Burst Balloons

You are given `n` balloons, indexed from `0` to `n - 1`. Each balloon is painted with a number on it represented by an array `nums`. You are asked to burst all the balloons. If you burst the `ith` balloon, you will get `nums[i - 1] * nums[i] * nums[i + 1]` coins. If `i - 1` or `i + 1` goes out of bounds of the array, then treat it as if there is a balloon with a `1` painted on it. Return _the maximum coins you can collect by bursting the balloons wisely_.   **Example 1:** **Input:** nums = [3,1,5,8] **Output:** 167 **Explanation:** nums = [3,1,5,8] --> [3,5,8] --> [3,8] --> [8] --> [] coins = 3*1*5 + 3*5*8 + 1*3*8 + 1*8*1 = 167 ``` **Example 2:** **Input:** nums = [1,5] **Output:** 10 ```   **Constraints:** - `n == nums.length` - `1 <= n <= 300` - `0 <= nums[i] <= 100`