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Lean statement

Reconstruction of the 35-move Snaky certificate

Lean is a language for mathematical statements and proofs that a computer can verify. This page shows one statement file from OpenAI’s release, possible paper matches and independent reports. The code-like names below identify the definitions or theorems selected by the proof-verification settings.

Theorem selected for verification: OAI.SnakyCertificate.certificate_correct

Lean statement file: SnakyCertificate.leanShow on the mapOpenAI’s Lean catalogue does not list this as a main result; the release’s Lean notes for family 187 link it.

The Lean statement

The lines of the Lean statement that state the theorem, then the definitions in the file that it uses.

theorem certificate_correct :    TableValid ∧ placementCount = 1837 ∧    Output 557 (-1, 0) 118 19 {p | p.1 ≤ -3 ∧ p.2 ≤ -2} ∧    Output 595 (-1, 0) 222 27 {p | p.1 = -2 ∧ p.2 ≤ -2} ∧    Output 603 (-1, 0) 275 27 {p | p.1 ≤ -3 ∧ p.2 = 0} ∧    Output 615 (1, 0) 686 34 {(1, -1)} ∧    AllRows := by  sorry

A Lean statement states the theorem and leaves its proof as sorry on purpose. OpenAI’s proof is in a separate solution module, and a program called Comparator checks that proof against this statement.

Definitions needed to read it

Local definitions the statement names, followed through the definitions they name in turn. The match is by name in the source text, so a name reached only through notation can be missed; the full file is below.

  • abbreviation OAI.SnakyCertificate.Cell line 11

    abbrev Cell := ℤ × ℤ
  • definition OAI.SnakyCertificate.origin line 13

    def origin : Cell := (0, 0)
  • structure OAI.SnakyCertificate.Term line 37

    structure Term where  child : ℕ  rotation : Fin 8  xDigit : Fin 10  yDigit : Fin 10  deriving DecidableEq, Repr
  • structure OAI.SnakyCertificate.Entry line 46

    structure Entry where  index : ℕ  terms : List Term  deriving DecidableEq, Repr
  • definition OAI.SnakyCertificate.emptyEntry line 51

    def emptyEntry : Entry := ⟨0, []⟩
  • definition OAI.SnakyCertificate.entry_6 line 53

    def entry_6 : Entry := ⟨6, [⟨0, 0, 0, 3⟩]⟩
  • definition OAI.SnakyCertificate.entry_7 line 55

    def entry_7 : Entry := ⟨7, [⟨4, 0, 3, 4⟩, ⟨6, 0, 5, 4⟩]⟩
  • definition OAI.SnakyCertificate.entry_8 line 57

    def entry_8 : Entry := ⟨8, [⟨0, 4, 8, 3⟩, ⟨6, 4, 3, 4⟩]⟩
  • definition OAI.SnakyCertificate.entry_9 line 59

    def entry_9 : Entry := ⟨9, [⟨0, 4, 5, 4⟩, ⟨6, 4, 0, 5⟩]⟩
  • definition OAI.SnakyCertificate.entry_10 line 61

    def entry_10 : Entry := ⟨10, [⟨2, 0, 2, 3⟩, ⟨2, 6, 2, 4⟩]⟩
  • definition OAI.SnakyCertificate.entry_11 line 63

    def entry_11 : Entry := ⟨11, [⟨6, 4, 2, 5⟩, ⟨6, 6, 2, 3⟩]⟩
  • definition OAI.SnakyCertificate.entry_12 line 65

    def entry_12 : Entry := ⟨12, [⟨0, 6, 5, 4⟩, ⟨0, 0, 0, 3⟩]⟩
  • definition OAI.SnakyCertificate.entry_13 line 67

    def entry_13 : Entry := ⟨13, [⟨6, 6, 0, 3⟩, ⟨6, 4, 0, 5⟩]⟩
  • definition OAI.SnakyCertificate.entry_14 line 69

    def entry_14 : Entry := ⟨14, [⟨0, 6, 5, 4⟩, ⟨3, 6, 1, 4⟩]⟩
  • definition OAI.SnakyCertificate.entry_15 line 71

    def entry_15 : Entry := ⟨15, [⟨0, 6, 6, 4⟩, ⟨3, 6, 2, 4⟩]⟩
  • definition OAI.SnakyCertificate.entry_16 line 73

    def entry_16 : Entry := ⟨16, [⟨3, 6, 3, 4⟩, ⟨0, 6, 7, 4⟩]⟩
  • definition OAI.SnakyCertificate.entry_17 line 75

    def entry_17 : Entry := ⟨17, [⟨0, 6, 5, 4⟩, ⟨3, 0, 3, 3⟩]⟩
  • definition OAI.SnakyCertificate.entry_18 line 77

    def entry_18 : Entry := ⟨18, [⟨3, 6, 2, 4⟩, ⟨3, 0, 4, 3⟩]⟩
  • definition OAI.SnakyCertificate.entry_19 line 79

    def entry_19 : Entry := ⟨19, [⟨6, 4, 1, 5⟩, ⟨6, 0, 6, 5⟩]⟩
  • definition OAI.SnakyCertificate.entry_20 line 81

    def entry_20 : Entry := ⟨20, [⟨6, 4, 0, 5⟩, ⟨6, 0, 5, 5⟩]⟩
  • definition OAI.SnakyCertificate.entry_21 line 83

    def entry_21 : Entry := ⟨21, [⟨4, 6, 2, 3⟩, ⟨6, 0, 6, 5⟩]⟩
  • definition OAI.SnakyCertificate.entry_22 line 85

    def entry_22 : Entry := ⟨22, [⟨0, 6, 7, 5⟩, ⟨3, 0, 5, 4⟩]⟩
  • definition OAI.SnakyCertificate.entry_23 line 87

    def entry_23 : Entry := ⟨23, [⟨0, 6, 6, 4⟩, ⟨0, 0, 1, 3⟩]⟩
  • definition OAI.SnakyCertificate.entry_24 line 89

    def entry_24 : Entry := ⟨24, [⟨0, 0, 0, 3⟩, ⟨17, 0, 5, 4⟩]⟩

84 more definitions are reached the same way; the full file lists them.

Possible paper match, with no recorded review

Atlas selected this possible match by comparing words in the Lean statement with every statement in the family. No review of whether the statements mean the same thing is recorded.

Words of the Lean statement, its names split into words, that also appear in the theorem: row, envelope, array, terms, point, disjoint, base, certificate and two more. Shared only with the release’s name for the Lean statement or OpenAI’s note on it: conditional, avoids, four, move, maker and breaker.

Proposition 10 of Snaky in 21 Maker moves

Proposition

The 35-move certificate has 616 cards, including its six base cards, and 1,837 placement terms. Every card satisfies A_i^{35}\subsetneq T_i^{35}, o\in T_i^{35}\setminus A_i^{35}, and h_i^{35}\le34. Four of its conditional interfaces are

\begin{array}{c|c|r|r|l} i&A_i^{35}&|T_i^{35}|&h_i^{35}&\text{region disjoint from }T_i^{35}\\ \hline 557&\{(-1,0)\}&118&19&\{(x,y):x\le-3,\ y\le-2\}\\ 595&\{(-1,0)\}&222&27&\{(x,y):x=-2,\ y\le-2\}\\ 603&\{(-1,0)\}&275&27&\{(x,y):x\le-3,\ y=0\}\\ 615&\{(1,0)\}&686&34&\{(1,-1)\}. \end{array}

Each row applies at any Maker turn with its required point owned and its entire envelope free of Breaker, regardless of all other ownership. For row 615 there is also a Breaker-turn conclusion: if Maker owns \{o,(1,0)\} and Breaker avoids T_{615}^{35}, then after any legal next reply Maker wins within 33 further claims, unless already victorious.

Appendix, The 35-move construction and its conditional interfaces Read it in the paper TeX source, line 150
Show the TeX
The 35-move certificate has 616 cards, including its six base cards,
and 1,837 placement terms.  Every card satisfies
\(A_i^{35}\subsetneq T_i^{35}\),
\(o\in T_i^{35}\setminus A_i^{35}\), and \(h_i^{35}\le34\).
Four of its conditional interfaces are
\begin{equation}
\begin{array}{c|c|r|r|l}
 i&A_i^{35}&|T_i^{35}|&h_i^{35}&\text{region disjoint from }T_i^{35}\\ \hline
 557&\{(-1,0)\}&118&19&\{(x,y):x\le-3,\ y\le-2\}\\
 595&\{(-1,0)\}&222&27&\{(x,y):x=-2,\ y\le-2\}\\
 603&\{(-1,0)\}&275&27&\{(x,y):x\le-3,\ y=0\}\\
 615&\{(1,0)\}&686&34&\{(1,-1)\}.
\end{array}
\end{equation}
Each row applies at any Maker turn with its required point owned and
its entire envelope free of Breaker, regardless of all other ownership.
For row 615 there is also a Breaker-turn conclusion: if Maker owns
\(\{o,(1,0)\}\) and Breaker avoids \(T_{615}^{35}\), then after any
legal next reply Maker wins within 33 further claims, unless already
victorious.

Other possible paper matches, closest wording first

  • Proposition 5 of Snaky in 21 Maker moves. Words of the Lean statement, its names split into words, that also appear in the theorem: child, list, data, valid, placement and heights. Shared only with the release’s name for the Lean statement or OpenAI’s note on it: appendix and finite.
  • Proposition 8 of Snaky in 21 Maker moves. Words of the Lean statement, its names split into words, that also appear in the theorem: placed, max, valid, height, required and cell.
  • Proposition 7 of Snaky in 21 Maker moves. Words of the Lean statement, its names split into words, that also appear in the theorem: cells. Shared only with the release’s name for the Lean statement or OpenAI’s note on it: four, finite, position, maker and breaker.
  • Corollary 6 of Snaky in 21 Maker moves. Words of the Lean statement, its names split into words, that also appear in the theorem: empty and cell. Shared only with the release’s name for the Lean statement or OpenAI’s note on it: finite, maker and breaker.
  • Theorem 11 of Snaky in 21 Maker moves. Words of the Lean statement, its names split into words, that also appear in the theorem: empty and required. Shared only with the release’s name for the Lean statement or OpenAI’s note on it: position, maker and breaker.
  • Proposition 9 of Snaky in 21 Maker moves. Words of the Lean statement, its names split into words, that also appear in the theorem: empty. Shared only with the release’s name for the Lean statement or OpenAI’s note on it: move, position, maker and breaker.

How Atlas selects possible matches: it compares words in the Lean statement with every statement in the family. It also splits Lean names into words. The release’s label and note receive less weight; a main theorem wins a close match. If the Lean wording yields no clear match, Atlas uses the catalogue description. This selects passages to compare; it does not establish that they mean the same thing.

Reported Comparator runs

three independent groups report that Comparator accepted runs for this Lean statement file: Carlos Toledo’s cert-machine; MathVet; Neal McBurnett’s openai-math-lean-tooling. Each group reports its own Comparator run for this statement file. Atlas has not repeated the runs.

For a configured theorem, Comparator tests whether OpenAI’s proof proves the exact Lean statement. Some files instead configure definitions for comparison by name and type. Acceptance does not establish that the statement means the same thing as the paper’s theorem.

Carlos Toledo’s cert-machine

How they ran it, in their words

Every Comparator challenge re-run on Linux with nanoda switched on, decided by a preregistered rule; every family’s challenge statements read against OpenAI’s headline, clause by clause. Decider: Comparator (leanprover/comparator d03acab1 = tag v4.34.0, built with the release’s toolchain v4.34.1), lean4export 076e8e57, landrun 811cfff5, nanoda_lib 3a240721 — on GitHub’s Linux runners (.github/workflows/openai-math-kernel.yml), one j…

  • Accepted Their term: “CERTIFIED”.

    Re-run through Comparator with the independent nanoda kernel switched on: Lean’s kernel and nanoda both accept OpenAI’s solution.

    Reported 10 October 2026, at the release version shown here. Original verification report

MathVet

How they ran it, in their words

An independent, model-assisted, pre-referee reading of each family’s challenge statements against its headline claim under a published rubric (PROTOCOL.md), with its own Comparator runs per challenge. Its protocol describes a planned error-rate study; this import does not establish that the study has been completed.

  • Accepted Their term: “comparator-sandboxed-pass”.

    Re-run through Comparator in a sandboxed virtual machine: accepted.

    Reported 8 October 2026, at the release version shown here. Original verification report

Neal McBurnett’s openai-math-lean-tooling

How they ran it, in their words

Each challenge’s solution is built and checked by Comparator at the pinned release, on Lean leanprover/lean4:v4.34.1, recording the verdict, the check time and the peak memory; the run was still in progress at this snapshot (192 accepted, 224 pending).

  • Accepted Their term: “accepted”.

    Re-run through Comparator with Lean’s kernel: accepted (the check took 1093 s; peak memory 8.7 GiB).

    Reported 11 October 2026, at the release version shown here. Original verification report

What an accepted Comparator run would establish

If Comparator is run under this configuration and accepts, the solution proves the configured theorem using only the allowed axioms, and the Lean kernel accepts every step.

This configuration lists no definition holes, so every definition the statement uses is compared as it is written in this file.

Allowed axioms: propext, Quot.sound, Classical.choice

Acceptance leaves open whether the Lean statement means the same thing as the paper’s theorem, whether the paper’s other claims are correct, and whether the result is new. Those questions require comparing the definitions and statements, reviewing the paper’s arguments, and reading the earlier literature.

Do family 187’s Lean statements express the advertised result?

These assessments compare all the family’s Lean statements with the whole result OpenAI describes in its catalogue. They do not assess this statement alone. Each group uses its own published rules.

MathVet and cert-machine agree on how much of the advertised result the Lean statements express.

  • MathVet

    Finds the whole advertised result stated or implied Their term: “full”.

    The challenge statements imply the headline claim after unpacking definitions or one routine step. Their record

    Their note: SnakyPrototype.snaky_winning_strategy_21_with_legal_states : ∃ σ : Policy Cell, (∀ r M B, σ r M B ∉ M ∧ σ r M B ∉ B) ∧ ∀ β, LegalRepliesBeforeFinal σ 21 β ∅ ∅ → HasSnaky (playState σ 21 β ∅ ∅ 21).1 ∧ ...card = 21 ∧ ... on ℤ×ℤ with all 8 dihedral orientations plus translations, Maker first. The other two challenges are supporting: SnakyCertificate.certificate_correct checks a 610-row certificate table (TableValid ∧ placementCount = 1837 ∧ Output 557 ...), and SnakyConditional is actually the N=35 strategy from the empty board, NOT the 'four conditional winning templates' the docs describe (docs/Lean mismatch).

    Definitions the group asks readers to compare with the paper: Hand-rolled game model: Policy α := ℕ → Finset α → Finset α → α, playState σ N β M₀ B₀ with Breaker as a fixed sequence β : ℕ → Cell (equivalent to an adaptive Breaker against a deterministic σ) and LegalRepliesBeforeFinal constraining Breaker only for k + 1 < N; looks faithful (final reply unused).

  • Carlos Toledo’s cert-machine

    Finds the whole advertised result stated or implied Their term: “MATCHES”.

    The challenge statements state the headline as OpenAI wrote it. Their record

Read the complete assessments on the family page.

OpenAI’s own note on what this Lean statement covers

“The linked supplements reconstruct the older $35$-move appendix's finite recursive certificate and prove four conditional winning templates from partial positions, assuming the required Maker cells are present and Breaker avoids the corresponding finite envelope.”

An AI agent drafted an interpretation of that note, classifying this statement as “states a supporting result”. No human review of the draft is recorded.

Supporting material

The complete Lean statement file

1,398 lines, copied from release version fd4aeeb. A name defined in this file links to its line; pointing at the name shows its definition.

Declared in this fileOpenAI’s library at fd4aeebOther linked names open the current documentation for Mathlib, Lean’s mathematical library.

Links in the file: 1,366 to its own declarations, 68 to Mathlib’s documentation. 670 declared names also link to the same declaration in OpenAI’s library. OpenAI uses Mathlib version d13f23b. The linked documentation describes the current version, so names that have since changed may be missing there.

import Mathlibnamespace OAInamespace SnakyCertificateinstance rotationModulus_neZero : NeZero 8 := @Nat.instNeZeroSucc 7instance digitModulus_neZero : NeZero 10 := @Nat.instNeZeroSucc 9abbrev Cell := ℤ × ℤdef origin : Cell := (0, 0)def snaky : Finset Cell := {(0, 0), (1, 0), (2, 0), (3, 0), (3, 1), (4, 1)}def orient (r : Fin 8) (p : Cell) : Cell :=  match r.val with  | 0 => (p.1, p.2)  | 1 => (p.2, p.1)  | 2 => (p.1, -p.2)  | 3 => (-p.2, p.1)  | 4 => (-p.1, p.2)  | 5 => (p.2, -p.1)  | 6 => (-p.1, -p.2)  | _ => (-p.2, -p.1)def placement (r : Fin 8) (t p : Cell) : Cell := orient r p + tdef basePoint (i : Fin 6) : Cell := ![(0,0),(1,0),(2,0),(3,0),(3,1),(4,1)] idef baseEnvelope (i : Fin 6) : Finset Cell :=  snaky.image (placement 0 (-basePoint i))def baseRequired (i : Fin 6) : Finset Cell := (baseEnvelope i).erase originstructure Term where  child : ℕ  rotation : Fin 8  xDigit : Fin 10  yDigit : Fin 10  deriving DecidableEq, Reprdef Term.shift (t : Term) : Cell := ((t.xDigit.val : ℤ) - 4, (t.yDigit.val : ℤ) - 4)structure Entry where  index : ℕ  terms : List Term  deriving DecidableEq, Reprdef emptyEntry : Entry := ⟨0, []⟩def entry_6 : Entry := ⟨6, [⟨0, 0, 0, 3⟩]⟩def entry_7 : Entry := ⟨7, [⟨4, 0, 3, 4⟩, ⟨6, 0, 5, 4⟩]⟩def entry_8 : Entry := ⟨8, [⟨0, 4, 8, 3⟩, ⟨6, 4, 3, 4⟩]⟩def entry_9 : Entry := ⟨9, [⟨0, 4, 5, 4⟩, ⟨6, 4, 0, 5⟩]⟩def entry_10 : Entry := ⟨10, [⟨2, 0, 2, 3⟩, ⟨2, 6, 2, 4⟩]⟩def entry_11 : Entry := ⟨11, [⟨6, 4, 2, 5⟩, ⟨6, 6, 2, 3⟩]⟩def entry_12 : Entry := ⟨12, [⟨0, 6, 5, 4⟩, ⟨0, 0, 0, 3⟩]⟩def entry_13 : Entry := ⟨13, [⟨6, 6, 0, 3⟩, ⟨6, 4, 0, 5⟩]⟩def entry_14 : Entry := ⟨14, [⟨0, 6, 5, 4⟩, ⟨3, 6, 1, 4⟩]⟩def entry_15 : Entry := ⟨15, [⟨0, 6, 6, 4⟩, ⟨3, 6, 2, 4⟩]⟩def entry_16 : Entry := ⟨16, [⟨3, 6, 3, 4⟩, ⟨0, 6, 7, 4⟩]⟩def entry_17 : Entry := ⟨17, [⟨0, 6, 5, 4⟩, ⟨3, 0, 3, 3⟩]⟩def entry_18 : Entry := ⟨18, [⟨3, 6, 2, 4⟩, ⟨3, 0, 4, 3⟩]⟩def entry_19 : Entry := ⟨19, [⟨6, 4, 1, 5⟩, ⟨6, 0, 6, 5⟩]⟩def entry_20 : Entry := ⟨20, [⟨6, 4, 0, 5⟩, ⟨6, 0, 5, 5⟩]⟩def entry_21 : Entry := ⟨21, [⟨4, 6, 2, 3⟩, ⟨6, 0, 6, 5⟩]⟩def entry_22 : Entry := ⟨22, [⟨0, 6, 7, 5⟩, ⟨3, 0, 5, 4⟩]⟩def entry_23 : Entry := ⟨23, [⟨0, 6, 6, 4⟩, ⟨0, 0, 1, 3⟩]⟩def entry_24 : Entry := ⟨24, [⟨0, 0, 0, 3⟩, ⟨17, 0, 5, 4⟩]⟩def entry_25 : Entry := ⟨25, [⟨0, 0, 0, 3⟩, ⟨14, 0, 5, 4⟩]⟩def entry_26 : Entry := ⟨26, [⟨0, 4, 6, 4⟩, ⟨6, 0, 6, 5⟩]⟩def entry_27 : Entry := ⟨27, [⟨0, 6, 5, 4⟩, ⟨6, 4, 0, 5⟩]⟩def entry_28 : Entry := ⟨28, [⟨6, 1, 4, 5⟩, ⟨0, 6, 6, 4⟩]⟩def entry_29 : Entry := ⟨29, [⟨1, 4, 7, 3⟩, ⟨6, 3, 4, 5⟩]⟩def entry_30 : Entry := ⟨30, [⟨0, 0, 1, 3⟩, ⟨14, 0, 6, 4⟩]⟩def entry_31 : Entry := ⟨31, [⟨0, 0, 1, 4⟩, ⟨17, 0, 6, 5⟩]⟩def entry_32 : Entry := ⟨32, [⟨0, 4, 8, 3⟩, ⟨6, 3, 4, 5⟩]⟩def entry_33 : Entry := ⟨33, [⟨0, 0, 2, 4⟩, ⟨17, 0, 7, 5⟩]⟩def entry_34 : Entry := ⟨34, [⟨6, 1, 4, 5⟩, ⟨1, 6, 5, 4⟩]⟩def entry_35 : Entry := ⟨35, [⟨0, 0, 2, 4⟩, ⟨14, 0, 7, 5⟩]⟩def entry_36 : Entry := ⟨36, [⟨0, 0, 3, 4⟩, ⟨17, 0, 8, 5⟩]⟩def entry_37 : Entry := ⟨37, [⟨6, 3, 4, 5⟩, ⟨2, 4, 6, 3⟩]⟩def entry_38 : Entry := ⟨38, [⟨3, 0, 3, 3⟩, ⟨16, 0, 2, 4⟩]⟩def entry_39 : Entry := ⟨39, [⟨0, 0, 1, 3⟩, ⟨17, 0, 6, 4⟩]⟩def entry_40 : Entry := ⟨40, [⟨3, 0, 4, 3⟩, ⟨16, 0, 3, 4⟩]⟩def entry_41 : Entry := ⟨41, [⟨6, 3, 3, 5⟩, ⟨1, 4, 6, 3⟩]⟩def entry_42 : Entry := ⟨42, [⟨0, 6, 6, 4⟩, ⟨6, 4, 1, 5⟩]⟩def entry_43 : Entry := ⟨43, [⟨2, 4, 5, 3⟩, ⟨6, 3, 3, 5⟩]⟩def entry_44 : Entry := ⟨44, [⟨4, 4, 1, 5⟩, ⟨7, 0, 4, 5⟩]⟩def entry_45 : Entry := ⟨45, [⟨6, 4, 0, 5⟩, ⟨7, 0, 4, 5⟩]⟩def entry_46 : Entry := ⟨46, [⟨6, 6, 0, 3⟩, ⟨7, 0, 4, 5⟩]⟩def entry_47 : Entry := ⟨47, [⟨6, 3, 3, 5⟩, ⟨6, 2, 7, 3⟩]⟩def entry_48 : Entry := ⟨48, [⟨6, 3, 4, 5⟩, ⟨6, 2, 8, 3⟩]⟩def entry_49 : Entry := ⟨49, [⟨4, 7, 3, 1⟩, ⟨7, 1, 5, 4⟩]⟩def entry_50 : Entry := ⟨50, [⟨6, 3, 3, 5⟩, ⟨7, 1, 5, 4⟩]⟩def entry_51 : Entry := ⟨51, [⟨10, 2, 5, 3⟩, ⟨10, 0, 5, 4⟩, ⟨26, 2, 3, 4⟩, ⟨26, 0, 3, 3⟩]⟩def entry_52 : Entry := ⟨52, [⟨0, 0, 0, 3⟩, ⟨0, 4, 7, 3⟩]⟩def entry_53 : Entry := ⟨53, [⟨6, 4, 3, 4⟩, ⟨3, 1, 4, 5⟩]⟩def entry_54 : Entry := ⟨54, [⟨22, 0, 2, 3⟩, ⟨3, 6, 1, 4⟩]⟩def entry_55 : Entry := ⟨55, [⟨7, 4, 0, 5⟩, ⟨7, 0, 4, 5⟩]⟩def entry_56 : Entry := ⟨56, [⟨7, 4, 0, 5⟩, ⟨7, 6, 0, 3⟩]⟩def entry_57 : Entry := ⟨57, [⟨0, 6, 5, 4⟩, ⟨7, 0, 4, 5⟩]⟩def entry_58 : Entry := ⟨58, [⟨0, 4, 5, 4⟩, ⟨7, 0, 4, 5⟩]⟩def entry_59 : Entry := ⟨59, [⟨0, 6, 5, 4⟩, ⟨7, 4, 0, 5⟩]⟩def entry_60 : Entry := ⟨60, [⟨6, 6, 1, 3⟩, ⟨49, 1, 6, 4⟩]⟩def entry_61 : Entry := ⟨61, [⟨6, 0, 5, 4⟩, ⟨14, 1, 4, 5⟩]⟩def entry_62 : Entry := ⟨62, [⟨6, 6, 0, 3⟩, ⟨53, 0, 1, 5⟩]⟩def entry_63 : Entry := ⟨63, [⟨4, 3, 4, 3⟩, ⟨50, 0, 5, 4⟩]⟩def entry_64 : Entry := ⟨64, [⟨6, 6, 3, 4⟩, ⟨49, 1, 8, 5⟩]⟩def entry_65 : Entry := ⟨65, [⟨6, 6, 0, 3⟩, ⟨49, 1, 5, 4⟩]⟩def entry_66 : Entry := ⟨66, [⟨6, 3, 4, 5⟩, ⟨53, 5, 6, 4⟩]⟩def entry_67 : Entry := ⟨67, [⟨6, 1, 4, 5⟩, ⟨9, 2, 5, 4⟩]⟩def entry_68 : Entry := ⟨68, [⟨6, 4, 0, 5⟩, ⟨44, 0, 5, 4⟩]⟩def entry_69 : Entry := ⟨69, [⟨6, 3, 4, 5⟩, ⟨34, 0, 6, 5⟩]⟩def entry_70 : Entry := ⟨70, [⟨4, 3, 4, 3⟩, ⟨41, 0, 5, 4⟩]⟩def entry_71 : Entry := ⟨71, [⟨6, 1, 4, 5⟩, ⟨23, 2, 4, 3⟩]⟩def entry_72 : Entry := ⟨72, [⟨0, 5, 3, 8⟩, ⟨8, 6, 5, 4⟩]⟩def entry_73 : Entry := ⟨73, [⟨4, 3, 3, 4⟩, ⟨50, 0, 4, 5⟩]⟩def entry_74 : Entry := ⟨74, [⟨2, 7, 4, 3⟩, ⟨53, 0, 3, 3⟩]⟩def entry_75 : Entry := ⟨75, [⟨0, 0, 1, 3⟩, ⟨9, 0, 7, 3⟩]⟩def entry_76 : Entry := ⟨76, [⟨0, 7, 5, 7⟩, ⟨14, 0, 7, 5⟩]⟩def entry_77 : Entry := ⟨77, [⟨0, 5, 3, 7⟩, ⟨12, 0, 5, 4⟩]⟩def entry_78 : Entry := ⟨78, [⟨6, 4, 3, 4⟩, ⟨52, 0, 5, 4⟩]⟩def entry_79 : Entry := ⟨79, [⟨6, 1, 5, 5⟩, ⟨48, 0, 3, 4⟩]⟩def entry_80 : Entry := ⟨80, [⟨0, 6, 6, 4⟩, ⟨13, 4, 2, 4⟩]⟩def entry_81 : Entry := ⟨81, [⟨4, 3, 4, 3⟩, ⟨43, 0, 5, 4⟩]⟩def entry_82 : Entry := ⟨82, [⟨6, 1, 4, 5⟩, ⟨36, 0, 1, 3⟩]⟩def entry_83 : Entry := ⟨83, [⟨0, 7, 5, 7⟩, ⟨67, 2, 6, 3⟩]⟩def entry_84 : Entry := ⟨84, [⟨6, 3, 4, 5⟩, ⟨67, 0, 6, 4⟩]⟩def entry_85 : Entry := ⟨85, [⟨9, 0, 6, 3⟩, ⟨8, 4, 5, 4⟩]⟩def entry_86 : Entry := ⟨86, [⟨0, 6, 5, 4⟩, ⟨67, 3, 1, 5⟩]⟩def entry_87 : Entry := ⟨87, [⟨0, 5, 3, 7⟩, ⟨24, 2, 5, 3⟩]⟩def entry_88 : Entry := ⟨88, [⟨0, 6, 6, 4⟩, ⟨67, 3, 2, 5⟩]⟩def entry_89 : Entry := ⟨89, [⟨8, 3, 3, 1⟩, ⟨7, 1, 5, 4⟩]⟩def entry_90 : Entry := ⟨90, [⟨31, 0, 3, 3⟩, ⟨54, 6, 0, 3⟩, ⟨54, 0, 5, 4⟩, ⟨31, 6, 2, 4⟩]⟩def entry_91 : Entry := ⟨91, [⟨6, 3, 4, 5⟩, ⟨74, 5, 7, 3⟩]⟩def entry_92 : Entry := ⟨92, [⟨6, 1, 4, 5⟩, ⟨33, 0, 2, 3⟩]⟩def entry_93 : Entry := ⟨93, [⟨4, 3, 4, 3⟩, ⟨47, 0, 5, 4⟩]⟩def entry_94 : Entry := ⟨94, [⟨6, 1, 4, 5⟩, ⟨27, 3, 3, 6⟩]⟩def entry_95 : Entry := ⟨95, [⟨0, 5, 3, 7⟩, ⟨29, 0, 2, 5⟩]⟩def entry_96 : Entry := ⟨96, [⟨6, 1, 5, 5⟩, ⟨70, 0, 3, 5⟩]⟩def entry_97 : Entry := ⟨97, [⟨6, 6, 0, 3⟩, ⟨44, 0, 5, 4⟩]⟩def entry_98 : Entry := ⟨98, [⟨6, 6, 2, 3⟩, ⟨44, 0, 7, 4⟩]⟩def entry_99 : Entry := ⟨99, [⟨2, 1, 3, 2⟩, ⟨24, 0, 5, 4⟩]⟩def entry_100 : Entry := ⟨100, [⟨0, 6, 5, 4⟩, ⟨48, 0, 1, 4⟩]⟩def entry_101 : Entry := ⟨101, [⟨0, 7, 4, 6⟩, ⟨24, 0, 5, 4⟩]⟩def entry_102 : Entry := ⟨102, [⟨6, 3, 4, 5⟩, ⟨25, 2, 6, 3⟩]⟩def entry_103 : Entry := ⟨103, [⟨6, 3, 4, 5⟩, ⟨71, 0, 6, 4⟩]⟩def entry_104 : Entry := ⟨104, [⟨6, 0, 5, 4⟩, ⟨75, 0, 3, 4⟩]⟩def entry_105 : Entry := ⟨105, [⟨6, 5, 4, 3⟩, ⟨77, 0, 4, 5⟩]⟩def entry_106 : Entry := ⟨106, [⟨6, 1, 4, 5⟩, ⟨36, 6, 5, 4⟩]⟩def entry_107 : Entry := ⟨107, [⟨6, 6, 0, 3⟩, ⟨63, 1, 5, 3⟩]⟩def entry_108 : Entry := ⟨108, [⟨4, 6, 1, 3⟩, ⟨63, 1, 5, 3⟩]⟩def entry_109 : Entry := ⟨109, [⟨4, 6, 1, 3⟩, ⟨55, 0, 5, 4⟩]⟩def entry_110 : Entry := ⟨110, [⟨6, 6, 1, 3⟩, ⟨63, 1, 6, 3⟩]⟩def entry_111 : Entry := ⟨111, [⟨6, 7, 4, 3⟩, ⟨83, 0, 4, 5⟩]⟩def entry_112 : Entry := ⟨112, [⟨4, 1, 5, 4⟩, ⟨93, 0, 3, 5⟩]⟩def entry_113 : Entry := ⟨113, [⟨1, 6, 6, 4⟩, ⟨36, 6, 7, 5⟩]⟩def entry_114 : Entry := ⟨114, [⟨6, 0, 6, 5⟩, ⟨67, 3, 2, 5⟩]⟩def entry_115 : Entry := ⟨115, [⟨6, 2, 7, 3⟩, ⟨70, 7, 2, 5⟩]⟩def entry_116 : Entry := ⟨116, [⟨0, 7, 4, 6⟩, ⟨24, 2, 5, 4⟩]⟩def entry_117 : Entry := ⟨117, [⟨6, 1, 4, 5⟩, ⟨100, 0, 5, 4⟩]⟩def entry_118 : Entry := ⟨118, [⟨4, 7, 3, 1⟩, ⟨61, 1, 5, 4⟩]⟩def entry_119 : Entry := ⟨119, [⟨6, 6, 1, 3⟩, ⟨55, 0, 6, 4⟩]⟩def entry_120 : Entry := ⟨120, [⟨4, 0, 4, 5⟩, ⟨58, 2, 5, 4⟩]⟩def entry_121 : Entry := ⟨121, [⟨9, 3, 4, 5⟩, ⟨7, 1, 5, 4⟩]⟩def entry_122 : Entry := ⟨122, [⟨6, 6, 3, 3⟩, ⟨105, 1, 4, 5⟩]⟩def entry_123 : Entry := ⟨123, [⟨6, 6, 1, 3⟩, ⟨64, 2, 2, 5⟩]⟩def entry_124 : Entry := ⟨124, [⟨6, 1, 4, 5⟩, ⟨31, 2, 5, 4⟩]⟩def entry_125 : Entry := ⟨125, [⟨3, 0, 4, 3⟩, ⟨31, 2, 4, 5⟩]⟩def entry_126 : Entry := ⟨126, [⟨6, 3, 4, 5⟩, ⟨46, 1, 5, 7⟩]⟩def entry_127 : Entry := ⟨127, [⟨7, 0, 4, 5⟩, ⟨44, 2, 5, 4⟩]⟩def entry_128 : Entry := ⟨128, [⟨9, 6, 1, 5⟩, ⟨57, 0, 6, 5⟩]⟩def entry_129 : Entry := ⟨129, [⟨6, 4, 2, 5⟩, ⟨58, 1, 3, 6⟩]⟩def entry_130 : Entry := ⟨130, [⟨6, 1, 4, 5⟩, ⟨60, 0, 5, 4⟩]⟩def entry_131 : Entry := ⟨131, [⟨45, 3, 4, 5⟩, ⟨7, 1, 5, 4⟩]⟩def entry_132 : Entry := ⟨132, [⟨6, 3, 4, 5⟩, ⟨89, 0, 5, 6⟩]⟩def entry_133 : Entry := ⟨133, [⟨6, 7, 3, 1⟩, ⟨92, 0, 5, 5⟩]⟩def entry_134 : Entry := ⟨134, [⟨6, 7, 3, 0⟩, ⟨82, 0, 5, 4⟩]⟩def entry_135 : Entry := ⟨135, [⟨7, 0, 4, 5⟩, ⟨75, 4, 2, 5⟩, ⟨44, 0, 5, 4⟩]⟩def entry_136 : Entry := ⟨136, [⟨6, 3, 3, 7⟩, ⟨102, 2, 3, 3⟩]⟩def entry_137 : Entry := ⟨137, [⟨4, 1, 4, 3⟩, ⟨96, 0, 3, 4⟩]⟩def entry_138 : Entry := ⟨138, [⟨27, 0, 5, 4⟩, ⟨10, 1, 4, 7⟩]⟩def entry_139 : Entry := ⟨139, [⟨28, 1, 4, 5⟩, ⟨27, 0, 5, 4⟩]⟩def entry_140 : Entry := ⟨140, [⟨6, 7, 3, 2⟩, ⟨82, 0, 5, 6⟩]⟩def entry_141 : Entry := ⟨141, [⟨7, 0, 4, 5⟩, ⟨78, 2, 1, 3⟩]⟩def entry_142 : Entry := ⟨142, [⟨72, 4, 2, 3⟩, ⟨32, 1, 4, 3⟩, ⟨55, 2, 5, 4⟩]⟩def entry_143 : Entry := ⟨143, [⟨6, 6, 3, 4⟩, ⟨108, 0, 8, 5⟩]⟩def entry_144 : Entry := ⟨144, [⟨7, 0, 4, 5⟩, ⟨104, 4, 1, 5⟩, ⟨55, 0, 5, 4⟩]⟩def entry_145 : Entry := ⟨145, [⟨0, 5, 4, 5⟩, ⟨91, 0, 3, 4⟩]⟩def entry_146 : Entry := ⟨146, [⟨36, 6, 5, 4⟩, ⟨24, 1, 4, 5⟩]⟩def entry_147 : Entry := ⟨147, [⟨53, 0, 1, 5⟩, ⟨44, 2, 5, 4⟩]⟩def entry_148 : Entry := ⟨148, [⟨7, 1, 5, 4⟩, ⟨46, 1, 4, 5⟩, ⟨94, 0, 5, 3⟩, ⟨97, 1, 4, 5⟩]⟩def entry_149 : Entry := ⟨149, [⟨16, 1, 4, 3⟩, ⟨24, 2, 5, 4⟩]⟩def entry_150 : Entry := ⟨150, [⟨4, 6, 1, 3⟩, ⟨126, 5, 2, 5⟩]⟩def entry_151 : Entry := ⟨151, [⟨2, 1, 4, 3⟩, ⟨101, 2, 6, 3⟩]⟩def entry_152 : Entry := ⟨152, [⟨6, 3, 4, 5⟩, ⟨73, 1, 7, 4⟩]⟩def entry_153 : Entry := ⟨153, [⟨59, 4, 0, 4⟩, ⟨27, 0, 5, 4⟩]⟩def entry_154 : Entry := ⟨154, [⟨7, 6, 4, 3⟩, ⟨104, 0, 7, 5⟩]⟩def entry_155 : Entry := ⟨155, [⟨7, 1, 5, 4⟩, ⟨55, 3, 4, 5⟩]⟩def entry_156 : Entry := ⟨156, [⟨11, 0, 2, 4⟩, ⟨98, 2, 2, 4⟩, ⟨33, 0, 2, 3⟩]⟩def entry_157 : Entry := ⟨157, [⟨6, 3, 4, 5⟩, ⟨57, 1, 5, 6⟩]⟩def entry_158 : Entry := ⟨158, [⟨66, 0, 3, 4⟩, ⟨45, 1, 4, 5⟩, ⟨46, 3, 4, 5⟩]⟩def entry_159 : Entry := ⟨159, [⟨45, 3, 4, 5⟩, ⟨65, 1, 4, 5⟩, ⟨7, 3, 3, 4⟩]⟩def entry_160 : Entry := ⟨160, [⟨63, 1, 8, 3⟩, ⟨32, 3, 4, 3⟩]⟩def entry_161 : Entry := ⟨161, [⟨15, 1, 4, 5⟩, ⟨86, 0, 5, 4⟩]⟩def entry_162 : Entry := ⟨162, [⟨7, 3, 3, 4⟩, ⟨127, 1, 4, 5⟩, ⟨63, 0, 3, 5⟩, ⟨157, 0, 3, 3⟩]⟩def entry_163 : Entry := ⟨163, [⟨44, 2, 5, 4⟩, ⟨49, 1, 5, 4⟩, ⟨56, 4, 0, 4⟩]⟩def entry_164 : Entry := ⟨164, [⟨6, 1, 4, 5⟩, ⟨110, 0, 5, 4⟩]⟩def entry_165 : Entry := ⟨165, [⟨0, 7, 5, 8⟩, ⟨107, 0, 7, 5⟩]⟩def entry_166 : Entry := ⟨166, [⟨2, 7, 4, 5⟩, ⟨107, 0, 6, 4⟩]⟩def entry_167 : Entry := ⟨167, [⟨57, 0, 5, 4⟩, ⟨57, 4, 0, 4⟩]⟩def entry_168 : Entry := ⟨168, [⟨6, 1, 5, 5⟩, ⟨152, 0, 3, 4⟩]⟩def entry_169 : Entry := ⟨169, [⟨28, 3, 4, 5⟩, ⟨63, 1, 8, 3⟩]⟩def entry_170 : Entry := ⟨170, [⟨4, 6, 1, 3⟩, ⟨127, 2, 5, 4⟩]⟩def entry_171 : Entry := ⟨171, [⟨6, 0, 5, 4⟩, ⟨91, 0, 0, 5⟩]⟩def entry_172 : Entry := ⟨172, [⟨63, 1, 5, 3⟩, ⟨55, 6, 0, 4⟩, ⟨64, 0, 1, 3⟩]⟩def entry_173 : Entry := ⟨173, [⟨63, 1, 5, 3⟩, ⟨64, 6, 4, 5⟩, ⟨55, 6, 0, 4⟩]⟩def entry_174 : Entry := ⟨174, [⟨58, 3, 4, 5⟩, ⟨57, 1, 4, 5⟩, ⟨84, 0, 3, 4⟩]⟩def entry_175 : Entry := ⟨175, [⟨141, 0, 5, 4⟩, ⟨7, 2, 4, 3⟩, ⟨63, 1, 5, 3⟩]⟩def entry_176 : Entry := ⟨176, [⟨63, 1, 5, 3⟩, ⟨64, 6, 4, 5⟩, ⟨55, 2, 5, 4⟩]⟩def entry_177 : Entry := ⟨177, [⟨6, 1, 4, 5⟩, ⟨136, 3, 5, 4⟩]⟩def entry_178 : Entry := ⟨178, [⟨37, 0, 3, 4⟩, ⟨68, 1, 4, 5⟩, ⟨46, 3, 4, 5⟩]⟩def entry_179 : Entry := ⟨179, [⟨6, 6, 0, 3⟩, ⟨148, 5, 5, 4⟩]⟩def entry_180 : Entry := ⟨180, [⟨7, 3, 3, 4⟩, ⟨63, 0, 3, 5⟩, ⟨155, 0, 4, 5⟩, ⟨132, 0, 3, 3⟩]⟩def entry_181 : Entry := ⟨181, [⟨24, 3, 4, 5⟩, ⟨87, 2, 6, 4⟩, ⟨90, 0, 7, 5⟩]⟩def entry_182 : Entry := ⟨182, [⟨12, 2, 7, 3⟩, ⟨139, 0, 7, 4⟩]⟩def entry_183 : Entry := ⟨183, [⟨64, 2, 1, 5⟩, ⟨63, 3, 0, 3⟩, ⟨55, 2, 5, 4⟩]⟩def entry_184 : Entry := ⟨184, [⟨34, 3, 4, 2⟩, ⟨35, 2, 5, 4⟩]⟩def entry_185 : Entry := ⟨185, [⟨44, 3, 4, 5⟩, ⟨49, 0, 4, 5⟩, ⟨84, 0, 3, 4⟩]⟩def entry_186 : Entry := ⟨186, [⟨7, 6, 0, 3⟩, ⟨141, 2, 5, 4⟩]⟩def entry_187 : Entry := ⟨187, [⟨6, 4, 3, 4⟩, ⟨108, 3, 4, 5⟩]⟩def entry_188 : Entry := ⟨188, [⟨6, 3, 4, 5⟩, ⟨112, 5, 7, 4⟩]⟩def entry_189 : Entry := ⟨189, [⟨12, 0, 5, 4⟩, ⟨86, 4, 1, 4⟩]⟩def entry_190 : Entry := ⟨190, [⟨46, 0, 5, 4⟩, ⟨85, 2, 3, 3⟩, ⟨111, 3, 4, 3⟩]⟩def entry_191 : Entry := ⟨191, [⟨6, 4, 3, 4⟩, ⟨145, 0, 4, 5⟩]⟩def entry_192 : Entry := ⟨192, [⟨64, 1, 3, 1⟩, ⟨103, 0, 3, 4⟩, ⟨55, 3, 4, 5⟩]⟩def entry_193 : Entry := ⟨193, [⟨6, 6, 2, 3⟩, ⟨162, 1, 7, 4⟩]⟩def entry_194 : Entry := ⟨194, [⟨0, 0, 0, 3⟩, ⟨146, 4, 2, 5⟩]⟩def entry_195 : Entry := ⟨195, [⟨6, 6, 0, 3⟩, ⟨162, 1, 5, 4⟩]⟩def entry_196 : Entry := ⟨196, [⟨6, 3, 4, 5⟩, ⟨187, 5, 6, 4⟩]⟩def entry_197 : Entry := ⟨197, [⟨63, 3, 0, 3⟩, ⟨63, 1, 5, 3⟩]⟩def entry_198 : Entry := ⟨198, [⟨7, 4, 0, 5⟩, ⟨131, 1, 5, 4⟩]⟩def entry_199 : Entry := ⟨199, [⟨55, 1, 4, 5⟩, ⟨64, 3, 5, 1⟩, ⟨84, 0, 3, 4⟩]⟩def entry_200 : Entry := ⟨200, [⟨103, 0, 3, 4⟩, ⟨64, 3, 5, 1⟩, ⟨55, 1, 4, 5⟩]⟩def entry_201 : Entry := ⟨201, [⟨45, 3, 5, 7⟩, ⟨82, 0, 6, 5⟩]⟩def entry_202 : Entry := ⟨202, [⟨150, 0, 5, 4⟩, ⟨7, 0, 4, 5⟩, ⟨108, 0, 5, 4⟩]⟩def entry_203 : Entry := ⟨203, [⟨18, 6, 1, 3⟩, ⟨107, 0, 5, 4⟩, ⟨163, 0, 5, 4⟩]⟩def entry_204 : Entry := ⟨204, [⟨2, 5, 4, 2⟩, ⟨166, 2, 5, 3⟩]⟩def entry_205 : Entry := ⟨205, [⟨4, 1, 4, 3⟩, ⟨168, 0, 3, 4⟩]⟩def entry_206 : Entry := ⟨206, [⟨28, 3, 4, 5⟩, ⟨135, 2, 8, 4⟩]⟩def entry_207 : Entry := ⟨207, [⟨28, 3, 4, 5⟩, ⟨127, 0, 8, 4⟩]⟩def entry_208 : Entry := ⟨208, [⟨7, 4, 0, 5⟩, ⟨127, 0, 5, 4⟩]⟩def entry_209 : Entry := ⟨209, [⟨25, 0, 5, 4⟩, ⟨81, 5, 5, 7⟩]⟩def entry_210 : Entry := ⟨210, [⟨58, 2, 5, 4⟩, ⟨57, 0, 5, 4⟩, ⟨117, 1, 4, 5⟩]⟩def entry_211 : Entry := ⟨211, [⟨49, 5, 5, 4⟩, ⟨6, 6, 0, 3⟩]⟩def entry_212 : Entry := ⟨212, [⟨6, 0, 5, 4⟩, ⟨188, 0, 0, 5⟩]⟩def entry_213 : Entry := ⟨213, [⟨6, 0, 7, 5⟩, ⟨191, 0, 3, 5⟩]⟩def entry_214 : Entry := ⟨214, [⟨7, 3, 3, 4⟩, ⟨108, 3, 4, 5⟩, ⟨95, 0, 5, 2⟩]⟩def entry_215 : Entry := ⟨215, [⟨107, 1, 4, 6⟩, ⟨24, 0, 5, 4⟩]⟩def entry_216 : Entry := ⟨216, [⟨7, 6, 0, 3⟩, ⟨155, 5, 5, 4⟩]⟩def entry_217 : Entry := ⟨217, [⟨111, 1, 1, 3⟩, ⟨55, 4, 0, 4⟩, ⟨64, 0, 1, 3⟩]⟩def entry_218 : Entry := ⟨218, [⟨0, 5, 3, 7⟩, ⟨182, 0, 2, 4⟩]⟩def entry_219 : Entry := ⟨219, [⟨0, 5, 3, 7⟩, ⟨179, 2, 6, 4⟩]⟩def entry_220 : Entry := ⟨220, [⟨56, 4, 0, 4⟩, ⟨63, 1, 5, 3⟩, ⟨144, 2, 5, 4⟩, ⟨154, 6, 5, 4⟩, ⟨155, 1, 5, 4⟩]⟩def entry_221 : Entry := ⟨221, [⟨6, 6, 0, 3⟩, ⟨180, 5, 5, 4⟩]⟩def entry_222 : Entry := ⟨222, [⟨6, 1, 4, 5⟩, ⟨158, 5, 5, 4⟩]⟩def entry_223 : Entry := ⟨223, [⟨63, 1, 5, 3⟩, ⟨135, 2, 5, 4⟩, ⟨128, 0, 3, 3⟩, ⟨111, 3, 4, 3⟩, ⟨127, 0, 5, 4⟩]⟩def entry_224 : Entry := ⟨224, [⟨6, 1, 4, 5⟩, ⟨212, 0, 6, 3⟩]⟩def entry_225 : Entry := ⟨225, [⟨111, 7, 7, 5⟩, ⟨61, 4, 4, 5⟩]⟩def entry_226 : Entry := ⟨226, [⟨10, 6, 0, 3⟩, ⟨203, 0, 5, 4⟩, ⟨33, 0, 2, 3⟩, ⟨193, 0, 2, 4⟩]⟩def entry_227 : Entry := ⟨227, [⟨6, 1, 5, 5⟩, ⟨212, 0, 7, 3⟩]⟩def entry_228 : Entry := ⟨228, [⟨82, 0, 6, 5⟩, ⟨68, 3, 5, 7⟩]⟩def entry_229 : Entry := ⟨229, [⟨171, 0, 7, 3⟩, ⟨45, 1, 4, 5⟩, ⟨46, 3, 4, 5⟩]⟩def entry_230 : Entry := ⟨230, [⟨10, 6, 3, 4⟩, ⟨193, 0, 5, 5⟩, ⟨203, 0, 8, 5⟩, ⟨33, 0, 5, 4⟩]⟩def entry_231 : Entry := ⟨231, [⟨6, 3, 4, 5⟩, ⟨222, 0, 6, 4⟩]⟩def entry_232 : Entry := ⟨232, [⟨24, 2, 5, 4⟩, ⟨107, 1, 4, 6⟩]⟩def entry_233 : Entry := ⟨233, [⟨32, 3, 3, 1⟩, ⟨133, 0, 6, 4⟩]⟩def entry_234 : Entry := ⟨234, [⟨180, 4, 4, 5⟩, ⟨37, 0, 3, 4⟩, ⟨129, 0, 5, 3⟩, ⟨63, 0, 3, 5⟩]⟩def entry_235 : Entry := ⟨235, [⟨7, 3, 3, 4⟩, ⟨110, 0, 6, 4⟩, ⟨70, 0, 3, 5⟩]⟩def entry_236 : Entry := ⟨236, [⟨38, 1, 4, 5⟩, ⟨122, 7, 3, 4⟩, ⟨181, 0, 2, 3⟩, ⟨30, 1, 4, 3⟩]⟩def entry_237 : Entry := ⟨237, [⟨6, 3, 4, 5⟩, ⟨172, 0, 7, 4⟩]⟩def entry_238 : Entry := ⟨238, [⟨6, 3, 4, 5⟩, ⟨178, 5, 7, 4⟩]⟩def entry_239 : Entry := ⟨239, [⟨0, 4, 7, 3⟩, ⟨174, 4, 3, 5⟩]⟩def entry_240 : Entry := ⟨240, [⟨6, 1, 4, 5⟩, ⟨237, 0, 2, 4⟩]⟩def entry_241 : Entry := ⟨241, [⟨131, 1, 5, 4⟩, ⟨159, 1, 5, 4⟩, ⟨61, 0, 4, 5⟩]⟩def entry_242 : Entry := ⟨242, [⟨6, 1, 4, 5⟩, ⟨190, 0, 5, 4⟩]⟩def entry_243 : Entry := ⟨243, [⟨6, 0, 5, 4⟩, ⟨233, 0, 2, 5⟩]⟩def entry_244 : Entry := ⟨244, [⟨99, 4, 2, 5⟩, ⟨99, 0, 4, 5⟩, ⟨11, 7, 3, 3⟩, ⟨173, 2, 5, 4⟩]⟩def entry_245 : Entry := ⟨245, [⟨64, 0, 1, 3⟩, ⟨175, 4, 0, 4⟩, ⟨143, 6, 4, 5⟩, ⟨186, 6, 0, 4⟩]⟩def entry_246 : Entry := ⟨246, [⟨64, 6, 4, 5⟩, ⟨175, 2, 5, 4⟩, ⟨186, 0, 5, 4⟩, ⟨143, 0, 1, 3⟩]⟩def entry_247 : Entry := ⟨247, [⟨6, 4, 3, 4⟩, ⟨229, 0, 4, 5⟩]⟩def entry_248 : Entry := ⟨248, [⟨186, 0, 7, 4⟩, ⟨143, 0, 3, 3⟩, ⟨175, 2, 7, 4⟩, ⟨64, 6, 6, 5⟩]⟩def entry_249 : Entry := ⟨249, [⟨0, 7, 4, 5⟩, ⟨225, 1, 4, 1⟩]⟩def entry_250 : Entry := ⟨250, [⟨6, 1, 4, 5⟩, ⟨238, 0, 2, 4⟩]⟩def entry_251 : Entry := ⟨251, [⟨6, 2, 5, 4⟩, ⟨239, 4, 3, 6⟩]⟩def entry_252 : Entry := ⟨252, [⟨111, 3, 4, 3⟩, ⟨154, 6, 5, 4⟩, ⟨144, 2, 5, 4⟩, ⟨63, 1, 5, 3⟩, ⟨155, 1, 5, 4⟩]⟩def entry_253 : Entry := ⟨253, [⟨29, 3, 3, 0⟩, ⟨177, 1, 6, 2⟩]⟩def entry_254 : Entry := ⟨254, [⟨96, 7, 4, 5⟩, ⟨108, 0, 8, 5⟩]⟩def entry_255 : Entry := ⟨255, [⟨69, 0, 3, 3⟩, ⟨205, 0, 5, 5⟩, ⟨7, 3, 3, 4⟩]⟩def entry_256 : Entry := ⟨256, [⟨0, 5, 4, 5⟩, ⟨231, 0, 3, 4⟩]⟩def entry_257 : Entry := ⟨257, [⟨4, 1, 5, 4⟩, ⟨235, 0, 4, 5⟩]⟩def entry_258 : Entry := ⟨258, [⟨6, 4, 3, 4⟩, ⟨227, 0, 4, 5⟩]⟩def entry_259 : Entry := ⟨259, [⟨6, 4, 3, 4⟩, ⟨231, 1, 7, 2⟩]⟩def entry_260 : Entry := ⟨260, [⟨0, 5, 4, 6⟩, ⟨231, 0, 3, 5⟩]⟩def entry_261 : Entry := ⟨261, [⟨6, 3, 4, 5⟩, ⟨242, 0, 6, 4⟩]⟩def entry_262 : Entry := ⟨262, [⟨0, 7, 5, 7⟩, ⟨213, 0, 3, 4⟩]⟩def entry_263 : Entry := ⟨263, [⟨144, 6, 0, 4⟩, ⟨143, 0, 1, 3⟩, ⟨175, 0, 5, 4⟩, ⟨55, 6, 0, 4⟩]⟩def entry_264 : Entry := ⟨264, [⟨6, 4, 3, 4⟩, ⟨250, 1, 7, 4⟩]⟩def entry_265 : Entry := ⟨265, [⟨6, 6, 3, 4⟩, ⟨247, 0, 4, 6⟩]⟩def entry_266 : Entry := ⟨266, [⟨6, 3, 3, 5⟩, ⟨242, 0, 5, 4⟩]⟩def entry_267 : Entry := ⟨267, [⟨175, 4, 1, 4⟩, ⟨144, 2, 6, 4⟩, ⟨55, 2, 6, 4⟩, ⟨143, 4, 5, 3⟩]⟩def entry_268 : Entry := ⟨268, [⟨6, 0, 5, 4⟩, ⟨251, 0, 4, 2⟩]⟩def entry_269 : Entry := ⟨269, [⟨28, 3, 3, 6⟩, ⟨202, 0, 7, 5⟩]⟩def entry_270 : Entry := ⟨270, [⟨63, 0, 3, 7⟩, ⟨6, 7, 3, 2⟩]⟩def entry_271 : Entry := ⟨271, [⟨107, 2, 7, 3⟩, ⟨107, 3, 4, 6⟩]⟩def entry_272 : Entry := ⟨272, [⟨1, 1, 3, 1⟩, ⟨249, 0, 4, 5⟩]⟩def entry_273 : Entry := ⟨273, [⟨6, 1, 4, 5⟩, ⟨223, 0, 5, 4⟩]⟩def entry_274 : Entry := ⟨274, [⟨6, 7, 3, 1⟩, ⟨240, 0, 5, 5⟩]⟩def entry_275 : Entry := ⟨275, [⟨63, 1, 5, 3⟩, ⟨198, 4, 0, 4⟩, ⟨44, 2, 5, 4⟩]⟩def entry_276 : Entry := ⟨276, [⟨7, 3, 3, 4⟩, ⟨177, 0, 5, 4⟩, ⟨63, 0, 3, 5⟩]⟩def entry_277 : Entry := ⟨277, [⟨14, 3, 4, 5⟩, ⟨204, 2, 3, 0⟩, ⟨33, 1, 3, 2⟩]⟩def entry_278 : Entry := ⟨278, [⟨63, 3, 3, 3⟩, ⟨162, 1, 8, 4⟩]⟩def entry_279 : Entry := ⟨279, [⟨6, 3, 4, 5⟩, ⟨234, 5, 7, 4⟩]⟩def entry_280 : Entry := ⟨280, [⟨184, 0, 1, 5⟩, ⟨116, 2, 4, 3⟩]⟩def entry_281 : Entry := ⟨281, [⟨36, 4, 5, 4⟩, ⟨163, 2, 5, 4⟩, ⟨189, 0, 4, 5⟩]⟩def entry_282 : Entry := ⟨282, [⟨56, 0, 5, 4⟩, ⟨64, 0, 1, 3⟩, ⟨55, 0, 5, 4⟩, ⟨265, 0, 1, 3⟩]⟩def entry_283 : Entry := ⟨283, [⟨64, 0, 1, 3⟩, ⟨196, 1, 4, 3⟩, ⟨55, 2, 5, 4⟩]⟩def entry_284 : Entry := ⟨284, [⟨45, 1, 4, 5⟩, ⟨224, 0, 5, 4⟩, ⟨46, 3, 4, 5⟩]⟩def entry_285 : Entry := ⟨285, [⟨6, 3, 4, 5⟩, ⟨273, 0, 6, 4⟩]⟩def entry_286 : Entry := ⟨286, [⟨6, 7, 3, 0⟩, ⟨261, 0, 3, 4⟩]⟩def entry_287 : Entry := ⟨287, [⟨64, 0, 1, 3⟩, ⟨55, 0, 5, 4⟩, ⟨56, 0, 5, 4⟩, ⟨264, 4, 4, 5⟩]⟩def entry_288 : Entry := ⟨288, [⟨130, 1, 4, 2⟩, ⟨96, 0, 1, 4⟩]⟩def entry_289 : Entry := ⟨289, [⟨6, 1, 4, 5⟩, ⟨279, 0, 2, 4⟩]⟩def entry_290 : Entry := ⟨290, [⟨67, 2, 5, 2⟩, ⟨231, 4, 5, 5⟩]⟩def entry_291 : Entry := ⟨291, [⟨89, 3, 3, 4⟩, ⟨202, 0, 8, 4⟩, ⟨55, 4, 3, 4⟩]⟩def entry_292 : Entry := ⟨292, [⟨39, 0, 3, 4⟩, ⟨219, 3, 3, 4⟩, ⟨79, 1, 4, 3⟩]⟩def entry_293 : Entry := ⟨293, [⟨2, 7, 4, 3⟩, ⟨280, 0, 5, 4⟩]⟩def entry_294 : Entry := ⟨294, [⟨63, 1, 5, 3⟩, ⟨196, 3, 1, 3⟩]⟩def entry_295 : Entry := ⟨295, [⟨63, 1, 5, 3⟩, ⟨64, 2, 1, 5⟩, ⟨55, 0, 5, 4⟩, ⟨265, 4, 4, 3⟩]⟩def entry_296 : Entry := ⟨296, [⟨107, 1, 4, 5⟩, ⟨209, 3, 3, 4⟩, ⟨65, 1, 4, 5⟩]⟩def entry_297 : Entry := ⟨297, [⟨6, 4, 3, 4⟩, ⟨289, 1, 7, 4⟩]⟩def entry_298 : Entry := ⟨298, [⟨24, 2, 7, 3⟩, ⟨24, 6, 3, 3⟩, ⟨107, 4, 3, 4⟩, ⟨195, 0, 7, 4⟩]⟩def entry_299 : Entry := ⟨299, [⟨6, 4, 3, 4⟩, ⟨284, 0, 4, 5⟩]⟩def entry_300 : Entry := ⟨300, [⟨64, 3, 5, 1⟩, ⟨240, 2, 5, 1⟩, ⟨55, 3, 4, 5⟩]⟩def entry_301 : Entry := ⟨301, [⟨59, 0, 5, 4⟩, ⟨57, 0, 5, 4⟩, ⟨258, 4, 4, 5⟩]⟩def entry_302 : Entry := ⟨302, [⟨125, 0, 5, 3⟩, ⟨162, 4, 3, 6⟩]⟩def entry_303 : Entry := ⟨303, [⟨49, 4, 4, 5⟩, ⟨44, 1, 4, 5⟩, ⟨63, 0, 3, 5⟩, ⟨261, 0, 3, 4⟩]⟩def entry_304 : Entry := ⟨304, [⟨55, 4, 3, 4⟩, ⟨202, 0, 8, 4⟩, ⟨131, 3, 3, 4⟩]⟩def entry_305 : Entry := ⟨305, [⟨6, 1, 4, 5⟩, ⟨278, 0, 1, 4⟩]⟩def entry_306 : Entry := ⟨306, [⟨4, 1, 4, 3⟩, ⟨288, 0, 6, 4⟩]⟩def entry_307 : Entry := ⟨307, [⟨0, 7, 4, 6⟩, ⟨273, 0, 5, 5⟩]⟩def entry_308 : Entry := ⟨308, [⟨6, 6, 3, 4⟩, ⟨299, 0, 4, 6⟩]⟩def entry_309 : Entry := ⟨309, [⟨28, 6, 3, 4⟩, ⟨268, 1, 5, 7⟩]⟩def entry_310 : Entry := ⟨310, [⟨6, 1, 4, 5⟩, ⟨281, 0, 5, 3⟩]⟩def entry_311 : Entry := ⟨311, [⟨6, 3, 3, 5⟩, ⟨278, 0, 2, 4⟩]⟩def entry_312 : Entry := ⟨312, [⟨9, 2, 5, 4⟩, ⟨272, 0, 4, 5⟩]⟩def entry_313 : Entry := ⟨313, [⟨162, 4, 4, 5⟩, ⟨148, 5, 6, 3⟩]⟩def entry_314 : Entry := ⟨314, [⟨6, 3, 4, 5⟩, ⟨305, 0, 6, 4⟩]⟩def entry_315 : Entry := ⟨315, [⟨6, 0, 5, 4⟩, ⟨296, 0, 4, 5⟩]⟩def entry_316 : Entry := ⟨316, [⟨6, 6, 3, 4⟩, ⟨306, 0, 5, 8⟩]⟩def entry_317 : Entry := ⟨317, [⟨263, 2, 6, 4⟩, ⟨26, 3, 4, 3⟩, ⟨99, 0, 5, 5⟩]⟩def entry_318 : Entry := ⟨318, [⟨64, 3, 5, 1⟩, ⟨63, 0, 3, 5⟩, ⟨261, 0, 3, 4⟩, ⟨55, 1, 4, 5⟩]⟩def entry_319 : Entry := ⟨319, [⟨39, 2, 3, 4⟩, ⟨109, 4, 0, 5⟩, ⟨266, 1, 4, 5⟩, ⟨122, 4, 4, 5⟩]⟩def entry_320 : Entry := ⟨320, [⟨19, 1, 4, 3⟩, ⟨267, 2, 6, 4⟩, ⟨115, 7, 4, 3⟩]⟩def entry_321 : Entry := ⟨321, [⟨165, 1, 3, 4⟩, ⟨97, 0, 7, 5⟩, ⟨223, 3, 4, 7⟩]⟩def entry_322 : Entry := ⟨322, [⟨96, 0, 1, 4⟩, ⟨205, 1, 5, 2⟩]⟩def entry_323 : Entry := ⟨323, [⟨165, 6, 4, 5⟩, ⟨278, 0, 1, 4⟩, ⟨25, 1, 4, 5⟩]⟩def entry_324 : Entry := ⟨324, [⟨6, 3, 4, 5⟩, ⟨298, 0, 3, 4⟩]⟩def entry_325 : Entry := ⟨325, [⟨25, 0, 6, 5⟩, ⟨313, 1, 6, 4⟩, ⟨24, 2, 6, 3⟩]⟩def entry_326 : Entry := ⟨326, [⟨63, 1, 5, 3⟩, ⟨255, 7, 0, 4⟩]⟩def entry_327 : Entry := ⟨327, [⟨24, 2, 6, 3⟩, ⟨195, 4, 2, 4⟩, ⟨195, 0, 6, 4⟩, ⟨24, 6, 2, 3⟩]⟩def entry_328 : Entry := ⟨328, [⟨49, 0, 4, 5⟩, ⟨44, 3, 4, 5⟩, ⟨285, 0, 3, 4⟩]⟩def entry_329 : Entry := ⟨329, [⟨0, 7, 4, 6⟩, ⟨305, 0, 5, 5⟩]⟩def entry_330 : Entry := ⟨330, [⟨63, 1, 5, 3⟩, ⟨268, 0, 4, 5⟩, ⟨144, 0, 5, 4⟩, ⟨154, 4, 5, 4⟩, ⟨155, 5, 5, 4⟩]⟩def entry_331 : Entry := ⟨331, [⟨113, 0, 1, 4⟩, ⟨15, 0, 3, 4⟩, ⟨298, 4, 4, 5⟩, ⟨90, 2, 5, 4⟩]⟩def entry_332 : Entry := ⟨332, [⟨67, 4, 3, 4⟩, ⟨289, 2, 5, 1⟩]⟩def entry_333 : Entry := ⟨333, [⟨317, 0, 5, 4⟩, ⟨1, 5, 4, 3⟩]⟩def entry_334 : Entry := ⟨334, [⟨67, 6, 3, 2⟩, ⟨289, 0, 5, 5⟩]⟩def entry_335 : Entry := ⟨335, [⟨196, 3, 1, 3⟩, ⟨162, 1, 5, 4⟩]⟩def entry_336 : Entry := ⟨336, [⟨25, 6, 2, 3⟩, ⟨199, 3, 2, 4⟩, ⟨65, 0, 6, 4⟩, ⟨304, 0, 2, 4⟩]⟩def entry_337 : Entry := ⟨337, [⟨107, 3, 3, 7⟩, ⟨230, 2, 1, 5⟩]⟩def entry_338 : Entry := ⟨338, [⟨241, 0, 6, 4⟩, ⟨275, 4, 2, 4⟩, ⟨107, 4, 2, 4⟩]⟩def entry_339 : Entry := ⟨339, [⟨4, 1, 4, 3⟩, ⟨322, 0, 6, 4⟩]⟩def entry_340 : Entry := ⟨340, [⟨25, 3, 3, 6⟩, ⟨300, 4, 4, 6⟩, ⟨24, 3, 3, 6⟩]⟩def entry_341 : Entry := ⟨341, [⟨162, 5, 5, 4⟩, ⟨259, 4, 4, 5⟩, ⟨208, 2, 5, 4⟩, ⟨143, 0, 1, 3⟩]⟩def entry_342 : Entry := ⟨342, [⟨210, 0, 5, 2⟩, ⟨88, 1, 4, 3⟩, ⟨260, 4, 4, 3⟩, ⟨290, 0, 4, 3⟩]⟩def entry_343 : Entry := ⟨343, [⟨0, 5, 4, 5⟩, ⟨250, 0, 5, 4⟩]⟩def entry_344 : Entry := ⟨344, [⟨7, 1, 5, 4⟩, ⟨108, 3, 4, 5⟩, ⟨262, 4, 5, 2⟩]⟩def entry_345 : Entry := ⟨345, [⟨6, 0, 5, 5⟩, ⟨320, 4, 4, 7⟩]⟩def entry_346 : Entry := ⟨346, [⟨60, 1, 4, 3⟩, ⟨255, 0, 1, 4⟩, ⟨276, 0, 1, 4⟩]⟩def entry_347 : Entry := ⟨347, [⟨6, 6, 3, 4⟩, ⟨339, 0, 5, 8⟩]⟩def entry_348 : Entry := ⟨348, [⟨312, 1, 5, 5⟩, ⟨114, 4, 3, 4⟩, ⟨139, 3, 4, 5⟩]⟩def entry_349 : Entry := ⟨349, [⟨14, 1, 4, 5⟩, ⟨17, 1, 4, 5⟩, ⟨332, 0, 3, 4⟩]⟩def entry_350 : Entry := ⟨350, [⟨24, 4, 2, 5⟩, ⟨107, 2, 6, 4⟩, ⟨271, 4, 5, 5⟩, ⟨215, 0, 5, 5⟩]⟩def entry_351 : Entry := ⟨351, [⟨163, 0, 5, 4⟩, ⟨287, 4, 1, 4⟩, ⟨25, 4, 1, 5⟩]⟩def entry_352 : Entry := ⟨352, [⟨214, 0, 4, 5⟩, ⟨91, 0, 3, 4⟩, ⟨63, 0, 3, 5⟩, ⟨344, 0, 4, 5⟩, ⟨180, 4, 4, 5⟩]⟩def entry_353 : Entry := ⟨353, [⟨6, 4, 0, 5⟩, ⟨347, 0, 1, 3⟩]⟩def entry_354 : Entry := ⟨354, [⟨138, 2, 5, 4⟩, ⟨114, 5, 4, 3⟩, ⟨312, 0, 5, 5⟩, ⟨182, 2, 2, 4⟩]⟩def entry_355 : Entry := ⟨355, [⟨12, 2, 7, 3⟩, ⟨167, 0, 7, 4⟩, ⟨342, 0, 6, 6⟩]⟩def entry_356 : Entry := ⟨356, [⟨24, 2, 6, 3⟩, ⟨24, 6, 2, 3⟩, ⟨211, 4, 2, 4⟩, ⟨179, 0, 6, 4⟩]⟩def entry_357 : Entry := ⟨357, [⟨82, 6, 2, 3⟩, ⟨283, 0, 5, 6⟩]⟩def entry_358 : Entry := ⟨358, [⟨6, 0, 5, 4⟩, ⟨346, 0, 4, 6⟩]⟩def entry_359 : Entry := ⟨359, [⟨134, 0, 4, 6⟩, ⟨24, 7, 3, 2⟩, ⟨323, 0, 5, 5⟩]⟩def entry_360 : Entry := ⟨360, [⟨155, 4, 4, 5⟩, ⟨7, 3, 3, 4⟩, ⟨337, 0, 5, 2⟩, ⟨228, 4, 5, 2⟩]⟩def entry_361 : Entry := ⟨361, [⟨6, 4, 3, 4⟩, ⟨352, 0, 4, 5⟩]⟩def entry_362 : Entry := ⟨362, [⟨4, 0, 3, 4⟩, ⟨345, 0, 4, 3⟩]⟩def entry_363 : Entry := ⟨363, [⟨137, 1, 4, 2⟩, ⟨248, 0, 2, 4⟩]⟩def entry_364 : Entry := ⟨364, [⟨63, 0, 3, 5⟩, ⟨314, 2, 3, 1⟩]⟩def entry_365 : Entry := ⟨365, [⟨6, 1, 4, 5⟩, ⟨354, 0, 4, 3⟩]⟩def entry_366 : Entry := ⟨366, [⟨6, 3, 4, 5⟩, ⟨357, 0, 6, 2⟩]⟩def entry_367 : Entry := ⟨367, [⟨6, 2, 5, 4⟩, ⟨361, 4, 4, 6⟩]⟩def entry_368 : Entry := ⟨368, [⟨6, 1, 4, 5⟩, ⟨366, 0, 2, 4⟩]⟩def entry_369 : Entry := ⟨369, [⟨6, 0, 5, 4⟩, ⟨367, 4, 1, 2⟩]⟩def entry_370 : Entry := ⟨370, [⟨199, 3, 1, 4⟩, ⟨286, 1, 5, 4⟩, ⟨24, 6, 1, 3⟩, ⟨319, 0, 5, 3⟩]⟩def entry_371 : Entry := ⟨371, [⟨267, 6, 2, 4⟩, ⟨137, 1, 4, 2⟩]⟩def entry_372 : Entry := ⟨372, [⟨40, 1, 4, 3⟩, ⟨333, 0, 2, 4⟩, ⟨120, 1, 3, 3⟩, ⟨161, 0, 4, 2⟩]⟩def entry_373 : Entry := ⟨373, [⟨156, 2, 7, 4⟩, ⟨226, 4, 3, 5⟩, ⟨80, 0, 5, 4⟩, ⟨327, 0, 5, 5⟩, ⟨156, 6, 3, 4⟩]⟩def entry_374 : Entry := ⟨374, [⟨65, 4, 3, 4⟩, ⟨335, 0, 7, 4⟩, ⟨24, 2, 7, 3⟩, ⟨163, 4, 3, 4⟩]⟩def entry_375 : Entry := ⟨375, [⟨24, 3, 3, 6⟩, ⟨327, 6, 3, 3⟩]⟩def entry_376 : Entry := ⟨376, [⟨162, 1, 5, 4⟩, ⟨285, 3, 1, 3⟩]⟩def entry_377 : Entry := ⟨377, [⟨29, 3, 3, 0⟩, ⟨362, 0, 7, 2⟩]⟩def entry_378 : Entry := ⟨378, [⟨295, 0, 5, 4⟩, ⟨176, 4, 1, 4⟩, ⟨183, 4, 1, 4⟩, ⟨172, 6, 1, 4⟩, ⟨294, 4, 1, 4⟩]⟩def entry_379 : Entry := ⟨379, [⟨63, 0, 3, 5⟩, ⟨64, 1, 3, 1⟩, ⟨55, 3, 4, 5⟩, ⟨368, 0, 5, 4⟩]⟩def entry_380 : Entry := ⟨380, [⟨101, 4, 2, 5⟩, ⟨271, 0, 2, 5⟩, ⟨223, 0, 5, 4⟩, ⟨192, 3, 1, 4⟩]⟩def entry_381 : Entry := ⟨381, [⟨211, 6, 3, 4⟩, ⟨24, 0, 7, 5⟩, ⟨163, 4, 3, 4⟩, ⟨341, 0, 7, 4⟩]⟩def entry_382 : Entry := ⟨382, [⟨124, 1, 5, 3⟩, ⟨2, 7, 4, 3⟩]⟩def entry_383 : Entry := ⟨383, [⟨192, 3, 2, 4⟩, ⟨271, 0, 3, 5⟩, ⟨197, 0, 6, 4⟩, ⟨172, 0, 6, 4⟩, ⟨215, 4, 3, 5⟩]⟩def entry_384 : Entry := ⟨384, [⟨173, 2, 6, 4⟩, ⟨282, 4, 2, 4⟩, ⟨220, 2, 6, 4⟩, ⟨246, 2, 6, 4⟩, ⟨263, 2, 6, 4⟩, ⟨183, 6, 2, 4⟩, ⟨295, 0, 6, 4⟩]⟩def entry_385 : Entry := ⟨385, [⟨63, 1, 5, 3⟩, ⟨64, 2, 1, 5⟩, ⟨55, 0, 5, 4⟩, ⟨369, 4, 1, 5⟩]⟩def entry_386 : Entry := ⟨386, [⟨217, 4, 1, 4⟩, ⟨172, 0, 5, 4⟩, ⟨173, 4, 1, 4⟩, ⟨217, 0, 5, 4⟩, ⟨294, 0, 5, 4⟩, ⟨294, 4, 1, 4⟩]⟩def entry_387 : Entry := ⟨387, [⟨14, 1, 4, 6⟩, ⟨370, 0, 5, 4⟩]⟩def entry_388 : Entry := ⟨388, [⟨6, 3, 4, 5⟩, ⟨374, 0, 3, 4⟩]⟩def entry_389 : Entry := ⟨389, [⟨197, 5, 4, 1⟩, ⟨215, 7, 3, 2⟩, ⟨271, 3, 3, 2⟩, ⟨236, 0, 5, 5⟩, ⟨192, 6, 4, 1⟩]⟩def entry_390 : Entry := ⟨390, [⟨372, 2, 5, 0⟩, ⟨167, 5, 4, 1⟩, ⟨12, 7, 3, 1⟩]⟩def entry_391 : Entry := ⟨391, [⟨6, 5, 5, 1⟩, ⟨388, 0, 3, 5⟩]⟩def entry_392 : Entry := ⟨392, [⟨24, 7, 3, 1⟩, ⟨107, 1, 4, 5⟩, ⟨236, 0, 5, 5⟩, ⟨364, 2, 4, 1⟩]⟩def entry_393 : Entry := ⟨393, [⟨107, 3, 4, 5⟩, ⟨348, 0, 6, 3⟩, ⟨65, 3, 4, 5⟩, ⟨303, 0, 4, 5⟩]⟩def entry_394 : Entry := ⟨394, [⟨226, 4, 1, 4⟩, ⟨226, 0, 5, 4⟩, ⟨327, 4, 3, 4⟩, ⟨327, 6, 3, 3⟩, ⟨226, 6, 1, 3⟩, ⟨226, 2, 5, 3⟩]⟩def entry_395 : Entry := ⟨395, [⟨211, 4, 2, 4⟩, ⟨376, 0, 6, 4⟩, ⟨24, 2, 6, 3⟩, ⟨236, 3, 2, 5⟩]⟩def entry_396 : Entry := ⟨396, [⟨107, 3, 4, 5⟩, ⟨365, 1, 7, 3⟩, ⟨303, 0, 4, 5⟩, ⟨65, 3, 4, 5⟩]⟩def entry_397 : Entry := ⟨397, [⟨24, 3, 4, 5⟩, ⟨374, 0, 3, 4⟩, ⟨65, 5, 5, 1⟩]⟩def entry_398 : Entry := ⟨398, [⟨257, 0, 1, 3⟩, ⟨363, 0, 5, 4⟩, ⟨130, 1, 4, 2⟩, ⟨177, 1, 4, 2⟩]⟩def entry_399 : Entry := ⟨399, [⟨192, 6, 4, 1⟩, ⟨271, 3, 3, 2⟩, ⟨173, 1, 4, 5⟩, ⟨319, 1, 3, 5⟩, ⟨215, 7, 3, 2⟩]⟩def entry_400 : Entry := ⟨400, [⟨283, 4, 2, 4⟩, ⟨252, 4, 2, 4⟩, ⟨176, 4, 2, 4⟩, ⟨197, 0, 6, 4⟩, ⟨283, 0, 6, 4⟩, ⟨245, 4, 2, 4⟩]⟩def entry_401 : Entry := ⟨401, [⟨24, 7, 3, 2⟩, ⟨286, 0, 4, 6⟩, ⟨364, 2, 4, 2⟩, ⟨319, 1, 3, 6⟩]⟩def entry_402 : Entry := ⟨402, [⟨29, 3, 3, 0⟩, ⟨384, 0, 5, 4⟩]⟩def entry_403 : Entry := ⟨403, [⟨202, 1, 4, 5⟩, ⟨180, 0, 4, 5⟩, ⟨314, 4, 5, 4⟩, ⟨63, 0, 3, 5⟩, ⟨388, 0, 3, 4⟩]⟩def entry_404 : Entry := ⟨404, [⟨82, 6, 2, 3⟩, ⟨388, 4, 4, 6⟩]⟩def entry_405 : Entry := ⟨405, [⟨391, 0, 4, 3⟩, ⟨301, 0, 5, 2⟩, ⟨42, 1, 4, 3⟩]⟩def entry_406 : Entry := ⟨406, [⟨295, 1, 4, 5⟩, ⟨172, 7, 4, 1⟩, ⟨245, 3, 4, 5⟩, ⟨197, 5, 4, 1⟩, ⟨236, 0, 5, 5⟩, ⟨176, 3, 4, 5⟩, ⟨364, 2, 4, 1⟩]⟩def entry_407 : Entry := ⟨407, [⟨285, 0, 3, 7⟩, ⟨314, 6, 5, 4⟩]⟩def entry_408 : Entry := ⟨408, [⟨357, 0, 5, 2⟩, ⟨229, 7, 2, 4⟩, ⟨223, 4, 2, 4⟩, ⟨223, 0, 6, 4⟩]⟩def entry_409 : Entry := ⟨409, [⟨136, 6, 4, 3⟩, ⟨384, 0, 5, 4⟩, ⟨133, 4, 4, 3⟩, ⟨110, 3, 4, 3⟩]⟩def entry_410 : Entry := ⟨410, [⟨0, 4, 5, 4⟩, ⟨405, 0, 3, 7⟩]⟩def entry_411 : Entry := ⟨411, [⟨252, 0, 7, 4⟩, ⟨263, 0, 7, 4⟩, ⟨300, 3, 3, 4⟩, ⟨379, 1, 7, 4⟩, ⟨173, 0, 7, 4⟩, ⟨246, 0, 7, 4⟩]⟩def entry_412 : Entry := ⟨412, [⟨0, 0, 0, 3⟩, ⟨403, 4, 3, 6⟩]⟩def entry_413 : Entry := ⟨413, [⟨3, 7, 4, 3⟩, ⟨403, 0, 4, 7⟩]⟩def entry_414 : Entry := ⟨414, [⟨374, 0, 2, 5⟩, ⟨199, 2, 4, 2⟩, ⟨185, 2, 4, 2⟩]⟩def entry_415 : Entry := ⟨415, [⟨177, 1, 4, 2⟩, ⟨164, 1, 4, 2⟩, ⟨205, 1, 5, 2⟩, ⟨384, 0, 3, 4⟩, ⟨371, 0, 5, 4⟩]⟩def entry_416 : Entry := ⟨416, [⟨176, 2, 5, 4⟩, ⟨385, 4, 1, 4⟩, ⟨197, 4, 1, 4⟩, ⟨295, 0, 5, 4⟩, ⟨245, 2, 5, 4⟩, ⟨220, 2, 5, 4⟩]⟩def entry_417 : Entry := ⟨417, [⟨409, 0, 2, 4⟩, ⟨11, 1, 4, 2⟩, ⟨270, 4, 4, 2⟩]⟩def entry_418 : Entry := ⟨418, [⟨68, 4, 1, 3⟩, ⟨62, 6, 1, 3⟩, ⟨147, 6, 1, 3⟩, ⟨413, 0, 4, 2⟩]⟩def entry_419 : Entry := ⟨419, [⟨243, 0, 4, 2⟩, ⟨164, 1, 4, 2⟩, ⟨402, 0, 2, 4⟩, ⟨253, 0, 2, 4⟩, ⟨377, 0, 2, 4⟩]⟩def entry_420 : Entry := ⟨420, [⟨29, 3, 3, 0⟩, ⟨415, 0, 6, 4⟩]⟩def entry_421 : Entry := ⟨421, [⟨24, 6, 2, 3⟩, ⟨397, 1, 5, 3⟩, ⟨25, 6, 2, 3⟩, ⟨241, 4, 2, 4⟩]⟩def entry_422 : Entry := ⟨422, [⟨45, 1, 3, 7⟩, ⟨106, 6, 2, 3⟩, ⟨419, 1, 6, 6⟩]⟩def entry_423 : Entry := ⟨423, [⟨378, 4, 2, 4⟩, ⟨386, 0, 5, 4⟩, ⟨226, 3, 3, 5⟩, ⟨386, 4, 2, 4⟩, ⟨378, 0, 5, 4⟩]⟩def entry_424 : Entry := ⟨424, [⟨55, 1, 4, 5⟩, ⟨394, 0, 6, 4⟩, ⟨216, 3, 4, 5⟩]⟩def entry_425 : Entry := ⟨425, [⟨386, 0, 5, 4⟩, ⟨226, 1, 4, 5⟩, ⟨378, 4, 2, 4⟩, ⟨378, 0, 5, 4⟩, ⟨386, 4, 2, 4⟩]⟩def entry_426 : Entry := ⟨426, [⟨300, 6, 4, 1⟩, ⟨252, 1, 4, 5⟩, ⟨397, 0, 3, 4⟩, ⟨291, 1, 4, 1⟩, ⟨328, 0, 4, 5⟩, ⟨319, 1, 3, 5⟩]⟩def entry_427 : Entry := ⟨427, [⟨45, 1, 3, 7⟩, ⟨106, 6, 2, 3⟩, ⟨420, 1, 6, 4⟩]⟩def entry_428 : Entry := ⟨428, [⟨26, 3, 4, 3⟩, ⟨416, 0, 5, 4⟩, ⟨244, 0, 5, 4⟩, ⟨329, 0, 4, 3⟩]⟩def entry_429 : Entry := ⟨429, [⟨128, 0, 6, 3⟩, ⟨28, 3, 4, 5⟩]⟩def entry_430 : Entry := ⟨430, [⟨277, 7, 1, 3⟩, ⟨338, 4, 3, 4⟩, ⟨336, 1, 4, 3⟩, ⟨375, 2, 4, 3⟩, ⟨277, 6, 3, 1⟩]⟩def entry_431 : Entry := ⟨431, [⟨73, 4, 3, 3⟩, ⟨302, 1, 5, 2⟩, ⟨415, 0, 6, 4⟩, ⟨398, 0, 6, 4⟩]⟩def entry_432 : Entry := ⟨432, [⟨42, 3, 4, 3⟩, ⟨428, 0, 5, 4⟩, ⟨274, 0, 4, 3⟩]⟩def entry_433 : Entry := ⟨433, [⟨63, 0, 3, 5⟩, ⟨7, 3, 3, 4⟩, ⟨427, 0, 5, 2⟩, ⟨422, 0, 5, 2⟩]⟩def entry_434 : Entry := ⟨434, [⟨418, 0, 4, 5⟩, ⟨263, 2, 5, 4⟩, ⟨295, 0, 5, 4⟩, ⟨176, 2, 5, 4⟩, ⟨116, 0, 4, 3⟩]⟩def entry_435 : Entry := ⟨435, [⟨6, 4, 3, 4⟩, ⟨431, 0, 5, 6⟩]⟩def entry_436 : Entry := ⟨436, [⟨51, 1, 5, 4⟩, ⟨60, 3, 4, 3⟩, ⟨274, 4, 4, 3⟩, ⟨428, 0, 5, 4⟩]⟩def entry_437 : Entry := ⟨437, [⟨55, 7, 4, 0⟩, ⟨427, 0, 5, 2⟩, ⟨63, 0, 3, 5⟩, ⟨422, 0, 5, 2⟩]⟩def entry_438 : Entry := ⟨438, [⟨0, 0, 1, 3⟩, ⟨432, 0, 4, 6⟩]⟩def entry_439 : Entry := ⟨439, [⟨176, 2, 5, 4⟩, ⟨295, 0, 5, 4⟩, ⟨263, 2, 5, 4⟩, ⟨418, 0, 4, 5⟩, ⟨149, 0, 4, 3⟩]⟩def entry_440 : Entry := ⟨440, [⟨6, 6, 1, 3⟩, ⟨435, 0, 2, 5⟩]⟩def entry_441 : Entry := ⟨441, [⟨6, 6, 3, 4⟩, ⟨435, 0, 4, 6⟩]⟩def entry_442 : Entry := ⟨442, [⟨63, 0, 3, 5⟩, ⟨7, 1, 5, 4⟩, ⟨433, 0, 4, 5⟩, ⟨201, 0, 3, 2⟩]⟩def entry_443 : Entry := ⟨443, [⟨6, 0, 5, 4⟩, ⟨438, 0, 3, 4⟩]⟩def entry_444 : Entry := ⟨444, [⟨194, 0, 5, 3⟩, ⟨160, 3, 4, 1⟩, ⟨142, 7, 4, 1⟩, ⟨236, 0, 5, 5⟩, ⟨353, 4, 1, 2⟩, ⟨412, 0, 5, 3⟩]⟩def entry_445 : Entry := ⟨445, [⟨9, 4, 3, 4⟩, ⟨432, 0, 5, 7⟩]⟩def entry_446 : Entry := ⟨446, [⟨4, 6, 4, 3⟩, ⟨438, 0, 6, 5⟩]⟩def entry_447 : Entry := ⟨447, [⟨0, 0, 0, 3⟩, ⟨436, 4, 4, 6⟩]⟩def entry_448 : Entry := ⟨448, [⟨9, 4, 1, 3⟩, ⟨436, 0, 3, 6⟩]⟩def entry_449 : Entry := ⟨449, [⟨26, 3, 4, 3⟩, ⟨244, 0, 5, 4⟩, ⟨439, 0, 5, 4⟩, ⟨307, 0, 4, 3⟩]⟩def entry_450 : Entry := ⟨450, [⟨6, 1, 5, 5⟩, ⟨440, 0, 6, 4⟩]⟩def entry_451 : Entry := ⟨451, [⟨1, 5, 4, 3⟩, ⟨449, 0, 5, 4⟩]⟩def entry_452 : Entry := ⟨452, [⟨24, 1, 5, 7⟩, ⟨451, 0, 3, 8⟩, ⟨25, 3, 3, 7⟩]⟩def entry_453 : Entry := ⟨453, [⟨359, 0, 4, 3⟩, ⟨226, 7, 3, 1⟩, ⟨386, 4, 2, 4⟩, ⟨389, 1, 5, 4⟩, ⟨414, 4, 3, 3⟩]⟩def entry_454 : Entry := ⟨454, [⟨58, 0, 6, 3⟩, ⟨436, 0, 3, 6⟩]⟩def entry_455 : Entry := ⟨455, [⟨20, 2, 4, 5⟩, ⟨118, 3, 0, 5⟩, ⟨39, 2, 3, 4⟩]⟩def entry_456 : Entry := ⟨456, [⟨308, 4, 4, 3⟩, ⟨64, 2, 1, 5⟩, ⟨63, 1, 5, 3⟩, ⟨55, 0, 5, 4⟩]⟩def entry_457 : Entry := ⟨457, [⟨28, 7, 3, 2⟩, ⟨454, 0, 5, 4⟩]⟩def entry_458 : Entry := ⟨458, [⟨130, 1, 4, 2⟩, ⟨177, 1, 4, 2⟩, ⟨450, 0, 1, 4⟩]⟩def entry_459 : Entry := ⟨459, [⟨97, 2, 7, 3⟩, ⟨448, 0, 5, 4⟩, ⟨65, 2, 7, 3⟩]⟩def entry_460 : Entry := ⟨460, [⟨183, 6, 1, 4⟩, ⟨173, 2, 5, 4⟩, ⟨295, 0, 5, 4⟩, ⟨282, 4, 1, 4⟩, ⟨246, 2, 5, 4⟩, ⟨263, 2, 5, 4⟩, ⟨220, 2, 5, 4⟩]⟩def entry_461 : Entry := ⟨461, [⟨4, 1, 4, 3⟩, ⟨458, 0, 6, 4⟩]⟩def entry_462 : Entry := ⟨462, [⟨452, 0, 3, 2⟩, ⟨86, 0, 5, 4⟩, ⟨328, 1, 5, 4⟩]⟩def entry_463 : Entry := ⟨463, [⟨170, 0, 6, 3⟩, ⟨76, 1, 3, 2⟩, ⟨447, 0, 5, 4⟩]⟩def entry_464 : Entry := ⟨464, [⟨63, 0, 3, 5⟩, ⟨224, 0, 5, 4⟩, ⟨315, 0, 7, 3⟩, ⟨306, 0, 5, 5⟩, ⟨358, 0, 7, 3⟩, ⟨461, 0, 5, 5⟩]⟩def entry_465 : Entry := ⟨465, [⟨55, 3, 4, 5⟩, ⟨285, 0, 3, 4⟩, ⟨64, 1, 3, 1⟩]⟩def entry_466 : Entry := ⟨466, [⟨395, 4, 3, 4⟩, ⟨360, 4, 2, 6⟩, ⟨417, 1, 5, 4⟩, ⟨325, 4, 3, 4⟩, ⟨324, 4, 3, 5⟩]⟩def entry_467 : Entry := ⟨467, [⟨64, 7, 5, 7⟩, ⟨314, 6, 5, 4⟩, ⟨443, 1, 5, 7⟩]⟩def entry_468 : Entry := ⟨468, [⟨6, 6, 3, 4⟩, ⟨464, 0, 4, 7⟩]⟩def entry_469 : Entry := ⟨469, [⟨55, 5, 4, 3⟩, ⟨443, 1, 5, 7⟩, ⟨314, 6, 5, 4⟩]⟩def entry_470 : Entry := ⟨470, [⟨6, 4, 3, 4⟩, ⟨468, 0, 4, 2⟩]⟩def entry_471 : Entry := ⟨471, [⟨6, 5, 4, 3⟩, ⟨466, 0, 5, 6⟩]⟩def entry_472 : Entry := ⟨472, [⟨6, 5, 5, 0⟩, ⟨466, 0, 6, 3⟩]⟩def entry_473 : Entry := ⟨473, [⟨121, 5, 5, 4⟩, ⟨436, 0, 3, 7⟩, ⟨445, 4, 5, 4⟩]⟩def entry_474 : Entry := ⟨474, [⟨463, 0, 6, 5⟩, ⟨70, 0, 3, 5⟩, ⟨83, 1, 5, 3⟩]⟩def entry_475 : Entry := ⟨475, [⟨63, 1, 5, 3⟩, ⟨261, 1, 4, 3⟩, ⟨457, 0, 2, 5⟩, ⟨269, 2, 2, 5⟩]⟩def entry_476 : Entry := ⟨476, [⟨0, 0, 1, 3⟩, ⟨473, 0, 5, 3⟩]⟩def entry_477 : Entry := ⟨477, [⟨55, 1, 4, 5⟩, ⟨154, 7, 4, 5⟩, ⟨154, 3, 4, 0⟩, ⟨471, 2, 5, 4⟩]⟩def entry_478 : Entry := ⟨478, [⟨25, 3, 4, 5⟩, ⟨165, 2, 4, 5⟩, ⟨190, 0, 7, 4⟩]⟩def entry_479 : Entry := ⟨479, [⟨55, 0, 5, 4⟩, ⟨443, 0, 4, 5⟩, ⟨443, 4, 1, 5⟩]⟩def entry_480 : Entry := ⟨480, [⟨108, 1, 4, 5⟩, ⟨4, 1, 5, 4⟩]⟩def entry_481 : Entry := ⟨481, [⟨303, 1, 5, 4⟩, ⟨429, 2, 1, 4⟩, ⟨309, 1, 1, 4⟩, ⟨206, 2, 1, 4⟩, ⟨169, 2, 1, 4⟩, ⟨207, 2, 1, 4⟩]⟩def entry_482 : Entry := ⟨482, [⟨6, 1, 4, 5⟩, ⟨218, 2, 4, 3⟩]⟩def entry_483 : Entry := ⟨483, [⟨173, 1, 4, 5⟩, ⟨292, 7, 3, 1⟩, ⟨319, 1, 3, 5⟩, ⟨192, 6, 4, 1⟩, ⟨475, 1, 4, 5⟩]⟩def entry_484 : Entry := ⟨484, [⟨25, 4, 1, 5⟩, ⟨107, 2, 5, 4⟩, ⟨349, 3, 1, 5⟩, ⟨163, 2, 5, 4⟩]⟩def entry_485 : Entry := ⟨485, [⟨484, 0, 5, 4⟩, ⟨2, 3, 4, 3⟩]⟩def entry_486 : Entry := ⟨486, [⟨2, 5, 4, 2⟩, ⟨485, 0, 5, 3⟩]⟩def entry_487 : Entry := ⟨487, [⟨2, 3, 4, 3⟩, ⟨481, 0, 5, 4⟩]⟩def entry_488 : Entry := ⟨488, [⟨0, 6, 6, 4⟩, ⟨247, 0, 2, 5⟩]⟩def entry_489 : Entry := ⟨489, [⟨356, 1, 3, 3⟩, ⟨197, 4, 1, 4⟩, ⟨172, 6, 1, 4⟩]⟩def entry_490 : Entry := ⟨490, [⟨64, 1, 3, 1⟩, ⟨471, 0, 5, 1⟩, ⟨470, 1, 5, 1⟩, ⟨111, 0, 3, 1⟩]⟩def entry_491 : Entry := ⟨491, [⟨6, 3, 3, 5⟩, ⟨273, 0, 5, 4⟩]⟩def entry_492 : Entry := ⟨492, [⟨62, 4, 3, 4⟩, ⟨107, 4, 3, 4⟩, ⟨487, 0, 6, 6⟩]⟩def entry_493 : Entry := ⟨493, [⟨225, 0, 1, 4⟩, ⟨455, 0, 5, 3⟩, ⟨236, 1, 5, 5⟩, ⟨221, 0, 5, 4⟩]⟩def entry_494 : Entry := ⟨494, [⟨297, 4, 4, 5⟩, ⟨268, 4, 1, 5⟩, ⟨162, 5, 5, 4⟩]⟩def entry_495 : Entry := ⟨495, [⟨25, 6, 1, 3⟩, ⟨167, 4, 1, 4⟩, ⟨456, 4, 1, 4⟩]⟩def entry_496 : Entry := ⟨496, [⟨25, 0, 7, 5⟩, ⟨107, 6, 3, 4⟩, ⟨163, 6, 3, 4⟩, ⟨494, 0, 7, 4⟩]⟩def entry_497 : Entry := ⟨497, [⟨36, 2, 3, 4⟩, ⟨167, 0, 7, 4⟩, ⟨410, 0, 7, 3⟩]⟩def entry_498 : Entry := ⟨498, [⟨14, 1, 4, 6⟩, ⟨298, 2, 2, 4⟩]⟩def entry_499 : Entry := ⟨499, [⟨493, 0, 5, 4⟩, ⟨25, 1, 4, 5⟩, ⟨478, 0, 2, 4⟩]⟩def entry_500 : Entry := ⟨500, [⟨1, 5, 3, 6⟩, ⟨351, 0, 5, 4⟩]⟩def entry_501 : Entry := ⟨501, [⟨6, 4, 0, 5⟩, ⟨316, 0, 1, 3⟩]⟩def entry_502 : Entry := ⟨502, [⟨215, 6, 2, 3⟩, ⟨232, 0, 4, 3⟩, ⟨192, 7, 1, 4⟩, ⟨173, 0, 5, 4⟩, ⟨271, 2, 2, 3⟩]⟩def entry_503 : Entry := ⟨503, [⟨63, 0, 3, 5⟩, ⟨55, 7, 4, 0⟩, ⟨420, 1, 7, 2⟩, ⟨419, 1, 7, 4⟩]⟩def entry_504 : Entry := ⟨504, [⟨381, 0, 3, 4⟩, ⟨310, 4, 4, 5⟩, ⟨159, 0, 5, 6⟩, ⟨351, 4, 3, 4⟩, ⟨496, 0, 3, 4⟩]⟩def entry_505 : Entry := ⟨505, [⟨173, 1, 4, 5⟩, ⟨499, 0, 5, 4⟩, ⟨183, 1, 4, 5⟩, ⟨282, 1, 4, 5⟩]⟩def entry_506 : Entry := ⟨506, [⟨99, 0, 4, 5⟩, ⟨200, 7, 1, 4⟩, ⟨318, 5, 5, 4⟩, ⟨173, 0, 5, 4⟩]⟩def entry_507 : Entry := ⟨507, [⟨151, 0, 2, 4⟩, ⟨33, 3, 4, 3⟩, ⟨481, 0, 5, 4⟩]⟩def entry_508 : Entry := ⟨508, [⟨6, 0, 5, 4⟩, ⟨393, 0, 1, 5⟩]⟩def entry_509 : Entry := ⟨509, [⟨252, 0, 6, 4⟩, ⟨241, 4, 2, 4⟩, ⟨455, 0, 6, 3⟩, ⟨68, 2, 6, 4⟩]⟩def entry_510 : Entry := ⟨510, [⟨6, 4, 3, 4⟩, ⟨508, 0, 7, 4⟩]⟩def entry_511 : Entry := ⟨511, [⟨15, 1, 4, 5⟩, ⟨331, 0, 5, 3⟩, ⟨380, 4, 2, 4⟩]⟩def entry_512 : Entry := ⟨512, [⟨62, 0, 5, 4⟩, ⟨107, 0, 5, 4⟩, ⟨507, 0, 4, 6⟩]⟩def entry_513 : Entry := ⟨513, [⟨6, 4, 3, 4⟩, ⟨396, 0, 4, 5⟩]⟩def entry_514 : Entry := ⟨514, [⟨57, 0, 5, 4⟩, ⟨443, 4, 1, 5⟩, ⟨510, 0, 1, 5⟩]⟩def entry_515 : Entry := ⟨515, [⟨2, 6, 2, 4⟩, ⟨512, 1, 1, 5⟩]⟩def entry_516 : Entry := ⟨516, [⟨329, 0, 4, 3⟩, ⟨244, 4, 2, 4⟩, ⟨10, 1, 4, 5⟩, ⟨506, 4, 2, 4⟩]⟩def entry_517 : Entry := ⟨517, [⟨496, 0, 2, 3⟩, ⟨140, 0, 4, 2⟩, ⟨193, 1, 4, 2⟩]⟩def entry_518 : Entry := ⟨518, [⟨9, 6, 3, 4⟩, ⟨514, 0, 7, 4⟩]⟩def entry_519 : Entry := ⟨519, [⟨498, 0, 4, 3⟩, ⟨311, 4, 3, 4⟩, ⟨38, 1, 4, 5⟩, ⟨408, 0, 3, 4⟩]⟩def entry_520 : Entry := ⟨520, [⟨254, 0, 2, 3⟩, ⟨200, 5, 6, 4⟩, ⟨271, 6, 5, 3⟩, ⟨215, 2, 5, 3⟩, ⟨252, 4, 2, 4⟩]⟩def entry_521 : Entry := ⟨521, [⟨492, 4, 5, 1⟩, ⟨2, 7, 4, 2⟩]⟩def entry_522 : Entry := ⟨522, [⟨176, 3, 4, 6⟩, ⟨338, 2, 3, 3⟩, ⟨252, 1, 4, 6⟩]⟩def entry_523 : Entry := ⟨523, [⟨303, 1, 5, 4⟩, ⟨25, 4, 1, 5⟩, ⟨107, 2, 5, 4⟩, ⟨511, 4, 1, 6⟩]⟩def entry_524 : Entry := ⟨524, [⟨504, 4, 5, 3⟩, ⟨504, 0, 3, 3⟩, ⟨180, 0, 4, 5⟩, ⟨180, 4, 4, 5⟩, ⟨261, 0, 3, 4⟩]⟩def entry_525 : Entry := ⟨525, [⟨303, 1, 5, 4⟩, ⟨25, 4, 1, 5⟩, ⟨430, 0, 4, 6⟩, ⟨107, 2, 5, 4⟩]⟩def entry_526 : Entry := ⟨526, [⟨359, 0, 4, 3⟩, ⟨416, 4, 2, 4⟩, ⟨327, 5, 4, 3⟩, ⟨489, 0, 5, 4⟩, ⟨399, 3, 2, 4⟩]⟩def entry_527 : Entry := ⟨527, [⟨387, 4, 4, 3⟩, ⟨38, 3, 4, 5⟩, ⟨491, 0, 5, 4⟩, ⟨519, 0, 6, 4⟩]⟩def entry_528 : Entry := ⟨528, [⟨414, 1, 3, 5⟩, ⟨386, 1, 4, 6⟩, ⟨502, 5, 4, 3⟩, ⟨226, 4, 1, 5⟩, ⟨359, 5, 3, 4⟩]⟩def entry_529 : Entry := ⟨529, [⟨55, 4, 3, 4⟩, ⟨441, 0, 4, 3⟩, ⟨63, 3, 3, 3⟩, ⟨64, 6, 7, 5⟩]⟩def entry_530 : Entry := ⟨530, [⟨456, 7, 4, 2⟩, ⟨336, 0, 5, 5⟩, ⟨283, 7, 4, 2⟩, ⟨271, 5, 5, 5⟩]⟩def entry_531 : Entry := ⟨531, [⟨425, 0, 5, 4⟩, ⟨336, 3, 4, 3⟩, ⟨340, 6, 4, 3⟩, ⟨394, 1, 5, 4⟩, ⟨423, 0, 5, 4⟩, ⟨526, 0, 5, 4⟩, ⟨401, 4, 4, 3⟩, ⟨453, 0, 5, 4⟩]⟩def entry_532 : Entry := ⟨532, [⟨504, 4, 5, 3⟩, ⟨6, 7, 3, 0⟩]⟩def entry_533 : Entry := ⟨533, [⟨318, 4, 4, 5⟩, ⟨319, 7, 5, 1⟩, ⟨407, 4, 4, 1⟩, ⟨173, 3, 4, 5⟩, ⟨217, 1, 4, 5⟩]⟩def entry_534 : Entry := ⟨534, [⟨434, 0, 4, 6⟩, ⟨12, 6, 1, 3⟩]⟩def entry_535 : Entry := ⟨535, [⟨444, 0, 4, 5⟩, ⟨426, 0, 4, 5⟩, ⟨25, 0, 5, 4⟩, ⟨321, 4, 4, 2⟩]⟩def entry_536 : Entry := ⟨536, [⟨307, 0, 4, 3⟩, ⟨244, 0, 5, 4⟩, ⟨26, 3, 4, 3⟩, ⟨534, 0, 5, 2⟩]⟩def entry_537 : Entry := ⟨537, [⟨373, 2, 2, 4⟩, ⟨271, 3, 3, 3⟩, ⟨176, 1, 4, 6⟩, ⟨330, 1, 4, 6⟩]⟩def entry_538 : Entry := ⟨538, [⟨63, 3, 3, 3⟩, ⟨470, 0, 4, 5⟩, ⟨64, 6, 7, 5⟩, ⟨55, 4, 3, 4⟩]⟩def entry_539 : Entry := ⟨539, [⟨51, 1, 5, 4⟩, ⟨488, 3, 4, 3⟩, ⟨428, 0, 5, 4⟩, ⟨516, 0, 5, 4⟩]⟩def entry_540 : Entry := ⟨540, [⟨334, 0, 4, 3⟩, ⟨51, 1, 5, 4⟩, ⟨88, 3, 4, 3⟩, ⟨536, 0, 5, 4⟩]⟩def entry_541 : Entry := ⟨541, [⟨236, 0, 5, 5⟩, ⟨142, 7, 4, 1⟩, ⟨160, 3, 4, 1⟩, ⟨194, 0, 5, 3⟩, ⟨501, 4, 1, 2⟩, ⟨412, 0, 5, 3⟩]⟩def entry_542 : Entry := ⟨542, [⟨6, 5, 5, 0⟩, ⟨442, 0, 4, 5⟩]⟩def entry_543 : Entry := ⟨543, [⟨493, 3, 2, 6⟩, ⟨107, 2, 5, 4⟩, ⟨318, 5, 5, 4⟩]⟩def entry_544 : Entry := ⟨544, [⟨263, 2, 7, 4⟩, ⟨9, 6, 3, 4⟩, ⟨451, 1, 8, 3⟩]⟩def entry_545 : Entry := ⟨545, [⟨256, 0, 4, 5⟩, ⟨448, 0, 5, 4⟩, ⟨153, 0, 6, 3⟩, ⟨343, 0, 4, 5⟩]⟩def entry_546 : Entry := ⟨546, [⟨64, 0, 4, 3⟩, ⟨482, 7, 4, 3⟩, ⟨443, 0, 7, 5⟩, ⟨64, 6, 7, 5⟩]⟩def entry_547 : Entry := ⟨547, [⟨443, 0, 7, 5⟩, ⟨510, 4, 7, 5⟩, ⟨131, 3, 3, 4⟩]⟩def entry_548 : Entry := ⟨548, [⟨426, 0, 4, 5⟩, ⟨541, 0, 4, 5⟩, ⟨25, 0, 5, 4⟩, ⟨321, 4, 4, 2⟩]⟩def entry_549 : Entry := ⟨549, [⟨385, 0, 6, 4⟩, ⟨385, 4, 2, 4⟩, ⟨330, 0, 6, 4⟩, ⟨252, 6, 2, 4⟩, ⟨326, 0, 6, 4⟩, ⟨529, 0, 2, 4⟩]⟩def entry_550 : Entry := ⟨550, [⟨424, 0, 4, 6⟩, ⟨172, 7, 4, 2⟩, ⟨215, 1, 5, 5⟩, ⟨456, 7, 4, 2⟩]⟩def entry_551 : Entry := ⟨551, [⟨300, 6, 4, 3⟩, ⟨172, 7, 4, 3⟩, ⟨319, 3, 5, 7⟩, ⟨527, 4, 5, 7⟩, ⟨176, 5, 4, 3⟩]⟩def entry_552 : Entry := ⟨552, [⟨443, 4, 1, 5⟩, ⟨64, 2, 1, 5⟩, ⟨504, 1, 3, 3⟩, ⟨404, 5, 2, 3⟩]⟩def entry_553 : Entry := ⟨553, [⟨63, 0, 3, 5⟩, ⟨261, 4, 5, 4⟩, ⟨471, 0, 5, 1⟩, ⟨442, 0, 4, 5⟩, ⟨504, 0, 3, 3⟩, ⟨180, 0, 4, 5⟩]⟩def entry_554 : Entry := ⟨554, [⟨30, 6, 5, 4⟩, ⟨96, 7, 4, 5⟩, ⟨474, 0, 4, 5⟩]⟩def entry_555 : Entry := ⟨555, [⟨504, 5, 3, 5⟩, ⟨513, 0, 1, 5⟩, ⟨55, 0, 5, 4⟩, ⟨443, 4, 1, 5⟩, ⟨471, 1, 1, 5⟩]⟩def entry_556 : Entry := ⟨556, [⟨34, 1, 4, 2⟩, ⟨549, 0, 3, 4⟩]⟩def entry_557 : Entry := ⟨557, [⟨460, 0, 5, 4⟩, ⟨460, 4, 2, 4⟩, ⟨460, 2, 5, 4⟩, ⟨411, 4, 5, 4⟩, ⟨531, 0, 3, 6⟩, ⟨531, 4, 4, 6⟩, ⟨406, 5, 5, 4⟩]⟩def entry_558 : Entry := ⟨558, [⟨180, 5, 5, 4⟩, ⟨443, 4, 1, 5⟩, ⟨513, 0, 1, 5⟩, ⟨442, 1, 5, 4⟩]⟩def entry_559 : Entry := ⟨559, [⟨228, 4, 5, 2⟩, ⟨7, 3, 3, 4⟩, ⟨155, 4, 4, 5⟩, ⟨538, 5, 4, 5⟩]⟩def entry_560 : Entry := ⟨560, [⟨517, 5, 5, 4⟩, ⟨416, 5, 4, 3⟩, ⟨359, 5, 3, 4⟩, ⟨356, 6, 3, 4⟩, ⟨483, 0, 4, 6⟩]⟩def entry_561 : Entry := ⟨561, [⟨295, 0, 5, 4⟩, ⟨173, 2, 5, 4⟩, ⟨263, 6, 1, 4⟩, ⟨236, 1, 5, 5⟩, ⟨546, 4, 5, 4⟩, ⟨176, 2, 5, 4⟩, ⟨535, 0, 4, 5⟩]⟩def entry_562 : Entry := ⟨562, [⟨6, 7, 3, 0⟩, ⟨559, 0, 4, 5⟩]⟩def entry_563 : Entry := ⟨563, [⟨167, 0, 7, 4⟩, ⟨538, 0, 3, 4⟩, ⟨514, 0, 7, 4⟩, ⟨330, 4, 3, 4⟩, ⟨545, 0, 5, 5⟩]⟩def entry_564 : Entry := ⟨564, [⟨560, 0, 4, 3⟩, ⟨421, 0, 3, 4⟩, ⟨401, 1, 3, 4⟩, ⟨340, 3, 3, 4⟩, ⟨509, 0, 3, 4⟩, ⟨528, 0, 4, 3⟩, ⟨423, 5, 4, 3⟩, ⟨425, 5, 4, 3⟩, ⟨336, 0, 3, 4⟩]⟩def entry_565 : Entry := ⟨565, [⟨443, 4, 4, 5⟩, ⟨131, 3, 3, 4⟩, ⟨538, 0, 3, 4⟩, ⟨459, 0, 5, 5⟩, ⟨144, 4, 3, 4⟩]⟩def entry_566 : Entry := ⟨566, [⟨314, 0, 3, 4⟩, ⟨180, 0, 4, 5⟩, ⟨442, 0, 4, 5⟩, ⟨466, 0, 6, 3⟩, ⟨504, 0, 3, 3⟩]⟩def entry_567 : Entry := ⟨567, [⟨21, 1, 4, 3⟩, ⟨561, 0, 6, 4⟩, ⟨500, 4, 3, 1⟩]⟩def entry_568 : Entry := ⟨568, [⟨538, 4, 6, 4⟩, ⟨547, 0, 2, 4⟩, ⟨275, 0, 6, 4⟩, ⟨565, 0, 2, 4⟩, ⟨330, 0, 6, 4⟩]⟩def entry_569 : Entry := ⟨569, [⟨34, 3, 4, 2⟩, ⟨568, 4, 5, 4⟩]⟩def entry_570 : Entry := ⟨570, [⟨569, 0, 2, 5⟩, ⟨2, 7, 4, 3⟩]⟩def entry_571 : Entry := ⟨571, [⟨293, 0, 4, 3⟩, ⟨570, 0, 4, 3⟩, ⟨382, 0, 4, 3⟩, ⟨556, 4, 2, 4⟩]⟩def entry_572 : Entry := ⟨572, [⟨564, 1, 6, 6⟩, ⟨465, 3, 3, 4⟩, ⟨385, 4, 3, 4⟩, ⟨364, 7, 3, 4⟩, ⟨499, 1, 6, 5⟩]⟩def entry_573 : Entry := ⟨573, [⟨527, 2, 3, 1⟩, ⟨499, 4, 3, 4⟩, ⟨527, 6, 5, 1⟩, ⟨499, 0, 5, 4⟩, ⟨407, 4, 4, 1⟩, ⟨531, 7, 2, 4⟩, ⟨407, 0, 4, 1⟩]⟩def entry_574 : Entry := ⟨574, [⟨497, 0, 2, 4⟩, ⟨539, 4, 4, 6⟩, ⟨355, 0, 2, 4⟩, ⟨390, 3, 2, 4⟩, ⟨544, 0, 2, 4⟩, ⟨462, 1, 4, 5⟩, ⟨563, 4, 5, 4⟩, ⟨540, 4, 4, 6⟩, ⟨518, 0, 2, 4⟩, ⟨495, 4, 2, 4⟩]⟩def entry_575 : Entry := ⟨575, [⟨314, 4, 5, 4⟩, ⟨504, 4, 5, 3⟩, ⟨180, 4, 4, 5⟩, ⟨442, 4, 4, 5⟩, ⟨559, 0, 4, 5⟩]⟩def entry_576 : Entry := ⟨576, [⟨495, 0, 5, 4⟩, ⟨544, 4, 5, 4⟩, ⟨462, 3, 3, 5⟩, ⟨540, 0, 3, 6⟩, ⟨355, 4, 5, 4⟩, ⟨539, 0, 3, 6⟩, ⟨497, 4, 5, 4⟩, ⟨390, 1, 5, 4⟩, ⟨563, 0, 2, 4⟩, ⟨518, 4, 5, 4⟩]⟩def entry_577 : Entry := ⟨577, [⟨64, 7, 5, 4⟩, ⟨64, 1, 3, 1⟩, ⟨443, 1, 5, 4⟩, ⟨443, 7, 3, 1⟩]⟩def entry_578 : Entry := ⟨578, [⟨574, 4, 4, 5⟩, ⟨2, 1, 4, 3⟩]⟩def entry_579 : Entry := ⟨579, [⟨2, 1, 4, 3⟩, ⟨576, 4, 4, 5⟩]⟩def entry_580 : Entry := ⟨580, [⟨2, 7, 4, 2⟩, ⟨579, 0, 3, 3⟩]⟩def entry_581 : Entry := ⟨581, [⟨578, 4, 5, 3⟩, ⟨2, 5, 4, 2⟩]⟩def entry_582 : Entry := ⟨582, [⟨40, 3, 4, 3⟩, ⟨446, 5, 5, 3⟩, ⟨523, 0, 7, 0⟩, ⟨480, 4, 5, 3⟩, ⟨567, 4, 5, 4⟩]⟩def entry_583 : Entry := ⟨583, [⟨25, 5, 4, 3⟩, ⟨525, 0, 5, 4⟩, ⟨582, 0, 2, 8⟩, ⟨221, 3, 3, 7⟩]⟩def entry_584 : Entry := ⟨584, [⟨263, 1, 4, 5⟩, ⟨236, 4, 3, 5⟩, ⟨548, 3, 3, 4⟩, ⟨295, 3, 4, 5⟩, ⟨577, 0, 4, 5⟩, ⟨173, 1, 4, 5⟩]⟩def entry_585 : Entry := ⟨585, [⟨236, 2, 5, 1⟩, ⟨300, 4, 4, 5⟩, ⟨479, 1, 4, 5⟩, ⟨577, 0, 4, 5⟩, ⟨183, 3, 4, 5⟩, ⟨527, 6, 5, 1⟩]⟩def entry_586 : Entry := ⟨586, [⟨465, 4, 4, 5⟩, ⟨558, 1, 4, 5⟩, ⟨385, 1, 4, 5⟩, ⟨379, 4, 4, 5⟩, ⟨524, 0, 4, 5⟩, ⟨469, 2, 4, 5⟩, ⟨467, 2, 4, 5⟩, ⟨527, 4, 5, 5⟩, ⟨553, 0, 4, 5⟩, ⟨552, 1, 4, 5⟩, ⟨555, 1, 4, 5⟩, ⟨564, 0, 6, 4⟩, ⟨583, 0, 5, 2⟩]⟩def entry_587 : Entry := ⟨587, [⟨300, 2, 4, 1⟩, ⟨479, 1, 4, 5⟩, ⟨319, 3, 5, 5⟩, ⟨477, 6, 4, 1⟩, ⟨252, 3, 4, 5⟩, ⟨467, 2, 4, 5⟩]⟩def entry_588 : Entry := ⟨588, [⟨3, 1, 3, 3⟩, ⟨586, 0, 4, 5⟩]⟩def entry_589 : Entry := ⟨589, [⟨4, 1, 4, 3⟩, ⟨588, 0, 4, 5⟩]⟩def entry_590 : Entry := ⟨590, [⟨295, 7, 4, 3⟩, ⟨173, 7, 4, 3⟩, ⟨577, 0, 4, 7⟩, ⟨490, 0, 4, 7⟩, ⟨217, 5, 4, 3⟩]⟩def entry_591 : Entry := ⟨591, [⟨524, 0, 4, 5⟩, ⟨529, 1, 4, 1⟩, ⟨529, 3, 4, 1⟩, ⟨538, 1, 4, 1⟩, ⟨538, 3, 4, 1⟩, ⟨197, 5, 4, 1⟩]⟩def entry_592 : Entry := ⟨592, [⟨588, 0, 4, 5⟩, ⟨108, 7, 3, 0⟩]⟩def entry_593 : Entry := ⟨593, [⟨2, 7, 4, 2⟩, ⟨586, 0, 4, 5⟩]⟩def entry_594 : Entry := ⟨594, [⟨30, 1, 4, 3⟩, ⟨476, 1, 4, 3⟩, ⟨588, 0, 4, 5⟩]⟩def entry_595 : Entry := ⟨595, [⟨460, 4, 2, 4⟩, ⟨460, 2, 5, 4⟩, ⟨586, 1, 5, 4⟩, ⟨411, 4, 5, 4⟩, ⟨551, 1, 2, 4⟩, ⟨406, 5, 5, 4⟩, ⟨572, 0, 2, 4⟩]⟩def entry_596 : Entry := ⟨596, [⟨385, 5, 4, 2⟩, ⟨592, 0, 5, 6⟩, ⟨330, 1, 4, 6⟩, ⟨529, 5, 4, 6⟩, ⟨385, 1, 4, 6⟩, ⟨330, 5, 4, 2⟩]⟩def entry_597 : Entry := ⟨597, [⟨24, 6, 2, 3⟩, ⟨221, 0, 6, 4⟩, ⟨199, 3, 2, 4⟩, ⟨594, 1, 6, 5⟩]⟩def entry_598 : Entry := ⟨598, [⟨594, 0, 5, 6⟩, ⟨456, 5, 4, 2⟩, ⟨254, 1, 3, 2⟩, ⟨554, 1, 3, 2⟩, ⟨465, 0, 4, 6⟩]⟩def entry_599 : Entry := ⟨599, [⟨578, 4, 5, 3⟩, ⟨492, 0, 3, 1⟩, ⟨512, 4, 3, 1⟩, ⟨586, 4, 4, 5⟩, ⟨485, 0, 5, 3⟩, ⟨579, 4, 5, 3⟩]⟩def entry_600 : Entry := ⟨600, [⟨448, 0, 4, 5⟩, ⟨278, 2, 1, 4⟩, ⟨592, 5, 5, 3⟩, ⟨403, 5, 5, 4⟩, ⟨146, 5, 4, 3⟩]⟩def entry_601 : Entry := ⟨601, [⟨437, 6, 4, 1⟩, ⟨553, 0, 4, 5⟩, ⟨592, 0, 5, 5⟩, ⟨236, 4, 3, 5⟩, ⟨469, 4, 4, 1⟩]⟩def entry_602 : Entry := ⟨602, [⟨553, 0, 4, 7⟩, ⟨467, 4, 4, 3⟩, ⟨592, 0, 5, 7⟩, ⟨437, 6, 4, 3⟩, ⟨236, 4, 3, 7⟩]⟩def entry_603 : Entry := ⟨603, [⟨505, 1, 5, 4⟩, ⟨505, 5, 5, 4⟩, ⟨586, 5, 5, 4⟩, ⟨551, 7, 5, 4⟩, ⟨531, 6, 4, 2⟩, ⟨586, 1, 5, 4⟩, ⟨585, 1, 5, 4⟩, ⟨585, 5, 5, 4⟩, ⟨551, 3, 5, 4⟩, ⟨573, 1, 5, 4⟩, ⟨533, 5, 5, 4⟩, ⟨533, 1, 5, 4⟩]⟩def entry_604 : Entry := ⟨604, [⟨597, 0, 3, 4⟩, ⟨375, 2, 4, 3⟩, ⟨597, 1, 4, 3⟩, ⟨375, 3, 3, 4⟩, ⟨350, 3, 4, 3⟩, ⟨350, 2, 3, 4⟩]⟩def entry_605 : Entry := ⟨605, [⟨400, 5, 4, 3⟩, ⟨383, 6, 3, 4⟩, ⟨530, 4, 4, 3⟩, ⟨596, 1, 3, 4⟩, ⟨522, 2, 4, 3⟩, ⟨598, 0, 4, 3⟩, ⟨537, 3, 3, 4⟩, ⟨520, 1, 4, 3⟩, ⟨550, 4, 4, 3⟩]⟩def entry_606 : Entry := ⟨606, [⟨123, 1, 4, 3⟩, ⟨274, 0, 4, 3⟩, ⟨605, 0, 6, 4⟩, ⟨119, 1, 4, 3⟩]⟩def entry_607 : Entry := ⟨607, [⟨420, 3, 1, 2⟩, ⟨419, 3, 1, 4⟩, ⟨589, 0, 5, 5⟩, ⟨314, 0, 3, 4⟩, ⟨571, 1, 7, 3⟩]⟩def entry_608 : Entry := ⟨608, [⟨486, 4, 4, 5⟩, ⟨515, 1, 4, 5⟩, ⟨580, 0, 4, 5⟩, ⟨521, 0, 4, 5⟩, ⟨581, 4, 4, 5⟩, ⟨593, 0, 4, 5⟩, ⟨599, 4, 4, 5⟩, ⟨606, 1, 6, 2⟩]⟩def entry_609 : Entry := ⟨609, [⟨286, 4, 4, 5⟩, ⟨107, 3, 4, 5⟩, ⟨532, 4, 4, 5⟩, ⟨542, 0, 4, 5⟩, ⟨221, 3, 4, 5⟩, ⟨562, 4, 4, 5⟩, ⟨575, 4, 4, 5⟩, ⟨604, 1, 6, 4⟩]⟩def entry_610 : Entry := ⟨610, [⟨221, 2, 5, 4⟩, ⟨286, 5, 5, 4⟩, ⟨107, 2, 5, 4⟩, ⟨472, 1, 5, 4⟩, ⟨566, 1, 5, 4⟩, ⟨532, 5, 5, 4⟩, ⟨542, 1, 5, 4⟩, ⟨609, 0, 2, 6⟩]⟩def entry_611 : Entry := ⟨611, [⟨456, 2, 5, 4⟩, ⟨456, 4, 1, 4⟩, ⟨594, 7, 1, 3⟩, ⟨594, 1, 5, 5⟩]⟩def entry_612 : Entry := ⟨612, [⟨589, 1, 5, 5⟩, ⟨589, 7, 0, 3⟩]⟩def entry_613 : Entry := ⟨613, [⟨607, 5, 5, 4⟩, ⟨503, 3, 1, 4⟩, ⟨592, 7, 1, 3⟩, ⟨592, 5, 5, 3⟩, ⟨607, 7, 1, 4⟩, ⟨612, 4, 1, 4⟩, ⟨612, 0, 5, 4⟩]⟩def entry_614 : Entry := ⟨614, [⟨608, 1, 7, 5⟩, ⟨543, 3, 5, 6⟩, ⟨370, 6, 3, 4⟩, ⟨392, 7, 3, 4⟩, ⟨610, 3, 5, 6⟩, ⟨600, 0, 6, 4⟩, ⟨613, 0, 6, 4⟩]⟩def entry_615 : Entry := ⟨615, [⟨602, 7, 6, 4⟩, ⟨614, 1, 4, 3⟩, ⟨533, 5, 6, 4⟩, ⟨590, 7, 6, 4⟩, ⟨611, 6, 3, 4⟩, ⟨587, 3, 3, 4⟩, ⟨601, 5, 6, 4⟩, ⟨406, 1, 6, 4⟩, ⟨591, 3, 3, 4⟩, ⟨586, 3, 3, 4⟩, ⟨584, 5, 6, 4⟩, ⟨406, 3, 3, 4⟩]⟩def tableChunk_0 : Array Entry := #[entry_6, entry_7, entry_8, entry_9, entry_10, entry_11, entry_12, entry_13, entry_14, entry_15, entry_16, entry_17, entry_18, entry_19, entry_20, entry_21, entry_22, entry_23, entry_24, entry_25]def tableChunk_1 : Array Entry := #[entry_26, entry_27, entry_28, entry_29, entry_30, entry_31, entry_32, entry_33, entry_34, entry_35, entry_36, entry_37, entry_38, entry_39, entry_40, entry_41, entry_42, entry_43, entry_44, entry_45]def tableChunk_2 : Array Entry := #[entry_46, entry_47, entry_48, entry_49, entry_50, entry_51, entry_52, entry_53, entry_54, entry_55, entry_56, entry_57, entry_58, entry_59, entry_60, entry_61, entry_62, entry_63, entry_64, entry_65]def tableChunk_3 : Array Entry := #[entry_66, entry_67, entry_68, entry_69, entry_70, entry_71, entry_72, entry_73, entry_74, entry_75, entry_76, entry_77, entry_78, entry_79, entry_80, entry_81, entry_82, entry_83, entry_84, entry_85]def tableChunk_4 : Array Entry := #[entry_86, entry_87, entry_88, entry_89, entry_90, entry_91, entry_92, entry_93, entry_94, entry_95, entry_96, entry_97, entry_98, entry_99, entry_100, entry_101, entry_102, entry_103, entry_104, entry_105]def tableChunk_5 : Array Entry := #[entry_106, entry_107, entry_108, entry_109, entry_110, entry_111, entry_112, entry_113, entry_114, entry_115, entry_116, entry_117, entry_118, entry_119, entry_120, entry_121, entry_122, entry_123, entry_124, entry_125]def tableChunk_6 : Array Entry := #[entry_126, entry_127, entry_128, entry_129, entry_130, entry_131, entry_132, entry_133, entry_134, entry_135, entry_136, entry_137, entry_138, entry_139, entry_140, entry_141, entry_142, entry_143, entry_144, entry_145]def tableChunk_7 : Array Entry := #[entry_146, entry_147, entry_148, entry_149, entry_150, entry_151, entry_152, entry_153, entry_154, entry_155, entry_156, entry_157, entry_158, entry_159, entry_160, entry_161, entry_162, entry_163, entry_164, entry_165]def tableChunk_8 : Array Entry := #[entry_166, entry_167, entry_168, entry_169, entry_170, entry_171, entry_172, entry_173, entry_174, entry_175, entry_176, entry_177, entry_178, entry_179, entry_180, entry_181, entry_182, entry_183, entry_184, entry_185]def tableChunk_9 : Array Entry := #[entry_186, entry_187, entry_188, entry_189, entry_190, entry_191, entry_192, entry_193, entry_194, entry_195, entry_196, entry_197, entry_198, entry_199, entry_200, entry_201, entry_202, entry_203, entry_204, entry_205]def tableChunk_10 : Array Entry := #[entry_206, entry_207, entry_208, entry_209, entry_210, entry_211, entry_212, entry_213, entry_214, entry_215, entry_216, entry_217, entry_218, entry_219, entry_220, entry_221, entry_222, entry_223, entry_224, entry_225]def tableChunk_11 : Array Entry := #[entry_226, entry_227, entry_228, entry_229, entry_230, entry_231, entry_232, entry_233, entry_234, entry_235, entry_236, entry_237, entry_238, entry_239, entry_240, entry_241, entry_242, entry_243, entry_244, entry_245]def tableChunk_12 : Array Entry := #[entry_246, entry_247, entry_248, entry_249, entry_250, entry_251, entry_252, entry_253, entry_254, entry_255, entry_256, entry_257, entry_258, entry_259, entry_260, entry_261, entry_262, entry_263, entry_264, entry_265]def tableChunk_13 : Array Entry := #[entry_266, entry_267, entry_268, entry_269, entry_270, entry_271, entry_272, entry_273, entry_274, entry_275, entry_276, entry_277, entry_278, entry_279, entry_280, entry_281, entry_282, entry_283, entry_284, entry_285]def tableChunk_14 : Array Entry := #[entry_286, entry_287, entry_288, entry_289, entry_290, entry_291, entry_292, entry_293, entry_294, entry_295, entry_296, entry_297, entry_298, entry_299, entry_300, entry_301, entry_302, entry_303, entry_304, entry_305]def tableChunk_15 : Array Entry := #[entry_306, entry_307, entry_308, entry_309, entry_310, entry_311, entry_312, entry_313, entry_314, entry_315, entry_316, entry_317, entry_318, entry_319, entry_320, entry_321, entry_322, entry_323, entry_324, entry_325]def tableChunk_16 : Array Entry := #[entry_326, entry_327, entry_328, entry_329, entry_330, entry_331, entry_332, entry_333, entry_334, entry_335, entry_336, entry_337, entry_338, entry_339, entry_340, entry_341, entry_342, entry_343, entry_344, entry_345]def tableChunk_17 : Array Entry := #[entry_346, entry_347, entry_348, entry_349, entry_350, entry_351, entry_352, entry_353, entry_354, entry_355, entry_356, entry_357, entry_358, entry_359, entry_360, entry_361, entry_362, entry_363, entry_364, entry_365]def tableChunk_18 : Array Entry := #[entry_366, entry_367, entry_368, entry_369, entry_370, entry_371, entry_372, entry_373, entry_374, entry_375, entry_376, entry_377, entry_378, entry_379, entry_380, entry_381, entry_382, entry_383, entry_384, entry_385]def tableChunk_19 : Array Entry := #[entry_386, entry_387, entry_388, entry_389, entry_390, entry_391, entry_392, entry_393, entry_394, entry_395, entry_396, entry_397, entry_398, entry_399, entry_400, entry_401, entry_402, entry_403, entry_404, entry_405]def tableChunk_20 : Array Entry := #[entry_406, entry_407, entry_408, entry_409, entry_410, entry_411, entry_412, entry_413, entry_414, entry_415, entry_416, entry_417, entry_418, entry_419, entry_420, entry_421, entry_422, entry_423, entry_424, entry_425]def tableChunk_21 : Array Entry := #[entry_426, entry_427, entry_428, entry_429, entry_430, entry_431, entry_432, entry_433, entry_434, entry_435, entry_436, entry_437, entry_438, entry_439, entry_440, entry_441, entry_442, entry_443, entry_444, entry_445]def tableChunk_22 : Array Entry := #[entry_446, entry_447, entry_448, entry_449, entry_450, entry_451, entry_452, entry_453, entry_454, entry_455, entry_456, entry_457, entry_458, entry_459, entry_460, entry_461, entry_462, entry_463, entry_464, entry_465]def tableChunk_23 : Array Entry := #[entry_466, entry_467, entry_468, entry_469, entry_470, entry_471, entry_472, entry_473, entry_474, entry_475, entry_476, entry_477, entry_478, entry_479, entry_480, entry_481, entry_482, entry_483, entry_484, entry_485]def tableChunk_24 : Array Entry := #[entry_486, entry_487, entry_488, entry_489, entry_490, entry_491, entry_492, entry_493, entry_494, entry_495, entry_496, entry_497, entry_498, entry_499, entry_500, entry_501, entry_502, entry_503, entry_504, entry_505]def tableChunk_25 : Array Entry := #[entry_506, entry_507, entry_508, entry_509, entry_510, entry_511, entry_512, entry_513, entry_514, entry_515, entry_516, entry_517, entry_518, entry_519, entry_520, entry_521, entry_522, entry_523, entry_524, entry_525]def tableChunk_26 : Array Entry := #[entry_526, entry_527, entry_528, entry_529, entry_530, entry_531, entry_532, entry_533, entry_534, entry_535, entry_536, entry_537, entry_538, entry_539, entry_540, entry_541, entry_542, entry_543, entry_544, entry_545]def tableChunk_27 : Array Entry := #[entry_546, entry_547, entry_548, entry_549, entry_550, entry_551, entry_552, entry_553, entry_554, entry_555, entry_556, entry_557, entry_558, entry_559, entry_560, entry_561, entry_562, entry_563, entry_564, entry_565]def tableChunk_28 : Array Entry := #[entry_566, entry_567, entry_568, entry_569, entry_570, entry_571, entry_572, entry_573, entry_574, entry_575, entry_576, entry_577, entry_578, entry_579, entry_580, entry_581, entry_582, entry_583, entry_584, entry_585]def tableChunk_29 : Array Entry := #[entry_586, entry_587, entry_588, entry_589, entry_590, entry_591, entry_592, entry_593, entry_594, entry_595, entry_596, entry_597, entry_598, entry_599, entry_600, entry_601, entry_602, entry_603, entry_604, entry_605]def tableChunk_30 : Array Entry := #[entry_606, entry_607, entry_608, entry_609, entry_610, entry_611, entry_612, entry_613, entry_614, entry_615]def table : Array Entry := ((((tableChunk_0 ++ (tableChunk_1 ++ tableChunk_2)) ++ ((tableChunk_3 ++ tableChunk_4) ++ (tableChunk_5 ++ tableChunk_6))) ++ (((tableChunk_7 ++ tableChunk_8) ++ (tableChunk_9 ++ tableChunk_10)) ++ ((tableChunk_11 ++ tableChunk_12) ++ (tableChunk_13 ++ tableChunk_14)))) ++ ((((tableChunk_15 ++ tableChunk_16) ++ (tableChunk_17 ++ tableChunk_18)) ++ ((tableChunk_19 ++ tableChunk_20) ++ (tableChunk_21 ++ tableChunk_22))) ++ (((tableChunk_23 ++ tableChunk_24) ++ (tableChunk_25 ++ tableChunk_26)) ++ ((tableChunk_27 ++ tableChunk_28) ++ (tableChunk_29 ++ tableChunk_30)))))def entryAt (i : ℕ) : Entry := table[i - 6]?.getD emptyEntrydef TableValid : Prop :=  table.size = 610 ∧ ∀ k, k < table.size →    let e := table[k]?.getD emptyEntry    e.index = k + 6 ∧ e.terms ≠ [] ∧ ∀ t ∈ e.terms, t.child < e.indexdef placementCount : ℕ := (table.toList.map fun e => e.terms.length).sumstructure RowData where  A : Finset Cell  H : Finset Cell  height : ℕ  deriving DecidableEqdef emptyRow : RowData := ⟨∅, ∅, 0⟩def baseRow (i : Fin 6) : RowData := ⟨baseRequired i, baseEnvelope i, 1⟩def placeRow (t : Term) (d : RowData) : RowData :=  ⟨d.A.image (placement t.rotation t.shift),   d.H.image (placement t.rotation t.shift), d.height⟩def unionA (ds : List RowData) : Finset Cell := (ds.map RowData.A).foldr (· ∪ ·) ∅def unionH (ds : List RowData) : Finset Cell := (ds.map RowData.H).foldr (· ∪ ·) ∅def commonH (ds : List RowData) : Finset Cell :=  match ds with  | [] => ∅  | d :: rest => (rest.map RowData.H).foldr (· ∩ ·) d.Hdef forkRow (ds : List RowData) : RowData :=  ⟨(unionA ds ∪ commonH ds).erase origin,   insert origin (unionH ds), 1 + (ds.map RowData.height).foldr max 0⟩def rowAt (i : ℕ) : RowData :=  if h : i < 6 then baseRow ⟨i, h⟩ else    forkRow ((entryAt i).terms.map fun t =>      placeRow t (if _ : t.child < i then rowAt t.child else emptyRow))termination_by idef Output (i : ℕ) (p : Cell) (size height : ℕ) (omitted : Set Cell) : Prop :=  (rowAt i).A = {p} ∧ (rowAt i).H.card = size ∧ (rowAt i).height = height ∧  Disjoint (↑(rowAt i).H : Set Cell) omitteddef AllRows : Prop := ∀ i, i < 616 →  (rowAt i).A ⊆ (rowAt i).H ∧ origin ∈ (rowAt i).H ∧  origin ∉ (rowAt i).A ∧ (rowAt i).height ≤ 34theorem certificate_correct :    TableValid ∧ placementCount = 1837 ∧    Output 557 (-1, 0) 118 19 {p | p.1 ≤ -3 ∧ p.2 ≤ -2} ∧    Output 595 (-1, 0) 222 27 {p | p.1 = -2 ∧ p.2 ≤ -2} ∧    Output 603 (-1, 0) 275 27 {p | p.1 ≤ -3 ∧ p.2 = 0} ∧    Output 615 (1, 0) 686 34 {(1, -1)} ∧    AllRows := by  sorryend SnakyCertificateend OAI
Every extracted statement of the accompanying papers

The statements the atlas extracted automatically from each accompanying paper’s TeX source, with links to the full sources.

Snaky in 21 Maker moves

Theorem

In this game, there is one globally legal Maker policy that completes an allowed copy of S within at most 21 actual Maker claims against every legal continuation of Breaker. Equivalently, extend the policy by fresh claims after an earlier win: its Maker set after claim 21 contains a target whenever the first 20 Breaker replies are legal.

Section 1, Introduction Read it in the paper TeX source, line 25
Show the TeX
In this game, there is one globally legal Maker policy that completes
an allowed copy of $S$ within at most $21$ actual Maker claims against
every legal continuation of Breaker. Equivalently, extend the policy by
fresh claims after an earlier win: its Maker set after claim $21$
contains a target whenever the first $20$ Breaker replies are legal.
Configuration and file facts
OpenAI’s Lean catalogue
OpenAI’s Lean catalogue does not list this as a main result; the release’s Lean notes for family 187 link it.
Solution module
OAI.Combinatorics.SnakyCertificate.Main
Allowed axioms
propext, Quot.sound, Classical.choiceThe axioms this configuration allows a proof to use. A replay shows which of them a proof uses.
Imports
Mathlib
Imports from outside Mathlib
None
Local vocabulary
670 local vocabulary declarations
Lines of Lean, without comments or blank lines
718
Second proof-verification program (nanoda)
Off in OpenAI's configuration.

Statement comparison

A shareable summary of this page: the proposed paper match, what the Lean statement expresses, and which reviews are recorded.

Plectis Atlas

Reconstruction of the 35-move Snaky certificate

Family 187: Snaky in 21 Maker moves

Candidate pairing

Proposition

The 35-move certificate has 616 cards, including its six base cards, and 1,837 placement terms. Every card satisfies A_i^{35}\subsetneq T_i^{35}, o\in T_i^{35}\setminus A_i^{35}, and h_i^{35}\le34. Four of its conditional interfaces are

\begin{array}{c|c|r|r|l} i&A_i^{35}&|T_i^{35}|&h_i^{35}&\text{region disjoint from }T_i^{35}\\ \hline 557&\{(-1,0)\}&118&19&\{(x,y):x\le-3,\ y\le-2\}\\ 595&\{(-1,0)\}&222&27&\{(x,y):x=-2,\ y\le-2\}\\ 603&\{(-1,0)\}&275&27&\{(x,y):x\le-3,\ y=0\}\\ 615&\{(1,0)\}&686&34&\{(1,-1)\}. \end{array}

Each row applies at any Maker turn with its required point owned and its entire envelope free of Breaker, regardless of all other ownership. For row 615 there is also a Breaker-turn conclusion: if Maker owns \{o,(1,0)\} and Breaker avoids T_{615}^{35}, then after any legal next reply Maker wins within 33 further claims, unless already victorious.

Snaky in 21 Maker moves

TeX label r35:conditional, build/route35.tex, line 150

The Lean statement says

theorem certificate_correct :    TableValid ∧ placementCount = 1837 ∧    Output 557 (-1, 0) 118 19 {p | p.1 ≤ -3 ∧ p.2 ≤ -2} ∧    Output 595 (-1, 0) 222 27 {p | p.1 = -2 ∧ p.2 ≤ -2} ∧    Output 603 (-1, 0) 275 27 {p | p.1 ≤ -3 ∧ p.2 = 0} ∧    Output 615 (1, 0) 686 34 {(1, -1)} ∧    AllRows := by  sorry

A Lean statement states the theorem and leaves its proof as sorry on purpose. OpenAI’s proof is in a separate solution module, and a program called Comparator checks that proof against this statement.

Atlas selected this possible match because the two statements share words. No review of whether they mean the same thing is recorded.three independent groups report that Comparator accepted runs for this file at the release version shown here.Statement review: none recorded

670 local vocabulary declarationsAllowed axioms: propext, Quot.sound, Classical.choiceopenai/math at fd4aeebwcook04.github.io/plectis-atlas/statements/SnakyCertificate.html

Recorded comparisons with the paper

Atlas records no contributed comparison of this statement with the paper.

Contributed Comparator run reports

Atlas records no contributed report of running Comparator for this statement file.

Questions to resolve when comparing this statement with the paper

  • 670 local vocabulary declarations to read.

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