Minimum Increment Operations to Make Heights Strictly +/-1 Monotonic

Given an integer array nums representing house heights from left to right, one operation increments any single element by 1. Make the final array satisfy either: strictly increasing with adjacent difference 1: [a, a+1, ..., a+n-1], or strictly decreasing with adjacent difference 1: [b, b-1, ..., b-(n-1)]. Only increments are allowed (no decrements). Return the minimum number of operations needed to reach either form. Input Line 1: integer n Line 2: n integers nums Output The minimum number of increment operations. Constraints 1 <= n <= 2e5 -1e9 <= nums[i] <= 1e9 Example Input 3 1 1 1 Output 3