abcBalance.c File Reference

#include "base/abc/abc.h"

Go to the source code of this file.

Functions
static ABC_NAMESPACE_IMPL_START void	Abc_NtkBalancePerform (Abc_Ntk_t *pNtk, Abc_Ntk_t *pNtkAig, int fDuplicate, int fSelective, int fUpdateLevel)
	DECLARATIONS ///. More...
static Abc_Obj_t *	Abc_NodeBalance_rec (Abc_Ntk_t *pNtkNew, Abc_Obj_t *pNode, Vec_Vec_t *vStorage, int Level, int fDuplicate, int fSelective, int fUpdateLevel)
static Vec_Ptr_t *	Abc_NodeBalanceCone (Abc_Obj_t *pNode, Vec_Vec_t *vSuper, int Level, int fDuplicate, int fSelective)
static int	Abc_NodeBalanceCone_rec (Abc_Obj_t *pNode, Vec_Ptr_t *vSuper, int fFirst, int fDuplicate, int fSelective)
static void	Abc_NtkMarkCriticalNodes (Abc_Ntk_t *pNtk)
static Vec_Ptr_t *	Abc_NodeBalanceConeExor (Abc_Obj_t *pNode)
Abc_Ntk_t *	Abc_NtkBalance (Abc_Ntk_t *pNtk, int fDuplicate, int fSelective, int fUpdateLevel)
	FUNCTION DEFINITIONS ///. More...
int	Abc_NodeBalanceFindLeft (Vec_Ptr_t *vSuper)
void	Abc_NodeBalancePermute (Abc_Ntk_t *pNtkNew, Vec_Ptr_t *vSuper, int LeftBound)
int	Abc_NodeBalanceConeExor_rec (Abc_Obj_t *pNode, Vec_Ptr_t *vSuper, int fFirst)
Vec_Ptr_t *	Abc_NodeFindCone_rec (Abc_Obj_t *pNode)
void	Abc_NtkBalanceAttach (Abc_Ntk_t *pNtk)
void	Abc_NtkBalanceDetach (Abc_Ntk_t *pNtk)
int	Abc_NtkBalanceLevel_rec (Abc_Obj_t *pNode)
void	Abc_NtkBalanceLevel (Abc_Ntk_t *pNtk)

Function Documentation

Abc_Obj_t * Abc_NodeBalance_rec ( Abc_Ntk_t *  pNtkNew, Abc_Obj_t *  pNodeOld, Vec_Vec_t *  vStorage, int  Level, int  fDuplicate, int  fSelective, int  fUpdateLevel  )

static

Function*************************************************************

Synopsis [Rebalances the multi-input node rooted at pNodeOld.]

Description []

SideEffects []

SeeAlso []

Definition at line 241 of file abcBalance.c.

{
    Abc_Aig_t * pMan = (Abc_Aig_t *)pNtkNew->pManFunc;
    Abc_Obj_t * pNodeNew, * pNode1, * pNode2;
    Vec_Ptr_t * vSuper;
    int i, LeftBound;
    assert( !Abc_ObjIsComplement(pNodeOld) );
    // return if the result if known
    if ( pNodeOld->pCopy )
        return pNodeOld->pCopy;
    assert( Abc_ObjIsNode(pNodeOld) );
    // get the implication supergate
//    Abc_NodeBalanceConeExor( pNodeOld );
    vSuper = Abc_NodeBalanceCone( pNodeOld, vStorage, Level, fDuplicate, fSelective );
    if ( vSuper->nSize == 0 )
    { // it means that the supergate contains two nodes in the opposite polarity
        pNodeOld->pCopy = Abc_ObjNot(Abc_AigConst1(pNtkNew));
        return pNodeOld->pCopy;
    }
    // for each old node, derive the new well-balanced node
    for ( i = 0; i < vSuper->nSize; i++ )
    {
        pNodeNew = Abc_NodeBalance_rec( pNtkNew, Abc_ObjRegular((Abc_Obj_t *)vSuper->pArray[i]), vStorage, Level + 1, fDuplicate, fSelective, fUpdateLevel );
        vSuper->pArray[i] = Abc_ObjNotCond( pNodeNew, Abc_ObjIsComplement((Abc_Obj_t *)vSuper->pArray[i]) );
    }
    if ( vSuper->nSize < 2 )
        printf( "BUG!\n" );
    // sort the new nodes by level in the decreasing order
    Vec_PtrSort( vSuper, (int (*)(void))Abc_NodeCompareLevelsDecrease );
    // balance the nodes
    assert( vSuper->nSize > 1 );
    while ( vSuper->nSize > 1 )
    {
        // find the left bound on the node to be paired
        LeftBound = (!fUpdateLevel)? 0 : Abc_NodeBalanceFindLeft( vSuper );
        // find the node that can be shared (if no such node, randomize choice)
        Abc_NodeBalancePermute( pNtkNew, vSuper, LeftBound );
        // pull out the last two nodes
        pNode1 = (Abc_Obj_t *)Vec_PtrPop(vSuper);
        pNode2 = (Abc_Obj_t *)Vec_PtrPop(vSuper);
        Abc_VecObjPushUniqueOrderByLevel( vSuper, Abc_AigAnd(pMan, pNode1, pNode2) );
    }
    // make sure the balanced node is not assigned
    assert( pNodeOld->pCopy == NULL );
    // mark the old node with the new node
    pNodeOld->pCopy = (Abc_Obj_t *)vSuper->pArray[0];
    vSuper->nSize = 0;
//    if ( Abc_ObjRegular(pNodeOld->pCopy) == Abc_AigConst1(pNtkNew) )
//        printf( "Constant node\n" );
//    assert( pNodeOld->Level >= Abc_ObjRegular(pNodeOld->pCopy)->Level );
    return pNodeOld->pCopy;
}

Vec_Ptr_t * Abc_NodeBalanceCone ( Abc_Obj_t *  pNode, Vec_Vec_t *  vStorage, int  Level, int  fDuplicate, int  fSelective  )

static

Function*************************************************************

Synopsis [Collects the nodes in the cone delimited by fMarkA==1.]

Description [Returns -1 if the AND-cone has the same node in both polarities. Returns 1 if the AND-cone has the same node in the same polarity. Returns 0 if the AND-cone has no repeated nodes.]

SideEffects []

SeeAlso []

Definition at line 307 of file abcBalance.c.

{
    Vec_Ptr_t * vNodes;
    int RetValue, i;
    assert( !Abc_ObjIsComplement(pNode) );
    // extend the storage
    if ( Vec_VecSize( vStorage ) <= Level )
        Vec_VecPush( vStorage, Level, 0 );
    // get the temporary array of nodes
    vNodes = Vec_VecEntry( vStorage, Level );
    Vec_PtrClear( vNodes );
    // collect the nodes in the implication supergate
    RetValue = Abc_NodeBalanceCone_rec( pNode, vNodes, 1, fDuplicate, fSelective );
    assert( vNodes->nSize > 1 );
    // unmark the visited nodes
    for ( i = 0; i < vNodes->nSize; i++ )
        Abc_ObjRegular((Abc_Obj_t *)vNodes->pArray[i])->fMarkB = 0;
    // if we found the node and its complement in the same implication supergate, 
    // return empty set of nodes (meaning that we should use constant-0 node)
    if ( RetValue == -1 )
        vNodes->nSize = 0;
    return vNodes;
}

int Abc_NodeBalanceCone_rec ( Abc_Obj_t *  pNode, Vec_Ptr_t *  vSuper, int  fFirst, int  fDuplicate, int  fSelective  )

static

Function*************************************************************

Synopsis [Collects the nodes in the cone delimited by fMarkA==1.]

Description [Returns -1 if the AND-cone has the same node in both polarities. Returns 1 if the AND-cone has the same node in the same polarity. Returns 0 if the AND-cone has no repeated nodes.]

SideEffects []

SeeAlso []

Definition at line 345 of file abcBalance.c.

{
    int RetValue1, RetValue2, i;
    // check if the node is visited
    if ( Abc_ObjRegular(pNode)->fMarkB )
    {
        // check if the node occurs in the same polarity
        for ( i = 0; i < vSuper->nSize; i++ )
            if ( vSuper->pArray[i] == pNode )
                return 1;
        // check if the node is present in the opposite polarity
        for ( i = 0; i < vSuper->nSize; i++ )
            if ( vSuper->pArray[i] == Abc_ObjNot(pNode) )
                return -1;
        assert( 0 );
        return 0;
    }
    // if the new node is complemented or a PI, another gate begins
    if ( !fFirst && (Abc_ObjIsComplement(pNode) || !Abc_ObjIsNode(pNode) || (!fDuplicate && !fSelective && (Abc_ObjFanoutNum(pNode) > 1)) || Vec_PtrSize(vSuper) > 10000) )
    {
        Vec_PtrPush( vSuper, pNode );
        Abc_ObjRegular(pNode)->fMarkB = 1;
        return 0;
    }
    assert( !Abc_ObjIsComplement(pNode) );
    assert( Abc_ObjIsNode(pNode) );
    // go through the branches
    RetValue1 = Abc_NodeBalanceCone_rec( Abc_ObjChild0(pNode), vSuper, 0, fDuplicate, fSelective );
    RetValue2 = Abc_NodeBalanceCone_rec( Abc_ObjChild1(pNode), vSuper, 0, fDuplicate, fSelective );
    if ( RetValue1 == -1 || RetValue2 == -1 )
        return -1;
    // return 1 if at least one branch has a duplicate
    return RetValue1 || RetValue2;
}

Vec_Ptr_t * Abc_NodeBalanceConeExor ( Abc_Obj_t *  pNode )

static

Function*************************************************************

Synopsis []

Description []

SideEffects []

SeeAlso []

Definition at line 428 of file abcBalance.c.

{
    Vec_Ptr_t * vSuper;
    if ( !pNode->fExor )
        return NULL;
    vSuper = Vec_PtrAlloc( 10 );
    Abc_NodeBalanceConeExor_rec( pNode, vSuper, 1 );
    printf( "%d ", Vec_PtrSize(vSuper) );
    Vec_PtrFree( vSuper );
    return NULL;
}

int Abc_NodeBalanceConeExor_rec	(	Abc_Obj_t *	pNode,
		Vec_Ptr_t *	vSuper,
		int	fFirst
	)

Function*************************************************************

Synopsis []

Description []

SideEffects []

SeeAlso []

Definition at line 392 of file abcBalance.c.

{
    int RetValue1, RetValue2, i;
    // check if the node occurs in the same polarity
    for ( i = 0; i < vSuper->nSize; i++ )
        if ( vSuper->pArray[i] == pNode )
            return 1;
    // if the new node is complemented or a PI, another gate begins
    if ( !fFirst && (!pNode->fExor || !Abc_ObjIsNode(pNode)) )
    {
        Vec_PtrPush( vSuper, pNode );
        return 0;
    }
    assert( !Abc_ObjIsComplement(pNode) );
    assert( Abc_ObjIsNode(pNode) );
    assert( pNode->fExor );
    // go through the branches
    RetValue1 = Abc_NodeBalanceConeExor_rec( Abc_ObjFanin0(Abc_ObjFanin0(pNode)), vSuper, 0 );
    RetValue2 = Abc_NodeBalanceConeExor_rec( Abc_ObjFanin1(Abc_ObjFanin0(pNode)), vSuper, 0 );
    if ( RetValue1 == -1 || RetValue2 == -1 )
        return -1;
    // return 1 if at least one branch has a duplicate
    return RetValue1 || RetValue2;
}

int Abc_NodeBalanceFindLeft

(

Vec_Ptr_t *

vSuper

)

Function*************************************************************

Synopsis [Finds the left bound on the next candidate to be paired.]

Description [The nodes in the array are in the decreasing order of levels. The last node in the array has the smallest level. By default it would be paired with the next node on the left. However, it may be possible to pair it with some other node on the left, in such a way that the new node is shared. This procedure finds the index of the left-most node, which can be paired with the last node.]

SideEffects []

SeeAlso []

Definition at line 154 of file abcBalance.c.

{
    Abc_Obj_t * pNodeRight, * pNodeLeft;
    int Current;
    // if two or less nodes, pair with the first
    if ( Vec_PtrSize(vSuper) < 3 )
        return 0;
    // set the pointer to the one before the last
    Current = Vec_PtrSize(vSuper) - 2;
    pNodeRight = (Abc_Obj_t *)Vec_PtrEntry( vSuper, Current );
    // go through the nodes to the left of this one
    for ( Current--; Current >= 0; Current-- )
    {
        // get the next node on the left
        pNodeLeft = (Abc_Obj_t *)Vec_PtrEntry( vSuper, Current );
        // if the level of this node is different, quit the loop
        if ( Abc_ObjRegular(pNodeLeft)->Level != Abc_ObjRegular(pNodeRight)->Level )
            break;
    }
    Current++;    
    // get the node, for which the equality holds
    pNodeLeft = (Abc_Obj_t *)Vec_PtrEntry( vSuper, Current );
    assert( Abc_ObjRegular(pNodeLeft)->Level == Abc_ObjRegular(pNodeRight)->Level );
    return Current;
}

void Abc_NodeBalancePermute	(	Abc_Ntk_t *	pNtkNew,
		Vec_Ptr_t *	vSuper,
		int	LeftBound
	)

Function*************************************************************

Synopsis [Moves closer to the end the node that is best for sharing.]

Description [If there is no node with sharing, randomly chooses one of the legal nodes.]

SideEffects []

SeeAlso []

Definition at line 192 of file abcBalance.c.

{
    Abc_Obj_t * pNode1, * pNode2, * pNode3;
    int RightBound, i;
    // get the right bound
    RightBound = Vec_PtrSize(vSuper) - 2;
    assert( LeftBound <= RightBound );
    if ( LeftBound == RightBound )
        return;
    // get the two last nodes
    pNode1 = (Abc_Obj_t *)Vec_PtrEntry( vSuper, RightBound + 1 );
    pNode2 = (Abc_Obj_t *)Vec_PtrEntry( vSuper, RightBound     );
    // find the first node that can be shared
    for ( i = RightBound; i >= LeftBound; i-- )
    {
        pNode3 = (Abc_Obj_t *)Vec_PtrEntry( vSuper, i );
        if ( Abc_AigAndLookup( (Abc_Aig_t *)pNtkNew->pManFunc, pNode1, pNode3 ) )
        {
            if ( pNode3 == pNode2 )
                return;
            Vec_PtrWriteEntry( vSuper, i,          pNode2 );
            Vec_PtrWriteEntry( vSuper, RightBound, pNode3 );
            return;
        }
    }
/*
    // we did not find the node to share, randomize choice
    {
        int Choice = rand() % (RightBound - LeftBound + 1);
        pNode3 = Vec_PtrEntry( vSuper, LeftBound + Choice );
        if ( pNode3 == pNode2 )
            return;
        Vec_PtrWriteEntry( vSuper, LeftBound + Choice, pNode2 );
        Vec_PtrWriteEntry( vSuper, RightBound,         pNode3 );
    }
*/
}

Vec_Ptr_t* Abc_NodeFindCone_rec

(

Abc_Obj_t *

pNode

)

Function*************************************************************

Synopsis [Collects the nodes in the implication supergate.]

Description []

SideEffects []

SeeAlso []

Definition at line 453 of file abcBalance.c.

{
    Vec_Ptr_t * vNodes;
    Abc_Obj_t * pNodeC, * pNodeT, * pNodeE;
    int RetValue, i;
    assert( !Abc_ObjIsComplement(pNode) );
    if ( Abc_ObjIsCi(pNode) )
        return NULL;
    // start the new array
    vNodes = Vec_PtrAlloc( 4 );
    // if the node is the MUX collect its fanins
    if ( Abc_NodeIsMuxType(pNode) )
    {
        pNodeC = Abc_NodeRecognizeMux( pNode, &pNodeT, &pNodeE );
        Vec_PtrPush( vNodes, Abc_ObjRegular(pNodeC) );
        Vec_PtrPushUnique( vNodes, Abc_ObjRegular(pNodeT) );
        Vec_PtrPushUnique( vNodes, Abc_ObjRegular(pNodeE) );
    }
    else
    {
        // collect the nodes in the implication supergate
        RetValue = Abc_NodeBalanceCone_rec( pNode, vNodes, 1, 1, 0 );
        assert( vNodes->nSize > 1 );
        // unmark the visited nodes
        Vec_PtrForEachEntry( Abc_Obj_t *, vNodes, pNode, i )
            Abc_ObjRegular(pNode)->fMarkB = 0;
        // if we found the node and its complement in the same implication supergate, 
        // return empty set of nodes (meaning that we should use constant-0 node)
        if ( RetValue == -1 )
            vNodes->nSize = 0;
    }
    // call for the fanin
    Vec_PtrForEachEntry( Abc_Obj_t *, vNodes, pNode, i )
    {
        pNode = Abc_ObjRegular(pNode);
        if ( pNode->pCopy )
            continue;
        pNode->pCopy = (Abc_Obj_t *)Abc_NodeFindCone_rec( pNode );
    }
    return vNodes;
}

Abc_Ntk_t* Abc_NtkBalance	(	Abc_Ntk_t *	pNtk,
		int	fDuplicate,
		int	fSelective,
		int	fUpdateLevel
	)

FUNCTION DEFINITIONS ///.

Function*************************************************************

Synopsis [Balances the AIG network.]

Description []

SideEffects []

SeeAlso []

Definition at line 53 of file abcBalance.c.

{
//    extern void Abc_NtkHaigTranfer( Abc_Ntk_t * pNtkOld, Abc_Ntk_t * pNtkNew );
    Abc_Ntk_t * pNtkAig;
    assert( Abc_NtkIsStrash(pNtk) );
    // compute the required times
    if ( fSelective )
    {
        Abc_NtkStartReverseLevels( pNtk, 0 );
        Abc_NtkMarkCriticalNodes( pNtk );
    }
    // perform balancing
    pNtkAig = Abc_NtkStartFrom( pNtk, ABC_NTK_STRASH, ABC_FUNC_AIG );
    // transfer HAIG
//    Abc_NtkHaigTranfer( pNtk, pNtkAig );
    // perform balancing
    Abc_NtkBalancePerform( pNtk, pNtkAig, fDuplicate, fSelective, fUpdateLevel );
    Abc_NtkFinalize( pNtk, pNtkAig );
    Abc_AigCleanup( (Abc_Aig_t *)pNtkAig->pManFunc );
    // undo the required times
    if ( fSelective )
    {
        Abc_NtkStopReverseLevels( pNtk );
        Abc_NtkCleanMarkA( pNtk );
    }
    if ( pNtk->pExdc )
        pNtkAig->pExdc = Abc_NtkDup( pNtk->pExdc );
    // make sure everything is okay
    if ( !Abc_NtkCheck( pNtkAig ) )
    {
        printf( "Abc_NtkBalance: The network check has failed.\n" );
        Abc_NtkDelete( pNtkAig );
        return NULL;
    }
//Abc_NtkPrintCiLevels( pNtkAig );
    return pNtkAig;
}

void Abc_NtkBalanceAttach

(

Abc_Ntk_t *

pNtk

)

Function*************************************************************

Synopsis [Attaches the implication supergates to internal nodes.]

Description []

SideEffects []

SeeAlso []

Definition at line 506 of file abcBalance.c.

{
    Abc_Obj_t * pNode;
    int i;
    Abc_NtkCleanCopy( pNtk );
    Abc_NtkForEachCo( pNtk, pNode, i )
    {
        pNode = Abc_ObjFanin0(pNode);
        if ( pNode->pCopy )
            continue;
        pNode->pCopy = (Abc_Obj_t *)Abc_NodeFindCone_rec( pNode );
    }
}

void Abc_NtkBalanceDetach

(

Abc_Ntk_t *

pNtk

)

Function*************************************************************

Synopsis [Attaches the implication supergates to internal nodes.]

Description []

SideEffects []

SeeAlso []

Definition at line 531 of file abcBalance.c.

{
    Abc_Obj_t * pNode;
    int i;
    Abc_NtkForEachNode( pNtk, pNode, i )
        if ( pNode->pCopy )
        {
            Vec_PtrFree( (Vec_Ptr_t *)pNode->pCopy );
            pNode->pCopy = NULL;
        }
}

void Abc_NtkBalanceLevel

(

Abc_Ntk_t *

pNtk

)

Function*************************************************************

Synopsis [Compute levels of implication supergates.]

Description []

SideEffects []

SeeAlso []

Definition at line 590 of file abcBalance.c.

{
    Abc_Obj_t * pNode;
    int i;
    Abc_NtkForEachObj( pNtk, pNode, i )
        pNode->Level = 0;
    Abc_NtkForEachCo( pNtk, pNode, i )
        Abc_NtkBalanceLevel_rec( Abc_ObjFanin0(pNode) );
}

int Abc_NtkBalanceLevel_rec

(

Abc_Obj_t *

pNode

)

Function*************************************************************

Synopsis [Compute levels of implication supergates.]

Description []

SideEffects []

SeeAlso []

Definition at line 554 of file abcBalance.c.

{
    Vec_Ptr_t * vSuper;
    Abc_Obj_t * pFanin;
    int i, LevelMax;
    assert( !Abc_ObjIsComplement(pNode) );
    if ( pNode->Level > 0 )
        return pNode->Level;
    if ( Abc_ObjIsCi(pNode) )
        return 0;
    vSuper = (Vec_Ptr_t *)pNode->pCopy;
    assert( vSuper != NULL );
    LevelMax = 0;
    Vec_PtrForEachEntry( Abc_Obj_t *, vSuper, pFanin, i )
    {
        pFanin = Abc_ObjRegular(pFanin);
        Abc_NtkBalanceLevel_rec(pFanin);
        if ( LevelMax < (int)pFanin->Level )
            LevelMax = pFanin->Level;
    }
    pNode->Level = LevelMax + 1;
    return pNode->Level;
}

void Abc_NtkBalancePerform ( Abc_Ntk_t *  pNtk, Abc_Ntk_t *  pNtkAig, int  fDuplicate, int  fSelective, int  fUpdateLevel  )

static

DECLARATIONS ///.

CFile****************************************************************

FileName [abcBalance.c]

SystemName [ABC: Logic synthesis and verification system.]

PackageName [Network and node package.]

Synopsis [Performs global balancing of the AIG by the number of levels.]

Author [Alan Mishchenko]

Affiliation [UC Berkeley]

Date [Ver. 1.0. Started - June 20, 2005.]

Revision [

Id:

abcBalance.c,v 1.00 2005/06/20 00:00:00 alanmi Exp

]

Function*************************************************************

Synopsis [Balances the AIG network.]

Description []

SideEffects []

SeeAlso []

Definition at line 102 of file abcBalance.c.

{
    ProgressBar * pProgress;
    Vec_Vec_t * vStorage;
    Abc_Obj_t * pNode;
    int i;
    // transfer level
    Abc_NtkForEachCi( pNtk, pNode, i )
        pNode->pCopy->Level = pNode->Level;
    // set the level of PIs of AIG according to the arrival times of the old network
    Abc_NtkSetNodeLevelsArrival( pNtk );
    // allocate temporary storage for supergates
    vStorage = Vec_VecStart( 10 );
    // perform balancing of POs
    pProgress = Extra_ProgressBarStart( stdout, Abc_NtkCoNum(pNtk) );
    if ( pNtk->nBarBufs == 0 )
    {
        Abc_NtkForEachCo( pNtk, pNode, i )
        {
            Extra_ProgressBarUpdate( pProgress, i, NULL );
            Abc_NodeBalance_rec( pNtkAig, Abc_ObjFanin0(pNode), vStorage, 0, fDuplicate, fSelective, fUpdateLevel );
        }
    }
    else
    {
        Abc_NtkForEachLiPo( pNtk, pNode, i )
        {
            Extra_ProgressBarUpdate( pProgress, i, NULL );
            Abc_NodeBalance_rec( pNtkAig, Abc_ObjFanin0(pNode), vStorage, 0, fDuplicate, fSelective, fUpdateLevel );
            if ( i < pNtk->nBarBufs )
                Abc_ObjFanout0(Abc_ObjFanout0(pNode))->Level = Abc_ObjFanin0(pNode)->Level;
        }
    }
    Extra_ProgressBarStop( pProgress );
    Vec_VecFree( vStorage );
}

void Abc_NtkMarkCriticalNodes ( Abc_Ntk_t *  pNtk )

static

Function*************************************************************

Synopsis [Marks the nodes on the critical and near critical paths.]

Description []

SideEffects []

SeeAlso []

Definition at line 612 of file abcBalance.c.

{
    Abc_Obj_t * pNode;
    int i, Counter = 0;
    Abc_NtkForEachNode( pNtk, pNode, i )
        if ( Abc_ObjRequiredLevel(pNode) - pNode->Level <= 1 )
            pNode->fMarkA = 1, Counter++;
    printf( "The number of nodes on the critical paths = %6d  (%5.2f %%)\n", Counter, 100.0 * Counter / Abc_NtkNodeNum(pNtk) );
}