/**
 * This program was used to generate the rule tables in apeirodic-hat.cpp.
 *
 * Some data was generated by this program itself, based on manual keyboard+mouse control.
 * Some of minor manual control tools have been removed, but the process was as follows:
 * 
 * * Run with `-symbol "12,6,4" -dual -canvas 101010 -smart 1 stamplen=0` and draw the hat shape, the table output is hatcorners
 * * Place hats into clusters as shown in the paper, obtaining the table hats[0]
 * * Place clusters into superclusters as shown in the paper, obtaining the table hats[1]
 * * Repeat for hats[2], hats[3], hats[4] and hats[5] (the paper does not specify precisely the coordinates to arrange the clusters; but we can multiply the previous hats by scaling factor
 * * for an approximate, and fix manually so that it matches)
 * * 'CON Lx' lines state the rules deduced; the rules should be the same for L1 and L2 (except the matrix codes returned by matcode), so we conjecture that this set of rules is complete
 * * Fill the table `hatid` to declare the correspondence between L1 and L2 matrices
 * * Run again, and we get rules (prefixed by RULE1 and RULE0)

 **/

#include "../rogueviz/rogueviz.h"

namespace rogueviz {

int toplev = 5;

vector<hyperpoint> hatcorners_add;

vector<hyperpoint> hatcorners[2];

vector<transmatrix> hats[8];

vector<int> hattype;

hyperpoint pt(ld x, ld y) { return hpxy(x, y); }

transmatrix rot;

transmatrix sca;

transmatrix U;

transmatrix mt(ld a, ld b, ld c, ld d, ld e, ld f, ld g, ld h, ld i) {
  transmatrix T = Id;
  T[0][0] = a;
  T[0][1] = b;
  T[0][2] = c;
  T[1][0] = d;
  T[1][1] = e;
  T[1][2] = f;
  T[2][0] = g;
  T[2][1] = h;
  T[2][2] = i;
  return T;
  }

map<string, int> hatid;

void init() {
  rot = Id;
  hatcorners[0] = {
   pt(-1.1160254038,1.4330127019),
   pt(-0.0915063509,2.0245190528),
   pt(0.2500000000,1.4330127019),
   pt(-0.0915063509,0.8415063509),
   pt(0.9330127019,0.2500000000),
   pt(0.9330127019,-0.9330127019),
   pt(0.2500000000,-0.9330127019),
   pt(-0.0915063509,-1.5245190528),
   pt(-1.1160254038,-0.9330127019),
   pt(-2.1405444566,-1.5245190528),
   pt(-2.4820508076,-0.9330127019),
   pt(0,0),
   pt(-1.7990381057,0.2500000000),
   pt(-1.1160254038,0.2500000000),
   };
  hatcorners[0][11] = mid(hatcorners[0][10], hatcorners[0][12]);
  hatcorners[1] = hatcorners[0];
  for(auto& h: hatcorners[1]) h = MirrorX * h;
  reverse(hatcorners[1].begin(), hatcorners[1].end());

  hats[0] = {
    mt(0.5000000000,-0.8660254038,-1.3660254038, -0.8660254038,-0.5000000000,-0.0000000000, 0.0000000000,0.0000000000,1.0000000000) * MirrorX,
    mt(0.5000000000,-0.8660254038,0.6830127019, 0.8660254038,0.5000000000,1.6830127019, 0.0000000000,0.0000000000,1.0000000000),
    mt(-1.0000000000,0.0000000000,-2.2320508076, -0.0000000000,-1.0000000000,-1.8660254038, 0.0000000000,0.0000000000,1.0000000000),
    mt(-0.5000000000,-0.8660254038,-4.5310889132, 0.8660254038,-0.5000000000,-1.6160254038, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,-0.8660254038,-3.4150635095, 0.8660254038,0.5000000000,1.6830127019, 0.0000000000,0.0000000000,1.0000000000),
    mt(1.0000000000,-0.0000000000,-2.0490381057, 0.0000000000,1.0000000000,3.5490381057, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,0.8660254038,0.2500000000, -0.8660254038,0.5000000000,3.2990381057, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,-0.8660254038,-5.4641016151, 0.8660254038,0.5000000000,0.5000000000, 0.0000000000,0.0000000000,1.0000000000),
    };

  hats[1] = {
    mt(1.0000000000,0.0000000000,0.0000000000, 0.0000000000,1.0000000000,0.0000000000, 0.0000000000,0.0000000000,1.0000000000),
    mt(-0.5000000000,0.8660254038,-0.8660254038, -0.8660254038,-0.5000000000,7.0980762114, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,0.8660254038,-5.8971143170, -0.8660254038,0.5000000000,4.4820508076, 0.0000000000,0.0000000000,1.0000000000),
    mt(1.0000000000,-0.0000000000,-6.1471143170, 0.0000000000,1.0000000000,-1.1830127019, 0.0000000000,0.0000000000,1.0000000000),
    mt(-0.5000000000,-0.8660254038,-4.5310889132, 0.8660254038,-0.5000000000,-3.9820508076, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,-0.8660254038,-9.5621778265, 0.8660254038,0.5000000000,-6.5980762114, 0.0000000000,0.0000000000,1.0000000000),
    mt(1.0000000000,-0.0000000000,-14.3432667397, 0.0000000000,1.0000000000,-3.5490381057, 0.0000000000,0.0000000000,1.0000000000),
    };
  hattype = {7, 8, 8, 8, 8, 8, 8};

  ld q7 = 1, q8 = 0;
  ld val;
  for(int a=0; a<100; a++) {
    ld nq7 = q7 + q8;
    ld nq8 = q7 * 5 + q8 * 6;
    println(hlog, format("%.20f", val = (nq7 + nq8) / (q7 + q8)));
    q7 = nq7; q8 = nq8;
    }
  val = sqrt(val);
  println(hlog, "root: ", format("%.20f", val));
  for(int a=-50; a<50; a++)
  for(int b=1; b<50; b++)
  for(int c=-50; c<50; c++)
  for(int d=1; d<50; d++) {
    ld err = abs(a*1./b + c * sqrt(1./d) - val);
    if(err < 1e-6)
      println(hlog, tie(a,b,c,d), " : ", err);
    }
  val = (3 + sqrt(5)) / 2; // scaling each axis

  sca = Id; sca[0][0] = sca[1][1] = val;

  hats[2] = {
    mt(1.0000000000,0.0000000000,0.0000000000, 0.0000000000,1.0000000000,0.0000000000, 0.0000000000,0.0000000000,1.0000000000),
    mt(-0.5000000000,0.8660254038,1.1830127025, -0.8660254038,-0.5000000000,15.3791651251, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,0.8660254038,-12.0442286339, -0.8660254038,0.5000000000,10.3971143173, 0.0000000000,0.0000000000,1.0000000000),
    mt(1.0000000000,0.0000000000,-14.3432667399, 0.0000000000,1.0000000000,-3.5490381057, 0.0000000000,0.0000000000,1.0000000000),
    mt(-0.5000000000,-0.8660254038,-12.7272413356, 0.8660254038,-0.5000000000,-13.4461524228, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,-0.8660254038,-25.9544826718, 0.8660254038,0.5000000000,-18.4282032304, 0.0000000000,0.0000000000,1.0000000000),
    mt(1.0000000000,0.0000000000,-36.8826859024, 0.0000000000,1.0000000000,-9.4641016152, 0.0000000000,0.0000000000,1.0000000000),
    };

  hats[3] = {
    mt(1.0000000000,0.0000000000,0.0000000000, 0.0000000000,1.0000000000,0.0000000000, 0.0000000000,0.0000000000,1.0000000000),
    mt(-0.5000000000,0.8660254038,7.3301270200, -0.8660254038,-0.5000000000,37.8564064623, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,0.8660254038,-28.4365334803, -0.8660254038,0.5000000000,26.9592921447, 0.0000000000,0.0000000000,1.0000000000),
    mt(1.0000000000,0.0000000000,-36.8826859027, 0.0000000000,1.0000000000,-9.4641016152, 0.0000000000,0.0000000000,1.0000000000),
    mt(-0.5000000000,-0.8660254038,-33.2176223915, 0.8660254038,-0.5000000000,-39.4724318658, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,-0.8660254038,-68.9842828915, 0.8660254038,0.5000000000,-50.3695461828, 0.0000000000,0.0000000000,1.0000000000),
    mt(1.0000000000,0.0000000000,-96.3047909683, 0.0000000000,1.0000000000,-24.8432667403, 0.0000000000,0.0000000000,1.0000000000),
    };

  hats[4] = {
    mt(1.0000000000,0.0000000000,0.0000000000, 0.0000000000,1.0000000000,0.0000000000, 0.0000000000,0.0000000000,1.0000000000),
    mt(-0.5000000000,0.8660254038,23.7224318656, -0.8660254038,-0.5000000000,97.0070415601, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,0.8660254038,-71.4663337016, -0.8660254038,0.5000000000,70.7307621167, 0.0000000000,0.0000000000,1.0000000000),
    mt(1.0000000000,0.0000000000,-96.3047909682, 0.0000000000,1.0000000000,-24.8432667399, 0.0000000000,0.0000000000,1.0000000000),
    mt(-0.5000000000,-0.8660254038,-86.4926131352, 0.8660254038,-0.5000000000,-108.0871685769, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,-0.8660254038,-181.6813787030, 0.8660254038,0.5000000000,-134.3634480195, 0.0000000000,0.0000000000,1.0000000000),
    mt(1.0000000000,0.0000000000,-252.0316870025, 0.0000000000,1.0000000000,-65.0656986057, 0.0000000000,0.0000000000,1.0000000000),
    };

  hats[5] = {
    mt(1.0000000000,0.0000000000,0.0000000000, 0.0000000000,1.0000000000,0.0000000000, 0.0000000000,0.0000000000,1.0000000000),
    mt(-0.5000000000,0.8660254038,66.7522320948, -0.8660254038,-0.5000000000,251.9817055201, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,0.8660254038,-184.1634295166, -0.8660254038,0.5000000000,185.4829942043, 0.0000000000,0.0000000000,1.0000000000),
    mt(1.0000000000,0.0000000000,-252.0316870019, 0.0000000000,1.0000000000,-65.0656986045, 0.0000000000,0.0000000000,1.0000000000),
    mt(-0.5000000000,-0.8660254038,-225.8272043260, 0.8660254038,-0.5000000000,-287.9050992716, 0.0000000000,0.0000000000,1.0000000000),
    mt(0.5000000000,-0.8660254038,-476.7428659331, 0.8660254038,0.5000000000,-354.4038105811, 0.0000000000,0.0000000000,1.0000000000),
    mt(1.0000000000,0.0000000000,-659.7902700392, 0.0000000000,1.0000000000,-170.3538290768, 0.0000000000,0.0000000000,1.0000000000),
    };

  hats[6] = hats[5];

  auto acs = inverse(sca);

  println(hlog, "shifts:");
  indenter ind(2);
  for(int i=0; i<7; i++) {

    transmatrix S = gpushxto0(hats[1][i] * C0) * hats[1][i];
    // println(hlog, "S = ", kz(S));
    transmatrix S0 = inverse(S);
    // transmatrix S1 = S;

    auto& t = hats[6][i];
    auto& t3 = hats[5][i];
    auto& t2 = hats[4][i];
    auto& t1 = hats[3][i];

    hyperpoint fix2 = t2 * C0 - sca * t1 * C0;

    hyperpoint cfix3 = acs * fix2;

    hyperpoint rfix3 = t3 * C0 - sca * t2 * C0;

    t = sca * t * acs * acs * rgpushxto0(rfix3) * sca;

    println(hlog, kz(rfix3-cfix3), " from ", fix2, " .. ", S0 * cfix3 - acs * fix2);

    // t = t * rgpushxto0(sca * (t3 * C0 - bt3 * C0));
    // t = t * 
    }

  hatid["R0A000L0.000"] = -1;
  int nextid = 8;

  hatid["R0A011L6.147"] = hatid["R0A014L14.343"] = nextid++;
  hatid["R0A016L8.196"] = hatid["R0A015L22.539"] = nextid++;
  hatid["R0A016L8.196"] = hatid["R0A015L22.539"] = nextid++;
  hatid["R0A191L6.147"] = hatid["R0A194L14.343"] = nextid++;
  hatid["R0A196L8.196"] = hatid["R0A195L22.539"] = nextid++;
  hatid["R1A023L6.903"] = hatid["R1A019L15.060"] = nextid++;
  hatid["R1A126L5.555"] = hatid["R1A131L15.741"] = nextid++;
  hatid["R1A185L7.579"] = hatid["R1A191L21.879"] = nextid++;
  hatid["R1A238L3.558"] = hatid["R1A232L11.654"] = nextid++;
  hatid["R1A327L4.885"] = hatid["R1A320L10.974"] = nextid++;
  hatid["R2A037L6.054"] = hatid["R2A025L14.053"] = nextid++;
  hatid["R2A092L2.046"] = hatid["R2A096L3.188"] = nextid++;
  hatid["R2A138L8.858"] = hatid["R2A145L25.101"] = nextid++;
  hatid["R2A221L4.953"] = hatid["R2A226L12.883"] = nextid++;
  hatid["R2A300L2.571"] = hatid["R2A279L2.571"] = nextid++;
  hatid["R3A226L7.005"] = hatid["R3A233L16.845"] = nextid++;
  hatid["R4A000L5.143"] = hatid["R4A339L10.197"] = nextid++;
  hatid["R4A097L4.093"] = hatid["R4A085L4.171"] = nextid++;
  hatid["R4A152L9.906"] = hatid["R4A156L21.728"] = nextid++;
  hatid["R4A198L11.809"] = hatid["R4A205L27.793"] = nextid++;
  hatid["R4A281L4.171"] = hatid["R4A286L6.625"] = nextid++;
  hatid["R5A087L5.006"] = hatid["R5A080L5.503"] = nextid++;
  hatid["R5A143L7.731"] = hatid["R5A139L13.041"] = nextid++;
  hatid["R5A246L6.309"] = hatid["R5A251L9.388"] = nextid++;
  hatid["R5A305L6.626"] = hatid["R5A311L15.426"] = nextid++;
  hatid["R5A358L8.119"] = hatid["R5A352L19.349"] = nextid++;

  println(hlog, "nextid = ", nextid);
  };

void draw_cross(hyperpoint h) {
  transmatrix T = rgpushxto0(h);
  shiftmatrix sId = shiftless(Id);
  for(int i=0; i<12; i++)
    queueline(sId * T * C0, sId * T * xspinpush0(30._deg * i, 0.1), 0xFFFFFFFF);
  }

void draw_shape(transmatrix T, vector<hyperpoint> sh, color_t lc, color_t fc) {
  for(hyperpoint h: sh) curvepoint(h);
  curvepoint(sh[0]);
  queuecurve(shiftless(Id) * T, lc, fc, PPR::LINE);
  }

/*
void draw_superhat(transmatrix T, const vector<transmatrix>& ms, int q, color_t lc, color_t fc) {
  for(auto& m: ms)
    draw_shape(T * m, hatcorners, lc, fc);
  }
*/

hyperpoint sh;

color_t coltables[8] = { 0xFF000080, 0x00FF0080, 0x0000FF80, 0xFFFF0080, 0xFF00FF80, 0x00FFFF80, 0xFFFFFF80, 0x4080C080 };

vector<int> curlabel;

ld ldist = 9999;

hyperpoint hfound, hfound1;

int connection_mode = 0;

int found_pairs, found_pairs_swap;

using pthash = int;

pthash makehash(hyperpoint h) {
  return int(floor(h[0] * 10 + .31)) + int(floor(h[1] * 10 + .31)) * 10000;
  }

map<pair<pthash, pthash>, vector<int> > seen_edges;

string name(int x) { return s0 + char('A' + x); }

string matcode(transmatrix T) {
  vector<ld> res(3);
  hyperpoint h = kz(T * C0);

  transmatrix S = gpushxto0(T * C0) * T;
  ld alpha = atan2(S * xpush0(1)) / degree;
  int ialpha = gmod(floor(alpha + .5), 360);

  int hangle = gmod(floor(atan2(h) / degree + .3), 360);

  h[2] = ialpha/60;
  swap(h[1], h[2]); swap(h[0], h[1]);
  // return lalign(0, h);

  return format("R%dA%03dL%.3f", ialpha/60, hangle, hypot_d(2, h));
  }

int ghatid(string s) {
  if(hatid.count(s)) return hatid[s];
  return -999;
  }

void edge_connect(vector<int> l1, vector<int> l2) {
  transmatrix T1 = Id;
  transmatrix T2 = Id;
  transmatrix W = Id;
  int idx = 0;
  for(int i=toplev; i>0; i--) {
    T1 = T1 * hats[i][l1[idx]];
    T2 = T2 * hats[i][l2[idx]];
    transmatrix W1 = inverse(T1) * T2;
    if(!eqmatrix(W1, Id))
      println(hlog, "CON L", i, " ", matcode(W1), " :: ", matcode(W), " ", tie(l1[idx], l2[idx]), " REV ", matcode(inverse(W1)));
    if(i == 1) println(hlog, "RULE1 {", l1[idx], ", ", l2[idx], ", ", ghatid(matcode(W1)), ", ", ghatid(matcode(W)), ", ", ghatid(matcode(inverse(W1))), "},");
    W = W1;
    idx++;
    }

  println(hlog, "CON L0 ", make_pair(make_pair(l1[idx], name(l1[idx+1])), make_pair(l2[idx], name(l2[idx+1]))), " :: ", matcode(W));
  println(hlog, "RULE0 {", l1[idx], ", ", l1[idx+1], ", ", l2[idx], ", ", l2[idx+1], ", ", ghatid(matcode(W)), "},");
  }

vector<pair<hyperpoint, hyperpoint> > extedges;

void edge_label(vector<int>& lbl, hyperpoint a, hyperpoint b) {
  auto ha = makehash(a);
  auto hb = makehash(b);

  if(connection_mode >= 2) return;

  if(connection_mode == 1) {
    if(seen_edges.count({ha, hb})) {
      extedges.emplace_back(a, b);
      /* vid.linewidth *= 10;
      queueline(shiftless(Id) * a, shiftless(Id) * b, 0xFF00FF80);
      vid.linewidth /= 10;
      */
      }
    return;
    }

  if(seen_edges.count({hb, ha})) {
    edge_connect(lbl, seen_edges[{hb, ha}]);
    edge_connect(seen_edges[{hb, ha}], lbl);
    seen_edges.erase({hb, ha});
    found_pairs++;
    return;
    }
  if(seen_edges.count({ha, hb})) {
    println(hlog, "CON ", lbl, " TO ", seen_edges[{hb, ha}], " SWAP");
    seen_edges.erase({ha, hb});
    found_pairs_swap++;
    return;
    }
  seen_edges[{ha, hb}] = lbl;
  }

void point_label(vector<int>& lbl, hyperpoint h) {
  if(lbl == curlabel) draw_cross(h);
  ld dist = hdist(unshift(mouseh), h);
  if(dist < ldist) {
    ldist = dist;
    curlabel = lbl;
    hfound = h;
    println(hlog, "found: ", lbl, " at: ", dist);
    }
  }

void draw_superhat_label(transmatrix T, const vector<transmatrix>& ms, int q, color_t lc, color_t fc, vector<int>& label) {
  for(int i=0; i<q; i++) {
    auto& hc = hatcorners[i == 0];
    for(int j=0; j<isize(hc); j++) {
      
      label.push_back(i);
      label.push_back(j);
      point_label(label, T * ms[i] * hc[j]);

      edge_label(label, T * ms[i] * hc[j], T * ms[i] * hc[(j+1)%isize(hc)]);
      label.pop_back();
      label.pop_back();
      }
    }
  for(int i=0; i<q; i++) {
    auto& hc = hatcorners[i == 0];
    draw_shape(T * ms[i], hc, lc, fc);
    }
  }

void draw_recurse_label(transmatrix T, int levs, int t, color_t col, vector<int>& label) {
  if(levs == 0) {
    draw_superhat_label(T, hats[0], t, 0xFFFFFFFF, col, label);
    return;
    }

  if(connection_mode == 2 && levs == toplev-1) {
   int eid = 0;
   for(auto e: extedges) {
     queueline(shiftless(Id) * T * e.first, shiftless(Id) * T * e.second, col);
     label.push_back(eid++);
     point_label(label, T * e.first);
     label.pop_back();
     }
   return;
   }

  transmatrix scap = Id;
  for(int i=1; i<levs; i++) scap = scap * sca;
  scap = inverse(scap);

  for(int i=0; i<t-1; i++) {
    auto col1 = col;
    if(col == 0) col1 = coltables[i];
    label.push_back(i);
    draw_recurse_label(T * hats[levs][i], levs-1, hattype[i], col1, label);
    label.pop_back();
    }
  }

int next_hattype = 7;

void hatframe() {
  if(isize(hatcorners_add) >= 2) draw_shape(Id, hatcorners_add, 0xFF0000FF, 0xFF000080);

  transmatrix B = rgpushxto0( unshift(ggmatrix(cwt.at)) * C0 );

  vector<int> glabel;

  draw_recurse_label(B, toplev, 8, 0, glabel);
  if(connection_mode == 0) {
    println(hlog, "CON found = ", found_pairs, " swap = ", found_pairs_swap, " not found = ", isize(seen_edges));
    // seen_edges.clear(); found_pairs = 0;
    connection_mode = 1;
    }
  else if(connection_mode == 1) {
    connection_mode = 2;
    toplev++;
    }

  draw_cross(C0);
  }

string writematrix(transmatrix T) {
  return format("mt(%.10f,%.10f,%.10f, %.10f,%.10f,%.10f, %.10f,%.10f,%.10f)",
    T[0][0], 
    T[0][1], 
    T[0][2], 
    T[1][0], 
    T[1][1], 
    T[1][2], 
    T[2][0], 
    T[2][1], 
    T[2][2]
    );
  }

void hatter() {
  cmode = sm::NORMAL | sm::CENTER | sm::PANNING;
  clearMessages();
  dialog::init();
  gamescreen();

  shiftpoint s = mapeditor::full_mouseh();
  sh = unshift(s);

  dialog::add_key_action('a', [] {
    hatcorners_add.push_back(sh);
    println(hlog, "hatcorners = {");
    for(auto h: hatcorners_add) println(hlog, format("  pt(%.10f,%.10f),", h[0], h[1]));
    println(hlog, "  }");
    });

  /* dialog::add_key_action('b', [] {
    if(hats.empty()) return;
    hats.pop_back();
    hattype.pop_back();
    }); */

  dialog::add_key_action('[', [] {
    // hyperpoint h = currentmap->get_corner(cwt.at, 0);
    // rot = rot * gpushxto0(h);
    rot = rot * spin(60._deg);
    // rot = rot * rgpushxto0(h);
    });

  dialog::add_key_action(']', [] {
    // hyperpoint h = currentmap->get_corner(cwt.at, 0);
    // rot = rot * gpushxto0(h);
    rot = MirrorX * rot;
    // rot = rot * rgpushxto0(h);
    });

  dialog::add_key_action('7', [] { next_hattype = 7; });
  dialog::add_key_action('8', [] { next_hattype = 8; });

  dialog::add_key_action('f', [] { hfound1 = hfound; });
  dialog::add_key_action('b', [] { 
    int id = curlabel[0];
    hats[toplev][id] = rgpushxto0(hfound1 - hfound) * hats[toplev][id];

    println(hlog, "hats[", toplev, "] = {");
      for(auto h: hats[toplev]) println(hlog, "  ", writematrix(h), ",");
      println(hlog, "  }");
    });

  dialog::add_key_action('q', [] {
    exit(0);
    });

  dialog::add_key_action('g', [] {
    ldist = 9999;
    });

  keyhandler = [] (int sym, int uni) { dialog::handleNavigation(sym, uni); };
  }

void enable_hatter() {
  init();
  mapeditor::snapping = true;
  rv_hook(hooks_frame, 100, hatframe);
  pushScreen(hatter);
  }
  
auto hathook = arg::add3("-hatter", enable_hatter);

}