<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>

class Solution:
    def sumOfBeauties(self, nums: List[int]) -> int:
        n = len(nums)
        res = 0
        
        # Precompute the maximum from the left side for each index
        left_max = [0] * n
        left_max[0] = nums[0]
        for i in range(1, n):
            left_max[i] = max(left_max[i-1], nums[i-1])
        
        # Precompute the minimum from the right side for each index
        right_min = [0] * n
        right_min[n-1] = nums[n-1]
        for i in range(n-2, -1, -1):
            right_min[i] = min(right_min[i+1], nums[i+1])
        
        # Calculate beauty of each element
        for i in range(1, n-1):
            if left_max[i] < nums[i] < right_min[i]:
                res += 2
            elif nums[i-1] < nums[i] < nums[i+1]:
                res += 1
        
        return res

793