# Turing Machine simulator # with a Fibonacci sequence setup to demo # 25/12/2013 v2 # Andi Fugard newTape = function(initTape = c(" "), pos = 1, state = " ", blank = " ") { stopifnot(length(initTape) > 0) list(cells = initTape, pos = pos, state = state, blank = blank) } tapesEqual = function(t1, t2) { length(t1$cells) == length(t2$cells) && t1$cells == t2$cells && t1$pos == t2$pos && t1$state == t2$state && t1$blank == t2$blank } runStep = function(tape, quints) { quint = subset(quints, s1 == tape$state & i == tape$cells[tape$pos]) newTape = tape if (nrow(quint) == 1) { # relax this when we go nondeterministic newTape = tape newTape$cells[tape$pos] = quint$o newTape$state = quint$s2 stopifnot(quint$d == "L" || quint$d == "R") if (quint$d == "R") { newTape$pos = newTape$pos + 1 if (newTape$pos > length(newTape$cells)) newTape$cells = c(newTape$cells, newTape$blank) } else if (quint$d == "L") { newTape$pos = newTape$pos - 1 if (newTape$pos < 1) { newTape$cells = c(newTape$blank, newTape$cells) newTape$pos = 1 } } } newTape } printTape = function(tape, iteration.number = "") { res = rbind(as.character(tape$cells) ,rep("", length(tape$cells)) ,rep("", length(tape$cells))) colnames(res) = rep("", length(tape$cells)) rownames(res) = c(paste("(", iteration.number, ")", sep = ""),"","") res[2,tape$pos] = "^" res[3,tape$pos] = as.character(tape$state) print(res, quote = F) } runProgram = function(startTape, program, maxSteps = 10000) { printTape(startTape, 0) tapeRes = runStep(startTape, program) printTape(tapeRes, 1) i = 2 finished = F while (i <= maxSteps && !finished) { tapeRes.prev = tapeRes tapeRes = runStep(tapeRes.prev, program) if (!tapesEqual(tapeRes, tapeRes.prev)) { printTape(tapeRes, i) } else finished = T i = i + 1 } } # Fibonaci fibprog = data.frame( s1 = c("A", "A", "B", "B", "C", "C", "D", "D", "E", "E", "F", "F", "G", "G", "H", "H", "I", "I", "J", "J", "K", "K", "L", "L", "M", "M", "N", "N", "O", "O"), s2 = c("B", "H", "B", "C", "C", "D", "D", "E", "E", "F", "F", "G", "G", "A", "I", "M", "I", "J", "J", "K", "K", "L", "L", "H", "M", "N", "N", "O", "O", "A"), i = c("1", "*", "1", "*", "1", "*", "1", "*", "1", "*", "1", "*", "1", "p", "1", "*", "1", "*", "1", "*", "1", "*", "1", "p", "p", "*", "p", "*", "1", "*"), o = c("p", "*", "1", "*", "1", "*", "1", "1", "1", "*", "1", "*", "1", "p", "p", "*", "1", "*", "1", "1", "1", "*", "1", "p", "1", "*", "1", "*", "1", "*"), d = c("R", "R", "R", "R", "R", "R", "R", "L", "L", "L", "L", "L", "L", "R", "R", "L", "R", "R", "R", "L", "L", "L", "L", "R", "L", "L", "L", "R", "R", "R"), stringsAsFactors = F ) fibprog # Run up 1,1,2,3,5,8 (317 steps) startTape = newTape(as.character(c(1,"*",1)) ,pos = 1 ,state = "A" ,blank = "*") runProgram(startTape, fibprog, maxSteps = 317)
Standard input is empty
s1 s2 i o d
1 A B 1 p R
2 A H * * R
3 B B 1 1 R
4 B C * * R
5 C C 1 1 R
6 C D * * R
7 D D 1 1 R
8 D E * 1 L
9 E E 1 1 L
10 E F * * L
11 F F 1 1 L
12 F G * * L
13 G G 1 1 L
14 G A p p R
15 H I 1 p R
16 H M * * L
17 I I 1 1 R
18 I J * * R
19 J J 1 1 R
20 J K * 1 L
21 K K 1 1 L
22 K L * * L
23 L L 1 1 L
24 L H p p R
25 M M p 1 L
26 M N * * L
27 N N p 1 L
28 N O * * R
29 O O 1 1 R
30 O A * * R
(0) 1 * 1
^
A
(1) p * 1
^
B
(2) p * 1
^
C
(3) p * 1 *
^
C
(4) p * 1 * *
^
D
(5) p * 1 * 1
^
E
(6) p * 1 * 1
^
F
(7) p * 1 * 1
^
F
(8) p * 1 * 1
^
G
(9) p * 1 * 1
^
A
(10) p * 1 * 1
^
H
(11) p * p * 1
^
I
(12) p * p * 1
^
J
(13) p * p * 1 *
^
J
(14) p * p * 1 1
^
K
(15) p * p * 1 1
^
K
(16) p * p * 1 1
^
L
(17) p * p * 1 1
^
H
(18) p * p * 1 1
^
M
(19) p * 1 * 1 1
^
M
(20) p * 1 * 1 1
^
N
(21) * 1 * 1 * 1 1
^
N
(22) * 1 * 1 * 1 1
^
O
(23) * 1 * 1 * 1 1
^
O
(24) * 1 * 1 * 1 1
^
A
(25) * 1 * p * 1 1
^
B
(26) * 1 * p * 1 1
^
C
(27) * 1 * p * 1 1
^
C
(28) * 1 * p * 1 1 *
^
C
(29) * 1 * p * 1 1 * *
^
D
(30) * 1 * p * 1 1 * 1
^
E
(31) * 1 * p * 1 1 * 1
^
F
(32) * 1 * p * 1 1 * 1
^
F
(33) * 1 * p * 1 1 * 1
^
F
(34) * 1 * p * 1 1 * 1
^
G
(35) * 1 * p * 1 1 * 1
^
A
(36) * 1 * p * 1 1 * 1
^
H
(37) * 1 * p * p 1 * 1
^
I
(38) * 1 * p * p 1 * 1
^
I
(39) * 1 * p * p 1 * 1
^
J
(40) * 1 * p * p 1 * 1 *
^
J
(41) * 1 * p * p 1 * 1 1
^
K
(42) * 1 * p * p 1 * 1 1
^
K
(43) * 1 * p * p 1 * 1 1
^
L
(44) * 1 * p * p 1 * 1 1
^
L
(45) * 1 * p * p 1 * 1 1
^
H
(46) * 1 * p * p p * 1 1
^
I
(47) * 1 * p * p p * 1 1
^
J
(48) * 1 * p * p p * 1 1
^
J
(49) * 1 * p * p p * 1 1 *
^
J
(50) * 1 * p * p p * 1 1 1
^
K
(51) * 1 * p * p p * 1 1 1
^
K
(52) * 1 * p * p p * 1 1 1
^
K
(53) * 1 * p * p p * 1 1 1
^
L
(54) * 1 * p * p p * 1 1 1
^
H
(55) * 1 * p * p p * 1 1 1
^
M
(56) * 1 * p * p 1 * 1 1 1
^
M
(57) * 1 * p * 1 1 * 1 1 1
^
M
(58) * 1 * p * 1 1 * 1 1 1
^
N
(59) * 1 * 1 * 1 1 * 1 1 1
^
N
(60) * 1 * 1 * 1 1 * 1 1 1
^
O
(61) * 1 * 1 * 1 1 * 1 1 1
^
O
(62) * 1 * 1 * 1 1 * 1 1 1
^
A
(63) * 1 * 1 * p 1 * 1 1 1
^
B
(64) * 1 * 1 * p 1 * 1 1 1
^
B
(65) * 1 * 1 * p 1 * 1 1 1
^
C
(66) * 1 * 1 * p 1 * 1 1 1
^
C
(67) * 1 * 1 * p 1 * 1 1 1
^
C
(68) * 1 * 1 * p 1 * 1 1 1 *
^
C
(69) * 1 * 1 * p 1 * 1 1 1 * *
^
D
(70) * 1 * 1 * p 1 * 1 1 1 * 1
^
E
(71) * 1 * 1 * p 1 * 1 1 1 * 1
^
F
(72) * 1 * 1 * p 1 * 1 1 1 * 1
^
F
(73) * 1 * 1 * p 1 * 1 1 1 * 1
^
F
(74) * 1 * 1 * p 1 * 1 1 1 * 1
^
F
(75) * 1 * 1 * p 1 * 1 1 1 * 1
^
G
(76) * 1 * 1 * p 1 * 1 1 1 * 1
^
G
(77) * 1 * 1 * p 1 * 1 1 1 * 1
^
A
(78) * 1 * 1 * p p * 1 1 1 * 1
^
B
(79) * 1 * 1 * p p * 1 1 1 * 1
^
C
(80) * 1 * 1 * p p * 1 1 1 * 1
^
C
(81) * 1 * 1 * p p * 1 1 1 * 1
^
C
(82) * 1 * 1 * p p * 1 1 1 * 1
^
C
(83) * 1 * 1 * p p * 1 1 1 * 1
^
D
(84) * 1 * 1 * p p * 1 1 1 * 1 *
^
D
(85) * 1 * 1 * p p * 1 1 1 * 1 1
^
E
(86) * 1 * 1 * p p * 1 1 1 * 1 1
^
E
(87) * 1 * 1 * p p * 1 1 1 * 1 1
^
F
(88) * 1 * 1 * p p * 1 1 1 * 1 1
^
F
(89) * 1 * 1 * p p * 1 1 1 * 1 1
^
F
(90) * 1 * 1 * p p * 1 1 1 * 1 1
^
F
(91) * 1 * 1 * p p * 1 1 1 * 1 1
^
G
(92) * 1 * 1 * p p * 1 1 1 * 1 1
^
A
(93) * 1 * 1 * p p * 1 1 1 * 1 1
^
H
(94) * 1 * 1 * p p * p 1 1 * 1 1
^
I
(95) * 1 * 1 * p p * p 1 1 * 1 1
^
I
(96) * 1 * 1 * p p * p 1 1 * 1 1
^
I
(97) * 1 * 1 * p p * p 1 1 * 1 1
^
J
(98) * 1 * 1 * p p * p 1 1 * 1 1
^
J
(99) * 1 * 1 * p p * p 1 1 * 1 1 *
^
J
(100) * 1 * 1 * p p * p 1 1 * 1 1 1
^
K
(101) * 1 * 1 * p p * p 1 1 * 1 1 1
^
K
(102) * 1 * 1 * p p * p 1 1 * 1 1 1
^
K
(103) * 1 * 1 * p p * p 1 1 * 1 1 1
^
L
(104) * 1 * 1 * p p * p 1 1 * 1 1 1
^
L
(105) * 1 * 1 * p p * p 1 1 * 1 1 1
^
L
(106) * 1 * 1 * p p * p 1 1 * 1 1 1
^
H
(107) * 1 * 1 * p p * p p 1 * 1 1 1
^
I
(108) * 1 * 1 * p p * p p 1 * 1 1 1
^
I
(109) * 1 * 1 * p p * p p 1 * 1 1 1
^
J
(110) * 1 * 1 * p p * p p 1 * 1 1 1
^
J
(111) * 1 * 1 * p p * p p 1 * 1 1 1
^
J
(112) * 1 * 1 * p p * p p 1 * 1 1 1 *
^
J
(113) * 1 * 1 * p p * p p 1 * 1 1 1 1
^
K
(114) * 1 * 1 * p p * p p 1 * 1 1 1 1
^
K
(115) * 1 * 1 * p p * p p 1 * 1 1 1 1
^
K
(116) * 1 * 1 * p p * p p 1 * 1 1 1 1
^
K
(117) * 1 * 1 * p p * p p 1 * 1 1 1 1
^
L
(118) * 1 * 1 * p p * p p 1 * 1 1 1 1
^
L
(119) * 1 * 1 * p p * p p 1 * 1 1 1 1
^
H
(120) * 1 * 1 * p p * p p p * 1 1 1 1
^
I
(121) * 1 * 1 * p p * p p p * 1 1 1 1
^
J
(122) * 1 * 1 * p p * p p p * 1 1 1 1
^
J
(123) * 1 * 1 * p p * p p p * 1 1 1 1
^
J
(124) * 1 * 1 * p p * p p p * 1 1 1 1
^
J
(125) * 1 * 1 * p p * p p p * 1 1 1 1 *
^
J
(126) * 1 * 1 * p p * p p p * 1 1 1 1 1
^
K
(127) * 1 * 1 * p p * p p p * 1 1 1 1 1
^
K
(128) * 1 * 1 * p p * p p p * 1 1 1 1 1
^
K
(129) * 1 * 1 * p p * p p p * 1 1 1 1 1
^
K
(130) * 1 * 1 * p p * p p p * 1 1 1 1 1
^
K
(131) * 1 * 1 * p p * p p p * 1 1 1 1 1
^
L
(132) * 1 * 1 * p p * p p p * 1 1 1 1 1
^
H
(133) * 1 * 1 * p p * p p p * 1 1 1 1 1
^
M
(134) * 1 * 1 * p p * p p 1 * 1 1 1 1 1
^
M
(135) * 1 * 1 * p p * p 1 1 * 1 1 1 1 1
^
M
(136) * 1 * 1 * p p * 1 1 1 * 1 1 1 1 1
^
M
(137) * 1 * 1 * p p * 1 1 1 * 1 1 1 1 1
^
N
(138) * 1 * 1 * p 1 * 1 1 1 * 1 1 1 1 1
^
N
(139) * 1 * 1 * 1 1 * 1 1 1 * 1 1 1 1 1
^
N
(140) * 1 * 1 * 1 1 * 1 1 1 * 1 1 1 1 1
^
O
(141) * 1 * 1 * 1 1 * 1 1 1 * 1 1 1 1 1
^
O
(142) * 1 * 1 * 1 1 * 1 1 1 * 1 1 1 1 1
^
O
(143) * 1 * 1 * 1 1 * 1 1 1 * 1 1 1 1 1
^
A
(144) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1
^
B
(145) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1
^
B
(146) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1
^
B
(147) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1
^
C
(148) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1
^
C
(149) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1
^
C
(150) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1
^
C
(151) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1
^
C
(152) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 *
^
C
(153) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * *
^
D
(154) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1
^
E
(155) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1
^
F
(156) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1
^
F
(157) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1
^
F
(158) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1
^
F
(159) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1
^
F
(160) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1
^
F
(161) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1
^
G
(162) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1
^
G
(163) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1
^
G
(164) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1
^
A
(165) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1
^
B
(166) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1
^
B
(167) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1
^
C
(168) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1
^
C
(169) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1
^
C
(170) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1
^
C
(171) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1
^
C
(172) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1
^
C
(173) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1
^
D
(174) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 *
^
D
(175) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1
^
E
(176) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1
^
E
(177) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1
^
F
(178) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1
^
F
(179) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1
^
F
(180) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1
^
F
(181) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1
^
F
(182) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1
^
F
(183) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1
^
G
(184) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1
^
G
(185) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1
^
A
(186) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1
^
B
(187) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1
^
C
(188) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1
^
C
(189) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1
^
C
(190) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1
^
C
(191) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1
^
C
(192) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1
^
C
(193) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1
^
D
(194) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1
^
D
(195) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 *
^
D
(196) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
E
(197) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
E
(198) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
E
(199) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
F
(200) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
F
(201) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
F
(202) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
F
(203) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
F
(204) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
F
(205) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
G
(206) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
A
(207) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1
^
H
(208) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1
^
I
(209) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1
^
I
(210) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1
^
I
(211) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1
^
I
(212) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1
^
I
(213) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1
^
J
(214) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1
^
J
(215) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1
^
J
(216) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 *
^
J
(217) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 1
^
K
(218) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 1
^
K
(219) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 1
^
K
(220) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 1
^
K
(221) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 1
^
L
(222) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 1
^
L
(223) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 1
^
L
(224) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 1
^
L
(225) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 1
^
L
(226) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 1
^
H
(227) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1
^
I
(228) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1
^
I
(229) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1
^
I
(230) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1
^
I
(231) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1
^
J
(232) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1
^
J
(233) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1
^
J
(234) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1
^
J
(235) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 *
^
J
(236) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 1
^
K
(237) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 1
^
K
(238) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 1
^
K
(239) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 1
^
K
(240) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 1
^
K
(241) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 1
^
L
(242) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 1
^
L
(243) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 1
^
L
(244) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 1
^
L
(245) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 1
^
H
(246) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1
^
I
(247) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1
^
I
(248) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1
^
I
(249) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1
^
J
(250) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1
^
J
(251) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1
^
J
(252) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1
^
J
(253) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1
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(254) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 *
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(255) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 1
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K
(256) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 1
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(257) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 1
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(258) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 1
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(259) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 1
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(260) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 1
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(261) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 1
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(262) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 1
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(263) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 1
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(264) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 1
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(265) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1
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(266) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1
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(267) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1
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(268) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1
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(269) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1
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(270) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1
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(271) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1
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(272) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1
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(273) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 *
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(274) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 1
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(275) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 1
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(276) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 1
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(277) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 1
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(278) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 1
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(279) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 1
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(280) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 1
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(281) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 1
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(282) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 1
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(283) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 1
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(284) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1
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(285) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1
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(286) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1
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(287) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1
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(288) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1
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(289) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1
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(290) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1
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(291) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1
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(293) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1 1
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(294) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1 1
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(295) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1 1
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(296) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1 1
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(297) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1 1
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(298) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1 1
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(299) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1 1
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(300) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1 1
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(301) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1 1
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(302) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1 1
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(303) * 1 * 1 * 1 1 * p p p * p p p p p * 1 1 1 1 1 1 1 1
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(304) * 1 * 1 * 1 1 * p p p * p p p p 1 * 1 1 1 1 1 1 1 1
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(305) * 1 * 1 * 1 1 * p p p * p p p 1 1 * 1 1 1 1 1 1 1 1
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(306) * 1 * 1 * 1 1 * p p p * p p 1 1 1 * 1 1 1 1 1 1 1 1
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(307) * 1 * 1 * 1 1 * p p p * p 1 1 1 1 * 1 1 1 1 1 1 1 1
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(308) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1 1 1 1 1 1
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(309) * 1 * 1 * 1 1 * p p p * 1 1 1 1 1 * 1 1 1 1 1 1 1 1
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(310) * 1 * 1 * 1 1 * p p 1 * 1 1 1 1 1 * 1 1 1 1 1 1 1 1
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(311) * 1 * 1 * 1 1 * p 1 1 * 1 1 1 1 1 * 1 1 1 1 1 1 1 1
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(312) * 1 * 1 * 1 1 * 1 1 1 * 1 1 1 1 1 * 1 1 1 1 1 1 1 1
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(313) * 1 * 1 * 1 1 * 1 1 1 * 1 1 1 1 1 * 1 1 1 1 1 1 1 1
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O
(314) * 1 * 1 * 1 1 * 1 1 1 * 1 1 1 1 1 * 1 1 1 1 1 1 1 1
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(315) * 1 * 1 * 1 1 * 1 1 1 * 1 1 1 1 1 * 1 1 1 1 1 1 1 1
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(316) * 1 * 1 * 1 1 * 1 1 1 * 1 1 1 1 1 * 1 1 1 1 1 1 1 1
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(317) * 1 * 1 * 1 1 * 1 1 1 * 1 1 1 1 1 * 1 1 1 1 1 1 1 1
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A