Bundle Min-Hashing for Logo Recognition - Semantic Scholar

Bundle Min-Hashing for Logo Recognition! !"#$%&'()*+#,-.'(%/&#,'0/#&1%,"' 2345*#6/%'7)*835&-'%&6'7)*83"#,'9/:/)&'0%+.';3-:+3,-'
Contributions! 2)5=%5)&F'V+W#I"G0)-)'I4%::/XI%5)&'+>',#",/#=%4' !  Y/#46:'%&'/&:"%&I#D+%:#6'I4%::/X#,' !  (#",/#=%4'I%&'#%:/4>':I%4#'H/"1'4%,-#'&3*+#,')$'I4%::#:' !  VZ#&'$#H'",%/&/&-'/*%-#:'%=%/4%+4#' '

Bundle Min-Hashing Query / Test Image

Visual Words

Image Description

Querying

1P-WGC-RANSAC Re-ranking

Synthetic Query Expansion Index of Reference Images

Synthetic Database Augmentation

k-nn Classification

Spatial Re-Ranking!

Fast Spatial Re-ranking! [#)*#",/I'=#,/XI%5)&')$',#",/#=%4',#:34":'/*8,)=#'/*%-#':#%,I1' 7)&=#&5)&%4'(;\!;7'1%:':8##6'%&6',)+3:"&#::'/::3#:' 23I1'+#E#,F'ND8)/&"D+%:#6'(;\!;7']^1/4+/&Q_`' !  S#"#,*/&/:5IF'%44'$#%"3,#'I),,#:8)&6#&I#:'>/#46'%'1>8)"1#:/:')&I#' !  2),#',)+3:"F',#a3/,#:'$#H#,'I),,#:8)&6#&I#:.'' *)6#4'/:'I)&:",%/'")':/*/4%,/">G%b&#'",%&:$),*:' !  K&/5%44>'#:5*%"#6'",%&:$),*%5)&:'%,#',#X'+>'#:5*%5&-'$344>' 8,)W#I5=#'",%&:$),*%5)&'%:'0)I%4'V85*/c%5)&'L0VM':"#8'' L#C-C'+>'0#%:"D2#6/%&DV$D!a3%,#:M')&'/&4/#,'I),,#:8)&6#&I#:' ]^1/4+/&Q_`'^1/4+/&.'dC.'713*.'VC.'K:%,6.'2C.'!/=/I.'dC.'e/::#,*%&.';C'' !"#$%&'($&()$*+,'-)&.',+(/$'*0%+"1,+()$2'+34'5+2&'26+7+,'8+&%.)3/''L79^('PQQ_M'

Projective Transformations Need Checking! f:5*%"#6'8,)W#I5=#'",%&:$),*%5)&:'*3:"'+#'I1#IB#6'$),':%&/">' ;'",%&:$),*%5)&'#:5*%"#6'$,)*'%':/&-4#'$#%"3,#'I),,#:8)&6#&I#'/:' I)&:",%/'")'4#::'6#-,##:D)$D$,##6)*'"1%&'%'8,)W#I5=#'",%&:$),*%5)&' gh'8,#=#&":'6#-#&#,%"#6',#:34":C' '

1-Point RANSAC followed by LO! ^,)W#I5=#',#D#:5*%5)&')$'/&/5%4'",%&:$),*%5)&'6)#:'&)"'/*8,)=#',#D,%&B/&-C' \)'%66/5)&%4'$%4:#'$#%"3,#'I),,#:8)&6#&I#:'I%&'+#'#4/*/&%"#6C' T)8'NQ'#:5*%"#6'",%&:$),*%5)&'1>8)"1#:#:'8,)W#I"#6'/&")'I%&6/6%"#'/*%-#'

Query image

RANSAC with LO step

RANSAC without LO step

1-Point RANSAC followed by LO! ^,)W#I5=#',#D#:5*%5)&')$'/&/5%4'",%&:$),*%5)&'6)#:'&)"'/*8,)=#',#D,%&B/&-C' \)'%66/5)&%4'$%4:#'$#%"3,#'I),,#:8)&6#&I#:'I%&'+#'#4/*/&%"#6C' T)8'NQ'#:5*%"#6'",%&:$),*%5)&'1>8)"1#:#:'8,)W#I"#6'/&")'I%&6/6%"#'/*%-#'

Query image

RANSAC with LO step

RANSAC without LO step

1P-WGC-RANSAC! V3,'%88,)%I1F'' ND8)/&"D+%:#6'(;\!;7'/&I),8),%5&-'H#%B'-#)*#",/I'I)&:/:"#&I>'Li[7M' !  j'6#-,##:D)$D$,##6)*'L",%&:4%5)&.':I%4/&-.',)"%5)&M' !  ^,)W#I5=#',#X&#*#&"')$'")8'1>8)"1#:#:'I%&'+#')*/E#6'L)85)&%4M' !  i[7DI)&:",%/&"':8##6:'38'1>8)"1#:/:'#=%43%5)&F' K$'%'$#%"3,#'I),,#:8)&6#&I#'/:'&)"'i[7DI)&:/:"#&"'H/"1',#:8#I"'")'I3,,#&"' #:5*%5)&')$'",%&:4%5)&.':I%4#'%&6',)"%5)&F' gh'S/,#I"4>'",#%"#6'%:')3"4/#,C';=)/6:'I)*83"%5)&')$'I):"4>'#,,),'$3&I5)&C'

1P-WGC-RANSAC Experiments! Vm$),6no'6%"%:#".'!KJT'$#%"3,#:.':/*/4%,',#:34":')&'J4/IB,0)-):DRP' Method [Philbin07], bow [Philbin07] bow+SP bow, tf-idf 1p-ransac, incl. lo 1p-ransac, no lo 1p-wgc-ransac, incl. lo 1p-wgc-ransac, no lo [Philbin07], bow [Philbin07], bow+SP [Arandjelovic12], bow [Arandjelovic12], bow+SP bow, tf-idf 1p-ransac, incl. lo 1p-ransac, no lo 1p-wgc-ransac, incl. lo 1p-wgc-ransac, no lo

Voc 100K 100K 100K 100K 100K 100K 100K 1M 1M 1M 1M 1M 1M 1M 1M 1M

mAP Time 0.535 − 0.597 − 0.571 − 0.678 160s 0.680 72s 0.693 115s 0.692 53s 0.618 − 0.645 − 0.636 − 0.672 − 0.647 − 0.712 54s 0.711 15s 0.704 50s 0.703 12s

NM'V3"8#,$),*:']^1/4+/&Q_`'%&6' ];,%&6W#4)=/INP`'

]^1/4+/&Q_`'^1/4+/&.'dC.'713*.'VC.'K:%,6.'2C.'!/=/I.'dC.'e/::#,*%&.';C.'!"#$%&'($&()$*+,'-)&.',+(/$'*0%+"1,+()$2'+34'5+2&'26+7+,'8+&%.)3/'L79^(kQ_M' ];,%&6W#4)=/INP`';,%&6W#4)=/I.'(C.'e/::#,*%&.';C.'!"#$$%&"'()*%$+$#,-($%*"-./0%1(-2%&-%'34#-+$%-56$7&%#$&#'$+8/.'L79^(lNPM'

1P-WGC-RANSAC Experiments! Vm$),6no'6%"%:#".'!KJT'$#%"3,#:.':/*/4%,',#:34":')&'J4/IB,0)-):DRP' Method [Philbin07], bow [Philbin07] bow+SP bow, tf-idf 1p-ransac, incl. lo 1p-ransac, no lo 1p-wgc-ransac, incl. lo 1p-wgc-ransac, no lo [Philbin07], bow [Philbin07], bow+SP [Arandjelovic12], bow [Arandjelovic12], bow+SP bow, tf-idf 1p-ransac, incl. lo 1p-ransac, no lo 1p-wgc-ransac, incl. lo 1p-wgc-ransac, no lo

Voc 100K 100K 100K 100K 100K 100K 100K 1M 1M 1M 1M 1M 1M 1M 1M 1M

mAP Time 0.535 − 0.597 − 0.571 − 0.678 160s 0.680 72s 0.693 115s 0.692 53s 0.618 − 0.645 − 0.636 − 0.672 − 0.647 − 0.712 54s 0.711 15s 0.704 50s 0.703 12s

NM'V3"8#,$),*:']^1/4+/&Q_`'%&6' ];,%&6W#4)=/INP`' PM'S,)88/&-'0V',#X&#*#&"'6)#:'&)"' %p#I"'8#,$),*%&I#'L*;^M'+3"'>/#46:' *%W),':8##638'

]^1/4+/&Q_`'^1/4+/&.'dC.'713*.'VC.'K:%,6.'2C.'!/=/I.'dC.'e/::#,*%&.';C.'!"#$%&'($&()$*+,'-)&.',+(/$'*0%+"1,+()$2'+34'5+2&'26+7+,'8+&%.)3/'L79^(kQ_M' ];,%&6W#4)=/INP`';,%&6W#4)=/I.'(C.'e/::#,*%&.';C.'!"#$$%&"'()*%$+$#,-($%*"-./0%1(-2%&-%'34#-+$%-56$7&%#$&#'$+8/.'L79^(lNPM'

1P-WGC-RANSAC Experiments! Vm$),6no'6%"%:#".'!KJT'$#%"3,#:.':/*/4%,',#:34":')&'J4/IB,0)-):DRP' Method [Philbin07], bow [Philbin07] bow+SP bow, tf-idf 1p-ransac, incl. lo 1p-ransac, no lo 1p-wgc-ransac, incl. lo 1p-wgc-ransac, no lo [Philbin07], bow [Philbin07], bow+SP [Arandjelovic12], bow [Arandjelovic12], bow+SP bow, tf-idf 1p-ransac, incl. lo 1p-ransac, no lo 1p-wgc-ransac, incl. lo 1p-wgc-ransac, no lo

Voc 100K 100K 100K 100K 100K 100K 100K 1M 1M 1M 1M 1M 1M 1M 1M 1M

mAP Time 0.535 − 0.597 − 0.571 − 0.678 160s 0.680 72s 0.693 115s 0.692 53s 0.618 − 0.645 − 0.636 − 0.672 − 0.647 − 0.712 54s 0.711 15s 0.704 50s 0.703 12s

NM'V3"8#,$),*:']^1/4+/&Q_`'%&6' ];,%&6W#4)=/INP`' PM'S,)88/&-'0V',#X&#*#&"'6)#:'&)"' %p#I"'8#,$),*%&I#'L*;^M'+3"'>/#46:' *%W),':8##638' RM'i[7'I)&:",%/&"')Z#&'>/#46:' :4/-1"4>'+#E#,'8#,$),*%&I#'%&6'/:' $%:"#,' '

]^1/4+/&Q_`'^1/4+/&.'dC.'713*.'VC.'K:%,6.'2C.'!/=/I.'dC.'e/::#,*%&.';C.'!"#$%&'($&()$*+,'-)&.',+(/$'*0%+"1,+()$2'+34'5+2&'26+7+,'8+&%.)3/'L79^(kQ_M' ];,%&6W#4)=/INP`';,%&6W#4)=/I.'(C.'e/::#,*%&.';C.'!"#$$%&"'()*%$+$#,-($%*"-./0%1(-2%&-%'34#-+$%-56$7&%#$&#'$+8/.'L79^(lNPM'

1P-WGC-RANSAC Experiments! Vm$),6no'6%"%:#".'!KJT'$#%"3,#:.':/*/4%,',#:34":')&'J4/IB,0)-):DRP' Method [Philbin07], bow [Philbin07] bow+SP bow, tf-idf 1p-ransac, incl. lo 1p-ransac, no lo 1p-wgc-ransac, incl. lo 1p-wgc-ransac, no lo [Philbin07], bow [Philbin07], bow+SP [Arandjelovic12], bow [Arandjelovic12], bow+SP bow, tf-idf 1p-ransac, incl. lo 1p-ransac, no lo 1p-wgc-ransac, incl. lo 1p-wgc-ransac, no lo

Voc 100K 100K 100K 100K 100K 100K 100K 1M 1M 1M 1M 1M 1M 1M 1M 1M

mAP Time 0.535 − 0.597 − 0.571 − 0.678 160s 0.680 72s 0.693 115s 0.692 53s 0.618 − 0.645 − 0.636 − 0.672 − 0.647 − 0.712 54s 0.711 15s 0.704 50s 0.703 12s

NM'V3"8#,$),*:']^1/4+/&Q_`'%&6' ];,%&6W#4)=/INP`' PM'S,)88/&-'0V',#X&#*#&"'6)#:'&)"' %p#I"'8#,$),*%&I#'L*;^M'+3"'>/#46:' *%W),':8##638' RM'i[7'I)&:",%/&"')Z#&'>/#46:' :4/-1"4>'+#E#,'8#,$),*%&I#'%&6'/:' $%:"#,' jM'(#%4D5*#'8#,$),*%&I#F' h'jQQ'/*%-#:G:.'q'PCn'*:G/*%-#' L:/&-4#D"1,#%6'8#,$),*%&I#'/&I4C'KGVM'

]^1/4+/&Q_`'^1/4+/&.'dC.'713*.'VC.'K:%,6.'2C.'!/=/I.'dC.'e/::#,*%&.';C.'!"#$%&'($&()$*+,'-)&.',+(/$'*0%+"1,+()$2'+34'5+2&'26+7+,'8+&%.)3/'L79^(kQ_M' ];,%&6W#4)=/INP`';,%&6W#4)=/I.'(C.'e/::#,*%&.';C.'!"#$$%&"'()*%$+$#,-($%*"-./0%1(-2%&-%'34#-+$%-56$7&%#$&#'$+8/.'L79^(lNPM'

Boosting Recall by Warping!

Boosting Recall by Warping! K&$#,'%,5XI/%4'=%,/%5)&:'$,)*':/&-4#'/*%-#F' [#&#,%"#'%b&#'",%&:$),*#6'=#,:/)&:')$'"1#'),/-/&%4'/*%-#'LrH%,8/&-sM'

Synthetic Query Expansion! 'SynQE warped versions ' query image ' ' ' '

multiple queries

image database

merging results

warped versions

' '#m8%&:/)&'!>&tf'%4:)'H),B:'/$'"1#'")8D*):"',#",/#=#6' /*%-#:'H#,#'&)"',#",/#=#6'I),,#I"4>C'

Synthetic Database Augmentation! 'SynAUG query image

' '

single query

image database

' ' ' R,6'I%:#F'u)"1'!>&tf'v'!>&;'+>'!>&tf'%&6'!>&;'' +%-D)$DH),6:'*)6#4' ' K*84/I%5)&:')$'=/:3%4'=)I%+34%,>':/c#F' !  7)&",)4:':",/I"&#::')$'=/:3%4'6#:I,/85)&' !  7)&",)4:'"1#'&3*+#,')$'/*%-#:',#"3,'8#,'a3#,>'H),6'' Lg',#:8)&:#',%5)M' ' VZ#&'=)I%+34%,>')$'N'*/44/)&'=/:3%4'H),6:'/:'3:#6F' u%-D)$DH),6:':544',#"3,&:'+#"H##&'_QDwnx')$'"1#'6%"%+%:#y']T),,#:%&/Qw`'' (#:345&-'/::3#:F':I%4%+/4/">'%&6':8##6' ]T),,#:%&/Qw`'T),,#:%&/.'0C.'!c3**#,.'2C.'z'J/"c-/++)&.';!""" 9$+(3)3/':1$(;D:#&:/5=#'1%:1/&-'"#I1&/a3#' !  ;44)H:'%88,)m/*%"#':/*/4%,/">':#%,I1')$':8%,:#':#":'

;&'/*%-#'/:'*)6#4#6'%:':#"')$'=/:3%4'H),6')II3,,#&I#:F' ' I = {v0 , ..., vl−1 } !/*/4%,/">')$'/*%-#:'*)6#4#6'%:')=#,4%8'+#"H##&':#":')$'=/:3%4'H),6:' 'D'B&)H&'%:'d%II%,6':/*/4%,/">F' |I1 ∩ I2 | ovr(I , I ) = 1 2 ' |I1 ∪ I2 |

0/&#%,':I%&')=#,'6%"%+%:#'")'I)*83"#'''''''''''''''''''''''/&$#%:/+4#y' ovr(I1 , I2 ) gh'2/&D{%:1'%88,)m/*%"#:'"1/:':/*/4%,/">'+3"'%44)H:':3+D4/&#%,':#%,I1' '

Min-Hash: Definition! ;&'/*%-#'/:'*)6#4#6'%:':#"')$'=/:3%4'H),6')II3,,#&I#:F' I = {v0 , ..., vl−1 } ' vi {%:1'$3&I5)&'''''''''''''%::/-&:'''''''%'1%:1'=%43#' h(vi ) D'S,%H&'6#"#,*/&/:5I%44>'$,)*'3&/$),*',%&6)*'6/:",/+35)&'

' T1#'*/&D1%:1'/:'6#X'%:''mh(I) = argmin h(vi ) '

vi ∈I

^,)+%+/4/">')$')+"%/&/&-'/6#&5I%4'*/&D1%:1'$),'"H)'6/p#,#&"':#":F' P (mh(I1 ) = mh(I2 )) = ovr(I1 , I2 ) =

|I1 ∩ I2 | |I1 ∪ I2 |

Min-Hash: Example! ' '

} }

I1 = I2 =

[/=#&'"H)'/*%-#:'

2 1

, ,

5 2

, ,

7 4

, ,

9 9

,

14

}

}

ovr(I1 , I2 ) = |I1 ∩ I2 | 2 = |I1 ∪ I2 | 7

9/:3%4'H),6:'I)&:/6#,#6'H1#&'I)*835&-'"1#'*/&D1%:1'+>' argmin h(vi )

}

' '

1

,

2

,

4

,

5

,

7

,

9

,

14

} = |I1 ∪ I2 |

\3*+#,')$'=/:3%4'H),6:'%88#%,/&-'/&'+)"1'/*%-#:'g''|I1

2/&D1%:1'%::/-&:'#%I1'%'=/:3%4'H),6'%'1%:1'=%43#C' T1#&'"1#'H),6'H/"1'"1#':*%44#:"'1%:1'=%43#'/:':#4#I"#6C'

vi ∈I

∩ I2 |

71%&I#')$'6,%H/&-'%'*/&D1%:1'"1%"'/:'%'' |I ∩ I | 1 2 =/:3%4'H),6'%88#%,/&-'/&'+)"1'/*%-#:'g' '''''''''''g'#a3%4'")')=#,4%8'

|I1 ∪ I2 |

Min-Hash: Sketches! ;'*/&D{%:1'/:'%'=/:3%4'H),6'|'%':/&-4#'*/&D1%:1'/:'&)"'*),#'6/:5&I5=#' "1%&'%':/&-4#'=/:3%4'H),6' NC  K&I,#%:#'6/:I,/*/&%5=#&#::F'-,)38'*34584#'*/&D1%:1#:'/&")'' #D"384#:'I%44#6''}$#%&'(%$rF' (mh1 , . . . , mhk ) gh'S,%:5I%44>'/&I,#%:#:'8,#I/:/)&.'+3"',#I%44':3p#,:' PC  K&I,#%:#',#I%44F',#8#%"'8,)I#::')'5*#:'%&6'I)*83"#')':B#"I1#:C'' '$),'%':B#"I1'I)44/:/)&')$')':B#"I1#:')$':/c#'#F'

P (collision) = 1 − (1 − ovr(I1 , I2 )k )n

Min-Hash: Indexing & Search! 7

,

2

i-th sketch

(

7

,

14

K&6#m/&-F' NC  f%I1':B#"I1'/:'/&:#,"#6'/&")'%'1%:1'"%+4#'+>' 1%:1/&-'"1#'#D"384#'/":#4$'/&")'1%:1'B#>:C' PC  T1#'*D"1':B#"I1'/:'/&:#,"#6'/&")'"1#'*D"1'1%:1'"%+4#' !#%,I1F'

1st hash table

NC  2/&D1%:1#:'%&6':B#"I1#:'%,#'I)*83"#6'H/"1'"1#' :%*#'1%:1'$3&I5)&:'%:'$),'/&6#m/&-'

•  K$':B#"I1'/:'I)&"%/'/&'1%:1'"%+4#'LrI)44/:/)&sM' "1#&':/*/4%,/">')$'/*%-#:'/:'h'Q' •  (#",/#=#'%::)I/%"#6'/*%-#:'

i-th hash table

7

PC  t3#,>'*D"1'1%:1'"%+4#'/$'/"'I)&"%/&:'*D"1'a3#,>' :B#"I1' 7

2

(

(

(

1st sketch

14

From Min-Hashing to Bundle Min-hashing! V+:#,=%5)&'NF' (#-34%,'2/&D{%:1F'!B#"I1#:')$':/c#'P'8#,$),*'*3I1'+#E#,'"1%&')$':/c#'R' r!/*/4%,s'/*%-#:.'#C-C':1)H/&-':%*#')+W#I"'3:3%44>'1%=#')=#,4%8'I4):#'")' QC'L(#8),"#6'QCQNw'/&']0##NQ`M'

K*8),"%&"'8%,"'

P (collision) = 1 − (1 − ovr(I1 , I2 )k )n

Bundle Min-hashing! central visual word

bundling

9

min-hashing

7 2

14

set of neighbors

}

7

2

,

9

,

14

}

?

K6#%F'T1#':8%5%4'&#/-1+),:')$'I#&",%4'$#%"3,#:'%,#'%--,#-%"#6'/&")'+3&64#:C'' f%I1'+3&64#'/:'%'r*/I,)D+%-D)$DH),6:sC' T1#'+3&64#:'%,#'/&6#m#6'+>',#-34%,'*/&D1%:1/&-'

From Min-Hashing to Bundle Min-hashing!

'

u3&64#'2/&D{%:1F'

}

2/&D{%:1F'

2

2

,

7

,

9

,

14

}

'V&#':#"')$'=/:3%4'H),6:'8#,'/*%-#' 'V&#':#"')$'=/:3%4'H),6:'8#,'I#&",%4'$#%"3,#'

!  K&I,#%:#:')=#,4%8'' !  r*/I,)D+%-D)$DH),6:s' !  T1#'+3&64#:'/C#C'"1#':#":'%,#'/&6#m#6'+>',#-34%,'*/&D1%:1/&-'

(

2

,

9

(

14

,

7

(

7

sketches

(

bundling

9

14

central min-hashing visual word + set of neighbors

From Min-Hashing to Bundle Min-hashing! V+:#,=%5)&'PF'7)*+/&/&-'=/:3%4'H),6'4%+#4')$'I#&",%4'$#%"3,#'H/"1':/&-4#' */&D1%:1'$,)*'&#/-1+),1))6'H),B:'#=#&'+#E#,'

K*8),"%&"'8%,"'

P (collision) = 1 − (1 − ovr(I1 , I2 )k )n

Bundle Min-hashing! 9

min-hashing

7 2

14

2

,

9

,

14

}

!B#"I1#:')$':/c#'PF' !  J/,:"':B#"I1'I)*8)&#&"F' !  !#I)&6':B#"I1'I)*8)&#&"F'

(

7

,

2

(

7

,

14

set of neighbors

}

7

sketches

(

bundling

(

central visual word

'9/:3%4'H),6'4%+#4')$'"1#'I#&",%4'$#%"3,#' '9/:3%4'H),6'6,%H&'+>'*/&D1%:1'

Bundling Strategy: Radius + Scale band! u3&64#'6#:I,/+#:'/*%-#',#-/)&'6#8#&6#&"')&4>')&'I#&",%4'$#%"3,#' Location of central feature

Bundle radius

smax

scale of central feature s min

fbI/#&"':#%,I1'$),':8%5%4'&#/-1+),:'+>'3:#')$'%'BD6'",##'

Bundle Min-Hashing! K&6#m/&-F' !  S#"#,*/&#'I#&",%4'$#%"3,#'%&6'/":':8%5%4'&#/-1+),:' !  7)*83"#'*/&D1%:1#:'$),':8%5%4'&#/-1+),:' !  u3/46':B#"I1#:'$,)*'=/:3%4'H),6')$'I#&",%4'$#%"3,#'v':/&-4#'*/&D1%:1' !  !"),#':B#"I1#:'/&'1%:1'"%+4#:' ' t3#,>F' !  t3#,>'1%:1'"%+4#:'$),'/*%-#:'H/"1':%*#':B#"I1#:'%:'a3#,>'/*%-#' !  (#D,%&B',#:34"'4/:"'+>'I):/&#':/*/4%,/">'+#"H##&'$344'+%-D)$DH),6:'1/:")-,%*:C' K&I,#%:#:'"1#'8#,$),*%&I#.'+#E#,'"1%&',%&B/&-'+>':B#"I1'I)44/:/)&'I)3&"''

Bundle Min-Hashing vs. Bag-of-Words! fm8#,/*#&":')&'J4/IB,0)-):DRP.':/*/4%,',#:34":')&'Vm$),6'%&6''I)&:3*85)&' jM  ^,#I/:/)&D*#*),>'",%6#D)p'I%&'+#'%6W3:"#6'#.-C'+>'&3*+#,')$':B#"I1#:'

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