/**************************************************************************
 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
 *                                                                        *
 * Author: The ALICE Off-line Project.                                    *
 * Contributors are mentioned in the code where appropriate.              *
 *                                                                        *
 * Permission to use, copy, modify and distribute this software and its   *
 * documentation strictly for non-commercial purposes is hereby granted   *
 * without fee, provided that the above copyright notice appears in all   *
 * copies and that both the copyright notice and this permission notice   *
 * appear in the supporting documentation. The authors make no claims     *
 * about the suitability of this software for any purpose. It is          *
 * provided "as is" without express or implied warranty.                  *
 **************************************************************************/

/* $Id: AliTRDgtuParam.cxx 28397 2008-09-02 09:33:00Z cblume $ */

////////////////////////////////////////////////////////////////////////////
//                                                                        //
//  Parameters for GTU simulation                                         //
//                                                                        //
//  Author: J. Klein (Jochen.Klein@cern.ch)                               //
//                                                                        //
////////////////////////////////////////////////////////////////////////////

#include <limits>

#include "TROOT.h"
#include "TMath.h"
#include "TMatrix.h"
#include "TDecompLU.h"
#include "TGraphAsymmErrors.h"
#include "TCanvas.h"

#include "AliLog.h"
#include "AliTRDgtuParam.h"
#include "AliTRDgeometry.h"
#include "AliTRDpadPlane.h"

ClassImp(AliTRDgtuParam)

Bool_t AliTRDgtuParam::fgUseGTUconst = kTRUE;
Bool_t AliTRDgtuParam::fgUseGTUmerge = kTRUE;
Bool_t AliTRDgtuParam::fgLimitNoTracklets = kTRUE;
Int_t  AliTRDgtuParam::fgMaxNoTracklets = 62;

// ----- matching windows -----
      Int_t     AliTRDgtuParam::fgDeltaY     = 19;
      Int_t     AliTRDgtuParam::fgDeltaAlpha = 21;
// ----- reference layers -----
      Int_t     AliTRDgtuParam::fgRefLayers[] = { 3, 2, 1 };

// ----- Bin widths (granularity) -----
const Float_t 	AliTRDgtuParam::fgkBinWidthY  = 160e-4;
const Float_t 	AliTRDgtuParam::fgkBinWidthdY = 140e-4;

// ----- Bit widths (used for internal representation) -----
const Int_t 	AliTRDgtuParam::fgkBitWidthY      = 13;
const Int_t 	AliTRDgtuParam::fgkBitWidthdY     = 7;
const Int_t 	AliTRDgtuParam::fgkBitWidthYProj  = 10;
const Int_t 	AliTRDgtuParam::fgkBitExcessY 	  = 4;
const Int_t 	AliTRDgtuParam::fgkBitExcessAlpha = 10;
const Int_t 	AliTRDgtuParam::fgkBitExcessYProj = 2;

// pt higher than the one for smallest possible a != 0
const Int_t    AliTRDgtuParam::fgkPtInfinity      = std::numeric_limits<Int_t>::max();

// ----- geometry constants used in GTU -----
const Bool_t    AliTRDgtuParam::fgZChannelMap[5][16][6][16] = {

{  /* --- Stack 0 --- */

/*  . x x . . . . . . . . . . . . .  */
/*  x . . . . . . . . . . . . . . .  */
/*  X . . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  x . . . . . . . . . . . . . . .  */

{{0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . x x . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  . X . . . . . . . . . . . . . .  */
/*  . x x . . . . . . . . . . . . .  */
/*  . x x . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */

{{0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . x x . . . . . . . . . . .  */
/*  . x x . . . . . . . . . . . . .  */
/*  . . X . . . . . . . . . . . . .  */
/*  . . x x . . . . . . . . . . . .  */
/*  . . x x . . . . . . . . . . . .  */
/*  . x x . . . . . . . . . . . . .  */

{{0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . x x . . . . . . . . . .  */
/*  . . x x . . . . . . . . . . . .  */
/*  . . . X . . . . . . . . . . . .  */
/*  . . . x x . . . . . . . . . . .  */
/*  . . . x x . . . . . . . . . . .  */
/*  . . x x . . . . . . . . . . . .  */

{{0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . x x . . . . . . . . .  */
/*  . . . x x . . . . . . . . . . .  */
/*  . . . . X . . . . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */
/*  . . . x x . . . . . . . . . . .  */

{{0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . x x . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */
/*  . . . . . X . . . . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */

{{0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */
/*  . . . . . . X . . . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . . x x . . . . . .  */
/*  . . . . . . x x x . . . . . . .  */
/*  . . . . . . . X . . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . . x x x . . . . .  */
/*  . . . . . . . x x x . . . . . .  */
/*  . . . . . . . . X . . . . . . .  */
/*  . . . . . . . x x x . . . . . .  */
/*  . . . . . . . x x x . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . . . x x x . . . .  */
/*  . . . . . . . . x x x . . . . .  */
/*  . . . . . . . . . X . . . . . .  */
/*  . . . . . . . . x x x . . . . .  */
/*  . . . . . . . . x x x . . . . .  */
/*  . . . . . . . . x x . . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . . . . x x x . . .  */
/*  . . . . . . . . . x x x . . . .  */
/*  . . . . . . . . . . X . . . . .  */
/*  . . . . . . . . . x x x . . . .  */
/*  . . . . . . . . . x x x . . . .  */
/*  . . . . . . . . . x x . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0}},

/*  . . . . . . . . . . . x x x . .  */
/*  . . . . . . . . . . x x x . . .  */
/*  . . . . . . . . . . . X . . . .  */
/*  . . . . . . . . . . x x x . . .  */
/*  . . . . . . . . . . x x x . . .  */
/*  . . . . . . . . . . x x . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0}},

/*  . . . . . . . . . . . . x x x .  */
/*  . . . . . . . . . . . x x x . .  */
/*  . . . . . . . . . . . . X . . .  */
/*  . . . . . . . . . . . x x x . .  */
/*  . . . . . . . . . . . x x x . .  */
/*  . . . . . . . . . . . x x . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0}},

/*  . . . . . . . . . . . . . x x x  */
/*  . . . . . . . . . . . . x x x .  */
/*  . . . . . . . . . . . . . X . .  */
/*  . . . . . . . . . . . . x x x .  */
/*  . . . . . . . . . . . . x x x .  */
/*  . . . . . . . . . . . . x x . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0}},

/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . x x x  */
/*  . . . . . . . . . . . . . . X .  */
/*  . . . . . . . . . . . . . x x x  */
/*  . . . . . . . . . . . . . x x x  */
/*  . . . . . . . . . . . . . x x .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0}},

/*  . . . . . . . . . . . . . . . x  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . . X  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . x x  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1}}},

{  /* --- Stack 1 --- */

/*  x x x . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  X . . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  x . . . . . . . . . . . . . . .  */

{{1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . x x x . . . . . . . . . . . .  */
/*  x x x . . . . . . . . . . . . .  */
/*  . X . . . . . . . . . . . . . .  */
/*  x x x . . . . . . . . . . . . .  */
/*  x x x . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */

{{0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . x x x . . . . . . . . . . .  */
/*  . x x x . . . . . . . . . . . .  */
/*  . . X . . . . . . . . . . . . .  */
/*  . x x x . . . . . . . . . . . .  */
/*  . x x x . . . . . . . . . . . .  */
/*  . x x . . . . . . . . . . . . .  */

{{0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . x x x . . . . . . . . . .  */
/*  . . x x x . . . . . . . . . . .  */
/*  . . . X . . . . . . . . . . . .  */
/*  . . x x x . . . . . . . . . . .  */
/*  . . x x x . . . . . . . . . . .  */
/*  . . x x . . . . . . . . . . . .  */

{{0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . x x x . . . . . . . . .  */
/*  . . . x x x . . . . . . . . . .  */
/*  . . . . X . . . . . . . . . . .  */
/*  . . . x x x . . . . . . . . . .  */
/*  . . . x x x . . . . . . . . . .  */
/*  . . . x x . . . . . . . . . . .  */

{{0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . x x x . . . . . . . .  */
/*  . . . . x x x . . . . . . . . .  */
/*  . . . . . X . . . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */

{{0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . x x x . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */
/*  . . . . . . X . . . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */

{{0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . X . . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . . x x . . . . . .  */
/*  . . . . . . . . x x . . . . . .  */
/*  . . . . . . . . X . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . . . x x . . . . .  */
/*  . . . . . . . . . x x . . . . .  */
/*  . . . . . . . . . X . . . . . .  */
/*  . . . . . . . . x x . . . . . .  */
/*  . . . . . . . . x x . . . . . .  */
/*  . . . . . . . . x x . . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . . . . x x . . . .  */
/*  . . . . . . . . . . x x . . . .  */
/*  . . . . . . . . . . X . . . . .  */
/*  . . . . . . . . . x x . . . . .  */
/*  . . . . . . . . . x x . . . . .  */
/*  . . . . . . . . . x x . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0}},

/*  . . . . . . . . . . . x x . . .  */
/*  . . . . . . . . . . . x x . . .  */
/*  . . . . . . . . . . . X . . . .  */
/*  . . . . . . . . . . x x . . . .  */
/*  . . . . . . . . . . x x . . . .  */
/*  . . . . . . . . . . x x . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0}},

/*  . . . . . . . . . . . . x x . .  */
/*  . . . . . . . . . . . . x x . .  */
/*  . . . . . . . . . . . . X . . .  */
/*  . . . . . . . . . . . x x . . .  */
/*  . . . . . . . . . . . x x . . .  */
/*  . . . . . . . . . . . x x . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0}},

/*  . . . . . . . . . . . . . x x .  */
/*  . . . . . . . . . . . . . x x .  */
/*  . . . . . . . . . . . . . X . .  */
/*  . . . . . . . . . . . . x x . .  */
/*  . . . . . . . . . . . . x x . .  */
/*  . . . . . . . . . . . . x x . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0}},

/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . X .  */
/*  . . . . . . . . . . . . . x x .  */
/*  . . . . . . . . . . . . . x x .  */
/*  . . . . . . . . . . . . . x x .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0}},

/*  . . . . . . . . . . . . . . . x  */
/*  . . . . . . . . . . . . . . . x  */
/*  . . . . . . . . . . . . . . . X  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . x x  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1}}},

{  /* --- Stack 2 --- */

/*  x x . . . . . . . . . .          */
/*  x x . . . . . . . . . .          */
/*  X . . . . . . . . . . .          */
/*  x . . . . . . . . . . .          */
/*  x . . . . . . . . . . .          */
/*  x . . . . . . . . . . .          */

{{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . x x . . . . . . . . .          */
/*  . x x . . . . . . . . .          */
/*  . X . . . . . . . . . .          */
/*  x x . . . . . . . . . .          */
/*  x x . . . . . . . . . .          */
/*  x x . . . . . . . . . .          */

{{0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . x x . . . . . . . .          */
/*  . . x x . . . . . . . .          */
/*  . . X . . . . . . . . .          */
/*  . x x . . . . . . . . .          */
/*  . x x . . . . . . . . .          */
/*  . x x . . . . . . . . .          */

{{0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . x x . . . . . . .          */
/*  . . . x x . . . . . . .          */
/*  . . . X . . . . . . . .          */
/*  . . x x x . . . . . . .          */
/*  . . x x x . . . . . . .          */
/*  . . x x x . . . . . . .          */

{{0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . x x x . . . . . .          */
/*  . . . x x x . . . . . .          */
/*  . . . . X . . . . . . .          */
/*  . . . x x x . . . . . .          */
/*  . . . x x x . . . . . .          */
/*  . . . x x x . . . . . .          */

{{0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . x x x . . . . .          */
/*  . . . . x x x . . . . .          */
/*  . . . . . X . . . . . .          */
/*  . . . . x x x . . . . .          */
/*  . . . . x x x . . . . .          */
/*  . . . . x x x . . . . .          */

{{0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . x x x . . . .          */
/*  . . . . . x x x . . . .          */
/*  . . . . . . X . . . . .          */
/*  . . . . . x x x . . . .          */
/*  . . . . . x x x . . . .          */
/*  . . . . . x x x . . . .          */

{{0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . x x x . . .          */
/*  . . . . . . x x x . . .          */
/*  . . . . . . . X . . . .          */
/*  . . . . . . x x x . . .          */
/*  . . . . . . x x x . . .          */
/*  . . . . . . x x x . . .          */

{{0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . x x . . .          */
/*  . . . . . . . x x . . .          */
/*  . . . . . . . . X . . .          */
/*  . . . . . . . x x x . .          */
/*  . . . . . . . x x x . .          */
/*  . . . . . . . x x x . .          */

{{0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . . x x . .          */
/*  . . . . . . . . x x . .          */
/*  . . . . . . . . . X . .          */
/*  . . . . . . . . . x x .          */
/*  . . . . . . . . . x x .          */
/*  . . . . . . . . . x x .          */

{{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0}},

/*  . . . . . . . . . x x .          */
/*  . . . . . . . . . x x .          */
/*  . . . . . . . . . . X .          */
/*  . . . . . . . . . . x x          */
/*  . . . . . . . . . . x x          */
/*  . . . . . . . . . . x x          */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0}},

/*  . . . . . . . . . . x x          */
/*  . . . . . . . . . . x x          */
/*  . . . . . . . . . . . X          */
/*  . . . . . . . . . . . x          */
/*  . . . . . . . . . . . x          */
/*  . . . . . . . . . . . x          */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0}},

/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */
/*  . . . . . . . . . . . .          */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}},

{  /* --- Stack 3 --- */

/*  x . . . . . . . . . . . . . . .  */
/*  x . . . . . . . . . . . . . . .  */
/*  X . . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */

{{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  x x . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  . X . . . . . . . . . . . . . .  */
/*  . x x . . . . . . . . . . . . .  */
/*  . x x . . . . . . . . . . . . .  */
/*  . x x . . . . . . . . . . . . .  */

{{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . x x . . . . . . . . . . . . .  */
/*  . x x . . . . . . . . . . . . .  */
/*  . . X . . . . . . . . . . . . .  */
/*  . . x x . . . . . . . . . . . .  */
/*  . . x x . . . . . . . . . . . .  */
/*  . . x x . . . . . . . . . . . .  */

{{0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . x x . . . . . . . . . . . .  */
/*  . . x x . . . . . . . . . . . .  */
/*  . . . X . . . . . . . . . . . .  */
/*  . . . x x . . . . . . . . . . .  */
/*  . . . x x . . . . . . . . . . .  */
/*  . . . x x . . . . . . . . . . .  */

{{0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . x x . . . . . . . . . . .  */
/*  . . . x x . . . . . . . . . . .  */
/*  . . . . X . . . . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */

{{0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . x x . . . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */
/*  . . . . . X . . . . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */

{{0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . x x . . . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */
/*  . . . . . . X . . . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */

{{0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . x x . . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */
/*  . . . . . . . X . . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */

{{0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . . X . . . . . . .  */
/*  . . . . . . . . x x . . . . . .  */
/*  . . . . . . . . x x . . . . . .  */
/*  . . . . . . . . x x . . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . x x x . . . . . .  */
/*  . . . . . . . . x x . . . . . .  */
/*  . . . . . . . . . X . . . . . .  */
/*  . . . . . . . . . x x . . . . .  */
/*  . . . . . . . . . x x . . . . .  */
/*  . . . . . . . . . x x . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0}},

/*  . . . . . . . . x x x . . . . .  */
/*  . . . . . . . . . x x x . . . .  */
/*  . . . . . . . . . . X . . . . .  */
/*  . . . . . . . . . . x x . . . .  */
/*  . . . . . . . . . . x x . . . .  */
/*  . . . . . . . . . . x x . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0}},

/*  . . . . . . . . . x x x . . . .  */
/*  . . . . . . . . . . x x x . . .  */
/*  . . . . . . . . . . . X . . . .  */
/*  . . . . . . . . . . x x x . . .  */
/*  . . . . . . . . . . x x x . . .  */
/*  . . . . . . . . . . . x x . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0}},

/*  . . . . . . . . . . x x x . . .  */
/*  . . . . . . . . . . . x x x . .  */
/*  . . . . . . . . . . . . X . . .  */
/*  . . . . . . . . . . . x x x . .  */
/*  . . . . . . . . . . . x x x . .  */
/*  . . . . . . . . . . . . x x . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0}},

/*  . . . . . . . . . . . x x x . .  */
/*  . . . . . . . . . . . . x x x .  */
/*  . . . . . . . . . . . . . X . .  */
/*  . . . . . . . . . . . . x x x .  */
/*  . . . . . . . . . . . . x x x .  */
/*  . . . . . . . . . . . . . x x .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0}},

/*  . . . . . . . . . . . . x x x .  */
/*  . . . . . . . . . . . . . x x x  */
/*  . . . . . . . . . . . . . . X .  */
/*  . . . . . . . . . . . . . x x x  */
/*  . . . . . . . . . . . . . x x x  */
/*  . . . . . . . . . . . . . . x x  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1}},

/*  . . . . . . . . . . . . . x x x  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . . X  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . . x  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}}},

{  /* --- Stack 4 --- */

/*  x . . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  X . . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */
/*  x x . . . . . . . . . . . . . .  */

{{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  x x . . . . . . . . . . . . . .  */
/*  x x x . . . . . . . . . . . . .  */
/*  . X . . . . . . . . . . . . . .  */
/*  x x x . . . . . . . . . . . . .  */
/*  x x x . . . . . . . . . . . . .  */
/*  . x x . . . . . . . . . . . . .  */

{{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  x x x . . . . . . . . . . . . .  */
/*  . x x x . . . . . . . . . . . .  */
/*  . . X . . . . . . . . . . . . .  */
/*  . x x x . . . . . . . . . . . .  */
/*  . x x x . . . . . . . . . . . .  */
/*  . . x x . . . . . . . . . . . .  */

{{1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . x x x . . . . . . . . . . . .  */
/*  . . x x x . . . . . . . . . . .  */
/*  . . . X . . . . . . . . . . . .  */
/*  . . x x x . . . . . . . . . . .  */
/*  . . x x x . . . . . . . . . . .  */
/*  . . . x x . . . . . . . . . . .  */

{{0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . x x x . . . . . . . . . . .  */
/*  . . . x x x . . . . . . . . . .  */
/*  . . . . X . . . . . . . . . . .  */
/*  . . . x x x . . . . . . . . . .  */
/*  . . . x x x . . . . . . . . . .  */
/*  . . . . x x . . . . . . . . . .  */

{{0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . x x x . . . . . . . . . .  */
/*  . . . . x x x . . . . . . . . .  */
/*  . . . . . X . . . . . . . . . .  */
/*  . . . . x x x . . . . . . . . .  */
/*  . . . . x x x . . . . . . . . .  */
/*  . . . . . x x . . . . . . . . .  */

{{0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . x x x . . . . . . . . .  */
/*  . . . . . x x x . . . . . . . .  */
/*  . . . . . . X . . . . . . . . .  */
/*  . . . . . x x x . . . . . . . .  */
/*  . . . . . x x x . . . . . . . .  */
/*  . . . . . . x x . . . . . . . .  */

{{0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . x x x . . . . . . . .  */
/*  . . . . . . x x x . . . . . . .  */
/*  . . . . . . . X . . . . . . . .  */
/*  . . . . . . x x x . . . . . . .  */
/*  . . . . . . x x x . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */

{{0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . x x . . . . . . . .  */
/*  . . . . . . . x x x . . . . . .  */
/*  . . . . . . . . X . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . . x x . . . . . .  */

{{0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0}},

/*  . . . . . . . x x . . . . . . .  */
/*  . . . . . . . . . x x . . . . .  */
/*  . . . . . . . . . X . . . . . .  */
/*  . . . . . . . . x x . . . . . .  */
/*  . . . . . . . . x x . . . . . .  */
/*  . . . . . . . . . x x . . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0}},

/*  . . . . . . . . x x . . . . . .  */
/*  . . . . . . . . . . x x . . . .  */
/*  . . . . . . . . . . X . . . . .  */
/*  . . . . . . . . . x x . . . . .  */
/*  . . . . . . . . . x x . . . . .  */
/*  . . . . . . . . . . x x . . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0}},

/*  . . . . . . . . . x x . . . . .  */
/*  . . . . . . . . . . . x x . . .  */
/*  . . . . . . . . . . . X . . . .  */
/*  . . . . . . . . . . x x . . . .  */
/*  . . . . . . . . . . x x . . . .  */
/*  . . . . . . . . . . . x x . . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0}},

/*  . . . . . . . . . . x x . . . .  */
/*  . . . . . . . . . . . . x x . .  */
/*  . . . . . . . . . . . . X . . .  */
/*  . . . . . . . . . . . x x . . .  */
/*  . . . . . . . . . . . x x . . .  */
/*  . . . . . . . . . . . . x x . .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0}},

/*  . . . . . . . . . . . x x . . .  */
/*  . . . . . . . . . . . . . x x .  */
/*  . . . . . . . . . . . . . X . .  */
/*  . . . . . . . . . . . . x x . .  */
/*  . . . . . . . . . . . . x x . .  */
/*  . . . . . . . . . . . . . x x .  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0}},

/*  . . . . . . . . . . . . x x . .  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . X .  */
/*  . . . . . . . . . . . . . x x .  */
/*  . . . . . . . . . . . . . x x .  */
/*  . . . . . . . . . . . . . . x x  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1}},

/*  . . . . . . . . . . . . . x x .  */
/*  . . . . . . . . . . . . . . . x  */
/*  . . . . . . . . . . . . . . . X  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . x x  */
/*  . . . . . . . . . . . . . . . x  */

{{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}}}

};
const Float_t   AliTRDgtuParam::fgkRadius[6] = { 300.65, 313.25, 325.85, 338.45, 351.05, 363.65 };
const Float_t   AliTRDgtuParam::fgkThickness = 3.;
const Float_t   AliTRDgtuParam::fgkRow0Pos[6][5] = {
  {301, 177, 53, -57, -181},
  {301, 177, 53, -57, -181},
  {315, 184, 53, -57, -188},
  {329, 191, 53, -57, -195},
  {343, 198, 53, -57, -202},
  {347, 200, 53, -57, -204}
};
const Float_t   AliTRDgtuParam::fgkInnerPadLength[] = {7.5, 7.5, 8.0, 8.5, 9.0, 9.0};
const Float_t   AliTRDgtuParam::fgkOuterPadLength[] = {7.5, 7.5, 7.5, 7.5, 7.5, 8.5};
const Float_t   AliTRDgtuParam::fgkAcoeff[32][6] = {
  {-3440, -3303,  3174,  3057,     0,     0},
  {-3481,     0,  -171,     0,  3140,     0},
  {-2850, -1380,     0,  1277,  2441,     0},
  {-3481,     0,  -171,     0,  3140,     0},
  {    0, -3568, -3431,  3303,  3185,     0},
  {-2783, -1378,  -136,  1275,  2510,     0},
  {-1500, -2857,  1384,     0,     0,  2461},
  {    0, -3609,     0,  -171,     0,  3268},
  {-3685,     0,  3400, -3276,     0,  3049},
  {    0, -3609,     0,  -171,     0,  3268},
  {-1498, -2792,  1382,  -132,     0,  2528},
  {-1850, -1777,     0,     0,  1585,  1531},
  {-3481,     0,  -171,     0,  3140,     0},
  {    0, -2953, -1431,     0,  1328,  2544},
  {-1808, -1776,   -89,     0,  1631,  1530},
  {-2932,     0,     0, -1314,  2511,  1223},
  {    0, -3609,     0,  -171,     0,  3268},
  {-1849, -1738,     0,   -82,  1583,  1574},
  {    0,     0, -3696, -3559,  3431,  3313},
  {-2863,     0,  -140, -1312,  2582,  1221},
  {    0, -2886, -1429,  -136,  1327,  2613},
  {-1806, -1736,   -89,   -82,  1629,  1572},
  {   -1,    -1,    -1,    -1,    -1,    -1},
  {   -1,    -1,    -1,    -1,    -1,    -1},
  {   -1,    -1,    -1,    -1,    -1,    -1},
  {   -1,    -1,    -1,    -1,    -1,    -1},
  {   -1,    -1,    -1,    -1,    -1,    -1},
  {   -1,    -1,    -1,    -1,    -1,    -1},
  {   -1,    -1,    -1,    -1,    -1,    -1},
  {   -1,    -1,    -1,    -1,    -1,    -1},
  {   -1,    -1,    -1,    -1,    -1,    -1},
  {   -1,    -1,    -1,    -1,    -1,    -1}
};
const Int_t     AliTRDgtuParam::fgkMaskID[] = {
  -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,  0,
  -1, -1, -1, -1, -1, -1, -1,  1, -1, -1, -1,  2, -1,  3,  4,  5,
  -1, -1, -1, -1, -1, -1, -1,  6, -1, -1, -1,  7, -1,  8,  9, 10,
  -1, -1, -1, 11, -1, 12, 13, 14, -1, 15, 16, 17, 18, 19, 20, 21
};

AliTRDgtuParam::AliTRDgtuParam() :
  fVertexSize(20.0),
  fCurrTrackletMask(0),
  fMagField(0.5),
  fGeo(0x0)
{
  // default ctor
  fGeo = new AliTRDgeometry();
  for (Int_t iLayer = 0; iLayer < 6; iLayer++) {
    fAki[iLayer] = 0.;
    fBki[iLayer] = 0.;
    fCki[iLayer] = 0.;
  }

  GenerateZChannelMap();
}

AliTRDgtuParam::~AliTRDgtuParam()
{
  // dtor

  delete fGeo;
}

AliTRDgtuParam* AliTRDgtuParam::Instance()
{
  // get (or create) the single instance

  static AliTRDgtuParam instance;
  return &instance;
}

Bool_t AliTRDgtuParam::IsInZChannel(Int_t stack, Int_t layer, Int_t zchannel, Int_t zpos) const
{
  return (fZSubChannel[stack][zchannel][layer][zpos] != 0);
}

Int_t AliTRDgtuParam::GetZSubchannel(Int_t stack, Int_t layer, Int_t zchannel, Int_t zpos) const
{
  return fZSubChannel[stack][zchannel][layer][zpos];
}

Int_t AliTRDgtuParam::GetRefLayer(Int_t refLayerIdx)
{
  // returns the reference layer indexed by refLayerIdx

  if (refLayerIdx >= 0 && refLayerIdx < fgkNRefLayers)
    return fgRefLayers[refLayerIdx];
  else
    return -1;
}

Int_t AliTRDgtuParam::GenerateZChannelMap()
{
  // generate the z-channel map
  // assuming that the tracks come from the vertex
  // +/- fVertexSize in z-direction

  if (fgUseGTUconst) {
    for (Int_t iStack = 0; iStack < fGeo->Nstack(); iStack++) {
      for (Int_t iChannel = 0; iChannel < fGeo->GetRowMax(fgkFixLayer, iStack, 0); iChannel++) {
	for (Int_t iLayer = 0; iLayer < fGeo->Nlayer(); iLayer++) {
	  for (Int_t iRow = 0; iRow < fGeo->GetRowMax(iLayer, iStack, 0); iRow++) {
	    if (fgZChannelMap[iStack][iChannel][iLayer][iRow] != 0) {
	      fZChannelMap[iStack][iChannel][iLayer][iRow] = 1;
	      fZSubChannel[iStack][iChannel % fgkNZChannels][iLayer][iRow] = iChannel / fgkNZChannels + 1;
	    }
	  }
	}
      }
    }

    return kTRUE;
  }
  else {
    Int_t iSec = 0; // sector is irrelevant
    Bool_t collision = kFALSE;

    for (Int_t iStack = 0; iStack < fGeo->Nstack(); iStack++) {

      Float_t x[6] = { 0 };
      Float_t z[6][16] = {{ 0 }};
      Float_t dZ[6][16] = {{ 0 }};

      for (Int_t iLayer = 0; iLayer < fGeo->Nlayer(); iLayer++) {
	AliTRDpadPlane *pp = fGeo->GetPadPlane(iLayer, iStack);
	x[iLayer]  = fGeo->GetTime0(iLayer) - fGeo->CdrHght(); // ???
	for (Int_t iRow = 0; iRow < fGeo->GetRowMax(iLayer, iStack, iSec); iRow++) {
	  z[iLayer][iRow]  = pp->GetRowPos(iRow); // this is the right (pos. z-direction) border of the pad
	  dZ[iLayer][iRow] = pp->GetRowSize(iRow); // length of the pad in z-direction
	  for (Int_t i = 0; i < fgkNZChannels; i++)
	    fZSubChannel[iStack][i][iLayer][iRow] = 0;
	}
      }

      for (Int_t fixRow = 0; fixRow < fGeo->GetRowMax(fgkFixLayer, iStack, iSec); fixRow++) {

	Double_t fixZmin = z[fgkFixLayer][fixRow] - dZ[fgkFixLayer][fixRow];
	Double_t fixZmax = z[fgkFixLayer][fixRow];
	Double_t fixX    = x[fgkFixLayer] + 1.5; // ??? 1.5 from where?

	for (Int_t iLayer = 0; iLayer < fGeo->Nlayer(); iLayer++) {
	  Double_t leftZ, rightZ;

	  if (iLayer <= fgkFixLayer) {
	    leftZ  = (fixZmin + fVertexSize) * (x[iLayer] + 1.5) / fixX - fVertexSize;
	    rightZ = (fixZmax - fVertexSize) * (x[iLayer] + 1.5) / fixX + fVertexSize;
	  }
	  else {
	    leftZ  = (fixZmin - fVertexSize) * (x[iLayer] + 1.5) / fixX + fVertexSize;
	    rightZ = (fixZmax + fVertexSize) * (x[iLayer] + 1.5) / fixX - fVertexSize;
	  }

	  Double_t epsilon = 0.001;
	  for (Int_t iRow = 0; iRow < fGeo->GetRowMax(iLayer, iStack, iSec); iRow++) {
	    if ( (z[iLayer][iRow] )                    > (leftZ  + epsilon) &&
		 (z[iLayer][iRow] - dZ[iLayer][iRow] ) < (rightZ - epsilon) ) {
	      fZChannelMap[iStack][fixRow][iLayer][iRow] = 1;
	      if (fZSubChannel[iStack][fixRow % fgkNZChannels][iLayer][iRow] != 0) {
		AliError("Collision in Z-Channel assignment occured! No reliable tracking!!!");
		collision = kTRUE;
	      }
	      else
		fZSubChannel[iStack][fixRow % fgkNZChannels][iLayer][iRow] = fixRow / fgkNZChannels + 1;
	    }

	  }
	}
      }
    }

    return ~collision;
  }
}

Bool_t AliTRDgtuParam::DisplayZChannelMap(Int_t zchannel, Int_t subchannel) const
{
  // display the z-channel map

  if (zchannel >= fgkNZChannels) {
    AliError("Invalid Z channel!");
    return kFALSE;
  }

  Int_t zchmin = zchannel >= 0 ? zchannel : 0;
  Int_t zchmax = zchannel >= 0 ? zchannel + 1 : fgkNZChannels;
  Int_t i = 0;
  Int_t j = 0;
  TCanvas *c = new TCanvas("zchmap", "Z-Chhannel Mapping");
  c->cd();
  TGraph **graphz = new TGraph*[fgkNZChannels];
  for (Int_t zch = zchmin; zch < zchmax; zch++)
    graphz[zch] = new TGraph;
  TGraphAsymmErrors *graph = new TGraphAsymmErrors();
  graph->SetTitle("Z-Channel Map");
  graph->SetPoint(i, 0, 0); // vertex
  graph->SetPointError(i++, 20, 20, 0, 0);
  //  graph->SetRange //????
  for (Int_t iLayer = 0; iLayer < fGeo->Nlayer(); iLayer++) {
    for (Int_t iStack = 0; iStack < fGeo->Nstack(); iStack++) {
      AliTRDpadPlane *pp = fGeo->GetPadPlane(iLayer, iStack);
      for (Int_t iRow = 0; iRow < fGeo->GetRowMax(iLayer, iStack, 0); iRow++) {
	graph->SetPoint(i, pp->GetRowPos(iRow), fGeo->GetTime0(iLayer) - fGeo->CdrHght());
	graph->SetPointError(i++, pp->GetRowSize(iRow), 0, 0, 0);
	for (Int_t zch = zchmin; zch < zchmax; zch++)
	  if (fZSubChannel[iStack][zch][iLayer][iRow] != 0)
	    if (subchannel == 0 || fZSubChannel[iStack][zch][iLayer][iRow] == subchannel)
	      graphz[zch]->SetPoint(j++, pp->GetRowPos(iRow)  - pp->GetRowSize(iRow)/2, fGeo->GetTime0(iLayer) - fGeo->CdrHght());
      }
    }
  }
  graph->SetMarkerStyle(kDot);
  graph->Draw("AP");
  gROOT->Add(graph);
  for (Int_t zch = zchmin; zch < zchmax; zch++) {
    graphz[zch]->SetMarkerStyle(kCircle);
    graphz[zch]->SetMarkerColor(zch+2);
    graphz[zch]->SetMarkerSize(0.3 + zch*0.2);
    graphz[zch]->Draw("P");
    gROOT->Add(graphz[zch]);
  }
  delete [] graphz;
  return kTRUE;
}

Int_t AliTRDgtuParam::GetCiAlpha(Int_t layer) const
{
  // get the constant for the calculation of alpha

  Int_t ci = TMath::Nint(GetChamberThickness() / fGeo->GetTime0(layer) * GetBinWidthY() / GetBinWidthdY() * (1 << (GetBitExcessAlpha() + GetBitExcessY() + 1)) );
  return ci;
}

Int_t AliTRDgtuParam::GetCiYProj(Int_t layer) const
{
  // get the constant for the calculation of y_proj

  Int_t ci = 0;

  if (fgUseGTUconst) {
    Float_t xmid = (fgkRadius[0] + fgkRadius[5]) / 2.;
    ci = TMath::Nint(- (fgkRadius[layer] - xmid) * fgkBinWidthdY / (fgkBinWidthY * fgkThickness) * (1 << GetBitExcessYProj()));
  } else {
    Float_t xmid = (fGeo->GetTime0(0) + fGeo->GetTime0(fGeo->Nlayer()-1)) / 2.;
    ci = TMath::Nint(- (fGeo->GetTime0(layer) - xmid) / GetChamberThickness() * GetBinWidthdY() / GetBinWidthY() * (1 << GetBitExcessYProj()) );
  }

  return ci;
}

Int_t AliTRDgtuParam::GetYt(Int_t stack, Int_t layer, Int_t zrow) const
{
  // return yt for the calculation of y'

  Int_t yt = 0;

  if (fgUseGTUconst) {
    yt = TMath::Nint (- ( (layer % 2 ? 1. : -1.) *
			  GetZrow(stack, layer, zrow) * TMath::Tan(- 2./180. * TMath::Pi()) / fgkBinWidthY ));
  } else {
    yt = TMath::Nint (- ( (layer % 2 ? 1. : -1.) *
			  (GetGeo()->GetPadPlane(layer, stack)->GetRowPos(zrow) - GetGeo()->GetPadPlane(layer, stack)->GetRowSize(zrow) / 2.) *
			  TMath::Tan(- 2./180. * TMath::Pi()) ) / fgkBinWidthY );
  }

  return yt;
}

Bool_t AliTRDgtuParam::GenerateRecoCoefficients(Int_t trackletMask)
{
  // calculate the coefficients for the straight line fit
  // depending on the mask of contributing tracklets

  fCurrTrackletMask = trackletMask;

  TMatrix a(GetNLayers(), 3);
  TMatrix b(3, GetNLayers());
  TMatrix c(3, 3);

  for (Int_t layer = 0; layer < GetNLayers(); layer++) {
      if ( (trackletMask & (1 << layer)) == 0) {
	  a(layer, 0) = 0;
	  a(layer, 1) = 0;
	  a(layer, 2) = 0;
      }
      else {
	  a(layer, 0) = 1;
	  a(layer, 1) = fGeo->GetTime0(layer);
	  a(layer, 2) = (layer % 2 ? 1 : -1) * fGeo->GetTime0(layer);
      }
  }

  b.Transpose(a);
  c = b * a;
  c.InvertFast();
  b = c * b;

  for (Int_t layer = 0; layer < GetNLayers(); layer++) {
      fAki[layer] = b.GetMatrixArray()[layer];
      fBki[layer] = b.GetMatrixArray()[GetNLayers() + layer];
      fCki[layer] = b.GetMatrixArray()[2 * GetNLayers() + layer];
    }
  return kTRUE;
}

Int_t AliTRDgtuParam::GetAki(Int_t k, Int_t i)
{
  // get A_ki for the calculation of the tracking parameters
  if (fgUseGTUconst) {
    Int_t maskId = fgkMaskID[k];
    return fgkAcoeff[maskId][i];
  } else {
    if (fCurrTrackletMask != k)
      GenerateRecoCoefficients(k);
    return -(((Int_t) fAki[i]) << 9);
  }
}

Float_t AliTRDgtuParam::GetBki(Int_t k, Int_t i)
{
  // get B_ki for the calculation of the tracking parameters

  if (fCurrTrackletMask != k)
    GenerateRecoCoefficients(k);

  return fBki[i];
}

Float_t AliTRDgtuParam::GetCki(Int_t k, Int_t i)
{
  // get B_ki for the calculation of the tracking parameters

  if (fCurrTrackletMask != k)
    GenerateRecoCoefficients(k);

  return fCki[i];
}

/*
Float_t AliTRDgtuParam::GetD(Int_t k) const
{
  // get the determinant for the calculation of the tracking parameters

  TMatrix t(3, 3);
  for (Int_t i = 0; i < GetNLayers(); i++) {
    if ( !((k >> i) & 0x1) )
      continue;
    Float_t xi = fGeo->GetTime0(i);
    t(0,0) += 1;
    t(1,0) += xi;
    t(2,0) += TMath::Power(-1, i) * xi;
    t(0,1) += xi;
    t(1,1) += TMath::Power(xi, 2);
    t(2,1) += TMath::Power(-1, i) * TMath::Power(xi, 2);
    t(0,2) += TMath::Power(-1, i) * xi;
    t(1,2) += TMath::Power(-1, i) * TMath::Power(xi, 2);
    t(2,2) += TMath::Power(xi, 2);
  }
  return t.Determinant();
}

Bool_t AliTRDgtuParam::GetFitParams(TVectorD& rhs, Int_t k)
{
  // calculate the fitting parameters
  // will be changed!

  TMatrix t(3,3);
  for (Int_t i = 0; i < GetNLayers(); i++) {
    if ( !((k >> i) & 0x1) )
      continue;
    Float_t xi = fGeo->GetTime0(i);
    t(0,0) += 1;
    t(1,0) += xi;
    t(2,0) += TMath::Power(-1, i) * xi;
    t(0,1) += xi;
    t(1,1) += TMath::Power(xi, 2);
    t(2,1) += TMath::Power(-1, i) * TMath::Power(xi, 2);
    t(0,2) -= TMath::Power(-1, i) * xi;
    t(1,2) -= TMath::Power(-1, i) * TMath::Power(xi, 2);
    t(2,2) -= TMath::Power(xi, 2);
  }
  TDecompLU lr(t);
  lr.Solve(rhs);
  return lr.Decompose();
}
*/

Bool_t AliTRDgtuParam::GetIntersectionPoints(Int_t k, Float_t &x1, Float_t &x2)
{
  // get the x-coord. of the assumed circle/straight line intersection points

  Int_t l1 = -1;
  Int_t l2 = -1;
  Int_t nHits = 0;
  for (Int_t layer = 0; layer < GetNLayers(); layer++) {
    if ( (k >> layer) & 0x1 ) {
      if (l1 < 0)
	l1 = layer;
      l2 = layer;
      nHits++;
    }
  }

  if ( (l1 >= 0) && (l2 >= 0) ) {
    x1 = fGeo->GetTime0(l1) + 10./6 * (nHits -1);
    x2 = fGeo->GetTime0(l2) - 10./6 * (nHits -1);
    return kTRUE;
  }
  else
    return kFALSE;
}

Int_t AliTRDgtuParam::GetPt(Int_t layerMask, Int_t a, Float_t /* b */, Float_t x1, Float_t x2, Float_t magField)
{
  // returns 0.3 * B * 1/a (1/128 GeV/c)
  // a : offset, b : slope (not used)

  // protect against division by zero, covers both cases
  if ((a >> 2) == 0)
    return fgkPtInfinity;

  if (fgUseGTUconst) {
    //----- calculation as in the GTU ----
    const Int_t maskIdLut[64] = {
      -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,  0,
      -1, -1, -1, -1, -1, -1, -1,  1, -1, -1, -1,  2, -1,  3,  4,  5,
      -1, -1, -1, -1, -1, -1, -1,  6, -1, -1, -1,  7, -1,  8,  9, 10,
      -1, -1, -1, 11, -1, 12, 13, 14, -1, 15, 16, 17, 18, 19, 20, 21
    };

    const Int_t c1Lut[32] = {
      -2371, -2474, -2474, -2474, -2563, -2448, -2578, -2578,
      -2578, -2670, -2557, -2578, -2578, -2670, -2557, -2578,
      -2670, -2557, -2763, -2557, -2644, -2523,    -1,    -1,
      -1,    -1,    -1,    -1,    -1,    -1,    -1,    -1
    };

    Int_t layerMaskId = maskIdLut[layerMask];
    Int_t c1 = c1Lut[layerMaskId];
    Int_t c1Ext = c1 << 8;
    Int_t ptRawStage4 = c1Ext / (a >> 2);
    Int_t ptRawComb4 = ptRawStage4;
    Int_t ptExtComb4 = (ptRawComb4 > 0) ? ptRawComb4 + 33 : ptRawComb4 - 30;

    return ((Int_t) ptExtComb4/2);
  }
  else {
    //----- simple calculation -----
    Float_t c1 = x1 * x2 / 2. / 10000.; // conversion cm to m
    Float_t r = 0;
    if ( (a >> 1) != 0)
      r = (0.3 * magField / 2. / (fgkBinWidthY/100.)) * (((Int_t) c1) << 8) / (a >> 1); //??? why shift of a?

    Int_t pt = (Int_t) (2 * r);
    if (pt >= 0)
      pt += 32;
    else
      pt -= 29;
    pt /= 2;
    return pt;
  }
}