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@ -792,7 +792,7 @@
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 1min 11s, sys: 146 ms, total: 1min 11s\n",
"CPU times: user 1min 11s, sys: 122 ms, total: 1min 11s\n",
"Wall time: 1min 11s\n"
]
}
@ -853,7 +853,33 @@
"- Can you generate a winning strategy for any power of 2 (without proving it is shortest)?\n",
"- Can you prove there are no shorter winning strategies for *N* = 16?\n",
"- Can you prove the conjecture in general?\n",
"- Can you *understand* and *explain* how the strategy works, rather than just listing the moves?"
"- Can you *understand* and *explain* how the strategy works, rather than just listing the moves?\n",
"\n",
"# A Proof of the Conjecture (from John Lamping)\n",
"\n",
"John Lamping came up with this proof of the conjecture:\n",
"\n",
"First, consider n = 3. If the three coins start out different, the devil can guarantee that they are still different after any flip you call for. If you ask for 1 flip, the devil makes the flip apply to one of the two matching coins. If you ask for 2 flips, the devil makes the flip apply to a pair of non-matching coins. If you ask for all 3 flips, they will still disagree, as well. So there is no strategy for 3 coins.\n",
"\n",
"We can generalize this to any prime number of coins, p, different from 2. If the p coins start out different, the devil can still make sure that any flip will leave the coins not matching. If the flip is of all coins, they will still disagree. Suppose it is not of all coins. The devil tries the flip on the current orientation of the table. If that leaves coins different, good. If not, the devil rotates the table by one position. We show that in that position, the coins will disagree after the flip. We know that there are at least two coins that the player asked to be flipped differently. With an odd number of coins, (LFFLF, for example) we also know there must be two adjacent coins that the player asked to be flipped the same. So there must be a subsequence that is either LFF or FLL. We know that the coins initially agreed on the last two positions, because the flip led to all the coins matching. After the rotation, those two positions will be flipped differently, leading to different coins.\n",
"\n",
"Now, consider any multiple of p (say 12, for example, 3 × 4). We can pick out p equally spaced points on the table (every 4th coin in the example), and apply the devil's strategy for p coins to those p coins: If those p start out different, the devil can always make sure they stay different.\n",
"\n",
"So for any number of coins that has a factor other than 2, the devil wins.\n",
"\n",
"Now we have to show that for any number that is a power of 2, the devil loses.\n",
"We proceed by induction. Suppose that we have a sequence of flip operations that guarantees a win for $2^n$ coins. We assume that there are $2^n - 1$ of them, $o_1, ... o_{2^n-1}$. Each operation specifies, for each of the n coins, whether to flip it or to leave alone, like LFFF. We create two new sequences, also of $2^n-1$ operations, but operating on $2^{n+1}$ coins. The first, called $d$ for double, does $o$ on the first $2^n$ coins, and then repeats the same pattern on the second $2^n$ coins. So if $o_i$ is LFFF, $d_i$ is LFFFLFFF. The second, for single, does $o$ on the first $2^n$ coins, and leaves the second $2^n$ coins alone. So if $o_i$ is LFFF, $s_i$ is LFFFLLLL. Then the following sequence of operations guarantees a win on $2^(n+1)$ coins: \n",
"\n",
" $d_1, ... d_{2^n-1}, s_1, d_1, ... d_{2^n-1}, s_2, .... d_1, ... d_{2^n-1}, s_{2^n-1}, d_1, ... d_{2^n-1}$\n",
" \n",
"That is, we do each operation of $s$, with a complete copy of $d$ between each $s$ operation, as well as at the beginning and at the end. The total number of operations is $2^n×(2^n - 1) + 2^n - 1 = 2^{n+1} -1.$\n",
"\n",
"Before explaining why this works, lets use it to generate the sequences we know. \n",
"For one coin, we win with a sequence of a single operation, F. \n",
"For two coins, d is the single operation FF, while s is the single operation FL. Combining them according to the procedure gives FF, FL, FF.\n",
"For four coins, d is FFFF, FLFL, FFFF, while s is FFLL, FLLL, FFLL, combining them gives FFFF, FLFL, FFFF, FFLL, FFFF, FLFL, FFFF, FLLL, FFFF, FLFL, FFFF, FFLL, FFFF, FLFL, FFFF. That is the answer that we all came up with.\n",
"\n",
"To see why it works, consider all pairs of opposite coins on the table with $2^{n+1}$ coins, and consider the XOR of each pair of opposite coins. There are $2^n$ of these XORs, and there is a natural correspondence between each XOR pair and a single coin in the original game. Now, s complements the XOR of a pair exactly when o flips the corresponding coin in the original game. Meanwhile, every operation in d leaves the XOR of each pair unchanged. So, since the sequence of o operations explores all coins positions, the sequence of s operations explores all XOR states. And the interposed d operations don't interfere with that exploration. In one of those states, the XORs will all be 0, meaning that each pair of opposite coins will agree. But in that state, when opposite pairs of coins agree, d is equivalent to o, just operating on pairs of coins, rather than single coins. So it explores all possible combinations of heads and tails, given that opposites agree. That will include the state where all coins are heads.\n"
]
},
{
@ -978,18 +1004,20 @@
"name": "stdout",
"output_type": "stream",
"text": [
" 1: HHTH | rot: HTHH | flip: 0123 HTTT\n",
" 2: HTTT | rot: TTHT | flip: 0 2 HTTT\n",
" 3: HTTT | rot: THTT | flip: 0123 HHHT\n",
" 4: HHHT | rot: HHTH | flip: 01 HTTT\n",
" 5: HTTT | rot: TTHT | flip: 0123 HHHT\n",
" 6: HHHT | rot: HTHH | flip: 0 2 HTTT\n",
" 7: HTTT | rot: TTHT | flip: 0123 HHHT\n",
" 1: HHTH | rot: THHH | flip: 0123 HTTT\n",
" 2: HTTT | rot: THTT | flip: 0 2 HHHT\n",
" 3: HHHT | rot: THHH | flip: 0123 HTTT\n",
" 4: HTTT | rot: THTT | flip: 01 HTTT\n",
" 5: HTTT | rot: THTT | flip: 0123 HHHT\n",
" 6: HHHT | rot: HHHT | flip: 0 2 HTTT\n",
" 7: HTTT | rot: THTT | flip: 0123 HHHT\n",
" 8: HHHT | rot: THHH | flip: 012 HHTT\n",
" 9: HHTT | rot: HTTH | flip: 0123 HHTT\n",
" 10: HHTT | rot: TTHH | flip: 0 2 HHTT\n",
" 11: HHTT | rot: HHTT | flip: 0123 HHTT\n",
" 12: HHTT | rot: TTHH | flip: 01 HHHH\n"
" 9: HHTT | rot: TTHH | flip: 0123 HHTT\n",
" 10: HHTT | rot: HTTH | flip: 0 2 HHTT\n",
" 11: HHTT | rot: TTHH | flip: 0123 HHTT\n",
" 12: HHTT | rot: THHT | flip: 01 HTHT\n",
" 13: HTHT | rot: HTHT | flip: 0123 HTHT\n",
" 14: HTHT | rot: THTH | flip: 0 2 HHHH\n"
]
},
{
@ -1030,241 +1058,190 @@
"name": "stdout",
"output_type": "stream",
"text": [
" 1: HTTHTTHT | rot: HTTHTTHT | flip: 01234567 HHTHHTHT\n",
" 2: HHTHHTHT | rot: THHTHHTH | flip: 0 2 4 6 HHHHHTTT\n",
" 3: HHHHHTTT | rot: TTTHHHHH | flip: 01234567 HHHTTTTT\n",
" 4: HHHTTTTT | rot: TTHHHTTT | flip: 01 45 HHHHTHTT\n",
" 5: HHHHTHTT | rot: THHHHTHT | flip: 01234567 HHTTTTHT\n",
" 6: HHTTTTHT | rot: TTHTHHTT | flip: 0 2 4 6 HHTHTTTT\n",
" 7: HHTHTTTT | rot: THTTTTHH | flip: 01234567 HHHHTTHT\n",
" 8: HHHHTTHT | rot: HHHHTTHT | flip: 012 456 HHHTTTTT\n",
" 9: HHHTTTTT | rot: TTHHHTTT | flip: 01234567 HHHHHTTT\n",
" 10: HHHHHTTT | rot: TTTHHHHH | flip: 0 2 4 6 HHTHHTHT\n",
" 11: HHTHHTHT | rot: THHTHTHH | flip: 01234567 HTHTTHTT\n",
" 12: HTHTTHTT | rot: HTHTTHTT | flip: 01 45 HHTHTTTT\n",
" 13: HHTHTTTT | rot: TTTTHHTH | flip: 01234567 HHHHTTHT\n",
" 14: HHHHTTHT | rot: HHTTHTHH | flip: 0 2 4 6 HHTTTTHT\n",
" 15: HHTTTTHT | rot: HTTTTHTH | flip: 01234567 HHHHTHTT\n",
" 16: HHHHTHTT | rot: HTHTTHHH | flip: 0123 HHHTHTHT\n",
" 17: HHHTHTHT | rot: THTHTHHH | flip: 01234567 HTHTHTTT\n",
" 18: HTHTHTTT | rot: HTTTHTHT | flip: 0 2 4 6 HTTTTTTT\n",
" 19: HTTTTTTT | rot: TTTTHTTT | flip: 01234567 HHHHHHHT\n",
" 20: HHHHHHHT | rot: HHTHHHHH | flip: 01 45 HHTTTHTT\n",
" 21: HHTTTHTT | rot: HTTHHTTT | flip: 01234567 HHHTHHTT\n",
" 22: HHHTHHTT | rot: HHTHHTTH | flip: 0 2 4 6 HHHTTHHT\n",
" 23: HHHTTHHT | rot: HHHTTHHT | flip: 01234567 HHTTHTTT\n",
" 24: HHTTHTTT | rot: TTTHHTTH | flip: 012 456 HHHHHHHT\n",
" 25: HHHHHHHT | rot: HHHHHTHH | flip: 01234567 HTTTTTTT\n",
" 26: HTTTTTTT | rot: TTTTHTTT | flip: 0 2 4 6 HTHTHTTT\n",
" 27: HTHTHTTT | rot: THTTTHTH | flip: 01234567 HHHTHTHT\n",
" 28: HHHTHTHT | rot: HTHHHTHT | flip: 01 45 HHHTHHTT\n",
" 29: HHHTHHTT | rot: TTHHHTHH | flip: 01234567 HHTTTHTT\n",
" 30: HHTTTHTT | rot: HTTTHTTH | flip: 0 2 4 6 HHTTHTTT\n",
" 31: HHTTHTTT | rot: TTTHHTTH | flip: 01234567 HHHTTHHT\n",
" 32: HHHTTHHT | rot: TTHHTHHH | flip: 01234 6 HHHTTHHT\n",
" 33: HHHTTHHT | rot: THHHTTHH | flip: 01234567 HHTTHTTT\n",
" 34: HHTTHTTT | rot: HHTTHTTT | flip: 0 2 4 6 HHTTTHTT\n",
" 35: HHTTTHTT | rot: THTTHHTT | flip: 01234567 HHHTHHTT\n",
" 36: HHHTHHTT | rot: TTHHHTHH | flip: 01 45 HHHHHHHT\n",
" 37: HHHHHHHT | rot: THHHHHHH | flip: 01234567 HTTTTTTT\n",
" 38: HTTTTTTT | rot: THTTTTTT | flip: 0 2 4 6 HHHTHTHT\n",
" 39: HHHTHTHT | rot: HTHTHHHT | flip: 01234567 HTHTHTTT\n",
" 1: HTTHTTHT | rot: TTHTTHTH | flip: 01234567 HHTHHTHT\n",
" 2: HHTHHTHT | rot: THHTHTHH | flip: 0 2 4 6 HHHTTTTT\n",
" 3: HHHTTTTT | rot: HTTTTTHH | flip: 01234567 HHHHHTTT\n",
" 4: HHHHHTTT | rot: HTTTHHHH | flip: 01 45 HHTHTTTT\n",
" 5: HHTHTTTT | rot: TTHHTHTT | flip: 01234567 HHHHTTHT\n",
" 6: HHHHTTHT | rot: THHHHTTH | flip: 0 2 4 6 HHHHTHTT\n",
" 7: HHHHTHTT | rot: TTHHHHTH | flip: 01234567 HHTTTTHT\n",
" 8: HHTTTTHT | rot: HTTTTHTH | flip: 012 456 HHTHHTHT\n",
" 9: HHTHHTHT | rot: THHTHHTH | flip: 01234567 HTHTTHTT\n",
" 10: HTHTTHTT | rot: HTHTTHTT | flip: 0 2 4 6 HHHTTTTT\n",
" 11: HHHTTTTT | rot: TTTHHHTT | flip: 01234567 HHHHHTTT\n",
" 12: HHHHHTTT | rot: HHHHTTTH | flip: 01 45 HHHHTHTT\n",
" 13: HHHHTHTT | rot: THHHHTHT | flip: 01234567 HHTTTTHT\n",
" 14: HHTTTTHT | rot: TTHTHHTT | flip: 0 2 4 6 HHTHTTTT\n",
" 15: HHTHTTTT | rot: TTHHTHTT | flip: 01234567 HHHHTTHT\n",
" 16: HHHHTTHT | rot: THTHHHHT | flip: 0123 HHHTHTHT\n",
" 17: HHHTHTHT | rot: HTHTHTHH | flip: 01234567 HTHTHTTT\n",
" 18: HTHTHTTT | rot: HTHTTTHT | flip: 0 2 4 6 HTTTTTTT\n",
" 19: HTTTTTTT | rot: THTTTTTT | flip: 01234567 HHHHHHHT\n",
" 20: HHHHHHHT | rot: HHHTHHHH | flip: 01 45 HHTTHTTT\n",
" 21: HHTTHTTT | rot: THHTTHTT | flip: 01234567 HHHTTHHT\n",
" 22: HHHTTHHT | rot: TTHHTHHH | flip: 0 2 4 6 HHHTHHTT\n",
" 23: HHHTHHTT | rot: HHTTHHHT | flip: 01234567 HHTTTHTT\n",
" 24: HHTTTHTT | rot: HHTTTHTT | flip: 012 456 HTHTHTTT\n",
" 25: HTHTHTTT | rot: TTTHTHTH | flip: 01234567 HHHTHTHT\n",
" 26: HHHTHTHT | rot: HHTHTHTH | flip: 0 2 4 6 HHHHHHHT\n",
" 27: HHHHHHHT | rot: HHHHHTHH | flip: 01234567 HTTTTTTT\n",
" 28: HTTTTTTT | rot: TTTTTHTT | flip: 01 45 HHTTHTTT\n",
" 29: HHTTHTTT | rot: HTTTHHTT | flip: 01234567 HHHTTHHT\n",
" 30: HHHTTHHT | rot: HTTHHTHH | flip: 0 2 4 6 HHTTTHTT\n",
" 31: HHTTTHTT | rot: HTTHHTTT | flip: 01234567 HHHTHHTT\n",
" 32: HHHTHHTT | rot: HHTHHTTH | flip: 01234 6 HHTTHTTT\n",
" 33: HHTTHTTT | rot: TTHTTTHH | flip: 01234567 HHHTTHHT\n",
" 34: HHHTTHHT | rot: THHHTTHH | flip: 0 2 4 6 HHHTHHTT\n",
" 35: HHHTHHTT | rot: THHTTHHH | flip: 01234567 HHTTTHTT\n",
" 36: HHTTTHTT | rot: THTTHHTT | flip: 01 45 HTTTTTTT\n",
" 37: HTTTTTTT | rot: TTTTTHTT | flip: 01234567 HHHHHHHT\n",
" 38: HHHHHHHT | rot: HHHHHHTH | flip: 0 2 4 6 HHHTHTHT\n",
" 39: HHHTHTHT | rot: HTHTHTHH | flip: 01234567 HTHTHTTT\n",
" 40: HTHTHTTT | rot: HTHTTTHT | flip: 012 456 HHTTTHTT\n",
" 41: HHTTTHTT | rot: HTTHHTTT | flip: 01234567 HHHTHHTT\n",
" 41: HHTTTHTT | rot: HHTTTHTT | flip: 01234567 HHHTHHTT\n",
" 42: HHHTHHTT | rot: THHHTHHT | flip: 0 2 4 6 HHHTTHHT\n",
" 43: HHHTTHHT | rot: HTHHHTTH | flip: 01234567 HHTTHTTT\n",
" 44: HHTTHTTT | rot: HTTHTTTH | flip: 01 45 HHHTHTHT\n",
" 45: HHHTHTHT | rot: THHHTHTH | flip: 01234567 HTHTHTTT\n",
" 46: HTHTHTTT | rot: THTHTHTT | flip: 0 2 4 6 HHHHHHHT\n",
" 47: HHHHHHHT | rot: HHHHTHHH | flip: 01234567 HTTTTTTT\n",
" 48: HTTTTTTT | rot: TTTTTTHT | flip: 0123 HHHHTTHT\n",
" 49: HHHHTTHT | rot: HHTTHTHH | flip: 01234567 HHTHTTTT\n",
" 50: HHTHTTTT | rot: HTHTTTTH | flip: 0 2 4 6 HHTTTTHT\n",
" 51: HHTTTTHT | rot: TTTTHTHH | flip: 01234567 HHHHTHTT\n",
" 52: HHHHTHTT | rot: HHTHTTHH | flip: 01 45 HHHHHTTT\n",
" 53: HHHHHTTT | rot: HHHHTTTH | flip: 01234567 HHHTTTTT\n",
" 54: HHHTTTTT | rot: HTTTTTHH | flip: 0 2 4 6 HTHTTHTT\n",
" 55: HTHTTHTT | rot: HTTHTHTT | flip: 01234567 HHTHHTHT\n",
" 56: HHTHHTHT | rot: THHTHHTH | flip: 012 456 HHHTTTTT\n",
" 57: HHHTTTTT | rot: HHHTTTTT | flip: 01234567 HHHHHTTT\n",
" 58: HHHHHTTT | rot: HHHHHTTT | flip: 0 2 4 6 HTHTTHTT\n",
" 59: HTHTTHTT | rot: HTTHTTHT | flip: 01234567 HHTHHTHT\n",
" 60: HHTHHTHT | rot: THHTHHTH | flip: 01 45 HHTHTTTT\n",
" 61: HHTHTTTT | rot: TTTHHTHT | flip: 01234567 HHHHTTHT\n",
" 62: HHHHTTHT | rot: HTHHHHTT | flip: 0 2 4 6 HHTTTTHT\n",
" 63: HHTTTTHT | rot: HHTTTTHT | flip: 01234567 HHHHTHTT\n",
" 64: HHHHTHTT | rot: HHTHTTHH | flip: 012345 HHHHTTHT\n",
" 65: HHHHTTHT | rot: HHHTTHTH | flip: 01234567 HHTHTTTT\n",
" 66: HHTHTTTT | rot: HHTHTTTT | flip: 0 2 4 6 HHHHTHTT\n",
" 67: HHHHTHTT | rot: THTTHHHH | flip: 01234567 HHTTTTHT\n",
" 68: HHTTTTHT | rot: HTTTTHTH | flip: 01 45 HTHTTHTT\n",
" 69: HTHTTHTT | rot: THTTHTTH | flip: 01234567 HHTHHTHT\n",
" 70: HHTHHTHT | rot: THTHHTHH | flip: 0 2 4 6 HHHHHTTT\n",
" 71: HHHHHTTT | rot: TTTHHHHH | flip: 01234567 HHHTTTTT\n",
" 72: HHHTTTTT | rot: HHTTTTTH | flip: 012 456 HHHHTTHT\n",
" 73: HHHHTTHT | rot: HHTTHTHH | flip: 01234567 HHTHTTTT\n",
" 74: HHTHTTTT | rot: TTTHHTHT | flip: 0 2 4 6 HHTTTTHT\n",
" 75: HHTTTTHT | rot: HHTTTTHT | flip: 01234567 HHHHTHTT\n",
" 76: HHHHTHTT | rot: HTHTTHHH | flip: 01 45 HHTHHTHT\n",
" 77: HHTHHTHT | rot: THTHHTHH | flip: 01234567 HTHTTHTT\n",
" 78: HTHTTHTT | rot: HTHTTHTT | flip: 0 2 4 6 HHHTTTTT\n",
" 79: HHHTTTTT | rot: HHTTTTTH | flip: 01234567 HHHHHTTT\n",
" 80: HHHHHTTT | rot: HHHHHTTT | flip: 0123 HTTTTTTT\n",
" 81: HTTTTTTT | rot: HTTTTTTT | flip: 01234567 HHHHHHHT\n",
" 82: HHHHHHHT | rot: HHHTHHHH | flip: 0 2 4 6 HTHTHTTT\n",
" 83: HTHTHTTT | rot: HTHTTTHT | flip: 01234567 HHHTHTHT\n",
" 84: HHHTHTHT | rot: HTHTHTHH | flip: 01 45 HHHTHHTT\n",
" 85: HHHTHHTT | rot: THHHTHHT | flip: 01234567 HHTTTHTT\n",
" 86: HHTTTHTT | rot: THHTTTHT | flip: 0 2 4 6 HHTTHTTT\n",
" 87: HHTTHTTT | rot: TTTHHTTH | flip: 01234567 HHHTTHHT\n",
" 88: HHHTTHHT | rot: THHHTTHH | flip: 012 456 HHHTHHTT\n",
" 89: HHHTHHTT | rot: HTTHHHTH | flip: 01234567 HHTTTHTT\n",
" 90: HHTTTHTT | rot: THTTHHTT | flip: 0 2 4 6 HHHTTHHT\n",
" 91: HHHTTHHT | rot: HTTHHTHH | flip: 01234567 HHTTHTTT\n",
" 92: HHTTHTTT | rot: HTTTHHTT | flip: 01 45 HTTTTTTT\n",
" 93: HTTTTTTT | rot: THTTTTTT | flip: 01234567 HHHHHHHT\n",
" 94: HHHHHHHT | rot: HHHHHTHH | flip: 0 2 4 6 HTHTHTTT\n",
" 95: HTHTHTTT | rot: THTHTHTT | flip: 01234567 HHHTHTHT\n",
" 96: HHHTHTHT | rot: HTHTHTHH | flip: 01234 6 HTHTHTTT\n",
" 97: HTHTHTTT | rot: THTHTTTH | flip: 01234567 HHHTHTHT\n",
" 98: HHHTHTHT | rot: HTHTHTHH | flip: 0 2 4 6 HTTTTTTT\n",
" 99: HTTTTTTT | rot: TTTTTTHT | flip: 01234567 HHHHHHHT\n",
" 100: HHHHHHHT | rot: HHTHHHHH | flip: 01 45 HHTTTHTT\n",
" 101: HHTTTHTT | rot: HTTTHTTH | flip: 01234567 HHHTHHTT\n",
" 102: HHHTHHTT | rot: HHTHHTTH | flip: 0 2 4 6 HHHTTHHT\n",
" 103: HHHTTHHT | rot: HHHTTHHT | flip: 01234567 HHTTHTTT\n",
" 104: HHTTHTTT | rot: TTTHHTTH | flip: 012 456 HHHHHHHT\n",
" 105: HHHHHHHT | rot: HHTHHHHH | flip: 01234567 HTTTTTTT\n",
" 106: HTTTTTTT | rot: THTTTTTT | flip: 0 2 4 6 HHHTHTHT\n",
" 107: HHHTHTHT | rot: THHHTHTH | flip: 01234567 HTHTHTTT\n",
" 108: HTHTHTTT | rot: THTHTTTH | flip: 01 45 HHHTHHTT\n",
" 109: HHHTHHTT | rot: HTTHHHTH | flip: 01234567 HHTTTHTT\n",
" 110: HHTTTHTT | rot: HTTTHTTH | flip: 0 2 4 6 HHTTHTTT\n",
" 111: HHTTHTTT | rot: HTTHTTTH | flip: 01234567 HHHTTHHT\n",
" 112: HHHTTHHT | rot: TTHHTHHH | flip: 0123 HHHHHTTT\n",
" 113: HHHHHTTT | rot: TTHHHHHT | flip: 01234567 HHHTTTTT\n",
" 114: HHHTTTTT | rot: TTTTTHHH | flip: 0 2 4 6 HHTHHTHT\n",
" 115: HHTHHTHT | rot: HTHHTHHT | flip: 01234567 HTHTTHTT\n",
" 116: HTHTTHTT | rot: HTTHTHTT | flip: 01 45 HHTTTTHT\n",
" 117: HHTTTTHT | rot: TTTTHTHH | flip: 01234567 HHHHTHTT\n",
" 118: HHHHTHTT | rot: HHHHTHTT | flip: 0 2 4 6 HHHHTTHT\n",
" 119: HHHHTTHT | rot: THHHHTTH | flip: 01234567 HHTHTTTT\n",
" 120: HHTHTTTT | rot: TTHHTHTT | flip: 012 456 HHTHHTHT\n",
" 121: HHTHHTHT | rot: THTHHTHH | flip: 01234567 HTHTTHTT\n",
" 122: HTHTTHTT | rot: THTHTTHT | flip: 0 2 4 6 HHHHHTTT\n",
" 123: HHHHHTTT | rot: HHHHTTTH | flip: 01234567 HHHTTTTT\n",
" 124: HHHTTTTT | rot: HHTTTTTH | flip: 01 45 HHTHTTTT\n",
" 125: HHTHTTTT | rot: TTHHTHTT | flip: 01234567 HHHHTTHT\n",
" 126: HHHHTTHT | rot: TTHTHHHH | flip: 0 2 4 6 HHTTTTHT\n",
" 127: HHTTTTHT | rot: HHTTTTHT | flip: 01234567 HHHHTHTT\n",
" 128: HHHHTHTT | rot: HHHTHTTH | flip: 0123456 HHHTTTHT\n",
" 129: HHHTTTHT | rot: HHHTTTHT | flip: 01234567 HHHTHTTT\n",
" 130: HHHTHTTT | rot: HHHTHTTT | flip: 0 2 4 6 HTTHTTTT\n",
" 131: HTTHTTTT | rot: HTTHTTTT | flip: 01234567 HHHHTHHT\n",
" 132: HHHHTHHT | rot: THHHHTHH | flip: 01 45 HHHHTHHT\n",
" 133: HHHHTHHT | rot: THHHHTHH | flip: 01234567 HTTHTTTT\n",
" 134: HTTHTTTT | rot: THTTTTHT | flip: 0 2 4 6 HHHTHTTT\n",
" 135: HHHTHTTT | rot: THHHTHTT | flip: 01234567 HHHTTTHT\n",
" 136: HHHTTTHT | rot: HTHHHTTT | flip: 012 456 HHTTHTHT\n",
" 137: HHTTHTHT | rot: THTHHTTH | flip: 01234567 HHTHTHTT\n",
" 138: HHTHTHTT | rot: HTTHHTHT | flip: 0 2 4 6 HHTTTTTT\n",
" 139: HHTTTTTT | rot: TTTHHTTT | flip: 01234567 HHHHHHTT\n",
" 140: HHHHHHTT | rot: HHHHHTTH | flip: 01 45 HHTHTHTT\n",
" 141: HHTHTHTT | rot: THTTHHTH | flip: 01234567 HHTTHTHT\n",
" 142: HHTTHTHT | rot: THTHHTTH | flip: 0 2 4 6 HHHHHHTT\n",
" 143: HHHHHHTT | rot: HHTTHHHH | flip: 01234567 HHTTTTTT\n",
" 144: HHTTTTTT | rot: THHTTTTT | flip: 0123 HTTHTTTT\n",
" 145: HTTHTTTT | rot: TTTHTTHT | flip: 01234567 HHHHTHHT\n",
" 146: HHHHTHHT | rot: HHHHTHHT | flip: 0 2 4 6 HHHTTTHT\n",
" 147: HHHTTTHT | rot: TTTHTHHH | flip: 01234567 HHHTHTTT\n",
" 148: HHHTHTTT | rot: THHHTHTT | flip: 01 45 HHHTTTHT\n",
" 149: HHHTTTHT | rot: THHHTTTH | flip: 01234567 HHHTHTTT\n",
" 150: HHHTHTTT | rot: TTHHHTHT | flip: 0 2 4 6 HTTHTTTT\n",
" 151: HTTHTTTT | rot: TTHTTHTT | flip: 01234567 HHHHTHHT\n",
" 152: HHHHTHHT | rot: HTHHHHTH | flip: 012 456 HHTHTHTT\n",
" 153: HHTHTHTT | rot: HTHTHTTH | flip: 01234567 HHTTHTHT\n",
" 154: HHTTHTHT | rot: HTTHTHTH | flip: 0 2 4 6 HHHHHHTT\n",
" 155: HHHHHHTT | rot: TTHHHHHH | flip: 01234567 HHTTTTTT\n",
" 156: HHTTTTTT | rot: TTTHHTTT | flip: 01 45 HHTHTHTT\n",
" 157: HHTHTHTT | rot: HTHTTHHT | flip: 01234567 HHTTHTHT\n",
" 158: HHTTHTHT | rot: HTTHTHTH | flip: 0 2 4 6 HHHHHHTT\n",
" 159: HHHHHHTT | rot: HHHHHTTH | flip: 01234567 HHTTTTTT\n",
" 160: HHTTTTTT | rot: HHTTTTTT | flip: 01234 6 HHHTHTTT\n",
" 161: HHHTHTTT | rot: HHHTHTTT | flip: 01234567 HHHTTTHT\n",
" 162: HHHTTTHT | rot: HHTTTHTH | flip: 0 2 4 6 HHHHTHHT\n",
" 163: HHHHTHHT | rot: HTHHTHHH | flip: 01234567 HTTHTTTT\n",
" 164: HTTHTTTT | rot: THTTTTHT | flip: 01 45 HHHTHTTT\n",
" 165: HHHTHTTT | rot: HTHTTTHH | flip: 01234567 HHHTTTHT\n",
" 166: HHHTTTHT | rot: HHHTTTHT | flip: 0 2 4 6 HTTHTTTT\n",
" 167: HTTHTTTT | rot: THTTHTTT | flip: 01234567 HHHHTHHT\n",
" 168: HHHHTHHT | rot: HHTHHTHH | flip: 012 456 HHTHTHTT\n",
" 169: HHTHTHTT | rot: THHTHTHT | flip: 01234567 HHTTHTHT\n",
" 170: HHTTHTHT | rot: HTHTHHTT | flip: 0 2 4 6 HHTTTTTT\n",
" 171: HHTTTTTT | rot: THHTTTTT | flip: 01234567 HHHHHHTT\n",
" 172: HHHHHHTT | rot: TTHHHHHH | flip: 01 45 HHHHHHTT\n",
" 173: HHHHHHTT | rot: HHHHHTTH | flip: 01234567 HHTTTTTT\n",
" 174: HHTTTTTT | rot: TTHHTTTT | flip: 0 2 4 6 HHTHTHTT\n",
" 175: HHTHTHTT | rot: HHTHTHTT | flip: 01234567 HHTTHTHT\n",
" 176: HHTTHTHT | rot: HTHHTTHT | flip: 0123 HTTHTTTT\n",
" 177: HTTHTTTT | rot: HTTTTHTT | flip: 01234567 HHHHTHHT\n",
" 178: HHHHTHHT | rot: THHHHTHH | flip: 0 2 4 6 HHHTHTTT\n",
" 179: HHHTHTTT | rot: HTTTHHHT | flip: 01234567 HHHTTTHT\n",
" 180: HHHTTTHT | rot: THHHTTTH | flip: 01 45 HHHHTHHT\n",
" 181: HHHHTHHT | rot: HHHTHHTH | flip: 01234567 HTTHTTTT\n",
" 182: HTTHTTTT | rot: HTTTTHTT | flip: 0 2 4 6 HHHTTTHT\n",
" 183: HHHTTTHT | rot: HTHHHTTT | flip: 01234567 HHHTHTTT\n",
" 184: HHHTHTTT | rot: TTTHHHTH | flip: 012 456 HHHHHHTT\n",
" 185: HHHHHHTT | rot: HHHTTHHH | flip: 01234567 HHTTTTTT\n",
" 186: HHTTTTTT | rot: HTTTTTTH | flip: 0 2 4 6 HHTTHTHT\n",
" 187: HHTTHTHT | rot: HTHTHHTT | flip: 01234567 HHTHTHTT\n",
" 188: HHTHTHTT | rot: HHTHTHTT | flip: 01 45 HHTTTTTT\n",
" 189: HHTTTTTT | rot: TTTTHHTT | flip: 01234567 HHHHHHTT\n",
" 190: HHHHHHTT | rot: HHHHTTHH | flip: 0 2 4 6 HHTTHTHT\n",
" 191: HHTTHTHT | rot: HHTTHTHT | flip: 01234567 HHTHTHTT\n",
" 192: HHTHTHTT | rot: TTHHTHTH | flip: 012345 HHHTTHTT\n",
" 193: HHHTTHTT | rot: TTHTTHHH | flip: 01234567 HHTHHTTT\n",
" 194: HHTHHTTT | rot: HHTHHTTT | flip: 0 2 4 6 HHHTTHTT\n",
" 195: HHHTTHTT | rot: HHTTHTTH | flip: 01234567 HHTHHTTT\n",
" 196: HHTHHTTT | rot: HTHHTTTH | flip: 01 45 HHHHHTHT\n",
" 197: HHHHHTHT | rot: THHHHHTH | flip: 01234567 HTHTTTTT\n",
" 198: HTHTTTTT | rot: THTTTTTH | flip: 0 2 4 6 HHHHHTHT\n",
" 199: HHHHHTHT | rot: HTHTHHHH | flip: 01234567 HTHTTTTT\n",
" 200: HTHTTTTT | rot: THTHTTTT | flip: 012 456 HHHHHTHT\n",
" 201: HHHHHTHT | rot: HHHHTHTH | flip: 01234567 HTHTTTTT\n",
" 202: HTHTTTTT | rot: THTTTTTH | flip: 0 2 4 6 HHHHHTHT\n",
" 203: HHHHHTHT | rot: THHHHHTH | flip: 01234567 HTHTTTTT\n",
" 204: HTHTTTTT | rot: HTHTTTTT | flip: 01 45 HHTHHTTT\n",
" 205: HHTHHTTT | rot: HHTHHTTT | flip: 01234567 HHHTTHTT\n",
" 206: HHHTTHTT | rot: HHTTHTTH | flip: 0 2 4 6 HHTHHTTT\n",
" 207: HHTHHTTT | rot: TTHHTHHT | flip: 01234567 HHHTTHTT\n",
" 208: HHHTTHTT | rot: THTTHHHT | flip: 0123 HHHHHTHT\n",
" 209: HHHHHTHT | rot: HHHHTHTH | flip: 01234567 HTHTTTTT\n",
" 210: HTHTTTTT | rot: HTTTTTHT | flip: 0 2 4 6 HTHTTTTT\n",
" 211: HTHTTTTT | rot: TTHTHTTT | flip: 01234567 HHHHHTHT\n",
" 212: HHHHHTHT | rot: HHTHTHHH | flip: 01 45 HHTHHTTT\n",
" 213: HHTHHTTT | rot: HTHHTTTH | flip: 01234567 HHHTTHTT\n",
" 214: HHHTTHTT | rot: HTTHHHTT | flip: 0 2 4 6 HHTHHTTT\n",
" 215: HHTHHTTT | rot: THHTTTHH | flip: 01234567 HHHTTHTT\n",
" 216: HHHTTHTT | rot: TTHTTHHH | flip: 012 456 HHHTTHTT\n",
" 217: HHHTTHTT | rot: HHTTHTTH | flip: 01234567 HHTHHTTT\n",
" 218: HHTHHTTT | rot: HTTTHHTH | flip: 0 2 4 6 HHHTTHTT\n",
" 219: HHHTTHTT | rot: HTTHHHTT | flip: 01234567 HHTHHTTT\n",
" 220: HHTHHTTT | rot: THHTHHTT | flip: 01 45 HTHTTTTT\n",
" 221: HTHTTTTT | rot: TTHTHTTT | flip: 01234567 HHHHHTHT\n",
" 222: HHHHHTHT | rot: THTHHHHH | flip: 0 2 4 6 HHHHHTHT\n",
" 223: HHHHHTHT | rot: HHHTHTHH | flip: 01234567 HTHTTTTT\n",
" 224: HTHTTTTT | rot: TTTHTHTT | flip: 01234 6 HHHTHHHT\n",
" 225: HHHTHHHT | rot: HHTHHHTH | flip: 01234567 HTTTHTTT\n",
" 226: HTTTHTTT | rot: HTTTHTTT | flip: 0 2 4 6 HTTTHTTT\n",
" 227: HTTTHTTT | rot: TTTHTTTH | flip: 01234567 HHHTHHHT\n",
" 228: HHHTHHHT | rot: HHHTHHHT | flip: 01 45 HTTTHTTT\n",
" 229: HTTTHTTT | rot: TTTHTTTH | flip: 01234567 HHHTHHHT\n",
" 230: HHHTHHHT | rot: HTHHHTHH | flip: 0 2 4 6 HTTTHTTT\n",
" 231: HTTTHTTT | rot: HTTTHTTT | flip: 01234567 HHHTHHHT\n",
" 232: HHHTHHHT | rot: HTHHHTHH | flip: 012 456 HTHTHTHT\n",
" 233: HTHTHTHT | rot: THTHTHTH | flip: 01234567 HTHTHTHT\n",
" 234: HTHTHTHT | rot: HTHTHTHT | flip: 0 2 4 6 TTTTTTTT\n",
" 235: TTTTTTTT | rot: TTTTTTTT | flip: 01234567 HHHHHHHH\n"
" 43: HHHTTHHT | rot: TTHHTHHH | flip: 01234567 HHTTHTTT\n",
" 44: HHTTHTTT | rot: TTHHTTHT | flip: 01 45 HHHHHHHT\n",
" 45: HHHHHHHT | rot: HHHHTHHH | flip: 01234567 HTTTTTTT\n",
" 46: HTTTTTTT | rot: TTHTTTTT | flip: 0 2 4 6 HTHTHTTT\n",
" 47: HTHTHTTT | rot: THTTTHTH | flip: 01234567 HHHTHTHT\n",
" 48: HHHTHTHT | rot: HTHTHHHT | flip: 0123 HHHHTTHT\n",
" 49: HHHHTTHT | rot: TTHTHHHH | flip: 01234567 HHTHTTTT\n",
" 50: HHTHTTTT | rot: TTHHTHTT | flip: 0 2 4 6 HHHHTHTT\n",
" 51: HHHHTHTT | rot: HHTHTTHH | flip: 01234567 HHTTTTHT\n",
" 52: HHTTTTHT | rot: THTHHTTT | flip: 01 45 HTHTTHTT\n",
" 53: HTHTTHTT | rot: THTTHTTH | flip: 01234567 HHTHHTHT\n",
" 54: HHTHHTHT | rot: HHTHHTHT | flip: 0 2 4 6 HHHTTTTT\n",
" 55: HHHTTTTT | rot: TTTTTHHH | flip: 01234567 HHHHHTTT\n",
" 56: HHHHHTTT | rot: THHHHHTT | flip: 012 456 HTHTTHTT\n",
" 57: HTHTTHTT | rot: THTHTTHT | flip: 01234567 HHTHHTHT\n",
" 58: HHTHHTHT | rot: HTHHTHHT | flip: 0 2 4 6 HHHTTTTT\n",
" 59: HHHTTTTT | rot: HHTTTTTH | flip: 01234567 HHHHHTTT\n",
" 60: HHHHHTTT | rot: HHHHHTTT | flip: 01 45 HHTHTTTT\n",
" 61: HHTHTTTT | rot: THTTTTHH | flip: 01234567 HHHHTTHT\n",
" 62: HHHHTTHT | rot: THTHHHHT | flip: 0 2 4 6 HHHHTHTT\n",
" 63: HHHHTHTT | rot: HHHTHTTH | flip: 01234567 HHTTTTHT\n",
" 64: HHTTTTHT | rot: TTTHTHHT | flip: 012345 HHHTHTHT\n",
" 65: HHHTHTHT | rot: THTHTHHH | flip: 01234567 HTHTHTTT\n",
" 66: HTHTHTTT | rot: HTHTHTTT | flip: 0 2 4 6 HTTTTTTT\n",
" 67: HTTTTTTT | rot: TTTTTTTH | flip: 01234567 HHHHHHHT\n",
" 68: HHHHHHHT | rot: HHHHTHHH | flip: 01 45 HHHTHHTT\n",
" 69: HHHTHHTT | rot: HHHTHHTT | flip: 01234567 HHTTTHTT\n",
" 70: HHTTTHTT | rot: TTHHTTTH | flip: 0 2 4 6 HHHTTHHT\n",
" 71: HHHTTHHT | rot: HTHHHTTH | flip: 01234567 HHTTHTTT\n",
" 72: HHTTHTTT | rot: THTTTHHT | flip: 012 456 HTHTHTTT\n",
" 73: HTHTHTTT | rot: TTHTHTHT | flip: 01234567 HHHTHTHT\n",
" 74: HHHTHTHT | rot: THHHTHTH | flip: 0 2 4 6 HHHHHHHT\n",
" 75: HHHHHHHT | rot: HHHTHHHH | flip: 01234567 HTTTTTTT\n",
" 76: HTTTTTTT | rot: TTTTTHTT | flip: 01 45 HHTTHTTT\n",
" 77: HHTTHTTT | rot: HHTTHTTT | flip: 01234567 HHHTTHHT\n",
" 78: HHHTTHHT | rot: TTHHTHHH | flip: 0 2 4 6 HHHTHHTT\n",
" 79: HHHTHHTT | rot: HHTHHTTH | flip: 01234567 HHTTTHTT\n",
" 80: HHTTTHTT | rot: THTTHHTT | flip: 0123 HHHHTTHT\n",
" 81: HHHHTTHT | rot: TTHTHHHH | flip: 01234567 HHTHTTTT\n",
" 82: HHTHTTTT | rot: HTTTTHHT | flip: 0 2 4 6 HHTTTTHT\n",
" 83: HHTTTTHT | rot: HTHHTTTT | flip: 01234567 HHHHTHTT\n",
" 84: HHHHTHTT | rot: HHHHTHTT | flip: 01 45 HHHTTTTT\n",
" 85: HHHTTTTT | rot: THHHTTTT | flip: 01234567 HHHHHTTT\n",
" 86: HHHHHTTT | rot: HHHHHTTT | flip: 0 2 4 6 HTHTTHTT\n",
" 87: HTHTTHTT | rot: TTHTTHTH | flip: 01234567 HHTHHTHT\n",
" 88: HHTHHTHT | rot: THHTHTHH | flip: 012 456 HHTTTTHT\n",
" 89: HHTTTTHT | rot: THHTTTTH | flip: 01234567 HHHHTHTT\n",
" 90: HHHHTHTT | rot: HHTHTTHH | flip: 0 2 4 6 HHHHTTHT\n",
" 91: HHHHTTHT | rot: HTTHTHHH | flip: 01234567 HHTHTTTT\n",
" 92: HHTHTTTT | rot: HTTTTHHT | flip: 01 45 HTHTTHTT\n",
" 93: HTHTTHTT | rot: THTTHTHT | flip: 01234567 HHTHHTHT\n",
" 94: HHTHHTHT | rot: HTHTHHTH | flip: 0 2 4 6 HHHTTTTT\n",
" 95: HHHTTTTT | rot: TTHHHTTT | flip: 01234567 HHHHHTTT\n",
" 96: HHHHHTTT | rot: HHTTTHHH | flip: 01234 6 HHHHTHTT\n",
" 97: HHHHTHTT | rot: TTHHHHTH | flip: 01234567 HHTTTTHT\n",
" 98: HHTTTTHT | rot: TTHTHHTT | flip: 0 2 4 6 HHTHTTTT\n",
" 99: HHTHTTTT | rot: TTTHHTHT | flip: 01234567 HHHHTTHT\n",
" 100: HHHHTTHT | rot: HHTTHTHH | flip: 01 45 HHHTTTTT\n",
" 101: HHHTTTTT | rot: HHTTTTTH | flip: 01234567 HHHHHTTT\n",
" 102: HHHHHTTT | rot: HHHHTTTH | flip: 0 2 4 6 HHTHHTHT\n",
" 103: HHTHHTHT | rot: HTHHTHHT | flip: 01234567 HTHTTHTT\n",
" 104: HTHTTHTT | rot: HTTHTTHT | flip: 012 456 HHHHHTTT\n",
" 105: HHHHHTTT | rot: TTHHHHHT | flip: 01234567 HHHTTTTT\n",
" 106: HHHTTTTT | rot: HHTTTTTH | flip: 0 2 4 6 HHTHHTHT\n",
" 107: HHTHHTHT | rot: THHTHHTH | flip: 01234567 HTHTTHTT\n",
" 108: HTHTTHTT | rot: THTTHTTH | flip: 01 45 HHTTTTHT\n",
" 109: HHTTTTHT | rot: HTTTTHTH | flip: 01234567 HHHHTHTT\n",
" 110: HHHHTHTT | rot: TTHHHHTH | flip: 0 2 4 6 HHHHTTHT\n",
" 111: HHHHTTHT | rot: THHHHTTH | flip: 01234567 HHTHTTTT\n",
" 112: HHTHTTTT | rot: HTTTTHHT | flip: 0123 HHHTHHTT\n",
" 113: HHHTHHTT | rot: HHTTHHHT | flip: 01234567 HHTTTHTT\n",
" 114: HHTTTHTT | rot: TTHHTTTH | flip: 0 2 4 6 HHHTTHHT\n",
" 115: HHHTTHHT | rot: HHHTTHHT | flip: 01234567 HHTTHTTT\n",
" 116: HHTTHTTT | rot: THHTTHTT | flip: 01 45 HTHTHTTT\n",
" 117: HTHTHTTT | rot: TTTHTHTH | flip: 01234567 HHHTHTHT\n",
" 118: HHHTHTHT | rot: THTHTHHH | flip: 0 2 4 6 HHHHHHHT\n",
" 119: HHHHHHHT | rot: HHHHTHHH | flip: 01234567 HTTTTTTT\n",
" 120: HTTTTTTT | rot: TTHTTTTT | flip: 012 456 HHHTHHTT\n",
" 121: HHHTHHTT | rot: HTHHTTHH | flip: 01234567 HHTTTHTT\n",
" 122: HHTTTHTT | rot: TTHHTTTH | flip: 0 2 4 6 HHHTTHHT\n",
" 123: HHHTTHHT | rot: THHHTTHH | flip: 01234567 HHTTHTTT\n",
" 124: HHTTHTTT | rot: TTTHHTTH | flip: 01 45 HHHTHTHT\n",
" 125: HHHTHTHT | rot: HHTHTHTH | flip: 01234567 HTHTHTTT\n",
" 126: HTHTHTTT | rot: TTTHTHTH | flip: 0 2 4 6 HHHHHHHT\n",
" 127: HHHHHHHT | rot: HTHHHHHH | flip: 01234567 HTTTTTTT\n",
" 128: HTTTTTTT | rot: THTTTTTT | flip: 0123456 HHHHHTHT\n",
" 129: HHHHHTHT | rot: HHHHHTHT | flip: 01234567 HTHTTTTT\n",
" 130: HTHTTTTT | rot: TTTHTHTT | flip: 0 2 4 6 HHHHHTHT\n",
" 131: HHHHHTHT | rot: HTHHHHHT | flip: 01234567 HTHTTTTT\n",
" 132: HTHTTTTT | rot: TTTHTHTT | flip: 01 45 HHTHHTTT\n",
" 133: HHTHHTTT | rot: THHTTTHH | flip: 01234567 HHHTTHTT\n",
" 134: HHHTTHTT | rot: HHHTTHTT | flip: 0 2 4 6 HHHTTHTT\n",
" 135: HHHTTHTT | rot: THTTHHHT | flip: 01234567 HHTHHTTT\n",
" 136: HHTHHTTT | rot: HTTTHHTH | flip: 012 456 HHTHHTTT\n",
" 137: HHTHHTTT | rot: HHTTTHHT | flip: 01234567 HHHTTHTT\n",
" 138: HHHTTHTT | rot: TTHTTHHH | flip: 0 2 4 6 HHTHHTTT\n",
" 139: HHTHHTTT | rot: TTHHTHHT | flip: 01234567 HHHTTHTT\n",
" 140: HHHTTHTT | rot: HHHTTHTT | flip: 01 45 HTHTTTTT\n",
" 141: HTHTTTTT | rot: TTTHTHTT | flip: 01234567 HHHHHTHT\n",
" 142: HHHHHTHT | rot: HHTHTHHH | flip: 0 2 4 6 HHHHHTHT\n",
" 143: HHHHHTHT | rot: HHHHTHTH | flip: 01234567 HTHTTTTT\n",
" 144: HTHTTTTT | rot: TTHTHTTT | flip: 0123 HHTHHTTT\n",
" 145: HHTHHTTT | rot: TTHHTHHT | flip: 01234567 HHHTTHTT\n",
" 146: HHHTTHTT | rot: HTTHHHTT | flip: 0 2 4 6 HHTHHTTT\n",
" 147: HHTHHTTT | rot: TTTHHTHH | flip: 01234567 HHHTTHTT\n",
" 148: HHHTTHTT | rot: HHHTTHTT | flip: 01 45 HTHTTTTT\n",
" 149: HTHTTTTT | rot: THTTTTTH | flip: 01234567 HHHHHTHT\n",
" 150: HHHHHTHT | rot: THHHHHTH | flip: 0 2 4 6 HHHHHTHT\n",
" 151: HHHHHTHT | rot: HHHTHTHH | flip: 01234567 HTHTTTTT\n",
" 152: HTHTTTTT | rot: HTHTTTTT | flip: 012 456 HHHTTHTT\n",
" 153: HHHTTHTT | rot: HHHTTHTT | flip: 01234567 HHTHHTTT\n",
" 154: HHTHHTTT | rot: TTTHHTHH | flip: 0 2 4 6 HHTHHTTT\n",
" 155: HHTHHTTT | rot: THHTTTHH | flip: 01234567 HHHTTHTT\n",
" 156: HHHTTHTT | rot: TTHHHTTH | flip: 01 45 HHHHHTHT\n",
" 157: HHHHHTHT | rot: THTHHHHH | flip: 01234567 HTHTTTTT\n",
" 158: HTHTTTTT | rot: TTHTHTTT | flip: 0 2 4 6 HTHTTTTT\n",
" 159: HTHTTTTT | rot: THTTTTTH | flip: 01234567 HHHHHTHT\n",
" 160: HHHHHTHT | rot: THTHHHHH | flip: 01234 6 HHTHTTHT\n",
" 161: HHTHTTHT | rot: TTHTHHTH | flip: 01234567 HHTHTTHT\n",
" 162: HHTHTTHT | rot: THTTHTHH | flip: 0 2 4 6 HHHHTTTT\n",
" 163: HHHHTTTT | rot: THHHHTTT | flip: 01234567 HHHHTTTT\n",
" 164: HHHHTTTT | rot: HHHTTTTH | flip: 01 45 HHTHTTHT\n",
" 165: HHTHTTHT | rot: HHTHTTHT | flip: 01234567 HHTHTTHT\n",
" 166: HHTHTTHT | rot: TTHTHHTH | flip: 0 2 4 6 HHHHTTTT\n",
" 167: HHHHTTTT | rot: TTTHHHHT | flip: 01234567 HHHHTTTT\n",
" 168: HHHHTTTT | rot: HHHHTTTT | flip: 012 456 HHHHTTTT\n",
" 169: HHHHTTTT | rot: TTHHHHTT | flip: 01234567 HHHHTTTT\n",
" 170: HHHHTTTT | rot: TTTHHHHT | flip: 0 2 4 6 HHTHTTHT\n",
" 171: HHTHTTHT | rot: TTHTHHTH | flip: 01234567 HHTHTTHT\n",
" 172: HHTHTTHT | rot: TTHTHHTH | flip: 01 45 HHHHTTTT\n",
" 173: HHHHTTTT | rot: HTTTTHHH | flip: 01234567 HHHHTTTT\n",
" 174: HHHHTTTT | rot: HTTTTHHH | flip: 0 2 4 6 HHTHTTHT\n",
" 175: HHTHTTHT | rot: THHTHTTH | flip: 01234567 HHTHTTHT\n",
" 176: HHTHTTHT | rot: TTHTHHTH | flip: 0123 HHHTHHHT\n",
" 177: HHHTHHHT | rot: HTHHHTHH | flip: 01234567 HTTTHTTT\n",
" 178: HTTTHTTT | rot: TTTHTTTH | flip: 0 2 4 6 HHHTHHHT\n",
" 179: HHHTHHHT | rot: HHHTHHHT | flip: 01234567 HTTTHTTT\n",
" 180: HTTTHTTT | rot: TTHTTTHT | flip: 01 45 HHHTHHHT\n",
" 181: HHHTHHHT | rot: HHHTHHHT | flip: 01234567 HTTTHTTT\n",
" 182: HTTTHTTT | rot: THTTTHTT | flip: 0 2 4 6 HHHTHHHT\n",
" 183: HHHTHHHT | rot: HHTHHHTH | flip: 01234567 HTTTHTTT\n",
" 184: HTTTHTTT | rot: TTTHTTTH | flip: 012 456 HHHHHHHH\n"
]
},
{