module newsyz;

localf module_syz, module_syz_old;
localf simplify_syz, icont, mod, remove_cont,ordcheck;
localf complsb, complsb_sd, sortlsb, find_pos, find_pos, reduce, lres_setup, dpm_sort1, comp_pos;
localf fres,minres,sres,minsres,lres, create_base_ord, simplify_k, simplify_by_k, remove_k, remove_k1, extract_nonzero;
localf nonzero, phi, syz_check, renumber_pos, compress, compress_h;
localf syz_check0,phi0,todpmlist,dpmlisttollist;

/* F : a list of (lists or polynomials), 
   V : a variable list, H >1=> over GF(H), H=0,1=> over Q 
   O : term order
   return: [GS,G]
   GS : a GB of syz(F) wrt [1,O] (POT), G: a GB of F wrt [1,O]
*/

// return [dpmlist F,rank N]
def todpmlist(F,V)
{
  K = length(F);
  for ( I = 0; I < K; I++ ) if ( F[I] ) break;
  if ( I == K ) return [];
  if ( type(F[I]) <= 2 ) {
    // F is a polynimial list
    F = map(dp_ptod,F,V);
    F = map(dpm_dptodpm,F,1);
    N = 1;
  } else if ( type(F[I]) == 9 ) {
    // F is a dpoly list
    F = map(dpm_dptodpm,F,1);
    N = 1;
  } else if ( type(F[I]) == 4 ) {
    // F is a list of poly lists
    N = length(F[0]);
    F = map(dpm_ltod,F,V);
  } else if ( type(F[I]) == 26 ) {
    // F is a DPM list
    for ( N = 0, T = F; T != []; T = cdr(T) ) {
      for ( A = car(T); A; A = dpm_rest(A) ) {
        N1 = dpm_hp(A);
        if ( N1 > N ) N = N1;
      }
    } 
  } else {
    error("todpmlist: arugument type is invalid.");
  }
  return [F,N];
}

def module_syz(F,V,H,Ord)
{
  if ( type(Weyl=getopt(weyl)) == -1 ) Weyl = 0;
  if ( type(DP=getopt(dp)) == -1 ) DP = 0;
  if ( type(F4=getopt(f4)) == -1 ) F4 = 0;
  dp_ord(Ord);
  K = length(F);
  for ( I = 0; I < K; I++ ) if ( F[I] ) break;
  if ( I == K ) return [[],[],[]];
  L = todpmlist(F,V);
  F = L[0]; N = L[1];
  dp_ord([1,Ord]);
  B = [];
  for ( I = 0; I < K; I++ ) {
    B = cons(F[I]+dpm_dptodpm(dp_ptod(1,V),N+I+1),B);
  }
  B = reverse(B);
  if ( H >= 2 ) {
    // finite field
    if ( Weyl )
      G = nd_weyl_gr(B,V,H,[1,Ord]|dp=1);
    else if ( F4 )
      G = nd_f4(B,V,H,[1,Ord]|dp=1);
    else
      G = nd_gr(B,V,H,[1,Ord]|dp=1);
  } else {
    if ( Weyl )
      G = nd_weyl_gr(B,V,0,[1,Ord]|dp=1,homo=H);
    else if ( F4 ) {
      Ind = 0;
      while ( 1 ) {
        G = nd_f4_trace(B,V,H,-lprime(Ind),[1,Ord]|dp=1);
        if ( G ) break;
        else Ind++;
      }
    } else
      G = nd_gr(B,V,0,[1,Ord]|dp=1,homo=H);
  }
  G0 = []; S0 = []; Gen0 = [];
  for ( T = G; T != []; T = cdr(T) ) {
    H = car(T);
    if ( dpm_hp(H) > N ) {
      S0 = cons(dpm_shift(H,N),S0);
    } else {
      L = dpm_split(H,N);
      G0 = cons(L[0],G0);
      Gen0 = cons(dpm_shift(L[1],N),Gen0);
	}
  }
#if 0
  S0 = reverse(S0); G0 = reverse(G0); Gen0 = reverse(Gen0);
#endif
  if ( !DP ) {
    S0 = map(dpm_dtol,S0,V); G0 = map(dpm_dtol,G0,V); Gen0 = map(dpm_dtol,Gen0,V);
  }
  return [S0,G0,Gen0];
}

def module_syz_old(F,V,H,O)
{
	Weyl = type(getopt(weyl)) != -1 ? 1 : 0;
	K = length(F);
	if ( type(F[0]) <= 2 ) {
		for ( T = [], S = F; S != []; S = cdr(S) )
			T = cons([car(S)],T);
		F = reverse(T);
	}
	N = length(F[0]);
	B = [];
	for ( I = 0; I < K; I++ ) {
		E = vector(N+K);
		for ( J = 0; J < N; J++ ) E[J] = F[I][J];
		E[N+I] = 1;
		B = cons(vtol(E),B);
	}
	B = reverse(B);
	if ( H >= 2 ) {
		if ( Weyl )
			G = nd_weyl_gr(B,V,H,[1,O]);
		else
			G = nd_gr(B,V,H,[1,O]);
	} else {
		if ( Weyl )
			G = nd_weyl_gr_trace(B,V,H,-1,[1,O]);
		else
			G = nd_gr_trace(B,V,H,-1,[1,O]);
	}
	G0 = []; S0 = []; Gen0 = [];
	for ( T = G; T != []; T = cdr(T) ) {
		H = car(T);
		for ( J = 0; J < N; J++ ) if ( H[J] ) break;
		if ( J == N ) {
			H1 = vector(K);
			for ( J = 0; J < K; J++ ) H1[J] = H[N+J];
			S0 = cons(vtol(H1),S0);
		} else {
			H1 = vector(N);
			for ( J = 0; J < N; J++ ) H1[J] = H[J];
			G0 = cons(vtol(H1),G0);
			H1 = vector(K);
			for ( J = 0; J < K; J++ ) H1[J] = H[N+J];
			Gen0 = cons(vtol(H1),Gen0);
		}
	}
	return [S0,G0,Gen0];
}

def fres(F,V,H,O)
{
  if ( type(Weyl=getopt(weyl)) == -1 ) Weyl = 0;
  if ( type(F4=getopt(f4)) == -1 ) F4 = 0;
  if ( type(DP=getopt(dp)) == -1 ) DP = 0;
  L = todpmlist(F,V); F = L[0];
  R = [F];
  while ( 1 ) {
    if ( Weyl )
      L = module_syz(car(R),V,H,O|weyl=1,dp=1,f4=F4);
    else
      L = module_syz(car(R),V,H,O|dp=1,f4=F4);
    L = L[0];
    L = ordcheck(L,V);
    if ( L == [] ) {
      R = reverse(R);
      if ( DP ) return R;
      else return map(dpmlisttollist,R,V);
    }
    R = cons(L,R);	
  }
}

def minres(F,V,H,O)
{
  if ( type(Weyl=getopt(weyl)) == -1 ) Weyl = 0;
  if ( type(F4=getopt(f4)) == -1 ) F4 = 0;
  if ( type(DP=getopt(dp)) == -1 ) DP = 0;
  L = todpmlist(F,V); F = L[0];
  R = [F];
  while ( 1 ) {
    if ( Weyl )
      L = module_syz(car(R),V,H,O|weyl=1,dp=1,f4=F4);
    else
      L = module_syz(car(R),V,H,O|dp=1,f4=F4);
    L = L[0];
    L = ordcheck(L,V);
    if ( L == [] ) break;
    S = dpm_simplify_syz(L,R[0]);
    if ( S[0] == [] && S[1] == [] ) {
      R = cdr(R); break;
    }
    R = append([S[0],S[1]],cdr(R));	
    if ( R[0] == [] ) {
      R = cdr(R); break;
    }
  }
  R = reverse(R);
  if ( DP ) return R;
  else return map(dpmlisttollist,R,V);
}

def dpmlisttollist(F,V)
{
  return map(dpm_dtol,F,V);
}

def sres(F,V,H,Ord)
{
  if ( type(DP=getopt(dp)) == -1 ) DP = 0;
  dpm_set_schreyer(0);
  dp_ord(Ord);
  K = length(F);
  K = length(F);
  for ( I = 0; I < K; I++ ) if ( F[I] ) break;
  if ( I == K ) return [[],[],[]];
  L = todpmlist(F,V);
  F = L[0]; N = L[1];
  G = nd_gr(F,V,H,[0,Ord]|dp=1);
  G = reverse(G);
  R = [G];
  dp_ord([0,Ord]);
  while ( 1 ) {
    S = dpm_schreyer_base(R[0]);
    print(["length",length(S)]);
    if ( S == [] ) break;
    else R = cons(S,R);
  }
  dp_ord([0,0]);
  R = reverse(R);
  if ( DP ) return R;
  else return map(dpmlisttollist,R,V);
}

def minsres(F,V,H,Ord)
{
  if ( type(DP=getopt(dp)) == -1 ) DP = 0;
  R = sres(F,V,H,Ord|dp=1);
  R = ltov(reverse(R));
  M = length(R);
  for ( I = 0; I < M; I++ ) R[I] = map(dpm_sort,R[I]);
  R = vtol(R);
  for ( T = R, U = []; length(T) >= 2; ) {
    Z = dpm_simplify_syz(T[0],T[1]);
    U = cons(Z[0],U);
    T = cons(Z[1],cdr(cdr(T)));
  }
  U = cons(T[0],U);
  if ( DP ) return U;
  else return map(dpmlisttollist,U,V);
}

def ordcheck(D,V)
{
  B=map(dpm_dtol,D,V);
  dp_ord([1,0]);
  D = map(dpm_sort,D);
  D1 = map(dpm_ltod,B,V);
  if ( D != D1 ) 
    print("afo");
  return D1;
}

def complsb(A,B)
{
  AL = A[3]; AD = A[4];
  BL = B[3]; BD = B[4];
  if ( AD > BD ) return 1;
  else if ( AD < BD ) return -1;
  else if ( AL < BL ) return 1;
  else if ( AL > BL ) return -1;
  else return 0;
}

def complsb_sd(A,B)
{
  AL = A[3]; AD = A[4];
  BL = B[3]; BD = B[4];
  if ( AD-AL > BD-BL ) return 1;
  else if ( AD-AL < BD-BL ) return -1;
  else if ( AL > BL ) return 1;
  else if ( AL < BL ) return -1;
  else return 0;
}

def sortlsb(A)
{
  S = [];
  N = length(A);
  for ( I = 0; I < N; I++ ) S = append(cdr(vtol(A[I])),S);
//  S = qsort(S,newsyz.complsb_sd);
  S = qsort(S,newsyz.complsb);
  return S;
}
/* D=[in,sum,deg,lev,ind] */
/* B=[0 B1 B2 ...] */
/* C=[0 C1 C2 ...] */
/* H=[0 H1 H2 ...] */
/* Z=[0 Z1 Z2 ...] */
/* Zi=[0 L1 L2 ...] */
/* Lj=[I1,I2,...] */
/* One=<<0,...,0>> */

extern Rtime,Stime,Ptime$

// B is sorted wrt positon
def find_pos(HF,B)
{
  Len = length(B);
  Pos = dpm_hp(HF);
  First = 0; Last = Len-1;
  if ( B[First][0] == HF ) return B[First][2];
  if ( B[Last][0] == HF ) return B[Last][2];
  while ( 1 ) {
    Mid = idiv(First+Last,2); 
    PosM = dpm_hp(B[Mid][0]);
    if ( PosM == Pos ) break;
    else if ( PosM < Pos )
      First = Mid;
    else
      Last = Mid;
  }
  for ( I = Mid; I < Len && dpm_hp(B[I][0]) == Pos; I++ )
    if ( HF == B[I][0] ) return B[I][2];
  for ( I = Mid-1; I >= 1 && dpm_hp(B[I][0]) == Pos; I-- )
    if ( HF == B[I][0] ) return B[I][2];
  error("find_pos : cannot happen");
}

def reduce(D,B,Bpos,C,H,Z,K,Kind,G,One,Top)
{
  M = D[0]; Ind = D[2]; I = D[3];
  if ( I == 1 ) {
    C[I][Ind] = G[Ind];
    dpm_insert_to_zlist(Z[1],dpm_hp(G[Ind]),Ind);
    H[I][Ind] = G[Ind];
  } else {
    /* M is in F(I-1) => phi(M) is in F(I-2) */
    /* reduction in F(I-2) */
    T0 = time()[0];
    dpm_set_schreyer_level(I-2);
    CI = C[I-1]; ZI = Z[I-1]; BI = B[I-1]; BposI = Bpos[I-1];
    Len = size(CI);
    T=dpm_hc(M); EM=dpm_hp(M);
    XiM = T*dpm_ht(CI[EM]);
    EXiM = dpm_hp(XiM);
    ZIE = ZI[EXiM];
    for ( ZIE = ZI[EXiM]; ZIE != []; ZIE = cdr(ZIE) ) {
      J = car(ZIE);
      if ( J > EM && dpm_redble(XiM,dpm_ht(CI[J])) ) break;
    }
    Ptime += time()[0]-T0;
    T0 = time()[0];
    QR = dpm_sp_nf(CI,ZI,EM,J|top=Top);
    Rtime += time()[0]-T0;
    G = QR[0]; F = QR[1];
    if ( F ) {
      HF = dpm_ht(F); EF = dpm_hp(HF);
      /* find HF in B[I-1] */
    T0 = time()[0];
    J = find_pos(HF,BposI);
    Stime += time()[0]-T0;
      /* F=Ret[0]*Ret[1] */
      Ret = dpm_remove_cont(F);
      CI[J] = Ret[1];
      Kind[I-1][J] = 2;
      dpm_insert_to_zlist(ZI,EF,J);
      dpm_set_schreyer_level(I-1);
      Tail = -Ret[0]*dpm_dptodpm(One,J);
      G += Tail;
      dpm_set_schreyer_level(0);
      Ret = dpm_remove_cont(G); G = Ret[1];
      C[I][Ind] = G;
      Kind[I][Ind] = 1;
      K[I] = cons([G,Tail],K[I]);
      dpm_insert_to_zlist(Z[I],EM,Ind);
      /* level <- 0 */
      BI[J][3] = 0;
    } else {
      Kind[I][Ind] = 0;
      Ret = dpm_remove_cont(G); G = Ret[1];
      H[I][Ind] = G;
      C[I][Ind] = G;
      dpm_insert_to_zlist(Z[I],EM,Ind);
    }
  }
}

def lres_setup(F,V,H,Ord)
{
  dpm_set_schreyer(0);
  dp_ord(Ord);
  K = length(F);
  if ( type(F[0]) <= 2 ) {
    // F is a polynimial list
    F = map(dp_ptod,F,V);
    F = map(dpm_dptodpm,F,1);
    N = 1;
  } else if ( type(F[0]) == 9 ) {
    // F is a dpoly list
    F = map(dpm_dptodpm,F,1);
    N = 1;
  } else if ( type(F[0]) == 4 ) {
    // F is a list of poly lists
    N = length(F[0]);
    F = map(dpm_ltod,F,V);
  } else if ( type(F[0]) == 26 ) {
    // F is a DPM list
    for ( N = 0, T = F; T != []; T = cdr(T) ) {
      for ( A = car(T); A; A = dpm_rest(A) ) {
        N1 = dpm_hp(A);
        if ( N1 > N ) N = N1;
      }
    } 
  } else {
    error("lres_setup: arugument type is invalid.");
  }
  G = nd_gr(F,V,H,[0,Ord]|dp=1);
  G = reverse(G);
  dp_ord([0,Ord]);
  One = dp_ptod(1,V);
  return [G,One];
}

def dpm_sort1(L)
{
  return [dpm_sort(L[0]),L[1]];
}

def comp_pos(A,B)
{
  PA = dpm_hp(A[0]); PB = dpm_hp(B[0]);
  if ( PA > PB ) return 1;
  else if ( PA < PB ) return -1;
  else return 0;
}

def lres(F,V,H,Ord)
{
  T0 = time();
  if ( type(Top=getopt(top)) == -1 ) Top = 0;
  if ( type(DP=getopt(dp)) == -1 ) DP = 0;
  if ( type(NoSimpK=getopt(nosimpk)) == -1 ) NoSimpK = 0;
  if ( type(NoPreProj=getopt(nopreproj)) == -1 ) NoPreProj = 0;
  Rtime = Stime = Ptime = 0;
  L = lres_setup(F,V,H,Ord);
  G = L[0];
  One = L[1];
  F = dpm_schreyer_frame(G);
  G = ltov(cons(0,L[0]));
  F = reverse(F);
  F = ltov(F);
  N = length(F);
  for ( I = 0; I < N; I++ ) {
    FI = F[I]; FI[0] = []; 
    FI = map(ltov,FI);
    F[I] = FI;
  }
  R = sortlsb(F);
  B = vector(N+1);
  Bpos = vector(N+1);
  C = vector(N+1);
  H = vector(N+1);
  Z = vector(N+1);
  K = vector(N+1);
  L = vector(N+1);
  K = vector(N+1);
  D = vector(N+1);
  Kind = vector(N+1);

  for ( I = 1; I <= N; I++ ) {
    FI = F[I-1]; Len = length(FI);
    B[I] = FI;
    T = vector(Len-1);
    for ( J = 1; J < Len; J++ ) T[J-1] = FI[J];
    Bpos[I] = qsort(T,newsyz.comp_pos);
    C[I] = vector(Len);
    H[I] = vector(Len);
    Kind[I] = vector(Len);
    K[I] = [];
    Max = 0;
    for ( J = 1; J < Len; J++ )
      if ( (Pos = dpm_hp(FI[J][0])) > Max ) Max = Pos;
    Z[I] = ZI = vector(Max+1);
    for ( J = 1; J <= Max; J++ ) ZI[J] = [];
  }
  T1 = time(); Ftime = T1[0]-T0[0];
  R = ltov(R); Len = length(R);
  print(["Len",Len]);
  for ( I = 0, NF = 0; I < Len; I++ ) {
    if ( !((I+1)%100) ) print(".",2);
    if ( !((I+1)%10000) ) print(I+1);
    if ( !R[I][3] ) continue;
    NF++;
    reduce(R[I],B,Bpos,C,H,Z,K,Kind,G,One,Top);
  }
  print("");
  print(["NF",NF]);
  T0 = time();
  dpm_set_schreyer_level(0);
  D[1] = map(dpm_sort,H[1]);
  for ( I = 2; I <= N; I++ ) {
    // HTT = [Head,Tab,TailTop]
    HTT = create_base_ord(K[I],length(Kind[I-1]));
    Head = HTT[0]; Tab = HTT[1]; TailTopPos = HTT[2];
    if ( !NoPreProj )
      Tab = map(remove_k,map(dpm_sort,Tab),Kind[I-1]);
    else
      Tab = map(dpm_sort,Tab);
    TailTop = dpm_dptodpm(One,TailTopPos);
    if ( !NoSimpK ) {
      print("simplify_k "+rtostr(I)+"...",2);
      simplify_k(Head,Tab,TailTop,One);
      print("done");
    }   
    HI = map(remove_k,map(dpm_sort,H[I]),Kind[I-1]);
    Len = length(HI);
    print("simplify_by_k "+rtostr(I)+"...",2);
    D[I] = vector(Len);
    for ( J = 0; J < Len; J++ ) {
      D[I][J] = simplify_by_k(HI[J],Tab,TailTop,One);
      if ( NoPreProj )
        D[I][J] = remove_k(D[I][J],Kind[I-1]);
    }
    print("done");
  }
  dp_ord([1,0]);
  T1 = time();
  print(["Frame",Ftime,"Prep",Ptime,"Reduce",Rtime,"Search",Stime,"Minimalize",T1[0]-T0[0]]);
//  return [C,H,K,Kind,D];
  D = compress_h(D);
  if ( DP ) return D;
  else return vtol(map(dpmlisttollist,D,V));
}

def create_base_ord(K,N)
{
  Tab = vector(N);
  Ks = [];
  for ( T = K; T != []; T = cdr(T) ) {
    Ks = cons(I=dpm_hp(car(T)[1]),Ks);
    Tab[I] = car(T)[0];
  }
  Others = [];
  for ( I = N-1; I >= 1; I-- )
    if ( !Tab[I] ) Others = cons(I,Others);
  Ks = reverse(Ks);
  dp_ord([4,append(Ks,Others),0]);
  return [ltov(Ks),Tab,car(Others)];
}

/* Head = [i1,i2,...], Tab[i1] = K[0], Tab[i2] = K[1],... */

def simplify_k(Head,Tab,TailTop,One)
{
  N = length(Tab);
  Len = length(Head);
  for ( I = Len-1; I >= 0; I-- ) {
    M = 1;
    R = Tab[Head[I]];
    H = dpm_hm(R); R = dpm_rest(R);
    while ( R && dpm_dptodpm(One,dpm_hp(R)) > TailTop ) {
      Pos = dpm_hp(R); Red = Tab[Pos];
      CRed = dp_hc(dpm_hc(Red));
      CR = dpm_extract(R,Pos);
      L = dpm_remove_cont(CRed*R-CR*Red);
      R = L[1]; M *= CRed/L[0];
    }
    Tab[Head[I]] = M*H+R;
  }
}

def simplify_by_k(F,Tab,TailTop,One)
{
  R = F;
  M = 1;
  while ( R && dpm_dptodpm(One,dpm_hp(R)) > TailTop ) {
    Pos = dpm_hp(R); Red = Tab[Pos];
    CRed = dp_hc(dpm_hc(Red));
    CR = dpm_extract(R,Pos);
    L = dpm_remove_cont(CRed*R-CR*Red);
    R = L[1]; M *= CRed/L[0];
  }
  return (1/M)*R;
}

/* Kind[I]=0 => phi(ei)\in H, Kind[I]=1 => phi(ei)\in K */
def remove_k(F,Kind)
{
  R = [];
  for ( T = F; T; T = dpm_rest(T) )
    if ( Kind[dpm_hp(T)] != 1 ) R = cons(dpm_hm(T),R);
  for ( S = 0; R != []; R = cdr(R) )
    S += car(R);
  return S;
}

def remove_k1(F,Kind)
{
  return [remove_k(F[0],Kind),F[1]];
}

def extract_nonzero(A)
{
  N = length(A);
  R = [];
  for ( C = I = 0; I < N; I++ )
    if ( A[I] ) R=cons(A[I],R);
  return reverse(R);;
}

def nonzero(A)
{
  N = length(A);
  for ( C = I = 0; I < N; I++ )
    if ( A[I] ) C++;
  return C;
}

def phi(C,F)
{
  R = 0;
  for ( T = F; T; T = dpm_rest(T) ) {
    Coef = dpm_hc(T); Pos = dpm_hp(T);
    R += Coef*C[Pos];
  }
  return R;
}

def syz_check(H,I)
{
  HI = H[I];
//  dpm_set_schreyer_level(I-1);
  HI1 = H[I+1];
  Len = size(HI1)[0];
  for ( J = 1; J < Len; J++ ) {
    F = HI1[J];
    R = phi(HI,F);
    if ( R ) print([J,"NG"]);
  }
}

// for compressed C
def phi0(C,F)
{
  R = 0;
  for ( T = F; T; T = dpm_rest(T) ) {
    Coef = dpm_hc(T); Pos = dpm_hp(T);
    R += Coef*C[Pos-1];
  }
  return R;
}

// for compressed H
def syz_check0(H,I)
{
  HI = H[I];
//  dpm_set_schreyer_level(I-1);
  HI1 = H[I+1];
  Len = length(HI1);
  for ( J = 0; J < Len; J++ ) {
    F = HI1[J];
    R = phi0(HI,F);
    if ( R ) print([J,"NG"]);
  }
}

// renumber position
def renumber_pos(F,Tab)
{
  L = [];
  for ( T = F; T; T = dpm_rest(T) )
    L = cons(dpm_hm(T),L);
  R = 0;
  for ( T = L; T != []; T = cdr(T) )
    R += dpm_dptodpm(dpm_hc(car(T)),Tab[dpm_hp(car(T))]);
  return R;
}

// compress H1 and renumber H
def compress(H,H1)
{
  // create index table for H1
  L1 = length(H1);
  Tmp = vector(L1);
  Tab = vector(L1);
  for ( I = 1, J = 1; I < L1; I++ )
    if ( H1[I] ) {
      Tab[I] = J;
      Tmp[J++] = H1[I];
    }
  NH1 = vector(J);
  for ( I = 1; I < J; I++ )
    NH1[I] = Tmp[I];
  if ( H )
    H = map(renumber_pos,H,Tab);
  return [H,NH1];
}

def compress_h(H)
{
  // H = [0,H[1],...,H[L-1]]
  L = length(H);
  NH = vector(L-1);
  H1 = H[1];
  for ( I = 2; I < L; I++ ) {
    R = compress(H[I],H1);
    H1 = R[0];
    NH[I-2] = cdr(vtol(R[1]));
  }
  R = compress(0,H1);
  NH[L-2] = cdr(vtol(R[1]));
  return NH;
}
endmodule$
end$