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Advanced Maths & Ingame Calculator
- Author(s)
- looking_for_help
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- 57.23 KB
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- May 4, 2013
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- May 30, 2014
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This bundle is marked as recommended. It works and satisfies the submission rules.
Advanced Mathematics & Ingame Calculator
vJass Version 1.2.0.0
1. Introduction
This is a math library designed to provide advanced mathematic functions and functionalities that are not supported by the World Editor. Mathematics are important for various things like calculating a units armor, physic systems with kinematics or differential equations, movement, artificial intelligence, statistics for balancing and many more. Therefore it is quite annoying that the World Editor lacks of many important math functions. The aim of this system is to close this gap - The library provides extremly efficient functions to calculate logarithms, hyperbolic functions and their inverses as well as typecheck or rounding functions and many more. Not only "complicated" functions are provided but also very easy ones like the absolute value of a real number, to finally have a full and complete list of important functions which every Math library should provide.
Further the library is designed modular, so that further and more advanced extensions can be easily added or removed from the system core. As a first Extension, there is a MathParser library included to the system which provides a fully functional interpreter for mathematic expressions, making it possible to implement an ingame calculator to the game. Further Plug-Ins or Extensions will follow.
2. System Code
Enclosed is the systems code. The system uses Newton-Cotes formulars to compute logarithms, hyperbolic functions and their inverses at an extremly high precision with a minimal overhead. Only four divisions are used in the worst case to compute the natural logarithm of a number, apart from that only additions and multiplications are used, making these functions very efficient. Some functions of the library already exist in the standard editor, like the min/max functions or abs. These are included for better readability to not have to use BJs. For more details about the interpreter, see section 3.
JASS:
library Maths/* v 1.2.0.0
**********************************************************************************
*
* Advanced Mathematics
* ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
* By looking_for_help aka eey
*
* This system provides a large amount of standard mathematical functions that
* miss in standard Jass like logarithmic, hyperbolic, typecheck or rounding
* functions. It can be extended with various optional libraries.
*
***********************************************************************************
*
* Requirements
* ¯¯¯¯¯¯¯¯¯¯¯¯
* */ uses ErrorMessage /* hiveworkshop.com/forums/jass-resources-412/snippet-error-message-239210/
*
***********************************************************************************
*
* Implementation
* ¯¯¯¯¯¯¯¯¯¯¯¯¯¯
* To use this system, just copy this script to your trigger editor, then you
* can use it straight away. To see how the evaluation function works, compare
* the example IngameCalculator trigger.
*
**********************************************************************************
*
* Available Plug-Ins and Extensions
* ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
* library MathParser
* - A library that allows you to parse string expressions. Compare the
* IngameCalculator Trigger for an example usage.
*
* library Matrices
* - A library that allows you to perform Matrix and Vector operations
* like solving a System of Linear Equations, compute the inverse of
* a Matrix, perform Matrix multiplication and so on.
*
**********************************************************************************
*
* System API
* ¯¯¯¯¯¯¯¯¯¯
* struct Math
* ¯ ¯ ¯ ¯ ¯ ¯
* readonly static real Pi
* - Refer to this field for the number Pi, the ratio of a circle's
* circumference to its diameter
*
* readonly static real E
* - Refer to this field for the number E, the base of the natural
* exponential function.
*
* readonly static real Phi
* - Refer to this field for the number Phi, the golden ratio.
*
* readonly static real Inf
* - Refer to this field for 2^128, the biggest real number Wc3 can
* handle. You can use -Math.Inf to get the smallest real number.
*
* readonly static integer MinInt
* - Refer to this field for -2147483648, the smallest integer number
* that Wc3 can handle.
*
* readonly static integer MaxInt
* - Refer to this field for 2147483647, the biggest integer number
* that Wc3 can handle.
*
* static method abs takes real r returns real
* - Computes the absolute value of a number.
*
* static method sig takes real r returns real
* - Extracts the sign of a real number.
*
* static method max takes real r1, real r2 returns real
* - Returns the bigger of two values r1 and r2.
*
* static method min takes real r1, real r2 returns real
* - Returns the smaller of two values r1 and r2.
*
* static method mod takes real r1, real r2 returns real
* - Computes the rest of the division r1/r2.
*
* static method modInt takes integer n1, integer n2 returns integer
* - Computes the modulo of n1/n2.
*
* static method multiMod takes integer n1, integer n2, integer mod returns integer
* - Computes the modulo of n1*n2/mod. Use this to compute the
* modulo of very large numbers.
*
* static method expMod takes integer x, integer n, integer modulo returns integer
* - Computes the modulo of x^n/modulo. Use this to compute the
* modulo of extremly large numbers.
*
* static method digits takes real r returns integer
* - Returns the number of digits before the comma of a given real number.
*
* static method isDigit takes string s returns boolean
* - Determines whether a string is a digit or not.
*
* static method isInteger takes real r returns boolean
* - Determines whether a real is integer or not.
*
* static method isEven takes real r returns boolean
* - Determines the parity of a real number.
*
* static method isPrime takes real r returns boolean
* - Determines whether a number is a prime or not by using a deterministic
* version of the Miller-Rabin test.
*
* static method sinh takes real r returns real
* - Computes the hyperbolic sine of a real number.
*
* static method cosh takes real r returns real
* - Computes the hyperbolic cosine of a real number.
*
* static method tanh takes real r returns real
* - Computes the hyperbolic tangent of a real number.
*
* static method asinh takes real r returns real
* - Computes the inverse hyperbolic sine of a real number.
*
* static method acosh takes real r returns real
* - Computes the inverse hyperbolic cosine of a real number.
*
* static method atanh takes real r returns real
* - Computes the inverse hyperbolic tangent of a real number.
*
* static method ln takes real r returns real
* - Computes the natural logarithm to a number by using Newton-Cotes.
* Reaches extremly high accuracies very efficiently. This method
* is used to compute all other logarithms and inverse hyperbolic
* functions.
*
* static method log2 takes real r returns real
* - Computes the binary logarithm to a number.
*
* static method log10 takes real r returns real
* - Computes the common logarithm to a number.
*
* static method log takes real r1, real r2 returns real
* - Computes the logarithm of a number r2 to the base r1.
*
* static method floor takes real r returns real
* - Rounds a number to the next smallest integer.
*
* static method ceil takes real r returns real
* - Rounds a number to the next largest integer.
*
* static method round takes real r returns real
* - Rounds a number to the nearest whole number.
*
* static method fractional takes real r returns real
* - Computes the fractional part of a number.
*
* static method mergeFloat takes real r returns real
* - Merges the fracional and the non fractional parts of a number
* together to an integer number.
*
* static method factorial takes real r returns real
* - Computes the factorial of a number r. If r is not a natural
* number, the gamma function as an extension to the factorial
* function is used.
*
*********************************************************************************/
globals
/*************************************************************************
* Customizable globals
*************************************************************************/
// Do you want the system to store primes that were once detected?
private constant boolean STORE_DETECTED_PRIMES = true
/*************************************************************************
* End of customizable globals
*************************************************************************/
public hashtable h
private constant real E_INV = 0.3678794
private constant real LOG_02_FACTOR = 1.4429504
private constant real LOG_10_FACTOR = 0.4342945
private constant real LN_FACTOR = 1.2840254
private constant real LN_FACTOR_INV = 0.7788008
endglobals
struct Math //extends array
// Constants
static constant real Pi = 3.141593
static constant real E = 2.718282
static constant real Phi = 1.618034
static constant real Inf = Pow(2.0, 128.0)
static constant integer MinInt = -2147483648
static constant integer MaxInt = 2147483647
// Absolute value
static method abs takes real r returns real
if r < 0 then
return -r
endif
return r
endmethod
// Signum
static method sig takes real r returns real
if r > 0 then
return 1.0
elseif r < 0 then
return -1.0
endif
return 0.0
endmethod
// Min-Max
static method max takes real r1, real r2 returns real
if r1 < r2 then
return r2
endif
return r1
endmethod
static method min takes real r1, real r2 returns real
if r1 < r2 then
return r1
endif
return r2
endmethod
// Modulus
static method mod takes real r1, real r2 returns real
local real modulus = r1 - I2R(R2I(r1/r2))*r2
if modulus < 0 then
set modulus = modulus + r2
endif
return modulus
endmethod
static method modInt takes integer n1, integer n2 returns integer
local integer modulus = n1 - (n1/n2)*n2
if modulus < 0 then
set modulus = modulus + n2
endif
return modulus
endmethod
static method multiMod takes integer n1, integer n2, integer mod returns integer
local integer factor1 = R2I(floor(n1/mod))
local integer factor2 = R2I(floor(n2/mod))
local integer modulus
if factor1 == 0 then
set factor1 = 1
endif
if factor2 == 0 then
set factor2 = 1
endif
if n1 > mod/2 and n2 > mod/2 then
set n1 = (n1 - factor1*mod)*(n2 - factor2*mod)
else
set n1 = n1*n2
endif
set n2 = mod
set modulus = n1 - (n1/n2)*n2
if modulus < 0 then
set modulus = modulus + n2
endif
return modulus
endmethod
static method expMod takes integer x, integer n, integer modulo returns integer
local string exponent = ""
local integer result = 1
local integer stringLen
local integer i = 0
loop
if modInt(n, 2) == 1 then
set exponent = "1"+exponent
else
set exponent = "0"+exponent
endif
set n = n/2
exitwhen n < 1
endloop
set stringLen = StringLength(exponent)
loop
exitwhen i >= stringLen
set result = multiMod(result, result, modulo)
if SubString(exponent, i, i + 1) == "1" then
set result = multiMod(result, x, modulo)
endif
set i = i + 1
endloop
return result
endmethod
// Digits
static method digits takes real r returns integer
local string s = R2S(r)
local integer i = 0
loop
exitwhen SubString(s, i, i + 1) == "."
set i = i + 1
endloop
if r < 0 then
return i - 1
endif
return i
endmethod
// Logarithms
static method ln takes real r returns real
local real sum = 0.0
local real sign = 1.0
debug if r < 0.0 then
debug call ThrowError(true, "Maths", "ln", "Math", 0, "Logarithm of negative number is undefined!")
debug endif
if r < 1.0 then
set r = 1.0/r
set sign = -1.0
endif
loop
exitwhen r < E
set r = r*E_INV
set sum = sum + 1.0
endloop
loop
exitwhen r < LN_FACTOR
set r = r*LN_FACTOR_INV
set sum = sum + 0.25
endloop
return sign*(sum + 0.125*(r - 1.0)*(1 + 9.0/(2.0 + r) + 4.5/(0.5 + r) + 1.0/r))
endmethod
static method log2 takes real r returns real
return LOG_02_FACTOR*ln(r)
endmethod
static method log10 takes real r returns real
return LOG_10_FACTOR*ln(r)
endmethod
static method log takes real base, real arg returns real
return ln(arg)/ln(base)
endmethod
// Hyperbolic functions
static method sinh takes real r returns real
return 0.5*(Pow(E, r) - Pow(E, -r))
endmethod
static method cosh takes real r returns real
return 0.5*(Pow(E, r) + Pow(E, -r))
endmethod
static method tanh takes real r returns real
return sinh(r)/cosh(r)
endmethod
static method asinh takes real r returns real
return ln(r + SquareRoot(r*r + 1))
endmethod
static method acosh takes real r returns real
return ln(r + SquareRoot(r*r - 1))
endmethod
static method atanh takes real r returns real
return 0.5*ln((1 + r)/(1 - r))
endmethod
// Rounding
static method floor takes real r returns real
if r < 0 then
return -I2R(R2I(-r))
endif
return I2R(R2I(r))
endmethod
static method ceil takes real r returns real
if floor(r) == r then
return r
elseif r < 0 then
return -(I2R(R2I(-r)) + 1.0)
endif
return I2R(R2I(r)) + 1.0
endmethod
static method round takes real r returns real
if r > 0 then
return I2R(R2I(r + 0.5))
endif
return I2R(R2I(r - 0.5))
endmethod
static method fractional takes real r returns real
return r - floor(r)
endmethod
static method mergeFloat takes real r returns real
local real afterC = fractional(r)
local real beforeC = floor(r)
local string beforeComma = R2S(beforeC)
local string afterComma = R2S(afterC)
local string subString
local integer i = 0
local integer stringLen = StringLength(beforeComma)
local integer endPosition = 0
if afterC == 0 then
return beforeC
endif
loop
exitwhen SubString(beforeComma, i, i + 1) == "."
set i = i + 1
endloop
set beforeComma = SubString(beforeComma, 0, i)
set i = StringLength(afterComma)
loop
set subString = SubString(afterComma, i, i + 1)
exitwhen subString == "."
if endPosition == 0 and subString != "0" and subString != "" then
set endPosition = i
endif
set i = i - 1
endloop
return S2R(beforeComma+SubString(afterComma, i + 1, endPosition + 1))
endmethod
// Type checks
static method isDigit takes string s returns boolean
return not (StringLength(s) != 1 or S2R(s) == 0 and s != "0")
endmethod
static method isInteger takes real r returns boolean
return I2R(R2I(r)) == r
endmethod
static method isEven takes real r returns boolean
return mod(r, 2.0) == 0
endmethod
static method isPrime takes integer n returns boolean
local integer s
local integer d
local integer a = 2
local integer temp
local integer counter
local integer dSave
local integer modulus
local boolean firstTest = false
local boolean secondTest = false
if n == 2 or n == 7 or n == 61 then
return true
elseif isEven(n) or n < 2 then
return false
endif
static if STORE_DETECTED_PRIMES then
if LoadBoolean(h, n, 0) then
return LoadBoolean(h, n, 1)
endif
endif
if n < 157 then
set a = n
loop
exitwhen a == 1
if modInt(n, a) == 0 and a != n then
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, false)
endif
return false
endif
set a = a - 1
endloop
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, true)
endif
return true
endif
set s = R2I(floor(log2(n - 1)))
loop
set temp = R2I(Pow(2, I2R(s)))
exitwhen modInt(n - 1, temp) == 0
set s = s - 1
endloop
set d = (n - 1)/(R2I(Pow(2, I2R(s))))
set dSave = d
set a = 2
set counter = 0
loop
exitwhen counter > s
set modulus = expMod(a, d, n)
if (counter == 0 and modulus == 1) or (counter > 0 and modulus - n == -1) then
set firstTest = true
exitwhen true
endif
set d = 2*d
set counter = counter + 1
if counter == 1 then
set d = dSave
endif
endloop
if not firstTest then
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, false)
endif
return false
endif
set a = 7
set d = dSave
set counter = 0
loop
exitwhen counter > s
set modulus = expMod(a, d, n)
if (counter == 0 and modulus == 1) or (counter > 0 and modulus - n == -1) then
if firstTest then
set secondTest = true
exitwhen true
endif
endif
set d = 2*d
set counter = counter + 1
if counter == 1 then
set d = dSave
endif
endloop
if not secondTest then
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, false)
endif
return false
endif
set a = 61
set d = dSave
set counter = 0
loop
exitwhen counter > s
set modulus = expMod(a, d, n)
if (counter == 0 and modulus == 1) or (counter > 0 and modulus - n == -1) then
if secondTest then
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, true)
endif
return true
endif
endif
set d = 2*d
set counter = counter + 1
if counter == 1 then
set d = dSave
endif
endloop
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, false)
endif
return false
endmethod
// Factorial
static method factorial takes real r returns real
local real z = 1.0
if floor(r) == r then
debug if r < 0 then
debug call ThrowError(true, "Maths", "factorial", "Math", 0, "Factorial of negative number is not defined!")
debug endif
if r == 0 then
return 1.0
endif
loop
exitwhen r == 0.0
set z = z*r
set r = r - 1.0
endloop
return z
endif
set r = r + 1.0
return SquareRoot((2.0*Pi)/(r))*Pow(((1.0/E)*(r + 1.0/(12.0*r - 1.0/(10.0*r)))), r)
endmethod
endstruct
private module Init
private static method onInit takes nothing returns nothing
set h = InitHashtable()
endmethod
endmodule
private struct Inits extends array
implement Init
endstruct
endlibraryMath struct (function list)
readonly static real PiRefer to this field for the number pi, the ratio of a circle's circumference to its diameter
readonly static real ERefer to this field for the number E, the base of the natural exponential function.
readonly static real PhiRefer to this field for the number Phi, the golden ratio.
readonly static real InfRefer to this field for 2^128, the biggest real number Wc3 can handle. You can use -Math.Inf to get the smallest real number.
readonly static integer MinIntRefer to this field for -2147483648, the smallest integer number that Wc3 can handle.
readonly static integer MaxIntRefer to this field for 2147483647, the biggest integer number that Wc3 can handle.
static method abs takes real r returns realComputes the absolute value of a number.
static method sig takes real r returns realExtracts the sign of a real number.
static method max takes real r1, real r2 returns realReturns the bigger of two values r1 and r2.
static method min takes real r1, real r2 returns realReturns the smaller of two values r1 and r2.
static method mod takes real r1, real r2 returns realComputes the rest of the division r1/r2.
static method modInt takes integer n1, integer n2 returns integerComputes the modulo of n1/n2.
static method multiMod takes integer n1, integer n2, integer mod returns integerComputes the modulo of n1*n2/mod. Use this to compute themodulo of very large numbers.
static method expMod takes integer x, integer n, integer modulo returns integerComputes the modulo of x^n/modulo. Use this to compute the modulo of extremly large numbers.
static method digits takes real r returns integerReturns the number of digits before the comma of a given real number.
static method isDigit takes string s returns booleanDetermines whether a string is a digit or not.
static method isInteger takes real r returns booleanDetermines whether a real is integer or not.
static method isEven takes real r returns booleanDetermines the parity of a real number.
static method isPrime takes real r returns booleanDetermines whether a number is a prime or not by using a deterministic version of the Miller-Rabin test. Works for values about ~100000.
static method sinh takes real r returns realComputes the hyperbolic sine of a real number.
static method cosh takes real r returns realComputes the hyperbolic cosine of a real number.
static method tanh takes real r returns realComputes the hyperbolic tangent of a real number.
static method asinh takes real r returns realComputes the inverse hyperbolic sine of a real number.
static method acosh takes real r returns realComputes the inverse hyperbolic cosine of a real number.
static method atanh takes real r returns realComputes the inverse hyperbolic tangent of a real number.
static method ln takes real r returns realComputes the natural logarithm to a number by using Newton-Cotes. Reaches extremly high accuracies very efficiently. This method is used to compute all other logarithms and inverse hyperbolic functions.
static method log2 takes real r returns realComputes the binary logarithm to a number.
static method log10 takes real r returns realComputes the common logarithm to a number.
static method log takes real r1, real r2 returns realComputes the logarithm of a number r2 to the base r1. If you want to compute the logarithm to the bases 2, 10 or E, you should use the specific functions as they are faster.
static method floor takes real r returns realRounds a number to the next smallest integer.
static method ceil takes real r returns realRounds a number to the next largest integer.
static method round takes real r returns realRounds a number to the nearest whole number.
static method fractional takes real r returns realComputes the fractional part of a number.
static method mergeFloat takes real r returns realMerges the fracional and the non fractional parts of a number together to an integer number.
static method factorial takes real r returns realComputes the factorial of a number r. If r is not a natural number, the gamma function as an extension to the factorial function is used.
3. Implementation and Available Extensions
To implement this system, just copy and paste the Math and the IngameCalculator triggers to your map. The only requirement is vJass, then you can use it right away, same applies for the available Extensions.
3.1. MathParser
This is one Extension to the Math library, a Math Parser library making it possible to dynamically evaluate mathematic expressions. This can be used to implement an ingame calculator to the game which makes ingame calculations very comfortable. This can be also useful for several things like: mathematic minigames or riddles, calculations during debugging or as a comfort function for maps that have a complex stat/skill system. Also maps with economy simulation parts could benefit from this. The math interpreter is based on standard Matlab conventions and supports the following symbols:
- Numbers with or without decimal point, e.g.: 3, 4.3, 55.2
- Arithmetic operators: +, -, *, /
- Power: ^
- Parenthesis: ( )
- Result memory (stores the last computed result): ans
- Clear screen: clc
The interpreter is designed to be very robust towards the different typing styles of mathematical expressions. So you can write for example 5*(1+2) or 5(1+2), the interpreter will automatically bring it into an understandable form. With the formatExpression method it is garantueed that the expression will also follow the standard conventions in terms of spacing and operator placement. Finally the interpreter is provided with various syntax and math error messages which will throw exceptions if the entered expression is invalid. These error messages can be optionally turned of in the system configuration. Enclosed is the Plug-In code:
JASS:
library MathParser /* v 1.1.0.0
**********************************************************************************
*
* MathParser
* ¯¯¯¯¯¯¯¯¯¯
* By looking_for_help aka eey
*
* This system provides methods for parsing mathematically string expressions,
* represented as strings. Also methods for formating string expressions are
* provided, making it possible to implement an ingame calculator to the game.
*
***********************************************************************************
*
* Requirements
* ¯¯¯¯¯¯¯¯¯¯¯¯
* */ uses Maths /* hiveworkshop.com/forums/spells-569/advanced-maths-ingame-calculator-234024/?prev=r%3D20%26page%3D5
*
***********************************************************************************
*
* Implementation
* ¯¯¯¯¯¯¯¯¯¯¯¯¯¯
* To use this system, you need the library Math. Once you implemented it, just
* copy this script to your trigger editor, then you can use it straight away. To
* see how the evaluation function works, compare the example IngameCalculator
* trigger for an example usage.
*
***********************************************************************************
*
* System API
* ¯¯¯¯¯¯¯¯¯¯
* readonly static real ans
* - Stores the last result of the evaluation method. Initialized as 0.
*
* static method calculate takes string expression returns real
* - Use this method to calculate a mathematic expression presented as
* a string. Allowed values are numbers, the decimal seperator, basic
* arithmetic operators like +, -, *, / and ^ as well as parenthesis.
* You can also put "ans" into the expression to refer to the last
* calculation result. Error messages on math and syntax errors will
* be displayed if specified so in the configurable globals. The
* syntax parsing strictly follows Matlab conventions.
*
* static method formatExpression takes string expression returns string
* - Use this method to format an user defined expression so that it
* looks nice. Compare the IngameCalculator trigger for an example
* usage.
*
*********************************************************************************/
globals
/*************************************************************************
* Customizable globals
*************************************************************************/
// Do you want the system to display error messages on math errors?
private constant boolean DISPLAY_MATH_ERRORS = true
// Do you want the system to display error messages on syntax errors?
private constant boolean DISPLAY_SYNTAX_ERRORS = true
/*************************************************************************
* End of customizable globals
*************************************************************************/
endglobals
private module Init
private static method onInit takes nothing returns nothing
call init()
endmethod
endmodule
struct MathParser extends array
readonly static real ans = 0.0
private static constant integer ADDITION = 1
private static constant integer SUBSTRACTION = 2
private static constant integer MULTIPLICATION = 3
private static constant integer DIVISION = 4
private static constant integer EXPONENTIATION = 5
private static method getPriority takes string op returns integer
return LoadInteger(Maths_h, StringHash(op), 0)
endmethod
private static method error takes string s, integer flag returns nothing
local real crashThread
if flag == 0 then
static if DISPLAY_MATH_ERRORS then
call DisplayTimedTextToPlayer(GetLocalPlayer(), 0.0, 0.0, 60.0, "|cffff0000Math Error!|r "+s)
endif
else
static if DISPLAY_SYNTAX_ERRORS then
call DisplayTimedTextToPlayer(GetLocalPlayer(), 0.0, 0.0, 60.0, "|cffff0000Syntax Error!|r "+s)
endif
endif
set crashThread = 0/0
endmethod
private static method convertExpression takes string expression returns string
local integer stringLen = StringLength(expression)
local integer i = 0
local integer stackCounter = -1
local string postfix = ""
local string array stack
local string actualChar
local string prevChar
local boolean decimalDetected = false
local boolean numberDetected = false
local boolean numberOnceDetected = false
local boolean unaryOperator = false
local integer openBraces = 0
loop
exitwhen i > stringLen
set prevChar = SubString(expression, i - 1, i)
set actualChar = SubString(expression, i, i + 1)
set unaryOperator = not (prevChar == ")" or Math.isDigit(prevChar))
if actualChar == ")" and openBraces < 1 then
call thistype.error("Unbalanced parenthesis!", 1)
endif
if actualChar == "m" or actualChar == "p" or actualChar == "M" or actualChar == "P" then
call thistype.error("Undefined symbols used!", 1)
endif
if actualChar == "+" and unaryOperator and prevChar != "^" then
set actualChar = "p"
elseif actualChar == "-" and unaryOperator and prevChar != "^" then
set actualChar = "m"
elseif actualChar == "-" and unaryOperator and prevChar == "^" then
set actualChar = "M"
elseif actualChar == "+" and unaryOperator and prevChar == "^" then
set actualChar = "P"
endif
if Math.isDigit(actualChar) then
set postfix = postfix+actualChar
set numberDetected = true
set numberOnceDetected = true
elseif actualChar == "." then
if decimalDetected == false and Math.isDigit(SubString(expression, i - 1, i)) and Math.isDigit(SubString(expression, i + 1, i + 2)) then
set postfix = postfix+actualChar
set decimalDetected = true
else
call thistype.error("Incorrect use of decimal point!", 1)
endif
elseif thistype.isOperator(actualChar) or actualChar == "(" or actualChar == ")" then
set decimalDetected = false
if numberDetected then
set numberDetected = false
set postfix = postfix+" "
endif
if thistype.getPriority(actualChar) > thistype.getPriority(stack[stackCounter]) or actualChar == "(" then
set stackCounter = stackCounter + 1
set stack[stackCounter] = actualChar
if actualChar == "(" then
set openBraces = openBraces + 1
endif
elseif openBraces > 0 and actualChar != ")" and actualChar != "(" and thistype.getPriority(actualChar) <= thistype.getPriority(stack[stackCounter]) then
loop
exitwhen stack[stackCounter] == "("
set postfix = postfix+stack[stackCounter]+" "
set stackCounter = stackCounter - 1
endloop
set stackCounter = stackCounter + 1
set stack[stackCounter] = actualChar
else
if actualChar == ")" then
set openBraces = openBraces - 1
loop
exitwhen stack[stackCounter] == "("
set postfix = postfix+stack[stackCounter]+" "
set stackCounter = stackCounter - 1
endloop
set stack[stackCounter] = ""
set stackCounter = stackCounter - 1
else
loop
exitwhen stackCounter < 0
set postfix = postfix+stack[stackCounter]+" "
set stackCounter = stackCounter - 1
endloop
set stackCounter = stackCounter + 1
set stack[stackCounter] = actualChar
endif
endif
else
if i != stringLen then
call thistype.error("Undefined symbols used!", 1)
endif
endif
set i = i + 1
endloop
if not numberOnceDetected then
call thistype.error("Invalid expression!", 1)
endif
if stackCounter >= 0 then
if openBraces > 0 then
call thistype.error("Unbalanced parenthesis!", 1)
endif
loop
exitwhen stackCounter < 0
if stack[stackCounter] != "(" then
if numberDetected then
set postfix = postfix+" "+stack[stackCounter]+" "
set numberDetected = false
else
set postfix = postfix+stack[stackCounter]+" "
endif
endif
set stackCounter = stackCounter - 1
endloop
endif
set stringLen = StringLength(postfix)
if Math.isDigit(SubString(postfix, stringLen - 1, stringLen)) then
set postfix = postfix+" "
endif
return postfix
endmethod
private static method subCalc takes string op1, string op2, string op returns real
local real r1 = S2R(op1)
local real r2 = S2R(op2)
local integer localOp
if op1 == null or op2 == null then
call thistype.error("Unbalanced operators!", 1)
endif
set localOp = LoadInteger(Maths_h, StringHash(op), 1)
if localOp < MULTIPLICATION then
if localOp == ADDITION then
return r1 + r2
else
return r1 - r2
endif
else
if localOp == MULTIPLICATION then
return r1*r2
elseif localOp == DIVISION then
if r2 == 0 then
call thistype.error("Division by zero!", 0)
endif
return r1/r2
else
if r1 < 0.0 and not Math.isInteger(r2) then
call thistype.error("(N-th) square root from negativ value not defined!", 0)
endif
return Pow(r1, r2)
endif
endif
call thistype.error("Undefined operators!", 1)
return 0.0
endmethod
private static method isOperator takes string s returns boolean
return s == "+" or s == "-" or s == "*" or s == "/" or s == "^" or s == "(" or s == "p" or s == "m" or s == "P" or s == "M"
endmethod
private static method prepareExpression takes string expression returns string
local integer stringLen = StringLength(expression)
local integer i = 0
local string actualChar
local string prevChar
local string nextChar
loop
exitwhen i > stringLen
set actualChar = SubString(expression, i, i + 1)
if actualChar == " " then
set expression = SubString(expression, 0, i)+SubString(expression, i + 1, stringLen)
set i = i - 1
endif
set i = i + 1
endloop
set i = 0
set stringLen = StringLength(expression)
loop
exitwhen i > stringLen
if SubString(expression, i, i + 3) == "ans" then
set expression = SubString(expression, 0, i)+"("+R2S(ans)+")"+SubString(expression, i + 3, stringLen)
set stringLen = StringLength(expression)
endif
set prevChar = SubString(expression, i - 1, i)
set actualChar = SubString(expression, i, i + 1)
set nextChar = SubString(expression, i + 1, i + 2)
if actualChar == "+" then
if SubString(expression, i + 1, i + 2) == "+" then
if Math.isDigit(SubString(expression, i - 1, i)) then
set expression = SubString(expression, 0, i)+"+"+SubString(expression, i + 2, stringLen)
else
set expression = SubString(expression, 0, i)+SubString(expression, i + 2, stringLen)
endif
set i = i - 1
elseif SubString(expression, i + 1, i + 2) == "-" then
set expression = SubString(expression, 0, i)+"-"+SubString(expression, i + 2, stringLen)
set i = i - 1
endif
elseif actualChar == "-" then
if SubString(expression, i + 1, i + 2) == "+" then
set expression = SubString(expression, 0, i)+"-"+SubString(expression, i + 2, stringLen)
set i = i - 1
elseif SubString(expression, i + 1, i + 2) == "-" then
if Math.isDigit(SubString(expression, i - 1, i)) then
set expression = SubString(expression, 0, i)+"+"+SubString(expression, i + 2, stringLen)
else
set expression = SubString(expression, 0, i)+SubString(expression, i + 2, stringLen)
endif
set i = i - 1
endif
elseif actualChar == "(" and (Math.isDigit(prevChar) or prevChar == ")") then
set expression = SubString(expression, 0, i)+"*"+SubString(expression, i, stringLen)
set stringLen = StringLength(expression)
set i = i - 1
elseif actualChar == ")" and Math.isDigit(nextChar) then
set expression = SubString(expression, 0, i + 1)+"*"+SubString(expression, i + 1, stringLen)
set stringLen = StringLength(expression)
set i = i - 1
endif
set i = i + 1
endloop
return expression
endmethod
private static method evaluateExpression takes string postfix returns real
local integer stringLen = StringLength(postfix)
local integer i = 0
local integer position = 0
local integer counter = 0
local integer stackCounter = -1
local string actualToken
local string array stack
local real result = 0.0
loop
exitwhen i == stringLen
if SubString(postfix, i, i + 1) == " " then
set actualToken = SubString(postfix, position, position + counter)
if Math.isDigit(SubString(actualToken, 0, 1)) then
set stackCounter = stackCounter + 1
set stack[stackCounter] = actualToken
else
if not (actualToken == "m " or actualToken == "p " or actualToken == "M " or actualToken == "P ") then
set result = thistype.subCalc(stack[stackCounter - 1], stack[stackCounter], actualToken)
set stack[stackCounter] = ""
set stack[stackCounter - 1] = R2S(result)
set stackCounter = stackCounter - 1
else
if actualToken == "m " or actualToken == "M " then
if S2R(stack[stackCounter]) > 0 then
set stack[stackCounter] = "-"+stack[stackCounter]
else
set stack[stackCounter] = SubString(stack[stackCounter], 1, StringLength(stack[stackCounter]))
endif
endif
endif
endif
set position = i + 1
set counter = 0
endif
set i = i + 1
set counter = counter + 1
endloop
return S2R(stack[0])
endmethod
static method calculate takes string expression returns real
set ans = thistype.evaluateExpression(thistype.convertExpression(thistype.prepareExpression(expression)))
return ans
endmethod
static method formatExpression takes string expression returns string
local integer i = 0
local integer stringLen = StringLength(expression)
local string prevChar
local string nextChar
local string actualChar
local string prevAnsToken
local string nextAnsToken
local boolean unaryOperator = false
loop
exitwhen i > stringLen
if SubString(expression, i, i + 1) == " " then
set expression = SubString(expression, 0, i)+SubString(expression, i + 1, stringLen)
set i = i - 1
endif
set i = i + 1
endloop
set i = 0
set stringLen = StringLength(expression)
loop
exitwhen i > stringLen
set actualChar = SubString(expression, i, i + 1)
if actualChar == "+" then
if SubString(expression, i + 1, i + 2) == "+" then
if Math.isDigit(SubString(expression, i - 1, i)) then
set expression = SubString(expression, 0, i)+"+"+SubString(expression, i + 2, stringLen)
else
set expression = SubString(expression, 0, i)+SubString(expression, i + 2, stringLen)
endif
set i = i - 1
elseif SubString(expression, i + 1, i + 2) == "-" then
set expression = SubString(expression, 0, i)+"-"+SubString(expression, i + 2, stringLen)
set i = i - 1
endif
elseif actualChar == "-" then
if SubString(expression, i + 1, i + 2) == "+" then
set expression = SubString(expression, 0, i)+"-"+SubString(expression, i + 2, stringLen)
set i = i - 1
elseif SubString(expression, i + 1, i + 2) == "-" then
if Math.isDigit(SubString(expression, i - 1, i)) then
set expression = SubString(expression, 0, i)+"+"+SubString(expression, i + 2, stringLen)
else
set expression = SubString(expression, 0, i)+SubString(expression, i + 2, stringLen)
endif
set i = i - 1
endif
endif
set i = i + 1
endloop
set i = 0
set stringLen = StringLength(expression)
loop
exitwhen i > stringLen
set actualChar = SubString(expression, i, i + 1)
set prevChar = SubString(expression, i - 1, i)
set nextChar = SubString(expression, i + 1, i + 2)
set prevAnsToken = SubString(expression, i - 3, i)
set nextAnsToken = SubString(expression, i + 1, i + 4)
set unaryOperator = not (prevChar == ")" or Math.isDigit(prevChar) or prevAnsToken == "ans")
if actualChar == "+" and not unaryOperator then
set expression = SubString(expression, 0, i)+" + "+SubString(expression, i + 1, stringLen)
set stringLen = StringLength(expression)
set i = i + 1
elseif actualChar == "+" and unaryOperator then
set expression = SubString(expression, 0, i)+SubString(expression, i + 1, stringLen)
set stringLen = StringLength(expression)
set i = i - 1
elseif actualChar == "-" and not unaryOperator then
set expression = SubString(expression, 0, i)+" - "+SubString(expression, i + 1, stringLen)
set stringLen = StringLength(expression)
set i = i + 1
elseif actualChar == "(" and (Math.isDigit(prevChar) or prevChar == ")") then
set expression = SubString(expression, 0, i)+"*"+SubString(expression, i, stringLen)
set stringLen = StringLength(expression)
set i = i - 1
elseif actualChar == ")" and Math.isDigit(nextChar) then
set expression = SubString(expression, 0, i + 1)+"*"+SubString(expression, i + 1, stringLen)
set stringLen = StringLength(expression)
set i = i - 1
endif
if prevAnsToken == "ans" and (Math.isDigit(actualChar) or actualChar == "(" or SubString(expression, i, i + 3) == "ans") then
set expression = SubString(expression, 0, i)+"*"+SubString(expression, i, stringLen)
set stringLen = StringLength(expression)
set i = i - 1
elseif nextAnsToken == "ans" and (Math.isDigit(actualChar) or actualChar == ")") then
set expression = SubString(expression, 0, i + 1)+"*"+SubString(expression, i + 1, stringLen)
set stringLen = StringLength(expression)
set i = i - 1
endif
set i = i + 1
endloop
return expression
endmethod
private static method init takes nothing returns nothing
call SaveInteger(Maths_h, StringHash("+"), 0, 1)
call SaveInteger(Maths_h, StringHash("-"), 0, 1)
call SaveInteger(Maths_h, StringHash("*"), 0, 2)
call SaveInteger(Maths_h, StringHash("/"), 0, 2)
call SaveInteger(Maths_h, StringHash("m"), 0, 3)
call SaveInteger(Maths_h, StringHash("p"), 0, 3)
call SaveInteger(Maths_h, StringHash("^"), 0, 4)
call SaveInteger(Maths_h, StringHash("M"), 0, 5)
call SaveInteger(Maths_h, StringHash("P"), 0, 5)
call SaveInteger(Maths_h, StringHash("("), 0, 6)
call SaveInteger(Maths_h, StringHash("+ "), 1, ADDITION)
call SaveInteger(Maths_h, StringHash("- "), 1, SUBSTRACTION)
call SaveInteger(Maths_h, StringHash("* "), 1, MULTIPLICATION)
call SaveInteger(Maths_h, StringHash("/ "), 1, DIVISION)
call SaveInteger(Maths_h, StringHash("^ "), 1, EXPONENTIATION)
endmethod
implement Init
endstruct
endlibrary
JASS:
library IngameCalculator uses MathParser
globals
/*************************************************************************
* Customizable globals
*************************************************************************/
// Define a command before performing a calculation, e.g. "-calc ".
// Use an empty string for no command.
private constant string commandString = ""
// Type in this string to clear the screen.
private constant string clearScreen = "clc"
/*************************************************************************
* End of customizable globals
*************************************************************************/
endglobals
private struct Calculator extends array
readonly static string expression
private static method onEnter takes nothing returns nothing
set expression = GetEventPlayerChatString()
if SubString(expression, 0, StringLength(commandString)) == commandString then
set expression = SubString(expression, StringLength(commandString), StringLength(expression))
if expression == clearScreen then
call ClearTextMessages()
else
call DisplayTimedTextToPlayer(GetLocalPlayer(), 0.0, 0.0, 60.0, MathParser.formatExpression(expression)+" = "+R2S(MathParser.calculate(expression)))
endif
endif
endmethod
implement CalcInit
endstruct
module CalcInit
private static method onInit takes nothing returns nothing
local trigger t = CreateTrigger()
local code c = function thistype.onEnter
local integer i = 0
loop
exitwhen i > 11
call TriggerRegisterPlayerChatEvent(t, Player(i), "", false)
set i = i + 1
endloop
call TriggerAddCondition(t, Filter(c))
set t = null
set c = null
endmethod
endmodule
endlibraryMathParser struct
readonly static real ansStores the last result of the evaluation method. Initialized as 0.
static method calculate takes string expression returns realUse this method to calculate a mathematic expression presented as a string. Allowed values are numbers, the decimal seperator, basic arithmetic operators like +, -, *, / and ^ as well as parenthesis. You can also put "ans" into the expression to refer to the last calculation result. Error messages on math and syntax errors will be displayed if specified so in the configurable globals. The syntax parsing strictly follows Matlab conventions.
static method formatExpression takes string expression returns stringUse this method to format an user defined expression so that it looks nice. Compare the IngameCalculator trigger for an example usage.
3.2. Matrices
This is another Extension to the basic Maths library which gives you the possiblity to perform Matrix operations in Warcraft 3. Matrices can basically be used like 2D-Arrays with this library. The library also provides advanced methods to initialize, reshape or to perform calculations with Matrices. Gaußian Eliminiation with pivotising is implemented as well as solving a System of Linear Equations (SLE), inverting or transposing a Matrix as well as calculating the norm, condition or trace.
This library will serve as a base for more advanced libraries in the future which allow curve fitting, trajectory interpolation and many more.
JASS:
library Matrices /* v 1.1.0.1
**********************************************************************************
*
* Matrices
* ¯¯¯¯¯¯¯¯
* By looking_for_help aka eey
*
* This system provides advanced methods for handling Matrices in Warcraft 3.
* Features like Matrix multiplication, calculation of norms or trace as well as
* solving a system of linear equations with Gauss-Elimination are implemented.
* The system also provides a big variety of functions to initialize, copy or
* reshape Matrices.
*
* Credits go to Magtheridon for helping with the Systems API.
*
**********************************************************************************
*
* Requirements
* ¯¯¯¯¯¯¯¯¯¯¯¯
* */ uses Maths /* hiveworkshop.com/forums/spells-569/advanced-maths-ingame-calculator-234024/?prev=r%3D20%26page%3D5
*
**********************************************************************************
*
* Implementation
* ¯¯¯¯¯¯¯¯¯¯¯¯¯¯
* To use this system just copy it into an empty trigger in your map. As this
* system uses the Math library you should install it first to get the system
* to work. The Math library can be found under the link above.
*
**********************************************************************************
*
* System API
* ¯¯¯¯¯¯¯¯¯¯
*
* Struct usage
* -----------------------------
*
* struct Matrix
* - This struct provides the methods and logic to use Matrices in
* Warcraft 3 with this system. Use the create method to allocate a
* new instance of a Matrix of your desired size. The Matrix can then
* be used like a 2D-Array (example displayed above) and provides
* various methods to perform advanced Matrix operations.
*
* 0 1 2
* 0 [0][0][0]
* local Matrix mat = Matrix.create(3, 3) = 1 [0][0][0]
* 2 [0][0][0]
*
*
* Operators
* -----------------------------
*
* [] operators
* - Use the [] operators to access directly to the values of a given
* Matrix. For example mat[2][1] will return the element in the third
* row, second column. Note that the indices are, like Wc3 arrays,
* zero-based.
*
*
* Fields
* -----------------------------
*
* readonly integer n
* - Specifies the number of rows of a given Matrix.
*
* readonly integer m
* - Specifies the number of columns of a given Matrix.
*
* readonly static Matrix Invalid_Matrix
* - An invalid Matrix of the size 0 x 0. You can't create such a Matrix,
* so if you need one, use this field. Some algorithms, such as solveSLE
* return such a Matrix if no solution for a given System of Linear
* Equations could be found. You can use the method isValid() to
* determine wether a Matrix is valid or not.
*
* static constant integer ONE_NORM
* - Use this as a parameter for the norm method to specify that the method
* should calculate the one norm (maximum of column sum absolute values).
*
* static constant integer EUCLIDEAN_NORM
* - Use this as a parameter for the norm method to specify that the method
* should calculate the euclidean norm (square root of sum of squares).
*
* static constant integer INFINITY_NORM
* - Use this as a parameter for the norm method to specify that the method
* should calculate the infinity norm (maximum of row sum absolute values).
*
* static constant integer METHOD_ROW_WISE
* - Use this as a parameter for methods like initStepWise or reShape to
* specify whether the method should be applied row-wise.
*
* static constant integer METHOD_COL_WISE
* - Use this as a parameter for methods like initStepWise or reShape to
* specify whether the method should be applied col-wise.
*
*
* Methods
* -----------------------------
*
* static method create takes integer nDim, integer mDim returns Matrix
* - Creates a new n x m Matrix with the maximum size of MAX_MATRIX_SIZE
* (specified in the globals block). The Matrix is initialized with
* zeros.
*
* method destroy takes nothing returns nothing
* - Destroys a given Matrix to free its memory usage.
*
* method display takes nothing returns nothing
* - Use this method to display a Matrix ingame. This is especially
* meant for debugging issues.
*
* method isValid takes nothing returns boolean
* - Checks whether a given Matrix is valid (means: not empty) or not.
*
* method isEqual takes Matrix mat returns boolean
* - Checks whether two Matrices are equal or not. If A == B then
* A.isEqual(B) returns true.
*
* method init takes real value returns nothing
* - Use this method to initialize a Matrix with a desired real value.
* Note that this method does not create a new instance of the Matrix
* object, as well as all methods that only initialize the values of a
* Matrix.
*
* method eye takes nothing returns nothing
* - Use this method to initialize an Identity Matrix.
*
* method diag takes real value, integer whichDiagonal returns nothing
* - Use this method to initialize a Diagonal Matrix with a desired real
* value. Use the second argument to specify which diagonal you want
* to set (zero is the main diagonal, negative values address the
* upper, positive values the lower diagonals).
*
* method rand takes real lowerBound, real upperBound returns nothing
* - Use this method to initialize a Matrix with random real values.
*
* method initStepWise takes real startValue, real steps returns nothing
* - Use this method to initialize a matrix from a given start value in
* ascending or descending order specified by the steps parameter.
*
* method assign takes nothing returns Matrix
* - Use this method to assign a Matrix to another Matrix. For example
* set B = A.assign() will copy A to B. Note that A and B must be of
* equal size for this operation to work.
*
* method addScalar takes real value returns Matrix
* - This method performs a element-wise addition of a given real value
* and returns the new Matrix. Example: A.addScalar(2.0) will add the
* value 2.0 to all elements of the Matrix A.
*
* method subScalar takes real value returns Matrix
* - This method performs a element-wise subtraction of a given real
* value.
*
* method mulScalar takes real value returns Matrix
* - This method performs a element-wise multiplication by a given real
* value.
*
* method divScalar takes real value returns Matrix
* - This method performs a element-wise division by a given real value.
*
* method abs takes nothing returns Matrix
* - This method performs the abs function on all Matrix elements.
*
* method add takes Matrix whichMatrix returns Matrix
* - Matrix addition. The expression A.add(B) where both A and B are
* Matrices returns the resulting Matrix A + B. Note that the Matrices
* must follow common Matrix calculation rules, like here that A and B
* have the same size.
*
* method sub takes Matrix whichMatrix returns MAtrix
* - Matrix substraction. Same as the add method, A.sub(B) performs
* A - B.
*
* method multiply takes Matrix whichMatrix returns Matrix
* - Matrix multiplication. The expression A.multiply(B) performs the
* operation A*B. Note that A's number of columns must equal B's
* number of rows for this operation to be well-defined.
*
* method transpose takes nothing returns Matrix
* - Matrix transposition. The expression A.transpose() computes A^T.
*
* method invert takes nothing returns Matrix
* - Matrix inversion. Use A.invert() to calculate A^-1, the inverse
* of the Matrix A. Be aware of the fact that not every Matrix is
* invertable.
*
* method gauss takes nothing returns Matrix
* - Use this method to perform a Gauss-Elimination with pivotising.
* The result is a upper triangular Matrix.
*
* method solveSLE takes Matrix b returns Matrix
* - Use this method to solve a System of Linear Equations following
* the common notation A*x = b. To calculate x use A.solveSLE(b)
* where A is the system Matrix and b is the solution vector. If the
* SLE has no unique solution, an invalid vector of size 0 x 0 is
* returned.
*
* method dotProduct takes Matrix b returns real
* - Use this method to calculate the dot product of two Vectors. Use
* it like a.dotProduct(b), which results in a^T*b. Calling this
* method is faster than performing the transposition manualy and
* should therefore be used if possible. To check whether two Vectors
* are orthogonal, the dot product must be zero.
*
* method crossProduct takes Matrix b returns Matrix
* - Use this method to calculate the cross product of two Vectors.
* This implementation only supports calculation of cross products
* for Vectors in R^3.
*
* method trace takes nothing returns real
* - Returns the trace of a given Matrix. Which is defined as the sum
* over its diagonal elements.
*
* method det takes nothing returns real
* - Returns the determinant of a given Matrix. From A.det() == 0
* follows for example that A is not invertable.
*
* method rank takes nothing returns integer
* - Returns the rank of a given Matrix. A square Matrix must have full
* rank to be invertable, which means that A.rank() == A.n must return
* true.
*
* method norm takes integer whichNorm returns real
* - Computes the norm of a given Matrix. You can choose between different
* norms by using the constants defined in the Matrix struct. Valid
* values for the whichNorm parameter are ONE_NORM, EUCLIDEAN_NORM
* and the INFINITY_NORM.
*
* method cond takes integer whichNorm returns real
* - Computes the condition of a Matrix. You can specify which Norm you
* want to use for that purpose by the parameter whichNorm (see method
* norm). Note that the Matrix must be invertable otherwise the
* condition will be infinity.
*
* method subMatrix takes integer startRow, integer startCol, integer endRow,
* integer endCol returns Matrix
* - This method can be used to get a sub Matrix out of another Matrix.
* With the parameters startRow and startCol you can specify where
* the submatrix should begin and the parameters endRow as well as
* endCol define where to end the sub Matrix. If A is for example
* a 3 x 3 Matrix, A.subMatrix(0, 0, 2, 0) will return the first
* column Vector of A, while A.subMatrix(0, 0, 1, 1) will return
* the first 2 x 2 sub Matrix of A and so on.
*
* method embed takes Matrix subMat, integer startRow, integer startCol
* returns Matrix
* - This method embeds one Matrix into another. If you have for example
* the 3 x 3 Matrix A and the 2 x 2 Matrix B then A.embed(B, 0, 0)
* will assign the upper left sub matrix of A to the values of B. The
* parameters startRow and startCol specify where the embeding should
* start. Of course the sub matrix must fit into the Matrix you want to
* embed it into, otherwise an error will be thrown.
*
* method concatH takes Matrix mat returns Matrix
* - Use this method to concatenate two Matrices. The Matrices must
* have the same amount of rows for this operation to work. The Matrices
* will get concatenated horizontal, resulting for two n x m
* Matrices in a n x 2*m Matrix. Example: A.concatH(B) will concate-
* nate A to B (from the left side).
*
* method concatV takes Matrix mat returns Matrix
* - Use this method to concatenate two Matrices. The Matrices must
* have the same amount of columns for this operation to work. The
* Matrices will get concatenated vertically, resulting for two n x m
* Matrices in a 2*n x m Matrix. Example: A.concatV(B) will stack
* the Matrix B on A.
*
* method reShape takes integer newN, integer newM, integer whichMethod
* returns Matrix
* - Use this method to reshape a Matrix. If you have for example a
* 3 x 2 Matrix A, by performing A.reShape(2, 3, METHOD_ROW_WISE)
* the Matrix will get a 2 x 3 Matrix. The third parameter whichMethod
* determines whether the operation should be done row-wise or
* column-wise. METHOD_ROW_WISE and METHOD_COL_WISE are valid
* parameters. This can also be used to make a Vektor of a Matrix
* (or vice versa): A.reShape(6, 1, METHOD_COL_WISE) will stack
* all column Vektors of A to one 6 x 1 Vektor.
*
* method switchRow takes integer whichRow, integer newRow returns Matrix
* - Use this method to switch two different rows of a Matrix. The
* expression A.switchRow(0, 2) will switch the first with the third
* row. Note that both parameters whichRow and newRow must not exceed
* Matrix dimensions.
*
* method switchCol takes integer whichCol, integer newCol returns Matrix
* - Use this method to switch two different columns of a Matrix. Same
* rules as for switchRow apply here.
*
*********************************************************************************/
globals
/*************************************************************************
* Configurable globals
*************************************************************************/
// Accuracy for considering a Matrix too close to singularity
private constant real EPSILON = 0.01
// Do you want the system to display debug error messages?
private constant boolean DISPLAY_MATRIX_ERRORS = true
// Biggest possible n x n-Matrix
private constant integer MAX_MATRIX_SIZE = 50
/*************************************************************************
* End of configurable globals
*************************************************************************/
endglobals
private struct MatrixRow
real array values[MAX_MATRIX_SIZE]
integer maxCols
method operator [] takes integer column returns real
return this.values[column]
endmethod
method operator []= takes integer column, real value returns nothing
debug if column < 0 or column >= maxCols then
debug call ThrowError(true, "Matrices", "[]=", "MatrixRow", this, "Can't access Matrix! Index exceeds Matrix dimensions!")
debug endif
set this.values[column] = value
endmethod
static method create takes integer cols returns thistype
local thistype this = MatrixRow.allocate()
set this.maxCols = cols
return this
endmethod
endstruct
private module Inits
private static method onInit takes nothing returns nothing
set Matrix.Invalid_Matrix = Matrix.createInvalid()
endmethod
endmodule
struct Matrix
private MatrixRow array matRow[MAX_MATRIX_SIZE]
static constant integer ONE_NORM = 1
static constant integer EUCLIDEAN_NORM = 2
static constant integer INFINITY_NORM = 3
static constant integer METHOD_ROW_WISE = 0
static constant integer METHOD_COL_WISE = 1
readonly static Matrix Invalid_Matrix
readonly integer n
readonly integer m
method operator [] takes integer row returns MatrixRow
debug if row < 0 or row >= n then
debug call ThrowError(true, "Matrices", "[]", "Matrix", this, "Can't access Matrix! Index exceeds Matrix dimensions!")
debug endif
return this.matRow[row]
endmethod
static method create takes integer nDim, integer mDim returns thistype
local integer i = 0
local thistype this
if nDim < 1 or mDim < 1 then
debug call ThrowError(true, "Matrices", "create", "Matrix", 0, "Invalid Matrix!")
endif
set this = Matrix.allocate()
loop
exitwhen i > nDim - 1
set this.matRow[i] = MatrixRow.create(mDim)
set i = i + 1
endloop
set this.n = nDim
set this.m = mDim
return this
endmethod
private static method createInvalid takes nothing returns thistype
local thistype this = Matrix.allocate()
set this.n = 0
set this.m = 0
return this
endmethod
method isValid takes nothing returns boolean
return this.n == 0
endmethod
method isEqual takes Matrix mat returns boolean
local integer i = 0
local integer j = 0
if this.n != mat.n or this.m != mat.m then
return false
endif
loop
exitwhen i >= n
loop
exitwhen j >= m
if this.matRow[i][j] != mat[i][j] then
return false
endif
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return true
endmethod
method addScalar takes real value returns Matrix
local integer i = 0
local integer j = 0
local Matrix mat
debug if n < 1 then
debug call ThrowError(true, "Matrices", "addScalar", "Matrix", this, "Invalid Matrix!")
debug endif
set mat = Matrix.create(n, m)
loop
exitwhen i >= n
loop
exitwhen j >= m
set mat[i][j] = this.matRow[i][j] + value
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return mat
endmethod
method subScalar takes real value returns Matrix
local integer i = 0
local integer j = 0
local Matrix mat
debug if n < 1 then
debug call ThrowError(true, "Matrices", "subScalar", "Matrix", this, "Invalid Matrix!")
debug endif
set mat = Matrix.create(n, m)
loop
exitwhen i >= n
loop
exitwhen j >= m
set mat[i][j] = this.matRow[i][j] - value
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return mat
endmethod
method multScalar takes real value returns Matrix
local integer i = 0
local integer j = 0
local Matrix mat
debug if n < 1 then
debug call ThrowError(true, "Matrices", "multScalar", "Matrix", this, "Invalid Matrix!")
debug endif
set mat = Matrix.create(n, m)
loop
exitwhen i >= n
loop
exitwhen j >= m
set mat[i][j] = this.matRow[i][j]*value
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return mat
endmethod
method divScalar takes real value returns Matrix
local integer i = 0
local integer j = 0
local Matrix mat
debug if n < 1 then
debug call ThrowError(true, "Matrices", "divScalar", "Matrix", this, "Invalid Matrix!")
debug endif
set mat = Matrix.create(n, m)
loop
exitwhen i >= n
loop
exitwhen j >= m
set mat[i][j] = this.matRow[i][j]/value
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return mat
endmethod
method abs takes nothing returns Matrix
local integer i = 0
local integer j = 0
local Matrix mat
debug if n < 1 then
debug call ThrowError(true, "Matrices", "abs", "Matrix", this, "Invalid Matrix!")
debug endif
set mat = Matrix.create(n, m)
loop
exitwhen i >= n
loop
exitwhen j >= m
if this.matRow[i][j] >= 0 then
set mat[i][j] = this.matRow[i][j]
else
set mat[i][j] = -this.matRow[i][j]
endif
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return mat
endmethod
method eye takes real value returns nothing
local integer i = 0
local integer j = 0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "eye", "Matrix", this, "Invalid Matrix!")
debug endif
loop
exitwhen j >= n
loop
exitwhen i >= m
if i != j then
set this.matRow[j][i] = 0.0
else
set this.matRow[j][i] = 1.0
endif
set i = i + 1
endloop
set i = 0
set j = j + 1
endloop
endmethod
method diag takes real value, integer whichDiagonal returns nothing
local integer i = 0
local integer j = 0
local integer minDim
debug if n < 1 then
debug call ThrowError(true, "Matrices", "diag", "Matrix", this, "Invalid Matrix!")
debug endif
if n <= m then
set minDim = n - 1
else
set minDim = m - 1
endif
debug if whichDiagonal > minDim then
debug call ThrowError(true, "Matrices", "diag", "Matrix", this, "Diagonal Index exceeds Matrix dimensions!")
debug endif
loop
exitwhen j >= n
loop
exitwhen i >= m
if i != j - whichDiagonal then
set this.matRow[j][i] = 0.0
else
set this.matRow[j][i] = value
endif
set i = i + 1
endloop
set i = 0
set j = j + 1
endloop
endmethod
method init takes real value returns nothing
local integer i = 0
local integer j = 0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "init", "Matrix", this, "Invalid Matrix!")
debug endif
loop
exitwhen j >= n
loop
exitwhen i >= m
set this.matRow[j][i] = value
set i = i + 1
endloop
set i = 0
set j = j + 1
endloop
endmethod
method rand takes real lowerBound, real upperBound returns nothing
local integer i = 0
local integer j = 0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "rand", "Matrix", this, "Invalid Matrix!")
debug endif
loop
exitwhen j >= n
loop
exitwhen i >= m
set this.matRow[j][i] = GetRandomReal(lowerBound, upperBound)
set i = i + 1
endloop
set i = 0
set j = j + 1
endloop
endmethod
method initStepWise takes real startValue, real step, integer whichMethod returns nothing
local integer i = 0
local integer j = 0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "initStepWise", "Matrix", this, "Invalid Matrix!")
debug endif
debug if (whichMethod != METHOD_ROW_WISE and whichMethod != METHOD_COL_WISE) then
debug call ThrowError(true, "Matrices", "initStepWise", "Matrix", this, "Invalid method for initializing!")
debug endif
if whichMethod == METHOD_ROW_WISE then
loop
exitwhen j >= n
loop
exitwhen i >= m
set this.matRow[j][i] = startValue
set startValue = startValue + step
set i = i + 1
endloop
set i = 0
set j = j + 1
endloop
elseif whichMethod == METHOD_COL_WISE then
loop
exitwhen j >= m
loop
exitwhen i >= n
set this.matRow[i][j] = startValue
set startValue = startValue + step
set i = i + 1
endloop
set i = 0
set j = j + 1
endloop
endif
endmethod
method add takes Matrix mat returns Matrix
local Matrix result
local integer i = 0
local integer j = 0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "add", "Matrix", this, "Invalid Matrix!")
debug endif
debug if mat.n != this.n or mat.m != this.m then
debug call ThrowError(true, "Matrices", "add", "Matrix", this, "Matrices must be of same dimension!")
debug endif
set result = Matrix.create(n, m)
loop
exitwhen j >= n
loop
exitwhen i >= m
set result[j][i] = this.matRow[j][i] + mat[j][i]
set i = i + 1
endloop
set i = 0
set j = j + 1
endloop
return result
endmethod
method sub takes Matrix mat returns Matrix
local Matrix result
local integer i = 0
local integer j = 0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "sub", "Matrix", this, "Invalid Matrix!")
debug endif
debug if mat.n != this.n or mat.m != this.m then
debug call ThrowError(true, "Matrices", "sub", "Matrix", this, "Matrices must be of same dimension!")
debug endif
set result = Matrix.create(n, m)
loop
exitwhen j >= n
loop
exitwhen i >= m
set result[j][i] = this.matRow[j][i] - mat[j][i]
set i = i + 1
endloop
set i = 0
set j = j + 1
endloop
return result
endmethod
method multiply takes Matrix mat returns Matrix
local Matrix result
local integer i = 0
local integer j = 0
local integer k = 0
local real temp = 0.0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "multiply", "Matrix", this, "Invalid Matrix!")
debug endif
debug if this.m != mat.n then
debug call ThrowError(true, "Matrices", "multiply", "Matrix", this, "Matrix dimensions must agree!")
debug endif
set result = Matrix.create(n, mat.m)
loop
exitwhen j >= result.n
loop
exitwhen k >= result.m
loop
exitwhen i >= this.m
set temp = temp + this.matRow[j][i]*mat[i][k]
set i = i + 1
endloop
set result[j][k] = temp
set i = 0
set temp = 0.0
set k = k + 1
endloop
set k = 0
set j = j + 1
endloop
return result
endmethod
method transpose takes nothing returns Matrix
local Matrix mat = Matrix.create(m, n)
local integer i = 0
local integer j = 0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "transpose", "Matrix", this, "Invalid Matrix!")
debug endif
loop
exitwhen j >= m
loop
exitwhen i >= n
set mat[j][i] = this.matRow[i][j]
set i = i + 1
endloop
set i = 0
set j = j + 1
endloop
return mat
endmethod
method gauss takes nothing returns Matrix
local Matrix mat
local integer i = 0
local integer j = 0
local integer k = 0
local integer row
local real maxVal = -Math.Inf
local real pivot
debug if n < 1 then
debug call ThrowError(true, "Matrices", "gauss", "Matrix", this, "Invalid Matrix!")
debug endif
set mat = this.assign()
loop
exitwhen i >= n - 1
set j = i + 1
set row = i
loop
exitwhen j >= n
set pivot = Math.abs(mat[j][i])
if pivot > maxVal then
set maxVal = pivot
set row = j
endif
set j = j + 1
endloop
if row != i then
set j = 0
loop
exitwhen j >= m
set pivot = mat[i][j]
set mat[i][j] = mat[row][j]
set mat[row][j] = pivot
set j = j + 1
endloop
endif
set j = i + 1
loop
exitwhen j >= n
set pivot = mat[j][i]/mat[i][i]
set k = i
loop
exitwhen k >= n
set mat[j][k] = mat[j][k] - pivot*mat[i][k]
set k = k + 1
endloop
set j = j + 1
endloop
set i = i + 1
endloop
return mat
endmethod
method invert takes nothing returns Matrix
local Matrix mat
local Matrix inv
local integer i = 0
local integer j = 0
local integer k = 0
local integer row
local real maxVal = -Math.Inf
local real pivot
local real temp_inv
debug if n < 1 then
debug call ThrowError(true, "Matrices", "invert", "Matrix", this, "Invalid Matrix!")
debug endif
set mat = this.assign()
set inv = Matrix.create(n, n)
call inv.eye(n)
loop
exitwhen i >= n - 1
set j = i + 1
set row = i
loop
exitwhen j >= n
set pivot = Math.abs(mat[j][i])
if pivot > maxVal then
set maxVal = pivot
set row = j
endif
set j = j + 1
endloop
if row != i then
set j = 0
loop
exitwhen j >= m
set pivot = mat[i][j]
set mat[i][j] = mat[row][j]
set mat[row][j] = pivot
set temp_inv = inv[i][j]
set inv[i][j] = inv[row][j]
set inv[row][j] = temp_inv
set j = j + 1
endloop
endif
set j = i + 1
loop
exitwhen j >= n
set pivot = mat[j][i]/mat[i][i]
set k = 0
loop
exitwhen k >= n
set mat[j][k] = mat[j][k] - pivot*mat[i][k]
set inv[j][k] = inv[j][k] - pivot*inv[i][k]
set k = k + 1
endloop
set j = j + 1
endloop
set i = i + 1
endloop
set i = n - 1
loop
exitwhen i < 0
set j = i - 1
loop
exitwhen j < 0
set pivot = mat[j][i]/mat[i][i]
set mat[j][i] = mat[j][i] - pivot*mat[i][i]
set k = 0
loop
exitwhen k >= m
set inv[j][k] = inv[j][k] - pivot*inv[i][k]
set k = k + 1
endloop
set j = j - 1
endloop
set i = i - 1
endloop
set i = 0
loop
exitwhen i >= n
set j = 0
loop
exitwhen j >= m
set inv[i][j] = inv[i][j]/mat[i][i]
set j = j + 1
endloop
set i = i + 1
endloop
call mat.destroy()
return inv
endmethod
method trace takes nothing returns real
local integer i = 0
local integer minDim
local real result = 0.0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "trace", "Matrix", this, "Invalid Matrix!")
debug endif
if n <= m then
set minDim = n - 1
else
set minDim = m - 1
endif
loop
exitwhen i > minDim
set result = result + this.matRow[i][i]
set i = i + 1
endloop
return result
endmethod
method assign takes nothing returns Matrix
local integer i = 0
local integer j = 0
local Matrix mat = Matrix.create(n, m)
if n < 1 then
set mat = Invalid_Matrix
return mat
endif
loop
exitwhen i >= n
loop
exitwhen j >= m
set mat[i][j] = this.matRow[i][j]
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return mat
endmethod
method rank takes nothing returns integer
local Matrix mat = this.assign()
local integer minDim
local integer i
local integer rank
debug if n < 1 then
debug call ThrowError(true, "Matrices", "rank", "Matrix", this, "Invalid Matrix!")
debug endif
if n <= m then
set minDim = n - 1
else
set minDim = m - 1
endif
set i = minDim
set rank = minDim + 1
set mat = this.gauss()
loop
exitwhen i < 1
if Math.abs(mat[i][i]) < EPSILON then
set rank = rank - 1
endif
set i = i - 1
endloop
return rank
endmethod
method cond takes integer whichNorm returns real
local Matrix mat
local real result
debug if n < 1 then
debug call ThrowError(true, "Matrices", "cond", "Matrix", this, "Invalid Matrix!")
debug endif
set mat = this.assign()
set mat = this.multiply(mat.invert())
set result = mat.norm(whichNorm)
call mat.destroy()
return result
endmethod
method det takes nothing returns real
local Matrix mat
local integer i = 0
local real result = 1.0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "det", "Matrix", this, "Invalid Matrix!")
debug endif
debug if n != m then
debug call ThrowError(true, "Matrices", "det", "Matrix", this, "Matrix must be square!")
debug endif
set mat = this.assign()
set mat = mat.gauss()
loop
exitwhen i >= n
set result = result*mat[i][i]
set i = i + 1
endloop
if Math.abs(result) < EPSILON then
set result = 0.0
endif
call mat.destroy()
return result
endmethod
method solveSLE takes Matrix b returns Matrix
local Matrix mat
local Matrix sol
local Matrix x
local integer i = 0
local integer j = 0
local integer k = 0
local integer row
local real maxVal = -Math.Inf
local real pivot
debug if n < 1 then
debug call ThrowError(true, "Matrices", "solveSLE", "Matrix", this, "Invalid Matrix!")
debug endif
debug if this.n != this.m or b.n != this.n or b.m > 1 then
debug call ThrowError(true, "Matrices", "solveSLE", "Matrix", this, "Invalid Matrices used! Can't solve SLE!")
debug endif
set mat = this.assign()
set sol = b.assign()
set x = Matrix.create(b.n, 1)
loop
exitwhen i >= n - 1
set j = i + 1
set row = i
loop
exitwhen j >= n
set pivot = Math.abs(mat[j][i])
if pivot > maxVal then
set maxVal = pivot
set row = j
endif
set j = j + 1
endloop
if Math.abs(pivot) < EPSILON then
return Matrix.Invalid_Matrix
endif
if row != i then
set j = 0
loop
exitwhen j >= m
set pivot = mat[i][j]
set mat[i][j] = mat[row][j]
set mat[row][j] = pivot
set j = j + 1
endloop
set pivot = sol[i][0]
set sol[i][0] = sol[row][0]
set sol[row][0] = pivot
endif
set j = i + 1
loop
exitwhen j >= n
set pivot = mat[j][i]/mat[i][i]
set k = i
loop
exitwhen k >= n
set mat[j][k] = mat[j][k] - pivot*mat[i][k]
set k = k + 1
endloop
set sol[j][0] = sol[j][0] - pivot*sol[i][0]
set j = j + 1
endloop
set i = i + 1
endloop
set x[x.n - 1][0] = sol[x.n - 1][0]/mat[n - 1][n - 1]
set i = x.n - 2
loop
exitwhen i < 0
set pivot = sol[i][0]
set j = i + 1
loop
exitwhen j >= n
set pivot = pivot - mat[i][j]*x[j][0]
set j = j + 1
endloop
set x[i][0] = pivot/mat[i][i]
set i = i - 1
endloop
call sol.destroy()
call mat.destroy()
return x
endmethod
method norm takes integer whichNorm returns real
local integer i = 0
local integer j = 0
local real result
local real maxVal = -Math.Inf
debug if n < 1 then
debug call ThrowError(true, "Matrices", "norm", "Matrix", this, "Invalid Matrix!")
debug endif
debug if whichNorm != ONE_NORM and whichNorm != EUCLIDEAN_NORM and whichNorm != INFINITY_NORM then
debug call ThrowError(true, "Matrices", "[]", "Matrix", this, "Invalid Norm used!")
debug endif
if whichNorm == ONE_NORM then
set result = 0.0
loop
exitwhen i >= m
loop
exitwhen j >= n
set result = result + Math.abs(this.matRow[j][i])
set j = j + 1
endloop
if result > maxVal then
set maxVal = result
endif
set result = 0.0
set j = 0
set i = i + 1
endloop
return maxVal
elseif whichNorm == EUCLIDEAN_NORM then
set result = 0.0
loop
exitwhen i >= n
loop
exitwhen j >= m
set result = result + this.matRow[i][j]*this.matRow[i][j]
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return SquareRoot(result)
else
set result = 0.0
loop
exitwhen i >= n
loop
exitwhen j >= m
set result = result + Math.abs(this.matRow[i][j])
set j = j + 1
endloop
if result > maxVal then
set maxVal = result
endif
set result = 0.0
set j = 0
set i = i + 1
endloop
return maxVal
endif
endmethod
method dotProduct takes Matrix mat returns real
local real temp = 0.0
local integer i = 0
local integer j = 0
debug if n < 1 or mat.n < 1 then
debug call ThrowError(true, "Matrices", "dotProduct", "Matrix", this, "Invalid Matrix!")
debug endif
debug if mat.m != 1 or this.m != 1 then
debug call ThrowError(true, "Matrices", "dotProduct", "Matrix", this, "Dot-Product is only defined for Vectors!")
debug endif
debug if mat.n != this.n then
debug call ThrowError(true, "Matrices", "dotProduct", "Matrix", this, "Dot-Product is only defined for Vectors of same length!")
debug endif
loop
exitwhen i > n
set temp = temp + this.matRow[i][1]*mat[i][1]
set i = i + 1
endloop
return temp
endmethod
method crossProduct takes Matrix mat returns Matrix
local Matrix result
debug if n < 1 or mat.n < 1 then
debug call ThrowError(true, "Matrices", "crossProduct", "Matrix", this, "Invalid Matrix!")
debug endif
debug if mat.m != 1 or this.m != 1 then
debug call ThrowError(true, "Matrices", "crossProduct", "Matrix", this, "Cross-Product is only defined for Vectors!")
debug endif
debug if mat.n != this.n then
debug call ThrowError(true, "Matrices", "crossProduct", "Matrix", this, "Cross-Product is only defined for Vectors of same length!")
debug endif
debug if mat.n != 3 or this.n != 3 then
debug call ThrowError(true, "Matrices", "crossProduct", "Matrix", this, "This implementation only supports Cross-Products for Vectors in R^3")
debug endif
set result = Matrix.create(3, 1)
set result[0][0] = this.matRow[1][0]*mat[2][0] - this.matRow[2][0]*mat[1][0]
set result[1][0] = this.matRow[2][0]*mat[0][0] - this.matRow[0][0]*mat[2][0]
set result[2][0] = this.matRow[0][0]*mat[1][0] - this.matRow[1][0]*mat[0][0]
return result
endmethod
method reShape takes integer newN, integer newM, integer whichMethod returns Matrix
local Matrix mat
local integer i = 0
local integer j = 0
local integer row = 0
local integer col = 0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "reShape", "Matrix", this, "Invalid Matrix!")
debug endif
debug if newN*newM != n*m then
debug call ThrowError(true, "Matrices", "reShape", "Matrix", this, "Reshape not possible! Dimension missmatch!")
debug endif
debug if newN < 1 or newM < 1 then
debug call ThrowError(true, "Matrices", "reShape", "Matrix", this, "Reshape not possible! Index must be greater than zero!")
debug endif
debug if n == 0 then
debug call ThrowError(true, "Matrices", "reShape", "Matrix", this, "Reshape not possible! Matrix is invalid!")
debug endif
debug if whichMethod != METHOD_ROW_WISE and whichMethod != METHOD_COL_WISE then
debug call ThrowError(true, "Matrices", "reShape", "Matrix", this, "Invalid method for reshaping!")
debug endif
set mat = Matrix.create(newN, newM)
if whichMethod == METHOD_ROW_WISE then
loop
exitwhen i >= n
loop
exitwhen j >= m
set mat[row][col] = this.matRow[i][j]
set col = col + 1
if col >= mat.m then
set row = row + 1
set col = 0
endif
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
elseif whichMethod == METHOD_COL_WISE then
loop
exitwhen i >= m
loop
exitwhen j >= n
set mat[row][col] = this.matRow[j][i]
set col = col + 1
if col >= mat.m then
set row = row + 1
set col = 0
endif
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
endif
return mat
endmethod
method embed takes Matrix subMat, integer startRow, integer startCol returns Matrix
local Matrix mat
local integer i = 0
local integer j = 0
debug if n == 0 or subMat.n == 0 then
debug call ThrowError(true, "Matrices", "embed", "Matrix", this, "Can't embed sub Matrix! This is an invalid Matrix!")
debug endif
debug if startRow < 0 or startCol < 0 then
debug call ThrowError(true, "Matrices", "embed", "Matrix", this, "Can't merge Matrices! Index must be greater than 0!")
debug endif
debug if startRow + subMat.n - 1 > n or startCol + subMat.m - 1 > m then
debug call ThrowError(true, "Matrices", "embed", "Matrix", this, "Can't merge Matrices! Matrices don't fit!")
debug endif
set mat = this.assign()
loop
exitwhen i >= subMat.n
loop
exitwhen j >= subMat.m
set mat[i + startRow][j + startCol] = subMat[i][j]
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return mat
endmethod
method subMatrix takes integer startRow, integer startCol, integer endRow, integer endCol returns Matrix
local Matrix mat
local integer i = 0
local integer j = 0
debug if n == 0 then
debug call ThrowError(true, "Matrices", "subMatrix", "Matrix", this, "Can't determine sub Matrix! This is an invalid Matrix!")
debug endif
debug if endRow < startRow or endCol < startCol then
debug call ThrowError(true, "Matrices", "subMatrix", "Matrix", this, "Can't determine sub Matrix! Size of sub Matrix smaller 1 x 1!")
debug endif
debug if endRow > n - 1 or endCol > m - 1 then
debug call ThrowError(true, "Matrices", "subMatrix", "Matrix", this, "Sub Matrix exceeds Matrix dimensions!")
debug endif
set mat = Matrix.create(endRow - startRow + 1, endCol - startCol + 1)
loop
exitwhen i >= mat.n
loop
exitwhen j >= mat.m
set mat[i][j] = this.matRow[i + startRow][j + startCol]
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return mat
endmethod
method concatV takes Matrix mat returns Matrix
local Matrix result
local integer i = 0
local integer j = 0
debug if n == 0 or m == 0 then
debug call ThrowError(true, "Matrices", "concatV", "Matrix", this, "Can't concat Invalid Matrices!")
debug endif
debug if m != mat.m then
debug call ThrowError(true, "Matrices", "concatV", "Matrix", this, "Can't concat Matrices! Matrix column dimensions must be equal!")
debug endif
set result = Matrix.create(n + mat.n, m)
loop
exitwhen i >= n
loop
exitwhen j >= m
set result[i][j] = mat[i][j]
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
set i = 0
set j = 0
loop
exitwhen i >= n
loop
exitwhen j >= m
set result[i + n][j] = this.matRow[i][j]
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return result
endmethod
method concatH takes Matrix mat returns Matrix
local Matrix result
local integer i = 0
local integer j = 0
debug if n == 0 or m == 0 then
debug call ThrowError(true, "Matrices", "concatH", "Matrix", this, "Can't concat Invalid Matrices!")
debug endif
debug if n != mat.n then
debug call ThrowError(true, "Matrices", "concatH", "Matrix", this, "Can't concat Matrices! Matrix row dimensions must be equal!")
debug endif
set result = Matrix.create(n, m + mat.m)
loop
exitwhen i >= n
loop
exitwhen j >= m
set result[i][j] = this.matRow[i][j]
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
set i = 0
set j = 0
loop
exitwhen i >= n
loop
exitwhen j >= m
set result[i][j + m] = mat[i][j]
set j = j + 1
endloop
set j = 0
set i = i + 1
endloop
return result
endmethod
method switchRow takes integer whichRow, integer newRow returns nothing
local real temp
local integer i = 0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "switchRow", "Matrix", this, "Invalid Matrix!")
debug endif
debug if whichRow < 0 or whichRow >= n or newRow < 0 or newRow >= n then
debug call ThrowError(true, "Matrices", "switchRow", "Matrix", this, "Can't switch row. Index exceeds Matrix dimensions!")
debug endif
loop
exitwhen i >= this.m
set temp = this.matRow[newRow][i]
set this.matRow[newRow][i] = this.matRow[whichRow][i]
set this.matRow[whichRow][i] = temp
set i = i + 1
endloop
endmethod
method switchCol takes integer whichCol, integer newCol returns nothing
local real temp
local integer i = 0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "switchCol", "Matrix", this, "Invalid Matrix!")
debug endif
debug if whichCol < 0 or whichCol >= n or newCol < 0 or newCol >= n then
debug call ThrowError(true, "Matrices", "switchCol", "Matrix", this, "Can't switch column. Index exceeds Matrix dimensions!")
debug endif
loop
exitwhen i >= this.n
set temp = this.matRow[i][newCol]
set this.matRow[i][newCol] = this.matRow[i][whichCol]
set this.matRow[i][whichCol] = temp
set i = i + 1
endloop
endmethod
method display takes nothing returns nothing
local string s = ""
local integer i = 0
local integer j = 0
debug if n < 1 then
debug call ThrowError(true, "Matrices", "display", "Matrix", this, "Invalid Matrix!")
debug endif
loop
exitwhen j >= this.n
loop
exitwhen i >= this.m
set s = s + " " + R2S(this.matRow[j][i])
set i = i + 1
endloop
call DisplayTimedTextToPlayer(GetLocalPlayer(), 0.0, 0.0, 60.0, s)
set s = ""
set i = 0
set j = j + 1
endloop
endmethod
implement Inits
endstruct
endlibrary
JASS:
scope Example initializer Init
private function Init takes nothing returns nothing
/**********************************************************************************
*
* Example Code
* ¯¯¯¯¯¯¯¯¯¯¯¯
*
* Solves the Linear System of Equations A*x = b for
*
* [1][4][7] [x1] [1] [ 0]
* [17][5][8] * [x2] = [2] with the solution x = [ 2] approximately.
* [3][6][9] [x3] [3] [-1]
*
* Feel free to try out more.
*
**********************************************************************************/
// Create a 3 x 3 system Matrix A
local Matrix A = Matrix.create(3, 3)
// Create a 3 x 1 solution Vector b
local Matrix b = Matrix.create(3, 1)
// Instanciate the unknown Vector x
local Matrix x
// Initialize Matrix A in ascending order (col-wise)
call A.initStepWise(1.0, 1.0, Matrix.METHOD_COL_WISE)
// Set the element in the second row, first column of A to 17.0
set A[1][0] = 17.0
// Initialize Vector b (row-wise)
call b.initStepWise(1.0, 1.0, Matrix.METHOD_ROW_WISE)
// Solve SLE
set x = A.solveSLE(b)
// Display A, b and x
call A.display()
call DisplayTimedTextToPlayer(GetLocalPlayer(), 0.0, 0.0, 60.0, " ")
call b.display()
call DisplayTimedTextToPlayer(GetLocalPlayer(), 0.0, 0.0, 60.0, " ")
call x.display()
endfunction
endscopeMatrix struct
[] operatorsUse the [] operators to access directly to the values of a given Matrix. For example mat[2][1] will return the element in the third row, second column. Note that the indices are, like Wc3 arrays, zero-based.
readonly integer nSpecifies the number of rows of a given Matrix.
readonly integer mSpecifies the number of columns of a given Matrix.
readonly static Matrix Invalid_MatrixAn invalid Matrix of the size 0 x 0. You can't create such a Matrix, so if you need one, use this field. Some algorithms, such as solveSLE return such a Matrix if no solution for a given System of Linear Equations could be found. You can use the method isValid() to determine wether a Matrix is valid or not.
static constant integer ONE_NORMUse this as a parameter for the norm method to specify that the method should calculate the one norm (maximum of column sum absolute values).
static constant integer EUCLIDEAN_NORMUse this as a parameter for the norm method to specify that the method should calculate the euclidean norm (square root of sum of squares).
static constant integer INFINITY_NORMUse this as a parameter for the norm method to specify that the method should calculate the infinity norm (maximum of row sum absolute values).
static constant integer METHOD_ROW_WISEUse this as a parameter for methods like initStepWise or reShape to specify whether the method should be applied row-wise.
static constant integer METHOD_COL_WISEUse this as a parameter for methods like initStepWise or reShape to specify whether the method should be applied col-wise.
static method create takes integer nDim, integer mDim returns MatrixCreates a new n x m Matrix with the maximum size of MAX_MATRIX_SIZE (specified in the globals block). The Matrix is initialized with zeros.
method destroy takes nothing returns nothingDestroys a given Matrix to free its memory usage.
method display takes nothing returns nothingUse this method to display a Matrix ingame. This is especially meant for debugging issues.
method isValid takes nothing returns booleanChecks whether a given Matrix is valid (means: not empty) or not.
method isEqual takes Matrix mat returns booleanChecks whether two Matrices are equal or not. If A == B then A.isEqual(B) returns true.
method init takes real value returns nothingUse this method to initialize a Matrix with a desired real value. Note that this method does not create a new instance of the Matrix object, as well as all methods that only initialize the values of a Matrix.
method eye takes nothing returns nothingUse this method to initialize an Identity Matrix.
method diag takes real value, integer whichDiagonal returns nothingUse this method to initialize a Diagonal Matrix with a desired real value. Use the second argument to specify which diagonal you want to set (zero is the main diagonal, negative values address the upper, positive values the lower diagonals).
method rand takes real lowerBound, real upperBound returns nothingUse this method to initialize a Matrix with random real values.
method initStepWise takes real startValue, real steps returns nothingUse this method to initialize a matrix from a given start value in ascending or descending order specified by the steps parameter.
method assign takes nothing returns MatrixUse this method to assign a Matrix to another Matrix. For example set B = A.assign() will copy A to B. Note that A and B must be of equal size for this operation to work.
method addScalar takes real value returns MatrixThis method performs a element-wise addition of a given real value and returns the new Matrix. Example: A.addScalar(2.0) will add the value 2.0 to all elements of the Matrix A.
method subScalar takes real value returns MatrixThis method performs a element-wise subtraction of a given real value.
method mulScalar takes real value returns MatrixThis method performs a element-wise multiplication by a given real value.
method divScalar takes real value returns MatrixThis method performs a element-wise division by a given real value.
method abs takes nothing returns MatrixThis method performs the abs function on all Matrix elements.
method add takes Matrix whichMatrix returns MatrixMatrix addition. The expression A.add(B) where both A and B are Matrices returns the resulting Matrix A + B. Note that the Matrices must follow common Matrix calculation rules, like here that A and B have the same size.
method sub takes Matrix whichMatrix returns MatrixMatrix substraction. Same as the add method, A.sub(B) performs A - B.
method multiply takes Matrix whichMatrix returns MatrixMatrix multiplication. The expression A.multiply(B) performs the operation A*B. Note that A's number of columns must equal B's number of rows for this operation to be well-defined.
method transpose takes nothing returns MatrixMatrix transposition. The expression A.transpose() computes A^T.
method invert takes nothing returns MatrixMatrix inversion. Use A.invert() to calculate A^-1, the inverse of the Matrix A. Be aware of the fact that not every Matrix is invertable.
method gauss takes nothing returns MatrixUse this method to perform a Gauss-Elimination with pivotising. The result is a upper triangular Matrix.
method solveSLE takes Matrix b returns MatrixUse this method to solve a System of Linear Equations following the common notation A*x = b. To calculate x use A.solveSLE(b) where A is the system Matrix and b is the solution vector. If the SLE has no unique solution, an invalid vector of size 0 x 0 is returned.
method dotProduct takes Matrix b returns realUse this method to calculate the dot product of two Vectors. Use it like a.dotProduct(b), which results in a^T*b. Calling this method is faster than performing the transposition manualy and should therefore be used if possible. To check whether two Vectors are orthogonal, the dot product must be zero.
method crossProduct takes Matrix b returns MatrixUse this method to calculate the cross product of two Vectors. This implementation only supports calculation of cross products for Vectors in R^3.
method trace takes nothing returns realReturns the trace of a given Matrix. Which is defined as the sum over its diagonal elements.
method det takes nothing returns realReturns the determinant of a given Matrix. From A.det() == 0 follows for example that A is not invertable.
method rank takes nothing returns integerReturns the rank of a given Matrix. A square Matrix must have full rank to be invertable, which means that A.rank() == A.n must return true.
method norm takes integer whichNorm returns realComputes the norm of a given Matrix. You can choose between different norms by using the constants defined in the Matrix struct. Valid values for the whichNorm parameter are ONE_NORM, EUCLIDEAN_NORM and the INFINITY_NORM.
method cond takes integer whichNorm returns realComputes the condition of a Matrix. You can specify which Norm you want to use for that purpose by the parameter whichNorm (see method norm). Note that the Matrix must be invertable otherwise the condition will be infinity.
method subMatrix takes integer startRow, integer startCol, integer endRow, integer endCol returns MatrixThis method can be used to get a sub Matrix out of another Matrix. With the parameters startRow and startCol you can specify where the submatrix should begin and the parameters endRow as well as endCol define where to end the sub Matrix. If A is for example a 3 x 3 Matrix, A.subMatrix(0, 0, 2, 0) will return the first column Vector of A, while A.subMatrix(0, 0, 1, 1) will return the first 2 x 2 sub Matrix of A and so on.
method embed takes Matrix subMat, integer startRow, integer startCol returns MatrixThis method embeds one Matrix into another. If you have for example the 3 x 3 Matrix A and the 2 x 2 Matrix B then A.embed(B, 0, 0) will assign the upper left sub matrix of A to the values of B. The parameters startRow and startCol specify where the embeding should start. Of course the sub matrix must fit into the Matrix you want to embed it into, otherwise an error will be thrown.
method concatH takes Matrix mat returns MatrixUse this method to concatenate two Matrices. The Matrices must have the same amount of rows for this operation to work. The Matrices will get concatenated horizontal, resulting for two n x m Matrices in a n x 2*m Matrix. Example: A.concatH(B) will concatenate A to B (from the left side).
method concatV takes Matrix mat returns MatrixUse this method to concatenate two Matrices. The Matrices must have the same amount of columns for this operation to work. The Matrices will get concatenated vertically, resulting for two n x m Matrices in a 2*n x m Matrix. Example: A.concatV(B) will stack the Matrix B on A.
method reShape takes integer newN, integer newM, integer whichMethod returns MatrixUse this method to reshape a Matrix. If you have for example a 3 x 2 Matrix A, by performing A.reShape(2, 3, METHOD_ROW_WISE) the Matrix will get a 2 x 3 Matrix. The third parameter whichMethod determines whether the operation should be done row-wise or column-wise. METHOD_ROW_WISE and METHOD_COL_WISE are valid parameters. This can also be used to make a Vektor of a Matrix (or vice versa): A.reShape(6, 1, METHOD_COL_WISE) will stack all column Vektors of A to one 6 x 1 Vektor.
method switchRow takes integer whichRow, integer newRow returns MatrixUse this method to switch two different rows of a Matrix. The expression A.switchRow(0, 2) will switch the first with the third row. Note that both parameters whichRow and newRow must not exceed Matrix dimensions.
method switchCol takes integer whichCol, integer newCol returns MatrixUse this method to switch two different columns of a Matrix. Same rules as for switchRow apply here.
4. Screenshots
Enclosed are some screenshots of the testmap, showing some of the ingame calculations from the MathParser Extension.
5. Accuracy and Performance
The following tables show the accuracy of the natural logarithm function which is used to calculate al other logarithms as well as the hyperbolic functions and their inverses. Also performance for all math functions is displayed in an extra table. Finally the efficiency of the isPrime method is analysed and compared towards the standard brute force attempt.
As it is shown in the following table, the logarithm reaches extremly high accuracies. This is important because
many other functions can be computed by using logarithms, therefore high acuracy is required. The logarithm
functions Ln1 to Ln5 from the table were taken from this Snippet by BlinkBoy.
The following table shows the OP-Limit values for new math functions. As the table shows, nearly all functions
are very efficient and can be used without any problems. Critical methods in terms of performance are isPrime,
mergeFloat and the factorial of an integer number.
The diagram shows the efficiency of the isPrime method. The system uses a deterministic version of the Miller-
Rabin test. While the standard brute-force attempt can only detect primes up to ~5003 before it hits the OP-Limit,
this method can detect much higher primes. As the diagram shows, the OP-Limit is quite alternating but stays
basically at the same mean. This method allows to detect primes efficiently up to ~100000.
Hope you enjoy it!
Greetings,
lfh
Keywords:
Advanced Mathematics, Math, Calculator, Ingame calculator, interpreter, logarithm, hyperbolic
Contents
Reviews
- Joined
- Dec 12, 2012
- Messages
- 1,007
Because the custom ones are more accurate than the native ones. Try this:
JASS:
function AccuracyTest takes nothing returns nothing
call BJDebugMsg(R2S(bj_PI*bj_PI*bj_PI*bj_PI*bj_PI*bj_PI*bj_PI*bj_PI))
call BJDebugMsg(R2S(Math.Pi*Math.Pi*Math.Pi*Math.Pi*Math.Pi*Math.Pi*Math.Pi*Math.Pi))
endfunctionIt will display
9488.462 for bj_PI and
9488.537 for Math.Pi while
9488.531... is the correct value.
The value 3.141593 is the best in terms of accuracy which doesn't bug (higher accuracies can cause bugs under some circumstances). Therefore it makes sense to use custom values for both Pi and E.
What do you mean? Input them into the system?
- Joined
- Mar 6, 2006
- Messages
- 9,240
- Joined
- Dec 12, 2008
- Messages
- 7,379
Wasn't the limit 9 digits of precision? (Hence why
0.031250000 actually works)
- Joined
- Dec 12, 2012
- Messages
- 1,007
The
0.031250000 = 3.125000 E-02
real datatype has float precision, therefore 7 significant digits.0.031250000 actually has only 7 significant digits, because leading zeros can get shifted away by using the "best" exponent, which is done on OS level:0.031250000 = 3.125000 E-02
- Joined
- Dec 12, 2008
- Messages
- 7,379
I see.
We weren't even sure they were floats though lol
For all we know, Blizzard could be implementing their own Float-like datatype because the coders wanted to confuse their managers with lots of uncommon words like mantissa so they look like they know what they're doing
We weren't even sure they were floats though lol
For all we know, Blizzard could be implementing their own Float-like datatype because the coders wanted to confuse their managers with lots of uncommon words like mantissa so they look like they know what they're doing
- Joined
- Jul 6, 2009
- Messages
- 1,885
Signum function is usually written as sgn(), not sig().
Code Reviewer
- Joined
- May 9, 2006
- Messages
- 3,522
See http://www.hiveworkshop.com/forums/2353639-post42.html - he is implementing it with maths reference in mind, as opposed computer science.
- Joined
- Dec 12, 2012
- Messages
- 1,007
Update to Version 1.1.0.0
- Reworked the basic Maths library
- Removed redundant functions like rand, sin, cos etc
- Now using ErrorMessage for having normal behaviour and standard output
- Renamed the StringParser library to MathParser
- MathParser library is now no longer an optional module but a seperated struct which requires Maths
- Added the new library Matrices to the documentation as well as to the testmap
- Reworked the basic Maths library
- Removed redundant functions like rand, sin, cos etc
- Now using ErrorMessage for having normal behaviour and standard output
- Renamed the StringParser library to MathParser
- MathParser library is now no longer an optional module but a seperated struct which requires Maths
- Added the new library Matrices to the documentation as well as to the testmap
- Joined
- Mar 19, 2010
- Messages
- 870
I know what that means
- Joined
- Oct 29, 2012
- Messages
- 1,474
1+1 ? Very good tool for noobs tho! 5/5 works perfectly
- Joined
- Jul 12, 2008
- Messages
- 3,138
I don't think you understand what this is actually capable of. This isn't a "1+1" sort of calculator. It's not something you take out to do your homework with. It's for all sorts of high level calculations that you might need to be automatically done in-game. Yeah, even if you know calculus, you're not going to be there in-game to pause and run the calculation on paper every time the trigger needing it goes through. You need a system that can automatically run these calculations for your script throughout the game, and that's what this does.
It's not just "noobs" who would find use in this. In fact, it's noobs (likely you, even) who won't find use in this because they've never tried to use that sort of math while scripting and don't see this system's potential for use. It really annoys me when some newbie goes to a very advanced and adequate system and tries to pretend he's above its level.
- Joined
- Oct 29, 2012
- Messages
- 1,474
Mr. Dude , I know that this tool is useful while scripting , But scripting in game? XD
I am noob I accept? -_____________-
- Joined
- Oct 16, 2008
- Messages
- 10,450
You don't script in-game, no one even said that... I think you're misunderstanding his explanation...
Sometimes you want to make systems that require such complex calculations, that is where this system comes in...
or maybe you simply thought that the included calculator is the core of this system, which is not as that is just a simple example of how to use this system...
and unless you actually know those calculations in real life, I doubt that you'll likely to use this system (or at least use it effectively)...
Code Reviewer
- Joined
- May 9, 2006
- Messages
- 3,522
Hi,
Depending on the response, this might become useful:
http://www.hiveworkshop.com/forums/lab-715/jass-benchmarking-results-245362/index5.html#post2463882
Depending on the response, this might become useful:
http://www.hiveworkshop.com/forums/lab-715/jass-benchmarking-results-245362/index5.html#post2463882
- Joined
- Jan 25, 2011
- Messages
- 64
The last thing it needs is binary to decimal converter (and vice-versa). I made one if you want.
+rep, i have tried to do an ingame calculator many times (many fails)
+rep, i have tried to do an ingame calculator many times (many fails)
- Joined
- Jul 17, 2011
- Messages
- 1,864
so many fucking noob comments.. anyway you have an error in the matrix lib line 1168 should be debug endif instead of just endif
- Joined
- Dec 12, 2012
- Messages
- 1,007
Hi, yes why not. You can post it in the Jass section, once it got approved I can add it to this collection.
Nice find, thanks! Updated Matrix library to version 1.1.0.1.
Spell Reviewer
- Joined
- Nov 18, 2012
- Messages
- 1,870
I would make the same question.
A cientific calculator would be much better than implementing the system and increasing the map size with add-ins.
Or... this is useful when the user doesn't have a calculator at home. I still like the idea.
- Joined
- Nov 16, 2012
- Messages
- 663
Helpful for Math Assignments. 
+Rep !
+Rep !
- Joined
- Jul 13, 2012
- Messages
- 86
Geez, at least you don't have to get a calculator, or alt-tab for a calculator. THIS IS GREAT
Many haters, keep hating...
- Joined
- Feb 6, 2014
- Messages
- 2,466
Very well done. Very useful. Everything is there.
I might use this for complex in-game calculation.
I might use this for complex in-game calculation.
- Joined
- Jul 12, 2008
- Messages
- 3,138
Here we go, another one...
This isn't just for spitting out answers to do your math homework. This is for allowing your triggers to automatically do calculations in-game that they couldn't normally, when needing to calculate certain integer or real values to use for something.
If you don't know what this could be used for, you probably don't know anywhere near enough about writing code to have a use for this in the first place.
I'm not saying I'm pro; I don't write JASS and won't have much use for this system myself, however I at least have a good enough understanding of it to know what it can be used for.
- Joined
- Feb 6, 2014
- Messages
- 2,466
Hahaha, another one bites the dust.
Tutorial Reviewer
- Joined
- Jun 9, 2011
- Messages
- 13,183
bullshit detected. If you can create a system that calculate something you can obviously calculate whatever it is, in game by yourself since both of you are using the same language (in the end it all ends up as jass).
- Joined
- Feb 6, 2014
- Messages
- 2,466
But it is easier, example instead of creating all the codes for calculating logarithms, factorials, natural logarithms, isPrime, etc., with this system, it is already at your disposal with just using a function and some copy pasting.
Just like the reason why people use systems, for easy use.
Tutorial Reviewer
- Joined
- Jun 9, 2011
- Messages
- 13,183
I never said that it couldn't be useful. However I fail to see why you would used so advanced calculations in wc3 modding so the usage seems limited. Anyway, did not come here to say that.
This is what I replied to.
- Joined
- Feb 6, 2014
- Messages
- 2,466
A lot of natural phenomenon has a logarithmic rate. Maybe you want to imitate/simulate that or something. It's depends on someone's creativity if he will find this useful or not. Maybe this is useful in Missile system that wants a very accurate representation of i.e. projectile motions. Another example is if you want to create a spell called Capacitor Charging that increases damage based on the exponential rate of a capacitor's increase in voltage. It would be impossible to do this if you don't know how to create a custom log function. This system allows us to use a lot of mathematical functions out there.
>This is what I replied to
For example you want to know if a certain variable is prime for whatever reason, there is no way to do this using a native Jass function. Then this will come in handy.
Last edited:
Tutorial Reviewer
- Joined
- Jun 9, 2011
- Messages
- 13,183
If there's a system for it, you can do it yourself. Since this calculator can check if it's a prime number, then your code can as well. Worth it? depends.
Once again, I never said that it isn't handy. The quote stated that it simply was impossible to do the math without the system, which is wrong.
- Joined
- Feb 6, 2014
- Messages
- 2,466
Tell me, how can a someone simply make a code that check if a number is prime number? It's not something you can easily do without having to research a lot. From my perspective, that is what Infernal Tater mean. There is no native function that checks if a number is prime. One does not simply able to know if a number is prime in-game. People couldn't normally do that and people couldn't normally make a function that checks if a number is prime.
- Joined
- Dec 12, 2008
- Messages
- 7,379
I like this.
How about Modular Matrix Exponentiation?
How about Modular Matrix Exponentiation?
- Joined
- Jul 12, 2008
- Messages
- 3,138
You can't normally; not without writing complex code to do so.
Sure, if a number is seven, you know yourself that it is prime, but the game will have no clue unless you write code to determine it; there is no in-game function for it.
Just like you can't normally save data as an elaborate encoded line of text that players can type to load in future games, without using a system either written by yourself or someone else.
It's a system. It doesn't mean you can't do it yourself, but you can't do it without writing a lot of code yourself; the point of this system is to save you the time. Every system can technically be done yourself; it was made by another human being, and you're a human being. You could spend years learning to JASS. You could then spend weeks writing your own systems. You can do it all yourself if you want to, and there's nothing wrong with that. But that doesn't mean that everything is "useless", it saves other people time.
When you buy food, by your definition, it would be "useless" because you can obtain and cook food yourself; all your purchase did was save you time. When you bought your computer/bought parts to build your computer, you could have spend your life learning how to build computer parts, and built it yourself. So your motherboard was useless. Your house is "useless" because you could build one yourself over time.
Do you see the point I'm trying to make? Just because you can do something yourself doesn't make it useless. Everything you get is prepared by other people to save you time and effort. That doesn't make it useless.
Last edited:
- Joined
- Dec 12, 2008
- Messages
- 7,379
Oooh! I know!
Pollard-Rho for Integer Factorization!
Just for the heck of it!
Pollard-Rho for Integer Factorization!
Just for the heck of it!
- Joined
- Dec 12, 2012
- Messages
- 1,007
Of course. But thats nothing new, right?
The whole point of systems is that not everyone has do do everything himself
Maybe you misunderstood something here. This is not really a single system but more a math framework. So the calculator and the math core (where the isPrime function is located) are not the same thing.
Of course you can write your own prime checking method, but doing this efficient is not as easy as it seems at first. Thats why this library uses the Miller-Rabin test which is very efficient.
But Shadow Flux and InfernalTater explained that quite nicely already
Magtheridon96 said:
Hm, maybe, I will take a look at it
- Joined
- Aug 1, 2013
- Messages
- 4,657
I was wondering...
vs
I am sorry for not trying to understand your "isPrime", but as far as I can see, mine is much easier to understand and may be quite a bit faster.
Another approach would be slightly the same but instead of "i+=2", you do "nextPrime()", knowing integers are 2^31-1 at max and the squareroot of that is <46341, you only need all primes listed until 46337 (the last prime before 46341)... which actually fits inside a normal array.... so:
Another approach is to store all primes until 2^31-1 in a hashtable (because there are more than 8190) and check if num is equal to that value... but who cares.
also
JASS:
static method isPrime takes integer n returns boolean
local integer s
local integer d
local integer a = 2
local integer temp
local integer counter
local integer dSave
local integer modulus
local boolean firstTest = false
local boolean secondTest = false
if n == 2 or n == 7 or n == 61 then
return true
elseif isEven(n) or n < 2 then
return false
endif
static if STORE_DETECTED_PRIMES then
if LoadBoolean(h, n, 0) then
return LoadBoolean(h, n, 1)
endif
endif
if n < 157 then
set a = n
loop
exitwhen a == 1
if modInt(n, a) == 0 and a != n then
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, false)
endif
return false
endif
set a = a - 1
endloop
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, true)
endif
return true
endif
set s = R2I(floor(log2(n - 1)))
loop
set temp = R2I(Pow(2, I2R(s)))
exitwhen modInt(n - 1, temp) == 0
set s = s - 1
endloop
set d = (n - 1)/(R2I(Pow(2, I2R(s))))
set dSave = d
set a = 2
set counter = 0
loop
exitwhen counter > s
set modulus = expMod(a, d, n)
if (counter == 0 and modulus == 1) or (counter > 0 and modulus - n == -1) then
set firstTest = true
exitwhen true
endif
set d = 2*d
set counter = counter + 1
if counter == 1 then
set d = dSave
endif
endloop
if not firstTest then
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, false)
endif
return false
endif
set a = 7
set d = dSave
set counter = 0
loop
exitwhen counter > s
set modulus = expMod(a, d, n)
if (counter == 0 and modulus == 1) or (counter > 0 and modulus - n == -1) then
if firstTest then
set secondTest = true
exitwhen true
endif
endif
set d = 2*d
set counter = counter + 1
if counter == 1 then
set d = dSave
endif
endloop
if not secondTest then
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, false)
endif
return false
endif
set a = 61
set d = dSave
set counter = 0
loop
exitwhen counter > s
set modulus = expMod(a, d, n)
if (counter == 0 and modulus == 1) or (counter > 0 and modulus - n == -1) then
if secondTest then
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, true)
endif
return true
endif
endif
set d = 2*d
set counter = counter + 1
if counter == 1 then
set d = dSave
endif
endloop
static if STORE_DETECTED_PRIMES then
call SaveBoolean(h, n, 0, true)
call SaveBoolean(h, n, 1, false)
endif
return false
endmethod
JASS:
//Returns wether num is a prime or not.
static method isPrime takes integer num returns boolean
local integer i
local real x
local integer max
if num == 2 then
//num is 2. (Only even prime.)
return true
endif
if num == 1 or num <= 0 or modInt(num, 2) == 0 then
//num is 1, not positive or num is dividable by 2. (2 itself is already filtered out.)
return false
endif
set i = 3
set max = R2I(SquareRoot(num))//No need to check if 99*x = 101. At max 10*10 would be "usefull" to check.
loop
exitwhen i > max
//If num is dividable by i, then it is not a prime.
//if modInt(num, i) == 0. then
// return false
//endif
//Now that we are talking about uninteresting stuff. Lets remove half of the mod:
set x = I2R(num)/i
if x == R2I(x) then
// num/i is an integer.
return false
endif
set i = i +2
endloop
return true
endmethodAnother approach would be slightly the same but instead of "i+=2", you do "nextPrime()", knowing integers are 2^31-1 at max and the squareroot of that is <46341, you only need all primes listed until 46337 (the last prime before 46341)... which actually fits inside a normal array.... so:
JASS:
function isPrime takes integer num returns boolean
local integer i
local real x
local integer max
if num == 1 or num <= 0 then
return false
endif
set i = 0
set max = R2I(SquareRoot(num))
loop
exitwhen PRIMES[i] > max
set x = I2R(num)/PRIMES[i]
if x == R2I(x) then
return false
endif
set i = i +1
endloop
return true
endfunction
function Init takes nothing returns nothing
set PRIMES[0] = 2
set PRIMES[1] = 3
set PRIMES[2] = 5
set PRIMES[3] = 7
set PRIMES[4] = 11
set PRIMES[5] = 13
set PRIMES[6] = 17
set PRIMES[7] = 19
set PRIMES[8] = 23
set PRIMES[9] = 29
set PRIMES[10] = 31
set PRIMES[11] = 37
set PRIMES[12] = 41
set PRIMES[13] = 43
set PRIMES[14] = 47
set PRIMES[15] = 53
set PRIMES[16] = 59
set PRIMES[17] = 61
set PRIMES[18] = 67
set PRIMES[19] = 71
set PRIMES[20] = 73
set PRIMES[21] = 79
set PRIMES[22] = 83
set PRIMES[23] = 89
set PRIMES[24] = 97
set PRIMES[25] = 101
set PRIMES[26] = 103
set PRIMES[27] = 107
set PRIMES[28] = 109
set PRIMES[29] = 113
set PRIMES[30] = 127
set PRIMES[31] = 131
set PRIMES[32] = 137
set PRIMES[33] = 139
set PRIMES[34] = 149
set PRIMES[35] = 151
set PRIMES[36] = 157
set PRIMES[37] = 163
set PRIMES[38] = 167
set PRIMES[39] = 173
set PRIMES[40] = 179
set PRIMES[41] = 181
set PRIMES[42] = 191
set PRIMES[43] = 193
set PRIMES[44] = 197
set PRIMES[45] = 199
set PRIMES[46] = 211
set PRIMES[47] = 223
set PRIMES[48] = 227
set PRIMES[49] = 229
set PRIMES[50] = 233
set PRIMES[51] = 239
set PRIMES[52] = 241
set PRIMES[53] = 251
set PRIMES[54] = 257
set PRIMES[55] = 263
set PRIMES[56] = 269
set PRIMES[57] = 271
set PRIMES[58] = 277
set PRIMES[59] = 281
set PRIMES[60] = 283
set PRIMES[61] = 293
set PRIMES[62] = 307
set PRIMES[63] = 311
set PRIMES[64] = 313
set PRIMES[65] = 317
set PRIMES[66] = 331
set PRIMES[67] = 337
set PRIMES[68] = 347
set PRIMES[69] = 349
set PRIMES[70] = 353
set PRIMES[71] = 359
set PRIMES[72] = 367
set PRIMES[73] = 373
set PRIMES[74] = 379
set PRIMES[75] = 383
set PRIMES[76] = 389
set PRIMES[77] = 397
set PRIMES[78] = 401
set PRIMES[79] = 409
set PRIMES[80] = 419
set PRIMES[81] = 421
set PRIMES[82] = 431
set PRIMES[83] = 433
set PRIMES[84] = 439
set PRIMES[85] = 443
set PRIMES[86] = 449
set PRIMES[87] = 457
set PRIMES[88] = 461
set PRIMES[89] = 463
set PRIMES[90] = 467
set PRIMES[91] = 479
set PRIMES[92] = 487
set PRIMES[93] = 491
set PRIMES[94] = 499
set PRIMES[95] = 503
set PRIMES[96] = 509
set PRIMES[97] = 521
set PRIMES[98] = 523
set PRIMES[99] = 541
set PRIMES[100] = 547
set PRIMES[101] = 557
set PRIMES[102] = 563
set PRIMES[103] = 569
set PRIMES[104] = 571
set PRIMES[105] = 577
set PRIMES[106] = 587
set PRIMES[107] = 593
set PRIMES[108] = 599
set PRIMES[109] = 601
set PRIMES[110] = 607
set PRIMES[111] = 613
set PRIMES[112] = 617
set PRIMES[113] = 619
set PRIMES[114] = 631
set PRIMES[115] = 641
set PRIMES[116] = 643
set PRIMES[117] = 647
set PRIMES[118] = 653
set PRIMES[119] = 659
set PRIMES[120] = 661
set PRIMES[121] = 673
set PRIMES[122] = 677
set PRIMES[123] = 683
set PRIMES[124] = 691
set PRIMES[125] = 701
set PRIMES[126] = 709
set PRIMES[127] = 719
set PRIMES[128] = 727
set PRIMES[129] = 733
set PRIMES[130] = 739
set PRIMES[131] = 743
set PRIMES[132] = 751
set PRIMES[133] = 757
set PRIMES[134] = 761
set PRIMES[135] = 769
set PRIMES[136] = 773
set PRIMES[137] = 787
set PRIMES[138] = 797
set PRIMES[139] = 809
set PRIMES[140] = 811
set PRIMES[141] = 821
set PRIMES[142] = 823
set PRIMES[143] = 827
set PRIMES[144] = 829
set PRIMES[145] = 839
set PRIMES[146] = 853
set PRIMES[147] = 857
set PRIMES[148] = 859
set PRIMES[149] = 863
set PRIMES[150] = 877
set PRIMES[151] = 881
set PRIMES[152] = 883
set PRIMES[153] = 887
set PRIMES[154] = 907
set PRIMES[155] = 911
set PRIMES[156] = 919
set PRIMES[157] = 929
set PRIMES[158] = 937
set PRIMES[159] = 941
set PRIMES[160] = 947
set PRIMES[161] = 953
set PRIMES[162] = 967
set PRIMES[163] = 971
set PRIMES[164] = 977
set PRIMES[165] = 983
set PRIMES[166] = 991
set PRIMES[167] = 997
set PRIMES[168] = 1009
set PRIMES[169] = 1013
set PRIMES[170] = 1019
set PRIMES[171] = 1021
set PRIMES[172] = 1031
set PRIMES[173] = 1033
set PRIMES[174] = 1039
set PRIMES[175] = 1049
set PRIMES[176] = 1051
set PRIMES[177] = 1061
set PRIMES[178] = 1063
set PRIMES[179] = 1069
set PRIMES[180] = 1087
set PRIMES[181] = 1091
set PRIMES[182] = 1093
set PRIMES[183] = 1097
set PRIMES[184] = 1103
set PRIMES[185] = 1109
set PRIMES[186] = 1117
set PRIMES[187] = 1123
set PRIMES[188] = 1129
set PRIMES[189] = 1151
set PRIMES[190] = 1153
set PRIMES[191] = 1163
set PRIMES[192] = 1171
set PRIMES[193] = 1181
set PRIMES[194] = 1187
set PRIMES[195] = 1193
set PRIMES[196] = 1201
set PRIMES[197] = 1213
set PRIMES[198] = 1217
set PRIMES[199] = 1223
set PRIMES[200] = 1229
set PRIMES[201] = 1231
set PRIMES[202] = 1237
set PRIMES[203] = 1249
set PRIMES[204] = 1259
set PRIMES[205] = 1277
set PRIMES[206] = 1279
set PRIMES[207] = 1283
set PRIMES[208] = 1289
set PRIMES[209] = 1291
set PRIMES[210] = 1297
set PRIMES[211] = 1301
set PRIMES[212] = 1303
set PRIMES[213] = 1307
set PRIMES[214] = 1319
set PRIMES[215] = 1321
set PRIMES[216] = 1327
set PRIMES[217] = 1361
set PRIMES[218] = 1367
set PRIMES[219] = 1373
set PRIMES[220] = 1381
set PRIMES[221] = 1399
set PRIMES[222] = 1409
set PRIMES[223] = 1423
set PRIMES[224] = 1427
set PRIMES[225] = 1429
set PRIMES[226] = 1433
set PRIMES[227] = 1439
set PRIMES[228] = 1447
set PRIMES[229] = 1451
set PRIMES[230] = 1453
set PRIMES[231] = 1459
set PRIMES[232] = 1471
set PRIMES[233] = 1481
set PRIMES[234] = 1483
set PRIMES[235] = 1487
set PRIMES[236] = 1489
set PRIMES[237] = 1493
set PRIMES[238] = 1499
set PRIMES[239] = 1511
set PRIMES[240] = 1523
set PRIMES[241] = 1531
set PRIMES[242] = 1543
set PRIMES[243] = 1549
set PRIMES[244] = 1553
set PRIMES[245] = 1559
set PRIMES[246] = 1567
set PRIMES[247] = 1571
set PRIMES[248] = 1579
set PRIMES[249] = 1583
set PRIMES[250] = 1597
set PRIMES[251] = 1601
set PRIMES[252] = 1607
set PRIMES[253] = 1609
set PRIMES[254] = 1613
set PRIMES[255] = 1619
set PRIMES[256] = 1621
set PRIMES[257] = 1627
set PRIMES[258] = 1637
set PRIMES[259] = 1657
set PRIMES[260] = 1663
set PRIMES[261] = 1667
set PRIMES[262] = 1669
set PRIMES[263] = 1693
set PRIMES[264] = 1697
set PRIMES[265] = 1699
set PRIMES[266] = 1709
set PRIMES[267] = 1721
set PRIMES[268] = 1723
set PRIMES[269] = 1733
set PRIMES[270] = 1741
set PRIMES[271] = 1747
set PRIMES[272] = 1753
set PRIMES[273] = 1759
set PRIMES[274] = 1777
set PRIMES[275] = 1783
set PRIMES[276] = 1787
set PRIMES[277] = 1789
set PRIMES[278] = 1801
set PRIMES[279] = 1811
set PRIMES[280] = 1823
set PRIMES[281] = 1831
set PRIMES[282] = 1847
set PRIMES[283] = 1861
set PRIMES[284] = 1867
set PRIMES[285] = 1871
set PRIMES[286] = 1873
set PRIMES[287] = 1877
set PRIMES[288] = 1879
set PRIMES[289] = 1889
set PRIMES[290] = 1901
set PRIMES[291] = 1907
set PRIMES[292] = 1913
set PRIMES[293] = 1931
set PRIMES[294] = 1933
set PRIMES[295] = 1949
set PRIMES[296] = 1951
set PRIMES[297] = 1973
set PRIMES[298] = 1979
set PRIMES[299] = 1987
set PRIMES[300] = 1993
set PRIMES[301] = 1997
set PRIMES[302] = 1999
set PRIMES[303] = 2003
set PRIMES[304] = 2011
set PRIMES[305] = 2017
set PRIMES[306] = 2027
set PRIMES[307] = 2029
set PRIMES[308] = 2039
set PRIMES[309] = 2053
set PRIMES[310] = 2063
set PRIMES[311] = 2069
set PRIMES[312] = 2081
set PRIMES[313] = 2083
set PRIMES[314] = 2087
set PRIMES[315] = 2089
set PRIMES[316] = 2099
set PRIMES[317] = 2111
set PRIMES[318] = 2113
set PRIMES[319] = 2129
set PRIMES[320] = 2131
set PRIMES[321] = 2137
set PRIMES[322] = 2141
set PRIMES[323] = 2143
set PRIMES[324] = 2153
set PRIMES[325] = 2161
set PRIMES[326] = 2179
set PRIMES[327] = 2203
set PRIMES[328] = 2207
set PRIMES[329] = 2213
set PRIMES[330] = 2221
set PRIMES[331] = 2237
set PRIMES[332] = 2239
set PRIMES[333] = 2243
set PRIMES[334] = 2251
set PRIMES[335] = 2267
set PRIMES[336] = 2269
set PRIMES[337] = 2273
set PRIMES[338] = 2281
set PRIMES[339] = 2287
set PRIMES[340] = 2293
set PRIMES[341] = 2297
set PRIMES[342] = 2309
set PRIMES[343] = 2311
set PRIMES[344] = 2333
set PRIMES[345] = 2339
set PRIMES[346] = 2341
set PRIMES[347] = 2347
set PRIMES[348] = 2351
set PRIMES[349] = 2357
set PRIMES[350] = 2371
set PRIMES[351] = 2377
set PRIMES[352] = 2381
set PRIMES[353] = 2383
set PRIMES[354] = 2389
set PRIMES[355] = 2393
set PRIMES[356] = 2399
set PRIMES[357] = 2411
set PRIMES[358] = 2417
set PRIMES[359] = 2423
set PRIMES[360] = 2437
set PRIMES[361] = 2441
set PRIMES[362] = 2447
set PRIMES[363] = 2459
set PRIMES[364] = 2467
set PRIMES[365] = 2473
set PRIMES[366] = 2477
set PRIMES[367] = 2503
set PRIMES[368] = 2521
set PRIMES[369] = 2531
set PRIMES[370] = 2539
set PRIMES[371] = 2543
set PRIMES[372] = 2549
set PRIMES[373] = 2551
set PRIMES[374] = 2557
set PRIMES[375] = 2579
set PRIMES[376] = 2591
set PRIMES[377] = 2593
set PRIMES[378] = 2609
set PRIMES[379] = 2617
set PRIMES[380] = 2621
set PRIMES[381] = 2633
set PRIMES[382] = 2647
set PRIMES[383] = 2657
set PRIMES[384] = 2659
set PRIMES[385] = 2663
set PRIMES[386] = 2671
set PRIMES[387] = 2677
set PRIMES[388] = 2683
set PRIMES[389] = 2687
set PRIMES[390] = 2689
set PRIMES[391] = 2693
set PRIMES[392] = 2699
set PRIMES[393] = 2707
set PRIMES[394] = 2711
set PRIMES[395] = 2713
set PRIMES[396] = 2719
set PRIMES[397] = 2729
set PRIMES[398] = 2731
set PRIMES[399] = 2741
set PRIMES[400] = 2749
set PRIMES[401] = 2753
set PRIMES[402] = 2767
set PRIMES[403] = 2777
set PRIMES[404] = 2789
set PRIMES[405] = 2791
set PRIMES[406] = 2797
set PRIMES[407] = 2801
set PRIMES[408] = 2803
set PRIMES[409] = 2819
set PRIMES[410] = 2833
set PRIMES[411] = 2837
set PRIMES[412] = 2843
set PRIMES[413] = 2851
set PRIMES[414] = 2857
set PRIMES[415] = 2861
set PRIMES[416] = 2879
set PRIMES[417] = 2887
set PRIMES[418] = 2897
set PRIMES[419] = 2903
set PRIMES[420] = 2909
set PRIMES[421] = 2917
set PRIMES[422] = 2927
set PRIMES[423] = 2939
set PRIMES[424] = 2953
set PRIMES[425] = 2957
set PRIMES[426] = 2963
set PRIMES[427] = 2969
set PRIMES[428] = 2971
set PRIMES[429] = 2999
set PRIMES[430] = 3001
set PRIMES[431] = 3011
set PRIMES[432] = 3019
set PRIMES[433] = 3023
set PRIMES[434] = 3037
set PRIMES[435] = 3041
set PRIMES[436] = 3049
set PRIMES[437] = 3061
set PRIMES[438] = 3067
set PRIMES[439] = 3079
set PRIMES[440] = 3083
set PRIMES[441] = 3089
set PRIMES[442] = 3109
set PRIMES[443] = 3119
set PRIMES[444] = 3121
set PRIMES[445] = 3137
set PRIMES[446] = 3163
set PRIMES[447] = 3167
set PRIMES[448] = 3169
set PRIMES[449] = 3181
set PRIMES[450] = 3187
set PRIMES[451] = 3191
set PRIMES[452] = 3203
set PRIMES[453] = 3209
set PRIMES[454] = 3217
set PRIMES[455] = 3221
set PRIMES[456] = 3229
set PRIMES[457] = 3251
set PRIMES[458] = 3253
set PRIMES[459] = 3257
set PRIMES[460] = 3259
set PRIMES[461] = 3271
set PRIMES[462] = 3299
set PRIMES[463] = 3301
set PRIMES[464] = 3307
set PRIMES[465] = 3313
set PRIMES[466] = 3319
set PRIMES[467] = 3323
set PRIMES[468] = 3329
set PRIMES[469] = 3331
set PRIMES[470] = 3343
set PRIMES[471] = 3347
set PRIMES[472] = 3359
set PRIMES[473] = 3361
set PRIMES[474] = 3371
set PRIMES[475] = 3373
set PRIMES[476] = 3389
set PRIMES[477] = 3391
set PRIMES[478] = 3407
set PRIMES[479] = 3413
set PRIMES[480] = 3433
set PRIMES[481] = 3449
set PRIMES[482] = 3457
set PRIMES[483] = 3461
set PRIMES[484] = 3463
set PRIMES[485] = 3467
set PRIMES[486] = 3469
set PRIMES[487] = 3491
set PRIMES[488] = 3499
set PRIMES[489] = 3511
set PRIMES[490] = 3517
set PRIMES[491] = 3527
set PRIMES[492] = 3529
set PRIMES[493] = 3533
set PRIMES[494] = 3539
set PRIMES[495] = 3541
set PRIMES[496] = 3547
set PRIMES[497] = 3557
set PRIMES[498] = 3559
set PRIMES[499] = 3571
set PRIMES[500] = 3581
set PRIMES[501] = 3583
set PRIMES[502] = 3593
set PRIMES[503] = 3607
set PRIMES[504] = 3613
set PRIMES[505] = 3617
set PRIMES[506] = 3623
set PRIMES[507] = 3631
set PRIMES[508] = 3637
set PRIMES[509] = 3643
set PRIMES[510] = 3659
set PRIMES[511] = 3671
set PRIMES[512] = 3673
set PRIMES[513] = 3677
set PRIMES[514] = 3691
set PRIMES[515] = 3697
set PRIMES[516] = 3701
set PRIMES[517] = 3709
set PRIMES[518] = 3719
set PRIMES[519] = 3727
set PRIMES[520] = 3733
set PRIMES[521] = 3739
set PRIMES[522] = 3761
set PRIMES[523] = 3767
set PRIMES[524] = 3769
set PRIMES[525] = 3779
set PRIMES[526] = 3793
set PRIMES[527] = 3797
set PRIMES[528] = 3803
set PRIMES[529] = 3821
set PRIMES[530] = 3823
set PRIMES[531] = 3833
set PRIMES[532] = 3847
set PRIMES[533] = 3851
set PRIMES[534] = 3853
set PRIMES[535] = 3863
set PRIMES[536] = 3877
set PRIMES[537] = 3881
set PRIMES[538] = 3889
set PRIMES[539] = 3907
set PRIMES[540] = 3911
set PRIMES[541] = 3917
set PRIMES[542] = 3919
set PRIMES[543] = 3923
set PRIMES[544] = 3929
set PRIMES[545] = 3931
set PRIMES[546] = 3943
set PRIMES[547] = 3947
set PRIMES[548] = 3967
set PRIMES[549] = 3989
set PRIMES[550] = 4001
set PRIMES[551] = 4003
set PRIMES[552] = 4007
set PRIMES[553] = 4013
set PRIMES[554] = 4019
set PRIMES[555] = 4021
set PRIMES[556] = 4027
set PRIMES[557] = 4049
set PRIMES[558] = 4051
set PRIMES[559] = 4057
set PRIMES[560] = 4073
set PRIMES[561] = 4079
set PRIMES[562] = 4091
set PRIMES[563] = 4093
set PRIMES[564] = 4099
set PRIMES[565] = 4111
set PRIMES[566] = 4127
set PRIMES[567] = 4129
set PRIMES[568] = 4133
set PRIMES[569] = 4139
set PRIMES[570] = 4153
set PRIMES[571] = 4157
set PRIMES[572] = 4159
set PRIMES[573] = 4177
set PRIMES[574] = 4201
set PRIMES[575] = 4211
set PRIMES[576] = 4217
set PRIMES[577] = 4219
set PRIMES[578] = 4229
set PRIMES[579] = 4231
set PRIMES[580] = 4241
set PRIMES[581] = 4243
set PRIMES[582] = 4253
set PRIMES[583] = 4259
set PRIMES[584] = 4261
set PRIMES[585] = 4271
set PRIMES[586] = 4273
set PRIMES[587] = 4283
set PRIMES[588] = 4289
set PRIMES[589] = 4297
set PRIMES[590] = 4327
set PRIMES[591] = 4337
set PRIMES[592] = 4339
set PRIMES[593] = 4349
set PRIMES[594] = 4357
set PRIMES[595] = 4363
set PRIMES[596] = 4373
set PRIMES[597] = 4391
set PRIMES[598] = 4397
set PRIMES[599] = 4409
set PRIMES[600] = 4421
set PRIMES[601] = 4423
set PRIMES[602] = 4441
set PRIMES[603] = 4447
set PRIMES[604] = 4451
set PRIMES[605] = 4457
set PRIMES[606] = 4463
set PRIMES[607] = 4481
set PRIMES[608] = 4483
set PRIMES[609] = 4493
set PRIMES[610] = 4507
set PRIMES[611] = 4513
set PRIMES[612] = 4517
set PRIMES[613] = 4519
set PRIMES[614] = 4523
set PRIMES[615] = 4547
set PRIMES[616] = 4549
set PRIMES[617] = 4561
set PRIMES[618] = 4567
set PRIMES[619] = 4583
set PRIMES[620] = 4591
set PRIMES[621] = 4597
set PRIMES[622] = 4603
set PRIMES[623] = 4621
set PRIMES[624] = 4637
set PRIMES[625] = 4639
set PRIMES[626] = 4643
set PRIMES[627] = 4649
set PRIMES[628] = 4651
set PRIMES[629] = 4657
set PRIMES[630] = 4663
set PRIMES[631] = 4673
set PRIMES[632] = 4679
set PRIMES[633] = 4691
set PRIMES[634] = 4703
set PRIMES[635] = 4721
set PRIMES[636] = 4723
set PRIMES[637] = 4729
set PRIMES[638] = 4733
set PRIMES[639] = 4751
set PRIMES[640] = 4759
set PRIMES[641] = 4783
set PRIMES[642] = 4787
set PRIMES[643] = 4789
set PRIMES[644] = 4793
set PRIMES[645] = 4799
set PRIMES[646] = 4801
set PRIMES[647] = 4813
set PRIMES[648] = 4817
set PRIMES[649] = 4831
set PRIMES[650] = 4861
set PRIMES[651] = 4871
set PRIMES[652] = 4877
set PRIMES[653] = 4889
set PRIMES[654] = 4903
set PRIMES[655] = 4909
set PRIMES[656] = 4919
set PRIMES[657] = 4931
set PRIMES[658] = 4933
set PRIMES[659] = 4937
set PRIMES[660] = 4943
set PRIMES[661] = 4951
set PRIMES[662] = 4957
set PRIMES[663] = 4967
set PRIMES[664] = 4969
set PRIMES[665] = 4973
set PRIMES[666] = 4987
set PRIMES[667] = 4993
set PRIMES[668] = 4999
set PRIMES[669] = 5003
set PRIMES[670] = 5009
set PRIMES[671] = 5011
set PRIMES[672] = 5021
set PRIMES[673] = 5023
set PRIMES[674] = 5039
set PRIMES[675] = 5051
set PRIMES[676] = 5059
set PRIMES[677] = 5077
set PRIMES[678] = 5081
set PRIMES[679] = 5087
set PRIMES[680] = 5099
set PRIMES[681] = 5101
set PRIMES[682] = 5107
set PRIMES[683] = 5113
set PRIMES[684] = 5119
set PRIMES[685] = 5147
set PRIMES[686] = 5153
set PRIMES[687] = 5167
set PRIMES[688] = 5171
set PRIMES[689] = 5179
set PRIMES[690] = 5189
set PRIMES[691] = 5197
set PRIMES[692] = 5209
set PRIMES[693] = 5227
set PRIMES[694] = 5231
set PRIMES[695] = 5233
set PRIMES[696] = 5237
set PRIMES[697] = 5261
set PRIMES[698] = 5273
set PRIMES[699] = 5279
set PRIMES[700] = 5281
set PRIMES[701] = 5297
set PRIMES[702] = 5303
set PRIMES[703] = 5309
set PRIMES[704] = 5323
set PRIMES[705] = 5333
set PRIMES[706] = 5347
set PRIMES[707] = 5351
set PRIMES[708] = 5381
set PRIMES[709] = 5387
set PRIMES[710] = 5393
set PRIMES[711] = 5399
set PRIMES[712] = 5407
set PRIMES[713] = 5413
set PRIMES[714] = 5417
set PRIMES[715] = 5419
set PRIMES[716] = 5431
set PRIMES[717] = 5437
set PRIMES[718] = 5441
set PRIMES[719] = 5443
set PRIMES[720] = 5449
set PRIMES[721] = 5471
set PRIMES[722] = 5477
set PRIMES[723] = 5479
set PRIMES[724] = 5483
set PRIMES[725] = 5501
set PRIMES[726] = 5503
set PRIMES[727] = 5507
set PRIMES[728] = 5519
set PRIMES[729] = 5521
set PRIMES[730] = 5527
set PRIMES[731] = 5531
set PRIMES[732] = 5557
set PRIMES[733] = 5563
set PRIMES[734] = 5569
set PRIMES[735] = 5573
set PRIMES[736] = 5581
set PRIMES[737] = 5591
set PRIMES[738] = 5623
set PRIMES[739] = 5639
set PRIMES[740] = 5641
set PRIMES[741] = 5647
set PRIMES[742] = 5651
set PRIMES[743] = 5653
set PRIMES[744] = 5657
set PRIMES[745] = 5659
set PRIMES[746] = 5669
set PRIMES[747] = 5683
set PRIMES[748] = 5689
set PRIMES[749] = 5693
set PRIMES[750] = 5701
set PRIMES[751] = 5711
set PRIMES[752] = 5717
set PRIMES[753] = 5737
set PRIMES[754] = 5741
set PRIMES[755] = 5743
set PRIMES[756] = 5749
set PRIMES[757] = 5779
set PRIMES[758] = 5783
set PRIMES[759] = 5791
set PRIMES[760] = 5801
set PRIMES[761] = 5807
set PRIMES[762] = 5813
set PRIMES[763] = 5821
set PRIMES[764] = 5827
set PRIMES[765] = 5839
set PRIMES[766] = 5843
set PRIMES[767] = 5849
set PRIMES[768] = 5851
set PRIMES[769] = 5857
set PRIMES[770] = 5861
set PRIMES[771] = 5867
set PRIMES[772] = 5869
set PRIMES[773] = 5879
set PRIMES[774] = 5881
set PRIMES[775] = 5897
set PRIMES[776] = 5903
set PRIMES[777] = 5923
set PRIMES[778] = 5927
set PRIMES[779] = 5939
set PRIMES[780] = 5953
set PRIMES[781] = 5981
set PRIMES[782] = 5987
set PRIMES[783] = 6007
set PRIMES[784] = 6011
set PRIMES[785] = 6029
set PRIMES[786] = 6037
set PRIMES[787] = 6043
set PRIMES[788] = 6047
set PRIMES[789] = 6053
set PRIMES[790] = 6067
set PRIMES[791] = 6073
set PRIMES[792] = 6079
set PRIMES[793] = 6089
set PRIMES[794] = 6091
set PRIMES[795] = 6101
set PRIMES[796] = 6113
set PRIMES[797] = 6121
set PRIMES[798] = 6131
set PRIMES[799] = 6133
set PRIMES[800] = 6143
set PRIMES[801] = 6151
set PRIMES[802] = 6163
set PRIMES[803] = 6173
set PRIMES[804] = 6197
set PRIMES[805] = 6199
set PRIMES[806] = 6203
set PRIMES[807] = 6211
set PRIMES[808] = 6217
set PRIMES[809] = 6221
set PRIMES[810] = 6229
set PRIMES[811] = 6247
set PRIMES[812] = 6257
set PRIMES[813] = 6263
set PRIMES[814] = 6269
set PRIMES[815] = 6271
set PRIMES[816] = 6277
set PRIMES[817] = 6287
set PRIMES[818] = 6299
set PRIMES[819] = 6301
set PRIMES[820] = 6311
set PRIMES[821] = 6317
set PRIMES[822] = 6323
set PRIMES[823] = 6329
set PRIMES[824] = 6337
set PRIMES[825] = 6343
set PRIMES[826] = 6353
set PRIMES[827] = 6359
set PRIMES[828] = 6361
set PRIMES[829] = 6367
set PRIMES[830] = 6373
set PRIMES[831] = 6379
set PRIMES[832] = 6389
set PRIMES[833] = 6397
set PRIMES[834] = 6421
set PRIMES[835] = 6427
set PRIMES[836] = 6449
set PRIMES[837] = 6451
set PRIMES[838] = 6469
set PRIMES[839] = 6473
set PRIMES[840] = 6481
set PRIMES[841] = 6491
set PRIMES[842] = 6521
set PRIMES[843] = 6529
set PRIMES[844] = 6547
set PRIMES[845] = 6551
set PRIMES[846] = 6553
set PRIMES[847] = 6563
set PRIMES[848] = 6569
set PRIMES[849] = 6571
set PRIMES[850] = 6577
set PRIMES[851] = 6581
set PRIMES[852] = 6599
set PRIMES[853] = 6607
set PRIMES[854] = 6619
set PRIMES[855] = 6637
set PRIMES[856] = 6653
set PRIMES[857] = 6659
set PRIMES[858] = 6661
set PRIMES[859] = 6673
set PRIMES[860] = 6679
set PRIMES[861] = 6689
set PRIMES[862] = 6691
set PRIMES[863] = 6701
set PRIMES[864] = 6703
set PRIMES[865] = 6709
set PRIMES[866] = 6719
set PRIMES[867] = 6733
set PRIMES[868] = 6737
set PRIMES[869] = 6761
set PRIMES[870] = 6763
set PRIMES[871] = 6779
set PRIMES[872] = 6781
set PRIMES[873] = 6791
set PRIMES[874] = 6793
set PRIMES[875] = 6803
set PRIMES[876] = 6823
set PRIMES[877] = 6827
set PRIMES[878] = 6829
set PRIMES[879] = 6833
set PRIMES[880] = 6841
set PRIMES[881] = 6857
set PRIMES[882] = 6863
set PRIMES[883] = 6869
set PRIMES[884] = 6871
set PRIMES[885] = 6883
set PRIMES[886] = 6899
set PRIMES[887] = 6907
set PRIMES[888] = 6911
set PRIMES[889] = 6917
set PRIMES[890] = 6947
set PRIMES[891] = 6949
set PRIMES[892] = 6959
set PRIMES[893] = 6961
set PRIMES[894] = 6967
set PRIMES[895] = 6971
set PRIMES[896] = 6977
set PRIMES[897] = 6983
set PRIMES[898] = 6991
set PRIMES[899] = 6997
set PRIMES[900] = 7001
set PRIMES[901] = 7013
set PRIMES[902] = 7019
set PRIMES[903] = 7027
set PRIMES[904] = 7039
set PRIMES[905] = 7043
set PRIMES[906] = 7057
set PRIMES[907] = 7069
set PRIMES[908] = 7079
set PRIMES[909] = 7103
set PRIMES[910] = 7109
set PRIMES[911] = 7121
set PRIMES[912] = 7127
set PRIMES[913] = 7129
set PRIMES[914] = 7151
set PRIMES[915] = 7159
set PRIMES[916] = 7177
set PRIMES[917] = 7187
set PRIMES[918] = 7193
set PRIMES[919] = 7207
set PRIMES[920] = 7211
set PRIMES[921] = 7213
set PRIMES[922] = 7219
set PRIMES[923] = 7229
set PRIMES[924] = 7237
set PRIMES[925] = 7243
set PRIMES[926] = 7247
set PRIMES[927] = 7253
set PRIMES[928] = 7283
set PRIMES[929] = 7297
set PRIMES[930] = 7307
set PRIMES[931] = 7309
set PRIMES[932] = 7321
set PRIMES[933] = 7331
set PRIMES[934] = 7333
set PRIMES[935] = 7349
set PRIMES[936] = 7351
set PRIMES[937] = 7369
set PRIMES[938] = 7393
set PRIMES[939] = 7411
set PRIMES[940] = 7417
set PRIMES[941] = 7433
set PRIMES[942] = 7451
set PRIMES[943] = 7457
set PRIMES[944] = 7459
set PRIMES[945] = 7477
set PRIMES[946] = 7481
set PRIMES[947] = 7487
set PRIMES[948] = 7489
set PRIMES[949] = 7499
set PRIMES[950] = 7507
set PRIMES[951] = 7517
set PRIMES[952] = 7523
set PRIMES[953] = 7529
set PRIMES[954] = 7537
set PRIMES[955] = 7541
set PRIMES[956] = 7547
set PRIMES[957] = 7549
set PRIMES[958] = 7559
set PRIMES[959] = 7561
set PRIMES[960] = 7573
set PRIMES[961] = 7577
set PRIMES[962] = 7583
set PRIMES[963] = 7589
set PRIMES[964] = 7591
set PRIMES[965] = 7603
set PRIMES[966] = 7607
set PRIMES[967] = 7621
set PRIMES[968] = 7639
set PRIMES[969] = 7643
set PRIMES[970] = 7649
set PRIMES[971] = 7669
set PRIMES[972] = 7673
set PRIMES[973] = 7681
set PRIMES[974] = 7687
set PRIMES[975] = 7691
set PRIMES[976] = 7699
set PRIMES[977] = 7703
set PRIMES[978] = 7717
set PRIMES[979] = 7723
set PRIMES[980] = 7727
set PRIMES[981] = 7741
set PRIMES[982] = 7753
set PRIMES[983] = 7757
set PRIMES[984] = 7759
set PRIMES[985] = 7789
set PRIMES[986] = 7793
set PRIMES[987] = 7817
set PRIMES[988] = 7823
set PRIMES[989] = 7829
set PRIMES[990] = 7841
set PRIMES[991] = 7853
set PRIMES[992] = 7867
set PRIMES[993] = 7873
set PRIMES[994] = 7877
set PRIMES[995] = 7879
set PRIMES[996] = 7883
set PRIMES[997] = 7901
set PRIMES[998] = 7907
set PRIMES[999] = 7919
set PRIMES[1000] = 7927
set PRIMES[1001] = 7933
set PRIMES[1002] = 7937
set PRIMES[1003] = 7949
set PRIMES[1004] = 7951
set PRIMES[1005] = 7963
set PRIMES[1006] = 7993
set PRIMES[1007] = 8009
set PRIMES[1008] = 8011
set PRIMES[1009] = 8017
set PRIMES[1010] = 8039
set PRIMES[1011] = 8053
set PRIMES[1012] = 8059
set PRIMES[1013] = 8069
set PRIMES[1014] = 8081
set PRIMES[1015] = 8087
set PRIMES[1016] = 8089
set PRIMES[1017] = 8093
set PRIMES[1018] = 8101
set PRIMES[1019] = 8111
set PRIMES[1020] = 8117
set PRIMES[1021] = 8123
set PRIMES[1022] = 8147
set PRIMES[1023] = 8161
set PRIMES[1024] = 8167
set PRIMES[1025] = 8171
set PRIMES[1026] = 8179
set PRIMES[1027] = 8191
set PRIMES[1028] = 8209
set PRIMES[1029] = 8219
set PRIMES[1030] = 8221
set PRIMES[1031] = 8231
set PRIMES[1032] = 8233
set PRIMES[1033] = 8237
set PRIMES[1034] = 8243
set PRIMES[1035] = 8263
set PRIMES[1036] = 8269
set PRIMES[1037] = 8273
set PRIMES[1038] = 8287
set PRIMES[1039] = 8291
set PRIMES[1040] = 8293
set PRIMES[1041] = 8297
set PRIMES[1042] = 8311
set PRIMES[1043] = 8317
set PRIMES[1044] = 8329
set PRIMES[1045] = 8353
set PRIMES[1046] = 8363
set PRIMES[1047] = 8369
set PRIMES[1048] = 8377
set PRIMES[1049] = 8387
set PRIMES[1050] = 8389
set PRIMES[1051] = 8419
set PRIMES[1052] = 8423
set PRIMES[1053] = 8429
set PRIMES[1054] = 8431
set PRIMES[1055] = 8443
set PRIMES[1056] = 8447
set PRIMES[1057] = 8461
set PRIMES[1058] = 8467
set PRIMES[1059] = 8501
set PRIMES[1060] = 8513
set PRIMES[1061] = 8521
set PRIMES[1062] = 8527
set PRIMES[1063] = 8537
set PRIMES[1064] = 8539
set PRIMES[1065] = 8543
set PRIMES[1066] = 8563
set PRIMES[1067] = 8573
set PRIMES[1068] = 8581
set PRIMES[1069] = 8597
set PRIMES[1070] = 8599
set PRIMES[1071] = 8609
set PRIMES[1072] = 8623
set PRIMES[1073] = 8627
set PRIMES[1074] = 8629
set PRIMES[1075] = 8641
set PRIMES[1076] = 8647
set PRIMES[1077] = 8663
set PRIMES[1078] = 8669
set PRIMES[1079] = 8677
set PRIMES[1080] = 8681
set PRIMES[1081] = 8689
set PRIMES[1082] = 8693
set PRIMES[1083] = 8699
set PRIMES[1084] = 8707
set PRIMES[1085] = 8713
set PRIMES[1086] = 8719
set PRIMES[1087] = 8731
set PRIMES[1088] = 8737
set PRIMES[1089] = 8741
set PRIMES[1090] = 8747
set PRIMES[1091] = 8753
set PRIMES[1092] = 8761
set PRIMES[1093] = 8779
set PRIMES[1094] = 8783
set PRIMES[1095] = 8803
set PRIMES[1096] = 8807
set PRIMES[1097] = 8819
set PRIMES[1098] = 8821
set PRIMES[1099] = 8831
set PRIMES[1100] = 8837
set PRIMES[1101] = 8839
set PRIMES[1102] = 8849
set PRIMES[1103] = 8861
set PRIMES[1104] = 8863
set PRIMES[1105] = 8867
set PRIMES[1106] = 8887
set PRIMES[1107] = 8893
set PRIMES[1108] = 8923
set PRIMES[1109] = 8929
set PRIMES[1110] = 8933
set PRIMES[1111] = 8941
set PRIMES[1112] = 8951
set PRIMES[1113] = 8963
set PRIMES[1114] = 8969
set PRIMES[1115] = 8971
set PRIMES[1116] = 8999
set PRIMES[1117] = 9001
set PRIMES[1118] = 9007
set PRIMES[1119] = 9011
set PRIMES[1120] = 9013
set PRIMES[1121] = 9029
set PRIMES[1122] = 9041
set PRIMES[1123] = 9043
set PRIMES[1124] = 9049
set PRIMES[1125] = 9059
set PRIMES[1126] = 9067
set PRIMES[1127] = 9091
set PRIMES[1128] = 9103
set PRIMES[1129] = 9109
set PRIMES[1130] = 9127
set PRIMES[1131] = 9133
set PRIMES[1132] = 9137
set PRIMES[1133] = 9151
set PRIMES[1134] = 9157
set PRIMES[1135] = 9161
set PRIMES[1136] = 9173
set PRIMES[1137] = 9181
set PRIMES[1138] = 9187
set PRIMES[1139] = 9199
set PRIMES[1140] = 9203
set PRIMES[1141] = 9209
set PRIMES[1142] = 9221
set PRIMES[1143] = 9227
set PRIMES[1144] = 9239
set PRIMES[1145] = 9241
set PRIMES[1146] = 9257
set PRIMES[1147] = 9277
set PRIMES[1148] = 9281
set PRIMES[1149] = 9283
set PRIMES[1150] = 9293
set PRIMES[1151] = 9311
set PRIMES[1152] = 9319
set PRIMES[1153] = 9323
set PRIMES[1154] = 9337
set PRIMES[1155] = 9341
set PRIMES[1156] = 9343
set PRIMES[1157] = 9349
set PRIMES[1158] = 9371
set PRIMES[1159] = 9377
set PRIMES[1160] = 9391
set PRIMES[1161] = 9397
set PRIMES[1162] = 9403
set PRIMES[1163] = 9413
set PRIMES[1164] = 9419
set PRIMES[1165] = 9421
set PRIMES[1166] = 9431
set PRIMES[1167] = 9433
set PRIMES[1168] = 9437
set PRIMES[1169] = 9439
set PRIMES[1170] = 9461
set PRIMES[1171] = 9463
set PRIMES[1172] = 9467
set PRIMES[1173] = 9473
set PRIMES[1174] = 9479
set PRIMES[1175] = 9491
set PRIMES[1176] = 9497
set PRIMES[1177] = 9511
set PRIMES[1178] = 9521
set PRIMES[1179] = 9533
set PRIMES[1180] = 9539
set PRIMES[1181] = 9547
set PRIMES[1182] = 9551
set PRIMES[1183] = 9587
set PRIMES[1184] = 9601
set PRIMES[1185] = 9613
set PRIMES[1186] = 9619
set PRIMES[1187] = 9623
set PRIMES[1188] = 9629
set PRIMES[1189] = 9631
set PRIMES[1190] = 9643
set PRIMES[1191] = 9649
set PRIMES[1192] = 9661
set PRIMES[1193] = 9677
set PRIMES[1194] = 9679
set PRIMES[1195] = 9689
set PRIMES[1196] = 9697
set PRIMES[1197] = 9719
set PRIMES[1198] = 9721
set PRIMES[1199] = 9733
set PRIMES[1200] = 9739
set PRIMES[1201] = 9743
set PRIMES[1202] = 9749
set PRIMES[1203] = 9767
set PRIMES[1204] = 9769
set PRIMES[1205] = 9781
set PRIMES[1206] = 9787
set PRIMES[1207] = 9791
set PRIMES[1208] = 9803
set PRIMES[1209] = 9811
set PRIMES[1210] = 9817
set PRIMES[1211] = 9829
set PRIMES[1212] = 9833
set PRIMES[1213] = 9839
set PRIMES[1214] = 9851
set PRIMES[1215] = 9857
set PRIMES[1216] = 9859
set PRIMES[1217] = 9871
set PRIMES[1218] = 9883
set PRIMES[1219] = 9887
set PRIMES[1220] = 9901
set PRIMES[1221] = 9907
set PRIMES[1222] = 9923
set PRIMES[1223] = 9929
set PRIMES[1224] = 9931
set PRIMES[1225] = 9941
set PRIMES[1226] = 9949
set PRIMES[1227] = 9967
set PRIMES[1228] = 9973
set PRIMES[1229] = 10007
set PRIMES[1230] = 10009
set PRIMES[1231] = 10037
set PRIMES[1232] = 10039
set PRIMES[1233] = 10061
set PRIMES[1234] = 10067
set PRIMES[1235] = 10069
set PRIMES[1236] = 10079
set PRIMES[1237] = 10091
set PRIMES[1238] = 10093
set PRIMES[1239] = 10099
set PRIMES[1240] = 10103
set PRIMES[1241] = 10111
set PRIMES[1242] = 10133
set PRIMES[1243] = 10139
set PRIMES[1244] = 10141
set PRIMES[1245] = 10151
set PRIMES[1246] = 10159
set PRIMES[1247] = 10163
set PRIMES[1248] = 10169
set PRIMES[1249] = 10177
set PRIMES[1250] = 10181
set PRIMES[1251] = 10193
set PRIMES[1252] = 10211
set PRIMES[1253] = 10223
set PRIMES[1254] = 10243
set PRIMES[1255] = 10247
set PRIMES[1256] = 10253
set PRIMES[1257] = 10259
set PRIMES[1258] = 10267
set PRIMES[1259] = 10271
set PRIMES[1260] = 10273
set PRIMES[1261] = 10289
set PRIMES[1262] = 10301
set PRIMES[1263] = 10303
set PRIMES[1264] = 10313
set PRIMES[1265] = 10321
set PRIMES[1266] = 10331
set PRIMES[1267] = 10333
set PRIMES[1268] = 10337
set PRIMES[1269] = 10343
set PRIMES[1270] = 10357
set PRIMES[1271] = 10369
set PRIMES[1272] = 10391
set PRIMES[1273] = 10399
set PRIMES[1274] = 10427
set PRIMES[1275] = 10429
set PRIMES[1276] = 10433
set PRIMES[1277] = 10453
set PRIMES[1278] = 10457
set PRIMES[1279] = 10459
set PRIMES[1280] = 10463
set PRIMES[1281] = 10477
set PRIMES[1282] = 10487
set PRIMES[1283] = 10499
set PRIMES[1284] = 10501
set PRIMES[1285] = 10513
set PRIMES[1286] = 10529
set PRIMES[1287] = 10531
set PRIMES[1288] = 10559
set PRIMES[1289] = 10567
set PRIMES[1290] = 10589
set PRIMES[1291] = 10597
set PRIMES[1292] = 10601
set PRIMES[1293] = 10607
set PRIMES[1294] = 10613
set PRIMES[1295] = 10627
set PRIMES[1296] = 10631
set PRIMES[1297] = 10639
set PRIMES[1298] = 10651
set PRIMES[1299] = 10657
set PRIMES[1300] = 10663
set PRIMES[1301] = 10667
set PRIMES[1302] = 10687
set PRIMES[1303] = 10691
set PRIMES[1304] = 10709
set PRIMES[1305] = 10711
set PRIMES[1306] = 10723
set PRIMES[1307] = 10729
set PRIMES[1308] = 10733
set PRIMES[1309] = 10739
set PRIMES[1310] = 10753
set PRIMES[1311] = 10771
set PRIMES[1312] = 10781
set PRIMES[1313] = 10789
set PRIMES[1314] = 10799
set PRIMES[1315] = 10831
set PRIMES[1316] = 10837
set PRIMES[1317] = 10847
set PRIMES[1318] = 10853
set PRIMES[1319] = 10859
set PRIMES[1320] = 10861
set PRIMES[1321] = 10867
set PRIMES[1322] = 10883
set PRIMES[1323] = 10889
set PRIMES[1324] = 10891
set PRIMES[1325] = 10903
set PRIMES[1326] = 10909
set PRIMES[1327] = 10937
set PRIMES[1328] = 10939
set PRIMES[1329] = 10949
set PRIMES[1330] = 10957
set PRIMES[1331] = 10973
set PRIMES[1332] = 10979
set PRIMES[1333] = 10987
set PRIMES[1334] = 10993
set PRIMES[1335] = 11003
set PRIMES[1336] = 11027
set PRIMES[1337] = 11047
set PRIMES[1338] = 11057
set PRIMES[1339] = 11059
set PRIMES[1340] = 11069
set PRIMES[1341] = 11071
set PRIMES[1342] = 11083
set PRIMES[1343] = 11087
set PRIMES[1344] = 11093
set PRIMES[1345] = 11113
set PRIMES[1346] = 11117
set PRIMES[1347] = 11119
set PRIMES[1348] = 11131
set PRIMES[1349] = 11149
set PRIMES[1350] = 11159
set PRIMES[1351] = 11161
set PRIMES[1352] = 11171
set PRIMES[1353] = 11173
set PRIMES[1354] = 11177
set PRIMES[1355] = 11197
set PRIMES[1356] = 11213
set PRIMES[1357] = 11239
set PRIMES[1358] = 11243
set PRIMES[1359] = 11251
set PRIMES[1360] = 11257
set PRIMES[1361] = 11261
set PRIMES[1362] = 11273
set PRIMES[1363] = 11279
set PRIMES[1364] = 11287
set PRIMES[1365] = 11299
set PRIMES[1366] = 11311
set PRIMES[1367] = 11317
set PRIMES[1368] = 11321
set PRIMES[1369] = 11329
set PRIMES[1370] = 11351
set PRIMES[1371] = 11353
set PRIMES[1372] = 11369
set PRIMES[1373] = 11383
set PRIMES[1374] = 11393
set PRIMES[1375] = 11399
set PRIMES[1376] = 11411
set PRIMES[1377] = 11423
set PRIMES[1378] = 11437
set PRIMES[1379] = 11443
set PRIMES[1380] = 11447
set PRIMES[1381] = 11467
set PRIMES[1382] = 11471
set PRIMES[1383] = 11483
set PRIMES[1384] = 11489
set PRIMES[1385] = 11491
set PRIMES[1386] = 11497
set PRIMES[1387] = 11503
set PRIMES[1388] = 11519
set PRIMES[1389] = 11527
set PRIMES[1390] = 11549
set PRIMES[1391] = 11551
set PRIMES[1392] = 11579
set PRIMES[1393] = 11587
set PRIMES[1394] = 11593
set PRIMES[1395] = 11597
set PRIMES[1396] = 11617
set PRIMES[1397] = 11621
set PRIMES[1398] = 11633
set PRIMES[1399] = 11657
set PRIMES[1400] = 11677
set PRIMES[1401] = 11681
set PRIMES[1402] = 11689
set PRIMES[1403] = 11699
set PRIMES[1404] = 11701
set PRIMES[1405] = 11717
set PRIMES[1406] = 11719
set PRIMES[1407] = 11731
set PRIMES[1408] = 11743
set PRIMES[1409] = 11777
set PRIMES[1410] = 11779
set PRIMES[1411] = 11783
set PRIMES[1412] = 11789
set PRIMES[1413] = 11801
set PRIMES[1414] = 11807
set PRIMES[1415] = 11813
set PRIMES[1416] = 11821
set PRIMES[1417] = 11827
set PRIMES[1418] = 11831
set PRIMES[1419] = 11833
set PRIMES[1420] = 11839
set PRIMES[1421] = 11863
set PRIMES[1422] = 11867
set PRIMES[1423] = 11887
set PRIMES[1424] = 11897
set PRIMES[1425] = 11903
set PRIMES[1426] = 11909
set PRIMES[1427] = 11923
set PRIMES[1428] = 11927
set PRIMES[1429] = 11933
set PRIMES[1430] = 11939
set PRIMES[1431] = 11941
set PRIMES[1432] = 11953
set PRIMES[1433] = 11959
set PRIMES[1434] = 11969
set PRIMES[1435] = 11971
set PRIMES[1436] = 11981
set PRIMES[1437] = 11987
set PRIMES[1438] = 12007
set PRIMES[1439] = 12011
set PRIMES[1440] = 12037
set PRIMES[1441] = 12041
set PRIMES[1442] = 12043
set PRIMES[1443] = 12049
set PRIMES[1444] = 12071
set PRIMES[1445] = 12073
set PRIMES[1446] = 12097
set PRIMES[1447] = 12101
set PRIMES[1448] = 12107
set PRIMES[1449] = 12109
set PRIMES[1450] = 12113
set PRIMES[1451] = 12119
set PRIMES[1452] = 12143
set PRIMES[1453] = 12149
set PRIMES[1454] = 12157
set PRIMES[1455] = 12161
set PRIMES[1456] = 12163
set PRIMES[1457] = 12197
set PRIMES[1458] = 12203
set PRIMES[1459] = 12211
set PRIMES[1460] = 12227
set PRIMES[1461] = 12239
set PRIMES[1462] = 12241
set PRIMES[1463] = 12251
set PRIMES[1464] = 12253
set PRIMES[1465] = 12263
set PRIMES[1466] = 12269
set PRIMES[1467] = 12277
set PRIMES[1468] = 12281
set PRIMES[1469] = 12289
set PRIMES[1470] = 12301
set PRIMES[1471] = 12323
set PRIMES[1472] = 12329
set PRIMES[1473] = 12343
set PRIMES[1474] = 12347
set PRIMES[1475] = 12373
set PRIMES[1476] = 12377
set PRIMES[1477] = 12379
set PRIMES[1478] = 12391
set PRIMES[1479] = 12401
set PRIMES[1480] = 12409
set PRIMES[1481] = 12413
set PRIMES[1482] = 12421
set PRIMES[1483] = 12433
set PRIMES[1484] = 12437
set PRIMES[1485] = 12451
set PRIMES[1486] = 12457
set PRIMES[1487] = 12473
set PRIMES[1488] = 12479
set PRIMES[1489] = 12487
set PRIMES[1490] = 12491
set PRIMES[1491] = 12497
set PRIMES[1492] = 12503
set PRIMES[1493] = 12511
set PRIMES[1494] = 12517
set PRIMES[1495] = 12527
set PRIMES[1496] = 12539
set PRIMES[1497] = 12541
set PRIMES[1498] = 12547
set PRIMES[1499] = 12553
set PRIMES[1500] = 12569
set PRIMES[1501] = 12577
set PRIMES[1502] = 12583
set PRIMES[1503] = 12589
set PRIMES[1504] = 12601
set PRIMES[1505] = 12611
set PRIMES[1506] = 12613
set PRIMES[1507] = 12619
set PRIMES[1508] = 12637
set PRIMES[1509] = 12641
set PRIMES[1510] = 12647
set PRIMES[1511] = 12653
set PRIMES[1512] = 12659
set PRIMES[1513] = 12671
set PRIMES[1514] = 12689
set PRIMES[1515] = 12697
set PRIMES[1516] = 12703
set PRIMES[1517] = 12713
set PRIMES[1518] = 12721
set PRIMES[1519] = 12739
set PRIMES[1520] = 12743
set PRIMES[1521] = 12757
set PRIMES[1522] = 12763
set PRIMES[1523] = 12781
set PRIMES[1524] = 12791
set PRIMES[1525] = 12799
set PRIMES[1526] = 12809
set PRIMES[1527] = 12821
set PRIMES[1528] = 12823
set PRIMES[1529] = 12829
set PRIMES[1530] = 12841
set PRIMES[1531] = 12853
set PRIMES[1532] = 12889
set PRIMES[1533] = 12893
set PRIMES[1534] = 12899
set PRIMES[1535] = 12907
set PRIMES[1536] = 12911
set PRIMES[1537] = 12917
set PRIMES[1538] = 12919
set PRIMES[1539] = 12923
set PRIMES[1540] = 12941
set PRIMES[1541] = 12953
set PRIMES[1542] = 12959
set PRIMES[1543] = 12967
set PRIMES[1544] = 12973
set PRIMES[1545] = 12979
set PRIMES[1546] = 12983
set PRIMES[1547] = 13001
set PRIMES[1548] = 13003
set PRIMES[1549] = 13007
set PRIMES[1550] = 13009
set PRIMES[1551] = 13033
set PRIMES[1552] = 13037
set PRIMES[1553] = 13043
set PRIMES[1554] = 13049
set PRIMES[1555] = 13063
set PRIMES[1556] = 13093
set PRIMES[1557] = 13099
set PRIMES[1558] = 13103
set PRIMES[1559] = 13109
set PRIMES[1560] = 13121
set PRIMES[1561] = 13127
set PRIMES[1562] = 13147
set PRIMES[1563] = 13151
set PRIMES[1564] = 13159
set PRIMES[1565] = 13163
set PRIMES[1566] = 13171
set PRIMES[1567] = 13177
set PRIMES[1568] = 13183
set PRIMES[1569] = 13187
set PRIMES[1570] = 13217
set PRIMES[1571] = 13219
set PRIMES[1572] = 13229
set PRIMES[1573] = 13241
set PRIMES[1574] = 13249
set PRIMES[1575] = 13259
set PRIMES[1576] = 13267
set PRIMES[1577] = 13291
set PRIMES[1578] = 13297
set PRIMES[1579] = 13309
set PRIMES[1580] = 13313
set PRIMES[1581] = 13327
set PRIMES[1582] = 13331
set PRIMES[1583] = 13337
set PRIMES[1584] = 13339
set PRIMES[1585] = 13367
set PRIMES[1586] = 13381
set PRIMES[1587] = 13397
set PRIMES[1588] = 13399
set PRIMES[1589] = 13411
set PRIMES[1590] = 13417
set PRIMES[1591] = 13421
set PRIMES[1592] = 13441
set PRIMES[1593] = 13451
set PRIMES[1594] = 13457
set PRIMES[1595] = 13463
set PRIMES[1596] = 13469
set PRIMES[1597] = 13477
set PRIMES[1598] = 13487
set PRIMES[1599] = 13499
set PRIMES[1600] = 13513
set PRIMES[1601] = 13523
set PRIMES[1602] = 13537
set PRIMES[1603] = 13553
set PRIMES[1604] = 13567
set PRIMES[1605] = 13577
set PRIMES[1606] = 13591
set PRIMES[1607] = 13597
set PRIMES[1608] = 13613
set PRIMES[1609] = 13619
set PRIMES[1610] = 13627
set PRIMES[1611] = 13633
set PRIMES[1612] = 13649
set PRIMES[1613] = 13669
set PRIMES[1614] = 13679
set PRIMES[1615] = 13681
set PRIMES[1616] = 13687
set PRIMES[1617] = 13691
set PRIMES[1618] = 13693
set PRIMES[1619] = 13697
set PRIMES[1620] = 13709
set PRIMES[1621] = 13711
set PRIMES[1622] = 13721
set PRIMES[1623] = 13723
set PRIMES[1624] = 13729
set PRIMES[1625] = 13751
set PRIMES[1626] = 13757
set PRIMES[1627] = 13759
set PRIMES[1628] = 13763
set PRIMES[1629] = 13781
set PRIMES[1630] = 13789
set PRIMES[1631] = 13799
set PRIMES[1632] = 13807
set PRIMES[1633] = 13829
set PRIMES[1634] = 13831
set PRIMES[1635] = 13841
set PRIMES[1636] = 13859
set PRIMES[1637] = 13873
set PRIMES[1638] = 13877
set PRIMES[1639] = 13879
set PRIMES[1640] = 13883
set PRIMES[1641] = 13901
set PRIMES[1642] = 13903
set PRIMES[1643] = 13907
set PRIMES[1644] = 13913
set PRIMES[1645] = 13921
set PRIMES[1646] = 13931
set PRIMES[1647] = 13933
set PRIMES[1648] = 13963
set PRIMES[1649] = 13967
set PRIMES[1650] = 13997
set PRIMES[1651] = 13999
set PRIMES[1652] = 14009
set PRIMES[1653] = 14011
set PRIMES[1654] = 14029
set PRIMES[1655] = 14033
set PRIMES[1656] = 14051
set PRIMES[1657] = 14057
set PRIMES[1658] = 14071
set PRIMES[1659] = 14081
set PRIMES[1660] = 14083
set PRIMES[1661] = 14087
set PRIMES[1662] = 14107
set PRIMES[1663] = 14143
set PRIMES[1664] = 14149
set PRIMES[1665] = 14153
set PRIMES[1666] = 14159
set PRIMES[1667] = 14173
set PRIMES[1668] = 14177
set PRIMES[1669] = 14197
set PRIMES[1670] = 14207
set PRIMES[1671] = 14221
set PRIMES[1672] = 14243
set PRIMES[1673] = 14249
set PRIMES[1674] = 14251
set PRIMES[1675] = 14281
set PRIMES[1676] = 14293
set PRIMES[1677] = 14303
set PRIMES[1678] = 14321
set PRIMES[1679] = 14323
set PRIMES[1680] = 14327
set PRIMES[1681] = 14341
set PRIMES[1682] = 14347
set PRIMES[1683] = 14369
set PRIMES[1684] = 14387
set PRIMES[1685] = 14389
set PRIMES[1686] = 14401
set PRIMES[1687] = 14407
set PRIMES[1688] = 14411
set PRIMES[1689] = 14419
set PRIMES[1690] = 14423
set PRIMES[1691] = 14431
set PRIMES[1692] = 14437
set PRIMES[1693] = 14447
set PRIMES[1694] = 14449
set PRIMES[1695] = 14461
set PRIMES[1696] = 14479
set PRIMES[1697] = 14489
set PRIMES[1698] = 14503
set PRIMES[1699] = 14519
set PRIMES[1700] = 14533
set PRIMES[1701] = 14537
set PRIMES[1702] = 14543
set PRIMES[1703] = 14549
set PRIMES[1704] = 14551
set PRIMES[1705] = 14557
set PRIMES[1706] = 14561
set PRIMES[1707] = 14563
set PRIMES[1708] = 14591
set PRIMES[1709] = 14593
set PRIMES[1710] = 14621
set PRIMES[1711] = 14627
set PRIMES[1712] = 14629
set PRIMES[1713] = 14633
set PRIMES[1714] = 14639
set PRIMES[1715] = 14653
set PRIMES[1716] = 14657
set PRIMES[1717] = 14669
set PRIMES[1718] = 14683
set PRIMES[1719] = 14699
set PRIMES[1720] = 14713
set PRIMES[1721] = 14717
set PRIMES[1722] = 14723
set PRIMES[1723] = 14731
set PRIMES[1724] = 14737
set PRIMES[1725] = 14741
set PRIMES[1726] = 14747
set PRIMES[1727] = 14753
set PRIMES[1728] = 14759
set PRIMES[1729] = 14767
set PRIMES[1730] = 14771
set PRIMES[1731] = 14779
set PRIMES[1732] = 14783
set PRIMES[1733] = 14797
set PRIMES[1734] = 14813
set PRIMES[1735] = 14821
set PRIMES[1736] = 14827
set PRIMES[1737] = 14831
set PRIMES[1738] = 14843
set PRIMES[1739] = 14851
set PRIMES[1740] = 14867
set PRIMES[1741] = 14869
set PRIMES[1742] = 14879
set PRIMES[1743] = 14887
set PRIMES[1744] = 14891
set PRIMES[1745] = 14897
set PRIMES[1746] = 14923
set PRIMES[1747] = 14929
set PRIMES[1748] = 14939
set PRIMES[1749] = 14947
set PRIMES[1750] = 14951
set PRIMES[1751] = 14957
set PRIMES[1752] = 14969
set PRIMES[1753] = 14983
set PRIMES[1754] = 15013
set PRIMES[1755] = 15017
set PRIMES[1756] = 15031
set PRIMES[1757] = 15053
set PRIMES[1758] = 15061
set PRIMES[1759] = 15073
set PRIMES[1760] = 15077
set PRIMES[1761] = 15083
set PRIMES[1762] = 15091
set PRIMES[1763] = 15101
set PRIMES[1764] = 15107
set PRIMES[1765] = 15121
set PRIMES[1766] = 15131
set PRIMES[1767] = 15137
set PRIMES[1768] = 15139
set PRIMES[1769] = 15149
set PRIMES[1770] = 15161
set PRIMES[1771] = 15173
set PRIMES[1772] = 15187
set PRIMES[1773] = 15193
set PRIMES[1774] = 15199
set PRIMES[1775] = 15217
set PRIMES[1776] = 15227
set PRIMES[1777] = 15233
set PRIMES[1778] = 15241
set PRIMES[1779] = 15259
set PRIMES[1780] = 15263
set PRIMES[1781] = 15269
set PRIMES[1782] = 15271
set PRIMES[1783] = 15277
set PRIMES[1784] = 15287
set PRIMES[1785] = 15289
set PRIMES[1786] = 15299
set PRIMES[1787] = 15307
set PRIMES[1788] = 15313
set PRIMES[1789] = 15319
set PRIMES[1790] = 15329
set PRIMES[1791] = 15331
set PRIMES[1792] = 15349
set PRIMES[1793] = 15359
set PRIMES[1794] = 15361
set PRIMES[1795] = 15373
set PRIMES[1796] = 15377
set PRIMES[1797] = 15383
set PRIMES[1798] = 15391
set PRIMES[1799] = 15401
set PRIMES[1800] = 15413
set PRIMES[1801] = 15427
set PRIMES[1802] = 15439
set PRIMES[1803] = 15443
set PRIMES[1804] = 15451
set PRIMES[1805] = 15461
set PRIMES[1806] = 15467
set PRIMES[1807] = 15473
set PRIMES[1808] = 15493
set PRIMES[1809] = 15497
set PRIMES[1810] = 15511
set PRIMES[1811] = 15527
set PRIMES[1812] = 15541
set PRIMES[1813] = 15551
set PRIMES[1814] = 15559
set PRIMES[1815] = 15569
set PRIMES[1816] = 15581
set PRIMES[1817] = 15583
set PRIMES[1818] = 15601
set PRIMES[1819] = 15607
set PRIMES[1820] = 15619
set PRIMES[1821] = 15629
set PRIMES[1822] = 15641
set PRIMES[1823] = 15643
set PRIMES[1824] = 15647
set PRIMES[1825] = 15649
set PRIMES[1826] = 15661
set PRIMES[1827] = 15667
set PRIMES[1828] = 15671
set PRIMES[1829] = 15679
set PRIMES[1830] = 15683
set PRIMES[1831] = 15727
set PRIMES[1832] = 15731
set PRIMES[1833] = 15733
set PRIMES[1834] = 15737
set PRIMES[1835] = 15739
set PRIMES[1836] = 15749
set PRIMES[1837] = 15761
set PRIMES[1838] = 15767
set PRIMES[1839] = 15773
set PRIMES[1840] = 15787
set PRIMES[1841] = 15791
set PRIMES[1842] = 15797
set PRIMES[1843] = 15803
set PRIMES[1844] = 15809
set PRIMES[1845] = 15817
set PRIMES[1846] = 15823
set PRIMES[1847] = 15859
set PRIMES[1848] = 15877
set PRIMES[1849] = 15881
set PRIMES[1850] = 15887
set PRIMES[1851] = 15889
set PRIMES[1852] = 15901
set PRIMES[1853] = 15907
set PRIMES[1854] = 15913
set PRIMES[1855] = 15919
set PRIMES[1856] = 15923
set PRIMES[1857] = 15937
set PRIMES[1858] = 15959
set PRIMES[1859] = 15971
set PRIMES[1860] = 15973
set PRIMES[1861] = 15991
set PRIMES[1862] = 16001
set PRIMES[1863] = 16007
set PRIMES[1864] = 16033
set PRIMES[1865] = 16057
set PRIMES[1866] = 16061
set PRIMES[1867] = 16063
set PRIMES[1868] = 16067
set PRIMES[1869] = 16069
set PRIMES[1870] = 16073
set PRIMES[1871] = 16087
set PRIMES[1872] = 16091
set PRIMES[1873] = 16097
set PRIMES[1874] = 16103
set PRIMES[1875] = 16111
set PRIMES[1876] = 16127
set PRIMES[1877] = 16139
set PRIMES[1878] = 16141
set PRIMES[1879] = 16183
set PRIMES[1880] = 16187
set PRIMES[1881] = 16189
set PRIMES[1882] = 16193
set PRIMES[1883] = 16217
set PRIMES[1884] = 16223
set PRIMES[1885] = 16229
set PRIMES[1886] = 16231
set PRIMES[1887] = 16249
set PRIMES[1888] = 16253
set PRIMES[1889] = 16267
set PRIMES[1890] = 16273
set PRIMES[1891] = 16301
set PRIMES[1892] = 16319
set PRIMES[1893] = 16333
set PRIMES[1894] = 16339
set PRIMES[1895] = 16349
set PRIMES[1896] = 16361
set PRIMES[1897] = 16363
set PRIMES[1898] = 16369
set PRIMES[1899] = 16381
set PRIMES[1900] = 16411
set PRIMES[1901] = 16417
set PRIMES[1902] = 16421
set PRIMES[1903] = 16427
set PRIMES[1904] = 16433
set PRIMES[1905] = 16447
set PRIMES[1906] = 16451
set PRIMES[1907] = 16453
set PRIMES[1908] = 16477
set PRIMES[1909] = 16481
set PRIMES[1910] = 16487
set PRIMES[1911] = 16493
set PRIMES[1912] = 16519
set PRIMES[1913] = 16529
set PRIMES[1914] = 16547
set PRIMES[1915] = 16553
set PRIMES[1916] = 16561
set PRIMES[1917] = 16567
set PRIMES[1918] = 16573
set PRIMES[1919] = 16603
set PRIMES[1920] = 16607
set PRIMES[1921] = 16619
set PRIMES[1922] = 16631
set PRIMES[1923] = 16633
set PRIMES[1924] = 16649
set PRIMES[1925] = 16651
set PRIMES[1926] = 16657
set PRIMES[1927] = 16661
set PRIMES[1928] = 16673
set PRIMES[1929] = 16691
set PRIMES[1930] = 16693
set PRIMES[1931] = 16699
set PRIMES[1932] = 16703
set PRIMES[1933] = 16729
set PRIMES[1934] = 16741
set PRIMES[1935] = 16747
set PRIMES[1936] = 16759
set PRIMES[1937] = 16763
set PRIMES[1938] = 16787
set PRIMES[1939] = 16811
set PRIMES[1940] = 16823
set PRIMES[1941] = 16829
set PRIMES[1942] = 16831
set PRIMES[1943] = 16843
set PRIMES[1944] = 16871
set PRIMES[1945] = 16879
set PRIMES[1946] = 16883
set PRIMES[1947] = 16889
set PRIMES[1948] = 16901
set PRIMES[1949] = 16903
set PRIMES[1950] = 16921
set PRIMES[1951] = 16927
set PRIMES[1952] = 16931
set PRIMES[1953] = 16937
set PRIMES[1954] = 16943
set PRIMES[1955] = 16963
set PRIMES[1956] = 16979
set PRIMES[1957] = 16981
set PRIMES[1958] = 16987
set PRIMES[1959] = 16993
set PRIMES[1960] = 17011
set PRIMES[1961] = 17021
set PRIMES[1962] = 17027
set PRIMES[1963] = 17029
set PRIMES[1964] = 17033
set PRIMES[1965] = 17041
set PRIMES[1966] = 17047
set PRIMES[1967] = 17053
set PRIMES[1968] = 17077
set PRIMES[1969] = 17093
set PRIMES[1970] = 17099
set PRIMES[1971] = 17107
set PRIMES[1972] = 17117
set PRIMES[1973] = 17123
set PRIMES[1974] = 17137
set PRIMES[1975] = 17159
set PRIMES[1976] = 17167
set PRIMES[1977] = 17183
set PRIMES[1978] = 17189
set PRIMES[1979] = 17191
set PRIMES[1980] = 17203
set PRIMES[1981] = 17207
set PRIMES[1982] = 17209
set PRIMES[1983] = 17231
set PRIMES[1984] = 17239
set PRIMES[1985] = 17257
set PRIMES[1986] = 17291
set PRIMES[1987] = 17293
set PRIMES[1988] = 17299
set PRIMES[1989] = 17317
set PRIMES[1990] = 17321
set PRIMES[1991] = 17327
set PRIMES[1992] = 17333
set PRIMES[1993] = 17341
set PRIMES[1994] = 17351
set PRIMES[1995] = 17359
set PRIMES[1996] = 17377
set PRIMES[1997] = 17383
set PRIMES[1998] = 17387
set PRIMES[1999] = 17389
set PRIMES[2000] = 17393
set PRIMES[2001] = 17401
set PRIMES[2002] = 17417
set PRIMES[2003] = 17419
set PRIMES[2004] = 17431
set PRIMES[2005] = 17443
set PRIMES[2006] = 17449
set PRIMES[2007] = 17467
set PRIMES[2008] = 17471
set PRIMES[2009] = 17477
set PRIMES[2010] = 17483
set PRIMES[2011] = 17489
set PRIMES[2012] = 17491
set PRIMES[2013] = 17497
set PRIMES[2014] = 17509
set PRIMES[2015] = 17519
set PRIMES[2016] = 17539
set PRIMES[2017] = 17551
set PRIMES[2018] = 17569
set PRIMES[2019] = 17573
set PRIMES[2020] = 17579
set PRIMES[2021] = 17581
set PRIMES[2022] = 17597
set PRIMES[2023] = 17599
set PRIMES[2024] = 17609
set PRIMES[2025] = 17623
set PRIMES[2026] = 17627
set PRIMES[2027] = 17657
set PRIMES[2028] = 17659
set PRIMES[2029] = 17669
set PRIMES[2030] = 17681
set PRIMES[2031] = 17683
set PRIMES[2032] = 17707
set PRIMES[2033] = 17713
set PRIMES[2034] = 17729
set PRIMES[2035] = 17737
set PRIMES[2036] = 17747
set PRIMES[2037] = 17749
set PRIMES[2038] = 17761
set PRIMES[2039] = 17783
set PRIMES[2040] = 17789
set PRIMES[2041] = 17791
set PRIMES[2042] = 17807
set PRIMES[2043] = 17827
set PRIMES[2044] = 17837
set PRIMES[2045] = 17839
set PRIMES[2046] = 17851
set PRIMES[2047] = 17863
set PRIMES[2048] = 17881
set PRIMES[2049] = 17891
set PRIMES[2050] = 17903
set PRIMES[2051] = 17909
set PRIMES[2052] = 17911
set PRIMES[2053] = 17921
set PRIMES[2054] = 17923
set PRIMES[2055] = 17929
set PRIMES[2056] = 17939
set PRIMES[2057] = 17957
set PRIMES[2058] = 17959
set PRIMES[2059] = 17971
set PRIMES[2060] = 17977
set PRIMES[2061] = 17981
set PRIMES[2062] = 17987
set PRIMES[2063] = 17989
set PRIMES[2064] = 18013
set PRIMES[2065] = 18041
set PRIMES[2066] = 18043
set PRIMES[2067] = 18047
set PRIMES[2068] = 18049
set PRIMES[2069] = 18059
set PRIMES[2070] = 18061
set PRIMES[2071] = 18077
set PRIMES[2072] = 18089
set PRIMES[2073] = 18097
set PRIMES[2074] = 18119
set PRIMES[2075] = 18121
set PRIMES[2076] = 18127
set PRIMES[2077] = 18131
set PRIMES[2078] = 18133
set PRIMES[2079] = 18143
set PRIMES[2080] = 18149
set PRIMES[2081] = 18169
set PRIMES[2082] = 18181
set PRIMES[2083] = 18191
set PRIMES[2084] = 18199
set PRIMES[2085] = 18211
set PRIMES[2086] = 18217
set PRIMES[2087] = 18223
set PRIMES[2088] = 18229
set PRIMES[2089] = 18233
set PRIMES[2090] = 18251
set PRIMES[2091] = 18253
set PRIMES[2092] = 18257
set PRIMES[2093] = 18269
set PRIMES[2094] = 18287
set PRIMES[2095] = 18289
set PRIMES[2096] = 18301
set PRIMES[2097] = 18307
set PRIMES[2098] = 18311
set PRIMES[2099] = 18313
set PRIMES[2100] = 18329
set PRIMES[2101] = 18341
set PRIMES[2102] = 18353
set PRIMES[2103] = 18367
set PRIMES[2104] = 18371
set PRIMES[2105] = 18379
set PRIMES[2106] = 18397
set PRIMES[2107] = 18401
set PRIMES[2108] = 18413
set PRIMES[2109] = 18427
set PRIMES[2110] = 18433
set PRIMES[2111] = 18439
set PRIMES[2112] = 18443
set PRIMES[2113] = 18451
set PRIMES[2114] = 18457
set PRIMES[2115] = 18461
set PRIMES[2116] = 18481
set PRIMES[2117] = 18493
set PRIMES[2118] = 18503
set PRIMES[2119] = 18517
set PRIMES[2120] = 18521
set PRIMES[2121] = 18523
set PRIMES[2122] = 18539
set PRIMES[2123] = 18541
set PRIMES[2124] = 18553
set PRIMES[2125] = 18583
set PRIMES[2126] = 18587
set PRIMES[2127] = 18593
set PRIMES[2128] = 18617
set PRIMES[2129] = 18637
set PRIMES[2130] = 18661
set PRIMES[2131] = 18671
set PRIMES[2132] = 18679
set PRIMES[2133] = 18691
set PRIMES[2134] = 18701
set PRIMES[2135] = 18713
set PRIMES[2136] = 18719
set PRIMES[2137] = 18731
set PRIMES[2138] = 18743
set PRIMES[2139] = 18749
set PRIMES[2140] = 18757
set PRIMES[2141] = 18773
set PRIMES[2142] = 18787
set PRIMES[2143] = 18793
set PRIMES[2144] = 18797
set PRIMES[2145] = 18803
set PRIMES[2146] = 18839
set PRIMES[2147] = 18859
set PRIMES[2148] = 18869
set PRIMES[2149] = 18899
set PRIMES[2150] = 18911
set PRIMES[2151] = 18913
set PRIMES[2152] = 18917
set PRIMES[2153] = 18919
set PRIMES[2154] = 18947
set PRIMES[2155] = 18959
set PRIMES[2156] = 18973
set PRIMES[2157] = 18979
set PRIMES[2158] = 19001
set PRIMES[2159] = 19009
set PRIMES[2160] = 19013
set PRIMES[2161] = 19031
set PRIMES[2162] = 19037
set PRIMES[2163] = 19051
set PRIMES[2164] = 19069
set PRIMES[2165] = 19073
set PRIMES[2166] = 19079
set PRIMES[2167] = 19081
set PRIMES[2168] = 19087
set PRIMES[2169] = 19121
set PRIMES[2170] = 19139
set PRIMES[2171] = 19141
set PRIMES[2172] = 19157
set PRIMES[2173] = 19163
set PRIMES[2174] = 19181
set PRIMES[2175] = 19183
set PRIMES[2176] = 19207
set PRIMES[2177] = 19211
set PRIMES[2178] = 19213
set PRIMES[2179] = 19219
set PRIMES[2180] = 19231
set PRIMES[2181] = 19237
set PRIMES[2182] = 19249
set PRIMES[2183] = 19259
set PRIMES[2184] = 19267
set PRIMES[2185] = 19273
set PRIMES[2186] = 19289
set PRIMES[2187] = 19301
set PRIMES[2188] = 19309
set PRIMES[2189] = 19319
set PRIMES[2190] = 19333
set PRIMES[2191] = 19373
set PRIMES[2192] = 19379
set PRIMES[2193] = 19381
set PRIMES[2194] = 19387
set PRIMES[2195] = 19391
set PRIMES[2196] = 19403
set PRIMES[2197] = 19417
set PRIMES[2198] = 19421
set PRIMES[2199] = 19423
set PRIMES[2200] = 19427
set PRIMES[2201] = 19429
set PRIMES[2202] = 19433
set PRIMES[2203] = 19441
set PRIMES[2204] = 19447
set PRIMES[2205] = 19457
set PRIMES[2206] = 19463
set PRIMES[2207] = 19469
set PRIMES[2208] = 19471
set PRIMES[2209] = 19477
set PRIMES[2210] = 19483
set PRIMES[2211] = 19489
set PRIMES[2212] = 19501
set PRIMES[2213] = 19507
set PRIMES[2214] = 19531
set PRIMES[2215] = 19541
set PRIMES[2216] = 19543
set PRIMES[2217] = 19553
set PRIMES[2218] = 19559
set PRIMES[2219] = 19571
set PRIMES[2220] = 19577
set PRIMES[2221] = 19583
set PRIMES[2222] = 19597
set PRIMES[2223] = 19603
set PRIMES[2224] = 19609
set PRIMES[2225] = 19661
set PRIMES[2226] = 19681
set PRIMES[2227] = 19687
set PRIMES[2228] = 19697
set PRIMES[2229] = 19699
set PRIMES[2230] = 19709
set PRIMES[2231] = 19717
set PRIMES[2232] = 19727
set PRIMES[2233] = 19739
set PRIMES[2234] = 19751
set PRIMES[2235] = 19753
set PRIMES[2236] = 19759
set PRIMES[2237] = 19763
set PRIMES[2238] = 19777
set PRIMES[2239] = 19793
set PRIMES[2240] = 19801
set PRIMES[2241] = 19813
set PRIMES[2242] = 19819
set PRIMES[2243] = 19841
set PRIMES[2244] = 19843
set PRIMES[2245] = 19853
set PRIMES[2246] = 19861
set PRIMES[2247] = 19867
set PRIMES[2248] = 19889
set PRIMES[2249] = 19891
set PRIMES[2250] = 19913
set PRIMES[2251] = 19919
set PRIMES[2252] = 19927
set PRIMES[2253] = 19937
set PRIMES[2254] = 19949
set PRIMES[2255] = 19961
set PRIMES[2256] = 19963
set PRIMES[2257] = 19973
set PRIMES[2258] = 19979
set PRIMES[2259] = 19991
set PRIMES[2260] = 19993
set PRIMES[2261] = 19997
set PRIMES[2262] = 20011
set PRIMES[2263] = 20021
set PRIMES[2264] = 20023
set PRIMES[2265] = 20029
set PRIMES[2266] = 20047
set PRIMES[2267] = 20051
set PRIMES[2268] = 20063
set PRIMES[2269] = 20071
set PRIMES[2270] = 20089
set PRIMES[2271] = 20101
set PRIMES[2272] = 20107
set PRIMES[2273] = 20113
set PRIMES[2274] = 20117
set PRIMES[2275] = 20123
set PRIMES[2276] = 20129
set PRIMES[2277] = 20143
set PRIMES[2278] = 20147
set PRIMES[2279] = 20149
set PRIMES[2280] = 20161
set PRIMES[2281] = 20173
set PRIMES[2282] = 20177
set PRIMES[2283] = 20183
set PRIMES[2284] = 20201
set PRIMES[2285] = 20219
set PRIMES[2286] = 20231
set PRIMES[2287] = 20233
set PRIMES[2288] = 20249
set PRIMES[2289] = 20261
set PRIMES[2290] = 20269
set PRIMES[2291] = 20287
set PRIMES[2292] = 20297
set PRIMES[2293] = 20323
set PRIMES[2294] = 20327
set PRIMES[2295] = 20333
set PRIMES[2296] = 20341
set PRIMES[2297] = 20347
set PRIMES[2298] = 20353
set PRIMES[2299] = 20357
set PRIMES[2300] = 20359
set PRIMES[2301] = 20369
set PRIMES[2302] = 20389
set PRIMES[2303] = 20393
set PRIMES[2304] = 20399
set PRIMES[2305] = 20407
set PRIMES[2306] = 20411
set PRIMES[2307] = 20431
set PRIMES[2308] = 20441
set PRIMES[2309] = 20443
set PRIMES[2310] = 20477
set PRIMES[2311] = 20479
set PRIMES[2312] = 20483
set PRIMES[2313] = 20507
set PRIMES[2314] = 20509
set PRIMES[2315] = 20521
set PRIMES[2316] = 20533
set PRIMES[2317] = 20543
set PRIMES[2318] = 20549
set PRIMES[2319] = 20551
set PRIMES[2320] = 20563
set PRIMES[2321] = 20593
set PRIMES[2322] = 20599
set PRIMES[2323] = 20611
set PRIMES[2324] = 20627
set PRIMES[2325] = 20639
set PRIMES[2326] = 20641
set PRIMES[2327] = 20663
set PRIMES[2328] = 20681
set PRIMES[2329] = 20693
set PRIMES[2330] = 20707
set PRIMES[2331] = 20717
set PRIMES[2332] = 20719
set PRIMES[2333] = 20731
set PRIMES[2334] = 20743
set PRIMES[2335] = 20747
set PRIMES[2336] = 20749
set PRIMES[2337] = 20753
set PRIMES[2338] = 20759
set PRIMES[2339] = 20771
set PRIMES[2340] = 20773
set PRIMES[2341] = 20789
set PRIMES[2342] = 20807
set PRIMES[2343] = 20809
set PRIMES[2344] = 20849
set PRIMES[2345] = 20857
set PRIMES[2346] = 20873
set PRIMES[2347] = 20879
set PRIMES[2348] = 20887
set PRIMES[2349] = 20897
set PRIMES[2350] = 20899
set PRIMES[2351] = 20903
set PRIMES[2352] = 20921
set PRIMES[2353] = 20929
set PRIMES[2354] = 20939
set PRIMES[2355] = 20947
set PRIMES[2356] = 20959
set PRIMES[2357] = 20963
set PRIMES[2358] = 20981
set PRIMES[2359] = 20983
set PRIMES[2360] = 21001
set PRIMES[2361] = 21011
set PRIMES[2362] = 21013
set PRIMES[2363] = 21017
set PRIMES[2364] = 21019
set PRIMES[2365] = 21023
set PRIMES[2366] = 21031
set PRIMES[2367] = 21059
set PRIMES[2368] = 21061
set PRIMES[2369] = 21067
set PRIMES[2370] = 21089
set PRIMES[2371] = 21101
set PRIMES[2372] = 21107
set PRIMES[2373] = 21121
set PRIMES[2374] = 21139
set PRIMES[2375] = 21143
set PRIMES[2376] = 21149
set PRIMES[2377] = 21157
set PRIMES[2378] = 21163
set PRIMES[2379] = 21169
set PRIMES[2380] = 21179
set PRIMES[2381] = 21187
set PRIMES[2382] = 21191
set PRIMES[2383] = 21193
set PRIMES[2384] = 21211
set PRIMES[2385] = 21221
set PRIMES[2386] = 21227
set PRIMES[2387] = 21247
set PRIMES[2388] = 21269
set PRIMES[2389] = 21277
set PRIMES[2390] = 21283
set PRIMES[2391] = 21313
set PRIMES[2392] = 21317
set PRIMES[2393] = 21319
set PRIMES[2394] = 21323
set PRIMES[2395] = 21341
set PRIMES[2396] = 21347
set PRIMES[2397] = 21377
set PRIMES[2398] = 21379
set PRIMES[2399] = 21383
set PRIMES[2400] = 21391
set PRIMES[2401] = 21397
set PRIMES[2402] = 21401
set PRIMES[2403] = 21407
set PRIMES[2404] = 21419
set PRIMES[2405] = 21433
set PRIMES[2406] = 21467
set PRIMES[2407] = 21481
set PRIMES[2408] = 21487
set PRIMES[2409] = 21491
set PRIMES[2410] = 21493
set PRIMES[2411] = 21499
set PRIMES[2412] = 21503
set PRIMES[2413] = 21517
set PRIMES[2414] = 21521
set PRIMES[2415] = 21523
set PRIMES[2416] = 21529
set PRIMES[2417] = 21557
set PRIMES[2418] = 21559
set PRIMES[2419] = 21563
set PRIMES[2420] = 21569
set PRIMES[2421] = 21577
set PRIMES[2422] = 21587
set PRIMES[2423] = 21589
set PRIMES[2424] = 21599
set PRIMES[2425] = 21601
set PRIMES[2426] = 21611
set PRIMES[2427] = 21613
set PRIMES[2428] = 21617
set PRIMES[2429] = 21647
set PRIMES[2430] = 21649
set PRIMES[2431] = 21661
set PRIMES[2432] = 21673
set PRIMES[2433] = 21683
set PRIMES[2434] = 21701
set PRIMES[2435] = 21713
set PRIMES[2436] = 21727
set PRIMES[2437] = 21737
set PRIMES[2438] = 21739
set PRIMES[2439] = 21751
set PRIMES[2440] = 21757
set PRIMES[2441] = 21767
set PRIMES[2442] = 21773
set PRIMES[2443] = 21787
set PRIMES[2444] = 21799
set PRIMES[2445] = 21803
set PRIMES[2446] = 21817
set PRIMES[2447] = 21821
set PRIMES[2448] = 21839
set PRIMES[2449] = 21841
set PRIMES[2450] = 21851
set PRIMES[2451] = 21859
set PRIMES[2452] = 21863
set PRIMES[2453] = 21871
set PRIMES[2454] = 21881
set PRIMES[2455] = 21893
set PRIMES[2456] = 21911
set PRIMES[2457] = 21929
set PRIMES[2458] = 21937
set PRIMES[2459] = 21943
set PRIMES[2460] = 21961
set PRIMES[2461] = 21977
set PRIMES[2462] = 21991
set PRIMES[2463] = 21997
set PRIMES[2464] = 22003
set PRIMES[2465] = 22013
set PRIMES[2466] = 22027
set PRIMES[2467] = 22031
set PRIMES[2468] = 22037
set PRIMES[2469] = 22039
set PRIMES[2470] = 22051
set PRIMES[2471] = 22063
set PRIMES[2472] = 22067
set PRIMES[2473] = 22073
set PRIMES[2474] = 22079
set PRIMES[2475] = 22091
set PRIMES[2476] = 22093
set PRIMES[2477] = 22109
set PRIMES[2478] = 22111
set PRIMES[2479] = 22123
set PRIMES[2480] = 22129
set PRIMES[2481] = 22133
set PRIMES[2482] = 22147
set PRIMES[2483] = 22153
set PRIMES[2484] = 22157
set PRIMES[2485] = 22159
set PRIMES[2486] = 22171
set PRIMES[2487] = 22189
set PRIMES[2488] = 22193
set PRIMES[2489] = 22229
set PRIMES[2490] = 22247
set PRIMES[2491] = 22259
set PRIMES[2492] = 22271
set PRIMES[2493] = 22273
set PRIMES[2494] = 22277
set PRIMES[2495] = 22279
set PRIMES[2496] = 22283
set PRIMES[2497] = 22291
set PRIMES[2498] = 22303
set PRIMES[2499] = 22307
set PRIMES[2500] = 22343
set PRIMES[2501] = 22349
set PRIMES[2502] = 22367
set PRIMES[2503] = 22369
set PRIMES[2504] = 22381
set PRIMES[2505] = 22391
set PRIMES[2506] = 22397
set PRIMES[2507] = 22409
set PRIMES[2508] = 22433
set PRIMES[2509] = 22441
set PRIMES[2510] = 22447
set PRIMES[2511] = 22453
set PRIMES[2512] = 22469
set PRIMES[2513] = 22481
set PRIMES[2514] = 22483
set PRIMES[2515] = 22501
set PRIMES[2516] = 22511
set PRIMES[2517] = 22531
set PRIMES[2518] = 22541
set PRIMES[2519] = 22543
set PRIMES[2520] = 22549
set PRIMES[2521] = 22567
set PRIMES[2522] = 22571
set PRIMES[2523] = 22573
set PRIMES[2524] = 22613
set PRIMES[2525] = 22619
set PRIMES[2526] = 22621
set PRIMES[2527] = 22637
set PRIMES[2528] = 22639
set PRIMES[2529] = 22643
set PRIMES[2530] = 22651
set PRIMES[2531] = 22669
set PRIMES[2532] = 22679
set PRIMES[2533] = 22691
set PRIMES[2534] = 22697
set PRIMES[2535] = 22699
set PRIMES[2536] = 22709
set PRIMES[2537] = 22717
set PRIMES[2538] = 22721
set PRIMES[2539] = 22727
set PRIMES[2540] = 22739
set PRIMES[2541] = 22741
set PRIMES[2542] = 22751
set PRIMES[2543] = 22769
set PRIMES[2544] = 22777
set PRIMES[2545] = 22783
set PRIMES[2546] = 22787
set PRIMES[2547] = 22807
set PRIMES[2548] = 22811
set PRIMES[2549] = 22817
set PRIMES[2550] = 22853
set PRIMES[2551] = 22859
set PRIMES[2552] = 22861
set PRIMES[2553] = 22871
set PRIMES[2554] = 22877
set PRIMES[2555] = 22901
set PRIMES[2556] = 22907
set PRIMES[2557] = 22921
set PRIMES[2558] = 22937
set PRIMES[2559] = 22943
set PRIMES[2560] = 22961
set PRIMES[2561] = 22963
set PRIMES[2562] = 22973
set PRIMES[2563] = 22993
set PRIMES[2564] = 23003
set PRIMES[2565] = 23011
set PRIMES[2566] = 23017
set PRIMES[2567] = 23021
set PRIMES[2568] = 23027
set PRIMES[2569] = 23029
set PRIMES[2570] = 23039
set PRIMES[2571] = 23041
set PRIMES[2572] = 23053
set PRIMES[2573] = 23057
set PRIMES[2574] = 23059
set PRIMES[2575] = 23063
set PRIMES[2576] = 23071
set PRIMES[2577] = 23081
set PRIMES[2578] = 23087
set PRIMES[2579] = 23099
set PRIMES[2580] = 23117
set PRIMES[2581] = 23131
set PRIMES[2582] = 23143
set PRIMES[2583] = 23159
set PRIMES[2584] = 23167
set PRIMES[2585] = 23173
set PRIMES[2586] = 23189
set PRIMES[2587] = 23197
set PRIMES[2588] = 23201
set PRIMES[2589] = 23203
set PRIMES[2590] = 23209
set PRIMES[2591] = 23227
set PRIMES[2592] = 23251
set PRIMES[2593] = 23269
set PRIMES[2594] = 23279
set PRIMES[2595] = 23291
set PRIMES[2596] = 23293
set PRIMES[2597] = 23297
set PRIMES[2598] = 23311
set PRIMES[2599] = 23321
set PRIMES[2600] = 23327
set PRIMES[2601] = 23333
set PRIMES[2602] = 23339
set PRIMES[2603] = 23357
set PRIMES[2604] = 23369
set PRIMES[2605] = 23371
set PRIMES[2606] = 23399
set PRIMES[2607] = 23417
set PRIMES[2608] = 23431
set PRIMES[2609] = 23447
set PRIMES[2610] = 23459
set PRIMES[2611] = 23473
set PRIMES[2612] = 23497
set PRIMES[2613] = 23509
set PRIMES[2614] = 23531
set PRIMES[2615] = 23537
set PRIMES[2616] = 23539
set PRIMES[2617] = 23549
set PRIMES[2618] = 23557
set PRIMES[2619] = 23561
set PRIMES[2620] = 23563
set PRIMES[2621] = 23567
set PRIMES[2622] = 23581
set PRIMES[2623] = 23593
set PRIMES[2624] = 23599
set PRIMES[2625] = 23603
set PRIMES[2626] = 23609
set PRIMES[2627] = 23623
set PRIMES[2628] = 23627
set PRIMES[2629] = 23629
set PRIMES[2630] = 23633
set PRIMES[2631] = 23663
set PRIMES[2632] = 23669
set PRIMES[2633] = 23671
set PRIMES[2634] = 23677
set PRIMES[2635] = 23687
set PRIMES[2636] = 23689
set PRIMES[2637] = 23719
set PRIMES[2638] = 23741
set PRIMES[2639] = 23743
set PRIMES[2640] = 23747
set PRIMES[2641] = 23753
set PRIMES[2642] = 23761
set PRIMES[2643] = 23767
set PRIMES[2644] = 23773
set PRIMES[2645] = 23789
set PRIMES[2646] = 23801
set PRIMES[2647] = 23813
set PRIMES[2648] = 23819
set PRIMES[2649] = 23827
set PRIMES[2650] = 23831
set PRIMES[2651] = 23833
set PRIMES[2652] = 23857
set PRIMES[2653] = 23869
set PRIMES[2654] = 23873
set PRIMES[2655] = 23879
set PRIMES[2656] = 23887
set PRIMES[2657] = 23893
set PRIMES[2658] = 23899
set PRIMES[2659] = 23909
set PRIMES[2660] = 23911
set PRIMES[2661] = 23917
set PRIMES[2662] = 23929
set PRIMES[2663] = 23957
set PRIMES[2664] = 23971
set PRIMES[2665] = 23977
set PRIMES[2666] = 23981
set PRIMES[2667] = 23993
set PRIMES[2668] = 24001
set PRIMES[2669] = 24007
set PRIMES[2670] = 24019
set PRIMES[2671] = 24023
set PRIMES[2672] = 24029
set PRIMES[2673] = 24043
set PRIMES[2674] = 24049
set PRIMES[2675] = 24061
set PRIMES[2676] = 24071
set PRIMES[2677] = 24077
set PRIMES[2678] = 24083
set PRIMES[2679] = 24091
set PRIMES[2680] = 24097
set PRIMES[2681] = 24103
set PRIMES[2682] = 24107
set PRIMES[2683] = 24109
set PRIMES[2684] = 24113
set PRIMES[2685] = 24121
set PRIMES[2686] = 24133
set PRIMES[2687] = 24137
set PRIMES[2688] = 24151
set PRIMES[2689] = 24169
set PRIMES[2690] = 24179
set PRIMES[2691] = 24181
set PRIMES[2692] = 24197
set PRIMES[2693] = 24203
set PRIMES[2694] = 24223
set PRIMES[2695] = 24229
set PRIMES[2696] = 24239
set PRIMES[2697] = 24247
set PRIMES[2698] = 24251
set PRIMES[2699] = 24281
set PRIMES[2700] = 24317
set PRIMES[2701] = 24329
set PRIMES[2702] = 24337
set PRIMES[2703] = 24359
set PRIMES[2704] = 24371
set PRIMES[2705] = 24373
set PRIMES[2706] = 24379
set PRIMES[2707] = 24391
set PRIMES[2708] = 24407
set PRIMES[2709] = 24413
set PRIMES[2710] = 24419
set PRIMES[2711] = 24421
set PRIMES[2712] = 24439
set PRIMES[2713] = 24443
set PRIMES[2714] = 24469
set PRIMES[2715] = 24473
set PRIMES[2716] = 24481
set PRIMES[2717] = 24499
set PRIMES[2718] = 24509
set PRIMES[2719] = 24517
set PRIMES[2720] = 24527
set PRIMES[2721] = 24533
set PRIMES[2722] = 24547
set PRIMES[2723] = 24551
set PRIMES[2724] = 24571
set PRIMES[2725] = 24593
set PRIMES[2726] = 24611
set PRIMES[2727] = 24623
set PRIMES[2728] = 24631
set PRIMES[2729] = 24659
set PRIMES[2730] = 24671
set PRIMES[2731] = 24677
set PRIMES[2732] = 24683
set PRIMES[2733] = 24691
set PRIMES[2734] = 24697
set PRIMES[2735] = 24709
set PRIMES[2736] = 24733
set PRIMES[2737] = 24749
set PRIMES[2738] = 24763
set PRIMES[2739] = 24767
set PRIMES[2740] = 24781
set PRIMES[2741] = 24793
set PRIMES[2742] = 24799
set PRIMES[2743] = 24809
set PRIMES[2744] = 24821
set PRIMES[2745] = 24841
set PRIMES[2746] = 24847
set PRIMES[2747] = 24851
set PRIMES[2748] = 24859
set PRIMES[2749] = 24877
set PRIMES[2750] = 24889
set PRIMES[2751] = 24907
set PRIMES[2752] = 24917
set PRIMES[2753] = 24919
set PRIMES[2754] = 24923
set PRIMES[2755] = 24943
set PRIMES[2756] = 24953
set PRIMES[2757] = 24967
set PRIMES[2758] = 24971
set PRIMES[2759] = 24977
set PRIMES[2760] = 24979
set PRIMES[2761] = 24989
set PRIMES[2762] = 25013
set PRIMES[2763] = 25031
set PRIMES[2764] = 25033
set PRIMES[2765] = 25037
set PRIMES[2766] = 25057
set PRIMES[2767] = 25073
set PRIMES[2768] = 25087
set PRIMES[2769] = 25097
set PRIMES[2770] = 25111
set PRIMES[2771] = 25117
set PRIMES[2772] = 25121
set PRIMES[2773] = 25127
set PRIMES[2774] = 25147
set PRIMES[2775] = 25153
set PRIMES[2776] = 25163
set PRIMES[2777] = 25169
set PRIMES[2778] = 25171
set PRIMES[2779] = 25183
set PRIMES[2780] = 25189
set PRIMES[2781] = 25219
set PRIMES[2782] = 25229
set PRIMES[2783] = 25237
set PRIMES[2784] = 25243
set PRIMES[2785] = 25247
set PRIMES[2786] = 25253
set PRIMES[2787] = 25261
set PRIMES[2788] = 25301
set PRIMES[2789] = 25303
set PRIMES[2790] = 25307
set PRIMES[2791] = 25309
set PRIMES[2792] = 25321
set PRIMES[2793] = 25339
set PRIMES[2794] = 25343
set PRIMES[2795] = 25349
set PRIMES[2796] = 25357
set PRIMES[2797] = 25367
set PRIMES[2798] = 25373
set PRIMES[2799] = 25391
set PRIMES[2800] = 25409
set PRIMES[2801] = 25411
set PRIMES[2802] = 25423
set PRIMES[2803] = 25439
set PRIMES[2804] = 25447
set PRIMES[2805] = 25453
set PRIMES[2806] = 25457
set PRIMES[2807] = 25463
set PRIMES[2808] = 25469
set PRIMES[2809] = 25471
set PRIMES[2810] = 25523
set PRIMES[2811] = 25537
set PRIMES[2812] = 25541
set PRIMES[2813] = 25561
set PRIMES[2814] = 25577
set PRIMES[2815] = 25579
set PRIMES[2816] = 25583
set PRIMES[2817] = 25589
set PRIMES[2818] = 25601
set PRIMES[2819] = 25603
set PRIMES[2820] = 25609
set PRIMES[2821] = 25621
set PRIMES[2822] = 25633
set PRIMES[2823] = 25639
set PRIMES[2824] = 25643
set PRIMES[2825] = 25657
set PRIMES[2826] = 25667
set PRIMES[2827] = 25673
set PRIMES[2828] = 25679
set PRIMES[2829] = 25693
set PRIMES[2830] = 25703
set PRIMES[2831] = 25717
set PRIMES[2832] = 25733
set PRIMES[2833] = 25741
set PRIMES[2834] = 25747
set PRIMES[2835] = 25759
set PRIMES[2836] = 25763
set PRIMES[2837] = 25771
set PRIMES[2838] = 25793
set PRIMES[2839] = 25799
set PRIMES[2840] = 25801
set PRIMES[2841] = 25819
set PRIMES[2842] = 25841
set PRIMES[2843] = 25847
set PRIMES[2844] = 25849
set PRIMES[2845] = 25867
set PRIMES[2846] = 25873
set PRIMES[2847] = 25889
set PRIMES[2848] = 25903
set PRIMES[2849] = 25913
set PRIMES[2850] = 25919
set PRIMES[2851] = 25931
set PRIMES[2852] = 25933
set PRIMES[2853] = 25939
set PRIMES[2854] = 25943
set PRIMES[2855] = 25951
set PRIMES[2856] = 25969
set PRIMES[2857] = 25981
set PRIMES[2858] = 25997
set PRIMES[2859] = 25999
set PRIMES[2860] = 26003
set PRIMES[2861] = 26017
set PRIMES[2862] = 26021
set PRIMES[2863] = 26029
set PRIMES[2864] = 26041
set PRIMES[2865] = 26053
set PRIMES[2866] = 26083
set PRIMES[2867] = 26099
set PRIMES[2868] = 26107
set PRIMES[2869] = 26111
set PRIMES[2870] = 26113
set PRIMES[2871] = 26119
set PRIMES[2872] = 26141
set PRIMES[2873] = 26153
set PRIMES[2874] = 26161
set PRIMES[2875] = 26171
set PRIMES[2876] = 26177
set PRIMES[2877] = 26183
set PRIMES[2878] = 26189
set PRIMES[2879] = 26203
set PRIMES[2880] = 26209
set PRIMES[2881] = 26227
set PRIMES[2882] = 26237
set PRIMES[2883] = 26249
set PRIMES[2884] = 26251
set PRIMES[2885] = 26261
set PRIMES[2886] = 26263
set PRIMES[2887] = 26267
set PRIMES[2888] = 26293
set PRIMES[2889] = 26297
set PRIMES[2890] = 26309
set PRIMES[2891] = 26317
set PRIMES[2892] = 26321
set PRIMES[2893] = 26339
set PRIMES[2894] = 26347
set PRIMES[2895] = 26357
set PRIMES[2896] = 26371
set PRIMES[2897] = 26387
set PRIMES[2898] = 26393
set PRIMES[2899] = 26399
set PRIMES[2900] = 26407
set PRIMES[2901] = 26417
set PRIMES[2902] = 26423
set PRIMES[2903] = 26431
set PRIMES[2904] = 26437
set PRIMES[2905] = 26449
set PRIMES[2906] = 26459
set PRIMES[2907] = 26479
set PRIMES[2908] = 26489
set PRIMES[2909] = 26497
set PRIMES[2910] = 26501
set PRIMES[2911] = 26513
set PRIMES[2912] = 26539
set PRIMES[2913] = 26557
set PRIMES[2914] = 26561
set PRIMES[2915] = 26573
set PRIMES[2916] = 26591
set PRIMES[2917] = 26597
set PRIMES[2918] = 26627
set PRIMES[2919] = 26633
set PRIMES[2920] = 26641
set PRIMES[2921] = 26647
set PRIMES[2922] = 26669
set PRIMES[2923] = 26681
set PRIMES[2924] = 26683
set PRIMES[2925] = 26687
set PRIMES[2926] = 26693
set PRIMES[2927] = 26699
set PRIMES[2928] = 26701
set PRIMES[2929] = 26711
set PRIMES[2930] = 26713
set PRIMES[2931] = 26717
set PRIMES[2932] = 26723
set PRIMES[2933] = 26729
set PRIMES[2934] = 26731
set PRIMES[2935] = 26737
set PRIMES[2936] = 26759
set PRIMES[2937] = 26777
set PRIMES[2938] = 26783
set PRIMES[2939] = 26801
set PRIMES[2940] = 26813
set PRIMES[2941] = 26821
set PRIMES[2942] = 26833
set PRIMES[2943] = 26839
set PRIMES[2944] = 26849
set PRIMES[2945] = 26861
set PRIMES[2946] = 26863
set PRIMES[2947] = 26879
set PRIMES[2948] = 26881
set PRIMES[2949] = 26891
set PRIMES[2950] = 26893
set PRIMES[2951] = 26903
set PRIMES[2952] = 26921
set PRIMES[2953] = 26927
set PRIMES[2954] = 26947
set PRIMES[2955] = 26951
set PRIMES[2956] = 26953
set PRIMES[2957] = 26959
set PRIMES[2958] = 26981
set PRIMES[2959] = 26987
set PRIMES[2960] = 26993
set PRIMES[2961] = 27011
set PRIMES[2962] = 27017
set PRIMES[2963] = 27031
set PRIMES[2964] = 27043
set PRIMES[2965] = 27059
set PRIMES[2966] = 27061
set PRIMES[2967] = 27067
set PRIMES[2968] = 27073
set PRIMES[2969] = 27077
set PRIMES[2970] = 27091
set PRIMES[2971] = 27103
set PRIMES[2972] = 27107
set PRIMES[2973] = 27109
set PRIMES[2974] = 27127
set PRIMES[2975] = 27143
set PRIMES[2976] = 27179
set PRIMES[2977] = 27191
set PRIMES[2978] = 27197
set PRIMES[2979] = 27211
set PRIMES[2980] = 27239
set PRIMES[2981] = 27241
set PRIMES[2982] = 27253
set PRIMES[2983] = 27259
set PRIMES[2984] = 27271
set PRIMES[2985] = 27277
set PRIMES[2986] = 27281
set PRIMES[2987] = 27283
set PRIMES[2988] = 27299
set PRIMES[2989] = 27329
set PRIMES[2990] = 27337
set PRIMES[2991] = 27361
set PRIMES[2992] = 27367
set PRIMES[2993] = 27397
set PRIMES[2994] = 27407
set PRIMES[2995] = 27409
set PRIMES[2996] = 27427
set PRIMES[2997] = 27431
set PRIMES[2998] = 27437
set PRIMES[2999] = 27449
set PRIMES[3000] = 27457
set PRIMES[3001] = 27479
set PRIMES[3002] = 27481
set PRIMES[3003] = 27487
set PRIMES[3004] = 27509
set PRIMES[3005] = 27527
set PRIMES[3006] = 27529
set PRIMES[3007] = 27539
set PRIMES[3008] = 27541
set PRIMES[3009] = 27551
set PRIMES[3010] = 27581
set PRIMES[3011] = 27583
set PRIMES[3012] = 27611
set PRIMES[3013] = 27617
set PRIMES[3014] = 27631
set PRIMES[3015] = 27647
set PRIMES[3016] = 27653
set PRIMES[3017] = 27673
set PRIMES[3018] = 27689
set PRIMES[3019] = 27691
set PRIMES[3020] = 27697
set PRIMES[3021] = 27701
set PRIMES[3022] = 27733
set PRIMES[3023] = 27737
set PRIMES[3024] = 27739
set PRIMES[3025] = 27743
set PRIMES[3026] = 27749
set PRIMES[3027] = 27751
set PRIMES[3028] = 27763
set PRIMES[3029] = 27767
set PRIMES[3030] = 27773
set PRIMES[3031] = 27779
set PRIMES[3032] = 27791
set PRIMES[3033] = 27793
set PRIMES[3034] = 27799
set PRIMES[3035] = 27803
set PRIMES[3036] = 27809
set PRIMES[3037] = 27817
set PRIMES[3038] = 27823
set PRIMES[3039] = 27827
set PRIMES[3040] = 27847
set PRIMES[3041] = 27851
set PRIMES[3042] = 27883
set PRIMES[3043] = 27893
set PRIMES[3044] = 27901
set PRIMES[3045] = 27917
set PRIMES[3046] = 27919
set PRIMES[3047] = 27941
set PRIMES[3048] = 27943
set PRIMES[3049] = 27947
set PRIMES[3050] = 27953
set PRIMES[3051] = 27961
set PRIMES[3052] = 27967
set PRIMES[3053] = 27983
set PRIMES[3054] = 27997
set PRIMES[3055] = 28001
set PRIMES[3056] = 28019
set PRIMES[3057] = 28027
set PRIMES[3058] = 28031
set PRIMES[3059] = 28051
set PRIMES[3060] = 28057
set PRIMES[3061] = 28069
set PRIMES[3062] = 28081
set PRIMES[3063] = 28087
set PRIMES[3064] = 28097
set PRIMES[3065] = 28099
set PRIMES[3066] = 28109
set PRIMES[3067] = 28111
set PRIMES[3068] = 28123
set PRIMES[3069] = 28151
set PRIMES[3070] = 28163
set PRIMES[3071] = 28181
set PRIMES[3072] = 28183
set PRIMES[3073] = 28201
set PRIMES[3074] = 28211
set PRIMES[3075] = 28219
set PRIMES[3076] = 28229
set PRIMES[3077] = 28277
set PRIMES[3078] = 28279
set PRIMES[3079] = 28283
set PRIMES[3080] = 28289
set PRIMES[3081] = 28297
set PRIMES[3082] = 28307
set PRIMES[3083] = 28309
set PRIMES[3084] = 28319
set PRIMES[3085] = 28349
set PRIMES[3086] = 28351
set PRIMES[3087] = 28387
set PRIMES[3088] = 28393
set PRIMES[3089] = 28403
set PRIMES[3090] = 28409
set PRIMES[3091] = 28411
set PRIMES[3092] = 28429
set PRIMES[3093] = 28433
set PRIMES[3094] = 28439
set PRIMES[3095] = 28447
set PRIMES[3096] = 28463
set PRIMES[3097] = 28477
set PRIMES[3098] = 28493
set PRIMES[3099] = 28499
set PRIMES[3100] = 28513
set PRIMES[3101] = 28517
set PRIMES[3102] = 28537
set PRIMES[3103] = 28541
set PRIMES[3104] = 28547
set PRIMES[3105] = 28549
set PRIMES[3106] = 28559
set PRIMES[3107] = 28571
set PRIMES[3108] = 28573
set PRIMES[3109] = 28579
set PRIMES[3110] = 28591
set PRIMES[3111] = 28597
set PRIMES[3112] = 28603
set PRIMES[3113] = 28607
set PRIMES[3114] = 28619
set PRIMES[3115] = 28621
set PRIMES[3116] = 28627
set PRIMES[3117] = 28631
set PRIMES[3118] = 28643
set PRIMES[3119] = 28649
set PRIMES[3120] = 28657
set PRIMES[3121] = 28661
set PRIMES[3122] = 28663
set PRIMES[3123] = 28669
set PRIMES[3124] = 28687
set PRIMES[3125] = 28697
set PRIMES[3126] = 28703
set PRIMES[3127] = 28711
set PRIMES[3128] = 28723
set PRIMES[3129] = 28729
set PRIMES[3130] = 28751
set PRIMES[3131] = 28753
set PRIMES[3132] = 28759
set PRIMES[3133] = 28771
set PRIMES[3134] = 28789
set PRIMES[3135] = 28793
set PRIMES[3136] = 28807
set PRIMES[3137] = 28813
set PRIMES[3138] = 28817
set PRIMES[3139] = 28837
set PRIMES[3140] = 28843
set PRIMES[3141] = 28859
set PRIMES[3142] = 28867
set PRIMES[3143] = 28871
set PRIMES[3144] = 28879
set PRIMES[3145] = 28901
set PRIMES[3146] = 28909
set PRIMES[3147] = 28921
set PRIMES[3148] = 28927
set PRIMES[3149] = 28933
set PRIMES[3150] = 28949
set PRIMES[3151] = 28961
set PRIMES[3152] = 28979
set PRIMES[3153] = 29009
set PRIMES[3154] = 29017
set PRIMES[3155] = 29021
set PRIMES[3156] = 29023
set PRIMES[3157] = 29027
set PRIMES[3158] = 29033
set PRIMES[3159] = 29059
set PRIMES[3160] = 29063
set PRIMES[3161] = 29077
set PRIMES[3162] = 29101
set PRIMES[3163] = 29123
set PRIMES[3164] = 29129
set PRIMES[3165] = 29131
set PRIMES[3166] = 29137
set PRIMES[3167] = 29147
set PRIMES[3168] = 29153
set PRIMES[3169] = 29167
set PRIMES[3170] = 29173
set PRIMES[3171] = 29179
set PRIMES[3172] = 29191
set PRIMES[3173] = 29201
set PRIMES[3174] = 29207
set PRIMES[3175] = 29209
set PRIMES[3176] = 29221
set PRIMES[3177] = 29231
set PRIMES[3178] = 29243
set PRIMES[3179] = 29251
set PRIMES[3180] = 29269
set PRIMES[3181] = 29287
set PRIMES[3182] = 29297
set PRIMES[3183] = 29303
set PRIMES[3184] = 29311
set PRIMES[3185] = 29327
set PRIMES[3186] = 29333
set PRIMES[3187] = 29339
set PRIMES[3188] = 29347
set PRIMES[3189] = 29363
set PRIMES[3190] = 29383
set PRIMES[3191] = 29387
set PRIMES[3192] = 29389
set PRIMES[3193] = 29399
set PRIMES[3194] = 29401
set PRIMES[3195] = 29411
set PRIMES[3196] = 29423
set PRIMES[3197] = 29429
set PRIMES[3198] = 29437
set PRIMES[3199] = 29443
set PRIMES[3200] = 29453
set PRIMES[3201] = 29473
set PRIMES[3202] = 29483
set PRIMES[3203] = 29501
set PRIMES[3204] = 29527
set PRIMES[3205] = 29531
set PRIMES[3206] = 29537
set PRIMES[3207] = 29567
set PRIMES[3208] = 29569
set PRIMES[3209] = 29573
set PRIMES[3210] = 29581
set PRIMES[3211] = 29587
set PRIMES[3212] = 29599
set PRIMES[3213] = 29611
set PRIMES[3214] = 29629
set PRIMES[3215] = 29633
set PRIMES[3216] = 29641
set PRIMES[3217] = 29663
set PRIMES[3218] = 29669
set PRIMES[3219] = 29671
set PRIMES[3220] = 29683
set PRIMES[3221] = 29717
set PRIMES[3222] = 29723
set PRIMES[3223] = 29741
set PRIMES[3224] = 29753
set PRIMES[3225] = 29759
set PRIMES[3226] = 29761
set PRIMES[3227] = 29789
set PRIMES[3228] = 29803
set PRIMES[3229] = 29819
set PRIMES[3230] = 29833
set PRIMES[3231] = 29837
set PRIMES[3232] = 29851
set PRIMES[3233] = 29863
set PRIMES[3234] = 29867
set PRIMES[3235] = 29873
set PRIMES[3236] = 29879
set PRIMES[3237] = 29881
set PRIMES[3238] = 29917
set PRIMES[3239] = 29921
set PRIMES[3240] = 29927
set PRIMES[3241] = 29947
set PRIMES[3242] = 29959
set PRIMES[3243] = 29983
set PRIMES[3244] = 29989
set PRIMES[3245] = 30011
set PRIMES[3246] = 30013
set PRIMES[3247] = 30029
set PRIMES[3248] = 30047
set PRIMES[3249] = 30059
set PRIMES[3250] = 30071
set PRIMES[3251] = 30089
set PRIMES[3252] = 30091
set PRIMES[3253] = 30097
set PRIMES[3254] = 30103
set PRIMES[3255] = 30109
set PRIMES[3256] = 30113
set PRIMES[3257] = 30119
set PRIMES[3258] = 30133
set PRIMES[3259] = 30137
set PRIMES[3260] = 30139
set PRIMES[3261] = 30161
set PRIMES[3262] = 30169
set PRIMES[3263] = 30181
set PRIMES[3264] = 30187
set PRIMES[3265] = 30197
set PRIMES[3266] = 30203
set PRIMES[3267] = 30211
set PRIMES[3268] = 30223
set PRIMES[3269] = 30241
set PRIMES[3270] = 30253
set PRIMES[3271] = 30259
set PRIMES[3272] = 30269
set PRIMES[3273] = 30271
set PRIMES[3274] = 30293
set PRIMES[3275] = 30307
set PRIMES[3276] = 30313
set PRIMES[3277] = 30319
set PRIMES[3278] = 30323
set PRIMES[3279] = 30341
set PRIMES[3280] = 30347
set PRIMES[3281] = 30367
set PRIMES[3282] = 30389
set PRIMES[3283] = 30391
set PRIMES[3284] = 30403
set PRIMES[3285] = 30427
set PRIMES[3286] = 30431
set PRIMES[3287] = 30449
set PRIMES[3288] = 30467
set PRIMES[3289] = 30469
set PRIMES[3290] = 30491
set PRIMES[3291] = 30493
set PRIMES[3292] = 30497
set PRIMES[3293] = 30509
set PRIMES[3294] = 30517
set PRIMES[3295] = 30529
set PRIMES[3296] = 30539
set PRIMES[3297] = 30553
set PRIMES[3298] = 30557
set PRIMES[3299] = 30559
set PRIMES[3300] = 30577
set PRIMES[3301] = 30593
set PRIMES[3302] = 30631
set PRIMES[3303] = 30637
set PRIMES[3304] = 30643
set PRIMES[3305] = 30649
set PRIMES[3306] = 30661
set PRIMES[3307] = 30671
set PRIMES[3308] = 30677
set PRIMES[3309] = 30689
set PRIMES[3310] = 30697
set PRIMES[3311] = 30703
set PRIMES[3312] = 30707
set PRIMES[3313] = 30713
set PRIMES[3314] = 30727
set PRIMES[3315] = 30757
set PRIMES[3316] = 30763
set PRIMES[3317] = 30773
set PRIMES[3318] = 30781
set PRIMES[3319] = 30803
set PRIMES[3320] = 30809
set PRIMES[3321] = 30817
set PRIMES[3322] = 30829
set PRIMES[3323] = 30839
set PRIMES[3324] = 30841
set PRIMES[3325] = 30851
set PRIMES[3326] = 30853
set PRIMES[3327] = 30859
set PRIMES[3328] = 30869
set PRIMES[3329] = 30871
set PRIMES[3330] = 30881
set PRIMES[3331] = 30893
set PRIMES[3332] = 30911
set PRIMES[3333] = 30931
set PRIMES[3334] = 30937
set PRIMES[3335] = 30941
set PRIMES[3336] = 30949
set PRIMES[3337] = 30971
set PRIMES[3338] = 30977
set PRIMES[3339] = 30983
set PRIMES[3340] = 31013
set PRIMES[3341] = 31019
set PRIMES[3342] = 31033
set PRIMES[3343] = 31039
set PRIMES[3344] = 31051
set PRIMES[3345] = 31063
set PRIMES[3346] = 31069
set PRIMES[3347] = 31079
set PRIMES[3348] = 31081
set PRIMES[3349] = 31091
set PRIMES[3350] = 31121
set PRIMES[3351] = 31123
set PRIMES[3352] = 31139
set PRIMES[3353] = 31147
set PRIMES[3354] = 31151
set PRIMES[3355] = 31153
set PRIMES[3356] = 31159
set PRIMES[3357] = 31177
set PRIMES[3358] = 31181
set PRIMES[3359] = 31183
set PRIMES[3360] = 31189
set PRIMES[3361] = 31193
set PRIMES[3362] = 31219
set PRIMES[3363] = 31223
set PRIMES[3364] = 31231
set PRIMES[3365] = 31237
set PRIMES[3366] = 31247
set PRIMES[3367] = 31249
set PRIMES[3368] = 31253
set PRIMES[3369] = 31259
set PRIMES[3370] = 31267
set PRIMES[3371] = 31271
set PRIMES[3372] = 31277
set PRIMES[3373] = 31307
set PRIMES[3374] = 31319
set PRIMES[3375] = 31321
set PRIMES[3376] = 31327
set PRIMES[3377] = 31333
set PRIMES[3378] = 31337
set PRIMES[3379] = 31357
set PRIMES[3380] = 31379
set PRIMES[3381] = 31387
set PRIMES[3382] = 31391
set PRIMES[3383] = 31393
set PRIMES[3384] = 31397
set PRIMES[3385] = 31469
set PRIMES[3386] = 31477
set PRIMES[3387] = 31481
set PRIMES[3388] = 31489
set PRIMES[3389] = 31511
set PRIMES[3390] = 31513
set PRIMES[3391] = 31517
set PRIMES[3392] = 31531
set PRIMES[3393] = 31541
set PRIMES[3394] = 31543
set PRIMES[3395] = 31547
set PRIMES[3396] = 31567
set PRIMES[3397] = 31573
set PRIMES[3398] = 31583
set PRIMES[3399] = 31601
set PRIMES[3400] = 31607
set PRIMES[3401] = 31627
set PRIMES[3402] = 31643
set PRIMES[3403] = 31649
set PRIMES[3404] = 31657
set PRIMES[3405] = 31663
set PRIMES[3406] = 31667
set PRIMES[3407] = 31687
set PRIMES[3408] = 31699
set PRIMES[3409] = 31721
set PRIMES[3410] = 31723
set PRIMES[3411] = 31727
set PRIMES[3412] = 31729
set PRIMES[3413] = 31741
set PRIMES[3414] = 31751
set PRIMES[3415] = 31769
set PRIMES[3416] = 31771
set PRIMES[3417] = 31793
set PRIMES[3418] = 31799
set PRIMES[3419] = 31817
set PRIMES[3420] = 31847
set PRIMES[3421] = 31849
set PRIMES[3422] = 31859
set PRIMES[3423] = 31873
set PRIMES[3424] = 31883
set PRIMES[3425] = 31891
set PRIMES[3426] = 31907
set PRIMES[3427] = 31957
set PRIMES[3428] = 31963
set PRIMES[3429] = 31973
set PRIMES[3430] = 31981
set PRIMES[3431] = 31991
set PRIMES[3432] = 32003
set PRIMES[3433] = 32009
set PRIMES[3434] = 32027
set PRIMES[3435] = 32029
set PRIMES[3436] = 32051
set PRIMES[3437] = 32057
set PRIMES[3438] = 32059
set PRIMES[3439] = 32063
set PRIMES[3440] = 32069
set PRIMES[3441] = 32077
set PRIMES[3442] = 32083
set PRIMES[3443] = 32089
set PRIMES[3444] = 32099
set PRIMES[3445] = 32117
set PRIMES[3446] = 32119
set PRIMES[3447] = 32141
set PRIMES[3448] = 32143
set PRIMES[3449] = 32159
set PRIMES[3450] = 32173
set PRIMES[3451] = 32183
set PRIMES[3452] = 32189
set PRIMES[3453] = 32191
set PRIMES[3454] = 32203
set PRIMES[3455] = 32213
set PRIMES[3456] = 32233
set PRIMES[3457] = 32237
set PRIMES[3458] = 32251
set PRIMES[3459] = 32257
set PRIMES[3460] = 32261
set PRIMES[3461] = 32297
set PRIMES[3462] = 32299
set PRIMES[3463] = 32303
set PRIMES[3464] = 32309
set PRIMES[3465] = 32321
set PRIMES[3466] = 32323
set PRIMES[3467] = 32327
set PRIMES[3468] = 32341
set PRIMES[3469] = 32353
set PRIMES[3470] = 32359
set PRIMES[3471] = 32363
set PRIMES[3472] = 32369
set PRIMES[3473] = 32371
set PRIMES[3474] = 32377
set PRIMES[3475] = 32381
set PRIMES[3476] = 32401
set PRIMES[3477] = 32411
set PRIMES[3478] = 32413
set PRIMES[3479] = 32423
set PRIMES[3480] = 32429
set PRIMES[3481] = 32441
set PRIMES[3482] = 32443
set PRIMES[3483] = 32467
set PRIMES[3484] = 32479
set PRIMES[3485] = 32491
set PRIMES[3486] = 32497
set PRIMES[3487] = 32503
set PRIMES[3488] = 32507
set PRIMES[3489] = 32531
set PRIMES[3490] = 32533
set PRIMES[3491] = 32537
set PRIMES[3492] = 32561
set PRIMES[3493] = 32563
set PRIMES[3494] = 32569
set PRIMES[3495] = 32573
set PRIMES[3496] = 32579
set PRIMES[3497] = 32587
set PRIMES[3498] = 32603
set PRIMES[3499] = 32609
set PRIMES[3500] = 32611
set PRIMES[3501] = 32621
set PRIMES[3502] = 32633
set PRIMES[3503] = 32647
set PRIMES[3504] = 32653
set PRIMES[3505] = 32687
set PRIMES[3506] = 32693
set PRIMES[3507] = 32707
set PRIMES[3508] = 32713
set PRIMES[3509] = 32717
set PRIMES[3510] = 32719
set PRIMES[3511] = 32749
set PRIMES[3512] = 32771
set PRIMES[3513] = 32779
set PRIMES[3514] = 32783
set PRIMES[3515] = 32789
set PRIMES[3516] = 32797
set PRIMES[3517] = 32801
set PRIMES[3518] = 32803
set PRIMES[3519] = 32831
set PRIMES[3520] = 32833
set PRIMES[3521] = 32839
set PRIMES[3522] = 32843
set PRIMES[3523] = 32869
set PRIMES[3524] = 32887
set PRIMES[3525] = 32909
set PRIMES[3526] = 32911
set PRIMES[3527] = 32917
set PRIMES[3528] = 32933
set PRIMES[3529] = 32939
set PRIMES[3530] = 32941
set PRIMES[3531] = 32957
set PRIMES[3532] = 32969
set PRIMES[3533] = 32971
set PRIMES[3534] = 32983
set PRIMES[3535] = 32987
set PRIMES[3536] = 32993
set PRIMES[3537] = 32999
set PRIMES[3538] = 33013
set PRIMES[3539] = 33023
set PRIMES[3540] = 33029
set PRIMES[3541] = 33037
set PRIMES[3542] = 33049
set PRIMES[3543] = 33053
set PRIMES[3544] = 33071
set PRIMES[3545] = 33073
set PRIMES[3546] = 33083
set PRIMES[3547] = 33091
set PRIMES[3548] = 33107
set PRIMES[3549] = 33113
set PRIMES[3550] = 33119
set PRIMES[3551] = 33149
set PRIMES[3552] = 33151
set PRIMES[3553] = 33161
set PRIMES[3554] = 33179
set PRIMES[3555] = 33181
set PRIMES[3556] = 33191
set PRIMES[3557] = 33199
set PRIMES[3558] = 33203
set PRIMES[3559] = 33211
set PRIMES[3560] = 33223
set PRIMES[3561] = 33247
set PRIMES[3562] = 33287
set PRIMES[3563] = 33289
set PRIMES[3564] = 33301
set PRIMES[3565] = 33311
set PRIMES[3566] = 33317
set PRIMES[3567] = 33329
set PRIMES[3568] = 33331
set PRIMES[3569] = 33343
set PRIMES[3570] = 33347
set PRIMES[3571] = 33349
set PRIMES[3572] = 33353
set PRIMES[3573] = 33359
set PRIMES[3574] = 33377
set PRIMES[3575] = 33391
set PRIMES[3576] = 33403
set PRIMES[3577] = 33409
set PRIMES[3578] = 33413
set PRIMES[3579] = 33427
set PRIMES[3580] = 33457
set PRIMES[3581] = 33461
set PRIMES[3582] = 33469
set PRIMES[3583] = 33479
set PRIMES[3584] = 33487
set PRIMES[3585] = 33493
set PRIMES[3586] = 33503
set PRIMES[3587] = 33521
set PRIMES[3588] = 33529
set PRIMES[3589] = 33533
set PRIMES[3590] = 33547
set PRIMES[3591] = 33563
set PRIMES[3592] = 33569
set PRIMES[3593] = 33577
set PRIMES[3594] = 33581
set PRIMES[3595] = 33587
set PRIMES[3596] = 33589
set PRIMES[3597] = 33599
set PRIMES[3598] = 33601
set PRIMES[3599] = 33613
set PRIMES[3600] = 33617
set PRIMES[3601] = 33619
set PRIMES[3602] = 33623
set PRIMES[3603] = 33629
set PRIMES[3604] = 33637
set PRIMES[3605] = 33641
set PRIMES[3606] = 33647
set PRIMES[3607] = 33679
set PRIMES[3608] = 33703
set PRIMES[3609] = 33713
set PRIMES[3610] = 33721
set PRIMES[3611] = 33739
set PRIMES[3612] = 33749
set PRIMES[3613] = 33751
set PRIMES[3614] = 33757
set PRIMES[3615] = 33767
set PRIMES[3616] = 33769
set PRIMES[3617] = 33773
set PRIMES[3618] = 33791
set PRIMES[3619] = 33797
set PRIMES[3620] = 33809
set PRIMES[3621] = 33811
set PRIMES[3622] = 33827
set PRIMES[3623] = 33829
set PRIMES[3624] = 33851
set PRIMES[3625] = 33857
set PRIMES[3626] = 33863
set PRIMES[3627] = 33871
set PRIMES[3628] = 33889
set PRIMES[3629] = 33893
set PRIMES[3630] = 33911
set PRIMES[3631] = 33923
set PRIMES[3632] = 33931
set PRIMES[3633] = 33937
set PRIMES[3634] = 33941
set PRIMES[3635] = 33961
set PRIMES[3636] = 33967
set PRIMES[3637] = 33997
set PRIMES[3638] = 34019
set PRIMES[3639] = 34031
set PRIMES[3640] = 34033
set PRIMES[3641] = 34039
set PRIMES[3642] = 34057
set PRIMES[3643] = 34061
set PRIMES[3644] = 34123
set PRIMES[3645] = 34127
set PRIMES[3646] = 34129
set PRIMES[3647] = 34141
set PRIMES[3648] = 34147
set PRIMES[3649] = 34157
set PRIMES[3650] = 34159
set PRIMES[3651] = 34171
set PRIMES[3652] = 34183
set PRIMES[3653] = 34211
set PRIMES[3654] = 34213
set PRIMES[3655] = 34217
set PRIMES[3656] = 34231
set PRIMES[3657] = 34253
set PRIMES[3658] = 34259
set PRIMES[3659] = 34261
set PRIMES[3660] = 34267
set PRIMES[3661] = 34273
set PRIMES[3662] = 34283
set PRIMES[3663] = 34297
set PRIMES[3664] = 34301
set PRIMES[3665] = 34303
set PRIMES[3666] = 34313
set PRIMES[3667] = 34319
set PRIMES[3668] = 34327
set PRIMES[3669] = 34337
set PRIMES[3670] = 34351
set PRIMES[3671] = 34361
set PRIMES[3672] = 34367
set PRIMES[3673] = 34369
set PRIMES[3674] = 34381
set PRIMES[3675] = 34403
set PRIMES[3676] = 34421
set PRIMES[3677] = 34429
set PRIMES[3678] = 34439
set PRIMES[3679] = 34457
set PRIMES[3680] = 34469
set PRIMES[3681] = 34471
set PRIMES[3682] = 34483
set PRIMES[3683] = 34487
set PRIMES[3684] = 34499
set PRIMES[3685] = 34501
set PRIMES[3686] = 34511
set PRIMES[3687] = 34513
set PRIMES[3688] = 34519
set PRIMES[3689] = 34537
set PRIMES[3690] = 34543
set PRIMES[3691] = 34549
set PRIMES[3692] = 34583
set PRIMES[3693] = 34589
set PRIMES[3694] = 34591
set PRIMES[3695] = 34603
set PRIMES[3696] = 34607
set PRIMES[3697] = 34613
set PRIMES[3698] = 34631
set PRIMES[3699] = 34649
set PRIMES[3700] = 34651
set PRIMES[3701] = 34667
set PRIMES[3702] = 34673
set PRIMES[3703] = 34679
set PRIMES[3704] = 34687
set PRIMES[3705] = 34693
set PRIMES[3706] = 34703
set PRIMES[3707] = 34721
set PRIMES[3708] = 34729
set PRIMES[3709] = 34739
set PRIMES[3710] = 34747
set PRIMES[3711] = 34757
set PRIMES[3712] = 34759
set PRIMES[3713] = 34763
set PRIMES[3714] = 34781
set PRIMES[3715] = 34807
set PRIMES[3716] = 34819
set PRIMES[3717] = 34841
set PRIMES[3718] = 34843
set PRIMES[3719] = 34847
set PRIMES[3720] = 34849
set PRIMES[3721] = 34871
set PRIMES[3722] = 34877
set PRIMES[3723] = 34883
set PRIMES[3724] = 34897
set PRIMES[3725] = 34913
set PRIMES[3726] = 34919
set PRIMES[3727] = 34939
set PRIMES[3728] = 34949
set PRIMES[3729] = 34961
set PRIMES[3730] = 34963
set PRIMES[3731] = 34981
set PRIMES[3732] = 35023
set PRIMES[3733] = 35027
set PRIMES[3734] = 35051
set PRIMES[3735] = 35053
set PRIMES[3736] = 35059
set PRIMES[3737] = 35069
set PRIMES[3738] = 35081
set PRIMES[3739] = 35083
set PRIMES[3740] = 35089
set PRIMES[3741] = 35099
set PRIMES[3742] = 35107
set PRIMES[3743] = 35111
set PRIMES[3744] = 35117
set PRIMES[3745] = 35129
set PRIMES[3746] = 35141
set PRIMES[3747] = 35149
set PRIMES[3748] = 35153
set PRIMES[3749] = 35159
set PRIMES[3750] = 35171
set PRIMES[3751] = 35201
set PRIMES[3752] = 35221
set PRIMES[3753] = 35227
set PRIMES[3754] = 35251
set PRIMES[3755] = 35257
set PRIMES[3756] = 35267
set PRIMES[3757] = 35279
set PRIMES[3758] = 35281
set PRIMES[3759] = 35291
set PRIMES[3760] = 35311
set PRIMES[3761] = 35317
set PRIMES[3762] = 35323
set PRIMES[3763] = 35327
set PRIMES[3764] = 35339
set PRIMES[3765] = 35353
set PRIMES[3766] = 35363
set PRIMES[3767] = 35381
set PRIMES[3768] = 35393
set PRIMES[3769] = 35401
set PRIMES[3770] = 35407
set PRIMES[3771] = 35419
set PRIMES[3772] = 35423
set PRIMES[3773] = 35437
set PRIMES[3774] = 35447
set PRIMES[3775] = 35449
set PRIMES[3776] = 35461
set PRIMES[3777] = 35491
set PRIMES[3778] = 35507
set PRIMES[3779] = 35509
set PRIMES[3780] = 35521
set PRIMES[3781] = 35527
set PRIMES[3782] = 35531
set PRIMES[3783] = 35533
set PRIMES[3784] = 35537
set PRIMES[3785] = 35543
set PRIMES[3786] = 35569
set PRIMES[3787] = 35573
set PRIMES[3788] = 35591
set PRIMES[3789] = 35593
set PRIMES[3790] = 35597
set PRIMES[3791] = 35603
set PRIMES[3792] = 35617
set PRIMES[3793] = 35671
set PRIMES[3794] = 35677
set PRIMES[3795] = 35729
set PRIMES[3796] = 35731
set PRIMES[3797] = 35747
set PRIMES[3798] = 35753
set PRIMES[3799] = 35759
set PRIMES[3800] = 35771
set PRIMES[3801] = 35797
set PRIMES[3802] = 35801
set PRIMES[3803] = 35803
set PRIMES[3804] = 35809
set PRIMES[3805] = 35831
set PRIMES[3806] = 35837
set PRIMES[3807] = 35839
set PRIMES[3808] = 35851
set PRIMES[3809] = 35863
set PRIMES[3810] = 35869
set PRIMES[3811] = 35879
set PRIMES[3812] = 35897
set PRIMES[3813] = 35899
set PRIMES[3814] = 35911
set PRIMES[3815] = 35923
set PRIMES[3816] = 35933
set PRIMES[3817] = 35951
set PRIMES[3818] = 35963
set PRIMES[3819] = 35969
set PRIMES[3820] = 35977
set PRIMES[3821] = 35983
set PRIMES[3822] = 35993
set PRIMES[3823] = 35999
set PRIMES[3824] = 36007
set PRIMES[3825] = 36011
set PRIMES[3826] = 36013
set PRIMES[3827] = 36017
set PRIMES[3828] = 36037
set PRIMES[3829] = 36061
set PRIMES[3830] = 36067
set PRIMES[3831] = 36073
set PRIMES[3832] = 36083
set PRIMES[3833] = 36097
set PRIMES[3834] = 36107
set PRIMES[3835] = 36109
set PRIMES[3836] = 36131
set PRIMES[3837] = 36137
set PRIMES[3838] = 36151
set PRIMES[3839] = 36161
set PRIMES[3840] = 36187
set PRIMES[3841] = 36191
set PRIMES[3842] = 36209
set PRIMES[3843] = 36217
set PRIMES[3844] = 36229
set PRIMES[3845] = 36241
set PRIMES[3846] = 36251
set PRIMES[3847] = 36263
set PRIMES[3848] = 36269
set PRIMES[3849] = 36277
set PRIMES[3850] = 36293
set PRIMES[3851] = 36299
set PRIMES[3852] = 36307
set PRIMES[3853] = 36313
set PRIMES[3854] = 36319
set PRIMES[3855] = 36341
set PRIMES[3856] = 36343
set PRIMES[3857] = 36353
set PRIMES[3858] = 36373
set PRIMES[3859] = 36383
set PRIMES[3860] = 36389
set PRIMES[3861] = 36433
set PRIMES[3862] = 36451
set PRIMES[3863] = 36457
set PRIMES[3864] = 36467
set PRIMES[3865] = 36469
set PRIMES[3866] = 36473
set PRIMES[3867] = 36479
set PRIMES[3868] = 36493
set PRIMES[3869] = 36497
set PRIMES[3870] = 36523
set PRIMES[3871] = 36527
set PRIMES[3872] = 36529
set PRIMES[3873] = 36541
set PRIMES[3874] = 36551
set PRIMES[3875] = 36559
set PRIMES[3876] = 36563
set PRIMES[3877] = 36571
set PRIMES[3878] = 36583
set PRIMES[3879] = 36587
set PRIMES[3880] = 36599
set PRIMES[3881] = 36607
set PRIMES[3882] = 36629
set PRIMES[3883] = 36637
set PRIMES[3884] = 36643
set PRIMES[3885] = 36653
set PRIMES[3886] = 36671
set PRIMES[3887] = 36677
set PRIMES[3888] = 36683
set PRIMES[3889] = 36691
set PRIMES[3890] = 36697
set PRIMES[3891] = 36709
set PRIMES[3892] = 36713
set PRIMES[3893] = 36721
set PRIMES[3894] = 36739
set PRIMES[3895] = 36749
set PRIMES[3896] = 36761
set PRIMES[3897] = 36767
set PRIMES[3898] = 36779
set PRIMES[3899] = 36781
set PRIMES[3900] = 36787
set PRIMES[3901] = 36791
set PRIMES[3902] = 36793
set PRIMES[3903] = 36809
set PRIMES[3904] = 36821
set PRIMES[3905] = 36833
set PRIMES[3906] = 36847
set PRIMES[3907] = 36857
set PRIMES[3908] = 36871
set PRIMES[3909] = 36877
set PRIMES[3910] = 36887
set PRIMES[3911] = 36899
set PRIMES[3912] = 36901
set PRIMES[3913] = 36913
set PRIMES[3914] = 36919
set PRIMES[3915] = 36923
set PRIMES[3916] = 36929
set PRIMES[3917] = 36931
set PRIMES[3918] = 36943
set PRIMES[3919] = 36947
set PRIMES[3920] = 36973
set PRIMES[3921] = 36979
set PRIMES[3922] = 36997
set PRIMES[3923] = 37003
set PRIMES[3924] = 37013
set PRIMES[3925] = 37019
set PRIMES[3926] = 37021
set PRIMES[3927] = 37039
set PRIMES[3928] = 37049
set PRIMES[3929] = 37057
set PRIMES[3930] = 37061
set PRIMES[3931] = 37087
set PRIMES[3932] = 37097
set PRIMES[3933] = 37117
set PRIMES[3934] = 37123
set PRIMES[3935] = 37139
set PRIMES[3936] = 37159
set PRIMES[3937] = 37171
set PRIMES[3938] = 37181
set PRIMES[3939] = 37189
set PRIMES[3940] = 37199
set PRIMES[3941] = 37201
set PRIMES[3942] = 37217
set PRIMES[3943] = 37223
set PRIMES[3944] = 37243
set PRIMES[3945] = 37253
set PRIMES[3946] = 37273
set PRIMES[3947] = 37277
set PRIMES[3948] = 37307
set PRIMES[3949] = 37309
set PRIMES[3950] = 37313
set PRIMES[3951] = 37321
set PRIMES[3952] = 37337
set PRIMES[3953] = 37339
set PRIMES[3954] = 37357
set PRIMES[3955] = 37361
set PRIMES[3956] = 37363
set PRIMES[3957] = 37369
set PRIMES[3958] = 37379
set PRIMES[3959] = 37397
set PRIMES[3960] = 37409
set PRIMES[3961] = 37423
set PRIMES[3962] = 37441
set PRIMES[3963] = 37447
set PRIMES[3964] = 37463
set PRIMES[3965] = 37483
set PRIMES[3966] = 37489
set PRIMES[3967] = 37493
set PRIMES[3968] = 37501
set PRIMES[3969] = 37507
set PRIMES[3970] = 37511
set PRIMES[3971] = 37517
set PRIMES[3972] = 37529
set PRIMES[3973] = 37537
set PRIMES[3974] = 37547
set PRIMES[3975] = 37549
set PRIMES[3976] = 37561
set PRIMES[3977] = 37567
set PRIMES[3978] = 37571
set PRIMES[3979] = 37573
set PRIMES[3980] = 37579
set PRIMES[3981] = 37589
set PRIMES[3982] = 37591
set PRIMES[3983] = 37607
set PRIMES[3984] = 37619
set PRIMES[3985] = 37633
set PRIMES[3986] = 37643
set PRIMES[3987] = 37649
set PRIMES[3988] = 37657
set PRIMES[3989] = 37663
set PRIMES[3990] = 37691
set PRIMES[3991] = 37693
set PRIMES[3992] = 37699
set PRIMES[3993] = 37717
set PRIMES[3994] = 37747
set PRIMES[3995] = 37781
set PRIMES[3996] = 37783
set PRIMES[3997] = 37799
set PRIMES[3998] = 37811
set PRIMES[3999] = 37813
set PRIMES[4000] = 37831
set PRIMES[4001] = 37847
set PRIMES[4002] = 37853
set PRIMES[4003] = 37861
set PRIMES[4004] = 37871
set PRIMES[4005] = 37879
set PRIMES[4006] = 37889
set PRIMES[4007] = 37897
set PRIMES[4008] = 37907
set PRIMES[4009] = 37951
set PRIMES[4010] = 37957
set PRIMES[4011] = 37963
set PRIMES[4012] = 37967
set PRIMES[4013] = 37987
set PRIMES[4014] = 37991
set PRIMES[4015] = 37993
set PRIMES[4016] = 37997
set PRIMES[4017] = 38011
set PRIMES[4018] = 38039
set PRIMES[4019] = 38047
set PRIMES[4020] = 38053
set PRIMES[4021] = 38069
set PRIMES[4022] = 38083
set PRIMES[4023] = 38113
set PRIMES[4024] = 38119
set PRIMES[4025] = 38149
set PRIMES[4026] = 38153
set PRIMES[4027] = 38167
set PRIMES[4028] = 38177
set PRIMES[4029] = 38183
set PRIMES[4030] = 38189
set PRIMES[4031] = 38197
set PRIMES[4032] = 38201
set PRIMES[4033] = 38219
set PRIMES[4034] = 38231
set PRIMES[4035] = 38237
set PRIMES[4036] = 38239
set PRIMES[4037] = 38261
set PRIMES[4038] = 38273
set PRIMES[4039] = 38281
set PRIMES[4040] = 38287
set PRIMES[4041] = 38299
set PRIMES[4042] = 38303
set PRIMES[4043] = 38317
set PRIMES[4044] = 38321
set PRIMES[4045] = 38327
set PRIMES[4046] = 38329
set PRIMES[4047] = 38333
set PRIMES[4048] = 38351
set PRIMES[4049] = 38371
set PRIMES[4050] = 38377
set PRIMES[4051] = 38393
set PRIMES[4052] = 38431
set PRIMES[4053] = 38447
set PRIMES[4054] = 38449
set PRIMES[4055] = 38453
set PRIMES[4056] = 38459
set PRIMES[4057] = 38461
set PRIMES[4058] = 38501
set PRIMES[4059] = 38543
set PRIMES[4060] = 38557
set PRIMES[4061] = 38561
set PRIMES[4062] = 38567
set PRIMES[4063] = 38569
set PRIMES[4064] = 38593
set PRIMES[4065] = 38603
set PRIMES[4066] = 38609
set PRIMES[4067] = 38611
set PRIMES[4068] = 38629
set PRIMES[4069] = 38639
set PRIMES[4070] = 38651
set PRIMES[4071] = 38653
set PRIMES[4072] = 38669
set PRIMES[4073] = 38671
set PRIMES[4074] = 38677
set PRIMES[4075] = 38693
set PRIMES[4076] = 38699
set PRIMES[4077] = 38707
set PRIMES[4078] = 38711
set PRIMES[4079] = 38713
set PRIMES[4080] = 38723
set PRIMES[4081] = 38729
set PRIMES[4082] = 38737
set PRIMES[4083] = 38747
set PRIMES[4084] = 38749
set PRIMES[4085] = 38767
set PRIMES[4086] = 38783
set PRIMES[4087] = 38791
set PRIMES[4088] = 38803
set PRIMES[4089] = 38821
set PRIMES[4090] = 38833
set PRIMES[4091] = 38839
set PRIMES[4092] = 38851
set PRIMES[4093] = 38861
set PRIMES[4094] = 38867
set PRIMES[4095] = 38873
set PRIMES[4096] = 38891
set PRIMES[4097] = 38903
set PRIMES[4098] = 38917
set PRIMES[4099] = 38921
set PRIMES[4100] = 38923
set PRIMES[4101] = 38933
set PRIMES[4102] = 38953
set PRIMES[4103] = 38959
set PRIMES[4104] = 38971
set PRIMES[4105] = 38977
set PRIMES[4106] = 38993
set PRIMES[4107] = 39019
set PRIMES[4108] = 39023
set PRIMES[4109] = 39041
set PRIMES[4110] = 39043
set PRIMES[4111] = 39047
set PRIMES[4112] = 39079
set PRIMES[4113] = 39089
set PRIMES[4114] = 39097
set PRIMES[4115] = 39103
set PRIMES[4116] = 39107
set PRIMES[4117] = 39113
set PRIMES[4118] = 39119
set PRIMES[4119] = 39133
set PRIMES[4120] = 39139
set PRIMES[4121] = 39157
set PRIMES[4122] = 39161
set PRIMES[4123] = 39163
set PRIMES[4124] = 39181
set PRIMES[4125] = 39191
set PRIMES[4126] = 39199
set PRIMES[4127] = 39209
set PRIMES[4128] = 39217
set PRIMES[4129] = 39227
set PRIMES[4130] = 39229
set PRIMES[4131] = 39233
set PRIMES[4132] = 39239
set PRIMES[4133] = 39241
set PRIMES[4134] = 39251
set PRIMES[4135] = 39293
set PRIMES[4136] = 39301
set PRIMES[4137] = 39313
set PRIMES[4138] = 39317
set PRIMES[4139] = 39323
set PRIMES[4140] = 39341
set PRIMES[4141] = 39343
set PRIMES[4142] = 39359
set PRIMES[4143] = 39367
set PRIMES[4144] = 39371
set PRIMES[4145] = 39373
set PRIMES[4146] = 39383
set PRIMES[4147] = 39397
set PRIMES[4148] = 39409
set PRIMES[4149] = 39419
set PRIMES[4150] = 39439
set PRIMES[4151] = 39443
set PRIMES[4152] = 39451
set PRIMES[4153] = 39461
set PRIMES[4154] = 39499
set PRIMES[4155] = 39503
set PRIMES[4156] = 39509
set PRIMES[4157] = 39511
set PRIMES[4158] = 39521
set PRIMES[4159] = 39541
set PRIMES[4160] = 39551
set PRIMES[4161] = 39563
set PRIMES[4162] = 39569
set PRIMES[4163] = 39581
set PRIMES[4164] = 39607
set PRIMES[4165] = 39619
set PRIMES[4166] = 39623
set PRIMES[4167] = 39631
set PRIMES[4168] = 39659
set PRIMES[4169] = 39667
set PRIMES[4170] = 39671
set PRIMES[4171] = 39679
set PRIMES[4172] = 39703
set PRIMES[4173] = 39709
set PRIMES[4174] = 39719
set PRIMES[4175] = 39727
set PRIMES[4176] = 39733
set PRIMES[4177] = 39749
set PRIMES[4178] = 39761
set PRIMES[4179] = 39769
set PRIMES[4180] = 39779
set PRIMES[4181] = 39791
set PRIMES[4182] = 39799
set PRIMES[4183] = 39821
set PRIMES[4184] = 39827
set PRIMES[4185] = 39829
set PRIMES[4186] = 39839
set PRIMES[4187] = 39841
set PRIMES[4188] = 39847
set PRIMES[4189] = 39857
set PRIMES[4190] = 39863
set PRIMES[4191] = 39869
set PRIMES[4192] = 39877
set PRIMES[4193] = 39883
set PRIMES[4194] = 39887
set PRIMES[4195] = 39901
set PRIMES[4196] = 39929
set PRIMES[4197] = 39937
set PRIMES[4198] = 39953
set PRIMES[4199] = 39971
set PRIMES[4200] = 39979
set PRIMES[4201] = 39983
set PRIMES[4202] = 39989
set PRIMES[4203] = 40009
set PRIMES[4204] = 40013
set PRIMES[4205] = 40031
set PRIMES[4206] = 40037
set PRIMES[4207] = 40039
set PRIMES[4208] = 40063
set PRIMES[4209] = 40087
set PRIMES[4210] = 40093
set PRIMES[4211] = 40099
set PRIMES[4212] = 40111
set PRIMES[4213] = 40123
set PRIMES[4214] = 40127
set PRIMES[4215] = 40129
set PRIMES[4216] = 40151
set PRIMES[4217] = 40153
set PRIMES[4218] = 40163
set PRIMES[4219] = 40169
set PRIMES[4220] = 40177
set PRIMES[4221] = 40189
set PRIMES[4222] = 40193
set PRIMES[4223] = 40213
set PRIMES[4224] = 40231
set PRIMES[4225] = 40237
set PRIMES[4226] = 40241
set PRIMES[4227] = 40253
set PRIMES[4228] = 40277
set PRIMES[4229] = 40283
set PRIMES[4230] = 40289
set PRIMES[4231] = 40343
set PRIMES[4232] = 40351
set PRIMES[4233] = 40357
set PRIMES[4234] = 40361
set PRIMES[4235] = 40387
set PRIMES[4236] = 40423
set PRIMES[4237] = 40427
set PRIMES[4238] = 40429
set PRIMES[4239] = 40433
set PRIMES[4240] = 40459
set PRIMES[4241] = 40471
set PRIMES[4242] = 40483
set PRIMES[4243] = 40487
set PRIMES[4244] = 40493
set PRIMES[4245] = 40499
set PRIMES[4246] = 40507
set PRIMES[4247] = 40519
set PRIMES[4248] = 40529
set PRIMES[4249] = 40531
set PRIMES[4250] = 40543
set PRIMES[4251] = 40559
set PRIMES[4252] = 40577
set PRIMES[4253] = 40583
set PRIMES[4254] = 40591
set PRIMES[4255] = 40597
set PRIMES[4256] = 40609
set PRIMES[4257] = 40627
set PRIMES[4258] = 40637
set PRIMES[4259] = 40639
set PRIMES[4260] = 40693
set PRIMES[4261] = 40697
set PRIMES[4262] = 40699
set PRIMES[4263] = 40709
set PRIMES[4264] = 40739
set PRIMES[4265] = 40751
set PRIMES[4266] = 40759
set PRIMES[4267] = 40763
set PRIMES[4268] = 40771
set PRIMES[4269] = 40787
set PRIMES[4270] = 40801
set PRIMES[4271] = 40813
set PRIMES[4272] = 40819
set PRIMES[4273] = 40823
set PRIMES[4274] = 40829
set PRIMES[4275] = 40841
set PRIMES[4276] = 40847
set PRIMES[4277] = 40849
set PRIMES[4278] = 40853
set PRIMES[4279] = 40867
set PRIMES[4280] = 40879
set PRIMES[4281] = 40883
set PRIMES[4282] = 40897
set PRIMES[4283] = 40903
set PRIMES[4284] = 40927
set PRIMES[4285] = 40933
set PRIMES[4286] = 40939
set PRIMES[4287] = 40949
set PRIMES[4288] = 40961
set PRIMES[4289] = 40973
set PRIMES[4290] = 40993
set PRIMES[4291] = 41011
set PRIMES[4292] = 41017
set PRIMES[4293] = 41023
set PRIMES[4294] = 41039
set PRIMES[4295] = 41047
set PRIMES[4296] = 41051
set PRIMES[4297] = 41057
set PRIMES[4298] = 41077
set PRIMES[4299] = 41081
set PRIMES[4300] = 41113
set PRIMES[4301] = 41117
set PRIMES[4302] = 41131
set PRIMES[4303] = 41141
set PRIMES[4304] = 41143
set PRIMES[4305] = 41149
set PRIMES[4306] = 41161
set PRIMES[4307] = 41177
set PRIMES[4308] = 41179
set PRIMES[4309] = 41183
set PRIMES[4310] = 41189
set PRIMES[4311] = 41201
set PRIMES[4312] = 41203
set PRIMES[4313] = 41213
set PRIMES[4314] = 41221
set PRIMES[4315] = 41227
set PRIMES[4316] = 41231
set PRIMES[4317] = 41233
set PRIMES[4318] = 41243
set PRIMES[4319] = 41257
set PRIMES[4320] = 41263
set PRIMES[4321] = 41269
set PRIMES[4322] = 41281
set PRIMES[4323] = 41299
set PRIMES[4324] = 41333
set PRIMES[4325] = 41341
set PRIMES[4326] = 41351
set PRIMES[4327] = 41357
set PRIMES[4328] = 41381
set PRIMES[4329] = 41387
set PRIMES[4330] = 41389
set PRIMES[4331] = 41399
set PRIMES[4332] = 41411
set PRIMES[4333] = 41413
set PRIMES[4334] = 41443
set PRIMES[4335] = 41453
set PRIMES[4336] = 41467
set PRIMES[4337] = 41479
set PRIMES[4338] = 41491
set PRIMES[4339] = 41507
set PRIMES[4340] = 41513
set PRIMES[4341] = 41519
set PRIMES[4342] = 41521
set PRIMES[4343] = 41539
set PRIMES[4344] = 41543
set PRIMES[4345] = 41549
set PRIMES[4346] = 41579
set PRIMES[4347] = 41593
set PRIMES[4348] = 41597
set PRIMES[4349] = 41603
set PRIMES[4350] = 41609
set PRIMES[4351] = 41611
set PRIMES[4352] = 41617
set PRIMES[4353] = 41621
set PRIMES[4354] = 41627
set PRIMES[4355] = 41641
set PRIMES[4356] = 41647
set PRIMES[4357] = 41651
set PRIMES[4358] = 41659
set PRIMES[4359] = 41669
set PRIMES[4360] = 41681
set PRIMES[4361] = 41687
set PRIMES[4362] = 41719
set PRIMES[4363] = 41729
set PRIMES[4364] = 41737
set PRIMES[4365] = 41759
set PRIMES[4366] = 41761
set PRIMES[4367] = 41771
set PRIMES[4368] = 41777
set PRIMES[4369] = 41801
set PRIMES[4370] = 41809
set PRIMES[4371] = 41813
set PRIMES[4372] = 41843
set PRIMES[4373] = 41849
set PRIMES[4374] = 41851
set PRIMES[4375] = 41863
set PRIMES[4376] = 41879
set PRIMES[4377] = 41887
set PRIMES[4378] = 41893
set PRIMES[4379] = 41897
set PRIMES[4380] = 41903
set PRIMES[4381] = 41911
set PRIMES[4382] = 41927
set PRIMES[4383] = 41941
set PRIMES[4384] = 41947
set PRIMES[4385] = 41953
set PRIMES[4386] = 41957
set PRIMES[4387] = 41959
set PRIMES[4388] = 41969
set PRIMES[4389] = 41981
set PRIMES[4390] = 41983
set PRIMES[4391] = 41999
set PRIMES[4392] = 42013
set PRIMES[4393] = 42017
set PRIMES[4394] = 42019
set PRIMES[4395] = 42023
set PRIMES[4396] = 42043
set PRIMES[4397] = 42061
set PRIMES[4398] = 42071
set PRIMES[4399] = 42073
set PRIMES[4400] = 42083
set PRIMES[4401] = 42089
set PRIMES[4402] = 42101
set PRIMES[4403] = 42131
set PRIMES[4404] = 42139
set PRIMES[4405] = 42157
set PRIMES[4406] = 42169
set PRIMES[4407] = 42179
set PRIMES[4408] = 42181
set PRIMES[4409] = 42187
set PRIMES[4410] = 42193
set PRIMES[4411] = 42197
set PRIMES[4412] = 42209
set PRIMES[4413] = 42221
set PRIMES[4414] = 42223
set PRIMES[4415] = 42227
set PRIMES[4416] = 42239
set PRIMES[4417] = 42257
set PRIMES[4418] = 42281
set PRIMES[4419] = 42283
set PRIMES[4420] = 42293
set PRIMES[4421] = 42299
set PRIMES[4422] = 42307
set PRIMES[4423] = 42323
set PRIMES[4424] = 42331
set PRIMES[4425] = 42337
set PRIMES[4426] = 42349
set PRIMES[4427] = 42359
set PRIMES[4428] = 42373
set PRIMES[4429] = 42379
set PRIMES[4430] = 42391
set PRIMES[4431] = 42397
set PRIMES[4432] = 42403
set PRIMES[4433] = 42407
set PRIMES[4434] = 42409
set PRIMES[4435] = 42433
set PRIMES[4436] = 42437
set PRIMES[4437] = 42443
set PRIMES[4438] = 42451
set PRIMES[4439] = 42457
set PRIMES[4440] = 42461
set PRIMES[4441] = 42463
set PRIMES[4442] = 42467
set PRIMES[4443] = 42473
set PRIMES[4444] = 42487
set PRIMES[4445] = 42491
set PRIMES[4446] = 42499
set PRIMES[4447] = 42509
set PRIMES[4448] = 42533
set PRIMES[4449] = 42557
set PRIMES[4450] = 42569
set PRIMES[4451] = 42571
set PRIMES[4452] = 42577
set PRIMES[4453] = 42589
set PRIMES[4454] = 42611
set PRIMES[4455] = 42641
set PRIMES[4456] = 42643
set PRIMES[4457] = 42649
set PRIMES[4458] = 42667
set PRIMES[4459] = 42677
set PRIMES[4460] = 42683
set PRIMES[4461] = 42689
set PRIMES[4462] = 42697
set PRIMES[4463] = 42701
set PRIMES[4464] = 42703
set PRIMES[4465] = 42709
set PRIMES[4466] = 42719
set PRIMES[4467] = 42727
set PRIMES[4468] = 42737
set PRIMES[4469] = 42743
set PRIMES[4470] = 42751
set PRIMES[4471] = 42767
set PRIMES[4472] = 42773
set PRIMES[4473] = 42787
set PRIMES[4474] = 42793
set PRIMES[4475] = 42797
set PRIMES[4476] = 42821
set PRIMES[4477] = 42829
set PRIMES[4478] = 42839
set PRIMES[4479] = 42841
set PRIMES[4480] = 42853
set PRIMES[4481] = 42859
set PRIMES[4482] = 42863
set PRIMES[4483] = 42899
set PRIMES[4484] = 42901
set PRIMES[4485] = 42923
set PRIMES[4486] = 42929
set PRIMES[4487] = 42937
set PRIMES[4488] = 42943
set PRIMES[4489] = 42953
set PRIMES[4490] = 42961
set PRIMES[4491] = 42967
set PRIMES[4492] = 42979
set PRIMES[4493] = 42989
set PRIMES[4494] = 43003
set PRIMES[4495] = 43013
set PRIMES[4496] = 43019
set PRIMES[4497] = 43037
set PRIMES[4498] = 43049
set PRIMES[4499] = 43051
set PRIMES[4500] = 43063
set PRIMES[4501] = 43067
set PRIMES[4502] = 43093
set PRIMES[4503] = 43103
set PRIMES[4504] = 43117
set PRIMES[4505] = 43133
set PRIMES[4506] = 43151
set PRIMES[4507] = 43159
set PRIMES[4508] = 43177
set PRIMES[4509] = 43189
set PRIMES[4510] = 43201
set PRIMES[4511] = 43207
set PRIMES[4512] = 43223
set PRIMES[4513] = 43237
set PRIMES[4514] = 43261
set PRIMES[4515] = 43271
set PRIMES[4516] = 43283
set PRIMES[4517] = 43291
set PRIMES[4518] = 43313
set PRIMES[4519] = 43319
set PRIMES[4520] = 43321
set PRIMES[4521] = 43331
set PRIMES[4522] = 43391
set PRIMES[4523] = 43397
set PRIMES[4524] = 43399
set PRIMES[4525] = 43403
set PRIMES[4526] = 43411
set PRIMES[4527] = 43427
set PRIMES[4528] = 43441
set PRIMES[4529] = 43451
set PRIMES[4530] = 43457
set PRIMES[4531] = 43481
set PRIMES[4532] = 43487
set PRIMES[4533] = 43499
set PRIMES[4534] = 43517
set PRIMES[4535] = 43541
set PRIMES[4536] = 43543
set PRIMES[4537] = 43573
set PRIMES[4538] = 43577
set PRIMES[4539] = 43579
set PRIMES[4540] = 43591
set PRIMES[4541] = 43597
set PRIMES[4542] = 43607
set PRIMES[4543] = 43609
set PRIMES[4544] = 43613
set PRIMES[4545] = 43627
set PRIMES[4546] = 43633
set PRIMES[4547] = 43649
set PRIMES[4548] = 43651
set PRIMES[4549] = 43661
set PRIMES[4550] = 43669
set PRIMES[4551] = 43691
set PRIMES[4552] = 43711
set PRIMES[4553] = 43717
set PRIMES[4554] = 43721
set PRIMES[4555] = 43753
set PRIMES[4556] = 43759
set PRIMES[4557] = 43777
set PRIMES[4558] = 43781
set PRIMES[4559] = 43783
set PRIMES[4560] = 43787
set PRIMES[4561] = 43789
set PRIMES[4562] = 43793
set PRIMES[4563] = 43801
set PRIMES[4564] = 43853
set PRIMES[4565] = 43867
set PRIMES[4566] = 43889
set PRIMES[4567] = 43891
set PRIMES[4568] = 43913
set PRIMES[4569] = 43933
set PRIMES[4570] = 43943
set PRIMES[4571] = 43951
set PRIMES[4572] = 43961
set PRIMES[4573] = 43963
set PRIMES[4574] = 43969
set PRIMES[4575] = 43973
set PRIMES[4576] = 43987
set PRIMES[4577] = 43991
set PRIMES[4578] = 43997
set PRIMES[4579] = 44017
set PRIMES[4580] = 44021
set PRIMES[4581] = 44027
set PRIMES[4582] = 44029
set PRIMES[4583] = 44041
set PRIMES[4584] = 44053
set PRIMES[4585] = 44059
set PRIMES[4586] = 44071
set PRIMES[4587] = 44087
set PRIMES[4588] = 44089
set PRIMES[4589] = 44101
set PRIMES[4590] = 44111
set PRIMES[4591] = 44119
set PRIMES[4592] = 44123
set PRIMES[4593] = 44129
set PRIMES[4594] = 44131
set PRIMES[4595] = 44159
set PRIMES[4596] = 44171
set PRIMES[4597] = 44179
set PRIMES[4598] = 44189
set PRIMES[4599] = 44201
set PRIMES[4600] = 44203
set PRIMES[4601] = 44207
set PRIMES[4602] = 44221
set PRIMES[4603] = 44249
set PRIMES[4604] = 44257
set PRIMES[4605] = 44263
set PRIMES[4606] = 44267
set PRIMES[4607] = 44269
set PRIMES[4608] = 44273
set PRIMES[4609] = 44279
set PRIMES[4610] = 44281
set PRIMES[4611] = 44293
set PRIMES[4612] = 44351
set PRIMES[4613] = 44357
set PRIMES[4614] = 44371
set PRIMES[4615] = 44381
set PRIMES[4616] = 44383
set PRIMES[4617] = 44389
set PRIMES[4618] = 44417
set PRIMES[4619] = 44449
set PRIMES[4620] = 44453
set PRIMES[4621] = 44483
set PRIMES[4622] = 44491
set PRIMES[4623] = 44497
set PRIMES[4624] = 44501
set PRIMES[4625] = 44507
set PRIMES[4626] = 44519
set PRIMES[4627] = 44531
set PRIMES[4628] = 44533
set PRIMES[4629] = 44537
set PRIMES[4630] = 44543
set PRIMES[4631] = 44549
set PRIMES[4632] = 44563
set PRIMES[4633] = 44579
set PRIMES[4634] = 44587
set PRIMES[4635] = 44617
set PRIMES[4636] = 44621
set PRIMES[4637] = 44623
set PRIMES[4638] = 44633
set PRIMES[4639] = 44641
set PRIMES[4640] = 44647
set PRIMES[4641] = 44651
set PRIMES[4642] = 44657
set PRIMES[4643] = 44683
set PRIMES[4644] = 44687
set PRIMES[4645] = 44699
set PRIMES[4646] = 44701
set PRIMES[4647] = 44711
set PRIMES[4648] = 44729
set PRIMES[4649] = 44741
set PRIMES[4650] = 44753
set PRIMES[4651] = 44771
set PRIMES[4652] = 44773
set PRIMES[4653] = 44777
set PRIMES[4654] = 44789
set PRIMES[4655] = 44797
set PRIMES[4656] = 44809
set PRIMES[4657] = 44819
set PRIMES[4658] = 44839
set PRIMES[4659] = 44843
set PRIMES[4660] = 44851
set PRIMES[4661] = 44867
set PRIMES[4662] = 44879
set PRIMES[4663] = 44887
set PRIMES[4664] = 44893
set PRIMES[4665] = 44909
set PRIMES[4666] = 44917
set PRIMES[4667] = 44927
set PRIMES[4668] = 44939
set PRIMES[4669] = 44953
set PRIMES[4670] = 44959
set PRIMES[4671] = 44963
set PRIMES[4672] = 44971
set PRIMES[4673] = 44983
set PRIMES[4674] = 44987
set PRIMES[4675] = 45007
set PRIMES[4676] = 45013
set PRIMES[4677] = 45053
set PRIMES[4678] = 45061
set PRIMES[4679] = 45077
set PRIMES[4680] = 45083
set PRIMES[4681] = 45119
set PRIMES[4682] = 45121
set PRIMES[4683] = 45127
set PRIMES[4684] = 45131
set PRIMES[4685] = 45137
set PRIMES[4686] = 45139
set PRIMES[4687] = 45161
set PRIMES[4688] = 45179
set PRIMES[4689] = 45181
set PRIMES[4690] = 45191
set PRIMES[4691] = 45197
set PRIMES[4692] = 45233
set PRIMES[4693] = 45247
set PRIMES[4694] = 45259
set PRIMES[4695] = 45263
set PRIMES[4696] = 45281
set PRIMES[4697] = 45289
set PRIMES[4698] = 45293
set PRIMES[4699] = 45307
set PRIMES[4700] = 45317
set PRIMES[4701] = 45319
set PRIMES[4702] = 45329
set PRIMES[4703] = 45337
set PRIMES[4704] = 45341
set PRIMES[4705] = 45343
set PRIMES[4706] = 45361
set PRIMES[4707] = 45377
set PRIMES[4708] = 45389
set PRIMES[4709] = 45403
set PRIMES[4710] = 45413
set PRIMES[4711] = 45427
set PRIMES[4712] = 45433
set PRIMES[4713] = 45439
set PRIMES[4714] = 45481
set PRIMES[4715] = 45491
set PRIMES[4716] = 45497
set PRIMES[4717] = 45503
set PRIMES[4718] = 45523
set PRIMES[4719] = 45533
set PRIMES[4720] = 45541
set PRIMES[4721] = 45553
set PRIMES[4722] = 45557
set PRIMES[4723] = 45569
set PRIMES[4724] = 45587
set PRIMES[4725] = 45589
set PRIMES[4726] = 45599
set PRIMES[4727] = 45613
set PRIMES[4728] = 45631
set PRIMES[4729] = 45641
set PRIMES[4730] = 45659
set PRIMES[4731] = 45667
set PRIMES[4732] = 45673
set PRIMES[4733] = 45677
set PRIMES[4734] = 45691
set PRIMES[4735] = 45697
set PRIMES[4736] = 45707
set PRIMES[4737] = 45737
set PRIMES[4738] = 45751
set PRIMES[4739] = 45757
set PRIMES[4740] = 45763
set PRIMES[4741] = 45767
set PRIMES[4742] = 45779
set PRIMES[4743] = 45817
set PRIMES[4744] = 45821
set PRIMES[4745] = 45823
set PRIMES[4746] = 45827
set PRIMES[4747] = 45833
set PRIMES[4748] = 45841
set PRIMES[4749] = 45853
set PRIMES[4750] = 45863
set PRIMES[4751] = 45869
set PRIMES[4752] = 45887
set PRIMES[4753] = 45893
set PRIMES[4754] = 45943
set PRIMES[4755] = 45949
set PRIMES[4756] = 45953
set PRIMES[4757] = 45959
set PRIMES[4758] = 45971
set PRIMES[4759] = 45979
set PRIMES[4760] = 45989
set PRIMES[4761] = 46021
set PRIMES[4762] = 46027
set PRIMES[4763] = 46049
set PRIMES[4764] = 46051
set PRIMES[4765] = 46061
set PRIMES[4766] = 46073
set PRIMES[4767] = 46091
set PRIMES[4768] = 46093
set PRIMES[4769] = 46099
set PRIMES[4770] = 46103
set PRIMES[4771] = 46133
set PRIMES[4772] = 46141
set PRIMES[4773] = 46147
set PRIMES[4774] = 46153
set PRIMES[4775] = 46171
set PRIMES[4776] = 46181
set PRIMES[4777] = 46183
set PRIMES[4778] = 46187
set PRIMES[4779] = 46199
set PRIMES[4780] = 46219
set PRIMES[4781] = 46229
set PRIMES[4782] = 46237
set PRIMES[4783] = 46261
set PRIMES[4784] = 46271
set PRIMES[4785] = 46273
set PRIMES[4786] = 46279
set PRIMES[4787] = 46301
set PRIMES[4788] = 46307
set PRIMES[4789] = 46309
set PRIMES[4790] = 46327
set PRIMES[4791] = 46337
endfunctionalso
JASS:
//Returns the x-root of base
static method root takes real base, real x returns real
return Pow(base, 1/x)
endmethod
Last edited:
- Joined
- Dec 12, 2008
- Messages
- 7,379
Test the speed of Pow(x, y) vs. Exp(y*Log(x))
- Joined
- Dec 12, 2012
- Messages
- 1,007
Well, just lets benchmark it then:
JASS:
scope MyScope initializer onInit
private function onInit takes nothing returns nothing
local integer i = 0
local player p = GetLocalPlayer()
local integer prime = 90127 // Change prime number here
loop
set i = i + 1
call Math.isPrime(prime) // Insert isPrime method here
call DisplayTimedTextToPlayer(p, 0.0, 0.0, 60.0, I2S(i))
endloop
endfunction
endscopeWe evaluate it on three different primes, a "very small" one (17), a "quite big" one (8093) and a "very big" one (90127). Results show the OP limit of the benchmark above:
Code:
n Math.isPrime(n) isPrime(n)
--------------------------------------------------
17 2173 2117
8093 2027 194
90127 1998 60At "very small" primes, the algorithms perform almost equal with Math.prime still being a bit faster. However, such small prime numbers are quite uninteresting.
Looking at larger primes it becomes quite obvious which algorithm is superior in terms of performance and scale. Math.isPrime is more than 10 times faster than your approach for "quite big" numbers like 8093 and more than 33 times faster at "very big" numbers like 90127. Also note that the performance stays very stable for a huge range of numbers, while your approach rapidly decreases in performances, already coming close to the OP limit for the biggest test number.
It might be a bit easier to understand since its the "naive" approach, but the Math library aims for maximum performance and accuracy, not as a math tutorial.
That would be about 105097565 primes. Given that each integer would require 32 bit, that would be more than 420 MB of RAM. However, since a hashtable always requires a key/value pair it would be at least the double, meaning 840 MB of RAM. I don't think that it would be desireable to waste almost 1 GB of RAM for doing prime calculations. And you would also have to somehow fill the hashtable, which would already cause a lot of problems (if possible at all).
- Joined
- Apr 16, 2012
- Messages
- 4,041
Conclusion: naive code is not necessarily better code
- Joined
- Feb 6, 2014
- Messages
- 2,466
Hmmm I'm curious, how did you do your tests?
- Joined
- Dec 12, 2012
- Messages
- 1,007
What do you mean? Everything is described in the post above.
- Joined
- Feb 6, 2014
- Messages
- 2,466
What does those numbers mean (SI unit??)?
- Joined
- Dec 12, 2012
- Messages
- 1,007
The numbers denote the (dimensionless) OP limit of the benchmark like described in the post. A number of (for example) 2027 means that the loop was executed 2027 times before it hit the OP limit and the operation was cancelled. Therefore large number means better.
- Joined
- Sep 6, 2013
- Messages
- 6,742
Screenshots are broken, I wanted to note.
- Joined
- Jul 9, 2012
- Messages
- 158
This is awesome! I am however not experienced in JASS. Was wondering if any1 could help me get the library to return a value of an exponential function? For instance, a real variable with value x = exp(r), where r is a value I determine.
Thanks!
Thanks!
- Joined
- Feb 27, 2007
- Messages
- 4,992
JASS:
native Pow takes real x, real power returns real
constant real bj_E = 2.71828
set x = Pow(bj_E, r)These are all available in GUI as well.
Similar threads
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