```
import Mathlib.Data.ZMod.Basic
import Mathlib.Order.Bounds.Basic
/-!
# USA Mathematical Olympiad 1998, Problem 4
A computer screen shows a 98 × 98 chessboard, colored in the usual way.
One can select with a mouse any rectangle with sides on the lines of the
chessboard and click the mouse button: as a result, the colors in the
selected rectangle switch (black becomes white, white becomes black).
Find, with proof, the minimum number of mouse clicks needed to make the
chessboard all one color.
-/
namespace Usa1998P4
def chessboard : Type := Fin 98 × Fin 98
def coloring := chessboard → ZMod 2
def all_same_color (f : coloring) : Prop :=
∃ c : ZMod 2, ∀ s : chessboard, f s = c
structure Rectangle where
x : ℕ
y : ℕ
width : ℕ
height : ℕ
def recolor_rect (f : coloring) (r : Rectangle) : coloring :=
fun ⟨x, y⟩ ↦ if r.x ≤ x.val ∧
r.y ≤ y.val ∧
x.val < r.x + r.width ∧
y.val < r.y + r.height
then
f ⟨x, y⟩ + 1
else
f ⟨x, y⟩
def start_coloring : coloring := fun ⟨x, y⟩ ↦ x.val + y.val
def possible_num_clicks : Set ℕ :=
{ n : ℕ | ∃ rs : List Rectangle,
(all_same_color (rs.foldl recolor_rect start_coloring) ∧
rs.length = n) }
/- determine -/ abbrev min_clicks : ℕ := sorry
theorem usa1998_p4 : IsLeast possible_num_clicks min_clicks := sorry
```

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