You are given a 0-indexed integer array `nums`. For each index `i` (`1 <= i <= nums.length - 2`) the beauty of `nums[i]` equals:

- `2`, if `nums[j] < nums[i] < nums[k]`, for all `0 <= j < i` and for all `i < k <= nums.length - 1`.
- `1`, if `nums[i - 1] < nums[i] < nums[i + 1]`, and the previous condition is not satisfied.
- `0`, if none of the previous conditions holds.

Return the sum of beauty of all `nums[i]` where `1 <= i <= nums.length - 2`.

Example 1:

    Input: nums = [1,2,3]
    Output: 2
    Explanation: For each index i in the range 1 <= i <= 1:
    - The beauty of nums[1] equals 2.

Example 2:

    Input: nums = [2,4,6,4]
    Output: 1
    Explanation: For each index i in the range 1 <= i <= 2:
    - The beauty of nums[1] equals 1.
    - The beauty of nums[2] equals 0.

Example 3:

    Input: nums = [3,2,1]
    Output: 0
    Explanation: For each index i in the range 1 <= i <= 1:
    - The beauty of nums[1] equals 0.

Constraints:

- `3 <= nums.length <= 105`
- `1 <= nums[i] <= 105`