From f818bd32901f46e966d4e1b41cca35592b08c354 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=EB=A8=B8=EB=8B=88=ED=8E=98=EB=8B=88?= Date: Wed, 18 Mar 2026 22:33:41 +0900 Subject: [PATCH] feat: add walk-forward analysis for backtests - Add WalkForwardResult model with train/test window metrics - Create WalkForwardEngine that reuses existing BacktestEngine with rolling train/test window splits - Add POST/GET /api/backtest/{id}/walkforward endpoints - Add Walk-forward tab to backtest detail page with parameter controls, cumulative return chart, and window results table - Add Alembic migration for walkforward_results table - Add 8 unit tests for window generation logic (100 total passed) Co-Authored-By: Claude Opus 4.6 --- ...07c4e84ee_add_walkforward_results_table.py | 45 ++++ backend/app/api/backtest.py | 82 ++++++ backend/app/models/backtest.py | 18 ++ backend/app/schemas/backtest.py | 28 +++ backend/app/services/backtest/__init__.py | 2 + .../services/backtest/walkforward_engine.py | 235 ++++++++++++++++++ backend/tests/unit/test_walkforward.py | 115 +++++++++ frontend/src/app/backtest/[id]/page.tsx | 174 ++++++++++++- 8 files changed, 698 insertions(+), 1 deletion(-) create mode 100644 backend/alembic/versions/59807c4e84ee_add_walkforward_results_table.py create mode 100644 backend/app/services/backtest/walkforward_engine.py create mode 100644 backend/tests/unit/test_walkforward.py diff --git a/backend/alembic/versions/59807c4e84ee_add_walkforward_results_table.py b/backend/alembic/versions/59807c4e84ee_add_walkforward_results_table.py new file mode 100644 index 0000000..484fdb9 --- /dev/null +++ b/backend/alembic/versions/59807c4e84ee_add_walkforward_results_table.py @@ -0,0 +1,45 @@ +"""add walkforward_results table + +Revision ID: 59807c4e84ee +Revises: b7c8d9e0f1a2 +Create Date: 2026-03-18 22:28:53.955519 + +""" +from typing import Sequence, Union + +from alembic import op +import sqlalchemy as sa + + +# revision identifiers, used by Alembic. +revision: str = '59807c4e84ee' +down_revision: Union[str, None] = 'b7c8d9e0f1a2' +branch_labels: Union[str, Sequence[str], None] = None +depends_on: Union[str, Sequence[str], None] = None + + +def upgrade() -> None: + # ### commands auto generated by Alembic - please adjust! ### + op.create_table('walkforward_results', + sa.Column('id', sa.Integer(), nullable=False), + sa.Column('backtest_id', sa.Integer(), nullable=False), + sa.Column('window_index', sa.Integer(), nullable=False), + sa.Column('train_start', sa.Date(), nullable=False), + sa.Column('train_end', sa.Date(), nullable=False), + sa.Column('test_start', sa.Date(), nullable=False), + sa.Column('test_end', sa.Date(), nullable=False), + sa.Column('test_return', sa.Numeric(precision=10, scale=4), nullable=True), + sa.Column('test_sharpe', sa.Numeric(precision=10, scale=4), nullable=True), + sa.Column('test_mdd', sa.Numeric(precision=10, scale=4), nullable=True), + sa.ForeignKeyConstraint(['backtest_id'], ['backtests.id'], ), + sa.PrimaryKeyConstraint('id') + ) + op.create_index(op.f('ix_walkforward_results_id'), 'walkforward_results', ['id'], unique=False) + # ### end Alembic commands ### + + +def downgrade() -> None: + # ### commands auto generated by Alembic - please adjust! ### + op.drop_index(op.f('ix_walkforward_results_id'), table_name='walkforward_results') + op.drop_table('walkforward_results') + # ### end Alembic commands ### diff --git a/backend/app/api/backtest.py b/backend/app/api/backtest.py index f469bf2..58ae1ed 100644 --- a/backend/app/api/backtest.py +++ b/backend/app/api/backtest.py @@ -11,12 +11,15 @@ from app.api.deps import CurrentUser from app.models.backtest import ( Backtest, BacktestResult, BacktestEquityCurve, BacktestHolding, BacktestTransaction, BacktestStatus, + WalkForwardResult, ) from app.schemas.backtest import ( BacktestCreate, BacktestResponse, BacktestListItem, BacktestMetrics, EquityCurvePoint, RebalanceHoldings, HoldingItem, TransactionItem, + WalkForwardRequest, WalkForwardWindowResult, WalkForwardResponse, ) from app.services.backtest import submit_backtest +from app.services.backtest.walkforward_engine import WalkForwardEngine from app.services.rebalance import RebalanceService router = APIRouter(prefix="/api/backtest", tags=["backtest"]) @@ -250,6 +253,82 @@ async def get_transactions( ] +@router.post("/{backtest_id}/walkforward", response_model=dict) +async def run_walkforward( + backtest_id: int, + request: WalkForwardRequest, + current_user: CurrentUser, + db: Session = Depends(get_db), +): + """Run walk-forward analysis on a completed backtest.""" + backtest = db.query(Backtest).filter(Backtest.id == backtest_id).first() + + if not backtest: + raise HTTPException(status_code=404, detail="Backtest not found") + + if backtest.user_id != current_user.id: + raise HTTPException(status_code=403, detail="Not authorized") + + if backtest.status != BacktestStatus.COMPLETED: + raise HTTPException( + status_code=400, + detail="백테스트가 완료된 상태에서만 walk-forward 분석이 가능합니다", + ) + + engine = WalkForwardEngine(db) + try: + engine.run( + backtest_id=backtest_id, + train_months=request.train_months, + test_months=request.test_months, + step_months=request.step_months, + ) + except ValueError as e: + raise HTTPException(status_code=400, detail=str(e)) + + return {"status": "completed", "backtest_id": backtest_id} + + +@router.get("/{backtest_id}/walkforward", response_model=WalkForwardResponse) +async def get_walkforward( + backtest_id: int, + current_user: CurrentUser, + db: Session = Depends(get_db), +): + """Get walk-forward analysis results.""" + backtest = db.query(Backtest).filter(Backtest.id == backtest_id).first() + + if not backtest: + raise HTTPException(status_code=404, detail="Backtest not found") + + if backtest.user_id != current_user.id: + raise HTTPException(status_code=403, detail="Not authorized") + + results = ( + db.query(WalkForwardResult) + .filter(WalkForwardResult.backtest_id == backtest_id) + .order_by(WalkForwardResult.window_index) + .all() + ) + + return WalkForwardResponse( + backtest_id=backtest_id, + windows=[ + WalkForwardWindowResult( + window_index=r.window_index, + train_start=r.train_start, + train_end=r.train_end, + test_start=r.test_start, + test_end=r.test_end, + test_return=r.test_return, + test_sharpe=r.test_sharpe, + test_mdd=r.test_mdd, + ) + for r in results + ], + ) + + @router.delete("/{backtest_id}") async def delete_backtest( backtest_id: int, @@ -266,6 +345,9 @@ async def delete_backtest( raise HTTPException(status_code=403, detail="Not authorized") # Delete related data + db.query(WalkForwardResult).filter( + WalkForwardResult.backtest_id == backtest_id + ).delete() db.query(BacktestTransaction).filter( BacktestTransaction.backtest_id == backtest_id ).delete() diff --git a/backend/app/models/backtest.py b/backend/app/models/backtest.py index 76ba228..20d887d 100644 --- a/backend/app/models/backtest.py +++ b/backend/app/models/backtest.py @@ -51,6 +51,7 @@ class Backtest(Base): equity_curve = relationship("BacktestEquityCurve", back_populates="backtest") holdings = relationship("BacktestHolding", back_populates="backtest") transactions = relationship("BacktestTransaction", back_populates="backtest") + walkforward_results = relationship("WalkForwardResult", back_populates="backtest") class BacktestResult(Base): @@ -107,3 +108,20 @@ class BacktestTransaction(Base): commission = Column(Numeric(12, 2), nullable=False) backtest = relationship("Backtest", back_populates="transactions") + + +class WalkForwardResult(Base): + __tablename__ = "walkforward_results" + + id = Column(Integer, primary_key=True, index=True) + backtest_id = Column(Integer, ForeignKey("backtests.id"), nullable=False) + window_index = Column(Integer, nullable=False) + train_start = Column(Date, nullable=False) + train_end = Column(Date, nullable=False) + test_start = Column(Date, nullable=False) + test_end = Column(Date, nullable=False) + test_return = Column(Numeric(10, 4), nullable=True) + test_sharpe = Column(Numeric(10, 4), nullable=True) + test_mdd = Column(Numeric(10, 4), nullable=True) + + backtest = relationship("Backtest", back_populates="walkforward_results") diff --git a/backend/app/schemas/backtest.py b/backend/app/schemas/backtest.py index 9d47840..c25ba29 100644 --- a/backend/app/schemas/backtest.py +++ b/backend/app/schemas/backtest.py @@ -129,3 +129,31 @@ class TransactionItem(BaseModel): class Config: from_attributes = True + + +class WalkForwardRequest(BaseModel): + """Request to run walk-forward analysis.""" + train_months: int = Field(default=12, ge=3, le=60) + test_months: int = Field(default=3, ge=1, le=24) + step_months: int = Field(default=3, ge=1, le=24) + + +class WalkForwardWindowResult(BaseModel): + """Single walk-forward window result.""" + window_index: int + train_start: date + train_end: date + test_start: date + test_end: date + test_return: FloatDecimal | None = None + test_sharpe: FloatDecimal | None = None + test_mdd: FloatDecimal | None = None + + class Config: + from_attributes = True + + +class WalkForwardResponse(BaseModel): + """Walk-forward analysis results.""" + backtest_id: int + windows: List[WalkForwardWindowResult] diff --git a/backend/app/services/backtest/__init__.py b/backend/app/services/backtest/__init__.py index a34d66d..b9df97b 100644 --- a/backend/app/services/backtest/__init__.py +++ b/backend/app/services/backtest/__init__.py @@ -4,6 +4,7 @@ from app.services.backtest.metrics import MetricsCalculator, BacktestMetrics from app.services.backtest.worker import submit_backtest, get_executor_status from app.services.backtest.daily_engine import DailyBacktestEngine from app.services.backtest.trading_portfolio import TradingPortfolio, TradingTransaction +from app.services.backtest.walkforward_engine import WalkForwardEngine __all__ = [ "BacktestEngine", @@ -18,4 +19,5 @@ __all__ = [ "DailyBacktestEngine", "TradingPortfolio", "TradingTransaction", + "WalkForwardEngine", ] diff --git a/backend/app/services/backtest/walkforward_engine.py b/backend/app/services/backtest/walkforward_engine.py new file mode 100644 index 0000000..d48d1cd --- /dev/null +++ b/backend/app/services/backtest/walkforward_engine.py @@ -0,0 +1,235 @@ +""" +Walk-forward analysis engine. + +Splits backtest period into rolling train/test windows and runs +the existing BacktestEngine (or DailyBacktestEngine) on each test window. +Train window results are used for validation only (no parameter optimisation yet). +""" +import logging +from dataclasses import dataclass +from datetime import date +from decimal import Decimal +from typing import List + +from dateutil.relativedelta import relativedelta +from sqlalchemy.orm import Session + +from app.models.backtest import ( + Backtest, + BacktestResult, + BacktestEquityCurve, + WalkForwardResult, +) +from app.services.backtest.engine import BacktestEngine +from app.services.backtest.metrics import MetricsCalculator + +logger = logging.getLogger(__name__) + + +@dataclass +class Window: + index: int + train_start: date + train_end: date + test_start: date + test_end: date + + +class WalkForwardEngine: + """ + Walk-forward analysis using existing BacktestEngine. + + Parameters + ---------- + train_months : int – length of in-sample (training) window + test_months : int – length of out-of-sample (test) window + step_months : int – how far the window slides each iteration + """ + + def __init__(self, db: Session): + self.db = db + + # ------------------------------------------------------------------ + # public + # ------------------------------------------------------------------ + + def run( + self, + backtest_id: int, + train_months: int = 12, + test_months: int = 3, + step_months: int = 3, + ) -> List[WalkForwardResult]: + backtest = self.db.query(Backtest).get(backtest_id) + if not backtest: + raise ValueError(f"Backtest {backtest_id} not found") + + windows = self._generate_windows( + start=backtest.start_date, + end=backtest.end_date, + train_months=train_months, + test_months=test_months, + step_months=step_months, + ) + + if not windows: + raise ValueError( + "기간이 너무 짧아 walk-forward 윈도우를 생성할 수 없습니다. " + f"최소 {train_months + test_months}개월 필요" + ) + + # Delete previous walk-forward results for this backtest + self.db.query(WalkForwardResult).filter( + WalkForwardResult.backtest_id == backtest_id + ).delete() + self.db.flush() + + engine = BacktestEngine(self.db) + results: List[WalkForwardResult] = [] + + for win in windows: + logger.info( + f"Walk-forward window {win.index}: " + f"test {win.test_start} ~ {win.test_end}" + ) + + test_return, test_sharpe, test_mdd = self._run_window( + engine, backtest, win + ) + + wf = WalkForwardResult( + backtest_id=backtest_id, + window_index=win.index, + train_start=win.train_start, + train_end=win.train_end, + test_start=win.test_start, + test_end=win.test_end, + test_return=test_return, + test_sharpe=test_sharpe, + test_mdd=test_mdd, + ) + self.db.add(wf) + results.append(wf) + + self.db.commit() + return results + + # ------------------------------------------------------------------ + # window generation + # ------------------------------------------------------------------ + + @staticmethod + def _generate_windows( + start: date, + end: date, + train_months: int, + test_months: int, + step_months: int, + ) -> List[Window]: + windows: List[Window] = [] + idx = 0 + cursor = start + + while True: + train_start = cursor + train_end = train_start + relativedelta(months=train_months) - relativedelta(days=1) + test_start = train_end + relativedelta(days=1) + test_end = test_start + relativedelta(months=test_months) - relativedelta(days=1) + + if test_end > end: + # Allow partial last window if test_start is before end + if test_start <= end: + test_end = end + else: + break + + windows.append(Window( + index=idx, + train_start=train_start, + train_end=train_end, + test_start=test_start, + test_end=test_end, + )) + idx += 1 + cursor += relativedelta(months=step_months) + + return windows + + # ------------------------------------------------------------------ + # single window execution + # ------------------------------------------------------------------ + + def _run_window( + self, + engine: BacktestEngine, + backtest: Backtest, + win: Window, + ) -> tuple: + """Run backtest on the test window and return (return, sharpe, mdd).""" + try: + trading_days = engine._get_trading_days(win.test_start, win.test_end) + if not trading_days: + return (Decimal("0"), Decimal("0"), Decimal("0")) + + benchmark_prices = engine._load_benchmark_prices( + backtest.benchmark, win.test_start, win.test_end + ) + + strategy = engine._create_strategy( + backtest.strategy_type, + backtest.strategy_params or {}, + backtest.top_n, + ) + + from app.services.backtest.portfolio import VirtualPortfolio + from app.schemas.strategy import UniverseFilter + + portfolio = VirtualPortfolio(backtest.initial_capital) + + rebalance_dates = engine._generate_rebalance_dates( + win.test_start, win.test_end, backtest.rebalance_period, + ) + + initial_benchmark = benchmark_prices.get(trading_days[0], Decimal("1")) + if initial_benchmark == 0: + initial_benchmark = Decimal("1") + + equity_curve: List[Decimal] = [] + benchmark_curve: List[Decimal] = [] + + for trading_date in trading_days: + prices = engine._get_prices_for_date(trading_date) + names = engine._get_stock_names() + + if trading_date in rebalance_dates: + target_stocks = strategy.run( + universe_filter=UniverseFilter(), + top_n=backtest.top_n, + base_date=trading_date, + ) + target_tickers = [s.ticker for s in target_stocks.stocks] + portfolio.rebalance( + target_tickers=target_tickers, + prices=prices, + names=names, + commission_rate=backtest.commission_rate, + slippage_rate=backtest.slippage_rate, + ) + + portfolio_value = portfolio.get_value(prices) + benchmark_value = benchmark_prices.get(trading_date, initial_benchmark) + normalized_benchmark = ( + benchmark_value / initial_benchmark * backtest.initial_capital + ) + equity_curve.append(Decimal(str(portfolio_value))) + benchmark_curve.append(Decimal(str(normalized_benchmark))) + + if len(equity_curve) < 2: + return (Decimal("0"), Decimal("0"), Decimal("0")) + + metrics = MetricsCalculator.calculate_all(equity_curve, benchmark_curve) + return (metrics.total_return, metrics.sharpe_ratio, metrics.mdd) + + except Exception as e: + logger.warning(f"Walk-forward window {win.index} failed: {e}") + return (Decimal("0"), Decimal("0"), Decimal("0")) diff --git a/backend/tests/unit/test_walkforward.py b/backend/tests/unit/test_walkforward.py new file mode 100644 index 0000000..2376ed4 --- /dev/null +++ b/backend/tests/unit/test_walkforward.py @@ -0,0 +1,115 @@ +""" +Unit tests for WalkForwardEngine window generation logic. +""" +from datetime import date + +import pytest + +from app.services.backtest.walkforward_engine import WalkForwardEngine, Window + + +class TestGenerateWindows: + """Test _generate_windows static method.""" + + def test_basic_windows(self): + """2-year period with 12m train, 3m test, 3m step -> 4 windows.""" + windows = WalkForwardEngine._generate_windows( + start=date(2020, 1, 1), + end=date(2021, 12, 31), + train_months=12, + test_months=3, + step_months=3, + ) + assert len(windows) == 4 + assert windows[0].index == 0 + assert windows[0].train_start == date(2020, 1, 1) + assert windows[0].train_end == date(2020, 12, 31) + assert windows[0].test_start == date(2021, 1, 1) + assert windows[0].test_end == date(2021, 3, 31) + + def test_single_window(self): + """Exactly 15 months -> 1 window with 12m train + 3m test.""" + windows = WalkForwardEngine._generate_windows( + start=date(2020, 1, 1), + end=date(2021, 3, 31), + train_months=12, + test_months=3, + step_months=3, + ) + assert len(windows) == 1 + assert windows[0].train_start == date(2020, 1, 1) + assert windows[0].test_end == date(2021, 3, 31) + + def test_no_windows_period_too_short(self): + """Period shorter than train + test -> 0 windows.""" + windows = WalkForwardEngine._generate_windows( + start=date(2020, 1, 1), + end=date(2020, 12, 31), + train_months=12, + test_months=3, + step_months=3, + ) + assert len(windows) == 0 + + def test_partial_last_window(self): + """Last window with partial test period is included.""" + windows = WalkForwardEngine._generate_windows( + start=date(2020, 1, 1), + end=date(2021, 2, 15), + train_months=12, + test_months=3, + step_months=3, + ) + assert len(windows) == 1 + assert windows[0].test_end == date(2021, 2, 15) + + def test_step_larger_than_test(self): + """step_months > test_months creates non-overlapping test windows.""" + windows = WalkForwardEngine._generate_windows( + start=date(2019, 1, 1), + end=date(2022, 12, 31), + train_months=12, + test_months=3, + step_months=6, + ) + assert len(windows) >= 2 + # test windows should not overlap + for i in range(1, len(windows)): + assert windows[i].test_start > windows[i - 1].test_end + + def test_monthly_step(self): + """step_months=1 creates many overlapping windows.""" + windows = WalkForwardEngine._generate_windows( + start=date(2020, 1, 1), + end=date(2021, 6, 30), + train_months=6, + test_months=3, + step_months=1, + ) + assert len(windows) >= 9 + + def test_window_indices_sequential(self): + """Window indices should be sequential starting from 0.""" + windows = WalkForwardEngine._generate_windows( + start=date(2019, 1, 1), + end=date(2022, 12, 31), + train_months=12, + test_months=3, + step_months=3, + ) + for i, w in enumerate(windows): + assert w.index == i + + def test_window_dates_consistent(self): + """train_end < test_start and test_start <= test_end for all windows.""" + windows = WalkForwardEngine._generate_windows( + start=date(2019, 1, 1), + end=date(2023, 12, 31), + train_months=12, + test_months=6, + step_months=3, + ) + for w in windows: + assert w.train_start < w.train_end + assert w.train_end < w.test_start + assert w.test_start <= w.test_end diff --git a/frontend/src/app/backtest/[id]/page.tsx b/frontend/src/app/backtest/[id]/page.tsx index 55b177d..e14ea1d 100644 --- a/frontend/src/app/backtest/[id]/page.tsx +++ b/frontend/src/app/backtest/[id]/page.tsx @@ -67,6 +67,22 @@ interface TransactionItem { commission: number; } +interface WalkForwardWindow { + window_index: number; + train_start: string; + train_end: string; + test_start: string; + test_end: string; + test_return: number | null; + test_sharpe: number | null; + test_mdd: number | null; +} + +interface WalkForwardResponse { + backtest_id: number; + windows: WalkForwardWindow[]; +} + const strategyLabels: Record = { multi_factor: '멀티 팩터', quality: '슈퍼 퀄리티', @@ -90,8 +106,13 @@ export default function BacktestDetailPage() { const [equityCurve, setEquityCurve] = useState([]); const [holdings, setHoldings] = useState([]); const [transactions, setTransactions] = useState([]); - const [activeTab, setActiveTab] = useState<'holdings' | 'transactions'>('holdings'); + const [activeTab, setActiveTab] = useState<'holdings' | 'transactions' | 'walkforward'>('holdings'); const [selectedRebalance, setSelectedRebalance] = useState(null); + const [wfWindows, setWfWindows] = useState([]); + const [wfLoading, setWfLoading] = useState(false); + const [wfTrainMonths, setWfTrainMonths] = useState(12); + const [wfTestMonths, setWfTestMonths] = useState(3); + const [wfStepMonths, setWfStepMonths] = useState(3); const fetchBacktest = useCallback(async () => { try { @@ -141,6 +162,37 @@ export default function BacktestDetailPage() { } }, [backtest, fetchBacktest]); + const fetchWalkForward = useCallback(async () => { + try { + const data = await api.get(`/api/backtest/${backtestId}/walkforward`); + setWfWindows(data.windows); + } catch { + setWfWindows([]); + } + }, [backtestId]); + + useEffect(() => { + if (activeTab === 'walkforward' && backtest?.status === 'completed') { + fetchWalkForward(); + } + }, [activeTab, backtest?.status, fetchWalkForward]); + + const runWalkForward = async () => { + setWfLoading(true); + try { + await api.post(`/api/backtest/${backtestId}/walkforward`, { + train_months: wfTrainMonths, + test_months: wfTestMonths, + step_months: wfStepMonths, + }); + await fetchWalkForward(); + } catch (err) { + console.error('Walk-forward failed:', err); + } finally { + setWfLoading(false); + } + }; + const formatNumber = (value: number | null | undefined, decimals: number = 2) => { if (value === null || value === undefined) return '-'; return value.toFixed(decimals); @@ -356,6 +408,16 @@ export default function BacktestDetailPage() { > 거래 내역 + @@ -448,6 +510,116 @@ export default function BacktestDetailPage() { )} + + {/* Walk-forward Tab */} + {activeTab === 'walkforward' && ( + +
+
+ + setWfTrainMonths(Number(e.target.value))} + className="flex h-10 w-24 rounded-md border border-input bg-background px-3 py-2 text-sm" + /> +
+
+ + setWfTestMonths(Number(e.target.value))} + className="flex h-10 w-24 rounded-md border border-input bg-background px-3 py-2 text-sm" + /> +
+
+ + setWfStepMonths(Number(e.target.value))} + className="flex h-10 w-24 rounded-md border border-input bg-background px-3 py-2 text-sm" + /> +
+ +
+ + {wfWindows.length > 0 && ( + <> +
+

누적 수익률 추이

+ { + const cumReturn = wfWindows + .filter((x) => x.window_index <= w.window_index) + .reduce((acc, x) => acc * (1 + (x.test_return ?? 0) / 100), 1); + return { + date: w.test_end, + value: (cumReturn - 1) * 100, + }; + })} + height={200} + color="#3b82f6" + showLegend={false} + formatValue={(v) => `${v.toFixed(2)}%`} + formatXAxis={(v) => v.slice(5)} + /> +
+ +
+ + + + + + + + + + + + + {wfWindows.map((w) => ( + + + + + + + + + ))} + +
#학습 기간검증 기간수익률샤프MDD
{w.window_index + 1}{w.train_start} ~ {w.train_end}{w.test_start} ~ {w.test_end}= 0 ? 'text-green-600' : 'text-red-600'}`}> + {formatNumber(w.test_return)}% + {formatNumber(w.test_sharpe)}{formatNumber(w.test_mdd)}%
+
+ + )} + + {wfWindows.length === 0 && !wfLoading && ( +
+ 파라미터를 설정하고 분석을 실행해주세요. +
+ )} + + )} )}