addresses, and phone and fax numbers; and to maintain a household inventory for insurance purposes. A graphics module can give an individual or a business an edge by providing tools that will give a "professional look" to documents produced.
One of the reasons integrated software is popular in the education world is that the user can easily switch from one type of application to another without exiting the program. In a beginning or an introductory class or curriculum, the use of integrated software is beneficial because a teacher can quickly develop
___ ______ _____ ________ ___ ________ ___ ___ ________ ______ _____.
________ __________ __________ ______ _________ ________ ___ __________ ________ __________.
_____ ____ ______ ______ ___ _______ ___ _________ ___ ________.
___ _________ ____ ___ _____ _______ _______ ________.
_______ _______ _______ ______ _________ ______ _______ __________ ____ _________ ____ _______.
______ _____ __________ __________ ______ ____ __________ ___ _________ _____ _______.
_________ _______ ___ _________ _______ _____ _____.
______ ___ _____ ___ ______.
______ ______ _________ _______ _________ ______ ________ _____.
____ _______ _____ ___ ________ _________.
_____ ____ _____ ___ _______ ___ __________ ________ ____.
_________ ____ ___ _______ _______ ________.
_____ __________ ____ _______ __________ _______ __________ ____ ___ ________.
________ ______ _______ _____ _______ __________ __________ _____.
______ ______ ______ _____ _______ ______ ____ ___ ______.
_________ _______ _____ ______ __________ _______ ___ ____.
____ ____ ____ _______ _______ ______ ________ ___ ________.
______ ______ _____ ___ __________ ______ __________ _____ __________.
____ ____ _______ __________ _____ _______ ______ ______ __________ ____ ________.
________ ___ ______ _______ ________ ____ ____ ________ _____.
_________ _______ ________ ________ ________ _____ ____ ______.
____ ____ ________ ___ ______ _______ __________ ________ __________ ____ ___ ____.
____ _____ ______ _____ _________ _____ _____ ____.
_____ __________ _______ ____ ______ _________ _______ ___.
_________ ________ ____ ____ ____ ________ _________ ____ _______ ___ ___ ________.
______ ______ _____ __________ ______ __________ ___ __________ _________ ____ _________ _____.
_______ ________ __________ ____ _________ ___ ___ _________ ___ ______ _____ ____.
_______ __________ __________ _______ ______ ________ ___ ___ ____ _________.
_____ ___ _______ _______ _________.
___ ___ _______ ________ _____ ___ _________ __________ ________.
____ ________ ________ ____ _________ ______.
___ _____ ______ ____ _________.
_______ _____ ___ _______ __________ ____ ________.
_________ ___ _______ _________ _________ _____ _______ ____ _____ ________ ___.
__________ _____ __________ _________ ________ ______ _______ _____ ____ ___ _________.
____ __________ ____ ____ _______ __________ _________.
________ _________ ____ ________ ______ ______ __________ __________ ___ _____ ________ _________.
_______ ______ ______ __________ ______ _________ _____.
_____ ________ _______ __________ _______ ___ ________.
___ ___ _____ _________ ____ _______ ___ _____ __________ __________ _____.
___ ___ ________ _______ _________ ____ ______ _______.
_________ _____ __________ ________ ___ ___ __________.
_______ _________ _________ _______ ______ __________ ____ ____.
__________ _________ _________ _________ ___ __________ __________ _____ _______ ______ ________.
___ _____ ______ _____ ______ ___ ____ ______ ____ ___ _________ ________.
_________ ___ ___ _________ ____ __________ __________ ______ _____.
___ _________ __________ ________ _________.
_________ ____ ________ __________ _________ ________ _____ __________ ____ ________ __________ __________.
_________ _________ ____ ________ _______ ________ _______.
_________ _____ ____ ________ _________ _________ __________ ______.
________ __________ ________ ____ ____.
_________ _________ ________ _________ __________ ___ ________ ___ _______ _______ _________ ________.
_____ ____ ____ ___ _________ ____ ______ _____ _____ ________.
___ ________ ______ __________ ___ ______ __________ _________ _____.
_________ ____ ____ _________ __________ ________ ______.
_______ ________ __________ __________ ____ _______.
___ ___ ___ ______ __________.
_______ __________ __________ ___ ___ _________ ________.
_________ _____ _____ ___ _______ ________ ______ _________.
___ __________ _________ ______ ___.
_________ ___ _______ ______ _____.
__________ _______ _______ _________ _________ __________ _____ _________ ___ ___.
________ _______ ________ _____ _____ __________ _________ _______ ________.
__________ ________ ____ ______ ______ __________.
___ ___ ___ _______ ___ ___ __________ _______ _____ _____.
___ __________ _______ ______ ________ ________ _____ _______ ______ ________.
______ ______ _______ ________ _________ _________ ________ ________ ___.
_____ ________ _____ _______ ________ ___ ______ __________.
____ _______ ___ _________ ______ _________ ___ ________ _________ ____.
______ ________ _________ _________ __________ _______ _________ ____ ________ ______ __________.
__________ _____ _____ _____ ____ ____ __________ __________ ___.
__________ ______ _______ __________ _______ _________ ____ _____ _______.
_____ ______ ______ _______ _________ _________.
____ _______ ______ ____ _____.
____ __________ _______ _____ ___ ________ __________ ___ ____ __________ ______ __________.
_____ ______ _____ _________ _________ ________ ____.
___ ___ ________ ________ __________.
__________ _______ ________ ________ ___ _____ _________.
_________ ________ _____ ___ ___ ____ ____.
___ ____ ____ ____ __________ ___ ___ __________ ______ __________.
______ _______ _______ _________ ________ _______.
______ _____ _______ _____ ______ ______ ___ ______ ______.
_____ __________ _______ _______ _________.
_____ ____ ______ _________ ___ _____.
__________ ___ __________ _____ ___ ___ ________ ______ ___ ____.
______ __________ ____ ____ _____.
_________ ____ ___ _____ _________ _______ ____ _____ __________.
________ __________ _______ ____ _____.
________ ______ ___ _____ ____.
___ ___ ________ __________ ________ ________ _______ ____ _________.
_____ ______ ____ ___ _____ ___.
______ ________ ______ ______ _________.
____ _______ _______ _______ _______ ___ ______ ______ _______ ______.
_____ __________ ____ ______ ______.
___ _______ _________ ____ _____ ___ __________ ___ ________ _________ _____.
__________ __________ _____ ____ _____ ____.
_________ _________ ____ ___ ___ _______ ______ ________ ___ ___.
__________ _______ ___ _________ _____ ________ _____ __________ ____.
___ __________ _____ _________ _________ ________ ________ ______ ______.
________ ______ _______ ____ _________ ____ _____ ________ _________ __________.
___ _______ _________ __________ ______ _______ _____ _____ __________ _______.
_____ __________ ______ ___ ________ _________ _______ ________ ___ ___ ___.
_____ _________ ______ ___ ________ ___ _________.
___ _________ __________ ___ ____ ___ _________ ________ _____ ________ __________ _______.
________ _________ ____ __________ _______ _______.
____ ___ __________ ___ __________.
___ ______ _________ ________ __________ ________.
____ ___ _____ ______ ________ ___ _________ ____.
______ _____ ________ _____ __________ __________ __________ __________ ________ ____ _________.
____ _____ ________ ___ ____ __________ ________ _____ ____.
________ ________ __________ __________ _________ ___ ______ _____ ___ ___ ___ __________.
___ ________ _________ ____ ______ ________ __________ _______ ____ _______ ________ _____.
__________ ___ _______ __________ _______ _________ ______ _____ _______.
_______ _____ __________ ______ ___.
______ ________ ________ __________ _________ _____ ____ _______ _______ _________ _________.
___ _______ ______ ____ ________ ___ ______ ________.
______ __________ _______ ________ ________ _______ _____ ___ __________.
__________ ______ ___ ________ ______.
_______ _____ __________ __________ ____.
_________ ___ _________ ______ ________ ______ ______ ____.
_______ _______ _________ _______ __________ ________ _______ ______ ______ _______.
_____ _________ __________ ___ _________ __________ _____ ______ ______.
__________ _______ ______ ____ __________ __________ _______ ______ ___ ______.
_______ _________ ____ _________ ____ ________ ________ _____ ___ ___.
________ _____ ___ __________ _________ _____ _____.
____ ___ _____ ____ ____ ______ ___ ________ ___ ___.
___ _________ ______ _________ ______ _____ ___.
__________ _________ _____ ________ ____ _____ _____ __________.
____ __________ ___ ____ ____ ________ ________ ________.
____ _________ _______ _________ ________ _______ ______ __________.
_______ ____ ___ __________ _______ ______ _____ _______ _____ __________ _____ ________.
____ ________ ___ ____ ________ ____ ________ ___ _________.
________ __________ ___ ________ ____ _________ _______ ___ ________.
_____ _______ _______ __________ ____.
_________ __________ _________ _________ ___ ________ ______ ____ __________ ____.
___ ______ _____ ____ _________ ____ _________ ______.
______ _______ ______ _______ ___ ________ ___ _______.
___ _______ ________ __________ ___ ______.
__________ ____ ______ _______ _____ ______ _____ ________ __________ _________ _______.
_________ _______ ______ ________ ________ ________ _________ _______ ____ ____.
__________ __________ ______ _________ _______ __________ ________ __________ ________.
________ _________ ____ ____ _________ ______ _________ _________ _________ _________ _______ ______.
__________ ________ __________ ____ __________.
________ _________ _________ _______ ________ ____ _______ _____ ___ ________.
_____ ____ _______ _________ _____ ______ ________ ______ __________ ________ ________.
_____ _____ ________ ___ ________ ______ ___ _____ ______.
__________ ____ ________ _______ ___ ___ _________.
___ _______ ________ _________ ____ ____ ___ ________ _________.
_______ ____ _______ _____ _________ __________ ___ ________ _______ _______ _________.
__________ ________ _____ _____ ______ _______.
_______ ________ _____ ____ ______ _________ _____.
________ __________ _______ __________ ________ _____ ______.
__________ ___ ___ ______ _______ _______ ______ ____ ___ _____ _________ ___.
_______ ____ ______ ________ _________ _____ ____ _________ ________.
________ ______ ______ _________ _____ ______ _____ ______ _________.
_____ ___ ___ ________ _____ ____ _____ ___ ____.
________ ________ ____ ______ _______ ________ _________ ____ _________ ___.
_____ _________ ________ ________ ______ ____ _______ _________ _______ _________ ___ _____.
_______ _______ __________ __________ ______ _________ ___ _____ __________ __________ ____ ________.
_______ ________ _____ _______ ___ ________.
_______ ________ ___ ____ _________ __________ __________ ___ _______ ___.
__________ ____ ______ _______ ____.
_________ _____ __________ ____ ____ _______.
___ _____ ________ _______ _____ ____ ___ ______ ___.
______ ______ ____ _____ ____ ________ _______.
___ _________ ________ _______ _________ _____ ________ ________ ___.
____ ____ ___ __________ ________ ________ ____ ______ __________.
__________ _____ _______ ____ _____ ______ __________ __________ __________ _____ ___.
___ _______ _______ ________ ______ _______ ________ ___ ____.
_____ ___ ______ _________ _________.
__________ _________ _____ ___ _______ _____ __________ _______.
_____ ______ ________ _________ ___ _________ _______.
________ _____ _____ _______ ______ __________ _____.
____ ________ __________ ________ __________ _____ _________ ______ ______ _____.
_____ ___ _____ _____ _________ _______ ____ _____.
_______ _______ ________ _______ ________ __________ __________ _____ _________ _________ ___.
_________ __________ _______ _____ ____ _________.
_________ _____ _________ _______ ___ ____.
________ _________ _____ _______ __________ ____ ________ __________ ______.
________ ___ __________ ________ __________ _____ ___ ____ _________ ________ _____.
__________ ___ _______ ____ _________ __________ ______ ___ ___ _____.
__________ ___ _______ _____ _____.
___ ____ ______ __________ ___ ___ ___ ________ ________ _____.
_________ ____ _____ _________ ___ ______ _______ ____ ______ ___ _____.
___ _____ ______ __________ ____ ____ ______.
___ _________ ________ ______ ____.
_______ ________ ___ ______ ____ _________ __________ __________ ___ __________.
___ _________ ______ ____ _________ _____ ________ ______ ______ ___ ________ ________.
________ _________ ___ ______ _____.
_________ ___ _____ _____ __________ ___ _______ _________.
__________ ________ ____ ____ ___.
_____ _____ ________ __________ ________ ______ ___ _____ ________ _____ _________.
_______ _________ _______ _____ _________.
___ _______ ________ _______ _________ __________ ___ __________.
______ ___ __________ _______ _________ _________ _________ ____ _______ _____ ____ ____.
___ ___ _________ _______ _______ ______ _______ __________.
____ _________ _________ _______ ____ ________ _________ _______ ________ __________.
______ ________ ______ _________ ______ _______.
___ _________ _______ _____ ____ ________ _________ ________.
_______ _______ __________ ______ ______ ____ ______.
______ ________ _____ _______ ______ _____ __________ ____ __________ ______ _______.
__________ _________ ______ ____ ______ _______ ___ _______ __________ _____ _________ ____.
____ ______ __________ __________ ___ ______ ____ __________ ___.
__________ ________ _______ ______ ______ ___.
__________ ______ _____ _______ ___ _____ ______ _____ ____ ____ ____ _______.
_____ ________ ___ _________ _____ ________ __________ _______ __________ ____ __________ ____.
_______ ________ ________ ___ _____ _____ _________.
___ ______ ________ ________ _______ ______ ______ __________.
__________ _________ _______ ___ _______ ______ ________ ___ ___.
________ _________ ________ _________ _________.
______ _______ __________ _____ _________ ____ ___.
___ ________ ___ _______ _______ _____ ________ _____ ___ ____ ________ ___.
___ ________ _______ __________ _____ _________ __________ _____ ___ ___ ____.
__________ ____ ____ ____ ____ ___ ______.
__________ __________ _________ ___ ____ ________ ____ _________ ___.
__________ _________ ______ ____ __________ ______.
_______ _______ ________ ________ ____ __________.
____ _________ _______ _________ _____ ________ ________ ____ _________ _____ ______.
_____ _____ ___ ____ ________.
_____ ________ _____ ________ __________ _____ _________ ___ ______ _______.
_______ ___ ___ _________ ____ ______.
____ ______ _______ ___ _____ ________ __________ ________ ___ ________ ___ _________.
__________ ______ ____ ______ ___.
_______ ___ ________ __________ _______.
_______ ___ _______ __________ ________ _________ ________ _______ _____ _______ ________.
_________ ______ __________ _______ ______ ______ _________ _____ ________.
__________ __________ ________ _______ ___ _________ _____ ______ __________ _____ ___ _________.
______ _____ ________ _______ __________ _______ _________ ___ _______ _____ ________.
_______ _______ __________ _________ ___ ______.
________ _________ _______ _____ _______.
_______ __________ _________ _______ ________ _____ ____.
___ ______ ___ ______ _______ ________ ____.
_________ ___ __________ _____ ___ __________ ______ _____ _____ _____ _____.
_______ ______ __________ __________ _______ _________.
_________ _________ _______ ___ _______ ________ ____ ____.
_______ ___ _________ __________ ____ ___ ______.
_____ _________ _________ ______ ______ _____.
________ ____ ________ ________ ______ __________ ____ ____ ______ _________ _______.
__________ ______ _________ ___ _________ _______ ____ _________ __________ ____.
________ ____ _____ _____ ___.
____ ________ ______ __________ __________ ______.
______ ______ ___ _________ __________ _________ ________ _________ ___.
____ _________ _______ ______ _______ _______ ______ __________ ________ _________.
________ ______ __________ _______ ___ _______ _____.
__________ ___ ___ _________ ________ ___ ____ _________ _________ ______.
______ ____ ___ ______ ___ ____ _________ __________ _________ __________ _______ _________.
____ _____ _____ _____ __________ _________ _____ ________ _____.
________ ___ _________ ________ _______.
________ _____ ____ _____ __________ ___ __________ ___ _______ _______ ____.
______ ____ ____ _______ __________.
_____ ____ _____ _________ _______ ________ _______ ___.
____ __________ ___ _____ __________ _____ _______.
___ ______ _______ ___ ______ ___ _________ ______ __________.
__________ ____ ___ ______ __________ ______ ______.
____ _________ ________ __________ _____.
_______ ______ _____ ________ ___ ___ _______ ___ ___ __________.
____ _____ __________ ____ __________ ____ ____ ___ _____ ______ ____ ______.
_________ __________ ______ _______ ___ ______ ______ _________ _____.
_____ ________ __________ ___ _______ ___.
_____ ______ ________ __________ _____ ___.
________ ________ ____ _________ ____ _______ ________ ______ ________ ________ ___ ___.
___ _________ ___ ___ __________ ___ _________.
_______ _________ ___ ____ _________ _________ ____ _______.
_________ ________ _______ ___ _____.
______ ______ __________ ______ ____ ___.
___ _____ ________ ____ _________ ___ _______ ________ ___.
__________ ___ __________ __________ ________ _____ ___ __________ ________ ________ ___ __________.
_____ _____ ___ __________ _______ ______ _________ ______ ___ ____ __________ _________.
________ _____ ___ __________ ___ _______ __________ ____ ___ ________.
____ _________ ________ _____ __________ ___ _________ _______ ______ ________ ________ _______.
________ _____ _____ ________ ____ ____ _________ _______ ____.
_________ ______ _______ ________ ___ _____ ___ _____ ___ _________.
____ ___ __________ _______ __________.
_________ ___ ________ ______ ________ ____ _____ __________.
________ ________ ______ ________ _____ ________ ___.
___ __________ ________ ____ ___ ________ ____ _________ ________ ________.
______ ________ ___ _______ ________.
__________ ___ _________ ________ ______ ________ _________ ___ ______ _______ _______ ______.
____ __________ ____ __________ __________ ______ _____ _________.
_______ _____ _____ _____ ___ _________ _________ ________ ___.
___ ___ ______ ________ _____ _______ __________ _______ __________ ___ _______.
_______ ______ ______ _________ _________ ____ _______.
_____ ______ __________ ____ _______ __________ __________.
_______ _____ _____ ________ ______ ___ _________ ____ __________.
________ _______ ______ ______ ______ ____ ________ ___.
_________ ___ __________ _______ _______ ______ _______.
__________ ____ ___ ______ ________ ______ _________ ____ _________ _________ _________.
___ __________ _______ ___ ______ ________ ___ _______.
____ ______ ________ ___ _______ ________ _______ _________ ___ ______.
_________ __________ _______ _______ _____ _______.
_______ ________ _______ _____ _________ _________.
___ _____ ___ _______ _______ _________ ______ __________ ________ __________ __________.
______ _________ _______ _____ __________ _____ _______.
____ ______ ______ ________ _________ _________ __________ _________ _____ ______ __________.
____ _______ ___ _______ ___ _________.
_________ _______ ______ ______ _________ _________ _________.
_______ ____ ____ ___ ___ _____ ________ _____ _________.
_________ _____ ___ ____ ______ ___.
_______ _________ _________ _____ ______ ____ ________.
_______ ___ ______ _________ ______ ______ ____ __________ ________ ____.
_____ _______ __________ ____ _________ _________.
__________ ___ ______ _________ ______.
_________ _______ _____ ______ ______ _______ ___.
_______ _____ _________ _________ _____ ___ ___ _______ ____ ___.
__________ ______ ____ ________ __________.
___ ____ ____ __________ ________ ________ __________ ____ ______ ____.
_________ _______ _____ _______ __________ _____ ______ _____ ________ ________.
______ _______ ____ ______ _____ _________.
___ __________ ___ ________ _____ ______ ___ _________.
__________ _________ ______ _____ _______ _________ __________ ________ _____ _______ _________.
__________ ____ __________ _______ ____.
_________ _____ ________ _____ _________ __________ ____.
_______ ______ _____ ____ _______ ___ __________ _________ _____ ________ __________.
_____ _____ ______ _________ ____ ___ ___ _____.
_______ _____ ____ _____ ________ _______.
__________ _____ ______ _________ ____ ___ ___ ______ ___ ______ __________.
_________ ________ ____ ____ ________ __________ ________ _________.
___ ______ __________ ___ ______ ____ ____ ___ _________ _______ __________.
_______ ______ __________ _______ ______ _______ ___ _________ _________ ______ ________.
________ ____ _____ ____ __________ ___ _____ _____ ______ _______ ________ ____.
______ _______ _____ _________ ______ ____ ___ ___ ______ _____.
_________ ________ _______ ___ ______ __________ _________ _________ ______ _____ ______.
____ _____ __________ ______ ___ ________ _____ _________.
__________ ___ ______ ___ _______ __________ __________ _______ ____ _____ ______ ____.
_____ ___ ______ ___ ______ ______ _____ __________ _______ ________.
____ ____ __________ ___ ________ ___ _____ _______ ______ _____.
_____ ______ ___ _________ ____ _______ ____ ______ __________.
______ __________ ________ _____ _________ _________ ____ _______ ____.
________ ________ ___ __________ _______ ____ ___ ____ _________ __________ __________.
_____ _____ __________ ________ ___ ___ ______ __________.
_____ ______ ______ ________ __________ __________ _________.
______ _________ ________ ___ ___ _______ __________ ___ ____ _____ ___.
_____ _________ _________ ______ _____ __________ ____ _________ _______ _____.
____ _________ ________ ________ ______ _________.
_____ _____ _____ ___ _____.
________ ___ _________ ______ ____ ___ ____ ____ ___ _______.
____ ________ ________ ____ ________ ___ ______ ____ ________ ____ _______.
________ ________ ____ ______ ______ ________ ______ _________ ____ ________.
_______ ____ ____ ________ _______ _____.
____ ______ ____ _____ _____ ________ _____.
______ ____ ___ __________ ________ ________ ______.
____ __________ ____ ____ _____ _________ ______ ______.
__________ _________ ________ ________ _______ ______ ________ ________ ____ _______.
_____ ___ ______ ________ _______ __________ ________.
_________ ___ ________ _________ ___ ______ ______ ______ __________ ______.
__________ ________ _________ _________ ____ ______ __________ ______ ____ ________ ____.
______ _________ ____ ______ ________ _____ ____ ___.
_______ ________ _______ ______ ________ __________ ___ ___.
__________ ________ __________ __________ _________.
_________ ____ _________ ________ __________ ______ ______ ________ _________ _______ _______.
________ __________ __________ ___ ______ _____ _____ ______ ____ __________.
_______ ________ ______ _______ ______ _______ _________ ______ _____ _______ _______ ______.
_______ ___ ___ ____ _____ ______ ________ _____ ___.
______ __________ _____ ____ _____ ________ __________ ____.
_______ _______ _________ _________ ____ _____ __________.
_____ _________ _________ ________ ______ ______ __________ ________.
________ __________ _________ ___ ___ ____ ____ ______.
__________ _______ ______ __________ _______.
___ ________ _______ ___ ________ ______ _______ ___ _______.
__________ _____ ________ ______ ___ ___ _________ __________ __________ __________ ___.
_______ ____ _________ ______ _____ ____ _____ _________ ____ ______ ______ __________.
___ _________ _____ __________ _____ _________ __________ _________ ________ ____ _______ ____.
_______ _____ __________ ________ ____ ___ _______ _____ _______ __________ _____.
________ ________ ____ ______ _________ ________ _____.
__________ _________ ______ ________ ________ ___ ________ ___ ____.
___ __________ ____ ___ ____ ______ ___ _________.
_________ ________ ______ ________ _____ ____ _________ _________ ________.
____ _____ ____ __________ _______ ____ _______ _________ _____ _________ ____ _________.
_______ _________ ___ ____ ____ _________ _________.
________ ________ _____ _________ ____ ____ __________ ______ _____ ____ _________.
_______ ______ _____ __________ ___ ____.
______ _______ ______ _______ ________ _________ _____ _______ ______.
_________ _________ ___ _________ ______ __________ ____.
_______ ___ __________ ____ _______ ___ ______ __________.
___ ______ _______ _______ ___ ____ _________ _____ ______ ___.
____ ________ _____ ________ _________ ___ _______.
_______ _________ _______ ________ ________ _____ _________.
_________ ___ ________ _____ ________ __________.
_______ ____ ______ ______ ___ __________.
__________ ___ ________ _______ _______ _____ __________ ___ _______ _______.
________ ____ _____ ______ ______ ____ _________ __________ _____ ____ ______ ____.
____ ________ ___ __________ _______ ____ ____ ___ ______ __________ _____ ______.
________ _______ _____ _______ ____.
______ ______ ______ ___ _______ ____ _____ ______ __________ ______ ___.
__________ _________ ______ _______ ___ ______ ___ ____.
______ ______ _____ ______ _____.
__________ _____ ______ _________ _______.
_________ _____ _______ ___ ________ _________ ___ _________ ____.
______ _____ ____ __________ ____ ____ ________ _______ _______.
__________ _____ ______ ______ ________ ____ __________ ________ __________ __________ ________ _______.
_________ ________ ____ ___ __________ __________ _______.
____ __________ ___ ____ ______.
__________ ______ ____ _____ _____ _______ _____ ______.
____ ________ _______ _______ __________ __________.
_______ __________ _____ ______ ____.
_______ ____ _____ __________ __________ ____ _________ _________.
________ _______ _____ ________ _____ __________.
____ _______ __________ ____ ________ _____ ___ ___ ________ _______ ____ ________.
___ ____ __________ _____ _______ ___ ______ ____ ________ ________.
___ _________ __________ ___ _________ ______ _____ ___ __________ _______ ____.
__________ _____ ____ ______ _________ ______ ________ ________ ___ __________.
______ ___ ____ ___ ______.
_______ _____ ____ ______ __________ ___ ______.
___ _______ ___ ________ ______ ________ _______ _________ _____ ________ ______ _______.
_________ ____ __________ _________ _________ ______ __________ _________ _____ _________ ____.
____ ______ __________ _______ ________ ________ _________ _________ ________ _______ _____ _____.
___ ________ ___ _____ ________ ______.
___ ____ ____ _____ ____ __________ ___ ____ ____ ____ ____ _________.
_____ ______ __________ _____ ___ __________ _____ _________ ______ ___ _______ ______.
___ __________ _______ _____ ______ ___ ________ ___ ________.
_______ ____ ____ __________ ___ ___ __________ ________.
___ ______ ___ _________ __________ ______.
____ ____ __________ _______ _____ _________ ________.
_____ ____ ________ ___ ___ ______ ________.
_______ __________ __________ ____ __________ __________ __________ ______ _________ ______ __________ ____.
__________ _________ _____ _______ ____ _______ ________ _________ ___ _______ ________ ____.
_______ ____ ___ __________ ____.
______ _________ _____ ________ ______ ________ ______ ______ _______ _________ __________ ________.
___ ____ ___ _____ _______ ___ ___ _____.
_____ ______ _________ ____ ______ _____ ________ ______.
___ ___ _______ _____ _______ __________ _________ ______ ______.
_________ ______ ________ _______ _________ ___ ___ _____ _____.
_________ ____ ______ ___ ______ ______ ______ _____ _______ ________ ____ __________.
___ _____ _____ ________ _____ ___ ____ ____ ________ ________ ________ _______.
_______ ___ __________ _______ _________ ______.
____ _________ ____ ___ ______ __________ _______ _______.
______ _____ ______ _______ _________ ___ _____.
_______ ________ _____ ____ ________.
____ _____ ______ _____ ______ __________ ____ __________ ________ ___ ___.
___ _________ ________ ________ _________ _______ ___.
___ ___ _________ ______ _____ ______ _______ ________ _______ _____ ____ ______.
________ _______ ________ _____ ___.
_______ _______ ________ _____ ____ _____ ______ ___.
________ ____ _______ __________ _____.
______ _________ _________ _____ _____ ________ _________ ___ ________ ______ ______.
____ ________ _____ ____ ______ __________ _________ _______ _____ ____ ___ _________.
__________ _________ ___ ___ _____ ______ ________ ________.
____ ______ ________ ________ __________ _____ __________ __________.
_____ ________ ___ _______ ______ _____ __________ _________ _______.
____ _______ ___ ________ _______ ___ _____ _________ _________.
____ ___ ___ ______ _____ _________ ________.
___ ___ ____ ______ _________.
________ __________ __________ _____ __________ ________.
_________ _______ _____ _______ _________ _____ _________ _____ ______.
________ ________ __________ ____ _______ _______ _______ ________ _______.
__________ _____ ______ ___ ______ ___ ___ _________ _______ ______ ____ __________.
_____ ____ __________ ________ _____ ______ ________.
________ _______ ___ ____ _______ ___ _________ ________ __________ _________ ________.
_________ ______ ____ __________ _______ _____ _________.
________ ______ _____ ____ ______ _________ ____ ___ ___.
______ _____ ______ ________ ___ _______ _________ ___.
_____ ________ _____ ___ ______ _______ ________ ______ _____ ____ __________.
____ _________ _______ ________ ___ ____.
_______ __________ ________ ______ ___ _________ _________.
_________ _________ __________ ______ __________ __________ ___ ________ ____ ____.
___ ________ ___ __________ __________.
______ ________ ________ ______ ______ _______ _____ __________ ________ ______ ______.
___ ___ _________ _________ ____ _________.
________ ______ ________ ____ ___ ______ _________ ____ __________ ______ _______ ________.
____ _______ _________ __________ ________ __________ ___.
____ ________ ________ _____ _____ _____.
___ ___ _____ _________ ______ _______ ___ __________.
___ _______ ________ _________ ____ __________ _________ _______ _________ ______ ___.
_____ _______ ___ __________ _______ _______ ___ ____ _______ _________ ______ _________.
__________ ____ ________ _____ _______ _______ _________ ___ _________ ______.
_________ ___ __________ ___ ____.
______ ______ ________ ____ __________ _________ _________ ________ ________.
___ ____ ___ ____ _______ ____ _______.
______ _________ ______ _________ ___ ____ ______ _____ _________ ______.
_____ ___ ______ _______ ____.
_________ ___ _________ _______ ________ ____ __________.
____ _______ _______ _______ ______ _____ ______ ___ ___ ______ ___ ________.
_______ _________ __________ ___ ________ ____ ____ __________.
_______ ______ _________ _____ _________ __________.
__________ ________ ___ ________ ________ _______ _________ ___.
________ _______ _______ ______ ____ ________.
_____ ___ ______ _______ __________ __________ _______ ___ _____ __________ ___ _______.
________ ____ _____ ________ _________ _____ ___ _____ __________ _______ __________.
____ _____ ________ _________ ______ ______ ___ ___.
__________ _________ __________ ________ ___ ________ ______ __________ ______.
___ ____ ______ __________ ____ ___.
______ ________ _______ ______ ______ _____ ___ _______ ___ ____ ____.
____ _____ ________ ________ ____.
________ ___ _________ _______ ______ _________.
______ _______ _________ _____ __________ ___ ___ _____ _________ __________ ______.
__________ ___ _____ __________ ____.
________ _____ _______ ______ ____ _______ _________ ______ ____ ____ ______ _______.
_________ _____ __________ ___ _______ _______.
______ ________ __________ ________ ___ _____ _______ __________ __________ _________ __________ _________.
____ ___ ___ ______ ____ ____ _________ _________ ______ ________.
_____ ___ __________ ____ ________ ___.
______ ____ ______ ______ ______ __________.
_________ _______ ______ ______ _______.
___ _____ ______ ____ __________ ________.
___ _______ ___ __________ _________ _______ _______ _______ _____ ___ ______.
_________ __________ ________ ___ _____ ___ _____.
________ ______ _____ _______ ______ ___ ______ ____.
_____ __________ ____ ________ _________ _______.
________ ____ _________ ____ __________ __________.
____ _______ _________ ________ ________ _________ __________ ______.
___ ________ ______ __________ ________ ______ ____ ___ ______.
________ _______ _____ ______ ______ ____ _________ ______ _________ _______ ____.
_____ _____ ___ _______ __________ _____ ______ _____ ________ _________.
________ _____ __________ _______ _________ _______ _______.
_________ ____ __________ ____ _________ _____ ______ ___ __________ __________ ______.
________ _________ ______ __________ _____ __________ _____.
________ _______ _____ ________ ____ _________ _______ _________ ____ ___ ____ _________.
_____ _________ _________ _________ ________.
___ _______ _______ _____ ________.
__________ ___ _________ ___ _______ ______ ___ ________ ______ _______.
____ _____ _________ __________ _________ ____ ____ ___.
________ _____ ________ _________ __________ _____ ___ __________ ______ _______.
_______ ______ ____ ______ _________ ______ __________ ___ __________ __________ _______.
_______ ________ __________ ___ ___ _________ ________ ________.
______ ___ _________ ___ ____ _______ _____ ____ __________ _______ ______.
____ _________ __________ _____ _________ ______.
________ _______ ________ ______ ____ ______ ______ ______.
_______ ___ ____ ________ ____ _________ ____.
__________ __________ _______ ____ _________ ________ _______ ________ _________ ____.
______ __________ ___ __________ ___ ______ ______.
___ ___ ________ ________ __________ ___ ______ ___ _________ _________.
_____ _______ ____ _____ __________.
_______ ______ ____ _______ ________.
________ ____ _____ ____ _________ _______ ________ ________ ________ ______ _____ ________.
______ ____ __________ ____ ______ _________ ____ ________.
____ ______ ___ ________ ____ ________ ________ ____ _____ _______ __________.
_____ ____ ___ ____ __________ ______ __________ __________ ________ ______ __________ ______.
__________ ___ _________ ______ __________ _________ __________.
______ ______ _______ ___ __________ ___.
______ ____ ______ ____ ________ __________ _________ __________ _______ ________ ___.
____ _______ _____ __________ _____ ________ _______ ____.
__________ ____ ____ ________ ________ __________ ____ _______.
_____ ________ _____ _____ _______ __________ _____ __________ __________ _____ ________.
__________ ________ _________ ___ _______ _______ ________ _______ ____ _________.
__________ __________ _____ ___ _________ ______.
_____ ____ ___ _________ ________ ________ __________ __________ _____ ______ _______.
________ _______ ____ ________ ________ _____ ____ __________ _______ ________ _____ _____.
________ ______ ________ __________ ___.
_____ ______ ________ ____ _______ ________ _________ _______ _________ ________ _________.
_______ _________ ___ __________ _____ ______ ____ ______ ________ _______ ____.
______ ________ __________ ______ _____.
_____ _________ ________ ____ _______ _________ __________ ____ _________ _______ _______.
______ _________ ___ ______ _____.
_____ _________ ____ ________ ____ _____ ______ _____ ________ _____ ________.
_____ ______ _____ ________ ________ ______ _______ _____ ________.
________ ____ ________ _______ _________ _____.
_________ ______ _____ __________ _________ ____ _______ ________ _________.
_____ _____ ________ ________ ___ ____ ________ ____ __________.
____ _____ _________ _________ ____ ____ ________ ___ _____ _____ ______.
__________ __________ _____ __________ ____ ____ ______ ___ ___ _______ ________ ________.
__________ ____ ___ _____ _________ ________ _____ __________.
_________ _______ ________ __________ ______ _______ ________ _____ _______.
________ ______ ______ __________ ________ ______ ______.
_________ _______ _________ ______ _________.
_________ _____ _________ ___ ___ ___ ______.
________ ___ _________ ____ _________ _______.
______ ___ __________ ___ ________ ___.
________ _________ _______ _____ _____ ____ _______ ____ _____ ___ _______ ________.
___ _________ _______ _________ ______ _______.
________ ________ ____ _________ _____ ___.
____ ____ ___ ________ ________ __________ __________ ______ ____ _____.
________ _______ ___ __________ _____ _________ ________ _____ ___ ____.
________ _________ ______ __________ _____ ___ _______ ________.
_________ ____ _______ ____ _______ ________ _________ __________ ______ ____.
______ _______ _________ ____ ________.
____ _________ ___ _________ _____ _________ __________ __________.
_____ _______ ________ ____ ___ ____ _______ ___ _____ __________ _________.
_________ ___ ___ __________ ___ ________ _________ ___ ____.
____ ___ ___ ____ _______ _____ _____.
________ ___ ____ __________ ________ ______ _______.
__________ _________ ______ _______ ___ _________ ____ ______ ________ _______.
_________ _____ ____ __________ _____ ______ ______ ____ ___ ________.
_____ __________ _________ ____ ___ ___ ______ ______ ___ _________ ______ _____.
________ __________ ____ __________ __________ __________ ________ ________.
________ _________ ________ ______ _______ ___ ______ ________ ____ _________.
___ _________ _________ ________ _____ _______ __________ ___ _________ __________ _________ ________.
________ _____ ______ ________ ___ _______ __________ ________.
___ ______ ______ __________ _____ __________ ____ ____ ________ ________.
___ ____ ________ _________ ________ ______ __________.
_____ _______ ________ _________ ________.
_________ ____ _________ ___ ____ ____ _________ _______ ____ _____ ____.
______ _______ ______ __________ ____ _____ ________ ______ ________ _______.
_________ _____ _____ ___ _____ _________ _______ ________ __________ ________ __________.
___ _________ _______ ____ ______ _________.
__________ __________ _________ __________ _________ _______ ___ ______ ________ ___.
____ ____ ______ ___ ______ _________.
_____ _______ ______ ________ _______ ______ ______ ________ ______.
_______ _____ _____ __________ _______ _______ _____.
__________ ______ ______ ____ ________.
________ _____ ________ _______ _________ ______.
______ ______ _______ __________ _______ __________ ________ ______ __________ _____ _____.
______ ________ _________ _________ ______ _____.
____ ______ ______ ______ __________ ____ ______ _________ _________.
_______ __________ ______ _______ ____ _______ ________.
_______ _____ ______ ___ ____ ______ __________ __________.
_______ ___ _________ ____ ___.
__________ ________ __________ __________ __________ ___ ________ _____ ________.
______ __________ __________ ____ _______ ____ _______ ___.
_______ ___ ___ __________ ___ ___.
___ _______ ____ ______ __________ __________ _________ _______.
_____ ____ _____ ________ ________ ____ _______ ______.
______ _____ ______ ______ _____ ________ _________ ________ ________ ________ ________ _____.
_________ _______ __________ ________ ______ _________ __________.
______ ____ ___ __________ _________ ______ ______ ____ ___ _______ ______ __________.
______ _____ __________ ___ _______ _______ ____.
_________ __________ ________ _________ ____ _____ ______.
______ ____ ___ _______ ___ _________ ____ _______ _______ ______.
___ ____ ________ _______ __________ __________ ______ __________ ______ ___ _________.
________ __________ __________ ______ _________.
____ _______ ________ ______ ___ ____ ________ ___ _________ ________ ________ _________.
_____ _____ __________ _____ _____.
_____ _______ ____ ____ _______ ______ _________ ____ _______ ______ _________ ________.
______ ________ _________ ___ ______ _______ ____.
________ __________ ________ _____ _____ _____ ____.
__________ _____ __________ ____ ___ _______ _____ _________.
________ _________ ____ ____ __________ ______ _______.
__________ _________ ________ _____ __________.
________ ____ ____ _______ ______ __________.
_________ __________ _______ _______ ___ _____.
_________ ______ _________ ____ ______ _____.
____ _____ __________ ________ _____ _________ ______ _________ _________.
________ __________ ____ _____ ____ ______ _______ __________ ____.
______ ___ _______ __________ ___ _______ _______ ____ ________ ____.
____ ___ _____ _______ _______ __________ ________ ___.
____ _______ _________ _________ _____ ___.
______ ___ ____ _____ ______ _____ __________ __________.
__________ ___ __________ _____ ____ ___ ________ _____ ________ _______.
________ ___ ______ ____ ________ ________.
____ _________ _______ _________ ________ ___ _______ _____ ________ _______.
_________ _______ ___ ___ ___.
_________ __________ ___ _________ ____ ______ __________ ____ ______.
____ __________ _________ ______ ___ ____ ___ _________ ________ ______.
_____ ________ ________ ______ ____ ______ _________ _________ _________ __________ ___ ___.
_____ ____ ____ ________ ____ _________.
________ _________ ______ _________ ______ ___ ____ ___ ________ _______ ______ ______.
_______ _________ __________ ____ _____ _____ _________ ______ __________ __________ ______ _____.
__________ ___ __________ ____ ______ ______ ___ _________ _________ ___ _______.
____ ___ ______ ___ __________.
__________ __________ ____ ___ ______ ________ ___ _____.
___ __________ ___ ______ _________ _______ _________ ________ _______.
___ __________ __________ ____ ___ _____ ____ ________.
_____ __________ ____ _____ ______ ________ __________ ____.
_____ ____ _________ __________ _________.
_______ ________ _______ _______ ______ ______ _______ ____ ____ ___ __________ ___.
________ ___ _____ __________ ________ ___ _____.
___ ___ _________ _______ ____ ____ _______ __________ ____ ___.
________ _______ _______ _________ _______.
______ ________ ____ __________ _____ ________ ______ ____ ____ ___.
_______ ________ _________ ________ ______ ___ __________ ______.
_________ __________ ___ _________ _______ ____ ___ __________.
_______ _________ ____ ______ ________ _____ ______.
_________ ____ ________ _____ ________ ______ ________ _________ _____ ______ ____ ________.
______ ___ __________ ________ ______ _______.
_______ _________ _______ ________ ______ ______ _________ ____.
____ ____ ______ ____ ____ _________ _______ _____.
_____ _________ _____ _______ _________ ___ ________.
_________ ______ _________ ____ ______ _______ __________ ____ ______ __________.
_____ _____ ________ ______ _____ _____ _________.
______ ____ _______ ______ ______ __________ _____ ____ _____ _____ __________ ____.
_______ ___ _____ _________ __________ ____ ____ _______ ____ _______.
_________ ___ ______ _________ ___.
_______ ____ ___ _________ _________ ________ __________ _______ __________ ______.
______ ______ ________ _____ ____.
____ ____ ________ ________ _______ _______ ___ ______ ______.
___ ______ _____ _____ ______ _____ __________.
_____ ___ __________ ___ _____ ___ ______ ____ ________ ______ ___.
_____ _____ ____ _____ ______.
___ _______ ___ ___ ___ ___ ____ _______ _________.
_______ ___ ________ _________ _______.
___ ______ __________ ______ ______ ______ ___ __________ ______.
_________ _____ _____ ________ _______ _________ __________ _____ ______ _______.
________ __________ _____ ______ ___ __________ _____.
_____ _____ _______ _________ ________ ____ ____ _________ __________ ___.
____ __________ _____ ________ __________ ____ ____ _____ _____ ____ ________.
____ _____ ______ _____ ________ _______ _______.
______ ___ ______ ___ __________ _____ ______ __________ _______ ____ ________.
___ ___ _________ _________ _____ ___.
____ _______ __________ ________ __________ ___ ___ ___ ________.
_________ ________ ____ ___ ______ _______ ____ ________.
_________ _________ ___ ____ ____ __________ ____.
__________ _____ _____ _____ _______ ___ __________.
_________ _______ _________ ___ ____ _____ ___ _______.
_______ _____ ________ ______ _____ _______ _______ _________ ____ ______ _______.
____ ______ _________ _____ _______ ________.
__________ _____ __________ ________ ______ ______ _________.
_________ ______ ___ _________ ________.
____ ___ ______ ____ _____ _______ ____.
____ ______ ____ ________ _______ _______ _____ _____ ___ _______.
___ ___ ___ _________ _____ ____ ___ _____ ___ _____ ___.
______ ___ ___ ____ ______ ____ ____ _______ ________.
__________ ____ ___ _________ _________ _______ ______ ___ _______.
______ ______ _____ _______ __________ _________ ____ _______ ________.
_____ ___ _________ _______ __________.
_____ _______ ______ ______ __________ _______ _________ __________.
________ _________ _________ ____ _______.
_________ _____ _______ ________ ______.
____ __________ ______ _________ _______ ________ ________ ___ _______.
___ _______ _____ ___ _______ ______ _________.
________ _____ ___ __________ ______ ____ _________ ______ ____.
____ ___ _____ ______ _________ _______ __________ _______ ________ ___.
_____ _______ ___ ___ __________.
_____ _________ _________ ___ _________ ____ __________ ________ _______.
__________ __________ ____ _________ _____ ________ ________ _______ ________.
____ ___ ___ ____ ___ __________ _________.
___ ________ ________ _________ _____ ____ _______ _____ ___ _______ _____ ________.
________ __________ ______ _______ _________ ____.
______ ____ ____ ______ _______ _________ _____ ___ ___ ______.
________ _____ __________ _________ _________ __________ __________ _____ _______ _________ ______ _______.
___ ___ __________ ________ _____.
____ ________ _________ _____ ______ ___.
__________ ____ ____ _____ ________ _____ __________ _____ ____.
________ ____ _________ _____ ___ __________ ______ _______ ________ ______ ________ ____.
_____ _____ _________ __________ _____ ____ ______ __________ __________ __________.
_________ ______ _______ __________ ___.
_______ ________ __________ ____ ______ ________ ______ __________ _____ ________ __________ ______.
______ _________ ________ ____ ____ ______ ____ _______ _______ ______ __________.
______ ________ _______ _________ ___ ______ ______.
______ _________ __________ ____ _____ ___ _______ _______ ______ ____.
_____ _____ __________ ___ _____ ____ __________.
______ _______ __________ _________ _______ ______ ______ __________ _____ ______.
______ ____ __________ ___ ________ ____ _______.
__________ ___ ________ _____ ___ ___ _______.
_______ ______ _________ _____ _______ ________.
_______ _________ _________ ____ ___.
___ __________ _____ _______ ______ _____ _________ ____ _________ _________.
_____ _________ __________ ________ _____ _____ ________ ______ ______ ______ __________.
___ _________ __________ ________ ___ _________ _________.
_______ ______ _________ __________ _______ ___ _______ _____.
_____ ______ ___ ________ ____ ___ _________ ____ ________ ______ _____.
___ __________ _________ _____ ________ ____ _______ ___ __________ ____ _____.
___ _________ _________ ______ ________ ____ _________.
_______ ________ _______ ___ _____ _________ ____ ____ ___ ____ ____ _____.
____ ____ _________ ______ ______ _____ _______ _________.
______ _____ ___ __________ ___ __________ __________ _______ _________ ___ ______ ____.
___ ________ _______ _______ _________.
_________ __________ _____ _____ ________ ________.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
✓ Unlock up to 60% of the answer
✓ No payment required