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nt
s
.
Li
[13]
c
a
l
c
ul
a
t
e
d
52
i
n
va
ri
a
nt
m
om
e
nt
s
,
a
nd
s
e
ve
n
pop
ul
a
r
i
nva
r
i
a
nt
m
om
e
nt
s
a
re
a
ppro
a
c
h
e
d
.
In
t
h
i
s
pa
p
e
r
,
a
nov
e
l
m
e
t
hod
for
f
a
c
e
re
c
ogni
t
i
on
i
s
propos
e
d,
us
i
ng
w
a
ve
l
e
t
s
a
t
e
a
c
h
s
c
a
l
e
ba
s
e
d
on
c
urv
e
l
e
t
t
r
a
ns
for
m
a
nd
i
m
prov
e
d
S
uppor
t
v
e
c
t
or
m
a
c
h
i
ne
(S
V
M
)
c
l
a
s
s
i
f
i
e
r
.
S
e
c
t
i
on
2
of
t
hi
s
p
a
pe
r
e
xp
l
a
i
ns
t
h
e
de
s
i
gn
of
t
h
e
fa
c
e
re
c
ogni
t
i
on
s
ys
t
e
m
,
i
n
vol
v
i
ng
c
urve
l
e
t
a
n
d
Inva
r
i
a
n
t
M
om
e
nt
s
m
e
t
hod
a
nd
t
h
e
pr
i
nc
i
pl
e
of
S
V
M
a
s
a
c
l
a
s
s
i
fi
c
a
t
i
on
m
e
t
hod
.
S
e
c
t
i
on
3
pr
e
s
e
n
t
s
t
he
e
xpe
ri
m
e
n
t
a
l
re
s
u
l
t
s
t
h
a
t
e
va
l
u
a
t
e
t
h
e
a
do
pt
e
d
t
e
c
hn
i
q
ue
s
pe
rf
orm
a
nc
e
.
Con
c
l
us
i
ons
a
r
e
re
v
i
e
w
e
d
i
n
S
e
c
t
i
on
4.
2.
P
R
O
P
O
S
ED
S
Y
S
TEM
D
ES
I
G
N
T
he
prop
os
e
d
s
ys
t
e
m
i
s
b
a
s
e
d
on
de
c
om
pos
i
t
i
on
of
f
a
c
e
i
m
a
ge
us
i
ng
c
ur
ve
l
e
t
t
ra
ns
f
orm
,
a
nd
t
h
e
n
re
duc
i
ng
t
h
e
di
m
e
ns
i
on
of
c
ur
ve
l
e
t
c
oe
ffi
c
i
e
nt
s
t
o
f
e
e
d
t
he
i
nva
ri
a
n
t
m
o
m
e
n
t
a
l
g
ori
t
hm
fo
r
i
nv
a
ri
a
nt
f
e
a
t
ure
s
e
xt
r
a
c
t
i
on
.
T
h
e
fe
a
t
ure
s
e
t
s
produ
c
e
d
by
c
urv
e
l
e
t
t
ra
n
s
form
a
nd
i
nva
ri
a
nt
m
o
m
e
n
t
a
re
us
e
d
t
o
t
ra
i
n
a
nd
t
e
s
t
t
he
S
V
M
c
l
a
s
s
i
fi
e
r.
T
he
fl
ow
c
h
a
r
t
of
t
he
propos
e
d
a
l
gori
t
h
m
i
s
s
how
n
i
n
F
i
gur
e
1.
F
i
gure
1
.
B
l
oc
k
d
i
a
gra
m
o
f
p
r
opos
e
d
s
ys
t
e
m
3.
C
U
R
V
ELET
TR
A
N
S
F
O
R
M
T
he
c
urve
l
e
t
t
r
a
ns
for
m
r
e
pr
e
s
e
n
t
s
on
e
of
t
h
e
m
u
l
t
i
s
c
a
l
e
g
e
om
e
t
r
i
c
t
ra
ns
for
m
fa
m
i
l
y
,
w
h
i
c
h
w
a
s
de
ve
l
op
e
d
t
o
ge
t
r
i
d
of
t
ra
di
t
i
on
a
l
m
u
l
t
i
s
c
a
l
e
r
e
pre
s
e
nt
a
t
i
ons
m
e
t
hods
s
u
c
h
a
s
w
a
v
e
l
e
t
s
[
14,
15]
.
T
h
e
c
urv
e
l
e
t
t
ra
n
s
for
m
s
o
l
ve
d
t
he
prob
l
e
m
of
i
s
o
t
ropi
c
s
c
a
l
i
ng
of
w
a
v
e
l
e
t
,
w
h
i
c
h
m
a
k
e
s
i
t
f
i
t
for
f
a
c
e
fe
a
t
ur
e
s
e
xt
r
a
c
t
i
on
.
T
he
r
e
a
r
e
t
w
o
d
i
ff
e
re
n
t
i
m
pl
e
m
e
nt
a
t
i
on
m
e
t
ho
ds
of
c
urve
l
e
t
t
ra
ns
for
m
:
-
Curv
e
l
e
t
vi
a
une
qua
l
l
y
s
pa
c
e
d
f
a
s
t
F
ouri
e
r
t
r
a
ns
form
(U
S
F
F
T
).
-
Curv
e
l
e
t
vi
a
w
ra
pp
i
ng
of
s
pe
c
i
a
l
l
y
s
e
l
e
c
t
e
d
F
ouri
e
r
s
a
m
pl
e
s
.
B
ot
h
a
re
s
h
a
re
d
t
h
e
s
a
m
e
p
rope
rt
i
e
s
of
s
i
m
pl
i
c
i
t
y
,
f
a
s
t
a
nd
l
e
s
s
re
d
unda
nt
;
c
o
m
p
a
re
w
i
t
h
t
he
i
r
e
a
r
l
i
e
r
ge
ne
r
a
t
i
on
ve
rs
i
ons
.
T
he
fi
rs
t
m
e
t
hod
h
a
s
b
e
e
n
t
a
k
e
n
i
n
t
h
i
s
pa
pe
r
,
w
hi
c
h
i
s
d
e
s
c
r
i
be
d
a
s
fo
l
l
ow
s
.
-
A
ppl
y
t
he
2D
F
F
T
a
nd
ob
t
a
i
n
F
our
i
e
r
s
a
m
p
l
e
s
̂
[
1
,
2
]
,
−
2
≤
1
,
2
<
2
.
-
F
or
e
a
c
h
s
c
a
l
e
/
a
ngl
e
pa
i
r
(
,
)
,
re
s
a
m
pl
e
(or
i
n
t
e
r
pol
a
t
e
)
̂
[
1
,
2
]
t
o
ob
t
a
i
n
s
a
m
pl
e
d
v
a
l
u
e
s
̂
[
1
,
2
−
1
t
a
n
]
for
(
1
,
2
)
∈
.
-
M
ul
t
i
p
l
y
t
h
e
i
nt
e
rpo
l
a
t
e
d
(o
r
s
h
a
re
d)
o
bj
e
c
t
̂
w
i
t
h
t
he
p
a
ra
bol
i
c
w
i
ndow
Ũ
,
e
ff
e
c
t
i
v
e
l
y
l
oc
a
l
i
z
i
ng
̂
n
e
a
r
t
he
pa
r
a
l
l
e
l
ogr
a
m
w
i
t
h
ori
e
nt
a
t
i
on
,
a
nd
obt
a
i
n
:
̂
,
[
1
,
2
]
=
̂
[
1
,
2
−
1
t
a
n
]
∗
Ũ
[
1
,
2
]
-
A
ppl
y
t
he
i
n
ve
rs
e
2D
F
F
T
t
o
e
a
c
h
̂
,
,
he
nc
e
c
ol
l
e
c
t
i
ng
t
h
e
d
i
s
c
re
t
e
c
o
e
ff
i
c
i
e
n
t
s
(
,
,
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
K
O
M
N
IK
A
T
e
l
e
c
o
m
m
u
n
Co
m
pu
t
E
l
Co
nt
ro
l
F
ac
e
r
e
c
og
ni
t
i
on
bas
e
d
o
n
c
ur
v
e
l
e
t
s
,
i
nv
ar
i
ant
m
om
e
n
t
s
f
e
a
t
ur
e
s
and
S
V
M
(
Moham
m
e
d
G
haz
al
)
735
4.
M
O
M
EN
T
I
N
V
A
R
I
A
N
TS
M
om
e
n
t
i
n
va
r
i
a
n
t
s
a
r
e
i
n
va
r
i
a
n
t
und
e
r
s
c
a
l
i
ng
,
s
hi
f
t
i
ng
a
nd
r
ot
a
t
i
on
.
T
he
y
a
re
w
i
d
e
l
y
us
e
d
i
n
pa
t
t
e
rn
re
c
og
ni
t
i
on
[1
6,
17
]
.
T
he
d
e
ri
va
t
i
on
d
e
t
a
i
l
s
of
m
o
m
e
nt
i
nva
ri
a
n
t
s
t
ha
t
ha
ve
b
e
e
n
us
e
d
i
n
f
a
c
e
fe
a
t
ur
e
s
e
xt
r
a
c
t
i
on
a
re
di
s
c
us
s
e
d
by
H
u
(
1962)
.
S
o
t
ha
t
,
t
h
e
g
e
n
e
ra
l
l
i
ne
a
r
t
r
a
ns
for
m
a
t
i
o
n
i
s
pr
e
s
e
n
t
e
d
b
e
l
ow
:
ω
1
=
λ
20
+
λ
02
,
(
1)
ω
2
=
(
λ
20
−
λ
02
)
2
+
4
λ
11
2
(2)
ω
3
=
(
λ
30
−
3
λ
12
)
2
+
(
3
λ
21
−
λ
03
)
2
(3)
ω
4
=
(
λ
30
+
λ
12
)
2
+
(
λ
21
+
λ
03
)
2
(4)
ω
5
=(
λ
30
−
3
λ
12
)
(
λ
30
+
λ
12
)
[(
λ
30
+
λ
12
)
2
−
3(
λ
21
+
λ
03
)
2
]
+
(3
λ
21
−
λ
03
)
(
λ
21
+
λ
0
3
)
[3
(
λ
30
+
λ
12
)
2
−
(
λ
21
+
λ
03
)
2
]
(5)
ω
6
=(
λ
20
−
λ
02
)
[(
λ
30
+
λ
12
)
2
−
(
λ
21
+
λ
03
)
2
]
+4
λ
11
(
λ
30
+
λ
12
)
(
λ
21
+
λ
03
)
(6)
ω
7
=
(3
λ
21
−
λ
03
)
(
λ
30
+
λ
12
)
[(
λ
30
+
λ
12
)
2
−
3
(
λ
21
+
λ
03
)
2
]
+
(3
λ
12
−
λ
30
)
(
λ
21
+
λ
0
3
)
[3
(
λ
30
+
λ
12
)
2
−
(
λ
21
+
λ
03
)
2
]
.
(7)
T
he
a
b
ove
for
m
u
l
a
s
a
r
e
us
e
d
t
o
c
a
l
c
ul
a
t
e
t
he
fe
a
t
ure
s
of
f
a
c
e
i
m
a
ge
s
.
F
i
gure
2
s
how
s
a
n
e
x
a
m
p
l
e
of
t
h
e
e
xt
r
a
c
t
e
d
f
e
a
t
ure
s
by
Curv
e
l
e
t
a
n
d
m
o
m
e
n
t
i
nv
a
ri
a
nt
s
.
F
i
gure
2
.
In
t
e
rfa
c
e
of
fe
a
t
u
re
s
e
xt
ra
c
t
i
on
5.
C
LA
S
S
I
F
I
C
A
TI
O
N
In
t
h
i
s
p
a
p
e
r
,
s
uppo
rt
ve
c
t
or
m
a
c
hi
n
e
(S
V
M
)
w
a
s
us
e
d
fo
r
c
l
a
s
s
i
f
i
c
a
t
i
on
of
f
a
c
e
i
m
a
g
e
s
[
1
8,
19]
.
M
a
ny
k
e
rn
e
l
func
t
i
o
ns
a
n
d
di
ffe
r
e
nt
pa
ra
m
e
t
e
rs
ha
v
e
be
e
n
c
o
ns
i
de
re
d
t
o
e
nh
a
n
c
e
t
he
p
e
rfor
m
a
n
c
e
of
t
h
e
c
l
a
s
s
i
fi
e
r
.
T
he
d
a
t
a
c
a
n
be
s
e
p
a
ra
t
e
d
by
s
e
v
e
ra
l
l
i
n
e
a
r
c
l
a
s
s
i
fi
e
rs
,
b
ut
t
h
e
re
i
s
onl
y
on
e
c
l
a
s
s
i
fi
e
r
t
h
a
t
c
a
n
m
a
x
i
m
i
z
e
t
h
e
d
i
s
t
a
n
c
e
be
t
w
e
e
n
i
t
a
n
d
t
h
e
ne
a
r
e
s
t
d
a
t
a
poi
n
t
of
e
a
c
h
c
l
a
s
s
.
T
hi
s
l
i
ne
a
r
c
l
a
s
s
i
fi
e
r
i
s
n
a
m
e
d
b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
1693
-
693
0
T
E
L
K
O
M
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IK
A
T
e
l
e
c
o
m
m
u
n
Co
m
pu
t
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l
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l
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V
ol
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18
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o.
2
,
A
pri
l
2
020:
73
3
-
73
9
736
opt
i
m
a
l
s
e
p
a
ra
t
i
n
g
hyp
e
r
p
l
a
n
e
[20
]
.
S
o
i
t
i
s
ne
e
d
ed
t
o
fi
nd
ω
,
w
hi
c
h
re
pre
s
e
nt
s
t
he
c
oe
ffi
c
i
e
nt
of
t
he
hyp
e
rp
l
a
n
e
.
T
h
e
s
u
pport
v
e
c
t
or
m
a
c
hi
n
e
S
V
M
i
s
a
s
up
e
rvi
s
e
d
l
e
a
rn
i
ng
m
ode
l
i
n
t
he
f
i
e
l
d
of
m
a
c
h
i
n
e
l
e
a
rni
n
g.
It
i
s
g
e
n
e
ra
l
l
y
us
e
d
for
pa
t
t
e
rn
re
c
ogn
i
t
i
on,
c
l
a
s
s
i
fi
c
a
t
i
on
a
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s
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i
on
a
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a
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s
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h
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V
M
de
p
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nd
s
on
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t
ru
c
t
u
ra
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k
m
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a
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on
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he
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for
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ons
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t
h
e
opt
i
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h
ype
r
pl
a
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s
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g
m
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t
a
t
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t
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fe
a
t
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pa
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m
a
k
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e
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rni
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t
or
ge
t
t
he
gl
oba
l
o
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i
m
i
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a
t
i
o
n.
P
r
obl
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de
s
c
ri
p
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:
A
s
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m
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t
h
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ra
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ni
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a
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(
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2
[21]
.
6.
EX
P
ER
I
M
EN
TA
L
R
ES
U
L
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S
T
o
c
l
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fy
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ff
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y
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propos
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hod
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w
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ff
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nt
da
t
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b
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ha
v
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us
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a
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va
l
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rs
t
da
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a
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d
Y
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l
e
[22]
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o
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da
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ba
s
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c
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ra
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l
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Re
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a
b
(O
R
L
)
[23]
.
T
a
bl
e
1
s
u
m
m
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ri
z
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t
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prop
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rt
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s
[
2
4]
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T
a
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1.
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us
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To
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a
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p
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m
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g
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Y
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l
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15
11
165
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RL
40
10
400
M
os
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gh
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Re
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[25
]
a
re
Evaluation Warning : The document was created with Spire.PDF for Python.
T
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(O
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No
T
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b
l
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4.
Th
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t
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of
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pe
rf
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D
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N
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20
96%
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A
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M
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of
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3
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q
.
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c
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t
s
ha
r
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f
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r
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ut
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c
a
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on
i
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ha
ndw
r
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t
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n
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al
R
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,
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2
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S
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e
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al
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,
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ul
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