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Matrix Chain Multiplication

1. You are given an array(arr) of positive integers of length N which represents the dimensions of N-1 matrices such that the ith matrix is of dimension arr[i-1] x arr[i]. 2. You have to find the minimum number of multiplications needed to multiply the given chain of matrices.

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Matrix Chain Multiplication

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1. You are given an array(arr) of positive integers of length N which represents the dimensions of N-1 matrices such that the ith matrix is of dimension arr[i-1] x arr[i]. 2. You have to find the minimum number of multiplications needed to multiply the given chain of matrices.

Constraints

2 <= N <= 1000 1 <= arr[i] <= 500

Format

Input

A number N arr1 arr2.. N integers

Output

Check the sample output and question video.

Example

Sample Input

3 1 2 3

Sample Output

6

Question Video

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