Given

`n`

balloons, indexed from `0`

to `n-1`

. Each balloon is painted with a number on it represented by array `nums`

. You are asked to burst all the balloons. If the you burst balloon `i`

you will get `nums[left] * nums[i] * nums[right]`

coins. Here `left`

and `right`

are adjacent indices of `i`

. After the burst, the `left`

and `right`

then becomes adjacent.
Find the maximum coins you can collect by bursting the balloons wisely.

Note:

(1) You may imagine

(2) 0 ≤

(1) You may imagine

`nums[-1] = nums[n] = 1`

. They are not real therefore you can not burst them.(2) 0 ≤

`n`

≤ 500, 0 ≤ `nums[i]`

≤ 100
Example:

Given

`[3, 1, 5, 8]`

Return

`167`

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

**Understand the problem:**

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