/** * scripts/regions.test.ts — validation for the committed `public/regions.geo.json`. * * The dataset is REAL named sub-national administrative regions (Natural * Earth admin-1: states, provinces, governorates, oblasts, …) that the * coarsening step (`scripts/coarsen-regions.mjs`, v0.14) has merged down to a * ~100×100 km (10,000 km²) floor: every small non-island region was dissolved * into its nearest same-country neighbor, so the only regions left below the * floor are islands (no same-country sibling nearby). One feature per named * region, each carrying `properties = { name, parent }` where `parent` is the * country's ISO_A3 (the RegionMap key the map resolves ownership through). * Tiny or uncovered countries collapse to a single whole-country region * (`-01`). * * v0.17 (`scripts/fill-gaps.mjs`) additionally fills the no-one's-land left * between merged sub-regions: per country, the uncovered slivers of the * country's landmass (≥ 25 km²) were added as extra parts of the nearest * region, so the regions now cover the landmass almost completely (the * sampling test below measures that per country). * * This test is self-contained (no import of the generator) and deliberately * dependency-free — it re-implements the same planar area model the * generator/analysis use, so the area-based assertions measure the same * quantity: * * x = lon · 111.32 · cos(midLat), y = lat · 110.574 (km) * * with a shoelace per OUTER ring, each ring measured at its own mean latitude. * Outer rings only — a region's inner rings (holes) are lakes and are ignored * by design, the same way the coverage band already absorbed them. * * No geojson/@turf types are imported: the project keeps `@types/geojson` * OUT of the tsc program (see tsconfig `types`) so maplibre-gl's d.ts stays * in its loose (skipLibCheck) mode; the one coverage test below uses an * inline even-odd ray cast instead of a geometry library. * * It reads each file exactly once and runs in O(total vertices). */ import { readFileSync } from 'node:fs'; import path from 'node:path'; import { fileURLToPath } from 'node:url'; import { describe, expect, it } from 'vitest'; const here = path.dirname(fileURLToPath(import.meta.url)); const root = path.resolve(here, '..'); // --- area model (planar approximation; matches scripts/generate-regions.mjs) -- const KM_LON = 111.32; const KM_LAT = 110.574; const rad = (deg: number) => (deg * Math.PI) / 180; type Ring = [number, number][]; type Geometry = | { type: 'Polygon'; coordinates: Ring[] } | { type: 'MultiPolygon'; coordinates: Ring[][] }; function ringAreaKm2(ring: Ring, midLat: number): number { const kx = KM_LON * Math.cos(rad(midLat)); let a = 0; const n = ring.length; for (let i = 0; i < n; i++) { const [lon1, lat1] = ring[i]; const [lon2, lat2] = ring[(i + 1) % n]; a += lon1 * kx * (lat2 * KM_LAT) - lon2 * kx * (lat1 * KM_LAT); } return Math.abs(a / 2); } function outerRings(geom: Geometry): Ring[] { if (geom.type === 'Polygon') return [geom.coordinates[0]]; if (geom.type === 'MultiPolygon') return geom.coordinates.map((p) => p[0]); return []; } /** Sum of a feature's outer-ring areas, each ring at its own mean latitude. */ function featureAreaKm2(geom: Geometry): number { let total = 0; for (const ring of outerRings(geom)) { let lat = 0; for (const [, la] of ring) lat += la; total += ringAreaKm2(ring, ring.length ? lat / ring.length : 0); } return total; } function median(nums: number[]): number { if (!nums.length) return 0; const s = [...nums].sort((a, b) => a - b); const m = Math.floor(s.length / 2); return s.length % 2 ? s[m] : (s[m - 1] + s[m]) / 2; } /** Raw min/max bbox [w, s, e, n] of a geometry (all coordinates). */ function rawBBox(geom: Geometry): [number, number, number, number] { const polys = geom.type === 'Polygon' ? [geom.coordinates] : geom.coordinates; let w = Infinity, s = Infinity, e = -Infinity, n = -Infinity; for (const poly of polys) for (const ring of poly) for (const [lo, la] of ring) { if (lo < w) w = lo; if (lo > e) e = lo; if (la < s) s = la; if (la > n) n = la; } return [w, s, e, n]; } /** * Even-odd ray cast: is `[lon, lat]` inside `ring`? Planar, in raw lon/lat * space (no antimeridian handling — the polygons and the sample points live * in the same unwrapped space, so containment is mathematically consistent * even for countries that cross the date line). Used only as a fast, * deterministic coverage proxy (see the sampling test), never for areas. */ function pointInRing(pt: [number, number], ring: Ring): boolean { const [x, y] = pt; let inside = false; for (let i = 0, j = ring.length - 1; i < ring.length; j = i++) { const [xi, yi] = ring[i]; const [xj, yj] = ring[j]; if (yi > y !== yj > y && x < ((xj - xi) * (y - yi)) / (yj - yi) + xi) inside = !inside; } return inside; } /** Is a point inside a (Multi)Polygon: inside the outer ring, outside all holes. */ function pointInGeom(pt: [number, number], geom: Geometry): boolean { if (geom.type === 'Polygon') { if (!pointInRing(pt, geom.coordinates[0])) return false; return geom.coordinates.slice(1).every((h) => !pointInRing(pt, h)); } if (geom.type === 'MultiPolygon') return geom.coordinates.some((p) => pointInGeom(pt, { type: 'Polygon', coordinates: p })); return false; } // ------------------------------------------------------------------------------ interface RegionFeature { type: 'Feature'; id: string; properties: { name: string; parent: string }; geometry: Geometry; } interface CountryFeature { type: 'Feature'; id: string; properties: { name: string }; geometry: Geometry; } // Read each file exactly once. const regions = JSON.parse( readFileSync(path.join(root, 'public', 'regions.geo.json'), 'utf8'), ) as { type: 'FeatureCollection'; features: RegionFeature[] }; const countries = JSON.parse( readFileSync(path.join(root, 'public', 'countries.geo.json'), 'utf8'), ) as { type: 'FeatureCollection'; features: CountryFeature[] }; // Precompute once (O(total vertices)). const countryIds = new Set(countries.features.map((c) => c.id)); const countryArea = new Map(); for (const c of countries.features) countryArea.set(c.id, featureAreaKm2(c.geometry)); const regionArea = new Map(); for (const f of regions.features) regionArea.set(f.id, featureAreaKm2(f.geometry)); const sumByParent = new Map(); for (const f of regions.features) sumByParent.set(f.properties.parent, (sumByParent.get(f.properties.parent) ?? 0) + (regionArea.get(f.id) ?? 0)); const countByParent = new Map(); for (const f of regions.features) countByParent.set(f.properties.parent, (countByParent.get(f.properties.parent) ?? 0) + 1); // Raw bboxes for the sampling test's cheap reject (O(total vertices)). const regionBB = new Map(); for (const f of regions.features) regionBB.set(f.id, rawBBox(f.geometry)); // --- island/close-neighbor helpers (mirror scripts/coarsen-regions.mjs) ------ interface LonInt { a: number; b: number; full: boolean; } interface RegionBBox { latMin: number; latMax: number; lon: LonInt; } const COARSE_FLOOR_KM2 = 10_000; // the coarsener's ~100×100 km floor const CLOSE_DEG = 0.2; // "spatially close" bbox gap (both lat and lon ≤ this) /** * Unwrap a ring's longitudes to a continuous line (np.unwrap shortest-diff * scheme, anchored at the first vertex's [0,360) value). `full` when the * unwrapped span is ≥ 300° (a full-360° antimeridian band, e.g. Antarctica). * Must stay in sync with the coarsening script. */ function unwrapRing(ring: Ring) { const n = ring.length; const norm = (x: number) => ((x % 360) + 360) % 360; const u: number[] = new Array(n); u[0] = norm(ring[0][0]); for (let i = 1; i < n; i++) { // the previous UNWRAPPED value may lie outside [0,360); normalize it // before measuring the shortest signed difference, or a bogus ~180° jump // is inserted and the ring's span balloons. const a = norm(u[i - 1]); const b = norm(ring[i][0]); const d = (((b - a) % 360) + 540) % 360 - 180; u[i] = u[i - 1] + d; } let min = Infinity; let max = -Infinity; for (const v of u) { if (v < min) min = v; if (v > max) max = v; } return { lons: u, full: max - min >= 300 }; } /** * Cyclic 1-D gap (degrees) between two tight longitude intervals in their own * unwrapped spaces; a `full` interval is close to everything. */ function lonGap(intA: LonInt, intB: LonInt): number { if (intA.full || intB.full) return 0; let best = Infinity; for (const k of [-1, 0, 1]) { const a2 = intB.a + 360 * k; const b2 = intB.b + 360 * k; const gap = intA.b < a2 ? a2 - intA.b : b2 < intA.a ? intA.a - b2 : 0; if (gap < best) best = gap; } return best; } // Per-region bbox in antimeridian-safe unwrapped longitude space. const regionBBox = new Map(); for (const f of regions.features) { const polys = f.geometry.type === 'Polygon' ? [f.geometry.coordinates] : f.geometry.coordinates; let latMin = Infinity; let latMax = -Infinity; let a = Infinity; let b = -Infinity; let full = false; for (const poly of polys) { const outer = poly[0]; for (const [, la] of outer) { if (la < latMin) latMin = la; if (la > latMax) latMax = la; } const { lons, full: fl } = unwrapRing(outer); if (fl) full = true; for (const v of lons) { if (v < a) a = v; if (v > b) b = v; } } regionBBox.set(f.id, { latMin, latMax, lon: { a, b, full } }); } /** Bounding-box closeness (same definition the coarsening script uses). */ function bboxesClose(x: RegionBBox, y: RegionBBox): boolean { const latGap = x.latMax < y.latMin ? y.latMin - x.latMax : y.latMax < x.latMin ? x.latMin - y.latMax : 0; if (latGap > CLOSE_DEG) return false; return lonGap(x.lon, y.lon) <= CLOSE_DEG; } describe('regions.geo.json', () => { it('is a valid GeoJSON FeatureCollection of well-formed features', () => { expect(regions.type).toBe('FeatureCollection'); expect(Array.isArray(regions.features)).toBe(true); expect(regions.features.length).toBeGreaterThan(0); for (const f of regions.features) { expect(f.type, `${f.id ?? '?'}: not a Feature`).toBe('Feature'); expect(typeof f.id, `${f.id ?? '?'}: id must be a string`).toBe('string'); expect(f.id.length, `${f.id ?? '?'}: empty id`).toBeGreaterThan(0); expect(typeof f.properties?.name, `${f.id}: missing name`).toBe('string'); expect(f.properties.name.length, `${f.id}: empty name`).toBeGreaterThan(0); expect(typeof f.properties.parent, `${f.id}: missing parent`).toBe('string'); expect(countryIds.has(f.properties.parent), `${f.id}: unknown parent ${f.properties.parent}`).toBe(true); const g = f.geometry; expect( !!g && (g.type === 'Polygon' || g.type === 'MultiPolygon'), `${f.id}: bad geometry type ${g?.type}`, ).toBe(true); if (g) { const polys = g.type === 'Polygon' ? [g.coordinates] : g.coordinates; for (const poly of polys) for (const ring of poly) expect(ring.length, `${f.id}: ring with ${ring.length} pts`).toBeGreaterThanOrEqual(3); } } }); it('has globally unique feature ids (ISO 3166-2 disambiguated on within-country collision)', () => { const seen = new Set(); const dups = new Set(); for (const f of regions.features) { if (seen.has(f.id)) dups.add(f.id); seen.add(f.id); } expect( dups.size, `duplicate ids: ${[...dups].slice(0, 10).join(', ')}`, ).toBe(0); expect(seen.size).toBe(regions.features.length); }); it('covers every one of the 177 countries with at least one region', () => { const counts = countries.features.map((c) => countByParent.get(c.id) ?? 0); for (const c of countries.features) { expect(countByParent.get(c.id) ?? 0, `country ${c.id} has no regions`).toBeGreaterThanOrEqual(1); } const min = Math.min(...counts); const max = Math.max(...counts); const med = median(counts); const maxCountry = [...countByParent.entries()].sort((a, b) => b[1] - a[1])[0]; const maxCountryName = countries.features.find((c) => c.id === maxCountry[0])?.properties.name ?? ''; console.log( `\n per-country region count: min ${min} / median ${med} / max ${max}` + ` (max: ${maxCountry[0]} ${maxCountryName} with ${maxCountry[1]})`, ); }); it('has sane region areas: median >= 100 km2, and no non-Antarctica region >= 5,000,000 km2', () => { const areas = regions.features.map((f) => regionArea.get(f.id) ?? 0); const med = median(areas); const maxRegion = regions.features.reduce((m, f) => ((regionArea.get(f.id) ?? 0) > (regionArea.get(m.id) ?? 0) ? f : m)); const minRegion = regions.features.reduce((m, f) => ((regionArea.get(f.id) ?? 0) < (regionArea.get(m.id) ?? 0) ? f : m)); const tiny = areas.filter((a) => a < 1).length; // Antarctica (ATA) is a full-360° wrap ring, so the planar model can't // measure it (it reports ~21.8M km2 for a ~14M km2 landmass) — exempt it. for (const f of regions.features) { if (f.properties.parent === 'ATA') continue; const a = regionArea.get(f.id) ?? 0; expect(a < 5_000_000, `${f.id}: area ${Math.round(a).toLocaleString('en-US')} km2 is absurdly large`).toBe(true); } expect(med, `median region area ${med.toFixed(1)} km2 is too small`).toBeGreaterThanOrEqual(100); console.log( `\n region area: min ${minRegion.id} (${minRegion.properties.name}) ≈ ${(regionArea.get(minRegion.id) ?? 0).toExponential(2)} km2` + ` / median ${med.toLocaleString('en-US')} km2` + ` / max ${maxRegion.id} (${maxRegion.properties.name}) ≈ ${Math.round(regionArea.get(maxRegion.id) ?? 0).toLocaleString('en-US')} km2` + ` — ${tiny} regions < 1 km2 (legit micro-regions: tiny islands, small urban districts, degenerate disputed enclaves)`, ); }); it('leaves only islands below the ~10,000 km2 coarsening floor (non-island small regions merged)', () => { // v0.14 coarsening: every region smaller than the floor that has a // same-country sibling within CLOSE_DEG of its bbox is dissolved into its // nearest such neighbor, so a below-floor region may only survive if it // is an island. Count the non-island residuals below the floor and allow // a small tolerance band (strictly < 1% of all regions) — the coarsener's // fixed point leaves none, and this catches a regression in the merge // logic (e.g. a broken neighbor test that exempts land regions) without // being brittle to one or two borderline cases. const smallNonIslands: string[] = []; let smallIslands = 0; let smallTotal = 0; for (const f of regions.features) { const a = regionArea.get(f.id) ?? 0; if (a >= COARSE_FLOOR_KM2) continue; smallTotal++; const bb = regionBBox.get(f.id)!; let hasNeighbor = false; for (const g of regions.features) { if (g.id === f.id || g.properties.parent !== f.properties.parent) continue; if (bboxesClose(bb, regionBBox.get(g.id)!)) { hasNeighbor = true; break; } } if (hasNeighbor) { smallNonIslands.push(`${f.id} (${Math.round(a)} km2)`); } else smallIslands++; } const frac = regions.features.length ? smallNonIslands.length / regions.features.length : 0; expect( frac < 0.01, `${smallNonIslands.length} non-island region(s) below the ${COARSE_FLOOR_KM2} km2 floor ` + `(${(100 * frac).toFixed(2)}% of all regions): ${smallNonIslands.slice(0, 10).join(', ')}`, ).toBe(true); console.log( `\n below-floor regions: ${smallTotal} — ${smallIslands} islands (exempt, no same-country neighbor within ${CLOSE_DEG}°)` + ` / ${smallNonIslands.length} non-island residuals (must stay < 1% of all regions)`, ); }); it('leaves exactly one enclosed hole: KZ-KZY (the real Aral Sea), still large', () => { // v0.15 filled every small hole; v0.16 smoothing never touches holes; and // v0.17's gap-filler explicitly keeps the Aral hole (its centroid matches a // pre-existing hole and it lies inside another country's landmass) while // dropping phantom holes. So the whole file must contain exactly one hole, // on KZ-KZY, at a realistic size (~5,860 km2 planar; the real Aral has // shrunk to roughly this by the 2020s) — no new holes of any size. let holes = 0; let maxHole = 0; const holeIds: string[] = []; let kzkzyHoleArea = 0; for (const f of regions.features) { const polys = f.geometry.type === 'Polygon' ? [f.geometry.coordinates] : f.geometry.coordinates; for (const poly of polys) { for (let i = 1; i < poly.length; i++) { holes++; let lat = 0; for (const [, la] of poly[i]) lat += la; const area = ringAreaKm2(poly[i], poly[i].length ? lat / poly[i].length : 0); if (area > maxHole) maxHole = area; holeIds.push(f.id); if (f.id === 'KZ-KZY') kzkzyHoleArea = area; } } } expect(holes, `expected exactly 1 hole (KZ-KZY), found ${holes}: ${[...new Set(holeIds)].join(', ')}`).toBe(1); expect(holeIds, 'the one remaining hole is KZ-KZY').toEqual(['KZ-KZY']); expect( kzkzyHoleArea >= 5_000 && kzkzyHoleArea <= 7_000, `KZ-KZY hole is ${Math.round(kzkzyHoleArea).toLocaleString('en-US')} km2 — outside the 5,000–7,000 km2 Aral band`, ).toBe(true); console.log( `\n holes: exactly 1 (KZ-KZY ≈ ${Math.round(kzkzyHoleArea).toLocaleString('en-US')} km2) — the Aral hole survived v0.17's fill`, ); }); it('sums to within [40%, 190%] of each country area (median in [70%, 130%])', () => { // The band is a planar-approximation sanity check. It is wider than a naive // [40%, 110%] because Natural Earth's admin-1 polygons are digitized // independently of the admin-0 country polygons (they are NOT clipped to // them). v0.17's gap fill removed the large UNDER-fills (the old minimum // was Brunei at ~52% — its regions now cover the landmass, ≈ 79%), but // the OVER-fill tail is a pre-existing admin-1 artifact: a few tiny island // nations (Vanuatu 178.9%, Solomon Is. 133%, Bahamas 129%) have admin-1 // polygons that extend beyond their own country polygon, and the fill // only added area *inside* the country, so it can't shrink that tail. // The band brackets the measured [78.8%, 178.9%] with margin while still // catching a genuinely missing or doubled-up region. const ratios: number[] = []; let minRatio = Infinity; let maxRatio = -Infinity; let minId = ''; let maxId = ''; for (const c of countries.features) { const ca = countryArea.get(c.id) ?? 0; if (ca <= 0) continue; const ratio = (sumByParent.get(c.id) ?? 0) / ca; ratios.push(ratio); if (ratio < minRatio) { minRatio = ratio; minId = c.id; } if (ratio > maxRatio) { maxRatio = ratio; maxId = c.id; } expect( ratio >= 0.4 && ratio <= 1.9, `${c.id}: coverage ${(100 * ratio).toFixed(1)}% is outside [40%, 190%]`, ).toBe(true); } const medRatio = median(ratios); expect( medRatio >= 0.7 && medRatio <= 1.3, `median coverage ${(100 * medRatio).toFixed(1)}% is outside [70%, 130%]`, ).toBe(true); console.log( `\n coverage range: min ${minId} ${(100 * minRatio).toFixed(1)}%` + ` / median ${(100 * medRatio).toFixed(1)}%` + ` / max ${maxId} ${(100 * maxRatio).toFixed(1)}% (band 40–190%)`, ); }); it('covers each country\'s landmass with no significant no-one\'s-land (v0.17 gap fill, grid-sampled)', () => { // The v0.17 fill (scripts/fill-gaps.mjs) assigned every uncovered sliver of // each country's landmass (≥ 25 km²) to its nearest region, so the residual // no-one's-land per country should be small everywhere. Measuring the // exact union is too slow, so this samples a 25×25 grid over each // country's raw bbox (skipping points outside the country polygon) and // counts the fraction of in-land sample points that fall in NONE of the // country's regions — a fast, deterministic proxy (same planar space, // inline even-odd ray cast; antimeridian-safe because points and polygons // share the raw coordinate space). Sampling over-counts coastline // mismatch (admin-0 vs admin-1 edges), so the thresholds are generous: // they catch a real regression (a whole sliver left unfilled) without // being brittle to digitization fuzz. const N = 25; const results: { id: string; name: string; frac: number; land: number }[] = []; for (const c of countries.features) { const [w, s, e, n] = rawBBox(c.geometry); if (e - w < 0.01 || n - s < 0.01) continue; // degenerate (point-like) country const regs = regions.features.filter((f) => f.properties.parent === c.id); let land = 0; let uncov = 0; for (let i = 0; i < N; i++) { const la = s + ((i + 0.5) / N) * (n - s); for (let j = 0; j < N; j++) { const lo = w + ((j + 0.5) / N) * (e - w); const pt: [number, number] = [lo, la]; if (!pointInGeom(pt, c.geometry)) continue; land++; // cheap bbox reject first, then the full containment test if (!regs.some((f) => { const [rw, rs, re, rn] = regionBB.get(f.id)!; if (lo < rw || lo > re || la < rs || la > rn) return false; return pointInGeom(pt, f.geometry); })) uncov++; } } if (land >= 4) results.push({ id: c.id, name: c.properties.name, frac: uncov / land, land }); } expect(results.length, `only ${results.length} countries sampled (expected ~176)`).toBeGreaterThanOrEqual(150); const fracs = results.map((r) => r.frac).sort((a, b) => a - b); const med = median(fracs); const p90 = fracs[Math.floor(fracs.length * 0.9)]; const worst = results.reduce((m, r) => (r.frac > m.frac ? r : m)); const over20 = results.filter((r) => r.frac > 0.2).sort((a, b) => b.frac - a.frac); expect( med <= 0.05, `median country gap ${(100 * med).toFixed(1)}% > 5% — significant no-one's-land remains`, ).toBe(true); expect( p90 <= 0.15, `p90 country gap ${(100 * p90).toFixed(1)}% > 15% — many countries have real gaps`, ).toBe(true); expect( worst.frac <= 0.4, `worst country ${worst.id} (${worst.name}) gap ${(100 * worst.frac).toFixed(1)}% > 40%`, ).toBe(true); expect( over20.length <= 3, `${over20.length} countries with > 20% gap: ${over20.map((r) => `${r.id} ${(100 * r.frac).toFixed(1)}%`).join(', ')}`, ).toBe(true); console.log( `\n no-one's-land (grid-sampled, N=${N}): median ${(100 * med).toFixed(1)}% / p90 ${(100 * p90).toFixed(1)}%` + ` / max ${worst.id} (${worst.name}) ${(100 * worst.frac).toFixed(1)}%` + (over20.length ? ` — >20%: ${over20.map((r) => `${r.id} ${(100 * r.frac).toFixed(1)}%`).join(', ')}` : ' — no country > 20%'), ); }); it('is at the v0.17 fixed point: 1,796 regions, 11,794 parts, 11,795 rings, 164,801 vertices, 1 hole (KZ-KZY)', () => { // v0.17 (scripts/fill-gaps.mjs) APPENDED cleaned gap pieces to the v0.16 // fixed point: it never moves an existing border, merges a part, or // removes a ring — it only adds new parts (+6,768: 5,026 → 11,794) and // keeps the single KZ-KZY hole. The region count (1,796), the // per-feature ids/names/parents and their order are unchanged; only the // part/ring/vertex totals and the hole's part structure moved. Pinning // the signature guards against a non-idempotent or destructive re-run. // The fill is byte-deterministic per input and idempotent (a second run // on the filled file changes nothing). const polysOf = (g: Geometry) => (g.type === 'Polygon' ? [g.coordinates] : g.coordinates); let verts = 0, rings = 0, parts = 0, holes = 0; const holeIds: string[] = []; for (const f of regions.features) { const polys = polysOf(f.geometry); parts += polys.length; for (const poly of polys) { rings += poly.length; holes += Math.max(0, poly.length - 1); if (poly.length > 1) holeIds.push(f.id); for (const ring of poly) verts += ring.length; } } expect(regions.features.length, 'region count').toBe(1796); // unchanged by the fill expect(parts, 'parts').toBe(11_794); // v0.16: 5,026 → +6,768 appended gap pieces expect(rings, 'rings').toBe(11_795); // every appended part is a single-ring polygon (+1 hole = KZ-KZY, pre-existing) expect(holes, 'holes').toBe(1); // the single KZ-KZY hole, unchanged expect(holeIds, 'the one remaining hole is KZ-KZY').toEqual(['KZ-KZY']); expect(verts, 'total vertices (incl. ring closure)').toBe(164_801); // v0.16: 111,175 console.log( `\n v0.17 gap fill: ${regions.features.length} regions, ${parts} parts, ${rings} rings, ` + `${holes} hole (KZ-KZY), ${verts} vertices — v0.16 topology preserved, 6,768 gap pieces appended`, ); }); });