<p>You are given <code>n</code> balloons, indexed from <code>0</code> to <code>n - 1</code>. Each balloon is painted with a number on it represented by an array <code>nums</code>. You are asked to burst all the balloons.</p>

<p>If you burst the <code>i<sup>th</sup></code> balloon, you will get <code>nums[i - 1] * nums[i] * nums[i + 1]</code> coins. If <code>i - 1</code> or <code>i + 1</code> goes out of bounds of the array, then treat it as if there is a balloon with a <code>1</code> painted on it.</p>

<p>Return <em>the maximum coins you can collect by bursting the balloons wisely</em>.</p>

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

<pre>
<strong>Input:</strong> nums = [3,1,5,8]
<strong>Output:</strong> 167
<strong>Explanation:</strong>
nums = [3,1,5,8] --&gt; [3,5,8] --&gt; [3,8] --&gt; [8] --&gt; []
coins =  3*1*5    +   3*5*8   +  1*3*8  + 1*8*1 = 167</pre>

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

<pre>
<strong>Input:</strong> nums = [1,5]
<strong>Output:</strong> 10
</pre>

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

<ul>
	<li><code>n == nums.length</code></li>
	<li><code>1 &lt;= n &lt;= 300</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 100</code></li>
</ul>

class Solution {
public:
    int solve(vector<int>& nums, int left, int right, vector<vector<int>>& dp) {
        if (left > right) {
            return 0;
        }

        if (dp[left][right] != -1) {
            return dp[left][right];
        }

        int result = 0;
        for (int i = left; i <= right; i++) {
            int gain = nums[left - 1] * nums[i] * nums[right + 1];
            int remaining = solve(nums, left, i - 1, dp) + solve(nums, i + 1, right, dp);
            result = max(result, remaining + gain);
        }

        dp[left][right] = result;
        return result;
    }

    int maxCoins(vector<int>& nums) {
        nums.push_back(1);
        nums.insert(nums.begin(), 1);

        int n = nums.size();
        vector<vector<int>> dp(n, vector<int>(n, -1));

        return solve(nums, 1, n - 2, dp);
    }
};
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