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v
id
ed
s
o
m
e
n
o
v
el
w
a
y
s
to
en
h
a
n
ce
t
h
e
s
ec
u
r
it
y
o
f
th
e
P
la
y
f
a
ir
cip
h
er
[
7
]
.
E
n
cr
y
p
tio
n
ca
n
b
e
d
ef
in
ed
as
ch
an
g
i
n
g
t
h
e
o
r
ig
i
n
al
m
e
s
s
a
g
e
in
to
o
th
er
f
o
r
m
[
8
]
.
C
r
y
p
to
g
r
ap
h
y
ca
n
b
e
u
s
ed
a
n
d
d
ev
elo
p
ed
u
s
i
n
g
d
if
f
er
e
n
t
m
et
h
o
d
s
a
n
d
alg
o
r
it
h
m
s
b
u
t
s
o
m
e
al
g
o
r
it
h
m
s
n
ee
d
m
o
d
if
icat
io
n
to
f
it
an
y
la
n
g
u
a
g
e
s
,
b
ec
au
s
e
t
h
e
o
r
ig
i
n
al
f
o
r
m
at
o
f
al
g
o
r
ith
m
s
u
c
h
as
P
la
y
Fair
w
as
d
ev
elo
p
ed
,
u
s
ed
,
an
d
d
esi
g
n
e
d
f
o
r
E
n
g
li
s
h
lan
g
u
ag
e,
an
d
as
w
e
k
n
o
w
E
n
g
li
s
h
lan
g
u
a
g
e
h
a
s
o
n
l
y
2
6
alp
h
ab
ets
an
d
t
h
e
o
r
ig
i
n
al
P
la
y
Fair
h
a
s
a
5
x
5
tab
le
th
at
ca
n
s
u
p
p
o
r
t o
n
l
y
2
6
alp
h
ab
ets
w
it
h
t
w
o
le
tter
s
J
an
d
I
s
h
ar
e
th
e
s
a
m
e
ce
ll.
B
u
t
t
h
is
is
s
till
n
o
t
u
s
e
f
u
l
w
h
e
n
it
co
m
es
to
t
h
e
o
th
er
lan
g
u
a
g
es
a
n
d
ad
d
in
g
n
e
w
c
h
ar
ac
ter
s
,
s
y
m
b
o
ls
,
an
d
n
u
m
b
er
s
.
So
w
e
n
ee
d
to
d
ev
elo
p
s
o
m
et
h
i
n
g
w
h
ic
h
ca
n
ac
ce
p
t
an
y
n
u
m
b
er
o
f
c
h
ar
ac
ter
s
o
r
s
ig
n
s
f
o
r
ex
a
m
p
le
I
tal
ian
la
n
g
u
a
g
e
h
as
o
n
l
y
2
1
letter
s
,
A
r
ab
ic
2
8
,
R
u
s
s
ia
n
3
3
letter
s
[
9
-
1
1
]
.
Di
f
f
er
en
t
k
e
y
b
o
ar
d
s
,
d
ev
ices,
an
d
s
o
o
n
.
T
h
er
ef
o
r
e,
in
th
i
s
s
t
u
d
y
w
e
ai
m
to
d
esig
n
an
d
d
ev
elo
p
m
o
d
i
f
icati
o
n
th
a
n
ca
n
f
it
a
n
y
lan
g
u
a
g
es,
a
n
y
n
u
m
b
er
o
f
ch
ar
ac
ter
s
,
s
y
m
b
o
l
s
,
k
e
y
s
,
etc.
,
an
d
w
h
ic
h
ca
n
p
r
o
ce
s
s
b
lo
ck
s
o
f
m
o
r
e
th
a
n
t
wo
ch
ar
ac
ter
s
at
o
n
ce
.
T
h
is
m
o
d
if
icatio
n
s
h
o
u
ld
b
e
ea
s
y
to
u
s
e
a
n
d
s
i
m
p
le
as
p
o
s
s
ib
le,
av
o
id
co
m
p
lex
it
y
,
b
e
f
ast
an
d
ea
s
y
in
e
x
ec
u
tio
n
an
d
i
m
p
le
m
en
tatio
n
,
b
e
f
r
ee
o
f
c
o
m
p
le
x
it
y
,
a
v
o
id
er
r
o
r
s
,
an
d
b
e
s
tr
o
n
g
an
d
h
ar
d
to
b
r
ea
k
.
W
e
r
ev
iew
ed
s
ev
e
r
a
l stu
d
ies i
n
d
ica
tin
g
m
a
n
y
a
s
p
ec
ts
o
f th
e
s
u
b
ject
o
f th
e
s
tu
d
y:
S
af
w
at
Ha
m
ad
,
i
n
t
h
is
m
o
d
i
f
i
ca
tio
n
,
t
h
e
a
u
t
h
o
r
u
s
ed
a
g
r
id
o
f
8
X8
co
d
o
n
m
atr
ix
u
s
i
n
g
i
n
t
er
w
ea
v
in
g
o
n
DN
A
–
e
n
co
d
e
d
at
a;
th
is
b
io
in
f
o
r
m
atics
e
n
cr
y
p
t
io
n
te
ch
n
iq
u
e
d
ep
en
d
s
o
n
t
h
e
s
a
m
e
r
u
les
o
f
P
la
y
Fair
m
et
h
o
d
.
T
h
e
p
u
r
p
o
s
e
is
to
en
h
an
ce
a
n
d
i
m
p
r
o
v
e
th
e
en
co
d
i
n
g
b
y
u
s
i
n
g
clas
s
ic
P
la
y
Fair
,
s
o
th
e
y
ca
n
e
n
cr
y
p
t
an
y
t
y
p
e
o
f
d
ata
an
d
at
th
e
s
a
m
e
ti
m
e
b
en
ef
it
f
r
o
m
t
h
e
co
n
c
ep
ts
o
f
b
io
lo
g
ical
in
f
o
r
m
atic
s
.
A
l
s
o
th
e
m
o
d
i
f
icatio
n
o
p
ti
m
iz
es th
e
s
ec
u
r
it
y
o
f
en
cr
y
p
tio
n
a
n
d
v
id
eo
s
teg
a
n
o
g
r
ap
h
y
[
1
2
]
.
Seth
A
,
B
is
w
as
SS
.
,
i
n
t
h
i
s
p
ap
er
,
th
e
class
ical
P
la
y
Fair
C
ip
h
er
i
s
m
o
d
i
f
ied
to
1
0
*
9
m
atr
i
x
.
T
h
e
ap
p
r
o
ac
h
p
r
o
p
o
s
ed
co
m
b
in
es
t
h
e
P
la
y
f
air
a
lg
o
r
it
h
m
en
cr
y
p
tio
n
a
n
d
th
e
o
p
ti
m
iz
ed
ch
ao
tic
g
en
eti
c
alg
o
r
ith
m
.
T
h
e
s
tr
in
g
en
cr
y
p
ted
o
n
ce
w
it
h
th
e
P
la
y
f
air
cip
h
er
is
ag
ai
n
s
u
b
j
ec
ted
to
en
cr
y
p
tio
n
u
s
i
n
g
th
e
Gen
e
tic
A
l
g
o
r
ith
m
w
it
h
a
P
s
eu
d
o
-
r
an
d
o
m
n
u
m
b
er
g
e
n
er
ated
b
y
1
-
D
c
h
ao
tic
m
ap
[
1
3
]
.
Deep
th
i
,
in
t
h
i
s
pa
p
er
,
th
e
au
th
o
r
m
ak
e
s
a
co
m
p
ar
is
o
n
b
et
w
ee
n
m
an
y
m
o
d
i
f
icatio
n
s
o
n
P
lay
f
ai
r
cip
h
er
an
d
s
h
o
w
s
t
h
e
w
ea
k
n
ess
es
i
n
th
e
s
e
m
o
d
i
f
icatio
n
s
o
n
th
e
o
r
ig
i
n
al
P
la
y
f
air
an
d
f
o
u
n
d
th
at
n
o
o
n
e
d
is
cu
s
s
ed
th
e
e
f
f
e
c
ts
o
f
b
r
ea
k
i
n
g
t
h
e
cip
h
er
te
x
t
,
an
d
n
o
o
n
e
p
r
o
v
ed
th
e
p
o
w
er
o
f
h
i
s
m
o
d
if
icatio
n
[
1
4
]
.
So
n
al
Na
m
d
ev
,
Vi
m
al
G
u
p
ta
(
2
0
1
6
)
,
in
th
i
s
p
ap
er
,
au
t
h
o
r
p
r
o
p
o
s
es
an
d
d
is
cu
s
s
e
s
a
m
o
d
if
icatio
n
o
n
P
lay
f
air
cip
h
er
b
ased
o
n
m
e
r
g
in
g
w
it
h
DN
A
a
n
d
a
m
i
n
o
ac
id
i
m
p
le
m
e
n
tatio
n
.
He
p
r
o
v
ed
th
at
t
h
e
w
ea
k
alg
o
r
ith
m
ca
n
b
ec
o
m
e
m
o
r
e
p
o
w
er
f
u
l
i
n
en
cr
y
p
tio
n
b
y
ad
d
in
g
co
n
f
u
s
io
n
an
d
d
if
f
u
s
io
n
o
n
th
e
p
r
o
ce
s
s
,
a
n
e
w
b
io
lo
g
ical
m
etr
ic
w
it
h
clas
s
ic
P
lay
f
air
i
m
p
r
o
v
e
s
en
cr
y
p
tio
n
p
r
o
ce
s
s
[
1
5
]
.
Z
a
k
ar
i
y
a
u
et
al.
,
a
n
e
w
m
o
d
if
icatio
n
o
n
clas
s
ical
P
la
y
f
air
w
it
h
1
7
X1
7
m
atr
i
x
w
as
p
r
o
p
o
s
ed
w
h
ic
h
allo
w
s
u
s
i
n
g
a
lo
n
g
k
e
y
w
it
h
m
o
r
e
t
h
an
6
4
ch
ar
ac
ter
(
lo
n
g
k
e
y
w
o
r
d
)
[
1
6
]
.
I
f
w
e
a
n
al
y
ze
th
e
p
r
ev
io
u
s
s
tu
d
ie
s
w
e
f
i
n
d
a
lo
t
o
f
p
r
o
b
le
m
s
s
u
c
h
as
w
ea
k
n
es
s
es
a
n
d
co
m
p
le
x
it
y
,
u
s
i
n
g
d
ata
s
te
g
a
n
o
g
r
ap
h
y
in
e
n
cr
y
p
ti
n
g
v
id
eo
w
il
l
a
f
f
ec
t
t
h
e
q
u
a
lit
y
o
f
v
id
eo
lik
e
d
i
s
to
r
tio
n
[
1
7
]
,
an
d
m
o
d
if
icatio
n
p
r
o
ce
s
s
g
o
es
t
h
r
o
u
g
h
m
an
y
co
m
p
licated
s
tep
s
.
Mo
r
eo
v
er
t
h
e
s
ec
u
r
i
t
y
o
f
t
h
ese
m
o
d
i
f
icatio
n
s
h
a
s
n
o
t
b
ee
n
p
r
o
v
ed
,
an
d
u
s
ed
in
E
n
g
lis
h
la
n
g
u
a
g
e
o
n
l
y
.
Ma
y
b
e
w
e
d
o
n
’
t
n
ee
d
th
i
s
a
m
o
u
n
t
o
f
c
h
ar
ac
ter
s
i
n
ca
s
e
o
f
lan
g
u
a
g
e
s
w
it
h
2
1
letter
s
.
Mo
d
if
icatio
n
i
s
n
o
t
test
ed
in
a
p
r
o
p
er
m
et
h
o
d
,
an
d
b
lo
ck
s
ize
is
s
till
t
h
e
s
a
m
e.
B
u
t
i
n
o
u
r
m
e
th
o
d
(
K
A
J
)
w
e
p
r
o
v
ed
it
is
p
o
w
er
f
u
l
u
s
i
n
g
I
n
d
ex
o
f
C
o
in
cid
e
n
ce
m
et
h
o
d
,
a
cc
ep
tin
g
an
y
a
m
o
u
n
t
o
f
ch
ar
ac
ter
s
,
u
s
ed
in
an
y
la
n
g
u
a
g
e,
an
d
s
u
p
p
o
r
t
an
y
b
lo
ck
s
ize.
I
n
th
i
s
s
t
u
d
y
w
e
p
r
o
p
o
s
ed
a
m
o
d
if
icatio
n
f
o
r
th
e
f
ir
s
t
ti
m
e
t
h
at
ca
n
h
elp
p
eo
p
le
w
it
h
d
if
f
er
en
t
lan
g
u
a
g
es
an
d
u
s
i
n
g
m
o
r
e
s
y
m
b
o
l
s
to
b
e
ab
le
to
en
cr
y
p
t
an
d
d
ec
r
y
p
t
m
es
s
ag
e
s
w
it
h
o
u
t
n
ee
d
i
n
g
to
alter
tab
les.
I
t
is
o
n
l
y
o
n
e
d
esig
n
th
at
ca
n
b
e
u
s
ed
u
n
i
v
er
s
all
y
.
T
h
e
im
p
o
r
tan
ce
o
f
t
h
e
s
tu
d
y
also
lies
i
n
th
e
p
o
s
s
ib
ilit
y
o
f
g
e
n
er
ati
n
g
u
s
ef
u
l
id
ea
s
o
n
t
h
e
d
ev
e
lo
p
in
g
a
n
d
en
h
a
n
cin
g
cr
y
p
to
g
r
a
p
h
y
a
n
d
m
a
k
in
g
it
u
n
i
v
er
s
al
f
r
o
m
th
e
p
o
in
t
o
f
v
i
e
w
o
f
r
esear
ch
er
s
to
i
m
p
r
o
v
e
th
e
ar
t
o
f
cr
y
p
to
g
r
ap
h
y
a
n
d
m
ak
e
n
e
w
p
r
o
s
p
ec
ts
,
to
h
elp
p
eo
p
le
w
it
h
o
t
h
er
la
n
g
u
a
g
es
u
s
e
t
h
e
P
la
y
Fair
al
g
o
r
ith
m
w
it
h
o
u
t
a
n
ee
d
to
m
a
k
e
n
e
w
r
ec
ta
n
g
les
,
s
q
u
ar
es,
o
r
co
n
f
u
s
ed
,
an
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2.
P
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AI
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ip
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Alg
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W
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e
1
8
5
4
[
1
8
]
.
A
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les.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
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n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
5
4
0
0
-
5
4
1
1
5402
2
.
1
.
P
ra
ct
ica
l e
x
a
m
ple
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w
i
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te
x
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u
s
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la
y
f
air
C
ip
h
er
A
l
g
o
r
ith
m
?
(
E
x
a
m
p
le
2
.
1
)
.
I
n
itiall
y
S
h
o
li
ag
r
ee
d
w
it
h
Mo
h
a
m
ed
a
k
e
y
w
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r
d
i
s
“L
I
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”.
T
h
e
p
lain
tex
t
is
:
U
n
iv
er
s
it
y
o
f
U
n
is
za
at
T
R
.
First
:
C
r
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te
a
tab
le
o
f
5
x
5
,
an
d
ap
p
ly
2
6
letter
s
i
n
2
5
s
q
u
ar
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s
u
ch
t
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at
t
h
ese
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w
o
letter
s
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J
&
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in
co
r
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ate
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tical
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d
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w
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lied
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y
m
a
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letter
s
ar
e
d
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p
licated
,
as
s
h
o
w
n
i
n
T
ab
le
1
.
T
h
i
r
d
:
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f
b
o
th
letter
s
ar
e
th
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s
a
m
e
(
o
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l
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letter
i
s
lef
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,
ad
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ter
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ir
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tter
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p
t th
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ab
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1
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P
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ir
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esig
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w
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e
y
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m
p
le
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B
C
D
F
G
H
M
N
O
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Q
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S
T
U
V
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Z
2
.
2
.
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ncry
ptio
n r
ule
s
a.
I
f
b
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th
le
tter
s
ap
p
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m
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ep
lace
t
h
e
m
w
it
h
t
h
e
letter
s
to
t
h
eir
i
m
m
ed
iate
r
i
g
h
t,
r
esp
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tiv
e
l
y
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if
a
letter
in
t
h
e
o
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ig
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air
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th
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w
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o
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h
e
f
ir
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t
letter
to
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ep
lace
w
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th
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h
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en
d
l
etter
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.
b.
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f
b
o
th
letter
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ap
p
ea
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th
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s
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m
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co
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r
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le,
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lace
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e
m
w
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t
h
e
letter
s
i
m
m
ed
iatel
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elo
w,
r
esp
ec
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el
y
(
i
f
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letter
in
th
e
o
r
ig
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al
p
air
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a
s
o
n
t
h
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o
tto
m
s
id
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co
l
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m
n
g
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t
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f
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co
lu
m
n
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n
d
u
s
e
th
e
f
ir
s
t le
tter
to
r
ep
lace
w
it
h
t
h
e
en
d
lett
er
).
c.
I
f
t
h
e
letter
s
ar
e
n
o
t
o
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th
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s
a
m
e
r
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w
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m
n
,
i
m
a
g
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e
cr
ea
tin
g
s
q
u
ar
e
o
r
r
ec
tan
g
le
w
it
h
t
h
e
to
w
letter
s
o
n
th
e
o
p
p
o
s
ite
s
id
e
[
1
9
]
.
Un
i
v
er
s
it
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f
U
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Un
iv
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s
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T
ab
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1
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ly
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tio
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et
th
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cip
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t b
y
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s
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g
T
ab
le
2
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a
b
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2
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s
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ate
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lt
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M
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En
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r
y
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t
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3
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3
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IS
3
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3
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TR
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w
h
e
n
w
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lied
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cr
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les
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th
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p
lain
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s
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g
T
ab
le
1
w
e
g
o
t
t
h
e
f
o
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w
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n
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lt
f
r
o
m
T
ab
le
2
.
C
: SP
L
W
I
T
R
KYE
T
OSP
KR
AGZ
K
SYUS
2
.
3
.
Dec
ry
ptio
n r
ules
a.
I
f
th
e
letter
s
ap
p
ea
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n
th
e
s
a
m
e
r
o
w
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u
r
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le,
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ep
lace
th
e
m
w
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th
t
h
e
lette
r
s
to
th
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m
m
ed
iate
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t,
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y
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f
t
h
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is
at
t
h
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tar
t o
f
r
o
w
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to
th
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d
o
f
th
e
r
o
w
)
.
b.
I
f
th
e
letter
s
ap
p
ea
r
o
n
th
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s
am
e
co
lu
m
n
o
f
y
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r
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le,
r
ep
l
ac
e
th
e
m
w
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e
letter
s
i
m
m
ed
iatel
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o
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e,
r
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el
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f
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letter
at
th
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tar
t o
f
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n
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ain
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n
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co
l
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m
n
(
s
a
m
e)
.
c.
I
f
th
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letter
s
ar
e
n
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t
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m
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r
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m
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ep
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o
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m
e
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u
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tan
g
le
d
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b
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th
e
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r
ig
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p
air
.
No
te:
T
h
e
o
r
d
er
is
i
m
p
o
r
tan
t
–
t
h
e
f
ir
s
t
letter
o
f
t
h
e
e
n
cr
y
p
ted
p
air
is
th
e
o
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e
th
at
lies
o
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t
h
e
s
a
m
e
r
o
w
as
t
h
e
f
ir
s
t
letter
o
f
th
e
p
lain
te
x
t p
air
[
1
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
8708
Mo
d
ifyin
g
p
la
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ir
cip
h
er a
l
g
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ith
m
u
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g
K
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p
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l m
eth
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3
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IT
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2
OF
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3
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AG
2
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ZK
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SY
3
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TR
w
h
e
n
w
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ap
p
lied
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r
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u
s
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n
g
T
ab
le
1
,
w
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g
o
t t
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w
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l
t f
r
o
m
T
ab
le
3
.
C
: SP
L
W
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T
R
KYE
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K
R
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G
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;
P
: U
n
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v
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Un
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R
3.
K
AJ
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A
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M
KA
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Sp
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lg
o
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et
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ak
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P
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Fair
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s
e
b
y
p
eo
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le
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a
n
2
6
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s
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lp
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et
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t
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ch
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s
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I
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p
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p
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ig
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e
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ar
y
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ec
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s
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w
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v
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w
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d
s
ev
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n
d
s
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m
b
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l
s
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w
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er
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r
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w
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ill
f
o
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u
s
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g
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E
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(
w
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id
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n
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Pla
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ith
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w
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s
o
m
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la
n
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s
u
c
h
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talia
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(
2
1
letter
s
)
,
an
d
A
r
ab
ic
(
2
8
letter
s
)
.
B
y
t
h
is
,
w
e
ca
n
p
er
f
o
r
m
o
u
r
an
al
y
s
i
s
an
d
p
r
o
v
e
th
e
w
o
r
k
ab
ilit
y
o
f
o
u
r
m
eth
o
d
.
T
h
e
m
et
h
o
d
u
s
es
s
p
ir
al
s
h
ap
e
w
ith
t
w
o
a
x
es (
X,
Y)
an
d
th
e
letter
s
ar
e
s
p
r
ea
d
o
n
th
a
t
ax
is
w
i
th
i
n
cir
cle
s
d
ep
en
d
in
g
o
n
th
e
la
n
g
u
a
g
e
u
s
ed
.
Fo
r
ex
a
m
p
le,
E
n
g
lis
h
s
tar
t
f
r
o
m
le
f
t
-
to
-
r
i
g
h
t,
b
u
t
in
A
r
ab
ic
it
s
tar
t
s
f
r
o
m
r
ig
h
t
-
to
-
lef
t
a
n
d
s
o
o
n
.
Mo
r
eo
v
er
,
E
n
g
lis
h
s
tar
ts
at
t
h
e
le
f
t
s
id
e
o
f
t
h
e
x
a
x
is
a
n
d
th
e
A
r
ab
ic
s
t
ar
ts
at
t
h
e
r
ig
h
t
s
id
e
o
f
t
h
e
x
a
x
is
.
A
s
in
t
h
e
P
la
y
Fair
t
h
e
k
e
y
s
h
o
u
ld
b
e
p
lace
d
f
ir
s
t
a
n
d
th
en
t
h
e
r
est
o
f
letter
s
o
f
alp
h
ab
ets
ar
e
co
n
tin
u
o
u
s
l
y
s
p
r
ea
d
o
n
ax
is
w
i
th
i
n
cir
cle
s
u
n
til
n
o
n
e
i
s
lef
t
(
w
e
ca
n
ad
d
an
y
n
u
m
b
er
s
,
lett
er
s
o
r
s
y
m
b
o
ls
b
y
ex
ten
d
i
n
g
t
h
e
cir
cle
a
n
d
t
h
u
s
ad
d
m
o
r
e
c
ir
cles)
.
E
ac
h
cir
cle
h
as
4
le
tter
s
o
f
alp
h
ab
et
s
,
an
d
if
th
e
la
s
t
cir
cle
is
n
o
t
f
u
ll
y
u
s
ed
,
it
d
o
es
n
o
t
m
a
tter
b
ec
au
s
e
th
e
r
u
le
3
w
ill
b
e
also
m
o
d
if
ied
.
T
h
e
f
o
llo
w
in
g
i
m
ag
e
s
s
h
o
w
h
o
w
t
h
e
letter
s
o
f
alp
h
ab
ets
w
a
s
d
is
tr
ib
u
te
d
o
n
th
e
ax
is
f
o
r
lan
g
u
a
g
es (
E
n
g
li
s
h
-
Fig
u
r
e
1
,
A
r
ab
ic
-
Fi
g
u
r
e
2
,
an
d
I
talian
-
F
ig
u
r
e
3
)
.
Fig
u
r
e
1
.
E
n
g
li
s
h
la
n
g
u
a
g
e
-
l
etter
s
o
f
alp
h
ab
ets
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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n
t J
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&
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o
m
p
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n
g
,
Vo
l.
9
,
No
.
6
,
Dec
em
b
er
2
0
1
9
:
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4
0
0
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5
4
1
1
5404
Fig
u
r
e
1
s
h
o
w
s
t
h
e
letter
s
f
i
t
t
h
e
s
e
v
en
cir
cles.
W
e
d
id
n
’
t
ad
d
o
r
d
elete
cir
cles.
T
h
e
em
p
t
y
p
o
s
itio
n
s
d
o
n
o
t
m
atter
an
d
w
e
d
o
n
’
t
n
ee
d
to
ad
d
an
y
t
h
i
n
g
.
Fig
u
r
e
2
s
h
o
w
s
t
h
e
let
te
r
s
f
it
t
h
e
s
e
v
e
n
cir
cles.
W
e
d
id
n
’
t
ad
d
o
r
d
elete
cir
cles,
th
er
e
ar
e
n
o
e
m
p
t
y
p
o
s
itio
n
s
.
Fig
u
r
e
3
s
h
o
w
s
t
h
e
letter
s
f
i
t
to
t
h
e
f
iv
e
cir
cles,
o
n
l
y
o
n
e
letter
is
in
cir
cle
s
ix
t
h
an
d
w
e
d
elete
d
cir
cle
s
ev
en
.
T
h
ese
ex
a
m
p
le
s
s
h
o
w
th
e
f
le
x
ib
ilit
y
o
f
th
e
n
e
w
m
o
d
i
f
icat
io
n
w
h
ich
f
it
s
S
h
an
n
o
n
r
u
les o
f
s
i
m
p
licit
y
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al
g
o
r
i
th
m
d
e
s
ig
n
.
Fig
u
r
e
2
.
A
r
ab
ic
lan
g
u
a
g
e
-
le
tter
s
o
f
alp
h
ab
et
Fig
u
r
e
3
.
I
talia
n
lan
g
u
ag
e
-
let
ter
o
f
alp
h
ab
et
3
.
1
.
T
he
rule
s
f
o
r
K
AJ
m
et
ho
d
a.
T
h
er
e
is
n
o
n
ee
d
to
cr
ea
te
tab
l
es,
an
d
th
e
letter
s
I
&
J
d
o
n
o
t
n
ee
d
to
s
h
ar
e
s
a
m
e
p
o
s
itio
n
.
b.
T
h
e
k
e
y
w
o
r
d
s
h
o
u
ld
b
e
p
lace
d
lef
t
-
to
-
r
i
g
h
t
f
ir
s
t
o
n
X
-
a
x
i
s
f
o
r
lan
g
u
ag
e
s
w
r
itte
n
le
f
t
-
to
-
r
ig
h
t,
a
n
d
t
h
en
th
e
e
m
p
t
y
p
o
s
i
tio
n
s
o
n
b
o
th
ax
es
ar
e
f
illed
i
n
w
ith
t
h
e
r
est
o
f
letter
s
o
f
th
e
alp
h
ab
et
an
d
m
ak
i
n
g
s
u
r
e
n
o
let
ter
s
ar
e
d
u
p
licated
.
c.
T
h
e
k
e
y
w
o
r
d
s
h
o
u
ld
b
e
p
lace
d
r
ig
h
t
–
to
-
le
f
t
f
ir
s
t
o
n
X
Ax
i
s
f
o
r
la
n
g
u
a
g
es
w
r
itte
n
r
ig
h
t
–
to
-
le
f
t,
an
d
th
e
n
th
e
e
m
p
t
y
p
o
s
itio
n
s
o
n
b
o
th
a
x
es
ar
e
f
illed
i
n
w
it
h
t
h
e
r
es
t
l
etter
s
o
f
th
e
alp
h
ab
et
w
it
h
m
ak
in
g
s
u
r
e
n
o
letter
s
ar
e
d
u
p
lica
ted
.
d.
I
f
b
o
th
let
ter
s
ar
e
t
h
e
s
a
m
e
(
o
r
o
n
l
y
o
n
e
le
tter
is
lef
t)
,
ad
d
an
"
X
"
af
ter
th
e
f
ir
s
t le
t
ter
.
E
n
cr
y
p
t
t
h
e
n
e
w
p
air
an
d
co
n
tin
u
e.
B
u
t
w
it
h
lan
g
u
ag
e
s
w
it
h
n
o
x
letter
s
,
w
e
r
ec
o
m
m
e
n
d
u
s
in
g
v
o
w
el
f
r
o
m
t
h
at
lan
g
u
ag
e
s
o
th
e
r
ec
eiv
er
ca
n
ea
s
il
y
f
i
g
u
r
e
th
at
.
e.
I
f
t
h
e
la
n
g
u
a
g
e
is
w
r
itte
n
le
f
t
-
to
-
r
ig
h
t,
s
tar
t
s
p
r
ea
d
in
g
c
h
ar
ac
ter
o
n
X
Ax
es
le
f
t
s
id
e
a
n
d
t
h
en
g
o
d
o
w
n
to
Y
Ax
es
a
n
d
co
n
tin
u
e
s
p
r
ea
d
in
g
letter
s
o
n
Ax
es
w
it
h
i
n
cir
cle
s
.
B
u
t
if
t
h
e
lan
g
u
ag
e
i
s
w
r
i
tt
en
r
ig
h
t
-
to
-
le
f
t,
s
tar
t
s
p
r
ea
d
in
g
ch
ar
ac
ter
o
n
X
Ax
es
r
i
g
h
t
s
id
e
a
n
d
th
e
n
g
o
u
p
to
Y
Ax
es
a
n
d
co
n
ti
n
u
e
s
p
r
e
ad
in
g
le
tter
s
o
n
Ax
es
w
i
th
i
n
cir
cles.
3
.
2
.
E
ncry
ptio
n r
ule
s
a.
I
f
b
o
th
letter
s
ap
p
ea
r
o
n
th
e
s
a
m
e
r
o
w
(
X
-
a
x
es),
r
ep
lace
th
e
m
w
it
h
th
e
letter
s
to
th
eir
i
m
m
ed
iate
r
ig
h
t,
r
esp
ec
tiv
el
y
(
if
a
le
tter
in
t
h
e
o
r
ig
in
al
p
a
ir
w
as
o
n
th
e
e
n
d
o
f
t
h
e
r
o
w
(X
-
ax
e
s
)
,
g
o
b
ac
k
to
th
e
s
tar
t
o
f
th
e
r
o
w
(
X
-
a
x
es),
an
d
u
s
e
t
h
e
f
ir
s
t le
tter
to
r
ep
lace
w
it
h
t
h
e
en
d
letter
)
.
b.
I
f
b
o
th
letter
s
ap
p
ea
r
o
n
th
e
s
a
m
e
co
l
u
m
n
(
Y
-
ax
e
s
)
o
f
y
o
u
r
tab
le,
r
ep
lace
th
e
m
w
it
h
t
h
e
letter
s
i
m
m
ed
iatel
y
b
elo
w
,
r
e
s
p
ec
ti
v
el
y
(
i
f
a
letter
in
th
e
o
r
ig
i
n
al
p
air
w
as
o
n
t
h
e
b
o
tto
m
s
id
e
o
f
t
h
e
co
lu
m
n
(Y
-
ax
e
s
)
g
o
b
ac
k
to
th
e
s
tar
t o
f
th
e
co
l
u
m
n
(
Y
-
a
x
es)
an
d
u
s
e
th
e
f
ir
s
t le
tter
to
r
ep
lace
w
it
h
t
h
e
en
d
letter
)
.
c.
I
f
th
e
letter
s
ar
e
n
o
t
o
n
t
h
e
s
a
m
e
r
o
w
o
r
co
lu
m
n
,
g
o
d
ir
ec
tl
y
to
th
e
letter
o
n
th
e
s
a
m
e
cir
cle
o
n
th
e
o
th
er
Ax
es (
le
f
t
-
to
-
r
i
g
h
t f
o
r
lan
g
u
ag
es u
s
e
le
f
t
–
to
-
r
i
g
h
t a
n
d
r
ig
h
t
–
to
-
lef
t
f
o
r
lan
g
u
a
g
es
u
s
e
r
i
g
h
t
–
to
-
le
f
t)
.
3
.
3
.
Dec
ry
ptio
n
rules
a.
I
f
b
o
th
letter
s
ap
p
ea
r
o
n
th
e
s
a
m
e
r
o
w
(
X
-
ax
e
s
)
,
r
ep
lace
t
h
e
m
w
i
th
t
h
e
letter
s
to
th
ei
r
i
m
m
ed
iate
lef
t
,
r
esp
ec
tiv
el
y
(
i
f
a
letter
i
n
th
e
o
r
ig
in
al
p
air
w
a
s
o
n
t
h
e
s
t
ar
t
o
f
th
e
r
o
w
(
X
-
a
x
es),
g
o
b
ac
k
to
th
e
en
d
o
f
th
e
r
o
w
(
X
-
a
x
es),
an
d
u
s
e
t
h
e
last
let
ter
to
r
ep
lace
w
i
th
t
h
e
f
ir
s
t le
tter
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2
0
8
8
-
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Mo
d
ifyin
g
p
la
yfa
ir
cip
h
er a
l
g
o
r
ith
m
u
s
in
g
K
A
J
s
p
ir
a
l m
eth
o
d
to
fit a
n
y
la
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a
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e
.
..
(
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b
r
a
h
im
A
.
S
h
o
li)
5405
b.
I
f
b
o
th
letter
s
ap
p
ea
r
o
n
th
e
s
a
m
e
co
l
u
m
n
(
Y
-
ax
e
s
)
,
r
ep
lace
th
e
m
w
it
h
t
h
e
letter
s
i
m
m
ed
iatel
y
u
p
,
r
esp
ec
tiv
el
y
(
i
f
a
let
ter
in
t
h
e
o
r
ig
in
al
p
air
w
as
o
n
t
h
e
s
tar
t
s
id
e
o
f
t
h
e
co
lu
m
n
(
Y
-
ax
e
s
)
g
o
b
ac
k
to
t
h
e
en
d
o
f
th
e
co
lu
m
n
(Y
-
a
x
es)
a
n
d
u
s
e
th
e
en
d
letter
to
r
ep
lace
w
it
h
th
e
f
ir
s
t le
tter
)
.
c.
I
f
th
e
let
ter
s
ar
e
n
o
t
o
n
t
h
e
s
a
m
e
r
o
w
o
r
co
lu
m
n
,
g
o
d
ir
ec
tly
to
th
e
letter
o
n
t
h
e
s
a
m
e
cir
cle
o
n
th
e
o
th
er
ax
es
(
r
ig
h
t
–
to
-
le
f
t
(
r
et
u
r
n
s
)
f
o
r
lan
g
u
ag
e
s
u
s
e
le
f
t
–
to
-
r
ig
h
t
an
d
lef
t
–
to
-
r
i
g
h
t
f
o
r
la
n
g
u
a
g
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les
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it
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t d
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tab
les.
3
.
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.
1
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x
a
m
p
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in
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n
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lis
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g
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f
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llo
w
in
g
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x
a
m
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n
g
l
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la
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g
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a
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s
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to
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ak
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it
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n
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er
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ab
le
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n
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ea
s
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t
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al
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ze
.
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j
u
s
t
u
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e
t
h
e
s
a
m
e
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ata
w
e
u
s
ed
in
t
h
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r
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i
n
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et
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in
ex
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m
p
le
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.
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.
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n
cr
y
p
t
th
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f
o
llo
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n
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te
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t
u
s
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n
g
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la
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Fa
ir
cip
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er
b
y
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ly
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m
e
th
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d
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n
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o
li
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w
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th
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h
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m
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k
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u
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h
en
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ap
p
lied
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d
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r
y
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t
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cip
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te
x
t
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g
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4
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t
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I
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8
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2
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x
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m
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a
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itiall
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li a
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it
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k
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ب
حن
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tex
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اج
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ly
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b
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r
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p
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s
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R
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tà
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p
ly
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cr
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ted
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eth
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Fig
u
r
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n
er
ate
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n
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er
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e
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r
o
ce
s
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.
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h
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r
esu
lt (
p
lain
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t)
=
Un
ivers
ità
d
i U
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is
z
a
p
r
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o
TR.
4.
RE
SU
L
T
S AN
D
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AL
Y
SI
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I
f
w
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co
m
p
ar
e
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e
t
w
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s
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.
2
.
1
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d
3
.
4
.
1
)
w
e
f
i
n
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o
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ig
d
if
f
er
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ce
s
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n
d
ee
d
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i
s
h
as
p
r
o
v
ed
th
e
v
alid
it
y
(
u
s
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le,
s
t
r
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n
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w
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f
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e
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d
,
an
d
as
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e
s
aid
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it is
s
u
b
j
ec
ted
f
o
r
m
o
d
if
y
in
g
b
ec
a
u
s
e
t
h
is
i
s
o
n
l
y
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ir
s
t i
m
ag
in
at
io
n
f
o
r
th
e
K
A
J
m
et
h
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d
.
Or
ig
i
n
al
P
la
y
Fair
-
P
: U
n
i
v
er
s
it
y
o
f
U
n
is
za
at
T
R
=
C
: SP
L
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T
R
KYE
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KR
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K
SYUS
KA
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-
R
es
u
lt: U
n
i
v
er
s
it
y
o
f
U
n
is
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at
T
R
=
C
:VOB
Z
I
VT
KQZ
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A
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OKT
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UB
PT
P
V
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
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l.
9
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.
6
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atio
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n
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i
th
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er
t
w
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a
m
p
les
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a
n
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talian
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1
0
N
0
-
1
0
O
1
0
0
O
2
1
2
P
2
1
2
P
2
1
2
Q
0
-
1
0
Q
1
0
0
R
2
1
2
R
0
-
1
0
S
4
3
12
S
1
0
0
T
2
1
2
T
3
2
6
U
1
0
0
U
1
0
0
V
0
-
1
0
V
4
3
12
W
1
0
0
W
0
-
1
0
X
0
-
1
0
X
0
-
1
0
Y
2
1
2
Y
1
0
0
Z
1
0
0
Z
2
1
2
24
26
24
32
No
w
w
e
w
il
l a
p
p
l
y
r
esu
l
ts
o
f
e
q
u
atio
n
1
o
n
th
e
eq
u
a
tio
n
2
to
d
eter
m
in
e
t
h
e
len
g
t
h
o
f
t
h
e
k
e
y
.
=
0
.
027
(
−
1
)
−
0
.
038
+
0
.
065
(
5
)
1
-
Or
ig
i
n
al
P
la
y
Fair
:
=
0
.
027
(
−
1
)
−
0
.
038
+
0
.
065
=
0
.
027
∗
24
(
24
−
1
)
0
.
0
4
7
1
0
1
4
4
9
−
0
.
038
∗
24
+
0
.
065
=
=
0
.
648
0
.
2
3
6
3
3
3
3
2
7
=
2
.
741890059
(
6
)
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