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Burst Balloons

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.

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Burst Balloons

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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.

Constraints

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

Format

Input

A number N a1 a2.. N integers

Output

Check the sample output and question video.

Example

Sample Input

3 1 2 3

Sample Output

12

Question Video

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