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3
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57,
1
1
8
b
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test
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s
&
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ac
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1
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2252
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8792
IJ
A
P
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Vo
l.
7
,
No
.
2
,
A
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1
8
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–
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100
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2.
VO
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AB
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2
.
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n
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en
t
in
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y
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te
m
s
Mo
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an
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is
m
eth
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[
2
5
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h
as
b
ee
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s
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.
T
h
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s
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tate
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lo
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.
[
]
[
]
*
+
(
1
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W
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j
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Ma
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S
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m
v
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s
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p
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Q
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Ass
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t
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(
1
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th
en
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[
]
(
2
)
(
3
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W
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(
)
(
4
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M
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f
ied
.
(
5
)
W
h
er
e,
=
r
ig
h
t e
ig
e
n
v
ec
to
r
m
atr
ix
o
f
J
R
=
lef
t e
ig
e
n
v
ec
to
r
m
atr
i
x
o
f
J
R
∧
=
d
iag
o
n
al
ei
g
en
v
al
u
e
m
atr
ix
o
f
J
R
an
d
(
6
)
Fro
m
th
e
eq
u
a
tio
n
s
(
5
)
an
d
(
8
)
,
w
e
ca
n
w
r
ite,
(
7
)
O
r
∑
(
8
)
W
h
er
e
i
is
th
e
i
t
h
co
lu
m
n
r
ig
h
t e
ig
e
n
v
ec
to
r
an
d
t
h
e
ith
r
o
w
le
f
t
ei
g
en
v
ec
to
r
o
f
J
R
.
i
is
th
e
i
th
E
i
g
e
n
v
al
u
e
o
f
J
R
.
T
h
e
ith
m
o
d
al
r
ea
ctiv
e
p
o
w
er
v
ar
iatio
n
i
s
g
i
v
e
n
b
y
,
(
9
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
Melea
g
r
is
Ga
llo
p
a
vo
A
lg
o
r
ith
m
fo
r
S
o
lvin
g
Op
tima
l R
ea
ctiv
e
P
o
w
er P
r
o
b
lem
(
K
.
Len
in
)
101
w
h
er
e,
∑
(
1
0
)
W
h
er
e
j
i is th
e
j
th
ele
m
e
n
t o
f
i
T
h
e
co
r
r
esp
o
n
d
in
g
it
h
m
o
d
al
v
o
ltag
e
v
ar
iatio
n
i
s
m
a
th
e
m
ati
ca
ll
y
g
iv
e
n
b
y
,
[
⁄
]
(
1
1
)
W
h
en
|
i
|
=
0
t
h
en
t
h
e
it
h
m
o
d
al
v
o
ltag
e
w
i
ll
g
et
co
llap
s
e
d
.
I
n
E
q
u
atio
n
(
8
)
,
ass
u
m
e
ΔQ
=
e
k
w
h
er
e
e
k
h
a
s
all
its
ele
m
e
n
ts
ze
r
o
ex
ce
p
t th
e
k
t
h
o
n
e
b
ein
g
1
.
T
h
en
,
∑
(
1
2
)
k
th
ele
m
e
n
t o
f
V
–
Q
s
en
s
iti
v
it
y
at
b
u
s
k
is
g
iv
en
b
y
,
∑
∑
(
1
3
)
3.
P
RO
B
L
E
M
F
O
R
M
UL
AT
I
O
N
T
h
e
k
ey
o
b
j
ec
tiv
es
o
f
th
e
r
ea
ctiv
e
p
o
w
er
d
is
p
atch
p
r
o
b
lem
i
s
to
m
i
n
i
m
ize
th
e
s
y
s
te
m
r
ea
l
p
o
w
er
lo
s
s
an
d
also
to
m
ax
i
m
ize
th
e
s
tati
c
v
o
ltag
e
s
tab
ilit
y
m
ar
g
in
(
S
V
SM)
.
3
.
1
.
M
ini
m
iza
t
io
n o
f
re
a
l po
w
er
lo
s
s
R
ea
l p
o
w
er
lo
s
s
(
P
lo
s
s
)
Min
i
m
izatio
n
in
tr
a
n
s
m
i
s
s
io
n
l
in
e
s
is
m
at
h
e
m
atica
ll
y
g
iv
e
n
as,
∑
(
1
4
)
W
h
er
e
n
i
s
t
h
e
n
u
m
b
er
o
f
tr
an
s
m
i
s
s
io
n
li
n
es,
g
k
is
t
h
e
c
o
n
d
u
ctan
ce
o
f
b
r
a
n
ch
k
,
V
i
an
d
Vj
ar
e
v
o
ltag
e
m
a
g
n
i
tu
d
e
at
b
u
s
i a
n
d
b
u
s
j
,
an
d
ij
is
th
e
v
o
lta
g
e
an
g
le
d
if
f
er
en
ce
b
et
w
ee
n
b
u
s
i a
n
d
b
u
s
j
.
3
.
2
.
M
ini
m
iza
t
io
n o
f
v
o
lt
a
g
e
dev
ia
t
io
n
A
t lo
ad
b
u
s
e
s
m
in
i
m
izat
io
n
o
f
th
e
v
o
lta
g
e
d
ev
iatio
n
m
a
g
n
it
u
d
es (
VD)
is
s
tated
as f
o
llo
w
s
,
Min
i
m
ize
VD
=
∑
|
|
(
1
5
)
W
h
er
e
n
l is t
h
e
n
u
m
b
er
o
f
lo
a
d
b
u
s
s
es a
n
d
Vk
is
t
h
e
v
o
ltag
e
m
ag
n
it
u
d
e
at
b
u
s
k
.
3
.
3
.
Sy
s
t
em
co
n
s
t
ra
ints
T
h
ese
ar
e
th
e
f
o
llo
w
in
g
co
n
s
tr
ain
t
s
s
u
b
j
ec
ted
to
o
b
j
ec
tiv
e
f
u
n
ctio
n
as
g
i
v
e
n
b
elo
w
,
L
o
ad
f
lo
w
eq
u
alit
y
co
n
s
tr
ai
n
ts
:
–
∑
[
]
(
1
6
)
∑
[
]
(
1
7
)
W
h
er
e,
n
b
is
th
e
n
u
m
b
er
o
f
b
u
s
e
s
,
P
G
an
d
QG
ar
e
th
e
r
ea
l
an
d
r
ea
ctiv
e
p
o
w
er
o
f
t
h
e
g
e
n
er
ato
r
,
P
D
an
d
QD
ar
e
th
e
r
ea
l
an
d
r
ea
ctiv
e
lo
ad
o
f
th
e
g
en
er
ato
r
,
an
d
Gij
an
d
B
ij
ar
e
th
e
m
u
tu
al
co
n
d
u
ctan
ce
an
d
s
u
s
ce
p
tan
ce
b
et
w
ee
n
b
u
s
i a
n
d
b
u
s
j
.
Gen
er
ato
r
b
u
s
v
o
lta
g
e
(
V
Gi
)
in
eq
u
alit
y
co
n
s
tr
ai
n
t:
(
1
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
E
Vo
l.
7
,
No
.
2
,
A
u
g
u
s
t
2
0
1
8
:
9
9
–
1
1
0
102
L
o
ad
b
u
s
v
o
lta
g
e
(
V
Li
)
in
eq
u
a
lit
y
co
n
s
tr
ain
t:
(
1
9
)
S
w
itc
h
ab
le
r
ea
ctiv
e
p
o
w
er
co
m
p
e
n
s
atio
n
s
(
Q
Ci
)
in
eq
u
a
lit
y
c
o
n
s
tr
ain
t:
(
2
0
)
R
ea
cti
v
e
p
o
w
er
g
e
n
er
atio
n
(
Q
Gi
)
in
eq
u
alit
y
co
n
s
tr
ain
t:
(
2
1
)
T
r
an
s
f
o
r
m
er
s
tap
s
etti
n
g
(
T
i
)
i
n
eq
u
alit
y
co
n
s
tr
ain
t:
(
2
2
)
T
r
an
s
m
is
s
io
n
li
n
e
f
lo
w
(
S
Li
)
in
eq
u
alit
y
co
n
s
tr
ain
t:
(
2
3
)
W
h
er
e,
n
c,
n
g
a
n
d
n
t a
r
e
n
u
m
b
er
s
o
f
th
e
s
w
i
tch
ab
le
r
ea
cti
v
e
p
o
w
er
s
o
u
r
ce
s
,
g
e
n
er
ato
r
s
an
d
tr
an
s
f
o
r
m
er
s
.
4.
M
E
L
E
AG
RIS
G
A
L
L
O
P
A
V
O
AL
G
O
R
I
T
H
M
(
M
G
A)
MG
A
i
s
b
ased
o
n
th
e
Me
leag
r
is
Gallo
p
av
o
b
eh
av
io
u
r
.
I
t
co
n
s
i
s
ts
o
f
s
e
v
er
al
g
r
o
u
p
s
a
n
d
e
ac
h
g
r
o
u
p
en
co
m
p
as
s
a
lead
in
g
m
ale
M
elea
g
r
is
Gal
lo
p
av
o
,
co
u
p
le
o
f
Me
leag
r
is
Ga
llo
p
av
o
,
an
d
P
o
u
lts
.
Dep
e
n
d
o
n
t
h
e
f
it
n
es
s
v
al
u
es
o
f
t
h
e
Me
leag
r
is
Gallo
p
av
o
th
e
y
d
i
v
id
e
th
e
m
s
el
v
es
i
n
to
s
ev
er
al
g
r
o
u
p
s
an
d
id
en
tit
y
o
f
th
e
Me
leag
r
is
Gallo
p
av
o
(
lead
in
g
m
ale
Me
lea
g
r
is
Gallo
p
av
o
,
co
u
p
le
o
f
Me
lea
g
r
is
Gal
lo
p
av
o
,
an
d
P
o
u
lts
)
h
as
b
ee
n
d
eter
m
in
ed
.
B
ased
u
p
o
n
th
e
b
est
f
it
n
ess
v
al
u
es
Me
lea
g
r
is
Gallo
p
av
o
w
o
u
ld
b
e
ac
ted
as
p
o
u
ltr
y
,
&
also
as
h
ea
d
p
o
u
ltr
y
i
n
a
g
r
o
u
p
.
An
d
w
h
ic
h
h
a
s
w
o
r
s
t
f
it
n
es
s
v
al
u
es
w
o
u
ld
b
e
d
esig
n
a
ted
as
P
o
u
lts
.
R
e
m
ai
n
i
n
g
all
w
o
u
ld
b
e
th
e
co
m
m
o
n
Me
lea
g
r
is
Ga
llo
p
a
vo
an
d
i
t
ar
b
itra
r
il
y
c
h
o
o
s
es
w
h
ic
h
g
r
o
u
p
to
li
v
e
in
.
M
o
t
h
er
-
c
h
ild
r
elatio
n
s
h
ip
b
et
w
ee
n
th
e
Fe
m
ale
Me
leag
r
i
s
Gallo
p
av
o
a
n
d
t
h
e
P
o
u
lts
is
al
s
o
ar
b
itra
r
il
y
es
tab
lis
h
ed
as
s
h
o
w
n
in
Fi
g
u
r
e
1
,
2
,
3
.
Fig
u
r
e
1
.
Me
leag
r
is
g
allo
p
av
o
Fig
u
r
e
2
.
Fe
m
ale
m
elea
g
r
is
g
allo
p
av
o
w
it
h
p
o
u
lts
Fig
u
r
e
3
.
Me
leag
r
is
g
allo
p
av
o
in
g
r
o
u
p
S
u
p
r
e
m
ac
y
r
elatio
n
s
h
ip
an
d
m
o
th
er
-
ch
ild
r
elatio
n
s
h
ip
in
a
g
r
o
u
p
w
i
ll
r
e
m
ai
n
u
n
c
h
an
g
ed
&
o
n
l
y
u
p
d
ate
ev
er
y
s
e
v
er
al
(
G)
ti
m
e
s
tep
s
.
I
n
th
e
as a
g
r
o
u
p
-
m
ate
Me
leag
r
is
Gallo
p
av
o
f
o
llo
w
t
h
eir
p
o
u
ltr
y
(
lead
in
g
m
ale
Me
lea
g
r
is
Gallo
p
av
o
)
to
ex
p
lo
r
e
f
o
o
d
,
at
th
e
s
a
m
e
ti
m
e
it
p
r
ev
en
t
th
e
s
a
m
e
o
n
es
to
ea
t
th
eir
o
w
n
f
o
o
d
.
A
l
w
a
y
s
th
e
o
v
er
r
id
in
g
in
d
i
v
id
u
als
h
av
e
th
e
lead
to
g
r
ab
m
o
r
e
f
o
o
d
an
d
Me
leag
r
is
Gallo
p
av
o
w
o
u
ld
ar
b
itra
r
ily
p
in
c
h
th
e
h
ig
h
-
qu
a
lit
y
f
o
o
d
w
h
ic
h
h
as
b
ee
n
alr
ea
d
y
f
o
u
n
d
b
y
o
th
er
Me
leag
r
i
s
Gallo
p
av
o
.
I
n
th
e
r
eg
io
n
o
f
th
e
m
o
th
er
Me
leag
r
is
Gallo
p
av
o
P
o
u
lts
al
w
a
y
s
s
ea
r
ch
f
o
r
f
o
o
d
.
I
n
th
e
p
r
o
j
ec
t
ed
MG
A
ad
d
itio
n
al
p
ar
am
eter
s
ar
e
eli
m
i
n
ated
,
in
o
r
d
er
t
o
u
p
s
u
r
g
e
t
h
e
s
ea
r
ch
to
w
ar
d
s
g
lo
b
al
o
p
tim
izatio
n
s
o
lu
tio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
Melea
g
r
is
Ga
llo
p
a
vo
A
lg
o
r
ith
m
fo
r
S
o
lvin
g
Op
tima
l R
ea
ctiv
e
P
o
w
er P
r
o
b
lem
(
K
.
Len
in
)
103
A
l
w
a
y
s
ad
v
an
ta
g
e
s
f
o
r
th
e
d
o
m
in
a
n
t
i
n
d
iv
id
u
als
i
n
g
r
ab
th
e
f
o
o
d
.
B
etter
f
itn
es
s
p
o
u
ltry
w
ill
h
a
v
e
h
ig
h
p
r
io
r
it
y
f
o
r
f
o
o
d
ac
ce
s
s
w
h
e
n
co
m
p
ar
ed
w
i
th
w
o
r
s
e
f
it
n
es
s
v
al
u
es
p
o
u
ltr
y
.
I
t
h
as
b
ee
n
s
i
m
u
la
ted
th
at
th
e
p
o
u
ltr
y
w
it
h
b
etter
f
it
n
ess
v
al
u
es
ca
n
e
x
p
lo
r
e
f
o
r
f
o
o
d
in
a
w
id
er
r
an
g
e
o
f
p
lace
s
th
a
n
th
a
t
o
f
th
e
w
it
h
p
o
u
ltr
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2
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2
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2
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W
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2
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et
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Gal
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Nu
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all
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m
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ar
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t
w
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iv
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if
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x
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in
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Me
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m
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s
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tim
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ac
h
in
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v
id
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a
l
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o
p
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d
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M
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te
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s
if
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(
ex
p
lo
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)
&
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t
ev
a
lu
at
es
th
e
v
al
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e
f
r
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t
h
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ir
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te
p
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Sin
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t
h
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d
P
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ab
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le
Me
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I
n
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f
P
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p
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Me
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p
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m
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3
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W
ith
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104
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3
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3
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(
)
(
3
4
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{
(
|
|
)
[
]
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3
5
)
T
h
e
f
ir
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lo
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s
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h
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E
q
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(
2
7
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.
A
f
ter
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s
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Me
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p
av
o
f
o
r
m
u
la
as f
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w
s
:
(
)
(
3
6
)
[
]
is
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f
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I
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I
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N:
2252
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8792
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I
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-
8792
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