Minimum Decaying Sweep Value

You are given an integer array nums of length n.

Choose a starting index s and an initial value x. A sweep then visits every index exactly once, one per step:

• the first visited index is s;
• each later step visits an index adjacent to the contiguous range of already-visited indices, extending that range by one to the left or right;
• which side extends at each step is not under your control, so you must plan for the worst case.

The k-th visited index (1-indexed) receives the value x - (k - 1). The sweep succeeds if every index j receives a value of at least nums[j].

Return the minimum x such that, for the best choice of s, the sweep succeeds no matter how the visiting order unfolds.

Examples

Example 1

Input: nums = [5,3,1,6,2,4]
Output: 9
Explanation: Start at index 0 with x = 9. Whatever order the range grows in, every element still receives at least its value; no smaller x can guarantee this from any start.

Example 2

Input: nums = [7,7]
Output: 8
Explanation: One element is visited second and receives x - 1, so x = 8 is needed.