<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:
    def maxCoins(self, nums: List[int]) -> int:
        dp = [[-1 for i in range(len(nums) + 1)]for i in range(len(nums) + 1)]
        nums = [1] + nums + [1]

        def recur(l, r):
            if l > r:
                return 0
            if dp[l][r] != -1:
                return dp[l][r]
            _max = -maxsize
            for i in range(l, r + 1):
                curr = nums[l - 1] * nums[i] * nums[r + 1]
                curr += recur(l, i - 1) + recur(i + 1, r)
                _max = max(_max, curr)
            dp[l][r] = _max
            return dp[l][r]

        return recur(1, len(nums) - 2)
        # def solve(i,j):
        #     if i>j:
        #         return 0
        #     if dp[i][j]!=-1:
        #         return dp[i][j]
        #     maxi=-maxsize
        #     for k in range(i,j+1):
        #         coins=nums[i-1]*nums[k]*nums[j+1]+solve(i,k-1)+solve(k+1,j)
        #         maxi=max(maxi,coins)
        #     dp[i][j]=maxi
        #     return dp[i][j]
        
        # n=len(nums)
        # dp=[[-1 for j in range(n+1)] for j in range(n+1)]
        # nums.insert(0,1)
        # nums.append(1)
        # return solve(1,n)
21576