Get Number of Perfect Packaging

Problem Overview

• Count ways to label n parcels with 5 stamps so adjacent stamps increase, decrease, or just differ according to adjacent price comparisons.
• Input: prices[0..n-1]. Output: number of valid labelings modulo 1e9+7 (return 0 if none).
• Real-world context: Amazon parcel packaging where stamp labels must reflect price trends.
• Constraints: 1 ≤ n ≤ 1e5; 1 ≤ prices[i] ≤ 1e5.
• An Amazon interviews coding interview problem and common interview question.