<p>Given an array <code>arr</code> of positive integers, consider all binary trees such that:</p>

<ul>
	<li>Each node has either <code>0</code> or <code>2</code> children;</li>
	<li>The values of <code>arr</code> correspond to the values of each <strong>leaf</strong> in an in-order traversal of the tree.</li>
	<li>The value of each non-leaf node is equal to the product of the largest leaf value in its left and right subtree, respectively.</li>
</ul>

<p>Among all possible binary trees considered, return <em>the smallest possible sum of the values of each non-leaf node</em>. It is guaranteed this sum fits into a <strong>32-bit</strong> integer.</p>

<p>A node is a <strong>leaf</strong> if and only if it has zero children.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/tree1.jpg" style="width: 500px; height: 169px;" />
<pre>
<strong>Input:</strong> arr = [6,2,4]
<strong>Output:</strong> 32
<strong>Explanation:</strong> There are two possible trees shown.
The first has a non-leaf node sum 36, and the second has non-leaf node sum 32.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/tree2.jpg" style="width: 224px; height: 145px;" />
<pre>
<strong>Input:</strong> arr = [4,11]
<strong>Output:</strong> 44
</pre>

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

<ul>
	<li><code>2 &lt;= arr.length &lt;= 40</code></li>
	<li><code>1 &lt;= arr[i] &lt;= 15</code></li>
	<li>It is guaranteed that the answer fits into a <strong>32-bit</strong> signed integer (i.e., it is less than 2<sup>31</sup>).</li>
</ul>

class Solution {
private:
    int fn(int i, int j, vector<int> &a, vector<vector<int>> &dp, vector<vector<int>> &maxSub) {
        if (j < i) return 0;
        if (i == j) return 0;
        if (dp[i][j] != -1) return dp[i][j];
        int ans = 1e9;
        for (int k=i; k<j; k++){
            ans = min(ans, maxSub[i][k] * maxSub[k+1][j] + fn(i, k, a, dp, maxSub) + fn(k+1, j, a, dp, maxSub));
        }
        dp[i][j] = ans;
        return dp[i][j];
    }
public:
    int mctFromLeafValues(vector<int>& a) {
        int n = a.size();
        vector<vector<int>> dp(n, vector<int> (n, -1)), maxSub(n, vector<int> (n, 1e9));
        for (int i=0; i<n; i++){
            maxSub[i][i] = a[i];
            for (int j=i+1; j<n; j++){
                maxSub[i][j] = max(maxSub[i][j-1], a[j]); 
            }
        }
        return fn(0, n-1, a, dp, maxSub);
    }
};
11300