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253 lines
6.2 KiB
Plaintext
253 lines
6.2 KiB
Plaintext
@chapter Expression Evaluation
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@c man begin EXPRESSION EVALUATION
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When evaluating an arithmetic expression, FFmpeg uses an internal
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formula evaluator, implemented through the @file{libavutil/eval.h}
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interface.
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An expression may contain unary, binary operators, constants, and
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functions.
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Two expressions @var{expr1} and @var{expr2} can be combined to form
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another expression "@var{expr1};@var{expr2}".
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@var{expr1} and @var{expr2} are evaluated in turn, and the new
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expression evaluates to the value of @var{expr2}.
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The following binary operators are available: @code{+}, @code{-},
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@code{*}, @code{/}, @code{^}.
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The following unary operators are available: @code{+}, @code{-}.
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The following functions are available:
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@table @option
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@item sinh(x)
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Compute hyperbolic sine of @var{x}.
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@item cosh(x)
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Compute hyperbolic cosine of @var{x}.
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@item tanh(x)
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Compute hyperbolic tangent of @var{x}.
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@item sin(x)
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Compute sine of @var{x}.
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@item cos(x)
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Compute cosine of @var{x}.
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@item tan(x)
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Compute tangent of @var{x}.
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@item atan(x)
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Compute arctangent of @var{x}.
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@item asin(x)
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Compute arcsine of @var{x}.
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@item acos(x)
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Compute arccosine of @var{x}.
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@item exp(x)
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Compute exponential of @var{x} (with base @code{e}, the Euler's number).
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@item log(x)
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Compute natural logarithm of @var{x}.
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@item abs(x)
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Compute absolute value of @var{x}.
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@item squish(x)
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Compute expression @code{1/(1 + exp(4*x))}.
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@item gauss(x)
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Compute Gauss function of @var{x}, corresponding to
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@code{exp(-x*x/2) / sqrt(2*PI)}.
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@item isinf(x)
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Return 1.0 if @var{x} is +/-INFINITY, 0.0 otherwise.
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@item isnan(x)
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Return 1.0 if @var{x} is NAN, 0.0 otherwise.
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@item mod(x, y)
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Compute the remainder of division of @var{x} by @var{y}.
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@item max(x, y)
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Return the maximum between @var{x} and @var{y}.
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@item min(x, y)
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Return the maximum between @var{x} and @var{y}.
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@item eq(x, y)
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Return 1 if @var{x} and @var{y} are equivalent, 0 otherwise.
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@item gte(x, y)
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Return 1 if @var{x} is greater than or equal to @var{y}, 0 otherwise.
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@item gt(x, y)
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Return 1 if @var{x} is greater than @var{y}, 0 otherwise.
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@item lte(x, y)
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Return 1 if @var{x} is lesser than or equal to @var{y}, 0 otherwise.
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@item lt(x, y)
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Return 1 if @var{x} is lesser than @var{y}, 0 otherwise.
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@item st(var, expr)
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Allow to store the value of the expression @var{expr} in an internal
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variable. @var{var} specifies the number of the variable where to
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store the value, and it is a value ranging from 0 to 9. The function
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returns the value stored in the internal variable.
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Note, Variables are currently not shared between expressions.
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@item ld(var)
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Allow to load the value of the internal variable with number
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@var{var}, which was previously stored with st(@var{var}, @var{expr}).
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The function returns the loaded value.
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@item while(cond, expr)
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Evaluate expression @var{expr} while the expression @var{cond} is
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non-zero, and returns the value of the last @var{expr} evaluation, or
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NAN if @var{cond} was always false.
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@item ceil(expr)
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Round the value of expression @var{expr} upwards to the nearest
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integer. For example, "ceil(1.5)" is "2.0".
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@item floor(expr)
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Round the value of expression @var{expr} downwards to the nearest
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integer. For example, "floor(-1.5)" is "-2.0".
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@item trunc(expr)
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Round the value of expression @var{expr} towards zero to the nearest
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integer. For example, "trunc(-1.5)" is "-1.0".
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@item sqrt(expr)
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Compute the square root of @var{expr}. This is equivalent to
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"(@var{expr})^.5".
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@item not(expr)
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Return 1.0 if @var{expr} is zero, 0.0 otherwise.
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@item pow(x, y)
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Compute the power of @var{x} elevated @var{y}, it is equivalent to
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"(@var{x})^(@var{y})".
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@item random(x)
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Return a pseudo random value between 0.0 and 1.0. @var{x} is the index of the
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internal variable which will be used to save the seed/state.
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@item hypot(x, y)
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This function is similar to the C function with the same name; it returns
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"sqrt(@var{x}*@var{x} + @var{y}*@var{y})", the length of the hypotenuse of a
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right triangle with sides of length @var{x} and @var{y}, or the distance of the
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point (@var{x}, @var{y}) from the origin.
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@item gcd(x, y)
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Return the greatest common divisor of @var{x} and @var{y}. If both @var{x} and
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@var{y} are 0 or either or both are less than zero then behavior is undefined.
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@item if(x, y)
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Evaluate @var{x}, and if the result is non-zero return the result of
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the evaluation of @var{y}, return 0 otherwise.
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@item ifnot(x, y)
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Evaluate @var{x}, and if the result is zero return the result of the
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evaluation of @var{y}, return 0 otherwise.
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@item taylor(expr, x) taylor(expr, x, id)
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Evaluate a taylor series at x.
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expr represents the LD(id)-th derivates of f(x) at 0. If id is not specified
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then 0 is assumed.
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note, when you have the derivatives at y instead of 0
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taylor(expr, x-y) can be used
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When the series does not converge the results are undefined.
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@item root(expr, max)
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Finds x where f(x)=0 in the interval 0..max.
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f() must be continuous or the result is undefined.
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@end table
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The following constants are available:
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@table @option
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@item PI
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area of the unit disc, approximately 3.14
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@item E
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exp(1) (Euler's number), approximately 2.718
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@item PHI
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golden ratio (1+sqrt(5))/2, approximately 1.618
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@end table
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Assuming that an expression is considered "true" if it has a non-zero
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value, note that:
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@code{*} works like AND
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@code{+} works like OR
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and the construct:
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@example
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if A then B else C
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@end example
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is equivalent to
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@example
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if(A,B) + ifnot(A,C)
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@end example
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In your C code, you can extend the list of unary and binary functions,
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and define recognized constants, so that they are available for your
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expressions.
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The evaluator also recognizes the International System number
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postfixes. If 'i' is appended after the postfix, powers of 2 are used
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instead of powers of 10. The 'B' postfix multiplies the value for 8,
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and can be appended after another postfix or used alone. This allows
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using for example 'KB', 'MiB', 'G' and 'B' as postfix.
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Follows the list of available International System postfixes, with
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indication of the corresponding powers of 10 and of 2.
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@table @option
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@item y
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-24 / -80
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@item z
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-21 / -70
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@item a
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-18 / -60
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@item f
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-15 / -50
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@item p
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-12 / -40
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@item n
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-9 / -30
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@item u
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-6 / -20
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@item m
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-3 / -10
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@item c
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-2
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@item d
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-1
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@item h
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2
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@item k
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3 / 10
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@item K
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3 / 10
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@item M
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6 / 20
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@item G
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9 / 30
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@item T
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12 / 40
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@item P
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15 / 40
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@item E
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18 / 50
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@item Z
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21 / 60
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@item Y
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24 / 70
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@end table
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@c man end
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