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| # Variables: | 41 |
| # Callers: | 1 |
| # Callings: | 3 |
| # Words: | 133 |
| # Keywords: | 69 |
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..
.. Array Arguments ..
..
Purpose
=======
PZUNGR2 generates an M-by-N complex distributed matrix Q denoting
A(IA:IA+M-1,JA:JA+N-1) with orthonormal rows, which is defined as the
last M rows of a product of K elementary reflectors of order N
Q = H(1)' H(2)' . . . H(k)'
as returned by PZGERQF.
Notes
=====
Each global data object is described by an associated description
vector. This vector stores the information required to establish
the mapping between an object element and its corresponding process
and memory location.
Let A be a generic term for any 2D block cyclicly distributed array.
Such a global array has an associated description vector DESCA.
In the following comments, the character _ should be read as
"of the global array".
NOTATION STORED IN EXPLANATION
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
M_A (global) DESCA( M_ ) The number of rows in the global
array A.
N_A (global) DESCA( N_ ) The number of columns in the global
array A.
MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
the rows of the array.
NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
row of the array A is distributed.
CSRC_A (global) DESCA( CSRC_ ) The process column over which the
first column of the array A is
distributed.
LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
array. LLD_A >= MAX(1,LOCr(M_A)).
Let K be the number of rows or columns of a distributed matrix,
and assume that its process grid has dimension p x q.
LOCr( K ) denotes the number of elements of K that a process
would receive if K were distributed over the p processes of its
process column.
Similarly, LOCc( K ) denotes the number of elements of K that a
process would receive if K were distributed over the q processes of
its process row.
The values of LOCr() and LOCc() may be determined via a call to the
ScaLAPACK tool function, NUMROC:
LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
An upper bound for these quantities may be computed by:
LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
Arguments
=========
M (global input) INTEGER
The number of rows to be operated on i.e the number of rows
of the distributed submatrix Q. M >= 0.
N (global input) INTEGER
The number of columns to be operated on i.e the number of
columns of the distributed submatrix Q. N >= M >= 0.
K (global input) INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.
A (local input/local output) COMPLEX*16 pointer into the
local memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
On entry, the i-th row must contain the vector which defines
the elementary reflector H(i), IA+M-K <= i <= IA+M-1, as
returned by PZGERQF in the K rows of its distributed
matrix argument A(IA+M-K:IA+M-1,JA:*). On exit, this array
contains the local pieces of the M-by-N distributed matrix Q.
IA (global input) INTEGER
The row index in the global array A indicating the first
row of sub( A ).
JA (global input) INTEGER
The column index in the global array A indicating the
first column of sub( A ).
DESCA (global and local input) INTEGER array of dimension DLEN_.
The array descriptor for the distributed matrix A.
TAU (local input) COMPLEX*16, array, dimension LOCr(IA+M-1)
This array contains the scalar factors TAU(i) of the
elementary reflectors H(i) as returned by PZGERQF.
TAU is tied to the distributed matrix A.
WORK (local workspace/local output) COMPLEX*16 array,
dimension (LWORK)
On exit, WORK(1) returns the minimal and optimal LWORK.
LWORK (local or global input) INTEGER
The dimension of the array WORK.
LWORK is local input and must be at least
LWORK >= NqA0 + MAX( 1, MpA0 ), where
IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ),
IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ),
IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ),
MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ),
NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
INDXG2P and NUMROC are ScaLAPACK tool functions;
MYROW, MYCOL, NPROW and NPCOL can be determined by calling
the subroutine BLACS_GRIDINFO.
If LWORK = -1, then LWORK is global input and a workspace
query is assumed; the routine only calculates the minimum
and optimal size for all work arrays. Each of these
values is returned in the first entry of the corresponding
work array, and no error message is issued by PXERBLA.
INFO (local output) INTEGER
= 0: successful exit
< 0: If the i-th argument is an array and the j-entry had
an illegal value, then INFO = -(i*100+j), if the i-th
argument is a scalar and had an illegal value, then
INFO = -i.
=====================================================================
.. Parameters ..
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001 SUBROUTINE PZUNGR2( M , N , K , A , IA , JA , DESCA , TAU , WORK , LWORK ,
002 $INFO )
003
004 * -- ScaLAPACK routine(version 1.7) --
005 * University of Tennessee , Knoxville , Oak Ridge National Laboratory ,
006 * and University of California , Berkeley.
007 * May 25 , 2001
008
009 * .. Scalar Arguments ..
010 INTEGER IA , INFO , JA , K , LWORK , M , N
011 INTEGER BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ ,
012 $LLD_ , MB_ , M_ , NB_ , N_ , RSRC_
013 PARAMETER( BLOCK_CYCLIC_2D = 1 , DLEN_ = 9 , DTYPE_ = 1 ,
014 $CTXT_ = 2 , M_ = 3 , N_ = 4 , MB_ = 5 , NB_ = 6 ,
015 $RSRC_ = 7 , CSRC_ = 8 , LLD_ = 9 )
016 COMPLEX*16 ONE , ZERO
017 PARAMETER( ONE =( 1.0D + 0 , 0.0D + 0 ) ,
018 $ZERO =( 0.0D + 0 , 0.0D + 0 ) )
019 * ..
020 * .. Local Scalars ..
021 LOGICAL LQUERY
022 CHARACTER COLBTOP , ROWBTOP
023 INTEGER IACOL , IAROW , I , ICTXT , II , LWMIN , MP , MPA0 ,
024 $MYCOL , MYROW , NPCOL , NPROW , NQA0
025 COMPLEX*16 TAUI
026 * ..
027 * .. External Subroutines ..
028 EXTERNAL BLACS_ABORT , BLACS_GRIDINFO , CHK1MAT ,
029 $PB_TOPGET , PB_TOPSET , PXERBLA , PZELSET ,
030 $PZLACGV , PZLARFC , PZLASET , PZSCAL
031 * ..
032 * .. External Functions ..
033 INTEGER INDXG2L , INDXG2P , NUMROC
034 EXTERNAL INDXG2L , INDXG2P , NUMROC
035 * ..
036 * .. Intrinsic Functions ..
037 INTRINSIC DBLE , DCMPLX , DCONJG , MAX , MIN , MOD
038 * ..
039 * .. Executable Statements ..
040
041 * Get grid parameters
042
043 ICTXT = DESCA( CTXT_ )
044 CALL BLACS_GRIDINFO( ICTXT , NPROW , NPCOL , MYROW , MYCOL )
045
046 * Test the input parameters
047
048 INFO = 0
049 IF( NPROW.EQ. - 1 ) THEN
049
050 INFO = - (700 + CTXT_)
051 ELSE
051
052 CALL CHK1MAT( M , 1 , N , 2 , IA , JA , DESCA , 7 , INFO )
053 IF( INFO.EQ.0 ) THEN
053
054 IAROW = INDXG2P( IA , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
055 $ NPROW )
056 IACOL = INDXG2P( JA , DESCA( NB_ ) , MYCOL , DESCA( CSRC_ ) ,
057 $ NPCOL )
058 MPA0 = NUMROC( M + MOD( IA - 1 , DESCA( MB_ ) ) , DESCA( MB_ ) ,
059 $ MYROW , IAROW , NPROW )
060 NQA0 = NUMROC( N + MOD( JA - 1 , DESCA( NB_ ) ) , DESCA( NB_ ) ,
061 $ MYCOL , IACOL , NPCOL )
062 LWMIN = NQA0 + MAX( 1 , MPA0 )
063
064 WORK( 1 ) = DCMPLX( DBLE( LWMIN ) )
065 LQUERY =( LWORK.EQ. - 1 )
066 IF( N.LT.M ) THEN
066
067 INFO = - 2
068 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
068
069 INFO = - 3
070 ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
070
071 INFO = - 10
072 END IF
073 END IF
074 END IF
075 IF( INFO.NE.0 ) THEN
075
076 CALL PXERBLA( ICTXT , 'PZUNGR2' , - INFO )
077 CALL BLACS_ABORT( ICTXT , 1 )
078 RETURN
079 ELSE IF( LQUERY ) THEN
079
080 RETURN
081 END IF
082
083 * Quick return if possible
084
085 IF( M.LE.0 )
085
086 $ RETURN
087
088 CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
089 CALL PB_TOPGET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
090 CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , ' ' )
091 CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , 'I - ring' )
092
093 IF( K.LT.M ) THEN
094
095 * Initialise rows ia : ia + m - k - 1 to rows of the unit matrix
096
096
097 CALL PZLASET ( 'All' , M - K , N - M , ZERO , ZERO , A , IA , JA , DESCA )
098 CALL PZLASET ( 'All' , M - K , M , ZERO , ONE , A , IA , JA + N - M , DESCA )
099
100 END IF
101
102 TAUI = ZERO
103 MP = NUMROC( IA + M - 1 , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) , NPROW )
104
105 DO 10 I = IA + M - K , IA + M - 1
106
107 * Apply H(i)' to A(ia : i , ja : ja + n - m + i - ia) from the right
108
108
109 CALL PZLACGV ( I - IA + N - M , A , I , JA , DESCA , DESCA( M_ ) )
110 CALL PZELSET( A , I , JA + N - M + I - IA , DESCA , ONE )
111 CALL PZLARFC ( 'Right' , I - IA , I - IA + N - M + 1 , A , I , JA , DESCA ,
112 $ DESCA( M_ ) , TAU , A , IA , JA , DESCA , WORK )
113 II = INDXG2L( I , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) , NPROW )
114 IAROW = INDXG2P( I , DESCA( MB_ ) , MYROW , DESCA( RSRC_ ) ,
115 $ NPROW )
116 IF( MYROW.EQ.IAROW )
116
117 $ TAUI = TAU( MIN( II , MP ) )
118 CALL PZSCAL( I - IA + N - M , - TAUI , A , I , JA , DESCA , DESCA( M_ ) )
119 CALL PZLACGV ( I - IA + N - M , A , I , JA , DESCA , DESCA( M_ ) )
120 CALL PZELSET( A , I , JA + N - M + I - IA , DESCA , ONE - DCONJG( TAUI ) )
121
122 * Set A(i , ja + n - m + i - ia + 1 : ja + n - 1) to zero
123
124 CALL PZLASET ( 'All' , 1 , IA + M - 1 - I , ZERO , ZERO , A , I ,
125 $ JA + N - M + I - IA + 1 , DESCA )
126
127 10 CONTINUE
128
128
129 CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Rowwise' , ROWBTOP )
130 CALL PB_TOPSET( ICTXT , 'Broadcast' , 'Columnwise' , COLBTOP )
131
132 WORK( 1 ) = DCMPLX( DBLE( LWMIN ) )
133
134 RETURN
135
136 * End of PZUNGR2
137
138 END26
13
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Variables in Routine PZUNGR2()
| Summary Report |
| Data Type | Quantity | Size(byte) |
| CHARACTER | 2 | 2 |
| COMPLEX*16 | 3 | ? |
| INTEGER | 34 | 136 |
| LOGICAL | 1 | 1 |
| REAL | 1 | 4 |
| TOTAL | 41 | 143 |
List of Variables
CHARACTER
COMPLEX*16
INTEGER
| BLOCK_CYCLIC_2D | CSRC_ | CTXT_ | DLEN_ | DTYPE_ |
| I | IA | IACOL | IAROW | ICTXT |
| II | INDXG2L | INDXG2P | INFO | JA |
| K | LLD_ | LWMIN | LWORK | M |
| M_ | MB_ | MP | MPA0 | MYCOL |
| MYROW | N | N_ | NB_ | NPCOL |
| NPROW | NQA0 | NUMROC | RSRC_ | |
LOGICAL
REAL
Variables Dependence Graph Put the mouse over a right hand side variable to display the corresponding line of the dependence | | - | | - | - | | I | <--- | KDO 10 I = IA+M-K, IA+M-1, MDO 10 I = IA+M-K, IA+M-1, IADO 10 I = IA+M-K, IA+M-1 |
| IACOL | <--- | INDXG2PIACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),, JAIACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),, MYCOLIACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),, CSRC_IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),, NB_IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),, NPCOLIACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), |
| IAROW | <--- | INDXG2PIAROW = INDXG2P( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),{2IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),}, MB_IAROW = INDXG2P( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),{2IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),}, MYROWIAROW = INDXG2P( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),{2IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),}, NPROWIAROW = INDXG2P( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),{2IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),}, RSRC_IAROW = INDXG2P( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),{2IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),}, IIAROW = INDXG2P( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ),, IAIAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), |
| ICTXT | <--- | CTXT_ICTXT = DESCA( CTXT_ ) |
| II | <--- | INDXG2LII = INDXG2L( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), MB_II = INDXG2L( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), MYROWII = INDXG2L( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), NPROWII = INDXG2L( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), RSRC_II = INDXG2L( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), III = INDXG2L( I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ) |
| INFO | <--- | CTXT_INFO = -(700+CTXT_) |
| LWMIN | <--- | MPA0LWMIN = NQA0 + MAX( 1, MPA0 ), NQA0LWMIN = NQA0 + MAX( 1, MPA0 ) |
| MP | <--- | MMP = NUMROC( IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), MB_MP = NUMROC( IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), MYROWMP = NUMROC( IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), NPROWMP = NUMROC( IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), NUMROCMP = NUMROC( IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), RSRC_MP = NUMROC( IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ), IAMP = NUMROC( IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ) |
| MPA0 | <--- | IAROWMPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),, MMPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),, MB_MPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),, MYROWMPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),, NPROWMPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),, NUMROCMPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ),, IAMPA0 = NUMROC( M+MOD( IA-1, DESCA( MB_ ) ), DESCA( MB_ ), |
| NQA0 | <--- | JANQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),, MYCOLNQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),, NNQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),, NB_NQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),, NPCOLNQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),, NUMROCNQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ),, IACOLNQA0 = NUMROC( N+MOD( JA-1, DESCA( NB_ ) ), DESCA( NB_ ), |
| TAUI | <--- | ZEROTAUI = ZERO |
| WORK | <--- | LWMINWORK( 1 ) = DCMPLX( DBLE( LWMIN ) ){2WORK( 1 ) = DCMPLX( DBLE( LWMIN ) )} |
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Analysis elements of the routine PZUNGR2() Put the mouse over each element to display detailed matching information
Assigned variables |
| | | BLOCK_CYCLIC_2D , CSRC_ , CTXT_ , DLEN_ , DTYPE_ , I , IACOL , IAROW , ICTXT , II , INFO , LLD_ , LQUERY , LWMIN , M_ , MB_ , MP , MPA0 , N_ , NB_ , NQA0 , ONE , RSRC_ , TAUI , WORK , ZERO |
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Active variables |
| | | A , BLOCK_CYCLIC_2D , COLBTOP , CSRC_ , CTXT_ , DESCA , DLEN_ , DTYPE_ , I , IA , IACOL , IAROW , ICTXT , II , INDXG2L , INDXG2P , INFO , JA , K , LLD_ , LQUERY , LWMIN , LWORK , M , M_ , MB_ , MP , MPA0 , MYCOL , MYROW , N , N_ , NB_ , NPCOL , NPROW , NQA0 , NUMROC , ONE , ROWBTOP , RSRC_ , TAU , TAUI , WORK , ZERO |
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Accessed arrays [ array name : associated index ] |
| | A | : i,ja+n-m+i-ia+1:ja+n-1 , ia:i,ja:ja+n-m+i-ia |
| | DESCA | : CSRC_ , CTXT_ , M_ , M_ , M_ , M_ , MB_ , MB_ , MB_ , MB_ , MB_ , NB_ , NB_ , RSRC_ , RSRC_ , RSRC_ , RSRC_ |
| | INDXG2L | : I, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW |
| | NUMROC | : IA+M-1, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW |
| | TAU | : MIN( II, MP ) |
| | WORK | : 1 , 1 |
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Conditional statements [ statement : associated predicate ] |
| | do | : ( 10 I = IA + M - K , IA + M - 1 ) |
| | if | : ( NPROW.EQ. - 1 ) , ( INFO.EQ.0 ) , ( N.LT.M ) , ( K.LT.0 .OR. K.GT.M ) , ( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) , ( INFO.NE.0 ) , ( LQUERY ) , ( possible ) , ( M.LE.0 ) , ( K.LT.M ) , ( MYROW.EQ.IAROW ) |
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| List of variables | BLOCK_CYCLIC_2D COLBTOP CSRC_ CTXT_ DLEN_ DTYPE_ I
| IA IACOL IAROW ICTXT II INDXG2L INDXG2P INFO
| JA K LLD_ LQUERY LWMIN LWORK M M_
| MB_ MP MPA0 MYCOL MYROW N N_ NB_
| NPCOL NPROW NQA0 NUMROC ONE ROWBTOP RSRC_ TAUI
| WORK ZERO | | close
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BLOCK_CYCLIC_2D
COLBTOP
CSRC_
CTXT_
DLEN_
DTYPE_
I
IA
IACOL
IAROW
ICTXT
II
INDXG2L
INDXG2P
INFO
JA
K
LLD_
LQUERY
LWMIN
LWORK
M
M_
MB_
MP
MPA0
MYCOL
MYROW
N
N_
NB_
NPCOL
NPROW
NQA0
NUMROC
ONE
ROWBTOP
RSRC_
TAUI
WORK
ZERO
542#512#533
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