import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem amc12_2000_p1
  (i m o : ℕ)
  (h₀ : i ≠ m ∧ m ≠ o ∧ o ≠ i)
  (h₁ : i*m*o = 2001) :
  i+m+o ≤ 671 := by sorry