Problem Statement

Amazon manages a warehouse with sequentially numbered product slots starting from 1. You are given an array inventory[n] where inventory[i] is the product ID in the i th slot. A perfect slot is a slot where the product ID equals its slot number. You are allowed to perform the following operation any number of times (possibly zero): Choose any index i , remove the product in the i th slot. When you remove a product at position i , all products to its right shift one slot to the left. Determine the maximum number of perfect slots achievable after any number of removals. Example n = 7 inventory = [1, 3, 2, 5, 4, 5, 3] Optimal removals: (Assuming 1-based indexing of inventory) Remove inventory[2] = 3 → inventory = [1, 2, 5, 4, 5, 3] Remove inventory[6] = 3 → inventory = [1, 2, 5, 4, 5] Perfect slots in final inventory: inventory[1] = 1, inventory[2] = 2, inventory[4] = 4, inventory[5] = 5 Hence, the maximum possible perfect slots is 4. Note that there can be more than one final a