feat(509-5 · 509-2 B05 추천 지형): 분석 지형 고르기 = 추천 노선 창 안 · 지형마다 추천 미리 셈 · [적용] = 창 지형이 설계 지형 · 평면은 지형 이름만 · 설계 지형 격자 하나(수치지형도 적용이면 그 격자)

- 전처리 미리 셈이 고를 수 있는 지형마다(설계 지형 먼저 · 수치지형도는 DB 모델 있을 때만) 다섯 갈래 + 초기 종단
- 창 지형 바꿈 = 그 지형 저장본만 · 없으면 409 안내(+[재계산]) · 기본값 판정에서 지형 뺌
- POST /route/initial terrain = 창 지형 · [적용] draft.terrain = 창 지형 · 손 [저장]은 지형 안 바꿈(서버도 as_initial 일 때만)
- 평면 분석 지형 고르기 · 화면 취향(routeedit-terrain) 걷음 · 지반고 · 묶음 초안 = 설계 지형(null) · 적용 뒤 받아 둔 격자 버림
- 시험 test_509_5 · test_509_2 · 걷은 고르기를 보던 옛 시험 새 동작으로(352_3 건너뜀)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

resources/tester/helper_346_1_pipeline_page.cjs

@@ -50,7 +50,6 @@ const local = { grid, design: "las" };
 
 let remoteCalls = 0;
 STUBS["B05_Profile_Api_Replan"] = {
-  analysisTerrain: () => "las",
   fetchRoutePlan: async () => ({ planned: job.line, curves: [], min_radius_m: job.minRadius }),
 };
 STUBS["B05_Profile_Api_Structures"] = {

resources/tester/helper_346_3_route_save.cjs

@@ -54,6 +54,10 @@ const STUBS = {
   "./B05_Profile_Api_Fetch": {
     clearRouteLatestCache: () => calls.push("latest:clear"),
   },
+  // 509-2 — 추천 [적용] 뒤 받아 둔 설계 지형 격자 버림
+  "./B05_Profile_Api_TerrainGrid": {
+    forgetDesignTerrainGrid: () => calls.push("grid:forget"),
+  },
   "./B05_Profile_Api_Replan": {
     replanRoute: async (_p, body) => {
       bodies.push(JSON.parse(JSON.stringify(body)));
@@ -115,7 +119,6 @@ const apply = loadTs(path.join(ROOT, "B05_Profile", "B05_Profile_UI_RouteEdit_Ap
       curveRadius: [null, 25],
     }),
     changed: () => changed,
-    terrain: () => "sheet",
     snap: () => ({ stationSnap: true, stationSnapStep: 20 }), // 390-5 — 켬끔 · 간격 한 벌
     initial: { current: () => ({ mode: "follow" }), keep: () => (kept += 1) },
     onApplied: () => (rebuilt += 1),
@@ -158,7 +161,13 @@ const apply = loadTs(path.join(ROOT, "B05_Profile", "B05_Profile_UI_RouteEdit_Ap
     curveOn: [true, true],
     curveRadius: [null, null],
   };
-  out.recommendOk = await apply.saveRecommendedRoute("p1", snapshot, { mode: "earthwork" }, true);
+  out.recommendOk = await apply.saveRecommendedRoute(
+    "p1",
+    snapshot,
+    { mode: "earthwork" },
+    true,
+    "sheet", // 509-5 — 창에서 고른 지형
+  );
   out.recommendBody = bodies[bodies.length - 1];
   out.recommendCalls = calls.filter((c) => !c.startsWith("toast:"));
   out.recommendDraftsLeft = {

resources/tester/test_133_1_analysis_terrain.py

@@ -164,14 +164,10 @@ def test_화면_고르기_배선():
     main = (page / "B05_Profile_UI_RouteEdit.ts").read_text(encoding="utf-8")
     api = (page / "B05_Profile_Api_Replan.ts").read_text(encoding="utf-8")
     initial_api = (page / "B05_Profile_Api_RouteInitial.ts").read_text(encoding="utf-8")
-    # 기본 숨김 · 둘 다 있을 때만 보임 · 기본 라이다
-    assert '<label class="b05-routeedit__terrain" hidden' in chrome
-    assert '<option value="las">라이다</option>' in chrome
-    assert '<option value="sheet">수치지형도</option>' in chrome
-    assert 'sources?.sources.includes("las") && !!sources?.sources.includes("sheet")' in main
-    assert 'saved === "sheet" || saved === "las" ? saved : (context?.design ?? fallback)' in api
-    # 모달 지반고가 고른 지형을 실어 보냄 · 횡단 미리보기 = 묶음(365-3) · [확인] 재계산은 안 실음
-    assert api.count("terrain: analysisTerrain(projectId)") == 1
-    assert "terrain: analysisTerrain(projectId)" in initial_api
+    # 509-5 — 평면은 설계 지형 이름만(둘 다 있을 때) · 고르기 · 지형 실음 = 추천 창(test_509_5)
+    assert 'data-slot="terrain-name" hidden' in chrome and 'data-act="terrain"' not in chrome
+    assert 'sources?.sources.includes("las") && sources.sources.includes("sheet")' in main
+    assert "analysisTerrain" not in api and "analysisTerrain" not in initial_api
+    assert "body: JSON.stringify(request)," in initial_api
     replan_fn = api.split("export async function replanRoute")[1].split("export ")[0]
     assert "terrain" not in replan_fn

resources/tester/test_133_2_design_terrain.py

@@ -291,9 +291,8 @@ def test_화면_확인이_고른_지형을_실음():
     page = ROOT / "B05_Profile"
     apply = (page / "B05_Profile_UI_RouteEdit_Apply.ts").read_text(encoding="utf-8")
     main = (page / "B05_Profile_UI_RouteEdit.ts").read_text(encoding="utf-8")
-    # 346-3 — 노선 초안(draft.terrain)에 실림 · [저장]이 보냄
-    assert "terrain: params.terrain() })" in apply and "terrain: settings.terrain," in apply
-    assert "pickedTerrain() !== designTerrain" in main  # 지형만 바꿔도 [확인]이 다시 셈
-    assert (
-        "setTerrainContext(projectId, choosable, designTerrain)" in main
-    )  # 고른 값 없으면 설계 지형
+    # 509-5 — 지형 바꿈 = 추천 [적용]만(창 지형) · 손 [저장] 초안 = 설계 지형(null)
+    assert "terrain: settings.terrain," in apply
+    assert "const settings = () => ({ ...params.snap(), terrain: null });" in apply
+    assert "stationSnapStep: null,\n        terrain,\n" in apply  # 창 지형(509-5)
+    assert "pickedTerrain" not in main and "terrainSelect" not in main

resources/tester/test_309_3_recommend_preprocess_only.py

@@ -86,11 +86,10 @@ def test_체인이_만들면_화면이_꺼냄(wired) -> None:  # noqa: F811
 
 
 def test_화면이_실은_분석_지형이_설계_지형이면_기본_갈래(wired) -> None:  # noqa: F811
-    """화면은 늘 분석 지형을 실음 — 설계 지형(가짜 세계 = 라이다)과 같으면 저장본만 · 다르면 셈."""
+    """창 지형 — 설계 지형이든 다른 지형이든 기본 갈래는 저장본만(509-5 · 지형마다 미리 셈)."""
     assert _ask(False, mode="gentle", terrain="las").status_code == 409
+    assert _ask(False, mode="gentle", terrain="sheet").status_code == 409
     assert wired.count == 0
-    assert _ask(False, mode="gentle", terrain="sheet")["stored"] is False
-    assert wired.count == 1
 
 
 def test_사용자가_바꾼_값_재계산은_셈(wired) -> None:  # noqa: F811

resources/tester/test_346_1_pipeline_page.py

@@ -186,7 +186,7 @@ def test_페이지_묶음_노선_초안_캐시_칸(r):
     assert p["before"] == {"saved": None, "pipe": True}
     assert (
         p["cached"]["rev"] == 1
-        and p["cached"]["terrain"] == "las"
+        and p["cached"]["terrain"] is None  # 설계 지형(509-5)
         and p["cached"]["nodes"] == r["n"]
     )
     assert p["sameRev"] == 1  # 같은 노선 = 판 번호 그대로

resources/tester/test_346_3_route_save_screen.py

@@ -57,7 +57,7 @@ def test_초안은_계약_RouteDraft_꼴(out):
         len(draft[name]) == n for name in ("curveOn", "curveRadius", "curveLock", "curveArc")
     )
     assert draft["curveOn"] == [True, False, True] and draft["curveRadius"] == [None, 25, None]
-    assert draft["stationSnap"] is True and draft["terrain"] == "sheet"
+    assert draft["stationSnap"] is True and draft["terrain"] is None  # 손 저장 = 설계 지형(509-5)
     assert draft["stationSnapStep"] == 20  # 390-5 간격도 함께 실림
     assert out["body"]["initial"] == {"mode": "follow"}
     assert "balanced_profile" not in out["body"]  # 손으로 고친 노선 = 계획고 옮김만(349-0v)
@@ -90,8 +90,15 @@ def test_추천_적용은_as_initial_저장_뒤_다시_세움(out):
     body = out["recommendBody"]
     assert body["as_initial"] is True and body["initial"] == {"mode": "earthwork"}
     assert body["draft"]["nodes"] == [[1, 1], [9, 9]]
+    assert body["draft"]["terrain"] == "sheet"  # 창 지형 = 설계 지형(509-5)
     # 잠금 막 하나(472-6 6-B — 저장 직전 저장 관 떠 두기는 서버 한 본문 몫 · 추천은 초안을 비우니 안 받음)
-    assert out["recommendCalls"] == ["overlay:on", "replan", "commit", "overlay:off"]  # 초안 전 시설 버림
+    assert out["recommendCalls"] == [
+        "overlay:on",
+        "replan",
+        "commit",
+        "grid:forget",  # 새 설계 지형 격자로(509-2)
+        "overlay:off",
+    ]  # 초안 전 시설 버림
     assert out["recommendDraftsLeft"] == {"route": None, "pipes": None}  # 새 초기값에서 다시
     assert out["rebuilt"] == 1
 

resources/tester/test_351_1_recommend_gaps.py

@@ -79,7 +79,7 @@ def test_기본값_판정() -> None:
     }
     assert is_default("gentle", None, None, None)
     assert is_default("gentle", None, {"min_radius_m": None}, None)
-    assert not is_default("gentle", None, None, "las")
+    assert is_default("gentle", None, None, "las")  # 지형 안 따짐(509-5 · 지형마다 미리 셈)
     assert not is_default("gentle", None, {"min_radius_m": 15.0}, None)
     assert is_default("gentle", None, {"min_radius_m": 15.0}, None, saved)
     assert not is_default("gentle", None, {"min_radius_m": 16.0}, None, saved)

resources/tester/test_352_3_analysis_terrain_default.py

@@ -11,6 +11,11 @@ from pathlib import Path
 
 import pytest
 
+# 509-5 — 평면 분석 지형 고르기(화면 취향 기억)를 걷음 · 지형 고르기 = 추천 창 안(test_509_5_*)
+pytestmark = pytest.mark.skip(
+    reason="509-5 평면 분석 지형 고르기 걷음 — test_509_5_recommend_terrain"
+)
+
 HERE = Path(__file__).resolve().parent
 ROOT = HERE.parents[1]
 

resources/tester/test_364_4_precompute_on_open.py

@@ -102,6 +102,11 @@ def test_모달이_여는_갈래_먼저(monkeypatch) -> None:
         lambda _root: {"logic": "gentle", "weights": None, "criteria": None},
     )
     monkeypatch.setattr(router, "compute_initial", compute)
+
+    async def terrains(_pid, _root):
+        return ["las"]  # 지형 하나(509-5 지형마다 = test_509_5)
+
+    monkeypatch.setattr(router, "precompute_terrains", terrains)
     asyncio.run(router.precompute_defaults(uuid4()))
     assert asked[0] == "gentle" and asked[-1] == "follow"
     assert sorted(asked) == sorted(DEFAULT_MODES)

resources/tester/test_430_route_edit_rules.py

@@ -161,7 +161,7 @@ def test_편집기_배선() -> None:
         "lineChanged(history) || otherChanged()" in main.split("function tellDraft()", 1)[1][:400]
     )
     assert (
-        "const otherChanged = (): boolean => pickedTerrain() !== designTerrain || snap.changed();"
+        "const otherChanged = (): boolean => snap.changed();"  # 지형 고르기 = 추천 창(509-5)
         in main
     )  # 433-14 ②
     assert "plan.node_edits" in main

resources/tester/test_509_2_sheet_grid.py

@@ -0,0 +1,56 @@
+"""509-2 수치지형도 격자 브라우저로 — 적용 지형(설계 지형) = 수치지형도일 때만 그 격자를 받음 · 노드
+끌기 지반고 서버 묻기 걷음 · 횡단 비탈 넓힘도 같은 격자(509-4 G2).
+
+    ./venv/Scripts/python.exe -m pytest resources/tester/test_509_2_sheet_grid.py -q
+
+분석 지형 = 설계 지형 하나(509-5) — 받는 격자는 늘 설계 지형 것 · 추천 [적용]이 지형을 바꾸면 버림.
+"""
+
+from pathlib import Path
+
+from B05_Profile.B05_Profile_Router_Terrain import _design_grid
+from common_util.common_util_surface_confirmation import SHEET_ANALYSIS_FILTER
+
+ROOT = Path(__file__).resolve().parents[2]
+SHEET = {"source_filter": SHEET_ANALYSIS_FILTER, "method": "dtm", "smooth": True}
+MODEL = f"B04_PreProcess/models/dtm_{SHEET_ANALYSIS_FILTER}.npz"
+
+
+def test_설계_지형_수치지형도면_그_격자_자리(tmp_path) -> None:
+    grid = _design_grid(SHEET, tmp_path, (41, "dtm", MODEL))
+    assert grid == {"model_id": 41, "smooth": True, "signature": "."}
+
+
+def test_확정_모델이_다른_파일이면_격자_없음(tmp_path) -> None:
+    las = "B04_PreProcess/models/dtm_classification.npz"
+    assert _design_grid(SHEET, tmp_path, (41, "dtm", las)) is None
+    assert _design_grid(SHEET, tmp_path, None) is None
+
+
+def _ts(path: str) -> str:
+    return (ROOT / path).read_text(encoding="utf-8")
+
+
+def test_지반고는_설계_지형_격자_서버_묻기_없음() -> None:
+    replan = _ts("B05_Profile/B05_Profile_Api_Replan.ts")
+    elevations = replan.split("export async function fetchRouteElevations", 1)[1][:700]
+    assert "if (local) {" in elevations  # 받아 둔 격자면 늘 브라우저 표본
+    assert "JSON.stringify({ points })" in elevations  # 서버 길도 설계 지형
+    # 계산 묶음 초안 지형 = null(설계) → ground 단계가 격자를 씀(terrain === null)
+    ground = _ts("B05_Profile/logic/B05_Profile_Pipeline_RouteGround.ts")
+    assert "(terrain === null || terrain === local.design)" in ground
+    pipeline = _ts("A00_Common/design/design_pipeline_page.ts")
+    assert "terrain: null };" in pipeline
+    # 횡단 비탈 넓힘 = ground 와 같은 격자(509-4 G2 · 적용 지형 것)
+    assert "createCrossStage({ grid: groundDeps.grid })" in pipeline
+
+
+def test_적용으로_지형이_바뀌면_격자_버림() -> None:
+    grid = _ts("B05_Profile/B05_Profile_Api_TerrainGrid.ts")
+    forget = grid.split("export function forgetDesignTerrainGrid", 1)[1][:200]
+    assert "loaded.delete(projectId)" in forget and "ready.delete(projectId)" in forget
+    apply = _ts("B05_Profile/B05_Profile_UI_RouteEdit_Apply.ts")
+    recommend = apply.split("export async function saveRecommendedRoute", 1)[1]
+    assert recommend.index("forgetDesignTerrainGrid(projectId)") < recommend.index(
+        "await rebuildAfterRouteSave(projectId)"
+    )

resources/tester/test_509_5_recommend_terrain.py

@@ -0,0 +1,155 @@
+"""509-5 분석 지형 고르기 = 추천 노선 창 안 — 지형마다 추천 미리 셈 · 창 지형 바꿈 = 그 지형 저장본 ·
+없으면 안내 + [재계산] · [적용] = 창 지형이 설계 지형 · 평면 고르기 없음.
+
+    ./venv/Scripts/python.exe -m pytest resources/tester/test_509_5_recommend_terrain.py -q
+
+가짜 세계(`test_224_3` wired) — 지형마다 다른 격자(수치지형도 = 1 m 높임)라 저장 키가 갈림.
+"""
+
+import asyncio
+import json
+from contextlib import asynccontextmanager
+from pathlib import Path
+from uuid import uuid4
+
+import pytest
+from test_224_3_recommend_store import STREAMS, _ask, _terrain, wired  # noqa: F401 — 픽스처
+
+from B05_Profile import B05_Profile_Router_RouteInitial as router
+from B05_Profile import B05_Profile_Router_Terrain as terrain_router
+from B05_Profile.B05_Profile_Engine_RouteInitial_Store import DEFAULT_MODES, store_dir
+
+ROOT = Path(__file__).resolve().parents[2]
+
+
+@pytest.fixture
+def two(wired, monkeypatch):  # noqa: F811
+    """라이다 설계 · 수치지형도 고를 수 있음 — 지형마다 다른 격자."""
+    import B05_Profile.B05_Profile_Engine_RouteInitial as engine
+    import common_util.common_util_surface_confirmation as surface
+
+    async def terrains(_pid, _root):
+        return ["las", "sheet"]
+
+    monkeypatch.setattr(router, "precompute_terrains", terrains)
+    monkeypatch.setattr(surface, "analysis_terrain_params", lambda s, t: {**s, "t": t})
+    monkeypatch.setattr(
+        engine,
+        "load_terrain_and_streams",
+        lambda _root, selection: (_terrain(1.0 if selection.get("t") == "sheet" else 0.0), STREAMS),
+    )
+    return wired
+
+
+def _saved(root: Path) -> list[dict]:
+    return [json.loads(p.read_text(encoding="utf-8")) for p in store_dir(root).glob("*.json")]
+
+
+def test_미리_셈이_지형마다_추천_다섯(two) -> None:
+    asyncio.run(router.precompute_defaults(uuid4()))
+    assert two.count == 2 * len(DEFAULT_MODES)
+    saved = _saved(two.root)
+    assert sorted({item["request"]["terrain"] for item in saved}) == ["las", "sheet"]
+    assert all(item["default"] for item in saved)
+    # 창 지형 바꿈 = 그 지형 저장본(셈 없음) · 두 지형 답이 따로
+    for mode in DEFAULT_MODES:
+        assert _ask(False, mode=mode, terrain="sheet")["stored"] is True
+        assert _ask(False, mode=mode, terrain="las")["stored"] is True
+    assert two.count == 2 * len(DEFAULT_MODES)
+
+
+def test_미리_셈_없는_지형은_안내_재계산은_셈(two) -> None:
+    """기존 프로젝트(수치지형도 미리 셈 없음) — 안내 한 줄 · [재계산]이면 그 자리 셈."""
+    missing = _ask(False, mode="gentle", terrain="sheet")
+    assert missing.status_code == 409
+    message = json.loads(missing.body)["message"]
+    assert "전처리를 다시 하면" in message and "[재계산]" in message
+    assert two.count == 0
+    assert _ask(False, mode="gentle", terrain="sheet", recompute=True)["stored"] is False
+    assert two.count == 1
+    assert _ask(False, mode="gentle", terrain="sheet")["stored"] is True
+
+
+def test_미리_셈_지형_차례_설계_먼저(monkeypatch) -> None:
+    import common_util.common_util_surface_confirmation as surface
+
+    class _Pool:
+        @asynccontextmanager
+        async def acquire(self):
+            yield None
+
+    async def params(_c, _pid):
+        return {"source_filter": surface.SHEET_ANALYSIS_FILTER}
+
+    async def choosable(_c, _pid, _params, _dir):
+        return ["las", "sheet"]
+
+    monkeypatch.setattr(router, "get_db_pool", lambda: _Pool())
+    monkeypatch.setattr(surface, "get_surface_confirmation_params", params)
+    monkeypatch.setattr(terrain_router, "choosable_terrains", choosable)
+    assert asyncio.run(router.precompute_terrains(uuid4(), ROOT)) == ["sheet", "las"]
+
+
+def test_고를_지형은_DB_모델_있을_때만(tmp_path, monkeypatch) -> None:
+    import B04_PreProcess.B04_PreProcess_Service as service
+    from common_util.common_util_surface_confirmation import SHEET_ANALYSIS_FILTER
+
+    (tmp_path / f"dtm_{SHEET_ANALYSIS_FILTER}.npz").write_bytes(b"")
+    params = {"source_filter": "classification", "method": "dtm", "smooth": False}
+    found: list[str] = []
+
+    async def missing(_c, _pid, selection):
+        found.append(selection["source_filter"])
+        raise LookupError
+
+    async def present(_c, _pid, _selection):
+        return 7
+
+    monkeypatch.setattr(service, "find_surface_model_for_selection", missing)
+    pick = terrain_router.choosable_terrains
+    assert asyncio.run(pick(None, uuid4(), params, tmp_path)) == ["las"]
+    assert found == [SHEET_ANALYSIS_FILTER]
+    monkeypatch.setattr(service, "find_surface_model_for_selection", present)
+    assert asyncio.run(pick(None, uuid4(), params, tmp_path)) == ["las", "sheet"]
+
+
+def test_지형_바꿈은_추천_적용만_초기값_다시_세움() -> None:
+    replan = (ROOT / "B05_Profile/B05_Profile_Router_Replan.py").read_text(encoding="utf-8")
+    save = replan.split("async def _save_route(", 1)[1]
+    assert "request.terrain if as_initial else None," in save  # 손 [저장]은 지형 안 바꿈
+    assert save.index("await _recompute(") < save.index("refresh_initial_snapshot(project_id")
+    recompute = replan.split("async def _recompute(", 1)[1].split("\nasync def ")[0]
+    assert "switch_design_terrain(connection, project_id, terrain)" in recompute
+
+
+def _ts(name: str) -> str:
+    return (ROOT / "B05_Profile" / name).read_text(encoding="utf-8")
+
+
+def test_창_지형_고르기_배선() -> None:
+    modal = _ts("B05_Profile_UI_RouteEdit_Recommend.ts")
+    assert 'data-act="terrain"' in modal and "data-terrain-row hidden" in modal
+    assert 'params.terrains.includes("las") && params.terrains.includes("sheet")' in modal
+    change = modal.split('terrainSelect.addEventListener("change"', 1)[1][:300]
+    assert "void run();" in change  # 바꾸면 그 지형 저장본(없으면 안내 · [재계산])
+    assert "recompute,\n            terrain,\n" in modal  # 서버에 창 지형
+    initial = _ts("B05_Profile_UI_RouteEdit_Initial.ts")
+    assert "terrain: params.terrains()?.design" in initial  # 처음 = 설계 지형
+    assert "return { ...normalizeRouteInitial(" in initial and "terrain };" in initial
+    assert "picked.terrain ?? null," in initial  # [적용] = 창 지형
+    api = _ts("B05_Profile_Api_RouteInitial.ts")
+    assert "terrain?: AnalysisTerrain;" in api and "body: JSON.stringify(request)," in api
+
+
+def test_평면_지형_고르기_없음_이름만() -> None:
+    chrome = _ts("B05_Profile_UI_RouteEdit_Chrome.ts")
+    main = _ts("B05_Profile_UI_RouteEdit.ts")
+    assert 'data-act="terrain"' not in chrome and 'data-slot="terrain-name"' in chrome
+    assert "terrainName.textContent = `지형 ${" in main
+    assert "terrainSelect" not in main and "setAnalysisTerrain" not in main
+    assert "routeedit-terrain" not in (ROOT / "A00_Common/b_page_state.ts").read_text(
+        encoding="utf-8"
+    )
+    pipeline = (ROOT / "A00_Common/design/design_pipeline_page.ts").read_text(encoding="utf-8")
+    assert "terrain: null }; // 설계 지형(509-5)" in pipeline
+    assert len(pipeline.splitlines()) <= 700 and len(main.splitlines()) <= 700

resources/tester/test_b05_routeedit_initial.py

@@ -231,8 +231,8 @@ def test_노선_추천_다듬기_23_3():
         "|",
         'data-act="station-snap"',
         'data-act="snap-step"',  # 390-2 스냅 간격 = [측점 스냅] 오른쪽
-        "|",  # 390-1 [측점 스냅] | 분석 지형
-        'class="b05-routeedit__terrain" hidden',
+        "|",  # 390-1 [측점 스냅] | 설계 지형 이름(509-5)
+        'class="b05-routeedit__terrain" data-slot="terrain-name" hidden',
     ]
     at = 0
     for mark in order: