Sum of Beauty in the Array
<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. For each index <code>i</code> (<code>1 &lt;= i &lt;= nums.length - 2</code>) the <strong>beauty</strong> of <code>nums[i]</code> equals:</p>

<ul>
	<li><code>2</code>, if <code>nums[j] &lt; nums[i] &lt; nums[k]</code>, for <strong>all</strong> <code>0 &lt;= j &lt; i</code> and for <strong>all</strong> <code>i &lt; k &lt;= nums.length - 1</code>.</li>
	<li><code>1</code>, if <code>nums[i - 1] &lt; nums[i] &lt; nums[i + 1]</code>, and the previous condition is not satisfied.</li>
	<li><code>0</code>, if none of the previous conditions holds.</li>
</ul>

<p>Return<em> the <strong>sum of beauty</strong> of all </em><code>nums[i]</code><em> where </em><code>1 &lt;= i &lt;= nums.length - 2</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3]
<strong>Output:</strong> 2
<strong>Explanation:</strong> For each index i in the range 1 &lt;= i &lt;= 1:
- The beauty of nums[1] equals 2.
</pre>

<p><strong class="example">Example 2:</strong></p>

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

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,2,1]
<strong>Output:</strong> 0
<strong>Explanation:</strong> For each index i in the range 1 &lt;= i &lt;= 1:
- The beauty of nums[1] equals 0.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>3 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
</ul>
Array
impl Solution {
    pub fn sum_of_beauties(nums: Vec<i32>) -> i32 {
        let n = nums.len();
        let mut right: Vec<i32> = vec![0; n];
        right[n - 1] = nums[n - 1];
        for i in (1..n - 1).rev() {
            right[i] = right[i + 1].min(nums[i]);
        }
        let mut ans = 0;
        let mut l = nums[0];
        for i in 1..n - 1 {
            let r = right[i + 1];
            if l < nums[i] && nums[i] < r {
                ans += 2;
            } else if nums[i - 1] < nums[i] && nums[i] < nums[i + 1] {
                ans += 1;
            }
            l = l.max(nums[i]);
        }
        ans
    }
}
