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I
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1027
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O
n
e
s
u
itab
le
a
p
p
r
o
ac
h
f
o
r
a
d
d
r
ess
in
g
s
tatis
tical
in
v
en
to
r
y
m
an
ag
e
m
en
t
p
r
o
b
l
em
s
is
th
e
s
tatis
tical
in
v
en
to
r
y
c
o
n
tr
o
l
(
SIC)
m
e
th
o
d
[
3
]
.
I
n
th
is
s
tu
d
y
,
th
e
p
r
o
b
ab
ilis
tic
SIC
ap
p
r
o
ac
h
,
s
p
ec
if
ically
th
e
p
r
o
b
a
b
ilis
tic
(
Q
,
r
)
in
v
en
to
r
y
m
o
d
el
,
is
co
n
s
id
er
ed
m
o
r
e
a
p
p
r
o
p
r
iate.
T
h
is
is
b
ec
au
s
e
th
e
d
em
an
d
f
o
r
ch
l
o
r
in
e
g
as
ex
h
ib
its
v
ar
iab
ilit
y
a
n
d
u
n
ce
r
tain
ty
,
m
ak
in
g
it
d
if
f
icu
lt
t
o
p
r
e
d
ict
with
p
r
ec
is
io
n
.
Ho
w
ev
er
,
k
ey
s
tatis
tical
ch
ar
ac
ter
is
tics
s
u
ch
as
th
e
e
x
p
ec
ted
v
alu
e,
v
ar
ia
n
ce
,
a
n
d
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
o
f
d
e
m
an
d
ca
n
b
e
esti
m
ated
f
r
o
m
h
is
to
r
ical
d
ata,
allo
win
g
f
o
r
th
e
a
p
p
licatio
n
o
f
a
p
r
o
b
a
b
ilis
tic
m
o
d
el.
R
esear
ch
o
n
p
r
o
b
ab
ilis
tic
in
v
en
to
r
y
m
o
d
els
,
s
p
ec
if
ically
th
e
ec
o
n
o
m
ic
o
r
d
er
q
u
a
n
tity
(
E
OQ)
o
r
p
r
o
b
a
b
il
is
tic
(
r
,
Q
)
m
o
d
els
,
h
a
s
b
ee
n
co
n
d
u
cted
ac
r
o
s
s
v
ar
io
u
s
f
ield
s
u
s
in
g
d
em
an
d
d
is
tr
ib
u
tio
n
s
s
u
ch
as
th
e
n
o
r
m
al
an
d
g
a
m
m
a
d
is
tr
ib
u
tio
n
s
[
4
]
−
[
9]
.
T
h
e
p
r
o
b
a
b
ilis
tic
E
OQ
m
o
d
el
u
n
d
er
u
n
if
o
r
m
l
y
d
is
tr
ib
u
ted
d
em
an
d
h
as
also
b
ee
n
e
x
am
in
ed
b
y
[
1
0
]
.
Ad
d
itio
n
ally
,
[
1
1
]
co
m
p
ar
e
d
tr
an
s
p
o
r
tatio
n
in
v
e
n
to
r
y
m
o
d
els
u
n
d
e
r
g
am
m
a,
ex
p
o
n
e
n
tial,
an
d
u
n
if
o
r
m
d
e
m
an
d
d
is
tr
ib
u
tio
n
s
.
R
esear
ch
o
n
ch
lo
r
in
e
g
as
in
v
e
n
to
r
y
m
o
d
els
h
as
also
b
ee
n
c
o
n
d
u
cte
d
b
y
[
1
2
]
,
wh
o
ap
p
lied
th
e
E
OQ
m
o
d
el
with
a
n
o
r
m
ally
d
is
tr
i
b
u
ted
d
em
a
n
d
ass
u
m
p
tio
n
to
m
an
ag
e
ch
lo
r
i
n
e
g
as
in
v
en
to
r
y
at
PT
T
o
y
a
I
n
d
o
Ma
n
u
n
g
g
al.
T
h
eir
f
i
n
d
in
g
s
i
n
d
icate
d
th
at
t
h
e
E
OQ
m
et
h
o
d
y
ield
ed
a
m
o
r
e
o
p
tim
a
l
in
v
en
to
r
y
p
o
licy
co
m
p
ar
ed
to
th
e
co
m
p
an
y
’
s
e
x
is
tin
g
ap
p
r
o
ac
h
.
I
n
a
d
d
itio
n
,
a
s
tu
d
y
b
y
[
1
3
]
ex
am
in
e
d
ch
l
o
r
in
e
g
as
i
n
v
en
to
r
y
at
PDAM
T
ir
ta
Mu
s
i
u
s
in
g
th
e
E
OQ
m
o
d
el
u
n
d
er
th
e
a
s
s
u
m
p
tio
n
o
f
ex
p
o
n
en
tially
d
is
tr
ib
u
ted
d
em
an
d
.
Ho
wev
er
,
th
er
e
h
as
b
ee
n
li
m
ited
d
ev
elo
p
m
en
t
o
f
in
v
en
to
r
y
m
o
d
els
f
o
r
ch
lo
r
i
n
e
g
a
s
u
s
in
g
alter
n
ativ
e
p
r
o
b
a
b
ilit
y
d
is
tr
ib
u
tio
n
s
.
Fu
r
th
er
m
o
r
e,
n
o
p
r
i
o
r
s
tu
d
ies
h
av
e
an
aly
ze
d
th
e
r
elatio
n
s
h
i
p
b
etwe
en
o
p
tim
al
in
v
en
to
r
y
p
o
licies
an
d
th
e
v
a
lu
es
o
f
th
e
ak
aik
e
in
f
o
r
m
atio
n
cr
iter
io
n
(
AI
C
)
an
d
th
e
b
a
y
esian
in
f
o
r
m
atio
n
cr
iter
io
n
(
B
I
C
)
in
ev
alu
atin
g
th
e
g
o
o
d
n
ess
-
of
-
f
it
o
f
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
s
f
o
r
ch
l
o
r
in
e
g
as
d
em
a
n
d
.
T
h
is
s
tu
d
y
aim
s
to
co
m
p
ar
e
th
e
o
p
tim
al
s
o
lu
tio
n
s
o
f
p
r
o
b
a
b
ilis
tic
(
Q
,
r
)
in
v
en
to
r
y
m
o
d
els
u
n
d
er
v
ar
io
u
s
p
r
o
b
a
b
ilit
y
d
is
tr
ib
u
tio
n
s
th
at
s
atis
f
y
th
e
d
is
tr
ib
u
tio
n
al
ass
u
m
p
tio
n
test
s
.
T
h
e
an
aly
s
is
is
co
n
d
u
cted
u
s
in
g
Py
th
o
n
s
o
f
twar
e.
R
esear
ch
o
n
p
r
o
b
ab
ilis
tic
in
v
en
to
r
y
m
o
d
el
s
(
Q
,
r
)
with
n
o
n
-
n
o
r
m
al
d
is
tr
ib
u
tio
n
s
is
s
till
r
ar
e
d
u
e
to
th
e
co
m
p
lex
ity
o
f
m
o
d
el
d
ev
elo
p
m
en
t.
T
h
is
s
tu
d
y
em
p
h
asizes
th
e
d
ev
elo
p
m
e
n
t
o
f
a
p
r
o
b
ab
ilis
tic
in
v
en
to
r
y
m
o
d
el
at
PDAM,
with
d
em
an
d
p
ar
am
eter
s
f
o
r
ch
lo
r
in
e
g
as
d
is
tr
ib
u
ted
ac
co
r
d
i
n
g
to
a
n
o
n
-
n
o
r
m
al
p
r
o
b
a
b
ilit
y
d
is
tr
ib
u
tio
n
.
I
t th
e
n
co
m
p
a
r
es th
e
r
esu
lts
o
f
th
e
o
p
tim
al
p
o
licies f
r
o
m
t
h
ese
in
v
en
to
r
y
m
o
d
els.
I
n
m
o
d
elin
g
in
v
e
n
to
r
y
s
y
s
tem
s
th
at
in
v
o
lv
e
t
h
e
d
e
m
an
d
o
r
c
o
n
s
u
m
p
tio
n
o
f
ch
l
o
r
in
e
g
as
c
h
em
icals,
it
is
s
o
m
etim
es
n
ec
ess
ar
y
to
g
en
e
r
ate
f
o
r
ec
asts
u
s
in
g
ap
p
r
o
p
r
i
ate
tim
e
s
er
ies
m
eth
o
d
s
.
On
e
s
u
ch
m
eth
o
d
is
th
e
s
ea
s
o
n
al
au
to
r
eg
r
ess
iv
e
in
teg
r
ated
m
o
v
in
g
av
er
a
g
e
(
SAR
I
MA
)
m
o
d
el.
SAR
I
MA
h
as
b
e
en
s
h
o
wn
to
p
r
o
v
id
e
m
o
r
e
ac
cu
r
ate
a
n
d
r
eliab
le
f
o
r
ec
asts
co
m
p
ar
ed
to
s
ev
e
r
al
o
th
er
ap
p
r
o
ac
h
es,
s
u
ch
a
s
th
e
h
o
lt
-
win
ter
s
m
eth
o
d
[
1
4
]
.
A
co
m
p
ar
ativ
e
s
t
u
d
y
co
n
d
u
cte
d
b
y
[
1
5
]
on
f
o
r
e
ca
s
tin
g
m
o
n
th
ly
r
i
v
er
f
lo
ws in
wester
n
C
u
b
a
also
d
em
o
n
s
tr
ated
th
at
SAR
I
MA
o
u
tp
er
f
o
r
m
ed
th
e
h
o
lt
-
win
ter
s
m
eth
o
d
in
ca
p
tu
r
in
g
s
ea
s
o
n
al
an
d
in
ter
-
an
n
u
al
v
ar
iab
ilit
y
.
Acc
o
r
d
in
g
ly
,
t
h
is
r
esear
ch
em
p
lo
y
s
th
e
S
AR
I
MA
m
o
d
el.
Mo
r
eo
v
er
,
SAR
I
MA
r
em
ain
s
co
m
p
etitiv
e
with
v
ar
io
u
s
m
ac
h
in
e
lear
n
in
g
f
o
r
ec
asti
n
g
tech
n
iq
u
es,
as
r
ep
o
r
ted
b
y
[
1
6
]
,
[
1
7
]
.
On
e
ap
p
licatio
n
o
f
SAR
I
MA
is
f
o
r
ec
asti
n
g
d
e
m
an
d
in
th
e
f
ash
io
n
s
ec
to
r
:
p
r
ed
ictin
g
lo
n
g
-
ter
m
s
ales
o
f
h
ig
h
ly
s
ea
s
o
n
al
s
h
o
e
m
o
d
els
b
ased
o
n
h
is
to
r
ical
d
a
ta
u
s
in
g
th
e
Pro
p
h
et
an
d
SAR
I
MA
alg
o
r
ith
m
s
.
Her
e,
SAR
I
MA
p
r
o
v
id
es
b
etter
f
o
r
ec
asti
n
g
r
esu
lts
th
an
Pro
p
h
et
[
1
8
]
.
An
o
th
er
ap
p
licatio
n
is
p
latelet
d
em
a
n
d
f
o
r
ec
asti
n
g
u
s
in
g
th
e
SAR
I
MA
m
o
d
el
to
o
p
tim
ize
th
e
al
lo
ca
tio
n
o
f
b
l
o
o
d
b
an
k
r
eso
u
r
ce
s
an
d
clin
ical
s
u
p
p
lies
[
1
9
]
.
T
o
d
ate,
PDAM
h
a
s
n
ev
er
esti
m
ated
ch
lo
r
in
e
g
as d
em
an
d
,
lead
i
n
g
to
e
x
ce
s
s
iv
e
o
r
d
er
s
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
2
.
1
.
SARI
M
A
f
o
r
ec
a
s
t
ing
m
et
ho
d
T
h
e
g
en
e
r
al
f
o
r
m
o
f
t
h
e
SAR
I
MA
(
,
,
)
(
,
,
)
ca
n
b
e
ex
p
r
ess
ed
as
(
1
)
:
(
)
(
)
(
1
−
)
(
1
−
)
=
(
)
(
)
(
1
)
H
er
e
,
p
,
d
,
an
d
q
r
ep
r
esen
t
th
e
n
o
n
-
s
ea
s
o
n
al
AR
,
d
if
f
er
en
ci
n
g
,
a
n
d
MA
o
r
d
e
r
s
,
r
esp
ec
tiv
e
ly
,
an
d
P
,
D
,
an
d
Q
r
ep
r
esen
t
th
e
s
ea
s
o
n
al
A
R
,
d
if
f
er
en
cin
g
,
an
d
MA
o
r
d
er
s
,
r
esp
ec
tiv
ely
.
(
)
d
en
o
tes
th
e
n
o
n
-
s
ea
s
o
n
al
A
R
co
m
p
o
n
en
t,
Φ
(
)
d
en
o
tes
th
e
s
ea
s
o
n
al
AR
co
m
p
o
n
en
t,
(
1
−
)
ᵈ
is
th
e
n
o
n
-
s
ea
s
o
n
al
d
if
f
er
en
cin
g
o
p
er
ato
r
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
15
,
No
.
3
,
Sep
tem
b
er
20
26
:
1
0
2
6
-
1
0
3
7
1028
(
1
−
ᴸ
)
ᴰ
is
th
e
s
ea
s
o
n
al
d
if
f
er
en
cin
g
o
p
er
ato
r
,
(
)
d
en
o
tes
th
e
n
o
n
-
s
ea
s
o
n
al
MA
co
m
p
o
n
en
t,
Θ
(
)
d
en
o
tes th
e
s
ea
s
o
n
al
MA
co
m
p
o
n
en
t,
an
d
r
ep
r
esen
ts
th
e
er
r
o
r
ter
m
at
p
er
io
d
t
[
2
0
]
.
Data
s
tatio
n
ar
ity
test
in
g
m
u
s
t
b
e
p
er
f
o
r
m
e
d
f
ir
s
t,
in
clu
d
i
n
g
test
s
f
o
r
m
ea
n
an
d
v
ar
ian
ce
s
t
atio
n
ar
ity
.
I
f
th
e
d
ata
d
o
es
n
o
t
m
ee
t
th
e
d
ata
s
tatio
n
ar
ity
r
eq
u
ir
em
e
n
ts
,
tr
an
s
f
o
r
m
atio
n
a
n
d
d
if
f
e
r
en
tiatio
n
m
u
s
t
b
e
p
er
f
o
r
m
ed
.
I
f
th
e
d
ata
is
s
tatio
n
ar
y
,
t
h
e
n
ex
t
s
tep
is
to
p
lo
t
th
e
a
u
t
o
co
r
r
elatio
n
f
u
n
ctio
n
(
AC
F)
an
d
p
ar
tial
au
to
co
r
r
elatio
n
f
u
n
ctio
n
(
P
AC
F)
f
o
r
SAR
I
MA
m
o
d
el
id
en
tific
atio
n
.
E
s
tim
atio
n
o
f
SAR
I
MA
(
,
,
)
(
,
,
)
m
o
d
el
co
ef
f
icien
ts
ca
n
b
e
esti
m
ated
u
s
in
g
th
e
m
ax
im
u
m
L
ik
elih
o
o
d
m
et
h
o
d
[
2
1
]
.
(
,
,
2
)
=
(
2
2
)
−
/
2
(
1
−
2
)
1
/
2
[
−
(
,
)
/
2
2
]
(
2
)
wh
er
e
n
is
th
e
n
u
m
b
er
o
f
o
b
s
er
v
atio
n
s
o
r
d
ata.
ϕ
is
th
e
au
to
r
eg
r
ess
iv
e
p
ar
am
eter
,
μ
is
th
e
m
ea
n
o
f
th
e
s
tatio
n
ar
y
p
r
o
ce
s
s
,
an
d
2
is
th
e
v
ar
ian
ce
o
f
th
e
e
r
r
o
r
.
(
,
)
is
a
q
u
an
tity
r
ep
r
esen
tin
g
th
e
s
u
m
o
f
s
q
u
ar
e
s
.
Fin
ally
,
v
er
if
y
th
e
SAR
I
MA
m
o
d
els
o
b
tain
ed
b
ased
o
n
AC
F
an
d
PAC
F
v
alu
es
u
s
in
g
m
ea
n
ab
s
o
l
u
te
p
er
ce
n
tag
e
e
r
r
o
r
(
MA
PE)
.
T
h
e
SAR
I
MA
m
o
d
el
with
th
e
s
m
allest
MA
PE
v
alu
e
is
s
elec
t
ed
f
o
r
th
e
f
o
r
ec
asti
n
g
an
d
p
r
o
b
ab
ilis
tic
in
v
en
to
r
y
m
o
d
elin
g
s
tag
es.
Acc
o
r
d
in
g
t
o
[
2
2
]
,
th
e
er
r
o
r
i
n
tim
e
s
er
ies
d
ata
an
aly
s
is
ca
n
b
e
ca
lcu
lated
u
s
in
g
th
e
MA
PE.
MA
PE
ass
es
s
es
th
e
m
ag
n
itu
d
e
o
f
t
h
e
d
if
f
e
r
en
ce
b
etwe
en
f
o
r
ec
aste
d
v
alu
es
an
d
ac
tu
al
o
b
s
er
v
ed
d
ata.
T
h
e
eq
u
atio
n
f
o
r
ca
lcu
latin
g
MA
PE
is
g
iv
en
as
(
3
)
:
=
1
∑
|
−
̂
|
=
1
×
100%
(
3
)
wh
er
e
n
r
ep
r
esen
ts
th
e
to
tal
n
u
m
b
er
o
f
d
ata
p
o
in
ts
,
is
th
e
a
ctu
al
d
ata
in
p
er
io
d
t,
an
d
̂
is
th
e
f
o
r
ec
asted
d
ata
f
o
r
p
er
io
d
ttt.
T
h
e
cr
iter
i
a
f
o
r
in
ter
p
r
etin
g
th
e
MA
PE
v
alu
e
ar
e
as
f
o
llo
ws:
ex
ce
llen
t
f
o
r
MA
PE
<
1
0
%,
g
o
o
d
f
o
r
1
0
%
≤
MA
PE
<
2
0
%,
f
air
f
o
r
2
0
% ≤
MA
PE
<
5
0
%
,
an
d
p
o
o
r
f
o
r
MA
PE
≥
5
0
%.
2
.
2
.
P
a
ra
met
er
s
a
nd
v
a
ria
bl
es o
f
t
he
pr
o
ba
bil
is
t
ic
inv
ent
o
ry
mo
del
T
h
e
p
ar
am
eter
s
an
d
v
ar
ia
b
les
u
s
ed
in
th
is
r
esear
ch
m
o
d
el
ar
e
p
r
esen
ted
in
d
etail
in
T
ab
le
1
.
T
h
is
p
r
esen
tatio
n
aim
s
t
o
cl
ar
if
y
th
e
m
ai
n
co
m
p
o
n
en
ts
th
at
m
ak
e
u
p
th
e
m
o
d
el,
th
er
eb
y
f
ac
ilit
atin
g
an
u
n
d
er
s
tan
d
i
n
g
o
f
th
e
m
o
d
el
’
s
s
tr
u
ctu
r
e
a
n
d
m
ec
h
a
n
is
m
s
.
I
n
ad
d
itio
n
,
th
e
T
ab
le
1
also
h
elp
s
id
en
tify
th
e
r
elatio
n
s
h
ip
s
b
etwe
en
v
ar
ia
b
les an
d
th
e
r
o
le
o
f
ea
c
h
p
a
r
a
m
eter
in
th
e
an
al
y
s
is
p
r
o
ce
s
s
.
T
ab
le
1
.
Def
in
i
n
g
v
a
r
iab
les an
d
p
ar
am
eter
s
V
a
r
i
a
b
l
e
s a
n
d
p
a
r
a
m
e
t
e
r
s
Th
e
d
e
f
i
n
i
n
g
v
a
r
i
a
b
l
e
s
a
n
d
p
a
r
a
me
t
e
r
s
η
S
e
r
v
i
c
e
l
e
v
e
l
,
r
e
p
r
e
s
e
n
t
i
n
g
t
h
e
p
r
o
b
a
b
i
l
i
t
y
t
h
a
t
d
e
ma
n
d
c
a
n
b
e
f
u
l
f
i
l
l
e
d
w
i
t
h
o
u
t
e
x
p
e
r
i
e
n
c
i
n
g
a
st
o
c
k
o
u
t
.
N
E
x
p
e
c
t
e
d
i
n
v
e
n
t
o
r
y
s
h
o
r
t
a
g
e
p
e
r
c
y
c
l
e
,
i
.
e
.
,
t
h
e
a
m
o
u
n
t
o
f
d
e
ma
n
d
t
h
a
t
c
a
n
n
o
t
b
e
f
u
l
f
i
l
l
e
d
.
E
x
p
e
c
t
e
d
d
e
ma
n
d
d
u
r
i
n
g
t
h
e
l
e
a
d
t
i
m
e
p
e
r
i
o
d
.
P
r
o
p
o
r
t
i
o
n
o
f
u
n
f
u
l
f
i
l
l
e
d
d
e
ma
n
d
,
w
h
e
r
e
η
=1
-
α
.
r
R
e
o
r
d
e
r
p
o
i
n
t
,
t
h
e
i
n
v
e
n
t
o
r
y
l
e
v
e
l
a
t
w
h
i
c
h
a
n
e
w
o
r
d
e
r
i
s
p
l
a
c
e
d
X
R
a
n
d
o
m
v
a
r
i
a
b
l
e
r
e
p
r
e
s
e
n
t
i
n
g
t
h
e
d
e
man
d
f
o
r
c
h
l
o
r
i
n
e
g
a
s.
(
)
P
r
o
b
a
b
i
l
i
t
y
d
e
n
si
t
y
f
u
n
c
t
i
o
n
o
f
d
e
ma
n
d
.
D
E
x
p
e
c
t
e
d
d
e
ma
n
d
o
v
e
r
t
h
e
p
l
a
n
n
i
n
g
h
o
r
i
z
o
n
(
k
g
/
y
e
a
r
)
.
L
L
e
a
d
t
i
me
,
d
e
f
i
n
e
d
a
s
t
h
e
t
i
me
i
n
t
e
r
v
a
l
f
r
o
m
p
l
a
c
i
n
g
a
n
o
r
d
e
r
u
n
t
i
l
t
h
e
g
o
o
d
s a
r
r
i
v
e
(
y
e
a
r
s)
.
O
r
d
e
r
q
u
a
n
t
i
t
y
o
r
l
o
t
s
i
z
e
f
o
r
e
a
c
h
r
e
p
l
e
n
i
s
h
me
n
t
(
k
g
)
.
U
n
i
t
p
r
i
c
e
p
e
r
k
i
l
o
g
r
a
m
.
O
r
d
e
r
i
n
g
o
r
c
o
mm
u
n
i
c
a
t
i
o
n
c
o
s
t
p
e
r
o
r
d
e
r
(
I
D
R
p
e
r
mess
a
g
e
)
.
ℎ
H
o
l
d
i
n
g
c
o
st
p
e
r
u
n
i
t
(
p
e
r
c
e
n
t
a
g
e
p
e
r
u
n
i
t
p
e
r
y
e
a
r
)
,
c
a
l
c
u
l
a
t
e
d
a
s
a
p
e
r
c
e
n
t
a
g
e
o
f
t
h
e
u
n
i
t
p
r
i
c
e
a
n
d
p
r
o
p
o
r
t
i
o
n
a
l
t
o
t
h
e
q
u
a
n
t
i
t
y
st
o
r
e
d
a
n
d
t
h
e
s
t
o
r
a
g
e
d
u
r
a
t
i
o
n
.
U
n
i
t
s
h
o
r
t
a
g
e
c
o
st
(
I
D
R
p
e
r
u
n
i
t
)
,
p
r
o
p
o
r
t
i
o
n
a
l
t
o
t
h
e
n
u
m
b
e
r
o
f
u
n
i
t
s
t
h
a
t
c
a
n
n
o
t
b
e
f
u
l
f
i
l
l
e
d
.
T
o
t
a
l
c
o
st
o
f
t
h
e
i
n
v
e
n
t
o
r
y
s
y
st
e
m.
ss
S
a
f
e
t
y
st
o
c
k
,
r
e
p
r
e
s
e
n
t
i
n
g
t
h
e
b
u
f
f
e
r
q
u
a
n
t
i
t
y
k
e
p
t
i
n
t
h
e
w
a
r
e
h
o
u
se
t
o
p
r
e
v
e
n
t
st
o
c
k
o
u
t
s.
2
.
3
.
No
rma
l
pr
o
ba
bil
is
t
ic
in
v
ent
o
ry
mo
del
Su
p
p
o
s
e
th
e
d
em
an
d
f
o
r
ch
e
m
icals
f
o
llo
ws
a
n
o
r
m
al
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
,
with
a
co
r
r
esp
o
n
d
in
g
n
o
r
m
al
p
r
o
b
a
b
ilit
y
d
en
s
ity
f
u
n
ctio
n
f
(
x
)
.
I
n
th
at
ca
s
e,
th
e
o
r
d
er
q
u
an
tity
p
er
cy
cle
(
Q
)
,
t
h
e
r
eo
r
d
er
p
o
in
t
(
r
)
,
an
d
th
e
e
x
p
ec
ted
n
u
m
b
e
r
o
f
in
v
en
to
r
y
s
h
o
r
tag
es (
N
)
ar
e
f
o
r
m
u
lated
as d
escr
ib
ed
in
th
e
(
4
)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
P
r
o
b
a
b
ilis
tic
in
ve
n
to
r
y
mo
d
eli
n
g
fo
r
ch
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in
e
g
a
s
u
s
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g
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i
ta
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n
d
P
yth
o
n
…
(
Oki
Dw
ip
u
r
w
a
n
i)
1029
=
+
(
4
)
=
√
2
(
+
)
ℎ
(
5
)
=
∫
(
−
)
(
)
∞
=
[
(
)
−
Ψ
(
)
]
(
6
)
wh
er
e
r
ep
r
esen
ts
th
e
s
tan
d
ar
d
ized
n
o
r
m
al
v
alu
e
.
T
h
e
n
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an
d
(
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en
o
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th
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p
r
o
b
ab
i
lity
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en
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(
PDF)
an
d
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m
u
lativ
e
d
is
tr
ib
u
tio
n
f
u
n
ct
io
n
(
C
DF)
o
f
th
e
s
tan
d
ar
d
n
o
r
m
al
d
is
tr
ib
u
tio
n
,
r
esp
ec
tiv
ely
[
2
3
]
.
T
h
e
to
tal
c
o
s
t is ca
lcu
lated
as
(
7
)
:
(
)
(
)
2
u
TL
R
C
A
DT
O
Dp
h
R
D
z
R
f
z
dz
TT
=
+
+
−
+
+
−
(
7
)
2
.
4
.
T
esting
t
he
pr
o
ba
bil
it
y
dis
t
rib
utio
n o
f
da
t
a
s
t
a
t
is
t
ics wit
h ko
lmo
g
o
r
o
v
-
s
mirno
v
(
K
S)
T
o
d
eter
m
i
n
e
th
e
s
tatis
tical
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
o
f
th
e
d
em
an
d
d
ata,
th
e
k
o
lm
o
g
o
r
o
v
–
s
m
ir
n
o
v
(
KS)
test
s
tatis
tic
is
u
s
ed
[
2
4
]
.
I
f
r
ep
r
esen
ts
th
e
o
r
d
e
r
ed
r
esid
u
al
d
ata
f
r
o
m
t
h
e
s
m
allest
to
th
e
lar
g
est
v
alu
e
,
th
e
KS statis
t
ic
ca
n
b
e
ca
lcu
lated
u
s
in
g
(
8
)
:
_
=
|
(
)
−
0
(
)
|
(
8
)
wh
er
e
(
)
d
en
o
tes
th
e
cu
m
u
lativ
e
d
is
tr
ib
u
tio
n
f
u
n
ctio
n
(
C
DF)
o
f
th
e
s
p
ec
if
ied
t
h
eo
r
etica
l
d
is
tr
ib
u
tio
n
,
a
n
d
0
(
)
r
ep
r
esen
ts
th
e
e
m
p
ir
ical
cu
m
u
lativ
e
d
is
tr
ib
u
tio
n
f
u
n
ctio
n
(
E
C
DF)
o
f
th
e
o
b
s
er
v
ed
d
ata.
T
h
e
h
y
p
o
th
eses
ar
e
d
ef
in
ed
as
f
o
llo
ws:
0
:
t
h
e
r
esid
u
als
f
o
llo
w
th
e
s
p
e
cif
ied
d
is
tr
ib
u
tio
n
,
an
d
1
:
T
h
e
r
esid
u
als
d
o
n
o
t
f
o
llo
w
th
e
s
p
ec
if
ied
d
is
tr
ib
u
tio
n
.
T
h
e
n
u
ll
h
y
p
o
th
es
is
0
is
r
ejec
ted
if
th
e
KS
test
s
tatis
t
ic
ex
ce
ed
s
th
e
cr
itical
v
alu
e,
i.e
.
,
_
>
,
,
o
r
if
th
e
p
-
va
lu
e
is
less
th
an
th
e
s
ig
n
if
ica
n
ce
lev
el,
i.e
.
,
_
<
[
2
5
]
,
[
2
6
]
Alo
n
g
s
id
e
th
e
KS
s
tatis
tic,
o
n
e
ca
n
ass
ess
th
e
g
o
o
d
n
ess
-
of
-
f
it
o
f
a
p
r
o
b
ab
ilit
y
d
is
tr
ib
u
tio
n
th
r
o
u
g
h
th
e
AI
C
an
d
th
e
B
I
C
.
T
h
eir
f
o
r
m
u
latio
n
s
ar
e
as
(
9
)
an
d
(
1
0
)
:
=
−
2
lo
g
(
)
+
2
(
+
1
)
(
9
)
=
−
2
lo
g
(
)
+
(
+
1
)
lo
g
(
)
(
10
)
wh
er
e
L
d
en
o
tes
th
e
esti
m
ated
lik
elih
o
o
d
f
u
n
ctio
n
,
p
is
th
e
n
u
m
b
e
r
o
f
p
ar
am
eter
s
in
th
e
m
o
d
el,
an
d
n
is
th
e
n
u
m
b
er
o
f
o
b
s
er
v
atio
n
s
in
th
e
d
ataset
[
2
7
]
.
2
.
5
.
H
a
dley
-
wit
hin
a
lg
o
rit
h
m
T
h
e
Had
d
le
y
-
W
ith
in
alg
o
r
ith
m
f
o
r
o
b
tain
in
g
th
e
o
p
tim
al
Q
an
d
r
v
alu
es
in
th
e
(
Q
,
r
)
m
o
d
el
h
as
s
ev
er
al
s
tag
es
[
2
8
]
.
First,
d
eter
m
in
e
th
e
i
n
itial
o
r
d
er
q
u
a
n
tity
p
er
cy
cle
(
Q
0
)
.
Seco
n
d
,
f
in
d
th
e
p
r
o
b
ab
ilit
y
o
f
in
v
en
to
r
y
s
h
o
r
ta
g
e
(
α
)
.
I
n
th
is
s
ec
o
n
d
s
tag
e,
t
h
e
r
eo
r
d
er
p
o
i
n
t
(
r
)
v
alu
e
will
b
e
o
b
tain
ed
.
T
h
e
th
ir
d
s
tep
is
to
en
ter
th
e
r
v
al
u
e
o
b
tain
ed
in
th
e
s
ec
o
n
d
s
tep
i
n
to
th
e
o
r
d
e
r
q
u
an
tity
p
e
r
cy
cle
(
Q
)
in
(
4
)
.
T
h
e
f
o
u
r
th
s
tep
is
an
iter
atio
n
in
wh
ich
th
e
n
ew
α
an
d
r
v
alu
es
ar
e
r
ec
alcu
lated
u
s
in
g
th
e
s
am
e
f
o
r
m
u
la,
th
en
r
etu
r
n
in
g
to
Step
2
.
At
th
is
s
tag
e,
if
a
n
ew
r
v
alu
e
is
o
b
tain
ed
th
at
is
r
elativ
ely
cl
o
s
e
to
th
e
p
r
ev
io
u
s
iter
atio
n
’
s
r
,
th
en
th
e
iter
atio
n
is
co
m
p
lete.
T
h
e
r
-
v
alu
e
f
o
r
t
h
e
Q
-
v
alu
e
in
th
is
s
tep
is
th
e
o
p
tim
al
v
alu
e.
Ho
wev
er
,
if
it
is
s
til
l
s
ig
n
i
f
ican
tly
d
if
f
er
en
t,
r
etu
r
n
to
t
h
e
s
ec
o
n
d
s
tep
,
s
tar
tin
g
f
r
o
m
th
e
last
r
an
d
Q
v
al
u
es
o
b
tain
e
d
.
T
h
e
Had
ley
-
W
ith
i
n
alg
o
r
ith
m
was
ch
o
s
en
f
o
r
it
s
s
im
p
licity
an
d
ab
ilit
y
to
ac
co
m
m
o
d
ate
th
e
o
p
tim
izati
o
n
o
f
p
r
o
b
ab
ilis
tic
in
v
en
to
r
y
m
o
d
els th
at
will b
e
d
ev
elo
p
e
d
wi
th
n
o
n
-
n
o
r
m
ally
d
is
tr
ib
u
ted
d
em
a
n
d
.
2
.
6
.
Resea
r
ch
met
ho
d
Fig
u
r
e
1
p
r
esen
ts
a
f
lo
wch
ar
t
illu
s
tr
atin
g
th
e
o
v
er
all
r
esear
ch
m
eth
o
d
o
l
o
g
y
,
s
p
ec
if
ically
f
o
cu
s
in
g
o
n
th
e
ap
p
licatio
n
o
f
th
e
SA
R
I
MA
f
o
r
ec
asti
n
g
m
eth
o
d
an
d
th
e
(
Q,
r)
p
r
o
b
ab
ilis
tic
in
v
en
to
r
y
m
o
d
el.
T
h
is
f
lo
wch
ar
t
p
r
o
v
id
es
a
s
y
s
tem
atic
o
v
er
v
iew
o
f
t
h
e
r
esear
ch
s
tag
es,
f
r
o
m
d
ata
p
r
o
ce
s
s
in
g
to
th
e
an
aly
s
is
o
f
r
esu
lts
.
Ad
d
itio
n
ally
,
th
is
v
is
u
aliza
tio
n
h
elp
s
clar
if
y
th
e
r
elatio
n
s
h
ip
s
b
etwe
en
p
r
o
ce
s
s
es
an
d
f
ac
ilit
ates
u
n
d
er
s
tan
d
i
n
g
o
f
th
e
im
p
lem
e
n
tatio
n
f
lo
w
o
f
th
e
m
et
h
o
d
s
u
s
ed
in
th
is
s
tu
d
y
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
15
,
No
.
3
,
Sep
tem
b
er
20
26
:
1
0
2
6
-
1
0
3
7
1030
Fig
u
r
e
1
.
Flo
wch
ar
t
o
f
r
esear
c
h
m
eth
o
d
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
SARI
M
A
A
g
r
ap
h
ical
r
ep
r
esen
tatio
n
o
f
th
e
ch
lo
r
in
e
g
as d
em
an
d
d
ata
i
s
p
r
esen
ted
in
Fig
u
r
e
2
,
wh
ich
illu
s
tr
ates
th
e
v
o
latilit
y
o
b
s
er
v
ed
in
th
e
tim
e
s
er
ies
f
r
o
m
J
an
u
ar
y
2
0
1
6
to
J
u
ly
2
0
2
3
.
Fo
r
ec
asti
n
g
f
o
r
th
e
p
er
io
d
f
r
o
m
Au
g
u
s
t
to
Dec
em
b
er
2
0
2
3
is
n
ec
ess
ar
y
,
as
th
e
in
v
en
to
r
y
m
o
d
elin
g
p
r
o
ce
s
s
r
eq
u
ir
es
co
m
p
lete
an
n
u
al
av
er
a
g
e
d
em
an
d
d
ata.
Fig
u
r
e
2
.
T
im
e
s
er
ies g
r
ap
h
o
f
ch
lo
r
in
e
g
as d
em
an
d
f
r
o
m
J
an
u
ar
y
2
0
1
6
to
J
u
ly
2
0
2
3
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
P
r
o
b
a
b
ilis
tic
in
ve
n
to
r
y
mo
d
eli
n
g
fo
r
ch
lo
r
in
e
g
a
s
u
s
in
g
min
i
ta
b
a
n
d
P
yth
o
n
…
(
Oki
Dw
ip
u
r
w
a
n
i)
1031
T
h
e
d
ataset
is
d
iv
id
ed
in
to
t
wo
s
eg
m
en
ts
:
th
e
tr
ain
in
g
d
at
a,
u
s
ed
to
d
ev
elo
p
th
e
SAR
I
MA
m
o
d
el,
co
n
s
is
ts
o
f
tim
e
s
er
ies
d
ata
f
r
o
m
J
an
u
ar
y
2
0
1
6
to
Dec
em
b
er
2
0
2
1
;
wh
ile
th
e
test
in
g
d
ata,
u
s
ed
to
ev
alu
ate
th
e
m
o
d
el
’
s
p
e
r
f
o
r
m
an
ce
,
in
clu
d
e
s
d
ata
f
r
o
m
J
an
u
a
r
y
2
0
2
2
to
J
u
ly
2
0
2
3
.
T
h
e
d
ata
f
r
o
m
a
s
in
g
le
d
if
f
er
en
tiatio
n
(
=
1
)
p
r
o
v
id
es
AC
F
an
d
PAC
F
v
alu
es,
n
o
n
e
o
f
wh
ich
ar
e
s
ig
n
if
ican
t.
T
h
is
m
ea
n
s
th
at
in
id
e
n
tify
in
g
th
e
SAR
I
MA
m
o
d
el,
it
will
b
e
n
ec
ess
ar
y
to
tr
y
co
m
b
in
atio
n
s
o
f
=
{
0
,
1
}
,
=
{
0
,
1
}
,
=
{
0
,
1
}
,
an
d
=
{
0
,
1
}
,
r
esu
ltin
g
in
a
t
o
tal
o
f
1
6
co
m
b
in
atio
n
s
f
o
r
th
e
p
ar
am
eter
v
alu
es
p
,
q
,
P
,
an
d
Q
th
at
n
ee
d
to
b
e
test
ed
.
T
h
e
o
p
tim
al
m
o
d
el
id
e
n
tifie
d
is
SAR
I
MA
(
0
,
1
,
0
)
(
0
,
1
,
1
)
¹²,
wh
ich
y
ield
s
a
MA
PE
o
f
5
.
4
8
%,
as
ca
lcu
lated
u
s
in
g
in
(3
)
.
T
h
is
MA
PE
v
alu
e
in
d
icate
s
th
at
th
e
SAR
I
M
A
(
0
,
1
,
0
)
(
0
,
1
,
1
)
¹²
m
o
d
el
d
e
m
o
n
s
tr
ates
v
er
y
h
ig
h
p
r
ed
ictiv
e
ac
cu
r
ac
y
.
T
h
e
p
l
o
ts
o
f
th
e
test
in
g
d
ata
an
d
th
e
f
o
r
ec
ast
ar
e
p
r
esen
ted
in
Fig
u
r
e
3
.
Data
p
r
ep
r
o
ce
s
s
in
g
an
d
m
o
d
elin
g
u
s
in
g
th
e
SAR
I
MA
ap
p
r
o
ac
h
in
Min
itab
s
o
f
twar
e.
I
n
Fig
u
r
e
3
,
th
e
b
l
u
e
lin
e
r
ep
r
esen
ts
th
e
ac
tu
al
ch
lo
r
in
e
g
as
d
ata
f
r
o
m
J
an
u
ar
y
2
0
2
2
to
J
u
ly
2
0
2
3
,
wh
ile
th
e
r
e
d
lin
e
illu
s
tr
ates
th
e
p
r
ed
icted
an
d
f
o
r
ec
asted
v
alu
es
f
r
o
m
J
an
u
ar
y
2
0
2
2
to
Dec
em
b
er
2
0
2
3
.
T
h
e
g
r
ee
n
an
d
p
u
r
p
le
lin
es
in
d
icate
th
e
lo
wer
an
d
u
p
p
er
co
n
f
id
en
c
e
b
o
u
n
d
s
o
f
th
e
f
o
r
ec
ast,
r
esp
ec
tiv
ely
.
Fig
u
r
e
3
.
Gr
a
p
h
o
f
test
in
g
d
ata
an
d
f
o
r
ec
ast d
ata
f
r
o
m
Au
g
u
s
t 2
0
2
3
t
o
Dec
em
b
er
2
0
2
3
3
.
2
.
Chlo
rine
g
a
s
dema
nd
dis
t
ributio
n t
esting
T
h
e
p
r
o
b
a
b
ilit
y
d
is
tr
ib
u
tio
n
o
f
an
n
u
al
ch
lo
r
i
n
e
g
as
d
em
an
d
d
ata
f
r
o
m
2
0
1
6
to
2
0
2
3
was
ev
alu
ated
u
s
in
g
th
e
k
o
lm
o
g
o
r
o
v
–
s
m
ir
n
o
v
an
d
cr
am
ér
–
v
o
n
m
is
es
test
s
,
as
d
ef
in
ed
in
(
8
)
an
d
(
1
0
)
.
T
h
ese
test
s
wer
e
u
s
ed
to
v
er
if
y
th
at
th
e
d
ata
d
is
tr
ib
u
t
io
n
alig
n
s
with
th
e
m
o
d
el
ass
u
m
p
tio
n
s
em
p
lo
y
e
d
in
th
e
an
al
y
s
is
.
T
h
e
r
esu
lts
o
f
th
ese
test
s
p
r
o
v
id
e
a
s
tr
o
n
g
b
a
s
is
f
o
r
d
eter
m
in
in
g
t
h
e
m
o
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I
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as f
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with
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i
s
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(
1
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=
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(
+
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ℎ
(1
7
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
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f
&
C
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m
m
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T
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
2
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6
I
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t J I
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,
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15
,
No
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3
,
Sep
tem
b
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20
26
:
1
0
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(
a)
(
b
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f
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im
als.
DATA AV
AI
L
AB
I
L
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Y
T
h
e
d
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th
at
s
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f
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m
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estrictio
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ap
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.
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s
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th
e
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m
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o
f
PDAM
.
RE
F
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R
E
NC
E
S
[
1
]
O
.
I
.
D
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e
z
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e
B
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.
M
o
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.
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2
]
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d
D
.
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[
3
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C
.
P
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La
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V
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(
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9
0
0
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-
9.
[
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