capd::autodiff Namespace Reference

Namespaces
	Acos
	AcosConst
	AcosFunTime
	AcosTime
	Add
	Asin
	AsinConst
	AsinFunTime
	AsinTime
	Atan
	AtanConst
	AtanFunTime
	AtanTime
	ConstMinusConst
	ConstMinusFunTime
	ConstMinusTime
	ConstMinusVar
	ConstPlusConst
	ConstPlusFunTime
	ConstPlusTime
	ConstPlusVar
	Cube
	CubeConst
	CubeFunTime
	CubeTime
	Div
	DivConstByConst
	DivFunTimeByConst
	DivFunTimeByFunTime
	DivFunTimeByTime
	DivTimeByConst
	DivVarByConst
	DivVarByFunTime
	DivVarByTime
	Exp
	ExpConst
	ExpFunTime
	ExpTime
	FunTimeMinusConst
	FunTimeMinusFunTime
	FunTimeMinusTime
	FunTimeMinusVar
	FunTimePlusFunTime
	FunTimePlusVar
	HalfIntPow
	HalfIntPowConst
	HalfIntPowFunTime
	HalfIntPowTime
	Log
	LogConst
	LogFunTime
	LogTime
	Mul
	MulConstByConst
	MulConstByFunTime
	MulConstByTime
	MulConstByVar
	MulFunTimeByFunTime
	MulFunTimeByVar
	MulTimeByFunTime
	MulTimeByVar
	NaturalPow
	natural powers x^c for c=2,3,4 are hand optimized and implemented in EvalSqr.h, EvalCubePow.h and EvalQuarticPow.h, respectively.
	NaturalPowConst
	NaturalPowFunTime
	NaturalPowTime
	NegIntPow
	NegIntPowConst
	NegIntPowFunTime
	NegIntPowTime
	OneMinusSqr
	OneMinusSqrConst
	OneMinusSqrFunTime
	OneMinusSqrTime
	Pow
	PowConst
	PowFunTime
	PowTime
	Quartic
	QuarticConst
	QuarticFunTime
	QuarticTime
	Sin
	SinConst
	SinFunTime
	SinTime
	Sqr
	SqrConst
	SqrFunTime
	Sqrt
	SqrtConst
	SqrtFunTime
	SqrTime
	SqrtTime
	Sub
	TimeMinusConst
	TimeMinusFunTime
	TimeMinusVar
	TimePlusFunTime
	TimePlusVar
	UnaryMinus
	UnaryMinusConst
	UnaryMinusFunTime
	UnaryMinusTime
	VarMinusConst
	VarMinusFunTime
	VarMinusTime

Classes
class	AbstractNode
class	DagIndexer
struct	Int4
struct	MaskIterator
struct	MultiindexData
	Stores information about decomposition of a Multiinex 'z' into possible sums of x+y=z Used to optimizs convolutions. All the data here is redundant and precomputed to avoid extra runtime computation. More...
struct	Node

Typedefs
typedef __size_type	VarNo
typedef __size_type	DerNo
typedef __size_type	CoeffNo
typedef __size_type	JetSize
typedef __size_type	Order
typedef __size_type	Degree
typedef __size_type	Dim
typedef Int4	MyNode

Enumerations
enum	NodeType {   NODE_ADD =0, NODE_CONST_PLUS_VAR =1, NODE_CONST_PLUS_CONST =2, NODE_CONST_PLUS_TIME =3,   NODE_CONST_PLUS_FUNTIME =4, NODE_TIME_PLUS_VAR =5, NODE_TIME_PLUS_FUNTIME =6, NODE_FUNTIME_PLUS_VAR =7,   NODE_FUNTIME_PLUS_FUNTIME =8, NODE_SUB =10, NODE_CONST_MINUS_CONST =11, NODE_CONST_MINUS_VAR =12,   NODE_CONST_MINUS_TIME =13, NODE_CONST_MINUS_FUNTIME =14, NODE_TIME_MINUS_CONST =15, NODE_TIME_MINUS_FUNTIME =16,   NODE_TIME_MINUS_VAR =17, NODE_FUNTIME_MINUS_CONST =18, NODE_FUNTIME_MINUS_TIME =19, NODE_FUNTIME_MINUS_FUNTIME =20,   NODE_FUNTIME_MINUS_VAR =21, NODE_VAR_MINUS_CONST =22, NODE_VAR_MINUS_TIME =23, NODE_VAR_MINUS_FUNTIME =24,   NODE_UNARY_MINUS =30, NODE_UNARY_MINUS_CONST =31, NODE_UNARY_MINUS_TIME =32, NODE_UNARY_MINUS_FUNTIME =33,   NODE_MUL =40, NODE_MUL_CONST_BY_VAR =41, NODE_MUL_CONST_BY_CONST =42, NODE_MUL_CONST_BY_TIME =43,   NODE_MUL_CONST_BY_FUNTIME =44, NODE_MUL_TIME_BY_VAR =45, NODE_MUL_TIME_BY_FUNTIME =46, NODE_MUL_FUNTIME_BY_VAR =47,   NODE_MUL_FUNTIME_BY_FUNTIME =48, NODE_DIV =50, NODE_DIV_VAR_BY_CONST =51, NODE_DIV_VAR_BY_TIME =52,   NODE_DIV_VAR_BY_FUNTIME =53, NODE_DIV_TIME_BY_CONST =54, NODE_DIV_FUNTIME_BY_CONST =55, NODE_DIV_FUNTIME_BY_TIME =56,   NODE_DIV_FUNTIME_BY_FUNTIME =57, NODE_DIV_CONST_BY_CONST =58, NODE_SQR =60, NODE_SQR_CONST =61,   NODE_SQR_TIME =62, NODE_SQR_FUNTIME =63, NODE_SQRT =64, NODE_SQRT_CONST =65,   NODE_SQRT_TIME =66, NODE_SQRT_FUNTIME =67, NODE_POW =70, NODE_POW_CONST =71,   NODE_POW_TIME =72, NODE_POW_FUNTIME =73, NODE_NATURAL_POW =74, NODE_NATURAL_POW_CONST =75,   NODE_NATURAL_POW_TIME =76, NODE_NATURAL_POW_FUNTIME =77, NODE_NEG_INT_POW =78, NODE_NEG_INT_POW_CONST =79,   NODE_NEG_INT_POW_TIME =80, NODE_NEG_INT_POW_FUNTIME =81, NODE_HALF_INT_POW =82, NODE_HALF_INT_POW_CONST =83,   NODE_HALF_INT_POW_TIME =84, NODE_HALF_INT_POW_FUNTIME =85, NODE_CUBE =86, NODE_CUBE_CONST =87,   NODE_CUBE_TIME =88, NODE_CUBE_FUNTIME =89, NODE_QUARTIC =90, NODE_QUARTIC_CONST =91,   NODE_QUARTIC_TIME =92, NODE_QUARTIC_FUNTIME =93, NODE_EXP =100, NODE_EXP_CONST =101,   NODE_EXP_TIME =102, NODE_EXP_FUNTIME =103, NODE_LOG =104, NODE_LOG_CONST =105,   NODE_LOG_TIME =106, NODE_LOG_FUNTIME =107, NODE_SIN =110, NODE_SIN_CONST =111,   NODE_SIN_TIME =112, NODE_SIN_FUNTIME =113, NODE_ATAN, NODE_ATAN_CONST,   NODE_ATAN_TIME, NODE_ATAN_FUNTIME, NODE_ONE_MINUS_SQR, NODE_ONE_MINUS_SQR_CONST,   NODE_ONE_MINUS_SQR_TIME, NODE_ONE_MINUS_SQR_FUNTIME, NODE_ASIN, NODE_ASIN_CONST,   NODE_ASIN_TIME, NODE_ASIN_FUNTIME, NODE_ACOS, NODE_ACOS_CONST,   NODE_ACOS_TIME, NODE_ACOS_FUNTIME, NODE_NULL, NODE_CONST,   NODE_TIME, NODE_PARAM, NODE_VAR, NODE_COS }

Functions
Node	operator+ (const Node &x, const Node &y)
Node	operator+ (const Node &x, double y)
Node	operator+ (double x, const Node &y)
Node	operator- (const Node &x, const Node &y)
Node	operator- (const Node &x, double y)
Node	operator- (double x, const Node &y)
Node	operator- (const Node &x)
Node	operator* (const Node &x, const Node &y)
Node	operator* (const Node &x, double y)
Node	operator* (double x, const Node &y)
Node	operator^ (const Node &x, double y)
Node	operator/ (const Node &x, const Node &y)
Node	operator/ (const Node &x, double y)
Node	operator/ (double x, const Node &y)
Node &	operator+= (Node &x, const Node &y)
Node &	operator+= (Node &x, double y)
Node &	operator-= (Node &x, const Node &y)
Node &	operator-= (Node &x, double y)
Node &	operator*= (Node &x, const Node &y)
Node &	operator*= (Node &x, double y)
Node &	operator/= (Node &x, const Node &y)
Node &	operator/= (Node &x, double y)
int	sumAndFindMax (const int a[], const int b[], int c[], const int n)
int	findMax (const int c[], const int n)
__size_type	index (__size_type dim, __size_type j, __size_type c)
__size_type	index (__size_type dim, __size_type j, __size_type c, __size_type k)
template<class T >
void	Int4ToAbstractNode (const std::vector< MyNode > &node, std::vector< AbstractNode< T > * > &out, capd::autodiff::DagIndexer< T > &dag)
	CAPD_MAKE_DAG_NODE (Acos)
	CAPD_MAKE_DAG_NODE (AcosConst)
	CAPD_MAKE_DAG_NODE (AcosTime)
	CAPD_MAKE_DAG_NODE (AcosFunTime)
	CAPD_MAKE_DAG_NODE (Add)
	CAPD_MAKE_DAG_NODE (ConstPlusVar)
	CAPD_MAKE_DAG_NODE (ConstPlusConst)
	CAPD_MAKE_DAG_NODE (ConstPlusTime)
	CAPD_MAKE_DAG_NODE (ConstPlusFunTime)
	CAPD_MAKE_DAG_NODE (TimePlusVar)
	CAPD_MAKE_DAG_NODE (TimePlusFunTime)
	CAPD_MAKE_DAG_NODE (FunTimePlusVar)
	CAPD_MAKE_DAG_NODE (FunTimePlusFunTime)
	CAPD_MAKE_DAG_NODE (Asin)
	CAPD_MAKE_DAG_NODE (AsinConst)
	CAPD_MAKE_DAG_NODE (AsinTime)
	CAPD_MAKE_DAG_NODE (AsinFunTime)
	CAPD_MAKE_DAG_NODE (Atan)
	CAPD_MAKE_DAG_NODE (AtanConst)
	CAPD_MAKE_DAG_NODE (AtanTime)
	CAPD_MAKE_DAG_NODE (AtanFunTime)
	CAPD_MAKE_DAG_NODE (Div)
	CAPD_MAKE_DAG_NODE (DivVarByConst)
	CAPD_MAKE_DAG_NODE (DivVarByTime)
	CAPD_MAKE_DAG_NODE (DivVarByFunTime)
	CAPD_MAKE_DAG_NODE (DivTimeByConst)
	CAPD_MAKE_DAG_NODE (DivFunTimeByConst)
	CAPD_MAKE_DAG_NODE (DivFunTimeByTime)
	CAPD_MAKE_DAG_NODE (DivFunTimeByFunTime)
	CAPD_MAKE_DAG_NODE (DivConstByConst)
	CAPD_MAKE_DAG_NODE (Exp)
	CAPD_MAKE_DAG_NODE (ExpConst)
	CAPD_MAKE_DAG_NODE (ExpTime)
	CAPD_MAKE_DAG_NODE (ExpFunTime)
	CAPD_MAKE_DAG_NODE (HalfIntPow)
	CAPD_MAKE_DAG_NODE (HalfIntPowConst)
	CAPD_MAKE_DAG_NODE (HalfIntPowTime)
	CAPD_MAKE_DAG_NODE (HalfIntPowFunTime)
	CAPD_MAKE_DAG_NODE (Log)
	CAPD_MAKE_DAG_NODE (LogConst)
	CAPD_MAKE_DAG_NODE (LogTime)
	CAPD_MAKE_DAG_NODE (LogFunTime)
	CAPD_MAKE_DAG_NODE (Mul)
	CAPD_MAKE_DAG_NODE (MulConstByVar)
	CAPD_MAKE_DAG_NODE (MulConstByConst)
	CAPD_MAKE_DAG_NODE (MulConstByTime)
	CAPD_MAKE_DAG_NODE (MulConstByFunTime)
	CAPD_MAKE_DAG_NODE (MulTimeByVar)
	CAPD_MAKE_DAG_NODE (MulTimeByFunTime)
	CAPD_MAKE_DAG_NODE (MulFunTimeByVar)
	CAPD_MAKE_DAG_NODE (MulFunTimeByFunTime)
	CAPD_MAKE_DAG_NODE (NaturalPow)
	CAPD_MAKE_DAG_NODE (NaturalPowConst)
	CAPD_MAKE_DAG_NODE (NaturalPowTime)
	CAPD_MAKE_DAG_NODE (NaturalPowFunTime)
	CAPD_MAKE_DAG_NODE (NegIntPow)
	CAPD_MAKE_DAG_NODE (NegIntPowConst)
	CAPD_MAKE_DAG_NODE (NegIntPowTime)
	CAPD_MAKE_DAG_NODE (NegIntPowFunTime)
	CAPD_MAKE_DAG_NODE (OneMinusSqr)
	CAPD_MAKE_DAG_NODE (OneMinusSqrTime)
	CAPD_MAKE_DAG_NODE (OneMinusSqrFunTime)
	CAPD_MAKE_DAG_NODE (OneMinusSqrConst)
	CAPD_MAKE_DAG_NODE (Pow)
	CAPD_MAKE_DAG_NODE (PowConst)
	CAPD_MAKE_DAG_NODE (PowTime)
	CAPD_MAKE_DAG_NODE (PowFunTime)
	CAPD_MAKE_DAG_NODE (Quartic)
	CAPD_MAKE_DAG_NODE (QuarticTime)
	CAPD_MAKE_DAG_NODE (QuarticFunTime)
	CAPD_MAKE_DAG_NODE (QuarticConst)
	CAPD_MAKE_DAG_NODE (Sin)
	CAPD_MAKE_DAG_NODE (SinConst)
	CAPD_MAKE_DAG_NODE (SinTime)
	CAPD_MAKE_DAG_NODE (SinFunTime)
	CAPD_MAKE_DAG_NODE (Sqr)
	CAPD_MAKE_DAG_NODE (SqrTime)
	CAPD_MAKE_DAG_NODE (SqrFunTime)
	CAPD_MAKE_DAG_NODE (SqrConst)
	CAPD_MAKE_DAG_NODE (Sqrt)
	CAPD_MAKE_DAG_NODE (SqrtConst)
	CAPD_MAKE_DAG_NODE (SqrtTime)
	CAPD_MAKE_DAG_NODE (SqrtFunTime)
	CAPD_MAKE_DAG_NODE (Sub)
	CAPD_MAKE_DAG_NODE (ConstMinusVar)
	CAPD_MAKE_DAG_NODE (ConstMinusFunTime)
	CAPD_MAKE_DAG_NODE (ConstMinusTime)
	CAPD_MAKE_DAG_NODE (ConstMinusConst)
	CAPD_MAKE_DAG_NODE (TimeMinusConst)
	CAPD_MAKE_DAG_NODE (TimeMinusFunTime)
	CAPD_MAKE_DAG_NODE (TimeMinusVar)
	CAPD_MAKE_DAG_NODE (FunTimeMinusConst)
	CAPD_MAKE_DAG_NODE (FunTimeMinusTime)
	CAPD_MAKE_DAG_NODE (FunTimeMinusFunTime)
	CAPD_MAKE_DAG_NODE (FunTimeMinusVar)
	CAPD_MAKE_DAG_NODE (VarMinusConst)
	CAPD_MAKE_DAG_NODE (VarMinusTime)
	CAPD_MAKE_DAG_NODE (VarMinusFunTime)
	CAPD_MAKE_DAG_NODE (Cube)
	CAPD_MAKE_DAG_NODE (CubeTime)
	CAPD_MAKE_DAG_NODE (CubeFunTime)
	CAPD_MAKE_DAG_NODE (CubeConst)
	CAPD_MAKE_DAG_NODE (UnaryMinus)
	CAPD_MAKE_DAG_NODE (UnaryMinusConst)
	CAPD_MAKE_DAG_NODE (UnaryMinusTime)
	CAPD_MAKE_DAG_NODE (UnaryMinusFunTime)
template<class T >
bool	getMask (MaskIterator< T > i)
template<class T >
bool	getMask (MaskIterator< T > i, unsigned j)
template<class T >
bool	getMask (T *)
template<class T >
bool	getMask (T *, unsigned)

Variables
__size_type	capd_c2jet_indices [21][20][20]

Typedef Documentation

CoeffNo

typedef __size_type capd::autodiff::CoeffNo

Degree

typedef __size_type capd::autodiff::Degree

DerNo

typedef __size_type capd::autodiff::DerNo

Dim

typedef __size_type capd::autodiff::Dim

JetSize

typedef __size_type capd::autodiff::JetSize

Order

typedef __size_type capd::autodiff::Order

VarNo

typedef __size_type capd::autodiff::VarNo

Function Documentation

findMax()

int capd::autodiff::findMax ( const int  c[], const int  n  )

inline

index() [1/2]

__size_type capd::autodiff::index ( __size_type  dim, __size_type  j, __size_type  c  )

inline

index() [2/2]

__size_type capd::autodiff::index ( __size_type  dim, __size_type  j, __size_type  c, __size_type  k  )

inline

sumAndFindMax()

int capd::autodiff::sumAndFindMax ( const int  a[], const int  b[], int  c[], const int  n  )

inline

Variable Documentation

capd_c2jet_indices

__size_type capd::autodiff::capd_c2jet_indices

Initial value:

={
{},
{{2}},
{{3,4},{4,5}},
{{4,5,6},{5,7,8},{6,8,9}},
{{5,6,7,8},{6,9,10,11},{7,10,12,13},{8,11,13,14}},
{{6,7,8,9,10},{7,11,12,13,14},{8,12,15,16,17},{9,13,16,18,19},{10,14,17,19,20}},
{{7,8,9,10,11,12},{8,13,14,15,16,17},{9,14,18,19,20,21},{10,15,19,22,23,24},{11,16,20,23,25,26},{12,17,21,24,26,27}},
{{8,9,10,11,12,13,14},{9,15,16,17,18,19,20},{10,16,21,22,23,24,25},{11,17,22,26,27,28,29},{12,18,23,27,30,31,32},{13,19,24,28,31,33,34},{14,20,25,29,32,34,35}},
{{9,10,11,12,13,14,15,16},{10,17,18,19,20,21,22,23},{11,18,24,25,26,27,28,29},{12,19,25,30,31,32,33,34},{13,20,26,31,35,36,37,38},{14,21,27,32,36,39,40,41},{15,22,28,33,37,40,42,43},{16,23,29,34,38,41,43,44}},
{{10,11,12,13,14,15,16,17,18},{11,19,20,21,22,23,24,25,26},{12,20,27,28,29,30,31,32,33},{13,21,28,34,35,36,37,38,39},{14,22,29,35,40,41,42,43,44},{15,23,30,36,41,45,46,47,48},{16,24,31,37,42,46,49,50,51},{17,25,32,38,43,47,50,52,53},{18,26,33,39,44,48,51,53,54}},
{{11,12,13,14,15,16,17,18,19,20},{12,21,22,23,24,25,26,27,28,29},{13,22,30,31,32,33,34,35,36,37},{14,23,31,38,39,40,41,42,43,44},{15,24,32,39,45,46,47,48,49,50},{16,25,33,40,46,51,52,53,54,55},{17,26,34,41,47,52,56,57,58,59},{18,27,35,42,48,53,57,60,61,62},{19,28,36,43,49,54,58,61,63,64},{20,29,37,44,50,55,59,62,64,65}},
{{12,13,14,15,16,17,18,19,20,21,22},{13,23,24,25,26,27,28,29,30,31,32},{14,24,33,34,35,36,37,38,39,40,41},{15,25,34,42,43,44,45,46,47,48,49},{16,26,35,43,50,51,52,53,54,55,56},{17,27,36,44,51,57,58,59,60,61,62},{18,28,37,45,52,58,63,64,65,66,67},{19,29,38,46,53,59,64,68,69,70,71},{20,30,39,47,54,60,65,69,72,73,74},{21,31,40,48,55,61,66,70,73,75,76},{22,32,41,49,56,62,67,71,74,76,77}},
{{13,14,15,16,17,18,19,20,21,22,23,24},{14,25,26,27,28,29,30,31,32,33,34,35},{15,26,36,37,38,39,40,41,42,43,44,45},{16,27,37,46,47,48,49,50,51,52,53,54},{17,28,38,47,55,56,57,58,59,60,61,62},{18,29,39,48,56,63,64,65,66,67,68,69},{19,30,40,49,57,64,70,71,72,73,74,75},{20,31,41,50,58,65,71,76,77,78,79,80},{21,32,42,51,59,66,72,77,81,82,83,84},{22,33,43,52,60,67,73,78,82,85,86,87},{23,34,44,53,61,68,74,79,83,86,88,89},{24,35,45,54,62,69,75,80,84,87,89,90}},
{{14,15,16,17,18,19,20,21,22,23,24,25,26},{15,27,28,29,30,31,32,33,34,35,36,37,38},{16,28,39,40,41,42,43,44,45,46,47,48,49},{17,29,40,50,51,52,53,54,55,56,57,58,59},{18,30,41,51,60,61,62,63,64,65,66,67,68},{19,31,42,52,61,69,70,71,72,73,74,75,76},{20,32,43,53,62,70,77,78,79,80,81,82,83},{21,33,44,54,63,71,78,84,85,86,87,88,89},{22,34,45,55,64,72,79,85,90,91,92,93,94},{23,35,46,56,65,73,80,86,91,95,96,97,98},{24,36,47,57,66,74,81,87,92,96,99,100,101},{25,37,48,58,67,75,82,88,93,97,100,102,103},{26,38,49,59,68,76,83,89,94,98,101,103,104}},
{{15,16,17,18,19,20,21,22,23,24,25,26,27,28},{16,29,30,31,32,33,34,35,36,37,38,39,40,41},{17,30,42,43,44,45,46,47,48,49,50,51,52,53},{18,31,43,54,55,56,57,58,59,60,61,62,63,64},{19,32,44,55,65,66,67,68,69,70,71,72,73,74},{20,33,45,56,66,75,76,77,78,79,80,81,82,83},{21,34,46,57,67,76,84,85,86,87,88,89,90,91},{22,35,47,58,68,77,85,92,93,94,95,96,97,98},{23,36,48,59,69,78,86,93,99,100,101,102,103,104},{24,37,49,60,70,79,87,94,100,105,106,107,108,109},{25,38,50,61,71,80,88,95,101,106,110,111,112,113},{26,39,51,62,72,81,89,96,102,107,111,114,115,116},{27,40,52,63,73,82,90,97,103,108,112,115,117,118},{28,41,53,64,74,83,91,98,104,109,113,116,118,119}},
{{16,17,18,19,20,21,22,23,24,25,26,27,28,29,30},{17,31,32,33,34,35,36,37,38,39,40,41,42,43,44},{18,32,45,46,47,48,49,50,51,52,53,54,55,56,57},{19,33,46,58,59,60,61,62,63,64,65,66,67,68,69},{20,34,47,59,70,71,72,73,74,75,76,77,78,79,80},{21,35,48,60,71,81,82,83,84,85,86,87,88,89,90},{22,36,49,61,72,82,91,92,93,94,95,96,97,98,99},{23,37,50,62,73,83,92,100,101,102,103,104,105,106,107},{24,38,51,63,74,84,93,101,108,109,110,111,112,113,114},{25,39,52,64,75,85,94,102,109,115,116,117,118,119,120},{26,40,53,65,76,86,95,103,110,116,121,122,123,124,125},{27,41,54,66,77,87,96,104,111,117,122,126,127,128,129},{28,42,55,67,78,88,97,105,112,118,123,127,130,131,132},{29,43,56,68,79,89,98,106,113,119,124,128,131,133,134},{30,44,57,69,80,90,99,107,114,120,125,129,132,134,135}},
{{17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32},{18,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47},{19,34,48,49,50,51,52,53,54,55,56,57,58,59,60,61},{20,35,49,62,63,64,65,66,67,68,69,70,71,72,73,74},{21,36,50,63,75,76,77,78,79,80,81,82,83,84,85,86},{22,37,51,64,76,87,88,89,90,91,92,93,94,95,96,97},{23,38,52,65,77,88,98,99,100,101,102,103,104,105,106,107},{24,39,53,66,78,89,99,108,109,110,111,112,113,114,115,116},{25,40,54,67,79,90,100,109,117,118,119,120,121,122,123,124},{26,41,55,68,80,91,101,110,118,125,126,127,128,129,130,131},{27,42,56,69,81,92,102,111,119,126,132,133,134,135,136,137},{28,43,57,70,82,93,103,112,120,127,133,138,139,140,141,142},{29,44,58,71,83,94,104,113,121,128,134,139,143,144,145,146},{30,45,59,72,84,95,105,114,122,129,135,140,144,147,148,149},{31,46,60,73,85,96,106,115,123,130,136,141,145,148,150,151},{32,47,61,74,86,97,107,116,124,131,137,142,146,149,151,152}},
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