Problem:
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Matrix-chain Multiplication

The goal of the matrix-chain multiplication problem is to find the most efficient way to multiply given $n$ matrices $M_1, M_2, M_3,...,M_n$.

Write a program which reads dimensions of $M_i$, and finds the minimum number of scalar multiplications to compute the maxrix-chain multiplication $M_1M_2...M_n$.

Input

In the first line, an integer $n$ is given. In the following $n$ lines, the dimension of matrix $M_i$ ($i = 1...n$) is given by two integers $r$ and $c$ which respectively represents the number of rows and columns of $M_i$.

Output

Print the minimum number of scalar multiplication in a line.

Constraints

$1 \leq n \leq 100$

$1 \leq r, c \leq 100$

Sample Input 1

6
30 35
35 15
15 5
5 10
10 20
20 25

Sample Output 1

15125

Solution in JAVA (judge verdict: Accepted)

import java.util.Scanner;
import java.lang.Math;
public class Main {
    public static void main(String[] args){
        final Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int[] p=new int[n+1];
        int[][] m=new int[n+1][n+1];

for(int i = 1; i <= n; i++)
    {
        p[i - 1] = sc.nextInt();
        p[i] = sc.nextInt();
    }

for(int i = 1; i <= n; i++) m[i][i] = 0;

for(int j = 2; j <= n; j++)
    {
        for(int i = 1; i <= n - j + 1; i++)
            {
                int k = i + j - 1;
                m[i][k] = 200000;
                for(int l = i; l <= k - 1; l++)
                    {
                        m[i][k] = ((m[i][k] < m[i][l] + m[l + 1][k] + p[i - 1] * p[l] * p[k]) ? m[i][k] : (m[i][l] + m[l + 1][k] + p[i - 1] * p[l] * p[k]));
                    }
            }
    }
System.out.println(m[1][n]);
}
}