Wednesday, June 15, 2011

Identification of homophone sequences in the Zodiac 408 cipher

In my previous post I mentioned an algorithm that I thought would identify homophone sequences used in the Zodiac 408 cipher. I wrote a small test program. Here's the output (note that here I have not used Unicode characters but the encoding scheme from this site).

The output shows the cipher being split on successive symbols and then shows the subsequences found (and within which of the splits it was found). It's clear that lots of subsequences are found (validating that the Zodiac 408 uses simple sequential homophone sequences) and it finds the longer sequences used.

This technique looks pretty viable for this type of cipher. However, tests on the Zodiac 340 show that it isn't working there. Either The Zodiac switched from a sequential pattern for the homophones, or there's some scrambling (in the form of transposition).

I've marked in bold a few very likely sequences (long ones, or those that occur frequently). These are all actual sequences used by The Zodiac.

!: 5 (7 A f r \ z c)
#: 10 (A f L d r \ z)
%: 11 (P Z U B)
3: (% P B) found in 2 3 4 8
(: 4 (# A f l E L d r \ z)
): 8 (S ( # A f l E L d r \ 8)
3: () E L) found in 2 3 5 7
+: 8 (G 6 K ! I 7 T t N Q D 5 ) S ( # A f l E L d r \ 8)
3: (+ 6 E) found in 2 3 4 5
3: (+ E 8) found in 2 4 5 7
3: (+ N E) found in 2 3 4 5
3: (+ T 8) found in 2 4 5 7
3: (+ T #) found in 2 4 5 7
3: (+ T 5) found in 2 4 6 7
3: (+ G 8) found in 2 4 5 7
3: (+ G I) found in 2 4 5 7
3: (+ G #) found in 2 4 5 7
3: (+ 6 8) found in 2 4 5 7
3: (+ 6 N) found in 2 3 4 5
3: (+ 6 I) found in 2 3 4 5 7
3: (+ 6 5) found in 2 3 4 7
3: (+ D 8) found in 2 4 5 7
3: (+ t 8) found in 2 4 5 7
3: (+ D #) found in 2 4 5 7
3: (+ t D) found in 2 4 5 7
3: (+ t #) found in 2 4 5 7
4: (+ 6 N E) found in 2 3 4 5
/: 6 (Z)
5: 8 (S ( # A f l E L d r \)
3: (5 L \) found in 3 4 6 7
3: (5 L r) found in 3 4 5 6
6: 8 (! 7 T t N Q 5 S ( # A f l E L d r \ 8)
3: (6 t L) found in 2 3 4 5
3: (6 N E) found in 2 3 4 5
3: (6 N L) found in 2 3 4 5
3: (6 N 5) found in 2 3 4 5
3: (6 E L) found in 2 3 4 5
3: (6 5 L) found in 2 3 4 5
4: (6 N 5 L) found in 2 3 4 5
4: (6 N E L) found in 2 3 4 5
7: 3 (j _)
8: 8 ()
9: 14 (P Z U k O R p X W V + e G Y F 6)
3: (9 R Y) found in 3 4 6 11
3: (9 P W) found in 3 4 5 9 13
3: (9 W +) found in 3 5 8 9
3: (9 Z W) found in 3 4 5 9 13
3: (9 U W) found in 3 4 5 11
3: (9 O W) found in 3 4 5 11 13
3: (9 R W) found in 3 4 5 11 13
3: (9 p W) found in 3 4 5 9
3: (9 P +) found in 3 5 9 13
3: (9 P Z) found in 3 4 5 13
3: (9 P U) found in 2 3 4 5 6 7 8
3: (9 P k) found in 2 3 4 5 6 7 8
3: (9 P R) found in 3 4 5 6 13
3: (9 P p) found in 3 4 5 7 9
3: (9 P e) found in 2 3 5 8 9
3: (9 P G) found in 3 6 8 13
3: (9 P F) found in 3 5 9 13
3: (9 P V) found in 3 5 6 9 13
3: (9 Z +) found in 3 5 9 13
3: (9 O +) found in 3 5 11 13
3: (9 R +) found in 3 5 11 13
3: (9 V +) found in 3 5 8 9
3: (9 Z p) found in 3 4 5 7 9
3: (9 Z V) found in 3 5 9 13
3: (9 U k) found in 2 3 4 5 6 7 8
3: (9 U p) found in 3 4 5 7
3: (9 U G) found in 3 6 8 11
3: (9 U V) found in 3 5 6 11
3: (9 O R) found in 3 4 5 11 13
3: (9 O G) found in 3 4 8 11 13
3: (9 O V) found in 3 5 11 13
3: (9 R e) found in 3 5 6 11
3: (9 R G) found in 3 4 6 11 13
3: (9 R V) found in 3 5 6 11 13
3: (9 e G) found in 3 6 8 11 13
3: (9 V e) found in 3 8 9 11
3: (9 V G) found in 3 6 8 11
4: (9 P U k) found in 2 3 4 5 6 7 8
4: (9 P U p) found in 3 4 5 7
4: (9 P p W) found in 3 4 5 9
4: (9 P R V) found in 3 5 6 13
4: (9 P Z W) found in 3 4 5 13
4: (9 P R W) found in 3 4 5 13
4: (9 O R W) found in 3 4 11 13
4: (9 Z p W) found in 3 4 5 9
=: 7 (p X)
@: 6 (K ! I 7 T t N Q D 5 ) S ( # A f l E L d r \ 8)
3: (@ 5 L) found in 2 3 4 5
3: (@ 5 #) found in 2 3 4 5
3: (@ K 5) found in 2 3 4 5
3: (@ 5 E) found in 2 3 4 5
3: (@ K L) found in 2 3 4 5
3: (@ E L) found in 2 3 4 5
3: (@ t L) found in 2 3 4 5
3: (@ K #) found in 2 3 4 5
3: (@ K T) found in 2 3 4 5
3: (@ K E) found in 2 3 4 5
3: (@ K t) found in 2 3 4 5
4: (@ 5 E L) found in 2 3 4 5
A: 8 (f z j _)
B: 12 (k O R p X)
3: (B O R) found in 3 7 10 11
D: 6 (5 ) S ( # A f l E L d r \ 8)
3: (D 5 L) found in 2 3 4 5
3: (D E L) found in 2 3 4 5
E: 9 (L d r \ z)
3: (E L r) found in 3 4 5 7
3: (E L \) found in 3 4 5 7
F: 6 (6 H @ K ! I 7 T t N Q D 5 ) S ( # A f l E L d r \)
G: 7 (6 K ! I 7 T t N Q D 5 ) S ( # A f l E L d r \ 8)
3: (G I N) found in 2 3 4 5
3: (G I 5) found in 2 3 4 5
3: (G I 8) found in 2 3 4 5
3: (G I )) found in 2 3 4 5
H: 8 (@ K ! I 7 T t N Q D 5 ) S ( # A f l E L d r \)
3: (H ) E) found in 2 3 5 6
3: (H N E) found in 2 3 5 6
3: (H D E) found in 2 3 5 6 7
3: (H I E) found in 2 3 5 6 7
3: (H 5 E) found in 2 3 5 6 7
3: (H T E) found in 2 5 6 7
3: (H t E) found in 2 5 6 7
3: (H @ E) found in 2 5 6 7
3: (H # E) found in 2 3 6 7
3: (H D L) found in 2 5 6 7
3: (H I L) found in 2 3 4 5 6
3: (H 5 L) found in 2 3 4 5 6
3: (H t L) found in 2 4 5 6
3: (H I r) found in 3 5 6 7
3: (H I )) found in 2 3 4 5 6
3: (H D d) found in 2 5 6 7
3: (H I N) found in 2 3 5 6
3: (H D 5) found in 2 5 6 7
3: (H I 5) found in 2 3 4 5 6
3: (H I t) found in 2 4 5 6
3: (H @ t) found in 2 5 6 7
4: (H I 5 L) found in 2 3 4 5 6
4: (H I 5 E) found in 2 3 5 6
4: (H D 5 E) found in 2 5 6 7
4: (H I t L) found in 2 4 5 6
4: (H I N E) found in 2 3 5 6
4: (H I ) E) found in 2 3 5 6
I: 11 (7 T t N Q 5 ) S ( # A f l E L d r \ 8)
3: (I 5 L) found in 4 5 6 7 8
J: 6 (I 7 T t N Q D 5 ) S ( # A f l E L)
K: 5 (! I 7 T t N Q 5 ) S ( # A f l E L d r \ 8)
L: 8 (d r \ z)
M: 8 (J I 7 T t N Q D 5 ) S ( # A f l E L)
3: (M N E) found in 2 4 5 7
3: (M E L) found in 2 4 5 7
3: (M I 5) found in 2 3 4 5
3: (M I L) found in 2 3 4 5
3: (M ) L) found in 2 3 5 7
3: (M t L) found in 2 4 5 7
3: (M 5 L) found in 2 3 4 5 7
3: (M N L) found in 2 4 5 7
4: (M N E L) found in 2 4 5 7
4: (M I 5 L) found in 2 3 4 5
N: 6 (Q # A f l E L d r \ z)
O: 7 (R p X W V + G F 6 H @ K ! M J ^ I 7 T t N Q D 5 ) S ( #)
3: (O G #) found in 3 4 5 6
3: (O ^ #) found in 3 4 5 6
3: (O X #) found in 3 4 5 6
3: (O W #) found in 3 4 5 6
3: (O K 5) found in 2 3 4 6
3: (O R 5) found in 2 3 4 6
3: (O G 5) found in 2 3 4 6
3: (O ^ 5) found in 2 3 4 6
3: (O X 5) found in 2 3 4 6
3: (O W 5) found in 2 3 4 6
3: (O H 5) found in 2 3 4 6
3: (O R +) found in 2 3 4 6
3: (O p +) found in 2 3 4 5
3: (O W +) found in 2 3 4 5
3: (O + 6) found in 2 3 4 6
3: (O R K) found in 2 3 4 6
3: (O M N) found in 2 3 4 5
3: (O G N) found in 2 3 4 5
3: (O ^ N) found in 2 3 4 5
3: (O I N) found in 2 3 4 5
3: (O 6 N) found in 2 3 4 5
3: (O M )) found in 2 3 4 5
3: (O R D) found in 2 3 4 6
3: (O R W) found in 2 3 4 6
3: (O R 6) found in 2 3 4 6
3: (O R H) found in 2 3 4 6
3: (O G )) found in 2 3 4 5
3: (O G I) found in 2 3 4 5
3: (O p W) found in 2 3 4 5
3: (O ^ )) found in 2 3 4 5
3: (O I )) found in 2 3 4 5
3: (O ^ D) found in 2 3 4 5 6
3: (O W D) found in 2 3 4 6
3: (O H D) found in 2 3 4 6
3: (O ^ I) found in 2 3 4 5
3: (O W 6) found in 2 3 4 6
4: (O R K 5) found in 2 3 4 6
4: (O G I )) found in 2 3 4 5
4: (O G I N) found in 2 3 4 5
4: (O ^ I )) found in 2 3 4 5
4: (O ^ I N) found in 2 3 4 5
4: (O p W +) found in 2 3 4 5
P: 11 (Z U k O R p X W V + e G Y F 6 H)
3: (P O R) found in 3 5 9 10
3: (P O +) found in 3 5 9 10
3: (P O X) found in 3 5 9 10
3: (P R F) found in 3 5 9 10
3: (P R V) found in 3 5 6 9
3: (P R +) found in 3 5 9 10
3: (P R H) found in 3 5 6 9
3: (P R G) found in 3 6 9 10
3: (P R W) found in 3 4 5 9
3: (P R X) found in 3 5 9 10
3: (P V +) found in 3 5 7 9
3: (P U V) found in 3 5 6 7 9
3: (P p V) found in 3 5 7 9
3: (P W +) found in 3 5 7 9
3: (P U +) found in 3 5 7 9
3: (P p +) found in 3 5 7 9
3: (P U 6) found in 3 5 8 9
3: (P e 6) found in 3 5 8 9
3: (P U H) found in 3 5 6 9
3: (P U G) found in 3 6 8 9
3: (P k W) found in 3 4 5 7
3: (P U W) found in 3 4 5 7 9
3: (P p W) found in 3 4 5 7 9
3: (P U k) found in 2 3 4 5 6 7 8
3: (P U Y) found in 2 3 5 9
3: (P e Y) found in 2 3 5 9
3: (P U e) found in 3 5 8 9
3: (P U p) found in 3 4 5 7
4: (P O R X) found in 3 5 9 10
4: (P p W +) found in 3 5 7 9
4: (P U k W) found in 3 4 5 7
4: (P U p W) found in 3 4 5 7
Q: 5 (# A f L d r \ z)
R: 12 (p X W V + G F 6 H @ K ! M J ^ I 7 T t N Q D 5 ) S ( #)
3: (R H D) found in 3 8 10 11
3: (R W D) found in 3 6 10 11
3: (R p )) found in 3 6 7 10
3: (R I )) found in 3 6 7 10
3: (R H 5) found in 3 7 10 11
3: (R H I) found in 3 7 8 10
3: (R p 5) found in 3 6 7 10
3: (R p W) found in 3 6 7 10
3: (R p I) found in 3 6 7 10
3: (R X 5) found in 3 9 10 11
3: (R V 5) found in 3 7 10 11
3: (R 6 5) found in 3 7 10 11
3: (R W 5) found in 3 6 7 10 11
3: (R F 5) found in 3 7 10 11
3: (R + 5) found in 3 7 10 11
3: (R I 5) found in 3 6 7 10
3: (R K 5) found in 3 6 10 11
3: (R + 6) found in 3 7 10 11
4: (R p I )) found in 3 6 7 10
4: (R p W 5) found in 3 6 7 10
4: (R p I 5) found in 3 6 7 10
4: (R + 6 5) found in 3 7 10 11
S: 6 (( # A f l E L d r \ z)
T: 7 (Q # A f L d r \ z)
U: 10 (k O R p X W V + G F 6 H @ K ! q M J ^)
3: (U + 6) found in 3 4 5 9
3: (U p +) found in 3 4 5 7 8
3: (U V +) found in 3 5 7 8 9
3: (U k +) found in 3 4 5 7 8
3: (U + @) found in 3 5 8 9
3: (U W +) found in 3 4 5 7 8 9
3: (U G M) found in 3 6 8 9
3: (U 6 M) found in 3 5 8 9
3: (U R 6) found in 3 4 5 9
3: (U 6 @) found in 3 5 8 9
3: (U W 6) found in 3 4 5 9
3: (U k p) found in 3 4 5 8
3: (U p W) found in 3 4 5 7 8
3: (U V M) found in 3 5 6 9
3: (U K M) found in 3 4 6 9
3: (U k M) found in 3 4 5 6
3: (U R M) found in 3 4 5 9
3: (U H M) found in 3 5 6 9
3: (U W M) found in 3 4 5 9
3: (U F @) found in 3 5 8 9
3: (U k O) found in 2 3 5 7 8
3: (U O R) found in 2 5 8 9
3: (U k V) found in 3 5 7 8
3: (U V @) found in 3 5 8 9
3: (U V H) found in 3 5 6 9
3: (U k R) found in 2 3 4 5 8
3: (U k q) found in 2 3 4 8
3: (U k W) found in 3 4 5 7 8
3: (U W @) found in 3 5 8 9
3: (U W q) found in 3 4 8 9
4: (U k V +) found in 3 5 7 8
4: (U V H M) found in 3 5 6 9
4: (U k p +) found in 3 4 5 8
4: (U k p W) found in 3 4 5 8
4: (U k W +) found in 3 4 5 7 8
4: (U p W +) found in 3 4 5 7 8
4: (U W + 6) found in 3 4 5 9
5: (U k p W +) found in 3 4 5 8
V: 9 (+ G 6 @ K ! I 7 T t N Q D 5 ) S ( # A f l E L d r \)
3: (V G I) found in 2 4 6 8
3: (V G #) found in 2 4 6 8
3: (V t D) found in 2 3 6 8
3: (V T d) found in 2 3 7 8
3: (V T 5) found in 2 3 7 8
3: (V T r) found in 2 3 6 8
3: (V t r) found in 2 3 6 8
3: (V 6 I) found in 2 3 6 8
3: (V I N) found in 2 3 4 6
3: (V I )) found in 2 3 4 6
W: 9 (+ G 6 @ K ! I 7 T t N Q D 5 ) S ( # A f l E L d r \)
3: (W + T) found in 2 4 5 6
3: (W T #) found in 2 4 5 7
3: (W T d) found in 2 4 6 7
3: (W + 6) found in 2 3 4 5
3: (W + E) found in 2 3 4 5
3: (W + N) found in 2 3 4 5
3: (W 6 I) found in 2 4 5 7
3: (W G I) found in 2 4 5 7
3: (W 6 E) found in 2 3 4 5 8
3: (W 6 N) found in 2 3 4 5
3: (W t #) found in 2 4 5 7
3: (W N E) found in 2 3 4 5
3: (W D E) found in 2 3 4 5
3: (W D #) found in 2 4 5 7
3: (W G #) found in 2 4 5 7
4: (W + 6 N) found in 2 3 4 5
4: (W + N E) found in 2 3 4 5
4: (W 6 N E) found in 2 3 4 5
4: (W + 6 E) found in 2 3 4 5
5: (W + 6 N E) found in 2 3 4 5
X: 9 (! 7 T t N Q 5 S ( # A f l E L d r \ 8)
3: (X E L) found in 2 3 4 5
3: (X 5 L) found in 2 3 4 5
3: (X 5 #) found in 2 3 4 5
3: (X 5 E) found in 2 3 4 5
4: (X 5 E L) found in 2 3 4 5
Y: 10 (F 6 H @ K ! q)
Z: 8 (p X W V + G F 6 H @ K ! J I 7 T t N Q D 5 ) S ( # A f l E L)
3: (Z p V) found in 2 4 5 6
3: (Z V T) found in 2 4 5 6
3: (Z V +) found in 2 4 5 6
3: (Z W N) found in 2 3 4 5
3: (Z p N) found in 2 3 4 5
3: (Z I N) found in 2 3 4 5
3: (Z N E) found in 2 3 4 5
3: (Z 6 N) found in 2 3 4 5
3: (Z + N) found in 2 3 4 5
3: (Z K L) found in 2 3 4 7
3: (Z K 5) found in 2 3 4 7
3: (Z p W) found in 2 3 4 5 6
3: (Z W T) found in 2 4 5 6
3: (Z W D) found in 2 3 4 5
3: (Z W E) found in 2 3 4 5
3: (Z W 6) found in 2 3 4 5
3: (Z W +) found in 2 3 4 5 6
3: (Z W 5) found in 2 3 4 6
3: (Z p T) found in 2 4 5 6
3: (Z p I) found in 2 3 4 5
3: (Z p #) found in 2 3 5 6
3: (Z p D) found in 2 3 4 5
3: (Z p E) found in 2 3 4 5
3: (Z p 6) found in 2 3 4 5
3: (Z p )) found in 2 3 4 5
3: (Z p +) found in 2 3 4 5 6
3: (Z p 5) found in 2 3 4 6
3: (Z + T) found in 2 4 5 6
3: (Z I E) found in 2 3 4 5
3: (Z I )) found in 2 3 4 5
3: (Z X 5) found in 2 4 6 7
3: (Z D E) found in 2 3 4 5
3: (Z 6 E) found in 2 3 4 5
3: (Z ) E) found in 2 3 4 5
3: (Z + E) found in 2 3 4 5
3: (Z + 6) found in 2 3 4 5
4: (Z p W 5) found in 2 3 4 6
4: (Z p W N) found in 2 3 4 5
4: (Z p + N) found in 2 3 4 5
4: (Z p 6 N) found in 2 3 4 5
4: (Z p I N) found in 2 3 4 5
4: (Z p N E) found in 2 3 4 5
4: (Z p I )) found in 2 3 4 5
4: (Z p ) E) found in 2 3 4 5
4: (Z p W +) found in 2 3 4 5 6
4: (Z p W 6) found in 2 3 4 5
4: (Z p W D) found in 2 3 4 5
4: (Z p W T) found in 2 4 5 6
4: (Z p W E) found in 2 3 4 5
4: (Z p + 6) found in 2 3 4 5
4: (Z p + T) found in 2 4 5 6
4: (Z p + E) found in 2 3 4 5
4: (Z p 6 E) found in 2 3 4 5
4: (Z p I E) found in 2 3 4 5
4: (Z p D E) found in 2 3 4 5
4: (Z W + N) found in 2 3 4 5
4: (Z W 6 N) found in 2 3 4 5
4: (Z W N E) found in 2 3 4 5
4: (Z + 6 N) found in 2 3 4 5
4: (Z + N E) found in 2 3 4 5
4: (Z 6 N E) found in 2 3 4 5
4: (Z I N E) found in 2 3 4 5
4: (Z V + T) found in 2 4 5 6
4: (Z I ) E) found in 2 3 4 5
4: (Z W + 6) found in 2 3 4 5
4: (Z W + T) found in 2 4 5 6
4: (Z W + E) found in 2 3 4 5
4: (Z W 6 E) found in 2 3 4 5
4: (Z W D E) found in 2 3 4 5
4: (Z + 6 E) found in 2 3 4 5
5: (Z p I ) E) found in 2 3 4 5
5: (Z p W N E) found in 2 3 4 5
5: (Z W + N E) found in 2 3 4 5
5: (Z W 6 N E) found in 2 3 4 5
5: (Z p W + E) found in 2 3 4 5
5: (Z p W 6 E) found in 2 3 4 5
5: (Z p W D E) found in 2 3 4 5
5: (Z W + 6 E) found in 2 3 4 5
5: (Z p W + N) found in 2 3 4 5
5: (Z p W 6 N) found in 2 3 4 5
5: (Z W + 6 N) found in 2 3 4 5
5: (Z p W + T) found in 2 4 5 6
5: (Z p W + 6) found in 2 3 4 5
5: (Z p + N E) found in 2 3 4 5
5: (Z p 6 N E) found in 2 3 4 5
5: (Z p I N E) found in 2 3 4 5
5: (Z + 6 N E) found in 2 3 4 5
5: (Z p + 6 E) found in 2 3 4 5
5: (Z p + 6 N) found in 2 3 4 5
6: (Z p W + N E) found in 2 3 4 5
6: (Z p W 6 N E) found in 2 3 4 5
6: (Z p W + 6 E) found in 2 3 4 5
6: (Z W + 6 N E) found in 2 3 4 5
6: (Z p W + 6 N) found in 2 3 4 5
6: (Z p + 6 N E) found in 2 3 4 5
\: 5 (z c j)
^: 6 (I 7 T t N Q D 5 ) S ( # A f l E)
3: (^ I N) found in 2 3 4 5
3: (^ N E) found in 2 3 4 5
3: (^ I 5) found in 2 3 4 5
3: (^ D 5) found in 2 3 4 5
3: (^ I E) found in 2 3 4 5
3: (^ I )) found in 2 3 4 5
3: (^ I #) found in 2 3 4 5
3: (^ D E) found in 2 3 4 5
3: (^ ) E) found in 2 3 4 5
3: (^ D )) found in 2 3 4 5
3: (^ ) #) found in 2 3 4 5
4: (^ I N E) found in 2 3 4 5
4: (^ I ) E) found in 2 3 4 5
4: (^ I ) #) found in 2 3 4 5
_: 8 ()
c: 6 (j)
d: 6 (r \ z)
e: 10 (G F 6 H @ K ! q)
f: 3 (j _)
j: 2 ()
k: 9 (O R p X W V + G F 6 H @ K ! q M J ^ I)
3: (k V 6) found in 3 5 7 8
3: (k V ^) found in 3 5 7 8
3: (k V G) found in 3 5 7 8
3: (k V +) found in 3 5 7 8
3: (k V I) found in 3 5 7 8
3: (k V M) found in 3 5 7 8
3: (k + 6) found in 3 4 5 7 8
3: (k p 6) found in 3 4 5 8
3: (k W 6) found in 3 4 5 7 8
3: (k 6 I) found in 3 5 7 8
3: (k 6 M) found in 3 5 7 8
3: (k 6 H) found in 3 4 5 8
3: (k + ^) found in 3 5 7 8
3: (k O ^) found in 3 5 7 8
3: (k W ^) found in 3 5 7 8
3: (k ^ I) found in 3 5 7 8
3: (k + G) found in 3 5 7 8
3: (k O G) found in 3 5 7 8
3: (k W G) found in 3 5 7 8
3: (k G I) found in 3 5 7 8
3: (k p +) found in 3 4 5 8
3: (k W +) found in 3 4 5 7 8
3: (k + I) found in 3 5 7 8
3: (k + M) found in 3 5 7 8
3: (k + H) found in 3 4 5 8
3: (k p W) found in 3 4 5 8
3: (k p I) found in 3 4 5 8
3: (k p M) found in 3 4 5 8
3: (k p H) found in 3 4 5 8
3: (k O R) found in 2 3 5 8
3: (k O M) found in 3 5 7 8
3: (k R H) found in 3 4 5 8
3: (k W I) found in 3 5 7 8
3: (k W M) found in 3 4 5 7 8
3: (k W H) found in 3 4 5 8
3: (k K I) found in 3 4 5 8
4: (k V + ^) found in 3 5 7 8
4: (k W + ^) found in 3 5 7 8
4: (k + 6 I) found in 3 5 7 8
4: (k V 6 I) found in 3 5 7 8
4: (k W 6 I) found in 3 5 7 8
4: (k + G I) found in 3 5 7 8
4: (k V G I) found in 3 5 7 8
4: (k W G I) found in 3 5 7 8
4: (k V + I) found in 3 5 7 8
4: (k W + I) found in 3 5 7 8
4: (k p 6 H) found in 3 4 5 8
4: (k + 6 H) found in 3 4 5 8
4: (k W 6 H) found in 3 4 5 8
4: (k + 6 M) found in 3 5 7 8
4: (k V 6 M) found in 3 5 7 8
4: (k W 6 M) found in 3 5 7 8
4: (k p + 6) found in 3 4 5 8
4: (k p W 6) found in 3 4 5 8
4: (k V + 6) found in 3 5 7 8
4: (k W + 6) found in 3 4 5 7 8
4: (k p + H) found in 3 4 5 8
4: (k p W H) found in 3 4 5 8
4: (k W + H) found in 3 4 5 8
4: (k p W M) found in 3 4 5 8
4: (k V + M) found in 3 5 7 8
4: (k W + M) found in 3 5 7 8
4: (k V + G) found in 3 5 7 8
4: (k W + G) found in 3 5 7 8
4: (k p W +) found in 3 4 5 8
5: (k V + 6 M) found in 3 5 7 8
5: (k W + 6 M) found in 3 5 7 8
5: (k V + 6 I) found in 3 5 7 8
5: (k W + 6 I) found in 3 5 7 8
5: (k p W + 6) found in 3 4 5 8
5: (k p W 6 H) found in 3 4 5 8
5: (k p + 6 H) found in 3 4 5 8
5: (k W + 6 H) found in 3 4 5 8
5: (k V + G I) found in 3 5 7 8
5: (k W + G I) found in 3 5 7 8
5: (k p W + H) found in 3 4 5 8
6: (k p W + 6 H) found in 3 4 5 8
l: 5 (L d r \ z)
p: 6 (X W V + G F 6 H @ K ! I 7 T t N Q D 5 ) S ( # A f l E L d r \)
3: (p + E) found in 2 3 4 5
3: (p + N) found in 2 3 4 5
3: (p W +) found in 2 3 4 5
3: (p + 6) found in 2 3 4 5
3: (p D E) found in 2 3 4 5
3: (p ) E) found in 2 3 4 5
3: (p N E) found in 2 3 4 5
3: (p W E) found in 2 3 4 5
3: (p I E) found in 2 3 4 5
3: (p 6 E) found in 2 3 4 5
3: (p W D) found in 2 3 4 5
3: (p I )) found in 2 3 4 5
3: (p W N) found in 2 3 4 5
3: (p I N) found in 2 3 4 5
3: (p 6 N) found in 2 3 4 5
3: (p W 6) found in 2 3 4 5
4: (p W 6 N) found in 2 3 4 5
4: (p + 6 N) found in 2 3 4 5
4: (p 6 N E) found in 2 3 4 5
4: (p W + N) found in 2 3 4 5
4: (p W N E) found in 2 3 4 5
4: (p + N E) found in 2 3 4 5
4: (p I N E) found in 2 3 4 5
4: (p W + 6) found in 2 3 4 5
4: (p W 6 E) found in 2 3 4 5
4: (p + 6 E) found in 2 3 4 5
4: (p W + E) found in 2 3 4 5
4: (p W D E) found in 2 3 4 5
4: (p I ) E) found in 2 3 4 5
5: (p W + 6 N) found in 2 3 4 5
5: (p + 6 N E) found in 2 3 4 5
5: (p W + 6 E) found in 2 3 4 5
5: (p W + N E) found in 2 3 4 5
5: (p W 6 N E) found in 2 3 4 5
6: (p W + 6 N E) found in 2 3 4 5
q: 16 (M J ^ I 7)
r: 7 (\ z c)
t: 7 (Q # A f l E L d r \ z)
z: 4 (j _)

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