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c
ial
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telli
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se
s
M
a
n
h
a
tt
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(M
D),
a
g
o
o
d
a
n
d
sim
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,
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v
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ri
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t
o
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e
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m
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e
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s
wh
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re
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ro
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ime
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tes
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d
o
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re
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se
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a
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a
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trate
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s
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k
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ifi
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ll
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it
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o
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d
v
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lu
e
f
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c
a
lcu
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lt
s,
a
n
d
a
tt
e
m
p
ted
t
o
imp
r
o
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e
th
is
v
a
l
u
e
in
v
a
rio
u
s
wa
y
s.
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fo
r
tu
n
a
tely
,
to
o
u
r
k
n
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wle
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g
e
,
n
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n
e
o
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th
e
p
re
se
n
ted
re
se
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rc
h
h
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s
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e
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b
le
to
fin
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l
p
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th
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ll
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is
w
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rk
d
isc
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ss
e
s
th
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d
e
tailed
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n
s
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o
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re
late
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fa
c
to
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th
a
t
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n
tri
b
u
te
to
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ts
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a
k
n
e
ss
.
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is
p
a
p
e
r
d
isc
o
v
e
r
e
d
th
a
t
th
e
d
istri
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ti
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f
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v
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with
i
n
th
e
d
o
m
a
in
,
n
o
t
lo
w
b
o
u
n
d
v
a
l
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e
s,
is
th
e
c
rit
ica
l
issu
e
th
a
t
c
o
m
p
l
ica
tes
th
e
se
a
rc
h
.
Th
e
M
D'
s
su
m
m
a
ti
o
n
m
e
t
h
o
d
fo
r
a
ll
ti
les
h
a
s
a
n
imp
a
c
t
o
n
t
h
e
c
a
lcu
la
ted
d
u
p
li
c
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ti
o
n
v
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lu
e
s.
Th
e
to
tal
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u
m
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e
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n
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d
e
s i
n
t
h
e
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m
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l
p
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lso
a
ff
e
c
ts t
h
e
se
a
rc
h
p
e
rfo
rm
a
n
c
e
.
K
ey
w
o
r
d
s
:
Do
m
ain
n
o
d
e
Heu
r
is
tic
Ma
n
h
attan
d
is
tan
ce
Op
tim
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n
Path
f
in
d
in
g
Sli
d
e
tiles
p
u
zz
le
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC BY
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mo
h
am
m
ed
Na
y
ef
Al
R
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ai
Dep
ar
tm
en
t o
f
So
f
twar
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E
n
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in
g
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Facu
lty
o
f
I
n
f
o
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m
atio
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T
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n
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lo
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y
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ar
q
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Un
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Z
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J
o
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m
ail:
r
ef
ai@
zu
.
ed
u
.
jo
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
Ma
n
h
atta
n
d
is
tan
ce
(
MD
)
,
also
k
n
o
wn
as
th
e
tax
ica
b
d
is
tan
ce
o
r
L
1
d
is
tan
ce
,
is
a
m
ea
s
u
r
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o
f
th
e
d
is
tan
ce
b
etwe
en
two
p
o
in
ts
in
a
g
r
id
-
lik
e
s
y
s
tem
wh
er
e
m
o
v
em
en
t
is
r
estricte
d
to
h
o
r
izo
n
tal
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d
v
er
tical
d
ir
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tio
n
s
.
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t
is
n
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m
ed
af
te
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t
h
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g
r
id
-
lik
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s
tr
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t
lay
o
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t
o
f
Ma
n
h
attan
[
1
]
,
[
2
]
.
T
h
e
MD
b
etwe
en
two
p
o
in
ts
(
x
1
,
y
1
)
an
d
(
x
2
,
y
2
)
is
d
ef
in
e
d
as
:
|
1
−
2
|
+
|
1
−
2
|
;
wh
er
e
"|
"
r
e
p
r
esen
ts
th
e
ab
s
o
lu
te
v
alu
e.
T
h
e
r
esu
lt
is
th
e
s
u
m
o
f
th
e
a
b
s
o
lu
te
d
if
f
er
en
ce
s
b
etwe
en
th
e
x
-
co
o
r
d
in
ates a
n
d
th
e
y
-
c
o
o
r
d
in
ates o
f
t
h
e
two
p
o
in
ts
[
3
]
.
Fo
r
ex
am
p
le,
th
e
MD
b
etwe
en
(
1
,
2
)
an
d
(
4
,
6
)
is
:
|
1
−
4
|
+
|
2
−
6
|
=
3
+
4
=
7
.
No
te
th
at
th
e
MD
is
alwa
y
s
g
r
ea
ter
th
an
o
r
eq
u
al
to
th
e
E
u
clid
ea
n
d
is
tan
ce
(
th
e
s
tr
aig
h
t
-
lin
e
d
is
tan
ce
b
etwe
en
two
p
o
i
n
ts
)
,
an
d
it
is
co
m
m
o
n
ly
u
s
ed
in
a
p
p
licatio
n
s
s
u
ch
as
im
ag
e
p
r
o
ce
s
s
in
g
,
co
m
p
u
ter
v
is
io
n
,
an
d
m
ac
h
in
e
lear
n
in
g
[
4
]
,
[
5
]
.
MD
is
a
g
o
o
d
h
eu
r
is
tic
u
s
ed
in
m
an
y
ty
p
es
o
f
r
esear
ch
f
iel
d
s
lik
e
d
ata
m
in
in
g
[
6
]
,
[
7
]
,
m
ac
h
in
e
lear
n
in
g
[
8
]
,
f
ac
e
r
ec
o
g
n
itio
n
[
9
]
,
a
n
d
p
ath
f
i
n
d
in
g
[
1
0
]
.
I
t
is
s
im
p
le
an
d
n
ee
d
s
a
s
m
all
am
o
u
n
t
o
f
ca
lcu
lati
o
n
.
A
ls
o
,
it
ap
p
ea
r
s
Evaluation Warning : The document was created with Spire.PDF for Python.
2424
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N
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2
2
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2
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8
9
3
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I
n
t J Ar
tif
I
n
tell
,
Vo
l.
1
4
,
No
.
3
,
J
u
n
e
2
0
2
5
:
2
4
2
3
-
2
4
3
2
b
etter
in
m
an
y
r
esear
ch
co
m
p
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ed
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o
th
er
h
e
u
r
is
tics
lik
e
E
u
clid
ea
n
d
is
tan
ce
[
9
]
.
MD
h
eu
r
is
tic
is
u
s
ed
to
ca
lcu
late
th
e
ab
s
o
lu
te
d
if
f
e
r
en
ce
b
etwe
en
two
v
alu
es
as
in
(
1
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.
W
h
en
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er
e
ar
e
m
a
n
y
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es
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ciate
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with
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ch
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th
er
[
1
1
]
,
[
1
2
]
,
MD
will
b
e
th
e
s
u
m
o
f
th
em
as
in
(
2
)
.
An
ex
am
p
le
f
o
r
MD
s
u
m
is
s
lid
e
tile
p
u
zz
les
wh
ich
will c
alcu
late
ea
ch
eq
u
iv
alen
t
p
air
in
d
if
f
er
en
t lo
ca
tio
n
s
f
o
r
t
h
e
two
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o
d
es a
n
d
th
e
n
s
u
m
th
e
r
esu
lt f
o
r
all
tiles
.
=
|
−
|
(
1
)
=
∑
|
−
|
−
1
=
1
(
2
)
Un
f
o
r
tu
n
atel
y
,
MD
is
n
o
t
p
r
ac
tical
alo
n
e
to
f
in
d
a
g
o
al
f
o
r
a
lar
g
e
s
lid
in
g
tile
p
u
zz
le.
As
t
h
e
d
esire
d
q
u
ality
b
o
u
n
d
p
r
o
d
u
ce
will
n
o
t
ac
ce
p
t
th
e
s
o
lu
tio
n
as
q
u
ick
ly
as
p
o
s
s
ib
le
[
1
3
]
,
o
th
er
h
eu
r
is
tics
r
elate
d
to
th
e
d
o
m
ain
u
s
ed
with
MD
in
s
lid
e
tile
p
u
zz
les
lik
e
m
is
p
lace
d
tile,
an
d
lin
ea
r
co
n
f
lict
(
L
C
)
[
1
4
]
.
Pre
v
io
u
s
s
tu
d
ies
f
o
cu
s
o
n
MD
wea
k
n
ess
r
elate
d
to
th
e
lo
w
b
o
u
n
d
ar
y
v
al
u
e
g
en
er
ated
at
th
e
ca
lcu
latio
n
f
o
r
ac
tu
al
s
o
lu
tio
n
co
s
t
[
1
5
]
.
So
m
e
s
tu
d
ies
f
o
cu
s
o
n
im
p
r
o
v
in
g
MD
b
y
ca
lcu
latin
g
wit
h
o
th
er
h
eu
r
is
tics
lik
e
m
is
s
tile
an
d
LC
[
1
2
]
,
[
1
6
]
.
O
th
er
s
tu
d
ies
f
o
c
u
s
o
n
in
v
en
ti
n
g
n
ew
h
e
u
r
is
tics
s
im
ilar
to
M
Ds
b
u
t
m
o
r
e
e
f
f
ec
tiv
e
lik
e
wal
k
in
g
d
is
tan
ce
(
W
D)
[
1
7
]
.
Oth
er
s
ch
a
n
g
e
t
h
e
way
to
tally
as
in
th
e
d
atab
ase
p
atter
n
wh
ich
p
r
o
v
id
es
th
e
b
est
e
x
is
tin
g
ad
m
is
s
ib
le
h
eu
r
is
tics
f
o
r
th
is
s
lid
e
tile
p
u
z
zle
[
1
8
]
.
T
h
e
s
tu
d
y
em
p
lo
y
s
a
n
o
v
el
m
et
h
o
d
f
o
r
h
y
b
r
id
izin
g
t
h
e
Vio
la
-
J
o
n
es
f
ac
e
d
etec
tio
n
alg
o
r
it
h
m
to
tr
ac
k
an
d
id
en
tify
h
u
m
a
n
f
ac
es in
v
i
d
e
o
s
eq
u
en
ce
s
u
s
in
g
MD
m
ea
s
u
r
e
eq
u
atio
n
s
[
1
9
]
.
Sli
d
e
tile
p
u
zz
les,
also
k
n
o
wn
as
s
lid
in
g
p
u
zz
les
o
r
s
lid
in
g
tile
p
u
zz
les,
ar
e
a
t
y
p
e
o
f
p
u
z
zle
g
am
e
wh
er
e
th
e
p
lay
er
m
u
s
t sli
d
e
til
es o
r
b
lo
ck
s
with
in
a
co
n
f
in
ed
s
p
ac
e
to
r
ea
r
r
an
g
e
th
em
in
to
a
s
p
ec
if
ic
p
atter
n
o
r
im
ag
e.
T
h
e
p
u
zz
les
ty
p
ically
co
n
s
is
t
o
f
a
g
r
id
o
f
s
q
u
ar
e
tile
s
o
r
b
lo
ck
s
,
with
o
n
e
em
p
ty
s
p
ac
e
th
at
allo
ws
f
o
r
th
e
s
lid
in
g
o
f
ad
jace
n
t
tiles
.
T
h
e
o
b
jectiv
e
o
f
th
e
g
a
m
e
is
to
r
ea
r
r
an
g
e
th
e
tiles
s
o
th
at
th
ey
f
o
r
m
a
s
p
ec
if
ic
p
atter
n
o
r
im
ag
e,
o
f
ten
b
y
m
o
v
in
g
th
em
ar
o
u
n
d
i
n
a
s
p
ec
if
ic
s
eq
u
en
ce
.
T
h
e
p
u
zz
les
ca
n
r
an
g
e
in
d
if
f
icu
lty
,
with
s
o
m
e
r
eq
u
ir
in
g
o
n
ly
a
f
ew
m
o
v
es
to
s
o
lv
e
an
d
o
th
er
s
b
ei
n
g
m
u
ch
m
o
r
e
co
m
p
le
x
.
Sli
d
e
tile
p
u
zz
les
h
av
e
b
ee
n
po
p
u
lar
f
o
r
m
an
y
y
ea
r
s
,
with
s
o
m
e
o
f
th
e
ea
r
lies
t
v
er
s
io
n
s
d
atin
g
b
ac
k
to
th
e
late
1
9
th
ce
n
tu
r
y
.
T
h
ey
h
av
e
s
in
ce
b
ee
n
ad
ap
te
d
to
a
wid
e
r
an
g
e
o
f
f
o
r
m
ats,
in
clu
d
in
g
elec
tr
o
n
i
c
g
am
es,
m
o
b
ile
ap
p
s
,
an
d
o
n
l
in
e
v
er
s
io
n
s
.
So
m
e
p
o
p
u
lar
v
a
r
iatio
n
s
o
f
th
e
p
u
z
zle
in
clu
d
e
th
e
1
5
-
p
u
zz
le,
th
e
2
4
-
p
u
zz
le,
an
d
th
e
R
u
b
ik
'
s
C
u
b
e.
Acc
o
r
d
in
g
to
Al
-
R
ef
ai
an
d
J
am
h
awi
[
2
0
]
,
t
h
e
m
em
o
r
y
u
s
ag
e
in
s
lid
e
tile
p
u
zz
les
was
c
o
m
p
a
r
ed
u
s
in
g
d
ep
th
-
f
ir
s
t
f
r
o
n
tier
s
ea
r
ch
es,
b
lin
d
alg
o
r
ith
m
s
,
an
d
b
r
ea
d
t
h
-
f
ir
s
t
f
r
o
n
tier
s
ea
r
ch
e
s
as a
n
ex
am
p
le
o
f
a
cy
clic
g
r
a
p
h
.
T
h
e
b
id
ir
ec
tio
n
al
s
ea
r
ch
alg
o
r
ith
m
A*
(
B
A*
)
with
th
r
ee
h
eu
r
is
tics
,
s
u
ch
as
L
C
,
MD
,
an
d
W
D,
h
as
b
ee
n
u
s
ed
tr
ied
to
co
n
tr
o
l
s
o
l
v
e
th
e
f
if
tee
n
p
u
zz
le
p
r
o
b
lem
i
n
th
e
r
esear
ch
a
r
ticle
[
2
1
]
.
Au
th
o
r
s
th
e
lar
g
e
s
tate
s
p
ac
e.
T
h
e
alg
o
r
ith
m
is
ef
f
ec
tiv
ely
ass
is
ted
b
y
th
e
t
h
r
ee
af
o
r
em
en
tio
n
ed
h
eu
r
is
tics
in
r
e
d
u
cin
g
th
e
n
u
m
b
er
o
f
g
en
er
ated
s
tates
an
d
ex
p
a
n
d
in
g
f
ewe
r
n
o
d
es.
Yiu
et
a
l.
[
2
2
]
i
n
tr
o
d
u
ce
d
a
n
o
v
el
d
esig
n
a
n
d
o
p
tim
izatio
n
m
eth
o
d
f
o
r
m
u
lti
-
weig
h
ted
-
h
eu
r
is
tics
f
u
n
ctio
n
(
MWH)
s
ea
r
ch
in
g
al
g
o
r
ith
m
s
ca
lled
ev
o
l
u
tio
n
ar
y
h
eu
r
is
tic
A*
s
ea
r
ch
(
E
HA*
)
to
r
ed
u
ce
t
h
e
ef
f
o
r
t
o
n
h
eu
r
is
tic
f
u
n
ctio
n
d
esig
n
v
ia
g
en
etic
alg
o
r
ith
m
(
GA)
,
o
p
tim
ize
th
e
p
er
f
o
r
m
an
c
e
o
f
A*
s
ea
r
ch
a
n
d
its
v
a
r
ian
ts
,
i
n
clu
d
in
g
b
u
t
n
o
t
lim
ited
to
W
A*
an
d
m
u
lti
-
h
e
u
r
is
tic
A*
(
MH
A
)
*
,
an
d
g
u
ar
an
tee
th
e
co
m
p
leten
ess
an
d
o
p
tim
ality
.
T
h
e
p
r
im
ar
y
g
o
al
o
f
[
2
3
]
w
as to
u
s
e
th
e
s
n
a
k
e
g
am
e
as a
co
m
p
ar
ativ
e
to
o
l to
an
aly
ze
th
e
v
ar
iatio
n
s
in
s
ea
r
ch
alg
o
r
ith
m
o
p
tim
ality
b
etw
ee
n
h
u
m
an
a
g
en
ts
an
d
a
r
tific
ial
in
tellig
en
ce
(
AI
)
.
T
h
is
p
ap
er
f
o
cu
s
es
o
n
th
e
d
o
m
ain
o
f
t
h
e
s
lid
e
tile
p
u
zz
le
a
n
d
th
e
MD
ca
lc
u
lated
v
alu
e
f
o
r
ea
ch
n
o
d
e
i
n
d
etail
to
f
in
d
th
e
m
ain
wea
k
n
ess
r
ea
s
o
n
f
o
r
its
v
alu
e
t
o
ap
p
r
o
v
e
o
r
r
ejec
t th
e
law
b
o
u
n
d
ar
y
r
ea
s
o
n
.
T
h
is
s
tu
d
y
will
b
e
ex
p
er
im
en
tal
an
d
r
ely
o
n
s
lid
e
tile
p
u
zz
les
s
ize
5
×
2
an
d
3
×
3
to
b
e
th
e
c
ase
s
tu
d
y
.
MD
h
eu
r
is
tic
will
b
e
co
m
p
u
te
d
b
y
co
u
n
tin
g
t
h
e
n
u
m
b
er
o
f
g
r
id
u
n
its
th
at
ea
ch
tile
is
d
is
p
lace
d
f
r
o
m
its
g
o
al
p
o
s
itio
n
an
d
th
e
n
s
u
m
m
in
g
all
tile
v
alu
es
with
o
u
t
th
e
b
lan
k
l
o
ca
tio
n
[
1
8
]
.
MD
ef
f
icien
t
co
m
p
u
tatio
n
p
o
s
s
ib
le
s
im
p
lifie
d
p
r
o
b
lem
as in
d
iv
id
u
al
tiles
ca
n
m
o
v
e
in
d
ep
en
d
en
tly
o
f
ea
ch
o
th
er
[
2
4
]
–
[
2
6
]
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
e
r
esear
ch
er
s
b
e
g
an
th
is
r
esear
ch
b
y
r
ea
d
in
g
p
r
ev
io
u
s
r
esear
ch
in
o
r
d
er
to
f
i
n
d
o
u
t
th
e
latest
d
ev
elo
p
m
e
n
ts
in
s
cien
ce
in
th
i
s
f
ield
,
as e
x
p
lain
ed
in
th
e
p
r
ev
io
u
s
s
ec
tio
n
.
T
h
e
r
esear
ch
er
s
th
en
wo
r
k
ed
o
n
all
th
e
d
o
m
ain
s
o
f
th
e
s
lid
e
tile
p
u
zz
le
f
o
r
th
e
ca
s
e
s
tu
d
y
,
aim
in
g
to
d
eter
m
in
e
th
e
n
o
d
e
lev
el,
p
ath
,
an
d
MD
v
alu
e.
T
h
e
g
o
al
n
o
d
e
was
lo
ca
ted
at
l
ev
el
0
,
wh
ich
is
co
n
s
id
er
ed
th
e
r
ef
er
en
ce
f
o
r
all
p
ap
er
ca
lc
u
latio
n
s
an
d
r
esu
lts
.
Af
ter
all
tr
ials
an
d
ca
lcu
latio
n
s
,
r
esear
ch
er
s
wr
ite
d
o
wn
t
h
e
r
esu
lts
an
d
r
ec
o
m
m
en
d
ati
o
n
s
.
T
h
e
f
o
llo
win
g
s
u
b
-
s
ec
tio
n
s
d
escr
ib
e
th
e
ca
lc
u
latio
n
s
u
s
ed
to
o
b
tain
th
e
r
es
u
lts
.
2
.
1
.
Do
m
a
in
c
o
llect
i
o
n
T
h
is
r
esear
ch
m
eth
o
d
tak
es th
e
in
itial n
o
d
e
f
o
r
th
e
ca
s
e
s
tu
d
y
as sh
o
wn
in
Fig
u
r
e
1
th
en
g
e
n
er
ates a
ll
th
eir
r
elate
d
n
o
d
es
th
at
ca
n
b
e
r
ea
ch
e
d
b
y
leg
al
m
o
v
es
t
o
ex
tr
ac
t
all
th
e
r
ea
ch
a
b
le
d
o
m
ain
s
.
No
d
es
wer
e
g
en
er
ated
b
y
u
s
in
g
a
b
r
ea
d
t
h
-
f
ir
s
t
s
ea
r
ch
with
f
r
o
n
tier
b
o
u
n
d
ar
y
[
2
0
]
.
T
h
e
c
o
llected
d
ata
is
s
av
ed
in
an
ar
r
ay
o
f
ar
r
a
y
s
f
o
r
ea
ch
le
v
el
n
o
d
e
i
n
an
o
r
d
er
l
y
way
f
r
o
m
g
o
al
le
v
el
to
m
a
x
im
u
m
r
ea
ch
ab
le
n
o
d
es
lev
el
.
Fig
u
r
e
1
(
a)
s
h
o
ws s
lid
e
tile p
u
zz
le
g
o
al
s
tate
f
o
r
3
×
3
an
d
Fig
u
r
e
1
(
b
)
s
h
o
ws s
lid
e
tile p
u
zz
le
g
o
al
s
tate
f
o
r
2
×
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
Th
e
ma
in
w
ea
kn
ess
es o
f u
s
in
g
M
a
n
h
a
tta
n
d
is
ta
n
ce
fo
r
s
o
lvin
g
s
lid
in
g
…
(
Mo
h
a
mme
d
N
a
ye
f
A
l R
efa
i
)
2425
1
2
3
4
5
6
7
8
(
a)
1
2
3
4
5
6
7
8
9
(
b
)
Fig
u
r
e
1.
Sli
d
e
tile p
u
zz
le
g
o
al
s
tate
f
o
r
(
a)
3
×
3
an
d
(
b
)
2
×
5
2
.
2
.
M
a
nh
a
t
t
a
n dis
t
a
nce
ca
l
cula
t
io
n
MD
was
ca
lcu
lated
f
o
r
ea
ch
n
o
d
e
in
th
e
two
d
o
m
ain
s
f
o
r
th
e
ca
s
e
s
tu
d
y
co
m
p
ar
is
o
n
b
et
wee
n
ea
ch
n
o
d
e
an
d
th
e
g
o
al
n
o
d
e.
E
ac
h
tile
co
o
r
d
in
ates
(
x
1
,
y
1
)
in
an
y
n
o
d
e
co
m
p
a
r
ed
to
its
g
o
al
n
o
d
e
co
o
r
d
in
ates
(
x
0
,
y
0
)
.
T
h
e
s
u
m
f
o
r
all
tiles
co
n
s
id
er
s
th
e
f
i
n
al
MD
h
e
u
r
is
tic
r
esu
lt
f
o
r
ea
ch
n
o
d
e
wh
ich
is
u
s
ed
to
g
u
id
e
to
r
ea
ch
th
e
g
o
al
n
o
d
e.
T
h
e
d
ata
wer
e
co
llected
to
c
h
ec
k
t
h
e
d
u
p
licatio
n
o
f
v
alu
es
at
d
if
f
er
en
t
lev
els
an
d
its
ef
f
ec
t
o
n
MD
h
eu
r
is
tic
o
p
tim
al
p
ath
g
u
id
in
g
.
Als
o
,
ex
tr
ac
t
th
e
f
ir
s
t
tile
f
r
o
m
ea
ch
n
o
d
e
g
en
er
ated
to
f
in
d
th
e
r
a
n
g
e
o
f
lev
el
f
o
u
n
d
o
n
an
d
at
th
e
s
am
e
tim
e
MD
v
al
u
e
f
o
r
th
em
.
T
h
e
em
p
ty
tile
d
o
es
n
o
t
in
clu
d
e
at
MD
ca
lcu
late
v
alu
e
b
ec
au
s
e
it
in
cr
ea
s
es
th
e
tab
le
MD
r
esu
lt
r
an
g
e
an
d
at
th
e
s
am
e
tim
e
in
cr
ea
s
es
th
e
r
an
g
e
o
f
lev
els
wh
er
e
th
e
s
am
e
v
alu
e
ap
p
ea
r
s
.
2
.
3
.
No
des
in ea
ch
pa
t
h
All
n
o
d
es
at
ea
ch
lev
el
ar
e
co
n
s
id
er
ed
as
i
n
itial
n
o
d
es
f
o
r
th
e
p
r
ev
i
o
u
s
lev
el
th
en
ex
tr
ac
t
t
h
e
allo
wed
o
p
tim
al
p
ath
n
o
d
es
f
r
o
m
th
e
m
to
th
e
g
o
al
n
o
d
e.
T
h
is
ch
ec
k
will
r
em
o
v
e
th
e
n
o
d
es
th
at
f
al
l
in
lev
el
m
ax
im
u
m
th
an
th
e
in
itial n
o
d
e
o
r
ev
en
if
its
n
eig
h
b
o
r
is
in
th
e
s
am
e
lev
el
th
er
e
will n
o
t b
e
a
d
ir
ec
t o
p
tim
al
p
ath
b
etwe
en
th
em
.
T
h
e
l
o
ca
l
m
ax
im
a
n
o
d
e
s
u
n
d
er
th
e
in
itial
n
o
d
e
lev
el
will
b
e
r
em
o
v
e
d
as
th
ey
ca
n
’
t c
o
n
s
id
er
th
e
o
p
tim
al
p
ath
f
o
r
th
e
n
o
d
e
c
h
o
s
en
.
Af
te
r
r
em
o
v
in
g
all
lo
ca
l
m
ax
im
a
n
o
d
es
in
th
e
f
ir
s
t
b
elo
w
lev
el,
t
h
en
th
eir
p
ar
en
t
will
b
ec
o
m
e
l
o
ca
l m
ax
im
a
u
n
less
th
ey
f
all
in
th
e
in
itial n
o
d
e
p
ath
s
.
T
h
is
s
ce
n
ar
io
will
b
e
r
e
p
ea
t
ed
u
n
til r
ea
ch
es th
e
g
o
al
s
tate
wh
ich
will
ex
tr
ac
t
th
e
o
p
tim
al
p
at
h
n
o
d
es
f
r
o
m
th
e
in
itial
s
tate
to
th
e
g
o
al
s
tate.
T
h
e
wo
r
k
d
o
n
e
f
o
r
all
n
o
d
es
f
alls
at
a
lev
el
g
r
ea
te
r
th
an
lev
el
0
f
o
r
th
e
two
d
o
m
a
in
s
.
T
h
e
p
ath
s
e
x
tr
ac
ted
f
o
r
th
e
to
p
-
le
v
el
d
o
m
ain
s
n
o
d
e
test
f
o
r
MD
to
ch
ec
k
if
it
is
v
alu
e
o
p
tim
al
th
r
o
u
g
h
th
e
d
if
f
er
en
t le
v
els.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
D
o
m
a
in lev
els re
s
ult
T
h
e
d
o
m
ain
f
o
r
t
h
e
two
ca
s
e
s
tu
d
ies
was
co
llected
in
le
v
els
f
o
r
ea
c
h
lev
el
a
n
d
t
h
e
n
o
d
es
c
o
u
n
t
in
it,
as
s
h
o
wn
in
T
ab
le
s
1
an
d
2
.
T
h
e
lev
el
c
o
u
n
t
in
cr
ea
s
es
u
n
til
r
ea
ch
in
g
th
e
m
ax
im
u
m
co
u
n
t
at
lev
el
2
4
f
o
r
s
lid
e
tile
p
u
zz
le
3
×
3
,
v
alu
e
2
4
,
0
4
7
,
an
d
lev
el
3
6
f
o
r
s
lid
e
tile
p
u
zz
le
2
×
5
,
v
alu
e
1
3
3
,
1
0
7
.
T
h
e
d
o
m
ai
n
is
a
cy
cle
p
o
ly
g
o
n
with
1
2
ed
g
es a
r
o
u
n
d
ea
ch
n
o
d
e
[
2
0
]
.
T
ab
le
1
.
Sli
d
e
tile p
u
zz
le
3
×
3
lev
els co
u
n
t n
o
d
es
Le
v
e
l
n
o
.
N
o
d
e
s
c
o
u
n
t
Le
v
e
l
n
o
.
N
o
d
e
s
c
o
u
n
t
Le
v
e
l
n
o
.
N
o
d
e
s
c
o
u
n
t
Le
v
e
l
n
o
.
N
o
d
e
s
c
o
u
n
t
0
1
8
1
1
6
16
4
,
4
8
5
24
24
,
047
1
2
9
1
5
2
17
5
,
6
3
8
25
15
,
578
2
4
10
2
8
6
18
9
,
5
2
9
26
14
,
560
3
8
11
3
9
6
19
10
,
878
27
6
,
2
7
4
4
16
12
7
4
8
20
16
,
993
28
3
,
9
1
0
5
20
13
1
,
0
2
4
21
17
,
110
29
7
6
0
6
39
14
1
,
8
9
3
22
23
,
952
30
2
2
1
7
62
15
2
,
5
1
2
23
20
,
224
31
2
T
ab
le
2
.
Sli
d
e
tile p
u
zz
le
5
×
2
lev
els co
u
n
t n
o
d
es
Le
v
e
l
n
o
.
N
o
d
e
s
c
o
u
n
t
Le
v
e
l
n
o
.
N
o
d
e
s
c
o
u
n
t
Le
v
e
l
n
o
.
N
o
d
e
s
c
o
u
n
t
Le
v
e
l
n
o
.
N
o
d
e
s
c
o
u
n
t
1
14
8
5
1
28
5
4
,
5
9
7
42
6
0
,
1
1
9
1
2
15
1
,
2
3
2
29
6
5
,
9
6
6
43
4
5
,
8
4
0
2
3
16
1
,
7
8
3
30
7
8
,
4
3
3
44
3
3
,
4
2
2
3
6
17
2
,
5
3
0
31
9
1
,
7
2
5
45
2
3
,
2
2
3
4
11
18
3
,
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6
7
32
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5
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4
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9
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6
0
2
27
4
4
,
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6
4
41
7
5
,
7
4
2
55
2
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2426
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M
a
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M
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2429
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Evaluation Warning : The document was created with Spire.PDF for Python.
2430
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CO
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k
n
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es
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at
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ch
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t
h
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s
li
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til
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p
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.
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h
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d
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d
r
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as
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s
f
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d
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t
h
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r
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wo
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h
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p
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p
p
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th
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t l
o
w
b
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n
o
t
th
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cr
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l iss
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t
h
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t c
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at
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.
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m
m
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ti
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f
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f
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th
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f
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h
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n
d
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f
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f
u
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x
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d
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d
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to
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t
h
e
g
o
a
l
s
ta
te
in
s
li
d
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til
e
p
u
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es.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
is
r
esear
ch
is
f
u
n
d
e
d
b
y
th
e
Dea
n
s
h
ip
o
f
Scien
tific
R
esear
ch
in
Z
ar
q
a
Un
iv
er
s
ity
,
J
o
r
d
an
.
AUTHO
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NT
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B
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h
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u
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C
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ax
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.
3
,
J
u
n
e
2
0
2
5
:
2
4
2
3
-
2
4
3
2
Dr
.
Ze
y
a
d
Mo
h
a
m
m
e
d
J
a
m
h
a
wi
is
P
h
.
D
.
in
c
o
m
p
u
ter
i
n
fo
rm
a
ti
o
n
sy
ste
m
s
(a
rti
ficia
l
in
tell
ig
e
n
c
e
),
Om
d
u
rm
a
n
Isla
m
ic
Un
i
v
e
rsity
,
S
u
d
a
n
2
0
1
3
-
2
0
1
6
.
M
a
ste
r
d
e
g
re
e
in
c
o
m
p
u
ter
i
n
fo
rm
a
ti
o
n
sy
ste
m
,
Ar
a
b
Ac
a
d
e
m
y
fo
r
Ba
n
k
in
g
a
n
d
F
i
n
a
n
c
e
,
Am
m
a
n
,
Jo
rd
a
n
2
0
0
9
-
2
0
1
2
.
P
r
o
fe
ss
io
n
a
l
d
ip
lo
m
a
sp
e
c
ializa
ti
o
n
in
E
-
g
o
v
e
rn
m
e
n
t,
J
o
rd
a
n
ian
Un
i
v
e
rsity
,
J
o
rd
a
n
2
0
0
7
-
2
0
0
8
.
B
.
S
.
in
c
o
m
p
u
ter
sc
ien
c
e
,
M
u
’ta
Un
i
v
e
rsity
,
Al
k
a
ra
k
,
Jo
r
d
a
n
,
1
9
8
8
-
9
2
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
z
_
jam
h
a
wi@a
su
.
e
d
u
.
j
o
.
Dr
.
Ahm
e
d
Ali
O
t
o
o
m
is
c
h
a
irma
n
o
f
De
p
a
rtme
n
t
o
f
Cy
b
e
rse
c
u
rit
y
a
n
d
C
lo
u
d
Co
m
p
u
ti
n
g
in
Ap
p
li
e
d
S
c
ien
c
e
P
riv
a
te
U
n
iv
e
rsit
y
,
P
h
.
D
.
in
c
o
m
p
u
ter
sc
ien
c
e
(
d
istri
b
u
te
d
sy
ste
m
s) Am
m
a
n
Ara
b
Un
iv
e
rsity
fo
r
g
ra
d
u
a
te stu
d
ies
2
0
0
7
,
m
a
ste
r
d
e
g
re
e
in
c
o
m
p
u
ter sc
ien
c
e
,
USA.
B
.
S
.
in
c
o
m
p
u
ter
sc
ien
c
e
,
M
u
’ta
Un
i
v
e
rsity
,
Al
k
a
ra
k
,
Jo
r
d
a
n
,
1
9
8
8
-
9
2
.
He
c
a
n
b
e
c
o
n
tac
te
d
a
t
e
m
a
il
:
a
_
o
to
o
m
@a
su
.
e
d
u
.
jo
.
Ada
i
Al
-
Mo
m
a
n
i
re
c
e
iv
e
d
t
h
e
B.
S
c
.
d
e
g
re
e
s
i
n
c
o
m
p
u
ter
sc
ien
c
e
fro
m
Ja
d
a
ra
Un
iv
e
rsity
,
Jo
r
d
a
n
,
M
.
S
c
.
d
e
g
re
e
s
in
i
n
fo
rm
a
ti
o
n
tec
h
n
o
l
o
g
y
fr
o
m
Un
iv
e
rsit
y
Ten
a
g
a
Na
sio
n
a
l
,
M
a
lay
sia
,
in
2
0
1
0
a
n
d
2
0
1
6
,
re
sp
e
c
ti
v
e
ly
a
n
d
th
e
P
h
.
D.
d
e
g
re
e
in
c
o
m
p
u
ter
sc
ien
c
e
s
fro
m
Un
iv
e
rsiti
S
u
lt
a
n
Zain
a
l
A
b
id
in
,
M
a
lay
sia
in
2
0
2
3
.
His
re
se
a
rc
h
in
t
e
re
sts
in
c
lu
d
e
i
n
tern
e
t
o
f
th
in
g
s
a
n
d
c
o
m
p
u
ter i
n
fo
rm
a
ti
o
n
sy
ste
m
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
o
a
lmo
m
a
n
i@z
u
.
e
d
u
.
jo
.
As
so
c
.
Pro
f.
H
a
y
e
l
K
h
a
fa
je
h
o
b
tai
n
e
d
h
is
P
h
.
D.
in
c
o
m
p
u
ter
i
n
fo
rm
a
ti
o
n
sy
ste
m
s
in
2
0
0
8
in
Jo
r
d
a
n
.
He
jo
in
e
d
Zarq
a
Un
iv
e
rsit
y
,
J
o
rd
a
n
i
n
2
0
0
9
.
In
2
0
1
0
,
h
e
se
rv
e
d
a
s
h
e
a
d
o
f
th
e
CIS
De
p
a
rtme
n
t
fo
r
two
y
e
a
rs.
S
i
n
c
e
a
c
a
d
e
m
ic
y
e
a
r
2
0
1
4
/2
0
1
5
,
h
e
h
a
s
se
rv
e
d
a
n
d
h
e
sti
ll
a
s
th
e
v
ice
d
e
a
n
o
f
t
h
e
IT
Co
l
leg
e
a
t
Z
a
rq
a
.
He
h
a
s
wo
rk
e
d
fo
r
2
3
y
e
a
r
s
in
th
e
e
d
u
c
a
ti
o
n
a
l
f
ield
a
s
p
ro
g
ra
m
m
e
r,
tea
c
h
e
r’s
su
p
e
rv
iso
r,
h
e
a
d
o
f
I
T
d
iv
isio
n
,
a
n
d
m
a
n
a
g
e
r
o
f
ICDL
Ce
n
ter.
He
h
a
s
p
u
b
li
sh
e
d
m
a
n
y
e
d
u
c
a
ti
o
n
a
l
c
o
m
p
u
ter
b
o
o
k
s
fo
r
th
e
M
i
n
istry
o
f
E
d
u
c
a
ti
o
n
in
Jo
r
d
a
n
.
I
n
2
0
1
3
,
h
e
p
u
b
li
sh
e
d
h
is
I
n
tro
d
u
c
ti
o
n
to
Ja
v
a
P
ro
g
ra
m
m
in
g
b
o
o
k
f
o
r
u
n
i
v
e
rsity
stu
d
e
n
ts.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
in
f
o
rm
a
ti
o
n
re
tri
e
v
a
l,
A
I
,
a
n
d
E
-
lea
rn
in
g
.
He
is
th
e
a
u
th
o
r
o
f
se
v
e
ra
l
p
u
b
l
ica
ti
o
n
s
o
n
t
h
e
se
to
p
ics
.
He
c
a
n
b
e
c
o
n
tac
t
e
d
a
t
e
m
a
il
:
h
a
y
e
lk
h
@z
u
.
e
d
u
.
j
o
.
Dr
.
Is
sa
Ato
u
m
is
m
e
m
b
e
r
in
F
a
c
u
lt
y
o
f
In
f
o
rm
a
ti
o
n
Tec
h
n
o
lo
g
y
,
P
h
il
a
d
e
l
p
h
ia
Un
iv
e
rsity
,
P
h
.
D
.
i
n
so
ftwa
re
e
n
g
in
e
e
rin
g
,
Un
ima
s
Un
iv
e
rsit
y
M
a
l
a
y
sia
,
2
0
1
5
.
M
a
ste
r
d
e
g
re
e
in
c
o
m
p
u
ter
in
f
o
rm
a
ti
o
n
sy
ste
m
,
P
h
il
a
d
e
lp
h
ia
Un
iv
e
rsit
y
,
Jo
r
d
a
n
2
0
1
2
.
B
.
S
.
in
c
o
m
p
u
ter
sc
ien
c
e
,
Ya
rm
o
u
k
Un
i
v
e
rsity
,
Jo
r
d
a
n
,
1
9
9
7
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
i
a
to
u
m
@P
h
i
lad
e
lp
h
ia.ed
u
.
jo
.
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