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Encyclopedia > Variable

In computer science and mathematics, a variable (pronounced /ˈværiəbəl/) (sometimes called an object or identifier in computer science) is a symbolic representation used to denote a quantity or expression. In mathematics, a variable often represents an "unknown" quantity that has the potential to change; in computer science, it represents a place where a quantity can be stored. Variables are often contrasted with constants, which are known and unchanging. Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... This article presents the essential definitions. ... Quantity is a kind of property which exists as magnitude or multitude. ... This article does not cite any references or sources. ... In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ...

In applied statistics, a variable is a measurable factor, characteristic, or attribute of an individual or a system—in other words, something that might be expected to vary over time or between individuals. Random variables are an idealisation of this in mathematical statistics, where they are defined as measurable functions from a probability space to a measurable space. Applied statistics is the use of statistics and statistical theory in real-life situations. ... In probability theory, a random variable is a quantity whose values are random and to which a probability distribution is assigned. ... Mathematical statistics uses probability theory and other branches of mathematics to study statistics from a purely mathematical standpoint. ... In mathematics, measurable functions are well-behaved functions between measurable spaces. ... In mathematics, the definition of the probability space is the foundation of probability theory. ...

x commonly represents an unknown variable. Even though any letter can be used, x is the most common choice. This usage can be traced back to the Arabic word šay' شيء = “thing”, which in translated algebra texts and similar was taken into Old Spanish with the pronunciation “šei”, which was written xei, which was soon habitually abbreviated to x. (The Spanish pronunciation of “x” has changed since.) But some sources say that this x is an abbreviation of Latin causa which was a translation of Arabic شيء. That started the habit of using letters to represent quantities in algebra. In mathematics, an “italicized x” ($x!$) is often used to avoid potential confusion with the multiplication symbol. By extension beyond mathematics, “X” has come to represent a generic placeholder variable whose value is unknown or secret, as in project X or mister X. This article is about the branch of mathematics. ... Look up pronunciation in Wiktionary, the free dictionary. ... This article is about the branch of mathematics. ... This article or section does not adequately cite its references or sources. ...

## General overview

Variables are used in open sentences. For instance, in the formula x + 1 = 5, x is a variable which represents an "unknown" number. Variables are often represented by letters of the Roman alphabet, but are also represented by letters of other alphabets, such as the Greek alphabet, as well as various other symbols. In this sense, variables are used as a "fill-in-the-blank" within many fields (mathematics, linguistics, etc.) An open sentence is a sentence which contains variables. ... For other uses, see X (disambiguation). ... For other uses, see Number (disambiguation). ... For other uses, see Letter (disambiguation). ... The Latin alphabet, also called the Roman alphabet, is the most widely used alphabetic writing system in the world today. ... ABCs redirects here, for the Alien Big Cats, see British big cats. ... The Greek alphabet (Greek: ) is an alphabet consisting of 24 letters that has been used to write the Greek language since the late 8th or early 8th century BC. It was the first alphabet in the narrow sense, that is, a writing system using a separate symbol for each vowel...

### Variable Naming Conventions

In general mathematics, the most common letters for variables are "x", "y", "n", "a" and "b". "x" and "y" are most often used because they correspond to the two axis on a graph, while "a" and "b" are used as the coefficients of x and y in the general form of a linear equation. "n" is most often used in elementary schools.

## In applied statistics

In statistics, variables refer to measurable attributes, as these typically vary over time or between individuals. Variables can be discrete (taking values from a finite or countable set), continuous (having a continuous distribution function), or neither. Temperature is a continuous variable, while the number of legs of an animal is a discrete variable. This concept of a variable is widely used in the natural, medical and social sciences. In mathematics, a probability distribution is called discrete, if it is fully characterized by a probability mass function. ... In mathematics the term countable set is used to describe the size of a set, e. ... By one convention, a probability distribution is called continuous if its cumulative distribution function is continuous. ... In mathematics, a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output. ... In probability theory, the cumulative distribution function (abbreviated cdf) completely describes the probability distribution of a real-valued random variable, X. For every real number x, the cdf is given by where the right-hand side represents the probability that the random variable X takes on a value less than... The Michelsonâ€“Morley experiment was used to disprove that light propagated through a luminiferous aether. ... Medical research (or experimental medicine) is basic research and applied research conducted to aid the body of knowledge in the field of medicine. ... The social sciences are groups of academic disciplines that study the human aspects of the world. ...

In causal models, a distinction is made between "independent variables" and "dependent variables", the latter being expected to vary in value in response to changes in the former. In other words, an independent variable is presumed to potentially affect a dependent one. In experiments, independent variables include factors that can be altered or chosen by the researcher independent of other factors. A causal system is a system that depends only on the current and previous inputs. ... In an experimental design, the independent variable (argument of a function, also called a predictor variable) is the variable that is manipulated or selected by the experimenter to determine its relationship to an observed phenomenon (the dependent variable). ... In experimental design, a dependent variable (also known as response variable, responding variable or regressand) is a factor whose values in different treatment conditions are compared. ...

For example, in an experiment to test whether or not the boiling point of water changes with altitude, the altitude is under direct control and is the independent variable, and the boiling point is presumed to depend upon it and is therefore the dependent variable. The collection of results from an experiment, or information to be used to draw conclusions, is known as data. It is often important to consider which variables to allow for, or to directly control or eliminate, in the design of experiments. For other uses, see Data (disambiguation). ... The first statistician to consider a methodology for the design of experiments was Sir Ronald A. Fisher. ...

While independent variables can refer to quantities and qualities that are under experimental control, they can also include extraneous factors that influence results in a confusing or undesired manner.

In general, if strongly confounding variables exist that can substantially affect the result, then this makes it more difficult to interpret the results. For example, a study into the incidence of cancer with age will also have to take into account variables such as income (poorer people may have less healthy lives), location (some cancers vary depending on diet and sunlight), stress and lifestyle issues (cancer may be related to these more than age), and so on. Failure to at least consider these factors can lead to grossly inaccurate deductions. For this reason, controlling unwanted variables is important in research. In statistics, a spurious relationship (or, sometimes, spurious correlation) is a mathematical relationship in which two occurrences have no logical connection, yet it may be implied that they do, due to a certain third, unseen factor (referred to as a confounding factor or lurking variable). The spurious relationship gives an... In medical terms, stress is the disruption of homeostasis through physical or psychological stimuli. ... Look up deduction in Wiktionary, the free dictionary. ...

Extraneous variables are variables other than the independent variable that may bear any effect on the behavior of the person being studied. ... An intervening variable is a hypothetical construct that attempts to explain relationships between variables, and especially the relationships between independent variables and dependent variables. ...

## In mathematics

Variables are useful in mathematics because they allow instructions to be specified in a general way. If one were forced to use actual values, then the instructions would only apply in a more narrow set of situations. For example:

Specify a mathematical definition for finding the number twice that of ANY number: double(x) = x + x.
Now, all we need to do to find the double of a number is replace x with any number we want.
• double(1) = 1 + 1 = 2
• double(3) = 3 + 3 = 6
• double(55) = 55 + 55 = 110
• etc.

In the above example, the variable x is a "placeholder" for any number. One important thing we are assuming is that the value of each occurrence of x is the same—that x does not get a new value between the first x and the second x.

(Note that in computer programming languages without referential transparency, changes such as this can occur. Variables in computer programming are also useful for this reason. The term "variable", as used by programmers, is much more vague than the meaning of "variable" as used by mathematicians.) A programming language is an artificial language that can be used to control the behavior of a machine, particularly a computer. ... Referential transparency is a property of parts of computer programs. ...

## In computer programming

Variables in computer programming are very different from variables in mathematics and the apparent similarity is source of much confusion. Variables in most of mathematics (those that are extensional and referentially transparent) are time-independent unknowns, while in programming a variable can associate with different values at different times (as they are intensional). Programming redirects here. ...

In computer programming a variable is a special value (also often called a reference) that has the property of being able to be associated with another value (or not). What is variable across time is the association. Obtaining the value associated with a variable is often called dereferencing, and creating or changing the association is called assignment.

Variables are usually named by an identifier, but they can be anonymous, and variables can be associated with other variables.

In the computing context, variable identifiers often consist of alphanumeric strings. These identifiers are then used to refer to values in computer memory. This convention of matching identifiers to values is but one of several alternative programmatic conventions for accessing values in computer memory (see also: reflection (computer science)). In computer programming and formal language theory, (and other branches of mathematics), a string is an ordered sequence of symbols. ... In computer science, a value is a sequence of bits that is interpreted according to some data type. ... The terms storage (U.K.) or memory (U.S.) refer to the parts of a digital computer that retain physical state (data) for some interval of time, possibly even after electrical power to the computer is turned off. ... In computer science, reflection is the process by which a computer program of the appropriate type can be modified in the process of being executed, in a manner that depends on abstract features of its code and its runtime behavior. ...

### Variable naming conventions

In some programming languages, specific characters (known as sigils) are prefixed or appended to variable identifiers to indicate the variable's type. For example: In computer programming, a naming convention is a set of rules for choosing the character sequence to be used for identifiers in source code and documentation. ... Identifiers (IDs) are lexical tokens that name entities. ... A namespace is a context in which a group of one or more identifiers might exist. ... In computer programming, a sigil is a symbol attached to a variable name, showing the variables datatype. ...

• in BASIC, the suffix \$ on a variable name indicates that its value is a string;
• in Perl, the sigils \$, @, %, and & indicate scalar, array, hash, and subroutine variables, respectively.
• in spreadsheets variables can refer to cells (e.g. \$A\$2), named ranges, or values in associated source code or functions.

BASIC (Beginners All-purpose Symbolic Instruction Code) is a family of high-level programming languages. ... In computer programming and formal language theory, (and other branches of mathematics), a string is an ordered sequence of symbols. ... Wikibooks has a book on the topic of Perl Programming Perl is a dynamic programming language created by Larry Wall and first released in 1987. ... Screenshot of a spreadsheet under OpenOffice A spreadsheet is a rectangular table (or grid) of information, often financial information. ...

### Variables in source code

In computer source code, a variable name is one way to bind a variable to a memory location; the corresponding value is stored as a data object in that location so that the object can be accessed and manipulated later via the variable's name. Source code (commonly just source or code) is any series of statements written in some human-readable computer programming language. ... In programming languages, name binding refers to the association of values with identifiers. ... An object is fundamental concept in object-oriented programming. ...

### Scope and extent

The scope of a variable describes where in a program's text, the variable may be used, while the extent (or lifetime) describes when in a program's execution a variable has a value. The scope of a variable is actually a property of the name of the variable, and the extent is a property of the variable itself. In computer programming, scope is an enclosing context where values and expressions are associated. ...

A variable name's scope affects its extent.

Scope is a lexical aspect of a variable. Most languages define a specific scope for each variable (as well as any other named entity), which may differ within a given program. The scope of a variable is the portion of the program code for which the variable's name has meaning and for which the variable is said to be "visible". Entrance into that scope typically begins a variable's lifetime and exit from that scope typically ends its lifetime. For instance, a variable with "lexical scope" is meaningful only within a certain block of statements or subroutine. A "global variable", or one with indefinite scope, may be referred to anywhere in the program. It is erroneous to refer to a variable where it is out of scope. Lexical analysis of a program can determine whether variables are used out of scope. In compiled languages, such analysis can be performed statically at compile time. This article or section should be merged with scope (programming) In computer science, static scoping, as opposed to dynamic scoping, is a way that the scope (programming) of free variables is determined according to its position in program code. ... In computer science, a subroutine (function, method, procedure, or subprogram) is a portion of code within a larger program, which performs a specific task and can be relatively independent of the remaining code. ... In computer programming, a global variable is a variable that is accessible in every scope. ... In computer science, lexical analysis is the process of converting a sequence of characters into a sequence of tokens. ... In computer science, compile time, as opposed to runtime, is the time when a compiler compiles code written in a programming language into an executable form. ...

Extent, on the other hand, is a runtime (dynamic) aspect of a variable. Each binding of a variable to a value can have its own extent at runtime. The extent of the binding is the portion of the program's execution time during which the variable continues to refer to the same value or memory location. A running program may enter and leave a given extent many times, as in the case of a closure. This article or section should be merged with scope (programming) Dynamic variable scoping is when you scope a variable in a programming language by replacing the existing variable of that name with a new variable temporarily, for instance for the duration of a function call. ... In computer science, binding refers to the creation of a simple reference to something which is larger and more complicated and used frequently. ... In computer science, a closure is a function that is evaluated in an environment containing one or more bound variables. ...

In portions of code, a variable in scope may never have been given a value, or its value may have been destroyed. Such variables are described as "out of extent" or "unbound". In many languages, it is an error to try to use the value of a variable when it is out of extent. In other languages, doing so may yield unpredictable results. Such a variable may, however, be assigned a new value, which gives it a new extent. By contrast, it is permissible for a variable binding to extend beyond its scope, as occurs in Lisp closures and C static variables. When execution passes back into the variable's scope, the variable may once again be used. In computer science, undefined behavior is a feature of some programming languages â€” most famously C. In these languages, to simplify the specification and allow some flexibility in implementation, the specification leaves the results of certain operations specifically undefined. ... In computer programming, static variables typically have a broader scope than other variables. ...

For space efficiency, a memory space needed for a variable may be allocated only when the variable is first used and freed when it is no longer needed. A variable is only needed when it is in scope, but beginning each variable's lifetime when it enters scope may give space to unused variables. To avoid wasting such space, compilers often warn programmers if a variable is declared but not used.

It is considered good programming practice to make the scope of variables as narrow as feasible so that different parts of a program do not accidentally interact with each other by modifying each other's variables. Doing so also prevents action at a distance. Common techniques for doing so are to have different sections of a program use different namespaces, or to make individual variables "private" through either dynamic variable scoping or lexical variable scoping. This article needs cleanup. ... In many programming languages, a namespace is a context for identifiers. ... This article or section should be merged with scope (programming) Dynamic variable scoping is when you scope a variable in a programming language by replacing the existing variable of that name with a new variable temporarily, for instance for the duration of a function call. ... This article or section should be merged with scope (programming) In computer science, static scoping, as opposed to dynamic scoping, is a way that the scope (programming) of free variables is determined according to its position in program code. ...

Many programming languages employ a reserved value (often named null or nil) to indicate an invalid or uninitialized variable. In computer programming, null is a special value for a pointer (or other kind of reference) used to signify that the pointer intentionally does not have a target. ...

### Typed and untyped variables

In statically-typed languages such as Java or ML, a variable also has a type, meaning that only values of a given class (or set of classes) can be stored in it. In dynamically-typed languages such as Python, it is values, not variables, which carry type. In Common Lisp, both situations exist simultaneously: a variable is given a type (if undeclared, it is assumed to be `T`, the universal supertype) which exists at compile time. Values also have types, which can be checked and queried at runtime. See type system. On computer science, a datatype (often simply type) is a name or label for a set of values and some operations which can be performed on that set of values. ... â€œJava languageâ€ redirects here. ... ML is a general-purpose functional programming language developed by Robin Milner and others in the late 1970s at the University of Edinburgh, whose syntax is inspired by ISWIM. Historically, ML stands for metalanguage as it was conceived to develop proof tactics in the LCF theorem prover (the language of... In computer science, a type system defines how a programming language classifies values and expressions into types, how it can manipulate those types and how they interact. ... Python is a high-level programming language first released by Guido van Rossum in 1991. ... Common Lisp, commonly abbreviated CL, is a dialect of the Lisp programming language, published in ANSI standard X3. ... In computer science, a subtype is a datatype that is generally related to another datatype (the supertype) by some notion of substitutability, meaning that computer programs written to operate on elements of the supertype can also operate on elements of the subtype. ... In computer science, a type system defines how a programming language classifies values and expressions into types, how it can manipulate those types and how they interact. ...

Typing of variables also allows polymorphisms to be resolved at compile time. However, this is different from the polymorphism used in object-oriented function calls (referred to as virtual functions in C++) which resolves the call based on the value type as opposed to the supertypes the variable is allowed to have. The Greek meaning of the words poly and morph together imply that a single entity can take on multiple forms. In the field of computer science, there are two fundamentally different types of polymorphism; subtype polymorphism, and parametric polymorphism. ... This article or section should be merged with Virtual method In many object oriented programming languages such as C++, C#, VB.NET, a virtual function is a function that can be overridden with specialized implementations in subclasses. ... C++ (pronounced see plus plus, IPA: ) is a general-purpose programming language with high-level and low-level capabilities. ...

Variables often store simple data-like integers and literal strings, but some programming languages allow a variable to store values of other datatypes as well. Such languages may also enable functions to be parametric polymorphic. These functions operate like variables to represent data of multiple types. For example, a function named `length` may determine the length of a list. Such a `length` function may be parametric polymorphic by including a type variable in its type signature, since the amount of elements in the list is independent of the elements' types. In computer science, a datatype or data type (often simply a type) is a name or label for a set of values and some operations which one can perform on that set of values. ... Polymorphism refers to features of various programming languages which allow a single piece of source code to operate on a variable whose type is not fixed. ... A type signature defines the inputs and outputs for a function or method. ...

### Parameters

The formal parameters of functions are also referred to as variables. For instance, in this Python code segment,

` def addtwo(x): return x + 2 addtwo(5) # yields 7 `

and its equivalent code segment in Lisp,

` (defun addtwo (x) (+ x 2)) (addtwo 5) ; yields 7 `

the variable named x is a parameter because it is given a value when the function is called. The integer 5 is the argument which gives `x` its value. In most languages, function parameters have local scope [citation needed]. This specific variable named x can only be referred to within the addtwo function (though of course other functions can also have variables called x).

### Memory allocation

The specifics of variable allocation and the representation of their values vary widely, both among programming languages and among implementations of a given language. Many language implementations allocate space for local variables, whose extent lasts for a single function call on the call stack, and whose memory is automatically reclaimed when the function returns. (More generally, in name binding, the name of a variable is bound to the address of some particular block (contiguous sequence) of bytes in memory, and operations on the variable manipulate that block. Referencing is more common for variables whose values have large or unknown sizes when the code is compiled. Such variables reference the location of the value instead of the storing value itself, which is allocated from a pool of memory called the heap. In computer science, a local variable is a variable that is given local scope. ... In computer science, a call stack is a special stack which stores information about the active subroutines of a computer program. ... In programming languages, name binding refers to the association of values with identifiers. ... This article is about a general notion of reference in computing. ... In computer science, dynamic memory allocation is the allocation of memory storage for use in a computer program during the runtime of that program. ...

Bound variables have values. A value, however, is an abstraction, an idea; in implementation, a value is represented by some data object, which is stored somewhere in computer memory. The program, or the runtime environment, must set aside memory for each data object and, since memory is finite, ensure that this memory is yielded for reuse when the object is no longer needed to represent some variable's value. In strictly mathematical branches of computer science the term object is used in a purely mathematical sense to refer to any thing. While this interpretation is useful in the discussion of abstract theory, it is not concrete enough to serve as a primitive datatype in the discussion of more concrete...

Objects allocated from the heap must be reclaimed specially when the objects are no longer needed. In a garbage-collected language (such as C#, Java, and Lisp), the runtime environment automatically reclaims objects when extant variables can no longer refer to them. In non-garbage-collected languages, such as C, the program (and thus the programmer) must explicitly allocate memory, and then later free it, to reclaim its memory. Failure to do so leads to memory leaks, in which the heap is depleted as the program runs, risking eventual failure from exhausting available memory. In computer science, garbage collection (GC) is a form of automatic memory management. ... The title given to this article is incorrect due to technical limitations. ... â€œJava languageâ€ redirects here. ... For the programming language, see Lisp (programming language). ... C is a general-purpose, block structured, procedural, imperative computer programming language developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system. ... In computing, malloc is a subroutine provided in the C programming languages and C++ programming languages standard library for performing dynamic memory allocation. ... In computer science, a memory leak is a particular kind of unintentional memory consumption by a computer program where the program fails to release memory when no longer needed. ...

When a variable refers to a data structure created dynamically, some of its components may be only indirectly accessed through the variable. In such circumstances, garbage collectors (or analogous program features in languages that lack garbage collectors) must deal with a case where only a portion of the memory reachable from the variable needs to be reclaimed. A binary tree, a simple type of branching linked data structure. ...

### Constants

A constant variable is a variable whose value cannot be changed once it is initially bound to a value. In other words, constant variables cannot be assigned to. In purely functional programming, all variables are constant, because there is no assignment. This article does not cite any references or sources. ... Purely functional is a term in computing used to describe algorithms, data structures or programming languages that exclude destructive modifications (updates). ...

Although a constant value is specified only once, the constant variable can be referenced multiple times in a program. Using a constant instead of specifying a value multiple times in the program can not only simplify code maintenance, but it can also supply a meaningful name for it and consolidate such constant assignments to a standard code location (for example, at the beginning).

Programming languages provide one of two kinds of constant variables:

Static constant or Manifest constant
Languages such as Visual Basic allow assigning a fixed value to static constant which will be known at compile time. Such a constant has the same value each time its program runs. Changing the value is accomplished by changing (and possibly recompiling) the code. E.g.: `CONST a = 60`.
Dynamic constant
Languages such as C++ and Java allow initializing a dynamic constant with a value that is computed at runtime. Thus, unlike static constants, the values of dynamic constants cannot be determined at compile time. E.g.: `final int a = b + 20;`.

For variables which are references, do not confuse constant references with immutable objects. For example, when a non-constant reference references an immutable object, that reference can be changed so that it references a different object, but the object it originally pointed to cannot be changed (i.e. other references that reference it still see the same information). In computer science, compile time, as opposed to runtime, is the time when a compiler compiles code written in a programming language into an executable form. ... In computer science, runtime or run time describes the operation of a computer program, the duration of its execution, from beginning to termination (compare compile time). ... In computer science, an immutable object, as opposed to a mutable object, is a kind of object whose internal states cannot be modified after it is created. ...

Conversely, a constant reference may reference a mutable object. In this case, the reference will always reference the same object (the reference cannot be changed); however, the object that the reference references can still be changed (and other references that also reference that object will see the change), as shown in the following example:

` final StringBuffer sampleDynamicConstant = new StringBuffer ("InitialValueOfDynamicConstant"); sampleDynamicConstant.append("_AppendedText"); System.out.println(sampleDynamicConstant); `

The above code produces the following output:

` InitialValueOfDynamicConstant_AppendedText `

In languages where a variable can be an object (i.e. C++), such a variable being constant is equivalent to the immutability of that object.

### Variable interpolation

Variable interpolation (also variable substitution, variable expansion) is the process of calculating and evaluating an expression or string literal containing one or more variables, yielding a result in which the variables are replaced with their corresponding values in memory. It is a specialized instance of concatenation. Concatenation is a standard operation in computer programming languages (a subset of formal language theory). ...

Languages that support variable interpolation include Perl, PHP, Ruby, and most Unix shells. In these languages, variable interpolation only occurs when the string literal is double-quoted, but not when it is single-quoted. The variables are recognized because variables start with a sigil (typically "\$") in these languages. Ruby uses the "#" symbol for interpolation, and lets you interpolate any expression, not just variables. Wikibooks has a book on the topic of Perl Programming Perl is a dynamic programming language created by Larry Wall and first released in 1987. ... For other uses, see PHP (disambiguation). ... This article does not cite any references or sources. ... Screenshot of a sample Bash session, taken on Gentoo Linux. ... In computer programming, a sigil is a symbol attached to a variable name, showing the variables datatype. ... This article does not cite any references or sources. ...

For example, the following Perl code: Wikibooks has a book on the topic of Perl Programming Perl is a dynamic programming language created by Larry Wall and first released in 1987. ...

` my \$name = "Nancy"; print "\$name said Hello World to the crowd of people."; `

produces the output:

` Nancy said Hello World to the crowd of people. `

Look up variable in Wiktionary, the free dictionary.

Wikipedia does not have an article with this exact name. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 150 languages. ... In computer programming, a global variable is a variable that is accessible in every scope. ... In computer science, a local variable is a variable that is given local scope. ... In computer programming, static variables typically have a broader scope than other variables. ... An undefined variable in a computer program is a variable that is accessed by the program but which has not been previously declared by that program. ... An unreferenced variable in a computer program is a variable that is declared but which is never used. ...

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