You are given three positive integers: `n`, `index`, and `maxSum`. You want to construct an array `nums` (0-indexed) that satisfies the following conditions:

- `nums.length == n`
- `nums[i]` is a positive integer where `0 <= i < n`.
- `abs(nums[i] - nums[i+1]) <= 1` where `0 <= i < n-1`.
- The sum of all the elements of `nums` does not exceed `maxSum`.
- `nums[index]` is maximized.

Return `nums[index]` of the constructed array.

Note that `abs(x)` equals `x` if `x >= 0`, and `-x` otherwise.

Example 1:

    Input: n = 4, index = 2,  maxSum = 6
    Output: 2
    Explanation: nums = [1,2,2,1] is one array that satisfies all the conditions.
    There are no arrays that satisfy all the conditions and have nums[2] == 3, so 2 is the maximum nums[2].

Example 2:

    Input: n = 6, index = 1,  maxSum = 10
    Output: 3

Constraints:

- `1 <= n <= maxSum <= 109`
- `0 <= index < n`