ocaml/test/nucleic.ml

(***********************************************************************)
(*                                                                     *)
(*                         Caml Special Light                          *)
(*                                                                     *)
(*            Xavier Leroy, projet Cristal, INRIA Rocquencourt         *)
(*                                                                     *)
(*  Copyright 1995 Institut National de Recherche en Informatique et   *)
(*  Automatique.  Distributed only by permission.                      *)
(*                                                                     *)
(***********************************************************************)

(* $Id$ *)

(* Use floating-point arithmetic *)

external (+) : float -> float -> float = "%addfloat"
external (-) : float -> float -> float = "%subfloat"
external ( * ) : float -> float -> float = "%mulfloat"
external (/) : float -> float -> float = "%divfloat"

(* -- MATH UTILITIES --------------------------------------------------------*)

let constant_pi        =  3.14159265358979323846
let constant_minus_pi  = -3.14159265358979323846
let constant_pi2       =  1.57079632679489661923
let constant_minus_pi2 = -1.57079632679489661923

(* -- POINTS ----------------------------------------------------------------*)

type pt = { x : float; y : float; z : float }

let
pt_sub p1 p2
  = { x = p1.x - p2.x; y = p1.y - p2.y; z = p1.z - p2.z }

let
pt_dist p1 p2
  = let dx = p1.x - p2.x
    and dy = p1.y - p2.y
    and dz = p1.z - p2.z
    in
      sqrt ((dx * dx) + (dy * dy) + (dz * dz))

let
pt_phi p
  = let b = atan2 p.x p.z
    in
      atan2 ((cos b) * p.z + (sin b) * p.x) p.y

let
pt_theta p
  =  atan2 p.x p.z

(* -- COORDINATE TRANSFORMATIONS --------------------------------------------*)

(*
   The notation for the transformations follows "Paul, R.P. (1981) Robot
   Manipulators.  MIT Press." with the exception that our transformation
   matrices don't have the perspective terms and are the transpose of
   Paul's one.  See also "M\"antyl\"a, M. (1985) An Introduction to
   Solid Modeling, Computer Science Press" Appendix A.
  
   The components of a transformation matrix are named like this:
  
    a  b  c
    d  e  f
    g  h  i
   tx ty tz
  
   The components tx, ty, and tz are the translation vector.
*)

type tfo =
  {a: float;   b: float;   c: float;
   d: float;   e: float;   f: float;
   g: float;   h: float;   i: float;
   tx: float;  ty: float;  tz: float}

let tfo_id =
  {a=1.0; b=0.0; c=0.0;
   d=0.0; e=1.0; f=0.0;
   g=0.0; h=0.0; i=1.0;
   tx=0.0; ty=0.0; tz=0.0}

(*
   The function "tfo-apply" multiplies a transformation matrix, tfo, by a
   point vector, p.  The result is a new point.
*)

let
tfo_apply t p
  = { x = ((p.x * t.a) + (p.y * t.d) + (p.z * t.g) + t.tx);
      y = ((p.x * t.b) + (p.y * t.e) + (p.z * t.h) + t.ty);
      z = ((p.x * t.c) + (p.y * t.f) + (p.z * t.i) + t.tz) }

(*
   The function "tfo-combine" multiplies two transformation matrices A and B.
   The result is a new matrix which cumulates the transformations described
   by A and B.
*)

let
tfo_combine a b =
(* <HAND_CSE> *)
  (* Hand elimination of common subexpressions.
     Assumes lots of float registers (32 is perfect, 16 still OK).
     Loses on the I386, of course. *)
  let a_a = a.a  and a_b = a.b  and a_c = a.c  and a_d = a.d
  and a_e = a.e  and a_f = a.f  and a_g = a.g  and a_h = a.h
  and a_i = a.i  and a_tx = a.tx  and a_ty = a.ty  and a_tz = a.tz
  and b_a = b.a  and b_b = b.b  and b_c = b.c  and b_d = b.d
  and b_e = b.e  and b_f = b.f  and b_g = b.g  and b_h = b.h
  and b_i = b.i  and b_tx = b.tx  and b_ty = b.ty  and b_tz = b.tz in
    { a = ((a_a * b_a) + (a_b * b_d) + (a_c * b_g));
      b = ((a_a * b_b) + (a_b * b_e) + (a_c * b_h));
      c = ((a_a * b_c) + (a_b * b_f) + (a_c * b_i));
      d = ((a_d * b_a) + (a_e * b_d) + (a_f * b_g));
      e = ((a_d * b_b) + (a_e * b_e) + (a_f * b_h));
      f = ((a_d * b_c) + (a_e * b_f) + (a_f * b_i));
      g = ((a_g * b_a) + (a_h * b_d) + (a_i * b_g));
      h = ((a_g * b_b) + (a_h * b_e) + (a_i * b_h));
      i = ((a_g * b_c) + (a_h * b_f) + (a_i * b_i));
      tx = ((a_tx * b_a) + (a_ty * b_d) + (a_tz * b_g) + b_tx);
      ty = ((a_tx * b_b) + (a_ty * b_e) + (a_tz * b_h) + b_ty);
      tz = ((a_tx * b_c) + (a_ty * b_f) + (a_tz * b_i) + b_tz)
    }
(* </HAND_CSE> *)
 (* Original without CSE *)
(* <NO_CSE> *) (***
    { a = ((a.a * b.a) + (a.b * b.d) + (a.c * b.g));
      b = ((a.a * b.b) + (a.b * b.e) + (a.c * b.h));
      c = ((a.a * b.c) + (a.b * b.f) + (a.c * b.i));
      d = ((a.d * b.a) + (a.e * b.d) + (a.f * b.g));
      e = ((a.d * b.b) + (a.e * b.e) + (a.f * b.h));
      f = ((a.d * b.c) + (a.e * b.f) + (a.f * b.i));
      g = ((a.g * b.a) + (a.h * b.d) + (a.i * b.g));
      h = ((a.g * b.b) + (a.h * b.e) + (a.i * b.h));
      i = ((a.g * b.c) + (a.h * b.f) + (a.i * b.i));
      tx = ((a.tx * b.a) + (a.ty * b.d) + (a.tz * b.g) + b.tx);
      ty = ((a.tx * b.b) + (a.ty * b.e) + (a.tz * b.h) + b.ty);
      tz = ((a.tx * b.c) + (a.ty * b.f) + (a.tz * b.i) + b.tz)
    }
  ***) (* </NO_CSE> *)

(*
   The function "tfo-inv-ortho" computes the inverse of a homogeneous
   transformation matrix.
*)

let
tfo_inv_ortho t =
  { a = t.a; b = t.d; c = t.g;
    d = t.b; e = t.e; f = t.h;
    g = t.c; h = t.f; i = t.i;
    tx = (-.((t.a * t.tx) + (t.b * t.ty) + (t.c * t.tz)));
    ty = (-.((t.d * t.tx) + (t.e * t.ty) + (t.f * t.tz)));
    tz = (-.((t.g * t.tx) + (t.h * t.ty) + (t.i * t.tz)))
  }

(*
   Given three points p1, p2, and p3, the function "tfo-align" computes
   a transformation matrix such that point p1 gets mapped to (0,0,0), p2 gets
   mapped to the Y axis and p3 gets mapped to the YZ plane.
*)

let
tfo_align p1 p2 p3
  = let x31 = p3.x - p1.x in
    let y31 = p3.y - p1.y in
    let z31 = p3.z - p1.z in
    let rotpy = pt_sub p2 p1 in
    let phi = pt_phi rotpy in
    let theta = pt_theta rotpy in
    let sinp = sin phi in
    let sint = sin theta in
    let cosp = cos phi in
    let cost = cos theta in
    let sinpsint = sinp * sint in
    let sinpcost = sinp * cost in
    let cospsint = cosp * sint in
    let cospcost = cosp * cost in
    let rotpz =
      { x = ((cost * x31) - (sint * z31));
        y = ((sinpsint * x31) + (cosp * y31) + (sinpcost * z31));
        z = ((cospsint * x31) + (-.(sinp * y31)) + (cospcost * z31)) } in
    let rho = pt_theta rotpz in
    let cosr = cos rho in
    let sinr = sin rho in
    let x = (-.(p1.x * cost)) + (p1.z * sint) in
    let y = ((-.(p1.x * sinpsint)) - (p1.y * cosp)) - (p1.z * sinpcost) in
    let z = ((-.(p1.x * cospsint) + (p1.y * sinp))) - (p1.z * cospcost) in
      { a = ((cost * cosr) - (cospsint * sinr));
        b = sinpsint;
        c = ((cost * sinr) + (cospsint * cosr));
        d = (sinp * sinr);
        e = cosp;
        f = (-.(sinp * cosr));
        g = ((-.(sint * cosr)) - (cospcost * sinr));
        h = sinpcost;
        i = ((-.(sint * sinr) + (cospcost * cosr)));
        tx = ((x * cosr) - (z * sinr));
        ty = y;
        tz = ((x * sinr + (z * cosr)))
      }

(* -- NUCLEIC ACID CONFORMATIONS DATA BASE ----------------------------------*)

(*
   Numbering of atoms follows the paper:
  
   IUPAC-IUB Joint Commission on Biochemical Nomenclature (JCBN)
   (1983) Abbreviations and Symbols for the Description of
   Conformations of Polynucleotide Chains.  Eur. J. Biochem 131,
   9-15.
*)

(* Define remaining atoms for each nucleotide type. *)

type nuc_specific =
  A of pt*pt*pt*pt*pt*pt*pt*pt
| C of pt*pt*pt*pt*pt*pt
| G of pt*pt*pt*pt*pt*pt*pt*pt*pt
| U of pt*pt*pt*pt*pt

(*
   A n6 n7 n9 c8 h2 h61 h62 h8
   C n4 o2 h41 h42 h5 h6
   G n2 n7 n9 c8 o6 h1 h21 h22 h8
   U o2 o4 h3 h5 h6
*)

(* Define part common to all 4 nucleotide types. *)

type nuc =
  N of tfo*tfo*tfo*tfo*
       pt*pt*pt*pt*pt*pt*pt*pt*pt*pt*pt*pt*
       pt*pt*pt*pt*pt*pt*pt*pt*pt*pt*pt*pt*
       pt*nuc_specific

(*
    dgf_base_tfo  ; defines the standard position for wc and wc_dumas
    p_o3'_275_tfo ; defines the standard position for the connect function
    p_o3'_180_tfo
    p_o3'_60_tfo
    p o1p o2p o5' c5' h5' h5'' c4' h4' o4' c1' h1' c2' h2'' o2' h2' c3'
    h3' o3' n1 n3 c2 c4 c5 c6
*)

let is_A = function
     N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
      p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
      c3',h3',o3',n1,n3,c2,c4,c5,c6,A(_,_,_,_,_,_,_,_)) -> true
   | _ -> false

let is_C = function
     N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
      p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
      c3',h3',o3',n1,n3,c2,c4,c5,c6,C(_,_,_,_,_,_)) -> true
  | _ -> false

let is_G = function
     N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
      p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
      c3',h3',o3',n1,n3,c2,c4,c5,c6,G(_,_,_,_,_,_,_,_,_)) -> true
  | _ -> false

let
nuc_C1'
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = c1'

let
nuc_C2 
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = c2

let
nuc_C3'
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = c3'

let
nuc_C4 
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = c4

let
nuc_C4'
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = c4'

let
nuc_N1 
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = n1

let
nuc_O3'
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = o3'

let
nuc_P
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = p

let
nuc_dgf_base_tfo
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = dgf_base_tfo

let
nuc_p_o3'_180_tfo
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = p_o3'_180_tfo

let
nuc_p_o3'_275_tfo
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = p_o3'_275_tfo

let
nuc_p_o3'_60_tfo
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,_))
  = p_o3'_60_tfo

let
rA_N9  
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,A (n6,n7,n9,c8,h2,h61,h62,h8)))
  = n9

let
rG_N9  
(N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,G (n2,n7,n9,c8,o6,h1,h21,h22,h8)))
  = n9

(* Database of nucleotide conformations: *)

let rA
  = N(
      {    a= -0.0018; b= -0.8207; c=0.5714; (* dgf_base_tfo *)
           d=0.2679; e= -0.5509; f= -0.7904;
           g=0.9634; h=0.1517; i=0.2209;
           tx=0.0073; ty=8.4030; tz=0.6232 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 5.4550; y = 8.2120; z = -2.8810 }, (* C5'  *)
      { x = 5.4546; y = 8.8508; z = -1.9978 }, (* H5'  *)
      { x = 5.7588; y = 8.6625; z = -3.8259 }, (* H5'' *)
      { x = 6.4970; y = 7.1480; z = -2.5980 }, (* C4'  *)
      { x = 7.4896; y = 7.5919; z = -2.5214 }, (* H4'  *)
      { x = 6.1630; y = 6.4860; z = -1.3440 }, (* O4'  *)
      { x = 6.5400; y = 5.1200; z = -1.4190 }, (* C1'  *)
      { x = 7.2763; y = 4.9681; z = -0.6297 }, (* H1'  *)
      { x = 7.1940; y = 4.8830; z = -2.7770 }, (* C2'  *)
      { x = 6.8667; y = 3.9183; z = -3.1647 }, (* H2'' *)
      { x = 8.5860; y = 5.0910; z = -2.6140 }, (* O2'  *)
      { x = 8.9510; y = 4.7626; z = -1.7890 }, (* H2'  *)
      { x = 6.5720; y = 6.0040; z = -3.6090 }, (* C3'  *)
      { x = 5.5636; y = 5.7066; z = -3.8966 }, (* H3'  *)
      { x = 7.3801; y = 6.3562; z = -4.7350 }, (* O3'  *)
      { x = 4.7150; y = 0.4910; z = -0.1360 }, (* N1   *)
      { x = 6.3490; y = 2.1730; z = -0.6020 }, (* N3   *)
      { x = 5.9530; y = 0.9650; z = -0.2670 }, (* C2   *)
      { x = 5.2900; y = 2.9790; z = -0.8260 }, (* C4   *)
      { x = 3.9720; y = 2.6390; z = -0.7330 }, (* C5   *)
      { x = 3.6770; y = 1.3160; z = -0.3660 }, (* C6 *)
      (A (
      { x = 2.4280; y = 0.8450; z = -0.2360 }, (* N6   *)
      { x = 3.1660; y = 3.7290; z = -1.0360 }, (* N7   *)
      { x = 5.3170; y = 4.2990; z = -1.1930 }, (* N9   *)
      { x = 4.0100; y = 4.6780; z = -1.2990 }, (* C8   *)
      { x = 6.6890; y = 0.1903; z = -0.0518 }, (* H2   *)
      { x = 1.6470; y = 1.4460; z = -0.4040 }, (* H61  *)
      { x = 2.2780; y = -0.1080; z = -0.0280 }, (* H62  *)
      { x = 3.4421; y = 5.5744; z = -1.5482 }) (* H8   *)
      )
    )

let rA01
  = N(
      {    a= -0.0043; b= -0.8175; c=0.5759; (* dgf_base_tfo *)
           d=0.2617; e= -0.5567; f= -0.7884;
           g=0.9651; h=0.1473; i=0.2164;
           tx=0.0359; ty=8.3929; tz=0.5532 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 5.4352; y = 8.2183; z = -2.7757 }, (* C5'  *)
      { x = 5.3830; y = 8.7883; z = -1.8481 }, (* H5'  *)
      { x = 5.7729; y = 8.7436; z = -3.6691 }, (* H5'' *)
      { x = 6.4830; y = 7.1518; z = -2.5252 }, (* C4'  *)
      { x = 7.4749; y = 7.5972; z = -2.4482 }, (* H4'  *)
      { x = 6.1626; y = 6.4620; z = -1.2827 }, (* O4'  *)
      { x = 6.5431; y = 5.0992; z = -1.3905 }, (* C1'  *)
      { x = 7.2871; y = 4.9328; z = -0.6114 }, (* H1'  *)
      { x = 7.1852; y = 4.8935; z = -2.7592 }, (* C2'  *)
      { x = 6.8573; y = 3.9363; z = -3.1645 }, (* H2'' *)
      { x = 8.5780; y = 5.1025; z = -2.6046 }, (* O2'  *)
      { x = 8.9516; y = 4.7577; z = -1.7902 }, (* H2'  *)
      { x = 6.5522; y = 6.0300; z = -3.5612 }, (* C3'  *)
      { x = 5.5420; y = 5.7356; z = -3.8459 }, (* H3'  *)
      { x = 7.3487; y = 6.4089; z = -4.6867 }, (* O3'  *)
      { x = 4.7442; y = 0.4514; z = -0.1390 }, (* N1   *)
      { x = 6.3687; y = 2.1459; z = -0.5926 }, (* N3   *)
      { x = 5.9795; y = 0.9335; z = -0.2657 }, (* C2   *)
      { x = 5.3052; y = 2.9471; z = -0.8125 }, (* C4   *)
      { x = 3.9891; y = 2.5987; z = -0.7230 }, (* C5   *)
      { x = 3.7016; y = 1.2717; z = -0.3647 }, (* C6 *)
      (A (
      { x = 2.4553; y = 0.7925; z = -0.2390 }, (* N6   *)
      { x = 3.1770; y = 3.6859; z = -1.0198 }, (* N7   *)
      { x = 5.3247; y = 4.2695; z = -1.1710 }, (* N9   *)
      { x = 4.0156; y = 4.6415; z = -1.2759 }, (* C8   *)
      { x = 6.7198; y = 0.1618; z = -0.0547 }, (* H2   *)
      { x = 1.6709; y = 1.3900; z = -0.4039 }, (* H61  *)
      { x = 2.3107; y = -0.1627; z = -0.0373 }, (* H62  *)
      { x = 3.4426; y = 5.5361; z = -1.5199 }) (* H8   *)
      )
    )

let rA02
  = N(
      {    a=0.5566; b=0.0449; c=0.8296; (* dgf_base_tfo *)
           d=0.5125; e=0.7673; f= -0.3854;
           g= -0.6538; h=0.6397; i=0.4041;
           tx= -9.1161; ty= -3.7679; tz= -2.9968 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 4.5778; y = 6.6594; z = -4.0364 }, (* C5'  *)
      { x = 4.9220; y = 7.1963; z = -4.9204 }, (* H5'  *)
      { x = 3.7996; y = 5.9091; z = -4.1764 }, (* H5'' *)
      { x = 5.7873; y = 5.8869; z = -3.5482 }, (* C4'  *)
      { x = 6.0405; y = 5.0875; z = -4.2446 }, (* H4'  *)
      { x = 6.9135; y = 6.8036; z = -3.4310 }, (* O4'  *)
      { x = 7.7293; y = 6.4084; z = -2.3392 }, (* C1'  *)
      { x = 8.7078; y = 6.1815; z = -2.7624 }, (* H1'  *)
      { x = 7.1305; y = 5.1418; z = -1.7347 }, (* C2'  *)
      { x = 7.2040; y = 5.1982; z = -0.6486 }, (* H2'' *)
      { x = 7.7417; y = 4.0392; z = -2.3813 }, (* O2'  *)
      { x = 8.6785; y = 4.1443; z = -2.5630 }, (* H2'  *)
      { x = 5.6666; y = 5.2728; z = -2.1536 }, (* C3'  *)
      { x = 5.1747; y = 5.9805; z = -1.4863 }, (* H3'  *)
      { x = 4.9997; y = 4.0086; z = -2.1973 }, (* O3'  *)
      { x = 10.3245; y = 8.5459; z = 1.5467 }, (* N1   *)
      { x = 9.8051; y = 6.9432; z = -0.1497 }, (* N3   *)
      { x = 10.5175; y = 7.4328; z = 0.8408 }, (* C2   *)
      { x = 8.7523; y = 7.7422; z = -0.4228 }, (* C4   *)
      { x = 8.4257; y = 8.9060; z = 0.2099 }, (* C5   *)
      { x = 9.2665; y = 9.3242; z = 1.2540 }, (* C6 *)
      (A (
      { x = 9.0664; y = 10.4462; z = 1.9610 }, (* N6   *)
      { x = 7.2750; y = 9.4537; z = -0.3428 }, (* N7   *)
      { x = 7.7962; y = 7.5519; z = -1.3859 }, (* N9   *)
      { x = 6.9479; y = 8.6157; z = -1.2771 }, (* C8   *)
      { x = 11.4063; y = 6.9047; z = 1.1859 }, (* H2   *)
      { x = 8.2845; y = 11.0341; z = 1.7552 }, (* H61  *)
      { x = 9.6584; y = 10.6647; z = 2.7198 }, (* H62  *)
      { x = 6.0430; y = 8.9853; z = -1.7594 }) (* H8   *)
      )
    )
let rA03
  = N(
      {    a= -0.5021; b=0.0731; c=0.8617; (* dgf_base_tfo *)
           d= -0.8112; e=0.3054; f= -0.4986;
           g= -0.2996; h= -0.9494; i= -0.0940;
           tx=6.4273; ty= -5.1944; tz= -3.7807 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 4.1214; y = 6.7116; z = -1.9049 }, (* C5'  *)
      { x = 3.3465; y = 5.9610; z = -2.0607 }, (* H5'  *)
      { x = 4.0789; y = 7.2928; z = -0.9837 }, (* H5'' *)
      { x = 5.4170; y = 5.9293; z = -1.8186 }, (* C4'  *)
      { x = 5.4506; y = 5.3400; z = -0.9023 }, (* H4'  *)
      { x = 5.5067; y = 5.0417; z = -2.9703 }, (* O4'  *)
      { x = 6.8650; y = 4.9152; z = -3.3612 }, (* C1'  *)
      { x = 7.1090; y = 3.8577; z = -3.2603 }, (* H1'  *)
      { x = 7.7152; y = 5.7282; z = -2.3894 }, (* C2'  *)
      { x = 8.5029; y = 6.2356; z = -2.9463 }, (* H2'' *)
      { x = 8.1036; y = 4.8568; z = -1.3419 }, (* O2'  *)
      { x = 8.3270; y = 3.9651; z = -1.6184 }, (* H2'  *)
      { x = 6.7003; y = 6.7565; z = -1.8911 }, (* C3'  *)
      { x = 6.5898; y = 7.5329; z = -2.6482 }, (* H3'  *)
      { x = 7.0505; y = 7.2878; z = -0.6105 }, (* O3'  *)
      { x = 9.6740; y = 4.7656; z = -7.6614 }, (* N1   *)
      { x = 9.0739; y = 4.3013; z = -5.3941 }, (* N3   *)
      { x = 9.8416; y = 4.2192; z = -6.4581 }, (* C2   *)
      { x = 7.9885; y = 5.0632; z = -5.6446 }, (* C4   *)
      { x = 7.6822; y = 5.6856; z = -6.8194 }, (* C5   *)
      { x = 8.5831; y = 5.5215; z = -7.8840 }, (* C6 *)
      (A (
      { x = 8.4084; y = 6.0747; z = -9.0933 }, (* N6   *)
      { x = 6.4857; y = 6.3816; z = -6.7035 }, (* N7   *)
      { x = 6.9740; y = 5.3703; z = -4.7760 }, (* N9   *)
      { x = 6.1133; y = 6.1613; z = -5.4808 }, (* C8   *)
      { x = 10.7627; y = 3.6375; z = -6.4220 }, (* H2   *)
      { x = 7.6031; y = 6.6390; z = -9.2733 }, (* H61  *)
      { x = 9.1004; y = 5.9708; z = -9.7893 }, (* H62  *)
      { x = 5.1705; y = 6.6830; z = -5.3167 }) (* H8   *)
      )
    )

let rA04
  = N(
      {    a= -0.5426; b= -0.8175; c=0.1929; (* dgf_base_tfo *)
           d=0.8304; e= -0.5567; f= -0.0237;
           g=0.1267; h=0.1473; i=0.9809;
           tx= -0.5075; ty=8.3929; tz=0.2229 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 5.4352; y = 8.2183; z = -2.7757 }, (* C5'  *)
      { x = 5.3830; y = 8.7883; z = -1.8481 }, (* H5'  *)
      { x = 5.7729; y = 8.7436; z = -3.6691 }, (* H5'' *)
      { x = 6.4830; y = 7.1518; z = -2.5252 }, (* C4'  *)
      { x = 7.4749; y = 7.5972; z = -2.4482 }, (* H4'  *)
      { x = 6.1626; y = 6.4620; z = -1.2827 }, (* O4'  *)
      { x = 6.5431; y = 5.0992; z = -1.3905 }, (* C1'  *)
      { x = 7.2871; y = 4.9328; z = -0.6114 }, (* H1'  *)
      { x = 7.1852; y = 4.8935; z = -2.7592 }, (* C2'  *)
      { x = 6.8573; y = 3.9363; z = -3.1645 }, (* H2'' *)
      { x = 8.5780; y = 5.1025; z = -2.6046 }, (* O2'  *)
      { x = 8.9516; y = 4.7577; z = -1.7902 }, (* H2'  *)
      { x = 6.5522; y = 6.0300; z = -3.5612 }, (* C3'  *)
      { x = 5.5420; y = 5.7356; z = -3.8459 }, (* H3'  *)
      { x = 7.3487; y = 6.4089; z = -4.6867 }, (* O3'  *)
      { x = 3.6343; y = 2.6680; z = 2.0783 }, (* N1   *)
      { x = 5.4505; y = 3.9805; z = 1.2446 }, (* N3   *)
      { x = 4.7540; y = 3.3816; z = 2.1851 }, (* C2   *)
      { x = 4.8805; y = 3.7951; z = 0.0354 }, (* C4   *)
      { x = 3.7416; y = 3.0925; z = -0.2305 }, (* C5   *)
      { x = 3.0873; y = 2.4980; z = 0.8606 }, (* C6 *)
      (A (
      { x = 1.9600; y = 1.7805; z = 0.7462 }, (* N6   *)
      { x = 3.4605; y = 3.1184; z = -1.5906 }, (* N7   *)
      { x = 5.3247; y = 4.2695; z = -1.1710 }, (* N9   *)
      { x = 4.4244; y = 3.8244; z = -2.0953 }, (* C8   *)
      { x = 5.0814; y = 3.4352; z = 3.2234 }, (* H2   *)
      { x = 1.5423; y = 1.6454; z = -0.1520 }, (* H61  *)
      { x = 1.5716; y = 1.3398; z = 1.5392 }, (* H62  *)
      { x = 4.2675; y = 3.8876; z = -3.1721 }) (* H8   *)
      )
    )

let rA05
  = N(
      {    a= -0.5891; b=0.0449; c=0.8068; (* dgf_base_tfo *)
           d=0.5375; e=0.7673; f=0.3498;
           g= -0.6034; h=0.6397; i= -0.4762;
           tx= -0.3019; ty= -3.7679; tz= -9.5913 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 4.5778; y = 6.6594; z = -4.0364 }, (* C5'  *)
      { x = 4.9220; y = 7.1963; z = -4.9204 }, (* H5'  *)
      { x = 3.7996; y = 5.9091; z = -4.1764 }, (* H5'' *)
      { x = 5.7873; y = 5.8869; z = -3.5482 }, (* C4'  *)
      { x = 6.0405; y = 5.0875; z = -4.2446 }, (* H4'  *)
      { x = 6.9135; y = 6.8036; z = -3.4310 }, (* O4'  *)
      { x = 7.7293; y = 6.4084; z = -2.3392 }, (* C1'  *)
      { x = 8.7078; y = 6.1815; z = -2.7624 }, (* H1'  *)
      { x = 7.1305; y = 5.1418; z = -1.7347 }, (* C2'  *)
      { x = 7.2040; y = 5.1982; z = -0.6486 }, (* H2'' *)
      { x = 7.7417; y = 4.0392; z = -2.3813 }, (* O2'  *)
      { x = 8.6785; y = 4.1443; z = -2.5630 }, (* H2'  *)
      { x = 5.6666; y = 5.2728; z = -2.1536 }, (* C3'  *)
      { x = 5.1747; y = 5.9805; z = -1.4863 }, (* H3'  *)
      { x = 4.9997; y = 4.0086; z = -2.1973 }, (* O3'  *)
      { x = 10.2594; y = 10.6774; z = -1.0056 }, (* N1   *)
      { x = 9.7528; y = 8.7080; z = -2.2631 }, (* N3   *)
      { x = 10.4471; y = 9.7876; z = -1.9791 }, (* C2   *)
      { x = 8.7271; y = 8.5575; z = -1.3991 }, (* C4   *)
      { x = 8.4100; y = 9.3803; z = -0.3580 }, (* C5   *)
      { x = 9.2294; y = 10.5030; z = -0.1574 }, (* C6 *)
      (A (
      { x = 9.0349; y = 11.3951; z = 0.8250 }, (* N6   *)
      { x = 7.2891; y = 8.9068; z = 0.3121 }, (* N7   *)
      { x = 7.7962; y = 7.5519; z = -1.3859 }, (* N9   *)
      { x = 6.9702; y = 7.8292; z = -0.3353 }, (* C8   *)
      { x = 11.3132; y = 10.0537; z = -2.5851 }, (* H2   *)
      { x = 8.2741; y = 11.2784; z = 1.4629 }, (* H61  *)
      { x = 9.6733; y = 12.1368; z = 0.9529 }, (* H62  *)
      { x = 6.0888; y = 7.3990; z = 0.1403 }) (* H8   *)
      )
    )

let rA06
  = N(
      {    a= -0.9815; b=0.0731; c= -0.1772; (* dgf_base_tfo *)
           d=0.1912; e=0.3054; f= -0.9328;
           g= -0.0141; h= -0.9494; i= -0.3137;
           tx=5.7506; ty= -5.1944; tz=4.7470 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 4.1214; y = 6.7116; z = -1.9049 }, (* C5'  *)
      { x = 3.3465; y = 5.9610; z = -2.0607 }, (* H5'  *)
      { x = 4.0789; y = 7.2928; z = -0.9837 }, (* H5'' *)
      { x = 5.4170; y = 5.9293; z = -1.8186 }, (* C4'  *)
      { x = 5.4506; y = 5.3400; z = -0.9023 }, (* H4'  *)
      { x = 5.5067; y = 5.0417; z = -2.9703 }, (* O4'  *)
      { x = 6.8650; y = 4.9152; z = -3.3612 }, (* C1'  *)
      { x = 7.1090; y = 3.8577; z = -3.2603 }, (* H1'  *)
      { x = 7.7152; y = 5.7282; z = -2.3894 }, (* C2'  *)
      { x = 8.5029; y = 6.2356; z = -2.9463 }, (* H2'' *)
      { x = 8.1036; y = 4.8568; z = -1.3419 }, (* O2'  *)
      { x = 8.3270; y = 3.9651; z = -1.6184 }, (* H2'  *)
      { x = 6.7003; y = 6.7565; z = -1.8911 }, (* C3'  *)
      { x = 6.5898; y = 7.5329; z = -2.6482 }, (* H3'  *)
      { x = 7.0505; y = 7.2878; z = -0.6105 }, (* O3'  *)
      { x = 6.6624; y = 3.5061; z = -8.2986 }, (* N1   *)
      { x = 6.5810; y = 3.2570; z = -5.9221 }, (* N3   *)
      { x = 6.5151; y = 2.8263; z = -7.1625 }, (* C2   *)
      { x = 6.8364; y = 4.5817; z = -5.8882 }, (* C4   *)
      { x = 7.0116; y = 5.4064; z = -6.9609 }, (* C5   *)
      { x = 6.9173; y = 4.8260; z = -8.2361 }, (* C6 *)
      (A (
      { x = 7.0668; y = 5.5163; z = -9.3763 }, (* N6   *)
      { x = 7.2573; y = 6.7070; z = -6.5394 }, (* N7   *)
      { x = 6.9740; y = 5.3703; z = -4.7760 }, (* N9   *)
      { x = 7.2238; y = 6.6275; z = -5.2453 }, (* C8   *)
      { x = 6.3146; y = 1.7741; z = -7.3641 }, (* H2   *)
      { x = 7.2568; y = 6.4972; z = -9.3456 }, (* H61  *)
      { x = 7.0437; y = 5.0478; z = -10.2446 }, (* H62  *)
      { x = 7.4108; y = 7.6227; z = -4.8418 }) (* H8   *)
      )
    )

let rA07
  = N(
      {    a=0.2379; b=0.1310; c= -0.9624; (* dgf_base_tfo *)
           d= -0.5876; e= -0.7696; f= -0.2499;
           g= -0.7734; h=0.6249; i= -0.1061;
           tx=30.9870; ty= -26.9344; tz=42.6416 },
      {    a=0.7529; b=0.1548; c=0.6397; (* P_O3'_275_tfo *)
           d=0.2952; e= -0.9481; f= -0.1180;
           g=0.5882; h=0.2777; i= -0.7595;
           tx= -58.8919; ty= -11.3095; tz=6.0866 },
      {    a= -0.0239; b=0.9667; c= -0.2546; (* P_O3'_180_tfo *)
           d=0.9731; e= -0.0359; f= -0.2275;
           g= -0.2290; h= -0.2532; i= -0.9399;
           tx=3.5401; ty= -29.7913; tz=52.2796 },
      {    a= -0.8912; b= -0.4531; c=0.0242; (* P_O3'_60_tfo *)
           d= -0.1183; e=0.1805; f= -0.9764;
           g=0.4380; h= -0.8730; i= -0.2145;
           tx=19.9023; ty=54.8054; tz=15.2799 },
      { x = 41.8210; y = 8.3880; z = 43.5890 }, (* P    *)
      { x = 42.5400; y = 8.0450; z = 44.8330 }, (* O1P  *)
      { x = 42.2470; y = 9.6920; z = 42.9910 }, (* O2P  *)
      { x = 40.2550; y = 8.2030; z = 43.7340 }, (* O5'  *)
      { x = 39.3505; y = 8.4697; z = 42.6565 }, (* C5'  *)
      { x = 39.1377; y = 7.5433; z = 42.1230 }, (* H5'  *)
      { x = 39.7203; y = 9.3119; z = 42.0717 }, (* H5'' *)
      { x = 38.0405; y = 8.9195; z = 43.2869 }, (* C4'  *)
      { x = 37.3687; y = 9.3036; z = 42.5193 }, (* H4'  *)
      { x = 37.4319; y = 7.8146; z = 43.9387 }, (* O4'  *)
      { x = 37.1959; y = 8.1354; z = 45.3237 }, (* C1'  *)
      { x = 36.1788; y = 8.5202; z = 45.3970 }, (* H1'  *)
      { x = 38.1721; y = 9.2328; z = 45.6504 }, (* C2'  *)
      { x = 39.1555; y = 8.7939; z = 45.8188 }, (* H2'' *)
      { x = 37.7862; y = 10.0617; z = 46.7013 }, (* O2'  *)
      { x = 37.3087; y = 9.6229; z = 47.4092 }, (* H2'  *)
      { x = 38.1844; y = 10.0268; z = 44.3367 }, (* C3'  *)
      { x = 39.1578; y = 10.5054; z = 44.2289 }, (* H3'  *)
      { x = 37.0547; y = 10.9127; z = 44.3441 }, (* O3'  *)
      { x = 34.8811; y = 4.2072; z = 47.5784 }, (* N1   *)
      { x = 35.1084; y = 6.1336; z = 46.1818 }, (* N3   *)
      { x = 34.4108; y = 5.1360; z = 46.7207 }, (* C2   *)
      { x = 36.3908; y = 6.1224; z = 46.6053 }, (* C4   *)
      { x = 36.9819; y = 5.2334; z = 47.4697 }, (* C5   *)
      { x = 36.1786; y = 4.1985; z = 48.0035 }, (* C6 *)
      (A (
      { x = 36.6103; y = 3.2749; z = 48.8452 }, (* N6   *)
      { x = 38.3236; y = 5.5522; z = 47.6595 }, (* N7   *)
      { x = 37.3887; y = 7.0024; z = 46.2437 }, (* N9   *)
      { x = 38.5055; y = 6.6096; z = 46.9057 }, (* C8   *)
      { x = 33.3553; y = 5.0152; z = 46.4771 }, (* H2   *)
      { x = 37.5730; y = 3.2804; z = 49.1507 }, (* H61  *)
      { x = 35.9775; y = 2.5638; z = 49.1828 }, (* H62  *)
      { x = 39.5461; y = 6.9184; z = 47.0041 }) (* H8   *)
      )
    )

let rA08
  = N(
      {    a=0.1084; b= -0.0895; c= -0.9901; (* dgf_base_tfo *)
           d=0.9789; e= -0.1638; f=0.1220;
           g= -0.1731; h= -0.9824; i=0.0698;
           tx= -2.9039; ty=47.2655; tz=33.0094 },
      {    a=0.7529; b=0.1548; c=0.6397; (* P_O3'_275_tfo *)
           d=0.2952; e= -0.9481; f= -0.1180;
           g=0.5882; h=0.2777; i= -0.7595;
           tx= -58.8919; ty= -11.3095; tz=6.0866 },
      {    a= -0.0239; b=0.9667; c= -0.2546; (* P_O3'_180_tfo *)
           d=0.9731; e= -0.0359; f= -0.2275;
           g= -0.2290; h= -0.2532; i= -0.9399;
           tx=3.5401; ty= -29.7913; tz=52.2796 },
      {    a= -0.8912; b= -0.4531; c=0.0242; (* P_O3'_60_tfo *)
           d= -0.1183; e=0.1805; f= -0.9764;
           g=0.4380; h= -0.8730; i= -0.2145;
           tx=19.9023; ty=54.8054; tz=15.2799 },
      { x = 41.8210; y = 8.3880; z = 43.5890 }, (* P    *)
      { x = 42.5400; y = 8.0450; z = 44.8330 }, (* O1P  *)
      { x = 42.2470; y = 9.6920; z = 42.9910 }, (* O2P  *)
      { x = 40.2550; y = 8.2030; z = 43.7340 }, (* O5'  *)
      { x = 39.4850; y = 8.9301; z = 44.6977 }, (* C5'  *)
      { x = 39.0638; y = 9.8199; z = 44.2296 }, (* H5'  *)
      { x = 40.0757; y = 9.0713; z = 45.6029 }, (* H5'' *)
      { x = 38.3102; y = 8.0414; z = 45.0789 }, (* C4'  *)
      { x = 37.7842; y = 8.4637; z = 45.9351 }, (* H4'  *)
      { x = 37.4200; y = 7.9453; z = 43.9769 }, (* O4'  *)
      { x = 37.2249; y = 6.5609; z = 43.6273 }, (* C1'  *)
      { x = 36.3360; y = 6.2168; z = 44.1561 }, (* H1'  *)
      { x = 38.4347; y = 5.8414; z = 44.1590 }, (* C2'  *)
      { x = 39.2688; y = 5.9974; z = 43.4749 }, (* H2'' *)
      { x = 38.2344; y = 4.4907; z = 44.4348 }, (* O2'  *)
      { x = 37.6374; y = 4.0386; z = 43.8341 }, (* H2'  *)
      { x = 38.6926; y = 6.6079; z = 45.4637 }, (* C3'  *)
      { x = 39.7585; y = 6.5640; z = 45.6877 }, (* H3'  *)
      { x = 37.8238; y = 6.0705; z = 46.4723 }, (* O3'  *)
      { x = 33.9162; y = 6.2598; z = 39.7758 }, (* N1   *)
      { x = 34.6709; y = 6.5759; z = 42.0215 }, (* N3   *)
      { x = 33.7257; y = 6.5186; z = 41.0858 }, (* C2   *)
      { x = 35.8935; y = 6.3324; z = 41.5018 }, (* C4   *)
      { x = 36.2105; y = 6.0601; z = 40.1932 }, (* C5   *)
      { x = 35.1538; y = 6.0151; z = 39.2537 }, (* C6 *)
      (A (
      { x = 35.3088; y = 5.7642; z = 37.9649 }, (* N6   *)
      { x = 37.5818; y = 5.8677; z = 40.0507 }, (* N7   *)
      { x = 37.0932; y = 6.3197; z = 42.1810 }, (* N9   *)
      { x = 38.0509; y = 6.0354; z = 41.2635 }, (* C8   *)
      { x = 32.6830; y = 6.6898; z = 41.3532 }, (* H2   *)
      { x = 36.2305; y = 5.5855; z = 37.5925 }, (* H61  *)
      { x = 34.5056; y = 5.7512; z = 37.3528 }, (* H62  *)
      { x = 39.1318; y = 5.8993; z = 41.2285 }) (* H8   *)
      )
    )

let rA09
  = N(
      {    a=0.8467; b=0.4166; c= -0.3311; (* dgf_base_tfo *)
           d= -0.3962; e=0.9089; f=0.1303;
           g=0.3552; h=0.0209; i=0.9346;
           tx= -42.7319; ty= -26.6223; tz= -29.8163 },
      {    a=0.7529; b=0.1548; c=0.6397; (* P_O3'_275_tfo *)
           d=0.2952; e= -0.9481; f= -0.1180;
           g=0.5882; h=0.2777; i= -0.7595;
           tx= -58.8919; ty= -11.3095; tz=6.0866 },
      {    a= -0.0239; b=0.9667; c= -0.2546; (* P_O3'_180_tfo *)
           d=0.9731; e= -0.0359; f= -0.2275;
           g= -0.2290; h= -0.2532; i= -0.9399;
           tx=3.5401; ty= -29.7913; tz=52.2796 },
      {    a= -0.8912; b= -0.4531; c=0.0242; (* P_O3'_60_tfo *)
           d= -0.1183; e=0.1805; f= -0.9764;
           g=0.4380; h= -0.8730; i= -0.2145;
           tx=19.9023; ty=54.8054; tz=15.2799 },
      { x = 41.8210; y = 8.3880; z = 43.5890 }, (* P    *)
      { x = 42.5400; y = 8.0450; z = 44.8330 }, (* O1P  *)
      { x = 42.2470; y = 9.6920; z = 42.9910 }, (* O2P  *)
      { x = 40.2550; y = 8.2030; z = 43.7340 }, (* O5'  *)
      { x = 39.3505; y = 8.4697; z = 42.6565 }, (* C5'  *)
      { x = 39.1377; y = 7.5433; z = 42.1230 }, (* H5'  *)
      { x = 39.7203; y = 9.3119; z = 42.0717 }, (* H5'' *)
      { x = 38.0405; y = 8.9195; z = 43.2869 }, (* C4'  *)
      { x = 37.6479; y = 8.1347; z = 43.9335 }, (* H4'  *)
      { x = 38.2691; y = 10.0933; z = 44.0524 }, (* O4'  *)
      { x = 37.3999; y = 11.1488; z = 43.5973 }, (* C1'  *)
      { x = 36.5061; y = 11.1221; z = 44.2206 }, (* H1'  *)
      { x = 37.0364; y = 10.7838; z = 42.1836 }, (* C2'  *)
      { x = 37.8636; y = 11.0489; z = 41.5252 }, (* H2'' *)
      { x = 35.8275; y = 11.3133; z = 41.7379 }, (* O2'  *)
      { x = 35.6214; y = 12.1896; z = 42.0714 }, (* H2'  *)
      { x = 36.9316; y = 9.2556; z = 42.2837 }, (* C3'  *)
      { x = 37.1778; y = 8.8260; z = 41.3127 }, (* H3'  *)
      { x = 35.6285; y = 8.9334; z = 42.7926 }, (* O3'  *)
      { x = 38.1482; y = 15.2833; z = 46.4641 }, (* N1   *)
      { x = 37.3641; y = 13.0968; z = 45.9007 }, (* N3   *)
      { x = 37.5032; y = 14.1288; z = 46.7300 }, (* C2   *)
      { x = 37.9570; y = 13.3377; z = 44.7113 }, (* C4   *)
      { x = 38.6397; y = 14.4660; z = 44.3267 }, (* C5   *)
      { x = 38.7473; y = 15.5229; z = 45.2609 }, (* C6 *)
      (A (
      { x = 39.3720; y = 16.6649; z = 45.0297 }, (* N6   *)
      { x = 39.1079; y = 14.3351; z = 43.0223 }, (* N7   *)
      { x = 38.0132; y = 12.4868; z = 43.6280 }, (* N9   *)
      { x = 38.7058; y = 13.1402; z = 42.6620 }, (* C8   *)
      { x = 37.0731; y = 14.0857; z = 47.7306 }, (* H2   *)
      { x = 39.8113; y = 16.8281; z = 44.1350 }, (* H61  *)
      { x = 39.4100; y = 17.3741; z = 45.7478 }, (* H62  *)
      { x = 39.0412; y = 12.9660; z = 41.6397 }) (* H8   *)
      )
    )

let rA10
  = N(
      {    a=0.7063; b=0.6317; c= -0.3196; (* dgf_base_tfo *)
           d= -0.0403; e= -0.4149; f= -0.9090;
           g= -0.7068; h=0.6549; i= -0.2676;
           tx=6.4402; ty= -52.1496; tz=30.8246 },
      {    a=0.7529; b=0.1548; c=0.6397; (* P_O3'_275_tfo *)
           d=0.2952; e= -0.9481; f= -0.1180;
           g=0.5882; h=0.2777; i= -0.7595;
           tx= -58.8919; ty= -11.3095; tz=6.0866 },
      {    a= -0.0239; b=0.9667; c= -0.2546; (* P_O3'_180_tfo *)
           d=0.9731; e= -0.0359; f= -0.2275;
           g= -0.2290; h= -0.2532; i= -0.9399;
           tx=3.5401; ty= -29.7913; tz=52.2796 },
      {    a= -0.8912; b= -0.4531; c=0.0242; (* P_O3'_60_tfo *)
           d= -0.1183; e=0.1805; f= -0.9764;
           g=0.4380; h= -0.8730; i= -0.2145;
           tx=19.9023; ty=54.8054; tz=15.2799 },
      { x = 41.8210; y = 8.3880; z = 43.5890 }, (* P    *)
      { x = 42.5400; y = 8.0450; z = 44.8330 }, (* O1P  *)
      { x = 42.2470; y = 9.6920; z = 42.9910 }, (* O2P  *)
      { x = 40.2550; y = 8.2030; z = 43.7340 }, (* O5'  *)
      { x = 39.4850; y = 8.9301; z = 44.6977 }, (* C5'  *)
      { x = 39.0638; y = 9.8199; z = 44.2296 }, (* H5'  *)
      { x = 40.0757; y = 9.0713; z = 45.6029 }, (* H5'' *)
      { x = 38.3102; y = 8.0414; z = 45.0789 }, (* C4'  *)
      { x = 37.7099; y = 7.8166; z = 44.1973 }, (* H4'  *)
      { x = 38.8012; y = 6.8321; z = 45.6380 }, (* O4'  *)
      { x = 38.2431; y = 6.6413; z = 46.9529 }, (* C1'  *)
      { x = 37.3505; y = 6.0262; z = 46.8385 }, (* H1'  *)
      { x = 37.8484; y = 8.0156; z = 47.4214 }, (* C2'  *)
      { x = 38.7381; y = 8.5406; z = 47.7690 }, (* H2'' *)
      { x = 36.8286; y = 8.0368; z = 48.3701 }, (* O2'  *)
      { x = 36.8392; y = 7.3063; z = 48.9929 }, (* H2'  *)
      { x = 37.3576; y = 8.6512; z = 46.1132 }, (* C3'  *)
      { x = 37.5207; y = 9.7275; z = 46.1671 }, (* H3'  *)
      { x = 35.9985; y = 8.2392; z = 45.9032 }, (* O3'  *)
      { x = 39.9117; y = 2.2278; z = 48.8527 }, (* N1   *)
      { x = 38.6207; y = 3.6941; z = 47.4757 }, (* N3   *)
      { x = 38.9872; y = 2.4888; z = 47.9057 }, (* C2   *)
      { x = 39.2961; y = 4.6720; z = 48.1174 }, (* C4   *)
      { x = 40.2546; y = 4.5307; z = 49.0912 }, (* C5   *)
      { x = 40.5932; y = 3.2189; z = 49.4985 }, (* C6 *)
      (A (
      { x = 41.4938; y = 2.9317; z = 50.4229 }, (* N6   *)
      { x = 40.7195; y = 5.7755; z = 49.5060 }, (* N7   *)
      { x = 39.1730; y = 6.0305; z = 47.9170 }, (* N9   *)
      { x = 40.0413; y = 6.6250; z = 48.7728 }, (* C8   *)
      { x = 38.5257; y = 1.5960; z = 47.4838 }, (* H2   *)
      { x = 41.9907; y = 3.6753; z = 50.8921 }, (* H61  *)
      { x = 41.6848; y = 1.9687; z = 50.6599 }, (* H62  *)
      { x = 40.3571; y = 7.6321; z = 49.0452 }) (* H8   *)
      )
    )

let rAs = [rA01;rA02;rA03;rA04;rA05;rA06;rA07;rA08;rA09;rA10]

let rC
  = N(
      {    a= -0.0359; b= -0.8071; c=0.5894; (* dgf_base_tfo *)
           d= -0.2669; e=0.5761; f=0.7726;
           g= -0.9631; h= -0.1296; i= -0.2361;
           tx=0.1584; ty=8.3434; tz=0.5434 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 5.2430; y = -8.2420; z = 2.8260 }, (* C5'  *)
      { x = 5.1974; y = -8.8497; z = 1.9223 }, (* H5'  *)
      { x = 5.5548; y = -8.7348; z = 3.7469 }, (* H5'' *)
      { x = 6.3140; y = -7.2060; z = 2.5510 }, (* C4'  *)
      { x = 7.2954; y = -7.6762; z = 2.4898 }, (* H4'  *)
      { x = 6.0140; y = -6.5420; z = 1.2890 }, (* O4'  *)
      { x = 6.4190; y = -5.1840; z = 1.3620 }, (* C1'  *)
      { x = 7.1608; y = -5.0495; z = 0.5747 }, (* H1'  *)
      { x = 7.0760; y = -4.9560; z = 2.7270 }, (* C2'  *)
      { x = 6.7770; y = -3.9803; z = 3.1099 }, (* H2'' *)
      { x = 8.4500; y = -5.1930; z = 2.5810 }, (* O2'  *)
      { x = 8.8309; y = -4.8755; z = 1.7590 }, (* H2'  *)
      { x = 6.4060; y = -6.0590; z = 3.5580 }, (* C3'  *)
      { x = 5.4021; y = -5.7313; z = 3.8281 }, (* H3'  *)
      { x = 7.1570; y = -6.4240; z = 4.7070 }, (* O3'  *)
      { x = 5.2170; y = -4.3260; z = 1.1690 }, (* N1   *)
      { x = 4.2960; y = -2.2560; z = 0.6290 }, (* N3   *)
      { x = 5.4330; y = -3.0200; z = 0.7990 }, (* C2   *)
      { x = 2.9930; y = -2.6780; z = 0.7940 }, (* C4   *)
      { x = 2.8670; y = -4.0630; z = 1.1830 }, (* C5   *)
      { x = 3.9570; y = -4.8300; z = 1.3550 }, (* C6 *)
      (C (
      { x = 2.0187; y = -1.8047; z = 0.5874 }, (* N4   *)
      { x = 6.5470; y = -2.5560; z = 0.6290 }, (* O2   *)
      { x = 1.0684; y = -2.1236; z = 0.7109 }, (* H41  *)
      { x = 2.2344; y = -0.8560; z = 0.3162 }, (* H42  *)
      { x = 1.8797; y = -4.4972; z = 1.3404 }, (* H5   *)
      { x = 3.8479; y = -5.8742; z = 1.6480 }) (* H6   *)
      )
    )

let rC01
  = N(
      {    a= -0.0137; b= -0.8012; c=0.5983; (* dgf_base_tfo *)
           d= -0.2523; e=0.5817; f=0.7733;
           g= -0.9675; h= -0.1404; i= -0.2101;
           tx=0.2031; ty=8.3874; tz=0.4228 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 5.2416; y = -8.2422; z = 2.8181 }, (* C5'  *)
      { x = 5.2050; y = -8.8128; z = 1.8901 }, (* H5'  *)
      { x = 5.5368; y = -8.7738; z = 3.7227 }, (* H5'' *)
      { x = 6.3232; y = -7.2037; z = 2.6002 }, (* C4'  *)
      { x = 7.3048; y = -7.6757; z = 2.5577 }, (* H4'  *)
      { x = 6.0635; y = -6.5092; z = 1.3456 }, (* O4'  *)
      { x = 6.4697; y = -5.1547; z = 1.4629 }, (* C1'  *)
      { x = 7.2354; y = -5.0043; z = 0.7018 }, (* H1'  *)
      { x = 7.0856; y = -4.9610; z = 2.8521 }, (* C2'  *)
      { x = 6.7777; y = -3.9935; z = 3.2487 }, (* H2'' *)
      { x = 8.4627; y = -5.1992; z = 2.7423 }, (* O2'  *)
      { x = 8.8693; y = -4.8638; z = 1.9399 }, (* H2'  *)
      { x = 6.3877; y = -6.0809; z = 3.6362 }, (* C3'  *)
      { x = 5.3770; y = -5.7562; z = 3.8834 }, (* H3'  *)
      { x = 7.1024; y = -6.4754; z = 4.7985 }, (* O3'  *)
      { x = 5.2764; y = -4.2883; z = 1.2538 }, (* N1   *)
      { x = 4.3777; y = -2.2062; z = 0.7229 }, (* N3   *)
      { x = 5.5069; y = -2.9779; z = 0.9088 }, (* C2   *)
      { x = 3.0693; y = -2.6246; z = 0.8500 }, (* C4   *)
      { x = 2.9279; y = -4.0146; z = 1.2149 }, (* C5   *)
      { x = 4.0101; y = -4.7892; z = 1.4017 }, (* C6 *)
      (C (
      { x = 2.1040; y = -1.7437; z = 0.6331 }, (* N4   *)
      { x = 6.6267; y = -2.5166; z = 0.7728 }, (* O2   *)
      { x = 1.1496; y = -2.0600; z = 0.7287 }, (* H41  *)
      { x = 2.3303; y = -0.7921; z = 0.3815 }, (* H42  *)
      { x = 1.9353; y = -4.4465; z = 1.3419 }, (* H5   *)
      { x = 3.8895; y = -5.8371; z = 1.6762 }) (* H6   *)
      )
    )

let rC02
  = N(
      {    a=0.5141; b=0.0246; c=0.8574; (* dgf_base_tfo *)
           d= -0.5547; e= -0.7529; f=0.3542;
           g=0.6542; h= -0.6577; i= -0.3734;
           tx= -9.1111; ty= -3.4598; tz= -3.2939 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 4.3825; y = -6.6585; z = 4.0489 }, (* C5'  *)
      { x = 4.6841; y = -7.2019; z = 4.9443 }, (* H5'  *)
      { x = 3.6189; y = -5.8889; z = 4.1625 }, (* H5'' *)
      { x = 5.6255; y = -5.9175; z = 3.5998 }, (* C4'  *)
      { x = 5.8732; y = -5.1228; z = 4.3034 }, (* H4'  *)
      { x = 6.7337; y = -6.8605; z = 3.5222 }, (* O4'  *)
      { x = 7.5932; y = -6.4923; z = 2.4548 }, (* C1'  *)
      { x = 8.5661; y = -6.2983; z = 2.9064 }, (* H1'  *)
      { x = 7.0527; y = -5.2012; z = 1.8322 }, (* C2'  *)
      { x = 7.1627; y = -5.2525; z = 0.7490 }, (* H2'' *)
      { x = 7.6666; y = -4.1249; z = 2.4880 }, (* O2'  *)
      { x = 8.5944; y = -4.2543; z = 2.6981 }, (* H2'  *)
      { x = 5.5661; y = -5.3029; z = 2.2009 }, (* C3'  *)
      { x = 5.0841; y = -6.0018; z = 1.5172 }, (* H3'  *)
      { x = 4.9062; y = -4.0452; z = 2.2042 }, (* O3'  *)
      { x = 7.6298; y = -7.6136; z = 1.4752 }, (* N1   *)
      { x = 8.6945; y = -8.7046; z = -0.2857 }, (* N3   *)
      { x = 8.6943; y = -7.6514; z = 0.6066 }, (* C2   *)
      { x = 7.7426; y = -9.6987; z = -0.3801 }, (* C4   *)
      { x = 6.6642; y = -9.5742; z = 0.5722 }, (* C5   *)
      { x = 6.6391; y = -8.5592; z = 1.4526 }, (* C6 *)
      (C (
      { x = 7.9033; y = -10.6371; z = -1.3010 }, (* N4   *)
      { x = 9.5840; y = -6.8186; z = 0.6136 }, (* O2   *)
      { x = 7.2009; y = -11.3604; z = -1.3619 }, (* H41  *)
      { x = 8.7058; y = -10.6168; z = -1.9140 }, (* H42  *)
      { x = 5.8585; y = -10.3083; z = 0.5822 }, (* H5   *)
      { x = 5.8197; y = -8.4773; z = 2.1667 }) (* H6   *)
      )
    )

let rC03
  = N(
      {    a= -0.4993; b=0.0476; c=0.8651; (* dgf_base_tfo *)
           d=0.8078; e= -0.3353; f=0.4847;
           g=0.3132; h=0.9409; i=0.1290;
           tx=6.2989; ty= -5.2303; tz= -3.8577 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 3.9938; y = -6.7042; z = 1.9023 }, (* C5'  *)
      { x = 3.2332; y = -5.9343; z = 2.0319 }, (* H5'  *)
      { x = 3.9666; y = -7.2863; z = 0.9812 }, (* H5'' *)
      { x = 5.3098; y = -5.9546; z = 1.8564 }, (* C4'  *)
      { x = 5.3863; y = -5.3702; z = 0.9395 }, (* H4'  *)
      { x = 5.3851; y = -5.0642; z = 3.0076 }, (* O4'  *)
      { x = 6.7315; y = -4.9724; z = 3.4462 }, (* C1'  *)
      { x = 7.0033; y = -3.9202; z = 3.3619 }, (* H1'  *)
      { x = 7.5997; y = -5.8018; z = 2.4948 }, (* C2'  *)
      { x = 8.3627; y = -6.3254; z = 3.0707 }, (* H2'' *)
      { x = 8.0410; y = -4.9501; z = 1.4724 }, (* O2'  *)
      { x = 8.2781; y = -4.0644; z = 1.7570 }, (* H2'  *)
      { x = 6.5701; y = -6.8129; z = 1.9714 }, (* C3'  *)
      { x = 6.4186; y = -7.5809; z = 2.7299 }, (* H3'  *)
      { x = 6.9357; y = -7.3841; z = 0.7235 }, (* O3'  *)
      { x = 6.8024; y = -5.4718; z = 4.8475 }, (* N1   *)
      { x = 7.9218; y = -5.5700; z = 6.8877 }, (* N3   *)
      { x = 7.8908; y = -5.0886; z = 5.5944 }, (* C2   *)
      { x = 6.9789; y = -6.3827; z = 7.4823 }, (* C4   *)
      { x = 5.8742; y = -6.7319; z = 6.6202 }, (* C5   *)
      { x = 5.8182; y = -6.2769; z = 5.3570 }, (* C6 *)
      (C (
      { x = 7.1702; y = -6.7511; z = 8.7402 }, (* N4   *)
      { x = 8.7747; y = -4.3728; z = 5.1568 }, (* O2   *)
      { x = 6.4741; y = -7.3461; z = 9.1662 }, (* H41  *)
      { x = 7.9889; y = -6.4396; z = 9.2429 }, (* H42  *)
      { x = 5.0736; y = -7.3713; z = 6.9922 }, (* H5   *)
      { x = 4.9784; y = -6.5473; z = 4.7170 }) (* H6   *)
      )
    )

let rC04
  = N(
      {    a= -0.5669; b= -0.8012; c=0.1918; (* dgf_base_tfo *)
           d= -0.8129; e=0.5817; f=0.0273;
           g= -0.1334; h= -0.1404; i= -0.9811;
           tx= -0.3279; ty=8.3874; tz=0.3355 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 5.2416; y = -8.2422; z = 2.8181 }, (* C5'  *)
      { x = 5.2050; y = -8.8128; z = 1.8901 }, (* H5'  *)
      { x = 5.5368; y = -8.7738; z = 3.7227 }, (* H5'' *)
      { x = 6.3232; y = -7.2037; z = 2.6002 }, (* C4'  *)
      { x = 7.3048; y = -7.6757; z = 2.5577 }, (* H4'  *)
      { x = 6.0635; y = -6.5092; z = 1.3456 }, (* O4'  *)
      { x = 6.4697; y = -5.1547; z = 1.4629 }, (* C1'  *)
      { x = 7.2354; y = -5.0043; z = 0.7018 }, (* H1'  *)
      { x = 7.0856; y = -4.9610; z = 2.8521 }, (* C2'  *)
      { x = 6.7777; y = -3.9935; z = 3.2487 }, (* H2'' *)
      { x = 8.4627; y = -5.1992; z = 2.7423 }, (* O2'  *)
      { x = 8.8693; y = -4.8638; z = 1.9399 }, (* H2'  *)
      { x = 6.3877; y = -6.0809; z = 3.6362 }, (* C3'  *)
      { x = 5.3770; y = -5.7562; z = 3.8834 }, (* H3'  *)
      { x = 7.1024; y = -6.4754; z = 4.7985 }, (* O3'  *)
      { x = 5.2764; y = -4.2883; z = 1.2538 }, (* N1   *)
      { x = 3.8961; y = -3.0896; z = -0.1893 }, (* N3   *)
      { x = 5.0095; y = -3.8907; z = -0.0346 }, (* C2   *)
      { x = 3.0480; y = -2.6632; z = 0.8116 }, (* C4   *)
      { x = 3.4093; y = -3.1310; z = 2.1292 }, (* C5   *)
      { x = 4.4878; y = -3.9124; z = 2.3088 }, (* C6 *)
      (C (
      { x = 2.0216; y = -1.8941; z = 0.4804 }, (* N4   *)
      { x = 5.7005; y = -4.2164; z = -0.9842 }, (* O2   *)
      { x = 1.4067; y = -1.5873; z = 1.2205 }, (* H41  *)
      { x = 1.8721; y = -1.6319; z = -0.4835 }, (* H42  *)
      { x = 2.8048; y = -2.8507; z = 2.9918 }, (* H5   *)
      { x = 4.7491; y = -4.2593; z = 3.3085 }) (* H6   *)
      )
    )

let rC05
  = N(
      {    a= -0.6298; b=0.0246; c=0.7763; (* dgf_base_tfo *)
           d= -0.5226; e= -0.7529; f= -0.4001;
           g=0.5746; h= -0.6577; i=0.4870;
           tx= -0.0208; ty= -3.4598; tz= -9.6882 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 4.3825; y = -6.6585; z = 4.0489 }, (* C5'  *)
      { x = 4.6841; y = -7.2019; z = 4.9443 }, (* H5'  *)
      { x = 3.6189; y = -5.8889; z = 4.1625 }, (* H5'' *)
      { x = 5.6255; y = -5.9175; z = 3.5998 }, (* C4'  *)
      { x = 5.8732; y = -5.1228; z = 4.3034 }, (* H4'  *)
      { x = 6.7337; y = -6.8605; z = 3.5222 }, (* O4'  *)
      { x = 7.5932; y = -6.4923; z = 2.4548 }, (* C1'  *)
      { x = 8.5661; y = -6.2983; z = 2.9064 }, (* H1'  *)
      { x = 7.0527; y = -5.2012; z = 1.8322 }, (* C2'  *)
      { x = 7.1627; y = -5.2525; z = 0.7490 }, (* H2'' *)
      { x = 7.6666; y = -4.1249; z = 2.4880 }, (* O2'  *)
      { x = 8.5944; y = -4.2543; z = 2.6981 }, (* H2'  *)
      { x = 5.5661; y = -5.3029; z = 2.2009 }, (* C3'  *)
      { x = 5.0841; y = -6.0018; z = 1.5172 }, (* H3'  *)
      { x = 4.9062; y = -4.0452; z = 2.2042 }, (* O3'  *)
      { x = 7.6298; y = -7.6136; z = 1.4752 }, (* N1   *)
      { x = 8.5977; y = -9.5977; z = 0.7329 }, (* N3   *)
      { x = 8.5951; y = -8.5745; z = 1.6594 }, (* C2   *)
      { x = 7.7372; y = -9.7371; z = -0.3364 }, (* C4   *)
      { x = 6.7596; y = -8.6801; z = -0.4476 }, (* C5   *)
      { x = 6.7338; y = -7.6721; z = 0.4408 }, (* C6 *)
      (C (
      { x = 7.8849; y = -10.7881; z = -1.1289 }, (* N4   *)
      { x = 9.3993; y = -8.5377; z = 2.5743 }, (* O2   *)
      { x = 7.2499; y = -10.8809; z = -1.9088 }, (* H41  *)
      { x = 8.6122; y = -11.4649; z = -0.9468 }, (* H42  *)
      { x = 6.0317; y = -8.6941; z = -1.2588 }, (* H5   *)
      { x = 5.9901; y = -6.8809; z = 0.3459 }) (* H6   *)
      )
    )

let rC06
  = N(
      {    a= -0.9837; b=0.0476; c= -0.1733; (* dgf_base_tfo *)
           d= -0.1792; e= -0.3353; f=0.9249;
           g= -0.0141; h=0.9409; i=0.3384;
           tx=5.7793; ty= -5.2303; tz=4.5997 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 3.9938; y = -6.7042; z = 1.9023 }, (* C5'  *)
      { x = 3.2332; y = -5.9343; z = 2.0319 }, (* H5'  *)
      { x = 3.9666; y = -7.2863; z = 0.9812 }, (* H5'' *)
      { x = 5.3098; y = -5.9546; z = 1.8564 }, (* C4'  *)
      { x = 5.3863; y = -5.3702; z = 0.9395 }, (* H4'  *)
      { x = 5.3851; y = -5.0642; z = 3.0076 }, (* O4'  *)
      { x = 6.7315; y = -4.9724; z = 3.4462 }, (* C1'  *)
      { x = 7.0033; y = -3.9202; z = 3.3619 }, (* H1'  *)
      { x = 7.5997; y = -5.8018; z = 2.4948 }, (* C2'  *)
      { x = 8.3627; y = -6.3254; z = 3.0707 }, (* H2'' *)
      { x = 8.0410; y = -4.9501; z = 1.4724 }, (* O2'  *)
      { x = 8.2781; y = -4.0644; z = 1.7570 }, (* H2'  *)
      { x = 6.5701; y = -6.8129; z = 1.9714 }, (* C3'  *)
      { x = 6.4186; y = -7.5809; z = 2.7299 }, (* H3'  *)
      { x = 6.9357; y = -7.3841; z = 0.7235 }, (* O3'  *)
      { x = 6.8024; y = -5.4718; z = 4.8475 }, (* N1   *)
      { x = 6.6920; y = -5.0495; z = 7.1354 }, (* N3   *)
      { x = 6.6201; y = -4.5500; z = 5.8506 }, (* C2   *)
      { x = 6.9254; y = -6.3614; z = 7.4926 }, (* C4   *)
      { x = 7.1046; y = -7.2543; z = 6.3718 }, (* C5   *)
      { x = 7.0391; y = -6.7951; z = 5.1106 }, (* C6 *)
      (C (
      { x = 6.9614; y = -6.6648; z = 8.7815 }, (* N4   *)
      { x = 6.4083; y = -3.3696; z = 5.6340 }, (* O2   *)
      { x = 7.1329; y = -7.6280; z = 9.0324 }, (* H41  *)
      { x = 6.8204; y = -5.9469; z = 9.4777 }, (* H42  *)
      { x = 7.2954; y = -8.3135; z = 6.5440 }, (* H5   *)
      { x = 7.1753; y = -7.4798; z = 4.2735 }) (* H6   *)
      )
    )

let rC07
  = N(
      {    a=0.0033; b=0.2720; c= -0.9623; (* dgf_base_tfo *)
           d=0.3013; e= -0.9179; f= -0.2584;
           g= -0.9535; h= -0.2891; i= -0.0850;
           tx=43.0403; ty=13.7233; tz=34.5710 },
      {    a=0.9187; b=0.2887; c=0.2694; (* P_O3'_275_tfo *)
           d=0.0302; e= -0.7316; f=0.6811;
           g=0.3938; h= -0.6176; i= -0.6808;
           tx= -48.4330; ty=26.3254; tz=13.6383 },
      {    a= -0.1504; b=0.7744; c= -0.6145; (* P_O3'_180_tfo *)
           d=0.7581; e=0.4893; f=0.4311;
           g=0.6345; h= -0.4010; i= -0.6607;
           tx= -31.9784; ty= -13.4285; tz=44.9650 },
      {    a= -0.6236; b= -0.7810; c= -0.0337; (* P_O3'_60_tfo *)
           d= -0.6890; e=0.5694; f= -0.4484;
           g=0.3694; h= -0.2564; i= -0.8932;
           tx=12.1105; ty=30.8774; tz=46.0946 },
      { x = 33.3400; y = 11.0980; z = 46.1750 }, (* P    *)
      { x = 34.5130; y = 10.2320; z = 46.4660 }, (* O1P  *)
      { x = 33.4130; y = 12.3960; z = 46.9340 }, (* O2P  *)
      { x = 31.9810; y = 10.3390; z = 46.4820 }, (* O5'  *)
      { x = 30.8152; y = 11.1619; z = 46.2003 }, (* C5'  *)
      { x = 30.4519; y = 10.9454; z = 45.1957 }, (* H5'  *)
      { x = 31.0379; y = 12.2016; z = 46.4400 }, (* H5'' *)
      { x = 29.7081; y = 10.7448; z = 47.1428 }, (* C4'  *)
      { x = 28.8710; y = 11.4416; z = 47.0982 }, (* H4'  *)
      { x = 29.2550; y = 9.4394; z = 46.8162 }, (* O4'  *)
      { x = 29.3907; y = 8.5625; z = 47.9460 }, (* C1'  *)
      { x = 28.4416; y = 8.5669; z = 48.4819 }, (* H1'  *)
      { x = 30.4468; y = 9.2031; z = 48.7952 }, (* C2'  *)
      { x = 31.4222; y = 8.9651; z = 48.3709 }, (* H2'' *)
      { x = 30.3701; y = 8.9157; z = 50.1624 }, (* O2'  *)
      { x = 30.0652; y = 8.0304; z = 50.3740 }, (* H2'  *)
      { x = 30.1622; y = 10.6879; z = 48.6120 }, (* C3'  *)
      { x = 31.0952; y = 11.2399; z = 48.7254 }, (* H3'  *)
      { x = 29.1076; y = 11.1535; z = 49.4702 }, (* O3'  *)
      { x = 29.7883; y = 7.2209; z = 47.5235 }, (* N1   *)
      { x = 29.1825; y = 5.0438; z = 46.8275 }, (* N3   *)
      { x = 28.8008; y = 6.2912; z = 47.2263 }, (* C2   *)
      { x = 30.4888; y = 4.6890; z = 46.7186 }, (* C4   *)
      { x = 31.5034; y = 5.6405; z = 47.0249 }, (* C5   *)
      { x = 31.1091; y = 6.8691; z = 47.4156 }, (* C6 *)
      (C (
      { x = 30.8109; y = 3.4584; z = 46.3336 }, (* N4   *)
      { x = 27.6171; y = 6.5989; z = 47.3189 }, (* O2   *)
      { x = 31.7923; y = 3.2301; z = 46.2638 }, (* H41  *)
      { x = 30.0880; y = 2.7857; z = 46.1215 }, (* H42  *)
      { x = 32.5542; y = 5.3634; z = 46.9395 }, (* H5   *)
      { x = 31.8523; y = 7.6279; z = 47.6603 }) (* H6   *)
      )
    )

let rC08
  = N(
      {    a=0.0797; b= -0.6026; c= -0.7941; (* dgf_base_tfo *)
           d=0.7939; e=0.5201; f= -0.3150;
           g=0.6028; h= -0.6054; i=0.5198;
           tx= -36.8341; ty=41.5293; tz=1.6628 },
      {    a=0.9187; b=0.2887; c=0.2694; (* P_O3'_275_tfo *)
           d=0.0302; e= -0.7316; f=0.6811;
           g=0.3938; h= -0.6176; i= -0.6808;
           tx= -48.4330; ty=26.3254; tz=13.6383 },
      {    a= -0.1504; b=0.7744; c= -0.6145; (* P_O3'_180_tfo *)
           d=0.7581; e=0.4893; f=0.4311;
           g=0.6345; h= -0.4010; i= -0.6607;
           tx= -31.9784; ty= -13.4285; tz=44.9650 },
      {    a= -0.6236; b= -0.7810; c= -0.0337; (* P_O3'_60_tfo *)
           d= -0.6890; e=0.5694; f= -0.4484;
           g=0.3694; h= -0.2564; i= -0.8932;
           tx=12.1105; ty=30.8774; tz=46.0946 },
      { x = 33.3400; y = 11.0980; z = 46.1750 }, (* P    *)
      { x = 34.5130; y = 10.2320; z = 46.4660 }, (* O1P  *)
      { x = 33.4130; y = 12.3960; z = 46.9340 }, (* O2P  *)
      { x = 31.9810; y = 10.3390; z = 46.4820 }, (* O5'  *)
      { x = 31.8779; y = 9.9369; z = 47.8760 }, (* C5'  *)
      { x = 31.3239; y = 10.6931; z = 48.4322 }, (* H5'  *)
      { x = 32.8647; y = 9.6624; z = 48.2489 }, (* H5'' *)
      { x = 31.0429; y = 8.6773; z = 47.9401 }, (* C4'  *)
      { x = 31.0779; y = 8.2331; z = 48.9349 }, (* H4'  *)
      { x = 29.6956; y = 8.9669; z = 47.5983 }, (* O4'  *)
      { x = 29.2784; y = 8.1700; z = 46.4782 }, (* C1'  *)
      { x = 28.8006; y = 7.2731; z = 46.8722 }, (* H1'  *)
      { x = 30.5544; y = 7.7940; z = 45.7875 }, (* C2'  *)
      { x = 30.8837; y = 8.6410; z = 45.1856 }, (* H2'' *)
      { x = 30.5100; y = 6.6007; z = 45.0582 }, (* O2'  *)
      { x = 29.6694; y = 6.4168; z = 44.6326 }, (* H2'  *)
      { x = 31.5146; y = 7.5954; z = 46.9527 }, (* C3'  *)
      { x = 32.5255; y = 7.8261; z = 46.6166 }, (* H3'  *)
      { x = 31.3876; y = 6.2951; z = 47.5516 }, (* O3'  *)
      { x = 28.3976; y = 8.9302; z = 45.5933 }, (* N1   *)
      { x = 26.2155; y = 9.6135; z = 44.9910 }, (* N3   *)
      { x = 27.0281; y = 8.8961; z = 45.8192 }, (* C2   *)
      { x = 26.7044; y = 10.3489; z = 43.9595 }, (* C4   *)
      { x = 28.1088; y = 10.3837; z = 43.7247 }, (* C5   *)
      { x = 28.8978; y = 9.6708; z = 44.5535 }, (* C6 *)
      (C (
      { x = 25.8715; y = 11.0249; z = 43.1749 }, (* N4   *)
      { x = 26.5733; y = 8.2371; z = 46.7484 }, (* O2   *)
      { x = 26.2707; y = 11.5609; z = 42.4177 }, (* H41  *)
      { x = 24.8760; y = 10.9939; z = 43.3427 }, (* H42  *)
      { x = 28.5089; y = 10.9722; z = 42.8990 }, (* H5   *)
      { x = 29.9782; y = 9.6687; z = 44.4097 }) (* H6   *)
      )
    )

let rC09
  = N(
      {    a=0.8727; b=0.4760; c= -0.1091; (* dgf_base_tfo *)
           d= -0.4188; e=0.6148; f= -0.6682;
           g= -0.2510; h=0.6289; i=0.7359;
           tx= -8.1687; ty= -52.0761; tz= -25.0726 },
      {    a=0.9187; b=0.2887; c=0.2694; (* P_O3'_275_tfo *)
           d=0.0302; e= -0.7316; f=0.6811;
           g=0.3938; h= -0.6176; i= -0.6808;
           tx= -48.4330; ty=26.3254; tz=13.6383 },
      {    a= -0.1504; b=0.7744; c= -0.6145; (* P_O3'_180_tfo *)
           d=0.7581; e=0.4893; f=0.4311;
           g=0.6345; h= -0.4010; i= -0.6607;
           tx= -31.9784; ty= -13.4285; tz=44.9650 },
      {    a= -0.6236; b= -0.7810; c= -0.0337; (* P_O3'_60_tfo *)
           d= -0.6890; e=0.5694; f= -0.4484;
           g=0.3694; h= -0.2564; i= -0.8932;
           tx=12.1105; ty=30.8774; tz=46.0946 },
      { x = 33.3400; y = 11.0980; z = 46.1750 }, (* P    *)
      { x = 34.5130; y = 10.2320; z = 46.4660 }, (* O1P  *)
      { x = 33.4130; y = 12.3960; z = 46.9340 }, (* O2P  *)
      { x = 31.9810; y = 10.3390; z = 46.4820 }, (* O5'  *)
      { x = 30.8152; y = 11.1619; z = 46.2003 }, (* C5'  *)
      { x = 30.4519; y = 10.9454; z = 45.1957 }, (* H5'  *)
      { x = 31.0379; y = 12.2016; z = 46.4400 }, (* H5'' *)
      { x = 29.7081; y = 10.7448; z = 47.1428 }, (* C4'  *)
      { x = 29.4506; y = 9.6945; z = 47.0059 }, (* H4'  *)
      { x = 30.1045; y = 10.9634; z = 48.4885 }, (* O4'  *)
      { x = 29.1794; y = 11.8418; z = 49.1490 }, (* C1'  *)
      { x = 28.4388; y = 11.2210; z = 49.6533 }, (* H1'  *)
      { x = 28.5211; y = 12.6008; z = 48.0367 }, (* C2'  *)
      { x = 29.1947; y = 13.3949; z = 47.7147 }, (* H2'' *)
      { x = 27.2316; y = 13.0683; z = 48.3134 }, (* O2'  *)
      { x = 27.0851; y = 13.3391; z = 49.2227 }, (* H2'  *)
      { x = 28.4131; y = 11.5507; z = 46.9391 }, (* C3'  *)
      { x = 28.4451; y = 12.0512; z = 45.9713 }, (* H3'  *)
      { x = 27.2707; y = 10.6955; z = 47.1097 }, (* O3'  *)
      { x = 29.8751; y = 12.7405; z = 50.0682 }, (* N1   *)
      { x = 30.7172; y = 13.1841; z = 52.2328 }, (* N3   *)
      { x = 30.0617; y = 12.3404; z = 51.3847 }, (* C2   *)
      { x = 31.1834; y = 14.3941; z = 51.8297 }, (* C4   *)
      { x = 30.9913; y = 14.8074; z = 50.4803 }, (* C5   *)
      { x = 30.3434; y = 13.9610; z = 49.6548 }, (* C6 *)
      (C (
      { x = 31.8090; y = 15.1847; z = 52.6957 }, (* N4   *)
      { x = 29.6470; y = 11.2494; z = 51.7616 }, (* O2   *)
      { x = 32.1422; y = 16.0774; z = 52.3606 }, (* H41  *)
      { x = 31.9392; y = 14.8893; z = 53.6527 }, (* H42  *)
      { x = 31.3632; y = 15.7771; z = 50.1491 }, (* H5   *)
      { x = 30.1742; y = 14.2374; z = 48.6141 }) (* H6   *)
      )
    )

let rC10
  = N(
      {    a=0.1549; b=0.8710; c= -0.4663; (* dgf_base_tfo *)
           d=0.6768; e= -0.4374; f= -0.5921;
           g= -0.7197; h= -0.2239; i= -0.6572;
           tx=25.2447; ty= -14.1920; tz=50.3201 },
      {    a=0.9187; b=0.2887; c=0.2694; (* P_O3'_275_tfo *)
           d=0.0302; e= -0.7316; f=0.6811;
           g=0.3938; h= -0.6176; i= -0.6808;
           tx= -48.4330; ty=26.3254; tz=13.6383 },
      {    a= -0.1504; b=0.7744; c= -0.6145; (* P_O3'_180_tfo *)
           d=0.7581; e=0.4893; f=0.4311;
           g=0.6345; h= -0.4010; i= -0.6607;
           tx= -31.9784; ty= -13.4285; tz=44.9650 },
      {    a= -0.6236; b= -0.7810; c= -0.0337; (* P_O3'_60_tfo *)
           d= -0.6890; e=0.5694; f= -0.4484;
           g=0.3694; h= -0.2564; i= -0.8932;
           tx=12.1105; ty=30.8774; tz=46.0946 },
      { x = 33.3400; y = 11.0980; z = 46.1750 }, (* P    *)
      { x = 34.5130; y = 10.2320; z = 46.4660 }, (* O1P  *)
      { x = 33.4130; y = 12.3960; z = 46.9340 }, (* O2P  *)
      { x = 31.9810; y = 10.3390; z = 46.4820 }, (* O5'  *)
      { x = 31.8779; y = 9.9369; z = 47.8760 }, (* C5'  *)
      { x = 31.3239; y = 10.6931; z = 48.4322 }, (* H5'  *)
      { x = 32.8647; y = 9.6624; z = 48.2489 }, (* H5'' *)
      { x = 31.0429; y = 8.6773; z = 47.9401 }, (* C4'  *)
      { x = 30.0440; y = 8.8473; z = 47.5383 }, (* H4'  *)
      { x = 31.6749; y = 7.6351; z = 47.2119 }, (* O4'  *)
      { x = 31.9159; y = 6.5022; z = 48.0616 }, (* C1'  *)
      { x = 31.0691; y = 5.8243; z = 47.9544 }, (* H1'  *)
      { x = 31.9300; y = 7.0685; z = 49.4493 }, (* C2'  *)
      { x = 32.9024; y = 7.5288; z = 49.6245 }, (* H2'' *)
      { x = 31.5672; y = 6.1750; z = 50.4632 }, (* O2'  *)
      { x = 31.8416; y = 5.2663; z = 50.3200 }, (* H2'  *)
      { x = 30.8618; y = 8.1514; z = 49.3749 }, (* C3'  *)
      { x = 31.1122; y = 8.9396; z = 50.0850 }, (* H3'  *)
      { x = 29.5351; y = 7.6245; z = 49.5409 }, (* O3'  *)
      { x = 33.1890; y = 5.8629; z = 47.7343 }, (* N1   *)
      { x = 34.4004; y = 4.2636; z = 46.4828 }, (* N3   *)
      { x = 33.2062; y = 4.8497; z = 46.7851 }, (* C2   *)
      { x = 35.5600; y = 4.6374; z = 47.0822 }, (* C4   *)
      { x = 35.5444; y = 5.6751; z = 48.0577 }, (* C5   *)
      { x = 34.3565; y = 6.2450; z = 48.3432 }, (* C6 *)
      (C (
      { x = 36.6977; y = 4.0305; z = 46.7598 }, (* N4   *)
      { x = 32.1661; y = 4.5034; z = 46.2348 }, (* O2   *)
      { x = 37.5405; y = 4.3347; z = 47.2259 }, (* H41  *)
      { x = 36.7033; y = 3.2923; z = 46.0706 }, (* H42  *)
      { x = 36.4713; y = 5.9811; z = 48.5428 }, (* H5   *)
      { x = 34.2986; y = 7.0426; z = 49.0839 }) (* H6   *)
      )
    )

let rCs = [rC01;rC02;rC03;rC04;rC05;rC06;rC07;rC08;rC09;rC10]

let rG
  = N(
      {    a= -0.0018; b= -0.8207; c=0.5714; (* dgf_base_tfo *)
           d=0.2679; e= -0.5509; f= -0.7904;
           g=0.9634; h=0.1517; i=0.2209;
           tx=0.0073; ty=8.4030; tz=0.6232 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 5.4550; y = 8.2120; z = -2.8810 }, (* C5'  *)
      { x = 5.4546; y = 8.8508; z = -1.9978 }, (* H5'  *)
      { x = 5.7588; y = 8.6625; z = -3.8259 }, (* H5'' *)
      { x = 6.4970; y = 7.1480; z = -2.5980 }, (* C4'  *)
      { x = 7.4896; y = 7.5919; z = -2.5214 }, (* H4'  *)
      { x = 6.1630; y = 6.4860; z = -1.3440 }, (* O4'  *)
      { x = 6.5400; y = 5.1200; z = -1.4190 }, (* C1'  *)
      { x = 7.2763; y = 4.9681; z = -0.6297 }, (* H1'  *)
      { x = 7.1940; y = 4.8830; z = -2.7770 }, (* C2'  *)
      { x = 6.8667; y = 3.9183; z = -3.1647 }, (* H2'' *)
      { x = 8.5860; y = 5.0910; z = -2.6140 }, (* O2'  *)
      { x = 8.9510; y = 4.7626; z = -1.7890 }, (* H2'  *)
      { x = 6.5720; y = 6.0040; z = -3.6090 }, (* C3'  *)
      { x = 5.5636; y = 5.7066; z = -3.8966 }, (* H3'  *)
      { x = 7.3801; y = 6.3562; z = -4.7350 }, (* O3'  *)
      { x = 4.7150; y = 0.4910; z = -0.1360 }, (* N1   *)
      { x = 6.3490; y = 2.1730; z = -0.6020 }, (* N3   *)
      { x = 5.9530; y = 0.9650; z = -0.2670 }, (* C2   *)
      { x = 5.2900; y = 2.9790; z = -0.8260 }, (* C4   *)
      { x = 3.9720; y = 2.6390; z = -0.7330 }, (* C5   *)
      { x = 3.6770; y = 1.3160; z = -0.3660 }, (* C6 *)
      (G (
      { x = 6.8426; y = 0.0056; z = -0.0019 }, (* N2   *)
      { x = 3.1660; y = 3.7290; z = -1.0360 }, (* N7   *)
      { x = 5.3170; y = 4.2990; z = -1.1930 }, (* N9   *)
      { x = 4.0100; y = 4.6780; z = -1.2990 }, (* C8   *)
      { x = 2.4280; y = 0.8450; z = -0.2360 }, (* O6   *)
      { x = 4.6151; y = -0.4677; z = 0.1305 }, (* H1   *)
      { x = 6.6463; y = -0.9463; z = 0.2729 }, (* H21  *)
      { x = 7.8170; y = 0.2642; z = -0.0640 }, (* H22  *)
      { x = 3.4421; y = 5.5744; z = -1.5482 }) (* H8   *)
      )
    )

let rG01
  = N(
      {    a= -0.0043; b= -0.8175; c=0.5759; (* dgf_base_tfo *)
           d=0.2617; e= -0.5567; f= -0.7884;
           g=0.9651; h=0.1473; i=0.2164;
           tx=0.0359; ty=8.3929; tz=0.5532 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 5.4352; y = 8.2183; z = -2.7757 }, (* C5'  *)
      { x = 5.3830; y = 8.7883; z = -1.8481 }, (* H5'  *)
      { x = 5.7729; y = 8.7436; z = -3.6691 }, (* H5'' *)
      { x = 6.4830; y = 7.1518; z = -2.5252 }, (* C4'  *)
      { x = 7.4749; y = 7.5972; z = -2.4482 }, (* H4'  *)
      { x = 6.1626; y = 6.4620; z = -1.2827 }, (* O4'  *)
      { x = 6.5431; y = 5.0992; z = -1.3905 }, (* C1'  *)
      { x = 7.2871; y = 4.9328; z = -0.6114 }, (* H1'  *)
      { x = 7.1852; y = 4.8935; z = -2.7592 }, (* C2'  *)
      { x = 6.8573; y = 3.9363; z = -3.1645 }, (* H2'' *)
      { x = 8.5780; y = 5.1025; z = -2.6046 }, (* O2'  *)
      { x = 8.9516; y = 4.7577; z = -1.7902 }, (* H2'  *)
      { x = 6.5522; y = 6.0300; z = -3.5612 }, (* C3'  *)
      { x = 5.5420; y = 5.7356; z = -3.8459 }, (* H3'  *)
      { x = 7.3487; y = 6.4089; z = -4.6867 }, (* O3'  *)
      { x = 4.7442; y = 0.4514; z = -0.1390 }, (* N1   *)
      { x = 6.3687; y = 2.1459; z = -0.5926 }, (* N3   *)
      { x = 5.9795; y = 0.9335; z = -0.2657 }, (* C2   *)
      { x = 5.3052; y = 2.9471; z = -0.8125 }, (* C4   *)
      { x = 3.9891; y = 2.5987; z = -0.7230 }, (* C5   *)
      { x = 3.7016; y = 1.2717; z = -0.3647 }, (* C6 *)
      (G (
      { x = 6.8745; y = -0.0224; z = -0.0058 }, (* N2   *)
      { x = 3.1770; y = 3.6859; z = -1.0198 }, (* N7   *)
      { x = 5.3247; y = 4.2695; z = -1.1710 }, (* N9   *)
      { x = 4.0156; y = 4.6415; z = -1.2759 }, (* C8   *)
      { x = 2.4553; y = 0.7925; z = -0.2390 }, (* O6   *)
      { x = 4.6497; y = -0.5095; z = 0.1212 }, (* H1   *)
      { x = 6.6836; y = -0.9771; z = 0.2627 }, (* H21  *)
      { x = 7.8474; y = 0.2424; z = -0.0653 }, (* H22  *)
      { x = 3.4426; y = 5.5361; z = -1.5199 }) (* H8   *)
      )
    )

let rG02
  = N(
      {    a=0.5566; b=0.0449; c=0.8296; (* dgf_base_tfo *)
           d=0.5125; e=0.7673; f= -0.3854;
           g= -0.6538; h=0.6397; i=0.4041;
           tx= -9.1161; ty= -3.7679; tz= -2.9968 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 4.5778; y = 6.6594; z = -4.0364 }, (* C5'  *)
      { x = 4.9220; y = 7.1963; z = -4.9204 }, (* H5'  *)
      { x = 3.7996; y = 5.9091; z = -4.1764 }, (* H5'' *)
      { x = 5.7873; y = 5.8869; z = -3.5482 }, (* C4'  *)
      { x = 6.0405; y = 5.0875; z = -4.2446 }, (* H4'  *)
      { x = 6.9135; y = 6.8036; z = -3.4310 }, (* O4'  *)
      { x = 7.7293; y = 6.4084; z = -2.3392 }, (* C1'  *)
      { x = 8.7078; y = 6.1815; z = -2.7624 }, (* H1'  *)
      { x = 7.1305; y = 5.1418; z = -1.7347 }, (* C2'  *)
      { x = 7.2040; y = 5.1982; z = -0.6486 }, (* H2'' *)
      { x = 7.7417; y = 4.0392; z = -2.3813 }, (* O2'  *)
      { x = 8.6785; y = 4.1443; z = -2.5630 }, (* H2'  *)
      { x = 5.6666; y = 5.2728; z = -2.1536 }, (* C3'  *)
      { x = 5.1747; y = 5.9805; z = -1.4863 }, (* H3'  *)
      { x = 4.9997; y = 4.0086; z = -2.1973 }, (* O3'  *)
      { x = 10.3245; y = 8.5459; z = 1.5467 }, (* N1   *)
      { x = 9.8051; y = 6.9432; z = -0.1497 }, (* N3   *)
      { x = 10.5175; y = 7.4328; z = 0.8408 }, (* C2   *)
      { x = 8.7523; y = 7.7422; z = -0.4228 }, (* C4   *)
      { x = 8.4257; y = 8.9060; z = 0.2099 }, (* C5   *)
      { x = 9.2665; y = 9.3242; z = 1.2540 }, (* C6 *)
      (G (
      { x = 11.6077; y = 6.7966; z = 1.2752 }, (* N2   *)
      { x = 7.2750; y = 9.4537; z = -0.3428 }, (* N7   *)
      { x = 7.7962; y = 7.5519; z = -1.3859 }, (* N9   *)
      { x = 6.9479; y = 8.6157; z = -1.2771 }, (* C8   *)
      { x = 9.0664; y = 10.4462; z = 1.9610 }, (* O6   *)
      { x = 10.9838; y = 8.7524; z = 2.2697 }, (* H1   *)
      { x = 12.2274; y = 7.0896; z = 2.0170 }, (* H21  *)
      { x = 11.8502; y = 5.9398; z = 0.7984 }, (* H22  *)
      { x = 6.0430; y = 8.9853; z = -1.7594 }) (* H8   *)
      )
    )

let rG03
  = N(
      {    a= -0.5021; b=0.0731; c=0.8617; (* dgf_base_tfo *)
           d= -0.8112; e=0.3054; f= -0.4986;
           g= -0.2996; h= -0.9494; i= -0.0940;
           tx=6.4273; ty= -5.1944; tz= -3.7807 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 4.1214; y = 6.7116; z = -1.9049 }, (* C5'  *)
      { x = 3.3465; y = 5.9610; z = -2.0607 }, (* H5'  *)
      { x = 4.0789; y = 7.2928; z = -0.9837 }, (* H5'' *)
      { x = 5.4170; y = 5.9293; z = -1.8186 }, (* C4'  *)
      { x = 5.4506; y = 5.3400; z = -0.9023 }, (* H4'  *)
      { x = 5.5067; y = 5.0417; z = -2.9703 }, (* O4'  *)
      { x = 6.8650; y = 4.9152; z = -3.3612 }, (* C1'  *)
      { x = 7.1090; y = 3.8577; z = -3.2603 }, (* H1'  *)
      { x = 7.7152; y = 5.7282; z = -2.3894 }, (* C2'  *)
      { x = 8.5029; y = 6.2356; z = -2.9463 }, (* H2'' *)
      { x = 8.1036; y = 4.8568; z = -1.3419 }, (* O2'  *)
      { x = 8.3270; y = 3.9651; z = -1.6184 }, (* H2'  *)
      { x = 6.7003; y = 6.7565; z = -1.8911 }, (* C3'  *)
      { x = 6.5898; y = 7.5329; z = -2.6482 }, (* H3'  *)
      { x = 7.0505; y = 7.2878; z = -0.6105 }, (* O3'  *)
      { x = 9.6740; y = 4.7656; z = -7.6614 }, (* N1   *)
      { x = 9.0739; y = 4.3013; z = -5.3941 }, (* N3   *)
      { x = 9.8416; y = 4.2192; z = -6.4581 }, (* C2   *)
      { x = 7.9885; y = 5.0632; z = -5.6446 }, (* C4   *)
      { x = 7.6822; y = 5.6856; z = -6.8194 }, (* C5   *)
      { x = 8.5831; y = 5.5215; z = -7.8840 }, (* C6 *)
      (G (
      { x = 10.9733; y = 3.5117; z = -6.4286 }, (* N2   *)
      { x = 6.4857; y = 6.3816; z = -6.7035 }, (* N7   *)
      { x = 6.9740; y = 5.3703; z = -4.7760 }, (* N9   *)
      { x = 6.1133; y = 6.1613; z = -5.4808 }, (* C8   *)
      { x = 8.4084; y = 6.0747; z = -9.0933 }, (* O6   *)
      { x = 10.3759; y = 4.5855; z = -8.3504 }, (* H1   *)
      { x = 11.6254; y = 3.3761; z = -7.1879 }, (* H21  *)
      { x = 11.1917; y = 3.0460; z = -5.5593 }, (* H22  *)
      { x = 5.1705; y = 6.6830; z = -5.3167 }) (* H8   *)
      )
    )

let rG04
  = N(
      {    a= -0.5426; b= -0.8175; c=0.1929; (* dgf_base_tfo *)
           d=0.8304; e= -0.5567; f= -0.0237;
           g=0.1267; h=0.1473; i=0.9809;
           tx= -0.5075; ty=8.3929; tz=0.2229 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 5.4352; y = 8.2183; z = -2.7757 }, (* C5'  *)
      { x = 5.3830; y = 8.7883; z = -1.8481 }, (* H5'  *)
      { x = 5.7729; y = 8.7436; z = -3.6691 }, (* H5'' *)
      { x = 6.4830; y = 7.1518; z = -2.5252 }, (* C4'  *)
      { x = 7.4749; y = 7.5972; z = -2.4482 }, (* H4'  *)
      { x = 6.1626; y = 6.4620; z = -1.2827 }, (* O4'  *)
      { x = 6.5431; y = 5.0992; z = -1.3905 }, (* C1'  *)
      { x = 7.2871; y = 4.9328; z = -0.6114 }, (* H1'  *)
      { x = 7.1852; y = 4.8935; z = -2.7592 }, (* C2'  *)
      { x = 6.8573; y = 3.9363; z = -3.1645 }, (* H2'' *)
      { x = 8.5780; y = 5.1025; z = -2.6046 }, (* O2'  *)
      { x = 8.9516; y = 4.7577; z = -1.7902 }, (* H2'  *)
      { x = 6.5522; y = 6.0300; z = -3.5612 }, (* C3'  *)
      { x = 5.5420; y = 5.7356; z = -3.8459 }, (* H3'  *)
      { x = 7.3487; y = 6.4089; z = -4.6867 }, (* O3'  *)
      { x = 3.6343; y = 2.6680; z = 2.0783 }, (* N1   *)
      { x = 5.4505; y = 3.9805; z = 1.2446 }, (* N3   *)
      { x = 4.7540; y = 3.3816; z = 2.1851 }, (* C2   *)
      { x = 4.8805; y = 3.7951; z = 0.0354 }, (* C4   *)
      { x = 3.7416; y = 3.0925; z = -0.2305 }, (* C5   *)
      { x = 3.0873; y = 2.4980; z = 0.8606 }, (* C6 *)
      (G (
      { x = 5.1433; y = 3.4373; z = 3.4609 }, (* N2   *)
      { x = 3.4605; y = 3.1184; z = -1.5906 }, (* N7   *)
      { x = 5.3247; y = 4.2695; z = -1.1710 }, (* N9   *)
      { x = 4.4244; y = 3.8244; z = -2.0953 }, (* C8   *)
      { x = 1.9600; y = 1.7805; z = 0.7462 }, (* O6   *)
      { x = 3.2489; y = 2.2879; z = 2.9191 }, (* H1   *)
      { x = 4.6785; y = 3.0243; z = 4.2568 }, (* H21  *)
      { x = 5.9823; y = 3.9654; z = 3.6539 }, (* H22  *)
      { x = 4.2675; y = 3.8876; z = -3.1721 }) (* H8   *)
      )
    )

let rG05
  = N(
      {    a= -0.5891; b=0.0449; c=0.8068; (* dgf_base_tfo *)
           d=0.5375; e=0.7673; f=0.3498;
           g= -0.6034; h=0.6397; i= -0.4762;
           tx= -0.3019; ty= -3.7679; tz= -9.5913 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 4.5778; y = 6.6594; z = -4.0364 }, (* C5'  *)
      { x = 4.9220; y = 7.1963; z = -4.9204 }, (* H5'  *)
      { x = 3.7996; y = 5.9091; z = -4.1764 }, (* H5'' *)
      { x = 5.7873; y = 5.8869; z = -3.5482 }, (* C4'  *)
      { x = 6.0405; y = 5.0875; z = -4.2446 }, (* H4'  *)
      { x = 6.9135; y = 6.8036; z = -3.4310 }, (* O4'  *)
      { x = 7.7293; y = 6.4084; z = -2.3392 }, (* C1'  *)
      { x = 8.7078; y = 6.1815; z = -2.7624 }, (* H1'  *)
      { x = 7.1305; y = 5.1418; z = -1.7347 }, (* C2'  *)
      { x = 7.2040; y = 5.1982; z = -0.6486 }, (* H2'' *)
      { x = 7.7417; y = 4.0392; z = -2.3813 }, (* O2'  *)
      { x = 8.6785; y = 4.1443; z = -2.5630 }, (* H2'  *)
      { x = 5.6666; y = 5.2728; z = -2.1536 }, (* C3'  *)
      { x = 5.1747; y = 5.9805; z = -1.4863 }, (* H3'  *)
      { x = 4.9997; y = 4.0086; z = -2.1973 }, (* O3'  *)
      { x = 10.2594; y = 10.6774; z = -1.0056 }, (* N1   *)
      { x = 9.7528; y = 8.7080; z = -2.2631 }, (* N3   *)
      { x = 10.4471; y = 9.7876; z = -1.9791 }, (* C2   *)
      { x = 8.7271; y = 8.5575; z = -1.3991 }, (* C4   *)
      { x = 8.4100; y = 9.3803; z = -0.3580 }, (* C5   *)
      { x = 9.2294; y = 10.5030; z = -0.1574 }, (* C6 *)
      (G (
      { x = 11.5110; y = 10.1256; z = -2.7114 }, (* N2   *)
      { x = 7.2891; y = 8.9068; z = 0.3121 }, (* N7   *)
      { x = 7.7962; y = 7.5519; z = -1.3859 }, (* N9   *)
      { x = 6.9702; y = 7.8292; z = -0.3353 }, (* C8   *)
      { x = 9.0349; y = 11.3951; z = 0.8250 }, (* O6   *)
      { x = 10.9013; y = 11.4422; z = -0.9512 }, (* H1   *)
      { x = 12.1031; y = 10.9341; z = -2.5861 }, (* H21  *)
      { x = 11.7369; y = 9.5180; z = -3.4859 }, (* H22  *)
      { x = 6.0888; y = 7.3990; z = 0.1403 }) (* H8   *)
      )
    )

let rG06
  = N(
      {    a= -0.9815; b=0.0731; c= -0.1772; (* dgf_base_tfo *)
           d=0.1912; e=0.3054; f= -0.9328;
           g= -0.0141; h= -0.9494; i= -0.3137;
           tx=5.7506; ty= -5.1944; tz=4.7470 },
      {    a= -0.8143; b= -0.5091; c= -0.2788; (* P_O3'_275_tfo *)
           d= -0.0433; e= -0.4257; f=0.9038;
           g= -0.5788; h=0.7480; i=0.3246;
           tx=1.5227; ty=6.9114; tz= -7.0765 },
      {    a=0.3822; b= -0.7477; c=0.5430; (* P_O3'_180_tfo *)
           d=0.4552; e=0.6637; f=0.5935;
           g= -0.8042; h=0.0203; i=0.5941;
           tx= -6.9472; ty= -4.1186; tz= -5.9108 },
      {    a=0.5640; b=0.8007; c= -0.2022; (* P_O3'_60_tfo *)
           d= -0.8247; e=0.5587; f= -0.0878;
           g=0.0426; h=0.2162; i=0.9754;
           tx=6.2694; ty= -7.0540; tz=3.3316 },
      { x = 2.8930; y = 8.5380; z = -3.3280 }, (* P    *)
      { x = 1.6980; y = 7.6960; z = -3.5570 }, (* O1P  *)
      { x = 3.2260; y = 9.5010; z = -4.4020 }, (* O2P  *)
      { x = 4.1590; y = 7.6040; z = -3.0340 }, (* O5'  *)
      { x = 4.1214; y = 6.7116; z = -1.9049 }, (* C5'  *)
      { x = 3.3465; y = 5.9610; z = -2.0607 }, (* H5'  *)
      { x = 4.0789; y = 7.2928; z = -0.9837 }, (* H5'' *)
      { x = 5.4170; y = 5.9293; z = -1.8186 }, (* C4'  *)
      { x = 5.4506; y = 5.3400; z = -0.9023 }, (* H4'  *)
      { x = 5.5067; y = 5.0417; z = -2.9703 }, (* O4'  *)
      { x = 6.8650; y = 4.9152; z = -3.3612 }, (* C1'  *)
      { x = 7.1090; y = 3.8577; z = -3.2603 }, (* H1'  *)
      { x = 7.7152; y = 5.7282; z = -2.3894 }, (* C2'  *)
      { x = 8.5029; y = 6.2356; z = -2.9463 }, (* H2'' *)
      { x = 8.1036; y = 4.8568; z = -1.3419 }, (* O2'  *)
      { x = 8.3270; y = 3.9651; z = -1.6184 }, (* H2'  *)
      { x = 6.7003; y = 6.7565; z = -1.8911 }, (* C3'  *)
      { x = 6.5898; y = 7.5329; z = -2.6482 }, (* H3'  *)
      { x = 7.0505; y = 7.2878; z = -0.6105 }, (* O3'  *)
      { x = 6.6624; y = 3.5061; z = -8.2986 }, (* N1   *)
      { x = 6.5810; y = 3.2570; z = -5.9221 }, (* N3   *)
      { x = 6.5151; y = 2.8263; z = -7.1625 }, (* C2   *)
      { x = 6.8364; y = 4.5817; z = -5.8882 }, (* C4   *)
      { x = 7.0116; y = 5.4064; z = -6.9609 }, (* C5   *)
      { x = 6.9173; y = 4.8260; z = -8.2361 }, (* C6 *)
      (G (
      { x = 6.2717; y = 1.5402; z = -7.4250 }, (* N2   *)
      { x = 7.2573; y = 6.7070; z = -6.5394 }, (* N7   *)
      { x = 6.9740; y = 5.3703; z = -4.7760 }, (* N9   *)
      { x = 7.2238; y = 6.6275; z = -5.2453 }, (* C8   *)
      { x = 7.0668; y = 5.5163; z = -9.3763 }, (* O6   *)
      { x = 6.5754; y = 2.9964; z = -9.1545 }, (* H1   *)
      { x = 6.1908; y = 1.1105; z = -8.3354 }, (* H21  *)
      { x = 6.1346; y = 0.9352; z = -6.6280 }, (* H22  *)
      { x = 7.4108; y = 7.6227; z = -4.8418 }) (* H8   *)
      )
    )

let rG07
  = N(
      {    a=0.0894; b= -0.6059; c=0.7905; (* dgf_base_tfo *)
           d= -0.6810; e=0.5420; f=0.4924;
           g= -0.7268; h= -0.5824; i= -0.3642;
           tx=34.1424; ty=45.9610; tz= -11.8600 },
      {    a= -0.8644; b= -0.4956; c= -0.0851; (* P_O3'_275_tfo *)
           d= -0.0427; e=0.2409; f= -0.9696;
           g=0.5010; h= -0.8345; i= -0.2294;
           tx=4.0167; ty=54.5377; tz=12.4779 },
      {    a=0.3706; b= -0.6167; c=0.6945; (* P_O3'_180_tfo *)
           d= -0.2867; e= -0.7872; f= -0.5460;
           g=0.8834; h=0.0032; i= -0.4686;
           tx= -52.9020; ty=18.6313; tz= -0.6709 },
      {    a=0.4155; b=0.9025; c= -0.1137; (* P_O3'_60_tfo *)
           d=0.9040; e= -0.4236; f= -0.0582;
           g= -0.1007; h= -0.0786; i= -0.9918;
           tx= -7.6624; ty= -25.2080; tz=49.5181 },
      { x = 31.3810; y = 0.1400; z = 47.5810 }, (* P    *)
      { x = 29.9860; y = 0.6630; z = 47.6290 }, (* O1P  *)
      { x = 31.7210; y = -0.6460; z = 48.8090 }, (* O2P  *)
      { x = 32.4940; y = 1.2540; z = 47.2740 }, (* O5'  *)
      { x = 33.8709; y = 0.7918; z = 47.2113 }, (* C5'  *)
      { x = 34.1386; y = 0.5870; z = 46.1747 }, (* H5'  *)
      { x = 34.0186; y = -0.0095; z = 47.9353 }, (* H5'' *)
      { x = 34.7297; y = 1.9687; z = 47.6685 }, (* C4'  *)
      { x = 35.7723; y = 1.6845; z = 47.8113 }, (* H4'  *)
      { x = 34.6455; y = 2.9768; z = 46.6660 }, (* O4'  *)
      { x = 34.1690; y = 4.1829; z = 47.2627 }, (* C1'  *)
      { x = 35.0437; y = 4.7633; z = 47.5560 }, (* H1'  *)
      { x = 33.4145; y = 3.7532; z = 48.4954 }, (* C2'  *)
      { x = 32.4340; y = 3.3797; z = 48.2001 }, (* H2'' *)
      { x = 33.3209; y = 4.6953; z = 49.5217 }, (* O2'  *)
      { x = 33.2374; y = 5.6059; z = 49.2295 }, (* H2'  *)
      { x = 34.2724; y = 2.5970; z = 48.9773 }, (* C3'  *)
      { x = 33.6373; y = 1.8935; z = 49.5157 }, (* H3'  *)
      { x = 35.3453; y = 3.1884; z = 49.7285 }, (* O3'  *)
      { x = 34.0511; y = 7.8930; z = 43.7791 }, (* N1   *)
      { x = 34.9937; y = 6.3369; z = 45.3199 }, (* N3   *)
      { x = 35.0882; y = 7.3126; z = 44.4200 }, (* C2   *)
      { x = 33.7190; y = 5.9650; z = 45.5374 }, (* C4   *)
      { x = 32.5845; y = 6.4770; z = 44.9458 }, (* C5   *)
      { x = 32.7430; y = 7.5179; z = 43.9914 }, (* C6 *)
      (G (
      { x = 36.3030; y = 7.7827; z = 44.1036 }, (* N2   *)
      { x = 31.4499; y = 5.8335; z = 45.4368 }, (* N7   *)
      { x = 33.2760; y = 4.9817; z = 46.4043 }, (* N9   *)
      { x = 31.9235; y = 4.9639; z = 46.2934 }, (* C8   *)
      { x = 31.8602; y = 8.1000; z = 43.3695 }, (* O6   *)
      { x = 34.2623; y = 8.6223; z = 43.1283 }, (* H1   *)
      { x = 36.5188; y = 8.5081; z = 43.4347 }, (* H21  *)
      { x = 37.0888; y = 7.3524; z = 44.5699 }, (* H22  *)
      { x = 31.0815; y = 4.4201; z = 46.7218 }) (* H8   *)
      )
    )

let rG08
  = N(
      {    a=0.2224; b=0.6335; c=0.7411; (* dgf_base_tfo *)
           d= -0.3644; e= -0.6510; f=0.6659;
           g=0.9043; h= -0.4181; i=0.0861;
           tx= -47.6824; ty= -0.5823; tz= -31.7554 },
      {    a= -0.8644; b= -0.4956; c= -0.0851; (* P_O3'_275_tfo *)
           d= -0.0427; e=0.2409; f= -0.9696;
           g=0.5010; h= -0.8345; i= -0.2294;
           tx=4.0167; ty=54.5377; tz=12.4779 },
      {    a=0.3706; b= -0.6167; c=0.6945; (* P_O3'_180_tfo *)
           d= -0.2867; e= -0.7872; f= -0.5460;
           g=0.8834; h=0.0032; i= -0.4686;
           tx= -52.9020; ty=18.6313; tz= -0.6709 },
      {    a=0.4155; b=0.9025; c= -0.1137; (* P_O3'_60_tfo *)
           d=0.9040; e= -0.4236; f= -0.0582;
           g= -0.1007; h= -0.0786; i= -0.9918;
           tx= -7.6624; ty= -25.2080; tz=49.5181 },
      { x = 31.3810; y = 0.1400; z = 47.5810 }, (* P    *)
      { x = 29.9860; y = 0.6630; z = 47.6290 }, (* O1P  *)
      { x = 31.7210; y = -0.6460; z = 48.8090 }, (* O2P  *)
      { x = 32.4940; y = 1.2540; z = 47.2740 }, (* O5'  *)
      { x = 32.5924; y = 2.3488; z = 48.2255 }, (* C5'  *)
      { x = 33.3674; y = 2.1246; z = 48.9584 }, (* H5'  *)
      { x = 31.5994; y = 2.5917; z = 48.6037 }, (* H5'' *)
      { x = 33.0722; y = 3.5577; z = 47.4258 }, (* C4'  *)
      { x = 33.0310; y = 4.4778; z = 48.0089 }, (* H4'  *)
      { x = 34.4173; y = 3.3055; z = 47.0316 }, (* O4'  *)
      { x = 34.5056; y = 3.3910; z = 45.6094 }, (* C1'  *)
      { x = 34.7881; y = 4.4152; z = 45.3663 }, (* H1'  *)
      { x = 33.1122; y = 3.1198; z = 45.1010 }, (* C2'  *)
      { x = 32.9230; y = 2.0469; z = 45.1369 }, (* H2'' *)
      { x = 32.7946; y = 3.6590; z = 43.8529 }, (* O2'  *)
      { x = 33.5170; y = 3.6707; z = 43.2207 }, (* H2'  *)
      { x = 32.2730; y = 3.8173; z = 46.1566 }, (* C3'  *)
      { x = 31.3094; y = 3.3123; z = 46.2244 }, (* H3'  *)
      { x = 32.2391; y = 5.2039; z = 45.7807 }, (* O3'  *)
      { x = 39.3337; y = 2.7157; z = 44.1441 }, (* N1   *)
      { x = 37.4430; y = 3.8242; z = 45.0824 }, (* N3   *)
      { x = 38.7276; y = 3.7646; z = 44.7403 }, (* C2   *)
      { x = 36.7791; y = 2.6963; z = 44.7704 }, (* C4   *)
      { x = 37.2860; y = 1.5653; z = 44.1678 }, (* C5   *)
      { x = 38.6647; y = 1.5552; z = 43.8235 }, (* C6 *)
      (G (
      { x = 39.5123; y = 4.8216; z = 44.9936 }, (* N2   *)
      { x = 36.2829; y = 0.6110; z = 44.0078 }, (* N7   *)
      { x = 35.4394; y = 2.4314; z = 44.9931 }, (* N9   *)
      { x = 35.2180; y = 1.1815; z = 44.5128 }, (* C8   *)
      { x = 39.2907; y = 0.6514; z = 43.2796 }, (* O6   *)
      { x = 40.3076; y = 2.8048; z = 43.9352 }, (* H1   *)
      { x = 40.4994; y = 4.9066; z = 44.7977 }, (* H21  *)
      { x = 39.0738; y = 5.6108; z = 45.4464 }, (* H22  *)
      { x = 34.3856; y = 0.4842; z = 44.4185 }) (* H8   *)
      )
    )

let rG09
  = N(
      {    a= -0.9699; b= -0.1688; c= -0.1753; (* dgf_base_tfo *)
           d= -0.1050; e= -0.3598; f=0.9271;
           g= -0.2196; h=0.9176; i=0.3312;
           tx=45.6217; ty= -38.9484; tz= -12.3208 },
      {    a= -0.8644; b= -0.4956; c= -0.0851; (* P_O3'_275_tfo *)
           d= -0.0427; e=0.2409; f= -0.9696;
           g=0.5010; h= -0.8345; i= -0.2294;
           tx=4.0167; ty=54.5377; tz=12.4779 },
      {    a=0.3706; b= -0.6167; c=0.6945; (* P_O3'_180_tfo *)
           d= -0.2867; e= -0.7872; f= -0.5460;
           g=0.8834; h=0.0032; i= -0.4686;
           tx= -52.9020; ty=18.6313; tz= -0.6709 },
      {    a=0.4155; b=0.9025; c= -0.1137; (* P_O3'_60_tfo *)
           d=0.9040; e= -0.4236; f= -0.0582;
           g= -0.1007; h= -0.0786; i= -0.9918;
           tx= -7.6624; ty= -25.2080; tz=49.5181 },
      { x = 31.3810; y = 0.1400; z = 47.5810 }, (* P    *)
      { x = 29.9860; y = 0.6630; z = 47.6290 }, (* O1P  *)
      { x = 31.7210; y = -0.6460; z = 48.8090 }, (* O2P  *)
      { x = 32.4940; y = 1.2540; z = 47.2740 }, (* O5'  *)
      { x = 33.8709; y = 0.7918; z = 47.2113 }, (* C5'  *)
      { x = 34.1386; y = 0.5870; z = 46.1747 }, (* H5'  *)
      { x = 34.0186; y = -0.0095; z = 47.9353 }, (* H5'' *)
      { x = 34.7297; y = 1.9687; z = 47.6685 }, (* C4'  *)
      { x = 34.5880; y = 2.8482; z = 47.0404 }, (* H4'  *)
      { x = 34.3575; y = 2.2770; z = 49.0081 }, (* O4'  *)
      { x = 35.5157; y = 2.1993; z = 49.8389 }, (* C1'  *)
      { x = 35.9424; y = 3.2010; z = 49.8893 }, (* H1'  *)
      { x = 36.4701; y = 1.2820; z = 49.1169 }, (* C2'  *)
      { x = 36.1545; y = 0.2498; z = 49.2683 }, (* H2'' *)
      { x = 37.8262; y = 1.4547; z = 49.4008 }, (* O2'  *)
      { x = 38.0227; y = 1.6945; z = 50.3094 }, (* H2'  *)
      { x = 36.2242; y = 1.6797; z = 47.6725 }, (* C3'  *)
      { x = 36.4297; y = 0.8197; z = 47.0351 }, (* H3'  *)
      { x = 37.0289; y = 2.8480; z = 47.4426 }, (* O3'  *)
      { x = 34.3005; y = 3.5042; z = 54.6070 }, (* N1   *)
      { x = 34.7693; y = 3.7936; z = 52.2874 }, (* N3   *)
      { x = 34.4484; y = 4.2541; z = 53.4939 }, (* C2   *)
      { x = 34.9354; y = 2.4584; z = 52.2785 }, (* C4   *)
      { x = 34.8092; y = 1.5915; z = 53.3422 }, (* C5   *)
      { x = 34.4646; y = 2.1367; z = 54.6085 }, (* C6 *)
      (G (
      { x = 34.2514; y = 5.5708; z = 53.6503 }, (* N2   *)
      { x = 35.0641; y = 0.2835; z = 52.9337 }, (* N7   *)
      { x = 35.2669; y = 1.6690; z = 51.1915 }, (* N9   *)
      { x = 35.3288; y = 0.3954; z = 51.6563 }, (* C8   *)
      { x = 34.3151; y = 1.5317; z = 55.6650 }, (* O6   *)
      { x = 34.0623; y = 3.9797; z = 55.4539 }, (* H1   *)
      { x = 33.9950; y = 6.0502; z = 54.5016 }, (* H21  *)
      { x = 34.3512; y = 6.1432; z = 52.8242 }, (* H22  *)
      { x = 35.5414; y = -0.6006; z = 51.2679 }) (* H8   *)
      )
    )

let rG10
  = N(
      {    a= -0.0980; b= -0.9723; c=0.2122; (* dgf_base_tfo *)
           d= -0.9731; e=0.1383; f=0.1841;
           g= -0.2083; h= -0.1885; i= -0.9597;
           tx=17.8469; ty=38.8265; tz=37.0475 },
      {    a= -0.8644; b= -0.4956; c= -0.0851; (* P_O3'_275_tfo *)
           d= -0.0427; e=0.2409; f= -0.9696;
           g=0.5010; h= -0.8345; i= -0.2294;
           tx=4.0167; ty=54.5377; tz=12.4779 },
      {    a=0.3706; b= -0.6167; c=0.6945; (* P_O3'_180_tfo *)
           d= -0.2867; e= -0.7872; f= -0.5460;
           g=0.8834; h=0.0032; i= -0.4686;
           tx= -52.9020; ty=18.6313; tz= -0.6709 },
      {    a=0.4155; b=0.9025; c= -0.1137; (* P_O3'_60_tfo *)
           d=0.9040; e= -0.4236; f= -0.0582;
           g= -0.1007; h= -0.0786; i= -0.9918;
           tx= -7.6624; ty= -25.2080; tz=49.5181 },
      { x = 31.3810; y = 0.1400; z = 47.5810 }, (* P    *)
      { x = 29.9860; y = 0.6630; z = 47.6290 }, (* O1P  *)
      { x = 31.7210; y = -0.6460; z = 48.8090 }, (* O2P  *)
      { x = 32.4940; y = 1.2540; z = 47.2740 }, (* O5'  *)
      { x = 32.5924; y = 2.3488; z = 48.2255 }, (* C5'  *)
      { x = 33.3674; y = 2.1246; z = 48.9584 }, (* H5'  *)
      { x = 31.5994; y = 2.5917; z = 48.6037 }, (* H5'' *)
      { x = 33.0722; y = 3.5577; z = 47.4258 }, (* C4'  *)
      { x = 34.0333; y = 3.3761; z = 46.9447 }, (* H4'  *)
      { x = 32.0890; y = 3.8338; z = 46.4332 }, (* O4'  *)
      { x = 31.6377; y = 5.1787; z = 46.5914 }, (* C1'  *)
      { x = 32.2499; y = 5.8016; z = 45.9392 }, (* H1'  *)
      { x = 31.9167; y = 5.5319; z = 48.0305 }, (* C2'  *)
      { x = 31.1507; y = 5.0820; z = 48.6621 }, (* H2'' *)
      { x = 32.0865; y = 6.8890; z = 48.3114 }, (* O2'  *)
      { x = 31.5363; y = 7.4819; z = 47.7942 }, (* H2'  *)
      { x = 33.2398; y = 4.8224; z = 48.2563 }, (* C3'  *)
      { x = 33.3166; y = 4.5570; z = 49.3108 }, (* H3'  *)
      { x = 34.2528; y = 5.7056; z = 47.7476 }, (* O3'  *)
      { x = 28.2782; y = 6.3049; z = 42.9364 }, (* N1   *)
      { x = 30.4001; y = 5.8547; z = 43.9258 }, (* N3   *)
      { x = 29.6195; y = 6.1568; z = 42.8913 }, (* C2   *)
      { x = 29.7005; y = 5.7006; z = 45.0649 }, (* C4   *)
      { x = 28.3383; y = 5.8221; z = 45.2343 }, (* C5   *)
      { x = 27.5519; y = 6.1461; z = 44.0958 }, (* C6 *)
      (G (
      { x = 30.1838; y = 6.3385; z = 41.6890 }, (* N2   *)
      { x = 27.9936; y = 5.5926; z = 46.5651 }, (* N7   *)
      { x = 30.2046; y = 5.3825; z = 46.3136 }, (* N9   *)
      { x = 29.1371; y = 5.3398; z = 47.1506 }, (* C8   *)
      { x = 26.3361; y = 6.3024; z = 44.0495 }, (* O6   *)
      { x = 27.8122; y = 6.5394; z = 42.0833 }, (* H1   *)
      { x = 29.7125; y = 6.5595; z = 40.8235 }, (* H21  *)
      { x = 31.1859; y = 6.2231; z = 41.6389 }, (* H22  *)
      { x = 28.9406; y = 5.1504; z = 48.2059 }) (* H8   *)
      )
    )

let rGs = [rG01;rG02;rG03;rG04;rG05;rG06;rG07;rG08;rG09;rG10]

let rU
  = N(
      {    a= -0.0359; b= -0.8071; c=0.5894; (* dgf_base_tfo *)
           d= -0.2669; e=0.5761; f=0.7726;
           g= -0.9631; h= -0.1296; i= -0.2361;
           tx=0.1584; ty=8.3434; tz=0.5434 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 5.2430; y = -8.2420; z = 2.8260 }, (* C5'  *)
      { x = 5.1974; y = -8.8497; z = 1.9223 }, (* H5'  *)
      { x = 5.5548; y = -8.7348; z = 3.7469 }, (* H5'' *)
      { x = 6.3140; y = -7.2060; z = 2.5510 }, (* C4'  *)
      { x = 7.2954; y = -7.6762; z = 2.4898 }, (* H4'  *)
      { x = 6.0140; y = -6.5420; z = 1.2890 }, (* O4'  *)
      { x = 6.4190; y = -5.1840; z = 1.3620 }, (* C1'  *)
      { x = 7.1608; y = -5.0495; z = 0.5747 }, (* H1'  *)
      { x = 7.0760; y = -4.9560; z = 2.7270 }, (* C2'  *)
      { x = 6.7770; y = -3.9803; z = 3.1099 }, (* H2'' *)
      { x = 8.4500; y = -5.1930; z = 2.5810 }, (* O2'  *)
      { x = 8.8309; y = -4.8755; z = 1.7590 }, (* H2'  *)
      { x = 6.4060; y = -6.0590; z = 3.5580 }, (* C3'  *)
      { x = 5.4021; y = -5.7313; z = 3.8281 }, (* H3'  *)
      { x = 7.1570; y = -6.4240; z = 4.7070 }, (* O3'  *)
      { x = 5.2170; y = -4.3260; z = 1.1690 }, (* N1   *)
      { x = 4.2960; y = -2.2560; z = 0.6290 }, (* N3   *)
      { x = 5.4330; y = -3.0200; z = 0.7990 }, (* C2   *)
      { x = 2.9930; y = -2.6780; z = 0.7940 }, (* C4   *)
      { x = 2.8670; y = -4.0630; z = 1.1830 }, (* C5   *)
      { x = 3.9570; y = -4.8300; z = 1.3550 }, (* C6 *)
      (U (
      { x = 6.5470; y = -2.5560; z = 0.6290 }, (* O2   *)
      { x = 2.0540; y = -1.9000; z = 0.6130 }, (* O4   *)
      { x = 4.4300; y = -1.3020; z = 0.3600 }, (* H3   *)
      { x = 1.9590; y = -4.4570; z = 1.3250 }, (* H5   *)
      { x = 3.8460; y = -5.7860; z = 1.6240 }) (* H6   *)
      )
    )

let rU01
  = N(
      {    a= -0.0137; b= -0.8012; c=0.5983; (* dgf_base_tfo *)
           d= -0.2523; e=0.5817; f=0.7733;
           g= -0.9675; h= -0.1404; i= -0.2101;
           tx=0.2031; ty=8.3874; tz=0.4228 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 5.2416; y = -8.2422; z = 2.8181 }, (* C5'  *)
      { x = 5.2050; y = -8.8128; z = 1.8901 }, (* H5'  *)
      { x = 5.5368; y = -8.7738; z = 3.7227 }, (* H5'' *)
      { x = 6.3232; y = -7.2037; z = 2.6002 }, (* C4'  *)
      { x = 7.3048; y = -7.6757; z = 2.5577 }, (* H4'  *)
      { x = 6.0635; y = -6.5092; z = 1.3456 }, (* O4'  *)
      { x = 6.4697; y = -5.1547; z = 1.4629 }, (* C1'  *)
      { x = 7.2354; y = -5.0043; z = 0.7018 }, (* H1'  *)
      { x = 7.0856; y = -4.9610; z = 2.8521 }, (* C2'  *)
      { x = 6.7777; y = -3.9935; z = 3.2487 }, (* H2'' *)
      { x = 8.4627; y = -5.1992; z = 2.7423 }, (* O2'  *)
      { x = 8.8693; y = -4.8638; z = 1.9399 }, (* H2'  *)
      { x = 6.3877; y = -6.0809; z = 3.6362 }, (* C3'  *)
      { x = 5.3770; y = -5.7562; z = 3.8834 }, (* H3'  *)
      { x = 7.1024; y = -6.4754; z = 4.7985 }, (* O3'  *)
      { x = 5.2764; y = -4.2883; z = 1.2538 }, (* N1   *)
      { x = 4.3777; y = -2.2062; z = 0.7229 }, (* N3   *)
      { x = 5.5069; y = -2.9779; z = 0.9088 }, (* C2   *)
      { x = 3.0693; y = -2.6246; z = 0.8500 }, (* C4   *)
      { x = 2.9279; y = -4.0146; z = 1.2149 }, (* C5   *)
      { x = 4.0101; y = -4.7892; z = 1.4017 }, (* C6 *)
      (U (
      { x = 6.6267; y = -2.5166; z = 0.7728 }, (* O2   *)
      { x = 2.1383; y = -1.8396; z = 0.6581 }, (* O4   *)
      { x = 4.5223; y = -1.2489; z = 0.4716 }, (* H3   *)
      { x = 2.0151; y = -4.4065; z = 1.3290 }, (* H5   *)
      { x = 3.8886; y = -5.7486; z = 1.6535 }) (* H6   *)
      )
    )

let rU02
  = N(
      {    a=0.5141; b=0.0246; c=0.8574; (* dgf_base_tfo *)
           d= -0.5547; e= -0.7529; f=0.3542;
           g=0.6542; h= -0.6577; i= -0.3734;
           tx= -9.1111; ty= -3.4598; tz= -3.2939 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 4.3825; y = -6.6585; z = 4.0489 }, (* C5'  *)
      { x = 4.6841; y = -7.2019; z = 4.9443 }, (* H5'  *)
      { x = 3.6189; y = -5.8889; z = 4.1625 }, (* H5'' *)
      { x = 5.6255; y = -5.9175; z = 3.5998 }, (* C4'  *)
      { x = 5.8732; y = -5.1228; z = 4.3034 }, (* H4'  *)
      { x = 6.7337; y = -6.8605; z = 3.5222 }, (* O4'  *)
      { x = 7.5932; y = -6.4923; z = 2.4548 }, (* C1'  *)
      { x = 8.5661; y = -6.2983; z = 2.9064 }, (* H1'  *)
      { x = 7.0527; y = -5.2012; z = 1.8322 }, (* C2'  *)
      { x = 7.1627; y = -5.2525; z = 0.7490 }, (* H2'' *)
      { x = 7.6666; y = -4.1249; z = 2.4880 }, (* O2'  *)
      { x = 8.5944; y = -4.2543; z = 2.6981 }, (* H2'  *)
      { x = 5.5661; y = -5.3029; z = 2.2009 }, (* C3'  *)
      { x = 5.0841; y = -6.0018; z = 1.5172 }, (* H3'  *)
      { x = 4.9062; y = -4.0452; z = 2.2042 }, (* O3'  *)
      { x = 7.6298; y = -7.6136; z = 1.4752 }, (* N1   *)
      { x = 8.6945; y = -8.7046; z = -0.2857 }, (* N3   *)
      { x = 8.6943; y = -7.6514; z = 0.6066 }, (* C2   *)
      { x = 7.7426; y = -9.6987; z = -0.3801 }, (* C4   *)
      { x = 6.6642; y = -9.5742; z = 0.5722 }, (* C5   *)
      { x = 6.6391; y = -8.5592; z = 1.4526 }, (* C6 *)
      (U (
      { x = 9.5840; y = -6.8186; z = 0.6136 }, (* O2   *)
      { x = 7.8505; y = -10.5925; z = -1.2223 }, (* O4   *)
      { x = 9.4601; y = -8.7514; z = -0.9277 }, (* H3   *)
      { x = 5.9281; y = -10.2509; z = 0.5782 }, (* H5   *)
      { x = 5.8831; y = -8.4931; z = 2.1028 }) (* H6   *)
      )
    )

let rU03
  = N(
      {    a= -0.4993; b=0.0476; c=0.8651; (* dgf_base_tfo *)
           d=0.8078; e= -0.3353; f=0.4847;
           g=0.3132; h=0.9409; i=0.1290;
           tx=6.2989; ty= -5.2303; tz= -3.8577 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 3.9938; y = -6.7042; z = 1.9023 }, (* C5'  *)
      { x = 3.2332; y = -5.9343; z = 2.0319 }, (* H5'  *)
      { x = 3.9666; y = -7.2863; z = 0.9812 }, (* H5'' *)
      { x = 5.3098; y = -5.9546; z = 1.8564 }, (* C4'  *)
      { x = 5.3863; y = -5.3702; z = 0.9395 }, (* H4'  *)
      { x = 5.3851; y = -5.0642; z = 3.0076 }, (* O4'  *)
      { x = 6.7315; y = -4.9724; z = 3.4462 }, (* C1'  *)
      { x = 7.0033; y = -3.9202; z = 3.3619 }, (* H1'  *)
      { x = 7.5997; y = -5.8018; z = 2.4948 }, (* C2'  *)
      { x = 8.3627; y = -6.3254; z = 3.0707 }, (* H2'' *)
      { x = 8.0410; y = -4.9501; z = 1.4724 }, (* O2'  *)
      { x = 8.2781; y = -4.0644; z = 1.7570 }, (* H2'  *)
      { x = 6.5701; y = -6.8129; z = 1.9714 }, (* C3'  *)
      { x = 6.4186; y = -7.5809; z = 2.7299 }, (* H3'  *)
      { x = 6.9357; y = -7.3841; z = 0.7235 }, (* O3'  *)
      { x = 6.8024; y = -5.4718; z = 4.8475 }, (* N1   *)
      { x = 7.9218; y = -5.5700; z = 6.8877 }, (* N3   *)
      { x = 7.8908; y = -5.0886; z = 5.5944 }, (* C2   *)
      { x = 6.9789; y = -6.3827; z = 7.4823 }, (* C4   *)
      { x = 5.8742; y = -6.7319; z = 6.6202 }, (* C5   *)
      { x = 5.8182; y = -6.2769; z = 5.3570 }, (* C6 *)
      (U (
      { x = 8.7747; y = -4.3728; z = 5.1568 }, (* O2   *)
      { x = 7.1154; y = -6.7509; z = 8.6509 }, (* O4   *)
      { x = 8.7055; y = -5.3037; z = 7.4491 }, (* H3   *)
      { x = 5.1416; y = -7.3178; z = 6.9665 }, (* H5   *)
      { x = 5.0441; y = -6.5310; z = 4.7784 }) (* H6   *)
      )
    )

let rU04
  = N(
      {    a= -0.5669; b= -0.8012; c=0.1918; (* dgf_base_tfo *)
           d= -0.8129; e=0.5817; f=0.0273;
           g= -0.1334; h= -0.1404; i= -0.9811;
           tx= -0.3279; ty=8.3874; tz=0.3355 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 5.2416; y = -8.2422; z = 2.8181 }, (* C5'  *)
      { x = 5.2050; y = -8.8128; z = 1.8901 }, (* H5'  *)
      { x = 5.5368; y = -8.7738; z = 3.7227 }, (* H5'' *)
      { x = 6.3232; y = -7.2037; z = 2.6002 }, (* C4'  *)
      { x = 7.3048; y = -7.6757; z = 2.5577 }, (* H4'  *)
      { x = 6.0635; y = -6.5092; z = 1.3456 }, (* O4'  *)
      { x = 6.4697; y = -5.1547; z = 1.4629 }, (* C1'  *)
      { x = 7.2354; y = -5.0043; z = 0.7018 }, (* H1'  *)
      { x = 7.0856; y = -4.9610; z = 2.8521 }, (* C2'  *)
      { x = 6.7777; y = -3.9935; z = 3.2487 }, (* H2'' *)
      { x = 8.4627; y = -5.1992; z = 2.7423 }, (* O2'  *)
      { x = 8.8693; y = -4.8638; z = 1.9399 }, (* H2'  *)
      { x = 6.3877; y = -6.0809; z = 3.6362 }, (* C3'  *)
      { x = 5.3770; y = -5.7562; z = 3.8834 }, (* H3'  *)
      { x = 7.1024; y = -6.4754; z = 4.7985 }, (* O3'  *)
      { x = 5.2764; y = -4.2883; z = 1.2538 }, (* N1   *)
      { x = 3.8961; y = -3.0896; z = -0.1893 }, (* N3   *)
      { x = 5.0095; y = -3.8907; z = -0.0346 }, (* C2   *)
      { x = 3.0480; y = -2.6632; z = 0.8116 }, (* C4   *)
      { x = 3.4093; y = -3.1310; z = 2.1292 }, (* C5   *)
      { x = 4.4878; y = -3.9124; z = 2.3088 }, (* C6 *)
      (U (
      { x = 5.7005; y = -4.2164; z = -0.9842 }, (* O2   *)
      { x = 2.0800; y = -1.9458; z = 0.5503 }, (* O4   *)
      { x = 3.6834; y = -2.7882; z = -1.1190 }, (* H3   *)
      { x = 2.8508; y = -2.8721; z = 2.9172 }, (* H5   *)
      { x = 4.7188; y = -4.2247; z = 3.2295 }) (* H6   *)
      )
    )

let rU05
  = N(
      {    a= -0.6298; b=0.0246; c=0.7763; (* dgf_base_tfo *)
           d= -0.5226; e= -0.7529; f= -0.4001;
           g=0.5746; h= -0.6577; i=0.4870;
           tx= -0.0208; ty= -3.4598; tz= -9.6882 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 4.3825; y = -6.6585; z = 4.0489 }, (* C5'  *)
      { x = 4.6841; y = -7.2019; z = 4.9443 }, (* H5'  *)
      { x = 3.6189; y = -5.8889; z = 4.1625 }, (* H5'' *)
      { x = 5.6255; y = -5.9175; z = 3.5998 }, (* C4'  *)
      { x = 5.8732; y = -5.1228; z = 4.3034 }, (* H4'  *)
      { x = 6.7337; y = -6.8605; z = 3.5222 }, (* O4'  *)
      { x = 7.5932; y = -6.4923; z = 2.4548 }, (* C1'  *)
      { x = 8.5661; y = -6.2983; z = 2.9064 }, (* H1'  *)
      { x = 7.0527; y = -5.2012; z = 1.8322 }, (* C2'  *)
      { x = 7.1627; y = -5.2525; z = 0.7490 }, (* H2'' *)
      { x = 7.6666; y = -4.1249; z = 2.4880 }, (* O2'  *)
      { x = 8.5944; y = -4.2543; z = 2.6981 }, (* H2'  *)
      { x = 5.5661; y = -5.3029; z = 2.2009 }, (* C3'  *)
      { x = 5.0841; y = -6.0018; z = 1.5172 }, (* H3'  *)
      { x = 4.9062; y = -4.0452; z = 2.2042 }, (* O3'  *)
      { x = 7.6298; y = -7.6136; z = 1.4752 }, (* N1   *)
      { x = 8.5977; y = -9.5977; z = 0.7329 }, (* N3   *)
      { x = 8.5951; y = -8.5745; z = 1.6594 }, (* C2   *)
      { x = 7.7372; y = -9.7371; z = -0.3364 }, (* C4   *)
      { x = 6.7596; y = -8.6801; z = -0.4476 }, (* C5   *)
      { x = 6.7338; y = -7.6721; z = 0.4408 }, (* C6 *)
      (U (
      { x = 9.3993; y = -8.5377; z = 2.5743 }, (* O2   *)
      { x = 7.8374; y = -10.6990; z = -1.1008 }, (* O4   *)
      { x = 9.2924; y = -10.3081; z = 0.8477 }, (* H3   *)
      { x = 6.0932; y = -8.6982; z = -1.1929 }, (* H5   *)
      { x = 6.0481; y = -6.9515; z = 0.3446 }) (* H6   *)
      )
    )

let rU06
  = N(
      {    a= -0.9837; b=0.0476; c= -0.1733; (* dgf_base_tfo *)
           d= -0.1792; e= -0.3353; f=0.9249;
           g= -0.0141; h=0.9409; i=0.3384;
           tx=5.7793; ty= -5.2303; tz=4.5997 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 3.9938; y = -6.7042; z = 1.9023 }, (* C5'  *)
      { x = 3.2332; y = -5.9343; z = 2.0319 }, (* H5'  *)
      { x = 3.9666; y = -7.2863; z = 0.9812 }, (* H5'' *)
      { x = 5.3098; y = -5.9546; z = 1.8564 }, (* C4'  *)
      { x = 5.3863; y = -5.3702; z = 0.9395 }, (* H4'  *)
      { x = 5.3851; y = -5.0642; z = 3.0076 }, (* O4'  *)
      { x = 6.7315; y = -4.9724; z = 3.4462 }, (* C1'  *)
      { x = 7.0033; y = -3.9202; z = 3.3619 }, (* H1'  *)
      { x = 7.5997; y = -5.8018; z = 2.4948 }, (* C2'  *)
      { x = 8.3627; y = -6.3254; z = 3.0707 }, (* H2'' *)
      { x = 8.0410; y = -4.9501; z = 1.4724 }, (* O2'  *)
      { x = 8.2781; y = -4.0644; z = 1.7570 }, (* H2'  *)
      { x = 6.5701; y = -6.8129; z = 1.9714 }, (* C3'  *)
      { x = 6.4186; y = -7.5809; z = 2.7299 }, (* H3'  *)
      { x = 6.9357; y = -7.3841; z = 0.7235 }, (* O3'  *)
      { x = 6.8024; y = -5.4718; z = 4.8475 }, (* N1   *)
      { x = 6.6920; y = -5.0495; z = 7.1354 }, (* N3   *)
      { x = 6.6201; y = -4.5500; z = 5.8506 }, (* C2   *)
      { x = 6.9254; y = -6.3614; z = 7.4926 }, (* C4   *)
      { x = 7.1046; y = -7.2543; z = 6.3718 }, (* C5   *)
      { x = 7.0391; y = -6.7951; z = 5.1106 }, (* C6 *)
      (U (
      { x = 6.4083; y = -3.3696; z = 5.6340 }, (* O2   *)
      { x = 6.9679; y = -6.6901; z = 8.6800 }, (* O4   *)
      { x = 6.5626; y = -4.3957; z = 7.8812 }, (* H3   *)
      { x = 7.2781; y = -8.2254; z = 6.5350 }, (* H5   *)
      { x = 7.1657; y = -7.4312; z = 4.3503 }) (* H6   *)
      )
    )

let rU07
  = N(
      {    a= -0.9434; b=0.3172; c=0.0971; (* dgf_base_tfo *)
           d=0.2294; e=0.4125; f=0.8816;
           g=0.2396; h=0.8539; i= -0.4619;
           tx=8.3625; ty= -52.7147; tz=1.3745 },
      {    a=0.2765; b= -0.1121; c= -0.9545; (* P_O3'_275_tfo *)
           d= -0.8297; e=0.4733; f= -0.2959;
           g=0.4850; h=0.8737; i=0.0379;
           tx= -14.7774; ty= -45.2464; tz=21.9088 },
      {    a=0.1063; b= -0.6334; c= -0.7665; (* P_O3'_180_tfo *)
           d= -0.5932; e= -0.6591; f=0.4624;
           g= -0.7980; h=0.4055; i= -0.4458;
           tx=43.7634; ty=4.3296; tz=28.4890 },
      {    a=0.7136; b= -0.5032; c= -0.4873; (* P_O3'_60_tfo *)
           d=0.6803; e=0.3317; f=0.6536;
           g= -0.1673; h= -0.7979; i=0.5791;
           tx= -17.1858; ty=41.4390; tz= -27.0751 },
      { x = 21.3880; y = 15.0780; z = 45.5770 }, (* P    *)
      { x = 21.9980; y = 14.5500; z = 46.8210 }, (* O1P  *)
      { x = 21.1450; y = 14.0270; z = 44.5420 }, (* O2P  *)
      { x = 22.1250; y = 16.3600; z = 44.9460 }, (* O5'  *)
      { x = 21.5037; y = 16.8594; z = 43.7323 }, (* C5'  *)
      { x = 20.8147; y = 17.6663; z = 43.9823 }, (* H5'  *)
      { x = 21.1086; y = 16.0230; z = 43.1557 }, (* H5'' *)
      { x = 22.5654; y = 17.4874; z = 42.8616 }, (* C4'  *)
      { x = 22.1584; y = 17.7243; z = 41.8785 }, (* H4'  *)
      { x = 23.0557; y = 18.6826; z = 43.4751 }, (* O4'  *)
      { x = 24.4788; y = 18.6151; z = 43.6455 }, (* C1'  *)
      { x = 24.9355; y = 19.0840; z = 42.7739 }, (* H1'  *)
      { x = 24.7958; y = 17.1427; z = 43.6474 }, (* C2'  *)
      { x = 24.5652; y = 16.7400; z = 44.6336 }, (* H2'' *)
      { x = 26.1041; y = 16.8773; z = 43.2455 }, (* O2'  *)
      { x = 26.7516; y = 17.5328; z = 43.5149 }, (* H2'  *)
      { x = 23.8109; y = 16.5979; z = 42.6377 }, (* C3'  *)
      { x = 23.5756; y = 15.5686; z = 42.9084 }, (* H3'  *)
      { x = 24.2890; y = 16.7447; z = 41.2729 }, (* O3'  *)
      { x = 24.9420; y = 19.2174; z = 44.8923 }, (* N1   *)
      { x = 25.2655; y = 20.5636; z = 44.8883 }, (* N3   *)
      { x = 25.1663; y = 21.2219; z = 43.8561 }, (* C2   *)
      { x = 25.6911; y = 21.1219; z = 46.0494 }, (* C4   *)
      { x = 25.8051; y = 20.4068; z = 47.2048 }, (* C5   *)
      { x = 26.2093; y = 20.9962; z = 48.2534 }, (* C6 *)
      (U (
      { x = 25.4692; y = 19.0221; z = 47.2053 }, (* O2   *)
      { x = 25.0502; y = 18.4827; z = 46.0370 }, (* O4   *)
      { x = 25.9599; y = 22.1772; z = 46.0966 }, (* H3   *)
      { x = 25.5545; y = 18.4409; z = 48.1234 }, (* H5   *)
      { x = 24.7854; y = 17.4265; z = 45.9883 }) (* H6   *)
      )
    )

let rU08
  = N(
      {    a= -0.0080; b= -0.7928; c=0.6094; (* dgf_base_tfo *)
           d= -0.7512; e=0.4071; f=0.5197;
           g= -0.6601; h= -0.4536; i= -0.5988;
           tx=44.1482; ty=30.7036; tz=2.1088 },
      {    a=0.2765; b= -0.1121; c= -0.9545; (* P_O3'_275_tfo *)
           d= -0.8297; e=0.4733; f= -0.2959;
           g=0.4850; h=0.8737; i=0.0379;
           tx= -14.7774; ty= -45.2464; tz=21.9088 },
      {    a=0.1063; b= -0.6334; c= -0.7665; (* P_O3'_180_tfo *)
           d= -0.5932; e= -0.6591; f=0.4624;
           g= -0.7980; h=0.4055; i= -0.4458;
           tx=43.7634; ty=4.3296; tz=28.4890 },
      {    a=0.7136; b= -0.5032; c= -0.4873; (* P_O3'_60_tfo *)
           d=0.6803; e=0.3317; f=0.6536;
           g= -0.1673; h= -0.7979; i=0.5791;
           tx= -17.1858; ty=41.4390; tz= -27.0751 },
      { x = 21.3880; y = 15.0780; z = 45.5770 }, (* P    *)
      { x = 21.9980; y = 14.5500; z = 46.8210 }, (* O1P  *)
      { x = 21.1450; y = 14.0270; z = 44.5420 }, (* O2P  *)
      { x = 22.1250; y = 16.3600; z = 44.9460 }, (* O5'  *)
      { x = 23.5096; y = 16.1227; z = 44.5783 }, (* C5'  *)
      { x = 23.5649; y = 15.8588; z = 43.5222 }, (* H5'  *)
      { x = 23.9621; y = 15.4341; z = 45.2919 }, (* H5'' *)
      { x = 24.2805; y = 17.4138; z = 44.7151 }, (* C4'  *)
      { x = 25.3492; y = 17.2309; z = 44.6030 }, (* H4'  *)
      { x = 23.8497; y = 18.3471; z = 43.7208 }, (* O4'  *)
      { x = 23.4090; y = 19.5681; z = 44.3321 }, (* C1'  *)
      { x = 24.2595; y = 20.2496; z = 44.3524 }, (* H1'  *)
      { x = 23.0418; y = 19.1813; z = 45.7407 }, (* C2'  *)
      { x = 22.0532; y = 18.7224; z = 45.7273 }, (* H2'' *)
      { x = 23.1307; y = 20.2521; z = 46.6291 }, (* O2'  *)
      { x = 22.8888; y = 21.1051; z = 46.2611 }, (* H2'  *)
      { x = 24.0799; y = 18.1326; z = 46.0700 }, (* C3'  *)
      { x = 23.6490; y = 17.4370; z = 46.7900 }, (* H3'  *)
      { x = 25.3329; y = 18.7227; z = 46.5109 }, (* O3'  *)
      { x = 22.2515; y = 20.1624; z = 43.6698 }, (* N1   *)
      { x = 22.4760; y = 21.0609; z = 42.6406 }, (* N3   *)
      { x = 23.6229; y = 21.3462; z = 42.3061 }, (* C2   *)
      { x = 21.3986; y = 21.6081; z = 42.0236 }, (* C4   *)
      { x = 20.1189; y = 21.3012; z = 42.3804 }, (* C5   *)
      { x = 19.1599; y = 21.8516; z = 41.7578 }, (* C6 *)
      (U (
      { x = 19.8919; y = 20.3745; z = 43.4387 }, (* O2   *)
      { x = 20.9790; y = 19.8423; z = 44.0440 }, (* O4   *)
      { x = 21.5235; y = 22.3222; z = 41.2097 }, (* H3   *)
      { x = 18.8732; y = 20.1200; z = 43.7312 }, (* H5   *)
      { x = 20.8545; y = 19.1313; z = 44.8608 }) (* H6   *)
      )
    )

let rU09
  = N(
      {    a= -0.0317; b=0.1374; c=0.9900; (* dgf_base_tfo *)
           d= -0.3422; e= -0.9321; f=0.1184;
           g=0.9391; h= -0.3351; i=0.0765;
           tx= -32.1929; ty=25.8198; tz= -28.5088 },
      {    a=0.2765; b= -0.1121; c= -0.9545; (* P_O3'_275_tfo *)
           d= -0.8297; e=0.4733; f= -0.2959;
           g=0.4850; h=0.8737; i=0.0379;
           tx= -14.7774; ty= -45.2464; tz=21.9088 },
      {    a=0.1063; b= -0.6334; c= -0.7665; (* P_O3'_180_tfo *)
           d= -0.5932; e= -0.6591; f=0.4624;
           g= -0.7980; h=0.4055; i= -0.4458;
           tx=43.7634; ty=4.3296; tz=28.4890 },
      {    a=0.7136; b= -0.5032; c= -0.4873; (* P_O3'_60_tfo *)
           d=0.6803; e=0.3317; f=0.6536;
           g= -0.1673; h= -0.7979; i=0.5791;
           tx= -17.1858; ty=41.4390; tz= -27.0751 },
      { x = 21.3880; y = 15.0780; z = 45.5770 }, (* P    *)
      { x = 21.9980; y = 14.5500; z = 46.8210 }, (* O1P  *)
      { x = 21.1450; y = 14.0270; z = 44.5420 }, (* O2P  *)
      { x = 22.1250; y = 16.3600; z = 44.9460 }, (* O5'  *)
      { x = 21.5037; y = 16.8594; z = 43.7323 }, (* C5'  *)
      { x = 20.8147; y = 17.6663; z = 43.9823 }, (* H5'  *)
      { x = 21.1086; y = 16.0230; z = 43.1557 }, (* H5'' *)
      { x = 22.5654; y = 17.4874; z = 42.8616 }, (* C4'  *)
      { x = 23.0565; y = 18.3036; z = 43.3915 }, (* H4'  *)
      { x = 23.5375; y = 16.5054; z = 42.4925 }, (* O4'  *)
      { x = 23.6574; y = 16.4257; z = 41.0649 }, (* C1'  *)
      { x = 24.4701; y = 17.0882; z = 40.7671 }, (* H1'  *)
      { x = 22.3525; y = 16.9643; z = 40.5396 }, (* C2'  *)
      { x = 21.5993; y = 16.1799; z = 40.6133 }, (* H2'' *)
      { x = 22.4693; y = 17.4849; z = 39.2515 }, (* O2'  *)
      { x = 23.0899; y = 17.0235; z = 38.6827 }, (* H2'  *)
      { x = 22.0341; y = 18.0633; z = 41.5279 }, (* C3'  *)
      { x = 20.9509; y = 18.1709; z = 41.5846 }, (* H3'  *)
      { x = 22.7249; y = 19.3020; z = 41.2100 }, (* O3'  *)
      { x = 23.8580; y = 15.0648; z = 40.5757 }, (* N1   *)
      { x = 25.1556; y = 14.5982; z = 40.4523 }, (* N3   *)
      { x = 26.1047; y = 15.3210; z = 40.7448 }, (* C2   *)
      { x = 25.3391; y = 13.3315; z = 40.0020 }, (* C4   *)
      { x = 24.2974; y = 12.5148; z = 39.6749 }, (* C5   *)
      { x = 24.5450; y = 11.3410; z = 39.2610 }, (* C6 *)
      (U (
      { x = 22.9633; y = 12.9979; z = 39.8053 }, (* O2   *)
      { x = 22.8009; y = 14.2648; z = 40.2524 }, (* O4   *)
      { x = 26.3414; y = 12.9194; z = 39.8855 }, (* H3   *)
      { x = 22.1227; y = 12.3533; z = 39.5486 }, (* H5   *)
      { x = 21.7989; y = 14.6788; z = 40.3650 }) (* H6   *)
      )
    )

let rU10
  = N(
      {    a= -0.9674; b=0.1021; c= -0.2318; (* dgf_base_tfo *)
           d= -0.2514; e= -0.2766; f=0.9275;
           g=0.0306; h=0.9555; i=0.2933;
           tx=27.8571; ty= -42.1305; tz= -24.4563 },
      {    a=0.2765; b= -0.1121; c= -0.9545; (* P_O3'_275_tfo *)
           d= -0.8297; e=0.4733; f= -0.2959;
           g=0.4850; h=0.8737; i=0.0379;
           tx= -14.7774; ty= -45.2464; tz=21.9088 },
      {    a=0.1063; b= -0.6334; c= -0.7665; (* P_O3'_180_tfo *)
           d= -0.5932; e= -0.6591; f=0.4624;
           g= -0.7980; h=0.4055; i= -0.4458;
           tx=43.7634; ty=4.3296; tz=28.4890 },
      {    a=0.7136; b= -0.5032; c= -0.4873; (* P_O3'_60_tfo *)
           d=0.6803; e=0.3317; f=0.6536;
           g= -0.1673; h= -0.7979; i=0.5791;
           tx= -17.1858; ty=41.4390; tz= -27.0751 },
      { x = 21.3880; y = 15.0780; z = 45.5770 }, (* P    *)
      { x = 21.9980; y = 14.5500; z = 46.8210 }, (* O1P  *)
      { x = 21.1450; y = 14.0270; z = 44.5420 }, (* O2P  *)
      { x = 22.1250; y = 16.3600; z = 44.9460 }, (* O5'  *)
      { x = 23.5096; y = 16.1227; z = 44.5783 }, (* C5'  *)
      { x = 23.5649; y = 15.8588; z = 43.5222 }, (* H5'  *)
      { x = 23.9621; y = 15.4341; z = 45.2919 }, (* H5'' *)
      { x = 24.2805; y = 17.4138; z = 44.7151 }, (* C4'  *)
      { x = 23.8509; y = 18.1819; z = 44.0720 }, (* H4'  *)
      { x = 24.2506; y = 17.8583; z = 46.0741 }, (* O4'  *)
      { x = 25.5830; y = 18.0320; z = 46.5775 }, (* C1'  *)
      { x = 25.8569; y = 19.0761; z = 46.4256 }, (* H1'  *)
      { x = 26.4410; y = 17.1555; z = 45.7033 }, (* C2'  *)
      { x = 26.3459; y = 16.1253; z = 46.0462 }, (* H2'' *)
      { x = 27.7649; y = 17.5888; z = 45.6478 }, (* O2'  *)
      { x = 28.1004; y = 17.9719; z = 46.4616 }, (* H2'  *)
      { x = 25.7796; y = 17.2997; z = 44.3513 }, (* C3'  *)
      { x = 25.9478; y = 16.3824; z = 43.7871 }, (* H3'  *)
      { x = 26.2154; y = 18.4984; z = 43.6541 }, (* O3'  *)
      { x = 25.7321; y = 17.6281; z = 47.9726 }, (* N1   *)
      { x = 25.5136; y = 18.5779; z = 48.9560 }, (* N3   *)
      { x = 25.2079; y = 19.7276; z = 48.6503 }, (* C2   *)
      { x = 25.6482; y = 18.1987; z = 50.2518 }, (* C4   *)
      { x = 25.9847; y = 16.9266; z = 50.6092 }, (* C5   *)
      { x = 26.0918; y = 16.6439; z = 51.8416 }, (* C6 *)
      (U (
      { x = 26.2067; y = 15.9515; z = 49.5943 }, (* O2   *)
      { x = 26.0713; y = 16.3497; z = 48.3080 }, (* O4   *)
      { x = 25.4890; y = 18.9105; z = 51.0618 }, (* H3   *)
      { x = 26.4742; y = 14.9310; z = 49.8682 }, (* H5   *)
      { x = 26.2346; y = 15.6394; z = 47.4975 }) (* H6   *)
      )
    )

let rUs = [rU01;rU02;rU03;rU04;rU05;rU06;rU07;rU08;rU09;rU10]

let rG'
  = N(
      {    a= -0.2067; b= -0.0264; c=0.9780; (* dgf_base_tfo *)
           d=0.9770; e= -0.0586; f=0.2049;
           g=0.0519; h=0.9979; i=0.0379;
           tx=1.0331; ty= -46.8078; tz= -36.4742 },
      {    a= -0.8644; b= -0.4956; c= -0.0851; (* P_O3'_275_tfo *)
           d= -0.0427; e=0.2409; f= -0.9696;
           g=0.5010; h= -0.8345; i= -0.2294;
           tx=4.0167; ty=54.5377; tz=12.4779 },
      {    a=0.3706; b= -0.6167; c=0.6945; (* P_O3'_180_tfo *)
           d= -0.2867; e= -0.7872; f= -0.5460;
           g=0.8834; h=0.0032; i= -0.4686;
           tx= -52.9020; ty=18.6313; tz= -0.6709 },
      {    a=0.4155; b=0.9025; c= -0.1137; (* P_O3'_60_tfo *)
           d=0.9040; e= -0.4236; f= -0.0582;
           g= -0.1007; h= -0.0786; i= -0.9918;
           tx= -7.6624; ty= -25.2080; tz=49.5181 },
      { x = 31.3810; y = 0.1400; z = 47.5810 }, (* P    *)
      { x = 29.9860; y = 0.6630; z = 47.6290 }, (* O1P  *)
      { x = 31.7210; y = -0.6460; z = 48.8090 }, (* O2P  *)
      { x = 32.4940; y = 1.2540; z = 47.2740 }, (* O5'  *)
      { x = 32.1610; y = 2.2370; z = 46.2560 }, (* C5'  *)
      { x = 31.2986; y = 2.8190; z = 46.5812 }, (* H5'  *)
      { x = 32.0980; y = 1.7468; z = 45.2845 }, (* H5'' *)
      { x = 33.3476; y = 3.1959; z = 46.1947 }, (* C4'  *)
      { x = 33.2668; y = 3.8958; z = 45.3630 }, (* H4'  *)
      { x = 33.3799; y = 3.9183; z = 47.4216 }, (* O4'  *)
      { x = 34.6515; y = 3.7222; z = 48.0398 }, (* C1'  *)
      { x = 35.2947; y = 4.5412; z = 47.7180 }, (* H1'  *)
      { x = 35.1756; y = 2.4228; z = 47.4827 }, (* C2'  *)
      { x = 34.6778; y = 1.5937; z = 47.9856 }, (* H2'' *)
      { x = 36.5631; y = 2.2672; z = 47.4798 }, (* O2'  *)
      { x = 37.0163; y = 2.6579; z = 48.2305 }, (* H2'  *)
      { x = 34.6953; y = 2.5043; z = 46.0448 }, (* C3'  *)
      { x = 34.5444; y = 1.4917; z = 45.6706 }, (* H3'  *)
      { x = 35.6679; y = 3.3009; z = 45.3487 }, (* O3'  *)
      { x = 37.4804; y = 4.0914; z = 52.2559 }, (* N1   *)
      { x = 36.9670; y = 4.1312; z = 49.9281 }, (* N3   *)
      { x = 37.8045; y = 4.2519; z = 50.9550 }, (* C2   *)
      { x = 35.7171; y = 3.8264; z = 50.3222 }, (* C4   *)
      { x = 35.2668; y = 3.6420; z = 51.6115 }, (* C5   *)
      { x = 36.2037; y = 3.7829; z = 52.6706 }, (* C6 *)
      (G (
      { x = 39.0869; y = 4.5552; z = 50.7092 }, (* N2   *)
      { x = 33.9075; y = 3.3338; z = 51.6102 }, (* N7   *)
      { x = 34.6126; y = 3.6358; z = 49.5108 }, (* N9   *)
      { x = 33.5805; y = 3.3442; z = 50.3425 }, (* C8   *)
      { x = 35.9958; y = 3.6512; z = 53.8724 }, (* O6   *)
      { x = 38.2106; y = 4.2053; z = 52.9295 }, (* H1   *)
      { x = 39.8218; y = 4.6863; z = 51.3896 }, (* H21  *)
      { x = 39.3420; y = 4.6857; z = 49.7407 }, (* H22  *)
      { x = 32.5194; y = 3.1070; z = 50.2664 }) (* H8   *)
      )
    )

let rU'
  = N(
      {    a= -0.0109; b=0.5907; c=0.8068; (* dgf_base_tfo *)
           d=0.2217; e= -0.7853; f=0.5780;
           g=0.9751; h=0.1852; i= -0.1224;
           tx= -1.4225; ty= -11.0956; tz= -2.5217 },
      {    a= -0.8313; b= -0.4738; c= -0.2906; (* P_O3'_275_tfo *)
           d=0.0649; e=0.4366; f= -0.8973;
           g=0.5521; h= -0.7648; i= -0.3322;
           tx=1.6833; ty=6.8060; tz= -7.0011 },
      {    a=0.3445; b= -0.7630; c=0.5470; (* P_O3'_180_tfo *)
           d= -0.4628; e= -0.6450; f= -0.6082;
           g=0.8168; h= -0.0436; i= -0.5753;
           tx= -6.8179; ty= -3.9778; tz= -5.9887 },
      {    a=0.5855; b=0.7931; c= -0.1682; (* P_O3'_60_tfo *)
           d=0.8103; e= -0.5790; f=0.0906;
           g= -0.0255; h= -0.1894; i= -0.9816;
           tx=6.1203; ty= -7.1051; tz=3.1984 },
      { x = 2.6760; y = -8.4960; z = 3.2880 }, (* P    *)
      { x = 1.4950; y = -7.6230; z = 3.4770 }, (* O1P  *)
      { x = 2.9490; y = -9.4640; z = 4.3740 }, (* O2P  *)
      { x = 3.9730; y = -7.5950; z = 3.0340 }, (* O5'  *)
      { x = 5.2430; y = -8.2420; z = 2.8260 }, (* C5'  *)
      { x = 5.1974; y = -8.8497; z = 1.9223 }, (* H5'  *)
      { x = 5.5548; y = -8.7348; z = 3.7469 }, (* H5'' *)
      { x = 6.3140; y = -7.2060; z = 2.5510 }, (* C4'  *)
      { x = 5.8744; y = -6.2116; z = 2.4731 }, (* H4'  *)
      { x = 7.2798; y = -7.2260; z = 3.6420 }, (* O4'  *)
      { x = 8.5733; y = -6.9410; z = 3.1329 }, (* C1'  *)
      { x = 8.9047; y = -6.0374; z = 3.6446 }, (* H1'  *)
      { x = 8.4429; y = -6.6596; z = 1.6327 }, (* C2'  *)
      { x = 9.2880; y = -7.1071; z = 1.1096 }, (* H2'' *)
      { x = 8.2502; y = -5.2799; z = 1.4754 }, (* O2'  *)
      { x = 8.7676; y = -4.7284; z = 2.0667 }, (* H2'  *)
      { x = 7.1642; y = -7.4416; z = 1.3021 }, (* C3'  *)
      { x = 7.4125; y = -8.5002; z = 1.2260 }, (* H3'  *)
      { x = 6.5160; y = -6.9772; z = 0.1267 }, (* O3'  *)
      { x = 9.4531; y = -8.1107; z = 3.4087 }, (* N1   *)
      { x = 11.5931; y = -9.0015; z = 3.6357 }, (* N3   *)
      { x = 10.8101; y = -7.8950; z = 3.3748 }, (* C2   *)
      { x = 11.1439; y = -10.2744; z = 3.9206 }, (* C4   *)
      { x = 9.7056; y = -10.4026; z = 3.9332 }, (* C5   *)
      { x = 8.9192; y = -9.3419; z = 3.6833 }, (* C6 *)
      (U (
      { x = 11.3013; y = -6.8063; z = 3.1326 }, (* O2   *)
      { x = 11.9431; y = -11.1876; z = 4.1375 }, (* O4   *)
      { x = 12.5840; y = -8.8673; z = 3.6158 }, (* H3   *)
      { x = 9.2891; y = -11.2898; z = 4.1313 }, (* H5   *)
      { x = 7.9263; y = -9.4537; z = 3.6977 }) (* H6   *)
      )
    )

(* -- PARTIAL INSTANTIATIONS ------------------------------------------------*)

type variable =
  { id : int;
    t : tfo;
    n : nuc }

let mk_var i t n = { id = i; t = t; n = n }

let absolute_pos v p = tfo_apply v.t p

let atom_pos atom v = absolute_pos v (atom v.n)

let rec get_var id (v::lst) =
  if id = v.id then v else get_var id lst

(* -- SEARCH ----------------------------------------------------------------*)

(* Sequential backtracking algorithm *)

let rec search (partial_inst : variable list) l constraint =
  match l with
    [] -> [partial_inst]
  | (h::t) ->
      let rec try_assignments = function
        [] -> []
      | v::vs ->
          if constraint v partial_inst then
            (search (v::partial_inst) t constraint) @ (try_assignments vs)
          else
            try_assignments vs
      in
        try_assignments (h partial_inst)


(* -- DOMAINS ---------------------------------------------------------------*)

(* Primary structure:   strand A CUGCCACGUCUG, strand B CAGACGUGGCAG
  
   Secondary structure: strand A CUGCCACGUCUG
                                 ||||||||||||
                                 GACGGUGCAGAC strand B
  
   Tertiary structure:
  
      5' end of strand A C1----G12 3' end of strand B
                       U2-------A11
                      G3-------C10
                      C4-----G9
                       C5---G8
                          A6
                        G6-C7
                       C5----G8
                      A4-------U9
                      G3--------C10
                       A2-------U11
     5' end of strand B C1----G12 3' end of strand A
  
   "helix", "stacked" and "connected" describe the spatial relationship
   between two consecutive nucleotides. E.g. the nucleotides C1 and U2
   from the strand A.
  
   "wc" (stands for Watson-Crick and is a type of base-pairing),
   and "wc-dumas" describe the spatial relationship between 
   nucleotides from two chains that are growing in opposite directions.
   E.g. the nucleotides C1 from strand A and G12 from strand B.
*)

(* Dynamic Domains *)

(* Given,
     "refnuc" a nucleotide which is already positioned,
     "nucl" the nucleotide to be placed,
     and "tfo" a transformation matrix which expresses the desired
     relationship between "refnuc" and "nucl",
   the function "dgf-base" computes the transformation matrix that
   places the nucleotide "nucl" in the given relationship to "refnuc".
*)

let
dgf_base tfo v nucl
  = let x = if is_A v.n then
                tfo_align (atom_pos nuc_C1' v)
                          (atom_pos rA_N9   v)
                          (atom_pos nuc_C4  v)
              else if is_C v.n then
                tfo_align (atom_pos nuc_C1' v)
                          (atom_pos nuc_N1  v)
                          (atom_pos nuc_C2  v)
              else if is_G v.n then
                tfo_align (atom_pos nuc_C1' v)
                          (atom_pos rG_N9   v)
                          (atom_pos nuc_C4  v)
              else
                tfo_align (atom_pos nuc_C1' v)
                          (atom_pos nuc_N1  v)
                          (atom_pos nuc_C2  v)
    in
      tfo_combine (nuc_dgf_base_tfo nucl)
                  (tfo_combine tfo (tfo_inv_ortho x))

(* Placement of first nucleotide. *)

let
reference n i partial_inst = [ mk_var i tfo_id n ]

(* The transformation matrix for wc is from:
  
   Chandrasekaran R. et al (1989) A Re-Examination of the Crystal
   Structure of A-DNA Using Fiber Diffraction Data. J. Biomol.
   Struct. & Dynamics 6(6):1189-1202.
*)

let wc_tfo
  = (
      {    a= -1.0000; b=0.0028; c= -0.0019;
           d=0.0028; e=0.3468; f= -0.9379;
           g= -0.0019; h= -0.9379; i= -0.3468;
           tx= -0.0080; ty=6.0730; tz=8.7208 }
    )

let
wc nucl i j partial_inst
  = [ mk_var i (dgf_base wc_tfo (get_var j partial_inst) nucl) nucl ]

let wc_dumas_tfo
  = (
      {    a= -0.9737; b= -0.1834; c=0.1352;
           d= -0.1779; e=0.2417; f= -0.9539;
           g=0.1422; h= -0.9529; i= -0.2679;
           tx=0.4837; ty=6.2649; tz=8.0285 }
    )

let
wc_dumas nucl i j partial_inst
  = [ mk_var i (dgf_base wc_dumas_tfo (get_var j partial_inst) nucl) nucl ]

let helix5'_tfo
  = (
      {    a=0.9886; b= -0.0961; c=0.1156;
           d=0.1424; e=0.8452; f= -0.5152;
           g= -0.0482; h=0.5258; i=0.8492;
           tx= -3.8737; ty=0.5480; tz=3.8024 }
    )

let
helix5' nucl i j partial_inst
  = [ mk_var i (dgf_base helix5'_tfo (get_var j partial_inst) nucl) nucl ]

let helix3'_tfo
  = (
      {    a=0.9886; b=0.1424; c= -0.0482;
           d= -0.0961; e=0.8452; f=0.5258;
           g=0.1156; h= -0.5152; i=0.8492;
           tx=3.4426; ty=2.0474; tz= -3.7042 }
    )

let
helix3' nucl i j partial_inst
  = [ mk_var i (dgf_base helix3'_tfo (get_var j partial_inst) nucl) nucl ]

let g37_a38_tfo
  = (
      {    a=0.9991; b=0.0164; c= -0.0387;
           d= -0.0375; e=0.7616; f= -0.6470;
           g=0.0189; h=0.6478; i=0.7615;
           tx= -3.3018; ty=0.9975; tz=2.5585 }
    )

let
g37_a38 nucl i j partial_inst
  = mk_var i (dgf_base g37_a38_tfo (get_var j partial_inst) nucl) nucl

let
stacked5' nucl i j partial_inst
  = (g37_a38 nucl i j partial_inst) :: (helix5' nucl i j partial_inst)

let a38_g37_tfo
  = (
      {    a=0.9991; b= -0.0375; c=0.0189;
           d=0.0164; e=0.7616; f=0.6478;
           g= -0.0387; h= -0.6470; i=0.7615;
           tx=3.3819; ty=0.7718; tz= -2.5321 }
    )

let
a38_g37 nucl i j partial_inst
  = mk_var i (dgf_base a38_g37_tfo (get_var j partial_inst) nucl) nucl

let   
stacked3' nucl i j partial_inst
  = (a38_g37 nucl i j partial_inst) :: (helix3' nucl i j partial_inst)

let
p_o3' nucls i j partial_inst
  = let refnuc = get_var j partial_inst in
    let align = tfo_inv_ortho
                    (tfo_align (atom_pos nuc_O3' refnuc)
                               (atom_pos nuc_C3' refnuc)
                               (atom_pos nuc_C4' refnuc)) in
    let rec generate domains = function
      [] -> domains
    | n::ns ->
         generate
           ((mk_var i (tfo_combine (nuc_p_o3'_60_tfo n) align) n)::
            (mk_var i (tfo_combine (nuc_p_o3'_180_tfo n) align) n)::
            (mk_var i (tfo_combine (nuc_p_o3'_275_tfo n) align) n)::domains)
           ns
    in
      generate [] nucls

(* -- PROBLEM STATEMENT -----------------------------------------------------*)

(* Define anticodon problem -- Science 253:1255 Figure 3a, 3b and 3c *)

let
anticodon_domains
  = [
     reference rC  27;
     helix5'   rC  28 27;
     helix5'   rA  29 28;
     helix5'   rG  30 29;
     helix5'   rA  31 30;
     wc        rU  39 31;
     helix5'   rC  40 39;
     helix5'   rU  41 40;
     helix5'   rG  42 41;
     helix5'   rG  43 42;
     stacked3' rA  38 39;
     stacked3' rG  37 38;
     stacked3' rA  36 37;
     stacked3' rA  35 36;
     stacked3' rG  34 35; (* <-. Distance      *)
     p_o3'     rCs 32 31; (*   | Constraint    *)
     p_o3'     rUs 33 32  (* <-' 3.0 Angstroms *)
    ]

(* Anticodon constraint *)

let
anticodon_constraint v partial_inst =
  let rec dist j = let p = atom_pos nuc_P (get_var j partial_inst) in
                   let o3' = atom_pos nuc_O3' v in
                     pt_dist p o3'
  in
      if v.id = 33 then
        (dist 34) <= 3.0
      else
        true

let
anticodon () = search [] anticodon_domains anticodon_constraint

(* Define pseudoknot problem -- Science 253:1255 Figure 4a and 4b *)

let
pseudoknot_domains
  = [
     reference rA  23;
     wc_dumas  rU   8 23;
     helix3'   rG  22 23;
     wc_dumas  rC   9 22;
     helix3'   rG  21 22;
     wc_dumas  rC  10 21;
     helix3'   rC  20 21;
     wc_dumas  rG  11 20;
     helix3'   rU' 19 20; (* <-.               *)
     wc_dumas  rA  12 19; (*   | Distance      *)
(*                             | Constraint    *)
(*  Helix 1                    | 4.0 Angstroms *)
     helix3'   rC   3 19; (*   |               *)
     wc_dumas  rG  13  3; (*   |               *)
     helix3'   rC   2  3; (*   |               *)
     wc_dumas  rG  14  2; (*   |               *)
     helix3'   rC   1  2; (*   |               *)
     wc_dumas  rG' 15  1; (*   |               *)
(*                             |               *)
(*  L2 LOOP                    |               *)
     p_o3'     rUs 16 15; (*   |               *)
     p_o3'     rCs 17 16; (*   |               *)
     p_o3'     rAs 18 17; (* <-'               *)
(*                                             *)
(*  L1 LOOP                                    *)
     helix3'   rU   7  8; (* <-.               *)
     p_o3'     rCs  4  3; (*   | Constraint    *)
     stacked5' rU   5  4; (*   | 4.5 Angstroms *)
     stacked5' rC   6  5  (* <-'               *)
    ]
  
(* Pseudoknot constraint *)

let
pseudoknot_constraint v partial_inst =
    let rec dist j =
        let p = atom_pos nuc_P (get_var j partial_inst) in
        let o3' = atom_pos nuc_O3' v in
        pt_dist p o3'
    in
      if v.id = 18 then
        (dist 19) <= 4.0
      else if v.id = 6 then
        (dist 7) <= 4.5
      else
        true

let
pseudoknot () = search [] pseudoknot_domains pseudoknot_constraint

(* -- TESTING ---------------------------------------------------------------*)

let list_of_atoms = function
  (N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,
   A (n6,n7,n9,c8,h2,h61,h62,h8)))
  -> [|p;o1p;o2p;o5';c5';h5';h5'';c4';h4';o4';c1';h1';c2';h2'';o2';h2';c3';
     h3';o3';n1;n3;c2;c4;c5;c6;n6;n7;n9;c8;h2;h61;h62;h8|]

| (N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,
   C (n4,o2,h41,h42,h5,h6)))
  -> [|p;o1p;o2p;o5';c5';h5';h5'';c4';h4';o4';c1';h1';c2';h2'';o2';h2';c3';
     h3';o3';n1;n3;c2;c4;c5;c6;n4;o2;h41;h42;h5;h6|]

| (N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,
   G (n2,n7,n9,c8,o6,h1,h21,h22,h8)))
  -> [|p;o1p;o2p;o5';c5';h5';h5'';c4';h4';o4';c1';h1';c2';h2'';o2';h2';c3';
     h3';o3';n1;n3;c2;c4;c5;c6;n2;n7;n9;c8;o6;h1;h21;h22;h8|]

| (N(dgf_base_tfo,p_o3'_275_tfo,p_o3'_180_tfo,p_o3'_60_tfo,
   p,o1p,o2p,o5',c5',h5',h5'',c4',h4',o4',c1',h1',c2',h2'',o2',h2',
   c3',h3',o3',n1,n3,c2,c4,c5,c6,
   U (o2,o4,h3,h5,h6)))
  -> [|p;o1p;o2p;o5';c5';h5';h5'';c4';h4';o4';c1';h1';c2';h2'';o2';h2';c3';
     h3';o3';n1;n3;c2;c4;c5;c6;o2;o4;h3;h5;h6|]

let maximum (x::xs) =
  let rec iter m = function
    [] -> m
  | (a::b) -> iter (if a > m then a else m) b
  in
    iter x xs

let
var_most_distant_atom v =
  let atoms = list_of_atoms v.n in
  let max_dist = ref 0.0 in
  for i = 0 to pred (Array.length atoms) do
    let p = atoms.(i) in
    let distance = 
      let pos = absolute_pos v p
      in sqrt ((pos.x * pos.x) + (pos.y * pos.y) + (pos.z * pos.z)) in
    if distance > !max_dist then max_dist := distance
  done;
  !max_dist

let
sol_most_distant_atom s = maximum (List.map var_most_distant_atom s)

let
most_distant_atom sols = maximum (List.map sol_most_distant_atom sols)

let
check () = List.length (pseudoknot ())

let
run () = most_distant_atom (pseudoknot ())

let main () = Printf.printf "%.4f" (run ()); print_newline()

let _ = main ()