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#include <math.h>
#include <time.h>
#include <stdio.h>
#include <stdlib.h>
#include <Riostream.h>
#include <assert.h>

#include "TVector2.h"
#include "TFile.h"
#include "TString.h"
#include "TF1.h"
#include "TF3.h"
#include "TH1.h"
#include "TH2.h"
#include "TH3.h"
#include "TProfile.h"
#include "TProfile2D.h"
#include "TMath.h"
#include "TText.h"
#include "TRandom3.h"
#include "TArray.h"
#include "TLegend.h"
#include "TStyle.h"
#include "TMinuit.h"
#include "TCanvas.h"
#include "TLatex.h"
#include "TPaveStats.h"
#include "TASImage.h"
#include "TSpline.h"


#define BohrR 1963.6885 // Bohr Radius for pions
#define FmToGeV 0.19733 // conversion to fm
#define PI 3.1415926
#define masspiC 0.1395702 // pi+ mass (GeV/c^2)
double kappa3 = 0.1; // 0.1 (default), 
double kappa4 = 0.5; // 0.5 (default), 

using namespace std;

int CollisionType_def=0;// 0=PbPb, 1=pPb, 2=pp
bool MCcase_def=0;// MC data?
int CHARGE_def=-1;// -1 or +1: + or - pions for same-charge case, --+ or ++- for mixed-charge case
bool SameCharge_def=kTRUE;// 3-pion same-charge?
bool AddCC=kTRUE;
bool Gaussian=1;// Gaussian or Exponential?
bool UseC2Bkg=1;// use Pythia/DPMJET bkg?
//
bool MuonCorrection=1;// apply Muon correction?
bool IncludeExpansion=kTRUE;// Include EdgeWorth coefficients?
bool FixExpansionAvg=1;
int Mbin_def=2;// 0-19 (0=1050-2000 pions, 19=0-5 pions)
int EDbin_def=0;// 0-2: Kt3 bin
int Ktbin_def=1;// 1-6, 10=full range
double MRCShift=1.0;// 1.0=full Momentum Resolution Correction. 1.1 for 10% systematic increase
bool FitRangeShift=0;// 30% reduction in Fit Range
bool ExtremeFitRangeC2=0;// 1.2 GeV/c fit range for C2?
//
//
bool SaveToFile_def=kFALSE;// Save outputs to file?
int SourceType=0;// 0=Therminator, 1=Therminator with 50fm cut (keep at 0 for default), 2=Gaussian
bool ConstantFSI=kFALSE;// Constant FSI's for each kt bin?
bool GofP=kFALSE;// Include momentum dependence of coherent fraction?
bool ChargeConstraint=kFALSE;// Include Charge Constraint for coherent states?
bool LinkN=kFALSE;// Make N(++)=N(+-)?
bool GeneratedSignal=kFALSE;// Was the QS+FSI signal generated in MC? 
bool Tricubic=kFALSE;// Tricubic or Trilinear interpolation?  Tricubic was found to be unstable.
bool IncludeSS=kTRUE;// Include same-charge two-pion correlations in the fit?
bool IncludeOS=kFALSE;// Include mixed-charge two-pion correlations in the fit?
//
//
double ExpPower=2;// default Gaussian(2), Exponential(1)
//
//
const int Sbins_2=1;// 2-particle Species bins. 1=Pion-Pion only. max=6 (pi-pi, pi-k, pi-p, k-p, k-k, p-p)
const int Sbins_3=1;// 3-particle Species bins. 1=Pion-Pion-Pion only. max=10
const int fitlimitLowBin = 3;
const int fitlimitHighBin = 14;// max = 20 (100MeV)
bool LHC11h=kTRUE;// always kTRUE
bool ExplicitLoop=kFALSE;// always kFALSE
bool PairCut=kTRUE;// always kTRUE
int FSIindex;
int Ktlowbin;
int Kthighbin;
int MomResCentBin;// momentum resolution centrality bin
float TwoFrac;// Lambda parameter
float OneFrac;// Lambda^{1/2}
float ThreeFrac;// Lambda^{3/2}
float Q2Limit;
float Q3Limit;

double lambda_PM = 0.7;


TH1D *CoulCorr2SS;
TH1D *CoulCorr2OS;
TH1D *CoulCorr2SS_2;// for interpolation in transition from Therminator to Gauss K factors
TH1D *CoulCorr2OS_2;// for interpolation in transition from Therminator to Gauss K factors
//

void ReadCoulCorrections(int);
void ReadMomResFile(int);
void ReadMuonCorrections(int,int);
double CoulCorr2(int, double);
double CoulCorrGRS(bool, double, double, double);
double Dfitfunction_c3(Double_t *x, Double_t *par);
double Gamov(int, double);
double C2ssFitFunction(Double_t *x, Double_t *par);
double C2osFitFunction(Double_t *x, Double_t *par);
double cubicInterpolate(double[4], double);
double bicubicInterpolate(double[4][4], double, double);
double tricubicInterpolate(double[4][4][4], double, double, double);
void DrawALICELogo(Bool_t, Float_t, Float_t, Float_t, Float_t);

//
void fcnC2_Global(int&, double*, double&, double[], int);

const int BINRANGE_C2global=400;// 40
double C2ssFitting[BINRANGE_C2global];
double C2osFitting[BINRANGE_C2global];
double C2ssFitting_e[BINRANGE_C2global];
double C2osFitting_e[BINRANGE_C2global];
double K2SS[BINRANGE_C2global];
double K2OS[BINRANGE_C2global];
double K2SS_e[BINRANGE_C2global];
double K2OS_e[BINRANGE_C2global];
double Chi2_C2global;
double NFitPoints_C2global;
double Chi2_C3global;
double NFitPoints_C3global;

const int BINS_OSL=40;// out,side,long bins
double A[BINS_OSL][BINS_OSL][BINS_OSL];// out,side,long
double B[BINS_OSL][BINS_OSL][BINS_OSL];// out,side,long
double A_e[BINS_OSL][BINS_OSL][BINS_OSL];// out,side,long
double B_e[BINS_OSL][BINS_OSL][BINS_OSL];// out,side,long
double avg_q[BINS_OSL][BINS_OSL][BINS_OSL];// out,side,long
double K_OSL[BINS_OSL][BINS_OSL][BINS_OSL];// out,side,long
double K_OSL_e[BINS_OSL][BINS_OSL][BINS_OSL];// out,side,long
double Chi2_OSL;
double NFitPoints_OSL;

const int BINRANGE_3=40;// q12,q13,q23
int BINLIMIT_3=20;
double A_3[BINRANGE_3][BINRANGE_3][BINRANGE_3];// q12,q13,q23
double A_3_e[BINRANGE_3][BINRANGE_3][BINRANGE_3];// q12,q13,q23
double B_3[BINRANGE_3][BINRANGE_3][BINRANGE_3];// q12,q13,q23
double BinCenters[400];
double BinWidthQ2;
double Chi2_c3;
double NFitPoints_c3;
void fcn_c3(int&, double*, double&, double[], int);

double C3_base[BINRANGE_3][BINRANGE_3][BINRANGE_3];
double N_term1[BINRANGE_3][BINRANGE_3][BINRANGE_3];
double N_term2[BINRANGE_3][BINRANGE_3][BINRANGE_3];
double N_term3[BINRANGE_3][BINRANGE_3][BINRANGE_3];
double N_term4[BINRANGE_3][BINRANGE_3][BINRANGE_3];
double N_term5[BINRANGE_3][BINRANGE_3][BINRANGE_3];


TH3D *MomRes3d[2][5];// SC/MC, term#
TH1D *MomRes1d[2][5];// SC/MC, term#
TH1D *MomResC2[2];// SC/MC
int MRC2index;// index for C2 MRC 

double AvgP[6][20];// kt bin, qinv bin

TH1D *C2muonCorrection_SC;
TH1D *C2muonCorrection_MC;
TH1D *C3muonCorrection;

TF1 *StrongSC;// same-charge pion strong FSI
TF1 *MixedChargeSysFit;// mixed-charge 3-pion cumulant residue obtained from Plot_plotsTPR.C
TF1 *BkgMCFit;// Pythia or DPMJET fit 
//


void Plot_PDCumulants_TPR(bool SaveToFile=SaveToFile_def, int CollisionType=CollisionType_def, bool MCcase=MCcase_def, bool SameCharge=SameCharge_def, int EDbin=EDbin_def, int CHARGE=CHARGE_def, int Mbin=Mbin_def, int Ktbin=Ktbin_def){
  
  EDbin_def=EDbin;
  Ktbin_def=Ktbin;
  CollisionType_def=CollisionType;
  SaveToFile_def=SaveToFile;
  MCcase_def=MCcase;
  CHARGE_def=CHARGE;
  SameCharge_def=SameCharge;// 3-pion same-charge
  Mbin_def=Mbin;
  //
  if(CollisionType==0){
    Q3Limit = 0.1 + 0.1*Mbin/16.;
  }else{
    Q3Limit = 0.3 + 0.2*fabs(Mbin-10)/9.;
  }
  if(FitRangeShift) Q3Limit -= 0.3*Q3Limit;
  Q2Limit = Q3Limit/sqrt(2.);
  if(ExtremeFitRangeC2) Q2Limit = 1.2;
  //Q2Limit = (0.3 + 0.2*fabs(Mbin-10)/9.) / sqrt(2.);
  //cout<<Q2Limit<<endl;

  
  // PbPb then pPb then pp
  //double Nch_means[3][20]={{1828,1407,1071,896,757,619,496,402,324,252,171,117,83,63,50,36,   36,36,36,36},  {71,71,71,71,71,71,71,71,71,71,71,71,   71,57,45,32,23,16,9.7,5},   {47,47,47,47,47,47,47,47,47,47,47,47,47,   47,37,27,20,15,8.6,4.6}};
  
  //kappa3 = 0.1;
  //kappa4 = 0.5;
  //kappa3 = 0.05 + 0.25*(Mbin/19.);// linear dependence of kappa3
  
  //double MainFitParams[8]={0};
  //
  //double RefMainFitParams[8]={6.71377,  5.39974,  1.3822,  1.82065,  6.71377,  5.39974,  1.3822,  1.82065};

  if(Gaussian) ExpPower=2.;
  else ExpPower=1.;
  
  if(CollisionType==0){
    if(Mbin==0) FSIindex = 0;// 0-5% Therm
    else if(Mbin==1) FSIindex = 1;// 0-10% Therm
    else if(Mbin<=3) FSIindex = 2;// 10-20% Therm
    else if(Mbin<=5) FSIindex = 3;// 20-30% Therm
    else if(Mbin<=7) FSIindex = 4;// 30-40% Therm
    else if(Mbin<=9) FSIindex = 5;// 40-50% Therm
    else FSIindex = 6;// EW R=4.0 fm
    // next bin is 3.0 fm which is used for interpolation
  }else{
    if(Mbin<=14) FSIindex = 8;// EW R=2.5 fm
    else if(Mbin<=16) FSIindex = 9;// EW R=2.0 fm
    else FSIindex = 10;// EW R=1.7 fm
    // last bin is 1.25 fm which is used for interpolation
  }

  // chooses lambda=0.7 for R=10,8,6,4,2
  if(Mbin<=2) MRC2index=138;
  else if(Mbin<=5) MRC2index=106;
  else if(Mbin<=9) MRC2index=74;
  else if(Mbin<=13) MRC2index=42;// was 9 by mistake, now 13 (corrected on 22/10/2013)
  else MRC2index=10;
  

  
  TwoFrac = lambda_PM;
  OneFrac = sqrt(TwoFrac);
  ThreeFrac = pow(TwoFrac,3/2.);
  
  if(CollisionType==0 && Mbin<10) BINLIMIT_3=20;
  else BINLIMIT_3=40;

  Ktlowbin=(Ktbin)*2+3;// kt bins are 0.5 GeV/c wide (0-0.5, 0.5-1.0 ...)
  Kthighbin=(Ktbin)*2+4;
  if(Ktbin==2) {cout<<"Kthighbin increased"<<endl; Kthighbin = 20;}// to make <KT3> comparible to <kT> 
  
  
  BkgMCFit=new TF1("BkgMCFit","[0]*([1] + [2]*exp(-pow([3]*x,2)))",0,2.0);
  BkgMCFit->SetParameter(0,1); 
  BkgMCFit->SetParameter(1,1.001);
  BkgMCFit->SetParameter(2,0.04102);
  BkgMCFit->SetParameter(3,1.874);
  BkgMCFit->SetLineColor(1);
  if(!MCcase){
    // kt bin(0.2<kt<0.3, 0.3<kt<1.0), Mult bin(low to high)
    float paramsPP_0[2][10]={{1.00014,1.00019,9.99733e-01,9.99379e-01,9.99488e-01, 9.99488e-01,9.99488e-01,9.99488e-01,9.99488e-01,9.99488e-01},{9.97267e-01,9.98918e-01,9.99117e-01,9.98878e-01,9.99457e-01, 9.99457e-01,9.99457e-01,9.99457e-01,9.99457e-01,9.99457e-01}};
    float paramsPP_1[2][10]={{1.00198,1.00156,1.00109,1.00068,1.00079, 1.00079,1.00079,1.00079,1.00079,1.00079},
			     {9.98091e-01,9.98893e-01,9.99782e-01,9.99595e-01,1.00037, 1.00037,1.00037,1.00037,1.00037,1.00037}};
    float paramsPP_2[2][10]={{4.51532e-02,4.30415e-02,4.10306e-02,3.42739e-02,2.95607e-02, 2.95607e-02,2.95607e-02,2.95607e-02,2.95607e-02,2.95607e-02},
			     {9.89882e-02,1.00657e-01,8.93560e-02,7.55225e-02,6.52689e-02, 6.52689e-02,6.52689e-02,6.52689e-02,6.52689e-02,6.52689e-02}};
    float paramsPP_3[2][10]={{1.57172,1.91807,1.87353,1.88549,2.22286, 2.22286,2.22286,2.22286,2.22286,2.22286},
			     {1.49834,1.65562,1.66501,1.75097,1.78597, 1.78597,1.78597,1.78597,1.78597,1.78597}};
    //////////////
    float paramsPPb_0[2][10]={{9.99479e-01,9.98772e-01,9.99295e-01,9.99532e-01,9.99430e-01,9.99642e-01,9.99424e-01, 9.99424e-01,9.99424e-01,9.99424e-01},
			      {9.91941e-01,9.96569e-01,9.97183e-01,9.98106e-01,9.98591e-01,9.98717e-01,9.98517e-01, 9.98517e-01,9.98517e-01,9.98517e-01}};
    float paramsPPb_1[2][10]={{1.00093,1.00023,1.00068,1.00082,1.00077,1.00087,1.00069, 1.00069,1.00069,1.00069},
			      {9.93727e-01,9.98118e-01,9.98630e-01,9.99584e-01,1.00005,1.00017,9.99972e-01, 9.99972e-01,9.99972e-01,9.99972e-01}};
    float paramsPPb_2[2][10]={{3.05502e-02,2.21034e-02,1.39907e-02,9.82480e-03,6.48672e-03,5.37259e-03,4.54498e-03, 4.54498e-03,4.54498e-03,4.54498e-03},
			      {8.86336e-02,5.53244e-02,3.59877e-02,2.57145e-02,1.82072e-02,1.44253e-02,1.28923e-02, 1.28923e-02,1.28923e-02, 1.28923e-02}};
    float paramsPPb_3[2][10]={{1.69217,1.51289,1.63134,1.71567,1.71918,1.78037,2.10736, 2.10736,2.10736,2.10736},
			      {1.21996,1.34570,1.35660,1.37801,1.39951,1.39093,1.33747, 1.33747,1.33747,1.33747}};

    int ktindexBkg = Ktbin - 1;
    if(ktindexBkg > 1) ktindexBkg = 1;
    if(CollisionType==2){
      BkgMCFit->FixParameter(0, paramsPP_0[ktindexBkg][19-Mbin]);
      BkgMCFit->FixParameter(1, paramsPP_1[ktindexBkg][19-Mbin]);
      BkgMCFit->FixParameter(2, paramsPP_2[ktindexBkg][19-Mbin]);
      BkgMCFit->FixParameter(3, paramsPP_3[ktindexBkg][19-Mbin]);
    }else if(CollisionType==1){
      BkgMCFit->FixParameter(0, paramsPPb_0[ktindexBkg][19-Mbin]);
      BkgMCFit->FixParameter(1, paramsPPb_1[ktindexBkg][19-Mbin]);
      BkgMCFit->FixParameter(2, paramsPPb_2[ktindexBkg][19-Mbin]);
      BkgMCFit->FixParameter(3, paramsPPb_3[ktindexBkg][19-Mbin]);
    }else{// no Bkg for PbPb
      BkgMCFit->FixParameter(0, 1);
      BkgMCFit->FixParameter(1, 1);
      BkgMCFit->FixParameter(2, 0);
      BkgMCFit->FixParameter(3, 1);
    }
    
  }
  // Core-Halo modeling of single-particle and triple-particle core fraction 
  //float AvgN[10]={1.99266, 3.97789, 6.4624, 8.94042, 11.4194, 13.8987, 16.385, 18.8756, 21.3691, 26.0742};// 13c (avg total pion mult)/2.  2.0sigma
  //
  
  // bin centers from QS+FSI
  double BinCenterPbPbCentral[40]={0.00206385, 0.00818515, 0.0129022, 0.0177584, 0.0226881, 0.027647, 0.032622, 0.0376015, 0.042588, 0.0475767, 0.0525692, 0.0575625, 0.0625569, 0.0675511, 0.0725471, 0.0775436, 0.0825399, 0.0875364, 0.0925339, 0.0975321, 0.102529, 0.107527, 0.112525, 0.117523, 0.122522, 0.12752, 0.132519, 0.137518, 0.142516, 0.147515, 0.152514, 0.157513, 0.162513, 0.167512, 0.172511, 0.177511, 0.18251, 0.187509, 0.192509, 0.197509};
  double BinCenterPbPbPeripheral[40]={0.00206385, 0.00818515, 0.0129022, 0.0177584, 0.0226881, 0.027647, 0.032622, 0.0376015, 0.042588, 0.0475767, 0.0525692, 0.0575625, 0.0625569, 0.0675511, 0.0725471, 0.0775436, 0.0825399, 0.0875364, 0.0925339, 0.0975321, 0.102529, 0.107527, 0.112525, 0.117523, 0.122522, 0.12752, 0.132519, 0.137518, 0.142516, 0.147515, 0.152514, 0.157513, 0.162513, 0.167512, 0.172511, 0.177511, 0.18251, 0.187509, 0.192509, 0.197509};
  double BinCenterpPbAndpp[40]={0.00359275, 0.016357, 0.0257109, 0.035445, 0.045297, 0.0552251, 0.0651888, 0.0751397, 0.0851088, 0.0951108, 0.105084, 0.115079, 0.12507, 0.135059, 0.145053, 0.155049, 0.16505, 0.175038, 0.185039, 0.195034, 0.205023, 0.215027, 0.225024, 0.235023, 0.245011, 0.255017, 0.265017, 0.275021, 0.285021, 0.295017, 0.305018, 0.315018, 0.325013, 0.335011, 0.345016, 0.355019, 0.365012, 0.375016, 0.385017, 0.395016};
  if(CollisionType==0){
    for(int i=0; i<40; i++){
      if(Mbin<10) BinCenters[i] = BinCenterPbPbCentral[i];
      else BinCenters[i] = BinCenterPbPbPeripheral[i];
    }
    BinWidthQ2 = 0.005;
  }else{
    for(int i=0; i<40; i++){
      BinCenters[i] = BinCenterpPbAndpp[i];
    }
    BinWidthQ2 = 0.01;
  }
  

  // extend BinCenters for high q
  for(int index=40; index<400; index++){
    if(CollisionType==0) BinCenters[index] = (index+0.5)*(0.005);
    else BinCenters[index] = (index+0.5)*(0.010);
  }
  // Set 0's to 3-particle fit arrays
  for(int i=1; i<=BINLIMIT_3; i++){// bin number
    for(int j=1; j<=BINLIMIT_3; j++){// bin number
      for(int k=1; k<=BINLIMIT_3; k++){// bin number
	A_3[i-1][j-1][k-1]=0;
	A_3_e[i-1][j-1][k-1]=0;
	B_3[i-1][j-1][k-1]=0;
      }
    }
  }

  // same-charge pion strong FSI (obtained from ratio of CoulStrong to Coul at R=7 Gaussian from Lednicky's code)
  StrongSC=new TF1("StrongSC","[0]+[1]*exp(-pow([2]*x,2))",0,1000);
  StrongSC->FixParameter(0,9.99192e-01);
  StrongSC->FixParameter(1,-8.01113e-03);
  StrongSC->FixParameter(2,5.35912e-02);
  // mixed-charge 3-pion cumulant residue obtained from Plot_plotsTPR.C
  MixedChargeSysFit=new TF1("MixedChargeSysFit","[0]+[1]*exp(-pow([2]*x/0.19733,2))",0,.5);
  MixedChargeSysFit->FixParameter(0,1); 
  MixedChargeSysFit->FixParameter(1,.06);
  MixedChargeSysFit->FixParameter(2,5.5 - 6*(Mbin/19.));
  
  
  gStyle->SetOptStat(0);
  gStyle->SetOptDate(0);
  gStyle->SetOptFit(0111);

  TFile *_file0;
  if(CollisionType==0){// PbPb
    if(MCcase) {
      if(Mbin<=1){
	_file0 = new TFile("Results/PDC_12a17a_R10_2.root","READ");
      }else{
	_file0 = new TFile("Results/PDC_12a17e_R10.root","READ");
      }
    }else{
      //_file0 = new TFile("Results/PDC_10h_11h_0to50_50to100.root","READ");
      //_file0 = new TFile("Results/PDC_10h_11h_0to50_50to100_3Ktbins.root","READ");
      //_file0 = new TFile("Results/PDC_10h_2Kt3bins.root","READ");
      //_file0 = new TFile("Results/PDC_10h_NewNorm.root","READ");
      //_file0 = new TFile("Results/PDC_10h_dEta0p03dPhi0p03.root","READ");
      //_file0 = new TFile("Results/PDC_10h_noPID.root","READ");
      //_file0 = new TFile("Results/PDC_10h_1percentCentral.root","READ");
      //_file0 = new TFile("Results/PDC_10h_11h_2Kt3bins.root","READ");// v5 and before
      //_file0 = new TFile("Results/PDC_10h_dEta0p025dPhi0p055.root","READ");
      //_file0 = new TFile("Results/PDC_11h_3Kt3bins_FB5and7overlap.root","READ");
      //_file0 = new TFile("Results/PDC_10h_11h_V0binning.root","READ");
      //_file0 = new TFile("Results/PDC_10h_11h_lowerMultBins.root","READ");
      _file0 = new TFile("Results/PDC_10h_11h_NclsFix.root","READ");// standard
    }
  }else if(CollisionType==1){// pPb
    if(!MCcase){
      //_file0 = new TFile("Results/PDC_13c_kMB.root","READ");
      //_file0 = new TFile("Results/PDC_13bc.root","READ");
      //_file0 = new TFile("Results/PDC_13bc_3Ktbins.root","READ");
      //_file0 = new TFile("Results/PDC_13bc_kAnyINT_kINT7.root","READ");
      //_file0 = new TFile("Results/PDC_13bc_2Kt3bins.root","READ");
      //_file0 = new TFile("Results/PDC_13bc_kINT7.root","READ");// paper v1
      //_file0 = new TFile("Results/PDC_13c_posEta.root","READ");// eta sub-range
      //_file0 = new TFile("Results/PDC_13c_negEta.root","READ");// eta sub-range
      //_file0 = new TFile("Results/PDC_13c_0p4to0p8eta.root","READ");// eta sub-range
      //_file0 = new TFile("Results/PDC_13c_neg0p4toneg0p8eta.root","READ");// eta sub-range
      //_file0 = new TFile("Results/PDC_13bc_dEta0p025dPhi0p055_kINT7_kHighMult.root","READ");
      //_file0 = new TFile("Results/PDC_13bc_FB5and7overlap_V0binning.root","READ");
      //_file0 = new TFile("Results/PDC_13bc_kAnyINT_V0binning.root","READ");
      //_file0 = new TFile("Results/PDC_13bcd_kHighMult.root","READ");
      //_file0 = new TFile("Results/PDC_13bcd_kINT7.root","READ");
      //_file0 = new TFile("Results/PDC_13f_kHighMult.root","READ");
      //_file0 = new TFile("Results/PDC_13e_kHighMult.root","READ");
      //_file0 = new TFile("Results/PDC_13bcd_kINT7_plus_kHighMult.root","READ");// v5 and before
      //_file0 = new TFile("Results/PDC_13bcde_kINT7_NclsFix.root","READ");
      //_file0 = new TFile("Results/PDC_13e_kHighMult_NclsFix.root","READ");
      _file0 = new TFile("Results/PDC_13bcde_kINT7_kHighMult_NclsFix.root","READ");// standard
    }else{
      _file0 = new TFile("Results/PDC_13b2_efix_p1234_R2_2Ktbins.root","READ");// standard (gen level)
      //_file0 = new TFile("Results/PDC_13b2_efix_p1234_R2_RecLevel.root","READ");// Reconstructed tracks
      //_file0 = new TFile("Results/PDC_13b2_p1_noTTC.root","READ");
    }
  }else{// pp
    if(!MCcase){
      //_file0 = new TFile("Results/PDC_10cde.root","READ");
      //_file0 = new TFile("Results/PDC_10cde_3Ktbins.root","READ");
      //_file0 = new TFile("Results/PDC_10e_kHighMult.root","READ");
      //_file0 = new TFile("Results/PDC_10e_kAnyINT.root","READ");
      //_file0 = new TFile("Results/PDC_10cde_kAnyINT.root","READ");
      //_file0 = new TFile("Results/PDC_10cde_kAnyINT_Plus_kHighMult.root","READ");
      //_file0 = new TFile("Results/K0sRange_10cde.root","READ");// for K0s peak removal
      //_file0 = new TFile("Results/PDC_10cde_2Kt3bins.root","READ");
      //_file0 = new TFile("Results/PDC_10e_kHighMult.root","READ");
      //_file0 = new TFile("Results/PDC_10cde_kMB.root","READ");
      //_file0 = new TFile("Results/PDC_10cde_kMB_plus_kHighMult_2Kt3bins.root","READ");// v2 paper
      //_file0 = new TFile("Results/PDC_10cde_kMB_plus_kHighMult_AOD147.root","READ");// v5 and before
      //_file0 = new TFile("Results/PDC_10cde_FB5and7overlap.root","READ");
      //_file0 = new TFile("Results/PDC_10d_noTTC.root","READ");
      //_file0 = new TFile("Results/PDC_10cde_kMB.root","READ");
      _file0 = new TFile("Results/PDC_10cde_kMB_kHighMult_NclsFix.root","READ");// standard
    }else{
      _file0 = new TFile("Results/PDC_10f6a_R2_2Ktbins.root","READ");// standard
      //_file0 = new TFile("Results/PDC_10f6a_R2_AOD161.root","READ");
      //_file0 = new TFile("Results/PDC_10f6a_R10_genLevel_2Ktbins.root","READ");
    }
  }
  
  ReadCoulCorrections(FSIindex);
  ReadMomResFile(Mbin);
  ReadMuonCorrections(CollisionType,Mbin);
  //
  /////////////////////////////////////////////////////////


  double NormQcutLow;
  double NormQcutHigh;
  if(CollisionType==0) {// PbPb
    if(Mbin<10){
      NormQcutLow = 0.15;// was 0.15
      NormQcutHigh = 0.175;// was 0.175
    }else{
      NormQcutLow = 0.3;// was 0.3
      NormQcutHigh = 0.35;// was 0.35
    }
  }else{// pPb and pp
    NormQcutLow = 1.0;// was 1.0
    NormQcutHigh = 1.2;// was 1.2
  }
  
  
  TList *MyList;
  TDirectoryFile *tdir;
  if(!MCcase) tdir = (TDirectoryFile*)_file0->Get("PWGCF.outputThreePionRadiiAnalysis.root");
  

  if(CollisionType==0){
    if(!MCcase){
      if(Mbin<6) MyList=(TList*)tdir->Get("ThreePionRadiiOutput_1");
      else MyList=(TList*)tdir->Get("ThreePionRadiiOutput_2");
    }else{
      MyList=(TList*)_file0->Get("MyList");
    }
  }else {
    if(!MCcase) {
      if(CollisionType==2 && Mbin<15) MyList=(TList*)tdir->Get("ThreePionRadiiOutput_2");
      else MyList=(TList*)tdir->Get("ThreePionRadiiOutput_1");
    }else MyList=(TList*)_file0->Get("MyList");
  }
  _file0->Close();
  
  TH1D *Events = (TH1D*)MyList->FindObject("fEvents2");
  //
  cout<<"#Events = "<<Events->Integral(Mbin+1,Mbin+1)<<endl;

  // below lines determine fractional cross-sections without correction for efficiency
  //TH1F *fMultDist3 = (TH1F*)MyList->FindObject("fMultDist3");// total event count before track cuts
  //for(int mm=19; mm>=10; mm--){
  //cout<<"fracton of cross-section = "<<Events->GetBinContent(mm+1)/fMultDist3->GetEntries()<<endl;
  //}
  
  TF1 *Unity = new TF1("Unity","1",0,10);
  Unity->SetLineStyle(2); Unity->SetLineColor(1);
  
  // Explicit Loop Histos
  TH2D *Two_ex_2d[2][2][Sbins_2][2];
  TH1D *Two_ex[2][2][Sbins_2][2];
      
  // Normalizations
  double NormH_pc[5]={0};
  
  double norm_ex_2[6][2]={{0}};
  
  // 3d method histograms
  TH3D *Three_3d[2][2][2][Sbins_3][5];
  TH1D *Three_1d[2][2][2][Sbins_3][5];
  ///////////////////////////////////
  // Create Histograms
  
  // 2-particle
  for(int c1=0; c1<2; c1++){
    for(int c2=0; c2<2; c2++){
      for(int sc=0; sc<Sbins_2; sc++){
	for(int term=0; term<2; term++){
	  
	  TString *name2_ex = new TString("Explicit2_Charge1_");
	  *name2_ex += c1;
	  name2_ex->Append("_Charge2_");
	  *name2_ex += c2;
	  name2_ex->Append("_SC_");
	  *name2_ex += sc;
	  name2_ex->Append("_M_");
	  *name2_ex += Mbin;
	  name2_ex->Append("_ED_");
	  *name2_ex += 0;// EDbin
	  name2_ex->Append("_Term_");
	  *name2_ex += term+1;
	  
	  if(sc==0 || sc==3 || sc==5){
	    if( (c1+c2)==1 ) {if(c1!=0) continue;}// skip degenerate histogram
	  }
	  	  
	  Two_ex_2d[c1][c2][sc][term] = (TH2D*)MyList->FindObject(name2_ex->Data());
	  Two_ex_2d[c1][c2][sc][term]->Sumw2();
	  TString *proname = new TString(name2_ex->Data());
	  proname->Append("_pro");
	  
	  if(Ktbin==10) {Ktlowbin=1; Kthighbin=Two_ex_2d[c1][c2][sc][term]->GetNbinsX();}//full kt interval
	  Two_ex[c1][c2][sc][term] = (TH1D*)Two_ex_2d[c1][c2][sc][term]->ProjectionY(proname->Data(),Ktlowbin,Kthighbin);// bins:5-6 (kt:0.2-0.3)
	  
	  norm_ex_2[sc][term] = Two_ex[c1][c2][sc][term]->Integral(Two_ex[c1][c2][sc][term]->GetXaxis()->FindBin(NormQcutLow),Two_ex[c1][c2][sc][term]->GetXaxis()->FindBin(NormQcutHigh));
	  Two_ex[c1][c2][sc][term]->Scale(norm_ex_2[sc][0]/norm_ex_2[sc][term]);
	  
	  Two_ex[c1][c2][sc][term]->SetMarkerStyle(20);
	  Two_ex[c1][c2][sc][term]->GetXaxis()->SetTitle("#font[12]{q}_{inv}");
	  Two_ex[c1][c2][sc][term]->GetYaxis()->SetTitle("#font[12]{C}_{2}");
	  Two_ex[c1][c2][sc][term]->SetTitle("");
	  
	}// term
      }// sc
      
      // 3-particle
      for(int c3=0; c3<2; c3++){
	for(int sc=0; sc<Sbins_3; sc++){
	  for(int term=0; term<5; term++){
	   
	    TString *name3_ex = new TString("Explicit3_Charge1_");
	    *name3_ex += c1;
	    name3_ex->Append("_Charge2_");
	    *name3_ex += c2;
	    name3_ex->Append("_Charge3_");
	    *name3_ex += c3;
	    name3_ex->Append("_SC_");
	    *name3_ex += sc;
	    name3_ex->Append("_M_");
	    *name3_ex += Mbin;
	    name3_ex->Append("_ED_");
	    *name3_ex += EDbin;
	    name3_ex->Append("_Term_");
	    *name3_ex += term+1;
	    
	    
	    TString *name3_pc = new TString("PairCut3_Charge1_");
	    *name3_pc += c1;
	    name3_pc->Append("_Charge2_");
	    *name3_pc += c2;
	    name3_pc->Append("_Charge3_");
	    *name3_pc += c3;
	    name3_pc->Append("_SC_");
	    *name3_pc += sc;
	    name3_pc->Append("_M_");
	    *name3_pc += Mbin;
	    name3_pc->Append("_ED_");
	    *name3_pc += EDbin;
	    name3_pc->Append("_Term_");
	    *name3_pc += term+1;
	    
	    ///////////////////////////////////////
	    // skip degenerate histograms
	    if(sc==0 || sc==6 || sc==9){// Identical species
	      if( (c1+c2+c3)==1) {if(c1!=0 || c2!=0 || c3!=1) continue;}
	      if( (c1+c2+c3)==2) {if(c1!=0) continue;}
	    }else if(sc!=5){
	      if( (c1+c2)==1) {if(c1!=0) continue;}
	    }else {}// do nothing for pi-k-p case
	    
	    /////////////////////////////////////////
	    	    
	   
	    if(PairCut){
	      
	      TString *nameNorm=new TString("PairCut3_Charge1_");
	      *nameNorm += c1;
	      nameNorm->Append("_Charge2_");
	      *nameNorm += c2;
	      nameNorm->Append("_Charge3_");
	      *nameNorm += c3;
	      nameNorm->Append("_SC_");
	      *nameNorm += sc;
	      nameNorm->Append("_M_");
	      *nameNorm += Mbin;
	      nameNorm->Append("_ED_");
	      *nameNorm += 0;// EDbin
	      nameNorm->Append("_Term_");
	      *nameNorm += term+1;
	      nameNorm->Append("_Norm");
	      NormH_pc[term] = ((TH1D*)MyList->FindObject(nameNorm->Data()))->Integral();
	      	      
	      if(NormH_pc[term] > 0){
		
		if(sc<=2) {
		 
		  TString *name_3d = new TString(name3_pc->Data());
		  name_3d->Append("_3D");
		  Three_3d[c1][c2][c3][sc][term] = (TH3D*)MyList->FindObject(name_3d->Data());
		  Three_3d[c1][c2][c3][sc][term]->Sumw2();
		  Three_3d[c1][c2][c3][sc][term]->Scale(NormH_pc[0]/NormH_pc[term]);
		  TString *name_Q3 = new TString(name3_pc->Data());
		  name_Q3->Append("_Q3");
		  Three_1d[c1][c2][c3][sc][term] = (TH1D*)MyList->FindObject(name_Q3->Data());
		  Three_1d[c1][c2][c3][sc][term]->Sumw2();
		  Three_1d[c1][c2][c3][sc][term]->Scale(NormH_pc[0]/NormH_pc[term]);
		  //cout<<"Scale factor = "<<NormH_pc[0]/NormH_pc[term]<<endl;

		  
		}
		
	      }else{
		cout<<"normalization = 0.  Skipping this SC.  SC="<<sc<<"  c1="<<c1<<"  c2="<<c2<<"  c3="<<c3<<endl;
	      }	      
	      
	      
	     
	    }// pair cut
	  }// term
	  
	}// SC
	
	
      }// c3

    }// c2
  }// c1

 
  cout<<"Done getting Histograms"<<endl;
  


  TCanvas *can1 = new TCanvas("can1", "can1",11,53,800,800);
  can1->SetHighLightColor(2);
  //can1->Range(-0.7838115,-1.033258,0.7838115,1.033258);
  gStyle->SetOptFit(0111);
  can1->SetFillColor(10);
  can1->SetBorderMode(0);
  can1->SetBorderSize(2);
  can1->SetFrameFillColor(0);
  can1->SetFrameBorderMode(0);
  can1->SetFrameBorderMode(0);
  gPad->SetRightMargin(0.025); gPad->SetLeftMargin(0.1); gPad->SetTopMargin(0.02); 
  gPad->SetGridx(0);
  gPad->SetGridy(0);
  TLegend *legend1 = new TLegend(.4,.67,.87,.87,NULL,"brNDC");
  legend1->SetBorderSize(1);
  legend1->SetTextSize(.04);// small .03; large .036 
  legend1->SetFillColor(0);
  
  TLatex *Specif_System = new TLatex(0.23, 0.9,"ALICE p-Pb #sqrt{#font[12]{s}_{NN}}=5.02 TeV, #LT#font[12]{N}_{ch}#GT = 9.8 #pm 0.5");
  TLatex *Specif_KT3 = new TLatex(0.23, 0.8,"0.16<#font[12]{K}_{T,3}<0.3 GeV/#font[12]{c}");
  TLatex *Specif_kT = new TLatex(0.23, 0.8,"0.2<#font[12]{k}_{T}<0.3 GeV/#font[12]{c}");
  TLatex *Specif_FSI = new TLatex(0.23, 0.7,"FSI uncorrected"); 
  TLatex *Specif_Disclaimer = new TLatex(0.23, 0.6,"Statistical errors only");
  Specif_FSI->SetTextFont(42); Specif_System->SetTextFont(42); Specif_KT3->SetTextFont(42); Specif_Disclaimer->SetTextFont(42);
  Specif_kT->SetTextFont(42);
  Specif_FSI->SetTextSize(0.04); Specif_System->SetTextSize(0.04); Specif_KT3->SetTextSize(0.04); Specif_Disclaimer->SetTextSize(0.04);
  Specif_kT->SetTextSize(0.04);
  Specif_FSI->SetNDC(); Specif_System->SetNDC(); Specif_KT3->SetNDC(); Specif_Disclaimer->SetNDC();
  Specif_kT->SetNDC();

  /////////////////////////
  // 2-particle legend
  // 0 = pi-pi
  // 1 = pi-k
  // 2 = pi-p
  // 3 = k-k
  // 4 = k-p
  // 5 = p-p
  /////////////////////////
  TH1D *Two_pipi_mp = (TH1D*)Two_ex[0][1][0][0]->Clone();
  Two_pipi_mp->Divide(Two_ex[0][1][0][1]);

  // Normalization range counting.  Just to evaluate required normalization width in qinv.
  //cout<<Two_ex[0][0][0][0]->Integral(Two_ex[0][0][0][0]->GetXaxis()->FindBin(0), Two_ex[0][0][0][0]->GetXaxis()->FindBin(0.1))<<endl;
  //cout<<Two_ex[0][0][0][0]->Integral(Two_ex[0][0][0][0]->GetXaxis()->FindBin(1.06), Two_ex[0][0][0][0]->GetXaxis()->FindBin(1.1))<<endl;
  //cout<<Two_ex[0][0][0][0]->Integral(Two_ex[0][0][0][0]->GetXaxis()->FindBin(0.15), Two_ex[0][0][0][0]->GetXaxis()->FindBin(0.175))<<endl;
  


  const int SCOI_2=0;
 
  TH1D *Two_ex_clone_mm=(TH1D*)Two_ex[0][0][SCOI_2][0]->Clone();
  Two_ex_clone_mm->Divide(Two_ex[0][0][SCOI_2][1]);
  TH1D *Two_ex_clone_mp=(TH1D*)Two_ex[0][1][SCOI_2][0]->Clone();
  Two_ex_clone_mp->Divide(Two_ex[0][1][SCOI_2][1]);
  TH1D *Two_ex_clone_pp=(TH1D*)Two_ex[1][1][SCOI_2][0]->Clone();
  Two_ex_clone_pp->Divide(Two_ex[1][1][SCOI_2][1]);
  
  
  Two_ex_clone_mm->GetYaxis()->SetTitle("#font[12]{C}_{2}");
  Two_ex_clone_mm->SetTitle("");
  Two_ex_clone_mp->GetYaxis()->SetTitle("#font[12]{C}_{2}");
  Two_ex_clone_mm->SetMarkerColor(2);
  Two_ex_clone_mm->SetLineColor(2);
  Two_ex_clone_mp->SetMarkerColor(1);
  Two_ex_clone_pp->SetMarkerColor(4);
  Two_ex_clone_pp->SetLineColor(4);
  Two_ex_clone_mm->GetXaxis()->SetRangeUser(0,0.6);
  Two_ex_clone_mm->SetMinimum(0.95);
  Two_ex_clone_mm->SetMaximum(2.4);
  

  if(MCcase){
    Two_ex_clone_mp->SetMarkerColor(4);
    Two_ex_clone_mp->SetLineColor(4);
    Two_ex_clone_mm->Add(Two_ex_clone_pp);
    Two_ex_clone_mm->Scale(0.5);
    Two_ex_clone_mm->GetYaxis()->SetTitle("#font[12]{C}_{2}^{MC}");
    Two_ex_clone_mm->GetYaxis()->SetTitleOffset(1.3);
    Two_ex_clone_mm->SetMinimum(0.95);
    Two_ex_clone_mm->SetMaximum(1.3);
    Two_ex_clone_mm->DrawCopy();
    gStyle->SetOptFit(1111);
    Two_ex_clone_mm->Fit(BkgMCFit,"","",0,1.8);
    //BkgMCFit->Draw("same");
    Two_ex_clone_mp->DrawCopy("same");
    legend1->AddEntry(Two_ex_clone_mm,"same-charge","p");
    //legend1->AddEntry(Two_ex_clone_pp,"++","p");
    legend1->AddEntry(Two_ex_clone_mp,"mixed-charge","p");
    legend1->Draw("same");
  }
 
  //for(int i=0; i<100; i++){
  //cout<<Two_ex_clone_mm->GetBinContent(i+1)<<", ";
  //}

  TF1 *C2osFit_CMS = new TF1("C2osFit_CMS","[0] + [1]*exp(-pow([2]*x,2))",0,2);
  C2osFit_CMS->FixParameter(0, 9.93558e-01);
  C2osFit_CMS->FixParameter(1, 5.19578e-02);
  C2osFit_CMS->FixParameter(2, 1.89425e+00);

  /////////////////////////////////////////////////////
  // Global fitting C2os and C2ss
  double C2ssSys_e[BINRANGE_C2global]={0};
  double C2osSys_e[BINRANGE_C2global]={0};
  //
  const int npar=10;// 10 
  TMinuit MyMinuit(npar);
  MyMinuit.SetFCN(fcnC2_Global);
  double arglist_C2 = 0; int dummy=0;
  MyMinuit.mnexcm("SET NOWarnings",&arglist_C2,1, dummy);  
  arglist_C2 = -1;
  MyMinuit.mnexcm("SET PRint",&arglist_C2,1, dummy);
  double OutputPar[npar]={0};
  double OutputPar_e[npar]={0};

  double par[npar];               // the start values
  double stepSize[npar];          // step sizes 
  double minVal[npar];            // minimum bound on parameter 
  double maxVal[npar];            // maximum bound on parameter
  string parName[npar];

  TH1D *temp_mm=(TH1D*)Two_ex[0][0][SCOI_2][0]->Clone();
  temp_mm->Divide(Two_ex[0][0][SCOI_2][1]);
  TH1D *temp_mp=(TH1D*)Two_ex[0][1][SCOI_2][0]->Clone();
  temp_mp->Divide(Two_ex[0][1][SCOI_2][1]);
  TH1D *temp_pp=(TH1D*)Two_ex[1][1][SCOI_2][0]->Clone();
  temp_pp->Divide(Two_ex[1][1][SCOI_2][1]);
  TH1D *C2ssRaw=(TH1D*)temp_mm->Clone();// MRC uncorrected
  TH1D *C2osRaw=(TH1D*)temp_mp->Clone();// MRC uncorrected
  C2ssRaw->SetMarkerStyle(24);
  C2osRaw->SetMarkerStyle(21);//21
  C2ssRaw->SetMarkerColor(2);
  C2osRaw->SetMarkerColor(4);
  
  for(int i=0; i<BINRANGE_C2global; i++){
    if(i >= temp_mm->GetNbinsX()) continue;// bin limit
    
    C2ssFitting[i] = (temp_mm->GetBinContent(i+1) + temp_pp->GetBinContent(i+1))/2.;
    double MRC_SC = 1.0;
    double MRC_MC = 1.0;
    if(MomResC2[0]->GetBinContent(i+1) > 0) MRC_SC = (MomResC2[0]->GetBinContent(i+1)-1)*MRCShift + 1;
    if(MomResC2[1]->GetBinContent(i+1) > 0) MRC_MC = (MomResC2[1]->GetBinContent(i+1)-1)*MRCShift + 1;
    if(!GeneratedSignal && !MCcase) C2ssFitting[i] *= MRC_SC;
    C2ssFitting_e[i] = pow(MRC_SC*sqrt(pow(temp_mm->GetBinError(i+1),2) + pow(temp_pp->GetBinError(i+1),2))/sqrt(2.),2);
    C2ssRaw->SetBinContent(i+1, (temp_mm->GetBinContent(i+1) + temp_pp->GetBinContent(i+1))/2.);
    C2ssRaw->SetBinError(i+1, pow(sqrt(pow(temp_mm->GetBinError(i+1),2) + pow(temp_pp->GetBinError(i+1),2))/sqrt(2.),2));
    C2ssFitting_e[i] = sqrt(C2ssFitting_e[i]);
    C2osFitting[i] = temp_mp->GetBinContent(i+1);
    if(!GeneratedSignal && !MCcase) C2osFitting[i] *= MRC_MC;
    C2osFitting_e[i] = pow(MRC_MC*temp_mp->GetBinError(i+1),2);
    C2osRaw->SetBinContent(i+1, temp_mp->GetBinContent(i+1));
    C2osRaw->SetBinError(i+1, temp_mp->GetBinError(i+1));
    C2osFitting_e[i] += pow((MRC_MC-1)*0.1 * temp_mp->GetBinContent(i+1),2);
    C2osFitting_e[i] = sqrt(C2osFitting_e[i]);
    //
    C2ssSys_e[i] = pow((MRC_SC-1)*0.1 * (temp_mm->GetBinContent(i+1) + temp_pp->GetBinContent(i+1))/2.,2);
    C2ssSys_e[i] = sqrt(C2ssSys_e[i]);
    C2osSys_e[i] = pow((MRC_MC-1)*0.1 * temp_mp->GetBinContent(i+1),2);
    C2osSys_e[i] = sqrt(C2osSys_e[i]);
    //
    if(UseC2Bkg) C2ssFitting[i] /= BkgMCFit->Eval(BinCenters[i]);
    //
    // method with undilution for plotting purposes
    //C2ssFitting[i] = (C2ssFitting[i] - (1-lambda_PM)) / (CoulCorr2(+1, BinCenters[i]) * lambda_PM);
    // divide CMS background
    //C2ssFitting[i] /= C2osFit_CMS->Eval(BinCenters[i]);
    //
    K2SS[i] = CoulCorr2(+1, BinCenters[i]);
    K2OS[i] = CoulCorr2(-1, BinCenters[i]);
    //K2SS[i] = 1;
    //K2OS[i] = 1;
    //
    K2SS_e[i] = 0.0;
    K2OS_e[i] = 0.0;
  }
  
    
    
    

  C2ssFitting[0]=-1000; C2osFitting[0]=-1000;
  C2ssFitting_e[0]=1000; C2osFitting_e[0]=1000;
  K2SS_e[0]=1000; K2OS_e[0]=1000;
  int ierflg=0;
  double arglist[10];
  //arglist[0]=2;// improve Minimization Strategy (1 is default)
  //MyMinuit.mnexcm("SET STR",arglist,1,ierflg);
  //arglist[0] = 0;
  //MyMinuit.mnexcm("SCAN", arglist,1,ierflg);
  arglist[0] = 5000;// 5000
  MyMinuit.mnexcm("MIGRAD", arglist ,1,ierflg);
  
  TF1 *fitC2ss_Base = new TF1("fitC2ss_Base",C2ssFitFunction, 0.005,2, npar);//0.2
  TF1 *fitC2ss_Expan = new TF1("fitC2ss_Expan",C2ssFitFunction, 0.005,2, npar);//0.2
  fitC2ss_Base->SetLineStyle(2);
  TH1D *fitC2ss_h = new TH1D("fitC2ss_h","",Two_ex_clone_mm->GetNbinsX(),Two_ex_clone_mm->GetXaxis()->GetBinLowEdge(1), Two_ex_clone_mm->GetXaxis()->GetBinUpEdge(Two_ex_clone_mm->GetNbinsX()));

  for(int ft=0; ft<2; ft++){// Gaussian or EW
    if(ft==1 && !IncludeExpansion) continue;
    par[0] = 1.0; par[1]=0.7; par[2]=0.5; par[3]=7.2; par[4] = .1; par[5] = .0; par[6] = .0; par[7] = 0.; par[8] = 0.; par[9] = 0.;// was par[1]=0.5
    stepSize[0] = 0.01; stepSize[1] = 0.01;  stepSize[2] = 0.02; stepSize[3] = 0.2; stepSize[4] = 0.01; stepSize[5] = 0.001; stepSize[6] = 0.001; stepSize[7] = 0.001; stepSize[8]=0.001; stepSize[9]=0.01;
    minVal[0] = 0.955; minVal[1] = 0.5; minVal[2] = 0.; minVal[3] = 0.1; minVal[4] = 0.001; minVal[5] = -10.; minVal[6] = -10.; minVal[7] = -10.; minVal[8]=-10; minVal[9] = 0.995;// minVal[1] was 0.2
    maxVal[0] = 1.1; maxVal[1] = 1.3; maxVal[2] = 0.99; maxVal[3] = 15.; maxVal[4] = 2.; maxVal[5] = 10.; maxVal[6] = 10.; maxVal[7] = 10.; maxVal[8]=10.; maxVal[9]=1.1;// maxVal[1] was 1.0
    if(Gaussian==kFALSE) {maxVal[1]=2.0; maxVal[3]=20.0;}
    
    parName[0] = "Norm"; parName[1] = "#Lambda"; parName[2] = "G"; parName[3] = "Rch"; parName[4] = "Rcoh"; 
    parName[5] = "coeff_3"; parName[6] = "coeff_4"; parName[7] = "coeff_5"; parName[8]="coeff_6"; parName[9]="Norm_2";
    
    for (int i=0; i<npar; i++){
      MyMinuit.DefineParameter(i, parName[i].c_str(), par[i], stepSize[i], minVal[i], maxVal[i]);
    }
    
    //MyMinuit.DefineParameter(1, parName[1].c_str(), 0.7, stepSize[1], minVal[1], maxVal[1]); MyMinuit.FixParameter(1);// lambda
    //MyMinuit.DefineParameter(0, parName[0].c_str(), .998, stepSize[0], minVal[0], maxVal[0]); MyMinuit.FixParameter(0);// N
    MyMinuit.DefineParameter(2, parName[2].c_str(), 0., stepSize[2], minVal[2], maxVal[2]); MyMinuit.FixParameter(2);// G
    MyMinuit.DefineParameter(4, parName[4].c_str(), 0., stepSize[4], minVal[4], maxVal[4]); MyMinuit.FixParameter(4);// Rcoh
    MyMinuit.DefineParameter(7, parName[7].c_str(), 0, stepSize[7], minVal[7], maxVal[7]); MyMinuit.FixParameter(7);// k5
    MyMinuit.DefineParameter(8, parName[8].c_str(), 0, stepSize[8], minVal[8], maxVal[8]); MyMinuit.FixParameter(8);// k6
    
    //
    if(ft==0){
      MyMinuit.DefineParameter(5, parName[5].c_str(), 0, stepSize[5], minVal[5], maxVal[5]); MyMinuit.FixParameter(5);// k3 
      MyMinuit.DefineParameter(6, parName[6].c_str(), 0, stepSize[6], minVal[6], maxVal[6]); MyMinuit.FixParameter(6);// k4
    }else{// IncludeExpansion
      if(FixExpansionAvg){
	if(Gaussian){ 
	  MyMinuit.DefineParameter(5, parName[5].c_str(), kappa3, stepSize[5], minVal[5], maxVal[5]); MyMinuit.FixParameter(5);// k3 
	  MyMinuit.DefineParameter(6, parName[6].c_str(), kappa4, stepSize[6], minVal[6], maxVal[6]); MyMinuit.FixParameter(6);// k4
	}else{
	  MyMinuit.DefineParameter(5, parName[5].c_str(), 0, stepSize[5], minVal[5], maxVal[5]); MyMinuit.FixParameter(5);// k3 
	  MyMinuit.DefineParameter(6, parName[6].c_str(), 0, stepSize[6], minVal[6], maxVal[6]); MyMinuit.FixParameter(6);// k4
	}
      }else{
	Int_t err=0;
	Double_t tmp[1];
	tmp[0] = 5+1;
	MyMinuit.mnexcm( "RELease", tmp,  1,  err );// kappa3
	tmp[0] = 6+1;
	MyMinuit.mnexcm( "RELease", tmp,  1,  err );// kappa4
	//
      }
    }
    
    if(IncludeSS==kFALSE){
      MyMinuit.DefineParameter(3, parName[3].c_str(), 9.1, stepSize[3], minVal[3], maxVal[3]); MyMinuit.FixParameter(3);// Rch
      MyMinuit.DefineParameter(0, parName[0].c_str(), .998, stepSize[0], minVal[0], maxVal[0]); MyMinuit.FixParameter(0);// N
      MyMinuit.DefineParameter(5, parName[5].c_str(), 0, stepSize[5], minVal[5], maxVal[5]); MyMinuit.FixParameter(5);// k3 
      MyMinuit.DefineParameter(6, parName[6].c_str(), 0, stepSize[6], minVal[6], maxVal[6]); MyMinuit.FixParameter(6);// k4
    }
    if(IncludeOS==kFALSE){
      MyMinuit.DefineParameter(9, parName[9].c_str(), 1.002, stepSize[9], minVal[9], maxVal[9]); MyMinuit.FixParameter(9);// N_2
    }
    

    // Do the minimization!
    if(!MCcase){
      cout<<"Start C2 Global fit"<<endl;
      MyMinuit.Migrad();// generally the best minimization algorithm
      cout<<"End C2 Global fit"<<endl;
    }
    for (int i=0; i<npar; i++){
      MyMinuit.GetParameter(i,OutputPar[i],OutputPar_e[i]);
    }
    MyMinuit.mnexcm("SHOw PARameters", &arglist_C2, 1, ierflg);
    cout<<"C2 fit: Chi2/NDF = "<<Chi2_C2global/(NFitPoints_C2global - MyMinuit.GetNumFreePars())<<"   Chi^2="<<Chi2_C2global<<endl;
    
    if(ft==0){// Gaussian or Exponential
      for(int i=0; i<npar; i++) {
	fitC2ss_Base->FixParameter(i,OutputPar[i]);
	fitC2ss_Base->SetParError(i,OutputPar_e[i]);
      }
      for(int bin=1; bin<=Two_ex_clone_mm->GetNbinsX(); bin++){
	double qinv = Two_ex_clone_mm->GetXaxis()->GetBinCenter(bin);
	if(!MCcase) fitC2ss_h->SetBinContent(bin, fitC2ss_Base->Eval(qinv));// Base fit
      }
      
    }else{// Edgeworth or Laguerre
      for(int i=0; i<npar; i++) {
	fitC2ss_Expan->FixParameter(i,OutputPar[i]);
	fitC2ss_Expan->SetParError(i,OutputPar_e[i]);
      }
      for(int bin=1; bin<=Two_ex_clone_mm->GetNbinsX(); bin++){
	//double qinv = Two_ex_clone_mm->GetXaxis()->GetBinCenter(bin);
	//if(!MCcase) fitC2ss_h->SetBinContent(bin, fitC2ss_Expan->Eval(qinv));// uncomment to show expansion
      }
      
      double lambdaStar=0, lambdaStar_e=0;
      if(Gaussian){
	lambdaStar = OutputPar[1]*pow(1 + OutputPar[6]/8.,2);
	lambdaStar_e = pow(OutputPar_e[1]*(1 + OutputPar[6]/8.),2);
	lambdaStar_e = sqrt(lambdaStar_e);
      }else{
	lambdaStar = OutputPar[1]*pow(1 - OutputPar[5] + OutputPar[6],2);
	lambdaStar_e = pow(OutputPar_e[1]*(1 - OutputPar[5] + OutputPar[6]),2);
	lambdaStar_e = sqrt(lambdaStar_e);
      }
      cout<<"lambda* = "<<lambdaStar<<" +- "<<lambdaStar_e<<endl;
    }
    //if(ft==0) {MainFitParams[0]=OutputPar[3]; MainFitParams[2]=OutputPar[1];}
    //else {MainFitParams[4]=OutputPar[3]; MainFitParams[6]=OutputPar[1];}
  }// ft
  

  TH1D *C2_ss=(TH1D*)Two_ex_clone_mm->Clone();
  TH1D *C2_os=(TH1D*)Two_ex_clone_mp->Clone();
  TH1D *C2_ss_Momsys=(TH1D*)Two_ex_clone_mm->Clone();
  TH1D *C2_os_Momsys=(TH1D*)Two_ex_clone_mp->Clone();
  TH1D *C2_ss_Ksys=(TH1D*)Two_ex_clone_mm->Clone();
  TH1D *C2_os_Ksys=(TH1D*)Two_ex_clone_mp->Clone();
  TH1D *K2_ss = (TH1D*)Two_ex_clone_mm->Clone();
  TH1D *K2_os = (TH1D*)Two_ex_clone_mp->Clone();
  
  for(int i=0; i<BINRANGE_C2global; i++){ 
    C2_ss->SetBinContent(i+1, C2ssFitting[i]);
    C2_os->SetBinContent(i+1, C2osFitting[i]);
    C2_ss_Momsys->SetBinContent(i+1, C2ssFitting[i]);
    C2_os_Momsys->SetBinContent(i+1, C2osFitting[i]);
    C2_ss_Ksys->SetBinContent(i+1, C2ssFitting[i]);
    C2_os_Ksys->SetBinContent(i+1, C2osFitting[i]);
    double Toterror_ss = sqrt(fabs(pow(C2ssFitting_e[i],2)-pow(C2ssSys_e[i],2)));
    double Toterror_os = sqrt(fabs(pow(C2osFitting_e[i],2)-pow(C2osSys_e[i],2)));
    C2_ss->SetBinError(i+1, Toterror_ss);
    C2_os->SetBinError(i+1, Toterror_os);
    C2_ss_Momsys->SetBinError(i+1, C2ssSys_e[i]);
    C2_os_Momsys->SetBinError(i+1, C2osSys_e[i]);
    C2_ss_Ksys->SetBinError(i+1, OutputPar[1]*K2SS_e[i]);
    C2_os_Ksys->SetBinError(i+1, OutputPar[1]*K2OS_e[i]);
    //
    K2_ss->SetBinContent(i+1, K2SS[i]); K2_ss->SetBinError(i+1, 0);
    K2_os->SetBinContent(i+1, K2OS[i]); K2_os->SetBinError(i+1, 0);
  }
  
  C2_ss_Momsys->SetMarkerSize(0);
  C2_ss_Momsys->SetFillStyle(1000);
  C2_ss_Momsys->SetFillColor(kRed-10);
  C2_os_Momsys->SetMarkerSize(0);
  C2_os_Momsys->SetFillStyle(1000);
  C2_os_Momsys->SetFillColor(kBlue-10);
  C2_ss_Ksys->SetMarkerSize(0);
  C2_ss_Ksys->SetFillStyle(3004);
  C2_ss_Ksys->SetFillColor(kRed);
  C2_os_Ksys->SetMarkerSize(0);
  C2_os_Ksys->SetFillStyle(3004);
  C2_os_Ksys->SetFillColor(kBlue);


  C2_ss->GetXaxis()->SetRangeUser(0,Q2Limit);// 0,0.098
  C2_ss->GetYaxis()->SetRangeUser(0.95,2.4);//0.98,1.3
  C2_ss->GetXaxis()->SetTitleOffset(.8);
  C2_ss->GetYaxis()->SetTitleOffset(.85);
  C2_ss->GetXaxis()->SetTitle("#font[12]{q} (GeV/c)");
  C2_ss->GetYaxis()->SetTitle("#font[12]{C}_{2}");
  C2_ss->GetXaxis()->SetTitleSize(0.05);
  C2_ss->GetYaxis()->SetTitleSize(0.05);
  C2_os->GetXaxis()->SetRangeUser(0,0.6);
  C2_os->GetYaxis()->SetRangeUser(0.98,1.3);
  C2_os->GetXaxis()->SetTitleOffset(.8);
  C2_os->GetYaxis()->SetTitleOffset(.8);
  C2_os->GetXaxis()->SetTitle("#font[12]{q} (GeV/c)");
  C2_os->GetXaxis()->SetTitleSize(0.05);
  C2_os->GetYaxis()->SetTitleSize(0.05);

  //C2_ss->SetMarkerSize(1.5);
  //C2_os->SetMarkerSize(1.5);
  C2_os->SetMarkerStyle(25);
  C2_os->SetMarkerColor(4);
  
  
  fitC2ss_h->SetLineWidth(2);
  fitC2ss_h->SetLineColor(2);

  TH1D *temp_hist_ss=new TH1D("temp_hist_ss","",100,0,0.5);
  TH1D *temp_hist_os=new TH1D("temp_hist_os","",100,0,0.5);
  TH1D *temp_fit=new TH1D("temp_fit","",100,0,0.5);
  
  // PbPb, M16
  double temp_points_ss[100]={-1000, 1.31587, 1.40841, 1.4426, 1.36602, 1.37548, 1.34059, 1.30318, 1.27143, 1.28487, 1.26105, 1.21905, 1.2025, 1.19743, 1.15297, 1.16947, 1.14259, 1.13562, 1.13135, 1.10088, 1.10227, 1.08037, 1.0824, 1.08069, 1.0657, 1.06808, 1.05341, 1.0493, 1.05081, 1.04546, 1.04644, 1.03703, 1.03975, 1.04479, 1.03218, 1.02657, 1.02588, 1.02756, 1.02345, 1.02306, 1.02024, 1.01551, 1.01133, 1.01025, 1.00697, 1.01819, 1.00651, 1.01293, 1.00529, 0.997971, 1.00141, 1.00665, 1.01479, 1.01668, 1.00657, 1.01188, 1.0042, 0.995877, 1.01094, 1.0036, 1.00312, 0.994031, 1.0084, 1.00604, 1.00329, 1.00677, 0.997553, 0.992874, 0.993799, 0.995368, 0.999215, 1.00508, 0.993053, 0.996744, 0.990297, 0.990715, 1.00114, 0.996376, 0.984527, 0.99474, 0.993457, 1.00723, 0.999042, 0.996589, 0.988385, 0.9916, 0.995184, 0.988197, 1.00019, 0.998052, 0.985506, 0.99024, 0.996102, 0.995797, 0.991887, 0.99276, 0.992561, 0.991261, 0.996243};
  double temp_points_ss_e[100]={1000, 0.206703, 0.0920405, 0.0637848, 0.0465513, 0.0380257, 0.0318382, 0.0270753, 0.0236593, 0.0216127, 0.0195971, 0.0176654, 0.0163346, 0.0153927, 0.0141902, 0.0136715, 0.0128887, 0.0124019, 0.0119795, 0.0113642, 0.0111615, 0.0106718, 0.0104775, 0.0102842, 0.0100296, 0.00990822, 0.00962737, 0.0094588, 0.00935572, 0.00923423, 0.0091266, 0.00897368, 0.00889453, 0.00883246, 0.00864815, 0.00853381, 0.00846384, 0.00839173, 0.00829825, 0.00822044, 0.00817065, 0.00805352, 0.00798793, 0.00791266, 0.00784862, 0.00788769, 0.00775376, 0.00772075, 0.00766719, 0.00757909, 0.00754696, 0.00755056, 0.00756756, 0.00754031, 0.00746571, 0.00745114, 0.00739226, 0.00729679, 0.00737659, 0.00730319, 0.00730321, 0.0072228, 0.00728131, 0.00726075, 0.0072364, 0.00723868, 0.00716992, 0.00712198, 0.00713157, 0.00713724, 0.00714391, 0.007175, 0.00708838, 0.00711573, 0.00709965, 0.00707786, 0.00713124, 0.00712164, 0.00703573, 0.00712383, 0.00709407, 0.00720098, 0.00713966, 0.00716466, 0.00710145, 0.00711087, 0.00714815, 0.00710751, 0.00717636, 0.00718936, 0.00712875, 0.00715855, 0.00718908, 0.00719846, 0.00719133, 0.00720147, 0.00721384, 0.00720763, 0.0072536};
 
 
  for(int bin=1; bin<100; bin++){
    //cout<<C2_ss->GetBinContent(bin)<<", ";
    //cout<<C2_ss->GetBinError(bin)<<", ";
    //cout<<fitC2ss_h->GetBinContent(bin)<<", ";
    temp_hist_ss->SetBinContent(bin, temp_points_ss[bin-1]);
    temp_hist_ss->SetBinError(bin, temp_points_ss_e[bin-1]);
    //temp_hist_os->SetBinContent(bin, temp_points_os[bin-1]);
    //temp_hist_os->SetBinError(bin, temp_points_os_e[bin-1]);
    //temp_fit->SetBinContent(bin, temp_points_fit[bin-1]);
  }
  //cout<<endl;
  temp_hist_ss->SetMarkerStyle(20);
  temp_hist_ss->SetMarkerColor(1);
  temp_hist_os->SetMarkerStyle(24);
  temp_hist_os->SetMarkerColor(1);
  temp_fit->SetLineColor(1);
  C2_os->SetMarkerStyle(24);
  C2_os->SetMarkerColor(2);
  
  if(!MCcase){

    //C2_ss->SetMaximum(1.6);
    C2_ss->DrawCopy();
    //legend1->AddEntry(C2_ss,"same-charge","p");
    C2_os->DrawCopy("same");
    //legend1->AddEntry(C2_os,"mixed-charge","p");
    /*
    Specif_System->Draw("same");
    Specif_kT->Draw("same");
    Specif_FSI->Draw("same");
    Specif_Disclaimer->Draw("same");

    TLatex *Stats1 = new TLatex(.5,.55, "#lambda = 0.41 #pm 0.004");
    Stats1->SetNDC();
    Stats1->SetTextSize(0.06);
    //Stats1->Draw("same");
    TLatex *Stats2 = new TLatex(.5,.45, "R_{inv} = 1.59 #pm 0.01 fm");
    Stats2->SetNDC();
    Stats2->SetTextSize(0.06);
    */
    //Stats2->Draw("same");
    /*TF1 *BkgFitC2 = new TF1("BkgFitC2","1+[0]*exp(-pow([1]*x/0.19733,2))",0,1);
    BkgFitC2->SetParameter(0,0.08);
    BkgFitC2->SetParameter(1,0.5);
    BkgFitC2->SetLineColor(1);
    C2_ss->Fit(BkgFitC2,"IME","",0.2,0.8);
    BkgFitC2->Draw("same");*/
    
    //fitC2ss_h->SetLineColor(1);
    Unity->Draw("same");
    fitC2ss_h->Draw("C same");
    //temp_hist_ss->Draw("same");
    //temp_hist_os->Draw("same");
    //temp_fit->Draw("C same");
    //fitC2ss_Base->Draw("C same");
    //fitC2ss_Expan->Draw("C same");
    //legend1->AddEntry(C2_ss,"p-Pb (++)","p");
    //legend1->AddEntry(C2_os,"p-Pb (-+)","p");
    //legend1->AddEntry(temp_hist_ss,"Pb-Pb (++), Mbin 16","p");
    //legend1->AddEntry(temp_hist_os,"Pb-Pb (-+), <Nch>=36","p");
    legend1->Draw("same");
  }
  
  
 
  cout<<"============================================"<<endl;
  cout<<"Start 3-pion section"<<endl;
  
  TCanvas *can2 = new TCanvas("can2", "can2",800,0,800,800);//800,0,600,900
  can2->SetHighLightColor(2);
  gStyle->SetOptFit(0111);
  can2->SetFillColor(10);
  can2->SetBorderMode(0);
  can2->SetBorderSize(2);
  can2->SetGridx();
  can2->SetGridy();
  can2->SetFrameFillColor(0);
  can2->SetFrameBorderMode(0);
  can2->SetFrameBorderMode(0);
  can2->cd();
  gPad->SetRightMargin(0.02);
  
  TLegend *legend2 = new TLegend(.58,.55, .97,.65,NULL,"brNDC");
  legend2->SetBorderSize(1);
  legend2->SetTextSize(.03);// small .03; large .06
  legend2->SetFillColor(0);

  /////////////////////////////////////////////
  TH3D *C3QS_3d = new TH3D("C3QS_3d","",BINRANGE_3,0,.4, BINRANGE_3,0,.4, BINRANGE_3,0,.4);
  TH3D *Combinatorics_3d = new TH3D("Combinatorics_3d","",BINRANGE_3,0,.4, BINRANGE_3,0,.4, BINRANGE_3,0,.4);
  
  //
  const float Q3HistoLimit=0.5;
  const int Q3BINS = int((Q3HistoLimit+0.0001)/0.01);
  TH1D *num_withRS = new TH1D("num_withRS","",Q3BINS,0,Q3HistoLimit);
  TH1D *num_withGRS = new TH1D("num_withGRS","",Q3BINS,0,Q3HistoLimit);
  TH1D *num_withTM = new TH1D("num_withTM","",Q3BINS,0,Q3HistoLimit);
  TH1D *Cterm1 = new TH1D("Cterm1","",Q3BINS,0,Q3HistoLimit);
  TH1D *Cterm1_noMRC = new TH1D("Cterm1_noMRC","",Q3BINS,0,Q3HistoLimit);
  TH1D *Cterm2 = new TH1D("Cterm2","",Q3BINS,0,Q3HistoLimit);
  TH1D *Cterm3 = new TH1D("Cterm3","",Q3BINS,0,Q3HistoLimit);
  TH1D *Cterm4 = new TH1D("Cterm4","",Q3BINS,0,Q3HistoLimit);
  TH1D *num_QS = new TH1D("num_QS","",Q3BINS,0,Q3HistoLimit);
  TH1D *Combinatorics_1d = new TH1D("Combinatorics_1d","",Q3BINS,0,Q3HistoLimit);
  TH1D *Combinatorics_1d_noMRC = new TH1D("Combinatorics_1d_noMRC","",Q3BINS,0,Q3HistoLimit);
  TH1D *Coul_Riverside = new TH1D("Coul_Riverside","",Q3BINS,0,Q3HistoLimit);
  TH1D *Coul_GRiverside = new TH1D("Coul_GRiverside","",Q3BINS,0,Q3HistoLimit);
  TH1D *c3_hist = new TH1D("c3_hist","",Q3BINS,0,Q3HistoLimit);
   
  if(SameCharge) {Cterm1_noMRC->Sumw2(); Combinatorics_1d_noMRC->Sumw2();}
  //
  double num_QS_e[Q3BINS];
  double c3_e[Q3BINS];
  
  for(int ii=0; ii<Q3BINS; ii++){
    num_QS_e[ii]=0.;
    c3_e[ii]=0.;
  }
  
  // CB=Charge Bin. 0 means pi-, 1 means pi+
  int CB1=0, CB2=0, CB3=0;
  int CP12=1, CP13=1, CP23=1;
  int CB1_2=0, CB2_2=0, CB3_2=0;
  if(CHARGE==-1) {
    if(SameCharge) {CB1=0; CB2=0; CB3=0;}
    else {CB1=0; CB2=0; CB3=1; CP12=+1, CP13=-1, CP23=-1;}
  }else {
    if(SameCharge) {CB1=1; CB2=1; CB3=1;}
    else {CB1=0; CB2=1; CB3=1; CP12=-1, CP13=-1, CP23=+1;}
  }
  if(AddCC){
    if(CHARGE==-1) {
      if(SameCharge) {CB1_2=1; CB2_2=1; CB3_2=1;}
      else {CB1_2=0; CB2_2=1; CB3_2=1;};
    }else {
      if(SameCharge) {CB1_2=0; CB2_2=0; CB3_2=0;}
      else {CB1_2=0; CB2_2=0; CB3_2=1;}
    }
  }

  
  // SC = species combination.  Always 0 meaning pi-pi-pi.
  int SCBin=0;
  //
    
  TH1D *GenSignalExpected_num=new TH1D("GenSignalExpected_num","",Q3BINS,0,Q3HistoLimit);
  TH1D *GenSignalExpected_den=new TH1D("GenSignalExpected_den","",Q3BINS,0,Q3HistoLimit);
  //
  double value_num; 
  double value_num_e;
  double N3_QS;
  double N3_QS_e;
  
  for(int i=2; i<=BINLIMIT_3; i++){// bin number
    double Q12 = BinCenters[i-1];// true center
    //int Q12bin = int(Q12/0.01)+1;
    //
    for(int j=2; j<=BINLIMIT_3; j++){// bin number
      double Q13 = BinCenters[j-1];// true center
      //int Q13bin = int(Q13/0.01)+1;
      //
      for(int k=2; k<=BINLIMIT_3; k++){// bin number
	double Q23 = BinCenters[k-1];// true center
	//int Q23bin = int(Q23/0.01)+1;
	//
	
	double Q3 = sqrt(pow(Q12,2) + pow(Q13,2) + pow(Q23,2));
       	int Q3bin = Cterm1->GetXaxis()->FindBin(Q3);
	
	if(Q12 < sqrt(pow(Q13,2)+pow(Q23,2) - 2*Q13*Q23)) continue;// not all configurations are possible
	if(Q12 > sqrt(pow(Q13,2)+pow(Q23,2) + 2*Q13*Q23)) continue;// not all configurations are possible
	
	
       	//
	double G_12 = Gamov(CP12, Q12);// point-source Coulomb correlation
	double G_13 = Gamov(CP13, Q13);
	double G_23 = Gamov(CP23, Q23);
	double K2_12 = CoulCorr2(CP12, Q12);// finite-source Coulomb+Strong correlation from Therminator.
	double K2_13 = CoulCorr2(CP13, Q13);
	double K2_23 = CoulCorr2(CP23, Q23);
	double K3 = 1.;// 3-body Coulomb+Strong correlation
	if(SameCharge || CHARGE==-1) K3 = CoulCorrGRS(SameCharge, Q12, Q13, Q23);
	else K3 = CoulCorrGRS(SameCharge, Q23, Q12, Q13);
	
	if(MCcase && !GeneratedSignal) { K2_12=1.; K2_13=1.; K2_23=1.; K3=1.;}
	if(K3==0) continue;

	double TERM1=Three_3d[CB1][CB2][CB3][SCBin][0]->GetBinContent(i,j,k);// N3 (3-pion yield per q12,q13,q23 cell). 3-pions from same-event
	double TERM2=Three_3d[CB1][CB2][CB3][SCBin][1]->GetBinContent(i,j,k);// N2*N1. 1 and 2 from same-event
	double TERM3=Three_3d[CB1][CB2][CB3][SCBin][2]->GetBinContent(i,j,k);// N2*N1. 1 and 3 from same-event
	double TERM4=Three_3d[CB1][CB2][CB3][SCBin][3]->GetBinContent(i,j,k);// N2*N1. 2 and 3 from same-event
	double TERM5=Three_3d[CB1][CB2][CB3][SCBin][4]->GetBinContent(i,j,k);// N1*N1*N1. All from different events (pure combinatorics)
	if(AddCC){
	  if(CHARGE==-1){// base is (SC,MC,MC)
	    TERM1 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][0]->GetBinContent(j,k,i);
	    TERM2 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][1]->GetBinContent(j,k,i);
	    TERM3 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][2]->GetBinContent(j,k,i);
	    TERM4 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][3]->GetBinContent(j,k,i);
	    TERM5 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][4]->GetBinContent(j,k,i);
	  }else {// base is (MC,MC,SC)
	    TERM1 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][0]->GetBinContent(k,i,j);
	    TERM2 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][1]->GetBinContent(k,i,j);
	    TERM3 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][2]->GetBinContent(k,i,j);
	    TERM4 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][3]->GetBinContent(k,i,j);
	    TERM5 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][4]->GetBinContent(k,i,j);
	  }
	}
	
	if(TERM1==0 && TERM2==0 && TERM3==0 && TERM4==0 && TERM5==0) continue;
	if(TERM1==0 || TERM2==0 || TERM3==0 || TERM4==0 || TERM5==0) continue;
	
	double muonCorr_C3=1.0, muonCorr_C2_12=1.0, muonCorr_C2_13=1.0, muonCorr_C2_23=1.0;
	if(MuonCorrection && !MCcase){
	  if(SameCharge){
	    muonCorr_C3 = C3muonCorrection->GetBinContent(C3muonCorrection->GetXaxis()->FindBin(Q3));
	    muonCorr_C2_12 = C2muonCorrection_SC->GetBinContent(C2muonCorrection_SC->GetXaxis()->FindBin(Q12));
	    muonCorr_C2_13 = C2muonCorrection_SC->GetBinContent(C2muonCorrection_SC->GetXaxis()->FindBin(Q13));
	    muonCorr_C2_23 = C2muonCorrection_SC->GetBinContent(C2muonCorrection_SC->GetXaxis()->FindBin(Q23));
	  }else{
	    muonCorr_C3 = C3muonCorrection->GetBinContent(C3muonCorrection->GetXaxis()->FindBin(Q3));
	    if(CHARGE==-1){// pi-pi-pi+
	      muonCorr_C2_12 = C2muonCorrection_SC->GetBinContent(C2muonCorrection_SC->GetXaxis()->FindBin(Q12));
	      muonCorr_C2_13 = C2muonCorrection_MC->GetBinContent(C2muonCorrection_MC->GetXaxis()->FindBin(Q13));
	      muonCorr_C2_23 = C2muonCorrection_MC->GetBinContent(C2muonCorrection_MC->GetXaxis()->FindBin(Q23));
	    }else{// pi-pi+pi+
	      muonCorr_C2_12 = C2muonCorrection_MC->GetBinContent(C2muonCorrection_MC->GetXaxis()->FindBin(Q12));
	      muonCorr_C2_13 = C2muonCorrection_MC->GetBinContent(C2muonCorrection_MC->GetXaxis()->FindBin(Q13));
	      muonCorr_C2_23 = C2muonCorrection_SC->GetBinContent(C2muonCorrection_SC->GetXaxis()->FindBin(Q23));
	    }
	  }
	}

	// apply momentum resolution correction
	if(!MCcase && !GeneratedSignal){
	  int MRC_Q3bin = int(Q3/0.01) + 1;
	  if(SameCharge){
	    TERM1 *= (MomRes1d[0][0]->GetBinContent(MRC_Q3bin)-1)*MRCShift+1;
	    TERM2 *= (MomRes1d[0][1]->GetBinContent(MRC_Q3bin)-1)*MRCShift+1;
	    TERM3 *= (MomRes1d[0][2]->GetBinContent(MRC_Q3bin)-1)*MRCShift+1;
	    TERM4 *= (MomRes1d[0][3]->GetBinContent(MRC_Q3bin)-1)*MRCShift+1;
	    TERM5 *= (MomRes1d[0][4]->GetBinContent(MRC_Q3bin)-1)*MRCShift+1;
	  }else{
	    // removed due to over-correction of 1-D MRC approximation
	    TERM1 *= (MomRes1d[1][0]->GetBinContent(MRC_Q3bin)-1)*MRCShift+1;
	    TERM2 *= (MomRes1d[1][1]->GetBinContent(MRC_Q3bin)-1)*MRCShift+1;
	    TERM3 *= (MomRes1d[1][2]->GetBinContent(MRC_Q3bin)-1)*MRCShift+1;
	    TERM4 *= (MomRes1d[1][3]->GetBinContent(MRC_Q3bin)-1)*MRCShift+1;
	    TERM5 *= (MomRes1d[1][4]->GetBinContent(MRC_Q3bin)-1)*MRCShift+1;
	  }
	}
	//
	
	TwoFrac=lambda_PM;// 0.7
	OneFrac=pow(TwoFrac,.5); ThreeFrac=pow(TwoFrac,1.5);
	
	
	// Purify.  Isolate pure 3-pion QS correlations using Lambda and K3 (removes lower order correlations)
	N3_QS = TERM1;
	N3_QS -= ( pow(1-OneFrac,3) + 3*OneFrac*pow(1-OneFrac,2) )*TERM5;
	N3_QS -= (1-OneFrac)*(TERM2 + TERM3 + TERM4 - 3*(1-TwoFrac)*TERM5);
	N3_QS /= ThreeFrac;
	N3_QS /= K3;
	N3_QS *=  muonCorr_C3;

	num_QS->Fill(Q3, N3_QS);
	
	// Isolate 3-pion cumulant
	value_num = N3_QS;
	value_num -= (TERM2 - (1-TwoFrac)*TERM5)/K2_12/TwoFrac * muonCorr_C2_12;
	value_num -= (TERM3 - (1-TwoFrac)*TERM5)/K2_13/TwoFrac * muonCorr_C2_13;
	value_num -= (TERM4 - (1-TwoFrac)*TERM5)/K2_23/TwoFrac * muonCorr_C2_23;
	value_num += 2*TERM5;
	
	
	
	
	// errors
	N3_QS_e = TERM1;
	N3_QS_e += pow(( pow(1-OneFrac,3) +3*OneFrac*pow(1-OneFrac,2) )*sqrt(TERM5),2);
	N3_QS_e += (pow((1-OneFrac),2)*(TERM2 + TERM3 + TERM4) + pow((1-OneFrac)*3*(1-TwoFrac)*sqrt(TERM5),2));
	N3_QS_e /= pow(ThreeFrac,2);
	N3_QS_e /= pow(K3,2);
	num_QS_e[Q3bin-1] += N3_QS_e;
	// errors 
	value_num_e = N3_QS_e;
	value_num_e += (pow(1/K2_12/TwoFrac*sqrt(TERM2),2) + pow((1-TwoFrac)/K2_12/TwoFrac*sqrt(TERM5),2));
	value_num_e += (pow(1/K2_13/TwoFrac*sqrt(TERM3),2) + pow((1-TwoFrac)/K2_13/TwoFrac*sqrt(TERM5),2));
	value_num_e += (pow(1/K2_23/TwoFrac*sqrt(TERM4),2) + pow((1-TwoFrac)/K2_23/TwoFrac*sqrt(TERM5),2));
	value_num_e += pow(2*sqrt(TERM5),2);
	
	c3_e[Q3bin-1] += value_num_e + TERM5;// add baseline stat error


	// Fill histograms
	c3_hist->Fill(Q3, value_num + TERM5);// for cumulant correlation function
	C3QS_3d->SetBinContent(i,j,k, N3_QS);
	C3QS_3d->SetBinError(i,j,k, N3_QS_e);
	//
	Coul_Riverside->Fill(Q3, G_12*G_13*G_23*TERM5);
	Coul_GRiverside->Fill(Q3, TERM5*CoulCorrGRS(SameCharge, Q12, Q13, Q23));
	num_withGRS->Fill(Q3, N3_QS);
	Cterm1->Fill(Q3, TERM1);
	Cterm2->Fill(Q3, TERM2);
	Cterm3->Fill(Q3, TERM3);
	Cterm4->Fill(Q3, TERM4);
	Combinatorics_1d->Fill(Q3, TERM5);
	Combinatorics_3d->Fill(Q12,Q13,Q23, TERM5);
	
	double Q3_m = sqrt(pow((i-0.5)*(0.005),2) + pow((j-0.5)*(0.005),2) + pow((k-0.5)*(0.005),2));
	Cterm1_noMRC->Fill(Q3_m, Three_3d[CB1][CB2][CB3][SCBin][0]->GetBinContent(i,j,k));
	Combinatorics_1d_noMRC->Fill(Q3_m, Three_3d[CB1][CB2][CB3][SCBin][4]->GetBinContent(i,j,k));
	
	//
	A_3[i-1][j-1][k-1] = value_num + TERM5;
	B_3[i-1][j-1][k-1] = TERM5;
	A_3_e[i-1][j-1][k-1] = sqrt(value_num_e + TERM5);

	//if(i==j && i==k && i==4) cout<<A_3[i-1][j-1][k-1]<<"  "<<B_3[i-1][j-1][k-1]<<"  "<<A_3_e[i-1][j-1][k-1]<<endl;
	///////////////////////////////////////////////////////////
	
      }
    }
  }
  
  
 
  ////////////////////////////

  // Intermediate steps
  num_withRS->Sumw2();
  num_withGRS->Sumw2();
  num_withTM->Sumw2();
  Cterm1->Sumw2();
  Cterm2->Sumw2();
  Cterm3->Sumw2();
  Cterm4->Sumw2();
  Combinatorics_1d->Sumw2();
  Combinatorics_3d->Sumw2();
  for(int i=0; i<Q3BINS; i++) {c3_hist->SetBinError(i+1, sqrt(c3_e[i])); num_QS->SetBinError(i+1, sqrt(num_QS_e[i]));}
 

  num_withRS->Divide(Combinatorics_1d);
  num_withGRS->Divide(Combinatorics_1d);
  num_withTM->Divide(Combinatorics_1d);
  Cterm1->Divide(Combinatorics_1d);
  Cterm1_noMRC->Divide(Combinatorics_1d_noMRC);
  Cterm2->Divide(Combinatorics_1d);
  Cterm3->Divide(Combinatorics_1d);
  Cterm4->Divide(Combinatorics_1d);
  c3_hist->Divide(Combinatorics_1d);
  num_QS->Divide(Combinatorics_1d);
 
 

  ///////////////////////////////////////////////////////////////////////////////////////////////////
  
  
  Cterm1->SetMarkerStyle(20);
  Cterm1->SetMarkerColor(4);
  Cterm1->SetLineColor(4);
  Cterm1->GetXaxis()->SetTitle("#font[12]{Q}_{3} (GeV/#font[12]{c})");
  Cterm1->GetYaxis()->SetTitle("#font[12]{C}_{3}");
  //Cterm1->SetTitle("#pi^{-}#pi^{-}#pi^{-}");
  Cterm1->SetMinimum(0.97);
  Cterm1->SetMaximum(5.7);// 6.1 for same-charge
  Cterm1->GetXaxis()->SetRangeUser(0,Q3Limit);
  Cterm1->GetYaxis()->SetTitleOffset(1.4);
  Cterm1->Draw();
  legend2->AddEntry(Cterm1,"#font[12]{C}_{3} raw","p");
  //
  Cterm2->SetMarkerStyle(20);
  Cterm2->SetMarkerColor(7);
  
  Cterm3->SetMarkerStyle(25);
  Cterm3->SetMarkerColor(8);
  Cterm4->SetMarkerStyle(26);
  Cterm4->SetMarkerColor(9);
  //Cterm2->Draw("same");
  //Cterm3->Draw("same");
  //Cterm4->Draw("same");
  //legend2->AddEntry(Cterm1,"++-","p");
  
  
  if(MCcase){
    double C3points_HIJING_mmm[10]={0, 0.961834, 1.01827, 0.999387, 1.00202, 1.00081, 1.00082, 1.00037, 0.999074, 0.999099};
    double C3points_HIJING_mmm_e[10]={0, 0.0833895, 0.015158, 0.0047978, 0.00235067, 0.00138155, 0.00087485, 0.000612203, 0.000450162, 0.000346943};
    double C3points_HIJING_ppp[10]={0, 1.13015, 1.00623, 1.00536, 1.00293, 0.999964, 1.00116, 1.0007, 1.00037, 1.00105};
    double C3points_HIJING_ppp_e[10]={0, 0.0977058, 0.0150694, 0.0048196, 0.00235518, 0.00138376, 0.000877562, 0.000614069, 0.000452051, 0.00034856};
    TH1D *C3_HIJING_mmm=(TH1D*)Cterm1->Clone();
    TH1D *C3_HIJING_ppp=(TH1D*)Cterm1->Clone();
    for(int i=0; i<10; i++){
      C3_HIJING_mmm->SetBinContent(i+1, C3points_HIJING_mmm[i]);
      C3_HIJING_mmm->SetBinError(i+1, C3points_HIJING_mmm_e[i]);
      C3_HIJING_ppp->SetBinContent(i+1, C3points_HIJING_ppp[i]);
      C3_HIJING_ppp->SetBinError(i+1, C3points_HIJING_ppp_e[i]);
    }
    C3_HIJING_mmm->SetMarkerColor(2);
    C3_HIJING_mmm->SetLineColor(2);
    C3_HIJING_ppp->SetMarkerColor(4);
    C3_HIJING_ppp->SetLineColor(4);
    //C3_HIJING_mmm->Draw("same");
    //C3_HIJING_ppp->Draw("same");
    //legend2->AddEntry(C3_HIJING_mmm,"---","p");
    //legend2->AddEntry(C3_HIJING_ppp,"+++","p");
  }

  num_QS->SetMarkerStyle(24);
  num_QS->SetMarkerColor(4);
  num_QS->SetLineColor(4);
  num_QS->GetXaxis()->SetTitle("#font[12]{Q}_{3}");
  num_QS->GetYaxis()->SetTitle("#font[12]{C}_{3}^{QS}");
  num_QS->GetXaxis()->SetRangeUser(0,.12);
  num_QS->SetMaximum(6);
  //num_QS->Draw("same");
  //legend2->AddEntry(num_QS,"C_{3}^{QS}","p");
 
  c3_hist->GetXaxis()->SetTitle("#font[12]{Q}_{3} (GeV/#font[12]{c})");
  c3_hist->GetYaxis()->SetTitle("#font[12]{C}_{3} or #font[12]{#bf{c}}_{3}");
  c3_hist->GetYaxis()->SetTitleOffset(1.4);
  c3_hist->GetXaxis()->SetRangeUser(0,Q3Limit);
  c3_hist->GetYaxis()->SetRangeUser(0.9,4);
  c3_hist->SetMarkerStyle(25);
  c3_hist->SetMarkerColor(2);
  c3_hist->SetLineColor(2);
  c3_hist->SetMaximum(3);
  c3_hist->SetMinimum(.7);
  if(!MCcase) c3_hist->Draw("same");
  legend2->AddEntry(c3_hist,"#font[12]{#bf{c}}_{3} (cumulant correlation)","p");
  c3_hist->Draw();
  
  //for(int i=1; i<=15; i++) cout<<c3_hist->GetBinContent(i)<<", ";
  //cout<<endl;
  //for(int i=1; i<=15; i++) cout<<c3_hist->GetBinError(i)<<", ";
  //cout<<endl;

  const int npar_c3=5;// 10 
  TMinuit MyMinuit_c3(npar_c3);
  MyMinuit_c3.SetFCN(fcn_c3);
  int ierflg_c3=0;
  double arglist_c3 = 0;
  MyMinuit_c3.mnexcm("SET NOWarnings",&arglist_c3,1, ierflg_c3);  
  arglist_c3 = -1;
  MyMinuit_c3.mnexcm("SET PRint",&arglist_c3,1, ierflg_c3);
  //arglist_c3=2;// improve Minimization Strategy (1 is default)
  //MyMinuit_c3.mnexcm("SET STR",&arglist_c3,1,ierflg_c3);
  //arglist_c3 = 0;
  //MyMinuit_c3.mnexcm("SCAN", &arglist_c3,1,ierflg_c3);
  arglist_c3 = 5000;
  MyMinuit_c3.mnexcm("MIGRAD", &arglist_c3 ,1,ierflg_c3);
  
  TF1 *c3Fit1D_Base=new TF1("c3Fit1D_Base","[0]*(1+[1]*exp(-pow([2]*x/0.19733,[3]) * [4]/2.))",0,1);
  c3Fit1D_Base->FixParameter(3,ExpPower);
  TF1 *c3Fit1D_Expan;
  if(Gaussian) {
    c3Fit1D_Base->FixParameter(4,1.0);
    c3Fit1D_Expan=new TF1("c3Fit1D_Expan","[0]*(1+[1]*exp(-pow([2]*x/0.19733,2)/2.) * pow(1 + ([3]/(6.*pow(2,1.5))*(8.*pow([2]*x/sqrt(3.)/0.19733,3) - 12.*pow([2]*x/sqrt(3.)/0.19733,1))) + ([4]/(24.*pow(2,2))*(16.*pow([2]*x/sqrt(3.)/0.19733,4) -48.*pow([2]*x/sqrt(3.)/0.19733,2) + 12)),3))",0,1);
  }else {
    c3Fit1D_Base->FixParameter(4,sqrt(3.));
    c3Fit1D_Expan=new TF1("c3Fit1D_Expan","[0]*(1+[1]*exp(-pow([2]*x/0.19733,1) * sqrt(3.)/2.) * pow(1 + [3]*([2]*x/sqrt(3.)/0.19733 - 1) + [4]/2*(pow([2]*x/sqrt(3.)/0.19733,2) - 4*[2]*x/sqrt(3.)/0.19733 + 2),3))",0,1);
  }
  double OutputPar_c3[npar_c3]={0};
  double OutputPar_c3_e[npar_c3]={0};
  
  double par_c3[npar_c3];               // the start values
  double stepSize_c3[npar_c3];          // step sizes 
  double minVal_c3[npar_c3];            // minimum bound on parameter 
  double maxVal_c3[npar_c3];            // maximum bound on parameter
  string parName_c3[npar_c3];
  if(SameCharge && !MCcase){
    for(int ft=0; ft<2; ft++){// Gaussian, Edgeworth
      if(ft==1 && !IncludeExpansion) continue;
      par_c3[0] = 1.0; par_c3[1] = .5; par_c3[2] = 5; par_c3[3] = kappa3; par_c3[4] = kappa4;// was par_c3[3] = 0.; par_c3[4] = 0.;
      stepSize_c3[0] = 0.01; stepSize_c3[1] = 0.1; stepSize_c3[2] = 0.2; stepSize_c3[3] = 0.01; stepSize_c3[4] = 0.01;
      minVal_c3[0] = 0.95; minVal_c3[1] = 0.2; minVal_c3[2] = 0.5; minVal_c3[3] = -1; minVal_c3[4] = -1;// was minVal_c3[3] = -1; minVal_c3[4] = -1;
      maxVal_c3[0] = 1.1; maxVal_c3[1] = 2.5; maxVal_c3[2] = 15.; maxVal_c3[3] = +1; maxVal_c3[4] = +1;// was minVal_c3[3] = +1; minVal_c3[4] = +1;
      parName_c3[0] = "N"; parName_c3[1] = "#lambda_{3}"; parName_c3[2] = "R_{inv}"; parName_c3[3] = "coeff_{3}"; parName_c3[4] = "coeff_{4}";
      c3Fit1D_Base->SetParName(0,"N"); c3Fit1D_Base->SetParName(1,"#lambda_{3}"); c3Fit1D_Base->SetParName(2,"R_{inv}");
      if(!Gaussian) {maxVal_c3[1] = 5.0; maxVal_c3[2] = 20.;}
      for (int i=0; i<npar_c3; i++){
	MyMinuit_c3.DefineParameter(i, parName_c3[i].c_str(), par_c3[i], stepSize_c3[i], minVal_c3[i], maxVal_c3[i]);
      }
      //
      if(!FixExpansionAvg) {
	maxVal_c3[1] = 2.0;
	/*double RadiusFix;
	if(CollisionType==0) RadiusFix = 10 - 7*Mbin/15.;
	else RadiusFix = 2.5 - 1.25*(Mbin-12)/7.;
	MyMinuit_c3.DefineParameter(2, parName_c3[2].c_str(), RadiusFix, stepSize_c3[2], minVal_c3[2], maxVal_c3[2]); MyMinuit_c3.FixParameter(2);
	MyMinuit_c3.DefineParameter(1, parName_c3[1].c_str(), 2.0, stepSize_c3[1], minVal_c3[1], maxVal_c3[1]); MyMinuit_c3.FixParameter(1);
	*/
      }
      // kappa_3 and kappa_4 
      if(ft==0){// Gaussian
	MyMinuit_c3.DefineParameter(3, parName_c3[3].c_str(), 0., stepSize_c3[3], minVal_c3[3], maxVal_c3[3]); MyMinuit_c3.FixParameter(3);
	MyMinuit_c3.DefineParameter(4, parName_c3[4].c_str(), 0., stepSize_c3[4], minVal_c3[4], maxVal_c3[4]); MyMinuit_c3.FixParameter(4);
      }else{// Edgeworth
	if(FixExpansionAvg){
	  if(Gaussian){
	    MyMinuit_c3.DefineParameter(3, parName_c3[3].c_str(), kappa3, stepSize_c3[3], minVal_c3[3], maxVal_c3[3]); MyMinuit_c3.FixParameter(3);
	    MyMinuit_c3.DefineParameter(4, parName_c3[4].c_str(), kappa4, stepSize_c3[4], minVal_c3[4], maxVal_c3[4]); MyMinuit_c3.FixParameter(4);
	  }else{
	    MyMinuit_c3.DefineParameter(3, parName_c3[3].c_str(), 0, stepSize_c3[3], minVal_c3[3], maxVal_c3[3]); MyMinuit_c3.FixParameter(3);
	    MyMinuit_c3.DefineParameter(4, parName_c3[4].c_str(), 0, stepSize_c3[4], minVal_c3[4], maxVal_c3[4]); MyMinuit_c3.FixParameter(4);
	  }
	  }else{
	  Int_t err=0;
	  Double_t tmp[1];
	  tmp[0] = 3+1;
	  MyMinuit_c3.mnexcm( "RELease", tmp,  1,  err );// kappa3
	  tmp[0] = 4+1;
	  MyMinuit_c3.mnexcm( "RELease", tmp,  1,  err );// kappa4
	}
      }
            
    
      /////////////////////////////////////////////////////////////
      // Do the minimization!
      cout<<"Start Three-d fit"<<endl;
      MyMinuit_c3.Migrad();// Minuit's best minimization algorithm
      cout<<"End Three-d fit"<<endl;
      /////////////////////////////////////////////////////////////
      MyMinuit_c3.mnexcm("SHOw PARameters", &arglist_c3, 1, ierflg);
      cout<<"c3 Fit: Chi2 = "<<Chi2_c3<<"   NDF = "<<(NFitPoints_c3-MyMinuit_c3.GetNumFreePars())<<endl;
      
      for(int i=0; i<npar_c3; i++){
	MyMinuit_c3.GetParameter(i,OutputPar_c3[i],OutputPar_c3_e[i]);
      }
      if(ft==0){
	c3Fit1D_Base->SetParameter(0,OutputPar_c3[0]); c3Fit1D_Base->SetParError(0,OutputPar_c3_e[0]);
	c3Fit1D_Base->SetParameter(1,OutputPar_c3[1]); c3Fit1D_Base->SetParError(1,OutputPar_c3_e[1]);
	c3Fit1D_Base->SetParameter(2,OutputPar_c3[2]); c3Fit1D_Base->SetParError(2,OutputPar_c3_e[2]);
	c3Fit1D_Base->SetLineStyle(2);
	c3Fit1D_Base->Draw("same");
      }else{
	c3Fit1D_Expan->SetParameter(0,OutputPar_c3[0]); c3Fit1D_Expan->SetParError(0,OutputPar_c3_e[0]);
	c3Fit1D_Expan->SetParameter(1,OutputPar_c3[1]); c3Fit1D_Expan->SetParError(1,OutputPar_c3_e[1]);
	c3Fit1D_Expan->SetParameter(2,OutputPar_c3[2]); c3Fit1D_Expan->SetParError(2,OutputPar_c3_e[2]);
	c3Fit1D_Expan->SetParameter(3,OutputPar_c3[3]); c3Fit1D_Expan->SetParError(3,OutputPar_c3_e[3]);
	c3Fit1D_Expan->SetParameter(4,OutputPar_c3[4]); c3Fit1D_Expan->SetParError(4,OutputPar_c3_e[4]);
	c3Fit1D_Expan->SetLineStyle(1);
	//c3Fit1D_Expan->Draw("same");
	double lambdaStar=0, lambdaStar_e=0;
	if(Gaussian){
	  lambdaStar = OutputPar_c3[1]*pow(1 + OutputPar_c3[4]/8.,3);
	  lambdaStar_e = pow(OutputPar_c3_e[1]*pow(1 + OutputPar_c3[4]/8.,3),2);
	  lambdaStar_e = sqrt(lambdaStar_e);
	}else{
	  lambdaStar = OutputPar_c3[1]*pow(1 - OutputPar_c3[3] + OutputPar_c3[4],3);
	  lambdaStar_e = pow(OutputPar_c3_e[1]*pow(1 - OutputPar_c3[3] + OutputPar_c3[4],3),2);
	  lambdaStar_e = sqrt(lambdaStar_e);
	}
	cout<<"lambda*_3 = "<<lambdaStar<<" +- "<<lambdaStar_e<<endl;
      }
      //if(ft==0) {MainFitParams[1]=OutputPar_c3[2]; MainFitParams[3]=OutputPar_c3[1];}
      //else {MainFitParams[5]=OutputPar_c3[2]; MainFitParams[7]=OutputPar_c3[1];}
    }// fit type
  }// SC and !MC

  // project 3D EW fit onto 1D histogram
  if(SameCharge && !MCcase){
    for(int i=2; i<=BINLIMIT_3; i++){// bin number
      double Q12 = BinCenters[i-1];// true center
      for(int j=2; j<=BINLIMIT_3; j++){// bin number
	double Q13 = BinCenters[j-1];// true center
	for(int k=2; k<=BINLIMIT_3; k++){// bin number
	  double Q23 = BinCenters[k-1];// true center
	  //	
	  double Q3 = sqrt(pow(Q12,2) + pow(Q13,2) + pow(Q23,2));
	  
	  if(Q12 < sqrt(pow(Q13,2)+pow(Q23,2) - 2*Q13*Q23)) continue;// not all configurations are possible
	  if(Q12 > sqrt(pow(Q13,2)+pow(Q23,2) + 2*Q13*Q23)) continue;// not all configurations are possible
	  	  
	  double TERM5=Three_3d[CB1][CB2][CB3][SCBin][4]->GetBinContent(i,j,k);// N1*N1*N1. All from different events (pure combinatorics)
	  if(TERM5==0) continue;
	  //
	  if(AddCC){
	    if(CHARGE==-1){// base is (SC,MC,MC)
	      TERM5 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][4]->GetBinContent(j,k,i);
	    }else {// base is (MC,MC,SC)
	      TERM5 += Three_3d[CB1_2][CB2_2][CB3_2][SCBin][4]->GetBinContent(k,i,j);
	    }
	  }
	  //
	  int MRC_Q3bin = int(Q3/0.01) + 1;
	  TERM5 *= (MomRes1d[0][4]->GetBinContent(MRC_Q3bin)-1)*MRCShift+1;
	  //
	  double radius_exp = c3Fit1D_Expan->GetParameter(2)/FmToGeV;
	  double arg12 = Q12*radius_exp;
	  double arg13 = Q13*radius_exp;
	  double arg23 = Q23*radius_exp;
	  
	  Float_t EW12 = 1 + c3Fit1D_Expan->GetParameter(3)/(6.*pow(2.,1.5))*(8.*pow(arg12,3) - 12.*arg12);
	  EW12 += c3Fit1D_Expan->GetParameter(4)/(24.*pow(2.,2))*(16.*pow(arg12,4) -48.*pow(arg12,2) + 12);
	  Float_t EW13 = 1 + c3Fit1D_Expan->GetParameter(3)/(6.*pow(2.,1.5))*(8.*pow(arg13,3) - 12.*arg13);
	  EW13 += c3Fit1D_Expan->GetParameter(4)/(24.*pow(2.,2))*(16.*pow(arg13,4) -48.*pow(arg13,2) + 12);
	  Float_t EW23 = 1 + c3Fit1D_Expan->GetParameter(3)/(6.*pow(2.,1.5))*(8.*pow(arg23,3) - 12.*arg23);
	  EW23 += c3Fit1D_Expan->GetParameter(4)/(24.*pow(2.,2))*(16.*pow(arg23,4) -48.*pow(arg23,2) + 12);
	  //
	  double cumulant_fitvalue=0;
	  cumulant_fitvalue = c3Fit1D_Expan->GetParameter(0)*(c3Fit1D_Expan->GetParameter(1)*EW12*EW13*EW23*exp(-pow(radius_exp,ExpPower)/2. * (pow(Q12,ExpPower)+pow(Q13,ExpPower)+pow(Q23,ExpPower)))*TERM5 + TERM5);
	  
	  GenSignalExpected_num->Fill(Q3, cumulant_fitvalue);
	  GenSignalExpected_den->Fill(Q3, TERM5);
	  ///////////////////////////////////////////////////////////
	  
	  
	  
	}
      }
    }
  }
  GenSignalExpected_num->Sumw2();
  GenSignalExpected_num->Divide(GenSignalExpected_den);
 
  TSpline3 *c3Fit1D_ExpanSpline = new TSpline3(GenSignalExpected_num);
  if(CollisionType==0) c3Fit1D_ExpanSpline->SetLineColor(1);
  if(CollisionType==1) c3Fit1D_ExpanSpline->SetLineColor(2);
  if(CollisionType==2) c3Fit1D_ExpanSpline->SetLineColor(4);
  c3Fit1D_ExpanSpline->SetLineWidth(2);
  double xpoints[1000], ypoints[1000];
  bool splineOnly=kFALSE;
  for(int iii=0; iii<1000; iii++){
    xpoints[iii] = 0 + (iii+0.5)*0.001;
    if(!Gaussian && CollisionType!=0 && c3Fit1D_Expan->Eval(xpoints[iii]) < 2.2) splineOnly=kTRUE;
    if(!Gaussian && CollisionType==0 && c3Fit1D_Expan->Eval(xpoints[iii]) < 2.0) splineOnly=kTRUE;// 2.0 or 1.4 for Mbin=3 in Fig 2
    if(!splineOnly){
      ypoints[iii] = c3Fit1D_Expan->Eval(xpoints[iii]);
      if(c3Fit1D_Expan->Eval(xpoints[iii])<2 && fabs(c3Fit1D_Expan->Eval(xpoints[iii])-c3Fit1D_ExpanSpline->Eval(xpoints[iii])) < 0.01) splineOnly=kTRUE;
    }
    else {ypoints[iii] = c3Fit1D_ExpanSpline->Eval(xpoints[iii]); splineOnly=kTRUE;}
  }
  TGraph *gr_c3Spline = new TGraph(1000,xpoints,ypoints);
  gr_c3Spline->SetLineWidth(2);
  if(CollisionType==0) gr_c3Spline->SetLineColor(1);
  if(CollisionType==1) gr_c3Spline->SetLineColor(2);
  if(CollisionType==2) gr_c3Spline->SetLineColor(4);
  
  gr_c3Spline->Draw("c same");
  
  double ChiSqSum_1D=0, SumNDF_1D=0;
  for(int bin=1; bin<=300; bin++){
    double binCenter = c3_hist->GetXaxis()->GetBinCenter(bin);
    if(binCenter > Q3Limit) continue;
    if(c3_hist->GetBinError(bin)==0) continue;
    int grIndex=1;
    for(int gr=0; gr<999; gr++){
      if(binCenter > xpoints[gr] && (binCenter < xpoints[gr+1])) {grIndex=gr; break;}
    }

    //ChiSqSum_1D += pow((c3_hist->GetBinContent(bin)-ypoints[grIndex]) / c3_hist->GetBinError(bin),2);
    ChiSqSum_1D += pow((c3_hist->GetBinContent(bin)-c3Fit1D_Base->Eval(binCenter)) / c3_hist->GetBinError(bin),2);
    //cout<<c3_hist->GetBinContent(bin)<<"  "<<c3Fit1D_Base->Eval(binCenter)<<"  "<<c3_hist->GetBinError(bin)<<endl;
    //cout<<c3_hist->GetBinContent(bin)<<"  "<<ypoints[grIndex]<<"  "<<c3_hist->GetBinError(bin)<<endl;

    SumNDF_1D++;
  }
  cout<<"1D Chi2/NDF = "<<ChiSqSum_1D / (SumNDF_1D-3.)<<endl;

  // uncomment to display fit box
  //c3_hist->GetListOfFunctions()->Add(c3Fit1D_Base);
  
  // Fit Range Systematics
  //for(int i=0; i<8; i++){cout<<MainFitParams[i]<<",  ";}
  //cout<<endl;
  //for(int i=0; i<4; i++){cout<<int(100*(MainFitParams[i]-RefMainFitParams[i])/MainFitParams[i])<<"$\\%$ & ";}// Gaussian
  //cout<<endl;
  //for(int i=4; i<8; i++){cout<<int(100*(MainFitParams[i]-RefMainFitParams[i])/MainFitParams[i])<<"$\\%$ & ";}// Edgeworth
  //cout<<endl;
  
  
  //TString *lamName=new TString("#lambda_{3}=");
  //TString *RName=new TString("#R_{inv,3}=");
  //*lamName += int(100*c3Fit1D_Base->GetParameter(1))/100.; lamName->Append(" #pm "); *lamName += int(100*c3Fit1D_Base->GetParError(1))/100.;
  //*RName += round(100*c3Fit1D_Base->GetParameter(2))/100; RName->Append(" #pm "); *RName += int(100*c3Fit1D_Base->GetParError(2))/100.; RName->Append(" fm");
  //TLatex *fitBox1=new TLatex(0.5,0.9,lamName->Data());
  //fitBox1->SetNDC(kTRUE);
  //fitBox1->Draw();
  //TLatex *fitBox2=new TLatex(0.5,0.8,"R_{inv,3} = 2.62 #pm 0.12");
  //fitBox2->SetNDC(kTRUE);
  //fitBox2->Draw();
  //TLatex *fitBox3=new TLatex(0.5,0.5,"<N_{rec,pions}>=103");
  //fitBox3->SetNDC(kTRUE);
  //fitBox3->Draw();
  
    //TPaveStats *c3Stats=(TPaveStats*)c3Fit1D_Base->FindObject("stats");
    //c3Stats->SetX1NDC(0.15);
    //c3Stats->SetX2NDC(0.52);
    //c3Stats->SetY1NDC(.2);
    //c3Stats->SetY2NDC(.3);
    //c3Stats->Draw("same");
    

    // The below 1D fit method has less well defined bin centers
    //TF1 *c3Fit1D=new TF1("c3Fit1D","[0]*(1+[1]*exp(-pow([2]*x/0.19733,2)/2.))",0,1);
    //TF1 *c3Fit1D=new TF1("c3Fit1D","[0]*(1+[1]*exp(-pow([2]*x/0.19733,2)/2.) * (1 + (-0.12/(6.*pow(2,1.5))*(8.*pow([2]*x/0.19733,3) - 12.*pow([2]*x/0.19733,1))) + (0.43/(24.*pow(2,2))*(16.*pow([2]*x/0.19733,4) -48.*pow([2]*x/0.19733,2) + 12))))",0,1);
    //TF1 *c3Fit1D=new TF1("c3Fit1D","[0]*(1+[1]*exp(-pow([2]*x/0.19733,2)/2.) * (1 + ([3]/(6.*pow(2,1.5))*(8.*pow([2]*x/0.19733,3) - 12.*pow([2]*x/0.19733,1))) + ([4]/(24.*pow(2,2))*(16.*pow([2]*x/0.19733,4) -48.*pow([2]*x/0.19733,2) + 12))))",0,1);
    //c3Fit1D->SetLineColor(4);
    //c3Fit1D->SetParameter(0,1); c3Fit1D->SetParName(0,"N");
    //c3Fit1D->SetParameter(1,0.5); c3Fit1D->SetParName(1,"#lambda_{3}");
    //c3Fit1D->SetParameter(2,5); c3Fit1D->SetParName(2,"R_{inv}");
    //c3Fit1D->SetParLimits(2,0.5,15);
    //c3Fit1D->SetLineColor(1);
    //
    //c3Fit1D->FixParameter(0,OutputPar_c3[0]);
    //c3Fit1D->FixParameter(1,OutputPar_c3[1]);
    //c3Fit1D->FixParameter(2,OutputPar_c3[2]);
    //c3Fit1D->SetParName(3,"coeff_{3}"); c3Fit1D->SetParName(4,"coeff_{4}");
    //c3Fit1D->SetParameter(3,.24); c3Fit1D->SetParameter(3,.16);
    //c3_hist->Fit(c3Fit1D,"IMEN","",0.0,Q3Limit);
    //c3Fit1D->Draw("same");
    //cout<<"1d fit: Chi2/NDF = "<<c3Fit1D->GetChisquare()/c3Fit1D->GetNDF()<<endl;
    //dentimesFit_c3->DrawCopy("l same");
    //
    //c3Fit1D->FixParameter(0, fitcopy_c3->GetParameter(0));
    //c3Fit1D->FixParameter(1, fitcopy_c3->GetParameter(1));
    //c3Fit1D->FixParameter(2, fitcopy_c3->GetParameter(2));
    
    //TF1 *c3Fit1D_2=new TF1("c3Fit1D_2","[0]*(1+[1]*exp(-pow([2]*x/0.19733,2)/2.))",0,1);
    //c3Fit1D=new TF1("c3Fit1D","[0]*(1+[1]*exp(-pow([2]*x/0.19733,2)/2.) * pow(1 + ([3]/(6.*pow(2,1.5))*(8.*pow([2]*x/sqrt(3.)/0.19733,3) - 12.*pow([2]*x/sqrt(3.)/0.19733,1))) + ([4]/(24.*pow(2,2))*(16.*pow([2]*x/sqrt(3.)/0.19733,4) -48.*pow([2]*x/sqrt(3.)/0.19733,2) + 12)),3))",0,1);
    //c3Fit1D->FixParameter(0,OutputPar_c3[0]);
    //c3Fit1D->FixParameter(1,OutputPar_c3[1]);
    //c3Fit1D->FixParameter(2,OutputPar_c3[2]);
    //c3Fit1D->FixParameter(3,OutputPar_c3[3]);
    //c3Fit1D->FixParameter(4,OutputPar_c3[4]);
    //c3Fit1D->SetLineColor(4);
    //c3Fit1D->Draw("same");


  //MomRes1d[1][0]->Draw();

  //for(int i=1; i<50; i++) cout<<c3_hist->GetBinContent(i)<<", ";
  //cout<<endl;
  //for(int i=1; i<50; i++) cout<<c3_hist->GetBinError(i)<<", ";
  // pp M2, pi-
  

  Cterm1->Draw("same");
  legend2->Draw("same");
  
  /*if(SameCharge==kTRUE && MCcase==kFALSE){
    TString *savename=new TString("C3c3_SC_");
    if(CollisionType==0) savename->Append("PbPb_K");
    if(CollisionType==1) savename->Append("pPb_K");
    if(CollisionType==2) savename->Append("pp_K");
    *savename += EDbin;
    savename->Append("_M");
    *savename += Mbin;
    savename->Append(".eps");
    can2->SaveAs(savename->Data());
    }*/

  //for(int ii=0; ii<10; ii++) cout<<c3_hist->GetBinContent(ii+1)<<", ";
  //Coul_GRiverside->Draw();
  //Coul_Riverside->Draw("same");
  /*
  TLegend *legend4 = new TLegend(.3,.8, .5,.95,NULL,"brNDC");
  legend4->SetBorderSize(0);
  legend4->SetTextFont(42);//42
  legend4->SetTextSize(.04);// small .03; large .06
  legend4->SetFillColor(0);

  gPad->SetRightMargin(0.025); gPad->SetLeftMargin(0.1); gPad->SetTopMargin(0.02); 
  TwoFrac=lambda_PM; OneFrac=pow(TwoFrac,.5), ThreeFrac=pow(TwoFrac,1.5);
  gPad->SetGridx(0);
  gPad->SetGridy(0);

  TH1D *c3_Extended = (TH1D*)Three_1d[CB1][CB2][CB3][SCBin][0]->Clone();
  c3_Extended->Add(Three_1d[CB1][CB2][CB3][SCBin][4], -( pow(1-OneFrac,3) + 3*OneFrac*pow(1-OneFrac,2) ));
  c3_Extended->Add(Three_1d[CB1][CB2][CB3][SCBin][1], -(1-OneFrac));
  c3_Extended->Add(Three_1d[CB1][CB2][CB3][SCBin][2], -(1-OneFrac));
  c3_Extended->Add(Three_1d[CB1][CB2][CB3][SCBin][3], -(1-OneFrac));
  c3_Extended->Add(Three_1d[CB1][CB2][CB3][SCBin][4], (1-OneFrac)*3*(1-TwoFrac));
  c3_Extended->Scale(1/ThreeFrac);
  //
  c3_Extended->Add(Three_1d[CB1][CB2][CB3][SCBin][1], -1/TwoFrac);
  c3_Extended->Add(Three_1d[CB1][CB2][CB3][SCBin][2], -1/TwoFrac);
  c3_Extended->Add(Three_1d[CB1][CB2][CB3][SCBin][3], -1/TwoFrac);
  c3_Extended->Add(Three_1d[CB1][CB2][CB3][SCBin][4], 3*(1-TwoFrac)/TwoFrac);
  c3_Extended->Add(Three_1d[CB1][CB2][CB3][SCBin][4], 3);
  //
  c3_Extended->Divide(Three_1d[CB1][CB2][CB3][SCBin][4]);
  c3_Extended->GetXaxis()->SetTitle("#font[12]{Q}_{3} (GeV/#font[12]{c})");
  c3_Extended->GetYaxis()->SetTitle("#font[12]{#bf{c}}_{3}^{#pm#pm#pm}");
  c3_Extended->SetMinimum(0.9); c3_Extended->SetMaximum(2.0);
  c3_Extended->SetMarkerStyle(24);
  c3_Extended->SetMarkerColor(2);
  c3_Extended->SetLineColor(2);
  
  //
  TH1D *C3_Extended = (TH1D*)Three_1d[CB1][CB2][CB3][SCBin][0]->Clone();
  C3_Extended->Divide(Three_1d[CB1][CB2][CB3][SCBin][4]);
  C3_Extended->GetXaxis()->SetTitle("#font[12]{Q}_{3} (GeV/c)");
  C3_Extended->GetYaxis()->SetTitle("#font[12]{C}_{3}");
  c3_Extended->GetXaxis()->SetTitleOffset(0.83);
  c3_Extended->GetYaxis()->SetTitleOffset(0.8);
  c3_Extended->GetYaxis()->SetTitleSize(0.05);
  c3_Extended->GetXaxis()->SetTitleSize(0.05);
  C3_Extended->SetMarkerStyle(20);
  C3_Extended->SetMarkerColor(4);
  c3_Extended->GetXaxis()->SetRangeUser(0,2);
  c3_Extended->SetMarkerStyle(20);
  c3_Extended->Draw();
  //cout<<c3_Extended->GetBinError(40)<<"  "<<Three_1d[CB1][CB2][CB3][SCBin][0]->GetBinError(40)/Three_1d[CB1][CB2][CB3][SCBin][4]->GetBinContent(40)<<"  "<<Three_1d[CB1][CB2][CB3][SCBin][1]->GetBinError(40)/Three_1d[CB1][CB2][CB3][SCBin][4]->GetBinContent(40)<<endl;
  //legend4->AddEntry(c3_Extended,"c_{3}, #pi^{#pm}#pi^{#pm}#pi^{#pm}, Coulomb Uncorrected","p");
  //legend4->AddEntry(C3_Extended,"C_{3}, #pi^{#pm}#pi^{#pm}#pi^{#pm}, Coulomb Uncorrected","p");
  //legend4->Draw("same");
  //Unity->Draw("same");
  */
  //Specif_System->Draw("same");
  //Specif_KT3->Draw("same");
  //Specif_FSI->Draw("same");
  //Specif_Disclaimer->Draw("same");
 

  /*
  gPad->SetGridx(0); gPad->SetGridy(0);
  int binLow=20;
  int binHigh=50;
  //TwoFrac=0.9; OneFrac=pow(TwoFrac,0.5); ThreeFrac=pow(TwoFrac,1.5);
  TH1D *K0sProjection = (TH1D*)(Three_3d[0][0][1][SCBin][0]->ProjectionY("K0sProjection",binLow,binHigh,binLow,binHigh));
  TH1D *K0sProjection_term1 = (TH1D*)(Three_3d[0][0][1][SCBin][0]->ProjectionY("K0sProjection_term1",binLow,binHigh,binLow,binHigh));
  TH1D *K0sProjection_term2 = (TH1D*)(Three_3d[0][0][1][SCBin][1]->ProjectionY("K0sProjection_term2",binLow,binHigh,binLow,binHigh));
  TH1D *K0sProjection_term3 = (TH1D*)(Three_3d[0][0][1][SCBin][2]->ProjectionY("K0sProjection_term3",binLow,binHigh,binLow,binHigh));
  TH1D *K0sProjection_term4 = (TH1D*)(Three_3d[0][0][1][SCBin][3]->ProjectionY("K0sProjection_term4",binLow,binHigh,binLow,binHigh));
  TH1D *K0sProjection_term5 = (TH1D*)(Three_3d[0][0][1][SCBin][4]->ProjectionY("K0sProjection_term5",binLow,binHigh,binLow,binHigh));
  K0sProjection_term1->Add(K0sProjection_term5, -( pow(1-OneFrac,3) + 3*OneFrac*pow(1-OneFrac,2) ));
  K0sProjection_term1->Add(K0sProjection_term2, -(1-OneFrac));
  K0sProjection_term1->Add(K0sProjection_term3, -(1-OneFrac));
  K0sProjection_term1->Add(K0sProjection_term4, -(1-OneFrac));
  K0sProjection_term1->Add(K0sProjection_term5, (1-OneFrac)*3*(1-TwoFrac));
  K0sProjection_term1->Scale(1/ThreeFrac);
  //
  K0sProjection_term1->Add(K0sProjection_term2, -1/TwoFrac);
  K0sProjection_term1->Add(K0sProjection_term3, -1/TwoFrac);
  K0sProjection_term1->Add(K0sProjection_term4, -1/TwoFrac);
  K0sProjection_term1->Add(K0sProjection_term5, 3*(1-TwoFrac)/TwoFrac);
  K0sProjection_term1->Add(K0sProjection_term5, 3);
  //
  K0sProjection->Divide(K0sProjection_term5);
  K0sProjection_term1->Divide(K0sProjection_term5);
  K0sProjection_term1->GetXaxis()->SetRangeUser(0,.5);
  K0sProjection_term1->SetMarkerStyle(24);
  K0sProjection_term1->SetMarkerColor(4);
  K0sProjection->SetMarkerStyle(20);
  K0sProjection->SetMarkerColor(4);
  K0sProjection->SetMinimum(0.92);
  K0sProjection->GetXaxis()->SetTitle("#font[12]{q_{13}^{#pm#mp}} (GeV/#font[12]{c})");
  K0sProjection->GetYaxis()->SetTitle("#font[12]{C_{3}} or #font[12]{#bf{c}_{3}}"); 
  K0sProjection->GetXaxis()->SetTitleOffset(1.2); K0sProjection->GetYaxis()->SetTitleOffset(1.3);
  
  K0sProjection->Draw();
  // Sys errors
  TH1D *Sys_K0sProjection=(TH1D*)K0sProjection->Clone();
  TH1D *Sys_K0sProjection_term1=(TH1D*)K0sProjection_term1->Clone();
  Sys_K0sProjection->SetMarkerSize(0); Sys_K0sProjection_term1->SetMarkerSize(0);
  Sys_K0sProjection->SetFillColor(kBlue-10); Sys_K0sProjection_term1->SetFillColor(kBlue-10);
  Sys_K0sProjection->SetFillStyle(1000); Sys_K0sProjection_term1->SetFillStyle(1000);
  for(int i=0; i<Sys_K0sProjection->GetNbinsX(); i++) { 
    Sys_K0sProjection->SetBinError(i+1, 0.01 * Sys_K0sProjection->GetBinContent(i+1));
    Sys_K0sProjection_term1->SetBinError(i+1, 0.01 * Sys_K0sProjection_term1->GetBinContent(i+1));
  }
  for(int i=0; i<Sys_K0sProjection->GetNbinsX(); i++) cout<<K0sProjection->GetBinContent(i+1)<<", ";
  cout<<endl;
  for(int i=0; i<Sys_K0sProjection->GetNbinsX(); i++) cout<<K0sProjection->GetBinError(i+1)<<", ";
  cout<<endl;
  for(int i=0; i<Sys_K0sProjection->GetNbinsX(); i++) cout<<K0sProjection_term1->GetBinContent(i+1)<<", ";
  cout<<endl;
  for(int i=0; i<Sys_K0sProjection->GetNbinsX(); i++) cout<<K0sProjection_term1->GetBinError(i+1)<<", ";
  cout<<endl;

  Sys_K0sProjection->Draw("E2 same");
  Sys_K0sProjection_term1->Draw("E2 same");
  K0sProjection->Draw("same");
  K0sProjection_term1->Draw("same");

  //legend4->AddEntry(K0sProjection,"#font[12]{C_{3}^{#pm#pm#mp}} projection","p");
  //legend4->AddEntry(K0sProjection_term1,"#font[12]{#bf{c}_{3}^{#pm#pm#mp}} projection","p");
  //legend4->Draw("same");
  */
  
  

    
  //////////////////////////////////////////////////////////////////////////////////////

  


 
  
  if(SaveToFile){
    TString *savefilename = new TString("OutFiles/OutFile");
    if(!Gaussian) savefilename->Append("ExpFit");
    if(CollisionType==0) savefilename->Append("PbPb");
    else if(CollisionType==1) savefilename->Append("pPb");
    else savefilename->Append("pp");
    //
    if(MCcase) savefilename->Append("MonteCarlo");
    //
    if(SameCharge) savefilename->Append("SC");
    else savefilename->Append("MC");
    //
    if(CHARGE==1) savefilename->Append("Pos");
    else savefilename->Append("Neg");
    //
       
    savefilename->Append("Kt3_");
    *savefilename += EDbin+1;
        
    savefilename->Append("_M");
    *savefilename += Mbin;
    savefilename->Append(".root");
    TFile *savefile = new TFile(savefilename->Data(),"RECREATE");
    can1->Write("can1");
    C2_ss->Write("C2_ss");
    C2_os->Write("C2_os");
    fitC2ss_h->Write("fitC2ss_h");
    fitC2ss_Base->Write("fitC2ss_Base");
    fitC2ss_Expan->Write("fitC2ss_Expan");
    Cterm1->Write("C3");
    c3_hist->Write("c3");
    Combinatorics_1d->Write("Combinatorics_1d");
    c3Fit1D_Base->Write("c3Fit1D_Base");
    c3Fit1D_Expan->Write("c3Fit1D_Expan");
    c3Fit1D_ExpanSpline->Write("c3Fit1D_ExpanSpline");
    gr_c3Spline->Write("gr_c3Spline");
    MyMinuit_c3.Write("MyMinuit_c3");
    //
    savefile->Close();
  }
  
  
}
void ReadCoulCorrections(int index){
  ///////////////////////
  TString *fname2 = new TString("KFile.root");
 
  TFile *File=new TFile(fname2->Data(),"READ");
  if(index>=12) cout<<"FSI index not acceptable in 2-particle Coulomb read"<<endl;
  TString *nameSS = new TString("K2ss_");
  TString *nameOS = new TString("K2os_");
  *nameSS += index;
  *nameOS += index;
  TString *nameSS_2 = new TString("K2ss_");
  TString *nameOS_2 = new TString("K2os_");
  *nameSS_2 += index+1; *nameOS_2 += index+1;
  /*if(index<9) {*nameSS_2 += index+1; *nameOS_2 += index+1;}
    else {*nameSS_2 += index; *nameOS_2 += index;}*/
  TH1D *temp_ss = (TH1D*)File->Get(nameSS->Data());
  TH1D *temp_os = (TH1D*)File->Get(nameOS->Data());
  TH1D *temp_ss_2 = (TH1D*)File->Get(nameSS_2->Data());
  TH1D *temp_os_2 = (TH1D*)File->Get(nameOS_2->Data());

  CoulCorr2SS = (TH1D*)temp_ss->Clone();
  CoulCorr2OS = (TH1D*)temp_os->Clone();
  CoulCorr2SS_2 = (TH1D*)temp_ss_2->Clone();
  CoulCorr2OS_2 = (TH1D*)temp_os_2->Clone();
  
  //
  CoulCorr2SS->SetDirectory(0);
  CoulCorr2OS->SetDirectory(0);
  CoulCorr2SS_2->SetDirectory(0);
  CoulCorr2OS_2->SetDirectory(0);
  
  File->Close(); 
}
double CoulCorr2(int chargeproduct, double Q2){// returns K2
  int indexL=0;
  int indexH=0;
  double slope=0;
  double value1=1.0, value2=1.0;

  indexL = int(fabs(Q2 - CoulCorr2SS->GetXaxis()->GetBinWidth(1)/2.)/(CoulCorr2SS->GetXaxis()->GetBinWidth(1)));
  indexH = indexL+1;
  
  
  if(indexH >= CoulCorr2SS->GetNbinsX()) {
    return (Gamov(chargeproduct, Q2) * CoulCorr2SS->GetBinContent(CoulCorr2SS->GetNbinsX()-1) / Gamov(chargeproduct, CoulCorr2SS->GetXaxis()->GetBinCenter(CoulCorr2SS->GetNbinsX()-1)));
  }
  // Low index value
  if(chargeproduct==1){
    slope = (CoulCorr2SS->GetBinContent(indexL+1) - CoulCorr2SS->GetBinContent(indexH+1));
    slope /= (CoulCorr2SS->GetXaxis()->GetBinCenter(indexL+1) - CoulCorr2SS->GetXaxis()->GetBinCenter(indexH+1));
    value1 = slope*(Q2 - CoulCorr2SS->GetXaxis()->GetBinCenter(indexL+1)) + CoulCorr2SS->GetBinContent(indexL+1);
  }else {
    slope = (CoulCorr2OS->GetBinContent(indexL+1) - CoulCorr2OS->GetBinContent(indexH+1));
    slope /= (CoulCorr2OS->GetXaxis()->GetBinCenter(indexL+1) - CoulCorr2OS->GetXaxis()->GetBinCenter(indexH+1));
    value1 = slope*(Q2 - CoulCorr2OS->GetXaxis()->GetBinCenter(indexL+1)) + CoulCorr2OS->GetBinContent(indexL+1);
  }
  // High index value
  if(chargeproduct==1){
    slope = (CoulCorr2SS_2->GetBinContent(indexL+1) - CoulCorr2SS_2->GetBinContent(indexH+1));
    slope /= (CoulCorr2SS_2->GetXaxis()->GetBinCenter(indexL+1) - CoulCorr2SS_2->GetXaxis()->GetBinCenter(indexH+1));
    value2 = slope*(Q2 - CoulCorr2SS_2->GetXaxis()->GetBinCenter(indexL+1)) + CoulCorr2SS_2->GetBinContent(indexL+1);
  }else {
    slope = (CoulCorr2OS_2->GetBinContent(indexL+1) - CoulCorr2OS_2->GetBinContent(indexH+1));
    slope /= (CoulCorr2OS_2->GetXaxis()->GetBinCenter(indexL+1) - CoulCorr2OS_2->GetXaxis()->GetBinCenter(indexH+1));
    value2 = slope*(Q2 - CoulCorr2OS_2->GetXaxis()->GetBinCenter(indexL+1)) + CoulCorr2OS_2->GetBinContent(indexL+1);
  }
  
  if(value1>0 && value2>0){// interpolation only done between 9 and 12 Mbin.
    return (value1 + (value2-value1)/(2.));// always use the half-way point.
  }else if(value1>0){
    return value1;
  }else if(value2>0){
    return value2;
  }else return 1.0;
  
  
  //
  // old way with Gaussian sources for low mult systems
  /*if(indexH >= CoulCorr2SS->GetNbinsX()) {
    return (Gamov(chargeproduct, Q2) * CoulCorr2SS->GetBinContent(CoulCorr2SS->GetNbinsX()-1) / Gamov(chargeproduct, CoulCorr2SS->GetXaxis()->GetBinCenter(CoulCorr2SS->GetNbinsX()-1)));
  }
  if(chargeproduct==1){
    slope = (CoulCorr2SS->GetBinContent(indexL+1) - CoulCorr2SS->GetBinContent(indexH+1));
    slope /= (CoulCorr2SS->GetXaxis()->GetBinCenter(indexL+1) - CoulCorr2SS->GetXaxis()->GetBinCenter(indexH+1));
    value1 = slope*(Q2 - CoulCorr2SS->GetXaxis()->GetBinCenter(indexL+1)) + CoulCorr2SS->GetBinContent(indexL+1);
  }else {
    slope = (CoulCorr2OS->GetBinContent(indexL+1) - CoulCorr2OS->GetBinContent(indexH+1));
    slope /= (CoulCorr2OS->GetXaxis()->GetBinCenter(indexL+1) - CoulCorr2OS->GetXaxis()->GetBinCenter(indexH+1));
    value1 = slope*(Q2 - CoulCorr2OS->GetXaxis()->GetBinCenter(indexL+1)) + CoulCorr2OS->GetBinContent(indexL+1);
  }
  if(Mbin_def<=9 || Mbin_def>12) return value1;
  else{// interpolate in K factor transition region
    if(chargeproduct==1){
      slope = (CoulCorr2SS_2->GetBinContent(indexL+1) - CoulCorr2SS_2->GetBinContent(indexH+1));
      slope /= (CoulCorr2SS_2->GetXaxis()->GetBinCenter(indexL+1) - CoulCorr2SS_2->GetXaxis()->GetBinCenter(indexH+1));
      value2 = slope*(Q2 - CoulCorr2SS_2->GetXaxis()->GetBinCenter(indexL+1)) + CoulCorr2SS_2->GetBinContent(indexL+1);
    }else {
      slope = (CoulCorr2OS_2->GetBinContent(indexL+1) - CoulCorr2OS_2->GetBinContent(indexH+1));
      slope /= (CoulCorr2OS_2->GetXaxis()->GetBinCenter(indexL+1) - CoulCorr2OS_2->GetXaxis()->GetBinCenter(indexH+1));
      value2 = slope*(Q2 - CoulCorr2OS_2->GetXaxis()->GetBinCenter(indexL+1)) + CoulCorr2OS_2->GetBinContent(indexL+1);
    }

    if(value1>0 && value2>0){// interpolation only done between 9 and 12 Mbin.
      return (value1 + (Mbin_def-9)*(value2-value1)/(3.));
    }else if(value1>0){
      return value1;
    }else if(value2>0){
      return value2;
    }else return 1.0;
    
  }
  */
  //
  
}

//----------------------------------------------------------------------
  

//________________________________________________________________________
void fcnC2_Global(int& npar, double* deriv, double& f, double par[], int flag){
  
  double qinvSS=0;
  
  double Rch=par[3]/FmToGeV;
  double CSS=0, COS=0;
  double SumChi2=0;
  double Expan=0;
  NFitPoints_C2global=0;
  if(LinkN) par[9]=par[0];// Link N factors

  for(int i=1; i<BINRANGE_C2global; i++){
    
    qinvSS = BinCenters[i];
    if(qinvSS > Q2Limit) continue;
    
    //
    double arg=qinvSS*Rch;
    if(Gaussian){// Edgeworth expansion
      Expan = 1 + par[5]/(6.*pow(2,1.5)) * (8.*pow(arg,3) - 12.*pow(arg,1));
      Expan += par[6]/(24.*pow(2,2)) * (16.*pow(arg,4) -48.*pow(arg,2) + 12);
      Expan += par[7]/(120.*pow(2,2.5)) * (32.*pow(arg,5) - 160.*pow(arg,3) + 120*arg);
      Expan += par[8]/(720.*pow(2,3)) * (64.*pow(arg,6) - 480.*pow(arg,4) + 720.*pow(arg,2) - 120);
    }else{
      Expan = 1 + par[5] * (arg - 1);
      Expan += par[6]/2. * (pow(arg,2) - 4*arg + 2);
      Expan += par[7] * 0.;
      Expan += par[8] * 0.;
    }
    //Expan = 1.0;
    //
    
    // old way without undilution
    /*CSS = 1 + exp(-pow(Rch*qinvSS,ExpPower))*pow(Expan,2);
    CSS *= par[1]*K2SS[i];
    CSS += 1-par[1];
    CSS *= par[0];*/
    // undilution method 
    //CSS = 1 + par[1]*exp(-pow(Rch*qinvSS,ExpPower))*pow(Expan,2);
    //CSS *= par[0];
    // undilution method with correct normalization location (was previously applied to C2^QS)
    CSS = 1 + par[1]*exp(-pow(Rch*qinvSS,ExpPower))*pow(Expan,2);
    CSS *= lambda_PM * K2SS[i];
    CSS += 1-lambda_PM;
    CSS *= par[0];

    //
    COS = 1;
    COS *= par[1]*K2OS[i];
    COS += 1-par[1];
    COS *= par[9];// different Norm
    //
    if(C2ssFitting[i] > 0){
      if(IncludeSS) {
	//double errorSS = sqrt(pow( (CSS/par[0] - (1-par[1]))/K2SS[i] * K2SS_e[i] * par[0],2) + pow(C2ssFitting_e[i],2));
	double errorSS = sqrt(pow(C2ssFitting_e[i],2));// new way with undilution already done in C2ssFitting[i]
	SumChi2 += pow((CSS - C2ssFitting[i])/errorSS,2);
	NFitPoints_C2global++;
      }
    }
    if(IncludeOS) {
      double errorOS = sqrt(pow( (COS/par[9] - (1-par[1]))/K2OS[i] * K2OS_e[i] * par[9],2) + pow(C2osFitting_e[i],2));
      SumChi2 += pow((COS - C2osFitting[i])/errorOS,2);
      NFitPoints_C2global++;
    }
  }
    
  
  f = SumChi2;
  Chi2_C2global = f;
  
}
//________________________________________________________________________
double C2ssFitFunction(Double_t *x, Double_t *par)
{
  double Rch=par[3]/FmToGeV;
  int qbin = int(fabs(x[0]/BinWidthQ2));
    
  double qinvSS = BinCenters[qbin];
  
  double arg=qinvSS*Rch;
  double Expan = 1;
  if(Gaussian){// Edgeworth expansion
    Expan += par[5]/(6.*pow(2,1.5))*(8.*pow(arg,3) - 12.*pow(arg,1));
    Expan += par[6]/(24.*pow(2,2))*(16.*pow(arg,4) -48.*pow(arg,2) + 12);
    Expan += par[7]/(120.*pow(2,2.5))*(32.*pow(arg,5) - 160.*pow(arg,3) + 120*arg);
    Expan += par[8]/(720.*pow(2,3))*(64.*pow(arg,6) - 480.*pow(arg,4) + 720.*pow(arg,2) - 120);
  }else{// Laguerre
    Expan = 1 + par[5] * (arg - 1);
    Expan += par[6]/2. * (pow(arg,2) - 4*arg + 2);
    Expan += par[7] * 0.;
    Expan += par[8] * 0.;
  }

  // old way without undilution
  /*double CSS = 1 + exp(-pow(Rch*qinvSS,ExpPower))*pow(Expan,2);
  double K2=1.0;
  if(qbin < BINRANGE_C2global) K2=K2SS[qbin];
  CSS *= par[1]*K2;
  CSS += 1-par[1];
  CSS *= par[0];*/
  // undilution method
  //double CSS = 1 + par[1]*exp(-pow(Rch*qinvSS,ExpPower))*pow(Expan,2);
  //CSS *= par[0];
  // undilution method with correct normalization location (was previously applied to C2^QS)
  double CSS = 1 + par[1]*exp(-pow(Rch*qinvSS,ExpPower))*pow(Expan,2);
  CSS *= lambda_PM * K2SS[qbin];
  CSS += 1-lambda_PM;
  CSS *= par[0];

  return CSS;
}
//________________________________________________________________________
double C2osFitFunction(Double_t *x, Double_t *par)
{
  if(LinkN) par[9]=par[0];// Link N factors
  int qbin = int(fabs(x[0]/BinWidthQ2));
    
  //double qinvOS = BinCenters[qbin];
  
  double COS = 1;
  double K2=1.0;
  if(qbin < BINRANGE_C2global) K2=K2OS[qbin];
  COS *= par[1]*K2;
  COS += 1-par[1];
  COS *= par[9];
  return COS;
}
//__________________________________________________________________________

void fcn_c3(int& npar, double* deriv, double& f, double par[], int flag){

  double q12=0, q13=0, q23=0;
  double Expan12=0, Expan13=0, Expan23=0;
  double C=0;
  double Rch=par[2]/FmToGeV;
  double SumChi2=0;
  //double lnL=0, term1=0, term2=0;
  NFitPoints_c3=0;
  //double SumChi2_test=0;

  for(int i=0; i<=BINLIMIT_3; i++){// q12
    for(int j=0; j<=BINLIMIT_3; j++){// q13
      for(int k=0; k<=BINLIMIT_3; k++){// q23
	
	if(B_3[i][j][k] == 0) continue;
	if(A_3[i][j][k] == 0) continue;
	if(A_3_e[i][j][k] == 0) continue;

	q12 = BinCenters[i];
	q13 = BinCenters[j];
	q23 = BinCenters[k];
	double q3 = sqrt(pow(q12,2)+pow(q13,2)+pow(q23,2));
	if(q3 > Q3Limit) continue;
	//
	double arg12 = q12*Rch;
	double arg13 = q13*Rch;
	double arg23 = q23*Rch;
	if(Gaussian){// Edgeworth expansion
	  Expan12 = 1 + par[3]/(6.*pow(2,1.5))*(8*pow(arg12,3) - 12*pow(arg12,1)) + par[4]/(24.*pow(2,2))*(16*pow(arg12,4) -48*pow(arg12,2) + 12);
	  Expan13 = 1 + par[3]/(6.*pow(2,1.5))*(8*pow(arg13,3) - 12*pow(arg13,1)) + par[4]/(24.*pow(2,2))*(16*pow(arg13,4) -48*pow(arg13,2) + 12);
	  Expan23 = 1 + par[3]/(6.*pow(2,1.5))*(8*pow(arg23,3) - 12*pow(arg23,1)) + par[4]/(24.*pow(2,2))*(16*pow(arg23,4) -48*pow(arg23,2) + 12);
	}else{// Laguerre expansion
	  Expan12 = 1 + par[3]*(arg12 - 1) + par[4]/2.*(pow(arg12,2) - 4*arg12 + 2);
	  Expan13 = 1 + par[3]*(arg13 - 1) + par[4]/2.*(pow(arg13,2) - 4*arg13 + 2);
	  Expan23 = 1 + par[3]*(arg23 - 1) + par[4]/2.*(pow(arg23,2) - 4*arg23 + 2);
	}
	//
	C = 1 + par[1]*exp(-(pow(arg12,ExpPower)+pow(arg13,ExpPower)+pow(arg23,ExpPower))/2.)*Expan12*Expan13*Expan23;
	C *= par[0];// Norm
	
	double error = pow(A_3_e[i][j][k]/B_3[i][j][k],2);
	error += pow(sqrt(B_3[i][j][k])*A_3[i][j][k]/pow(B_3[i][j][k],2),2);
	error = sqrt(error);
	SumChi2 += pow( (C - A_3[i][j][k]/B_3[i][j][k])/error,2);
	//if(q3<0.05) SumChi2_test += pow( (C - A_3[i][j][k]/B_3[i][j][k])/error,2);
	//
	/*if(A_3[i][j][k] >= 1) term1 = C*(A_3[i][j][k]+B_3[i][j][k])/(A_3[i][j][k]*(C+1));
	else term1 = 0;
	term2 = (A_3[i][j][k]+B_3[i][j][k])/(B_3[i][j][k]*(C+1));
	
	if(term1 > 0.0 && term2 > 0.0){
	  lnL += A_3[i][j][k]*log(term1) + B_3[i][j][k]*log(term2);
	}else if(term1==0 && term2 > 0.0){
	  lnL += B_3[i][j][k]*log(term2);
	}else {cout<<"WARNING -- term1 and term2 are negative"<<endl;}
	*/
	float DegenerateCount=1.;
	//if(i==j && i==k) DegenerateCount=1;
	//else if(i==j || i==k || j==k) DegenerateCount=3;//3
	//else DegenerateCount=6;//6
	NFitPoints_c3 += 1/DegenerateCount;
	
      }
    }
  }
  //f = -2.0*lnL;// log-liklihood minimization
  f = SumChi2;// Chi2 minimization
  Chi2_c3 = f;
  //Chi2_c3 = SumChi2_test;
  
}
//________________________________________________________________________
double Dfitfunction_c3(Double_t *x, Double_t *par)
{
  double Rch = par[2]/FmToGeV;
  double arg12 = x[0]*Rch;
  double arg13 = x[1]*Rch;
  double arg23 = x[2]*Rch;
  double Expan12 = 1, Expan13 = 1, Expan23 = 1;
  if(Gaussian){// Edworth Expansion
    Expan12 += par[3]/(6.*pow(2,1.5))*(8*pow(arg12,3) - 12*pow(arg12,1)) + par[4]/(24.*pow(2,2))*(16*pow(arg12,4) -48*pow(arg12,2) + 12);
    Expan13 += par[3]/(6.*pow(2,1.5))*(8*pow(arg13,3) - 12*pow(arg13,1)) + par[4]/(24.*pow(2,2))*(16*pow(arg13,4) -48*pow(arg13,2) + 12);
    Expan23 += par[3]/(6.*pow(2,1.5))*(8*pow(arg23,3) - 12*pow(arg23,1)) + par[4]/(24.*pow(2,2))*(16*pow(arg23,4) -48*pow(arg23,2) + 12);
  }else{// Laguerre Expansion
    Expan12 = 1 + par[3]*(arg12 - 1) + par[4]/2.*(pow(arg12,2) - 4*arg12 + 2);
    Expan13 = 1 + par[3]*(arg13 - 1) + par[4]/2.*(pow(arg13,2) - 4*arg13 + 2);
    Expan23 = 1 + par[3]*(arg23 - 1) + par[4]/2.*(pow(arg23,2) - 4*arg23 + 2);
  }
  
  //
  double C = 1 + par[1]*exp(-(pow(arg12,ExpPower)+pow(arg13,ExpPower)+pow(arg23,ExpPower))/2.)*Expan12*Expan13*Expan23;
  C *= par[0];// Norm
  
  return C;
}
//________________________________________________________________________
double CoulCorrGRS(bool SC, double Q_12, double Q_13, double Q_23){
 
  int index12L = int(fabs(Q_12 - CoulCorr2SS->GetXaxis()->GetBinWidth(1)/2.)/(CoulCorr2SS->GetXaxis()->GetBinWidth(1)));
  int index12H = index12L+1;
  int index13L = int(fabs(Q_13 - CoulCorr2SS->GetXaxis()->GetBinWidth(1)/2.)/(CoulCorr2SS->GetXaxis()->GetBinWidth(1)));
  int index13H = index13L+1;
  int index23L = int(fabs(Q_23 - CoulCorr2SS->GetXaxis()->GetBinWidth(1)/2.)/(CoulCorr2SS->GetXaxis()->GetBinWidth(1)));
  int index23H = index23L+1;

  if(Tricubic){
    // Tricubic Interpolation
    double arr[4][4][4]={{{0}}};
    for(int x=0; x<4; x++){
      for(int y=0; y<4; y++){
	for(int z=0; z<4; z++){
	  if(SC){
	    arr[x][y][z] = CoulCorr2SS->GetBinContent((index12L)+x)*CoulCorr2SS->GetBinContent((index23L)+y)*CoulCorr2SS->GetBinContent((index13L)+z);
	  }else{
	    arr[x][y][z] = CoulCorr2SS->GetBinContent((index12L)+x)*CoulCorr2OS->GetBinContent((index23L)+y)*CoulCorr2OS->GetBinContent((index13L)+z);
	  }
	  
	}
      }
    }
    return tricubicInterpolate(arr, Q_12, Q_23, Q_13);
  }else{
    // Trilinear Interpolation.  See for instance: https://en.wikipedia.org/wiki/Trilinear_interpolation
    //
    double value1=1.0, value2=1.0;
    //
    double xd = (Q_12-CoulCorr2SS->GetXaxis()->GetBinCenter(index12L+1));
    xd /= (CoulCorr2SS->GetXaxis()->GetBinCenter(index12H+1)-CoulCorr2SS->GetXaxis()->GetBinCenter(index12L+1));
    double yd = (Q_13-CoulCorr2SS->GetXaxis()->GetBinCenter(index13L+1));
    yd /= (CoulCorr2SS->GetXaxis()->GetBinCenter(index13H+1)-CoulCorr2SS->GetXaxis()->GetBinCenter(index13L+1));
    double zd = (Q_23-CoulCorr2SS->GetXaxis()->GetBinCenter(index23L+1));
    zd /= (CoulCorr2SS->GetXaxis()->GetBinCenter(index23H+1)-CoulCorr2SS->GetXaxis()->GetBinCenter(index23L+1));
    //
    if(SC){
      double c00 = CoulCorr2SS->GetBinContent(index12L+1)*CoulCorr2SS->GetBinContent(index13L+1)*CoulCorr2SS->GetBinContent(index23L+1)*(1-xd);
      c00 += CoulCorr2SS->GetBinContent(index12H+1)*CoulCorr2SS->GetBinContent(index13L+1)*CoulCorr2SS->GetBinContent(index23L+1)*xd;
      double c10 = CoulCorr2SS->GetBinContent(index12L+1)*CoulCorr2SS->GetBinContent(index13H+1)*CoulCorr2SS->GetBinContent(index23L+1)*(1-xd);
      c10 += CoulCorr2SS->GetBinContent(index12H+1)*CoulCorr2SS->GetBinContent(index13H+1)*CoulCorr2SS->GetBinContent(index23L+1)*xd;
      double c01 = CoulCorr2SS->GetBinContent(index12L+1)*CoulCorr2SS->GetBinContent(index13L+1)*CoulCorr2SS->GetBinContent(index23H+1)*(1-xd);
      c01 += CoulCorr2SS->GetBinContent(index12H+1)*CoulCorr2SS->GetBinContent(index13L+1)*CoulCorr2SS->GetBinContent(index23H+1)*xd;
      double c11 = CoulCorr2SS->GetBinContent(index12L+1)*CoulCorr2SS->GetBinContent(index13H+1)*CoulCorr2SS->GetBinContent(index23H+1)*(1-xd);
      c11 += CoulCorr2SS->GetBinContent(index12H+1)*CoulCorr2SS->GetBinContent(index13H+1)*CoulCorr2SS->GetBinContent(index23H+1)*xd;
      //
      double c0 = c00*(1-yd) + c10*yd;
      double c1 = c01*(1-yd) + c11*yd;
      value1 = (c0*(1-zd) + c1*zd);
    }else{
      double c00 = CoulCorr2SS->GetBinContent(index12L+1)*CoulCorr2OS->GetBinContent(index13L+1)*CoulCorr2OS->GetBinContent(index23L+1)*(1-xd);
      c00 += CoulCorr2SS->GetBinContent(index12H+1)*CoulCorr2OS->GetBinContent(index13L+1)*CoulCorr2OS->GetBinContent(index23L+1)*xd;
      double c10 = CoulCorr2SS->GetBinContent(index12L+1)*CoulCorr2OS->GetBinContent(index13H+1)*CoulCorr2OS->GetBinContent(index23L+1)*(1-xd);
      c10 += CoulCorr2SS->GetBinContent(index12H+1)*CoulCorr2OS->GetBinContent(index13H+1)*CoulCorr2OS->GetBinContent(index23L+1)*xd;
      double c01 = CoulCorr2SS->GetBinContent(index12L+1)*CoulCorr2OS->GetBinContent(index13L+1)*CoulCorr2OS->GetBinContent(index23H+1)*(1-xd);
      c01 += CoulCorr2SS->GetBinContent(index12H+1)*CoulCorr2OS->GetBinContent(index13L+1)*CoulCorr2OS->GetBinContent(index23H+1)*xd;
      double c11 = CoulCorr2SS->GetBinContent(index12L+1)*CoulCorr2OS->GetBinContent(index13H+1)*CoulCorr2OS->GetBinContent(index23H+1)*(1-xd);
      c11 += CoulCorr2SS->GetBinContent(index12H+1)*CoulCorr2OS->GetBinContent(index13H+1)*CoulCorr2OS->GetBinContent(index23H+1)*xd;
      //
      double c0 = c00*(1-yd) + c10*yd;
      double c1 = c01*(1-yd) + c11*yd;
      value1 = (c0*(1-zd) + c1*zd);
    }
    
    //if(Mbin_def<=9 || Mbin_def>12) return value1;// old way for v5
    //
    // interpolation for K factor tansition
    if(SC){
      double c00 = CoulCorr2SS_2->GetBinContent(index12L+1)*CoulCorr2SS_2->GetBinContent(index13L+1)*CoulCorr2SS_2->GetBinContent(index23L+1)*(1-xd);
      c00 += CoulCorr2SS_2->GetBinContent(index12H+1)*CoulCorr2SS_2->GetBinContent(index13L+1)*CoulCorr2SS_2->GetBinContent(index23L+1)*xd;
      double c10 = CoulCorr2SS_2->GetBinContent(index12L+1)*CoulCorr2SS_2->GetBinContent(index13H+1)*CoulCorr2SS_2->GetBinContent(index23L+1)*(1-xd);
      c10 += CoulCorr2SS_2->GetBinContent(index12H+1)*CoulCorr2SS_2->GetBinContent(index13H+1)*CoulCorr2SS_2->GetBinContent(index23L+1)*xd;
      double c01 = CoulCorr2SS_2->GetBinContent(index12L+1)*CoulCorr2SS_2->GetBinContent(index13L+1)*CoulCorr2SS_2->GetBinContent(index23H+1)*(1-xd);
      c01 += CoulCorr2SS_2->GetBinContent(index12H+1)*CoulCorr2SS_2->GetBinContent(index13L+1)*CoulCorr2SS_2->GetBinContent(index23H+1)*xd;
      double c11 = CoulCorr2SS_2->GetBinContent(index12L+1)*CoulCorr2SS_2->GetBinContent(index13H+1)*CoulCorr2SS_2->GetBinContent(index23H+1)*(1-xd);
      c11 += CoulCorr2SS_2->GetBinContent(index12H+1)*CoulCorr2SS_2->GetBinContent(index13H+1)*CoulCorr2SS_2->GetBinContent(index23H+1)*xd;
      //
      double c0 = c00*(1-yd) + c10*yd;
      double c1 = c01*(1-yd) + c11*yd;
      value2 = (c0*(1-zd) + c1*zd);
    }else{
      double c00 = CoulCorr2SS_2->GetBinContent(index12L+1)*CoulCorr2OS_2->GetBinContent(index13L+1)*CoulCorr2OS_2->GetBinContent(index23L+1)*(1-xd);
      c00 += CoulCorr2SS_2->GetBinContent(index12H+1)*CoulCorr2OS_2->GetBinContent(index13L+1)*CoulCorr2OS_2->GetBinContent(index23L+1)*xd;
      double c10 = CoulCorr2SS_2->GetBinContent(index12L+1)*CoulCorr2OS_2->GetBinContent(index13H+1)*CoulCorr2OS_2->GetBinContent(index23L+1)*(1-xd);
      c10 += CoulCorr2SS_2->GetBinContent(index12H+1)*CoulCorr2OS_2->GetBinContent(index13H+1)*CoulCorr2OS_2->GetBinContent(index23L+1)*xd;
      double c01 = CoulCorr2SS_2->GetBinContent(index12L+1)*CoulCorr2OS_2->GetBinContent(index13L+1)*CoulCorr2OS_2->GetBinContent(index23H+1)*(1-xd);
      c01 += CoulCorr2SS_2->GetBinContent(index12H+1)*CoulCorr2OS_2->GetBinContent(index13L+1)*CoulCorr2OS_2->GetBinContent(index23H+1)*xd;
      double c11 = CoulCorr2SS_2->GetBinContent(index12L+1)*CoulCorr2OS_2->GetBinContent(index13H+1)*CoulCorr2OS_2->GetBinContent(index23H+1)*(1-xd);
      c11 += CoulCorr2SS_2->GetBinContent(index12H+1)*CoulCorr2OS_2->GetBinContent(index13H+1)*CoulCorr2OS_2->GetBinContent(index23H+1)*xd;
      //
      double c0 = c00*(1-yd) + c10*yd;
      double c1 = c01*(1-yd) + c11*yd;
      value2 = (c0*(1-zd) + c1*zd);
    }
    
    if(value1>0 && value2>0){
      return (value1 + (value2-value1)/(2.));// always take the half-way point
      //return (value1 + (Mbin_def-9)*(value2-value1)/(3.));// old way for v5
    }else if(value1>0){
      return value1;
    }else if(value2>0){
      return value2;
    }else return 1.0;
    
  }
  
}

double Gamov(int chargeProduct, double qinv){
  
  double arg = chargeProduct*2.*PI/(BohrR*qinv/2.);
  
  return arg/(exp(arg)-1);
}
void ReadMomResFile(int Mbin){
 
  int MRCindex_L=0, MRCindex_H=0;
  float MRCindex_weight=0;
  if(Mbin<=2) {MRCindex_L=0; MRCindex_H=1; MRCindex_weight = Mbin/2.;}
  else if(Mbin<=6) {MRCindex_L=1; MRCindex_H=2; MRCindex_weight = fabs(Mbin-3)/3.;}
  else if(Mbin<=11) {MRCindex_L=2; MRCindex_H=3; MRCindex_weight = fabs(Mbin-7)/4.;}
  else {MRCindex_L=3; MRCindex_H=4; MRCindex_weight = fabs(Mbin-12)/7.;}
 
  
  TH1D *temp_L[2][5];
  TH1D *temp_H[2][5];
  TH1D *tempC2_L[2];
  TH1D *tempC2_H[2];
  TString *momresfilenameL = new TString("MomResFile_M");
  *momresfilenameL += MRCindex_L;
  momresfilenameL->Append(".root");
  TFile *MomResFileL = new TFile(momresfilenameL->Data(),"READ");
  TString *names1D_L[2][5];// SC/MC, term#
  for(int ChProd=0; ChProd<2; ChProd++){
    for(int term=0; term<5; term++){
      //
      if(ChProd==0) {names1D_L[ChProd][term] = new TString("MRC3_SC_term");}
      else {names1D_L[ChProd][term] = new TString("MRC3_MC_term");}
      *names1D_L[ChProd][term] += term+1;
      temp_L[ChProd][term] = (TH1D*)MomResFileL->Get(names1D_L[ChProd][term]->Data());
      temp_L[ChProd][term]->SetDirectory(0);
      
    }
    TString *C2MRCname=new TString("MomResHisto_");
    if(ChProd==0) C2MRCname->Append("pp");
    else C2MRCname->Append("mp");
    tempC2_L[ChProd]=(TH1D*)(((TH2D*)(MomResFileL->Get(C2MRCname->Data())))->ProjectionY("C2MRCproL",MRC2index,MRC2index));
    tempC2_L[ChProd]->SetDirectory(0);
  }
  
  //
  TString *momresfilenameH = new TString("MomResFile_M");
  *momresfilenameH += MRCindex_H;
  momresfilenameH->Append(".root");
  TFile *MomResFileH = new TFile(momresfilenameH->Data(),"READ");
  TString *names1D_H[2][5];// SC/MC, term#
  for(int ChProd=0; ChProd<2; ChProd++){
    for(int term=0; term<5; term++){
      //
      if(ChProd==0) {names1D_H[ChProd][term] = new TString("MRC3_SC_term");}
      else {names1D_H[ChProd][term] = new TString("MRC3_MC_term");}
      *names1D_H[ChProd][term] += term+1;
      temp_H[ChProd][term] = (TH1D*)MomResFileH->Get(names1D_H[ChProd][term]->Data());
      temp_H[ChProd][term]->SetDirectory(0);
      MomRes1d[ChProd][term] = (TH1D*)MomResFileH->Get(names1D_H[ChProd][term]->Data());
      MomRes1d[ChProd][term]->SetDirectory(0);
    }
    TString *C2MRCname=new TString("MomResHisto_");
    if(ChProd==0) C2MRCname->Append("pp");
    else C2MRCname->Append("mp");
    tempC2_H[ChProd]=(TH1D*)(((TH2D*)(MomResFileH->Get(C2MRCname->Data())))->ProjectionY("C2MRCproH",MRC2index,MRC2index));
    tempC2_H[ChProd]->SetDirectory(0);
    TString *name=new TString("MomResC2_");
    *name += ChProd;
    MomResC2[ChProd] = (TH1D*)(((TH2D*)(MomResFileH->Get(C2MRCname->Data())))->ProjectionY(name->Data(),MRC2index,MRC2index));
    MomResC2[ChProd]->SetDirectory(0);
  }
  
  for(int ChProd=0; ChProd<2; ChProd++){
    // C3 MRC
    for(int term=0; term<5; term++){
      for(int bin=1; bin<=temp_H[ChProd][term]->GetNbinsX(); bin++){
	double value=1;
	if(temp_L[ChProd][term]->GetBinContent(bin)>0 && temp_H[ChProd][term]->GetBinContent(bin)>0){// both have entries
	  value = temp_L[ChProd][term]->GetBinContent(bin) + MRCindex_weight * temp_H[ChProd][term]->GetBinContent(bin);
	}else if(temp_L[ChProd][term]->GetBinContent(bin)>0){
	  value = temp_L[ChProd][term]->GetBinContent(bin);
	}else if(temp_H[ChProd][term]->GetBinContent(bin)>0){
	  value = temp_H[ChProd][term]->GetBinContent(bin);
	}else value=1.0;
	
	MomRes1d[ChProd][term]->SetBinContent(bin,value);
      }
    }
    // C2 MRC
    for(int bin=1; bin<=tempC2_H[ChProd]->GetNbinsX(); bin++){
      double value=1;
      if(tempC2_L[ChProd]->GetBinContent(bin)>0 && tempC2_H[ChProd]->GetBinContent(bin)>0){// both have entries
	value = tempC2_L[ChProd]->GetBinContent(bin)*(1-MRCindex_weight) + MRCindex_weight * tempC2_H[ChProd]->GetBinContent(bin);
      }else if(tempC2_L[ChProd]->GetBinContent(bin)>0){
	value = tempC2_L[ChProd]->GetBinContent(bin);
      }else if(tempC2_H[ChProd]->GetBinContent(bin)>0){
	value = tempC2_H[ChProd]->GetBinContent(bin);
      }else value=1.0;
      MomResC2[ChProd]->SetBinContent(bin,value);
    } 
  }

  for(int ChProd=0; ChProd<2; ChProd++){
    for(int term=0; term<5; term++){
      for(int i=0; i<MomRes1d[0][0]->GetNbinsX(); i++){
	if(SourceType==0 && Mbin<10){
	  if(MomRes1d[ChProd][term]->GetXaxis()->GetBinCenter(i+1) > 0.1) MomRes1d[ChProd][term]->SetBinContent(i+1, 1.0);
	}else if(SourceType==0 && Mbin>=10){
	  if(MomRes1d[ChProd][term]->GetXaxis()->GetBinCenter(i+1) > 0.2) MomRes1d[ChProd][term]->SetBinContent(i+1, 1.0);
	}else{
	  if(MomRes1d[ChProd][term]->GetXaxis()->GetBinCenter(i+1) > 0.5) MomRes1d[ChProd][term]->SetBinContent(i+1, 1.0);
	}

      }
    }
    
  }
  
  MomResFileL->Close();
  MomResFileH->Close();

}
double cubicInterpolate (double p[4], double x) {
  return p[1] + 0.5 * x*(p[2] - p[0] + x*(2.0*p[0] - 5.0*p[1] + 4.0*p[2] - p[3] + x*(3.0*(p[1] - p[2]) + p[3] - p[0])));// Paulinternet
}
double bicubicInterpolate (double p[4][4], double x, double y) {
	double arr[4];
	arr[0] = cubicInterpolate(p[0], y);
	arr[1] = cubicInterpolate(p[1], y);
	arr[2] = cubicInterpolate(p[2], y);
	arr[3] = cubicInterpolate(p[3], y);
	return cubicInterpolate(arr, x);
}
double tricubicInterpolate (double p[4][4][4], double x, double y, double z) {
	double arr[4];
	arr[0] = bicubicInterpolate(p[0], y, z);
	arr[1] = bicubicInterpolate(p[1], y, z);
	arr[2] = bicubicInterpolate(p[2], y, z);
	arr[3] = bicubicInterpolate(p[3], y, z);
	return cubicInterpolate(arr, x);
}
//____________________________________________________________________________________________________
void ReadMuonCorrections(int ct, int mbin){
  TString *name = new TString("MuonCorrection_");
  if(ct==0){// PbPb
    if(mbin<=1) *name += 0;
    else if(mbin<=3) *name += 1;
    else if(mbin<=5) *name += 2;
    else if(mbin<=7) *name += 3;
    else if(mbin<10) *name += 4;
    else *name += 5;
  }else *name += 6;
  name->Append(".root");
  TFile *muonfile=new TFile(name->Data(),"READ");
  C2muonCorrection_SC = (TH1D*)muonfile->Get("C2muonCorrection_SC");
  C2muonCorrection_MC = (TH1D*)muonfile->Get("C2muonCorrection_MC");
  if(SameCharge_def) C3muonCorrection = (TH1D*)muonfile->Get("C3muonCorrection_SC");
  else C3muonCorrection = (TH1D*)muonfile->Get("C3muonCorrection_MC");
  //
  C2muonCorrection_SC->SetDirectory(0);
  C2muonCorrection_MC->SetDirectory(0);
  C3muonCorrection->SetDirectory(0);
  //
  muonfile->Close();
}
//____________________________________________________________________________________________________
void DrawALICELogo(Bool_t prel, Float_t x1, Float_t y1, Float_t x2, Float_t y2)
{
  // revision on July 24th or 25th 2012
  // correct for aspect ratio of figure plus aspect ratio of pad (coordinates are NDC!)
  x2 = x1 + (y2 - y1) * (466. / 523) * gPad->GetWh() * gPad->GetHNDC() / (gPad->GetWNDC() * gPad->GetWw());
  // Printf("%f %f %f %f", x1, x2, y1, y2);
  
  TPad *myPadLogo = new TPad("myPadLogo", "Pad for ALICE Logo", x1, y1, x2, y2);
  myPadLogo->SetLeftMargin(0);
  myPadLogo->SetTopMargin(0);
  myPadLogo->SetRightMargin(0);
  myPadLogo->SetBottomMargin(0);
  myPadLogo->Draw();
  myPadLogo->cd();
  TASImage *myAliceLogo = new TASImage((prel) ? "~/Pictures/2011-Nov-24-ALICE_PRELIMARY_logo_BLACK_small_usage_design.eps" : "~/Pictures/2011-Nov-24-ALICE_PERFORMANCE_logo_BLACK_small_usage_design.eps");
  myAliceLogo->Draw();
}
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