lnd.xprv/autopilot/agent.go

package autopilot

import (
	"bytes"
	"fmt"
	"math/rand"
	"net"
	"sync"
	"sync/atomic"
	"time"

	"github.com/btcsuite/btcd/btcec"
	"github.com/btcsuite/btcutil"
	"github.com/davecgh/go-spew/spew"
	"github.com/lightningnetwork/lnd/lnwire"
)

// Config couples all the items that an autopilot agent needs to function.
// All items within the struct MUST be populated for the Agent to be able to
// carry out its duties.
type Config struct {
	// Self is the identity public key of the Lightning Network node that
	// is being driven by the agent. This is used to ensure that we don't
	// accidentally attempt to open a channel with ourselves.
	Self *btcec.PublicKey

	// Heuristic is an attachment heuristic which will govern to whom we
	// open channels to, and also what those channels look like in terms of
	// desired capacity. The Heuristic will take into account the current
	// state of the graph, our set of open channels, and the amount of
	// available funds when determining how channels are to be opened.
	// Additionally, a heuristic make also factor in extra-graph
	// information in order to make more pertinent recommendations.
	Heuristic AttachmentHeuristic

	// ChanController is an interface that is able to directly manage the
	// creation, closing and update of channels within the network.
	ChanController ChannelController

	// ConnectToPeer attempts to connect to the peer using one of its
	// advertised addresses. The boolean returned signals whether the peer
	// was already connected.
	ConnectToPeer func(*btcec.PublicKey, []net.Addr) (bool, error)

	// DisconnectPeer attempts to disconnect the peer with the given public
	// key.
	DisconnectPeer func(*btcec.PublicKey) error

	// WalletBalance is a function closure that should return the current
	// available balance of the backing wallet.
	WalletBalance func() (btcutil.Amount, error)

	// Graph is an abstract channel graph that the Heuristic and the Agent
	// will use to make decisions w.r.t channel allocation and placement
	// within the graph.
	Graph ChannelGraph

	// Constraints is the set of constraints the autopilot must adhere to
	// when opening channels.
	Constraints *HeuristicConstraints

	// TODO(roasbeef): add additional signals from fee rates and revenue of
	// currently opened channels
}

// channelState is a type that represents the set of active channels of the
// backing LN node that the Agent should be aware of. This type contains a few
// helper utility methods.
type channelState map[lnwire.ShortChannelID]Channel

// Channels returns a slice of all the active channels.
func (c channelState) Channels() []Channel {
	chans := make([]Channel, 0, len(c))
	for _, channel := range c {
		chans = append(chans, channel)
	}
	return chans
}

// ConnectedNodes returns the set of nodes we currently have a channel with.
// This information is needed as we want to avoid making repeated channels with
// any node.
func (c channelState) ConnectedNodes() map[NodeID]struct{} {
	nodes := make(map[NodeID]struct{})
	for _, channels := range c {
		nodes[channels.Node] = struct{}{}
	}

	// TODO(roasbeef): add outgoing, nodes, allow incoming and outgoing to
	// per node
	//  * only add node is chan as funding amt set

	return nodes
}

// Agent implements a closed-loop control system which seeks to autonomously
// optimize the allocation of satoshis within channels throughput the network's
// channel graph. An agent is configurable by swapping out different
// AttachmentHeuristic strategies. The agent uses external signals such as the
// wallet balance changing, or new channels being opened/closed for the local
// node as an indicator to re-examine its internal state, and the amount of
// available funds in order to make updated decisions w.r.t the channel graph.
// The Agent will automatically open, close, and splice in/out channel as
// necessary for it to step closer to its optimal state.
//
// TODO(roasbeef): prob re-word
type Agent struct {
	// Only to be used atomically.
	started uint32
	stopped uint32

	// cfg houses the configuration state of the Ant.
	cfg Config

	// chanState tracks the current set of open channels.
	chanState channelState

	// stateUpdates is a channel that any external state updates that may
	// affect the heuristics of the agent will be sent over.
	stateUpdates chan interface{}

	// balanceUpdates is a channel where notifications about updates to the
	// wallet's balance will be sent. This channel will be buffered to
	// ensure we have at most one pending update of this type to handle at
	// a given time.
	balanceUpdates chan *balanceUpdate

	// nodeUpdates is a channel that changes to the graph node landscape
	// will be sent over. This channel will be buffered to ensure we have
	// at most one pending update of this type to handle at a given time.
	nodeUpdates chan *nodeUpdates

	// pendingOpenUpdates is a channel where updates about channel pending
	// opening will be sent. This channel will be buffered to ensure we
	// have at most one pending update of this type to handle at a given
	// time.
	pendingOpenUpdates chan *chanPendingOpenUpdate

	// chanOpenFailures is a channel where updates about channel open
	// failures will be sent. This channel will be buffered to ensure we
	// have at most one pending update of this type to handle at a given
	// time.
	chanOpenFailures chan *chanOpenFailureUpdate

	// totalBalance is the total number of satoshis the backing wallet is
	// known to control at any given instance. This value will be updated
	// when the agent receives external balance update signals.
	totalBalance btcutil.Amount

	// failedNodes lists nodes that we've previously attempted to initiate
	// channels with, but didn't succeed.
	failedNodes map[NodeID]struct{}

	// pendingConns tracks the nodes that we are attempting to make
	// connections to. This prevents us from making duplicate connection
	// requests to the same node.
	pendingConns map[NodeID]struct{}

	// pendingOpens tracks the channels that we've requested to be
	// initiated, but haven't yet been confirmed as being fully opened.
	// This state is required as otherwise, we may go over our allotted
	// channel limit, or open multiple channels to the same node.
	pendingOpens map[NodeID]Channel
	pendingMtx   sync.Mutex

	quit chan struct{}
	wg   sync.WaitGroup
}

// New creates a new instance of the Agent instantiated using the passed
// configuration and initial channel state. The initial channel state slice
// should be populated with the set of Channels that are currently opened by
// the backing Lightning Node.
func New(cfg Config, initialState []Channel) (*Agent, error) {
	a := &Agent{
		cfg:                cfg,
		chanState:          make(map[lnwire.ShortChannelID]Channel),
		quit:               make(chan struct{}),
		stateUpdates:       make(chan interface{}),
		balanceUpdates:     make(chan *balanceUpdate, 1),
		nodeUpdates:        make(chan *nodeUpdates, 1),
		chanOpenFailures:   make(chan *chanOpenFailureUpdate, 1),
		pendingOpenUpdates: make(chan *chanPendingOpenUpdate, 1),
		failedNodes:        make(map[NodeID]struct{}),
		pendingConns:       make(map[NodeID]struct{}),
		pendingOpens:       make(map[NodeID]Channel),
	}

	for _, c := range initialState {
		a.chanState[c.ChanID] = c
	}

	return a, nil
}

// Start starts the agent along with any goroutines it needs to perform its
// normal duties.
func (a *Agent) Start() error {
	if !atomic.CompareAndSwapUint32(&a.started, 0, 1) {
		return nil
	}

	rand.Seed(time.Now().Unix())
	log.Infof("Autopilot Agent starting")

	a.wg.Add(1)
	go a.controller()

	return nil
}

// Stop signals the Agent to gracefully shutdown. This function will block
// until all goroutines have exited.
func (a *Agent) Stop() error {
	if !atomic.CompareAndSwapUint32(&a.stopped, 0, 1) {
		return nil
	}

	log.Infof("Autopilot Agent stopping")

	close(a.quit)
	a.wg.Wait()

	return nil
}

// balanceUpdate is a type of external state update that reflects an
// increase/decrease in the funds currently available to the wallet.
type balanceUpdate struct {
}

// nodeUpdates is a type of external state update that reflects an addition or
// modification in channel graph node membership.
type nodeUpdates struct{}

// chanOpenUpdate is a type of external state update that indicates a new
// channel has been opened, either by the Agent itself (within the main
// controller loop), or by an external user to the system.
type chanOpenUpdate struct {
	newChan Channel
}

// chanPendingOpenUpdate is a type of external state update that indicates a new
// channel has been opened, either by the agent itself or an external subsystem,
// but is still pending.
type chanPendingOpenUpdate struct{}

// chanOpenFailureUpdate is a type of external state update that indicates
// a previous channel open failed, and that it might be possible to try again.
type chanOpenFailureUpdate struct{}

// chanCloseUpdate is a type of external state update that indicates that the
// backing Lightning Node has closed a previously open channel.
type chanCloseUpdate struct {
	closedChans []lnwire.ShortChannelID
}

// OnBalanceChange is a callback that should be executed each time the balance
// of the backing wallet changes.
func (a *Agent) OnBalanceChange() {
	select {
	case a.balanceUpdates <- &balanceUpdate{}:
	default:
	}
}

// OnNodeUpdates is a callback that should be executed each time our channel
// graph has new nodes or their node announcements are updated.
func (a *Agent) OnNodeUpdates() {
	select {
	case a.nodeUpdates <- &nodeUpdates{}:
	default:
	}
}

// OnChannelOpen is a callback that should be executed each time a new channel
// is manually opened by the user or any system outside the autopilot agent.
func (a *Agent) OnChannelOpen(c Channel) {
	a.wg.Add(1)
	go func() {
		defer a.wg.Done()

		select {
		case a.stateUpdates <- &chanOpenUpdate{newChan: c}:
		case <-a.quit:
		}
	}()
}

// OnChannelPendingOpen is a callback that should be executed each time a new
// channel is opened, either by the agent or an external subsystems, but is
// still pending.
func (a *Agent) OnChannelPendingOpen() {
	select {
	case a.pendingOpenUpdates <- &chanPendingOpenUpdate{}:
	default:
	}
}

// OnChannelOpenFailure is a callback that should be executed when the
// autopilot has attempted to open a channel, but failed. In this case we can
// retry channel creation with a different node.
func (a *Agent) OnChannelOpenFailure() {
	select {
	case a.chanOpenFailures <- &chanOpenFailureUpdate{}:
	default:
	}
}

// OnChannelClose is a callback that should be executed each time a prior
// channel has been closed for any reason. This includes regular
// closes, force closes, and channel breaches.
func (a *Agent) OnChannelClose(closedChans ...lnwire.ShortChannelID) {
	a.wg.Add(1)
	go func() {
		defer a.wg.Done()

		select {
		case a.stateUpdates <- &chanCloseUpdate{closedChans: closedChans}:
		case <-a.quit:
		}
	}()
}

// mergeNodeMaps merges the Agent's set of nodes that it already has active
// channels open to, with the other sets of nodes that should be removed from
// consideration during heuristic selection. This ensures that the Agent doesn't
// attempt to open any "duplicate" channels to the same node.
func mergeNodeMaps(c map[NodeID]Channel,
	skips ...map[NodeID]struct{}) map[NodeID]struct{} {

	numNodes := len(c)
	for _, skip := range skips {
		numNodes += len(skip)
	}

	res := make(map[NodeID]struct{}, len(c)+numNodes)
	for nodeID := range c {
		res[nodeID] = struct{}{}
	}
	for _, skip := range skips {
		for nodeID := range skip {
			res[nodeID] = struct{}{}
		}
	}

	return res
}

// mergeChanState merges the Agent's set of active channels, with the set of
// channels awaiting confirmation. This ensures that the agent doesn't go over
// the prescribed channel limit or fund allocation limit.
func mergeChanState(pendingChans map[NodeID]Channel,
	activeChans channelState) []Channel {

	numChans := len(pendingChans) + len(activeChans)
	totalChans := make([]Channel, 0, numChans)

	for _, activeChan := range activeChans.Channels() {
		totalChans = append(totalChans, activeChan)
	}
	for _, pendingChan := range pendingChans {
		totalChans = append(totalChans, pendingChan)
	}

	return totalChans
}

// weightedChoice draws a random index from the map of channel candidates, with
// a probability propotional to their score.
func weightedChoice(s map[NodeID]*AttachmentDirective) (NodeID, error) {
	// Calculate the sum of scores found in the map.
	var sum float64
	for _, v := range s {
		sum += v.Score
	}

	if sum <= 0 {
		return NodeID{}, fmt.Errorf("non-positive sum")
	}

	// Create a map of normalized scores such, that they sum to 1.0.
	norm := make(map[NodeID]float64)
	for k, v := range s {
		norm[k] = v.Score / sum
	}

	// Pick a random number in the range [0.0, 1.0), and iterate the map
	// until the number goes below 0. This means that each index is picked
	// with a probablity equal to their normalized score.
	//
	// Example:
	// Items with scores [1, 5, 2, 2]
	// Normalized scores [0.1, 0.5, 0.2, 0.2]
	// Imagine they each occupy a "range" equal to their normalized score
	// in [0, 1.0]:
	// [|-0.1-||-----0.5-----||--0.2--||--0.2--|]
	// The following loop is now equivalent to "hitting" the intervals.
	r := rand.Float64()
	for k, v := range norm {
		r -= v
		if r <= 0 {
			return k, nil
		}
	}
	return NodeID{}, fmt.Errorf("no choice made")
}

// chooseN picks at random min[n, len(s)] nodes if from the
// AttachmentDirectives map, with a probability weighted by their score.
func chooseN(n int, s map[NodeID]*AttachmentDirective) (
	map[NodeID]*AttachmentDirective, error) {

	// Keep a map of nodes not yet choosen.
	rem := make(map[NodeID]*AttachmentDirective)
	for k, v := range s {
		rem[k] = v
	}

	// Pick a weighted choice from the remaining nodes as long as there are
	// nodes left, and we haven't already picked n.
	chosen := make(map[NodeID]*AttachmentDirective)
	for len(chosen) < n && len(rem) > 0 {
		choice, err := weightedChoice(rem)
		if err != nil {
			return nil, err
		}

		chosen[choice] = rem[choice]
		delete(rem, choice)
	}

	return chosen, nil
}

// controller implements the closed-loop control system of the Agent. The
// controller will make a decision w.r.t channel placement within the graph
// based on: its current internal state of the set of active channels open,
// and external state changes as a result of decisions it  makes w.r.t channel
// allocation, or attributes affecting its control loop being updated by the
// backing Lightning Node.
func (a *Agent) controller() {
	defer a.wg.Done()

	// We'll start off by assigning our starting balance, and injecting
	// that amount as an initial wake up to the main controller goroutine.
	a.OnBalanceChange()

	// TODO(roasbeef): do we in fact need to maintain order?
	//  * use sync.Cond if so
	updateBalance := func() {
		newBalance, err := a.cfg.WalletBalance()
		if err != nil {
			log.Warnf("unable to update wallet balance: %v", err)
			return
		}

		a.totalBalance = newBalance
	}

	// TODO(roasbeef): add 10-minute wake up timer
	for {
		select {
		// A new external signal has arrived. We'll use this to update
		// our internal state, then determine if we should trigger a
		// channel state modification (open/close, splice in/out).
		case signal := <-a.stateUpdates:
			log.Infof("Processing new external signal")

			switch update := signal.(type) {
			// A new channel has been opened successfully. This was
			// either opened by the Agent, or an external system
			// that is able to drive the Lightning Node.
			case *chanOpenUpdate:
				log.Debugf("New channel successfully opened, "+
					"updating state with: %v",
					spew.Sdump(update.newChan))

				newChan := update.newChan
				a.chanState[newChan.ChanID] = newChan

				a.pendingMtx.Lock()
				delete(a.pendingOpens, newChan.Node)
				a.pendingMtx.Unlock()

				updateBalance()
			// A channel has been closed, this may free up an
			// available slot, triggering a new channel update.
			case *chanCloseUpdate:
				log.Debugf("Applying closed channel "+
					"updates: %v",
					spew.Sdump(update.closedChans))

				for _, closedChan := range update.closedChans {
					delete(a.chanState, closedChan)
				}

				updateBalance()
			}

		// A new channel has been opened by the agent or an external
		// subsystem, but is still pending confirmation.
		case <-a.pendingOpenUpdates:
			updateBalance()

		// The balance of the backing wallet has changed, if more funds
		// are now available, we may attempt to open up an additional
		// channel, or splice in funds to an existing one.
		case <-a.balanceUpdates:
			log.Debug("Applying external balance state update")

			updateBalance()

		// The channel we tried to open previously failed for whatever
		// reason.
		case <-a.chanOpenFailures:
			log.Debug("Retrying after previous channel open " +
				"failure.")

			updateBalance()

		// New nodes have been added to the graph or their node
		// announcements have been updated. We will consider opening
		// channels to these nodes if we haven't stabilized.
		case <-a.nodeUpdates:
			log.Infof("Node updates received, assessing " +
				"need for more channels")

		// The agent has been signalled to exit, so we'll bail out
		// immediately.
		case <-a.quit:
			return
		}

		a.pendingMtx.Lock()
		log.Debugf("Pending channels: %v", spew.Sdump(a.pendingOpens))
		a.pendingMtx.Unlock()

		// With all the updates applied, we'll obtain a set of the
		// current active channels (confirmed channels), and also
		// factor in our set of unconfirmed channels.
		confirmedChans := a.chanState
		a.pendingMtx.Lock()
		totalChans := mergeChanState(a.pendingOpens, confirmedChans)
		a.pendingMtx.Unlock()

		// Now that we've updated our internal state, we'll consult our
		// channel attachment heuristic to determine if we should open
		// up any additional channels or modify existing channels.
		availableFunds, numChans, needMore := a.cfg.Heuristic.NeedMoreChans(
			totalChans, a.totalBalance,
		)
		if !needMore {
			continue
		}

		log.Infof("Triggering attachment directive dispatch, "+
			"total_funds=%v", a.totalBalance)

		err := a.openChans(availableFunds, numChans, totalChans)
		if err != nil {
			log.Errorf("Unable to open channels: %v", err)
		}
	}
}

// openChans queries the agent's heuristic for a set of channel candidates, and
// attempts to open channels to them.
func (a *Agent) openChans(availableFunds btcutil.Amount, numChans uint32,
	totalChans []Channel) error {

	// We're to attempt an attachment so we'll obtain the set of
	// nodes that we currently have channels with so we avoid
	// duplicate edges.
	connectedNodes := a.chanState.ConnectedNodes()
	a.pendingMtx.Lock()
	nodesToSkip := mergeNodeMaps(a.pendingOpens,
		a.pendingConns, connectedNodes, a.failedNodes,
	)
	a.pendingMtx.Unlock()

	// Gather the set of all nodes in the graph, except those we
	// want to skip.
	selfPubBytes := a.cfg.Self.SerializeCompressed()
	nodes := make(map[NodeID]struct{})
	if err := a.cfg.Graph.ForEachNode(func(node Node) error {
		nID := NodeID(node.PubKey())

		// If we come across ourselves, them we'll continue in
		// order to avoid attempting to make a channel with
		// ourselves.
		if bytes.Equal(nID[:], selfPubBytes) {
			return nil
		}

		// Additionally, if this node is in the blacklist, then
		// we'll skip it.
		if _, ok := nodesToSkip[nID]; ok {
			return nil
		}

		nodes[nID] = struct{}{}
		return nil
	}); err != nil {
		return fmt.Errorf("unable to get graph nodes: %v", err)
	}

	// Use the heuristic to calculate a score for each node in the
	// graph.
	scores, err := a.cfg.Heuristic.NodeScores(
		a.cfg.Graph, totalChans, availableFunds, nodes,
	)
	if err != nil {
		return fmt.Errorf("unable to calculate node scores : %v", err)
	}

	log.Debugf("Got scores for %d nodes", len(scores))

	// Now use the score to make a weighted choice which
	// nodes to attempt to open channels to.
	chanCandidates, err := chooseN(int(numChans), scores)
	if err != nil {
		return fmt.Errorf("Unable to make weighted choice: %v",
			err)
	}

	if len(chanCandidates) == 0 {
		log.Infof("No eligible candidates to connect to")
		return nil
	}

	log.Infof("Attempting to execute channel attachment "+
		"directives: %v", spew.Sdump(chanCandidates))

	// Before proceeding, check to see if we have any slots
	// available to open channels. If there are any, we will attempt
	// to dispatch the retrieved directives since we can't be
	// certain which ones may actually succeed. If too many
	// connections succeed, we will they will be ignored and made
	// available to future heuristic selections.
	a.pendingMtx.Lock()
	defer a.pendingMtx.Unlock()
	if uint16(len(a.pendingOpens)) >= a.cfg.Constraints.MaxPendingOpens {
		log.Debugf("Reached cap of %v pending "+
			"channel opens, will retry "+
			"after success/failure",
			a.cfg.Constraints.MaxPendingOpens)
		return nil
	}

	// For each recommended attachment directive, we'll launch a
	// new goroutine to attempt to carry out the directive. If any
	// of these succeed, then we'll receive a new state update,
	// taking us back to the top of our controller loop.
	for _, chanCandidate := range chanCandidates {
		// Skip candidates which we are already trying
		// to establish a connection with.
		nodeID := chanCandidate.NodeID
		if _, ok := a.pendingConns[nodeID]; ok {
			continue
		}
		a.pendingConns[nodeID] = struct{}{}

		a.wg.Add(1)
		go a.executeDirective(*chanCandidate)
	}
	return nil
}

// executeDirective attempts to connect to the channel candidate specified by
// the given attachment directive, and open a channel of the given size.
//
// NOTE: MUST be run as a goroutine.
func (a *Agent) executeDirective(directive AttachmentDirective) {
	defer a.wg.Done()

	// We'll start out by attempting to connect to the peer in order to
	// begin the funding workflow.
	nodeID := directive.NodeID
	pub, err := btcec.ParsePubKey(nodeID[:], btcec.S256())
	if err != nil {
		log.Errorf("Unable to parse pubkey %x: %v", nodeID, err)
		return
	}

	alreadyConnected, err := a.cfg.ConnectToPeer(pub, directive.Addrs)
	if err != nil {
		log.Warnf("Unable to connect to %x: %v",
			pub.SerializeCompressed(), err)

		// Since we failed to connect to them, we'll mark them as
		// failed so that we don't attempt to connect to them again.
		a.pendingMtx.Lock()
		delete(a.pendingConns, nodeID)
		a.failedNodes[nodeID] = struct{}{}
		a.pendingMtx.Unlock()

		// Finally, we'll trigger the agent to select new peers to
		// connect to.
		a.OnChannelOpenFailure()

		return
	}

	// The connection was successful, though before progressing we must
	// check that we have not already met our quota for max pending open
	// channels. This can happen if multiple directives were spawned but
	// fewer slots were available, and other successful attempts finished
	// first.
	a.pendingMtx.Lock()
	if uint16(len(a.pendingOpens)) >=
		a.cfg.Constraints.MaxPendingOpens {
		// Since we've reached our max number of pending opens, we'll
		// disconnect this peer and exit. However, if we were
		// previously connected to them, then we'll make sure to
		// maintain the connection alive.
		if alreadyConnected {
			// Since we succeeded in connecting, we won't add this
			// peer to the failed nodes map, but we will remove it
			// from a.pendingConns so that it can be retried in the
			// future.
			delete(a.pendingConns, nodeID)
			a.pendingMtx.Unlock()
			return
		}

		err = a.cfg.DisconnectPeer(pub)
		if err != nil {
			log.Warnf("Unable to disconnect peer %x: %v",
				pub.SerializeCompressed(), err)
		}

		// Now that we have disconnected, we can remove this node from
		// our pending conns map, permitting subsequent connection
		// attempts.
		delete(a.pendingConns, nodeID)
		a.pendingMtx.Unlock()
		return
	}

	// If we were successful, we'll track this peer in our set of pending
	// opens. We do this here to ensure we don't stall on selecting new
	// peers if the connection attempt happens to take too long.
	delete(a.pendingConns, nodeID)
	a.pendingOpens[nodeID] = Channel{
		Capacity: directive.ChanAmt,
		Node:     nodeID,
	}
	a.pendingMtx.Unlock()

	// We can then begin the funding workflow with this peer.
	err = a.cfg.ChanController.OpenChannel(pub, directive.ChanAmt)
	if err != nil {
		log.Warnf("Unable to open channel to %x of %v: %v",
			pub.SerializeCompressed(), directive.ChanAmt, err)

		// As the attempt failed, we'll clear the peer from the set of
		// pending opens and mark them as failed so we don't attempt to
		// open a channel to them again.
		a.pendingMtx.Lock()
		delete(a.pendingOpens, nodeID)
		a.failedNodes[nodeID] = struct{}{}
		a.pendingMtx.Unlock()

		// Trigger the agent to re-evaluate everything and possibly
		// retry with a different node.
		a.OnChannelOpenFailure()

		// Finally, we should also disconnect the peer if we weren't
		// already connected to them beforehand by an external
		// subsystem.
		if alreadyConnected {
			return
		}

		err = a.cfg.DisconnectPeer(pub)
		if err != nil {
			log.Warnf("Unable to disconnect peer %x: %v",
				pub.SerializeCompressed(), err)
		}
	}

	// Since the channel open was successful and is currently pending,
	// we'll trigger the autopilot agent to query for more peers.
	a.OnChannelPendingOpen()
}