public class Solution
extends Object
2012 - Sum of Beauty in the Array\.
Medium
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