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: Wrong Answer)

import java.util.*;
public class Main {
	Scanner sc = new Scanner(System.in);
	
	int n;
	int[][] M;
	int[][] DP;
	
	int min = Integer.MAX_VALUE;
	
	public void input() {
		n = sc.nextInt();
		M = new int[n][2];
		DP = new int[n][n];
		for(int i=0; i<n; i++) {
			M[i][0] = sc.nextInt(); //r（行数）
			M[i][1] = sc.nextInt(); //c（列数）
		}
	}
	
	public int matrix(int i, int j) {
		if(i == j) return 0;
		if(DP[i][j] == 0) {
			for(int k=i; k<j; k++) {
				int q = matrix(i,k)+matrix(k+1,j)+(M[i][0]*M[k][1]*M[j][1]);
				min = Math.min(min, q);
			}
			DP[i][j] = min;
		}
		return DP[i][j];
	}
	
	public void output() {
		System.out.println( matrix(0,n-1) );
		
	}
	
	public static void main(String[] args) {
		Main obj = new Main();
		obj.input();
		obj.output();
	}
}