Judge's Notes for Probability Paradox
Below is the output from paradoxGauss.java with debug switched to true,
showing the augmented linear system, with the rightmost column of
numbers being the constant side of the equations. To the right of
the numbers are the prefixes that correspond to the main diagonal
variable. The bottom prefix is empty. That is the initial
state prefix, and the corresponding variable is the one that we want to
solve for.
The first matrix system is the intial one, and after the input data
comes the final row reduced matrix, all in integers. The final
answer is just the quotient of the two nonzero entries at the right end
of the final line.
After the dataset displays, at the very bottom line of the whole
output, is a line labeled "maxCalc", the largest integer used:
too big for the int type.
The determinant version, paradox.java, has the same initial
systems. The only other calculation in its debug version is the
largest number used in the calculation of determinants: 29 = 512, so that version does not need long integers.
2 -1 0 0 H
-1 2 0 1 T
-1 -1 2 0
n: 2, a: TT, b: HH
2 -1 0 0 H
0 -3 0 -2 T
0 0 -4 -2
1/2
2 -1 0 0 0 0 TH
-1 1 0 0 0 0 T
0 -1 2 0 0 1 HH
0 -1 -1 2 0 0 H
0 -1 0 -1 2 0
n: 3, a: HHH, b: THH
2 -1 0 0 0 0 TH
0 -1 0 0 0 0 T
0 0 2 0 0 1 HH
0 0 0 -4 0 -1 H
0 0 0 0 8 1
1/8
2 0 -1 0 0 TH
0 1 0 0 1 TT
-1 -1 2 0 0 T
0 0 -1 1 0
n: 3, a: TTH, b: THH
2 0 -1 0 0 TH
0 1 0 0 1 TT
0 0 -3 0 -2 T
0 0 0 3 2
2/3
2 -1 0 0 0 0 0 0 0 0 HTHT
-1 2 0 0 0 -1 0 0 0 0 HTH
0 -1 2 0 0 0 0 -1 0 0 HT
0 0 -1 1 0 0 0 0 0 0 H
0 0 0 0 2 0 0 -1 0 1 THHT
0 0 0 -1 -1 2 0 0 0 0 THH
0 0 -1 0 0 -1 2 0 0 0 TH
0 0 0 0 0 0 -1 1 0 0 T
0 0 0 -1 0 0 0 -1 2 0
n: 5, a: THHTH, b: HTHTT
2 -1 0 0 0 0 0 0 0 0 HTHT
0 -3 0 0 0 2 0 0 0 0 HTH
0 0 6 0 0 -2 0 -3 0 0 HT
0 0 0 -6 0 2 0 3 0 0 H
0 0 0 0 2 0 0 -1 0 1 THHT
0 0 0 0 0 10 0 -6 0 3 THH
0 0 0 0 0 0 -60 39 0 -12 TH
0 0 0 0 0 0 0 21 0 12 T
0 0 0 0 0 0 0 0 -420 -225
15/28
2 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 THHHTHTH
-1 2 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 THHHTHT
0 -1 2 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 THHHTH
0 0 -1 2 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 THHHT
0 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 THHH
0 0 0 0 -1 2 0 0 0 0 0 0 0 0 -1 0 0 0 THH
0 0 0 0 0 -1 2 0 0 0 0 0 0 0 -1 0 0 0 TH
0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 T
0 0 0 0 0 -1 0 0 2 0 0 0 0 0 0 0 0 1 HTTHHHTH
0 0 0 0 0 0 0 0 -1 2 0 0 0 -1 0 0 0 0 HTTHHHT
0 0 0 0 0 0 0 0 0 -1 2 0 0 0 0 -1 0 0 HTTHHH
0 0 0 0 0 0 0 0 0 0 -1 2 0 0 -1 0 0 0 HTTHH
0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 0 0 0 HTTH
0 0 0 0 0 0 0 -1 0 0 0 0 -1 2 0 0 0 0 HTT
0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 2 0 0 0 HT
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 H
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 2 0
n: 9, a: HTTHHHTHT, b: THHHTHTHH
2 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 THHHTHTH
0 -4 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 THHHTHT
0 0 8 0 0 -4 0 0 0 0 0 0 0 -2 -1 0 0 0 THHHTH
0 0 0 -16 0 4 0 0 0 0 0 0 0 10 1 0 0 0 THHHT
0 0 0 0 32 -4 0 0 0 0 0 0 0 -10 -1 -16 0 0 THHH
0 0 0 0 0 -60 0 0 0 0 0 0 0 10 33 16 0 0 THH
0 0 0 0 0 0 120 0 0 0 0 0 0 -10 -93 -16 0 0 TH
0 0 0 0 0 0 0 -120 0 0 0 0 0 10 93 16 0 0 T
0 0 0 0 0 0 0 0 120 0 0 0 0 -10 -33 -16 0 60 HTTHHHTH
0 0 0 0 0 0 0 0 0 -240 0 0 0 130 33 16 0 -60 HTTHHHT
0 0 0 0 0 0 0 0 0 0 480 0 0 -130 -33 -256 0 60 HTTHHH
0 0 0 0 0 0 0 0 0 0 0 -960 0 130 513 256 0 -60 HTTHH
0 0 0 0 0 0 0 0 0 0 0 0 1920 -130 -1473 -256 0 60 HTTH
0 0 0 0 0 0 0 0 0 0 0 0 0 -3550 2961 512 0 -60 HTT
0 0 0 0 0 0 0 0 0 0 0 0 0 0 13692 -12336 0 780 HT
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1356 0 -780 H
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10985091600 6294554700
259/452
2 1
n: 1, a: T, b: H
2 1
1/2
1 0 0 0 T
0 1 0 1 H
-1 -1 2 0
n: 2, a: HT, b: TH
1 0 0 0 T
0 1 0 1 H
0 0 2 1
1/2
2 0 0 0 0 0 0 0 0 -1 0 0 HHTTT
-1 2 0 0 0 0 0 0 -1 0 0 0 HHTT
0 -1 2 0 0 0 0 0 -1 0 0 0 HHT
0 0 -1 1 0 0 0 0 0 0 0 0 HH
0 0 0 -1 2 0 0 0 0 -1 0 0 H
0 0 0 0 0 2 0 -1 0 0 0 1 THHTH
0 -1 0 0 0 -1 2 0 0 0 0 0 THHT
0 0 0 -1 0 0 -1 2 0 0 0 0 THH
0 0 0 0 0 0 0 -1 2 -1 0 0 TH
0 0 0 0 0 0 0 0 -1 1 0 0 T
0 0 0 0 -1 0 0 0 0 -1 2 0
n: 6, a: THHTHT, b: HHTTTH
2 0 0 0 0 0 0 0 0 -1 0 0 HHTTT
0 -4 0 0 0 0 0 0 2 1 0 0 HHTT
0 0 8 0 0 0 0 0 -6 -1 0 0 HHT
0 0 0 -8 0 0 0 0 6 1 0 0 HH
0 0 0 0 16 0 0 0 -6 -9 0 0 H
0 0 0 0 0 2 0 -1 0 0 0 1 THHTH
0 0 0 0 0 0 8 -2 -2 -1 0 2 THHT
0 0 0 0 0 0 0 14 -8 -2 0 2 THH
0 0 0 0 0 0 0 0 -20 16 0 -2 TH
0 0 0 0 0 0 0 0 0 4 0 2 T
0 0 0 0 0 0 0 0 0 0 -640 -310
31/64
2 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 HHTTTHH
-1 2 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 HHTTTH
0 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 HHTTT
0 0 -1 2 0 0 0 0 0 0 0 0 -1 0 0 0 HHTT
0 0 0 -1 2 0 0 0 0 0 0 0 -1 0 0 0 HHT
0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 HH
0 0 0 0 0 -1 2 0 0 0 0 0 0 -1 0 0 H
0 0 0 0 0 0 0 2 -1 0 0 0 0 0 0 1 THTHTHT
0 0 0 0 0 -1 0 -1 2 0 0 0 0 0 0 0 THTHTH
0 0 0 0 0 0 0 0 -1 2 0 0 0 -1 0 0 THTHT
0 0 0 0 0 -1 0 0 0 -1 2 0 0 0 0 0 THTH
0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 0 0 THT
0 0 0 0 0 -1 0 0 0 0 0 -1 2 0 0 0 TH
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 T
0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 2 0
n: 8, a: THTHTHTT, b: HHTTTHHH
2 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 HHTTTHH
0 -4 0 0 1 0 0 0 0 0 0 2 0 0 0 0 HHTTTH
0 0 8 0 -1 0 0 0 0 0 0 -2 0 -4 0 0 HHTTT
0 0 0 -16 1 0 0 0 0 0 0 2 8 4 0 0 HHTT
0 0 0 0 31 0 0 0 0 0 0 -2 -24 -4 0 0 HHT
0 0 0 0 0 -31 0 0 0 0 0 2 24 4 0 0 HH
0 0 0 0 0 0 62 0 0 0 0 -2 -24 -35 0 0 H
0 0 0 0 0 0 0 2 -1 0 0 0 0 0 0 1 THTHTHT
0 0 0 0 0 0 0 0 -93 0 0 4 48 8 0 -31 THTHTH
0 0 0 0 0 0 0 0 0 186 0 -4 -48 -101 0 31 THTHT
0 0 0 0 0 0 0 0 0 0 -372 16 192 125 0 -31 THTH
0 0 0 0 0 0 0 0 0 0 0 728 -192 -497 0 31 THT
0 0 0 0 0 0 0 0 0 0 0 0 -21328 19313 0 -1023 TH
0 0 0 0 0 0 0 0 0 0 0 0 0 2015 0 1023 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -9704240 -4889444
131/260
2 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 HTHTHTHH
-1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 HTHTHTH
0 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 HTHTHT
0 0 -1 2 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 HTHTH
0 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 HTHT
0 0 0 0 -1 2 0 0 0 0 0 0 0 -1 0 0 0 0 HTH
0 0 0 0 0 -1 2 0 0 0 0 0 0 0 0 -1 0 0 HT
0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 H
0 0 0 0 0 -1 0 0 2 0 0 0 0 0 0 0 0 1 THHHTHHT
0 0 0 0 0 0 0 0 -1 2 0 0 -1 0 0 0 0 0 THHHTHH
0 0 0 0 -1 0 0 0 0 -1 2 0 0 0 0 0 0 0 THHHTH
0 0 0 0 0 0 0 0 0 0 -1 2 0 0 0 -1 0 0 THHHT
0 0 0 0 0 0 0 -1 0 0 0 -1 2 0 0 0 0 0 THHH
0 0 0 0 0 0 -1 0 0 0 0 0 -1 2 0 0 0 0 THH
0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 2 0 0 0 TH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 T
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 2 0
n: 9, a: THHHTHHTT, b: HTHTHTHHH
2 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 HTHTHTHH
0 -4 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 HTHTHTH
0 0 6 0 0 0 -1 0 0 0 0 0 0 0 0 -4 0 0 HTHTHT
0 0 0 -12 0 0 1 0 0 0 0 0 0 6 0 4 0 0 HTHTH
0 0 0 0 24 0 -1 0 0 0 0 0 0 -6 0 -16 0 0 HTHT
0 0 0 0 0 -48 1 0 0 0 0 0 0 30 0 16 0 0 HTH
0 0 0 0 0 0 95 0 0 0 0 0 0 -30 0 -64 0 0 HT
0 0 0 0 0 0 0 -95 0 0 0 0 0 30 0 64 0 0 H
0 0 0 0 0 0 0 0 -9120 0 0 0 0 2880 0 1584 0 -4560 THHHTHHT
0 0 0 0 0 0 0 0 0 18240 0 0 -9120 -2880 0 -1584 0 4560 THHHTHH
0 0 0 0 0 0 0 0 0 0 -36480 0 9120 7680 0 14256 0 -4560 THHHTH
0 0 0 0 0 0 0 0 0 0 0 72960 -9120 -7680 0 -50736 0 4560 THHHT
0 0 0 0 0 0 0 0 0 0 0 0 -136800 30720 0 99888 0 -4560 THHH
0 0 0 0 0 0 0 0 0 0 0 0 0 199680 0 -192048 0 4560 THH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -7587840 7357104 0 -114000 TH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 230736 0 114000 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -319953920 -157447680
249/506
2 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 HTHTHTHH
-1 2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 HTHTHTH
0 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 HTHTHT
0 0 -1 2 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 HTHTH
0 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 HTHT
0 0 0 0 -1 2 0 0 0 0 0 0 0 -1 0 0 0 0 HTH
0 0 0 0 0 -1 2 0 0 0 0 0 0 0 0 -1 0 0 HT
0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 H
0 0 0 0 0 0 0 0 2 0 0 0 -1 0 0 0 0 1 THHHTTHH
0 0 0 0 0 0 -1 0 -1 2 0 0 0 0 0 0 0 0 THHHTTH
0 0 0 0 0 0 0 0 0 -1 2 0 0 0 0 -1 0 0 THHHTT
0 0 0 0 0 -1 0 0 0 0 -1 2 0 0 0 0 0 0 THHHT
0 0 0 0 0 0 0 -1 0 0 0 -1 2 0 0 0 0 0 THHH
0 0 0 0 0 0 -1 0 0 0 0 0 -1 2 0 0 0 0 THH
0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 2 0 0 0 TH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 T
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 2 0
n: 9, a: THHHTTHHT, b: HTHTHTHHH
2 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 HTHTHTHH
0 -4 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 HTHTHTH
0 0 6 0 0 0 -1 0 0 0 0 0 0 0 0 -4 0 0 HTHTHT
0 0 0 -12 0 0 1 0 0 0 0 0 0 6 0 4 0 0 HTHTH
0 0 0 0 24 0 -1 0 0 0 0 0 0 -6 0 -16 0 0 HTHT
0 0 0 0 0 -48 1 0 0 0 0 0 0 30 0 16 0 0 HTH
0 0 0 0 0 0 95 0 0 0 0 0 0 -30 0 -64 0 0 HT
0 0 0 0 0 0 0 -95 0 0 0 0 0 30 0 64 0 0 H
0 0 0 0 0 0 0 0 2 0 0 0 -1 0 0 0 0 1 THHHTTHH
0 0 0 0 0 0 0 0 0 -380 0 0 95 60 0 128 0 -95 THHHTTH
0 0 0 0 0 0 0 0 0 0 760 0 -95 -60 0 -508 0 95 THHHTT
0 0 0 0 0 0 0 0 0 0 0 -9120 570 3240 0 4632 0 -570 THHHT
0 0 0 0 0 0 0 0 0 0 0 0 17670 -6120 0 -10776 0 570 THHH
0 0 0 0 0 0 0 0 0 0 0 0 0 -23640 0 22680 0 -570 THH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 898320 -869592 0 14250 TH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -28728 0 -14250 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18864720 9320070
83/168
2 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 THHHHHHH
-1 2 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 THHHHHH
0 -1 2 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 THHHHH
0 0 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 THHHH
0 0 0 -1 2 0 0 0 0 0 0 0 0 0 -1 0 0 THHH
0 0 0 0 -1 2 0 0 0 0 0 0 0 0 -1 0 0 THH
0 0 0 0 0 -1 2 0 0 0 0 0 0 0 -1 0 0 TH
0 0 0 0 0 0 0 2 0 0 0 0 0 0 -1 0 1 TTHHHHHH
0 0 0 0 0 0 0 -1 2 0 0 0 0 0 -1 0 0 TTHHHHH
0 0 0 0 0 0 0 0 -1 2 0 0 0 0 -1 0 0 TTHHHH
0 0 0 0 0 0 0 0 0 -1 2 0 0 0 -1 0 0 TTHHH
0 0 0 0 0 0 0 0 0 0 -1 2 0 0 -1 0 0 TTHH
0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 0 0 TTH
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 TT
0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 2 0 0 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0
n: 9, a: TTHHHHHHH, b: THHHHHHHH
2 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 THHHHHHH
0 -4 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 THHHHHH
0 0 8 0 0 0 0 0 0 0 0 0 0 0 -7 0 0 THHHHH
0 0 0 -16 0 0 0 0 0 0 0 0 0 0 15 0 0 THHHH
0 0 0 0 32 0 0 0 0 0 0 0 0 0 -31 0 0 THHH
0 0 0 0 0 -64 0 0 0 0 0 0 0 0 63 0 0 THH
0 0 0 0 0 0 128 0 0 0 0 0 0 0 -127 0 0 TH
0 0 0 0 0 0 0 2 0 0 0 0 0 0 -1 0 1 TTHHHHHH
0 0 0 0 0 0 0 0 -4 0 0 0 0 0 3 0 -1 TTHHHHH
0 0 0 0 0 0 0 0 0 8 0 0 0 0 -7 0 1 TTHHHH
0 0 0 0 0 0 0 0 0 0 -16 0 0 0 15 0 -1 TTHHH
0 0 0 0 0 0 0 0 0 0 0 32 0 0 -31 0 1 TTHH
0 0 0 0 0 0 0 0 0 0 0 0 -64 0 63 0 -1 TTH
0 0 0 0 0 0 0 0 0 0 0 0 0 64 -63 0 1 TT
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -3 0 -2 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2
2/3
2 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 TTHTHTHT
-1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 TTHTHTH
0 -1 2 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 TTHTHT
0 0 -1 2 0 0 0 0 0 0 0 0 0 0 0 -1 0 TTHTH
0 0 0 -1 2 0 -1 0 0 0 0 0 0 0 0 0 0 TTHT
0 0 0 0 -1 2 0 0 0 0 0 0 0 0 0 -1 0 TTH
0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 TT
0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 -1 1 THTHTHTH
0 0 0 0 0 0 -1 -1 2 0 0 0 0 0 0 0 0 THTHTHT
0 0 0 0 0 0 0 0 -1 2 0 0 0 0 0 -1 0 THTHTH
0 0 0 0 0 0 -1 0 0 -1 2 0 0 0 0 0 0 THTHT
0 0 0 0 0 0 0 0 0 0 -1 2 0 0 0 -1 0 THTH
0 0 0 0 0 0 -1 0 0 0 0 -1 2 0 0 0 0 THT
0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 0 TH
0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 2 0 0 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0
n: 9, a: THTHTHTHT, b: TTHTHTHTH
2 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 TTHTHTHT
0 -4 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 TTHTHTH
0 0 8 0 0 0 -5 0 0 0 0 0 0 0 0 -2 0 TTHTHT
0 0 0 -16 0 0 5 0 0 0 0 0 0 0 0 10 0 TTHTH
0 0 0 0 32 0 -21 0 0 0 0 0 0 0 0 -10 0 TTHT
0 0 0 0 0 -64 21 0 0 0 0 0 0 0 0 42 0 TTH
0 0 0 0 0 0 43 0 0 0 0 0 0 0 0 -42 0 TT
0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 -1 1 THTHTHTH
0 0 0 0 0 0 0 0 -172 0 0 0 0 0 0 127 -43 THTHTHT
0 0 0 0 0 0 0 0 0 344 0 0 0 0 0 -299 43 THTHTH
0 0 0 0 0 0 0 0 0 0 -688 0 0 0 0 635 -43 THTHT
0 0 0 0 0 0 0 0 0 0 0 1376 0 0 0 -1323 43 THTH
0 0 0 0 0 0 0 0 0 0 0 0 -2752 0 0 2667 -43 THT
0 0 0 0 0 0 0 0 0 0 0 0 0 5504 0 -5419 43 TH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -11008 10795 -43 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 213 43
43/213
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 HHHHHTHT
-1 2 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 HHHHHTH
0 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 HHHHHT
0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 HHHHH
0 0 0 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 HHHH
0 0 0 0 -1 2 0 0 0 0 0 0 0 0 0 -1 0 0 HHH
0 0 0 0 0 -1 2 0 0 0 0 0 0 0 0 -1 0 0 HH
0 0 0 0 0 0 -1 2 0 0 0 0 0 0 0 -1 0 0 H
0 0 0 0 0 0 0 0 2 0 0 0 0 -1 0 0 0 1 THHHHHTH
0 0 0 0 0 0 0 0 -1 2 0 0 0 0 0 -1 0 0 THHHHHT
0 0 0 -1 0 0 0 0 0 -1 2 0 0 0 0 0 0 0 THHHHH
0 0 0 0 0 0 0 0 0 0 -1 2 0 0 0 -1 0 0 THHHH
0 0 0 0 0 0 0 0 0 0 0 -1 2 0 0 -1 0 0 THHH
0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 0 0 THH
0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 TH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 T
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 2 0
n: 9, a: THHHHHTHT, b: HHHHHTHTH
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 HHHHHTHT
0 -4 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 HHHHHTH
0 0 8 0 0 0 0 0 0 0 0 0 0 -2 0 -5 0 0 HHHHHT
0 0 0 -8 0 0 0 0 0 0 0 0 0 2 0 5 0 0 HHHHH
0 0 0 0 16 0 0 0 0 0 0 0 0 -2 0 -13 0 0 HHHH
0 0 0 0 0 -32 0 0 0 0 0 0 0 2 0 29 0 0 HHH
0 0 0 0 0 0 64 0 0 0 0 0 0 -2 0 -61 0 0 HH
0 0 0 0 0 0 0 -128 0 0 0 0 0 2 0 125 0 0 H
0 0 0 0 0 0 0 0 2 0 0 0 0 -1 0 0 0 1 THHHHHTH
0 0 0 0 0 0 0 0 0 -4 0 0 0 1 0 2 0 -1 THHHHHT
0 0 0 0 0 0 0 0 0 0 16 0 0 -4 0 -9 0 2 THHHHH
0 0 0 0 0 0 0 0 0 0 0 -32 0 4 0 25 0 -2 THHHH
0 0 0 0 0 0 0 0 0 0 0 0 64 -4 0 -57 0 2 THHH
0 0 0 0 0 0 0 0 0 0 0 0 0 -124 0 121 0 -2 THH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 248 -245 0 2 TH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -3 0 -2 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15872 10540
85/128
2 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 THHTHHTT
-1 2 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 THHTHHT
0 -1 2 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 THHTHH
0 0 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 THHTH
0 0 0 -1 2 0 0 0 0 0 0 0 0 -1 0 0 0 THHT
0 0 0 0 -1 2 0 0 0 0 0 0 0 0 0 -1 0 THH
0 0 0 0 0 -1 2 0 0 0 0 0 0 0 -1 0 0 TH
-1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 TTHHTHHT
0 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 -1 0 TTHHTHH
0 0 0 0 0 0 0 0 -1 2 0 0 0 0 -1 0 0 TTHHTH
0 0 0 0 0 0 0 0 0 -1 2 0 0 -1 0 0 0 TTHHT
0 0 0 0 0 0 0 0 0 0 -1 2 0 0 0 -1 0 TTHH
0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 0 0 TTH
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 TT
0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 2 0 0 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0
n: 9, a: TTHHTHHTH, b: THHTHHTTT
2 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 THHTHHTT
0 -4 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 THHTHHT
0 0 8 -2 0 0 0 0 0 0 0 0 -1 0 0 -4 0 THHTHH
0 0 0 -14 0 0 0 0 0 0 0 0 1 0 8 4 0 THHTH
0 0 0 0 28 0 0 0 0 0 0 0 -1 -14 -8 -4 0 THHT
0 0 0 0 0 -56 0 0 0 0 0 0 1 14 8 32 0 THH
0 0 0 0 0 0 112 0 0 0 0 0 -1 -14 -64 -32 0 TH
0 0 0 0 0 0 0 -4 0 0 0 0 1 0 0 0 -2 TTHHTHHT
0 0 0 0 0 0 0 0 8 0 0 0 -1 0 0 -4 2 TTHHTHH
0 0 0 0 0 0 0 0 0 -16 0 0 1 0 8 4 -2 TTHHTH
0 0 0 0 0 0 0 0 0 0 32 0 -1 -16 -8 -4 2 TTHHT
0 0 0 0 0 0 0 0 0 0 0 -64 1 16 8 36 -2 TTHH
0 0 0 0 0 0 0 0 0 0 0 0 127 -16 -72 -36 2 TTH
0 0 0 0 0 0 0 0 0 0 0 0 0 -111 72 36 -2 TT
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1094232 -1031748 32258 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -62484 -32258
127/246
2 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 TTHTHTHT
-1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 TTHTHTH
0 -1 2 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 TTHTHT
0 0 -1 2 0 0 0 0 0 0 0 0 -1 0 0 0 0 TTHTH
0 0 0 -1 2 0 -1 0 0 0 0 0 0 0 0 0 0 TTHT
0 0 0 0 -1 2 0 0 0 0 0 0 -1 0 0 0 0 TTH
0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 TT
0 0 0 0 0 0 -1 2 0 0 0 0 0 0 0 0 1 THHHTHHT
0 0 0 0 0 0 0 -1 2 0 0 -1 0 0 0 0 0 THHHTHH
0 0 0 0 0 0 0 0 -1 2 0 0 0 0 -1 0 0 THHHTH
0 0 0 0 0 0 -1 0 0 -1 2 0 0 0 0 0 0 THHHT
0 0 0 0 0 0 0 0 0 0 -1 2 0 0 0 -1 0 THHH
0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 0 0 THH
0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 0 TH
0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 2 0 0 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0
n: 9, a: THHHTHHTH, b: TTHTHTHTH
2 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 TTHTHTHT
0 -4 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 TTHTHTH
0 0 8 0 0 0 -5 0 0 0 0 0 -2 0 0 0 0 TTHTHT
0 0 0 -16 0 0 5 0 0 0 0 0 10 0 0 0 0 TTHTH
0 0 0 0 32 0 -21 0 0 0 0 0 -10 0 0 0 0 TTHT
0 0 0 0 0 -64 21 0 0 0 0 0 42 0 0 0 0 TTH
0 0 0 0 0 0 43 0 0 0 0 0 -42 0 0 0 0 TT
0 0 0 0 0 0 0 -86 0 0 0 0 42 0 0 0 -43 THHHTHHT
0 0 0 0 0 0 0 0 172 0 0 -86 -42 0 0 0 43 THHHTHH
0 0 0 0 0 0 0 0 0 -344 0 86 42 0 172 0 -43 THHHTH
0 0 0 0 0 0 0 0 0 0 688 -86 -378 0 -172 0 43 THHHT
0 0 0 0 0 0 0 0 0 0 0 -1290 378 0 172 688 -43 THHH
0 0 0 0 0 0 0 0 0 0 0 0 2202 0 -1462 -688 43 THH
0 0 0 0 0 0 0 0 0 0 0 0 0 -4404 3664 688 -43 TH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -98384 87376 -5461 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11008 5461
127/256
2 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 THHHHHHH
-1 2 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 THHHHHH
0 -1 2 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 THHHHH
0 0 -1 2 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 THHHH
0 0 0 -1 2 0 0 -1 0 0 0 0 0 0 0 0 0 0 THHH
0 0 0 0 -1 2 0 -1 0 0 0 0 0 0 0 0 0 0 THH
0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 TH
0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 T
0 0 0 0 0 0 0 -1 2 0 0 0 0 0 0 0 0 1 HHHHHHHH
0 0 0 0 0 0 0 -1 -1 2 0 0 0 0 0 0 0 0 HHHHHHH
0 0 0 0 0 0 0 -1 0 -1 2 0 0 0 0 0 0 0 HHHHHH
0 0 0 0 0 0 0 -1 0 0 -1 2 0 0 0 0 0 0 HHHHH
0 0 0 0 0 0 0 -1 0 0 0 -1 2 0 0 0 0 0 HHHH
0 0 0 0 0 0 0 -1 0 0 0 0 -1 2 0 0 0 0 HHH
0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 2 0 0 0 HH
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 2 0 0 H
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 2 0
n: 9, a: HHHHHHHHH, b: THHHHHHHH
2 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 THHHHHHH
0 -4 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 THHHHHH
0 0 8 0 0 0 0 -7 0 0 0 0 0 0 0 0 0 0 THHHHH
0 0 0 -16 0 0 0 15 0 0 0 0 0 0 0 0 0 0 THHHH
0 0 0 0 32 0 0 -31 0 0 0 0 0 0 0 0 0 0 THHH
0 0 0 0 0 -64 0 63 0 0 0 0 0 0 0 0 0 0 THH
0 0 0 0 0 0 128 -127 0 0 0 0 0 0 0 0 0 0 TH
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 T
0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 HHHHHHHH
0 0 0 0 0 0 0 0 0 -4 0 0 0 0 0 0 0 -1 HHHHHHH
0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 1 HHHHHH
0 0 0 0 0 0 0 0 0 0 0 -16 0 0 0 0 0 -1 HHHHH
0 0 0 0 0 0 0 0 0 0 0 0 32 0 0 0 0 1 HHHH
0 0 0 0 0 0 0 0 0 0 0 0 0 -64 0 0 0 -1 HHH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 128 0 0 1 HH
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -256 0 -1 H
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 512 1
1/512
2 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 TTTHHHHT
-1 2 0 0 0 0 0 0 0 0 0 0 0 -1 0 TTTHHHH
0 -1 2 0 0 0 0 0 0 0 0 0 -1 0 0 TTTHHH
0 0 -1 2 0 0 0 0 0 0 0 0 -1 0 0 TTTHH
0 0 0 -1 2 0 0 0 0 0 0 0 -1 0 0 TTTH
0 0 0 0 0 2 0 0 0 0 0 0 -1 0 1 TTTTTHHH
0 0 0 0 0 -1 2 0 0 0 0 0 -1 0 0 TTTTTHH
0 0 0 0 0 0 -1 2 0 0 0 0 -1 0 0 TTTTTH
0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 TTTTT
0 0 0 0 -1 0 0 0 -1 2 0 0 0 0 0 TTTT
0 0 0 0 -1 0 0 0 0 -1 2 0 0 0 0 TTT
0 0 0 0 0 0 0 0 0 0 -1 2 0 -1 0 TT
0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 T
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0
n: 9, a: TTTTTHHHH, b: TTTHHHHTT
2 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 TTTHHHHT
0 -4 0 0 0 0 0 0 0 0 0 0 0 3 0 TTTHHHH
0 0 8 0 0 0 0 0 0 0 0 0 -4 -3 0 TTTHHH
0 0 0 -16 0 0 0 0 0 0 0 0 12 3 0 TTTHH
0 0 0 0 32 0 0 0 0 0 0 0 -28 -3 0 TTTH
0 0 0 0 0 2 0 0 0 0 0 0 -1 0 1 TTTTTHHH
0 0 0 0 0 0 -4 0 0 0 0 0 3 0 -1 TTTTTHH
0 0 0 0 0 0 0 8 0 0 0 0 -7 0 1 TTTTTH
0 0 0 0 0 0 0 0 -8 0 0 0 7 0 -1 TTTTT
0 0 0 0 0 0 0 0 0 -64 0 0 56 3 -4 TTTT
0 0 0 0 0 0 0 0 0 0 128 0 -112 -9 4 TTT
0 0 0 0 0 0 0 0 0 0 0 -256 112 137 -4 TT
0 0 0 0 0 0 0 0 0 0 0 0 400 -393 4 T
0 0 0 0 0 0 0 0 0 0 0 0 0 -7 -4
4/7
2 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 HTTHTHHH
-1 2 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 HTTHTHH
0 -1 2 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 HTTHTH
0 0 -1 2 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 HTTHT
0 0 0 -1 2 0 0 -1 0 0 0 0 0 0 0 0 0 0 HTTH
0 0 0 0 -1 2 0 0 0 0 0 0 0 -1 0 0 0 0 HTT
0 0 0 0 0 -1 2 -1 0 0 0 0 0 0 0 0 0 0 HT
0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 H
0 0 0 0 0 -1 0 0 2 0 0 0 0 0 0 0 0 1 TTTHTTHT
0 0 0 0 0 0 0 -1 -1 2 0 0 0 0 0 0 0 0 TTTHTTH
0 0 0 0 0 0 0 0 0 -1 2 0 0 -1 0 0 0 0 TTTHTT
0 0 0 0 0 0 0 -1 0 0 -1 2 0 0 0 0 0 0 TTTHT
0 0 0 0 0 0 0 -1 0 0 0 -1 2 0 0 0 0 0 TTTH
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 TTT
0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 2 0 0 0 TT
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 2 0 0 T
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 2 0
n: 9, a: TTTHTTHTH, b: HTTHTHHHT
2 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 HTTHTHHH
0 -4 0 0 0 0 2 1 0 0 0 0 0 0 0 0 0 0 HTTHTHH
0 0 8 0 0 0 -6 -1 0 0 0 0 0 0 0 0 0 0 HTTHTH
0 0 0 -16 0 8 6 1 0 0 0 0 0 0 0 0 0 0 HTTHT
0 0 0 0 32 -8 -6 -17 0 0 0 0 0 0 0 0 0 0 HTTH
0 0 0 0 0 -56 6 17 0 0 0 0 0 32 0 0 0 0 HTT
0 0 0 0 0 0 106 -73 0 0 0 0 0 -32 0 0 0 0 HT
0 0 0 0 0 0 0 -33 0 0 0 0 0 32 0 0 0 0 H
0 0 0 0 0 0 0 0 195888 0 0 0 0 -94976 0 0 0 97944 TTTHTTHT
0 0 0 0 0 0 0 0 0 -391776 0 0 0 284928 0 0 0 -97944 TTTHTTH
0 0 0 0 0 0 0 0 0 0 783552 0 0 -676704 0 0 0 97944 TTTHTT
0 0 0 0 0 0 0 0 0 0 0 -1567104 0 1436512 0 0 0 -97944 TTTHT
0 0 0 0 0 0 0 0 0 0 0 0 3134208 -2956128 0 0 0 97944 TTTH
0 0 0 0 0 0 0 0 0 0 0 0 0 -178080 0 0 0 -97944 TTT
0 0 0 0 0 0 0 0 0 0 0 0 0 0 2350656 0 0 1273272 TT
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -23506560 0 -12634776 T
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 47013120 25171608
257/480
maxCalc: 10985091600