An alternative to field-normalization in the aggregation of

Wo
r
k
in
gP
ap
e
r
E
conom
i
cS
e
r
i
e
s1
4–2
5
Ap
r
i
l2
0
1
5
I
S
SN2
3
4
0
5
0
3
1
D
ep
a
r
t
am
en
tod
eE
conom
í
a
Un
i
v
e
r
s
id
adC
a
r
lo
sI
I
Id
eM
ad
r
id
C/ M
ad
r
id
,1
2
6
,2
8
9
0
3G
e
t
a
f
e(
Sp
a
in
)
F
a
x(
3
4
)9
1
6
2
4
9
8
7
5
“ANALTERNAT
IVETOF
IELD
-NORMAL
IZAT
IONINTHEAGGREGAT
ION OF
HETEROGENEOUSSC
IENT
IF
ICF
IELDS
”
b
An
ton
ioP
e
r
i
an
e
s
-Rod
r
i
g
u
e
za andJ
a
v
i
e
rR
u
i
z
-C
a
s
t
i
l
lo
a
D
ep
a
r
t
am
en
tod
eB
ib
l
io
t
e
conom
í
ayDo
c
um
en
t
a
c
ión
,Un
i
v
e
r
s
id
adC
a
r
lo
sI
I
I
,SC
Im
a
goR
e
s
e
a
r
ch
G
ro
up
b
D
ep
a
r
t
am
en
tod
eE
conom
í
a
,Un
i
v
e
r
s
id
adC
a
r
lo
sI
I
I
Ab
s
t
r
a
c
t.Apo
s
s
ib
l
eso
l
u
t
iontoth
ep
rob
l
emo
fa
g
g
r
e
g
a
t
in
gh
e
t
e
ro
g
en
eo
u
sf
i
e
ld
sinth
ea
l
l
s
c
i
en
c
e
s
c
a
s
er
e
l
i
e
sonth
eno
rm
a
l
i
z
a
t
iono
fth
er
awc
i
t
a
t
ion
sr
e
c
e
i
v
e
db
ya
l
lp
ub
l
i
c
a
t
ion
s
.Inth
i
sp
ap
e
r
,w
e
s
t
ud
yana
l
t
e
rn
a
t
i
v
eso
l
u
t
ionth
a
tdo
e
sno
tr
e
q
u
i
r
ean
yc
i
t
a
t
ionno
rm
a
l
i
z
a
t
i
on
.Pro
v
id
e
don
eu
s
e
ss
i
z
e
ands
c
a
l
e
ind
ep
end
en
tind
i
c
a
to
r
s
,th
ec
i
t
a
t
ionimp
a
c
to
fan
yr
e
s
e
a
r
chun
i
tc
anb
ec
a
l
c
u
l
a
t
e
da
sth
e
a
v
e
r
a
g
e(w
e
i
gh
t
e
db
yth
ep
ub
l
i
c
a
t
iono
u
tp
u
t
)o
fth
ec
i
t
a
t
ionimp
a
c
tth
a
tth
eun
i
ta
ch
i
e
v
e
sina
l
lf
i
e
ld
s
.
Th
etwoa
l
t
e
rn
a
t
i
v
e
sa
r
eco
n
f
ron
t
e
d wh
enth
er
e
s
e
a
r
cho
u
tp
u
to
fth
e5
0
0un
i
v
e
r
s
i
t
i
e
sinth
e2
0
1
3
e
d
i
t
iono
fth
e CWT
SL
e
id
en R
an
k
in
gi
se
v
a
l
u
a
t
e
du
s
in
gtwoc
i
t
a
t
ionimp
a
c
tind
i
c
a
to
r
sw
i
thv
e
r
y
d
i
f
f
e
r
en
tp
rop
e
r
t
i
e
s
.W
eu
s
ea
l
a
r
g
eW
ebo
fS
c
i
en
c
ed
a
t
a
s
e
tcon
s
i
s
t
in
go
f3
.
6m
i
l
l
iona
r
t
i
c
l
e
sp
ub
l
i
sh
e
d
inth
e2
0
0
5
2
0
0
8p
e
r
iod
,andac
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
emd
i
s
t
in
g
u
i
sh
in
gb
e
tw
e
en5
,
1
1
9c
l
u
s
t
e
r
s
.Th
em
a
in
twof
ind
in
g
sa
r
ea
sfo
l
low
s
.F
i
r
s
t
l
y
,d
i
f
f
e
r
en
c
e
sinp
rod
u
c
t
ionandc
i
t
a
t
ionp
r
a
c
t
i
c
e
sb
e
tw
e
enth
e3
,
3
3
2
c
l
u
s
t
e
r
sw
i
th mo
r
eth
an2
5
0p
ub
l
i
c
a
t
ion
sa
c
co
un
tfo
r2
2
.
5%o
fth
eo
v
e
r
a
l
lc
i
t
a
t
ionin
e
q
u
a
l
i
t
y
.A
f
t
e
r
th
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
ewh
e
r
ec
l
u
s
t
e
rm
e
anc
i
t
a
t
ion
sa
r
eu
s
e
da
sno
rm
a
l
i
z
a
t
ion
f
a
c
to
r
s
,th
i
sf
i
g
u
r
ei
sr
e
d
u
c
e
dto4
.
3%
.S
e
cond
l
y
,th
ed
i
f
f
e
r
en
c
e
sb
e
tw
e
enth
eun
i
v
e
r
s
i
t
yr
an
k
in
g
s
a
c
co
rd
in
gtoth
etwoso
l
u
t
ion
sfo
rth
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
ema
r
eo
fasm
a
l
lo
rd
e
ro
f
m
a
gn
i
t
ud
efo
rbo
thc
i
t
a
t
ion
imp
a
c
t
ind
i
c
a
to
r
s
.
A
cknow
l
edg
em
en
t
s.
Th
i
s
i
sth
eth
i
rdv
e
r
s
iono
fap
ap
e
rw
i
thth
es
am
et
i
t
l
ep
ub
l
i
sh
e
d
inth
i
ss
e
r
i
e
s
in
D
e
c
emb
e
r,2
0
1
4
,andF
eb
r
u
a
r
y
,2
0
1
5
.Th
i
sr
e
s
e
a
r
chp
ro
j
e
c
tb
u
i
ld
sone
a
r
l
i
e
rwo
r
ks
t
a
r
t
e
db
yJ
a
v
i
e
r
R
u
i
z
-C
a
s
t
i
l
lod
u
r
in
gar
e
s
e
a
r
chv
i
s
i
ttoth
eC
en
t
r
efo
rS
c
i
en
c
eandT
e
chno
lo
g
yS
t
ud
i
e
s(CWT
S
)o
f
L
e
id
en Un
i
v
e
r
s
i
t
y
.Th
ea
u
tho
r
sg
r
a
t
e
f
u
l
l
ya
c
know
l
e
d
g
eCWT
Sfo
rth
eu
s
eo
fi
t
sd
a
t
a.R
u
i
z
-C
a
s
t
i
l
lo
a
c
know
l
e
d
g
e
sf
in
an
c
i
a
ls
uppo
r
tf
rom th
e Sp
an
i
sh MEC th
ro
u
gh g
r
an
t ECO
2
0
1
12
9
7
6
2
.
Con
v
e
r
s
a
t
ion
sw
i
th An
ton
io V
i
l
l
a
r
,P
e
d
ro A
lb
a
r
r
án
,andL
udo W
a
l
tm
ana
r
ed
e
ep
l
yapp
r
e
c
i
a
t
e
d
.A
l
l
r
em
a
in
in
gsho
r
t
com
in
g
sa
r
eth
ea
u
tho
r
s
’so
l
e
r
e
spo
n
s
ib
i
l
i
t
y
.
1
I
.INTRODUCT
ION
A
si
sw
e
l
lknown
,th
ecomp
a
r
i
sono
fth
ec
i
t
a
t
ionimp
a
c
to
fr
e
s
e
a
r
chun
i
t
si
sp
l
a
g
u
e
dw
i
th
ob
s
t
a
c
l
e
so
fa
l
lso
r
t
s
.Fo
ro
u
rp
u
rpo
s
e
sinth
i
sp
ap
e
r
,i
ti
su
s
e
f
u
ltod
i
s
t
in
g
u
i
shb
e
tw
e
enth
efo
l
low
in
g
th
r
e
eb
a
s
i
cd
i
f
f
i
c
u
l
t
i
e
s
.
(
i
)Howc
anw
ecomp
a
r
eth
ec
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
so
fr
e
s
e
a
r
chun
i
t
so
fd
i
f
f
e
r
en
t
s
i
z
e
se
v
eni
fth
e
ywo
r
kinth
es
am
ehomo
g
en
eo
u
ss
c
i
en
t
i
f
i
cf
i
e
ld
?Fo
re
x
amp
l
e
,howc
anw
ecomp
a
r
e
th
eo
u
tp
u
to
fth
el
a
r
g
eE
conom
i
c
sd
ep
a
r
tm
en
ta
tH
a
r
v
a
rdUn
i
v
e
r
s
i
t
yw
i
thth
eo
u
tp
u
to
fth
er
e
l
a
t
i
v
e
l
y
sm
a
l
lE
conom
i
c
sd
ep
a
r
tm
en
ta
tJohn
s Hop
k
in
s
? Th
en
e
x
ttwod
i
f
f
i
c
u
l
t
i
e
sh
a
v
etodo w
i
thth
e
h
e
t
e
ro
g
en
e
i
t
yo
fs
c
i
en
t
i
f
i
cf
i
e
ld
s
:th
ew
e
l
lknownd
i
f
f
e
r
en
c
e
sinp
rod
u
c
t
ionandc
i
t
a
t
ionp
r
a
c
t
i
c
e
s
m
a
k
e
si
timpo
s
s
ib
l
e tod
i
r
e
c
t
l
ycomp
a
r
eth
er
awc
i
t
a
t
ion
sr
e
c
e
i
v
e
db
ya
r
t
i
c
l
e
sb
e
lon
g
in
gtod
i
f
f
e
r
en
t
f
i
e
ld
s
.G
i
v
enac
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
em
,th
a
ti
s
,ar
u
l
efo
ra
s
s
i
gn
in
gan
ys
e
to
fa
r
t
i
c
l
e
stoan
umb
e
ro
f
s
c
i
en
t
i
f
i
cf
i
e
ld
s
,f
i
e
ldh
e
t
e
ro
g
en
e
i
t
yp
r
e
s
en
t
sth
efo
l
low
in
gc
l
a
s
s
i
ch
ind
r
an
c
e
sinth
ee
v
a
l
u
a
t
iono
f
r
e
s
e
a
r
chun
i
t
s
’p
e
r
fo
rm
an
c
e
.(
i
i
) Howc
an w
ecomp
a
r
eth
ec
i
t
a
t
ionimp
a
c
to
ftwor
e
s
e
a
r
chun
i
t
s
wo
r
k
in
gind
i
f
f
e
r
en
tf
i
e
ld
s
?Fo
re
x
amp
l
e
,howc
anw
ecomp
a
r
eth
ec
i
t
a
t
ionimp
a
c
to
fM
ITin O
r
g
an
i
c
Ch
em
i
s
t
r
yw
i
thth
ec
i
t
a
t
ion
imp
a
c
to
fO
x
fo
rdUn
i
v
e
r
s
i
t
y
inS
t
a
t
i
s
t
i
c
sandP
rob
ab
i
l
i
t
y
?F
in
a
l
l
y
,(
i
i
i
)how
c
anw
ecomp
a
r
eth
ec
i
t
a
t
ion
imp
a
c
to
ftwor
e
s
e
a
r
chun
i
t
st
a
k
in
g
in
toa
c
co
un
tth
e
i
ro
u
tp
u
t
ina
l
lf
i
e
ld
s
?
Fo
re
x
amp
l
e
,howc
anw
ecomp
a
r
eth
ec
i
t
a
t
ionimp
a
c
to
fM
ITand O
x
fo
rdUn
i
v
e
r
s
i
t
yinwh
a
tw
ec
a
l
l
th
ea
l
l
s
c
i
e
n
c
e
sc
a
s
e
?
A
si
sw
e
l
lknown
,th
eso
l
u
t
iontoth
ef
i
r
s
t twop
rob
l
em
sr
e
q
u
i
r
e
ss
i
z
e
-ands
c
a
l
e
ind
ep
end
en
t
c
i
t
a
t
ion
imp
a
c
t
ind
i
c
a
to
r
s
.
W
ew
i
l
lr
e
f
e
rto
ind
i
c
a
to
r
sw
i
thth
e
s
etwop
rop
e
r
t
i
e
sa
sa
dm
i
s
s
i
b
l
eind
i
c
a
to
r
s
.
G
i
v
enanadm
i
s
s
ib
l
e
ind
i
c
a
to
r
,
inth
i
sp
ap
e
rw
ea
r
econ
c
e
rn
e
dw
i
thth
etwot
yp
e
so
fso
l
u
t
ion
sth
a
tth
e
th
i
rdp
rob
l
emadm
i
t
s
.F
i
r
s
t
l
y
,th
ep
rob
l
emc
anb
eso
l
v
e
dintwos
t
ep
s
. On
ef
i
r
s
tu
s
e
ssom
eso
r
to
f
no
rm
a
l
i
z
a
t
ion p
ro
c
e
d
u
r
eto m
a
k
eth
ec
i
t
a
t
ion
so
fa
r
t
i
c
l
e
sina
l
lf
i
e
ld
sa
tl
e
a
s
tapp
ro
x
im
a
t
e
l
y
comp
a
r
ab
l
e
.Th
en
,on
eapp
l
i
e
sth
ec
i
t
a
t
ionind
i
c
a
to
rtoe
a
chun
i
t
’
sno
rm
a
l
i
z
e
dc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
.
S
e
cond
l
y
,con
s
id
e
rth
eT
op1
0%ind
i
c
a
to
ru
s
e
dinth
econ
s
t
r
u
c
t
iono
fth
ein
f
l
u
en
t
i
a
lL
e
id
enand
2
1
SC
Im
a
g
or
an
k
in
g
s
.
Inth
eL
e
id
enR
an
k
in
gth
i
sind
i
c
a
to
ri
sd
e
f
in
e
da
s“
T
h
ep
r
o
p
o
r
t
i
o
no
fp
u
b
l
i
c
a
t
i
o
n
so
fa
u
n
i
v
e
r
s
i
t
yt
h
a
t
,c
om
p
a
r
e
dw
i
t
ho
t
h
e
rs
im
i
l
a
rp
u
b
l
i
c
a
t
i
o
n
s
,b
e
l
o
n
gt
ot
h
et
o
p1
0%m
o
s
t
f
r
e
q
u
e
n
t
l
yc
i
t
e
d…P
u
b
l
i
c
a
t
i
o
n
sa
r
e
c
o
n
s
i
d
e
r
e
ds
im
i
l
a
ri
ft
h
e
yw
e
r
ep
u
b
l
i
s
h
e
di
nt
h
es
am
ef
i
e
l
da
n
dt
h
es
am
ep
u
b
l
i
c
a
t
i
o
na
n
di
ft
h
e
yh
a
v
et
h
es
am
ed
o
c
um
e
n
t
2
t
y
p
e
”(W
a
lm
ane
ta
l
.
,2
0
1
2
a
)
.
No
t
eth
a
tth
i
sw
a
yo
fcomp
u
t
in
gth
i
sp
a
r
t
i
c
u
l
a
rind
i
c
a
to
rinnth
ea
l
l
3
s
c
i
en
c
e
sc
a
s
edo
e
sno
tr
e
q
u
i
r
ean
yk
indo
fp
r
io
rc
i
t
a
t
ionno
rm
a
l
i
z
a
t
ion
.
Fo
ro
u
rp
u
rpo
s
e
s
,i
ti
su
s
e
f
u
l
tov
i
ewth
i
sp
ro
c
e
d
u
r
ea
sth
ea
v
e
r
a
g
e(w
e
i
gh
t
e
db
yth
ep
ub
l
i
c
a
t
iono
u
tp
u
t
)o
fth
eun
i
t
’
sT
op1
0%
p
e
r
fo
rm
an
c
eine
a
chf
i
e
ld
.W
eno
t
eth
a
tth
i
simpo
r
t
an
tp
r
e
c
e
d
en
tc
anb
ee
x
t
end
e
dtoa
n
yadm
i
s
s
ib
l
e
ind
i
c
a
to
r
.Th
u
s
,g
i
v
enac
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
emandanadm
i
s
s
ib
l
ec
i
t
a
t
ion
ind
i
c
a
to
r
,w
ec
ancomp
u
t
eth
e
c
i
t
a
t
ionimp
a
c
to
far
e
s
e
a
r
chun
i
tinth
ea
l
l
s
c
i
en
c
e
sc
a
s
ea
sth
eapp
rop
r
i
a
t
ew
e
i
gh
t
e
da
v
e
r
a
g
eo
fth
e
un
i
t
’
sc
i
t
a
t
ion
imp
a
c
t
ine
a
chf
i
e
ld
.Ind
ep
end
en
t
l
yo
fth
econ
c
ep
t
u
a
l
in
t
e
r
e
s
to
fth
i
sp
ropo
s
a
l
,w
em
u
s
t
comp
a
r
eth
econ
s
e
q
u
en
c
e
so
fadop
t
in
gi
tv
e
r
s
u
sth
e po
s
s
ib
i
l
i
t
yo
ffo
l
low
in
ga no
rm
a
l
i
z
a
t
ion
p
ro
c
e
d
u
r
e
.
In
t
u
i
t
i
v
e
l
y
,th
eb
e
t
t
e
rth
ep
e
r
fo
rm
an
c
eo
fth
e no
rm
a
l
i
z
a
t
ion p
ro
c
e
d
u
r
eine
l
im
in
a
t
in
gth
e
comp
a
r
ab
i
l
i
t
yd
i
f
f
i
c
u
l
t
i
e
sa
c
ro
s
sf
i
e
ld
s
,th
esm
a
l
l
e
rth
ed
i
f
f
e
r
en
c
e
sw
i
l
lb
eb
e
tw
e
enth
etwoapp
ro
a
ch
e
s
.
U
s
in
ga m
e
a
s
u
r
in
gf
r
am
ewo
r
kin
t
rod
u
c
e
dinC
r
e
spoe
ta
l
.(
2
0
1
3
)
,r
e
c
en
tr
e
s
e
a
r
chh
a
se
s
t
ab
l
i
sh
e
dth
a
t
d
i
f
f
e
r
en
tso
u
r
c
e(o
rc
i
t
in
g
s
id
e
)andt
a
r
g
e
t(o
rc
i
t
e
d
s
id
e
)no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e
sp
e
r
fo
rmq
u
i
t
ew
e
l
l
ine
l
im
in
a
t
in
g mo
s
to
fth
ee
f
f
e
c
tino
v
e
r
a
l
lc
i
t
a
t
ionin
e
q
u
a
l
i
t
yth
a
tc
anb
ea
t
t
r
ib
u
t
e
dtod
i
f
f
e
r
en
c
e
sin
p
rod
u
c
t
ionandc
i
t
a
t
ionp
r
a
c
t
i
c
e
sb
e
tw
e
enf
i
e
ld
s(W
a
l
tm
an&V
anE
c
k
,2
0
1
3
,C
r
e
spoe
ta
l
.
,2
0
1
3
,2
0
1
4
,
andL
ie
ta
l
.
,2
0
1
3
)
.
Th
e
r
e
fo
r
e,w
ee
xp
e
c
tth
a
tth
ed
i
f
f
e
r
en
c
e
sb
e
tw
e
enth
etwoapp
ro
a
ch
e
sfo
rso
l
v
in
g
th
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
em wo
u
ldb
eo
fasm
a
l
lo
rd
e
ro
fm
a
gn
i
t
ud
e
.How
e
v
e
r,th
i
si
san
1S
C
Im
a
goi
s
ar
e
s
e
a
r
chg
ro
upf
romth
eC
o
n
s
e
j
oS
u
p
er
i
o
rd
eI
n
v
e
s
t
i
g
a
c
i
o
n
e
sC
i
e
n
t
í
f
i
c
a
s
,Un
i
v
e
r
s
i
t
yo
fG
r
an
ad
a
,E
x
t
r
em
ad
u
r
a
,C
a
r
lo
s
I
I
I(M
ad
r
id
)and A
l
c
a
l
ád
eH
en
a
r
e
sinSp
a
in
.T
h
eSC
Im
a
g
oI
n
s
t
i
t
u
t
i
o
n
sR
a
nk
i
n
g
s(
S
IR
;www
.
s
c
im
a
go
i
r
.
com)i
sab
ib
l
iom
e
t
r
i
c
r
an
k
in
go
fr
e
s
e
a
r
ch
in
s
t
i
t
u
t
ion
sba
s
edonE
l
s
e
v
i
e
r
’
sS
cop
u
sd
a
t
ab
a
s
e
.
2As
im
i
l
a
rd
e
f
in
i
t
ioni
sapp
l
i
edinth
eSC
Im
a
gor
an
k
in
g(Bo
rnm
ann e
ta
l
.
,2
0
1
2
)
,a
sw
e
l
la
sinth
eInC
i
t
e
sso
f
tw
a
r
e(
s
e
e
‘p
e
r
c
en
t
i
l
eIs
ub
j
e
c
ta
r
e
a
inh
t
tp
://
i
n
c
i
t
e
s
.
i
s
i
know
l
ed
g
e
.
com/
common/h
e
lp/h_
g
lo
s
s
a
r
y
.h
t
lm
)
.
3N
a
t
u
r
a
l
l
y
,e
v
e
r
y
th
in
gth
a
tw
es
a
yfo
rth
ea
l
ls
c
i
en
c
e
sc
a
s
ec
anb
ee
q
u
a
l
l
yapp
l
i
eda
to
th
e
ra
g
g
r
e
g
a
t
ionl
e
v
e
l
s
,a
sinth
ec
a
s
e
o
fa
g
g
r
e
g
a
t
in
ga
r
t
i
c
l
e
sin O
r
g
an
i
cCh
em
i
s
t
r
y
,Ino
r
g
an
i
cCh
em
i
s
t
r
y
,Ch
em
i
c
a
lEn
g
in
e
e
r
in
g
,ando
th
e
rr
e
l
a
t
eds
ub
f
i
e
ld
sin
to
th
ed
i
s
c
ip
l
in
eo
fCh
em
i
s
t
r
y
.
3
emp
i
r
i
c
a
lq
u
e
s
t
ionth
a
th
a
sn
e
v
e
rb
e
enin
v
e
s
t
i
g
a
t
e
d
b
e
fo
r
e
. Tocon
f
ron
tth
i
sq
u
e
s
t
ion
,
inth
i
sp
ap
e
rw
e
cond
u
c
tth
efo
l
low
in
ge
x
e
r
c
i
s
e
.
•R
u
i
z
-C
a
s
t
i
l
lo& W
a
l
tm
an(
2
0
1
5
)app
l
yth
ep
ub
l
i
c
a
t
ion
l
e
v
e
la
l
go
r
i
thm
i
cm
e
thodo
lo
g
y
in
t
rod
u
c
e
d
b
yW
a
l
tm
an &V
anE
c
k(
2
0
1
2
)toa W
ebo
fS
c
i
en
c
e(Wo
Sh
e
r
e
a
f
t
e
r
)d
a
t
a
s
e
tcon
s
i
s
t
in
go
f9
.
4m
i
l
l
ion
p
ub
l
i
c
a
t
ion
sf
rom th
e2
0
0
3
2
0
1
2p
e
r
iod
. Th
i
si
s don
ea
lon
gas
e
q
u
en
c
eo
ftw
e
l
v
eind
ep
end
en
t
c
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
em
sine
a
cho
fwh
i
chth
es
am
es
e
to
fp
ub
l
i
c
a
t
ion
si
sa
s
s
i
gn
e
dtoanin
c
r
e
a
s
in
gn
umb
e
r
o
fc
l
u
s
t
e
r
s
.Inth
i
sp
ap
e
r
,w
eu
s
eth
ec
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
emr
e
comm
end
e
dinR
u
i
z
-C
a
s
t
i
l
lo & W
a
l
tm
an
(
2
0
1
5
)
,con
s
i
s
t
in
go
f5
,
1
1
9c
l
u
s
t
e
r
s
.Fo
rth
ee
v
a
l
u
a
t
iono
fr
e
s
e
a
r
chun
i
t
s
’c
i
t
a
t
ionimp
a
c
t
,w
efo
c
u
son
th
e3
.
6m
i
l
l
ionp
ub
l
i
c
a
t
ion
sinth
e2
0
0
5
2
0
0
8p
e
r
iod
,andth
ec
i
t
a
t
ion
sth
e
yr
e
c
e
i
v
ed
u
r
in
gaf
i
v
e
-y
e
a
r
c
i
t
a
t
ionw
indowfo
re
a
chy
e
a
r
inth
a
tp
e
r
iod
.
•O
u
rr
e
s
e
a
r
chun
i
t
sa
r
eth
e5
0
0un
i
v
e
r
s
i
t
i
e
sinth
e2
0
1
3e
d
i
t
iono
fth
eCWT
SL
e
id
enR
an
k
in
g
(W
a
l
tm
ane
ta
l
.
,2
0
1
2
a
)
.W
ean
a
l
y
z
eth
eapp
ro
x
im
a
t
e
l
y2
.
4m
i
l
l
iona
r
t
i
c
l
e
s–
abo
u
t6
7%o
fth
eto
t
a
l
–fo
r
wh
i
cha
t
l
e
a
s
ton
ea
u
tho
rb
e
lon
g
stoon
eo
fth
e
s
eun
i
v
e
r
s
i
t
i
es
.W
eu
s
eaf
r
a
c
t
ion
a
lco
un
t
in
gapp
ro
a
chto
so
l
v
eth
ep
rob
l
emo
fth
ea
s
s
i
gnm
en
to
fr
e
spon
s
ib
i
l
i
t
yfo
rp
ub
l
i
c
a
t
ion
sw
i
ths
e
v
e
r
a
lco
a
u
tho
r
swo
r
k
in
g
in d
i
f
f
e
r
en
tin
s
t
i
t
u
t
ion
s
. Th
eto
t
a
ln
umb
e
ro
fa
r
t
i
c
l
e
s co
r
r
e
spond
in
gtoth
e5
0
0 un
i
v
e
r
s
i
t
i
e
si
s
app
ro
x
im
a
t
e
l
y1
.
9m
i
l
l
iona
r
t
i
c
l
e
s–
abo
u
t5
0%o
fth
eto
t
a
l
.
• W
ee
v
a
l
u
a
t
eth
ec
i
t
a
t
ionimp
a
c
to
fe
a
chun
i
v
e
r
s
i
t
yu
s
in
gtwoadm
i
s
s
ib
l
eind
i
c
a
to
r
s
.F
i
r
s
t
l
y
,th
e
Top1
0%ind
i
c
a
to
ra
l
r
e
ad
ym
en
t
ion
e
d
.S
e
cond
l
y
,on
ech
a
r
a
c
t
e
r
i
s
t
i
co
fth
i
sind
i
c
a
to
ri
sth
a
ti
ti
sno
t
mono
ton
i
cinth
es
en
s
eth
a
ti
ti
sin
v
a
r
i
an
ttoan
yadd
i
t
ion
a
lc
i
t
a
t
ionth
a
tah
i
gh
imp
a
c
ta
r
t
i
c
l
em
i
gh
t
r
e
c
e
i
v
e
.Con
s
e
q
u
en
t
l
y
,w
eb
e
l
i
e
v
eth
a
t
i
t
i
s
in
t
e
r
e
s
t
in
gtou
s
eas
e
cond
ind
i
c
a
to
rpo
s
s
e
s
s
in
gth
i
sp
rop
e
r
t
y
.
In p
a
r
t
i
c
u
l
a
r
,w
es
e
l
e
c
ta m
emb
e
ro
fth
eFo
s
t
e
r
,G
r
e
e
r
,and Tho
rb
e
c
k
e(FGT h
e
r
e
a
f
t
e
r
)f
am
i
l
y
,
in
t
rod
u
c
e
dinA
lb
a
r
r
áne
ta
l
.(
2
0
1
1
a
)
.W
eapp
l
yth
i
sind
i
c
a
to
rtoth
es
e
tfo
rm
e
db
yth
e1
0%o
fth
e mo
s
t
h
i
gh
l
yc
i
t
e
dp
ub
l
i
c
a
t
ion
s
inth
ewo
r
ld
,r
e
f
e
r
r
e
dtoa
sth
es
e
to
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
s.
4
•L
ie
ta
l
.(
2
0
1
3
)ind
i
c
a
t
eth
a
tth
eb
e
s
ta
l
t
e
rn
a
t
i
v
eamon
ga w
id
es
e
to
ff
i
e
ld
-no
rm
a
l
i
z
a
t
ion
p
ro
c
e
d
u
r
e
si
sth
etwo
-p
a
r
am
e
t
e
rs
y
s
t
emd
e
v
e
lop
e
dinR
ad
i
c
c
i &C
a
s
t
e
l
l
ano(
2
0
1
2
)
.4 How
e
v
e
r
,d
i
f
f
e
r
en
t
r
e
s
u
l
t
sind
i
c
a
t
eth
a
tth
es
t
and
a
rd
,on
e
-p
a
r
am
e
t
e
rf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e
,in wh
i
chno
rm
a
l
i
z
e
d
c
i
t
a
t
ions
co
r
e
sine
v
e
r
yf
i
e
lda
r
ee
q
u
a
ltoth
eo
r
i
g
in
a
lr
awc
i
t
a
t
ion
sd
i
v
id
e
db
yth
ef
i
e
ld m
e
anc
i
t
a
t
ion
,
e
xh
ib
i
t
sagoodp
e
r
fo
rm
an
c
e(R
ad
i
c
ch
ie
ta
l
.
,2
0
0
8
,C
r
e
spoe
ta
l
.
,2
0
1
3
,2
0
1
4
,L
ie
ta
l
.
,2
0
1
3
,andR
u
i
z
C
a
s
t
i
l
lo
,2
0
1
4
)
.G
i
v
eni
t
ss
imp
l
i
c
i
t
yandgoodp
e
r
fo
rm
an
c
e
,inth
i
sp
ap
e
rw
eadop
tth
i
sp
ro
c
e
d
u
r
einth
e
so
l
u
t
iontoth
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
em
.
• Anind
i
c
a
to
ri
ss
a
idto b
eadd
i
t
i
v
e
l
yd
e
compo
s
ab
l
ei
f
,fo
ran
yp
a
r
t
i
t
ion o
fac
i
t
a
t
ion
d
i
s
t
r
ib
u
t
ionin
toan
umb
e
ro
fd
i
s
jo
in
ts
ub
g
ro
up
s
,th
ec
i
t
a
t
ionimp
a
c
to
fth
een
t
i
r
ed
i
s
t
r
ib
u
t
ionc
anb
e
e
xp
r
e
s
s
e
da
sth
ea
v
e
r
a
g
e(w
e
i
gh
t
e
db
yth
es
ub
g
ro
up
s
’o
u
tp
u
t
)o
fth
es
ub
g
ro
up
s
’c
i
t
a
t
ionimp
a
c
t
.A
s
w
i
l
lb
es
e
en b
e
low
,th
ef
a
c
tth
a
t bo
th o
fo
u
rind
i
c
a
to
r
s po
s
s
e
s
sth
i
sp
rop
e
r
t
yf
a
c
i
l
i
t
a
t
e
s th
e
comp
a
r
ab
i
l
i
t
yo
fth
etwoso
l
u
t
ion
stoth
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
emth
a
tcon
s
t
i
t
u
t
e
sth
em
a
in
a
imo
fth
ep
ap
e
r
.
• W
ep
r
e
s
en
ttwot
yp
e
so
fr
e
s
u
l
t
s
.F
i
r
s
t
l
y
,w
ea
s
s
e
s
sth
ep
e
r
fo
rm
an
c
eo
fth
es
t
and
a
rdf
i
e
ld
no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e
inf
a
c
i
l
i
t
a
t
in
gth
ecomp
a
r
ab
i
l
i
t
yo
fth
ec
i
t
a
t
ion
sr
e
c
e
i
v
e
db
ya
r
t
i
c
l
e
sb
e
lon
g
in
g
tod
i
f
f
e
r
en
tc
l
u
s
t
e
r
s
.S
e
cond
l
y
,w
ea
s
s
e
s
sth
econ
s
e
q
u
en
c
e
so
fadop
t
in
gth
etwoso
l
u
t
ion
stoth
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
emb
ycomp
a
r
in
gth
eco
r
r
e
spond
in
gun
i
v
e
r
s
i
t
yr
an
k
in
g
sa
c
co
rd
in
gtoth
e
twoadm
i
s
s
ib
l
ec
i
t
a
t
ion
imp
a
c
t
ind
i
c
a
to
r
s
.
•Th
e two m
a
inf
ind
in
g
sa
r
eth
efo
l
low
in
g
.F
i
r
s
t
l
y
,d
i
f
f
e
r
en
c
e
sinp
rod
u
c
t
ionandc
i
t
a
t
ion
p
r
a
c
t
i
c
e
sb
e
tw
e
en3
,
3
3
2c
l
u
s
t
e
r
sw
i
th mo
r
eth
an2
5
0p
ub
l
i
c
a
t
ion
sa
c
co
un
tfo
r2
2
.
5%o
fth
eo
v
e
r
a
l
l
c
i
t
a
t
ionin
e
q
u
a
l
i
t
y
.A
f
t
e
rth
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e
,wh
e
r
ec
l
u
s
t
e
rm
e
anc
i
t
a
t
ion
sa
r
e
u
s
e
da
sno
rm
a
l
i
z
a
t
ionf
a
c
to
r
s
,th
i
sf
i
g
u
r
ei
sr
e
d
u
c
e
dto4
.
3%
.S
e
cond
l
y
,th
ed
i
f
f
e
r
en
c
e
sb
e
tw
e
enth
e
T
a
r
g
e
t(o
rc
i
t
eds
id
e
) no
rm
a
l
i
z
a
t
ion p
ro
c
ed
u
r
e
sd
ep
end onag
i
v
enc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
emin
c
l
ud
in
ga n
umb
e
ro
f
h
e
t
e
ro
g
en
eo
u
sf
i
e
ld
s
.Tor
e
co
gn
i
z
eth
i
sf
e
a
t
u
r
e
,i
ti
su
s
e
f
u
ltor
e
f
e
rtoth
e
s
ep
ro
c
ed
u
r
e
sa
sf
i
e
ld
no
rm
a
l
i
z
edno
rm
a
l
i
z
a
t
ion
p
ro
c
ed
u
r
e
s
.Th
i
s
i
sth
ep
r
a
c
t
i
c
ew
efo
l
low
inth
i
sp
ap
e
r
.
4
5
un
i
v
e
r
s
i
t
yr
an
k
in
g
sob
t
a
in
e
dw
i
thth
etwo m
e
thod
sfo
rso
l
v
in
gth
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
emi
s
o
fav
e
r
ysm
a
l
lo
rd
e
ro
fm
a
gn
i
t
ud
efo
rbo
thc
i
t
a
t
ion
imp
a
c
t
ind
i
c
a
to
r
s
.
Th
er
e
s
to
fth
ep
ap
e
ri
so
r
g
an
i
z
e
din
tofo
u
rs
e
c
t
ion
s
.S
e
c
t
ionI
Iin
t
rod
u
c
e
sth
ec
i
t
a
t
ionimp
a
c
t
ind
i
c
a
to
r
s
,andi
t
sp
rop
e
r
t
i
e
s
.S
e
c
t
ionI
I
Ip
r
e
s
en
t
sth
etwoso
l
u
t
ion
stoth
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ion
p
rob
l
em
.S
e
c
t
ionIVd
e
s
c
r
ib
e
sth
ed
a
t
a
,and
in
c
l
ud
e
sth
eemp
i
r
i
c
a
lr
e
s
u
l
t
s
,wh
i
l
eS
e
c
t
ionVcon
c
l
ud
e
s
.
I
I
.C
ITAT
IONIMPACTIND
ICATORS
I
I
.
1
. No
t
a
t
ion
I
ti
snowcon
v
en
i
en
ttoin
t
rod
u
c
esom
eno
t
a
t
ion
s
.G
i
v
enas
e
tD o
fN d
i
s
t
in
c
ta
r
t
i
c
l
e
s
,andJ
s
c
i
en
t
i
f
i
cf
i
e
ld
sind
e
x
e
db
yj=1
,…
,J
,ac
l
a
s
s
i
f
i
c
a
t
i
o
ns
y
s
t
emi
sana
s
s
i
gnm
en
to
fa
r
t
i
c
l
e
sinD toth
eJ
f
i
e
ld
s
.L
e
tIb
eth
en
umb
e
ro
fr
e
s
e
a
r
chun
i
t
s
,ind
e
x
e
db
yi=1
,…
,I
.Fo
rs
imp
l
i
c
i
t
y
,inth
i
sS
e
c
t
ionw
e
a
s
s
um
eth
a
tth
e
r
ei
snoco
a
u
tho
r
sh
ip
,soth
a
te
a
cha
r
t
i
c
l
einD b
e
lon
g
stoas
in
g
l
eun
i
tinI
.
L
e
tc
e
i
jkb
th
en
umb
e
ro
fc
i
t
a
t
ion
sr
e
c
e
i
v
e
db
yth
ektha
r
t
i
c
l
eo
fun
i
tiinf
i
e
ldj
.Th
enc
c
}d
eno
t
e
sth
e
i
j={
i
jk
c
i
t
a
t
i
o
nd
i
s
t
r
i
b
u
t
i
o
no
fu
n
i
t
i
i
n
f
i
e
l
d
j
,
wh
i
l
ec
eno
t
e
sth
ec
i
t
a
t
i
o
nd
i
s
t
r
i
b
u
t
i
o
no
f
f
i
e
l
dj
,th
a
t
i
s
,th
eun
iono
fa
l
l
jd
r
e
s
e
a
r
chun
i
t
s
’c
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sinth
a
tf
i
e
ld
:c
c
}
.Und
e
rth
es
imp
l
i
f
y
in
ga
s
s
ump
t
iono
f
j=∪i{
i
j
5
nocoa
u
tho
r
sh
ip
,th
es
e
to
fd
i
s
t
r
ib
u
t
ion
sc
o
rmap
a
r
t
i
t
iono
fc
.
F
in
a
l
l
y
,l
e
tC=∪j{
c
}=∪i∪j
i
jf
j
j
{
c
}b
eth
eo
v
e
r
a
l
lc
i
t
a
t
i
o
nd
i
s
t
r
i
b
u
t
i
o
n
,o
rth
ec
i
t
a
t
iond
i
s
t
r
ib
u
t
ioninth
ea
l
l
s
c
i
en
c
e
sc
a
s
e
.Fo
rl
a
t
e
r
i
j
r
e
f
e
r
en
c
e
,l
e
tNi
eth
en
umb
e
ro
fa
r
t
i
c
l
e
sind
i
s
t
r
ib
u
t
ionc
,l
e
tNi=Σj N
eth
eto
t
a
ln
umb
e
ro
f
jb
i
j
i
jb
a
r
t
i
c
l
e
sp
ub
l
i
sh
e
db
yun
i
ti
,
andl
e
tNj=Σi N
eth
eto
t
a
ln
umb
e
ro
fa
r
t
i
c
l
e
sinf
i
e
ldj
.O
fco
u
r
s
e
,
th
e
i
jb
.
to
t
a
ln
umb
e
ro
fa
r
t
i
c
l
e
s
inth
ea
l
l
s
c
i
en
c
e
sc
a
s
e
i
sN =ΣiΣjNi
j
Ino
u
rcon
t
e
x
t
, wh
e
r
eine
v
e
r
yf
i
e
ldjw
eh
a
v
ec
c
}
,th
ee
v
a
l
u
a
t
iono
fan
yc
i
t
a
t
ion
j= ∪i{
i
j
d
i
s
t
r
ib
u
t
ioni
sdon
et
a
k
in
gin
toa
c
co
un
tak
e
ych
a
r
a
c
t
e
r
i
s
t
i
co
fd
i
s
t
r
ib
u
t
ionc
,s
a
yθj.Th
u
s
,ac
i
t
a
t
i
o
n
j
5M
o
r
eg
en
e
r
a
l
l
y
, inth
i
sS
e
c
t
ionw
ea
s
s
um
eth
a
tth
ea
s
s
i
gnm
en
to
fa
r
t
i
c
l
e
sinD toth
eIr
e
s
e
a
r
chun
i
t
si
ss
u
chth
a
tth
es
e
t
o
fd
i
s
t
r
ib
u
t
ion
sc
o
rmap
a
r
t
i
t
iono
fc
.
i
jf
j
6
im
p
a
c
ti
n
d
i
c
a
t
o
ri
saf
un
c
t
ionF d
e
f
in
e
dinth
ep
rod
u
c
tsp
a
c
eo
fa
l
lc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sandth
e
ch
a
r
a
c
t
e
r
i
s
t
i
csp
a
c
e
,soth
a
t–
g
i
v
enθj–th
ee
xp
r
e
s
s
ionFi
(
c
;θj)d
eno
t
e
sth
ec
i
t
a
t
ionimp
a
c
to
f
j=F
i
j
un
i
tiinf
i
e
ldj
,wh
i
l
eFj=F(
c
;θj)d
eno
t
e
sth
ec
i
t
a
t
ionimp
a
c
to
ff
i
e
ldja
sawho
l
e
.Toc
l
a
r
i
f
yth
i
s
j
no
t
ion
,con
s
id
e
rth
efo
l
low
in
gth
r
e
e
ind
i
c
a
to
r
sth
a
tw
i
l
lb
eu
s
e
d
inth
i
sp
ap
e
r
.
1
.L
e
tµi
ndµj b
eth
em
e
anc
i
t
a
t
iono
fd
i
s
t
r
ib
u
t
ion
sc
ndc
,r
e
sp
e
c
t
i
v
e
l
y
.Th
eR
e
l
a
t
i
v
em
e
a
n
ja
i
ja
j
c
i
t
a
t
i
o
n
i
n
d
i
c
a
t
o
r
,M
,
i
sd
e
f
in
e
da
s
Mi
c
;
µj)=µi
/µj
.
j=M(
i
j
j
(
1
)
Inth
i
sc
a
s
e
,θj=µj
.Fo
rf
i
e
ld
ja
sawho
l
e
,Mj=µj
/µj =1
.
2
.L
e
tXjb
eth
es
e
to
fth
e1
0% mo
s
tc
i
t
e
da
r
t
i
c
l
e
sinc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc
,andl
e
tXi
eth
e
j
jb
s
ub
s
e
to
fa
r
t
i
c
l
e
sinXjco
r
r
e
spond
in
gtoun
i
ti
,soth
a
t
Xj=∪i{
Xij} w
i
thXijnonemp
t
yfo
rsom
ei
.
I
fn
sth
en
umb
e
ro
fa
r
t
i
c
l
e
s
inXij,th
enth
e
T
o
p1
0%
i
n
d
i
c
a
t
o
r
,T
,i
sd
e
f
in
e
da
s
i
ji
Ti
(
c
;
Xj)=n
/Ni
.
j =T
i
j
i
j
j
(
2
)
Inth
i
sc
a
s
e
,θj=Xj
.I
fn
sth
en
umb
e
ro
fa
r
t
i
c
l
e
sinXj
,th
enfo
rf
i
e
ldja
sawho
l
e
,Tj=T(
c
;
j=Σ
in
i
ji
j
Xj)=n
/Nj =0
.
1
0
.
j
3
.L
e
tz
eth
eC
r
i
t
i
c
a
lC
i
t
a
t
i
o
nL
i
n
e–
CCLh
e
r
e
a
f
t
e
r–fo
rc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc
,andd
eno
t
eth
e
jb
j
a
r
t
i
c
l
e
sinc
i
thc
i
t
a
t
ion
se
q
u
a
ltoo
rg
r
e
a
t
e
rth
anz
sh
i
g
h
im
p
a
c
ta
r
t
i
c
l
e
s
.Fo
ran
yh
i
ghimp
a
c
ta
r
t
i
c
l
e
jw
ja
w
i
thc
i
t
a
t
ion
sc
,th
e
CCLn
o
rm
a
l
i
z
e
dh
i
g
h
im
p
a
c
tg
a
pi
sd
e
f
in
e
da
s(
c
)
/
z
.Con
s
id
e
rth
ef
am
i
l
yo
fFGT
i
l
i
l-z
j
j
ind
i
c
a
to
r
sin
t
rod
u
c
e
din A
lb
a
r
r
áne
ta
l
.(
2
0
1
1
a
)a
sf
un
c
t
ion
so
fno
rm
a
l
i
z
e
dh
i
gh
imp
a
c
tg
ap
s
. Th
e
s
e
condm
emb
e
ro
fth
i
sf
am
i
l
y
,r
e
f
e
r
r
e
dtoa
sth
eA
v
e
r
a
g
eo
fh
i
g
h
im
p
a
c
tg
a
p
s,
A
,i
sd
e
f
in
e
da
s
c
;
z
)=(
1
/Ni
)
[
Σl(
c
z
)
/
z
]
,
Ai
j=A(
i
j
j
j
i
lj
j
7
(
3
)
wh
e
r
eth
es
um
i
so
v
e
rth
eh
i
gh
imp
a
c
ta
r
t
i
c
l
e
s
inc
h
a
tb
e
lon
gtoc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc
.Inth
i
sc
a
s
e
,
jt
i
j
θj=z
.Fo
rth
een
t
i
r
ef
i
e
ld
ja
sawho
l
e
,w
eh
a
v
eAj=A(
c
;
z
)=(
1
/Nj
)
[
Σk(
c
z
)
/
z
]
,wh
e
r
eth
es
um
j
j
j
kj
j
i
so
v
e
rth
eh
i
gh
imp
a
c
ta
r
t
i
c
l
e
s
in
c
.
j
Tof
a
c
i
l
i
t
a
t
eth
ecomp
a
r
i
son w
i
th Ti
,inth
es
e
q
u
e
lw
ew
i
l
la
lw
a
y
sf
i
xz
sth
en
umb
e
ro
f
j
ja
th
c
i
t
a
t
ion
so
fth
ea
r
t
i
c
l
einth
e9
0
p
e
r
c
en
t
i
l
eo
fc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc
.Inth
a
tc
a
s
e
,th
es
e
to
fh
i
gh
j
imp
a
c
ta
r
t
i
c
l
e
sco
in
c
id
e
sw
i
thth
es
e
to
fth
e1
0% mo
s
tc
i
t
e
da
r
t
i
c
l
e
s
inc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc
.Ino
th
e
r
j
wo
rd
s
,fo
rbo
thind
i
c
a
to
r
sw
eh
a
v
e θj= z
. Th
etwo m
a
ind
i
f
f
e
r
en
c
e
sb
e
tw
e
enT andA a
r
eth
e
j
fo
l
low
in
g
.F
i
r
s
t
l
y
,on
eo
r mo
r
ec
i
t
a
t
ion
sr
e
c
e
i
v
e
db
yah
i
gh
imp
a
c
ta
r
t
i
c
l
ein
c
r
e
a
s
e
sAi
u
tdo
e
sno
t
jb
ch
an
g
eTi
.Ino
th
e
r wo
rd
s
,A i
s mono
ton
i
cb
u
tTi
sno
t
.S
e
cond
l
y
,Ti
s mo
r
erob
u
s
ttoe
x
t
r
em
e
j
ob
s
e
r
v
a
t
ion
sth
anA.
I
I
.
2
.S
i
z
e-ands
c
a
l
e
ind
ep
end
en
c
e
Con
s
id
e
rth
efo
l
low
in
gtwod
i
f
f
i
c
u
l
t
i
e
sfo
rcomp
a
r
in
gth
ec
i
t
a
t
ion
imp
a
c
to
fan
yp
a
iro
fr
e
s
e
a
r
ch
un
i
t
s
:th
etwoun
i
t
sm
a
yb
eo
fd
i
f
f
e
r
en
ts
i
z
e
s
,andi
fth
e
y wo
r
kind
i
f
f
e
r
en
tf
i
e
ld
s
,th
enth
e
i
rr
aw
c
i
t
a
t
ion
sa
r
eno
td
i
r
e
c
t
l
ycomp
a
r
ab
l
e
.Tos
e
ehowtoo
v
e
r
com
eth
ef
i
r
s
td
i
f
f
i
c
u
l
t
y
,a
s
s
um
eth
a
tw
eh
a
v
e
twoc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sc
ndc
o
run
i
t
su andvinf
i
e
ldj
.Inth
ee
x
amp
l
eg
i
v
eninth
e
u
j a
v
jf
r
In
t
rod
u
c
t
ion
,ui
sH
a
r
v
a
rd
,vi
sJohn Hop
k
in
s
,andj
i
sE
conom
i
c
s
.G
i
v
enan
yd
i
s
t
r
ib
u
t
ionc
,l
e
tc
b
e
n
ind
i
c
a
to
rFi
ss
a
idtob
es
i
z
e
i
n
d
e
p
e
n
d
e
n
ti
f
,fo
ran
yc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
th
er
thr
ep
l
i
c
ao
f
i
t
.G
i
v
enθ,a
r
r
t
c
,
F(
c
;
θ)=F(
c
;
θ)fo
ra
l
lr
.N
e
x
t
,
l
e
t
c
eth
er
r
ep
l
i
c
ao
fd
i
s
t
r
ib
u
t
ionc
i
thr=Nv
,and
l
e
t
c
e
u
j w
j
u
jb
v
jb
r
t
th
et
r
ep
l
i
c
ao
fd
i
s
t
r
ib
u
t
ionc
i
tht=Nu
. Now
c
ndc
a
v
eth
es
am
es
i
z
ee
q
u
a
ltoNv
im
e
sNu
.
v
j w
j
jt
j
u
ja
v
jh
r
t
Th
u
s
,i
f Fi
ss
i
z
e
ind
ep
end
en
t
,soth
a
tF(
c
) =F(
c
)andF(
c
;θj) =F(
c
;θj)
,th
ef
i
r
s
t
j
u
j;θ
j
v
j
u
j;θ
v
j
d
i
f
f
i
c
u
l
t
y
i
so
v
e
r
com
e
.
8
Tos
e
ehowtoh
and
l
eth
es
e
condd
i
f
f
i
c
u
l
t
y
,l
e
tc
ndc
etwoc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sfo
run
i
ti
i
ja
lwb
inf
i
e
ld
j
,andfo
run
i
t
vinf
i
e
ldw.Inth
ee
x
amp
l
em
en
t
ion
e
d
inth
eIn
t
rod
u
c
t
ion
,
i= M
IT
,j= O
r
g
an
i
c
Ch
em
i
s
t
r
y
,v= O
x
fo
rdUn
i
v
e
r
s
i
t
y
,andw =S
t
a
t
i
s
t
i
c
sandP
rob
ab
i
l
i
t
y
.A
nind
i
c
a
to
r
Fi
ss
a
idtob
es
c
a
l
e
i
n
d
e
p
e
n
d
e
n
ti
f
,fo
ran
yc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc
,an
ych
a
r
a
c
t
e
r
i
s
t
i
cθ,andan
yλ>0
,F(
λc
;λθ)=F(
c
;θ)
.
N
e
x
t
,l
e
t b=θj/θw,andcon
s
id
e
rth
eno
rm
a
l
i
z
e
dd
i
s
t
r
ib
u
t
ionc
’
c
’
}
,wh
e
r
ec
’
/bfo
ra
l
lk
i
j={
i
jk
i
jk=c
i
jk
=1
,
.
.
,Ni
. No
t
eth
a
tθ’
/b=θw,soth
a
tc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sc
’
ndc
r
enowcomp
a
r
ab
l
e
j
j=θ
j
i
ja
lw a
und
e
rθw. Th
u
s
,i
fFi
ss
c
a
l
e
ind
ep
end
en
t
,soth
a
tF(
c
;θj) =F(
c
’
;θ’
) =F(
c
’
;θw)
,th
es
e
cond
i
j
i
j
j
i
j
d
i
f
f
i
c
u
l
t
y
i
so
v
e
r
com
e
.
Anind
i
c
a
to
r Fi
ss
a
idtob
ea
dm
i
s
s
i
b
l
ei
fi
ti
ss
i
z
e
-ands
c
a
l
e
ind
ep
end
en
t
.T
h
eh
ind
e
xi
san
impo
r
t
an
te
x
amp
l
eo
fanind
i
c
a
to
rth
a
ti
sn
e
i
th
e
rs
i
z
e
-no
rs
c
a
l
e
ind
ep
end
en
t
. Onth
econ
t
r
a
r
y
,t
h
e
th
r
e
eind
i
c
a
to
r
sd
e
f
in
e
d
ine
xp
r
e
s
s
ion
s(
1
)
,(
2
)
,and(
3
)a
r
egoode
x
amp
l
e
so
fadm
i
s
s
ib
l
e
ind
i
c
a
to
r
s
.
I
I
.
3
.Th
eadd
i
t
i
v
ed
e
compo
s
ab
i
l
i
t
yp
rop
e
r
t
y
Th
efo
l
low
in
gp
rop
e
r
t
yi
sv
e
r
ycon
v
en
i
en
t
.G
i
v
en θ,a
nind
ic
a
to
rFi
ss
a
idtob
ea
d
d
i
t
i
v
e
l
y
d
e
c
om
p
o
s
a
b
l
ei
ffo
ran
yp
a
r
t
i
t
iono
fac
i
t
a
t
iond
i
s
t
r
ib
u
t
ioncin
toG d
i
s
jo
in
ts
ub
g
ro
up
s
,ind
e
x
e
db
yg=
1
,
.
.
.
,G,th
ec
i
t
a
t
ion
imp
a
c
to
fd
i
s
t
r
ib
u
t
ion
cc
anb
ee
xp
r
e
s
s
e
da
sfo
l
low
s
:
F(
c
;
θ)=Σg(
n
/n
)
F(
c
;
θ)
,
g
g
sth
en
umb
e
ro
fp
ub
l
i
c
a
t
ion
sins
ub
g
ro
upg
,andn=Σgn
sth
en
umb
e
ro
fp
ub
l
i
c
a
t
ion
sin
wh
e
r
en
gi
gi
d
i
s
t
r
ib
u
t
ionc
.Toi
l
l
u
s
t
r
a
t
eth
eu
s
e
f
u
ln
e
s
so
fth
i
sp
rop
e
r
t
y
,con
s
id
e
rth
efo
l
low
in
gth
r
e
es
i
t
u
a
t
ion
sin
wh
i
chth
e
ind
i
c
a
to
rFi
sa
s
s
um
e
dtob
eadm
i
s
s
ib
l
e
.
c
}
,andth
ed
i
s
t
r
ib
u
t
ion
sc
,i=
A.Und
e
ro
u
ra
s
s
ump
t
ion
s
,ine
v
e
r
yf
i
e
ld jw
eh
a
v
ec
j=∪i{
i
j
i
j
1
,…
,I
,con
s
t
i
t
u
t
eap
a
r
t
i
t
iono
f
c
.I
f
Fi
sadd
i
t
i
v
e
l
yd
e
compo
s
ab
l
e
,th
enw
ec
anw
r
i
t
e
j
F(
c
;
θj
)
,=Σi(
Ni
/Nj
)
F(
c
;
θj
)
.
j
j
i
j
9
(
4
)
Th
i
si
sav
e
r
yn
a
t
u
r
a
lcond
i
t
ion
,ind
i
c
a
t
in
gth
a
tth
ec
i
t
a
t
ionimp
a
c
to
ff
i
e
ld ja
sa who
l
ec
anb
e
e
xp
r
e
s
s
e
da
sth
ew
e
i
gh
t
e
da
v
e
r
a
g
eo
fth
er
e
s
e
a
r
chun
i
t
s
’c
i
t
a
t
ion
imp
a
c
tund
e
racommonθj
.
B.A
s
s
um
eth
a
tco
un
t
r
yvcon
s
i
s
t
so
fRr
e
g
ion
s
,ind
e
x
e
db
yr=1
,…
,R,anda
s
s
um
eth
a
tth
eR
c
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sinf
i
e
ldj
,c
,fo
rmap
a
r
t
i
t
iono
fth
ec
i
t
a
t
iond
i
s
t
r
ib
u
t
iono
fco
un
t
r
yvinth
a
t
v
r
j
f
i
e
ld
,c
.I
f
Fi
sadd
i
t
i
v
e
l
yd
e
compo
s
ab
l
e
,th
enw
ec
anw
r
i
t
e
v
j
F(
c
;
θj
)=Σr(
Nvr
/Nv)
F(
c
;
θj
)
,
v
j
j
v
r
j
(
5
)
wh
e
r
eNvr
sth
en
umb
e
ro
fp
ub
l
i
c
a
t
ion
sinr
e
g
ionr
,soth
a
tNv
.E
q
u
a
t
ion(
5
)ind
i
c
a
t
e
sth
a
t
ji
j=Σ
rNi
r
j
th
ec
i
t
a
t
ionimp
a
c
to
fco
un
t
r
yvinf
i
e
ldjc
anb
ee
xp
r
e
s
s
e
da
sth
ew
e
i
gh
t
e
da
v
e
r
a
g
eo
fth
er
e
g
ion
s
’
c
i
t
a
t
ion
imp
a
c
t
inf
i
e
ldjund
e
racommonθj
.
C.
A
s
s
um
eth
a
tc
anb
ep
a
r
t
i
t
ion
e
din
toSh
e
t
e
ro
g
en
eo
u
ss
ub
f
i
e
ld
s
,ind
e
x
e
db
ys=1
,…
,S,so
jc
th
a
tc
c
}
,wh
e
r
ec
sth
ec
i
t
a
t
iond
i
s
t
r
ib
u
t
iono
fs
ub
f
i
e
ldsinf
i
e
ldj
.I
fFi
sadd
i
t
i
v
e
l
y
j= ∪s{
s
j
s
ji
d
e
compo
s
ab
l
e
,th
enw
ec
anw
r
i
t
e
F(
c
;
θj
)=Σs(
Ns
/Nj
)
F(
c
;
θj
)
,
j
j
s
j
(
6
)
wh
e
r
eNs
sth
en
umb
e
ro
fp
ub
l
i
c
a
t
ion
sins
ub
f
i
e
lds
,soth
a
tNj=ΣsNs
.E
q
u
a
t
ion(
6
)ind
i
c
a
t
e
sth
a
t
ji
j
th
ec
i
t
a
t
ionimp
a
c
tinf
i
e
ldja
sa who
l
ec
anb
ee
xp
r
e
s
s
e
da
sth
ew
e
i
gh
t
e
da
v
e
r
a
g
eo
fth
es
ub
f
i
e
ld
c
i
t
a
t
ionimp
a
c
tv
a
l
u
e
s
.How
e
v
e
r
,th
i
se
xp
r
e
s
s
ionadd
sc
i
t
a
t
ionimp
a
c
tv
a
l
u
e
sco
r
r
e
spond
in
gtor
aw
tth
ef
i
e
ld
c
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
so
fh
e
t
e
ro
g
en
eo
u
ss
ub
f
i
e
ld
su
s
in
ga
sr
e
f
e
r
en
c
eth
ech
a
r
a
c
t
e
r
i
s
t
i
cθja
l
e
v
e
l
.Th
u
s
,a
l
tho
u
ghth
i
sd
e
compo
s
i
t
ioni
sm
a
th
em
a
t
i
c
a
l
l
ypo
s
s
ib
l
e
,i
tdo
e
sno
tp
ro
v
id
eas
a
t
i
s
f
a
c
to
r
y
so
l
u
t
iontoth
ea
g
g
r
e
g
a
t
ionp
rob
l
em m
en
t
ion
e
dinno
t
e1
.S
u
chaso
l
u
t
ionw
i
l
lh
a
v
etow
a
i
tun
t
i
lth
e
n
e
x
tS
e
c
t
ion
.
F
in
a
l
l
y
,no
t
eth
efo
l
low
in
gtwopo
in
t
s
.F
i
r
s
t
l
y
,e
q
u
a
t
ion(
4
)c
anb
ew
r
i
t
t
ena
sfo
l
low
s
:
Σi(
Ni
/Nj
)[
F(
c
,
θj
)
/
F(
c
;
θj
)
]=1
,
j
i
j
j
10
soth
a
tth
ev
a
l
u
eon
ec
ans
e
r
v
ea
sab
en
chm
a
r
kfo
re
v
a
l
u
a
t
in
gth
er
e
s
e
a
r
chun
i
t
sinth
eu
s
u
a
lw
a
y
.Th
e
s
am
ec
anb
es
a
ido
fe
q
u
a
t
ion
s(
5
)and(
6
)
.S
e
cond
l
y
,th
eth
r
e
eadm
i
s
s
ib
l
eind
i
c
a
to
r
sin
t
rod
u
c
e
din
e
xp
r
e
s
s
ion
s(
1
)
,(
2
)
,and(
3
)a
r
eadd
i
t
i
v
e
l
yd
e
compo
s
ab
l
e
.
I
I
I
.THESOLUT
IONSTOTHEALL
-SC
IENCESAGGREGAT
IONPROBLEM
I
I
I
.
1
.Th
e so
lu
t
iontoth
ea
l
l
s
c
i
en
c
e
sagg
r
eg
a
t
ionp
rob
l
emu
s
ingth
est
and
a
rdf
i
e
ld
no
rm
a
l
i
z
a
t
ionp
ro
c
edu
r
e
D
i
f
f
e
r
en
c
e
sinp
rod
u
c
t
ionandc
i
t
a
t
ionp
r
a
c
t
i
c
e
sa
c
ro
s
sf
i
e
ld
sm
a
k
e
si
timpo
s
s
ib
l
e tod
i
r
e
c
t
l
y
a
g
g
r
e
g
a
t
eth
er
awc
i
t
a
t
ion
sr
e
c
e
i
v
e
db
ya
r
t
i
c
l
e
sind
i
f
f
e
r
en
tf
i
e
ld
s
.Ino
rd
e
rtoso
l
v
eth
ea
l
l
s
c
i
en
c
e
s
a
g
g
r
e
g
a
t
ion p
rob
l
em
, on
e po
s
s
ib
i
l
i
t
yi
sto u
s
ea no
rm
a
l
i
z
a
t
ion p
ro
c
e
d
u
r
e
.A
sind
i
c
a
t
e
dinth
e
In
t
rod
u
c
t
ion
,g
i
v
eni
t
ss
imp
l
i
c
i
t
yandgoodp
e
r
fo
rm
an
c
e
,inth
i
sp
ap
e
rw
eadop
tth
es
t
and
a
rdf
i
e
ld
no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
einwh
i
chth
er
awc
i
t
a
t
ions
co
r
e
sinan
yf
i
e
lda
r
eno
rm
a
l
i
z
e
du
s
in
gth
ef
i
e
ld
m
e
anc
i
t
a
t
iona
sth
eno
rm
a
l
i
z
a
t
ionf
a
c
to
r
.
Fo
rm
a
l
l
y
,fo
ran
ya
r
t
i
c
l
ekinc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc
,th
eno
rm
a
l
i
z
e
dn
umb
e
ro
fc
i
t
a
t
ion
sc
*
s
i
j
i
jki
d
e
f
in
e
da
s
c
*
µj
.
i
j
k=c
i
j
k/
Th
en
o
rm
a
l
i
z
e
do
v
e
r
a
l
lc
i
t
a
t
i
o
nd
i
s
t
r
i
b
u
t
i
o
ni
sC* =∪i{
c*
}
,wh
e
r
ec*
c
*
}i
sth
en
o
rm
a
l
i
z
e
d
i
i=∪j∪k {
i
jk
c
i
t
a
t
i
o
nd
i
s
t
r
i
b
u
t
i
o
no
fu
n
i
tii
nt
h
ea
l
l
s
c
i
e
n
c
e
sc
a
s
e
.S
in
c
eno
rm
a
l
i
z
e
dc
i
t
a
t
ion
sa
r
enowcomp
a
r
ab
l
e
,i
tm
a
k
e
s
.
G
i
v
enth
ek
e
ych
a
r
a
c
t
e
r
i
s
t
i
c θ*o
fd
i
s
t
r
ib
u
t
ion
s
en
s
etoapp
l
yan
yind
i
c
a
to
rtoc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc*
i
C*,f
o
ran
yi
,l
e
tF
*i=F(
c*
;θ*
)b
eth
ec
i
t
a
t
ionimp
a
c
to
fd
i
s
t
r
ib
u
t
ionc*
c
co
rd
in
gtoth
eind
i
c
a
to
r
i
ia
*va
r
enowcomp
a
r
ab
l
e
,
F.Fo
ran
yp
a
i
ro
fr
e
s
e
a
r
chun
i
t
suandv
,th
ec
i
t
a
t
ionimp
a
c
tv
a
l
u
e
sF
*uandF
6
andc
anb
eu
s
e
dtor
an
kth
etwoun
i
t
s
inq
u
e
s
t
ion
.
S
in
c
eFi
sa
s
s
um
e
dtob
eadd
i
t
i
v
e
l
yd
e
compo
s
ab
l
e
,
w
ec
anw
r
i
t
e
6T
h
ea
g
g
r
e
g
a
t
iono
fSh
e
t
e
ro
g
en
eo
u
ss
ubf
i
e
ld
se
x
am
in
edins
i
t
u
a
t
ion CinS
ub
s
e
c
t
ionI
I
.
3
,adm
i
t
sas
im
i
l
a
rso
l
u
t
ion
:
;
θ*
)=Σs(
Nsj/Nj)
F(
c*
;
θ*
)
.
F(
c*
j
s
j
11
F
*=F(
C*;θ*
)=Σi(
Ni/N)
F
*i.
Th
u
s,i
fw
er
an
kun
i
v
e
r
s
i
t
i
e
sb
yth
er
a
t
ioF
*i/F
*,i =1
,…
,I
,th
enth
ev
a
l
u
eon
ec
ans
e
r
v
ea
sa
b
en
chm
a
r
kfo
re
v
a
l
u
a
t
in
gth
er
e
s
e
a
r
chun
i
t
s
inth
eu
s
u
a
lw
a
y
.
Fo
r
l
a
t
e
rr
e
f
e
r
en
c
e
,s
in
c
ec*
c*
}
,
fo
re
a
chiw
ec
anw
r
i
t
e
:
i=∪j{
i
j
F
*i =
F(
c*
;
θ*
)=Σj(
Nij/Ni)F
(
c*
;
θ*
)=χi(c*
,
j=1
,…
,J
,
θ*
)
.
i
i
j
i
j
(
7
)
No
t
eth
a
t
,fo
re
a
ch i
,
F
*id
ep
end
son
l
yonc*
,
j=1
,…
,J
,
andth
ecommony
a
rd
s
t
i
c
kθ*
,th
a
t
i
s
,
F
*i=
i
j
χi(c*
,
j=1
,…
,J
,
θ*
)
.
i
j
I
I
I
.
2
.Aso
lu
t
iontoth
ea
l
l
s
c
i
en
c
e
sagg
r
eg
a
t
ionp
rob
l
emw
i
thou
tf
i
e
ld
-no
rm
a
l
i
z
a
t
ion
Fo
ran
yun
i
ti
inan
yf
i
e
ldj
,g
i
v
enθjth
ee
xp
r
e
s
s
ionFij=F(
c
;θj)i
sth
ec
i
t
a
t
ionimp
a
c
to
fi
inj
i
j
a
c
co
rd
in
gtoind
i
c
a
to
rF.Acon
v
en
i
en
tm
e
a
s
u
r
eo
fc
i
t
a
t
ionimp
a
c
tfo
run
i
tiinth
ea
l
l
s
c
i
en
c
e
sc
a
s
e
,
Φi,c
anb
ed
e
f
in
eda
sth
ew
e
i
gh
t
e
da
v
e
r
a
g
eo
fth
ev
a
l
u
e
sFija
ch
i
e
v
e
dina
l
lf
i
e
ld
s
,w
i
thw
e
i
gh
t
se
q
u
a
l
toth
er
e
l
a
t
i
v
e
impo
r
t
an
c
eo
fe
a
chf
i
e
ldinth
eto
t
a
lp
rod
u
c
t
iono
fun
i
ti
.
Add
in
gup“
adm
i
s
s
ib
l
e
”F(
c
;
s
j
θj
)v
a
l
u
e
sfo
rd
i
f
f
e
r
en
tf
i
e
ld
sund
e
rch
a
r
a
c
t
e
r
i
s
t
i
cθjine
a
cho
fth
emsho
u
ldpo
s
enop
rob
l
ema
ta
l
l
.
No
t
eth
a
tth
i
sm
e
a
s
u
r
e
, Fi,i
saf
un
c
t
ionϕi o
fe
v
e
r
yc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc
nde
v
e
r
yθjfo
ra
l
lj=
i
ja
1
,…
,J
:
7
Φi=ϕi(
c
,
θj,
j=1
,…
,J
)=Σj(
Nij/Ni)
Fij.
i
j
(
8
)
c*
}
,wh
e
r
ec*
A
f
t
e
rth
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e
,w
eh
a
v
eC* =∪j{
j
j=∪i∪k
{
c
*
}i
sth
en
o
rm
a
l
i
z
e
dc
i
t
a
t
i
o
nd
i
s
t
r
i
b
u
t
i
o
no
ff
i
e
l
dj
.L
e
tθ*
eth
ech
a
r
a
c
t
e
r
i
s
t
i
co
fc*
n
a
lo
go
u
stoth
e
i
jk
jb
ja
c
h
a
r
a
c
t
e
r
i
s
t
i
cθ*o
fC*,soth
a
tθ*= Σj(
Nj/N)
θ*
,andθ*
/µj
.Th
e
r
e
fo
r
e
,s
in
c
eFi
ss
c
a
l
e
j
j= θ
j
ind
ep
end
en
t
,
Fij=F(
c
;
θj)=F(
c*
;
θ*
)fo
ra
l
lj
.H
en
c
e
,e
q
u
a
t
ion(
8
)c
ann
ew
r
i
t
t
ena
sfo
l
low
s
:
i
j
i
j
j
7T
h
ea
g
g
r
e
g
a
t
iono
fSh
e
t
e
ro
g
en
eo
u
ss
ubf
i
e
ld
se
x
am
in
ed
ins
i
t
u
a
t
ionC
inS
ub
s
e
c
t
ionI
I
.
3
,adm
i
t
sas
im
i
l
a
rso
l
u
t
ion
:F(
c
;
j
θj)=Σs(
Nsj/Nj)
F(
c
;
θsj)
,wh
e
r
eθsji
sth
ech
a
r
a
c
t
e
r
i
s
t
i
co
fc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc
tth
es
ub
f
i
e
ld
l
e
v
e
lfo
re
v
e
r
yj
=1
,…
,J
.
s
j
s
ja
12
Φi=ϕ(
c
,
θj,
j=1
,…
,J
)=Σj(
Nij/Ni)F
(
c*
;
θ*
)
.
i
j
i
j
j
(
9
)
Th
ecomp
a
r
i
sono
fe
xp
r
e
s
s
ion
s(
7
)and(
9)i
l
l
u
s
t
r
a
t
eth
ed
i
f
f
e
r
en
c
e
sb
e
tw
e
enth
etwoso
l
u
t
ion
stoth
e
a
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
em wh
enth
ee
v
a
l
u
a
t
iono
fth
eun
i
t
s
’c
i
t
a
t
ionimp
a
c
ti
sm
ad
ew
i
th
add
i
t
i
v
e
l
yd
e
compo
s
ab
l
eind
i
c
a
to
r
s
.Fo
ran
yi
,F(
c*
;θ*
)ine
q
u
a
t
ion(
7
)m
e
a
s
u
r
e
sth
ec
i
t
a
t
ionimp
a
c
t
i
j
o
fun
i
ti
inf
i
e
ldju
s
in
ga
sr
e
f
e
r
en
c
eth
ech
a
r
a
c
t
e
r
i
s
t
i
cθ*o
fth
eo
v
e
r
a
l
lno
rm
a
l
i
z
e
dc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
C*. How
e
v
e
r
,F(
c*
;θ*
)=F(
c
;θj)ine
q
u
a
t
ion(
9
)m
e
a
s
u
r
e
sth
ec
i
t
a
t
ionimp
a
c
to
fun
i
tiinf
i
e
ldj
i
j
j
i
j
u
s
in
ga
sr
e
f
e
r
en
c
eth
ech
a
r
a
c
t
e
r
i
s
t
i
cθ*
fe
a
chc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc*
r
,wh
a
ti
sth
es
am
e
,u
s
in
ga
s
jo
jo
r
e
f
e
r
en
c
eth
ech
a
r
a
c
t
e
r
i
s
t
i
cθjo
fe
a
chc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionc
r
io
rtoapp
l
y
in
gth
es
t
and
a
rdf
i
e
ld
jp
no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e
. Con
s
e
q
u
en
t
l
y
,comp
u
t
in
gΦi= ϕ(
c
,θj,j=1
,…
,J
)a
vo
id
sth
epo
s
s
ib
l
e
i
j
e
r
ro
r
scomm
i
t
t
e
d
inth
eno
rm
a
l
i
z
a
t
iono
fr
awc
i
t
a
t
ions
co
r
e
su
s
in
gth
ep
ro
c
e
d
u
r
e
in(
7
)
.
I
t
i
scon
v
en
i
en
ttocomp
u
t
eth
ew
e
i
gh
t
e
da
v
e
r
a
g
eo
fth
eFiv
a
l
u
e
sa
sfo
l
low
s
:
Φ=Σi(
Ni/N)Φi=Σi(
Ni/N)Σj(
Nij/Ni)
Fij=ΣiΣj(
Nij/N)
Fij.
(
1
0
)
Th
u
s,a
sb
e
fo
r
e
,
i
fw
er
an
kun
i
v
e
r
s
i
t
i
e
sb
yth
er
a
t
io
Fi/F,
i=1
,…
,I
,
th
enth
ev
a
l
u
eon
ec
ans
e
r
v
ea
sa
b
en
chm
a
r
kfo
re
v
a
l
u
a
t
in
gth
er
e
s
e
a
r
chun
i
t
s
inth
eu
s
u
a
lw
a
y.
Inp
r
a
c
t
i
c
e
,w
eh
a
v
ein
fo
rm
a
t
ioncon
c
e
rn
in
gsom
e–
th
e5
0
0 LRun
i
v
e
r
s
i
t
i
e
s–b
u
tno
ta
l
l
r
e
s
e
a
r
chun
i
t
s
.Th
e
r
e
fo
r
e
,w
ec
anno
tcomp
u
t
eΦ u
s
in
ge
xp
r
e
s
s
ion(
1
0
)
.S
t
a
r
t
in
gf
romth
a
te
xp
r
e
s
s
ion
,
w
eh
a
v
e
Φ=ΣiΣj(
Nij/N)
Fij=Σj(
Nj/N)Σi(
Nij/Nj)
Fij.
S
in
c
ec
c
}
,andFi
sadd
i
t
i
v
e
l
yd
e
compo
s
ab
l
e
,Σi(
Nij/Nj)
Fij=Fj,wh
e
r
eFj=F(
c
,θj)c
anb
e
j
j=∪i{
i
j
comp
u
t
e
dw
i
tho
u
rd
a
t
a
.Th
e
r
e
fo
r
e
,w
ec
ancomp
u
t
eΦ a
sfo
l
low
s
Φ=Σj(
Nj/N)Fj.
13
Onth
eo
th
e
rh
and
,s
in
c
e Fj=F
(c
,θj)=F
*j=F
(c*
,θ*
)
,w
eh
a
v
eF
*=Φ.F
in
a
l
l
y
,no
t
eth
a
twh
enF
j
j
j
=M,
F
*=Φ =1
,wh
i
l
ewh
enF=T,
F
*=Φ =0
.
1
0
.
I
I
I
.
3
.Th
ea
imo
fth
ep
ap
e
r
Th
em
a
ina
imo
fth
i
sp
ap
e
ri
sth
ecomp
a
r
i
sonb
e
tw
e
enth
er
an
k
in
g
so
fr
e
s
e
a
r
chun
i
t
sob
t
a
in
e
d
w
i
thand w
i
tho
u
tth
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ion p
ro
c
e
d
u
r
e
,(F
*1, …
,F
*I)and(
Φ1, …
,ΦI)
,
r
e
sp
e
c
t
i
v
e
l
y
.Tound
e
r
s
t
andth
ew
a
yth
er
e
s
u
l
t
sw
i
l
lb
ep
r
e
s
en
t
e
d
,r
e
c
a
l
lth
a
t
,fo
ran
yj
,Xji
sth
es
e
to
f
h
i
gh
imp
a
c
ta
r
t
i
c
l
e
sind
i
s
t
r
ib
u
t
ionc
,th
a
ti
s
,th
es
e
to
fa
r
t
i
c
l
e
sinc
i
thc
i
t
a
t
ion
se
q
u
a
ltoo
rg
r
e
a
t
e
r
j
jw
th
anz
,o
rth
es
e
to
fth
e1
0% mo
s
tc
i
t
e
da
r
t
i
c
l
e
si
nc
.L
e
tu
sd
eno
t
eb
y
X=(X1,…
,
Xj
,…
,
XJ)th
es
e
t
j
j
o
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
sinth
ea
l
l
s
c
i
en
c
e
sc
a
s
e
. Onth
eo
th
e
rh
and
,l
e
tY b
eth
es
e
to
fth
e1
0% mo
s
t
c
i
t
e
da
r
t
i
c
l
e
s
inth
eo
v
e
r
a
l
lno
rm
a
l
i
z
e
dc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionC*=∪j{
c*
}
,and
l
e
t
Yjb
eth
es
ubs
e
to
f
j
a
r
t
i
c
l
e
s
inY b
e
lon
g
in
gtof
i
e
ldj
,soth
a
t
Y=(Y1,…
,
Yj
,…
,
YJ)
.
Und
e
rth
eun
i
v
e
r
s
a
l
i
t
ycond
i
t
ion
,th
a
ti
s
,i
fa
l
lf
i
e
ld
sa
r
ee
q
u
a
l
l
yd
i
s
t
r
ib
u
t
e
de
x
c
ep
tfo
ras
c
a
l
e
f
a
c
to
r
,th
enth
eno
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
ew
i
l
le
l
im
in
a
t
ea
l
ld
i
f
f
e
r
en
c
e
sb
e
tw
e
enc
i
t
a
t
ionp
r
a
c
t
i
c
e
s
a
c
ro
s
sc
l
u
s
t
e
r
s
,andth
etwoso
l
u
t
ion
stoth
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
emw
i
l
lco
in
c
id
e
.
Th
er
e
a
son
i
sth
a
t
inth
i
ss
i
t
u
a
t
ionw
ewo
u
ldh
a
v
e
z
*
/µj=z
*fo
ra
l
lj
.Con
s
e
q
u
en
t
l
y
,
Yj=Xjfo
ra
l
lj
,and
Y=
j=z
j
X.S
in
c
ec
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sc*
ndc
a
v
eth
es
am
en
umb
e
ro
fa
r
t
i
c
l
e
sando
u
rind
i
c
a
to
r
sa
r
ea
i
ja
i
jh
c
;z
)=F(
c*
;z
*
)=F(
c*
;z
*
)=F
*ij
f
un
c
t
ionso
l
e
l
yo
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
s
,w
ewo
u
ldh
a
v
eFij=F(
i
j
j
i
j
j
i
j
fo
ra
l
liandj
.Inv
i
ewo
fe
q
u
a
t
ion
s(
7
)and(
8
)
,w
ewo
u
ldh
a
v
eF
*i=Φifo
ra
l
li
.Ino
th
e
rwo
rd
s
,th
e
r
an
k
in
g
s(
F
*1, …
,
F
*I)and(
Φ1, …
,
ΦI)w
i
l
lb
e
id
en
t
i
c
a
l
.
A
sw
eknow
,inp
r
a
c
t
i
c
eth
eun
i
v
e
r
s
a
l
i
t
ycond
i
t
ioni
sno
ts
a
t
i
s
f
i
e
d(A
lb
a
r
r
án e
ta
l
.
,2
0
1
1b
,
W
a
l
tm
an e
ta
l
.
,2
0
1
2b
,Th
e
lw
a
l
l& W
i
l
son
,2
0
1
4
, and B
r
z
e
z
in
s
k
i, 2
0
1
5
)
.Con
s
e
q
u
en
t
l
y
,th
e
p
e
r
fo
rm
an
c
eo
fth
ef
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
ec
anno
tb
ep
e
r
f
e
c
t
,andth
es
e
t
sY andX w
i
l
lno
t
14
co
in
c
id
e
.Inth
i
ss
i
t
u
a
t
ion
,w
esho
u
ld m
e
a
s
u
r
eth
econ
s
e
q
u
en
c
e
so
fadop
t
in
gth
etwoso
l
u
t
ion
stoth
e
a
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
emu
s
in
gind
i
c
a
to
r
sw
i
thd
i
f
f
e
r
en
tp
rop
e
r
t
i
e
s
.Th
er
e
a
son
,o
fco
u
r
s
e
,i
s
th
a
twh
en
e
v
e
rY andX d
i
f
f
e
r
,th
a
ti
s
,wh
enth
es
e
to
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
sund
e
rth
etwoso
l
u
t
ion
s
d
i
f
f
e
r
,th
econ
s
e
q
u
en
c
e
sfo
rth
eun
i
v
e
r
s
i
t
yr
an
k
in
g
sm
i
gh
tb
eo
fad
i
f
f
e
r
en
to
rd
e
ro
fm
a
gn
i
t
ud
e
d
ep
end
in
gonth
ec
i
t
a
t
ion
imp
a
c
t
ind
i
c
a
to
rw
eu
s
e
.
F
in
a
l
l
y
,no
t
eth
a
t
,g
en
e
r
a
l
l
y
,F
*i≠Fi fo
ra
l
li=1
,…
,I
. How
e
v
e
r
,
i
t
i
se
a
s
ytoe
s
t
ab
l
i
shth
a
tth
i
s
i
sno
tth
ec
a
s
efo
rth
er
e
l
a
t
i
v
em
e
an
ind
i
c
a
to
r
M.A
sam
a
t
t
e
ro
ff
a
c
t
,
M
*i=(
1
/
Ni)ΣjΣkc
*
(
1/
Ni)ΣjΣkc
µj
i
j
k =
i
j
k/
i
ss
imp
l
yth
eM
e
anNo
rm
a
l
i
z
e
dC
i
t
a
t
ionS
co
r
e
ind
i
c
a
to
r
.How
e
v
e
r
,
Mi=Σj(
Nij/
Ni)Mij=Σj(
Nij/Ni)(
µi
/µj
)=(
1/
Ni)ΣjΣkc
µj=M
*i
.
j
i
j
k/
Th
e
r
e
fo
r
e
,inth
eemp
i
r
i
c
a
lp
a
r
to
fth
ep
ap
e
rw
ew
i
l
lon
l
ys
t
ud
yth
eun
i
v
e
r
s
i
t
yr
an
k
in
g
sob
t
a
in
e
dw
i
th
th
e
ind
i
c
a
to
r
sTandA,n
am
e
l
y
,th
etop1
0%andth
ea
v
e
r
a
g
eo
fh
i
gh
imp
a
c
tg
ap
s
.
IV
.EMP
IR
ICALRESULTS
IV
.
1
.Th
ed
a
t
aandd
e
s
c
r
ip
t
i
v
es
t
a
t
i
s
t
i
c
s
O
u
rd
a
t
a
s
e
tr
e
s
u
l
t
sf
romth
eapp
l
i
c
a
t
ion o
fa p
ub
l
i
c
a
t
ion
l
e
v
e
la
l
go
r
i
thm
i
cm
e
thodo
lo
g
y to
9
,
4
4
6
,
6
2
2d
i
s
t
in
c
ta
r
t
i
c
l
e
sp
ub
l
i
sh
e
din2
0
0
3
2
0
1
2(
s
e
eR
u
i
z
-C
a
s
t
i
l
lo & W
a
l
tm
an
,2
0
1
5
)
.P
ub
l
i
c
a
t
ion
sin
lo
c
a
ljo
u
rn
a
l
s
,a
sw
e
l
la
spop
u
l
a
rm
a
g
a
z
in
e
sandt
r
ad
ejo
u
rn
a
l
s
,h
a
v
eb
e
ene
x
c
l
ud
e
d(
s
e
eR
u
i
z
-C
a
s
t
i
l
lo&
W
a
l
tm
an
,2
0
1
5
,fo
rth
ed
e
t
a
i
l
s
)
.W
ewo
r
kw
i
thjo
u
rn
a
l
sinth
es
c
i
en
c
e
s
,th
eso
c
i
a
ls
c
i
en
c
e
s
,andth
ea
r
t
s
andh
um
an
i
t
i
e
s
,a
l
tho
u
gh m
an
ya
r
t
sandh
um
an
i
t
i
e
sjo
u
rn
a
l
sa
r
ee
x
c
l
ud
e
db
e
c
a
u
s
eth
e
ya
r
eo
falo
c
a
l
n
a
t
u
r
e
. Th
ec
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
emcon
s
i
s
t
so
f5
,
1
1
9c
l
u
s
t
e
r
s
,andc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sr
e
f
e
rtoth
e
c
i
t
a
t
ion
sr
e
c
e
i
v
e
db
yth
e
s
ea
r
t
i
c
l
e
sd
u
r
in
gaf
i
v
e
y
e
a
rc
i
t
a
t
ionw
indowfo
re
a
chy
e
a
r
inth
a
tp
e
r
iod
.
Inth
i
s
p
ap
e
r
,w
efo
c
u
sonth
es
e
to
f3
,
6
1
4
,
4
4
7d
i
s
t
in
c
ta
r
t
i
c
l
e
sp
ub
l
i
sh
e
dinth
ep
e
r
iod2
0
0
5
2
0
0
8
.Int
e
rm
so
f
15
th
eno
t
a
t
ionin
t
rod
u
c
e
dinS
e
c
t
ionI
I
.
1
,w
eh
a
v
eC = ∪j{
c
}=(c
,…
,c
i
thJ= 5
,
1
1
9
,andN =
j
1
N) w
3
,
6
1
4
,
4
4
7
.
Weso
r
tc
l
u
s
t
e
r
sin d
e
c
r
e
a
s
in
go
rd
e
rb
ys
i
z
e
, wh
e
r
es
i
z
ei
sm
e
a
s
u
r
e
da
sth
en
umb
e
ro
f
p
ub
l
i
c
a
t
ion
s
,andg
ro
upc
l
u
s
t
e
r
sin
tot
end
e
c
i
l
ec
l
a
s
s
e
s
,ind
e
x
e
db
yd =1
,…
,1
0
.
.Fo
re
a
chd
e
c
i
l
e
,th
e
a
v
e
r
a
g
en
umb
e
ro
fp
ub
l
i
c
a
t
ion
sp
e
rc
l
u
s
t
e
r
,d
eno
t
e
db
ymd,andth
ea
v
e
r
a
g
en
umb
e
ro
fc
i
t
a
t
ion
sp
e
r
p
ub
l
i
c
a
t
ion
,d
eno
t
e
db
yµd,a
r
einT
ab
l
e1
. No
t
eth
ep
r
e
s
en
c
eo
fal
a
r
g
en
umb
e
ro
fsm
a
l
lc
l
u
s
t
e
r
sw
i
th
l
e
s
sth
ano
re
q
u
a
lto1
0
0p
ub
l
i
c
a
t
ion
s(
t
yp
i
c
a
l
l
ya
c
comp
an
i
e
db
yalow m
e
anc
i
t
a
t
ionp
e
ra
r
t
i
c
l
e
)
.
How
e
v
e
r
,th
es
e
to
fsm
a
l
lc
l
u
s
t
e
r
sin
c
l
ud
e
sav
e
r
ysm
a
l
lp
ropo
r
t
iono
fth
e3
.
6m
i
l
l
iona
r
t
i
c
l
e
sinth
e
en
t
i
r
ed
a
t
a
s
e
t(
s
e
erowD
inT
ab
l
e1
)
.
T
ab
l
e1a
roundh
e
r
e
Th
er
es
e
a
r
chun
i
t
sa
r
eun
i
v
e
r
s
i
t
i
e
s
.A
sin W
a
l
tm
ane
ta
l
.(
2
0
1
2b
)
,p
ub
l
i
c
a
t
ion
sa
r
ea
s
s
i
gn
e
dto
un
i
v
e
r
s
i
t
i
e
su
s
in
gth
ef
r
a
c
t
ion
a
lco
un
t
in
gm
e
thodth
a
tt
a
k
e
s
in
toa
c
co
un
tth
eadd
r
e
s
s
l
in
e
sapp
e
a
r
in
g
in
e
a
chp
ub
l
i
c
a
t
ion
.W
ea
r
eon
l
ycon
c
e
rn
e
dw
i
thth
e2
,
4
2
0
,
0
5
4d
i
s
t
in
c
ta
r
t
i
c
l
e
s
,o
r6
7%o
fth
eto
t
a
l
,w
i
th
a
tl
e
a
s
ton
eadd
r
e
s
sl
in
eb
e
lon
g
in
gtoanLRun
i
v
e
r
s
i
t
y
.Anya
r
t
i
c
l
eo
fth
i
st
yp
ei
sf
u
l
l
ya
s
s
i
gn
e
dtoan
LRun
i
v
e
r
s
i
t
yon
l
y
i
fa
l
ladd
r
e
s
s
e
sm
en
t
ion
e
d
inth
ep
ub
l
i
c
a
t
ionb
e
lon
gtoth
eun
i
v
e
r
s
i
t
y
inq
u
e
s
t
ion
.I
f
ap
ub
l
i
c
a
t
ioni
sco
a
u
tho
r
e
db
ytwoo
r mo
r
eLRun
i
v
e
r
s
i
t
i
e
s
,th
eni
ti
sa
s
s
i
gn
e
df
r
a
c
t
ion
a
l
l
ytoa
l
lo
f
th
eminp
ropo
r
t
iontoth
en
umb
e
ro
fadd
r
e
s
sl
in
e
sine
a
chc
a
s
e
.Fo
re
x
amp
l
e
,i
fth
eadd
r
e
s
sl
i
s
to
fan
a
r
t
i
c
l
econ
t
a
in
sf
i
v
eadd
r
e
s
s
e
sandtwoo
fth
emb
e
lon
gtoap
a
r
t
i
c
u
l
a
run
i
v
e
r
s
i
t
y
,th
en0
.
4o
fth
ea
r
t
i
c
l
e
i
sa
s
s
i
gn
e
dtoth
i
sun
i
v
e
r
s
i
t
y
,andon
l
y0
.
2o
fth
ea
r
t
i
c
l
ei
sa
s
s
i
gn
e
dtoe
a
cho
fth
eo
th
e
rth
r
e
e
un
i
v
e
r
s
i
t
i
e
s
.F
in
a
l
l
y
,con
s
id
e
rap
ub
l
i
c
a
t
ionco
a
u
tho
r
e
db
yanLRun
i
v
e
r
s
i
t
yandanun
knownn
umb
e
r
o
fo
th
e
rin
s
t
i
t
u
t
ion
so
u
t
s
id
eth
eL
e
id
enR
an
k
in
g
.A
s
s
um
e
,fo
re
x
amp
l
e
,th
a
tth
ep
ub
l
i
c
a
t
ionh
a
sfou
r
add
r
e
s
s
l
in
e
s
,twoo
fwh
i
chco
r
r
e
spondtoth
eLRun
i
v
e
r
s
i
t
y
.Inth
i
sc
a
s
e
,on
l
y0
.
5o
fth
ea
r
t
i
c
l
ew
i
l
lb
e
a
s
s
i
gn
e
dtoth
eLRun
i
v
e
r
s
i
t
y
. Th
i
sp
ro
c
e
d
u
r
eimp
l
i
e
sth
a
tth
eto
t
a
lf
r
a
c
t
ion
a
ln
umb
e
ro
fa
r
t
i
c
l
e
s
a
s
s
i
gn
e
dtoLRun
i
v
e
r
s
i
t
i
e
sw
i
l
lb
esm
a
l
l
e
rth
anth
eto
t
a
ln
umb
e
ro
fa
r
t
i
c
l
e
sw
i
tha
tl
e
a
s
ton
eadd
r
e
s
s
16
l
in
eb
e
lon
g
in
gtoanLRun
i
v
e
r
s
i
t
y
.I
tt
u
rn
so
u
tth
a
tth
i
sn
umb
e
ri
s1
,
8
8
6
,
1
0
6
.
1
,o
r5
2
.
2%o
fth
eto
t
a
l
.
Th
ed
i
s
t
r
ib
u
t
iono
fth
i
sto
t
a
lamon
gth
e5
0
0un
i
v
e
r
s
i
t
i
e
si
sinco
l
umn
s1and2inT
ab
l
e Ainth
e
App
end
i
x
.
F
in
a
l
l
y
,w
ecomp
a
r
eth
es
k
ewn
e
s
sandc
i
t
a
t
ionin
e
q
u
a
l
i
t
yo
fth
eth
r
e
ed
i
s
t
r
ib
u
t
ion
scon
s
i
s
t
in
go
f
3
.
6
,2
.
4
,and1
.
9m
i
l
l
iona
r
t
i
c
l
e
su
s
in
gth
eCh
a
r
a
c
t
e
r
i
s
t
i
cS
co
r
e
sandS
c
a
l
e
sapp
ro
a
ch(
S
ch
ub
e
r
te
ta
l
.
,
1
9
8
7
)
,a
sw
e
l
la
stwoind
i
c
a
to
r
so
fc
i
t
a
t
ionin
e
q
u
a
l
i
t
yands
k
ewn
e
s
sth
a
ta
r
erob
u
s
ttoe
x
t
r
em
e
ob
s
e
r
v
a
t
ion
s(G
ro
en
e
v
e
ldand M
e
e
d
en
,1
9
8
4
)
. Th
er
e
s
u
l
t
sa
r
ein T
ab
l
e Binth
e App
end
i
x
.
In
t
e
r
e
s
t
in
g
l
yeno
u
gh
,th
es
k
ewn
e
s
sandc
i
t
a
t
ionin
e
q
u
a
l
i
t
yo
fth
eth
r
e
ed
i
s
t
r
ib
u
t
ion
sa
r
eo
fth
es
am
e
o
rd
e
ro
fm
a
gn
i
t
ud
e
.
IV
.
2
.Th
ep
e
r
fo
rm
an
c
eo
fth
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
edu
r
e
W
ec
an e
s
t
im
a
t
eth
eimp
a
c
to
fth
es
t
and
a
rd f
i
e
ld
-no
rm
a
l
i
z
a
t
ion p
ro
c
e
d
u
r
eu
s
in
gth
e
m
e
a
s
u
r
em
en
tf
r
am
ewo
r
kin
t
rod
u
c
e
din C
r
e
spo e
ta
l
.(
2
0
1
3
)
.W
ef
i
r
s
te
s
t
im
a
t
eth
ee
f
f
e
c
tono
v
e
r
a
l
l
c
i
t
a
t
ionin
e
q
u
a
l
i
t
yth
a
tc
anb
ea
t
t
r
ib
u
t
e
dtod
i
f
f
e
r
en
c
e
sinp
rod
u
c
t
ionandc
i
t
a
t
ionp
r
a
c
t
i
c
e
sb
e
tw
e
en
c
l
u
s
t
e
r
sth
ro
u
ghth
et
e
rmIDCC(
I
n
e
q
u
a
l
i
t
yd
u
etoDi
f
f
e
r
en
c
e
sinCi
t
a
t
ionimp
a
c
tb
e
tw
e
enCl
u
s
t
e
r
s
)
.
Th
en
,w
ea
s
s
e
s
sth
ep
e
r
fo
rm
an
c
eo
fth
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
eb
yth
er
e
d
u
c
t
ioni
t
ind
u
c
e
sinth
eIDCCt
e
rm
.Inapp
l
i
c
a
t
ion
s
,i
ti
scon
v
en
i
en
tto p
a
r
t
i
t
ione
a
chc
l
u
s
t
e
rc
i
t
a
t
ion
d
i
s
t
r
ib
u
t
ionin
to1
0
0p
e
r
c
en
t
i
l
e
s
,ind
e
x
e
db
yπ=1
,
.
.
.
,1
0
0
.G
i
v
enth
em
an
yc
l
u
s
t
e
r
sw
i
thv
e
r
yf
ew
p
ub
l
i
c
a
t
ion
s(
s
e
eT
ab
l
e1
)
,w
eapp
l
yth
i
sm
e
thodtoth
ec
i
t
a
t
iond
i
s
t
r
ib
u
t
ionC
’r
e
s
t
r
i
c
t
e
dtoth
e3
,
3
3
2
c
l
u
s
t
e
r
sw
i
th mo
r
eth
an2
5
0p
ub
l
i
c
a
t
ion
s
.Th
i
sd
i
s
t
r
ib
u
t
ionin
c
l
ud
e
s3
,
4
4
1
,
6
6
6m
i
l
l
ionp
ub
l
i
c
a
t
io
n
s,o
r
9
5
.
2
%o
fth
eto
t
a
l
.
A
s
s
um
efo
ra mom
en
tth
a
t
,inan
yc
l
u
s
t
e
rj
,w
ed
i
s
r
e
g
a
rdth
ec
i
t
a
t
ionin
e
q
u
a
l
i
t
yw
i
th
ine
v
e
r
y
π
p
e
r
c
en
t
i
l
eb
ya
s
s
i
gn
in
gtoe
v
e
r
ya
r
t
i
c
l
einth
a
tp
e
r
c
en
t
i
l
eth
em
e
anc
i
t
a
t
iono
fth
ep
e
r
c
en
t
i
l
ei
t
s
e
l
f
,µj.
π
π
sth
a
t
,ona
v
e
r
a
g
e
,th
ec
i
t
a
t
ionimp
a
c
to
f
Th
ein
t
e
rp
r
e
t
a
t
iono
fth
ef
a
c
tth
a
t
,fo
re
x
amp
l
e,µj =2µl i
17
c
l
u
s
t
e
rji
stw
i
c
ea
sl
a
r
g
ea
sth
ec
i
t
a
t
ionimp
a
c
to
fc
l
u
s
t
e
rlinsp
i
t
eo
fth
ef
a
c
tth
a
tbo
thq
u
an
t
i
t
i
e
s
r
ep
r
e
s
en
tacommonund
e
r
l
y
in
gph
enom
enon
,n
am
e
l
y
,th
es
am
ed
e
g
r
e
eo
fc
i
t
a
t
i
o
nim
p
a
c
tinbo
thc
l
u
s
t
e
r
s
.
π
π
Ino
th
e
rwo
rd
s
,fo
ran
yπ,th
ed
i
s
t
an
c
eb
e
tw
e
enµj andµl i
sen
t
i
r
e
l
ya
t
t
r
ib
u
t
ab
l
etoth
ed
i
f
f
e
r
en
c
e
sin
th
ep
rod
u
c
t
ionandc
i
t
a
t
ionp
r
a
c
t
i
c
e
sth
a
tp
r
e
v
a
i
linth
etwoc
l
u
s
t
e
r
sfo
rp
ub
l
i
c
a
t
ion
sh
a
v
in
gth
es
am
e
d
e
g
r
e
eo
fe
x
c
e
l
l
en
c
e
.Th
u
s
,th
ec
i
t
a
t
ion
in
e
q
u
a
l
i
t
yb
e
tw
e
enc
l
u
s
t
e
r
sa
te
a
chp
e
r
c
en
t
i
l
e
,d
eno
t
e
db
yI
(
π)
,i
s
en
t
i
r
e
l
ya
t
t
r
ib
u
t
ab
l
etoth
ed
i
f
f
e
r
en
c
e
sinc
i
t
a
t
ionp
r
a
c
t
i
c
e
sb
e
tw
e
enth
e3
,
3
3
2c
l
u
s
t
e
r
sho
ld
in
gcon
s
t
an
t
en
c
e
,th
et
e
rmIDCC
,wh
i
chi
se
q
u
a
ltoac
e
r
t
a
in
th
ed
e
g
r
e
eo
fe
x
c
e
l
l
en
c
eina
l
lc
l
u
s
t
e
r
sa
tq
u
an
t
i
l
eπ. H
w
e
i
gh
t
e
da
v
e
r
a
g
eo
fth
e
s
eq
u
an
t
i
t
i
e
s,p
ro
v
id
e
sagood m
e
a
s
u
r
eo
fth
eto
t
a
limp
a
c
tono
v
e
r
a
l
lc
i
t
a
t
ion
in
e
q
u
a
l
i
t
yth
a
tc
anb
ea
t
t
r
ib
u
t
e
dtos
u
chd
i
f
f
e
r
en
c
e
s(
fo
rd
e
t
a
i
l
s
,s
e
e
C
r
e
spoe
ta
l
.
,2
0
1
3
)
.
W
eu
s
eth
er
a
t
io
ID
CC/I
(
C
’)
(
1
1
)
toa
s
s
e
s
sth
er
e
l
a
t
i
v
ee
f
f
e
c
tono
v
e
r
a
l
lc
i
t
a
t
ionin
e
q
u
a
l
i
t
y
,I
(
C
’)
,a
t
t
r
ib
u
t
e
dtoth
ed
i
f
f
e
r
en
c
e
sinc
i
t
a
t
ion
p
r
a
c
t
i
c
e
sb
e
tw
e
enc
l
u
s
t
e
r
s
.F
in
a
l
l
y
,w
ea
r
ein
t
e
r
e
s
t
e
dine
s
t
im
a
t
in
ghowimpo
r
t
an
ts
c
a
l
ed
i
f
f
e
r
en
c
e
s
b
e
tw
e
enc
l
u
s
t
e
rc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sa
r
eina
c
co
un
t
in
gfo
rth
ee
f
f
e
c
tm
e
a
s
u
r
e
db
ye
xp
r
e
s
s
ion(
1
1
)
.Fo
r
th
a
tp
u
rpo
s
e
,w
eu
s
eth
er
e
l
a
t
i
v
ech
an
g
e
inth
eIDPCt
e
rm
,th
a
t
i
s
,th
er
a
t
io
[
ID
CC –ID
CC*
]
/ID
CC,
(
1
2
)
wh
e
r
e ID
CC
*i
sth
et
e
rmth
a
tm
e
a
s
u
r
e
sth
ee
f
f
e
c
tono
v
e
r
a
l
lc
i
t
a
t
ionin
e
q
u
a
l
i
t
ya
t
t
r
ib
u
t
e
dtoth
e
d
i
f
f
e
r
en
c
e
s
inc
l
u
s
t
e
rd
i
s
t
r
ib
u
t
ion
sa
f
t
e
rapp
l
y
in
gth
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e
.
I
tsho
u
ldb
eno
t
e
dth
a
t
,u
s
in
gth
es
i
z
e
-ands
c
a
l
e
ind
ep
end
en
tt
e
chn
i
q
u
eknowna
sCh
a
r
a
c
t
e
r
i
s
t
i
c
S
co
r
e
sandS
c
a
l
e
s
,R
u
i
z
-C
a
s
t
i
l
lo & W
a
l
tm
an(
2
0
1
5
)showth
a
t
,a
sinp
r
e
v
io
u
sr
e
s
e
a
r
ch
,th
e4
,
1
6
1
s
i
gn
i
f
i
c
an
tc
l
u
s
t
e
r
sw
i
th mo
r
eth
an1
0
0p
ub
l
i
c
a
t
ion
sa
r
eh
i
gh
l
ys
k
ew
e
dands
im
i
l
a
r
l
yd
i
s
t
r
ib
u
t
e
d
.S
in
c
e
th
e mo
r
es
im
i
l
a
rc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sa
r
e
,th
eb
e
t
t
e
rsho
u
ld wo
r
kan
yno
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e
,w
e
e
xp
e
c
tr
e
a
son
ab
l
ygoodr
e
s
u
l
t
sino
u
rc
a
s
e
.Th
ee
s
t
im
a
t
e
so
fe
xp
r
e
s
s
ion
s(
1
1
)and(
1
2
)a
r
ep
r
e
s
en
t
e
din
18
T
ab
l
e2.Fo
rcomp
a
r
i
sonp
u
rpo
s
e
s
,w
ein
c
l
ud
eth
er
e
s
u
l
t
sf
romC
r
e
spoe
ta
l
.(
2
0
1
3
)andL
ie
ta
l
.(
2
0
1
3
)
fo
r2
1
9and1
7
2 Wo
Ss
ub
f
i
e
ld
s
,r
e
sp
e
c
t
i
v
e
l
y
.
T
ab
l
e2a
roundh
e
r
e
I
tc
anb
eob
s
e
r
v
e
dth
a
tth
ee
f
f
e
c
to
fth
ed
i
f
f
e
r
en
c
e
sinc
i
t
a
t
ionp
r
a
c
t
i
c
e
sb
e
tw
e
enth
e3
,
3
3
2
c
l
u
s
t
e
r
sr
ep
r
e
s
en
t
s2
2
.
5%o
fo
v
e
r
a
l
lc
i
t
a
t
ionin
e
q
u
a
l
i
t
y
,ag
r
e
a
t
e
rp
e
r
c
en
t
a
g
eth
anwh
a
th
a
sb
e
enfo
und
inth
ep
r
e
v
io
u
sl
i
t
e
r
a
t
u
r
efo
r2
1
9o
r1
7
2s
ub
f
i
e
ld
s
.N
e
v
e
r
th
e
l
e
s
s
,th
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ion
p
ro
c
e
d
u
r
er
ed
u
c
e
sth
i
se
f
f
e
c
tdownto4
.
3%o
fth
en
ewo
v
e
r
a
l
lc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
,wh
i
chi
sq
u
i
t
ean
a
ch
i
e
v
em
en
t
. Onth
eo
th
e
rh
and
,f
i
e
ld
-no
rm
a
l
i
z
a
t
iong
en
e
r
a
t
e
san8
4
.
3%r
e
d
u
c
t
iono
fth
eIDCCt
e
rm
,a
comp
a
r
ab
l
ef
i
g
u
r
ew
i
thwh
a
ti
sfo
undinth
ep
r
e
v
io
u
sl
i
t
e
r
a
t
u
r
e
.Th
u
s
,fo
rth
el
a
r
g
e
s
t3
,
3
3
2o
fth
e5
,
1
1
9
c
l
u
s
t
e
r
s
,th
ep
e
r
fo
rm
an
c
eo
fth
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e
i
sr
e
a
son
ab
l
ygood
.
F
in
a
l
l
y
,i
ti
sv
e
r
yin
s
t
r
u
c
t
i
v
etos
t
ud
yhowI
(
π)ch
an
g
e
sw
i
thπ bo
thb
e
fo
r
eanda
f
t
e
rth
es
t
and
a
rd
f
i
e
ld
-no
rm
a
l
i
z
a
t
ion
.Th
er
e
s
u
l
t
sapp
e
a
rinF
i
g
u
r
e1(
s
in
c
eI
(
π)i
sv
e
r
yh
i
ghfo
rπ<2
5,fo
rc
l
a
r
i
t
yth
e
s
e
p
e
r
c
en
t
il
e
sa
r
eom
i
t
t
e
df
rom F
i
g
u
r
e2
)
, wh
i
chw
a
r
r
an
t
s th
efo
l
low
in
gtwocomm
en
t
s
.F
i
r
s
t
l
y
,th
e
s
i
gn
i
f
i
c
an
t
imp
a
c
to
ff
i
e
ld
-no
rm
a
l
i
z
a
t
ion
i
sr
e
ad
i
l
yapp
a
r
en
t
.S
e
cond
l
y
,
i
t
i
su
s
e
f
u
lto
in
fo
rm
a
l
l
yp
a
r
t
i
t
ion
th
es
uppo
r
to
fo
u
rc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sin
toth
efo
l
low
in
gth
r
e
ein
t
e
r
v
a
l
s
:[
0
,4
7
]
,[
4
8
,9
7
]
,and[
9
8
,
π)v
a
l
u
e
sa
r
ev
e
r
yh
i
gh
.Th
i
sm
e
an
sth
a
t
,s
in
c
einth
e
s
etwo
1
0
0
]
.Inth
ef
i
r
s
tandth
eth
i
rdon
e
,I
(
in
t
e
r
v
a
l
sc
l
u
s
t
e
rc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sd
i
f
f
e
rb
y mo
r
eth
anas
c
a
l
ef
a
c
to
r
,th
eun
i
v
e
r
s
a
l
i
t
ycond
i
t
ionc
an
h
a
rd
l
yb
es
a
t
i
s
f
i
e
dinth
em
. How
e
v
e
r
,I
(
π)i
sapp
ro
x
im
a
t
e
l
ycon
s
t
an
tfo
raw
id
er
an
g
eo
fin
t
e
rm
e
d
i
a
t
e
v
a
l
u
e
s
inth
es
e
cond
in
t
e
r
v
a
l
.
F
igu
r
e1a
roundh
e
r
e
IV
.
3
.D
i
f
f
e
r
en
c
e
sb
e
tw
e
enth
etwoapp
ro
a
ch
e
s
Insp
i
t
eo
fth
egoodp
e
r
fo
rm
an
c
eo
fth
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
ew
esho
u
ldno
t
fo
r
g
e
tth
a
tth
ed
i
f
f
e
r
en
c
e
sinp
rod
u
c
t
ionandc
i
t
a
t
ionp
r
a
c
t
i
c
e
sb
e
tw
e
enc
l
u
s
t
e
r
sr
em
a
in
in
ga
f
t
e
r
no
rm
a
l
i
z
a
t
iona
r
es
t
i
l
lr
e
spon
s
ib
l
efo
r4
.
3%o
fth
eo
v
e
r
a
l
lc
i
t
a
t
ionin
e
q
u
a
l
i
t
yI
(
C
’)
. Mo
r
eo
v
e
r
,w
e
19
sho
u
ldt
a
k
ein
toa
c
co
un
tth
a
tth
e1
,
7
8
7c
l
u
s
t
e
r
sw
i
thl
e
s
sth
an2
5
0p
ub
l
i
c
a
t
ion
sm
u
s
tb
eb
ro
u
gh
tb
a
c
k
in
toth
ean
a
l
y
s
i
s
.Th
e
r
e
fo
r
e
,w
ee
xp
e
c
tth
a
ts
e
t
so
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
sb
e
fo
r
eanda
f
t
e
rth
ef
i
e
ld
no
rm
a
l
i
z
a
t
ionin
t
rod
u
c
e
dinS
e
c
t
ionI
I
I
.
3,n
am
e
l
y
,th
es
e
t
sX =(X1,…
,Xj
,…
,XJ)andY =(Y1,…
,
Yj
,…
,YJ)
,p
r
e
s
en
tsom
ed
i
f
f
e
r
en
c
e
s wo
r
ths
t
ud
y
in
g
.A
sab
en
chm
a
r
k
,w
ef
i
r
s
td
e
f
in
eth
es
e
tB o
f
h
i
gh
imp
a
c
ta
r
t
i
c
l
e
s–
th
a
t
i
s
,th
e1
0% mo
s
tc
i
t
e
da
r
t
i
c
l
e
s–
inth
eo
rd
e
r
e
do
v
e
r
a
l
lc
i
t
a
t
iond
i
s
t
r
ib
u
t
ionC
wh
e
r
ea
r
t
i
c
l
e
sf
roma
l
lc
l
u
s
t
e
r
sa
r
eo
rd
e
r
e
da
c
co
rd
in
gtoth
e
i
rr
awc
i
t
a
t
ion
sp
r
io
rtoth
eapp
l
i
c
a
t
iono
f
an
yno
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e
.L
e
tBjb
eth
es
ub
s
e
to
fB w
i
tha
r
t
i
c
l
e
s
inf
i
e
ldj
,po
s
s
ib
l
yemp
t
yfo
rm
an
y
8
j
,soth
a
t
B=(B1,…
,
Bj
,…
,
BJ)
.
N
e
x
t
,w
ecomp
a
r
eth
es
e
t
sX andY,and
X andBf
romth
efo
l
low
in
g
twopo
in
t
so
fv
i
ew
.
1
.Inth
ef
i
r
s
tp
l
a
c
e
,w
ecomp
u
t
eth
en
umb
e
ro
fc
l
u
s
t
e
r
swh
e
r
eY andB a
r
eemp
t
y
,a
sw
e
l
la
sth
e
n
umb
e
ro
fa
r
t
i
c
l
e
sinth
ein
t
e
r
s
e
c
t
ion
sb
e
tw
e
enth
etwop
a
i
r
s
:X∩B,andX∩Y.Th
er
e
s
u
l
t
sa
r
ein
T
ab
l
e3
.A
. Twocomm
en
t
sa
r
eino
rd
e
r
.F
i
r
s
t
l
y
,a
l
tho
u
ghth
en
umb
e
ro
femp
t
yc
l
u
s
t
e
r
sinB i
s
r
e
l
a
t
i
v
e
l
yl
a
r
g
e
,th
ep
e
r
c
en
t
a
g
eo
fm
i
s
s
in
ga
r
t
i
c
l
e
si
ssm
a
l
l
:on
l
y2
.
7%o
fa
l
lh
i
gh
imp
a
c
ta
r
t
i
c
l
e
sinX
a
r
em
i
s
s
e
dfo
rth
i
sr
e
a
son
.Th
i
sp
e
r
c
en
t
a
g
ei
sn
e
g
l
i
g
ib
l
efo
rY.S
e
cond
l
y
,th
ep
e
r
c
en
t
a
g
eo
fa
r
t
i
c
l
e
sin
X∩Bi
sc
lo
s
etotwoth
i
rd
so
fth
eto
t
a
l
.G
i
v
enth
ew
a
yB h
a
sb
e
encon
s
t
r
u
c
t
e
d
,th
i
si
ssom
ewh
a
t
s
u
rp
r
i
s
in
g
.Int
u
rn
,th
es
e
tX∩Y r
ep
r
e
s
en
t
s9
4
.
8
%o
fth
eto
t
a
l
. Th
u
s
,on
l
yapp
ro
x
im
a
t
e
l
y 5%o
f
a
r
t
i
c
l
e
s
inX a
r
eno
tfo
und
inth
eno
rm
a
l
i
z
e
ds
e
tY.
I
t
i
swo
r
thr
e
v
i
ew
in
gth
es
i
t
u
a
t
ionwh
enw
er
e
s
t
r
i
c
tth
ea
t
t
en
t
iontoth
e3
,
3
3
2c
l
u
s
t
e
r
sw
i
thmo
r
e
th
an2
5
0p
ub
l
i
c
a
t
ion
s
,th
a
ti
s
, wh
enth
eo
v
e
r
a
l
lc
i
t
a
t
iond
i
s
t
r
ib
u
t
ioni
sC
’. Th
er
e
s
u
l
t
sfo
rth
e
co
r
r
e
spond
in
gs
e
t
sX’
,Y’
,andB’a
r
einT
ab
l
e3
.B
.Th
en
umb
e
ro
femp
t
yc
l
u
s
t
e
r
sinB’d
e
c
r
e
a
s
e
s
8
Du
etot
i
e
s
,a
sw
e
l
la
sth
ep
r
e
s
en
c
eo
fc
l
u
s
t
e
r
sw
i
thf
ew
e
rth
an1
0p
ub
l
i
c
a
t
ion
s
,
i
t
i
su
s
u
a
l
l
yno
tpo
s
s
ib
l
eto m
a
k
eane
x
a
c
t
d
i
s
t
in
c
t
ionb
e
tw
e
enp
ub
l
i
c
a
t
ion
sth
a
tb
e
lon
gtoth
etop1
0%andp
ub
l
i
c
a
t
ion
sth
a
tdono
tb
e
lon
gtoth
a
ts
e
tine
v
e
r
y
c
l
u
s
t
e
r
.Ino
rd
e
rtoendupw
i
the
x
a
c
t
l
y1
0%topp
ub
l
i
c
a
t
ion
sinth
ed
a
t
a
s
e
t
,w
es
e
l
e
c
tth
etop1
0%p
ub
l
i
c
a
t
ion
sine
a
ch
c
l
u
s
t
e
rfo
l
low
in
gth
ef
r
a
c
t
ion
a
lp
ro
c
ed
u
r
er
e
comm
end
ed
in W
a
l
tm
an&S
ch
r
e
ib
e
r(
2
0
1
3
)
.
20
con
s
id
e
r
ab
l
y
,wh
i
l
e
i
tb
e
com
e
sz
e
ro
inth
eno
rm
a
l
i
z
e
dc
a
s
e
.In
t
e
r
e
s
t
in
g
l
y
,th
ep
e
r
c
en
t
a
g
e
so
fa
r
t
i
c
l
e
s
in
th
e
in
t
e
r
s
e
c
t
ion
sX’
∩B’
,and
X’
∩Y’r
em
a
ine
s
s
en
t
i
a
l
l
yth
es
am
ea
sb
e
fo
r
e
.
T
ab
l
e3a
roundh
e
r
e
2
.Inth
es
e
condp
l
a
c
e
,F
i
g
u
r
e2
.Ashow
sah
i
s
to
g
r
amo
fth
ed
i
s
t
r
ib
u
t
iono
fth
ep
ropo
r
t
iono
f
h
i
gh
imp
a
c
ta
r
t
i
c
l
e
sinB andY o
v
e
rth
e5
,
1
1
9c
l
u
s
t
e
r
s
.A
se
xp
e
c
t
e
d
,th
ed
i
s
t
r
ib
u
t
iono
fth
e
s
e
p
ropo
r
t
ion
sfo
rs
e
tBi
sw
a
yo
f
fth
em
a
r
k
.Th
ep
e
r
c
en
t
a
g
eo
fa
r
t
i
c
l
e
sinc
l
u
s
t
e
rj
inth
ein
t
e
r
v
a
l[
0
.
0
9
,
0
.
1
1
]
,w
i
tha1
0%d
e
v
i
a
t
ionf
romth
ep
ropo
r
t
ion0
.
1
0
,t
a
k
e
sp
l
a
c
einon
l
y2
8
2o
fth
e5
,
1
1
9c
l
u
s
t
e
r
s
,
andin
c
l
ud
e
s8
.
3
%o
fa
l
lh
i
gh
imp
a
c
ta
r
t
i
c
l
e
s
.A
f
t
e
rno
rm
a
l
i
z
a
t
ion
,a
l
tho
u
ghth
e
s
em
a
gn
i
t
ud
e
sin
cr
e
a
s
e
to2
,
2
4
4c
l
u
s
t
e
r
sandap
e
r
c
en
t
a
g
eo
f5
6
.
1%a
r
t
i
c
l
e
s
,th
e
ya
r
es
t
i
l
lno
tv
e
r
yl
a
r
g
e
.F
u
r
th
e
rmo
r
e
,an
in
sp
e
c
t
iono
fth
et
a
i
l
so
fth
eY h
i
s
to
g
r
amin F
i
g
u
r
e2
.Bind
i
c
a
t
e
sth
a
t
,fo
rm
an
yc
l
u
s
t
e
r
s
,th
e
p
e
r
c
en
t
a
g
eo
fa
r
t
i
c
l
e
sinYji
sno
tin
c
l
ud
e
dinth
ein
t
e
r
v
a
l[
0
.
0
5
,0
.
1
4
5
)
.C
l
e
a
r
l
y
,e
v
ena
l
low
in
gfo
r
r
andomv
a
r
i
a
t
ion
,th
eimp
a
c
to
fth
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
ei
sf
a
rf
romp
e
r
f
e
c
t.In
o
th
e
rwo
rd
s
,th
eun
i
v
e
r
s
a
l
i
t
ycond
i
t
ioni
sno
ts
a
t
i
s
f
i
e
d
.F
in
a
l
l
y,wh
enw
er
e
s
t
r
i
c
tth
ea
t
t
en
t
iontoth
e
3
,
3
3
2c
l
u
s
t
e
r
sw
i
th mo
r
eth
an2
5
0p
ub
l
i
c
a
t
ion
s
,F
i
g
u
r
e2
.Ci
l
l
u
s
t
r
a
t
e
sth
eg
r
e
a
t
e
rcon
c
en
t
r
a
t
iono
f
c
l
u
s
t
e
r
stow
a
rd
sth
e1
0%p
e
r
c
en
t
a
g
e
.A
f
t
e
rno
rm
a
l
i
z
a
t
ion
,1
,
8
2
9c
l
u
s
t
e
r
sin
c
l
ud
in
g5
7
.
6
%o
fth
eto
t
a
l
a
r
t
i
c
l
e
sa
r
e
in
c
l
ud
e
d
inth
e
in
t
e
r
v
a
l[
0
.
0
9
,0
.
1
1
]
.
F
igu
r
e2a
roundh
e
r
e
Inb
r
i
e
f
,a
l
tho
u
ghth
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e wo
r
k
sw
e
l
lfo
rth
e3
,
3
3
2c
l
u
s
t
e
r
s
w
i
th mo
r
eth
an2
5
0p
ub
l
i
c
a
t
ion
s
,th
eun
i
v
e
r
s
a
l
i
t
ycond
i
t
ionfo
rth
e5
,
1
1
9c
l
u
s
t
e
r
si
sno
ts
a
t
i
s
f
i
e
d
.Th
i
s
l
e
ad
stoth
econ
c
l
u
s
ionth
a
tth
es
e
t
so
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
sb
e
fo
r
eanda
f
t
e
rf
i
e
ld
-no
rm
a
l
i
z
a
t
ion
,X and
Y,p
r
e
s
en
tsom
ed
i
f
f
e
r
en
c
e
s
:app
ro
x
im
a
t
e
l
y5%o
fa
r
t
i
c
l
e
sinX a
r
eno
tfo
undinY,andth
ep
e
r
c
en
t
a
g
e
o
fa
r
t
i
c
l
e
sinac
l
u
s
t
e
rw
i
tha1
0%d
e
v
i
a
t
ionf
rom0
.
1
0t
a
k
e
sp
l
a
c
einon
l
y1
,
8
2
9c
l
u
s
t
e
r
swh
i
chin
c
l
ud
e
5
7
.
6%o
fth
eto
t
a
ln
umb
e
ro
fa
r
t
i
c
l
e
s
.
21
IV
.
4
.D
i
f
f
e
r
en
c
e
sin un
i
v
e
r
s
i
t
yr
ank
ing
s und
e
rth
etwo so
lu
t
ion
sto a
l
l
-s
c
i
en
c
e
s
agg
r
eg
a
t
ionp
rob
l
em
Th
eun
i
v
e
r
s
i
t
yr
an
k
in
g
sw
i
thandw
i
tho
u
tno
rm
a
l
i
z
a
t
iona
c
co
rd
in
gtoth
etop1
0%
ind
i
c
a
to
r
,Ti*
andTi,anda
c
co
rd
in
gtoth
ea
v
e
r
a
g
eo
fh
i
gh
imp
a
c
tg
ap
s
,
A
*iandAi,a
r
ep
r
e
s
en
t
e
d
inT
ab
l
eA
inth
e
9
App
end
i
x
. Un
i
v
e
r
s
i
t
i
e
sa
r
eo
rd
e
r
e
da
c
co
rd
in
gtoth
eind
i
c
a
to
r Ti.
R
e
c
a
l
lth
a
t
,und
e
rth
ef
r
a
c
t
ion
a
l
app
ro
a
ch
,th
ea
r
t
i
c
l
e
sa
s
s
i
gn
e
dtoth
eun
iono
fth
e5
0
0LRun
i
v
e
r
s
i
t
i
e
sr
ep
r
e
s
en
ton
l
y5
2
.
1%o
fth
e
to
t
a
l
.N
e
v
e
r
th
e
l
e
s
s
,th
ew
e
i
gh
t
e
da
v
e
r
a
g
eo
fth
eTian
dTi* v
a
l
u
e
sfo
rth
e
s
eun
i
v
e
r
s
i
t
i
e
s
,u
s
in
ga
s
w
e
i
gh
t
sth
e
i
rr
e
l
a
t
i
v
ep
ub
l
i
c
a
t
iono
u
tp
u
t
,i
s1
.
1
4and1
.
1
3
,r
e
sp
e
c
t
i
v
e
l
y
.S
im
i
l
a
r
l
y
,th
e
s
ef
i
g
u
r
e
sfo
rth
e
AiandAi*v
a
l
u
e
sa
r
e1
.
1
8and1
.
1
6
.Th
i
s
ind
i
c
a
t
e
sth
a
tth
econ
t
r
ib
u
t
iono
fth
e
s
eun
i
v
e
r
s
i
t
i
e
s
i
sc
l
e
a
r
l
y
abo
v
eth
ewo
r
lda
v
e
r
a
g
ea
c
co
rd
in
gtobo
th
ind
i
c
a
to
r
s
.
W
en
e
x
ta
r
r
i
v
etoth
ek
e
yemp
i
r
i
c
a
lq
u
e
s
t
iono
fth
ep
ap
e
r
,n
am
e
l
y
,th
econ
s
e
q
u
en
c
e
so
fadop
t
in
g
th
etwoso
l
u
t
ion
stoth
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
em
in
t
rod
u
c
e
d
inS
e
c
t
ionI
I
I
.
2
.W
eb
e
g
inw
i
thth
e
comp
a
r
i
sono
fun
i
v
e
r
s
i
t
yr
an
k
in
g
sa
c
co
rd
in
gtoTi andT
*i. Bo
tht
h
eP
e
a
r
son andth
eSp
e
a
rm
an
co
r
r
e
l
a
t
ionco
e
f
f
i
c
i
en
t
sb
e
tw
e
en un
i
v
e
r
s
i
t
yv
a
l
u
e
sa
r
e0
.
9
9
. How
e
v
e
r
,h
i
ghco
r
r
e
l
a
t
ion
sb
e
tw
e
en
un
i
v
e
r
s
i
t
yv
a
l
u
e
sandr
an
k
s do no
tp
r
e
c
l
ud
eimpo
r
t
an
td
i
f
f
e
r
en
c
e
sfo
rind
i
v
id
u
a
l un
i
v
e
r
s
i
t
i
e
s
.In
an
a
l
y
z
in
gth
econ
s
e
q
u
en
c
e
so
fgo
in
gf
romTitoT
*i,w
em
u
s
tt
a
k
etwoa
sp
e
c
t
sin
toa
c
co
un
t
.F
i
r
s
t
l
y
,w
e
sho
u
ldan
a
l
y
z
eth
er
e
r
an
k
in
g
sth
a
tt
a
k
ep
l
a
c
eins
u
cha mo
v
e
.S
e
cond
l
y
,w
esho
u
ldcomp
a
r
eth
e
r
t
un
a
t
e
l
y
,w
eh
a
v
ear
e
l
e
v
an
tin
s
t
an
c
ew
i
th
d
i
f
f
e
r
en
c
e
sb
e
tw
e
enth
eun
i
v
e
r
s
i
t
yv
a
l
u
e
sth
em
s
e
l
v
e
s
.10 Fo
wh
i
chtocomp
a
r
eo
u
rr
e
s
u
l
t
s
:th
ed
i
f
f
e
r
en
c
e
sfo
undinR
u
i
z
-C
a
s
t
i
l
lo & W
a
l
tm
an(
2
0
1
5
)ingo
in
gf
rom
9T
h
isi
sa
l
soth
eT
op1
0%ind
i
c
a
to
rcomp
u
t
edinRu
i
z
C
a
s
t
i
l
lo &
W
a
l
tm
an(
2
0
1
5)
.M
ino
rd
i
f
f
e
r
en
c
e
sb
e
tw
e
enth
etwo
r
an
k
in
g
sa
r
ed
u
etoro
und
ede
r
ro
r
s(Comp
a
r
eth
er
an
k
in
gund
e
rc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
em8inT
ab
l
eCinth
eApp
end
i
xinth
e
wo
r
k
in
gp
ap
e
rv
e
r
s
iono
fRu
i
z
C
a
s
t
i
l
lo & W
a
l
tm
an–h
t
tp
://hd
l
.h
and
l
e
.n
e
t/
1
0
0
1
6/
1
8
3
8
5–w
i
thth
er
an
k
in
ginco
l
umn3in
T
ab
l
eA
inth
eApp
end
i
xtoth
i
sp
ap
e
r
)
.
1
0A
spo
in
t
edo
u
tb
yW
a
l
tm
an e
ta
l
.(
2
0
1
2
b)
,s
in
c
eun
i
v
e
r
s
i
t
yv
a
l
u
ed
i
s
t
r
ib
u
t
ion
sa
r
esom
ewh
a
ts
k
ew
ed
,anin
c
r
e
a
s
einth
e
r
an
ko
faun
i
v
e
r
s
i
t
yb
y
,s
a
y
,1
0po
s
i
t
ion
si
s mu
ch mo
r
es
i
gn
i
f
i
c
an
tinth
etopo
fth
er
an
k
in
gth
anf
u
r
th
e
rdownth
el
i
s
t
.
Th
e
r
e
fo
r
e
,as
t
a
t
em
en
ts
u
cha
s“Un
i
v
e
r
s
i
t
yui
sp
e
r
fo
rm
in
g2
0%b
e
t
t
e
rth
anun
i
v
e
r
s
i
t
y
va
c
co
rd
in
gtoth
etop1
0%ind
i
c
a
to
r
”
sr
an
k
ed2
0po
s
i
t
ion
sh
i
gh
e
rth
anun
i
v
e
r
s
i
t
yva
c
co
rd
in
gtoth
e
i
s mo
r
ein
fo
rm
a
t
i
v
eth
anas
t
a
t
em
en
ts
u
cha
s“Un
i
v
e
r
s
i
t
yui
top1
0%
ind
i
c
a
to
r
.
”
22
th
eun
i
v
e
r
s
i
t
yr
an
k
in
g
sa
c
co
rd
in
gtoTi u
s
in
gth
eW
ebo
fS
c
i
en
c
ec
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
emw
i
th 2
3
6jo
u
rn
a
l
s
ub
j
e
c
tc
a
t
e
go
r
i
e
s
,o
rs
ub
f
i
e
ld
s
,andth
ec
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
em w
ea
r
eu
s
in
ginth
i
sp
ap
e
rw
i
th5
,
1
1
9
c
l
u
s
t
e
r
s
.Th
er
e
s
u
l
t
sfo
rbo
ths
i
t
u
a
t
ion
sa
r
e
inT
ab
l
e4
.
T
ab
l
e4a
roundh
e
r
e
A
sm
u
cha
s3
7
.
2%o
fun
i
v
e
r
s
i
t
i
e
se
xp
e
r
i
en
c
ev
e
r
ysm
a
l
lr
e
r
an
k
in
g
so
fl
e
s
sth
ano
re
q
u
a
ltof
i
v
e
po
s
i
t
ion
s
,wh
i
l
e7
0un
i
v
e
r
s
i
t
i
e
s
,o
r1
4
.
0
%o
fth
eto
t
a
l,e
xp
e
r
i
en
c
er
e
r
an
k
in
g
sg
r
e
a
t
e
rth
an2
5po
s
i
t
ion
s
.
Th
e
s
ef
i
g
u
r
e
sa
r
e2
0
.
2%and3
9
.
0%wh
en go
in
gf
romth
eWo
S c
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
emtoo
u
rd
a
t
a
s
e
t
.
Amon
gth
ef
i
r
s
t1
0
0un
i
v
e
r
s
i
t
i
e
s
,6
0e
xp
e
r
i
en
c
esm
a
l
lr
e
r
an
k
in
g
singo
in
gf
romTitoT
*i,wh
i
l
eon
l
y4
4
a
r
einth
i
ss
i
t
u
a
t
ioninth
ech
an
g
eb
e
tw
e
enc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
em
s
.A
sf
a
ra
sth
ec
a
rd
in
a
lch
an
g
e
si
s
con
c
e
rn
e
d
,8
2
.
8
%o
fun
i
v
e
r
s
i
t
i
e
sh
a
v
ech
an
g
e
s
intop1
0%
ind
i
c
a
to
rv
a
l
u
e
ssm
a
l
l
e
rth
ano
re
q
u
a
lto0
.
0
5
wh
engo
in
gf
romTitoT
*i.Th
i
sp
e
r
c
en
t
a
g
ei
s7
1%amon
gth
ef
i
r
s
t1
0
0un
i
v
e
r
s
i
t
i
e
s
.Th
e
s
ef
i
g
u
r
e
sa
r
e
5
0
.
1
%and6
0
.
0%
inth
ech
an
g
eb
e
tw
e
enc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
em
s
.Fo
rmo
s
tun
i
v
e
r
s
i
t
i
e
s
,th
ed
i
f
f
e
r
en
c
e
sa
r
e
mo
r
eo
r
l
e
s
sn
e
g
l
i
g
ib
l
e
.A
l
tho
u
ghfo
rsom
eun
i
v
e
r
s
i
t
i
e
smo
r
es
i
gn
i
f
i
c
an
td
i
f
f
e
r
en
c
e
sc
anb
eob
s
e
r
v
e
d
,th
e
con
c
l
u
s
ioni
sc
l
e
a
r
.Th
ed
i
f
f
e
r
en
c
e
sob
s
e
r
v
e
dinun
i
v
e
r
s
i
t
yr
an
k
in
g
sa
c
co
rd
in
gtoth
etop1
0%ind
i
c
a
to
r
wh
en w
eadop
tth
etwoso
l
u
t
ion
sfo
rso
l
v
in
gth
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
ema
r
econ
s
id
e
r
ab
l
y
f
ew
e
rth
ana
c
co
rd
in
gtoth
es
am
eind
i
c
a
to
rwh
enw
e mo
v
ef
romth
e Wo
Sc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
emtoo
u
r
d
a
t
a
s
e
t
.
Th
er
e
s
u
l
t
sfo
rth
ecomp
a
r
i
sonb
e
tw
e
enun
i
v
e
r
s
i
t
yr
an
k
in
g
sa
c
co
rd
in
gtoth
ea
v
e
r
a
g
eo
fh
i
gh
imp
a
c
tg
ap
sa
r
einT
ab
l
e5
.A
l
tho
u
ghas
y
s
t
em
a
t
i
ccomp
a
r
i
sonb
e
tw
e
enth
eind
i
c
a
to
r
sTi andAii
s
b
e
yondth
es
cop
eo
fth
i
sp
ap
e
r
,b
ycomp
a
r
in
gth
eco
r
r
e
spond
in
gr
an
k
in
g
sinT
ab
l
eAinth
eApp
end
i
x
x
t
r
em
e
th
efo
l
low
in
gth
r
e
epo
in
t
sa
r
e wo
r
themph
a
s
i
z
in
g
.F
i
r
s
t
l
y
,th
el
a
c
ko
frob
u
s
tn
e
s
so
fAitoe
ob
s
e
r
v
a
t
ion
si
sv
e
r
yapp
a
r
en
t
.Th
efo
l
low
in
gun
i
v
e
r
s
i
t
i
e
sg
a
inal
a
r
g
en
umb
e
ro
fpo
s
i
t
ion
s(
inb
r
a
c
k
e
t
s
)
d
u
etoth
eimp
a
c
to
fh
i
gh
l
y
c
i
t
e
da
r
t
i
c
l
e
s
:Un
i
v
e
r
s
i
t
yo
f Gö
t
t
in
g
en(
2
6
4)
,th
eUn
i
v
e
r
s
i
t
yo
fF
lo
r
id
a(
2
0
2
)
,
23
L
undUni
v
e
r
s
i
t
y(
1
9
1
)
,O
s
a
k
aUn
i
v
e
r
s
i
t
y(
3
1
8
)
,andToho
k
uUn
i
v
e
r
s
i
t
y(
3
1
1
)
.Inth
er
an
k
in
ga
c
co
rd
in
g
toTi,t
h
e
s
eun
i
v
e
r
s
i
t
i
e
so
c
c
up
ypo
s
i
t
ion
s2
6
5
,2
4
8
,2
8
1
,3
9
7
,and4
0
7
,r
e
sp
e
c
t
i
v
e
l
y
.11 S
e
cond
l
y
,b
e
c
a
u
s
e
th
eh
i
gh
imp
a
c
ta
r
t
i
c
l
e
so
fc
e
r
t
a
inun
i
v
e
r
s
i
t
i
e
sr
e
c
e
i
v
ec
i
t
a
t
ion
sc
lo
s
etoth
eCCL
s
,th
e
ydo
lo
s
epo
s
i
t
ion
s
(
inb
r
a
c
k
e
t
s
)wh
enw
e mo
v
ef
romTitoAi.Th
i
si
sth
ec
a
s
e
,fo
re
x
amp
l
e
,o
f Un
i
v
e
r
s
i
t
yo
fT
e
x
a
s
SW
M
e
d
i
c
a
lC
en
t
e
r(
loo
s
in
g2
8
2 po
s
i
t
ion
s
)
, LondonS
choo
lo
fH
y
g
i
en
eand T
rop
i
c
a
lM
e
d
i
c
in
e(
2
1
6
)
,
L
an
c
a
s
t
e
r Un
i
v
e
r
s
i
t
y(
2
2
4
)
, Un
i
v
e
r
s
i
t
yo
fE
x
e
t
e
r(
2
0
1
7
)
,andP
a
r
i
sÉ
co
l
ePo
l
i
t
e
chn
i
q
u
e(
2
0
8
)
.Inth
e
r
an
k
in
ga
c
co
rd
in
gtoTi,t
h
e
s
eun
i
v
e
r
s
i
t
i
e
so
c
c
up
ypo
s
i
t
ion
s1
0
,1
3
,7
7
,9
1
,and9
5
,r
e
sp
e
c
t
i
v
e
l
y
.Th
i
rd
l
y
,
th
er
an
g
eo
fv
a
r
i
a
t
ionandth
ein
e
q
u
a
l
i
t
ye
xh
ib
i
t
e
db
yAi v
a
l
u
e
sa
r
econ
s
id
e
r
ab
l
yg
r
e
a
t
e
rth
antho
s
e
e
xh
ib
i
t
e
db
yth
eTi v
a
l
u
e
s
.Fo
re
x
amp
l
e
,th
eco
e
f
f
i
c
i
en
t
so
fv
a
r
i
a
t
ionfo
rth
eAiandth
eTi v
a
l
u
e
sa
r
e
1
.
3
6and0
.
3
5
.Th
u
s
,th
e
r
ei
snodo
ub
tth
a
tbo
thind
i
c
a
to
r
sg
en
e
r
a
t
econ
s
id
e
r
ab
l
yd
i
f
f
e
r
en
tun
i
v
e
r
s
i
t
y
r
an
k
in
g
s
. Con
s
e
q
u
en
t
l
y
,i
ti
simpo
r
t
an
ttoe
x
am
in
eth
econ
s
e
q
u
en
c
e
so
fadop
t
in
gth
etwoso
l
u
t
ion
sto
th
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
emu
s
in
gth
ea
v
e
r
a
g
eo
fh
i
gh
imp
a
c
tg
ap
s
ind
i
c
a
to
r
.
T
ab
l
e5a
roundh
e
r
e
Th
eP
e
a
r
sonco
r
r
e
l
a
t
ionco
e
f
f
i
c
i
en
tb
e
tw
e
enth
eAi andA
*i un
i
v
e
r
s
i
t
yv
a
l
u
e
si
s0
.
4
8
,wh
i
l
eth
e
Sp
e
a
rm
an co
r
r
e
l
a
t
ion co
e
f
f
i
c
i
en
tb
e
tw
e
enr
an
k
si
s0
.
9
9
. How
e
v
e
r
,th
elow P
e
a
r
son co
r
r
e
l
a
t
ion
co
e
f
f
i
c
i
en
ti
sd
u
etoth
ep
r
e
s
en
c
eo
fth
e Un
i
v
e
r
s
i
t
yo
f Gö
t
t
in
g
en
. W
i
tho
u
tth
i
s un
i
v
e
r
s
i
t
y
,th
i
s
co
r
r
e
l
a
t
ionco
e
f
f
i
c
i
en
tb
e
com
e
s0
.
9
9
.Inan
yc
a
s
e
,a
sb
e
fo
r
e
,h
i
ghco
r
r
e
l
a
t
ion
sb
e
tw
e
enun
i
v
e
r
s
i
t
yv
a
l
u
e
s
andr
an
k
sdono
tp
r
e
c
l
ud
eimpo
r
t
an
td
i
f
f
e
r
en
c
e
sfo
rind
i
v
id
u
a
lun
i
v
e
r
s
i
t
i
e
s
.T
h
eo
rd
in
a
ld
i
f
f
e
r
en
c
e
sin
un
i
v
e
r
s
i
t
yr
an
k
in
g
sa
c
co
rd
in
gtoth
i
sind
i
c
a
to
rw
i
thand w
i
tho
u
tf
i
e
ld
-no
rm
a
l
i
z
a
t
iona
r
em
u
chsm
a
l
l
e
r
th
antho
s
eob
t
a
in
e
dw
i
thth
etop1
0%ind
i
c
a
to
r
.Fo
re
x
amp
l
e
,6
6
.
6
%o
fun
i
v
e
r
s
i
t
i
e
se
xp
e
r
i
en
c
ev
e
r
y
sm
a
l
lr
e
r
an
k
in
g
so
fl
e
s
sth
ano
re
q
u
a
ltof
i
v
epo
s
i
t
ion
s
, wh
i
l
e2
0un
i
v
e
r
s
i
t
i
e
s
,o
r4
.
0%o
fth
eto
t
a
l
,
1
1W
eno
t
eth
a
tth
eUn
i
v
e
r
s
i
t
yo
f Gö
t
t
in
g
eni
sq
u
i
t
easp
e
c
i
a
lc
a
s
e
.Th
eM
ean No
rm
a
l
i
z
edC
i
t
a
t
ionS
co
r
e
,andh
en
c
eth
eAi
v
a
l
u
eo
fth
eUn
i
v
e
r
s
i
t
yo
f Gö
t
t
in
g
eni
sknowntob
es
t
ron
g
l
yd
e
t
e
rm
in
edb
yas
in
g
l
ee
x
t
r
em
e
l
yh
i
gh
l
yc
i
t
edp
ub
l
i
c
a
t
ion(
s
e
e
W
a
l
tm
an e
ta
l
.
,2
0
1
2
b
,fo
r mo
r
ed
e
t
a
i
l
sonth
i
sc
a
s
e
)
.
24
e
xp
e
r
i
en
c
er
e
r
an
k
in
g
sg
r
e
a
t
e
rth
an1
6po
s
i
t
ion
s
.Amon
gth
ef
i
r
s
t1
0
0un
i
v
e
r
s
i
t
i
e
s
,7
8e
xp
e
r
i
en
c
esm
a
l
l
r
e
r
an
k
in
g
s
ingo
in
gf
romAitoA
*i(
incomp
a
r
i
sonw
i
th6
0wh
engo
in
gf
romTitoT
*i)
.
A
sf
a
ra
sth
ec
a
rd
in
a
lch
an
g
e
sa
r
econ
c
e
rn
e
d
,w
esho
u
ldr
e
c
a
l
lth
eh
i
ghco
e
f
f
i
c
i
en
to
fv
a
r
i
a
t
iono
f
th
e5
0
0Ai v
a
l
u
e
s
,e
q
u
a
lto1
.
3
6
. How
e
v
e
r
,no
rm
a
l
i
z
a
t
ionr
ad
i
c
a
l
l
ych
an
g
e
sth
es
i
t
u
a
t
ion
:th
er
an
g
eo
f
v
a
r
i
a
t
ionandth
eco
e
f
f
i
c
i
en
to
fv
a
r
i
a
t
iono
fth
eA
*iv
a
l
u
e
sa
r
enow m
u
chsm
a
l
l
e
rth
anb
e
fo
r
e(
s
e
eT
ab
l
e
A
)
. Con
s
e
q
u
en
t
l
y
,th
ec
a
rd
in
a
lchan
g
e
sb
e
tw
e
enAitoA
*i a
r
em
u
chl
a
r
g
e
rth
anb
e
tw
e
enTitoT
*i:
4
1
.
8
%o
fun
i
v
e
r
s
i
t
i
e
sh
a
v
ech
an
g
e
s
in
ind
i
c
a
to
rv
a
l
u
e
ssm
a
l
l
e
rth
ano
re
q
u
a
lto0
.
0
5wh
engo
in
gf
rom Ai
toA
*i–
incomp
a
r
i
sonto8
2
.
8
% wh
engo
in
gf
romTitoT
*i.
V
.CONCLUS
IONS
Th
eh
e
t
e
ro
g
en
ei
t
yo
fth
ef
i
e
ld
sd
i
s
t
in
g
u
i
sh
e
d
inan
yc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
empo
s
e
sa
g
r
a
v
ea
g
g
r
e
g
a
t
ion
p
rob
l
emwh
enon
ei
sin
t
e
r
e
s
t
e
dine
v
a
l
u
a
t
in
gth
ec
i
t
a
t
ionimp
a
c
to
fas
e
to
fr
e
s
e
a
r
chun
i
t
sinth
ea
l
l
s
c
i
en
c
e
sc
a
s
e
.Inth
i
sp
ap
e
r
,w
eh
a
v
ean
a
l
y
z
e
dtwopo
s
s
ib
l
eso
l
u
t
ion
stoth
i
sp
rob
l
em
.Th
ef
i
r
s
tso
l
u
t
ion
r
e
l
i
e
sonp
r
io
rno
rm
a
l
i
z
a
t
iono
fth
er
awc
i
t
a
t
ion
sr
e
c
e
i
v
e
db
ya
l
lp
ub
l
i
c
a
t
ion
s
.Inp
a
r
t
i
c
u
l
a
r
,w
efo
c
u
son
th
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
ein wh
i
chf
i
e
ld m
e
anc
i
t
a
t
ion
sa
r
eu
s
e
da
sno
rm
a
l
i
z
a
t
ion
f
a
c
to
r
s
. Th
es
e
condso
l
u
t
ione
x
t
end
sth
eapp
ro
a
chadop
t
e
dinth
eL
e
id
enandSC
Im
a
gor
an
k
in
g
sfo
r
comp
u
t
in
gth
eTop1
0%
ind
i
c
a
to
r
inth
ea
l
l
s
c
i
en
c
e
sc
a
s
etoan
yadm
i
s
s
ib
l
e
ind
i
c
a
to
r
.Th
i
sso
l
u
t
iondo
e
s
no
tr
e
q
u
i
r
ean
yp
r
io
rf
i
e
ld
-no
rm
a
l
i
z
a
t
ion
:th
ec
i
t
a
t
ion
imp
a
c
to
fan
yr
e
s
e
a
r
chun
i
tinth
ea
l
l
-s
c
i
en
c
e
s
c
a
s
e
i
sc
a
l
c
u
l
a
t
e
da
sth
eapp
rop
r
i
a
t
e
l
yw
e
i
gh
t
e
ds
umo
fth
ec
i
t
a
t
ion
imp
a
c
tth
a
tth
eun
i
ta
ch
i
e
v
e
s
ine
a
chf
i
e
ld
.
Con
c
ep
t
u
a
l
l
y
,th
ed
i
f
f
e
r
en
c
ei
sc
l
e
a
r
.Th
eu
s
u
a
lso
l
u
t
ions
t
a
r
t
sb
yd
e
t
e
rm
in
in
gth
es
e
to
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
sinth
eo
v
e
r
a
l
lno
rm
a
l
i
z
e
dc
i
t
a
t
iond
i
s
t
r
ib
u
t
io
nfo
rp
ub
l
i
c
a
t
ion
sina
l
lf
i
e
ld
s
.G
i
v
ena
c
i
t
a
t
ionind
i
c
a
to
r
,t
h
ek
e
yr
e
f
e
r
en
c
efo
re
a
chr
e
s
e
a
r
chun
i
ti
sth
eun
i
q
u
eno
rm
a
l
i
z
e
dn
umb
e
ro
fc
i
t
a
t
ion
s
th
a
td
e
t
e
rm
in
e
sth
es
e
to
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
sfo
ra
l
ls
c
i
en
c
e
st
a
k
ento
g
e
th
e
r
.Th
ea
l
t
e
rn
a
t
i
v
eso
l
u
t
ion
p
r
e
s
e
r
v
e
sth
eun
i
t
s
’k
e
yr
e
f
e
r
en
c
ea
tth
el
e
v
e
lo
fe
a
chind
i
v
id
u
a
lf
i
e
ld
.Ino
th
e
r wo
rd
s
,th
ed
i
f
f
e
r
en
c
e
25
bo
i
l
sdowntoth
ew
a
yth
es
e
to
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
sinth
ea
l
l
s
c
i
en
c
e
sc
a
s
ei
scon
s
t
r
u
c
t
e
d
.Inth
eu
s
u
a
l
so
l
u
t
ion
,
i
t
i
sb
u
i
l
tup
inas
in
g
l
es
t
ro
k
ea
f
t
e
rno
rm
a
l
i
z
a
t
ion
.Inth
ea
l
t
e
rn
a
t
i
v
eso
l
u
t
ion
,
i
t
i
sb
u
i
l
tupf
rom
th
es
e
to
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
sine
a
chf
i
e
ld
.Inth
i
sc
a
s
e
,a
l
lf
i
e
ld
sa
r
et
r
e
a
t
e
df
a
i
r
l
yinth
es
en
s
eth
a
te
a
ch
con
t
r
ib
u
t
e
stoth
eo
v
e
r
a
l
ls
e
to
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
s
inth
es
am
ep
ropo
r
t
ionto
i
t
ss
i
z
e
.
Inp
r
a
c
t
i
c
e
,th
e mo
r
ef
i
e
ldc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sd
i
f
f
e
ron
l
yb
yas
c
a
l
ef
a
c
to
r
,th
eb
e
t
t
e
rw
i
l
lb
eth
e
p
e
r
fo
rm
an
c
eo
fth
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
eine
l
im
in
a
t
in
gth
ee
f
f
e
c
to
fd
i
f
f
e
r
en
c
es
b
e
tw
e
enf
i
e
ldono
v
e
r
a
l
lc
i
t
a
t
ionin
e
q
u
a
l
i
t
y
,th
e mo
r
eth
etwos
e
t
so
fh
i
gh
imp
a
c
ta
r
t
i
c
l
e
sw
i
l
lr
e
s
emb
l
e
e
a
cho
th
e
r
,andth
esm
a
l
l
e
rw
i
l
lb
eth
ed
i
f
f
e
r
en
c
eb
e
tw
e
enth
etwoapp
ro
a
ch
e
sind
ep
end
en
t
l
yo
fth
e
c
i
t
a
t
ion
imp
a
c
t
ind
i
c
a
to
rw
ec
a
r
etou
s
e
inth
ee
v
a
l
u
a
t
iono
fth
er
e
s
e
a
r
chun
i
t
s
.
U
s
in
gal
a
r
g
e Wo
Sd
a
t
a
s
e
tcon
s
i
s
t
in
go
f3
.
6m
i
l
l
ionp
ub
l
i
c
a
t
ion
sinth
e2
0
0
5
2
0
0
8p
e
r
iodandan
a
l
go
r
i
thm
i
c
a
l
l
ycon
s
t
r
u
c
t
e
dp
ub
l
i
c
a
t
ion
l
e
v
e
lc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
emth
a
td
i
s
t
in
g
u
i
sh
e
sb
e
tw
e
en5
,
1
1
9
c
l
u
s
t
e
r
s
,t
h
etwoa
l
t
e
rn
a
t
i
v
e
sh
a
v
eb
e
encon
f
ron
t
e
dwh
enth
ec
i
t
a
t
ionimp
a
c
to
fth
e5
0
0LRun
i
v
e
r
s
i
t
i
e
s
a
r
ee
v
a
l
u
a
t
e
du
s
in
gtwoind
i
c
a
to
r
sw
i
thv
e
r
yd
i
f
f
e
r
en
tp
rop
e
r
t
i
e
s
:th
e Top1
0%ind
i
c
a
to
r
,andth
e
A
v
e
r
a
g
eo
fh
i
gh
imp
a
c
tg
ap
s
.
Th
esh
ap
eo
fth
ec
i
t
a
t
ion d
i
s
t
r
ib
u
t
ion
so
f4
,
1
6
1s
i
gn
i
f
i
c
an
tc
l
u
s
t
e
r
sw
i
th mo
r
eth
an 1
0
0
p
ub
l
i
c
a
t
ion
s
ino
u
rd
a
t
a
s
e
th
a
sb
e
enp
r
e
v
io
u
s
l
yshowntob
eh
i
gh
l
ys
k
ew
e
dandr
e
a
son
ab
l
ys
im
i
l
a
r(R
u
i
z
C
a
s
t
i
l
lo & W
a
l
tm
an
,2
0
1
5
)
.P
r
e
v
io
u
sr
e
s
u
l
t
sw
i
th Wo
Sc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
em
sth
a
td
i
s
t
in
g
u
i
sha
t mo
s
t
b
e
tw
e
en2
3
5s
ub
f
i
e
ld
sind
i
c
a
t
eth
a
t
,wh
enth
i
si
sth
ec
a
s
e
,th
es
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
ionp
ro
c
e
d
u
r
e
p
e
r
fo
rmsw
e
l
linr
e
d
u
c
in
gth
eo
v
e
r
a
l
lc
i
t
a
t
ionin
e
q
u
a
l
i
t
ya
t
t
r
ib
u
t
e
dtoth
ed
i
f
f
e
r
en
c
e
sinp
rod
u
c
t
ionand
c
i
t
a
t
ionp
r
a
c
t
i
c
e
sb
e
tw
e
enf
i
e
ld
s
.Inth
i
sp
ap
e
r
,w
eh
a
v
eshownth
a
twh
enw
er
e
s
t
r
i
c
to
u
ra
t
t
en
t
ionto
3
,
3
3
2c
l
u
s
t
e
r
sw
i
th mo
r
eth
an2
5
0p
ub
l
i
c
a
t
ion
sth
i
si
sa
l
soth
ec
a
s
e
.N
e
v
e
r
th
e
l
e
s
s
, ap
r
i
o
r
ii
ti
sno
t
ob
v
io
u
s wh
a
ttoe
xp
e
c
twh
en w
econ
f
ron
tth
etwo so
l
u
t
ion
stoth
ea
l
l
s
c
i
en
c
e
sa
g
g
r
e
g
a
t
ionp
rob
l
em
w
i
thandw
i
tho
u
tp
r
io
rf
i
e
ld
-no
rm
a
l
i
z
a
t
ionfo
rth
e5
,
1
1
9c
l
u
s
t
e
r
s
.
26
In
t
e
r
e
s
t
in
g
l
yeno
u
gh
,th
ed
i
f
f
e
r
en
c
e
sb
e
tw
e
enth
eun
i
v
e
r
s
i
t
yr
an
k
in
g
sob
t
a
in
e
dw
i
thbo
thso
l
u
t
ion
s
i
so
fasm
a
l
lo
rd
e
ro
fm
a
gn
i
t
ud
eind
ep
end
en
t
l
yo
fth
ec
i
t
a
t
ionimp
a
c
tind
i
c
a
to
ru
s
e
dinth
econ
s
t
r
u
c
t
i
on
o
fth
eun
i
v
e
r
s
i
t
yr
an
k
in
g
s
.Inp
a
r
t
i
c
u
l
a
r
,th
e
s
ed
i
f
f
e
r
en
c
e
sa
r
econ
s
id
e
r
ab
l
ysm
a
l
l
e
rth
anth
e on
e
s
ob
t
a
in
e
dinR
u
i
z
-C
a
s
t
i
l
lo & W
a
l
tm
an(
2
0
1
5)wh
enw
e mo
v
ef
romth
e Wo
Sc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
emw
i
th
2
3
6s
ub
f
i
e
ld
stoth
eon
eu
s
e
d
inth
i
sp
ap
e
rw
i
th5
,
1
1
9c
l
u
s
t
e
r
s
.
Inp
r
in
c
ip
l
e
,
i
ts
e
em
sp
r
e
f
e
r
ab
l
etoe
v
a
l
u
a
t
eth
ec
i
t
a
t
ion
imp
a
c
to
fr
e
s
e
a
r
chun
i
t
s
inth
ea
l
l
s
c
i
en
c
e
s
c
a
s
ea
vo
id
in
gan
yk
indo
fp
r
io
rno
rm
a
l
i
z
a
t
ionop
e
r
a
t
ion
. How
e
v
e
r
,th
eemp
i
r
i
c
a
le
v
id
en
c
ew
eh
a
v
e
p
r
e
s
en
t
e
dind
i
c
a
t
e
sth
a
tth
em
e
thodr
e
l
y
in
gonth
ep
r
io
rs
t
and
a
rdf
i
e
ld
-no
rm
a
l
i
z
a
t
iondo
e
sno
tl
e
adto
v
e
r
yd
i
f
f
e
r
en
tr
e
s
u
l
t
s
.Th
i
si
sacon
v
en
i
en
tcon
c
l
u
s
ion
,s
in
c
eth
e
r
ea
r
ein
s
t
an
c
e
swh
enno
rm
a
l
i
z
a
t
ioni
s
s
t
ron
g
l
yad
v
i
s
ab
l
e
;fo
re
x
amp
l
e
, wh
en on
ei
sin
t
e
r
e
s
t
e
dins
t
ud
y
in
gth
er
e
s
e
a
r
ch un
i
t
s
’c
i
t
a
t
i
on
d
i
s
t
r
ib
u
t
ion
sinth
ea
l
l
s
c
i
en
c
e
sc
a
s
e–
a
sw
edointh
ecomp
an
ionp
ap
e
rP
e
r
i
an
e
s
-Rod
r
i
g
u
e
z &R
u
i
z
C
a
s
t
i
l
lo(
2
0
1
4
)
.
I
tsho
u
ldb
eno
t
e
dth
a
t
,b
e
fo
r
eb
e
in
ga
c
c
ep
t
e
d
,
i
two
u
ldb
ead
v
i
s
ab
l
etor
ep
l
i
c
a
t
eth
er
e
s
u
l
t
so
fth
i
s
p
ap
e
rfo
ro
th
e
rd
a
t
a
s
e
t
s
,o
th
e
rc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
em
s
,o
th
e
rt
yp
e
so
fr
e
s
e
a
r
chun
i
t
s
,ando
th
e
rw
a
y
so
f
a
s
s
i
gn
in
gr
e
spon
s
ib
i
l
i
t
yb
e
tw
e
enr
e
s
e
a
r
chun
i
t
s
inth
ec
a
s
eo
fco
a
u
tho
r
e
dp
ub
l
i
c
a
t
ion
s
.
27
REFERENCES
A
lb
a
r
r
án
,P
.
,O
r
t
uño,I
.
, &Ru
i
z
C
a
s
t
i
l
lo
,J
.(
2
0
1
1a
)
.Th
em
e
a
s
u
r
em
en
to
flow
-andh
i
gh
imp
a
c
tinc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
s
:
t
e
chn
i
c
a
lr
e
s
u
l
t
s
.J
o
u
r
n
a
lo
fI
n
f
o
rm
e
t
r
i
c
s
,
5
,4
8
–6
3
.
A
lb
a
r
r
án
,P
.
,C
r
e
spo
,J
.
,O
r
t
uño
,I
.
,&Ru
i
zC
a
s
t
i
l
lo
,J
.(
2
0
1
1b)
.Th
es
k
ewn
e
s
so
fs
c
i
en
c
ein2
1
9s
ubf
i
e
ld
sandan
umb
e
ro
f
a
g
g
r
e
g
a
t
e
s
.S
c
i
e
n
t
om
e
t
r
i
c
s,
8
8
,3
8
5
–3
9
7
.
Bo
rnm
ann
,L
.
,D
e Mo
y
a An
e
gón
,F
.
,L
e
yd
e
sdo
r
f
f
,L
.(
2
0
1
2
)Th
en
ew E
x
c
e
l
l
en
c
eInd
i
c
a
to
rinth
e Wo
r
ldR
epo
r
to
fth
e
SC
Im
a
goIn
s
t
i
t
u
t
ion
sR
an
k
in
g
s2
0
1
1
.Jo
u
rn
a
lo
fIn
fo
rm
e
t
r
i
c
s
,6
,
3
3
3
3
3
5
.
B
r
z
e
z
in
s
k
i
,M
.(
2
0
1
5)
.Pow
e
r
l
aw
s
inc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
s
:E
v
id
e
n
c
ef
romS
cop
u
s
,S
c
i
e
n
t
om
e
t
r
i
c
s,
1
0
3
:2
1
3
2
2
8
.
C
r
e
spo
,J
.A
.
,L
i
,Y
.
, & Ru
i
zC
a
s
t
i
l
lo
,J
.(
2
0
1
3
)
.Th
em
e
a
s
u
r
em
en
to
fth
ee
f
f
e
c
tonc
i
t
a
t
ionin
e
q
u
a
l
i
t
yo
fd
i
f
f
e
r
en
c
e
sin
c
i
t
a
t
ionp
r
a
c
t
i
c
e
sa
c
ro
s
ss
c
i
en
t
i
f
i
cf
i
e
ld
s
.PL
oSONE,
8
,e
5
8
7
2
7
.
C
r
e
spo
,J
.A
.
,H
e
r
ran
z
,N
.
,L
i
,Y
.
, &Ru
i
z
C
a
s
t
i
l
lo
,J
.(
2
0
1
4
)
.Th
ee
f
f
e
c
tonc
i
t
a
t
ionin
e
q
u
a
l
i
t
yo
fd
i
f
f
e
r
en
c
e
sinc
i
t
a
t
ion
p
r
a
c
t
i
c
e
sa
tth
eW
ebo
fS
c
i
en
c
es
ub
j
e
c
tc
a
t
e
go
r
yl
e
v
e
l
.J
o
u
r
n
a
lo
ft
h
e Am
e
r
i
c
a
nS
o
c
i
e
t
yf
o
rI
n
f
o
rm
a
t
i
o
nS
c
i
e
n
c
ea
n
dT
e
c
h
n
o
l
o
g
y
,6
5
,
1
2
4
4
–1
2
5
6
.
G
ro
en
ev
e
ld
,R
.A
.
,M
e
ed
en
,G
.(
1
9
8
4
)
.M
e
a
s
u
r
in
gs
k
ewn
e
s
sandk
u
r
to
s
i
s
.
T
h
eS
t
a
t
i
s
t
i
c
i
a
n,
3
3
:3
9
1
–3
9
9
.
L
i
,Y
.
,C
a
s
t
e
l
l
ano
,C
.
,R
ad
i
c
ch
i
,F
.
, & Ru
i
zC
a
s
t
i
l
lo
,J
.(
2
0
1
3
)
. Qu
an
t
i
t
a
t
i
v
ee
v
a
l
u
a
t
iono
fa
l
t
e
rn
a
t
i
v
ef
i
e
ldno
rm
a
l
i
z
a
t
ion
p
ro
c
ed
u
r
e
s
.J
o
u
r
n
a
lo
fI
n
f
o
rm
e
t
r
i
c
s
,
7
,7
4
6
–7
5
5
.
P
e
r
i
an
e
sRod
r
i
g
u
e
z
,A
.
,andRu
i
zC
a
s
t
i
l
lo
,J
.(
2
0
1
4
)
.Un
i
v
e
r
s
i
t
yc
i
t
a
t
ion d
i
s
t
r
ib
u
t
ion
s
. Wo
r
k
in
gP
ap
e
r1
42
6
,Un
i
v
e
r
s
id
ad
C
a
r
lo
sI
I
I(
h
t
tp
://hd
l
.h
and
l
e
.n
e
t/
1
0
0
1
6/
1
9
8
1
1)
.
R
ad
i
c
ch
i
,F
.
,&C
a
st
e
l
l
ano
,C
.(
2
0
1
2
)
.Ar
e
v
e
r
s
een
g
in
e
e
r
in
gapp
ro
a
chtoth
es
upp
r
e
s
s
iono
fc
i
t
a
t
ionb
i
a
s
e
sr
e
v
e
a
l
sun
i
v
e
r
s
a
l
p
rop
e
r
t
i
e
so
fc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
s
.PL
oSONE,
7
,e
3
3
8
3
3
.
R
ad
i
c
ch
i
,F
.
, Fo
r
t
un
a
to
,S
.
,and C
a
s
t
e
l
l
ano
,C
.(
2
0
0
8)
,“
Un
i
v
e
r
s
a
l
i
t
yo
fC
i
t
a
t
ion D
i
s
t
r
ibu
t
ion
s
: Tow
a
rd An Ob
j
e
c
t
i
v
e
M
e
a
s
u
r
eo
fS
c
i
en
t
i
f
i
cImp
a
c
t”
,PNAS,
1
0
5
:
1
7
2
6
8
1
7
2
7
2
.
R
u
i
zC
a
s
t
i
l
lo
,J
.(
2
0
1
4
)
.Th
ecomp
a
r
i
sono
fc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
em
b
a
s
edno
rm
a
l
i
z
a
t
ionp
ro
c
ed
u
r
e
sw
i
thso
u
r
c
eno
rm
a
l
i
z
a
t
ion
a
l
t
e
rn
a
t
i
v
e
s
in W
a
l
tm
anandV
anE
c
k
.J
o
u
r
n
a
lo
fI
n
f
o
rm
e
t
r
i
c
s
,
8
,2
5
–2
8
.
R
u
i
zC
a
s
t
i
l
lo
,J
.& W
a
l
tm
an
,L
.(
2
0
1
5
)
.F
i
e
ld
no
rm
a
l
i
z
edc
i
t
a
t
ionimp
a
c
tind
i
c
a
to
r
su
s
in
ga
l
go
r
i
thm
i
c
a
l
l
ycon
s
t
r
u
c
t
ed
c
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
em
so
fs
c
i
en
c
e
.
J
o
u
r
n
a
lo
fI
n
f
o
rm
e
t
r
i
c
s
,
9
,1
0
2
1
1
7
.
S
ch
ub
e
r
t
,A
.
,G
l
än
z
e
l
,W
.
, &B
r
a
un
,T
.(
1
9
8
7
)
.S
ub
j
e
c
tf
i
e
ldch
a
r
a
c
t
e
r
i
s
t
i
cc
i
t
a
t
ions
co
r
e
sands
c
a
l
e
sfo
ra
s
s
e
s
s
in
gr
e
s
e
a
r
ch
p
e
r
fo
rm
an
c
e
.S
c
i
e
n
t
om
e
t
r
i
c
s,
1
2
,2
6
7
–2
9
2
.
Th
e
lw
a
l
l
,M
.
,&W
i
l
son
,P
.(
2
0
1
4
)
,D
i
s
t
r
ib
u
t
ion
sfo
rc
i
t
eda
r
t
i
c
l
e
sf
rom
ind
i
v
id
u
a
ls
ub
j
e
c
t
sandy
e
a
r
s
.J
o
u
r
n
a
lo
fI
n
f
o
rm
e
t
r
i
c
s
,
8
,
8
2
4
8
3
9
.
W
a
l
tm
an
,L
.
, &V
anE
c
k
,N
.J
.(
2
0
1
2
)
. An
ew m
e
thodo
lo
g
yfo
rcon
s
t
r
u
c
t
in
gap
ub
l
i
c
a
t
ionl
e
v
e
lc
l
a
s
s
i
f
i
c
a
t
ions
y
s
t
emo
f
s
c
i
en
c
e
.J
o
u
r
n
a
lo
ft
h
eAm
e
r
i
c
a
nS
o
c
i
e
t
y
f
o
rI
n
f
o
rm
a
t
i
o
nS
c
i
e
n
c
ea
n
dT
e
c
h
n
o
l
o
g
y
,
6
3
,2
3
7
8
–2
3
9
2
.
W
a
l
tm
an
,L
.
,C
a
l
e
roM
ed
in
a,C
.
,Ko
s
t
en
,J
.
, No
yon
s
,E
.C
.M
.
,T
i
j
s
s
en
,R
.J
.W
.
,V
anE
c
k
,N
.J
.
,V
anL
e
e
uw
en
,T
.N
.
,V
an
R
a
an
,A
.F
.J
.
,V
i
s
s
e
r
,M
.S
.
, & Wo
u
t
e
r
s
,P
.(
2
0
1
2a
)
.Th
eL
e
id
en R
an
k
in
g2
0
1
1/
2
0
1
2
:D
a
t
aco
l
l
e
c
t
ion
,ind
i
c
a
to
r
s
,and
J
o
u
r
n
a
lo
ft
h
eAm
e
r
i
c
a
nS
o
c
i
e
t
y
f
o
rI
n
f
o
rm
a
t
i
o
nS
c
i
e
n
c
ea
n
dT
e
c
h
n
o
l
o
g
y
,
6
3
,2
4
1
9
–2
4
3
2
.
in
t
e
rp
r
e
t
a
t
ion
.
W
a
l
tm
an
,L
.
,V
an E
c
k
,N
.J
.
, &V
anR
a
an
,A
.F
.J
.(
2
0
1
2b)
.Un
i
v
e
r
s
a
l
i
t
yo
fc
i
t
a
t
iond
i
s
t
r
ib
u
t
ion
sr
e
v
i
s
i
t
ed
.J
o
u
r
n
a
lo
ft
h
e
Am
e
r
i
c
a
nS
o
c
i
e
t
y
f
o
rI
n
f
o
rm
a
t
i
o
nS
c
i
e
n
c
ea
n
dT
e
c
h
n
o
l
o
g
y,
6
3
,7
2
–7
7
.
W
a
l
tman
,L
.
,andS
ch
r
e
ib
e
r
,M
.(
2
0
1
3
)
. Onth
ec
a
l
c
u
l
a
t
iono
fp
e
r
c
en
t
i
l
e
-b
a
s
edb
ib
l
iom
e
t
r
i
cind
i
c
a
to
r
s.
J
o
u
r
n
a
lo
ft
h
e Am
e
r
i
c
a
n
S
o
c
i
e
t
y
f
o
rI
n
f
o
rm
a
t
i
o
nS
c
i
e
n
c
ea
n
dT
e
c
h
n
o
l
o
g
y,
6
4
,
3
7
2
3
7
9
.
28
W
a
l
tm
an
,L
.
,&V
anE
c
k
,N
.J
.(
2
0
1
3)
.As
y
s
t
em
a
t
i
cemp
i
r
i
c
a
lcomp
a
r
i
sono
fd
i
f
f
e
r
en
tapp
ro
a
ch
e
sfo
rno
rm
a
l
i
z
in
gc
i
t
a
t
ion
imp
a
c
t
ind
i
c
a
to
r
s
.
J
o
u
r
n
a
lo
fI
n
f
o
rm
e
t
r
i
c
s
,
7
,8
3
3
–8
4
9
.
29
APPEND
IX
T
ab
l
eA
. Numb
e
ro
fpub
l
i
c
a
t
ion
s
,andc
i
t
a
t
ionimp
a
c
tind
i
c
a
to
r
sfo
rth
e5
0
0L
e
id
enR
ank
ingun
i
v
e
r
s
i
t
i
e
s
R
ankT
1
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
2
1
2
2
2
3
2
4
2
5
2
6
2
7
2
8
2
9
3
0
3
1
3
2
3
3
3
4
3
5
3
6
3
7
3
8
3
9
4
0
4
1
4
2
4
3
4
4
4
5
4
6
4
7
4
8
4
9
5
0
5
1
Un
i
v
e
r
s
i
t
y
M
IT
H
a
r
v
a
rdUn
i
v
P
r
in
c
e
tonUn
i
v
S
t
an
fo
rdUn
i
v
C
a
l
t
e
ch
Un
i
vC
a
l
i
f-B
e
r
k
e
l
e
y
Un
i
vC
a
l
i
f-S
an
t
aB
a
rb
a
r
a
Un
i
vC
a
l
i
f-S
anF
r
an
c
i
s
co
Y
a
l
eUn
i
v
Un
i
vT
e
x
a
s-SW M
edC
t
r
Un
i
vCh
i
c
a
go
Un
i
vW
a
sh
in
g
ton-S
e
a
t
t
l
e
LondonS
chH
y
g&T
rop M
ed
Un
i
vC
a
l
i
f-S
anD
i
e
go
E
co
l
ePo
l
y
t
e
chF
éd
é
r
a
l
eL
a
u
s
ann
e
No
rthw
e
s
t
e
rnUn
i
v
C
a
rn
e
g
i
eM
e
l
lonUn
i
v
Un
i
vC
a
l
i
f-Lo
sAn
g
e
l
e
s
Co
l
umb
i
aUn
i
v
ETHZ
u
r
i
ch
W
e
i
zm
annIn
s
tS
c
i
R
i
c
eUn
i
v
Un
i
vP
enn
Un
i
vC
a
l
i
f-S
an
t
aC
r
u
z
Un
i
vCo
lo
r
ado-Bo
u
ld
e
r
Un
i
vO
x
fo
rd
D
u
k
eUn
i
v
W
a
sh
in
g
tonUn
iv-S
tLo
u
i
s
John
sHop
k
in
sUn
i
v
NYU
G
eo
r
g
i
aIn
s
tT
e
chno
l
Emo
r
yUn
i
v
Un
i
vC
amb
r
id
g
e
Co
rn
e
l
lUn
i
v
Un
i
vM
i
ch
i
g
an
Un
i
vC
a
l
i
f-R
i
v
e
r
s
id
e
Imp
e
r
i
a
lCo
l
lLondon
D
a
r
tmo
u
thCo
l
l
Bo
s
tonUn
i
v
T
u
f
t
sUn
i
v
Un
i
vCo
l
lLondon
Un
i
vC
a
l
i
f-I
r
v
in
e
I
c
ahnS
ch M
ed M
tS
in
a
i
B
a
y
lo
rCo
l
lM
ed
Un
i
vNC
a
ro
l
in
a-Ch
ap
e
lH
i
l
l
V
and
e
rb
i
l
tUn
i
v
Un
i
vI
l
l
ino
i
sU
rb
an
aCh
amp
a
i
gn
Un
i
vTe
x
a
s-A
u
s
t
in
Un
i
vW
i
s
con
s
in-M
ad
i
son
Un
i
vB
r
i
s
to
l
Un
i
vM
a
r
y
l
and-Co
l
l
e
g
eP
a
r
k
Numb
e
ra
r
t
i
c
l
e
s
8
3
4
6
.
9
6
2
6
8
6
9
.
0
3
4
5
4
8
.
1
8
1
1
9
3
6
.
9
6
5
2
6
4
.
7
6
9
1
8
5
.
5
5
4
1
9
2
.
3
3
8
7
5
7
.
9
1
8
6
7
3
.
4
9
1
2
0
5
.
7
8
6
1
3
3
.
8
2
1
2
5
2
2
.
5
8
1
2
7
5
.
7
1
9
9
8
9
.
1
9
3
7
4
3
.
5
6
8
0
7
9
.
5
9
2
9
1
1
.
5
2
1
3
2
6
7
.
1
0
1
0
6
6
5
.
6
1
6
7
0
6
.
3
2
2
5
2
3
.
1
6
2
0
8
2
.
2
5
1
1
4
3
8
.
5
1
1
7
4
6
.
3
3
4
3
3
5
.
5
0
1
0
9
1
0
.
7
0
9
0
1
7
.
7
5
7
6
7
5
.
8
7
1
2
8
9
4
.
3
9
6
3
6
3
.
6
0
5
3
6
5
.
3
1
5
7
3
2
.
1
5
1
1
1
4
5
.
3
0
1
0
3
6
8
.
5
0
1
4
2
8
6
.
4
6
2
9
5
5
.
9
4
9
1
2
4
.
6
2
1
9
5
9
.
2
9
5
4
1
0
.
1
3
3
3
3
4
.
4
2
1
0
1
3
7
.
8
8
5
6
1
4
.
2
7
2
9
4
0
.
9
2
4
7
4
3
.
1
8
8
0
7
3
.
4
3
6
1
6
0
.
7
9
8
9
5
7
.
9
0
6
9
1
5
.
1
3
1
1
1
2
2
.
7
8
5
2
1
4
.
8
5
5
7
5
0
.
5
0
‰
2
.
3
1
7
.
4
3
1
.
2
6
3
.
3
0
1
.
4
6
2
.
5
4
1
.
1
6
2
.
4
2
2
.
4
0
0
.
3
3
1
.
7
0
3
.
4
6
0
.
3
5
2
.
7
6
1
.
0
4
2
.
2
4
0
.
8
1
3
.
6
7
2
.
9
5
1
.
8
6
0
.
7
0
0
.
5
8
3
.
1
6
0
.
4
8
1
.
2
0
3
.
0
2
2
.
4
9
2
.
1
2
3
.
5
7
1
.
7
6
1
.
4
8
1
.
5
9
3
.
0
8
2
.
8
7
3
.
9
5
0
.
8
2
2
.
5
2
0
.
5
4
1
.
5
0
0
.
9
2
2
.
8
0
1
.
5
5
0
.
8
1
1
.
3
1
2
.
2
3
1
.
7
0
2
.
4
8
1
.
9
1
3
.
0
8
1
.
4
4
1
.
5
9
30
T
2
.
4
1
2
.
2
7
2
.
2
2
2
.
1
9
2
.
1
2
2
.
0
7
1
.
9
4
1
.
9
3
1
.
8
8
1
.
8
2
1
.
8
0
1
.
8
0
1
.
7
9
1
.
7
7
1
.
7
7
1
.
7
7
1
.
7
6
1
.
7
3
1
.
7
3
1
.
7
3
1
.
7
3
1
.
7
2
1
.
7
1
1
.
7
1
1
.
7
0
1
.
6
8
1
.
6
8
1
.
6
5
1
.
6
3
1
.
6
3
1
.
6
2
1
.
6
2
1
.
6
2
1
.
6
0
1
.
6
0
1
.
5
8
1
.
5
8
1
.
5
8
1
.
5
6
1
.
5
6
1
.
5
5
1
.
5
4
1
.
5
3
1
.
5
3
1
.
5
2
1
.
5
0
1
.
5
0
1
.
5
0
1
.
5
0
1
.
4
8
1
.
4
8
Top1
0%
T
* R
ankT
*
2
.
4
5
1
2
.
1
9
4
2
.
3
1
2
2
.
1
9
3
2
.
1
4
5
2
.
0
9
6
1
.
9
8
7
1
.
8
2
9
1
.
8
6
8
1
.
7
1
2
1
1
.
7
9
1
1
1
.
7
6
1
4
1
.
7
0
2
2
1
.
7
5
1
5
1
.
7
9
1
2
1
.
7
8
1
3
1
.
8
2
1
0
1
.
7
1
1
9
1
.
7
1
2
0
1
.
7
3
1
7
1
.
7
3
1
8
1
.
7
4
1
6
1
.
6
6
2
7
1
.
6
6
2
6
1
.
6
7
2
4
1
.
6
6
2
8
1
.
6
3
2
9
1
.
6
0
3
2
1
.
5
9
3
4
1
.
6
7
2
5
1
.
6
8
2
3
1
.
5
5
3
8
1
.
6
1
3
0
1
.
5
9
3
3
1
.
5
9
3
5
1
.
5
5
3
7
1
.
6
0
3
1
1
.
5
7
3
6
1
.
5
3
4
3
1
.
5
2
4
4
1
.
5
3
4
1
1
.
5
4
3
9
1
.
4
4
5
2
1
.
4
6
5
1
1
.
4
9
4
7
1
.
4
6
5
0
1
.
5
3
4
0
1
.
5
3
4
2
1
.
4
8
4
8
1
.
4
7
4
9
1
.
5
2
4
5
A
v
e
r
ag
eh
ighimp
a
c
tg
ap
s
A
A
* R
ankA R
ankA
*
3
.
4
6 3
.
6
6
4
3
3
.
0
8 3
.
0
9
2
1
2
.
9
5 3
.
1
9
3
0
2
6
2
.
7
8 2
.
8
8
3
2
3
.
0
1 3
.
1
3
2
4
2
3
2
.
6
4 2
.
8
0
9
6
2
.
5
8 2
.
7
2
4
0
3
9
2
.
1
0 2
.
0
7
1
8
1
7
2
.
1
3 2
.
1
8
1
6
1
6
1
.
7
5 1
.
7
7
2
9
2
2
9
3
2
.
1
2 2
.
2
2
3
2
3
0
2
.
0
3 2
.
0
6
8
7
2
.
4
5 2
.
3
8
2
1
9
2
2
5
2
.
1
3 2
.
1
4
1
3
1
3
2
.
1
2 2
.
2
4
6
1
5
8
2
.
0
3 2
.
1
2
2
3
2
2
1
.
8
4 2
.
0
7
1
1
1
9
8
1
.
9
8 2
.
0
4
5
4
1
.
9
9 2
.
0
4
1
4
1
2
1
.
8
8 2
.
0
0
3
4
3
1
1
.
8
7 1
.
9
6
1
2
3
1
2
1
1
.
9
3 2
.
0
7
1
5
7
1
5
0
1
.
8
4 1
.
8
6
1
5
1
4
1
.
8
7 2
.
0
1
2
0
3
1
9
4
1
.
7
9 1
.
8
2
6
4
6
3
2
.
0
7 2
.
1
3
1
1
9
1
.
9
4 1
.
9
4
1
9
1
9
1
.
6
8 1
.
7
2
3
3
3
2
1
.
7
9 1
.
8
2
1
0
8
1
.
7
7 1
.
9
0
3
8
3
6
1
.
8
1 1
.
9
3
4
3
4
1
1
.
6
1 1
.
6
1
4
8
5
0
2
.
2
9 2
.
0
3
6
1
1
1
.
7
8 1
.
8
3
1
7
1
5
1
.
7
8 1
.
8
2
7
5
1
.
6
5 1
.
7
5
1
1
9
1
1
6
1
.
6
7 1
.
7
4
2
5
2
4
1
.
6
5 1
.
7
0
2
0
7
2
0
5
1
.
6
6 1
.
6
8
5
1
5
2
1
.
6
7 1
.
6
8
1
0
5
1
0
8
1
.
7
1 1
.
7
3
2
0
1
8
1
.
6
0 1
.
6
5
5
2
4
9
1
.
5
3 1
.
5
0
1
3
6
1
4
4
1
.
4
7 1
.
4
5
7
5
8
0
1
.
7
3 1
.
7
4
2
8
2
8
1
.
4
0 1
.
4
1
5
5
5
6
1
.
6
3 1
.
7
2
2
6
2
5
1
.
5
4 1
.
6
6
4
1
3
8
1
.
5
1 1
.
5
5
2
1
2
0
1
.
5
8 1
.
6
2
5
8
5
7
1
.
5
3 1
.
6
2
5
3
4
8
R
ankT
5
2
5
3
5
4
5
5
5
6
5
7
5
8
5
9
6
0
6
1
6
2
6
3
6
4
6
5
6
6
6
7
6
8
6
9
7
0
7
1
7
2
7
3
7
4
7
5
7
6
7
7
7
8
7
9
8
0
8
1
8
2
8
3
8
4
8
5
8
6
8
7
8
8
8
9
9
0
9
1
9
2
9
3
9
4
9
5
9
6
9
7
9
8
9
9
1
0
0
1
0
1
1
0
2
1
0
3
1
0
4
1
0
5
1
0
6
Un
i
v
e
r
s
i
t
y
Un
i
vL
a
u
s
ann
e
Un
i
vM
a
s
s
a
ch
u
s
e
t
t
sM
edS
ch
Un
i
vV
i
r
g
in
i
a
Un
i
vEd
inb
u
r
gh
Un
i
vTw
en
t
e
Un
i
vM
a
s
s
a
ch
u
s
e
t
t
s-Amh
e
r
s
t
Un
i
vM
inn
e
so
t
a-Tw
inC
i
t
i
e
s
Un
i
vP
i
t
t
sb
u
r
gh
O
r
e
gonH
l
th&S
c
iUn
i
v
Un
i
vSoC
a
l
i
f
Un
i
vS
tAnd
r
ew
s
Un
i
vRo
ch
e
s
t
e
r
W
a
g
en
in
g
enUn
i
v&R
e
sC
t
r
B
rownUn
i
v
Un
i
vB
a
s
e
l
Un
i
vU
t
ah
Un
i
vZ
u
r
i
ch
T
e
chUn
i
vD
enm
a
r
k
D
u
rh
amUn
i
v
E
r
a
sm
u
sUn
i
vRo
t
t
e
rd
am
Un
i
vD
ub
l
inT
r
in
i
t
yCo
l
l
Un
i
vD
und
e
e
K
in
g
'
sCo
l
lLondon
D
e
l
f
tUn
i
vT
e
chno
l
Un
i
vTo
ron
to
L
an
c
a
s
t
e
rUn
i
v
Un
i
vCo
lo
r
ado-D
en
v
e
r
L
e
id
enUn
i
v
S
ton
yB
roo
kUn
i
v-SUNY
Un
i
vC
a
l
i
f-D
a
v
i
s
P
ennS
t
a
t
eUn
i
v
T
e
chUn
i
vM
ün
ch
en
Un
i
vC
in
c
inn
a
t
i
Y
e
sh
i
v
aUn
i
v
Un
i
vYo
r
k
Un
i
vAm
s
t
e
rd
am
R
u
t
g
e
r
sS
t
a
t
eUn
i
v
Un
i
vE
a
s
tAn
g
l
i
a
VUUn
i
vAm
s
t
e
rd
am
Un
i
vE
x
e
t
e
r
Un
i
vB
r
i
t
i
shCo
l
umb
i
a
Ind
i
an
aUn
i
v-B
loom
in
g
ton
U
t
r
e
ch
tUn
i
v
P
a
r
i
sT
e
ch-É
co
l
ePo
l
y
t
e
ch
Un
i
vG
en
e
v
a
Un
i
vNo
t
r
eD
am
e
A
r
i
zon
aS
t
a
t
eUn
i
v
Un
i
vIow
a
G
eo
r
g
e
townUn
i
v
K
a
tho
l
i
e
k
eUn
i
vL
e
u
v
en
A
u
s
t
r
a
l
i
anN
a
t
lUn
i
v
C
a
s
eW
e
s
t
e
rnR
e
s
e
r
veUn
i
v
E
indho
v
enUn
i
vT
e
chno
l
O
r
e
gonS
t
a
t
eUn
i
v
Un
i
vSh
e
f
f
i
e
ld
Numb
e
ra
r
t
i
c
l
e
s
2
6
8
1
.
1
0
1
8
6
9
.
9
7
5
3
6
2
.
9
6
5
6
8
0
.
6
2
2
1
5
8
.
4
5
2
9
9
5
.
7
2
1
0
5
9
1
.
1
0
9
9
7
0
.
5
7
2
1
0
7
.
9
5
6
5
0
6
.
7
6
1
7
9
3
.
0
3
4
4
8
9
.
9
9
3
5
6
9
.
5
8
3
8
7
5
.
4
8
3
3
3
3
.
6
6
5
4
1
3
.
6
3
5
6
3
5
.
5
3
3
4
0
7
.
9
9
2
4
4
7
.
5
7
5
1
1
7
.
3
2
2
0
3
4
.
7
4
1
9
3
8
.
1
2
4
9
7
8
.
3
3
3
4
2
5
.
5
1
1
6
2
8
6
.
5
8
1
4
7
4
.
6
9
3
9
6
7
.
3
0
4
8
9
2
.
5
2
3
2
8
8
.
9
5
9
6
2
6
.
6
7
9
5
5
8
.
6
6
4
6
8
2
.
1
6
4
8
9
3
.
6
4
2
9
1
4
.
8
0
2
5
7
7
.
9
0
6
3
3
5
.
5
2
4
4
0
5
.
1
5
1
6
1
3
.
7
8
5
1
8
9
.
5
6
1
6
1
9
.
9
5
9
7
7
6
.
6
4
3
2
2
3
.
4
3
7
4
6
3
.
7
8
1
2
9
4
.
3
8
3
9
4
4
.
6
2
2
1
3
0
.
6
8
4
3
7
8
.
2
7
5
7
5
0
.
5
5
2
2
7
6
.
9
3
8
4
9
5
.
1
6
4
1
7
7
.
7
3
5
2
1
0
.
0
5
2
7
3
7
.
8
2
3
1
1
2
.
9
0
5
1
4
6
.
7
5
‰
0
.
7
4
0
.
5
2
1
.
4
8
1
.
5
7
0
.
6
0
0
.
8
3
2
.
9
3
2
.
7
6
0
.
5
8
1
.
8
0
0
.
5
0
1
.
2
4
0
.
9
9
1
.
0
7
0
.
9
2
1
.
5
0
1
.
5
6
0
.
9
4
0
.
6
8
1
.
4
2
0
.
5
6
0
.
5
4
1
.
3
8
0
.
9
5
4
.
5
1
0
.
4
1
1
.
1
0
1
.
3
5
0
.
9
1
2
.
6
6
2
.
6
4
1
.
3
0
1
.
3
5
0
.
8
1
0
.
7
1
1
.
7
5
1
.
2
2
0
.
4
5
1
.
4
4
0
.
4
5
2
.
7
0
0
.
8
9
2
.
0
6
0
.
3
6
1
.
0
9
0
.
5
9
1
.
2
1
1
.
5
9
0
.
6
3
2
.
3
5
1
.
1
6
1
.
4
4
0
.
7
6
0
.
8
6
1
.
4
2
31
Top1
0%
T
T
* R
ankT
*
1
.
4
8 1
.
4
0
6
3
1
.
4
7 1
.
4
2
5
9
1
.
4
6 1
.
4
4
5
5
1
.
4
4 1
.
4
1
6
0
1
.
4
4 1
.
4
9
4
6
1
.
4
4 1
.
4
3
5
6
1
.
4
3 1
.
4
1
6
1
1
.
4
2 1
.
3
6
7
2
1
.
4
2 1
.
4
2
5
8
1
.
4
2 1
.
4
4
5
4
1
.
4
2 1
.
4
4
5
3
1
.
4
1 1
.
4
1
6
2
1
.
4
1 1
.
3
6
7
4
1
.
4
0 1
.
4
0
6
5
1
.
3
9 1
.
3
1
8
2
1
.
3
9 1
.
3
7
6
9
1
.
3
9 1
.
3
5
7
5
1
.
3
8 1
.
3
7
7
0
1
.
3
7 1
.
3
8
6
7
1
.
3
7 1
.
3
2
8
1
1
.
3
6 1
.
3
3
7
7
1
.
3
6 1
.
3
1
8
3
1
.
3
5 1
.
3
1
8
6
1
.
3
5 1
.
4
0
6
4
1
.
3
5 1
.
3
2
8
0
1
.
3
5 1
.
4
3
5
7
1
.
3
5 1
.
2
7
1
0
1
1
.
3
5 1
.
3
0
8
8
1
.
3
4 1
.
3
5
7
6
1
.
3
4 1
.
3
6
7
3
1
.
3
4 1
.
3
7
7
1
1
.
3
4 1
.
3
0
9
2
1
.
3
3 1
.
3
0
8
9
1
.
3
3 1
.
2
8
9
6
1
.
3
3 1
.
3
1
8
7
1
.
3
2 1
.
2
9
9
3
1
.
3
1 1
.
3
8
6
8
1
.
3
1 1
.
2
9
9
4
1
.
3
0 1
.
2
7
9
9
1
.
3
0 1
.
3
1
8
5
1
.
3
0 1
.
3
0
9
0
1
.
2
9 1
.
3
0
9
1
1
.
2
9 1
.
2
7
1
0
0
1
.
2
8 1
.
3
9
6
6
1
.
2
8 1
.
2
8
9
8
1
.
2
8 1
.
3
1
8
4
1
.
2
7 1
.
2
9
9
5
1
.
2
7 1
.
2
7
1
0
2
1
.
2
7 1
.
2
4
1
0
9
1
.
2
6 1
.
2
6
1
0
5
1
.
2
6 1
.
2
8
9
7
1
.
2
6 1
.
2
3
1
1
1
1
.
2
5 1
.
3
3
7
8
1
.
2
5 1
.
1
9
1
3
2
1
.
2
5 1
.
2
6
1
0
3
A
v
e
r
ag
eh
ighimp
a
c
tg
ap
s
A
A
* R
ankA R
ankA
*
1
.
6
8 1
.
6
7
1
3
7
1
4
3
1
.
5
1 1
.
5
0
2
3
3
2
4
2
1
.
3
7 1
.
4
0
7
0
7
1
1
.
4
1 1
.
4
3
5
9
6
0
1
.
4
2 1
.
5
4
2
2
3
2
0
7
1
.
3
0 1
.
4
0
1
5
9
1
5
5
1
.
5
7 1
.
6
3
2
2
2
1
1
.
3
9 1
.
3
9
2
9
2
9
1
.
6
0 1
.
6
0
1
9
4
2
0
0
1
.
3
9 1
.
4
8
5
0
4
5
2
.
1
0 2
.
2
3
1
7
1
1
6
5
1
.
5
3 1
.
5
7
8
0
7
7
1
.
1
5 1
.
1
4
1
5
1
1
5
9
1
.
5
0 1
.
5
5
9
4
1
0
0
1
.
3
4 1
.
3
5
1
3
9
1
4
0
1
.
3
5 1
.
3
9
7
1
7
0
1
.
2
7 1
.
3
0
7
2
7
4
1
.
2
5 1
.
3
3
1
4
6
1
3
9
1
.
3
0 1
.
3
7
2
1
7
2
0
3
1
.
3
2 1
.
3
1
8
1
8
2
1
.
7
7 1
.
8
3
1
8
0
1
7
8
1
.
9
8 1
.
9
8
1
6
3
1
7
2
1
.
3
8 1
.
4
0
7
8
7
9
1
.
6
7 1
.
7
7
1
0
1
9
6
1
.
3
6 1
.
3
9
1
2
1
0
1
.
3
3 1
.
3
9
3
0
1
3
0
1
1
.
2
9 1
.
2
6
1
1
4
1
1
9
1
.
2
3 1
.
2
4
9
2
9
7
1
.
3
6 1
.
4
3
1
4
0
1
3
3
1
.
2
8 1
.
3
2
3
6
3
5
1
.
4
8 1
.
5
0
2
7
2
7
1
.
2
9 1
.
3
6
9
1
8
6
1
.
1
7 1
.
1
6
1
0
0
1
0
6
1
.
3
4 1
.
3
2
1
6
0
1
7
3
1
.
2
4 1
.
2
4
2
1
6
2
1
3
1
.
2
6 1
.
2
8
6
0
6
1
1
.
4
0 1
.
4
8
8
8
8
4
1
.
5
4 1
.
5
5
2
6
4
2
6
9
1
.
2
0 1
.
2
0
8
6
9
0
1
.
2
1 1
.
2
4
2
9
8
3
0
4
1
.
2
7 1
.
3
1
3
5
3
4
1
.
1
7 1
.
2
5
1
6
8
1
6
3
1
.
2
2 1
.
2
0
4
9
5
4
1
.
5
0 1
.
6
7
3
0
3
2
9
2
1
.
4
4 1
.
4
9
1
0
2
1
0
2
1
.
4
4 1
.
5
5
2
2
2
2
0
9
1
.
9
5 1
.
7
7
5
7
6
6
1
.
1
0 1
.
1
7
8
4
8
1
1
.
1
5 1
.
1
9
2
5
1
2
4
6
1
.
3
1 1
.
3
3
3
9
4
0
1
.
3
2 1
.
3
6
1
0
6
1
0
5
1
.
2
1 1
.
2
1
8
5
8
7
1
.
2
2 1
.
3
7
1
9
5
1
7
7
1
.
2
5 1
.
2
9
1
6
1
1
6
4
1
.
1
7 1
.
2
0
9
3
9
2
R
ankT
1
0
7
1
0
8
1
0
9
1
1
0
1
1
1
1
1
2
1
1
3
1
1
4
1
1
5
1
1
6
1
1
7
1
1
8
1
1
9
1
2
0
1
2
1
1
2
2
1
2
3
1
2
4
1
2
5
1
2
6
1
2
7
1
2
8
1
2
9
1
3
0
1
3
1
1
3
2
1
3
3
1
3
4
1
3
5
1
3
6
1
3
7
1
3
8
1
3
9
1
4
0
1
4
1
1
4
2
1
4
3
1
4
4
1
4
5
1
4
6
1
4
7
1
4
8
1
4
9
1
5
0
1
5
1
1
5
2
1
5
3
1
5
4
1
5
5
1
5
6
1
5
7
1
5
8
1
5
9
1
6
0
1
6
1
Un
i
v
e
r
s
i
t
y
M
i
ch
i
g
anS
t
a
t
eUn
i
v
Oh
ioS
t
a
t
eUn
i
v
Un
i
vAb
e
rd
e
en
A
a
rh
u
sUn
i
v
M
a
x
im
i
l
i
an
sUn
i
vM
ün
ch
en
Un
i
vG
l
a
s
gow
Un
i
vT
e
x
a
sH
l
thS
c
iC
t
rSAn
ton
io
Un
i
vM
e
lbo
u
rn
e
Un
i
vCop
enh
a
g
en
P
a
r
i
sD
id
e
ro
tUn
i
v
Un
i
vS
t
u
t
t
g
a
r
t
Un
i
vF
r
e
ib
u
r
g
Un
i
vN
i
c
eSoph
i
aAn
t
ipo
l
i
s
Un
i
vA
r
i
zon
a
Un
i
vW
ü
r
zb
u
r
g
M
cM
a
s
t
e
rUn
i
v
K
a
r
l
s
r
uh
eIn
s
tT
e
chno
l
Un
i
vB
e
rn
No
r
th
e
a
s
t
e
rnUn
i
v
Un
i
vN
ew M
e
x
ico
P
a
r
i
sD
e
s
c
a
r
t
e
sUn
i
v
M
cG
i
l
lUn
i
v
Un
i
vP
a
r
i
sS
ud1
1
Un
i
vSo
u
th
amp
ton
W
a
k
eFo
r
e
s
tUn
i
v
Hon
gKon
gUn
i
vS
c
i&T
e
chno
l
Un
i
vNo
t
t
in
gh
am
Un
i
vD
e
l
aw
a
r
e
Un
i
vQ
u
e
en
s
l
and
Un
i
vM
a
r
y
l
and-B
a
l
t
imo
r
e
Un
i
vP
a
r
i
sE
s
tC
r
é
t
e
i
l
Un
i
vP
i
e
r
r
e& M
a
r
i
eC
u
r
i
e
Un
i
vG
ron
in
g
en
T
u
l
an
eUn
i
v
P
u
rd
u
eUn
i
v-L
a
f
a
y
et
t
e
Un
i
vW
a
rw
i
c
k
F
lo
r
id
aS
t
a
t
eUn
i
v
S
to
c
kho
lmUn
i
v
Un
i
vB
ath
Un
i
vL
ib
r
eB
r
u
x
e
l
l
e
s
Un
i
vSC
a
ro
l
in
a
Un
i
vE
r
l
an
g
enN
ü
rnb
e
r
g
Co
lo
r
adoS
t
a
t
eUn
i
v
Un
i
vM
i
am
i-M
i
am
i
Un
i
vL
i
v
e
rpoo
l
K
a
ro
l
in
s
k
aIn
s
t
R
adbo
udUn
i
vN
i
jm
e
g
en
Un
i
vH
aw
a
i
i-M
ano
a
Un
i
vL
e
ed
s
Un
i
vBonn
Un
i
vR
e
ad
in
g
Go
e
th
eUn
i
vF
r
an
k
f
u
r
t
Un
i
vC
a
tho
l
i
q
u
eLo
u
v
a
in
N
ew
c
a
s
t
l
eUn
i
v
Mon
a
shUn
i
v
Numb
e
ra
r
t
i
c
l
e
s
5
9
2
3
.
0
3
9
3
3
9
.
3
5
2
7
0
0
.
2
0
5
3
9
1
.
1
3
6
3
6
2
.
3
9
4
2
2
0
.
4
1
6
0
2
.
8
5
7
2
7
8
.
9
7
7
7
6
4
.
5
7
2
6
6
2
.
0
9
2
2
0
9
.
0
5
3
7
1
9
.
6
1
1
2
3
7
.
6
9
6
4
3
4
.
6
2
3
2
0
0
.
8
9
4
9
9
1
.
5
0
3
5
9
3
.
1
4
3
6
4
0
.
7
4
1
3
5
5
.
6
3
2
7
7
9
.
7
8
2
8
3
1
.
7
2
8
4
9
1
.
3
4
4
5
5
9
.
2
2
4
7
4
6
.
2
8
2
5
8
0
.
4
7
2
8
3
5
.
5
4
5
2
6
9
.
3
6
2
8
3
3
.
8
7
6
7
1
5
.
1
1
3
6
1
4
.
6
1
8
8
4
.
3
3
6
6
5
2
.
5
2
5
4
0
5
.
1
1
1
7
8
4
.
6
4
6
6
1
9
.
3
0
2
6
1
3
.
8
4
3
0
6
8
.
6
3
2
6
1
3
.
9
2
1
8
4
6
.
1
2
2
4
9
8
.
5
7
2
5
3
9
.
8
0
4
0
3
2
.
1
6
3
3
3
5
.
5
4
4
0
2
6
.
1
5
3
7
7
8
.
5
2
6
8
9
6
.
3
2
4
9
0
5
.
5
4
2
7
4
3
.
2
7
5
1
3
3
.
1
5
3
8
8
4
.
1
2
1
9
4
7
.
9
1
3
5
3
3
.
2
1
2
8
6
3
.
3
2
3
5
6
2
.
1
6
4
9
0
1
.
9
0
‰
1
.
6
4
2
.
5
8
0
.
7
5
1
.
4
9
1
.
7
6
1
.
1
7
0
.
1
7
2
.
0
1
2
.
1
5
0
.
7
4
0
.
6
1
1
.
0
3
0
.
3
4
1
.
7
8
0
.
8
9
1
.
3
8
0
.
9
9
1
.
0
1
0
.
3
8
0
.
7
7
0
.
7
8
2
.
3
5
1
.
2
6
1
.
3
1
0
.
7
1
0
.
7
8
1
.
4
6
0
.
7
8
1
.
8
6
1
.
0
0
0
.
2
4
1
.
8
4
1
.
5
0
0
.
4
9
1
.
8
3
0
.
7
2
0
.
8
5
0
.
7
2
0
.
5
1
0
.
6
9
0
.
7
0
1
.
1
2
0
.
9
2
1
.
1
1
1
.
0
5
1
.
9
1
1
.
3
6
0
.
7
6
1
.
4
2
1
.
0
7
0
.
5
4
0
.
9
8
0
.
7
9
0
.
9
9
1
.
3
6
32
Top1
0%
T
T
* R
ankT
*
1
.
2
4 1
.
2
5
1
0
6
1
.
2
4 1
.
2
4
1
0
8
1
.
2
4 1
.
2
0
1
2
1
1
.
2
3 1
.
1
8
1
3
6
1
.
2
3 1
.
1
9
1
3
0
1
.
2
3 1
.
2
0
1
2
2
1
.
2
3 1
.
1
6
1
4
3
1
.
2
3 1
.
2
2
1
1
3
1
.
2
3 1
.
1
9
1
3
3
1
.
2
2 1
.
2
3
1
1
2
1
.
2
2 1
.
3
3
7
9
1
.
2
2 1
.
2
0
1
2
5
1
.
2
2 1
.
1
9
1
2
9
1
.
2
1 1
.
2
1
1
1
8
1
.
2
1 1
.
1
8
1
3
4
1
.
2
1 1
.
2
2
1
1
4
1
.
2
1 1
.
2
6
1
0
4
1
.
2
0 1
.
1
7
1
3
9
1
.
2
0 1
.
2
1
1
1
9
1
.
2
0 1
.
2
0
1
2
6
1
.
1
9 1
.
1
5
1
4
8
1
.
1
9 1
.
1
7
1
4
0
1
.
1
9 1
.
2
3
1
1
0
1
.
1
9 1
.
2
2
1
1
5
1
.
1
9 1
.
1
4
1
5
5
1
.
1
9 1
.
2
4
1
0
7
1
.
1
9 1
.
2
0
1
2
8
1
.
1
8 1
.
2
0
1
2
0
1
.
1
8 1
.
1
5
1
4
6
1
.
1
8 1
.
1
4
1
5
1
1
.
1
8 1
.
2
0
1
2
7
1
.
1
8 1
.
1
9
1
3
1
1
.
1
7 1
.
1
6
1
4
4
1
.
1
7 1
.
1
3
1
6
0
1
.
1
7 1
.
2
1
1
1
6
1
.
1
7 1
.
2
0
1
2
3
1
.
1
7 1
.
2
0
1
2
4
1
.
1
7 1
.
1
7
1
4
1
1
.
1
6 1
.
2
1
1
1
7
1
.
1
6 1
.
1
4
1
5
3
1
.
1
6 1
.
1
7
1
3
8
1
.
1
5 1
.
1
4
1
5
4
1
.
1
5 1
.
1
2
1
6
4
1
.
1
5 1
.
1
2
1
6
6
1
.
1
5 1
.
1
4
1
5
7
1
.
1
4 1
.
0
8
1
9
0
1
.
1
4 1
.
1
2
1
6
5
1
.
1
4 1
.
1
4
1
5
2
1
.
1
4 1
.
1
3
1
5
8
1
.
1
4 1
.
1
4
1
5
0
1
.
1
3 1
.
1
1
1
6
8
1
.
1
3 1
.
1
1
1
7
1
1
.
1
3 1
.
1
2
1
6
2
1
.
1
3 1
.
1
4
1
5
6
1
.
1
2 1
.
1
1
1
7
0
A
v
e
r
ag
eh
ighimp
a
c
tg
ap
s
A
A
* R
ankA R
ankA
*
1
.
1
6 1
.
2
1
7
7
7
6
1
.
2
2 1
.
2
7
3
7
3
7
1
.
2
1 1
.
1
6
2
0
1
2
2
1
1
.
0
8 1
.
0
8
9
5
1
0
3
1
.
2
2 1
.
2
2
6
5
6
5
1
.
2
7 1
.
3
0
1
0
9
1
1
1
1
.
0
2 1
.
0
0
4
6
3
4
6
9
1
.
2
8 1
.
3
1
4
7
4
6
1
.
2
4 1
.
2
2
4
4
4
7
1
.
2
5 1
.
3
2
1
9
6
1
9
0
1
.
4
9 1
.
6
2
1
9
8
1
8
7
1
.
0
9 1
.
1
2
1
5
6
1
5
6
1
.
1
6 1
.
2
0
3
5
9
3
5
8
1
.
2
3 1
.
2
7
6
2
5
9
0
.
9
7 0
.
9
8
2
2
0
2
2
0
1
.
4
8 1
.
4
8
6
9
7
2
1
.
2
8 1
.
3
6
1
3
3
1
2
2
1
.
3
4 1
.
3
2
1
1
8
1
3
0
1
.
2
7 1
.
3
6
3
3
0
3
2
0
1
.
2
5 1
.
3
4
1
8
5
1
7
9
1
.
1
4 1
.
1
3
2
0
8
2
1
6
1
.
1
6 1
.
1
8
4
2
4
2
1
.
2
6 1
.
3
3
9
9
9
5
1
.
3
1 1
.
3
2
8
7
8
8
1
.
1
6 1
.
1
5
2
2
4
2
2
8
0
.
9
4 1
.
0
5
2
4
6
2
2
9
1
.
0
3 1
.
0
7
1
0
8
1
0
7
1
.
0
4 1
.
0
8
2
2
8
2
2
4
1
.
1
3 1
.
1
3
6
7
6
9
1
.
0
1 0
.
9
9
1
7
7
1
8
5
0
.
9
2 0
.
9
6
4
3
6
4
3
3
1
.
0
4 1
.
0
9
7
6
7
5
1
.
0
5 1
.
0
6
1
0
4
1
0
4
1
.
1
6 1
.
1
5
2
9
4
2
9
9
1
.
0
8 1
.
1
6
7
3
6
7
1
.
0
6 1
.
1
0
2
3
9
2
3
5
1
.
2
4 1
.
2
8
1
6
6
1
6
6
1
.
2
3 1
.
2
2
2
0
9
2
1
7
1
.
0
0 1
.
0
7
3
1
0
3
0
5
1
.
1
2 1
.
1
6
2
3
5
2
3
2
0
.
9
9 1
.
0
2
2
6
1
2
5
9
1
.
1
6 1
.
1
8
1
2
5
1
3
1
1
.
0
6 1
.
0
4
1
8
1
1
9
5
1
.
1
8 1
.
2
0
1
2
2
1
2
7
1
.
0
2 1
.
0
2
1
6
2
1
7
0
1
.
1
4 1
.
1
1
6
3
6
8
1
.
0
6 1
.
0
7
1
1
3
1
1
3
1
.
0
8 1
.
0
6
2
2
7
2
3
3
1
.
0
5 1
.
0
7
1
1
0
1
1
0
1
.
0
8 1
.
0
9
1
4
8
1
5
3
1
.
0
9 1
.
0
9
2
9
0
2
9
4
1
.
0
7 1
.
0
9
1
6
7
1
7
4
0
.
9
5 0
.
9
6
2
4
2
2
4
5
1
.
0
6 1
.
0
8
1
6
9
1
7
5
0
.
9
8 1
.
0
3
1
2
1
1
1
8
R
ankT
1
6
2
1
6
3
1
6
4
1
6
5
1
6
6
1
6
7
1
6
8
1
6
9
1
7
0
1
7
1
1
7
2
1
7
3
1
7
4
1
7
5
1
7
6
1
7
7
1
7
8
1
7
9
1
8
0
1
8
1
1
8
2
1
8
3
1
8
4
1
8
5
1
8
6
1
8
7
1
8
8
1
8
9
1
9
0
1
9
1
1
9
2
1
9
3
1
9
4
1
9
5
1
9
6
1
9
7
1
9
8
1
9
9
2
0
0
2
0
1
2
0
2
2
0
3
2
0
4
2
0
5
2
0
6
2
0
7
2
0
8
2
0
9
2
1
0
2
1
1
2
1
2
2
1
3
2
1
4
2
1
5
2
1
6
Un
i
v
e
r
s
i
t
y
Un
i
vO
t
t
aw
a
Un
i
vBo
rd
e
a
u
xS
e
g
a
l
en
T
e
chUn
i
vB
e
r
l
in
H
umbo
ld
tUn
i
vB
e
r
l
in
RWTHA
a
ch
enUn
i
v
e
r
s
i
t
y
N
a
t
lUn
i
vS
in
g
apo
r
e
Un
i
vC
en
tF
lo
r
id
a
Un
i
v Mon
tp
e
l
l
i
e
r2
Q
u
e
en M
a
r
yUn
i
vLondon
Un
i
vG
eo
r
g
i
a
Un
i
vN
ewS W
a
l
e
s
V
i
enn
aUn
i
vT
e
chno
l
Un
i
vS
ydn
e
y
Jo
s
ephFo
u
r
i
e
rUn
i
v
Un
i
vV
e
rmon
t
Un
i
vS
u
s
s
e
x
Un
i
vS
t
r
a
sbo
u
r
g
Ph
i
l
ipp
sUn
i
vM
a
rb
u
r
g
Un
i
vM
an
ch
e
s
t
e
r
Un
i
vConn
e
c
t
i
c
u
t
Q
u
e
en
'
sUn
i
v
G
u
t
enb
e
r
gUn
i
vM
a
in
z
Un
i
vV
i
enn
a
G
eo
r
g
eW
a
sh
in
g
tonUn
i
v
Un
i
vSF
lo
r
id
a-T
amp
a
No
rw
e
g
i
anUn
i
vS
c
i&T
e
chno
l
P
a
u
lS
ab
a
t
i
e
rUn
i
v
M
edCo
l
lW
i
s
con
s
in
T
e
chUn
i
vD
r
e
sd
en
Un
i
vA
u
c
k
l
and
M
a
a
s
t
r
i
ch
tUn
i
v
Iow
aS
t
a
t
eUn
i
v
Un
i
vA
l
ab
am
a-B
i
rm
in
gh
am
Un
i
vHon
gKon
g
T
e
x
a
sA&MUn
i
v-Co
l
l
e
g
eS
tn
Un
i
vA
lb
e
r
t
a
Un
i
vAntw
e
rp
Ch
a
lm
e
r
sUn
i
vT
e
chno
l
Un
i
vH
e
l
s
in
k
i
Un
i
vT
üb
in
g
en
Uni
vH
amb
u
r
g
Ind
i
an
aUn
i
v-P
u
rd
u
e
M
edUn
i
vSC
a
ro
l
in
a
F
r
e
i
eUn
i
vB
e
r
l
in
Un
i
vO
t
a
go
R
uh
rUn
i
vBo
ch
um
D
r
e
x
e
lUn
i
v
G
eo
r
g
eM
a
sonUn
i
v
W
a
sh
in
g
tonS
t
a
t
eUn
i
v
Un
i
vR
e
g
en
sb
u
r
g
Un
i
vD
u
i
sb
u
r
gE
s
s
en
H
e
id
e
lb
e
r
gUn
i
v
Un
i
vM
ed& D
en
tN
ewJ
e
r
s
e
y
Un
i
vB
i
rm
in
gh
am
C
i
t
yUn
i
vHon
gKon
g
Numb
e
ra
r
t
i
c
l
e
s
3
7
5
7
.
3
8
1
4
3
3
.
6
7
1
8
4
2
.
1
4
4
7
9
7
.
2
9
3
5
9
6
.
6
7
9
1
5
5
.
4
8
2
1
5
3
.
0
4
2
1
1
6
.
0
8
1
8
2
4
.
7
8
4
4
9
8
.
9
2
5
1
8
8
.
4
4
1
6
1
6
.
4
9
7
4
4
8
.
8
4
2
8
0
3
.
9
0
1
8
3
6
.
3
1
1
6
3
3
.
7
0
3
1
0
1
.
5
1
2
3
1
4
.
6
1
8
2
1
3
.
3
8
4
5
1
4
.
3
9
3
1
7
5
.
8
3
2
9
5
6
.
6
7
3
3
4
5
.
8
3
2
0
5
5
.
0
4
2
9
8
5
.
6
3
2
8
7
0
.
0
2
3
6
5
8
.
6
1
2
0
4
0
.
4
8
2
9
6
5
.
3
9
3
2
3
8
.
1
1
3
2
8
3
.
2
1
4
5
6
0
.
0
0
4
5
7
7
.
5
2
5
4
2
0
.
8
0
7
1
9
5
.
1
0
7
6
2
8
.
3
9
2
4
0
1
.
8
8
1
5
6
6
.
2
2
6
2
4
5
.
5
2
4
2
6
6
.
2
9
3
4
8
3
.
3
9
3
6
3
5
.
8
8
2
3
2
5
.
9
5
4
5
5
8
.
5
6
2
6
1
2
.
8
3
3
1
2
5
.
6
0
1
9
0
0
.
9
2
1
2
4
0
.
8
2
2
9
6
4
.
1
8
2
4
7
7
.
4
3
2
6
5
8
.
1
4
5
9
1
3
.
3
3
2
9
9
1
.
3
9
5
1
3
6
.
7
0
3
0
1
9
.
8
2
‰
1
.
0
4
0
.
4
0
0
.
5
1
1
.
3
3
1
.
0
0
2
.
5
3
0
.
6
0
0
.
5
9
0
.
5
0
1
.
2
4
1
.
4
4
0
.
4
5
2
.
0
6
0
.
7
8
0
.
5
1
0
.
4
5
0
.
8
6
0
.
6
4
2
.
2
7
1
.
2
5
0
.
8
8
0
.
8
2
0
.
9
3
0
.
5
7
0
.
8
3
0
.
7
9
1
.
0
1
0
.
5
6
0
.
8
2
0
.
9
0
0
.
9
1
1
.
2
6
1
.
2
7
1
.
5
0
1
.
9
9
2
.
1
1
0
.
6
6
0
.
4
3
1
.
7
3
1
.
1
8
0
.
9
6
1
.
0
1
0
.
6
4
1
.
2
6
0
.
7
2
0
.
8
6
0
.
5
3
0
.
3
4
0
.
8
2
0
.
6
9
0
.
7
4
1
.
6
4
0
.
8
3
1
.
4
2
0
.
8
4
33
Top1
0%
T
T
* R
ankT
*
1
.
1
2 1
.
1
1
1
7
7
1
.
1
2 1
.
1
1
1
7
5
1
.
1
2 1
.
1
8
1
3
7
1
.
1
2 1
.
0
9
1
8
3
1
.
1
2 1
.
1
3
1
5
9
1
.
1
2 1
.
1
6
1
4
5
1
.
1
1 1
.
1
5
1
4
9
1
.
1
1 1
.
1
3
1
6
1
1
.
1
1 1
.
1
5
1
4
7
1
.
1
1 1
.
1
1
1
7
4
1
.
1
0 1
.
0
8
1
9
4
1
.
1
0 1
.
1
8
1
3
5
1
.
1
0 1
.
0
9
1
8
4
1
.
1
0 1
.
1
1
1
7
6
1
.
1
0 1
.
0
4
2
2
1
1
.
1
0 1
.
0
8
1
8
8
1
.
0
9 1
.
0
7
1
9
5
1
.
0
9 1
.
0
8
1
9
2
1
.
0
9 1
.
0
8
1
8
9
1
.
0
9 1
.
0
9
1
8
5
1
.
0
9 1
.
0
7
1
9
8
1
.
0
9 1
.
0
4
2
1
2
1
.
0
9 1
.
1
1
1
6
9
1
.
0
8 1
.
0
7
1
9
6
1
.
0
8 1
.
0
3
2
2
3
1
.
0
8 1
.
1
0
1
7
8
1
.
0
8 1
.
0
8
1
9
3
1
.
0
8 1
.
0
3
2
2
6
1
.
0
8 1
.
0
9
1
8
6
1
.
0
8 1
.
0
4
2
1
3
1
.
0
8 1
.
0
2
2
3
4
1
.
0
8 1
.
0
7
1
9
9
1
.
0
8 1
.
0
3
2
2
4
1
.
0
8 1
.
0
6
2
0
1
1
.
0
7 1
.
1
1
1
7
2
1
.
0
7 1
.
0
6
2
0
6
1
.
0
7 1
.
0
1
2
4
3
1
.
0
7 1
.
1
2
1
6
3
1
.
0
7 1
.
0
3
2
2
8
1
.
0
7 1
.
0
6
2
0
4
1
.
0
7 1
.
0
6
2
0
3
1
.
0
7 1
.
0
5
2
1
0
1
.
0
7 1
.
0
2
2
3
5
1
.
0
6 1
.
0
3
2
2
9
1
.
0
6 1
.
0
1
2
4
5
1
.
0
6 1
.
0
7
2
0
0
1
.
0
6 1
.
0
5
2
0
8
1
.
0
6 1
.
1
2
1
6
7
1
.
0
6 1
.
0
3
2
2
7
1
.
0
6 1
.
0
3
2
2
5
1
.
0
6 1
.
0
9
1
8
7
1
.
0
5 1
.
0
1
2
4
9
1
.
0
5 0
.
9
8
2
6
7
1
.
0
5 1
.
0
5
2
1
1
1
.
0
5 1
.
1
7
1
4
2
A
v
e
r
ag
eh
ighimp
a
c
tg
ap
s
A
A
* R
ankA R
ankA
*
1
.
0
1 1
.
0
3
1
6
5
1
6
8
1
.
1
4 1
.
1
4
3
3
4
3
4
1
0
.
9
9 1
.
0
5
3
1
4
3
1
1
0
.
9
7 0
.
9
7
1
2
8
1
3
4
1
.
1
2 1
.
3
5
1
5
5
1
2
6
1
.
0
4 1
.
0
8
4
5
4
3
0
.
9
8 1
.
0
9
2
9
3
2
7
8
1
.
2
8 1
.
2
7
2
4
3
2
4
9
1
.
0
7 1
.
3
3
3
0
2
2
7
3
1
.
0
2 1
.
0
3
1
3
0
1
3
6
1
.
0
6 1
.
0
7
1
0
7
1
0
9
1
.
0
0 1
.
1
1
3
3
5
3
2
7
1
.
0
2 1
.
0
5
6
6
6
4
1
.
1
0 1
.
1
5
2
2
1
2
1
0
1
.
0
1 1
.
0
2
3
0
9
3
1
8
1
.
0
8 1
.
1
1
3
1
9
3
2
4
1
.
1
4 1
.
1
5
1
8
2
1
8
6
1
.
0
2 1
.
0
5
2
7
1
2
7
5
1
.
0
5 1
.
0
9
5
4
5
3
1
.
0
0 1
.
0
2
1
3
8
1
3
7
1
.
0
1 1
.
0
4
2
1
0
2
0
8
1
.
1
0 1
.
1
3
2
0
6
2
0
4
1
.
0
4 1
.
0
9
1
8
7
1
8
4
1
.
2
9 1
.
2
8
2
4
8
2
5
2
1
.
0
6 1
.
0
7
2
1
8
2
1
5
0
.
9
7 1
.
0
2
2
3
6
2
3
0
0
.
8
8 0
.
9
2
2
1
2
2
0
2
0
.
8
1 0
.
8
1
3
3
3
3
3
9
0
.
9
1 0
.
9
5
2
4
4
2
4
0
1
.
2
5 1
.
2
5
1
5
4
1
6
1
0
.
9
8 0
.
9
8
2
1
1
2
1
4
1
.
1
2 1
.
1
4
1
1
6
1
1
5
0
.
9
3 0
.
9
2
1
4
5
1
5
2
1
.
0
7 1
.
1
1
9
7
9
9
1
.
0
4 1
.
1
1
6
8
6
2
0
.
9
3 0
.
9
7
7
4
7
3
0
.
9
6 0
.
9
7
2
7
5
2
8
1
0
.
9
0 0
.
9
3
3
6
3
3
6
3
1
.
0
3 1
.
0
3
8
3
8
5
1
.
0
1 1
.
0
3
1
4
3
1
4
7
1
.
0
8 1
.
1
0
1
7
2
1
7
1
0
.
8
8 0
.
8
8
2
1
3
2
1
2
0
.
9
5 0
.
9
1
2
8
3
2
9
5
0
.
9
4 0
.
9
5
1
4
4
1
4
8
0
.
9
7 0
.
9
7
2
5
9
2
6
3
0
.
8
9 0
.
9
6
2
3
7
2
2
6
1
.
2
3 1
.
3
0
2
7
2
2
7
2
0
.
9
6 1
.
0
5
3
9
1
3
8
2
0
.
8
9 0
.
9
0
2
5
0
2
4
8
0
.
9
3 0
.
9
5
2
7
6
2
7
9
0
.
9
4 0
.
9
8
2
6
2
2
5
6
1
.
0
4 1
.
0
6
8
9
8
9
0
.
8
6 0
.
8
4
2
5
6
2
6
6
0
.
9
4 0
.
9
4
1
2
0
1
2
8
0
.
9
1 1
.
0
4
2
4
0
2
1
9
R
ankT
2
1
7
2
1
8
2
1
9
2
2
0
2
2
1
2
2
2
2
2
3
2
2
4
2
2
5
2
2
6
2
2
7
2
2
8
2
2
9
2
3
0
2
3
1
2
3
2
2
3
3
2
3
4
2
3
5
2
3
6
2
3
7
2
3
8
2
3
9
2
4
0
2
4
1
2
4
2
2
4
3
2
4
4
2
4
5
2
4
6
2
4
7
2
4
8
2
4
9
2
5
0
2
5
1
2
5
2
2
5
3
2
5
4
2
5
5
2
5
6
2
5
7
2
5
8
2
5
9
2
6
0
2
6
1
2
6
2
2
6
3
2
6
4
2
6
5
2
6
6
2
6
7
2
6
8
2
6
9
2
7
0
2
7
1
Un
i
v
e
r
s
i
t
y
Un
i
vC
l
a
udeB
e
rn
a
rdL
yon1
Un
i
vBo
rd
e
a
u
x1S
c
iT
e
chno
l
Un
i
vI
l
l
ino
i
s-Ch
i
c
a
go
V
i
r
g
in
i
aT
e
ch
Un
i
vL
e
i
c
e
s
t
e
r
S
imonF
r
a
s
e
rUn
i
v
V
r
i
j
eUn
i
vB
r
u
s
s
e
l
Un
i
vW
a
t
e
r
loo
Un
i
vW
e
s
t
e
rnA
u
s
t
r
a
l
i
a
Poh
an
gUn
i
vS
c
i&T
e
chno
l
Un
i
vT
e
x
a
s-M
ed
i
c
a
lB
r
an
ch
K
i
e
lUn
i
v
V
i
r
g
in
i
aCommonw
e
a
l
thUn
i
v
NC
a
ro
l
in
aS
t
a
t
eUn
i
v
H
e
in
r
i
chH
e
in
eUn
i
vD
ü
s
s
e
ldo
r
f
Un
i
v Wo
l
lon
gon
g
Un
i
vHo
u
s
ton-Ho
u
s
ton
Gh
en
tUn
i
v
Um
e
åUn
i
v
T
e
chUn
i
vD
a
rm
s
t
ad
t
Un
i
vW
e
s
t
e
rn On
t
a
r
io
Un
i
vC
a
l
g
a
r
y
Thom
a
sJe
f
f
e
r
sonUn
i
v
G
i
e
s
s
enUn
i
v
C
a
rd
i
f
fUn
i
v
e
r
s
i
t
y
H
eb
r
ewUn
i
vJ
e
r
u
s
a
l
em
W
a
yn
eS
t
a
t
eUn
i
v
Un
i
v Mon
t
r
é
a
l
Sw
edUn
i
vA
g
rS
c
i
Un
i
vB
e
r
g
en
Un
i
vO
s
lo
Un
i
vF
lo
r
id
a
Un
i
vN
eb
r
a
s
k
a-L
in
co
ln
Un
i
vAd
e
l
a
id
e
Un
i
vCo
l
lCo
r
k
M
edUn
i
vW
i
en
D
a
lho
u
s
i
eUn
i
v
Un
i
vCo
lo
gn
e
A
i
xM
a
r
s
e
i
l
l
eUn
i
v
Un
i
vM
ün
s
t
e
r
Un
i
vB
a
r
c
e
lon
a
H
anno
v
e
rM
edS
ch
Un
i
vC
ap
eTown
L
a
v
a
lUn
i
v
F
r
i
ed
r
i
chS
ch
i
l
l
e
rUn
i
vJ
en
a
Upp
s
a
l
aUn
i
v
Un
i
vM
i
l
anB
i
co
c
c
a
Mon
tp
e
l
l
i
e
r1Un
i
v
Un
i
vGö
t
t
in
g
en
Un
i
vB
r
em
en
Un
i
vV
i
c
to
r
i
a
Un
i
vT
enn
e
s
s
e
e-Kno
x
v
i
l
l
e
Un
i
vCo
l
lD
ub
l
in
Un
i
vPo
l
i
t
è
cn
i
c
aV
a
l
èn
c
i
a
Un
i
vN
ew
c
a
s
t
l
e
Numb
e
ra
r
t
i
c
l
e
s
3
5
5
2
.
7
0
1
9
5
2
.
9
5
5
0
3
5
.
2
2
3
9
2
7
.
5
6
2
5
9
8
.
3
6
2
1
1
2
.
2
5
1
8
6
5
.
9
6
3
9
1
9
.
2
9
3
7
0
4
.
2
4
2
4
1
3
.
9
3
2
3
7
5
.
5
7
2
6
6
8
.
9
3
2
8
0
6
.
9
3
4
8
7
8
.
5
1
2
4
7
5
.
6
7
1
5
3
9
.
7
6
2
0
4
9
.
0
9
6
6
7
1
.
6
1
2
4
4
6
.
2
2
2
0
0
2
.
4
9
4
6
4
7
.
5
0
5
1
2
8
.
0
9
2
1
2
2
.
0
6
2
0
2
6
.
4
9
3
5
2
4
.
3
7
5
5
9
6
.
6
8
3
7
8
9
.
4
0
4
7
9
0
.
2
6
1
8
3
5
.
0
9
2
5
2
2
.
7
0
5
2
3
5
.
4
1
1
0
4
9
9
.
5
4
2
9
5
0
.
0
5
2
9
7
4
.
9
6
1
7
1
3
.
4
4
2
9
9
1
.
2
9
3
0
3
6
.
5
8
2
9
5
8
.
5
0
3
4
2
9
.
3
8
3
7
6
0
.
0
0
5
5
5
7
.
7
9
1
7
5
2
.
3
6
1
9
7
0
.
3
3
3
6
1
3
.
5
9
2
6
8
9
.
3
4
4
9
1
2
.
0
1
8
1
6
.
5
8
1
0
9
2
.
5
7
3
6
4
6
.
8
2
1
3
1
1
.
9
9
1
7
9
6
.
9
4
4
3
4
5
.
5
7
2
7
6
2
.
6
5
2
2
2
5
.
8
3
1
5
3
1
.
9
4
‰
0
.
9
8
0
.
5
4
1
.
3
9
1
.
0
9
0
.
7
2
0
.
5
8
0
.
5
2
1
.
0
8
1
.
0
2
0
.
6
7
0
.
6
6
0
.
7
4
0
.
7
8
1
.
3
5
0
.
6
8
0
.
4
3
0
.
5
7
1
.
8
5
0
.
6
8
0
.
5
5
1
.
2
9
1
.
4
2
0
.
5
9
0
.
5
6
0
.
9
8
1
.
5
5
1
.
0
5
1
.
3
3
0
.
5
1
0
.
7
0
1
.
4
5
2
.
9
0
0
.
8
2
0
.
8
2
0
.
4
7
0
.
8
3
0
.
8
4
0
.
8
2
0
.
9
5
1
.
0
4
1
.
5
4
0
.
4
8
0
.
5
5
1
.
0
0
0
.
7
4
1
.
3
6
0
.
2
3
0
.
3
0
1
.
0
1
0
.
3
6
0
.
5
0
1
.
2
0
0
.
7
6
0
.
6
2
0
.
4
2
34
Top1
0%
T
T
* R
ankT
*
1
.
0
4 1
.
0
4
2
1
4
1
.
0
4 1
.
1
0
1
7
9
1
.
0
4 1
.
0
2
2
4
0
1
.
0
4 1
.
0
7
1
9
7
1
.
0
4 1
.
0
4
2
1
7
1
.
0
4 1
.
0
8
1
9
1
1
.
0
4 1
.
0
5
2
0
7
1
.
0
4 1
.
0
9
1
8
2
1
.
0
4 1
.
0
4
2
2
0
1
.
0
3 1
.
0
9
1
8
1
1
.
0
3 0
.
9
3
2
9
8
1
.
0
3 1
.
0
0
2
5
2
1
.
0
3 0
.
9
8
2
6
4
1
.
0
3 1
.
0
6
2
0
5
1
.
0
3 1
.
0
4
2
1
8
1
.
0
3 1
.
0
4
2
2
2
1
.
0
3 1
.
1
0
1
8
0
1
.
0
3 1
.
0
2
2
3
8
1
.
0
3 0
.
9
9
2
6
0
1
.
0
2 1
.
1
1
1
7
3
1
.
0
2 1
.
0
1
2
4
4
1
.
0
2 1
.
0
0
2
5
5
1
.
0
2 0
.
9
5
2
8
3
1
.
0
2 1
.
0
2
2
3
9
1
.
0
2 0
.
9
8
2
6
6
1
.
0
2 1
.
0
1
2
4
1
1
.
0
2 1
.
0
0
2
5
4
1
.
0
2 0
.
9
7
2
7
7
1
.
0
2 0
.
9
7
2
7
8
1
.
0
1 0
.
9
9
2
5
8
1
.
0
1 1
.
0
0
2
5
0
1
.
0
1 1
.
0
1
2
4
8
1
.
0
1 1
.
0
2
2
3
2
1
.
0
1 1
.
0
3
2
3
1
1
.
0
1 1
.
0
2
2
3
6
1
.
0
1 0
.
9
8
2
7
1
1
.
0
1 1
.
0
1
2
4
7
1
.
0
1 0
.
9
8
2
6
3
1
.
0
0 1
.
0
2
2
3
3
1
.
0
0 0
.
9
8
2
7
0
1
.
0
0 0
.
9
7
2
8
0
1
.
0
0 0
.
9
6
2
8
2
1
.
0
0 0
.
9
8
2
6
5
0
.
9
9 0
.
9
7
2
7
9
0
.
9
9 1
.
0
0
2
5
1
0
.
9
9 0
.
9
8
2
6
8
0
.
9
9 1
.
0
1
2
4
2
0
.
9
9 0
.
9
3
3
0
1
0
.
9
9 0
.
9
9
2
5
6
0
.
9
8 0
.
9
7
2
7
3
0
.
9
8 1
.
0
2
2
3
7
0
.
9
8 0
.
9
9
2
6
1
0
.
9
8 0
.
9
8
2
6
9
0
.
9
8 1
.
0
4
2
1
6
0
.
9
8 1
.
0
4
2
1
9
A
v
e
r
ag
eh
ighimp
a
c
tg
ap
s
A
A
* R
ankA R
ankA
*
1
.
0
2 1
.
0
3
1
7
8
1
8
2
1
.
1
2 1
.
1
7
2
8
5
2
8
3
0
.
9
1 0
.
9
4
1
3
2
1
3
2
0
.
8
3 0
.
8
9
2
0
5
1
9
6
0
.
9
6 0
.
9
6
2
6
3
2
7
0
0
.
9
3 0
.
9
7
2
9
9
3
0
0
1
.
0
9 1
.
1
0
2
9
6
3
0
2
0
.
8
6 0
.
9
5
1
9
3
1
8
0
0
.
9
4 0
.
9
5
1
8
6
1
9
3
0
.
8
9 0
.
9
7
2
8
9
2
8
0
0
.
8
3 0
.
8
1
3
0
0
3
1
3
0
.
9
5 0
.
9
5
2
6
0
2
6
2
1
.
0
6 1
.
0
7
2
2
5
2
2
7
0
.
9
4 1
.
0
0
1
3
4
1
2
4
0
.
9
1 0
.
9
1
2
7
9
2
8
6
0
.
9
3 0
.
9
3
3
6
1
3
6
5
0
.
8
6 0
.
9
4
3
2
1
3
1
2
0
.
9
7 0
.
9
8
8
2
8
3
0
.
8
7 0
.
8
5
2
9
1
2
9
7
0
.
9
9 1
.
0
5
2
9
7
2
9
6
0
.
9
0 0
.
9
1
1
4
7
1
5
1
0
.
9
2 0
.
9
1
1
2
6
1
3
5
0
.
8
1 0
.
7
9
3
2
8
3
3
8
0
.
9
4 0
.
9
6
3
0
5
3
0
7
0
.
9
0 0
.
9
0
2
1
5
2
1
8
0
.
9
1 0
.
9
4
1
1
5
1
1
4
0
.
8
9 0
.
8
9
1
9
2
2
0
1
0
.
9
2 0
.
9
5
1
4
1
1
3
8
0
.
8
8 0
.
8
5
3
3
7
3
4
9
1
.
1
6 1
.
1
4
2
2
9
2
3
6
0
.
8
6 0
.
8
6
1
3
5
1
4
2
0
.
8
9 0
.
9
2
4
6
4
4
0
.
8
3 0
.
8
8
2
6
6
2
5
8
0
.
8
6 0
.
8
7
2
5
7
2
6
0
0
.
8
7 0
.
8
7
3
5
2
3
5
7
0
.
9
4 0
.
9
5
2
3
4
2
3
7
0
.
8
4 0
.
8
3
2
5
8
2
6
4
0
.
9
3 0
.
9
6
2
3
8
2
3
9
0
.
9
9 1
.
0
3
1
9
0
1
8
9
0
.
8
8 0
.
9
0
1
9
7
1
9
8
0
.
9
4 0
.
9
5
1
1
2
1
1
2
0
.
8
8 0
.
8
7
3
4
5
3
5
3
0
.
9
3 0
.
9
1
3
1
1
3
2
6
0
.
9
1 0
.
8
9
1
9
9
2
1
1
0
.
8
9 0
.
9
4
2
6
9
2
6
5
0
.
9
4 0
.
9
2
1
2
9
1
4
1
0
.
9
2 0
.
9
6
4
4
5
4
4
7
0
.
9
1 0
.
8
9
4
0
9
4
1
9
2
9
.
5
0 2
.
5
2
1
5
1
0
.
9
1 0
.
9
6
3
9
0
3
8
7
0
.
8
0 0
.
8
4
3
6
0
3
5
6
0
.
9
6 0
.
9
9
1
5
0
1
4
9
0
.
9
9 0
.
9
5
2
4
1
2
5
3
1
.
0
5 1
.
1
5
2
7
4
2
6
1
0
.
8
3 0
.
8
8
3
7
8
3
7
6
R
ankT
2
7
2
2
7
3
2
7
4
2
7
5
2
7
6
2
7
7
2
7
8
2
7
9
2
8
0
2
8
1
2
8
2
2
8
3
2
8
4
2
8
5
2
8
6
2
8
7
2
8
8
2
8
9
2
9
0
2
9
1
2
9
2
2
9
3
2
9
4
2
9
5
2
9
6
2
9
7
2
9
8
2
9
9
3
0
0
3
0
1
3
0
2
3
0
3
3
0
4
3
0
5
3
0
6
3
0
7
3
0
8
3
0
9
3
1
0
3
1
1
3
1
2
3
1
3
3
1
4
3
1
5
3
1
6
3
1
7
3
1
8
3
1
9
3
2
0
3
2
1
3
2
2
3
2
3
3
2
4
3
2
5
3
2
6
Un
i
v
e
r
s
i
t
y
Un
i
vR
enn
e
s1
K
an
s
a
sS
t
a
t
eUn
i
v
Un
i
vSo
u
th
e
rnD
enm
a
r
k
Yo
r
kUn
i
v
Un
i
vB
u
f
f
a
lo-SUNY
Po
l
i
t
e
cn
i
co M
i
l
ano
M
a
c
q
u
a
r
i
eUn
i
v
Po
l
i
t
e
cn
i
coTo
r
ino
Un
i
vL
i
è
g
e
L
undUn
i
v
Un
i
vT
r
i
e
s
t
e
Un
i
vPo
l
i
t
è
cn
i
c
aC
a
t
a
l
un
y
a
Un
i
vGo
th
enb
u
r
g
Un
i
vRo
s
to
c
k
A
a
l
toUn
i
v
Un
i
vG
u
e
lph
Ind
i
anIn
s
tT
e
chno
lM
ad
r
a
s
Un
i
vS
u
r
r
e
y
Un
i
vLo
u
i
s
v
i
l
l
e
Un
i
vTo
r
ino
Lo
u
ghbo
ro
u
ghUn
i
v
Un
i
vS
e
v
i
l
l
e
Un
i
vP
ado
v
a
Un
i
vS
c
i&T
e
chno
lCh
in
a
Inn
sb
r
u
c
kM
edUn
i
v
KTHRo
y
a
lIn
s
tT
e
chno
l
Un
i
vK
an
s
a
s
Ch
in
e
s
eUn
i
vHon
gKon
g
Un
i
vA
u
tónom
aB
a
r
c
e
lon
a
Un
i
vM
i
l
an
Q
u
e
en
'
sUn
i
vB
e
l
f
a
s
t
Un
i
vO
k
l
ahom
a
N
an
y
an
gT
e
chno
lUn
i
v
Q
u
e
en
s
l
andUn
i
vT
e
chno
l
Un
i
vK
en
t
u
c
k
y
C
l
em
sonUn
i
v
T
emp
l
eUn
i
v
Un
i
vU
lm
Un
i
vS
t
r
a
th
c
l
yd
eG
l
a
s
gow
Un
i
vNo
v
aL
i
sbo
a
Un
i
vM
i
s
sou
r
i-Co
l
umb
i
a
Un
i
vP
a
v
i
a
Un
i
vTo
k
yo
H
en
r
iPo
in
c
a
r
éUn
i
v
Un
i
vL
e
ip
z
i
g
Un
i
vZ
a
r
a
go
z
a
Un
i
vA
u
tónom
aM
ad
r
id
S
a
a
r
l
andUn
i
v
Un
i
vPo
r
to
H
un
anUn
i
v
Lo
u
i
s
i
an
aS
t
a
t
eUn
i
v
Ko
r
e
aAd
vIn
s
tS
c
i&T
e
chno
l
Hon
gKon
gPo
l
y
t
e
chUn
i
v
Un
i
vT
a
sm
an
i
a
G
u
e
r
i
c
k
eUn
i
vM
a
gd
eb
u
r
g
Numb
e
ra
r
t
i
c
l
e
s
1
9
9
2
.
8
4
2
0
8
0
.
5
8
1
8
3
8
.
7
0
1
6
0
8
.
1
5
3
7
1
0
.
7
6
2
0
8
7
.
1
7
1
3
2
9
.
5
2
1
6
4
4
.
4
7
2
3
3
3
.
7
7
6
8
2
5
.
6
3
1
2
1
5
.
8
6
1
7
1
1
.
7
2
4
2
0
0
.
6
1
1
6
8
2
.
1
4
2
1
0
1
.
9
7
2
8
4
6
.
2
1
1
9
2
5
.
5
3
1
8
6
6
.
5
3
2
4
1
9
.
7
2
3
4
0
2
.
6
2
1
9
4
1
.
0
7
2
2
4
3
.
7
3
5
0
2
2
.
9
6
4
8
3
3
.
6
1
1
5
0
6
.
7
3
3
1
3
5
.
0
4
3
3
2
1
.
6
6
4
6
5
2
.
1
7
4
1
3
9
.
0
7
6
0
8
1
.
8
2
2
7
4
0
.
3
6
3
0
6
0
.
2
0
5
5
7
8
.
5
2
1
4
2
7
.
7
6
4
6
8
9
.
9
7
1
8
7
3
.
0
7
2
0
3
8
.
6
4
2
3
2
5
.
4
2
1
8
2
5
.
4
0
1
2
9
0
.
3
2
4
0
2
9
.
1
9
2
0
8
2
.
0
3
1
4
6
2
3
.
3
3
1
8
0
4
.
1
6
2
9
1
5
.
1
5
2
3
8
7
.
3
3
3
6
5
3
.
1
4
1
9
4
6
.
7
1
2
8
6
3
.
2
8
1
3
8
5
.
9
3
3
2
7
6
.
9
2
3
8
3
7
.
4
5
3
5
3
9
.
8
4
1
2
7
9
.
0
0
1
5
6
2
.
5
4
‰
0
.
5
5
0
.
5
8
0
.
5
1
0
.
4
4
1
.
0
3
0
.
5
8
0
.
3
7
0
.
4
5
0
.
6
5
1
.
8
9
0
.
3
4
0
.
4
7
1
.
1
6
0
.
4
7
0
.
5
8
0
.
7
9
0
.
5
3
0
.
5
2
0
.
6
7
0
.
9
4
0
.
5
4
0
.
6
2
1
.
3
9
1
.
3
4
0
.
4
2
0
.
8
7
0
.
9
2
1
.
2
9
1
.
1
5
1
.
6
8
0
.
7
6
0
.
8
5
1
.
5
4
0
.
4
0
1
.
3
0
0
.
5
2
0
.
5
6
0
.
6
4
0
.
5
1
0
.
3
6
1
.
1
1
0
.
5
8
4
.
0
5
0
.
5
0
0
.
8
1
0
.
6
6
1
.
0
1
0
.
5
4
0
.
7
9
0
.
3
8
0
.
9
1
1
.
0
6
0
.
9
8
0
.
3
5
0
.
4
3
35
Top1
0%
T
T
* R
ankT
*
0
.
9
8 0
.
9
7
2
7
2
0
.
9
8 0
.
9
9
2
5
7
0
.
9
7 0
.
9
3
2
9
9
0
.
9
7 1
.
0
1
2
4
6
0
.
9
7 0
.
9
5
2
8
4
0
.
9
7 1
.
0
5
2
0
9
0
.
9
6 0
.
9
7
2
7
6
0
.
9
6 1
.
0
4
2
1
5
0
.
9
6 0
.
9
4
2
9
0
0
.
9
6 0
.
9
3
3
0
2
0
.
9
6 0
.
9
7
2
7
4
0
.
9
5 1
.
0
6
2
0
2
0
.
9
5 0
.
9
2
3
0
7
0
.
9
5 0
.
9
5
2
8
9
0
.
9
5 1
.
0
3
2
3
0
0
.
9
5 0
.
8
9
3
2
3
0
.
9
4 1
.
0
0
2
5
3
0
.
9
4 0
.
9
9
2
6
2
0
.
9
3 0
.
8
8
3
2
6
0
.
9
3 0
.
8
9
3
2
5
0
.
9
3 0
.
9
7
2
7
5
0
.
9
3 0
.
9
3
3
0
0
0
.
9
2 0
.
9
5
2
8
7
0
.
9
2 0
.
9
4
2
9
4
0
.
9
2 0
.
8
7
3
3
4
0
.
9
2 0
.
9
5
2
8
5
0
.
9
2 0
.
9
2
3
0
5
0
.
9
2 0
.
9
4
2
9
2
0
.
9
2 0
.
8
9
3
2
1
0
.
9
2 0
.
9
3
2
9
7
0
.
9
2 0
.
9
4
2
9
5
0
.
9
1 0
.
9
0
3
1
7
0
.
9
1 0
.
9
9
2
5
9
0
.
9
1 0
.
9
3
3
0
3
0
.
9
1 0
.
9
0
3
1
3
0
.
9
1 0
.
9
6
2
8
1
0
.
9
0 0
.
8
9
3
1
9
0
.
9
0 0
.
9
1
3
0
9
0
.
9
0 0
.
9
3
2
9
6
0
.
8
9 0
.
9
1
3
1
1
0
.
8
9 0
.
9
1
3
0
8
0
.
8
9 0
.
9
2
3
0
4
0
.
8
8 0
.
8
9
3
2
2
0
.
8
8 0
.
8
9
3
2
4
0
.
8
8 0
.
8
7
3
3
0
0
.
8
8 0
.
9
4
2
9
1
0
.
8
7 0
.
9
0
3
1
5
0
.
8
7 0
.
8
6
3
4
2
0
.
8
7 0
.
8
7
3
3
3
0
.
8
7 0
.
9
5
2
8
6
0
.
8
6 0
.
8
6
3
3
8
0
.
8
6 0
.
9
2
3
0
6
0
.
8
6 0
.
9
5
2
8
8
0
.
8
6 0
.
8
1
3
6
1
0
.
8
6 0
.
8
8
3
2
7
A
v
e
r
ag
eh
ighimp
a
c
tg
ap
s
A
A
* R
ankA R
ankA
*
0
.
8
8 0
.
9
1
3
2
2
3
2
3
0
.
7
1 0
.
7
8
3
5
4
3
4
2
0
.
9
6 0
.
9
4
3
2
0
3
3
3
0
.
7
9 0
.
7
9
3
7
7
3
8
6
0
.
8
8 0
.
9
0
2
0
2
2
0
6
0
.
8
4 0
.
9
4
3
2
4
3
0
6
0
.
8
3 0
.
8
5
3
9
5
3
9
6
0
.
7
8 0
.
9
0
3
7
2
3
6
1
0
.
9
5 0
.
9
5
2
8
2
2
9
0
0
.
8
9 0
.
9
0
9
0
9
3
1
.
0
0 1
.
0
3
3
8
5
3
8
8
0
.
7
5 1
.
0
2
3
7
6
3
3
1
0
.
9
7 0
.
9
6
1
5
2
1
6
2
0
.
8
0 0
.
7
7
3
6
8
3
8
1
0
.
9
0 1
.
0
3
3
0
7
2
9
1
0
.
8
0 0
.
7
2
2
7
7
3
0
3
0
.
5
1 0
.
5
7
4
1
1
4
0
5
0
.
6
7 0
.
7
4
3
8
0
3
7
1
0
.
7
3 0
.
7
1
3
2
3
3
3
4
0
.
7
6 0
.
7
6
2
5
5
2
5
7
0
.
7
2 0
.
7
6
3
6
5
3
5
9
0
.
6
9 0
.
7
2
3
4
8
3
4
4
0
.
8
1 0
.
8
7
1
5
3
1
4
6
0
.
5
9 0
.
6
4
2
3
2
2
2
3
0
.
7
2 0
.
7
3
3
9
6
4
0
4
0
.
7
2 0
.
7
7
2
7
8
2
7
4
1
.
0
2 1
.
0
2
1
9
1
1
9
7
0
.
7
8 0
.
7
8
1
7
9
1
8
3
0
.
8
5 0
.
8
6
1
8
3
1
8
8
0
.
8
2 0
.
8
2
1
1
7
1
2
0
0
.
8
5 0
.
8
8
2
7
3
2
7
7
0
.
7
3 0
.
7
4
2
8
0
2
8
5
0
.
8
4 0
.
9
0
1
2
7
1
1
7
0
.
7
3 0
.
7
4
4
0
3
4
0
8
0
.
7
9 0
.
8
1
1
7
6
1
7
6
0
.
6
9 0
.
7
3
3
7
3
3
7
2
0
.
7
6 0
.
7
7
3
4
7
3
4
8
0
.
7
9 0
.
8
0
3
1
2
3
1
9
0
.
9
3 0
.
9
7
3
3
2
3
2
8
0
.
8
4 0
.
8
4
3
9
7
4
0
6
0
.
8
5 0
.
8
7
1
8
9
1
9
2
0
.
8
8 0
.
9
4
3
1
3
3
0
8
0
.
8
9 0
.
9
0
3
1
3
3
0
.
7
1 0
.
7
4
3
7
4
3
7
7
0
.
7
4 0
.
7
6
2
8
8
2
8
7
0
.
7
5 0
.
7
8
3
1
5
3
1
7
0
.
8
9 0
.
9
3
2
0
4
1
9
9
0
.
7
4 0
.
7
8
3
5
8
3
5
4
0
.
6
6 0
.
6
7
3
0
8
3
1
4
0
.
5
2 0
.
5
6
4
5
0
4
4
8
0
.
8
2 0
.
8
5
2
4
5
2
4
3
0
.
6
9 0
.
7
4
2
4
9
2
3
8
0
.
6
9 0
.
7
4
2
6
5
2
5
4
0
.
5
9 0
.
5
6
4
4
6
4
5
5
0
.
6
7 0
.
7
1
4
0
2
4
0
1
R
ankT
3
2
7
3
2
8
3
2
9
3
3
0
3
3
1
3
3
2
3
3
3
3
3
4
3
3
5
3
3
6
3
3
7
3
3
8
3
3
9
3
4
0
3
4
1
3
4
2
3
4
3
3
4
4
3
4
5
3
4
6
3
4
7
3
4
8
3
4
9
3
5
0
3
5
1
3
5
2
3
5
3
3
5
4
3
5
5
3
5
6
3
5
7
3
5
8
3
5
9
3
6
0
3
6
1
3
6
2
3
6
3
3
6
4
3
6
5
3
6
6
3
6
7
3
6
8
3
6
9
3
7
0
3
7
1
3
7
2
3
7
3
3
7
4
3
7
5
3
7
6
3
7
7
3
7
8
3
7
9
3
8
0
3
8
1
Un
i
v
e
r
s
i
t
y
Un
i
vM
an
i
tob
a
Un
i
vB
u
r
g
und
y
Un
i
vP
a
rm
a
Un
i
vF
lo
r
en
c
e
D
a
l
i
anUn
i
vT
e
chno
l
P
e
k
in
gUn
i
v
G
r
i
f
f
i
thUn
i
v
T
e
chn
ion-I
s
r
a
e
lIn
s
tT
e
chno
l
Un
i
vBo
lo
gn
a
Un
i
vL
üb
e
c
k
T
e
chUn
i
vL
i
sbon
L
e
ibn
i
zUn
i
vH
anno
v
e
r
M
a
s
s
e
yUn
i
v
T
e
lA
v
i
vUn
i
v
SEUn
i
v
Un
i
vT
u
r
k
u
Un
i
vV
al
en
c
i
a
Ind
i
anIn
s
tT
e
chno
lKh
a
r
a
gp
u
r
T
s
in
gh
u
aUn
i
v
Un
i
vM
i
s
s
i
s
s
ipp
i
S
unY
a
t
s
enUn
i
v
Un
i
vP
e
r
u
g
i
a
L
an
zho
uUn
i
v
Un
i
vF
e
r
r
a
r
a
O
k
l
ahom
aS
t
a
t
eUn
i
v -S
t
i
l
lw
a
t
e
r
S
t
e
l
l
enbo
s
chUn
i
v
Un
i
v Mod
en
a&R
e
g
g
ioEm
i
l
i
a
N
a
t
lT
s
in
gH
u
aUni
v
Un
i
vS
an
t
i
a
god
eCompo
s
t
e
l
a
A
ub
u
rnUn
i
v
N
an
k
a
iUn
i
v
Un
i
vA
v
e
i
ro
Un
i
vN
an
t
e
s
Un
i
vB
a
s
q
u
eCo
un
t
r
y
A
r
i
s
to
t
l
eUn
i
vTh
e
s
s
a
lon
i
k
i
Un
i
vW
i
tw
a
t
e
r
s
r
and
Am
i
r
k
ab
i
rUn
i
vT
e
chno
l
Sh
a
r
i
fUn
i
vT
e
chno
l
H
a
rb
inIn
s
tT
e
chno
l
N
a
t
lS
unY
a
ts
enUn
i
v
N
an
j
in
gUn
i
v
Un
i
vG
eno
a
Un
i
vL
i
sbon
K
yo
toUn
i
v
Un
i
vG
r
an
ad
a
N
a
t
lC
en
tUn
i
v
Un
i
vN
ap
e
l
sF
ed
e
r
i
coI
I
F
ud
anUn
i
v
To
k
yo M
ed& D
en
tUn
i
v
Un
i
vP
i
s
a
B
a
rI
l
anUn
i
v
Un
i
vE
a
s
t
e
rnF
in
l
and
Un
i
vC
a
t
to
l
i
c
aS
a
c
roC
uo
r
e
L
u
th
e
rUn
i
vH
a
l
l
eW
i
t
t
enb
e
r
g
Pon
t
i
f
i
c
i
aUn
i
vC
a
tó
l
i
c
aCh
i
l
e
Numb
e
ra
r
t
i
c
l
e
s
3
0
1
5
.
7
9
1
3
1
0
.
6
0
1
7
4
0
.
6
8
3
8
8
9
.
8
5
2
7
9
2
.
9
1
6
3
9
1
.
9
0
1
4
5
3
.
8
4
4
9
4
7
.
9
1
5
6
3
7
.
1
8
1
2
1
7
.
2
9
2
3
3
8
.
1
2
8
7
0
.
3
3
1
4
6
6
.
5
8
6
5
7
0
.
6
1
1
7
9
6
.
2
1
2
3
0
9
.
0
6
3
5
8
8
.
4
1
2
3
5
9
.
1
3
8
3
6
1
.
9
8
1
7
0
8
.
5
1
3
3
7
2
.
9
3
1
8
0
4
.
4
6
2
3
2
5
.
1
4
1
4
2
0
.
5
7
1
5
2
3
.
4
4
1
3
9
3
.
4
9
1
6
1
0
.
2
7
3
1
1
4
.
6
4
2
6
1
8
.
8
9
2
1
1
0
.
6
5
2
8
9
3
.
0
1
1
7
0
4
.
1
2
1
3
9
8
.
2
1
2
2
8
7
.
0
7
4
1
7
3
.
9
4
1
4
5
7
.
1
4
9
3
6
.
3
3
1
4
5
3
.
7
4
3
1
9
7
.
9
3
1
5
8
8
.
2
0
4
6
3
8
.
3
1
2
5
7
4
.
4
6
1
5
5
2
.
9
5
1
1
9
2
3
.
4
6
2
7
6
4
.
7
2
1
6
6
6
.
5
7
3
9
8
3
.
8
9
5
0
7
7
.
2
7
1
6
3
5
.
6
1
3
7
3
4
.
6
6
1
7
3
5
.
9
3
1
5
2
2
.
6
4
1
5
7
6
.
3
2
1
8
1
1
.
8
8
1
1
6
9
.
1
2
‰
0
.
8
3
0
.
3
6
0
.
4
8
1
.
0
8
0
.
7
7
1
.
7
7
0
.
4
0
1
.
3
7
1
.
5
6
0
.
3
4
0
.
6
5
0
.
2
4
0
.
4
1
1
.
8
2
0
.
5
0
0
.
6
4
0
.
9
9
0
.
6
5
2
.
3
1
0
.
4
7
0
.
9
3
0
.
5
0
0
.
6
4
0
.
3
9
0
.
4
2
0
.
3
9
0
.
4
5
0
.
8
6
0
.
7
2
0
.
5
8
0
.
8
0
0
.
4
7
0
.
3
9
0
.
6
3
1
.
1
5
0
.
4
0
0
.
2
6
0
.
4
0
0
.
8
8
0
.
4
4
1
.
2
8
0
.
7
1
0
.
4
3
3
.
3
0
0
.
7
6
0
.
4
6
1
.
1
0
1
.
4
0
0
.
4
5
1
.
0
3
0
.
4
8
0
.
4
2
0
.
4
4
0
.
5
0
0
.
3
2
36
Top1
0%
T
T
* R
ankT
*
0
.
8
6 0
.
8
7
3
3
7
0
.
8
6 0
.
8
4
3
4
9
0
.
8
6 0
.
9
0
3
1
6
0
.
8
6 0
.
8
3
3
5
8
0
.
8
6 0
.
9
0
3
1
4
0
.
8
5 0
.
8
6
3
4
3
0
.
8
5 0
.
8
9
3
2
0
0
.
8
5 0
.
8
6
3
4
0
0
.
8
5 0
.
8
7
3
2
9
0
.
8
5 0
.
8
0
3
6
4
0
.
8
5 0
.
9
4
2
9
3
0
.
8
5 0
.
9
0
3
1
2
0
.
8
5 0
.
8
3
3
5
7
0
.
8
4 0
.
8
6
3
3
9
0
.
8
4 0
.
8
3
3
5
4
0
.
8
4 0
.
8
4
3
5
2
0
.
8
4 0
.
8
4
3
5
1
0
.
8
4 0
.
9
1
3
1
0
0
.
8
3 0
.
8
7
3
3
1
0
.
8
3 0
.
8
6
3
4
1
0
.
8
3 0
.
8
3
3
5
3
0
.
8
3 0
.
7
9
3
6
6
0
.
8
3 0
.
8
7
3
3
2
0
.
8
3 0
.
8
3
3
5
5
0
.
8
3 0
.
8
5
3
4
4
0
.
8
1 0
.
8
1
3
6
0
0
.
8
1 0
.
8
4
3
4
7
0
.
8
1 0
.
8
5
3
4
6
0
.
8
1 0
.
7
9
3
6
7
0
.
8
1 0
.
8
0
3
6
3
0
.
8
0 0
.
8
8
3
2
8
0
.
8
0 0
.
8
5
3
4
5
0
.
7
9 0
.
7
7
3
7
4
0
.
7
9 0
.
8
1
3
5
9
0
.
7
8 0
.
8
1
3
6
2
0
.
7
8 0
.
7
6
3
7
7
0
.
7
8 0
.
8
7
3
3
5
0
.
7
8 0
.
8
9
3
1
8
0
.
7
8 0
.
8
4
3
5
0
0
.
7
8 0
.
8
3
3
5
6
0
.
7
7 0
.
7
7
3
7
3
0
.
7
7 0
.
7
7
3
7
5
0
.
7
7 0
.
7
5
3
8
0
0
.
7
7 0
.
7
8
3
7
0
0
.
7
6 0
.
7
8
3
7
1
0
.
7
6 0
.
8
7
3
3
6
0
.
7
6 0
.
7
3
3
8
9
0
.
7
6 0
.
7
5
3
7
8
0
.
7
6 0
.
7
5
3
8
1
0
.
7
6 0
.
7
5
3
7
9
0
.
7
6 0
.
7
8
3
6
9
0
.
7
6 0
.
7
2
3
9
4
0
.
7
5 0
.
7
3
3
9
2
0
.
7
5 0
.
7
3
3
9
1
0
.
7
5 0
.
7
3
3
8
8
A
v
e
r
ag
eh
ighimp
a
c
tg
ap
s
A
A
* R
ankA R
ankA
*
0
.
7
2 0
.
7
4
2
8
7
2
8
8
0
.
6
7 0
.
6
9
4
2
4
4
2
6
0
.
9
2 1
.
0
0
3
3
8
3
3
2
0
.
7
5 0
.
7
5
2
3
0
2
3
1
0
.
6
9 0
.
7
4
3
0
4
2
9
8
0
.
7
4 0
.
7
6
1
2
4
1
2
5
0
.
6
5 0
.
6
3
4
1
9
4
2
4
0
.
7
6 0
.
8
4
1
7
4
1
5
7
0
.
7
4 0
.
7
8
1
4
9
1
4
5
0
.
6
8 0
.
6
6
4
3
5
4
4
3
0
.
7
3 0
.
7
7
3
3
1
3
2
5
0
.
8
3 0
.
8
9
4
5
1
4
4
9
0
.
9
9 0
.
9
4
3
5
6
3
7
0
0
.
7
0 0
.
7
4
1
3
1
1
2
3
0
.
9
9 0
.
6
2
3
1
6
3
9
9
0
.
6
9 0
.
6
7
3
3
9
3
5
1
0
.
6
8 0
.
7
0
2
6
8
2
6
8
0
.
6
5 0
.
7
2
3
4
9
3
3
5
0
.
6
9 0
.
7
4
9
8
9
1
0
.
6
7 0
.
6
9
3
9
3
3
9
3
0
.
6
5 0
.
6
8
2
8
4
2
8
4
0
.
7
5 0
.
7
7
3
6
7
3
6
9
0
.
6
4 0
.
7
3
3
5
3
3
3
7
0
.
9
9 1
.
0
3
3
6
4
3
6
2
0
.
6
4 0
.
7
1
4
1
0
4
0
7
0
.
6
4 0
.
6
7
4
2
1
4
2
2
0
.
6
4 0
.
6
8
4
0
4
4
0
3
0
.
5
7 0
.
6
2
3
1
7
3
1
0
0
.
6
6 0
.
7
0
3
2
7
3
2
2
0
.
7
1 0
.
7
3
3
5
1
3
5
2
0
.
6
0 0
.
6
1
3
2
9
3
2
9
0
.
6
3 0
.
6
8
4
0
0
3
9
4
0
.
5
7 0
.
5
9
4
3
7
4
3
5
0
.
5
8 0
.
6
1
3
6
9
3
6
8
0
.
5
3 0
.
5
8
2
8
1
2
7
6
0
.
7
5 0
.
7
6
3
9
8
4
0
2
0
.
7
9 0
.
8
4
4
4
8
4
4
6
0
.
5
3 0
.
6
2
4
4
2
4
2
8
0
.
9
0 0
.
8
8
2
3
1
2
4
1
0
.
6
1 0
.
7
5
4
1
2
3
9
2
0
.
6
9 0
.
6
2
2
1
4
2
3
4
0
.
8
4 0
.
8
6
2
8
6
2
8
9
0
.
5
5 0
.
5
9
4
3
0
4
2
3
0
.
7
2 0
.
7
5
5
6
5
5
0
.
5
7 0
.
5
8
3
4
1
3
4
3
0
.
5
2 0
.
5
9
4
2
7
4
1
5
0
.
6
6 0
.
6
7
2
5
2
2
5
1
0
.
5
9 0
.
6
1
2
2
6
2
2
2
0
.
5
4 0
.
5
4
4
2
6
4
3
1
0
.
6
6 0
.
6
7
2
6
7
2
6
7
0
.
5
6 0
.
5
8
4
1
4
4
1
2
0
.
5
5 0
.
5
3
4
3
2
4
4
2
0
.
5
7 0
.
5
7
4
2
2
4
2
7
0
.
6
8 0
.
6
8
3
8
2
3
9
0
0
.
5
2 0
.
5
4
4
6
7
4
6
7
R
ankT
3
8
2
3
8
3
3
8
4
3
8
5
3
8
6
3
8
7
3
8
8
3
8
9
3
9
0
3
9
1
3
9
2
3
9
3
3
9
4
3
9
5
3
9
6
3
9
7
3
9
8
3
9
9
4
0
0
4
0
1
4
0
2
4
0
3
4
0
4
4
0
5
4
0
6
4
0
7
4
0
8
4
0
9
4
1
0
4
1
1
4
1
2
4
1
3
4
1
4
4
1
5
4
1
6
4
1
7
4
1
8
4
1
9
4
2
0
4
2
1
4
2
2
4
2
3
4
2
4
4
2
5
4
2
6
4
2
7
4
2
8
4
2
9
4
3
0
4
3
1
4
3
2
4
3
3
4
3
4
4
3
5
4
3
6
Un
i
v
e
r
s
i
t
y
W
uh
anUn
i
v
Un
i
vP
a
t
r
a
s
L
in
köp
in
gUn
i
v
Un
i
vO
u
l
u
F
l
ind
e
r
sUn
i
v
Ind
i
anIn
s
tS
c
i
S
eo
u
lN
a
t
lUn
i
v
N
a
t
lT
e
chUn
i
vA
th
en
s
X
i
am
enUn
i
v
To
k
yoIn
s
tT
e
chno
l
WV
i
r
g
in
i
aUn
i
v
Un
i
vS
a
in
sM
a
l
a
y
s
i
a
S
ap
i
en
z
aUn
i
vRom
a
Un
i
vB
a
r
iA
ldo Mo
ro
Te
x
a
sT
e
chUn
i
v
O
s
a
k
aUn
i
v
N
a
t
lCh
un
gH
s
in
gUn
i
v
Un
i
vO
v
i
edo
N
a
t
lT
a
iw
anUn
i
v
Un
i
vRom
aTo
rV
e
r
g
a
t
a
N
a
t
lCh
i
aoT
un
gUn
i
v
N
a
go
y
aUn
i
v
Un
i
vKw
aZ
u
l
uN
a
t
a
l
Sh
an
gh
a
iUn
i
v
Sh
an
gh
a
iJ
i
aoTon
gUn
i
v
Toho
k
uUn
i
v
Un
i
vM
u
r
c
i
a
M
idd
l
eE
a
s
tT
e
chUn
i
v
Un
i
vU
l
s
an
SCh
in
aUn
i
vT
e
chno
l
ECh
in
aNo
rm
a
lUn
i
v
ECh
in
aUn
i
vS
c
i&T
e
chno
l
Comp
l
u
t
en
s
eUn
i
v
Un
ivCo
imb
r
a
X
i
'
anJ
i
ao
ton
gUn
i
v
Un
i
vL
j
ub
l
j
an
a
Zh
e
j
i
an
gUn
i
v
T
e
chUn
i
vM
ad
r
id
Sh
andon
gUn
i
v
K
y
u
sh
uUn
i
v
Yon
s
e
iUn
i
v
K
e
ioUn
i
v
Un
i
vW
a
r
s
aw
N
a
t
l&K
apod
i
s
t
r
i
anUn
i
vA
th
en
s
Ewh
a Wom
an
sUn
i
v
Un
i
vF
edS
an
t
aC
a
t
a
r
in
a
C
en
tSUn
i
v
J
i
l
inUn
i
v
M
ah
ido
lUn
i
v
Un
i
vS
i
en
a
N
a
t
lCh
en
gK
un
gUn
i
v
B
enG
u
r
ionUn
i
vN
e
g
e
v
Un
i
vC
a
t
an
i
a
Un
i
vS
a
s
k
a
t
ch
ew
an
Un
i
vS
c
i&T
e
chno
lB
e
i
j
in
g
Numb
e
ra
r
t
i
c
l
e
s
3
3
2
3
.
0
7
2
2
9
2
.
8
7
2
3
9
3
.
1
6
1
8
3
7
.
4
9
1
1
8
3
.
1
1
3
1
5
5
.
2
7
9
5
4
3
.
9
1
2
1
0
9
.
0
0
1
5
9
4
.
1
6
5
4
7
4
.
2
9
1
8
3
7
.
3
9
1
1
9
0
.
9
9
6
4
4
3
.
7
4
2
1
6
2
.
8
3
2
1
0
9
.
3
7
9
7
0
0
.
6
5
1
8
8
9
.
9
8
1
8
9
5
.
0
9
8
4
0
2
.
7
4
2
3
6
5
.
6
4
3
4
2
4
.
9
3
5
7
7
5
.
6
5
1
1
2
2
.
0
9
1
6
2
1
.
0
0
7
4
4
5
.
4
1
9
2
9
8
.
6
7
1
6
1
3
.
3
4
1
8
1
5
.
8
8
1
6
3
4
.
9
1
1
6
2
8
.
7
6
1
1
7
9
.
6
7
1
7
5
2
.
0
0
4
5
1
5
.
2
3
1
6
8
5
.
4
7
2
9
6
7
.
7
9
2
8
9
0
.
8
4
9
4
8
7
.
9
1
1
5
9
7
.
8
1
3
7
0
1
.
1
5
6
3
9
2
.
0
0
5
2
7
9
.
3
3
2
9
8
8
.
3
9
1
8
2
3
.
6
6
5
4
5
4
.
0
6
1
1
6
1
.
1
8
1
1
9
3
.
5
3
1
8
5
6
.
3
9
3
4
0
0
.
1
5
1
6
5
2
.
7
5
1
8
1
7
.
8
0
5
3
0
9
.
5
7
3
5
4
9
.
0
1
1
7
4
5
.
1
2
2
7
9
1
.
7
3
9
8
2
.
5
0
‰
0
.
9
2
0
.
6
3
0
.
6
6
0
.
5
1
0
.
3
3
0
.
8
7
2
.
6
4
0
.
5
8
0
.
4
4
1
.
5
1
0
.
5
1
0
.
3
3
1
.
7
8
0
.
6
0
0
.
5
8
2
.
6
8
0
.
5
2
0
.
5
2
2
.
3
2
0
.
6
5
0
.
9
5
1
.
6
0
0
.
3
1
0
.
4
5
2
.
0
6
2
.
5
7
0
.
4
5
0
.
5
0
0
.
4
5
0
.
4
5
0
.
3
3
0
.
4
8
1
.
2
5
0
.
4
7
0
.
8
2
0
.
8
0
2
.
6
2
0
.
4
4
1
.
0
2
1
.
7
7
1
.
4
6
0
.
8
3
0
.
5
0
1
.
5
1
0
.
3
2
0
.
3
3
0
.
5
1
0
.
9
4
0
.
4
6
0
.
5
0
1
.
4
7
0
.
9
8
0
.
4
8
0
.
7
7
0
.
2
7
37
Top1
0%
T
T
* R
ankT
*
0
.
7
5 0
.
7
1
4
0
0
0
.
7
4 0
.
7
3
3
9
0
0
.
7
4 0
.
7
5
3
8
2
0
.
7
4 0
.
7
4
3
8
3
0
.
7
4 0
.
7
0
4
0
7
0
.
7
4 0
.
7
7
3
7
6
0
.
7
2 0
.
7
2
3
9
3
0
.
7
2 0
.
8
4
3
4
8
0
.
7
2 0
.
7
0
4
0
8
0
.
7
1 0
.
7
4
3
8
7
0
.
7
1 0
.
7
4
3
8
5
0
.
7
1 0
.
6
9
4
1
1
0
.
7
1 0
.
7
2
3
9
8
0
.
7
1 0
.
7
0
4
0
6
0
.
7
1 0
.
7
1
4
0
1
0
.
7
1 0
.
7
1
4
0
3
0
.
7
0 0
.
7
2
3
9
6
0
.
7
0 0
.
6
7
4
1
7
0
.
7
0 0
.
7
2
3
9
7
0
.
7
0 0
.
7
1
4
0
2
0
.
7
0 0
.
7
9
3
6
5
0
.
6
9 0
.
7
0
4
0
4
0
.
6
9 0
.
7
2
3
9
5
0
.
6
9 0
.
7
9
3
6
8
0
.
6
9 0
.
7
4
3
8
6
0
.
6
8 0
.
7
0
4
0
9
0
.
6
8 0
.
7
2
3
9
9
0
.
6
8 0
.
7
4
3
8
4
0
.
6
6 0
.
6
8
4
1
6
0
.
6
6 0
.
7
7
3
7
2
0
.
6
6 0
.
6
9
4
1
0
0
.
6
6 0
.
6
7
4
2
0
0
.
6
6 0
.
6
8
4
1
3
0
.
6
5 0
.
6
3
4
2
9
0
.
6
5 0
.
6
8
4
1
2
0
.
6
5 0
.
6
7
4
1
9
0
.
6
5 0
.
6
5
4
2
1
0
.
6
5 0
.
7
0
4
0
5
0
.
6
4 0
.
6
7
4
1
8
0
.
6
4 0
.
6
5
4
2
2
0
.
6
4 0
.
6
3
4
2
7
0
.
6
4 0
.
6
4
4
2
6
0
.
6
3 0
.
6
4
4
2
5
0
.
6
3 0
.
6
0
4
3
7
0
.
6
3 0
.
6
3
4
3
0
0
.
6
3 0
.
6
4
4
2
4
0
.
6
3 0
.
6
8
4
1
4
0
.
6
2 0
.
6
2
4
3
3
0
.
6
2 0
.
6
0
4
4
1
0
.
6
1 0
.
6
3
4
2
8
0
.
6
1 0
.
6
8
4
1
5
0
.
6
0 0
.
6
2
4
3
5
0
.
6
0 0
.
6
2
4
3
6
0
.
5
9 0
.
5
8
4
4
6
0
.
5
9 0
.
6
4
4
2
3
A
v
e
r
ag
eh
ighimp
a
c
tg
ap
s
A
A
* R
ankA R
ankA
*
0
.
4
4 0
.
4
6
3
5
5
3
5
5
0
.
5
6 0
.
5
9
3
7
5
3
7
4
0
.
5
7 0
.
5
9
3
6
6
3
6
6
0
.
6
7 0
.
6
8
3
8
4
3
8
9
0
.
4
7 0
.
4
5
4
7
1
4
7
6
0
.
5
6 0
.
6
2
3
1
8
3
0
9
0
.
5
9 0
.
6
2
1
0
3
1
0
1
0
.
4
8 0
.
5
5
4
0
7
3
9
5
0
.
5
7 0
.
6
1
4
2
0
4
1
8
0
.
6
9 0
.
7
4
1
7
0
1
6
0
0
.
5
2 0
.
5
4
4
1
5
4
1
4
0
.
5
1 0
.
5
4
4
6
5
4
6
3
0
.
5
8 0
.
6
0
1
7
3
1
6
9
0
.
5
6 0
.
5
6
3
8
7
3
9
1
0
.
6
1 0
.
6
4
3
7
1
3
7
5
0
.
7
1 0
.
7
2
7
9
7
8
0
.
4
4 0
.
4
7
4
3
1
4
2
9
0
.
4
7 0
.
4
8
4
2
3
4
2
5
0
.
5
2 0
.
5
7
1
4
2
1
2
9
0
.
5
3 0
.
5
6
3
7
9
3
7
8
0
.
4
6 0
.
5
2
3
4
2
3
3
0
0
.
6
0 0
.
6
4
1
8
4
1
8
1
0
.
6
3 0
.
7
5
4
5
2
4
3
4
0
.
4
3 0
.
4
8
4
5
3
4
5
0
0
.
5
0 0
.
5
5
1
7
5
1
5
8
0
.
6
2 0
.
6
6
9
6
9
4
0
.
5
1 0
.
5
3
4
3
3
4
3
2
0
.
4
2 0
.
4
5
4
4
1
4
3
8
0
.
4
2 0
.
4
2
4
5
5
4
5
8
0
.
4
5 0
.
5
0
4
4
9
4
3
9
0
.
4
0 0
.
4
5
4
7
9
4
7
8
0
.
4
9 0
.
5
5
4
2
8
4
2
0
0
.
5
8 0
.
5
9
2
5
4
2
5
0
0
.
4
4 0
.
4
4
4
4
7
4
5
2
0
.
5
5 0
.
5
3
3
3
6
3
4
7
0
.
5
4 0
.
5
5
3
4
3
3
4
5
0
.
4
2 0
.
4
4
1
5
8
1
5
4
0
.
3
8 0
.
4
2
4
6
8
4
5
9
0
.
4
7 0
.
5
2
3
2
6
3
1
5
0
.
5
4 0
.
5
5
1
8
8
1
9
1
0
.
5
0 0
.
5
3
2
4
7
2
4
4
0
.
4
9 0
.
4
9
3
5
7
3
6
0
1
.
8
0 1
.
4
9
2
0
0
2
4
7
0
.
4
3 0
.
4
5
2
7
0
2
7
1
0
.
5
6 0
.
6
0
4
5
8
4
5
7
0
.
3
2 0
.
3
3
4
8
8
4
9
0
0
.
5
5 0
.
6
1
4
0
6
3
9
7
0
.
3
5 0
.
3
9
3
9
2
3
7
9
0
.
4
6 0
.
4
5
4
4
4
4
5
1
0
.
4
3 0
.
4
4
4
3
9
4
4
5
0
.
3
8 0
.
4
4
2
9
5
2
8
2
0
.
4
9 0
.
5
2
3
2
5
3
2
1
0
.
5
0 0
.
5
1
4
2
5
4
3
0
0
.
4
0 0
.
4
0
3
9
4
3
9
8
0
.
3
6 0
.
4
2
4
8
9
4
8
9
R
ankT
4
3
7
4
3
8
4
3
9
4
4
0
4
4
1
4
4
2
4
4
3
4
4
4
4
4
5
4
4
6
4
4
7
4
4
8
4
4
9
4
5
0
4
5
1
4
5
2
4
5
3
4
5
4
4
5
5
4
5
6
4
5
7
4
5
8
4
5
9
4
6
0
4
6
1
4
6
2
4
6
3
4
6
4
4
6
5
4
6
6
4
6
7
4
6
8
4
6
9
4
7
0
4
7
1
4
7
2
4
7
3
4
7
4
4
7
5
4
7
6
4
7
7
4
7
8
4
7
9
4
8
0
4
8
1
4
8
2
4
8
3
4
8
4
4
8
5
4
8
6
4
8
7
4
8
8
4
8
9
4
9
0
4
9
1
Un
i
v
e
r
s
i
t
y
Un
i
vP
a
l
e
rmo
T
a
rb
i
a
t Mod
a
r
e
sUn
i
v
Ko
r
e
aUn
i
v
B
e
i
j
in
gNo
rm
a
lUn
i
v
C
a
i
roUn
i
v
Un
i
vT
s
u
k
uba
Ch
ib
aUn
i
v
H
an
y
an
gUn
i
v
E
g
eUn
i
v
K
y
un
gH
e
eUn
i
v
S
un
g
k
y
un
kw
anUn
i
v
Ton
g
j
iUn
i
v
H
i
ro
sh
im
aUn
i
v
T
i
an
j
inUn
i
v
S
i
ch
u
anUn
i
v
Ch
in
aA
g
rUn
i
v
No
r
thw
e
s
t
e
rnPo
l
y
t
e
chUn
i
v
Ho
k
k
aidoUn
i
v
Un
i
vT
eh
r
an
Chonb
u
kN
a
t
lUn
i
v
J
a
g
i
e
l
lon
i
anUn
i
vK
r
a
kow
S
t
a
t
eUn
i
vC
amp
in
a
s
Lomono
so
v Mo
s
cowS
t
a
t
eUn
i
v
W
a
s
ed
aUn
i
v
Ch
un
gn
am N
a
t
lUn
i
v
Un
i
vP
r
e
to
r
i
a
Un
i
vB
u
eno
sA
i
r
e
s
F
edUn
i
vR
ioG
r
and
eS
u
l
Ch
u
l
a
lon
g
ko
rnUn
i
v
S
tP
e
t
e
r
sb
u
r
gS
t
a
t
eUn
i
v
Un
i
vS
ãoP
a
u
lo
Un
i
vCh
i
l
e
Ch
a
r
le
sUn
i
vP
r
a
g
u
e
B
an
a
r
a
sH
ind
uUn
i
v
K
an
a
z
aw
aUn
i
v
Chonn
am N
a
t
lUn
i
v
Ch
an
gG
un
gUn
i
v
N
a
t
lY
an
gM
in
gUn
i
v
Inh
aUn
i
v
K
y
un
gpoo
kN
a
t
lUn
i
v
Un
i
vF
ed M
in
a
sG
e
r
a
i
s
Kob
eUn
i
v
N
a
t
lA
u
tonomo
u
sUn
i
vM
e
x
i
co
H
u
a
zhon
gUn
i
vS
c
i&T
e
chnol
K
in
gS
a
udUn
i
v
F
edUn
i
vR
iod
eJ
an
e
i
ro
O
k
a
y
am
aUn
i
v
I
s
t
anb
u
lUn
i
v
Un
i
vM
a
l
a
y
a
Un
i
vB
e
l
g
r
ad
e
F
edUn
i
vV
i
ço
s
a
F
edUn
i
vS
ãoP
a
u
lo
G
a
z
iUn
i
v
T
eh
r
anUn
i
vM
edS
c
i
Un
i
vZ
a
g
r
eb
Numb
e
ra
r
t
i
c
l
e
s
2
1
7
8
.
7
2
9
3
4
.
3
1
3
7
7
2
.
2
1
1
5
2
4
.
8
4
1
3
9
7
.
8
6
3
4
1
5
.
3
6
2
6
7
8
.
0
8
3
0
1
4
.
9
4
1
8
6
0
.
3
7
1
4
5
3
.
4
7
3
8
4
2
.
3
0
1
4
7
5
.
4
0
3
4
8
8
.
4
9
2
6
9
2
.
0
5
3
6
1
2
.
1
9
1
6
9
1
.
9
8
1
2
0
8
.
4
3
6
4
6
3
.
4
8
1
9
8
6
.
6
6
1
3
2
4
.
5
1
2
3
8
7
.
2
0
4
1
9
1
.
2
6
2
8
4
1
.
2
6
1
8
8
3
.
8
4
1
4
3
2
.
6
4
1
3
3
5
.
3
4
3
0
8
7
.
4
6
2
5
5
5
.
7
8
1
7
0
7
.
0
3
8
8
9
.
7
8
1
0
6
9
0
.
1
9
1
9
3
5
.
2
3
3
6
8
8
.
1
8
1
2
7
1
.
2
7
2
0
1
4
.
7
0
1
8
4
1
.
8
6
1
9
0
9
.
0
7
1
8
9
5
.
9
9
2
0
6
3
.
4
1
2
1
2
2
.
7
7
2
0
1
9
.
7
9
2
5
3
9
.
5
1
5
1
8
2
.
2
9
3
8
4
0
.
6
9
8
7
8
.
8
5
3
2
2
1
.
9
6
3
0
0
7
.
1
9
2
7
3
9
.
4
3
1
1
1
5
.
7
8
2
2
3
1
.
3
5
5
0
6
.
1
7
1
8
0
6
.
3
2
1
9
9
1
.
2
0
1
0
7
6
.
2
0
2
0
3
8
.
5
8
‰
0
.
6
0
0
.
2
6
1
.
0
4
0
.
4
2
0
.
3
9
0
.
9
4
0
.
7
4
0
.
8
3
0
.
5
1
0
.
4
0
1
.
0
6
0
.
4
1
0
.
9
7
0
.
7
4
1
.
0
0
0
.
4
7
0
.
3
3
1
.
7
9
0
.
5
5
0
.
3
7
0
.
6
6
1
.
1
6
0
.
7
9
0
.
5
2
0
.
4
0
0
.
3
7
0
.
8
5
0
.
7
1
0
.
4
7
0
.
2
5
2
.
9
6
0
.
5
4
1
.
0
2
0
.
3
5
0
.
5
6
0
.
5
1
0
.
5
3
0
.
5
2
0
.
5
7
0
.
5
9
0
.
5
6
0
.
7
0
1
.
4
3
1
.
0
6
0
.
2
4
0
.
8
9
0
.
8
3
0
.
7
6
0
.
3
1
0
.
6
2
0
.
1
4
0
.
5
0
0
.
5
5
0
.
3
0
0
.
5
6
38
Top1
0%
T
T
* R
ankT
*
0
.
5
8 0
.
5
7
4
4
7
0
.
5
8 0
.
5
8
4
4
5
0
.
5
8 0
.
5
9
4
4
2
0
.
5
8 0
.
6
2
4
3
1
0
.
5
7 0
.
6
0
4
3
8
0
.
5
7 0
.
5
9
4
4
3
0
.
5
7 0
.
5
6
4
5
0
0
.
5
7 0
.
6
2
4
3
4
0
.
5
6 0
.
5
5
4
5
4
0
.
5
6 0
.
5
7
4
4
8
0
.
5
6 0
.
5
4
4
5
5
0
.
5
6 0
.
6
2
4
3
2
0
.
5
6 0
.
5
5
4
5
3
0
.
5
5 0
.
5
7
4
4
9
0
.
5
5 0
.
6
0
4
3
9
0
.
5
5 0
.
5
6
4
5
2
0
.
5
4 0
.
5
9
4
4
4
0
.
5
4 0
.
5
4
4
5
7
0
.
5
4 0
.
6
0
4
4
0
0
.
5
2 0
.
5
6
4
5
1
0
.
5
2 0
.
5
3
4
6
0
0
.
5
2 0
.
5
3
4
5
8
0
.
5
2 0
.
5
3
4
5
9
0
.
5
1 0
.
5
1
4
6
5
0
.
5
1 0
.
5
4
4
5
6
0
.
5
1 0
.
5
1
4
6
3
0
.
5
1 0
.
5
0
4
6
7
0
.
5
1 0
.
5
1
4
6
4
0
.
5
1 0
.
4
9
4
7
2
0
.
5
0 0
.
5
2
4
6
2
0
.
5
0 0
.
5
1
4
6
6
0
.
4
8 0
.
4
9
4
7
0
0
.
4
8 0
.
5
2
4
6
1
0
.
4
8 0
.
5
0
4
6
8
0
.
4
8 0
.
4
6
4
8
0
0
.
4
8 0
.
4
7
4
7
5
0
.
4
8 0
.
4
7
4
7
7
0
.
4
7 0
.
4
3
4
8
9
0
.
4
7 0
.
4
9
4
7
1
0
.
4
7 0
.
4
7
4
7
8
0
.
4
6 0
.
4
9
4
6
9
0
.
4
6 0
.
4
7
4
7
6
0
.
4
6 0
.
4
8
4
7
4
0
.
4
5 0
.
4
5
4
8
1
0
.
4
4 0
.
4
9
4
7
3
0
.
4
4 0
.
4
6
4
7
9
0
.
4
4 0
.
4
3
4
8
6
0
.
4
4 0
.
4
5
4
8
2
0
.
4
4 0
.
4
3
4
8
8
0
.
4
2 0
.
4
4
4
8
5
0
.
4
2 0
.
4
4
4
8
4
0
.
4
1 0
.
3
8
4
9
5
0
.
4
1 0
.
4
4
4
8
3
0
.
4
0 0
.
4
0
4
9
1
0
.
4
0 0
.
4
3
4
8
7
A
v
e
r
ag
eh
ighimp
a
c
tg
ap
s
A
A
* R
ankA R
ankA
*
0
.
4
6 0
.
4
7
4
0
8
4
1
0
0
.
3
2 0
.
3
0
4
9
4
4
9
5
0
.
4
2 0
.
4
5
3
4
4
3
3
6
0
.
3
8 0
.
4
0
4
6
9
4
6
8
0
.
3
8 0
.
4
1
4
7
5
4
7
2
0
.
4
6 0
.
4
8
3
4
0
3
4
0
0
.
3
9 0
.
3
8
4
0
5
4
1
1
0
.
4
0 0
.
4
3
3
8
9
3
8
0
0
.
3
3 0
.
3
4
4
6
4
4
6
4
0
.
3
2 0
.
3
2
4
8
4
4
8
3
0
.
3
2 0
.
3
3
3
8
3
3
8
5
0
.
3
6 0
.
4
0
4
7
4
4
7
0
0
.
4
1 0
.
4
1
3
6
2
3
6
4
0
.
3
5 0
.
3
5
4
1
7
4
2
1
0
.
3
4 0
.
3
8
3
8
8
3
7
3
0
.
3
7 0
.
3
7
4
6
1
4
6
6
0
.
2
9 0
.
3
5
4
9
0
4
8
7
0
.
4
0 0
.
4
0
2
5
3
2
5
5
0
.
4
3 0
.
4
2
4
2
9
4
3
6
0
.
3
5 0
.
3
8
4
8
5
4
8
0
0
.
4
0 0
.
4
2
4
1
3
4
1
3
0
.
3
6 0
.
3
8
3
5
0
3
4
6
0
.
4
6 0
.
4
9
3
7
0
3
6
7
0
.
4
1 0
.
4
3
4
4
3
4
4
1
0
.
3
3 0
.
3
3
4
8
3
4
8
1
0
.
3
5 0
.
3
4
4
8
6
4
8
5
0
.
3
5 0
.
3
6
3
9
9
4
0
0
0
.
3
7 0
.
3
8
4
1
8
4
1
7
0
.
3
0 0
.
3
1
4
7
7
4
7
7
0
.
3
6 0
.
3
8
4
9
2
4
9
2
0
.
3
6 0
.
3
6
1
6
4
1
6
7
0
.
2
9 0
.
3
0
4
7
0
4
7
1
0
.
3
4 0
.
3
5
3
8
1
3
8
4
0
.
4
1 0
.
4
3
4
7
6
4
7
5
0
.
3
2 0
.
3
3
4
6
0
4
6
1
0
.
3
3 0
.
3
4
4
6
6
4
6
5
0
.
2
5 0
.
2
3
4
8
1
4
8
6
0
.
2
6 0
.
2
5
4
7
8
4
8
2
0
.
2
6 0
.
2
8
4
7
3
4
7
3
0
.
3
7 0
.
3
8
4
3
8
4
4
0
0
.
3
4 0
.
3
6
4
5
4
4
5
3
0
.
3
7 0
.
3
8
4
1
6
4
1
6
0
.
3
7 0
.
3
6
3
0
6
3
1
6
0
.
3
2 0
.
3
4
3
8
6
3
8
3
0
.
3
2 0
.
3
6
4
9
5
4
9
3
0
.
4
8 0
.
4
8
3
4
6
3
5
0
0
.
3
5 0
.
3
5
4
0
1
4
0
9
0
.
3
0 0
.
3
0
4
3
4
4
3
7
0
.
2
8 0
.
2
6
4
9
3
4
9
4
0
.
2
8 0
.
3
0
4
6
2
4
6
2
0
.
2
4 0
.
2
2
5
0
0
5
0
0
0
.
2
6 0
.
2
5
4
8
0
4
8
4
0
.
2
4 0
.
2
6
4
8
2
4
7
9
0
.
2
1 0
.
2
0
4
9
7
4
9
9
0
.
3
2 0
.
3
3
4
5
9
4
6
0
R
ankT
4
9
2
4
9
3
4
9
4
4
9
5
4
9
6
4
9
7
4
9
8
4
9
9
5
0
0
Un
i
v
e
r
s
i
t
y
Un
i
vN
a
c
lL
aP
l
a
t
a
Un
i
vE
s
t
ad
u
a
lP
a
u
l
i
s
t
a
N
ihonUn
i
v
An
k
a
r
aUn
i
v
P
u
s
anN
a
t
lUn
i
v
H
a
c
e
t
t
ep
eUn
i
v
Kon
k
u
kUn
i
v
F
edUn
i
vP
a
r
an
á
C
a
tho
l
i
cUn
i
vKo
r
e
a
Un
iono
fL
e
id
enR
an
k
in
g
un
i
v
e
r
s
i
t
i
e
s
A
v
e
r
a
g
eo
v
e
rth
e5
0
0v
a
l
u
e
s
SD
CV
Top1
0%
T
T
* R
ankT
*
0
.
3
9 0
.
4
0
4
9
2
0
.
3
9 0
.
4
1
4
9
0
0
.
3
9 0
.
3
9
4
9
3
0
.
3
8 0
.
3
8
4
9
4
0
.
3
7 0
.
3
8
4
9
6
0
.
3
6 0
.
3
6
4
9
7
0
.
3
6 0
.
3
5
4
9
8
0
.
3
6 0
.
3
3
5
0
0
0
.
3
5 0
.
3
5
4
9
9
A
v
e
r
ag
eh
ighimp
a
c
tg
ap
s
A
A
* R
ankA R
ankA
*
0
.
2
4 0
.
2
4
4
9
1
4
9
1
0
.
2
6 0
.
2
7
4
5
7
4
5
6
0
.
2
5 0
.
2
7
4
7
2
4
7
4
0
.
2
1 0
.
2
1
4
8
7
4
8
8
0
.
3
1 0
.
3
3
4
5
6
4
5
4
0
.
2
9 0
.
2
9
4
4
0
4
4
4
0
.
2
1 0
.
2
1
4
9
6
4
9
6
0
.
2
4 0
.
2
6
4
9
8
4
9
7
0
.
1
8 0
.
1
9
4
9
9
4
9
8
5
2
0
.
7
9
1
.
1
4
1
.
1
3
1
.
1
8
1
.
1
6
1
.
0
4
0
.
7
7
0
.
7
4
1
.
0
1
0
.
3
6
0
.
3
5
1
.
0
1
0
.
3
5
0
.
3
5
1
.
0
1
1
.
3
7
1
.
3
6
0
.
9
8
0
.
5
2
0
.
5
2
Numb
e
ra
r
t
i
c
l
e
s
1
4
0
2
.
4
1
2
5
8
5
.
9
1
2
1
1
4
.
8
6
2
0
3
4
.
9
2
2
1
8
1
.
5
2
2
7
4
5
.
6
0
1
2
3
8
.
6
7
9
2
0
.
7
0
1
2
2
3
.
5
4
‰
0
.
3
9
0
.
7
2
0
.
5
9
0
.
5
6
0
.
6
0
0
.
7
6
0
.
3
4
0
.
2
5
0
.
3
4
1
8
8
2
3
7
0
.
3
3
3
7
6
4
.
7
4
2
7
7
5
.
2
1
0
.
7
4
39
T
ab
l
eB
. Ch
a
r
a
c
t
e
r
i
s
t
i
c
so
fo
v
e
r
a
l
lc
i
t
a
t
iond
i
s
t
r
ibu
t
ion
sfo
rth
een
t
i
r
ed
a
t
a
s
e
to
fd
i
s
t
in
c
ta
r
t
i
c
l
e
s(
3
.
6m
i
l
l
ion
)
,
d
i
s
t
in
c
ta
r
t
i
c
l
e
sw
i
tha
tl
e
a
s
ton
eLRun
i
v
e
r
s
i
t
y(
2
.
4m
i
l
l
ion
)
,andth
ef
r
a
c
t
ion
a
lcoun
t
ingfo
rLRun
i
v
e
r
s
i
t
i
e
s(
1
.
9
m
i
l
l
ion
)
D
i
s
t
r
ibu
t
ion
s
F
i
r
s
tm
e
an S
e
cond m
e
an
µ1
µ2
P
e
r
c
en
t
ag
eo
fa
r
t
i
c
l
e
sinc
a
t
ego
r
y
:P
e
r
c
en
t
ag
eo
fc
i
t
a
t
ion
sinc
a
t
ego
r
y
:
1
2
3
1
2
3
3
.
6m
i
l
l
ion
8
.
7
2
4
.
0
7
2
.
0
2
0
.
2
7
.
8
2
2
.
6
3
2
.
2
4
5
.
2
2
.
4m
i
l
l
ion
9
.
8
2
6
.
5
7
1
.
5
2
0
.
8
7
.
7
2
3
.
0
3
2
.
9
4
4
.
1
1
.
9m
i
l
l
ion
9
.
8
2
5
.
0
7
0
.
9
2
0
.
7
8
.
4
2
6
.
3
3
1
.
6
4
2
.
1
D
i
s
t
r
ibu
t
ion
s
Robu
s
tco
e
f
f
i
c
i
en
t
o
fv
a
r
i
a
t
ion
GMind
ex
o
fsk
ewn
e
s
s
3
.
6m
i
l
l
ion
0
.
7
5
0
.
6
4
2
,
4m
i
l
l
ion
0
.
7
5
0
.
7
1
1
.
9m
i
l
l
ion
0
.
9
4
0
.
7
5
µ1 = m
e
anc
i
t
a
t
ion
µ2 = m
e
anc
i
t
a
t
iono
fa
r
t
i
c
l
e
sw
i
thc
i
t
a
t
ion
sabo
v
eµ1
C
a
t
ego
r
y1=a
r
t
i
c
l
e
sw
i
tha
lowc
i
t
a
t
ion
,b
e
lowµ1
C
a
t
ego
r
y2=a
r
t
i
c
l
e
sw
i
thaf
a
i
rn
umb
e
ro
fc
i
t
a
t
ion
s,abo
v
e
µ1andb
e
lowµ2
C
a
t
ego
r
y3=a
r
t
i
c
l
e
sw
i
thar
em
a
r
k
ab
l
eo
ro
u
t
s
t
and
in
gn
umb
e
ro
fc
i
t
a
t
ion
s,abo
v
e
µ2
40
T
ab
l
e1
.M
e
an numb
e
ro
fpub
l
i
c
a
t
ion
sp
e
rc
lu
s
t
e
r
,m,andm
e
an c
i
t
a
t
ionp
e
rpub
l
i
ca
t
ion
,µ,inth
ep
a
r
t
i
t
ionb
y
d
e
c
i
l
e
so
fth
eo
v
e
r
a
l
lc
i
t
a
t
iond
i
s
t
r
ibu
t
ion
m
µ
D
e
c
i
l
e
s
1
2
,
4
7
2
.
7
1
0
.
5
2
1
,
4
3
5
.
3
9
.
4
3
1
,
0
1
5
.
9
8
.
0
4
7
3
7
.
3
7
.
4
5
5
4
2
.
1
6
.
9
6
3
7
7
.
4
5
.
8
7
2
5
0
.
8
5
.
1
8
1
5
1
.
3
4
.
5
9
7
0
.
5
3
.
7
1
0
6
.
0
1
.
2
A.Numb
e
ro
fc
lu
s
t
e
r
s
5
,
1
1
9
a
B
.Numb
e
ro
fsm
a
l
lc
lu
s
t
e
r
s
8
5
8
b
C
.Numb
e
ro
fs
ign
i
f
i
c
an
tc
lu
s
t
e
r
s
4
,
1
6
1
D
. %o
fa
r
t
i
c
l
e
sinsm
a
l
lc
lu
s
t
e
r
s
0
.
8
9%
a
S
m
a
l
lc
lu
s
t
e
r
sh
a
vel
e
s
sth
ano
requ
a
lto1
0
0pub
l
i
c
a
t
ion
s
b
S
ign
i
f
i
c
an
tc
lu
s
t
e
r
sh
a
v
e mo
r
eth
an1
0
0pub
l
i
c
a
t
ion
s
-
41
T
ab
l
e2. Th
ee
f
f
e
c
tono
v
e
r
a
l
lc
i
t
a
t
ionin
equ
a
l
i
t
y
,I
(
C
’)
,o
fth
ed
i
f
f
e
r
en
c
esinc
i
t
a
t
ionimp
a
c
tb
e
tw
e
enc
lu
s
t
e
r
s
b
e
fo
r
eanda
f
t
e
rs
t
and
a
rdf
i
e
ld
no
rm
a
l
i
z
a
t
ion,andth
eimp
a
c
to
fno
rm
a
l
i
z
a
t
iononth
i
se
f
f
e
c
t
No
rm
a
l
i
z
a
t
ionimp
a
c
t=
1
0
0[
ID
CC –IDC
C*/
IDC
C]
B
e
fo
r
eno
rm
a
l
i
z
a
t
ion,1
0
0[
ID
CC/I
(
C
’)
]
2
2
.
5%
-
A
f
t
e
rno
rm
a
l
i
z
a
t
ion,1
0
0[
IDCC*
/I
(
C
’)
]
4
.
3%
8
4
.
3%
R
e
su
l
t
sf
romC
r
e
spoe
ta
l
.(
2
0
1
4
)fo
r2
1
9sub
f
i
e
ld
s
B
e
fo
r
eno
rm
a
l
i
z
a
t
ion,1
0
0[
ID
CC/I
(
C
’)
]
1
8
.
1%
A
f
t
e
rno
rm
a
l
i
z
a
t
ion,1
0
0[
IDCC*
/I
(
C
’)
]
3
.
3%
8
7
.
3%
R
e
su
lt
sf
romL
ie
ta
l
.(
2
0
1
3
)fo
r1
7
2sub
f
i
e
ld
s
B
e
fo
r
eno
rm
a
l
i
z
a
t
ion,1
0
0[
ID
CC/I
(
C
’)
]
A
v
e
r
ag
eo
v
e
rs
ixon
ey
e
a
rd
a
t
a
s
e
t
s(S
td
.d
e
v
.
)
1
3
.
1%(0
.
9
)
A
f
t
e
rno
rm
a
l
i
z
a
t
ion,1
0
0[
IDCC*
/I
(
C
’)
]
A
v
e
r
ag
eo
v
e
rs
ixon
ey
e
a
rd
a
t
a
s
e
t
s(S
td
.d
e
v
.
)
2
.
9 %(
0
.
4
)
42
7
9
.
4% (
4
.
3
)
0
,
4
0
,
3
5
0
,
3
0
,
2
5
0
,
2
0
,
1
5
0
,
1
0
,
0
5
0
2
5
3
0
3
5
4
0
4
5
5
0
5
5
6
0
ip
ir
aw
6
5
7
0
7
5
8
0
8
5
9
0
9
5
1
0
0
ip
ino
rm
F
igu
r
e1
.O
v
e
r
a
l
lc
i
t
a
t
ionin
equ
a
l
i
t
ydu
etod
i
f
f
e
r
en
c
e
sinc
i
t
a
t
ionpr
a
c
t
i
c
e
s
,I
(
π)
,a
safun
c
t
iono
fπ.R
e
su
l
t
s
fo
rth
e[
2
5
,1
0
0
]p
e
r
c
en
t
i
l
ein
t
e
r
v
a
l
43
T
ab
l
e3.
A
.Emp
t
yc
lu
s
t
e
r
sinth
es
e
t
so
fh
ighimp
a
c
ta
r
t
i
c
l
e
sBandY,andp
e
r
c
en
t
ag
eo
fa
r
t
i
c
l
e
sinth
e
in
t
e
r
s
e
c
t
ion
sB∩X,andY∩X
S
e
t
so
fh
ighimp
a
c
t
a
r
t
i
c
l
e
s
Numb
e
ro
f
emp
t
yc
lu
s
t
e
r
s
%o
fa
r
t
i
c
le
sinX
inth
eemp
t
yc
lu
s
t
e
r
s
%o
fa
r
t
i
c
l
e
sinth
e
in
t
e
r
s
e
c
t
ionw
i
thX
B
1
,
0
7
8
2
.
6
7
6
5
.
8
Y
3
0
8
0
.
0
3
9
4
.
8
T
ab
l
e3
.b
.Emp
t
yc
lu
s
t
e
r
sinth
es
e
t
so
fh
ighimp
a
c
ta
r
t
i
c
l
e
sB
’andY
’,andp
e
r
c
en
t
ag
eo
fa
r
t
i
c
l
e
sinth
e
in
t
e
r
s
e
c
t
ion
sB
’∩X
’ andY
’,
’∩X
’
S
e
t
so
fh
ighimp
a
c
t
a
r
t
i
c
l
e
s
Numb
e
ro
f
emp
t
yc
lu
s
t
e
r
s
%o
fa
r
t
i
c
l
e
sin X
inth
eemp
t
yc
lu
s
t
e
r
s
%o
fa
r
t
i
c
l
e
sinth
e
in
t
e
r
s
e
c
t
ionw
i
thX
B
’
1
1
7
1
.
3
7
6
6
.
6
Y
’
3
0
8
0
.
0
0
9
4
.
9
-
44
2
2
0
0
2
0
0
0
Numb
e
ro
fc
lu
s
t
e
r
s
1
8
0
0
1
6
0
0
1
4
0
0
1
2
0
0
1
0
0
0
8
0
0
6
0
0
4
0
0
2
0
0
0
<
2
2
3
4
5
6
7
8
9
1
0 1
1 1
2 1
3 1
4 1
5
%
F
igu
r
e2
.A
.H
igh
imp
a
c
ta
r
t
i
c
l
e
sinth
eo
v
e
r
a
l
lun
-no
rm
a
l
i
z
edc
i
t
a
t
iond
i
s
t
r
ibu
t
ionC. H
i
s
tog
r
amo
fth
e
d
i
s
t
r
ibu
t
iono
v
e
r5
,
1
1
9c
lu
s
t
e
r
so
fth
ep
e
r
c
en
t
ag
eth
a
tth
e
s
ea
r
t
i
c
l
e
sr
ep
r
e
s
en
tine
a
chc
lu
s
t
e
r
7
0
0
Numb
e
ro
fc
lu
s
t
e
r
s
6
0
0
5
0
0
4
0
0
3
0
0
2
0
0
1
0
0
0
>
6 6
.
0 6
.
5 7
.
0 7
.
5 8
.
0 8
.
5 9
.
0 9
.
51
0
.
01
0
.
51
1
.
01
1
.
51
2
.
01
2
.
51
3
.
01
3
.
51
4
.
01
4
.
51
5
.
0
%
i
s
tog
r
amo
fth
e
F
igu
r
e2
.B
.H
igh
imp
a
c
ta
r
t
i
c
l
e
sinth
eo
v
e
r
a
l
lno
rm
a
l
i
z
edc
it
a
t
iond
i
s
t
r
ibu
t
ionC*. H
d
i
s
t
r
ibu
t
iono
v
e
r5
,
1
1
9c
lu
s
t
e
r
so
fth
ep
e
r
c
en
t
ag
eth
a
tth
e
s
ea
r
t
i
c
l
e
sr
ep
r
e
s
en
tine
a
chc
lu
s
t
e
r
45
6
0
0
Numb
e
ro
fc
lu
s
t
e
r
s
5
0
0
4
0
0
3
0
0
2
0
0
1
0
0
0
>
6 6
.
0 6
.
5 7
.
0 7
.
5 8
.
0 8
.
5 9
.
0 9
.
51
0
.
01
0
.
51
1
.
01
1
.
51
2
.
01
2
.
51
3
.
01
3
.
51
4
.
01
4
.
51
5
.
0
%
*
. H
i
s
tog
r
am o
fth
e
F
igu
r
e2
.C
. H
igh
imp
a
c
ta
r
t
i
c
l
e
sinth
eo
v
e
r
a
l
l no
rm
a
l
i
z
ed c
i
t
a
t
ion d
i
s
t
r
ibu
t
ion C'
d
i
s
t
r
ibu
t
iono
v
e
r3
,
3
3
2c
lu
s
t
e
r
sw
i
th mor
eth
an2
5
0pub
l
i
c
a
t
ion
so
fth
ep
e
r
c
en
t
a
g
eth
a
tth
e
s
ea
r
t
i
c
l
e
sr
ep
r
e
s
en
tin
e
a
chc
lu
s
t
e
r
46
T
ab
l
e4
.A
.Un
i
v
e
r
s
i
t
yre
r
ank
inga
c
co
rd
ingtoth
eTop1
0%ind
i
c
a
to
rT
a
F
romth
e WoSc
l
a
s
s
.s
y
s
t
emtog
r
anu
l
a
r
i
t
yl
e
v
e
l8
F
i
r
s
t1
0
0
un
i
v
e
r
s
i
t
i
e
s
>5
0po
s
i
t
ion
s
2
6–5
0
1
6–2
5
6–1
5
≤ 5po
s
i
t
ion
s
Noch
ang
eb
To
t
a
l
0
7
1
3
3
6
4
4
1
0
0
N
ex
t4
0
0
un
i
v
e
r
s
i
t
i
e
s
8
1
1
0
7
7
4
8
1
5
7
4
0
0
To
t
a
l
8
1
1
1
4
8
7
1
1
7
1
0
1
5
0
0
F
romTitoT*i
F
i
r
s
t1
0
0
R
em
a
in
ing4
0
0
un
i
v
e
r
s
i
t
i
e
s
un
i
v
e
r
s
i
t
i
e
s
0
1
4
3
5
5
2
8
1
0
0
1
1
5
8
6
5
1
4
0
1
0
8
1
8
4
0
0
To
t
a
l
1
1
5
9
6
9
1
7
5
1
6
0
2
6
5
0
0
T
ab
l
e4
.B
.Un
i
v
e
r
s
i
t
yd
i
f
f
e
r
en
c
e
sinTiv
a
lu
e
s
F
romTitoT*i
c
F
romth
e WoSc
l
a
s
s
.s
y
s
t
emtog
r
anu
l
a
r
i
t
yl
e
v
e
l8
N
ex
t4
0
0
F
i
r
s
t1
0
0un
i
v
e
rs
i
t
i
e
s
un
i
v
e
r
s
i
t
i
e
s
>0
.
2
0
>0
.
1
0and≤0
.
2
>0
.
0
5and≤0
.
1
≤0
.
0
5
To
t
a
l
1
1
2
2
7
6
0
1
0
0
1
6
6
6
1
2
4
9
4
4
0
0
To
t
a
l
F
i
r
s
t1
0
0
un
i
v
e
r
s
i
t
i
e
s
1
7
7
8
1
5
1
2
5
4
5
0
0
0
3
2
6
7
1
1
0
0
aT
ab
l
e6
.A
inRu
i
zC
a
s
t
i
l
lo& W
a
l
tm
an(
2
0
1
5
)
bN
o
ta
v
a
i
l
ab
l
e
cT
ab
l
e6
.B
inRu
i
zC
a
s
t
i
l
lo& W
a
l
tm
an(
2
0
1
5
)
47
N
ex
t4
0
0
un
i
v
e
r
s
i
t
i
e
s
0
8
4
9
3
4
3
4
0
0
To
t
a
l
0
1
1
7
5
4
1
4
5
0
0
T
ab
l
e5
.A
.Un
i
v
e
r
s
i
t
yr
e
r
ank
ing
sa
c
co
rd
ingtoth
eAv
e
r
ag
eo
fh
igh
imp
a
c
tg
ap
sin
d
i
c
a
to
rA
>5
0po
s
i
t
ion
s
2
6–5
0
1
6–2
5
6–1
5
≤ 5po
s
i
t
ion
s
Noch
ang
e
To
t
a
l
F
i
r
s
t1
0
0
un
i
v
e
r
s
i
t
i
e
s
R
em
a
in
ing4
0
0
un
i
v
e
r
s
i
t
i
e
s
To
t
a
l
0
0
1
2
1
7
0
8
1
0
0
1
6
1
2
1
2
6
2
2
0
3
5
4
0
0
1
6
1
3
1
4
7
2
9
0
4
3
5
0
0
F
i
r
s
t1
0
0
un
i
v
e
r
s
i
t
i
e
s
R
em
a
in
ing4
0
0
un
i
v
e
r
s
i
t
i
e
s
To
t
a
l
5
5
7
3
1
7
1
0
0
3
3
8
1
5
7
2
0
2
4
0
0
8
9
5
1
8
8
2
0
9
5
0
0
T
ab
l
e5
.B
.Un
i
v
e
r
s
i
t
yd
i
f
fe
r
en
c
e
sinAiv
a
lu
e
s
>0
.
2
0
>0
.
1
0and≤0
.
2
>0
.
0
5and≤0
.
1
≤0
.
0
5
To
t
a
l
48