─────╷─────────── $𝖘𝖍𝖐𝖚/𝖘𝖍𝖎𝖐𝖆𝖐𝖚-𝖗𝖚𝖑𝖊𝖘.𝖘𝖆𝖕𝖕𝖍𝖎𝖗𝖊 ───────────────────────────────────────────────────────
0┊---------------------------------| Shikaku Rules in Sapphire |----------------------------------
1┊--|∙An∙n×m∙grid∙of∙cells,∙k∙have∙numbers∙in∙them
2┊--|∙divide∙grid∙into∙non-overlapping∙rectangles,∙each∙containing∙a∙single∙number∙which∙is
3┊--|∙the∙area∙of∙the∙rectangle
4┊
5┊∀i∈{0⋯k⨫1}
6┊∙∙⦗x∙i⦘∈{0⋯n⨫1}
7┊∙∙⦗y∙i⦘∈{0⋯m⨫1}
8┊∙∙⦗lft∙i⦘∈{0⋯n⨫1}∙∧∙⦗rgt∙i⦘∈{0⋯n⨫1}∙∧∙⦗rgt∙i⦘>=⦗lft∙i⦘
9┊∙∙⦗bot∙i⦘∈{0⋯m⨫1}∙∧∙⦗top∙i⦘∈{0⋯m⨫1}∙∧∙⦗top∙i⦘>=⦗bot∙i⦘
10┊∙∙⦗x∙i⦘>=⦗lft∙i⦘∙∧∙⦗x∙i⦘<=⦗rgt∙i⦘
11┊∙∙⦗y∙i⦘>=⦗bot∙i⦘∙∧∙⦗y∙i⦘<=⦗top∙i⦘
12┊∙∙⦗wd∙i⦘=⦗rgt∙i⦘+1⨫⦗lft∙i⦘
13┊∙∙⦗ht∙i⦘=⦗top∙i⦘+1⨫⦗bot∙i⦘
14┊∙∙⦗wd∙i⦘·⦗ht∙i⦘=⦗sz∙i⦘
15┊∙∙∀j∈{0⋯k⨫1}
16┊∙∙∙∙j¬=i∙⇒∙⦗lft∙j⦘>⦗rgt∙i⦘∙∨∙⦗bot∙j⦘>⦗top∙i⦘∙∨∙⦗rgt∙j⦘<⦗lft∙i⦘∙∨∙⦗top∙j⦘<⦗bot∙i⦘
17┊∙∙⦗wd∙i⦘∈{0⋯n}∙∙--|∙These∙are∙a∙solver∙hack∙to∙make∙sure∙the∙xov's∙⟨⦗wd∙i⦘∙⋮∙0⋯<k⟩∙are∙defined
18┊∙∙⦗ht∙i⦘∈{0⋯m}
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