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tai
n
i
n
g
th
e
h
ar
d
co
n
s
tr
ain
ts
f
r
o
m
a
n
y
v
io
latio
n
s
.
I
n
[
1
2
,
1
3
]
a
class
-
o
r
ien
ted
r
e
p
r
esen
tatio
n
o
f
T
i
m
etab
l
e
is
u
s
ed
,
w
h
ich
i
m
p
licit
l
y
a
v
o
id
s
class
r
o
o
m
co
n
ten
tio
n
s
,
th
e
i
n
s
tr
u
cto
r
-
o
r
ien
ted
r
ep
r
esen
tat
io
n
o
f
t
i
m
et
ab
le
is
u
s
ed
w
h
ic
h
i
m
p
lic
itl
y
av
o
id
s
in
s
tr
u
cto
r
s
ti
m
e
tab
le
co
n
te
n
tio
n
s
.
I
n
th
is
p
ap
er
,
b
o
th
C
las
s
-
o
r
ie
n
ted
an
d
I
n
s
tr
u
c
to
r
-
o
r
ien
ted
r
ep
r
esen
tatio
n
s
o
f
a
ti
m
etab
le,
w
h
ich
a
v
o
id
class
clash
e
s
an
d
in
s
tr
u
c
to
r
clash
e
s
ar
e
u
s
ed
in
p
ar
allel.
A
cr
o
s
s
t
h
e
liter
at
u
r
e,
v
ar
io
u
s
alg
o
r
ith
m
ic
clas
s
es
h
av
e
b
e
en
p
r
o
p
o
s
ed
to
ad
d
r
ess
th
e
s
ch
ed
u
li
n
g
p
r
o
b
lem
at
ac
ad
e
m
ic
i
n
s
ti
tu
ti
o
n
s
.
T
h
ese
alg
o
r
ith
m
s
in
cl
u
d
e
:
A
l
g
o
r
ith
m
s
f
all
i
n
g
u
n
d
er
th
e
g
en
etic
al
g
o
r
ith
m
s
class
w
h
ic
h
ar
e
o
f
ten
u
s
ed
to
tack
le
h
u
g
e
a
m
o
u
n
ts
o
f
d
ata,
an
d
s
i
m
u
lated
a
n
n
ea
l
in
g
al
g
o
r
ith
m
s
w
h
ich
le
n
d
th
e
m
s
el
v
es
f
air
l
y
w
ell
to
p
r
o
b
le
m
s
w
it
h
lar
g
e
s
ea
r
ch
s
p
ac
es.
Neit
h
er
o
f
t
h
ese
clas
s
es
o
f
al
g
o
r
ith
m
s
w
i
ll
b
e
lev
er
ag
ed
i
n
th
e
c
u
r
r
en
t
w
o
r
k
.
I
n
th
e
f
o
r
m
er
clas
s
o
f
al
g
o
r
ith
m
s
lar
g
e
m
e
m
o
r
y
s
izes
ar
e
r
eq
u
ir
ed
[
1
4
,
1
5
]
,
w
h
ile
i
n
t
h
e
latter
ca
te
g
o
r
y
c
er
tain
d
is
ad
v
a
n
ta
g
es
ar
e
co
m
m
o
n
l
y
e
n
co
u
n
ter
ed
.
T
h
ese
d
ea
l
w
i
th
t
h
e
f
ac
t
t
h
at
th
e
o
p
ti
m
al
s
o
lu
t
io
n
u
s
u
all
y
d
ep
en
d
s
o
n
th
e
in
i
tial
s
ta
te
w
h
er
e
th
e
s
p
ee
d
o
f
co
n
v
er
g
e
n
ce
is
r
ath
er
to
o
s
lo
w
th
an
m
a
n
y
o
t
h
er
alg
o
r
it
h
m
s
[
1
6
,
1
7
]
.
Fu
r
th
er
m
o
r
e,
in
t
h
is
w
o
r
k
n
o
co
n
s
id
er
atio
n
w
ill
b
e
g
iv
e
n
to
T
ab
u
’
s
s
ea
r
ch
al
g
o
r
ith
m
w
h
ic
h
is
cl
ass
i
f
ied
u
n
d
er
th
e
lo
ca
l
s
ea
r
c
h
f
a
m
i
l
y
a
n
d
w
o
u
ld
r
eq
u
ir
e
a
lar
g
e
n
u
m
b
er
o
f
iter
atio
n
s
f
o
r
its
co
n
v
er
g
e
n
ce
[
1
8
]
.
I
n
th
is
p
ap
er
,
a
n
o
v
el
tech
n
iq
u
e
is
p
r
o
p
o
s
ed
;
th
is
tech
n
iq
u
e
is
m
ad
e
-
u
p
o
f
t
w
o
s
tag
e
s
:
I
n
th
e
f
ir
s
t,
an
i
n
itial
s
o
lu
tio
n
is
cr
ea
ted
in
a
w
a
y
th
a
t
w
o
u
ld
a
v
o
id
an
y
cla
s
h
e
s
lev
er
a
g
i
n
g
C
las
s
-
o
r
ie
n
ted
an
d
I
n
s
tr
u
c
to
r
-
o
r
ien
ted
r
ep
r
esen
tat
io
n
s
w
it
h
v
ar
io
u
s
o
t
h
er
f
u
n
cti
o
n
s
to
m
a
k
e
s
u
r
e
t
h
at
n
o
ti
m
e
s
lo
ts
ar
e
s
elec
ted
i
n
w
a
y
s
t
h
at
w
o
u
ld
e
n
d
u
p
in
cla
s
h
e
s
.
I
n
th
e
s
ec
o
n
d
s
tag
e,
t
h
e
h
ill
-
cli
m
b
i
n
g
al
g
o
r
ith
m
,
w
it
h
s
o
m
e
m
o
d
i
f
icatio
n
s
,
p
er
th
e
p
r
o
ce
d
u
r
e
o
u
tl
in
ed
in
s
ec
tio
n
3
,
is
u
s
ed
,
lev
er
a
g
i
n
g
th
e
n
u
m
b
er
o
f
ad
v
an
ta
g
es
it
e
n
tail
s
i
n
cl
u
d
in
g
i
ts
lo
w
p
o
w
er
r
eq
u
ir
e
m
en
ts
,
its
r
ath
er
f
ast
co
n
v
er
g
en
ce
a
n
d
its
r
ea
s
o
n
ab
le
r
eq
u
ir
e
m
e
n
t
s
o
f
lo
w
m
e
m
o
r
y
s
izes [
1
9
]
.
T
h
e
r
est
o
f
t
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
w
s
:
s
ec
tio
n
2
d
etails
th
e
co
m
m
o
n
p
r
o
b
le
m
o
f
s
c
h
o
o
l
ti
m
etab
li
n
g
.
Sectio
n
3
ill
u
s
tr
a
tes
th
e
m
o
d
i
f
ied
Hill
C
li
m
b
in
g
A
lg
o
r
it
h
m
.
S
ec
tio
n
4
elab
o
r
ates
th
e
m
ec
h
a
n
ic
s
o
f
t
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e,
a
s
s
ec
tio
n
5
e
x
p
lain
s
t
h
e
m
ai
n
r
es
u
lt
s
an
d
o
f
f
er
s
p
e
r
tin
e
n
t
an
al
y
s
e
s
.
Fi
n
all
y
,
s
ec
tio
n
6
p
r
o
v
id
es th
e
co
n
cl
u
s
io
n
s
.
2.
P
RO
B
L
E
M
ST
AT
E
M
E
NT
:
DE
SCR
I
P
T
I
O
N
AND
R
E
Q
UIRE
M
E
NT
S
T
h
e
p
r
o
b
lem
o
f
s
c
h
o
o
l
ti
m
eta
b
le
s
ch
ed
u
li
n
g
h
as
tr
ad
itio
n
al
l
y
b
ee
n
d
ef
in
ed
b
y
a
p
r
o
ce
s
s
th
at
w
o
u
ld
en
s
u
r
e
i
n
teg
r
it
y
a
n
d
co
n
s
is
t
en
c
y
as
w
e
co
m
b
i
n
e
i
n
s
tr
u
c
to
r
,
class
r
o
o
m
an
d
co
u
r
s
e
ti
m
es
to
g
et
h
er
i
n
t
o
co
m
m
o
n
l
y
f
ea
s
ib
le
ti
m
e
s
lo
ts
,
s
atis
f
y
in
g
a
ce
r
tain
g
r
o
u
p
o
f
co
n
s
tr
ai
n
ts
t
h
at
w
o
u
ld
m
a
k
e
th
e
s
tr
u
ct
u
r
e
o
f
th
e
tar
g
eted
s
c
h
o
o
l
ti
m
e
tab
le
s
o
u
n
d
an
d
co
r
r
ec
t
.
T
h
e
b
asic
f
ac
to
r
s
o
f
th
e
s
c
h
o
o
l
ti
m
etab
le
-
s
c
h
ed
u
li
n
g
p
r
o
b
lem
co
n
tain
f
r
o
m
t
h
r
ee
l
a
y
er
s
,
t
h
ese
t
h
r
e
e
la
y
er
s
ar
e
f
ea
t
u
r
ed
in
th
e
s
a
m
e
d
ia
g
r
a
m
.
L
a
y
er
1
co
n
ta
in
s
th
e
m
o
s
t e
s
s
e
n
tial c
o
m
p
o
n
en
t
s
in
t
h
e
p
r
o
ce
s
s
,
viz.,
I
n
s
tr
u
c
to
r
s
,
C
las
s
es a
n
d
C
o
u
r
s
es.
L
a
y
er
2
f
ea
tu
r
es
th
e
m
o
s
t
i
m
p
o
r
tan
t
h
ar
d
co
n
s
tr
ai
n
ts
(
C
l
ass
r
o
o
m
clas
h
e
s
,
I
n
s
tr
u
cto
r
cl
ash
e
s
,
lectu
r
e
a
n
d
d
a
y
teac
h
i
n
g
lo
ad
s
)
th
a
t
m
a
k
e
th
e
o
v
er
all
s
tr
u
ct
u
r
e
o
f
t
h
e
ti
m
etab
le
lo
g
icall
y
co
r
r
ec
t.
L
a
y
er
3
co
n
tai
n
s
a
g
r
o
u
p
o
f
s
o
f
t
co
n
s
tr
ain
ts
(
I
n
s
tr
u
cto
r
s
’
p
r
ef
er
en
ce
s
,
Dail
y
w
o
r
k
i
n
g
lo
ad
s
(
h
o
u
r
s
)
,
d
esi
r
ed
L
ast
L
ec
tu
r
e
a
n
d
P
r
ef
er
en
ce
s
o
f
th
e
C
las
s
es)
w
h
er
e
th
e
s
e
co
n
s
tr
ai
n
t
s
ar
e
m
e
an
t to
en
h
an
ce
t
h
e
Sc
h
o
o
l T
im
etab
le
q
u
alit
y
[
2
0
,
2
1
]
.
2
.
1
.
L
a
y
er
1
:
ins
t
ruct
o
rs,
cla
s
s
es,
co
urs
e
s
T
h
e
I
n
s
tr
u
cto
r
s
:
I
(
j)
;
j=
1
,
2
,
3
,
…
,
ḽ
;
ar
e
an
ess
en
tial
ele
m
en
t
in
an
y
s
ch
o
o
l
ti
m
etab
le
-
s
ch
ed
u
lin
g
m
ec
h
a
n
i
s
m
,
w
h
er
e
ea
ch
o
n
e
o
f
th
e
in
s
tr
u
ct
o
r
s
h
as
a
p
ar
a
m
eter
ca
lled
S
p
ec
ia
lty
,
w
h
i
ch
is
an
i
m
p
o
r
ta
n
t
ch
ar
ac
ter
is
tic
t
h
at
ca
n
tak
e
v
alu
es
f
o
r
P
r
im
ar
y
L
e
v
el
I
n
s
tr
u
cto
r
,
Dip
lo
m
a
an
d
B
ac
h
elo
r
'
s
d
eg
r
ee
s
o
r
ev
en
th
o
s
e
th
at
ar
e
ab
o
v
e.
T
h
ese
v
alu
es
h
e
lp
th
e
p
r
o
g
r
a
m
m
in
g
p
r
o
ce
s
s
to
d
ete
r
m
i
n
e
th
e
cla
s
s
lev
e
l
an
i
n
s
tr
u
cto
r
ca
n
teac
h
.
Mo
r
e
s
p
ec
if
icall
y
,
an
in
s
tr
u
cto
r
w
ith
a
P
r
i
m
ar
y
L
e
v
el
I
n
s
tr
u
cto
r
s
p
ec
ialt
y
ca
n
o
n
l
y
teac
h
p
r
i
m
ar
y
lev
el
clas
s
es,
w
h
ile
th
at
w
it
h
a
Dip
lo
m
a
s
p
ec
ial
t
y
ca
n
teac
h
b
o
th
p
r
im
ar
y
a
n
d
in
ter
m
ed
iate
lev
el
class
e
s
an
d
th
e
in
s
tr
u
cto
r
w
h
o
s
e
s
p
ec
ial
t
y
is
at
th
e
B
ac
h
elo
r
'
s
d
eg
r
ee
o
r
ab
o
v
e
ca
n
teac
h
all
class
lev
els.
T
h
e
C
lass
e
s
:
C
(
j)
;
j=
1
,
2
,
3
,
…
,
Ҫ
;
t
h
e
class
e
s
co
n
s
tit
u
te
t
h
e
s
ec
o
n
d
m
o
s
t
i
m
p
o
r
tan
t
ele
m
e
n
t
i
n
s
c
h
o
o
l
ti
m
etab
le
s
ch
ed
u
lin
g
,
w
it
h
ea
c
h
cla
s
s
p
o
s
s
ess
in
a
p
ar
a
m
eter
ca
lled
t
h
e
C
la
ss
-
Leve
l
.
T
h
is
p
ar
a
m
ete
r
ca
n
tak
e
o
n
v
alu
e
s
o
f
p
r
i
m
ar
y
,
i
n
ter
m
ed
iate
o
r
s
ec
o
n
d
ar
y
,
w
i
th
th
e
v
al
u
es
in
d
icatin
g
t
h
e
s
p
ec
ialt
y
o
f
th
e
i
n
s
tr
u
cto
r
th
a
t
allo
w
s
h
i
m
to
teac
h
a
p
ar
ticu
lar
class
,
an
d
f
in
al
l
y
,
t
h
e
C
o
u
r
s
es
:
K
(
j
)
;
j=
1
,
2
,
3
,
…
,
Ḳ
;
w
h
ic
h
ar
e
th
e
la
s
t
ele
m
en
t
in
th
e
s
ch
o
o
l
t
i
m
etab
le
s
c
h
ed
u
li
n
g
p
r
o
ce
s
s
,
w
h
er
e
ea
c
h
co
u
r
s
e
h
as
a
p
ar
a
m
e
ter
c
alled
C
o
u
r
s
e
typ
e.
T
h
is
p
ar
am
eter
h
a
s
t
w
o
v
alu
es:
s
cien
tific
co
u
r
s
es
s
u
ch
as
P
h
ysics
,
Ma
th
ema
tic
s
an
d
C
h
emist
r
y
,
an
d
n
o
n
-
s
c
ien
t
if
ic
o
n
es
s
u
c
h
a
s
A
r
ts
,
S
p
o
r
ts
,
Hi
s
to
ry
an
d
C
o
mp
u
ter
s
kills
.
T
h
is
p
ar
a
m
e
ter
is
u
s
u
al
l
y
w
e
ig
h
ed
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
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
558
-
6
5
7
3
6560
in
m
o
r
e
h
ea
v
il
y
i
n
a
s
s
i
g
n
i
n
g
s
cien
ti
f
ic
co
u
r
s
es
to
ea
r
l
y
ti
m
e
s
lo
ts
,
a
n
d
th
o
s
e
t
h
at
ar
e
n
o
n
-
s
cien
ti
f
ic
co
u
r
s
es
to
later
ti
m
e
s
lo
t
s
;
s
o
m
et
h
i
n
g
t
h
a
t
w
o
u
ld
co
n
tr
ib
u
te
m
o
r
e
p
o
s
iti
v
el
y
to
w
ar
d
s
s
tu
d
e
n
ts
’
lear
n
i
n
g
ap
p
etites.
All
o
f
th
ese
e
le
m
e
n
t
s
ar
e
s
c
h
ed
u
led
t
o
tak
e
p
lace
w
it
h
i
n
ce
r
tai
n
ti
m
e
s
lo
ts
d
u
r
i
n
g
s
c
h
o
o
l
d
a
y
,
T
S
(
j
)
=
1
,
2
,
3
,
…
,
Ṣ
.
T
h
e
s
o
lu
tio
n
s
p
ac
e
o
f
s
u
c
h
a
p
r
o
b
lem
t
h
u
s
b
ec
o
m
es:
=
×
×
×
(
1
)
Ass
u
m
in
g
t
h
at
t
h
e
i
n
s
tr
u
cto
r
te
ac
h
es
j
u
s
t
o
n
e
o
r
t
w
o
co
u
r
s
es,
a
class
r
o
o
m
tak
e
s
s
o
m
e
b
u
t
n
o
t
al
l
co
u
r
s
es,
a
n
d
it
is
o
f
te
n
k
n
o
wn
w
h
ic
h
i
n
s
tr
u
cto
r
teac
h
es
wh
at
co
u
r
s
e
a
n
d
at
w
h
ic
h
cla
s
s
r
o
o
m
.
I
n
ad
d
itio
n
,
lectu
r
es
ta
k
e
p
lace
d
u
r
i
n
g
a
li
m
ited
ti
m
e
f
r
a
m
e
(
e.
g
.
d
a
y
)
,
w
h
ich
i
n
h
er
en
tl
y
li
m
i
ts
t
h
e
ac
tu
al
ti
m
es
lo
ts
.
As
a
r
es
u
lt
s
,
SP
A
C
E
i
s
r
ed
u
c
ed
to
V
,
w
h
er
e
V
SP
A
C
E
,
w
h
ic
h
r
ep
r
esen
t
s
o
n
l
y
th
o
s
e
l
ec
tu
r
es
t
h
e
t
i
m
e
s
ch
ed
u
lin
g
o
f
w
h
ic
h
m
a
k
e
s
s
e
n
s
e,
s
u
c
h
th
at
,
,
,
=
{
;
ℎ
;
ℎ
(
2
)
w
h
er
e
,
,
,
r
ep
r
esen
ts
a
n
ele
m
e
n
t
o
f
,
,
,
.
2
.
2
.
L
a
y
er
2
:
ha
rd
co
ns
t
ra
in
t
s
T
h
e
s
ec
o
n
d
la
y
er
r
ef
er
s
to
t
h
e
h
ar
d
co
n
s
tr
ai
n
ts
,
w
h
ich
e
n
co
m
p
as
s
es
th
o
s
e
co
n
s
tr
ain
t
s
th
at
m
a
k
e
th
e
s
tr
u
ct
u
r
e
o
f
t
h
e
ti
m
etab
l
e
s
o
u
n
d
a
n
d
co
r
r
ec
t
w
h
ich
h
as
to
b
e
s
ati
s
f
ied
in
all
ca
s
e
s
a
n
d
at
a
ll
ti
m
e
s
.
T
h
ese
co
n
s
tr
ain
t
s
i
n
clu
d
e:
a.
C
las
s
r
o
o
m
clas
h
(
co
n
f
l
ict)
C
las
s
r
o
o
m
clas
h
r
e
f
er
s
to
a
s
it
u
atio
n
w
h
er
eb
y
w
e
w
o
u
l
d
allo
c
ate
m
o
r
e
th
a
n
o
n
e
in
s
tr
u
cto
r
to
th
e
s
a
m
e
clas
s
r
o
o
m
ti
m
etab
le
in
th
e
s
a
m
e
ti
m
e
s
lo
t.
T
h
is
p
r
o
b
l
em
o
cc
u
r
s
b
ec
au
s
e
t
h
e
ad
m
i
n
is
tr
ato
r
ca
n
n
o
t
s
ee
th
e
ti
m
etab
le
f
o
r
all
class
r
o
o
m
s
at
th
e
s
a
m
e
ti
m
e.
C
o
n
s
e
q
u
en
tl
y
,
th
e
ap
p
licatio
n
o
f
t
h
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
av
o
id
s
t
h
is
p
r
o
b
lem
b
y
u
s
in
g
a
C
las
s
-
o
r
ien
ted
r
ep
r
esen
ta
tio
n
o
f
t
h
e
ti
m
etab
le,
w
h
ic
h
allo
w
s
s
ee
in
g
t
h
e
e
n
tir
e
ti
m
etab
le
f
o
r
all
class
r
o
o
m
s
al
l a
t th
e
s
a
m
e
ti
m
e.
C
la
s
s
clas
h
es c
an
b
e
r
ep
r
esen
ted
as:
∑
(
1
,
1
,
1
+
v
1
,
2
,
1
)
=
1
;
∀
∈
V
∈
(
3
)
w
h
ic
h
m
ea
n
s
t
h
at
f
o
r
an
y
cla
s
s
r
o
o
m
c
1
,
n
o
t
w
o
co
u
r
s
es
(
k
1
,
k
2
)
ar
e
as
s
ig
n
ed
to
it
at
t
h
e
s
a
m
e
ti
m
e
s
lo
t
s
1
r
eg
ar
d
less
o
f
th
e
in
s
tr
u
c
to
r
wh
o
g
ets
ass
ig
n
ed
to
th
at
p
ar
ti
cu
lar
co
u
r
s
e.
I
n
s
tr
u
cto
r
s
clas
h
(
co
n
f
lict)
:
T
h
is
is
q
u
ite
th
e
o
p
p
o
s
ite
o
f
th
e
clas
s
r
o
o
m
clas
h
p
r
o
b
lem
s
u
c
h
th
at
o
n
e
ca
n
n
o
t
allo
ca
te
m
o
r
e
th
a
n
o
n
e
class
r
o
o
m
i
n
th
e
s
a
m
e
t
i
m
e
s
lo
t
f
o
r
a
g
i
v
e
n
i
n
s
tr
u
cto
r
’
s
ti
m
etab
le.
S
u
ch
a
p
r
o
b
lem
u
s
u
all
y
o
cc
u
r
s
s
i
n
ce
th
e
ad
m
in
is
tr
ato
r
ca
n
n
o
t
s
ee
t
h
e
ti
m
etab
les
f
o
r
all
in
s
tr
u
cto
r
s
al
l
at
t
h
e
s
a
m
e
ti
m
e.
Her
e,
a
g
ain
,
th
e
p
r
o
p
o
s
ed
s
o
lu
tio
n
a
v
o
id
s
th
is
p
r
o
b
le
m
u
s
i
n
g
I
n
s
tr
u
ct
o
r
-
o
r
ien
te
d
r
ep
r
esen
tatio
n
o
f
a
ti
m
etab
le
s
u
c
h
t
h
at
it
allo
w
s
d
is
p
la
y
i
n
g
th
e
ti
m
etab
les
f
o
r
all
in
s
tr
u
cto
r
s
all
at
th
e
s
a
m
e
ti
m
e.
I
n
s
tr
u
c
to
r
clash
ca
n
b
e
r
ep
r
esen
ted
in
th
e
f
o
r
m
:
∑
(
1
,
1
,
1
+
v
2
,
1
,
1
)
=
1
;
∀
∈
∈
(
4
)
T
h
is
m
ea
n
s
th
at
f
o
r
an
y
g
i
v
e
n
in
s
tr
u
cto
r
i
k
,
n
o
t
w
o
clas
s
r
o
o
m
s
(
c
i
,
c
j
)
ar
e
ass
ig
n
ed
to
h
i
m
/h
er
i
n
th
e
s
a
m
e
ti
m
e
s
lo
t
s
k
r
eg
ar
d
les
s
o
f
w
h
ich
co
u
r
s
e
s
h
e/s
h
e
i
s
a
s
s
ig
n
ed
to
.
F
in
all
y
,
th
e
L
ec
tu
r
e
s
(
w
ee
k
l
y
)
lo
ad
:
I
n
ev
er
y
Sc
h
o
o
l
p
o
lic
y
,
ea
c
h
co
u
r
s
e
h
as
a
p
r
eset
n
u
m
b
e
r
o
f
lect
u
r
es
p
er
w
ee
k
p
er
ea
ch
clas
s
r
o
o
m
.
T
h
is
co
n
s
tr
ai
n
t
r
ea
d
il
y
i
m
p
li
es
t
h
at
w
e
ca
n
n
o
t
p
o
s
s
ib
l
y
i
n
cr
ea
s
e
o
r
d
ec
r
ea
s
e
t
h
e
n
u
m
b
er
o
f
lect
u
r
es
f
o
r
a
co
u
r
s
e
in
a
n
y
g
i
v
en
cla
s
s
r
o
o
m
.
T
h
er
ef
o
r
e,
th
e
r
eq
u
ir
ed
n
u
m
b
er
o
f
lectu
r
e
s
f
o
r
co
u
r
s
e
k
1
t
au
g
h
t
at
cla
s
s
r
o
o
m
c
1
d
u
r
in
g
t
h
e
w
ee
k
r
eg
ar
d
less
th
e
ti
m
e
s
lo
t d
is
tr
ib
u
tio
n
o
r
th
e
p
ar
ticu
lar
in
s
tr
u
cto
r
o
f
th
e
c
o
u
r
s
e
is
g
iv
e
n
b
y
:
≡
∑
∑
∑
1
,
1
;
∀
∈
∈
∈
∈
(5
)
w
h
er
e
D
(
j
)
=
1
,
…
,
5
;
w
h
ic
h
r
ep
r
esen
ts
th
e
w
ee
k
l
y
s
c
h
o
o
l
d
ay
s
.
Si
m
ilar
l
y
,
t
h
e
n
u
m
b
er
o
f
lectu
r
es
h
as
to
b
e
tau
g
h
t
b
y
i
n
s
tr
u
cto
r
i
1
d
u
r
i
n
g
th
e
w
ee
k
r
eg
ar
d
les
s
o
f
co
u
r
s
e
s
g
et
tau
g
h
t,
t
h
e
ti
m
e
s
lo
ts
o
r
th
e
cla
s
s
r
o
o
m
s
is
g
iv
e
n
b
y
:
≥
∑
∑
∑
∑
1
;
∀
∈
∈
∈
∈
∈
(
6
)
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
C
o
u
r
s
es ti
meta
b
lin
g
b
a
s
ed
o
n
h
ill climb
in
g
a
lg
o
r
ith
m
(
A
b
d
o
u
l R
jo
u
b
)
6561
b.
Da
y
lo
ad
T
h
e
n
u
m
b
er
o
f
lect
u
r
es
p
er
co
u
r
s
e
f
o
r
ea
c
h
clas
s
r
o
o
m
m
u
s
t
b
e
d
i
v
id
ed
in
to
f
i
v
e
w
o
r
k
in
g
d
a
y
s
.
Fo
r
ex
a
m
p
le,
if
a
g
iv
e
n
clas
s
r
o
o
m
ca
ter
s
f
o
r
f
i
v
e
Ma
th
co
u
r
s
e
lectu
r
es,
th
e
n
ea
ch
d
a
y
ca
n
h
av
e
n
o
m
o
r
e
th
an
o
n
e
lectu
r
e
f
o
r
th
e
s
a
m
e
co
u
r
s
e.
C
o
n
s
eq
u
e
n
tl
y
,
th
r
ee
ca
s
es
w
ill
ar
is
e
as
s
u
m
i
n
g
th
at
t
h
er
e
ar
e
5
s
ch
o
o
l
d
ay
s
(
w
o
r
k
i
n
g
d
a
y
s
)
i
n
a
g
i
v
en
w
ee
k
:
C
ase
1
:
C
la
s
s
c
h
a
s
les
s
th
a
n
f
i
v
e
lectu
r
e
s
o
f
co
u
r
s
e
k
d
u
r
i
n
g
th
e
w
ee
k
∑
∑
∑
1
,
1
<
5
;
∀
∈
,
∀
∈
,
∀
∈
∈
∈
5
=
1
(
7
)
T
h
en
,
1
,
=
{
0
,
1
}
;
∀
∈
(
8
)
w
h
er
e
,
,
,
≡
{
1
;
ℎ
0
;
ℎ
(
9
)
C
ase
2
:
C
la
s
s
c
h
a
s
ex
ac
t
l
y
f
i
v
e
lectu
r
es o
f
co
u
r
s
e
k
d
u
r
in
g
t
h
e
w
ee
k
∑
∑
∑
1
,
1
=
5
;
∀
∈
,
∀
∈
,
∀
∈
∈
∈
5
=
1
(
1
0
)
T
h
en
,
1
,
=
1
;
∀
∈
(
1
1
)
C
ase
3
:
C
la
s
s
c
h
a
s
m
o
r
e
t
h
an
f
i
v
e
lectu
r
e
s
o
f
co
u
r
s
e
k
d
u
r
i
n
g
th
e
w
ee
k
∑
∑
∑
1
,
1
>
5
;
∈
∈
5
=
1
∀
∈
,
∀
∈
,
∀
∈
(
1
2
)
T
h
en
,
1
≤
1
,
≤
2
;
∀
∈
(
1
3
)
s
u
c
h
th
a
t
∑
1
,
5
=
1
=
∑
∑
∑
1
,
1
∈
∈
5
=
1
(
1
4
)
T
h
e
f
in
al
an
d
d
ef
in
i
te
co
n
s
tr
ain
t
i
s
th
a
t
n
o
f
r
ee
lect
u
r
es
ar
e
allo
w
ed
to
b
e
ass
ig
n
ed
to
an
y
cla
s
s
r
o
o
m
b
ef
o
r
e
th
e
last
lect
u
r
e
in
t
h
at
p
ar
ticu
lar
class
r
o
o
m
o
n
a
g
i
v
en
d
ay
.
1
≠
0
;
∀
<
,
∀
∈
,
∀
∈
(
1
5
)
2
.
3
.
L
a
y
er
3
:
s
o
f
t
co
ns
t
ra
int
s
So
f
t
co
n
s
tr
ain
ts
r
ef
er
to
t
h
e
p
ar
a
m
eter
s
t
h
at
ar
e
s
o
m
e
w
h
at
le
s
s
i
m
p
o
r
ta
n
t
t
h
an
t
h
eir
h
ar
d
co
u
n
ter
p
ar
t
s
ar
e.
Her
e,
alth
o
u
g
h
th
e
s
e
w
o
u
ld
s
h
o
w
u
p
in
th
e
co
m
p
u
ter
p
r
o
g
r
a
m
,
it
w
o
u
ld
n
o
t
b
e
v
er
y
n
ec
ess
ar
y
to
ac
co
u
n
t
f
o
r
all
o
f
th
e
m
.
Def
i
n
ite
l
y
,
t
h
e
m
o
r
e
co
n
tai
n
ed
it
is
,
t
h
e
b
et
ter
th
e
s
ch
ed
u
le.
A
s
m
en
tio
n
e
d
ea
r
lier
,
la
y
er
3
is
m
ad
e
u
p
o
f
t
w
o
co
n
s
tr
ai
n
ts
:
C
las
s
r
o
o
m
p
r
ef
er
e
n
ce
s
:
P
r
ef
er
en
ce
s
o
f
cla
s
s
r
o
o
m
s
i
m
p
licitl
y
r
e
f
er
to
t
h
e
th
r
e
e
co
n
s
tr
ain
ts
a
s
s
o
ciate
d
w
it
h
cl
ass
r
o
o
m
s
:
Scie
n
ti
f
ic
C
o
u
r
s
e
s
:
Scien
ti
f
ic
co
u
r
s
es
s
u
ch
a
s
P
h
ysics
,
Ma
th
ema
tics
,
C
h
emist
r
y
an
d
B
io
lo
g
y
ar
e
t
o
b
e
co
n
s
id
er
ed
d
u
r
in
g
th
e
ea
r
l
y
ti
m
e
s
lo
ts
.
No
n
-
Scien
ti
f
ic
C
o
u
r
s
es
:
No
n
-
Scien
tific
co
u
r
s
e
s
s
u
c
h
a
s
A
r
ts
,
S
p
o
r
ts
,
His
to
r
y
a
n
d
C
o
mp
u
ter
s
kills
ar
e
to
b
e
co
n
s
i
d
er
ed
f
o
r
th
e
latter
ti
m
e
s
lo
ts
.
T
h
e
I
n
s
tr
u
cto
r
p
r
ef
er
en
ce
s
w
h
ich
i
s
an
e
s
s
en
tia
l
p
ar
t
o
f
th
e
teac
h
in
g
p
r
o
ce
s
s
ad
d
r
ess
es
th
e
i
n
s
tr
u
cto
r
s
’
co
n
v
e
n
ie
n
ce
a
n
d
co
m
f
o
r
t
lev
el
s
d
u
r
in
g
t
h
e
s
e
m
ester
,
s
u
c
h
t
h
at
th
e
teac
h
i
n
g
ef
f
o
r
t
is
r
e
f
lecte
d
m
o
r
e
p
o
s
iti
v
el
y
o
n
th
e
o
v
er
all
ed
u
ca
tio
n
al
p
r
o
ce
s
s
.
Hen
ce
,
s
ev
er
al
in
s
tr
u
cto
r
-
ce
n
tr
ic
f
ac
ets
ar
e
co
n
s
id
er
ed
.
T
h
ese
in
clu
d
e
an
i
n
s
tr
u
cto
r
’
s
p
r
ef
er
en
ce
o
n
w
h
et
h
er
h
e/
s
h
e
w
o
u
ld
r
ath
er
s
tar
t
th
eir
d
ail
y
t
ea
ch
in
g
i
n
th
e
f
ir
s
t
lectu
r
e
s
lo
t
o
f
ea
c
h
d
a
y
o
r
n
o
t
.
A
l
s
o
,
an
in
s
tr
u
cto
r
’
s
p
r
ef
er
e
n
ce
to
ca
ll
it
a
n
ea
r
l
y
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u
it
s
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o
n
a
n
y
p
ar
tic
u
lar
d
a
y
o
f
ch
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ice,
a
n
d
f
i
n
all
y
w
h
et
h
e
r
th
e
i
n
s
tr
u
cto
r
s
till
h
ap
p
en
s
to
b
e
a
s
tu
d
en
t
o
f
t
h
e
i
n
s
tit
u
t
io
n
h
i
m
s
el
f
/h
er
s
el
f
w
it
h
ce
r
tai
n
co
n
v
en
ie
n
ce
-
d
r
iv
en
n
ee
d
s
t
h
at
n
ee
d
to
b
e
ac
co
m
m
o
d
ated
b
y
t
h
e
ti
m
etab
le
o
r
g
an
izer
s
.
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
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
558
-
6
5
7
3
6562
3.
E
F
F
I
CI
E
N
T
H
I
L
L
C
L
I
M
B
I
NG
A
L
G
O
R
I
T
H
M
T
h
e
Hill
C
li
m
b
in
g
A
l
g
o
r
ith
m
(
HC
A
)
is
a
m
at
h
e
m
atica
l
te
ch
n
iq
u
e
th
at
b
elo
n
g
s
to
th
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teg
o
r
y
o
f
lo
ca
l
s
ea
r
ch
a
lg
o
r
it
h
m
s
[
2
0
-
2
2
]
.
I
t
is
a
r
ep
etiti
v
e
al
g
o
r
ith
m
th
at
s
tar
t
s
w
it
h
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n
in
i
tial
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o
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latio
n
ch
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en
f
r
o
m
th
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t
io
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s
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t
th
en
g
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t
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o
u
g
h
a
p
r
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ce
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s
th
at
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m
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r
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es
t
h
ese
s
o
lu
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s
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y
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cr
e
m
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n
ta
ll
y
ch
an
g
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t
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ts
in
o
r
d
er
to
cr
ea
te
n
e
w
s
o
l
u
tio
n
s
.
I
n
t
h
e
p
r
o
ce
s
s
,
s
o
l
u
tio
n
s
t
h
at
h
av
e
h
i
g
h
er
co
s
t
v
alu
e
s
ar
e
ad
o
p
ted
in
a
n
e
f
f
o
r
t
to
g
e
n
er
ate
a
n
e
w
p
o
p
u
la
tio
n
a
n
d
t
h
e
p
r
o
ce
s
s
is
r
ep
ea
ted
u
n
til
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o
f
u
r
th
er
i
m
p
r
o
v
e
m
en
t
s
ca
n
b
e
ac
h
ie
v
e
d
[
2
3
]
.
Un
d
er
th
e
p
r
o
p
o
s
ed
tech
n
iq
u
e,
th
e
Hill
C
li
m
b
in
g
al
g
o
r
ith
m
i
s
m
o
d
if
ied
to
b
e
u
s
ed
as a
n
o
p
ti
m
izat
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n
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o
r
ith
m
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e
th
e
o
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ti
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i
za
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n
p
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ce
s
s
co
n
tin
u
e
s
as
lo
n
g
as
th
e
ca
lcu
lated
h
e
u
r
is
tic
v
al
u
e
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i.e
.
,
co
s
t
v
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lu
e,
o
f
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h
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o
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iz
ed
s
o
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s
le
s
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th
a
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ze
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o
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h
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th
a
t
t
h
e
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r
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ce
s
s
is
s
to
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h
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alu
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ch
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g
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h
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co
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ec
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ti
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e
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tio
n
s
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t
h
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u
ld
in
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icate
th
at
n
o
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m
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t
ca
n
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h
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a
n
d
th
e
s
o
lu
t
io
n
i
s
f
in
all
y
r
ea
ch
ed
[
2
4
]
.
T
h
e
h
eu
r
i
s
tic
v
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e
is
a
li
n
ea
r
f
u
n
ctio
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o
f
s
o
f
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tr
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;
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u
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r
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t
d
eg
r
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e
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u
r
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en
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tio
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s
th
e
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e
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n
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ain
t
s
.
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t
ch
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s
i
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t
h
e
t
w
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s
tr
ain
ts
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cla
s
s
p
r
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ce
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atis
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ied
f
o
r
all
clas
s
es i
n
th
e
s
c
h
o
o
l,
s
u
c
h
th
at:
=
{
0
;
ℎ
′
−
1
;
ℎ
−
2
;
ℎ
ℎ
(
1
6
)
w
h
er
e
r
ep
r
esen
ts
a
m
ea
s
u
r
e
o
f
th
e
cla
s
s
p
r
ef
er
e
n
ce
co
n
s
tr
ai
n
ts
f
o
r
class
c.
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n
ad
d
itio
n
,
it
c
h
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k
s
i
f
t
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e
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n
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ai
n
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n
s
tr
u
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r
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s
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er
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al
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r
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ce
s
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ail
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w
o
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h
o
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r
s
a
n
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last
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r
e
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en
ce
s
ar
e
s
at
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f
ied
f
o
r
all
in
s
tr
u
cto
r
s
,
s
u
ch
t
h
at:
=
{
0
;
ℎ
,
ℎ
−
1
;
ℎ
−
2
;
ℎ
−
3
;
ℎ
(
1
7
)
w
h
er
e
r
ep
r
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ts
th
e
m
ea
s
u
r
e
m
en
t
o
f
th
e
i
n
s
tr
u
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r
's
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e
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ce
s
,
d
aily
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k
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o
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r
s
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d
last
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r
e
p
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ef
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en
ce
s
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r
in
s
tr
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r
i
.
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a
r
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lt,
th
e
h
eu
r
i
s
tic
p
ar
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m
et
er
is
g
iv
e
n
as
:
=
∑
Ҫ
=
1
+
∑
ḽ
=
1
(
1
8
)
T
h
e
in
itial
a
n
d
o
p
ti
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al
v
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e
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is
0
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t
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e
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s
s
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m
o
r
in
s
tr
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cto
r
.
Har
d
co
n
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tr
ai
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e
n
o
t c
o
n
s
id
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as M
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o
t p
r
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s
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n
les
s
all
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e
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ar
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ain
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ati
s
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ied
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T
h
e
in
p
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to
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th
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is
r
eq
u
ir
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to
r
u
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th
is
tech
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q
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e
is
:
〈
,
,
〉
as f
o
llo
w
s
:
-
C
o
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r
s
e
d
etails
: s
u
ch
as c
o
u
r
s
e
titl
e,
co
u
r
s
e
t
y
p
e
(
Scie
n
ti
f
ic
o
r
No
n
-
Sc
ien
t
if
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.
-
C
las
s
d
etail
s
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a
s
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m
e,
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s
s
d
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le
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(
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im
ar
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I
n
ter
m
ed
iate
o
r
Seco
n
d
ar
y
)
a
n
d
th
e
lis
t o
f
all
co
u
r
s
e
s
th
a
t a
r
e
tau
g
h
t i
n
a
g
i
v
e
n
class
r
o
o
m
.
-
I
n
s
tr
u
c
to
r
d
etails:
s
u
ch
as
h
i
s
/h
er
I
D
n
u
m
b
er
,
n
a
m
e,
n
u
m
b
er
o
f
le
ctu
r
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s
h
e/s
h
e
ca
n
teac
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i
n
s
tr
u
cto
r
s
p
ec
ialt
y
(
P
r
i
m
ar
y
lev
e
l,
Dip
lo
m
a
o
r
B
ac
h
elo
r
'
s
d
eg
r
ee
o
r
ab
o
v
e)
a
n
d
a
lis
t
o
f
all
class
r
o
o
m
s
a
n
d
th
e
co
u
r
s
e
s
th
at
ar
e
ta
u
g
h
t b
y
t
h
is
i
n
s
tr
u
cto
r
.
4.
T
H
E
P
RO
P
O
SE
D
T
I
M
E
T
A
B
L
E
SCH
E
DU
L
I
N
G
T
E
CH
NIQU
E
On
ce
all
r
eq
u
ir
ed
d
ata
w
ill
h
av
e
b
ee
n
id
en
t
if
ied
a
n
d
ac
co
u
n
ted
f
o
r
,
th
e
cr
ea
tio
n
p
r
o
ce
s
s
w
il
l
co
m
m
e
n
ce
i
n
t
h
r
ee
s
ep
ar
ate
p
h
ase
s
.
T
h
e
f
ir
s
t
p
h
ase
is
t
h
e
d
ata
o
r
g
an
izatio
n
p
h
a
s
e
(
DOP
)
w
h
ic
h
o
r
g
a
n
izes
al
l
th
e
d
ata
th
at
w
as
ac
co
u
n
ted
f
o
r
ea
r
lier
.
T
h
e
s
ec
o
n
d
p
h
ase
is
t
h
e
i
n
itia
l
s
tate
p
h
a
s
e
(
I
SP
)
w
h
ic
h
cr
ea
tes
a
n
in
itial
s
o
lu
tio
n
f
o
r
th
e
t
i
m
e
ta
b
le
an
d
th
e
th
ir
d
p
h
ase
i
s
th
e
s
atis
f
ied
s
o
f
t
co
n
s
tr
ai
n
ts
p
h
ase
(
SS
C
P
)
w
h
ic
h
i
m
p
r
o
v
es
th
e
i
n
itial
s
o
lu
tio
n
u
s
i
n
g
MH
C
A
to
s
ati
s
f
y
a
ll
o
f
th
e
s
o
f
t
co
n
s
tr
ain
ts
a
s
it
p
o
s
s
ib
l
y
ca
n
i
n
o
r
d
er
to
ac
h
iev
e
t
h
e
"
b
est"
f
in
al
s
o
l
u
tio
n
[
2
5
]
.
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
C
o
u
r
s
es ti
meta
b
lin
g
b
a
s
ed
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n
h
ill climb
in
g
a
lg
o
r
ith
m
(
A
b
d
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l R
jo
u
b
)
6563
4
.
1
.
T
he
da
t
a
o
rg
a
niza
t
i
o
n pha
s
e
(
DO
P
)
W
h
en
th
e
s
y
s
te
m
b
eg
i
n
s
to
b
u
ild
a
s
ch
o
o
l
ti
m
etab
le,
it
co
m
m
en
ce
s
b
y
o
r
g
an
izi
n
g
th
e
r
eq
u
ir
ed
d
ata
as
a
f
ir
s
t
tas
k
.
I
n
th
i
s
p
h
ase
(
DOP
)
,
th
e
s
y
s
te
m
s
tar
ts
t
h
e
cr
ea
tio
n
o
f
th
e
ti
m
etab
le
b
y
lo
ad
in
g
th
e
r
eq
u
ir
ed
d
ata
an
d
s
etti
n
g
u
p
th
e
d
ata
s
tr
u
ct
u
r
es.
Su
c
h
r
eq
u
ir
ed
d
ata
in
th
e
s
ch
o
o
l o
b
j
ec
t sp
lits
in
to
f
o
u
r
t
y
p
e
s
o
f
o
b
j
ec
ts
:
-
I
n
s
tr
u
c
to
r
Ob
j
ec
t:
co
n
tain
v
ar
iab
les
s
u
c
h
as
I
n
s
tr
u
cto
r
-
I
D,
I
n
s
tr
u
cto
r
-
T
o
tal
-
Nu
m
b
er
-
Of
-
L
ec
tu
r
e
s
an
d
C
las
s
-
C
o
u
r
s
e
-
Li
s
t
t
h
at
r
e
f
er
s
to
th
e
cla
s
s
e
s
a
n
d
co
u
r
s
e
s
w
h
ich
t
h
i
s
i
n
s
tr
u
cto
r
teac
h
e
s
a
n
d
th
e
I
n
s
tr
u
cto
r
-
Nu
m
b
er
-
Of
-
L
a
s
t
-
L
ec
tu
r
e.
-
C
las
s
Ob
j
ec
t:
co
n
tain
s
v
ar
iab
les
s
u
c
h
as
C
las
s
-
I
D,
C
lass
-
T
o
tal
-
N
u
m
b
er
-
Of
-
L
ec
t
u
r
es,
C
l
ass
-
C
o
u
r
s
e
-
L
is
t
th
at
r
ef
er
s
to
ea
ch
co
u
r
s
e
w
it
h
its
in
s
t
r
u
cto
r
s
,
C
las
s
-
L
a
s
t
-
L
e
ctu
r
e
th
at
r
ef
er
s
to
th
e
in
d
e
x
o
f
last
lect
u
r
e
in
th
e
clas
s
ti
m
etab
le
an
d
C
la
s
s
-
Nu
m
b
er
-
Of
-
L
a
s
t
-
L
ec
tu
r
e
t
h
at
r
ef
er
s
to
th
e
to
tal
n
u
m
b
er
o
f
la
s
t le
ctu
r
e
s
.
-
C
o
u
r
s
e
Ob
j
ec
t: c
o
n
tain
s
v
ar
ia
b
les s
u
c
h
as
C
o
u
r
s
e
-
I
D
an
d
C
o
u
r
s
e
-
T
y
p
e.
-
C
las
s
-
C
o
u
r
s
e
Ob
j
ec
t:
co
n
tain
s
s
o
m
e
v
ar
iab
les
th
a
t
li
n
k
C
l
ass
-
I
D,
C
o
u
r
s
e
-
I
D,
N
u
m
b
er
-
Of
-
L
ec
tu
r
e
s
an
d
I
n
s
tr
u
c
to
r
-
I
D
w
it
h
th
e
I
n
s
tr
u
ct
o
r
Ob
j
ec
t,
C
lass
o
b
j
ec
t a
n
d
C
o
u
r
s
e
o
b
j
ec
t.
On
ce
t
h
e
r
eq
u
ir
ed
d
ata
is
lo
ad
ed
an
d
s
p
lit
in
to
th
e
s
aid
o
b
j
ec
ts
,
t
h
e
al
g
o
r
ith
m
co
m
m
en
ce
s
t
h
e
s
c
h
o
o
l
ti
m
etab
le
g
e
n
er
atio
n
.
T
h
e
I
C
T
NL
F
u
n
ct
io
n
ill
u
s
tr
ates
h
o
w
m
an
y
ti
m
es
ea
ch
s
p
ec
i
f
ic
co
u
r
s
e
is
g
o
n
e
th
r
o
u
g
h
f
o
r
a
s
p
ec
if
ic
i
n
s
tr
u
cto
r
an
d
h
o
w
m
a
n
y
ti
m
es
ea
c
h
s
p
ec
i
f
ic
co
u
r
s
e
i
s
g
o
n
e
th
r
o
u
g
h
f
o
r
a
s
p
ec
if
ic
cla
s
s
r
o
o
m
.
A
lo
o
p
s
elec
ts
th
e
n
ex
t
o
b
j
ec
t
f
r
o
m
C
la
s
s
-
C
o
u
r
s
es
li
s
t,
an
d
th
en
f
i
n
d
s
th
e
i
n
s
tr
u
cto
r
o
b
j
ec
t
th
at
h
a
s
th
e
s
a
m
e
I
n
s
tr
u
c
to
r
-
I
D.
T
h
is
is
p
er
f
o
r
m
ed
i
n
o
r
d
er
to
ad
d
t
h
e
n
u
m
b
er
o
f
lect
u
r
es
f
o
r
t
h
e
C
la
s
s
-
C
o
u
r
s
es
o
b
j
ec
t
to
th
e
to
tal
n
u
m
b
er
o
f
lect
u
r
es
o
f
th
e
i
n
s
tr
u
cto
r
o
b
j
ec
t
an
d
th
en
t
h
e
s
a
m
e
p
r
o
c
ed
u
r
e
is
r
ep
ea
ted
f
o
r
th
e
class
o
b
j
ec
t.
I
t
is
q
u
ite
ev
id
en
t
th
a
t
t
h
e
co
m
p
lex
it
y
o
f
th
i
s
f
u
n
ctio
n
is
(
(
ḽ
+
Ҫ
)
)
.
W
h
er
e
CKO
is
t
h
e
n
u
m
b
er
o
f
class
-
co
u
r
s
e
o
b
j
ec
ts
,
w
h
ic
h
ca
n
b
e
d
escr
ib
ed
as:
=
∑
∑
∑
,
;
∀
∈
,
∀
∈
,
∀
∈
∈
∈
∈
(
1
9
)
=
∑
∑
;
∀
∈
∈
∈
,
∀
∈
Th
e
to
tal
n
u
m
b
er
o
f
lect
u
r
es
f
o
r
an
y
in
s
tr
u
cto
r
i
is
:
=
∑
∑
∑
∑
;
∀
∈
,
∀
∈
,
∀
∈
,
∀
∈
∈
∈
∈
∈
,
∀
∈
(
2
0
)
Si
m
i
lar
l
y
,
t
h
e
to
tal
n
u
m
b
er
o
f
lectu
r
es
f
o
r
an
y
cla
s
s
c
is
:
=
∑
∑
∑
∑
;
∀
∈
,
∀
∈
,
∀
∈
,
∀
∈
,
∀
∈
∈
∈
∈
∈
(
2
1
)
Fro
m
(
1
0
)
,
th
e
to
tal
n
u
m
b
er
o
f
lect
u
r
es
i
n
t
h
e
s
c
h
o
o
l
is
th
e
s
u
m
m
atio
n
o
f
t
h
e
to
tal
n
u
m
b
e
r
o
f
lectu
r
e
s
o
f
al
l
class
r
o
o
m
s
,
as
g
i
v
en
b
y
:
Ω
=
∑
;
∀
∈
∈
(
2
2
)
As a
r
esu
lt,
t
h
e
p
r
o
b
ab
ilit
y
to
s
ch
ed
u
le
th
e
lect
u
r
es o
f
t
h
e
n
e
x
t in
s
tr
u
c
to
r
(
f+1
)
is
:
+
1
=
(
1
ḽ
−
)
(
Ω
−
−
∑
1
Ω
)
(
2
3
)
w
h
er
e
z
is
t
h
e
n
u
m
b
er
o
f
lectu
r
es r
eser
v
ed
f
o
r
in
s
tr
u
cto
r
(
f+1
)
in
th
e
p
r
o
ce
s
s
.
On
ce
t
h
e
to
tal
n
u
m
b
er
o
f
lect
u
r
es
i
s
ca
lcu
lated
,
an
I
L
L
f
u
n
ctio
n
w
i
ll
f
i
n
d
t
h
e
i
n
d
ex
f
o
r
l
ast
lect
u
r
e
f
o
r
ea
ch
clas
s
r
o
o
m
,
i.e
.
,
th
e
t
i
m
e
s
lo
t
o
f
t
h
e
last
lectu
r
e
with
i
n
t
h
e
w
ee
k
,
in
o
r
d
er
to
in
itialize
i
n
s
tr
u
cto
r
’
s
ti
m
etab
le
s
an
d
cla
s
s
ti
m
etab
les
as
w
e
ll
as
th
at
f
o
r
t
h
e
s
c
h
o
o
l
as
a
w
h
o
le.
A
n
e
w
p
ar
a
m
eter
is
as
s
ig
n
ed
(
(
Ҫ
)
)
to
d
is
tr
ib
u
tes
th
e
cla
s
s
lect
u
r
e
s
o
v
er
th
e
f
i
v
e
w
ee
k
l
y
d
a
y
s
e
v
en
h
an
d
ed
l
y
to
f
in
d
t
h
e
m
a
x
i
m
u
m
ti
m
e
s
lo
ts
f
o
r
o
n
e
w
o
r
k
i
n
g
d
a
y
.
T
h
e
n
,
w
h
er
e
t
h
er
e
r
e
m
ain
lect
u
r
es
u
n
ac
co
u
n
ted
f
o
r
,
t
h
e
I
L
L
in
cr
ea
s
es
t
h
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
ti
m
e
s
lo
t
s
b
y
o
n
e
,
an
d
d
is
tr
ib
u
tes
th
ese
lect
u
r
es
o
v
er
th
er
e
m
a
in
i
n
g
in
s
tr
u
cto
r
s
s
tar
tin
g
f
r
o
m
th
e
f
ir
s
t d
a
y
o
f
t
h
e
w
ee
k
,
s
u
c
h
th
at:
=
{
5
;
(
5
)
=
0
5
+
1
;
ℎ
(
2
4
)
w
h
er
e
is
t
h
e
m
a
x
i
m
u
m
n
u
m
b
er
o
f
tim
e
s
lo
ts
o
f
class
c
f
o
r
an
y
w
o
r
k
i
n
g
d
a
y
.
Fo
r
th
e
en
tire
s
ch
o
o
l,
th
e
in
d
e
x
f
o
r
th
e
la
s
t le
ct
u
r
e
is
g
i
v
en
b
y
:
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
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
558
-
6
5
7
3
6564
=
(
)
;
∀
∈
(
2
5
)
T
h
e
NL
L
I
Fu
n
ctio
n
in
g
e
n
er
al
co
u
n
t
s
h
o
w
m
a
n
y
w
e
e
k
l
y
lect
u
r
es
ar
e
s
c
h
ed
u
led
to
tak
e
p
la
ce
in
ti
m
e
s
lo
t
f
o
r
th
e
w
h
o
le
s
ch
o
o
l,
an
d
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e
n
it
d
is
tr
ib
u
te
s
th
e
s
e
l
ec
tu
r
es
a
m
o
n
g
s
t
i
n
s
tr
u
cto
r
s
ev
en
-
h
an
d
ed
l
y
.
T
h
is
h
ap
p
en
s
co
m
m
e
n
s
u
r
ate
w
it
h
t
h
e
f
air
n
es
s
cr
iter
io
n
t
h
a
t
w
ar
r
an
ts
th
at
th
e
lect
u
r
e
d
is
tr
ib
u
tio
n
p
r
o
ce
s
s
i
s
b
ias
f
r
ee
d
e
v
o
id
o
f
a
n
y
f
av
o
r
i
tis
m
p
r
ac
tices,
p
er
t
h
e
s
o
f
t
co
n
s
tr
ai
n
ts
i
n
s
ec
t
io
n
2
.
As
a
r
es
u
lt
o
f
t
h
is
f
u
n
ctio
n
,
ea
ch
i
n
s
tr
u
cto
r
g
ets
h
i
s
/
h
er
o
wn
s
h
ar
e
o
f
t
h
e
Nu
m
b
er
o
f
L
ast
L
ec
t
u
r
es
(
N
L
L
)
.
First,
th
e
n
u
m
b
er
o
f
a
ll lec
t
u
r
es
th
at
ta
k
e
p
lac
e
ti
m
e
s
lo
t a
cr
o
s
s
th
e
s
c
h
o
o
l is g
i
v
en
b
y
:
=
∑
∑
;
∀
∈
Ҫ
Ҫ
=
1
5
=
1
(
2
6
)
T
h
en
f
o
r
all
in
s
tr
u
cto
r
s
,
i
f
i
n
s
tr
u
cto
r
i
teac
h
e
s
a
class
s
u
c
h
th
a
t
=
,
th
e
n
th
e
n
u
m
b
er
o
f
in
s
tr
u
cto
r
s
w
h
o
teac
h
lect
u
r
es
in
th
a
t c
lass
r
o
o
m
w
i
th
in
t
h
at
ti
m
e
s
lo
t is
g
i
v
en
b
y
:
=
+
1
(
2
7
)
w
h
er
e
t
h
er
e
s
t
ill
e
x
i
s
ts
ca
s
es
o
f
m
o
r
e
lectu
r
es
t
h
an
t
h
er
e
ar
e
in
s
tr
u
cto
r
s
,
th
e
n
t
h
e
r
e
m
ai
n
i
n
g
n
o
n
-
d
i
s
tr
ib
u
ted
lectu
r
es
ar
e
d
is
tr
ib
u
ted
r
an
d
o
m
l
y
ac
r
o
s
s
i
n
s
tr
u
cto
r
s
,
s
u
ch
t
h
at
t
h
e
r
an
d
o
m
p
r
o
b
ab
ilit
y
to
s
elec
t
an
y
o
n
e
o
f
th
e
m
is
:
=
1
(
2
8
)
4
.
2
.
T
he
ini
t
ia
l st
a
t
e
ph
a
s
e
(
I
SP)
I
n
itiall
y
,
an
d
as
ex
p
lain
ed
i
n
[
1
6
,
1
7
]
,
th
e
f
ir
s
t
s
tep
is
to
cr
ea
te
a
r
an
d
o
m
in
itia
l
s
o
lu
tio
n
an
d
th
e
n
p
er
f
o
r
m
ad
d
itio
n
al
o
p
er
atio
n
s
o
n
it
w
it
h
t
h
e
o
b
j
ec
tiv
e
o
f
s
atis
f
y
i
n
g
t
h
e
h
ar
d
co
n
s
tr
ain
t
s
th
er
eb
y
ar
r
iv
i
n
g
at
th
e
co
r
r
ec
t
i
n
itial
s
o
l
u
tio
n
[
1
8
]
.
I
n
f
ac
t,
th
is
h
a
s
b
ee
n
a
r
ath
er
ti
m
e
-
co
n
s
u
m
i
n
g
m
et
h
o
d
.
I
n
t
h
e
p
r
o
p
o
s
ed
tech
n
iq
u
e,
th
e
i
n
itial
s
o
lu
tio
n
w
h
ich
i
s
cr
ea
ted
in
th
e
in
i
ti
al
s
tate
p
h
ase
(
I
SP
)
,
k
ee
p
s
all
h
ar
d
co
n
s
tr
ain
t
s
d
ev
o
id
f
r
o
m
an
y
v
io
latio
n
s
s
o
as
to
m
ain
tain
i
n
te
g
r
it
y
an
d
c
o
r
r
ec
tn
ess
o
f
t
h
e
ti
m
etab
le
s
tr
u
ctu
r
e
t
h
r
o
u
g
h
o
u
t.
T
h
e
I
SP
p
r
o
ce
s
s
ca
n
b
e
s
p
lit
in
to
th
r
ee
m
ain
p
ar
ts
i
n
a
w
a
y
t
h
at
w
o
u
ld
u
n
d
er
s
co
r
e
its
r
ath
er
i
m
p
o
r
tan
t
f
u
n
ct
io
n
s
:
4
.
2
.
1
.
Co
m
m
o
n
brea
k
a
rr
a
y
(
CB
A)
W
h
en
an
i
n
s
tr
u
cto
r
is
p
ick
ed
an
d
a
s
p
ec
if
ic
clas
s
r
o
o
m
is
id
en
ti
f
ied
,
a
t
w
o
-
d
i
m
e
n
s
io
n
al
ar
r
ay
ca
ll
e
d
th
e
co
m
m
o
n
-
b
r
ea
k
-
ar
r
a
y
(
C
B
A
)
is
g
e
n
er
ated
.
First,
th
e
i
n
s
tr
u
cto
r
ti
m
etab
le
an
d
th
e
cl
ass
r
o
o
m
ti
m
etab
le
co
n
tain
th
r
ee
t
y
p
es
o
f
ti
m
e
s
lo
ts
as
s
h
o
w
n
i
n
F
ig
u
r
e
1
(a
)
an
d
1
(
b
)
:
ti
m
e
s
lo
ts
r
eser
v
ed
f
o
r
th
e
clas
s
r
o
o
m
(
T
SR
C
)
,
ti
m
e
s
lo
ts
r
e
s
er
v
ed
b
y
t
h
e
i
n
s
tr
u
cto
r
(
T
SR
I
)
an
d
als
o
th
e
r
e
m
ain
in
g
n
o
n
-
r
eser
v
ed
ti
m
e
s
lo
ts
(
N
R
T
S).
W
h
en
t
h
e
i
n
s
tr
u
cto
r
ti
m
e
tab
le
is
o
v
er
lap
p
ed
w
it
h
a
cla
s
s
r
o
o
m
ti
m
etab
le,
t
h
e
co
m
m
o
n
b
r
e
ak
ar
r
a
y
(
C
B
A
)
w
il
l
b
e
g
en
er
ated
as
s
h
o
w
n
ag
a
i
n
in
F
ig
u
r
e
1
(
c
)
.
No
w
,
t
h
e
g
en
er
ated
C
B
A
h
a
s
t
w
o
t
y
p
es
o
f
T
im
e
S
lo
ts
:
a
No
n
-
R
e
s
er
v
ed
t
i
m
e
s
lo
t
th
at
is
r
ep
r
ese
n
ted
b
y
Y/Yes
an
d
a
r
eser
v
ed
ti
m
e
s
lo
t
(
b
y
ei
t
h
er
an
i
n
s
tr
u
cto
r
o
r
a
class
r
o
o
m
)
th
at
i
s
r
ep
r
esen
te
d
b
y
an
N
/No
as ill
u
s
tr
ated
b
y
(
2
9
)
.
,
=
,
,
(
2
9
)
w
h
er
e,
,
is
i
n
s
tr
u
cto
r
i
’
s
ti
m
et
ab
le
an
d
,
is
cla
s
s
r
o
o
m
c
’
s
o
c
cu
p
an
c
y
ti
m
etab
le
as
g
i
v
en
in
(
30
)
an
d
(
31
)
,
r
esp
ec
tiv
el
y
.
4
.
2
.
2
.
T
i
m
e
s
lo
t
s
el
ec
t
io
n
(
ST
S)
f
un
ct
io
n
T
h
e
ST
S
is
an
im
p
o
r
tan
t
f
u
n
ct
io
n
th
at
o
f
f
er
s
s
e
v
er
al
ad
v
a
n
ta
g
es
i
n
th
e
p
r
o
p
o
s
ed
tech
n
iq
u
e,
a
m
o
n
g
s
t
w
h
ic
h
th
a
t
o
f
m
i
n
i
m
izi
n
g
t
h
e
s
ea
r
ch
s
p
ac
e,
p
er
eq
u
atio
n
3
0
,
b
y
av
o
id
i
n
g
ti
m
e
s
lo
ts
w
it
h
a
lab
el
o
f
(
N)
in
th
e
C
B
A
;
a
s
a
co
n
s
eq
u
e
n
ce
,
t
h
e
ex
ec
u
tio
n
ti
m
e
is
f
u
r
th
er
r
ed
u
ce
d
.
Fu
r
th
er
m
o
r
e,
t
h
e
ST
S
f
u
n
ct
io
n
a
v
o
id
s
s
i
m
u
lta
n
eo
u
s
clas
s
r
o
o
m
a
n
d
in
s
tr
u
cto
r
co
n
f
lic
ts
(
clas
h
es)
as
it
o
n
l
y
s
ea
r
ch
e
s
f
o
r
th
e
s
e
t
o
f
ti
m
e
s
lo
ts
t
h
at
s
t
ill
ex
h
ib
it
t
h
e
lab
el
(
Y)
i
n
t
h
e
C
B
A
,
s
a
y
Y
C
B
A
,
w
h
ic
h
m
ea
n
s
th
at
th
e
s
e
ti
m
e
s
lo
ts
ar
e
s
til
l
No
n
-
R
eser
v
ed
,
as
i
s
g
iv
e
n
b
y
(
31
)
.
Ω
(
,
)
=
|
,
|
×
|
,
|
(
3
0
)
,
,
,
∶
,
→
,
,
,
→
,
(
3
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
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lec
&
C
o
m
p
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n
g
I
SS
N:
2
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8
8
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8708
C
o
u
r
s
es ti
meta
b
lin
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b
a
s
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h
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a
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ith
m
(
A
b
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u
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6565
,
,
,
,
w
h
er
e
,
(
,
)
=
1
,
…
,
ɖ
is
d
a
y
s
t
h
at
h
av
e
,
(
,
)
=
1
,
…
,
n
o
n
r
eser
v
ed
ti
m
e
s
lo
ts
.
Fig
u
r
e
1
.
C
o
m
m
o
n
-
b
r
ea
k
-
a
r
r
ay
(
C
B
A
)
i
m
p
le
m
en
tatio
n
On
ce
th
e
C
B
A
is
g
e
n
er
ated
p
er
s
ec
tio
n
4
.
2
.
1
,
th
e
(
S
T
S)
ad
o
p
ts
o
n
e
r
an
d
o
m
No
n
-
R
ese
r
v
ed
T
im
e
Slo
t
f
r
o
m
t
h
e
C
B
A
in
o
r
d
er
to
ch
e
ck
i
f
a
p
ar
ticu
lar
t
i
m
e
s
lo
t
i
s
a
p
p
r
o
p
r
iate
(
v
alid
)
f
o
r
th
e
cla
s
s
/co
u
r
s
e.
W
h
e
n
t
h
i
s
o
cc
u
r
s
,
th
e
co
u
r
s
e
w
ill
b
e
ass
i
g
n
ed
to
t
h
is
ti
m
e
s
lo
t.
As
a
r
esu
l
t,
th
i
s
ti
m
e
s
lo
t
w
il
l
b
e
m
ap
p
ed
to
th
e
cla
s
s
r
o
o
m
a
n
d
in
s
tr
u
c
to
r
ti
m
etab
les
a
n
d
u
p
d
ated
in
t
h
e
C
B
A
w
it
h
a
n
(
N
)
;
o
t
h
er
w
is
e
t
h
is
ti
m
e
s
lo
t
w
ill
b
e
u
p
d
ated
b
y
th
e
C
B
A
w
it
h
a
(
U
/Un
d
er
d
e
m
an
d
)
.
T
h
is
p
r
o
ce
d
u
r
e
w
ill
b
e
r
ep
ea
ted
u
n
til
all
ti
m
e
s
lo
ts
s
tar
t
ex
h
ib
it
in
g
eit
h
er
(
N
o
r
U
)
.
Fig
u
r
e
2
ill
u
s
tr
ate
s
an
e
x
a
m
p
le
th
at
s
c
h
ed
u
l
e
s
a
P
h
y
C
o
u
r
s
e
a
t
th
r
ee
lect
u
r
es
p
er
w
ee
k
.
S0
:
De
s
ig
n
ate
th
e
C
B
A
ar
r
ay
th
at
is
cr
ea
ted
p
er
s
ec
ti
o
n
4
.
2
.
1
.
S1
:
Div
id
e
th
e
C
B
A
in
to
f
iv
e
n
o
d
es
to
r
ep
r
esen
t
th
e
w
o
r
k
i
n
g
d
a
y
s
p
er
w
ee
k
.
S2
:
R
e
m
o
v
e
all
ti
m
e
s
lo
ts
w
i
th
th
e
lab
el
N
(
R
e
s
er
v
ed
T
im
e
Slo
ts
)
.
S3
:
I
n
o
r
d
er
to
s
ch
ed
u
le
t
h
e
f
ir
s
t
lect
u
r
e
o
f
t
h
e
P
h
y
co
u
r
s
e,
th
e
ST
S
f
u
n
ctio
n
d
es
ig
n
ate
s
T
S3
f
o
r
T
h
u
r
s
d
a
y
,
T
S3
w
ill
b
e
i
m
p
lic
itl
y
u
p
d
ated
w
it
h
lab
el
(
N
)
an
d
th
en
r
e
m
o
v
ed
f
r
o
m
s
ea
r
ch
s
p
ac
e.
No
te
th
at
th
i
s
d
a
y
b
ec
o
m
e
s
e
m
p
t
y
,
an
d
,
co
n
s
eq
u
en
tl
y
,
t
h
e
ST
S
f
u
n
ct
io
n
n
e
g
le
cts
a
n
y
f
u
r
t
h
er
co
n
s
id
er
atio
n
o
f
it
an
d
th
e
s
ea
r
c
h
s
p
ac
e
is
r
e
s
tr
icted
o
n
l
y
to
f
o
u
r
d
a
y
s
.
I
n
S4
:
T
h
e
ST
S
co
n
tin
u
es
to
s
c
h
ed
u
le
th
e
s
ec
o
n
d
lectu
r
e
o
f
t
h
e
P
h
y
co
u
r
s
e.
I
t
d
esig
n
ates
a
s
T
S4
f
o
r
Su
n
d
a
y
;
T
S4
is
t
h
en
u
p
d
ated
i
m
p
licitl
y
w
it
h
lab
el
(
N
)
an
d
th
e
n
w
ill,
a
g
ain
,
b
e
r
e
m
o
v
ed
f
r
o
m
s
ea
r
ch
s
p
ac
e.
S5
:
T
h
e
ST
S
d
esig
n
ate
s
T
S2
f
o
r
T
u
esd
a
y
in
o
r
d
er
to
s
ch
ed
u
le
t
h
e
la
s
t
lec
tu
r
e
o
f
th
e
P
h
y
co
u
r
s
e.
T
S2
is
f
i
n
a
ll
y
i
m
p
licitl
y
u
p
d
ated
w
ith
a
l
ab
el
o
f
(
N
)
w
h
ich
w
ill
co
n
s
eq
u
en
t
l
y
b
e
r
e
m
o
v
ed
f
r
o
m
s
ea
r
ch
s
p
ac
e.
S6
:
Di
s
p
l
ay
s
th
e
e
n
d
r
es
u
lt
o
f
t
h
e
C
B
A
p
r
o
ce
s
s
.
I
n
f
ac
t,
s
u
c
h
s
u
b
s
et
o
f
C
B
A
w
o
u
ld
o
n
l
y
b
e
av
ailab
le
i
f
t
h
e
co
r
r
esp
o
n
d
in
g
s
u
b
s
ets
o
f
t
h
e
i
n
s
tr
u
cto
r
an
d
clas
s
r
o
o
m
ti
m
etab
les
a
r
e
b
o
th
av
ailab
le,
s
u
c
h
th
a
t
,
,
,
=
,
,
,
,
,
,
(
3
2
)
w
h
er
e
,
,
,
,
r
ep
r
esen
ts
all
av
ailab
le
n
o
n
-
r
eser
v
ed
ti
m
e
s
lo
ts
f
o
r
in
s
tr
u
ct
o
r
i’
s
ti
m
etab
le
w
h
ic
h
is
f
il
led
b
y
a
(
–
)
d
en
o
tatio
n
.
,
,
,
r
ep
r
esen
ts
all
av
ailab
le
n
o
n
-
r
eser
v
ed
ti
m
e
s
lo
ts
i
n
class
c
’
s
ti
m
etab
le
w
h
ic
h
is
f
illed
w
it
h
a
(
–
)
d
en
o
tatio
n
.
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
E
n
g
,
Vo
l.
10
,
No
.
6
,
Dec
em
b
er
2
0
2
0
:
6
558
-
6
5
7
3
6566
Fig
u
r
e
2
.
Select
t
i
m
e
s
lo
t (
STS)
f
u
n
ctio
n
So
,
in
s
tead
o
f
s
ea
r
c
h
i
n
g
∑
5
=
1
,
it
is
n
e
ed
ed
to
s
ea
r
ch
∑
᾽
ɖ
=
1
,
w
h
er
e
is
th
e
to
tal
n
u
m
b
er
o
f
tau
g
h
t
ti
m
e
s
lo
t
s
d
u
r
i
n
g
d
a
y
d
,
an
d
᾽
is
t
h
e
n
u
m
b
er
o
f
a
v
ailab
le
n
o
n
-
r
eser
v
ed
ti
m
e
s
l
o
ts
f
o
r
d
a
y
d
.
T
h
e
r
elativ
e
p
er
ce
n
t i
m
p
r
o
v
e
m
en
t c
an
b
e
m
ea
s
u
r
ed
as
R
ela
tive
P
ercen
t
(
ε
)
=
|
∑
−
∑
᾽
ɖ
=
1
5
=
1
|
∑
5
=
1
×
100%
(
3
3
)
T
h
e
w
o
r
s
t
ca
s
e
w
il
l
m
an
i
f
e
s
t
its
el
f
d
u
r
i
n
g
t
h
e
i
n
itial
s
tate
wh
er
e
all
t
i
m
e
s
lo
ts
f
o
r
b
o
th
t
h
e
in
s
tr
u
cto
r
an
d
t
h
e
cla
s
s
r
o
o
m
t
i
m
e
tab
les
w
o
u
ld
s
h
o
w
as
n
o
n
-
r
eser
v
ed
s
tat
u
s
.
On
t
h
e
o
t
h
er
ex
tr
e
m
e
,
th
e
b
e
s
t
ca
s
e
w
il
l
ap
p
ea
r
w
h
e
n
b
o
th
ti
m
etab
le
s
r
ef
lect
t
h
e
s
a
m
e
ti
m
eslo
t,
i
n
wh
ich
ca
s
e
t
h
e
r
elati
v
e
p
er
ce
n
t
i
m
p
r
o
v
e
m
e
n
t
w
o
u
ld
ap
p
r
o
ac
h
1
0
0
%.
A
s
a
r
esu
lt,
t
h
e
r
elativ
e
p
er
ce
n
t i
m
p
r
o
v
e
m
e
n
t a
ch
ie
v
ed
is
:
|
∑
−
∑
᾽
ɖ
=
1
5
=
1
|
∑
5
=
1
×
100%
<
100%
(
3
4
)
No
w
r
ev
er
ti
n
g
to
th
e
P
h
y
co
u
r
s
e
w
h
ich
h
as
t
h
r
ee
lectu
r
es
p
er
w
ee
k
,
t
h
e
ST
S
f
u
n
ctio
n
,
in
th
is
ca
s
e,
w
il
l
b
e
r
ep
ea
ted
th
r
ee
ti
m
es
in
th
e
p
r
o
ce
s
s
o
f
u
p
d
atin
g
t
h
e
t
h
r
ee
tab
les
(
I
n
s
tr
u
cto
r
T
im
etab
l
e,
C
las
s
T
i
m
etab
l
e
an
d
C
B
A
)
.
I
n
t
h
is
e
x
a
m
p
le,
th
e
ST
S
f
u
n
c
tio
n
co
m
m
it
s
T
S4
f
o
r
S
u
n
d
a
y
,
T
S2
f
o
r
T
u
esd
a
y
a
n
d
T
S3
f
o
r
T
h
u
r
s
d
a
y
,
w
it
h
a
f
i
n
al
r
es
u
lt
a
s
s
h
o
w
n
in
Fig
u
r
e
3
,
n
o
ti
n
g
t
h
at
t
h
e
r
ed
s
lo
ts
ar
e
u
s
ed
to
d
en
o
te
th
e
ti
m
e
s
lo
t
s
th
at
h
a
v
e
b
ee
n
c
h
an
g
ed
.
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
C
o
u
r
s
es ti
meta
b
lin
g
b
a
s
ed
o
n
h
ill climb
in
g
a
lg
o
r
ith
m
(
A
b
d
o
u
l R
jo
u
b
)
6567
Fig
u
r
e
3
.
Fin
al
r
es
u
lt a
f
ter
s
ett
in
g
3
l
ec
t
u
r
es o
f
p
h
y
c
o
u
r
s
e
4
.
2
.
3
.
Swa
p
t
i
m
e
s
lo
t
s
f
un
ct
i
o
n f
o
r
t
w
o
ins
t
ruct
o
rs
(
ST
SI
)
W
h
en
th
e
ST
S
f
u
n
ctio
n
f
ail
s
to
s
elec
t
ap
p
r
o
p
r
iate
ti
m
e
s
lo
ts
f
r
o
m
C
B
A
,
t
h
en
it
w
o
u
ld
b
e
ess
e
n
tial
to
ex
ec
u
te
t
h
e
ST
SI
f
u
n
ctio
n
.
T
h
is
f
u
n
ct
io
n
d
ea
ls
w
it
h
p
o
ten
tia
ll
y
e
m
er
g
i
n
g
ca
s
e
s
o
f
t
w
o
in
s
t
r
u
cto
r
s
s
h
o
w
i
n
g
at
th
e
s
a
m
e
ti
m
e
an
d
s
tr
iv
e
s
to
s
w
ap
ar
o
u
n
d
th
e
ti
m
e
s
lo
t
s
b
et
w
ee
n
t
h
e
m
.
A
s
a
n
o
t
h
er
ex
a
m
p
le,
Fig
u
r
e
4
o
u
tli
n
e
s
th
e
p
r
o
ce
s
s
o
f
s
ch
ed
u
lin
g
a
M
ath
co
u
r
s
e
w
i
th
f
i
v
e
lect
u
r
es
p
er
w
ee
k
f
o
r
in
s
tr
u
cto
r
(
Mr
.
J
a
ck
)
an
d
class
r
o
o
m
(
C
6
)
.
T
h
e
f
ir
s
t
f
o
u
r
lectu
r
es
f
o
r
th
is
Ma
t
h
co
u
r
s
e
ar
e
alr
e
ad
y
s
ch
ed
u
le
d
th
r
o
u
g
h
t
h
e
C
B
A
p
r
o
ce
s
s
u
s
in
g
th
e
ST
S
f
u
n
ctio
n
(
th
o
s
e
co
lo
r
ed
as
g
r
ee
n
)
,
w
h
er
e
t
h
e
last
lectu
r
e
is
s
h
o
w
n
to
h
a
v
e
f
ail
ed
,
w
h
er
e
it
w
o
u
ld
r
eq
u
ir
e
th
e
h
elp
o
f
t
h
e
ST
SI
f
u
n
ctio
n
.
T
h
e
f
o
llo
w
i
n
g
s
tep
s
s
e
r
v
e
to
o
u
tlin
e
t
h
i
s
p
r
o
ce
s
s
.
I
n
S1
,
th
e
p
r
o
ce
s
s
b
eg
in
s
b
y
l
o
ad
in
g
Mr
.
J
ac
k
’
s
a
n
d
C
6
ti
m
etab
les.
S2
s
elec
ts
a
No
n
-
R
e
s
er
v
ed
ti
m
e
s
lo
t
f
r
o
m
Mr
.
Ja
ck
tim
etab
le
an
d
f
etch
e
s
th
e
co
r
r
esp
o
n
d
in
g
co
u
r
s
e
f
r
o
m
t
h
e
C
6
ti
m
et
ab
le,
in
w
h
ic
h
ca
s
e
th
e
T
i
m
e
Slo
t
w
o
u
ld
b
e
T
S4
a
s
co
lo
r
ed
in
r
ed
w
h
er
e
th
e
co
r
r
esp
o
n
d
in
g
co
u
r
s
e
is
A
r
t)
.
T
h
is
is
f
u
l
f
illed
b
y
:
〈
∗
,
∗
〉
=
,
1
,
(
3
5
)
w
h
er
e
i
1
r
ep
r
esen
ts
t
h
e
i
n
s
tr
u
cto
r
to
b
e
s
ch
ed
u
led
,
w
h
ich
r
ep
r
esen
ts
Mr
.
J
ac
k
in
t
h
i
s
ca
s
e.
T
h
e
p
r
o
ce
s
s
th
en
f
etc
h
es
th
e
in
s
tr
u
cto
r
w
h
o
tea
ch
es
th
is
co
u
r
s
e
a
s
s
h
o
w
n
i
n
S
3
,
w
h
o
h
ap
p
en
s
to
b
e
M
r
.
Liu
).
Af
ter
lo
ad
in
g
M
r
.
Liu
’
s
ti
m
etab
le,
t
h
e
alg
o
r
it
h
m
p
ick
s
o
n
e
No
n
-
R
eser
v
ed
ti
m
e
s
lo
t
f
r
o
m
M
r
.
Liu
’
s
an
d
th
e
C
6
ti
m
etab
les
t
h
at
o
v
er
lap
s
in
s
a
m
e
ti
m
e
s
lo
t;
h
e
r
e,
th
e
ti
m
e
s
lo
t
h
ap
p
en
s
to
b
e
T
s
2
w
h
er
e
it
i
s
co
lo
r
ed
in
b
lu
e.
T
h
is
is
s
u
m
m
ed
u
p
b
y
:
〈
,
〉
=
,
2
,
(
3
6
)
w
h
er
e
i
2
r
ep
r
esen
ts
t
h
e
i
n
s
tr
u
cto
r
w
h
o
s
e
lectu
r
e
w
i
ll
b
e
s
wap
p
ed
,
w
h
ich
r
ep
r
ese
n
ts
t
h
at
f
o
r
Mr
.
Liu
,
i
n
th
is
ca
s
e.
I
n
S4
,
n
o
w
s
w
ap
t
h
e
co
n
ten
ts
o
f
T
S4
an
d
T
S2
f
o
r
b
o
th
Mr
.
Liu
’
s
a
n
d
th
e
C
6
T
i
m
e
tab
les
s
o
t
h
at
T
S4
b
ec
o
m
e
s
No
n
-
R
eser
v
ed
,
w
h
er
e
th
e
A
r
t
co
u
r
s
e
w
ill
b
e
s
et
f
o
r
T
S2
.
Fin
all
y
,
i
n
S5
,
s
et
th
e
Ma
th
co
u
r
s
e
in
to
th
e
t
i
m
e
s
lo
t
T
S4
f
o
r
b
o
th
Mr
.
J
ac
k
an
d
C
6
ti
m
etab
les.
A
t
th
e
en
d
o
f
t
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