Burst Balloons

hard
1. You are given an array(arr) of length N which represents N number of balloons.
2. Each balloon is painted with a number on it.
3. You have to collect maximum coins by bursting all the balloons.
4. If you burst a balloon with index i, you will get (arr[i-1] * arr[i] * arr[i+1]) number of coins.
5. If arr[i-1] and arr[i+1] don't exist, then you may assume their value as 1. 

Input Format

A number N a1 a2.. N integers

Output Format

Check the sample output and question video.

Constraints

1 <= N <= 1000
1 <= arr[i] <= 100

Notice

Try First, Check Solution later

1. You should first read the question and watch the question video.
2. Think of a solution approach, then try and submit the question on editor tab.
3. We strongly advise you to watch the solution video for prescribed approach.

Example

Input
3
1
2
3
Output
12
Previous
Target Sum Pair 2
Next
Min Max Value Expression

Related Questions