feature/profitTracker: integrate profit report with profit tracker

This commit is contained in:
Andy Cheng 2023-06-16 18:06:47 +08:00
parent a197352c6e
commit 027acfe3b5
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GPG Key ID: 936427CF651A9D28
4 changed files with 137 additions and 171 deletions

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@ -164,7 +164,20 @@ func (e *GeneralOrderExecutor) BindProfitStats(profitStats *types.ProfitStats) {
} }
func (e *GeneralOrderExecutor) BindProfitTracker(profitTracker *report.ProfitTracker) { func (e *GeneralOrderExecutor) BindProfitTracker(profitTracker *report.ProfitTracker) {
profitTracker.Bind(e.tradeCollector, e.session) e.session.Subscribe(types.KLineChannel, profitTracker.Market.Symbol, types.SubscribeOptions{Interval: profitTracker.Interval})
e.tradeCollector.OnProfit(func(trade types.Trade, profit *types.Profit) {
profitTracker.AddProfit(*profit)
})
e.tradeCollector.OnTrade(func(trade types.Trade, profit fixedpoint.Value, netProfit fixedpoint.Value) {
profitTracker.AddTrade(trade)
})
// Rotate profitStats slice
e.session.MarketDataStream.OnKLineClosed(types.KLineWith(profitTracker.Market.Symbol, profitTracker.Interval, func(kline types.KLine) {
profitTracker.Rotate()
}))
} }
func (e *GeneralOrderExecutor) Bind() { func (e *GeneralOrderExecutor) Bind() {

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@ -2,7 +2,6 @@ package report
import ( import (
"fmt" "fmt"
"github.com/c9s/bbgo/pkg/bbgo"
"github.com/c9s/bbgo/pkg/data/tsv" "github.com/c9s/bbgo/pkg/data/tsv"
"github.com/c9s/bbgo/pkg/datatype/floats" "github.com/c9s/bbgo/pkg/datatype/floats"
"github.com/c9s/bbgo/pkg/fixedpoint" "github.com/c9s/bbgo/pkg/fixedpoint"
@ -12,134 +11,104 @@ import (
// AccumulatedProfitReport For accumulated profit report output // AccumulatedProfitReport For accumulated profit report output
type AccumulatedProfitReport struct { type AccumulatedProfitReport struct {
// AccumulatedProfitMAWindow Accumulated profit SMA window, in number of trades // ProfitMAWindow Accumulated profit SMA window
AccumulatedProfitMAWindow int `json:"accumulatedProfitMAWindow"` ProfitMAWindow int `json:"ProfitMAWindow"`
// IntervalWindow interval window, in days // ShortTermProfitWindow The window to sum up the short-term profit
IntervalWindow int `json:"intervalWindow"` ShortTermProfitWindow int `json:"shortTermProfitWindow"`
// NumberOfInterval How many intervals to output to TSV
NumberOfInterval int `json:"NumberOfInterval"`
// TsvReportPath The path to output report to // TsvReportPath The path to output report to
TsvReportPath string `json:"tsvReportPath"` TsvReportPath string `json:"tsvReportPath"`
// AccumulatedDailyProfitWindow The window to sum up the daily profit, in days symbol string
AccumulatedDailyProfitWindow int `json:"accumulatedDailyProfitWindow"`
Symbol string types.IntervalWindow
// Accumulated profit // Accumulated profit
accumulatedProfit fixedpoint.Value accumulatedProfit fixedpoint.Value
accumulatedProfitPerDay floats.Slice accumulatedProfitPerInterval floats.Slice
previousAccumulatedProfit fixedpoint.Value
// Accumulated profit MA // Accumulated profit MA
accumulatedProfitMA *indicator.SMA profitMA *indicator.SMA
accumulatedProfitMAPerDay floats.Slice profitMAPerInterval floats.Slice
// Daily profit // Profit of each interval
dailyProfit floats.Slice ProfitPerInterval floats.Slice
// Accumulated fee // Accumulated fee
accumulatedFee fixedpoint.Value accumulatedFee fixedpoint.Value
accumulatedFeePerDay floats.Slice accumulatedFeePerInterval floats.Slice
// Win ratio // Win ratio
winRatioPerDay floats.Slice winRatioPerInterval floats.Slice
// Profit factor // Profit factor
profitFactorPerDay floats.Slice profitFactorPerInterval floats.Slice
// Trade number // Trade number
dailyTrades floats.Slice accumulatedTrades int
accumulatedTrades int accumulatedTradesPerInterval floats.Slice
previousAccumulatedTrades int
// Extra values // Extra values
extraValues [][2]string strategyParameters [][2]string
} }
func (r *AccumulatedProfitReport) Initialize(Symbol string, session *bbgo.ExchangeSession, orderExecutor *bbgo.GeneralOrderExecutor, TradeStats *types.TradeStats) { func (r *AccumulatedProfitReport) Initialize(symbol string, interval types.Interval, window int) {
r.Symbol = Symbol r.symbol = symbol
r.Interval = interval
r.Window = window
if r.AccumulatedProfitMAWindow <= 0 { if r.ProfitMAWindow <= 0 {
r.AccumulatedProfitMAWindow = 60 r.ProfitMAWindow = 60
} }
if r.IntervalWindow <= 0 {
r.IntervalWindow = 7 if r.Window <= 0 {
r.Window = 7
} }
if r.AccumulatedDailyProfitWindow <= 0 {
r.AccumulatedDailyProfitWindow = 7 if r.ShortTermProfitWindow <= 0 {
r.ShortTermProfitWindow = 7
} }
if r.NumberOfInterval <= 0 {
r.NumberOfInterval = 1
}
r.accumulatedProfitMA = &indicator.SMA{IntervalWindow: types.IntervalWindow{Interval: types.Interval1d, Window: r.AccumulatedProfitMAWindow}}
session.Subscribe(types.KLineChannel, r.Symbol, types.SubscribeOptions{Interval: types.Interval1d}) r.profitMA = &indicator.SMA{IntervalWindow: types.IntervalWindow{Interval: r.Interval, Window: r.ProfitMAWindow}}
// Record profit
orderExecutor.TradeCollector().OnProfit(func(trade types.Trade, profit *types.Profit) {
if profit == nil {
return
}
r.RecordProfit(profit.Profit)
})
// Record trade
orderExecutor.TradeCollector().OnTrade(func(trade types.Trade, profit fixedpoint.Value, netProfit fixedpoint.Value) {
r.RecordTrade(trade.Fee)
})
// Record daily status
session.MarketDataStream.OnKLineClosed(types.KLineWith(r.Symbol, types.Interval1d, func(kline types.KLine) {
r.DailyUpdate(TradeStats)
}))
} }
func (r *AccumulatedProfitReport) AddExtraValue(valueAndTitle [2]string) { func (r *AccumulatedProfitReport) AddStrategyParameter(title string, value string) {
r.extraValues = append(r.extraValues, valueAndTitle) r.strategyParameters = append(r.strategyParameters, [2]string{title, value})
} }
func (r *AccumulatedProfitReport) RecordProfit(profit fixedpoint.Value) { func (r *AccumulatedProfitReport) AddTrade(trade types.Trade) {
r.accumulatedProfit = r.accumulatedProfit.Add(profit) r.accumulatedFee = r.accumulatedFee.Add(trade.Fee)
}
func (r *AccumulatedProfitReport) RecordTrade(fee fixedpoint.Value) {
r.accumulatedFee = r.accumulatedFee.Add(fee)
r.accumulatedTrades += 1 r.accumulatedTrades += 1
} }
func (r *AccumulatedProfitReport) DailyUpdate(tradeStats *types.TradeStats) { func (r *AccumulatedProfitReport) Rotate(ps *types.ProfitStats, ts *types.TradeStats) {
// Daily profit
r.dailyProfit.Update(r.accumulatedProfit.Sub(r.previousAccumulatedProfit).Float64())
r.previousAccumulatedProfit = r.accumulatedProfit
// Accumulated profit // Accumulated profit
r.accumulatedProfitPerDay.Update(r.accumulatedProfit.Float64()) r.accumulatedProfit.Add(ps.AccumulatedNetProfit)
r.accumulatedProfitPerInterval.Update(r.accumulatedProfit.Float64())
// Accumulated profit MA // Profit of each interval
r.accumulatedProfitMA.Update(r.accumulatedProfit.Float64()) r.ProfitPerInterval.Update(ps.AccumulatedNetProfit.Float64())
r.accumulatedProfitMAPerDay.Update(r.accumulatedProfitMA.Last(0))
// Profit MA
r.profitMA.Update(r.accumulatedProfit.Float64())
r.profitMAPerInterval.Update(r.profitMA.Last(0))
// Accumulated Fee // Accumulated Fee
r.accumulatedFeePerDay.Update(r.accumulatedFee.Float64()) r.accumulatedFeePerInterval.Update(r.accumulatedFee.Float64())
// Trades
r.accumulatedTradesPerInterval.Update(float64(r.accumulatedTrades))
// Win ratio // Win ratio
r.winRatioPerDay.Update(tradeStats.WinningRatio.Float64()) r.winRatioPerInterval.Update(ts.WinningRatio.Float64())
// Profit factor // Profit factor
r.profitFactorPerDay.Update(tradeStats.ProfitFactor.Float64()) r.profitFactorPerInterval.Update(ts.ProfitFactor.Float64())
// Daily trades
r.dailyTrades.Update(float64(r.accumulatedTrades - r.previousAccumulatedTrades))
r.previousAccumulatedTrades = r.accumulatedTrades
} }
// Output Accumulated profit report to a TSV file // Output Accumulated profit report to a TSV file
func (r *AccumulatedProfitReport) Output(symbol string) { func (r *AccumulatedProfitReport) Output() {
if r.TsvReportPath != "" { if r.TsvReportPath != "" {
tsvwiter, err := tsv.AppendWriterFile(r.TsvReportPath) tsvwiter, err := tsv.AppendWriterFile(r.TsvReportPath)
if err != nil { if err != nil {
@ -150,46 +119,34 @@ func (r *AccumulatedProfitReport) Output(symbol string) {
titles := []string{ titles := []string{
"#", "#",
"Symbol", "Symbol",
"accumulatedProfit", "Total Net Profit",
"accumulatedProfitMA", fmt.Sprintf("Total Net Profit %sMA%d", r.Interval, r.Window),
fmt.Sprintf("%dd profit", r.AccumulatedDailyProfitWindow), fmt.Sprintf("%s %d Net Profit", r.Interval, r.ShortTermProfitWindow),
"accumulatedFee", "accumulatedFee",
"accumulatedNetProfit",
"winRatio", "winRatio",
"profitFactor", "profitFactor",
"60D trades", fmt.Sprintf("%s %d Trades", r.Interval, r.Window),
} }
for i := 0; i < len(r.extraValues); i++ { for i := 0; i < len(r.strategyParameters); i++ {
titles = append(titles, r.extraValues[i][0]) titles = append(titles, r.strategyParameters[i][0])
} }
_ = tsvwiter.Write(titles) _ = tsvwiter.Write(titles)
// Output data row // Output data row
for i := 0; i <= r.NumberOfInterval-1; i++ { for i := 0; i <= r.Window-1; i++ {
accumulatedProfit := r.accumulatedProfitPerDay.Index(r.IntervalWindow * i)
accumulatedProfitStr := fmt.Sprintf("%f", accumulatedProfit)
accumulatedProfitMA := r.accumulatedProfitMAPerDay.Index(r.IntervalWindow * i)
accumulatedProfitMAStr := fmt.Sprintf("%f", accumulatedProfitMA)
intervalAccumulatedProfit := r.dailyProfit.Tail(r.AccumulatedDailyProfitWindow+r.IntervalWindow*i).Sum() - r.dailyProfit.Tail(r.IntervalWindow*i).Sum()
intervalAccumulatedProfitStr := fmt.Sprintf("%f", intervalAccumulatedProfit)
accumulatedFee := fmt.Sprintf("%f", r.accumulatedFeePerDay.Index(r.IntervalWindow*i))
accumulatedNetProfit := fmt.Sprintf("%f", accumulatedProfit-r.accumulatedFeePerDay.Index(r.IntervalWindow*i))
winRatio := fmt.Sprintf("%f", r.winRatioPerDay.Index(r.IntervalWindow*i))
profitFactor := fmt.Sprintf("%f", r.profitFactorPerDay.Index(r.IntervalWindow*i))
trades := r.dailyTrades.Tail(60+r.IntervalWindow*i).Sum() - r.dailyTrades.Tail(r.IntervalWindow*i).Sum()
tradesStr := fmt.Sprintf("%f", trades)
values := []string{ values := []string{
fmt.Sprintf("%d", i+1), fmt.Sprintf("%d", i+1),
symbol, accumulatedProfitStr, r.symbol,
accumulatedProfitMAStr, fmt.Sprintf("%f", r.accumulatedProfitPerInterval.Last(i)),
intervalAccumulatedProfitStr, fmt.Sprintf("%f", r.profitMAPerInterval.Last(i)),
accumulatedFee, fmt.Sprintf("%f", r.accumulatedProfitPerInterval.Last(i)-r.accumulatedProfitPerInterval.Last(i+r.ShortTermProfitWindow)),
accumulatedNetProfit, fmt.Sprintf("%f", r.accumulatedFeePerInterval.Last(i)),
winRatio, profitFactor, fmt.Sprintf("%f", r.winRatioPerInterval.Last(i)),
tradesStr, fmt.Sprintf("%f", r.profitFactorPerInterval.Last(i)),
fmt.Sprintf("%f", r.accumulatedTradesPerInterval.Last(i)),
} }
for j := 0; j < len(r.extraValues); j++ { for j := 0; j < len(r.strategyParameters); j++ {
values = append(values, r.extraValues[j][1]) values = append(values, r.strategyParameters[j][1])
} }
_ = tsvwiter.Write(values) _ = tsvwiter.Write(values)
} }

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@ -1,64 +1,59 @@
package report package report
import ( import (
"github.com/c9s/bbgo/pkg/bbgo"
"github.com/c9s/bbgo/pkg/fixedpoint"
"github.com/c9s/bbgo/pkg/types" "github.com/c9s/bbgo/pkg/types"
) )
type ProfitTracker struct { type ProfitTracker struct {
types.IntervalWindow types.IntervalWindow
// Accumulated profit report
AccumulatedProfitReport *AccumulatedProfitReport `json:"accumulatedProfitReport"`
Market types.Market
ProfitStatsSlice []*types.ProfitStats ProfitStatsSlice []*types.ProfitStats
CurrentProfitStats **types.ProfitStats CurrentProfitStats **types.ProfitStats
market types.Market tradeStats *types.TradeStats
} }
// InitOld is for backward capability. ps is the ProfitStats of the strategy, market is the strategy market // InitOld is for backward capability. ps is the ProfitStats of the strategy, Market is the strategy Market
func (p *ProfitTracker) InitOld(ps **types.ProfitStats, market types.Market) { func (p *ProfitTracker) InitOld(market types.Market, ps **types.ProfitStats, ts *types.TradeStats) {
p.market = market p.Market = market
if *ps == nil { if *ps == nil {
*ps = types.NewProfitStats(p.market) *ps = types.NewProfitStats(p.Market)
} }
p.tradeStats = ts
p.CurrentProfitStats = ps p.CurrentProfitStats = ps
p.ProfitStatsSlice = append(p.ProfitStatsSlice, *ps) p.ProfitStatsSlice = append(p.ProfitStatsSlice, *ps)
if p.AccumulatedProfitReport != nil {
p.AccumulatedProfitReport.Initialize(p.Market.Symbol, p.Interval, p.Window)
}
} }
// Init initialize the tracker with the given market // Init initialize the tracker with the given Market
func (p *ProfitTracker) Init(market types.Market) { func (p *ProfitTracker) Init(market types.Market, ts *types.TradeStats) {
p.market = market ps := types.NewProfitStats(p.Market)
*p.CurrentProfitStats = types.NewProfitStats(p.market) p.InitOld(market, &ps, ts)
p.ProfitStatsSlice = append(p.ProfitStatsSlice, *p.CurrentProfitStats)
}
func (p *ProfitTracker) Bind(tradeCollector *bbgo.TradeCollector, session *bbgo.ExchangeSession) {
session.Subscribe(types.KLineChannel, p.market.Symbol, types.SubscribeOptions{Interval: p.Interval})
tradeCollector.OnProfit(func(trade types.Trade, profit *types.Profit) {
p.AddProfit(*profit)
})
tradeCollector.OnTrade(func(trade types.Trade, profit fixedpoint.Value, netProfit fixedpoint.Value) {
p.AddTrade(trade)
})
// Rotate profitStats slice
session.MarketDataStream.OnKLineClosed(types.KLineWith(p.market.Symbol, p.Interval, func(kline types.KLine) {
p.Rotate()
}))
} }
// Rotate the tracker to make a new ProfitStats to record the profits // Rotate the tracker to make a new ProfitStats to record the profits
func (p *ProfitTracker) Rotate() { func (p *ProfitTracker) Rotate() {
*p.CurrentProfitStats = types.NewProfitStats(p.market) *p.CurrentProfitStats = types.NewProfitStats(p.Market)
p.ProfitStatsSlice = append(p.ProfitStatsSlice, *p.CurrentProfitStats) p.ProfitStatsSlice = append(p.ProfitStatsSlice, *p.CurrentProfitStats)
// Truncate // Truncate
if len(p.ProfitStatsSlice) > p.Window { if len(p.ProfitStatsSlice) > p.Window {
p.ProfitStatsSlice = p.ProfitStatsSlice[len(p.ProfitStatsSlice)-p.Window:] p.ProfitStatsSlice = p.ProfitStatsSlice[len(p.ProfitStatsSlice)-p.Window:]
} }
if p.AccumulatedProfitReport != nil {
p.AccumulatedProfitReport.Rotate(*p.CurrentProfitStats, p.tradeStats)
}
} }
func (p *ProfitTracker) AddProfit(profit types.Profit) { func (p *ProfitTracker) AddProfit(profit types.Profit) {
@ -67,4 +62,8 @@ func (p *ProfitTracker) AddProfit(profit types.Profit) {
func (p *ProfitTracker) AddTrade(trade types.Trade) { func (p *ProfitTracker) AddTrade(trade types.Trade) {
(*p.CurrentProfitStats).AddTrade(trade) (*p.CurrentProfitStats).AddTrade(trade)
if p.AccumulatedProfitReport != nil {
p.AccumulatedProfitReport.AddTrade(trade)
}
} }

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@ -39,8 +39,6 @@ type Strategy struct {
ProfitStats *types.ProfitStats `persistence:"profit_stats"` ProfitStats *types.ProfitStats `persistence:"profit_stats"`
TradeStats *types.TradeStats `persistence:"trade_stats"` TradeStats *types.TradeStats `persistence:"trade_stats"`
ProfitTracker *report.ProfitTracker `json:"profitTracker" persistence:"profit_tracker"`
// Symbol is the market symbol you want to trade // Symbol is the market symbol you want to trade
Symbol string `json:"symbol"` Symbol string `json:"symbol"`
@ -104,8 +102,7 @@ type Strategy struct {
// StrategyController // StrategyController
bbgo.StrategyController bbgo.StrategyController
// Accumulated profit report ProfitTracker *report.ProfitTracker `json:"profitTracker" persistence:"profit_tracker"`
AccumulatedProfitReport *report.AccumulatedProfitReport `json:"accumulatedProfitReport"`
} }
func (s *Strategy) ID() string { func (s *Strategy) ID() string {
@ -330,8 +327,23 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
s.TradeStats = types.NewTradeStats(s.Symbol) s.TradeStats = types.NewTradeStats(s.Symbol)
} }
if s.ProfitTracker.CurrentProfitStats == nil { if s.ProfitTracker != nil {
s.ProfitTracker.InitOld(&s.ProfitStats, s.Market) if s.ProfitTracker.CurrentProfitStats == nil {
s.ProfitTracker.InitOld(s.Market, &s.ProfitStats, s.TradeStats)
}
// Add strategy parameters to report
if s.ProfitTracker.AccumulatedProfitReport != nil {
s.ProfitTracker.AccumulatedProfitReport.AddStrategyParameter("window", fmt.Sprintf("%d", s.Window))
s.ProfitTracker.AccumulatedProfitReport.AddStrategyParameter("multiplier", fmt.Sprintf("%f", s.SupertrendMultiplier))
s.ProfitTracker.AccumulatedProfitReport.AddStrategyParameter("fastDEMA", fmt.Sprintf("%d", s.FastDEMAWindow))
s.ProfitTracker.AccumulatedProfitReport.AddStrategyParameter("slowDEMA", fmt.Sprintf("%d", s.SlowDEMAWindow))
s.ProfitTracker.AccumulatedProfitReport.AddStrategyParameter("takeProfitAtrMultiplier", fmt.Sprintf("%f", s.TakeProfitAtrMultiplier))
s.ProfitTracker.AccumulatedProfitReport.AddStrategyParameter("stopLossByTriggeringK", fmt.Sprintf("%t", s.StopLossByTriggeringK))
s.ProfitTracker.AccumulatedProfitReport.AddStrategyParameter("stopByReversedSupertrend", fmt.Sprintf("%t", s.StopByReversedSupertrend))
s.ProfitTracker.AccumulatedProfitReport.AddStrategyParameter("stopByReversedDema", fmt.Sprintf("%t", s.StopByReversedDema))
s.ProfitTracker.AccumulatedProfitReport.AddStrategyParameter("stopByReversedLinGre", fmt.Sprintf("%t", s.StopByReversedLinGre))
}
} }
// Interval profit report // Interval profit report
@ -361,25 +373,6 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
// AccountValueCalculator // AccountValueCalculator
s.AccountValueCalculator = bbgo.NewAccountValueCalculator(s.session, s.Market.QuoteCurrency) s.AccountValueCalculator = bbgo.NewAccountValueCalculator(s.session, s.Market.QuoteCurrency)
// Accumulated profit report
if bbgo.IsBackTesting {
if s.AccumulatedProfitReport == nil {
s.AccumulatedProfitReport = &report.AccumulatedProfitReport{}
}
s.AccumulatedProfitReport.Initialize(s.Symbol, session, s.orderExecutor, s.TradeStats)
// Add strategy parameters to report
s.AccumulatedProfitReport.AddExtraValue([2]string{"window", fmt.Sprintf("%d", s.Window)})
s.AccumulatedProfitReport.AddExtraValue([2]string{"multiplier", fmt.Sprintf("%f", s.SupertrendMultiplier)})
s.AccumulatedProfitReport.AddExtraValue([2]string{"fastDEMA", fmt.Sprintf("%d", s.FastDEMAWindow)})
s.AccumulatedProfitReport.AddExtraValue([2]string{"slowDEMA", fmt.Sprintf("%d", s.SlowDEMAWindow)})
s.AccumulatedProfitReport.AddExtraValue([2]string{"takeProfitAtrMultiplier", fmt.Sprintf("%f", s.TakeProfitAtrMultiplier)})
s.AccumulatedProfitReport.AddExtraValue([2]string{"stopLossByTriggeringK", fmt.Sprintf("%t", s.StopLossByTriggeringK)})
s.AccumulatedProfitReport.AddExtraValue([2]string{"stopByReversedSupertrend", fmt.Sprintf("%t", s.StopByReversedSupertrend)})
s.AccumulatedProfitReport.AddExtraValue([2]string{"stopByReversedDema", fmt.Sprintf("%t", s.StopByReversedDema)})
s.AccumulatedProfitReport.AddExtraValue([2]string{"stopByReversedLinGre", fmt.Sprintf("%t", s.StopByReversedLinGre)})
}
// For drawing // For drawing
profitSlice := floats.Slice{1., 1.} profitSlice := floats.Slice{1., 1.}
price, _ := session.LastPrice(s.Symbol) price, _ := session.LastPrice(s.Symbol)
@ -527,10 +520,14 @@ func (s *Strategy) Run(ctx context.Context, orderExecutor bbgo.OrderExecutor, se
bbgo.OnShutdown(ctx, func(ctx context.Context, wg *sync.WaitGroup) { bbgo.OnShutdown(ctx, func(ctx context.Context, wg *sync.WaitGroup) {
defer wg.Done() defer wg.Done()
if bbgo.IsBackTesting { // Output profit report
// Output accumulated profit report if s.ProfitTracker != nil {
defer s.AccumulatedProfitReport.Output(s.Symbol) if s.ProfitTracker.AccumulatedProfitReport != nil {
s.ProfitTracker.AccumulatedProfitReport.Output()
}
}
if bbgo.IsBackTesting {
// Draw graph // Draw graph
if s.DrawGraph { if s.DrawGraph {
if err := s.Draw(&profitSlice, &cumProfitSlice); err != nil { if err := s.Draw(&profitSlice, &cumProfitSlice); err != nil {