# Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006

level: medium

position: ........2..9...4.3.34..271.8...4.6...9.1.7.......2..9..432......15..8...7..3....1 initial

# Autosolve

position: ........2..9...4.3.34..271.8.1.4.6...9.1.7.......2.19..432......15..8...7..3....1 autosolve

# Pair Reduction Variants

## Pair Reduction Analysis

The following important HDP chains were detected:

```* DIS # A1: 5,6 => CTR => A1: 1
* DIS # H4: 5,7 => CTR => H4: 2,3
* DIS # I6: 5,7 => CTR => I6: 4,8
* CNT   3 HDP CHAINS /  31 HYP OPENED
```

See Appendix: Full HDP Chains for full list of HDP chains.

## Pair Reduction

The following important HDP chains were detected:

```* DIS # A1: 5,6 => CTR => A1: 1
* DIS A1: 1 # H4: 5,7 => CTR => H4: 2,3
* DIS A1: 1 + H4: 2,3 # I6: 5,7 => CTR => I6: 4,8
* DIS A1: 1 + H4: 2,3 + I6: 4,8 # H5: 2,3 => CTR => H5: 4,5,8
* DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 # H8: 4,6,7 => CTR => H8: 2,3
* DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # A8: 2 => CTR => A8: 6,9
* PRF A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 # E7: 6,9 => SOL
* STA A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 + E7: 6,9
* CNT   7 HDP CHAINS /  52 HYP OPENED
```

See Appendix: Full HDP Chains for full list of HDP chains.

# Details

## Positions

 ........2..9...4.3.34..271.8...4.6...9.1.7.......2..9..432......15..8...7..3....1 initial ........2..9...4.3.34..271.8.1.4.6...9.1.7.......2.19..432......15..8...7..3....1 autosolve 178934562269715483534862719821549637396187254457623198643291875915478326782356941 solved

level: medium

## Pairing Analysis

```--------------------------------------------------
* PAIRS (8)
A3: 5,6
A5: 3,4
C5: 2,6
A6: 3,4
C6: 6,7
D4: 5,9
I4: 5,7
A7: 6,9

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
A1,A2: 1.. / A1 = 1  =>  8 pairs (_) / A2 = 1  =>  0 pairs (X)
E7,F7: 1.. / E7 = 1  =>  8 pairs (_) / F7 = 1  =>  9 pairs (_)
A2,B2: 2.. / A2 = 2  => 14 pairs (_) / B2 = 2  => 27 pairs (_)
B4,C5: 2.. / B4 = 2  => 17 pairs (_) / C5 = 2  => 14 pairs (_)
B4,H4: 2.. / B4 = 2  => 17 pairs (_) / H4 = 2  => 14 pairs (_)
A2,A8: 2.. / A2 = 2  => 14 pairs (_) / A8 = 2  => 27 pairs (_)
C5,C9: 2.. / C5 = 2  => 14 pairs (_) / C9 = 2  => 17 pairs (_)
E1,F1: 3.. / E1 = 3  =>  8 pairs (_) / F1 = 3  =>  0 pairs (X)
A5,A6: 3.. / A5 = 3  => 14 pairs (_) / A6 = 3  =>  9 pairs (_)
G8,H8: 3.. / G8 = 3  =>  8 pairs (_) / H8 = 3  =>  0 pairs (X)
F4,H4: 3.. / F4 = 3  => 13 pairs (_) / H4 = 3  => 15 pairs (_)
A6,F6: 3.. / A6 = 3  =>  9 pairs (_) / F6 = 3  => 14 pairs (_)
E1,E5: 3.. / E1 = 3  =>  8 pairs (_) / E5 = 3  =>  0 pairs (X)
G5,G8: 3.. / G5 = 3  =>  0 pairs (X) / G8 = 3  =>  8 pairs (_)
D1,F1: 4.. / D1 = 4  =>  8 pairs (_) / F1 = 4  =>  8 pairs (_)
A5,A6: 4.. / A5 = 4  =>  9 pairs (_) / A6 = 4  => 14 pairs (_)
D8,F9: 4.. / D8 = 4  =>  8 pairs (_) / F9 = 4  =>  8 pairs (_)
A6,I6: 4.. / A6 = 4  => 14 pairs (_) / I6 = 4  =>  9 pairs (_)
F9,H9: 4.. / F9 = 4  =>  8 pairs (_) / H9 = 4  =>  8 pairs (_)
D1,D8: 4.. / D1 = 4  =>  8 pairs (_) / D8 = 4  =>  8 pairs (_)
F1,F9: 4.. / F1 = 4  =>  8 pairs (_) / F9 = 4  =>  8 pairs (_)
B4,B6: 5.. / B4 = 5  => 14 pairs (_) / B6 = 5  => 13 pairs (_)
C5,E5: 6.. / C5 = 6  => 17 pairs (_) / E5 = 6  => 14 pairs (_)
C1,C6: 7.. / C1 = 7  => 13 pairs (_) / C6 = 7  => 10 pairs (_)
E5,D6: 8.. / E5 = 8  => 14 pairs (_) / D6 = 8  =>  8 pairs (_)
B9,C9: 8.. / B9 = 8  => 13 pairs (_) / C9 = 8  => 15 pairs (_)
D6,I6: 8.. / D6 = 8  =>  8 pairs (_) / I6 = 8  => 14 pairs (_)
C1,C9: 8.. / C1 = 8  => 13 pairs (_) / C9 = 8  => 15 pairs (_)
G1,I3: 9.. / G1 = 9  => 12 pairs (_) / I3 = 9  => 12 pairs (_)
D4,F4: 9.. / D4 = 9  =>  8 pairs (_) / F4 = 9  => 13 pairs (_)
A7,A8: 9.. / A7 = 9  =>  9 pairs (_) / A8 = 9  => 15 pairs (_)
* DURATION: 0:00:31.649234  START: 23:08:13.167515  END: 23:08:44.816749 2019-04-30
* CP COUNT: (31)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A6,A7,C5,C6,D4,I4)
* ........2..9...4.3.34..271.8.1.4.6...9.1.7.......2.19..432......15..8...7..3....1
* PAIR A3: 5,6 BLK 1
A1: 5,6,1                                # reduction candidate for 5,6
A1: 5,6 => CTR
* ....31..2129...4.3.34..271.8.1.4362..92167...3..82519494321....215..8...7..3..2.1
A1: 1                                    #  8 pairs
A2: 5,6,1,2                              # reduction candidate for 5,6
A2: 5,6                                  # 27 pairs
* PAIR A3: 5,6 ROW 3
D3: 5,6,8,9                              # reduction candidate for 5,6
D3: 5,6                                  # 11 pairs
E3: 5,6,8,9                              # reduction candidate for 5,6
E3: 5,6                                  # 11 pairs
I3: 5,6,8,9                              # reduction candidate for 5,6
I3: 5,6                                  # 15 pairs
* PAIR A5: 3,4 ROW 5
H5: 3,4,2,5,8                            # reduction candidate for 3,4
H5: 3,4                                  # 10 pairs
H5: 2,5,8                                #  8 pairs
* PAIR C5: 2,6 COL C
C9: 2,6,8                                # reduction candidate for 2,6
C9: 8                                    # 15 pairs
C9: 2,6                                  # 13 pairs
* PAIR C6: 6,7 BLK 4
B6: 6,7,5                                # reduction candidate for 6,7
B6: 6,7                                  # 14 pairs
B6: 5                                    # 13 pairs
* PAIR C6: 6,7 COL C
C1: 6,7,8                                # reduction candidate for 6,7
C1: 6,7                                  # 15 pairs
C1: 8                                    # 13 pairs
* PAIR D4: 5,9 BLK 5
F4: 5,9,3                                # reduction candidate for 5,9
F4: 5,9                                  # 15 pairs
F4: 3                                    # 13 pairs
* PAIR D4: 5,9 COL D
D1: 5,9,4,6,7,8                          # reduction candidate for 5,9
D1: 5,9                                  # 11 pairs
D3: 5,9,6,8                              # reduction candidate for 5,9
D3: 5,9                                  # 10 pairs
* PAIR I4: 5,7 BLK 6
H4: 5,7,2,3                              # reduction candidate for 5,7
H4: 5,7 => CTR
* 1.8.395622695714835346827198219436..496157..8357826194.43215876.15..8...7823....1
H4: 2,3                                  #  9 pairs
I6: 5,7,4,8                              # reduction candidate for 5,7
I6: 5,7 => CTR
* ....3...2..9...4.3.34..271.821.4.63.39.167...4..82319..432......15..83..7..3....1
I6: 4,8                                  # 10 pairs
* PAIR I4: 5,7 ROW 4
B4: 5,7,2                                # reduction candidate for 5,7
B4: 2                                    # 17 pairs
B4: 5,7                                  # 14 pairs
* PAIR I4: 5,7 COL I
I7: 5,7,6,8,9                            # reduction candidate for 5,7
I7: 5,7                                  # 14 pairs
I7: 6,8,9                                #  8 pairs
* PAIR A7: 6,9 BLK 7
A8: 6,9,2                                # reduction candidate for 6,9
A8: 2                                    # 27 pairs
A8: 6,9                                  # 14 pairs
* PAIR A7: 6,9 ROW 7
E7: 6,9,1,5,7                            # reduction candidate for 6,9
E7: 6,9                                  # 14 pairs
F7: 6,9,1,5                              # reduction candidate for 6,9
F7: 6,9                                  # 13 pairs
I7: 6,9,5,7,8                            # reduction candidate for 6,9
I7: 6,9                                  # 11 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060514-absurd-base-pr-000.dot
* REASONING
* DIS # A1: 5,6 => CTR => A1: 1
* DIS # H4: 5,7 => CTR => H4: 2,3
* DIS # I6: 5,7 => CTR => I6: 4,8
* CNT   3 HDP CHAINS /  31 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A3,A5,A6,A7,C5,C6,D4,I4)
* ........2..9...4.3.34..271.8.1.4.6...9.1.7.......2.19..432......15..8...7..3....1
* PAIR A3: 5,6 BLK 1
A1: 5,6,1                                # reduction candidate for 5,6
A1: 5,6 => CTR
* ....31..2129...4.3.34..271.8.1.4362..92167...3..82519494321....215..8...7..3..2.1
A2: 5,6,2                                # reduction candidate for 5,6
A2: 5,6                                  # 27 pairs
* RESTART
* PAIR A3: 5,6 BLK 1
A2: 5,6,2                                # reduction candidate for 5,6
A2: 5,6                                  # 27 pairs
A2: 2                                    # 14 pairs
* PAIR A3: 5,6 ROW 3
D3: 5,6,8,9                              # reduction candidate for 5,6
D3: 5,6                                  # 11 pairs
E3: 5,6,8,9                              # reduction candidate for 5,6
E3: 5,6                                  # 11 pairs
I3: 5,6,8,9                              # reduction candidate for 5,6
I3: 5,6                                  # 15 pairs
* PAIR A5: 3,4 ROW 5
H5: 3,4,2,5,8                            # reduction candidate for 3,4
H5: 3,4                                  # 10 pairs
H5: 2,5,8                                #  8 pairs
* PAIR C5: 2,6 COL C
C9: 2,6,8                                # reduction candidate for 2,6
C9: 8                                    # 15 pairs
C9: 2,6                                  # 13 pairs
* PAIR C6: 6,7 BLK 4
B6: 6,7,5                                # reduction candidate for 6,7
B6: 6,7                                  # 14 pairs
B6: 5                                    # 13 pairs
* PAIR C6: 6,7 COL C
C1: 6,7,8                                # reduction candidate for 6,7
C1: 6,7                                  # 15 pairs
C1: 8                                    # 13 pairs
* PAIR D4: 5,9 BLK 5
F4: 5,9,3                                # reduction candidate for 5,9
F4: 5,9                                  # 15 pairs
F4: 3                                    # 13 pairs
* PAIR D4: 5,9 COL D
D1: 5,9,4,6,7,8                          # reduction candidate for 5,9
D1: 5,9                                  # 11 pairs
D3: 5,9,6,8                              # reduction candidate for 5,9
D3: 5,9                                  # 10 pairs
* PAIR I4: 5,7 BLK 6
H4: 5,7,2,3                              # reduction candidate for 5,7
H4: 5,7 => CTR
* 1.8.395622695714835346827198219436..496157..8357826194.43215876.15..8...7823....1
I6: 5,7,4,8                              # reduction candidate for 5,7
I6: 5,7 => CTR
* 1...3...2..9...4.3.34..271.821.4.63.39.167...4..82319..432......15..83..7..3....1
* PAIR A7: 6,9 BLK 7
A8: 6,9,2                                # reduction candidate for 6,9
A8: 2                                    # 27 pairs
A8: 6,9                                  # 16 pairs
* PAIR A7: 6,9 ROW 7
E7: 6,9,1,5,7                            # reduction candidate for 6,9
E7: 6,9                                  # 17 pairs
F7: 6,9,1,5                              # reduction candidate for 6,9
F7: 6,9                                  # 16 pairs
I7: 6,9,5,8                              # reduction candidate for 6,9
I7: 6,9                                  # 13 pairs

* LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A3,A5,A6,A7,B4,C5,C6,D4,H4,I6)
* 1.......2..9...4.3.34..271.8.1.4.6.7.9.1.7.......2.19..432......15..8...7..3....1
* PAIR A3: 5,6 BLK 1
A2: 5,6,2                                # reduction candidate for 5,6
A2: 5,6                                  # 27 pairs
A2: 2                                    # 16 pairs
* PAIR A3: 5,6 ROW 3
D3: 5,6,8,9                              # reduction candidate for 5,6
D3: 5,6                                  # 13 pairs
E3: 5,6,8,9                              # reduction candidate for 5,6
E3: 5,6                                  # 13 pairs
I3: 5,6,8,9                              # reduction candidate for 5,6
I3: 5,6                                  # 17 pairs
* PAIR A5: 3,4 ROW 5
H5: 3,4,2,5,8                            # reduction candidate for 3,4
H5: 3,4                                  # 13 pairs
H5: 2,5,8                                # 11 pairs
* PAIR C5: 2,6 COL C
C9: 2,6,8                                # reduction candidate for 2,6
C9: 8                                    # 15 pairs
C9: 2,6                                  # 14 pairs
* PAIR C6: 6,7 BLK 4
B6: 6,7,5                                # reduction candidate for 6,7
B6: 5                                    # 15 pairs
B6: 6,7                                  # 14 pairs
* PAIR C6: 6,7 COL C
C1: 6,7,8                                # reduction candidate for 6,7
C1: 6,7                                  # 15 pairs
C1: 8                                    # 14 pairs
* PAIR D4: 5,9 BLK 5
F4: 5,9,3                                # reduction candidate for 5,9
F4: 5,9                                  # 15 pairs
F4: 3                                    # 14 pairs
* PAIR D4: 5,9 COL D
D1: 5,9,4,6,7,8                          # reduction candidate for 5,9
D1: 5,9                                  # 16 pairs
D3: 5,9,6,8                              # reduction candidate for 5,9
D3: 5,9                                  # 12 pairs
* PAIR H4: 2,3 BLK 6
G5: 2,3,5,8                              # reduction candidate for 2,3
G5: 2,3                                  # 11 pairs
H5: 2,3,4,5,8                            # reduction candidate for 2,3
H5: 2,3 => CTR
* 1...3.9.2.29...4.3.34.927188519436274921678353..8251949432..5862156783.97..3..2.1
* RESTART
* PAIR H4: 2,3 COL H
H8: 2,3,4,6,7                            # reduction candidate for 2,3
H8: 4,6,7 => CTR
* 1.......2..9...4.3.34..271.8.1.4.637.9.1.72......2.19..432.....215..83..7..3...21
* PAIR RESTART
* PAIR I6: 4,8 BLK 6
H5: 4,8,5                                # reduction candidate for 4,8
H5: 4,8                                  # 13 pairs
I5: 4,8,5                                # reduction candidate for 4,8
I5: 4,8                                  # 23 pairs
* PAIR A7: 6,9 BLK 7
A8: 6,9,2                                # reduction candidate for 6,9
A8: 2 => CTR
* 1...3...2.29...4.3.34..271.851943627.921673..3..8251949432...7.2154789367..3..241
* PAIR A7: 6,9 ROW 7
E7: 6,9,1,5                              # reduction candidate for 6,9
E7: 6,9 => SOLVED
* 178934562269715483534862719821549637396187254457623198643291875915478326782356941
* DURATION: 0:00:32.506753  START: 23:09:01.631236  END: 23:09:34.137989 2019-04-30
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060514-absurd-base-pr-001.dot
* REASONING
* DIS # A1: 5,6 => CTR => A1: 1
* DIS A1: 1 # H4: 5,7 => CTR => H4: 2,3
* DIS A1: 1 + H4: 2,3 # I6: 5,7 => CTR => I6: 4,8
* DIS A1: 1 + H4: 2,3 + I6: 4,8 # H5: 2,3 => CTR => H5: 4,5,8
* DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 # H8: 4,6,7 => CTR => H8: 2,3
* DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # A8: 2 => CTR => A8: 6,9
* PRF A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 # E7: 6,9 => SOL
* STA A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 + E7: 6,9
* CNT   7 HDP CHAINS /  52 HYP OPENED
```

```http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=May&YEAR=2006, 20060514, absurd
```

# Solution

position: 178934562269715483534862719821549637396187254457623198643291875915478326782356941 solved

See section Pair Reduction for the HDP chains leading to this result.

# Appendix: Full HDP Chains

## A1. Pair Reduction Analysis

Full list of HDP chains traversed:

```* DIS # A1: 5,6 => CTR => A1: 1
* INC # A1: 1 => UNS
* INC # A2: 5,6 => UNS
* INC # D3: 5,6 => UNS
* INC # E3: 5,6 => UNS
* INC # I3: 5,6 => UNS
* INC # H5: 3,4 => UNS
* INC # H5: 2,5,8 => UNS
* INC # C9: 2,6 => UNS
* INC # C9: 8 => UNS
* INC # B6: 6,7 => UNS
* INC # B6: 5 => UNS
* INC # C1: 6,7 => UNS
* INC # C1: 8 => UNS
* INC # F4: 5,9 => UNS
* INC # F4: 3 => UNS
* INC # D1: 5,9 => UNS
* INC # D3: 5,9 => UNS
* DIS # H4: 5,7 => CTR => H4: 2,3
* INC # H4: 2,3 => UNS
* DIS # I6: 5,7 => CTR => I6: 4,8
* INC # I6: 4,8 => UNS
* INC # B4: 5,7 => UNS
* INC # B4: 2 => UNS
* INC # I7: 5,7 => UNS
* INC # I7: 6,8,9 => UNS
* INC # A8: 6,9 => UNS
* INC # A8: 2 => UNS
* INC # E7: 6,9 => UNS
* INC # F7: 6,9 => UNS
* INC # I7: 6,9 => UNS
* CNT  31 HDP CHAINS /  31 HYP OPENED
```

## A2. Pair Reduction

Full list of HDP chains traversed:

```* DIS # A1: 5,6 => CTR => A1: 1
* INC A1: 1 # A2: 5,6 => UNS
* INC A1: 1 # A2: 5,6 => UNS
* INC A1: 1 # A2: 2 => UNS
* INC A1: 1 # D3: 5,6 => UNS
* INC A1: 1 # E3: 5,6 => UNS
* INC A1: 1 # I3: 5,6 => UNS
* INC A1: 1 # H5: 3,4 => UNS
* INC A1: 1 # H5: 2,5,8 => UNS
* INC A1: 1 # C9: 2,6 => UNS
* INC A1: 1 # C9: 8 => UNS
* INC A1: 1 # B6: 6,7 => UNS
* INC A1: 1 # B6: 5 => UNS
* INC A1: 1 # C1: 6,7 => UNS
* INC A1: 1 # C1: 8 => UNS
* INC A1: 1 # F4: 5,9 => UNS
* INC A1: 1 # F4: 3 => UNS
* INC A1: 1 # D1: 5,9 => UNS
* INC A1: 1 # D3: 5,9 => UNS
* DIS A1: 1 # H4: 5,7 => CTR => H4: 2,3
* DIS A1: 1 + H4: 2,3 # I6: 5,7 => CTR => I6: 4,8
* INC A1: 1 + H4: 2,3 + I6: 4,8 # A8: 6,9 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # A8: 2 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # E7: 6,9 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # F7: 6,9 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # I7: 6,9 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # A2: 5,6 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # A2: 2 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # D3: 5,6 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # E3: 5,6 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # I3: 5,6 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # H5: 3,4 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # H5: 2,5,8 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # C9: 2,6 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # C9: 8 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # B6: 6,7 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # B6: 5 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # C1: 6,7 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # C1: 8 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # F4: 5,9 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # F4: 3 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # D1: 5,9 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # D3: 5,9 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 # G5: 2,3 => UNS
* DIS A1: 1 + H4: 2,3 + I6: 4,8 # H5: 2,3 => CTR => H5: 4,5,8
* INC A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 # H8: 2,3 => UNS
* DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 # H8: 4,6,7 => CTR => H8: 2,3
* INC A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # H5: 4,8 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # I5: 4,8 => UNS
* INC A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # A8: 6,9 => UNS
* DIS A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 # A8: 2 => CTR => A8: 6,9
* PRF A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 # E7: 6,9 => SOL
* STA A1: 1 + H4: 2,3 + I6: 4,8 + H5: 4,5,8 + H8: 2,3 + A8: 6,9 + E7: 6,9
* CNT  52 HDP CHAINS /  52 HYP OPENED
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