|
| Double_t | TMath::ACos (Double_t) |
| | Returns the principal value of the arc cosine of x, expressed in radians.
|
| |
| Double_t | TMath::ACosH (Double_t) |
| | Returns the nonnegative area hyperbolic cosine of x.
|
| |
| Bool_t | TMath::AreEqualAbs (Double_t af, Double_t bf, Double_t epsilon) |
| | Comparing floating points.
|
| |
| Bool_t | TMath::AreEqualRel (Double_t af, Double_t bf, Double_t relPrec) |
| | Comparing floating points.
|
| |
| Double_t | TMath::ASin (Double_t) |
| | Returns the principal value of the arc sine of x, expressed in radians.
|
| |
| Double_t | TMath::ASinH (Double_t) |
| | Returns the area hyperbolic sine of x.
|
| |
| Double_t | TMath::ATan (Double_t) |
| | Returns the principal value of the arc tangent of x, expressed in radians.
|
| |
| Double_t | TMath::ATan2 (Double_t y, Double_t x) |
| | Returns the principal value of the arc tangent of y/x, expressed in radians.
|
| |
| Double_t | TMath::ATanH (Double_t) |
| | Returns the area hyperbolic tangent of x.
|
| |
| Double_t | TMath::BesselI (Int_t n, Double_t x) |
| | Computes the Integer Order Modified Bessel function I_n(x) for n=0,1,2,... and any real x.
|
| |
| Double_t | TMath::BesselI0 (Double_t x) |
| | Integer order modified Bessel function K_n(x)
|
| |
| Double_t | TMath::BesselI1 (Double_t x) |
| | Modified Bessel function K_0(x)
|
| |
| Double_t | TMath::BesselJ0 (Double_t x) |
| | Modified Bessel function K_1(x)
|
| |
| Double_t | TMath::BesselJ1 (Double_t x) |
| | Bessel function J0(x) for any real x.
|
| |
| Double_t | TMath::BesselK (Int_t n, Double_t x) |
| | Integer order modified Bessel function I_n(x)
|
| |
| Double_t | TMath::BesselK0 (Double_t x) |
| | Modified Bessel function I_0(x)
|
| |
| Double_t | TMath::BesselK1 (Double_t x) |
| | Modified Bessel function I_1(x)
|
| |
| Double_t | TMath::BesselY0 (Double_t x) |
| | Bessel function J1(x) for any real x.
|
| |
| Double_t | TMath::BesselY1 (Double_t x) |
| | Bessel function Y0(x) for positive x.
|
| |
| Double_t | TMath::Beta (Double_t p, Double_t q) |
| | Calculates Beta-function Gamma(p)*Gamma(q)/Gamma(p+q).
|
| |
| Double_t | TMath::BetaCf (Double_t x, Double_t a, Double_t b) |
| | Continued fraction evaluation by modified Lentz's method used in calculation of incomplete Beta function.
|
| |
| Double_t | TMath::BetaDist (Double_t x, Double_t p, Double_t q) |
| | Computes the probability density function of the Beta distribution (the distribution function is computed in BetaDistI).
|
| |
| Double_t | TMath::BetaDistI (Double_t x, Double_t p, Double_t q) |
| | Computes the distribution function of the Beta distribution.
|
| |
| Double_t | TMath::BetaIncomplete (Double_t x, Double_t a, Double_t b) |
| | Calculates the incomplete Beta-function.
|
| |
| Double_t | TMath::Binomial (Int_t n, Int_t k) |
| | Calculates the binomial coefficient n over k.
|
| |
| Double_t | TMath::BinomialI (Double_t p, Int_t n, Int_t k) |
| | Suppose an event occurs with probability p per trial Then the probability P of its occurring k or more times in n trials is termed a cumulative binomial probability the formula is:
|
| |
| Double_t | TMath::BreitWigner (Double_t x, Double_t mean=0, Double_t gamma=1) |
| | Calculates a Breit Wigner function with mean and gamma.
|
| |
| Double_t | TMath::BreitWignerRelativistic (Double_t x, Double_t median=0, Double_t gamma=1) |
| | Calculates a Relativistic Breit Wigner function with median and gamma.
|
| |
| void | TMath::BubbleHigh (Int_t Narr, Double_t *arr1, Int_t *arr2) |
| | Bubble sort variant to obtain the order of an array's elements into an index in order to do more useful things than the standard built in functions.
|
| |
| void | TMath::BubbleLow (Int_t Narr, Double_t *arr1, Int_t *arr2) |
| | Opposite ordering of the array arr2[] to that of BubbleHigh.
|
| |
| constexpr Double_t | TMath::C () |
| | Velocity of light in \( m s^{-1} \).
|
| |
| Double_t | TMath::CauchyDist (Double_t x, Double_t t=0, Double_t s=1) |
| | Computes the density of Cauchy distribution at point x by default, standard Cauchy distribution is used (t=0, s=1)
|
| |
| constexpr Double_t | TMath::Ccgs () |
| | \( cm s^{-1} \)
|
| |
| Double_t | TMath::Ceil (Double_t x) |
| | Rounds x upward, returning the smallest integral value that is not less than x.
|
| |
| Int_t | TMath::CeilNint (Double_t x) |
| | Returns the nearest integer of TMath::Ceil(x).
|
| |
| Double_t | TMath::ChisquareQuantile (Double_t p, Double_t ndf) |
| | Evaluate the quantiles of the chi-squared probability distribution function.
|
| |
| Double_t | TMath::Cos (Double_t) |
| | Returns the cosine of an angle of x radians.
|
| |
| Double_t | TMath::CosH (Double_t) |
| | Returns the hyperbolic cosine of x.
|
| |
| template<typename T > |
| T * | TMath::Cross (const T v1[3], const T v2[3], T out[3]) |
| | Calculates the Cross Product of two vectors: out = [v1 x v2].
|
| |
| constexpr Double_t | TMath::CUncertainty () |
| | Speed of light uncertainty.
|
| |
| constexpr Double_t | TMath::DegToRad () |
| | Conversion from degree to radian: \( \frac{\pi}{180} \).
|
| |
| Double_t | TMath::DiLog (Double_t x) |
| | Modified Struve functions of order 1.
|
| |
| constexpr Double_t | TMath::E () |
| | Base of natural log: \( e \).
|
| |
| Double_t | TMath::Erf (Double_t x) |
| | Computation of the error function erf(x).
|
| |
| Double_t | TMath::Erfc (Double_t x) |
| | Computes the complementary error function erfc(x).
|
| |
| Double_t | TMath::ErfcInverse (Double_t x) |
| | Returns the inverse of the complementary error function.
|
| |
| Double_t | TMath::ErfInverse (Double_t x) |
| | Returns the inverse error function.
|
| |
| constexpr Double_t | TMath::EulerGamma () |
| | Euler-Mascheroni Constant.
|
| |
| Double_t | TMath::Exp (Double_t x) |
| | Returns the base-e exponential function of x, which is e raised to the power x.
|
| |
| Double_t | TMath::Factorial (Int_t i) |
| | Computes factorial(n).
|
| |
| Double_t | TMath::FDist (Double_t F, Double_t N, Double_t M) |
| | Computes the density function of F-distribution (probability function, integral of density, is computed in FDistI).
|
| |
| Double_t | TMath::FDistI (Double_t F, Double_t N, Double_t M) |
| | Calculates the cumulative distribution function of F-distribution, this function occurs in the statistical test of whether two observed samples have the same variance.
|
| |
| Int_t | TMath::Finite (Double_t x) |
| | Check if it is finite with a mask in order to be consistent in presence of fast math.
|
| |
| Int_t | TMath::Finite (Float_t x) |
| | Check if it is finite with a mask in order to be consistent in presence of fast math.
|
| |
| Double_t | TMath::Floor (Double_t x) |
| | Rounds x downward, returning the largest integral value that is not greater than x.
|
| |
| Int_t | TMath::FloorNint (Double_t x) |
| | Returns the nearest integer of TMath::Floor(x).
|
| |
| Double_t | TMath::Freq (Double_t x) |
| | Computation of the normal frequency function freq(x).
|
| |
| constexpr Double_t | TMath::G () |
| | Gravitational constant in: \( m^{3} kg^{-1} s^{-2} \).
|
| |
| Double_t | TMath::Gamma (Double_t a, Double_t x) |
| | Computation of the normalized lower incomplete gamma function P(a,x) as defined in the Handbook of Mathematical Functions by Abramowitz and Stegun, formula 6.5.1 on page 260 .
|
| |
| Double_t | TMath::Gamma (Double_t z) |
| | Computation of gamma(z) for all z.
|
| |
| Double_t | TMath::GammaDist (Double_t x, Double_t gamma, Double_t mu=0, Double_t beta=1) |
| | Computes the density function of Gamma distribution at point x.
|
| |
| Double_t | TMath::Gaus (Double_t x, Double_t mean=0, Double_t sigma=1, Bool_t norm=kFALSE) |
| | Calculates a gaussian function with mean and sigma.
|
| |
| constexpr Double_t | TMath::Gcgs () |
| | \( cm^{3} g^{-1} s^{-2} \)
|
| |
| template<typename Iterator > |
| Double_t | TMath::GeomMean (Iterator first, Iterator last) |
| | Returns the geometric mean of an array defined by the iterators.
|
| |
| template<typename T > |
| Double_t | TMath::GeomMean (Long64_t n, const T *a) |
| | Returns the geometric mean of an array a of size n.
|
| |
| constexpr Double_t | TMath::GhbarC () |
| | \( \frac{G}{\hbar C} \) in \( (GeV/c^{2})^{-2} \)
|
| |
| constexpr Double_t | TMath::GhbarCUncertainty () |
| | \( \frac{G}{\hbar C} \) uncertainty.
|
| |
| constexpr Double_t | TMath::Gn () |
| | Standard acceleration of gravity in \( m s^{-2} \).
|
| |
| constexpr Double_t | TMath::GnUncertainty () |
| | Standard acceleration of gravity uncertainty.
|
| |
| constexpr Double_t | TMath::GUncertainty () |
| | Gravitational constant uncertainty.
|
| |
| constexpr Double_t | TMath::H () |
| | Planck's constant in \( J s \): \( h \).
|
| |
| ULong_t | TMath::Hash (const char *str) |
| |
| ULong_t | TMath::Hash (const void *txt, Int_t ntxt) |
| | Calculates hash index from any char string.
|
| |
| constexpr Double_t | TMath::Hbar () |
| | \( \hbar \) in \( J s \): \( \hbar = \frac{h}{2\pi} \)
|
| |
| constexpr Double_t | TMath::Hbarcgs () |
| | \( erg s \)
|
| |
| constexpr Double_t | TMath::HbarUncertainty () |
| | \( \hbar \) uncertainty.
|
| |
| constexpr Double_t | TMath::HC () |
| | \( hc \) in \( J m \)
|
| |
| constexpr Double_t | TMath::HCcgs () |
| | \( erg cm \)
|
| |
| constexpr Double_t | TMath::Hcgs () |
| | \( erg s \)
|
| |
| constexpr Double_t | TMath::HUncertainty () |
| | Planck's constant uncertainty.
|
| |
| Double_t | TMath::Hypot (Double_t x, Double_t y) |
| | Returns sqrt(x*x + y*y)
|
| |
| Long_t | TMath::Hypot (Long_t x, Long_t y) |
| | Returns sqrt(x*x + y*y)
|
| |
| Double_t | TMath::Infinity () |
| | Returns an infinity as defined by the IEEE standard.
|
| |
| constexpr Double_t | TMath::InvPi () |
| | \( \frac{1.}{\pi}\)
|
| |
| template<typename T > |
| Bool_t | TMath::IsInside (T xp, T yp, Int_t np, T *x, T *y) |
| | Function which returns kTRUE if point xp,yp lies inside the polygon defined by the np points in arrays x and y, kFALSE otherwise.
|
| |
| Bool_t | TMath::IsNaN (Double_t x) |
| |
| Bool_t | TMath::IsNaN (Float_t x) |
| |
| constexpr Double_t | TMath::K () |
| | Boltzmann's constant in \( J K^{-1} \): \( k \).
|
| |
| constexpr Double_t | TMath::Kcgs () |
| | \( erg K^{-1} \)
|
| |
| Double_t | TMath::KolmogorovProb (Double_t z) |
| | Calculates the Kolmogorov distribution function,.
|
| |
| Double_t | TMath::KolmogorovTest (Int_t na, const Double_t *a, Int_t nb, const Double_t *b, Option_t *option) |
| | Statistical test whether two one-dimensional sets of points are compatible with coming from the same parent distribution, using the Kolmogorov test.
|
| |
| template<class Element , typename Size > |
| Element | TMath::KOrdStat (Size n, const Element *a, Size k, Size *work=0) |
| | Returns k_th order statistic of the array a of size n (k_th smallest element out of n elements).
|
| |
| constexpr Double_t | TMath::KUncertainty () |
| | Boltzmann's constant uncertainty.
|
| |
| Double_t | TMath::Landau (Double_t x, Double_t mpv=0, Double_t sigma=1, Bool_t norm=kFALSE) |
| | The LANDAU function.
|
| |
| Double_t | TMath::LandauI (Double_t x) |
| | Returns the value of the Landau distribution function at point x.
|
| |
| Double_t | TMath::LaplaceDist (Double_t x, Double_t alpha=0, Double_t beta=1) |
| | Computes the probability density function of Laplace distribution at point x, with location parameter alpha and shape parameter beta.
|
| |
| Double_t | TMath::LaplaceDistI (Double_t x, Double_t alpha=0, Double_t beta=1) |
| | Computes the distribution function of Laplace distribution at point x, with location parameter alpha and shape parameter beta.
|
| |
| Double_t | TMath::Ldexp (Double_t x, Int_t exp) |
| | Returns the result of multiplying x (the significant) by 2 raised to the power of exp (the exponent).
|
| |
| constexpr Double_t | TMath::Ln10 () |
| | Natural log of 10 (to convert log to ln)
|
| |
| Double_t | TMath::LnGamma (Double_t z) |
| | Computation of ln[gamma(z)] for all z.
|
| |
| template<typename Iterator > |
| Iterator | TMath::LocMax (Iterator first, Iterator last) |
| | Returns index of array with the maximum element.
|
| |
| template<typename T > |
| Long64_t | TMath::LocMax (Long64_t n, const T *a) |
| | Returns index of array with the maximum element.
|
| |
| template<typename Iterator > |
| Iterator | TMath::LocMin (Iterator first, Iterator last) |
| | Returns index of array with the minimum element.
|
| |
| template<typename T > |
| Long64_t | TMath::LocMin (Long64_t n, const T *a) |
| | Returns index of array with the minimum element.
|
| |
| Double_t | TMath::Log (Double_t x) |
| | Returns the natural logarithm of x.
|
| |
| Double_t | TMath::Log10 (Double_t x) |
| | Returns the common (base-10) logarithm of x.
|
| |
| Double_t | TMath::Log2 (Double_t x) |
| | Returns the binary (base-2) logarithm of x.
|
| |
| constexpr Double_t | TMath::LogE () |
| | Base-10 log of e (to convert ln to log)
|
| |
| Double_t | TMath::LogNormal (Double_t x, Double_t sigma, Double_t theta=0, Double_t m=1) |
| | Computes the density of LogNormal distribution at point x.
|
| |
| template<typename T > |
| T | TMath::MaxElement (Long64_t n, const T *a) |
| | Returns maximum of array a of length n.
|
| |
| template<typename Iterator > |
| Double_t | TMath::Mean (Iterator first, Iterator last) |
| | Returns the weighted mean of an array defined by the iterators.
|
| |
| template<typename Iterator , typename WeightIterator > |
| Double_t | TMath::Mean (Iterator first, Iterator last, WeightIterator wfirst) |
| | Returns the weighted mean of an array defined by the first and last iterators.
|
| |
| template<typename T > |
| Double_t | TMath::Mean (Long64_t n, const T *a, const Double_t *w=0) |
| | Returns the weighted mean of an array a with length n.
|
| |
| template<typename T > |
| Double_t | TMath::Median (Long64_t n, const T *a, const Double_t *w=0, Long64_t *work=0) |
| | Same as RMS.
|
| |
| template<typename T > |
| T | TMath::MinElement (Long64_t n, const T *a) |
| | Returns minimum of array a of length n.
|
| |
| constexpr Double_t | TMath::MWair () |
| | Molecular weight of dry air 1976 US Standard Atmosphere in \( kg kmol^{-1} \) or \( gm mol^{-1} \)
|
| |
| constexpr Double_t | TMath::Na () |
| | Avogadro constant (Avogadro's Number) in \( mol^{-1} \).
|
| |
| constexpr Double_t | TMath::NaUncertainty () |
| | Avogadro constant (Avogadro's Number) uncertainty.
|
| |
| template<typename T > |
| Int_t | TMath::Nint (T x) |
| | Round to nearest integer. Rounds half integers to the nearest even integer.
|
| |
| template<typename T > |
| T * | TMath::Normal2Plane (const T v1[3], const T v2[3], const T v3[3], T normal[3]) |
| | Calculates a normal vector of a plane.
|
| |
| Double_t | TMath::Normalize (Double_t v[3]) |
| | Normalize a vector v in place.
|
| |
| Float_t | TMath::Normalize (Float_t v[3]) |
| | Normalize a vector v in place.
|
| |
| template<typename T > |
| T | TMath::NormCross (const T v1[3], const T v2[3], T out[3]) |
| | Calculates the Normalized Cross Product of two vectors.
|
| |
| Double_t | TMath::NormQuantile (Double_t p) |
| | Computes quantiles for standard normal distribution N(0, 1) at probability p.
|
| |
| Bool_t | TMath::Permute (Int_t n, Int_t *a) |
| | Simple recursive algorithm to find the permutations of n natural numbers, not necessarily all distinct adapted from CERNLIB routine PERMU.
|
| |
| constexpr Double_t | TMath::Pi () |
| | \( \pi\)
|
| |
| constexpr Double_t | TMath::PiOver2 () |
| | \( \frac{\pi}{2} \)
|
| |
| constexpr Double_t | TMath::PiOver4 () |
| | \( \frac{\pi}{4} \)
|
| |
| Double_t | TMath::Poisson (Double_t x, Double_t par) |
| | Computes the Poisson distribution function for (x,par).
|
| |
| Double_t | TMath::PoissonI (Double_t x, Double_t par) |
| | Computes the Discrete Poisson distribution function for (x,par).
|
| |
| Double_t | TMath::Power (Double_t x, Double_t y) |
| | Returns x raised to the power y.
|
| |
| Double_t | TMath::Power (Double_t x, Int_t y) |
| | Returns x raised to the power y.
|
| |
| LongDouble_t | TMath::Power (Long64_t x, Long64_t y) |
| | Returns x raised to the power y.
|
| |
| LongDouble_t | TMath::Power (LongDouble_t x, Long64_t y) |
| | Returns x raised to the power y.
|
| |
| LongDouble_t | TMath::Power (LongDouble_t x, LongDouble_t y) |
| | Returns x raised to the power y.
|
| |
| Double_t | TMath::Prob (Double_t chi2, Int_t ndf) |
| | Computation of the probability for a certain Chi-squared (chi2) and number of degrees of freedom (ndf).
|
| |
| constexpr Double_t | TMath::Qe () |
| | Elementary charge in \( C \) .
|
| |
| constexpr Double_t | TMath::QeUncertainty () |
| | Elementary charge uncertainty.
|
| |
| void | TMath::Quantiles (Int_t n, Int_t nprob, Double_t *x, Double_t *quantiles, Double_t *prob, Bool_t isSorted=kTRUE, Int_t *index=nullptr, Int_t type=7) |
| | Computes sample quantiles, corresponding to the given probabilities.
|
| |
| Double_t | TMath::QuietNaN () |
| | Returns a quiet NaN as defined by IEEE 754.
|
| |
| constexpr Double_t | TMath::R () |
| | Universal gas constant ( \( Na K \)) in \( J K^{-1} mol^{-1} \)
|
| |
| constexpr Double_t | TMath::RadToDeg () |
| | Conversion from radian to degree: \( \frac{180}{\pi} \).
|
| |
| constexpr Double_t | TMath::Rgair () |
| | Dry Air Gas Constant (R / MWair) in \( J kg^{-1} K^{-1} \)
|
| |
| template<typename Iterator > |
| Double_t | TMath::RMS (Iterator first, Iterator last) |
| | Returns the Standard Deviation of an array defined by the iterators.
|
| |
| template<typename Iterator , typename WeightIterator > |
| Double_t | TMath::RMS (Iterator first, Iterator last, WeightIterator wfirst) |
| | Returns the weighted Standard Deviation of an array defined by the iterators.
|
| |
| template<typename T > |
| Double_t | TMath::RMS (Long64_t n, const T *a, const Double_t *w=0) |
| | Returns the Standard Deviation of an array a with length n.
|
| |
| Bool_t | TMath::RootsCubic (const Double_t coef[4], Double_t &a, Double_t &b, Double_t &c) |
| | Calculates roots of polynomial of 3rd order a*x^3 + b*x^2 + c*x + d, where.
|
| |
| constexpr Double_t | TMath::RUncertainty () |
| | Universal gas constant uncertainty.
|
| |
| constexpr Double_t | TMath::Sigma () |
| | Stefan-Boltzmann constant in \( W m^{-2} K^{-4}\): \( \sigma \).
|
| |
| constexpr Double_t | TMath::SigmaUncertainty () |
| | Stefan-Boltzmann constant uncertainty.
|
| |
| Double_t | TMath::SignalingNaN () |
| | Returns a signaling NaN as defined by IEEE 754](http://en.wikipedia.org/wiki/NaN#Signaling_NaN).
|
| |
| Double_t | TMath::Sin (Double_t) |
| | Returns the sine of an angle of x radians.
|
| |
| Double_t | TMath::SinH (Double_t) |
| | Returns the hyperbolic sine of `x.
|
| |
| Double_t | TMath::Sq (Double_t x) |
| | Returns x*x.
|
| |
| Double_t | TMath::Sqrt (Double_t x) |
| | Returns the square root of x.
|
| |
| constexpr Double_t | TMath::Sqrt2 () |
| | \( \sqrt{2} \)
|
| |
| template<typename Iterator > |
| Double_t | TMath::StdDev (Iterator first, Iterator last) |
| | Same as RMS.
|
| |
| template<typename Iterator , typename WeightIterator > |
| Double_t | TMath::StdDev (Iterator first, Iterator last, WeightIterator wfirst) |
| | Same as RMS.
|
| |
| template<typename T > |
| Double_t | TMath::StdDev (Long64_t n, const T *a, const Double_t *w=0) |
| |
| Double_t | TMath::StruveH0 (Double_t x) |
| | Bessel function Y1(x) for positive x.
|
| |
| Double_t | TMath::StruveH1 (Double_t x) |
| | Struve functions of order 0.
|
| |
| Double_t | TMath::StruveL0 (Double_t x) |
| | Struve functions of order 1.
|
| |
| Double_t | TMath::StruveL1 (Double_t x) |
| | Modified Struve functions of order 0.
|
| |
| Double_t | TMath::Student (Double_t T, Double_t ndf) |
| | Computes density function for Student's t- distribution (the probability function (integral of density) is computed in StudentI).
|
| |
| Double_t | TMath::StudentI (Double_t T, Double_t ndf) |
| | Calculates the cumulative distribution function of Student's t-distribution second parameter stands for number of degrees of freedom, not for the number of samples if x has Student's t-distribution, the function returns the probability of x being less than T.
|
| |
| Double_t | TMath::StudentQuantile (Double_t p, Double_t ndf, Bool_t lower_tail=kTRUE) |
| | Computes quantiles of the Student's t-distribution 1st argument is the probability, at which the quantile is computed 2nd argument - the number of degrees of freedom of the Student distribution When the 3rd argument lower_tail is kTRUE (default)- the algorithm returns such x0, that.
|
| |
| Double_t | TMath::Tan (Double_t) |
| | Returns the tangent of an angle of x radians.
|
| |
| Double_t | TMath::TanH (Double_t) |
| | Returns the hyperbolic tangent of x.
|
| |
| constexpr Double_t | TMath::TwoPi () |
| | \( 2\pi\)
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| Double_t | TMath::Vavilov (Double_t x, Double_t kappa, Double_t beta2) |
| | Returns the value of the Vavilov density function.
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| Double_t | TMath::VavilovI (Double_t x, Double_t kappa, Double_t beta2) |
| | Returns the value of the Vavilov distribution function.
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| Double_t | TMath::Voigt (Double_t x, Double_t sigma, Double_t lg, Int_t r=4) |
| | Computation of Voigt function (normalised).
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