grcc.cc

// { ( [
//**************************************************************
// grcc.cc

/* #[ License : */
/*
 *   Copyright (C) 2023-2026 T. Kaneko
 *   When using this file you are requested to refer to the publication
 *   Comput.Phys.Commun. 92 (1995) 127-152
 *
 *   This file is part of FORM.
 *
 *   FORM is free software: you can redistribute it and/or modify it under the
 *   terms of the GNU General Public License as published by the Free Software
 *   Foundation, either version 3 of the License, or (at your option) any later
 *   version.
 *
 *   FORM is distributed in the hope that it will be useful, but WITHOUT ANY
 *   WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 *   FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more
 *   details.
 *
 *   You should have received a copy of the GNU General Public License along
 *   with FORM.  If not, see <http://www.gnu.org/licenses/>.
 */
/* #] License : */

#ifndef NOFORM
extern "C" {
#include "form3.h"
}
#endif

#include <iostream>
#include <iomanip>
#include <sstream>
#include <cstdio>
#include <stdlib.h>
#include <string.h>
#include <time.h>

//==============================================================
// new default values of options
// #define OLDDEFAULT

// new function for the output in python format
// #define NEWOUTPY

//==============================================================
// For debugging
//
// #define MONITOR     // in graph elimination
// #define CHECK       // check consistency

//==============================================================
// optimization : best combination depends on process by process
#define SIMPSEL

// optimization : lower and upper bound of deg of target node of connection.
#define MINMAXLEG

// optimization : optimization with respect to 'extonly' particles
#define OPTEXTONLY

// check unique interaction by name or by code
#define UNIQINTR

// possible extensions of the program
// #define ORBITS

// reverse direction of an edge of agraph when anti-particle flows on it.
// In this case the direction of edges will be diffrent
// from ones of original mgraph.
// #define EDGEPORDER

//--------------------------------------------------------------
#include "grcc.h"

#ifdef GRCC_NAMESPACE
using namespace Grcc;
#endif

#define MAXSTR   1024

//--------------------------------------------------------------
// Macro functions
#define CLWIGHTD(x)   (5*(x))
#define CLWIGHTO(x)   (3*(x)-2)
#define MAXSTRLEN      81

#define MASK(n)       ((1ul) << (n))

#define BOOLSTR(x) ((x) ? "True" : "False")

//--------------------------------------------------------------
// Static variables

static OptDef optDef0[] = {
 {"Step",       "Generate particle assigned graphs",               GRCC_AGraph, 0},
 {"Outgrf",     "Output to file (out.grf)",                              False, 0},
 {"Outgrp",     "Output to file (out.grp)",                              False, 0},
 {"OPI",        "Only 1PI graphs",                                       True , 0},
 {"NoSelfLoop", "Exclude graphs with loops consist of 1 edge",           True , 0},
 {"NoTadpole",  "Exclude graphs with tadpoles (2 edge connected)",       True , 0},
 {"No1PtBlock", "Exclude graphs with tadpole blocks (2 node connected)", False, 0},
 {"No2PtL1PI",  "Exclude graphs with 2-point subgraphs",                 False, 0},
 {"NoExtSelf",  "Exclude graphs with 2-pt subgraphs at ext. particles",  False, 0},
 {"NoAdj2PtV",  "Exclude graphs with an edge connecting 2-pt vertices",  False, 0},
 {"Block",      "Exclude graphs with more than one block",               False, 0},
 {"NoMultiEdge","Exclude graphs with multi-edges",                       False, 0},
 {"SymmInitial","Symmetrize initial particles",                          False, 0},
 {"SymmFinal",  "Symmetrize final particles",                            False, 0},
};
static OptDef optDef1[] = {
 {"Step",       "Generate particle assigned graphs",               GRCC_AGraph, 0},
 {"Outgrf",     "Ouput to file (out.grf)",                               False, 0},
 {"Outgrp",     "Ouput to file (out.grp)",                               False, 0},
 {"OPI",        "Only 1PI graphs",                                       False, 0},
 {"NoSelfLoop", "Exclude graphs with loops consist of 1 edge",           False, 0},
 {"NoTadpole",  "Exclude graphs with tadpoles (2 edge connected)",       False, 0},
 {"No1PtBlock", "Exclude graphs with tadpole blocks (2 node connected)", False, 0},
 {"No2PtL1PI",  "Exclude graphs with 2-point subgraphs",                 False, 0},
 {"NoExtSelf",  "Exclude graphs with 2-pt subgraphs at ext. particles",  False, 0},
 {"NoAdj2PtV",  "Exclude graphs with an edge connecting 2-pt vertices",  False, 0},
 {"Block",      "Exclude graphs with more than one block",               False, 0},
 {"NoMultiEdge","Exclude graphs with multi-edges",                       False, 0},
 {"SymmInitial","Symmetrize initial particles",                          False, 0},
 {"SymmFinal",  "Symmetrize final particles",                            False, 0},
};
#ifdef OLDDEFAULT
static OptDef *optDef = &(optDef0[0]);
static int nOptDef = sizeof(optDef0)/sizeof(OptDef);
#else
static OptDef *optDef = &(optDef1[0]);
static int nOptDef = sizeof(optDef1)/sizeof(OptDef);
#endif

    
static OptQGDef optQGDef[] = {
 {"onepi",      "onepr",    "one-particle illreducible"},
 {"onshell",    "offshell", "without self-energy part at external particles"},
 {"nosigma",    "sigma",    "no 2-point functions"},
 {"nosnail",    "snail",    "without snail"},
 {"notadpole",  "tadpole",  "without tadpole"},
 {"simple",     "notsimple", "without self-loop nor multi-edge"},
 {"bipart",     "nonbipart", "only bipartite graph"},
 {"cycli",      "cyclr",     "???"},
 {"floop",      "",          "without fermion loops of odd length"},
#ifdef GRCC_QGRAF_OPT_TOPOL
 {"topol",      "?",         "topology"},
#endif
};

static int nOptQGDef = sizeof(optQGDef)/sizeof(OptQGDef);
    
static int      prlevel = 2;
static ErExit  *erExit  = NULL;
static void    *erExitArg  = NULL;

//**************************************************************
// Utility functions
//==============================================================

static void   grcc_fprintf(FILE* out, const char* fmt, ...);
static void   erEnd(const char *msg);
static Bool   nextPart(int nelem, int nclist, int *clist, int *nl, int *r);
static void   prilist(int n, const int *a, const char *msg);
static int   *newArray(int size, int val);
static int   *deleteArray(int *a);
static int  **newMat(int n0, int n1, int val);
static int  **deleteMat(int **m, int n0);
static void   prIntArray(int n, int *p, const char *msg);
static void   prIntArrayErr(int n, int *p, const char *msg);
static int   *intdup(int n, int *v);
static int   *delintdup(int *v);
static void   bsort(int n, int *ord, int *a);
static void   sorti(int n, int *a);
static int    sortb(int n, int *a);
static int    toSList(int n, int *a);
static int    intSetAdd(int n, int *a, int v, const int size);
static int    intSListAdd(int n, int *a, int v, const int size);
static int    cmpArray(int na, int *a, int nb, int *b);
static Bool   leqArray(int n, int *a, int *b);
static void   prMomStr(int mom, const char *ms, int mn);
static void   listDiff(int na, int *a, int nb, int *b, int *np, int *p, int *nq, int *q, int *nr, int *r);
static Bool   isSubSList(int na, int *a, int nb, int *b);
static int    subtrSet(int na, int *a, int nb, int *b, int *c, int size);
static int    nextPerm(int nelem, int nclass, int *cl, int *r, int *q, int *p, int count);
static BigInt ipow(int n, int p);
static BigInt factorial(int n);

// for debugging
#ifdef CHECK
static Bool   isIn(int n, int *a, int v);
#endif

//==============================================================
// class Options
//--------------------------------------------------------------
Options::Options(void)
{
    if (nOptDef != GRCC_OPT_Size) {
        grcc_fprintf(GRCC_Stderr, "*** Options: inconsistent default values\n");
        grcc_fprintf(GRCC_Stderr, "nOptDef=%d, GRCC_OPT_Size=%d\n",
                nOptDef, GRCC_OPT_Size);
        GRCC_ABORT();
    }
    
    model  = NULL;
    proc   = NULL;
    sproc  = NULL;

    outmg  = NULL;
    endmg  = NULL;
    outag  = NULL;

    argmg  = NULL;
    argemg = NULL;
    argag  = NULL;

    setDefaultValues();

    // QGraf options
    if (nOptQGDef != GRCC_QGRAF_OPT_Size) {
        grcc_fprintf(GRCC_Stderr, "*** Options: inconsistent default values\n");
        grcc_fprintf(GRCC_Stderr, "nOptQGDef=%d, GRCC_QGRAF_OPT_Size=%d\n",
                nOptQGDef, GRCC_QGRAF_OPT_Size);
        GRCC_ABORT();
    }
    nqgopt = 0;
    for (int j = 0; j < nOptQGDef; j++) {
        qgref[nqgopt].name  = optQGDef[j].name;
        qgref[nqgopt].index = j;
        qgref[nqgopt].sign  = +1;
        nqgopt++;
        if (strlen(optQGDef[j].cname) > 0) {
            qgref[nqgopt].name  = optQGDef[j].cname;
            qgref[nqgopt].index = j;
            qgref[nqgopt].sign  = -1;
            nqgopt++;
        }
    }

    // default values
    for (int j = 0; j < GRCC_QGRAF_OPT_Size; j++) {
        qgopt[j] = 0;
    }

    // for output
    out   = new Output(this);

    // subrpocess
    sproc = NULL;

    // measuring time
    time0  = 0.0;
    time1  = 0.0;
}

//--------------------------------------------------------------
Options::~Options(void)
{
    outmg = NULL;
    outag = NULL;

    argmg = NULL;
    argag = NULL;

    delete out;
}

//--------------------------------------------------------------
void Options::setDefaultValues(void)
{
    int j;

    // default values
    for (j = 0; j < GRCC_OPT_Size; j++) {
        values[j] = optDef[j].defaultv;
    }

    values[GRCC_OPT_Step] = GRCC_AGraph;

    // print level
    prlevel = 1;
}

//--------------------------------------------------------------
void Options::setOldDefaultValues(void)
{
    int j;

    // default values
    for (j = 0; j < GRCC_OPT_Size; j++) {
        values[j] = optDef0[j].defaultv;
    }

    values[GRCC_OPT_Step] = GRCC_AGraph;

    // print level
    prlevel = 1;
}

//--------------------------------------------------------------
void Options::setOutMG(OutEGB *omg, void *pt)
{
    outmg = omg;
    argmg = pt;
}

//--------------------------------------------------------------
void Options::setEndMG(OutEGB *emg, void *pt)
{
    endmg  = emg;
    argemg = pt;
}

//--------------------------------------------------------------
void Options::setOutAG(OutEG *oag, void *pt)
{
    outag = oag;
    argag = pt;
}

//--------------------------------------------------------------
void Options::setErExit(ErExit *ere, void *erearg)
{
    erExit    = ere;
    erExitArg = erearg;
}

//--------------------------------------------------------------
void Options::printLevel(int l)
{
    prlevel = l;
}

//--------------------------------------------------------------
void Options::setValue(int ind, int val)
{
    if (0 <= ind && ind < GRCC_OPT_Size) {
        values[ind] = val;
    } else {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** Options::setValue : invalid index=%d ",
                    ind);
            grcc_fprintf(GRCC_Stderr, "(val=%d)\n", val);
        }
        erEnd("Options::setValue : invalid index");
    }
}

//--------------------------------------------------------------
int Options::getValue(int ind)
{
    if (0 <= ind && ind < GRCC_OPT_Size) {
        return values[ind];
    } else {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** Options::getValue : invalid index=%d\n", ind);
        }
        erEnd("Options::getValue : invalid index");
    }
    return -1;
}

//--------------------------------------------------------------
void Options::setQGrafOpt(int *qg)
{
    // reset options : default is to generate all connected graphs

#ifdef OLDDEFAULT
    values[GRCC_OPT_1PI]         = False;
    values[GRCC_OPT_NoSelfLoop]  = False;
    values[GRCC_OPT_NoTadpole]   = False;
    values[GRCC_OPT_No1PtBlock]  = False;
    values[GRCC_OPT_No2PtL1PI]   = False;
    values[GRCC_OPT_NoExtSelf]   = False;
    values[GRCC_OPT_NoAdj2PtV]   = False;
    values[GRCC_OPT_Block]       = False;
    values[GRCC_OPT_SymmInitial] = False;
    values[GRCC_OPT_SymmFinal]   = False;
#endif

    for (int j = 0; j < GRCC_QGRAF_OPT_Size; j++) {
        qgopt[j] = qg[j];
    }

    // {"onepi", "onepr"},
    if (qgopt[GRCC_QGRAF_OPT_ONEPI] > 0) {   
        values[GRCC_OPT_1PI] = True;
    } else if (qgopt[GRCC_QGRAF_OPT_ONEPI] < 0) {
        values[GRCC_OPT_1PI] = False;
    }

    // {"onshell", "offshell"}
    if (qgopt[GRCC_QGRAF_OPT_ONSHELL] > 0) {
        values[GRCC_OPT_NoExtSelf] = 1;
    } else if (qgopt[GRCC_QGRAF_OPT_ONSHELL] < 0) {
        values[GRCC_OPT_NoExtSelf] = 0;
    }

    // {"nosigma", "sigma"}

    // {"nosnail",    "snail"},
    if (qgopt[GRCC_QGRAF_OPT_NOSNAIL] > 0) {
        values[GRCC_OPT_NoTadpole]  = True;
        values[GRCC_OPT_No1PtBlock] = True;
    } else if (qgopt[GRCC_QGRAF_OPT_NOSNAIL] < 0) {
        values[GRCC_OPT_NoTadpole]  = False;
        values[GRCC_OPT_No1PtBlock] = False;
    }

    // {"notadpole", "tadpole"}
    if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] > 0) {
        values[GRCC_OPT_NoTadpole] = True;
    } else if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] < 0) {
        values[GRCC_OPT_NoTadpole] = False;
    }

    // {"simple",     "notsimple"},
    if (qgopt[GRCC_QGRAF_OPT_SIMPLE] > 0) {
        values[GRCC_OPT_NoSelfLoop]  = True;
        values[GRCC_OPT_NoMultiEdge] = True;
    } else if (qgopt[GRCC_QGRAF_OPT_SIMPLE] < 0) {
        values[GRCC_OPT_NoSelfLoop]  = False;
        values[GRCC_OPT_NoMultiEdge] = False;
    }

    // {"bipart",     "nonbipart"},
    // {"cycli",      "cyclr"},

#ifdef GRCC_QGRAF_OPT_TOPOL
    // {"topol",     ""},
    if (qgopt[GRCC_QGRAF_OPT_TOPOL] > 0) {
        values[GRCC_OPT_SymmInitial] = True;
        values[GRCC_OPT_SymmFinal]   = True;
    }
#endif
}

//--------------------------------------------------------------
void Options::print(void)
{
    int j;
    
    grcc_fprintf(GRCC_Stdout, "Options\n");
    grcc_fprintf(GRCC_Stdout, "+++ GRCC_OPT_Size=%d, print level=%d: ",
           GRCC_OPT_Size, prlevel);
    grcc_fprintf(GRCC_Stdout, "symbol = value (default)\n");
    for (j=0; j < GRCC_OPT_Size; j++) {
        grcc_fprintf(GRCC_Stdout, "   %4d GRCC_OPT_%-15s = %2d (%2d)\n", 
               j, optDef[j].name, values[j], optDef[j].defaultv);
    }
    grcc_fprintf(GRCC_Stdout, "    outgrf=%s, outgrp=%s\n", out->outgrf, out->outgrp);
    grcc_fprintf(GRCC_Stdout, "    GRCC_QGRAF_OPT_Size=%d:\n", GRCC_QGRAF_OPT_Size);
    for (j=0; j < GRCC_QGRAF_OPT_Size; j++) {
        grcc_fprintf(GRCC_Stdout, "   %4d %-10s = %2d\n", j, optQGDef[j].name, qgopt[j]);
    }
}

//--------------------------------------------------------------
const OptDef *Options::getDef(void)
{
    return optDef;
}

//--------------------------------------------------------------
const OptDef *Options::getOldDef(void)
{
    return optDef0;
}

//--------------------------------------------------------------
const OptQGDef *Options::getQGDef(void)
{
    return optQGDef;
}

//--------------------------------------------------------------
void Options::setOutputF(Bool outf, const char *fname)
{
    values[GRCC_OPT_Outgrf] = outf;
    out->setOutgrf(fname);
}

//--------------------------------------------------------------
void Options::setOutputP(Bool outp, const char *fname)
{
    values[GRCC_OPT_Outgrp] = outp;
    out->setOutgrp(fname);
}

//--------------------------------------------------------------
void Options::printModel(void)
{
    if (prlevel > 0) {
        if (model != NULL) {
            model->prModel();
        } else {
            grcc_fprintf(GRCC_Stdout, "*** model is not defined\n");
        }
    }
}

//--------------------------------------------------------------
void Options::outModel(void)
{
    if (out != NULL && model != NULL) {
        out->outModelF();
        out->outModelP();
    }
}

//--------------------------------------------------------------
void Options::begin(Model *mdl)
{
    model = mdl;
    if (out != NULL) {
        if (values[GRCC_OPT_Outgrf]) {
            out->outBeginF(model, values[GRCC_OPT_Outgrf]);
            if (model != NULL) {
                out->outModelF();
            }
        }
        if (values[GRCC_OPT_Outgrp]) {
            out->outBeginP(model, values[GRCC_OPT_Outgrp]);
            if (model != NULL) {
                out->outModelP();
            }
        }
    }
}

//--------------------------------------------------------------
void Options::end(void)
{
    if (prlevel > 1) {
        grcc_fprintf(GRCC_Stdout, "Optimization: ");
#ifdef SIMPSEL
        grcc_fprintf(GRCC_Stdout, "SIMPSEL=1 ");
#else
        grcc_fprintf(GRCC_Stdout, "SIMPSEL=0 ");
#endif
#ifdef MINMAXLEG
        grcc_fprintf(GRCC_Stdout, "MINMAXLEG=1 ");
#else
        grcc_fprintf(GRCC_Stdout, "MINMAXLEG=0 ");
#endif
#ifdef OPTEXTONLY
        grcc_fprintf(GRCC_Stdout, "OPTEXTONLY=1 ");
#else
        grcc_fprintf(GRCC_Stdout, "OPTEXTONLY=0 ");
#endif
        grcc_fprintf(GRCC_Stdout, "\n");
    }

    if (out != NULL && values[GRCC_OPT_Outgrf]) {
        out->outEndF();
    }
    if (out != NULL && values[GRCC_OPT_Outgrp]) {
        out->outEndP();
    }
    model = NULL;
}
//
//--------------------------------------------------------------
void Options::beginProc(Process *prc)
{
    proc = prc;
    if (out != NULL && values[GRCC_OPT_Outgrf]) {
        out->outProcBeginF(prc);
    }
    if (out != NULL && values[GRCC_OPT_Outgrp]) {
        out->outProcBeginP(prc);
    }
    if (proc != NULL) {
        proc->mgrcount = 0;
        proc->agrcount = 0;
    }
}

//--------------------------------------------------------------
void Options::endProc(void)
{
    int k;

    if (proc == NULL) {
        if (out != NULL && values[GRCC_OPT_Outgrf]) {
            out->outProcEndF();
        }
        if (out != NULL && values[GRCC_OPT_Outgrp]) {
            out->outProcEndP();
        }
        return;
    }
    if (prlevel > 0) {
        grcc_fprintf(GRCC_Stdout, "\n");
        grcc_fprintf(GRCC_Stdout, "+++ Proc %d: ext=%d, loop=%d, ",
               proc->id, proc->nExtern, proc->loop);
        if (model != NULL) {
            grcc_fprintf(GRCC_Stdout, "order=");
            prIntArray(model->ncouple, proc->clist, ": ");
            model->prParticleArray(proc->ninitl, proc->initlPart, "-->");
            model->prParticleArray(proc->nfinal, proc->finalPart, "");
        }
        grcc_fprintf(GRCC_Stdout, " (%8.2f sec)\n", proc->sec);
    
    
        grcc_fprintf(GRCC_Stdout, "    Proc    %d: Total M-Graphs=%ld, M-Graphs=",
               proc->id, proc->nMGraphs);
        proc->wMGraphs.print(" (Conn)\n");

        grcc_fprintf(GRCC_Stdout, "    Proc    %d: Total M-Graphs=%ld, M-Graphs=",
               proc->id, proc->nMOPI);
        proc->wMOPI.print(" (1PI)\n");
    
        grcc_fprintf(GRCC_Stdout, "    Proc    %d: Total A-Graphs=%ld, A-Graphs=",
               proc->id, proc->nAGraphs);
        proc->wAGraphs.print(" (Conn)\n");

        grcc_fprintf(GRCC_Stdout, "    Proc    %d: Total A-Graphs=%ld, A-Graphs=",
               proc->id, proc->nAOPI);
        proc->wAOPI.print(" (1PI)\n");

        grcc_fprintf(GRCC_Stdout, "#  { %d,{", proc->ninitl);
        for (k = 0; k < proc->ninitl; k++) {
            if (k != 0) {
                grcc_fprintf(GRCC_Stdout, ", ");
            }
            if (proc->model != NULL) {
                grcc_fprintf(GRCC_Stdout, "\"%s\"", proc->model->particleName(proc->initlPart[k]));
            } else {
                grcc_fprintf(GRCC_Stdout, "%d", proc->initlPart[k]);
            }
        }
        grcc_fprintf(GRCC_Stdout, "}, %d,{", proc->nfinal);
        for (k = 0; k < proc->nfinal; k++) {
            if (k != 0) {
                grcc_fprintf(GRCC_Stdout, ", ");
            }
            if (proc->model != NULL) {
                grcc_fprintf(GRCC_Stdout, "\"%s\"", proc->model->particleName(proc->finalPart[k]));
            } else {
                grcc_fprintf(GRCC_Stdout, "%d", proc->initlPart[k]);
            }
        }
        grcc_fprintf(GRCC_Stdout, "}, ");
        if (model != NULL) {
            grcc_fprintf(GRCC_Stdout, "{");
            for (k = 0; k < model->ncouple; k++) {
                if (k != 0) {
                    grcc_fprintf(GRCC_Stdout, ", ");
                }
                grcc_fprintf(GRCC_Stdout, "%d", proc->clist[k]);
            }
            grcc_fprintf(GRCC_Stdout, "},");
        }
        grcc_fprintf(GRCC_Stdout, "},%6ldL,%6ldL,%3ldL, -1.0, %4.2f},\n",
               proc->nAOPI, proc->wAOPI.num, proc->wAOPI.den, proc->sec);
    }

    if (out != NULL && values[GRCC_OPT_Outgrf]) {
        out->outProcEndF();
    }
    if (out != NULL && values[GRCC_OPT_Outgrp]) {
        out->outProcEndP();
    }
    proc = NULL;
}

//--------------------------------------------------------------
void Options::beginSubProc(SProcess *sprc)
{
    sproc = sprc;

    // 'beginProc' is called before
    if (out != NULL && values[GRCC_OPT_Outgrf]) {
        out->outSProcBeginF(sprc);
    }
    if (out != NULL && values[GRCC_OPT_Outgrp]) {
        out->outSProcBeginP(sprc);
    }
    if (proc != NULL) {
        return;
    }
    if (sprc != NULL) {
        sproc->mgrcount = 0;
        sproc->agrcount = 0;
    }
}

//--------------------------------------------------------------
void Options::endSubProc(void)
{
    MGraph *mgraph;

    if (sproc == NULL) {
        if (out != NULL && values[GRCC_OPT_Outgrf]) {
            out->outProcEndF();
        }
        if (out != NULL && values[GRCC_OPT_Outgrp]) {
            out->outProcEndP();
        }
        return;
    }
    mgraph = sproc->mgraph;
    if (sproc != NULL) {
        sproc->resultMGraph(mgraph->cDiag, mgraph->wscon,
                            mgraph->c1PI, mgraph->wsopi);
    }

    if (prlevel > 1) {
        grcc_fprintf(GRCC_Stdout, "\n");
        grcc_fprintf(GRCC_Stdout, "+++ Subproc %d: ext=%d, loop=%d, nodes=%d, edges=%d\n",
               sproc->id, sproc->nExtern, sproc->loop,
               sproc->nNodes, sproc->nEdges);
    
        grcc_fprintf(GRCC_Stdout, "    Subproc %d: Total M-Graphs=%ld, M-Wsum=",
               sproc->id, sproc->nMGraphs);
        sproc->wMGraphs.print(" (Conn)\n");

        grcc_fprintf(GRCC_Stdout, "    Subproc %d: Total M-Graphs=%ld, M-Wsum=",
               sproc->id, sproc->nMOPI);
        sproc->wMOPI.print(" (1PI)\n");
    
        grcc_fprintf(GRCC_Stdout, "    Subproc %d: Total A-Graphs=%ld, A-Wsum=", 
               sproc->id, sproc->nAGraphs);
        sproc->wAGraphs.print(" (Conn)\n");

        grcc_fprintf(GRCC_Stdout, "    Subproc %d: Total A-Graphs=%ld, A-Wsum=", 
               sproc->id, sproc->nAOPI);
        sproc->wAOPI.print(" (1PI)\n");
    }
    if (prlevel > 0) {
        grcc_fprintf(GRCC_Stdout, "\n");
        grcc_fprintf(GRCC_Stdout, "* Total %ld MGraphs; %ld 1PI", mgraph->cDiag, mgraph->c1PI);
        grcc_fprintf(GRCC_Stdout, " wscon = ");
        mgraph->wscon.print(" ( ");
        mgraph->wsopi.print(" 1PI)\n");

#ifdef MONITOR
        grcc_fprintf(GRCC_Stdout, "* refine:                     %ld\n", mgraph->nCallRefine);
        grcc_fprintf(GRCC_Stdout, "* discarded for refinement:   %ld\n", mgraph->discardRefine);
        grcc_fprintf(GRCC_Stdout, "* discarded for disconnected: %ld\n", mgraph->discardDisc);
        grcc_fprintf(GRCC_Stdout, "* discarded for duplication:  %ld\n", mgraph->discardIso);
#endif
    }
    
    if (proc != NULL) {
        return;
    }
    if (out != NULL && values[GRCC_OPT_Outgrf]) {
        out->outProcEndF();
    }
    if (out != NULL && values[GRCC_OPT_Outgrp]) {
        out->outProcEndP();
    }
}

//--------------------------------------------------------------
void Options::newMGraph(MGraph *mgr)
{
    MGraph *mgraph = mgr;

    if (proc != NULL) {
        proc->mgrcount++;
        mgr->egraph->mId = proc->mgrcount;
    } else if (sproc != NULL) {
        sproc->mgrcount++;
        mgr->egraph->mId = sproc->mgrcount;
    }

    if (out != NULL 
        && values[GRCC_OPT_Step] == GRCC_MGraph) {
        if (values[GRCC_OPT_Outgrf]) {
            out->outEGraphF(mgraph->egraph);
        }
        if (values[GRCC_OPT_Outgrp]) {
            out->outEGraphP(mgraph->egraph);
        }
    }
    if (sproc != NULL) {
        sproc->endMGraph(mgr);
    }
    if (endmg != NULL) {
        (*endmg)(mgr->egraph, argemg);
    } 
}

//--------------------------------------------------------------
void Options::newAGraph(EGraph *egraph)
{
    Fraction sf, zr;

    if (proc != NULL) {
        proc->agrcount++;
        egraph->sId = proc->agrcount;
    } else if (sproc != NULL) {
        sproc->agrcount++;
        egraph->sId = sproc->agrcount;
    }

    if (sproc != NULL) {
        zr = Fraction(0, 1);
        if ((egraph->nsym)*(egraph->esym) != 0) {
            sf = Fraction(egraph->extperm, egraph->nsym*egraph->esym);
        } else {
            sf = zr;
        }
        if (egraph->mgraph->opi) {
            sproc->resultAGraph(1, sf, 1, sf);
        } else {
            sproc->resultAGraph(1, sf, 0, zr);
        }
    }

    if (out != NULL && values[GRCC_OPT_Outgrf]) {
        out->outEGraphF(egraph);
    }
    if (out != NULL && values[GRCC_OPT_Outgrp]) {
        out->outEGraphP(egraph);
    }
    if (outag != NULL) {
        (*outag)(egraph, argag);
    }

    sproc->endAGraph(egraph);
}

//==============================================================
Output::Output(Options *optn)
{
    opt     = optn;
    model   = NULL;
    proc    = NULL;
    sproc   = NULL;
    outgrfp = NULL;
    outgrpp = NULL;
    procId  = -1;
    outgrf  = NULL;
    outgrp  = NULL;
    outproc = False;

}

//--------------------------------------------------------------
Output::~Output(void)
{
    if (outgrfp != NULL) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** file has not been closed : \"%s\"\n",
                    outgrf);
        }
        fclose(outgrfp);
        outgrfp = NULL;
        erEnd("file has not been closed");
    }
    if (outgrf != NULL) {
        free(outgrf);
        outgrf = NULL;
    }
    if (outgrpp != NULL) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** file has not been closed : \"%s\"\n",
                    outgrp);
        }
        fclose(outgrpp);
        outgrpp = NULL;
        erEnd("file has not been closed");
    }
    if (outgrp != NULL) {
        free(outgrp);
        outgrp = NULL;
    }
}

//--------------------------------------------------------------
void Output::setOutgrf(const char *fname)
{
    if (outgrf != NULL && strcmp(outgrf, fname) == 0) {
        return;
    }

    if (outgrf != NULL) {
        // delete outgrf;
        free(outgrf);
    }
    if (fname == NULL || strlen(fname) < 1) {
        outgrf = NULL;
    } else {
        outgrf = strdup(fname);
    }
}

//--------------------------------------------------------------
void Output::setOutgrp(const char *fname)
{
    if (outgrp != NULL && strcmp(outgrp, fname) == 0) {
        return;
    }

    if (outgrp != NULL) {
        free(outgrp);
    }
    if (fname == NULL || strlen(fname) < 1) {
        outgrp = NULL;
    } else {
        outgrp = strdup(fname);
    }
}

//--------------------------------------------------------------
Bool Output::outBeginF(Model *mdl, Bool pr)
{
    time_t tp;
    struct tm *tm;
    char   sdate[MAXSTRLEN];

    model = mdl;

    if (outgrf == NULL || strlen(outgrf) < 1) {
        outgrfp = NULL;
        return True;
    } else if (outgrfp != NULL) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** outBegin: \"%s\" is already opened\n",
                    outgrf);
        }
        erEnd("outBegin: file is already opened\n");
    }
 
    if (!pr) {
        return True;
    }
    if ((outgrfp = fopen(outgrf, "w")) == NULL) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** outBegin: cannot open %s\n", outgrf);
        }
        return False;
    }
    tp = time(NULL);
    tm = localtime(&tp);
    strftime(sdate, MAXSTRLEN, "%Y/%m/%d %H:%M:%S", tm);

    fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n");
    fprintf(outgrfp, "%% Generated by grcc at \"%s\"\n", sdate);
    fprintf(outgrfp, "Version={2,2,0,0};\n");
    if (model != NULL) {
        fprintf(outgrfp, "Model=\"./%s.mdl\";\n", model->name);
    } else {
        fprintf(outgrfp, "Model=\"./Phi34.mdl\";\n");
    }


    return True;
}

//--------------------------------------------------------------
Bool Output::outBeginP(Model *mdl, Bool pr)
{
    time_t tp;
    struct tm *tm;
    char   sdate[MAXSTRLEN];

    model = mdl;

    if (outgrp == NULL || strlen(outgrp) < 1) {
        outgrpp = NULL;
        return True;
    } else if (outgrpp != NULL) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** outBegin: \"%s\" is already opened\n",
                    outgrp);
        }
        erEnd("outBegin: file is already opened\n");
    }
 
    if (!pr) {
        return True;
    }
    if ((outgrpp = fopen(outgrp, "w")) == NULL) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** outBegin: cannot open %s\n", outgrp);
        }
        return False;
    }
    tp = time(NULL);
    tm = localtime(&tp);
    strftime(sdate, MAXSTRLEN, "%Y/%m/%d %H:%M:%S", tm);

    fprintf(outgrpp, "################################\n");
    fprintf(outgrpp, "# Generated by 'grcc' at \"%s\"\n", sdate);

    return True;
}

//--------------------------------------------------------------
void Output::outEndF(void)
{
    if (outgrfp == NULL) {
        return;
    }
    fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n");
    fprintf(outgrfp, "End=1;\n");
    fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n");
    fclose(outgrfp);
    outgrfp = NULL;

    free(outgrf);
    outgrf = NULL;
}

//--------------------------------------------------------------
void Output::outEndP(void)
{
    if (outgrpp == NULL) {
        return;
    }
    fprintf(outgrpp, "################################\n");
    fprintf(outgrpp, "# End\n");
    fprintf(outgrpp, "################################\n");
    fclose(outgrpp);
    outgrpp = NULL;

    free(outgrp);
    outgrp = NULL;
}

//--------------------------------------------------------------
void Output::outProcBeginF(Process *prc)
{
    int k, ex;

    if (prc == NULL) {
        return;
    }

    proc    = prc;
    sproc   = NULL;
    procId  = proc->id;

    if (outgrfp == NULL) {
        return;
    }
    if (outproc) {
        return;
    }
    outproc = True;

    fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n");
    fprintf(outgrfp, "Process=%d;\n", proc->id);
    fprintf(outgrfp, "External=%d;\n", proc->ninitl+proc->nfinal);
    for (k = 0, ex = 0; k < proc->ninitl; k++, ex++) {
        fprintf(outgrfp, "%4d= initial %s;\n", ex,
                proc->model->particleName(proc->initlPart[k]));
    }
    for (k = 0; k < proc->nfinal; k++, ex++) {
        fprintf(outgrfp, "%4d= final   %s;\n", ex,
                proc->model->particleName(proc->finalPart[k]));
    }
    fprintf(outgrfp, "Eend;\n");
    for (k = 0; k < proc->model->ncouple; k++) {
        fprintf(outgrfp, "%s=%d;  ", proc->model->cnlist[k], proc->clist[k]);
    }
    fprintf(outgrfp, "Loop=%d;\n", proc->loop);
    fprintf(outgrfp, "OPI=%s;\n", (opt->values[GRCC_OPT_1PI] > 0? "Yes" : "No"));
    fprintf(outgrfp, "Assign=%s;\n", (opt->values[GRCC_OPT_Step]==GRCC_AGraph ? "Yes" : "No"));
    fprintf(outgrfp, "%% Options : dummy values\n");
    fprintf(outgrfp, "Expand=Yes; ExpMin=0; ExpMax=-1;\n");
    fprintf(outgrfp, "Block=No; Tadpole=Yes; Extself=Yes;\n");
    fprintf(outgrfp, "Selfe=Yes; Countert=No; AnyCT=No;Undefp=No;\n");
}

//--------------------------------------------------------------
void Output::outProcBeginP(Process *prc)
{
    if (prc == NULL) {
        return;
    }

    proc    = prc;
    sproc   = NULL;
    procId  = proc->id;

    if (outgrpp == NULL) {
        return;
    }
    if (outproc) {
        return;
    }
    outproc = True;

    fprintf(outgrpp, "# Process=%d;\n", proc->id);
}

//--------------------------------------------------------------
void Output::outProcBegin0(int next, int couple, int loop)
{
    int k, ex;

    procId  = 0;

    if (outgrfp == NULL) {
        return;
    }
    if (outproc) {
        return;
    }
    outproc = True;

    fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n");
    fprintf(outgrfp, "Process=%d;\n", procId);
    fprintf(outgrfp, "External=%d;\n", next);
    int ninit = (next + 1) / 2;
    for (k = 0, ex = 0; k < ninit; k++, ex++) {
        fprintf(outgrfp, "%4d= initial undef;\n", ex);
    }
    for (k = 0; k < next - ninit; k++, ex++) {
        fprintf(outgrfp, "%4d= final   undef;\n", ex);
    }
    fprintf(outgrfp, "Eend;\n");
    fprintf(outgrfp, "GRCC_PHI=%d;  ", couple);
 // fprintf(outgrfp, "PHI=%d;  ", couple);
    fprintf(outgrfp, "Loop=%d;\n", loop);
    fprintf(outgrfp, "OPI=%s;\n", (opt->values[GRCC_OPT_1PI] > 0? "Yes" : "No"));
    fprintf(outgrfp, "Assign=No;\n");
    fprintf(outgrfp, "%% Options : dummy values\n");
    fprintf(outgrfp, "Expand=Yes; ExpMin=0; ExpMax=-1;\n");
    fprintf(outgrfp, "Block=No; Tadpole=Yes; Extself=Yes;\n");
    fprintf(outgrfp, "Selfe=Yes; Countert=No; AnyCT=No;Undefp=No;\n");
}

//--------------------------------------------------------------
void Output::outSProcBeginF(SProcess *sprc)
{
    int j, k, ex;
    PNodeClass *pnc;

    if (sprc == NULL) {
        return;
    }

    sproc  = sprc;
    procId = sproc->id;
    pnc    = sproc->pnclass;

    if (outgrfp == NULL) {
        return;
    }
    if (outproc) {
        return;
    }
    outproc = True;
    fprintf(outgrfp, "%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%\n");
    fprintf(outgrfp, "Process=%d;\n", sproc->id);
    fprintf(outgrfp, "External=%d;\n", sproc->nExtern);

    ex = 0;
    for (j = 0; j < pnc->nclass; j++) {
        if (pnc->type[j] == GRCC_AT_Initial) {
            for (k = 0; k < pnc->count[j]; k++) {
                fprintf(outgrfp, "%4d= initial %s;\n", ex,
                        model->particleName(pnc->particle[j]));
                ex++;
            }
        } else if (pnc->type[j] == GRCC_AT_Final) {
            for (k = 0; k < pnc->count[j]; k++) {
                fprintf(outgrfp, "%4d= final %s;\n", ex,
                        model->particleName(-pnc->particle[j]));
                ex++;
            }
        }
    }

    fprintf(outgrfp, "Eend;\n");
    for (k = 0; k < sproc->model->ncouple; k++) {
        fprintf(outgrfp, "%s=%d;  ", sproc->model->cnlist[k], sproc->clist[k]);
    }
    fprintf(outgrfp, "Loop=%d;\n", sproc->loop);
    fprintf(outgrfp, "OPI=%s;\n", (opt->values[GRCC_OPT_1PI] > 0? "Yes" : "No"));
    fprintf(outgrfp, "Assign=%s;\n", (opt->values[GRCC_OPT_Step]==GRCC_AGraph ? "Yes" : "No"));
    fprintf(outgrfp, "%% Options : dummy values\n");
    fprintf(outgrfp, "Expand=Yes; ExpMin=0; ExpMax=-1;\n");
    fprintf(outgrfp, "Block=No; Tadpole=Yes; Extself=Yes;\n");
    fprintf(outgrfp, "Selfe=Yes; Countert=No; AnyCT=No;Undefp=No;\n");
}

//--------------------------------------------------------------
void Output::outSProcBeginP(SProcess *sprc)
{
    if (sprc == NULL) {
        return;
    }

    sproc  = sprc;
    procId = sproc->id;

    if (outgrpp == NULL) {
        return;
    }
    if (outproc) {
        return;
    }
    outproc = True;
    fprintf(outgrpp, "# SProcess=%d;\n", sproc->id);
}

//--------------------------------------------------------------
void Output::outProcEndF(void)
{
    if (outgrfp == NULL) {
        return;
    }
    if (proc != NULL) {
        fprintf(outgrfp, "%%------------------------------\n");
        fprintf(outgrfp, "Pend=%d;\n", proc->id);
    } else if (sproc != NULL) {
        fprintf(outgrfp, "%%------------------------------\n");
        fprintf(outgrfp, "Pend=%d;\n", sproc->id);
    } else {
        fprintf(outgrfp, "%%------------------------------\n");
        fprintf(outgrfp, "Pend=1;\n");
    }
    fflush(outgrfp);
}

//--------------------------------------------------------------
void Output::outProcEndP(void)
{
    if (outgrpp == NULL) {
        return;
    }
    fflush(outgrpp);
}

//--------------------------------------------------------------
void Output::outEGraphF(EGraph *egraph)
{
    int nd, lg, ptcl, ed, intr, j, k, loop;
    Model *mdl = egraph->model;
    Bool popt;
    EFLine *fl;

    if (outgrfp == NULL) {
        return;
    }
    fprintf(outgrfp, "%%------------------------------\n");
    if (egraph->assigned) {
        fprintf(outgrfp, "Graph=%ld;\n", egraph->sId);
        fprintf(outgrfp, "%% AGraph=%ld;\n", egraph->aId);
    } else {
        fprintf(outgrfp, "Graph=%ld;\n", egraph->mId);
    }
    fprintf(outgrfp, "Gtype=%ld;\n", egraph->mId);
    if (egraph->assigned) {
        fprintf(outgrfp, "Sfactor=%ld;\n", 
                egraph->nsym * egraph->esym * egraph->fsign);
    } else {
        fprintf(outgrfp, "Sfactor=%ld;\n", egraph->nsym * egraph->esym);
    }
    fprintf(outgrfp, "%% ExtPerm=%ld; NSym=%ld; ESym=%ld; NSym1=%ld;"
                     " Multp=%ld;\n", 
            egraph->extperm, egraph->nsym, egraph->esym, egraph->nsym1,
            egraph->multp);

    fprintf(outgrfp, "Vertex=%d;\n", egraph->nNodes - egraph->nExtern);

    for (nd = 0; nd < egraph->nNodes; nd++) {
        fprintf(outgrfp, "%4d", nd);
        if (mdl != NULL && egraph->assigned && !egraph->isExternal(nd)) {
            intr = egraph->nodes[nd]->intrct;
            loop = mdl->interacts[intr]->loop;
            popt = False;

            // not tree vertex
            if (loop > 0) {
                fprintf(outgrfp, "[loop=%d", loop);
                popt = True;
            }

            // multiple coupling constants
            if (mdl->ncouple > 1) {
                if (popt) {
                    fprintf(outgrfp, ";order={");
                } else {
                    fprintf(outgrfp, "[order={");
                    popt = True;
                }
                for (j = 0; j < mdl->interacts[intr]->nclist; j++) {
                    if (j != 0) {
                        fprintf(outgrfp, ",");
                    }
                    fprintf(outgrfp, "%d", mdl->interacts[intr]->clist[j]);
                }
                fprintf(outgrfp, "}");
            }
            if (popt) {
                fprintf(outgrfp, "]");
            }
        } else if (!egraph->isExternal(nd)) {
            loop = egraph->nodes[nd]->extloop;
            // not tree vertex
            if (loop > 0) {
                fprintf(outgrfp, "[loop=%d]", loop);
            }
        }
        fprintf(outgrfp, "={");

        // list of legs
        for (lg = 0; lg < egraph->nodes[nd]->deg; lg++) {
            if (lg != 0) {
                fprintf(outgrfp, ", ");
            }
            ed = V2Iedge(egraph->nodes[nd]->edges[lg]);
         // fprintf(outgrfp, "%4d", egraph->nodes[nd]->edges[lg]);
            fprintf(outgrfp, "%4d", abs(egraph->nodes[nd]->edges[lg]));
            ptcl = egraph->edges[ed]->ptcl;
            if (mdl != NULL && ptcl != 0 && egraph->assigned) {
                if (egraph->nodes[nd]->edges[lg] < 0) {
                    ptcl = mdl->normalParticle(-ptcl);
                } else {
                    ptcl = mdl->normalParticle(ptcl);
                }
                fprintf(outgrfp, "[%s]", mdl->particleName(ptcl));
            } else {
                fprintf(outgrfp, "[undef]");
            }
        }
        fprintf(outgrfp, "};\n");
    }
    // print Fermion line as comment line
    if (egraph->nFlines >= 0) {
        fprintf(outgrfp, "%%  FLines=%d; FSign=%d; sId=%ld;\n",
                egraph->nFlines, egraph->fsign, egraph->sId);
    }
    for (j = 0; j < egraph->nFlines; j++) {
        fl = egraph->flines[j];
        fprintf(outgrfp, "%% %4d", j);
        if (fl->ftype == FL_Open) {
            fprintf(outgrfp, "[FOpen]=[");
        } else if (fl->ftype == FL_Closed) {
            fprintf(outgrfp, "[FLoop]=[");
        } else {
            fprintf(outgrfp, " ?%d", fl->ftype);
        }
        for (k = 0; k < fl->nlist; k++) {
            if (k != 0) {
                fprintf(outgrfp, ", ");
            }
            fprintf(outgrfp, "%d", fl->elist[k]);
        }
        fprintf(outgrfp, "];\n");
    }
    fprintf(outgrfp, "Vend;\n");
    fprintf(outgrfp, "Gend;\n");
}

//--------------------------------------------------------------
#ifdef NEWOUTPY
void Output::outEGraphP(EGraph *eg)
{
    if (outgrpp == NULL) {
        return;
    }

    if (eg->assigned) {
        grcc_fprintf(GRCC_Stdout, "outEGraphP:egraph:egraph[%ld]\n", eg->mId-1);
        eg->printPy(outgrpp, eg->mId);
        return;
    } else {
        grcc_fprintf(GRCC_Stdout, "outEGraphP:mgraph:egraph[%ld]\n", eg->mId-1);
        eg->mgraph->printPy(outgrpp, eg->mId);
        return;
    }
}
#else
void Output::outEGraphP(EGraph *eg)
{
    int      j, nd, lg, ed, k;
    ENode   *node;
    static char undef[] = "Undef";
    char    *s;
    EFLine  *fl;

    if (outgrpp == NULL) {
        return;
    }

    if (eg->assigned) {
        fprintf(outgrpp, "egraph[%ld] = {\n", eg->sId-1);
    } else {
        fprintf(outgrpp, "egraph[%ld] = {\n", eg->mId-1);
    }

    // process
    if (proc != NULL) {
        fprintf(outgrpp, "  \"Process\": {\n");
        proc->outProcP(outgrpp);
        fprintf(outgrpp, "  },\n");
    }

    // graph
    fprintf(outgrpp, "  \"GId\": [%ld, %ld, %ld],\n",
            eg->mId, eg->aId, eg->sId);
    fprintf(outgrpp, "  \"GParam\": {\"Assigned\":%d, "
            "\"NNodes\":%d, \"NEdges\":%d, \"NFLines\":%d},\n", 
            eg->assigned, eg->nNodes, eg->nEdges, eg->nFlines);
    fprintf(outgrpp, "  \"Sym\": {\"FSign\":%d, \"NSym\":%ld, "
            "\"ESym\":%ld, \"NSym1\":%ld, \"Multp\":%ld},\n", 
            eg->fsign, eg->nsym, eg->esym, eg->nsym1, eg->multp);

    // nodes
    fprintf(outgrpp, "  \"Nodes\": [\n");
    for (nd = 0; nd < eg->nNodes; nd++) {
        node = eg->nodes[nd];
        if (model==NULL) {
            s = undef;
        } else if(!eg->assigned) {
            if (eg->isExternal(nd)) {
                ed = Abs(eg->nodes[nd]->edges[0])-1;
                s = model->particleName(eg->edges[ed]->ptcl);
            } else {
                s = undef;
            }
        } else if (eg->isExternal(nd)) {
            s = model->particleName(node->intrct);
        } else {
            s = model->interacts[node->intrct]->name;
        }
        fprintf(outgrpp, "    [%d, \"%s\", %d, [", 
                nd, s, node->extloop);
        for (lg = 0; lg < eg->nodes[nd]->deg; lg++) {
            if (lg != 0) {
                fprintf(outgrpp, ", ");
            }
            fprintf(outgrpp, "%d", eg->nodes[nd]->edges[lg]);
        }
        fprintf(outgrpp, "]],\n");
    }
    fprintf(outgrpp, "  ],\n");

    // edges
    fprintf(outgrpp, "  \"Edges\": [\n");
    for (ed = 0; ed < eg->nEdges; ed++) {
        if (model != NULL) {
            s = model->particleName(eg->edges[ed]->ptcl);
            fprintf(outgrpp, "    [%d, \"%s\", [%d, %d]],\n", 
                    ed+1, s, eg->edges[ed]->nodes[0],
                    eg->edges[ed]->nodes[1]);
        } else {
            fprintf(outgrpp, "    [%d, \"Undef\", [%d, %d]],\n", 
                    ed+1, eg->edges[ed]->nodes[0],
                    eg->edges[ed]->nodes[1]);
        }
    }

    fprintf(outgrpp, "  ],\n");

    if (eg->nFlines >= 0) {
        // print Fermion line as comment line
        fprintf(outgrpp, "  \"FLines\": [\n");
        for (j = 0; j < eg->nFlines; j++) {
            fl = eg->flines[j];
            fprintf(outgrpp, "    [%d, ", j);
            if (fl->ftype == FL_Open) {
                fprintf(outgrpp, "\"FOpen\", ");
            } else if (fl->ftype == FL_Closed) {
                fprintf(outgrpp, "\"FLoop\", ");
            } else {
                fprintf(outgrpp, "\"Undef%d\", ", fl->ftype);
            }
            fprintf(outgrpp, "[");
            for (k = 0; k < fl->nlist; k++) {
                if (k != 0) {
                    fprintf(outgrpp, ", ");
                }
                fprintf(outgrpp, "%d", fl->elist[k]);
            }
            fprintf(outgrpp, "]],\n");
        }
        fprintf(outgrpp, "  ]\n");
    }
    
    // end of a graph
    fprintf(outgrpp, "};\n");
}
#endif

//--------------------------------------------------------------
void Output::outModelF(void)
{
    char        *mdlfn;
    FILE        *mdlfp;
    Particle    *pt;
    Interaction *vt;
    int          j, k, l, ln;
    const char        *ptn;

    if (model == NULL) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** Output::outModel : model is not defined\n");
        }
        return;
    }
    ln = strlen(model->name)+5;
    mdlfn = new char[ln];
    snprintf(mdlfn, ln, "%s.mdl", model->name);

    if ((mdlfp = fopen(mdlfn, "w")) == NULL) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** Output::outModel : cannot open \"%s\"\n",
                    mdlfn);
        }
        return;
    }

    for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp);
    fprintf(mdlfp, "%% File \"%s\"\n", mdlfn);
    fprintf(mdlfp, "%% Generated by graph generater\n");
    fprintf(mdlfp, " Version={2,2,0};\n");

    // copupling constants
    fprintf(mdlfp, " Order={");
    for (j = 0; j < model->ncouple; j++) {
        if (j != 0) {
            fprintf(mdlfp, ", ");
        }
        fprintf(mdlfp, "%s", model->cnlist[j]);
    }
    fprintf(mdlfp, "};\n");

    for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp);
    fprintf(mdlfp, "%% particles\n");
    for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp);
    for (j = 1; j < model->nParticles; j++) {
        pt = model->particles[j];
        fprintf(mdlfp, " Particle=%s; Antiparticle=%s;\n",
                pt->name, pt->aname);
        ptn = pt->typeGName();
        fprintf(mdlfp, " PType=%s; Charge=0; Color=1; Mass=0; Width=0;\n", ptn);
        fprintf(mdlfp, " PCode=%d; Massless; \n", pt->pcode);
        fprintf(mdlfp, " Pend;\n");
        fprintf(mdlfp, "%%\n");
    }
    for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp);
    fprintf(mdlfp, "%% interactions\n");
    for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp);
    for (j = 0; j < model->nInteracts; j++) {
        vt = model->interacts[j];
        fprintf(mdlfp, " Vertex={");
        for (k = 0; k < vt->nplist; k++) {
            if (k != 0) {
                fprintf(mdlfp, ", ");
            }
            fprintf(mdlfp, "%s", model->particleName(vt->plist[k]));
        }
        fprintf(mdlfp, "}; ");
        for (k = 0; k < model->ncouple; k++) {
            fprintf(mdlfp, "%s=%d; ", model->cnlist[k], vt->clist[k]);
        }
        fprintf(mdlfp, "FName=%s; Vend;\n", vt->name);
    }
    for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp);
    fprintf(mdlfp, " Mend;\n");
    for (l = 0; l < 60; l++) { putc('%', mdlfp); } putc('\n', mdlfp);
    fclose(mdlfp);
    delete[] mdlfn;
}

//--------------------------------------------------------------
void Output::outModelP(void)
{
    char        *mdlfn;
    FILE        *mdlfp;
    Particle    *pt;
    Interaction *vt;
    int          j, k, l, ln;
    const char        *ptn;

    if (model == NULL) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** Output::outModel : ");
            grcc_fprintf(GRCC_Stderr, "model is not defined\n");
        }
        return;
    }
    ln = strlen(model->name)+5;
    mdlfn = new char[ln];
    snprintf(mdlfn, ln, "%s.mdp", model->name);

    if ((mdlfp = fopen(mdlfn, "w")) == NULL) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** Output::outModel : cannot open \"%s\"\n",
                    mdlfn);
        }
        return;
    }

    for (l = 0; l < 60; l++) { putc('#', mdlfp); } putc('\n', mdlfp);
    fprintf(mdlfp, "# File \"%s\"\n", mdlfn);
    fprintf(mdlfp, "# Generated by graph generater grcc\n");

    // copupling constants
    fprintf(mdlfp, "Model={\n");
    fprintf(mdlfp, "  \"Model\": [");
    fprintf(mdlfp, "\"%s\", %d, [", 
            model->name, model->ncouple);
    for (j = 0; j < model->ncouple; j++) {
        if (j != 0) {
            fprintf(mdlfp, ", ");
        }
        fprintf(mdlfp, "\"%s\"", model->cnlist[j]);
    }
    fprintf(mdlfp, "], ");
    if (model->defpart == GRCC_DEFBYCODE) {
        fprintf(mdlfp, "\"ByCode\"");
    } else {
        fprintf(mdlfp, "\"ByName\"");
    }
    fprintf(mdlfp, "],\n");

    fprintf(mdlfp, "  \"Particles\": [\n");
    for (j = 1; j < model->nParticles; j++) {
        pt = model->particles[j];
        ptn = pt->typeName();
        fprintf(mdlfp, "    [\"%s\", %d, \"%s\", %d, \"%s\", %d],\n",
                pt->name, pt->pcode, pt->aname, pt->acode, 
                ptn, pt->extonly);
    }
    fprintf(mdlfp, "  ],\n");
    fprintf(mdlfp, "  \"Interactions\": [\n");
    for (j = 0; j < model->nInteracts; j++) {
        vt = model->interacts[j];
        fprintf(mdlfp, "    [\"%s\", %d, %d, [", vt->name, vt->id, vt->nplist);
        for (k = 0; k < vt->nplist; k++) {
            if (k != 0) {
                fprintf(mdlfp, ", ");
            }
            if (model->defpart == GRCC_DEFBYCODE) {
                fprintf(mdlfp, "%d", vt->plist[k]);
            } else {
                fprintf(mdlfp, "\"%s\"", model->particleName(vt->plist[k]));
            }
        }
        fprintf(mdlfp, "], [");
        for (k = 0; k < model->ncouple; k++) {
            if (k != 0) {
                fprintf(mdlfp, ",");
            }
            fprintf(mdlfp, "%d", vt->clist[k]);
        }
        fprintf(mdlfp, "]],\n");
    }
    fprintf(mdlfp, "  ],\n");
    fprintf(mdlfp, "};\n");
    fclose(mdlfp);
    delete[] mdlfn;
}

//**************************************************************
// model.cc

//==============================================================

static const char *ptypenames[]  = GRCC_PT_Table;
static const char *pgtypenames[] = GRCC_PT_GTable;

//==============================================================
// class Particle
//--------------------------------------------------------------
Particle::Particle(Model *modl, int pid, PInput *pinp)
{
    static char buff[100];
    static int  nbuff=100;
    int j;

    mdl     = modl;                   // the model
    id      = pid;                    // id of this particle
    if (pinp->name == NULL || strlen(pinp->name) < 1) {
        if (pinp->pcode != 0) {
            snprintf(buff, nbuff, "pa%d", pinp->pcode);
            name = strdup(buff);
        } else {
            snprintf(buff, nbuff, "pi%d", pid);
            name = strdup(buff);
        }
    } else {
        name = strdup(pinp->name);     // the name of the particle
    }
    if (pinp->aname == NULL) {
        if (pinp->acode != 0) {
            snprintf(buff, nbuff, "ap%d", Abs(pinp->acode));
            aname = strdup(buff);
        } else {
            snprintf(buff, nbuff, "ai%d", pid);
            aname = strdup(buff);
        }
    } else {
        aname   = strdup(pinp->aname); // the name of the anti-particle
    }
    pcode   = pinp->pcode;
    acode   = pinp->acode;
    if (Abs(mdl->defpart) == GRCC_DEFBYCODE) {
        neutral = (pcode == acode);
    } else if (Abs(mdl->defpart) == GRCC_DEFBYNAME) {
        neutral = ((strcmp(name, aname)==0) ? True : False);
    }

    // convert ptype string to its code.
    if (Abs(mdl->defpart) == GRCC_DEFBYCODE) {
        if (pinp->ptypec < GRCC_PT_Undef || pinp->ptypec > GRCC_PT_Size) {
            if (prlevel > 0) {
                grcc_fprintf(GRCC_Stderr, "*** particle type is not defined: %d\n",
                        pinp->ptypec);
            }
            erEnd("particle type is not defined (illegal code)");
        }
        ptype = pinp->ptypec;
    } else if (Abs(mdl->defpart) == GRCC_DEFBYNAME) {
        if (pinp->ptypen == NULL) {
            erEnd("particle type is not defined (NULL)");
        }
        ptype = -1;
        for (j = 0; j < GRCC_PT_Size; j++) {
            if (strcmp(pinp->ptypen, ptypenames[j]) == 0) {
                ptype = j;
                break;
            }
        }
        if (ptype < 0) {
            if (prlevel > 0) {
                grcc_fprintf(GRCC_Stderr, "*** particle type \"%s\" is not defined\n",
                        pinp->ptypen);
            }
            erEnd("particle type is not defined (name)");
        }
    }
    if (ptype == GRCC_PT_Undef && ptype != 0) {
        erEnd("illegal ptype");
    }

    extonly = pinp->extonly;
    cmindeg = 0;
    cmaxdeg = 0;
}

//--------------------------------------------------------------
Particle::~Particle(void)
{
    free(aname);
    free(name);
}

//--------------------------------------------------------------
char *Particle::particleName(int p)
{
    if (p < 0) {
        return aname;
    } else {
        return name;
    }
}

//--------------------------------------------------------------
int Particle::particleCode(int p)
{
    if (p < 0) {
        return acode;
    } else {
        return pcode;
    }
}

//--------------------------------------------------------------
int Particle::isNeutral(void)
{
    return neutral;
}

//--------------------------------------------------------------
const char *Particle::typeName(void)
{
    return ptypenames[ptype];
}

//--------------------------------------------------------------
const char *Particle::typeGName(void)
{
    return pgtypenames[ptype];
}

//--------------------------------------------------------------
char *Particle::aparticle(void)
{
    static char prtcl[] = "Particle";

    if (isNeutral()) {
        return prtcl;
    } else {
        return aname;
    }
}

//--------------------------------------------------------------
void Particle::prParticle(void)
{
    if (isNeutral()) {
        grcc_fprintf(GRCC_Stdout, "pid=%d, name=\"%s\", real_field, ", id, name);
    } else {
        grcc_fprintf(GRCC_Stdout, "pid=%d, name=\"%s\", aname=\"%s\", ", id, name, aname);
    }
    grcc_fprintf(GRCC_Stdout, "ptype=%s, pcode=%d, acode=%d, extonly=%d, cdeg=(%d,%d)\n", 
           ptypenames[ptype], pcode, acode, extonly, cmindeg, cmaxdeg);
}

//==============================================================
// class Interaction
//--------------------------------------------------------------
Interaction::Interaction(Model *modl, int iid, const char *nam, int icd, int *cpl, int nlgs, int *plst, int csm, int lp)
{
    static char buff[100];
    static int  nbuff=100;
    static Bool prmsg = True;
    Particle   *p;
    int         j, ndir, sdir, jdir, nmaj, jmaj, ngho, sgho, jgho, ptcl;
    Bool        ok;

    mdl    = modl;         // the model
    id     = iid;          // id of this interaction
    icode  = icd;          // id of this interaction
    csum   = csm;          // the total orders of coupling constants
    nlegs  = nlgs;         // the size of plist[]
    loop   = lp;           // the number of loops

    if (nam == NULL || strlen(nam) < 1) {
        snprintf(buff, nbuff, "vt%d", icd);
        name = strdup(buff);
    } else {
        name = strdup(nam);  // the name of the interaction
    }
    nclist = mdl->ncouple;
    clist  = new int[nclist];
    icode  = icd;
    for (j = 0; j < mdl->ncouple; j++) {
        clist[j] = cpl[j];
    }
    plist  = new int[nlegs];
    nplist = nlegs;
    for (j = 0; j < nlegs; j++) {
        plist[j] = plst[j];
    }
    nslist = 0;
    slist  = NULL;

    // check fermion number conservation
    ndir = 0;
    sdir = 0;
    jdir = 0;
    nmaj = 0;
    jmaj = 0;
    ngho = 0;
    sgho = 0;
    jgho = 0;
    ok = True;
    for (j = 0; j < nplist; j++) {
        if (plist[j] > 0) {
            p = mdl->particles[plist[j]];
            ptcl = 1;
        } else {
            p = mdl->particles[-plist[j]];
            ptcl = -1;
        }
            
        if (p->ptype == GRCC_PT_Dirac) {
            ndir++;
            if (ptcl > 0) {
                sdir++;
            } else {
                sdir--;
            }
            if (Abs(sdir) == 1) {
                jdir = j;
            } else if ((Abs(sdir) == 0 && j != jdir + 1) || Abs(sdir) > 1) {
                grcc_fprintf(GRCC_Stderr, "*** Interaction: Dirac and anti-Dirac should "
                        "arranged in pairs in an interaction.\n");
                ok = False;
            }
        } else if (p->ptype == GRCC_PT_Ghost) {
            ngho++;
            if (ptcl > 0) {
                sgho++;
            } else {
                sgho--;
            }
            if (Abs(sgho) == 1) {
                jgho = j;
            } else if ((Abs(sgho) == 0 && j != jgho + 1) || Abs(sgho) > 1) {
                grcc_fprintf(GRCC_Stderr, "*** Interaction: Ghost and anti-Ghost should "
                        "arranged in pairs in an interaction.\n");
                ok = False;
            }
        } else if (p->ptype == GRCC_PT_Majorana) {
            nmaj++;
            if (nmaj % 2 == 1) {
                jmaj = j;
            } else if (j != jmaj + 1) {
                grcc_fprintf(GRCC_Stderr, "*** Interaction: two Majoranas should "
                        "arranged in pairs in an interaction.\n");
                ok = False;
            }
        }
    }
    if (sdir != 0) {
        grcc_fprintf(GRCC_Stderr, "*** Interaction: Dirac number is not conserved\n");
        ok = False;
    }
    if (sgho != 0) {
        grcc_fprintf(GRCC_Stderr, "*** Interaction: Ghost number is not conserved\n");
        ok = False;
    }
    if (nmaj % 2 != 0) {
        grcc_fprintf(GRCC_Stderr, "*** Interaction: odd number of Majorana particles\n");
        ok = False;
    }
    if (ndir + nmaj + ngho > 2 && prmsg) {
        grcc_fprintf(GRCC_Stderr, "+++ Interaction: more than 2 "
                             "Dirac/Majorana/Ghost "
                             "particles are interacting.\n");
        grcc_fprintf(GRCC_Stderr, "    Interaction has %d Dirac, %d Ghost "
                             "and %d Majorana particles.\n", 
                             ndir, nmaj, ngho);
        grcc_fprintf(GRCC_Stderr, "    Sign factors related to fermions may "
                             "be inconsistent with your calculation method.\n");
        prmsg = False;
    }
    if (!ok) {
        prInteraction();
        erEnd("illegal Dirac/Majorana/Ghost interaction");
    }
}

//--------------------------------------------------------------
Interaction::~Interaction(void)
{
    if (slist != NULL) {
        delete[] slist;
    }
    if (plist != NULL) {
        delete[] plist;
    }
    if (clist != NULL) {
        delete[] clist;
    }
    free(name);
}

//--------------------------------------------------------------
void Interaction::prInteraction(void)
{
    int j;

    grcc_fprintf(GRCC_Stdout, "vid=%d, icode=%d, name=\"%s\", loop=%d, csum=%d, cpl=",
          id, icode, name, loop, csum);
    prIntArray(mdl->ncouple, clist, ", legs=[");
    for (j = 0; j < nplist; j++) {
        if (j != 0) {
            grcc_fprintf(GRCC_Stdout, ", ");
        }
        grcc_fprintf(GRCC_Stdout, "%s", mdl->particleName(plist[j]));
    }
    grcc_fprintf(GRCC_Stdout, "];\n");

}

//==============================================================
// class Model
//--------------------------------------------------------------
Model::Model(MInput *minp)
{
    static PInput pundef = {"undef", "undef", 0, 0, "undef", 0, 0};
    int j;

    if (minp->name == NULL || strlen(minp->name) < 1) {
        erEnd("model should have a name");
    }
    name    = strdup(minp->name);
    ncouple = minp->ncouple;
    if (ncouple >= GRCC_MAXNCPLG) {
        erEnd("too many coupling constants in the model (GRCC_MAXNCPLG)");
    }
    // cnlist = minp->cnamlist;
    cnlist = new char*[ncouple];
    for (j = 0; j < ncouple; j++) {
        cnlist[j] = strdup(minp->cnamlist[j]);
    }

    nParticles = 0;
    particles  = new Particle*[GRCC_MAXMPARTICLES];
    for (j = 0; j < GRCC_MAXMPARTICLES; j++) {
        particles[j] = NULL;
    }
    pdef = False;

    nInteracts = 0;
    interacts  = new Interaction*[GRCC_MAXMINTERACT];
    for (j = 0; j < GRCC_MAXMINTERACT; j++) {
        interacts[j] = NULL;
    }
    vdef       = False;

    if (particles == NULL || interacts == NULL) {
        erEnd("memory allocation failed");
    }

#ifdef UNIQINTR
    if (minp->defpart != GRCC_DEFBYNAME 
        && minp->defpart != GRCC_DEFBYCODE) {
        erEnd("illegal value of defpart");
    }
#else
    if (Abs(minp->defpart) != GRCC_DEFBYNAME 
        && Abs(minp->defpart) != GRCC_DEFBYCODE) {
        erEnd("illegal value of defpart");
    }
#endif

    defpart = minp->defpart;

    maxnlegs   = 0;
    maxcpl     = 0;
    maxloop    = 0;
    ncplgcp    = 0;
    cplgvl     = NULL;

    addParticle(&pundef);
}

//--------------------------------------------------------------
Model::~Model(void)
{
    int j;

    if (ncplgcp > 0) {
        for (j = ncplgcp-1; j >= 0; j--) {
            cplgvl[j] = delintdup(cplgvl[j]);
        }
        delete[] cplgvl;
        cplgnvl = delintdup(cplgnvl);
        cplglg  = delintdup(cplglg);
        cplgcp  = delintdup(cplgcp);
    }

    for (j = GRCC_MAXMINTERACT-1; j >= 0; j--) {
        if (interacts[j] != NULL) {
            interacts[j]->slist = delintdup(interacts[j]->slist);
            delete interacts[j];
            interacts[j] = NULL;
        }
    }
    delete[] interacts;
    interacts = NULL;

    for (j = GRCC_MAXMPARTICLES-1; j >= 0; j--) {
        if (particles[j] != NULL) {
            delete particles[j];
            particles[j] = NULL;
        }
    }
    delete[] particles;
    particles = NULL;

    for (j=ncouple-1; j>=0; j--) {
        free(cnlist[j]);
    }
    delete[] cnlist;

    free(name);
}

//--------------------------------------------------------------
void Model::prModel(void)
{
    static char hdr[] = "#=================================================\n";
    static char hd1[] = "#-------------------------------------------------\n";
    int j;

    grcc_fprintf(GRCC_Stdout, "%s", hdr);
    grcc_fprintf(GRCC_Stdout, "Model=\"%s\", ", name);
    grcc_fprintf(GRCC_Stdout, "coupling=[");
    for (j = 0; j < ncouple; j++) {
        if (j != 0) {
            grcc_fprintf(GRCC_Stdout, ", ");
        }
        grcc_fprintf(GRCC_Stdout, "\"%s\"", cnlist[j]);
    }
    grcc_fprintf(GRCC_Stdout, "];\n");
    grcc_fprintf(GRCC_Stdout, "%s", hd1);
    grcc_fprintf(GRCC_Stdout, "Particles=%d;\n", nParticles);
    for (j = 1; j < nParticles; j++) {
        particles[j]->prParticle();
    }
    grcc_fprintf(GRCC_Stdout, "EndParticle;\n");
    grcc_fprintf(GRCC_Stdout, "allPart (%d) = [", nallPart);
    for (j = 0; j < nallPart; j++) {
        if (j != 0) {
            grcc_fprintf(GRCC_Stdout, ", ");
        }
        grcc_fprintf(GRCC_Stdout, "%d", allPart[j]);
    }
    grcc_fprintf(GRCC_Stdout, "]\n");

    grcc_fprintf(GRCC_Stdout, "%s", hd1);
    grcc_fprintf(GRCC_Stdout, "Interactions=%d;\n", nInteracts);
    for (j = 0; j < nInteracts; j++) {
        interacts[j]->prInteraction();
    }
    grcc_fprintf(GRCC_Stdout, "EndInteraction;\n");
    grcc_fprintf(GRCC_Stdout, "%s", hd1);
    grcc_fprintf(GRCC_Stdout, "InteractionTable;\n");
    grcc_fprintf(GRCC_Stdout, "#  %d class in (total coupling, degree)\n", ncplgcp);
    for (j = 0; j < ncplgcp; j++) {
        grcc_fprintf(GRCC_Stdout, "  class=%d: cp=%d, lg=%d, vl=", j, cplgcp[j], cplglg[j]);
        prIntArray(cplgnvl[j], cplgvl[j], "\n");
    }
    grcc_fprintf(GRCC_Stdout, "EndInteractionTable;\n");
    grcc_fprintf(GRCC_Stdout, "%s", hdr);
}

//--------------------------------------------------------------
void Model::addParticle(PInput *pinp)
{
    int  nid, aid, pid, pcd, acd;

    if (nParticles >= GRCC_MAXMPARTICLES) {
        erEnd("particle table overflow (GRCC_MAXMPARTICLES)");
    }

    // uniqueness check
    if (Abs(defpart) == GRCC_DEFBYCODE) {
        pcd = findParticleCode(pinp->pcode);
        acd = findParticleCode(pinp->acode);
        if (pcd > 0 || acd > 0) {
            if (prlevel > 0) {
                grcc_fprintf(GRCC_Stderr, "*** particle code [%d, %d] ", 
                        pinp->pcode, pinp->acode);
                grcc_fprintf(GRCC_Stderr, "is already used.\n");
            }
            erEnd("particle code is already defined");
        }
    } else if (Abs(defpart) == GRCC_DEFBYNAME) {
        if (pinp->name == NULL || pinp->aname == NULL ||
            strlen(pinp->name) < 1 || strlen(pinp->aname) < 1) {
            erEnd("no name of particle or anti-particle.");
        }
        nid = findParticleName(pinp->name);
        aid = findParticleName(pinp->aname);
        if (nid > 0 || aid > 0) {
            if (prlevel > 0) {
                grcc_fprintf(GRCC_Stderr, "*** particle name [%s, %s] ", 
                        pinp->name, pinp->aname);
                grcc_fprintf(GRCC_Stderr, "is already used.\n");
            }
            erEnd("particle name is already defined.");
        }
    }

    pid = nParticles++;
    particles[pid] = new Particle(this, pid, pinp);
}

//--------------------------------------------------------------
void Model::addParticleEnd(void)
{
    int p, ap;

    pdef = True;

#ifdef OPTEXTONLY
    nallPart = 0;
    for (p = nParticles-1; p >= 1; p--) {
        if (!particles[p]->extonly) {
            ap = antiParticle(p);
            if (ap != p) {
                allPart[nallPart++] = ap;
            }
        }
    }
    for (p = 1; p < nParticles; p++) {
        if (!particles[p]->extonly) {
            allPart[nallPart++] = p;
        }
    }
    sorti(nallPart, allPart);
#else
    nallPart = 0;
    for (p = nParticles-1; p >= 1; p--) {
        ap = antiParticle(p);
        if (ap != p) {
            allPart[nallPart++] = ap;
        }
    }
    for (p = 1; p < nParticles; p++) {
        allPart[nallPart++] = p;
    }
    sorti(nallPart, allPart);
#endif
}

//--------------------------------------------------------------
void Model::addInteraction(IInput *iinp)
{
    int vid, nlegs, j, k, c;
    int csum, lp2, lp;
    int plist[GRCC_MAXLEGS];

    if (!pdef) {
        erEnd("call 'addParticleEnd' before 'addInteraction'");
    }
    if (nInteracts >= GRCC_MAXMINTERACT) {
        erEnd("too many interactions in the model (GRCC_MAXMINTERACT)");
    }
    nlegs = iinp->nplistn;
    if (nlegs >= GRCC_MAXLEGS) {
        erEnd("too many legs in an interaction (GRCC_MAXLEGS)");
    }

    // check identifier
    if (defpart == GRCC_DEFBYCODE) {
        if (iinp->icode < 0) {
            if (prlevel > 0) {
                grcc_fprintf(GRCC_Stderr, "*** vertex code %d should be positive\n",
                        iinp->icode);
            }
            erEnd("vertex code should be positive");
        } else {
            vid = findInteractionCode(iinp->icode);
            if (vid >= 0) {
                if (prlevel > 0) {
                    grcc_fprintf(GRCC_Stderr, "*** vertex code %d is already used\n",
                            iinp->icode);
                }
                erEnd("vertex code is already used");
            }
        }
    } else if (defpart == GRCC_DEFBYNAME) {
        if (iinp->name == NULL || strlen(iinp->name) < 1) {
            erEnd("no name of vertex\n");
        }
        vid = findInteractionName(iinp->name);
        if (vid >= 0) {
            if (prlevel > 0) {
                grcc_fprintf(GRCC_Stderr, "*** vertex name %s is already used\n",
                iinp->name);
                erEnd("vertex name is already used");
            }
        }
    } else {
#ifdef UNIQINTR
        // defpart =< 0
        erEnd("illegal value of defpart");
#else
        // don't care about duplicated name/code of interaction
        ;   
#endif
    }
    vid = nInteracts++;

    for (j = 0; j < nlegs; j++) {
        if (Abs(defpart) == GRCC_DEFBYCODE) {
            plist[j] = findParticleCode(iinp->plistc[j]);
            if (plist[j] == 0) {
                if (prlevel > 0) {
                    grcc_fprintf(GRCC_Stderr, "*** particle code %d ",
                            iinp->plistc[j]);
                    grcc_fprintf(GRCC_Stderr, "is not defined\n");
                }
                erEnd("particle is not defined (code)");
            }
        } else if (Abs(defpart) == GRCC_DEFBYNAME) {
            plist[j] = findParticleName(iinp->plistn[j]);
            if (plist[j] == 0) {
                if (prlevel > 0) {
                    grcc_fprintf(GRCC_Stderr, "*** particle name %s ",
                            iinp->plistn[j]);
                    grcc_fprintf(GRCC_Stderr, "is not defined\n");
                }
                erEnd("particle is not defined (name)");
            }
        }
    }

    csum = 0;
    for (j = 0; j < ncouple; j++) {
        c = iinp->cvallist[j];
        if (c < 0) {
            if (prlevel > 0) {
                grcc_fprintf(GRCC_Stderr, "*** illegal value of c-constants \n");
                for (k = 0; k < ncouple; k++) {
                      grcc_fprintf(GRCC_Stderr, "    %s = %d\n",
                              cnlist[k], iinp->cvallist[k]);
                }
            }
            erEnd("illegal value of c-constants");
        }
        csum += c;
    }
    if (csum < 0) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** illegal total coupling-constants %d\n",
                    csum);
            for (k = 0; k < ncouple; k++) {
                grcc_fprintf(GRCC_Stderr, "    %s = %d\n", 
                        cnlist[k], iinp->cvallist[k]);
            }
        }
        erEnd("illegal value of c-constants");
    }

    // assume : csum = nlegs - 2 + 2*loop
    lp2 = csum - nlegs + 2;
    if (lp2 % 2 != 0 || lp2 < 0) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** illegal coupling const : ");
            grcc_fprintf(GRCC_Stderr, "nlegs - 2 + 2*loop: 2*loop = %d\n", lp2);
        }
    }
    lp = lp2/2;

    maxnlegs = Max(maxnlegs, nlegs);
    maxloop  = Max(maxloop , lp);
    maxcpl   = Max(maxcpl  , csum);

    interacts[vid] = new Interaction(this, vid, iinp->name, iinp->icode, 
                             iinp->cvallist, nlegs, plist, csum, lp);
}

//--------------------------------------------------------------
void Model::addInteractionEnd(void)
{
    int lst[GRCC_MAXMINTERACT];
    int tcp[GRCC_MAXMINTERACT], tlg[GRCC_MAXMINTERACT];
    int tnvl[GRCC_MAXMINTERACT], *tvl[GRCC_MAXMINTERACT];
    Interaction *vt;
    int cp, lg, j, k, p;

    vdef = True;
    ncplgcp = 0;
    for (cp = 0; cp <= maxcpl; cp++) {

        for (lg = 0; lg <= maxnlegs; lg++) {
            k = 0;
            for (j = 0; j < nInteracts; j++) {
                vt = interacts[j];
                if (vt->csum == cp && vt->nlegs == lg) {
                    lst[k++] = j;
                }
            }
            if (k > 0) {
                tcp[ncplgcp]  = cp;
                tlg[ncplgcp]  = lg;
                tnvl[ncplgcp] = k;
                tvl[ncplgcp]  = intdup(k, lst);
                ncplgcp++;
            }
        }
    }
    cplgcp  = intdup(ncplgcp, tcp);
    cplglg  = intdup(ncplgcp, tlg);
    cplgnvl = intdup(ncplgcp, tnvl);
    cplgvl  = new int*[ncplgcp];
    for (j = 0; j < ncplgcp; j++) {
        if (cplgnvl[j] > 0) {
            cplgvl[j] = tvl[j];
        } else {
            cplgvl[j] = NULL;
        }
    }

    for (j = 0; j < nInteracts; j++) {
        vt = interacts[j];
        if (vt->slist != NULL) {
            erEnd("addInteractionEnd: vt->nslist != NULL");
        }
        vt->slist  = intdup(vt->nplist, vt->plist);
        vt->nslist = toSList(vt->nplist, vt->slist);
    }

    for (p = 0; p < nParticles; p++) {
        particles[p]->cmindeg = 0;
        particles[p]->cmaxdeg = 0;
    }
    for (j = 0; j < nInteracts; j++) {
        vt = interacts[j];
        for (k = 0; k < vt->nplist; k++) {
            p = abs(vt->plist[k]);
            if (particles[p]->cmindeg == 0) {
                particles[p]->cmindeg = vt->nlegs;
                particles[p]->cmaxdeg = vt->nlegs;
            } else {
                particles[p]->cmindeg = Min(particles[p]->cmindeg, vt->nlegs);
                particles[p]->cmaxdeg = Max(particles[p]->cmaxdeg, vt->nlegs);
            }
        }
    }
}

//--------------------------------------------------------------
int Model::findParticleName(const char *name)
{
    int j;

    for (j = 0; j < nParticles; j++) {
        if (strcmp(name, particles[j]->name) == 0) {
            return j;
        }
    }
    for (j = 0; j < nParticles; j++) {
        if (strcmp(name, particles[j]->aname) == 0) {
            return -j;
        }
    }
    return 0;
}

//--------------------------------------------------------------
int Model::findParticleCode(int pcd)
{
    int j;

    for (j = 0; j < nParticles; j++) {
        if (pcd == particles[j]->pcode) {
            return j;
        } else if (pcd == particles[j]->acode) {
            return -j;
        }
    }
    return 0;
}

//--------------------------------------------------------------
char *Model::particleName(int p)
{
    int q;

    if (Abs(p) >= nParticles) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "\n*** Model::particleName: ");
            grcc_fprintf(GRCC_Stderr, "illegal particle id=%d\n", p);
        }
        erEnd("Model::particleName: illegal particle");
    }
    if (p < 0) {
        q = - p;
    } else {
        q = p;
    }
    return particles[q]->particleName(p);
}

//--------------------------------------------------------------
int Model::particleCode(int p)
{
    int q;

    if (Abs(p) >= nParticles) {
        grcc_fprintf(GRCC_Stderr, "\n*** Model::particleCode: illegal particle id=%d\n",
                p);
        erEnd("Model::particleCode: illegal particle");
    }
    if (p < 0) {
        q = - p;
    } else {
        q = p;
    }
    return particles[q]->particleCode(p);
}

//--------------------------------------------------------------
void Model::prParticleArray(int n, int *a, const char *msg)
{
    int j;

    grcc_fprintf(GRCC_Stdout, "[");
    for (j = 0; j < n; j++) {
        if (j != 0) {
            grcc_fprintf(GRCC_Stdout, ", ");
        }
        grcc_fprintf(GRCC_Stdout, "%s", particleName(a[j]));
    }
    grcc_fprintf(GRCC_Stdout, "]%s", msg);
}

//--------------------------------------------------------------
int Model::findMClass(const int cpl, const int dgr)
{
    int j;

    for (j = 0; j < ncplgcp; j++) {
        if (cplgcp[j] == cpl && cplglg[j] == dgr) {
            return j;
        }
    }
    return -1;
}

//--------------------------------------------------------------
int Model::normalParticle(int pt)
{
    int ptc = Abs(pt);
    Particle *p;

    if (ptc >= nParticles) {
        return 0;
    }
    p = particles[ptc];
    if (p->isNeutral()) {
        return ptc;
    } else {
        return pt;
    }
}

//--------------------------------------------------------------
int Model::antiParticle(int pt)
{
    int ptc = Abs(pt);
    Particle *p;

    p = particles[ptc];
    if (p->isNeutral()) {
        return ptc;
    } else {
        return -pt;
    }
}

//--------------------------------------------------------------
int *Model::allParticles(int *len)
{
    *len = nallPart;
    return allPart;
}

//--------------------------------------------------------------
int Model::findInteractionName(const char *name)
{
    int j;

    for (j = 0; j < nInteracts; j++) {
        if (strcmp(name, interacts[j]->name) == 0) {
            return j;
        }
    }
    return -1;
}

//--------------------------------------------------------------
int Model::findInteractionCode(int icd)
{
    int j;

    for (j = 0; j < nInteracts; j++) {
        if (icd == interacts[j]->icode) {
            return j;
        }
    }
    return -1;
}

//--------------------------------------------------------------
void Model::printMInput(MInput *min)
{
    grcc_fprintf(GRCC_Stdout, "  \"Model\": [\"%s\", %d, [",
           min->name, min->ncouple);
    for (int j = 0; j < min->ncouple; j++) {
        if (j != 0) {
            grcc_fprintf(GRCC_Stdout, ", ");
        }
        grcc_fprintf(GRCC_Stdout, "\"%s\"", min->cnamlist[j]);
    }
    grcc_fprintf(GRCC_Stdout, "], ");
    if (min->defpart == GRCC_DEFBYCODE) {
        grcc_fprintf(GRCC_Stdout, "\"ByCode\"");
    } else {
        grcc_fprintf(GRCC_Stdout, "\"ByName\"");
    }
    grcc_fprintf(GRCC_Stdout, "],\n");
}

//--------------------------------------------------------------
void Model::printPInput(PInput *pin)
{
    grcc_fprintf(GRCC_Stdout, "    [\"%s\"(%d), \"%s\"(%d), \"%s\"(%d), %d],\n",
           pin->name, pin->pcode, pin->aname, pin->acode,
           pin->ptypen, pin->ptypec, pin->extonly);
}

//--------------------------------------------------------------
void Model::printIInput(IInput *iin)
{
    int j;

    grcc_fprintf(GRCC_Stdout, "    [\"%s\"(%d), %d, [", iin->name, iin->icode, iin->nplistn);
    for (j = 0; j < iin->nplistn; j++) {
        if (j != 0) {
            grcc_fprintf(GRCC_Stdout, ", ");
        }
        grcc_fprintf(GRCC_Stdout, "\"%s\"(%d)", iin->plistn[j], iin->plistc[j]);
    }
    grcc_fprintf(GRCC_Stdout, "], [");
    for (j = 0; j < GRCC_MAXNCPLG; j++) {
        if (j != 0) {
            grcc_fprintf(GRCC_Stdout, ", ");
        }
        grcc_fprintf(GRCC_Stdout, "%d", iin->cvallist[j]);
    }
    grcc_fprintf(GRCC_Stdout, "],\n");
}

//**************************************************************
// proc.cc

//==============================================================
// class PNodeClass
//--------------------------------------------------------------
PNodeClass::PNodeClass(SProcess *spc, int nnods, int nclss, NCInput *cls)
{
    //  Create a class of nodes
    //    nnodes : # nodes
    //    nclss  : # classes
    //    cls    : table of class inputs
    // 
    int j, k, nn, lp2;
    Bool ok = True;

    sproc    = spc;
    nnodes   = nnods;
    nclass   = nclss;
    deg      = new int[nclass];
    type     = new int[nclass];
    particle = new int[nclass];
    count    = new int[nclass];
    couple   = new int[nclass];
    cmindeg  = new int[nclass];
    cmaxdeg  = new int[nclass];
    for (j = 0; j < nclass; j++) {
        deg[j]      = cls[j].cldeg;
        count[j]    = cls[j].clnum;
        type[j]     = cls[j].cltyp;
        cmindeg[j]  = cls[j].cmind;
        cmaxdeg[j]  = cls[j].cmaxd;
        particle[j] = cls[j].ptcl;
        couple[j]   = cls[j].cple;
        lp2 = (couple[j]-deg[j]+2);
        if (!isATExternal(type[j]) && (lp2 % 2 != 0 || lp2 < 0)) {
            if (prlevel > 0) {
                grcc_fprintf(GRCC_Stderr, "*** PNodeClass: illegal loop: "
                       ": 2*loop=cpl[%d](%d)-deg[%d](%d)+2 =2*loop = %d\n",
                       j, couple[j], j, deg[j], lp2);
                for (k = 0; k < nclss; k++) {
                    grcc_fprintf(GRCC_Stderr, "k=%d, deg=%d, typ=%d, ptcl=%d, ",
                            k, deg[k], type[k], particle[k]);
                    grcc_fprintf(GRCC_Stderr, "cpl=%d, cnt=%d\n", 
                            couple[k], count[k]);
                }
            }
            ok = False;
        }
    }
    if (!ok) {
        erEnd("PNodeClass: illegal loop");
    }
    cl2nd   = new int[nclass+1];
    nd2cl   = new int[nnodes];
    cl2mcl  = new int[nnodes];

    nn = 0;
    for (j = 0; j < nclass; j++) {
        cl2nd[j]  = nn;
        for (k = 0; k < count[j]; k++, nn++) {
            nd2cl[nn]  = j;
        }
        if (isATExternal(type[j])) {
            cl2mcl[j] = -1;
        } else {
            cl2mcl[j] = spc->model->findMClass(couple[j], deg[j]);
            if (cl2mcl[j] < 0) {
                if (prlevel > 0) {
                    grcc_fprintf(GRCC_Stderr, "*** PNodeClass : no vertex : ");
                    grcc_fprintf(GRCC_Stderr, "coupling=%d, degree=%d\n",
                           couple[j], deg[j]);
                }
                erEnd("PNodeClass : no vertex");
            }
        }
    }
    cl2nd[nclass] = nnodes;
}
//--------------------------------------------------------------
PNodeClass::PNodeClass(SProcess *spc, int nnods, int nclss, int *dgs, int *typ, int *ptcl, int *cpl, int *cnt, int *cmind, int *cmaxd)
{
    //  Create a class of nodes
    //    nnodes : # nodes
    //    nclss  : # classes
    //    dgs  : degree of a node, which is common to the vertices in a class
    //    typ  : initial/final/vertex
    //    ptcl : particle code or list of possible interactions 
    //    cpl  : values of coupling constants.
    //    cnt  : the number of nodes in this class
    // 
    int j, k, nn, lp2;
    Bool ok = True;

    sproc    = spc;
    nnodes   = nnods;
    nclass   = nclss;
    deg      = new int[nclass];
    type     = new int[nclass];
    particle = new int[nclass];
    count    = new int[nclass];
    couple   = new int[nclass];
    cmindeg  = new int[nclass];
    cmaxdeg  = new int[nclass];
    for (j = 0; j < nclass; j++) {
        deg[j]      = dgs[j];
        type[j]     = typ[j];
        particle[j] = ptcl[j];
        count[j]    = cnt[j];
        couple[j]   = cpl[j];
        cmindeg[j]  = cmind[j];
        cmaxdeg[j]  = cmaxd[j];
        lp2 = (cpl[j]-dgs[j]+2);
        if (!isATExternal(type[j]) && (lp2 % 2 != 0 || lp2 < 0)) {
            if (prlevel > 0) {
                grcc_fprintf(GRCC_Stderr, "*** PNodeClass: illegal loop: "
                       ": 2*loop=cpl[%d](%d)-deg[%d](%d)+2 =2*loop = %d\n",
                       j, cpl[j], j, dgs[j], lp2);
                for (k = 0; k < nclss; k++) {
                    grcc_fprintf(GRCC_Stderr, "k=%d, dgs=%d, typ=%d, ptcl=%d, ",
                           k, dgs[k], typ[k], ptcl[k]);
                    grcc_fprintf(GRCC_Stderr, "cpl=%d, cnt=%d\n", cpl[k], cnt[k]);
                }
            }
            ok = False;
        }
    }
    if (!ok) {
        erEnd("PNodeClass: illegal loop");
    }
    cl2nd   = new int[nclass+1];
    nd2cl   = new int[nnodes];
    cl2mcl  = new int[nnodes];

    nn = 0;
    for (j = 0; j < nclass; j++) {
        cl2nd[j]  = nn;
        for (k = 0; k < count[j]; k++, nn++) {
            nd2cl[nn]  = j;
        }
        if (isATExternal(type[j])) {
            cl2mcl[j] = -1;
        } else {
            cl2mcl[j] = spc->model->findMClass(couple[j], deg[j]);
            if (cl2mcl[j] < 0) {
                if (prlevel > 0) {
                    grcc_fprintf(GRCC_Stderr, "*** PNodeClass : no vertex : ");
                    grcc_fprintf(GRCC_Stderr, "coupling=%d, degree=%d\n",
                           couple[j], deg[j]);
                }
                erEnd("PNodeClass : no vertex");
            }
        }
    }
    cl2nd[nclass] = nnodes;
}

//--------------------------------------------------------------
PNodeClass::~PNodeClass(void)
{
    delete[] cl2mcl;
    delete[] nd2cl;
    delete[] cl2nd;
    delete[] cmaxdeg;
    delete[] cmindeg;
    delete[] couple;
    delete[] count;
    delete[] particle;
    delete[] type;
    delete[] deg;
}

//--------------------------------------------------------------
void PNodeClass::prPNodeClass(void)
{
    int j;

    grcc_fprintf(GRCC_Stdout, "+++ PNodeClass: nclass=%d, nnodes=%d\n", nclass, nnodes);
    for (j = 0; j < nclass; j++) {
        prElem(j);
    }
    grcc_fprintf(GRCC_Stdout, "\n");
}

//--------------------------------------------------------------
void PNodeClass::prElem(int j)
{
    int tp;

    grcc_fprintf(GRCC_Stdout, "%3d: %-7s(%2d), ", j, GRCC_AT_NdStr(type[j]), type[j]);
    grcc_fprintf(GRCC_Stdout, "deg=%d, count=%d, nodes[%d--%d], couple=%d, cmindeg=%d, cmaxdeg=%d",
           deg[j], count[j], cl2nd[j], cl2nd[j+1], couple[j], cmindeg[j], cmaxdeg[j]);
    tp = type[j];
    if (isATExternal(tp)) {
        if (sproc->model != NULL) {
            grcc_fprintf(GRCC_Stdout, ", ptcl=%s ", sproc->model->particleName(particle[j]));
        } else {
            grcc_fprintf(GRCC_Stdout, ", ptcl=%d ", particle[j]);
        }
    }
    grcc_fprintf(GRCC_Stdout, "\n");

}

//==============================================================
// class SProcess
//--------------------------------------------------------------
SProcess::SProcess(Model *mdl, Process *prc, Options *opts, int sid, int *clst, int ncls, int *cdeg, int *ctyp, int *ptcl, int *cpl, int *cnum, int *cmind, int *cmaxd)
{
    // Construct a Subprocess object
    //    mdl            : model
    //    prc            : process (may be NULL)
    //    opts           : options
    //    sid            : id of the sprocess
    //    ncls           : the number of classes
    //    cdeg[ncls]     : the table of degrees of nodes.
    //    ctyp[ncls]     : the table of nodes in the classes
    //    ptcl[ncls]     : particle(External)/interaction code(Internal)
    //    cpl[ncls]      : the table of total order of coupling constants.
    //    cnum[ncls]     : the table of nodes in the classes
    //    cmind[ncls]    : the table of min(deg of connectable vertex)
    //    cmaxd[ncls]    : the table of max(deg of connectable vertex)

    int j, cp, lp2, ndeg, nvrt, tcpl0;
    bool ok;

    if (ncls < 1) {
        grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: no class %d\n", ncls);
        erEnd("SProcess::SProcess: no Class");
    }
    id       = sid;
    model    = mdl;
    proc     = prc;
    opt      = opts;
    nclass   = ncls;

    nNodes   = 0;
    nEdges   = 0;
    nExtern  = 0;
    tCouple  = 0;
    loop     = 0;
    mgraph   = NULL;
    egraph   = NULL;
    astack   = NULL;

    mgrcount = 0;
    agrcount = 0;
    extperm  = 1;

    // the results of the graph generation
    nMGraphs = 0;               // the number of generated M-graphs
    nMOPI    = 0;               // the number of 1PI M-graphs
    wMGraphs.setValue(0,1);   // the weighted sum of M-graphs
    wMOPI.setValue(0,1);      // the weighted sum of 1PI M-graphs

    nAGraphs = 0;               // the number of generated A-graphs
    nAOPI    = 0;               // the number of 1PI A-graphs
    wAGraphs.setValue(0,1);   // the weighted sum of A-graphs
    wAOPI.setValue(0,1);      // the weighted sum of 1PI A-graphs

    // check input
    nNodes  = 0;
    nExtern = 0;

    ndeg     = 0;
    nvrt     = 0;
    ok = True;

    tcpl0 = 0;
    for (j = 0; j < model->ncouple; j++) {
        clist[j] = clst[j];
        tcpl0 += clist[j];
    }
    for (j = 0; j < nclass; j++) {
        cp  = cpl[j];
        if (cp > 0) {
            lp2 = cpl[j] - cdeg[j] + 2;
            if (lp2 % 2 != 0 || lp2 < 0) {
                if (prlevel > 0) {
                    grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal loop:"
                           "class %d, cp=%d, deg=%d, lp2=%d\n",
                           j, cp, cdeg[j], lp2);
                }
                ok = False;
            }
        }
        tCouple +=      cp*cnum[j];
        ndeg    += cdeg[j]*cnum[j];

        if (!isATExternal(ctyp[j])) {
            nvrt += cnum[j];
        } else if (isATExternal(ctyp[j])) {
            if (model->normalParticle(ptcl[j]) == 0) {
                if (prlevel > 0) {
                    grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: ");
                    grcc_fprintf(GRCC_Stderr, "illegal particle code: ");
                    grcc_fprintf(GRCC_Stderr, "code: class %d, ptcl=%d\n", j, ptcl[j]);
                }
                ok = False;
            } else {
                nExtern += cnum[j];
            }
            extperm *= factorial(cnum[j]);
  
        } else {
            if (prlevel > 0) {
                grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal type: ");
                grcc_fprintf(GRCC_Stderr, "class %d, type=%d\n", j, ctyp[j]);
            }
            ok = False;
        }
    }
    if (tcpl0 != tCouple) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: ");
            grcc_fprintf(GRCC_Stderr, "illegal coupling constants:");
            grcc_fprintf(GRCC_Stderr, " %d != %d\n", tcpl0, tCouple);
        }
        ok = False;
    }
    if (ndeg == nExtern) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: ");
            grcc_fprintf(GRCC_Stderr, "no vertices: ");
            grcc_fprintf(GRCC_Stderr, "nExtern=%d, ndeg=%d\n", nExtern, ndeg);
        }
        ok = False;
    }
    if (ndeg % 2 == 0) {
        nEdges = ndeg/2;
    } else {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: ");
            grcc_fprintf(GRCC_Stderr, "illegal total deg = %d (not even)\n", ndeg);
        }
        ok = False;
    }
    nNodes = nvrt + nExtern;
    if (nNodes >= GRCC_MAXNODES) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: ");
            grcc_fprintf(GRCC_Stderr, "too many nodes = %d\n", nNodes);
            grcc_fprintf(GRCC_Stderr, "    nExtern=%d, nvert=%d (GRCC_MAXNODES)\n",
                    nExtern, nvert);
        }
        ok = False;
    }
    if (!ok) {
        prSProcess();
        erEnd("SProcess::SProcess: illegal input");
    }
    if (proc == NULL) {
        opt->beginProc(NULL);
    }

    lp2 = tCouple - nExtern + 2;
    if (lp2 % 2 != 0 || lp2 < 0) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal loop: "
                   "tCouple=%d, nExtern=%d, 2*loop=%d\n",
                   tCouple, nExtern, lp2);
        }
        ok = False;
    }
    loop = lp2/2;

    // stack for assignment
    if (opt->values[GRCC_OPT_Step] == GRCC_AGraph) {
        astack = new AStack(GRCC_MAXNSTACK, GRCC_MAXESTACK);
    }

    // save to PNodeClass object
    pnclass = new PNodeClass(this, nNodes, nclass, cdeg, ctyp, ptcl, cpl, cnum, cmind, cmaxd);
}

//--------------------------------------------------------------
SProcess::SProcess(Model *mdl, Process *prc, Options *opts, int sid, int *clst, int ncls, NCInput *cls)
{
    // Construct a Subprocess object
    //    mdl            : model
    //    prc            : process (may be NULL)
    //    opts           : options
    //    sid            : id of the sprocess
    //    ncls           : the number of classes
    //    cls            : input data of classes

    int j, cp, lp2, ndeg, nvrt, tcpl0;
    bool ok;

    if (ncls < 1) {
        grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: no class %d\n", ncls);
        erEnd("SProcess::SProcess: no Class");
    }
    id       = sid;
    model    = mdl;
    proc     = prc;
    opt      = opts;
    nclass   = ncls;

    nNodes   = 0;
    nEdges   = 0;
    nExtern  = 0;
    tCouple  = 0;
    loop     = 0;
    mgraph   = NULL;
    egraph   = NULL;
    astack   = NULL;

    mgrcount = 0;
    agrcount = 0;
    extperm  = 1;

    // the results of the graph generation
    nMGraphs = 0;               // the number of generated M-graphs
    nMOPI    = 0;               // the number of 1PI M-graphs
    wMGraphs.setValue(0,1);   // the weighted sum of M-graphs
    wMOPI.setValue(0,1);      // the weighted sum of 1PI M-graphs

    nAGraphs = 0;               // the number of generated A-graphs
    nAOPI    = 0;               // the number of 1PI A-graphs
    wAGraphs.setValue(0,1);   // the weighted sum of A-graphs
    wAOPI.setValue(0,1);      // the weighted sum of 1PI A-graphs

    // check input
    nNodes  = 0;
    nExtern = 0;

    ndeg     = 0;
    nvrt     = 0;
    ok = True;

    tcpl0 = 0;
    for (j = 0; j < model->ncouple; j++) {
        clist[j] = clst[j];
        tcpl0 += clist[j];
    }
    for (j = 0; j < nclass; j++) {
        cp  = cls[j].cple;
        if (cp > 0) {
            lp2 = cls[j].cple - cls[j].cldeg + 2;
            if (lp2 % 2 != 0 || lp2 < 0) {
                if (prlevel > 0) {
                    grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal loop: "
                           "class %d, cp=%d, deg=%d, lp2=%d\n",
                           j, cp, cls[j].cldeg, lp2);
                }
                ok = False;
            }
        }
        tCouple += cp*cls[j].clnum;
        ndeg    += cls[j].cldeg*cls[j].clnum;

        if (!isATExternal(cls[j].cltyp)) {
            nvrt += cls[j].clnum;
        } else if (isATExternal(cls[j].cltyp)) {
            if (model->normalParticle(cls[j].ptcl) == 0) {
                if (prlevel > 0) {
                    grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: ");
                    grcc_fprintf(GRCC_Stderr, "illegal particle code: ");
                    grcc_fprintf(GRCC_Stderr, "code: class %d, ptcl=%d\n", j, cls[j].ptcl);
                }
                ok = False;
            } else {
                nExtern += cls[j].clnum;
            }
            extperm *= factorial(cls[j].clnum);
  
        } else {
            if (prlevel > 0) {
                grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal type: ");
                grcc_fprintf(GRCC_Stderr, "class %d, type=%d\n", j, cls[j].cltyp);
            }
            ok = False;
        }
    }
    if (tcpl0 != tCouple) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: ");
            grcc_fprintf(GRCC_Stderr, "illegal coupling constants:");
            grcc_fprintf(GRCC_Stderr, " %d != %d\n", tcpl0, tCouple);
        }
        ok = False;
    }
    if (ndeg == nExtern) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: ");
            grcc_fprintf(GRCC_Stderr, "no vertices: ");
            grcc_fprintf(GRCC_Stderr, "nExtern=%d, ndeg=%d\n", nExtern, ndeg);
        }
        ok = False;
    }
    if (ndeg % 2 == 0) {
        nEdges = ndeg/2;
    } else {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: ");
            grcc_fprintf(GRCC_Stderr, "illegal total deg = %d (not even)\n", ndeg);
        }
        ok = False;
    }
    nNodes = nvrt + nExtern;
    if (nNodes >= GRCC_MAXNODES) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: ");
            grcc_fprintf(GRCC_Stderr, "too many nodes = %d\n", nNodes);
            grcc_fprintf(GRCC_Stderr, "    nExtern=%d, nvert=%d (GRCC_MAXNODES)\n",
                    nExtern, nvert);
        }
        ok = False;
    }
    if (!ok) {
        erEnd("SProcess::SProcess: illegal input");
    }
    if (proc == NULL) {
        opt->beginProc(NULL);
    }

    lp2 = tCouple - nExtern + 2;
    if (lp2 % 2 != 0 || lp2 < 0) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** SProcess::SProcess: illegal loop: "
                   "tCouple=%d, nExtern=%d, 2*loop=%d\n",
                   tCouple, nExtern, lp2);
        }
        ok = False;
    }
    loop = lp2/2;

    // stack for assignment
    if (opt->values[GRCC_OPT_Step] == GRCC_AGraph) {
        astack = new AStack(GRCC_MAXNSTACK, GRCC_MAXESTACK);
    }

    // save to PNodeClass object
    pnclass = new PNodeClass(this, nNodes, nclass, cls);
}

//--------------------------------------------------------------
SProcess::~SProcess(void)
{
    delete pnclass;
    delete astack;
    delete mgraph;
    model = NULL;
}

//--------------------------------------------------------------
void SProcess::prSProcess(void)
{
    grcc_fprintf(GRCC_Stdout, "\n");
    grcc_fprintf(GRCC_Stdout, "+++ Subprocess %d, class=%d\n", id, nclass);
    if (pnclass != NULL) {
        pnclass->prPNodeClass();
    } else {
        grcc_fprintf(GRCC_Stdout, "  pnclass = NULL\n");
   }
}

//--------------------------------------------------------------
BigInt SProcess::generate(void)
{
    //  Entry point of Feynman graph generation
    int  cldeg[GRCC_MAXNODES], clnum[GRCC_MAXNODES], cltyp[GRCC_MAXNODES];
    int  cmind[GRCC_MAXNODES], cmaxd[GRCC_MAXNODES];
    int  ncl;
    BigInt ng;

    ncl = toMNodeClass(cltyp, cldeg, clnum, cmind, cmaxd);

    opt->beginSubProc(this);

    mgraph = new MGraph(id, ncl, cldeg, clnum, cltyp, cmind, cmaxd, opt);

    ng = mgraph->generate();

    opt->endSubProc();

    delete mgraph;
    mgraph = NULL;

    return ng;
}

//--------------------------------------------------------------
int SProcess::toMNodeClass(int *cltyp, int *cldeg, int *clnum, int *cmind, int *cmaxd)
{
    int j;

    for (j = 0; j < nclass; j++) {
        if (isATExternal(pnclass->type[j])) {
            cltyp[j] = -1;
        } else {
            cltyp[j] = (pnclass->couple[j]-pnclass->deg[j]+2)/2;
        }
        cldeg[j] = pnclass->deg[j];
        clnum[j] = pnclass->count[j];
        cmind[j] = pnclass->cmindeg[j];
        cmaxd[j] = pnclass->cmaxdeg[j];
    }
    return nclass;
}

//--------------------------------------------------------------
void SProcess::assign(MGraph *mgr)
{
    PNodeClass *pnc;

    pnc = match(mgr);

    agraph = new Assign(this, mgr, pnc);

#ifdef CHECK
    agraph->checkAG("SProcess::assign");
#endif
    delete pnc;
    delete agraph;
    agraph = NULL;
}

//--------------------------------------------------------------
PNodeClass *SProcess::match(MGraph *mgr)
{
    PNodeClass *pnc = NULL;

    int typ[GRCC_MAXNODES], dgs[GRCC_MAXNODES];
    int cnt[GRCC_MAXNODES], ptcl[GRCC_MAXNODES];
    int cpl[GRCC_MAXNODES];
    int n2m[GRCC_MAXNODES];
    int cmind[GRCC_MAXNODES], cmaxd[GRCC_MAXNODES];
    int j, k, l, nd, mc, mcl, mclss;

    if (mgr->nNodes != nNodes) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** SProcess::match: different nNodes=%d != %d\n",
                   nNodes, mgr->nNodes);
        }
        erEnd("SProcess::match: different nNodes");
    }

    mcl = toMNodeClass(typ, dgs, cnt, cmind, cmaxd);

    nd = 0;
    for (j = 0; j < mcl; j++) {
        for (k = 0; k < cnt[j]; k++, nd++) {
            n2m[nd] = j;
        }
    }

    nd    = 0;
    mclss = mgr->curcl->nClasses;
    for (j = 0; j < mclss; j++) {
        for (k = 0; k < mgr->curcl->clist[j]; k++, nd++) {
            mc = mgr->nodes[nd]->clss;
            if (mc != n2m[nd]) {
                if (prlevel > 0) {
                    grcc_fprintf(GRCC_Stderr, "*** SProcess::match: ");
                    grcc_fprintf(GRCC_Stderr, "inconsistent class\n");
                    for (l = 0; l < nNodes; l++) {
                        grcc_fprintf(GRCC_Stderr, "    %d: %d, %d\n", 
                                j, mgr->nodes[l]->clss, n2m[l]);
                    }
                }
                erEnd("SProcess::match: inconsistent class");
            }
        }
    }
    for (j = 0; j < mcl; j++) {
        dgs[j]    = pnclass->deg[j];
        typ[j]    = pnclass->type[j];
        ptcl[j]   = pnclass->particle[j];
        cnt[j]    = pnclass->count[j];
        cpl[j]    = pnclass->couple[j];
        cmind[j]  = pnclass->cmindeg[j];
        cmaxd[j]  = pnclass->cmaxdeg[j];
    }
    pnc = new PNodeClass(this, nNodes, mcl, dgs, typ, ptcl, cpl, cnt, cmind, cmaxd);

    return pnc;
}

//--------------------------------------------------------------
void SProcess::resultMGraph(BigInt nmgraphs, Fraction mwsum, BigInt nmopi, Fraction mwopi)
{
    nMGraphs += nmgraphs;
    nMOPI    += nmopi;
    wMGraphs.add(mwsum);
    wMOPI.add(mwopi);
}

//--------------------------------------------------------------
void SProcess::resultAGraph(BigInt nmgraphs, Fraction mwsum, BigInt nmopi, Fraction mwopi)
{
    nAGraphs += nmgraphs;
    nAOPI    += nmopi;
    wAGraphs.add(mwsum);
    wAOPI.add(mwopi);
}

//--------------------------------------------------------------
void SProcess::endMGraph(MGraph *mgr)
{
    egraph = mgr->egraph;

    if (opt->values[GRCC_OPT_Step] != GRCC_MGraph) {
        assign(mgr);
    }
}

//--------------------------------------------------------------
void SProcess::endAGraph(EGraph *egr)
{
    egraph = egr;
}


//==============================================================
// class Process
//--------------------------------------------------------------
Process::Process(int pid, Model *modl, Options *optn, int nini, int *intlPrt, int nfin, int *finlPrt, int *coupling)
{
    //  Define a process and construct a set of sprocesses
    //    model     : Model object
    //    optn      : Option object
    //    initlPart : list of particle-id of initlPart particles
    //    finalPart : list of particle-id of final particles
    //    coupling  : list of coupling constants

    int j, lp2;
    Bool ok;
    char buff[MAXSTR];

    id        = pid;
    model     = modl;
    opt       = optn;
    ninitl    = nini;
    nfinal    = nfin;
    initlPart = intdup(ninitl, intlPrt);
    finalPart = intdup(nfinal, finlPrt);

    // count total number of coupling constants.
    ctotal = 0;
    for (j = 0; j < GRCC_MAXNCPLG; j++) {
        if (j < model->ncouple) {
            clist[j] = coupling[j];
            ctotal  += coupling[j];
        } else {
            clist[j] = 0;
        }
    }
    if (ctotal < 1) {
        erEnd("Process: coupling constant = 0");
    }

    nExtern   =  0;
    loop      = -1;
    maxnlegs  =  0;
    mgrcount = 0;
    agrcount = 0;

    // table of sprocesses 
    nSubproc  = 0;
    sproc   = NULL;

    // the results of the graph generation
    nMGraphs = 0;                 // the number of generated M-graphs
    nMOPI    = 0;                 // the number of 1PI M-graphs
    wMGraphs.setValue(0,1);       // the weighted sum of M-graphs
    wMOPI.setValue(0,1);          // the weighted sum of 1PI M-graphs

    nAGraphs = 0;                 // the number of generated A-graphs
    nAOPI    = 0;                 // the number of 1PI A-graphs
    wAGraphs.setValue(0,1);       // the weighted sum of A-graphs
    wAOPI.setValue(0,1);          // the weighted sum of 1PI A-graphs

    ok = True;

    // numbers
    nExtern  = ninitl + nfinal;
    maxnlegs = Max(nExtern, model->maxnlegs);
    
    // count loops
    lp2 = ctotal - nExtern + 2;
    if (lp2 % 2 != 0) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** cannot generate : 2*loop is odd : " 
                    "2*loop = %d, ctotal=%d, nExtern=%d\n",
                    lp2, ctotal, nExtern);
        }
        ok = False;
    } else if (lp2 < 0) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** cannot make a connected graph : "
                    "2*loop=%d, ctotal=%d, nExtern=%d\n",
                    lp2, ctotal, nExtern);
        }
        ok = False;
    }

    loop = lp2 / 2;

    if (!ok) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** Process: illegal input: lp2 = %d\n", lp2);
        }
        erEnd("Process: illegal input");
    }

    if (opt->out->outgrp != NULL) {
        snprintf(buff, MAXSTR, "out%d.prp", pid);
        prProcessP(buff);
    }

    // construct sprocesses
    mkSProcess();
}

//--------------------------------------------------------------
Process::~Process(void)
{
    initlPart = delintdup(initlPart);
    finalPart = delintdup(finalPart);
    for (int j = 0; j < nSubproc; j++) {
        delete sptbl[j];
    }
 // delete sproc;
}

//--------------------------------------------------------------
void Process::prProcess(void)
{
    grcc_fprintf(GRCC_Stdout, "+++ process options : OPI = %d, (Step) = %d, coupling=%d: ",
           opt->values[GRCC_OPT_1PI], opt->values[GRCC_OPT_Step], ctotal);
    prIntArray(model->ncouple, clist, "\n");
}

//--------------------------------------------------------------
void Process::prProcessP(const char *fname)
{
    FILE *fp;

    if ((fp = fopen(fname, "w")) == NULL) {
        grcc_fprintf(GRCC_Stderr, "*** cannot open \"%s\"\n", fname);
        return;
    }
    fprintf(fp, "Process = {\n");
    outProcP(fp);
    fprintf(fp, "};\n");
    fclose(fp);
}

//--------------------------------------------------------------
void Process::outProcP(FILE *fp)
{
    int   j;

    if (model == NULL) {
        return;
    }
    fprintf(fp, "    \"Model\": \"%s\",\n", model->name);
    fprintf(fp, "    \"Initial\": [");
    for (j = 0; j < ninitl; j++) {
        if (j != 0) {
            fprintf(fp, ", ");
        }
        fprintf(fp, "\"%s\"", model->particleName(initlPart[j]));
    }
    fprintf(fp, "],\n");
    fprintf(fp, "    \"Final\": [");
    for (j = 0; j < nfinal; j++) {
        if (j != 0) {
            fprintf(fp, ", ");
        }
        fprintf(fp, "\"%s\"", model->particleName(finalPart[j]));
    }
    fprintf(fp, "],\n");
    fprintf(fp, "    \"Couple\": [");
    for (j = 0; j < model->ncouple; j++) {
        if (j != 0) {
            fprintf(fp, ", ");
        }
        fprintf(fp, "%d", clist[j]);
    }
    fprintf(fp, "],\n");
    fprintf(fp, "    \"Options\": {\n");
    for (j = 0; j < GRCC_OPT_Size; j++) {
        if (j == GRCC_OPT_Outgrf || j == GRCC_OPT_Outgrp) {
            continue;
        }
        fprintf(fp, "      \"%s\":%d,\n", optDef[j].name, opt->values[j]);
    }
    fprintf(fp, "      \"%s\":", optDef[GRCC_OPT_Outgrf].name);
    if (opt->out->outgrf != NULL) {
        fprintf(fp, "\"%s\",\n", opt->out->outgrf);
    } else {
        fprintf(fp, "0,\n");
    }
    fprintf(fp, "      \"%s\":", optDef[GRCC_OPT_Outgrp].name);
    if (opt->out->outgrp != NULL) {
        fprintf(fp, "\"%s\",\n", opt->out->outgrp);
    } else {
        fprintf(fp, "0,\n");
    }
    fprintf(fp, "    }\n");
}

//--------------------------------------------------------------
void Process::mkSProcess(void)
{
    //  Construct sprocesses
    //  Each sprocess is a set of nodes whose degree and order of 
    //  coupling constants are determined.
    //  Only the total coupling constants are considered here even if
    //  two or more coupling constants are defined in the model

    NCInput cls[GRCC_MAXMINTERACT];
    int r, j, k, lin2, nvtx, nleg, nc, n0;
    int nl[GRCC_MAXMINTERACT];
    double proct0 = 0, proct1 = 0;

    if (model->ncplgcp < 1) {
        erEnd("function 'addInteractionEnd' has not been called");
    }
    // output file to start process
    opt->beginProc(this);

    // starting time
    Second(&proct0);

    // generate all possible number of (nl[i]), 
    //   \sum_i nl[i]*cplgcp[i] = (total number of coupling constants)

    r = -1;
    nSubproc = 0;
    ngraphs  = 0;
    nopi     = 0;
    wgraphs  = 0;
    wopi     = 0;

    // for partitions of (leg, order)
    
    while (nextPart(ctotal, model->ncplgcp, model->cplgcp, nl, &r)) {
        // count the total number of vertices and legs.
        nvtx = 0;
        nleg = 0;
        for (j = 0; j < model->ncplgcp; j++) {
            nvtx += nl[j];
            nleg += nl[j]*model->cplglg[j];
        }

        // count loops
        lin2 = nExtern + nleg;
        if (lin2 % 2 != 0) {
            continue;
        }
        loop = lin2/2 - nExtern - nvtx + 1;
        if (loop < 0) {
            continue;
        }

        nc = 0;
        if (opt->values[GRCC_OPT_SymmInitial]) {
            n0 = nc;
            for (j = 0; j < ninitl; j++) {
                for (k = n0; k < nc; k++) {
                    if (cls[k].ptcl == initlPart[j]) {
                        cls[k].clnum++;
                        break;
                    }
                }
                if (k >= nc) {
                    cls[nc].ptcl  = initlPart[j];
                    cls[nc].clnum = 1;
                    cls[nc].cple  = 0;
                    cls[nc].clnum = 1;
                    cls[nc].cldeg = 1;
                    cls[nc].cltyp = GRCC_AT_Initial;
                    cls[nc].ptcl  = initlPart[j];
                    cls[nc].cmind 
                        = model->particles[Abs(cls[nc].ptcl)]->cmindeg;
                    cls[nc].cmaxd 
                        = model->particles[Abs(cls[nc].ptcl)]->cmaxdeg;
                    if (opt->values[GRCC_OPT_NoExtSelf] > 0 && nExtern > 2) {
                        cls[nc].cmind = Max(cls[nc].cmind, 3);
                    }
                    nc++;
                }
            }
        } else {
            for (j = 0; j < ninitl; j++) {
                cls[nc].ptcl  = initlPart[j];
                cls[nc].clnum = 1;
                cls[nc].cple  = 0;
                cls[nc].cldeg = 1;
                cls[nc].cltyp = GRCC_AT_Initial;
                cls[nc].cmind = model->particles[Abs(cls[nc].ptcl)]->cmindeg;
                cls[nc].cmaxd = model->particles[Abs(cls[nc].ptcl)]->cmaxdeg;
                if (opt->values[GRCC_OPT_NoExtSelf] > 0 && nExtern > 2) {
                    cls[nc].cmind = Max(cls[nc].cmind, 3);
                }
                nc++;
            }
        }
        if (opt->values[GRCC_OPT_SymmFinal]) {
            n0 = nc;
            for (j = 0; j < nfinal; j++) {
                for (k = n0; k < nc; k++) {
                    if (cls[k].ptcl == model->antiParticle(finalPart[j])) {
                        cls[k].clnum++;
                        break;
                    }
                }
                if (k >= nc) {
                    cls[nc].ptcl  = model->antiParticle(finalPart[j]);
                    cls[nc].clnum = 1;
                    cls[nc].cple  = 0;
                    cls[nc].cldeg = 1;
                    cls[nc].cltyp = GRCC_AT_Final;
                    cls[nc].cmind 
                        = model->particles[Abs(cls[nc].ptcl)]->cmindeg;
                    cls[nc].cmaxd 
                        = model->particles[Abs(cls[nc].ptcl)]->cmaxdeg;
                    if (opt->values[GRCC_OPT_NoExtSelf] > 0 && nExtern > 2) {
                        cls[nc].cmind = Max(cls[nc].cmind, 3);
                    }
                    nc++;
                }
            }
        } else {
            for (j = 0; j < nfinal; j++) {
                cls[nc].ptcl  = model->antiParticle(finalPart[j]);
                cls[nc].cldeg = 1;
                cls[nc].cple  = 0;
                cls[nc].clnum = 1;
                cls[nc].cltyp = GRCC_AT_Final;
                cls[nc].cmind = model->particles[Abs(cls[nc].ptcl)]->cmindeg;
                cls[nc].cmaxd = model->particles[Abs(cls[nc].ptcl)]->cmaxdeg;
                if (opt->values[GRCC_OPT_NoExtSelf] > 0 && nExtern > 2) {
                    cls[nc].cmind = Max(cls[nc].cmind, 3);
                }
                nc++;
            }
        }
        for (j = 0; j < model->ncplgcp; j++) {
            if (nl[j] > 0) {
                cls[nc].ptcl  = 0;
                cls[nc].cple  = model->cplgcp[j];
                cls[nc].cldeg = model->cplglg[j];
                cls[nc].clnum = nl[j];
                // number of loops
                cls[nc].cltyp = (model->cplgcp[j] - model->cplglg[j] + 2)/2;
                cls[nc].cmind = 0;
                cls[nc].cmaxd = 0;
                nc++;
            }
        }
        // create a sprocess ??? to be rewritten
        sproc = new SProcess(model, this, opt, nSubproc, clist, nc, cls);
  
        // list of sprocesses
        if (nSubproc >= GRCC_MAXSUBPROCS) {
              erEnd("Subclass: too many sprocesses (GRCC_MAXSUBPROCS)");
        }
        sptbl[nSubproc++] = sproc;

        // generate M-graphs
        sproc->generate();

        // summation of the numbers and weighted numbers of graphs
        nMGraphs += sproc->nMGraphs;
        nMOPI    += sproc->nMOPI;
        wMGraphs.add(sproc->wMGraphs);
        wMOPI.add(sproc->wMOPI);

        nAGraphs += sproc->nAGraphs;
        nAOPI    += sproc->nAOPI;
        wAGraphs.add(sproc->wAGraphs);
        wAOPI.add(sproc->wAOPI);

        if (nAGraphs > 0) {
            ngraphs  = nAGraphs;
        } else {
            ngraphs  = nAGraphs;
        }
     // delete sproc;
     // sproc = NULL;
    }

    // ending time
    Second(&proct1);
    sec = proct1-proct0;

    // output file to finish process
    opt->endProc();
}

//**************************************************************
// mgraph.cc
//==============================================================
//--------------------------------------------------------------
MNodeClass::MNodeClass(int nnodes, int nclasses)
{
    // Input
    //   nnodes   : possible maximal number of nodes
    //   nclasses : possible maximal number of classes

    int j, k;

    nNodes   = nnodes;
    nClasses = nclasses;
    maxdeg   = 0;
    for (j = 0; j < nNodes; j++) {
        for (k = 0; k < nNodes; k++) {
            clmat[j][k] = 0;
        }
        clist[j]   = 0;
        ndcl[j]    = 0;
        flist[j]   = 0;
        clord[j]   = 0;
        cmindeg[j] = 0;
        cmaxdeg[j] = 0;
    }
    flist[nNodes] = 0;
    flg0 = 0;
    flg1 = 0;
    flg2 = 0;
}

//--------------------------------------------------------------
MNodeClass::~MNodeClass(void)
{
}

//==============================================================
// class MNodeClass
//--------------------------------------------------------------
void MNodeClass::init(int *cl, int mxdeg, int **adjmat)
{
    // initialize the object
    // Argument
    //   cl[j]        : list of number of nodes in the j-th class
    //   mxdeg        : maximum degree to nodes
    //   adjmat[j][k] : adjacency matrix

    int j;

    for (j = 0; j < nClasses; j++) {
        clist[j]  = cl[j];
        clord[j]  = j;
    }
    maxdeg   = mxdeg;
    mkNdCl();
    mkClMat(adjmat);
    mkFlist();
    flg0 = 0;
    flg1 = 0;
    flg2 = 0;
}

//--------------------------------------------------------------
void MNodeClass::copy(MNodeClass* mnc)
{
    // copy MNodeClass 'mnc' to this object

    int j, k;

    nClasses = mnc->nClasses;
    for (k = 0; k < nClasses; k++) {
        clist[k] = mnc->clist[k];
    }
    maxdeg   = mnc->maxdeg;
    for (j = 0; j < nNodes; j++) {
        ndcl[j]  = mnc->ndcl[j];
        clord[j] = mnc->clord[j];
        for (k = 0; k < nClasses; k++) {
            clmat[j][k] = mnc->clmat[j][k];
        }
    }
    for (k = 0; k < nClasses+1; k++) {
        flist[k] = mnc->flist[k];
    }
}

//--------------------------------------------------------------
void MNodeClass::mkFlist(void)
{
    //  Construct flist
    //    The set of nodes in class 'c' is [flist[c],...,flist[c+1]-1]

    int  j, f;

    f  = 0;
    for (j = 0; j < nClasses; j++) {
        flist[j] = f;
        f += clist[j];
    }
    flist[nClasses] = f;
}

//--------------------------------------------------------------
void MNodeClass::mkNdCl(void)
{
    //  Construct ndcl
    //    ndcl[nd] = (the class id in which node 'nd' belongs)

    int  c, k;
    int  nd = 0;

    for (c = 0; c < nClasses; c++) {
        for (k = 0; k < clist[c]; k++) {
            ndcl[nd++] = c;
        }
    }
}

//--------------------------------------------------------------
int MNodeClass::clCmp(int nd0, int nd1, int cn)
{
    //  Comparison of two nodes 'nd0' and 'nd1'
    //    in lexicographic ordering of [class, connection configuration]

    int cmp;
    // Wether two nodes are in a same class or not.

    cmp = ndcl[nd0] - ndcl[nd1];
    if (cmp != 0) {
        return cmp;
    }

    // Sign '-' signifies the reverse ordering
    cmp = - cmpMNCArray(clmat[nd0], clmat[nd1], cn);
    if (cmp != 0) {
        return cmp;
    }
    return cmp;
}
    
//--------------------------------------------------------------
void MNodeClass::mkClMat(int **adjmat)
{
    //  Construct a matrix 'clmat[nd][tc]' which is the number
    //  of edges connecting 'nd' and all nodes in class 'tc'.

    int  nd, td, tc;

    for (nd = 0; nd < nNodes; nd++) {
        for (td = 0; td < nNodes; td++) {
            tc = ndcl[td];                      // another node
            if (nd == td) {
                clmat[nd][tc] += CLWIGHTD(adjmat[nd][td]);
            } else {
                clmat[nd][tc] += CLWIGHTO(adjmat[nd][td]);
            }
        }
    }
}

//--------------------------------------------------------------
void MNodeClass::incMat(int nd, int td, int val)
{
    //  Increase the number of edges by 'val' between 'nd' and 'td'.

    int tdc = ndcl[td];             // class of 'td'
    clmat[nd][tdc] += val;          // modify matrix 'clmat'.
}

//--------------------------------------------------------------
void MNodeClass::printMat(void)
{
    //  Print configuration matrix.

    int j1, j2;

    grcc_fprintf(GRCC_Stdout, "\n");
  
    grcc_fprintf(GRCC_Stdout, "nClasses=%d", nClasses);
    grcc_fprintf(GRCC_Stdout, " clord="); prIntArray(nClasses, clord, "");
    grcc_fprintf(GRCC_Stdout, " flist="); prIntArray(nClasses, flist, "\n");
    grcc_fprintf(GRCC_Stdout, "flg = (%d, %d, %d)\n", flg0, flg1, flg2);

    // the first line
    grcc_fprintf(GRCC_Stdout, "nd: cl:   ");
    for (j2 = 0; j2 < nClasses; j2++) {
        grcc_fprintf(GRCC_Stdout, "%2d ", j2);
    }
    grcc_fprintf(GRCC_Stdout, "\n");
  
    // print raw
    for (j1 = 0; j1 < nNodes; j1++) {
        grcc_fprintf(GRCC_Stdout, "%2d; %2d: [", j1, ndcl[j1]);
        for (j2 = 0; j2 < nClasses; j2++) {
            grcc_fprintf(GRCC_Stdout, " %2d", clmat[j1][j2]);
        }
        grcc_fprintf(GRCC_Stdout, "]\n");
    }
}

//--------------------------------------------------------------
int MNodeClass::cmpMNCArray(int *a0, int *a1, int ma)
{
    int j, k;

    for (k = 0; k < ma; k++) {
        j = clord[k];
        if (a0[j] < a1[j]) {
            return -1;
        } else if (a0[j] > a1[j]) {
            return 1;
        }
    }
    return 0;
}

//--------------------------------------------------------------
void MNodeClass::reorder(MGraph *mg)
{
    int flg[GRCC_MAXNODES];
    int co, cn;
    int f0, f1, f2;
  
    f0 = 0;
    f1 = 0;
    f2 = 0;
    for (co = 0; co < nClasses; co++) {
        cn  = flist[co];
        if (mg->nodes[cn]->freelg < 1) {
            flg[co] = 0;
            f0++;
        } else if (mg->nodes[cn]->freelg < mg->nodes[cn]->deg) {
            flg[co] = mg->nodes[cn]->deg + maxdeg*clist[co];
            f1++;
        } else {
            flg[co] = maxdeg*(mg->nodes[cn]->deg + maxdeg*clist[co]);
            f2++;
        }
    }
    if (f0 < nClasses) {
        bsort(nClasses, clord, flg);
    }
    flg0 = f0;
    flg1 = f0 + f1;
    flg2 = f0 + f1 + f2;
}

//==============================================================
// class MNode : nodes in MGraph
//--------------------------------------------------------------
MNode::MNode(int vid, int vclss, NCInput *mgi)
{
    // Arguments
    //   vid    : identifier of the vertex
    //   vdeg   : degree of the node
    //   vextlp : external node (-1) or looped vertex
    //   vclss  : class of the node

    id      = vid;           // id of the node
    clss    = vclss;         // class to which the node belongs
    deg     = mgi->cldeg;    // degree of the node
    freelg  = mgi->cldeg;    // number of free legs
    extloop = mgi->cltyp;    // external node or not
    cmindeg = mgi->cmind;    // min(deg of connectable vertex)
    cmaxdeg = mgi->cmaxd;    // max(deg of connectable vertex)
}

//--------------------------------------------------------------
MNode::MNode(int vid, int vdeg, int vextlp, int vclss, int cmin, int cmax)
{
    // Arguments
    //   vid    : identifier of the vertex
    //   vdeg   : degree of the node
    //   vextlp : external node (-1) or looped vertex
    //   vclss  : class of the node

    id      = vid;       // id of the node
    deg     = vdeg;      // degree of the node
    freelg  = vdeg;      // number of free legs
    clss    = vclss;     // class to which the node belongs
    extloop = vextlp;    // external node or not
    cmindeg = cmin;      // min(deg of connectable vertex)
    cmaxdeg = cmax;      // max(deg of connectable vertex)
}

//===============================================================
//  class MGraph : scalar graph expressed by matrix form
//---------------------------------------------------------------
MGraph::MGraph(int pid, int ncl, int *cldeg, int *clnum, int *cltyp, int *cmind, int *cmaxd, Options *opts)
{
    int nn, ne, j, k;

    // initial conditions
    nClasses = ncl;
    clist    = new int[ncl];
    opt      = opts;
    mId      = -1;

    mindeg   = -1;
    maxdeg   = -1;
    ne = 0;
    nn = 0;
    for (j = 0; j < nClasses; j++) {
        clist[j] = clnum[j];
        nn += clnum[j];
        ne += cldeg[j]*clnum[j];
        if (mindeg < 0) {
            mindeg = cldeg[j];
        } else {
            mindeg = Min(mindeg, cldeg[j]);
        }
        if (maxdeg < 0) {
            maxdeg = cldeg[j];
        } else {
            maxdeg = Max(maxdeg, cldeg[j]);
        }
    }
    if (ne % 2 != 0) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "Sum of degrees are not even\n");
            for (j = 0; j < nClasses; j++) {
                grcc_fprintf(GRCC_Stderr, "class %2d: %2d %2d %2d\n", 
                       j, cldeg[j], clnum[j], cltyp[j]);
            }
        }
        erEnd("illegal degrees of nodes");
    }
    pId    = pid;
    nNodes = nn;
    nodes  = new MNode*[nNodes];
    group  = new SGroup();
#ifdef ORBITS
    orbits = new MOrbits();
#endif

    nEdges = ne / 2;
    nLoops = nEdges - nNodes + 1;

    egraph = new EGraph(nNodes, nEdges, maxdeg);
    nn = 0;
    nExtern = 0;
    for (j = 0; j < nClasses; j++) {
        for (k = 0; k < clist[j]; k++, nn++) {
            nodes[nn] = new MNode(nn, cldeg[j], cltyp[j], j, cmind[j], cmaxd[j]);
            egraph->setExtLoop(nn, cltyp[j]);
            if (cltyp[j] < 0) {
                nExtern++;
            }
        }
    }
    egraph->endSetExtLoop();

    init();
}

//---------------------------------------------------------------
MGraph::MGraph(int pid, int ncl, NCInput *mgi, Options *opts)
{
    int nn, ne, j, k;

    // initial conditions
    nClasses = ncl;
    clist    = new int[ncl];
    opt      = opts;
    mId      = -1;

    mindeg   = -1;
    maxdeg   = -1;
    ne = 0;
    nn = 0;
    for (j = 0; j < nClasses; j++) {
        clist[j] = mgi[j].clnum;
        nn += mgi[j].clnum;
        ne += mgi[j].cldeg*mgi[j].clnum;
        if (mindeg < 0) {
            mindeg = mgi[j].cldeg;
        } else {
            mindeg = Min(mindeg, mgi[j].cldeg);
        }
        if (maxdeg < 0) {
            maxdeg = mgi[j].cldeg;
        } else {
            maxdeg = Max(maxdeg, mgi[j].cldeg);
        }
    }
    if (ne % 2 != 0) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "Sum of degrees are not even\n");
            for (j = 0; j < nClasses; j++) {
                grcc_fprintf(GRCC_Stderr, "class %2d: %2d %2d %2d\n", 
                       j, mgi[j].cldeg, mgi[j].clnum, mgi[j].cltyp);
            }
        }
        erEnd("illegal degrees of nodes");
    }
    pId    = pid;
    nNodes = nn;
    if (nNodes < 0) {
        grcc_fprintf(GRCC_Stdout, "*** nNodes = %d\n", nNodes);
        erEnd("MGraph::MGrap : nNodes < 0");
    }
    nodes  = new MNode*[nNodes];
    group  = new SGroup();
#ifdef ORBITS
    orbits = new MOrbits();
#endif

    nEdges = ne / 2;
    nLoops = nEdges - nNodes + 1;

    egraph = new EGraph(nNodes, nEdges, maxdeg);
    nn = 0;
    nExtern = 0;
    for (j = 0; j < nClasses; j++) {
        for (k = 0; k < clist[j]; k++, nn++) {
            nodes[nn] = new MNode(nn, j, mgi+j);
            egraph->setExtLoop(nn, mgi[j].cltyp);
            if (mgi[j].cltyp < 0) {
                nExtern++;
            }
        }
    }
    egraph->endSetExtLoop();

    init();
}

//---------------------------------------------------------------
void MGraph::init(void)
{
    // generated set of graphs
    cDiag          = 0;
    c1PI           = 0;
    cNoTadpole     = 0;
    cNoTadBlock    = 0;
    c1PINoTadBlock = 0;

    // the current graph
    adjMat    = newMat(nNodes, nNodes, 0);
    nsym      = ToBigInt(0);
    esym      = ToBigInt(0);
    wscon     = Fraction(0, 1);
    wsopi     = Fraction(0, 1);

    // current node classification
    curcl    = new MNodeClass(nNodes, nClasses);

    // table of n-edge connected components
    mconn    = new MConn(nNodes, nEdges);

    // measures of efficiency
    ngen     = 0;
    ngconn   = 0;

#ifdef MONITOR
    nCallRefine    = 0;
    discardRefine  = 0;
    discardDisc    = 0;
    discardIso     = 0;
#endif

    // work space for isIsomorphic
    modmat = newMat(nNodes, nNodes, 0);

    // work space for bisearchME
    bidef = newArray(nNodes, 0);
    bilow = newArray(nNodes, 0);
    bicol = newArray(nNodes, 0);
    bicount = 0;
}

//---------------------------------------------------------------
MGraph::~MGraph(void)
{
    int j;

    // group->delGroup();

    bicol = deleteArray(bicol);
    bilow = deleteArray(bilow);
    bidef = deleteArray(bidef);


    modmat = deleteMat(modmat, nNodes);
    delete mconn;
    delete curcl;
    adjMat = deleteMat(adjMat, nNodes);
#ifdef ORBITS
    delete orbits;
#endif
    delete egraph;
    delete group;
    for (j = 0; j < nNodes; j++) {
        delete nodes[j];
        nodes[j] = NULL;
    }
    delete[] nodes;
    delete[] clist;

}
  
//---------------------------------------------------------------
void MGraph::printAdjMat(MNodeClass *cl)
{
    int j1, j2;

    grcc_fprintf(GRCC_Stdout, "      ");
    for (j2 = 0; j2 < nNodes; j2++) {
        grcc_fprintf(GRCC_Stdout, " %2d", j2);
    }
    grcc_fprintf(GRCC_Stdout, "\n");
    for (j1 = 0; j1 < nNodes; j1++) {
        grcc_fprintf(GRCC_Stdout, "%2d : [", j1);
        for (j2 = 0; j2 < nNodes; j2++) {
            grcc_fprintf(GRCC_Stdout, " %2d", adjMat[j1][j2]);
        }
        grcc_fprintf(GRCC_Stdout, "] %2d\n", cl->ndcl[j1]);
    }
}

//---------------------------------------------------------------
void MGraph::print(void)
{
    int j;

    grcc_fprintf(GRCC_Stdout, "MGraph: pId=%d, cDiag=%ld, c1PI=%ld\n", pId, cDiag, c1PI);
    grcc_fprintf(GRCC_Stdout, "     nNodes=%d, nEdges=%d, nExtern=%d, nLoops=%d "
           "mindeg=%d, maxdeg=%d, sym=(%ld, %ld)\n",
           nNodes, nEdges, nExtern, nLoops, mindeg, maxdeg, nsym, esym);
    grcc_fprintf(GRCC_Stdout, "  Nodes=%d\n", nNodes);
    for (j = 0; j < nNodes; j++) {
        grcc_fprintf(GRCC_Stdout, "    %2d: id=%d, deg=%d, clss=%d, extloop=%d, ",
               j, nodes[j]->id, nodes[j]->deg, nodes[j]->clss,
               nodes[j]->extloop);
        grcc_fprintf(GRCC_Stdout, "mind=%d, maxd=%d, freelg=%d\n",
               nodes[j]->cmindeg, nodes[j]->cmaxdeg, nodes[j]->freelg);
    }
        
    curcl->printMat();
    grcc_fprintf(GRCC_Stdout, "\n");
 
    printAdjMat(curcl);
}

//---------------------------------------------------------------
void MGraph::printPy(FILE *fp, long mId)
{
    fprintf(fp, "#TGraph : (gseq, gid, nodes, amat)\n");
    fprintf(fp, "(%ld, (%d, %d),\n", mId, pId, -1);
    fprintf(fp, "  [ # nodes: (cid, deg0, loop, part)\n");
    for (int j = 0; j < nNodes; j++) {
        fprintf(fp, "    (%2d,%2d,%2d,%2d),   # %2d\n",
                 nodes[j]->clss, nodes[j]->deg, nodes[j]->extloop, 0, j);
    }
    fprintf(fp, "  ],\n");
    fprintf(fp, "  [\n");
    fprintf(fp, "  #");
    for (int j2 = 0; j2 < nNodes; j2++) {
        fprintf(fp, " %4d", j2);
    }
    fprintf(fp, "\n");
    for (int j1 = 0; j1 < nNodes; j1++) {
        fprintf(fp, "    [");
        for (int j2 = 0; j2 < nNodes; j2++) {
            fprintf(fp, " %2d, ", adjMat[j1][j2]);
        }
        fprintf(fp, "],   # %2d\n", j1);
    }
    fprintf(fp, "  ], # nodes\n");
    fprintf(fp, "  [ # group of 2 elements\n");
    fprintf(fp, "    [],\n");
    fprintf(fp, "  ], # group\n");
    fprintf(fp, ")\n");
}

//---------------------------------------------------------------
Bool MGraph::isConnected(void)
{
    //  Check graph can be a connected one.
    //  If a connected component without free leg is not the whole graph then
    //  return False, otherwise return True.

    int j, n, nv;

    for (j = 0; j < nNodes; j++) {
        nodes[j]->visited = -1;
    }
    if (visit(0)) {
        return True;
    }
    nv = 0;
    for (n = 0; n < nNodes; n++) {
        if (nodes[n]->visited >= 0) {
            nv++;
        }
    }
    return (nv == nNodes);
}

//---------------------------------------------------------------
Bool MGraph::visit(int nd)
{
    //  Visiting connected node used for 'isConnected'
    //  If child nodes has free legs, then this function returns True.
    //  otherwise it returns False.
  
    int td;
  
    // This node has free legs.
    if (nodes[nd]->freelg > 0) {
        return True;
    }
    nodes[nd]->visited = 0;
    for (td = 0; td < nNodes; td++) {
        if ((adjMat[nd][td] > 0) && (nodes[td]->visited < 0)) {
            if (visit(td)) {
                return True;
            }
        }
    }
    // all the child nodes has no free legs.
    return False;
}

//---------------------------------------------------------------
Bool MGraph::isIsomorphic(MNodeClass *cl)
{
    //  Check whether the current graph is the Representative 
    //  of a isomorphic class.
    //    nsym = symmetry factor by the permutation of nodes.
    //    esym = symmetry factor by the permutation of edge.
    //  If this graph is not a representative, then returns False.

    int j1, j2, cmp, nself;
    int *perm;

    nsym = ToBigInt(0);
    esym = ToBigInt(1);

    group->newGroup(nNodes, cl->nClasses, cl->clist);

#ifdef ORBITS
    orbits->initPerm(nNodes);
#endif

    while (True) {
        perm = group->genNext();

        if (perm == NULL) {
            // calculate permutations of edges
            esym = ToBigInt(1);
            for (j1 = 0; j1 < nNodes; j1++) {
                if (adjMat[j1][j1] > 0) {
                    nself = adjMat[j1][j1]/2;
                    esym *= factorial(nself);
                    esym *= ipow(2, nself);
                }
                for (j2 = j1+1; j2 < nNodes; j2++) {
                    if (adjMat[j1][j2] > 0) {
                          esym *= factorial(adjMat[j1][j2]);
                    }
                }
            }
            return True;
        }
  
        permMat(nNodes, perm, adjMat, modmat);
        cmp = compMat(nNodes, adjMat, modmat);
        if (cmp < 0) {
            return False;
        } else if (cmp == 0) {
            // if ngroup < 0, symmetry group is $S_{-group}$.
            group->addGroup(perm);
  
            nsym = nsym + ToBigInt(1);
#ifdef ORBITS
            orbits->fromPerm(perm);
#endif
        }
    }
}

//---------------------------------------------------------------
void MGraph::permMat(int size, int *perm, int **mat0, int **mat1)
{
    // apply permutation to matrix 'mat0' and obtain 'mat1'

    int j1, j2;

    for (j1 = 0; j1 < size; j1++) {
        for (j2 = 0; j2 < size; j2++) {
            mat1[j1][j2] = mat0[perm[j1]][perm[j2]];
        }
    }
}

//---------------------------------------------------------------
int MGraph::compMat(int size, int **mat0, int **mat1)
{
    // comparison of matrix

    int j1, j2, cmp;

    for (j1 = 0; j1 < size; j1++) {
        for (j2 = 0; j2 < size; j2++) {
            cmp = mat0[j1][j2] - mat1[j1][j2];
            if (cmp != 0) {
                return cmp;
            }
        }
    }
    return 0;
}

//---------------------------------------------------------------
MNodeClass *MGraph::refineClass(MNodeClass *cl)
{
    //  Refine the classification
    //    cl : the current 'MNodeClass' object
    //    cn : the class number
    //  Returns (the new class number corresponds to 'cn') if OK, or
    //          'None' if ordering condition is not satisfied

    MNodeClass *ccl = cl;
    MNodeClass *xcl = NULL;
    MNodeClass *ncl = NULL;
    int         ucl[GRCC_MAXNODES];
    int         ccn = cl->nClasses;
    int         nucl, nce;
    int         td, cmp;
    int         nccl;

#ifdef MONITOR
    nCallRefine++;
#endif
    nucl = 0;
    while (ccl->nClasses != nucl) {    // repeat refinement.
        nce  = 0;
        nucl = 0;
        for (td = 1; td < nNodes; td++) {
          // 'td' is the next node and the current node is 'td-1'.
          // Count up the number of the elements in the current class 
          // corresponding to the current node
          nce++;
          cmp = ccl->clCmp(td-1, td, ccn);
  
          // the ordering condition is not satisfied.
          if (cmp > 0) {
            if (ccl != cl) {
                delete ccl;
            }
            return NULL;
  
          } else if (cmp < 0) {
              // 'td' is in the next class to the current node.
              ucl[nucl++] = nce;       // close the current class
  
              // start new class
              nce = 0;
          }
          // nothing to do for the case of 'cmp == 0'.
  
        }
  
        // close array 'ucl'.
        ucl[nucl++] = nce + 1;
    
#ifdef CHECK
        // inconsistent
        if (nucl < ccl->nClasses) {
            erEnd("refineClasses : smaller number of classes");
        }
#endif
  
        // preparation of the next repetition.
        xcl = new MNodeClass(nNodes, nucl);
        xcl->init(ucl, maxdeg, adjMat);
        ccn = xcl->nClasses;

        nccl = ccl->nClasses;

        if (ccl != cl) {
            delete ccl;
        }
        ccl = xcl;
        if (ccl->nClasses == nccl) {
            ccl->reorder(this);
            return ccl;
        }

        nucl = 0;
    }

    return ncl;
}

//---------------------------------------------------------------
void MGraph::biconnME(void)
{
    //  Count the number of 1PI components.

    int j, j1, root, vr, next, nart;
    MCOpi   mopi;
    MCBlock mblk;
    ULong   momset;

    // initialization
    bicount    = 0;
    mconn->init();
    mconn->initCEdges(this);

    for (j = 0; j < nNodes; j++) {
        bidef[j] = -1;
        bilow[j] = -1;
        bicol[j] =  0;
    }
    bipart = True;

    // find a root for the root of bisearch
    // root must be an external node
    // or an vertex when there are not external nodes.
    root = -1;
    vr   = -1;
    for (j = 0; j < nNodes; j++) {
        if (bidef[j] < 0) {
            if (isExternal(j)) {
                root = j;
                break;
            } else if (vr < 0) {
                vr = j;
            }
        }
    }
    // case (2)
    if (root < 0) {
        root = vr;
    }

    if (root >= 0) {
        bisearchME(root, -1, 0, 1, &mopi, &mblk, &momset, &next, &nart);

        mconn->nlpopic = 0;
        mconn->nctopic = 0;
        for (j = 0; j < mconn->nopic; j++) {
            if (mconn->opics[j].loop > 0) {
                mconn->nlpopic++;
            } else if (mconn->opics[j].ctloop > 0) {
                mconn->nctopic++;
            }
        } 

        mconn->ne0bridges  = 0;
        mconn->ne1bridges   = 0;
        for (j = 0; j < mconn->nbridges; j++) {
            if (mconn->bridges[j].next == 0) {
                mconn->ne0bridges++;
            }
            if (mconn->bridges[j].next == 1) {
                mconn->ne1bridges++;
            }
        }

        mconn->nselfloops = 0;
        for (j = 0; j < nNodes; j++) {
            mconn->nselfloops += adjMat[j][j]/2;
        }

        mconn->nmultiedges = 0;
        for (j = 0; j < nNodes; j++) {
            for (j1 = j+1; j1 < nNodes; j1++) {
                if (adjMat[j][j1] > 1) {
                    mconn->nmultiedges++;
                }
            }
        }

        mconn->na1blocks = 0;
        for (j = 0; j < mconn->nblocks; j++) {
            if (mconn->blocks[j].nartps == 1) {
                mconn->na1blocks++;
            }
        }
        mconn->neblocks = mconn->nblocks + mconn->nctopic;

#ifdef CHECK
        if (True) {
            if (isExternal(root)) {
                momset |= MASK(root);
            }
            ULong m = 0;
            for (j = 0; j < nExtern; j++) {
                m |= MASK(j);
            }
            bool ok = True;
            if (momset != m) {
                grcc_fprintf(GRCC_Stdout, "*** momset = %ld != %ld\n", momset, m);
                ok = False;
            }
            if (mconn->nbacked != nLoops) {
                grcc_fprintf(GRCC_Stdout, "*** nbacked = %d != %c\n", mconn->nbacked, nLoops);
                ok = False;
            }
            if (! ok) {
                print();
                egraph->print();
                mconn->print();
                erEnd("biconnME: illegal connection");
            }
        }
#endif

    // no vertex.
    } else {
        // no vertices
        // Connected ==> only when ex=2, loop=0 
        mconn->nopic      = 0;
        mconn->ne0bridges = 0;
        mconn->ne1bridges = 0;
    }
}

//---------------------------------------------------------------
void MGraph::bisearchME(int nd, int pd, int ned,  int col,
         MCOpi *mopi, MCBlock *mblk, ULong *momset, int *next, int *nart)
{
    //  Search biconnected component
    //    visit : pd --> nd --> td
    //    ned : the number of edges between pd and nd.
    //  Output
    //
    //                 |
    //                 x----+
    //                 |    |
    //             ----x pd |
    //                 |    |
    //            x----x nd |  n art. pints.
    //            |   /|\   |
    //            |  / | \  |
    //   m art p. x-x  |  x-x
    //             n1  x  n3
    //                 n2
    //
    //   output of bisearchME(n1, nd, ...) ==> npart = m
    //   output of bisearchME(n2, nd, ...) ==> npart = 1
    //   output of bisearchME(n3, nd, ...) ==> npart = n
    //
    //   output of bisearchME(nd, pd, ...) ==> npart = n+1
    //       n1 => block of (m+1) articulation points
    //       n2 => block of    2  articulation points
    //       n3 => no block
    //
    Bool newv;
    int  td, td0, lp, conn, next1, nart1, nart2, nvisit, ndart; 
    int  opit, opit0, blkt, l;
    MCOpi   mopi1;
    MCBlock mblk1;
    ULong   momset1, momset2, momset3;

    mopi->init();
    mblk->init();

    *momset = 0;     // # the set of momenta
    *next   = 0;     // # external below 'nd' inclusive
    *nart   = 0;     // # articulation points 'nd' inclusive
    nart1   = 0;     // # articulation points below 'nd'
    nart2   = 0;     // # 'nd' is articulation point then 1
    ndart   = 0;     // # the number of blocks attached to 'nd'

    newv = (bidef[nd] < 0);
    if (! newv) {
        grcc_fprintf(GRCC_Stdout, "*** nd=%d, pd=%d, bidef[nd]=%d\n", nd, pd, bidef[nd]);
        erEnd("bisearchME: illegal connection");
    }

    bidef[nd] = bicount;
    bilow[nd] = bicount;
    bicol[nd] = col;
    bicount++;

    opit0 = mconn->opistkptr;

    if (pd < 0) {
        mconn->pushNode(nd);
    }

    // external node and not the root
    if (isExternal(nd)) {
        if (pd >= 0) {
            // not the root
            *momset      = MASK(nd);
            mopi->next   = 1;
            mopi->nlegs  = 1;
            mopi->mom0lg = 0;
            mblk->nartps = 1;
            *next        = 1;
            *nart        = 1;
            mconn->addCEdge(nd, pd, *momset);
            return;
        }
    }

    nvisit = 0;
    td0    = -1;
    for (td = 0; td < nNodes; td++) {
        conn = adjMat[nd][td];

        // td is not adjacent to nd
        if (conn < 1) {
            continue;
        }
        nvisit++;
        td0 = td;

        momset1 = 0;
  
        // external node
        if (isExternal(td) && bidef[td] < 0) {
            bicol[td] = - col;
            (*next)++;
            ndart++;
            mconn->addArtic(nd, 1);
            mblk->nartps++;
            nart2 = 1;
            momset1  = MASK(td);
            mopi->nlegs++;
            mopi->next++;
            mconn->addCEdge(td, nd, momset1);
            *momset |= momset1;
            if (newv) {
                mconn->pushNode(td);
            }

        // self-loop : pd --> nd --> nd
        } else if (td == nd) {
            lp  = conn/2;
            mopi->loop   += lp;
            mopi->nedges += lp;
            ndart += lp;
            bipart = False;
            mconn->addArtic(nd, lp);
            mconn->addBlockSelf(nd, lp);
            mblk->nartps++;
            nart2  = 1;
            for (l = 0; l < lp; l++) {
                int m = nExtern + mconn->nbacked;
                mconn->nbacked++;
                momset1 = MASK(m);
                mconn->addCEdge(td, nd, momset1);
            }
  
        // back to the parent : pd --> nd --> pd,  pd is a vertex
        } else if (td == pd) {
            if (ned > 1) {
                bilow[nd] = Min(bilow[nd], bidef[pd]);
                mopi->loop += ned - 1;
                mblk->loop += ned - 1;
            } else {
                // cancel this visit
                nvisit--;
            }
  
        // td is already visited
        } else if (bidef[td] >= 0) {
            bipart &= (bicol[td] == - col);
            bilow[nd] = Min(bilow[nd], bidef[td]);
            if (bidef[nd] >= bidef[td]) {
                // new back-edge is found
                mopi->loop   += conn;
                mopi->nedges += conn;
                mblk->loop   += conn;
                mconn->pushEdge(td, nd);
                for (l = 0; l < conn; l++) {
                    int m = nExtern + mconn->nbacked;
                    mconn->nbacked++;
                    momset1 = MASK(m);
                    *momset |= momset1;
                    mconn->addCEdge(td, nd, momset1);
                }
            } else {
                // reverse direction of back-edge
                int cn = 0;

                for (int ed = 0; ed < mconn->sedges; ed++) {
                    if (mconn->cedges[ed].nodes[0] == nd &&
                        mconn->cedges[ed].nodes[1] == td &&
                        mconn->cedges[ed].momdir   > 0) {
                        cn++;
                        *momset &= ~ (mconn->cedges[ed].momset);
                    } else if (mconn->cedges[ed].nodes[1] == nd &&
                               mconn->cedges[ed].nodes[0] == td &&
                               mconn->cedges[ed].momdir   < 0) {
                        cn++;
                        *momset &= ~ (mconn->cedges[ed].momset);
                    }
                }
                if (cn != conn) {
                    grcc_fprintf(GRCC_Stdout, "*** revisit back-ed (%d --> %d) cn=%d != conn=%d\n",
                           nd, td, cn, conn);
                    grcc_fprintf(GRCC_Stdout, "    sedges = %d\n", mconn->sedges);
                    for (int ed = 0; ed < mconn->sedges; ed++) {
                        grcc_fprintf(GRCC_Stdout, "    %d : (%d --> %d) : [%2d*%2ld]\n", ed,
                            mconn->cedges[ed].nodes[0],
                            mconn->cedges[ed].nodes[1],
                            mconn->cedges[ed].momdir,
                            mconn->cedges[ed].momset);
                    }
                    print();
                    egraph->print();
                    mconn->print();
                    erEnd("bisearchME: illegal connection");
                }
            }

        // new node
        } else if (bidef[td] < 0) {

            // stack pointer
            if (pd < 0 && isExternal(nd)) {
                opit = opit0;
            } else {
                opit = mconn->opistkptr;
            }
            blkt = mconn->blkstkptr;
            mblk1.init();

            mconn->pushEdge(nd, td);

            // visit child
            bisearchME(td, nd, adjMat[td][nd], - col,
                &mopi1, &mblk1, &momset1, &next1, &nart1);
  
            // momset
            momset2 = 0;
            for (l = 0; l < conn - 1; l++) {
                int m = nExtern + mconn->nbacked;
                mconn->nbacked++;
                momset3 = MASK(m);
                mconn->addCEdge(nd, td, momset3);
                momset2 |= momset3;
            }
            mconn->addCEdge(td, nd, momset1 | momset2);
            *momset |= momset1;
            // articulation point of bridge
            if (bilow[td] > bidef[nd]) {

                // new OPI component (not including 'td')
                int mom0lg = (momset1 == 0) ? 1 : 0;
                mopi1.nlegs++;
                mopi1.mom0lg += mom0lg;

                mconn->addOPIc(&mopi1, opit);

                mopi1.init();
                mopi1.nlegs  = 1;
                mopi1.mom0lg = mom0lg;
                if (pd >= 0 || !isExternal(nd)) {
                    // opi
                    mconn->addBridge(nd, td, next1, nExtern);

                    // block
                    ndart++;
                    mconn->addArtic(nd, 1);
                    // discard nparts from nodes below td
                    mblk1.nartps = 2; 
                    mconn->addBlock(&mblk1, blkt);
                    mblk1.init();
                    mblk1.nartps = 1;

                    nart1 = 0;
                    nart2 = 1;  // nd is an articulation point
                }
            } else if (bilow[td] == bidef[nd]) {
                // articulation point of a block
                mopi1.nedges += conn;
                if (pd >= 0 || !isExternal(nd)) {
                    ndart++;
                    mconn->addArtic(nd, 1);
                    mblk1.nartps++;
                    mconn->addBlock(&mblk1, blkt);
                    mblk1.init();
                    mblk1.nartps = 1;
                    nart1 = 0;
                    nart2 = 1;  // nd is an articulation point
                }

            } else {
                // inside a block
                mopi1.nedges += conn;
            }

            bilow[nd] = Min(bilow[nd], bilow[td]);
            mopi->nlegs  += mopi1.nlegs;
            mopi->next   += mopi1.next;
            mopi->loop   += mopi1.loop;
            mopi->nedges += mopi1.nedges;
            mopi->ctloop += mopi1.ctloop;
            mopi->mom0lg += mopi1.mom0lg;

            mblk->nartps += mblk1.nartps;
            mblk->loop   += mblk1.loop;

            *next   += next1;
            *nart   += nart1;
        }  // of "if (bidef[td] < 0)"
    }  // end of for

    // no connection except for 'pd'==>'nd'.  Then 'nd' is an art. point
    if (nvisit == 0) {  
        nart2 = 1;
    }
    *nart += nart2;

    // add # loop inside counter terms
    if (newv) {
        if (pd >= 0) {
            mconn->pushNode(nd);
        }
        mopi->ctloop += Max(0, nodes[nd]->extloop);
    }

    // 'nd' is the root node
    if (pd < 0) {
        if (isExternal(nd)) {
            if (td0 >= 0) {
                mconn->addArtic(td0, 1);
            }
            if (mconn->nopic > 0) {
                (mconn->opics[mconn->nopic-1].next)++;
            }
        } else {
            mconn->addOPIc(mopi, opit0);
            if (ndart == 1) {           
                // 'nd' has only 1 child
                // the root is not really an art. point
                (*nart)--;
                mconn->addArtic(nd, -1);
                (mconn->blocks[mconn->nblocks-1].nartps)--;
            }
        }
    }
}

//---------------------------------------------------------------
BigInt MGraph::generate(void)
{
    //  Generate graphs
    //    the generation process starts from 'connectClass'.

    MNodeClass *cl;

    // Initial classification of nodes.
    cl = new MNodeClass(nNodes, nClasses);
    cl->init(clist, maxdeg, adjMat);
    cl->reorder(this);
    connectClass(cl);

    delete cl;

    return cDiag;
}

//---------------------------------------------------------------
void MGraph::connectClass(MNodeClass *cl)
{
    // Connect nodes in a class to others

    int sc, sn;
    MNodeClass *xcl;

    xcl = refineClass(cl);

    if (xcl == NULL) {
#ifdef MONITOR
        discardRefine++;
#endif
    } else {
        if (xcl->flg0 >= xcl->nClasses) {
            newGraph(xcl);
        } else {
            sc = xcl->clord[xcl->flg0];
            sn = xcl->flist[sc];
            connectNode(xcl->flg0, sn, xcl);
        }
    }
    if (xcl != cl && xcl != NULL) {
        delete xcl;
    }
}

//------------------------------------------------------------
void MGraph::connectNode(int so, int ss, MNodeClass *cl)
{
    int sc, sn;

    sc = cl->clord[so];
    if (ss >= cl->flist[sc+1]) {
        connectClass(cl);
        return;
    }

    for (sn = ss; sn < cl->flist[sc+1]; sn++) {
        connectLeg(so, sn, so, sn, cl);
        return;
    }
}

//------------------------------------------------------------
void MGraph::connectLeg(int so, int sn, int to, int ts, MNodeClass *cl)
{
    //  Add one connection between two legs.
    //    1. select another node to connect
    //    2. determine multiplicity of the connection

    int sc, tc, tn, maxself, nc2, nc, maxcon, ts1, ncm, to1;

    sc = cl->clord[so];

#ifdef CHECK
    if (sn >= cl->flist[sc+1]) {
        erEnd("connectLeg : illegal control");
        return;
    }
#endif

    // There remains no free legs in the node 'sn' : move to next node.
    if (nodes[sn]->freelg < 1) {

        if (!isConnected()) {
#ifdef MONITOR
            discardDisc++;
#endif
        } else {
            // next node in the current class.
            connectNode(so, sn+1, cl);
        }
        return;
    }

    // connect a free leg of the current node 'sn'.
    for (to1 = to; to1 < cl->nClasses; to1++) {
        tc = cl->clord[to1];
        if (to1 == to) {
            ts1 = ts;
        } else {
            ts1 = cl->flist[tc];
        }
#ifdef MINMAXLEG
        if (ts1 >= nNodes) {
            continue;
        }
        if ((nodes[sn]->cmindeg > 0 && nodes[ts1]->deg < nodes[sn]->cmindeg)
          ||(nodes[sn]->cmaxdeg > 0 && nodes[ts1]->deg > nodes[sn]->cmaxdeg)
          | (nodes[ts1]->cmindeg > 0 && nodes[sn]->deg < nodes[ts1]->cmindeg)
          ||(nodes[ts1]->cmaxdeg > 0 && nodes[sn]->deg > nodes[ts1]->cmaxdeg)) {
            continue;
        }
#endif
        for (tn = ts1; tn < cl->flist[tc+1]; tn++) {
            if (sc == tc && sn > tn) {
                continue;
    
            } else if (nodes[tn]->freelg < 1) {
                continue;
    
            // self-loop
            } else if (sn == tn) {
                if (opt->values[GRCC_OPT_NoSelfLoop] > 0) {
                     continue;
                }
                if (nNodes > 1) {
                    // there are two or more nodes in the graph : 
                    // avoid disconnected graph
                    maxself = Min((nodes[sn]->freelg)/2, (nodes[sn]->deg-1)/2);
                } else {
                    // there is only one node the graph.
                    maxself = nodes[sn]->freelg/2;
                }
      
                if ((nExtern > 1) && (opt->values[GRCC_OPT_1PI] > 0
                     || opt->values[GRCC_OPT_NoTadpole] > 0)
                    && nNodes > 1) {
                    // there are two or more nodes in the graph : 
                    // avoid to generate tadpole
                     maxself = Min((nodes[sn]->deg-2)/2, maxself);
                }
      
                // for the number of connection.
                for (nc2 = maxself; nc2 > 0; nc2--) {
                    nc = 2*nc2;
                    ncm = CLWIGHTD(nc);
                    adjMat[sn][sn] = nc;
                    nodes[sn]->freelg -= nc;
                    cl->incMat(sn, tn, ncm);
        
                    // next connection
                    connectLeg(so, sn, to1, tn+1, cl);
        
                    // restore the configuration
                    cl->incMat(tn, sn, - ncm);
                    adjMat[sn][sn] = 0;
                    nodes[sn]->freelg += nc;
                }
    
            // connections between different nodes.
            } else {
                // maximum possible connection number
                maxcon = Min(nodes[sn]->freelg, nodes[tn]->freelg);
      
                // avoid disconnected graphs.
                if (nNodes > 2 && nodes[sn]->deg == nodes[tn]->deg) {
                    maxcon = Min(maxcon, nodes[sn]->deg-1);
                }

                if (opt->values[GRCC_OPT_NoMultiEdge] > 0) {
                    maxcon = Min(maxcon, 1);
                }
      
#ifdef CHECK
                if ((adjMat[sn][tn] != 0) || 
                    (adjMat[sn][tn] != adjMat[tn][sn])) {
                    grcc_fprintf(GRCC_Stdout, "*** inconsistent connection: sn=%d, tn=%d",
                           sn, tn);
                    printAdjMat(cl);
                    erEnd("inconsistent connection ");
                }
#endif
      
                // vary number of connections
                for (nc = maxcon; nc > 0; nc--) {
                    ncm = CLWIGHTO(nc);
                    adjMat[sn][tn] = nc;
                    adjMat[tn][sn] = nc;
                    nodes[sn]->freelg -= nc;
                    nodes[tn]->freelg -= nc;
                    cl->incMat(sn, tn, ncm);
                    cl->incMat(tn, sn, ncm);
        
                    // next connection
                    connectLeg(so, sn, to1, tn+1, cl);
          
                    // restore configuration
                    cl->incMat(sn, tn, - ncm);
                    cl->incMat(tn, sn, - ncm);
                    adjMat[sn][tn] = 0;
                    adjMat[tn][sn] = 0;
                    nodes[sn]->freelg += nc;
                    nodes[tn]->freelg += nc;
                }
            }
        } 
    }
}

//------------------------------------------------------------
Bool MGraph::isOptM(void)
{
    Bool ok = True;

    opi       = (mconn->nopic == 1);
    opiloop   = (mconn->nlpopic <= 1);
    tadpole   = (mconn->ne0bridges >= ((nExtern == 1) ? 0 : 1));
    selfloop  = (mconn->nselfloops > 0);
    multiedge = (mconn->nmultiedges > 0);
    tadblock  = (mconn->na1blocks > 0);
    block     = (mconn->neblocks <= 1);
    extself   = (mconn->ne1bridges > 0);

    if (opt->values[GRCC_OPT_1PI] > 0) {
        ok = ok && opi;
    } else if (opt->values[GRCC_OPT_1PI] < 0) {
        ok = ok && !opi;
    }
    if (opt->values[GRCC_OPT_NoExtSelf] > 0) {
        ok = ok && !extself;
    } else if (opt->values[GRCC_OPT_NoExtSelf] < 0) {
        ok = ok && extself;
    }
    if (opt->values[GRCC_OPT_NoTadpole] > 0) {
#ifdef OLDOPT
        ok = ok && !tadpole;
#else
        if (nExtern > 1) {
            ok = ok && !tadpole;
        }
#endif
    } else if (opt->values[GRCC_OPT_NoTadpole] < 0) {
#ifdef OLDOPT
        ok = ok && !tadpole;
#else
        if (nExtern > 1) {
            ok = ok && tadpole;
        }
#endif
    }
    if (opt->values[GRCC_OPT_NoSelfLoop] > 0) {
    } else if (opt->values[GRCC_OPT_NoSelfLoop] < 0) {
        ok = ok && selfloop;
    }
    if (opt->values[GRCC_OPT_NoMultiEdge] > 0) {
    } else if (opt->values[GRCC_OPT_NoMultiEdge] < 0) {
        ok = ok && multiedge;
    }
    if (opt->values[GRCC_OPT_No1PtBlock] > 0) {
        if (nExtern > 1) {
            ok = ok && !tadblock;
        }
    } else if (opt->values[GRCC_OPT_No1PtBlock] < 0) {
        if (nExtern > 1) {
            ok = ok && tadblock;
        }
    }
    if (opt->values[GRCC_OPT_Block] > 0) {
        ok = ok && block;
    } else if (opt->values[GRCC_OPT_Block] < 0) {
        ok = ok && !block;
    }
    return ok;
}

//------------------------------------------------------------
void MGraph::newGraph(MNodeClass *cl)
{
    //  A new candidate diagram is obtained.
    //  It may be a disconnected graph
    //
    //  Things to be done in the steps followed by this function.
    //  1. convert data format which treat the edges as objects.
    //  2. definition of loop momenta to the edges.
    //  3. analysis of loop structure in a graph.
    //  4. assignment of particles to edges and vertices to nodes
    //  5. recalculate symmetry factor

    int connected;
    MNodeClass *xcl;
    Bool ok;
 
    ngen++;

    // refine class and check ordering condition
    xcl = refineClass(cl);
    if (xcl == NULL) {
#ifdef MONITOR
        discardRefine++;
#endif

    // check whether this is a connected graph or not.
    } else {
        connected = isConnected();
        if (!connected) {
#ifdef MONITOR
            discardDisc++;
#endif
  
        // connected graph : check isomorphism of the graph
        } else {
            ngconn++;
            if (!isIsomorphic(xcl)) {
#ifdef MONITOR
                discardIso++;
#endif
    
            // We got a new connected and a unique representation of a class.
            } else {
                biconnME();
                if (isOptM()) {
                    egraph->fromMGraph(this);
                    if (egraph->isOptE()) {
                        curcl->copy(xcl);
#ifdef ORBITS
                        orbits->toOrbits();
#endif
                        ok = True;
                        if (opt->outmg != NULL) {
                            if (opt->proc != NULL) {
                                egraph->mId = opt->proc->mgrcount + 1;
                                egraph->sId = opt->proc->agrcount + 1;
                            } else if (opt->sproc != NULL) {
                                egraph->mId = opt->sproc->mgrcount + 1;
                                egraph->sId = opt->sproc->agrcount + 1;
                            } else {
                                egraph->mId = cDiag;
                            }
                            ok = (*(opt->outmg))(egraph, opt->argmg);
                        }

                        if (ok) {
                            // # generated graphs
                            cDiag++;
                            wscon.add(1, nsym*esym);
          
                            // # generated 1PI graphs
                            if (opi) {
                                wsopi.add(1, nsym*esym);
                                c1PI++;
                            }
          
                            // # no tadpoles
                            if (!tadpole) {
                                cNoTadpole++;
                            }
                            // # no tadblocks
                            if (!tadblock) {
                                cNoTadBlock++;
                                if (opi) {
                                    c1PINoTadBlock++;
                                }
                            }
              
#ifdef MONITOR
                            grcc_fprintf(GRCC_Stdout, "\n");
                            grcc_fprintf(GRCC_Stdout, "Graph : %ld (%ld)", cDiag, ngen);
                            grcc_fprintf(GRCC_Stdout, " sym. factor = (%ld*%ld)\n", nsym, esym);
                            printAdjMat(cl);
                            // cl->printMat();
#  ifdef ORBITS
                            orbits->print();
#  endif
#endif
                            // go to next step
                            opt->newMGraph(this);
                        } else {
                        }
                    } else {
                    }
                } else {
                    ;
                }
            }
        }
    }
    if (xcl != cl && xcl != NULL) {
      delete xcl;
    }
}

//==============================================================
// class MOrbits: orbits of nodes
//--------------------------------------------------------------
MOrbits::MOrbits(void)
{
    nOrbits = 0;
    nNodes  = 0;
}

//--------------------------------------------------------------
MOrbits::~MOrbits(void)
{
}

//--------------------------------------------------------------
void MOrbits::print(void)
{
    int c;

    grcc_fprintf(GRCC_Stdout, "Orbits : nOrbits=%d: nd2or=", nOrbits);
    prIntArray(nNodes, nd2or, "\n");
    for (c = 0; c < nOrbits; c++) {
        grcc_fprintf(GRCC_Stdout, "    %2d: (%2d -- %2d) :", c, flist[c], flist[c+1]-1);
        prIntArray(flist[c+1]-flist[c], or2nd+flist[c], "\n");
    }
}

//---------------------------------------------------------------
void MOrbits::initPerm(int nnodes)
{
    int j;

    nNodes = nnodes;
    for (j = 0; j < nNodes; j++) {
        nd2or[j] = j;
    }
}

//---------------------------------------------------------------
void MOrbits::fromPerm(int *perm)
{
    // update the orbits of nodes by the permutation

    int j, j1, k, l;

    for (j = 0; j < nNodes; j++) {
        if (nd2or[j] != j) {
            // not the first element of an old orbit
            continue;
        }
        // merge orbits to orbit 'j'
        k = j;
        for (j1 = 0; j1 < nNodes && (k = perm[k]) != j; j1++) {
            if (nd2or[k] == j) {
                // 'k' is already in 'j'
                ;
            } else {
                // old orbit 'k' had several elements: merge to orbit 'j'
                for (l = 0; l < nNodes; l++) {
                    if (nd2or[l] == k) {
                        nd2or[l] = j;
                    }
                }
            }
        }     
#ifdef CHECK
        if (j1 >= nNodes) {
            grcc_fprintf(GRCC_Stdout, "*** fromPerm: illegal control: j=%d, k=%d\n", j, k);
            grcc_fprintf(GRCC_Stdout, "perm=");
            prIntArray(nNodes, perm,  " nd2or=");
            prIntArray(nNodes, nd2or, "\n");
            erEnd("fromPerm: illegal control");
        }
#endif
    }
}

//--------------------------------------------------------------
void MOrbits::toOrbits(void)
{
    // fill elements from 'nd2or'
    int nd, nel, k, lor;

    lor = -1;
    nel = 0;
    nOrbits = 0;
    for (nd = 0; nd < nNodes; nd++) {
        if (nd2or[nd] > lor) {
            // lowest element of a new orbit
            lor = nd2or[nd];
            flist[nOrbits++] = nel;
            for (k = nd; k < nNodes; k++) {
                if (nd2or[k] == lor) {
                    or2nd[nel++] = k;
                }
            }
        }
    }
    flist[nOrbits] = nNodes;
}

//**************************************************************
// n-edge connected components
//============================================================
// class MCEdge
//------------------------------------------------------------
MCEdge::MCEdge(void)
{
    ;
}

//------------------------------------------------------------
MCEdge::~MCEdge(void)
{
    ;
}

//============================================================
// class MCOpi: one n-edge connected component
//------------------------------------------------------------
MCOpi::MCOpi(void)
{
    init();
}

//------------------------------------------------------------
MCOpi::~MCOpi(void)
{
    nodes = NULL;
}

//------------------------------------------------------------
void MCOpi::init(void)
{
    nodes  = NULL;
    nnodes = 0;
    nlegs  = 0;
    next   = 0;
    nedges = 0;
    loop   = 0;
    ctloop = 0;
    mom0lg = 0;
}

//============================================================
// class MCBridge
//------------------------------------------------------------
MCBridge::MCBridge(void)
{
}

//------------------------------------------------------------
MCBridge::~MCBridge(void)
{
}

//============================================================
// class MCBlock
//------------------------------------------------------------
MCBlock::MCBlock(void)
{
    init();
}

//------------------------------------------------------------
MCBlock::~MCBlock(void)
{
}

//------------------------------------------------------------
void MCBlock::init(void)
{
    edges   = NULL;
    nmedges = 0;
    nartps  = 0;
    loop    = 0;
}

//============================================================
// class MConn: table of n-edge connected components
//------------------------------------------------------------
MConn::MConn(int nnod, int nedg)
{
    // nnod : the number of nodes
    // nedg : the number of edges

    snodes = nnod;
    sedges = nedg;

    cedges   = new MCEdge[sedges];
    opics    = new MCOpi[snodes];
    bridges  = new MCBridge[sedges];
    blocks   = new MCBlock[sedges];
    articuls = new int[snodes];

    // workspace
    opisp    = new int[snodes];
    opistk   = new int[snodes];
    blksp    = new Edge2n[sedges];
    blkstk   = new Edge2n[sedges];
    init();
}

//------------------------------------------------------------
MConn::~MConn(void)
{
    delete[] blkstk;
    delete[] blksp;
    delete[] opistk;
    delete[] opisp;

    delete[] articuls;
    delete[] blocks;
    delete[] bridges;
    delete[] opics;
    delete[] cedges;
}

//------------------------------------------------------------
void MConn::init(void)
{
    int j;

    nopic       = 0;
    nlpopic     = 0;
    nbacked     = 0;
    nctopic     = 0;
    nbridges    = 0;
    ne0bridges  = 0;
    ne1bridges  = 0;
    nselfloops  = 0;
    nmultiedges = 0;
    nbacked     = 0;

    nblocks     = 0;
    na1blocks   = 0;
    narticuls   = 0;
    neblocks    = 0;

    opistkptr   = 0;
    nopisp      = 0;
    blkstkptr   = 0;
    nblksp      = 0;

    for (j = 0; j < snodes; j++) {
        articuls[j] = 0;
    }
}

//------------------------------------------------------------
void MConn::pushNode(int nd)
{
    if (opistkptr >= snodes) {
        erEnd("MConn::pushNode: opistkptr >= snodes");
    }
    opistk[opistkptr++] = nd;
}

//------------------------------------------------------------
void MConn::pushEdge(int n0, int n1)
{
    if (blkstkptr >= sedges) {
        erEnd("MConn::pushEdge: blkstkptr >= sedges");
    }
    if (n0 <= n1) {
        blkstk[blkstkptr][0] = n0;
        blkstk[blkstkptr][1] = n1;
    } else {
        blkstk[blkstkptr][0] = n1;
        blkstk[blkstkptr][1] = n0;
    }
    blkstkptr++;
}


//------------------------------------------------------------
void MConn::initCEdges(MGraph *mg)
{
    int ed, n0, n1, e;

    ed = 0;
    for (n0 = 0; n0 < mg->nNodes; n0++) {
        for (e = 0; e < mg->adjMat[n0][n0]/2; e++, ed++) {
            cedges[ed].nodes[0] = n0;
            cedges[ed].nodes[1] = n0;
            cedges[ed].momdir   = 0;
        }
        for (n1 = n0+1; n1 < mg->nNodes; n1++) {
            for (e = 0; e < mg->adjMat[n0][n1]; e++, ed++) {
                cedges[ed].nodes[0] = n0;
                cedges[ed].nodes[1] = n1;
                cedges[ed].momdir   = 0;
            }
        }
    }
    if (ed != sedges) {
        grcc_fprintf(GRCC_Stdout, "*** ed=%d != sedges=%d\n", ed, sedges);
        erEnd("MConn::initCEdge: table overflow");
    }
}

//------------------------------------------------------------
void MConn::addCEdge(int n0, int n1, ULong momset)
{
    int m0, m1, dir, ed;

    if (n0 <= n1) {
        m0  = n0;
        m1  = n1;
        dir = 1;
    } else {
        m0  = n1;
        m1  = n0;
        dir = -1;
    }
    for (ed = 0; ed < sedges; ed++) {
        if (cedges[ed].nodes[0] == m0 && cedges[ed].nodes[1] == m1 &&
                cedges[ed].momdir   == 0) {
            cedges[ed].momdir = dir;
            cedges[ed].momset = momset;
            return;
        }
    }
}

//------------------------------------------------------------
void MConn::addOPIc(MCOpi *mopi, int stp)
{
    int j, nn;

    if (nopic >= snodes) {
        erEnd("MConn::addOPIc: table overflow");
    }

    nn = opistkptr - stp;
    for (j = 0; j < nn; j++) {
        opisp[nopisp+j] = opistk[stp+j];
    }
    opics[nopic].nnodes = nn;
    opics[nopic].nlegs  = mopi->nlegs;
    opics[nopic].nedges = mopi->nedges;
    opics[nopic].next   = mopi->next;
    opics[nopic].loop   = mopi->loop;
    opics[nopic].ctloop = mopi->ctloop;
    opics[nopic].mom0lg = mopi->mom0lg;
    opics[nopic].nodes  = opisp  + nopisp;
    nopisp   += nn;
    opistkptr = stp;
    
    nopic++;
}

//------------------------------------------------------------
void MConn::addBridge(int n0, int n1, int nex, int nextot)
{
    if (nbridges >= sedges) {
        erEnd("MConn::addBridge: table overflow");
    }
    if (n0 <= n1) {
        bridges[nbridges].nodes[0] = n0;
        bridges[nbridges].nodes[1] = n1;
    } else {
        bridges[nbridges].nodes[0] = n1;
        bridges[nbridges].nodes[1] = n0;
    }
    bridges[nbridges].next = Min(nex, nextot-nex);
    nbridges++;
}

//------------------------------------------------------------
void MConn::addArtic(int nd, int mul)
{
    articuls[nd] += mul;
    if (articuls[nd] == mul) {
        narticuls++;
    } else if (articuls[nd] == 0) {
        narticuls--;
    }
}

//------------------------------------------------------------
void MConn::addBlock(MCBlock *mblk, int stp)
{
    int j, nn;

    if (nopic >= snodes) {
        erEnd("MConn::addOPIc: table overflow");
    }

    nn = blkstkptr - stp;
    for (j = 0; j < nn; j++) {
        blksp[nblksp+j][0] = blkstk[stp+j][0];
        blksp[nblksp+j][1] = blkstk[stp+j][1];
    }
    blocks[nblocks].edges   = blksp + nblksp;
    blocks[nblocks].nmedges = nn;
    blocks[nblocks].nartps  = mblk->nartps;
    blocks[nblocks].loop    = mblk->loop;
    nblksp    += nn;
    blkstkptr = stp;
    
    nblocks++;
}

//------------------------------------------------------------
void MConn::addBlockSelf(int nd, int mult)
{
    MCBlock mblk;
    int j, stp;

    mblk.edges   = NULL;
    mblk.nmedges = 0;
    mblk.nartps  = 1;
    mblk.loop    = 1;

    for (j = 0; j < mult; j++) {
        stp = blkstkptr;
        pushEdge(nd, nd);
        addBlock(&mblk, stp);
    }
}

//------------------------------------------------------------
void MConn::print(void)
{
    int j, k;

    grcc_fprintf(GRCC_Stdout, "+++ MConn object: snodes=%d, sedges=%d\n", snodes, sedges);
    grcc_fprintf(GRCC_Stdout, "    nopic=%d, nlpopic=%d, nbacked=%d, nctopic=%d, "
           "nbridges=%d, ne0bridges=%d, ne1bridges=%d\n",
           nopic, nlpopic, nbacked, nctopic, 
           nbridges, ne0bridges, ne1bridges);
    grcc_fprintf(GRCC_Stdout, "    nblocks=%d, neblocks=%d, na1blocks=%d, narticuls=%d, nselfloop=%d\n",
           nblocks, neblocks, na1blocks, narticuls, nselfloops);
    grcc_fprintf(GRCC_Stdout, "    nmultiedges=%d\n", nmultiedges);

    grcc_fprintf(GRCC_Stdout, "  cEdges (%d)\n", sedges);
    if (sedges > 0) {
        for (j = 0; j < sedges; j++) {
            grcc_fprintf(GRCC_Stdout, "    %2d: (%d,%d)[%2d*%2ld] \n", j,
                   cedges[j].nodes[0], cedges[j].nodes[1], 
                   cedges[j].momdir, cedges[j].momset);
        }
    }
    grcc_fprintf(GRCC_Stdout, "\n");

    grcc_fprintf(GRCC_Stdout, "  1PI components (%d)\n", nopic);
    for (j = 0; j < nopic; j++) {
        grcc_fprintf(GRCC_Stdout, "    %d: nleg=%d, nnodes=%d, nedge=%d, ",
                j, opics[j].nlegs, opics[j].nnodes, opics[j].nedges);
        grcc_fprintf(GRCC_Stdout, "next=%d, loop=%d, ctlp=%d: m0lg=%d [",
                opics[j].next, opics[j].loop, opics[j].ctloop, 
                opics[j].mom0lg);
        for (k = 0; k < opics[j].nnodes; k++) {
            grcc_fprintf(GRCC_Stdout, " %d", opics[j].nodes[k]);
        }
        grcc_fprintf(GRCC_Stdout, "]\n");
    }

    grcc_fprintf(GRCC_Stdout, "  bridges (%d)\n", nbridges);
    if (nbridges > 0) {
        grcc_fprintf(GRCC_Stdout, "    ");
        for (j = 0; j < nbridges; j++) {
            grcc_fprintf(GRCC_Stdout, "(%d,%d)[mom=%d] ", 
                   bridges[j].nodes[0], bridges[j].nodes[1], bridges[j].next);
        }
        grcc_fprintf(GRCC_Stdout, "\n");
    }

    grcc_fprintf(GRCC_Stdout, "  blocks (%d)\n", nblocks);
    for (j = 0; j < nblocks; j++) {
        grcc_fprintf(GRCC_Stdout, "    %d: nmedges=%d, nartps=%d, loop=%d: [",
               j, blocks[j].nmedges, blocks[j].nartps, blocks[j].loop);
        for (k = 0; k < blocks[j].nmedges; k++) {
            grcc_fprintf(GRCC_Stdout, " (%d,%d)", blocks[j].edges[k][0], blocks[j].edges[k][1]);
        }
        grcc_fprintf(GRCC_Stdout, "]\n");
    }

    grcc_fprintf(GRCC_Stdout, "  articulation points (%d)\n", narticuls);
    if (narticuls > 0) {
        grcc_fprintf(GRCC_Stdout, "    ");
        for (j = 0; j < snodes; j++) {
            if (articuls[j] != 0) {
#if 0
                grcc_fprintf(GRCC_Stdout, "%d(%d) ", j, articuls[j]);
#else
                grcc_fprintf(GRCC_Stdout, "%d ", j);
#endif
            }
        }
        grcc_fprintf(GRCC_Stdout, "\n");
    }
}

//------------------------------------------------------------
void MConn::prEdges(void)
{
    int j;

    grcc_fprintf(GRCC_Stdout, "  cEdges (%d)", sedges);
    if (sedges > 0) {
        for (j = 0; j < sedges; j++) {
            if (j % 5 == 0) {
                grcc_fprintf(GRCC_Stdout, "\n    ");
            }
            grcc_fprintf(GRCC_Stdout, "(%d,%d)[%2d*%3ld] ", 
                   cedges[j].nodes[0], cedges[j].nodes[1], 
                   cedges[j].momdir, cedges[j].momset);
        }
        grcc_fprintf(GRCC_Stdout, "\n");
    }
}

//**************************************************************
// sgroup.cc
//==============================================================
// compile options
//============================================================
// table of group elements
//------------------------------------------------------------
SGroup::SGroup(void)
{
    // should be called before graph generation
    nnodes = -1;
    nelem  = 0;
    elem   = NULL;
}

//------------------------------------------------------------
SGroup::~SGroup(void)
{
    int j;

    if (elem != NULL) {
        for (j = GRCC_MAXGROUP-1; j >= 0; j--) {
            if (elem[j] != NULL) {
                delete[] elem[j];
                elem[j] = NULL;
            }
        }
        delete[] elem;
        elem = NULL;
    }
}

//------------------------------------------------------------
void SGroup::print(void)
{
    int j;

    grcc_fprintf(GRCC_Stdout, "SGroup : nnodes = %d, nelem=%ld, cgen=%d, csav=%d\n",
           nnodes, nelem, cgen, csav);
    grcc_fprintf(GRCC_Stdout, "  eclass =");
    prIntArray(neclass, eclass, "\n");
    for (j = 0; j < nelem; j++) {
        grcc_fprintf(GRCC_Stdout, "    %4d: ", j);
        prIntArray(nnodes, elem[j], "\n");
    }
}

//------------------------------------------------------------
void SGroup::newGroup(int nnd, int nclss, int *clss)
{
    int j;

    clearGroup();
    nnodes  = nnd;
    neclass = nclss;

    if (neclass > GRCC_MAXNODES) {
        erEnd("newGroup : too many classes (GRCC_MAXNODES)");
    }
    for (j = 0; j < neclass; j++) {
        eclass[j] = clss[j];
    }

    nelem = 0;
    if (elem == NULL) {
        elem  = new int*[GRCC_MAXGROUP];
        for (j = 0; j < GRCC_MAXGROUP; j++) {
            elem[j] = NULL;
        }
    }
}

//------------------------------------------------------------
void SGroup::clearGroup(void)
{
    nelem  = 0;
    csav   = -1;
    cgen   = -1;
}

//------------------------------------------------------------
void SGroup::delGroup(void)
{
    int j;

    for (j = 0; j < GRCC_MAXGROUP; j++) {
        if (elem[j] != NULL) {
            delete[] elem[j];
            elem[j] = NULL;
        }
    }
    delete[] elem;
    elem = NULL;
    clearGroup();
}

//------------------------------------------------------------
int *SGroup::genNext(void)
{
    cgen = nextPerm(nnodes, neclass, eclass, pgr, pgq, permg, cgen);
    if (cgen < 0) {
        return NULL;
    }
    return permg;
}

//------------------------------------------------------------
void SGroup::addGroup(int *p)
{
    int j;

    if (nelem >= GRCC_MAXGROUP) {
        erEnd("addGroup : too many elements (GRCC_MAXGROUP)");
    }
    if (elem[nelem] == NULL) {
        elem[nelem] = new int[GRCC_MAXNODES];
    }
    for (j = 0; j < nnodes; j++) {
        elem[nelem][j] = p[j];
    }
    nelem++;
}

//------------------------------------------------------------
BigInt SGroup::nElem(void)
{
    return nelem;
}

//------------------------------------------------------------
int *SGroup::nextElem(void)
{
    if (nelem < 0) {
        cgen = nextPerm(nelem, neclass, eclass,
                     psr, psq, perms, cgen);
        return perms;
    }
    if (cgen < 0) {
        cgen = 0;
    }
    if (cgen >= nelem) {
        return NULL;
    } else {
        return elem[cgen++];
    }
}

//**************************************************************
// egraph.cc
// Generate scalar connected Feynman graphs.
//==============================================================
static const char *GRCC_ND_names[] = GRCC_ND_NAMES;
static const char *GRCC_ED_names[] = GRCC_ED_NAMES;

//==============================================================
// class ENode
//--------------------------------------------------------------
ENode::ENode(void)
{ 
    id      = -1;
    egraph  = NULL;
    edges   = NULL;
    maxdeg  = 0;
    deg     = 0;

    klow    = NULL;
    extloop = 0;
    ndtype  = GRCC_ND_Undef;

    intrct  = -1;
}

//--------------------------------------------------------------
ENode::ENode(EGraph *egrph, int loops, int sdeg)

{ 
    id      = -1;
    egraph  = egrph;
    edges   = NULL;
    maxdeg  = sdeg;
    deg     = 0;

    klow    = NULL;
    extloop = 0;
    ndtype  = GRCC_ND_Undef;

    intrct  = -1;

    edges = new int[sdeg]; 
    klow  = new int[loops+1]; 
}

//--------------------------------------------------------------
ENode::~ENode(void)
{ 
    if (klow != NULL) {
        delete[] klow; 
        delete[] edges;
        klow  = NULL;
        edges = NULL;;
    }
}

//--------------------------------------------------------------
void ENode::copy(ENode *en)
{ 
    int d;

    deg = en->deg;
    extloop = en->extloop;
    ndtype  = en->ndtype;
    for (d = 0; d < deg; d++) {
        edges[d] = en->edges[d];
    }
}

//--------------------------------------------------------------
void ENode::initAss(EGraph *egrph, int nid, int sdg)
{
    id      = nid;
    egraph  = egrph;
    maxdeg  = sdg;
}

//--------------------------------------------------------------
void ENode::setId(EGraph *egrph, const int nid)
{ 
    id      = nid;
    egraph  = egrph;
}

//--------------------------------------------------------------
void ENode::setExtern(int typ, int pt)
{
    intrct  = pt;
    if (typ == GRCC_AT_Initial || typ == GRCC_AT_Final) {
        extloop = typ;
    } else {
        grcc_fprintf(GRCC_Stderr, "** ENode::setExternal:: illegal typ=%d\n",
                typ);
        erEnd("ENode::setExternal:: illegal typ");
    }
}

//--------------------------------------------------------------
void ENode::setType(int typ)
{ 
#ifdef CHECK
    if (ndtype != GRCC_ND_Undef && ndtype != typ) { 
        grcc_fprintf(GRCC_Stderr, "*** ndtype is already defined : old=%d, new = %d\n",
               ndtype, typ);
        erEnd("ndtype is already defined");
    }
#endif
    ndtype = typ;
}

//--------------------------------------------------------------
void ENode::print(void)
{
    int j;

    grcc_fprintf(GRCC_Stdout, "Enode %d deg=%d, extl=%2d, intr=%d ",
           id, deg, extloop, intrct);
    if (egraph->bicount > 0) {
        grcc_fprintf(GRCC_Stdout, "(%-8s) ", GRCC_ND_names[ndtype]);
    }
    grcc_fprintf(GRCC_Stdout, "edge=[");
    for (j = 0; j < deg; j++) {
        grcc_fprintf(GRCC_Stdout, " %2d", edges[j]);
    }
    grcc_fprintf(GRCC_Stdout, "]\n");
}

//==============================================================
// class EEdge
//--------------------------------------------------------------
EEdge::EEdge(void)
{
    id       = -1;
    egraph   = NULL;
    nodes[0] = -1;
    nodes[1] = -1;
    // nlegs[0] = -1;
    // nlegs[1] = -1;
    ptcl     = GRCC_PT_Undef;
    deleted  = False;

    edtype   = GRCC_ED_Undef;
    cut      = False;

    emom = NULL;
    lmom = NULL;

    momset = 0;
    momdir = 0;
}

//--------------------------------------------------------------
EEdge::EEdge(EGraph *egrph, int nedges, int nloops)
{
    id       = -1;
    egraph   = egrph;
    nodes[0] = -1;
    nodes[1] = -1;
    nlegs[0] = -1;
    nlegs[1] = -1;
    ptcl     = GRCC_PT_Undef;
    deleted  = False;

    edtype   = GRCC_ED_Undef;
    cut      = False;

    emom = new int[nedges];
    lmom = new int[nloops];
}

//--------------------------------------------------------------
EEdge::~EEdge(void)
{
    if (lmom != NULL) {
        delete[] lmom;
    }
    if (emom != NULL) {
        delete[] emom;
    }
}

//--------------------------------------------------------------
void EEdge::copy(EEdge *ee)
{
    nodes[0] = ee->nodes[0];
    nodes[1] = ee->nodes[1];
    id       = ee->id;
    ext      = ee->ext;
    dir      = ee->dir;
    edtype   = ee->edtype;
    cut      = ee->cut;
}

//--------------------------------------------------------------
void EEdge::setId(EGraph *egrph, const int eid)
{
    id      = eid;
    egraph  = egrph;
}

//--------------------------------------------------------------
void EEdge::setType(int typ)
{ 
#ifdef CHECK
    if (edtype != GRCC_ED_Undef) {
        erEnd("edtype is already defined");
    }
#endif
    edtype = typ;
}

//--------------------------------------------------------------
void EEdge::setEMom(int nedges, int *em, int dir)
{
    int e;

    for (e = 0; e < nedges; e++) {
        if (em[e] != 0) {
            emom[e] = dir;
        }
    }
}

//--------------------------------------------------------------
void EEdge::setLMom(int k, int dir)
{
    lmom[k] = dir;
}

//--------------------------------------------------------------
void EEdge::print(void)
{
    int zero, n, k;

    grcc_fprintf(GRCC_Stdout, "Edge %2d ext=%d ptcl=%2d ", id, ext, ptcl);
    if (egraph == NULL || !egraph->assigned) {
        grcc_fprintf(GRCC_Stdout, "[%d, %d]", nodes[0], nodes[1]);
    } else {
        grcc_fprintf(GRCC_Stdout, "[(%d,%d), (%d,%d))", nodes[0], nlegs[0], nodes[1], nlegs[1]);
    }
    if (momdir != 0) {
        grcc_fprintf(GRCC_Stdout, "[%2d*%2lu]", momdir, momset);
    }

    if (egraph != NULL && egraph->bicount > 0) {
        if (cut) {
            grcc_fprintf(GRCC_Stdout, " %-9s ", "Cut");
        } else {
            grcc_fprintf(GRCC_Stdout, " %-9s ", GRCC_ED_names[edtype]);
        }
        grcc_fprintf(GRCC_Stdout, "c%2d: ", opicomp);
        grcc_fprintf(GRCC_Stdout, "%s%d =", (ext)?"Q":"p", id);
        zero = True;
        for (n = 0; n < egraph->nEdges; n++) {
            if (emom[n] != 0) {
                prMomStr(emom[n], "Q", n);
                zero = False;
            }
        }
        for (k = 0; k < egraph->nLoops; k++) {
            if (lmom[k] != 0) {
                prMomStr(lmom[k], "k", k);
                zero = False;
            }
        }
        if (zero) {
            grcc_fprintf(GRCC_Stdout, " 0");
        }
    } else {
        if (egraph == NULL) {
            grcc_fprintf(GRCC_Stdout, " egraph=NULL");
        } else {
            grcc_fprintf(GRCC_Stdout, " egraph->bicount=%d", egraph->bicount);
        }
    }
    grcc_fprintf(GRCC_Stdout, "\n");
}

//==============================================================
// class EFLine
//--------------------------------------------------------------
EFLine::EFLine(void)
{
    ftype = FL_Open;
    fkind = 0;
    nlist = 0;
}

//--------------------------------------------------------------
void EFLine::print(const char *msg)
{
    if (ftype == FL_Open) {
        grcc_fprintf(GRCC_Stdout, " Open");
    } else if (ftype == FL_Closed) {
        grcc_fprintf(GRCC_Stdout, " Loop");
    } else {
        grcc_fprintf(GRCC_Stdout, " ?%d", ftype);
    }
    if (fkind == GRCC_PT_Dirac) {
        grcc_fprintf(GRCC_Stdout, " Dirac");
    } else if (fkind == GRCC_PT_Majorana) {
        grcc_fprintf(GRCC_Stdout, " Major");
    } else if (fkind == GRCC_PT_Ghost) {
        grcc_fprintf(GRCC_Stdout, " Ghost");
    } else {
        grcc_fprintf(GRCC_Stdout, " ?%d", fkind);
    }
    grcc_fprintf(GRCC_Stdout, " len=%d ", nlist);
    prIntArray(nlist, elist, msg);
}

//==============================================================
// class EGraph
//--------------------------------------------------------------
EGraph::EGraph(int nnodes, int nedges, int mxdeg)
{
    // Arguments
    //   nnodes : the number of nodes
    //   nedges : the number of edges
    //   mxdeg  : the maximum number of degrees of nodes

    int j;

    opt     = NULL;
    mgraph  = NULL;
    econn   = NULL;

    sNodes  = nnodes;
    sEdges  = nedges;
    sMaxdeg = mxdeg;
    sLoops  = sEdges - sNodes + 1;   // assume connected graph

    pId     = -1;
    mId     = -1;
    aId     = -1;
    sId     =  0;
    gSubId  = -1;
    assigned = False;

    nNodes  = sNodes;
    nEdges  = sEdges;
    nLoops  = 0;
    nExtern = 0;

    nsym    = 1;
    esym    = 1;
    extperm = 1;
    nsym1   = 1;
    multp   = 1;
    totalc  = 0;

    nodes = new ENode*[sNodes];
    for (j = 0; j < sNodes; j++) {
        nodes[j] = new ENode(this, sNodes, sMaxdeg);
    }
    edges = new EEdge*[sEdges];
    for (j = 0; j < sEdges; j++) {
        edges[j] = new EEdge(this, sEdges, sLoops);
    }

    bidef   = new int[sNodes];
    bilow   = new int[sNodes];
    bicount = -1;

    extMom  = new int[sEdges+1];

    fsign   = 1;
    nFlines = -1;
    for (j = 0; j < GRCC_MAXFLINES; j++) {
        flines[j] = NULL;
    }
}

//--------------------------------------------------------------
EGraph::~EGraph(void)
{
    int j;

    for (j = GRCC_MAXFLINES-1; j >= 0; j--) {
        if (flines[j] != NULL) {
            delete flines[j];
            flines[j] = NULL;
        }
    }

    delete[] extMom;

    delete[] bilow;
    delete[] bidef;

    for (j = 0; j < sEdges; j++) {
        delete edges[j];
        edges[j] = NULL;
    }
    delete[] edges;

    for (j = 0; j < sNodes; j++) {
        delete nodes[j];
        nodes[j] = NULL;
    }
    delete[] nodes;

}

//--------------------------------------------------------------
void EGraph::copy(EGraph *eg)
{
    int nd, ed;

#ifdef CHECK
    if (sNodes < eg->nNodes || sEdges < eg->nEdges || 
        sMaxdeg < eg->sMaxdeg || sLoops < eg->nLoops) {
        erEnd("EGraph::copy: sizes are too small");
    }
#endif
    model   = eg->model;
    proc    = eg->proc;
    sproc   = eg->sproc;
    mgraph  = eg->mgraph;
    opt     = mgraph->opt;
    econn   = mgraph->mconn;

    pId     = eg->pId;
    mId     = eg->mId;
    gSubId  = eg->gSubId;
    nNodes  = eg->nNodes;
    nEdges  = eg->nEdges;
    nExtern = eg->nExtern;
    nLoops  = eg->nLoops;

    for (nd = 0; nd < nNodes; nd++) {
        nodes[nd]->copy(eg->nodes[nd]);
    }
    for (ed = 0; ed < nEdges; ed++) {
        edges[ed]->copy(eg->edges[ed]);
    }

    nsym    = eg->nsym;
    esym    = eg->esym;
    extperm = eg->extperm;
    nsym1   = eg->nsym1;
    multp   = eg->multp;
    
    bicount = -1;
}

//--------------------------------------------------------------
void EGraph::setExtLoop(int nd, int val)
{
    // set the node 'nd' being an external node (-1) or a looped vertex
    nodes[nd]->extloop = val;
}

//--------------------------------------------------------------
void EGraph::endSetExtLoop(void)
{
    // end of calling 'setExtLoop'.

    int n;

    nExtern = 0;
    for (n = 0; n < nNodes; n++) {
        if (isExternal(n)) {
            nExtern++;
        }
    }
}

//--------------------------------------------------------------
void EGraph::fromDGraph(DGraph *dg)
{
    int deg[GRCC_MAXNODES];
    int maxdeg, nextern, nconn, tc;
    int n0, n1, e;

    if (dg->nnodes > GRCC_MAXNODES) {
        grcc_fprintf(GRCC_Stderr, "*** too many nodes (GRCC_MAXNODES)\n");
        GRCC_ABORT();
    }
    if (dg->nedges > GRCC_MAXEDGES) {
        grcc_fprintf(GRCC_Stderr, "*** too many edges (GRCC_MAXEDGES)\n");
        GRCC_ABORT();
    }

    for (e = 0; e < dg->nedges; e++) {
        if (dg->edges[e][0] >= dg->nnodes || dg->edges[e][0] >= dg->nnodes) {
            grcc_fprintf(GRCC_Stderr, "*** undefined node:");
            grcc_fprintf(GRCC_Stderr, "edge[%d] = {%d, %d}\n", 
                    e, dg->edges[e][0], dg->edges[e][0]);
            GRCC_ABORT();
        }
    }

    for (n0 = 0; n0 < dg->nnodes; n0++) {
        deg[n0] = 0;
    }
    for (e = 0; e < dg->nedges; e++) {
        deg[dg->edges[e][0]]++;
        deg[dg->edges[e][1]]++;
    }
    maxdeg  = 0;
    nextern = 0;
    for (n0 = 0; n0 < dg->nnodes; n0++) {
        maxdeg = Max(maxdeg, deg[n0]);
        if (deg[n0] == 1) {
            nextern++;
        } if (deg[n0] < 0) {
            grcc_fprintf(GRCC_Stderr, "+++ node %d is isolated\n", n0);
        }
    }

    mgraph = NULL;
    model  = NULL;
    proc   = NULL;
    sproc  = NULL;
    opt    = NULL;

    nNodes  = dg->nnodes;
    nEdges  = dg->nedges;
    nLoops  = 0;
    nExtern = nextern;

    pId     = 0;
    mId     = 0;
    aId     = 0;
    gSubId  = 0;
    nsym    = 1;
    nsym1   = 1;
    esym    = 1;
    extperm = 1;
    multp   = 1;
    maxdeg  = maxdeg;
    
    for (n0 = 0; n0 < dg->nnodes; n0++) {
        nodes[n0]->deg = 0;
        nodes[n0]->extloop = dg->nodes[n0].extloop;
    }
    for (e = 0; e < dg->nedges; e++) {
        n0 = dg->edges[e][0];
        n1 = dg->edges[e][1];
        edges[e]->nodes[0] = n0;
        edges[e]->nodes[1] = n1;
        edges[e]->ext = (isExternal(n0) || isExternal(n1));
        edges[e]->momdir = 0;

        nodes[n0]->edges[nodes[n0]->deg++] = I2Vedge(e, -1);
        nodes[n1]->edges[nodes[n1]->deg++] = I2Vedge(e, +1);
    }
    for (n0 = 0; n0 < dg->nnodes; n0++) {
        nodes[n0]->setId(this, n0);
        nodes[n0]->intrct = dg->nodes[n0].intrct;
    }

    for (e = 0; e < nEdges; e++) {
        edges[e]->setId(this, e);
    }
    tc = 0;
    for (n0 = 0; n0 < nNodes; n0++) {
        if (isExternal(n0)) {
            setExtern(n0, 1, GRCC_AT_Initial);
        } else {
            tc += 2*nodes[n0]->extloop + nodes[n0]->deg - 2;
        }
    }
    totalc = tc;

    // get the number of connected components
    nconn = connComp();
    nLoops = nEdges - nNodes + nconn;

    bicount = -1;
}


//--------------------------------------------------------------
void EGraph::fromMGraph(MGraph *mg)
{
    // construct EGraph from adjacency matrix.
    // This function should be called after
    //   EGraph(), setExtLoop() and endSetExtLoop().

    int n0, n1, m0, m1, ed, e;
    int j, ni, nf;
    PNodeClass *pnc;
    int k;

#ifdef CHECK
    if (sNodes < mg->nNodes || sEdges < mg->nEdges || sMaxdeg < mg->maxdeg) {
        erEnd("EGraph::fromMGraph: sizes are too small");
    }
    if (sLoops < mg->nLoops) {
        grcc_fprintf(GRCC_Stdout, "too small sLoops : %d < %d\n", sLoops, mg->nLoops);
        erEnd("too small sLoops");
    }
#endif
    mgraph  = mg;
    opt     = mgraph->opt;
    econn   = mgraph->mconn;
    sproc   = opt->sproc;
    if (sproc == NULL) {
        proc  = NULL;
        model = NULL;
    } else {
        proc  = sproc->proc;
        model = sproc->model;
    }

    nNodes  = mg->nNodes;
    nEdges  = mg->nEdges;
    nLoops  = mg->nLoops;
    nExtern = mg->nExtern;
    pId     = mg->pId;
    mId     = mg->cDiag;
    aId     = -1;
    if (opt->proc != NULL) {
        mId = mg->opt->proc->mgrcount;
        sId = mg->opt->proc->agrcount;
    } else if (mg->opt->sproc != NULL) {
        mId = mg->opt->sproc->mgrcount;
        sId = mg->opt->sproc->agrcount;
    } else {
        mId = mg->cDiag;
        sId = mg->cDiag;
    }
    gSubId  = 0;
    nsym    = mg->nsym;
    esym    = mg->esym;
    extperm = 1;
    nsym1   = nsym;
    multp   = 1;
    maxdeg  = mg->maxdeg;

    totalc  = 0;
    if (proc != NULL) {
        for (j = 0; j < proc->model->ncouple; j++) {
            totalc += proc->clist[j];
        }
    }
    for (ed = 0; ed < nEdges; ed++) {
        edges[ed]->edtype = GRCC_ED_Undef;
    }

    ed = 0;
    for (n0 = 0; n0 < nNodes; n0++) {
        nodes[n0]->deg = 0;
    }
    for (n0 = 0; n0 < nNodes; n0++) {
        for (e = 0; e < mg->adjMat[n0][n0]/2; e++, ed++) {
            edges[ed]->nodes[0] = n0;
            edges[ed]->nodes[1] = n0;
            nodes[n0]->edges[nodes[n0]->deg++] = I2Vedge(ed, -1);
            nodes[n0]->edges[nodes[n0]->deg++] = I2Vedge(ed, +1);
            edges[ed]->ext = isExternal(n0);
        }
        for (n1 = n0+1; n1 < nNodes; n1++) {
            for (e = 0; e < mg->adjMat[n0][n1]; e++, ed++) {
                edges[ed]->nodes[0] = n0;
                edges[ed]->nodes[1] = n1;
                nodes[n0]->edges[nodes[n0]->deg++] = I2Vedge(ed, -1);
                nodes[n1]->edges[nodes[n1]->deg++] = I2Vedge(ed, +1);
                edges[ed]->ext = (isExternal(n0) || isExternal(n1));
            }
        }
    }
#ifdef CHECK
    if (ed != nEdges) {
        grcc_fprintf(GRCC_Stdout, "*** EGraph::init: ed=%d != nEdges=%d\n",
               ed, nEdges+1);
        erEnd("EGraph::init: illegal connection");
    }
#endif

    for (j = 0; j < nNodes; j++) {
        nodes[j]->setId(this, j);
        nodes[j]->intrct = mg->nodes[j]->extloop;
    }

    for (j = 0; j < nEdges; j++) {
        edges[j]->setId(this, j);
    }

    ni = 0;
    nf = 0;
    if (proc != NULL) {
        ni = proc->ninitl;
        for (j = 0; j < ni; j++) {
            setExtern(j, proc->initlPart[j], GRCC_AT_Initial);
        }

        nf = proc->nfinal;
        for (j = 0; j <  nf; j++) {
            setExtern(j+ni, proc->finalPart[j], GRCC_AT_Final);
        }
        nExtern = ni + nf;
    } else if (sproc != NULL) {
        pnc = sproc->pnclass;
        for (j = 0; j < sproc->pnclass->nclass; j++) {
            if (pnc->type[j] == GRCC_AT_Initial 
                || pnc->type[j] == GRCC_AT_External) {
                for (k = pnc->cl2nd[j]; k < pnc->cl2nd[j+1]; k++) {
                    setExtern(j, k, GRCC_AT_Initial);
                    ni++;
                }
            } else if (sproc->pnclass->type[j] == GRCC_AT_Final) {
                for (k = pnc->cl2nd[j]; k < pnc->cl2nd[j+1]; k++) {
                    setExtern(j, k, GRCC_AT_Final);
                    nf++;
                }
            }
                    
        }
        nExtern = ni + nf;
    }
    totalc = 0;
    for (j = 0; j < nNodes; j++) {
        if (!isExternal(j)) {
            totalc += 2*nodes[j]->extloop + nodes[j]->deg - 2;
        }
    }

    for (ed = 0; ed < nEdges; ed++) {
        edges[ed]->momdir = 0;
    }
    for (e = 0; e < econn->sedges; e++) {
        m0 = econn->cedges[e].nodes[0];
        m1 = econn->cedges[e].nodes[1];

        bool found = False;
        for (ed = 0; ed < nEdges; ed++) {
            if (edges[ed]->momdir != 0) {
                continue;
            }
            n0 = edges[ed]->nodes[0];
            n1 = edges[ed]->nodes[1];
            if (m0 == n0 && m1 == n1) {
                edges[ed]->momdir = econn->cedges[e].momdir;
                edges[ed]->momset = econn->cedges[e].momset;
                found = True;
                break;
            } else if (m0 == n1 && m1 == n0) {
                edges[ed]->momdir = - econn->cedges[e].momdir;
                edges[ed]->momset =   econn->cedges[e].momset;
                found = True;
                break;
            }
        }

        if (! found) {
            grcc_fprintf(GRCC_Stdout, "*** EGraph::fromMGraph:edge (%d->%d) is not found\n", 
                   m0, m1);
        }
    }

    bicount = -1;
}

//--------------------------------------------------------------
ENode *EGraph::setExtern(int n0, int pt, int ndtyp)
{
    ENode *nd;
    int npt, ept, eg;

    nd = nodes[n0];
    if (nd->deg != 1) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** illegal external particle %d, %d, %d\n",
                    n0,pt,ndtyp);
        }
        erEnd("illegal external particle");
    }

    // particle comes into the node
    if (ndtyp == GRCC_AT_Initial) {
        npt = pt;
    } else if (ndtyp == GRCC_AT_Final) {
        npt = -pt;
    } else {
        npt = 0;
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** illegal type of an external particle : "
                   "node = %d, particle = %d, type = %d", n0, pt, ndtyp);
        }
        erEnd("illegal type of an external particle");
    }

    // edge attached to the external node
    eg = n0;

    // particle flows on e from leg=0 to 1.
    if (model != NULL){
        npt = model->normalParticle(npt);
        ept = model->normalParticle(npt);
    } else {
        npt = 0;
        ept = 0;
    }

    nd->setExtern(ndtyp, npt);
    edges[eg]->ptcl = ept;

    return nd;
}

//--------------------------------------------------------------
void EGraph::print(void)
{
    // print the EGraph
  
    int  nd, ed, nlp;
  
    nlp = nEdges - nNodes + 1;
    grcc_fprintf(GRCC_Stdout, "\nEGraph\n");
    grcc_fprintf(GRCC_Stdout, "    pId=%d, gSubId=%ld, mId=%ld, aId=%ld, sId=%ld\n",
           pId, gSubId, mId, aId, sId);
    grcc_fprintf(GRCC_Stdout, "    sNodes=%d, sEdges=%d, sMaxdeg=%d, sLoops=%d\n",
           sNodes, sEdges, sMaxdeg, sLoops);
    grcc_fprintf(GRCC_Stdout, "    nNodes=%d, nEdges=%d, nExtern=%d, nLoops=%d, totalc=%d\n",
           nNodes, nEdges, nExtern, nlp, totalc);
    grcc_fprintf(GRCC_Stdout, "    ");
    if (model == NULL) {
        grcc_fprintf(GRCC_Stdout, "model=NULL,");
    } else {
        grcc_fprintf(GRCC_Stdout, "model=\"%s\",", model->name);
    }
    if (proc == NULL) {
        grcc_fprintf(GRCC_Stdout, "proc=NULL,");
    } else {
        grcc_fprintf(GRCC_Stdout, "proc=%d,", proc->id);
    }
    if (sproc == NULL) {
        grcc_fprintf(GRCC_Stdout, "sproc=NULL,");
    } else {
        grcc_fprintf(GRCC_Stdout, "sproc=%d,", sproc->id);
    }
    grcc_fprintf(GRCC_Stdout, "\n");
    grcc_fprintf(GRCC_Stdout, "    assigned=%d, sym = (%ld * %ld) ", 
           assigned, nsym, esym);
    grcc_fprintf(GRCC_Stdout, "extperm=%ld, nsym1=%ld, multp=%ld\n", 
           extperm, nsym1, multp);

    grcc_fprintf(GRCC_Stdout, "  Nodes\n");
    for (nd = 0; nd < nNodes; nd++) {
        if (isExternal(nd)) {
            grcc_fprintf(GRCC_Stdout, "    %2d Extern ", nd);
        } else {
            grcc_fprintf(GRCC_Stdout, "    %2d Vertex ", nd);
        }
        nodes[nd]->print();
    }
    grcc_fprintf(GRCC_Stdout, "  Edges\n");
    for (ed = 0; ed < nEdges; ed++) {
        if (edges[ed]->ext) {
            grcc_fprintf(GRCC_Stdout, "    %2d Extern ", ed);
        } else {
            grcc_fprintf(GRCC_Stdout, "    %2d Intern ", ed);
        }
        edges[ed]->print();
    }
    if (bicount > 0) {
        grcc_fprintf(GRCC_Stdout, "  Biconn: nopicomp=%d, nopi2p=%d, opi2plp=%d, nadj2ptv=%d\n",
               nopicomp, nopi2p, opi2plp, nadj2ptv);
    }
    grcc_fprintf(GRCC_Stdout, "\n");

    if (nFlines > 0) {
        prFLines();
    }
}

//--------------------------------------------------------------
void EGraph::printPy(FILE *fp, long mId)
{
    if (!assigned) {
        mgraph->printPy(fp, mId);
        return;
    }

    fprintf(fp, "#AGraph : (gseq, {spid, gid, ...}, nodes, node-group)\n");
    fprintf(fp, "(%ld,\n", mId);

    //  {'proc':0, 'subproc':0, 'tgraph':1, ... }
    fprintf(fp, "  {'proc':%d, 'subproc':%d, ", proc->id, sproc->id);
    fprintf(fp, "'tgraph':%ld, ", mId);
    fprintf(fp, "'OPI':%s, ", BOOLSTR(opt->values[GRCC_OPT_1PI]));
    fprintf(fp, "'agraph':%ld, \n", aId);
    fprintf(fp, "   'nnodes':%d, 'nnsym':%ld, 'nesym':%ld, },\n",
                nNodes, nsym, esym);
    //  #nodes
    fprintf(fp, "  [ #nodes\n");
    for (int nd = 0; nd < nNodes; nd++) {
        ENode *end = nodes[nd];

        // #node  0: external=phi
        // #node  4: phi3=0
        fprintf(fp, "    [ #node  %d: ", nd);
        fprintf(fp, "\n");

        // {'deg':1, 'cid':-3, ..., }
        fprintf(fp, "      {'deg':%d, 'cid':%d, 'extern':%s, ",
                end->deg, 0, BOOLSTR(isExternal(nd)));
        fprintf(fp, "'intr':%d, 'loop':%d, },\n",
                end->intrct, end->extloop);

        // legs : (edge, leg, particle)
        // [ (0, 1, 0), ... ],
        fprintf(fp, "      [ ");
        for (int lg = 0; lg < end->deg; lg++) {
            int ed = V2Iedge(end->edges[lg]);
            int ptcl = edges[ed]->ptcl;
            int edlg = (edges[ed]->nodes[0] == nd) ? 1 : 0;
            int nnd  = edges[ed]->nodes[edlg];
            int nlg  = edges[ed]->nlegs[edlg];
            fprintf(fp, "(%d, %d, %d), ", nnd, ptcl, nlg);
        }
        fprintf(fp, "],\n");
        fprintf(fp, "    ],\n");   // end #node
    }
    fprintf(fp, "  ], #node\n");
    fprintf(fp, "  [ # group of 1 elements\n");
    fprintf(fp, "    [],    #\n");
    fprintf(fp, "  ], # group\n");
    fprintf(fp, ")\n");
}

//--------------------------------------------------------------
void EGraph::prFLines(void)
{
    int j;

    grcc_fprintf(GRCC_Stdout, "  Fermion lines %d, sign=%d (mId=%ld, aId=%ld)\n", 
            nFlines, fsign, mId, aId);
    for (j = 0; j < nFlines; j++) {
        grcc_fprintf(GRCC_Stdout, "%4d ", j);
        flines[j]->print("\n");
    }
}

//--------------------------------------------------------------
int EGraph::dirEdge(int n, int e)
{
    if (nodes[n]->edges[e] > 0) {
        return 1;
    } else {
        return -1;
    }
}

//--------------------------------------------------------------
int EGraph::cmpMom(int *lm0, int *em0, int *lm1, int *em1)
{
    int lp, ed, cmp, sgn = 0;

    for (lp = 0; lp < nLoops; lp++) {
        if (lm0[lp] != 0) {
            if (lm1[lp] == 0) {
                return 1;
            } else if (sgn == 0) {
                sgn = lm0[lp]*lm1[lp];   // cancel first non-zero elements
#ifdef CHECK
                if (Abs(sgn) != 1) {
                    erEnd("cmpMom : illegal element of lmom");
                }
#endif
            } else {
                cmp = lm0[lp] - sgn*lm1[lp];
                if (cmp != 0) {
                    return cmp;
                }
            }
        } else if (lm1[lp] != 0) {   // lm0[lp] == 0
            return -1;
        }
    }
    for (ed = 0; ed < nEdges; ed++) {
        if (em0[ed] != 0) {
            if (em1[ed] == 0) {
                return 1;
            } else if (sgn == 0) {
                sgn = em0[ed]*em1[ed];   // cancel first non-zero elements
#ifdef CHECK
                if (Abs(sgn) != 1) {
                    erEnd("cmpMom : illegal element of emom");
                }
#endif
            } else {
                cmp = em0[ed] - sgn*em1[ed];
                if (cmp != 0) {
                    return cmp;
                }
            }
        } else if (em1[ed] != 0) {   // em0[ed] == 0
            return -1;
        }
    }
    return 0;
}

//--------------------------------------------------------------
int EGraph::groupLMom(int *grp, int *ed2gr)
{
    //  grp[g] : the number of elements in the group g (in [0,...,(ngrp-1)])
    //  ed2gr[ed] : group number of edge ed.

    int ed0, ed1, cmp, ngrp = -1;

    for (ed0 = 0; ed0 < nEdges; ed0++) {
        ed2gr[ed0] = -1;
        grp[ed0]   = 0;
    }

    for (ed0 = 0; ed0 < nEdges; ed0++) {
        if (ed2gr[ed0] < 0) {
            ngrp++;
            ed2gr[ed0] = ngrp;
            grp[ngrp]++;
            for (ed1 = ed0+1; ed1 < nEdges; ed1++) {
                cmp = cmpMom(edges[ed0]->lmom, edges[ed0]->emom, 
                             edges[ed1]->lmom, edges[ed1]->emom);
                if (cmp == 0) {
                    ed2gr[ed1] = ngrp;
                    grp[ngrp]++;
                }
            }
        }
    }
    ngrp++;

    return ngrp;
}

//--------------------------------------------------------------
Bool EGraph::optQGrafM(Options *opt)
{
    int *qgopt = opt->qgopt;
    int nopis[GRCC_MAXEDGES];
    ULong mext = 0;
    mext = (~ mext) << nExtern;

#ifdef PRINT
    grcc_fprintf(GRCC_Stdout, "optQGrafM:");
    print();
#endif

#ifdef PRINT
    grcc_fprintf(GRCC_Stdout, "optQGrafM: %8ld\n", mId);
    econn->print();
#endif

    // count the number of self-energy 1PI components.
    int maxlegs = 0;
    for (int j = 0; j < econn->nopic; j++) {
        maxlegs = Max(maxlegs, econn->opics[j].nlegs);
    }
    if (maxlegs >= GRCC_MAXEDGES) {
        grcc_fprintf(GRCC_Stdout, "*** table overflow\n");
        GRCC_ABORT();
    }
    for (int k = 0; k < GRCC_MAXEDGES; k++) {
        nopis[k] = 0;
    }
    for (int j = 0; j < econn->nopic; j++) {
        nopis[econn->opics[j].nlegs]++;
    }

    //  
    if (qgopt[GRCC_QGRAF_OPT_ONEPI] > 0) {
        if (econn->nopic != 1) {
            return False;
        }
    } else if (qgopt[GRCC_QGRAF_OPT_ONEPI] < 0) {
        if (econn->nopic < 2) {
            return False;
        }
    }

    if (qgopt[GRCC_QGRAF_OPT_ONSHELL] != 0) {
        if (nExtern == 1) {
            if (qgopt[GRCC_QGRAF_OPT_ONSHELL] > 0) {
                if (econn->nopic != 1) {
                    return False;
                }
            } else if (qgopt[GRCC_QGRAF_OPT_ONSHELL] < 0) {
                if (econn->nopic == 1) {
                    return False;
                }
            }
        } else {
            if (qgopt[GRCC_QGRAF_OPT_ONSHELL] > 0) {
                if (econn->ne1bridges > 0) {
                    return False;
                }
            } else if (qgopt[GRCC_QGRAF_OPT_ONSHELL] < 0) {
                if (econn->ne1bridges <= 0) {
                    return False;
                }
            }
        }
    }

    if (qgopt[GRCC_QGRAF_OPT_NOSNAIL] != 0) {
        if (qgopt[GRCC_QGRAF_OPT_NOSNAIL] > 0) {
            if (nExtern == 1) {
                if (econn->nblocks != 1) {
                    return False;
                }
            } else {
                if (mgraph->mconn->ne0bridges >= 1 ||
                    mgraph->mconn->na1blocks  >= 1) {
                    return False;
                }
            }
        } else if (qgopt[GRCC_QGRAF_OPT_NOSNAIL] < 0) {
            if (nExtern == 1) {
                if (econn->nblocks == 1) {
                    return False;
                 }
            } else {
                if (mgraph->mconn->ne0bridges < 1 &&
                    mgraph->mconn->na1blocks  < 1) {
                    return False;
                }
            }
        }
    }

    if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] != 0) {
        if (nExtern == 1) {
            if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] > 0) {
                if (econn->nopic != 1) {
                    return False;
                }
            } else if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] < 0) {
                if (econn->nopic == 1) {
                    return False;
                }
            }
        } else {
            if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] > 0) {
                if (mgraph->mconn->ne0bridges != 0) {
                    return False;
                }
            } else if (qgopt[GRCC_QGRAF_OPT_NOTADPOLE] < 0) {
                if (mgraph->mconn->ne0bridges == 0) {
                    return False;
                }
            }
        }
    }

    if (qgopt[GRCC_QGRAF_OPT_NOSIGMA] != 0) {
        bool ok = True;
        if (nExtern != 2) {
            if (nopis[2] > 1) {
                ok = False;
            }
        }
        for (int j = 0; j < econn->nopic; j++) {
            if (econn->opics[j].nlegs >= 2 && 
                econn->opics[j].nlegs == econn->opics[j].mom0lg) {
                ok = False;
            }
        }

        // loop momenta
        for (int j = 0; j < econn->sedges - 1; j++) {
            ULong momj = econn->cedges[j].momset;
            if (momj == 0) {
                continue;
            }
            int extj = 0;
            if (econn->cedges[j].nodes[0] < nExtern) {
                extj = 1;
            } else if (econn->cedges[j].nodes[1] < nExtern) {
                extj = 1;
            }
            for (int k = j+1; k < econn->sedges; k++) {
                ULong momk = econn->cedges[k].momset;
                if (momk == 0) {
                     continue;
                }
                int extk = 0;
                if (econn->cedges[k].nodes[0] < nExtern) {
                    extk = 1;
                } else if (econn->cedges[k].nodes[1] < nExtern) {
                    extk = 1;
                }
                if ( momj == momk) {
                    // We have a pair of lines with equal momenta. Determine if they have a
                    // common two-point vertex. We want to keep this type of "insertion" when
                    // in GRCC_QGRAF_OPT_NOSIGMA mode.
                    int commonNode = -1;
                    bool common2PtVtx = False;
                    if      (econn->cedges[j].nodes[0] == econn->cedges[k].nodes[0])
                        commonNode = econn->cedges[j].nodes[0];
                    else if (econn->cedges[j].nodes[0] == econn->cedges[k].nodes[1])
                        commonNode = econn->cedges[j].nodes[0];
                    else if (econn->cedges[j].nodes[1] == econn->cedges[k].nodes[0])
                        commonNode = econn->cedges[j].nodes[1];
                    else if (econn->cedges[j].nodes[1] == econn->cedges[k].nodes[1])
                        commonNode = econn->cedges[j].nodes[1];
                    if (commonNode != -1) {
                        if (nodes[commonNode]->deg == 2) {
                            common2PtVtx = True;
                        }
                    }

                    if (nExtern == 2) {
                        if (extj + extk != 2 && common2PtVtx == False) {
                            ok = False;
                        }
                    } else {
                        if (common2PtVtx == False) {
                            ok = False;
                        }
                    }
                }
            }
        }
        if (qgopt[GRCC_QGRAF_OPT_NOSIGMA] > 0) {
            if (! ok) {
                return False;
            }
        } else if (qgopt[GRCC_QGRAF_OPT_NOSIGMA] < 0) {
            if (ok) {
                return False;
            }
        }
    }

    if (qgopt[GRCC_QGRAF_OPT_SIMPLE] > 0) {
        if (mgraph->selfloop || mgraph->multiedge) {
            return False;
        }
    } else if (qgopt[GRCC_QGRAF_OPT_SIMPLE] < 0) {
        if (!mgraph->selfloop && !mgraph->multiedge) {
            return False;
        }
    }

    if (qgopt[GRCC_QGRAF_OPT_BIPART] > 0) {
        if (! mgraph->bipart) {
            return False;
        }
    } else if (qgopt[GRCC_QGRAF_OPT_BIPART] < 0) {
        if (mgraph->bipart) {
            return False;
        }
    }
    // GRCC_QGRAF_OPT_CYCLI
    if (qgopt[GRCC_QGRAF_OPT_CYCLI] != 0) {
        int nb = 0;
        for (int k = 0; k < econn->nblocks; k++) {
            if (econn->blocks[k].loop > 0) {
                nb++;
            }
        }
        if (qgopt[GRCC_QGRAF_OPT_CYCLI] > 0) {
            if (nb > 1) {
                return False;
            }
        } else if (qgopt[GRCC_QGRAF_OPT_CYCLI] < 0) {
            if (nb <= 1) {
                return False;
            }
        }
    }

    return True;
}

//--------------------------------------------------------------
Bool EGraph::optQGrafA(Options *opt)
{
#ifdef PRINT
    grcc_fprintf(GRCC_Stdout, "optQGrafA: %8ld\n", mId);
    econn->print();
#endif
    Bool retval = True;
    if (opt->qgopt[GRCC_QGRAF_OPT_FLOOP] != 0) {
        for (int fl=0; fl < nFlines; fl++) {
            if (flines[fl]->ftype == FL_Closed) {
                if (flines[fl]->nlist % 2 != 0) {
                    retval = False;
                    break;
                }
            }
        }
        // `notfloop_' is the dual of `floop_', so flip the decision:
        if (opt->qgopt[GRCC_QGRAF_OPT_FLOOP] == -1) {
            retval = (retval == True ? False : True);
        }
    }
    return retval;
}

//--------------------------------------------------------------
Bool EGraph::isOptE(void)
{
    EGraph edupv = EGraph(sNodes, sEdges, sMaxdeg);
    EGraph *edup = &edupv;
    int    grp[GRCC_MAXEDGES], ed2gr[GRCC_MAXEDGES];
    int    g, ed, ngrp;
    Bool   ok;
    int    minopi2p;


 // if (opt->values[GRCC_OPT_No2PtL1PI] == 0
 //     && opt->values[GRCC_OPT_NoAdj2PtV] == 0) {
 //     return True;
 // }

    for (ed = 0; ed < nEdges; ed++) {
        edges[ed]->cut = False;
    }

    biconnE();

    // QGraf options
    if (! optQGrafM(opt)) {
        return False;
    }
        
    if (opt->values[GRCC_OPT_NoAdj2PtV] > 0) {
        if (nadj2ptv > 0) {
            return False;
        }
    } else if (opt->values[GRCC_OPT_NoAdj2PtV] < 0) {
        if (nadj2ptv < 1) {
            return False;
        }
    }
    if (opt->values[GRCC_OPT_No2PtL1PI] == 0) {
        return True;
    }

    if (nExtern == 2 && nopicomp == 1) {
        minopi2p = 2;
    } else {
        minopi2p = 1;
    }

    if (opi2plp > 0 && nopi2p >= minopi2p) {
        if (opt->values[GRCC_OPT_No2PtL1PI] > 0) {
            return False;
        } else if (opt->values[GRCC_OPT_No2PtL1PI] < 0) {
            return True;
        }
    }

    edup->copy(this);
    ngrp = groupLMom(grp, ed2gr);
    
    for (g = 0; g < ngrp; g++) {
        ok = True;
        if (grp[g] < 2) {
            continue;
        }
        for (ed = 0; ed < nEdges; ed++) {
            if (ed2gr[ed] == g) {
                if (edges[ed]->ext) {
                    ok = False;
                    break;
                }
                edup->edges[ed]->cut = True;
            } else {
                edup->edges[ed]->cut = False;
            }
        }
        if (ok) {
            edup->gSubId++;
            edup->biconnE();

            if (edup->nExtern == 2 && edup->nopicomp == 1) {
                minopi2p = 2;
            } else {
                minopi2p = 1;
            }

            if (edup->opi2plp > 0 && edup->nopi2p >= minopi2p) {
                if (opt->values[GRCC_OPT_No2PtL1PI] > 0) {
                    return False;
                } else if (opt->values[GRCC_OPT_No2PtL1PI] < 0) {
                    return True;
                }
            }
        }
    }

    if (opt->values[GRCC_OPT_No2PtL1PI] > 0) {
        return True;
    } else if (opt->values[GRCC_OPT_No2PtL1PI] < 0) {
        return False;
    } else {
        erEnd("isOptE: illegal control");
        return False;
    }
}

//--------------------------------------------------------------
int EGraph::findRoot(void)
{
    int root, vr, er, e, nd0, nd1;

    root = -1;
    vr   = -1;
    er   = -1;
    for (e = 0; e < nEdges; e++) {
        if (edges[e]->cut || edges[e]->edtype == GRCC_ED_Deleted) {
            continue;
        }
        if (edges[e]->visited) {
            continue;
        }
        if (root < 0) {
            if (edges[e]->ext) {
                nd0 = edges[e]->nodes[0];
                nd1 = edges[e]->nodes[1];
                if (isExternal(nd0) && !isExternal(nd1)) {
                    root = nd1;
                    break;
                } else if (!isExternal(nd0) && isExternal(nd1)) {
                    root = nd0;
                    break;
                }
            }
        }
        if (er < 0) {
            er = edges[e]->nodes[0];
        }
        if (vr < 0) {
            vr = edges[e]->nodes[0];
        }
    }
    // if root >= 0 : vertex adjacent to an external node
    if (root < 0) {
        // if vr >= 0 : a vertex
        if (vr >= 0) {
            root = vr;
        
        // no vertex, only external nodes;
        } else {
            root = er;
        }
    }
    return root;
}

//---------------------------------------------------------------
int EGraph::connComp(void)
{
    //  Count the number of connected component
    //  If a connected component without free leg is not the whole graph then
    //  return False, otherwise return True.

    int j, ncc, nelem;

    for (j = 0; j < nNodes; j++) {
        nodes[j]->visited = -1;
    }
    ncc   = 0;    // # connected components
    nelem = 0;    // # visited nodes
    while (nelem < nNodes) {
        for (j = 0; j < nNodes; j++) {
            if (nodes[j]->visited < 0) {
                break;
            }
        }
        if (j >= nNodes) {
            break;
        }
        nelem += connVisit(j, ncc);
        ncc++;
    }
    if (nelem != nNodes) {
        erEnd("EGraph::connComp: illegal control");
    }
    return ncc;
}

//---------------------------------------------------------------
int EGraph::connVisit(int nd, int ncc)
{
    //  Visiting connected node used for 'connComp'
  
    int e, en, nn, j, nelem;
  
    nelem = 1;
    nodes[nd]->visited = ncc;
    for (e = 0; e < nodes[nd]->deg; e++) {
        en = V2Iedge(nodes[nd]->edges[e]);
        for (j = 0; j < 2; j++) {
            nn = edges[en]->nodes[j];
            if (nodes[nn]->visited < 0) {
                nelem += connVisit(nn, ncc);
            }
        }
    }
    return nelem;
}

//--------------------------------------------------------------
void EGraph::biconnE(void)
{
    int e, ie, root;
    int extlst[GRCC_MAXEDGES], intlst[GRCC_MAXEDGES];
    int opiext, opiloop;

    nadj2ptv = 0;
    for (e = 0; e < nEdges; e++) {
        if (nodes[edges[e]->nodes[0]]->deg == 2 &&
            nodes[edges[e]->nodes[1]]->deg == 2 &&
            edges[e]->nodes[0] != edges[e]->nodes[1]) {
            nadj2ptv++;
        }
    }

    biinitE();      // initialization
    bconn = 0;      // the number of connected components

    opiext  = 0;
    opiloop = 0;

    for (e = 0; e < nEdges; e++) {
        // root of a spanning tree to be searched.
        root = findRoot();   
        if (root < 0) {
            // no root : end of search
            break;
        }

        // recursive search
        bisearchE(root, extlst, intlst, &opiext, &opiloop);

        // opi2plp = Max(opi2plp, opiloop);      // ???

        // adjust the #external for the root
        if (isExternal(root)) {
            opiext++;
        }

        // 2 point function
        if (opiext == 2) {
            opi2plp = Max(opi2plp, opiloop);
            nopi2p++;
        }
        for (ie = 0; ie < nEdges; ie++) {
            if (intlst[ie]) {
                edges[ie]->opicomp = nopicomp;
            }
        }
        nopicomp++;

        bconn++;    // the number of connected component
    }

    // momentum conservation of external particles
    extMomConsv();

#ifdef CHECK
    chkMomConsv();
#endif
    return;
}

//--------------------------------------------------------------
void EGraph::biinitE(void)
{
    int n, j, e;

    bicount = 0;                  // counter of visiting node
    loopm   = 0;                  // # of independent loop momentum 

    nopicomp = 0;
    opi2plp  = 0;
    nopi2p   = 0;

    for (n = 0; n < nNodes; n++) {
        bidef[n] = -1;
        bilow[n] = -1;
        nodes[n]->ndtype  = GRCC_ND_Undef;    
        for (j = 0; j < nLoops; j++) {
            nodes[n]->klow[j] = -1;
        }
    }

    for (e = 0; e < nEdges; e++) {
        // edges[e]->cut is defined before
        edges[e]->visited = False;
        edges[e]->conid   = -1;                  // connected component
        edges[e]->edtype  = GRCC_ED_Undef;    
        edges[e]->opicomp = -1;
        for (j = 0; j < nEdges; j++) {
            edges[e]->emom[j] = 0;            // coefficients of ext. mom.
        }
        for (j = 0; j < nLoops; j++) {
            edges[e]->lmom[j] = 0;            // coefficients of loop mom.
        }
    }
}

//--------------------------------------------------------------
void EGraph::bisearchE(int nd, int *extlst, int *intlst, int *opiext, int *opiloop)
{
    // Search in the spanning tree below 'nd'.
    // Arguments:
    //   nd      : input  : node to be visited
    //   extlst  : output : set of external lines in the current 1PI comp.
    //   intlst  : output : set of internal lines in the current 1PI comp.
    //   opiext  : output : no. external lines of the current 1PI component
    //   opiloop : output : no. loops of the current 1PI component
    //
    // EGraph variables
    //   bicount   : counter of visiting node
    //   loopm     : no. of independent loop momentum 
    //   nopicomp  : no. of OPI components
    //   opi2plp   : maximum number loops among 2-point looped OPI components
    //   nopi2p    : no. of 2-point OPI components
    //   edges[ie]->opicomp : OPI component no. of the edge
    //

    int k, e, ie, ed, td, dir, j;
    int opiext1, opiloop1;
    int extlst1[GRCC_MAXEDGES];   // set of external nodes below
    int intlst1[GRCC_MAXEDGES];   // set of vertices in the 1PI component

    (*opiext)  = 0;
    (*opiloop) = 0;

    // visit node 'nd'
    bidef[nd] = bicount;
    bilow[nd] = bicount;
    for (k = 0; k < nLoops; k++) {
        nodes[nd]->klow[k] = bicount;
    }
    bicount++;
    for (j = 0; j < nEdges; j++) {
        extlst[j] = False;
        intlst[j] = False;
    }

    // go to children : nd --> ed --> td
    for (e = 0; e < nodes[nd]->deg; e++) {
        ed = V2Iedge(nodes[nd]->edges[e]);

        // check this edge is already visited
        if (edges[ed]->edtype == GRCC_ED_Deleted) {
            // permanently deleted edge
            continue;
        } else if (edges[ed]->visited) {
            // already visited (backword visit)
            continue;
        } else if (edges[ed]->cut) {
            // cut edge : treat as nd is an external
            (*opiext)++;
            nodes[nd]->setType(GRCC_ND_CPoint);
            continue;
        } else if (!isExternal(nd) && edges[ed]->ext) {
            // external
            edges[ed]->setType(GRCC_ED_Extern);
            edges[ed]->visited = True;
            edges[ed]->emom[ed] = 1;
            extlst[ed] = True;
            (*opiext)++;
            nodes[nd]->setType(GRCC_ND_CPoint);
            continue;
        }
  
        // mark visited
        edges[ed]->visited = True;

        // momentum is assigned on the backward move. (nd) 1 --> 0 (td)
        td  = edges[ed]->nodes[0];
        dir = 1;
        if (td == nd) {
            td = edges[ed]->nodes[1];
            dir = -1;
        }
  
        // biconnected component
        if (bidef[td] >= 0) {
            // a back edge is found. Already visited. Don't go further
            bilow[nd] = Min(bilow[nd], bilow[td]);
            edges[ed]->setType(GRCC_ED_Back);
            intlst[ed] = True;
            (*opiloop)++;
    
            // create new loop momentum
            k = loopm++;
            nodes[nd]->klow[k] = Min(nodes[nd]->klow[k], nodes[td]->klow[k]);
            edges[ed]->setLMom(k, dir);
    
            // self-loop
            if (td == nd) {
                nodes[nd]->setType(GRCC_ND_CPoint);
            }
    
        } else {
            // not a back edge
            // go down further
            bisearchE(td, extlst1, intlst1, &opiext1, &opiloop1);
    
            // the set of external particles
            for (j = 0; j < nEdges; j++) {
                extlst[j] = extlst[j] || extlst1[j];
            }
    
            // loop momenta
            for (k = 0; k < nLoops; k++) {
                if (nodes[td]->klow[k] <= nodes[nd]->klow[k]) {
                    // inside loop 'k'
                    edges[ed]->setLMom(k, dir);
                }
                nodes[nd]->klow[k] = Min(nodes[nd]->klow[k], nodes[td]->klow[k]);
            }
                 
            // cut point ?
            if (bilow[td] >= bidef[nd]) {
                // a cut point is found
                if (nodes[nd]->ndtype == GRCC_ND_Undef) {
                    nodes[nd]->setType(GRCC_ND_CPoint);
#ifdef CHECK
                } else if (nodes[nd]->ndtype != GRCC_ND_CPoint) {
                    if (prlevel > 0) {
                        grcc_fprintf(GRCC_Stderr, "bisearch: node %d is a cut point ",
                                nd);
                        grcc_fprintf(GRCC_Stderr, "(not undef %d)\n", 
                                nodes[nd]->ndtype);
                    }
#endif
                }
            }  // cut point
                 
            // bridge ?
            if (bilow[td] > bidef[nd]) {
                // a bridge is found
                if (edges[ed]->edtype == GRCC_ED_Undef) {
                    edges[ed]->setType(GRCC_ED_Bridge);
                    nodes[td]->setType(GRCC_ND_CPoint);
#ifdef CHECK
                } else if (edges[ed]->edtype != GRCC_ED_Bridge) {
                    if (prlevel > 0) {
                        grcc_fprintf(GRCC_Stderr, "bisearch: edges %d is a bridge ", ed);
                        grcc_fprintf(GRCC_Stderr, "(not undef %d)\n", edges[ed]->edtype);
                    }
#endif
                }

                if (!edges[ed]->ext) {
                    // internal bridge 
                    opiext1++;            // from bridge
                    for (ie = 0; ie < nEdges; ie++) {
                        if (intlst1[ie]) {
                            // OPI component No.
                            edges[ie]->opicomp = nopicomp;
                            intlst1[ie] = False;
                        }
                    }
                    // 2pt OPI component
                    if (opiext1 == 2) {
                        opi2plp = Max(opi2plp, opiloop1);

                        // the number of 2pt looped OPI components
                        nopi2p++;
                    }
                    // the number of OPI components
                    nopicomp++;
                }
                opiext1  = 1;    // from bridge
                opiloop1 = 0;
    
            } else {
                // not a bridge

                bilow[nd] = Min(bilow[nd], bilow[td]);

                if (edges[ed]->edtype == GRCC_ED_Undef) {
                    edges[ed]->setType(GRCC_ED_Inloop);
#ifdef CHECK
                } else if (edges[ed]->edtype != GRCC_ED_Inloop) {
                    if (prlevel > 0) {
                        grcc_fprintf(GRCC_Stderr, "bisearch: ");
                        grcc_fprintf(GRCC_Stderr, "edges %d is not undef (%d)\n", 
                               ed, edges[ed]->edtype);
                    }
#endif
                }
                intlst1[ed] = True;
            }

            // merge to the current variables
            for (ie = 0; ie < nEdges; ie++) {
                intlst[ie] = intlst[ie] || intlst1[ie];
            }
            (*opiext)  += opiext1;
            (*opiloop) += opiloop1;
    
            // linear combination of external momenta
            edges[ed]->setEMom(nEdges, extlst1, dir);

        }  // end of a child
    }  // for (ed)

    return;
}

//--------------------------------------------------------------
void EGraph::extMomConsv(void)
{
    int e, ex, lex, rs;

    lex = -1;
    for (e = 0; e < nEdges; e++) {
        if (edges[e]->ext) {
            lex = e;
            extMom[e] = edges[e]->emom[e];
        } else {
            extMom[e] = 0;
        }
    }
    // eliminate momentum of the last external particle
    if (lex < 0) {
        return;
    }
    for (e = 0; e < nEdges; e++) {
        rs = edges[e]->emom[lex];
        if (rs != 0) {
            for (ex = 0; ex < nEdges; ex++) {
                edges[e]->emom[ex] -= rs*extMom[ex];
            }
        }
    }
}

//--------------------------------------------------------------
void EGraph::chkMomConsv(void)
{
    // check momentum conservation

    int  esum[GRCC_MAXEDGES];
    int  lsum[GRCC_MAXNODES];
    Bool ok, okn;
    int  n, ex, lk, ej, e, dir;

    if (bicount < 1) {
        return;
    }
    ok = True;
    for (n = 0; n < nNodes; n++) {
        if (isExternal(n)) {
            continue;
        }
        for (ex = 0; ex < nEdges; ex++) {
            esum[ex] = 0;
        }
        for (lk = 0; lk < nLoops; lk++) {
            lsum[lk] = 0;
        }
        for (ej = 0; ej < nodes[n]->deg; ej++) {
            e = V2Iedge(nodes[n]->edges[ej]);
            if (edges[e]->nodes[0] == edges[e]->nodes[0]) {
                continue;
            }
            dir = dirEdge(n, ej);
            for (ex = 0; ex < nEdges; ex++) {
                if (edges[e]->ext) {
                    esum[ex] += dir*edges[e]->emom[ex];
                }
            }
            for (lk = 0; lk < nLoops; lk++) {
                lsum[lk] += dir*edges[e]->lmom[lk];
            }
        }
  
        okn = True;
        for (ex = 0; ex < nEdges; ex++) {
            if (esum[ex] != 0) {
                okn = False;
                grcc_fprintf(GRCC_Stderr, "chkMomConsv:n=%d, esum[%d]=%d\n",
                        n, ex, esum[ex]);
            }
        }
  
        for (lk = 0; lk < nLoops; lk++) {
            if (lsum[lk] != 0) {
                okn = False;
                grcc_fprintf(GRCC_Stderr, "chkMomConsv:n=%d, lsum[%d]=%d\n",
                        n, lk, lsum[lk]);
   
            }
        }
  
        if (!okn) {
            ok = False;
            grcc_fprintf(GRCC_Stderr, "*** Violation of momentum conservation ");
            grcc_fprintf(GRCC_Stderr, "at node =%d\n",n);
       }
    }

    if (!ok) {
        print();
        erEnd("inconsistent momentum");
    }
}

//--------------------------------------------------------------
int  EGraph::legParticle(int ed, int el)
{
    // outgoing particle from (edge, leg) = (ed, el)

    return model->normalParticle((2*el-1)*edges[ed]->ptcl);
}

//--------------------------------------------------------------
int  EGraph::isFermion(int ed)
{
    // return if particle on the edge ed follows Fermi statistics or not.

    int ptcl, ptype;

    ptcl  = edges[ed]->ptcl;
    ptype = model->particles[Abs(ptcl)]->ptype;

    return (ptype == GRCC_PT_Dirac || ptype == GRCC_PT_Majorana 
            || ptype == GRCC_PT_Ghost);
}

//--------------------------------------------------------------
int  EGraph::fltrace(int fk, int nd0, int *fl)
{
    // fk  : kind of fermion
    //       = (GRCC_PT_Dirac, GRCC_PT_Majorana or GRCC_PT_Ghost)
    // nd0 : the last node visited
    // fl  : list of signed edge on the fermion line.
    //       fl[j] : 
    //       (V2Iedge(fl[j]), V2Ileg(fl[j])) is the next node
    //       fl[0] should be already defined

    int nfl, k, i, nd, nl, e, ed, el, fgcnt, fkind, lk;

    nfl = 1;
    // maximal possible length of a fline is nEdges
    for (k = 0; k < nEdges; k++) {
        if (k >= nfl) {
            grcc_fprintf(GRCC_Stdout, "*** fltrace:illegal contorl: k=%d, nEdges=%d\n", k, nEdges);
            break;
        }

        // get next node : nd0 ---- nd (nl)
        e  = fl[k];
        ed = V2Iedge(e);
        el = V2Ileg(e);
#ifdef CHECK
        if (ed > nEdges) {
            grcc_fprintf(GRCC_Stderr, "*** fltrace: ed=%d > nEdges=%d, fl=",
                    ed, nEdges);
            prIntArray(nNodes, fl, "\n");
            erEnd("fltrace: illegal fl");
        }
#endif
        nd = edges[ed]->nodes[el];
        nl = edges[ed]->nlegs[el];

        // end of the fline
        if (isExternal(nd) || nd == nd0) {
            fgcnt = 1;
            break;
        }

        // find leg of nd for going next
        fgcnt = 0;
        ed = 0;
        lk = 0;
        for (i = 0; i < nodes[nd]->deg; i++) {
            e  = nodes[nd]->edges[i];
            ed = V2Iedge(e);
            fkind = model->particles[Abs(edges[ed]->ptcl)]->ptype;
            // lk =  1 : (# of fkind particle) is even
            // lk = -1 : (# of fkind particle) is odd
            if (fkind == fk) {
                if (lk == 1) {
                    lk = -1;
                } else {
                    lk = 1;
                }
            } else {
                lk = 0;
            }
            if (!edges[ed]->visited) {
                if (!isFermion(ed)) {
                    edges[ed]->visited = True;
                } else {
                    if (fkind == fk) {
                        // i should be the neighbor of nl
                        // (nl, i) or (i, nl) should be a pair of fkind
                        // (nl, i) : lk = -1
                        // (i, nl) : lk =  1
                        if ((lk == 1 && nl == i+1) || (lk == -1 && nl == i-1)) {
                            edges[ed]->visited = True;
                            fgcnt++;
                            if (fgcnt == 1) {
                                // -e = (signed edge points the next node)
                                fl[nfl++] = - e;
                                break;
                            }
                        }
                    }
                }
            } // not visited
        }  // end of for k
        if (fgcnt == 0) {
            grcc_fprintf(GRCC_Stdout, "*** fline: Fermion number is not conserved\n");
            grcc_fprintf(GRCC_Stdout, "    nd=%d, e=%d, ed=%d, fgcnt=%d\n",
                   nd, e, ed, fgcnt);
            // erEnd("fline: Fermion number is not conserved");
        } else if (fgcnt > 1) {
            grcc_fprintf(GRCC_Stdout, "+++ fline: more than two fermions: check fsign\n");
            grcc_fprintf(GRCC_Stdout, "    nd=%d, e=%d, ed=%d, fgcnt=%d\n",
                   nd, e, ed, fgcnt);
        }
    }
    if (k >= nEdges || k >= nfl) {
        grcc_fprintf(GRCC_Stdout, "*** fline: illegal control\n");
        grcc_fprintf(GRCC_Stdout, "    nEdges=%d, nfl=%d, k=%d, ", nEdges, nfl, k);
        prIntArray(nfl, fl, "\n");
        erEnd("fline: illegal control");
    }
    return nfl;
}

//--------------------------------------------------------------
void EGraph::getFLines(void)
{
    int fl[GRCC_MAXNODES];
    int nextn, exto[GRCC_MAXNODES];
    int e, ed, nd, floop, nswap, nfl, fkind, el, ptcl;

    nFlines = 0;
    for (ed = 0; ed < nEdges; ed++) {
        edges[ed]->visited = False;
    }

    nextn = 0;
    for (ed = 0; ed < nEdges; ed++) {
        if (edges[ed]->visited) {
            continue;
        }
        if (!edges[ed]->ext) {
            continue;
        }
        el = 0;
        nd = edges[ed]->nodes[el];
        if (!isExternal(nd)) {
            el = 1;
            nd = edges[ed]->nodes[el];
            if (!isExternal(nd)) {
                erEnd("*** illegal control");
            }
        }
        if (!isFermion(ed)) {
            continue;
        }
        ptcl = legParticle(ed, 1-el);
        if (ptcl < 0) {
            continue;
        }

        //     el   ed   el1
        //      x----<----x       e = (signed edge of (ed, el1))
        //     nd   ptcl(>= 0)
        //  external

        fl[0] = - I2Vedge(ed, el);
        nfl   = 1;
        fkind = model->particles[Abs(edges[ed]->ptcl)]->ptype;
        edges[ed]->visited = True;

        nfl = fltrace(fkind, nd, fl);
        addFLine(FL_Open, fkind, nfl, fl);
        e  = fl[nfl-1];
        exto[nextn++] = edges[V2Iedge(e)]->nodes[V2Ileg(e)];
    }

    // closed Fermion line
    floop = 0;
    for (ed = 0; ed < nEdges; ed++) {
        if (edges[ed]->visited) {
            continue;
        }
        if (!isFermion(ed)) {
            continue;
        }
        el = 0;
        ptcl = legParticle(ed, 1-el);
        if (ptcl < 0) {
            el = 1;
        }
        nd = edges[ed]->nodes[el];

        //     el    ed  el1
        //      x----<----x       e = (signed edge of (ed, el1))
        //     nd   ptcl

        fl[0] = - I2Vedge(ed, el);
        nfl   = 1;
        edges[ed]->visited = True;

        fkind = model->particles[Abs(edges[ed]->ptcl)]->ptype;
        nfl = fltrace(fkind, nd, fl);
        addFLine(FL_Closed, fkind, nfl, fl);
        floop++;
    }
    if (nextn > 0) {
        nswap = sortb(nextn, exto);
    } else {
        nswap = 0;
    }
    if ((floop+nswap) % 2 == 0) {
        fsign = 1;
    } else {
        fsign = -1;
    }
}

//--------------------------------------------------------------
void EGraph::addFLine(const FLType ft, int fk, int nfl, int *fl)
{
    int j;

    if (nFlines >= GRCC_MAXFLINES) {
        erEnd("too many Fermion lines (GRCC_MAXEDGES)");
    }
    if (flines[nFlines] == NULL) {
        flines[nFlines] = new EFLine();
    }
    flines[nFlines]->ftype = ft;
    flines[nFlines]->fkind = fk;
    flines[nFlines]->nlist = nfl;
    for (j = 0; j < nfl; j++) {
        flines[nFlines]->elist[j] = fl[j];
    }
    nFlines++;
}


//**************************************************************
// assign.cc
//==============================================================
// Assign particles to the edges and interactions to nodes.
// Completed graph data is saved in the form of EGraph.

// method : selection of assignable node

//===============================================================
// class NCand
NCand::NCand(const NCandSt sta, const int dega, const int nilst, int *ilst)
{
    // candidate list of interactions attached to a vertex.

    int j;

    deg    = dega;
    st     = sta;
    nilist = nilst;
    for (j = 0; j < nilist; j++) {
        ilist[j] = ilst[j];
    }

#ifdef CHECK
    if (st == AS_Assigned) {
        if (nilist != 1) {
            erEnd("illegal assignment");
        }
    } else if (st == AS_AssExt) {
        if (nilist != 1) {
            erEnd("illegal assignment");
        }
    }
#endif
}

//---------------------------------------------------------------
NCand::~NCand(void)
{
}

//---------------------------------------------------------------
void NCand::prNCand(const char* msg)
{
    grcc_fprintf(GRCC_Stdout, "%d %d ",  st, deg);
    prIntArray(nilist, ilist, msg);
}

//===============================================================
// class ECand
ECand::ECand(int dt, int nplst, int *plst)
{
    int j;

    det    = dt;
    nplist = nplst;
    for (j = 0; j < nplist; j++) {
        plist[j] = plst[j];
    }

    if (det && nplist != 1) {
        if (prlevel > 0) {
            grcc_fprintf(GRCC_Stderr, "*** ECand : len(plist) != 1 : det=%d ", det);
            prIntArrayErr(nplist, plist, "\n");
        }
        erEnd("ECand : len(plist) != 1");
    }
}

//---------------------------------------------------------------
ECand::~ECand(void)
{
}

//---------------------------------------------------------------
void ECand::prECand(const char *msg)
{
    prIntArray(nplist, plist, "");
    grcc_fprintf(GRCC_Stdout, " (det=%d)%s", det, msg);
}

//===============================================================
// class ANode
ANode::ANode(int dg)
{
    int j;

    deg    = dg;
    nlegs  = 0;
    anodes = new int[deg];
    aedges = new int[deg];
    aelegs = new int[deg];
    cand   = NULL;
    for (j = 0; j < deg; j++) {
        anodes[j] = -1;
        aedges[j] = -1;
        aelegs[j] = -1;
    }
}

//---------------------------------------------------------------
ANode::~ANode(void)
{
    if (cand != NULL) {
        delete cand;
        cand = NULL;
    }
    if (aelegs != NULL) {
        delete[] aelegs;
        delete[] aedges;
        delete[] anodes;
        aelegs = NULL;
        aedges = NULL;
        anodes = NULL;
    }
}

//---------------------------------------------------------------
int ANode::newleg(void)
{
    // add a slot for a leg

    int lg = nlegs;

    nlegs++;
#ifdef CHECK
    if (nlegs > deg) {
        grcc_fprintf(GRCC_Stderr, "*** ANode::newleg : nlegs = %d > deg = %d\n",
                nlegs, deg);
        erEnd("ANode::newleg : nlegs > deg");
    }
#endif

    return lg;
}

//===============================================================
// class AEdge
AEdge::AEdge(int n0, int l0, int n1, int l1)
{
    nodes[0]  = n0;       // node of 0 side of the edge
    nodes[1]  = n1;       // node of 1 side of the edge
    nlegs[0]  = l0;       // leg ot the node of 0 side of the edge
    nlegs[1]  = l1;       // leg ot the node of 1 side of the edge
    ptcl   = GRCC_PT_Undef;    // particle defined in the model
    cand   = NULL;        // candidate
}

//---------------------------------------------------------------
AEdge::~AEdge(void)
{
    if (cand != NULL) {
        delete cand;
    }
}

//===============================================================
// class Assign
Assign::Assign(SProcess *sprc, MGraph *mgr, PNodeClass *pnc)
{
    Bool ok;
    int  j;

    if (sprc == NULL) {
        erEnd("Assign: sproc == NULL");
    }

    // pointers to related objects
    sproc        = sprc;
    model        = sproc->model;
    opt          = sproc->opt;
    mgraph       = mgr;
    pnclass      = pnc;

    egraph = mgraph->egraph;
    if (egraph == NULL) {
        erEnd("Assign: egraph == NULL");
    }

    astack       = sproc->astack;
    if (astack == NULL) {
        erEnd("Assign: astack == NULL");
    }

    nNodes       = mgraph->nNodes;
    nEdges       = mgraph->nEdges;
    nExtern      = sproc->nExtern;
    nETotal      = 0;               // total number of edges

    // counters of graphs
    nAGraphs     = 0;
    wAGraphs     = Fraction(0,1);
    nAOPI        = 0;
    wAOPI        = Fraction(0,1);

    nodes        = new ANode*[nNodes];
    edges        = new AEdge*[nEdges];

    for (j = 0; j < nNodes; j++) {
        nodes[j] = NULL;
    }
    for (j = 0; j < nEdges; j++) {
        edges[j] = NULL;
    }
    for (j = 0; j < model->ncouple; j++) {
        cplleft[j] = sproc->clist[j];
    }

    // initialize astack
    astack->setAGraph(this);
    astack->checkPoint(checkpoint0);

    // import from mgraph
    ok = fromMGraph();
#ifdef CHECK
    checkAG("Assign::Assign");
#endif

    if (ok) {
        // start assignment
        assignAllVertices();
    } else {
        // cannot assign
    }

    // restore from the stack
#ifdef CHECK
    astack->restoreMsg(checkpoint0, "Assign");  
#else
    astack->restore(checkpoint0);  
#endif
}

//===============================================================
Assign::~Assign(void)
{
    int j;

    for (j = 0; j < nEdges; j++) {
        delete edges[j];
        edges[j] = NULL;
    }
    delete[] edges;
    edges = NULL;

    for (j = 0; j < nNodes; j++) {
        delete nodes[j];
        nodes[j] = NULL;
    }
    delete[] nodes;
    nodes = NULL;
}

//---------------------------------------------------------------
void Assign::prCand(const char *msg)
{
    //  Print candidate table
    int    n, e, ne;
    AEdge *ed;

    grcc_fprintf(GRCC_Stdout, "\n");
    grcc_fprintf(GRCC_Stdout, "+++ Candidate list: %s\n", msg);
    grcc_fprintf(GRCC_Stdout, "  Nodes %d\n", nNodes);
    for (n = 0; n < nNodes; n++) {
       grcc_fprintf(GRCC_Stdout, "%d: edges=", n);
       prIntArray(nodes[n]->deg, nodes[n]->aedges, ": cand=");
       if (nodes[n]->cand == NULL) {
           grcc_fprintf(GRCC_Stdout, "NULL\n");
       } else {
           nodes[n]->cand->prNCand("\n");
       }
    }
    ne = Min(nEdges, nETotal);
    grcc_fprintf(GRCC_Stdout, "  Edges %d\n", ne);
    for (e = 0; e < ne; e++) {
       ed = edges[e];
       if (ed == NULL) {
           grcc_fprintf(GRCC_Stdout, "NULL_Edge\n");
       } else {
           grcc_fprintf(GRCC_Stdout, "%d: %d->%d: cand=", e, ed->nodes[0], ed->nodes[1]);
           if (edges[e]->cand == NULL) {
               grcc_fprintf(GRCC_Stdout, "NULL\n");
           } else {
               edges[e]->cand->prECand("\n");
           }
       }
    }
}

//===============================================================
void Assign::checkAG(const char *msg)
{
    int n, lg;
    Bool ok = True;

    for (n = 0; n < nNodes; n++) {
        for (lg = 0; lg < nodes[n]->deg; lg++) {
            if (nodes[n]->aedges[lg] < 0) {
                grcc_fprintf(GRCC_Stdout, "*** checkAG:%s: n=%d, lg=%d, aedges=%d\n",
                       msg, n, lg, nodes[n]->aedges[lg]);
                ok = False;
            }
        }
    }
    if (!ok) {
        prCand("checkAG");
        erEnd("checkAG: failed");
    }
}

//===============================================================
// control of the process of particle/interaction assignment

//---------------------------------------------------------------
Bool Assign::assignAllVertices(void)
{
    //  Entry point of the assignment procedure
    Bool   ok;

#ifdef CHECK
    checkCand("assignAllVertices:1");
#endif

    // start main part
#ifdef SIMPSEL
    ok = selectVertexSimp(-1);
#else
    ok = selectVertex();
#endif

#ifdef CHECK
    checkCand("assignAllVertices:2");
#endif

    return ok;
}

//---------------------------------------------------------------
Bool Assign::selectVertexSimp(int lastv)
{
    //  Select a vertex for assignment of particles to legs
    //
    //  Argument
    //    lastv : previously assigned vertex; Nothing when lastv<0.

    Bool ok;
    int v;

#ifdef CHECK
        checkCand("selectVertexSimp");
#endif

    // find a vertex to which interaction is assigned
    v = selUnAssVertexSimp(lastv);

    // no more vertex
    if (v < 0) {

        ok = allAssigned();
        if (ok) {
            if (!egraph->optQGrafA(opt)) {
                return False;
            } 
         // egraph->biconnE();      // necessary ???
            opt->newAGraph(egraph);
        }

        return ok;
    }

    // select a leg and assign a particle to it
    ok = selectLeg(v, -1);

    return ok;
}

//---------------------------------------------------------------
Bool Assign::selectVertex(void)
{
    //  Select a vertex for assignment of particles to legs
    //
    //  Argument
    //    lastv : previously assigned vertex; Nothing when lastv<0.

    Bool ok;
    int v;

#ifdef CHECK
        checkCand("selectVertex");
#endif

    // find a vertex to which interaction is assigned
    v = selUnAssVertex();

    // no more vertex
    if (v < 0) {

        ok = allAssigned();
        if (ok) {
            if (!egraph->optQGrafA(opt)) {
                return False;
            } 
            egraph->biconnE();
            opt->newAGraph(egraph);
        }

        return ok;
    }

    // select a leg and assign a particle to it
    ok = selectLeg(v, -1);

    return ok;
}

//---------------------------------------------------------------
Bool Assign::selectLeg(int v, int lastlg)
{
    //  Select a leg of vertex 'v' for assignment of particle,
    //  where the last assigned leg was 'lastlg'.

    int      pt, ln, j;
    Bool     ok;
    CheckPt  sav, sav0;
    int      nplist, plist[GRCC_MAXMPARTICLES2];

#ifdef CHECK
    checkNode(v, "selectLeg:0");
    checkCand("selectLeg");
#endif

    // find a leg to be assigned
    ln = selUnAssLeg(v, lastlg);

    // no more assignable leg for the current node
    if (ln < 0) {
        // move to next vertex
        ok = assignVertex(v);

        return ok;
    }

    // make the list of possible particles, incoming to the vertex
    astack->checkPoint(sav0);
    nplist = candPart(v, ln, plist, GRCC_MAXMPARTICLES2);

    // no candidate
    if (nplist < 1) {
        return False;
    }

    // assign each of possible particle to the leg 'lg'.
    astack->checkPoint(sav);
    for (j = 0; j < nplist; j++) {
        pt = plist[j];

        // try to assign 'pt' to (v, ln)
        if(assignPLeg(v, ln, pt)) {
            // move to next leg
            selectLeg(v, ln);
        }

#ifdef CHECK
        astack->restoreMsg(sav, "selectLeg2");
#else
        astack->restore(sav);
#endif
    }

#ifdef CHECK
    astack->restoreMsg(sav0, "selectLeg2");
#else
    astack->restore(sav0);
#endif
    return True;
}

//---------------------------------------------------------------
void Assign::saveCouple(int *sav)
{
    int j;

    if (model->ncouple > 1) {
        for (j = 0; j < model->ncouple; j++) {
            sav[j] = cplleft[j];
        }
    }
}

//---------------------------------------------------------------
void Assign::restoreCouple(int *sav)
{
    int j;

    if (model->ncouple > 1) {
        for (j = 0; j < model->ncouple; j++) {
            cplleft[j] = sav[j];
        }
    }
}

//---------------------------------------------------------------
Bool Assign::subCouple(int *cpl)
{
    int j;

    if (model->ncouple > 1) {
        for (j = 0; j < model->ncouple; j++) {
            cplleft[j] -= cpl[j];
            if (cplleft[j] < 0) {
                return False;
            }
        }
    }
    return True;
}

//---------------------------------------------------------------
Bool Assign::assignVertex(int v)
{
    //  Assign interactions to vertex 'v'

    Bool      done, ok;
    CheckPt   sav, sav1;
    NCand    *nc;
    int       ia, n, j, cl;
    NCandSt   vst;
    Bool      ok1;
    int       savc0[GRCC_MAXNCPLG], savc1[GRCC_MAXNCPLG];

#ifdef CHECK
    checkCand("assignVertex");
#endif

    // save the configuration
    astack->checkPoint(sav);
    saveCouple(savc0);

    // assign to all vertices with only one candidate
    done = False;
    for (n = 0; n < nNodes; n++) {

        // check if vertex
        cl = pnclass->nd2cl[n];
        if (!isATExternal(pnclass->type[cl])) {

            nc = nodes[n]->cand;
            if (nc->st == AS_UnAssLegs && nc->nilist == 1) {

                // bind interaction to the vertex
                ia = nc->ilist[0];
                vst = assignIVertex(n, ia);
                if (vst == AS_Impossible) {
                    // discard the current configuration
#ifdef CHECK
                    astack->restoreMsg(sav, "assignVertex");
#else
                    astack->restore(sav);
#endif
                    restoreCouple(savc0);
                    return False;

                } else if (vst == AS_Assigned) {
                    if (!subCouple(model->interacts[ia]->clist)) {
#ifdef CHECK
                        astack->restoreMsg(sav, "assignVertex");
#else
                        astack->restore(sav);
#endif
                        restoreCouple(savc0);
                        return False;
                    }
                }
                if (n == v) {
                    done = (vst == AS_Assigned);
                }
            }
        }
    }

    // uniquely determined
    ok = True;
    if (done) {
        // move to the next vertex
#ifdef SIMPSEL
        ok = selectVertexSimp(v);
#else
        ok = selectVertex();
#endif

#ifdef CHECK
        astack->restoreMsg(sav, "assignVertex");
#else
        astack->restore(sav);
#endif
        restoreCouple(savc0);

        return ok;
    }

    // there are still several possibilities.

    astack->checkPoint(sav1);
    saveCouple(savc1);
    for (j = 0; j < nodes[v]->cand->nilist; j++) {
        ia = nodes[v]->cand->ilist[j];

        // bind interaction to the vertex
        ok1 = True;
        vst = assignIVertex(v, ia);
        if (vst == AS_Assigned) {
            ok1 = subCouple(model->interacts[ia]->clist);
        }
        if (ok1 && (vst == AS_Assigned || vst == AS_Assigned0)) {
            // move to the next vertex
#ifdef SIMPSEL
            ok = selectVertexSimp(v);
#else
            ok = selectVertex();
#endif
        }

#ifdef CHECK
        astack->restoreMsg(sav1, "assignVertex");
#else
        astack->restore(sav1);
#endif
        restoreCouple(savc1);
    }

#ifdef CHECK
    astack->restoreMsg(sav, "assignVertex");
#else
    astack->restore(sav);
#endif
    restoreCouple(savc0);

    return ok;
}

//---------------------------------------------------------------
Bool Assign::allAssigned(void)
{
    // Assignment of particles and interactions is finished.
    // Check isomorphism etc. and count symmetry factor
    // The sign from Fermi statistics is calculated inf fillEGraph

    BigInt  nsym, esym, nsym1;
    MNodeClass *cl;
    Bool ok = True;
#ifdef OPTEXTONLY
#else
    Bool ext;
    int  e, p;
#endif

#ifdef CHECK
    checkCand("allAssigned");
#endif

    // check order of coupling constants
#ifdef CHECK
    if (!checkOrderCpl()) {
        erEnd("allAssigned: checkOrderCpl = False");
    }
#endif

    // check duplication by violating ordering condition
    if (!isOrdLegs()) {
        return False;
    }

    // classification of nodes
    cl = mgraph->curcl;

    // check isomorphism and calculate sfactor
    nsym = 0;
    esym = 0;

    ok = isIsomorphic(cl, &nsym, &esym, &nsym1);
    if (!ok || nsym < 1 || esym < 1) {
        return False;
    }

    //--------------------------
    // Now we got a new agraph.

    // Update counters
    nAGraphs++;
    wAGraphs.add(1,nsym*esym);
    if (mgraph->opi) {
        nAOPI++;
        wAOPI.add(1,nsym*esym);
    }

#ifdef CHECK
    checkAG("allAssigned");
#endif
    // fill information to resulting Egraph
    fillEGraph(nAGraphs, nsym, esym, nsym1);

#ifdef OPTEXTONLY
#else
    // check extonly particles
    for (e = 0; e < nEdges; e++) {
        p   = Abs(egraph->edges[e]->ptcl);
        ext = egraph->edges[e]->ext;
        if (!ext) {
            if (model->particles[p]->extonly) {
                return False;
            }
        }
    }
#endif

    return True;
}

//===============================================================
// Interface to MGraph and EGraph
//---------------------------------------------------------------
Bool Assign::fromMGraph(void)
{
    // Import from MGraph

    int     npall, *pall;
    int     np[1];
    Bool    ok;
    int     j, k, n, nn, n1, deg, nc, ptcl, cl, typ, mcl, cl1, typ1;
    int     lcn, ia;
    int     nilist, ilist[GRCC_MAXMINTERACT];
    NCandSt st;

    // create ANodes
    for (j = 0; j < nNodes; j++) {
        nodes[j] = new ANode(mgraph->nodes[j]->deg);
    }

    // initialization of edge table
    nETotal = 0;

    // List of all particles
    pall = model->allParticles(&npall);

    // add nodes
    for (n = 0; n < mgraph->nNodes; n++) {
        cl   = pnclass->nd2cl[n];
        typ  = pnclass->type[cl];

        // external particle
        if (isATExternal(typ)) {

#ifdef CHECK
            if (mgraph->nodes[n]->deg != 1) {
                grcc_fprintf(GRCC_Stdout, "*** assign:fromMGraph : "
                       "external but deg[%d] = %d != 1, type=%d\n",
                       n, mgraph->nodes[n]->deg, typ);
                mgraph->print();
                erEnd("assign:fromMGraph : illegal external particle");
            }
#endif
            np[0] = pnclass->particle[cl];
            nodes[n]->cand = new NCand(AS_AssExt, 1, 1, np);
            for (n1 = 0; n1 < mgraph->nNodes; n1++) {
                nc = mgraph->adjMat[n][n1];
                for (k = 0; k < nc; k++) {
                    addEdge(n, n1, 1, np);
                }
            }

        // vertex
        } else {

            // candidates of vertices
            deg    = mgraph->nodes[n]->deg;
            st     = AS_UnAssLegs;
            cl     = sproc->pnclass->nd2cl[n];     // class in the process
            mcl    = sproc->pnclass->cl2mcl[cl];   // class in the model

            if (nodes[n]->cand != NULL) {
                delete nodes[n]->cand;
            }
            lcn = model->ncouple;

            // multiple coupling constants are defined in the model.
            if (lcn > 1) {
                nilist = 0;
                for (j = 0; j < model->cplgnvl[mcl]; j++) {
                    ia = model->cplgvl[mcl][j];

                    // select by coupling constants
                    if (leqArray(lcn, model->interacts[ia]->clist, cplleft)) {
                        ilist[nilist++] = ia;
                    }
                }
                nodes[n]->cand = new NCand(st, deg, nilist, ilist);

            // there is only one coupling constant
            } else {
                nodes[n]->cand = 
                    new NCand(st, deg, model->cplgnvl[mcl], model->cplgvl[mcl]);
            }

            // vertices
            for (n1 = n; n1 < mgraph->nNodes; n1++) {
                cl1   = pnclass->nd2cl[n1];
                typ1  = pnclass->type[cl1];
                if (!isATExternal(typ1)) {
                    nc = mgraph->adjMat[n][n1];
                    if (n == n1) {
                        nc = nc/2;
                    }
                    for (k = 0; k < nc; k++) {
                        addEdge(n, n1, npall, pall);
                    }
                }
            }
        }
    }
#ifdef CHECK
    if (nETotal != nEdges) {
        grcc_fprintf(GRCC_Stdout, "*** Assign::fromMGraph nETotal=%d != nEdges=%d\n",
               nETotal, nEdges);
        erEnd("Assign::fromMGraph nETotal= != nEdges");
    }
#endif

    // assign particle of an edge next to an external particle
    for (n = 0; n < mgraph->nNodes; n++) {
        cl  = pnclass->nd2cl[n];
        typ = pnclass->type[cl];
        if (isATExternal(typ)) {

            cl   = pnclass->nd2cl[n];
            ptcl = pnclass->particle[cl];

            // particle ptcl     flows in to   the node and
            // particle (- ptcl) flows in from the edge.

#ifdef CHECK
            if (ptcl == 0) {
                erEnd("fromMGraph: ptcl=0");
            }
#endif
            ok = assignPLeg(n, 0, -ptcl);
            if (!ok) {
                // impossible config
                return False;
            }
            nn = nodes[n]->anodes[0];
            ok = updateCandNode(nn);
            if (!ok) {
                // impossible config
                return False;
            }
        }
    }

#ifdef CHECK
    checkCand("fromMGraph");
    checkAG("fromMGraph");
#endif

    return True;
}

//---------------------------------------------------------------
void Assign::addEdge(int n0, int n1, int nplist, int *plist)
{
    //  add an edge and set connection information
    //  n0 -- (new edge) -- n1, with candidates 'plist'

    int lg0, lg1, eid;
    AEdge *aed;

#ifdef CHECK
    if (n0 >= nNodes || n1 >= nNodes) {
        grcc_fprintf(GRCC_Stdout, "*** Assign::addEdge : undefined nodes %d: [%d, %d]",
              nETotal, n0, n1);
        erEnd("Assign::addEdge : undefined nodes");
    }
#endif

    // legs to be connected
    lg0 = nodes[n0]->newleg();
    lg1 = nodes[n1]->newleg();

    // create edge
#ifdef CHECK
    if (nETotal >= nEdges) {
        erEnd("too many edges");
    }
#endif

    aed = new AEdge(n0, lg0, n1, lg1);
    aed->cand = new ECand(False, nplist, plist);

#ifdef CHECK
    if (edges[nETotal] != NULL) {
        erEnd("edges[nETotal] != NULL");
    }
#endif

    // registor to the edge table
    eid = nETotal;
    edges[nETotal++] = aed;

    // connect edge and nodes
    connect(n0, lg0, eid, 0, n1, lg1);
}

//---------------------------------------------------------------
void Assign::connect(int n0, int l0, int eg, int el, int n1, int l1)
{
    //  Connect (n0, l0) -- (eg, el) -- (nl)

    ANode *nd0, *nd1;
    AEdge *ed;
    int    eo;

    nd0 = nodes[n0];
    nd1 = nodes[n1];
    ed  = edges[eg];
    eo  = 1 - el;

    nd0->anodes[l0] = n1;
    nd0->aedges[l0] = eg;
    nd0->aelegs[l0] = el;

    nd1->anodes[l1] = n0;
    nd1->aedges[l1] = eg;
    nd1->aelegs[l1] = eo;

    ed->nodes[el] = n0;
    ed->nlegs[el] = l0;

    ed->nodes[eo] = n1;
    ed->nlegs[eo] = l1;
}

//---------------------------------------------------------------
Bool Assign::fillEGraph(int aid, BigInt nsym, BigInt esym, BigInt nsym1)
{
    //  Set variables of egraph with the result of particle assignment
    //  Adjust the ordering of legs of vertices in a consistent way
    //  with the interaction defined in the model.

    ANode *an;
    ENode *en;
    int    work[3][GRCC_MAXLEGS];
    int    n, lr, e;
    int   *elist;
    int    lg, ed, eg;
#ifdef CHECK
    int    cl, ok = True;
#endif

    egraph->assigned = True;

    egraph->aId   = aid;
    egraph->nsym  = nsym;
    egraph->esym  = esym;
    egraph->bicount = -1;
    if (sproc != NULL) {
        egraph->extperm = sproc->extperm;
    } else {
        egraph->extperm = 1;
    }
    egraph->nsym1 = nsym1;
    egraph->multp = (egraph->extperm * egraph->nsym1) / egraph->nsym;

#ifdef CHECK
    checkAG("fillEGraph:0");
#endif
    // external node
    for (n = 0; n < nNodes; n++) {
        // vertices
#ifdef CHECK
        cl  = pnclass->nd2cl[n];
        if (isATExternal(pnclass->type[cl])) {
            ;
        } else if (nodes[n]->cand->st != AS_Assigned) {
            grcc_fprintf(GRCC_Stdout, "*** fillEGraph : node %d is not assigned", n);
            prCand("fillEGraph: node");
            erEnd("fillEGraph : node is not assigned");
        }
#endif

        an = nodes[n];
        en = egraph->nodes[n];

        en->initAss(egraph, n, an->deg);
        
        en->intrct = an->cand->ilist[0];
        elist = reordLeg(n, work[0], work[1], work[2]);
        for (lr = 0; lr < nodes[n]->deg; lr++) {
            if (elist == NULL) {
                lg = lr;
            } else {
                lg = elist[lr];
            }
#ifdef CHECK
            if (lg < 0 || lg >= nodes[n]->deg) {
                grcc_fprintf(GRCC_Stdout, "*** fillEGraph: n=%d, lr=%d: 0 <= lg=%d < %d\n",
                       n, lr, lg, nodes[n]->deg);
                erEnd("fillEGraph: illegal reordering");
            }
#endif
            ed = an->aedges[lg];
            eg = an->aelegs[lg];

            en->edges[lr] = I2Vedge(ed, 2*eg-1);

            egraph->edges[ed]->nodes[eg] = n;
            egraph->edges[ed]->nlegs[eg] = lr;
        }
    }
    // edges
    for (e = 0; e < nEdges; e++) {
#ifdef CHECK
        if (edges[e]->cand->nplist != 1) {
            grcc_fprintf(GRCC_Stdout, "*** fillEGraph : edge %d is not assigned", e);
            prCand("fillEGraph: edge");
            erEnd("fillEGraph : edge is not assigned");
        }
#endif
        egraph->edges[e]->ptcl = edges[e]->cand->plist[0];
    }
#ifdef EDGEPORDER
    for (e = 0; e < nEdges; e++) {
        if (egraph->edges[e]->ptcl < 0) {
            egraph->edges[e]->ptcl = - edges[e]->cand->plist[0];
            n  = egraph->edges[e]->nodes[0];
            lr = egraph->edges[e]->nlegs[0];
            egraph->edges[e]->nodes[0] = egraph->edges[e]->nodes[1];
            egraph->edges[e]->nlegs[0] = egraph->edges[e]->nlegs[1];
            egraph->edges[e]->nodes[1] = n;
            egraph->edges[e]->nlegs[1] = lr;

            egraph->nodes[n]->edges[lr] = - egraph->nodes[n]->edges[lr];
            n  = egraph->edges[e]->nodes[0];
            lr = egraph->edges[e]->nlegs[0];
            egraph->nodes[n]->edges[lr] = - egraph->nodes[n]->edges[lr];
        }
    }
#endif
#ifdef CHECK
    for (ed = 0; ed < nEdges; ed++) {
        n  = egraph->edges[ed]->nodes[0];
        lr = egraph->edges[ed]->nlegs[0];
        if (egraph->nodes[n]->edges[lr] != -ed-1) {
            grcc_fprintf(GRCC_Stderr, "+++ node[%d][%d]=%d != - (edge[%d][0] + 1) = %d\n", 
                    n, lr, egraph->nodes[n]->edges[lr], e, -ed-1);
            ok = False;
        }
        n = egraph->edges[ed]->nodes[1];
        lr = egraph->edges[ed]->nlegs[1];
        if (egraph->nodes[n]->edges[lr] != ed+1) {
            grcc_fprintf(GRCC_Stderr, "+++ node[%d][%d]=%d != + (edge[%d][0] + 1) = %d\n", 
                    n, lr, egraph->nodes[n]->edges[lr], e, ed+1);
            ok = False;
        }
    }
    if (!ok) {
        egraph->print();
        erEnd("fillEGraph: illegal connection");
    }
#endif


    // analyse fermion line and determine Fermi statistical sign factor
    egraph->getFLines();

#ifdef CHECK
    checkAG("fillEGraph:0");
#endif
    return True;

}

//---------------------------------------------------------------
int *Assign::reordLeg(int n, int *reord, int *plist, int *used)
{
    // Reorder legs of node 'n' in accordance with the definition 
    // of the interaction in the model
    //
    // plist[record[j]] = model->interacts[ia]->plist[j]

    int lg, ia, lr, deg, pt, ed;
    int *ilegs;
#ifdef CHECK
    Bool found;
#endif

    // external node
    if (nodes[n]->cand->st == AS_AssExt) {
        reord[0] = 0;
        return 0;
    }

    // degree of the node
    deg = nodes[n]->deg;

    if (deg <= 1) {
        reord[0] = 0;
        return 0;
    }

    // list of particles at the legs of the node 'n'
    for (lg = 0; lg < deg; lg++) {
        ed = nodes[n]->aedges[lg];
        pt = edges[ed]->cand->plist[0];
        plist[lg] = legEdgeParticle(n, lg, pt);
        used[lg]  = 0;
    }

    // list of legs in the interaction
    ia    = nodes[n]->cand->ilist[0];
    ilegs = model->interacts[ia]->plist;

    // reorder
#ifdef CHECK
    found = False;
#endif
    for (lr = 0; lr < deg; lr++) {
        for (lg = 0; lg < deg; lg++) {
            if (used[lg] == 0 && plist[lg] == ilegs[lr]) {
                reord[lr] = lg;
                used[lg]  = 1;
#ifdef CHECK
                found = True;
#endif
                break;
            }
        }

#ifdef CHECK
        if (!found) {
            grcc_fprintf(GRCC_Stdout, "*** reordLeg: illegal list of particles:"
                   "interaction %d ", ia);
            prIntArray(deg, ilegs, "; ");
            grcc_fprintf(GRCC_Stdout, "vertex %d ", n);
            prIntArray(deg, plist, "\n");
            prCand("reordLeg");
            erEnd("reordLeg: illegal list of particles");
        }
#endif
    }

    return reord;
}

//==============================================================
// Adjust the direction of a particle on an edge and on a leg of
// node.
//---------------------------------------------------------------
int Assign::getLegParticle(int n,  int ln)
{
    //  Get particle code of (n, ln) when particle 'pt' runs
    //  in the direction of the edge at (n, ln).
    //
    //  Get particle code in the direction the edge at (n, ln)
    //  when particle 'pt' is at leg (n, ln).
    //
    //  These two cases are realized by the same function

    ANode *nd;
    int    elg, ed, pt;

    nd  = nodes[n];
    elg = nd->aelegs[ln];
    ed  = nd->aedges[ln];
    pt  = edges[ed]->cand->plist[0];

    // normalization of sign for neutral particle
    if (elg == 0) {
        return model->normalParticle(-pt);
    } else {
        return model->normalParticle(pt);
    }
}

//---------------------------------------------------------------
int Assign::legEdgeParticle(int n, int ln, int pt)
{
    //  Get particle code of (n, ln) when particle 'pt' runs
    //  in the direction of the edge at (n, ln).
    //
    //  Get particle code in the direction the edge at (n, nl)
    //  when particle 'pt' is at leg (n, ln).
    //
    //  These two cases are realized by the same function

    // normalization of sign for neutral particle

    if (nodes[n]->aelegs[ln] == 0) {
        return model->normalParticle(-pt);
    } else {
        return model->normalParticle(pt);
    }
}

//---------------------------------------------------------------
int Assign::legPart(int v, int lg, int nplist, int *plist, int *rlist, const int size)
{
    // Convert list of candidate particles in 'plist' at (v, lg) ==> edge
    // or edge ==> (v, lg)

    int    j, nrlist;

    nrlist = 0;
    for (j = 0; j < nplist; j++) {
        nrlist = intSetAdd(nrlist, rlist, 
                           legEdgeParticle(v, lg, plist[j]), size);
    }
    return nrlist;
}

//---------------------------------------------------------------
int Assign::candPart(int v, int ln, int *plist, const int size)
{
    //  update candidate particles incoming to (v, ln)

    int      en;
    int      ntplist;
    ECand   *ec;

    en = nodes[v]->aedges[ln];

#ifdef CHECK
    if (edges[en]->cand->det) {
        grcc_fprintf(GRCC_Stdout, "*** candPart : particle of leg (%d, %d) "
               "is assigned to %d\n",
               v, ln, edges[en]->cand->plist[0]);
        checkCand("candPart");
        mgraph->printAdjMat(mgraph->curcl);
        prCand("candPart");
        erEnd("candPart : particle of leg is assigned");
    }
#endif

    ec = edges[en]->cand;

    ntplist = legPart(v, ln, ec->nplist, ec->plist, plist, size);

    return  ntplist;
}

//==============================================================
// tools for assignment

//---------------------------------------------------------------
int Assign::selUnAssVertexSimp(int lastv)
{
    //  Select a vertex for assignment to its leg.
    //  We take one with minimum number of candidates
    //
    //  There may be better method.

    int v0, v;

    // select vertex one by one in the sequential order of node number
    v0 = Max(lastv+1, nExtern);
    for (v = v0; v < nNodes; v++) {
        if (nodes[v]->cand->st == AS_UnAssLegs) {
            return v;
        }
    }
    return -1;
}

//---------------------------------------------------------------
int Assign::selUnAssVertex(void)
{
    //  Select a vertex for assignment to its leg.
    //  We take one with minimum number of candidates
    //
    //  There may be better method.

    int v0, v, nl;

    // select vertex one by one in the sequential order of node number
    v0 = -1;
    nl = 0;
    for (v = 0; v < nNodes; v++) {
        if (nodes[v]->cand->st == AS_UnAssLegs) {
            if (nodes[v]->cand->nilist == 1) {
                return v;
            } else if (nodes[v]->cand->nilist > 1) {
                // select node with fewer candidates
                if (v0 < 0 || nodes[v]->cand->nilist < nl) {
                    v0 = v;
                    nl = nodes[v]->cand->nilist;
                }
            }
        }
    }
    return v0;
}

//---------------------------------------------------------------
int Assign::selUnAssLeg(int v, int lastlg)
{
    // Select a leg of vertex 'v' for the assignment.
    // The lastly selected leg was 'lastlg'.

    int lg0, lg, e;
#ifdef CHECK
    int n0, n1;
#endif

    // lg0 = Max(lastlg, lastlg + 1);
    lg0 = lastlg + 1;

    for (lg = lg0; lg < nodes[v]->deg; lg++) {

#ifdef CHECK
        if (lastlg >= 0) {
            n0 = nodes[v]->anodes[lastlg];
        } else {
            n0 = -1;
        }
        n1 = nodes[v]->anodes[lg];
        if (n0 > n1) {
            grcc_fprintf(GRCC_Stdout, "*** selUnAssLeg: n0=%d > n1=%d\n", n0, n1);
            grcc_fprintf(GRCC_Stdout, "*** illegal connection\n");
            erEnd("selUnAssLeg: n0 > n1");
        }
#endif
  
        e  = nodes[v]->aedges[lg];
        if (!edges[e]->cand->det) {
            return lg;
        }

    }
    return -1;
}

//---------------------------------------------------------------
NCandSt Assign::assignIVertex(int v, int ia)
{
    //  Try to assign interaction 'ia' to 'v'

    int     lplist[GRCC_MAXLEGS], iplist[GRCC_MAXLEGS];
    int     lg, e, pt, deg;


    if (nodes[v]->cand->st == AS_Assigned || nodes[v]->cand->st == AS_AssExt) {
        return AS_Assigned0;
    }

    deg = nodes[v]->deg;
    if (deg != model->interacts[ia]->nlegs) {
        return AS_Impossible;
    }

    // list of particles at the legs of the vertex
    for (lg = 0; lg < deg; lg++) {
        e = nodes[v]->aedges[lg];
        if (edges[e]->cand->nplist != 1) {
            return AS_UnAssLegs;
        } else {
            pt = edges[e]->cand->plist[0];
            lplist[lg] = legEdgeParticle(v, lg, pt);
        }
        iplist[lg] = model->interacts[ia]->plist[lg];
    }

    sorti(deg, lplist);
    sorti(deg, iplist);

    // from interaction
    if (cmpArray(deg, lplist, deg, iplist) == 0) {
        // orders of coupling constants should be checked ???
        astack->pushNode(v);
        nodes[v]->cand->st = AS_Assigned;
        nodes[v]->cand->nilist = 1;
        nodes[v]->cand->ilist[0] = ia;
        return AS_Assigned;
    }

    return AS_Impossible;
}

//---------------------------------------------------------------
Bool Assign::assignPLeg(int n, int ln, int pt)
{
    //  A particle 'pt' is assigned to leg 'ln' of node 'n'

    ANode *nd;
    int e, ept; 
    Bool ok;

#ifdef CHECK
    checkNode(n, "assignPLeg0");
    checkCand("assignPLeg");
#endif

    // nodes and the edge
    nd  = nodes[n];
    e   = nd->aedges[ln];

    // already determined
    if (edges[e]->cand->det) {
        return True;
    }

    if (!isOrdPLeg(n, ln, pt)) {
        return False;
    }

    // particle on the edge
    ept = legEdgeParticle(n, ln, pt);

#ifdef CHECK
    if (!isIn(edges[e]->cand->nplist, edges[e]->cand->plist, ept)) {
        grcc_fprintf(GRCC_Stdout, "*** assignPLeg: particle %d is not in the cand. of e=%d",
                ept, e);
        edges[e]->cand->prECand("\n");
        prCand("assignPLeg");
        erEnd("assignPLeg: particle is not in the cand.");
    }
#endif

    // save the current configuration
    astack->pushEdge(e);

    // determine the particle on the edge
    edges[e]->cand->nplist   = 1;
    edges[e]->cand->plist[0] = ept;

    ok = detEdge(e);

    return ok;
}

//---------------------------------------------------------------
Bool Assign::detEdge(int e)
{
    Bool ok0, ok1;

    if (edges[e]->cand->nplist != 1) {
        return False;
    }
    edges[e]->cand->det = True;

    // update candidate list
    ok0 = updateCandNode(edges[e]->nodes[0]);
    if (ok0) {
        ok1 = updateCandNode(edges[e]->nodes[1]);
    } else {
        ok1 = False;
    }

    return (ok0 && ok1);
}

//---------------------------------------------------------------
Bool Assign::isOrdPLeg(int n, int ln, int pt)
{
    int e0, el, ln0, ep0, pt0, nn, n0, n1, ln1, pt1, e1, ep1;

    if (nodes[n]->deg < 2) {
        return True;
    }
    nn = nodes[n]->anodes[ln];
    if (n <= nn) {
        n0  = n;
        n1  = nn;
        ln0 = ln;
        pt0 = pt;
    } else {
        n0 = nn;
        n1 = n;
        e0  = nodes[n]->aedges[ln];
        el  = nodes[n]->aelegs[ln];
        ln0 = edges[e0]->nlegs[1-el];
        ep0 = legEdgeParticle(n,  ln,  pt);
        pt0 = legEdgeParticle(n0, ln0, ep0);
    }

    for (ln1 = 0; ln1 < nodes[n0]->deg; ln1++) {
        if (ln1 == ln0 || n1 != nodes[n0]->anodes[ln1]) {
            continue;
        }
        e1  = nodes[n0]->aedges[ln1];
        if (!edges[e1]->cand->det) {
            continue;
        }
        ep1 = edges[e1]->cand->plist[0];
        pt1 = legEdgeParticle(n0, ln1, ep1);
        if ((ln0 < ln1 && pt0 > pt1) ||
            (ln0 > ln1 && pt0 < pt1)) {
            return False;
        }
    }
    return True;
}

//==============================================================
// Operations of candidate
//---------------------------------------------------------------
Bool Assign::candPartClassify(int v, int *npdass, int *pdass, int *npuass, int *puass, const int size)
{
    // Construct the classified lists of particles possible to assign to
    // the legs of node v
    //
    // pdass = (duplicated set of particles where edges has a unique
    // candidate)
    // puass = (duplicated set of other candidate particles)

    int lg, e, npl, ass, jd, ju, j, pt, pts;

    jd = 0;
    ju = 0;
    for (lg = 0; lg < nodes[v]->deg; lg++) {
        e   = nodes[v]->aedges[lg];
        npl = edges[e]->cand->nplist;
        if (npl < 1) {
            return False;
        }
        ass = (npl == 1);
        for (j = 0; j < edges[e]->cand->nplist; j++) {
            pt  = edges[e]->cand->plist[j];
            pts = legEdgeParticle(v, lg, pt);
            if (ass) {
                jd = intSListAdd(jd, pdass, pts, size);
            } else {
                ju = intSListAdd(ju, puass, pts, size);
            }
        }
    }
    *npdass = jd;
    *npuass = ju;

    return True;
}

//---------------------------------------------------------------
Bool Assign::updateCandNode(int v)
{
    //  Update the configuration
    //  - nodes[v]->cand->ilist
    //  - edges[e]->cand->plist for the adjacent edge
    //  - nodes[n]->cand->unass for the adjacent node 'n' of 'e'

    int   npdass,  pdass[GRCC_MAXPSLIST];
    int   npuass,  puass[GRCC_MAXPSLIST];
    int    nsub0,   sub0[GRCC_MAXPSLIST];
    int  niplist, iplist[GRCC_MAXPSLIST];
    int      nd0,     d0[GRCC_MAXMPARTICLES2];
    int      nd1,     d1[GRCC_MAXMPARTICLES2];
    int      ns0,     s0[GRCC_MAXMPARTICLES2];
    int  neplist, eplist[GRCC_MAXMPARTICLES2];
    int  nitlist, itlist[GRCC_MAXMINTERACT];
    int e, it, j, k, i, lg;

    // external node
    if (nodes[v]->cand->st == AS_AssExt) {
#ifdef CHECK
        e = nodes[v]->aedges[0];
        if (e < 0 || edges[e]->cand->nplist != 1) {
            grcc_fprintf(GRCC_Stdout, "*** illegal external node: v=%d e=%d :", v, e);
            prCand("updateCandNode");
            erEnd("illegal external node");
        }
#endif

        return True;
    }

    // impossible configuration.
    if (nodes[v]->cand->nilist < 1) {
        return False;
    }

    // list of possible particles on the edges of the vertex.
    // pdass = (set of assigned particles)
    // puass = (list of particles of edges with two of more candidates)

    niplist = 0;
    nitlist = 0;
    if (!candPartClassify(v, &npdass, pdass, &npuass, puass, GRCC_MAXPSLIST)) {
        return False;
    }

    if (npdass < 1) {
        return False;
    }

    // from interaction : slist
    // Conditions :
    // 1. pdass \subset slist
    // 2. slist-pdass \subset puass
    // from interaction : slist
    //  conditions : pdass \subset slist \subset (pdass + puass)
    //  sub0 = slist  -   pdass,
    nitlist = 0;
    for (j = 0; j < nodes[v]->cand->nilist; j++) {
        it = nodes[v]->cand->ilist[j];
        // conditions: 
        // 1. pdass \subset slist <==> pdass-slist = \emptyset
        // 2. slist-pdass \subset puass <==> (slist-pdass)-puass = \emptyset
        if (isSubSList(npdass, pdass, 
                       model->interacts[it]->nslist, 
                       model->interacts[it]->slist) ) {
            nsub0 = subtrSet(model->interacts[it]->nslist, 
                             model->interacts[it]->slist,
                             npdass, pdass, sub0, GRCC_MAXPSLIST);
            if (nsub0 < 1) {
                // slist == pdass : no additional candidate particle
                nitlist = intSetAdd(nitlist, itlist, it, GRCC_MAXMINTERACT);

            } else {
                if (isSubSList(nsub0, sub0, npuass, puass)) {
                    nitlist = intSetAdd(nitlist, itlist, it, GRCC_MAXMINTERACT);
                    for (k = 0; k < nsub0; k++) {
                        niplist = intSetAdd(niplist,iplist,sub0[k],GRCC_MAXPSLIST);
                    }
                }
            }
        }
    }

    if (nitlist < 1) {
        return False;
    }

    if (nitlist != nodes[v]->cand->nilist) {
        astack->pushNode(v);
        nodes[v]->cand->nilist = nitlist;
        for (i = 0; i < nitlist; i++) {
            nodes[v]->cand->ilist[i] = itlist[i];
        }
#ifdef CHECK
    } else if (nitlist > nodes[v]->cand->nilist) {
        erEnd("larger ncand");
#endif
    }

    // edge
    for (lg = 0; lg < nodes[v]->deg; lg++) {
        e = nodes[v]->aedges[lg];
        if (edges[e]->cand->nplist > 1) {
            // elist = {candidate particles in the direction of the edge}
            // s0 = plist \cap elist
            neplist = legPart(v, lg, niplist, iplist, eplist, GRCC_MAXMPARTICLES2);
            listDiff(edges[e]->cand->nplist, edges[e]->cand->plist,
                     neplist, eplist,
                     &nd0, d0, &ns0, s0, &nd1, d1);

            if (ns0 < 1) {
                return False;
            }
            if (ns0 < edges[e]->cand->nplist) {
                astack->pushEdge(e);
                edges[e]->cand->nplist = ns0;
                for (i = 0; i < ns0; i++) {
                    edges[e]->cand->plist[i] = s0[i];
                }
            }
        }
    }
    for (lg = 0; lg < nodes[v]->deg; lg++) {
        e = nodes[v]->aedges[lg];
        if (edges[e]->cand->nplist == 1 && !edges[e]->cand->det) {
            if(!detEdge(e)) {
                return False;
            }
        }
    }

    return True;
}

//==============================================================
// Check order of coupling constants, duplication and isomorphism
//--------------------------------------------------------------
Bool Assign::checkOrderCpl(void)
{
    //  Check order of coupling constants

    int ord[GRCC_MAXNCPLG];
    int lcn, n, ia, j, cl;

    // list of coupling constants
    lcn = model->ncouple;

    if (lcn == 1) {
        return True;
    }

    // sum up for each coupling constants
    for (j = 0; j < GRCC_MAXNCPLG; j++) {
        ord[j] = 0;
    }
    for (n = 0; n < nNodes; n++) {
        cl = pnclass->nd2cl[n];
        if (!isATExternal(pnclass->type[cl])) {
            ia = nodes[n]->cand->ilist[0];
            for (j = 0; j < lcn; j++) {
                ord[j] += model->interacts[ia]->clist[j];
            }
        }
    }

    // comparison
    for (j = 0; j < lcn; j++) {
        if (sproc->clist[j] != ord[j]) {
            return False;
        }
    }
    return True;
}

//--------------------------------------------------------------
Bool Assign::isOrdLegs(void)
{
    //  Whether graph is duplicated because of the violation
    //  of ordering in the case of multiple connections
    //    v0 <-- v --> v1

    int v, l0, v0, l1, v1, e0, e1, q0, q1, p0, p1, cl;

    for (v = 0; v < nNodes; v++) {
        cl = pnclass->nd2cl[v];
        if (!isATExternal(pnclass->type[cl])) {
            for (l0 = 0; l0 < nodes[v]->deg; l0++) {
                v0 = nodes[v]->anodes[l0];
                for (l1 = l0+1; l1 < nodes[v]->deg; l1++) {
                    v1 = nodes[v]->anodes[l1];
    
                    if (v0 == v1 && v <= v0) {
                        // multiple connections (v, l0) and (v, l1)
                        e0 = nodes[v]->aedges[l0];
                        e1 = nodes[v]->aedges[l1];
                        q0 = edges[e0]->cand->plist[0];
                        q1 = edges[e1]->cand->plist[0];
                        p0 = legEdgeParticle(v, l0, q0);
                        p1 = legEdgeParticle(v, l1, q1);
                        if (p0 > p1) {
                            // violation of ordering
                            return False;
                        }
                    }
                }
            }
        }
    }

    return True;
}

//--------------------------------------------------------------
Bool Assign::isIsomorphic(MNodeClass *cl, BigInt *nsym, BigInt *esym, BigInt *nsym1)
{
    //  Check whether the current graph is the representive of 
    //  a isomorphic class.
    //  Returns (nsym, esym)
    //    nsym = symmetry factor by the permutation of nodes.
    //    esym = symmetry factor by the permutation of edge.
    //  If this graph is not a representative, then returns (0,0).

    int j, cmp, n, cln;
    BigInt ngelem;
    int *p;
    Bool invext;

    ngelem = mgraph->group->nElem();
#ifdef CHECK
    if (mgraph->nsym > 1 && ngelem <= 1) {
        grcc_fprintf(GRCC_Stdout, "*** isIsomorphic: illegal group: "
               "ngelem=%ld, mgraph->sym=(%ld, %ld)\n",
               ngelem, mgraph->nsym, mgraph->esym);
        erEnd("Assign::isIsomorphic: illegal group");
    }
#endif
    if (ngelem == 0) {
        *nsym  = 1;
        *nsym1 = 1;
    } else {
        *nsym  = 0;
        *nsym1 = 0;
        for (j = 0; j < ngelem; j++) {
            // check the graph is the representative and count 'nsym'.

            //p = mgraph->group->nextElem();
            p = mgraph->group->elem[j];

            cmp = cmpPermGraph(p, cl);

            if (cmp < 0) {        // duplicated graph
                return False;
            } else if(cmp == 0) { // not duplicated
                (*nsym)++;

                if (opt->values[GRCC_OPT_SymmInitial] || opt->values[GRCC_OPT_SymmFinal]) {
                    invext = True;
                    for (n = 0; n < nNodes; n++) {
                        cln = pnclass->nd2cl[n];
                        if (!isATExternal(pnclass->type[cln])) {
                            continue;
                        }
                        if (p[n] != n) {
                            invext = False;
                        }
                    }
                    if (invext) {
                        (*nsym1)++;
                    }
                } else {
                    (*nsym1)++;
                }
            }
        }
    }
    if (*nsym1 == 0) {
        *nsym1 = *nsym;
    }

    // calculate permutations of edges
    *esym = edgeSym();
    if (*esym < 1) {
        return False;
    }

    return True;
}

//--------------------------------------------------------------
int Assign::cmpPermGraph(int *p, MNodeClass *cl)
{
    //  compare the graph with one permutated by 'p'.

    int n, cmp, n1, n2, p1, p2, j;
    ANode *nd1, *np1;
    // ANode *nd2, *np2;
    int    njn, jn[GRCC_MAXLEGS];
    int    njp, jp[GRCC_MAXLEGS];

#ifdef CHECK
    if (p == NULL) {
        erEnd("Assign::cmpPermGraph: p==NULL");
    }
#endif
    for (n = 0; n < nNodes; n++) {
        if (!isATExternal(pnclass->type[pnclass->nd2cl[n]])) {
            cmp = cmpNodes(n, p[n], cl);
            if (cmp != 0) {
                return cmp;
            }
        }
    }

    njn = 0;
    njp = 0;
    for (n1 = 0; n1 < nNodes; n1++) {
        p1  = p[n1];
        nd1 = nodes[n1];
        np1 = nodes[p1];
        for (n2 = n1; n2 < nNodes; n2++) {
            if (mgraph->adjMat[n1][n2] == 0) {
                continue;
            }

            p2  = p[n2];
            if (p1 == n1 && p2 == n2) {
                continue;
            }
            cmp = mgraph->adjMat[n1][n2] - mgraph->adjMat[p1][p2];
            if (cmp != 0) {
                return cmp;
            }

            njn = 0;
            njp = 0;
            for (j = 0; j < nd1->deg; j++) {
                if (nd1->anodes[j] == n2) {
                    jn[njn++] = getLegParticle(n1, j);
                }
            }

            for (j = 0; j < np1->deg; j++) {
                if (np1->anodes[j] == p2) {
                    jp[njp++] = getLegParticle(p1, j);
                }
            }

            cmp = njn - njp;
            if (cmp != 0) {
                return cmp;
            }

            // ignore ordering for multiple connections
            if (mgraph->adjMat[n1][n2] >= 2) {
                sorti(njn, jn);
                sorti(njn, jp);
            }

            for (j = 0; j < njn; j++) {
                cmp = jn[j] - jp[j];
                if (cmp != 0) {
                    return cmp;
                }
            }
        }
    }

    return 0;
}

//--------------------------------------------------------------
int Assign::cmpNodes(int nd0, int nd1, MNodeClass *cn)
{
    //  Comparison of two nodes 'nd0' and 'nd1'
    //    Ordering is lexicographical (class, connection configuration)
    //

    int cmp;

    // Wether two nodes are in a same class or not.
    cmp = cn->ndcl[nd0] - cn->ndcl[nd1];
    if (cmp != 0) {
        return cmp;
    }

    // interaction
    cmp = nodes[nd0]->cand->ilist[0] - nodes[nd1]->cand->ilist[0];
    return cmp;
}

//--------------------------------------------------------------
BigInt Assign::edgeSym(void)
{
    //  calculate permutations of edges

    int lg[GRCC_MAXLEGS], lt[GRCC_MAXLEGS], lc;
    ANode *nd1;
    int n1, n2, j, k, mult;
    BigInt  esym;

    esym = 1;
    for (n1 = 0; n1 < nNodes; n1++) {
        nd1 = nodes[n1];
        for (n2 = n1; n2 < nNodes; n2++) {
            if (mgraph->adjMat[n1][n2] > 1) {
                lc = 0;
                for (j = 0; j < nd1->deg; j++) {
                    if (nd1->anodes[j] == n2) {
                        lg[lc] = 1;
                        lt[lc] = getLegParticle(n1, j);
                        lc++;
                    }
                }
                for (j = 0; j < lc-1; j++) {
                    if (lg[j] > 0) {
                        for (k = lc-1; k > j; k--) {
                            if (lt[j] == lt[k]) {
                                lg[j] += lg[k];
                                lg[k]  = 0;
                            }
                        }
                    }
                }

                // calculate symmetry factor
                for (j = 0; j < lc; j++) {
                    if (lg[j] < 1) {
                        continue;
                    }
                    mult = lg[j];
                    if (mult > 1) {
                        if (n1 == n2) {
                            // self-loop
                            esym *= ipow(2,mult/2)*factorial(mult/2);
                        } else {
                            esym *= factorial(mult);
                        }
                    }
                }
            }
        }
    }

    return esym;
}

#ifdef CHECK
//==============================================================
// check
//--------------------------------------------------------------
Bool Assign::checkCand(const char *msg)
{
    //  Check the consistency of Candidate data

    Bool  ok;
    ANode *na;
    NCand *nc;
    ECand *ec;
    int   n, lg, e;

    // check 'nodes->cand'
    ok = True;
    for (n = 0; n < nNodes; n++) {
        na = nodes[n];
        nc = na->cand;

        // check unassigned vertex
        if (nc->st == AS_UnAssLegs) {

        // check assigned vertex
        } else if (nc->st == AS_Assigned) {
            if (nc->nilist < 1) {
                grcc_fprintf(GRCC_Stdout, "*** checkCand:7:%s:status (%d) of node %d says"
                       " interaction is assigned to %d but ilist=",
                       msg, nc->st, n, nc->st);
                prIntArray(nc->nilist, nc->ilist, "\n");
                ok = False;
            }

            for (lg = 0; lg < nc->deg; lg++) {
                e  = na->aedges[lg];
                ec = edges[e]->cand;
                if (ec->nplist != 1) {
                    grcc_fprintf(GRCC_Stdout, "*** checkCand:8:%s:status (%d) of node %d says"
                          " interaction is assigned "
                          " but unassigned edge %d is found\n",
                          msg, nc->st, n, e);
                    ok = False;
                }
            }

        // external particle
        } else if (nc->st == AS_AssExt) {
            // pt  = nc->ilist[0];
            // *** pte = legEdgeParticle(n, 0, - pt);
        } else {
            grcc_fprintf(GRCC_Stdout, "*** checkCand:10:%s:illegal status of node %d : %d",
                   msg, n, nc->st);
            ok = False;
        }
    }

    // check edges

    for (e = 0; e < nEdges; e++) {
        ec = edges[e]->cand;
        if (ec != NULL && ec->nplist < 1) {
            grcc_fprintf(GRCC_Stdout, "*** checkCand:12:%s:illegal edge %d\n", msg, e);
            ok = False;
        }
    }

    if (!ok) {
        grcc_fprintf(GRCC_Stdout, "*** checkCand:15:%s:illegal configuration\n", msg);
        prCand("checkCand");
        grcc_fprintf(GRCC_Stdout, "*** checkCand:16:illegal configuration\n");
        erEnd("checkCand:16:illegal configuration");
    }
    return ok;
}

//--------------------------------------------------------------
void Assign::checkNode(int n, const char *msg)
{
    int j, it;

    for (j = 0; j < nodes[n]->cand->nilist; j++) {
        it = nodes[n]->cand->ilist[j];
        if (Abs(it) >= GRCC_MAXMINTERACT) {
            grcc_fprintf(GRCC_Stdout, "*** %s: n=%d, j=%d, it=%d\n", msg, n, j, it);
            nodes[n]->cand->prNCand(msg);
            grcc_fprintf(GRCC_Stdout, "\n");
            erEnd("checkNode:illegal it");
        }
    }
}
#endif // CHECK

//**************************************************************
// astack.cc
//==============================================================
// Assign particles to the edges and interactions to nodes.
// Completed graph data is saved in the form of EGraph.

//=============================================================
// stack operations
//--------------------------------------------------------------
void NStack::print(const char *msg)
{
    grcc_fprintf(GRCC_Stdout, "  node=%d, deg=%d, st=%d, ilist=", noden, deg, st);
    prilist(nilist, ilist, msg);
}

//--------------------------------------------------------------
void EStack::print(const char *msg)
{
    grcc_fprintf(GRCC_Stdout, "  edge=%d, det=%d, plist=", edgen, det);
    prilist(nplist, plist, msg);
}

//--------------------------------------------------------------
AStack::AStack(int nsize, int esize)
{
    int j;

    agraph  = NULL;

    nSize   = nsize;
    eSize   = esize;
    if (nSize > 0) {
        nStack = new NStack*[nSize];
    } else {
        nStack = NULL;
    }
    if (eSize > 0) {
        eStack = new EStack*[eSize];
    } else {
        eStack = NULL;
    }

    nStackP = 0;
    eStackP = 0;

    for (j = 0; j < nSize; j++) {
        nStack[j] = new NStack();
    }

    for (j = 0; j < eSize; j++) {
        eStack[j] = new EStack();
    }
}

//--------------------------------------------------------------
AStack::~AStack(void)
{
    int j;

    if (eStack != NULL) {
        for (j = eSize-1; j >= 0; j--) {
            if (eStack[j] != NULL) {
                delete eStack[j];
                eStack[j] = NULL;
            }
        }
        delete[] eStack;
        eStack = NULL;
    }

    if (nStack != NULL) {
        for (j = nSize-1; j >= 0; j--) {
            if (nStack[j] != NULL) {
                delete nStack[j];
                nStack[j] = NULL;
            }
        }
        delete[] nStack;
        nStack = NULL;
    }
}

//--------------------------------------------------------------
void AStack::setAGraph(Assign *ag)
{
    agraph = ag;
}

//--------------------------------------------------------------
void AStack::pushNode(int n)
{
    NCand  *nc;
    NStack *ns;
    int j;

#ifdef CHECK
    if (agraph == NULL) {
        erEnd("pushNode: agraph is not defined");
    }
#endif
    if (nStackP >= GRCC_MAXNSTACK) {
        erEnd("N-stack overflow (GRCC_MAXNSTACK)");
    }
    nc = agraph->nodes[n]->cand;
    if (nc->nilist >= GRCC_MAXMINTERACT) {
        erEnd("N-stack: too long list (GRCC_MAXMINTERACT)");
    }
    ns = nStack[nStackP];
    ns->noden  = n;
    ns->deg    = nc->deg;
    ns->st     = nc->st;
    ns->nilist = nc->nilist;
    for (j = 0; j < nc->nilist; j++) {
        ns->ilist[j] = nc->ilist[j];
    }
    nStackP++;
}

//--------------------------------------------------------------
void AStack::pushEdge(int e)
{
    ECand  *ec;
    EStack *es;
    int j;

#ifdef CHECK
    if (agraph == NULL) {
        erEnd("pushEdge: agraph is not defined");
    }
#endif
    if (eStackP >= GRCC_MAXESTACK) {
        erEnd("E-stack overflow (GRCC_MAXESTACK)");
    }
    ec = agraph->edges[e]->cand;
    if (ec->nplist >= GRCC_MAXMPARTICLES2) {
        erEnd("E-stack: Too long list (GRCC_MAXMPARTICLES)");
    }
    es = eStack[eStackP];
    es->edgen  = e;
    es->det    = ec->det;
    es->nplist = ec->nplist;
    for (j = 0; j < ec->nplist; j++) {
        es->plist[j] = ec->plist[j];
    }
    eStackP++;
}

//--------------------------------------------------------------
void AStack::checkPoint(CheckPt sav)
{
    sav[0] = nStackP;
    sav[1] = eStackP;
}

//--------------------------------------------------------------
void AStack::restoreNode(int spr)
{
    NStack *stc;
    int     sp, n, j;

    for (sp = nStackP-1; sp >= spr; sp--) {
        stc = nStack[sp];
        n = stc->noden;
        agraph->nodes[n]->cand->deg     = stc->deg;
        agraph->nodes[n]->cand->st      = stc->st;
        agraph->nodes[n]->cand->nilist  = stc->nilist;
        for (j = 0; j < stc->nilist; j++) {
            agraph->nodes[stc->noden]->cand->ilist[j]  = stc->ilist[j];
        }
    }
    nStackP = spr;
}

//--------------------------------------------------------------
void AStack::restoreEdge(int spr)
{
    EStack *stc;
    int     sp, e, j;

    for (sp = eStackP-1; sp >= spr; sp--) {
        stc = eStack[sp];
        e   = eStack[sp]->edgen;
        agraph->edges[e]->cand->det = stc->det;
        agraph->edges[e]->cand->nplist = stc->nplist;
        for (j = 0; j < stc->nplist; j++) {
            agraph->edges[e]->cand->plist[j] = stc->plist[j];
        }
    }
    eStackP = spr;
}

//--------------------------------------------------------------
void AStack::restore(CheckPt sav)
{
    restoreNode(sav[0]);
    restoreEdge(sav[1]);
}

#ifdef CHECK
//--------------------------------------------------------------
void AStack::restoreMsg(CheckPt sav, const char *msg)
{
    if (agraph == NULL) {
        erEnd("restore: agraph is not defined");
    }

    restore(sav);

    if (!agraph->checkCand("restore")) {
        grcc_fprintf(GRCC_Stdout, "restore is called from %s\n", msg);
    }
}
#endif

//--------------------------------------------------------------
void AStack::prStack(void)
{
    int j;

    grcc_fprintf(GRCC_Stdout, "+++ prStack : (%d, %d)", nStackP, eStackP);
    for (j = 0; j < nStackP; j++) {
        grcc_fprintf(GRCC_Stdout, "N:%4d ", j);
        nStack[j]->print("\n");
    }
    for (j = 0; j < eStackP; j++) {
        grcc_fprintf(GRCC_Stdout, "E:%4d ", j);
        eStack[j]->print("\n");
    }
}

//**************************************************************
// class Fraction
//==============================================================
Fraction::Fraction(BigInt n, BigInt d)
{
    BigInt g;

    g     = gcd(n, d);
    num   = n/g;
    den   = d/g;
    ratio = Real(n)/Real(d);
}

//--------------------------------------------------------------
void Fraction::print(const char *msg)
{
    double err = Abs(Real(num)/Real(den) - ratio);

    if (err > GRCC_FRACERROR) {
        grcc_fprintf(GRCC_Stdout, "%ld/%ld(%g)(overflow)%s", num, den, ratio, msg);
    } else {
        grcc_fprintf(GRCC_Stdout, "%ld/%ld(%g)%s", num, den, ratio, msg);
    }
}

//--------------------------------------------------------------
void Fraction::setValue(BigInt n, BigInt d) 
{ 
    num = n;  
    den = d; 
    ratio = Real(n)/Real(d); 
}

//--------------------------------------------------------------
void  Fraction::setValue(Fraction &f) 
{ 
    num   = f.num;  
    den   = f.den; 
    ratio = f.ratio; 
}

//--------------------------------------------------------------
BigInt Fraction::gcd(BigInt n0, BigInt n1)
{
    BigInt nn[2], r;
    int    nc;

    nn[0] = Abs(n0);
    nn[1] = Abs(n1);
    nc    = 0;

    while (1) {
        r = nn[nc] % nn[1-nc];
        if (r == 0) {
            return nn[1-nc];
        }
        nn[nc] = r;
        nc = 1 - nc;
    }
}

//--------------------------------------------------------------
void Fraction::normal(void)
{
    BigInt g;

    if (den == 0) {
        erEnd("Fraction: den==0");
    }
    g   = gcd(num, den);
    num /= g;
    den /= g;
    if (den < 0) {
        num = - num;
        den = - den;
    }
}

//--------------------------------------------------------------
void Fraction::add(BigInt n, BigInt d)
{
    BigInt g, d1;

    if (d < 0) {
        n = -n;
        d = -d;
    }
    if (den < 0) {
        num = - num;
        den = - den;
    }
    g    = gcd(den, d);
    d1   = d/g;
    num  = num * d1 + n * (den/g);
    den  = d1*den;
    g    = gcd(num, den);
    num /= g;
    den /= g;
    ratio += Real(n)/Real(d);
}

//--------------------------------------------------------------
void Fraction::add(Fraction f)
{
    double r = ratio + f.ratio;

    add(f.num, f.den);
    ratio = r;
}

//--------------------------------------------------------------
void Fraction::sub(Fraction f)
{
    double r = ratio - f.ratio;

    add(-f.num, f.den);
    ratio = r;
}

//--------------------------------------------------------------
Bool Fraction::isEq(Fraction f)
{
    return (num == f.num && den == f.den);
}

//**************************************************************
// common.cc
//==============================================================

// Wrapper function for printing messages. This allows the use
// of FORM MesPrint when compiled as part of FORM, and the
// usual fprintf to GRCC_Stdout or GRCC_Stderr otherwise.
static void grcc_fprintf(FILE* out, const char* fmt, ...)
{
    va_list args;
    va_start(args, fmt);

#ifndef NOFORM
    DUMMYUSE(out);
    // the second call of vsnprintf requires a copy of args
    va_list args_copy;
    va_copy(args_copy, args);
    // determine the required buffer size for the formatted string:
    const int len = vsnprintf(NULL, 0, fmt, args);
    char *buffer = new char[len+1];
    vsnprintf(buffer, len+1, fmt, args_copy);
    MLOCK(ErrorMessageLock);
    MesPrint("%s", buffer);
    MUNLOCK(ErrorMessageLock);
    delete[] buffer;
    va_end(args_copy);
#else
    vfprintf(out, fmt, args);
#endif

    va_end(args);
    return;
}

static void erEnd(const char *msg)
{
    if (erExit != NULL) {
        (*erExit)(msg, erExitArg);
    }
    grcc_fprintf(GRCC_Stderr, "*** Error : %s\n\n", msg);
    GRCC_ABORT();
}

#define MAXPART 100
//------------------------------------------------------------
static Bool nextPart(int nelem, int nclist, int *clist, int *nl, int *r)
{
    // Generate configuration nl[] sequentially such that
    //    sum_j^{nclist} nl[j]*clist[j] = nelem
    //    0 <= nl[j]    (j = 0, ..., nclis-1)
    // For control
    //    for the first call : *r < 0
    //    otherwise          : *r >= 0,  nl is the last configuration
    // Returns
    //    True  : succeeded
    //    False : no more configuration

    int rem, pn, j, c;

    if (*r < 0) {
        *r = 0;
        rem = nelem;
        for (j = 0; j < nclist; j++) {
            nl[j] = rem/clist[j];
            rem -= nl[j]*clist[j];
        }
        if (rem == 0) {
            return True;
        }
    } else {
        rem = 0;
    }
    for (c = 0; c < MAXPART; c++) {
        rem += nl[nclist-1]*clist[nclist-1];
        for (pn = nclist-2; pn >= 0 && nl[pn] == 0; pn--) {
            ;
        }
        if (pn < 0) {
            return False;
        }
        rem += clist[pn];
        nl[pn]--;
        for (j = pn+1; j < nclist; j++) {
            nl[j] = rem/clist[j];
            rem -= nl[j]*clist[j];
        }
        if (rem == 0) {
            return True;
        }
    }
    erEnd("*** nextPart : illegal control : too many repetition");
    return False;
}

//------------------------------------------------------------
static int   *intdup(int n, int *a)
{
    int *r, j;

    r = new int[n];
    for (j = 0; j < n; j++) {
        r[j] = a[j];
    }
    return r;
}

//------------------------------------------------------------
static int   *delintdup(int *a)
{
    if (a != NULL) {
        delete[] a;
    }
    return NULL;
}

//------------------------------------------------------------
static void   prilist(int n, const int *a, const char *msg)
{
    grcc_fprintf(GRCC_Stdout, "[");
    for (int j = 0; j < n; j++) {
        if (j!=0) grcc_fprintf(GRCC_Stdout, ", ");
        grcc_fprintf(GRCC_Stdout, "%d", a[j]);
    }
    grcc_fprintf(GRCC_Stdout, "]%s", msg);
}

//------------------------------------------------------------
static int nextPerm(int nelem, int nclass, int *cl, int *r, int *q, int *p, int count)
{
    // Sequential generation of all permutations.

    int  j, k, n, e, t;
    Bool b;

    for (j = 0; j < nelem; j++) {
        p[j] = j;
    }
    if (count < 1) {
        for (j = 0; j < nelem; j++) {
            q[j] = 0;
            r[j] = 0;
        }
        j = 0;
        for (k = 0; k < nclass; k++) {
            n = cl[k];
            for (e = 0; e < n; e++) {
                r[j] = n - e - 1;
                j++;
            }
        }
#ifdef CHECK
        if (j != nelem) {
            erEnd("inconsistent # elements");
        }
#endif
        return 1;
    }
    b = False;
    for (j = nelem-1; j >= 0; j--) {
        if (q[j] < r[j]) {
            for (k = j+1; k < nelem; k++) {
                q[k] = 0;
            }
            q[j]++;
            b = True;
            break;
        }
    }
    if (!b) {
        return (-count);
    }

    for (j = 0; j < nelem; j++) {
        k = j + q[j];
        t = p[j];
        p[j] = p[k];
        p[k] = t;
    }
    return count + 1;
}

//------------------------------------------------------------
static BigInt factorial(int n)
{
    // returns 1 for n < 1

    int r, j;

    r = 1;
    for (j = 2; j <= n; j++) {
        r *= j;
    }
    return r;
}

//------------------------------------------------------------
static BigInt ipow(int n, int p)
{
    int r, j;

    r = 1;
    for (j = 0; j < p; j++) {
        r *= n;
    }
    return r;
}

//------------------------------------------------------------
static int   *newArray(int size, int val)
{
    // memory allocation of an array

    int *a, j;

    a = new int[size];
    for (j = 0; j < size; j++) {
        a[j] = val;
    }
    return a;
}

//------------------------------------------------------------
static int   *deleteArray(int *a)
{
    // memory allocation of an array

    delete[] a;
    return NULL;
}

//------------------------------------------------------------
static int  **newMat(int n0, int n1, int val)
{
    int **m, j, k;

    m = new int*[n0];
    for (j = 0; j < n0; j++) {
        m[j] = new int[n1];
        for (k = 0; k < n1; k++) {
            m[j][k] = val;
        }
    }
    return m;
}

//------------------------------------------------------------
static int **deleteMat(int **m, int n0)
{
    int j;

    for (j = n0-1; j >= 0; j--) {
        delete[] m[j];
    }
    delete[] m;

    return NULL;
}

//------------------------------------------------------------
static void bsort(int n, int *ord, int *a)
{
    int i, j, t;

    for (j = n-1; j > 0; j--) {
        for (i = 0; i < j; i++) {
            if(a[ord[i+1]] < a[ord[i]]) {
                t = ord[i];
                ord[i] = ord[i+1];
                ord[i+1] = t;
            }
        }
    }
}

//--------------------------------------------------------------
static void prMomStr(int mom, const char *ms, int mn)
{
    if (mom == 0) {
        return;
    } else if (mom == 1) {
        grcc_fprintf(GRCC_Stdout, " + %s%d", ms, mn);
    } else if (mom > 0) {
        grcc_fprintf(GRCC_Stdout, " + %d*%s%d", mom, ms, mn);
    } else if (mom == -1) {
        grcc_fprintf(GRCC_Stdout, " - %s%d", ms, mn);
    } else {
        grcc_fprintf(GRCC_Stdout, " - %d*%s%d", -mom, ms, mn);
    }
}

//--------------------------------------------------------------
static void prIntArray(int n, int *p, const char *msg)
{

    int j;

    grcc_fprintf(GRCC_Stdout, "[");
    for (j = 0; j < n; j++) {
        if (j!=0) grcc_fprintf(GRCC_Stdout, ", ");
        grcc_fprintf(GRCC_Stdout, "%2d", p[j]);
    }
    grcc_fprintf(GRCC_Stdout, "]%s", msg);
}

//--------------------------------------------------------------
static void prIntArrayErr(int n, int *p, const char *msg)
{

    int j;

    grcc_fprintf(GRCC_Stderr, "[");
    for (j = 0; j < n; j++) {
        if (j!=0) grcc_fprintf(GRCC_Stderr, ", ");
        grcc_fprintf(GRCC_Stderr, "%2d", p[j]);
    }
    grcc_fprintf(GRCC_Stderr, "]%s", msg);
}

//--------------------------------------------------------------
static void sortrec(int l, int r, int *a)
{
    // quick sort : taken from N. Wirth
    int i,j, x, w;

    i = l;
    j = r;
    x = a[(l+r)/2];
    do {
        while(a[i] < x) i++;
        while(x < a[j]) j--;
        if (i <= j) {
            w = a[i];  a[i] = a[j];  a[j] = w;
            i++;  j--;
        }
    } while (i < j);
    if (l < j) sortrec(l, j, a);
    if (i < r) sortrec(i, r, a);
}

//--------------------------------------------------------------
static void sorti(int size, int *a)
{
    sortrec(0, size-1, a);    
}

//------------------------------------------------------------
static int sortb(int n, int *a)
{
    int i, j, t, nswap;

    nswap = 0;
    for (j = n-1; j > 0; j--) {
        for (i = 0; i < j; i++) {
            if(a[i+1] < a[i]) {
                t = a[i];
                a[i] = a[i+1];
                a[i+1] = t;
                nswap++;
            }
        }
    }

    // the sign of the permutation is (-1)^{nswap}
    return nswap;
}

#ifdef CHECK
//--------------------------------------------------------------
static Bool isIn(int n, int *a, int v)
{
    int j;

    for (j = 0; j < n; j++) {
        if (a[j] == v) {
            return True;
        }
    }
    return False;
}
#endif

//--------------------------------------------------------------
static int intSetAdd(int n, int *a, int v, const int size)
{
    // Add 'v' into 'a'.  
    // 'n' is the current # of element.
    // 'a' is assumed sorted without duplicated elements.
    // Size of 'a' should be large enough.

    int j, k;

    if (n >= size) {
        grcc_fprintf(GRCC_Stderr, "*** intSetAdd : array out of range (>%d)\n", size);
        erEnd("intSetAdd : array out of range (GRCC_MAXPSLIST)");
    }
    for (j = 0; j < n; j++) {
        if (a[j] > v) {
            break;
        } else if (a[j] == v) {
            return n;
        }
    }

    // 'j' can be equal to 'n'
    for (k = n-1; k >= j; k--) {
        a[k+1] = a[k];
    }
    a[j] = v;
    return n+1;
}

//--------------------------------------------------------------
static int intSListAdd(int n, int *a, int v, const int size)
{
    // Add 'v' into 'a'.  
    // 'n' is the current # of element.
    // 'a' is assumed sorted without duplicated elements.
    // Size of 'a' should be large enough.

    int j, k;

    if (n >= size) {
        grcc_fprintf(GRCC_Stderr, "*** intSListAdd : array out of range (>%d)\n", size);
        erEnd("intSListAdd : array out of range");
    }
    for (j = 0; j < n; j++) {
        if (a[j] >= v) {
            break;
        }
    }

    // 'j' can be equal to 'n'
    for (k = n-1; k >= j; k--) {
        a[k+1] = a[k];
    }
    a[j] = v;
    return n+1;
}

//--------------------------------------------------------------
static int    cmpArray(int na, int *a, int nb, int *b)
{
    int j, cmp;

    cmp = na - nb;
    if (cmp != 0) {
        return cmp;
    }
    for (j = 0; j < na; j++) {
        cmp = a[j] - b[j];
        if (cmp != 0) {
            return cmp;
        }
    }
    return 0;
}

//--------------------------------------------------------------
static Bool   leqArray(int n, int *a, int *b)
{
    int j;

    for (j = 0; j < n; j++) {
        if (a[j] > b[j]) {
            return False;
        }
    }
    return True;
}

//--------------------------------------------------------------
// convert list to sorted list
static int   toSList(int n, int *a)
{
    sorti(n, a);
    return n;
}

//--------------------------------------------------------------
// as set operation assuming a and b are sorted with duplication
//     p := a \ b;  q := a \cap b;  r := b \ a;
// p, q, r are sorted without duplication
static void   listDiff(int na, int *a, int nb, int *b, int *np, int *p, int *nq, int *q, int *nr, int *r)
{
    int ja, jb;

    *np = *nq = *nr = 0;
    ja = jb = 0;
    while (ja < na && jb < nb) {
        while (ja < na && a[ja] < b[jb]) {
            p[(*np)++] = a[ja++];
        }
        while (jb < nb && b[jb] < a[ja]) {
            r[(*nr)++] = b[jb++];
        }
        if (ja < na && jb < nb && a[ja] == b[jb]) {
            q[(*nq)++] = a[ja++];
            jb++; 
        }
    }
    for (; ja < na; ja++) {
        p[(*np)++] = a[ja];
    }
    for (; jb < nb; jb++) {
        r[(*nr)++] = b[jb];
    }
}

//--------------------------------------------------------------
static int isSubSList(int na, int *a, int nb, int *b)
{
    int ja, jb;

    ja = jb = 0;
    while (ja < na && jb < nb) {
        for ( ; jb < nb && b[jb] < a[ja]; jb++) {
            ;
        }
        if (jb >= nb || b[jb] > a[ja]) {
            return False;
        }
        for ( ; jb < nb && ja < na && b[jb] == a[ja]; jb++, ja++) {
            ;
        }
    }
    return (ja >= na);
}

//--------------------------------------------------------------
static int subtrSet(int na, int *a, int nb, int *b, int *c, int size)
{
    // set subtraction 'c' := 'a' - 'b'.  
    // 'a' and 'b' are sorted lists (not always unique)
    // 'c' is the set (sorted and unique elements)

    int ja, jb, jc;

    jc = 0;
    ja = jb = 0;
    while (ja < na && jb < nb) {
        while (ja < na && a[ja] < b[jb]) {
            if (jc == 0 || c[jc-1] != a[ja]) {
                if (jc >= size) {
                    erEnd("subsutSet: too small size of array (GRCC_MAXPSLIST)");
                }
                c[jc++] = a[ja];
            }
            ja++;
        }
        while (jb < nb && b[jb] < a[ja]) {
            ;
        }
        if (ja < na && jb < nb && a[ja] == b[jb]) {
            ja++;
            jb++; 
        }
    }
    for (; ja < na; ja++) {
        if (jc == 0 || c[jc-1] != a[ja]) {
            c[jc++] = a[ja];
        }
    }
    return jc;
}

// } ) ]