src/collision.cpp

   1 /*
   2 Minetest
   3 Copyright (C) 2013 celeron55, Perttu Ahola <celeron55@gmail.com>
   4
   5 This program is free software; you can redistribute it and/or modify
   6 it under the terms of the GNU Lesser General Public License as published by
   7 the Free Software Foundation; either version 2.1 of the License, or
   8 (at your option) any later version.
   9
  10 This program is distributed in the hope that it will be useful,
  11 but WITHOUT ANY WARRANTY; without even the implied warranty of
  12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  13 GNU Lesser General Public License for more details.
  14
  15 You should have received a copy of the GNU Lesser General Public License along
  16 with this program; if not, write to the Free Software Foundation, Inc.,
  17 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
  18 */
  19
  20 #include "collision.h"
  21 #include "mapblock.h"
  22 #include "map.h"
  23 #include "nodedef.h"
  24 #include "gamedef.h"
  25 #ifndef SERVER
  26 #include "clientenvironment.h"
  27 #endif
  28 #include "serverenvironment.h"
  29 #include "serverobject.h"
  30 #include "util/timetaker.h"
  31 #include "profiler.h"
  32
  33 // float error is 10 - 9.96875 = 0.03125
  34 //#define COLL_ZERO 0.032 // broken unit tests
  35 #define COLL_ZERO 0
  36
  37
  38 struct NearbyCollisionInfo {
  39         NearbyCollisionInfo(bool is_ul, bool is_obj, int bouncy,
  40                         const v3s16 &pos, const aabb3f &box) :
  41                 is_unloaded(is_ul),
  42                 is_object(is_obj),
  43                 bouncy(bouncy),
  44                 position(pos),
  45                 box(box)
  46         {}
  47
  48         bool is_unloaded;
  49         bool is_step_up = false;
  50         bool is_object;
  51         int bouncy;
  52         v3s16 position;
  53         aabb3f box;
  54 };
  55
  56
  57 // Helper function:
  58 // Checks for collision of a moving aabbox with a static aabbox
  59 // Returns -1 if no collision, 0 if X collision, 1 if Y collision, 2 if Z collision
  60 // The time after which the collision occurs is stored in dtime.
  61 int axisAlignedCollision(
  62                 const aabb3f &staticbox, const aabb3f &movingbox,
  63                 const v3f &speed, f32 d, f32 *dtime)
  64 {
  65         //TimeTaker tt("axisAlignedCollision");
  66
  67         f32 xsize = (staticbox.MaxEdge.X - staticbox.MinEdge.X) - COLL_ZERO;     // reduce box size for solve collision stuck (flying sand)
  68         f32 ysize = (staticbox.MaxEdge.Y - staticbox.MinEdge.Y); // - COLL_ZERO; // Y - no sense for falling, but maybe try later
  69         f32 zsize = (staticbox.MaxEdge.Z - staticbox.MinEdge.Z) - COLL_ZERO;
  70
  71         aabb3f relbox(
  72                         movingbox.MinEdge.X - staticbox.MinEdge.X,
  73                         movingbox.MinEdge.Y - staticbox.MinEdge.Y,
  74                         movingbox.MinEdge.Z - staticbox.MinEdge.Z,
  75                         movingbox.MaxEdge.X - staticbox.MinEdge.X,
  76                         movingbox.MaxEdge.Y - staticbox.MinEdge.Y,
  77                         movingbox.MaxEdge.Z - staticbox.MinEdge.Z
  78         );
  79
  80         if(speed.X > 0) // Check for collision with X- plane
  81         {
  82                 if (relbox.MaxEdge.X <= d) {
  83                         *dtime = -relbox.MaxEdge.X / speed.X;
  84                         if ((relbox.MinEdge.Y + speed.Y * (*dtime) < ysize) &&
  85                                         (relbox.MaxEdge.Y + speed.Y * (*dtime) > COLL_ZERO) &&
  86                                         (relbox.MinEdge.Z + speed.Z * (*dtime) < zsize) &&
  87                                         (relbox.MaxEdge.Z + speed.Z * (*dtime) > COLL_ZERO))
  88                                 return 0;
  89                 }
  90                 else if(relbox.MinEdge.X > xsize)
  91                 {
  92                         return -1;
  93                 }
  94         }
  95         else if(speed.X < 0) // Check for collision with X+ plane
  96         {
  97                 if (relbox.MinEdge.X >= xsize - d) {
  98                         *dtime = (xsize - relbox.MinEdge.X) / speed.X;
  99                         if ((relbox.MinEdge.Y + speed.Y * (*dtime) < ysize) &&
 100                                         (relbox.MaxEdge.Y + speed.Y * (*dtime) > COLL_ZERO) &&
 101                                         (relbox.MinEdge.Z + speed.Z * (*dtime) < zsize) &&
 102                                         (relbox.MaxEdge.Z + speed.Z * (*dtime) > COLL_ZERO))
 103                                 return 0;
 104                 }
 105                 else if(relbox.MaxEdge.X < 0)
 106                 {
 107                         return -1;
 108                 }
 109         }
 110
 111         // NO else if here
 112
 113         if(speed.Y > 0) // Check for collision with Y- plane
 114         {
 115                 if (relbox.MaxEdge.Y <= d) {
 116                         *dtime = -relbox.MaxEdge.Y / speed.Y;
 117                         if ((relbox.MinEdge.X + speed.X * (*dtime) < xsize) &&
 118                                         (relbox.MaxEdge.X + speed.X * (*dtime) > COLL_ZERO) &&
 119                                         (relbox.MinEdge.Z + speed.Z * (*dtime) < zsize) &&
 120                                         (relbox.MaxEdge.Z + speed.Z * (*dtime) > COLL_ZERO))
 121                                 return 1;
 122                 }
 123                 else if(relbox.MinEdge.Y > ysize)
 124                 {
 125                         return -1;
 126                 }
 127         }
 128         else if(speed.Y < 0) // Check for collision with Y+ plane
 129         {
 130                 if (relbox.MinEdge.Y >= ysize - d) {
 131                         *dtime = (ysize - relbox.MinEdge.Y) / speed.Y;
 132                         if ((relbox.MinEdge.X + speed.X * (*dtime) < xsize) &&
 133                                         (relbox.MaxEdge.X + speed.X * (*dtime) > COLL_ZERO) &&
 134                                         (relbox.MinEdge.Z + speed.Z * (*dtime) < zsize) &&
 135                                         (relbox.MaxEdge.Z + speed.Z * (*dtime) > COLL_ZERO))
 136                                 return 1;
 137                 }
 138                 else if(relbox.MaxEdge.Y < 0)
 139                 {
 140                         return -1;
 141                 }
 142         }
 143
 144         // NO else if here
 145
 146         if(speed.Z > 0) // Check for collision with Z- plane
 147         {
 148                 if (relbox.MaxEdge.Z <= d) {
 149                         *dtime = -relbox.MaxEdge.Z / speed.Z;
 150                         if ((relbox.MinEdge.X + speed.X * (*dtime) < xsize) &&
 151                                         (relbox.MaxEdge.X + speed.X * (*dtime) > COLL_ZERO) &&
 152                                         (relbox.MinEdge.Y + speed.Y * (*dtime) < ysize) &&
 153                                         (relbox.MaxEdge.Y + speed.Y * (*dtime) > COLL_ZERO))
 154                                 return 2;
 155                 }
 156                 //else if(relbox.MinEdge.Z > zsize)
 157                 //{
 158                 //      return -1;
 159                 //}
 160         }
 161         else if(speed.Z < 0) // Check for collision with Z+ plane
 162         {
 163                 if (relbox.MinEdge.Z >= zsize - d) {
 164                         *dtime = (zsize - relbox.MinEdge.Z) / speed.Z;
 165                         if ((relbox.MinEdge.X + speed.X * (*dtime) < xsize) &&
 166                                         (relbox.MaxEdge.X + speed.X * (*dtime) > COLL_ZERO) &&
 167                                         (relbox.MinEdge.Y + speed.Y * (*dtime) < ysize) &&
 168                                         (relbox.MaxEdge.Y + speed.Y * (*dtime) > COLL_ZERO))
 169                                 return 2;
 170                 }
 171                 //else if(relbox.MaxEdge.Z < 0)
 172                 //{
 173                 //      return -1;
 174                 //}
 175         }
 176
 177         return -1;
 178 }
 179
 180 // Helper function:
 181 // Checks if moving the movingbox up by the given distance would hit a ceiling.
 182 bool wouldCollideWithCeiling(
 183                 const std::vector<NearbyCollisionInfo> &cinfo,
 184                 const aabb3f &movingbox,
 185                 f32 y_increase, f32 d)
 186 {
 187         //TimeTaker tt("wouldCollideWithCeiling");
 188
 189         assert(y_increase >= 0);        // pre-condition
 190
 191         for (const auto &it : cinfo) {
 192                 const aabb3f &staticbox = it.box;
 193                 if ((movingbox.MaxEdge.Y - d <= staticbox.MinEdge.Y) &&
 194                                 (movingbox.MaxEdge.Y + y_increase > staticbox.MinEdge.Y) &&
 195                                 (movingbox.MinEdge.X < staticbox.MaxEdge.X) &&
 196                                 (movingbox.MaxEdge.X > staticbox.MinEdge.X) &&
 197                                 (movingbox.MinEdge.Z < staticbox.MaxEdge.Z) &&
 198                                 (movingbox.MaxEdge.Z > staticbox.MinEdge.Z))
 199                         return true;
 200         }
 201
 202         return false;
 203 }
 204
 205 static inline void getNeighborConnectingFace(const v3s16 &p, INodeDefManager *nodedef,
 206                 Map *map, MapNode n, int v, int *neighbors)
 207 {
 208         MapNode n2 = map->getNodeNoEx(p);
 209         if (nodedef->nodeboxConnects(n, n2, v))
 210                 *neighbors |= v;
 211 }
 212
 213 collisionMoveResult collisionMoveSimple(Environment *env, IGameDef *gamedef,
 214                 f32 pos_max_d, const aabb3f &box_0,
 215                 f32 stepheight, f32 dtime,
 216                 v3f *pos_f, v3f *speed_f,
 217                 v3f accel_f, ActiveObject *self,
 218                 bool collideWithObjects)
 219 {
 220         static bool time_notification_done = false;
 221         Map *map = &env->getMap();
 222         //TimeTaker tt("collisionMoveSimple");
 223         ScopeProfiler sp(g_profiler, "collisionMoveSimple avg", SPT_AVG);
 224
 225         collisionMoveResult result;
 226
 227         /*
 228                 Calculate new velocity
 229         */
 230         if (dtime > 0.5) {
 231                 if (!time_notification_done) {
 232                         time_notification_done = true;
 233                         infostream << "collisionMoveSimple: maximum step interval exceeded,"
 234                                         " lost movement details!"<<std::endl;
 235                 }
 236                 dtime = 0.5;
 237         } else {
 238                 time_notification_done = false;
 239         }
 240         *speed_f += accel_f * dtime;
 241
 242         // If there is no speed, there are no collisions
 243         if (speed_f->getLength() == 0)
 244                 return result;
 245
 246         // Limit speed for avoiding hangs
 247         speed_f->Y = rangelim(speed_f->Y, -5000, 5000);
 248         speed_f->X = rangelim(speed_f->X, -5000, 5000);
 249         speed_f->Z = rangelim(speed_f->Z, -5000, 5000);
 250
 251         /*
 252                 Collect node boxes in movement range
 253         */
 254         std::vector<NearbyCollisionInfo> cinfo;
 255         {
 256         //TimeTaker tt2("collisionMoveSimple collect boxes");
 257         ScopeProfiler sp2(g_profiler, "collisionMoveSimple collect boxes avg", SPT_AVG);
 258
 259         v3f newpos_f = *pos_f + *speed_f * dtime;
 260         v3f minpos_f(
 261                 MYMIN(pos_f->X, newpos_f.X),
 262                 MYMIN(pos_f->Y, newpos_f.Y) + 0.01 * BS, // bias rounding, player often at +/-n.5
 263                 MYMIN(pos_f->Z, newpos_f.Z)
 264         );
 265         v3f maxpos_f(
 266                 MYMAX(pos_f->X, newpos_f.X),
 267                 MYMAX(pos_f->Y, newpos_f.Y),
 268                 MYMAX(pos_f->Z, newpos_f.Z)
 269         );
 270         v3s16 min = floatToInt(minpos_f + box_0.MinEdge, BS) - v3s16(1, 1, 1);
 271         v3s16 max = floatToInt(maxpos_f + box_0.MaxEdge, BS) + v3s16(1, 1, 1);
 272
 273         bool any_position_valid = false;
 274
 275         v3s16 p;
 276         for (p.X = min.X; p.X <= max.X; p.X++)
 277         for (p.Y = min.Y; p.Y <= max.Y; p.Y++)
 278         for (p.Z = min.Z; p.Z <= max.Z; p.Z++) {
 279                 bool is_position_valid;
 280                 MapNode n = map->getNodeNoEx(p, &is_position_valid);
 281
 282                 if (is_position_valid) {
 283                         // Object collides into walkable nodes
 284
 285                         any_position_valid = true;
 286                         INodeDefManager *nodedef = gamedef->getNodeDefManager();
 287                         const ContentFeatures &f = nodedef->get(n);
 288
 289                         if (!f.walkable)
 290                                 continue;
 291
 292                         int n_bouncy_value = itemgroup_get(f.groups, "bouncy");
 293
 294                         int neighbors = 0;
 295                         if (f.drawtype == NDT_NODEBOX &&
 296                                 f.node_box.type == NODEBOX_CONNECTED) {
 297                                 v3s16 p2 = p;
 298
 299                                 p2.Y++;
 300                                 getNeighborConnectingFace(p2, nodedef, map, n, 1, &neighbors);
 301
 302                                 p2 = p;
 303                                 p2.Y--;
 304                                 getNeighborConnectingFace(p2, nodedef, map, n, 2, &neighbors);
 305
 306                                 p2 = p;
 307                                 p2.Z--;
 308                                 getNeighborConnectingFace(p2, nodedef, map, n, 4, &neighbors);
 309
 310                                 p2 = p;
 311                                 p2.X--;
 312                                 getNeighborConnectingFace(p2, nodedef, map, n, 8, &neighbors);
 313
 314                                 p2 = p;
 315                                 p2.Z++;
 316                                 getNeighborConnectingFace(p2, nodedef, map, n, 16, &neighbors);
 317
 318                                 p2 = p;
 319                                 p2.X++;
 320                                 getNeighborConnectingFace(p2, nodedef, map, n, 32, &neighbors);
 321                         }
 322                         std::vector<aabb3f> nodeboxes;
 323                         n.getCollisionBoxes(gamedef->ndef(), &nodeboxes, neighbors);
 324                         for (auto box : nodeboxes) {
 325                                 box.MinEdge += intToFloat(p, BS);
 326                                 box.MaxEdge += intToFloat(p, BS);
 327                                 cinfo.emplace_back(false, false, n_bouncy_value, p, box);
 328                         }
 329                 } else {
 330                         // Collide with unloaded nodes
 331                         aabb3f box = getNodeBox(p, BS);
 332                         cinfo.emplace_back(true, false, 0, p, box);
 333                 }
 334         }
 335
 336         // Do not move if world has not loaded yet, since custom node boxes
 337         // are not available for collision detection.
 338         if (!any_position_valid) {
 339                 *speed_f = v3f(0, 0, 0);
 340                 return result;
 341         }
 342
 343         } // tt2
 344
 345         if(collideWithObjects)
 346         {
 347                 ScopeProfiler sp2(g_profiler, "collisionMoveSimple objects avg", SPT_AVG);
 348                 //TimeTaker tt3("collisionMoveSimple collect object boxes");
 349
 350                 /* add object boxes to cinfo */
 351
 352                 std::vector<ActiveObject*> objects;
 353 #ifndef SERVER
 354                 ClientEnvironment *c_env = dynamic_cast<ClientEnvironment*>(env);
 355                 if (c_env != 0) {
 356                         f32 distance = speed_f->getLength();
 357                         std::vector<DistanceSortedActiveObject> clientobjects;
 358                         c_env->getActiveObjects(*pos_f, distance * 1.5, clientobjects);
 359                         for (auto &clientobject : clientobjects) {
 360                                 if (!self || (self != clientobject.obj)) {
 361                                         objects.push_back((ActiveObject*) clientobject.obj);
 362                                 }
 363                         }
 364                 }
 365                 else
 366 #endif
 367                 {
 368                         ServerEnvironment *s_env = dynamic_cast<ServerEnvironment*>(env);
 369                         if (s_env != NULL) {
 370                                 f32 distance = speed_f->getLength();
 371                                 std::vector<u16> s_objects;
 372                                 s_env->getObjectsInsideRadius(s_objects, *pos_f, distance * 1.5);
 373                                 for (u16 obj_id : s_objects) {
 374                                         ServerActiveObject *current = s_env->getActiveObject(obj_id);
 375                                         if (!self || (self != current)) {
 376                                                 objects.push_back((ActiveObject*)current);
 377                                         }
 378                                 }
 379                         }
 380                 }
 381
 382                 for (std::vector<ActiveObject*>::const_iterator iter = objects.begin();
 383                                 iter != objects.end(); ++iter) {
 384                         ActiveObject *object = *iter;
 385
 386                         if (object) {
 387                                 aabb3f object_collisionbox;
 388                                 if (object->getCollisionBox(&object_collisionbox) &&
 389                                                 object->collideWithObjects()) {
 390                                         cinfo.emplace_back(false, true, 0, v3s16(), object_collisionbox);
 391                                 }
 392                         }
 393                 }
 394         } //tt3
 395
 396         /*
 397                 Collision detection
 398         */
 399
 400         /*
 401                 Collision uncertainty radius
 402                 Make it a bit larger than the maximum distance of movement
 403         */
 404         f32 d = pos_max_d * 1.1;
 405         // A fairly large value in here makes moving smoother
 406         //f32 d = 0.15*BS;
 407
 408         // This should always apply, otherwise there are glitches
 409         assert(d > pos_max_d);  // invariant
 410
 411         int loopcount = 0;
 412
 413         while(dtime > BS * 1e-10) {
 414                 //TimeTaker tt3("collisionMoveSimple dtime loop");
 415                 ScopeProfiler sp2(g_profiler, "collisionMoveSimple dtime loop avg", SPT_AVG);
 416
 417                 // Avoid infinite loop
 418                 loopcount++;
 419                 if (loopcount >= 100) {
 420                         warningstream << "collisionMoveSimple: Loop count exceeded, aborting to avoid infiniite loop" << std::endl;
 421                         break;
 422                 }
 423
 424                 aabb3f movingbox = box_0;
 425                 movingbox.MinEdge += *pos_f;
 426                 movingbox.MaxEdge += *pos_f;
 427
 428                 int nearest_collided = -1;
 429                 f32 nearest_dtime = dtime;
 430                 int nearest_boxindex = -1;
 431
 432                 /*
 433                         Go through every nodebox, find nearest collision
 434                 */
 435                 for (u32 boxindex = 0; boxindex < cinfo.size(); boxindex++) {
 436                         NearbyCollisionInfo box_info = cinfo[boxindex];
 437                         // Ignore if already stepped up this nodebox.
 438                         if (box_info.is_step_up)
 439                                 continue;
 440
 441                         // Find nearest collision of the two boxes (raytracing-like)
 442                         f32 dtime_tmp;
 443                         int collided = axisAlignedCollision(box_info.box,
 444                                         movingbox, *speed_f, d, &dtime_tmp);
 445
 446                         if (collided == -1 || dtime_tmp >= nearest_dtime)
 447                                 continue;
 448
 449                         nearest_dtime = dtime_tmp;
 450                         nearest_collided = collided;
 451                         nearest_boxindex = boxindex;
 452                 }
 453
 454                 if (nearest_collided == -1) {
 455                         // No collision with any collision box.
 456                         *pos_f += *speed_f * dtime;
 457                         dtime = 0;  // Set to 0 to avoid "infinite" loop due to small FP numbers
 458                 } else {
 459                         // Otherwise, a collision occurred.
 460                         NearbyCollisionInfo &nearest_info = cinfo[nearest_boxindex];
 461                         const aabb3f& cbox = nearest_info.box;
 462                         // Check for stairs.
 463                         bool step_up = (nearest_collided != 1) && // must not be Y direction
 464                                         (movingbox.MinEdge.Y < cbox.MaxEdge.Y) &&
 465                                         (movingbox.MinEdge.Y + stepheight > cbox.MaxEdge.Y) &&
 466                                         (!wouldCollideWithCeiling(cinfo, movingbox,
 467                                                         cbox.MaxEdge.Y - movingbox.MinEdge.Y,
 468                                                         d));
 469
 470                         // Get bounce multiplier
 471                         float bounce = -(float)nearest_info.bouncy / 100.0;
 472
 473                         // Move to the point of collision and reduce dtime by nearest_dtime
 474                         if (nearest_dtime < 0) {
 475                                 // Handle negative nearest_dtime (can be caused by the d allowance)
 476                                 if (!step_up) {
 477                                         if (nearest_collided == 0)
 478                                                 pos_f->X += speed_f->X * nearest_dtime;
 479                                         if (nearest_collided == 1)
 480                                                 pos_f->Y += speed_f->Y * nearest_dtime;
 481                                         if (nearest_collided == 2)
 482                                                 pos_f->Z += speed_f->Z * nearest_dtime;
 483                                 }
 484                         } else {
 485                                 *pos_f += *speed_f * nearest_dtime;
 486                                 dtime -= nearest_dtime;
 487                         }
 488
 489                         bool is_collision = true;
 490                         if (nearest_info.is_unloaded)
 491                                 is_collision = false;
 492
 493                         CollisionInfo info;
 494                         if (nearest_info.is_object)
 495                                 info.type = COLLISION_OBJECT;
 496                         else
 497                                 info.type = COLLISION_NODE;
 498
 499                         info.node_p = nearest_info.position;
 500                         info.old_speed = *speed_f;
 501
 502                         // Set the speed component that caused the collision to zero
 503                         if (step_up) {
 504                                 // Special case: Handle stairs
 505                                 nearest_info.is_step_up = true;
 506                                 is_collision = false;
 507                         } else if (nearest_collided == 0) { // X
 508                                 if (fabs(speed_f->X) > BS * 3)
 509                                         speed_f->X *= bounce;
 510                                 else
 511                                         speed_f->X = 0;
 512                                 result.collides = true;
 513                         } else if (nearest_collided == 1) { // Y
 514                                 if(fabs(speed_f->Y) > BS * 3)
 515                                         speed_f->Y *= bounce;
 516                                 else
 517                                         speed_f->Y = 0;
 518                                 result.collides = true;
 519                         } else if (nearest_collided == 2) { // Z
 520                                 if (fabs(speed_f->Z) > BS * 3)
 521                                         speed_f->Z *= bounce;
 522                                 else
 523                                         speed_f->Z = 0;
 524                                 result.collides = true;
 525                         }
 526
 527                         info.new_speed = *speed_f;
 528                         if (info.new_speed.getDistanceFrom(info.old_speed) < 0.1 * BS)
 529                                 is_collision = false;
 530
 531                         if (is_collision) {
 532                                 result.collisions.push_back(info);
 533                         }
 534                 }
 535         }
 536
 537         /*
 538                 Final touches: Check if standing on ground, step up stairs.
 539         */
 540         aabb3f box = box_0;
 541         box.MinEdge += *pos_f;
 542         box.MaxEdge += *pos_f;
 543         for (const auto &box_info : cinfo) {
 544                 const aabb3f &cbox = box_info.box;
 545
 546                 /*
 547                         See if the object is touching ground.
 548
 549                         Object touches ground if object's minimum Y is near node's
 550                         maximum Y and object's X-Z-area overlaps with the node's
 551                         X-Z-area.
 552
 553                         Use 0.15*BS so that it is easier to get on a node.
 554                 */
 555                 if (cbox.MaxEdge.X - d > box.MinEdge.X && cbox.MinEdge.X + d < box.MaxEdge.X &&
 556                                 cbox.MaxEdge.Z - d > box.MinEdge.Z &&
 557                                 cbox.MinEdge.Z + d < box.MaxEdge.Z) {
 558                         if (box_info.is_step_up) {
 559                                 pos_f->Y += cbox.MaxEdge.Y - box.MinEdge.Y;
 560                                 box = box_0;
 561                                 box.MinEdge += *pos_f;
 562                                 box.MaxEdge += *pos_f;
 563                         }
 564                         if (fabs(cbox.MaxEdge.Y - box.MinEdge.Y) < 0.15 * BS) {
 565                                 result.touching_ground = true;
 566
 567                                 if (box_info.is_object)
 568                                         result.standing_on_object = true;
 569                         }
 570                 }
 571         }
 572
 573         return result;
 574 }