A9ROhmC1Uk
.
.
1
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
1
.
.
In
te
ll
ig
e
n
t
b
e
h
a
v
io
u
r
In
th
is
c
o
u
rs
e
,
w
e
w
il
l
c
o
n
s
id
e
r
w
h
a
t
it
ta
k
e
s
to
g
e
t
a
c
o
m
p
u
te
r
to
e
n
g
a
g
e
in
in
te
ll
ig
e
n
t
a
c
ti
v
it
ie
s
s
u
c
h
a
s
•
u
n
d
e
rs
ta
n
d
in
g
E
n
g
li
s
h
s
e
n
te
n
c
e
s
;
•
re
c
o
g
n
iz
in
g
o
b
je
c
ts
in
a
v
is
u
a
l
s
c
e
n
e
;
•
p
la
n
n
in
g
c
o
u
rs
e
s
o
f
a
c
ti
o
n
s
;
•
s
o
lv
in
g
re
c
re
a
ti
o
n
a
l
p
u
z
z
le
s
;
•
p
la
y
in
g
s
tr
a
te
g
ic
g
a
m
e
s
.
W
h
a
t
th
e
s
e
v
e
ry
d
if
fe
re
n
t
a
c
ti
v
it
ie
s
a
ll
h
a
v
e
in
c
o
m
m
o
n
,
is
th
a
t
w
h
e
n
th
e
y
a
re
p
e
rf
o
rm
e
d
b
y
p
e
o
p
le
,
th
e
y
a
p
p
e
a
r
to
re
q
u
ir
e
th
o
u
g
h
t.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
2
.
.
A
re
c
o
m
p
u
te
rs
e
le
c
tr
o
n
ic
b
ra
in
s
?
H
is
to
ri
c
a
ll
y,
m
o
d
e
ls
o
f
th
e
b
ra
in
h
a
v
e
o
ft
e
n
b
e
e
n
a
s
s
o
c
ia
te
d
w
it
h
th
e
m
o
s
t
a
d
v
a
n
c
e
d
te
c
h
n
o
lo
g
y
o
f
th
e
ti
m
e
.
•
c
lo
c
k
w
o
rk
•
s
te
a
m
e
n
g
in
e
•
te
le
p
h
o
n
e
s
w
it
c
h
b
o
a
rd
•
a
n
d
n
o
w
it
’s
.
.
.
c
o
m
p
u
te
rs
!
In
v
a
ri
a
b
ly
,
w
e
e
n
d
u
p
la
u
g
h
in
g
a
t
th
e
s
e
s
im
p
li
s
ti
c
m
o
d
e
ls
!
•
fo
u
n
d
to
b
e
s
im
p
li
s
ti
c
,
m
is
le
a
d
in
g
•
te
ll
u
s
v
e
ry
li
tt
le
a
b
o
u
t
w
h
a
t
w
e
a
re
,
a
n
d
h
o
w
w
e
d
o
w
h
a
t
w
e
d
o
W
h
y
s
h
o
u
ld
w
e
th
in
k
c
o
m
p
u
te
rs
a
re
a
n
y
d
if
fe
re
n
t?
?
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
3
.
.
T
h
e
b
ra
in
In
th
is
c
o
u
rs
e
,
a
s
in
m
u
c
h
o
f
A
I,
w
e
w
il
l
b
e
c
o
n
c
e
rn
e
d
w
it
h
th
in
k
in
g
(o
f
v
a
ri
o
u
s
s
o
rt
s
),
b
u
t
h
a
v
e
v
e
ry
li
tt
le
to
s
a
y
a
b
o
u
t
th
e
b
ra
in
.
H
e
re
is
a
u
s
e
fu
l
a
n
a
lo
g
y
:
th
e
s
tu
d
y
o
f
fl
ig
h
t
(b
e
fo
re
a
ir
p
la
n
e
s
)
•
w
e
m
ig
h
t
li
k
e
to
u
n
d
e
rs
ta
n
d
h
o
w
a
n
im
a
ls
li
k
e
b
ir
d
s
c
a
n
fl
y
•
w
e
m
ig
h
t
w
a
n
t
to
b
u
il
d
m
a
c
h
in
e
s
th
a
t
a
re
c
a
p
a
b
le
o
f
fl
ig
h
t
T
w
o
p
o
s
s
ib
le
s
tr
a
te
g
ie
s
:
1
.
s
tu
d
y
b
ir
d
s
,
th
e
ir
fe
a
th
e
rs
,
m
u
s
c
le
s
,
v
e
ry
c
a
re
fu
ll
y
a
n
d
c
o
n
s
tr
u
c
t
m
a
c
h
in
e
s
to
e
m
u
la
te
th
e
m
2
.
s
tu
d
y
a
e
ro
d
y
n
a
m
ic
s
:
p
ri
n
c
ip
le
s
o
f
fl
ig
h
t
a
p
p
li
c
a
b
le
to
a
n
y
th
in
g
W
e
w
il
l
b
e
fo
ll
o
w
in
g
th
e
s
e
c
o
n
d
s
tr
a
te
g
y
h
e
re
(f
o
r
th
in
k
in
g
,
n
o
t
fl
ig
h
t)
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
4
.
.
T
h
in
k
in
g
Q
:
W
h
a
t
is
th
in
k
in
g
?
A
:
T
h
in
k
in
g
is
a
p
ro
c
e
s
s
th
a
t
o
c
c
u
rs
in
th
e
b
ra
in
o
v
e
r
ti
m
e
,
b
u
t
la
rg
e
ly
u
n
c
o
n
s
c
io
u
s
ly
.
L
e
t’
s
lo
o
k
a
t
th
in
k
in
g
in
a
c
ti
o
n
.
.
.
R
e
a
d
th
is
s
e
n
te
n
c
e
:
T
h
e
tr
o
p
h
y
w
o
u
ld
n
o
t
fi
t
in
to
th
e
b
ro
w
n
s
u
it
c
a
s
e
b
e
c
a
u
s
e
it
w
a
s
to
o
s
m
a
ll
.
N
o
w
a
n
s
w
e
r
th
is
q
u
e
s
ti
o
n
:
W
h
a
t
w
a
s
to
o
s
m
a
ll
?
W
h
a
t
is
th
e
“ i
t
”?
H
o
w
d
id
y
o
u
fi
g
u
re
th
is
o
u
t?
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
5
.
.
U
s
in
g
w
h
a
t
y
o
u
k
n
o
w
O
b
s
e
rv
e
:
T
h
e
re
is
n
o
th
in
g
in
th
e
s
e
n
te
n
c
e
it
s
e
lf
th
a
t
g
iv
e
s
a
w
a
y
th
e
a
n
s
w
e
r!
T
o
s
e
e
th
is
,
re
p
la
c
e
“s
m
a
ll
”
b
y
“b
ig
”:
T
h
e
tr
o
p
h
y
w
o
u
ld
n
o
t
fi
t
in
to
th
e
b
ro
w
n
s
u
it
c
a
s
e
b
e
c
a
u
s
e
it
w
a
s
to
o
b
ig
.
N
o
w
w
h
a
t
is
th
e
“i
t
”?
S
o
y
o
u
h
a
v
e
to
u
s
e
a
lo
t
o
f
w
h
a
t
y
o
u
k
n
e
w
a
b
o
u
t
th
e
s
iz
e
s
o
f
th
in
g
s
,
th
in
g
s
fi
tt
in
g
in
s
id
e
o
f
o
th
e
r
th
in
g
s
e
tc
.
e
v
e
n
if
y
o
u
a
re
u
n
a
w
a
re
o
f
it
.
T
h
is
is
th
in
k
in
g
!
R
o
u
g
h
ly
:
B
ri
n
g
in
g
w
h
a
t
y
o
u
k
n
o
w
to
b
e
a
r
o
n
w
h
a
t
y
o
u
a
re
d
o
in
g
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
6
.
.
W
h
a
t
s
o
rt
o
f
p
ro
c
e
s
s
is
th
in
k
in
g
?
It
is
a
b
io
lo
g
ic
a
l
p
ro
c
e
s
s
th
a
t
h
a
p
p
e
n
s
in
th
e
b
ra
in
.
L
ik
e
d
ig
e
s
ti
o
n
in
th
e
s
to
m
a
c
h
?
L
ik
e
m
it
o
s
is
in
c
e
ll
s
?
K
e
y
C
o
n
je
c
tu
re
:
th
in
k
in
g
c
a
n
b
e
u
s
e
fu
ll
y
u
n
d
e
rs
to
o
d
a
s
a
c
o
m
p
u
ta
ti
o
n
a
l
p
ro
c
e
s
s
P
e
rh
a
p
s
th
in
k
in
g
h
a
s
m
o
re
in
c
o
m
m
o
n
w
it
h
m
u
lt
ip
li
c
a
ti
o
n
o
r
s
o
rt
in
g
a
li
s
t
o
f
n
a
m
e
s
,
th
a
n
w
it
h
d
ig
e
s
ti
o
n
o
r
m
it
o
s
is
.
T
h
is
is
e
x
tr
e
m
e
ly
c
o
n
tr
o
v
e
rs
ia
l!
W
e
w
il
l
s
p
e
n
d
m
o
s
t
o
f
th
e
c
o
u
rs
e
e
x
p
lo
ri
n
g
th
is
o
n
e
id
e
a
.
B
u
t
fi
rs
t
w
e
n
e
e
d
to
u
n
d
e
rs
ta
n
d
w
h
a
t
“c
o
m
p
u
ta
ti
o
n
a
l
p
ro
c
e
s
s
”
m
e
a
n
s
.
.
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
7
.
.
C
o
m
p
u
te
r
S
c
ie
n
c
e
It
’s
n
o
t
a
b
o
u
t
c
o
m
p
u
te
rs
!
H
a
v
in
g
p
ro
b
le
m
s
w
it
h
y
o
u
r
P
C
?
D
o
n
’t
a
s
k
a
C
o
m
p
u
te
r
S
c
ie
n
ti
s
t!
T
h
e
e
le
c
tr
o
n
ic
/
p
h
y
s
ic
a
l
p
ro
p
e
rt
ie
s
o
f
c
o
m
p
u
te
rs
p
la
y
li
tt
le
o
r
n
o
ro
le
in
C
o
m
p
u
te
r
S
c
ie
n
c
e
A
n
o
th
e
r
a
n
a
lo
g
y
to
th
in
k
a
b
o
u
t:
m
u
s
ic
a
l
in
s
tr
u
m
e
n
ts
v
s
.
m
u
s
ic
L
ik
e
m
u
s
ic
,
C
o
m
p
u
te
r
S
c
ie
n
c
e
is
n
o
t
a
b
o
u
t
a
n
y
th
in
g
p
h
y
s
ic
a
l!
C
o
m
p
u
te
r
S
c
ie
n
c
e
is
a
b
o
u
t
c
o
m
p
u
ta
ti
o
n
:
a
c
e
rt
a
in
fo
rm
o
f
m
a
n
ip
u
la
ti
o
n
o
f
s
y
m
b
o
ls
M
o
d
e
rn
e
le
c
tr
o
n
ic
c
o
m
p
u
te
rs
(l
ik
e
a
n
A
p
p
le
iM
a
c
o
r
a
D
e
ll
P
C
)
ju
s
t
h
a
p
p
e
n
to
p
ro
v
id
e
a
fa
s
t,
c
h
e
a
p
,
a
n
d
re
li
a
b
le
m
e
d
iu
m
fo
r
c
o
m
p
u
ta
ti
o
n
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
8
.
.
S
y
m
b
o
ls
a
n
d
s
y
m
b
o
li
c
s
tr
u
c
tu
re
s
•
S
im
p
le
s
t
s
o
rt
:
c
h
a
ra
c
te
rs
fr
o
m
a
n
a
lp
h
a
b
e
t
d
ig
it
s
:
3
,
7
,
V
le
tt
e
rs
:
a
,
R
,
α
o
p
e
ra
to
rs
:
+
,
×
,
∩
•
S
tr
in
g
to
g
e
th
e
r
in
to
m
o
re
c
o
m
p
le
x
o
n
e
s
n
u
m
e
ra
ls
:
3
3
5
.4
2
w
o
rd
s
:
“d
o
n
’t
”
•
M
o
re
c
o
m
p
le
x
g
ro
u
p
in
g
s
e
x
p
re
s
s
io
n
s
:
2
4
7
+
4
(x
−
1
)3
p
h
ra
s
e
s
:
“t
h
e
w
o
m
a
n
J
o
h
n
lo
v
e
d
”
•
In
to
tr
u
th
-v
a
lu
e
d
s
y
m
b
o
li
c
s
tr
u
c
tu
re
s
re
la
ti
o
n
s
:
2
4
7
+
4
(x
−
1
)3
>
z
! 5
s
e
n
te
n
c
e
s
:
“T
h
e
w
o
m
a
n
J
o
h
n
lo
v
e
d
h
a
d
b
ro
w
n
h
a
ir
.”
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
9
.
.
M
a
n
ip
u
la
ti
n
g
s
y
m
b
o
ls
T
h
e
id
e
a
:
ta
k
e
s
tr
in
g
s
o
f
s
y
m
b
o
ls
,
b
re
a
k
th
e
m
a
p
a
rt
,
c
o
m
p
a
re
th
e
m
,
a
n
d
re
a
s
s
e
m
b
le
th
e
m
a
c
c
o
rd
in
g
to
a
re
c
ip
e
c
a
ll
e
d
a
p
ro
c
e
d
u
re
.
It
is
im
p
o
rt
a
n
t
to
k
e
e
p
tr
a
c
k
o
f
w
h
e
re
y
o
u
a
re
,
a
n
d
fo
ll
o
w
th
e
in
s
tr
u
c
ti
o
n
s
in
th
e
p
ro
c
e
d
u
re
e
x
a
c
tl
y.
(Y
o
u
m
a
y
n
o
t
b
e
a
b
le
to
fi
g
u
re
w
h
y
y
o
u
a
re
d
o
in
g
th
e
s
te
p
s
in
v
o
lv
e
d
!)
T
h
e
s
y
m
b
o
ls
y
o
u
h
a
v
e
a
t
th
e
s
ta
rt
a
re
c
a
ll
e
d
th
e
in
p
u
ts
.
S
o
m
e
o
f
th
e
s
y
m
b
o
ls
y
o
u
e
n
d
u
p
w
it
h
w
il
l
b
e
d
e
s
ig
n
a
te
d
a
s
th
e
o
u
tp
u
ts
.
W
e
s
a
y
th
a
t
th
e
p
ro
c
e
d
u
re
is
c
a
ll
e
d
o
n
th
e
in
p
u
ts
a
n
d
re
tu
rn
s
o
r
p
ro
d
u
c
e
s
th
e
o
u
tp
u
ts
.
T
h
e
n
c
o
n
s
tr
u
c
t
m
o
re
c
o
m
p
le
x
p
ro
c
e
d
u
re
s
o
u
t
o
f
s
im
p
le
p
ro
c
e
d
u
re
s
.
In
th
e
n
e
x
t
fe
w
s
li
d
e
s
,
w
e
w
il
l
lo
o
k
a
t
a
n
in
te
re
s
ti
n
g
s
p
e
c
ia
l
c
a
s
e
:
a
ri
th
m
e
ti
c
!
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
1
0
.
.
A
ri
th
m
e
ti
c
p
ro
c
e
d
u
re
s
Im
a
g
in
e
y
o
u
a
re
e
x
p
la
in
in
g
to
s
o
m
e
o
n
e
(a
y
o
u
n
g
c
h
il
d
)
h
o
w
to
d
o
s
u
b
tr
a
c
ti
o
n
:
5
2
−
1
7
Y
o
u
m
ig
h
t
u
s
e
w
o
rd
s
li
k
e
th
is
:
F
ir
s
t,
y
o
u
h
a
v
e
to
s
u
b
tr
a
c
t
7
fr
o
m
2
.
B
u
t
s
in
c
e
7
is
b
ig
g
e
r
th
a
n
2
,
y
o
u
n
e
e
d
to
b
o
rr
o
w
1
0
fr
o
m
th
e
5
o
n
th
e
le
ft
.
T
h
a
t
c
h
a
n
g
e
s
th
e
2
to
a
1
2
a
n
d
c
h
a
n
g
e
s
th
e
5
to
a
4
.
S
o
y
o
u
s
u
b
tr
a
c
t
7
n
o
t
fr
o
m
2
b
u
t
fr
o
m
1
2
,
w
h
ic
h
g
iv
e
s
y
o
u
5
,
a
n
d
y
o
u
s
u
b
tr
a
c
t
1
n
o
t
fr
o
m
5
b
u
t
fr
o
m
4
w
h
ic
h
g
iv
e
s
y
o
u
3
.
S
o
th
e
a
n
s
w
e
r
is
3
5
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
1
1
.
.
A
v
e
ry
fi
rs
t
p
ro
c
e
d
u
re
L
e
t’
s
g
o
b
a
c
k
to
th
e
m
o
s
t
b
a
s
ic
fo
rm
o
f
a
ri
th
m
e
ti
c
w
e
c
a
n
im
a
g
in
e
:
a
d
d
in
g
tw
o
s
in
g
le
d
ig
it
n
u
m
b
e
rs
.
W
h
a
t
is
th
e
p
ro
c
e
d
u
re
th
e
re
?
H
e
re
’s
o
n
e
v
e
rs
io
n
:
c
a
ll
it
P
R
O
C
0
•
Y
o
u
w
il
l
b
e
g
iv
e
n
tw
o
d
ig
it
s
a
s
in
p
u
t
a
n
d
re
tu
rn
tw
o
d
ig
it
s
a
s
o
u
tp
u
t.
(F
o
r
e
x
a
m
p
le
,
g
iv
e
n
7
a
n
d
6
a
s
in
p
u
t,
y
o
u
w
il
l
re
tu
rn
1
3
a
s
o
u
tp
u
t.
)
•
T
o
d
o
s
o
,
y
o
u
w
il
l
u
s
e
a
ta
b
le
w
h
ic
h
is
o
n
th
e
n
e
x
t
p
a
g
e
.
•
T
o
a
d
d
th
e
tw
o
d
ig
it
s
,
fi
n
d
th
e
ro
w
fo
r
th
e
fi
rs
t
d
ig
it
o
n
th
e
ta
b
le
,
a
n
d
th
e
c
o
lu
m
n
fo
r
th
e
s
e
c
o
n
d
d
ig
it
,
a
n
d
re
tu
rn
a
s
o
u
tp
u
t
th
e
tw
o
d
ig
it
n
u
m
b
e
r
a
t
th
e
in
te
rs
e
c
ti
o
n
o
n
th
e
ta
b
le
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
1
2
.
.
A
ta
b
le
fo
r
a
d
d
it
io
n
7
+
6
=
1
3
↓
0
1
2
3
4
5
6
7
8
9
0
0
0
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
1
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
1
0
2
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
1
0
1
1
3
0
3
0
4
0
5
0
6
0
7
0
8
0
9
1
0
1
1
1
2
4
0
4
0
5
0
6
0
7
0
8
0
9
1
0
1
1
1
2
1
3
5
0
5
0
6
0
7
0
8
0
9
1
0
1
1
1
2
1
3
1
4
6
0
6
0
7
0
8
0
9
1
0
1
1
1
2
1
3
1
4
1
5
→
7
0
7
0
8
0
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
8
0
8
0
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
9
0
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
T
h
is
is
h
o
w
w
e
a
ll
le
a
rn
e
d
m
u
lt
ip
li
c
a
ti
o
n
!
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
1
3
.
.
P
ro
c
e
d
u
re
P
R
O
C
1
W
e
c
a
n
n
o
w
s
ta
rt
b
u
il
d
in
g
o
n
p
ro
c
e
d
u
re
P
R
O
C
0
to
d
o
m
o
re
.
T
h
e
fi
rs
t
th
in
g
w
e
w
il
l
n
e
e
d
is
to
b
e
a
b
le
to
a
d
d
th
re
e
d
ig
it
s
(w
h
ic
h
w
il
l
la
te
r
a
ll
o
w
u
s
to
h
a
n
d
le
c
a
rr
y
d
ig
it
s
).
H
e
re
is
a
p
ro
c
e
d
u
re
P
R
O
C
1
th
a
t
ta
k
e
s
th
re
e
d
ig
it
s
a
,
t,
a
n
d
b
,
a
s
in
p
u
t,
a
n
d
re
tu
rn
s
tw
o
d
ig
it
s
c
a
n
d
s
.
1
.
C
a
ll
P
R
O
C
0
o
n
t
a
n
d
b
to
g
e
t
u
a
n
d
v
.
2
.
C
a
ll
P
R
O
C
0
o
n
a
a
n
d
v
to
g
e
t
u
′
a
n
d
v
′
.
3
.
If
u
=
u
′
=
0
th
e
n
re
tu
rn
w
it
h
c
a
s
0
a
n
d
s
a
s
v
′
.
If
u
=
u
′
=
1
th
e
n
re
tu
rn
w
it
h
c
a
s
2
a
n
d
s
a
s
v
′
.
O
th
e
rw
is
e
,
re
tu
rn
w
it
h
c
a
s
1
a
n
d
s
a
s
v
′
.
N
o
te
th
a
t
w
e
d
o
n
o
t
s
a
y
w
h
y
w
e
d
o
a
n
y
o
f
th
is
!
(B
u
t
d
o
tr
y
it
o
u
t!
)
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
1
4
.
.
A
d
d
it
io
n
o
f
tw
o
n
u
m
b
e
rs
N
o
w
th
a
t
w
e
c
a
n
fo
ll
o
w
th
e
P
R
O
C
1
p
ro
c
e
d
u
re
e
x
a
c
tl
y,
w
e
c
a
n
b
u
il
d
o
n
it
to
d
o
s
o
m
e
th
in
g
th
a
t
w
e
m
a
y
s
ta
rt
to
re
c
o
g
n
iz
e
a
s
re
a
l
a
d
d
it
io
n
!
W
e
w
il
l
c
o
n
s
tr
u
c
t
a
n
o
th
e
r
p
ro
c
e
d
u
re
P
R
O
C
2
th
a
t
c
a
n
a
d
d
tw
o
s
tr
in
g
s
o
f
d
ig
it
s
:
in
p
u
t
o
f
P
R
O
C
2
:
tw
o
s
tr
in
g
s
o
f
d
ig
it
s
o
f
th
e
s
a
m
e
le
n
g
th
x
1
x
2
.
.
.
x
k
y
1
y
2
.
.
.
y
k
o
u
tp
u
t
o
f
P
R
O
C
2
:
o
n
e
s
tr
in
g
o
f
d
ig
it
s
o
f
th
a
t
le
n
g
th
+
1
z
0
z
1
z
2
.
.
.
z
k
F
o
r
e
x
a
m
p
le
,
g
iv
e
n
7
4
7
a
n
d
2
8
1
(w
it
h
th
re
e
d
ig
it
s
e
a
c
h
),
P
R
O
C
2
w
il
l
re
tu
rn
1
0
2
8
(w
it
h
fo
u
r
d
ig
it
s
).
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
1
5
.
.
T
h
e
p
ro
c
e
d
u
re
P
R
O
C
2
1
.
S
ta
rt
a
t
th
e
ri
g
h
t
h
a
n
d
s
id
e
o
f
th
e
in
p
u
ts
.
C
a
ll
P
R
O
C
1
w
it
h
a
a
s
th
e
d
ig
it
0
,
t
a
s
x
k
,
a
n
d
b
a
s
y
k
.
L
e
t
z
k
b
e
th
e
s
re
tu
rn
e
d
.
H
a
n
g
o
n
to
th
e
c
fo
r
th
e
n
e
x
t
s
te
p
.
2
.
N
o
w
m
o
v
e
o
v
e
r
o
n
e
s
te
p
to
th
e
le
ft
.
C
a
ll
P
R
O
C
1
w
it
h
a
a
s
th
e
c
re
tu
rn
e
d
in
th
e
p
re
v
io
u
s
s
te
p
,
t
a
s
x
k
−
1
,
a
n
d
b
a
s
y
k
−
1
.
L
e
t
z
k
−
1
b
e
th
e
s
re
tu
rn
e
d
.
H
a
n
g
o
n
to
th
e
c
fo
r
th
e
n
e
x
t
s
te
p
.
3
.
C
o
n
ti
n
u
e
th
is
w
a
y
th
ro
u
g
h
a
ll
th
e
d
ig
it
s
,
fr
o
m
ri
g
h
t
to
le
ft
,
fi
ll
in
g
o
u
t
z
k
−
2
,
z
k
−
3
,
.
.
.
,
z
3
,
z
2
,
z
1
.
4
.
L
e
t
z
0
b
e
th
e
fi
n
a
l
c
re
tu
rn
e
d
(f
ro
m
P
R
O
C
1
w
it
h
x
1
a
n
d
y
1
).
N
o
te
a
g
a
in
th
a
t
th
e
p
ro
c
e
d
u
re
d
o
e
s
n
o
t
e
x
p
la
in
w
h
a
t
it
a
ll
m
e
a
n
s
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
1
6
.
.
T
ry
in
g
P
R
O
C
2
W
e
c
a
n
tr
a
c
e
w
h
a
t
h
a
p
p
e
n
s
w
it
h
P
R
O
C
2
in
d
e
ta
il
.
L
e
t’
s
lo
o
k
a
t
w
h
a
t
P
R
O
C
2
d
o
e
s
w
h
e
n
th
e
x
i
a
re
7
4
7
a
n
d
th
e
y
i
a
re
2
8
1
.
1
.
F
ir
s
t,
w
e
c
a
ll
P
R
O
C
1
o
n
0
,
7
,
1
.
It
w
il
l
re
tu
rn
0
a
n
d
8
.
S
o
z
3
w
il
l
b
e
8
.
2
.
N
e
x
t,
w
e
c
a
ll
P
R
O
C
1
o
n
0
,
4
,
8
.
It
w
il
l
re
tu
rn
1
a
n
d
2
.
S
o
z
2
w
il
l
b
e
2
.
3
.
T
h
e
n
,
w
e
c
a
ll
P
R
O
C
1
o
n
1
,
7
,
2
.
It
w
il
l
re
tu
rn
1
a
n
d
0
.
S
o
z
1
w
il
l
b
e
0
a
n
d
z
0
w
il
l
b
e
1
.
S
o
P
R
O
C
2
w
il
l
re
tu
rn
1
0
2
8
,
w
h
ic
h
is
in
d
e
e
d
th
e
s
u
m
o
f
7
4
7
a
n
d
2
8
1
.
S
o
e
v
e
n
if
y
o
u
d
o
n
’t
w
h
y
y
o
u
a
re
d
o
in
g
a
ll
th
e
s
te
p
s
,
if
y
o
u
fo
ll
o
w
th
e
d
ir
e
c
ti
o
n
s
e
x
a
c
tl
y
,
y
o
u
w
il
l
b
e
a
d
d
in
g
th
e
n
u
m
b
e
rs
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
1
7
.
.
A
d
d
in
g
a
li
s
t
o
f
n
u
m
b
e
rs
W
e
c
a
n
n
o
w
c
o
n
s
id
e
r
a
m
o
re
g
e
n
e
ra
l
p
ro
c
e
d
u
re
P
R
O
C
3
th
a
t
u
s
e
s
P
R
O
C
2
to
a
d
d
a
n
y
li
s
t
o
f
n
u
m
b
e
rs
n
1
,
n
2
,
.
.
.
,
e
a
c
h
w
it
h
a
n
y
n
u
m
b
e
r
o
f
d
ig
it
s
.
1
.
L
e
t
s
u
m
b
e
th
e
s
in
g
le
d
ig
it
0
.
2
.
S
ta
rt
w
it
h
th
e
fi
rs
t
n
u
m
b
e
r
n
1
a
n
d
s
u
m
.
M
a
k
e
s
u
re
b
o
th
o
f
th
e
s
e
h
a
v
e
th
e
s
a
m
e
n
u
m
b
e
r
o
f
d
ig
it
s
b
y
u
s
in
g
a
P
R
O
C
4
(i
t
w
il
l
in
s
e
rt
0
’s
a
s
n
e
c
e
s
s
a
ry
to
th
e
le
ft
).
T
h
e
n
c
a
ll
P
R
O
C
2
o
n
th
e
tw
o
re
s
u
lt
in
g
n
u
m
b
e
rs
,
a
n
d
le
t
s
u
m
n
o
w
b
e
th
e
n
u
m
b
e
r
re
tu
rn
e
d
.
3
.
N
e
x
t,
d
o
th
e
s
a
m
e
th
in
g
w
it
h
th
e
n
e
w
s
u
m
a
n
d
n
2
,
to
p
ro
d
u
c
e
th
e
n
e
x
t
v
a
lu
e
o
f
s
u
m
.
4
.
C
o
n
ti
n
u
e
th
is
w
a
y
w
it
h
th
e
re
s
t
o
f
n
u
m
b
e
rs
,
n
3
,
n
4
,
.
.
.
.
5
.
R
e
tu
rn
a
s
o
u
tp
u
t
th
e
fi
n
a
l
v
a
lu
e
o
f
s
u
m
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
1
8
.
.
A
n
d
o
n
it
g
o
e
s
.
.
.
L
e
t’
s
a
s
s
u
m
e
w
e
a
lr
e
a
d
y
h
a
v
e
p
ro
c
e
d
u
re
s
to
d
o
+
,
×
,
−
,
÷
a
n
d
≤
,
a
s
w
e
ll
a
s
s
tr
in
g
o
p
e
ra
ti
o
n
s
(e
.g
.
u
ˆv
m
e
a
n
s
c
o
n
c
a
te
n
a
te
s
tr
in
g
s
u
a
n
d
v
).
W
e
c
a
n
u
s
e
th
e
s
e
to
d
e
fi
n
e
s
ti
ll
m
o
re
c
o
m
p
le
x
p
ro
c
e
d
u
re
s
.
O
n
th
e
n
e
x
t
s
li
d
e
,
w
e
w
il
l
c
o
n
s
id
e
r
a
m
y
s
te
ry
p
ro
c
e
d
u
re
c
a
ll
e
d
P
R
O
C
X
th
a
t
ta
k
e
s
o
n
e
p
o
s
it
iv
e
in
te
g
e
r
x
a
s
in
p
u
t
a
n
d
re
tu
rn
s
a
p
o
s
it
iv
e
in
te
g
e
r
y
a
s
o
u
tp
u
t.
T
ry
to
fi
g
u
re
o
u
t
w
h
a
t
th
is
p
ro
c
e
d
u
re
d
o
e
s
b
y
tr
y
in
g
it
o
u
t
o
n
s
o
m
e
s
a
m
p
le
in
p
u
ts
,
fo
r
e
x
a
m
p
le
,
1
3
7
6
4
1
.
Y
o
u
s
h
o
u
ld
b
e
a
b
le
to
fo
ll
o
w
th
e
p
ro
c
e
d
u
re
w
it
h
o
u
t
k
n
o
w
in
g
w
h
a
t
e
x
a
c
tl
y
y
o
u
a
re
s
u
p
p
o
s
e
d
to
b
e
c
a
lc
u
la
ti
n
g
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
1
9
.
.
T
h
e
P
R
O
C
X
p
ro
c
e
d
u
re
G
ro
u
p
th
e
d
ig
it
s
in
x
in
to
p
a
ir
s
s
ta
rt
in
g
fr
o
m
th
e
ri
g
h
t.
S
ta
rt
w
it
h
u
,
v
,
b
o
t,
to
p
,
a
n
d
s
id
e
a
ll
h
a
v
in
g
v
a
lu
e
0
.
T
h
e
n
,
w
o
rk
in
g
y
o
u
r
w
a
y
fr
o
m
le
ft
to
ri
g
h
t
o
n
th
e
g
ro
u
p
s
in
x
,
re
p
e
a
t
th
e
fo
ll
o
w
in
g
:
1
.
S
e
t
b
o
t
to
(b
o
t
−
u
)
ˆ(
th
e
n
e
x
t
g
ro
u
p
fr
o
m
x
)
2
.
S
e
t
s
id
e
to
2
×
to
p
3
.
S
e
t
v
to
th
e
la
rg
e
s
t
s
in
g
le
d
ig
it
s
u
c
h
th
a
t
v
×
(s
id
e
ˆv
)
≤
b
o
t
4
.
S
e
t
u
to
v
×
(s
id
e
ˆv
)
5
.
S
e
t
to
p
to
to
p
ˆv
T
h
e
a
n
s
w
e
r
y
to
re
tu
rn
is
th
e
fi
n
a
l
v
a
lu
e
o
f
to
p
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
2
0
.
.
L
e
s
s
o
n
:
a
ri
th
m
e
ti
c
a
s
s
y
m
b
o
l
m
a
n
ip
u
la
ti
o
n
A
ri
th
m
e
ti
c
c
a
n
b
e
b
u
il
t
fr
o
m
m
o
re
p
ri
m
it
iv
e
s
y
m
b
o
l
m
a
n
ip
u
la
ti
o
n
s
•
s
ta
rt
in
g
w
it
h
v
e
ry
s
im
p
le
o
p
e
ra
ti
o
n
s
(s
u
c
h
a
s
ta
b
le
lo
o
k
u
p
),
th
e
a
b
il
it
y
to
s
tr
in
g
a
n
d
u
n
s
tr
in
g
s
y
m
b
o
ls
,
c
o
m
p
a
re
th
e
m
e
tc
.,
w
e
c
a
n
b
u
il
d
p
ro
c
e
d
u
re
s
to
d
o
a
d
d
it
io
n
•
u
s
in
g
th
e
s
e
w
e
c
a
n
b
u
il
d
e
v
e
r
m
o
re
c
o
m
p
le
x
p
ro
c
e
d
u
re
s
,
to
d
o
m
u
lt
ip
li
c
a
ti
o
n
,
d
iv
is
io
n
,
te
s
ti
n
g
fo
r
p
ri
m
e
n
u
m
b
e
rs
,
e
tc
.
•
u
s
in
g
p
a
ir
s
o
f
n
u
m
b
e
rs
w
e
c
a
n
d
e
a
l
w
it
h
fr
a
c
ti
o
n
s
(r
a
ti
o
n
a
l
n
u
m
b
e
rs
);
a
n
d
u
s
in
g
n
u
m
b
e
rs
a
rr
a
n
g
e
d
in
to
m
a
tr
ic
e
s
,
w
e
c
a
n
s
o
lv
e
s
y
s
te
m
s
o
f
e
q
u
a
ti
o
n
s
,
p
e
rf
o
rm
n
u
m
e
ri
c
a
l
s
im
u
la
ti
o
n
s
,
e
tc
.
A
s
w
e
w
il
l
s
e
e
in
th
is
c
o
u
rs
e
,
th
e
re
a
re
a
ls
o
m
a
n
y
in
te
re
s
ti
n
g
c
a
s
e
s
o
f
s
y
m
b
o
l
m
a
n
ip
u
la
ti
o
n
th
a
t
a
re
n
o
t
n
u
m
e
ri
c
!
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
2
1
.
.
A
k
e
y
o
b
s
e
rv
a
ti
o
n
Y
o
u
d
o
n
’t
n
e
e
d
to
k
n
o
w
w
h
a
t
y
o
u
’r
e
d
o
in
g
!
T
o
g
e
t
m
e
a
n
in
g
fu
l
a
n
s
w
e
rs
,
y
o
u
d
o
n
o
t
h
a
v
e
to
u
n
d
e
rs
ta
n
d
w
h
a
t
th
e
s
y
m
b
o
ls
s
ta
n
d
fo
r,
o
r
w
h
y
th
e
m
a
n
ip
u
la
ti
o
n
s
a
re
c
o
rr
e
c
t.
T
h
e
s
y
m
b
o
ls
c
a
n
b
e
m
a
n
ip
u
la
te
d
c
o
m
p
le
te
ly
m
e
c
h
a
n
ic
a
ll
y
a
n
d
s
ti
ll
e
n
d
u
p
p
ro
d
u
c
in
g
s
ig
n
ifi
c
a
n
t
a
n
d
in
te
re
s
ti
n
g
re
s
u
lt
s
.
T
h
is
is
th
e
tr
ic
k
o
f
c
o
m
p
u
ta
ti
o
n
:
W
e
c
a
n
g
e
t
c
o
m
p
u
te
rs
to
p
e
rf
o
rm
a
w
id
e
v
a
ri
e
ty
o
f
v
e
ry
im
p
re
s
s
iv
e
a
c
ti
v
it
ie
s
p
re
c
is
e
ly
b
e
c
a
u
s
e
w
e
a
re
a
b
le
to
d
e
s
c
ri
b
e
th
o
s
e
a
c
ti
v
it
ie
s
a
s
a
ty
p
e
o
f
s
y
m
b
o
l
m
a
n
ip
u
la
ti
o
n
th
a
t
c
a
n
b
e
c
a
rr
ie
d
o
u
t
p
u
re
ly
m
e
c
h
a
n
ic
a
ll
y.
T
h
is
“t
ri
c
k
”
h
a
s
tu
rn
e
d
o
u
t
to
b
e
o
n
e
o
f
th
e
m
a
jo
r
in
v
e
n
ti
o
n
s
o
f
th
e
2
0
th
c
e
n
tu
ry
.
A
n
d
n
o
te
:
It
h
a
s
n
o
th
in
g
to
d
o
w
it
h
e
le
c
tr
o
n
ic
s
!
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
2
2
.
.
B
u
t
w
h
a
t
d
o
e
s
th
is
h
a
v
e
to
d
o
w
it
h
th
in
k
in
g
?
L
e
t
u
s
re
tu
rn
to
w
h
a
t
w
e
c
a
ll
e
d
th
e
K
e
y
C
o
n
je
c
tu
re
fr
o
m
e
a
rl
ie
r:
K
e
y
C
o
n
je
c
tu
re
:
th
in
k
in
g
c
a
n
b
e
u
s
e
fu
ll
y
u
n
d
e
rs
to
o
d
a
s
a
c
o
m
p
u
ta
ti
o
n
a
l
p
ro
c
e
s
s
W
h
a
t
d
o
e
s
th
is
c
o
n
tr
o
v
e
rs
ia
l
c
o
n
je
c
tu
re
a
m
o
u
n
t
to
?
•
n
o
t
th
a
t
th
e
b
ra
in
is
s
o
m
e
th
in
g
li
k
e
a
n
e
le
c
tr
o
n
ic
c
o
m
p
u
te
r
(w
h
ic
h
it
is
in
s
o
m
e
w
a
y
s
,
b
u
t
in
v
e
ry
m
a
n
y
o
th
e
r
w
a
y
s
is
n
o
t)
•
b
u
t
th
a
t
th
e
p
ro
c
e
s
s
o
f
th
in
k
in
g
c
a
n
b
e
u
s
e
fu
ll
y
u
n
d
e
rs
to
o
d
a
s
a
fo
rm
o
f
s
y
m
b
o
l
p
ro
c
e
s
s
in
g
th
a
t
c
a
n
b
e
c
a
rr
ie
d
o
u
t
p
u
re
ly
m
e
c
h
a
n
ic
a
ll
y
w
it
h
o
u
t
h
a
v
in
g
to
k
n
o
w
w
h
a
t
y
o
u
a
re
d
o
in
g
.
T
h
is
is
w
h
a
t
w
e
w
il
l
e
x
p
lo
re
in
th
is
c
o
u
rs
e
!
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
2
3
.
.
T
h
in
k
in
g
a
s
c
o
m
p
u
ta
ti
o
n
S
o
m
e
th
in
k
in
g
c
le
a
rl
y
a
p
p
e
a
rs
to
b
e
c
o
m
p
u
ta
ti
o
n
:
•
d
o
in
g
m
a
th
h
o
m
e
w
o
rk
•
fi
ll
in
g
o
u
t
a
ta
x
fo
rm
•
e
s
ti
m
a
ti
n
g
a
g
ro
c
e
ry
b
il
l
B
u
t
m
u
c
h
o
f
o
u
r
th
in
k
in
g
s
e
e
m
s
to
h
a
v
e
v
e
ry
li
tt
le
to
d
o
w
it
h
c
a
lc
u
la
ti
o
n
s
o
r
a
n
y
th
in
g
n
u
m
e
ri
c
a
l.
U
n
li
k
e
a
ri
th
m
e
ti
c
,
th
in
k
in
g
s
e
e
m
s
to
in
v
o
lv
e
id
e
a
s
a
b
o
u
t
a
n
u
n
b
o
u
n
d
e
d
v
a
ri
e
ty
o
f
s
u
b
je
c
ts
.
Y
o
u
c
a
n
th
in
k
a
b
o
u
t
a
n
y
th
in
g
;
b
u
t
it
is
a
lw
a
y
s
a
b
o
u
t
s
o
m
e
th
in
g
.
S
o
in
w
h
a
t
s
e
n
s
e
c
a
n
th
in
k
in
g
b
e
c
o
m
p
u
ta
ti
o
n
a
l?
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
2
4
.
.
A
n
e
x
a
m
p
le
C
o
n
s
id
e
r
th
e
fo
ll
o
w
in
g
:
I
k
n
o
w
th
a
t
m
y
k
e
y
s
a
re
e
it
h
e
r
in
m
y
c
o
a
t
p
o
c
k
e
t
o
r
o
n
th
e
fr
id
g
e
.
T
h
a
t’
s
w
h
e
re
I
a
lw
a
y
s
le
a
v
e
th
e
m
.
I
fe
e
l
m
y
c
o
a
t
p
o
c
k
e
t
a
n
d
I
s
e
e
th
a
t
th
e
re
is
n
o
th
in
g
th
e
re
.
S
o
m
y
k
e
y
s
m
u
s
t
b
e
o
n
th
e
fr
id
g
e
.
A
n
d
th
a
t’
s
w
h
e
re
I
s
h
o
u
ld
g
o
lo
o
k
in
g
.
T
h
is
is
th
in
k
in
g
th
a
t
o
b
v
io
u
s
ly
h
a
s
n
o
th
in
g
to
d
o
w
it
h
n
u
m
b
e
rs
.
B
u
t
it
is
c
le
a
rl
y
a
b
o
u
t
s
o
m
e
th
in
g
:
m
y
k
e
y
s
,
p
o
c
k
e
t,
re
fr
ig
e
ra
to
r.
C
a
n
w
e
u
n
d
e
rs
ta
n
d
it
a
s
a
fo
rm
o
f
c
o
m
p
u
ta
ti
o
n
?
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
2
5
.
.
G
o
tt
fr
ie
d
L
e
ib
n
iz
(1
6
4
6
-1
7
1
6
)
C
o
-i
n
v
e
n
to
r
o
f
th
e
c
a
lc
u
lu
s
(w
it
h
N
e
w
to
n
)
T
h
e
fi
rs
t
p
e
rs
o
n
to
s
e
ri
o
u
s
ly
c
o
n
s
id
e
r
th
e
id
e
a
th
a
t
o
rd
in
a
ry
th
in
k
in
g
w
a
s
c
o
m
p
u
ta
ti
o
n
•
th
e
ru
le
s
o
f
a
ri
th
m
e
ti
c
a
ll
o
w
u
s
to
d
e
a
l
w
it
h
a
b
s
tr
a
c
t
n
u
m
b
e
rs
in
te
rm
s
o
f
c
o
n
c
re
te
s
y
m
b
o
ls
m
a
n
ip
u
la
ti
o
n
s
o
n
n
u
m
e
ri
c
s
y
m
b
o
ls
m
ir
ro
r
re
la
ti
o
n
s
h
ip
s
a
m
o
n
g
th
e
n
u
m
b
e
rs
b
e
in
g
re
p
re
s
e
n
te
d
•
th
e
ru
le
s
o
f
lo
g
ic
a
ll
o
w
u
s
to
d
e
a
l
w
it
h
a
b
s
tr
a
c
t
id
e
a
s
in
te
rm
s
o
f
c
o
n
c
re
te
s
y
m
b
o
ls
m
a
n
ip
u
la
ti
o
n
s
o
n
p
ro
p
o
s
it
io
n
a
l
s
y
m
b
o
ls
m
ir
ro
r
re
la
ti
o
n
s
h
ip
s
a
m
o
n
g
id
e
a
s
b
e
in
g
re
p
re
s
e
n
te
d
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
2
6
.
.
P
ro
p
o
s
it
io
n
s
v
s
.
s
e
n
te
n
c
e
s
D
e
fi
n
it
io
n
:
A
p
ro
p
o
s
it
io
n
is
th
e
id
e
a
e
x
p
re
s
s
e
d
b
y
a
d
e
c
la
ra
ti
v
e
s
e
n
te
n
c
e
.
fo
r
e
x
a
m
p
le
,
th
e
id
e
a
th
a
t
•
m
y
k
e
y
s
a
re
in
m
y
c
o
a
t
p
o
c
k
e
t
•
d
in
o
s
a
u
rs
w
e
re
w
a
rm
-b
lo
o
d
e
d
•
s
o
m
e
b
o
d
y
w
il
l
fa
il
th
is
c
o
u
rs
e
T
h
e
y
a
re
a
b
s
tr
a
c
t
e
n
ti
ti
e
s
(l
ik
e
n
u
m
b
e
rs
)
b
u
t
h
a
v
e
s
p
e
c
ia
l
p
ro
p
e
rt
ie
s
:
•
T
h
e
y
a
re
c
o
n
s
id
e
re
d
to
h
o
ld
o
r
n
o
t
h
o
ld
.
A
s
e
n
te
n
c
e
is
c
o
n
s
id
e
re
d
to
b
e
tr
u
e
if
th
e
p
ro
p
o
s
it
io
n
it
e
x
p
re
s
s
e
s
h
o
ld
s
.
•
T
h
e
y
a
re
re
la
te
d
to
p
e
o
p
le
in
v
a
ri
o
u
s
w
a
y
s
:
p
e
o
p
le
c
a
n
b
e
li
e
v
e
th
e
m
,
d
is
b
e
li
e
v
e
th
e
m
,
fe
a
r
th
e
m
,
w
o
rr
y
a
b
o
u
t
th
e
m
,
re
g
re
t
th
e
m
,
e
tc
.
•
T
h
e
y
a
re
re
la
te
d
to
e
a
c
h
o
th
e
r
in
v
a
ri
o
u
s
w
a
y
s
:
e
n
ta
il
,
p
ro
v
id
e
e
v
id
e
n
c
e
,
c
o
n
tr
a
d
ic
t,
e
tc
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
2
7
.
.
A
fi
rs
t
c
lu
e
W
e
d
o
n
o
t
n
e
c
e
s
s
a
ri
ly
n
e
e
d
to
k
n
o
w
w
h
a
t
th
e
te
rm
s
in
a
s
e
n
te
n
c
e
m
e
a
n
to
b
e
a
b
le
to
th
in
k
a
b
o
u
t
it
.
E
x
a
m
p
le
:
T
h
e
s
n
a
rk
w
a
s
a
b
o
o
ju
m
.
A
n
d
n
o
w
a
n
s
w
e
r
th
e
fo
ll
o
w
in
g
:
•
W
h
a
t
k
in
d
o
f
th
in
g
w
a
s
th
e
s
n
a
rk
?
•
Is
th
e
re
a
n
y
th
in
g
th
a
t
w
a
s
a
b
o
o
ju
m
?
•
W
a
s
th
e
s
n
a
rk
e
it
h
e
r
a
b
e
e
ju
m
o
r
a
b
o
o
ju
m
?
•
G
iv
e
n
th
a
t
n
o
b
o
o
ju
m
is
e
v
e
ry
a
b
e
e
ju
m
,
w
a
s
th
e
s
n
a
rk
a
b
e
e
ju
m
?
W
e
c
a
n
s
ti
ll
fi
g
u
re
o
u
t
a
p
p
ro
p
ri
a
te
a
n
s
w
e
rs
u
s
in
g
s
im
p
le
ru
le
s
.
C
o
m
p
a
re
:
th
e
P
R
O
C
X
p
ro
c
e
d
u
re
!
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
2
8
.
.
S
o
m
e
re
la
te
d
th
o
u
g
h
ts
M
y
k
e
y
s
a
re
in
m
y
c
o
a
t
p
o
c
k
e
t
o
r
o
n
th
e
fr
id
g
e
.
N
o
th
in
g
is
in
m
y
c
o
a
t
p
o
c
k
e
t.
S
o
m
y
k
e
y
s
a
re
o
n
th
e
fr
id
g
e
.
C
o
m
p
a
re
to
th
is
:
H
e
n
ry
is
in
th
e
b
a
s
e
m
e
n
t
o
r
in
th
e
g
a
rd
e
n
.
N
o
b
o
d
y
is
in
th
e
b
a
s
e
m
e
n
t.
S
o
H
e
n
ry
is
in
th
e
g
a
rd
e
n
.
A
n
d
c
o
m
p
a
re
to
th
is
:
J
il
l
is
m
a
rr
ie
d
to
G
e
o
rg
e
o
r
J
a
c
k
.
N
o
b
o
d
y
is
m
a
rr
ie
d
to
G
e
o
rg
e
.
S
o
J
il
l
is
m
a
rr
ie
d
to
J
a
c
k
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
2
9
.
.
It
’s
a
ll
in
th
e
fo
rm
A
ll
th
re
e
e
x
a
m
p
le
s
a
re
re
a
ll
y
th
e
s
a
m
e
:
B
lu
e
th
in
g
is
g
re
e
n
th
in
g
o
r
y
e
ll
o
w
th
in
g
.
N
o
th
in
g
is
g
re
e
n
th
in
g
.
S
o
b
lu
e
th
in
g
is
y
e
ll
o
w
th
in
g
.
It
d
o
e
s
n
o
t
m
a
tt
e
r
w
h
e
th
e
r
•
b
lu
e
th
in
g
is
“m
y
k
e
y
s
”
o
r
“H
e
n
ry
”
o
r
“J
il
l”
•
g
re
e
n
th
in
g
is
“i
n
m
y
c
o
a
t
p
o
c
k
e
t
o
r
“i
n
th
e
b
a
s
e
m
e
n
t”
o
r
“m
a
rr
ie
d
to
G
e
o
rg
e
”
N
o
te
:
T
h
e
th
in
k
in
g
is
th
e
s
a
m
e
!
T
h
e
o
n
ly
th
in
g
th
a
t
m
a
tt
e
rs
is
th
a
t
it
is
th
e
s
a
m
e
te
rm
(t
h
e
b
lu
e
th
in
g
)
th
a
t
is
u
s
e
d
in
th
e
fi
rs
t
a
n
d
th
ir
d
s
e
n
te
n
c
e
s
,
e
tc
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
3
0
.
.
E
n
ta
il
m
e
n
t
A
c
o
ll
e
c
ti
o
n
o
f
s
e
n
te
n
c
e
s
,
S
1
,
S
2
,
.
.
.
S
n
e
n
ta
il
a
s
e
n
te
n
c
e
S
if
th
e
tr
u
th
o
f
S
is
im
p
li
c
it
in
th
e
tr
u
th
o
f
th
e
S
i
.
N
o
m
a
tt
e
r
w
h
a
t
th
e
te
rm
s
in
th
e
S
i
re
a
ll
y
m
e
a
n
,
if
th
e
S
i
s
e
n
te
n
c
e
s
a
re
a
ll
tr
u
e
,
th
e
n
S
m
u
s
t
a
ls
o
b
e
tr
u
e
.
F
o
r
e
x
a
m
p
le
,
T
h
e
s
n
a
rk
w
a
s
a
b
o
o
ju
m
.
E
n
ta
il
s
:
S
o
m
e
th
in
g
w
a
s
a
b
o
o
ju
m
.
M
y
k
e
y
s
a
re
in
m
y
c
o
a
t
p
o
c
k
e
t
o
r
o
n
th
e
fr
id
g
e
.
a
n
d
N
o
th
in
g
is
in
m
y
c
o
a
t
p
o
c
k
e
t.
E
n
ta
il
s
:
M
y
k
e
y
s
a
re
o
n
th
e
fr
id
g
e
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
3
1
.
.
C
a
n
th
is
b
e
h
o
w
w
e
th
in
k
?
?
S
u
p
p
o
s
e
w
e
a
re
to
ld
a
t
a
p
a
rt
y
:
G
e
o
rg
e
is
a
b
a
c
h
e
lo
r.
H
e
re
is
w
h
a
t
is
e
n
ta
il
e
d
:
•
S
o
m
e
b
o
d
y
is
a
b
a
c
h
e
lo
r.
•
G
e
o
rg
e
is
e
it
h
e
r
a
b
a
c
h
e
lo
r
o
r
a
fa
rm
e
r.
•
N
o
t
e
v
e
ry
o
n
e
is
n
o
t
a
b
a
c
h
e
lo
r.
•
It
is
n
o
t
th
e
c
a
s
e
th
a
t
G
e
o
rg
e
is
n
o
t
a
b
a
c
h
e
lo
r.
.
.
.
A
ll
tr
u
e
,
b
u
t
v
e
ry
v
e
ry
b
o
ri
n
g
!
B
u
t
w
h
e
n
w
e
th
in
k
a
b
o
u
t
it
,
w
e
th
in
k
a
b
o
u
t
•
G
e
o
rg
e
(w
h
o
w
e
m
a
y
k
n
o
w
a
lo
t
a
b
o
u
t)
•
b
e
in
g
a
b
a
c
h
e
lo
r
(w
h
ic
h
w
e
m
a
y
k
n
o
w
a
lo
t
a
b
o
u
t)
S
o
o
u
r
th
in
k
in
g
a
p
p
e
a
rs
to
d
e
p
e
n
d
o
n
w
h
a
t
th
e
te
rm
s
m
e
a
n
!
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
3
2
.
.
U
s
in
g
w
h
a
t
y
o
u
k
n
o
w
W
e
m
u
s
t
c
o
n
s
id
e
r
th
e
e
n
ta
il
m
e
n
ts
o
f
n
o
t
o
n
ly
G
e
o
rg
e
is
a
b
a
c
h
e
lo
r,
b
u
t
th
is
+
a
la
rg
e
c
o
ll
e
c
ti
o
n
o
f
o
th
e
r
s
e
n
te
n
c
e
s
w
e
m
ig
h
t
a
lr
e
a
d
y
k
n
o
w
:
G
e
o
rg
e
w
a
s
b
o
rn
in
B
o
s
to
n
,
c
o
ll
e
c
ts
s
ta
m
p
s
.
A
s
o
n
o
f
s
o
m
e
o
n
e
is
a
c
h
il
d
w
h
o
is
m
a
le
.
G
e
o
rg
e
is
th
e
o
n
ly
s
o
n
o
f
M
a
ry
a
n
d
F
re
d
.
A
m
a
n
is
a
n
a
d
u
lt
m
a
le
p
e
rs
o
n
.
A
b
a
c
h
e
lo
r
is
a
m
a
n
w
h
o
h
a
s
n
e
v
e
r
b
e
e
n
m
a
rr
ie
d
.
A
(t
ra
d
it
io
n
a
l)
m
a
rr
ia
g
e
is
a
c
o
n
tr
a
c
t
b
e
tw
e
e
n
a
m
a
n
a
n
d
a
w
o
m
a
n
,
e
n
a
c
te
d
b
y
a
w
e
d
d
in
g
a
n
d
d
is
s
o
lv
e
d
b
y
a
d
iv
o
rc
e
.
W
h
il
e
th
e
c
o
n
tr
a
c
t
is
in
e
ff
e
c
t,
th
e
m
a
n
(c
a
ll
e
d
th
e
h
u
s
b
a
n
d
)
a
n
d
th
e
w
o
m
a
n
(c
a
ll
e
d
th
e
w
if
e
)
a
re
s
a
id
to
b
e
m
a
rr
ie
d
.
A
w
e
d
d
in
g
is
a
c
e
re
m
o
n
y
w
h
e
re
.
.
.
b
ri
d
e
.
.
.
g
ro
o
m
.
.
.
b
o
u
q
u
e
t
.
.
.
T
h
e
te
rm
s
li
k
e
“G
e
o
rg
e
”
a
n
d
“b
a
c
h
e
lo
r”
a
n
d
“p
e
rs
o
n
”
a
n
d
“s
ta
m
p
s
”
a
p
p
e
a
r
in
m
a
n
y
p
la
c
e
s
a
n
d
li
n
k
th
e
s
e
s
e
n
te
n
c
e
s
to
g
e
th
e
r.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
3
3
.
.
T
h
e
w
e
b
o
f
b
e
li
e
f
s
w
a
s
s
in
s
,
.
.
.
.
.
.
G
eo
rg
e
b
or
n
B
os
to
n
F
re
d
s
is
th
e
o
n
ly
s
o
f
s
a
n
d
s
so
n
M
ar
y
ch
il
d
A
s
o
f
s
o
m
e
o
n
e
is
a
s
w
h
o
is
s
ad
u
lt
m
al
e
A
s
is
a
n
s
s
s
m
an
p
er
so
n
A
s
is
a
s
w
h
o
h
a
s
n
e
v
e
r
b
e
e
n
s
b
ac
h
el
or
m
ar
ri
ag
e
co
n
tr
ac
t
m
ar
ri
ed
A
s
is
a
s
.
.
.
.
.
.
s
a
id
to
b
e
s
@
@
! !
”
“”
##
! !
!!
$ $
@
@
# #
!!
@
@
E
a
c
h
s
e
n
te
n
c
e
w
e
b
e
li
e
v
e
is
li
n
k
e
d
to
m
a
n
y
o
th
e
rs
b
y
v
ir
tu
e
o
f
th
e
te
rm
s
th
a
t
a
p
p
e
a
r
in
th
e
m
.
It
is
th
e
jo
b
o
f
lo
g
ic
to
c
ra
w
l
o
v
e
r
th
is
w
e
b
lo
o
k
in
g
fo
r
c
o
n
n
e
c
ti
o
n
s
a
m
o
n
g
th
e
te
rm
s
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
3
4
.
.
U
s
in
g
w
h
a
t
y
o
u
k
n
o
w
W
h
e
n
w
e
in
c
lu
d
e
a
ll
th
e
s
e
o
th
e
r
fa
c
ts
,
h
e
re
a
re
s
o
m
e
e
n
ta
il
m
e
n
ts
w
e
g
e
t:
•
G
e
o
rg
e
h
a
s
n
e
v
e
r
b
e
e
n
th
e
g
ro
o
m
a
t
a
w
e
d
d
in
g
.
•
M
a
ry
h
a
s
a
n
u
n
m
a
rr
ie
d
s
o
n
b
o
rn
in
B
o
s
to
n
.
•
N
o
w
o
m
a
n
is
th
e
w
if
e
o
f
a
n
y
o
f
F
re
d
’s
c
h
il
d
re
n
.
T
h
e
c
o
n
c
lu
s
io
n
s
a
re
m
u
c
h
m
o
re
li
k
e
th
o
s
e
m
a
d
e
b
y
o
rd
in
a
ry
p
e
o
p
le
.
W
e
fi
n
d
w
h
e
re
th
e
s
a
m
e
te
rm
a
p
p
e
a
rs
(l
ik
e
w
e
d
id
w
it
h
th
e
b
lu
e
th
in
g
,
th
e
g
re
e
n
th
in
g
e
tc
.)
.
W
e
th
e
n
a
p
p
ly
s
im
p
le
ru
le
s
o
f
lo
g
ic
to
d
ra
w
c
o
n
c
lu
s
io
n
s
.
W
e
s
ti
ll
d
o
n
o
t
n
e
e
d
to
k
n
o
w
w
h
a
t
“G
e
o
rg
e
”
o
r
“b
a
c
h
e
lo
r”
m
e
a
n
s
!
N
o
w
,
th
e
b
ig
s
te
p
:
Im
a
g
in
e
d
ra
w
in
g
c
o
n
c
lu
s
io
n
s
fr
o
m
m
il
li
o
n
s
o
f
s
u
c
h
fa
c
ts
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
3
5
.
.
T
w
o
h
y
p
o
th
e
s
e
s
1
.
M
u
c
h
o
f
th
e
ri
c
h
n
e
s
s
o
f
m
e
a
n
in
g
th
a
t
w
e
e
x
p
e
ri
e
n
c
e
d
u
ri
n
g
th
in
k
in
g
m
a
y
b
e
a
c
c
o
u
n
te
d
fo
r
in
te
rm
s
o
f
s
im
p
le
s
y
m
b
o
li
c
m
a
n
ip
u
la
ti
o
n
s
o
v
e
r
a
ri
c
h
c
o
ll
e
c
ti
o
n
o
f
re
p
re
s
e
n
te
d
p
ro
p
o
s
it
io
n
s
2
.
T
o
b
u
il
d
c
o
m
p
u
te
rs
s
y
s
te
m
s
th
a
t
a
re
v
e
rs
a
ti
le
,
fl
e
x
ib
le
,
m
o
d
ifi
a
b
le
,
e
x
p
la
in
a
b
le
,
.
.
.
it
is
a
g
o
o
d
id
e
a
to
•
re
p
re
s
e
n
t
m
u
c
h
o
f
w
h
a
t
th
e
s
y
s
te
m
n
e
e
d
s
to
k
n
o
w
a
s
s
y
m
b
o
li
c
s
e
n
te
n
c
e
s
•
p
e
rf
o
rm
m
a
n
ip
u
la
ti
o
n
s
o
v
e
r
th
e
s
e
s
e
n
te
n
c
e
s
u
s
in
g
th
e
ru
le
s
o
f
s
y
m
b
o
li
c
lo
g
ic
to
d
e
ri
v
e
n
e
w
c
o
n
c
lu
s
io
n
s
•
h
a
v
e
th
e
s
y
s
te
m
a
c
t
b
a
s
e
d
o
n
th
e
c
o
n
c
lu
s
io
n
s
it
is
a
b
le
to
d
e
ri
v
e
S
y
s
te
m
s
b
u
il
t
th
is
w
a
y
a
re
c
a
ll
e
d
k
n
o
w
le
d
g
e
-b
a
s
e
d
s
y
s
te
m
s
a
n
d
th
e
c
o
ll
e
c
ti
o
n
o
f
s
e
n
te
n
c
e
s
is
c
a
ll
e
d
it
s
k
n
o
w
le
d
g
e
b
a
s
e
(K
B
).
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
3
6
.
.
S
u
m
m
a
ry
T
h
in
k
in
g
,
a
s
fa
r
a
s
w
e
a
re
c
o
n
c
e
rn
e
d
,
m
e
a
n
s
b
ri
n
g
in
g
w
h
a
t
y
o
u
k
n
o
w
to
b
e
a
r
o
n
w
h
a
t
y
o
u
a
re
d
o
in
g
.
B
u
t
h
o
w
d
o
e
s
th
is
w
o
rk
?
H
o
w
d
o
c
o
n
c
re
te
,
p
h
y
s
ic
a
l
e
n
ti
ti
e
s
li
k
e
p
e
o
p
le
e
n
g
a
g
e
w
it
h
s
o
m
e
th
in
g
fo
rm
le
s
s
a
n
d
a
b
s
tr
a
c
t
li
k
e
k
n
o
w
le
d
g
e
?
T
h
e
a
n
s
w
e
r
(v
ia
L
e
ib
n
iz
)
is
th
a
t
w
e
e
n
g
a
g
e
w
it
h
s
y
m
b
o
li
c
re
p
re
s
e
n
ta
ti
o
n
s
o
f
th
a
t
k
n
o
w
le
d
g
e
.
W
e
re
p
re
s
e
n
t
k
n
o
w
le
d
g
e
s
y
m
b
o
li
c
a
ll
y
a
s
a
c
o
ll
e
c
ti
o
n
o
f
s
e
n
te
n
c
e
s
in
a
k
n
o
w
le
d
g
e
b
a
s
e
,
a
n
d
th
e
n
c
o
m
p
u
te
e
n
ta
il
m
e
n
ts
o
f
th
o
s
e
s
e
n
te
n
c
e
s
,
a
s
w
e
n
e
e
d
th
e
m
.
S
o
c
o
m
p
u
ta
ti
o
n
o
v
e
r
a
k
n
o
w
le
d
g
e
b
a
s
e
is
th
e
d
ir
e
c
ti
o
n
th
a
t
w
e
w
il
l
b
e
p
u
rs
u
in
g
in
th
is
c
o
u
rs
e
,
a
lt
h
o
u
g
h
w
e
w
il
l
o
n
ly
e
v
e
r
d
e
a
l
w
it
h
ti
n
y
k
n
o
w
le
d
g
e
b
a
s
e
s
h
e
re
.
C
h
a
p
te
r
1
:
T
h
in
k
in
g
a
n
d
C
o
m
p
u
ta
ti
o
n
c ©
L
e
v
e
sq
u
e
2
0
1
1
3
7