1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688
use mint::Point2; use retain_mut::RetainMut; use slotmap::new_key_type; use slotmap::SlotMap; use std::cmp::{max, min}; new_key_type! { /// This handle is used to modify the associated object or to update its position. /// It is returned by the _insert_ method of a DenseGrid. pub struct DenseGridHandle; } /// State of an object, maintain() updates the internals of the densegrid and resets this to Unchanged #[derive(Clone, Copy, PartialEq, Eq)] enum ObjectState { Unchanged, NewPos, Removed, } /// The actual object stored in the store #[derive(Clone, Copy)] struct StoreObject<O: Copy> { /// User-defined object to be associated with a value obj: O, state: ObjectState, pos: Point2<f32>, cell_id: usize, } type CellObject = (DenseGridHandle, Point2<f32>); /// A single cell of the densegrid, can be empty #[derive(Default, Clone)] pub struct DenseGridCell { pub objs: Vec<CellObject>, pub dirty: bool, } /// DenseGrid is a point-based spatial partitioning structure that uses a simple Vec which acts as a /// grid instead of a tree. /// It is Dense because all cells within the bounding rectangle of the inserted points must be allocated, /// even if they are empty. /// /// ## Fast queries /// In theory, DenseGrid should be faster than a quadtree/r-tree because it has no log costs /// (calculating the cells around a point is trivial). /// However, it only works if the cell size is adapted to the problem, much like how a tree has to /// be balanced to be efficient. It is also memory hungry since all empty cells have to be allocated. /// /// ## Dynamicity /// DenseGrid's big advantage is that it is dynamic, supporting lazy positions updates /// and object removal in constant time. Once objects are in, there is almost no allocation happening /// if the objects don't move too much. [^1] /// /// Compare that to most immutable spatial partitioning structures out there, which pretty much require /// to rebuild the entire tree every time. /// /// A SlotMap is used for objects managing, adding a level of indirection between points and objects. /// SlotMap is used because removal doesn't alter handles given to the user, while still having constant time access. /// However it requires O to be copy, but SlotMap's author stated that they were working on a similar /// map where Copy isn't required. /// /// [^1]: If an object goes out of the boundaries, then the boundary has to grow. Therefore, all cells have /// to be reallocated and all the points have to be reinserted. /// This can be solved in constant time using a SparseGrid, which has yet to be implemented. /// /// /// ## About object managment /// /// In theory, you don't have to use the object managment directly, you can make your custom /// Handle -> Object map by specifying "`()`" to be the object type. /// _(This can be useful if your object is not Copy)_ /// Since `()` is zero sized, it should probably optimize away a lot of the object managment code. /// /// ```rust /// use flat_spatial::DenseGrid; /// let mut g: DenseGrid<()> = DenseGrid::new(10); /// let handle = g.insert([0.0, 0.0], ()); /// // Use handle however you want /// ``` /// /// ## Examples /// Here is a basic example that shows most of its capabilities: /// ```rust /// use flat_spatial::DenseGrid; /// /// let mut g: DenseGrid<i32> = DenseGrid::new(10); // Creates a new grid with a cell width of 10 with an integer as extra data /// let a = g.insert([0.0, 0.0], 0); // Inserts a new element with data: 0 /// /// { /// let mut before = g.query_around([0.0, 0.0], 5.0).map(|(id, _pos)| id); // Queries for objects around a given point /// assert_eq!(before.next(), Some(a)); /// assert_eq!(g.get(a).unwrap().1, &0); /// } /// let b = g.insert([0.0, 0.0], 1); // Inserts a new element, assigning a new unique and stable handle, with data: 1 /// /// g.remove(a); // Removes a value using the handle given by `insert` /// // This won't have an effect until g.maintain() is called /// /// g.maintain(); // Maintains the grid, which applies all removals and position updates (not needed for insertions) /// /// assert_eq!(g.handles().collect::<Vec<_>>(), vec![b]); // We check that the "a" object has been removed /// /// let after: Vec<_> = g.query_around([0.0, 0.0], 5.0).map(|(id, _pos)| id).collect(); // And that b is query-able /// assert_eq!(after, vec![b]); /// /// assert_eq!(g.get(b).unwrap().1, &1); // We also check that b still has his data associated /// assert_eq!(g.get(a), None); // But that a doesn't exist anymore /// ``` /// /// ## Schema /// Here is a schema showing a bit more visually how the structure works /// /// ![schema](https://i.imgur.com/2rkQbxB.png) #[derive(Clone)] pub struct DenseGrid<O: Copy> { start_x: i32, start_y: i32, cell_size: i32, width: i32, height: i32, cells: Vec<DenseGridCell>, objects: SlotMap<DenseGridHandle, StoreObject<O>>, // Cache maintain vec to avoid allocating every time maintain is called to_relocate: Vec<(usize, CellObject)>, } impl<O: Copy> DenseGrid<O> { /// Creates an empty grid that will center itself on the first coordinate given. /// The cell size should be about the same magnitude as your queries size. pub fn new(cell_size: i32) -> Self { Self::new_rect(cell_size, 0, 0, 0, 0) } /// Creates a new grid centered on zero with width and height defined by size. /// The cell size should be about the same magnitude as your queries size. /// /// Note that the size is counted in cells and not in absolute units (!) pub fn new_centered(cell_size: i32, size: i32) -> Self { Self::new_rect(cell_size, -size, -size, 2 * size, 2 * size) } /// Creates a new grid with a custom rect defining its boundaries. /// The cell size should be about the same magnitude as your queries size. /// /// Note that the coordinates are counted in cells and not in absolute units (!) pub fn new_rect(cell_size: i32, x: i32, y: i32, w: i32, h: i32) -> Self { assert!( cell_size > 0, "Cell size ({}) cannot be less than or equal to zero", cell_size ); Self { start_x: x * cell_size, start_y: y * cell_size, cell_size, width: w, height: h, cells: (0..w * h).map(|_| DenseGridCell::default()).collect(), objects: SlotMap::with_key(), to_relocate: vec![], } } /// Inserts a new object with a position and an associated object /// Returns the unique and stable handle to be used with get_obj /// May reallocate the grid if pos is out of the boundary /// /// # Example /// ```rust /// use flat_spatial::DenseGrid; /// let mut g: DenseGrid<()> = DenseGrid::new(10); /// let h = g.insert([5.0, 3.0], ()); /// ``` pub fn insert(&mut self, pos: impl Into<Point2<f32>>, obj: O) -> DenseGridHandle { let pos = pos.into(); self.check_resize(pos); let cell_id = self.get_cell_id(pos); let handle = self.objects.insert(StoreObject { obj, state: ObjectState::Unchanged, pos, cell_id, }); self.get_cell_mut(cell_id).objs.push((handle, pos)); handle } /// Lazily sets the position of an object (if it is not marked for deletion). /// This won't be taken into account until maintain() is called. /// May reallocate the grid if pos is out of the boundary. /// /// # Example /// ```rust /// use flat_spatial::DenseGrid; /// let mut g: DenseGrid<()> = DenseGrid::new(10); /// let h = g.insert([5.0, 3.0], ()); /// g.set_position(h, [3.0, 3.0]); /// ``` pub fn set_position(&mut self, handle: DenseGridHandle, pos: impl Into<Point2<f32>>) { let pos = pos.into(); self.check_resize(pos); let new_cell_id = self.get_cell_id(pos); let obj = self .objects .get_mut(handle) .expect("Object not in grid anymore"); let old_id = obj.cell_id; obj.cell_id = new_cell_id; obj.pos = pos; if obj.state != ObjectState::Removed { obj.state = ObjectState::NewPos } self.get_cell_mut(old_id).dirty = true; } /// Lazily removes an object from the grid. /// This won't be taken into account until maintain() is called. /// /// # Example /// ```rust /// use flat_spatial::DenseGrid; /// let mut g: DenseGrid<()> = DenseGrid::new(10); /// let h = g.insert([5.0, 3.0], ()); /// g.remove(h); /// ``` pub fn remove(&mut self, handle: DenseGridHandle) { let st = self .objects .get_mut(handle) .expect("Object not in grid anymore"); st.state = ObjectState::Removed; let id = st.cell_id; self.get_cell_mut(id).dirty = true; } /// Maintains the world, updating all the positions (and moving them to corresponding cells) and removing necessary objects. /// Runs in linear time O(C + O) where C is the number of cells and O the number of objects. /// # Example /// ```rust /// use flat_spatial::DenseGrid; /// let mut g: DenseGrid<()> = DenseGrid::new(10); /// let h = g.insert([5.0, 3.0], ()); /// g.remove(h); /// /// assert!(g.get(h).is_some()); /// g.maintain(); /// assert!(g.get(h).is_none()); /// ``` pub fn maintain(&mut self) { let Self { cells, objects, to_relocate, .. } = self; for (id, cell) in cells.iter_mut().filter(|x| x.dirty).enumerate() { cell.dirty = false; cell.objs.retain_mut(|(obj_id, obj_pos)| { let store_obj = objects.get_mut(*obj_id).unwrap(); match store_obj.state { ObjectState::NewPos => { store_obj.state = ObjectState::Unchanged; *obj_pos = store_obj.pos; let relocate = store_obj.cell_id != id; if relocate { to_relocate.push((store_obj.cell_id, (*obj_id, *obj_pos))); } !relocate } ObjectState::Removed => { objects.remove(*obj_id); false } _ => true, } }) } for (cell_id, obj) in to_relocate.drain(..) { self.cells[cell_id].objs.push(obj); } } /// Iterate over all handles pub fn handles<'a>(&'a self) -> impl Iterator<Item = DenseGridHandle> + 'a { self.objects.keys() } /// Read access to the cells pub fn cells(&self) -> &Vec<DenseGridCell> { &self.cells } /// Returns a reference to the associated object and its position, using the handle. /// /// # Example /// ```rust /// use flat_spatial::DenseGrid; /// let mut g: DenseGrid<i32> = DenseGrid::new(10); /// let h = g.insert([5.0, 3.0], 42); /// assert_eq!(g.get(h), Some(([5.0, 3.0].into(), &42))); /// ``` pub fn get(&self, id: DenseGridHandle) -> Option<(Point2<f32>, &O)> { self.objects.get(id).map(|x| (x.pos, &x.obj)) } /// Returns a mutable reference to the associated object and its position, using the handle. /// /// # Example /// ```rust /// use flat_spatial::DenseGrid; /// let mut g: DenseGrid<i32> = DenseGrid::new(10); /// let h = g.insert([5.0, 3.0], 42); /// *g.get_mut(h).unwrap().1 = 56; /// assert_eq!(g.get(h).unwrap().1, &56); /// ``` pub fn get_mut(&mut self, id: DenseGridHandle) -> Option<(Point2<f32>, &mut O)> { self.objects.get_mut(id).map(|x| (x.pos, &mut x.obj)) } /// Queries for all objects around a position within a certain radius. /// Try to keep the radius asked and the cell size of similar magnitude for better performance. /// /// # Example /// ```rust /// use flat_spatial::DenseGrid; /// /// let mut g: DenseGrid<()> = DenseGrid::new(10); /// let a = g.insert([0.0, 0.0], ()); /// /// let around: Vec<_> = g.query_around([2.0, 2.0], 5.0).map(|(id, _pos)| id).collect(); /// /// assert_eq!(vec![a], around); /// ``` #[rustfmt::skip] pub fn query_around(&self, pos: impl Into<Point2<f32>>, radius: f32) -> impl Iterator<Item=CellObject> + '_ { let pos = pos.into(); let cell = self.get_cell_id(pos) as i32; let (w, h) = (self.width, self.height); let y = cell / w; let x = cell - y * w; let rplus = (radius as i32) / self.cell_size; let x_diff = pos.x - (self.start_x + x * self.cell_size) as f32; let y_diff = pos.y - (self.start_y + y * self.cell_size) as f32; let remainder = radius - (rplus * self.cell_size) as f32; let left = x_diff < remainder; let bottom = y_diff < remainder; let right = self.cell_size as f32 - x_diff < remainder; let top = self.cell_size as f32 - y_diff < remainder; let x1 = max(0, x - rplus - left as i32); let y1 = max(0, y - rplus - bottom as i32); let x2 = min(w - 1, x + rplus + right as i32); let y2 = min(h - 1, y + rplus + top as i32); let radius2 = radius * radius; (y1..y2 + 1).flat_map(move |y| { (x1..x2 + 1).flat_map(move |x| { let cell_id = y * self.width + x; // Safety: min and max boundaries just above // Works because of invariant self.cells.len() == height * width let cell = unsafe { &self.cells.get_unchecked(cell_id as usize) }; cell.objs.iter().filter(move |(_, pos_obj)| { let x = pos_obj.x - pos.x; let y = pos_obj.y - pos.y; x * x + y * y < radius2 }).copied() }) }) } /// Queries for all objects in an aabb (aka a rect). /// Try to keep the rect's width/height of similar magnitudes to the cell size for better performance. /// /// # Example /// ```rust /// use flat_spatial::DenseGrid; /// /// let mut g: DenseGrid<()> = DenseGrid::new(10); /// let a = g.insert([0.0, 0.0], ()); /// /// let around: Vec<_> = g.query_aabb([-1.0, -1.0], [1.0, 1.0]).map(|(id, _pos)| id).collect(); /// /// assert_eq!(vec![a], around); /// ``` #[rustfmt::skip] pub fn query_aabb(&self, aa: impl Into<Point2<f32>>, bb: impl Into<Point2<f32>>) -> impl Iterator<Item=CellObject> + '_ { let aa = aa.into(); let bb = bb.into(); let ll = [aa.x.min(bb.x), aa.y.min(bb.y)].into(); // lower left let ur = [aa.x.max(bb.x), aa.y.max(bb.y)].into(); // upper right let (w, h) = (self.width, self.height); let cell = self.get_cell_id(ll) as i32; let y1 = cell / w; let x1 = cell - y1 * w; let cell2 = self.get_cell_id(ur) as i32; let y2 = cell2 / w; let x2 = cell2 - y2 * w; let x1 = x1.max(0); let y1 = y1.max(0); let x2 = x2.min(w-1); let y2 = y2.min(h-1); (y1..y2 + 1).flat_map(move |y| { (x1..x2 + 1).flat_map(move |x| { let cell_id = y * self.width + x; // Safety: min and max boundaries just above // Works because of invariant self.cells.len() == height * width let cell = unsafe { &self.cells.get_unchecked(cell_id as usize) }; cell.objs.iter().filter(move |(_, pos_obj)| { (pos_obj.x >= ll.x) && (pos_obj.x <= ur.x) && (pos_obj.y >= ll.y) && (pos_obj.y <= ur.y) }).copied() }) }) } /// Allows to look directly at what's in a cell covering a specific position /// /// # Example /// ```rust /// use flat_spatial::DenseGrid; /// /// let mut g: DenseGrid<()> = DenseGrid::new(10); /// let a = g.insert([2.0, 2.0], ()); /// /// let around = g.get_cell([1.0, 1.0]); /// /// assert_eq!(&vec![(a, [2.0, 2.0].into())], around); /// ``` pub fn get_cell(&mut self, pos: impl Into<mint::Point2<f32>>) -> &Vec<CellObject> { &self .cells .get(self.get_cell_id(pos.into())) .expect("get_cell error") .objs } /// Returns the (x, y, width, height) tuple representing the current allocated rect /// (x, y) are in absolute units and (width, height) are in cells pub fn get_rect(&self) -> (i32, i32, i32, i32) { (self.start_x, self.start_y, self.width, self.height) } /// Returns the number of objects currently available /// (removals that were not confirmed with maintain() are still counted) pub fn len(&self) -> usize { self.objects.len() } /// Checks if the grid contains objects or not /// (removals that were not confirmed with maintain() are still counted) pub fn is_empty(&self) -> bool { self.objects.is_empty() } fn check_resize(&mut self, pos: Point2<f32>) { debug_assert!(pos.x.is_finite()); debug_assert!(pos.y.is_finite()); if self.width == 0 && self.height == 0 { // First allocation, change start_x and start_y to match pos self.start_x = pos.x as i32 / self.cell_size; self.start_y = pos.y as i32 / self.cell_size; } let mut reallocate = false; let x = pos.x as i32; let y = pos.y as i32; if x <= self.start_x { let diff = 1 + (self.start_x - x) / self.cell_size; self.start_x -= self.cell_size * diff; self.width += diff; reallocate = true; } if y <= self.start_y { let diff = 1 + (self.start_y - y) / self.cell_size; self.start_y -= self.cell_size * diff; self.height += diff; reallocate = true; } let right = self.start_x + self.width as i32 * self.cell_size; if x >= right { self.width += 1 + (x - right) / self.cell_size; reallocate = true; } let up = self.start_y + self.height as i32 * self.cell_size; if y >= up { self.height += 1 + (y - up) / self.cell_size; self.cells .resize_with((self.width * self.height) as usize, DenseGridCell::default); } if reallocate { self.reallocate(); } } fn reallocate(&mut self) { self.cells .resize_with((self.width * self.height) as usize, DenseGridCell::default); for x in &mut self.cells { x.objs.clear(); x.dirty = false; } for (id, obj) in &mut self.objects { let cell_id = Self::get_cell_id_raw( self.width as i32, self.start_x, self.start_y, self.cell_size, obj.pos, ); obj.cell_id = cell_id; obj.state = ObjectState::Unchanged; self.cells .get_mut(cell_id) .unwrap() .objs .push((id, obj.pos)); } } fn get_cell_mut(&mut self, id: usize) -> &mut DenseGridCell { self.cells.get_mut(id).expect("get_cell error") } fn get_cell_id(&self, pos: Point2<f32>) -> usize { Self::get_cell_id_raw( self.width as i32, self.start_x, self.start_y, self.cell_size, pos, ) } fn get_cell_id_raw( width: i32, start_x: i32, start_y: i32, cell_size: i32, pos: Point2<f32>, ) -> usize { let i_x = (pos.x as i32 - start_x) / cell_size; let i_y = (pos.y as i32 - start_y) / cell_size; (i_y * width + i_x) as usize } } #[cfg(test)] mod tests { use super::DenseGrid; #[test] fn test_small_query() { let mut g: DenseGrid<()> = DenseGrid::new(10); let a = g.insert([5.0, 0.0], ()); let b = g.insert([11.0, 0.0], ()); let c = g.insert([5.0, 8.0], ()); let near: Vec<_> = g.query_around([6.0, 0.0], 2.0).map(|x| x.0).collect(); assert_eq!(near, vec![a]); let mid: Vec<_> = g.query_around([8.0, 0.0], 4.0).map(|x| x.0).collect(); assert!(mid.contains(&a)); assert!(mid.contains(&b)); let far: Vec<_> = g.query_around([6.0, 0.0], 10.0).map(|x| x.0).collect(); assert!(far.contains(&a)); assert!(far.contains(&b)); assert!(far.contains(&c)); } #[test] fn test_big_query_around() { let mut g: DenseGrid<()> = DenseGrid::new(10); for i in 0..100 { g.insert([i as f32, 0.0], ()); } let q: Vec<_> = g.query_around([15.0, 0.0], 9.5).map(|x| x.0).collect(); assert_eq!(q.len(), 19); // 1 middle, 8 left, 8 right } #[test] fn test_big_query_rect() { let mut g: DenseGrid<()> = DenseGrid::new(10); for i in 0..100 { g.insert([i as f32, 0.0], ()); } let q: Vec<_> = g .query_aabb([5.5, 1.0], [15.5, -1.0]) .map(|x| x.0) .collect(); assert_eq!(q.len(), 10); } #[test] fn test_distance_test() { let mut g: DenseGrid<()> = DenseGrid::new(10); let a = g.insert([3.0, 4.0], ()); let far: Vec<_> = g.query_around([0.0, 0.0], 5.1).map(|x| x.0).collect(); assert_eq!(far, vec![a]); let near: Vec<_> = g.query_around([0.0, 0.0], 4.9).map(|x| x.0).collect(); assert_eq!(near, vec![]); } #[test] fn test_change_position() { let mut g: DenseGrid<()> = DenseGrid::new(10); let a = g.insert([0.0, 0.0], ()); let before: Vec<_> = g.query_around([0.0, 0.0], 5.0).map(|x| x.0).collect(); assert_eq!(before, vec![a]); g.set_position(a, [30.0, 30.0]); g.maintain(); let before: Vec<_> = g.query_around([0.0, 0.0], 5.0).map(|x| x.0).collect(); assert_eq!(before, vec![]); let after: Vec<_> = g.query_around([30.0, 30.0], 5.0).map(|x| x.0).collect(); assert_eq!(after, vec![a]); } #[test] fn test_remove() { let mut g: DenseGrid<()> = DenseGrid::new(10); let a = g.insert([0.0, 0.0], ()); let before: Vec<_> = g.query_around([0.0, 0.0], 5.0).map(|x| x.0).collect(); assert_eq!(before, vec![a]); g.remove(a); let b = g.insert([0.0, 0.0], ()); g.maintain(); assert_eq!(g.handles().collect::<Vec<_>>(), vec![b]); let after: Vec<_> = g.query_around([0.0, 0.0], 5.0).map(|x| x.0).collect(); assert_eq!(after, vec![b]); } #[test] fn test_resize() { let mut g: DenseGrid<()> = DenseGrid::new(10); let a = g.insert([-1000.0, 0.0], ()); let q: Vec<_> = g.query_around([-1000.0, 0.0], 5.0).map(|x| x.0).collect(); assert_eq!(q, vec![a]); let b = g.insert([0.0, 1000.0], ()); let q: Vec<_> = g.query_around([0.0, 1000.0], 5.0).map(|x| x.0).collect(); assert_eq!(q, vec![b]); } }