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Evokation
  
 
Index
  

 

 

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
-
7
-
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
-
7
-
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
-
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
-
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
+
=
351
3+5+1
=
9
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
-
9
-
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
-
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
-
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
-
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

 

ADVENT 2065 ADVENT

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

NET ENTERS NETERS TEN

 

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
First Total
189
90
18
1+8
Add to Reduce
1+8+9
9+0
1+8
9
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
9
Essence of Number
9
9
9

 

 

 

 

THE, NET
THE WORLD WIDE WEB
THE, WEB
THE, LAW, OF, CLOSURE
THE WEB
THE NET
INTERNET
THE INTERNET
U TUBE
FACEBOOK
TWITTER
THE, PEOPLE, OF, PLANET, EARTH
THE, INTELLECT
INTELLIGENCE
SQUARIN G THE CIRCLE
CIRCLING THE SQUARE

 

 

 

 

3
THE
33
15
6
3
NET
39
12
3
6
Add to Reduce
72
27
9
-
Reduce to Deduce
7+2
2+7
-
6
Essence of Number
9
9
9

 

 

3
THE
33
15
6
3
WEB
30
12
3
6
Add to Reduce
63
27
9
-
Reduce to Deduce
6+3
2+7
-
6
Essence of Number
9
9
9

 

 

-
6
T
H
E
-
W
E
B
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
+
=
8
-
=
8
=
8
=
8
-
-
-
8
-
-
-
-
-
+
=
8
-
=
8
=
8
=
8
-
6
T
H
E
-
W
E
B
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
5
5
2
+
=
19
1+9
=
10
1+0
1
=
1
-
-
20
-
5
-
23
5
2
+
=
55
5+5
=
10
1+0
1
=
1
-
6
T
H
E
-
W
E
B
-
-
-
-
-
--
-
-
-
-
-
-
20
8
5
-
23
5
2
+
=
63
6+3
=
9
=
9
=
9
-
-
2
8
5
-
5
5
2
+
=
27
2+7
=
9
=
9
=
9
-
6
T
H
E
-
W
E
B
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
5
5
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
30
6
T
H
E
-
W
E
B
-
-
15
-
-
6
-
27
-
18
3+0
-
-
-
5
-
5
5
-
-
-
1+5
-
-
-
-
2+7
-
1+8
3
6
T
H
E
-
W
E
B
-
-
6
-
-
6
-
9
-
9
-
-
2
8
5
-T
5
5
2
-T
-
-
-
-
-
-
-
-
-
3
6
T
H
E
-
W
E
B
-
-
6
-
-
6
-
9
-
9

 

 

6
T
H
E
-
W
E
B
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
+
=
8
-
=
8
=
8
=
8
-
-
8
-
-
-
-
-
+
=
8
-
=
8
=
8
=
8
6
T
H
E
-
W
E
B
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
5
5
2
+
=
19
1+9
=
10
1+0
1
=
1
-
20
-
5
-
23
5
2
+
=
55
5+5
=
10
1+0
1
=
1
6
T
H
E
-
W
E
B
-
-
-
-
-
--
-
-
-
-
-
20
8
5
-
23
5
2
+
=
63
6+3
=
9
=
9
=
9
-
2
8
5
-
5
5
2
+
=
27
2+7
=
9
=
9
=
9
6
T
H
E
-
W
E
B
-T
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
5
-
5
5
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
6
T
H
E
-
W
E
B
-
-
15
-
-
6
-
27
-
18
-
-
-
5
-
5
5
-
-
-
1+5
-
-
-
-
2+7
-
1+8
6
T
H
E
-
W
E
B
-
-
6
-
-
6
-
9
-
9
-
2
8
5
-T
5
5
2
-T
-
-
-
-
-
-
-
-
-
6
T
H
E
-
W
E
B
-
-
6
-
-
6
-
9
-
9

 

 

3
THE
33
15
6
5
WORLD
72
27
9
4
WIDE
41
23
5
3
WEB
30
12
3
15
First Total
176
77
23
1+5
Add to Reduce
1+7+6
7+7
2+3
6
Second Total
14
14
5
-
Reduce to Deduce
1+4
1+4
-
6
Essence of Number
5
5
5

 

 

-
6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
6
-
-
-
-
-
9
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
8
-
-
-
15
-
-
-
-
-
9
-
-
-
-
-
-
+
=
32
3+2
=
5
=
5
=
5
-
6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
5
-
9
3
4
-
5
-
4
5
-
5
5
2
+
=
54
5+4
=
9
=
9
=
9
-
-
20
-
5
-
23
-
18
12
4
-
23
-
4
5
-
23
5
2
+
=
144
1+4+4
=
9
=
9
=
9
-
6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
23
15
18
12
4
-
23
9
4
5
-
23
5
2
+
=
176
1+7+6
=
14
1+4
5
=
5
-
-
2
8
5
-
5
6
9
3
4
-
5
9
4
5
-
5
5
2
+
=
77
7+7
=
14
1+4
5
=
5
-
6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
-
5
-
5
-
-
-
-
-
5
-
-
5
-
5
5
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
15
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
37
-
-
15
-
77
-
41
-
1+5
-
-
5
-
5
-
-
-
-
-
5
-
-
5
-
5
5
-
-
-
3+7
-
-
1+5
-
7+7
-
4+1
8
6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
10
-
-
6
-
14
-
5
-
-
2
8
5
-
5
6
9
3
4
-
5
9
4
5
-
5
5
2
-
-
1+0
-
-
-
-
1+4
-
-
8
6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
1
-
-
6
-
5
-
5

 

 

6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
6
-
-
-
-
-
9
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
8
-
-
-
15
-
-
-
-
-
9
-
-
-
-
-
-
+
=
32
3+2
=
5
=
5
=
5
6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
5
-
9
3
4
-
5
-
4
5
-
5
5
2
+
=
54
5+4
=
9
=
9
=
9
-
20
-
5
-
23
-
18
12
4
-
23
-
4
5
-
23
5
2
+
=
144
1+4+4
=
9
=
9
=
9
6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
23
15
18
12
4
-
23
9
4
5
-
23
5
2
+
=
176
1+7+6
=
14
1+4
5
=
5
-
2
8
5
-
5
6
9
3
4
-
5
9
4
5
-
5
5
2
+
=
77
7+7
=
14
1+4
5
=
5
6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-T
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
-
-
-
4
-
-
-
4
-
-
-
-
-
-
-
4
occurs
x
2
=
8
=
8
-
-
-
5
-
5
-
-
-
-
-
5
-
-
5
-
5
5
-
-
-
5
occurs
x
6
=
30
3+0
3
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
15
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
37
-
-
15
-
77
-
41
1+5
-
-
5
-
5
-
-
-
-
-
5
-
-
5
-
5
5
-
-
-
3+7
-
-
1+5
-
7+7
-
4+1
6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
10
-
-
6
-
14
-
5
-
2
8
5
-
5
6
9
3
4
-
5
9
4
5
-
5
5
2
-
-
1+0
-
-
-
-
1+4
-
-
6
T
H
E
-
W
O
R
L
D
-
W
I
D
E
-
W
E
B
-
-
1
-
-
6
-
5
-
5

 

 

-
6
T
H
E
--
N
E
T
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
5
-
-
+
=
13
1+3
=
4
=
4
=
4
-
`-
-
8
-
--
14
-
-
+
=
22
2+2
=
4
=
4
=
4
-
6
T
H
E
-
N
E
T
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
5
2
+
=
14
1+4
=
5
=
5
=
5
-
`-
20
-
5
-
-
5
20
+
=
50
5+0
=
5
=
5
=
5
-
6
T
H
E
-
N
E
T
-
-
-
-
-
-
-
-
-
-
-
`-
20
8
5
-
14
5
20
+
=
72
7+2
=
9
=
9
=
9
-
-
2
8
5
--
5
5
2
+
=
27
2+7
=
9
=
9
=
9
-
6
T
H
E
-
N
E
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
3
-
-
-
-
-
-
-
-
-
5
-
5
5
-
-
-
5
occurs
x
3
=
15
=
6
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
9
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
30
6
T
H
E
-
N
E
T
-
-
15
-
-
6
-
27
-
9
3+0
-
-
-
5
-
5
5
-
-
-
1+5
-
-
-
-
2+7
-
-
3
6
T
H
E
-
N
E
T
-
-
6
-
-
6
-
9
-
9
-
-
2
8
5
-T
5
5
2
-T
-
-
-
-
-
-
-
-
-
3
6
T
H
E
-
N
E
T
-
-
6
-
-
6
-
9
-
9

 

 

6
T
H
E
--
N
E
T
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
5
-
-
+
=
13
1+3
=
4
=
4
=
4
-
-
8
-
--
14
-
-
+
=
22
2+2
=
4
=
4
=
4
6
T
H
E
-
N
E
T
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
5
2
+
=
14
1+4
=
5
=
5
=
5
-
20
-
5
-
-
5
20
+
=
50
5+0
=
5
=
5
=
5
6
T
H
E
-
N
E
T
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
14
5
20
+
=
72
7+2
=
9
=
9
=
9
-
2
8
5
--
5
5
2
+
=
27
2+7
=
9
=
9
=
9
6
T
H
E
-
N
E
T
-T
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
5
-
5
5
-
--
-
5
occurs
x
3
=
15
=
6
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
6
T
H
E
-
N
E
T
-
-
15
-
-
6
-
27
-
9
-
-
-
5
-
5
5
-
-
-
1+5
-
-
-
-
2+7
-
-
6
T
H
E
-
N
E
T
-
-
6
-
-
6
-
9
-
9
-
2
8
5
-T
5
5
2
-T
-
-
-
-
-
-
-
-
-
6
T
H
E
-
N
E
T
-
-
6
-
-
6
-
9
-
9

 

 

-
8
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
-
-
9
5
-
-
-
5
-
-
+
=
19
1+9
=
10
1+0
1
=
1
-
-
9
14
-
-
-
14
-
-
+
=
37
3+7
=
10
1+0
1
=
1
-
8
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
5
9
-
5
2
+
=
23
2+3
=
5
=
5
=
5
-
-
-
-
20
5
18
-
5
20
+
=
68
6+8
=
14
1+4
5
=
5
-
8
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
-
`-
9
14
20
5
18
14
5
20
+
=
105
1+0+5
=
6
=
6
=
6
-
-
9
5
2
5
9
5
5
2
+
=
42
4+2
=
6
=
6
=
6
-
8
I
N
T
E
R
N
E
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
2
occurs
x
2
=
4
=
4
3
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
5
-
5
5
-
--
-
5
occurs
x
4
=
20
2+0
2
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
29
8
I
N
T
E
R
N
E
T
-
-
16
-
-
8
-
42
-
15
2+9
-
-
5
-
5
-
5
5
-
-
-
1+6
-
-
-
-
4+2
-
1+5
11
8
I
N
T
E
R
N
E
T
-
-
7
-
-
8
-
6
-
6
1+1
-
9
5
2
5
9
5
5
2
-
-
-
-
-
-
-
-
-
-
2
8
I
N
T
E
R
N
E
T
-
-
7
-
-
8
-
6
-
6

 

 

8
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
-
9
5
-
-
-
5
-
-
+
=
19
1+9
=
10
1+0
1
=
1
-
9
14
-
-
-
14
-
-
+
=
37
3+7
=
10
1+0
1
=
1
8
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
-
-
-
2
5
9
-
5
2
+
=
23
2+3
=
5
=
5
=
5
-
-
-
20
5
18
-
5
20
+
=
68
6+8
=
14
1+4
5
=
5
8
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
-
9
14
20
5
18
14
5
20
+
=
105
1+0+5
=
6
=
6
=
6
-
9
5
2
5
9
5
5
2
+
=
42
4+2
=
6
=
6
=
6
8
I
N
T
E
R
N
E
T
-T
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
-
-
2
occurs
x
2
=
4
-
4
-
-
5
-
5
-
5
5
-
-
-
5
occurs
x
4
=
20
2+0
2
-
9
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
8
I
N
T
E
R
N
E
T
-
-
16
-
-
8
-
42
-
15
-
-
5
-
5
-
5
5
-
-
-
1+6
-
-
-
-
4+2
-
1+5
8
I
N
T
E
R
N
E
T
-
-
7
-
-
8
-
6
-
6
-
9
5
2
5
9
5
5
2
-
-
-
-
-
-
-
-
-
-
8
I
N
T
E
R
N
E
T
-
-
7
-
-
8
-
6
-
6

 

 

-
11
T
H
E
-
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
9
5
-
-
-
5
-
-
+
=
27
2+7
=
9
-
9
=
9
-
-
-
8
-
-
9
14
-
-
-
14
-
-
+
=
45
4+5
=
9
-
9
=
9
-
11
T
H
E
-
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
-
2
5
9
-
5
2
+
=
30
3+0
=
3
-
3
=
3
-
-
20
-
5
-
-
-
20
5
18
-
5
20
+
=
93
9+3
=
12
1+2
3
=
3
-
11
T
H
E
-
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
-
-
20
8
5
-
9
14
20
5
18
14
5
20
+
=
138
1+3+8
=
12
1+2
3
=
3
-
-
2
8
5
-
9
5
2
5
9
5
5
2
+
=
57
5+7
=
12
1+2
3
=
3
-
11
T
H
E
-
I
N
T
E
R
N
E
T
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
5
-
5
-
5
5
-
-
-
5
occurs
x
5
=
25
2+5
7
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
21
11
T
H
E
-
I
N
T
E
R
N
E
T
-
-
24
-
-
11
-
57
-
30
2+1
1+1
-
-
5
-
-
5
-
5
-
5
5
-
--
-
2+4
-
-
1+1
-
5+7
-
3+0
3
2
T
H
E
-
I
N
T
E
R
N
E
T
-
-
6
-
-
2
-
12
-
3
-
-
2
8
5
-
9
5
2
5
9
5
5
2
-
-
-
-
-
-
-
1+2
-
-
3
2
T
H
E
-
I
N
T
E
R
N
E
T
-
-
6
-
-
2
-
3
-
3

 

 

11
T
H
E
-
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
9
5
-
-
-
5
-
-
+
=
27
2+7
=
9
-
9
=
9
-
-
8
-
-
9
14
-
-
-
14
-
-
+
=
45
4+5
=
9
-
9
=
9
11
T
H
E
-
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
-
2
-
5
-
-
-
2
5
9
-
5
2
+
=
30
3+0
=
3
-
3
=
3
-
20
-
5
-
-
-
20
5
18
-
5
20
+
=
93
9+3
=
12
1+2
3
=
3
11
T
H
E
-
I
N
T
E
R
N
E
T
-
-
-
-
-
-
-
-
-
-
`-
20
8
5
-
9
14
20
5
18
14
5
20
+
=
138
1+3+8
=
12
1+2
3
=
3
-
2
8
5
-
9
5
2
5
9
5
5
2
+
=
57
5+7
=
12
1+2
3
=
3
11
T
H
E
-
I
N
T
E
R
N
E
T
-T
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
-
-
-
-
2
-
-
2
occurs
x
3
=
6
=
6
--
-
-
5
-
-
5
-
5
-
5
5
-
-
-
5
occurs
x
5
=
25
2+5
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
9
-
-
-
9
-
-
-
-
-
9
occurs
x
2
=
18
1+8
9
11
T
H
E
-
I
N
T
E
R
N
E
T
-
-
24
-
-
11
-
57
-
30
1+1
-
-
5
-
-
5
-
5
-
5
5
-
--
-
2+4
-
-
1+1
-
5+7
-
3+0
2
T
H
E
-
I
N
T
E
R
N
E
T
-
-
6
-
-
2
-
12
-
3
-
2
8
5
-
9
5
2
5
9
5
5
2
-
-
-
-
-
-
-
1+2
-
-
2
T
H
E
-
I
N
T
E
R
N
E
T
-
-
6
-
-
2
-
3
-
3

 

 

-
7
Y
O
U
-
T
U
B
E
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
+
=
6
-
=
6
-
6
-
-
-
15
-
-
-
-
-
-
+
=
15
1+5
=
6
-
6
-
7
Y
O
U
-
T
U
B
E
-
-
-
-
-
-
-
-
-
-
7
-
3
-
2
3
2
5
+
=
22
2+2
=
4
-
4
-
-
25
-
21
-
20
21
2
5
+
=
94
9+4
=
13
1+3
4
-
7
Y
O
U
-
T
U
B
E
-
-
-
-
-
--
-
-
-
-
25
15
21
-
20
21
2
5
+
=
109
1+0+9
=
10
1+0
1
-
-
7
6
3
-
2
3
2
5
+
=
28
2+8
=
10
1+0
1
-
7
Y
O
U
-
T
U
B
E
-T
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
-
-
2
-
2
-
-
-
2
occurs
x
2
=
4
-
-
-
-
3
-
-
3
-
-
-
-
3
occurs
x
2
=
6
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
-
6
-
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
-
7
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
22
7
Y
O
U
-
T
U
B
E
-
-
23
-
-
7
-
15
2+2
-
-
-
-
-
-
-
-
5
-
-
2+3
-
-
-
-
1+5
4
7
Y
O
U
-
T
U
B
E
-
-
5
-
-
7
-
6
-
-
3
3
3
-T
2
3
2
5
-T
-
-
-
-
-
-
-
4
7
Y
O
U
-
T
U
B
E
-
-
5
-
-
7
-
6

 

 

7
Y
O
U
-
T
U
B
E
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
+
=
6
-
=
6
-
6
-
-
15
-
-
-
-
-
-
+
=
15
1+5
=
6
-
6
7
Y
O
U
-
T
U
B
E
-
-
-
-
-
-
-
-
-
7
-
3
-
2
3
2
5
+
=
22
2+2
=
4
-
4
-
25
-
21
-
20
21
2
5
+
=
94
9+4
=
13
1+3
4
7
Y
O
U
-
T
U
B
E
-
-
-
-
-
--
-
-
-
25
15
21
-
20
21
2
5
+
=
109
1+0+9
=
10
1+0
1
-
7
6
3
-
2
3
2
5
+
=
28
2+8
=
10
1+0
1
7
Y
O
U
-
T
U
B
E
-T
-
-
-
-
-
-
-
-
-
-
-
-
2
-
2
-
-
-
2
occurs
x
2
=
4
-
-
-
3
-
-
3
-
-
-
-
3
occurs
x
2
=
6
-
-
-
-
-
-
-
-
5
-
-
5
occurs
x
1
=
5
-
-
6
-
-
-
-
-
-
-
-
6
occurs
x
1
-
6
-
7
-
-
-
-
-
-
-
-
-
7
occurs
x
1
-
7
7
Y
O
U
-
T
U
B
E
-
-
23
-
-
7
-
15
-
-
-
-
-
-
-
-
5
-
-
2+3
-
-
-
-
1+5
7
Y
O
U
-
T
U
B
E
-
-
5
-
-
7
-
6
-
3
3
3
-T
2
3
2
5
-T
-
-
-
-
-
-
-
7
Y
O
U
-
T
U
B
E
-
-
5
-
-
7
-
6

 

 

-
7
M
Y
-
S
P
A
C
E
-
-
-
-T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
+
=
1
-
=
1
=
1
=
1
-
-
-
-
-
19
-
-
-
-
+
=
19
1+9
=
1
=
1
=
1
-
7
M
Y
-
S
P
A
C
E
-
-
-
-
-
-
-
-
-
-
-
-
4
7
--
-
7
1
3
5
+
=
27
2+7
=
9
=
9
=
9
-
-
13
25
-
-
16
1
3
5
+
=
63
6+3
=
9
=
9
=
9
-
7
M
Y
-
S
P
A
C
E
-
-
-
-
-
-
-
-
-
-
-
`-
13
25
-
19
16
1
3
5
+
=
82
8+2
=
10
1+0
1
=
1
-
-
4
7
-
1
7
1
3
5
+
=
31
3+1
=
10
1+0
1
=
1
-
7
M
Y
-
S
P
A
C
E
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
--
-
-
-
-
5
--
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
7
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
25
7
M
Y
-
S
P
A
C
E
-
-
20
-
-
7
-
28
-
19
2+5
-
-
-
-
-
-
-
-
5
-
-
2+0
-
-
-
-
2+8
-
1+9
7
7
M
Y
-
S
P
A
C
E
-
-
2
-
-
7
-
10
-
10
-
-
4
7
-
1
7
1
3
5
-
-
-
-
-
-
-
1+0
-
1+0
7
7
M
Y
-
S
P
A
C
E
-
-
2
-
-
7
-
1
-
1

 

 

-
7
M
Y
-
S
P
A
C
E
-
-
-
-T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
+
=
1
-
=
1
=
1
=
1
-
-
-
-
-
19
-
-
-
-
+
=
19
1+9
=
1
=
1
=
1
-
7
M
Y
-
S
P
A
C
E
-
-
-
-
-
-
-
-
-
-
-
-
4
7
--
-
7
1
3
5
+
=
27
2+7
=
9
=
9
=
9
-
-
13
25
-
-
16
1
3
5
+
=
63
6+3
=
9
=
9
=
9
-
7
M
Y
-
S
P
A
C
E
-
-
-
-
-
-
-
-
-
-
-
`-
13
25
-
19
16
1
3
5
+
=
82
8+2
=
10
1+0
1
=
1
-
-
4
7
-
1
7
1
3
5
+
=
31
3+1
=
10
1+0
1
=
1
-
7
M
Y
-
S
P
A
C
E
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
--
-
-
-
-
5
--
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
7
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
25
7
M
Y
-
S
P
A
C
E
-
-
20
-
-
7
-
28
-
19
2+5
-
-
-
-
-
-
-
-
5
-
-
2+0
-
-
-
-
2+8
-
1+9
7
7
M
Y
-
S
P
A
C
E
-
-
2
-
-
7
-
10
-
10
-
-
4
7
-
1
7
1
3
5
-
-
-
-
-
-
-
1+0
-
1+0
7
7
M
Y
-
S
P
A
C
E
-
-
2
-
-
7
-
1
-
1

 

 

7
M
Y
-
S
P
A
C
E
-
-
-
-T
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
+
=
1
-
=
1
=
1
=
1
-
-
-
-
19
-
-
-
-
+
=
19
1+9
=
1
=
1
=
1
7
M
Y
-
S
P
A
C
E
-
-
-
-
-
-
-
-
-
-
-
4
7
--
-
7
1
3
5
+
=
27
2+7
=
9
=
9
=
9
-
13
25
-
-
16
1
3
5
+
=
63
6+3
=
9
=
9
=
9
7
M
Y
-
S
P
A
C
E
-
-
-
-
-
-
-
-
-
-
`-
13
25
-
19
16
1
3
5
+
=
82
8+2
=
10
1+0
1
=
1
-
4
7
-
1
7
1
3
5
+
=
31
3+1
=
10
1+0
1
=
1
7
M
Y
-
S
P
A
C
E
-T
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
--
-
-
-
-
5
--
-
5
occurs
x
1
=
5
=
5
-
-
7
-
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
7
M
Y
-
S
P
A
C
E
-
-
20
-
-
7
-
28
-
19
-
-
-
-
-
-
-
-
5
-
-
2+0
-
-
-
-
2+8
-
1+9
7
M
Y
-
S
P
A
C
E
-
-
2
-
-
7
-
10
-
10
-
4
7
-
1
7
1
3
5
-
-
-
-
-
-
-
1+0
-
1+0
7
M
Y
-
S
P
A
C
E
-
-
2
-
-
7
-
1
-
1

 

 

7
M
Y
S
P
A
C
E
-
-
-
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
+
=
1
-
=
1
=
1
=
1
-
-
-
19
-
-
-
-
+
=
19
1+9
=
1
=
1
=
1
7
M
Y
S
P
A
C
E
-
-
-
-
-
-
-
-
-
-
-
4
7
-
7
1
3
5
+
=
27
2+7
=
9
=
9
=
9
-
13
25
-
16
1
3
5
+
=
63
6+3
=
9
=
9
=
9
7
M
Y
S
P
A
C
E
-
-
-
-
-
-
-
-
-
-
`-
13
25
19
16
1
3
5
+
=
82
8+2
=
10
1+0
1
=
1
-
4
7
1
7
1
3
5
+
=
31
3+1
=
10
1+0
1
=
1
7
M
Y
S
P
A
C
E
-T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
-
-
-
-
-
5
--
-
5
occurs
x
1
=
5
=
5
-
-
7
-
7
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
7
M
Y
S
P
A
C
E
-
-
20
-
-
7
-
28
-
19
-
-
-
-
-
-
-
5
-
-
2+0
-
-
-
-
2+8
-
1+9
7
M
Y
S
P
A
C
E
-
-
2
-
-
7
-
10
-
10
-
4
7
1
7
1
3
5
-
-
-
-
-
-
-
1+0
-
1+0
7
M
Y
S
P
A
C
E
-
-
2
-
-
7
-
1
-
1

 

 

-
8
F
A
C
E
B
O
O
K
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
+
=
12
1+2
=
3
=
3
=
3
-
-
-
-
-
-
-
15
15
-
+
=
30
3+0
=
3
=
3
=
3
-
8
F
A
C
E
B
O
O
K
-
-
-
-
-
-
-
-
-
-
-
-
6
1
3
5
2
-
-
2
+
=
19
1+9
=
10
1+0
1
=
1
-
-
6
1
3
5
2
-
-
11
+
=
28
2+8
=
10
1+0
1
=
1
-
8
F
A
C
E
B
O
O
K
-
-
-
-
-
-
-
-
-
-
-
`-
6
1
3
5
2
15
15
11
+
=
58
5+8
=
6
=
6
=
6
-
-
6
1
3
5
2
6
6
2
+
=
31
3+1
=
6
=
6
=
6
-
8
F
A
C
E
B
O
O
K
-T
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
-
2
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
--
-
5
occurs
x
1
=
5
=
5
-
-
6
-
-
-
-
6
6
-
-
-
6
occurs
x
3
=
18
1+8
9
7
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
-
9
NINE
9
-
-
-
-
-
28
8
F
A
C
E
B
O
O
K
-
-
17
-
-
8
-
31
-
22
2+8
-
-
-
-
5
-
-
-
-
-
-
2+6
-
-
-
-
3+1
-
2+2
10
8
F
A
C
E
B
O
O
K
-
-
8
-
-
8
-
4
-
4
1+0
-
6
1
3
5
2
6
6
2
-
-
-
-
-
-
-
-
-
-
1
8
F
A
C
E
B
O
O
K
-
-
8
-
-
8
-
4
-
4

 

 

8
F
A
C
E
B
O
O
K
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
6
-
+
=
12
1+2
=
3
=
3
=
3
-
-
-
-
-
-
15
15
-
+
=
30
3+0
=
3
=
3
=
3
8
F
A
C
E
B
O
O
K
-
-
-
-
-
-
-
-
-
-
-
6
1
3
5
2
-
-
2
+
=
19
1+9
=
10
1+0
1
=
1
-
6
1
3
5
2
-
-
11
+
=
28
2+8
=
10
1+0
1
=
1
8
F
A
C
E
B
O
O
K
-
-
-
-
-
-
-
-
-
-
`-
6
1
3
5
2
15
15
11
+
=
58
5+8
=
6
=
6
=
6
-
6
1
3
5
2
6
6
2
+
=
31
3+1
=
6
=
6
=
6
8
F
A
C
E
B
O
O
K
-T
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
=
1
-
-
-
-
-
2
-
-
2
-
-
2
occurs
x
2
=
4
=
4
-
-
-
3
-
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
5
-
-
-
-
--
-
5
occurs
x
1
=
5
=
5
-
6
-
-
-
-
6
6
-
-
-
6
occurs
x
3
=
18
1+8
9
8
F
A
C
E
B
O
O
K
-
-
17
-
-
8
-
31
-
22
-
-
-
-
5
-
-
-
-
-
-
2+6
-
-
-
-
3+1
-
2+2
8
F
A
C
E
B
O
O
K
-
-
8
-
-
8
-
4
-
4
-
6
1
3
5
2
6
6
2
-
-
-
-
-
-
-
-
-
-
8
F
A
C
E
B
O
O
K
-
-
8
-
-
8
-
4
-
4

 

 

-
7
T
W
I
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
9
-
-
-
-
+
=
9
-
=
9
=
9
=
9
-
7
T
W
I
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
2
5
-
2
2
5
9
+
=
25
2+5
=
7
1+0
7
=
7
-
-
20
23
-
20
20
5
18
+
=
106
1+0+6
=
7
1+0
7
=
7
-
7
T
W
I
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
`-
20
23
9
20
20
5
18
+
=
115
1+1+5
=
7
=
7
=
7
-
-
2
5
9
2
2
5
9
+
=
34
3+4
=
7
=
7
=
7
-
7
T
W
I
T
T
E
R
-T
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
ONE
1
-
-
-
-
-
-
-
2
-
-
2
2
-
-
-
-
2
occurs
x
3
=
6
=
6
3
-
-
-
-
-
-
-
-
-
-
3
THREE
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
5
-
-
-
5
-
--
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
7
SEVEN
7
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
9
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
4
29
7
T
W
I
T
T
E
R
-
-
16
-
-
7
-
34
-
22
2+9
-
-
-
9
-
-
5
9
-
-
1+6
-
-
-
-
3+4
-
2+2
11
7
T
W
I
T
T
E
R
-
-
7
-
-
7
-
7
-
7
1+1
-
2
5
9
2
2
5
9
-
-
-
-
-
-
-
-
-
-
2
7
T
W
I
T
T
E
R
-
-
7
-
-
7
-
7
-
7

 

 

-
7
T
W
I
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
+
=
9
-
=
9
=
9
=
9
-
-
-
-
9
-
-
-
-
+
=
9
-
=
9
=
9
=
9
-
7
T
W
I
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
-
2
5
-
2
2
5
9
+
=
25
2+5
=
7
1+0
7
=
7
-
-
20
23
-
20
20
5
18
+
=
106
1+0+6
=
7
1+0
7
=
7
-
7
T
W
I
T
T
E
R
-
-
-
-
-
-
-
-
-
-
-
`-
20
23
9
20
20
5
18
+
=
115
1+1+5
=
7
=
7
=
7
-
-
2
5
9
2
2
5
9
+
=
34
3+4
=
7
=
7
=
7
-
7
T
W
I
T
T
E
R
-T
-
-
-
-
-
-
-
-
-
-
-
2
-
-
2
2
-
-
-
-
2
occurs
x
3
=
6
=
6
-
-
-
5
-
-
-
5
-
--
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
9
-
-
-
9
-
-
9
occurs
x
2
=
18
1+8
4
29
7
T
W
I
T
T
E
R
-
-
16
-
-
7
-
34
-
22
2+9
-
-
-
9
-
-
5
9
-
-
1+6
-
-
-
-
3+4
-
2+2
11
7
T
W
I
T
T
E
R
-
-
7
-
-
7
-
7
-
7
1+1
-
2
5
9
2
2
5
9
-
-
-
-
-
-
-
-
-
-
2
7
T
W
I
T
T
E
R
-
-
7
-
-
7
-
7
-
7

 

 

Daily Mail, Wednesday. November 28,2017

Half of 11-year-year olds use social media...so much for ban on under 13s!

By Katherine Rushton Media and Technology Editor

SOCIAL media giants are letting children aged 11 nd 12 sign up for profiles despite a supposed ban n those under 13.
Nearly half of this age group have accounts on social net works such as Facebook and vitter - as do more than a quarter of ten-year-olds, according to communications watchdog Ofcom.

The revelations last night drew criticism that the companies are `turning a blind eye' to age limit breaches and are not sufficiently
protecting children. Facebook, Twitter, Instagram and Snapchat all claim that users must be 13 but do not demand proof of age. Users are asked to enter their date of birth - but they can easily lie. An Ofcom report, published today, found 51 per cent of 12year-olds have a social media account, along with 46 per cent of 11 year olds. One in ten children shared live videos of themselves on social media. Some platforms, 'including Instagram Live, allow them to broadcast to strangers. Yesterday, child safety experts, MPs and charities lambasted the social media giants for leaving children at risk.

John Carr, secretary of the UK Children's Charities' Coalition on Internet Safety, said: 'There is a gigantic amount of blind eye turning. They know that around the world are tens of millions of children on their websites, and they choose to do nothing about it because they don't have to do anything about it.'

Tory MP Damian Collins, chair of the Commons' digital, culture, media and sport select committee, said: 'If that number of young people are able to set up profiles online, then that suggests that not enough is done to check them.'
Andy Burrows, the NSPCC's associate head of child safety online, added: 'For too long sites like Face-book, Instagram and Snapchat have failed to protect children on their platforms and Government urgently needs to step in.'

Campaigners have called on social media companies to put much stricter controls in place.

Anyone with official ID, such as a passport, can already access online security 'tokens' to prove their age online - making it possible for social media firms to impose age checks.

However, Ofcom's report found many parents are happy for young children to go online. More than half of children aged three and four use the web.

Under a European data protection law due to come into force next year, parents will have to give consent before children under a certain age can sign up for a social media profile. This age will be set at 16 in many European countries but is expected to be 13 in Britain.

Yesterday, Mr Burrows called on the House of Lords to ensure stricter controls are put in place when an amendment to the bill is put to a vote next month.

A Facebook spokesman said yesterday: 'When we become aware that someone is under 13 and they have therefore lied about their age, we remove their account and we use cookies to prevent them from signing up again.'

3-year-olds watching YouTube

HALF of children aged three and four are watching videos on YouTtibe amid growing alarm over the platform's disturbing content.

Young children flock to the Googie-owned video vvebsite to watch cartoons and songs.

But the website also hosts sexualised child content and violent films masquemling as children's shows.

At this age, half of the children who use the platform access it through the YouTube Kids app. The app Is supposed to be safe for very young children Parents can control what they watch.
However, it has emerged that pranksters are targeting children with macabre cartoons-as Peppa Pig but are actually filled with extremely unsuitable content such as torture or sex scenes.

Children starting to spot fake news
OLDER children are becoming increasingly savvy about fake news on social media, according to Ofcom's report.

More than half of youngsters aged 12 to 15 use Facebook and Twitter to access news online - often clicking on stories that have been recommended by 'friends' in their network or by users they 'follow'.

But even though they like to access news in this way, they are extremely wary about which articles they can trust.
The majority of those in this age group who read news on social media make an effort to check if it is true. Some 86 per cent make 'at least one practical attempt' to check the veracity of an article.

For example, they might double check it with other news sources, read the comments posted at the end of the article, or check if it was published by an organisation they feel they can trust. The findings come amid growing concern about made-up news stories being planted online - often by malicious groups trying to divide people and sow discontent.

However, three quarters of youngsters aged 12 to 15 are aware that fake news stories exist. And nearly four out of ten claim to have spotted an invented story themselves. Nearly two thirds of 12 to 15-yearolds who find a fake news story will also try to take action.

A third said that they would alert their parents or another family member. One in five said they would leave a comment stating it was fake and 14 per cent would report it to the social media where they found it circulating.

What are YOUR
kids watching?
PAGES 26-27

Page 26

GONE are the days when children's TV consisted of safe, age-appropriate programming such as Playschool or The Magic Roundabout.

These days, if you see a youngster engrossed in a screen, they are most likely to be choosing clips to watch on YouTube. The video-sharing site has overtaken terrestrial television as the main source of children's entertainment.

Yet it is also leading youngsters down some very dark alleyways. Chillingly, even when they click on the cartoon characters they love, toddler and primary-age children are not safe.

Over the past year, parents have grown increasingly alarmed at the number of Counterfeit videos, which lure children with favourites such as Peppa Pig but descend into violence, torture, sexual themes or extreme language. Even on YouTube Kids — an app supposed to offer only filtered, child-friendly clips -- damaging material is slipping under the radar.

Despite parents repeatedly raising the alarm, Google-owned YouTube told the Mail earlier this month that over the previous 30 days, one in 200 videos meant for kids on the app have had to be removed for being 'inappropriate'.

Considering that a recent survey by Internet security experts Kaspersky Lab found the average child spends 40 minutes a day watching online videos on a mobile device — as many as 20 short clips a day — it's not hard to work out the risks of coming across such material, or the psychological harm it could cause.

As they get older, children increasingly search YouTube for school tutorials and entertainment such as pop videos and video games tips. Yet they are always just a few clicks away from videos, also aimed at them, offering advice on everything from how to hide self-harm cuts to how to take Class A drugs.

When asked how many human moderators the main YouTube site has globally — on top of automated monitoring — a spokesman would only say 'thousands'. Sonia Livingstone, professor of social psychology at the London School of Economics and a researcher on children's digital lives, told the Mail: `Parents really do need to pay attention to what their children are watching. But then I would point the finger firmly back at YouTube.

`With the YouTube Kids app, they are selling a flawed product [because inappropriate material is still slipping through]. If this were baby food they were selling, we wouldn't stand for this

So why is anyone creating spoof cartoons to traumatise children?

Professor Livingstone says there is a lucrative industry in duping them. Anyone putting a video on YouTube can make money if a viewer watches the ad that runs before it. It is estimated that it's possible to make up to £2,500 for every million views.
`The business model is pay per click,' says Professor Livingstone. 'They are reaching a huge amount of people for a small amount of investment, and the returns are good.'

WHILE she acknowledges that protecting free speech is important, Professor Livingstone says: `To promote the welfare of children is not Big Brother or pro-censorship. The psychological welfare of children is getting lost in this.' Consultant clinical psychologist Emma Citron works in adolescent and child mental health. She says: 'YouTube has been viewed as harmless and educational by parents. Kids can learn how to do their maths homework watching tutorials there.

`The people posting videos around children's cartoon characters are abusing that trust, just like any abuser does. `Even though you're not singling them out as individuals, it's like grooming kids for abuse. It's trying to corrupt children within their own platforms. It's sinister and exploit ative.' So what is your child really seeing on YouTube?

PEPPA PIG, VIOLENCE AND PORNOGRAPHY
ONE of the most cynical trends on YouTube is fake cartoons, which start like children's favourite programmes but quickly descend into sadistic, violent and disturbing plots.
In one fake Peppa Pig cartoon, a dentist with a huge syringe pulls out a character's teeth while she cries in pain. In another, the character asks to see pornography on her parents' computer and is shown drinking bleach.
While some clips are parodies supposed to amuse adults, just" as many are given keywords (which help videos appear in searches) designed to evade filters and entice youngsters.

One such channel, Superhero versus Superhero, has 1.6million subscribers and features actors dressed as Spiderman and Disney princess Elsa — but the plots include Elsa dealing with a gory injury and using automatic weapons.

Another channel, Fun Kid Toon, has more than 380 videos and features sexed-up versions of Disney's Mickey and Minnie mouse. In one episode, one of their baby twins cuts off the other's hand with a knife.

Richard Pursey, of cybersafety company SafeToNet, told the Mall: 'YouTube relies on users flagging harmful content. It is too slow. By the time content has been flagged to YouTube or the authorities, it will have been shared and seen by millions of children.

'Recently YouTube removed a counterfeit of children's cartoon Paw Patrol that showed children sleepwalking to their deaths. This was viewed over three million times before it was removed.'

YouTube says it removes the advertising stream from any user posting material which is aimed at children but also damaging to them — and recruits 'trusted flaggers' to look for this kind of material.

FRESH-FACED GIRL'S SWEARY TIRADES
YOU might hope a video channel starring a fresh-faced 12year-old talking about her life might be appropriate for youngsters her age. But you'd be wrong if your child is watching LtCorbis, who has more than 767,000 subscribers.
Her videos are a stream of swear words as she complains school is a waste of time, pokes fun at teachers and gives expletive-ridden video game commentaries. This is despite the fact that users are supposed to be over 13 to get an account. Look further and there are plenty of clips by other youngsters promoting similarly negative attitudes (and language), including videos giving tips on how to fake illness to skip school and cheat in exams.

TIPS ON HIDING SELF-HARM BLADES
THE rise of self-harm among young people is one of the UK's most pressing mental health issues. Girls are most at risk, with the number under 18 cutting themselves seriously enough to need hospital care almost quadrupling between 2005 and 2015, from 600 to 2311, according to NHS figures. Yet one young British You Tuber using the name LollysandCiggies has had her own YouTube channel for more than three years featuring clips advising others how to cover evidence that they cut themselves. The clips cover every eventuality, from hiding cuts in summer to what to say if a member of your family spots them. Plenty of others also offer the same tips. One clip, titled `How and when to hide your self-harm blades' has racked up 32,000 views since it was-uploaded a year ago.

Many videos feature video disclaimers, claiming they do not condone self-harm. Yet it, comments thanking them for the tips show they clearly encourage and normalise it.

YouTube says it removes videos showing self-harm as well as content that encourages people to commit harmful or dangerous acts. However, videos showing how to hide it are clearly not considered unsuitable as the clips are allowed to rack up tens of thousands of views.

Psychologist Emma Citron warns: 'If parents never get to the see the self-harm scars, these young people will never get the help they need.

TV PRESENTERS TAKE DRUGS ON SCREEN
IN A TV studio vaguely resembling a science lab, a chatty young woman happily declares that the cocaine she just snorted has given her 'confidence', before adding she might need a little more.

This is Drugs Lab, a series made for YouTube by a Dutch TV company, which shows its hosts taking a variety of dangerous and illegal drugs. Other episodes have titles such as `Bastiaan smiles after taking GHB' and 'Rens is off his rocks after taking MDMA. This glossy series is only the tip of the iceberg.

 

 

3
THE
33
15
6
6
PEOPLE
69
33
6
2
OF
21
12
3
6
PLANET
68
23
5
5
EARTH
52
25
7
22
Add to Reduce
243
108
27
2+2
Reduce to Deduce
2+4+3
1+0+8
2+7
4
Essence of Number
9
9
9

 

 

3
THE
33
15
6
9
INTELLECT
100
37
1
12
Add to Reduce
133
52
7
1+2
Reduce to Deduce
1+3+3
5+2
-
3
Essence of Number
7
7
7

 

 

12
INTELLIGENCE
115
61
7

 

SEVEN EVENS SEVEN

 

 

     

 

 

8
QUO VADIS
108
36
9
6
VOX POP
108
36
9

 

 

WHY SMASH ATOMS

A. K. Solomon 1940

VAN DE GRAAFF GENERATOR

Page 77

"Once the fairy tale hero has penetrated the ring of fire round The Magic Mountain he is free to woo the heroine in her castle on the mountain top."

 

 

S
=
1
-
8
SQUARING
106
52
7
T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CIRCLE
50
32
5
-
-
6
-
17
First Total
189
99
18
-
-
-
-
1+7
Add to Reduce
1+8+9
9+9
1+8
-
-
6
-
8
Second Total
18
18
9
-
-
-
-
-
Reduce to Deduce
1+8
1+8
-
-
-
6
-
8
Essence of Number
9
9
9

 

 

-
17
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
9
5
-
-
-
8
-
-
-
9
-
-
-
-
+
=
32
3+2
=
5
=
5
=
5
-
-
19
-
-
-
-
9
14
-
-
-
8
-
-
-
9
-
-
-
-
+
=
59
5+9
=
14
1+4
5
=
5
-
17
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
=
8
3
1
9
-
-
7
-
2
-
5
-
3
-
9
3
3
5
+
=
58
5+8
=
13
1+3
4
=
4
-
-
-
17
21
1
18
-
-
7
-
20
-
5
-
3
-
18
3
12
5
+
=
130
1+3+0
=
4
=
4
=
4
-
17
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
--
-
-
-
-
-
-
19
17
21
1
18
9
14
7
-
20
8
5
-
3
9
18
3
12
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
-
1
8
3
1
9
9
5
7
-
2
8
5
-
3
9
9
3
3
5
+
=
90
9+0
=
9
=
9
=
9
-
17
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
3
occurs
x
4
=
12
1+2
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
--
-
-
--
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
-
9
9
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
4
=
36
3+6
9
10
17
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
36
-
-
17
-
90
-
36
1+0
1+7
--
-
-
--
9
9
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
3+6
-
-
1+7
-
9+0
-
3+6
1
8
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
9
-
-
8
-
9
-
9
-
-
1
8
3
1
9
9
5
7
-
2
8
5
-
3
9
9
3
3
5
-
-
-
-
-
-
-
-
-
-
1
8
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
9
-
-
8
-
9
-
9

 

 

17
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
9
5
-
-
-
8
-
-
-
9
-
-
-
-
+
=
32
3+2
=
5
=
5
=
5
-
19
-
-
-
-
9
14
-
-
-
8
-
-
-
9
-
-
-
-
+
=
59
5+9
=
14
1+4
5
=
5
17
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
=
8
3
1
9
-
-
7
-
2
-
5
-
3
-
9
3
3
5
+
=
58
5+8
=
13
1+3
4
=
4
-
-
17
21
1
18
-
-
7
-
20
-
5
-
3
-
18
3
12
5
+
=
130
1+3+0
=
4
=
4
=
4
17
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
--
-
-
-
-
-
19
17
21
1
18
9
14
7
-
20
8
5
-
3
9
18
3
12
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
1
8
3
1
9
9
5
7
-
2
8
5
-
3
9
9
3
3
5
+
=
90
9+0
=
9
=
9
=
9
17
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
3
-
-
-
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
5
-
-
-
-
5
-
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
--
-
-
--
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
9
9
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
4
=
36
3+6
9
17
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
36
-
-
17
-
90
-
36
1+7
--
-
-
--
9
9
-
-
-
-
-
-
-
-
9
9
-
-
-
-
-
3+6
-
-
1+7
-
9+0
-
3+6
8
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
9
-
-
8
-
9
-
9
-
1
8
3
1
9
9
5
7
-
2
8
5
-
3
9
9
3
3
5
-
-
-
-
-
-
-
-
-
-
8
S
Q
U
A
R
I
N
G
-
T
H
E
-
C
I
R
C
L
E
-
-
9
-
-
8
-
9
-
9

 

 

17
S
Q
U
A
R
I
N
G
T
H
E
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
9
5
-
-
8
-
-
9
-
-
-
-
+
=
32
3+2
=
5
=
5
=
5
-
19
-
-
-
-
9
14
-
-
8
-
-
9
-
-
-
-
+
=
59
5+9
=
14
1+4
5
=
5
17
S
Q
U
A
R
I
N
G
T
H
E
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
=
8
3
1
9
-
-
7
2
-
5
3
-
9
3
3
5
+
=
58
5+8
=
13
1+3
4
=
4
-
-
17
21
1
18
-
-
7
20
-
5
3
-
18
3
12
5
+
=
130
1+3+0
=
4
=
4
=
4
17
S
Q
U
A
R
I
N
G
T
H
E
C
I
R
C
L
E
-
-
-
-
-
--
-
-
-
-
-
19
17
21
1
18
9
14
7
20
8
5
3
9
18
3
12
5
+
=
189
1+8+9
=
18
1+8
9
=
9
-
1
8
3
1
9
9
5
7
2
8
5
3
9
9
3
3
5
+
=
90
9+0
=
9
=
9
=
9
17
S
Q
U
A
R
I
N
G
T
H
E
C
I
R
C
L
E
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
3
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
5
-
-
5
occurs
x
3
=
15
1+5
6
-
--
-
-
--
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
8
occurs
x
2
=
16
1+6
7
-
-
-
-
-
9
9
-
-
-
-
-
-
9
9
-
-
-
-
-
9
occurs
x
4
=
36
3+6
9
17
S
Q
U
A
R
I
N
G
T
H
E
C
I
R
C
L
E
-
-
36
-
-
17
-
90
-
36
1+7
--
-
-
--
9
9
-
-
-
-
-
-
9
9
-
-
-
-
-
3+6
-
-
1+7
-
9+0
-
3+6
8
S
Q
U
A
R
I
N
G
T
H
E
C
I
R
C
L
E
-
-
9
-
-
8
-
9
-
9
-
1
8
3
1
9
9
5
7
2
8
5
3
9
9
3
3
5
-
-
-
-
-
-
-
-
-
-
8
S
Q
U
A
R
I
N
G
T
H
E
C
I
R
C
L
E
-
-
9
-
-
8
-
9
-
9

 

 

SACRED GEOMETRY

Miranda Lundy 2006

CIRCLING THE SQUARE

the marriage of heaven and earth

 

T
=
2
-
3
THE
33
15
6
M
=
4
-
8
MARRIAGE
72
45
9
O
=
6
-
2
OF
21
12
3
H
=
8
-
6
HEAVEN
55
28
1
A
=
1
-
3
AND
19
10
1
E
=
5
-
5
EARTH
52
25
7
-
-
26
-
27
Add to Reduce
252
135
27
-
-
2+6
-
2+7
Reduce to Deduce
2+5+2
1+3+5
2+7
-
-
8
-
9
Essence of Number
9
9
9

 

The circle is the shape traditionally assigned to the Heavens, and the square to the Earth. When these two shapes are unified by being made equal in area or perimeter we speak of 'squaring the circle', meaning that Heaven and Earth, or Spirit and Matter, are symbolically combined, or married. Fivefold Man exists between sixfold Heaven and fourfold Earth and Leonardo da Vinci's image opposite also shows how a man's span equals his height, that this measure equals seven of his feet and other important ratios.
Amazingly, the Earth and the Moon square the circle, for if the Moon (diameter 3) is drawn down to the Earth (diameter II) then a heavenly circle through the Moon (dotted below centre) has radius 7, and so circumference 44, the same as the perimeter of the square around the Earth. This works because irjelating the circumference of a circle to its diameter is practically 22/7. In Leonardo's image the Moon would fit above the man's head.
Also shown (below left and right) is a construction for a square using ruler and compasses. Octagons soon follow.

 

C
=
3
-
8
CIRCLING
75
48
3
T
=
2
-
3
THE
33
15
6
S
=
1
-
6
SQUARE
81
36
9
-
-
6
-
45
First Total
189
99
18
-
-
-
-
4+5
Add to Reduce
1+8+9
9+9
1+8
-
-
6
-
9
Second Total
18
18
9
-
-
-
-
-
Reduce to Deduce
1+8
1+8
-
-
-
6
-
9
Essence of Number
9
9
9

 

 

S
=
1
-
8
SQUARING
106
52
7
T
=
2
-
3
THE
33
15
6
C
=
3
-
6
CIRCLE
50
32
5
-
-
6
-
17
First Total
189
99
18
-
-
-
-
1+7
Add to Reduce
1+8+9
9+9
1+8
-
-
6
-
8
Second Total
18
18
9
-
-
-
-
-
Reduce to Deduce
1+8
1+8
-
-
-
6
-
8
Essence of Number
9
9
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
8
SQUARING
106
52
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6-
-
-
-
C
=
3
-
6
CIRCLE
50
32
5
-
-
-
-
-
5
-
-
-
-
-
-
6
-
17
First Total
189
99
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
1+7
Add to Reduce
1+8+9
9+9
1+8
-
-
-
-
-
-
-
-
-
-
-
-
6
-
8
Second Total
18
18
9
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
8
Essence of Number
9
9
9
-
1
2
3
4
5
6
7
8
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
8
SQUARING
106
52
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6-
-
-
-
C
=
3
-
6
CIRCLE
50
32
5
-
-
-
-
-
5
-
-
-
-
-
-
6
-
17
First Total
189
99
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
4
-
6
-
-
-
Q
=
8
2
1
Q
17
8
8
-
-
-
-
4
-
6
-
8
-
U
=
3
3
1
U
21
3
3
-
-
-
3
4
-
6
-
-
-
A
=
1
4
1
A
1
1
1
-
1
-
-
4
-
6
-
-
-
R
=
9
5
1
R
18
9
9
-
-
-
-
4
-
6
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
4
-
6
-
-
9
N
=
5
7
1
N
14
5
5
-
-
-
-
4
5
6
-
-
-
G
=
7
8
1
G
7
7
7
-
-
-
-
4
-
6
7
-
-
T
=
2
9
1
T
20
2
2
-
-
2
-
4
-
6
-
-
-
H
=
8
10
1
H
8
8
8
-
-
-
-
4
-
6
-
8
-
E
=
5
11
1
E
5
5
5
-
-
-
-
4
5
6
-
-
-
C
=
3
12
1
C
3
3
3
-
-
-
3
4
-
6
-
-
-
I
=
9
13
1
I
9
9
9
-
-
-
-
4
-
6
-
-
9
R
=
9
14
1
R
18
9
9
-
-
-
-
4
-
6
-
-
9
C
=
3
15
1
C
3
3
3
-
-
-
3
4
-
6
-
-
-
L
=
3
16
1
L
12
3
3
-
-
-
3
4
-
6
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
4
5
6
-
-
-
-
-
-
-
-
-
-
-
2
2
12
4
15
6
7
16
36
-
-
-
-
-
-
-
-
-
-
-
-
1+2
-
1+5
-
-
1+6
3+6
S
=
1
-
8
SQUARING
106
52
7
-
2
2
3
4
6
6
7
7
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CIRCLE
50
32
5
-
-
-
-
-
-
-
-
-
-
-
-
6
-
17
First Total
189
99
18
-
2
2
3
4
6
6
7
7
9
-
-
-
-
2+6
Add to Reduce
1+8+9
9+9
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Second Total
18
18
9
-
2
2
3
4
6
6
7
7
9
-
-
-
-
-
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Essence of Number
9
9
9
-
2
2
3
4
6
6
7
7
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
-
8
SQUARING
106
52
7
-
-
-
-
-
-
-
7
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
6-
-
-
-
C
=
3
-
6
CIRCLE
50
32
5
-
-
-
-
-
5
-
-
-
-
-
-
6
-
17
First Total
189
99
18
-
1
2
3
4
5
6
7
8
9
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
4
-
6
-
-
-
A
=
1
4
1
A
1
1
1
-
1
-
-
4
-
6
-
-
-
T
=
2
9
1
T
20
2
2
-
-
2
-
4
-
6
-
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
4
-
6
-
-
-
C
=
3
12
1
C
3
3
3
-
-
-
3
4
-
6
-
-
-
C
=
3
15
1
C
3
3
3
-
-
-
3
4
-
6
-
-
-
L
=
3
16
1
L
12
3
3
-
-
-
3
4
-
6
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
4
5
6
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
4
5
6
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
4
5
6
-
-
-
G
=
7
8
1
G
7
7
7
-
-
-
-
4
-
6
7
-
-
H
=
8
10
1
H
8
8
8
-
-
-
-
4
-
6
-
8
-
Q
=
8
2
1
Q
17
8
8
-
-
-
-
4
-
6
-
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
4
-
6
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
4
-
6
-
-
9
I
=
9
13
1
I
9
9
9
-
-
-
-
4
-
6
-
-
9
R
=
9
14
1
R
18
9
9
-
-
-
-
4
-
6
-
-
9
-
-
-
-
-
-
-
-
2
2
12
4
15
6
7
16
36
-
-
-
-
-
-
-
-
-
-
-
-
1+2
-
1+5
-
-
1+6
3+6
S
=
1
-
8
SQUARING
106
52
7
-
2
2
3
4
6
6
7
7
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
-
-
C
=
3
-
6
CIRCLE
50
32
5
-
-
-
-
-
-
-
-
-
-
-
-
6
-
17
First Total
189
99
18
-
2
2
3
4
6
6
7
7
9
-
-
-
-
2+6
Add to Reduce
1+8+9
9+9
1+8
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Second Total
18
18
9
-
2
2
3
4
6
6
7
7
9
-
-
-
-
-
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Essence of Number
9
9
9
-
2
2
3
4
6
6
7
7
9

 

 

-
-
-
-
-
-
-
-
-
-
1
2
3
5
7
8
9
S
=
1
-
8
SQUARING
106
52
7
-
-
-
-
-
7
-
-
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
C
=
3
-
6
CIRCLE
50
32
5
-
-
-
-
5
-
-
-
-
-
6
-
17
First Total
189
99
18
-
1
2
3
5
7
8
9
-
-
-
-
-
-
-
-
-
-
1
2
3
5
7
8
9
S
=
1
1
1
S
19
10
1
-
1
-
-
-
-
-
-
A
=
1
4
1
A
1
1
1
-
1
-
-
-
-
-
-
T
=
2
9
1
T
20
2
2
-
-
2
-
-
-
-
-
U
=
3
3
1
U
21
3
3
-
-
-
3
-
-
-
-
C
=
3
12
1
C
3
3
3
-
-
-
3
-
-
-
-
C
=
3
15
1
C
3
3
3
-
-
-
3
-
-
-
-
L
=
3
16
1
L
12
3
3
-
-
-
3
-
-
-
-
N
=
5
7
1
N
14
5
5
-
-
-
-
5
-
-
-
E
=
5
11
1
E
5
5
5
-
-
-
-
5
-
-
-
E
=
5
17
1
E
5
5
5
-
-
-
-
5
-
-
-
G
=
7
8
1
G
7
7
7
-
-
-
-
-
7
-
-
H
=
8
10
1
H
8
8
8
-
-
-
-
-
-
8
-
Q
=
8
2
1
Q
17
8
8
-
-
-
-
-
-
8
-
R
=
9
5
1
R
18
9
9
-
-
-
-
-
-
-
9
I
=
9
6
1
I
9
9
9
-
-
-
-
-
-
-
9
I
=
9
13
1
I
9
9
9
-
-
-
-
-
-
-
9
R
=
9
14
1
R
18
9
9
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
2
2
12
15
7
16
36
-
-
-
-
-
-
-
-
-
-
-
-
1+2
1+5
-
1+6
3+6
S
=
1
-
8
SQUARING
106
52
7
-
2
2
3
6
7
7
9
T
=
2
-
3
THE
33
15
6
-
-
-
-
-
-
-
-
C
=
3
-
6
CIRCLE
50
32
5
-
-
-
-
-
-
-
-
-
-
6
-
17
First Total
189
99
18
-
2
2
3
6
7
7
9
-
-
-
-
2+6
Add to Reduce
1+8+9
9+9
1+8
-
-
-
-
-
-
-
-
-
-
9
-
8
Second Total
18
18
9
-
2
2
3
6
7
7
9
-
-
-
-
-
Reduce to Deduce
1+8
1+8
-
-
-
-
-
-
-
-
-
-
-
9
-
8
Essence of Number
9
9
9
-
2
2
3
6
7
7
9

 

 

IN OUR TIME

Last broadcast on Thu, 18 Dec 2003, 21:30 on BBC Radio 4

"Melvyn Bragg and guests discuss the feat of astonishing intellectual engineering which provides us with millions of words in hundreds of languages. At the start of the twentieth century, in the depths of an ancient Egyptian turquoise mine on the Sinai peninsular, an archaeologist called Sir Flinders Petrie made an exciting discovery. Scratched onto rocks, pots and portable items, he found scribblings of a very unexpected but strangely familiar nature. He had expected to see the complex pictorial hieroglyphic script the Egyptian establishment had used for over 1000 years, but it seemed that at this very early period, 1700 BC, the mine workers and Semitic slaves had started using a new informal system of graffiti, one which was brilliantly simple, endlessly adaptable and perfectly portable: the Alphabet. This was probably the earliest example of an alphabetic script and it bears an uncanny resemblance to our own.

Did the alphabet really spring into life almost fully formed? How did it manage to conquer three quarters of the globe? And despite its Cyrillic and Arabic variations and the myriad languages it has been used to write, why is there essentially only one alphabet anywhere in the world?"

 

 

THE USBORNE BOOK OF FACTS AND LISTS

Lynn Bressler (no date)

Page 82

10 most spoken languages
Chinese 700,000,000 English 400,000,000 Russian 265,000,000 Spanish 240,000,000 Hindustani 230,000,000 Arabic 146,000,000 Portuguese 145,000,000 Bengali 144,000,000 German 119,000,000 Japanese 116,000,000

The first alphabet
The Phoenicians, who once lived where Syria, Jordan and Lebanon are today, had an alphabet of 29 letters as early as 1,700 BC. It was adopted by the Greeks and the Romans. Through the Romans, who went on to conquer most of Europe, it became the alphabet of Western countries.

Sounds strange
One tribe of Mexican Indians hold entire conversations just by whistling. The different pitches provide meaning.

The Rosetta Stone
 The Rosetta Stone was found by Napoleon in the sands of Egypt. It dates to about 196 BC.
On it is an inscription in hieroglyphics and a translation in Greek. , Because scholars knew ancient Greek, they could work out what the Egyptian hieroglyphics meant. From this they learned the language of the ancient Egyptians.

Did You KnowMany Chinese cannot understand each other. They have different ways of speaking (called dialects) in different
parts of the country. But today in schools allover China, the children are being taught one dialect (Mandarin), so that one day all Chinese will understand each other.

Translating computers
Computers can be used to help people of different nationalities, who do not know each others' language, talk to each other. By giving a computer a message in one language it will translate it into another specified language.

Worldwide language
English is spoken either as a first or second language in at least 45 countries. This is more than any other language. It is the language of international business and scientific conferences and is used by airtraffic controllers worldwide. In all, about one third of the world speaks it.

Page 83

Earliest writing Chinese writing has been found on pottery, and even on a tortoise shell, going back 6,000 years. Pictures made the basis for their writing, each picture showing an object or idea. Probably the earliest form of writing came from the Middle East, where Iraq and Iran are now. This region was then ruled by the Sumerians.

The most words

English has more words in it than any other language. There are about1 million in all, a third of which are technical terms. Most
people only use about 1 per cent of the words available, that is, about 10,000. William Shakespeare is reputed to have made most use of the English vocabulary.

A scientific word describing a process in the human cell is 207,000 letters long. This makes this single word equal in length to a short novel or about 80 typed sheets of A4 paper.

Many tongues
A Frenchman, named Georges Henri Schmidt, is fluent (meaning he reads and writes well) in 31 different languages.

International language
Esperanto was invented in the 1880s by a Pole, Dr Zamenhof. It was hoped that it would become the international language of Europe. It took words from many European countries and has a very easy grammar that can be learned in an hour or two.
The same language

The languages of India and Europe may originally come from just one source. Many words in different languages sound similar. For example, the word for King in Latin is Rex, in Indian, Raj, in Italian Re, in French Roi and in Spanish Rey. The original language has been named Indo-European. Basque, spoken in the French and Spanish Pyrenees, is an exception. It seems to have a different source which is still unknown.

Number of alphabets
There are 65 alphabets in use in the world today. Here are some of them: Roman
ABCDEFGHUKLMNOPQRS Greek  Russian (Cyrillic) Hebrew  Chinese (examples omitted)

 

 

Daily Mail, Monday, December 21, 2015

Page 45

ANSWERS TO CORRESPONDENTS
Charles Legge.

QUESTION If E is the most used letter of our alphabet, in what order of usage are the remaining 25 letters?

CODEBREAKERS are especially interested in frequency analysis. The most basic encryption text is achieved by simply replacing one letter by another. So to decipher such an encryption, it's useful to get a frequency count of all the letters. The most frequent letter might represent the most common letter in English, E followed by T, A, 0 and I. The least frequent are Q, Z and X.
Common percentages in standard Englist are: e 12.7, t 9.1, a 8.2, o 7.5, i 7.0, n 6.7, s 6.3 h 6.1, r 6.0, d 4.3, I 4.0, u 2.8, c 2.8, m 2.4, IA 2.4, f 2.2, y 2.0, g 2.0, p 1.9, b 1.5, v 1.0, k 0.8 x 0.2, j 0.2, q 0.1, z 0.1. The top 12 letter: constitute about 80 per cent of the total usage. The top eight letters constitute about 65 per cent of total use.
Codebreakers also look for common pairings, for example the consonants TE and vowels EA. Other pairings are OF, TO IN, IT, IS, BE, AS, AT, SO, WE, HE, BY, OR ON, DO, IF, ME, MY, UP. Common pairs of repeated letters are SS, EE, TT, FF, LL MM and 00. Common triplets are THE EST, FOR, AND, HIS, ENT and THA. The use of letter frequencies and frequency analysis plays a fundamental role in cryptograms and word puzzle games such as Hangman and Scrabble. An example of applying the knowledge of English letter frequency to solving cryptogram is found in Edgar Allan Poe's famous story The Gold-Bug, where the method is successfully applied to decipher a message instructing on the whereabouts of a treasure hidden by Captain Kidd.
A. D. Butler Warrington, Cheshire.

 

 

DAILY MAIL

Monday, October 8, 2007

Harry Bingham

Page 15

"YOU SAY POTATO, I SAY GHOUGHBTEIGHPTEAU !"

"...Yes you CAN spell potato like that. It's one of the amazing quirks which make English the world's dominant language

 

"ABOUT three years ago I started researching a book, This Little Britain, about the various ways in which we Brits have a history .
of being the exception.
In areas such as law, government, economics, agriculture and science, we've often been a uniquely British exception to a general European rule.
Ditto, in such things as men's fashion, Victorian sewers, drunken yobbishness, and - not least - in the whole area of language and literature.
Take spellings. George Bernard Shaw famously commented that English spelling would allow you to write the word 'fish' as 'ghoti' - and it would sound the same (in the latter, the sound 'f' would be from 'gh', as in 'rough'; 'i' would be from 'o' in 'women' and 'sh' as in 'ti' from 'nation').
But he couldn't have been trying all that hard, if that was the best example he came up with. How about 'potato' as in 'ghoughbteighpteau'? That's the sound 'p' as in hiccough, 'o' as in though, 't' as in debt, 'a' as in neighbour, 't' as in ptomaine, 'o' as in bureau. The fact is that with just 26 letters and 48 different sounds to cope with, there were always going to be problems. :
Throw in other pronunciation changes and an appetite for foreign borrowings, and it's no surprise that English has some of the most dangerously unpredictable spellings in the world.
If our spellings are painful, however, our grammar has its blessedly simple side. French nouns are either masculine or feminine; French verbs vary with every puff of the syntactical breeze.
But French is a pretty simple language. Italian has 50 different forms for every verb, ancient Greek more than 300, modern Turkish an eye popping two million. English, by contrast, has just four verb forms (bark, barks, barking, barked), two noun forms (dog, dogs), and just one adjectival form (snappy), thus making our language about the least inflected in the world.
If that's a curious fact, the reason why is perhaps odder still. Back in Alfred the Great's England, two language communities - English and Danish - inter­mingled. Each community could make out the basic words of the other language.

FOR example, the word 'horse' is 'hors' in Old English, 'hossit' in Old Norse. But all those tricksy little word endings would have made no sense at all. So they began to vanish.
Under pressure of trade, friendship and intermarriage, our ancient ancestors did away with inflections almost completely. Confusing at the time, no doubt, but a blessing for those who need to learn the language today.
And there are plenty of people learning it, of course. With about one-and a-half billion non-native speakers, English has become the world's own language - one that accounts for two-thirds of internet content, and a still larger proportion of the world's scientific and technical journals.
It's sometimes suggested that English has achieved its leadership because it's thelanguage of Shakespeare, because of its unique and beautiful literature.
That's nonsense, of course. English dominates because the British Isles exported English speakers and gunboats in the 19th century, and because America exported Hollywood, GIs and hamburgers in the 20th.
If those Mayflower settlers had chanced to speak Ubykh (a Caucasian language with 81 consonants and 'three vowels) or Rotokas (a Papua New Guinea language with just six consonants and five vowels), the world would most likely be speaking those fine languages today.
Such dominance has its down­side, of course. There are now about 6,800 languages left in the world, compared with perhaps twice that number back at the dawn of agriculture. The remaining languages are now dying at the rate of about one a fortnight.
English is big in other ways too. If you wanted to learn all the words in the Oxford English Dictionary, you'd have to deal with about 500,000 of them (ending with zyxt, a splendid last word by any standards and an archaic Kentish term for thou seest).
Having done that, you'd probably be a bit taken aback to learn the equivalent American dictionary, Webster's, offers a further 450,000 words or so, of which only about half are to be found in the OED, suggesting a pooled total word count of about 750,000.
But there are lots of words that never get in to either dictionary. Flora and fauna are mostly out. So are most acronyms, slang and dialect. Total that lot up and you'd get to a million or so. Next, you'd need to deal with scientific and technological terms, adding another million or so words.
Other languages-can't keep up. The official dictionary-based word count of German is fewer than 200,000. The French word­count is fewer than 100,000. The scale of our vocabulary is impossible to explain, except by recognising that English users are reckless adopters and inventors.
In the cultural realm, however, mere size is hardly likely to impress. In tenus of Nobel Prizes for literature, the United Kingdom trots home in the bronze medal position (beaten by gold­medallist France, and the silver­gong-holder, the US.).
If, on the other hand, you were looking at the total amount of literature produced by the British Isles then we would come in level with France, with 13 prizes.

BUT perhaps that's to measure things the wrong way. If you look at Nobel Prizes by language, then English wins by a country mile 26 laureates vs 13 for France).

More to the point, the Nobel Prize Committee is just that: a committee. Wouldn't it be better to let the world's reading public determine which literature it favours? Alas, there are no reliable global sales figures available.
We do, however, have an index of which authors have written the most translated books. British authors romp home in four of the top five places: Agatha Christie in first, then Enid Blyton, Shakespeare and Barbara Cartland in third to fifth. (The one interloper, Frenchman Jules Verne, is in second place.)
Looking more broadly, British authors dominate the top 40, with some 14 authors on the list, compared with 11 for the United States, and 15 for the entire rest of the world put together.
The obvious conclusion: that we Brits have some natural affinity for words and literature, the way that the Germans 'do' music, or the French 'do' visual art.
Such things run both deep and ancient. The vernacular literature of Alfred the Great's England was the most developed in Europe. It's perhaps not surprising that the same is arguably still true today."

"YOU SAY POTATO, I SAY GHOUGHBTEIGHPTEAU !"

 

 
 
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