# 2012. Sum of Beauty in the Array

<https://leetcode.com/problems/sum-of-beauty-in-the-array>

## Description

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`

## ac

```java
```